LMFDB - Embedded newform 104.2.u.a.67.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [104,2,Mod(11,104)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(104, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 7]))

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

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

chi := DirichletCharacter("104.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	104.u (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:	$0.830444181021$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.8
Character	$\chi$	$=$	104.67
Dual form			104.2.u.a.59.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.203272 + 1.39953i) q^{2} +(0.793616 + 1.37458i) q^{3} +(-1.91736 + 0.568969i) q^{4} +(0.203095 + 0.203095i) q^{5} +(-1.76245 + 1.39010i) q^{6} +(-0.207385 - 0.773970i) q^{7} +(-1.18603 - 2.56775i) q^{8} +(0.240346 - 0.416291i) q^{9} +O(q^{10})$	\(q+(0.203272 + 1.39953i) q^{2} +(0.793616 + 1.37458i) q^{3} +(-1.91736 + 0.568969i) q^{4} +(0.203095 + 0.203095i) q^{5} +(-1.76245 + 1.39010i) q^{6} +(-0.207385 - 0.773970i) q^{7} +(-1.18603 - 2.56775i) q^{8} +(0.240346 - 0.416291i) q^{9} +(-0.242953 + 0.325520i) q^{10} +(-0.587501 + 2.19258i) q^{11} +(-2.30375 - 2.18403i) q^{12} +(3.31919 - 1.40818i) q^{13} +(1.04104 - 0.447567i) q^{14} +(-0.117991 + 0.440350i) q^{15} +(3.35255 - 2.18184i) q^{16} +(-3.23700 - 1.86889i) q^{17} +(0.631467 + 0.251751i) q^{18} +(0.792632 + 2.95814i) q^{19} +(-0.504960 - 0.273851i) q^{20} +(0.899303 - 0.899303i) q^{21} +(-3.18801 - 0.376534i) q^{22} +(1.24741 + 2.16058i) q^{23} +(2.58833 - 3.66811i) q^{24} -4.91751i q^{25} +(2.64548 + 4.35906i) q^{26} +5.52467 q^{27} +(0.837997 + 1.36599i) q^{28} +(1.82695 - 1.05479i) q^{29} +(-0.640267 - 0.0756217i) q^{30} +(-5.25282 - 5.25282i) q^{31} +(3.73502 + 4.24848i) q^{32} +(-3.48014 + 0.932501i) q^{33} +(1.95757 - 4.91017i) q^{34} +(0.115071 - 0.199308i) q^{35} +(-0.223973 + 0.934930i) q^{36} +(-7.30393 - 1.95708i) q^{37} +(-3.97889 + 1.71062i) q^{38} +(4.56983 + 3.44495i) q^{39} +(0.280618 - 0.762373i) q^{40} +(-2.91916 - 0.782185i) q^{41} +(1.44140 + 1.07580i) q^{42} +(-3.07997 - 1.77822i) q^{43} +(-0.121061 - 4.53825i) q^{44} +(0.133359 - 0.0357336i) q^{45} +(-2.77022 + 2.18497i) q^{46} +(-7.51561 + 7.51561i) q^{47} +(5.65976 + 2.87682i) q^{48} +(5.50616 - 3.17898i) q^{49} +(6.88219 - 0.999590i) q^{50} -5.93271i q^{51} +(-5.56288 + 4.58851i) q^{52} +13.1159i q^{53} +(1.12301 + 7.73193i) q^{54} +(-0.564621 + 0.325984i) q^{55} +(-1.74139 + 1.45047i) q^{56} +(-3.43717 + 3.43717i) q^{57} +(1.84757 + 2.34246i) q^{58} +(-6.44108 + 1.72588i) q^{59} +(-0.0243134 - 0.911443i) q^{60} +(-3.55817 - 2.05431i) q^{61} +(6.28373 - 8.41923i) q^{62} +(-0.372041 - 0.0996881i) q^{63} +(-5.18665 + 6.09087i) q^{64} +(0.960104 + 0.388116i) q^{65} +(-2.01248 - 4.68101i) q^{66} +(-10.5799 - 2.83488i) q^{67} +(7.26984 + 1.74157i) q^{68} +(-1.97993 + 3.42934i) q^{69} +(0.302328 + 0.120531i) q^{70} +(7.61356 - 2.04005i) q^{71} +(-1.35399 - 0.123412i) q^{72} +(10.3306 + 10.3306i) q^{73} +(1.25431 - 10.6199i) q^{74} +(6.75952 - 3.90261i) q^{75} +(-3.20286 - 5.22085i) q^{76} +1.81883 q^{77} +(-3.89240 + 7.09586i) q^{78} -12.1132i q^{79} +(1.12400 + 0.237765i) q^{80} +(3.66343 + 6.34525i) q^{81} +(0.501309 - 4.24444i) q^{82} +(2.07891 - 2.07891i) q^{83} +(-1.21261 + 2.23596i) q^{84} +(-0.277858 - 1.03698i) q^{85} +(1.86260 - 4.67197i) q^{86} +(2.89979 + 1.67420i) q^{87} +(6.32680 - 1.09193i) q^{88} +(0.497728 - 1.85755i) q^{89} +(0.0771184 + 0.179377i) q^{90} +(-1.77824 - 2.27692i) q^{91} +(-3.62103 - 3.43287i) q^{92} +(3.05172 - 11.3892i) q^{93} +(-12.0460 - 8.99060i) q^{94} +(-0.439804 + 0.761763i) q^{95} +(-2.87572 + 8.50577i) q^{96} +(1.50062 + 5.60039i) q^{97} +(5.56832 + 7.05983i) q^{98} +(0.771550 + 0.771550i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 4 q^{3} - 6 q^{4} - 6 q^{6} - 10 q^{8} - 20 q^{9}+O(q^{10}) $ 48 * q - 4 * q^2 - 4 * q^3 - 6 * q^4 - 6 * q^6 - 10 * q^8 - 20 * q^9	$ 48 q - 4 q^{2} - 4 q^{3} - 6 q^{4} - 6 q^{6} - 10 q^{8} - 20 q^{9} - 6 q^{10} - 8 q^{11} + 8 q^{14} - 10 q^{16} - 12 q^{17} - 6 q^{18} - 8 q^{19} + 10 q^{20} - 20 q^{22} + 46 q^{24} - 2 q^{26} + 8 q^{27} + 12 q^{28} - 54 q^{30} + 16 q^{32} + 4 q^{33} - 46 q^{34} - 4 q^{35} + 30 q^{36} - 32 q^{40} - 16 q^{42} - 12 q^{43} - 16 q^{44} + 34 q^{46} + 46 q^{48} - 60 q^{49} + 86 q^{50} + 12 q^{52} + 32 q^{54} + 48 q^{56} + 36 q^{57} + 30 q^{58} - 64 q^{59} + 80 q^{60} + 42 q^{62} - 16 q^{65} + 8 q^{66} - 8 q^{67} - 32 q^{68} + 36 q^{70} - 24 q^{72} - 12 q^{73} + 38 q^{74} + 24 q^{75} - 94 q^{76} + 40 q^{78} - 108 q^{80} - 8 q^{81} + 54 q^{82} - 48 q^{83} - 72 q^{84} + 80 q^{86} - 108 q^{88} + 12 q^{89} + 104 q^{91} - 20 q^{92} + 26 q^{94} - 32 q^{96} + 4 q^{97} - 16 q^{98} + 168 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 4 * q^3 - 6 * q^4 - 6 * q^6 - 10 * q^8 - 20 * q^9 - 6 * q^10 - 8 * q^11 + 8 * q^14 - 10 * q^16 - 12 * q^17 - 6 * q^18 - 8 * q^19 + 10 * q^20 - 20 * q^22 + 46 * q^24 - 2 * q^26 + 8 * q^27 + 12 * q^28 - 54 * q^30 + 16 * q^32 + 4 * q^33 - 46 * q^34 - 4 * q^35 + 30 * q^36 - 32 * q^40 - 16 * q^42 - 12 * q^43 - 16 * q^44 + 34 * q^46 + 46 * q^48 - 60 * q^49 + 86 * q^50 + 12 * q^52 + 32 * q^54 + 48 * q^56 + 36 * q^57 + 30 * q^58 - 64 * q^59 + 80 * q^60 + 42 * q^62 - 16 * q^65 + 8 * q^66 - 8 * q^67 - 32 * q^68 + 36 * q^70 - 24 * q^72 - 12 * q^73 + 38 * q^74 + 24 * q^75 - 94 * q^76 + 40 * q^78 - 108 * q^80 - 8 * q^81 + 54 * q^82 - 48 * q^83 - 72 * q^84 + 80 * q^86 - 108 * q^88 + 12 * q^89 + 104 * q^91 - 20 * q^92 + 26 * q^94 - 32 * q^96 + 4 * q^97 - 16 * q^98 + 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.203272	+	1.39953i	0.143735	+	0.989616i
$2$	0.203272	+	1.39953i	0.143735	+	0.989616i
$3$	0.793616	+	1.37458i	0.458195	+	0.793616i	0.998866	−	0.0476177i	$-0.0151629\pi$
$3$	0.793616	+	1.37458i	0.458195	+	0.793616i	−0.540671	+	0.841234i	$0.681830\pi$
$4$	−1.91736	+	0.568969i	−0.958681	+	0.284485i
$5$	0.203095	+	0.203095i	0.0908267	+	0.0908267i	0.751060	−	0.660234i	$-0.229543\pi$
$5$	0.203095	+	0.203095i	0.0908267	+	0.0908267i	−0.660234	+	0.751060i	$0.729543\pi$
$6$	−1.76245	+	1.39010i	−0.719517	+	0.567507i
$7$	−0.207385	−	0.773970i	−0.0783840	−	0.292533i	0.915595	−	0.402101i	$-0.131720\pi$
$7$	−0.207385	−	0.773970i	−0.0783840	−	0.292533i	−0.993979	+	0.109568i	$0.965053\pi$
$8$	−1.18603	−	2.56775i	−0.419326	−	0.907836i
$9$	0.240346	−	0.416291i	0.0801153	−	0.138764i
$10$	−0.242953	+	0.325520i	−0.0768286	+	0.102939i
$11$	−0.587501	+	2.19258i	−0.177138	+	0.661089i	0.819039	+	0.573737i	$0.194507\pi$
$11$	−0.587501	+	2.19258i	−0.177138	+	0.661089i	−0.996178	+	0.0873516i	$0.972160\pi$
$12$	−2.30375	−	2.18403i	−0.665034	−	0.630475i
$13$	3.31919	−	1.40818i	0.920578	−	0.390559i
$13$	3.31919	−	1.40818i	0.920578	−	0.390559i
$14$	1.04104	−	0.447567i	0.278229	−	0.119617i
$15$	−0.117991	+	0.440350i	−0.0304653	+	0.113698i
$16$	3.35255	−	2.18184i	0.838137	−	0.545460i
$17$	−3.23700	−	1.86889i	−0.785089	−	0.453271i	0.0531419	−	0.998587i	$-0.483076\pi$
$17$	−3.23700	−	1.86889i	−0.785089	−	0.453271i	−0.838231	+	0.545316i	$0.816410\pi$
$18$	0.631467	+	0.251751i	0.148838	+	0.0593382i
$19$	0.792632	+	2.95814i	0.181842	+	0.678645i	0.995284	+	0.0969990i	$0.0309244\pi$
$19$	0.792632	+	2.95814i	0.181842	+	0.678645i	−0.813442	+	0.581646i	$0.802409\pi$
$20$	−0.504960	−	0.273851i	−0.112913	−	0.0612350i
$21$	0.899303	−	0.899303i	0.196244	−	0.196244i
$22$	−3.18801	−	0.376534i	−0.679685	−	0.0802774i
$23$	1.24741	+	2.16058i	0.260103	+	0.450511i	0.966269	−	0.257535i	$-0.0829102\pi$
$23$	1.24741	+	2.16058i	0.260103	+	0.450511i	−0.706166	+	0.708046i	$0.749577\pi$
$24$	2.58833	−	3.66811i	0.528340	−	0.748750i
$25$		−	4.91751i		−	0.983501i
$26$	2.64548	+	4.35906i	0.518822	+	0.854882i
$27$	5.52467			1.06322
$28$	0.837997	+	1.36599i	0.158366	+	0.258147i
$29$	1.82695	−	1.05479i	0.339256	−	0.195869i	−0.320687	−	0.947185i	$-0.603914\pi$
$29$	1.82695	−	1.05479i	0.339256	−	0.195869i	0.659943	+	0.751316i	$0.270580\pi$
$30$	−0.640267	−	0.0756217i	−0.116896	−	0.0138066i
$31$	−5.25282	−	5.25282i	−0.943435	−	0.943435i	0.0550487	−	0.998484i	$-0.482469\pi$
$31$	−5.25282	−	5.25282i	−0.943435	−	0.943435i	−0.998484	+	0.0550487i	$0.982469\pi$
$32$	3.73502	+	4.24848i	0.660265	+	0.751032i
$33$	−3.48014	+	0.932501i	−0.605815	+	0.162328i
$34$	1.95757	−	4.91017i	0.335720	−	0.842087i
$35$	0.115071	−	0.199308i	0.0194505	−	0.0336892i
$36$	−0.223973	+	0.934930i	−0.0373288	+	0.155822i
$37$	−7.30393	−	1.95708i	−1.20076	−	0.321742i	−0.397629	−	0.917546i	$-0.630167\pi$
$37$	−7.30393	−	1.95708i	−1.20076	−	0.321742i	−0.803130	+	0.595804i	$0.796833\pi$
$38$	−3.97889	+	1.71062i	−0.645461	+	0.277499i
$39$	4.56983	+	3.44495i	0.731758	+	0.551634i
$40$	0.280618	−	0.762373i	0.0443697	−	0.120542i
$41$	−2.91916	−	0.782185i	−0.455895	−	0.122157i	0.0235612	−	0.999722i	$-0.492500\pi$
$41$	−2.91916	−	0.782185i	−0.455895	−	0.122157i	−0.479457	+	0.877566i	$0.659166\pi$
$42$	1.44140	+	1.07580i	0.222413	+	0.165999i
$43$	−3.07997	−	1.77822i	−0.469691	−	0.271176i	0.246419	−	0.969163i	$-0.420746\pi$
$43$	−3.07997	−	1.77822i	−0.469691	−	0.271176i	−0.716110	+	0.697987i	$0.754079\pi$
$44$	−0.121061	−	4.53825i	−0.0182506	−	0.684166i
$45$	0.133359	−	0.0357336i	0.0198801	−	0.00532684i
$46$	−2.77022	+	2.18497i	−0.408447	+	0.322156i
$47$	−7.51561	+	7.51561i	−1.09626	+	1.09626i	−0.101420	+	0.994844i	$0.532339\pi$
$47$	−7.51561	+	7.51561i	−1.09626	+	1.09626i	−0.994844	+	0.101420i	$0.967661\pi$
$48$	5.65976	+	2.87682i	0.816916	+	0.415233i
$49$	5.50616	−	3.17898i	0.786594	−	0.454140i
$50$	6.88219	−	0.999590i	0.973289	−	0.141363i
$51$		−	5.93271i		−	0.830746i
$52$	−5.56288	+	4.58851i	−0.771432	+	0.636311i
$53$			13.1159i			1.80160i	0.434230	+	0.900802i	$0.357020\pi$
