LMFDB - Embedded newform 672.2.ch.a.11.1

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			11.1
Character	$\chi$	$=$	672.11
Dual form			672.2.ch.a.611.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 + 0.00202033i) q^{2} +(-1.50647 + 0.854722i) q^{3} +(1.99999 - 0.00571435i) q^{4} +(0.202706 + 1.53970i) q^{5} +(2.12874 - 1.21180i) q^{6} +(0.529096 + 2.59231i) q^{7} +(-2.82840 + 0.0121219i) q^{8} +(1.53890 - 2.57522i) q^{9} +O(q^{10})$	\(q+(-1.41421 + 0.00202033i) q^{2} +(-1.50647 + 0.854722i) q^{3} +(1.99999 - 0.00571435i) q^{4} +(0.202706 + 1.53970i) q^{5} +(2.12874 - 1.21180i) q^{6} +(0.529096 + 2.59231i) q^{7} +(-2.82840 + 0.0121219i) q^{8} +(1.53890 - 2.57522i) q^{9} +(-0.289779 - 2.17705i) q^{10} +(-4.75742 + 3.65049i) q^{11} +(-3.00804 + 1.71804i) q^{12} +(0.106525 + 0.257175i) q^{13} +(-0.753491 - 3.66500i) q^{14} +(-1.62139 - 2.14626i) q^{15} +(3.99993 - 0.0228573i) q^{16} +(-1.06215 + 1.83970i) q^{17} +(-2.17113 + 3.64502i) q^{18} +(-1.28670 - 0.987321i) q^{19} +(0.414208 + 3.07823i) q^{20} +(-3.01277 - 3.45300i) q^{21} +(6.72062 - 5.17218i) q^{22} +(5.94161 + 1.59205i) q^{23} +(4.25054 - 2.43576i) q^{24} +(2.50004 - 0.669883i) q^{25} +(-0.151169 - 0.363485i) q^{26} +(-0.117209 + 5.19483i) q^{27} +(1.07300 + 5.18157i) q^{28} +(1.01347 + 2.44673i) q^{29} +(2.29732 + 3.03199i) q^{30} +(-6.75813 - 3.90181i) q^{31} +(-5.65671 + 0.0404063i) q^{32} +(4.04675 - 9.56562i) q^{33} +(1.49839 - 2.60387i) q^{34} +(-3.88413 + 1.34012i) q^{35} +(3.06308 - 5.15922i) q^{36} +(2.55405 - 0.336247i) q^{37} +(1.82166 + 1.39368i) q^{38} +(-0.380290 - 0.296377i) q^{39} +(-0.591997 - 4.35244i) q^{40} +(-6.08980 - 6.08980i) q^{41} +(4.26767 + 4.87719i) q^{42} +(-1.92408 + 4.64514i) q^{43} +(-9.49393 + 7.32814i) q^{44} +(4.27702 + 1.84744i) q^{45} +(-8.40592 - 2.23949i) q^{46} +(2.12691 - 1.22797i) q^{47} +(-6.00624 + 3.45326i) q^{48} +(-6.44011 + 2.74316i) q^{49} +(-3.53423 + 0.952408i) q^{50} +(0.0276674 - 3.67930i) q^{51} +(0.214519 + 0.513739i) q^{52} +(-7.16108 - 9.33250i) q^{53} +(0.155264 - 7.34683i) q^{54} +(-6.58502 - 6.58502i) q^{55} +(-1.52792 - 7.32567i) q^{56} +(2.78226 + 0.387597i) q^{57} +(-1.43820 - 3.45814i) q^{58} +(0.142134 + 0.185232i) q^{59} +(-3.25502 - 4.28323i) q^{60} +(-4.16461 - 3.19562i) q^{61} +(9.56532 + 5.50433i) q^{62} +(7.49000 + 2.62677i) q^{63} +(7.99971 - 0.0685714i) q^{64} +(-0.374379 + 0.216148i) q^{65} +(-5.70363 + 13.5360i) q^{66} +(-8.42225 - 1.10881i) q^{67} +(-2.11378 + 3.68545i) q^{68} +(-10.3116 + 2.68005i) q^{69} +(5.49027 - 1.90307i) q^{70} +(-0.125081 - 0.125081i) q^{71} +(-4.32142 + 7.30242i) q^{72} +(2.43133 + 9.07386i) q^{73} +(-3.61129 + 0.480685i) q^{74} +(-3.19367 + 3.14600i) q^{75} +(-2.57903 - 1.96728i) q^{76} +(-11.9803 - 10.4012i) q^{77} +(0.538410 + 0.418371i) q^{78} +(3.02184 + 5.23399i) q^{79} +(0.846002 + 6.15407i) q^{80} +(-4.26356 - 7.92604i) q^{81} +(8.62458 + 8.59997i) q^{82} +(-2.61245 - 6.30700i) q^{83} +(-6.04524 - 6.88876i) q^{84} +(-3.04789 - 1.26248i) q^{85} +(2.71167 - 6.57310i) q^{86} +(-3.61803 - 2.81969i) q^{87} +(13.4116 - 10.3827i) q^{88} +(-14.3185 - 3.83663i) q^{89} +(-6.05235 - 2.60403i) q^{90} +(-0.610314 + 0.412217i) q^{91} +(11.8923 + 3.15014i) q^{92} +(13.5159 + 0.101636i) q^{93} +(-3.00543 + 1.74091i) q^{94} +(1.25936 - 2.18127i) q^{95} +(8.48713 - 4.89578i) q^{96} +8.21665 q^{97} +(9.10215 - 3.89242i) q^{98} +(2.07964 + 17.8692i) 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 $

$2$	−1.41421	+	0.00202033i	−0.999999	+	0.00142859i
$2$	−1.41421	+	0.00202033i	−0.999999	+	0.00142859i
$3$	−1.50647	+	0.854722i	−0.869761	+	0.493474i
$3$	−1.50647	+	0.854722i	−0.869761	+	0.493474i
$4$	1.99999	−	0.00571435i	0.999996	−	0.00285717i
$5$	0.202706	+	1.53970i	0.0906527	+	0.688575i	0.975073	+	0.221884i	$0.0712207\pi$
$5$	0.202706	+	1.53970i	0.0906527	+	0.688575i	−0.884420	+	0.466691i	$0.845446\pi$
$6$	2.12874	−	1.21180i	0.869055	−	0.494716i
$7$	0.529096	+	2.59231i	0.199979	+	0.979800i
$7$	0.529096	+	2.59231i	0.199979	+	0.979800i
$8$	−2.82840	+	0.0121219i	−0.999991	+	0.00428575i
$9$	1.53890	−	2.57522i	0.512967	−	0.858408i
$10$	−0.289779	−	2.17705i	−0.0916363	−	0.688445i
$11$	−4.75742	+	3.65049i	−1.43441	+	1.10067i	−0.456968	+	0.889483i	$0.651065\pi$
$11$	−4.75742	+	3.65049i	−1.43441	+	1.10067i	−0.977447	+	0.211182i	$0.932269\pi$
$12$	−3.00804	+	1.71804i	−0.868347	+	0.495957i
$13$	0.106525	+	0.257175i	0.0295448	+	0.0713275i	0.937963	−	0.346734i	$-0.112709\pi$
$13$	0.106525	+	0.257175i	0.0295448	+	0.0713275i	−0.908419	+	0.418062i	$0.862709\pi$
$14$	−0.753491	−	3.66500i	−0.201379	−	0.979513i
$15$	−1.62139	−	2.14626i	−0.418640	−	0.554161i
$16$	3.99993	−	0.0228573i	0.999984	−	0.00571432i
$17$	−1.06215	+	1.83970i	−0.257609	+	0.446193i	−0.965601	−	0.260028i	$-0.916268\pi$
$17$	−1.06215	+	1.83970i	−0.257609	+	0.446193i	0.707992	+	0.706221i	$0.249601\pi$
$18$	−2.17113	+	3.64502i	−0.511741	+	0.859140i
$19$	−1.28670	−	0.987321i	−0.295190	−	0.226507i	0.450539	−	0.892757i	$-0.351232\pi$
$19$	−1.28670	−	0.987321i	−0.295190	−	0.226507i	−0.745729	+	0.666250i	$0.767898\pi$
$20$	0.414208	+	3.07823i	0.0926197	+	0.688314i
$21$	−3.01277	−	3.45300i	−0.657440	−	0.753507i
$22$	6.72062	−	5.17218i	1.43284	−	1.10271i
$23$	5.94161	+	1.59205i	1.23891	+	0.331965i	0.818044	−	0.575156i	$-0.195059\pi$
$23$	5.94161	+	1.59205i	1.23891	+	0.331965i	0.420868	+	0.907122i	$0.361725\pi$
$24$	4.25054	−	2.43576i	0.867638	−	0.497197i
$25$	2.50004	−	0.669883i	0.500008	−	0.133977i
$26$	−0.151169	−	0.363485i	−0.0296467	−	0.0712852i
$27$	−0.117209	+	5.19483i	−0.0225570	+	0.999746i
$28$	1.07300	+	5.18157i	0.202778	+	0.979225i
$29$	1.01347	+	2.44673i	0.188196	+	0.454346i	0.989612	−	0.143761i	$-0.0459197\pi$
$29$	1.01347	+	2.44673i	0.188196	+	0.454346i	−0.801416	+	0.598107i	$0.795920\pi$
$30$	2.29732	+	3.03199i	0.419431	+	0.553562i
$31$	−6.75813	−	3.90181i	−1.21380	−	0.700786i	−0.250212	−	0.968191i	$-0.580500\pi$
$31$	−6.75813	−	3.90181i	−1.21380	−	0.700786i	−0.963584	+	0.267405i	$0.913834\pi$
$32$	−5.65671	+	0.0404063i	−0.999974	+	0.00714288i
$33$	4.04675	−	9.56562i	0.704448	−	1.66516i
$34$	1.49839	−	2.60387i	0.256972	−	0.446560i
$35$	−3.88413	+	1.34012i	−0.656538	+	0.226522i
$36$	3.06308	−	5.15922i	0.510513	−	0.859870i
$37$	2.55405	−	0.336247i	0.419883	−	0.0552787i	0.0823753	−	0.996601i	$-0.473749\pi$
$37$	2.55405	−	0.336247i	0.419883	−	0.0552787i	0.337508	+	0.941323i	$0.390416\pi$
$38$	1.82166	+	1.39368i	0.295513	+	0.226085i
$39$	−0.380290	−	0.296377i	−0.0608952	−	0.0474583i
$40$	−0.591997	−	4.35244i	−0.0936029	−	0.688181i
$41$	−6.08980	−	6.08980i	−0.951068	−	0.951068i	0.0477899	−	0.998857i	$-0.484782\pi$
$41$	−6.08980	−	6.08980i	−0.951068	−	0.951068i	−0.998857	+	0.0477899i	$0.984782\pi$
$42$	4.26767	+	4.87719i	0.658516	+	0.752567i
$43$	−1.92408	+	4.64514i	−0.293419	+	0.708377i	0.706580	+	0.707633i	$0.250237\pi$
$43$	−1.92408	+	4.64514i	−0.293419	+	0.708377i	−1.00000		0.000744158i	$0.999763\pi$
$44$	−9.49393	+	7.32814i	−1.43126	+	1.10476i
$45$	4.27702	+	1.84744i	0.637581	+	0.275400i
$46$	−8.40592	−	2.23949i	−1.23938	−	0.330195i
$47$	2.12691	−	1.22797i	0.310242	−	0.179118i	−0.336793	−	0.941579i	$-0.609342\pi$
$47$	2.12691	−	1.22797i	0.310242	−	0.179118i	0.647035	+	0.762460i	$0.276009\pi$
$48$	−6.00624	+	3.45326i	−0.866927	+	0.498436i
$49$	−6.44011	+	2.74316i	−0.920016	+	0.391880i
$50$	−3.53423	+	0.952408i	−0.499816	+	0.134691i
$51$	0.0276674	−	3.67930i	0.00387422	−	0.515204i
$52$	0.214519	+	0.513739i	0.0297485	+	0.0712428i
$53$	−7.16108	−	9.33250i	−0.983650	−	1.28192i	−0.959352	−	0.282213i	$-0.908932\pi$
$53$	−7.16108	−	9.33250i	−0.983650	−	1.28192i	−0.0242978	−	0.999705i	$-0.507735\pi$
$54$	0.155264	−	7.34683i	0.0211287	−	0.999777i
$55$	−6.58502	−	6.58502i	−0.887925	−	0.887925i
$56$	−1.52792	−	7.32567i	−0.204177	−	0.978934i
$57$	2.78226	+	0.387597i	0.368520	+	0.0513385i
$58$	−1.43820	−	3.45814i	−0.188845	−	0.454077i
$59$	0.142134	+	0.185232i	0.0185042	+	0.0241152i	0.802514	−	0.596634i	$-0.203495\pi$
$59$	0.142134	+	0.185232i	0.0185042	+	0.0241152i	−0.784010	+	0.620749i	$0.786829\pi$
$60$	−3.25502	−	4.28323i	−0.420222	−	0.552963i
$61$	−4.16461	−	3.19562i	−0.533224	−	0.409157i	0.306745	−	0.951792i	$-0.400760\pi$
$61$	−4.16461	−	3.19562i	−0.533224	−	0.409157i	−0.839969	+	0.542635i	$0.817427\pi$
$62$	9.56532	+	5.50433i	1.21480	+	0.699051i
$63$	7.49000	+	2.62677i	0.943651	+	0.330941i
$64$	7.99971	−	0.0685714i	0.999963	−	0.00857143i
$65$	−0.374379	+	0.216148i	−0.0464360	+	0.0268099i
$66$	−5.70363	+	13.5360i	−0.702069	+	1.66617i
$67$	−8.42225	−	1.10881i	−1.02894	−	0.135463i	−0.402893	−	0.915247i	$-0.631995\pi$
$67$	−8.42225	−	1.10881i	−1.02894	−	0.135463i	−0.626049	+	0.779784i	$0.715329\pi$
$68$	−2.11378	+	3.68545i	−0.256334	+	0.446927i
$69$	−10.3116	+	2.68005i	−1.24137	+	0.322640i
$70$	5.49027	−	1.90307i	0.656213	−	0.227460i
$71$	−0.125081	−	0.125081i	−0.0148444	−	0.0148444i	0.699646	−	0.714490i	$-0.253341\pi$
$71$	−0.125081	−	0.125081i	−0.0148444	−	0.0148444i	−0.714490	+	0.699646i	$0.753341\pi$
$72$	−4.32142	+	7.30242i	−0.509284	+	0.860599i
$73$	2.43133	+	9.07386i	0.284566	+	1.06201i	0.949156	+	0.314807i	$0.101940\pi$
$73$	2.43133	+	9.07386i	0.284566	+	1.06201i	−0.664590	+	0.747208i	$0.731394\pi$
$74$	−3.61129	+	0.480685i	−0.419804	+	0.0558784i
$75$	−3.19367	+	3.14600i	−0.368773	+	0.363268i
$76$	−2.57903	−	1.96728i	−0.295836	−	0.225663i
$77$	−11.9803	−	10.4012i	−1.36529	−	1.18533i
