LMFDB - Embedded newform 672.2.ch.a.11.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(11,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 12, 16]))

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

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

chi := DirichletCharacter("672.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.ch (of order $24$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$124$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.13
Character	$\chi$	$=$	672.11
Dual form			672.2.ch.a.611.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33331 + 0.471485i) q^{2} +(1.63784 + 0.563452i) q^{3} +(1.55540 - 1.25727i) q^{4} +(0.441991 + 3.35725i) q^{5} +(-2.44940 + 0.0209633i) q^{6} +(1.71134 + 2.01775i) q^{7} +(-1.48105 + 2.40967i) q^{8} +(2.36504 + 1.84569i) q^{9} +O(q^{10})$	\(q+(-1.33331 + 0.471485i) q^{2} +(1.63784 + 0.563452i) q^{3} +(1.55540 - 1.25727i) q^{4} +(0.441991 + 3.35725i) q^{5} +(-2.44940 + 0.0209633i) q^{6} +(1.71134 + 2.01775i) q^{7} +(-1.48105 + 2.40967i) q^{8} +(2.36504 + 1.84569i) q^{9} +(-2.17220 - 4.26785i) q^{10} +(3.37681 - 2.59112i) q^{11} +(3.25591 - 1.18280i) q^{12} +(1.65768 + 4.00200i) q^{13} +(-3.23308 - 1.88340i) q^{14} +(-1.16774 + 5.74769i) q^{15} +(0.838568 - 3.91111i) q^{16} +(2.36540 - 4.09699i) q^{17} +(-4.02354 - 1.34578i) q^{18} +(-5.29954 - 4.06648i) q^{19} +(4.90843 + 4.66619i) q^{20} +(1.66600 + 4.26901i) q^{21} +(-3.28065 + 5.04687i) q^{22} +(-0.715456 - 0.191706i) q^{23} +(-3.78345 + 3.11215i) q^{24} +(-6.24617 + 1.67366i) q^{25} +(-4.09708 - 4.55431i) q^{26} +(2.83361 + 4.35553i) q^{27} +(5.19867 + 0.986804i) q^{28} +(-1.11873 - 2.70084i) q^{29} +(-1.15299 - 8.21399i) q^{30} +(-7.15425 - 4.13051i) q^{31} +(0.725963 + 5.61008i) q^{32} +(6.99065 - 2.34117i) q^{33} +(-1.22213 + 6.57779i) q^{34} +(-6.01770 + 6.63724i) q^{35} +(5.99912 - 0.102695i) q^{36} +(-0.298809 + 0.0393389i) q^{37} +(8.98318 + 2.92321i) q^{38} +(0.460086 + 7.48866i) q^{39} +(-8.74448 - 3.90720i) q^{40} +(-1.05507 - 1.05507i) q^{41} +(-4.23406 - 4.90640i) q^{42} +(3.14924 - 7.60294i) q^{43} +(1.99458 - 8.27579i) q^{44} +(-5.15112 + 8.75583i) q^{45} +(1.04431 - 0.0817241i) q^{46} +(4.36881 - 2.52234i) q^{47} +(3.57716 - 5.93329i) q^{48} +(-1.14262 + 6.90612i) q^{49} +(7.53895 - 5.17647i) q^{50} +(6.18261 - 5.37743i) q^{51} +(7.60994 + 4.14058i) q^{52} +(-3.29150 - 4.28957i) q^{53} +(-5.83163 - 4.47125i) q^{54} +(10.1916 + 10.1916i) q^{55} +(-7.39668 + 1.13538i) q^{56} +(-6.38853 - 9.64628i) q^{57} +(2.76501 + 3.07359i) q^{58} +(1.67628 + 2.18457i) q^{59} +(5.41006 + 10.4081i) q^{60} +(7.59569 + 5.82838i) q^{61} +(11.4863 + 2.13411i) q^{62} +(0.323263 + 7.93067i) q^{63} +(-3.61299 - 7.13767i) q^{64} +(-12.7031 + 7.33411i) q^{65} +(-8.21684 + 6.41747i) q^{66} +(-4.40518 - 0.579954i) q^{67} +(-1.47185 - 9.34642i) q^{68} +(-1.06379 - 0.717109i) q^{69} +(4.89407 - 11.6867i) q^{70} +(-9.29859 - 9.29859i) q^{71} +(-7.95024 + 2.96542i) q^{72} +(-0.360091 - 1.34388i) q^{73} +(0.379856 - 0.193335i) q^{74} +(-11.1733 - 0.778234i) q^{75} +(-13.3556 + 0.337906i) q^{76} +(11.0071 + 2.37927i) q^{77} +(-4.14422 - 9.76775i) q^{78} +(3.78072 + 6.54839i) q^{79} +(13.5012 + 1.08661i) q^{80} +(2.18687 + 8.73027i) q^{81} +(1.90417 + 0.909277i) q^{82} +(6.96153 + 16.8066i) q^{83} +(7.95858 + 4.54543i) q^{84} +(14.8001 + 6.13042i) q^{85} +(-0.614231 + 11.6219i) q^{86} +(-0.310500 - 5.05390i) q^{87} +(1.24251 + 11.9746i) q^{88} +(-10.8012 - 2.89418i) q^{89} +(2.73977 - 14.1029i) q^{90} +(-5.23817 + 10.1936i) q^{91} +(-1.35385 + 0.601338i) q^{92} +(-9.39017 - 10.7962i) q^{93} +(-4.63572 + 5.42287i) q^{94} +(11.3099 - 19.5892i) q^{95} +(-1.97200 + 9.59746i) q^{96} -16.8335 q^{97} +(-1.73267 - 9.74668i) q^{98} +(12.7687 + 0.104434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9}+O(q^{10}) $ 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9	$ 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9} - 8 q^{10} - 4 q^{12} - 32 q^{13} - 32 q^{15} + 24 q^{16} - 4 q^{18} - 8 q^{19} - 8 q^{21} - 32 q^{22} - 44 q^{24} - 8 q^{25} - 16 q^{27} - 16 q^{28} - 36 q^{30} - 8 q^{33} + 64 q^{36} - 8 q^{37} - 4 q^{39} - 72 q^{40} - 68 q^{42} - 32 q^{43} - 4 q^{45} - 8 q^{46} - 16 q^{48} + 20 q^{51} + 16 q^{52} - 92 q^{54} - 32 q^{55} - 16 q^{57} + 24 q^{58} - 20 q^{60} - 8 q^{61} - 128 q^{64} - 20 q^{66} - 72 q^{67} - 16 q^{69} - 16 q^{70} - 4 q^{72} - 8 q^{73} + 16 q^{75} - 32 q^{76} + 136 q^{78} - 16 q^{79} - 48 q^{82} + 124 q^{84} + 48 q^{85} - 4 q^{87} - 8 q^{88} + 128 q^{90} - 64 q^{91} - 28 q^{93} - 64 q^{94} - 72 q^{96} - 64 q^{97} - 16 q^{99}+O(q^{100}) $ 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9 - 8 * q^10 - 4 * q^12 - 32 * q^13 - 32 * q^15 + 24 * q^16 - 4 * q^18 - 8 * q^19 - 8 * q^21 - 32 * q^22 - 44 * q^24 - 8 * q^25 - 16 * q^27 - 16 * q^28 - 36 * q^30 - 8 * q^33 + 64 * q^36 - 8 * q^37 - 4 * q^39 - 72 * q^40 - 68 * q^42 - 32 * q^43 - 4 * q^45 - 8 * q^46 - 16 * q^48 + 20 * q^51 + 16 * q^52 - 92 * q^54 - 32 * q^55 - 16 * q^57 + 24 * q^58 - 20 * q^60 - 8 * q^61 - 128 * q^64 - 20 * q^66 - 72 * q^67 - 16 * q^69 - 16 * q^70 - 4 * q^72 - 8 * q^73 + 16 * q^75 - 32 * q^76 + 136 * q^78 - 16 * q^79 - 48 * q^82 + 124 * q^84 + 48 * q^85 - 4 * q^87 - 8 * q^88 + 128 * q^90 - 64 * q^91 - 28 * q^93 - 64 * q^94 - 72 * q^96 - 64 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.33331	+	0.471485i	−0.942789	+	0.333390i
$2$	−1.33331	+	0.471485i	−0.942789	+	0.333390i
$3$	1.63784	+	0.563452i	0.945608	+	0.325309i
$3$	1.63784	+	0.563452i	0.945608	+	0.325309i
$4$	1.55540	−	1.25727i	0.777702	−	0.628633i
$5$	0.441991	+	3.35725i	0.197664	+	1.50141i	0.746447	+	0.665445i	$0.231758\pi$
$5$	0.441991	+	3.35725i	0.197664	+	1.50141i	−0.548783	+	0.835965i	$0.684909\pi$
$6$	−2.44940	+	0.0209633i	−0.999963	+	0.00855821i
$7$	1.71134	+	2.01775i	0.646826	+	0.762637i
$7$	1.71134	+	2.01775i	0.646826	+	0.762637i
$8$	−1.48105	+	2.40967i	−0.523629	+	0.851946i
$9$	2.36504	+	1.84569i	0.788348	+	0.615230i
$10$	−2.17220	−	4.26785i	−0.686911	−	1.34961i
$11$	3.37681	−	2.59112i	1.01815	−	0.781252i	0.0421667	−	0.999111i	$-0.486574\pi$
$11$	3.37681	−	2.59112i	1.01815	−	0.781252i	0.975980	+	0.217859i	$0.0699073\pi$
$12$	3.25591	−	1.18280i	0.939901	−	0.341446i
$13$	1.65768	+	4.00200i	0.459758	+	1.10996i	0.968495	+	0.249033i	$0.0801127\pi$
$13$	1.65768	+	4.00200i	0.459758	+	1.10996i	−0.508737	+	0.860922i	$0.669887\pi$
$14$	−3.23308	−	1.88340i	−0.864076	−	0.503361i
$15$	−1.16774	+	5.74769i	−0.301509	+	1.48405i
$16$	0.838568	−	3.91111i	0.209642	−	0.977778i
$17$	2.36540	−	4.09699i	0.573694	−	0.993667i	−0.422488	−	0.906368i	$-0.638843\pi$
$17$	2.36540	−	4.09699i	0.573694	−	0.993667i	0.996182	−	0.0872984i	$-0.0278234\pi$
$18$	−4.02354	−	1.34578i	−0.948357	−	0.317204i
$19$	−5.29954	−	4.06648i	−1.21580	−	0.932914i	−0.216736	−	0.976230i	$-0.569541\pi$
$19$	−5.29954	−	4.06648i	−1.21580	−	0.932914i	−0.999061	+	0.0433159i	$0.986208\pi$
$20$	4.90843	+	4.66619i	1.09756	+	1.04339i
$21$	1.66600	+	4.26901i	0.363551	+	0.931574i
$22$	−3.28065	+	5.04687i	−0.699436	+	1.07600i
$23$	−0.715456	−	0.191706i	−0.149183	−	0.0399734i	0.183455	−	0.983028i	$-0.441272\pi$
$23$	−0.715456	−	0.191706i	−0.149183	−	0.0399734i	−0.332638	+	0.943055i	$0.607939\pi$
$24$	−3.78345	+	3.11215i	−0.772294	+	0.635265i
$25$	−6.24617	+	1.67366i	−1.24923	+	0.334731i
$26$	−4.09708	−	4.55431i	−0.803503	−	0.893175i
$27$	2.83361	+	4.35553i	0.545328	+	0.838223i
$28$	5.19867	+	0.986804i	0.982457	+	0.186489i
$29$	−1.11873	−	2.70084i	−0.207742	−	0.501534i	0.785325	−	0.619084i	$-0.212496\pi$
$29$	−1.11873	−	2.70084i	−0.207742	−	0.501534i	−0.993067	+	0.117550i	$0.962496\pi$
$30$	−1.15299	−	8.21399i	−0.210506	−	1.49966i
$31$	−7.15425	−	4.13051i	−1.28494	−	0.741861i	−0.307193	−	0.951647i	$-0.599390\pi$
$31$	−7.15425	−	4.13051i	−1.28494	−	0.741861i	−0.977747	+	0.209786i	$0.932723\pi$
$32$	0.725963	+	5.61008i	0.128333	+	0.991731i
$33$	6.99065	−	2.34117i	1.21692	−	0.407545i
$34$	−1.22213	+	6.57779i	−0.209594	+	1.12808i
$35$	−6.01770	+	6.63724i	−1.01718	+	1.12190i
$36$	5.99912	−	0.102695i	0.999854	−	0.0171158i
$37$	−0.298809	+	0.0393389i	−0.0491239	+	0.00646728i	−0.155048	−	0.987907i	$-0.549553\pi$
$37$	−0.298809	+	0.0393389i	−0.0491239	+	0.00646728i	0.105924	+	0.994374i	$0.466220\pi$
$38$	8.98318	+	2.92321i	1.45726	+	0.474207i
$39$	0.460086	+	7.48866i	0.0736727	+	1.19915i
$40$	−8.74448	−	3.90720i	−1.38262	−	0.617783i
$41$	−1.05507	−	1.05507i	−0.164774	−	0.164774i	0.619904	−	0.784678i	$-0.287172\pi$
$41$	−1.05507	−	1.05507i	−0.164774	−	0.164774i	−0.784678	+	0.619904i	$0.787172\pi$
$42$	−4.23406	−	4.90640i	−0.653330	−	0.757074i
$43$	3.14924	−	7.60294i	0.480255	−	1.15944i	−0.479233	−	0.877688i	$-0.659085\pi$
$43$	3.14924	−	7.60294i	0.480255	−	1.15944i	0.959488	−	0.281750i	$-0.0909150\pi$
$44$	1.99458	−	8.27579i	0.300695	−	1.24762i
$45$	−5.15112	+	8.75583i	−0.767883	+	1.30524i
$46$	1.04431	−	0.0817241i	0.153975	−	0.0120496i
$47$	4.36881	−	2.52234i	0.637257	−	0.367921i	−0.146300	−	0.989240i	$-0.546736\pi$
$47$	4.36881	−	2.52234i	0.637257	−	0.367921i	0.783557	+	0.621320i	$0.213403\pi$
$48$	3.57716	−	5.93329i	0.516319	−	0.856396i
$49$	−1.14262	+	6.90612i	−0.163231	+	0.986588i
$50$	7.53895	−	5.17647i	1.06617	−	0.732063i
$51$	6.18261	−	5.37743i	0.865738	−	0.752991i
$52$	7.60994	+	4.14058i	1.05531	+	0.574195i
$53$	−3.29150	−	4.28957i	−0.452123	−	0.589218i	0.510563	−	0.859840i	$-0.329437\pi$
$53$	−3.29150	−	4.28957i	−0.452123	−	0.589218i	−0.962685	+	0.270623i	$0.912770\pi$
$54$	−5.83163	−	4.47125i	−0.793584	−	0.608460i
$55$	10.1916	+	10.1916i	1.37423	+	1.37423i
$56$	−7.39668	+	1.13538i	−0.988423	+	0.151722i
$57$	−6.38853	−	9.64628i	−0.846182	−	1.27768i
$58$	2.76501	+	3.07359i	0.363064	+	0.403582i
