LMFDB - Embedded newform 430.2.q.b.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			31.2
Character	$\chi$	$=$	430.31
Dual form			430.2.q.b.111.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.900969 + 0.433884i) q^{2} +(-0.993471 + 0.677337i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(0.601201 - 1.04131i) q^{6} +(-0.895490 - 1.55103i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-0.567823 + 1.44679i) q^{9} +O(q^{10})$	\(q+(-0.900969 + 0.433884i) q^{2} +(-0.993471 + 0.677337i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(0.601201 - 1.04131i) q^{6} +(-0.895490 - 1.55103i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-0.567823 + 1.44679i) q^{9} +(-0.955573 - 0.294755i) q^{10} +(1.01059 + 1.26724i) q^{11} +(-0.0898556 + 1.19904i) q^{12} +(3.87453 - 1.19513i) q^{13} +(1.47978 + 1.00889i) q^{14} +(-1.18897 - 0.179209i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-4.64418 + 4.30917i) q^{17} +(-0.116148 - 1.54988i) q^{18} +(1.64585 + 4.19355i) q^{19} +(0.988831 - 0.149042i) q^{20} +(1.94022 + 0.934359i) q^{21} +(-1.46034 - 0.703264i) q^{22} +(-4.73249 + 0.713308i) q^{23} +(-0.439287 - 1.11928i) q^{24} +(0.0747301 + 0.997204i) q^{25} +(-2.97228 + 2.75788i) q^{26} +(-1.21853 - 5.33872i) q^{27} +(-1.77098 - 0.266932i) q^{28} +(5.04517 + 3.43974i) q^{29} +(1.14898 - 0.354414i) q^{30} +(-0.0732282 + 0.977162i) q^{31} +(0.623490 + 0.781831i) q^{32} +(-1.86234 - 0.574456i) q^{33} +(2.31458 - 5.89746i) q^{34} +(0.398530 - 1.74608i) q^{35} +(0.777114 + 1.34600i) q^{36} +(-4.55060 + 7.88187i) q^{37} +(-3.30237 - 3.06415i) q^{38} +(-3.03973 + 3.81170i) q^{39} +(-0.826239 + 0.563320i) q^{40} +(-5.81655 + 2.80110i) q^{41} -2.15348 q^{42} +(-6.48618 + 0.964089i) q^{43} +1.62086 q^{44} +(-1.40031 + 0.674354i) q^{45} +(3.95433 - 2.69602i) q^{46} +(-7.18618 + 9.01118i) q^{47} +(0.881423 + 0.817841i) q^{48} +(1.89620 - 3.28431i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(1.69510 - 7.42672i) q^{51} +(1.48134 - 3.77439i) q^{52} +(7.40036 + 2.28271i) q^{53} +(3.41424 + 4.28132i) q^{54} +(-0.121127 + 1.61633i) q^{55} +(1.71141 - 0.527900i) q^{56} +(-4.47556 - 3.05138i) q^{57} +(-6.03799 - 0.910081i) q^{58} +(-0.341593 - 1.49662i) q^{59} +(-0.881423 + 0.817841i) q^{60} +(0.840510 + 11.2158i) q^{61} +(-0.357998 - 0.912165i) q^{62} +(2.75250 - 0.414873i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(3.65313 + 1.75926i) q^{65} +(1.92716 - 0.290472i) q^{66} +(-4.98755 - 12.7081i) q^{67} +(0.473445 + 6.31769i) q^{68} +(4.21844 - 3.91414i) q^{69} +(0.398530 + 1.74608i) q^{70} +(12.4442 + 1.87566i) q^{71} +(-1.28416 - 0.875528i) q^{72} +(14.1986 - 4.37968i) q^{73} +(0.680133 - 9.07575i) q^{74} +(-0.749686 - 0.940076i) q^{75} +(4.30482 + 1.32786i) q^{76} +(1.06056 - 2.70226i) q^{77} +(1.08487 - 4.75311i) q^{78} +(-3.15524 - 5.46504i) q^{79} +(0.500000 - 0.866025i) q^{80} +(1.40870 + 1.30708i) q^{81} +(4.02518 - 5.04741i) q^{82} +(9.48908 - 6.46955i) q^{83} +(1.94022 - 0.934359i) q^{84} -6.33541 q^{85} +(5.42554 - 3.68286i) q^{86} -7.34210 q^{87} +(-1.46034 + 0.703264i) q^{88} +(3.21864 - 2.19443i) q^{89} +(0.969046 - 1.21514i) q^{90} +(-5.32330 - 4.93930i) q^{91} +(-2.39297 + 4.14475i) q^{92} +(-0.589118 - 1.02038i) q^{93} +(2.56472 - 11.2368i) q^{94} +(-1.64585 + 4.19355i) q^{95} +(-1.14898 - 0.354414i) q^{96} +(-0.162228 - 0.203428i) q^{97} +(-0.283406 + 3.78179i) q^{98} +(-2.40727 + 0.742543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9}+O(q^{10}) $ 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9} - 4 q^{10} - 9 q^{11} - q^{12} - 11 q^{13} + 7 q^{14} - 6 q^{15} - 8 q^{16} - 11 q^{17} - 15 q^{18} + 31 q^{19} - 4 q^{20} + 4 q^{21} + 12 q^{22} + 4 q^{23} + 6 q^{24} + 4 q^{25} + 31 q^{26} + 44 q^{27} + 13 q^{29} + q^{30} - q^{31} - 8 q^{32} - 30 q^{33} - 25 q^{34} + 14 q^{35} - 36 q^{36} - 27 q^{37} - 4 q^{38} + 4 q^{39} - 4 q^{40} + 16 q^{41} + 4 q^{42} - 7 q^{43} - 30 q^{44} + 12 q^{45} - 52 q^{46} - 43 q^{47} - q^{48} - 23 q^{49} - 24 q^{50} - 7 q^{51} - 25 q^{52} + 73 q^{53} - 61 q^{54} + 27 q^{55} + 7 q^{56} + 136 q^{57} - 36 q^{58} + 58 q^{59} + q^{60} - 61 q^{61} + 27 q^{62} + 32 q^{63} - 8 q^{64} - q^{65} + 12 q^{66} + 39 q^{67} + 17 q^{68} - 34 q^{69} + 14 q^{70} + 60 q^{71} + 27 q^{72} + 3 q^{73} + 29 q^{74} - 12 q^{75} + 17 q^{76} - 27 q^{77} - 17 q^{78} - 2 q^{79} + 24 q^{80} - 165 q^{81} + 2 q^{82} + 74 q^{83} + 4 q^{84} - 8 q^{85} + 14 q^{86} + 88 q^{87} + 12 q^{88} + 23 q^{89} - 2 q^{90} - 39 q^{91} + 4 q^{92} - 46 q^{93} + 55 q^{94} - 31 q^{95} - q^{96} - 85 q^{97} + 33 q^{98} - 168 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9 - 4 * q^10 - 9 * q^11 - q^12 - 11 * q^13 + 7 * q^14 - 6 * q^15 - 8 * q^16 - 11 * q^17 - 15 * q^18 + 31 * q^19 - 4 * q^20 + 4 * q^21 + 12 * q^22 + 4 * q^23 + 6 * q^24 + 4 * q^25 + 31 * q^26 + 44 * q^27 + 13 * q^29 + q^30 - q^31 - 8 * q^32 - 30 * q^33 - 25 * q^34 + 14 * q^35 - 36 * q^36 - 27 * q^37 - 4 * q^38 + 4 * q^39 - 4 * q^40 + 16 * q^41 + 4 * q^42 - 7 * q^43 - 30 * q^44 + 12 * q^45 - 52 * q^46 - 43 * q^47 - q^48 - 23 * q^49 - 24 * q^50 - 7 * q^51 - 25 * q^52 + 73 * q^53 - 61 * q^54 + 27 * q^55 + 7 * q^56 + 136 * q^57 - 36 * q^58 + 58 * q^59 + q^60 - 61 * q^61 + 27 * q^62 + 32 * q^63 - 8 * q^64 - q^65 + 12 * q^66 + 39 * q^67 + 17 * q^68 - 34 * q^69 + 14 * q^70 + 60 * q^71 + 27 * q^72 + 3 * q^73 + 29 * q^74 - 12 * q^75 + 17 * q^76 - 27 * q^77 - 17 * q^78 - 2 * q^79 + 24 * q^80 - 165 * q^81 + 2 * q^82 + 74 * q^83 + 4 * q^84 - 8 * q^85 + 14 * q^86 + 88 * q^87 + 12 * q^88 + 23 * q^89 - 2 * q^90 - 39 * q^91 + 4 * q^92 - 46 * q^93 + 55 * q^94 - 31 * q^95 - q^96 - 85 * q^97 + 33 * q^98 - 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{17}{21}\right)$

Coefficient data

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

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

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