$78$	0.538410	+	0.418371i	0.0609629	+	0.0473712i
$79$	3.02184	+	5.23399i	0.339984	+	0.588869i	0.984429	−	0.175781i	$-0.0562450\pi$
$79$	3.02184	+	5.23399i	0.339984	+	0.588869i	−0.644445	+	0.764650i	$0.722912\pi$
$80$	0.846002	+	6.15407i	0.0945859	+	0.688046i
$81$	−4.26356	−	7.92604i	−0.473729	−	0.880671i
$82$	8.62458	+	8.59997i	0.952425	+	0.949708i
$83$	−2.61245	−	6.30700i	−0.286753	−	0.692284i	0.713209	−	0.700951i	$-0.247241\pi$
$83$	−2.61245	−	6.30700i	−0.286753	−	0.692284i	−0.999962	+	0.00866760i	$0.997241\pi$
$84$	−6.04524	−	6.88876i	−0.659590	−	0.751625i
$85$	−3.04789	−	1.26248i	−0.330590	−	0.136935i
$86$	2.71167	−	6.57310i	0.292407	−	0.708795i
$87$	−3.61803	−	2.81969i	−0.387893	−	0.302302i
$88$	13.4116	−	10.3827i	1.42968	−	1.10680i
$89$	−14.3185	−	3.83663i	−1.51776	−	0.406682i	−0.598756	−	0.800932i	$-0.704338\pi$
$89$	−14.3185	−	3.83663i	−1.51776	−	0.406682i	−0.919003	+	0.394249i	$0.871005\pi$
$90$	−6.05235	−	2.60403i	−0.637973	−	0.274489i
$91$	−0.610314	+	0.412217i	−0.0639783	+	0.0432121i
$92$	11.8923	+	3.15014i	1.23986	+	0.328424i
$93$	13.5159	+	0.101636i	1.40153	+	0.0105392i
$94$	−3.00543	+	1.74091i	−0.309986	+	0.179561i
$95$	1.25936	−	2.18127i	0.129207	−	0.223794i
$96$	8.48713	−	4.89578i	0.866214	−	0.499674i
$97$	8.21665			0.834275			0.417137	−	0.908843i	$-0.363033\pi$
$97$	8.21665			0.834275			0.417137	+	0.908843i	$0.363033\pi$
$98$	9.10215	−	3.89242i	0.919456	−	0.393194i
$99$	2.07964	+	17.8692i	0.209012	+	1.79592i
$100$	4.99623	−	1.35405i	0.499623	−	0.135405i
$101$	−1.72596	+	1.32438i	−0.171740	+	0.131780i	−0.691055	−	0.722802i	$-0.742854\pi$
$101$	−1.72596	+	1.32438i	−0.171740	+	0.131780i	0.519315	+	0.854583i	$0.326187\pi$
$102$	−0.0316942	+	5.20336i	−0.00313820	+	0.515209i
$103$	−7.95387	−	2.13123i	−0.783718	−	0.209997i	−0.155295	−	0.987868i	$-0.549633\pi$
$103$	−7.95387	−	2.13123i	−0.783718	−	0.209997i	−0.628423	+	0.777872i	$0.716299\pi$
$104$	−0.304414	−	0.726103i	−0.0298502	−	0.0712002i
$105$	4.70589	−	5.33871i	0.459248	−	0.521004i
$106$	10.1461	+	13.1837i	0.985480	+	1.28051i
$107$	−0.154849	−	1.17619i	−0.0149698	−	0.113707i	0.982329	−	0.187165i	$-0.0599299\pi$
$107$	−0.154849	−	1.17619i	−0.0149698	−	0.113707i	−0.997298	+	0.0734580i	$0.976597\pi$
$108$	−0.204733	+	10.3903i	−0.0197004	+	0.999806i
$109$	−2.39323	−	0.315075i	−0.229230	−	0.0301787i	0.0150359	−	0.999887i	$-0.495214\pi$
$109$	−2.39323	−	0.315075i	−0.229230	−	0.0301787i	−0.244266	+	0.969708i	$0.578547\pi$
$110$	9.32593	+	9.29932i	0.889192	+	0.886655i
$111$	−3.56020	+	2.68955i	−0.337919	+	0.255281i
$112$	2.17560	+	10.3570i	0.205575	+	0.978641i
$113$	14.6243			1.37574			0.687870	−	0.725834i	$-0.258546\pi$
$113$	14.6243			1.37574			0.687870	+	0.725834i	$0.258546\pi$
$114$	−3.93549	−	0.542524i	−0.368593	−	0.0508120i
$115$	−1.24688	+	9.47103i	−0.116273	+	0.883178i
$116$	2.04091	+	4.88764i	0.189494	+	0.453806i
$117$	0.826215	+	0.121440i	0.0763836	+	0.0112272i
$118$	−0.201382	−	0.261671i	−0.0185387	−	0.0240887i
$119$	−5.33105	−	1.78004i	−0.488696	−	0.163176i
$120$	4.61195	+	6.05082i	0.421011	+	0.552362i
$121$	6.45989	−	24.1086i	0.587263	−	2.19170i
$122$	5.89610	+	4.51087i	0.533808	+	0.408395i
$123$	14.3792	+	3.96902i	1.29653	+	0.357874i
$124$	−13.5385	−	7.76497i	−1.21579	−	0.697315i
$125$	4.50970	+	10.8874i	0.403360	+	0.973798i
$126$	−10.5978	−	3.69967i	−0.944123	−	0.329593i
$127$			5.79069i			0.513841i	0.966433	+	0.256920i	$0.0827079\pi$
$127$			5.79069i			0.513841i	−0.966433	+	0.256920i	$0.917292\pi$
$128$	−11.3131	+	0.113137i	−0.999950	+	0.00999996i
$129$	−1.07173	−	8.64231i	−0.0943608	−	0.760913i
$130$	0.529015	−	0.306436i	0.0463977	−	0.0268762i
$131$	2.35123	+	1.80416i	0.205428	+	0.157630i	0.706352	−	0.707861i	$-0.250340\pi$
$131$	2.35123	+	1.80416i	0.205428	+	0.157630i	−0.500924	+	0.865491i	$0.667006\pi$
$132$	8.03880	−	19.1543i	0.699688	−	1.66717i
$133$	1.87865	−	3.85791i	0.162900	−	0.334524i
$134$	11.9131	+	1.55108i	1.02913	+	0.133993i
$135$	−8.02225	+	0.872553i	−0.690445	+	0.0750974i
$136$	2.98189	−	5.21628i	0.255695	−	0.447293i
$137$	14.3948	−	3.85708i	1.22983	−	0.329533i	0.415319	−	0.909676i	$-0.363670\pi$
$137$	14.3948	−	3.85708i	1.22983	−	0.329533i	0.814514	+	0.580143i	$0.197003\pi$
$138$	14.5774	−	3.81099i	1.24091	−	0.324413i
$139$	−7.80470	+	18.8422i	−0.661986	+	1.59818i	0.132701	+	0.991156i	$0.457635\pi$
$139$	−7.80470	+	18.8422i	−0.661986	+	1.59818i	−0.794687	+	0.607020i	$0.792365\pi$
$140$	−7.76057	+	2.70243i	−0.655888	+	0.228397i
$141$	−2.15456	+	3.66783i	−0.181446	+	0.308887i
$142$	0.177143	+	0.176638i	0.0148655	+	0.0148231i
$143$	−1.44560	−	0.834618i	−0.120887	−	0.0697943i
$144$	6.09664	−	10.3359i	0.508054	−	0.861325i
$145$	−3.56179	+	2.05640i	−0.295791	+	0.170775i
$146$	−3.45675	−	12.8274i	−0.286083	−	1.06161i
$147$	7.35720	−	9.63699i	0.606812	−	0.794846i
$148$	5.10616	−	0.687086i	0.419723	−	0.0564781i
$149$	6.38760	−	0.840943i	0.523292	−	0.0688927i	0.135747	−	0.990744i	$-0.456657\pi$
$149$	6.38760	−	0.840943i	0.523292	−	0.0688927i	0.387545	+	0.921851i	$0.373323\pi$
$150$	4.51017	−	4.45556i	0.368254	−	0.363795i
$151$	−22.3201	+	5.98066i	−1.81639	+	0.486699i	−0.996331	−	0.0855836i	$-0.972725\pi$
$151$	−22.3201	+	5.98066i	−1.81639	+	0.486699i	−0.820056	+	0.572283i	$0.806058\pi$
$152$	3.65128	+	2.77694i	0.296158	+	0.225240i
$153$	3.10309	+	5.56640i	0.250870	+	0.450016i
$154$	16.9637	+	14.6853i	1.36698	+	1.18338i
$155$	4.63771	−	11.1964i	0.372510	−	0.899318i
$156$	−0.762271	−	0.590578i	−0.0610305	−	0.0472841i
$157$	−3.17874	+	24.1449i	−0.253691	+	1.92697i	0.106939	+	0.994266i	$0.465895\pi$
$157$	−3.17874	+	24.1449i	−0.253691	+	1.92697i	−0.360630	+	0.932709i	$0.617438\pi$
$158$	−4.28410	−	7.39586i	−0.340825	−	0.588383i
$159$	18.7646	+	7.93840i	1.48813	+	0.629556i
$160$	−1.20886	−	8.70145i	−0.0955688	−	0.687910i
$161$	−0.983400	+	16.2448i	−0.0775028	+	1.28027i
$162$	6.04559	+	11.2005i	0.474987	+	0.879993i
$163$	5.96795	−	7.77758i	0.467446	−	0.609187i	−0.498829	−	0.866700i	$-0.666236\pi$
$163$	5.96795	−	7.77758i	0.467446	−	0.609187i	0.966275	+	0.257513i	$0.0829031\pi$
$164$	−12.2144	−	12.1448i	−0.953781	−	0.948346i
$165$	15.5485	+	4.29178i	1.21045	+	0.334114i
$166$	3.70730	+	8.91416i	0.287742	+	0.691873i
$167$	−2.09803	−	2.09803i	−0.162350	−	0.162350i	0.621257	−	0.783607i	$-0.286622\pi$
$167$	−2.09803	−	2.09803i	−0.162350	−	0.162350i	−0.783607	+	0.621257i	$0.786622\pi$
$168$	8.56317	+	9.72996i	0.660663	+	0.750682i
$169$	9.13760	−	9.13760i	0.702892	−	0.702892i
$170$	4.31292	+	1.77925i	0.330786	+	0.136463i
$171$	−4.52268	+	1.79416i	−0.345858	+	0.137203i
$172$	−3.82160	+	9.30123i	−0.291394	+	0.709212i
$173$	11.4976	+	8.82246i	0.874150	+	0.670759i	0.945121	−	0.326719i	$-0.105943\pi$
$173$	11.4976	+	8.82246i	0.874150	+	0.670759i	−0.0709713	+	0.997478i	$0.522610\pi$
$174$	5.12236	+	3.98033i	0.388325	+	0.301748i
$175$	3.05930	+	6.12643i	0.231262	+	0.463115i
$176$	−18.9459	+	14.7105i	−1.42810	+	1.10884i
$177$	−0.372442	−	0.157562i	−0.0279945	−	0.0118431i
$178$	20.2572	+	5.39689i	1.51834	+	0.404514i
$179$	12.0779	+	1.59008i	0.902741	+	0.118848i	0.567585	−	0.823314i	$-0.307878\pi$
$179$	12.0779	+	1.59008i	0.902741	+	0.118848i	0.335156	+	0.942163i	$0.391211\pi$
$180$	8.56456	+	3.67042i	0.638365	+	0.273577i
$181$	1.68273	+	0.697011i	0.125077	+	0.0518084i	0.444344	−	0.895856i	$-0.353437\pi$
$181$	1.68273	+	0.697011i	0.125077	+	0.0518084i	−0.319267	+	0.947665i	$0.603437\pi$
$182$	0.862281	−	0.584195i	0.0639165	−	0.0433034i
$183$	9.00523	+	1.25452i	0.665686	+	0.0927368i
$184$	−16.8246	−	4.43093i	−1.24032	−	0.326653i
$185$	1.03544	+	3.86431i	0.0761271	+	0.284110i
$186$	−19.1145	−	0.116429i	−1.40155	−	0.00853697i
$187$	−1.66272	−	12.6296i	−0.121590	−	0.923567i
$188$	4.24679	−	2.46809i	0.309729	−	0.180004i
$189$	−13.5286	+	2.44472i	−0.984062	+	0.177827i
$190$	−1.77659	+	3.08733i	−0.128888	+	0.223978i
$191$	7.65915	+	13.2660i	0.554197	+	0.959897i	0.997966	+	0.0637557i	$0.0203079\pi$
$191$	7.65915	+	13.2660i	0.554197	+	0.959897i	−0.443769	+	0.896141i	$0.646359\pi$
$192$	−11.9927	+	6.94082i	−0.865499	+	0.500911i
$193$	−10.6837	+	18.5047i	−0.769029	+	1.33200i	0.169061	+	0.985606i	$0.445927\pi$
$193$	−10.6837	+	18.5047i	−0.769029	+	1.33200i	−0.938090	+	0.346392i	$0.887407\pi$
$194$	−11.6201	+	0.0166003i	−0.834274	+	0.00119184i
$195$	0.379245	−	0.645611i	0.0271583	−	0.0462331i
$196$	−12.8645	+	5.52310i	−0.918893	+	0.394507i
$197$	−0.557164	−	0.230785i	−0.0396963	−	0.0164427i	0.362747	−	0.931888i	$-0.381839\pi$
$197$	−0.557164	−	0.230785i	−0.0396963	−	0.0164427i	−0.402443	+	0.915445i	$0.631839\pi$
$198$	−2.97716	−	25.2666i	−0.211577	−	1.79562i
$199$	−5.64383	−	21.0631i	−0.400081	−	1.49312i	−0.812951	−	0.582332i	$-0.802140\pi$
$199$	−5.64383	−	21.0631i	−0.400081	−	1.49312i	0.412870	−	0.910790i	$-0.364526\pi$
$200$	−7.06299	+	1.92500i	−0.499429	+	0.136118i
$201$	13.6356	−	5.52829i	0.961781	−	0.389936i
$202$	2.43820	−	1.87644i	0.171551	−	0.132026i
$203$	−5.80645	+	3.92177i	−0.407533	+	0.275255i
$204$	0.0343099	−	7.35872i	0.00240217	−	0.515213i
$205$	8.14204	−	10.6109i	0.568665	−	0.741099i
$206$	11.2528	+	2.99795i	0.784017	+	0.208877i
$207$	13.2434	−	12.8510i	0.920483	−	0.893205i
$208$	0.431973	+	1.02625i	0.0299519	+	0.0711575i
$209$	9.72558			0.672733
$210$	−6.64434	+	7.55957i	−0.458503	+	0.521660i
$211$	20.8902	−	8.65300i	1.43814	−	0.595697i	0.478794	−	0.877927i	$-0.341074\pi$
