LMFDB - Embedded newform 112.2.w.c.37.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,2,Mod(37,112)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("112.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	112.w (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:	$0.894324502638$
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			37.8
Character	$\chi$	$=$	112.37
Dual form			112.2.w.c.109.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.262311 - 1.38967i) q^{2} +(2.91496 + 0.781062i) q^{3} +(-1.86239 - 0.729053i) q^{4} +(-0.745506 + 0.199758i) q^{5} +(1.85005 - 3.84597i) q^{6} +(-2.51194 - 0.830765i) q^{7} +(-1.50167 + 2.39687i) q^{8} +(5.28887 + 3.05353i) q^{9} +O(q^{10})$	\(q+(0.262311 - 1.38967i) q^{2} +(2.91496 + 0.781062i) q^{3} +(-1.86239 - 0.729053i) q^{4} +(-0.745506 + 0.199758i) q^{5} +(1.85005 - 3.84597i) q^{6} +(-2.51194 - 0.830765i) q^{7} +(-1.50167 + 2.39687i) q^{8} +(5.28887 + 3.05353i) q^{9} +(0.0820438 + 1.08841i) q^{10} +(-0.333193 + 1.24349i) q^{11} +(-4.85935 - 3.57980i) q^{12} +(-0.919058 + 0.919058i) q^{13} +(-1.81340 + 3.27286i) q^{14} -2.32914 q^{15} +(2.93696 + 2.71556i) q^{16} +(-3.95601 - 6.85200i) q^{17} +(5.63074 - 6.54883i) q^{18} +(0.478380 + 1.78534i) q^{19} +(1.53405 + 0.171487i) q^{20} +(-6.67332 - 4.38363i) q^{21} +(1.64065 + 0.789212i) q^{22} +(3.33211 + 1.92380i) q^{23} +(-6.24941 + 5.81389i) q^{24} +(-3.81425 + 2.20216i) q^{25} +(1.03611 + 1.51827i) q^{26} +(6.63016 + 6.63016i) q^{27} +(4.07253 + 3.37854i) q^{28} +(5.25154 - 5.25154i) q^{29} +(-0.610960 + 3.23675i) q^{30} +(2.44642 + 4.23733i) q^{31} +(4.54413 - 3.36910i) q^{32} +(-1.94249 + 3.36449i) q^{33} +(-10.5598 + 3.70020i) q^{34} +(2.03862 + 0.117561i) q^{35} +(-7.62373 - 9.54272i) q^{36} +(-1.28190 + 0.343485i) q^{37} +(2.60652 - 0.196478i) q^{38} +(-3.39686 + 1.96118i) q^{39} +(0.640710 - 2.08685i) q^{40} -2.84345i q^{41} +(-7.84229 + 8.12387i) q^{42} +(0.585764 + 0.585764i) q^{43} +(1.52711 - 2.07295i) q^{44} +(-4.55285 - 1.21993i) q^{45} +(3.54750 - 4.12591i) q^{46} +(-2.86095 + 4.95532i) q^{47} +(6.44012 + 10.2097i) q^{48} +(5.61966 + 4.17366i) q^{49} +(2.05976 + 5.87821i) q^{50} +(-6.17977 - 23.0632i) q^{51} +(2.38168 - 1.04160i) q^{52} +(2.54947 - 9.51475i) q^{53} +(10.9529 - 7.47460i) q^{54} -0.993590i q^{55} +(5.76334 - 4.77325i) q^{56} +5.57784i q^{57} +(-5.92039 - 8.67547i) q^{58} +(2.39390 - 8.93417i) q^{59} +(4.33777 + 1.69807i) q^{60} +(-1.71139 - 6.38698i) q^{61} +(6.53023 - 2.28823i) q^{62} +(-10.7485 - 12.0641i) q^{63} +(-3.48998 - 7.19862i) q^{64} +(0.501575 - 0.868753i) q^{65} +(4.16601 + 3.58197i) q^{66} +(5.94825 + 1.59383i) q^{67} +(2.37214 + 15.6452i) q^{68} +(8.21037 + 8.21037i) q^{69} +(0.698123 - 2.80217i) q^{70} +1.99534i q^{71} +(-15.2611 + 8.09134i) q^{72} +(-6.69237 + 3.86384i) q^{73} +(0.141075 + 1.87153i) q^{74} +(-12.8384 + 3.44004i) q^{75} +(0.410678 - 3.67375i) q^{76} +(1.87001 - 2.84677i) q^{77} +(1.83437 + 5.23497i) q^{78} +(-4.63378 + 8.02594i) q^{79} +(-2.73198 - 1.43778i) q^{80} +(4.98751 + 8.63862i) q^{81} +(-3.95146 - 0.745866i) q^{82} +(-4.78537 + 4.78537i) q^{83} +(9.23241 + 13.0292i) q^{84} +(4.31797 + 4.31797i) q^{85} +(0.967673 - 0.660369i) q^{86} +(19.4098 - 11.2063i) q^{87} +(-2.48015 - 2.66594i) q^{88} +(-1.84016 - 1.06242i) q^{89} +(-2.88957 + 6.00698i) q^{90} +(3.07214 - 1.54510i) q^{91} +(-4.80313 - 6.01213i) q^{92} +(3.82162 + 14.2625i) q^{93} +(6.13582 + 5.27563i) q^{94} +(-0.713270 - 1.23542i) q^{95} +(15.8775 - 6.27155i) q^{96} -9.01961 q^{97} +(7.27412 - 6.71470i) q^{98} +(-5.55926 + 5.55926i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8}+O(q^{10}) $ 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8	$ 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 24 q^{13} - 34 q^{14} - 40 q^{15} + 16 q^{16} + 8 q^{17} + 18 q^{18} - 4 q^{19} - 16 q^{20} - 8 q^{21} + 18 q^{24} - 10 q^{26} - 24 q^{27} - 10 q^{28} + 24 q^{29} - 4 q^{30} + 28 q^{31} + 16 q^{32} + 16 q^{33} - 44 q^{34} + 28 q^{35} - 72 q^{36} - 24 q^{37} + 20 q^{38} + 26 q^{40} + 6 q^{42} - 40 q^{43} + 6 q^{44} - 28 q^{45} - 14 q^{46} - 20 q^{47} + 56 q^{48} + 56 q^{50} + 24 q^{51} - 16 q^{52} - 16 q^{53} + 64 q^{54} + 40 q^{56} - 6 q^{58} - 20 q^{59} + 46 q^{60} + 8 q^{61} + 24 q^{62} - 16 q^{63} + 80 q^{64} + 8 q^{65} - 20 q^{66} + 48 q^{67} - 40 q^{69} + 82 q^{70} - 32 q^{72} - 8 q^{74} - 4 q^{75} - 36 q^{76} - 20 q^{77} + 116 q^{78} - 36 q^{79} - 28 q^{80} + 2 q^{82} - 8 q^{83} + 28 q^{84} - 20 q^{86} - 42 q^{88} - 20 q^{90} + 64 q^{91} + 76 q^{92} + 8 q^{93} - 72 q^{94} - 4 q^{95} - 120 q^{96} - 48 q^{97} - 2 q^{98} - 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 24 * q^13 - 34 * q^14 - 40 * q^15 + 16 * q^16 + 8 * q^17 + 18 * q^18 - 4 * q^19 - 16 * q^20 - 8 * q^21 + 18 * q^24 - 10 * q^26 - 24 * q^27 - 10 * q^28 + 24 * q^29 - 4 * q^30 + 28 * q^31 + 16 * q^32 + 16 * q^33 - 44 * q^34 + 28 * q^35 - 72 * q^36 - 24 * q^37 + 20 * q^38 + 26 * q^40 + 6 * q^42 - 40 * q^43 + 6 * q^44 - 28 * q^45 - 14 * q^46 - 20 * q^47 + 56 * q^48 + 56 * q^50 + 24 * q^51 - 16 * q^52 - 16 * q^53 + 64 * q^54 + 40 * q^56 - 6 * q^58 - 20 * q^59 + 46 * q^60 + 8 * q^61 + 24 * q^62 - 16 * q^63 + 80 * q^64 + 8 * q^65 - 20 * q^66 + 48 * q^67 - 40 * q^69 + 82 * q^70 - 32 * q^72 - 8 * q^74 - 4 * q^75 - 36 * q^76 - 20 * q^77 + 116 * q^78 - 36 * q^79 - 28 * q^80 + 2 * q^82 - 8 * q^83 + 28 * q^84 - 20 * q^86 - 42 * q^88 - 20 * q^90 + 64 * q^91 + 76 * q^92 + 8 * q^93 - 72 * q^94 - 4 * q^95 - 120 * q^96 - 48 * q^97 - 2 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.262311	−	1.38967i	0.185482	−	0.982648i
$2$	0.262311	−	1.38967i	0.185482	−	0.982648i
$3$	2.91496	+	0.781062i	1.68295	+	0.450946i	0.968557	−	0.248794i	$-0.0800341\pi$
$3$	2.91496	+	0.781062i	1.68295	+	0.450946i	0.714398	+	0.699740i	$0.246701\pi$
$4$	−1.86239	−	0.729053i	−0.931193	−	0.364526i
$5$	−0.745506	+	0.199758i	−0.333400	+	0.0893344i	−0.421636	−	0.906765i	$-0.638544\pi$
$5$	−0.745506	+	0.199758i	−0.333400	+	0.0893344i	0.0882353	+	0.996100i	$0.471877\pi$
$6$	1.85005	−	3.84597i	0.755279	−	1.57011i
$7$	−2.51194	−	0.830765i	−0.949423	−	0.313999i
$7$	−2.51194	−	0.830765i	−0.949423	−	0.313999i
$8$	−1.50167	+	2.39687i	−0.530920	+	0.847422i
$9$	5.28887	+	3.05353i	1.76296	+	1.01784i
$10$	0.0820438	+	1.08841i	0.0259445	+	0.344185i
$11$	−0.333193	+	1.24349i	−0.100462	+	0.374928i	−0.997791	−	0.0664342i	$-0.978838\pi$
$11$	−0.333193	+	1.24349i	−0.100462	+	0.374928i	0.897329	+	0.441362i	$0.145504\pi$
$12$	−4.85935	−	3.57980i	−1.40277	−	1.03340i
$13$	−0.919058	+	0.919058i	−0.254901	+	0.254901i	−0.822976	−	0.568076i	$-0.807688\pi$
$13$	−0.919058	+	0.919058i	−0.254901	+	0.254901i	0.568076	+	0.822976i	$0.307688\pi$
$14$	−1.81340	+	3.27286i	−0.484652	+	0.874707i
$15$	−2.32914			−0.601383
$16$	2.93696	+	2.71556i	0.734241	+	0.678889i
$17$	−3.95601	−	6.85200i	−0.959473	−	1.66186i	−0.723784	−	0.690026i	$-0.757599\pi$
$17$	−3.95601	−	6.85200i	−0.959473	−	1.66186i	−0.235688	−	0.971829i	$-0.575734\pi$
$18$	5.63074	−	6.54883i	1.32718	−	1.54357i
$19$	0.478380	+	1.78534i	0.109748	+	0.409585i	0.998840	−	0.0481427i	$-0.0153302\pi$
$19$	0.478380	+	1.78534i	0.109748	+	0.409585i	−0.889093	+	0.457727i	$0.848664\pi$
$20$	1.53405	+	0.171487i	0.343025	+	0.0383457i
$21$	−6.67332	−	4.38363i	−1.45624	−	0.956586i
$22$	1.64065	+	0.789212i	0.349788	+	0.168261i
$23$	3.33211	+	1.92380i	0.694793	+	0.401139i	0.805405	−	0.592725i	$-0.201948\pi$
$23$	3.33211	+	1.92380i	0.694793	+	0.401139i	−0.110612	+	0.993864i	$0.535281\pi$
$24$	−6.24941	+	5.81389i	−1.27566	+	1.18676i
$25$	−3.81425	+	2.20216i	−0.762850	+	0.440432i
$26$	1.03611	+	1.51827i	0.203198	+	0.297757i
$27$	6.63016	+	6.63016i	1.27598	+	1.27598i
$28$	4.07253	+	3.37854i	0.769635	+	0.638484i
$29$	5.25154	−	5.25154i	0.975187	−	0.975187i	−0.0245125	−	0.999700i	$-0.507803\pi$
$29$	5.25154	−	5.25154i	0.975187	−	0.975187i	0.999700	+	0.0245125i	$0.00780335\pi$
$30$	−0.610960	+	3.23675i	−0.111546	+	0.590947i
$31$	2.44642	+	4.23733i	0.439391	+	0.761047i	0.997643	−	0.0686244i	$-0.0218610\pi$
$31$	2.44642	+	4.23733i	0.439391	+	0.761047i	−0.558252	+	0.829672i	$0.688528\pi$
$32$	4.54413	−	3.36910i	0.803297	−	0.595579i
$33$	−1.94249	+	3.36449i	−0.338144	+	0.585683i
$34$	−10.5598	+	3.70020i	−1.81098	+	0.634580i
$35$	2.03862	+	0.117561i	0.344589	+	0.0198714i
$36$	−7.62373	−	9.54272i	−1.27062	−	1.59045i
$37$	−1.28190	+	0.343485i	−0.210743	+	0.0564685i	−0.362646	−	0.931927i	$-0.618127\pi$
$37$	−1.28190	+	0.343485i	−0.210743	+	0.0564685i	0.151903	+	0.988395i	$0.451460\pi$
$38$	2.60652	−	0.196478i	0.422834	−	0.0318730i
$39$	−3.39686	+	1.96118i	−0.543933	+	0.314040i
$40$	0.640710	−	2.08685i	0.101305	−	0.329960i
$41$		−	2.84345i		−	0.444072i	−0.975039	−	0.222036i	$-0.928730\pi$
$41$		−	2.84345i		−	0.444072i	0.975039	−	0.222036i	$-0.0712702\pi$
$42$	−7.84229	+	8.12387i	−1.21009	+	1.25354i
$43$	0.585764	+	0.585764i	0.0893282	+	0.0893282i	0.750359	−	0.661031i	$-0.229881\pi$
$43$	0.585764	+	0.585764i	0.0893282	+	0.0893282i	−0.661031	+	0.750359i	$0.729881\pi$
$44$	1.52711	−	2.07295i	0.230220	−	0.312509i
$45$	−4.55285	−	1.21993i	−0.678699	−	0.181857i
$46$	3.54750	−	4.12591i	0.523050	−	0.608333i
$47$	−2.86095	+	4.95532i	−0.417313	+	0.722807i	−0.995668	−	0.0929777i	$-0.970361\pi$
$47$	−2.86095	+	4.95532i	−0.417313	+	0.722807i	0.578355	+	0.815785i	$0.303695\pi$
$48$	6.44012	+	10.2097i	0.929551	+	1.47364i
$49$	5.61966	+	4.17366i	0.802809	+	0.596237i
$50$	2.05976	+	5.87821i	0.291294	+	0.831305i
$51$	−6.17977	−	23.0632i	−0.865341	−	3.22950i
$52$	2.38168	−	1.04160i	0.330280	−	0.144444i
$53$	2.54947	−	9.51475i	0.350197	−	1.30695i	−0.536226	−	0.844075i	$-0.680150\pi$
$53$	2.54947	−	9.51475i	0.350197	−	1.30695i	0.886422	−	0.462877i	$-0.153183\pi$
$54$	10.9529	−	7.47460i	1.49050	−	1.01716i
$55$		−	0.993590i		−	0.133976i