$53$			13.1159i			1.80160i	−0.434230	+	0.900802i	$0.642980\pi$
$54$	1.12301	+	7.73193i	0.152822	+	1.05218i
$55$	−0.564621	+	0.325984i	−0.0761334	+	0.0439556i
$56$	−1.74139	+	1.45047i	−0.232704	+	0.193827i
$57$	−3.43717	+	3.43717i	−0.455265	+	0.455265i
$58$	1.84757	+	2.34246i	0.242598	+	0.307580i
$59$	−6.44108	+	1.72588i	−0.838558	+	0.224691i	−0.652444	−	0.757837i	$-0.726256\pi$
$59$	−6.44108	+	1.72588i	−0.838558	+	0.224691i	−0.186114	+	0.982528i	$0.559589\pi$
$60$	−0.0243134	−	0.911443i	−0.00313884	−	0.117667i
$61$	−3.55817	−	2.05431i	−0.455577	−	0.263028i	0.254606	−	0.967045i	$-0.418054\pi$
$61$	−3.55817	−	2.05431i	−0.455577	−	0.263028i	−0.710183	+	0.704017i	$0.751388\pi$
$62$	6.28373	−	8.41923i	0.798034	−	1.06924i
$63$	−0.372041	−	0.0996881i	−0.0468728	−	0.0125595i
$64$	−5.18665	+	6.09087i	−0.648331	+	0.761359i
$65$	0.960104	+	0.388116i	0.119086	+	0.0481399i
$66$	−2.01248	−	4.68101i	−0.247719	−	0.576192i
$67$	−10.5799	−	2.83488i	−1.29254	−	0.346336i	−0.453917	−	0.891044i	$-0.649974\pi$
$67$	−10.5799	−	2.83488i	−1.29254	−	0.346336i	−0.838626	+	0.544708i	$0.816640\pi$
$68$	7.26984	+	1.74157i	0.881598	+	0.211197i
$69$	−1.97993	+	3.42934i	−0.238355	+	0.412844i
$70$	0.302328	+	0.120531i	0.0361351	+	0.0144062i
$71$	7.61356	−	2.04005i	0.903563	−	0.242109i	0.223017	−	0.974814i	$-0.428409\pi$
$71$	7.61356	−	2.04005i	0.903563	−	0.242109i	0.680546	+	0.732705i	$0.261743\pi$
$72$	−1.35399	−	0.123412i	−0.159569	−	0.0145442i
$73$	10.3306	+	10.3306i	1.20910	+	1.20910i	0.971319	+	0.237781i	$0.0764201\pi$
$73$	10.3306	+	10.3306i	1.20910	+	1.20910i	0.237781	+	0.971319i	$0.423580\pi$
$74$	1.25431	−	10.6199i	0.145811	−	1.23454i
$75$	6.75952	−	3.90261i	0.780523	−	0.450635i
$76$	−3.20286	−	5.22085i	−0.367393	−	0.598872i
$77$	1.81883			0.207275
$78$	−3.89240	+	7.09586i	−0.440727	+	0.803448i
$79$		−	12.1132i		−	1.36284i	−0.731892	−	0.681421i	$-0.761363\pi$
$79$		−	12.1132i		−	1.36284i	0.731892	−	0.681421i	$-0.238637\pi$
$80$	1.12400	+	0.237765i	0.125668	+	0.0265829i
$81$	3.66343	+	6.34525i	0.407048	+	0.705027i
$82$	0.501309	−	4.24444i	0.0553603	−	0.468720i
$83$	2.07891	−	2.07891i	0.228190	−	0.228190i	−0.583746	−	0.811936i	$-0.698414\pi$
$83$	2.07891	−	2.07891i	0.228190	−	0.228190i	0.811936	+	0.583746i	$0.198414\pi$
$84$	−1.21261	+	2.23596i	−0.132307	+	0.243964i
$85$	−0.277858	−	1.03698i	−0.0301379	−	0.112476i
$86$	1.86260	−	4.67197i	0.200849	−	0.503791i
$87$	2.89979	+	1.67420i	0.310890	+	0.179493i
$88$	6.32680	−	1.09193i	0.674439	−	0.116400i
$89$	0.497728	−	1.85755i	0.0527590	−	0.196899i	−0.934516	−	0.355921i	$-0.884167\pi$
$89$	0.497728	−	1.85755i	0.0527590	−	0.196899i	0.987275	+	0.159021i	$0.0508339\pi$
$90$	0.0771184	+	0.179377i	0.00812899	+	0.0189080i
$91$	−1.77824	−	2.27692i	−0.186410	−	0.238686i
$92$	−3.62103	−	3.43287i	−0.377519	−	0.357901i
$93$	3.05172	−	11.3892i	0.316449	−	1.18100i
$94$	−12.0460	−	8.99060i	−1.24245	−	0.927309i
$95$	−0.439804	+	0.761763i	−0.0451229	+	0.0781552i
$96$	−2.87572	+	8.50577i	−0.293502	+	0.868116i
$97$	1.50062	+	5.60039i	0.152365	+	0.568634i	0.999317	+	0.0369639i	$0.0117687\pi$
$97$	1.50062	+	5.60039i	0.152365	+	0.568634i	−0.846952	+	0.531670i	$0.821565\pi$
$98$	5.56832	+	7.05983i	0.562485	+	0.713150i
$99$	0.771550	+	0.771550i	0.0775437	+	0.0775437i
$100$	2.79791	+	9.42863i	0.279791	+	0.942863i
$101$	−4.06770	−	7.04546i	−0.404751	−	0.701050i	0.589541	−	0.807738i	$-0.299309\pi$
$101$	−4.06770	−	7.04546i	−0.404751	−	0.701050i	−0.994293	+	0.106688i	$0.965975\pi$
$102$	8.30300	−	1.20595i	0.822120	−	0.119407i
$103$	17.4099			1.71545			0.857723	−	0.514113i	$-0.171879\pi$
$103$	17.4099			1.71545			0.857723	+	0.514113i	$0.171879\pi$
$104$	−7.55252	−	6.85269i	−0.740586	−	0.671962i
$105$	0.365287			0.0356484
$106$	−18.3560	+	2.66609i	−1.78290	+	0.258953i
$107$	−0.736948	−	1.27643i	−0.0712434	−	0.123397i	0.828203	−	0.560428i	$-0.189363\pi$
$107$	−0.736948	−	1.27643i	−0.0712434	−	0.123397i	−0.899447	+	0.437031i	$0.856030\pi$
$108$	−10.5928	+	3.14337i	−1.01929	+	0.302471i
$109$	8.43246	+	8.43246i	0.807683	+	0.807683i	0.984283	−	0.176600i	$-0.0565098\pi$
$109$	8.43246	+	8.43246i	0.807683	+	0.807683i	−0.176600	+	0.984283i	$0.556510\pi$
$110$	−0.570995	−	0.723939i	−0.0544422	−	0.0690249i
$111$	−3.10634	−	11.5930i	−0.294841	−	1.10036i
$112$	−2.38395	−	2.14229i	−0.225262	−	0.202428i
$113$	−2.67940	+	4.64087i	−0.252057	+	0.436576i	−0.964092	−	0.265568i	$-0.914440\pi$
$113$	−2.67940	+	4.64087i	−0.252057	+	0.436576i	0.712035	+	0.702144i	$0.247774\pi$
$114$	−5.50910	−	4.11174i	−0.515975	−	0.385100i
$115$	−0.185459	+	0.692143i	−0.0172942	+	0.0645427i
$116$	−2.90278	+	3.06189i	−0.269516	+	0.284289i
$117$	0.211541	−	1.72020i	0.0195570	−	0.159033i
$118$	−3.72471	−	8.66366i	−0.342888	−	0.797554i
$119$	−0.775156	+	2.89292i	−0.0710585	+	0.265194i
$120$	1.27065	−	0.219298i	0.115994	−	0.0200191i
$121$	5.06401	+	2.92371i	0.460365	+	0.265792i
$122$	2.15179	−	5.39735i	0.194814	−	0.488653i
$123$	−1.24151	−	4.63338i	−0.111943	−	0.417778i
$124$	13.0603	+	7.08287i	1.17285	+	0.636060i
$125$	2.01419	−	2.01419i	0.180155	−	0.180155i
$126$	0.0638909	−	0.540946i	0.00569186	−	0.0481913i
$127$	−2.15128	−	3.72613i	−0.190895	−	0.330640i	0.754652	−	0.656125i	$-0.227806\pi$
$127$	−2.15128	−	3.72613i	−0.190895	−	0.330640i	−0.945547	+	0.325485i	$0.894472\pi$
$128$	−9.57865	−	6.02076i	−0.846641	−	0.532165i
$129$		−	5.64490i		−	0.497006i
$130$	−0.348018	+	1.42259i	−0.0305232	+	0.124769i
$131$	14.6076			1.27627			0.638136	−	0.769924i	$-0.279706\pi$
$131$	14.6076			1.27627			0.638136	+	0.769924i	$0.279706\pi$
$132$	6.14212	−	3.76804i	0.534603	−	0.327965i
$133$	2.12514	−	1.22695i	0.184273	−	0.106390i
$134$	1.81690	−	15.3831i	0.156956	−	1.32890i
$135$	1.12203	+	1.12203i	0.0965690	+	0.0965690i
$136$	−0.959627	+	10.5284i	−0.0822873	+	0.902800i
$137$	−15.3326	+	4.10837i	−1.30996	+	0.351002i	−0.845206	−	0.534440i	$-0.820522\pi$
$137$	−15.3326	+	4.10837i	−1.30996	+	0.351002i	−0.464750	+	0.885442i	$0.653856\pi$
$138$	−5.20192	−	2.07388i	−0.442817	−	0.176540i
$139$	−4.87379	+	8.44165i	−0.413390	+	0.716012i	−0.995258	−	0.0972713i	$-0.968989\pi$
$139$	−4.87379	+	8.44165i	−0.413390	+	0.716012i	0.581868	+	0.813283i	$0.302322\pi$
$140$	−0.107232	+	0.447617i	−0.00906273	+	0.0378305i
$141$	−16.2953	−	4.36632i	−1.37232	−	0.367711i
$142$	4.40273	+	10.2407i	0.369469	+	0.859381i
$143$	1.13752	+	8.10491i	0.0951244	+	0.677767i
$144$	−0.102509	−	1.92003i	−0.00854244	−	0.160003i
$145$	0.585265	+	0.156821i	0.0486036	+	0.0130233i
$146$	−12.3580	+	16.5578i	−1.02276	+	1.37033i
$147$	8.73955	+	5.04578i	0.720826	+	0.416169i
$148$	15.1178	−	0.403278i	1.24267	−	0.0331492i
$149$	7.97144	−	2.13594i	0.653046	−	0.174983i	0.0829402	−	0.996555i	$-0.473569\pi$
$149$	7.97144	−	2.13594i	0.653046	−	0.174983i	0.570106	+	0.821571i	$0.306902\pi$
$150$	6.83584	+	8.66686i	0.558144	+	0.707646i
$151$	−10.3500	+	10.3500i	−0.842268	+	0.842268i	−0.989153	−	0.146886i	$-0.953075\pi$
$151$	−10.3500	+	10.3500i	−0.842268	+	0.842268i	0.146886	+	0.989153i	$0.453075\pi$
$152$	6.65568	−	5.54374i	0.539847	−	0.449657i
$153$	−1.55600	+	0.898357i	−0.125795	+	0.0726279i
$154$	0.369717	+	2.54551i	0.0297927	+	0.205123i
$155$		−	2.13364i		−	0.171378i
$156$	−10.7221	−	4.00513i	−0.858453	−	0.320667i
$157$			18.5981i			1.48429i	0.670239	+	0.742146i	$0.266192\pi$
$157$			18.5981i			1.48429i	−0.670239	+	0.742146i	$0.733808\pi$
$158$	16.9528	−	2.46227i	1.34869	−	0.195888i
$159$	−18.0289	+	10.4090i	−1.42978	+	0.825485i
$160$	−0.104280	+	1.62141i	−0.00824409	+	0.128184i
$161$	1.41353	−	1.41353i	0.111402	−	0.111402i
$162$	−8.13568	+	6.41689i	−0.639200	+	0.504158i
$163$	−3.93325	+	1.05391i	−0.308076	+	0.0825487i	−0.409545	−	0.912290i	$-0.634312\pi$
$163$	−3.93325	+	1.05391i	−0.308076	+	0.0825487i	0.101469	+	0.994839i	$0.467646\pi$
$164$	6.04211	−	0.161178i	0.471810	−	0.0125859i
$165$	−0.896184	−	0.517412i	−0.0697679	−	0.0402805i
$166$	3.33208	+	2.48691i	0.258620	+	0.193022i
$167$	21.6215	+	5.79347i	1.67312	+	0.448312i	0.965950	−	0.258728i	$-0.0833033\pi$
$167$	21.6215	+	5.79347i	1.67312	+	0.448312i	0.707173	+	0.707040i	$0.249970\pi$
$168$	−3.37579	−	1.24258i	−0.260448	−	0.0958670i
$169$	9.03406	−	9.34803i	0.694928	−	0.719079i
$170$	1.39480	−	0.599658i	0.106976	−	0.0459917i
$171$	1.42196	+	0.381012i	0.108740	+	0.0291367i
$172$	6.91717	+	1.65709i	0.527429	+	0.126352i
$173$	−7.52545	+	13.0345i	−0.572149	+	0.990992i	0.424196	+	0.905571i	$0.360557\pi$
$173$	−7.52545	+	13.0345i	−0.572149	+	0.990992i	−0.996345	+	0.0854210i	$0.972776\pi$
$174$	−1.75364	+	4.39866i	−0.132943	+	0.333461i
$175$	−3.80600	+	1.01982i	−0.287707	+	0.0770908i
$176$	2.81424	+	8.63258i	0.212131	+	0.650705i
$177$	−7.48412	−	7.48412i	−0.562541	−	0.562541i
$178$	2.70086	+	0.318998i	0.202438	+	0.0239099i
$179$	−14.1062	+	8.14424i	−1.05435	+	0.608729i	−0.923864	−	0.382721i	$-0.874987\pi$
$179$	−14.1062	+	8.14424i	−1.05435	+	0.608729i	−0.130486	+	0.991450i	$0.541654\pi$
$180$	−0.235367	+	0.144392i	−0.0175432	+	0.0107623i
$181$	3.59813			0.267447			0.133724	−	0.991019i	$-0.457307\pi$
$181$	3.59813			0.267447			0.133724	+	0.991019i	$0.457307\pi$
$182$	2.82515	−	2.95153i	0.209414	−	0.218782i
$183$		−	6.52134i		−	0.482071i
$184$	4.06834	−	5.76555i	0.299922	−	0.425042i
$185$	−1.08592	−	1.88086i	−0.0798381	−	0.138284i
$186$	16.5598	+	1.95587i	1.21422	+	0.143412i
$187$	5.99943	−	5.99943i	0.438722	−	0.438722i
$188$	10.1340	−	18.6863i	0.739097	−	1.36284i
$189$	−1.14573	−	4.27593i	−0.0833397	−	0.311028i
$190$	−1.15551	−	0.460673i	−0.0838294	−	0.0334208i
$191$	−23.1278	−	13.3529i	−1.67347	−	0.966180i	−0.965671	−	0.259768i	$-0.916354\pi$
$191$	−23.1278	−	13.3529i	−1.67347	−	0.966180i	−0.707801	−	0.706411i	$-0.750313\pi$
$192$	−12.4886	−	2.29567i	−0.901289	−	0.165676i
$193$	2.87004	−	10.7111i	0.206590	−	0.771003i	−0.782369	−	0.622815i	$-0.785989\pi$
