LMFDB - Embedded newform 380.2.bj.a.43.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(23,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 4]))

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

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

chi := DirichletCharacter("380.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bj (of order $36$, degree $12$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$56$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			43.31
Character	$\chi$	$=$	380.43
Dual form			380.2.bj.a.327.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.181148 + 1.40256i) q^{2} +(-1.17040 - 1.67151i) q^{3} +(-1.93437 + 0.508144i) q^{4} +(1.98936 - 1.02100i) q^{5} +(2.13238 - 1.94436i) q^{6} +(-0.639752 + 2.38759i) q^{7} +(-1.06311 - 2.62103i) q^{8} +(-0.398042 + 1.09361i) q^{9} +O(q^{10})$	\(q+(0.181148 + 1.40256i) q^{2} +(-1.17040 - 1.67151i) q^{3} +(-1.93437 + 0.508144i) q^{4} +(1.98936 - 1.02100i) q^{5} +(2.13238 - 1.94436i) q^{6} +(-0.639752 + 2.38759i) q^{7} +(-1.06311 - 2.62103i) q^{8} +(-0.398042 + 1.09361i) q^{9} +(1.79238 + 2.60526i) q^{10} +(-0.626858 - 0.361917i) q^{11} +(3.11336 + 2.63859i) q^{12} +(1.65099 - 2.35785i) q^{13} +(-3.46464 - 0.464786i) q^{14} +(-4.03497 - 2.13026i) q^{15} +(3.48358 - 1.96588i) q^{16} +(3.26467 - 7.00111i) q^{17} +(-1.60596 - 0.360173i) q^{18} +(4.15065 - 1.33122i) q^{19} +(-3.32935 + 2.98587i) q^{20} +(4.73965 - 1.72509i) q^{21} +(0.394057 - 0.944769i) q^{22} +(0.282197 - 3.22553i) q^{23} +(-3.13681 + 4.84467i) q^{24} +(2.91512 - 4.06227i) q^{25} +(3.60612 + 1.88849i) q^{26} +(-3.61917 + 0.969755i) q^{27} +(0.0242799 - 4.94357i) q^{28} +(-2.79908 + 7.69040i) q^{29} +(2.25690 - 6.04519i) q^{30} +(7.25194 - 4.18691i) q^{31} +(3.38831 + 4.52983i) q^{32} +(0.128730 + 1.47139i) q^{33} +(10.4109 + 3.31067i) q^{34} +(1.16502 + 5.40297i) q^{35} +(0.214249 - 2.31771i) q^{36} +(-5.98915 + 5.98915i) q^{37} +(2.61900 + 5.58040i) q^{38} -5.87350 q^{39} +(-4.79098 - 4.12874i) q^{40} +(0.0129711 - 0.0735630i) q^{41} +(3.27813 + 6.33516i) q^{42} +(-0.184716 + 0.0161606i) q^{43} +(1.39648 + 0.381547i) q^{44} +(0.324725 + 2.58199i) q^{45} +(4.57513 - 0.188499i) q^{46} +(-4.16895 - 8.94034i) q^{47} +(-7.36318 - 3.52197i) q^{48} +(0.770881 + 0.445069i) q^{49} +(6.22566 + 3.35278i) q^{50} +(-15.5234 + 2.73720i) q^{51} +(-1.99549 + 5.39990i) q^{52} +(0.640075 + 0.0559993i) q^{53} +(-2.01575 - 4.90045i) q^{54} +(-1.61656 - 0.0799623i) q^{55} +(6.93807 - 0.861464i) q^{56} +(-7.08308 - 5.37979i) q^{57} +(-11.2933 - 2.53278i) q^{58} +(9.67177 - 3.52024i) q^{59} +(8.88760 + 2.07037i) q^{60} +(-8.53104 + 7.15839i) q^{61} +(7.18609 + 9.41286i) q^{62} +(-2.35644 - 1.65000i) q^{63} +(-5.73959 + 5.57289i) q^{64} +(0.877047 - 6.37628i) q^{65} +(-2.04040 + 0.447091i) q^{66} +(-0.481938 - 1.03352i) q^{67} +(-2.75751 + 15.2017i) q^{68} +(-5.72179 + 3.30348i) q^{69} +(-7.36696 + 2.61276i) q^{70} +(-7.49426 + 8.93131i) q^{71} +(3.28955 - 0.119352i) q^{72} +(-0.823444 + 0.576582i) q^{73} +(-9.48510 - 7.31525i) q^{74} +(-10.2020 - 0.118162i) q^{75} +(-7.35244 + 4.68419i) q^{76} +(1.26514 - 1.26514i) q^{77} +(-1.06397 - 8.23796i) q^{78} +(-0.875528 + 4.96536i) q^{79} +(4.92294 - 7.46757i) q^{80} +(8.53141 + 7.15870i) q^{81} +(0.105526 + 0.00486705i) q^{82} +(-0.387639 - 0.103868i) q^{83} +(-8.29164 + 5.74539i) q^{84} +(-0.653508 - 17.2610i) q^{85} +(-0.0561272 - 0.256149i) q^{86} +(16.1306 - 4.32219i) q^{87} +(-0.282174 + 2.02777i) q^{88} +(10.7879 - 1.90221i) q^{89} +(-3.56258 + 0.923170i) q^{90} +(4.57336 + 5.45032i) q^{91} +(1.09316 + 6.38277i) q^{92} +(-15.4862 - 7.22132i) q^{93} +(11.7842 - 7.46675i) q^{94} +(6.89797 - 6.88608i) q^{95} +(3.60596 - 10.9653i) q^{96} +(-2.85135 + 6.11475i) q^{97} +(-0.484593 + 1.16183i) q^{98} +(0.645311 - 0.541481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.181148	+	1.40256i	0.128091	+	0.991762i
$2$	0.181148	+	1.40256i	0.128091	+	0.991762i
$3$	−1.17040	−	1.67151i	−0.675733	−	0.965047i	−0.999819	−	0.0190196i	$-0.993946\pi$
$3$	−1.17040	−	1.67151i	−0.675733	−	0.965047i	0.324086	−	0.946028i	$-0.394943\pi$
$4$	−1.93437	+	0.508144i	−0.967185	+	0.254072i
$5$	1.98936	−	1.02100i	0.889670	−	0.456604i
$5$	1.98936	−	1.02100i	0.889670	−	0.456604i
$6$	2.13238	−	1.94436i	0.870542	−	0.793781i
$7$	−0.639752	+	2.38759i	−0.241804	+	0.902424i	0.733159	+	0.680057i	$0.238045\pi$
$7$	−0.639752	+	2.38759i	−0.241804	+	0.902424i	−0.974963	+	0.222367i	$0.928622\pi$
$8$	−1.06311	−	2.62103i	−0.375867	−	0.926674i
$9$	−0.398042	+	1.09361i	−0.132681	+	0.364537i
$10$	1.79238	+	2.60526i	0.566802	+	0.823854i
$11$	−0.626858	−	0.361917i	−0.189005	−	0.109122i	0.402512	−	0.915415i	$-0.368137\pi$
$11$	−0.626858	−	0.361917i	−0.189005	−	0.109122i	−0.591517	+	0.806293i	$0.701471\pi$
$12$	3.11336	+	2.63859i	0.898751	+	0.761695i
$13$	1.65099	−	2.35785i	0.457902	−	0.653951i	−0.522113	−	0.852876i	$-0.674856\pi$
$13$	1.65099	−	2.35785i	0.457902	−	0.653951i	0.980015	+	0.198925i	$0.0637450\pi$
$14$	−3.46464	−	0.464786i	−0.925963	−	0.124219i
$15$	−4.03497	−	2.13026i	−1.04182	−	0.550031i
$16$	3.48358	−	1.96588i	0.870895	−	0.491469i
$17$	3.26467	−	7.00111i	0.791799	−	1.69802i	0.0787606	−	0.996894i	$-0.474904\pi$
$17$	3.26467	−	7.00111i	0.791799	−	1.69802i	0.713038	−	0.701125i	$-0.247319\pi$
$18$	−1.60596	−	0.360173i	−0.378529	−	0.0848936i
$19$	4.15065	−	1.33122i	0.952223	−	0.305402i
$19$	4.15065	−	1.33122i	0.952223	−	0.305402i
$20$	−3.32935	+	2.98587i	−0.744465	+	0.667661i
$21$	4.73965	−	1.72509i	1.03428	−	0.376446i
$22$	0.394057	−	0.944769i	0.0840132	−	0.201425i
$23$	0.282197	−	3.22553i	0.0588422	−	0.672569i	−0.908298	−	0.418324i	$-0.862618\pi$
$23$	0.282197	−	3.22553i	0.0588422	−	0.672569i	0.967140	−	0.254245i	$-0.0818269\pi$
$24$	−3.13681	+	4.84467i	−0.640298	+	0.988914i
$25$	2.91512	−	4.06227i	0.583025	−	0.812454i
$26$	3.60612	+	1.88849i	0.707217	+	0.370364i
$27$	−3.61917	+	0.969755i	−0.696510	+	0.186629i
$28$	0.0242799	−	4.94357i	0.00458848	−	0.934246i
$29$	−2.79908	+	7.69040i	−0.519775	+	1.42807i	0.350993	+	0.936378i	$0.385844\pi$
$29$	−2.79908	+	7.69040i	−0.519775	+	1.42807i	−0.870768	+	0.491693i	$0.836378\pi$
$30$	2.25690	−	6.04519i	0.412051	−	1.10370i
$31$	7.25194	−	4.18691i	1.30249	−	0.751992i	0.321657	−	0.946856i	$-0.395760\pi$
$31$	7.25194	−	4.18691i	1.30249	−	0.751992i	0.980830	+	0.194865i	$0.0624267\pi$
$32$	3.38831	+	4.52983i	0.598975	+	0.800768i
$33$	0.128730	+	1.47139i	0.0224090	+	0.256136i
$34$	10.4109	+	3.31067i	1.78545	+	0.567775i
$35$	1.16502	+	5.40297i	0.196925	+	0.913268i
$36$	0.214249	−	2.31771i	0.0357081	−	0.386285i
$37$	−5.98915	+	5.98915i	−0.984611	+	0.984611i	−0.999883	−	0.0152725i	$-0.995138\pi$
$37$	−5.98915	+	5.98915i	−0.984611	+	0.984611i	0.0152725	+	0.999883i	$0.495138\pi$
$38$	2.61900	+	5.58040i	0.424858	+	0.905260i
$39$	−5.87350			−0.940513
$40$	−4.79098	−	4.12874i	−0.757521	−	0.652811i
$41$	0.0129711	−	0.0735630i	0.00202575	−	0.0114886i	−0.983778	−	0.179390i	$-0.942588\pi$
$41$	0.0129711	−	0.0735630i	0.00202575	−	0.0114886i	0.985804	+	0.167901i	$0.0536989\pi$
$42$	3.27813	+	6.33516i	0.505826	+	0.977537i
$43$	−0.184716	+	0.0161606i	−0.0281690	+	0.00246446i	−0.101232	−	0.994863i	$-0.532278\pi$
$43$	−0.184716	+	0.0161606i	−0.0281690	+	0.00246446i	0.0730626	+	0.997327i	$0.476723\pi$
$44$	1.39648	+	0.381547i	0.210528	+	0.0575204i
$45$	0.324725	+	2.58199i	0.0484072	+	0.384900i
$46$	4.57513	−	0.188499i	0.674566	−	0.0277927i
$47$	−4.16895	−	8.94034i	−0.608104	−	1.30408i	−0.933524	−	0.358514i	$-0.883284\pi$
$47$	−4.16895	−	8.94034i	−0.608104	−	1.30408i	0.325420	−	0.945569i	$-0.394494\pi$
$48$	−7.36318	−	3.52197i	−1.06278	−	0.508353i
$49$	0.770881	+	0.445069i	0.110126	+	0.0635812i
$50$	6.22566	+	3.35278i	0.880442	+	0.474154i
$51$	−15.5234	+	2.73720i	−2.17371	+	0.383284i
$52$	−1.99549	+	5.39990i	−0.276725	+	0.748832i
$53$	0.640075	+	0.0559993i	0.0879211	+	0.00769210i	0.131031	−	0.991378i	$-0.458171\pi$
$53$	0.640075	+	0.0559993i	0.0879211	+	0.00769210i	−0.0431103	+	0.999070i	$0.513727\pi$
$54$	−2.01575	−	4.90045i	−0.274309	−	0.666867i
$55$	−1.61656	−	0.0799623i	−0.217977	−	0.0107821i
$56$	6.93807	−	0.861464i	0.927138	−	0.115118i
$57$	−7.08308	−	5.37979i	−0.938177	−	0.712570i
$58$	−11.2933	−	2.53278i	−1.48289	−	0.332571i
$59$	9.67177	−	3.52024i	1.25916	−	0.458296i	0.375671	−	0.926753i	$-0.377412\pi$
$59$	9.67177	−	3.52024i	1.25916	−	0.458296i	0.883486	+	0.468457i	$0.155190\pi$
$60$	8.88760	+	2.07037i	1.14738	+	0.267283i
$61$	−8.53104	+	7.15839i	−1.09229	+	0.916538i	−0.996882	−	0.0789006i	$-0.974859\pi$
$61$	−8.53104	+	7.15839i	−1.09229	+	0.916538i	−0.0954049	+	0.995439i	$0.530415\pi$
$62$	7.18609	+	9.41286i	0.912634	+	1.19543i
$63$	−2.35644	−	1.65000i	−0.296884	−	0.207880i
$64$	−5.73959	+	5.57289i	−0.717448	+	0.696612i
$65$	0.877047	−	6.37628i	0.108784	−	0.790881i
$66$	−2.04040	+	0.447091i	−0.251156	+	0.0550331i
$67$	−0.481938	−	1.03352i	−0.0588781	−	0.126265i	0.874667	−	0.484724i	$-0.161080\pi$
$67$	−0.481938	−	1.03352i	−0.0588781	−	0.126265i	−0.933545	+	0.358459i	$0.883302\pi$
$68$	−2.75751	+	15.2017i	−0.334398	+	1.84347i
$69$	−5.72179	+	3.30348i	−0.688823	+	0.397692i
$70$	−7.36696	+	2.61276i	−0.880520	+	0.312284i
$71$	−7.49426	+	8.93131i	−0.889405	+	1.05995i	0.108424	+	0.994105i	$0.465419\pi$
$71$	−7.49426	+	8.93131i	−0.889405	+	1.05995i	−0.997830	+	0.0658473i	$0.979025\pi$
$72$	3.28955	−	0.119352i	0.387677	−	0.0140657i
$73$	−0.823444	+	0.576582i	−0.0963769	+	0.0674838i	−0.620772	−	0.783992i	$-0.713181\pi$
