LMFDB - Embedded newform 380.2.bj.a.23.3

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			23.3
Character	$\chi$	$=$	380.23
Dual form			380.2.bj.a.347.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40256 - 0.181148i) q^{2} +(-1.67151 - 1.17040i) q^{3} +(1.93437 + 0.508144i) q^{4} +(-0.660038 - 2.13643i) q^{5} +(2.13238 + 1.94436i) q^{6} +(-2.38759 + 0.639752i) q^{7} +(-2.62103 - 1.06311i) q^{8} +(0.398042 + 1.09361i) q^{9} +O(q^{10})$	\(q+(-1.40256 - 0.181148i) q^{2} +(-1.67151 - 1.17040i) q^{3} +(1.93437 + 0.508144i) q^{4} +(-0.660038 - 2.13643i) q^{5} +(2.13238 + 1.94436i) q^{6} +(-2.38759 + 0.639752i) q^{7} +(-2.62103 - 1.06311i) q^{8} +(0.398042 + 1.09361i) q^{9} +(0.538734 + 3.11605i) q^{10} +(-0.626858 + 0.361917i) q^{11} +(-2.63859 - 3.11336i) q^{12} +(-2.35785 + 1.65099i) q^{13} +(3.46464 - 0.464786i) q^{14} +(-1.39723 + 4.34358i) q^{15} +(3.48358 + 1.96588i) q^{16} +(7.00111 - 3.26467i) q^{17} +(-0.360173 - 1.60596i) q^{18} +(-4.15065 - 1.33122i) q^{19} +(-0.191142 - 4.46805i) q^{20} +(4.73965 + 1.72509i) q^{21} +(0.944769 - 0.394057i) q^{22} +(-3.22553 + 0.282197i) q^{23} +(3.13681 + 4.84467i) q^{24} +(-4.12870 + 2.82026i) q^{25} +(3.60612 - 1.88849i) q^{26} +(-0.969755 + 3.61917i) q^{27} +(-4.94357 + 0.0242799i) q^{28} +(2.79908 + 7.69040i) q^{29} +(2.74654 - 5.83905i) q^{30} +(7.25194 + 4.18691i) q^{31} +(-4.52983 - 3.38831i) q^{32} +(1.47139 + 0.128730i) q^{33} +(-10.4109 + 3.31067i) q^{34} +(2.94269 + 4.67866i) q^{35} +(0.214249 + 2.31771i) q^{36} +(-5.98915 + 5.98915i) q^{37} +(5.58040 + 2.61900i) q^{38} +5.87350 q^{39} +(-0.541290 + 6.30135i) q^{40} +(0.0129711 + 0.0735630i) q^{41} +(-6.33516 - 3.27813i) q^{42} +(0.0161606 - 0.184716i) q^{43} +(-1.39648 + 0.381547i) q^{44} +(2.07370 - 1.57221i) q^{45} +(4.57513 + 0.188499i) q^{46} +(8.94034 + 4.16895i) q^{47} +(-3.52197 - 7.36318i) q^{48} +(-0.770881 + 0.445069i) q^{49} +(6.30165 - 3.20768i) q^{50} +(-15.5234 - 2.73720i) q^{51} +(-5.39990 + 1.99549i) q^{52} +(0.0559993 + 0.640075i) q^{53} +(2.01575 - 4.90045i) q^{54} +(1.18696 + 1.10036i) q^{55} +(6.93807 + 0.861464i) q^{56} +(5.37979 + 7.08308i) q^{57} +(-2.53278 - 11.2933i) q^{58} +(-9.67177 - 3.52024i) q^{59} +(-4.90993 + 7.69211i) q^{60} +(-8.53104 - 7.15839i) q^{61} +(-9.41286 - 7.18609i) q^{62} +(-1.65000 - 2.35644i) q^{63} +(5.73959 + 5.57289i) q^{64} +(5.08350 + 3.94769i) q^{65} +(-2.04040 - 0.447091i) q^{66} +(1.03352 + 0.481938i) q^{67} +(15.2017 - 2.75751i) q^{68} +(5.72179 + 3.30348i) q^{69} +(-3.27978 - 7.09519i) q^{70} +(-7.49426 - 8.93131i) q^{71} +(0.119352 - 3.28955i) q^{72} +(0.576582 - 0.823444i) 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} +(-8.23796 - 1.06397i) q^{78} +(0.875528 + 4.96536i) q^{79} +(1.90067 - 8.73999i) q^{80} +(8.53141 - 7.15870i) q^{81} +(-0.00486705 - 0.105526i) q^{82} +(-0.103868 - 0.387639i) q^{83} +(8.29164 + 5.74539i) q^{84} +(-11.5958 - 12.8026i) q^{85} +(-0.0561272 + 0.256149i) q^{86} +(4.32219 - 16.1306i) q^{87} +(2.02777 - 0.282174i) q^{88} +(-10.7879 - 1.90221i) q^{89} +(-3.19331 + 1.82948i) q^{90} +(4.57336 - 5.45032i) q^{91} +(-6.38277 - 1.09316i) q^{92} +(-7.22132 - 15.4862i) q^{93} +(-11.7842 - 7.46675i) q^{94} +(-0.104475 + 9.74623i) q^{95} +(3.60596 + 10.9653i) q^{96} +(-6.11475 + 2.85135i) q^{97} +(1.16183 - 0.484593i) 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.40256	−	0.181148i	−0.991762	−	0.128091i
$2$	−1.40256	−	0.181148i	−0.991762	−	0.128091i
$3$	−1.67151	−	1.17040i	−0.965047	−	0.675733i	−0.0190196	−	0.999819i	$-0.506054\pi$
$3$	−1.67151	−	1.17040i	−0.965047	−	0.675733i	−0.946028	+	0.324086i	$0.894943\pi$
$4$	1.93437	+	0.508144i	0.967185	+	0.254072i
$5$	−0.660038	−	2.13643i	−0.295178	−	0.955442i
$5$	−0.660038	−	2.13643i	−0.295178	−	0.955442i
$6$	2.13238	+	1.94436i	0.870542	+	0.793781i
$7$	−2.38759	+	0.639752i	−0.902424	+	0.241804i	−0.680057	−	0.733159i	$-0.738045\pi$
$7$	−2.38759	+	0.639752i	−0.902424	+	0.241804i	−0.222367	+	0.974963i	$0.571378\pi$
$8$	−2.62103	−	1.06311i	−0.926674	−	0.375867i
$9$	0.398042	+	1.09361i	0.132681	+	0.364537i
$10$	0.538734	+	3.11605i	0.170363	+	0.985381i
$11$	−0.626858	+	0.361917i	−0.189005	+	0.109122i	−0.591517	−	0.806293i	$-0.701471\pi$
$11$	−0.626858	+	0.361917i	−0.189005	+	0.109122i	0.402512	+	0.915415i	$0.368137\pi$
$12$	−2.63859	−	3.11336i	−0.761695	−	0.898751i
$13$	−2.35785	+	1.65099i	−0.653951	+	0.457902i	−0.852876	−	0.522113i	$-0.825144\pi$
$13$	−2.35785	+	1.65099i	−0.653951	+	0.457902i	0.198925	+	0.980015i	$0.436255\pi$
$14$	3.46464	−	0.464786i	0.925963	−	0.124219i
$15$	−1.39723	+	4.34358i	−0.360764	+	1.12151i
$16$	3.48358	+	1.96588i	0.870895	+	0.491469i
$17$	7.00111	−	3.26467i	1.69802	−	0.791799i	0.701125	−	0.713038i	$-0.252681\pi$
$17$	7.00111	−	3.26467i	1.69802	−	0.791799i	0.996894	−	0.0787606i	$-0.0250963\pi$
$18$	−0.360173	−	1.60596i	−0.0848936	−	0.378529i
$19$	−4.15065	−	1.33122i	−0.952223	−	0.305402i
$19$	−4.15065	−	1.33122i	−0.952223	−	0.305402i
$20$	−0.191142	−	4.46805i	−0.0427407	−	0.999086i
$21$	4.73965	+	1.72509i	1.03428	+	0.376446i
$22$	0.944769	−	0.394057i	0.201425	−	0.0840132i
$23$	−3.22553	+	0.282197i	−0.672569	+	0.0588422i	−0.418324	−	0.908298i	$-0.637382\pi$
$23$	−3.22553	+	0.282197i	−0.672569	+	0.0588422i	−0.254245	+	0.967140i	$0.581827\pi$
$24$	3.13681	+	4.84467i	0.640298	+	0.988914i
$25$	−4.12870	+	2.82026i	−0.825740	+	0.564051i
$26$	3.60612	−	1.88849i	0.707217	−	0.370364i
$27$	−0.969755	+	3.61917i	−0.186629	+	0.696510i
$28$	−4.94357	+	0.0242799i	−0.934246	+	0.00458848i
$29$	2.79908	+	7.69040i	0.519775	+	1.42807i	0.870768	+	0.491693i	$0.163622\pi$
$29$	2.79908	+	7.69040i	0.519775	+	1.42807i	−0.350993	+	0.936378i	$0.614156\pi$
$30$	2.74654	−	5.83905i	0.501447	−	1.06606i
$31$	7.25194	+	4.18691i	1.30249	+	0.751992i	0.980830	−	0.194865i	$-0.0624267\pi$
$31$	7.25194	+	4.18691i	1.30249	+	0.751992i	0.321657	+	0.946856i	$0.395760\pi$
$32$	−4.52983	−	3.38831i	−0.800768	−	0.598975i
$33$	1.47139	+	0.128730i	0.256136	+	0.0224090i
$34$	−10.4109	+	3.31067i	−1.78545	+	0.567775i
$35$	2.94269	+	4.67866i	0.497405	+	0.790839i
$36$	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	$0.495138\pi$
$38$	5.58040	+	2.61900i	0.905260	+	0.424858i
$39$	5.87350			0.940513
$40$	−0.541290	+	6.30135i	−0.0855854	+	0.996331i
$41$	0.0129711	+	0.0735630i	0.00202575	+	0.0114886i	0.985804	−	0.167901i	$-0.0536989\pi$
$41$	0.0129711	+	0.0735630i	0.00202575	+	0.0114886i	−0.983778	+	0.179390i	$0.942588\pi$
$42$	−6.33516	−	3.27813i	−0.977537	−	0.505826i
$43$	0.0161606	−	0.184716i	0.00246446	−	0.0281690i	−0.994863	−	0.101232i	$-0.967722\pi$
$43$	0.0161606	−	0.184716i	0.00246446	−	0.0281690i	0.997327	+	0.0730626i	$0.0232773\pi$
$44$	−1.39648	+	0.381547i	−0.210528	+	0.0575204i
$45$	2.07370	−	1.57221i	0.309129	−	0.234372i
$46$	4.57513	+	0.188499i	0.674566	+	0.0277927i
$47$	8.94034	+	4.16895i	1.30408	+	0.608104i	0.945569	−	0.325420i	$-0.105506\pi$
$47$	8.94034	+	4.16895i	1.30408	+	0.608104i	0.358514	+	0.933524i	$0.383284\pi$
$48$	−3.52197	−	7.36318i	−0.508353	−	1.06278i
$49$	−0.770881	+	0.445069i	−0.110126	+	0.0635812i
$50$	6.30165	−	3.20768i	0.891188	−	0.453635i
$51$	−15.5234	−	2.73720i	−2.17371	−	0.383284i
$52$	−5.39990	+	1.99549i	−0.748832	+	0.276725i
$53$	0.0559993	+	0.640075i	0.00769210	+	0.0879211i	0.999070	−	0.0431103i	$-0.0137267\pi$
$53$	0.0559993	+	0.640075i	0.00769210	+	0.0879211i	−0.991378	+	0.131031i	$0.958171\pi$
$54$	2.01575	−	4.90045i	0.274309	−	0.666867i
$55$	1.18696	+	1.10036i	0.160050	+	0.148373i
$56$	6.93807	+	0.861464i	0.927138	+	0.115118i
$57$	5.37979	+	7.08308i	0.712570	+	0.938177i
$58$	−2.53278	−	11.2933i	−0.332571	−	1.48289i
$59$	−9.67177	−	3.52024i	−1.25916	−	0.458296i	−0.375671	−	0.926753i	$-0.622588\pi$
$59$	−9.67177	−	3.52024i	−1.25916	−	0.458296i	−0.883486	+	0.468457i	$0.844810\pi$
$60$	−4.90993	+	7.69211i	−0.633869	+	0.993047i
$61$	−8.53104	−	7.15839i	−1.09229	−	0.916538i	−0.0954049	−	0.995439i	$-0.530415\pi$
$61$	−8.53104	−	7.15839i	−1.09229	−	0.916538i	−0.996882	+	0.0789006i	$0.974859\pi$
$62$	−9.41286	−	7.18609i	−1.19543	−	0.912634i
$63$	−1.65000	−	2.35644i	−0.207880	−	0.296884i
$64$	5.73959	+	5.57289i	0.717448	+	0.696612i
$65$	5.08350	+	3.94769i	0.630531	+	0.489650i
$66$	−2.04040	−	0.447091i	−0.251156	−	0.0550331i
$67$	1.03352	+	0.481938i	0.126265	+	0.0588781i	0.484724	−	0.874667i	$-0.338920\pi$
$67$	1.03352	+	0.481938i	0.126265	+	0.0588781i	−0.358459	+	0.933545i	$0.616698\pi$
$68$	15.2017	−	2.75751i	1.84347	−	0.334398i
$69$	5.72179	+	3.30348i	0.688823	+	0.397692i
$70$	−3.27978	−	7.09519i	−0.392008	−	0.848037i
$71$	−7.49426	−	8.93131i	−0.889405	−	1.05995i	−0.997830	−	0.0658473i	$-0.979025\pi$
$71$	−7.49426	−	8.93131i	−0.889405	−	1.05995i	0.108424	−	0.994105i	$-0.465419\pi$
$72$	0.119352	−	3.28955i	0.0140657	−	0.387677i
$73$	0.576582	−	0.823444i	0.0674838	−	0.0963769i	−0.783992	−	0.620772i	$-0.786819\pi$
$73$	0.576582	−	0.823444i	0.0674838	−	0.0963769i	0.851475	+	0.524395i	$0.175708\pi$
$74$	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
$78$	−8.23796	−	1.06397i	−0.932766	−	0.120471i
$79$	0.875528	+	4.96536i	0.0985046	+	0.558647i	0.993617	+	0.112807i	$0.0359840\pi$