$193$	2.87004	−	10.7111i	0.206590	−	0.771003i	0.988959	−	0.148189i	$-0.0473443\pi$
$194$	−7.53288	+	3.23856i	−0.540829	+	0.232515i
$195$	0.228455	+	1.62776i	0.0163600	+	0.116566i
$196$	−8.74855	+	9.22809i	−0.624896	+	0.659149i
$197$	4.30867	−	16.0802i	0.306980	−	1.14567i	−0.624247	−	0.781227i	$-0.714594\pi$
$197$	4.30867	−	16.0802i	0.306980	−	1.14567i	0.931227	−	0.364439i	$-0.118739\pi$
$198$	−0.922972	+	1.23664i	−0.0655928	+	0.0878842i
$199$	3.05770	−	5.29609i	0.216755	−	0.375430i	−0.737059	−	0.675828i	$-0.763786\pi$
$199$	3.05770	−	5.29609i	0.216755	−	0.375430i	0.953814	+	0.300398i	$0.0971195\pi$
$200$	−12.6269	+	5.83233i	−0.892857	+	0.412408i
$201$	−4.49961	−	16.7928i	−0.317378	−	1.18447i
$202$	9.03348	−	7.12501i	0.635594	−	0.501314i
$203$	−1.19526	−	1.19526i	−0.0838905	−	0.0838905i
$204$	3.37553	+	11.3752i	0.236334	+	0.796420i
$205$	−0.434007	−	0.751723i	−0.0303124	−	0.0525026i
$206$	3.53893	+	24.3656i	0.246569	+	1.69763i
$207$	1.19924			0.0833528
$208$	8.05533	−	11.9629i	0.558537	−	0.829480i
$209$	−6.95165			−0.480856
$210$	0.0742526	+	0.511230i	0.00512392	+	0.0352782i
$211$	−6.47658	−	11.2178i	−0.445866	−	0.772263i	0.552246	−	0.833681i	$-0.313771\pi$
$211$	−6.47658	−	11.2178i	−0.445866	−	0.772263i	−0.998112	+	0.0614182i	$0.980438\pi$
$212$	−7.46253	−	25.1479i	−0.512529	−	1.72716i
$213$	8.84646	+	8.84646i	0.606150	+	0.606150i
$214$	1.63660	−	1.29084i	0.111876	−	0.0882401i
$215$	−0.264378	−	0.986673i	−0.0180304	−	0.0672905i
$216$	−6.55244	−	14.1859i	−0.445837	−	0.965232i
$217$	−2.97617	+	5.15488i	−0.202036	+	0.349936i
$218$	−10.0874	+	13.5155i	−0.683204	+	0.915389i
$219$	−6.00172	+	22.3987i	−0.405558	+	1.51356i
$220$	0.897107	−	0.946280i	0.0604829	−	0.0637982i
$221$	−13.3760	−	1.64491i	−0.899764	−	0.110648i
$222$	15.5934	−	6.70396i	1.04656	−	0.449940i
$223$	−1.31334	+	4.90147i	−0.0879480	+	0.328226i	−0.995856	−	0.0909428i	$-0.971012\pi$
$223$	−1.31334	+	4.90147i	−0.0879480	+	0.328226i	0.907908	+	0.419169i	$0.137679\pi$
$224$	2.51361	−	3.77187i	0.167948	−	0.252019i
$225$	−2.04711	−	1.18190i	−0.136474	−	0.0787935i
$226$	−7.03967	−	2.80655i	−0.468272	−	0.186689i
$227$	−0.177177	−	0.661235i	−0.0117597	−	0.0438877i	0.959797	−	0.280696i	$-0.0905653\pi$
$227$	−0.177177	−	0.661235i	−0.0117597	−	0.0438877i	−0.971556	+	0.236808i	$0.923899\pi$
$228$	4.63466	−	8.54595i	0.306938	−	0.565969i
$229$	3.26943	−	3.26943i	0.216050	−	0.216050i	−0.590782	−	0.806832i	$-0.701180\pi$
$229$	3.26943	−	3.26943i	0.216050	−	0.216050i	0.806832	+	0.590782i	$0.201180\pi$
$230$	−1.00637	−	0.118862i	−0.0663583	−	0.00783755i
$231$	1.44346	+	2.50014i	0.0949725	+	0.164497i
$232$	−4.87525	−	3.44012i	−0.320076	−	0.225855i
$233$		−	15.3725i		−	1.00708i	−0.863971	−	0.503542i	$-0.832030\pi$
$233$		−	15.3725i		−	1.00708i	0.863971	−	0.503542i	$-0.167970\pi$
$234$	2.45047	−	0.0536098i	0.160192	−	0.00350459i
$235$	−3.05276			−0.199140
$236$	11.3679	−	6.97392i	0.739988	−	0.453964i
$237$	16.6506	−	9.61323i	1.08157	−	0.624447i
$238$	−4.20630	−	0.496804i	−0.272654	−	0.0322030i
$239$	−5.60237	−	5.60237i	−0.362387	−	0.362387i	0.502304	−	0.864691i	$-0.332486\pi$
$239$	−5.60237	−	5.60237i	−0.362387	−	0.362387i	−0.864691	+	0.502304i	$0.832486\pi$
$240$	0.565201	+	1.73373i	0.0364836	+	0.111912i
$241$	15.3608	−	4.11592i	0.989476	−	0.265129i	0.272446	−	0.962171i	$-0.412167\pi$
$241$	15.3608	−	4.11592i	0.989476	−	0.265129i	0.717031	+	0.697042i	$0.245501\pi$
$242$	−3.06244	+	7.68154i	−0.196861	+	0.493788i
$243$	2.47229	−	4.28212i	0.158597	−	0.274698i
$244$	7.99114	+	1.91437i	0.511580	+	0.122555i
$245$	1.76391	+	0.472637i	0.112692	+	0.0301957i
$246$	6.23218	−	2.67936i	0.397350	−	0.170830i
$247$	6.79650	+	8.70248i	0.432451	+	0.553726i
$248$	−7.25789	+	19.7179i	−0.460877	+	1.25209i
$249$	4.50750	+	1.20778i	0.285651	+	0.0765400i
$250$	3.22835	+	2.40949i	0.204179	+	0.152390i
$251$	15.5466	+	8.97582i	0.981291	+	0.566549i	0.902660	−	0.430355i	$-0.141612\pi$
$251$	15.5466	+	8.97582i	0.981291	+	0.566549i	0.0786312	+	0.996904i	$0.474945\pi$
$252$	0.770056	−	0.0205418i	0.0485090	−	0.00129401i
$253$	−5.47010	+	1.46571i	−0.343902	+	0.0921483i
$254$	4.77753	−	3.76819i	0.299769	−	0.236438i
$255$	1.20490	−	1.20490i	0.0754539	−	0.0754539i
$256$	6.47916	−	14.6294i	0.404947	−	0.914340i
$257$	−19.5473	+	11.2857i	−1.21933	+	0.703980i	−0.964774	−	0.263078i	$-0.915262\pi$
$257$	−19.5473	+	11.2857i	−1.21933	+	0.703980i	−0.254555	+	0.967058i	$0.581929\pi$
$258$	7.90020	−	1.14745i	0.491845	−	0.0714371i
$259$			6.05889i			0.376481i
$260$	−2.06169	−	0.197890i	−0.127861	−	0.0122726i
$261$		−	1.01406i		−	0.0627685i
$262$	2.96931	+	20.4437i	0.183445	+	1.26302i
$263$	−2.99321	+	1.72813i	−0.184569	+	0.106561i	−0.589438	−	0.807814i	$-0.700651\pi$
$263$	−2.99321	+	1.72813i	−0.184569	+	0.106561i	0.404868	+	0.914375i	$0.367317\pi$
$264$	6.52199	+	7.83015i	0.401401	+	0.481912i
$265$	−2.66376	+	2.66376i	−0.163634	+	0.163634i
$266$	2.14913	+	2.72478i	0.131772	+	0.167067i
$267$	2.94836	−	0.790010i	0.180437	−	0.0483478i
$268$	21.8985	−	0.584157i	1.33766	−	0.0356831i
$269$	11.2159	+	6.47548i	0.683843	+	0.394817i	0.801301	−	0.598261i	$-0.204141\pi$
$269$	11.2159	+	6.47548i	0.683843	+	0.394817i	−0.117458	+	0.993078i	$0.537475\pi$
$270$	−1.34224	+	1.79839i	−0.0816859	+	0.109447i
$271$	9.57438	+	2.56545i	0.581602	+	0.155840i	0.537612	−	0.843192i	$-0.319326\pi$
$271$	9.57438	+	2.56545i	0.581602	+	0.155840i	0.0439898	+	0.999032i	$0.485993\pi$
$272$	−14.9298	+	0.797094i	−0.905253	+	0.0483309i
$273$	1.71858	−	4.25134i	0.104013	−	0.257303i
$274$	−8.86647	−	20.6234i	−0.535643	−	1.24590i
$275$	10.7820	+	2.88904i	0.650182	+	0.174216i
$276$	1.84505	−	7.70179i	0.111059	−	0.463594i
$277$	−4.72824	+	8.18955i	−0.284092	+	0.492062i	−0.972389	−	0.233367i	$-0.925026\pi$
$277$	−4.72824	+	8.18955i	−0.284092	+	0.492062i	0.688296	+	0.725430i	$0.258359\pi$
$278$	−12.8050	−	5.10506i	−0.767995	−	0.306181i
$279$	−3.44920	+	0.924210i	−0.206498	+	0.0553310i
$280$	−0.648250	−	0.0590859i	−0.0387403	−	0.00353106i
$281$	5.83221	+	5.83221i	0.347921	+	0.347921i	0.859334	−	0.511414i	$-0.170878\pi$
$281$	5.83221	+	5.83221i	0.347921	+	0.347921i	−0.511414	+	0.859334i	$0.670878\pi$
$282$	2.79841	−	23.6933i	0.166643	−	1.41092i
$283$	−0.217451	+	0.125545i	−0.0129261	+	0.00746290i	−0.506449	−	0.862270i	$-0.669042\pi$
$283$	−0.217451	+	0.125545i	−0.0129261	+	0.00746290i	0.493523	+	0.869733i	$0.335709\pi$
$284$	−13.4372	+	8.24339i	−0.797352	+	0.489155i
$285$	−1.39614			−0.0827004
$286$	−11.1118	+	3.23949i	−0.657056	+	0.191555i
$287$			2.42155i			0.142940i
$288$	2.66630	−	0.533753i	0.157113	−	0.0314517i
$289$	−1.51454	−	2.62325i	−0.0890904	−	0.154309i
$290$	−0.100508	+	0.850973i	−0.00590204	+	0.0499708i
$291$	−6.50730	+	6.50730i	−0.381464	+	0.381464i
$292$	−25.6852	−	13.9296i	−1.50311	−	0.815170i
$293$	−5.41972	−	20.2267i	−0.316624	−	1.18166i	−0.922468	−	0.386072i	$-0.873831\pi$
$293$	−5.41972	−	20.2267i	−0.316624	−	1.18166i	0.605845	−	0.795583i	$-0.292835\pi$
$294$	−5.28521	+	13.2569i	−0.308240	+	0.773159i
$295$	−1.65867	−	0.957632i	−0.0965714	−	0.0557555i
$296$	3.63742	+	21.0758i	0.211421	+	1.22501i
$297$	−3.24575	+	12.1133i	−0.188337	+	0.702885i
$298$	4.60968	+	10.7221i	0.267032	+	0.621114i
$299$	7.18287	+	5.41479i	0.415396	+	0.313145i
$300$	−10.7400	+	11.3287i	−0.620073	+	0.654062i
$301$	−0.737552	+	2.75258i	−0.0425118	+	0.158656i
$302$	−16.5889	−	12.3812i	−0.954585	−	0.712459i
$303$	6.45639	−	11.1828i	0.370910	−	0.642435i
$304$	9.11153	+	8.18793i	0.522582	+	0.469610i
$305$	−0.305426	−	1.13987i	−0.0174886	−	0.0652685i
$306$	−1.57357	−	1.99506i	−0.0899549	−	0.114050i
$307$	10.5407	+	10.5407i	0.601588	+	0.601588i	0.940734	−	0.339146i	$-0.110138\pi$
$307$	10.5407	+	10.5407i	0.601588	+	0.601588i	−0.339146	+	0.940734i	$0.610138\pi$
$308$	−3.48736	+	1.03486i	−0.198711	+	0.0589666i
$309$	13.8168	+	23.9313i	0.786008	+	1.36141i
$310$	2.98609	−	0.433709i	0.169599	−	0.0246330i
$311$	1.71529			0.0972653			0.0486327	−	0.998817i	$-0.484514\pi$
$311$	1.71529			0.0972653			0.0486327	+	0.998817i	$0.484514\pi$
$312$	3.42580	−	15.8200i	0.193948	−	0.895630i
$313$	−8.25608			−0.466661			−0.233331	−	0.972397i	$-0.574962\pi$
$313$	−8.25608			−0.466661			−0.233331	+	0.972397i	$0.574962\pi$
$314$	−26.0286	+	3.78047i	−1.46888	+	0.213344i
$315$	−0.0553134	−	0.0958057i	−0.00311656	−	0.00539804i
$316$	6.89204	+	23.2254i	0.387707	+	1.30653i
$317$	−9.53707	−	9.53707i	−0.535655	−	0.535655i	0.386595	−	0.922250i	$-0.373651\pi$
$317$	−9.53707	−	9.53707i	−0.535655	−	0.535655i	−0.922250	+	0.386595i	$0.873651\pi$
$318$	−18.2324	−	23.1161i	−1.02242	−	1.29629i
$319$	1.23938	+	4.62543i	0.0693919	+	0.258974i
$320$	−2.29040	+	0.183643i	−0.128037	+	0.0102659i
$321$	1.16971	−	2.02599i	0.0652867	−	0.113080i
$322$	2.26560	+	1.69094i	0.126257	+	0.0942325i
$323$	2.96268	−	11.0569i	0.164848	−	0.615220i
$324$	−10.6344	−	10.0818i	−0.590798	−	0.560097i
$325$	−6.92473	−	16.3221i	−0.384115	−	0.905389i
$326$	−2.27450	−	5.29046i	−0.125973	−	0.293012i
$327$	−4.89899	+	18.2833i	−0.270915	+	1.01107i
$328$	1.45376	+	8.42335i	0.0802707	+	0.465102i
$329$	7.37548	+	4.25823i	0.406623	+	0.234764i
$330$	0.541964	−	1.35941i	0.0298342	−	0.0748331i
$331$	−5.08215	−	18.9669i	−0.279340	−	1.04251i	−0.952877	−	0.303358i	$-0.901892\pi$
$331$	−5.08215	−	18.9669i	−0.279340	−	1.04251i	0.673536	−	0.739154i	$-0.264775\pi$
$332$	−2.80319	+	5.16886i	−0.153845	+	0.283678i
$333$	−2.57018	+	2.57018i	−0.140845	+	0.140845i
$334$	−3.71308	+	31.4376i	−0.203171	+	1.72019i
$335$	−1.57298	−	2.72447i	−0.0859408	−	0.148854i
$336$	1.05282	−	4.97709i	0.0574362	−	0.271523i
$337$			34.2794i			1.86732i	0.358165	+	0.933658i	$0.383402\pi$
$337$			34.2794i			1.86732i	−0.358165	+	0.933658i	$0.616598\pi$
$338$	14.9192	+	10.7432i	0.811498	+	0.584355i
$339$	−8.50568			−0.461965