$56$	5.76334	−	4.77325i	0.770158	−	0.637853i
$57$			5.57784i			0.738803i
$58$	−5.92039	−	8.67547i	−0.777386	−	1.13914i
$59$	2.39390	−	8.93417i	0.311660	−	1.16313i	−0.615400	−	0.788215i	$-0.711005\pi$
$59$	2.39390	−	8.93417i	0.311660	−	1.16313i	0.927059	−	0.374915i	$-0.122328\pi$
$60$	4.33777	+	1.69807i	0.560003	+	0.219220i
$61$	−1.71139	−	6.38698i	−0.219121	−	0.817769i	−0.984675	−	0.174398i	$-0.944202\pi$
$61$	−1.71139	−	6.38698i	−0.219121	−	0.817769i	0.765555	−	0.643371i	$-0.222465\pi$
$62$	6.53023	−	2.28823i	0.829340	−	0.290606i
$63$	−10.7485	−	12.0641i	−1.35419	−	1.51993i
$64$	−3.48998	−	7.19862i	−0.436247	−	0.899827i
$65$	0.501575	−	0.868753i	0.0622127	−	0.107755i
$66$	4.16601	+	3.58197i	0.512801	+	0.440910i
$67$	5.94825	+	1.59383i	0.726695	+	0.194717i	0.603157	−	0.797623i	$-0.293909\pi$
$67$	5.94825	+	1.59383i	0.726695	+	0.194717i	0.123538	+	0.992340i	$0.460576\pi$
$68$	2.37214	+	15.6452i	0.287664	+	1.89726i
$69$	8.21037	+	8.21037i	0.988413	+	0.988413i
$70$	0.698123	−	2.80217i	0.0834416	−	0.334924i
$71$			1.99534i			0.236803i	0.992966	+	0.118402i	$0.0377770\pi$
$71$			1.99534i			0.236803i	−0.992966	+	0.118402i	$0.962223\pi$
$72$	−15.2611	+	8.09134i	−1.79853	+	0.953574i
$73$	−6.69237	+	3.86384i	−0.783283	+	0.452229i	−0.837592	−	0.546296i	$-0.816038\pi$
$73$	−6.69237	+	3.86384i	−0.783283	+	0.452229i	0.0543096	+	0.998524i	$0.482704\pi$
$74$	0.141075	+	1.87153i	0.0163996	+	0.217560i
$75$	−12.8384	+	3.44004i	−1.48245	+	0.397222i
$76$	0.410678	−	3.67375i	0.0471080	−	0.421408i
$77$	1.87001	−	2.84677i	0.213108	−	0.324420i
$78$	1.83437	+	5.23497i	0.207701	+	0.592743i
$79$	−4.63378	+	8.02594i	−0.521341	+	0.902989i	0.478351	+	0.878169i	$0.341235\pi$
$79$	−4.63378	+	8.02594i	−0.521341	+	0.902989i	−0.999692	+	0.0248202i	$0.992099\pi$
$80$	−2.73198	−	1.43778i	−0.305444	−	0.160749i
$81$	4.98751	+	8.63862i	0.554168	+	0.959847i
$82$	−3.95146	−	0.745866i	−0.436366	−	0.0823672i
$83$	−4.78537	+	4.78537i	−0.525263	+	0.525263i	−0.919156	−	0.393893i	$-0.871128\pi$
$83$	−4.78537	+	4.78537i	−0.525263	+	0.525263i	0.393893	+	0.919156i	$0.371128\pi$
$84$	9.23241	+	13.0292i	1.00734	+	1.42160i
$85$	4.31797	+	4.31797i	0.468349	+	0.468349i
$86$	0.967673	−	0.660369i	0.104347	−	0.0712094i
$87$	19.4098	−	11.2063i	2.08095	−	1.20144i
$88$	−2.48015	−	2.66594i	−0.264385	−	0.284190i
$89$	−1.84016	−	1.06242i	−0.195057	−	0.112616i	0.399291	−	0.916824i	$-0.369256\pi$
$89$	−1.84016	−	1.06242i	−0.195057	−	0.112616i	−0.594348	+	0.804208i	$0.702590\pi$
$90$	−2.88957	+	6.00698i	−0.304588	+	0.633191i
$91$	3.07214	−	1.54510i	0.322048	−	0.161970i
$92$	−4.80313	−	6.01213i	−0.500761	−	0.626808i
$93$	3.82162	+	14.2625i	0.396283	+	1.47895i
$94$	6.13582	+	5.27563i	0.632861	+	0.544139i
$95$	−0.713270	−	1.23542i	−0.0731800	−	0.126751i
$96$	15.8775	−	6.27155i	1.62049	−	0.640088i
$97$	−9.01961			−0.915802			−0.457901	−	0.889003i	$-0.651399\pi$
$97$	−9.01961			−0.915802			−0.457901	+	0.889003i	$0.651399\pi$
$98$	7.27412	−	6.71470i	0.734797	−	0.678287i
$99$	−5.55926	+	5.55926i	−0.558727	+	0.558727i
$100$	8.70910	−	1.32048i	0.870910	−	0.132048i
$101$	−1.29142	+	4.81966i	−0.128501	+	0.479574i	−0.999940	−	0.0109304i	$-0.996521\pi$
$101$	−1.29142	+	4.81966i	−0.128501	+	0.479574i	0.871439	+	0.490504i	$0.163187\pi$
$102$	−33.6714	+	2.53813i	−3.33396	+	0.251313i
$103$	−10.1524	−	5.86151i	−1.00035	−	0.577551i	−0.0919971	−	0.995759i	$-0.529325\pi$
$103$	−10.1524	−	5.86151i	−1.00035	−	0.577551i	−0.908351	+	0.418208i	$0.862658\pi$
$104$	−0.822742	−	3.58299i	−0.0806765	−	0.351341i
$105$	5.85067	+	1.93497i	0.570967	+	0.188834i
$106$	−12.5536	−	6.03875i	−1.21932	−	0.586536i
$107$	6.97171	−	1.86807i	0.673981	−	0.180593i	0.0944336	−	0.995531i	$-0.469896\pi$
$107$	6.97171	−	1.86807i	0.673981	−	0.180593i	0.579547	+	0.814938i	$0.303229\pi$
$108$	−7.51418	−	17.1817i	−0.723052	−	1.65331i
$109$	10.9026	+	2.92133i	1.04428	+	0.279813i	0.739884	−	0.672734i	$-0.234880\pi$
$109$	10.9026	+	2.92133i	1.04428	+	0.279813i	0.304391	+	0.952547i	$0.401547\pi$
$110$	−1.38077	−	0.260629i	−0.131651	−	0.0248500i
$111$	−4.00498			−0.380136
$112$	−5.12148	−	9.26123i	−0.483935	−	0.875104i
$113$	9.15066			0.860821			0.430411	−	0.902633i	$-0.358369\pi$
$113$	9.15066			0.860821			0.430411	+	0.902633i	$0.358369\pi$
$114$	7.75137	+	1.46313i	0.725983	+	0.137034i
$115$	−2.86840	−	0.768586i	−0.267480	−	0.0716710i
$116$	−13.6091	+	5.95175i	−1.26357	+	0.552606i
$117$	−7.66715	+	2.05441i	−0.708829	+	0.189930i
$118$	−11.7876	−	5.67027i	−1.08514	−	0.521991i
$119$	4.24484	+	20.4983i	0.389124	+	1.87908i
$120$	3.49761	−	5.58266i	0.319286	−	0.509625i
$121$	8.09102	+	4.67135i	0.735547	+	0.424668i
$122$	−9.32473	+	0.702894i	−0.844222	+	0.0636371i
$123$	2.22091	−	8.28853i	0.200252	−	0.747352i
$124$	−1.46695	−	9.67512i	−0.131736	−	0.868852i
$125$	5.13239	−	5.13239i	0.459055	−	0.459055i
$126$	−19.5846	+	11.7724i	−1.74474	+	1.04877i
$127$	17.4281			1.54649			0.773245	−	0.634108i	$-0.218632\pi$
$127$	17.4281			1.54649			0.773245	+	0.634108i	$0.218632\pi$
$128$	−10.9192	+	2.96165i	−0.965129	+	0.261776i
$129$	1.24996	+	2.16500i	0.110053	+	0.190617i
$130$	−1.07571	−	0.924908i	−0.0943464	−	0.0811198i
$131$	2.71575	+	10.1353i	0.237276	+	0.885527i	0.977110	+	0.212737i	$0.0682377\pi$
$131$	2.71575	+	10.1353i	0.237276	+	0.885527i	−0.739833	+	0.672790i	$0.765096\pi$
$132$	6.07056	−	4.84981i	0.528375	−	0.422121i
$133$	0.281535	−	4.88208i	0.0244122	−	0.423330i
$134$	3.77520	−	7.84805i	0.326127	−	0.677969i
$135$	−6.26725	−	3.61840i	−0.539399	−	0.311422i
$136$	22.3640	+	0.807413i	1.91770	+	0.0692351i
$137$	−5.24143	+	3.02614i	−0.447806	+	0.258541i	−0.706903	−	0.707310i	$-0.749908\pi$
$137$	−5.24143	+	3.02614i	−0.447806	+	0.258541i	0.259097	+	0.965851i	$0.416575\pi$
$138$	13.5634	−	9.25607i	1.15459	−	0.787929i
$139$	−4.50305	−	4.50305i	−0.381944	−	0.381944i	0.489858	−	0.871802i	$-0.337048\pi$
$139$	−4.50305	−	4.50305i	−0.381944	−	0.381944i	−0.871802	+	0.489858i	$0.837048\pi$
$140$	−3.71098	−	1.70520i	−0.313635	−	0.144116i
$141$	−12.2100	+	12.2100i	−1.02827	+	1.02827i
$142$	2.77287	+	0.523399i	0.232694	+	0.0439227i
$143$	−0.836620	−	1.44907i	−0.0699616	−	0.121177i
$144$	7.24119	+	23.3303i	0.603432	+	1.94419i
$145$	−2.86602	+	4.96409i	−0.238010	+	0.412245i
$146$	3.61400	+	10.3137i	0.299097	+	0.853571i
$147$	13.1212	+	16.5554i	1.08222	+	1.36546i
$148$	2.63782	+	0.294874i	0.216827	+	0.0242385i
$149$	−14.6597	+	3.92804i	−1.20097	+	0.321798i	−0.803211	−	0.595694i	$-0.796877\pi$
$149$	−14.6597	+	3.92804i	−1.20097	+	0.321798i	−0.397754	+	0.917492i	$0.630210\pi$
$150$	1.41288	+	18.7436i	0.115361	+	1.53041i
$151$	−12.8763	+	7.43412i	−1.04786	+	0.604980i	−0.922049	−	0.387074i	$-0.873486\pi$
$151$	−12.8763	+	7.43412i	−1.04786	+	0.604980i	−0.125808	+	0.992055i	$0.540152\pi$
$152$	−4.99759	−	1.53437i	−0.405358	−	0.124454i
$153$		−	48.3192i		−	3.90637i
$154$	−3.46556	−	3.34545i	−0.279263	−	0.269584i
$155$	−2.67026	−	2.67026i	−0.214481	−	0.214481i
$156$	7.75607	−	1.17598i	0.620983	−	0.0941538i
$157$	−10.9861	−	2.94372i	−0.876786	−	0.234934i	−0.207766	−	0.978178i	$-0.566619\pi$
$157$	−10.9861	−	2.94372i	−0.876786	−	0.234934i	−0.669020	+	0.743244i	$0.733286\pi$
$158$	9.93795	+	8.54473i	0.790621	+	0.679782i
$159$	14.8632	−	25.7439i	1.17873	−	2.04162i
$160$	−2.71468	+	3.41941i	−0.214614	+	0.270328i
$161$	−6.77183	−	7.60065i	−0.533695	−	0.599015i
$162$	13.3131	−	4.66501i	1.04598	−	0.366518i
$163$	2.61713	+	9.76727i	0.204990	+	0.765032i	0.989453	+	0.144856i	$0.0462720\pi$
$163$	2.61713	+	9.76727i	0.204990	+	0.765032i	−0.784463	+	0.620176i	$0.787061\pi$
$164$	−2.07302	+	5.29559i	−0.161876	+	0.413516i
$165$	0.776055	−	2.89628i	0.0604158	−	0.225475i
$166$	5.39485	+	7.90536i	0.418721	+	0.613575i
$167$		−	2.61575i		−	0.202413i	−0.994865	−	0.101207i	$-0.967730\pi$
$167$		−	2.61575i		−	0.202413i	0.994865	−	0.101207i	$-0.0322703\pi$
$168$	20.5281	−	9.41234i	1.58378	−	0.726178i
$169$			11.3107i			0.870051i
$170$	7.13322	−	4.86792i	0.547093	−	0.373352i
$171$	−2.92150	+	10.9032i	−0.223412	+	0.833786i
$172$	−0.663866	−	1.51797i	−0.0506193	−	0.115744i
$173$	2.64600	+	9.87502i	0.201172	+	0.750784i	0.990582	+	0.136918i	$0.0437197\pi$
$173$	2.64600	+	9.87502i	0.201172	+	0.750784i	−0.789410	+	0.613866i	$0.789614\pi$
$174$	−10.4816	−	29.9129i	−0.794612	−	2.26769i
$175$	11.4106	−	2.36294i	0.862563	−	0.178622i
$176$	−4.35535	+	2.74729i	−0.328297	+	0.207085i
$177$	13.9563	−	24.1730i	1.04902	−	1.81695i
$178$	−1.95911	+	2.27854i	−0.146841	+	0.170784i
$179$	−15.0929	−	4.04414i	−1.12810	−	0.302273i	−0.353942	−	0.935267i	$-0.615159\pi$
$179$	−15.0929	−	4.04414i	−1.12810	−	0.302273i	−0.774156	+	0.632994i	$0.781826\pi$
$180$	7.58977	+	5.59126i	0.565708	+	0.416748i
$181$	12.8671	+	12.8671i	0.956407	+	0.956407i	0.999089	−	0.0426817i	$-0.0135901\pi$
$181$	12.8671	+	12.8671i	0.956407	+	0.956407i	−0.0426817	+	0.999089i	$0.513590\pi$
$182$	−1.34132	−	4.67457i	−0.0994256	−	0.346502i
$183$		−	19.9545i		−	1.47508i
$184$	−9.61482	+	5.09773i	−0.708814	+	0.375810i
$185$	0.887052	−	0.512140i	0.0652174	−	0.0376533i
$186$	20.8226	−	1.56960i	1.52679	−	0.115089i
$187$	9.83854	−	2.63623i	0.719465	−	0.192780i
$188$	8.94089	−	7.14293i	0.652081	−	0.520952i
$189$	−11.1464	−	22.1627i	−0.810785	−	1.61210i
$190$	−1.90393	+	0.667149i	−0.138126	+	0.0484001i
$191$	0.254497	−	0.440801i	0.0184147	−	0.0318952i	−0.856671	−	0.515863i	$-0.827471\pi$
$191$	0.254497	−	0.440801i	0.0184147	−	0.0318952i	0.875086	+	0.483968i	$0.160805\pi$
$192$	−4.55058	−	23.7096i	−0.328410	−	1.71109i
$193$	−2.41417	−	4.18147i	−0.173776	−	0.300989i	0.765961	−	0.642887i	$-0.222264\pi$
$193$	−2.41417	−	4.18147i	−0.173776	−	0.300989i	−0.939737	+	0.341898i	$0.888930\pi$
$194$	−2.36594	+	12.5343i	−0.169865	+	0.899911i
$195$	2.14062	−	2.14062i	0.153293	−	0.153293i
$196$	−7.42316	−	11.8700i	−0.530226	−	0.847857i