$79$	0.875528	+	4.96536i	0.0985046	+	0.558647i	−0.895112	+	0.445841i	$0.852905\pi$
$80$	1.90067	−	8.73999i	0.212502	−	0.977161i
$81$	8.53141	−	7.15870i	0.947935	−	0.795412i
$82$	−0.00486705	−	0.105526i	−0.000537475	−	0.0116534i
$83$	−0.103868	−	0.387639i	−0.0114009	−	0.0425489i	0.959991	−	0.280031i	$-0.0903447\pi$
$83$	−0.103868	−	0.387639i	−0.0114009	−	0.0425489i	−0.971392	+	0.237482i	$0.923678\pi$
$84$	8.29164	+	5.74539i	0.904693	+	0.626873i
$85$	−11.5958	−	12.8026i	−1.25774	−	1.38864i
$86$	−0.0561272	+	0.256149i	−0.00605236	+	0.0276212i
$87$	4.32219	−	16.1306i	0.463388	−	1.72939i
$88$	2.02777	−	0.282174i	0.216161	−	0.0300798i
$89$	−10.7879	−	1.90221i	−1.14352	−	0.201633i	−0.430375	−	0.902650i	$-0.641619\pi$
$89$	−10.7879	−	1.90221i	−1.14352	−	0.201633i	−0.713145	+	0.701017i	$0.752730\pi$
$90$	−3.19331	+	1.82948i	−0.336604	+	0.192844i
$91$	4.57336	−	5.45032i	0.479419	−	0.571349i
$92$	−6.38277	−	1.09316i	−0.665449	−	0.113970i
$93$	−7.22132	−	15.4862i	−0.748816	−	1.60584i
$94$	−11.7842	−	7.46675i	−1.21545	−	0.770136i
$95$	−0.104475	+	9.74623i	−0.0107189	+	0.999943i
$96$	3.60596	+	10.9653i	0.368032	+	1.11914i
$97$	−6.11475	+	2.85135i	−0.620859	+	0.289511i	−0.707483	−	0.706730i	$-0.750170\pi$
$97$	−6.11475	+	2.85135i	−0.620859	+	0.289511i	0.0866249	+	0.996241i	$0.472392\pi$
$98$	1.16183	−	0.484593i	0.117363	−	0.0489513i
$99$	−0.645311	−	0.541481i	−0.0648562	−	0.0544208i
$100$	−9.41953	+	3.35745i	−0.941953	+	0.335745i
$101$	0.0831138	−	0.471362i	0.00827013	−	0.0469023i	−0.980393	−	0.197050i	$-0.936864\pi$
$101$	0.0831138	−	0.471362i	0.00827013	−	0.0469023i	0.988664	+	0.150148i	$0.0479750\pi$
$102$	21.2767	+	6.65113i	2.10671	+	0.658560i
$103$	2.14424	+	0.574548i	0.211279	+	0.0566119i	0.362906	−	0.931826i	$-0.381785\pi$
$103$	2.14424	+	0.574548i	0.211279	+	0.0566119i	−0.151627	+	0.988438i	$0.548451\pi$
$104$	7.93519	−	1.82062i	0.778110	−	0.178527i
$105$	0.557195	−	11.2646i	0.0543767	−	1.09931i
$106$	0.0374058	−	0.907890i	0.00363318	−	0.0881821i
$107$	−1.57477	+	0.421958i	−0.152239	+	0.0407922i	−0.334133	−	0.942526i	$-0.608444\pi$
$107$	−1.57477	+	0.421958i	−0.152239	+	0.0407922i	0.181895	+	0.983318i	$0.441777\pi$
$108$	−3.71493	+	6.50805i	−0.357469	+	0.626237i
$109$	3.66902	+	4.37257i	0.351428	+	0.418816i	0.912581	−	0.408896i	$-0.134086\pi$
$109$	3.66902	+	4.37257i	0.351428	+	0.418816i	−0.561152	+	0.827712i	$0.689642\pi$
$110$	−1.46546	−	1.75834i	−0.139726	−	0.167652i
$111$	17.0207	−	3.00120i	1.61553	−	0.284862i
$112$	−9.57503	−	2.46508i	−0.904755	−	0.232928i
$113$	−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
$117$	−2.74406	−	1.92141i	−0.253689	−	0.177635i
$118$	12.9276	+	6.68938i	1.19008	+	0.615808i
$119$	−14.6272	+	12.2737i	−1.34087	+	1.12513i
$120$	8.27990	−	9.89925i	0.755848	−	0.903673i
$121$	−5.23803	+	9.07254i	−0.476185	+	0.824776i
$122$	10.6686	+	11.5855i	0.965889	+	1.04890i
$123$	0.0644170	−	0.138143i	0.00580829	−	0.0124559i
$124$	11.9004	+	11.7841i	1.06869	+	1.05824i
$125$	8.75039	+	6.95922i	0.782658	+	0.622451i
$126$	1.88736	+	3.60396i	0.168140	+	0.321066i
$127$	−6.48310	+	4.53951i	−0.575282	+	0.402817i	−0.824693	−	0.565581i	$-0.808652\pi$
$127$	−6.48310	+	4.53951i	−0.575282	+	0.402817i	0.249411	+	0.968398i	$0.419763\pi$
$128$	−7.04062	−	8.85606i	−0.622308	−	0.782772i
$129$	−0.243205	+	0.289841i	−0.0214130	+	0.0255191i
$130$	−6.41482	−	6.45775i	−0.562617	−	0.566382i
$131$	1.98232	−	5.44637i	0.173196	−	0.475852i	−0.822475	−	0.568801i	$-0.807407\pi$
$131$	1.98232	−	5.44637i	0.173196	−	0.475852i	0.995671	+	0.0929495i	$0.0296295\pi$
$132$	2.78080	+	0.996689i	0.242037	+	0.0867506i
$133$	10.7617	+	0.523014i	0.933156	+	0.0453511i
$134$	−1.36227	−	0.863169i	−0.117683	−	0.0745665i
$135$	8.37220	−	0.316975i	0.720564	−	0.0272809i
$136$	−21.8208	+	1.11383i	−1.87112	+	0.0955105i
$137$	−1.69719	+	0.148485i	−0.145001	+	0.0126859i	−0.159425	−	0.987210i	$-0.550964\pi$
$137$	−1.69719	+	0.148485i	−0.145001	+	0.0126859i	0.0144242	+	0.999896i	$0.495408\pi$
$138$	−7.42676	−	5.66983i	−0.632208	−	0.482648i
$139$	0.261126	−	1.48092i	0.0221485	−	0.125610i	−0.971729	−	0.236100i	$-0.924131\pi$
$139$	0.261126	−	1.48092i	0.0221485	−	0.125610i	0.993877	+	0.110490i	$0.0352419\pi$
$140$	3.31481	+	10.5456i	0.280153	+	0.891264i
$141$	−10.0645	−	17.4323i	−0.847586	−	1.46806i
$142$	8.89329	+	13.8843i	0.746308	+	1.16515i
$143$	0.880520	−	1.88828i	0.0736328	−	0.157906i
$144$	−0.763294	+	4.59218i	−0.0636078	+	0.382682i
$145$	14.5825	−	11.0560i	1.21101	−	0.918151i
$146$	−0.957858	+	1.05049i	−0.0792729	+	0.0869389i
$147$	1.80945	+	0.158306i	0.149241	+	0.0130569i
$148$	−14.6286	+	8.54189i	−1.20246	+	0.702139i
$149$	−17.8134	+	3.14098i	−1.45933	+	0.257319i	−0.846285	−	0.532731i	$-0.821166\pi$
$149$	−17.8134	+	3.14098i	−1.45933	+	0.257319i	−0.613042	+	0.790050i	$0.710055\pi$
$150$	−14.2876	−	2.01380i	−1.16657	−	0.164426i
$151$		−	15.5959i		−	1.26918i	−0.772851	−	0.634588i	$-0.781170\pi$
$151$		−	15.5959i		−	1.26918i	0.772851	−	0.634588i	$-0.218830\pi$
$152$	9.46373	+	7.90176i	0.767610	+	0.640917i
$153$	6.35701	+	6.35701i	0.513934	+	0.513934i
$154$	−2.00362	+	1.54526i	−0.161456	+	0.124521i
$155$	4.15850	−	18.2568i	0.334019	−	1.46642i
$156$	11.3615	+	2.98458i	0.909651	+	0.238958i
$157$	−0.223070	+	2.54970i	−0.0178029	+	0.203488i	0.982084	+	0.188444i	$0.0603444\pi$
$157$	−0.223070	+	2.54970i	−0.0178029	+	0.203488i	−0.999887	+	0.0150440i	$0.995211\pi$
$158$	−0.328517	−	7.12284i	−0.0261354	−	0.566663i
$159$	0.655543	−	1.13543i	0.0519880	−	0.0900458i
$160$	−4.24905	+	11.9141i	−0.335917	+	0.941892i
$161$	7.52070	−	2.73731i	0.592714	−	0.215730i
$162$	−13.2626	+	8.49509i	−1.04201	+	0.667437i
$163$	−4.92616	−	1.31996i	−0.385846	−	0.103387i	0.0606810	−	0.998157i	$-0.480673\pi$
$163$	−4.92616	−	1.31996i	−0.385846	−	0.103387i	−0.446527	+	0.894770i	$0.647339\pi$
$164$	−0.0122896	+	0.148889i	−0.000959655	+	0.0116263i
$165$	−0.696150	−	3.22849i	−0.0541952	−	0.251338i
$166$	0.0754607	+	0.562504i	0.00585689	+	0.0436587i
$167$	0.163790	+	1.87213i	0.0126745	+	0.144870i	0.999895	−	0.0144901i	$-0.00461250\pi$
$167$	0.163790	+	1.87213i	0.0126745	+	0.144870i	−0.987221	+	0.159360i	$0.949057\pi$
$168$	−10.5888	−	9.56029i	−0.816943	−	0.737593i
$169$	−1.61254	+	4.43042i	−0.124042	+	0.340802i
$170$	13.9446	+	20.0570i	1.06950	+	1.53830i
$171$	−0.196296	−	5.06907i	−0.0150112	−	0.387641i
$172$	0.125123	−	0.349098i	0.00954053	−	0.0266184i
$173$	3.94971	+	8.47018i	0.300291	+	0.643976i	0.997328	−	0.0730596i	$-0.0232763\pi$
$173$	3.94971	+	8.47018i	0.300291	+	0.643976i	−0.697037	+	0.717035i	$0.745499\pi$
$174$	−8.98419	+	21.8413i	−0.681089	+	1.65578i
$175$	8.05337	−	9.37495i	0.608778	−	0.708680i
$176$	−2.89519	+	0.0284397i	−0.218233	+	0.00214372i
$177$	12.0464	+	17.2040i	0.905461	+	1.29313i
$178$	14.7862	+	4.62218i	1.10827	+	0.346447i
$179$	1.06826	+	1.85029i	0.0798458	+	0.138297i	0.903183	−	0.429255i	$-0.141224\pi$
$179$	1.06826	+	1.85029i	0.0798458	+	0.138297i	−0.823337	+	0.567552i	$0.807891\pi$
$180$	4.81022	−	1.98750i	0.358533	−	0.148140i
$181$	−11.7983	+	4.29424i	−0.876963	+	0.319188i	−0.740984	−	0.671523i	$-0.765640\pi$
$181$	−11.7983	+	4.29424i	−0.876963	+	0.319188i	−0.135980	+	0.990712i	$0.543418\pi$
$182$	−7.40175	+	6.81597i	−0.548654	+	0.505233i
$183$	5.88151	+	21.9501i	0.434774	+	1.62260i
$184$	8.75421	+	2.68945i	0.645369	+	0.198269i
$185$	16.7485	+	8.84236i	1.23137	+	0.650103i
$186$	7.32307	+	23.0285i	0.536954	+	1.68853i
$187$	−3.20716	+	4.58030i	−0.234531	+	0.334945i
$188$	15.1755	+	12.6073i	1.10679	+	0.919480i
$189$		−	9.26150i		−	0.673675i
$190$	1.91205	−	13.6508i	0.138714	−	0.990332i
$191$			21.0578i			1.52369i	0.647759	+	0.761846i	$0.275707\pi$
$191$			21.0578i			1.52369i	−0.647759	+	0.761846i	$0.724293\pi$
$192$	−3.07124	−	16.0328i	−0.221648	−	1.15707i
$193$	−2.95928	+	4.22628i	−0.213013	+	0.304215i	−0.911413	−	0.411494i	$-0.865007\pi$
$193$	−2.95928	+	4.22628i	−0.213013	+	0.304215i	0.698399	+	0.715708i	$0.253896\pi$
$194$	9.09284	−	2.89153i	0.652828	−	0.207600i
$195$	−3.87674	−	12.5484i	−0.277619	−	0.898606i
$196$	−1.71733	+	0.469209i	−0.122666	+	0.0335149i
$197$	−6.31520	−	23.5686i	−0.449939	−	1.67920i	−0.702555	−	0.711629i	$-0.747958\pi$
$197$	−6.31520	−	23.5686i	−0.449939	−	1.67920i	0.252616	−	0.967567i	$-0.418709\pi$
$198$	0.807002	+	0.876358i	0.0573512	+	0.0622801i
$199$	−3.03004	+	1.10284i	−0.214794	+	0.0781786i	−0.447176	−	0.894446i	$-0.647570\pi$
$199$	−3.03004	+	1.10284i	−0.214794	+	0.0781786i	0.232382	+	0.972625i	$0.425348\pi$
$200$	13.8197	−	3.00270i	0.977200	−	0.212323i
$201$	−1.16348	−	2.01520i	−0.0820653	−	0.142141i
$202$	−0.201959	+	0.646059i	−0.0142098	+	0.0454566i
$203$	−11.6030	−	16.5708i	−0.814371	−	1.16304i
$204$	−28.6372	−	13.1829i	−2.00500	−	0.922986i
$205$	0.148601	−	0.0762663i	0.0103787	−	0.00532667i
$206$	−2.90336	−	1.19427i	−0.202287	−	0.0832085i
$207$	−1.59251	−	3.41515i	−0.110687	−	0.237369i
$208$	−11.4594	+	1.11609i	−0.794567	+	0.0773872i
$209$	3.08366	−	0.667703i	0.213301	−	0.0461860i
$210$	−2.82206	+	15.6984i	−0.194741	+	1.08329i
$211$	5.88126	−	16.1586i	0.404883	−	1.11241i	−0.554962	−	0.831876i	$-0.687267\pi$
$211$	5.88126	−	16.1586i	0.404883	−	1.11241i	0.959845	−	0.280531i	$-0.0905105\pi$