$59$	1.67628	+	2.18457i	0.218233	+	0.284407i	0.889621	−	0.456699i	$-0.150968\pi$
$59$	1.67628	+	2.18457i	0.218233	+	0.284407i	−0.671388	+	0.741106i	$0.734302\pi$
$60$	5.41006	+	10.4081i	0.698436	+	1.34369i
$61$	7.59569	+	5.82838i	0.972529	+	0.746248i	0.967273	−	0.253738i	$-0.0816602\pi$
$61$	7.59569	+	5.82838i	0.972529	+	0.746248i	0.00525618	+	0.999986i	$0.498327\pi$
$62$	11.4863	+	2.13411i	1.45876	+	0.271032i
$63$	0.323263	+	7.93067i	0.0407274	+	0.999170i
$64$	−3.61299	−	7.13767i	−0.451624	−	0.892208i
$65$	−12.7031	+	7.33411i	−1.57562	+	0.909684i
$66$	−8.21684	+	6.41747i	−1.01142	+	0.789937i
$67$	−4.40518	−	0.579954i	−0.538179	−	0.0708526i	−0.143463	−	0.989656i	$-0.545824\pi$
$67$	−4.40518	−	0.579954i	−0.538179	−	0.0708526i	−0.394716	+	0.918803i	$0.629157\pi$
$68$	−1.47185	−	9.34642i	−0.178488	−	1.13342i
$69$	−1.06379	−	0.717109i	−0.128065	−	0.0863298i
$70$	4.89407	−	11.6867i	0.584953	−	1.39683i
$71$	−9.29859	−	9.29859i	−1.10354	−	1.10354i	−0.993980	−	0.109559i	$-0.965056\pi$
$71$	−9.29859	−	9.29859i	−1.10354	−	1.10354i	−0.109559	−	0.993980i	$-0.534944\pi$
$72$	−7.95024	+	2.96542i	−0.936945	+	0.349478i
$73$	−0.360091	−	1.34388i	−0.0421454	−	0.157289i	0.941646	−	0.336604i	$-0.109278\pi$
$73$	−0.360091	−	1.34388i	−0.0421454	−	0.157289i	−0.983792	+	0.179315i	$0.942612\pi$
$74$	0.379856	−	0.193335i	0.0441573	−	0.0224747i
$75$	−11.1733	−	0.778234i	−1.29018	−	0.0898627i
$76$	−13.3556	+	0.337906i	−1.53199	+	0.0387604i
$77$	11.0071	+	2.37927i	1.25438	+	0.271143i
$78$	−4.14422	−	9.76775i	−0.469241	−	1.10598i
$79$	3.78072	+	6.54839i	0.425364	+	0.736752i	0.996454	−	0.0841353i	$-0.0268128\pi$
$79$	3.78072	+	6.54839i	0.425364	+	0.736752i	−0.571090	+	0.820887i	$0.693479\pi$
$80$	13.5012	+	1.08661i	1.50948	+	0.121487i
$81$	2.18687	+	8.73027i	0.242985	+	0.970030i
$82$	1.90417	+	0.909277i	0.210281	+	0.100413i
$83$	6.96153	+	16.8066i	0.764127	+	1.84477i	0.434624	+	0.900612i	$0.356881\pi$
$83$	6.96153	+	16.8066i	0.764127	+	1.84477i	0.329503	+	0.944155i	$0.393119\pi$
$84$	7.95858	+	4.54543i	0.868353	+	0.495947i
$85$	14.8001	+	6.13042i	1.60530	+	0.664937i
$86$	−0.614231	+	11.6219i	−0.0662342	+	1.25322i
$87$	−0.310500	−	5.05390i	−0.0332891	−	0.541835i
$88$	1.24251	+	11.9746i	0.132453	+	1.27649i
$89$	−10.8012	−	2.89418i	−1.14493	−	0.306782i	−0.363997	−	0.931400i	$-0.618588\pi$
$89$	−10.8012	−	2.89418i	−1.14493	−	0.306782i	−0.780931	+	0.624618i	$0.785255\pi$
$90$	2.73977	−	14.1029i	0.288797	−	1.48657i
$91$	−5.23817	+	10.1936i	−0.549109	+	1.06858i
$92$	−1.35385	+	0.601338i	−0.141149	+	0.0626938i
$93$	−9.39017	−	10.7962i	−0.973716	−	1.11951i
$94$	−4.63572	+	5.42287i	−0.478138	+	0.559327i
$95$	11.3099	−	19.5892i	1.16037	−	2.00981i
$96$	−1.97200	+	9.59746i	−0.201266	+	0.979537i
$97$	−16.8335			−1.70918			−0.854592	−	0.519299i	$-0.826193\pi$
$97$	−16.8335			−1.70918			−0.854592	+	0.519299i	$0.826193\pi$
$98$	−1.73267	−	9.74668i	−0.175026	−	0.984564i
$99$	12.7687	+	0.104434i	1.28330	+	0.0104960i
$100$	−7.61109	+	10.4563i	−0.761109	+	1.04563i
$101$	−8.10857	+	6.22192i	−0.806833	+	0.619105i	−0.927599	−	0.373576i	$-0.878131\pi$
$101$	−8.10857	+	6.22192i	−0.806833	+	0.619105i	0.120767	+	0.992681i	$0.461465\pi$
$102$	−5.70792	+	10.0848i	−0.565169	+	0.998540i
$103$	1.24351	+	0.333198i	0.122527	+	0.0328309i	0.319561	−	0.947566i	$-0.396464\pi$
$103$	1.24351	+	0.333198i	0.122527	+	0.0328309i	−0.197035	+	0.980397i	$0.563131\pi$
$104$	−12.0986	−	1.93269i	−1.18636	−	0.189516i
$105$	−13.5958	+	7.48005i	−1.32681	+	0.729978i
$106$	6.41104	+	4.16741i	0.622695	+	0.404775i
$107$	−1.14292	−	8.68130i	−0.110490	−	0.839253i	−0.953508	−	0.301368i	$-0.902557\pi$
$107$	−1.14292	−	8.68130i	−0.110490	−	0.839253i	0.843018	−	0.537885i	$-0.180777\pi$
$108$	9.88347	+	3.21202i	0.951037	+	0.309077i
$109$	−0.356759	−	0.0469683i	−0.0341714	−	0.00449874i	0.113421	−	0.993547i	$-0.463819\pi$
$109$	−0.356759	−	0.0469683i	−0.0341714	−	0.00449874i	−0.147592	+	0.989048i	$0.547152\pi$
$110$	−18.3936	−	8.78330i	−1.75376	−	0.837455i
$111$	−0.511567	−	0.103934i	−0.0485558	−	0.00986494i
$112$	9.32672	−	5.00123i	0.881292	−	0.472572i
$113$	−0.806366			−0.0758565			−0.0379283	−	0.999280i	$-0.512076\pi$
$113$	−0.806366			−0.0758565			−0.0379283	+	0.999280i	$0.512076\pi$
$114$	13.0659	+	9.84934i	1.22374	+	0.922475i
$115$	0.327380	−	2.48670i	0.0305284	−	0.231886i
$116$	−5.13575	−	2.79437i	−0.476843	−	0.259451i
$117$	−3.46595	+	12.5245i	−0.320428	+	1.15789i
$118$	−3.26499	−	2.12236i	−0.300567	−	0.195379i
$119$	12.3147	−	2.23857i	1.12889	−	0.205210i
$120$	−12.1205	−	11.3265i	−1.10645	−	1.03396i
$121$	1.84195	−	6.87425i	0.167450	−	0.624932i
$122$	−12.8754	−	4.18976i	−1.16568	−	0.379323i
$123$	−1.13355	−	2.32251i	−0.102209	−	0.209414i
$124$	−16.3209	+	2.57018i	−1.46566	+	0.230809i
$125$	−1.90038	−	4.58793i	−0.169975	−	0.410357i
$126$	−4.17020	−	10.4216i	−0.371511	−	0.928429i
$127$		−	12.2377i		−	1.08592i	−0.839760	−	0.542958i	$-0.817304\pi$
$127$		−	12.2377i		−	1.08592i	0.839760	−	0.542958i	$-0.182696\pi$
$128$	8.18252	+	7.81321i	0.723240	+	0.690597i
$129$	9.44185	−	10.6780i	0.831309	−	0.940142i
$130$	13.4791	−	15.7679i	1.18220	−	1.38294i
$131$	12.2647	+	9.41103i	1.07157	+	0.822246i	0.984750	−	0.173978i	$-0.0556622\pi$
$131$	12.2647	+	9.41103i	1.07157	+	0.822246i	0.0868221	+	0.996224i	$0.472329\pi$
$132$	7.92982	−	12.4306i	0.690202	−	1.08194i
$133$	−0.864191	−	17.6523i	−0.0749349	−	1.53065i
$134$	6.14689	−	1.30372i	0.531011	−	0.112624i
$135$	−13.3702	+	11.4382i	−1.15072	+	0.984448i
$136$	6.36912	+	11.7677i	0.546148	+	1.00907i
$137$	3.79176	−	1.01600i	0.323952	−	0.0868027i	−0.0931781	−	0.995649i	$-0.529703\pi$
$137$	3.79176	−	1.01600i	0.323952	−	0.0868027i	0.417130	+	0.908847i	$0.363036\pi$
$138$	1.75646	+	0.454566i	0.149520	+	0.0386952i
$139$	7.74067	−	18.6876i	0.656555	−	1.58506i	−0.146535	−	0.989205i	$-0.546812\pi$
$139$	7.74067	−	18.6876i	0.656555	−	1.58506i	0.803090	−	0.595858i	$-0.203188\pi$
$140$	−1.01519	+	17.8894i	−0.0857989	+	1.51193i
$141$	8.57664	−	1.66957i	0.722283	−	0.140603i
$142$	16.7820	+	8.01371i	1.40831	+	0.672496i
$143$	15.9673	+	9.21875i	1.33526	+	0.770910i
$144$	9.20195	−	7.70222i	0.766829	−	0.641852i
$145$	8.57296	−	4.94960i	0.711945	−	0.411042i
$146$	1.11373	+	1.62202i	0.0921728	+	0.134239i
$147$	−5.76269	+	10.6673i	−0.475299	+	0.879825i
$148$	−0.415309	+	0.436870i	−0.0341382	+	0.0359105i
$149$	4.52776	−	0.596091i	0.370928	−	0.0488337i	0.0572422	−	0.998360i	$-0.481769\pi$
$149$	4.52776	−	0.596091i	0.370928	−	0.0488337i	0.313686	+	0.949527i	$0.398436\pi$
$150$	15.2643	−	4.23039i	1.24632	−	0.345410i
$151$	−2.18315	+	0.584974i	−0.177663	+	0.0476045i	−0.346554	−	0.938030i	$-0.612648\pi$
$151$	−2.18315	+	0.584974i	−0.177663	+	0.0476045i	0.168891	+	0.985635i	$0.445981\pi$
$152$	17.6477	−	6.74748i	1.43142	−	0.547293i
$153$	13.1560	−	5.32378i	1.06360	−	0.430402i
$154$	−15.7976	+	2.01739i	−1.27301	+	0.162566i
$155$	10.7050	−	25.8443i	0.859850	−	2.07586i
$156$	10.1309	+	11.0695i	0.811118	+	0.886265i
$157$	1.20705	−	9.16846i	0.0963331	−	0.731723i	−0.873304	−	0.487175i	$-0.838027\pi$
$157$	1.20705	−	9.16846i	0.0963331	−	0.731723i	0.969637	−	0.244547i	$-0.0786394\pi$
$158$	−8.12831	−	6.94846i	−0.646654	−	0.552790i
$159$	−2.97399	−	8.88023i	−0.235853	−	0.704248i
$160$	−18.5136	+	4.91684i	−1.46363	+	0.388711i
$161$	−0.837576	−	1.77169i	−0.0660102	−	0.139628i
$162$	−7.03195	−	10.6090i	−0.552482	−	0.833525i
$163$	1.82761	−	2.38178i	0.143149	−	0.186556i	−0.716276	−	0.697817i	$-0.754155\pi$
$163$	1.82761	−	2.38178i	0.143149	−	0.186556i	0.859425	+	0.511261i	$0.170822\pi$
$164$	−2.96755	−	0.314557i	−0.231727	−	0.0245627i
$165$	10.9497	+	22.4346i	0.852433	+	1.74653i
$166$	−17.2059	−	19.1261i	−1.33544	−	1.48447i
$167$	8.29146	+	8.29146i	0.641613	+	0.641613i	0.950952	−	0.309339i	$-0.100108\pi$
$167$	8.29146	+	8.29146i	0.641613	+	0.641613i	−0.309339	+	0.950952i	$0.600108\pi$
$168$	−12.7543	−	2.30810i	−0.984017	−	0.178074i
$169$	−4.07570	+	4.07570i	−0.313516	+	0.313516i
$170$	−22.6235	−	1.19568i	−1.73514	−	0.0917045i
$171$	−5.02819	−	19.3987i	−0.384515	−	1.48346i
$172$	−4.66057	−	15.7851i	−0.355365	−	1.20360i
$173$	−6.81000	−	5.22550i	−0.517755	−	0.397287i	0.316562	−	0.948572i	$-0.397471\pi$
$173$	−6.81000	−	5.22550i	−0.517755	−	0.397287i	−0.834317	+	0.551284i	$0.814138\pi$
$174$	2.79683	+	6.59200i	0.212027	+	0.499738i
$175$	−14.0664	−	9.73900i	−1.06332	−	0.736199i
$176$	−7.30247	−	15.3799i	−0.550445	−	1.15931i
$177$	1.51458	+	4.52249i	0.113843	+	0.339931i
$178$	15.7659	−	1.23379i	1.18170	−	0.0924762i
$179$	−2.55411	−	0.336255i	−0.190903	−	0.0251329i	0.0344683	−	0.999406i	$-0.489026\pi$
$179$	−2.55411	−	0.336255i	−0.190903	−	0.0251329i	−0.225371	+	0.974273i	$0.572360\pi$
$180$	2.99633	+	20.0952i	0.223333	+	1.49781i
$181$	3.43952	+	1.42470i	0.255658	+	0.105897i	0.506832	−	0.862045i	$-0.330817\pi$
$181$	3.43952	+	1.42470i	0.255658	+	0.105897i	−0.251174	+	0.967942i	$0.580817\pi$
$182$	2.17796	−	16.0609i	0.161441	−	1.19051i
$183$	9.15653	+	13.8258i	0.676870	+	1.02203i
$184$	1.52157	−	1.44009i	0.112172	−	0.106165i
$185$	−0.264142	−	0.985790i	−0.0194201	−	0.0724767i
$186$	17.6102	+	9.96729i	1.29124	+	0.730837i
$187$	−2.62828	−	19.9638i	−0.192199	−	1.45990i
$188$	3.62403	−	9.41601i	0.264309	−	0.686733i
$189$	−3.93910	+	13.1713i	−0.286527	+	0.958072i
$190$	−5.84346	+	31.4509i	−0.423929	+	2.28169i
$191$	−10.0034	−	17.3265i	−0.723824	−	1.25370i	−0.959456	−	0.281858i	$-0.909049\pi$
$191$	−10.0034	−	17.3265i	−0.723824	−	1.25370i	0.235632	−	0.971842i	$-0.424284\pi$
$192$	−1.89578	−	13.7261i	−0.136816	−	0.990596i
$193$	−9.96959	+	17.2678i	−0.717627	+	1.24297i	0.244311	+	0.969697i	$0.421438\pi$
$193$	−9.96959	+	17.2678i	−0.717627	+	1.24297i	−0.961938	+	0.273269i	$0.911895\pi$
$194$	22.4442	−	7.93674i	1.61140	−	0.569825i
$195$	−24.9380	+	4.85455i	−1.78585	+	0.347641i