$211$	20.8902	−	8.65300i	1.43814	−	0.595697i	0.959347	+	0.282230i	$0.0910741\pi$
$212$	−14.3754	−	18.6240i	−0.987308	−	1.27910i
$213$	0.295340	+	0.0815212i	0.0202363	+	0.00558574i
$214$	0.221365	+	1.66307i	0.0151322	+	0.113685i
$215$	−7.54215	−	2.02091i	−0.514370	−	0.137825i
$216$	0.268544	−	14.6945i	0.0182721	−	0.999833i
$217$	6.53899	−	19.5836i	0.443895	−	1.32942i
$218$	3.38518	+	0.440748i	0.229273	+	0.0298512i
$219$	−11.4184	−	11.5914i	−0.771581	−	0.783273i
$220$	−13.2076	−	13.1324i	−0.890458	−	0.885384i
$221$	−0.586271	−	0.0771840i	−0.0394368	−	0.00519196i
$222$	5.02944	−	3.81078i	0.337554	−	0.255763i
$223$			1.73930i			0.116472i	0.998303	+	0.0582360i	$0.0185476\pi$
$223$			1.73930i			0.116472i	−0.998303	+	0.0582360i	$0.981452\pi$
$224$	−3.09769	−	14.6426i	−0.206973	−	0.978347i
$225$	2.12221	−	7.46904i	0.141481	−	0.497936i
$226$	−20.6819	+	0.0295459i	−1.37574	+	0.00196537i
$227$	−2.18275	+	16.5796i	−0.144874	+	1.10043i	0.752321	+	0.658796i	$0.228934\pi$
$227$	−2.18275	+	16.5796i	−0.144874	+	1.10043i	−0.897196	+	0.441633i	$0.854399\pi$
$228$	5.56672	+	0.759293i	0.368665	+	0.0502854i
$229$	−27.1620	+	3.57594i	−1.79491	+	0.236305i	−0.952928	−	0.303197i	$-0.901946\pi$
$229$	−27.1620	+	3.57594i	−1.79491	+	0.236305i	−0.841985	+	0.539501i	$0.818613\pi$
$230$	1.74422	−	13.3966i	0.115011	−	0.883343i
$231$	26.9382	+	5.42928i	1.77240	+	0.357220i
$232$	−2.89615	−	6.90804i	−0.190142	−	0.453535i
$233$	−0.574204	+	2.14296i	−0.0376174	+	0.140390i	−0.982181	−	0.187940i	$-0.939819\pi$
$233$	−0.574204	+	2.14296i	−0.0376174	+	0.140390i	0.944563	+	0.328330i	$0.106486\pi$
$234$	−1.16869	−	0.170073i	−0.0763996	−	0.0111180i
$235$	2.32185	+	3.02590i	0.151461	+	0.197388i
$236$	0.285325	+	0.369651i	0.0185731	+	0.0240622i
$237$	−9.02592	−	5.30201i	−0.586296	−	0.344402i
$238$	7.54283	+	2.50659i	0.488929	+	0.162478i
$239$		−	22.6306i		−	1.46385i	−0.681385	−	0.731926i	$-0.738622\pi$
$239$		−	22.6306i		−	1.46385i	0.681385	−	0.731926i	$-0.261378\pi$
$240$	−6.53449	−	8.54783i	−0.421800	−	0.551760i
$241$	3.01750	+	1.74215i	0.194374	+	0.112222i	0.594029	−	0.804444i	$-0.297537\pi$
$241$	3.01750	+	1.74215i	0.194374	+	0.112222i	−0.399655	+	0.916666i	$0.630870\pi$
$242$	−9.08695	+	34.1078i	−0.584131	+	2.19253i
$243$	13.1975	+	8.29618i	0.846619	+	0.532200i
$244$	−8.34745	−	6.36741i	−0.534391	−	0.407632i
$245$	−5.52909	−	9.35980i	−0.353241	−	0.597976i
$246$	−20.3432	−	5.58398i	−1.29704	−	0.356022i
$247$	0.116848	−	0.436082i	0.00743485	−	0.0277472i
$248$	19.1620	+	10.9540i	1.21679	+	0.695577i
$249$	9.32631	+	7.26840i	0.591031	+	0.460616i
$250$	−6.39967	−	15.3880i	−0.404751	−	0.973221i
$251$	−6.48579	+	15.6581i	−0.409380	+	0.988330i	0.575922	+	0.817505i	$0.304643\pi$
$251$	−6.48579	+	15.6581i	−0.409380	+	0.988330i	−0.985301	+	0.170825i	$0.945357\pi$
$252$	14.9949	+	5.21071i	0.944593	+	0.328244i
$253$	−34.0785	+	14.1158i	−2.14250	+	0.887451i
$254$	−0.0116991	−	8.18927i	−0.000734067	−	0.513840i
$255$	5.67062	−	0.703214i	0.355108	−	0.0440370i
$256$	15.9990	−	0.182855i	0.999935	−	0.0114285i
$257$	−8.40156	+	4.85064i	−0.524075	+	0.302575i	−0.738600	−	0.674144i	$-0.764513\pi$
$257$	−8.40156	+	4.85064i	−0.524075	+	0.302575i	0.214525	+	0.976718i	$0.431180\pi$
$258$	1.53312	+	12.2199i	0.0954477	+	0.760778i
$259$	2.22299	+	6.44297i	0.138130	+	0.400347i
$260$	−0.747521	+	0.434434i	−0.0463593	+	0.0269424i
$261$	7.86050	+	1.15537i	0.486553	+	0.0715154i
$262$	−3.32878	−	2.54671i	−0.205653	−	0.157336i
$263$	−15.6120	+	4.18323i	−0.962679	+	0.257949i	−0.705734	−	0.708477i	$-0.749383\pi$
$263$	−15.6120	+	4.18323i	−0.962679	+	0.257949i	−0.256945	+	0.966426i	$0.582716\pi$
$264$	−11.3299	+	27.1045i	−0.697305	+	1.66817i
$265$	12.9177	−	12.9177i	0.793526	−	0.793526i
$266$	−2.64902	+	5.45970i	−0.162422	+	0.334756i
$267$	24.8497	−	6.45857i	1.52077	−	0.395258i
$268$	−16.8508	−	2.16948i	−1.02932	−	0.132522i
$269$	0.662771	−	5.03424i	0.0404098	−	0.306943i	−0.959290	−	0.282425i	$-0.908861\pi$
$269$	0.662771	−	5.03424i	0.0404098	−	0.306943i	0.999699	−	0.0245187i	$-0.00780534\pi$
$270$	11.3434	−	1.25018i	0.690337	−	0.0760837i
$271$	14.5725	+	25.2403i	0.885216	+	1.53324i	0.845466	+	0.534029i	$0.179323\pi$
$271$	14.5725	+	25.2403i	0.885216	+	1.53324i	0.0397491	+	0.999210i	$0.487344\pi$
$272$	−4.20648	+	7.38296i	−0.255056	+	0.447658i
$273$	0.567090	−	1.14264i	0.0343218	−	0.0691558i
$274$	−20.3495	+	5.48381i	−1.22936	+	0.331289i
$275$	−9.44832	+	12.3133i	−0.569755	+	0.742519i
$276$	−20.6078	+	5.41900i	−1.24045	+	0.326185i
$277$	−2.57661	+	1.97710i	−0.154813	+	0.118793i	−0.683264	−	0.730172i	$-0.739440\pi$
$277$	−2.57661	+	1.97710i	−0.154813	+	0.118793i	0.528450	+	0.848964i	$0.322773\pi$
$278$	10.9994	−	26.6627i	0.659702	−	1.59912i
$279$	−20.4481	+	11.3992i	−1.22420	+	0.682452i
$280$	10.9696	−	3.83749i	0.655561	−	0.229334i
$281$	−8.41026	+	8.41026i	−0.501714	+	0.501714i	−0.911970	−	0.410256i	$-0.865439\pi$
$281$	−8.41026	+	8.41026i	−0.501714	+	0.501714i	0.410256	+	0.911970i	$0.365439\pi$
$282$	3.03959	−	5.19144i	0.181005	−	0.309146i
$283$	17.6453	−	13.5397i	1.04891	−	0.804854i	0.0676788	−	0.997707i	$-0.478441\pi$
$283$	17.6453	−	13.5397i	1.04891	−	0.804854i	0.981228	+	0.192853i	$0.0617740\pi$
$284$	−0.250875	−	0.249446i	−0.0148867	−	0.0148019i
$285$	−0.0328044	+	4.36242i	−0.00194316	+	0.258407i
$286$	2.04607	+	1.17741i	0.120987	+	0.0696215i
$287$	12.5646	−	19.0087i	0.741662	−	1.12205i
$288$	−8.60107	+	14.6295i	−0.506823	+	0.862050i
$289$	6.24367	+	10.8144i	0.367275	+	0.636138i
$290$	5.03298	−	2.91539i	0.295547	−	0.171197i
$291$	−12.3781	+	7.02295i	−0.725619	+	0.411693i
$292$	4.91450	+	18.1338i	0.287599	+	1.06120i
$293$	−19.5320	−	8.09042i	−1.14107	−	0.472647i	−0.269541	−	0.962989i	$-0.586872\pi$
$293$	−19.5320	−	8.09042i	−1.14107	−	0.472647i	−0.871530	+	0.490342i	$0.836872\pi$
$294$	−10.3852	+	13.6436i	−0.605676	+	0.795712i
$295$	−0.256391	+	0.256391i	−0.0149277	+	0.0149277i
$296$	−7.21980	+	0.982001i	−0.419642	+	0.0570777i
$297$	−18.4061	−	25.1418i	−1.06803	−	1.45888i
$298$	−9.03172	+	1.20218i	−0.523193	+	0.0696402i
$299$	0.223497	+	1.69763i	0.0129252	+	0.0981764i
$300$	−6.36933	+	6.31021i	−0.367734	+	0.364320i
$301$	−13.0596	−	2.53008i	−0.752746	−	0.145831i
$302$	31.5533	−	8.50302i	1.81569	−	0.489294i
$303$	1.46814	−	3.47035i	0.0843422	−	0.199366i
$304$	−5.16929	−	3.91981i	−0.296479	−	0.224816i
$305$	4.07611	−	7.06003i	0.233397	−	0.404256i
$306$	−4.39968	−	7.86579i	−0.251513	−	0.449658i
$307$	6.39406	−	2.64851i	0.364928	−	0.151158i	−0.192682	−	0.981261i	$-0.561719\pi$
$307$	6.39406	−	2.64851i	0.364928	−	0.151158i	0.557610	+	0.830103i	$0.311719\pi$
$308$	−24.0200	−	20.7339i	−1.36867	−	1.18142i
$309$	13.8039	−	3.58771i	0.785275	−	0.204098i
$310$	−6.53609	+	15.8435i	−0.371225	+	0.899850i
$311$	−1.32895	−	4.95971i	−0.0753579	−	0.281240i	0.917956	−	0.396681i	$-0.129838\pi$
$311$	−1.32895	−	4.95971i	−0.0753579	−	0.281240i	−0.993314	+	0.115442i	$0.963172\pi$
$312$	1.07921	+	0.833663i	0.0610980	+	0.0471968i
$313$	−6.75778	+	25.2204i	−0.381972	+	1.42554i	0.460912	+	0.887446i	$0.347522\pi$
$313$	−6.75778	+	25.2204i	−0.381972	+	1.42554i	−0.842885	+	0.538094i	$0.819144\pi$
$314$	4.44663	−	34.1525i	0.250938	−	1.92734i
$315$	−2.52617	+	12.0648i	−0.142334	+	0.679776i
$316$	6.07357	+	10.4507i	0.341665	+	0.587896i
$317$	−18.2894	+	23.8352i	−1.02723	+	1.33872i	−0.0877415	+	0.996143i	$0.527965\pi$
$317$	−18.2894	+	23.8352i	−1.02723	+	1.33872i	−0.939491	+	0.342573i	$0.888702\pi$
$318$	−26.5532	−	11.1887i	−1.48903	−	0.627429i
$319$	−13.7532	−	7.94044i	−0.770034	−	0.444579i
$320$	1.72716	+	12.3033i	0.0965514	+	0.687773i
$321$	1.23859	+	1.63955i	0.0691315	+	0.0915106i
$322$	1.35792	−	22.9756i	0.0756738	−	1.28038i
$323$	3.18305	−	1.31846i	0.177109	−	0.0733611i
$324$	−8.57238	−	15.8276i	−0.476243	−	0.879314i
$325$	0.438595	+	0.571588i	0.0243289	+	0.0317060i
$326$	−8.42423	+	11.0112i	−0.466575	+	0.609855i
$327$	3.87464	−	1.57090i	0.214268	−	0.0868708i
$328$	17.2982	+	17.1506i	0.955135	+	0.946983i
$329$	4.30863	+	4.86390i	0.237542	+	0.268155i
$330$	−21.9976	−	6.03807i	−1.21093	−	0.332385i
$331$	10.7212	−	1.41147i	0.589289	−	0.0775814i	0.170016	−	0.985441i	$-0.445618\pi$
$331$	10.7212	−	1.41147i	0.589289	−	0.0775814i	0.419274	+	0.907860i	$0.362285\pi$
$332$	−5.26091	−	12.5990i	−0.288730	−	0.691462i
$333$	3.06452	−	7.09470i	0.167935	−	0.388787i
$334$	2.97129	+	2.96282i	0.162582	+	0.162118i
$335$		−	13.1925i		−	0.720784i
$336$	−12.1298	−	13.7429i	−0.661735	−	0.749738i
$337$			6.01469i			0.327641i	0.986490	+	0.163821i	$0.0523818\pi$
$337$			6.01469i			0.327641i	−0.986490	+	0.163821i	$0.947618\pi$
$338$	−12.9040	+	12.9410i	−0.701887	+	0.703895i
$339$	−22.0311	+	12.4997i	−1.19657	+	0.678892i
$340$	−6.10297	−	2.50753i	−0.330980	−	0.135990i
$341$	46.3948	−	6.10799i	2.51242	−	0.330766i
$342$	6.39241	−	2.54645i	0.345662	−	0.137696i
$343$	−10.5185	−	15.2434i	−0.567948	−	0.823064i
$344$	5.38576	−	13.1616i	0.290381	−	0.709628i
$345$	−6.21670	−	15.3336i	−0.334696	−	0.825531i
$346$	−16.2779	−	12.4536i	−0.875107	−	0.669509i
$347$	4.39137	+	5.72295i	0.235741	+	0.307224i	0.896210	−	0.443629i	$-0.146309\pi$
$347$	4.39137	+	5.72295i	0.235741	+	0.307224i	−0.660469	+	0.750853i	$0.729643\pi$
$348$	−7.25214	−	5.61868i	−0.388756	−	0.301193i
$349$	19.0623	−	7.89588i	1.02038	−	0.422657i	0.191151	−	0.981561i	$-0.438778\pi$
$349$	19.0623	−	7.89588i	1.02038	−	0.422657i	0.829232	+	0.558904i	$0.188778\pi$
$350$	−4.33888	−	8.65790i	−0.231923	−	0.462784i