$197$	3.02638	+	3.02638i	0.215621	+	0.215621i	0.806650	−	0.591029i	$-0.201278\pi$
$197$	3.02638	+	3.02638i	0.215621	+	0.215621i	−0.591029	+	0.806650i	$0.701278\pi$
$198$	6.26731	+	9.18382i	0.445398	+	0.652665i
$199$	−6.56029	+	3.78758i	−0.465046	+	0.268495i	−0.714164	−	0.699979i	$-0.753193\pi$
$199$	−6.56029	+	3.78758i	−0.465046	+	0.268495i	0.249117	+	0.968473i	$0.419860\pi$
$200$	0.449456	−	12.4492i	0.0317813	−	0.880290i
$201$	16.0941	+	9.29191i	1.13519	+	0.655401i
$202$	6.35900	+	3.05890i	0.447417	+	0.215224i
$203$	−17.5543	+	8.82875i	−1.23207	+	0.619657i
$204$	−5.30519	+	47.4580i	−0.371438	+	3.32272i
$205$	0.568000	+	2.11981i	0.0396709	+	0.148054i
$206$	−10.8087	+	12.5710i	−0.753076	+	0.875865i
$207$	11.7487	+	20.3494i	0.816594	+	1.41438i
$208$	−5.19500	+	0.203486i	−0.360208	+	0.0141092i
$209$	−2.37945			−0.164590
$210$	4.22367	−	7.62295i	0.291461	−	0.526034i
$211$	6.60935	−	6.60935i	0.455006	−	0.455006i	−0.442006	−	0.897012i	$-0.645733\pi$
$211$	6.60935	−	6.60935i	0.455006	−	0.455006i	0.897012	+	0.442006i	$0.145733\pi$
$212$	−11.6849	+	15.8614i	−0.802519	+	1.08937i
$213$	−1.55848	+	5.81634i	−0.106785	+	0.398529i
$214$	−0.767245	−	10.1784i	−0.0524478	−	0.695783i
$215$	−0.553701	−	0.319680i	−0.0377621	−	0.0218020i
$216$	−25.8479	+	5.93532i	−1.75873	+	0.403848i
$217$	−2.62504	−	12.6763i	−0.178199	−	0.860524i
$218$	6.91955	−	14.3847i	0.468651	−	0.974254i
$219$	−22.5259	+	6.03580i	−1.52216	+	0.407862i
$220$	−0.724380	+	1.85045i	−0.0488377	+	0.124757i
$221$	9.93319	+	2.66159i	0.668179	+	0.179038i
$222$	−1.05055	+	5.56561i	−0.0705083	+	0.373540i
$223$	−20.4381			−1.36864			−0.684319	−	0.729183i	$-0.739900\pi$
$223$	−20.4381			−1.36864			−0.684319	+	0.729183i	$0.739900\pi$
$224$	−14.2135	+	4.68787i	−0.949680	+	0.313221i
$225$	−26.8974			−1.79316
$226$	2.40032	−	12.7164i	0.159667	−	0.845884i
$227$	−11.3952	−	3.05333i	−0.756326	−	0.202657i	−0.140004	−	0.990151i	$-0.544711\pi$
$227$	−11.3952	−	3.05333i	−0.756326	−	0.202657i	−0.616322	+	0.787494i	$0.711378\pi$
$228$	4.06654	−	10.3881i	0.269313	−	0.687968i
$229$	13.1330	−	3.51899i	0.867856	−	0.232541i	0.202696	−	0.979242i	$-0.435030\pi$
$229$	13.1330	−	3.51899i	0.867856	−	0.232541i	0.665160	+	0.746700i	$0.268363\pi$
$230$	−1.82050	+	3.78453i	−0.120040	+	0.249545i
$231$	7.67452	−	6.83764i	0.504946	−	0.449884i
$232$	4.70118	+	20.4734i	0.308648	+	1.34414i
$233$	−18.6628	−	10.7750i	−1.22264	−	0.705893i	−0.257162	−	0.966368i	$-0.582787\pi$
$233$	−18.6628	−	10.7750i	−1.22264	−	0.705893i	−0.965481	+	0.260475i	$0.916121\pi$
$234$	0.843779	+	11.1937i	0.0551595	+	0.731757i
$235$	1.14300	−	4.26572i	0.0745608	−	0.278265i
$236$	−10.9719	+	14.8936i	−0.714207	+	0.969490i
$237$	−19.7760	+	19.7760i	−1.28459	+	1.28459i
$238$	29.5994	−	0.522011i	1.91865	−	0.0338369i
$239$	14.5125			0.938733			0.469366	−	0.883004i	$-0.344482\pi$
$239$	14.5125			0.938733			0.469366	+	0.883004i	$0.344482\pi$
$240$	−6.84061	−	6.32492i	−0.441560	−	0.408272i
$241$	4.59046	+	7.95090i	0.295697	+	0.512163i	0.975147	−	0.221560i	$-0.0711147\pi$
$241$	4.59046	+	7.95090i	0.295697	+	0.512163i	−0.679450	+	0.733722i	$0.737781\pi$
$242$	8.61402	−	10.0185i	0.553730	−	0.644016i
$243$	0.510685	+	1.90590i	0.0327604	+	0.122264i
$244$	−1.46919	+	13.1427i	−0.0940549	+	0.841376i
$245$	−5.02321	−	1.98892i	−0.320921	−	0.127067i
$246$	−10.9358	−	5.26051i	−0.697241	−	0.335398i
$247$	−2.08049	−	1.20117i	−0.132378	−	0.0764287i
$248$	−13.8301	−	0.499310i	−0.878210	−	0.0317062i
$249$	−17.6868	+	10.2115i	−1.12086	+	0.647128i
$250$	−5.78607	−	8.47863i	−0.365943	−	0.536236i
$251$	9.13628	+	9.13628i	0.576677	+	0.576677i	0.933986	−	0.357309i	$-0.116306\pi$
$251$	9.13628	+	9.13628i	0.576677	+	0.576677i	−0.357309	+	0.933986i	$0.616306\pi$
$252$	11.2226	+	30.3042i	0.706957	+	1.90899i
$253$	−3.50246	+	3.50246i	−0.220198	+	0.220198i
$254$	4.57157	−	24.2193i	0.286846	−	1.51965i
$255$	9.21411	+	15.9593i	0.577010	+	0.999411i
$256$	1.25151	+	15.9510i	0.0782194	+	0.996936i
$257$	4.85503	−	8.40916i	0.302849	−	0.524549i	−0.673931	−	0.738794i	$-0.735396\pi$
$257$	4.85503	−	8.40916i	0.302849	−	0.524549i	0.976780	+	0.214245i	$0.0687290\pi$
$258$	3.33652	−	1.16914i	0.207723	−	0.0727873i
$259$	3.50541	+	0.202147i	0.217816	+	0.0125608i
$260$	−1.56749	+	1.25228i	−0.0972117	+	0.0776630i
$261$	43.8105	−	11.7390i	2.71180	−	0.726625i
$262$	14.7972	−	1.11540i	0.914172	−	0.0689098i
$263$	9.24140	−	5.33552i	0.569849	−	0.329002i	−0.187240	−	0.982314i	$-0.559954\pi$
$263$	9.24140	−	5.33552i	0.569849	−	0.329002i	0.757089	+	0.653312i	$0.226621\pi$
$264$	−5.14727	−	9.70826i	−0.316793	−	0.597502i
$265$			7.60258i			0.467023i
$266$	−6.71065	−	1.67186i	−0.411456	−	0.102509i
$267$	−4.53418	−	4.53418i	−0.277487	−	0.277487i
$268$	−9.91596	−	7.30492i	−0.605714	−	0.446219i
$269$	7.31835	+	1.96094i	0.446207	+	0.119561i	0.474924	−	0.880027i	$-0.342475\pi$
$269$	7.31835	+	1.96094i	0.446207	+	0.119561i	−0.0287169	+	0.999588i	$0.509142\pi$
$270$	−6.67236	+	7.76029i	−0.406067	+	0.472276i
$271$	5.62243	−	9.73834i	0.341538	−	0.591562i	−0.643180	−	0.765715i	$-0.722385\pi$
$271$	5.62243	−	9.73834i	0.341538	−	0.591562i	0.984719	+	0.174153i	$0.0557187\pi$
$272$	6.98836	−	30.8668i	0.423731	−	1.87158i
$273$	10.1620	−	2.10437i	0.615031	−	0.127362i
$274$	2.83047	+	8.07767i	0.170995	+	0.487990i
$275$	−1.46749	−	5.47674i	−0.0884929	−	0.330260i
$276$	−9.30509	−	21.2767i	−0.560101	−	1.28071i
$277$	5.50691	−	20.5521i	0.330878	−	1.23485i	−0.577391	−	0.816467i	$-0.695929\pi$
$277$	5.50691	−	20.5521i	0.330878	−	1.23485i	0.908269	−	0.418386i	$-0.137404\pi$
$278$	−7.43897	+	5.07657i	−0.446160	+	0.304472i
$279$			29.8809i			1.78892i
$280$	−3.34311	+	4.70976i	−0.199789	+	0.281462i
$281$		−	20.0973i		−	1.19891i	−0.800410	−	0.599453i	$-0.795385\pi$
$281$		−	20.0973i		−	1.19891i	0.800410	−	0.599453i	$-0.204615\pi$
$282$	13.7651	+	20.1707i	0.819699	+	1.20115i
$283$	5.29502	−	19.7613i	0.314756	−	1.17469i	−0.609460	−	0.792816i	$-0.708614\pi$
$283$	5.29502	−	19.7613i	0.314756	−	1.17469i	0.924216	−	0.381869i	$-0.124719\pi$
$284$	1.45471	−	3.71609i	0.0863210	−	0.220509i
$285$	−1.11422	−	4.15831i	−0.0660005	−	0.246317i
$286$	−2.23319	+	0.782522i	−0.132051	+	0.0462715i
$287$	−2.36223	+	7.14256i	−0.139438	+	0.421612i
$288$	34.3210	−	3.94309i	2.02238	−	0.232349i
$289$	−22.8000	+	39.4907i	−1.34117	+	2.32298i
$290$	6.14668	+	5.28497i	0.360946	+	0.310344i
$291$	−26.2918	−	7.04487i	−1.54125	−	0.412978i
$292$	15.2807	−	2.31687i	0.894237	−	0.135585i
$293$	−10.4368	−	10.4368i	−0.609726	−	0.609726i	0.333148	−	0.942875i	$-0.391889\pi$
$293$	−10.4368	−	10.4368i	−0.609726	−	0.609726i	−0.942875	+	0.333148i	$0.891889\pi$
$294$	26.4484	−	13.8916i	1.54250	−	0.810172i
$295$			7.13868i			0.415630i
$296$	1.10171	−	3.58835i	0.0640353	−	0.208569i
$297$	−10.4537	+	6.03544i	−0.606585	+	0.350212i
$298$	1.61331	+	21.4025i	0.0934566	+	1.23981i
$299$	−4.83048	+	1.29432i	−0.279354	+	0.0748527i
$300$	26.4181	+	2.95320i	1.52525	+	0.170503i
$301$	−0.984771	−	1.95803i	−0.0567612	−	0.112859i
$302$	6.95342	+	19.8439i	0.400124	+	1.14189i
$303$	−7.52890	+	13.0404i	−0.432524	+	0.749153i
$304$	−3.44320	+	6.54254i	−0.197481	+	0.375240i
$305$	2.55170	+	4.41967i	0.146110	+	0.253070i
$306$	−67.1479	−	12.6746i	−3.83859	−	0.724561i
$307$	4.72698	−	4.72698i	0.269783	−	0.269783i	−0.559230	−	0.829013i	$-0.688903\pi$
$307$	4.72698	−	4.72698i	0.269783	−	0.269783i	0.829013	+	0.559230i	$0.188903\pi$
$308$	−5.55813	+	3.93846i	−0.316704	+	0.224414i
$309$	−25.0157	−	25.0157i	−1.42310	−	1.42310i
$310$	−4.41124	+	3.01036i	−0.250541	+	0.170977i
$311$	−4.82684	+	2.78678i	−0.273705	+	0.158024i	−0.630570	−	0.776132i	$-0.717179\pi$
$311$	−4.82684	+	2.78678i	−0.273705	+	0.158024i	0.356865	+	0.934156i	$0.383846\pi$
$312$	0.400273	−	11.0869i	0.0226610	−	0.627671i
$313$	10.2429	+	5.91372i	0.578961	+	0.334263i	0.760720	−	0.649080i	$-0.224846\pi$
$313$	10.2429	+	5.91372i	0.578961	+	0.334263i	−0.181760	+	0.983343i	$0.558179\pi$
$314$	−6.97258	+	14.4949i	−0.393485	+	0.817996i
$315$	10.4230	+	6.84674i	0.587270	+	0.385770i
$316$	14.4812	−	11.5691i	0.814632	−	0.650814i
$317$	−1.17054	−	4.36851i	−0.0657441	−	0.245360i	0.925231	−	0.379403i	$-0.123871\pi$
$317$	−1.17054	−	4.36851i	−0.0657441	−	0.245360i	−0.990976	+	0.134043i	$0.957204\pi$
$318$	−31.8768	−	27.4079i	−1.78756	−	1.53696i
$319$	4.78048	+	8.28004i	0.267656	+	0.463593i
$320$	4.03978	+	4.66946i	0.225830	+	0.261031i
$321$	21.7814			1.21572
$322$	−12.3388	+	7.41691i	−0.687612	+	0.413328i
$323$	10.3407	−	10.3407i	0.575370	−	0.575370i
$324$	−2.99066	−	19.7246i	−0.166148	−	1.09581i
$325$	1.48161	−	5.52943i	0.0821848	−	0.306718i
$326$	14.2598	−	1.07490i	0.789779	−	0.0595332i
$327$	29.4988	+	17.0311i	1.63129	+	0.941824i
$328$	6.81537	+	4.26992i	0.376316	+	0.235767i
$329$	11.3032	−	10.0707i	0.623168	−	0.555214i
$330$	−3.82131	−	1.83819i	−0.210356	−	0.101189i
$331$	22.2142	−	5.95228i	1.22100	−	0.327167i	0.409934	−	0.912115i	$-0.365552\pi$
$331$	22.2142	−	5.95228i	1.22100	−	0.327167i	0.811071	+	0.584948i	$0.198885\pi$
$332$	12.4010	−	5.42342i	0.680593	−	0.297649i
$333$	−7.82866	−	2.09768i	−0.429008	−	0.114952i
$334$	−3.63505	−	0.686141i	−0.198901	−	0.0375440i
$335$	−4.75284			−0.259675
$336$	−7.69533	−	30.9963i	−0.419815	−	1.69099i
$337$	−16.6077			−0.904682			−0.452341	−	0.891845i	$-0.649411\pi$
$337$	−16.6077			−0.904682			−0.452341	+	0.891845i	$0.649411\pi$
$338$	15.7181	+	2.96691i	0.854954	+	0.161379i
$339$	26.6738	+	7.14723i	1.44872	+	0.388184i
$340$	−4.89370	−	11.1897i	−0.265398	−	0.606849i
$341$	−6.08423	+	1.63026i	−0.329479	+	0.0882838i
$342$	14.3855	+	6.91995i	0.777879	+	0.374188i
$343$	−10.6489	−	15.1526i	−0.574987	−	0.818162i
$344$	−2.28362	+	0.524376i	−0.123125	+	0.0282725i
$345$	−7.76097	−	4.48080i	−0.417837	−	0.241238i
$346$	14.4171	−	1.08676i	0.775070	−	0.0584244i
$347$	−4.00465	+	14.9456i	−0.214981	+	0.802320i	0.771192	+	0.636602i	$0.219661\pi$