$196$	6.90559	+	12.1784i	0.493256	+	0.869884i
$197$	−11.6133	−	4.81038i	−0.827412	−	0.342725i	−0.0715341	−	0.997438i	$-0.522789\pi$
$197$	−11.6133	−	4.81038i	−0.827412	−	0.342725i	−0.755878	+	0.654713i	$0.772789\pi$
$198$	−17.0738	+	5.88101i	−1.21338	+	0.417945i
$199$	0.309518	+	1.15514i	0.0219412	+	0.0818855i	0.976028	−	0.217644i	$-0.0698371\pi$
$199$	0.309518	+	1.15514i	0.0219412	+	0.0818855i	−0.954087	+	0.299529i	$0.903170\pi$
$200$	5.21792	−	17.5300i	0.368963	−	1.23956i
$201$	−6.88821	−	3.43198i	−0.485857	−	0.242073i
$202$	7.87766	−	12.1188i	0.554270	−	0.852675i
$203$	3.53510	−	6.87938i	0.248116	−	0.482838i
$204$	2.85560	−	16.1373i	0.199932	−	1.12983i
$205$	3.07579	−	4.00845i	0.214823	−	0.279963i
$206$	−1.81508	+	0.142042i	−0.126462	+	0.00989653i
$207$	−1.33826	−	1.77390i	−0.0930152	−	0.123295i
$208$	17.0424	−	3.12744i	1.18167	−	0.216849i
$209$	−28.4323			−1.96670
$210$	14.6006	−	16.3834i	1.00754	−	1.13056i
$211$	12.7268	−	5.27160i	0.876147	−	0.362912i	0.101146	−	0.994872i	$-0.467749\pi$
$211$	12.7268	−	5.27160i	0.876147	−	0.362912i	0.775001	+	0.631960i	$0.217749\pi$
$212$	−10.5127	−	2.53372i	−0.722018	−	0.174017i
$213$	−9.99030	−	20.4689i	−0.684524	−	1.40251i
$214$	5.61695	+	11.0360i	0.383967	+	0.754402i
$215$	26.9170	+	7.21238i	1.83572	+	0.491880i
$216$	−14.6921	+	0.377302i	−0.999670	+	0.0256721i
$217$	−3.90904	−	21.5042i	−0.265363	−	1.45980i
$218$	0.497814	−	0.105584i	0.0337162	−	0.00715102i
$219$	0.167439	−	2.40395i	0.0113145	−	0.162444i
$220$	28.6655	+	3.03851i	1.93263	+	0.204856i
$221$	20.3172	+	2.67482i	1.36669	+	0.179928i
$222$	0.731078	−	0.102621i	0.0490667	−	0.00688746i
$223$			23.3905i			1.56635i	0.621804	+	0.783173i	$0.286400\pi$
$223$			23.3905i			1.56635i	−0.621804	+	0.783173i	$0.713600\pi$
$224$	−10.0774	+	11.0656i	−0.673322	+	0.739350i
$225$	−17.8615	−	7.57022i	−1.19077	−	0.504681i
$226$	1.07513	−	0.380189i	0.0715167	−	0.0252898i
$227$	2.32096	−	17.6294i	0.154047	−	1.17011i	−0.723399	−	0.690431i	$-0.757421\pi$
$227$	2.32096	−	17.6294i	0.154047	−	1.17011i	0.877446	−	0.479675i	$-0.159246\pi$
$228$	−22.0647	−	6.97179i	−1.46127	−	0.461718i
$229$	−7.18645	+	0.946114i	−0.474894	+	0.0625210i	−0.364174	−	0.931331i	$-0.618649\pi$
$229$	−7.18645	+	0.946114i	−0.474894	+	0.0625210i	−0.110719	+	0.993852i	$0.535315\pi$
$230$	0.735943	+	3.46989i	0.0485266	+	0.228797i
$231$	16.6873	+	10.0988i	1.09794	+	0.664454i
$232$	8.16503	+	1.30432i	0.536060	+	0.0856329i
$233$	−4.66788	+	17.4207i	−0.305803	+	1.14127i	0.626449	+	0.779462i	$0.284507\pi$
$233$	−4.66788	+	17.4207i	−0.305803	+	1.14127i	−0.932252	+	0.361809i	$0.882159\pi$
$234$	−1.28392	−	18.3331i	−0.0839325	−	1.19847i
$235$	10.3991	+	13.5524i	0.678363	+	0.884059i
$236$	5.35389	+	1.29036i	0.348508	+	0.0839956i
$237$	2.50251	+	12.8555i	0.162555	+	0.835053i
$238$	−15.3638	+	8.79090i	−0.995888	+	0.569829i
$239$			4.75475i			0.307559i	0.988105	+	0.153780i	$0.0491446\pi$
$239$			4.75475i			0.307559i	−0.988105	+	0.153780i	$0.950855\pi$
$240$	21.5006	+	9.38699i	1.38786	+	0.605928i
$241$	−5.95852	−	3.44015i	−0.383822	−	0.221600i	0.295658	−	0.955294i	$-0.404461\pi$
$241$	−5.95852	−	3.44015i	−0.383822	−	0.221600i	−0.679480	+	0.733694i	$0.737794\pi$
$242$	0.785222	+	10.0339i	0.0504760	+	0.645005i
$243$	−1.33735	+	15.5310i	−0.0857910	+	0.996313i
$244$	19.1422	−	0.484312i	1.22545	−	0.0310049i
$245$	−23.6906	−	0.783617i	−1.51354	−	0.0500634i
$246$	2.60640	+	2.56216i	0.166178	+	0.163357i
$247$	7.48910	−	27.9497i	0.476520	−	1.77840i
$248$	20.5489	−	11.1219i	1.30486	−	0.706240i
$249$	1.93216	+	31.4491i	0.122445	+	1.99300i
$250$	4.69693	+	5.22111i	0.297060	+	0.330212i
$251$	3.84928	−	9.29300i	0.242965	−	0.586569i	−0.754610	−	0.656174i	$-0.772174\pi$
$251$	3.84928	−	9.29300i	0.242965	−	0.586569i	0.997575	+	0.0696050i	$0.0221739\pi$
$252$	10.4738	+	11.9290i	0.659785	+	0.751455i
$253$	−2.91269	+	1.20648i	−0.183119	+	0.0758506i
$254$	5.76987	+	16.3165i	0.362034	+	1.02379i
$255$	20.7861	+	18.3798i	1.30167	+	1.15099i
$256$	−14.5936	−	6.55947i	−0.912101	−	0.409967i
$257$	6.99958	−	4.04121i	0.436622	−	0.252084i	−0.265542	−	0.964099i	$-0.585551\pi$
$257$	6.99958	−	4.04121i	0.436622	−	0.252084i	0.702164	+	0.712016i	$0.252217\pi$
$258$	−7.55437	+	18.6887i	−0.470315	+	1.16351i
$259$	−0.590740	−	0.535599i	−0.0367068	−	0.0332805i
$260$	−10.5375	+	27.3786i	−0.653506	+	1.69795i
$261$	2.33908	−	8.45244i	0.144786	−	0.523193i
$262$	−20.7897	−	6.76516i	−1.28439	−	0.417953i
$263$	8.32211	−	2.22990i	0.513163	−	0.137502i	0.00706075	−	0.999975i	$-0.497752\pi$
$263$	8.32211	−	2.22990i	0.513163	−	0.137502i	0.506102	+	0.862473i	$0.331086\pi$
$264$	−4.71205	+	20.3125i	−0.290007	+	1.25015i
$265$	12.9464	−	12.9464i	0.795289	−	0.795289i
$266$	9.47500	+	23.1284i	0.580950	+	1.41809i
$267$	−16.0600	−	10.8262i	−0.982853	−	0.662551i
$268$	−7.58100	+	4.63642i	−0.463083	+	0.283215i
$269$	−1.38795	+	10.5425i	−0.0846248	+	0.642789i	0.895594	+	0.444872i	$0.146751\pi$
$269$	−1.38795	+	10.5425i	−0.0846248	+	0.642789i	−0.980219	+	0.197917i	$0.936582\pi$
$270$	12.4336	−	21.5545i	0.756685	−	1.31177i
$271$	0.340003	+	0.588902i	0.0206537	+	0.0357732i	0.876168	−	0.482007i	$-0.160092\pi$
$271$	0.340003	+	0.588902i	0.0206537	+	0.0357732i	−0.855514	+	0.517780i	$0.826759\pi$
$272$	−14.0403	−	12.6870i	−0.851315	−	0.769259i
$273$	−14.3229	+	13.7440i	−0.866860	+	0.831825i
$274$	−4.57655	+	3.14239i	−0.276479	+	0.189839i
$275$	−16.7555	+	21.8362i	−1.01039	+	1.31677i
$276$	−2.55621	+	0.222067i	−0.153866	+	0.0133669i
$277$	5.94555	−	4.56218i	0.357233	−	0.274115i	−0.414516	−	0.910042i	$-0.636049\pi$
$277$	5.94555	−	4.56218i	0.357233	−	0.274115i	0.771749	+	0.635928i	$0.219382\pi$
$278$	−1.50975	+	28.5659i	−0.0905485	+	1.71327i
$279$	−9.29648	−	22.9733i	−0.556566	−	1.37538i
$280$	−7.08104	−	24.3307i	−0.423173	−	1.45404i
$281$	−3.32942	+	3.32942i	−0.198617	+	0.198617i	−0.799407	−	0.600790i	$-0.794853\pi$
$281$	−3.32942	+	3.32942i	−0.198617	+	0.198617i	0.600790	+	0.799407i	$0.294853\pi$
$282$	−10.6481	+	6.26980i	−0.634085	+	0.373361i
$283$	−3.57370	+	2.74220i	−0.212434	+	0.163007i	−0.709498	−	0.704707i	$-0.751078\pi$
$283$	−3.57370	+	2.74220i	−0.212434	+	0.163007i	0.497064	+	0.867714i	$0.334412\pi$
$284$	−26.1539	−	2.77227i	−1.55195	−	0.164504i
$285$	29.5613	−	25.7115i	1.75106	−	1.52302i
$286$	−25.6358	−	4.76305i	−1.51588	−	0.281645i
$287$	0.323279	−	3.93444i	0.0190826	−	0.232242i
$288$	−8.63753	+	14.6080i	−0.508971	+	0.860784i
$289$	−2.69023	−	4.65962i	−0.158249	−	0.274095i
$290$	−9.09671	+	10.6413i	−0.534177	+	0.624881i
$291$	−27.5706	−	9.48488i	−1.61622	−	0.556013i
$292$	−2.24970	−	1.63754i	−0.131654	−	0.0958300i
$293$	21.6753	+	8.97821i	1.26629	+	0.524513i	0.911833	−	0.410561i	$-0.134667\pi$
$293$	21.6753	+	8.97821i	1.26629	+	0.524513i	0.354453	+	0.935074i	$0.384667\pi$
$294$	2.65395	−	16.9398i	0.154782	−	0.987949i
$295$	−6.59327	+	6.59327i	−0.383875	+	0.383875i
$296$	0.347757	−	0.778293i	0.0202129	−	0.0452374i
$297$	20.8543	+	7.36560i	1.21009	+	0.427395i
$298$	−5.75584	+	2.92954i	−0.333427	+	0.169704i
$299$	−0.418792	−	3.18104i	−0.0242194	−	0.183964i
$300$	−18.3574	+	12.8373i	−1.05986	+	0.741161i
$301$	20.7303	−	6.65686i	1.19487	−	0.383695i
$302$	2.63500	−	1.80927i	0.151627	−	0.104112i
$303$	−16.7863	+	5.62173i	−0.964348	+	0.322960i
$304$	−20.3485	+	17.3171i	−1.16707	+	0.993202i
$305$	−16.2101	+	28.0768i	−0.928189	+	1.60767i
$306$	−15.0309	+	13.3011i	−0.859262	+	0.760373i
$307$	7.70283	−	3.19062i	0.439624	−	0.182098i	−0.151882	−	0.988399i	$-0.548534\pi$
$307$	7.70283	−	3.19062i	0.439624	−	0.182098i	0.591506	+	0.806300i	$0.298534\pi$
$308$	20.1119	−	10.1381i	1.14598	−	0.577674i
$309$	1.84893	+	1.24638i	0.105182	+	0.0709043i
$310$	−2.08792	+	39.5056i	−0.118586	+	2.24377i
$311$	4.62118	+	17.2465i	0.262043	+	0.977957i	0.964036	+	0.265773i	$0.0856272\pi$
$311$	4.62118	+	17.2465i	0.262043	+	0.977957i	−0.701993	+	0.712184i	$0.747706\pi$
$312$	−18.7266	−	9.98241i	−1.06018	−	0.565143i
$313$	−6.08136	+	22.6959i	−0.343739	+	1.28285i	0.550340	+	0.834940i	$0.314498\pi$
$313$	−6.08136	+	22.6959i	−0.343739	+	1.28285i	−0.894079	+	0.447909i	$0.852169\pi$
$314$	2.71342	+	12.7935i	0.153127	+	0.721977i
$315$	−26.4824	+	4.59056i	−1.49211	+	0.258649i
$316$	14.1136	+	5.43204i	0.793953	+	0.305576i
$317$	−6.24926	+	8.14419i	−0.350993	+	0.457423i	−0.935168	−	0.354205i	$-0.884752\pi$
$317$	−6.24926	+	8.14419i	−0.350993	+	0.457423i	0.584175	+	0.811628i	$0.301418\pi$
$318$	8.15213	+	10.4379i	0.457149	+	0.585327i
$319$	−10.7759	−	6.22149i	−0.603337	−	0.348337i
$320$	22.3660	−	15.2845i	1.25030	−	0.854431i
$321$	3.01958	−	14.8626i	0.168537	−	0.829548i
$322$	1.95207	+	1.96729i	0.108784	+	0.109633i
$323$	−29.1959	+	12.0933i	−1.62450	+	0.672891i
$324$	14.3777	+	10.8296i	0.798763	+	0.601646i
$325$	−17.0521	−	22.2228i	−0.945883	−	1.23270i
$326$	−1.31378	+	4.03733i	−0.0727637	+	0.223607i
$327$	−0.557851	−	0.277943i	−0.0308492	−	0.0153703i
$328$	4.10496	−	0.979755i	0.226659	−	0.0540979i
$329$	12.5660	+	4.49859i	0.692785	+	0.248015i
$330$	−25.1769	−	24.7496i	−1.38594	−	1.36242i
$331$	5.91687	−	0.778970i	0.325220	−	0.0428161i	0.0338516	−	0.999427i	$-0.489223\pi$
$331$	5.91687	−	0.778970i	0.325220	−	0.0428161i	0.291369	+	0.956611i	$0.405889\pi$
$332$	31.9584	+	17.3886i	1.75394	+	0.954324i
$333$	−0.779304	−	0.458470i	−0.0427056	−	0.0251240i
$334$	−14.9643	−	7.14575i	−0.818813	−	0.390998i
$335$		−	15.0457i		−	0.822032i
$336$	18.0936	−	2.93607i	0.987089	−	0.160176i
$337$		−	18.1172i		−	0.986909i	−0.869772	−	0.493455i	$-0.835734\pi$
$337$		−	18.1172i		−	0.986909i	0.869772	−	0.493455i	$-0.164266\pi$
$338$	3.51252	−	7.35579i	0.191056	−	0.400102i
$339$	−1.32070	−	0.454348i	−0.0717305	−	0.0246768i
$340$	30.7278	−	9.07242i	1.66645	−	0.492021i
$341$	−34.8612	+	4.58956i	−1.88784	+	0.248539i
$342$	15.8503	+	23.4937i	0.857086	+	1.27039i