$212$	−0.216927	+	1.26660i	−0.0148986	+	0.0869903i
$213$	2.07349	+	23.7001i	0.142073	+	1.62390i
$214$	2.28515	−	0.306557i	0.156210	−	0.0209558i
$215$	−0.405301	+	0.0873937i	−0.0276413	+	0.00596020i
$216$	6.38934	−	8.45500i	0.434740	−	0.575290i
$217$	−19.9932	−	5.35717i	−1.35723	−	0.363669i
$218$	−4.35395	−	6.79744i	−0.294887	−	0.460381i
$219$	−1.92753	+	0.701562i	−0.130250	+	0.0474072i
$220$	1.73688	+	2.73166i	0.117100	+	0.184168i
$221$	−11.1177	+	19.2564i	−0.747855	+	1.29532i
$222$	−24.4162	+	1.12612i	−1.63871	+	0.0755799i
$223$	−1.86424	+	21.3084i	−0.124839	+	1.42692i	0.632836	+	0.774286i	$0.281891\pi$
$223$	−1.86424	+	21.3084i	−0.124839	+	1.42692i	−0.757675	+	0.652632i	$0.773665\pi$
$224$	12.9830	+	5.19193i	0.867466	+	0.346900i
$225$	−4.72765	−	3.39261i	−0.315177	−	0.226174i
$226$	7.57234	+	9.81844i	0.503704	+	0.653113i
$227$	−0.561061	−	0.561061i	−0.0372389	−	0.0372389i	0.688242	−	0.725481i	$-0.258383\pi$
$227$	−0.561061	−	0.561061i	−0.0372389	−	0.0372389i	−0.725481	+	0.688242i	$0.758383\pi$
$228$	6.80728	+	16.4350i	0.450823	+	1.08843i
$229$			21.6520i			1.43080i	0.698713	+	0.715402i	$0.253756\pi$
$229$			21.6520i			1.43080i	−0.698713	+	0.715402i	$0.746244\pi$
$230$	−2.61704	−	9.89888i	−0.172563	−	0.652713i
$231$	−3.59543	+	0.633971i	−0.236562	+	0.0417122i
$232$	0.839295	−	23.1325i	0.0551024	−	1.51872i
$233$	−4.43445	−	0.387965i	−0.290511	−	0.0254164i	−0.0590311	−	0.998256i	$-0.518801\pi$
$233$	−4.43445	−	0.387965i	−0.290511	−	0.0254164i	−0.231480	+	0.972840i	$0.574357\pi$
$234$	3.50066	+	3.19199i	0.228845	+	0.208667i
$235$	3.00572	−	21.8521i	0.196072	−	1.42548i
$236$	−16.9200	−	11.7241i	−1.10140	−	0.763174i
$237$	4.34803	−	9.32438i	0.282435	−	0.605684i
$238$	22.7389	−	14.5649i	1.47395	−	0.944103i
$239$	−14.9330	−	25.8647i	−0.965934	−	1.67305i	−0.707084	−	0.707129i	$-0.749990\pi$
$239$	−14.9330	−	25.8647i	−0.965934	−	1.67305i	−0.258850	−	0.965918i	$-0.583343\pi$
$240$	−13.4063	+	12.3844i	−0.865374	+	0.799412i
$241$	−3.86581	+	21.9241i	−0.249019	+	1.41225i	0.561953	+	0.827169i	$0.310050\pi$
$241$	−3.86581	+	21.9241i	−0.249019	+	1.41225i	−0.810971	+	0.585086i	$0.801061\pi$
$242$	8.99015	−	11.7760i	0.577909	−	0.756987i
$243$	−11.4412	+	1.00097i	−0.733951	+	0.0642124i
$244$	−12.8647	−	18.1820i	−0.823578	−	1.16398i
$245$	1.45967	+	1.35318i	0.0932549	+	0.0864512i
$246$	−0.115373	+	0.182085i	−0.00735593	+	0.0116093i
$247$	11.9844	−	3.71385i	0.762552	−	0.236306i
$248$	−14.5564	−	18.6836i	−0.924332	−	1.18641i
$249$	−0.280079	+	0.769510i	−0.0177493	+	0.0487657i
$250$	−11.0123	−	11.3459i	−0.696481	−	0.717576i
$251$	3.28704	−	3.91735i	0.207476	−	0.247261i	−0.652264	−	0.757992i	$-0.726181\pi$
$251$	3.28704	−	3.91735i	0.207476	−	0.247261i	0.859741	+	0.510731i	$0.170625\pi$
$252$	−1.99430	−	5.39667i	−0.125629	−	0.339958i
$253$	1.91982	−	1.34427i	0.120698	−	0.0845136i
$254$	9.91528	−	5.19256i	0.622140	−	0.325810i
$255$	4.39820	+	34.9714i	0.275426	+	2.18999i
$256$	8.27066	+	13.6966i	0.516916	+	0.856036i
$257$	−2.49070	+	5.34132i	−0.155366	+	0.333183i	−0.968548	−	0.248826i	$-0.919955\pi$
$257$	−2.49070	+	5.34132i	−0.155366	+	0.333183i	0.813183	+	0.582009i	$0.197733\pi$
$258$	0.393615	−	0.362464i	0.0245054	−	0.0225660i
$259$	10.4681	−	18.1312i	0.650454	−	1.12662i
$260$	7.82738	+	10.2194i	0.485434	+	0.633783i
$261$	−7.29615	+	6.12220i	−0.451620	+	0.378955i
$262$	−3.76693	+	7.27979i	−0.232722	+	0.449747i
$263$	22.1329	+	15.4976i	1.36477	+	0.955624i	0.999696	+	0.0246464i	$0.00784600\pi$
$263$	22.1329	+	15.4976i	1.36477	+	0.955624i	0.365076	+	0.930978i	$0.381043\pi$
$264$	−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
$268$	1.75432	+	1.45742i	0.107162	+	0.0890263i
$269$	19.4316	−	3.42631i	1.18476	−	0.208906i	0.453662	−	0.891174i	$-0.350117\pi$
$269$	19.4316	−	3.42631i	1.18476	−	0.208906i	0.731102	+	0.682268i	$0.239006\pi$
$270$	−11.8000	−	1.07203i	−0.718123	−	0.0652417i
$271$	−4.03952	−	4.81412i	−0.245384	−	0.292437i	0.629269	−	0.777188i	$-0.283355\pi$
$271$	−4.03952	−	4.81412i	−0.245384	−	0.292437i	−0.874652	+	0.484751i	$0.838910\pi$
$272$	30.8069	+	2.39058i	1.86794	+	0.144950i
$273$	−14.0235	+	3.75759i	−0.848742	+	0.227420i
$274$	2.40732	+	0.0991835i	0.145431	+	0.00599189i
$275$	1.56741	−	3.26215i	0.0945185	−	0.196715i
$276$	9.38943	+	9.29765i	0.565177	+	0.559653i
$277$	15.4368	+	4.13627i	0.927506	+	0.248525i	0.690791	−	0.723054i	$-0.257262\pi$
$277$	15.4368	+	4.13627i	0.927506	+	0.248525i	0.236715	+	0.971579i	$0.423929\pi$
$278$	−0.634513	+	2.02978i	−0.0380555	+	0.121738i
$279$	−1.69227	+	9.59737i	−0.101314	+	0.574579i
$280$	−2.73893	−	15.3913i	−0.163682	−	0.919807i
$281$	−20.1948	−	16.9455i	−1.20472	−	1.01088i	−0.999482	−	0.0321711i	$-0.989758\pi$
$281$	−20.1948	−	16.9455i	−1.20472	−	1.01088i	−0.205241	−	0.978712i	$-0.565798\pi$
$282$	10.9583	+	26.2730i	0.652558	+	1.56454i
$283$	4.67503	−	2.18000i	0.277902	−	0.129588i	−0.278671	−	0.960387i	$-0.589894\pi$
$283$	4.67503	−	2.18000i	0.277902	−	0.129588i	0.556573	+	0.830799i	$0.312116\pi$
$284$	−9.95829	−	21.0846i	−0.590916	−	1.25114i
$285$	11.5817	−	16.1687i	0.686039	−	0.957749i
$286$	−1.57705	+	2.48893i	−0.0932526	+	0.147174i
$287$	−0.0780318	−	0.167340i	−0.00460607	−	0.00987776i
$288$	1.90243	−	6.30256i	0.112102	−	0.371382i
$289$	27.4301	−	32.6899i	1.61353	−	1.92293i
$290$	−22.4557	+	12.8651i	−1.31864	+	0.755467i
$291$	13.5581	+	2.39066i	0.794790	+	0.140143i
$292$	1.53375	−	1.29986i	0.0897560	−	0.0760685i
$293$	0.621378	−	2.31901i	0.0363013	−	0.135478i	−0.945397	−	0.325921i	$-0.894326\pi$
$293$	0.621378	−	2.31901i	0.0363013	−	0.135478i	0.981698	+	0.190443i	$0.0609923\pi$
$294$	−2.50919	−	0.549813i	−0.146339	−	0.0320657i
$295$	−1.13702	+	22.9866i	−0.0661997	+	1.33833i
$296$	22.0649	−	9.33061i	1.28250	−	0.542330i
$297$	−0.701941	−	2.61968i	−0.0407307	−	0.152009i
$298$	25.5534	−	1.17856i	1.48027	−	0.0682722i
$299$	7.13943	−	5.99069i	0.412884	−	0.346451i
$300$	19.6744	+	5.41266i	1.13590	+	0.312500i
$301$	0.0795878	+	0.451365i	0.00458737	+	0.0260162i
$302$	−2.82517	+	21.8742i	−0.162570	+	1.25872i
$303$	−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
$307$	−11.5432	+	16.4854i	−0.658807	+	0.940874i	0.341193	+	0.939993i	$0.389169\pi$
$307$	−11.5432	+	16.4854i	−0.658807	+	0.940874i	−1.00000		0.000880386i	$0.999720\pi$
$308$	3.09013	−	1.80438i	0.176076	−	0.102814i
$309$	−2.91167	−	3.47000i	−0.165639	−	0.197401i
$310$	−9.13975	+	24.8530i	−0.519103	+	1.41156i
$311$	14.0012	+	8.08360i	0.793936	+	0.458379i	0.841346	−	0.540496i	$-0.181764\pi$
$311$	14.0012	+	8.08360i	0.793936	+	0.458379i	−0.0474105	+	0.998875i	$0.515097\pi$
$312$	−15.3946	−	6.24419i	−0.871549	−	0.353508i
$313$	20.4158	+	9.52006i	1.15397	+	0.538106i	0.902895	−	0.429862i	$-0.141438\pi$
$313$	20.4158	+	9.52006i	1.15397	+	0.538106i	0.251076	+	0.967967i	$0.419215\pi$
$314$	0.774743	−	3.53571i	0.0437213	−	0.199531i
$315$	−3.94532	+	5.08046i	−0.222294	+	0.286251i
$316$	−0.829524	+	10.0497i	−0.0466644	+	0.565343i
$317$	−8.56115	−	12.2266i	−0.480842	−	0.686713i	0.503297	−	0.864114i	$-0.332120\pi$
$317$	−8.56115	−	12.2266i	−0.480842	−	0.686713i	−0.984139	+	0.177400i	$0.943231\pi$
$318$	−1.12512	+	1.47377i	−0.0630938	+	0.0826448i
$319$	−4.53791	−	3.80776i	−0.254074	−	0.213193i
$320$	8.11778	−	15.9406i	0.453797	−	0.891105i
$321$	3.12611	+	1.13781i	0.174482	+	0.0635063i
$322$	−11.0441	+	2.47689i	−0.615465	+	0.138032i
$323$	−33.4051	+	4.23049i	−1.85871	+	0.235391i
$324$	20.1406	−	9.51240i	1.11892	−	0.528467i
$325$	5.07867	−	13.4662i	0.281714	−	0.746970i
$326$	6.67014	+	2.74369i	0.369425	+	0.151959i
$327$	−1.01513	−	11.6030i	−0.0561370	−	0.641649i
$328$	0.0442079	−	0.206600i	0.00244098	−	0.0114076i
$329$	−24.0130	−	4.23413i	−1.32388	−	0.233435i
$330$	0.391559	+	4.65427i	0.0215546	+	0.256209i
$331$	−5.25288	+	3.03275i	−0.288724	+	0.166695i	−0.637366	−	0.770561i	$-0.719976\pi$
$331$	−5.25288	+	3.03275i	−0.288724	+	0.166695i	0.348642	+	0.937256i	$0.386643\pi$
$332$	−0.00394199	−	0.802617i	−0.000216345	−	0.0440493i
$333$	−8.93373	−	4.16587i	−0.489566	−	0.228288i
$334$	0.109407	−	2.65545i	0.00598648	−	0.145300i
$335$	0.347467	−	2.52614i	0.0189841	−	0.138018i
$336$	13.1196	+	15.3271i	0.715735	+	0.836160i
$337$	1.80206	−	20.5977i	0.0981647	−	1.12203i	−0.774123	−	0.633035i	$-0.781809\pi$
$337$	1.80206	−	20.5977i	0.0981647	−	1.12203i	0.872288	−	0.488993i	$-0.162636\pi$
$338$	3.06426	−	5.92184i	0.166674	−	0.322106i
$339$	3.10668	+	17.6188i	0.168732	+	0.956924i
$340$	−15.9249	−	30.6573i	−0.863650	−	1.66262i
$341$	−6.06125			−0.328235
$342$	−0.642935	+	7.14525i	−0.0347659	+	0.386371i
$343$	13.7907	−	13.7907i	0.744626	−	0.744626i
$344$	−0.238731	+	0.466966i	−0.0128715	+	0.0251771i
$345$	3.28106	−	14.4047i	0.176647	−	0.775520i
$346$	−4.00536	−	12.5955i	−0.215330	−	0.677136i
$347$	−36.1212	−	3.16020i	−1.93909	−	0.169648i	−0.949520	−	0.313706i	$-0.898429\pi$
$347$	−36.1212	−	3.16020i	−1.93909	−	0.169648i	−0.989569	+	0.144058i	$0.953985\pi$
$348$	16.5574	−	29.0063i	0.887570	−	1.55490i
$349$	4.23126	+	2.44292i	0.226494	+	0.130767i	0.608954	−	0.793206i	$-0.291589\pi$
$349$	4.23126	+	2.44292i	0.226494	+	0.130767i	−0.382459	+	0.923972i	$0.624923\pi$
$350$	−12.9936	+	11.6901i	−0.694538	+	0.624863i