$2$	−0.900969	+	0.433884i	−0.637081	+	0.306802i
$2$	−0.900969	+	0.433884i	−0.637081	+	0.306802i
$3$	−0.993471	+	0.677337i	−0.573581	+	0.391061i	−0.815087	−	0.579338i	$-0.803311\pi$
$3$	−0.993471	+	0.677337i	−0.573581	+	0.391061i	0.241506	+	0.970399i	$0.422359\pi$
$4$	0.623490	−	0.781831i	0.311745	−	0.390916i
$5$	0.733052	+	0.680173i	0.327831	+	0.304182i
$5$	0.733052	+	0.680173i	0.327831	+	0.304182i
$6$	0.601201	−	1.04131i	0.245439	−	0.425113i
$7$	−0.895490	−	1.55103i	−0.338463	−	0.586236i	0.645681	−	0.763608i	$-0.276574\pi$
$7$	−0.895490	−	1.55103i	−0.338463	−	0.586236i	−0.984144	+	0.177372i	$0.943240\pi$
$8$	−0.222521	+	0.974928i	−0.0786730	+	0.344689i
$9$	−0.567823	+	1.44679i	−0.189274	+	0.482263i
$10$	−0.955573	−	0.294755i	−0.302179	−	0.0932098i
$11$	1.01059	+	1.26724i	0.304704	+	0.382087i	0.910483	−	0.413546i	$-0.135710\pi$
$11$	1.01059	+	1.26724i	0.304704	+	0.382087i	−0.605779	+	0.795633i	$0.707138\pi$
$12$	−0.0898556	+	1.19904i	−0.0259391	+	0.346133i
$13$	3.87453	−	1.19513i	1.07460	−	0.331471i	0.293554	−	0.955942i	$-0.405162\pi$
$13$	3.87453	−	1.19513i	1.07460	−	0.331471i	0.781048	+	0.624472i	$0.214686\pi$
$14$	1.47978	+	1.00889i	0.395487	+	0.269638i
$15$	−1.18897	−	0.179209i	−0.306991	−	0.0462715i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	−4.64418	+	4.30917i	−1.12638	+	1.04513i	−0.127802	+	0.991800i	$0.540792\pi$
$17$	−4.64418	+	4.30917i	−1.12638	+	1.04513i	−0.998577	+	0.0533277i	$0.983017\pi$
$18$	−0.116148	−	1.54988i	−0.0273763	−	0.365311i
$19$	1.64585	+	4.19355i	0.377584	+	0.962067i	0.985744	+	0.168253i	$0.0538126\pi$
$19$	1.64585	+	4.19355i	0.377584	+	0.962067i	−0.608160	+	0.793814i	$0.708092\pi$
$20$	0.988831	−	0.149042i	0.221109	−	0.0333269i
$21$	1.94022	+	0.934359i	0.423390	+	0.203894i
$22$	−1.46034	−	0.703264i	−0.311346	−	0.149936i
$23$	−4.73249	+	0.713308i	−0.986793	+	0.148735i	−0.622559	−	0.782573i	$-0.713907\pi$
$23$	−4.73249	+	0.713308i	−0.986793	+	0.148735i	−0.364233	+	0.931308i	$0.618669\pi$
$24$	−0.439287	−	1.11928i	−0.0896691	−	0.228473i
$25$	0.0747301	+	0.997204i	0.0149460	+	0.199441i
$26$	−2.97228	+	2.75788i	−0.582913	+	0.540864i
$27$	−1.21853	−	5.33872i	−0.234506	−	1.02744i
$28$	−1.77098	−	0.266932i	−0.334683	−	0.0504453i
$29$	5.04517	+	3.43974i	0.936865	+	0.638744i	0.932470	−	0.361246i	$-0.117649\pi$
$29$	5.04517	+	3.43974i	0.936865	+	0.638744i	0.00439490	+	0.999990i	$0.498601\pi$
$30$	1.14898	−	0.354414i	0.209775	−	0.0647069i
$31$	−0.0732282	+	0.977162i	−0.0131522	+	0.175504i	0.986759	+	0.162192i	$0.0518564\pi$
$31$	−0.0732282	+	0.977162i	−0.0131522	+	0.175504i	−0.999911	+	0.0133116i	$0.995763\pi$
$32$	0.623490	+	0.781831i	0.110218	+	0.138210i
$33$	−1.86234	−	0.574456i	−0.324192	−	0.0999999i
$34$	2.31458	−	5.89746i	0.396948	−	1.01141i
$35$	0.398530	−	1.74608i	0.0673639	−	0.295141i
$36$	0.777114	+	1.34600i	0.129519	+	0.224334i
$37$	−4.55060	+	7.88187i	−0.748114	+	1.29577i	0.200612	+	0.979671i	$0.435707\pi$
$37$	−4.55060	+	7.88187i	−0.748114	+	1.29577i	−0.948726	+	0.316100i	$0.897626\pi$
$38$	−3.30237	−	3.06415i	−0.535716	−	0.497072i
$39$	−3.03973	+	3.81170i	−0.486746	+	0.610360i
$40$	−0.826239	+	0.563320i	−0.130640	+	0.0890687i
$41$	−5.81655	+	2.80110i	−0.908392	+	0.437459i	−0.828913	−	0.559378i	$-0.811040\pi$
$41$	−5.81655	+	2.80110i	−0.908392	+	0.437459i	−0.0794794	+	0.996837i	$0.525326\pi$
$42$	−2.15348			−0.332289
$43$	−6.48618	+	0.964089i	−0.989133	+	0.147022i
$43$	−6.48618	+	0.964089i	−0.989133	+	0.147022i
$44$	1.62086			0.244354
$45$	−1.40031	+	0.674354i	−0.208746	+	0.100527i
$46$	3.95433	−	2.69602i	0.583035	−	0.397506i
$47$	−7.18618	+	9.01118i	−1.04821	+	1.31442i	−0.100623	+	0.994925i	$0.532084\pi$
$47$	−7.18618	+	9.01118i	−1.04821	+	1.31442i	−0.947589	+	0.319491i	$0.896488\pi$
$48$	0.881423	+	0.817841i	0.127223	+	0.118045i
$49$	1.89620	−	3.28431i	0.270885	−	0.469187i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	1.69510	−	7.42672i	0.237361	−	1.03995i
$52$	1.48134	−	3.77439i	0.205425	−	0.523413i
$53$	7.40036	+	2.28271i	1.01652	+	0.313554i	0.757861	−	0.652415i	$-0.226244\pi$
$53$	7.40036	+	2.28271i	1.01652	+	0.313554i	0.258656	+	0.965970i	$0.416720\pi$
$54$	3.41424	+	4.28132i	0.464619	+	0.582614i
$55$	−0.121127	+	1.61633i	−0.0163328	+	0.217945i
$56$	1.71141	−	0.527900i	0.228697	−	0.0705437i
$57$	−4.47556	−	3.05138i	−0.592802	−	0.404165i
$58$	−6.03799	−	0.910081i	−0.792827	−	0.119499i
$59$	−0.341593	−	1.49662i	−0.0444716	−	0.194843i	0.947812	−	0.318829i	$-0.103289\pi$
$59$	−0.341593	−	1.49662i	−0.0444716	−	0.194843i	−0.992284	+	0.123986i	$0.960432\pi$
$60$	−0.881423	+	0.817841i	−0.113791	+	0.105583i
$61$	0.840510	+	11.2158i	0.107616	+	1.43604i	0.745808	+	0.666161i	$0.232064\pi$
$61$	0.840510	+	11.2158i	0.107616	+	1.43604i	−0.638191	+	0.769878i	$0.720317\pi$
$62$	−0.357998	−	0.912165i	−0.0454659	−	0.115845i
$63$	2.75250	−	0.414873i	0.346782	−	0.0522690i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	3.65313	+	1.75926i	0.453115	+	0.218209i
$66$	1.92716	−	0.290472i	0.237217	−	0.0357547i
$67$	−4.98755	−	12.7081i	−0.609327	−	1.55254i	−0.818406	−	0.574641i	$-0.805142\pi$
$67$	−4.98755	−	12.7081i	−0.609327	−	1.55254i	0.209079	−	0.977899i	$-0.432953\pi$
$68$	0.473445	+	6.31769i	0.0574137	+	0.766133i
$69$	4.21844	−	3.91414i	0.507841	−	0.471208i
$70$	0.398530	+	1.74608i	0.0476335	+	0.208696i
$71$	12.4442	+	1.87566i	1.47686	+	0.222600i	0.837554	−	0.546355i	$-0.183985\pi$
$71$	12.4442	+	1.87566i	1.47686	+	0.222600i	0.639302	+	0.768955i	$0.279223\pi$
$72$	−1.28416	−	0.875528i	−0.151340	−	0.103182i
$73$	14.1986	−	4.37968i	1.66182	−	0.512603i	0.685340	−	0.728223i	$-0.259654\pi$
$73$	14.1986	−	4.37968i	1.66182	−	0.512603i	0.976477	+	0.215620i	$0.0691774\pi$
$74$	0.680133	−	9.07575i	0.0790639	−	1.05503i
$75$	−0.749686	−	0.940076i	−0.0865662	−	0.108551i
$76$	4.30482	+	1.32786i	0.493797	+	0.152316i
$77$	1.06056	−	2.70226i	0.120862	−	0.307951i