$343$	−15.8902	+	9.51321i	−0.857991	+	0.513665i
$344$	13.6564	+	18.8490i	0.736303	+	1.01627i
$345$	1.93733	−	3.88836i	0.104303	−	0.209342i
$346$	11.5436	+	3.75637i	0.620585	+	0.201944i
$347$	8.84225	+	11.5234i	0.474677	+	0.618611i	0.967913	−	0.251284i	$-0.0808529\pi$
$347$	8.84225	+	11.5234i	0.474677	+	0.618611i	−0.493236	+	0.869895i	$0.664186\pi$
$348$	−6.83705	−	7.47048i	−0.366504	−	0.400460i
$349$	18.1300	−	7.50968i	0.970475	−	0.401984i	0.159586	−	0.987184i	$-0.448984\pi$
$349$	18.1300	−	7.50968i	0.970475	−	0.401984i	0.810889	+	0.585200i	$0.198984\pi$
$350$	23.3465	+	6.35299i	1.24792	+	0.339582i
$351$	−12.7336	+	18.5602i	−0.679670	+	0.990670i
$352$	16.9878	+	17.0631i	0.905454	+	0.909467i
$353$	7.44648	+	4.29923i	0.396336	+	0.228825i	0.684902	−	0.728635i	$-0.259845\pi$
$353$	7.44648	+	4.29923i	0.396336	+	0.228825i	−0.288566	+	0.957460i	$0.593178\pi$
$354$	−4.15168	−	5.31575i	−0.220659	−	0.282529i
$355$	27.1078	−	35.3276i	1.43873	−	1.87499i
$356$	−20.4390	+	9.07839i	−1.08327	+	0.481153i
$357$	21.4309	+	3.27232i	1.13424	+	0.173189i
$358$	3.56395	−	0.755893i	0.188361	−	0.0399502i
$359$	−5.78009	+	21.5716i	−0.305061	+	1.13850i	0.627831	+	0.778350i	$0.283943\pi$
$359$	−5.78009	+	21.5716i	−0.305061	+	1.13850i	−0.932892	+	0.360155i	$0.882724\pi$
$360$	−13.4696	−	25.3803i	−0.709910	−	1.33766i
$361$	6.63130	+	24.7483i	0.349016	+	1.30254i
$362$	−5.25765	−	0.277874i	−0.276336	−	0.0146047i
$363$	6.89013	−	10.2211i	0.361638	−	0.536468i
$364$	4.66856	+	22.4409i	0.244699	+	1.17622i
$365$	4.35258	−	1.80290i	0.227824	−	0.0943680i
$366$	−18.7271	−	14.1168i	−0.978880	−	0.737897i
$367$	−1.67611	+	2.90312i	−0.0874925	+	0.151541i	−0.906451	−	0.422312i	$-0.861219\pi$
$367$	−1.67611	+	2.90312i	−0.0874925	+	0.151541i	0.818958	+	0.573853i	$0.194552\pi$
$368$	−1.34974	+	2.63747i	−0.0703602	+	0.137488i
$369$	−0.547954	−	4.44260i	−0.0285253	−	0.231273i
$370$	0.816966	+	1.18982i	0.0424721	+	0.0618558i
$371$	3.02239	−	13.9823i	0.156914	−	0.725927i
$372$	−28.1792	−	4.98650i	−1.46102	−	0.258538i
$373$	−1.90325	−	14.4566i	−0.0985464	−	0.748534i	−0.967362	−	0.253398i	$-0.918452\pi$
$373$	−1.90325	−	14.4566i	−0.0985464	−	0.748534i	0.868816	−	0.495136i	$-0.164882\pi$
$374$	12.9169	+	25.3786i	0.667919	+	1.31230i
$375$	−0.527446	−	8.58507i	−0.0272372	−	0.443331i
$376$	−0.392432	+	14.2631i	−0.0202381	+	0.735563i
$377$	8.95429	−	8.95429i	0.461169	−	0.461169i
$378$	−0.958054	−	19.4186i	−0.0492770	−	0.998785i
$379$	−14.8171	−	6.13745i	−0.761105	−	0.315260i	−0.0318412	−	0.999493i	$-0.510137\pi$
$379$	−14.8171	−	6.13745i	−0.761105	−	0.315260i	−0.729263	+	0.684233i	$0.760137\pi$
$380$	−7.03748	−	44.6887i	−0.361015	−	2.29248i
$381$	6.89533	−	20.0433i	0.353259	−	1.02685i
$382$	21.5068	+	18.3850i	1.10038	+	0.940659i
$383$	−1.36755	−	2.36866i	−0.0698785	−	0.121033i	0.828969	−	0.559294i	$-0.188928\pi$
$383$	−1.36755	−	2.36866i	−0.0698785	−	0.121033i	−0.898848	+	0.438261i	$0.855594\pi$
$384$	8.99930	+	17.4073i	0.459243	+	0.888310i
$385$	−3.12276	+	38.0053i	−0.159151	+	1.93693i
$386$	5.15099	−	27.7238i	0.262178	−	1.41110i
$387$	21.4808	−	12.1688i	1.09193	−	0.618574i
$388$	−26.1829	+	21.1642i	−1.32924	+	1.07445i
$389$	−10.0565	+	7.71666i	−0.509887	+	0.391250i	−0.831417	−	0.555649i	$-0.812470\pi$
$389$	−10.0565	+	7.71666i	−0.509887	+	0.391250i	0.321530	+	0.946899i	$0.395803\pi$
$390$	30.9611	−	18.2305i	1.56778	−	0.923135i
$391$	−2.47776	+	2.47776i	−0.125306	+	0.125306i
$392$	−14.9492	−	12.9816i	−0.755047	−	0.655671i
$393$	14.7850	+	22.3243i	0.745802	+	1.12611i
$394$	17.7521	+	0.938220i	0.894336	+	0.0472668i
$395$	−20.3136	+	15.5872i	−1.02209	+	0.784275i
$396$	19.9918	−	15.8912i	1.00463	−	0.798564i
$397$	15.2498	−	19.8740i	0.765367	−	0.997446i	−0.234313	−	0.972161i	$-0.575284\pi$
$397$	15.2498	−	19.8740i	0.765367	−	0.997446i	0.999680	−	0.0252845i	$-0.00804915\pi$
$398$	−0.957312	−	1.39422i	−0.0479857	−	0.0698858i
$399$	8.53080	−	29.3985i	0.427074	−	1.47177i
$400$	1.30802	+	25.8330i	0.0654011	+	1.29165i
$401$	−9.57243	−	16.5799i	−0.478024	−	0.827962i	0.521658	−	0.853155i	$-0.325314\pi$
$401$	−9.57243	−	16.5799i	−0.478024	−	0.827962i	−0.999683	+	0.0251920i	$0.991980\pi$
$402$	10.8022	+	1.32819i	0.538766	+	0.0662442i
$403$	4.67081	−	35.4784i	0.232670	−	1.76730i
$404$	−4.78950	+	19.8722i	−0.238286	+	0.988681i
$405$	−28.3432	+	11.2006i	−1.40838	+	0.556561i
$406$	−1.46985	+	10.8391i	−0.0729474	+	0.537933i
$407$	−0.907090	+	0.907090i	−0.0449628	+	0.0449628i
$408$	3.80109	+	22.8623i	0.188182	+	1.13185i
$409$	14.3651	−	3.84911i	0.710307	−	0.190326i	0.114464	−	0.993427i	$-0.463485\pi$
$409$	14.3651	−	3.84911i	0.710307	−	0.190326i	0.595843	+	0.803101i	$0.296818\pi$
$410$	−2.21105	+	6.79468i	−0.109196	+	0.335565i
$411$	6.78277	+	0.472430i	0.334569	+	0.0233033i
$412$	2.35308	−	1.04517i	0.115928	−	0.0514916i
$413$	−1.53923	+	7.12087i	−0.0757404	+	0.350395i
$414$	2.62067	+	1.73419i	0.128799	+	0.0852306i
$415$	−53.3472	+	30.8000i	−2.61871	+	1.51191i
$416$	−21.2481	+	12.2050i	−1.04177	+	0.598401i
$417$	23.2076	−	26.2459i	1.13648	−	1.28526i
$418$	37.9089	−	13.4054i	1.85418	−	0.655678i
$419$	25.1594	−	10.4214i	1.22912	−	0.509116i	0.328819	−	0.944393i	$-0.393349\pi$
$419$	25.1594	−	10.4214i	1.22912	−	0.509116i	0.900297	+	0.435277i	$0.143349\pi$
$420$	−11.7425	+	28.7280i	−0.572978	+	1.40178i
$421$	−7.23759	+	17.4731i	−0.352738	+	0.851586i	0.643542	+	0.765411i	$0.277464\pi$
$421$	−7.23759	+	17.4731i	−0.352738	+	0.851586i	−0.996280	+	0.0861747i	$0.972536\pi$
$422$	−14.4832	+	13.0291i	−0.705030	+	0.634248i
$423$	14.9879	+	2.09804i	0.728736	+	0.102010i
$424$	15.2113	−	1.57837i	0.738726	−	0.0766523i
$425$	−7.91773	+	29.5494i	−0.384066	+	1.43336i
$426$	22.9709	+	22.5810i	1.11294	+	1.09405i
$427$	1.23862	+	25.3006i	0.0599412	+	1.22438i
$428$	−12.6924	−	12.0660i	−0.613510	−	0.583232i
$429$	20.9576	+	24.0957i	1.01184	+	1.16335i
$430$	−39.2890	+	3.07463i	−1.89469	+	0.148272i
$431$	−10.9820	−	6.34046i	−0.528985	−	0.305409i	0.211618	−	0.977352i	$-0.432127\pi$
$431$	−10.9820	−	6.34046i	−0.528985	−	0.305409i	−0.740603	+	0.671943i	$0.765460\pi$
$432$	19.4112	−	7.43015i	0.933919	−	0.357483i
$433$		−	2.40765i		−	0.115704i	−0.998325	−	0.0578522i	$-0.981575\pi$
$433$		−	2.40765i		−	0.115704i	0.998325	−	0.0578522i	$-0.0184252\pi$
$434$	15.3508	+	26.8286i	0.736863	+	1.28781i
$435$	16.8300	−	3.27621i	0.806937	−	0.157082i
$436$	−0.613957	+	0.375487i	−0.0294032	+	0.0179825i
$437$	3.01202	+	3.92534i	0.144084	+	0.187775i
$438$	0.910178	+	3.28414i	0.0434900	+	0.156922i
$439$	−6.18583	+	23.0858i	−0.295233	+	1.10183i	0.645798	+	0.763508i	$0.276525\pi$
$439$	−6.18583	+	23.0858i	−0.295233	+	1.10183i	−0.941032	+	0.338318i	$0.890142\pi$
$440$	−39.6525	+	9.46409i	−1.89036	+	0.451183i
$441$	−15.4489	+	14.2243i	−0.735661	+	0.677350i
$442$	−28.3502	+	6.01292i	−1.34848	+	0.286005i
$443$	25.3932	−	3.34307i	1.20647	−	0.158834i	0.499647	−	0.866229i	$-0.333463\pi$
$443$	25.3932	−	3.34307i	1.20647	−	0.158834i	0.706819	+	0.707395i	$0.250130\pi$
$444$	−0.926366	+	0.481517i	−0.0439634	+	0.0228518i
$445$	4.94245	−	37.5417i	0.234295	−	1.77965i
$446$	−11.0283	−	31.1867i	−0.522204	−	1.47673i
$447$	7.75162	+	1.57487i	0.366639	+	0.0744889i
$448$	8.21894	−	19.5051i	0.388309	−	0.921529i
$449$			12.3086i			0.580879i	0.956893	+	0.290439i	$0.0938014\pi$
$449$			12.3086i			0.580879i	−0.956893	+	0.290439i	$0.906199\pi$
$450$	27.3841	+	1.67198i	1.29090	+	0.0788178i
$451$	−6.29656	−	0.828958i	−0.296493	−	0.0390341i
$452$	−1.25423	+	1.01382i	−0.0589938	+	0.0476859i
$453$	−3.90526	−	0.272007i	−0.183485	−	0.0127800i
$454$	5.21746	+	24.5997i	0.244867	+	1.15452i
$455$	−36.5377	−	13.0804i	−1.71291	−	0.613218i
$456$	32.7061	−	1.10764i	1.53160	−	0.0518701i
$457$	−18.0215	−	4.82885i	−0.843010	−	0.225884i	−0.188629	−	0.982048i	$-0.560404\pi$
$457$	−18.0215	−	4.82885i	−0.843010	−	0.225884i	−0.654382	+	0.756165i	$0.727071\pi$
$458$	9.13565	−	4.64976i	0.426881	−	0.217269i
$459$	24.5472	−	1.30670i	1.14577	−	0.0609914i
$460$	−2.61723	−	4.27943i	−0.122029	−	0.199529i
$461$	28.5164	−	11.8119i	1.32814	−	0.550135i	0.398018	−	0.917378i	$-0.369698\pi$
$461$	28.5164	−	11.8119i	1.32814	−	0.550135i	0.930125	+	0.367243i	$0.119698\pi$
$462$	−27.0107	−	5.59703i	−1.25665	−	0.260397i
$463$	−2.35798			−0.109585			−0.0547923	−	0.998498i	$-0.517450\pi$
$463$	−2.35798			−0.109585			−0.0547923	+	0.998498i	$0.517450\pi$
$464$	−11.5014	+	2.11062i	−0.533941	+	0.0979833i
$465$	32.0952	−	36.2970i	1.48838	−	1.68323i
$466$	−1.98991	−	25.4280i	−0.0921808	−	1.17793i
$467$	−3.80362	+	4.95698i	−0.176011	+	0.229381i	−0.873025	−	0.487676i	$-0.837845\pi$
$467$	−3.80362	+	4.95698i	−0.176011	+	0.229381i	0.697014	+	0.717057i	$0.254511\pi$
$468$	10.3556	+	23.8382i	0.478689	+	1.10192i
$469$	−6.36858	−	9.88105i	−0.294074	−	0.456265i
$470$	−20.2549	−	13.1664i	−0.934289	−	0.607322i
$471$	7.14294	−	14.3364i	0.329129	−	0.660585i
$472$	−7.74675	+	0.803825i	−0.356573	+	0.0369990i
$473$	−9.06573	−	33.8338i	−0.416843	−	1.55568i
$474$	−9.39776	−	15.9604i	−0.431654	−	0.733084i
$475$	39.9077	+	16.5303i	1.83109	+	0.758463i
$476$	16.3399	−	18.9647i	0.748937	−	0.869248i
$477$	0.132662	−	16.2201i	0.00607419	−	0.742668i
$478$	−2.24179	−	6.33953i	−0.102537	−	0.289963i
$479$	−18.6207	+	32.2519i	−0.850800	+	1.47363i	0.0296877	+	0.999559i	$0.490549\pi$
$479$	−18.6207	+	32.2519i	−0.850800	+	1.47363i	−0.880488	+	0.474069i	$0.842785\pi$
$480$	−33.0927	−	2.37851i	−1.51047	−	0.108564i
$481$	−0.652765	−	1.13062i	−0.0297635	−	0.0515519i
$482$	9.56650	+	1.77742i	0.435742	+	0.0809594i
$483$	−0.373557	−	3.37367i	−0.0169974	−	0.153507i
$484$	−5.77778	−	13.0081i	−0.262626	−	0.591276i
$485$	−7.44026	−	56.5144i	−0.337845	−	2.56619i
$486$	−5.53952	−	21.3381i	−0.251278	−	0.967915i
$487$	3.71057	+	13.8480i	0.168142	+	0.627514i	0.997619	+	0.0689724i	$0.0219721\pi$