$351$	−3.68867	−	10.1345i	−0.196887	−	0.540942i
$352$	4.06585	+	0.484571i	0.216710	+	0.0258277i
$353$	1.40982	−	5.26150i	0.0750369	−	0.280042i	−0.918205	−	0.396106i	$-0.870361\pi$
$353$	1.40982	−	5.26150i	0.0750369	−	0.280042i	0.993242	+	0.116065i	$0.0370279\pi$
$354$	−13.7793	−	26.3119i	−0.732363	−	1.39846i
$355$	−14.1347	+	21.9060i	−0.750190	+	1.16265i
$356$	−19.9013	−	9.16140i	−1.05477	−	0.485553i
$357$	38.8147	−	3.39584i	2.05429	−	0.179727i
$358$	−1.16313	−	2.78866i	−0.0614735	−	0.147385i
$359$	−14.6234	−	5.32249i	−0.771795	−	0.280910i	−0.0740478	−	0.997255i	$-0.523592\pi$
$359$	−14.6234	−	5.32249i	−0.771795	−	0.280910i	−0.697747	+	0.716344i	$0.745814\pi$
$360$	−7.10668	+	1.91624i	−0.374555	+	0.100995i
$361$	15.4557	+	11.0508i	0.813459	+	0.581622i
$362$	17.3258	−	3.88570i	0.910624	−	0.204228i
$363$	19.3740	−	9.03423i	1.01687	−	0.474174i
$364$	11.6161	−	8.21902i	0.608851	−	0.430794i
$365$	−2.13980	−	0.688325i	−0.112002	−	0.0360286i
$366$	−4.27297	−	31.8518i	−0.223352	−	1.66492i
$367$	−20.4897	+	14.3471i	−1.06956	+	0.748911i	−0.969258	−	0.246047i	$-0.920868\pi$
$367$	−20.4897	+	14.3471i	−1.06956	+	0.748911i	−0.100298	+	0.994957i	$0.531980\pi$
$368$	−11.7912	−	5.35794i	−0.614656	−	0.279302i
$369$	−0.0752862	+	0.0434665i	−0.00391924	+	0.00226278i
$370$	−21.8891	−	15.4359i	−1.13796	−	0.802476i
$371$	−0.543193	−	1.49241i	−0.0282012	−	0.0774821i
$372$	−6.09951	−	33.6255i	−0.316245	−	1.74340i
$373$	3.36231	−	0.900929i	0.174094	−	0.0466483i	−0.170719	−	0.985320i	$-0.554609\pi$
$373$	3.36231	−	0.900929i	0.174094	−	0.0466483i	0.344813	+	0.938671i	$0.387942\pi$
$374$	5.32797	−	5.84320i	0.275503	−	0.302145i
$375$	−6.48127	−	21.8739i	−0.334691	−	1.12956i
$376$	−19.0008	−	20.4315i	−0.979894	−	1.05368i
$377$	−19.2966	−	13.5116i	−0.993824	−	0.695883i
$378$	−1.67770	+	12.9898i	−0.0862918	+	0.668126i
$379$	26.6623			1.36955			0.684775	−	0.728754i	$-0.259900\pi$
$379$	26.6623			1.36955			0.684775	+	0.728754i	$0.259900\pi$
$380$	−5.15458	+	18.7997i	−0.264424	+	0.964406i
$381$	16.1496			0.827371
$382$	3.81459	−	29.5350i	0.195171	−	1.51114i
$383$	−8.25312	−	5.77890i	−0.421715	−	0.295288i	0.343391	−	0.939193i	$-0.388424\pi$
$383$	−8.25312	−	5.77890i	−0.421715	−	0.295288i	−0.765106	+	0.643905i	$0.777313\pi$
$384$	1.40330	+	23.0434i	0.0716118	+	1.17593i
$385$	−3.53793	−	1.86785i	−0.180310	−	0.0951945i
$386$	4.91616	−	5.39157i	0.250226	−	0.274423i
$387$	0.208440	−	0.0558514i	0.0105956	−	0.00283908i
$388$	−13.2771	+	2.40840i	−0.674042	+	0.122268i
$389$	8.65808	+	23.7879i	0.438982	+	1.20609i	0.940155	+	0.340747i	$0.110680\pi$
$389$	8.65808	+	23.7879i	0.438982	+	1.20609i	−0.501173	+	0.865347i	$0.667098\pi$
$390$	3.16426	+	18.3021i	0.160228	+	0.926764i
$391$	−21.6610	+	12.5060i	−1.09544	+	0.632455i
$392$	2.49366	−	0.347004i	0.125949	−	0.0175264i
$393$	−9.68793	+	6.78356i	−0.488691	+	0.342185i
$394$	4.58805	+	34.2005i	0.231143	+	1.72300i
$395$	10.0303	−	5.14784i	0.504679	−	0.259016i
$396$	−0.973122	−	1.37534i	−0.0489012	−	0.0691132i
$397$	1.79789	−	0.838372i	0.0902338	−	0.0420767i	−0.376977	−	0.926222i	$-0.623037\pi$
$397$	1.79789	−	0.838372i	0.0902338	−	0.0420767i	0.467211	+	0.884146i	$0.345259\pi$
$398$	4.44960	−	0.997923i	0.223038	−	0.0500214i
$399$	−17.3761	−	13.4697i	−0.869895	−	0.674331i
$400$	−19.9269	+	1.70807i	−0.996346	+	0.0854034i
$401$	−0.189817	−	0.0690879i	−0.00947903	−	0.00345008i	0.337276	−	0.941406i	$-0.390494\pi$
$401$	−0.189817	−	0.0690879i	−0.00947903	−	0.00345008i	−0.346755	+	0.937956i	$0.612717\pi$
$402$	1.26680	+	3.03721i	0.0631823	+	0.151482i
$403$	−24.0116	+	2.10074i	−1.19610	+	0.104645i
$404$	0.400293	−	0.869555i	0.0199153	−	0.0432620i
$405$	−20.9252	−	13.5018i	−1.03978	−	0.670909i
$406$	13.2722	+	25.3435i	0.658687	+	1.25777i
$407$	1.58677	−	5.92192i	0.0786535	−	0.293539i
$408$	37.7774	+	23.6774i	1.87026	+	1.17221i
$409$	−10.2941	−	28.2829i	−0.509013	−	1.39850i	−0.882257	−	0.470768i	$-0.843977\pi$
$409$	−10.2941	−	28.2829i	−0.509013	−	1.39850i	0.373245	−	0.927733i	$-0.378245\pi$
$410$	−0.222238	+	0.0800496i	−0.0109755	+	0.00395337i
$411$	3.01066	+	1.73821i	0.148505	+	0.0857394i
$412$	3.85581	+	2.20097i	0.189962	+	0.108434i
$413$	25.3443	+	2.21734i	1.24711	+	0.109108i
$414$	1.61495	+	5.07844i	0.0793704	+	0.249592i
$415$	−0.759608	+	0.477762i	−0.0372877	+	0.0234524i
$416$	16.2747	+	0.510458i	0.797935	+	0.0250273i
$417$	−2.16975	+	2.16975i	−0.106253	+	0.106253i
$418$	−4.44598	+	0.377898i	−0.217460	+	0.0184836i
$419$	−0.259791			−0.0126916			−0.00634581	−	0.999980i	$-0.502020\pi$
$419$	−0.259791			−0.0126916			−0.00634581	+	0.999980i	$0.502020\pi$
$420$	6.80185	−	21.5067i	0.331896	−	1.04942i
$421$	0.726968	+	4.12284i	0.0354303	+	0.200935i	0.997385	−	0.0722747i	$-0.0230258\pi$
$421$	0.726968	+	4.12284i	0.0354303	+	0.200935i	−0.961955	+	0.273210i	$0.911915\pi$
$422$	−11.1760	+	21.5981i	−0.544037	+	1.05138i
$423$	−1.00058	+	11.4367i	−0.0486498	+	0.556070i
$424$	0.533696	−	1.73719i	0.0259185	−	0.0843653i
$425$	−19.6983	+	33.2238i	−0.955507	+	1.61159i
$426$	1.38503	−	33.6165i	0.0671049	−	1.62873i
$427$	24.9482	+	11.6335i	1.20733	+	0.562986i
$428$	−3.26060	+	0.0160142i	−0.157607	+	0.000774075i
$429$	−3.68185	+	2.12572i	−0.177762	+	0.102631i
$430$	0.584291	−	0.0491558i	0.0281770	−	0.00237050i
$431$	17.8136	+	3.14102i	0.858050	+	0.151297i	0.585329	−	0.810796i	$-0.300965\pi$
$431$	17.8136	+	3.14102i	0.858050	+	0.151297i	0.272721	+	0.962093i	$0.412076\pi$
$432$	−10.4931	+	10.7013i	−0.504848	+	0.514865i
$433$	−2.61793	−	29.9231i	−0.125810	−	1.43801i	−0.752421	−	0.658682i	$-0.771114\pi$
$433$	−2.61793	−	29.9231i	−0.125810	−	1.43801i	0.626612	−	0.779332i	$-0.284441\pi$
$434$	27.0714	+	11.1355i	1.29947	+	0.534522i
$435$	−37.3149	+	1.41276i	−1.78911	+	0.0677365i
$436$	4.87535	+	10.3226i	0.233487	+	0.494361i
$437$	13.7637	+	3.12258i	0.658407	+	0.149373i
$438$	2.83056	−	0.634818i	0.135250	−	0.0303328i
$439$	30.2542	+	11.0116i	1.44395	+	0.525556i	0.940895	−	0.338697i	$-0.109986\pi$
$439$	30.2542	+	11.0116i	1.44395	+	0.525556i	0.503057	+	0.864253i	$0.332209\pi$
$440$	−1.94125	−	4.14595i	−0.0925455	−	0.197651i
$441$	−0.793575	−	0.665888i	−0.0377893	−	0.0317090i
$442$	19.0815	−	24.9943i	0.907614	−	1.18886i
$443$	−12.5399	−	17.9089i	−0.595790	−	0.850876i	0.402114	−	0.915590i	$-0.368276\pi$
$443$	−12.5399	−	17.9089i	−0.595790	−	0.850876i	−0.997904	+	0.0647132i	$0.979387\pi$
$444$	34.4493	+	2.84351i	1.63489	+	0.134947i
$445$	3.05652	+	24.3033i	0.144893	+	1.15208i
$446$	6.47470	−	29.5487i	0.306586	−	1.39917i
$447$	33.4514	+	15.5987i	1.58220	+	0.737791i
$448$	−17.2690	−	9.63387i	−0.815886	−	0.455157i
$449$	1.14795	+	0.662768i	0.0541750	+	0.0312780i	0.526843	−	0.849963i	$-0.323376\pi$
$449$	1.14795	+	0.662768i	0.0541750	+	0.0312780i	−0.472668	+	0.881241i	$0.656709\pi$
$450$	6.01627	+	5.61476i	0.283610	+	0.264682i
$451$	−0.0347547	−	0.0414191i	−0.00163654	−	0.00195035i
$452$	−8.84209	−	15.1427i	−0.415897	−	0.712253i
$453$	−18.2535	+	26.0687i	−0.857624	+	1.22481i
$454$	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	$0.350407\pi$
$458$	3.92222	−	30.3683i	0.183273	−	1.41902i
$459$	5.02605	+	28.5042i	0.234596	+	1.33046i
$460$	1.87741	+	14.3579i	0.0875345	+	0.669440i
$461$	1.90318	−	1.59696i	0.0886401	−	0.0743778i	−0.597391	−	0.801950i	$-0.703796\pi$
$461$	1.90318	−	1.59696i	0.0886401	−	0.0743778i	0.686031	+	0.727572i	$0.259351\pi$
$462$	5.15766	−	0.237879i	0.239956	−	0.0110672i
$463$	2.02324	+	7.55084i	0.0940280	+	0.350917i	0.996870	−	0.0790546i	$-0.0251901\pi$
$463$	2.02324	+	7.55084i	0.0940280	+	0.350917i	−0.902842	+	0.429972i	$0.858523\pi$
$464$	−5.36757	+	32.2928i	−0.249183	+	1.49915i
$465$	−28.3188	+	25.6493i	−1.31326	+	1.18946i
$466$	6.14933	+	1.34744i	0.284862	+	0.0624189i
$467$	−0.958618	+	3.57761i	−0.0443596	+	0.165552i	−0.984552	−	0.175091i	$-0.943978\pi$
$467$	−0.958618	+	3.57761i	−0.0443596	+	0.165552i	0.940193	+	0.340643i	$0.110645\pi$
$468$	−4.33168	−	5.11110i	−0.200232	−	0.236261i
$469$	−2.77594	−	0.489473i	−0.128181	−	0.0226018i
$470$	−8.17419	+	30.1045i	−0.377047	+	1.38862i
$471$	3.35704	−	4.00077i	0.154684	−	0.184346i
$472$	21.6076	+	19.5088i	0.994570	+	0.897966i
$473$	0.0567215	+	0.121640i	0.00260806	+	0.00559300i
$474$	−7.78749	+	12.2904i	−0.357691	+	0.564517i
$475$	20.8911	−	6.20968i	0.958551	−	0.284920i
$476$	−34.5312	+	16.3091i	−1.58273	+	0.747527i
$477$	−0.677703	+	0.316018i	−0.0310299	+	0.0144695i
$478$	16.2591	+	38.9819i	0.743675	+	1.78299i
$479$	17.1845	+	14.4195i	0.785181	+	0.658845i	0.944548	−	0.328374i	$-0.106501\pi$
$479$	17.1845	+	14.4195i	0.785181	+	0.658845i	−0.159366	+	0.987220i	$0.550945\pi$
$480$	21.0466	−	14.9414i	0.960643	−	0.681980i
$481$	4.23354	−	24.0096i	0.193033	−	1.09474i
$482$	9.39355	−	30.0497i	0.427865	−	1.36872i
$483$	−15.7747	−	4.22682i	−0.717774	−	0.192327i
$484$	−14.7425	+	14.8880i	−0.670111	+	0.676726i
$485$	10.1277	+	11.1818i	0.459875	+	0.507737i
$486$	16.2283	+	0.668619i	0.736130	+	0.0303292i
$487$	−27.6814	+	7.41721i	−1.25436	+	0.336106i	−0.824021	−	0.566560i	$-0.808274\pi$
$487$	−27.6814	+	7.41721i	−1.25436	+	0.336106i	−0.430343	+	0.902665i	$0.641607\pi$
$488$	14.7499	+	27.8318i	0.667698	+	1.25989i
$489$	6.68924	+	7.97192i	0.302498	+	0.360503i