$351$	−1.34847	+	0.523238i	−0.0719758	+	0.0279284i
$352$	26.7638	−	20.8420i	1.42652	−	1.11088i
$353$	30.0978	+	17.3770i	1.60194	+	0.924883i	0.991098	+	0.133133i	$0.0425039\pi$
$353$	30.0978	+	17.3770i	1.60194	+	0.924883i	0.610846	+	0.791749i	$0.290829\pi$
$354$	0.527031	+	0.222074i	0.0280114	+	0.0118031i
$355$	0.167232	−	0.217942i	0.00887578	−	0.0115671i
$356$	−28.6588	−	7.59141i	−1.51891	−	0.402344i
$357$	9.55250	−	1.87498i	0.505572	−	0.0992344i
$358$	−17.0839	−	2.22431i	−0.902910	−	0.117558i
$359$	3.24075	−	12.0946i	0.171040	−	0.638330i	−0.826152	−	0.563447i	$-0.809475\pi$
$359$	3.24075	−	12.0946i	0.171040	−	0.638330i	0.997192	−	0.0748834i	$-0.0238584\pi$
$360$	−12.1195	−	5.17345i	−0.638755	−	0.272665i
$361$	−4.23676	−	15.8118i	−0.222988	−	0.832201i
$362$	−2.38115	−	0.982322i	−0.125151	−	0.0516297i
$363$	10.8745	+	41.8404i	0.570766	+	2.19605i
$364$	−1.21827	+	0.827918i	−0.0638546	+	0.0433947i
$365$	−13.4782	+	5.58285i	−0.705481	+	0.292220i
$366$	−12.7378	−	1.75596i	−0.665817	−	0.0917857i
$367$	−6.93455	+	12.0110i	−0.361980	+	0.626969i	−0.988287	−	0.152609i	$-0.951233\pi$
$367$	−6.93455	+	12.0110i	−0.361980	+	0.626969i	0.626306	+	0.779577i	$0.284566\pi$
$368$	23.8025	+	6.23229i	1.24079	+	0.324880i
$369$	−25.0542	+	6.31100i	−1.30427	+	0.328538i
$370$	−1.47214	−	5.46287i	−0.0765329	−	0.284001i
$371$	20.4038	−	23.5015i	1.05931	−	1.22014i
$372$	27.0322	+	0.126037i	1.40156	+	0.00653473i
$373$	3.54403	+	26.9196i	0.183503	+	1.39384i	0.796921	+	0.604084i	$0.206461\pi$
$373$	3.54403	+	26.9196i	0.183503	+	1.39384i	−0.613418	+	0.789759i	$0.710206\pi$
$374$	2.37695	+	17.8576i	0.122909	+	0.923393i
$375$	−16.0994	−	12.5470i	−0.831371	−	0.647923i
$376$	−6.00088	+	3.49899i	−0.309472	+	0.180446i
$377$	−0.521277	+	0.521277i	−0.0268471	+	0.0268471i
$378$	19.1274	−	3.48469i	0.983807	−	0.179233i
$379$	−11.2444	−	4.65759i	−0.577587	−	0.239244i	0.0747135	−	0.997205i	$-0.476196\pi$
$379$	−11.2444	−	4.65759i	−0.577587	−	0.239244i	−0.652300	+	0.757961i	$0.726196\pi$
$380$	2.50624	−	4.36972i	0.128567	−	0.224162i
$381$	−4.94943	−	8.72351i	−0.253567	−	0.446919i
$382$	−10.8585	−	18.7455i	−0.555568	−	0.959104i
$383$	−12.6329	−	21.8808i	−0.645509	−	1.11805i	−0.984184	−	0.177151i	$-0.943312\pi$
$383$	−12.6329	−	21.8808i	−0.645509	−	1.11805i	0.338675	−	0.940904i	$-0.390021\pi$
$384$	16.9462	−	9.84002i	0.864782	−	0.502147i
$385$	13.5863	−	20.5545i	0.692422	−	1.04756i
$386$	15.0716	−	26.1912i	0.767125	−	1.33309i
$387$	9.00130	+	12.1033i	0.457562	+	0.615248i
$388$	16.4332	−	0.0469528i	0.834271	−	0.00238367i
$389$	−16.7198	+	12.8295i	−0.847726	+	0.650483i	−0.938458	−	0.345392i	$-0.887746\pi$
$389$	−16.7198	+	12.8295i	−0.847726	+	0.650483i	0.0907326	+	0.995875i	$0.471079\pi$
$390$	−0.535028	+	0.913797i	−0.0270922	+	0.0462719i
$391$	−9.23979	+	9.23979i	−0.467276	+	0.467276i
$392$	18.1820	−	7.83682i	0.918328	−	0.395819i
$393$	−5.08410	−	0.708268i	−0.256459	−	0.0357274i
$394$	0.788414	+	0.325253i	0.0397197	+	0.0163860i
$395$	−7.44623	+	5.71369i	−0.374661	+	0.287487i
$396$	4.26138	+	35.7263i	0.214142	+	1.79531i
$397$	4.10324	−	5.34745i	0.205936	−	0.268381i	−0.678954	−	0.734180i	$-0.737567\pi$
$397$	4.10324	−	5.34745i	0.205936	−	0.268381i	0.884890	+	0.465800i	$0.154233\pi$
$398$	8.02413	+	29.7763i	0.402213	+	1.49255i
$399$	0.467312	+	7.41755i	0.0233949	+	0.371342i
$400$	9.98468	−	2.73663i	0.499234	−	0.136832i
$401$	14.1794	+	24.5595i	0.708086	+	1.22644i	0.965566	+	0.260157i	$0.0837743\pi$
$401$	14.1794	+	24.5595i	0.708086	+	1.22644i	−0.257481	+	0.966283i	$0.582892\pi$
$402$	−19.2725	+	7.84573i	−0.961223	+	0.391309i
$403$	0.283535	−	2.15366i	0.0141239	−	0.107282i
$404$	−3.44434	+	2.65861i	−0.171362	+	0.132271i
$405$	11.3395	−	8.17126i	0.563463	−	0.406033i
$406$	8.20363	−	5.55795i	0.407139	−	0.275836i
$407$	−10.9232	+	10.9232i	−0.541443	+	0.541443i
$408$	−0.0336544	+	10.4069i	−0.00166614	+	0.515216i
$409$	−33.3899	+	8.94680i	−1.65103	+	0.442391i	−0.959900	−	0.280343i	$-0.909552\pi$
$409$	−33.3899	+	8.94680i	−1.65103	+	0.442391i	−0.691126	+	0.722734i	$0.742885\pi$
$410$	−11.4931	+	15.0225i	−0.567606	+	0.741910i
$411$	−18.3886	+	18.1141i	−0.907045	+	0.893505i
$412$	−15.9199	−	4.21700i	−0.784315	−	0.207757i
$413$	−0.404977	+	0.466460i	−0.0199276	+	0.0229530i
$414$	−18.7031	+	18.2008i	−0.919206	+	0.894519i
$415$	9.18135	−	5.30085i	0.450695	−	0.260209i
$416$	−0.612975	−	1.45046i	−0.0300535	−	0.0711146i
$417$	−4.34730	−	35.0561i	−0.212888	−	1.71670i
$418$	−13.7540	+	0.0196489i	−0.672732	+	0.000961058i
$419$	−20.0033	+	8.28563i	−0.977225	+	0.404780i	−0.813397	−	0.581709i	$-0.802384\pi$
$419$	−20.0033	+	8.28563i	−0.977225	+	0.404780i	−0.163828	+	0.986489i	$0.552384\pi$
$420$	9.38123	−	10.7043i	0.457757	−	0.522314i
$421$	8.29945	−	20.0366i	0.404490	−	0.976526i	−0.582071	−	0.813138i	$-0.697758\pi$
$421$	8.29945	−	20.0366i	0.404490	−	0.976526i	0.986562	−	0.163389i	$-0.0522424\pi$
$422$	−29.5257	+	12.2794i	−1.43729	+	0.597751i
$423$	0.110803	−	7.36701i	0.00538741	−	0.358196i
$424$	20.3675	+	26.3092i	0.989135	+	1.27769i
$425$	−1.42303	+	5.31084i	−0.0690273	+	0.257613i
$426$	−0.417838	−	0.114692i	−0.0202443	−	0.00555682i
$427$	6.08055	−	12.4867i	0.294258	−	0.604276i
$428$	−0.316418	−	2.35149i	−0.0152946	−	0.113664i
$429$	2.89112	+	0.0217405i	0.139585	+	0.00104964i
$430$	10.6703	+	2.84276i	0.514567	+	0.137090i
$431$	7.62288	+	4.40107i	0.367181	+	0.211992i	0.672226	−	0.740346i	$-0.265338\pi$
$431$	7.62288	+	4.40107i	0.367181	+	0.211992i	−0.305045	+	0.952338i	$0.598672\pi$
$432$	−0.350090	+	20.7817i	−0.0168437	+	0.999858i
$433$		−	0.593435i		−	0.0285187i	−0.999898	−	0.0142593i	$-0.995461\pi$
$433$		−	0.593435i		−	0.0285187i	0.999898	−	0.0142593i	$-0.00453904\pi$
$434$	−9.20795	+	27.7086i	−0.441996	+	1.33005i
$435$	3.60808	−	6.14225i	0.172994	−	0.294498i
$436$	−4.78825	−	0.616472i	−0.229316	−	0.0295237i
$437$	−6.07322	−	7.91477i	−0.290521	−	0.378615i
$438$	16.1714	+	16.3696i	0.772699	+	0.782170i
$439$	4.27780	−	15.9650i	0.204168	−	0.761966i	−0.785533	−	0.618819i	$-0.787611\pi$
$439$	4.27780	−	15.9650i	0.204168	−	0.761966i	0.989702	−	0.143147i	$-0.0457220\pi$
$440$	18.7049	+	18.5453i	0.891722	+	0.884111i
$441$	−2.84646	+	20.8062i	−0.135546	+	0.990771i
$442$	0.829267	+	0.107970i	0.0394442	+	0.00513561i
$443$	−15.3755	+	2.02422i	−0.730511	+	0.0961736i	−0.486601	−	0.873624i	$-0.661763\pi$
$443$	−15.3755	+	2.02422i	−0.730511	+	0.0961736i	−0.243910	+	0.969798i	$0.578430\pi$
$444$	−7.10500	+	5.39942i	−0.337189	+	0.256245i
$445$	3.00483	−	22.8239i	0.142443	−	1.08196i
$446$	−0.00351396	−	2.45974i	−0.000166391	−	0.116472i
$447$	−8.90395	+	6.72647i	−0.421142	+	0.318151i
$448$	4.41037	+	20.7014i	0.208370	+	0.978050i
$449$			33.5249i			1.58214i	0.611727	+	0.791069i	$0.290475\pi$
$449$			33.5249i			1.58214i	−0.611727	+	0.791069i	$0.709525\pi$
$450$	−2.98617	+	10.5671i	−0.140769	+	0.498138i
$451$	51.2025	+	6.74094i	2.41103	+	0.317418i
$452$	29.2485	−	0.0835685i	1.37574	−	0.00393073i
$453$	28.5128	−	28.0872i	1.33965	−	1.31965i
$454$	3.05338	−	23.4515i	0.143302	−	1.10064i
$455$	−0.758405	−	0.856143i	−0.0355546	−	0.0401366i
$456$	−7.87405	−	1.06255i	−0.368736	−	0.0497587i
$457$	30.2282	+	8.09962i	1.41401	+	0.378884i	0.883357	−	0.468702i	$-0.155278\pi$
$457$	30.2282	+	8.09962i	1.41401	+	0.378884i	0.530658	+	0.847586i	$0.321945\pi$
$458$	38.4055	−	5.11201i	1.79457	−	0.238869i
$459$	−9.43243	−	5.73333i	−0.440268	−	0.267609i
$460$	−2.43964	+	18.9491i	−0.113749	+	0.883506i
$461$	11.1416	−	4.61502i	0.518918	−	0.214943i	−0.107824	−	0.994170i	$-0.534388\pi$
$461$	11.1416	−	4.61502i	0.518918	−	0.214943i	0.626742	+	0.779227i	$0.284388\pi$
$462$	−38.1072	−	7.62373i	−1.77291	−	0.354688i
$463$	−17.6318			−0.819417			−0.409709	−	0.912216i	$-0.634370\pi$
$463$	−17.6318			−0.819417			−0.409709	+	0.912216i	$0.634370\pi$
$464$	4.10973	+	9.76358i	0.190789	+	0.453263i
$465$	2.58325	+	20.8310i	0.119796	+	0.966016i
$466$	0.807717	−	3.03176i	0.0374168	−	0.140444i
$467$	19.7972	−	25.8003i	0.916107	−	1.19389i	−0.0645015	−	0.997918i	$-0.520546\pi$
$467$	19.7972	−	25.8003i	0.916107	−	1.19389i	0.980609	−	0.195976i	$-0.0627876\pi$
$468$	1.65312	+	0.238158i	0.0764154	+	0.0110089i
$469$	−1.58180	−	22.4197i	−0.0730408	−	1.03525i
$470$	−3.28970	−	4.27457i	−0.151743	−	0.197171i
$471$	−15.8485	−	39.0905i	−0.730261	−	1.80120i
$472$	−0.404257	−	0.522189i	−0.0186074	−	0.0240357i
$473$	−7.80340	−	29.1227i	−0.358801	−	1.33906i
$474$	12.7753	+	7.47993i	0.586788	+	0.343564i
$475$	−3.87819	−	1.60640i	−0.177944	−	0.0737067i
$476$	−10.6722	−	3.52961i	−0.489161	−	0.161779i
$477$	−35.0535	+	4.07958i	−1.60499	+	0.186791i
$478$	0.0457212	+	32.0045i	0.00209124	+	1.46385i
$479$	5.23497	−	9.06724i	0.239192	−	0.414293i	−0.721291	−	0.692633i	$-0.756451\pi$
$479$	5.23497	−	9.06724i	0.239192	−	0.414293i	0.960483	+	0.278340i	$0.0897841\pi$
$480$	9.25843	+	12.0752i	0.422588	+	0.551157i
$481$	0.358545	+	0.621019i	0.0163483	+	0.0283160i
$482$	−4.27090	−	2.45768i	−0.194534	−	0.111944i
$483$	−12.4033	−	25.3129i	−0.564372	−	1.15178i
$484$	12.7820	−	48.2540i	0.580998	−	2.19336i
$485$	1.66556	+	12.6512i	0.0756292	+	0.574461i
$486$	−18.6808	−	11.7059i	−0.847378	−	0.530990i
$487$	0.554419	+	2.06912i	0.0251231	+	0.0937607i	0.977349	−	0.211634i	$-0.0678784\pi$
$487$	0.554419	+	2.06912i	0.0251231	+	0.0937607i	−0.952226	+	0.305394i	$0.901212\pi$
$488$	11.8179	+	8.98801i	0.534973	+	0.406868i
$489$	−2.34287	+	16.8176i	−0.105948	+	0.760520i