$487$	3.71057	+	13.8480i	0.168142	+	0.627514i	−0.829477	+	0.558541i	$0.811361\pi$
$488$	−25.2940	+	9.67099i	−1.14501	+	0.437785i
$489$	4.33535	−	2.87121i	0.196051	−	0.129841i
$490$	31.9563	−	10.1250i	1.44364	−	0.457399i
$491$	−25.8377	−	10.7023i	−1.16604	−	0.482990i	−0.286158	−	0.958182i	$-0.592378\pi$
$491$	−25.8377	−	10.7023i	−1.16604	−	0.482990i	−0.879882	+	0.475193i	$0.842378\pi$
$492$	−4.68314	−	2.18727i	−0.211132	−	0.0986096i
$493$	−13.7116	−	1.80516i	−0.617538	−	0.0813005i
$494$	3.19259	+	40.7964i	0.143642	+	1.83552i
$495$	5.29304	+	42.9139i	0.237905	+	1.92884i
$496$	−22.1542	+	24.5174i	−0.994753	+	1.10086i
$497$	2.84915	−	34.6753i	0.127802	−	1.55540i
$498$	−17.4039	−	41.0202i	−0.779887	−	1.83816i
$499$	10.5269	+	8.07760i	0.471250	+	0.361603i	0.816918	−	0.576754i	$-0.195681\pi$
$499$	10.5269	+	8.07760i	0.471250	+	0.361603i	−0.345668	+	0.938357i	$0.612348\pi$
$500$	−8.72411	−	4.74680i	−0.390154	−	0.212283i
$501$	8.90826	+	18.2519i	0.397992	+	0.815437i
$502$	−0.750767	+	14.2053i	−0.0335084	+	0.634012i
$503$	−13.2338	+	13.2338i	−0.590066	+	0.590066i	−0.937649	−	0.347583i	$-0.887002\pi$
$503$	−13.2338	+	13.2338i	−0.590066	+	0.590066i	0.347583	+	0.937649i	$0.387002\pi$
$504$	−19.5890	−	10.9667i	−0.872565	−	0.488498i
$505$	−24.4725	−	24.4725i	−1.08901	−	1.08901i
$506$	3.31467	−	2.98189i	0.147355	−	0.132561i
$507$	−8.97181	+	4.37889i	−0.398452	+	0.194473i
$508$	−15.3860	−	19.0345i	−0.682643	−	0.844520i
$509$	5.08824	−	6.63112i	0.225532	−	0.293919i	−0.666857	−	0.745186i	$-0.732361\pi$
$509$	5.08824	−	6.63112i	0.225532	−	0.293919i	0.892389	+	0.451266i	$0.149028\pi$
$510$	−36.3800	−	14.7056i	−1.61093	−	0.651174i
$511$	2.09537	−	3.02641i	0.0926936	−	0.133880i
$512$	22.5504	+	1.86511i	0.996597	+	0.0824269i
$513$	2.69486	−	34.6051i	0.118981	−	1.52785i
$514$	−7.42721	+	8.68836i	−0.327600	+	0.383227i
$515$	−0.569009	+	4.32205i	−0.0250735	+	0.190452i
$516$	1.26086	−	28.4795i	0.0555065	−	1.25374i
$517$	8.21699	−	19.8376i	0.361383	−	0.872455i
$518$	1.04016	+	0.435592i	0.0457022	+	0.0191388i
$519$	−8.20938	−	12.3956i	−0.360352	−	0.544108i
$520$	1.14106	−	41.4723i	0.0500388	−	1.81868i
$521$	13.5731	−	3.63691i	0.594650	−	0.159336i	0.0510727	−	0.998695i	$-0.483736\pi$
$521$	13.5731	−	3.63691i	0.594650	−	0.159336i	0.543578	+	0.839359i	$0.317069\pi$
$522$	0.866484	+	12.3725i	0.0379250	+	0.541530i
$523$	−17.6891	+	2.32881i	−0.773489	+	0.101832i	−0.506930	−	0.861987i	$-0.669220\pi$
$523$	−17.6891	+	2.32881i	−0.773489	+	0.101832i	−0.266559	+	0.963819i	$0.585887\pi$
$524$	30.9087	−	0.782013i	1.35025	−	0.0341624i
$525$	−17.5510	−	23.8766i	−0.765988	−	1.04206i
$526$	−10.0445	+	6.89688i	−0.437963	+	0.300718i
$527$	−33.8453	+	19.5406i	−1.47432	+	0.851202i
$528$	−3.29444	−	29.3044i	−0.143372	−	1.27531i
$529$	−19.4435	−	11.2257i	−0.845368	−	0.488073i
$530$	−11.1574	+	23.3655i	−0.484648	+	1.01493i
$531$	−0.0675617	+	8.26051i	−0.00293193	+	0.358476i
$532$	−23.5378	−	26.3699i	−1.02049	−	1.14328i
$533$	2.47341	−	5.97134i	0.107135	−	0.258647i
$534$	26.5172	+	6.86257i	1.14751	+	0.296973i
$535$	28.6402	−	7.67411i	1.23822	−	0.331781i
$536$	7.92178	−	9.75609i	0.342169	−	0.421399i
$537$	−3.99376	−	1.98985i	−0.172344	−	0.0858684i
$538$	−3.12008	−	14.7108i	−0.134516	−	0.634228i
$539$	14.0362	+	26.2813i	0.604580	+	1.13202i
$540$	−6.41516	+	34.6010i	−0.276064	+	1.48899i
$541$	−11.5345	−	8.85072i	−0.495906	−	0.380522i	0.330313	−	0.943872i	$-0.392846\pi$
$541$	−11.5345	−	8.85072i	−0.495906	−	0.380522i	−0.826219	+	0.563349i	$0.809513\pi$
$542$	−0.730985	−	0.624880i	−0.0313985	−	0.0268409i
$543$	4.83064	+	4.27143i	0.207303	+	0.183305i
$544$	24.7016	+	10.2958i	1.05907	+	0.441429i
$545$		−	1.21849i		−	0.0521944i
$546$	12.6167	−	25.0780i	0.539944	−	1.07324i
$547$	1.73057	+	4.17796i	0.0739938	+	0.178637i	0.956549	−	0.291572i	$-0.0941784\pi$
$547$	1.73057	+	4.17796i	0.0739938	+	0.178637i	−0.882555	+	0.470209i	$0.844178\pi$
$548$	4.62034	−	6.34754i	0.197371	−	0.271153i
$549$	7.20677	+	27.8037i	0.307578	+	1.18663i
$550$	12.0448	−	37.0143i	0.513591	−	1.57829i
$551$	−5.05419	+	18.8625i	−0.215316	+	0.803570i
$552$	3.30351	−	1.50130i	0.140607	−	0.0638995i
$553$	−6.74291	+	18.8351i	−0.286738	+	0.800949i
$554$	−5.77623	+	8.88601i	−0.245408	+	0.377530i
$555$	0.122823	−	1.76340i	0.00521356	−	0.0748521i
$556$	−11.4554	−	38.7989i	−0.485818	−	1.64544i
$557$	−3.76408	+	28.5910i	−0.159489	+	1.21144i	0.705154	+	0.709054i	$0.250878\pi$
$557$	−3.76408	+	28.5910i	−0.159489	+	1.21144i	−0.864643	+	0.502386i	$0.832456\pi$
$558$	23.2266	+	26.2473i	0.983261	+	1.11114i
$559$	35.6474			1.50773
$560$	20.9127	+	29.1017i	0.883724	+	1.22977i
$561$	6.94393	−	34.1784i	0.293173	−	1.44301i
$562$	2.86937	−	6.00891i	0.121037	−	0.253471i
$563$	−15.9202	−	2.09594i	−0.670957	−	0.0883332i	−0.212652	−	0.977128i	$-0.568210\pi$
$563$	−15.9202	−	2.09594i	−0.670957	−	0.0883332i	−0.458305	+	0.888795i	$0.651543\pi$
$564$	11.2411	−	13.3800i	0.473334	−	0.563398i
$565$	−0.356406	−	2.70718i	−0.0149941	−	0.113892i
$566$	3.47193	−	5.34113i	0.145936	−	0.224504i
$567$	−13.8730	+	19.3530i	−0.582612	+	0.812751i
$568$	36.1782	−	8.63485i	1.51800	−	0.362310i
$569$	38.5247	+	10.3227i	1.61504	+	0.432749i	0.949539	−	0.313648i	$-0.101551\pi$
$569$	38.5247	+	10.3227i	1.61504	+	0.432749i	0.665501	+	0.746397i	$0.268218\pi$
$570$	−27.2917	+	48.2190i	−1.14312	+	2.01967i
$571$	−19.3779	+	14.8692i	−0.810940	+	0.622256i	−0.928719	−	0.370783i	$-0.879089\pi$
$571$	−19.3779	+	14.8692i	−0.810940	+	0.622256i	0.117779	+	0.993040i	$0.462423\pi$
$572$	36.4261	−	5.73630i	1.52305	−	0.239847i
$573$	−6.62142	−	34.0145i	−0.276614	−	1.42098i
$574$	1.42400	+	5.39822i	0.0594364	+	0.225318i
$575$	4.78971			0.199745
$576$	4.62902	−	23.5494i	0.192876	−	0.981223i
$577$	−1.93822	+	3.35709i	−0.0806891	+	0.139758i	−0.903546	−	0.428491i	$-0.859045\pi$
$577$	−1.93822	+	3.35709i	−0.0806891	+	0.139758i	0.822857	+	0.568248i	$0.192379\pi$
$578$	5.78384	+	4.94429i	0.240576	+	0.205656i
$579$	−26.0582	+	22.6646i	−1.08294	+	0.941908i
$580$	7.11146	−	18.4771i	0.295287	−	0.767220i
$581$	−21.9980	+	42.8085i	−0.912630	+	1.77600i
$582$	41.2320	−	0.352885i	1.70912	−	0.0146276i
$583$	−22.2296	−	5.95639i	−0.920654	−	0.246689i
$584$	3.77161	+	1.12265i	0.156070	+	0.0464555i
$585$	−43.5798	−	6.10039i	−1.80180	−	0.252220i
$586$	−33.1329	−	1.75112i	−1.36871	−	0.0723380i
$587$	−26.1069	−	10.8138i	−1.07755	−	0.446334i	−0.227899	−	0.973685i	$-0.573185\pi$
$587$	−26.1069	−	10.8138i	−1.07755	−	0.446334i	−0.849648	+	0.527351i	$0.823185\pi$
$588$	4.44832	+	23.8372i	0.183446	+	0.983030i
$589$	21.1176	+	50.9824i	0.870135	+	2.10069i
$590$	5.68221	−	11.8995i	0.233933	−	0.489893i
$591$	−16.3103	−	14.4222i	−0.670915	−	0.593248i
$592$	−0.0967125	+	1.20166i	−0.00397486	+	0.0493881i
$593$	−16.8587	−	29.2002i	−0.692306	−	1.19911i	−0.971081	−	0.238752i	$-0.923262\pi$
$593$	−16.8587	−	29.2002i	−0.692306	−	1.19911i	0.278775	−	0.960356i	$-0.410072\pi$
$594$	−31.2779	+	0.0118738i	−1.28335	+	0.000487189i
$595$	12.9585	+	40.3542i	0.531245	+	1.65436i
$596$	6.29305	−	6.61976i	0.257774	−	0.271156i
$597$	−0.143923	+	2.06633i	−0.00589037	+	0.0845692i
$598$	2.05819	+	4.04385i	0.0841657	+	0.165365i
$599$	−6.76452	−	25.2456i	−0.276391	−	1.03151i	−0.954903	−	0.296916i	$-0.904042\pi$
$599$	−6.76452	−	25.2456i	−0.276391	−	1.03151i	0.678513	−	0.734589i	$-0.262625\pi$
$600$	18.4234	−	25.7712i	0.752133	−	1.05211i
$601$	29.0754	+	29.0754i	1.18601	+	1.18601i	0.978161	+	0.207850i	$0.0666466\pi$
$601$	29.0754	+	29.0754i	1.18601	+	1.18601i	0.207850	+	0.978161i	$0.433353\pi$
$602$	−24.5012	+	18.6496i	−0.998592	+	0.760102i
$603$	−9.34804	−	9.50222i	−0.380682	−	0.386960i
$604$	−2.66022	+	3.65468i	−0.108243	+	0.148707i
$605$	23.8927	+	3.14554i	0.971378	+	0.127884i
$606$	19.7307	−	15.4100i	0.801505	−	0.625987i
$607$	23.2934	−	13.4485i	0.945451	−	0.545857i	0.0537863	−	0.998552i	$-0.482871\pi$
$607$	23.2934	−	13.4485i	0.945451	−	0.545857i	0.891665	+	0.452696i	$0.149538\pi$
$608$	18.9660	−	32.6829i	0.769173	−	1.32547i
$609$	9.66613	−	9.27547i	0.391691	−	0.375861i
$610$	8.37529	−	45.0777i	0.339105	−	1.82514i
$611$	17.3365	+	13.3028i	0.701360	+	0.538172i
$612$	13.7696	−	24.8213i	0.556602	−	1.00334i
$613$	22.9875	+	29.9579i	0.928458	+	1.20999i	0.977445	+	0.211190i	$0.0677339\pi$
$613$	22.9875	+	29.9579i	0.928458	+	1.20999i	−0.0489875	+	0.998799i	$0.515599\pi$
$614$	−8.76590	+	7.88583i	−0.353763	+	0.318246i
$615$	7.29623	−	4.83215i	0.294212	−	0.194851i
$616$	−22.0353	+	22.9997i	−0.887827	+	0.926682i
$617$	−4.75643	−	4.75643i	−0.191487	−	0.191487i	0.604852	−	0.796338i	$-0.293232\pi$
$617$	−4.75643	−	4.75643i	−0.191487	−	0.191487i	−0.796338	+	0.604852i	$0.793232\pi$
$618$	−3.05284	−	0.790066i	−0.122803	−	0.0317811i
$619$	18.2010	+	23.7200i	0.731559	+	0.953387i	0.999951	−	0.00992317i	$-0.00315870\pi$
$619$	18.2010	+	23.7200i	0.731559	+	0.953387i	−0.268391	+	0.963310i	$0.586492\pi$
$620$	−15.8424	−	53.6574i	−0.636247	−	2.15493i
$621$	−1.19234	−	3.65941i	−0.0478470	−	0.146847i
$622$	−14.2929	−	20.8160i	−0.573092	−	0.834645i
$623$	−12.6449	−	26.7471i	−0.506606	−	1.07160i
$624$	29.6748	+	4.48030i	1.18794	+	0.179356i
$625$	−13.4379	+	7.75839i	−0.537517	+	0.310336i
$626$	−2.59248	−	33.1279i	−0.103616	−	1.32406i
$627$	−46.5675	−	16.0202i	−1.85973	−	0.639786i
$628$	−9.64973	−	15.7782i	−0.385066	−	0.629621i
$629$	−0.545631	+	1.31727i	−0.0217557	+	0.0525230i
$630$	33.1447	−	18.6067i	1.32052	−	0.741307i
$631$	−16.5893	−	16.5893i	−0.660411	−	0.660411i	0.295066	−	0.955477i	$-0.404658\pi$
$631$	−16.5893	−	16.5893i	−0.660411	−	0.660411i	−0.955477	+	0.295066i	$0.904658\pi$
$632$	−21.3789	−	0.588214i	−0.850406	−	0.0233979i
$633$	23.8147	−	1.46312i	0.946550	−	0.0581538i
$634$	4.49231	−	13.8051i	0.178412	−	0.548271i
$635$	41.0849	−	5.40893i	1.63041	−	0.214647i