$490$	−1.80216	−	2.16233i	−0.0814131	−	0.0976842i
$491$	−37.1458	+	6.54980i	−1.67637	+	0.295589i	−0.929345	−	0.369212i	$-0.879628\pi$
$491$	−37.1458	+	6.54980i	−1.67637	+	0.295589i	−0.747021	+	0.664801i	$0.768516\pi$
$492$	0.194803	−	0.234486i	0.00878239	−	0.0105715i
$493$	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
$497$	23.6070	+	16.5298i	1.05892	+	0.741464i
$498$	0.532223	−	1.02855i	0.0238495	−	0.0460905i
$499$	−2.13289	+	1.78970i	−0.0954811	+	0.0801182i	−0.689279	−	0.724496i	$-0.742072\pi$
$499$	−2.13289	+	1.78970i	−0.0954811	+	0.0801182i	0.593798	+	0.804614i	$0.297628\pi$
$500$	13.3902	+	17.9082i	0.598828	+	0.800877i
$501$	1.91737	−	3.32099i	0.0856620	−	0.148371i
$502$	−5.31991	+	4.89889i	−0.237439	+	0.218648i
$503$	−16.1730	+	34.6832i	−0.721120	+	1.54645i	0.112217	+	0.993684i	$0.464205\pi$
$503$	−16.1730	+	34.6832i	−0.721120	+	1.54645i	−0.833338	+	0.552764i	$0.813573\pi$
$504$	1.81953	+	7.93044i	0.0810485	+	0.353250i
$505$	−1.06189	+	0.133550i	−0.0472536	+	0.00594288i
$506$	−2.93618	+	1.53765i	−0.130529	+	0.0683571i
$507$	7.88077	−	5.51818i	0.349997	−	0.245071i
$508$	−14.8474	+	5.48676i	−0.658748	+	0.243435i
$509$	7.89744	−	9.41181i	0.350048	−	0.417171i	−0.562076	−	0.827086i	$-0.689997\pi$
$509$	7.89744	−	9.41181i	0.350048	−	0.417171i	0.912124	+	0.409915i	$0.134442\pi$
$510$	0.166246	−	49.8464i	0.00736149	−	2.20723i
$511$	−0.849840	+	2.33492i	−0.0375947	+	0.103291i
$512$	−9.11901	−	20.7085i	−0.403007	−	0.915197i
$513$	8.84302	−	13.7310i	0.390429	−	0.606236i
$514$	4.46094	−	7.04036i	0.196763	−	0.310537i
$515$	−0.187798	−	4.96026i	−0.00827535	−	0.218575i
$516$	−0.617730	+	0.437076i	−0.0271940	+	0.0192412i
$517$	−7.11314	+	0.622319i	−0.312836	+	0.0273696i
$518$	−17.9666	+	23.5339i	−0.789405	+	1.03402i
$519$	3.31155	−	18.7808i	0.145361	−	0.824384i
$520$	−9.12717	−	15.7513i	−0.400253	−	0.690742i
$521$	12.9120	+	22.3643i	0.565687	+	0.979798i	0.996985	+	0.0775890i	$0.0247222\pi$
$521$	12.9120	+	22.3643i	0.565687	+	0.979798i	−0.431299	+	0.902209i	$0.641944\pi$
$522$	11.3423	−	7.26509i	0.496441	−	0.317984i
$523$	0.162518	−	0.348522i	0.00710644	−	0.0152398i	−0.902723	−	0.430223i	$-0.858435\pi$
$523$	0.162518	−	0.348522i	0.00710644	−	0.0152398i	0.909829	+	0.414983i	$0.136213\pi$
$524$	6.60208	−	9.52800i	0.288413	−	0.416233i
$525$	−24.4338	+	6.24464i	−1.06638	+	0.272538i
$526$	−28.2354	−	25.7457i	−1.23112	−	1.12257i
$527$	64.4405	+	5.63782i	2.80707	+	0.245587i
$528$	4.87263	+	3.34101i	0.212054	+	0.145399i
$529$	−12.3262	+	2.17344i	−0.535921	+	0.0944973i
$530$	−1.96434	+	0.519327i	−0.0853253	+	0.0225581i
$531$		−	11.9784i		−	0.519816i
$532$	20.5513	+	6.48019i	0.891013	+	0.280952i
$533$	−0.152036	−	0.152036i	−0.00658539	−	0.00658539i
$534$	−19.3055	−	25.0319i	−0.835429	−	1.08323i
$535$	1.94089	+	3.08588i	0.0839121	+	0.133414i
$536$	−2.19653	−	2.36192i	−0.0948757	−	0.102019i
$537$	0.379970	−	4.34308i	0.0163969	−	0.187418i
$538$	−27.8747	+	1.28563i	−1.20176	+	0.0554272i
$539$	0.322156	−	0.557990i	0.0138762	−	0.0240343i
$540$	16.3560	+	3.64113i	0.703851	+	0.156689i
$541$	−16.7745	+	6.10541i	−0.721191	+	0.262492i	−0.676431	−	0.736506i	$-0.736474\pi$
$541$	−16.7745	+	6.10541i	−0.721191	+	0.262492i	−0.0447598	+	0.998998i	$0.514252\pi$
$542$	4.79362	+	7.48386i	0.205904	+	0.321459i
$543$	24.7470	+	6.63095i	1.06200	+	0.284561i
$544$	−42.7755	−	8.93355i	−1.83399	−	0.383023i
$545$	6.92001	−	10.7247i	0.296421	−	0.459395i
$546$	20.3496	−	2.72992i	0.870880	−	0.116830i
$547$	−3.20525	−	36.6362i	−0.137047	−	1.56645i	−0.684122	−	0.729367i	$-0.739814\pi$
$547$	−3.20525	−	36.6362i	−0.137047	−	1.56645i	0.547075	−	0.837083i	$-0.315741\pi$
$548$	−3.35845	−	0.575192i	−0.143466	−	0.0245710i
$549$	4.43278	−	12.1790i	0.189187	−	0.519786i
$550$	−2.78933	+	4.29143i	−0.118937	+	0.182987i
$551$	−1.38038	−	35.6463i	−0.0588061	−	1.51858i
$552$	−11.4850	−	14.7414i	−0.488835	−	0.627436i
$553$	−5.26700	−	11.2951i	−0.223976	−	0.480318i
$554$	−20.9018	−	8.59773i	−0.888032	−	0.365283i
$555$	−17.6462	−	34.3826i	−0.749038	−	1.45946i
$556$	1.25764	−	2.73196i	0.0533357	−	0.115861i
$557$	−3.57558	−	5.10646i	−0.151502	−	0.216368i	0.736226	−	0.676736i	$-0.236606\pi$
$557$	−3.57558	−	5.10646i	−0.151502	−	0.216368i	−0.887728	+	0.460368i	$0.847717\pi$
$558$	4.11207	−	13.1544i	0.174078	−	0.556869i
$559$	0.266860	+	0.462215i	0.0112870	+	0.0195496i
$560$	1.05341	+	22.0835i	0.0445147	+	0.933197i
$561$	10.7216	−	3.90235i	0.452667	−	0.164757i
$562$	25.2549	+	27.4254i	1.06531	+	1.15687i
$563$	−9.44215	−	35.2386i	−0.397939	−	1.48513i	−0.816716	−	0.577040i	$-0.804208\pi$
$563$	−9.44215	−	35.2386i	−0.397939	−	1.48513i	0.418777	−	0.908089i	$-0.362459\pi$
$564$	−10.6104	−	38.8347i	−0.446779	−	1.63524i
$565$	−9.15312	+	17.3371i	−0.385075	+	0.729378i
$566$	−6.95193	+	2.21072i	−0.292211	+	0.0929234i
$567$	−15.7897	+	22.5500i	−0.663105	+	0.947012i
$568$	10.1477	+	31.3765i	0.425788	+	1.31653i
$569$			1.84160i			0.0772037i	0.999255	+	0.0386019i	$0.0122904\pi$
$569$			1.84160i			0.0772037i	−0.999255	+	0.0386019i	$0.987710\pi$
$570$	−19.1730	+	20.5796i	−0.803067	+	0.861984i
$571$			2.51012i			0.105045i	0.998620	+	0.0525225i	$0.0167261\pi$
$571$			2.51012i			0.105045i	−0.998620	+	0.0525225i	$0.983274\pi$
$572$	2.66277	−	3.20521i	0.111336	−	0.134016i
$573$	24.6462	−	35.1984i	1.02961	−	1.47043i
$574$	0.0791313	+	0.248840i	0.00330288	+	0.0103864i
$575$	12.5214	−	10.2619i	0.522177	−	0.427952i
$576$	−3.80998	+	8.49511i	−0.158749	+	0.353963i
$577$	0.611312	+	2.28145i	0.0254493	+	0.0949779i	0.977482	−	0.211017i	$-0.0676776\pi$
$577$	0.611312	+	2.28145i	0.0254493	+	0.0949779i	−0.952033	+	0.305995i	$0.901011\pi$
$578$	−44.3941	+	40.8807i	−1.84655	+	1.70041i
$579$	9.89292	−	3.60073i	0.411136	−	0.149641i
$580$	33.8261	−	13.9764i	1.40455	−	0.580337i
$581$	0.495986	+	0.859073i	0.0205770	+	0.0356403i
$582$	−18.5830	−	5.80908i	−0.770292	−	0.240794i
$583$	−0.266757	−	0.380969i	−0.0110480	−	0.0157781i
$584$	−2.38665	+	1.54530i	−0.0987603	+	0.0639450i
$585$	−2.29379	+	7.13071i	−0.0948364	+	0.294819i
$586$	−1.29161	+	3.14000i	−0.0533558	+	0.129712i
$587$	2.51837	+	5.40065i	0.103944	+	0.222909i	0.951401	−	0.307956i	$-0.0996450\pi$
$587$	2.51837	+	5.40065i	0.103944	+	0.222909i	−0.847456	+	0.530865i	$0.821867\pi$
$588$	3.41970	+	1.22568i	0.141026	+	0.0505463i
$589$	−24.5266	−	27.0323i	−1.01060	−	1.11385i
$590$	5.75872	−	32.0342i	0.237083	−	1.31883i
$591$	−17.0289	+	46.7866i	−0.700476	+	1.92454i
$592$	−32.6376	+	9.08975i	−1.34140	+	0.373587i
$593$	0.0765286	+	0.874726i	0.00314265	+	0.0359207i	0.997604	−	0.0691812i	$-0.0220387\pi$
$593$	0.0765286	+	0.874726i	0.00314265	+	0.0359207i	−0.994461	+	0.105102i	$0.966483\pi$
$594$	0.509967	+	3.80142i	0.0209242	+	0.155974i
$595$	35.8764	+	23.1489i	1.47079	+	0.949014i
$596$	−36.0537	−	2.97594i	−1.47682	−	0.121899i
$597$	6.35552	+	1.70296i	0.260114	+	0.0696974i
$598$	−11.0987	+	7.10903i	−0.453860	+	0.290710i
$599$	−36.7367	+	13.3711i	−1.50102	+	0.546326i	−0.956324	−	0.292308i	$-0.905577\pi$
$599$	−36.7367	+	13.3711i	−1.50102	+	0.546326i	−0.544695	+	0.838634i	$0.683355\pi$
$600$	−26.6141	−	11.1556i	−1.08652	−	0.455425i
$601$	21.1660	−	36.6607i	0.863381	−	1.49542i	−0.00526496	−	0.999986i	$-0.501676\pi$
$601$	21.1660	−	36.6607i	0.863381	−	1.49542i	0.868646	−	0.495433i	$-0.164991\pi$
$602$	−0.0298631	−	0.647485i	−0.00121713	−	0.0263895i
$603$	−0.115669	+	1.32210i	−0.00471039	+	0.0538400i
$604$	7.92496	−	30.1682i	0.322462	−	1.22753i
$605$	22.8402	+	5.20249i	0.928585	+	0.211511i
$606$	1.09373	−	0.843522i	0.0444296	−	0.0342657i
$607$	−17.2427	−	17.2427i	−0.699858	−	0.699858i	0.264522	−	0.964380i	$-0.414786\pi$
$607$	−17.2427	−	17.2427i	−0.699858	−	0.699858i	−0.964380	+	0.264522i	$0.914786\pi$
$608$	14.2911	+	20.0939i	0.579582	+	0.814914i
$609$			41.2785i			1.67269i
$610$	17.7099	−	30.4396i	0.717054	−	1.23246i
$611$	−27.9629	+	4.93062i	−1.13126	+	0.199471i
$612$	9.06654	+	15.5271i	0.366493	+	0.627645i
$613$	−12.4381	−	1.08820i	−0.502372	−	0.0439519i	−0.166846	−	0.985983i	$-0.553358\pi$
$613$	−12.4381	−	1.08820i	−0.502372	−	0.0439519i	−0.335526	+	0.942031i	$0.608914\pi$
$614$	19.1764	−	21.0308i	0.773897	−	0.848736i
$615$	−0.337651	−	0.0464433i	−0.0136154	−	0.00187277i
$616$	−4.66096	+	1.97099i	−0.187796	+	0.0794133i
$617$	−5.08866	+	10.9127i	−0.204862	+	0.439327i	−0.981716	−	0.190354i	$-0.939037\pi$
$617$	−5.08866	+	10.9127i	−0.204862	+	0.439327i	0.776854	+	0.629681i	$0.216814\pi$
$618$	3.45522	+	5.39433i	0.138989	+	0.216992i
$619$	0.856612	+	1.48370i	0.0344302	+	0.0596348i	0.882727	−	0.469886i	$-0.155705\pi$
$619$	0.856612	+	1.48370i	0.0344302	+	0.0596348i	−0.848297	+	0.529521i	$0.822372\pi$
$620$	17.3212	−	33.2023i	0.695635	−	1.33344i
$621$	2.10665	−	11.9474i	0.0845370	−	0.479433i
$622$	−18.1733	−	13.8741i	−0.728681	−	0.556299i
$623$	26.9741	−	2.35993i	1.08069	−	0.0945485i
$624$	20.4608	+	11.5466i	0.819088	+	0.462233i
$625$	9.09232	−	23.2880i	0.363693	−	0.931519i
$626$	−26.9100	−	17.0508i	−1.07554	−	0.681486i
$627$	−5.93585	−	2.49305i	−0.237055	−	0.0995629i
$628$	−1.72711	+	4.81871i	−0.0689193	+	0.192287i
$629$	−22.3781	+	61.4833i	−0.892274	+	2.45150i
$630$	6.45388	−	6.41098i	0.257129	−	0.255419i