$73$	−0.823444	+	0.576582i	−0.0963769	+	0.0674838i	0.524395	+	0.851475i	$0.324292\pi$
$74$	−9.48510	−	7.31525i	−1.10262	−	0.850380i
$75$	−10.2020	−	0.118162i	−1.17803	−	0.0136441i
$76$	−7.35244	+	4.68419i	−0.843382	+	0.537314i
$77$	1.26514	−	1.26514i	0.144176	−	0.144176i
$78$	−1.06397	−	8.23796i	−0.120471	−	0.932766i
$79$	−0.875528	+	4.96536i	−0.0985046	+	0.558647i	0.895112	+	0.445841i	$0.147095\pi$
$79$	−0.875528	+	4.96536i	−0.0985046	+	0.558647i	−0.993617	+	0.112807i	$0.964016\pi$
$80$	4.92294	−	7.46757i	0.550402	−	0.834900i
$81$	8.53141	+	7.15870i	0.947935	+	0.795412i
$82$	0.105526	+	0.00486705i	0.0116534	+	0.000537475i
$83$	−0.387639	−	0.103868i	−0.0425489	−	0.0114009i	0.237482	−	0.971392i	$-0.423678\pi$
$83$	−0.387639	−	0.103868i	−0.0425489	−	0.0114009i	−0.280031	+	0.959991i	$0.590345\pi$
$84$	−8.29164	+	5.74539i	−0.904693	+	0.626873i
$85$	−0.653508	−	17.2610i	−0.0708829	−	1.87221i
$86$	−0.0561272	−	0.256149i	−0.00605236	−	0.0276212i
$87$	16.1306	−	4.32219i	1.72939	−	0.463388i
$88$	−0.282174	+	2.02777i	−0.0300798	+	0.216161i
$89$	10.7879	−	1.90221i	1.14352	−	0.201633i	0.430375	−	0.902650i	$-0.358381\pi$
$89$	10.7879	−	1.90221i	1.14352	−	0.201633i	0.713145	+	0.701017i	$0.247270\pi$
$90$	−3.56258	+	0.923170i	−0.375529	+	0.0973107i
$91$	4.57336	+	5.45032i	0.479419	+	0.571349i
$92$	1.09316	+	6.38277i	0.113970	+	0.665449i
$93$	−15.4862	−	7.22132i	−1.60584	−	0.748816i
$94$	11.7842	−	7.46675i	1.21545	−	0.770136i
$95$	6.89797	−	6.88608i	0.707716	−	0.706497i
$96$	3.60596	−	10.9653i	0.368032	−	1.11914i
$97$	−2.85135	+	6.11475i	−0.289511	+	0.620859i	−0.996241	−	0.0866249i	$-0.972392\pi$
$97$	−2.85135	+	6.11475i	−0.289511	+	0.620859i	0.706730	+	0.707483i	$0.250170\pi$
$98$	−0.484593	+	1.16183i	−0.0489513	+	0.117363i
$99$	0.645311	−	0.541481i	0.0648562	−	0.0544208i
$100$	−3.57471	+	9.33924i	−0.357471	+	0.933924i
$101$	0.0831138	+	0.471362i	0.00827013	+	0.0469023i	0.988664	−	0.150148i	$-0.0479750\pi$
$101$	0.0831138	+	0.471362i	0.00827013	+	0.0469023i	−0.980393	+	0.197050i	$0.936864\pi$
$102$	−6.65113	−	21.2767i	−0.658560	−	2.10671i
$103$	0.574548	+	2.14424i	0.0566119	+	0.211279i	0.988438	−	0.151627i	$-0.0484513\pi$
$103$	0.574548	+	2.14424i	0.0566119	+	0.211279i	−0.931826	+	0.362906i	$0.881785\pi$
$104$	−7.93519	−	1.82062i	−0.778110	−	0.178527i
$105$	7.66757	−	8.27101i	0.748278	−	0.807168i
$106$	0.0374058	+	0.907890i	0.00363318	+	0.0881821i
$107$	−0.421958	+	1.57477i	−0.0407922	+	0.152239i	−0.983318	−	0.181895i	$-0.941777\pi$
$107$	−0.421958	+	1.57477i	−0.0407922	+	0.152239i	0.942526	+	0.334133i	$0.108444\pi$
$108$	6.50805	−	3.71493i	0.626237	−	0.357469i
$109$	−3.66902	+	4.37257i	−0.351428	+	0.418816i	−0.912581	−	0.408896i	$-0.865914\pi$
$109$	−3.66902	+	4.37257i	−0.351428	+	0.418816i	0.561152	+	0.827712i	$0.310358\pi$
$110$	−0.180685	−	2.28182i	−0.0172277	−	0.217563i
$111$	17.0207	+	3.00120i	1.61553	+	0.284862i
$112$	2.46508	+	9.57503i	0.232928	+	0.904755i
$113$	−6.19964	−	6.19964i	−0.583213	−	0.583213i	0.352572	−	0.935785i	$-0.385307\pi$
$113$	−6.19964	−	6.19964i	−0.583213	−	0.583213i	−0.935785	+	0.352572i	$0.885307\pi$
$114$	6.26241	−	10.9090i	0.586528	−	1.02172i
$115$	−2.73187	−	6.70487i	−0.254748	−	0.625232i
$116$	1.50662	−	16.2984i	0.139886	−	1.51327i
$117$	1.92141	+	2.74406i	0.177635	+	0.253689i
$118$	6.68938	+	12.9276i	0.615808	+	1.19008i
$119$	14.6272	+	12.2737i	1.34087	+	1.12513i
$120$	−1.29385	+	12.8405i	−0.118112	+	1.17217i
$121$	−5.23803	−	9.07254i	−0.476185	−	0.824776i
$122$	−11.5855	−	10.6686i	−1.04890	−	0.965889i
$123$	−0.138143	+	0.0644170i	−0.0124559	+	0.00580829i
$124$	−11.9004	+	11.7841i	−1.06869	+	1.05824i
$125$	1.65167	−	11.0577i	0.147730	−	0.989028i
$126$	1.88736	−	3.60396i	0.168140	−	0.321066i
$127$	−4.53951	+	6.48310i	−0.402817	+	0.575282i	−0.968398	−	0.249411i	$-0.919763\pi$
$127$	−4.53951	+	6.48310i	−0.402817	+	0.575282i	0.565581	+	0.824693i	$0.308652\pi$
$128$	−8.85606	−	7.04062i	−0.782772	−	0.622308i
$129$	0.243205	+	0.289841i	0.0214130	+	0.0255191i
$130$	9.10202	+	0.0750618i	0.798300	+	0.00658336i
$131$	1.98232	+	5.44637i	0.173196	+	0.475852i	0.995671	−	0.0929495i	$-0.0296295\pi$
$131$	1.98232	+	5.44637i	0.173196	+	0.475852i	−0.822475	+	0.568801i	$0.807407\pi$
$132$	−0.996689	−	2.78080i	−0.0867506	−	0.242037i
$133$	0.523014	+	10.7617i	0.0453511	+	0.933156i
$134$	1.36227	−	0.863169i	0.117683	−	0.0745665i
$135$	−6.20973	+	5.62436i	−0.534448	+	0.484068i
$136$	−21.8208	−	1.11383i	−1.87112	−	0.0955105i
$137$	−0.148485	+	1.69719i	−0.0126859	+	0.145001i	−0.999896	−	0.0144242i	$-0.995408\pi$
$137$	−0.148485	+	1.69719i	−0.0126859	+	0.145001i	0.987210	+	0.159425i	$0.0509640\pi$
$138$	−5.66983	−	7.42676i	−0.482648	−	0.632208i
$139$	−0.261126	−	1.48092i	−0.0221485	−	0.125610i	0.971729	−	0.236100i	$-0.0758692\pi$
$139$	−0.261126	−	1.48092i	−0.0221485	−	0.125610i	−0.993877	+	0.110490i	$0.964758\pi$
$140$	−4.99907	−	9.85934i	−0.422499	−	0.833266i
$141$	−10.0645	+	17.4323i	−0.847586	+	1.46806i
$142$	−13.8843	−	8.89329i	−1.16515	−	0.746308i
$143$	−1.88828	+	0.880520i	−0.157906	+	0.0736328i
$144$	0.763294	+	4.59218i	0.0636078	+	0.382682i
$145$	2.28351	+	18.1568i	0.189635	+	1.50784i
$146$	−0.957858	−	1.05049i	−0.0792729	−	0.0869389i
$147$	−0.158306	−	1.80945i	−0.0130569	−	0.149241i
$148$	8.54189	−	14.6286i	0.702139	−	1.20246i
$149$	17.8134	+	3.14098i	1.45933	+	0.257319i	0.846285	−	0.532731i	$-0.178834\pi$
$149$	17.8134	+	3.14098i	1.45933	+	0.257319i	0.613042	+	0.790050i	$0.289945\pi$
$150$	−1.68235	−	14.3304i	−0.137363	−	1.17007i
$151$			15.5959i			1.26918i	0.772851	+	0.634588i	$0.218830\pi$
$151$			15.5959i			1.26918i	−0.772851	+	0.634588i	$0.781170\pi$
$152$	−7.90176	−	9.46373i	−0.640917	−	0.767610i
$153$	6.35701	+	6.35701i	0.513934	+	0.513934i
$154$	2.00362	+	1.54526i	0.161456	+	0.124521i
$155$	10.1519	−	15.7335i	0.815421	−	1.26375i
$156$	11.3615	−	2.98458i	0.909651	−	0.238958i
$157$	−2.54970	+	0.223070i	−0.203488	+	0.0178029i	−0.188444	−	0.982084i	$-0.560344\pi$
$157$	−2.54970	+	0.223070i	−0.203488	+	0.0178029i	−0.0150440	+	0.999887i	$0.504789\pi$
$158$	−7.12284	−	0.328517i	−0.566663	−	0.0261354i
$159$	−0.655543	−	1.13543i	−0.0519880	−	0.0900458i
$160$	11.3655	+	5.55201i	0.898524	+	0.438925i
$161$	7.52070	+	2.73731i	0.592714	+	0.215730i
$162$	−8.49509	+	13.2626i	−0.667437	+	1.04201i
$163$	−1.31996	−	4.92616i	−0.103387	−	0.385846i	0.894770	−	0.446527i	$-0.147339\pi$
$163$	−1.31996	−	4.92616i	−0.103387	−	0.385846i	−0.998157	+	0.0606810i	$0.980673\pi$
$164$	0.0122896	+	0.148889i	0.000959655	+	0.0116263i
$165$	1.75838	+	2.79569i	0.136889	+	0.217644i
$166$	0.0754607	−	0.562504i	0.00585689	−	0.0436587i
$167$	−1.87213	−	0.163790i	−0.144870	−	0.0126745i	0.0144901	−	0.999895i	$-0.495388\pi$
$167$	−1.87213	−	0.163790i	−0.144870	−	0.0126745i	−0.159360	+	0.987221i	$0.550943\pi$
$168$	−9.56029	−	10.5888i	−0.737593	−	0.816943i
$169$	1.61254	+	4.43042i	0.124042	+	0.340802i
$170$	24.0912	−	4.04338i	1.84771	−	0.310113i
$171$	−0.196296	+	5.06907i	−0.0150112	+	0.387641i
$172$	0.349098	−	0.125123i	0.0266184	−	0.00954053i
$173$	8.47018	+	3.94971i	0.643976	+	0.300291i	0.717035	−	0.697037i	$-0.245499\pi$
$173$	8.47018	+	3.94971i	0.643976	+	0.300291i	−0.0730596	+	0.997328i	$0.523276\pi$
$174$	8.98419	+	21.8413i	0.681089	+	1.65578i
$175$	7.83407	+	9.55897i	0.592200	+	0.722590i
$176$	−2.89519	−	0.0284397i	−0.218233	−	0.00214372i
$177$	−17.2040	−	12.0464i	−1.29313	−	0.905461i
$178$	4.62218	+	14.7862i	0.346447	+	1.10827i
$179$	−1.06826	+	1.85029i	−0.0798458	+	0.138297i	−0.903183	−	0.429255i	$-0.858776\pi$
$179$	−1.06826	+	1.85029i	−0.0798458	+	0.138297i	0.823337	+	0.567552i	$0.192109\pi$
$180$	−1.94016	−	4.82951i	−0.144611	−	0.359971i
$181$	−11.7983	−	4.29424i	−0.876963	−	0.319188i	−0.135980	−	0.990712i	$-0.543418\pi$
$181$	−11.7983	−	4.29424i	−0.876963	−	0.319188i	−0.740984	+	0.671523i	$0.765640\pi$
$182$	−6.81597	+	7.40175i	−0.505233	+	0.548654i
$183$	21.9501	+	5.88151i	1.62260	+	0.434774i
$184$	−8.75421	+	2.68945i	−0.645369	+	0.198269i
$185$	−5.79968	+	18.0295i	−0.426401	+	1.32556i
$186$	7.32307	−	23.0285i	0.536954	−	1.68853i
$187$	−4.58030	+	3.20716i	−0.334945	+	0.234531i
$188$	12.6073	+	15.1755i	0.919480	+	1.10679i
$189$		−	9.26150i		−	0.673675i
$190$	10.9077	+	8.42744i	0.791329	+	0.611391i
$191$		−	21.0578i		−	1.52369i	−0.647759	−	0.761846i	$-0.724293\pi$
$191$		−	21.0578i		−	1.52369i	0.647759	−	0.761846i	$-0.275707\pi$
$192$	16.0328	+	3.07124i	1.15707	+	0.221648i
$193$	4.22628	−	2.95928i	0.304215	−	0.213013i	−0.411494	−	0.911413i	$-0.634993\pi$
$193$	4.22628	−	2.95928i	0.304215	−	0.213013i	0.715708	+	0.698399i	$0.246104\pi$
$194$	−9.09284	−	2.89153i	−0.652828	−	0.207600i
$195$	−11.6845	+	5.99684i	−0.836746	+	0.429443i
$196$	−1.71733	−	0.469209i	−0.122666	−	0.0335149i
$197$	23.5686	+	6.31520i	1.67920	+	0.449939i	0.967567	−	0.252616i	$-0.0812909\pi$
$197$	23.5686	+	6.31520i	1.67920	+	0.449939i	0.711629	+	0.702555i	$0.247958\pi$
$198$	0.876358	+	0.807002i	0.0622801	+	0.0573512i
$199$	3.03004	+	1.10284i	0.214794	+	0.0781786i	0.447176	−	0.894446i	$-0.352430\pi$
$199$	3.03004	+	1.10284i	0.214794	+	0.0781786i	−0.232382	+	0.972625i	$0.574652\pi$
$200$	−13.7464	−	3.32198i	−0.972020	−	0.234899i
$201$	−1.16348	+	2.01520i	−0.0820653	+	0.142141i
$202$	−0.646059	+	0.201959i	−0.0454566	+	0.0142098i
$203$	−16.5708	−	11.6030i	−1.16304	−	0.814371i
$204$	28.6372	−	13.1829i	2.00500	−	0.922986i
$205$	−0.0493034	−	0.159587i	−0.00344350	−	0.0111460i
$206$	−2.90336	+	1.19427i	−0.202287	+	0.0832085i