$636$	−15.7906	−	10.0733i	−0.626137	−	0.399431i
$637$	−29.5324	+	6.87539i	−1.17012	+	0.272413i
$638$	17.3009	+	3.21446i	0.684951	+	0.127262i
$639$	−4.82927	−	39.1539i	−0.191043	−	1.54890i
$640$	−22.6143	+	30.9242i	−0.893911	+	1.22239i
$641$	22.9796	+	13.2673i	0.907641	+	0.524027i	0.879671	−	0.475582i	$-0.157763\pi$
$641$	22.9796	+	13.2673i	0.907641	+	0.524027i	0.0279694	+	0.999609i	$0.491096\pi$
$642$	2.98144	+	21.2400i	0.117668	+	0.838277i
$643$	13.2242	+	31.9259i	0.521510	+	1.25904i	0.936965	+	0.349422i	$0.113622\pi$
$643$	13.2242	+	31.9259i	0.521510	+	1.25904i	−0.415455	+	0.909614i	$0.636378\pi$
$644$	−3.53025	−	1.70263i	−0.139111	−	0.0670931i
$645$	40.0219	+	26.9791i	1.57586	+	1.06230i
$646$	33.2252	−	29.8895i	1.30723	−	1.17599i
$647$	−16.6405	+	4.45881i	−0.654206	+	0.175294i	−0.570630	−	0.821207i	$-0.693301\pi$
$647$	−16.6405	+	4.45881i	−0.654206	+	0.175294i	−0.0835761	+	0.996501i	$0.526634\pi$
$648$	−24.2759	−	7.66033i	−0.953647	−	0.300926i
$649$	11.3210	+	3.03345i	0.444387	+	0.119073i
$650$	33.2134	+	21.5899i	1.30274	+	0.846827i
$651$	5.71418	−	37.4230i	0.223957	−	1.46672i
$652$	−0.151866	−	6.00242i	−0.00594752	−	0.235073i
$653$	−18.6253	−	14.2917i	−0.728864	−	0.559277i	0.176302	−	0.984336i	$-0.443587\pi$
$653$	−18.6253	−	14.2917i	−0.728864	−	0.559277i	−0.905165	+	0.425059i	$0.860253\pi$
$654$	0.874831	+	0.107565i	0.0342086	+	0.00420613i
$655$	−26.1743	+	45.3353i	−1.02272	+	1.77140i
$656$	−5.01123	+	3.24174i	−0.195655	+	0.126569i
$657$	1.62875	−	3.84294i	0.0635435	−	0.149928i
$658$	−18.8753	−	0.0733283i	−0.735836	−	0.00285863i
$659$	15.1499	+	36.5751i	0.590156	+	1.42476i	0.883352	+	0.468710i	$0.155281\pi$
$659$	15.1499	+	36.5751i	0.590156	+	1.42476i	−0.293197	+	0.956052i	$0.594719\pi$
$660$	45.2375	+	21.1282i	1.76087	+	0.822415i
$661$	−32.7974	+	25.1664i	−1.27567	+	0.978858i	−0.275829	+	0.961207i	$0.588952\pi$
$661$	−32.7974	+	25.1664i	−1.27567	+	0.978858i	−0.999844	+	0.0176512i	$0.994381\pi$
$662$	−7.52172	+	3.82832i	−0.292340	+	0.148792i
$663$	31.7693	+	15.8287i	1.23382	+	0.614736i
$664$	−50.8087	−	8.11644i	−1.97176	−	0.314979i
$665$	58.8812	−	10.7035i	2.28332	−	0.415062i
$666$	1.25521	+	0.243851i	0.0486384	+	0.00944902i
$667$	0.282632	+	2.14680i	0.0109436	+	0.0831245i
$668$	23.3212	+	2.47201i	0.902323	+	0.0956450i
$669$	−13.1794	+	38.3099i	−0.509546	+	1.48115i
$670$	7.09380	+	20.0605i	0.274057	+	0.775003i
$671$	40.7513			1.57318
$672$	−22.7400	+	12.4455i	−0.877215	+	0.480097i
$673$	40.4873			1.56067			0.780335	−	0.625362i	$-0.215049\pi$
$673$	40.4873			1.56067			0.780335	+	0.625362i	$0.215049\pi$
$674$	8.54200	+	24.1558i	0.329025	+	0.930447i
$675$	−24.9889	−	22.4629i	−0.961822	−	0.864598i
$676$	−1.21513	+	11.4636i	−0.0467357	+	0.440908i
$677$	−4.72791	−	35.9120i	−0.181708	−	1.38021i	−0.802695	−	0.596390i	$-0.796601\pi$
$677$	−4.72791	−	35.9120i	−0.181708	−	1.38021i	0.620986	−	0.783821i	$-0.286732\pi$
$678$	1.97511	−	0.0169041i	0.0758538	−	0.000649196i
$679$	−28.8079	−	33.9658i	−1.10555	−	1.30349i
$680$	−36.6920	+	26.5840i	−1.40707	+	1.01945i
$681$	13.7347	−	27.5664i	0.526315	−	1.05635i
$682$	44.3167	−	22.5558i	1.69697	−	0.863706i
$683$	36.2635	−	27.8259i	1.38758	−	1.06473i	0.398532	−	0.917155i	$-0.369520\pi$
$683$	36.2635	−	27.8259i	1.38758	−	1.06473i	0.989051	−	0.147575i	$-0.0471467\pi$
$684$	−32.2102	−	23.8511i	−1.23159	−	0.911968i
$685$	5.08689	+	12.2808i	0.194360	+	0.469227i
$686$	16.7012	−	20.1760i	0.637654	−	0.770323i
$687$	−12.3033	−	2.49963i	−0.469402	−	0.0953670i
$688$	−27.0951	−	18.6926i	−1.03299	−	0.712650i
$689$	11.7106	−	20.2833i	0.446138	−	0.772733i
$690$	−0.749756	+	6.09779i	−0.0285427	+	0.232139i
$691$	24.9616	+	19.1537i	0.949585	+	0.728642i	0.962502	−	0.271275i	$-0.0874452\pi$
$691$	24.9616	+	19.1537i	0.949585	+	0.728642i	−0.0129174	+	0.999917i	$0.504112\pi$
$692$	−17.1622	+	0.434215i	−0.652407	+	0.0165064i
$693$	21.6409	+	25.9428i	0.822070	+	0.985484i
$694$	−17.2225	−	11.1953i	−0.653759	−	0.424967i
$695$	66.1604	+	17.7276i	2.50961	+	0.672447i
$696$	12.6381	+	6.73687i	0.479046	+	0.255360i
$697$	−6.81825	+	1.82694i	−0.258260	+	0.0692005i
$698$	−20.6321	+	18.5607i	−0.780936	+	0.702532i
$699$	−17.4610	+	25.9023i	−0.660435	+	0.979714i
$700$	−34.1234	+	2.53705i	−1.28974	+	0.0958913i
$701$	3.74296	+	9.03631i	0.141370	+	0.341297i	0.978668	−	0.205450i	$-0.0658659\pi$
$701$	3.74296	+	9.03631i	0.141370	+	0.341297i	−0.837298	+	0.546747i	$0.815866\pi$
$702$	8.22695	−	30.7501i	0.310506	−	1.16059i
$703$	1.74352	+	1.00662i	0.0657581	+	0.0379655i
$704$	−30.6949	−	14.7409i	−1.15686	−	0.555567i
$705$	9.39596	+	28.0560i	0.353872	+	1.05665i
$706$	−11.9554	−	2.22128i	−0.449949	−	0.0835990i
$707$	−26.4308	−	5.71321i	−0.994033	−	0.214868i
$708$	8.04175	+	5.13007i	0.302228	+	0.192800i
$709$	−20.6565	+	2.71948i	−0.775772	+	0.102132i	−0.508008	−	0.861352i	$-0.669618\pi$
$709$	−20.6565	+	2.71948i	−0.775772	+	0.102132i	−0.267764	+	0.963485i	$0.586285\pi$
$710$	−19.4866	+	59.8834i	−0.731318	+	2.24738i
$711$	−3.14473	+	22.4653i	−0.117937	+	0.842513i
$712$	22.9711	−	21.7409i	0.860880	−	0.814776i
$713$	4.32671	+	4.32671i	0.162036	+	0.162036i
$714$	−30.1167	+	5.74132i	−1.12709	+	0.214863i
$715$	−23.8923	+	57.6810i	−0.893520	+	2.15715i
$716$	−4.39544	+	2.68818i	−0.164265	+	0.100462i
$717$	−2.67907	+	7.78752i	−0.100052	+	0.290830i
$718$	−2.46405	−	31.4867i	−0.0919574	−	1.17507i
$719$	5.14528	−	2.97063i	0.191887	−	0.110786i	−0.400979	−	0.916087i	$-0.631330\pi$
$719$	5.14528	−	2.97063i	0.191887	−	0.110786i	0.592865	+	0.805302i	$0.297997\pi$
$720$	29.9255	+	27.4890i	1.11526	+	1.02445i
$721$	1.45576	+	3.07931i	0.0542154	+	0.114679i
$722$	−20.5100	−	29.8705i	−0.763303	−	1.11167i
$723$	−7.82074	−	8.99176i	−0.290857	−	0.334407i
$724$	7.14107	−	2.10841i	0.265396	−	0.0783585i
$725$	11.5080	+	14.9976i	0.427398	+	0.556996i
$726$	−4.36757	+	16.8764i	−0.162096	+	0.626342i
$727$	−37.3822	−	37.3822i	−1.38643	−	1.38643i	−0.832690	−	0.553740i	$-0.813200\pi$
$727$	−37.3822	−	37.3822i	−1.38643	−	1.38643i	−0.553740	−	0.832690i	$-0.686800\pi$
$728$	−16.8052	−	27.7194i	−0.622840	−	1.02735i
$729$	−10.9413	+	24.6837i	−0.405234	+	0.914213i
$730$	−4.95328	+	4.45599i	−0.183329	+	0.164923i
$731$	−23.7000	−	30.8864i	−0.876576	−	1.14238i
$732$	31.6248	+	9.99248i	1.16888	+	0.369333i
$733$	2.60492	+	1.99883i	0.0962150	+	0.0738284i	0.655749	−	0.754979i	$-0.272353\pi$
$733$	2.60492	+	1.99883i	0.0962150	+	0.0738284i	−0.559534	+	0.828808i	$0.689020\pi$
$734$	0.865998	−	4.66100i	0.0319646	−	0.172041i
$735$	−38.3599	−	14.6320i	−1.41493	−	0.539708i
$736$	0.556091	−	4.15294i	0.0204978	−	0.153079i
$737$	−16.3782	+	9.45596i	−0.603299	+	0.348315i
$738$	2.82521	+	5.66499i	0.103997	+	0.208531i
$739$	2.28338	+	0.300613i	0.0839956	+	0.0110582i	0.172407	−	0.985026i	$-0.444846\pi$
$739$	2.28338	+	0.300613i	0.0839956	+	0.0110582i	−0.0884112	+	0.996084i	$0.528179\pi$
$740$	−1.65025	−	1.20121i	−0.0606643	−	0.0441572i
$741$	28.0142	−	41.5574i	1.02913	−	1.52665i
$742$	2.56270	+	20.0677i	0.0940795	+	0.736710i
$743$	19.2251	+	19.2251i	0.705301	+	0.705301i	0.965543	−	0.260242i	$-0.0838025\pi$
$743$	19.2251	+	19.2251i	0.705301	+	0.705301i	−0.260242	+	0.965543i	$0.583802\pi$
$744$	39.9225	−	6.63753i	1.46363	−	0.243344i
$745$	4.00246	+	14.9374i	0.146639	+	0.547263i
$746$	9.35367	+	18.3777i	0.342462	+	0.672855i
$747$	−14.5555	+	52.5972i	−0.532557	+	1.92443i
$748$	−29.1878	−	27.7473i	−1.06721	−	1.01454i
$749$	15.5608	−	17.1628i	0.568578	−	0.627115i
$750$	4.75097	+	11.1978i	0.173481	+	0.408887i
$751$	−5.00830	−	8.67463i	−0.182755	−	0.316542i	0.760062	−	0.649850i	$-0.225168\pi$
$751$	−5.00830	−	8.67463i	−0.182755	−	0.316542i	−0.942818	+	0.333308i	$0.891835\pi$
$752$	−6.20160	−	19.2021i	−0.226149	−	0.700228i
$753$	11.5407	−	13.0516i	0.420565	−	0.475625i
$754$	−7.71699	+	16.1606i	−0.281036	+	0.588535i
$755$	−2.92884	−	7.07085i	−0.106591	−	0.257335i
$756$	10.4329	+	25.4392i	0.379443	+	0.925215i
$757$	38.6269	+	15.9998i	1.40392	+	0.581522i	0.950766	−	0.309910i	$-0.100299\pi$
$757$	38.6269	+	15.9998i	1.40392	+	0.581522i	0.453153	+	0.891433i	$0.350299\pi$
$758$	22.6495	+	1.19705i	0.822665	+	0.0434789i
$759$	−5.45032	+	0.334855i	−0.197834	+	0.0121545i
$760$	30.4531	+	56.2656i	1.10465	+	2.04097i
$761$	−12.9465	−	3.46901i	−0.469310	−	0.125751i	0.0164104	−	0.999865i	$-0.494776\pi$
$761$	−12.9465	−	3.46901i	−0.469310	−	0.125751i	−0.485721	+	0.874114i	$0.661443\pi$
$762$	0.256541	+	29.9749i	0.00929351	+	1.08588i
$763$	−0.515767	−	0.800230i	−0.0186720	−	0.0289703i
$764$	−37.3434	−	14.3727i	−1.35104	−	0.519986i
$765$	23.6881	+	41.8151i	0.856446	+	1.51183i
$766$	2.94015	+	2.51337i	0.106232	+	0.0908119i
$767$	−5.96392	+	10.3298i	−0.215345	+	0.372988i
$768$	−20.2061	−	18.9662i	−0.729123	−	0.684382i
$769$	−39.8183			−1.43588			−0.717942	−	0.696103i	$-0.754916\pi$
$769$	−39.8183			−1.43588			−0.717942	+	0.696103i	$0.754916\pi$
$770$	−13.7553	−	52.1449i	−0.495707	−	1.87917i
$771$	13.7412	−	2.67493i	0.494878	−	0.0963353i
$772$	6.20351	+	39.3929i	0.223269	+	1.41778i
$773$	21.4661	−	16.4715i	0.772081	−	0.592438i	−0.145791	−	0.989315i	$-0.546573\pi$
$773$	21.4661	−	16.4715i	0.772081	−	0.592438i	0.917872	+	0.396877i	$0.129906\pi$
$774$	−22.9030	+	26.3525i	−0.823232	+	0.947222i
$775$	51.5997	+	13.8261i	1.85352	+	0.496648i
$776$	24.9312	−	40.5632i	0.894980	−	1.45613i
$777$	−0.665755	−	1.21008i	−0.0238838	−	0.0434114i
$778$	9.77016	−	15.0302i	0.350277	−	0.538857i
$779$	1.30096	+	9.88177i	0.0466117	+	0.354051i
$780$	−32.6852	+	38.9045i	−1.17032	+	1.39300i
$781$	−55.4933	−	7.30583i	−1.98571	−	0.261423i
$782$	2.13538	−	4.47183i	0.0763611	−	0.159912i
$783$	8.59359	−	12.5258i	0.307110	−	0.447635i
$784$	26.0524	+	10.2602i	0.930444	+	0.366434i
$785$	31.3143			1.11766
$786$	−30.2384	−	22.7943i	−1.07857	−	0.813045i