$78$	1.08487	−	4.75311i	0.122837	−	0.538184i
$79$	−3.15524	−	5.46504i	−0.354993	−	0.614865i	0.632124	−	0.774867i	$-0.282183\pi$
$79$	−3.15524	−	5.46504i	−0.354993	−	0.614865i	−0.987117	+	0.160002i	$0.948850\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	1.40870	+	1.30708i	0.156522	+	0.145231i
$82$	4.02518	−	5.04741i	0.444506	−	0.557393i
$83$	9.48908	−	6.46955i	1.04156	−	0.710125i	0.0834479	−	0.996512i	$-0.473407\pi$
$83$	9.48908	−	6.46955i	1.04156	−	0.710125i	0.958114	+	0.286387i	$0.0924544\pi$
$84$	1.94022	−	0.934359i	0.211695	−	0.101947i
$85$	−6.33541			−0.687171
$86$	5.42554	−	3.68286i	0.585051	−	0.397133i
$87$	−7.34210			−0.787156
$88$	−1.46034	+	0.703264i	−0.155673	+	0.0749682i
$89$	3.21864	−	2.19443i	0.341175	−	0.232609i	−0.380595	−	0.924742i	$-0.624281\pi$
$89$	3.21864	−	2.19443i	0.341175	−	0.232609i	0.721771	+	0.692132i	$0.243329\pi$
$90$	0.969046	−	1.21514i	0.102146	−	0.128087i
$91$	−5.32330	−	4.93930i	−0.558033	−	0.517779i
$92$	−2.39297	+	4.14475i	−0.249485	+	0.432120i
$93$	−0.589118	−	1.02038i	−0.0610887	−	0.105809i
$94$	2.56472	−	11.2368i	0.264530	−	1.15898i
$95$	−1.64585	+	4.19355i	−0.168861	+	0.430250i
$96$	−1.14898	−	0.354414i	−0.117268	−	0.0361723i
$97$	−0.162228	−	0.203428i	−0.0164718	−	0.0206549i	0.773527	−	0.633763i	$-0.218490\pi$
$97$	−0.162228	−	0.203428i	−0.0164718	−	0.0206549i	−0.789999	+	0.613108i	$0.789919\pi$
$98$	−0.283406	+	3.78179i	−0.0286283	+	0.382018i
$99$	−2.40727	+	0.742543i	−0.241939	+	0.0746284i
$100$	0.826239	+	0.563320i	0.0826239	+	0.0563320i
$101$	−1.11894	−	0.168653i	−0.111339	−	0.0167816i	0.0931365	−	0.995653i	$-0.470311\pi$
$101$	−1.11894	−	0.168653i	−0.111339	−	0.0167816i	−0.204475	+	0.978872i	$0.565549\pi$
$102$	1.69510	+	7.42672i	0.167840	+	0.735354i
$103$	12.0515	−	11.1821i	1.18747	−	1.10181i	0.194812	−	0.980841i	$-0.437590\pi$
$103$	12.0515	−	11.1821i	1.18747	−	1.10181i	0.992656	−	0.120969i	$-0.0386001\pi$
$104$	0.303006	+	4.04333i	0.0297122	+	0.396481i
$105$	0.786754	+	2.00462i	0.0767793	+	0.195630i
$106$	−7.65792	+	1.15425i	−0.743803	+	0.112110i
$107$	8.07829	+	3.89030i	0.780958	+	0.376089i	0.781496	−	0.623910i	$-0.214457\pi$
$107$	8.07829	+	3.89030i	0.780958	+	0.376089i	−0.000538087		1.00000i	$0.500171\pi$
$108$	−4.93372	−	2.37595i	−0.474747	−	0.228626i
$109$	−7.08188	+	1.06742i	−0.678321	+	0.102240i	−0.479162	−	0.877727i	$-0.659059\pi$
$109$	−7.08188	+	1.06742i	−0.678321	+	0.102240i	−0.199159	+	0.979967i	$0.563821\pi$
$110$	−0.592166	−	1.50882i	−0.0564608	−	0.143860i
$111$	−0.817794	−	10.9127i	−0.0776215	−	1.03579i
$112$	−1.31288	+	1.21818i	−0.124056	+	0.115107i
$113$	3.42874	+	15.0223i	0.322549	+	1.41318i	0.833001	+	0.553272i	$0.186621\pi$
$113$	3.42874	+	15.0223i	0.322549	+	1.41318i	−0.510452	+	0.859906i	$0.670522\pi$
$114$	5.35628	+	0.807329i	0.501662	+	0.0756133i
$115$	−3.95433	−	2.69602i	−0.368744	−	0.251405i
$116$	5.83491	−	1.79983i	0.541758	−	0.167110i
$117$	−0.470940	+	6.28426i	−0.0435384	+	0.580980i
$118$	0.957123	+	1.20019i	0.0881103	+	0.110487i
$119$	10.8425	+	3.34446i	0.993929	+	0.306586i
$120$	0.439287	−	1.11928i	0.0401012	−	0.102176i
$121$	1.86313	−	8.16289i	0.169375	−	0.742081i
$122$	−5.62364	−	9.74043i	−0.509140	−	0.881857i
$123$	3.88128	−	6.72258i	0.349964	−	0.606155i
$124$	0.718319	+	0.666503i	0.0645070	+	0.0598537i
$125$	−0.623490	+	0.781831i	−0.0557666	+	0.0699291i
$126$	−2.29991	+	1.56805i	−0.204892	+	0.139693i
$127$	5.93738	−	2.85929i	0.526857	−	0.253721i	−0.151495	−	0.988458i	$-0.548409\pi$
$127$	5.93738	−	2.85929i	0.526857	−	0.253721i	0.678352	+	0.734737i	$0.262694\pi$
$128$	1.00000			0.0883883
$129$	5.79082	−	5.35113i	0.509853	−	0.471141i
$130$	−4.05467			−0.355618
$131$	−1.46646	+	0.706209i	−0.128125	+	0.0617018i	−0.496848	−	0.867838i	$-0.665509\pi$
$131$	−1.46646	+	0.706209i	−0.128125	+	0.0617018i	0.368723	+	0.929539i	$0.379795\pi$
$132$	−1.61028	+	1.09787i	−0.140157	+	0.0955572i
$133$	5.03050	−	6.30805i	0.436200	−	0.546977i
$134$	10.0075	+	9.28557i	0.864513	+	0.802151i
$135$	2.73801	−	4.74237i	0.235650	−	0.408158i
$136$	−3.16770	−	5.48662i	−0.271628	−	0.470474i
$137$	−1.44715	+	6.34037i	−0.123638	+	0.541694i	0.874731	+	0.484609i	$0.161038\pi$
$137$	−1.44715	+	6.34037i	−0.123638	+	0.541694i	−0.998369	+	0.0570856i	$0.981819\pi$
$138$	−2.10240	+	5.35684i	−0.178968	+	0.456004i
$139$	−8.87185	−	2.73660i	−0.752500	−	0.232116i	−0.105305	−	0.994440i	$-0.533582\pi$
$139$	−8.87185	−	2.73660i	−0.752500	−	0.232116i	−0.647195	+	0.762324i	$0.724058\pi$
$140$	−1.11666	−	1.40024i	−0.0943748	−	0.118342i
$141$	1.03565	−	13.8198i	0.0872177	−	1.16384i
$142$	−12.0257	+	3.70943i	−1.00917	+	0.311288i
$143$	5.43008	+	3.70217i	0.454086	+	0.309591i
$144$	1.53687	+	0.231646i	0.128072	+	0.0193038i
$145$	1.35876	+	5.95310i	0.112839	+	0.494378i
$146$	−10.8922	+	10.1065i	−0.901445	+	0.836419i
$147$	0.340768	+	4.54723i	0.0281061	+	0.375049i
$148$	3.32504	+	8.47206i	0.273317	+	0.696399i
$149$	5.69301	−	0.858083i	0.466389	−	0.0702969i	0.0883562	−	0.996089i	$-0.471839\pi$
$149$	5.69301	−	0.858083i	0.466389	−	0.0702969i	0.378033	+	0.925792i	$0.376601\pi$
$150$	1.08333	+	0.521703i	0.0884533	+	0.0425969i
$151$	−4.07833	−	1.96402i	−0.331890	−	0.159830i	0.260516	−	0.965470i	$-0.416107\pi$
$151$	−4.07833	−	1.96402i	−0.331890	−	0.159830i	−0.592406	+	0.805640i	$0.701822\pi$
$152$	−4.45465	+	0.671430i	−0.361320	+	0.0544602i
$153$	−3.59739	−	9.16601i	−0.290832	−	0.741028i
$154$	0.216936	+	2.89481i	0.0174812	+	0.233270i
$155$	−0.718319	+	0.666503i	−0.0576968	+	0.0535348i
$156$	1.08487	+	4.75311i	0.0868588	+	0.380553i
$157$	−6.65185	−	1.00260i	−0.530875	−	0.0800166i	−0.121866	−	0.992547i	$-0.538888\pi$
$157$	−6.65185	−	1.00260i	−0.530875	−	0.0800166i	−0.409010	+	0.912530i	$0.634126\pi$
$158$	5.21397	+	3.55482i	0.414801	+	0.282807i
$159$	−8.89821	+	2.74473i	−0.705674	+	0.217672i
$160$	−0.0747301	+	0.997204i	−0.00590793	+	0.0788359i