$340$	1.12276	+	1.83017i	0.0608903	+	0.0992549i
$341$	14.6033	−	8.43122i	0.790813	−	0.456576i
$342$	−0.244194	+	2.06752i	−0.0132045	+	0.111798i
$343$	−7.56843	−	7.56843i	−0.408657	−	0.408657i
$344$	−0.913073	+	10.0176i	−0.0492296	+	0.540114i
$345$	−1.09859	+	0.294367i	−0.0591462	+	0.0158482i
$346$	−19.7718	−	7.88254i	−1.06294	−	0.423768i
$347$	10.3503	−	17.9272i	0.555633	−	0.962384i	−0.442221	−	0.896906i	$-0.645809\pi$
$347$	10.3503	−	17.9272i	0.555633	−	0.962384i	0.997854	−	0.0654782i	$-0.0208573\pi$
$348$	−6.51251	−	1.56015i	−0.349107	−	0.0836326i
$349$	−14.7302	−	3.94695i	−0.788490	−	0.211275i	−0.157966	−	0.987445i	$-0.550494\pi$
$349$	−14.7302	−	3.94695i	−0.788490	−	0.211275i	−0.630525	+	0.776169i	$0.717160\pi$
$350$	−2.20091	−	5.11931i	−0.117644	−	0.273639i
$351$	18.3374	−	7.77972i	0.978780	−	0.415251i
$352$	−11.5095	+	5.69337i	−0.613458	+	0.303458i
$353$	26.0283	+	6.97426i	1.38535	+	0.371202i	0.873060	−	0.487612i	$-0.162132\pi$
$353$	26.0283	+	6.97426i	1.38535	+	0.371202i	0.512286	+	0.858815i	$0.328799\pi$
$354$	8.95293	−	11.9956i	0.475843	−	0.637557i
$355$	1.96060	+	1.13195i	0.104058	+	0.0600777i
$356$	0.102562	+	3.84478i	0.00543578	+	0.203773i
$357$	−4.59174	+	1.23035i	−0.243021	+	0.0651172i
$358$	−14.2655	−	18.0866i	−0.753955	−	0.955906i
$359$	17.2783	−	17.2783i	0.911913	−	0.911913i	−0.0845098	−	0.996423i	$-0.526932\pi$
$359$	17.2783	−	17.2783i	0.911913	−	0.911913i	0.996423	+	0.0845098i	$0.0269324\pi$
$360$	−0.249924	−	0.300052i	−0.0131721	−	0.0158141i
$361$	8.33213	−	4.81056i	0.438533	−	0.253187i
$362$	0.731399	+	5.03569i	0.0384415	+	0.264670i
$363$			9.28121i			0.487137i
$364$	4.70502	+	3.35392i	0.246610	+	0.175793i
$365$			4.19616i			0.219637i
$366$	9.12680	−	1.32560i	0.477066	−	0.0692904i
$367$	0.905546	−	0.522817i	0.0472691	−	0.0272908i	−0.476179	−	0.879348i	$-0.657979\pi$
$367$	0.905546	−	0.522817i	0.0472691	−	0.0272908i	0.523448	+	0.852057i	$0.324645\pi$
$368$	8.89603	+	4.52179i	0.463737	+	0.235714i
$369$	−1.02722	+	1.02722i	−0.0534751	+	0.0534751i
$370$	2.41158	−	1.90210i	0.125372	−	0.0988853i
$371$	10.1513	−	2.72003i	0.527029	−	0.141217i
$372$	0.628839	+	23.5735i	0.0326038	+	1.22223i
$373$	24.2536	+	14.0028i	1.25580	+	0.725039i	0.972256	−	0.233919i	$-0.0751551\pi$
$373$	24.2536	+	14.0028i	1.25580	+	0.725039i	0.283548	+	0.958958i	$0.408488\pi$
$374$	9.61589	+	7.17686i	0.497226	+	0.371107i
$375$	4.36717	+	1.17018i	0.225520	+	0.0604279i
$376$	28.2119	+	10.3844i	1.45492	+	0.535535i
$377$	4.57866	−	6.07371i	0.235813	−	0.312812i
$378$	5.75139	−	2.47266i	0.295820	−	0.127180i
$379$	−24.2227	−	6.49045i	−1.24424	−	0.333392i	−0.424129	−	0.905602i	$-0.639420\pi$
$379$	−24.2227	−	6.49045i	−1.24424	−	0.333392i	−0.820108	+	0.572209i	$0.806086\pi$
$380$	0.409843	−	1.71081i	0.0210245	−	0.0877627i
$381$	3.41458	−	5.91423i	0.174934	−	0.302995i
$382$	13.9865	−	35.0823i	0.715611	−	1.79497i
$383$	−18.0059	+	4.82468i	−0.920061	+	0.246530i	−0.687611	−	0.726079i	$-0.741341\pi$
$383$	−18.0059	+	4.82468i	−0.920061	+	0.246530i	−0.232449	+	0.972608i	$0.574674\pi$
$384$	0.674269	−	17.9448i	0.0344086	−	0.915743i
$385$	0.369395	+	0.369395i	0.0188261	+	0.0188261i
$386$	15.5739	+	1.83943i	0.792691	+	0.0936245i
$387$	−1.48052	+	0.854776i	−0.0752588	+	0.0434507i
$388$	−6.06369	−	9.88417i	−0.307837	−	0.501793i
$389$	−27.5165			−1.39514			−0.697572	−	0.716515i	$-0.745736\pi$
$389$	−27.5165			−1.39514			−0.697572	+	0.716515i	$0.745736\pi$
$390$	−2.23166	+	0.650607i	−0.113004	+	0.0329448i
$391$		−	9.32505i		−	0.471588i
$392$	−14.6933	−	10.3680i	−0.742124	−	0.523665i
$393$	11.5928	+	20.0794i	0.584781	+	1.01287i
$394$	23.3805	+	2.76146i	1.17789	+	0.139121i
$395$	2.46013	−	2.46013i	0.123782	−	0.123782i
$396$	−1.91833	−	1.04035i	−0.0963996	−	0.0522796i
$397$	3.63406	+	13.5625i	0.182388	+	0.680681i	0.995175	+	0.0981198i	$0.0312828\pi$
$397$	3.63406	+	13.5625i	0.182388	+	0.680681i	−0.812787	+	0.582562i	$0.802050\pi$
$398$	8.03358	+	3.20279i	0.402687	+	0.160542i
$399$	3.37309	+	1.94745i	0.168865	+	0.0974945i
$400$	−10.7292	−	16.4862i	−0.536460	−	0.824309i
$401$	2.77041	−	10.3393i	0.138348	−	0.516321i	−0.861614	−	0.507564i	$-0.830546\pi$
$401$	2.77041	−	10.3393i	0.138348	−	0.516321i	0.999962	−	0.00875651i	$-0.00278732\pi$
$402$	22.5873	−	9.71084i	1.12655	−	0.484333i
$403$	−24.8320	−	10.0382i	−1.23697	−	0.500039i
$404$	11.8079	+	11.1943i	0.587465	+	0.556937i
$405$	−0.544663	+	2.03271i	−0.0270645	+	0.101006i
$406$	1.42983	−	1.91576i	0.0709614	−	0.0950774i
$407$	8.58213	−	14.8647i	0.425401	−	0.736815i
$408$	−15.2337	+	7.03640i	−0.754181	+	0.348354i
$409$	1.81350	+	6.76808i	0.0896718	+	0.334660i	0.996158	−	0.0875760i	$-0.0279121\pi$
$409$	1.81350	+	6.76808i	0.0896718	+	0.334660i	−0.906486	+	0.422236i	$0.861245\pi$
$410$	0.963836	−	0.760210i	0.0476005	−	0.0375441i
$411$	−17.8155	−	17.8155i	−0.878775	−	0.878775i
$412$	−33.3810	+	9.90568i	−1.64456	+	0.488018i
$413$	2.67156	+	4.62729i	0.131459	+	0.227694i
$414$	0.243771	+	1.67837i	0.0119807	+	0.0824873i
$415$	0.844432			0.0414516
$416$	18.3799	+	8.84194i	0.901148	+	0.433512i
$417$	−15.4717			−0.757652
$418$	−1.41307	−	9.72904i	−0.0691157	−	0.475863i
$419$	−11.8842	−	20.5840i	−0.580580	−	1.00559i	−0.995411	−	0.0956958i	$-0.969492\pi$
$419$	−11.8842	−	20.5840i	−0.580580	−	1.00559i	0.414830	−	0.909899i	$-0.363841\pi$
$420$	−0.700388	+	0.207837i	−0.0341754	+	0.0101414i
$421$	−10.0457	−	10.0457i	−0.489596	−	0.489596i	0.418583	−	0.908179i	$-0.362527\pi$
$421$	−10.0457	−	10.0457i	−0.489596	−	0.489596i	−0.908179	+	0.418583i	$0.862527\pi$
$422$	14.3831	−	11.3444i	0.700158	−	0.552238i
$423$	1.32234	+	4.93503i	0.0642942	+	0.239949i
$424$	33.6782	−	15.5559i	1.63556	−	0.755460i
$425$	−9.19025	+	15.9180i	−0.445793	+	0.772136i
$426$	−10.5826	+	14.1791i	−0.512731	+	0.686980i
$427$	−0.852066	+	3.17995i	−0.0412343	+	0.153889i
$428$	2.13924	+	2.02808i	0.103404	+	0.0980309i
$429$	−10.2381	+	7.99581i	−0.494302	+	0.386041i
$430$	1.32714	−	0.570568i	0.0640002	−	0.0275152i
$431$	−1.94441	+	7.25665i	−0.0936591	+	0.349540i	−0.996813	−	0.0797770i	$-0.974579\pi$
$431$	−1.94441	+	7.25665i	−0.0936591	+	0.349540i	0.903154	+	0.429317i	$0.141246\pi$
$432$	18.5217	−	12.0539i	0.891127	−	0.579945i
$433$	−11.3356	−	6.54458i	−0.544752	−	0.314513i	0.202251	−	0.979334i	$-0.435174\pi$
$433$	−11.3356	−	6.54458i	−0.544752	−	0.314513i	−0.747003	+	0.664821i	$0.768508\pi$
$434$	−7.81938	−	3.11740i	−0.375342	−	0.149640i
$435$	0.248912	+	0.928952i	0.0119344	+	0.0445399i
$436$	−20.9659	−	11.3703i	−1.00408	−	0.544537i
$437$	−5.40256	+	5.40256i	−0.258439	+	0.258439i
$438$	−32.5676	−	3.84655i	−1.55614	−	0.183795i
$439$	0.725737	+	1.25701i	0.0346376	+	0.0599940i	0.882825	−	0.469703i	$-0.155639\pi$
$439$	0.725737	+	1.25701i	0.0346376	+	0.0599940i	−0.848187	+	0.529697i	$0.822306\pi$
$440$	1.50670	+	1.06317i	0.0718292	+	0.0506849i
$441$		−	3.05622i		−	0.145534i
$442$	−0.416860	−	19.0544i	−0.0198280	−	0.906326i
$443$	−18.0569			−0.857909			−0.428954	−	0.903326i	$-0.641118\pi$
$443$	−18.0569			−0.857909			−0.428954	+	0.903326i	$0.641118\pi$
$444$	12.5521	+	20.4606i	0.595695	+	0.971018i
$445$	0.478343	−	0.276172i	0.0226757	−	0.0130918i
$446$	−7.12671	−	0.841733i	−0.337459	−	0.0398572i
$447$	9.26230	+	9.26230i	0.438092	+	0.438092i
$448$	5.78978	+	2.75116i	0.273542	+	0.129980i
$449$	33.1966	−	8.89499i	1.56664	−	0.419780i	0.631883	−	0.775064i	$-0.282282\pi$
$449$	33.1966	−	8.89499i	1.56664	−	0.419780i	0.934759	+	0.355283i	$0.115616\pi$
$450$	1.23799	−	3.10524i	0.0583592	−	0.146383i
$451$	3.43001	−	5.94096i	0.161513	−	0.279749i
$452$	2.49688	−	10.4227i	0.117443	−	0.490243i
$453$	−22.4408	−	6.01299i	−1.05436	−	0.282515i
$454$	0.889402	−	0.382375i	0.0417417	−	0.0179457i
$455$	0.101280	−	0.823581i	0.00474807	−	0.0386101i
$456$	12.9024	+	4.74918i	0.604210	+	0.222401i
$457$	−21.1085	−	5.65600i	−0.987414	−	0.264577i	−0.271250	−	0.962509i	$-0.587437\pi$
$457$	−21.1085	−	5.65600i	−0.987414	−	0.264577i	−0.716164	+	0.697932i	$0.754104\pi$
$458$	5.24024	+	3.91108i	0.244861	+	0.182753i
$459$	−17.8834	−	10.3250i	−0.834724	−	0.481928i
$460$	−0.0382159	−	1.43261i	−0.00178182	−	0.0667958i
$461$	15.3365	−	4.10940i	0.714292	−	0.191394i	0.116669	−	0.993171i	$-0.462778\pi$
$461$	15.3365	−	4.10940i	0.714292	−	0.191394i	0.597623	+	0.801777i	$0.296112\pi$
$462$	−3.20560	+	2.52837i	−0.149138	+	0.117630i
$463$	3.31898	−	3.31898i	0.154246	−	0.154246i	−0.625765	−	0.780011i	$-0.715213\pi$
$463$	3.31898	−	3.31898i	0.154246	−	0.154246i	0.780011	+	0.625765i	$0.215213\pi$
$464$	3.82355	−	7.52233i	0.177504	−	0.349216i
$465$	2.93287	−	1.69329i	0.136009	−	0.0785246i
$466$	21.5142	−	3.12479i	0.996626	−	0.144753i
$467$			4.31326i			0.199594i	0.995008	+	0.0997968i	$0.0318193\pi$
$467$			4.31326i			0.199594i	−0.995008	+	0.0997968i	$0.968181\pi$
$468$	0.573140	+	3.41861i	0.0264934	+	0.158025i
$469$			8.77645i			0.405259i
$470$	−0.620540	−	4.27242i	−0.0286234	−	0.197072i
$471$	−25.5647	+	14.7598i	−1.17796	+	0.680094i
$472$	12.0710	+	14.4921i	0.555612	+	0.667054i
$473$	5.70839	−	5.70839i	0.262472	−	0.262472i
$474$	16.8386	+	21.3489i	0.773422	+	0.980588i
$475$	14.5467	−	3.89777i	0.667448	−	0.178842i
$476$	−0.159729	−	5.98782i	−0.00732118	−	0.274451i
$477$	5.46002	+	3.15235i	0.249997	+	0.144336i
$478$	6.70187	−	8.97948i	0.306537	−	0.410712i
$479$	14.5501	+	3.89868i	0.664810	+	0.178135i	0.575416	−	0.817861i	$-0.304840\pi$
$479$	14.5501	+	3.89868i	0.664810	+	0.178135i	0.0893943	+	0.995996i	$0.471507\pi$
$480$	−2.31152	+	1.14343i	−0.105506	+	0.0521904i
$481$	−26.9991	+	3.78931i	−1.23105	+	0.172778i
$482$	8.88276	+	20.6612i	0.404599	+	0.941094i
$483$	3.06481	+	0.821214i	0.139454	+	0.0373665i
$484$	−11.3730	−	2.72454i	−0.516956	−	0.123843i
$485$	−0.832642	+	1.44218i	−0.0378083	+	0.0654860i
$486$	6.49550	+	2.58960i	0.294642	+	0.117467i