$787$	3.30379	−	25.0947i	0.117767	−	0.894531i	−0.825942	−	0.563755i	$-0.809356\pi$
$787$	3.30379	−	25.0947i	0.117767	−	0.894531i	0.943709	−	0.330776i	$-0.107310\pi$
$788$	−24.1113	+	7.11889i	−0.858928	+	0.253600i
$789$	14.8867	+	1.03688i	0.529981	+	0.0369140i
$790$	19.7351	−	30.3600i	0.702143	−	1.08016i
$791$	−1.37997	−	1.62704i	−0.0490660	−	0.0578510i
$792$	−19.1627	+	30.6137i	−0.680917	+	1.08781i
$793$	−10.7339	+	40.0596i	−0.381173	+	1.42256i
$794$	−10.9624	+	33.6881i	−0.389041	+	1.19555i
$795$	28.4987	−	13.9094i	1.01075	−	0.493316i
$796$	1.93374	+	1.40756i	0.0685396	+	0.0498896i
$797$	−1.96629	−	4.74704i	−0.0696496	−	0.168149i	0.885221	−	0.465170i	$-0.154007\pi$
$797$	−1.96629	−	4.74704i	−0.0696496	−	0.168149i	−0.954871	+	0.297021i	$0.904007\pi$
$798$	2.48680	+	43.2194i	0.0880317	+	1.52995i
$799$		−	23.8653i		−	0.844295i
$800$	−13.9238	−	33.8265i	−0.492282	−	1.19595i
$801$	−20.2036	−	26.7806i	−0.713860	−	0.946245i
$802$	20.5802	+	17.5929i	0.726710	+	0.621225i
$803$	−4.69810	−	3.60498i	−0.165792	−	0.127217i
$804$	−15.0289	+	3.32219i	−0.530027	+	0.117165i
$805$	5.57780	−	3.59502i	0.196591	−	0.126708i
$806$	10.4999	+	49.5057i	0.369842	+	1.74376i
$807$	−8.21345	+	16.4849i	−0.289127	+	0.580297i
$808$	−2.98359	−	28.7539i	−0.104962	−	1.01156i
$809$	−30.6866	+	8.22245i	−1.07888	+	0.289086i	−0.754139	−	0.656715i	$-0.771945\pi$
$809$	−30.6866	+	8.22245i	−1.07888	+	0.289086i	−0.324745	+	0.945801i	$0.605279\pi$
$810$	32.5092	−	28.2971i	1.14226	−	0.994260i
$811$	9.19524	−	22.1993i	0.322889	−	0.779522i	−0.676195	−	0.736723i	$-0.736372\pi$
$811$	9.19524	−	22.1993i	0.322889	−	0.779522i	0.999084	−	0.0427995i	$-0.0136277\pi$
$812$	−3.15069	−	15.1448i	−0.110568	−	0.531478i
$813$	0.225052	+	1.15610i	0.00789293	+	0.0405463i
$814$	0.781749	−	1.63711i	0.0274003	−	0.0573805i
$815$	8.80404	+	5.08301i	0.308392	+	0.178050i
$816$	−15.8472	−	28.6902i	−0.554763	−	1.00436i
$817$	−47.6067	+	27.4858i	−1.66555	+	0.961605i
$818$	−17.3382	+	11.9049i	−0.606217	+	0.416247i
$819$	−31.2027	+	14.4402i	−1.09031	+	0.504583i
$820$	−0.255584	−	10.1019i	−0.00892539	−	0.352772i
$821$	−31.5942	+	4.15946i	−1.10265	+	0.145166i	−0.659807	−	0.751435i	$-0.729362\pi$
$821$	−31.5942	+	4.15946i	−1.10265	+	0.145166i	−0.442839	+	0.896601i	$0.646029\pi$
$822$	−9.26624	+	2.56808i	−0.323197	+	0.0895720i
$823$	−2.86056	+	0.766486i	−0.0997130	+	0.0267180i	−0.308331	−	0.951279i	$-0.599770\pi$
$823$	−2.86056	+	0.766486i	−0.0997130	+	0.0267180i	0.208618	+	0.977997i	$0.433104\pi$
$824$	−2.64459	+	2.50297i	−0.0921288	+	0.0871949i
$825$	−39.7465	+	26.3233i	−1.38379	+	0.916459i
$826$	−1.30512	−	10.2200i	−0.0454109	−	0.355600i
$827$	0.327050	−	0.789570i	0.0113727	−	0.0274560i	−0.918091	−	0.396369i	$-0.870270\pi$
$827$	0.327050	−	0.789570i	0.0113727	−	0.0274560i	0.929464	+	0.368913i	$0.120270\pi$
$828$	−4.31180	−	1.07659i	−0.149845	−	0.0374142i
$829$	−3.62904	+	27.5653i	−0.126042	+	0.957382i	0.805206	+	0.592995i	$0.202055\pi$
$829$	−3.62904	+	27.5653i	−0.126042	+	0.957382i	−0.931248	+	0.364387i	$0.881279\pi$
$830$	56.6063	−	66.2182i	1.96483	−	2.29847i
$831$	12.3084	−	4.12209i	0.426974	−	0.142994i
$832$	22.5757	−	26.2912i	0.782673	−	0.911483i
$833$	25.5916	+	21.0170i	0.886695	+	0.728197i
$834$	−18.5682	+	45.9357i	−0.642965	+	1.59062i
$835$	−24.1718	+	31.5013i	−0.836500	+	1.09015i
$836$	−44.2237	+	35.7469i	−1.52951	+	1.23633i
$837$	−2.28178	−	42.8648i	−0.0788698	−	1.48162i
$838$	−28.6316	+	25.7571i	−0.989062	+	0.889764i
$839$	−18.8037	−	18.8037i	−0.649175	−	0.649175i	0.303619	−	0.952794i	$-0.401805\pi$
$839$	−18.8037	−	18.8037i	−0.649175	−	0.649175i	−0.952794	+	0.303619i	$0.901805\pi$
$840$	2.11158	−	43.8397i	0.0728563	−	1.51261i
$841$	14.4631	−	14.4631i	0.498727	−	0.498727i
$842$	1.41162	−	26.7094i	0.0486478	−	0.920465i
$843$	−7.32904	+	3.57710i	−0.252425	+	0.123202i
$844$	13.1675	−	24.2004i	0.453243	−	0.833012i
$845$	−15.4846	−	11.8817i	−0.532686	−	0.408745i
$846$	−20.9726	+	4.26923i	−0.721053	+	0.146779i
$847$	17.0227	−	8.04760i	0.584908	−	0.276519i
$848$	−19.5371	+	9.27634i	−0.670908	+	0.318551i
$849$	−7.39825	+	2.47767i	−0.253907	+	0.0850335i
$850$	−3.37532	−	43.1314i	−0.115773	−	1.47940i
$851$	0.221326	+	0.0291382i	0.00758697	+	0.000998843i
$852$	−41.2738	−	19.2770i	−1.41402	−	0.660419i
$853$	49.3853	+	20.4561i	1.69092	+	0.700403i	0.999752	−	0.0222895i	$-0.00709557\pi$
$853$	49.3853	+	20.4561i	1.69092	+	0.700403i	0.691170	+	0.722692i	$0.257096\pi$
$854$	−13.5803	−	33.1494i	−0.464708	−	1.13435i
$855$	62.9040	−	25.4550i	2.15127	−	0.870541i
$856$	22.6118	+	10.1034i	0.772854	+	0.345326i
$857$	10.0926	+	37.6661i	0.344757	+	1.28665i	0.892896	+	0.450263i	$0.148670\pi$
$857$	10.0926	+	37.6661i	0.344757	+	1.28665i	−0.548139	+	0.836387i	$0.684664\pi$
$858$	−39.3037	−	22.2457i	−1.34180	−	0.759455i
$859$	−5.77355	−	43.8545i	−0.196991	−	1.49630i	−0.749062	−	0.662499i	$-0.769496\pi$
$859$	−5.77355	−	43.8545i	−0.196991	−	1.49630i	0.552071	−	0.833797i	$-0.313838\pi$
$860$	50.9346	−	22.6236i	1.73686	−	0.771458i
$861$	2.74634	−	6.26183i	0.0935952	−	0.213402i
$862$	17.6318	+	3.27593i	0.600541	+	0.111579i
$863$	−17.6402	−	30.5538i	−0.600480	−	1.04006i	−0.992748	−	0.120212i	$-0.961643\pi$
$863$	−17.6402	−	30.5538i	−0.600480	−	1.04006i	0.392268	−	0.919851i	$-0.371691\pi$
$864$	−22.3778	+	19.0587i	−0.761308	+	0.648391i
$865$	14.5334	−	25.1725i	0.494149	−	0.855892i
$866$	1.13517	+	3.21014i	0.0385747	+	0.109085i
$867$	−1.78070	−	9.14754i	−0.0604758	−	0.310667i
$868$	−33.1166	−	28.5330i	−1.12405	−	0.968473i
$869$	29.7344	+	12.3164i	1.00867	+	0.417805i
$870$	−20.8948	+	12.3033i	−0.708401	+	0.417120i
$871$	−4.98142	−	18.5909i	−0.168789	−	0.629930i
$872$	0.641556	−	0.790109i	0.0217258	−	0.0267565i
$873$	−39.8120	−	31.0694i	−1.34743	−	1.05154i
$874$	−5.86668	−	3.81356i	−0.198443	−	0.128995i
$875$	6.00508	−	11.6860i	0.203009	−	0.395059i
$876$	−2.76197	−	3.94963i	−0.0933183	−	0.133446i
$877$	−0.0633581	+	0.0825699i	−0.00213945	+	0.00278819i	−0.794422	−	0.607366i	$-0.792226\pi$
$877$	−0.0633581	+	0.0825699i	−0.00213945	+	0.00278819i	0.792282	+	0.610155i	$0.208893\pi$
$878$	−2.63701	−	33.6970i	−0.0889949	−	1.13722i
$879$	30.4419	+	26.9179i	1.02678	+	0.907918i
$880$	48.4067	−	31.3140i	1.63179	−	1.05560i
$881$	−36.9961			−1.24643			−0.623216	−	0.782050i	$-0.714174\pi$
$881$	−36.9961			−1.24643			−0.623216	+	0.782050i	$0.714174\pi$
$882$	13.8915	−	26.2493i	0.467751	−	0.883860i
$883$	−51.9668	+	21.5254i	−1.74882	+	0.724386i	−0.750868	+	0.660452i	$0.770365\pi$
$883$	−51.9668	+	21.5254i	−1.74882	+	0.724386i	−0.997954	+	0.0639341i	$0.979635\pi$
$884$	34.9645	−	21.3837i	1.17598	−	0.719213i
$885$	−14.5137	+	7.08373i	−0.487873	+	0.238117i
$886$	−32.2806	+	16.4298i	−1.08449	+	0.551971i
$887$	−23.2011	−	6.21672i	−0.779017	−	0.208737i	−0.152666	−	0.988278i	$-0.548786\pi$
$887$	−23.2011	−	6.21672i	−0.779017	−	0.208737i	−0.626351	+	0.779541i	$0.715452\pi$
$888$	1.00810	−	1.07878i	0.0338296	−	0.0362014i
$889$	24.6925	−	20.9428i	0.828161	−	0.702400i
$890$	11.1105	+	52.3848i	0.372425	+	1.75594i
$891$	30.0058	+	23.8140i	1.00523	+	0.797801i
$892$	29.4081	+	36.3817i	0.984656	+	1.21815i
$893$	−33.4097	−	4.39847i	−1.11801	−	0.147189i
$894$	−11.0778	+	1.55498i	−0.370497	+	0.0520064i
$895$		−	8.72342i		−	0.291592i
$896$	−1.76201	+	29.8814i	−0.0588645	+	0.998266i
$897$	1.10645	−	5.44601i	0.0369433	−	0.181837i
$898$	−5.80331	−	16.4111i	−0.193659	−	0.547646i
$899$	−3.15221	+	23.9434i	−0.105132	+	0.798558i
$900$	−37.2997	+	10.6819i	−1.24332	+	0.356064i
$901$	−25.3601	+	3.33871i	−0.844866	+	0.111229i
$902$	8.78607	−	1.86348i	0.292544	−	0.0620470i
$903$	37.7037	+	0.777631i	1.25470	+	0.0258779i
$904$	1.19427	−	1.94307i	0.0397207	−	0.0646257i
$905$	−3.26283	+	12.1770i	−0.108460	+	0.404779i
$906$	5.33515	−	1.47860i	0.177249	−	0.0491233i
$907$	−30.2582	−	39.4332i	−1.00471	−	1.30936i	−0.950465	−	0.310831i	$-0.899393\pi$
$907$	−30.2582	−	39.4332i	−1.00471	−	1.30936i	−0.0542414	−	0.998528i	$-0.517274\pi$
$908$	−18.5548	−	30.3389i	−0.615764	−	1.00683i
$909$	−30.6609	−	0.250771i	−1.01696	−	0.00831756i
$910$	54.8830	+	0.213214i	1.81935	+	0.00706798i
$911$			19.0128i			0.629922i	0.949105	+	0.314961i	$0.101991\pi$
$911$			19.0128i			0.629922i	−0.949105	+	0.314961i	$0.898009\pi$
$912$	−43.0849	+	16.8972i	−1.42668	+	0.559523i
$913$	67.0557	+	38.7146i	2.21922	+	1.28127i
$914$	26.3049	−	2.05853i	0.870088	−	0.0680902i
$915$	−42.3695	+	36.8516i	−1.40069	+	1.21828i
$916$	−9.98832	+	10.5069i	−0.330023	+	0.347156i
$917$	1.99999	+	40.8526i	0.0660456	+	1.34907i
$918$	−32.1128	+	13.3159i	−1.05988	+	0.439489i
$919$	−3.03291	+	11.3190i	−0.100046	+	0.373378i	−0.997736	−	0.0672497i	$-0.978578\pi$
$919$	−3.03291	+	11.3190i	−0.100046	+	0.373378i	0.897690	+	0.440628i	$0.145244\pi$
$920$	5.50726	+	4.47180i	0.181569	+	0.147431i
$921$	14.4138	−	0.885548i	0.474950	−	0.0291798i
$922$	−32.4520	+	29.1939i	−1.06875	+	0.961451i
$923$	21.7988	−	52.6270i	0.717517	−	1.73224i
$924$	38.6524	−	5.27257i	1.27157	−	0.173455i
$925$	1.80057	−	0.745821i	0.0592024	−	0.0245225i
$926$	3.14390	−	1.11175i	0.103315	−	0.0365344i
$927$	2.32598	+	3.08316i	0.0763952	+	0.101264i
$928$	14.3398	−	8.23686i	0.470727	−	0.270388i
$929$	4.65243	−	2.68608i	0.152641	−	0.0881274i	−0.421734	−	0.906720i	$-0.638578\pi$
$929$	4.65243	−	2.68608i	0.152641	−	0.0881274i	0.574375	+	0.818592i	$0.305245\pi$
$930$	−25.6792	+	63.5274i	−0.842053	+	2.08314i
$931$	34.1389	−	31.9528i	1.11886	−	1.04721i
$932$	14.6421	+	32.9651i	0.479617	+	1.07981i
$933$	−2.14880	+	30.8508i	−0.0703486	+	1.01001i
$934$	2.73425	−	8.40251i	0.0894674	−	0.274938i
$935$	65.8619	−	17.6476i	2.15391	−	0.577140i
$936$	−25.0466	−	26.9011i	−0.818673	−	0.879291i
$937$	11.3358	−	11.3358i	0.370324	−	0.370324i	−0.497271	−	0.867595i	$-0.665665\pi$
$937$	11.3358	−	11.3358i	0.370324	−	0.370324i	0.867595	+	0.497271i	$0.165665\pi$