$490$	7.83822	+	13.2256i	0.354095	+	0.597470i
$491$	36.7909	+	15.2393i	1.66035	+	0.687739i	0.998104	−	0.0615475i	$-0.0196036\pi$
$491$	36.7909	+	15.2393i	1.66035	+	0.687739i	0.662246	+	0.749287i	$0.269604\pi$
$492$	28.7809	+	7.85584i	1.29755	+	0.354168i
$493$	−5.57770	−	0.734318i	−0.251207	−	0.0330720i
$494$	−0.164367	+	0.616949i	−0.00739521	+	0.0277578i
$495$	−27.0916	+	6.82421i	−1.21768	+	0.306725i
$496$	−27.1213	−	15.4525i	−1.21778	−	0.693838i
$497$	0.258068	−	0.390428i	0.0115759	−	0.0175131i
$498$	−13.2041	−	10.2602i	−0.591688	−	0.459771i
$499$	−15.1042	−	11.5899i	−0.676157	−	0.518833i	0.212643	−	0.977130i	$-0.431793\pi$
$499$	−15.1042	−	11.5899i	−0.676157	−	0.518833i	−0.888799	+	0.458297i	$0.848460\pi$
$500$	9.08159	+	21.7489i	0.406141	+	0.972641i
$501$	4.95384	+	1.36738i	0.221321	+	0.0610902i
$502$	9.14065	−	22.1570i	0.407967	−	0.988914i
$503$	−11.1383	+	11.1383i	−0.496634	+	0.496634i	−0.910388	−	0.413755i	$-0.864217\pi$
$503$	−11.1383	+	11.1383i	−0.496634	+	0.496634i	0.413755	+	0.910388i	$0.364217\pi$
$504$	−21.2166	−	7.33876i	−0.945061	−	0.326894i
$505$	−2.38901	−	2.38901i	−0.106309	−	0.106309i
$506$	48.1657	−	20.0315i	2.14123	−	0.890511i
$507$	−5.95541	+	21.5756i	−0.264489	+	0.958207i
$508$	0.0330900	+	11.5813i	0.00146813	+	0.513839i
$509$	−4.06238	+	5.29419i	−0.180062	+	0.234661i	−0.874660	−	0.484737i	$-0.838915\pi$
$509$	−4.06238	+	5.29419i	−0.180062	+	0.234661i	0.694598	+	0.719398i	$0.255582\pi$
$510$	−8.01805	+	1.00595i	−0.355045	+	0.0445442i
$511$	−22.2358	+	11.1037i	−0.983655	+	0.491199i
$512$	−22.6255	+	0.290919i	−0.999917	+	0.0128569i
$513$	5.27978	−	6.56847i	0.233108	−	0.290005i
$514$	11.8718	−	6.87681i	0.523642	−	0.303323i
$515$	1.66917	−	12.6786i	0.0735524	−	0.558686i
$516$	−2.19284	−	17.2784i	−0.0965345	−	0.760640i
$517$	−5.63590	+	13.6063i	−0.247867	+	0.598403i
$518$	−3.15680	−	9.10724i	−0.138702	−	0.400149i
$519$	−24.8616	−	3.46347i	−1.09130	−	0.152030i
$520$	1.05627	−	0.615892i	0.0463207	−	0.0270086i
$521$	−4.35374	+	1.16658i	−0.190741	+	0.0511089i	−0.352925	−	0.935652i	$-0.614813\pi$
$521$	−4.35374	+	1.16658i	−0.190741	+	0.0511089i	0.162184	+	0.986761i	$0.448146\pi$
$522$	−11.1187	−	1.61805i	−0.486654	−	0.0708203i
$523$	4.10771	−	0.540790i	0.179618	−	0.0236471i	−0.0401808	−	0.999192i	$-0.512793\pi$
$523$	4.10771	−	0.540790i	0.179618	−	0.0236471i	0.219798	+	0.975545i	$0.429460\pi$
$524$	4.71274	+	3.59487i	0.205877	+	0.157043i
$525$	−9.84514	−	6.61444i	−0.429677	−	0.288678i
$526$	22.0703	−	5.94752i	0.962309	−	0.259324i
$527$	14.3563	−	8.28862i	0.625371	−	0.361058i
$528$	15.9681	−	38.3544i	0.694921	−	1.66916i
$529$	12.8496	+	7.41869i	0.558676	+	0.322552i
$530$	−18.2422	+	18.2944i	−0.792392	+	0.794659i
$531$	0.695745	−	0.0809720i	0.0301928	−	0.00351388i
$532$	3.73524	−	7.72653i	0.161943	−	0.334988i
$533$	0.917427	−	2.21486i	0.0397382	−	0.0959364i
$534$	−35.1296	+	9.18399i	−1.52021	+	0.397430i
$535$	1.77960	−	0.476842i	0.0769387	−	0.0206157i
$536$	23.8350	+	3.03407i	1.02951	+	0.131052i
$537$	−19.5540	+	7.92780i	−0.843817	+	0.342110i
$538$	−0.927128	+	7.12083i	−0.0399713	+	0.307001i
$539$	20.6244	−	36.5599i	0.888357	−	1.57475i
$540$	−16.0394	+	1.79094i	−0.690228	+	0.0770699i
$541$	−16.9806	−	13.0297i	−0.730052	−	0.560189i	0.175472	−	0.984485i	$-0.443855\pi$
$541$	−16.9806	−	13.0297i	−0.730052	−	0.560189i	−0.905524	+	0.424296i	$0.860522\pi$
$542$	−20.6596	−	35.6657i	−0.887405	−	1.53197i
$543$	−3.13074	+	0.388243i	−0.134353	+	0.0166611i
$544$	5.93395	−	10.4496i	0.254416	−	0.448021i
$545$		−	3.74873i		−	0.160578i
$546$	−0.799677	+	1.61708i	−0.0342230	+	0.0692047i
$547$	−1.09190	−	2.63609i	−0.0466864	−	0.112711i	0.898816	−	0.438326i	$-0.144429\pi$
$547$	−1.09190	−	2.63609i	−0.0466864	−	0.112711i	−0.945502	+	0.325615i	$0.894429\pi$
$548$	28.7675	−	7.79639i	1.22889	−	0.333045i
$549$	−14.6384	+	5.80707i	−0.624750	+	0.247840i
$550$	13.3370	−	17.4327i	0.568694	−	0.743332i
$551$	1.11167	−	4.14883i	0.0473589	−	0.176746i
$552$	29.1329	−	7.70525i	1.23998	−	0.327957i
$553$	−11.9693	+	10.6028i	−0.508985	+	0.450878i
$554$	3.63988	−	2.80125i	0.154644	−	0.119014i
$555$	−4.86277	−	4.93646i	−0.206413	−	0.209541i
$556$	−15.5017	+	37.7289i	−0.657417	+	1.60006i
$557$	−0.534295	+	4.05837i	−0.0226388	+	0.171959i	−0.999029	−	0.0440551i	$-0.985972\pi$
$557$	−0.534295	+	4.05837i	−0.0226388	+	0.171959i	0.976390	+	0.216014i	$0.0693056\pi$
$558$	28.8950	−	16.1622i	1.22322	−	0.684201i
$559$	−1.39958			−0.0591958
$560$	−15.5056	+	5.44919i	−0.655232	+	0.230270i
$561$	13.2996	+	17.6049i	0.561510	+	0.743281i
$562$	11.8769	−	11.9109i	0.500997	−	0.502430i
$563$	−8.34206	−	1.09825i	−0.351576	−	0.0462859i	−0.0473299	−	0.998879i	$-0.515071\pi$
$563$	−8.34206	−	1.09825i	−0.351576	−	0.0462859i	−0.304246	+	0.952593i	$0.598405\pi$
$564$	−4.28813	+	7.34793i	−0.180563	+	0.309404i
$565$	2.96443	+	22.5171i	0.124715	+	0.947301i
$566$	−24.9269	+	19.1837i	−1.04776	+	0.806352i
$567$	18.2909	−	15.2461i	0.768145	−	0.640276i
$568$	0.355295	+	0.352262i	0.0149078	+	0.0147806i
$569$	11.1903	+	2.99844i	0.469123	+	0.125701i	0.485634	−	0.874162i	$-0.338589\pi$
$569$	11.1903	+	2.99844i	0.469123	+	0.125701i	−0.0165103	+	0.999864i	$0.505256\pi$
$570$	0.0375788	−	6.16945i	0.00157400	−	0.258410i
$571$	11.2579	−	8.63852i	0.471130	−	0.361511i	−0.345742	−	0.938330i	$-0.612373\pi$
$571$	11.2579	−	8.63852i	0.471130	−	0.361511i	0.816872	+	0.576819i	$0.195706\pi$
$572$	−2.89596	−	1.66097i	−0.121086	−	0.0694486i
$573$	−22.8771	−	13.4384i	−0.955703	−	0.561399i
$574$	−17.7305	+	26.9078i	−0.740058	+	1.12311i
$575$	15.9207			0.663941
$576$	12.1342	−	20.7066i	0.505591	−	0.862773i
$577$	−0.181187	+	0.313825i	−0.00754290	+	0.0130647i	−0.869772	−	0.493453i	$-0.835734\pi$
$577$	−0.181187	+	0.313825i	−0.00754290	+	0.0130647i	0.862229	+	0.506518i	$0.169068\pi$
$578$	−8.85172	−	15.2812i	−0.368183	−	0.635613i
$579$	0.278294	−	37.0084i	0.0115655	−	1.53801i
$580$	−7.11181	+	4.13314i	−0.295302	+	0.171619i
$581$	14.9675	−	10.1093i	0.620955	−	0.419403i
$582$	17.4911	−	9.95695i	0.725030	−	0.412729i
$583$	68.1365	+	18.2571i	2.82192	+	0.756132i
$584$	−6.98678	−	25.6350i	−0.289115	−	1.06079i
$585$	−0.0195035	+	1.29674i	−0.000806370	+	0.0536137i
$586$	27.6387	+	11.4021i	1.14175	+	0.471017i
$587$	−39.0866	−	16.1902i	−1.61328	−	0.668241i	−0.620064	−	0.784551i	$-0.712893\pi$
$587$	−39.0866	−	16.1902i	−1.61328	−	0.668241i	−0.993213	+	0.116310i	$0.962893\pi$
$588$	14.6593	−	19.3159i	0.604538	−	0.796576i
$589$	4.84336	+	11.6929i	0.199567	+	0.481798i
$590$	0.362074	−	0.363110i	0.0149063	−	0.0149490i
$591$	1.03661	−	0.128550i	0.0426403	−	0.00528782i
$592$	10.2083	−	1.40334i	0.419560	−	0.0576771i
$593$	20.3788	+	35.2970i	0.836855	+	1.44948i	0.892511	+	0.451026i	$0.148942\pi$
$593$	20.3788	+	35.2970i	0.836855	+	1.44948i	−0.0556556	+	0.998450i	$0.517725\pi$
$594$	26.0809	+	35.5187i	1.07011	+	1.45735i
$595$	1.66010	−	8.56905i	0.0680576	−	0.351297i
$596$	12.7703	−	1.71838i	0.523093	−	0.0703876i
$597$	26.5053	+	26.9070i	1.08479	+	1.10123i
$598$	−0.319502	−	2.40035i	−0.0130654	−	0.0981578i
$599$	8.91657	+	33.2771i	0.364321	+	1.35967i	0.868339	+	0.495972i	$0.165188\pi$
$599$	8.91657	+	33.2771i	0.364321	+	1.35967i	−0.504017	+	0.863693i	$0.668145\pi$
$600$	8.99484	−	8.93685i	0.367213	−	0.364845i
$601$	14.3932	+	14.3932i	0.587111	+	0.587111i	0.936848	−	0.349737i	$-0.113729\pi$
$601$	14.3932	+	14.3932i	0.587111	+	0.587111i	−0.349737	+	0.936848i	$0.613729\pi$
$602$	18.4742	+	3.55169i	0.752953	+	0.144756i
$603$	−15.8165	+	19.9828i	−0.644096	+	0.813764i
$604$	−44.6059	+	12.0888i	−1.81499	+	0.491887i
$605$	38.4296	+	5.05935i	1.56238	+	0.205692i
$606$	−2.06924	+	4.91078i	−0.0840573	+	0.199487i
$607$	−29.9837	+	17.3111i	−1.21700	+	0.702635i	−0.964275	−	0.264904i	$-0.914660\pi$
$607$	−29.9837	+	17.3111i	−1.21700	+	0.702635i	−0.252724	+	0.967538i	$0.581326\pi$
$608$	7.31839	+	5.53300i	0.296800	+	0.224393i
$609$	5.39521	−	10.8709i	0.218625	−	0.440512i
$610$	−5.75022	+	9.99261i	−0.232820	+	0.404589i
$611$	0.542375	+	0.416179i	0.0219421	+	0.0168368i
$612$	6.23797	+	11.1150i	0.252155	+	0.449298i
$613$	10.9827	+	14.3129i	0.443587	+	0.578093i	0.960618	−	0.277873i	$-0.0896295\pi$
$613$	10.9827	+	14.3129i	0.443587	+	0.578093i	−0.517031	+	0.855967i	$0.672963\pi$
$614$	−9.03720	+	3.75847i	−0.364712	+	0.151679i
$615$	−3.19636	+	22.9442i	−0.128890	+	0.925200i
$616$	34.0113	+	29.2736i	1.37035	+	1.17947i
$617$	−3.94745	−	3.94745i	−0.158918	−	0.158918i	0.623169	−	0.782087i	$-0.285845\pi$
$617$	−3.94745	−	3.94745i	−0.158918	−	0.158918i	−0.782087	+	0.623169i	$0.785845\pi$
$618$	−19.5144	+	5.10167i	−0.784983	+	0.205219i
$619$	5.57023	+	7.25926i	0.223886	+	0.291774i	0.891768	−	0.452493i	$-0.149465\pi$
$619$	5.57023	+	7.25926i	0.223886	+	0.291774i	−0.667881	+	0.744268i	$0.732799\pi$
$620$	9.21140	−	22.4193i	0.369939	−	0.900379i
$621$	−8.96684	+	30.6791i	−0.359827	+	1.23111i
$622$	1.88944	+	7.01140i	0.0757596	+	0.281132i
$623$	2.36987	−	39.1479i	0.0949467	−	1.56843i
$624$	−1.52791	−	1.17680i	−0.0611654	−	0.0471095i
$625$	−4.64182	+	2.67996i	−0.185673	+	0.107198i
$626$	9.50598	−	35.6806i	0.379935	−	1.42608i
$627$	−14.6513	+	8.31267i	−0.585116	+	0.331976i
$628$	−6.21948	+	48.3078i	−0.248184	+	1.92769i
$629$	−2.09419	+	5.05583i	−0.0835009	+	0.201589i
$630$	3.54817	−	17.0673i	0.141362	−	0.679978i
$631$	22.4226	+	22.4226i	0.892629	+	0.892629i	0.994770	−	0.102141i	$-0.0325693\pi$