$487$	−17.2756	+	4.62898i	−0.782831	+	0.209759i	−0.628032	−	0.778187i	$-0.716139\pi$
$487$	−17.2756	+	4.62898i	−0.782831	+	0.209759i	−0.154798	+	0.987946i	$0.549473\pi$
$488$	−1.05484	+	11.5730i	−0.0477503	+	0.523884i
$489$	−4.57018	−	4.57018i	−0.206671	−	0.206671i
$490$	−0.302917	+	2.56471i	−0.0136844	+	0.115862i
$491$	15.4867	−	8.94124i	0.698904	−	0.403512i	−0.108035	−	0.994147i	$-0.534456\pi$
$491$	15.4867	−	8.94124i	0.698904	−	0.403512i	0.806939	+	0.590635i	$0.201123\pi$
$492$	5.01667	+	8.17748i	0.226169	+	0.368669i
$493$	−7.88512			−0.355128
$494$	−10.7978	+	11.2809i	−0.485818	+	0.507550i
$495$			0.313395i			0.0140861i
$496$	−29.0712	−	6.14953i	−1.30533	−	0.276122i
$497$	−3.15787	−	5.46959i	−0.141650	−	0.245345i
$498$	−0.774077	+	6.55388i	−0.0346872	+	0.293687i
$499$	−2.29278	+	2.29278i	−0.102639	+	0.102639i	−0.756561	−	0.653923i	$-0.773122\pi$
$499$	−2.29278	+	2.29278i	−0.102639	+	0.102639i	0.653923	+	0.756561i	$0.273122\pi$
$500$	−2.71592	+	5.00795i	−0.121460	+	0.223962i
$501$	9.19559	+	34.3184i	0.410828	+	1.53323i
$502$	−9.40174	+	23.5824i	−0.419620	+	1.05253i
$503$	−17.2984	−	9.98723i	−0.771297	−	0.445309i	0.0620400	−	0.998074i	$-0.480239\pi$
$503$	−17.2984	−	9.98723i	−0.771297	−	0.445309i	−0.833337	+	0.552765i	$0.813573\pi$
$504$	0.185280	+	1.07354i	0.00825301	+	0.0478193i
$505$	0.604768	−	2.25702i	0.0269118	−	0.100436i
$506$	−3.16322	−	7.35762i	−0.140622	−	0.327086i
$507$	20.0192	+	4.99933i	0.889086	+	0.222028i
$508$	6.24483	+	5.92032i	0.277070	+	0.262672i
$509$	0.745854	−	2.78356i	0.0330594	−	0.123379i	−0.947424	−	0.319980i	$-0.896324\pi$
$509$	0.745854	−	2.78356i	0.0330594	−	0.123379i	0.980484	+	0.196601i	$0.0629904\pi$
$510$	1.93122	+	1.44137i	0.0855158	+	0.0638251i
$511$	5.85314	−	10.1379i	0.258928	−	0.448476i
$512$	21.7914	+	6.09402i	0.963051	+	0.269320i
$513$	4.37903	+	16.3428i	0.193339	+	0.721551i
$514$	−19.7680	−	25.0630i	−0.871930	−	1.10548i
$515$	3.53585	+	3.53585i	0.155808	+	0.155808i
$516$	3.21178	+	10.8233i	0.141391	+	0.476470i
$517$	−12.0632	−	20.8940i	−0.530538	−	0.918918i
$518$	−8.47959	+	1.23160i	−0.372572	+	0.0541135i
$519$	−23.8893			−1.04862
$520$	−0.142131	−	2.92562i	−0.00623285	−	0.128297i
$521$	24.0994			1.05581			0.527906	−	0.849303i	$-0.322977\pi$
$521$	24.0994			1.05581			0.527906	+	0.849303i	$0.322977\pi$
$522$	1.41920	−	0.206129i	0.0621167	−	0.00902202i
$523$	17.5798	+	30.4491i	0.768712	+	1.33145i	0.938262	+	0.345926i	$0.112435\pi$
$523$	17.5798	+	30.4491i	0.768712	+	1.33145i	−0.169550	+	0.985522i	$0.554231\pi$
$524$	−28.0080	+	8.31127i	−1.22354	+	0.363080i
$525$	−4.42233	−	4.42233i	−0.193006	−	0.193006i
$526$	−3.02701	−	3.83781i	−0.131984	−	0.167336i
$527$	7.18649	+	26.8203i	0.313048	+	1.16831i
$528$	−9.63278	+	10.7194i	−0.419213	+	0.466500i
$529$	8.38794	−	14.5283i	0.364693	−	0.631667i
$530$	−4.26948	−	3.18655i	−0.185454	−	0.138415i
$531$	−0.829618	+	3.09618i	−0.0360023	+	0.134363i
$532$	−3.37656	+	3.56164i	−0.146392	+	0.154417i
$533$	−10.7907	+	1.51447i	−0.467397	+	0.0655990i
$534$	1.70496	+	3.96572i	0.0737808	+	0.171614i
$535$	0.109566	−	0.408906i	0.00473696	−	0.0176786i
$536$	5.26889	+	30.5288i	0.227581	+	1.31864i
$537$	−22.3899	−	12.9268i	−0.966195	−	0.557833i
$538$	−6.78275	+	17.0132i	−0.292425	+	0.733491i
$539$	3.73531	+	13.9404i	0.160891	+	0.600454i
$540$	−2.78974	−	1.51294i	−0.120051	−	0.0651065i
$541$	11.1945	−	11.1945i	0.481288	−	0.481288i	−0.424255	−	0.905543i	$-0.639464\pi$
$541$	11.1945	−	11.1945i	0.481288	−	0.481288i	0.905543	+	0.424255i	$0.139464\pi$
$542$	−1.64422	+	13.9211i	−0.0706251	+	0.597962i
$543$	2.85554	+	4.94594i	0.122543	+	0.212250i
$544$	−4.15037	−	20.7327i	−0.177945	−	0.888906i
$545$			3.42518i			0.146718i
$546$	6.29921	+	1.54102i	0.269581	+	0.0659498i
$547$	21.0720			0.900973			0.450486	−	0.892783i	$-0.351251\pi$
$547$	21.0720			0.900973			0.450486	+	0.892783i	$0.351251\pi$
$548$	27.0607	−	16.6010i	1.15597	−	0.709161i
$549$	−1.71038	+	0.987490i	−0.0729974	+	0.0421451i
$550$	−1.85161	+	15.6770i	−0.0789529	+	0.668471i
$551$	4.56832	+	4.56832i	0.194617	+	0.194617i
$552$	11.1539	+	1.01664i	0.474743	+	0.0432713i
$553$	−9.37525	+	2.51209i	−0.398676	+	0.106825i
$554$	−12.4226	−	4.95260i	−0.527787	−	0.210416i
$555$	1.72360	−	2.98537i	0.0731628	−	0.126722i
$556$	4.54178	−	18.9587i	0.192614	−	0.804029i
$557$	35.3694	+	9.47720i	1.49865	+	0.401562i	0.912647	−	0.408748i	$-0.134035\pi$
$557$	35.3694	+	9.47720i	1.49865	+	0.401562i	0.586002	+	0.810310i	$0.300701\pi$
$558$	−1.99458	−	4.63939i	−0.0844374	−	0.196401i
$559$	−12.7271	−	1.56511i	−0.538297	−	0.0661970i
$560$	−0.0490784	−	0.919255i	−0.00207394	−	0.0388456i
$561$	13.0080	+	3.48548i	0.549197	+	0.147157i
$562$	−6.97682	+	9.34787i	−0.294300	+	0.394316i
$563$	−7.36457	−	4.25194i	−0.310380	−	0.179198i	0.336717	−	0.941606i	$-0.390684\pi$
$563$	−7.36457	−	4.25194i	−0.310380	−	0.179198i	−0.647096	+	0.762408i	$0.724017\pi$
$564$	33.7284	−	0.899727i	1.42022	−	0.0378854i
$565$	−1.48671	+	0.398362i	−0.0625463	+	0.0167592i
$566$	−0.219906	−	0.278809i	−0.00924334	−	0.0117192i
$567$	4.15129	−	4.15129i	0.174338	−	0.174338i
$568$	−14.2683	−	17.1301i	−0.598683	−	0.718764i
$569$	−2.15664	+	1.24514i	−0.0904110	+	0.0521988i	−0.544524	−	0.838745i	$-0.683290\pi$
$569$	−2.15664	+	1.24514i	−0.0904110	+	0.0521988i	0.454113	+	0.890944i	$0.349956\pi$
$570$	−0.283796	−	1.95394i	−0.0118869	−	0.0818416i
$571$			32.2266i			1.34864i	0.738439	+	0.674320i	$0.235563\pi$
$571$			32.2266i			1.34864i	−0.738439	+	0.674320i	$0.764437\pi$
$572$	−6.79249	−	14.8928i	−0.284008	−	0.622701i
$573$		−	42.3882i		−	1.77079i
$574$	−3.38903	+	0.492233i	−0.141455	+	0.0205454i
$575$	10.6246	−	6.13414i	0.443078	−	0.255811i
$576$	1.28899	+	3.62307i	0.0537078	+	0.150961i
$577$	−3.92020	+	3.92020i	−0.163200	+	0.163200i	−0.783983	−	0.620783i	$-0.786815\pi$
$577$	−3.92020	+	3.92020i	−0.163200	+	0.163200i	0.620783	+	0.783983i	$0.286815\pi$
$578$	3.36346	−	2.65287i	0.139901	−	0.110345i
$579$	17.0010	−	4.55542i	0.706539	−	0.189317i
$580$	−1.21139	+	0.0323147i	−0.0503003	+	0.00134180i
$581$	−2.04015	−	1.17788i	−0.0846397	−	0.0488668i
$582$	−10.4299	−	7.78440i	−0.432333	−	0.322674i
$583$	−28.7577	−	7.70559i	−1.19102	−	0.319133i
$584$	14.2739	−	38.7786i	0.590656	−	1.60467i
$585$	0.392326	−	0.306401i	0.0162207	−	0.0126681i
$586$	27.2061	−	11.6966i	1.12388	−	0.483181i
$587$	20.1329	+	5.39459i	0.830972	+	0.222658i	0.649138	−	0.760671i	$-0.275130\pi$
$587$	20.1329	+	5.39459i	0.830972	+	0.222658i	0.181835	+	0.983329i	$0.441796\pi$
$588$	−19.6278	−	4.70205i	−0.809436	−	0.193909i
$589$	11.3751	−	19.7022i	0.468701	−	0.811814i
$590$	1.00307	−	2.51601i	0.0412959	−	0.103583i
$591$	25.5230	−	6.83887i	1.04988	−	0.281313i
$592$	−28.7568	+	9.37479i	−1.18190	+	0.385301i
$593$	−26.9784	−	26.9784i	−1.10787	−	1.10787i	−0.993430	−	0.114441i	$-0.963492\pi$
$593$	−26.9784	−	26.9784i	−1.10787	−	1.10787i	−0.114441	−	0.993430i	$-0.536508\pi$
$594$	−17.6127	−	2.08023i	−0.722657	−	0.0853528i
$595$	−0.744967	+	0.430107i	−0.0305407	+	0.0176327i
$596$	−14.0688	+	8.63087i	−0.576282	+	0.353534i
$597$	9.70656			0.397263
$598$	−6.11808	+	11.1533i	−0.250187	+	0.456092i
$599$		−	8.59618i		−	0.351230i	−0.984459	−	0.175615i	$-0.943809\pi$
$599$		−	8.59618i		−	0.351230i	0.984459	−	0.175615i	$-0.0561914\pi$
$600$	−18.0379	−	12.7281i	−0.736396	−	0.519623i
$601$	−3.37794	−	5.85076i	−0.137789	−	0.238658i	0.788870	−	0.614560i	$-0.210666\pi$
$601$	−3.37794	−	5.85076i	−0.137789	−	0.238658i	−0.926659	+	0.375902i	$0.877333\pi$
$602$	−4.00224	−	0.472703i	−0.163119	−	0.0192659i
$603$	−3.72297	+	3.72297i	−0.151611	+	0.151611i
$604$	13.9558	−	25.7334i	0.567854	−	1.04708i
$605$	0.434684	+	1.62226i	0.0176724	+	0.0659544i
$606$	16.9630	+	6.76276i	0.689076	+	0.274718i
$607$	38.1905	+	22.0493i	1.55010	+	0.894953i	0.998132	+	0.0610892i	$0.0194574\pi$
$607$	38.1905	+	22.0493i	1.55010	+	0.894953i	0.551971	+	0.833863i	$0.313876\pi$
$608$	−9.60712	+	14.4162i	−0.389620	+	0.584655i
$609$	0.694405	−	2.59155i	0.0281387	−	0.105015i
$610$	1.53319	−	0.659155i	0.0620770	−	0.0266884i
$611$	−14.3624	+	35.5291i	−0.581041	+	1.43735i
$612$	2.47228	−	2.60779i	0.0999359	−	0.105414i
$613$	−2.58306	+	9.64013i	−0.104329	+	0.389361i	−0.998268	−	0.0588272i	$-0.981264\pi$
$613$	−2.58306	+	9.64013i	−0.104329	+	0.389361i	0.893939	+	0.448188i	$0.147931\pi$
$614$	−12.6094	+	16.8946i	−0.508872	+	0.681810i
$615$	0.688871	−	1.19316i	0.0277779	−	0.0481128i
$616$	−2.15720	−	4.67030i	−0.0869160	−	0.188172i
$617$	3.14881	+	11.7515i	0.126766	+	0.473099i	0.999896	−	0.0143885i	$-0.00458015\pi$
$617$	3.14881	+	11.7515i	0.126766	+	0.473099i	−0.873130	+	0.487487i	$0.837913\pi$
$618$	−30.6840	+	24.2015i	−1.23429	+	0.973527i
$619$	−11.9483	−	11.9483i	−0.480243	−	0.480243i	0.424966	−	0.905209i	$-0.360286\pi$
$619$	−11.9483	−	11.9483i	−0.480243	−	0.480243i	−0.905209	+	0.424966i	$0.860286\pi$
$620$	1.21398	+	4.09096i	0.0487544	+	0.164297i
$621$	6.89152	+	11.9365i	0.276547	+	0.478994i
$622$	0.348670	+	2.40060i	0.0139804	+	0.0962553i
$623$	−1.54091			−0.0617351
$624$	22.8369	+	1.57875i	0.914207	+	0.0632006i
$625$	−23.7694			−0.950775
$626$	−1.67823	−	11.5546i	−0.0670755	−	0.461816i
$627$	−5.51695	−	9.55563i	−0.220326	−	0.381615i
$628$	−10.5818	−	35.6593i	−0.422258	−	1.42296i
$629$	19.9853	+	19.9853i	0.796866	+	0.796866i
$630$	0.122839	−	0.0968873i	0.00489403	−	0.00386008i
$631$	4.96268	+	18.5210i	0.197561	+	0.737309i	0.991589	+	0.129427i	$0.0413138\pi$
$631$	4.96268	+	18.5210i	0.197561	+	0.737309i	−0.794028	+	0.607882i	$0.792020\pi$
$632$	−31.1036	+	14.3667i	−1.23724	+	0.571475i
$633$	10.2798	−	17.8052i	0.408587	−	0.707694i
$634$	11.4088	−	15.2860i	0.453101	−	0.607085i
$635$	0.319843	−	1.19367i	0.0126926	−	0.0473693i
$636$	28.6455	−	30.2156i	1.13587	−	1.19813i
$637$	13.7994	−	18.3053i	0.546753	−	0.725282i
$638$	−6.22149	+	2.67477i	−0.246311	+	0.105895i