$207$	3.41515	+	1.59251i	0.237369	+	0.110687i
$208$	1.11609	−	11.4594i	0.0773872	−	0.794567i
$209$	−3.08366	−	0.667703i	−0.213301	−	0.0461860i
$210$	12.9896	+	9.25597i	0.896366	+	0.638723i
$211$	5.88126	+	16.1586i	0.404883	+	1.11241i	0.959845	+	0.280531i	$0.0905105\pi$
$211$	5.88126	+	16.1586i	0.404883	+	1.11241i	−0.554962	+	0.831876i	$0.687267\pi$
$212$	−1.26660	+	0.216927i	−0.0869903	+	0.0148986i
$213$	23.7001	+	2.07349i	1.62390	+	0.142073i
$214$	−2.28515	−	0.306557i	−0.156210	−	0.0209558i
$215$	−0.350967	+	0.220744i	−0.0239358	+	0.0150546i
$216$	6.38934	+	8.45500i	0.434740	+	0.575290i
$217$	5.35717	+	19.9932i	0.363669	+	1.35723i
$218$	−6.79744	−	4.35395i	−0.460381	−	0.294887i
$219$	1.92753	+	0.701562i	0.130250	+	0.0474072i
$220$	3.16767	−	0.666770i	0.213564	−	0.0449536i
$221$	−11.1177	−	19.2564i	−0.747855	−	1.29532i
$222$	−1.12612	+	24.4162i	−0.0755799	+	1.63871i
$223$	21.3084	−	1.86424i	1.42692	−	0.124839i	0.652632	−	0.757675i	$-0.273665\pi$
$223$	21.3084	−	1.86424i	1.42692	−	0.124839i	0.774286	+	0.632836i	$0.218109\pi$
$224$	−12.9830	+	5.19193i	−0.867466	+	0.346900i
$225$	3.28220	+	4.80496i	0.218813	+	0.320331i
$226$	7.57234	−	9.81844i	0.503704	−	0.653113i
$227$	0.561061	+	0.561061i	0.0372389	+	0.0372389i	0.725481	−	0.688242i	$-0.241617\pi$
$227$	0.561061	+	0.561061i	0.0372389	+	0.0372389i	−0.688242	+	0.725481i	$0.741617\pi$
$228$	16.4350	+	6.80728i	1.08843	+	0.450823i
$229$			21.6520i			1.43080i	0.698713	+	0.715402i	$0.253756\pi$
$229$			21.6520i			1.43080i	−0.698713	+	0.715402i	$0.746244\pi$
$230$	8.90913	−	5.04619i	0.587451	−	0.332736i
$231$	−3.59543	−	0.633971i	−0.236562	−	0.0417122i
$232$	23.1325	−	0.839295i	1.51872	−	0.0551024i
$233$	−0.387965	−	4.43445i	−0.0254164	−	0.290511i	−0.998256	−	0.0590311i	$-0.981199\pi$
$233$	−0.387965	−	4.43445i	−0.0254164	−	0.290511i	0.972840	−	0.231480i	$-0.0743567\pi$
$234$	−3.50066	+	3.19199i	−0.228845	+	0.208667i
$235$	−17.4216	−	13.5291i	−1.13646	−	0.882541i
$236$	−16.9200	+	11.7241i	−1.10140	+	0.763174i
$237$	9.32438	−	4.34803i	0.605684	−	0.282435i
$238$	−14.5649	+	22.7389i	−0.944103	+	1.47395i
$239$	14.9330	−	25.8647i	0.965934	−	1.67305i	0.258850	−	0.965918i	$-0.416657\pi$
$239$	14.9330	−	25.8647i	0.965934	−	1.67305i	0.707084	−	0.707129i	$-0.250010\pi$
$240$	−18.2440	+	0.511323i	−1.17764	+	0.0330057i
$241$	−3.86581	−	21.9241i	−0.249019	−	1.41225i	−0.810971	−	0.585086i	$-0.801061\pi$
$241$	−3.86581	−	21.9241i	−0.249019	−	1.41225i	0.561953	−	0.827169i	$-0.310050\pi$
$242$	11.7760	−	8.99015i	0.756987	−	0.577909i
$243$	1.00097	−	11.4412i	0.0642124	−	0.733951i
$244$	12.8647	−	18.1820i	0.823578	−	1.16398i
$245$	1.98798	+	0.0983340i	0.127007	+	0.00628233i
$246$	−0.115373	−	0.182085i	−0.00735593	−	0.0116093i
$247$	3.71385	−	11.9844i	0.236306	−	0.762552i
$248$	−18.6836	−	14.5564i	−1.18641	−	0.924332i
$249$	0.280079	+	0.769510i	0.0177493	+	0.0487657i
$250$	15.8083	+	0.313491i	0.999803	+	0.0198269i
$251$	3.28704	+	3.91735i	0.207476	+	0.247261i	0.859741	−	0.510731i	$-0.170625\pi$
$251$	3.28704	+	3.91735i	0.207476	+	0.247261i	−0.652264	+	0.757992i	$0.726181\pi$
$252$	5.39667	+	1.99430i	0.339958	+	0.125629i
$253$	−1.34427	+	1.91982i	−0.0845136	+	0.120698i
$254$	−9.91528	−	5.19256i	−0.622140	−	0.325810i
$255$	−28.0870	+	21.2947i	−1.75888	+	1.33352i
$256$	8.27066	−	13.6966i	0.516916	−	0.856036i
$257$	−5.34132	+	2.49070i	−0.333183	+	0.155366i	−0.582009	−	0.813183i	$-0.697733\pi$
$257$	−5.34132	+	2.49070i	−0.333183	+	0.155366i	0.248826	+	0.968548i	$0.419955\pi$
$258$	−0.362464	+	0.393615i	−0.0225660	+	0.0245054i
$259$	−10.4681	−	18.1312i	−0.650454	−	1.12662i
$260$	1.54354	+	12.7798i	0.0957260	+	0.792567i
$261$	−7.29615	−	6.12220i	−0.451620	−	0.378955i
$262$	−7.27979	+	3.76693i	−0.449747	+	0.232722i
$263$	15.4976	+	22.1329i	0.955624	+	1.36477i	0.930978	+	0.365076i	$0.118957\pi$
$263$	15.4976	+	22.1329i	0.955624	+	1.36477i	0.0246464	+	0.999696i	$0.492154\pi$
$264$	3.71970	−	1.90166i	0.228932	−	0.117039i
$265$	1.33052	−	0.542113i	0.0817330	−	0.0333017i
$266$	−14.9992	+	2.68302i	−0.919660	+	0.164507i
$267$	−15.8058	−	15.8058i	−0.967300	−	0.967300i
$268$	1.45742	+	1.75432i	0.0890263	+	0.107162i
$269$	−19.4316	−	3.42631i	−1.18476	−	0.208906i	−0.453662	−	0.891174i	$-0.649883\pi$
$269$	−19.4316	−	3.42631i	−1.18476	−	0.208906i	−0.731102	+	0.682268i	$0.760994\pi$
$270$	−9.01341	−	7.69070i	−0.548539	−	0.468041i
$271$	−4.03952	+	4.81412i	−0.245384	+	0.292437i	−0.874652	−	0.484751i	$-0.838910\pi$
$271$	−4.03952	+	4.81412i	−0.245384	+	0.292437i	0.629269	+	0.777188i	$0.283355\pi$
$272$	−2.39058	−	30.8069i	−0.144950	−	1.86794i
$273$	3.75759	−	14.0235i	0.227420	−	0.848742i
$274$	−2.40732	+	0.0991835i	−0.145431	+	0.00599189i
$275$	−3.29757	+	1.49144i	−0.198851	+	0.0899369i
$276$	9.38943	−	9.29765i	0.565177	−	0.559653i
$277$	−4.13627	−	15.4368i	−0.248525	−	0.927506i	−0.971579	−	0.236715i	$-0.923929\pi$
$277$	−4.13627	−	15.4368i	−0.248525	−	0.927506i	0.723054	−	0.690791i	$-0.242738\pi$
$278$	2.02978	−	0.634513i	0.121738	−	0.0380555i
$279$	1.69227	+	9.59737i	0.101314	+	0.574579i
$280$	12.9228	−	8.79752i	0.772284	−	0.525752i
$281$	−20.1948	+	16.9455i	−1.20472	+	1.01088i	−0.205241	+	0.978712i	$0.565798\pi$
$281$	−20.1948	+	16.9455i	−1.20472	+	1.01088i	−0.999482	+	0.0321711i	$0.989758\pi$
$282$	−26.2730	−	10.9583i	−1.56454	−	0.652558i
$283$	−2.18000	+	4.67503i	−0.129588	+	0.277902i	−0.960387	−	0.278671i	$-0.910106\pi$
$283$	−2.18000	+	4.67503i	−0.129588	+	0.277902i	0.830799	+	0.556573i	$0.187884\pi$
$284$	9.95829	−	21.0846i	0.590916	−	1.25114i
$285$	−19.5836	−	3.47053i	−1.16003	−	0.205577i
$286$	−1.57705	−	2.48893i	−0.0932526	−	0.147174i
$287$	0.167340	+	0.0780318i	0.00987776	+	0.00460607i
$288$	−6.30256	+	1.90243i	−0.371382	+	0.112102i
$289$	−27.4301	−	32.6899i	−1.61353	−	1.92293i
$290$	−25.0525	+	6.49185i	−1.47113	+	0.381214i
$291$	13.5581	−	2.39066i	0.794790	−	0.140143i
$292$	1.29986	−	1.53375i	0.0760685	−	0.0897560i
$293$	−2.31901	+	0.621378i	−0.135478	+	0.0363013i	−0.325921	−	0.945397i	$-0.605674\pi$
$293$	−2.31901	+	0.621378i	−0.135478	+	0.0363013i	0.190443	+	0.981698i	$0.439008\pi$
$294$	2.50919	−	0.549813i	0.146339	−	0.0320657i
$295$	15.6465	−	16.8779i	0.910975	−	0.982669i
$296$	22.0649	+	9.33061i	1.28250	+	0.542330i
$297$	2.61968	+	0.701941i	0.152009	+	0.0407307i
$298$	−1.17856	+	25.5534i	−0.0682722	+	1.48027i
$299$	−7.13943	−	5.99069i	−0.412884	−	0.346451i
$300$	19.7945	−	4.95552i	1.14284	−	0.286107i
$301$	0.0795878	−	0.451365i	0.00458737	−	0.0260162i
$302$	−21.8742	+	2.82517i	−1.25872	+	0.162570i
$303$	0.690610	−	0.690610i	0.0396745	−	0.0396745i
$304$	11.8421	−	12.7971i	0.679191	−	0.733962i
$305$	−9.66262	+	22.9508i	−0.553280	+	1.31416i
$306$	−7.76455	+	10.0677i	−0.443870	+	0.575531i
$307$	−16.4854	+	11.5432i	−0.940874	+	0.658807i	−0.939993	−	0.341193i	$-0.889169\pi$
$307$	−16.4854	+	11.5432i	−0.940874	+	0.658807i	−0.000880386		1.00000i	$0.500280\pi$
$308$	−1.80438	+	3.09013i	−0.102814	+	0.176076i
$309$	2.91167	−	3.47000i	0.165639	−	0.197401i
$310$	23.9062	+	11.3886i	1.35778	+	0.646830i
$311$	14.0012	−	8.08360i	0.793936	−	0.458379i	−0.0474105	−	0.998875i	$-0.515097\pi$
$311$	14.0012	−	8.08360i	0.793936	−	0.458379i	0.841346	+	0.540496i	$0.181764\pi$
$312$	6.24419	+	15.3946i	0.353508	+	0.871549i
$313$	9.52006	+	20.4158i	0.538106	+	1.15397i	0.967967	+	0.251076i	$0.0807845\pi$
$313$	9.52006	+	20.4158i	0.538106	+	1.15397i	−0.429862	+	0.902895i	$0.641438\pi$
$314$	−0.774743	−	3.53571i	−0.0437213	−	0.199531i
$315$	−6.37247	−	0.876522i	−0.359048	−	0.0493864i
$316$	−0.829524	−	10.0497i	−0.0466644	−	0.565343i
$317$	12.2266	+	8.56115i	0.686713	+	0.480842i	0.864114	−	0.503297i	$-0.167880\pi$
$317$	12.2266	+	8.56115i	0.686713	+	0.480842i	−0.177400	+	0.984139i	$0.556769\pi$
$318$	1.47377	−	1.12512i	0.0826448	−	0.0630938i
$319$	4.53791	−	3.80776i	0.254074	−	0.213193i
$320$	−5.72820	+	16.9466i	−0.320216	+	0.947345i
$321$	3.12611	−	1.13781i	0.174482	−	0.0635063i
$322$	−2.47689	+	11.0441i	−0.138032	+	0.615465i
$323$	4.23049	−	33.4051i	0.235391	−	1.85871i
$324$	−20.1406	−	9.51240i	−1.11892	−	0.528467i
$325$	−4.76541	−	13.5802i	−0.264337	−	0.753294i
$326$	6.67014	−	2.74369i	0.369425	−	0.151959i
$327$	11.6030	+	1.01513i	0.641649	+	0.0561370i
$328$	−0.206600	+	0.0442079i	−0.0114076	+	0.00244098i
$329$	24.0130	−	4.23413i	1.32388	−	0.233435i
$330$	−3.60261	+	2.97267i	−0.198317	+	0.163640i
$331$	−5.25288	−	3.03275i	−0.288724	−	0.166695i	0.348642	−	0.937256i	$-0.386643\pi$
$331$	−5.25288	−	3.03275i	−0.288724	−	0.166695i	−0.637366	+	0.770561i	$0.719976\pi$
$332$	0.802617	+	0.00394199i	0.0440493	+	0.000216345i
$333$	−4.16587	−	8.93373i	−0.228288	−	0.489566i
$334$	−0.109407	−	2.65545i	−0.00598648	−	0.145300i
$335$	−2.01397	−	1.56399i	−0.110035	−	0.0854497i
$336$	13.1196	−	15.3271i	0.715735	−	0.836160i
$337$	20.5977	−	1.80206i	1.12203	−	0.0981647i	0.488993	−	0.872288i	$-0.337364\pi$
$337$	20.5977	−	1.80206i	1.12203	−	0.0981647i	0.633035	+	0.774123i	$0.281809\pi$
$338$	−5.92184	+	3.06426i	−0.322106	+	0.166674i
$339$	−3.10668	+	17.6188i	−0.168732	+	0.956924i
$340$	10.0352	+	33.0570i	0.544234	+	1.79277i
$341$	−6.06125			−0.328235
$342$	−7.14525	+	0.642935i	−0.386371	+	0.0347659i
$343$	−13.7907	+	13.7907i	−0.744626	+	0.744626i
$344$	0.238731	+	0.466966i	0.0128715	+	0.0251771i
$345$	−8.00987	+	12.4138i	−0.431237	+	0.668334i
$346$	−4.00536	+	12.5955i	−0.215330	+	0.677136i
$347$	3.16020	+	36.1212i	0.169648	+	1.93909i	0.313706	+	0.949520i	$0.398429\pi$