$347$	−4.00465	+	14.9456i	−0.214981	+	0.802320i	−0.986173	+	0.165718i	$0.947006\pi$
$348$	−44.3186	+	6.71961i	−2.37572	+	0.360209i
$349$	13.7065	−	13.7065i	0.733694	−	0.733694i	−0.237656	−	0.971349i	$-0.576379\pi$
$349$	13.7065	−	13.7065i	0.733694	−	0.733694i	0.971349	+	0.237656i	$0.0763790\pi$
$350$	−0.290584	−	16.4769i	−0.0155323	−	0.880727i
$351$	−12.1870			−0.650494
$352$	2.67538	+	6.77317i	0.142598	+	0.361011i
$353$	1.15032	+	1.99241i	0.0612252	+	0.106045i	0.895013	−	0.446039i	$-0.147166\pi$
$353$	1.15032	+	1.99241i	0.0612252	+	0.106045i	−0.833788	+	0.552085i	$0.813833\pi$
$354$	−29.9317	−	25.7355i	−1.59085	−	1.36783i
$355$	−0.398584	−	1.48754i	−0.0211547	−	0.0789503i
$356$	2.65253	+	3.32020i	0.140584	+	0.175970i
$357$	−3.63691	+	63.0673i	−0.192485	+	3.33788i
$358$	−9.57907	+	19.9134i	−0.506270	+	1.05246i
$359$	6.28570	+	3.62905i	0.331747	+	0.191534i	0.656616	−	0.754225i	$-0.271987\pi$
$359$	6.28570	+	3.62905i	0.331747	+	0.191534i	−0.324870	+	0.945759i	$0.605320\pi$
$360$	9.76090	−	9.08066i	0.514445	−	0.478593i
$361$	13.4959	−	7.79186i	0.710310	−	0.410098i
$362$	21.2563	−	14.5059i	1.11721	−	0.762415i
$363$	19.9364	+	19.9364i	1.04639	+	1.04639i
$364$	−6.84796	+	0.637814i	−0.358931	+	0.0334305i
$365$	4.21737	−	4.21737i	0.220747	−	0.220747i
$366$	−27.7303	−	5.23428i	−1.44948	−	0.273600i
$367$	−13.4406	−	23.2797i	−0.701591	−	1.21519i	−0.967908	−	0.251306i	$-0.919140\pi$
$367$	−13.4406	−	23.2797i	−0.701591	−	1.21519i	0.266316	−	0.963886i	$-0.414193\pi$
$368$	4.56211	+	14.6987i	0.237817	+	0.766220i
$369$	8.68255	−	15.0386i	0.451995	−	0.782879i
$370$	−0.479024	−	1.36705i	−0.0249033	−	0.0710697i
$371$	−14.3086	+	21.7825i	−0.742867	+	1.13089i
$372$	3.28077	−	29.3484i	0.170100	−	1.52164i
$373$	1.29586	−	0.347226i	0.0670973	−	0.0179787i	−0.225114	−	0.974332i	$-0.572276\pi$
$373$	1.29586	−	0.347226i	0.0670973	−	0.0179787i	0.292212	+	0.956354i	$0.405609\pi$
$374$	−1.08274	−	14.3639i	−0.0559873	−	0.742738i
$375$	18.9694	−	10.9520i	0.979578	−	0.565559i
$376$	−7.58105	−	14.2986i	−0.390963	−	0.737393i
$377$			9.65295i			0.497152i
$378$	−33.7227	+	9.67642i	−1.73451	+	0.497701i
$379$	−15.3095	−	15.3095i	−0.786396	−	0.786396i	0.194506	−	0.980901i	$-0.437690\pi$
$379$	−15.3095	−	15.3095i	−0.786396	−	0.786396i	−0.980901	+	0.194506i	$0.937690\pi$
$380$	0.427698	+	2.82084i	0.0219404	+	0.144706i
$381$	50.8021	+	13.6124i	2.60267	+	0.697384i
$382$	−0.545812	−	0.469294i	−0.0279262	−	0.0240112i
$383$	−4.04897	+	7.01302i	−0.206893	+	0.358348i	−0.950734	−	0.310008i	$-0.899668\pi$
$383$	−4.04897	+	7.01302i	−0.206893	+	0.358348i	0.743842	+	0.668356i	$0.233002\pi$
$384$	−34.1422	+	0.104547i	−1.74231	+	0.00533513i
$385$	−0.825439	+	2.49584i	−0.0420683	+	0.127200i
$386$	−6.44415	+	2.25807i	−0.327998	+	0.114933i
$387$	1.30938	+	4.88668i	0.0665596	+	0.248404i
$388$	16.7980	+	6.57577i	0.852789	+	0.333834i
$389$	−4.79714	+	17.9032i	−0.243225	+	0.907727i	0.731043	+	0.682332i	$0.239034\pi$
$389$	−4.79714	+	17.9032i	−0.243225	+	0.907727i	−0.974267	+	0.225395i	$0.927633\pi$
$390$	−2.41326	−	3.53627i	−0.122200	−	0.179066i
$391$		−	30.4422i		−	1.53953i
$392$	−18.4426	+	7.20214i	−0.931491	+	0.363763i
$393$			31.6652i			1.59730i
$394$	4.99953	−	3.41183i	0.251873	−	0.171885i
$395$	1.85127	−	6.90902i	0.0931473	−	0.347631i
$396$	14.4065	−	6.30050i	0.723953	−	0.316612i
$397$	−4.35104	−	16.2383i	−0.218372	−	0.814977i	−0.984952	−	0.172828i	$-0.944710\pi$
$397$	−4.35104	−	16.2383i	−0.218372	−	0.814977i	0.766580	−	0.642149i	$-0.221957\pi$
$398$	3.54267	+	10.1102i	0.177578	+	0.506778i
$399$	4.63387	−	14.0112i	0.231984	−	0.701436i
$400$	−17.1824	−	3.89015i	−0.859120	−	0.194508i
$401$	−2.18786	+	3.78949i	−0.109257	+	0.189238i	−0.915469	−	0.402388i	$-0.868180\pi$
$401$	−2.18786	+	3.78949i	−0.109257	+	0.189238i	0.806213	+	0.591626i	$0.201514\pi$
$402$	17.1344	−	19.9281i	0.854585	−	0.993924i
$403$	−6.14276	−	1.64595i	−0.305993	−	0.0819905i
$404$	5.91891	−	8.03454i	0.294477	−	0.399734i
$405$	−5.44385	−	5.44385i	−0.270507	−	0.270507i
$406$	7.66439	+	26.7107i	0.380377	+	1.32563i
$407$		−	1.70848i		−	0.0846864i
$408$	64.5595	+	19.8212i	3.19617	+	0.981297i
$409$	−0.103105	+	0.0595279i	−0.00509823	+	0.00294347i	−0.502547	−	0.864550i	$-0.667604\pi$
$409$	−0.103105	+	0.0595279i	−0.00509823	+	0.00294347i	0.497449	+	0.867493i	$0.334270\pi$
$410$	3.09483	−	0.233287i	0.152843	−	0.0115212i
$411$	−17.6422	+	4.72721i	−0.870225	+	0.233176i
$412$	14.6344	+	18.3180i	0.720985	+	0.902465i
$413$	−13.4355	+	20.4533i	−0.661119	+	1.00644i
$414$	31.3609	−	10.9890i	1.54130	−	0.540082i
$415$	2.61161	−	4.52344i	0.128199	−	0.222047i
$416$	−1.07992	+	7.27273i	−0.0529476	+	0.356575i
$417$	−9.60906	−	16.6434i	−0.470558	−	0.815030i
$418$	−0.624156	+	3.30666i	−0.0305284	+	0.161734i
$419$	21.5456	−	21.5456i	1.05257	−	1.05257i	0.0540333	−	0.998539i	$-0.482792\pi$
$419$	21.5456	−	21.5456i	1.05257	−	1.05257i	0.998539	−	0.0540333i	$-0.0172077\pi$
$420$	−9.48550	−	7.86911i	−0.462845	−	0.383973i
$421$	−0.254915	−	0.254915i	−0.0124238	−	0.0124238i	0.700868	−	0.713291i	$-0.252796\pi$
$421$	−0.254915	−	0.254915i	−0.0124238	−	0.0124238i	−0.713291	+	0.700868i	$0.752796\pi$
$422$	−7.45113	−	10.9185i	−0.362716	−	0.531506i
$423$	−30.2624	+	17.4720i	−1.47141	+	0.849519i
$424$	18.9772	+	20.3988i	0.921613	+	0.990652i
$425$	30.1784	+	17.4235i	1.46387	+	0.845164i
$426$	7.67400	+	3.69147i	0.371807	+	0.178852i
$427$	−1.00718	+	17.4655i	−0.0487409	+	0.845213i
$428$	−14.3459	−	1.60369i	−0.693437	−	0.0775173i
$429$	−1.30690	−	4.87743i	−0.0630979	−	0.235484i
$430$	−0.589492	+	0.685609i	−0.0284278	+	0.0330630i
$431$	−12.1470	−	21.0393i	−0.585101	−	1.01343i	−0.994863	−	0.101232i	$-0.967721\pi$
$431$	−12.1470	−	21.0393i	−0.585101	−	1.01343i	0.409762	−	0.912193i	$-0.365612\pi$
$432$	1.46797	+	37.4771i	0.0706276	+	1.80312i
$433$	19.6797			0.945744			0.472872	−	0.881131i	$-0.343217\pi$
$433$	19.6797			0.945744			0.472872	+	0.881131i	$0.343217\pi$
$434$	−18.3045	+	0.322815i	−0.878645	+	0.0154956i
$435$	−12.2316	+	12.2316i	−0.586461	+	0.586461i
$436$	−18.1750	−	13.3892i	−0.870423	−	0.641226i
$437$	−1.84061	+	6.86925i	−0.0880483	+	0.328601i
$438$	2.47900	+	32.8869i	0.118451	+	1.57140i
$439$	−26.3901	−	15.2363i	−1.25953	−	0.727190i	−0.286548	−	0.958066i	$-0.592508\pi$
$439$	−26.3901	−	15.2363i	−1.25953	−	0.727190i	−0.972983	+	0.230876i	$0.925841\pi$
$440$	2.38151	+	1.49204i	0.113534	+	0.0711304i
$441$	16.9773	+	39.2337i	0.808441	+	1.86827i
$442$	6.30433	−	13.1057i	0.299866	−	0.623376i
$443$	3.77526	−	1.01158i	0.179368	−	0.0480615i	−0.168017	−	0.985784i	$-0.553736\pi$
$443$	3.77526	−	1.01158i	0.179368	−	0.0480615i	0.347385	+	0.937723i	$0.387070\pi$
$444$	7.45882	+	2.91984i	0.353980	+	0.138570i
$445$	1.58408	+	0.424452i	0.0750924	+	0.0201209i
$446$	−5.36114	+	28.4023i	−0.253857	+	1.34489i
$447$	−45.8004			−2.16628
$448$	2.78625	+	20.9818i	0.131638	+	0.991298i
$449$	38.0210			1.79432			0.897161	−	0.441704i	$-0.145626\pi$
$449$	38.0210			1.79432			0.897161	+	0.441704i	$0.145626\pi$
$450$	−7.05549	+	37.3787i	−0.332599	+	1.76205i
$451$	3.53581	+	0.947417i	0.166495	+	0.0446121i
$452$	−17.0421	−	6.67131i	−0.801591	−	0.313792i
$453$	−43.3404	+	11.6130i	−2.03631	+	0.545627i
$454$	−7.23222	+	15.0347i	−0.339425	+	0.705613i
$455$	−1.98165	+	1.76556i	−0.0929013	+	0.0827708i
$456$	−13.3694	−	8.37607i	−0.626077	−	0.392245i
$457$	−15.0844	−	8.70896i	−0.705616	−	0.407388i	0.103819	−	0.994596i	$-0.466894\pi$
$457$	−15.0844	−	8.70896i	−0.705616	−	0.407388i	−0.809436	+	0.587208i	$0.800227\pi$
$458$	−1.44531	−	19.1737i	−0.0675347	−	0.895929i
$459$	19.2009	−	71.6588i	0.896223	−	3.34475i
$460$	4.78173	+	3.52262i	0.222949	+	0.164243i
$461$	−27.4189	+	27.4189i	−1.27703	+	1.27703i	−0.334701	+	0.942324i	$0.608635\pi$
$461$	−27.4189	+	27.4189i	−1.27703	+	1.27703i	−0.942324	+	0.334701i	$0.891365\pi$
$462$	−7.48899	−	12.4587i	−0.348419	−	0.579630i
$463$	−40.5988			−1.88679			−0.943394	−	0.331674i	$-0.892387\pi$
$463$	−40.5988			−1.88679			−0.943394	+	0.331674i	$0.892387\pi$
$464$	29.6844	−	1.16273i	1.37807	−	0.0539784i
$465$	−5.69808	−	9.86936i	−0.264242	−	0.457681i
$466$	−19.8692	+	23.1089i	−0.920422	+	1.07050i
$467$	−2.38296	−	8.89334i	−0.110270	−	0.411535i	0.888619	−	0.458646i	$-0.151665\pi$
$467$	−2.38296	−	8.89334i	−0.110270	−	0.411535i	−0.998890	+	0.0471109i	$0.984999\pi$
$468$	15.7770	+	1.76366i	0.729291	+	0.0815253i
$469$	−13.6175	−	8.94520i	−0.628800	−	0.413051i
$470$	−5.62813	−	2.70733i	−0.259606	−	0.124880i
$471$	−29.7248	−	17.1616i	−1.36965	−	0.790767i
$472$	17.8192	+	19.1540i	0.820195	+	0.881637i
$473$	−0.923566	+	0.533221i	−0.0424656	+	0.0245175i
$474$	22.2948	+	32.6697i	1.02403	+	1.50057i
$475$	−5.75626	−	5.75626i	−0.264115	−	0.264115i
$476$	7.03883	−	41.2705i	0.322624	−	1.89163i
$477$	42.5374	−	42.5374i	1.94765	−	1.94765i
$478$	3.80677	−	20.1676i	0.174118	−	0.922444i
$479$	3.73955	+	6.47710i	0.170865	+	0.295946i	0.938722	−	0.344674i	$-0.112011\pi$
$479$	3.73955	+	6.47710i	0.170865	+	0.295946i	−0.767858	+	0.640620i	$0.778677\pi$
$480$	−10.5839	+	7.84713i	−0.483089	+	0.358171i
$481$	0.862460	−	1.49383i	0.0393248	−	0.0681126i
$482$	12.2533	−	4.29363i	0.558122	−	0.195569i
$483$	−13.8031	−	27.4448i	−0.628061	−	1.24878i
$484$	−11.6629	−	14.5986i	−0.530134	−	0.663575i
$485$	6.72417	−	1.80174i	0.305329	−	0.0818126i
$486$	2.78254	−	0.209746i	0.126218	−	0.00951429i
$487$	17.8451	−	10.3029i	0.808640	−	0.466868i	−0.0378436	−	0.999284i	$-0.512049\pi$
$487$	17.8451	−	10.3029i	0.808640	−	0.466868i	0.846483	+	0.532415i	$0.178716\pi$
$488$	17.8787	+	5.48916i	0.809331	+	0.248483i
$489$			30.5154i			1.37995i
$490$	−4.08159	+	6.45891i	−0.184387	+	0.291784i
$491$	1.13401	+	1.13401i	0.0511771	+	0.0511771i	0.732232	−	0.681055i	$-0.238479\pi$
$491$	1.13401	+	1.13401i	0.0511771	+	0.0511771i	−0.681055	+	0.732232i	$0.738479\pi$