$639$	0.980634	−	3.65977i	0.0387933	−	0.144778i
$640$	−0.722588	−	3.16816i	−0.0285628	−	0.125232i
$641$	−3.97192	−	2.29319i	−0.156881	−	0.0905755i	0.419504	−	0.907753i	$-0.362204\pi$
$641$	−3.97192	−	2.29319i	−0.156881	−	0.0905755i	−0.576386	+	0.817178i	$0.695537\pi$
$642$	3.07320	+	1.22521i	0.121290	+	0.0483553i
$643$	10.7606	+	40.1589i	0.424355	+	1.58371i	0.765328	+	0.643641i	$0.222577\pi$
$643$	10.7606	+	40.1589i	0.424355	+	1.58371i	−0.340973	+	0.940073i	$0.610756\pi$
$644$	−1.90599	+	3.51450i	−0.0751065	+	0.138491i
$645$	1.14645	−	1.14645i	0.0451414	−	0.0451414i
$646$	16.0766	+	1.89881i	0.632526	+	0.0747075i
$647$	−20.7662	−	35.9681i	−0.816402	−	1.41405i	−0.908316	−	0.418284i	$-0.862632\pi$
$647$	−20.7662	−	35.9681i	−0.816402	−	1.41405i	0.0919140	−	0.995767i	$-0.470702\pi$
$648$	11.9480	−	16.9324i	0.469363	−	0.665169i
$649$		−	15.1366i		−	0.594163i
$650$	21.4357	−	13.0092i	0.840777	−	0.510262i
$651$	−9.44776			−0.370287
$652$	6.94182	−	4.25863i	0.271863	−	0.166781i
$653$	−4.70452	+	2.71615i	−0.184102	+	0.106291i	−0.589218	−	0.807974i	$-0.700564\pi$
$653$	−4.70452	+	2.71615i	−0.184102	+	0.106291i	0.405117	+	0.914265i	$0.367231\pi$
$654$	−26.5838	−	3.13980i	−1.03951	−	0.122776i
$655$	2.96672	+	2.96672i	0.115920	+	0.115920i
$656$	−11.4932	+	3.74681i	−0.448735	+	0.146288i
$657$	6.78342	−	1.81761i	0.264647	−	0.0709118i
$658$	−4.46029	+	11.1878i	−0.173880	+	0.436145i
$659$	−7.46965	+	12.9378i	−0.290976	+	0.503986i	−0.974041	−	0.226372i	$-0.927313\pi$
$659$	−7.46965	+	12.9378i	−0.290976	+	0.503986i	0.683065	+	0.730358i	$0.260647\pi$
$660$	2.01270	+	0.482165i	0.0783443	+	0.0187682i
$661$	14.3738	+	3.85145i	0.559076	+	0.149804i	0.527282	−	0.849690i	$-0.323211\pi$
$661$	14.3738	+	3.85145i	0.559076	+	0.149804i	0.0317943	+	0.999494i	$0.489878\pi$
$662$	25.5116	−	10.9680i	0.991537	−	0.426285i
$663$	−8.35432	−	19.6918i	−0.324455	−	0.764766i
$664$	−7.80378	−	2.87246i	−0.302846	−	0.111473i
$665$	0.680790	+	0.182417i	0.0263999	+	0.00707384i
$666$	−4.11949	−	3.07460i	−0.159627	−	0.119138i
$667$	4.55790	+	2.63151i	0.176483	+	0.101892i
$668$	−44.7526	+	1.19381i	−1.73153	+	0.0461897i
$669$	−7.77977	+	2.08458i	−0.300783	+	0.0805946i
$670$	3.49324	−	2.75523i	0.134956	−	0.106444i
$671$	6.59468	−	6.59468i	0.254585	−	0.254585i
$672$	7.17959	+	0.461753i	0.276959	+	0.0178125i
$673$	19.6041	−	11.3184i	0.755682	−	0.436293i	−0.0720614	−	0.997400i	$-0.522958\pi$
$673$	19.6041	−	11.3184i	0.755682	−	0.436293i	0.827743	+	0.561107i	$0.189624\pi$
$674$	−47.9750	+	6.96803i	−1.84793	+	0.268398i
$675$		−	27.1676i		−	1.04568i
$676$	−12.0028	+	23.0637i	−0.461647	+	0.887064i
$677$		−	28.1241i		−	1.08090i	−0.841377	−	0.540448i	$-0.818255\pi$
$677$		−	28.1241i		−	1.08090i	0.841377	−	0.540448i	$-0.181745\pi$
$678$	−1.72896	−	11.9039i	−0.0664005	−	0.457168i
$679$	4.02333	−	2.32287i	0.154401	−	0.0891437i
$680$	−2.33315	+	1.94336i	−0.0894722	+	0.0745245i
$681$	0.768312	−	0.768312i	0.0294418	−	0.0294418i
$682$	14.7682	+	18.7239i	0.565502	+	0.716975i
$683$	−43.1843	+	11.5712i	−1.65240	+	0.442760i	−0.960284	−	0.279025i	$-0.909989\pi$
$683$	−43.1843	+	11.5712i	−1.65240	+	0.442760i	−0.692118	+	0.721785i	$0.743322\pi$
$684$	−2.94319	+	0.0785115i	−0.112536	+	0.00300196i
$685$	−3.94837	−	2.27959i	−0.150859	−	0.0870986i
$686$	9.05378	−	12.1307i	0.345675	−	0.463151i
$687$	7.08878	+	1.89943i	0.270454	+	0.0724679i
$688$	−14.2055	+	0.758425i	−0.541581	+	0.0289147i
$689$	18.4695	+	43.5341i	0.703632	+	1.65852i
$690$	−0.635288	−	1.47768i	−0.0241850	−	0.0562542i
$691$	18.4100	+	4.93295i	0.700350	+	0.187658i	0.591387	−	0.806388i	$-0.298580\pi$
$691$	18.4100	+	4.93295i	0.700350	+	0.187658i	0.108963	+	0.994046i	$0.465247\pi$
$692$	7.01280	−	29.2735i	0.266587	−	1.11281i
$693$	0.437149	−	0.757164i	0.0166059	−	0.0287623i
$694$	27.1936	+	10.8414i	1.03225	+	0.411535i
$695$	−2.70430	+	0.724614i	−0.102580	+	0.0274862i
$696$	0.859658	−	9.43158i	0.0325853	−	0.357503i
$697$	7.98750	+	7.98750i	0.302548	+	0.302548i
$698$	2.52963	−	21.4177i	0.0957480	−	0.810670i
$699$	21.1307	−	12.1998i	0.799238	−	0.461440i
$700$	6.71724	−	4.12085i	0.253888	−	0.155754i
$701$	−8.11837			−0.306627			−0.153313	−	0.988178i	$-0.548994\pi$
$701$	−8.11837			−0.306627			−0.153313	+	0.988178i	$0.548994\pi$
$702$	14.6154	+	24.0824i	0.551624	+	0.908930i
$703$		−	23.1573i		−	0.873395i
$704$	−10.3076	−	14.9506i	−0.388482	−	0.563470i
$705$	−2.42272	−	4.19627i	−0.0912449	−	0.158041i
$706$	−4.46986	+	37.8450i	−0.168225	+	1.42432i
$707$	−4.60940	+	4.60940i	−0.173354	+	0.173354i
$708$	18.6080	+	10.0915i	0.699331	+	0.379263i
$709$	−0.488166	−	1.82186i	−0.0183335	−	0.0684215i	0.956153	−	0.292867i	$-0.0946094\pi$
$709$	−0.488166	−	1.82186i	−0.0183335	−	0.0684215i	−0.974487	+	0.224446i	$0.927943\pi$
$710$	−1.18566	+	2.97400i	−0.0444972	+	0.111612i
$711$	−5.04262	−	2.91136i	−0.189113	−	0.109184i
$712$	−5.36003	+	0.925073i	−0.200876	+	0.0346686i
$713$	4.79670	−	17.9015i	0.179638	−	0.670418i
$714$	−2.65529	−	6.17618i	−0.0993716	−	0.231138i
$715$	−1.41504	+	1.87709i	−0.0529195	+	0.0701992i
$716$	22.4129	−	23.6415i	0.837611	−	0.883523i
$717$	3.25480	−	12.1471i	0.121553	−	0.453640i
$718$	27.6936	+	20.6693i	1.03352	+	0.771370i
$719$	−17.1820	+	29.7601i	−0.640780	+	1.10986i	0.344479	+	0.938794i	$0.388056\pi$
$719$	−17.1820	+	29.7601i	−0.640780	+	1.10986i	−0.985259	+	0.171069i	$0.945278\pi$
$720$	0.369129	−	0.410767i	0.0137566	−	0.0153084i
$721$	−3.61054	−	13.4747i	−0.134464	−	0.501825i
$722$	8.42620	+	10.6832i	0.313591	+	0.397588i
$723$	17.8483	+	17.8483i	0.663784	+	0.663784i
$724$	−6.89892	+	2.04723i	−0.256396	+	0.0760846i
$725$	−5.18693	−	8.98402i	−0.192638	−	0.333658i
$726$	−12.9893	+	1.88661i	−0.482079	+	0.0700186i
$727$	−20.4072			−0.756861			−0.378430	−	0.925630i	$-0.623536\pi$
$727$	−20.4072			−0.756861			−0.378430	+	0.925630i	$0.623536\pi$
$728$	−3.73750	+	7.26657i	−0.138521	+	0.269317i
$729$	29.8288			1.10477
$730$	−5.87265	+	0.852961i	−0.217356	+	0.0315695i
$731$	6.64658	+	11.5122i	0.245833	+	0.425795i
$732$	3.71044	+	12.5038i	0.137142	+	0.462153i
$733$	16.3864	+	16.3864i	0.605247	+	0.605247i	0.941700	−	0.336453i	$-0.109227\pi$
$733$	16.3864	+	16.3864i	0.605247	+	0.605247i	−0.336453	+	0.941700i	$0.609227\pi$
$734$	0.915769	+	1.16106i	0.0338017	+	0.0428556i
$735$	0.750185	+	2.79973i	0.0276710	+	0.103270i
$736$	−4.52006	+	13.3694i	−0.166612	+	0.492802i
$737$	12.4314	−	21.5319i	0.457917	−	0.793136i
$738$	−1.64643	−	1.22882i	−0.0606061	−	0.0452336i
$739$	10.5673	−	39.4378i	0.388725	−	1.45074i	−0.443486	−	0.896282i	$-0.646258\pi$
$739$	10.5673	−	39.4378i	0.388725	−	1.45074i	0.832211	−	0.554460i	$-0.187075\pi$
$740$	3.15225	+	2.98844i	0.115879	+	0.109857i
$741$	−6.56848	+	16.2488i	−0.241299	+	0.596914i
$742$	5.87023	+	13.6541i	0.215503	+	0.501259i
$743$	1.61384	−	6.02293i	0.0592060	−	0.220960i	−0.929984	−	0.367600i	$-0.880179\pi$
$743$	1.61384	−	6.02293i	0.0592060	−	0.220960i	0.989190	+	0.146641i	$0.0468461\pi$
$744$	−32.8640	+	5.67190i	−1.20485	+	0.207942i
$745$	2.05276	+	1.18516i	0.0752071	+	0.0434209i
$746$	−14.6673	+	36.7900i	−0.537007	+	1.34698i
$747$	−0.365775	−	1.36509i	−0.0133830	−	0.0499461i
$748$	−8.08959	+	14.9166i	−0.295785	+	0.545404i
$749$	−0.835088	+	0.835088i	−0.0305134	+	0.0305134i
$750$	−0.749978	+	6.34985i	−0.0273853	+	0.231864i
$751$	15.2301	+	26.3794i	0.555755	+	0.962597i	0.997844	+	0.0656254i	$0.0209042\pi$
$751$	15.2301	+	26.3794i	0.555755	+	0.962597i	−0.442089	+	0.896971i	$0.645762\pi$
$752$	−8.79859	+	41.5943i	−0.320852	+	1.51679i
$753$			28.4934i			1.03836i
$754$	9.43105	+	5.17335i	0.343459	+	0.188402i
$755$	−4.20404			−0.153001
$756$	4.62965	+	7.54661i	0.168379	+	0.274468i
$757$	−29.4578	+	17.0074i	−1.07066	+	0.618146i	−0.928362	−	0.371678i	$-0.878783\pi$
$757$	−29.4578	+	17.0074i	−1.07066	+	0.618146i	−0.142299	+	0.989824i	$0.545449\pi$
$758$	4.15979	−	35.2197i	0.151090	−	1.27924i
$759$	−6.35590	−	6.35590i	−0.230705	−	0.230705i
$760$	2.47764	+	0.225829i	0.0898733	+	0.00819166i
$761$	−29.3342	+	7.86008i	−1.06336	+	0.284928i	−0.747764	−	0.663965i	$-0.768872\pi$
$761$	−29.3342	+	7.86008i	−1.06336	+	0.284928i	−0.315600	+	0.948892i	$0.602206\pi$
$762$	8.97122	+	3.57661i	0.324993	+	0.129567i
$763$	4.77771	−	8.27524i	0.172965	−	0.299584i
$764$	51.9418	+	12.4432i	1.87919	+	0.450181i
$765$	−0.498467	−	0.133564i	−0.0180221	−	0.00482901i
$766$	−10.4124	−	24.2191i	−0.376214	−	0.875072i
$767$	−18.9488	+	14.7987i	−0.684203	+	0.534351i
$768$	25.2514	−	2.70402i	0.911180	−	0.0975728i
$769$	−14.4158	−	3.86269i	−0.519846	−	0.139292i	−0.0106506	−	0.999943i	$-0.503390\pi$
$769$	−14.4158	−	3.86269i	−0.519846	−	0.139292i	−0.509195	+	0.860651i	$0.670057\pi$
$770$	−0.441892	+	0.592067i	−0.0159247	+	0.0213366i
$771$	−31.0262	−	17.9130i	−1.11738	−	0.645120i
$772$	0.591401	+	22.1700i	0.0212850	+	0.797917i
$773$	−8.50020	+	2.27762i	−0.305731	+	0.0819204i	−0.408423	−	0.912793i	$-0.633921\pi$
$773$	−8.50020	+	2.27762i	−0.305731	+	0.0819204i	0.102692	+	0.994713i	$0.467254\pi$
$774$	−1.49723	−	1.89827i	−0.0538169	−	0.0682320i
$775$	−25.8308	+	25.8308i	−0.927869	+	0.927869i
$776$	12.6006	−	10.4955i	0.452335	−	0.376766i
$777$	−8.32846	+	4.80844i	−0.298782	+	0.172502i
$778$	−5.59333	−	38.5102i	−0.200531	−	1.38066i
$779$		−	9.25527i		−	0.331604i
$780$	−1.36418	−	2.99102i	−0.0488453	−	0.107096i
$781$			17.8919i			0.640223i
$782$	13.0507	−	1.89552i	0.466691	−	0.0677836i
$783$	10.0933	−	5.82736i	0.360704	−	0.208253i
$784$	11.5236	−	22.6712i	0.411558	−	0.809687i
$785$	−3.77718	+	3.77718i	−0.134813	+	0.134813i
$786$	−25.7452	+	20.3061i	−0.918299	+	0.724293i
$787$	22.2999	−	5.97524i	0.794906	−	0.212994i	0.161560	−	0.986863i	$-0.448348\pi$
$787$	22.2999	−	5.97524i	0.794906	−	0.212994i	0.633346	+	0.773869i	$0.281681\pi$
$788$	0.887848	+	33.2830i	0.0316283	+	1.18566i