$631$	−15.7341	+	18.7512i	−0.626366	+	0.746474i	−0.982151	−	0.188094i	$-0.939769\pi$
$631$	−15.7341	+	18.7512i	−0.626366	+	0.746474i	0.355785	+	0.934568i	$0.384214\pi$
$632$	2.98395	−	13.9451i	0.118695	−	0.554708i
$633$	−28.7427	+	20.1259i	−1.14242	+	0.799932i
$634$	9.79273	+	18.6994i	0.388919	+	0.742648i
$635$	13.9775	+	10.8545i	0.554679	+	0.430746i
$636$	1.84503	−	1.86324i	0.0731601	−	0.0738823i
$637$	1.08282	−	2.32212i	0.0429030	−	0.0920059i
$638$	5.67494	+	6.16266i	0.224673	+	0.243982i
$639$	6.78435	−	11.7508i	0.268385	−	0.464856i
$640$	−14.2733	+	20.8871i	−0.564202	+	0.825637i
$641$	10.8231	−	9.08164i	0.427486	−	0.358703i	−0.403516	−	0.914972i	$-0.632212\pi$
$641$	10.8231	−	9.08164i	0.427486	−	0.358703i	0.831002	+	0.556269i	$0.187768\pi$
$642$	−4.17845	−	2.16214i	−0.164910	−	0.0853328i
$643$	25.4189	+	17.7985i	1.00242	+	0.701905i	0.954888	−	0.296965i	$-0.0959744\pi$
$643$	25.4189	+	17.7985i	1.00242	+	0.701905i	0.0475354	+	0.998870i	$0.484863\pi$
$644$	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	$-0.947293\pi$
$647$	−29.2809	−	29.2809i	−1.15115	−	1.15115i	−0.164828	−	0.986322i	$-0.552707\pi$
$648$	−29.9716	+	9.69333i	−1.17739	+	0.380790i
$649$	7.33686	−	1.29369i	0.287997	−	0.0507817i
$650$	−9.56253	+	17.9672i	−0.375073	+	0.704731i
$651$	27.1489	+	32.3548i	1.06405	+	1.26808i
$652$	−8.85828	−	5.05649i	−0.346917	−	0.198027i
$653$	−35.0980	+	9.40449i	−1.37349	+	0.368026i	−0.868753	−	0.495246i	$-0.835078\pi$
$653$	−35.0980	+	9.40449i	−1.37349	+	0.368026i	−0.504739	+	0.863272i	$0.668411\pi$
$654$	−0.678078	+	16.4579i	−0.0265150	+	0.643554i
$655$	−12.9442	−	0.640278i	−0.505773	−	0.0250177i
$656$	−0.0994298	+	0.281762i	−0.00388208	+	0.0110010i
$657$	1.13003	+	0.302791i	0.0440867	+	0.0118130i
$658$	32.9127	+	10.2885i	1.28307	+	0.401089i
$659$	−4.82640	+	27.3719i	−0.188010	+	1.06626i	0.734017	+	0.679131i	$0.237643\pi$
$659$	−4.82640	+	27.3719i	−0.188010	+	1.06626i	−0.922027	+	0.387126i	$0.873468\pi$
$660$	0.293927	−	6.59884i	0.0114411	−	0.256860i
$661$	4.06988	+	3.41504i	0.158300	+	0.132830i	0.718497	−	0.695530i	$-0.244830\pi$
$661$	4.06988	+	3.41504i	0.158300	+	0.132830i	−0.560197	+	0.828359i	$0.689275\pi$
$662$	7.91688	−	3.30208i	0.307698	−	0.128339i
$663$	41.1210	−	19.1751i	1.59701	−	0.744698i
$664$	−0.139864	+	1.12644i	−0.00542776	+	0.0437142i
$665$	−5.98573	−	23.3368i	−0.232117	−	0.904964i
$666$	11.7755	+	7.46123i	0.456291	+	0.289117i
$667$	−11.1987	−	24.0157i	−0.433616	−	0.929892i
$668$	−0.634481	+	3.70463i	−0.0245488	+	0.143336i
$669$	28.0556	−	33.4353i	1.08469	−	1.29268i
$670$	−0.944951	+	3.48013i	−0.0365066	+	0.134449i
$671$	7.93849	+	1.39977i	0.306462	+	0.0540375i
$672$	−15.6246	−	23.8738i	−0.602734	−	0.920951i
$673$	8.69823	−	32.4622i	0.335292	−	1.25133i	−0.568260	−	0.822849i	$-0.692383\pi$
$673$	8.69823	−	32.4622i	0.335292	−	1.25133i	0.903552	−	0.428478i	$-0.140950\pi$
$674$	−6.25874	+	28.5631i	−0.241078	+	1.10021i
$675$	−6.20317	−	17.6774i	−0.238760	−	0.680405i
$676$	−5.37055	+	7.75068i	−0.206560	+	0.298103i
$677$	−5.66331	−	21.1358i	−0.217659	−	0.812313i	−0.985214	−	0.171330i	$-0.945194\pi$
$677$	−5.66331	−	21.1358i	−0.217659	−	0.812313i	0.767555	−	0.640983i	$-0.221473\pi$
$678$	−1.16569	−	25.2743i	−0.0447681	−	0.970655i
$679$	12.7753	−	10.7198i	0.490273	−	0.411388i
$680$	16.7822	+	45.8836i	0.643568	+	1.75955i
$681$	0.281151	+	1.59449i	0.0107737	+	0.0611009i
$682$	8.50129	+	1.09799i	0.325531	+	0.0420440i
$683$	−11.0742	+	11.0742i	−0.423742	+	0.423742i	−0.886490	−	0.462748i	$-0.846863\pi$
$683$	−11.0742	+	11.0742i	−0.423742	+	0.423742i	0.462748	+	0.886490i	$0.346863\pi$
$684$	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
$687$	25.3416	−	36.1915i	0.966842	−	1.38079i
$688$	0.419426	−	0.611704i	0.0159905	−	0.0233210i
$689$	−1.18879	−	1.41675i	−0.0452895	−	0.0539739i
$690$	−7.21128	+	19.6091i	−0.274529	+	0.746505i
$691$	1.11642	+	0.644565i	0.0424706	+	0.0245204i	0.521085	−	0.853505i	$-0.325527\pi$
$691$	1.11642	+	0.644565i	0.0424706	+	0.0245204i	−0.478614	+	0.878025i	$0.658861\pi$
$692$	3.33613	+	18.3915i	0.126821	+	0.699139i
$693$	1.88715	+	0.879993i	0.0716870	+	0.0334282i
$694$	50.0899	+	10.9757i	1.90139	+	0.416631i
$695$	−3.33624	+	0.419585i	−0.126551	+	0.0159158i
$696$	−28.4773	+	37.6839i	−1.07943	+	1.42840i
$697$	0.330971	+	0.472676i	0.0125364	+	0.0179039i
$698$	−5.49209	−	4.19284i	−0.207879	−	0.158701i
$699$	6.95816	+	5.83859i	0.263182	+	0.220836i
$700$	20.3420	−	14.0424i	0.768856	−	0.530752i
$701$	35.1615	+	12.7977i	1.32803	+	0.483364i	0.906023	−	0.423228i	$-0.139103\pi$
$701$	35.1615	+	12.7977i	1.32803	+	0.483364i	0.422009	+	0.906592i	$0.361325\pi$
$702$	3.33774	+	14.8825i	0.125975	+	0.561705i
$703$	32.8317	−	16.8860i	1.23827	−	0.636867i
$704$	−5.61483	−	1.41616i	−0.211617	−	0.0533736i
$705$	−30.5999	+	33.0081i	−1.15246	+	1.24316i
$706$	−2.93047	+	7.12421i	−0.110290	+	0.268123i
$707$	0.103113	+	1.17859i	0.00387798	+	0.0443255i
$708$	14.5600	+	39.4002i	0.547200	+	1.48075i
$709$	3.82149	+	0.673831i	0.143519	+	0.0253063i	0.244946	−	0.969537i	$-0.421230\pi$
$709$	3.82149	+	0.673831i	0.143519	+	0.0253063i	−0.101427	+	0.994843i	$0.532341\pi$
$710$	23.7930	−	28.1641i	0.892935	−	1.05698i
$711$	−5.08168	+	2.93391i	−0.190578	+	0.110030i
$712$	26.2533	+	16.4545i	0.983882	+	0.616659i
$713$	−24.5729	−	11.4585i	−0.920262	−	0.429125i
$714$	−55.0552	−	2.26832i	−2.06039	−	0.0848897i
$715$	−4.61537	−	0.634836i	−0.172605	−	0.0237415i
$716$	1.12621	+	4.12197i	0.0420883	+	0.154045i
$717$	−5.31150	+	60.7107i	−0.198362	+	2.26728i
$718$	19.5461	+	10.1141i	0.729455	+	0.377456i
$719$	−3.67193	−	20.8246i	−0.136940	−	0.776625i	−0.973489	−	0.228733i	$-0.926542\pi$
$719$	−3.67193	−	20.8246i	−0.136940	−	0.776625i	0.836549	−	0.547892i	$-0.184569\pi$
$720$	10.3147	−	1.40029i	0.384406	−	0.0521856i
$721$	−5.48714			−0.204352
$722$	−19.6758	−	18.2993i	−0.732257	−	0.681028i
$723$	32.1218	−	32.1218i	1.19462	−	1.19462i
$724$	−25.0044	+	2.31141i	−0.929283	+	0.0859027i
$725$	−33.2454	−	23.8572i	−1.23470	−	0.886036i
$726$	−28.8098	+	9.16153i	−1.06923	+	0.340016i
$727$	5.58256	+	0.488411i	0.207046	+	0.0181142i	0.190207	−	0.981744i	$-0.439084\pi$
$727$	5.58256	+	0.488411i	0.207046	+	0.0181142i	0.0168390	+	0.999858i	$0.494640\pi$
$728$	−17.7812	+	9.42346i	−0.659016	+	0.349257i
$729$	−8.63911	−	4.98779i	−0.319967	−	0.184733i
$730$	2.87652	+	1.35304i	0.106465	+	0.0500783i
$731$	−0.489896	−	1.34598i	−0.0181194	−	0.0497828i
$732$	0.223216	+	45.4483i	0.00825028	+	1.67982i
$733$	6.41608	−	23.9451i	0.236983	−	0.884434i	−0.740261	−	0.672319i	$-0.765298\pi$
$733$	6.41608	−	23.9451i	0.236983	−	0.884434i	0.977245	−	0.212115i	$-0.0680351\pi$
$734$	31.3371	−	16.4110i	1.15667	−	0.605741i
$735$	−0.856093	−	3.97025i	−0.0315775	−	0.146445i
$736$	15.5673	+	9.65080i	0.573817	+	0.355733i
$737$	−0.822292	+	0.0719412i	−0.0302895	+	0.00264999i
$738$	0.113468	−	0.0473266i	0.00417680	−	0.00174212i
$739$	−39.6990	−	14.4492i	−1.46035	−	0.531524i	−0.514888	−	0.857257i	$-0.672166\pi$
$739$	−39.6990	−	14.4492i	−1.46035	−	0.531524i	−0.945462	+	0.325734i	$0.894389\pi$
$740$	27.9046	+	25.6151i	1.02579	+	0.941628i
$741$	−24.3788	−	7.81891i	−0.895579	−	0.287235i
$742$	0.491515	+	2.19160i	0.0180441	+	0.0804561i
$743$	2.20359	−	1.02755i	0.0808418	−	0.0376971i	−0.381777	−	0.924255i	$-0.624688\pi$
$743$	2.20359	−	1.02755i	0.0808418	−	0.0376971i	0.462619	+	0.886557i	$0.346910\pi$
$744$	2.46376	+	48.2668i	0.0903257	+	1.76955i
$745$	18.4680	+	35.9839i	0.676614	+	1.31835i
$746$	−4.87906	+	0.654534i	−0.178635	+	0.0239642i
$747$	0.382582	−	0.267887i	0.0139980	−	0.00980147i
$748$	−8.53130	+	7.23031i	−0.311935	+	0.264366i
$749$	3.48995	−	2.01492i	0.127520	−	0.0736237i
$750$	5.12797	+	31.8536i	0.187247	+	1.16313i
$751$	−5.18557	−	14.2472i	−0.189224	−	0.519889i	0.808411	−	0.588618i	$-0.200328\pi$
$751$	−5.18557	−	14.2472i	−0.189224	−	0.519889i	−0.997635	+	0.0687291i	$0.978106\pi$
$752$	22.9488	+	32.0985i	0.836855	+	1.17051i
$753$	−10.0792	+	2.70072i	−0.367307	+	0.0984196i
$754$	24.6171	+	22.4464i	0.896501	+	0.817451i
$755$	−33.3196	+	10.2939i	−1.21262	+	0.374633i
$756$	4.70617	−	17.9152i	0.171162	−	0.651569i
$757$	−25.3645	−	17.7604i	−0.921887	−	0.645512i	0.0132066	−	0.999913i	$-0.495796\pi$
$757$	−25.3645	−	17.7604i	−0.921887	−	0.645512i	−0.935094	+	0.354400i	$0.884685\pi$
$758$	−37.3956	−	4.82983i	−1.35827	−	0.175427i
$759$	−4.78234			−0.173588
$760$	10.6352	−	25.4341i	0.385778	−	0.922592i
$761$	−3.98694			−0.144527			−0.0722633	−	0.997386i	$-0.523022\pi$
$761$	−3.98694			−0.144527			−0.0722633	+	0.997386i	$0.523022\pi$
$762$	−22.6509	−	2.92548i	−0.820555	−	0.105979i
$763$	−11.5575	−	8.09263i	−0.418409	−	0.292973i
$764$	−10.7004	+	40.7337i	−0.387127	+	1.47369i
$765$	9.38547	−	17.7772i	0.339332	−	0.642736i
$766$	10.5287	+	9.60031i	0.380417	+	0.346873i
$767$	28.6165	−	7.66777i	1.03328	−	0.276867i
$768$	2.20605	−	32.5740i	0.0796039	−	1.17541i
$769$	−11.0886	−	30.4656i	−0.399864	−	1.09862i	−0.962351	−	0.271811i	$-0.912378\pi$
$769$	−11.0886	−	30.4656i	−0.399864	−	1.09862i	0.562487	−	0.826806i	$-0.309845\pi$
$770$	4.62382	+	3.26067i	0.166631	+	0.117506i
$771$	10.4147	−	6.01295i	0.375078	−	0.216551i
$772$	−7.87190	+	6.67146i	−0.283316	+	0.240111i