$492$	−10.1790	+	13.8173i	−0.458903	+	0.622932i
$493$	−56.7587	−	15.2085i	−2.55628	−	0.684954i
$494$	−2.21497	+	2.57612i	−0.0996562	+	0.115905i
$495$	3.03396	−	5.25497i	0.136366	−	0.236193i
$496$	−4.32165	+	19.0883i	−0.194048	+	0.857090i
$497$	1.65766	−	5.01217i	0.0743560	−	0.224826i
$498$	9.55121	+	27.2575i	0.428000	+	1.22144i
$499$	8.63159	+	32.2136i	0.386403	+	1.44208i	0.835943	+	0.548816i	$0.184921\pi$
$499$	8.63159	+	32.2136i	0.386403	+	1.44208i	−0.449540	+	0.893260i	$0.648412\pi$
$500$	−13.3003	+	5.81671i	−0.594806	+	0.260131i
$501$	2.04307	−	7.62483i	0.0912775	−	0.340652i
$502$	15.0930	−	10.2999i	0.673633	−	0.459707i
$503$			20.7931i			0.927117i	0.886066	+	0.463558i	$0.153428\pi$
$503$			20.7931i			0.927117i	−0.886066	+	0.463558i	$0.846572\pi$
$504$	45.0568	−	7.64660i	2.00699	−	0.340607i
$505$		−	3.85105i		−	0.171370i
$506$	3.94855	+	5.78602i	0.175534	+	0.257220i
$507$	−8.83433	+	32.9702i	−0.392346	+	1.46426i
$508$	−32.4578	−	12.7060i	−1.44008	−	0.563736i
$509$	−10.3474	−	38.6171i	−0.458641	−	1.71167i	−0.677156	−	0.735839i	$-0.736788\pi$
$509$	−10.3474	−	38.6171i	−0.458641	−	1.71167i	0.218515	−	0.975834i	$-0.429879\pi$
$510$	24.5952	−	8.61831i	1.08909	−	0.381625i
$511$	20.0208	−	4.14595i	0.885666	−	0.183406i
$512$	22.4949	+	2.44492i	0.994145	+	0.108051i
$513$	−8.66534	+	15.0088i	−0.382584	+	0.662655i
$514$	−10.4125	−	8.95273i	−0.459274	−	0.394888i
$515$	8.73958	+	2.34176i	0.385112	+	0.103190i
$516$	−0.749514	−	4.94335i	−0.0329955	−	0.217619i
$517$	−5.20866	−	5.20866i	−0.229076	−	0.229076i
$518$	1.20043	−	4.81836i	0.0527437	−	0.211706i
$519$			30.8520i			1.35425i
$520$	1.32909	+	2.50679i	0.0582844	+	0.109930i
$521$	−16.0339	+	9.25715i	−0.702456	+	0.405563i	−0.808262	−	0.588824i	$-0.799591\pi$
$521$	−16.0339	+	9.25715i	−0.702456	+	0.405563i	0.105805	+	0.994387i	$0.466258\pi$
$522$	−4.82139	−	63.9615i	−0.211027	−	2.79952i
$523$	35.2333	−	9.44073i	1.54064	−	0.412814i	0.614170	−	0.789174i	$-0.289491\pi$
$523$	35.2333	−	9.44073i	1.54064	−	0.412814i	0.926474	+	0.376360i	$0.122824\pi$
$524$	2.33141	−	20.8558i	0.101848	−	0.911090i
$525$	35.1072	+	2.02453i	1.53220	+	0.0883576i
$526$	−4.99052	−	14.2421i	−0.217597	−	0.620985i
$527$	19.3561	−	33.5258i	0.843167	−	1.46041i
$528$	−14.8415	+	4.60645i	−0.645893	+	0.200470i
$529$	−4.09802	−	7.09799i	−0.178175	−	0.308608i
$530$	10.5651	+	1.99424i	0.458919	+	0.0866242i
$531$	39.9418	−	39.9418i	1.73333	−	1.73333i
$532$	−4.08362	+	8.88706i	−0.177047	+	0.385303i
$533$	2.61329	+	2.61329i	0.113194	+	0.113194i
$534$	−7.49040	+	5.11167i	−0.324141	+	0.221204i
$535$	−4.82429	+	2.78531i	−0.208572	+	0.120419i
$536$	−12.7525	+	11.8638i	−0.550825	+	0.512438i
$537$	−40.8366	−	23.5770i	−1.76223	−	1.01742i
$538$	4.64475	−	9.65574i	0.200250	−	0.416288i
$539$	−7.06235	+	5.59738i	−0.304197	+	0.241096i
$540$	9.03404	+	11.3080i	0.388763	+	0.486619i
$541$	0.613332	+	2.28899i	0.0263692	+	0.0984112i	0.977856	−	0.209277i	$-0.0671112\pi$
$541$	0.613332	+	2.28899i	0.0263692	+	0.0984112i	−0.951487	+	0.307689i	$0.900444\pi$
$542$	−12.0583	−	10.3678i	−0.517948	−	0.445336i
$543$	27.4572	+	47.5573i	1.17830	+	2.04088i
$544$	−41.0617	−	17.8082i	−1.76051	−	0.763522i
$545$	−8.71148			−0.373159
$546$	−0.258785	−	14.6738i	−0.0110750	−	0.627982i
$547$	−15.8419	+	15.8419i	−0.677351	+	0.677351i	−0.959400	−	0.282049i	$-0.908986\pi$
$547$	−15.8419	+	15.8419i	−0.677351	+	0.677351i	0.282049	+	0.959400i	$0.408986\pi$
$548$	11.9678	−	1.81456i	0.511239	−	0.0775143i
$549$	10.4515	−	39.0057i	0.446061	−	1.66472i
$550$	−7.99582	+	0.602722i	−0.340943	+	0.0257001i
$551$	11.8880	+	6.86355i	0.506446	+	0.292397i
$552$	−32.0085	+	7.34993i	−1.36237	+	0.312834i
$553$	18.3074	−	16.3111i	0.778511	−	0.693618i
$554$	−27.1161	−	13.0438i	−1.15205	−	0.554179i
$555$	2.98574	−	0.800026i	0.126737	−	0.0339592i
$556$	5.10345	+	11.6694i	0.216435	+	0.494892i
$557$	42.9377	+	11.5051i	1.81933	+	0.487488i	0.996706	−	0.0811008i	$-0.0258436\pi$
$557$	42.9377	+	11.5051i	1.81933	+	0.487488i	0.822622	+	0.568588i	$0.192510\pi$
$558$	41.5247	+	7.83809i	1.75788	+	0.331813i
$559$	−1.07670			−0.0455397
$560$	5.66810	+	5.88125i	0.239521	+	0.248528i
$561$	30.7380			1.29776
$562$	−27.9287	−	5.27175i	−1.17810	−	0.222375i
$563$	5.19184	+	1.39115i	0.218810	+	0.0586299i	0.366558	−	0.930395i	$-0.380536\pi$
$563$	5.19184	+	1.39115i	0.218810	+	0.0586299i	−0.147749	+	0.989025i	$0.547203\pi$
$564$	31.6414	−	13.8380i	1.33234	−	0.582684i
$565$	−6.82187	+	1.82791i	−0.286998	+	0.0769009i
$566$	−26.0728	−	12.5419i	−1.09592	−	0.527177i
$567$	−5.35165	−	25.8431i	−0.224748	−	1.08531i
$568$	−4.78257	−	2.99634i	−0.200672	−	0.125724i
$569$	4.37176	+	2.52404i	0.183274	+	0.105813i	0.588830	−	0.808257i	$-0.299589\pi$
$569$	4.37176	+	2.52404i	0.183274	+	0.105813i	−0.405556	+	0.914070i	$0.632922\pi$
$570$	−6.07097	+	0.457627i	−0.254285	+	0.0191679i
$571$	−9.72141	+	36.2808i	−0.406828	+	1.51830i	0.393830	+	0.919183i	$0.371150\pi$
$571$	−9.72141	+	36.2808i	−0.406828	+	1.51830i	−0.800658	+	0.599121i	$0.795517\pi$
$572$	0.501662	+	3.30866i	0.0209755	+	0.138342i
$573$	1.08614	−	1.08614i	0.0453742	−	0.0453742i
$574$	9.30618	+	5.15630i	0.388433	+	0.215220i
$575$	−16.9460			−0.706697
$576$	3.52317	−	48.7293i	0.146799	−	2.03039i
$577$	9.36395	+	16.2188i	0.389826	+	0.675199i	0.992426	−	0.122845i	$-0.0392016\pi$
$577$	9.36395	+	16.2188i	0.389826	+	0.675199i	−0.602599	+	0.798044i	$0.705868\pi$
$578$	48.8985	+	42.0434i	2.03391	+	1.74877i
$579$	−3.77124	−	14.0745i	−0.156727	−	0.584914i
$580$	8.95672	−	7.15558i	0.371908	−	0.297119i
$581$	15.9961	−	8.04504i	0.663629	−	0.333764i
$582$	−16.6867	+	34.6891i	−0.691686	+	1.43791i
$583$	10.9821	+	6.34050i	0.454831	+	0.262597i
$584$	0.788602	−	21.8430i	0.0326326	−	0.903868i
$585$	5.30553	−	3.06315i	0.219356	−	0.126646i
$586$	−17.2415	+	11.7661i	−0.712239	+	0.486053i
$587$	5.57210	+	5.57210i	0.229985	+	0.229985i	0.812686	−	0.582701i	$-0.198004\pi$
$587$	5.57210	+	5.57210i	0.229985	+	0.229985i	−0.582701	+	0.812686i	$0.698004\pi$
$588$	−12.3670	−	40.3985i	−0.510008	−	1.66601i
$589$	−6.39475	+	6.39475i	−0.263491	+	0.263491i
$590$	9.92043	+	1.87255i	0.408418	+	0.0770918i
$591$	6.45799	+	11.1856i	0.265646	+	0.460113i
$592$	−4.69765	−	2.47228i	−0.193072	−	0.101610i
$593$	−6.09225	+	10.5521i	−0.250179	+	0.433322i	−0.963575	−	0.267439i	$-0.913823\pi$
$593$	−6.09225	+	10.5521i	−0.250179	+	0.433322i	0.713396	+	0.700761i	$0.247156\pi$
$594$	5.64518	+	16.1104i	0.231624	+	0.661017i
$595$	−7.25925	−	14.4337i	−0.297600	−	0.591723i
$596$	30.1657	+	3.37213i	1.23563	+	0.138128i
$597$	−22.0813	+	5.91667i	−0.903728	+	0.242153i
$598$	0.531600	+	7.05231i	0.0217387	+	0.288391i
$599$	16.2977	−	9.40947i	0.665905	−	0.384461i	−0.128618	−	0.991694i	$-0.541054\pi$
$599$	16.2977	−	9.40947i	0.665905	−	0.384461i	0.794523	+	0.607234i	$0.207721\pi$
$600$	11.0337	−	35.9378i	0.450450	−	1.46716i
$601$		−	11.3877i		−	0.464514i	−0.972654	−	0.232257i	$-0.925389\pi$
$601$		−	11.3877i		−	0.464514i	0.972654	−	0.232257i	$-0.0746111\pi$
$602$	−2.97934	+	0.854896i	−0.121429	+	0.0348430i
$603$	26.5927	+	26.5927i	1.08294	+	1.08294i
$604$	29.4005	−	4.45772i	1.19629	−	0.181382i
$605$	−6.96504	−	1.86628i	−0.283169	−	0.0758750i
$606$	16.1470	+	13.8834i	0.655929	+	0.563973i
$607$	−16.9140	+	29.2959i	−0.686519	+	1.18909i	0.286438	+	0.958099i	$0.407529\pi$
$607$	−16.9140	+	29.2959i	−0.686519	+	1.18909i	−0.972957	+	0.230986i	$0.925805\pi$
$608$	8.18881	+	6.50111i	0.332100	+	0.263655i
$609$	−58.0660	+	12.0245i	−2.35295	+	0.487255i
$610$	6.81124	−	2.38670i	0.275779	−	0.0966346i
$611$	−1.92484	−	7.18361i	−0.0778708	−	0.290618i
$612$	−35.2272	+	89.9889i	−1.42398	+	3.63759i
$613$	−0.444885	+	1.66033i	−0.0179687	+	0.0670602i	−0.974328	−	0.225133i	$-0.927718\pi$
$613$	−0.444885	+	1.66033i	−0.0179687	+	0.0670602i	0.956359	+	0.292193i	$0.0943850\pi$
$614$	−5.32902	−	7.80890i	−0.215062	−	0.315142i
$615$			6.62280i			0.267057i
$616$	4.01521	+	8.75709i	0.161777	+	0.352833i
$617$		−	8.15102i		−	0.328148i	−0.986448	−	0.164074i	$-0.947536\pi$
$617$		−	8.15102i		−	0.328148i	0.986448	−	0.164074i	$-0.0524636\pi$
$618$	−41.3256	+	28.2018i	−1.66236	+	1.13444i
$619$	−8.73907	+	32.6147i	−0.351253	+	1.31089i	0.533882	+	0.845559i	$0.320733\pi$
$619$	−8.73907	+	32.6147i	−0.351253	+	1.31089i	−0.885135	+	0.465335i	$0.845934\pi$
$620$	3.02630	+	6.91983i	0.121539	+	0.277907i
$621$	9.33736	+	34.8475i	0.374695	+	1.39838i
$622$	2.60658	+	7.43874i	0.104514	+	0.298266i
$623$	3.73975	+	4.19746i	0.149830	+	0.168168i
$624$	−15.3022	−	3.46446i	−0.612576	−	0.138689i
$625$	8.20980	−	14.2198i	0.328392	−	0.568792i
$626$	10.9050	−	12.6830i	0.435850	−	0.506915i
$627$	−6.93601	−	1.85850i	−0.276997	−	0.0742212i
$628$	18.3142	+	13.4918i	0.730818	+	0.538381i
$629$	7.42477	+	7.42477i	0.296045	+	0.296045i
$630$	12.2488	−	12.6886i	0.488004	−	0.505526i
$631$			24.8235i			0.988206i	0.869403	+	0.494103i	$0.164504\pi$
$631$			24.8235i			0.988206i	−0.869403	+	0.494103i	$0.835496\pi$
$632$	−12.2787	−	23.1589i	−0.488422	−	0.921211i
$633$	24.4283	−	14.1037i	0.970938	−	0.560571i
$634$	−6.37786	+	0.480760i	−0.253297	+	0.0190934i
$635$	−12.9927	+	3.48139i	−0.515600	+	0.138155i
$636$	−46.4497	+	37.1089i	−1.84185	+	1.47146i
$637$	−9.00063	+	1.32896i	−0.356618	+	0.0526554i
$638$	12.7605	−	4.47137i	0.505194	−	0.177023i
$639$	−6.09283	+	10.5531i	−0.241029	+	0.417474i
$640$	7.54871	−	4.38912i	0.298389	−	0.173495i
$641$	−15.4186	−	26.7058i	−0.608998	−	1.05482i	−0.991406	−	0.130822i	$-0.958238\pi$
$641$	−15.4186	−	26.7058i	−0.608998	−	1.05482i	0.382408	−	0.923994i	$-0.375095\pi$
$642$	5.71349	−	30.2690i	0.225493	−	1.19462i
$643$	7.86848	−	7.86848i	0.310302	−	0.310302i	−0.534724	−	0.845027i	$-0.679584\pi$
$643$	7.86848	−	7.86848i	0.310302	−	0.310302i	0.845027	+	0.534724i	$0.179584\pi$
$644$	7.07049	+	19.0924i	0.278616	+	0.752345i
$645$	−1.36433	−	1.36433i	−0.0537204	−	0.0537204i