$789$	−4.75093	−	2.74295i	−0.169138	−	0.0976516i
$790$	3.94309	+	2.94294i	0.140289	+	0.104705i
$791$	4.14756	+	1.11134i	0.147470	+	0.0395145i
$792$	1.06606	−	2.89623i	0.0378808	−	0.102913i
$793$	−14.7031	−	1.80811i	−0.522122	−	0.0642079i
$794$	−18.2424	+	7.84283i	−0.647398	+	0.278332i
$795$	−5.77558	−	1.54756i	−0.204839	−	0.0548863i
$796$	−2.84940	+	11.8943i	−0.100994	+	0.421581i
$797$	−17.2646	+	29.9032i	−0.611544	+	1.05923i	0.379436	+	0.925218i	$0.376118\pi$
$797$	−17.2646	+	29.9032i	−0.611544	+	1.05923i	−0.990980	+	0.134007i	$0.957215\pi$
$798$	−2.03986	+	5.11659i	−0.0722103	+	0.181125i
$799$	38.3739	−	10.2822i	1.35757	−	0.363760i
$800$	20.8919	−	18.3670i	0.738641	−	0.649372i
$801$	−0.653653	−	0.653653i	−0.0230957	−	0.0230957i
$802$	15.0333	+	1.77558i	0.530845	+	0.0626979i
$803$	−28.7198	+	16.5814i	−1.01350	+	0.585145i
$804$	18.1820	+	29.6377i	0.641229	+	1.04524i
$805$	0.574160			0.0202365
$806$	9.00111	−	36.7936i	0.317051	−	1.29600i
$807$			20.5562i			0.723612i
$808$	−13.2665	+	18.8010i	−0.466715	+	0.661416i
$809$	−6.45115	−	11.1737i	−0.226810	−	0.392847i	0.730051	−	0.683393i	$-0.239496\pi$
$809$	−6.45115	−	11.1737i	−0.226810	−	0.392847i	−0.956861	+	0.290546i	$0.906163\pi$
$810$	−2.95555	−	0.349079i	−0.103847	−	0.0122654i
$811$	18.8656	−	18.8656i	0.662463	−	0.662463i	−0.293497	−	0.955960i	$-0.594819\pi$
$811$	18.8656	−	18.8656i	0.662463	−	0.662463i	0.955960	+	0.293497i	$0.0948192\pi$
$812$	2.97180	+	1.61167i	0.104290	+	0.0565587i
$813$	4.07196	+	15.1968i	0.142810	+	0.532974i
$814$	22.5481	+	8.98937i	0.790309	+	0.315077i
$815$	−1.01287	−	0.584778i	−0.0354791	−	0.0204839i
$816$	−12.9442	−	19.8897i	−0.453138	−	0.696279i
$817$	2.81895	−	10.5205i	0.0986226	−	0.368065i
$818$	−9.10348	+	3.91380i	−0.318296	+	0.136843i
$819$	−1.37525	+	0.193016i	−0.0480553	+	0.00674454i
$820$	1.25986	+	1.19439i	0.0439961	+	0.0417098i
$821$	−12.7023	+	47.4056i	−0.443313	+	1.65447i	0.277040	+	0.960858i	$0.410647\pi$
$821$	−12.7023	+	47.4056i	−0.443313	+	1.65447i	−0.720353	+	0.693608i	$0.756020\pi$
$822$	21.3120	−	28.5547i	0.743340	−	0.995961i
$823$	−14.9212	+	25.8443i	−0.520121	+	0.900876i	0.479606	+	0.877484i	$0.340780\pi$
$823$	−14.9212	+	25.8443i	−0.520121	+	0.900876i	−0.999726	+	0.0233914i	$0.992554\pi$
$824$	−20.6487	−	44.7041i	−0.719331	−	1.55734i
$825$	4.58558	+	17.1136i	0.159649	+	0.595820i
$826$	−5.93297	+	4.67953i	−0.206434	+	0.162822i
$827$	−39.0150	−	39.0150i	−1.35668	−	1.35668i	−0.877971	−	0.478714i	$-0.841103\pi$
$827$	−39.0150	−	39.0150i	−1.35668	−	1.35668i	−0.478714	−	0.877971i	$-0.658897\pi$
$828$	−2.29937	+	0.682329i	−0.0799087	+	0.0237126i
$829$	−17.4500	−	30.2242i	−0.606063	−	1.04973i	−0.991883	−	0.127157i	$-0.959415\pi$
$829$	−17.4500	−	30.2242i	−0.606063	−	1.04973i	0.385820	−	0.922574i	$-0.373919\pi$
$830$	0.171649	+	1.18181i	0.00595803	+	0.0410211i
$831$	−15.0096			−0.520678
$832$	−8.63844	+	27.5205i	−0.299484	+	0.954101i
$833$	−23.7646			−0.823395
$834$	−3.14496	−	21.6531i	−0.108901	−	0.749784i
$835$	3.21459	+	5.56784i	0.111246	+	0.192683i
$836$	13.3288	−	3.95528i	0.460987	−	0.136796i
$837$	−29.0201	−	29.0201i	−1.00308	−	1.00308i
$838$	26.3922	−	20.8164i	0.911703	−	0.719091i
$839$	−7.72729	−	28.8387i	−0.266776	−	0.995621i	−0.961154	−	0.276011i	$-0.910987\pi$
$839$	−7.72729	−	28.8387i	−0.266776	−	0.995621i	0.694379	−	0.719610i	$-0.255679\pi$
$840$	−0.433243	−	0.937965i	−0.0149483	−	0.0323629i
$841$	−12.2748	+	21.2606i	−0.423270	+	0.733126i
$842$	12.0172	−	16.1012i	0.414140	−	0.554884i
$843$	−3.38833	+	12.6454i	−0.116700	+	0.435531i
$844$	18.8005	+	17.8235i	0.647140	+	0.613512i
$845$	3.73331	−	0.0637651i	0.128430	−	0.00219359i
$846$	−6.63792	+	2.85380i	−0.228216	+	0.0981156i
$847$	1.21266	−	4.52573i	0.0416677	−	0.155506i
$848$	28.6167	+	43.9716i	0.982702	+	1.50999i
$849$	−0.345145	−	0.199270i	−0.0118454	−	0.00683892i
$850$	−24.1458	−	9.62635i	−0.828194	−	0.330181i
$851$	−4.88256	−	18.2220i	−0.167372	−	0.624641i
$852$	−21.9952	−	11.9285i	−0.753544	−	0.408664i
$853$	23.9776	−	23.9776i	0.820976	−	0.820976i	−0.165272	−	0.986248i	$-0.552850\pi$
$853$	23.9776	−	23.9776i	0.820976	−	0.820976i	0.986248	+	0.165272i	$0.0528502\pi$
$854$	−4.62363	−	0.546096i	−0.158218	−	0.0186870i
$855$	0.211410	+	0.366173i	0.00723007	+	0.0125229i
$856$	−2.40351	+	3.40619i	−0.0821502	+	0.116421i
$857$		−	14.2812i		−	0.487836i	−0.969796	−	0.243918i	$-0.921567\pi$
$857$		−	14.2812i		−	0.487836i	0.969796	−	0.243918i	$-0.0784328\pi$
$858$	−13.2715	−	12.7032i	−0.453081	−	0.433681i
$859$	−7.95874			−0.271549			−0.135774	−	0.990740i	$-0.543352\pi$
$859$	−7.95874			−0.271549			−0.135774	+	0.990740i	$0.543352\pi$
$860$	1.06829	+	1.74139i	0.0364286	+	0.0593807i
$861$	−3.32863	+	1.92178i	−0.113439	+	0.0654942i
$862$	−10.5511	−	1.24619i	−0.359373	−	0.0424454i
$863$	21.5136	+	21.5136i	0.732331	+	0.732331i	0.971081	−	0.238750i	$-0.0767377\pi$
$863$	21.5136	+	21.5136i	0.732331	+	0.732331i	−0.238750	+	0.971081i	$0.576738\pi$
$864$	20.6348	+	23.4715i	0.702009	+	0.798515i
$865$	−4.17561	+	1.11885i	−0.141975	+	0.0380421i
$866$	6.85514	−	17.1948i	0.232947	−	0.584302i
$867$	2.40392	−	4.16372i	0.0816415	−	0.141407i
$868$	2.77343	−	11.5771i	0.0941364	−	0.392953i
$869$	26.5592	+	7.11652i	0.900959	+	0.241411i
$870$	−1.24950	+	0.537189i	−0.0423620	+	0.0182124i
$871$	−39.1088	+	5.48891i	−1.32515	+	0.185984i
$872$	11.6512	−	31.6536i	0.394561	−	1.07193i
$873$	2.69206	+	0.721336i	0.0911125	+	0.0244135i
$874$	−8.65922	−	6.46285i	−0.292903	−	0.218609i
$875$	−1.97664	−	1.14121i	−0.0668225	−	0.0385800i
$876$	−1.23672	−	46.3612i	−0.0417848	−	1.56640i
$877$	−15.4279	+	4.13388i	−0.520962	+	0.139591i	−0.509711	−	0.860345i	$-0.670248\pi$
$877$	−15.4279	+	4.13388i	−0.520962	+	0.139591i	−0.0112504	+	0.999937i	$0.503581\pi$
$878$	−1.61171	+	1.27121i	−0.0543924	+	0.0429011i
$879$	23.5021	−	23.5021i	0.792706	−	0.792706i
$880$	−1.18167	+	2.32479i	−0.0398342	+	0.0783686i
$881$	12.4608	−	7.19424i	0.419814	−	0.242380i	−0.275183	−	0.961392i	$-0.588739\pi$
$881$	12.4608	−	7.19424i	0.419814	−	0.242380i	0.694998	+	0.719012i	$0.255405\pi$
$882$	4.27727	−	0.621243i	0.144023	−	0.0209183i
$883$		−	3.55013i		−	0.119472i	−0.998214	−	0.0597358i	$-0.980974\pi$
$883$		−	3.55013i		−	0.119472i	0.998214	−	0.0597358i	$-0.0190258\pi$
$884$	26.5824	−	4.45663i	0.894065	−	0.149893i
$885$		−	3.03997i		−	0.102187i
$886$	−3.67046	−	25.2711i	−0.123311	−	0.849001i
$887$	47.6836	−	27.5301i	1.60106	−	0.924371i	0.609782	−	0.792569i	$-0.291257\pi$
$887$	47.6836	−	27.5301i	1.60106	−	0.924371i	0.991276	−	0.131802i	$-0.0420764\pi$
$888$	−26.0838	+	21.7260i	−0.875313	+	0.729078i
$889$	−2.43777	+	2.43777i	−0.0817601	+	0.0817601i
$890$	0.483744	+	0.613318i	0.0162151	+	0.0205584i
$891$	−16.0648	+	4.30454i	−0.538190	+	0.144207i
$892$	−0.270629	−	10.1451i	−0.00906131	−	0.339684i
$893$	−28.1894	−	16.2751i	−0.943321	−	0.544627i
$894$	−11.0801	+	14.8456i	−0.370574	+	0.496512i
$895$	−4.51895	−	1.21085i	−0.151052	−	0.0404742i
$896$	−2.67342	+	8.66220i	−0.0893128	+	0.289384i
$897$	−1.74264	+	14.1707i	−0.0581851	+	0.473146i
$898$	19.1967	+	44.6514i	0.640603	+	1.49004i
$899$	−15.1373	−	4.05601i	−0.504856	−	0.135276i
$900$	4.59752	+	1.10139i	0.153251	+	0.0367129i
$901$	24.5121	−	42.4561i	0.816615	−	1.41442i
$902$	9.01177	+	3.59277i	0.300059	+	0.119626i
$903$	−4.36899	+	1.17067i	−0.145391	+	0.0389573i
$904$	15.0944	+	1.37581i	0.502033	+	0.0457587i
$905$	0.730762	+	0.730762i	0.0242913	+	0.0242913i
$906$	3.85378	−	32.6288i	0.128033	−	1.08402i
$907$	38.6201	−	22.2973i	1.28236	−	0.740370i	0.305079	−	0.952327i	$-0.401317\pi$
$907$	38.6201	−	22.2973i	1.28236	−	0.740370i	0.977279	+	0.211957i	$0.0679837\pi$
$908$	0.715935	+	1.16702i	0.0237591	+	0.0387288i
$909$	−3.91062			−0.129707
$910$	1.17321	−	0.0256668i	0.0388916	−	0.000850847i
$911$			22.8758i			0.757910i	0.925415	+	0.378955i	$0.123717\pi$
$911$			22.8758i			0.757910i	−0.925415	+	0.378955i	$0.876283\pi$
$912$	−4.02393	+	19.0226i	−0.133246	+	0.629903i
$913$	3.33683	+	5.77956i	0.110433	+	0.191275i
$914$	3.62498	−	30.6916i	0.119904	−	1.01519i
$915$	1.32445	−	1.32445i	0.0437850	−	0.0437850i
$916$	−4.40847	+	8.12888i	−0.145660	+	0.268586i
$917$	−3.02939	−	11.3058i	−0.100039	−	0.373352i
$918$	10.8149	−	27.1271i	0.356945	−	0.895327i
$919$	24.1895	+	13.9658i	0.797939	+	0.460690i	0.842750	−	0.538305i	$-0.180935\pi$
$919$	24.1895	+	13.9658i	0.797939	+	0.460690i	−0.0448109	+	0.998995i	$0.514269\pi$
$920$	1.99721	−	0.344693i	0.0658461	−	0.0113642i
$921$	−6.12379	+	22.8543i	−0.201786	+	0.753074i
$922$	8.86870	+	20.6285i	0.292075	+	0.679365i
$923$	22.3981	−	17.4926i	0.737243	−	0.575775i
$924$	−4.19013	−	3.97239i	−0.137845	−	0.130682i
$925$	−9.62396	+	35.9171i	−0.316434	+	1.18095i
$926$	5.31966	+	3.97035i	0.174815	+	0.130474i
$927$	4.18439	−	7.24757i	0.137433	−	0.238042i
$928$	11.3049	+	3.82209i	0.371103	+	0.125466i
$929$	7.54479	+	28.1575i	0.247536	+	0.923818i	0.972092	+	0.234602i	$0.0753785\pi$
$929$	7.54479	+	28.1575i	0.247536	+	0.923818i	−0.724555	+	0.689217i	$0.757955\pi$
$930$	2.96598	+	3.76044i	0.0972583	+	0.123310i
$931$	13.7682	+	13.7682i	0.451236	+	0.451236i
$932$	8.74646	+	29.4746i	0.286500	+	0.965471i
$933$	1.36128	+	2.35781i	0.0445665	+	0.0771914i
$934$	−6.03653	+	0.876763i	−0.197521	+	0.0286886i
$935$	2.43691			0.0796953
$936$	−4.66793	+	1.49703i	−0.152576	+	0.0489320i
$937$	7.52598			0.245863			0.122931	−	0.992415i	$-0.460770\pi$
$937$	7.52598			0.245863			0.122931	+	0.992415i	$0.460770\pi$
$938$	−12.2829	+	1.78400i	−0.401051	+	0.0582498i
$939$	−6.55216	−	11.3487i	−0.213822	−	0.370350i
$940$	5.85324	−	1.73693i	0.190912	−	0.0566523i
$941$	1.73699	+	1.73699i	0.0566241	+	0.0566241i	0.734852	−	0.678228i	$-0.237252\pi$
$941$	1.73699	+	1.73699i	0.0566241	+	0.0566241i	−0.678228	+	0.734852i	$0.737252\pi$
$942$	−25.8533	−	32.7783i	−0.842346	−	1.06797i