$161$	5.34426	+	6.70149i	0.421187	+	0.528152i
$162$	−1.83631	−	0.566428i	−0.144274	−	0.0445028i
$163$	−3.68924	+	9.40004i	−0.288964	+	0.736268i	0.710505	+	0.703692i	$0.248466\pi$
$163$	−3.68924	+	9.40004i	−0.288964	+	0.736268i	−0.999469	+	0.0325762i	$0.989629\pi$
$164$	−1.43657	+	6.29402i	−0.112177	+	0.491480i
$165$	−0.974463	−	1.68782i	−0.0758618	−	0.131396i
$166$	−5.74234	+	9.94602i	−0.445692	+	0.771961i
$167$	−4.14399	−	3.84506i	−0.320672	−	0.297540i	0.503368	−	0.864072i	$-0.332094\pi$
$167$	−4.14399	−	3.84506i	−0.320672	−	0.297540i	−0.824039	+	0.566532i	$0.808285\pi$
$168$	−1.34267	+	1.68366i	−0.103589	+	0.129897i
$169$	2.84255	−	1.93802i	0.218658	−	0.149078i
$170$	5.70800	−	2.74883i	0.437784	−	0.210826i
$171$	−7.00175			−0.535437
$172$	−3.29031	+	5.67220i	−0.250884	+	0.432501i
$173$	−14.7590			−1.12210			−0.561052	−	0.827781i	$-0.689603\pi$
$173$	−14.7590			−1.12210			−0.561052	+	0.827781i	$0.689603\pi$
$174$	6.61501	−	3.18562i	0.501482	−	0.241501i
$175$	1.47978	−	1.00889i	0.111861	−	0.0762653i
$176$	1.01059	−	1.26724i	0.0761760	−	0.0955217i
$177$	1.35308	+	1.25547i	0.101704	+	0.0943671i
$178$	−1.94777	+	3.37363i	−0.145991	+	0.252864i
$179$	−5.33742	−	9.24468i	−0.398937	−	0.690980i	0.594658	−	0.803979i	$-0.297288\pi$
$179$	−5.33742	−	9.24468i	−0.398937	−	0.690980i	−0.993595	+	0.112999i	$0.963954\pi$
$180$	−0.345848	+	1.51526i	−0.0257780	+	0.112941i
$181$	4.44297	−	11.3205i	0.330243	−	0.841446i	−0.665251	−	0.746620i	$-0.731675\pi$
$181$	4.44297	−	11.3205i	0.330243	−	0.841446i	0.995494	−	0.0948261i	$-0.0302295\pi$
$182$	6.93921	+	2.14046i	0.514368	+	0.158662i
$183$	−8.43192	−	10.5733i	−0.623306	−	0.781600i
$184$	0.357654	−	4.77256i	0.0263666	−	0.351838i
$185$	−8.69685	+	2.68262i	−0.639405	+	0.197230i
$186$	0.973505	+	0.663724i	0.0713808	+	0.0486666i
$187$	−10.1541	−	1.53049i	−0.742542	−	0.111920i
$188$	2.56472	+	11.2368i	0.187051	+	0.819525i
$189$	−7.18935	+	6.67075i	−0.522949	+	0.485225i
$190$	−0.336657	−	4.49237i	−0.0244236	−	0.325911i
$191$	−1.36127	−	3.46845i	−0.0984978	−	0.250968i	0.873128	−	0.487491i	$-0.162088\pi$
$191$	−1.36127	−	3.46845i	−0.0984978	−	0.250968i	−0.971626	+	0.236522i	$0.923992\pi$
$192$	1.18897	−	0.179209i	0.0858067	−	0.0129333i
$193$	24.0458	+	11.5799i	1.73086	+	0.833537i	0.986090	+	0.166211i	$0.0531533\pi$
$193$	24.0458	+	11.5799i	1.73086	+	0.833537i	0.744766	+	0.667325i	$0.232561\pi$
$194$	0.234426	+	0.112894i	0.0168308	+	0.00810530i
$195$	−4.82089	+	0.726632i	−0.345231	+	0.0520352i
$196$	−1.38552	−	3.53024i	−0.0989655	−	0.252160i
$197$	−1.08532	−	14.4826i	−0.0773261	−	1.03185i	−0.892032	−	0.451971i	$-0.850721\pi$
$197$	−1.08532	−	14.4826i	−0.0773261	−	1.03185i	0.814706	−	0.579874i	$-0.196898\pi$
$198$	1.84669	−	1.71348i	0.131239	−	0.121772i
$199$	3.05937	+	13.4040i	0.216873	+	0.950184i	0.959772	+	0.280780i	$0.0905932\pi$
$199$	3.05937	+	13.4040i	0.216873	+	0.950184i	−0.742899	+	0.669404i	$0.766550\pi$
$200$	−0.988831	−	0.149042i	−0.0699209	−	0.0105389i
$201$	13.5627	+	9.24686i	0.956636	+	0.652223i
$202$	1.08131	−	0.333539i	0.0760805	−	0.0234677i
$203$	0.817253	−	10.9055i	0.0573599	−	0.765415i
$204$	−4.74956	−	5.95576i	−0.332536	−	0.416987i
$205$	−6.16906	−	1.90290i	−0.430866	−	0.132905i
$206$	−6.00626	+	15.3037i	−0.418476	+	1.06626i
$207$	1.65521	−	7.25196i	0.115045	−	0.504046i
$208$	−2.02733	−	3.51145i	−0.140570	−	0.243475i
$209$	−3.65096	+	6.32364i	−0.252542	+	0.437416i
$210$	−1.57861	−	1.46474i	−0.108934	−	0.101076i
$211$	3.52845	−	4.42454i	0.242909	−	0.304598i	−0.645400	−	0.763845i	$-0.723309\pi$
$211$	3.52845	−	4.42454i	0.242909	−	0.304598i	0.888309	+	0.459247i	$0.151881\pi$
$212$	6.39874	−	4.36259i	0.439467	−	0.299624i
$213$	−13.6334	+	6.56551i	−0.934147	+	0.449861i
$214$	−8.96623			−0.612919
$215$	−5.41045	−	3.70500i	−0.368990	−	0.252679i
$216$	5.47602			0.372596
$217$	1.58119	−	0.761459i	0.107338	−	0.0516912i
$218$	5.91741	−	4.03442i	0.400778	−	0.273246i
$219$	−11.1394	+	13.9683i	−0.752728	+	0.943891i
$220$	1.18817	+	1.10246i	0.0801067	+	0.0743281i
$221$	−12.8440	+	22.2464i	−0.863980	+	1.49646i
$222$	5.47165	+	9.47717i	0.367233	+	0.636066i
$223$	−2.97598	+	13.0386i	−0.199286	+	0.873130i	0.772077	+	0.635529i	$0.219218\pi$
$223$	−2.97598	+	13.0386i	−0.199286	+	0.873130i	−0.971363	+	0.237601i	$0.923639\pi$
$224$	0.654318	−	1.66718i	0.0437185	−	0.111393i
$225$	−1.48518	−	0.458117i	−0.0990119	−	0.0305411i
$226$	−9.60711	−	12.0469i	−0.639056	−	0.801351i
$227$	−0.879577	+	11.7371i	−0.0583796	+	0.779022i	0.888795	+	0.458304i	$0.151543\pi$
$227$	−0.879577	+	11.7371i	−0.0583796	+	0.779022i	−0.947175	+	0.320717i	$0.896076\pi$
$228$	−5.17613	+	1.59662i	−0.342798	+	0.105739i
$229$	8.00889	+	5.46037i	0.529242	+	0.360831i	0.798269	−	0.602302i	$-0.205750\pi$
$229$	8.00889	+	5.46037i	0.529242	+	0.360831i	−0.269026	+	0.963133i	$0.586702\pi$
$230$	4.73249	+	0.713308i	0.312051	+	0.0470342i
$231$	0.776706	+	3.40297i	0.0511035	+	0.223899i
$232$	−4.47616	+	4.15327i	−0.293874	+	0.272675i
$233$	−0.626319	−	8.35765i	−0.0410315	−	0.547528i	−0.979405	−	0.201905i	$-0.935287\pi$
$233$	−0.626319	−	8.35765i	−0.0410315	−	0.547528i	0.938374	−	0.345623i	$-0.112332\pi$
$234$	−2.30234	−	5.86626i	−0.150508	−	0.383489i
$235$	−11.3970	+	1.71782i	−0.743458	+	0.112058i
$236$	−1.38308	−	0.666057i	−0.0900310	−	0.0433566i
$237$	6.83632	+	3.29220i	0.444067	+	0.213851i
$238$	−11.2198	+	1.69112i	−0.727275	+	0.109619i
$239$	−2.46987	−	6.29313i	−0.159763	−	0.407069i	0.828469	−	0.560035i	$-0.189212\pi$
$239$	−2.46987	−	6.29313i	−0.159763	−	0.407069i	−0.988231	+	0.152967i	$0.951117\pi$
$240$	0.0898556	+	1.19904i	0.00580016	+	0.0773977i
$241$	14.8160	−	13.7473i	0.954386	−	0.885540i	−0.0391303	−	0.999234i	$-0.512459\pi$
$241$	14.8160	−	13.7473i	0.954386	−	0.885540i	0.993516	+	0.113694i	$0.0362683\pi$
$242$	1.86313	+	8.16289i	0.119766	+	0.524731i
$243$	13.9597	+	2.10409i	0.895517	+	0.134977i