$347$	3.16020	+	36.1212i	0.169648	+	1.93909i	−0.144058	+	0.989569i	$0.546015\pi$
$348$	−29.0063	+	16.5574i	−1.55490	+	0.887570i
$349$	−4.23126	+	2.44292i	−0.226494	+	0.130767i	−0.608954	−	0.793206i	$-0.708411\pi$
$349$	−4.23126	+	2.44292i	−0.226494	+	0.130767i	0.382459	+	0.923972i	$0.375077\pi$
$350$	−11.9879	+	12.7194i	−0.640782	+	0.679879i
$351$	−3.68867	+	10.1345i	−0.196887	+	0.540942i
$352$	−0.484571	−	4.06585i	−0.0258277	−	0.216710i
$353$	−5.26150	+	1.40982i	−0.280042	+	0.0750369i	−0.396106	−	0.918205i	$-0.629639\pi$
$353$	−5.26150	+	1.40982i	−0.280042	+	0.0750369i	0.116065	+	0.993242i	$0.462972\pi$
$354$	13.7793	−	26.3119i	0.732363	−	1.39846i
$355$	−5.78995	+	25.4192i	−0.307298	+	1.34911i
$356$	−19.9013	+	9.16140i	−1.05477	+	0.485553i
$357$	3.39584	−	38.8147i	0.179727	−	2.05429i
$358$	−2.78866	−	1.16313i	−0.147385	−	0.0614735i
$359$	14.6234	−	5.32249i	0.771795	−	0.280910i	0.0740478	−	0.997255i	$-0.476408\pi$
$359$	14.6234	−	5.32249i	0.771795	−	0.280910i	0.697747	+	0.716344i	$0.254186\pi$
$360$	6.42224	−	3.59606i	0.338482	−	0.189529i
$361$	15.4557	−	11.0508i	0.813459	−	0.581622i
$362$	3.88570	−	17.3258i	0.204228	−	0.910624i
$363$	−9.03423	+	19.3740i	−0.474174	+	1.01687i
$364$	−11.6161	−	8.21902i	−0.608851	−	0.430794i
$365$	−1.04944	+	1.98777i	−0.0549302	+	0.104044i
$366$	−4.27297	+	31.8518i	−0.223352	+	1.66492i
$367$	−14.3471	+	20.4897i	−0.748911	+	1.06956i	0.246047	+	0.969258i	$0.420868\pi$
$367$	−14.3471	+	20.4897i	−0.748911	+	1.06956i	−0.994957	+	0.100298i	$0.968020\pi$
$368$	−5.35794	−	11.7912i	−0.279302	−	0.614656i
$369$	0.0752862	+	0.0434665i	0.00391924	+	0.00226278i
$370$	−26.3381	−	4.86841i	−1.36925	−	0.253096i
$371$	−0.543193	+	1.49241i	−0.0282012	+	0.0774821i
$372$	33.6255	+	6.09951i	1.74340	+	0.316245i
$373$	−0.900929	+	3.36231i	−0.0466483	+	0.174094i	−0.985320	−	0.170719i	$-0.945391\pi$
$373$	−0.900929	+	3.36231i	−0.0466483	+	0.174094i	0.938671	+	0.344813i	$0.112058\pi$
$374$	−5.32797	−	5.84320i	−0.275503	−	0.302145i
$375$	−20.4161	+	10.1812i	−1.05428	+	0.525753i
$376$	−19.0008	+	20.4315i	−0.979894	+	1.05368i
$377$	13.5116	+	19.2966i	0.695883	+	0.993824i
$378$	12.9898	−	1.67770i	0.668126	−	0.0862918i
$379$	−26.6623			−1.36955			−0.684775	−	0.728754i	$-0.740100\pi$
$379$	−26.6623			−1.36955			−0.684775	+	0.728754i	$0.740100\pi$
$380$	−9.84411	+	16.8254i	−0.504992	+	0.863124i
$381$	16.1496			0.827371
$382$	29.5350	−	3.81459i	1.51114	−	0.195171i
$383$	−5.77890	−	8.25312i	−0.295288	−	0.421715i	0.643905	−	0.765106i	$-0.277313\pi$
$383$	−5.77890	−	8.25312i	−0.295288	−	0.421715i	−0.939193	+	0.343391i	$0.888424\pi$
$384$	−1.40330	+	23.0434i	−0.0716118	+	1.17593i
$385$	1.22512	−	3.80853i	0.0624378	−	0.194101i
$386$	4.91616	+	5.39157i	0.250226	+	0.274423i
$387$	0.0558514	−	0.208440i	0.00283908	−	0.0105956i
$388$	2.40840	−	13.2771i	0.122268	−	0.674042i
$389$	−8.65808	+	23.7879i	−0.438982	+	1.20609i	0.501173	+	0.865347i	$0.332902\pi$
$389$	−8.65808	+	23.7879i	−0.438982	+	1.20609i	−0.940155	+	0.340747i	$0.889320\pi$
$390$	−10.5276	−	15.3020i	−0.533085	−	0.774846i
$391$	−21.6610	−	12.5060i	−1.09544	−	0.632455i
$392$	0.347004	−	2.49366i	0.0175264	−	0.125949i
$393$	6.78356	−	9.68793i	0.342185	−	0.488691i
$394$	−4.58805	+	34.2005i	−0.231143	+	1.72300i
$395$	3.32789	+	10.7718i	0.167444	+	0.541989i
$396$	−0.973122	+	1.37534i	−0.0489012	+	0.0691132i
$397$	0.838372	−	1.79789i	0.0420767	−	0.0902338i	−0.884146	−	0.467211i	$-0.845259\pi$
$397$	0.838372	−	1.79789i	0.0420767	−	0.0902338i	0.926222	+	0.376977i	$0.123037\pi$
$398$	−0.997923	+	4.44960i	−0.0500214	+	0.223038i
$399$	17.3761	−	13.4697i	0.869895	−	0.674331i
$400$	2.16914	−	19.8820i	0.108457	−	0.994101i
$401$	−0.189817	+	0.0690879i	−0.00947903	+	0.00345008i	−0.346755	−	0.937956i	$-0.612717\pi$
$401$	−0.189817	+	0.0690879i	−0.00947903	+	0.00345008i	0.337276	+	0.941406i	$0.390494\pi$
$402$	−3.03721	−	1.26680i	−0.151482	−	0.0631823i
$403$	2.10074	−	24.0116i	0.104645	−	1.19610i
$404$	−0.400293	−	0.869555i	−0.0199153	−	0.0432620i
$405$	24.2811	+	5.53070i	1.20654	+	0.274823i
$406$	13.2722	−	25.3435i	0.658687	−	1.25777i
$407$	5.92192	−	1.58677i	0.293539	−	0.0786535i
$408$	23.6774	+	37.7774i	1.17221	+	1.87026i
$409$	10.2941	−	28.2829i	0.509013	−	1.39850i	−0.373245	−	0.927733i	$-0.621755\pi$
$409$	10.2941	−	28.2829i	0.509013	−	1.39850i	0.882257	−	0.470768i	$-0.156023\pi$
$410$	0.214900	−	0.0980600i	0.0106131	−	0.00484284i
$411$	3.01066	−	1.73821i	0.148505	−	0.0857394i
$412$	−2.20097	−	3.85581i	−0.108434	−	0.189962i
$413$	2.21734	+	25.3443i	0.109108	+	1.24711i
$414$	−1.61495	+	5.07844i	−0.0793704	+	0.249592i
$415$	−0.877203	+	0.189149i	−0.0430602	+	0.00928494i
$416$	16.2747	−	0.510458i	0.797935	−	0.0250273i
$417$	−2.16975	+	2.16975i	−0.106253	+	0.106253i
$418$	0.377898	−	4.44598i	0.0184836	−	0.217460i
$419$	0.259791			0.0126916			0.00634581	−	0.999980i	$-0.497980\pi$
$419$	0.259791			0.0126916			0.00634581	+	0.999980i	$0.497980\pi$
$420$	−10.6291	+	19.8954i	−0.518645	+	0.970797i
$421$	0.726968	−	4.12284i	0.0354303	−	0.200935i	−0.961955	−	0.273210i	$-0.911915\pi$
$421$	0.726968	−	4.12284i	0.0354303	−	0.200935i	0.997385	+	0.0722747i	$0.0230258\pi$
$422$	−21.5981	+	11.1760i	−1.05138	+	0.544037i
$423$	11.4367	−	1.00058i	0.556070	−	0.0486498i
$424$	−0.533696	−	1.73719i	−0.0259185	−	0.0843653i
$425$	−18.9235	−	33.6711i	−0.917924	−	1.63329i
$426$	1.38503	+	33.6165i	0.0671049	+	1.62873i
$427$	−11.6335	−	24.9482i	−0.562986	−	1.20733i
$428$	0.0160142	−	3.26060i	0.000774075	−	0.157607i
$429$	3.68185	+	2.12572i	0.177762	+	0.102631i
$430$	−0.373185	−	0.452267i	−0.0179966	−	0.0218102i
$431$	17.8136	−	3.14102i	0.858050	−	0.151297i	0.272721	−	0.962093i	$-0.412076\pi$
$431$	17.8136	−	3.14102i	0.858050	−	0.151297i	0.585329	+	0.810796i	$0.300965\pi$
$432$	−10.7013	+	10.4931i	−0.514865	+	0.504848i
$433$	−29.9231	−	2.61793i	−1.43801	−	0.125810i	−0.658682	−	0.752421i	$-0.728886\pi$
$433$	−29.9231	−	2.61793i	−1.43801	−	0.125810i	−0.779332	+	0.626612i	$0.784441\pi$
$434$	−27.0714	+	11.1355i	−1.29947	+	0.534522i
$435$	27.6767	−	25.0678i	1.32700	−	1.20191i
$436$	4.87535	−	10.3226i	0.233487	−	0.494361i
$437$	−3.12258	−	13.7637i	−0.149373	−	0.658407i
$438$	−0.634818	+	2.83056i	−0.0303328	+	0.135250i
$439$	−30.2542	+	11.0116i	−1.44395	+	0.525556i	−0.940895	−	0.338697i	$-0.890014\pi$
$439$	−30.2542	+	11.0116i	−1.44395	+	0.525556i	−0.503057	+	0.864253i	$0.667791\pi$
$440$	1.50901	+	4.32207i	0.0719390	+	0.206047i
$441$	−0.793575	+	0.665888i	−0.0377893	+	0.0317090i
$442$	24.9943	−	19.0815i	1.18886	−	0.907614i
$443$	−17.9089	−	12.5399i	−0.850876	−	0.595790i	0.0647132	−	0.997904i	$-0.479387\pi$
$443$	−17.9089	−	12.5399i	−0.850876	−	0.595790i	−0.915590	+	0.402114i	$0.868276\pi$
$444$	−34.4493	+	2.84351i	−1.63489	+	0.134947i
$445$	19.5190	−	14.7986i	0.925288	−	0.701523i
$446$	6.47470	+	29.5487i	0.306586	+	1.39917i
$447$	−15.5987	−	33.4514i	−0.737791	−	1.58220i
$448$	−9.63387	−	17.2690i	−0.455157	−	0.815886i
$449$	−1.14795	+	0.662768i	−0.0541750	+	0.0312780i	−0.526843	−	0.849963i	$-0.676624\pi$
$449$	−1.14795	+	0.662768i	−0.0541750	+	0.0312780i	0.472668	+	0.881241i	$0.343291\pi$
$450$	−6.14470	+	5.47391i	−0.289664	+	0.258042i
$451$	−0.0347547	+	0.0414191i	−0.00163654	+	0.00195035i
$452$	15.1427	+	8.84209i	0.712253	+	0.415897i
$453$	26.0687	−	18.2535i	1.22481	−	0.857624i
$454$	−0.685289	+	0.888559i	−0.0321622	+	0.0417022i
$455$	14.6628	+	6.17327i	0.687405	+	0.289407i
$456$	−6.57047	+	24.2843i	−0.307690	+	1.13722i
$457$	−9.37911	+	9.37911i	−0.438736	+	0.438736i	−0.891587	−	0.452850i	$-0.850407\pi$
$457$	−9.37911	+	9.37911i	−0.438736	+	0.438736i	0.452850	+	0.891587i	$0.350407\pi$
$458$	−30.3683	+	3.92222i	−1.41902	+	0.183273i
$459$	−5.02605	+	28.5042i	−0.234596	+	1.33046i
$460$	8.69148	+	11.5815i	0.405242	+	0.539991i
$461$	1.90318	+	1.59696i	0.0886401	+	0.0743778i	0.686031	−	0.727572i	$-0.259351\pi$
$461$	1.90318	+	1.59696i	0.0886401	+	0.0743778i	−0.597391	+	0.801950i	$0.703796\pi$
$462$	0.237879	−	5.15766i	0.0110672	−	0.239956i
$463$	7.55084	+	2.02324i	0.350917	+	0.0940280i	0.429972	−	0.902842i	$-0.358523\pi$
$463$	7.55084	+	2.02324i	0.350917	+	0.0940280i	−0.0790546	+	0.996870i	$0.525190\pi$
$464$	5.36757	+	32.2928i	0.249183	+	1.49915i
$465$	−38.1806	+	1.44553i	−1.77058	+	0.0670350i
$466$	6.14933	−	1.34744i	0.284862	−	0.0624189i
$467$	−3.57761	+	0.958618i	−0.165552	+	0.0443596i	−0.340643	−	0.940193i	$-0.610645\pi$
$467$	−3.57761	+	0.958618i	−0.165552	+	0.0443596i	0.175091	+	0.984552i	$0.443978\pi$
$468$	−5.11110	−	4.33168i	−0.236261	−	0.200232i
$469$	2.77594	−	0.489473i	0.128181	−	0.0226018i
$470$	15.8195	−	26.8857i	0.729700	−	1.24015i
$471$	3.35704	+	4.00077i	0.154684	+	0.184346i
$472$	−19.5088	−	21.6076i	−0.897966	−	0.994570i
$473$	0.121640	+	0.0567215i	0.00559300	+	0.00260806i
$474$	7.78749	+	12.2904i	0.357691	+	0.564517i
$475$	6.69188	−	20.7417i	0.307045	−	0.951695i
$476$	−34.5312	−	16.3091i	−1.58273	−	0.747527i
$477$	−0.316018	+	0.677703i	−0.0144695	+	0.0310299i
$478$	38.9819	+	16.2591i	1.78299	+	0.743675i
$479$	−17.1845	+	14.4195i	−0.785181	+	0.658845i	−0.944548	−	0.328374i	$-0.893499\pi$
$479$	−17.1845	+	14.4195i	−0.785181	+	0.658845i	0.159366	+	0.987220i	$0.449055\pi$
$480$	−4.02202	−	25.4957i	−0.183579	−	1.16371i
$481$	4.23354	+	24.0096i	0.193033	+	1.09474i
$482$	30.0497	−	9.39355i	1.36872	−	0.427865i
$483$	−4.22682	−	15.7747i	−0.192327	−	0.717774i
$484$	14.7425	+	14.8880i	0.670111	+	0.676726i
$485$	0.570772	+	15.0757i	0.0259174	+	0.684551i
$486$	16.2283	−	0.668619i	0.736130	−	0.0303292i