$943$	−1.95141	−	7.28276i	−0.0635466	−	0.237159i
$944$	−17.8284	+	19.8395i	−0.580266	+	0.645721i
$945$	0.635726	−	1.10111i	0.0206802	−	0.0358191i
$946$	9.14940	+	6.82870i	0.297473	+	0.222020i
$947$	14.1576	−	52.8369i	0.460060	−	1.71697i	−0.212709	−	0.977116i	$-0.568229\pi$
$947$	14.1576	−	52.8369i	0.460060	−	1.71697i	0.672769	−	0.739852i	$-0.265105\pi$
$948$	−26.4556	+	27.9057i	−0.859238	+	0.906336i
$949$	48.8364	+	19.7418i	1.58530	+	0.640847i
$950$	8.41198	+	19.5662i	0.272921	+	0.634811i
$951$	5.54073	−	20.6783i	0.179670	−	0.670539i
$952$	8.34766	−	1.44070i	0.270549	−	0.0466933i
$953$	49.3129	+	28.4708i	1.59740	+	0.922261i	0.991985	+	0.126353i	$0.0403273\pi$
$953$	49.3129	+	28.4708i	1.59740	+	0.922261i	0.605418	+	0.795908i	$0.293006\pi$
$954$	−3.30193	+	8.28224i	−0.106904	+	0.268147i
$955$	−1.98525	−	7.40904i	−0.0642411	−	0.239751i
$956$	13.9293	+	7.55419i	0.450507	+	0.244320i
$957$	−5.37445	+	5.37445i	−0.173731	+	0.173731i
$958$	−2.49870	+	21.1557i	−0.0807293	+	0.683511i
$959$	6.35951	+	11.0150i	0.205359	+	0.355693i
$960$	−2.07013	−	3.00261i	−0.0668133	−	0.0969088i
$961$			24.1843i			0.780139i
$962$	−10.7914	−	37.0157i	−0.347928	−	1.19343i
$963$	−0.708489			−0.0228307
$964$	−27.1104	+	16.6315i	−0.873167	+	0.535665i
$965$	2.75826	−	1.59248i	0.0887915	−	0.0512638i
$966$	−0.526323	+	4.45622i	−0.0169342	+	0.143377i
$967$	−28.7702	−	28.7702i	−0.925189	−	0.925189i	0.0722014	−	0.997390i	$-0.476998\pi$
$967$	−28.7702	−	28.7702i	−0.925189	−	0.925189i	−0.997390	+	0.0722014i	$0.976998\pi$
$968$	1.50125	−	16.4707i	0.0482521	−	0.529389i
$969$	17.5498	−	4.70246i	0.563781	−	0.151065i
$970$	−2.18762	−	0.872153i	−0.0702403	−	0.0280031i
$971$	−27.3131	+	47.3076i	−0.876518	+	1.51817i	−0.0213803	+	0.999771i	$0.506806\pi$
$971$	−27.3131	+	47.3076i	−0.876518	+	1.51817i	−0.855137	+	0.518402i	$0.826527\pi$
$972$	−2.30387	+	9.61703i	−0.0738966	+	0.308466i
$973$	7.54434	+	2.02150i	0.241860	+	0.0648063i
$974$	−9.99002	−	23.2367i	−0.320101	−	0.744552i
$975$	16.9406	−	22.4721i	0.542533	−	0.719684i
$976$	−16.4111	+	0.876180i	−0.525307	+	0.0280458i
$977$	−3.60921	−	0.967085i	−0.115469	−	0.0309398i	0.200622	−	0.979669i	$-0.435704\pi$
$977$	−3.60921	−	0.967085i	−0.115469	−	0.0309398i	−0.316091	+	0.948729i	$0.602370\pi$
$978$	5.46711	−	7.32509i	0.174819	−	0.234230i
$979$	3.78041	+	2.18262i	0.120822	+	0.0697569i
$980$	−3.65096	+	0.0973919i	−0.116626	+	0.00311107i
$981$	5.53706	−	1.48365i	0.176785	−	0.0473694i
$982$	15.6615	+	19.8566i	0.499779	+	0.633648i
$983$	20.7574	−	20.7574i	0.662057	−	0.662057i	−0.293808	−	0.955865i	$-0.594922\pi$
$983$	20.7574	−	20.7574i	0.662057	−	0.662057i	0.955865	+	0.293808i	$0.0949225\pi$
$984$	−10.4249	+	8.68323i	−0.332333	+	0.276811i
$985$	4.14087	−	2.39073i	0.131939	−	0.0761751i
$986$	−1.60282	−	11.0354i	−0.0510442	−	0.351440i
$987$			13.5176i			0.430271i
$988$	−17.9828	−	12.8188i	−0.572108	−	0.407820i
$989$		−	8.87268i		−	0.282135i
$990$	−0.438606	+	0.0637044i	−0.0139398	+	0.00202466i
$991$	48.8698	−	28.2150i	1.55240	−	0.896279i	0.554455	−	0.832214i	$-0.312927\pi$
$991$	48.8698	−	28.2150i	1.55240	−	0.896279i	0.997946	−	0.0640655i	$-0.0204067\pi$
$992$	2.69710	−	41.9359i	0.0856330	−	1.33147i
$993$	22.0383	−	22.0383i	0.699363	−	0.699363i
$994$	7.01295	−	5.53135i	0.222437	−	0.175444i
$995$	1.69661	−	0.454605i	0.0537862	−	0.0144120i
$996$	−9.32970	+	0.248876i	−0.295623	+	0.00788594i
$997$	−52.4375	−	30.2748i	−1.66071	−	0.958812i	−0.972376	−	0.233420i	$-0.925008\pi$
$997$	−52.4375	−	30.2748i	−1.66071	−	0.958812i	−0.688336	−	0.725392i	$-0.741658\pi$
$998$	−3.67487	−	2.74275i	−0.116326	−	0.0868203i
$999$	−40.3518	−	10.8122i	−1.27667	−	0.342084i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	104.2.u.a.67.8	yes	48
3.2	odd	2		936.2.ed.d.379.5		48
4.3	odd	2		416.2.bk.a.15.4		48
8.3	odd	2	inner	104.2.u.a.67.10	yes	48
8.5	even	2		416.2.bk.a.15.3		48
13.7	odd	12	inner	104.2.u.a.59.10	yes	48
24.11	even	2		936.2.ed.d.379.3		48
39.20	even	12		936.2.ed.d.163.3		48
52.7	even	12		416.2.bk.a.111.3		48
104.59	even	12	inner	104.2.u.a.59.8	✓	48
104.85	odd	12		416.2.bk.a.111.4		48
312.59	odd	12		936.2.ed.d.163.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.u.a.59.8	✓	48	104.59	even	12	inner
104.2.u.a.59.10	yes	48	13.7	odd	12	inner
104.2.u.a.67.8	yes	48	1.1	even	1	trivial
104.2.u.a.67.10	yes	48	8.3	odd	2	inner
416.2.bk.a.15.3		48	8.5	even	2
416.2.bk.a.15.4		48	4.3	odd	2
416.2.bk.a.111.3		48	52.7	even	12
416.2.bk.a.111.4		48	104.85	odd	12
936.2.ed.d.163.3		48	39.20	even	12
936.2.ed.d.163.5		48	312.59	odd	12
936.2.ed.d.379.3		48	24.11	even	2
936.2.ed.d.379.5		48	3.2	odd	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:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.203272 + 1.39953i) q^{2} +(0.793616 + 1.37458i) q^{3} +(-1.91736 + 0.568969i) q^{4} +(0.203095 + 0.203095i) q^{5} +(-1.76245 + 1.39010i) q^{6} +(-0.207385 - 0.773970i) q^{7} +(-1.18603 - 2.56775i) q^{8} +(0.240346 - 0.416291i) q^{9} +O(q^{10})\)	\(q+(0.203272 + 1.39953i) q^{2} +(0.793616 + 1.37458i) q^{3} +(-1.91736 + 0.568969i) q^{4} +(0.203095 + 0.203095i) q^{5} +(-1.76245 + 1.39010i) q^{6} +(-0.207385 - 0.773970i) q^{7} +(-1.18603 - 2.56775i) q^{8} +(0.240346 - 0.416291i) q^{9} +(-0.242953 + 0.325520i) q^{10} +(-0.587501 + 2.19258i) q^{11} +(-2.30375 - 2.18403i) q^{12} +(3.31919 - 1.40818i) q^{13} +(1.04104 - 0.447567i) q^{14} +(-0.117991 + 0.440350i) q^{15} +(3.35255 - 2.18184i) q^{16} +(-3.23700 - 1.86889i) q^{17} +(0.631467 + 0.251751i) q^{18} +(0.792632 + 2.95814i) q^{19} +(-0.504960 - 0.273851i) q^{20} +(0.899303 - 0.899303i) q^{21} +(-3.18801 - 0.376534i) q^{22} +(1.24741 + 2.16058i) q^{23} +(2.58833 - 3.66811i) q^{24} -4.91751i q^{25} +(2.64548 + 4.35906i) q^{26} +5.52467 q^{27} +(0.837997 + 1.36599i) q^{28} +(1.82695 - 1.05479i) q^{29} +(-0.640267 - 0.0756217i) q^{30} +(-5.25282 - 5.25282i) q^{31} +(3.73502 + 4.24848i) q^{32} +(-3.48014 + 0.932501i) q^{33} +(1.95757 - 4.91017i) q^{34} +(0.115071 - 0.199308i) q^{35} +(-0.223973 + 0.934930i) q^{36} +(-7.30393 - 1.95708i) q^{37} +(-3.97889 + 1.71062i) q^{38} +(4.56983 + 3.44495i) q^{39} +(0.280618 - 0.762373i) q^{40} +(-2.91916 - 0.782185i) q^{41} +(1.44140 + 1.07580i) q^{42} +(-3.07997 - 1.77822i) q^{43} +(-0.121061 - 4.53825i) q^{44} +(0.133359 - 0.0357336i) q^{45} +(-2.77022 + 2.18497i) q^{46} +(-7.51561 + 7.51561i) q^{47} +(5.65976 + 2.87682i) q^{48} +(5.50616 - 3.17898i) q^{49} +(6.88219 - 0.999590i) q^{50} -5.93271i q^{51} +(-5.56288 + 4.58851i) q^{52} +13.1159i q^{53} +(1.12301 + 7.73193i) q^{54} +(-0.564621 + 0.325984i) q^{55} +(-1.74139 + 1.45047i) q^{56} +(-3.43717 + 3.43717i) q^{57} +(1.84757 + 2.34246i) q^{58} +(-6.44108 + 1.72588i) q^{59} +(-0.0243134 - 0.911443i) q^{60} +(-3.55817 - 2.05431i) q^{61} +(6.28373 - 8.41923i) q^{62} +(-0.372041 - 0.0996881i) q^{63} +(-5.18665 + 6.09087i) q^{64} +(0.960104 + 0.388116i) q^{65} +(-2.01248 - 4.68101i) q^{66} +(-10.5799 - 2.83488i) q^{67} +(7.26984 + 1.74157i) q^{68} +(-1.97993 + 3.42934i) q^{69} +(0.302328 + 0.120531i) q^{70} +(7.61356 - 2.04005i) q^{71} +(-1.35399 - 0.123412i) q^{72} +(10.3306 + 10.3306i) q^{73} +(1.25431 - 10.6199i) q^{74} +(6.75952 - 3.90261i) q^{75} +(-3.20286 - 5.22085i) q^{76} +1.81883 q^{77} +(-3.89240 + 7.09586i) q^{78} -12.1132i q^{79} +(1.12400 + 0.237765i) q^{80} +(3.66343 + 6.34525i) q^{81} +(0.501309 - 4.24444i) q^{82} +(2.07891 - 2.07891i) q^{83} +(-1.21261 + 2.23596i) q^{84} +(-0.277858 - 1.03698i) q^{85} +(1.86260 - 4.67197i) q^{86} +(2.89979 + 1.67420i) q^{87} +(6.32680 - 1.09193i) q^{88} +(0.497728 - 1.85755i) q^{89} +(0.0771184 + 0.179377i) q^{90} +(-1.77824 - 2.27692i) q^{91} +(-3.62103 - 3.43287i) q^{92} +(3.05172 - 11.3892i) q^{93} +(-12.0460 - 8.99060i) q^{94} +(-0.439804 + 0.761763i) q^{95} +(-2.87572 + 8.50577i) q^{96} +(1.50062 + 5.60039i) q^{97} +(5.56832 + 7.05983i) q^{98} +(0.771550 + 0.771550i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 4 q^{3} - 6 q^{4} - 6 q^{6} - 10 q^{8} - 20 q^{9}+O(q^{10}) \) 48 * q - 4 * q^2 - 4 * q^3 - 6 * q^4 - 6 * q^6 - 10 * q^8 - 20 * q^9	\( 48 q - 4 q^{2} - 4 q^{3} - 6 q^{4} - 6 q^{6} - 10 q^{8} - 20 q^{9} - 6 q^{10} - 8 q^{11} + 8 q^{14} - 10 q^{16} - 12 q^{17} - 6 q^{18} - 8 q^{19} + 10 q^{20} - 20 q^{22} + 46 q^{24} - 2 q^{26} + 8 q^{27} + 12 q^{28} - 54 q^{30} + 16 q^{32} + 4 q^{33} - 46 q^{34} - 4 q^{35} + 30 q^{36} - 32 q^{40} - 16 q^{42} - 12 q^{43} - 16 q^{44} + 34 q^{46} + 46 q^{48} - 60 q^{49} + 86 q^{50} + 12 q^{52} + 32 q^{54} + 48 q^{56} + 36 q^{57} + 30 q^{58} - 64 q^{59} + 80 q^{60} + 42 q^{62} - 16 q^{65} + 8 q^{66} - 8 q^{67} - 32 q^{68} + 36 q^{70} - 24 q^{72} - 12 q^{73} + 38 q^{74} + 24 q^{75} - 94 q^{76} + 40 q^{78} - 108 q^{80} - 8 q^{81} + 54 q^{82} - 48 q^{83} - 72 q^{84} + 80 q^{86} - 108 q^{88} + 12 q^{89} + 104 q^{91} - 20 q^{92} + 26 q^{94} - 32 q^{96} + 4 q^{97} - 16 q^{98} + 168 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 4 * q^3 - 6 * q^4 - 6 * q^6 - 10 * q^8 - 20 * q^9 - 6 * q^10 - 8 * q^11 + 8 * q^14 - 10 * q^16 - 12 * q^17 - 6 * q^18 - 8 * q^19 + 10 * q^20 - 20 * q^22 + 46 * q^24 - 2 * q^26 + 8 * q^27 + 12 * q^28 - 54 * q^30 + 16 * q^32 + 4 * q^33 - 46 * q^34 - 4 * q^35 + 30 * q^36 - 32 * q^40 - 16 * q^42 - 12 * q^43 - 16 * q^44 + 34 * q^46 + 46 * q^48 - 60 * q^49 + 86 * q^50 + 12 * q^52 + 32 * q^54 + 48 * q^56 + 36 * q^57 + 30 * q^58 - 64 * q^59 + 80 * q^60 + 42 * q^62 - 16 * q^65 + 8 * q^66 - 8 * q^67 - 32 * q^68 + 36 * q^70 - 24 * q^72 - 12 * q^73 + 38 * q^74 + 24 * q^75 - 94 * q^76 + 40 * q^78 - 108 * q^80 - 8 * q^81 + 54 * q^82 - 48 * q^83 - 72 * q^84 + 80 * q^86 - 108 * q^88 + 12 * q^89 + 104 * q^91 - 20 * q^92 + 26 * q^94 - 32 * q^96 + 4 * q^97 - 16 * q^98 + 168 * q^99

Introduction

L-functions

Modular forms

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