$244$	9.29294	+	6.33582i	0.594919	+	0.405609i
$245$	3.62391	−	1.11783i	0.231523	−	0.0714154i
$246$	−0.580097	+	7.74086i	−0.0369857	+	0.493539i
$247$	11.3888	+	14.2810i	0.724649	+	0.908681i
$248$	−0.936368	−	0.288831i	−0.0594594	−	0.0183408i
$249$	−5.04507	+	12.8546i	−0.319718	+	0.814628i
$250$	0.222521	−	0.974928i	0.0140735	−	0.0616599i
$251$	0.843139	+	1.46036i	0.0532185	+	0.0921771i	0.891407	−	0.453203i	$-0.149719\pi$
$251$	0.843139	+	1.46036i	0.0532185	+	0.0921771i	−0.838189	+	0.545380i	$0.816385\pi$
$252$	1.39180	−	2.41066i	0.0876749	−	0.151857i
$253$	−5.68654	−	5.27633i	−0.357509	−	0.331720i
$254$	−4.10879	+	5.15226i	−0.257808	+	0.323282i
$255$	6.29405	−	4.29121i	0.394148	−	0.268726i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	21.6099			1.34799			0.673996	−	0.738735i	$-0.264577\pi$
$257$	21.6099			1.34799			0.673996	+	0.738735i	$0.264577\pi$
$258$	−2.89558	+	7.33374i	−0.180271	+	0.456579i
$259$	16.3000			1.01284
$260$	3.65313	−	1.75926i	0.226558	−	0.109104i
$261$	−7.84135	+	5.34614i	−0.485368	+	0.330918i
$262$	1.01482	−	1.27254i	0.0626958	−	0.0786181i
$263$	−1.35147	−	1.25398i	−0.0833350	−	0.0773236i	0.637406	−	0.770528i	$-0.280008\pi$
$263$	−1.35147	−	1.25398i	−0.0833350	−	0.0773236i	−0.720741	+	0.693205i	$0.756198\pi$
$264$	0.974463	−	1.68782i	0.0599740	−	0.103878i
$265$	3.87221	+	6.70686i	0.237868	+	0.411999i
$266$	−1.79537	+	7.86601i	−0.110081	+	0.482296i
$267$	−1.71126	+	4.36021i	−0.104727	+	0.266841i
$268$	−13.0453	−	4.02393i	−0.796867	−	0.245801i
$269$	−8.48728	−	10.6427i	−0.517479	−	0.648898i	0.452593	−	0.891717i	$-0.350499\pi$
$269$	−8.48728	−	10.6427i	−0.517479	−	0.648898i	−0.970071	+	0.242820i	$0.921928\pi$
$270$	−0.409223	+	5.46070i	−0.0249045	+	0.332328i
$271$	−19.1607	+	5.91031i	−1.16393	+	0.359026i	−0.815752	−	0.578402i	$-0.803677\pi$
$271$	−19.1607	+	5.91031i	−1.16393	+	0.359026i	−0.348181	+	0.937427i	$0.613200\pi$
$272$	5.23456	+	3.56886i	0.317392	+	0.216394i
$273$	8.63412	+	1.30138i	0.522560	+	0.0787633i
$274$	−1.44715	−	6.34037i	−0.0874254	−	0.383036i
$275$	−1.18817	+	1.10246i	−0.0716496	+	0.0664811i
$276$	−0.430044	−	5.73854i	−0.0258856	−	0.345420i
$277$	−6.23509	−	15.8867i	−0.374630	−	0.954542i	−0.986526	−	0.163604i	$-0.947688\pi$
$277$	−6.23509	−	15.8867i	−0.374630	−	0.954542i	0.611896	−	0.790938i	$-0.290407\pi$
$278$	9.18063	−	1.38376i	0.550617	−	0.0829922i
$279$	−1.37217	−	0.660801i	−0.0821496	−	0.0395611i
$280$	1.61362	+	0.777077i	0.0964320	+	0.0464392i
$281$	−17.1248	+	2.58115i	−1.02158	+	0.153979i	−0.638408	−	0.769698i	$-0.720407\pi$
$281$	−17.1248	+	2.58115i	−1.02158	+	0.153979i	−0.383173	+	0.923677i	$0.625169\pi$
$282$	5.06311	+	12.9006i	0.301504	+	0.768218i
$283$	0.0448635	+	0.598661i	0.00266686	+	0.0355867i	0.998378	−	0.0569248i	$-0.0181295\pi$
$283$	0.0448635	+	0.598661i	0.00266686	+	0.0355867i	−0.995712	+	0.0925116i	$0.970510\pi$
$284$	9.22529	−	8.55982i	0.547420	−	0.507932i
$285$	−1.20535	−	5.28097i	−0.0713986	−	0.312818i
$286$	−6.49864	−	0.979513i	−0.384273	−	0.0579198i
$287$	9.55326	+	6.51330i	0.563911	+	0.384468i
$288$	−1.48518	+	0.458117i	−0.0875150	+	0.0269948i
$289$	1.72906	−	23.0727i	0.101709	−	1.35722i
$290$	−3.80715	−	4.77401i	−0.223564	−	0.280340i
$291$	0.298958	+	0.0922164i	0.0175252	+	0.00540582i
$292$	5.42849	−	13.8316i	0.317679	−	0.809432i
$293$	4.56671	−	20.0081i	0.266790	−	1.16888i	−0.646933	−	0.762547i	$-0.723949\pi$
$293$	4.56671	−	20.0081i	0.266790	−	1.16888i	0.913723	−	0.406337i	$-0.133194\pi$
$294$	−2.27999	−	3.94906i	−0.132972	−	0.230314i
$295$	0.767553	−	1.32944i	0.0446887	−	0.0774030i
$296$	−6.67165	−	6.19038i	−0.387782	−	0.359809i
$297$	5.53400	−	6.93942i	0.321115	−	0.402666i
$298$	−4.75691	+	3.24321i	−0.275561	+	0.187874i
$299$	−17.4837	+	8.41970i	−1.01111	+	0.486924i
$300$	−1.20240			−0.0694207
$301$	7.30364	+	9.19695i	0.420975	+	0.530103i
$302$	4.52660			0.260477
$303$	1.22587	−	0.590349i	0.0704245	−	0.0339146i
$304$	3.72218	−	2.53774i	0.213482	−	0.145549i
$305$	−7.01256	+	8.79347i	−0.401538	+	0.503513i
$306$	7.21812	+	6.69744i	0.412632	+	0.382867i
$307$	−12.4022	+	21.4813i	−0.707834	+	1.22600i	0.257826	+	0.966191i	$0.416994\pi$
$307$	−12.4022	+	21.4813i	−0.707834	+	1.22600i	−0.965659	+	0.259812i	$0.916339\pi$
$308$	−1.45146	−	2.51401i	−0.0827048	−	0.143249i
$309$	−4.39872	+	19.2721i	−0.250235	+	1.09635i
$310$	0.357998	−	0.912165i	0.0203329	−	0.0518075i
$311$	19.0958	+	5.89027i	1.08282	+	0.334006i	0.784291	−	0.620393i	$-0.213027\pi$
$311$	19.0958	+	5.89027i	1.08282	+	0.334006i	0.298531	+	0.954400i	$0.403503\pi$
$312$	−3.03973	−	3.81170i	−0.172091	−	0.215795i
$313$	−0.716060	+	9.55516i	−0.0404741	+	0.540089i	0.939706	+	0.341983i	$0.111098\pi$
$313$	−0.716060	+	9.55516i	−0.0404741	+	0.540089i	−0.980180	+	0.198107i	$0.936521\pi$
$314$	6.42812	−	1.98281i	0.362760	−	0.111897i
$315$	2.29991	+	1.56805i	0.129585	+	0.0883497i
$316$	−6.24001	−	0.940529i	−0.351028	−	0.0529089i
$317$	−2.81747	−	12.3442i	−0.158245	−	0.693317i	−0.990337	−	0.138680i	$-0.955714\pi$
$317$	−2.81747	−	12.3442i	−0.158245	−	0.693317i	0.832092	−	0.554637i	$-0.187143\pi$
$318$	6.82611	−	6.33371i	0.382789	−	0.355177i
$319$	0.739625	+	9.86961i	0.0414110	+	0.552592i
$320$	−0.365341	−	0.930874i	−0.0204232	−	0.0520374i
$321$	−10.6606	+	1.60683i	−0.595016	+	0.0896843i
$322$	−7.72268	−	3.71905i	−0.430368	−	0.207254i
$323$	−25.7144	−	12.3834i	−1.43079	−	0.689030i
$324$	1.90023	−	0.286413i	0.105568	−	0.0159118i
$325$	1.48134	+	3.77439i	0.0821698	+	0.209365i
$326$	−0.754631	−	10.0698i	−0.0417951	−	0.557717i
$327$	6.31264	−	5.85727i	0.349090	−	0.323908i
$328$	−1.43657	−	6.29402i	−0.0793212	−	0.347529i
$329$	20.4118	+	3.07658i	1.12534	+	0.169618i
$330$	1.61028	+	1.09787i	0.0886429	+	0.0604357i
$331$	3.82269	−	1.17914i	0.210114	−	0.0648117i	−0.187911	−	0.982186i	$-0.560172\pi$
$331$	3.82269	−	1.17914i	0.210114	−	0.0648117i	0.398026	+	0.917374i	$0.369696\pi$
$332$	0.858251	−	11.4526i	0.0471026	−	0.628541i