$646$	−11.6577	−	17.0826i	−0.458666	−	0.672107i
$647$	33.1866	−	19.1603i	1.30470	−	0.753268i	0.323492	−	0.946231i	$-0.395143\pi$
$647$	33.1866	−	19.1603i	1.30470	−	0.753268i	0.981206	+	0.192963i	$0.0618098\pi$
$648$	−28.1952	−	1.01794i	−1.10761	−	0.0399885i
$649$	10.3120	+	5.95361i	0.404780	+	0.233700i
$650$	−7.29546	−	3.50938i	−0.286152	−	0.137649i
$651$	2.24909	−	39.0013i	0.0881488	−	1.52858i
$652$	2.24675	−	20.0985i	0.0879894	−	0.787116i
$653$	−3.62018	−	13.5107i	−0.141669	−	0.528714i	−0.999881	−	0.0154198i	$-0.995092\pi$
$653$	−3.62018	−	13.5107i	−0.141669	−	0.528714i	0.858213	−	0.513294i	$-0.171575\pi$
$654$	31.4056	−	36.5262i	1.22805	−	1.42829i
$655$	−4.04922	−	7.01345i	−0.158216	−	0.274038i
$656$	7.72153	−	8.35109i	0.301475	−	0.326055i
$657$	−47.1935			−1.84119
$658$	−11.0300	−	18.3495i	−0.429993	−	0.715336i
$659$	−18.0981	+	18.0981i	−0.705003	+	0.705003i	−0.965480	−	0.260477i	$-0.916120\pi$
$659$	−18.0981	+	18.0981i	−0.705003	+	0.705003i	0.260477	+	0.965480i	$0.416120\pi$
$660$	−3.55685	+	4.82820i	−0.138450	+	0.187938i
$661$	7.80014	−	29.1105i	0.303390	−	1.13227i	−0.630932	−	0.775838i	$-0.717327\pi$
$661$	7.80014	−	29.1105i	0.303390	−	1.13227i	0.934322	−	0.356430i	$-0.116006\pi$
$662$	−2.44470	−	32.4319i	−0.0950160	−	1.26050i
$663$	26.8760	+	15.5169i	1.04378	+	0.602625i
$664$	−4.28387	−	18.6560i	−0.166246	−	0.723992i
$665$	0.765347	+	3.69586i	0.0296789	+	0.143319i
$666$	−4.96863	+	10.3290i	−0.192531	+	0.400242i
$667$	27.6016	−	7.39583i	1.06874	−	0.286368i
$668$	−1.90702	+	4.87155i	−0.0737850	+	0.188486i
$669$	−59.5763	−	15.9634i	−2.30335	−	0.617182i
$670$	−1.24672	+	6.60490i	−0.0481650	+	0.255169i
$671$	8.51239			0.328617
$672$	−45.0934	+	2.56332i	−1.73951	+	0.0988823i
$673$	−10.9832			−0.423371			−0.211686	−	0.977338i	$-0.567895\pi$
$673$	−10.9832			−0.423371			−0.211686	+	0.977338i	$0.567895\pi$
$674$	−4.35639	+	23.0793i	−0.167802	+	0.888983i
$675$	−39.8898	−	10.6884i	−1.53536	−	0.411398i
$676$	8.24607	−	21.0648i	0.317157	−	0.810185i
$677$	42.5236	−	11.3942i	1.63431	−	0.437913i	0.679153	−	0.733997i	$-0.262347\pi$
$677$	42.5236	−	11.3942i	1.63431	−	0.437913i	0.955162	+	0.296084i	$0.0956808\pi$
$678$	16.9291	−	35.1931i	0.650160	−	1.35158i
$679$	22.6567	+	7.49317i	0.869484	+	0.287561i
$680$	−16.8338	+	3.86545i	−0.645546	+	0.148233i
$681$	−30.8317	−	17.8007i	−1.18147	−	0.682125i
$682$	0.669576	+	8.88273i	0.0256394	+	0.340137i
$683$	−6.60660	+	24.6562i	−0.252794	+	0.943441i	0.716510	+	0.697577i	$0.245738\pi$
$683$	−6.60660	+	24.6562i	−0.252794	+	0.943441i	−0.969304	+	0.245864i	$0.920928\pi$
$684$	13.3899	−	18.1760i	0.511977	−	0.694976i
$685$	3.30302	−	3.30302i	0.126202	−	0.126202i
$686$	−23.8505	+	10.8238i	−0.910615	+	0.413256i
$687$	41.0309			1.56543
$688$	0.129692	+	3.31104i	0.00494448	+	0.126232i
$689$	6.40150	+	11.0877i	0.243878	+	0.422409i
$690$	−8.26263	+	9.60985i	−0.314553	+	0.365841i
$691$	11.6155	+	43.3496i	0.441875	+	1.64910i	0.724059	+	0.689738i	$0.242274\pi$
$691$	11.6155	+	43.3496i	0.441875	+	1.64910i	−0.282184	+	0.959360i	$0.591059\pi$
$692$	2.27153	−	20.3202i	0.0863507	−	0.772457i
$693$	18.5830	−	9.34608i	0.705908	−	0.355028i
$694$	19.7190	+	9.48555i	0.748523	+	0.360066i
$695$	4.25657	+	2.45753i	0.161461	+	0.0932195i
$696$	−2.28718	+	63.3510i	−0.0866952	+	2.40131i
$697$	−19.4833	+	11.2487i	−0.737983	+	0.426074i
$698$	−15.4522	−	22.6430i	−0.584876	−	0.857049i
$699$	−45.9855	−	45.9855i	−1.73933	−	1.73933i
$700$	−22.9737	−	3.91825i	−0.868325	−	0.148096i
$701$	−34.8486	+	34.8486i	−1.31621	+	1.31621i	−0.399466	+	0.916748i	$0.630804\pi$
$701$	−34.8486	+	34.8486i	−1.31621	+	1.31621i	−0.916748	+	0.399466i	$0.869196\pi$
$702$	−3.19678	+	16.9360i	−0.120655	+	0.639207i
$703$	−1.22647	−	2.12431i	−0.0462573	−	0.0801200i
$704$	10.1143	−	1.94123i	0.381196	−	0.0731630i
$705$	6.66358	−	11.5417i	0.250965	−	0.434684i
$706$	3.07054	−	1.07594i	0.115561	−	0.0404934i
$707$	7.24797	−	11.0338i	0.272588	−	0.414969i
$708$	−43.6154	+	34.8446i	−1.63917	+	1.30954i
$709$	33.8583	−	9.07232i	1.27158	−	0.340718i	0.440942	−	0.897536i	$-0.354644\pi$
$709$	33.8583	−	9.07232i	1.27158	−	0.340718i	0.830635	+	0.556818i	$0.187978\pi$
$710$	−2.17174	+	0.163705i	−0.0815041	+	0.00614374i
$711$	−49.0149	+	28.2988i	−1.83820	+	1.06129i
$712$	5.30979	−	2.81523i	0.198993	−	0.105505i
$713$			18.8257i			0.705027i
$714$	86.6890	+	21.5973i	3.24425	+	0.808260i
$715$	0.913167	+	0.913167i	0.0341505	+	0.0341505i
$716$	25.1605	+	18.5353i	0.940291	+	0.692696i
$717$	42.3033	+	11.3351i	1.57984	+	0.423318i
$718$	6.69200	−	7.78313i	0.249743	−	0.290464i
$719$	−19.3564	+	33.5263i	−0.721872	+	1.25032i	0.238377	+	0.971173i	$0.423385\pi$
$719$	−19.3564	+	33.5263i	−0.721872	+	1.25032i	−0.960249	+	0.279146i	$0.909949\pi$
$720$	−10.0588	−	15.9464i	−0.374868	−	0.594288i
$721$	20.6327	+	23.1580i	0.768403	+	0.862450i
$722$	−7.28802	−	20.7988i	−0.271232	−	0.774051i
$723$	7.17086	+	26.7620i	0.266687	+	0.995290i
$724$	−14.5828	−	33.3444i	−0.541964	−	1.23924i
$725$	−8.46597	+	31.5954i	−0.314418	+	1.17342i
$726$	32.9346	−	22.4756i	1.22232	−	0.834146i
$727$		−	11.1458i		−	0.413375i	−0.978407	−	0.206688i	$-0.933732\pi$
$727$		−	11.1458i		−	0.413375i	0.978407	−	0.206688i	$-0.0662684\pi$
$728$	−0.909942	+	9.68374i	−0.0337247	+	0.358903i
$729$		−	23.9706i		−	0.887798i
$730$	−4.75451	−	6.96703i	−0.175972	−	0.257861i
$731$	1.69637	−	6.33094i	0.0627425	−	0.234158i
$732$	−14.5479	+	37.1630i	−0.537706	+	1.37358i
$733$	2.45813	+	9.17387i	0.0907931	+	0.338845i	0.996348	−	0.0853844i	$-0.0272118\pi$
$733$	2.45813	+	9.17387i	0.0907931	+	0.338845i	−0.905555	+	0.424229i	$0.860545\pi$
$734$	−35.8768	+	12.5715i	−1.32424	+	0.464021i
$735$	−13.0890	−	9.72105i	−0.482795	−	0.358566i
$736$	21.6230	−	2.48424i	0.797035	−	0.0915701i
$737$	−3.96384	+	6.86557i	−0.146010	+	0.252896i
$738$	−18.6212	−	16.0107i	−0.685457	−	0.589362i
$739$	31.8880	+	8.54437i	1.17302	+	0.314310i	0.792154	−	0.610321i	$-0.208959\pi$
$739$	31.8880	+	8.54437i	1.17302	+	0.314310i	0.380865	+	0.924630i	$0.375626\pi$
$740$	−2.02541	+	0.307094i	−0.0744556	+	0.0112890i
$741$	−5.12636	−	5.12636i	−0.188321	−	0.188321i
$742$	26.5172	+	25.5981i	0.973477	+	0.939736i
$743$		−	46.1538i		−	1.69322i	−0.532214	−	0.846610i	$-0.678640\pi$
$743$		−	46.1538i		−	1.69322i	0.532214	−	0.846610i	$-0.321360\pi$
$744$	−39.9241	−	12.2576i	−1.46369	−	0.449385i
$745$	10.1442	−	5.85676i	0.371655	−	0.214575i
$746$	−0.142611	−	1.89191i	−0.00522137	−	0.0692677i
$747$	−39.9215	+	10.6969i	−1.46065	+	0.391380i
$748$	−20.2451	−	2.26314i	−0.740235	−	0.0827486i
$749$	−19.0644	−	1.09939i	−0.696599	−	0.0401708i
$750$	−10.2438	−	29.2342i	−0.374052	−	1.06748i
$751$	−8.69900	+	15.0671i	−0.317431	+	0.549807i	−0.979951	−	0.199237i	$-0.936154\pi$
$751$	−8.69900	+	15.0671i	−0.317431	+	0.549807i	0.662520	+	0.749044i	$0.269487\pi$
$752$	−21.8590	+	6.78451i	−0.797114	+	0.247405i
$753$	19.4959	+	33.7679i	0.710470	+	1.23057i
$754$	13.4144	+	2.53207i	0.488525	+	0.0922127i
$755$	8.11432	−	8.11432i	0.295310	−	0.295310i
$756$	4.60124	+	49.4018i	0.167346	+	1.79672i
$757$	3.24720	+	3.24720i	0.118021	+	0.118021i	0.763651	−	0.645629i	$-0.223405\pi$
$757$	3.24720	+	3.24720i	0.118021	+	0.118021i	−0.645629	+	0.763651i	$0.723405\pi$
$758$	−25.2910	+	17.2594i	−0.918612	+	0.626888i
$759$	−12.9452	+	7.47391i	−0.469881	+	0.271286i
$760$	4.03224	+	0.145577i	0.146265	+	0.00528063i
$761$	7.91882	+	4.57193i	0.287057	+	0.165732i	0.636614	−	0.771183i	$-0.280335\pi$
$761$	7.91882	+	4.57193i	0.287057	+	0.165732i	−0.349557	+	0.936915i	$0.613668\pi$
$762$	32.2427	−	67.0277i	1.16803	−	2.42816i
$763$	−24.9596	−	16.3957i	−0.903598	−	0.593562i
$764$	−0.795338	+	0.635400i	−0.0287743	+	0.0229880i
$765$	9.65212	+	36.0222i	0.348973	+	1.30239i
$766$	8.68372	+	7.46633i	0.313755	+	0.269770i
$767$	6.01089	+	10.4112i	0.217041	+	0.375925i
$768$	−8.81060	+	47.4740i	−0.317925	+	1.71307i
$769$	26.8105			0.966812			0.483406	−	0.875396i	$-0.339400\pi$
$769$	26.8105			0.966812			0.483406	+	0.875396i	$0.339400\pi$
$770$	3.25188	+	1.80178i	0.117189	+	0.0649315i
$771$	20.7203	−	20.7203i	0.746224	−	0.746224i
$772$	1.44761	+	9.54758i	0.0521006	+	0.343625i
$773$	1.37206	−	5.12058i	0.0493494	−	0.184175i	−0.936851	−	0.349727i	$-0.886274\pi$
$773$	1.37206	−	5.12058i	0.0493494	−	0.184175i	0.986201	+	0.165553i	$0.0529409\pi$
$774$	7.13435	−	0.537784i	0.256439	−	0.0193303i
$775$	−18.6626	−	10.7748i	−0.670379	−	0.387043i
$776$	13.5445	−	21.6188i	0.486218	−	0.776071i
$777$	10.0603	+	3.32719i	0.360910	+	0.119362i
$778$	23.6212	+	11.3627i	0.846862	+	0.407371i
$779$	5.07651	−	1.36025i	0.181885	−	0.0487359i
$780$	−5.54729	+	2.42604i	−0.198625	+	0.0868660i
$781$	−2.48119	−	0.664833i	−0.0887840	−	0.0237896i
$782$	−42.3047	−	7.98532i	−1.51281	−	0.285554i
$783$	69.6371			2.48863
$784$	5.17094	+	27.5184i	0.184676	+	0.982799i
$785$	8.77824			0.313309
$786$	44.0044	+	8.30614i	1.56958	+	0.296270i
$787$	−37.5883	−	10.0718i	−1.33988	−	0.359020i	−0.483490	−	0.875350i	$-0.660631\pi$
$787$	−37.5883	−	10.0718i	−1.33988	−	0.359020i	−0.856389	+	0.516331i	$0.827298\pi$
$788$	−3.42990	−	7.84268i	−0.122185	−	0.279384i
$789$	31.1057	−	8.33474i	1.10739	−	0.296725i
$790$	−9.11568	−	4.38497i	−0.324321	−	0.156010i
$791$	−22.9859	−	7.60204i	−0.817284	−	0.270297i
$792$	−4.97666	−	21.6730i	−0.176838	−	0.770117i
$793$	7.44287	+	4.29714i	0.264304	+	0.152596i
$794$	−23.7073	+	1.78704i	−0.841339	+	0.0634198i
$795$	−5.93809	+	22.1612i	−0.210602	+	0.785978i
$796$	14.9791	−	2.27115i	0.530921	−	0.0804986i
$797$	4.08133	−	4.08133i	0.144568	−	0.144568i	−0.631118	−	0.775686i	$-0.717404\pi$
$797$	4.08133	−	4.08133i	0.144568	−	0.144568i	0.775686	+	0.631118i	$0.217404\pi$
$798$	−18.2555	−	10.1149i	−0.646236	−	0.358062i
$799$	45.2718			1.60160
$800$	−9.91317	+	22.8575i	−0.350484	+	0.808135i
$801$	−6.48824	−	11.2380i	−0.229251	−	0.397074i