$487$	−7.41721	+	27.6814i	−0.336106	+	1.25436i	0.566560	+	0.824021i	$0.308274\pi$
$487$	−7.41721	+	27.6814i	−0.336106	+	1.25436i	−0.902665	+	0.430343i	$0.858393\pi$
$488$	27.8318	+	14.7499i	1.25989	+	0.667698i
$489$	−6.68924	+	7.97192i	−0.302498	+	0.360503i
$490$	0.222199	+	2.80608i	0.0100379	+	0.126766i
$491$	−37.1458	−	6.54980i	−1.67637	−	0.295589i	−0.747021	−	0.664801i	$-0.768516\pi$
$491$	−37.1458	−	6.54980i	−1.67637	−	0.295589i	−0.929345	+	0.369212i	$0.879628\pi$
$492$	0.234486	−	0.194803i	0.0105715	−	0.00878239i
$493$	44.7033	+	44.7033i	2.01333	+	2.01333i
$494$	17.4817	+	3.03795i	0.786539	+	0.136684i
$495$	0.730907	−	1.73606i	0.0328518	−	0.0780302i
$496$	17.0318	−	28.8419i	0.764749	−	1.29504i
$497$	−16.5298	−	23.6070i	−0.741464	−	1.05892i
$498$	−1.02855	+	0.532223i	−0.0460905	+	0.0238495i
$499$	2.13289	+	1.78970i	0.0954811	+	0.0801182i	0.689279	−	0.724496i	$-0.257928\pi$
$499$	2.13289	+	1.78970i	0.0954811	+	0.0801182i	−0.593798	+	0.804614i	$0.702372\pi$
$500$	2.42395	+	22.2289i	0.108402	+	0.994107i
$501$	1.91737	+	3.32099i	0.0856620	+	0.148371i
$502$	−4.89889	+	5.31991i	−0.218648	+	0.237439i
$503$	34.6832	−	16.1730i	1.54645	−	0.721120i	0.552764	−	0.833338i	$-0.313573\pi$
$503$	34.6832	−	16.1730i	1.54645	−	0.721120i	0.993684	+	0.112217i	$0.0357953\pi$
$504$	−1.81953	+	7.93044i	−0.0810485	+	0.353250i
$505$	0.646603	+	0.852851i	0.0287735	+	0.0379514i
$506$	−2.93618	−	1.53765i	−0.130529	−	0.0683571i
$507$	5.51818	−	7.88077i	0.245071	−	0.349997i
$508$	5.48676	−	14.8474i	0.243435	−	0.658748i
$509$	−7.89744	−	9.41181i	−0.350048	−	0.417171i	0.562076	−	0.827086i	$-0.310003\pi$
$509$	−7.89744	−	9.41181i	−0.350048	−	0.417171i	−0.912124	+	0.409915i	$0.865558\pi$
$510$	−34.9550	−	35.5364i	−1.54784	−	1.57358i
$511$	−0.849840	−	2.33492i	−0.0375947	−	0.103291i
$512$	20.7085	+	9.11901i	0.915197	+	0.403007i
$513$	−13.7310	+	8.84302i	−0.606236	+	0.390429i
$514$	−4.46094	−	7.04036i	−0.196763	−	0.310537i
$515$	3.33225	+	3.67906i	0.146837	+	0.162119i
$516$	−0.617730	−	0.437076i	−0.0271940	−	0.0192412i
$517$	−0.622319	+	7.11314i	−0.0273696	+	0.312836i
$518$	23.5339	−	17.9666i	1.03402	−	0.789405i
$519$	−3.31155	−	18.7808i	−0.145361	−	0.824384i
$520$	−17.6448	+	4.47994i	−0.773777	+	0.196458i
$521$	12.9120	−	22.3643i	0.565687	−	0.979798i	−0.431299	−	0.902209i	$-0.641944\pi$
$521$	12.9120	−	22.3643i	0.565687	−	0.979798i	0.996985	−	0.0775890i	$-0.0247222\pi$
$522$	7.26509	−	11.3423i	0.317984	−	0.496441i
$523$	−0.348522	+	0.162518i	−0.0152398	+	0.00710644i	−0.430223	−	0.902723i	$-0.641565\pi$
$523$	−0.348522	+	0.162518i	−0.0152398	+	0.00710644i	0.414983	+	0.909829i	$0.363787\pi$
$524$	−6.60208	−	9.52800i	−0.288413	−	0.416233i
$525$	6.80888	−	24.2826i	0.297164	−	1.05978i
$526$	−28.2354	+	25.7457i	−1.23112	+	1.12257i
$527$	−5.63782	−	64.4405i	−0.245587	−	2.80707i
$528$	3.34101	+	4.87263i	0.145399	+	0.212054i
$529$	12.3262	+	2.17344i	0.535921	+	0.0944973i
$530$	1.00137	+	1.76793i	0.0434967	+	0.0767940i
$531$			11.9784i			0.519816i
$532$	−6.48019	−	20.5513i	−0.280952	−	0.891013i
$533$	−0.152036	−	0.152036i	−0.00658539	−	0.00658539i
$534$	19.3055	−	25.0319i	0.835429	−	1.08323i
$535$	0.768409	+	3.56360i	0.0332212	+	0.154068i
$536$	−2.19653	+	2.36192i	−0.0948757	+	0.102019i
$537$	4.34308	−	0.379970i	0.187418	−	0.0163969i
$538$	1.28563	−	27.8747i	0.0554272	−	1.20176i
$539$	−0.322156	−	0.557990i	−0.0138762	−	0.0240343i
$540$	9.15393	−	14.0350i	0.393923	−	0.603972i
$541$	−16.7745	−	6.10541i	−0.721191	−	0.262492i	−0.0447598	−	0.998998i	$-0.514252\pi$
$541$	−16.7745	−	6.10541i	−0.721191	−	0.262492i	−0.676431	+	0.736506i	$0.736474\pi$
$542$	−7.48386	−	4.79362i	−0.321459	−	0.205904i
$543$	6.63095	+	24.7470i	0.284561	+	1.06200i
$544$	42.7755	−	8.93355i	1.83399	−	0.383023i
$545$	−2.83463	+	12.4447i	−0.121422	+	0.533072i
$546$	20.3496	+	2.72992i	0.870880	+	0.116830i
$547$	36.6362	+	3.20525i	1.56645	+	0.137047i	0.837083	−	0.547075i	$-0.184259\pi$
$547$	36.6362	+	3.20525i	1.56645	+	0.137047i	0.729367	+	0.684122i	$0.239814\pi$
$548$	−0.575192	−	3.35845i	−0.0245710	−	0.143466i
$549$	−4.43278	−	12.1790i	−0.189187	−	0.519786i
$550$	−2.68918	−	4.35489i	−0.114667	−	0.185693i
$551$	−1.38038	+	35.6463i	−0.0588061	+	1.51858i
$552$	14.7414	+	11.4850i	0.627436	+	0.488835i
$553$	−11.2951	−	5.26700i	−0.480318	−	0.223976i
$554$	20.9018	−	8.59773i	0.888032	−	0.365283i
$555$	36.9245	−	11.4076i	1.56736	−	0.484225i
$556$	1.25764	+	2.73196i	0.0533357	+	0.115861i
$557$	5.10646	+	3.57558i	0.216368	+	0.151502i	0.676736	−	0.736226i	$-0.263394\pi$
$557$	5.10646	+	3.57558i	0.216368	+	0.151502i	−0.460368	+	0.887728i	$0.652283\pi$
$558$	−13.1544	+	4.11207i	−0.556869	+	0.174078i
$559$	−0.266860	+	0.462215i	−0.0112870	+	0.0195496i
$560$	14.6800	+	16.5314i	0.620344	+	0.698578i
$561$	10.7216	+	3.90235i	0.452667	+	0.164757i
$562$	−27.4254	−	25.2549i	−1.15687	−	1.06531i
$563$	−35.2386	−	9.44215i	−1.48513	−	0.397939i	−0.577040	−	0.816716i	$-0.695792\pi$
$563$	−35.2386	−	9.44215i	−1.48513	−	0.397939i	−0.908089	+	0.418777i	$0.862459\pi$
$564$	10.6104	−	38.8347i	0.446779	−	1.63524i
$565$	−18.6631	−	6.00351i	−0.785165	−	0.252569i
$566$	−6.95193	−	2.21072i	−0.292211	−	0.0929234i
$567$	−22.5500	+	15.7897i	−0.947012	+	0.663105i
$568$	31.3765	+	10.1477i	1.31653	+	0.425788i
$569$			1.84160i			0.0772037i	0.999255	+	0.0386019i	$0.0122904\pi$
$569$			1.84160i			0.0772037i	−0.999255	+	0.0386019i	$0.987710\pi$
$570$	1.32011	−	28.0959i	0.0552935	−	1.17681i
$571$		−	2.51012i		−	0.105045i	−0.998620	−	0.0525225i	$-0.983274\pi$
$571$		−	2.51012i		−	0.105045i	0.998620	−	0.0525225i	$-0.0167261\pi$
$572$	3.20521	−	2.66277i	0.134016	−	0.111336i
$573$	−35.1984	+	24.6462i	−1.47043	+	1.02961i
$574$	−0.0791313	+	0.248840i	−0.00330288	+	0.0103864i
$575$	−12.2803	−	10.5492i	−0.512125	−	0.439931i
$576$	−3.80998	−	8.49511i	−0.158749	−	0.353963i
$577$	−2.28145	−	0.611312i	−0.0949779	−	0.0254493i	0.211017	−	0.977482i	$-0.432322\pi$
$577$	−2.28145	−	0.611312i	−0.0949779	−	0.0254493i	−0.305995	+	0.952033i	$0.598989\pi$
$578$	40.8807	−	44.3941i	1.70041	−	1.84655i
$579$	−9.89292	−	3.60073i	−0.411136	−	0.149641i
$580$	−13.6434	−	33.9617i	−0.566513	−	1.41018i
$581$	0.495986	−	0.859073i	0.0205770	−	0.0356403i
$582$	5.80908	+	18.5830i	0.240794	+	0.770292i
$583$	−0.380969	−	0.266757i	−0.0157781	−	0.0110480i
$584$	2.38665	+	1.54530i	0.0987603	+	0.0639450i
$585$	6.62407	+	3.49717i	0.273872	+	0.144590i
$586$	−1.29161	−	3.14000i	−0.0533558	−	0.129712i
$587$	−5.40065	−	2.51837i	−0.222909	−	0.103944i	0.307956	−	0.951401i	$-0.400355\pi$
$587$	−5.40065	−	2.51837i	−0.222909	−	0.103944i	−0.530865	+	0.847456i	$0.678133\pi$
$588$	1.22568	+	3.41970i	0.0505463	+	0.141026i
$589$	24.5266	−	27.0323i	1.01060	−	1.11385i
$590$	26.5067	+	18.8878i	1.09126	+	0.777599i
$591$	−17.0289	−	46.7866i	−0.700476	−	1.92454i
$592$	−9.08975	+	32.6376i	−0.373587	+	1.34140i
$593$	0.874726	+	0.0765286i	0.0359207	+	0.00314265i	0.105102	−	0.994461i	$-0.466483\pi$
$593$	0.874726	+	0.0765286i	0.0359207	+	0.00314265i	−0.0691812	+	0.997604i	$0.522039\pi$
$594$	−0.509967	+	3.80142i	−0.0209242	+	0.155974i
$595$	41.6302	+	9.48244i	1.70667	+	0.388742i
$596$	−36.0537	+	2.97594i	−1.47682	+	0.121899i
$597$	−1.70296	−	6.35552i	−0.0696974	−	0.260114i
$598$	7.10903	−	11.0987i	0.290710	−	0.453860i
$599$	36.7367	+	13.3711i	1.50102	+	0.546326i	0.956324	−	0.292308i	$-0.0944231\pi$
$599$	36.7367	+	13.3711i	1.50102	+	0.546326i	0.544695	+	0.838634i	$0.316645\pi$
$600$	10.5362	+	26.8654i	0.430137	+	1.09677i
$601$	21.1660	+	36.6607i	0.863381	+	1.49542i	0.868646	+	0.495433i	$0.164991\pi$
$601$	21.1660	+	36.6607i	0.863381	+	1.49542i	−0.00526496	+	0.999986i	$0.501676\pi$
$602$	0.647485	+	0.0298631i	0.0263895	+	0.00121713i
$603$	1.32210	−	0.115669i	0.0538400	−	0.00471039i
$604$	−7.92496	−	30.1682i	−0.322462	−	1.22753i
$605$	−19.6834	−	12.7005i	−0.800244	−	0.516351i
$606$	1.09373	+	0.843522i	0.0444296	+	0.0342657i
$607$	17.2427	+	17.2427i	0.699858	+	0.699858i	0.964380	−	0.264522i	$-0.0852142\pi$
$607$	17.2427	+	17.2427i	0.699858	+	0.699858i	−0.264522	+	0.964380i	$0.585214\pi$
$608$	20.0939	+	14.2911i	0.814914	+	0.579582i
$609$			41.2785i			1.67269i
$610$	−33.9403	−	9.39494i	−1.37420	−	0.380390i
$611$	−27.9629	−	4.93062i	−1.13126	−	0.199471i
$612$	−15.5271	−	9.06654i	−0.627645	−	0.366493i
$613$	−1.08820	−	12.4381i	−0.0439519	−	0.502372i	−0.985983	−	0.166846i	$-0.946642\pi$
$613$	−1.08820	−	12.4381i	−0.0439519	−	0.502372i	0.942031	−	0.335526i	$-0.108914\pi$
$614$	−19.1764	−	21.0308i	−0.773897	−	0.848736i
$615$	−0.209046	+	0.269192i	−0.00842956	+	0.0108549i
$616$	−4.66096	−	1.97099i	−0.187796	−	0.0794133i
$617$	−10.9127	+	5.08866i	−0.439327	+	0.204862i	−0.629681	−	0.776854i	$-0.716814\pi$
$617$	−10.9127	+	5.08866i	−0.439327	+	0.204862i	0.190354	+	0.981716i	$0.439037\pi$
$618$	5.39433	+	3.45522i	0.216992	+	0.138989i
$619$	−0.856612	+	1.48370i	−0.0344302	+	0.0596348i	−0.882727	−	0.469886i	$-0.844295\pi$
$619$	−0.856612	+	1.48370i	−0.0344302	+	0.0596348i	0.848297	+	0.529521i	$0.177628\pi$
$620$	−11.6427	+	35.5931i	−0.467581	+	1.42945i
$621$	2.10665	+	11.9474i	0.0845370	+	0.479433i
$622$	13.8741	+	18.1733i	0.556299	+	0.728681i
$623$	−2.35993	+	26.9741i	−0.0945485	+	1.08069i
$624$	−20.4608	+	11.5466i	−0.819088	+	0.462233i
$625$	−8.00410	−	23.6841i	−0.320164	−	0.947362i
$626$	−26.9100	+	17.0508i	−1.07554	+	0.681486i
$627$	2.49305	+	5.93585i	0.0995629	+	0.237055i
$628$	4.81871	−	1.72711i	0.192287	−	0.0689193i
$629$	22.3781	+	61.4833i	0.892274	+	2.45150i