$333$	−8.81947	−	11.0593i	−0.483304	−	0.606044i
$334$	5.40192	+	1.66627i	0.295580	+	0.0911743i
$335$	4.98755	−	12.7081i	0.272499	−	0.694317i
$336$	0.479194	−	2.09949i	0.0261422	−	0.114536i
$337$	−8.36821	−	14.4942i	−0.455846	−	0.789548i	0.542891	−	0.839803i	$-0.317330\pi$
$337$	−8.36821	−	14.4942i	−0.455846	−	0.789548i	−0.998736	+	0.0502554i	$0.983996\pi$
$338$	−1.72017	+	2.97943i	−0.0935651	+	0.162059i
$339$	−13.5815	−	12.6018i	−0.737647	−	0.684436i
$340$	−3.95006	+	4.95322i	−0.214222	+	0.268626i
$341$	−1.31230	+	0.894712i	−0.0710651	+	0.0484514i
$342$	6.30836	−	3.03794i	0.341117	−	0.164273i
$343$	−19.3290			−1.04367
$344$	0.503393	−	6.53809i	0.0271412	−	0.352510i
$345$	5.75463			0.309819
$346$	13.2974	−	6.40368i	0.714871	−	0.344264i
$347$	15.7072	−	10.7090i	0.843206	−	0.574888i	−0.0628609	−	0.998022i	$-0.520022\pi$
$347$	15.7072	−	10.7090i	0.843206	−	0.574888i	0.906067	+	0.423134i	$0.139070\pi$
$348$	−4.57773	+	5.74029i	−0.245392	+	0.307712i
$349$	10.4988	+	9.74143i	0.561986	+	0.521447i	0.909211	−	0.416335i	$-0.136686\pi$
$349$	10.4988	+	9.74143i	0.561986	+	0.521447i	−0.347225	+	0.937782i	$0.612876\pi$
$350$	−0.895490	+	1.55103i	−0.0478659	+	0.0829062i
$351$	−11.1017	−	19.2287i	−0.592566	−	1.02635i
$352$	−0.360675	+	1.58022i	−0.0192240	+	0.0842261i
$353$	1.66540	−	4.24337i	0.0886403	−	0.225852i	−0.879679	−	0.475569i	$-0.842242\pi$
$353$	1.66540	−	4.24337i	0.0886403	−	0.225852i	0.968319	+	0.249717i	$0.0803376\pi$
$354$	−1.76381	−	0.544064i	−0.0937455	−	0.0289167i
$355$	7.84648	+	9.83917i	0.416448	+	0.522209i
$356$	0.291114	−	3.88464i	0.0154290	−	0.205886i
$357$	−13.0370	+	4.02139i	−0.689993	+	0.212835i
$358$	8.81996	+	6.01335i	0.466149	+	0.317815i
$359$	−13.7212	−	2.06814i	−0.724178	−	0.109152i	−0.223398	−	0.974727i	$-0.571715\pi$
$359$	−13.7212	−	2.06814i	−0.724178	−	0.109152i	−0.500779	+	0.865575i	$0.666953\pi$
$360$	−0.345848	−	1.51526i	−0.0182278	−	0.0798612i
$361$	−0.949095	+	0.880631i	−0.0499524	+	0.0463490i
$362$	0.908804	+	12.1272i	0.0477657	+	0.637389i
$363$	3.67807	+	9.37157i	0.193049	+	0.491880i
$364$	−7.18072	+	1.08232i	−0.376372	+	0.0567290i
$365$	13.3872	+	6.44695i	0.700720	+	0.337449i
$366$	12.1845	+	5.86774i	0.636893	+	0.306711i
$367$	34.9326	−	5.26525i	1.82347	−	0.274844i	0.854038	−	0.520211i	$-0.174147\pi$
$367$	34.9326	−	5.26525i	1.82347	−	0.274844i	0.969430	+	0.245367i	$0.0789085\pi$
$368$	1.74850	+	4.45511i	0.0911470	+	0.232239i
$369$	−0.749835	−	10.0059i	−0.0390349	−	0.520884i
$370$	6.67165	−	6.19038i	0.346842	−	0.321823i
$371$	−3.08639	−	13.5223i	−0.160237	−	0.702045i
$372$	−1.16508	−	0.175607i	−0.0604064	−	0.00910480i
$373$	7.24879	+	4.94214i	0.375328	+	0.255894i	0.736261	−	0.676697i	$-0.236589\pi$
$373$	7.24879	+	4.94214i	0.375328	+	0.255894i	−0.360933	+	0.932592i	$0.617542\pi$
$374$	9.81259	−	3.02678i	0.507397	−	0.156511i
$375$	0.0898556	−	1.19904i	0.00464013	−	0.0619182i
$376$	−7.18618	−	9.01118i	−0.370599	−	0.464716i
$377$	23.6586	+	7.29773i	1.21848	+	0.375852i
$378$	3.58306	−	9.12948i	0.184293	−	0.469570i
$379$	5.53552	−	24.2527i	0.284341	−	1.24578i	−0.607826	−	0.794071i	$-0.707958\pi$
$379$	5.53552	−	24.2527i	0.284341	−	1.24578i	0.892166	−	0.451707i	$-0.149185\pi$
$380$	2.25248	+	3.90141i	0.115550	+	0.200138i
$381$	−3.96191	+	6.86223i	−0.202975	+	0.351563i
$382$	2.73136	+	2.53434i	0.139749	+	0.129668i
$383$	−16.7101	+	20.9538i	−0.853845	+	1.07069i	0.142874	+	0.989741i	$0.454366\pi$
$383$	−16.7101	+	20.9538i	−0.853845	+	1.07069i	−0.996718	+	0.0809465i	$0.974206\pi$
$384$	−0.993471	+	0.677337i	−0.0506979	+	0.0345652i
$385$	2.61545	−	1.25953i	0.133295	−	0.0641917i
$386$	−26.6889			−1.35843
$387$	2.28817	−	9.93158i	0.116314	−	0.504850i
$388$	−0.260194			−0.0132093
$389$	−13.5534	+	6.52699i	−0.687186	+	0.330931i	−0.744687	−	0.667414i	$-0.767401\pi$
$389$	−13.5534	+	6.52699i	−0.687186	+	0.330931i	0.0575006	+	0.998345i	$0.481687\pi$
$390$	4.02820	−	2.74638i	0.203976	−	0.139068i
$391$	18.9048	−	23.7058i	0.956056	−	1.19886i
$392$	2.78002	+	2.57948i	0.140412	+	0.130284i
$393$	0.978543	−	1.69489i	0.0493609	−	0.0854957i
$394$	7.26162	+	12.5775i	0.365835	+	0.633645i
$395$	1.40422	−	6.15227i	0.0706538	−	0.309554i
$396$	−0.920362	+	2.34504i	−0.0462499	+	0.117843i
$397$	32.0537	+	9.88727i	1.60873	+	0.496228i	0.963488	−	0.267750i	$-0.0862802\pi$
$397$	32.0537	+	9.88727i	1.60873	+	0.496228i	0.645242	+	0.763978i	$0.276756\pi$
$398$	−8.57218	−	10.7492i	−0.429684	−	0.538807i
$399$	−0.724982	+	9.67422i	−0.0362945	+	0.484317i
$400$	0.955573	−	0.294755i	0.0477786	−	0.0147378i
$401$	27.0231	+	18.4240i	1.34947	+	0.920051i	0.999858	−	0.0168441i	$-0.00536189\pi$
$401$	27.0231	+	18.4240i	1.34947	+	0.920051i	0.349609	+	0.936896i	$0.386314\pi$
$402$	−16.2316	−	2.44652i	−0.809558	−	0.122021i
$403$	0.884116	+	3.87356i	0.0440409	+	0.192956i
$404$	−0.829507	+	0.769670i	−0.0412695	+	0.0382925i
$405$	0.143608	+	1.91632i	0.00713594	+	0.0952225i
$406$	3.99539	+	10.1801i	0.198288	+	0.505230i
$407$	−14.5870	+	2.19863i	−0.723050	+	0.108982i
$408$	6.86332	+	3.30520i	0.339785	+	0.163632i
$409$	−17.4466	−	8.40185i	−0.862680	−	0.415445i	−0.0504116	−	0.998729i	$-0.516053\pi$
$409$	−17.4466	−	8.40185i	−0.862680	−	0.415445i	−0.812268	+	0.583284i	$0.801768\pi$
$410$	6.38377	−	0.962199i	0.315272	−	0.0475196i
$411$	−2.85687	−	7.27918i	−0.140919	−	0.359056i
$412$	−1.22857	−	16.3942i	−0.0605275	−	0.807684i
$413$	−2.01541	+	1.87003i	−0.0991719	+	0.0920181i
$414$	1.65521	+	7.25196i	0.0813492	+	0.356414i
$415$	11.3564	+	1.71170i	0.557464	+	0.0840241i
$416$	3.35013	+	2.28408i	0.164253	+	0.111986i
$417$	10.6675	−	3.29050i	0.522391	−	0.161136i
$418$	0.545673	−	7.28150i	0.0266897	−	0.356150i
$419$	22.5348	+	28.2577i	1.10090	+	1.38048i	0.917639	+	0.397415i	$0.130093\pi$
$419$	22.5348	+	28.2577i	1.10090	+	1.38048i	0.183257	+	0.983065i	$0.441336\pi$
$420$	2.05780	+	0.634749i	0.100411	+	0.0309726i