$802$	4.69225	+	4.03444i	0.165689	+	0.142461i
$803$	−2.57481	−	9.60933i	−0.0908631	−	0.339106i
$804$	−23.1991	−	29.0385i	−0.818168	−	1.02411i
$805$	6.56673	+	4.31361i	0.231447	+	0.152035i
$806$	−3.89864	+	8.10469i	−0.137324	+	0.285475i
$807$	19.8011	+	11.4322i	0.697031	+	0.402431i
$808$	−9.61280	−	10.3329i	−0.338177	−	0.363510i
$809$	−18.4321	+	10.6418i	−0.648037	+	0.374144i	−0.787704	−	0.616054i	$-0.788730\pi$
$809$	−18.4321	+	10.6418i	−0.648037	+	0.374144i	0.139667	+	0.990199i	$0.455397\pi$
$810$	−8.99316	+	6.13719i	−0.315987	+	0.215639i
$811$	12.6569	+	12.6569i	0.444442	+	0.444442i	0.893502	−	0.449060i	$-0.148241\pi$
$811$	12.6569	+	12.6569i	0.444442	+	0.444442i	−0.449060	+	0.893502i	$0.648241\pi$
$812$	39.1296	−	3.64450i	1.37318	−	0.127897i
$813$	23.9954	−	23.9954i	0.841556	−	0.841556i
$814$	−2.37424	−	0.448154i	−0.0832169	−	0.0157078i
$815$	−3.90218	−	6.75877i	−0.136687	−	0.236749i
$816$	44.4797	−	84.5173i	1.55710	−	2.95870i
$817$	−0.765569	+	1.32600i	−0.0267839	+	0.0463910i
$818$	0.0556787	+	0.158898i	0.00194676	+	0.00555573i
$819$	20.9661	+	1.20906i	0.732616	+	0.0422478i
$820$	0.487615	−	4.36200i	0.0170282	−	0.152328i
$821$	−49.6916	+	13.3148i	−1.73425	+	0.464691i	−0.981155	−	0.193222i	$-0.938106\pi$
$821$	−49.6916	+	13.3148i	−1.73425	+	0.464691i	−0.753094	+	0.657912i	$0.771440\pi$
$822$	1.94154	+	25.7569i	0.0677190	+	0.898374i
$823$	−21.8000	+	12.5862i	−0.759899	+	0.438728i	−0.829259	−	0.558864i	$-0.811237\pi$
$823$	−21.8000	+	12.5862i	−0.759899	+	0.438728i	0.0693606	+	0.997592i	$0.477904\pi$
$824$	29.2949	−	15.5320i	1.02054	−	0.541083i
$825$		−	17.1107i		−	0.595718i
$826$	24.8991	+	24.0361i	0.866352	+	0.836324i
$827$	−3.76090	−	3.76090i	−0.130779	−	0.130779i	0.638687	−	0.769466i	$-0.279478\pi$
$827$	−3.76090	−	3.76090i	−0.130779	−	0.130779i	−0.769466	+	0.638687i	$0.779478\pi$
$828$	−7.04489	−	46.4639i	−0.244827	−	1.61473i
$829$	4.47469	+	1.19899i	0.155412	+	0.0416426i	0.335686	−	0.941974i	$-0.391032\pi$
$829$	4.47469	+	1.19899i	0.155412	+	0.0416426i	−0.180274	+	0.983616i	$0.557698\pi$
$830$	−5.60105	−	4.81583i	−0.194415	−	0.167160i
$831$	32.1048	−	55.6072i	1.11370	−	1.92899i
$832$	9.82344	+	3.40846i	0.340566	+	0.118167i
$833$	6.36650	−	55.0170i	0.220586	−	1.90622i
$834$	−25.6494	+	8.98772i	−0.888167	+	0.311219i
$835$	0.522517	+	1.95006i	0.0180825	+	0.0674846i
$836$	4.43145	+	1.73475i	0.153265	+	0.0599974i
$837$	−11.8740	+	44.3144i	−0.410426	+	1.53173i
$838$	−24.2897	−	35.5930i	−0.839075	−	1.22954i
$839$		−	31.7342i		−	1.09559i	−0.836614	−	0.547793i	$-0.815468\pi$
$839$		−	31.7342i		−	1.09559i	0.836614	−	0.547793i	$-0.184532\pi$
$840$	−13.4236	+	11.1176i	−0.463160	+	0.383594i
$841$		−	26.1574i		−	0.901979i
$842$	−0.421115	+	0.287381i	−0.0145126	+	0.00990381i
$843$	15.6973	−	58.5830i	0.540642	−	2.01771i
$844$	−17.1277	+	7.49059i	−0.589561	+	0.257837i
$845$	−2.25939	−	8.43217i	−0.0777255	−	0.290075i
$846$	16.3422	+	46.6380i	0.561858	+	1.60345i
$847$	−16.4433	−	18.4559i	−0.565000	−	0.634151i
$848$	33.3255	−	21.0213i	1.14440	−	0.721873i
$849$	30.8695	−	53.4676i	1.05944	−	1.83500i
$850$	32.1291	−	37.3678i	1.10202	−	1.28170i
$851$	−4.93223	−	1.32159i	−0.169075	−	0.0453035i
$852$	7.14291	−	9.69605i	0.244712	−	0.332181i
$853$	25.3410	+	25.3410i	0.867661	+	0.867661i	0.992213	−	0.124552i	$-0.0397494\pi$
$853$	25.3410	+	25.3410i	0.867661	+	0.867661i	−0.124552	+	0.992213i	$0.539749\pi$
$854$	24.0071	+	5.98103i	0.821506	+	0.204667i
$855$		−	8.71197i		−	0.297943i
$856$	−5.99170	+	19.5155i	−0.204792	+	0.667027i
$857$	39.6000	−	22.8631i	1.35271	−	0.780987i	0.364082	−	0.931367i	$-0.381383\pi$
$857$	39.6000	−	22.8631i	1.35271	−	0.780987i	0.988628	+	0.150380i	$0.0480496\pi$
$858$	−7.12085	+	0.536766i	−0.243102	+	0.0183249i
$859$	35.5511	−	9.52588i	1.21299	−	0.325019i	0.405053	−	0.914293i	$-0.367253\pi$
$859$	35.5511	−	9.52588i	1.21299	−	0.325019i	0.807933	+	0.589274i	$0.200586\pi$
$860$	0.798142	+	0.999045i	0.0272164	+	0.0340671i
$861$	−12.4646	+	18.9752i	−0.424792	+	0.646674i
$862$	−32.4240	+	11.3616i	−1.10437	+	0.386977i
$863$	−2.15212	+	3.72758i	−0.0732590	+	0.126888i	−0.900328	−	0.435212i	$-0.856673\pi$
$863$	−2.15212	+	3.72758i	−0.0732590	+	0.126888i	0.827069	+	0.562101i	$0.190007\pi$
$864$	52.4660	+	7.79066i	1.78493	+	0.265044i
$865$	−3.94522	−	6.83333i	−0.134142	−	0.232340i
$866$	5.16219	−	27.3483i	0.175418	−	0.929333i
$867$	−97.3057	+	97.3057i	−3.30468	+	3.30468i
$868$	−4.35287	+	25.5220i	−0.147746	+	0.866273i
$869$	−8.43627	−	8.43627i	−0.286181	−	0.286181i
$870$	13.7895	+	20.2064i	0.467506	+	0.685062i
$871$	−6.93162	+	4.00197i	−0.234869	+	0.135602i
$872$	−23.3741	+	21.7451i	−0.791546	+	0.736383i
$873$	−47.7035	−	27.5416i	−1.61452	−	0.932143i
$874$	9.06320	+	4.35973i	0.306567	+	0.147470i
$875$	−17.1561	+	8.62844i	−0.579980	+	0.291694i
$876$	46.3524	+	5.18159i	1.56610	+	0.175070i
$877$	−14.7923	−	55.2056i	−0.499500	−	1.86416i	−0.503203	−	0.864168i	$-0.667845\pi$
$877$	−14.7923	−	55.2056i	−0.499500	−	1.86416i	0.00370287	−	0.999993i	$-0.498821\pi$
$878$	−28.0959	+	32.6770i	−0.948192	+	1.10279i
$879$	−22.2712	−	38.5748i	−0.751188	−	1.30110i
$880$	2.69815	−	2.91814i	0.0909546	−	0.0983704i
$881$	−46.7407			−1.57474			−0.787368	−	0.616484i	$-0.788557\pi$
$881$	−46.7407			−1.57474			−0.787368	+	0.616484i	$0.788557\pi$
$882$	58.9754	−	13.3014i	1.98581	−	0.447882i
$883$	−1.66705	+	1.66705i	−0.0561007	+	0.0561007i	−0.734601	−	0.678500i	$-0.762630\pi$
$883$	−1.66705	+	1.66705i	−0.0561007	+	0.0561007i	0.678500	+	0.734601i	$0.262630\pi$
$884$	−16.5590	−	12.1987i	−0.556939	−	0.410288i
$885$	−5.57575	+	20.8090i	−0.187427	+	0.699486i
$886$	−0.415471	−	5.51172i	−0.0139580	−	0.185170i
$887$	−14.2716	−	8.23972i	−0.479194	−	0.276663i	0.240887	−	0.970553i	$-0.422562\pi$
$887$	−14.2716	−	8.23972i	−0.479194	−	0.276663i	−0.720081	+	0.693890i	$0.755895\pi$
$888$	6.01416	−	9.59942i	0.201822	−	0.322135i
$889$	−43.7782	−	14.4786i	−1.46827	−	0.485597i
$890$	1.00537	−	2.09001i	0.0337001	−	0.0700573i
$891$	−12.4039	+	3.32361i	−0.415545	+	0.111345i
$892$	38.0637	+	14.9005i	1.27447	+	0.498905i
$893$	−10.2155	−	2.73725i	−0.341850	−	0.0915984i
$894$	−12.0139	+	63.6476i	−0.401806	+	2.12869i
$895$	12.0597			0.403112
$896$	29.8887	+	1.63179i	0.998513	+	0.0545141i
$897$	−15.0916			−0.503895
$898$	9.97332	−	52.8368i	0.332814	−	1.76319i
$899$	35.1000	+	9.40503i	1.17065	+	0.313675i
$900$	50.0934	+	19.6097i	1.66978	+	0.653655i
$901$	−75.2808	+	20.1714i	−2.50797	+	0.672008i
$902$	2.24408	−	4.66510i	0.0747197	−	0.155331i
$903$	−1.34122	−	6.47676i	−0.0446331	−	0.215533i
$904$	−13.7413	+	21.9329i	−0.457028	+	0.729479i
$905$	−12.1628	−	7.02222i	−0.404307	−	0.233426i
$906$	4.76966	+	63.2752i	0.158461	+	2.10218i
$907$	−1.14578	+	4.27611i	−0.0380450	+	0.141986i	−0.982336	−	0.187126i	$-0.940083\pi$
$907$	−1.14578	+	4.27611i	−0.0380450	+	0.141986i	0.944291	+	0.329112i	$0.106749\pi$
$908$	18.9962	+	13.9942i	0.630412	+	0.464414i
$909$	−21.5471	+	21.5471i	−0.714673	+	0.714673i
$910$	1.93375	+	3.21698i	0.0641031	+	0.106642i
$911$	−2.42550			−0.0803605			−0.0401802	−	0.999192i	$-0.512793\pi$
$911$	−2.42550			−0.0803605			−0.0401802	+	0.999192i	$0.512793\pi$
$912$	−15.1469	+	16.3819i	−0.501565	+	0.542459i
$913$	−4.35613	−	7.54503i	−0.144167	−	0.249704i
$914$	−16.0594	+	18.6779i	−0.531198	+	0.617809i
$915$	3.98607	+	14.8762i	0.131775	+	0.491792i
$916$	−27.0243	−	3.02097i	−0.892909	−	0.0998157i
$917$	1.59827	−	27.7154i	0.0527795	−	0.915245i
$918$	−94.5458	−	45.4799i	−3.12048	−	1.50106i
$919$	35.0592	+	20.2414i	1.15650	+	0.667703i	0.950462	−	0.310842i	$-0.100611\pi$
$919$	35.0592	+	20.2414i	1.15650	+	0.667703i	0.206034	+	0.978545i	$0.433944\pi$
$920$	6.14959	−	5.72103i	0.202746	−	0.188617i
$921$	17.4710	−	10.0869i	0.575690	−	0.332375i
$922$	30.9111	+	45.2956i	1.01800	+	1.49173i
$923$	−1.83383	−	1.83383i	−0.0603613	−	0.0603613i
$924$	−19.2779	+	7.13920i	−0.634197	+	0.234863i
$925$	4.13309	−	4.13309i	0.135895	−	0.135895i
$926$	−10.6495	+	56.4191i	−0.349965	+	1.85405i
$927$	−35.7966	−	62.0015i	−1.17571	−	2.03640i
$928$	6.17074	−	41.5567i	0.202564	−	1.36417i
$929$	−13.6726	+	23.6816i	−0.448583	+	0.776969i	−0.998294	−	0.0583859i	$-0.981405\pi$
$929$	−13.6726	+	23.6816i	−0.448583	+	0.776969i	0.549711	+	0.835355i	$0.314738\pi$
$930$	−15.2099	+	5.32963i	−0.498751	+	0.174765i
$931$	−4.76306	+	12.0296i	−0.156103	+	0.394254i
$932$	26.9019	+	33.6734i	0.881200	+	1.10301i
$933$	−16.2467	+	4.35329i	−0.531893	+	0.142520i
$934$	−12.9839	+	0.978722i	−0.424847	+	0.0320248i
$935$	−6.80808	+	3.93065i	−0.222648	+	0.128546i
$936$	6.58938	−	21.4622i	0.215381	−	0.701515i
$937$			6.30987i			0.206135i	0.994674	+	0.103067i	$0.0328657\pi$
$937$			6.30987i			0.206135i	−0.994674	+	0.103067i	$0.967134\pi$
$938$	−16.0029	+	16.5775i	−0.522515	+	0.541275i
$939$	25.2386	+	25.2386i	0.823630	+	0.823630i
$940$	−5.23863	+	7.11111i	−0.170865	+	0.231939i
$941$	26.3055	+	7.04854i	0.857535	+	0.229776i	0.660690	−	0.750659i	$-0.270264\pi$
$941$	26.3055	+	7.04854i	0.857535	+	0.229776i	0.196845	+	0.980435i	$0.436930\pi$
$942$	−31.6462	+	36.8062i	−1.03109	+	1.19921i
$943$	5.47021	−	9.47467i	0.178134	−	0.308538i
$944$	31.2920	−	19.7386i	1.01847	−	0.642435i
$945$	12.7369	+	14.2958i	0.414332	+	0.465042i
$946$	0.498742	+	1.42333i	0.0162155	+	0.0462763i
$947$	−5.93030	−	22.1322i	−0.192709	−	0.719200i	−0.992848	−	0.119385i	$-0.961908\pi$
$947$	−5.93030	−	22.1322i	−0.192709	−	0.719200i	0.800139	−	0.599815i	$-0.204759\pi$
$948$	51.2484	−	22.4128i	1.66447	−	0.727935i
$949$	2.59958	−	9.70178i	0.0843860	−	0.314933i
$950$	−9.50925	+	6.48939i	−0.308521	+	0.210544i
$951$		−	13.6483i		−	0.442577i
$952$	−55.5062	−	20.6074i	−1.79896	−	0.667889i
$953$			33.9914i			1.10109i	0.834806	+	0.550545i	$0.185580\pi$
$953$			33.9914i			1.10109i	−0.834806	+	0.550545i	$0.814420\pi$
$954$	−47.9551	−	70.2711i	−1.55260	−	2.27511i