$630$	0.0750169	−	9.09657i	0.00298874	−	0.362416i
$631$	−15.7341	−	18.7512i	−0.626366	−	0.746474i	0.355785	−	0.934568i	$-0.384214\pi$
$631$	−15.7341	−	18.7512i	−0.626366	−	0.746474i	−0.982151	+	0.188094i	$0.939769\pi$
$632$	13.9451	−	2.98395i	0.554708	−	0.118695i
$633$	20.1259	−	28.7427i	0.799932	−	1.14242i
$634$	−9.79273	+	18.6994i	−0.388919	+	0.742648i
$635$	−2.41150	+	17.5321i	−0.0956977	+	0.695739i
$636$	1.84503	+	1.86324i	0.0731601	+	0.0738823i
$637$	2.32212	−	1.08282i	0.0920059	−	0.0429030i
$638$	6.16266	+	5.67494i	0.243982	+	0.224673i
$639$	−6.78435	−	11.7508i	−0.268385	−	0.464856i
$640$	−24.8064	−	4.96432i	−0.980558	−	0.196232i
$641$	10.8231	+	9.08164i	0.427486	+	0.358703i	0.831002	−	0.556269i	$-0.187768\pi$
$641$	10.8231	+	9.08164i	0.427486	+	0.358703i	−0.403516	+	0.914972i	$0.632212\pi$
$642$	2.16214	+	4.17845i	0.0853328	+	0.164910i
$643$	17.7985	+	25.4189i	0.701905	+	1.00242i	0.998870	+	0.0475354i	$0.0151367\pi$
$643$	17.7985	+	25.4189i	0.701905	+	1.00242i	−0.296965	+	0.954888i	$0.595974\pi$
$644$	−15.9388	−	1.47338i	−0.628076	−	0.0580592i
$645$	0.779750	+	0.328286i	0.0307026	+	0.0129263i
$646$	47.6192	−	0.117741i	1.87355	−	0.00463244i
$647$	29.2809	+	29.2809i	1.15115	+	1.15115i	0.986322	+	0.164828i	$0.0527068\pi$
$647$	29.2809	+	29.2809i	1.15115	+	1.15115i	0.164828	+	0.986322i	$0.447293\pi$
$648$	9.69333	−	29.9716i	0.380790	−	1.17739i
$649$	−7.33686	−	1.29369i	−0.287997	−	0.0507817i
$650$	18.1839	−	9.14382i	0.713229	−	0.358650i
$651$	27.1489	−	32.3548i	1.06405	−	1.26808i
$652$	5.05649	+	8.85828i	0.198027	+	0.346917i
$653$	9.40449	−	35.0980i	0.368026	−	1.37349i	−0.495246	−	0.868753i	$-0.664922\pi$
$653$	9.40449	−	35.0980i	0.368026	−	1.37349i	0.863272	−	0.504739i	$-0.168411\pi$
$654$	0.678078	+	16.4579i	0.0265150	+	0.643554i
$655$	9.50429	+	8.81087i	0.371363	+	0.344269i
$656$	−0.0994298	−	0.281762i	−0.00388208	−	0.0110010i
$657$	−0.302791	−	1.13003i	−0.0118130	−	0.0440867i
$658$	10.2885	+	32.9127i	0.401089	+	1.28307i
$659$	4.82640	+	27.3719i	0.188010	+	1.06626i	0.922027	+	0.387126i	$0.126532\pi$
$659$	4.82640	+	27.3719i	0.188010	+	1.06626i	−0.734017	+	0.679131i	$0.762357\pi$
$660$	−4.82197	−	4.51440i	−0.187695	−	0.175723i
$661$	4.06988	−	3.41504i	0.158300	−	0.132830i	−0.560197	−	0.828359i	$-0.689275\pi$
$661$	4.06988	−	3.41504i	0.158300	−	0.132830i	0.718497	+	0.695530i	$0.244830\pi$
$662$	3.30208	−	7.91688i	0.128339	−	0.307698i
$663$	−19.1751	+	41.1210i	−0.744698	+	1.59701i
$664$	0.139864	+	1.12644i	0.00542776	+	0.0437142i
$665$	12.0281	+	20.8749i	0.466431	+	0.809494i
$666$	11.7755	−	7.46123i	0.456291	−	0.289117i
$667$	24.0157	+	11.1987i	0.929892	+	0.433616i
$668$	3.70463	−	0.634481i	0.143336	−	0.0245488i
$669$	−28.0556	−	33.4353i	−1.08469	−	1.29268i
$670$	1.82876	−	3.10804i	0.0706513	−	0.120074i
$671$	7.93849	−	1.39977i	0.306462	−	0.0540375i
$672$	23.8738	+	15.6246i	0.920951	+	0.602734i
$673$	−32.4622	+	8.69823i	−1.25133	+	0.335292i	−0.822849	−	0.568260i	$-0.807617\pi$
$673$	−32.4622	+	8.69823i	−1.25133	+	0.335292i	−0.428478	+	0.903552i	$0.640950\pi$
$674$	6.25874	+	28.5631i	0.241078	+	1.10021i
$675$	−6.61094	+	17.5290i	−0.254455	+	0.674692i
$676$	−5.37055	−	7.75068i	−0.206560	−	0.298103i
$677$	21.1358	+	5.66331i	0.812313	+	0.217659i	0.640983	−	0.767555i	$-0.278527\pi$
$677$	21.1358	+	5.66331i	0.812313	+	0.217659i	0.171330	+	0.985214i	$0.445194\pi$
$678$	−25.2743	−	1.16569i	−0.970655	−	0.0447681i
$679$	−12.7753	−	10.7198i	−0.490273	−	0.411388i
$680$	−44.5467	+	20.0632i	−1.70829	+	0.769389i
$681$	0.281151	−	1.59449i	0.0107737	−	0.0611009i
$682$	−1.09799	−	8.50129i	−0.0420440	−	0.325531i
$683$	11.0742	−	11.0742i	0.423742	−	0.423742i	−0.462748	−	0.886490i	$-0.653137\pi$
$683$	11.0742	−	11.0742i	0.423742	−	0.423742i	0.886490	+	0.462748i	$0.153137\pi$
$684$	−2.19611	−	9.90521i	−0.0839702	−	0.378735i
$685$	1.43744	+	3.52793i	0.0549217	+	0.134795i
$686$	−21.8404	−	16.8441i	−0.833872	−	0.643112i
$687$	36.1915	−	25.3416i	1.38079	−	0.966842i
$688$	−0.611704	+	0.419426i	−0.0233210	+	0.0159905i
$689$	1.18879	−	1.41675i	0.0452895	−	0.0539739i
$690$	−18.8621	−	8.98563i	−0.718066	−	0.342077i
$691$	1.11642	−	0.644565i	0.0424706	−	0.0245204i	−0.478614	−	0.878025i	$-0.658861\pi$
$691$	1.11642	−	0.644565i	0.0424706	−	0.0245204i	0.521085	+	0.853505i	$0.325527\pi$
$692$	−18.3915	−	3.33613i	−0.699139	−	0.126821i
$693$	0.879993	+	1.88715i	0.0334282	+	0.0716870i
$694$	−50.0899	+	10.9757i	−1.90139	+	0.416631i
$695$	−2.03149	−	2.67948i	−0.0770589	−	0.101638i
$696$	−28.4773	−	37.6839i	−1.07943	−	1.42840i
$697$	−0.472676	−	0.330971i	−0.0179039	−	0.0125364i
$698$	−4.19284	−	5.49209i	−0.158701	−	0.207879i
$699$	−6.95816	+	5.83859i	−0.263182	+	0.220836i
$700$	−20.0113	−	14.5097i	−0.756357	−	0.548417i
$701$	35.1615	−	12.7977i	1.32803	−	0.483364i	0.422009	−	0.906592i	$-0.361325\pi$
$701$	35.1615	−	12.7977i	1.32803	−	0.483364i	0.906023	+	0.423228i	$0.139103\pi$
$702$	−14.8825	−	3.33774i	−0.561705	−	0.125975i
$703$	−16.8860	+	32.8317i	−0.636867	+	1.23827i
$704$	5.61483	−	1.41616i	0.211617	−	0.0533736i
$705$	−2.22367	+	44.9550i	−0.0837482	+	1.69310i
$706$	−2.93047	−	7.12421i	−0.110290	−	0.268123i
$707$	−1.17859	−	0.103113i	−0.0443255	−	0.00387798i
$708$	39.4002	+	14.5600i	1.48075	+	0.547200i
$709$	−3.82149	+	0.673831i	−0.143519	+	0.0253063i	−0.244946	−	0.969537i	$-0.578770\pi$
$709$	−3.82149	+	0.673831i	−0.143519	+	0.0253063i	0.101427	+	0.994843i	$0.467659\pi$
$710$	−36.7010	−	3.51612i	−1.37736	−	0.131958i
$711$	−5.08168	−	2.93391i	−0.190578	−	0.110030i
$712$	−16.4545	−	26.2533i	−0.616659	−	0.983882i
$713$	−11.4585	−	24.5729i	−0.429125	−	0.920262i
$714$	55.0552	−	2.26832i	2.06039	−	0.0848897i
$715$	−2.85747	+	3.67961i	−0.106863	+	0.137610i
$716$	1.12621	−	4.12197i	0.0420883	−	0.154045i
$717$	−60.7107	+	5.31150i	−2.26728	+	0.198362i
$718$	10.1141	+	19.5461i	0.377456	+	0.729455i
$719$	3.67193	−	20.8246i	0.136940	−	0.776625i	−0.836549	−	0.547892i	$-0.815431\pi$
$719$	3.67193	−	20.8246i	0.136940	−	0.776625i	0.973489	−	0.228733i	$-0.0734583\pi$
$720$	6.20708	+	8.35619i	0.231324	+	0.311417i
$721$	−5.48714			−0.204352
$722$	18.2993	+	19.6758i	0.681028	+	0.732257i
$723$	−32.1218	+	32.1218i	−1.19462	+	1.19462i
$724$	25.0044	+	2.31141i	0.929283	+	0.0859027i
$725$	23.0808	+	33.7891i	0.857201	+	1.25489i
$726$	−28.8098	−	9.16153i	−1.06923	−	0.340016i
$727$	−0.488411	−	5.58256i	−0.0181142	−	0.207046i	−0.999858	−	0.0168390i	$-0.994640\pi$
$727$	−0.488411	−	5.58256i	−0.0181142	−	0.207046i	0.981744	−	0.190207i	$-0.0609158\pi$
$728$	9.42346	−	17.7812i	0.349257	−	0.659016i
$729$	8.63911	−	4.98779i	0.319967	−	0.184733i
$730$	−2.97807	−	1.11183i	−0.110223	−	0.0411505i
$731$	−0.489896	+	1.34598i	−0.0181194	+	0.0497828i
$732$	−45.4483	−	0.223216i	−1.67982	−	0.00825028i
$733$	−23.9451	+	6.41608i	−0.884434	+	0.236983i	−0.672319	−	0.740261i	$-0.734702\pi$
$733$	−23.9451	+	6.41608i	−0.884434	+	0.236983i	−0.212115	+	0.977245i	$0.568035\pi$
$734$	−31.3371	−	16.4110i	−1.15667	−	0.605741i
$735$	−2.16237	−	3.43802i	−0.0797603	−	0.126813i
$736$	15.5673	−	9.65080i	0.573817	−	0.355733i
$737$	−0.0719412	+	0.822292i	−0.00264999	+	0.0302895i
$738$	−0.0473266	+	0.113468i	−0.00174212	+	0.00417680i
$739$	39.6990	−	14.4492i	1.46035	−	0.531524i	0.514888	−	0.857257i	$-0.327834\pi$
$739$	39.6990	−	14.4492i	1.46035	−	0.531524i	0.945462	+	0.325734i	$0.105611\pi$
$740$	2.05715	−	37.8228i	0.0756222	−	1.39040i
$741$	−24.3788	+	7.81891i	−0.895579	+	0.287235i
$742$	−2.19160	−	0.491515i	−0.0804561	−	0.0180441i
$743$	−1.02755	+	2.20359i	−0.0376971	+	0.0808418i	−0.924255	−	0.381777i	$-0.875312\pi$
$743$	−1.02755	+	2.20359i	−0.0376971	+	0.0808418i	0.886557	+	0.462619i	$0.153090\pi$
$744$	−2.46376	+	48.2668i	−0.0903257	+	1.76955i
$745$	38.6441	−	11.9389i	1.41581	−	0.437406i
$746$	−4.87906	−	0.654534i	−0.178635	−	0.0239642i
$747$	0.267887	−	0.382582i	0.00980147	−	0.0139980i
$748$	7.23031	−	8.53130i	0.264366	−	0.311935i
$749$	−3.48995	−	2.01492i	−0.127520	−	0.0736237i
$750$	−17.9781	−	26.7906i	−0.656467	−	0.978255i
$751$	−5.18557	+	14.2472i	−0.189224	+	0.519889i	−0.997635	−	0.0687291i	$-0.978106\pi$
$751$	−5.18557	+	14.2472i	−0.189224	+	0.519889i	0.808411	+	0.588618i	$0.200328\pi$
$752$	−32.0985	−	22.9488i	−1.17051	−	0.836855i
$753$	2.70072	−	10.0792i	0.0984196	−	0.367307i
$754$	−24.6171	+	22.4464i	−0.896501	+	0.817451i
$755$	15.9234	+	31.0259i	0.579511	+	1.12915i
$756$	4.70617	+	17.9152i	0.171162	+	0.651569i
$757$	17.7604	+	25.3645i	0.645512	+	0.921887i	0.999913	−	0.0132066i	$-0.00420390\pi$
$757$	17.7604	+	25.3645i	0.645512	+	0.921887i	−0.354400	+	0.935094i	$0.615315\pi$
$758$	−4.82983	−	37.3956i	−0.175427	−	1.35827i
$759$	4.78234			0.173588
$760$	−25.3819	−	10.7591i	−0.920699	−	0.390274i
$761$	−3.98694			−0.144527			−0.0722633	−	0.997386i	$-0.523022\pi$
$761$	−3.98694			−0.144527			−0.0722633	+	0.997386i	$0.523022\pi$
$762$	2.92548	+	22.6509i	0.105979	+	0.820555i
$763$	−8.09263	−	11.5575i	−0.292973	−	0.418409i
$764$	10.7004	+	40.7337i	0.387127	+	1.47369i
$765$	19.1369	+	6.15590i	0.691896	+	0.222567i
$766$	10.5287	−	9.60031i	0.380417	−	0.346873i
$767$	7.66777	−	28.6165i	0.276867	−	1.03328i
$768$	−32.5740	+	2.20605i	−1.17541	+	0.0796039i
$769$	11.0886	−	30.4656i	0.399864	−	1.09862i	−0.562487	−	0.826806i	$-0.690155\pi$
$769$	11.0886	−	30.4656i	0.399864	−	1.09862i	0.962351	−	0.271811i	$-0.0876224\pi$
$770$	5.56364	+	1.02840i	0.200500	+	0.0370609i
$771$	10.4147	+	6.01295i	0.375078	+	0.216551i
$772$	−6.67146	+	7.87190i	−0.240111	+	0.283316i