$421$	10.8134	−	27.5522i	0.527014	−	1.34281i	−0.381273	−	0.924463i	$-0.624514\pi$
$421$	10.8134	−	27.5522i	0.527014	−	1.34281i	0.908287	−	0.418348i	$-0.137391\pi$
$422$	−1.25929	+	5.51731i	−0.0613013	+	0.268579i
$423$	−8.95681	−	15.5137i	−0.435495	−	0.754300i
$424$	−3.87221	+	6.70686i	−0.188051	+	0.325714i
$425$	−4.64418	−	4.30917i	−0.225276	−	0.209025i
$426$	9.43462	−	11.8306i	0.457109	−	0.573196i
$427$	16.6435	−	11.3473i	0.805433	−	0.549135i
$428$	8.07829	−	3.89030i	0.390479	−	0.188045i
$429$	−7.90225			−0.381524
$430$	6.48219	+	0.990578i	0.312599	+	0.0477699i
$431$	−8.11795			−0.391028			−0.195514	−	0.980701i	$-0.562637\pi$
$431$	−8.11795			−0.391028			−0.195514	+	0.980701i	$0.562637\pi$
$432$	−4.93372	+	2.37595i	−0.237374	+	0.114313i
$433$	−7.48917	+	5.10603i	−0.359907	+	0.245380i	−0.729750	−	0.683714i	$-0.760364\pi$
$433$	−7.48917	+	5.10603i	−0.359907	+	0.245380i	0.369844	+	0.929094i	$0.379411\pi$
$434$	−1.09421	+	1.37210i	−0.0525240	+	0.0658630i
$435$	−5.38214	−	4.99390i	−0.258054	−	0.239439i
$436$	−3.58093	+	6.20236i	−0.171496	+	0.297039i
$437$	−10.7803	−	18.6720i	−0.515690	−	0.893201i
$438$	3.97559	−	17.4182i	0.189961	−	0.832274i
$439$	−11.5140	+	29.3372i	−0.549534	+	1.40019i	0.338741	+	0.940880i	$0.389999\pi$
$439$	−11.5140	+	29.3372i	−0.549534	+	1.40019i	−0.888276	+	0.459311i	$0.848096\pi$
$440$	−1.54885	−	0.477757i	−0.0738385	−	0.0227762i
$441$	3.67500	+	4.60831i	0.175000	+	0.219443i
$442$	1.91967	−	25.6162i	0.0913092	−	1.21844i
$443$	10.5015	−	3.23930i	0.498943	−	0.153904i	−0.0350614	−	0.999385i	$-0.511163\pi$
$443$	10.5015	−	3.23930i	0.498943	−	0.153904i	0.534005	+	0.845482i	$0.320686\pi$
$444$	−9.04178	−	6.16458i	−0.429104	−	0.292558i
$445$	3.85202	+	0.580599i	0.182603	+	0.0275230i
$446$	−2.97598	−	13.0386i	−0.140917	−	0.617396i
$447$	−5.07463	+	4.70857i	−0.240022	+	0.222708i
$448$	0.133840	+	1.78597i	0.00632335	+	0.0843792i
$449$	−14.3188	−	36.4838i	−0.675747	−	1.72178i	−0.691989	−	0.721908i	$-0.743265\pi$
$449$	−14.3188	−	36.4838i	−0.675747	−	1.72178i	0.0162417	−	0.999868i	$-0.494830\pi$
$450$	1.53687	−	0.231646i	0.0724487	−	0.0109199i
$451$	−9.42781	−	4.54019i	−0.443938	−	0.213789i
$452$	13.8827	+	6.68555i	0.652986	+	0.314462i
$453$	5.38201	−	0.811207i	0.252869	−	0.0381138i
$454$	−4.30008	−	10.9564i	−0.201813	−	0.514211i
$455$	−0.542677	−	7.24152i	−0.0254411	−	0.339488i
$456$	3.97078	−	3.68435i	0.185949	−	0.172535i
$457$	3.55860	+	15.5913i	0.166464	+	0.729328i	0.987392	+	0.158296i	$0.0505999\pi$
$457$	3.55860	+	15.5913i	0.166464	+	0.729328i	−0.820927	+	0.571033i	$0.806543\pi$
$458$	−9.58492	−	1.44469i	−0.447874	−	0.0675062i
$459$	28.6645	+	19.5431i	1.33795	+	0.912196i
$460$	−4.57332	+	1.41068i	−0.213232	+	0.0657734i
$461$	−2.44255	+	32.5936i	−0.113761	+	1.51804i	0.589886	+	0.807486i	$0.299173\pi$
$461$	−2.44255	+	32.5936i	−0.113761	+	1.51804i	−0.703647	+	0.710549i	$0.748446\pi$
$462$	−2.17628	−	2.72897i	−0.101250	−	0.126963i
$463$	17.2609	+	5.32428i	0.802181	+	0.247440i	0.668624	−	0.743601i	$-0.266884\pi$
$463$	17.2609	+	5.32428i	0.802181	+	0.247440i	0.133558	+	0.991041i	$0.457360\pi$
$464$	2.23084	−	5.68410i	0.103564	−	0.263878i
$465$	0.262182	−	1.14870i	0.0121584	−	0.0532695i
$466$	4.19054	+	7.25823i	0.194123	+	0.336231i
$467$	1.99942	−	3.46309i	0.0925220	−	0.160253i	−0.816050	−	0.577982i	$-0.803840\pi$
$467$	1.99942	−	3.46309i	0.0925220	−	0.160253i	0.908572	+	0.417729i	$0.137174\pi$
$468$	4.61961	+	4.28637i	0.213541	+	0.198137i
$469$	−15.2444	+	19.1158i	−0.703919	+	0.882686i
$470$	9.52301	−	6.49268i	0.439264	−	0.299485i
$471$	7.28752	−	3.50949i	0.335791	−	0.161709i
$472$	1.53511			0.0706590
$473$	−7.77659	−	7.24524i	−0.357568	−	0.333137i
$474$	−7.58775			−0.348517
$475$	−4.05883	+	1.95463i	−0.186232	+	0.0896846i
$476$	9.37498	−	6.39176i	0.429702	−	0.292966i
$477$	−7.50470	+	9.41059i	−0.343616	+	0.430881i
$478$	4.95576	+	4.59828i	0.226671	+	0.210320i
$479$	5.76341	−	9.98252i	0.263337	−	0.456113i	−0.703790	−	0.710409i	$-0.748510\pi$
$479$	5.76341	−	9.98252i	0.263337	−	0.456113i	0.967127	+	0.254295i	$0.0818435\pi$
$480$	−0.601201	−	1.04131i	−0.0274410	−	0.0475291i
$481$	−8.21154	+	35.9771i	−0.374414	+	1.64042i
$482$	−7.38408	+	18.8143i	−0.336335	+	0.856969i
$483$	−9.84854	−	3.03787i	−0.448124	−	0.138228i
$484$	−5.22037	−	6.54613i	−0.237289	−	0.297551i
$485$	0.0194443	−	0.259466i	0.000882920	−	0.0117818i
$486$	−13.4902	+	4.16118i	−0.611928	+	0.188755i
$487$	15.0484	+	10.2598i	0.681909	+	0.464918i	0.854075	−	0.520150i	$-0.174124\pi$
$487$	15.0484	+	10.2598i	0.681909	+	0.464918i	−0.172166	+	0.985068i	$0.555076\pi$
$488$	−11.1217	−	1.67632i	−0.503454	−	0.0758834i
$489$	−2.70184	−	11.8375i	−0.122181	−	0.535312i
$490$	−2.78002	+	2.57948i	−0.125589	+	0.116529i
$491$	−1.51590	−	20.2283i	−0.0684116	−	0.912890i	−0.920814	−	0.390003i	$-0.872474\pi$
$491$	−1.51590	−	20.2283i	−0.0684116	−	0.912890i	0.852402	−	0.522887i	$-0.175145\pi$
$492$	−2.83598	−	7.22597i	−0.127856	−	0.325772i
$493$	−38.2531	+	5.76573i	−1.72283	+	0.259676i
$494$	−16.4572	−	7.92538i	−0.740446	−	0.356580i
$495$	−2.26971	−	1.09303i	−0.102016	−	0.0491282i
$496$	0.968958	−	0.146047i	0.0435075	−	0.00655770i
$497$	−8.23444	−	20.9810i	−0.369365	−	0.941127i
$498$	−1.03196	−	13.7706i	−0.0462433	−	0.617075i
$499$	−12.4206	+	11.5246i	−0.556022	+	0.515913i	−0.907370	−	0.420332i	$-0.861914\pi$
$499$	−12.4206	+	11.5246i	−0.556022	+	0.515913i	0.351349	+	0.936245i	$0.385723\pi$
$500$	0.222521	+	0.974928i	0.00995144	+	0.0436001i
$501$	6.72134	+	1.01308i	0.300287	+	0.0452611i
$502$	−1.39327	−	0.949914i	−0.0621846	−	0.0423968i
$503$	12.6069	−	3.88872i	0.562115	−	0.173390i	−0.000659577	−	1.00000i	$-0.500210\pi$
$503$	12.6069	−	3.88872i	0.562115	−	0.173390i	0.562775	+	0.826610i	$0.309734\pi$
$504$	−0.208018	+	2.77581i	−0.00926586	+	0.123644i
$505$	−0.705529	−	0.884705i	−0.0313956	−	0.0393689i
$506$	7.41271	+	2.28652i	0.329535	+	0.101648i