$631$	22.4226	+	22.4226i	0.892629	+	0.892629i	−0.102141	+	0.994770i	$0.532569\pi$
$632$	−8.61043	−	14.7672i	−0.342505	−	0.587407i
$633$	−24.0745	+	30.8908i	−0.956877	+	1.22780i
$634$	25.8169	−	33.7449i	1.02532	−	1.34018i
$635$	−8.91594	+	1.17381i	−0.353818	+	0.0465811i
$636$	37.5745	+	15.7695i	1.48993	+	0.625302i
$637$	−1.39151	−	1.36402i	−0.0551335	−	0.0540445i
$638$	19.4661	+	11.2017i	0.770668	+	0.443479i
$639$	−0.514598	+	0.129624i	−0.0203572	+	0.00512785i
$640$	−2.46743	−	17.3959i	−0.0975339	−	0.687634i
$641$	−22.9296	−	13.2384i	−0.905664	−	0.522885i	−0.0266304	−	0.999645i	$-0.508478\pi$
$641$	−22.9296	−	13.2384i	−0.905664	−	0.522885i	−0.879033	+	0.476760i	$0.841811\pi$
$642$	−1.75495	−	2.31617i	−0.0692622	−	0.0914117i
$643$	−8.93126	−	21.5620i	−0.352215	−	0.850321i	−0.996346	−	0.0854066i	$-0.972781\pi$
$643$	−8.93126	−	21.5620i	−0.352215	−	0.850321i	0.644132	−	0.764915i	$-0.277219\pi$
$644$	−1.87396	+	32.4952i	−0.0738445	+	1.28049i
$645$	13.0893	−	3.40199i	0.515392	−	0.133953i
$646$	−4.49884	+	1.87101i	−0.177004	+	0.0736141i
$647$	31.3653	−	8.40432i	1.23310	−	0.330408i	0.417314	−	0.908763i	$-0.362972\pi$
$647$	31.3653	−	8.40432i	1.23310	−	0.330408i	0.815785	+	0.578355i	$0.196305\pi$
$648$	12.1551	+	22.3663i	0.477499	+	0.878632i
$649$	−1.35238	−	0.362369i	−0.0530855	−	0.0142242i
$650$	−0.621421	−	0.807460i	−0.0243741	−	0.0316712i
$651$	6.88773	+	35.0911i	0.269951	+	1.37533i
$652$	11.8914	−	15.5892i	0.465703	−	0.610520i
$653$	−18.4766	−	14.1776i	−0.723045	−	0.554812i	0.180360	−	0.983601i	$-0.442274\pi$
$653$	−18.4766	−	14.1776i	−0.723045	−	0.554812i	−0.903405	+	0.428789i	$0.858940\pi$
$654$	−5.47638	+	2.22941i	−0.214144	+	0.0871768i
$655$	−2.30126	+	3.98590i	−0.0899177	+	0.155742i
$656$	−24.4980	−	24.2196i	−0.956487	−	0.945617i
$657$	27.1088	+	7.70255i	1.05762	+	0.300505i
$658$	−6.10314	−	6.86988i	−0.237925	−	0.267816i
$659$	0.371982	+	0.898045i	0.0144904	+	0.0349828i	0.930959	−	0.365123i	$-0.118973\pi$
$659$	0.371982	+	0.898045i	0.0144904	+	0.0349828i	−0.916469	+	0.400106i	$0.868973\pi$
$660$	31.1214	+	8.49467i	1.21140	+	0.330655i
$661$	24.6587	−	18.9213i	0.959112	−	0.735952i	−0.00540193	−	0.999985i	$-0.501719\pi$
$661$	24.6587	−	18.9213i	0.959112	−	0.735952i	0.964514	+	0.264033i	$0.0850528\pi$
$662$	−15.1592	+	2.01778i	−0.589178	+	0.0784232i
$663$	0.949170	−	0.384823i	0.0368627	−	0.0149453i
$664$	7.46550	+	17.8071i	0.289718	+	0.691048i
$665$	6.32085	+	2.11054i	0.245112	+	0.0818433i
$666$	−4.31955	+	10.0396i	−0.167379	+	0.389027i
$667$	2.12632	+	16.1510i	0.0823314	+	0.625369i
$668$	−4.20802	−	4.18405i	−0.162813	−	0.161886i
$669$	−1.48662	−	2.62020i	−0.0574759	−	0.101303i
$670$	0.0266532	+	18.6570i	0.00102970	+	0.720783i
$671$	31.4784			1.21521
$672$	17.1819	+	19.4109i	0.662805	+	0.748792i
$673$	1.32871			0.0512180			0.0256090	−	0.999672i	$-0.491848\pi$
$673$	1.32871			0.0512180			0.0256090	+	0.999672i	$0.491848\pi$
$674$	−0.0121517	−	8.50605i	−0.000468064	−	0.327641i
$675$	3.18690	+	13.0658i	0.122664	+	0.502903i
$676$	18.2229	−	18.3273i	0.700881	−	0.704897i
$677$	3.02936	+	23.0103i	0.116428	+	0.884357i	0.945593	+	0.325353i	$0.105483\pi$
$677$	3.02936	+	23.0103i	0.116428	+	0.884357i	−0.829165	+	0.559004i	$0.811184\pi$
$678$	31.1314	−	17.7218i	1.19559	−	0.680601i
$679$	4.34740	+	21.3001i	0.166838	+	0.817422i
$680$	8.63597	+	3.53385i	0.331174	+	0.135517i
$681$	−10.8827	−	26.8424i	−0.417027	−	1.02860i
$682$	−65.5997	+	8.73172i	−2.51194	+	0.334355i
$683$	26.0766	−	20.0093i	0.997794	−	0.765634i	0.0255669	−	0.999673i	$-0.491861\pi$
$683$	26.0766	−	20.0093i	0.997794	−	0.765634i	0.972227	+	0.234039i	$0.0751942\pi$
$684$	−9.03507	+	3.61414i	−0.345465	+	0.138190i
$685$	8.85667	+	21.3819i	0.338396	+	0.816960i
$686$	14.9063	+	21.5361i	0.569124	+	0.822252i
$687$	37.8622	−	28.6030i	1.44453	−	1.09127i
$688$	−7.59002	+	18.6242i	−0.289367	+	0.710042i
$689$	1.63725	−	2.83580i	0.0623742	−	0.108035i
$690$	8.82271	+	21.6723i	0.335875	+	0.825052i
$691$	−19.5036	−	14.9656i	−0.741952	−	0.569320i	0.167131	−	0.985935i	$-0.446550\pi$
$691$	−19.5036	−	14.9656i	−0.741952	−	0.569320i	−0.909083	+	0.416615i	$0.863216\pi$
$692$	23.0456	+	17.5791i	0.876063	+	0.668259i
$693$	−45.2220	+	14.8456i	−1.71784	+	0.563937i
$694$	−6.22190	−	8.08459i	−0.236180	−	0.306887i
$695$	−30.5934	−	8.19749i	−1.16048	−	0.310948i
$696$	10.2674	+	7.93135i	0.389185	+	0.300637i
$697$	17.6717	−	4.73512i	0.669363	−	0.179355i
$698$	−26.9422	+	11.2050i	−1.01978	+	0.424114i
$699$	−0.966612	−	3.71909i	−0.0365606	−	0.140669i
$700$	6.15359	+	12.2353i	0.232584	+	0.462452i
$701$	8.53901	+	20.6150i	0.322514	+	0.778617i	0.999107	+	0.0422600i	$0.0134558\pi$
$701$	8.53901	+	20.6150i	0.322514	+	0.778617i	−0.676593	+	0.736357i	$0.736544\pi$
$702$	1.90596	−	0.742694i	0.0719358	−	0.0280312i
$703$	−3.61828	−	2.08902i	−0.136466	−	0.0787888i
$704$	−37.8076	+	29.5291i	−1.42493	+	1.11292i
$705$	−6.08410	−	2.57388i	−0.229140	−	0.0969381i
$706$	−42.5998	−	24.5139i	−1.60326	−	0.922593i
$707$	−4.34639	−	3.77350i	−0.163463	−	0.141917i
$708$	−0.745782	−	0.312995i	−0.0280282	−	0.0117631i
$709$	−35.7392	+	4.70516i	−1.34222	+	0.176706i	−0.767185	−	0.641426i	$-0.778343\pi$
$709$	−35.7392	+	4.70516i	−1.34222	+	0.176706i	−0.575030	+	0.818132i	$0.695010\pi$
$710$	−0.236062	+	0.308554i	−0.00885925	+	0.0115798i
$711$	18.1290	+	0.272667i	0.679891	+	0.0102258i
$712$	40.5450	+	10.6780i	1.51949	+	0.400174i
$713$	−33.9423	−	33.9423i	−1.27115	−	1.27115i
$714$	−13.5055	+	2.67092i	−0.505430	+	0.0999565i
$715$	0.992031	−	2.39498i	0.0370999	−	0.0895670i
$716$	24.1647	+	3.11113i	0.903077	+	0.116268i
$717$	19.3429	+	34.0923i	0.722372	+	1.27320i
$718$	−4.55867	+	17.1109i	−0.170128	+	0.638574i
$719$	−31.0938	+	17.9520i	−1.15960	+	0.669497i	−0.951209	−	0.308548i	$-0.900157\pi$
$719$	−31.0938	+	17.9520i	−1.15960	+	0.669497i	−0.208394	+	0.978045i	$0.566824\pi$
$720$	17.1500	+	7.29187i	0.639144	+	0.271752i
$721$	1.31645	−	21.7465i	0.0490272	−	0.809882i
$722$	6.02363	+	22.3527i	0.224176	+	0.831881i
$723$	−6.03482	−	0.0453805i	−0.224438	−	0.00168772i
$724$	3.36944	+	1.38440i	0.125224	+	0.0514509i
$725$	4.17273	+	5.43801i	0.154971	+	0.201963i
$726$	−15.4634	−	59.1492i	−0.573902	−	2.19523i
$727$	13.3053	+	13.3053i	0.493467	+	0.493467i	0.909397	−	0.415930i	$-0.136544\pi$
$727$	13.3053	+	13.3053i	0.493467	+	0.493467i	−0.415930	+	0.909397i	$0.636544\pi$
$728$	1.72122	−	1.17331i	0.0637926	−	0.0434859i
$729$	−26.9725	−	1.21777i	−0.998982	−	0.0451024i
$730$	19.0497	−	7.92256i	0.705062	−	0.293227i
$731$	−6.50200	−	8.47357i	−0.240485	−	0.313406i
$732$	18.0175	+	2.45757i	0.665948	+	0.0908344i
$733$	−39.7745	−	30.5201i	−1.46910	−	1.12728i	−0.964549	−	0.263905i	$-0.914989\pi$
$733$	−39.7745	−	30.5201i	−1.46910	−	1.12728i	−0.504556	−	0.863379i	$-0.668344\pi$
$734$	9.78266	−	17.0001i	0.361084	−	0.627485i
$735$	16.3294	+	9.37442i	0.602320	+	0.345781i
$736$	−33.6743	−	8.76569i	−1.24125	−	0.323108i
$737$	44.1159	−	25.4703i	1.62503	−	0.938211i
$738$	35.4192	−	8.97571i	1.30380	−	0.330400i
$739$	8.41621	+	1.10802i	0.309595	+	0.0407590i	0.283723	−	0.958906i	$-0.408430\pi$
$739$	8.41621	+	1.10802i	0.309595	+	0.0407590i	0.0258723	+	0.999665i	$0.491764\pi$
$740$	2.09295	+	7.72268i	0.0769385	+	0.283891i
$741$	0.196701	+	0.756817i	0.00722600	+	0.0278024i
$742$	−28.8078	+	33.2773i	−1.05757	+	1.22165i
$743$	−37.9842	−	37.9842i	−1.39350	−	1.39350i	−0.817319	−	0.576186i	$-0.804540\pi$
$743$	−37.9842	−	37.9842i	−1.39350	−	1.39350i	−0.576186	−	0.817319i	$-0.695460\pi$
$744$	−38.2296	−	0.123629i	−1.40156	−	0.00453247i
$745$	2.58960	+	9.66453i	0.0948757	+	0.354081i
$746$	−5.06640	−	38.0628i	−0.185494	−	1.39358i
$747$	−20.2623	−	2.97823i	−0.741357	−	0.108968i
$748$	−3.39759	−	25.2496i	−0.124228	−	0.923216i
$749$	2.96712	−	1.02373i	0.108416	−	0.0374065i
$750$	22.7933	+	17.7116i	0.832295	+	0.646735i
$751$	−13.8702	−	24.0239i	−0.506131	−	0.876644i	−0.999975	−	0.00709356i	$-0.997742\pi$
$751$	−13.8702	−	24.0239i	−0.506131	−	0.876644i	0.493844	−	0.869550i	$-0.335591\pi$
$752$	8.47945	−	4.96043i	0.309214	−	0.180888i
$753$	−3.61266	−	29.1320i	−0.131653	−	1.06163i
$754$	0.736143	−	0.738249i	0.0268088	−	0.0268855i
$755$	−13.7329	−	33.1540i	−0.499790	−	1.20660i
$756$	−27.0431	+	4.96673i	−0.983550	+	0.180638i
$757$	−15.4654	−	6.40597i	−0.562099	−	0.232829i	0.0834972	−	0.996508i	$-0.473391\pi$
$757$	−15.4654	−	6.40597i	−0.562099	−	0.232829i	−0.645596	+	0.763679i	$0.723391\pi$
$758$	15.9114	+	6.56410i	0.577928	+	0.238419i
$759$	39.2732	−	50.3926i	1.42553	−	1.82914i
$760$	−3.53553	+	6.18478i	−0.128247	+	0.224345i
$761$	3.42784	+	0.918488i	0.124259	+	0.0332952i	0.320413	−	0.947278i	$-0.396178\pi$
$761$	3.42784	+	0.918488i	0.124259	+	0.0332952i	−0.196153	+	0.980573i	$0.562845\pi$
$762$	7.01717	+	12.3269i	0.254205	+	0.446556i
$763$	−0.449479	−	6.37070i	−0.0162722	−	0.230635i
$764$	15.3940	+	26.4882i	0.556937	+	0.958310i
$765$	−7.94157	+	5.90618i	−0.287128	+	0.213538i
$766$	17.9098	+	30.9185i	0.647106	+	1.11713i
$767$	−0.0324963	+	0.0562852i	−0.00117337	+	0.00203234i
$768$	−23.9457	+	13.9501i	−0.864064	+	0.503382i
$769$	−32.0125			−1.15440			−0.577201	−	0.816602i	$-0.695855\pi$
$769$	−32.0125			−1.15440			−0.577201	+	0.816602i	$0.695855\pi$
$770$	−19.1724	+	29.0959i	−0.690925	+	1.04854i
$771$	8.51075	−	14.4883i	0.306507	−	0.521785i
$772$	−21.2616	+	37.0703i	−0.765220	+	1.33419i
$773$	2.86484	−	2.19827i	0.103041	−	0.0790663i	−0.555956	−	0.831212i	$-0.687648\pi$