$938$	13.1500	+	10.1718i	0.429363	+	0.332120i
$939$	−22.7484	+	33.7458i	−0.742365	+	1.10125i
$940$	33.2137	+	8.00499i	1.08331	+	0.261094i
$941$	0.551920	−	4.19225i	0.0179921	−	0.136664i	−0.980091	−	0.198548i	$-0.936378\pi$
$941$	0.551920	−	4.19225i	0.0179921	−	0.136664i	0.998083	+	0.0618841i	$0.0197109\pi$
$942$	−2.76435	+	22.4825i	−0.0900673	+	0.732520i
$943$	0.552591	+	0.957116i	0.0179948	+	0.0311680i
$944$	9.94979	−	4.72422i	0.323838	−	0.153760i
$945$	−45.9605	−	7.40295i	−1.49510	−	0.240818i
$946$	28.0395	+	40.8364i	0.911642	+	1.32771i
$947$	−7.52110	+	9.80169i	−0.244403	+	0.318512i	−0.899406	−	0.437114i	$-0.856001\pi$
$947$	−7.52110	+	9.80169i	−0.244403	+	0.318512i	0.655003	+	0.755626i	$0.272667\pi$
$948$	20.0552	+	16.8492i	0.651361	+	0.547235i
$949$	4.78128	−	3.66880i	0.155207	−	0.119094i
$950$	−61.0029	−	3.22409i	−1.97920	−	0.104603i
$951$	−14.8241	+	9.81773i	−0.480706	+	0.318362i
$952$	−12.8445	+	32.9898i	−0.416291	+	1.06921i
$953$	−2.64537	+	2.64537i	−0.0856919	+	0.0856919i	−0.748653	−	0.662962i	$-0.769299\pi$
$953$	−2.64537	+	2.64537i	−0.0856919	+	0.0856919i	0.662962	+	0.748653i	$0.269299\pi$
$954$	7.47065	+	21.6889i	0.241871	+	0.702204i
$955$	53.7480	−	41.2423i	1.73924	−	1.33457i
$956$	5.97798	+	7.39556i	0.193342	+	0.239189i
$957$	−14.1438	−	16.2615i	−0.457203	−	0.525661i
$958$	9.62074	−	51.7810i	0.310832	−	1.67297i
$959$	8.53903	+	5.91210i	0.275740	+	0.190912i
$960$	45.2441	−	12.4314i	1.46025	−	0.401222i
$961$	18.6222	+	32.2545i	0.600715	+	1.04047i
$962$	1.40341	+	1.19970i	0.0452476	+	0.0386797i
$963$	13.3199	−	22.6411i	0.429229	−	0.729600i
$964$	−13.5931	+	2.14061i	−0.437804	+	0.0689444i
$965$	−62.3790	−	25.8382i	−2.00805	−	0.831762i
$966$	2.08870	+	4.32201i	0.0672028	+	0.139058i
$967$	22.6242	−	22.6242i	0.727545	−	0.727545i	−0.242585	−	0.970130i	$-0.577995\pi$
$967$	22.6242	−	22.6242i	0.727545	−	0.727545i	0.970130	+	0.242585i	$0.0779953\pi$
$968$	13.8366	+	14.6196i	0.444727	+	0.469891i
$969$	−54.6322	+	3.35647i	−1.75504	+	0.107825i
$970$	36.5658	+	71.8430i	1.17406	+	2.30674i
$971$	−3.37212	−	25.6138i	−0.108216	−	0.821985i	−0.956354	−	0.292209i	$-0.905610\pi$
$971$	−3.37212	−	25.6138i	−0.108216	−	0.821985i	0.848138	−	0.529775i	$-0.177724\pi$
$972$	17.4465	+	25.8384i	0.559595	+	0.828766i
$973$	50.9538	−	16.3622i	1.63351	−	0.524548i
$974$	−11.4764	−	16.7142i	−0.367729	−	0.535556i
$975$	−15.4072	−	46.0054i	−0.493426	−	1.47335i
$976$	29.1650	−	24.8201i	0.933548	−	0.794473i
$977$	0.435781	−	0.754795i	0.0139419	−	0.0241480i	−0.858970	−	0.512025i	$-0.828895\pi$
$977$	0.435781	−	0.754795i	0.0139419	−	0.0241480i	0.872912	+	0.487877i	$0.162229\pi$
$978$	−4.42661	+	5.87225i	−0.141547	+	0.187774i
$979$	−43.9729	+	18.2142i	−1.40538	+	0.582127i
$980$	−37.8337	+	28.5665i	−1.20855	+	0.912525i
$981$	−0.757063	−	0.769549i	−0.0241712	−	0.0245698i
$982$	39.4956	+	2.08739i	1.26035	+	0.0666113i
$983$	−8.50909	−	31.7564i	−0.271398	−	1.01287i	−0.958217	−	0.286042i	$-0.907660\pi$
$983$	−8.50909	−	31.7564i	−0.271398	−	1.01287i	0.686819	−	0.726828i	$-0.259006\pi$
$984$	7.27532	+	0.708266i	0.231929	+	0.0225787i
$985$	11.0167	−	41.1149i	0.351021	−	1.31003i
$986$	19.1328	−	4.05796i	0.609313	−	0.129232i
$987$	18.0463	+	14.4483i	0.574421	+	0.459894i
$988$	−23.4916	−	52.8889i	−0.747367	−	1.68262i
$989$	−3.71067	+	4.83584i	−0.117993	+	0.153771i
$990$	−27.2905	−	54.7218i	−0.867349	−	1.73917i
$991$	−7.82913	−	4.52015i	−0.248700	−	0.143587i	0.370469	−	0.928845i	$-0.379197\pi$
$991$	−7.82913	−	4.52015i	−0.248700	−	0.143587i	−0.619169	+	0.785258i	$0.712530\pi$
$992$	17.9787	−	43.1345i	0.570826	−	1.36952i
$993$	10.1298	+	2.05804i	0.321459	+	0.0653099i
$994$	12.5501	+	47.5760i	0.398064	+	1.50902i
$995$	−3.74129	+	1.54969i	−0.118607	+	0.0491285i
$996$	42.5451	+	46.4868i	1.34809	+	1.47299i
$997$	−3.36479	−	4.38507i	−0.106564	−	0.138877i	0.737027	−	0.675864i	$-0.236229\pi$
$997$	−3.36479	−	4.38507i	−0.106564	−	0.138877i	−0.843591	+	0.536987i	$0.819562\pi$
$998$	−17.8441	−	5.80662i	−0.564844	−	0.183805i
$999$	−1.01805	−	1.19000i	−0.0322097	−	0.0376500i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.ch.a.11.13	✓	992
3.2	odd	2	inner	672.2.ch.a.11.112	yes	992
7.2	even	3	inner	672.2.ch.a.107.97	yes	992
21.2	odd	6	inner	672.2.ch.a.107.28	yes	992
32.3	odd	8	inner	672.2.ch.a.515.28	yes	992
96.35	even	8	inner	672.2.ch.a.515.97	yes	992
224.163	odd	24	inner	672.2.ch.a.611.112	yes	992
672.611	even	24	inner	672.2.ch.a.611.13	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.ch.a.11.13	✓	992	1.1	even	1	trivial
672.2.ch.a.11.112	yes	992	3.2	odd	2	inner
672.2.ch.a.107.28	yes	992	21.2	odd	6	inner
672.2.ch.a.107.97	yes	992	7.2	even	3	inner
672.2.ch.a.515.28	yes	992	32.3	odd	8	inner
672.2.ch.a.515.97	yes	992	96.35	even	8	inner
672.2.ch.a.611.13	yes	992	672.611	even	24	inner
672.2.ch.a.611.112	yes	992	224.163	odd	24	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.ch (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33331 + 0.471485i) q^{2} +(1.63784 + 0.563452i) q^{3} +(1.55540 - 1.25727i) q^{4} +(0.441991 + 3.35725i) q^{5} +(-2.44940 + 0.0209633i) q^{6} +(1.71134 + 2.01775i) q^{7} +(-1.48105 + 2.40967i) q^{8} +(2.36504 + 1.84569i) q^{9} +O(q^{10})\)	\(q+(-1.33331 + 0.471485i) q^{2} +(1.63784 + 0.563452i) q^{3} +(1.55540 - 1.25727i) q^{4} +(0.441991 + 3.35725i) q^{5} +(-2.44940 + 0.0209633i) q^{6} +(1.71134 + 2.01775i) q^{7} +(-1.48105 + 2.40967i) q^{8} +(2.36504 + 1.84569i) q^{9} +(-2.17220 - 4.26785i) q^{10} +(3.37681 - 2.59112i) q^{11} +(3.25591 - 1.18280i) q^{12} +(1.65768 + 4.00200i) q^{13} +(-3.23308 - 1.88340i) q^{14} +(-1.16774 + 5.74769i) q^{15} +(0.838568 - 3.91111i) q^{16} +(2.36540 - 4.09699i) q^{17} +(-4.02354 - 1.34578i) q^{18} +(-5.29954 - 4.06648i) q^{19} +(4.90843 + 4.66619i) q^{20} +(1.66600 + 4.26901i) q^{21} +(-3.28065 + 5.04687i) q^{22} +(-0.715456 - 0.191706i) q^{23} +(-3.78345 + 3.11215i) q^{24} +(-6.24617 + 1.67366i) q^{25} +(-4.09708 - 4.55431i) q^{26} +(2.83361 + 4.35553i) q^{27} +(5.19867 + 0.986804i) q^{28} +(-1.11873 - 2.70084i) q^{29} +(-1.15299 - 8.21399i) q^{30} +(-7.15425 - 4.13051i) q^{31} +(0.725963 + 5.61008i) q^{32} +(6.99065 - 2.34117i) q^{33} +(-1.22213 + 6.57779i) q^{34} +(-6.01770 + 6.63724i) q^{35} +(5.99912 - 0.102695i) q^{36} +(-0.298809 + 0.0393389i) q^{37} +(8.98318 + 2.92321i) q^{38} +(0.460086 + 7.48866i) q^{39} +(-8.74448 - 3.90720i) q^{40} +(-1.05507 - 1.05507i) q^{41} +(-4.23406 - 4.90640i) q^{42} +(3.14924 - 7.60294i) q^{43} +(1.99458 - 8.27579i) q^{44} +(-5.15112 + 8.75583i) q^{45} +(1.04431 - 0.0817241i) q^{46} +(4.36881 - 2.52234i) q^{47} +(3.57716 - 5.93329i) q^{48} +(-1.14262 + 6.90612i) q^{49} +(7.53895 - 5.17647i) q^{50} +(6.18261 - 5.37743i) q^{51} +(7.60994 + 4.14058i) q^{52} +(-3.29150 - 4.28957i) q^{53} +(-5.83163 - 4.47125i) q^{54} +(10.1916 + 10.1916i) q^{55} +(-7.39668 + 1.13538i) q^{56} +(-6.38853 - 9.64628i) q^{57} +(2.76501 + 3.07359i) q^{58} +(1.67628 + 2.18457i) q^{59} +(5.41006 + 10.4081i) q^{60} +(7.59569 + 5.82838i) q^{61} +(11.4863 + 2.13411i) q^{62} +(0.323263 + 7.93067i) q^{63} +(-3.61299 - 7.13767i) q^{64} +(-12.7031 + 7.33411i) q^{65} +(-8.21684 + 6.41747i) q^{66} +(-4.40518 - 0.579954i) q^{67} +(-1.47185 - 9.34642i) q^{68} +(-1.06379 - 0.717109i) q^{69} +(4.89407 - 11.6867i) q^{70} +(-9.29859 - 9.29859i) q^{71} +(-7.95024 + 2.96542i) q^{72} +(-0.360091 - 1.34388i) q^{73} +(0.379856 - 0.193335i) q^{74} +(-11.1733 - 0.778234i) q^{75} +(-13.3556 + 0.337906i) q^{76} +(11.0071 + 2.37927i) q^{77} +(-4.14422 - 9.76775i) q^{78} +(3.78072 + 6.54839i) q^{79} +(13.5012 + 1.08661i) q^{80} +(2.18687 + 8.73027i) q^{81} +(1.90417 + 0.909277i) q^{82} +(6.96153 + 16.8066i) q^{83} +(7.95858 + 4.54543i) q^{84} +(14.8001 + 6.13042i) q^{85} +(-0.614231 + 11.6219i) q^{86} +(-0.310500 - 5.05390i) q^{87} +(1.24251 + 11.9746i) q^{88} +(-10.8012 - 2.89418i) q^{89} +(2.73977 - 14.1029i) q^{90} +(-5.23817 + 10.1936i) q^{91} +(-1.35385 + 0.601338i) q^{92} +(-9.39017 - 10.7962i) q^{93} +(-4.63572 + 5.42287i) q^{94} +(11.3099 - 19.5892i) q^{95} +(-1.97200 + 9.59746i) q^{96} -16.8335 q^{97} +(-1.73267 - 9.74668i) q^{98} +(12.7687 + 0.104434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9}+O(q^{10}) \) 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9	\( 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9} - 8 q^{10} - 4 q^{12} - 32 q^{13} - 32 q^{15} + 24 q^{16} - 4 q^{18} - 8 q^{19} - 8 q^{21} - 32 q^{22} - 44 q^{24} - 8 q^{25} - 16 q^{27} - 16 q^{28} - 36 q^{30} - 8 q^{33} + 64 q^{36} - 8 q^{37} - 4 q^{39} - 72 q^{40} - 68 q^{42} - 32 q^{43} - 4 q^{45} - 8 q^{46} - 16 q^{48} + 20 q^{51} + 16 q^{52} - 92 q^{54} - 32 q^{55} - 16 q^{57} + 24 q^{58} - 20 q^{60} - 8 q^{61} - 128 q^{64} - 20 q^{66} - 72 q^{67} - 16 q^{69} - 16 q^{70} - 4 q^{72} - 8 q^{73} + 16 q^{75} - 32 q^{76} + 136 q^{78} - 16 q^{79} - 48 q^{82} + 124 q^{84} + 48 q^{85} - 4 q^{87} - 8 q^{88} + 128 q^{90} - 64 q^{91} - 28 q^{93} - 64 q^{94} - 72 q^{96} - 64 q^{97} - 16 q^{99}+O(q^{100}) \) 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9 - 8 * q^10 - 4 * q^12 - 32 * q^13 - 32 * q^15 + 24 * q^16 - 4 * q^18 - 8 * q^19 - 8 * q^21 - 32 * q^22 - 44 * q^24 - 8 * q^25 - 16 * q^27 - 16 * q^28 - 36 * q^30 - 8 * q^33 + 64 * q^36 - 8 * q^37 - 4 * q^39 - 72 * q^40 - 68 * q^42 - 32 * q^43 - 4 * q^45 - 8 * q^46 - 16 * q^48 + 20 * q^51 + 16 * q^52 - 92 * q^54 - 32 * q^55 - 16 * q^57 + 24 * q^58 - 20 * q^60 - 8 * q^61 - 128 * q^64 - 20 * q^66 - 72 * q^67 - 16 * q^69 - 16 * q^70 - 4 * q^72 - 8 * q^73 + 16 * q^75 - 32 * q^76 + 136 * q^78 - 16 * q^79 - 48 * q^82 + 124 * q^84 + 48 * q^85 - 4 * q^87 - 8 * q^88 + 128 * q^90 - 64 * q^91 - 28 * q^93 - 64 * q^94 - 72 * q^96 - 64 * q^97 - 16 * q^99

Introduction

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