$773$	20.4392	−	14.3117i	0.735147	−	0.514755i	−0.145015	−	0.989429i	$-0.546323\pi$
$773$	20.4392	−	14.3117i	0.735147	−	0.514755i	0.880162	+	0.474674i	$0.157434\pi$
$774$	−0.302468	+	0.0405765i	−0.0108720	+	0.00145849i
$775$	−41.7493	+	3.16583i	−1.49968	+	0.113720i
$776$	19.0582	−	0.972820i	0.684151	−	0.0349222i
$777$	−38.7183	+	18.0547i	−1.38901	+	0.647707i
$778$	−7.83438	−	34.9324i	−0.280876	−	1.25239i
$779$	0.0440897	−	0.322601i	0.00157968	−	0.0115584i
$780$	−1.12268	−	26.2431i	−0.0401982	−	0.939654i
$781$	7.93023	+	2.88637i	0.283766	+	0.103282i
$782$	32.6464	−	13.6166i	1.16743	−	0.486928i
$783$	−30.5473	+	2.67254i	−1.09167	+	0.0955089i
$784$	−3.56038	+	0.0349739i	−0.127156	+	0.00124907i
$785$	5.59450	−	1.20632i	0.199676	−	0.0430555i
$786$	14.8168	−	7.75943i	0.528497	−	0.276770i
$787$	5.63660	−	21.0361i	0.200923	−	0.749855i	−0.789731	−	0.613454i	$-0.789780\pi$
$787$	5.63660	−	21.0361i	0.200923	−	0.749855i	0.990654	−	0.136401i	$-0.0435536\pi$
$788$	−0.239675	−	48.7995i	−0.00853807	−	1.73841i
$789$	−18.8569	−	51.8089i	−0.671323	−	1.84444i
$790$	−15.0006	+	5.40320i	−0.533699	+	0.192237i
$791$	18.7684	+	10.8360i	0.667328	+	0.385282i
$792$	1.11573	+	2.10527i	0.0396456	+	0.0748077i
$793$	31.9334	+	2.79381i	1.13399	+	0.0992110i
$794$	−2.67353	+	0.850185i	−0.0948801	+	0.0301719i
$795$	−2.85846	−	0.651095i	−0.101379	−	0.0230920i
$796$	−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	$0.253812\pi$
$798$	21.9311	+	22.0398i	0.776353	+	0.780202i
$799$	76.2026			2.69585
$800$	28.2582	+	1.21405i	0.999078	+	0.0429233i
$801$	−2.21378	−	12.5550i	−0.0782200	−	0.443608i
$802$	0.253716	+	0.131285i	0.00895902	+	0.00463584i
$803$	−0.0634168	+	0.724857i	−0.00223793	+	0.0255797i
$804$	−1.22658	−	4.48936i	−0.0432583	−	0.158327i
$805$	−10.8120	−	14.2608i	−0.381074	−	0.502625i
$806$	34.0583	+	1.40323i	1.19965	+	0.0494267i
$807$	−36.4903	−	17.0157i	−1.28452	−	0.598981i
$808$	−0.718954	+	1.14709i	−0.0252927	+	0.0403546i
$809$	16.6757	−	9.62775i	0.586288	−	0.338494i	−0.177340	−	0.984150i	$-0.556749\pi$
$809$	16.6757	−	9.62775i	0.586288	−	0.338494i	0.763628	+	0.645656i	$0.223416\pi$
$810$	26.9030	+	22.7277i	0.945277	+	0.798569i
$811$	52.0669	+	9.18080i	1.82832	+	0.322382i	0.978743	−	0.205088i	$-0.0657481\pi$
$811$	52.0669	+	9.18080i	1.82832	+	0.322382i	0.849574	+	0.527470i	$0.176859\pi$
$812$	−14.0241	−	37.9500i	−0.492151	−	1.33179i
$813$	1.11764	+	12.7747i	0.0391975	+	0.448029i
$814$	−3.29830	+	8.01844i	−0.115605	+	0.281046i
$815$	0.431444	+	11.3956i	0.0151128	+	0.399172i
$816$	−48.6961	−	40.0524i	−1.70470	−	1.40211i
$817$	−0.312974	+	0.745178i	−0.0109496	+	0.0260705i
$818$	9.31479	+	41.5334i	0.325684	+	1.45218i
$819$	7.78092	+	2.83202i	0.271887	+	0.0989589i
$820$	0.326204	−	0.0720167i	0.0113915	−	0.00251493i
$821$	−25.8923	−	21.7262i	−0.903649	−	0.758251i	0.0672514	−	0.997736i	$-0.478577\pi$
$821$	−25.8923	−	21.7262i	−0.903649	−	0.758251i	−0.970900	+	0.239485i	$0.923022\pi$
$822$	−3.90777	−	2.98332i	−0.136299	−	0.104055i
$823$	−11.6645	−	16.6586i	−0.406598	−	0.580683i	0.562672	−	0.826680i	$-0.309773\pi$
$823$	−11.6645	−	16.6586i	−0.406598	−	0.580683i	−0.969270	+	0.245997i	$0.920884\pi$
$824$	−5.00931	−	3.78548i	−0.174508	−	0.131873i
$825$	−6.43798	+	3.61821i	−0.224142	+	0.125970i
$826$	−35.1453	−	7.70103i	−1.22286	−	0.267953i
$827$	30.6741	+	14.3036i	1.06664	+	0.497385i	0.875022	−	0.484084i	$-0.160847\pi$
$827$	30.6741	+	14.3036i	1.06664	+	0.497385i	0.191623	+	0.981469i	$0.438625\pi$
$828$	−1.34512	−	7.41538i	−0.0467460	−	0.257702i
$829$	3.13939	+	1.81253i	0.109035	+	0.0629517i	0.553526	−	0.832832i	$-0.313282\pi$
$829$	3.13939	+	1.81253i	0.109035	+	0.0629517i	−0.444491	+	0.895784i	$0.646615\pi$
$830$	1.15194	−	0.532491i	0.0399846	−	0.0184830i
$831$	−20.9616	−	24.9811i	−0.727151	−	0.866585i
$832$	−22.7339	−	3.66409i	−0.788156	−	0.127029i
$833$	−3.94402	+	5.63265i	−0.136652	+	0.195160i
$834$	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
$838$	0.364373	+	0.0470607i	0.0125871	+	0.00162568i
$839$	−3.57945	−	20.3001i	−0.123577	−	0.700837i	−0.982143	−	0.188135i	$-0.939756\pi$
$839$	−3.57945	−	20.3001i	−0.123577	−	0.700837i	0.858567	−	0.512702i	$-0.171355\pi$
$840$	−13.4359	+	28.9324i	−0.463584	+	0.998263i
$841$	−29.0921	+	24.4112i	−1.00318	+	0.841765i
$842$	−0.272774	−	5.91424i	−0.00940041	−	0.203818i
$843$	13.9228	+	51.9607i	0.479528	+	1.78962i
$844$	19.5875	−	28.2683i	0.674228	−	0.973034i
$845$	10.5296	+	0.520842i	0.362231	+	0.0179175i
$846$	3.47511	−	15.8594i	0.119477	−	0.545258i
$847$	6.70209	−	25.0125i	0.230286	−	0.859441i
$848$	−1.06323	+	2.33984i	−0.0365115	+	0.0803504i
$849$	−10.3658	−	1.82778i	−0.355755	−	0.0627292i
$850$	33.6465	−	43.0301i	1.15407	−	1.47592i
$851$	17.6281	−	21.0083i	0.604282	−	0.720156i
$852$	−8.03216	+	46.8984i	−0.275177	+	1.60671i
$853$	−11.0695	−	23.7386i	−0.379013	−	0.812795i	−0.999590	−	0.0286494i	$-0.990879\pi$
$853$	−11.0695	−	23.7386i	−0.379013	−	0.812795i	0.620577	−	0.784145i	$-0.286898\pi$
$854$	−32.8841	−	20.8361i	−1.12527	−	0.712997i
$855$	−10.7002	+	3.76515i	−0.365938	+	0.128765i
$856$	4.57610	+	0.568191i	0.156408	+	0.0194204i
$857$	47.7637	−	22.2726i	1.63158	−	0.760817i	0.631682	−	0.775228i	$-0.282365\pi$
$857$	47.7637	−	22.2726i	1.63158	−	0.760817i	0.999896	+	0.0144106i	$0.00458718\pi$
$858$	5.54911	−	2.31450i	0.189443	−	0.0790156i
$859$	28.8366	+	24.1968i	0.983891	+	0.825583i	0.984672	−	0.174417i	$-0.0558041\pi$
$859$	28.8366	+	24.1968i	0.983891	+	0.825583i	−0.000780747		1.00000i	$0.500249\pi$
$860$	−0.828410	−	0.0368991i	−0.0282485	−	0.00125825i
$861$	−0.0654242	+	0.371039i	−0.00222965	+	0.0126450i
$862$	−24.4157	−	7.63237i	−0.831602	−	0.259960i
$863$	3.92637	+	1.05207i	0.133655	+	0.0358128i	0.325026	−	0.945705i	$-0.394627\pi$
$863$	3.92637	+	1.05207i	0.133655	+	0.0358128i	−0.191371	+	0.981518i	$0.561293\pi$
$864$	16.6557	−	13.1084i	0.566639	−	0.445957i
$865$	15.4890	−	14.0289i	0.526643	−	0.476998i
$866$	−1.74870	+	42.4433i	−0.0594233	+	1.44228i
$867$	−84.1101	+	22.5372i	−2.85653	+	0.765404i
$868$	−35.9521	−	20.5222i	−1.22029	−	0.696569i
$869$	−2.34588	−	2.79571i	−0.0795785	−	0.0948380i
$870$	52.5924	+	4.77804i	1.78305	+	0.161991i
$871$	−3.23256	+	0.569988i	−0.109531	+	0.0193133i
$872$	−4.96808	−	15.3612i	−0.168240	−	0.520196i
$873$	−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
$877$	24.3126	+	17.0239i	0.820978	+	0.574855i	0.906851	−	0.421451i	$-0.138479\pi$
$877$	24.3126	+	17.0239i	0.820978	+	0.574855i	−0.0858733	+	0.996306i	$0.527368\pi$
$878$	−40.4387	−	20.9250i	−1.36474	−	0.706184i
$879$	−3.75283	+	3.14899i	−0.126580	+	0.106213i
$880$	1.97170	+	6.16662i	0.0664659	+	0.207877i
$881$	23.0992	−	40.0091i	0.778233	−	1.34794i	−0.154726	−	0.987957i	$-0.549449\pi$
$881$	23.0992	−	40.0091i	0.778233	−	1.34794i	0.932959	−	0.359982i	$-0.117217\pi$
$882$	0.992415	+	1.07771i	0.0334163	+	0.0362882i
$883$	17.4881	−	37.5033i	0.588521	−	1.26209i	−0.356261	−	0.934386i	$-0.615949\pi$
$883$	17.4881	−	37.5033i	0.588521	−	1.26209i	0.944782	−	0.327700i	$-0.106274\pi$
$884$	−31.2907	+	31.5996i	−1.05242	+	1.06281i
$885$	28.8042	−	37.0916i	0.968241	−	1.24682i
$886$	14.3439	+	27.3899i	0.481893	+	0.920183i
$887$	−12.4354	+	8.70734i	−0.417539	+	0.292364i	−0.763405	−	0.645920i	$-0.776474\pi$
$887$	−12.4354	+	8.70734i	−0.417539	+	0.292364i	0.345866	+	0.938284i	$0.387585\pi$
$888$	−47.8023	−	10.2286i	−1.60414	−	0.343251i
$889$	12.5748	−	14.9861i	0.421745	−	0.502617i
$890$	0.115532	−	34.6405i	0.00387264	−	1.16115i
$891$	−2.75713	+	7.57515i	−0.0923673	+	0.253777i
$892$	−14.4339	+	40.2711i	−0.483282	+	1.34838i
$893$	−31.5584	−	29.2054i	−1.05606	−	0.977321i
$894$	−44.0921	−	27.9378i	−1.47466	−	0.934379i
$895$	3.24792	−	3.50354i	0.108566	−	0.117110i
$896$	22.4758	+	16.6404i	0.750863	+	0.555916i
$897$	−18.9452	+	1.65749i	−0.632561	+	0.0553419i
$898$	−1.49001	−	1.13752i	−0.0497223	−	0.0379597i
$899$	−11.9003	+	67.4898i	−0.396897	+	2.25091i
$900$	−7.42110	−	8.96489i	−0.247370	−	0.298830i
$901$	2.48169	+	4.29842i	0.0826771	+	0.143201i
$902$	0.0412427	+	0.0643886i	0.00137323	+	0.00214391i
$903$	0.395248	−	0.847612i	0.0131530	−	0.0282067i
$904$	9.65852	+	22.8403i	0.321238	+	0.759658i
$905$	16.9617	+	22.3720i	0.563826	+	0.743670i
$906$	30.3240	−	33.2564i	1.00745	−	1.10487i
$907$	28.0202	+	2.45145i	0.930395	+	0.0813990i	0.542267	−	0.840206i	$-0.317566\pi$
$907$	28.0202	+	2.45145i	0.930395	+	0.0813990i	0.388128	+	0.921605i	$0.373122\pi$
$908$	−0.800201	−	1.37040i	−0.0265556	−	0.0454783i
$909$	0.548569	−	0.0967275i	0.0181949	−	0.00320825i
$910$	19.4473	+	11.3146i	0.644672	+	0.375074i
$911$		−	1.12748i		−	0.0373552i	−0.999826	−	0.0186776i	$-0.994054\pi$
$911$		−	1.12748i		−	0.0373552i	0.999826	−	0.0186776i	$-0.00594561\pi$
$912$	4.81645	+	35.2505i	0.159489	+	1.16726i
$913$	0.205403	+	0.205403i	0.00679785	+	0.00679785i
$914$	14.8538	−	11.4558i	0.491320	−	0.378924i
$915$	43.0129	−	27.0534i	1.42196	−	0.894356i
$916$	−11.0023	+	41.8830i	−0.363527	+	1.38385i
$917$	−1.24863	+	14.2719i	−0.0412334	+	0.471299i
$918$	−1.88588	−	40.8894i	−0.0622434	−	1.34955i
$919$	−10.9955	+	19.0448i	−0.362708	+	0.628229i	−0.988406	−	0.151837i	$-0.951481\pi$
$919$	−10.9955	+	19.0448i	−0.362708	+	0.628229i	0.625698	+	0.780066i	$0.284814\pi$