$773$	−14.3117	+	20.4392i	−0.514755	+	0.735147i	−0.989429	−	0.145015i	$-0.953677\pi$
$773$	−14.3117	+	20.4392i	−0.514755	+	0.735147i	0.474674	+	0.880162i	$0.342566\pi$
$774$	0.302468	+	0.0405765i	0.0108720	+	0.00145849i
$775$	4.13195	−	41.6647i	0.148424	−	1.49664i
$776$	19.0582	+	0.972820i	0.684151	+	0.0349222i
$777$	−18.0547	+	38.7183i	−0.647707	+	1.38901i
$778$	−34.9324	−	7.83438i	−1.25239	−	0.280876i
$779$	−0.0440897	−	0.322601i	−0.00157968	−	0.0115584i
$780$	19.5550	−	17.5375i	0.700180	−	0.627944i
$781$	7.93023	−	2.88637i	0.283766	−	0.103282i
$782$	13.6166	−	32.6464i	0.486928	−	1.16743i
$783$	2.67254	−	30.5473i	0.0955089	−	1.09167i
$784$	3.56038	+	0.0349739i	0.127156	+	0.00124907i
$785$	−4.84452	+	3.04700i	−0.172908	+	0.108752i
$786$	14.8168	+	7.75943i	0.528497	+	0.276770i
$787$	21.0361	−	5.63660i	0.749855	−	0.200923i	0.136401	−	0.990654i	$-0.456446\pi$
$787$	21.0361	−	5.63660i	0.749855	−	0.200923i	0.613454	+	0.789731i	$0.289780\pi$
$788$	−48.7995	−	0.239675i	−1.73841	−	0.00853807i
$789$	18.8569	−	51.8089i	0.671323	−	1.84444i
$790$	−14.5053	+	6.61887i	−0.516076	+	0.235489i
$791$	18.7684	−	10.8360i	0.667328	−	0.385282i
$792$	−2.10527	−	1.11573i	−0.0748077	−	0.0396456i
$793$	2.79381	+	31.9334i	0.0992110	+	1.13399i
$794$	2.67353	+	0.850185i	0.0948801	+	0.0301719i
$795$	−2.46339	−	1.58948i	−0.0873674	−	0.0563731i
$796$	−6.42162	−	0.593614i	−0.227608	−	0.0210401i
$797$	−0.478172	+	0.478172i	−0.0169377	+	0.0169377i	−0.715525	−	0.698587i	$-0.753812\pi$
$797$	−0.478172	+	0.478172i	−0.0169377	+	0.0169377i	0.698587	+	0.715525i	$0.253812\pi$
$798$	22.0398	+	21.9311i	0.780202	+	0.776353i
$799$	−76.2026			−2.69585
$800$	28.2787	−	0.559231i	0.999805	−	0.0197718i
$801$	−2.21378	+	12.5550i	−0.0782200	+	0.443608i
$802$	−0.131285	−	0.253716i	−0.00463584	−	0.00895902i
$803$	0.724857	−	0.0634168i	0.0255797	−	0.00223793i
$804$	1.22658	−	4.48936i	0.0432583	−	0.158327i
$805$	17.7562	−	2.23312i	0.625823	−	0.0787071i
$806$	34.0583	−	1.40323i	1.19965	−	0.0494267i
$807$	17.0157	+	36.4903i	0.598981	+	1.28452i
$808$	1.14709	−	0.718954i	0.0403546	−	0.0252927i
$809$	−16.6757	−	9.62775i	−0.586288	−	0.338494i	0.177340	−	0.984150i	$-0.443251\pi$
$809$	−16.6757	−	9.62775i	−0.586288	−	0.338494i	−0.763628	+	0.645656i	$0.776584\pi$
$810$	−3.35868	+	35.0577i	−0.118012	+	1.23180i
$811$	52.0669	−	9.18080i	1.82832	−	0.322382i	0.849574	−	0.527470i	$-0.176859\pi$
$811$	52.0669	−	9.18080i	1.82832	−	0.322382i	0.978743	+	0.205088i	$0.0657481\pi$
$812$	37.9500	+	14.0241i	1.33179	+	0.492151i
$813$	12.7747	+	1.11764i	0.448029	+	0.0391975i
$814$	3.29830	+	8.01844i	0.115605	+	0.281046i
$815$	−7.65548	−	8.45223i	−0.268160	−	0.296069i
$816$	−48.6961	+	40.0524i	−1.70470	+	1.40211i
$817$	−0.745178	+	0.312974i	−0.0260705	+	0.0109496i
$818$	41.5334	+	9.31479i	1.45218	+	0.325684i
$819$	−7.78092	+	2.83202i	−0.271887	+	0.0989589i
$820$	0.176464	+	0.283647i	0.00616239	+	0.00990538i
$821$	−25.8923	+	21.7262i	−0.903649	+	0.758251i	−0.970900	−	0.239485i	$-0.923022\pi$
$821$	−25.8923	+	21.7262i	−0.903649	+	0.758251i	0.0672514	+	0.997736i	$0.478577\pi$
$822$	2.98332	+	3.90777i	0.104055	+	0.136299i
$823$	−16.6586	−	11.6645i	−0.580683	−	0.406598i	0.245997	−	0.969270i	$-0.420884\pi$
$823$	−16.6586	−	11.6645i	−0.580683	−	0.406598i	−0.826680	+	0.562672i	$0.809773\pi$
$824$	5.00931	−	3.78548i	0.174508	−	0.131873i
$825$	6.35245	+	3.76635i	0.221164	+	0.131127i
$826$	−35.1453	+	7.70103i	−1.22286	+	0.267953i
$827$	−14.3036	−	30.6741i	−0.497385	−	1.06664i	−0.981469	−	0.191623i	$-0.938625\pi$
$827$	−14.3036	−	30.6741i	−0.497385	−	1.06664i	0.484084	−	0.875022i	$-0.339153\pi$
$828$	−7.41538	−	1.34512i	−0.257702	−	0.0467460i
$829$	−3.13939	+	1.81253i	−0.109035	+	0.0629517i	−0.553526	−	0.832832i	$-0.686718\pi$
$829$	−3.13939	+	1.81253i	−0.109035	+	0.0629517i	0.444491	+	0.895784i	$0.353385\pi$
$830$	−0.424197	−	1.19607i	−0.0147241	−	0.0415162i
$831$	−20.9616	+	24.9811i	−0.727151	+	0.866585i
$832$	3.66409	+	22.7339i	0.127029	+	0.788156i
$833$	5.63265	−	3.94402i	0.195160	−	0.136652i
$834$	−3.43626	−	2.65017i	−0.118988	−	0.0917679i
$835$	−3.89158	+	1.58561i	−0.134674	+	0.0548721i
$836$	6.30422	−	0.275355i	0.218036	−	0.00952334i
$837$	−22.1858	+	22.1858i	−0.766852	+	0.766852i
$838$	0.0470607	+	0.364373i	0.00162568	+	0.0125871i
$839$	3.57945	−	20.3001i	0.123577	−	0.700837i	−0.858567	−	0.512702i	$-0.828645\pi$
$839$	3.57945	−	20.3001i	0.123577	−	0.700837i	0.982143	−	0.188135i	$-0.0602443\pi$
$840$	−29.8300	−	11.3039i	−1.02923	−	0.390022i
$841$	−29.0921	−	24.4112i	−1.00318	−	0.841765i
$842$	5.91424	+	0.272774i	0.203818	+	0.00940041i
$843$	51.9607	+	13.9228i	1.78962	+	0.479528i
$844$	−19.5875	−	28.2683i	−0.674228	−	0.973034i
$845$	7.73139	+	7.16732i	0.265968	+	0.246563i
$846$	3.47511	+	15.8594i	0.119477	+	0.545258i
$847$	25.0125	−	6.70209i	0.859441	−	0.230286i
$848$	2.33984	−	1.06323i	0.0803504	−	0.0365115i
$849$	10.3658	−	1.82778i	0.355755	−	0.0627292i
$850$	43.7979	−	32.6409i	1.50226	−	1.11957i
$851$	17.6281	+	21.0083i	0.604282	+	0.720156i
$852$	−46.8984	+	8.03216i	−1.60671	+	0.275177i
$853$	−23.7386	−	11.0695i	−0.812795	−	0.379013i	−0.0286494	−	0.999590i	$-0.509121\pi$
$853$	−23.7386	−	11.0695i	−0.812795	−	0.379013i	−0.784145	+	0.620577i	$0.786898\pi$
$854$	32.8841	−	20.8361i	1.12527	−	0.712997i
$855$	4.78501	+	10.2846i	0.163644	+	0.351727i
$856$	4.57610	−	0.568191i	0.156408	−	0.0194204i
$857$	22.2726	−	47.7637i	0.760817	−	1.63158i	−0.0144106	−	0.999896i	$-0.504587\pi$
$857$	22.2726	−	47.7637i	0.760817	−	1.63158i	0.775228	−	0.631682i	$-0.217635\pi$
$858$	−2.31450	+	5.54911i	−0.0790156	+	0.189443i
$859$	−28.8366	+	24.1968i	−0.983891	+	0.825583i	−0.984672	−	0.174417i	$-0.944196\pi$
$859$	−28.8366	+	24.1968i	−0.983891	+	0.825583i	0.000780747		1.00000i	$0.499751\pi$
$860$	0.566731	−	0.605343i	0.0193254	−	0.0206420i
$861$	−0.0654242	−	0.371039i	−0.00222965	−	0.0126450i
$862$	7.63237	+	24.4157i	0.259960	+	0.831602i
$863$	1.05207	+	3.92637i	0.0358128	+	0.133655i	0.981518	−	0.191371i	$-0.0612934\pi$
$863$	1.05207	+	3.92637i	0.0358128	+	0.133655i	−0.945705	+	0.325026i	$0.894627\pi$
$864$	−16.6557	−	13.1084i	−0.566639	−	0.445957i
$865$	20.8829	−	0.790636i	0.710040	−	0.0268824i
$866$	−1.74870	−	42.4433i	−0.0594233	−	1.44228i
$867$	−22.5372	+	84.1101i	−0.765404	+	2.85653i
$868$	−20.5222	−	35.9521i	−0.696569	−	1.22029i
$869$	2.34588	−	2.79571i	0.0795785	−	0.0948380i
$870$	40.1727	+	34.2774i	1.36198	+	1.16211i
$871$	−3.23256	−	0.569988i	−0.109531	−	0.0193133i
$872$	15.3612	+	4.96808i	0.520196	+	0.168240i
$873$	−5.55219	−	5.55219i	−0.187913	−	0.187913i
$874$	18.7388	−	6.87289i	0.633850	−	0.232479i
$875$	25.3445	+	11.0177i	0.856801	+	0.372465i
$876$	−4.08504	−	0.377621i	−0.138021	−	0.0127586i
$877$	−17.0239	−	24.3126i	−0.574855	−	0.820978i	0.421451	−	0.906851i	$-0.361521\pi$
$877$	−17.0239	−	24.3126i	−0.574855	−	0.820978i	−0.996306	+	0.0858733i	$0.972632\pi$
$878$	−20.9250	−	40.4387i	−0.706184	−	1.36474i
$879$	3.75283	+	3.14899i	0.126580	+	0.106213i
$880$	−5.78863	+	2.89941i	−0.195135	+	0.0977391i
$881$	23.0992	+	40.0091i	0.778233	+	1.34794i	0.932959	+	0.359982i	$0.117217\pi$
$881$	23.0992	+	40.0091i	0.778233	+	1.34794i	−0.154726	+	0.987957i	$0.549449\pi$
$882$	−1.07771	−	0.992415i	−0.0362882	−	0.0334163i
$883$	−37.5033	+	17.4881i	−1.26209	+	0.588521i	−0.934386	−	0.356261i	$-0.884051\pi$
$883$	−37.5033	+	17.4881i	−1.26209	+	0.588521i	−0.327700	+	0.944782i	$0.606274\pi$
$884$	31.2907	+	31.5996i	1.05242	+	1.06281i
$885$	−46.5243	−	6.39934i	−1.56390	−	0.215111i
$886$	14.3439	−	27.3899i	0.481893	−	0.920183i
$887$	−8.70734	+	12.4354i	−0.292364	+	0.417539i	−0.938284	−	0.345866i	$-0.887585\pi$
$887$	−8.70734	+	12.4354i	−0.292364	+	0.417539i	0.645920	+	0.763405i	$0.276474\pi$
$888$	−10.2286	−	47.8023i	−0.343251	−	1.60414i
$889$	−12.5748	−	14.9861i	−0.421745	−	0.502617i
$890$	24.2919	+	24.6959i	0.814265	+	0.827807i
$891$	−2.75713	−	7.57515i	−0.0923673	−	0.253777i
$892$	−40.2711	+	14.4339i	−1.34838	+	0.483282i
$893$	−29.2054	−	31.5584i	−0.977321	−	1.05606i
$894$	44.0921	−	27.9378i	1.47466	−	0.934379i
$895$	−0.236024	+	4.77159i	−0.00788940	+	0.159497i
$896$	22.4758	−	16.6404i	0.750863	−	0.555916i
$897$	−1.65749	+	18.9452i	−0.0553419	+	0.632561i
$898$	−1.13752	−	1.49001i	−0.0379597	−	0.0497223i
$899$	11.9003	+	67.4898i	0.396897	+	2.25091i
$900$	−8.79061	−	7.62675i	−0.293020	−	0.254225i
$901$	2.48169	−	4.29842i	0.0826771	−	0.143201i
$902$	−0.0643886	−	0.0412427i	−0.00214391	−	0.00137323i
$903$	−0.847612	+	0.395248i	−0.0282067	+	0.0131530i
$904$	−9.65852	+	22.8403i	−0.321238	+	0.759658i
$905$	−27.8556	+	3.50328i	−0.925950	+	0.116453i
$906$	30.3240	+	33.2564i	1.00745	+	1.10487i
$907$	−2.45145	−	28.0202i	−0.0813990	−	0.930395i	−0.921605	−	0.388128i	$-0.873122\pi$
$907$	−2.45145	−	28.0202i	−0.0813990	−	0.930395i	0.840206	−	0.542267i	$-0.182434\pi$
$908$	−1.37040	−	0.800201i	−0.0454783	−	0.0265556i
$909$	−0.548569	−	0.0967275i	−0.0181949	−	0.00320825i
$910$	−6.00226	+	21.6839i	−0.198973	+	0.718813i
$911$			1.12748i			0.0373552i	0.999826	+	0.0186776i	$0.00594561\pi$
$911$			1.12748i			0.0373552i	−0.999826	+	0.0186776i	$0.994054\pi$
$912$	−35.2505	−	4.81645i	−1.16726	−	0.159489i
$913$	0.205403	+	0.205403i	0.00679785	+	0.00679785i
$914$	−14.8538	−	11.4558i	−0.491320	−	0.378924i
$915$	49.6717	−	10.7106i	1.64210	−	0.354080i
$916$	−11.0023	−	41.8830i	−0.363527	−	1.38385i
$917$	−14.2719	+	1.24863i	−0.471299	+	0.0412334i
$918$	−40.8894	−	1.88588i	−1.34955	−	0.0622434i
$919$	10.9955	+	19.0448i	0.362708	+	0.628229i	0.988406	−	0.151837i	$-0.0485189\pi$