$955$	−0.101675	+	0.379457i	−0.00329014	+	0.0122790i
$956$	−27.0278	−	10.5803i	−0.874141	−	0.342193i
$957$	7.46771	+	27.8699i	0.241397	+	0.900905i
$958$	9.98197	−	3.49775i	0.322503	−	0.113007i
$959$	15.6802	−	3.24708i	0.506339	−	0.104854i
$960$	8.12866	+	16.7666i	0.262351	+	0.541140i
$961$	3.53001	−	6.11416i	0.113871	−	0.197231i
$962$	−1.84970	−	1.59039i	−0.0596366	−	0.0512761i
$963$	42.5767	+	11.4084i	1.37201	+	0.367630i
$964$	−2.75257	−	18.1543i	−0.0886544	−	0.584712i
$965$	2.63506	+	2.63506i	0.0848257	+	0.0848257i
$966$	−41.7601	+	11.9827i	−1.34361	+	0.385536i
$967$			50.2769i			1.61680i	0.588635	+	0.808399i	$0.299665\pi$
$967$			50.2769i			1.61680i	−0.588635	+	0.808399i	$0.700335\pi$
$968$	−23.3467	+	12.3783i	−0.750390	+	0.397854i
$969$	38.2194	−	22.0660i	1.22778	−	0.708861i
$970$	−0.740002	−	9.81702i	−0.0237600	−	0.315205i
$971$	−30.0778	+	8.05932i	−0.965243	+	0.258636i	−0.706818	−	0.707395i	$-0.749870\pi$
$971$	−30.0778	+	8.05932i	−0.965243	+	0.258636i	−0.258425	+	0.966031i	$0.583203\pi$
$972$	0.438411	−	3.92184i	0.0140620	−	0.125793i
$973$	7.57040	+	15.0524i	0.242696	+	0.482556i
$974$	−9.63668	−	27.5015i	−0.308779	−	0.881203i
$975$	8.63766	−	14.9609i	0.276626	−	0.479131i
$976$	12.3179	−	23.4057i	0.394287	−	0.749198i
$977$	22.6866	+	39.2943i	0.725808	+	1.25714i	0.958640	+	0.284620i	$0.0918674\pi$
$977$	22.6866	+	39.2943i	0.725808	+	1.25714i	−0.232832	+	0.972517i	$0.574799\pi$
$978$	42.4064	+	8.00451i	1.35601	+	0.255956i
$979$	1.93424	−	1.93424i	0.0618185	−	0.0618185i
$980$	7.90513	+	7.36632i	0.252520	+	0.235308i
$981$	48.7418	+	48.7418i	1.55621	+	1.55621i
$982$	1.87337	−	1.27844i	0.0597815	−	0.0407967i
$983$	−39.3690	+	22.7297i	−1.25568	+	0.724966i	−0.972231	−	0.234022i	$-0.924811\pi$
$983$	−39.3690	+	22.7297i	−1.25568	+	0.724966i	−0.283446	+	0.958988i	$0.591478\pi$
$984$	16.5315	+	17.7699i	0.527004	+	0.566483i
$985$	−2.86073	−	1.65164i	−0.0911504	−	0.0526257i
$986$	−36.0232	+	74.8868i	−1.14721	+	2.38488i
$987$	40.8143	−	20.5271i	1.29913	−	0.653385i
$988$	2.99896	+	3.75383i	0.0954095	+	0.119425i
$989$	0.824941	+	3.07872i	0.0262316	+	0.0978976i
$990$	−6.50685	−	5.59465i	−0.206801	−	0.177810i
$991$	−12.9817	−	22.4850i	−0.412379	−	0.714261i	0.582771	−	0.812637i	$-0.301969\pi$
$991$	−12.9817	−	22.4850i	−0.412379	−	0.714261i	−0.995149	+	0.0983759i	$0.968635\pi$
$992$	25.3929	+	11.0128i	0.806225	+	0.349655i
$993$	69.4027			2.20243
$994$	−6.53045	−	3.61835i	−0.207133	−	0.114767i
$995$	4.13413	−	4.13413i	0.131061	−	0.131061i
$996$	40.3845	−	6.12312i	1.27963	−	0.194018i
$997$	−11.7799	+	43.9631i	−0.373073	+	1.39233i	0.483068	+	0.875583i	$0.339522\pi$
$997$	−11.7799	+	43.9631i	−0.373073	+	1.39233i	−0.856141	+	0.516743i	$0.827144\pi$
$998$	47.0305	−	3.54514i	1.48872	−	0.112219i
$999$	−10.7766	−	6.22186i	−0.340956	−	0.196851i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.2.w.c.37.8	✓	48
4.3	odd	2		448.2.ba.c.177.1		48
7.2	even	3		784.2.m.j.197.2		24
7.3	odd	6		784.2.x.o.165.11		48
7.4	even	3	inner	112.2.w.c.53.11	yes	48
7.5	odd	6		784.2.m.k.197.2		24
7.6	odd	2		784.2.x.o.373.8		48
8.3	odd	2		896.2.ba.e.737.12		48
8.5	even	2		896.2.ba.f.737.1		48
16.3	odd	4		448.2.ba.c.401.12		48
16.5	even	4		896.2.ba.f.289.12		48
16.11	odd	4		896.2.ba.e.289.1		48
16.13	even	4	inner	112.2.w.c.93.11	yes	48
28.11	odd	6		448.2.ba.c.305.12		48
56.11	odd	6		896.2.ba.e.865.1		48
56.53	even	6		896.2.ba.f.865.12		48
112.11	odd	12		896.2.ba.e.417.12		48
112.13	odd	4		784.2.x.o.765.11		48
112.45	odd	12		784.2.x.o.557.8		48
112.53	even	12		896.2.ba.f.417.1		48
112.61	odd	12		784.2.m.k.589.2		24
112.67	odd	12		448.2.ba.c.81.1		48
112.93	even	12		784.2.m.j.589.2		24
112.109	even	12	inner	112.2.w.c.109.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.8	✓	48	1.1	even	1	trivial
112.2.w.c.53.11	yes	48	7.4	even	3	inner
112.2.w.c.93.11	yes	48	16.13	even	4	inner
112.2.w.c.109.8	yes	48	112.109	even	12	inner
448.2.ba.c.81.1		48	112.67	odd	12
448.2.ba.c.177.1		48	4.3	odd	2
448.2.ba.c.305.12		48	28.11	odd	6
448.2.ba.c.401.12		48	16.3	odd	4
784.2.m.j.197.2		24	7.2	even	3
784.2.m.j.589.2		24	112.93	even	12
784.2.m.k.197.2		24	7.5	odd	6
784.2.m.k.589.2		24	112.61	odd	12
784.2.x.o.165.11		48	7.3	odd	6
784.2.x.o.373.8		48	7.6	odd	2
784.2.x.o.557.8		48	112.45	odd	12
784.2.x.o.765.11		48	112.13	odd	4
896.2.ba.e.289.1		48	16.11	odd	4
896.2.ba.e.417.12		48	112.11	odd	12
896.2.ba.e.737.12		48	8.3	odd	2
896.2.ba.e.865.1		48	56.11	odd	6
896.2.ba.f.289.12		48	16.5	even	4
896.2.ba.f.417.1		48	112.53	even	12
896.2.ba.f.737.1		48	8.5	even	2
896.2.ba.f.865.12		48	56.53	even	6

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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.262311 - 1.38967i) q^{2} +(2.91496 + 0.781062i) q^{3} +(-1.86239 - 0.729053i) q^{4} +(-0.745506 + 0.199758i) q^{5} +(1.85005 - 3.84597i) q^{6} +(-2.51194 - 0.830765i) q^{7} +(-1.50167 + 2.39687i) q^{8} +(5.28887 + 3.05353i) q^{9} +O(q^{10})\)	\(q+(0.262311 - 1.38967i) q^{2} +(2.91496 + 0.781062i) q^{3} +(-1.86239 - 0.729053i) q^{4} +(-0.745506 + 0.199758i) q^{5} +(1.85005 - 3.84597i) q^{6} +(-2.51194 - 0.830765i) q^{7} +(-1.50167 + 2.39687i) q^{8} +(5.28887 + 3.05353i) q^{9} +(0.0820438 + 1.08841i) q^{10} +(-0.333193 + 1.24349i) q^{11} +(-4.85935 - 3.57980i) q^{12} +(-0.919058 + 0.919058i) q^{13} +(-1.81340 + 3.27286i) q^{14} -2.32914 q^{15} +(2.93696 + 2.71556i) q^{16} +(-3.95601 - 6.85200i) q^{17} +(5.63074 - 6.54883i) q^{18} +(0.478380 + 1.78534i) q^{19} +(1.53405 + 0.171487i) q^{20} +(-6.67332 - 4.38363i) q^{21} +(1.64065 + 0.789212i) q^{22} +(3.33211 + 1.92380i) q^{23} +(-6.24941 + 5.81389i) q^{24} +(-3.81425 + 2.20216i) q^{25} +(1.03611 + 1.51827i) q^{26} +(6.63016 + 6.63016i) q^{27} +(4.07253 + 3.37854i) q^{28} +(5.25154 - 5.25154i) q^{29} +(-0.610960 + 3.23675i) q^{30} +(2.44642 + 4.23733i) q^{31} +(4.54413 - 3.36910i) q^{32} +(-1.94249 + 3.36449i) q^{33} +(-10.5598 + 3.70020i) q^{34} +(2.03862 + 0.117561i) q^{35} +(-7.62373 - 9.54272i) q^{36} +(-1.28190 + 0.343485i) q^{37} +(2.60652 - 0.196478i) q^{38} +(-3.39686 + 1.96118i) q^{39} +(0.640710 - 2.08685i) q^{40} -2.84345i q^{41} +(-7.84229 + 8.12387i) q^{42} +(0.585764 + 0.585764i) q^{43} +(1.52711 - 2.07295i) q^{44} +(-4.55285 - 1.21993i) q^{45} +(3.54750 - 4.12591i) q^{46} +(-2.86095 + 4.95532i) q^{47} +(6.44012 + 10.2097i) q^{48} +(5.61966 + 4.17366i) q^{49} +(2.05976 + 5.87821i) q^{50} +(-6.17977 - 23.0632i) q^{51} +(2.38168 - 1.04160i) q^{52} +(2.54947 - 9.51475i) q^{53} +(10.9529 - 7.47460i) q^{54} -0.993590i q^{55} +(5.76334 - 4.77325i) q^{56} +5.57784i q^{57} +(-5.92039 - 8.67547i) q^{58} +(2.39390 - 8.93417i) q^{59} +(4.33777 + 1.69807i) q^{60} +(-1.71139 - 6.38698i) q^{61} +(6.53023 - 2.28823i) q^{62} +(-10.7485 - 12.0641i) q^{63} +(-3.48998 - 7.19862i) q^{64} +(0.501575 - 0.868753i) q^{65} +(4.16601 + 3.58197i) q^{66} +(5.94825 + 1.59383i) q^{67} +(2.37214 + 15.6452i) q^{68} +(8.21037 + 8.21037i) q^{69} +(0.698123 - 2.80217i) q^{70} +1.99534i q^{71} +(-15.2611 + 8.09134i) q^{72} +(-6.69237 + 3.86384i) q^{73} +(0.141075 + 1.87153i) q^{74} +(-12.8384 + 3.44004i) q^{75} +(0.410678 - 3.67375i) q^{76} +(1.87001 - 2.84677i) q^{77} +(1.83437 + 5.23497i) q^{78} +(-4.63378 + 8.02594i) q^{79} +(-2.73198 - 1.43778i) q^{80} +(4.98751 + 8.63862i) q^{81} +(-3.95146 - 0.745866i) q^{82} +(-4.78537 + 4.78537i) q^{83} +(9.23241 + 13.0292i) q^{84} +(4.31797 + 4.31797i) q^{85} +(0.967673 - 0.660369i) q^{86} +(19.4098 - 11.2063i) q^{87} +(-2.48015 - 2.66594i) q^{88} +(-1.84016 - 1.06242i) q^{89} +(-2.88957 + 6.00698i) q^{90} +(3.07214 - 1.54510i) q^{91} +(-4.80313 - 6.01213i) q^{92} +(3.82162 + 14.2625i) q^{93} +(6.13582 + 5.27563i) q^{94} +(-0.713270 - 1.23542i) q^{95} +(15.8775 - 6.27155i) q^{96} -9.01961 q^{97} +(7.27412 - 6.71470i) q^{98} +(-5.55926 + 5.55926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8}+O(q^{10}) \) 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8	\( 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 24 q^{13} - 34 q^{14} - 40 q^{15} + 16 q^{16} + 8 q^{17} + 18 q^{18} - 4 q^{19} - 16 q^{20} - 8 q^{21} + 18 q^{24} - 10 q^{26} - 24 q^{27} - 10 q^{28} + 24 q^{29} - 4 q^{30} + 28 q^{31} + 16 q^{32} + 16 q^{33} - 44 q^{34} + 28 q^{35} - 72 q^{36} - 24 q^{37} + 20 q^{38} + 26 q^{40} + 6 q^{42} - 40 q^{43} + 6 q^{44} - 28 q^{45} - 14 q^{46} - 20 q^{47} + 56 q^{48} + 56 q^{50} + 24 q^{51} - 16 q^{52} - 16 q^{53} + 64 q^{54} + 40 q^{56} - 6 q^{58} - 20 q^{59} + 46 q^{60} + 8 q^{61} + 24 q^{62} - 16 q^{63} + 80 q^{64} + 8 q^{65} - 20 q^{66} + 48 q^{67} - 40 q^{69} + 82 q^{70} - 32 q^{72} - 8 q^{74} - 4 q^{75} - 36 q^{76} - 20 q^{77} + 116 q^{78} - 36 q^{79} - 28 q^{80} + 2 q^{82} - 8 q^{83} + 28 q^{84} - 20 q^{86} - 42 q^{88} - 20 q^{90} + 64 q^{91} + 76 q^{92} + 8 q^{93} - 72 q^{94} - 4 q^{95} - 120 q^{96} - 48 q^{97} - 2 q^{98} - 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 24 * q^13 - 34 * q^14 - 40 * q^15 + 16 * q^16 + 8 * q^17 + 18 * q^18 - 4 * q^19 - 16 * q^20 - 8 * q^21 + 18 * q^24 - 10 * q^26 - 24 * q^27 - 10 * q^28 + 24 * q^29 - 4 * q^30 + 28 * q^31 + 16 * q^32 + 16 * q^33 - 44 * q^34 + 28 * q^35 - 72 * q^36 - 24 * q^37 + 20 * q^38 + 26 * q^40 + 6 * q^42 - 40 * q^43 + 6 * q^44 - 28 * q^45 - 14 * q^46 - 20 * q^47 + 56 * q^48 + 56 * q^50 + 24 * q^51 - 16 * q^52 - 16 * q^53 + 64 * q^54 + 40 * q^56 - 6 * q^58 - 20 * q^59 + 46 * q^60 + 8 * q^61 + 24 * q^62 - 16 * q^63 + 80 * q^64 + 8 * q^65 - 20 * q^66 + 48 * q^67 - 40 * q^69 + 82 * q^70 - 32 * q^72 - 8 * q^74 - 4 * q^75 - 36 * q^76 - 20 * q^77 + 116 * q^78 - 36 * q^79 - 28 * q^80 + 2 * q^82 - 8 * q^83 + 28 * q^84 - 20 * q^86 - 42 * q^88 - 20 * q^90 + 64 * q^91 + 76 * q^92 + 8 * q^93 - 72 * q^94 - 4 * q^95 - 120 * q^96 - 48 * q^97 - 2 * q^98 - 24 * q^99

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