$773$	2.86484	−	2.19827i	0.103041	−	0.0790663i	0.658997	+	0.752146i	$0.270981\pi$
$774$	−12.7542	−	17.0985i	−0.458440	−	0.614593i
$775$	−19.5093	−	5.22751i	−0.700796	−	0.187778i
$776$	−23.2400	+	0.0996018i	−0.834267	+	0.00357550i
$777$	−8.85582	−	7.80611i	−0.317701	−	0.280042i
$778$	23.6194	−	18.1775i	0.846796	−	0.651693i
$779$	1.82317	+	13.8484i	0.0653218	+	0.496169i
$780$	0.754797	−	1.29338i	0.0270261	−	0.0463105i
$781$	1.05167	+	0.138455i	0.0376316	+	0.00495430i
$782$	13.0483	−	13.0857i	0.466608	−	0.467943i
$783$	−12.8291	+	4.97801i	−0.458475	+	0.177900i
$784$	−25.6973	+	11.1197i	−0.917762	+	0.397131i
$785$	−37.8203			−1.34987
$786$	7.19143	+	0.991369i	0.256510	+	0.0353610i
$787$	−2.10773	+	16.0098i	−0.0751324	+	0.570687i	0.911929	+	0.410347i	$0.134592\pi$
$787$	−2.10773	+	16.0098i	−0.0751324	+	0.570687i	−0.987062	+	0.160340i	$0.948741\pi$
$788$	−1.11564	−	0.458384i	−0.0397431	−	0.0163292i
$789$	19.9436	−	19.6458i	0.710009	−	0.699411i
$790$	10.5190	−	8.09542i	0.374249	−	0.288022i
$791$	7.73767	+	37.9107i	0.275120	+	1.34795i
$792$	−6.09867	−	50.5160i	−0.216707	−	1.79501i
$793$	0.378196	−	1.41145i	0.0134302	−	0.0501220i
$794$	−5.79205	+	7.57071i	−0.205552	+	0.268674i
$795$	−8.41907	+	30.5011i	−0.298594	+	1.08176i
$796$	−11.4080	−	42.0937i	−0.404345	−	1.49197i
$797$	9.85140	+	23.7834i	0.348955	+	0.842451i	0.996744	+	0.0806315i	$0.0256937\pi$
$797$	9.85140	+	23.7834i	0.348955	+	0.842451i	−0.647789	+	0.761820i	$0.724306\pi$
$798$	−0.675864	−	10.4891i	−0.0239253	−	0.371308i
$799$			5.21718i			0.184570i
$800$	−14.1149	+	3.89035i	−0.499038	+	0.137545i
$801$	−31.9150	+	30.9692i	−1.12766	+	1.09424i
$802$	−20.1023	−	34.7036i	−0.709837	−	1.22543i
$803$	−44.6909	−	34.2926i	−1.57711	−	1.21016i
$804$	27.2395	−	11.1345i	0.960663	−	0.392682i
$805$	−25.2115	+	1.77877i	−0.888590	+	0.0626936i
$806$	−0.396628	+	3.04631i	−0.0139706	+	0.107302i
$807$	3.30443	+	8.15042i	0.116322	+	0.286908i
$808$	4.86566	−	3.76679i	0.171173	−	0.132515i
$809$	−11.8806	+	3.18341i	−0.417701	+	0.111923i	−0.461547	−	0.887116i	$-0.652705\pi$
$809$	−11.8806	+	3.18341i	−0.417701	+	0.111923i	0.0438462	+	0.999038i	$0.486039\pi$
$810$	−16.0199	+	11.5788i	−0.562883	+	0.406838i
$811$	−5.17025	+	12.4821i	−0.181552	+	0.438305i	−0.988287	−	0.152608i	$-0.951233\pi$
$811$	−5.17025	+	12.4821i	−0.181552	+	0.438305i	0.806735	+	0.590914i	$0.201233\pi$
$812$	−11.5904	+	7.87669i	−0.406745	+	0.276418i
$813$	−43.5264	−	25.5683i	−1.52654	−	0.896720i
$814$	15.4257	−	15.4698i	0.540669	−	0.542216i
$815$	13.1849	+	7.61230i	0.461847	+	0.266647i
$816$	0.0265692	−	14.7176i	0.000930108	−	0.515218i
$817$	7.06196	−	4.07722i	0.247067	−	0.142644i
$818$	47.2024	−	12.7201i	1.65039	−	0.444749i
$819$	0.122336	+	2.20606i	0.00427478	+	0.0770859i
$820$	16.2234	−	21.2683i	0.566545	−	0.742720i
$821$	−35.2267	+	4.63769i	−1.22942	+	0.161856i	−0.717120	−	0.696950i	$-0.754540\pi$
$821$	−35.2267	+	4.63769i	−1.22942	+	0.161856i	−0.512301	+	0.858806i	$0.671207\pi$
$822$	25.9688	−	25.6544i	0.905767	−	0.894800i
$823$	−23.3321	+	6.25181i	−0.813304	+	0.217924i	−0.641417	−	0.767192i	$-0.721653\pi$
$823$	−23.3321	+	6.25181i	−0.813304	+	0.217924i	−0.171887	+	0.985117i	$0.554986\pi$
$824$	22.5226	+	5.93157i	0.784611	+	0.206636i
$825$	3.70917	−	26.6253i	0.129137	−	0.926973i
$826$	0.571781	−	0.660492i	0.0198948	−	0.0229815i
$827$	−3.80689	+	9.19064i	−0.132379	+	0.319590i	−0.976145	−	0.217121i	$-0.930333\pi$
$827$	−3.80689	+	9.19064i	−0.132379	+	0.319590i	0.843766	+	0.536711i	$0.180333\pi$
$828$	26.4133	−	25.7775i	0.917927	−	0.895831i
$829$	1.01206	−	7.68737i	0.0351504	−	0.266993i	−0.964841	−	0.262834i	$-0.915343\pi$
$829$	1.01206	−	7.68737i	0.0351504	−	0.266993i	0.999991	−	0.00415917i	$-0.00132391\pi$
$830$	−12.9737	+	7.51508i	−0.450322	+	0.260852i
$831$	2.19171	−	5.18073i	0.0760297	−	0.179717i
$832$	0.869806	+	2.05002i	0.0301551	+	0.0710716i
$833$	1.79379	−	14.7615i	0.0621510	−	0.511457i
$834$	6.21883	+	49.5679i	0.215341	+	1.71640i
$835$	2.80505	−	3.65562i	0.0970728	−	0.126508i
$836$	19.4511	−	0.0555754i	0.672730	−	0.00192211i
$837$	21.0614	−	34.6500i	0.727987	−	1.19768i
$838$	28.2722	−	11.7581i	0.976645	−	0.406175i
$839$	4.97277	+	4.97277i	0.171679	+	0.171679i	0.787717	−	0.616038i	$-0.211263\pi$
$839$	4.97277	+	4.97277i	0.171679	+	0.171679i	−0.616038	+	0.787717i	$0.711263\pi$
$840$	−13.2454	+	15.1570i	−0.457011	+	0.522968i
$841$	15.5467	−	15.5467i	0.536094	−	0.536094i
$842$	−11.6967	+	28.3528i	−0.403095	+	0.977103i
$843$	5.48137	−	19.8582i	0.188788	−	0.683954i
$844$	41.7308	−	17.4253i	1.43643	−	0.599804i
$845$	15.9214	+	12.2169i	0.547713	+	0.420275i
$846$	−0.141815	+	10.4187i	−0.00487569	+	0.358204i
$847$	65.9149	+	3.99024i	2.26486	+	0.137106i
$848$	−28.8572	−	37.1657i	−0.990959	−	1.27628i
$849$	−15.0095	+	35.4791i	−0.515123	+	1.21764i
$850$	2.00174	−	7.51352i	0.0686592	−	0.257712i
$851$	15.7105	+	2.06833i	0.538549	+	0.0709013i
$852$	0.591143	+	0.161354i	0.0202522	+	0.00552790i
$853$	30.0926	+	12.4648i	1.03035	+	0.426785i	0.832839	−	0.553516i	$-0.186714\pi$
$853$	30.0926	+	12.4648i	1.03035	+	0.426785i	0.197511	+	0.980301i	$0.436714\pi$
$854$	−8.57396	+	17.6712i	−0.293395	+	0.604696i
$855$	−3.67924	−	6.59989i	−0.125827	−	0.225712i
$856$	0.452232	+	3.32487i	0.0154570	+	0.113642i
$857$	0.0171032	+	0.0638301i	0.000584235	+	0.00218039i	0.966217	−	0.257729i	$-0.0829741\pi$
$857$	0.0171032	+	0.0638301i	0.000584235	+	0.00218039i	−0.965633	+	0.259909i	$0.916307\pi$
$858$	−4.08870	−	0.0249047i	−0.139586	−	0.000850234i
$859$	−5.96615	−	45.3174i	−0.203562	−	1.54621i	−0.722484	−	0.691387i	$-0.757000\pi$
$859$	−5.96615	−	45.3174i	−0.203562	−	1.54621i	0.518922	−	0.854822i	$-0.326333\pi$
$860$	−15.0958	−	3.99871i	−0.514762	−	0.136355i
$861$	−2.68094	+	39.3753i	−0.0913663	+	1.34191i
$862$	−10.7893	−	6.20865i	−0.367484	−	0.211467i
$863$	12.7599	+	22.1008i	0.434353	+	0.752322i	0.997243	−	0.0742106i	$-0.0236437\pi$
$863$	12.7599	+	22.1008i	0.434353	+	0.752322i	−0.562890	+	0.826532i	$0.690310\pi$
$864$	0.453116	−	29.3904i	0.0154153	−	0.999881i
$865$	−11.2533	+	19.4913i	−0.382624	+	0.662724i
$866$	0.00119893	+	0.839243i	4.07415e−5	+	0.0285186i
$867$	−18.6492	−	10.9549i	−0.633359	−	0.372048i
$868$	12.9660	−	39.2044i	0.440095	−	1.33068i
$869$	−33.4828	−	13.8690i	−1.13583	−	0.470475i
$870$	−5.09019	+	8.69374i	−0.172573	+	0.294745i
$871$	−0.612025	−	2.28411i	−0.0207377	−	0.0773941i
$872$	6.77284	+	0.862148i	0.229357	+	0.0291960i
$873$	12.6446	−	21.1597i	0.427956	−	0.716148i
$874$	8.60481	+	11.1809i	0.291062	+	0.378200i
$875$	−25.8374	+	17.4510i	−0.873463	+	0.589952i
$876$	−22.9029	−	23.1174i	−0.773816	−	0.781065i
$877$	4.41210	−	5.74995i	0.148986	−	0.194162i	−0.712898	−	0.701268i	$-0.752618\pi$
$877$	4.41210	−	5.74995i	0.148986	−	0.194162i	0.861884	+	0.507105i	$0.169285\pi$
$878$	−6.01746	+	22.5865i	−0.203079	+	0.762257i
$879$	36.3394	−	4.50645i	1.22570	−	0.151999i
$880$	−26.4902	−	26.1892i	−0.892984	−	0.882836i
$881$	−20.3318			−0.684994			−0.342497	−	0.939519i	$-0.611273\pi$
$881$	−20.3318			−0.684994			−0.342497	+	0.939519i	$0.611273\pi$
$882$	3.98346	−	29.4301i	0.134130	−	0.990964i
$883$	−18.6957	+	7.74402i	−0.629161	+	0.260607i	−0.674396	−	0.738369i	$-0.735596\pi$
$883$	−18.6957	+	7.74402i	−0.629161	+	0.260607i	0.0452358	+	0.998976i	$0.485596\pi$
$884$	−1.17298	−	0.151017i	−0.0394515	−	0.00507926i
$885$	0.167103	−	0.605389i	0.00561709	−	0.0203499i
$886$	21.7401	−	2.89374i	0.730373	−	0.0972171i
$887$	−35.1357	−	9.41458i	−1.17974	−	0.316111i	−0.384917	−	0.922951i	$-0.625770\pi$
$887$	−35.1357	−	9.41458i	−1.17974	−	0.316111i	−0.794824	+	0.606841i	$0.792437\pi$
$888$	10.0371	−	7.65027i	0.336822	−	0.256726i
$889$	−15.0113	+	3.06383i	−0.503461	+	0.102758i
$890$	−4.20335	+	32.2840i	−0.140897	+	1.08216i
$891$	49.2175	+	22.1433i	1.64885	+	0.741830i
$892$	0.00993896	+	3.47858i	0.000332781	+	0.116472i
$893$	−3.94911	−	0.519910i	−0.132152	−	0.0173981i
$894$	12.5785	−	9.53065i	0.420687	−	0.318752i
$895$			18.9186i			0.632379i
$896$	−6.27902	−	29.2673i	−0.209767	−	0.977751i
$897$	−1.78769	−	2.36640i	−0.0596892	−	0.0790117i
$898$	−0.0677314	−	47.4113i	−0.00226022	−	1.58214i
$899$	2.69752	−	20.4897i	0.0899672	−	0.683369i
$900$	4.20173	−	14.9502i	0.140058	−	0.498338i
$901$	24.7751	−	3.26171i	0.825380	−	0.108663i
$902$	−72.4248	−	9.42967i	−2.41148	−	0.313974i
$903$	21.8365	−	7.35087i	0.726673	−	0.244622i
$904$	−41.3635	+	0.177275i	−1.37573	+	0.00589609i
$905$	−0.732090	+	2.73220i	−0.0243355	+	0.0908213i
$906$	−40.2664	+	39.7789i	−1.33776	+	1.32156i
$907$	−9.98888	−	13.0178i	−0.331675	−	0.432247i	0.597510	−	0.801861i	$-0.296157\pi$
$907$	−9.98888	−	13.0178i	−0.331675	−	0.432247i	−0.929186	+	0.369614i	$0.879490\pi$
$908$	−4.27074	+	33.1716i	−0.141730	+	1.10084i
$909$	0.754482	+	6.48283i	0.0250246	+	0.215022i
$910$	1.07427	+	1.20924i	0.0356119	+	0.0400858i
$911$			13.4126i			0.444380i	0.975003	+	0.222190i	$0.0713205\pi$
$911$			13.4126i			0.444380i	−0.975003	+	0.222190i	$0.928680\pi$
$912$	11.1377	+	1.48677i	0.368807	+	0.0492319i
$913$	35.4522	+	20.4683i	1.17330	+	0.677403i
$914$	−42.7654	−	11.3935i	−1.41455	−	0.376864i
$915$	−0.106177	+	14.1197i	−0.00351009	+	0.466782i
$916$	−54.3033	+	7.30706i	−1.79423	+	0.241432i
$917$	−3.43291	+	7.04967i	−0.113365	+	0.232801i
$918$	13.3510	+	8.08908i	0.440650	+	0.266979i
$919$	−3.40062	+	12.6913i	−0.112176	+	0.418647i	−0.999060	−	0.0433450i	$-0.986199\pi$
$919$	−3.40062	+	12.6913i	−0.112176	+	0.418647i	0.886884	+	0.461992i	$0.152865\pi$