$919$	10.9955	+	19.0448i	0.362708	+	0.628229i	−0.625698	+	0.780066i	$0.715186\pi$
$920$	−14.6694	+	14.2883i	−0.483635	+	0.471072i
$921$	38.5893	+	14.0453i	1.27156	+	0.462810i
$922$	−1.89508	+	2.95862i	−0.0624111	+	0.0974370i
$923$	8.68581	+	32.4159i	0.285897	+	1.06698i
$924$	7.27704	−	0.600660i	0.239397	−	0.0197602i
$925$	6.87044	+	41.7887i	0.225899	+	1.37400i
$926$	−1.46990	+	10.9570i	−0.0483040	+	0.360071i
$927$	−2.57366	−	0.225166i	−0.0845301	−	0.00739543i
$928$	−44.3203	+	13.3781i	−1.45489	+	0.439159i
$929$	2.40016	+	6.59438i	0.0787467	+	0.216355i	0.972819	−	0.231569i	$-0.0743859\pi$
$929$	2.40016	+	6.59438i	0.0787467	+	0.216355i	−0.894072	+	0.447924i	$0.852164\pi$
$930$	−8.94380	−	53.2888i	−0.293279	−	1.74741i
$931$	3.79214	+	0.821111i	0.124282	+	0.0269108i
$932$	3.00381	+	8.38074i	0.0983930	+	0.274520i
$933$	−29.8989	−	13.9421i	−0.978846	−	0.456444i
$934$	−1.99260	−	4.84418i	−0.0651999	−	0.158506i
$935$	−5.83738	+	11.0567i	−0.190903	+	0.361593i
$936$	5.14959	−	7.95332i	0.168320	−	0.259963i
$937$	−42.2334	−	29.5722i	−1.37971	−	0.966080i	−0.999146	−	0.0413243i	$-0.986842\pi$
$937$	−42.2334	−	29.5722i	−1.37971	−	0.966080i	−0.380560	−	0.924756i	$-0.624269\pi$
$938$	1.18937	+	3.80477i	0.0388344	+	0.124230i
$939$	22.9830	−	39.8077i	0.750021	−	1.29907i
$940$	40.5746	+	17.3176i	1.32340	+	0.564837i
$941$	−34.7687	−	12.6548i	−1.13343	−	0.412533i	−0.293891	−	0.955839i	$-0.594950\pi$
$941$	−34.7687	−	12.6548i	−1.13343	−	0.412533i	−0.839535	+	0.543305i	$0.817173\pi$
$942$	−5.00321	+	5.43320i	−0.163013	+	0.177023i
$943$	−0.233619	−	0.0625981i	−0.00760768	−	0.00203847i
$944$	26.7720	−	31.2765i	0.871356	−	1.01796i
$945$	−9.45598	−	18.4245i	−0.307603	−	0.599348i
$946$	−0.0575207	+	0.180882i	−0.00187016	+	0.00588099i
$947$	−28.7489	+	20.1302i	−0.934214	+	0.654143i	−0.938290	−	0.345848i	$-0.887591\pi$
$947$	−28.7489	+	20.1302i	−0.934214	+	0.654143i	0.00407689	+	0.999992i	$0.498702\pi$
$948$	−15.8274	+	13.1488i	−0.514050	+	0.427054i
$949$			2.89349i			0.0939267i
$950$	30.3038	+	5.62847i	0.983185	+	0.182612i
$951$		−	30.4569i		−	0.987632i
$952$	16.6193	−	51.3866i	0.538635	−	1.66545i
$953$	26.7389	−	18.7228i	0.866157	−	0.606490i	−0.0537813	−	0.998553i	$-0.517127\pi$
$953$	26.7389	−	18.7228i	0.866157	−	0.606490i	0.919938	+	0.392063i	$0.128238\pi$
$954$	−1.00777	−	0.320471i	−0.0326277	−	0.0103756i
$955$	−21.5000	−	41.8917i	−0.695724	−	1.35558i
$956$	−15.7429	+	57.6200i	−0.509163	+	1.86356i
$957$	−11.6759	−	3.12855i	−0.377428	−	0.101132i
$958$	−23.3373	−	21.4903i	−0.753993	−	0.694321i
$959$	−3.95720	−	1.44030i	−0.127785	−	0.0465098i
$960$	35.0308	−	10.2596i	1.13061	−	0.331129i
$961$	19.5605	−	33.8797i	0.630983	−	1.09289i
$962$	−32.9081	+	10.2871i	−1.06100	+	0.331669i
$963$	−1.55423	−	1.08828i	−0.0500843	−	0.0350694i
$964$	18.6185	+	40.4449i	0.599662	+	1.30264i
$965$	5.38619	−	10.2021i	0.173388	−	0.328417i
$966$	21.3593	−	8.78594i	0.687225	−	0.282683i
$967$	−1.42626	−	0.665078i	−0.0458656	−	0.0213875i	0.399550	−	0.916711i	$-0.369166\pi$
$967$	−1.42626	−	0.665078i	−0.0458656	−	0.0213875i	−0.445416	+	0.895324i	$0.646944\pi$
$968$	−18.2108	+	23.3742i	−0.585316	+	0.751274i
$969$	−60.7884	+	32.0262i	−1.95280	+	1.02883i
$970$	−21.0412	+	3.53148i	−0.675592	+	0.113389i
$971$	−16.8522	−	46.3010i	−0.540812	−	1.48587i	−0.845793	−	0.533511i	$-0.820872\pi$
$971$	−16.8522	−	46.3010i	−0.540812	−	1.48587i	0.304981	−	0.952358i	$-0.401350\pi$
$972$	3.87751	+	22.6401i	0.124371	+	0.726181i
$973$	3.70289	+	0.323961i	0.118709	+	0.0103857i
$974$	−40.1685	−	5.38867i	−1.28708	−	0.172664i
$975$	−17.1220	+	23.8598i	−0.548343	+	0.764124i
$976$	−15.6460	+	41.7078i	−0.500817	+	1.33503i
$977$	4.32375	+	16.1364i	0.138329	+	0.516251i	0.999962	+	0.00871895i	$0.00277536\pi$
$977$	4.32375	+	16.1364i	0.138329	+	0.516251i	−0.861633	+	0.507532i	$0.830558\pi$
$978$	−12.3929	−	7.93798i	−0.396280	−	0.253829i
$979$	−7.45095	−	2.71192i	−0.238133	−	0.0866734i
$980$	−3.89545	+	0.819964i	−0.124436	+	0.0261928i
$981$	−3.32146	−	5.75294i	−0.106046	−	0.183677i
$982$	2.45763	−	53.2858i	0.0784260	−	1.70042i
$983$	−61.8920	+	5.41485i	−1.97405	+	0.172707i	−0.998823	−	0.0485109i	$-0.984552\pi$
$983$	−61.8920	+	5.41485i	−1.97405	+	0.172707i	−0.975224	+	0.221218i	$0.928997\pi$
$984$	0.315700	+	0.293594i	0.0100642	+	0.00935943i
$985$	53.3344	−	11.5003i	1.69937	−	0.366431i
$986$	−54.6013	+	70.7971i	−1.73886	+	2.25464i
$987$	−35.1823	−	35.1823i	−1.11986	−	1.11986i
$988$	−1.09414	+	25.0695i	−0.0348091	+	0.797568i
$989$			0.600368i			0.0190906i
$990$	2.56734	+	0.710660i	0.0815955	+	0.0225862i
$991$	−11.2060	−	1.97592i	−0.355970	−	0.0627671i	−0.00719625	−	0.999974i	$-0.502291\pi$
$991$	−11.2060	−	1.97592i	−0.355970	−	0.0627671i	−0.348774	+	0.937207i	$0.613402\pi$
$992$	43.5378	+	18.6635i	1.38233	+	0.592566i
$993$	1.07872	+	12.3298i	0.0342321	+	0.391274i
$994$	30.1160	−	27.4605i	0.955223	−	0.870995i
$995$	7.15385	−	0.899709i	0.226792	−	0.0285227i
$996$	−0.932797	−	1.34620i	−0.0295568	−	0.0426559i
$997$	8.43096	−	3.93142i	0.267011	−	0.124509i	−0.284502	−	0.958675i	$-0.591828\pi$
$997$	8.43096	−	3.93142i	0.267011	−	0.124509i	0.551513	+	0.834166i	$0.314051\pi$
$998$	−2.12381	+	3.31571i	−0.0672279	+	0.104957i
$999$	15.8678	−	27.4838i	0.502034	−	0.869549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bj.a.43.31	yes	672
4.3	odd	2	inner	380.2.bj.a.43.11	yes	672
5.2	odd	4	inner	380.2.bj.a.347.3	yes	672
19.4	even	9	inner	380.2.bj.a.23.19	yes	672
20.7	even	4	inner	380.2.bj.a.347.19	yes	672
76.23	odd	18	inner	380.2.bj.a.23.3	✓	672
95.42	odd	36	inner	380.2.bj.a.327.11	yes	672
380.327	even	36	inner	380.2.bj.a.327.31	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.23.3	✓	672	76.23	odd	18	inner
380.2.bj.a.23.19	yes	672	19.4	even	9	inner
380.2.bj.a.43.11	yes	672	4.3	odd	2	inner
380.2.bj.a.43.31	yes	672	1.1	even	1	trivial
380.2.bj.a.327.11	yes	672	95.42	odd	36	inner
380.2.bj.a.327.31	yes	672	380.327	even	36	inner
380.2.bj.a.347.3	yes	672	5.2	odd	4	inner
380.2.bj.a.347.19	yes	672	20.7	even	4	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bj (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.181148 + 1.40256i) q^{2} +(-1.17040 - 1.67151i) q^{3} +(-1.93437 + 0.508144i) q^{4} +(1.98936 - 1.02100i) q^{5} +(2.13238 - 1.94436i) q^{6} +(-0.639752 + 2.38759i) q^{7} +(-1.06311 - 2.62103i) q^{8} +(-0.398042 + 1.09361i) q^{9} +O(q^{10})\)	\(q+(0.181148 + 1.40256i) q^{2} +(-1.17040 - 1.67151i) q^{3} +(-1.93437 + 0.508144i) q^{4} +(1.98936 - 1.02100i) q^{5} +(2.13238 - 1.94436i) q^{6} +(-0.639752 + 2.38759i) q^{7} +(-1.06311 - 2.62103i) q^{8} +(-0.398042 + 1.09361i) q^{9} +(1.79238 + 2.60526i) q^{10} +(-0.626858 - 0.361917i) q^{11} +(3.11336 + 2.63859i) q^{12} +(1.65099 - 2.35785i) q^{13} +(-3.46464 - 0.464786i) q^{14} +(-4.03497 - 2.13026i) q^{15} +(3.48358 - 1.96588i) q^{16} +(3.26467 - 7.00111i) q^{17} +(-1.60596 - 0.360173i) q^{18} +(4.15065 - 1.33122i) q^{19} +(-3.32935 + 2.98587i) q^{20} +(4.73965 - 1.72509i) q^{21} +(0.394057 - 0.944769i) q^{22} +(0.282197 - 3.22553i) q^{23} +(-3.13681 + 4.84467i) q^{24} +(2.91512 - 4.06227i) q^{25} +(3.60612 + 1.88849i) q^{26} +(-3.61917 + 0.969755i) q^{27} +(0.0242799 - 4.94357i) q^{28} +(-2.79908 + 7.69040i) q^{29} +(2.25690 - 6.04519i) q^{30} +(7.25194 - 4.18691i) q^{31} +(3.38831 + 4.52983i) q^{32} +(0.128730 + 1.47139i) q^{33} +(10.4109 + 3.31067i) q^{34} +(1.16502 + 5.40297i) q^{35} +(0.214249 - 2.31771i) q^{36} +(-5.98915 + 5.98915i) q^{37} +(2.61900 + 5.58040i) q^{38} -5.87350 q^{39} +(-4.79098 - 4.12874i) q^{40} +(0.0129711 - 0.0735630i) q^{41} +(3.27813 + 6.33516i) q^{42} +(-0.184716 + 0.0161606i) q^{43} +(1.39648 + 0.381547i) q^{44} +(0.324725 + 2.58199i) q^{45} +(4.57513 - 0.188499i) q^{46} +(-4.16895 - 8.94034i) q^{47} +(-7.36318 - 3.52197i) q^{48} +(0.770881 + 0.445069i) q^{49} +(6.22566 + 3.35278i) q^{50} +(-15.5234 + 2.73720i) q^{51} +(-1.99549 + 5.39990i) q^{52} +(0.640075 + 0.0559993i) q^{53} +(-2.01575 - 4.90045i) q^{54} +(-1.61656 - 0.0799623i) q^{55} +(6.93807 - 0.861464i) q^{56} +(-7.08308 - 5.37979i) q^{57} +(-11.2933 - 2.53278i) q^{58} +(9.67177 - 3.52024i) q^{59} +(8.88760 + 2.07037i) q^{60} +(-8.53104 + 7.15839i) q^{61} +(7.18609 + 9.41286i) q^{62} +(-2.35644 - 1.65000i) q^{63} +(-5.73959 + 5.57289i) q^{64} +(0.877047 - 6.37628i) q^{65} +(-2.04040 + 0.447091i) q^{66} +(-0.481938 - 1.03352i) q^{67} +(-2.75751 + 15.2017i) q^{68} +(-5.72179 + 3.30348i) q^{69} +(-7.36696 + 2.61276i) q^{70} +(-7.49426 + 8.93131i) q^{71} +(3.28955 - 0.119352i) q^{72} +(-0.823444 + 0.576582i) q^{73} +(-9.48510 - 7.31525i) q^{74} +(-10.2020 - 0.118162i) q^{75} +(-7.35244 + 4.68419i) q^{76} +(1.26514 - 1.26514i) q^{77} +(-1.06397 - 8.23796i) q^{78} +(-0.875528 + 4.96536i) q^{79} +(4.92294 - 7.46757i) q^{80} +(8.53141 + 7.15870i) q^{81} +(0.105526 + 0.00486705i) q^{82} +(-0.387639 - 0.103868i) q^{83} +(-8.29164 + 5.74539i) q^{84} +(-0.653508 - 17.2610i) q^{85} +(-0.0561272 - 0.256149i) q^{86} +(16.1306 - 4.32219i) q^{87} +(-0.282174 + 2.02777i) q^{88} +(10.7879 - 1.90221i) q^{89} +(-3.56258 + 0.923170i) q^{90} +(4.57336 + 5.45032i) q^{91} +(1.09316 + 6.38277i) q^{92} +(-15.4862 - 7.22132i) q^{93} +(11.7842 - 7.46675i) q^{94} +(6.89797 - 6.88608i) q^{95} +(3.60596 - 10.9653i) q^{96} +(-2.85135 + 6.11475i) q^{97} +(-0.484593 + 1.16183i) q^{98} +(0.645311 - 0.541481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Introduction

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