$920$	−0.0322779	−	20.4779i	−0.00106417	−	0.675138i
$921$	38.5893	−	14.0453i	1.27156	−	0.462810i
$922$	−2.95862	+	1.89508i	−0.0974370	+	0.0624111i
$923$	32.4159	+	8.68581i	1.06698	+	0.285897i
$924$	−7.27704	−	0.600660i	−0.239397	−	0.0197602i
$925$	7.83648	−	41.6184i	0.257662	−	1.36840i
$926$	−1.46990	−	10.9570i	−0.0483040	−	0.360071i
$927$	0.225166	+	2.57366i	0.00739543	+	0.0845301i
$928$	13.3781	−	44.3203i	0.439159	−	1.45489i
$929$	−2.40016	+	6.59438i	−0.0787467	+	0.216355i	−0.972819	−	0.231569i	$-0.925614\pi$
$929$	−2.40016	+	6.59438i	−0.0787467	+	0.216355i	0.894072	+	0.447924i	$0.147836\pi$
$930$	44.3653	−	30.8449i	1.45480	−	1.01145i
$931$	3.79214	−	0.821111i	0.124282	−	0.0269108i
$932$	−8.38074	−	3.00381i	−0.274520	−	0.0983930i
$933$	−13.9421	−	29.8989i	−0.456444	−	0.978846i
$934$	1.99260	−	4.84418i	0.0651999	−	0.158506i
$935$	11.9024	+	3.82872i	0.389249	+	0.125212i
$936$	5.14959	+	7.95332i	0.168320	+	0.259963i
$937$	29.5722	+	42.2334i	0.966080	+	1.37971i	0.924756	+	0.380560i	$0.124269\pi$
$937$	29.5722	+	42.2334i	0.966080	+	1.37971i	0.0413243	+	0.999146i	$0.486842\pi$
$938$	3.80477	+	1.18937i	0.124230	+	0.0388344i
$939$	−22.9830	−	39.8077i	−0.750021	−	1.29907i
$940$	16.9182	−	40.7428i	0.551811	−	1.32888i
$941$	−34.7687	+	12.6548i	−1.13343	+	0.412533i	−0.839535	−	0.543305i	$-0.817173\pi$
$941$	−34.7687	+	12.6548i	−1.13343	+	0.412533i	−0.293891	+	0.955839i	$0.594950\pi$
$942$	−5.43320	+	5.00321i	−0.177023	+	0.163013i
$943$	−0.0625981	−	0.233619i	−0.00203847	−	0.00760768i
$944$	−26.7720	−	31.2765i	−0.871356	−	1.01796i
$945$	−19.7866	+	6.11294i	−0.643658	+	0.198854i
$946$	−0.0575207	−	0.180882i	−0.00187016	−	0.00588099i
$947$	−20.1302	+	28.7489i	−0.654143	+	0.934214i	−0.999992	−	0.00407689i	$-0.998702\pi$
$947$	−20.1302	+	28.7489i	−0.654143	+	0.934214i	0.345848	+	0.938290i	$0.387591\pi$
$948$	13.1488	−	15.8274i	0.427054	−	0.514050i
$949$			2.89349i			0.0939267i
$950$	−30.4260	+	4.92508i	−0.987151	+	0.159791i
$951$			30.4569i			0.987632i
$952$	51.3866	−	16.6193i	1.66545	−	0.538635i
$953$	−18.7228	+	26.7389i	−0.606490	+	0.866157i	−0.998553	−	0.0537813i	$-0.982873\pi$
$953$	−18.7228	+	26.7389i	−0.606490	+	0.866157i	0.392063	+	0.919938i	$0.371762\pi$
$954$	1.00777	−	0.320471i	0.0326277	−	0.0103756i
$955$	44.9887	−	13.8990i	1.45580	−	0.449760i
$956$	−15.7429	−	57.6200i	−0.509163	−	1.86356i
$957$	3.12855	+	11.6759i	0.101132	+	0.377428i
$958$	−21.4903	−	23.3373i	−0.694321	−	0.753993i
$959$	3.95720	−	1.44030i	0.127785	−	0.0465098i
$960$	−32.2259	+	17.1438i	−1.04009	+	0.553312i
$961$	19.5605	+	33.8797i	0.630983	+	1.09289i
$962$	−10.2871	+	32.9081i	−0.331669	+	1.06100i
$963$	−1.08828	−	1.55423i	−0.0350694	−	0.0500843i
$964$	−18.6185	+	40.4449i	−0.599662	+	1.30264i
$965$	10.9824	+	3.53279i	0.353536	+	0.113725i
$966$	21.3593	+	8.78594i	0.687225	+	0.282683i
$967$	0.665078	+	1.42626i	0.0213875	+	0.0458656i	0.916711	−	0.399550i	$-0.130834\pi$
$967$	0.665078	+	1.42626i	0.0213875	+	0.0458656i	−0.895324	+	0.445416i	$0.853056\pi$
$968$	23.3742	−	18.2108i	0.751274	−	0.585316i
$969$	60.7884	+	32.0262i	1.95280	+	1.02883i
$970$	−12.1792	−	17.5177i	−0.391050	−	0.562461i
$971$	−16.8522	+	46.3010i	−0.540812	+	1.48587i	0.304981	+	0.952358i	$0.401350\pi$
$971$	−16.8522	+	46.3010i	−0.540812	+	1.48587i	−0.845793	+	0.533511i	$0.820872\pi$
$972$	−22.6401	−	3.87751i	−0.726181	−	0.124371i
$973$	0.323961	+	3.70289i	0.0103857	+	0.118709i
$974$	40.1685	−	5.38867i	1.28708	−	0.172664i
$975$	−24.2499	+	16.5648i	−0.776619	+	0.530498i
$976$	−15.6460	−	41.7078i	−0.500817	−	1.33503i
$977$	−16.1364	−	4.32375i	−0.516251	−	0.138329i	−0.00871895	−	0.999962i	$-0.502775\pi$
$977$	−16.1364	−	4.32375i	−0.516251	−	0.138329i	−0.507532	+	0.861633i	$0.669442\pi$
$978$	−7.93798	−	12.3929i	−0.253829	−	0.396280i
$979$	7.45095	−	2.71192i	0.238133	−	0.0866734i
$980$	2.13594	+	3.35926i	0.0682300	+	0.107308i
$981$	−3.32146	+	5.75294i	−0.106046	+	0.183677i
$982$	53.2858	−	2.45763i	1.70042	−	0.0784260i
$983$	5.41485	−	61.8920i	0.172707	−	1.97405i	−0.0485109	−	0.998823i	$-0.515448\pi$
$983$	5.41485	−	61.8920i	0.172707	−	1.97405i	0.221218	−	0.975224i	$-0.428997\pi$
$984$	−0.315700	+	0.293594i	−0.0100642	+	0.00935943i
$985$	−46.1846	+	29.0482i	−1.47156	+	0.925553i
$986$	−54.6013	−	70.7971i	−1.73886	−	2.25464i
$987$	35.1823	+	35.1823i	1.11986	+	1.11986i
$988$	25.0695	−	1.09414i	0.797568	−	0.0348091i
$989$			0.600368i			0.0190906i
$990$	1.33963	−	2.30254i	0.0425762	−	0.0731794i
$991$	−11.2060	+	1.97592i	−0.355970	+	0.0627671i	−0.348774	−	0.937207i	$-0.613402\pi$
$991$	−11.2060	+	1.97592i	−0.355970	+	0.0627671i	−0.00719625	+	0.999974i	$0.502291\pi$
$992$	−18.6635	−	43.5378i	−0.592566	−	1.38233i
$993$	12.3298	+	1.07872i	0.391274	+	0.0342321i
$994$	−30.1160	−	27.4605i	−0.955223	−	0.870995i
$995$	4.35610	+	5.74556i	0.138098	+	0.182147i
$996$	−0.932797	+	1.34620i	−0.0295568	+	0.0426559i
$997$	3.93142	−	8.43096i	0.124509	−	0.267011i	−0.834166	−	0.551513i	$-0.814051\pi$
$997$	3.93142	−	8.43096i	0.124509	−	0.267011i	0.958675	+	0.284502i	$0.0918283\pi$
$998$	3.31571	−	2.12381i	0.104957	−	0.0672279i
$999$	−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.23.3	✓	672
4.3	odd	2	inner	380.2.bj.a.23.19	yes	672
5.2	odd	4	inner	380.2.bj.a.327.31	yes	672
19.5	even	9	inner	380.2.bj.a.43.11	yes	672
20.7	even	4	inner	380.2.bj.a.327.11	yes	672
76.43	odd	18	inner	380.2.bj.a.43.31	yes	672
95.62	odd	36	inner	380.2.bj.a.347.19	yes	672
380.347	even	36	inner	380.2.bj.a.347.3	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.23.3	✓	672	1.1	even	1	trivial
380.2.bj.a.23.19	yes	672	4.3	odd	2	inner
380.2.bj.a.43.11	yes	672	19.5	even	9	inner
380.2.bj.a.43.31	yes	672	76.43	odd	18	inner
380.2.bj.a.327.11	yes	672	20.7	even	4	inner
380.2.bj.a.327.31	yes	672	5.2	odd	4	inner
380.2.bj.a.347.3	yes	672	380.347	even	36	inner
380.2.bj.a.347.19	yes	672	95.62	odd	36	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)

\(f(q)\)	\(=\)	\(q+(-1.40256 - 0.181148i) q^{2} +(-1.67151 - 1.17040i) q^{3} +(1.93437 + 0.508144i) q^{4} +(-0.660038 - 2.13643i) q^{5} +(2.13238 + 1.94436i) q^{6} +(-2.38759 + 0.639752i) q^{7} +(-2.62103 - 1.06311i) q^{8} +(0.398042 + 1.09361i) q^{9} +O(q^{10})\)	\(q+(-1.40256 - 0.181148i) q^{2} +(-1.67151 - 1.17040i) q^{3} +(1.93437 + 0.508144i) q^{4} +(-0.660038 - 2.13643i) q^{5} +(2.13238 + 1.94436i) q^{6} +(-2.38759 + 0.639752i) q^{7} +(-2.62103 - 1.06311i) q^{8} +(0.398042 + 1.09361i) q^{9} +(0.538734 + 3.11605i) q^{10} +(-0.626858 + 0.361917i) q^{11} +(-2.63859 - 3.11336i) q^{12} +(-2.35785 + 1.65099i) q^{13} +(3.46464 - 0.464786i) q^{14} +(-1.39723 + 4.34358i) q^{15} +(3.48358 + 1.96588i) q^{16} +(7.00111 - 3.26467i) q^{17} +(-0.360173 - 1.60596i) q^{18} +(-4.15065 - 1.33122i) q^{19} +(-0.191142 - 4.46805i) q^{20} +(4.73965 + 1.72509i) q^{21} +(0.944769 - 0.394057i) q^{22} +(-3.22553 + 0.282197i) q^{23} +(3.13681 + 4.84467i) q^{24} +(-4.12870 + 2.82026i) q^{25} +(3.60612 - 1.88849i) q^{26} +(-0.969755 + 3.61917i) q^{27} +(-4.94357 + 0.0242799i) q^{28} +(2.79908 + 7.69040i) q^{29} +(2.74654 - 5.83905i) q^{30} +(7.25194 + 4.18691i) q^{31} +(-4.52983 - 3.38831i) q^{32} +(1.47139 + 0.128730i) q^{33} +(-10.4109 + 3.31067i) q^{34} +(2.94269 + 4.67866i) q^{35} +(0.214249 + 2.31771i) q^{36} +(-5.98915 + 5.98915i) q^{37} +(5.58040 + 2.61900i) q^{38} +5.87350 q^{39} +(-0.541290 + 6.30135i) q^{40} +(0.0129711 + 0.0735630i) q^{41} +(-6.33516 - 3.27813i) q^{42} +(0.0161606 - 0.184716i) q^{43} +(-1.39648 + 0.381547i) q^{44} +(2.07370 - 1.57221i) q^{45} +(4.57513 + 0.188499i) q^{46} +(8.94034 + 4.16895i) q^{47} +(-3.52197 - 7.36318i) q^{48} +(-0.770881 + 0.445069i) q^{49} +(6.30165 - 3.20768i) q^{50} +(-15.5234 - 2.73720i) q^{51} +(-5.39990 + 1.99549i) q^{52} +(0.0559993 + 0.640075i) q^{53} +(2.01575 - 4.90045i) q^{54} +(1.18696 + 1.10036i) q^{55} +(6.93807 + 0.861464i) q^{56} +(5.37979 + 7.08308i) q^{57} +(-2.53278 - 11.2933i) q^{58} +(-9.67177 - 3.52024i) q^{59} +(-4.90993 + 7.69211i) q^{60} +(-8.53104 - 7.15839i) q^{61} +(-9.41286 - 7.18609i) q^{62} +(-1.65000 - 2.35644i) q^{63} +(5.73959 + 5.57289i) q^{64} +(5.08350 + 3.94769i) q^{65} +(-2.04040 - 0.447091i) q^{66} +(1.03352 + 0.481938i) q^{67} +(15.2017 - 2.75751i) q^{68} +(5.72179 + 3.30348i) q^{69} +(-3.27978 - 7.09519i) q^{70} +(-7.49426 - 8.93131i) q^{71} +(0.119352 - 3.28955i) q^{72} +(0.576582 - 0.823444i) 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} +(-8.23796 - 1.06397i) q^{78} +(0.875528 + 4.96536i) q^{79} +(1.90067 - 8.73999i) q^{80} +(8.53141 - 7.15870i) q^{81} +(-0.00486705 - 0.105526i) q^{82} +(-0.103868 - 0.387639i) q^{83} +(8.29164 + 5.74539i) q^{84} +(-11.5958 - 12.8026i) q^{85} +(-0.0561272 + 0.256149i) q^{86} +(4.32219 - 16.1306i) q^{87} +(2.02777 - 0.282174i) q^{88} +(-10.7879 - 1.90221i) q^{89} +(-3.19331 + 1.82948i) q^{90} +(4.57336 - 5.45032i) q^{91} +(-6.38277 - 1.09316i) q^{92} +(-7.22132 - 15.4862i) q^{93} +(-11.7842 - 7.46675i) q^{94} +(-0.104475 + 9.74623i) q^{95} +(3.60596 + 10.9653i) q^{96} +(-6.11475 + 2.85135i) q^{97} +(1.16183 - 0.484593i) 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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