$920$	3.41188	−	26.8030i	0.112486	−	0.883668i
$921$	−7.36872	+	9.45503i	−0.242808	+	0.311554i
$922$	−15.7473	+	6.54913i	−0.518611	+	0.215684i
$923$	0.0188434	−	0.0454919i	0.000620237	−	0.00149738i
$924$	53.9071	+	10.7046i	1.77341	+	0.352155i
$925$	6.15997	−	2.55155i	0.202539	−	0.0838943i
$926$	24.9350	−	0.0356219i	0.819416	−	0.00117061i
$927$	−17.7286	+	17.2032i	−0.582285	+	0.565029i
$928$	−5.83176	−	13.7995i	−0.191437	−	0.452990i
$929$	−15.1596	+	8.75241i	−0.497371	+	0.287157i	−0.727627	−	0.685973i	$-0.759377\pi$
$929$	−15.1596	+	8.75241i	−0.497371	+	0.287157i	0.230256	+	0.973130i	$0.426044\pi$
$930$	−3.69536	−	29.4543i	−0.121175	−	0.965844i
$931$	10.9949	+	2.82883i	0.360343	+	0.0927113i
$932$	−1.13616	+	4.28918i	−0.0372161	+	0.140497i
$933$	6.24120	+	6.33577i	0.204328	+	0.207424i
$934$	−27.9454	+	36.5271i	−0.914401	+	1.19520i
$935$	19.1088	−	5.12018i	0.624923	−	0.167448i
$936$	−2.33834	−	0.333467i	−0.0764311	−	0.0108997i
$937$	−28.3914	+	28.3914i	−0.927508	+	0.927508i	−0.997544	−	0.0700367i	$-0.977688\pi$
$937$	−28.3914	+	28.3914i	−0.927508	+	0.927508i	0.0700367	+	0.997544i	$0.477688\pi$
$938$	2.28230	+	31.7031i	0.0745197	+	1.03514i
$939$	−11.3760	−	43.7698i	−0.371242	−	1.42837i
$940$	4.66097	+	6.03850i	0.152024	+	0.196954i
$941$	4.09545	−	31.1080i	0.133508	−	1.01409i	−0.785224	−	0.619211i	$-0.787452\pi$
$941$	4.09545	−	31.1080i	0.133508	−	1.01409i	0.918732	−	0.394881i	$-0.129214\pi$
$942$	22.4921	+	55.2503i	0.732833	+	1.80015i
$943$	−26.4880	−	45.8785i	−0.862567	−	1.49401i
$944$	0.572760	+	0.737669i	0.0186417	+	0.0240091i
$945$	−6.50646	−	20.3345i	−0.211655	−	0.661480i
$946$	11.0945	+	41.1699i	0.360713	+	1.33855i
$947$	−9.07062	+	11.8211i	−0.294755	+	0.384133i	−0.917131	−	0.398586i	$-0.869501\pi$
$947$	−9.07062	+	11.8211i	−0.294755	+	0.384133i	0.622376	+	0.782719i	$0.286168\pi$
$948$	−18.0821	−	10.5524i	−0.587278	−	0.342726i
$949$	−2.07457	+	1.59187i	−0.0673434	+	0.0516744i
$950$	5.48783	+	2.26396i	0.178049	+	0.0734524i
$951$	7.17994	−	51.5393i	0.232826	−	1.67127i
$952$	15.0999	+	4.97006i	0.489391	+	0.161080i
$953$	−10.2244	+	10.2244i	−0.331199	+	0.331199i	−0.853042	−	0.521843i	$-0.825245\pi$
$953$	−10.2244	+	10.2244i	−0.331199	+	0.331199i	0.521843	+	0.853042i	$0.325245\pi$
$954$	49.5648	−	5.84021i	1.60472	−	0.189084i
$955$	−18.8732	+	14.4819i	−0.610722	+	0.468624i
$956$	−0.129319	−	45.2610i	−0.00418248	−	1.46385i
$957$	27.5057	+	0.206837i	0.889134	+	0.00668608i
$958$	−7.38504	+	12.8336i	−0.238600	+	0.414634i
$959$	17.6150	+	35.2750i	0.568818	+	1.13909i
$960$	−13.1178	−	17.0582i	−0.423375	−	0.550552i
$961$	14.9482	+	25.8911i	0.482201	+	0.835197i
$962$	−0.508314	−	0.877528i	−0.0163887	−	0.0282926i
$963$	−3.26726	−	1.41128i	−0.105286	−	0.0454777i
$964$	6.04492	+	3.46705i	0.194694	+	0.111666i
$965$	−30.6574	−	12.6987i	−0.986895	−	0.408785i
$966$	17.5921	+	35.7727i	0.566017	+	1.15097i
$967$	−14.7744	+	14.7744i	−0.475112	+	0.475112i	−0.903564	−	0.428452i	$-0.859059\pi$
$967$	−14.7744	+	14.7744i	−0.475112	+	0.475112i	0.428452	+	0.903564i	$0.359059\pi$
$968$	−17.9789	+	68.2672i	−0.577864	+	2.19419i
$969$	−3.66825	+	4.70684i	−0.117841	+	0.151205i
$970$	−2.38102	−	17.8881i	−0.0764498	−	0.574352i
$971$	−4.18183	−	31.7642i	−0.134201	−	1.01936i	−0.917506	−	0.397723i	$-0.869801\pi$
$971$	−4.18183	−	31.7642i	−0.134201	−	1.01936i	0.783304	−	0.621639i	$-0.213533\pi$
$972$	26.4423	+	16.5169i	0.848136	+	0.529779i
$973$	−52.9742	−	10.2628i	−1.69828	−	0.329012i
$974$	−0.788246	−	2.92505i	−0.0252570	−	0.0937247i
$975$	−1.14928	−	0.486203i	−0.0368064	−	0.0155710i
$976$	−16.7312	−	12.6871i	−0.535553	−	0.406103i
$977$	−0.644501	+	1.11631i	−0.0206194	+	0.0357139i	−0.876151	−	0.482037i	$-0.839897\pi$
$977$	−0.644501	+	1.11631i	−0.0206194	+	0.0357139i	0.855532	+	0.517751i	$0.173230\pi$
$978$	3.27933	−	23.7884i	0.104862	−	0.760670i
$979$	82.1247	−	34.0172i	2.62472	−	1.08719i
$980$	−11.1116	−	18.6879i	−0.354948	−	0.596964i
$981$	−4.49434	+	5.67824i	−0.143493	+	0.181292i
$982$	−52.0609	−	21.4773i	−1.66133	−	0.685367i
$983$	−1.58878	−	5.92942i	−0.0506743	−	0.189119i	0.935949	−	0.352135i	$-0.114544\pi$
$983$	−1.58878	−	5.92942i	−0.0506743	−	0.189119i	−0.986623	+	0.163016i	$0.947878\pi$
$984$	−40.7182	−	11.0517i	−1.29805	−	0.352314i
$985$	0.242399	−	0.904647i	0.00772349	−	0.0288244i
$986$	7.88953	+	1.02721i	0.251254	+	0.0327131i
$987$	−10.6481	−	3.64464i	−0.338933	−	0.116010i
$988$	0.231203	−	0.872829i	0.00735554	−	0.0277684i
$989$	−18.8274	+	24.5364i	−0.598677	+	0.780212i
$990$	38.2995	−	9.70561i	1.21724	−	0.308465i
$991$	29.4323	+	16.9928i	0.934948	+	0.539793i	0.888373	−	0.459122i	$-0.151836\pi$
$991$	29.4323	+	16.9928i	0.934948	+	0.539793i	0.0465752	+	0.998915i	$0.485169\pi$
$992$	38.3864	+	21.7983i	1.21877	+	0.692098i
$993$	−14.9447	+	11.2900i	−0.474256	+	0.358276i
$994$	−0.364174	+	0.552669i	−0.0115509	+	0.0175296i
$995$	31.2868	−	12.9594i	0.991858	−	0.410841i
$996$	18.6941	+	14.4834i	0.592344	+	0.458925i
$997$	−14.8321	−	19.3296i	−0.469739	−	0.612175i	0.497059	−	0.867716i	$-0.334413\pi$
$997$	−14.8321	−	19.3296i	−0.469739	−	0.612175i	−0.966798	+	0.255541i	$0.917746\pi$
$998$	21.3840	+	16.3600i	0.676897	+	0.517867i
$999$	1.44739	+	13.3073i	0.0457933	+	0.421023i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.ch.a.11.1	✓	992
3.2	odd	2	inner	672.2.ch.a.11.124	yes	992
7.2	even	3	inner	672.2.ch.a.107.82	yes	992
21.2	odd	6	inner	672.2.ch.a.107.43	yes	992
32.3	odd	8	inner	672.2.ch.a.515.43	yes	992
96.35	even	8	inner	672.2.ch.a.515.82	yes	992
224.163	odd	24	inner	672.2.ch.a.611.124	yes	992
672.611	even	24	inner	672.2.ch.a.611.1	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.ch.a.11.1	✓	992	1.1	even	1	trivial
672.2.ch.a.11.124	yes	992	3.2	odd	2	inner
672.2.ch.a.107.43	yes	992	21.2	odd	6	inner
672.2.ch.a.107.82	yes	992	7.2	even	3	inner
672.2.ch.a.515.43	yes	992	32.3	odd	8	inner
672.2.ch.a.515.82	yes	992	96.35	even	8	inner
672.2.ch.a.611.1	yes	992	672.611	even	24	inner
672.2.ch.a.611.124	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)

\(f(q)\)	\(=\)	\(q+(-1.41421 + 0.00202033i) q^{2} +(-1.50647 + 0.854722i) q^{3} +(1.99999 - 0.00571435i) q^{4} +(0.202706 + 1.53970i) q^{5} +(2.12874 - 1.21180i) q^{6} +(0.529096 + 2.59231i) q^{7} +(-2.82840 + 0.0121219i) q^{8} +(1.53890 - 2.57522i) q^{9} +O(q^{10})\)	\(q+(-1.41421 + 0.00202033i) q^{2} +(-1.50647 + 0.854722i) q^{3} +(1.99999 - 0.00571435i) q^{4} +(0.202706 + 1.53970i) q^{5} +(2.12874 - 1.21180i) q^{6} +(0.529096 + 2.59231i) q^{7} +(-2.82840 + 0.0121219i) q^{8} +(1.53890 - 2.57522i) q^{9} +(-0.289779 - 2.17705i) q^{10} +(-4.75742 + 3.65049i) q^{11} +(-3.00804 + 1.71804i) q^{12} +(0.106525 + 0.257175i) q^{13} +(-0.753491 - 3.66500i) q^{14} +(-1.62139 - 2.14626i) q^{15} +(3.99993 - 0.0228573i) q^{16} +(-1.06215 + 1.83970i) q^{17} +(-2.17113 + 3.64502i) q^{18} +(-1.28670 - 0.987321i) q^{19} +(0.414208 + 3.07823i) q^{20} +(-3.01277 - 3.45300i) q^{21} +(6.72062 - 5.17218i) q^{22} +(5.94161 + 1.59205i) q^{23} +(4.25054 - 2.43576i) q^{24} +(2.50004 - 0.669883i) q^{25} +(-0.151169 - 0.363485i) q^{26} +(-0.117209 + 5.19483i) q^{27} +(1.07300 + 5.18157i) q^{28} +(1.01347 + 2.44673i) q^{29} +(2.29732 + 3.03199i) q^{30} +(-6.75813 - 3.90181i) q^{31} +(-5.65671 + 0.0404063i) q^{32} +(4.04675 - 9.56562i) q^{33} +(1.49839 - 2.60387i) q^{34} +(-3.88413 + 1.34012i) q^{35} +(3.06308 - 5.15922i) q^{36} +(2.55405 - 0.336247i) q^{37} +(1.82166 + 1.39368i) q^{38} +(-0.380290 - 0.296377i) q^{39} +(-0.591997 - 4.35244i) q^{40} +(-6.08980 - 6.08980i) q^{41} +(4.26767 + 4.87719i) q^{42} +(-1.92408 + 4.64514i) q^{43} +(-9.49393 + 7.32814i) q^{44} +(4.27702 + 1.84744i) q^{45} +(-8.40592 - 2.23949i) q^{46} +(2.12691 - 1.22797i) q^{47} +(-6.00624 + 3.45326i) q^{48} +(-6.44011 + 2.74316i) q^{49} +(-3.53423 + 0.952408i) q^{50} +(0.0276674 - 3.67930i) q^{51} +(0.214519 + 0.513739i) q^{52} +(-7.16108 - 9.33250i) q^{53} +(0.155264 - 7.34683i) q^{54} +(-6.58502 - 6.58502i) q^{55} +(-1.52792 - 7.32567i) q^{56} +(2.78226 + 0.387597i) q^{57} +(-1.43820 - 3.45814i) q^{58} +(0.142134 + 0.185232i) q^{59} +(-3.25502 - 4.28323i) q^{60} +(-4.16461 - 3.19562i) q^{61} +(9.56532 + 5.50433i) q^{62} +(7.49000 + 2.62677i) q^{63} +(7.99971 - 0.0685714i) q^{64} +(-0.374379 + 0.216148i) q^{65} +(-5.70363 + 13.5360i) q^{66} +(-8.42225 - 1.10881i) q^{67} +(-2.11378 + 3.68545i) q^{68} +(-10.3116 + 2.68005i) q^{69} +(5.49027 - 1.90307i) q^{70} +(-0.125081 - 0.125081i) q^{71} +(-4.32142 + 7.30242i) q^{72} +(2.43133 + 9.07386i) q^{73} +(-3.61129 + 0.480685i) q^{74} +(-3.19367 + 3.14600i) q^{75} +(-2.57903 - 1.96728i) q^{76} +(-11.9803 - 10.4012i) q^{77} +(0.538410 + 0.418371i) q^{78} +(3.02184 + 5.23399i) q^{79} +(0.846002 + 6.15407i) q^{80} +(-4.26356 - 7.92604i) q^{81} +(8.62458 + 8.59997i) q^{82} +(-2.61245 - 6.30700i) q^{83} +(-6.04524 - 6.88876i) q^{84} +(-3.04789 - 1.26248i) q^{85} +(2.71167 - 6.57310i) q^{86} +(-3.61803 - 2.81969i) q^{87} +(13.4116 - 10.3827i) q^{88} +(-14.3185 - 3.83663i) q^{89} +(-6.05235 - 2.60403i) q^{90} +(-0.610314 + 0.412217i) q^{91} +(11.8923 + 3.15014i) q^{92} +(13.5159 + 0.101636i) q^{93} +(-3.00543 + 1.74091i) q^{94} +(1.25936 - 2.18127i) q^{95} +(8.48713 - 4.89578i) q^{96} +8.21665 q^{97} +(9.10215 - 3.89242i) q^{98} +(2.07964 + 17.8692i) 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

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