$507$	−1.51130	+	3.85073i	−0.0671192	+	0.171017i
$508$	1.46641	−	6.42476i	0.0650614	−	0.285053i
$509$	7.24918	+	12.5559i	0.321314	+	0.556533i	0.980759	−	0.195220i	$-0.0625421\pi$
$509$	7.24918	+	12.5559i	0.321314	+	0.556533i	−0.659445	+	0.751753i	$0.729209\pi$
$510$	−3.80885	+	6.59713i	−0.168659	+	0.292126i
$511$	−19.5077	−	18.1005i	−0.862970	−	0.800719i
$512$	0.623490	−	0.781831i	0.0275546	−	0.0345524i
$513$	20.3827	−	13.8967i	0.899918	−	0.613554i
$514$	−19.4699	+	9.37620i	−0.858780	+	0.413567i
$515$	16.4402			0.724440
$516$	−0.573162	−	7.86382i	−0.0252320	−	0.346185i
$517$	−18.6816			−0.821616
$518$	−14.6858	+	7.07233i	−0.645259	+	0.310740i
$519$	14.6626	−	9.99681i	0.643618	−	0.438811i
$520$	−2.52805	+	3.17007i	−0.110862	+	0.139017i
$521$	9.40287	+	8.72459i	0.411947	+	0.382231i	0.858745	−	0.512404i	$-0.171245\pi$
$521$	9.40287	+	8.72459i	0.411947	+	0.382231i	−0.446797	+	0.894635i	$0.647435\pi$
$522$	4.74521	−	8.21894i	0.207692	−	0.359733i
$523$	14.1807	+	24.5617i	0.620079	+	1.07401i	0.989470	+	0.144735i	$0.0462329\pi$
$523$	14.1807	+	24.5617i	0.620079	+	1.07401i	−0.369391	+	0.929274i	$0.620434\pi$
$524$	−0.362185	+	1.58684i	−0.0158221	+	0.0693213i
$525$	−0.786754	+	2.00462i	−0.0343367	+	0.0874886i
$526$	1.76171	+	0.543415i	0.0768142	+	0.0236940i
$527$	−3.87067	−	4.85367i	−0.168609	−	0.211429i
$528$	−0.145643	+	1.94348i	−0.00633831	+	0.0845789i
$529$	−0.0905112	+	0.0279190i	−0.00393527	+	0.00121387i
$530$	−6.39874	−	4.36259i	−0.277944	−	0.189499i
$531$	2.35926	+	0.355601i	0.102383	+	0.0154318i
$532$	−1.79537	−	7.86601i	−0.0778390	−	0.341035i
$533$	−19.1887	+	17.8045i	−0.831155	+	0.771199i
$534$	−0.350036	−	4.67090i	−0.0151475	−	0.202130i
$535$	3.27573	+	8.34642i	0.141622	+	0.360847i
$536$	13.4993	−	2.03469i	0.583081	−	0.0878853i
$537$	11.5643	+	5.56909i	0.499038	+	0.240324i
$538$	12.2645	+	5.90626i	0.528759	+	0.254637i
$539$	6.07828	−	0.916153i	0.261810	−	0.0394615i
$540$	−2.00061	−	5.09748i	−0.0860927	−	0.219361i
$541$	−1.49012	−	19.8842i	−0.0640651	−	0.854890i	−0.932980	−	0.359928i	$-0.882801\pi$
$541$	−1.49012	−	19.8842i	−0.0640651	−	0.854890i	0.868915	−	0.494962i	$-0.164818\pi$
$542$	14.6989	−	13.6385i	0.631370	−	0.585826i
$543$	3.25384	+	14.2560i	0.139635	+	0.611783i
$544$	−6.26464	−	0.944243i	−0.268594	−	0.0404841i
$545$	−5.91741	−	4.03442i	−0.253474	−	0.172816i
$546$	−8.34372	+	2.57370i	−0.357078	+	0.110144i
$547$	−3.12540	+	41.7055i	−0.133632	+	1.78320i	0.379800	+	0.925069i	$0.375993\pi$
$547$	−3.12540	+	41.7055i	−0.133632	+	1.78320i	−0.513433	+	0.858130i	$0.671626\pi$
$548$	4.05482	+	5.08458i	0.173213	+	0.217203i
$549$	−16.7042	−	5.15257i	−0.712918	−	0.219906i
$550$	0.592166	−	1.50882i	0.0252501	−	0.0643361i
$551$	−6.12115	+	26.8185i	−0.260770	+	1.14251i
$552$	2.87732	+	4.98366i	0.122467	+	0.212119i
$553$	−5.65098	+	9.78778i	−0.240304	+	0.416219i
$554$	12.5106	+	11.6082i	0.531525	+	0.493183i
$555$	6.82303	−	8.55582i	0.289622	−	0.363174i
$556$	−7.67107	+	5.23005i	−0.325326	+	0.221803i
$557$	−20.4830	+	9.86408i	−0.867892	+	0.417955i	−0.814187	−	0.580602i	$-0.802817\pi$
$557$	−20.4830	+	9.86408i	−0.867892	+	0.417955i	−0.0537043	+	0.998557i	$0.517103\pi$
$558$	1.52299			0.0644734
$559$	−23.9787	+	11.4873i	−1.01419	+	0.485859i
$560$	−1.79098			−0.0756827
$561$	11.1245	−	5.35726i	0.469676	−	0.226184i
$562$	14.3090	−	9.75572i	0.603589	−	0.411520i
$563$	−21.2487	+	26.6450i	−0.895525	+	1.12295i	0.0963008	+	0.995352i	$0.469299\pi$
$563$	−21.2487	+	26.6450i	−0.895525	+	1.12295i	−0.991826	+	0.127600i	$0.959273\pi$
$564$	−10.1591	−	9.42622i	−0.427773	−	0.396916i
$565$	−7.70431	+	13.3443i	−0.324123	+	0.561397i
$566$	−0.300170	−	0.519910i	−0.0126171	−	0.0218534i
$567$	0.765851	−	3.35541i	0.0321627	−	0.140914i
$568$	−4.59773	+	11.7148i	−0.192917	+	0.491543i
$569$	−32.8110	−	10.1209i	−1.37551	−	0.424288i	−0.483119	−	0.875554i	$-0.660496\pi$
$569$	−32.8110	−	10.1209i	−1.37551	−	0.424288i	−0.892389	+	0.451266i	$0.850972\pi$
$570$	3.37731	+	4.23501i	0.141460	+	0.177385i
$571$	3.18113	−	42.4493i	0.133126	−	1.77645i	−0.386730	−	0.922193i	$-0.626395\pi$
$571$	3.18113	−	42.4493i	0.133126	−	1.77645i	0.519856	−	0.854254i	$-0.325986\pi$
$572$	6.28007	−	1.93715i	0.262583	−	0.0809961i
$573$	3.70169	+	2.52377i	0.154640	+	0.105432i
$574$	−11.4332	−	1.72328i	−0.477213	−	0.0719283i
$575$	−1.06497	−	4.66595i	−0.0444125	−	0.194584i
$576$	1.13933	−	1.05714i	0.0474721	−	0.0440477i
$577$	−1.14988	−	15.3440i	−0.0478700	−	0.638781i	−0.968607	−	0.248597i	$-0.920030\pi$
$577$	−1.14988	−	15.3440i	−0.0478700	−	0.638781i	0.920737	−	0.390184i	$-0.127589\pi$
$578$	8.45303	+	21.5380i	0.351600	+	0.895861i
$579$	−31.7323	+	4.78288i	−1.31875	+	0.198770i
$580$	5.50149	+	2.64938i	0.228437	+	0.110009i
$581$	−18.5319	−	8.92447i	−0.768831	−	0.370249i
$582$	−0.309363	+	0.0466290i	−0.0128235	+	0.00193283i
$583$	4.58599	+	11.6849i	0.189932	+	0.483939i
$584$	1.11039	+	14.8172i	0.0459484	+	0.613138i
$585$	−4.61961	+	4.28637i	−0.190997	+	0.177220i
$586$	4.56671	+	20.0081i	0.188649	+	0.826525i
$587$	−25.9414	−	3.91004i	−1.07072	−	0.161385i	−0.410049	−	0.912063i	$-0.634489\pi$
$587$	−25.9414	−	3.91004i	−1.07072	−	0.161385i	−0.660667	+	0.750679i	$0.729727\pi$
$588$	3.76764	+	2.56873i	0.155375	+	0.105933i
$589$	−4.21831	+	1.30117i	−0.173812	+	0.0536140i
$590$	−0.114719	+	1.53081i	−0.00472289	+	0.0630226i
$591$	10.8879	+	13.6530i	0.447867	+	0.561608i
$592$	8.69685	+	2.68262i	0.357439	+	0.110255i
$593$	9.15752	−	23.3330i	0.376054	−	0.958171i	−0.610098	−	0.792326i	$-0.708870\pi$
$593$	9.15752	−	23.3330i	0.376054	−	0.958171i	0.986152	−	0.165845i	$-0.0530350\pi$
$594$	−1.97506	+	8.65331i	−0.0810378	+	0.355050i
$595$	5.67329	+	9.82643i	0.232582	+	0.402844i
$596$	2.87866	−	4.98598i	0.117914	−	0.204234i
$597$	−12.1184	−	11.2443i	−0.495974	−	0.460197i
$598$	12.0991	−	15.1718i	0.494769	−	0.620420i
$599$	12.2377	−	8.34352i	0.500019	−	0.340907i	−0.286903	−	0.957960i	$-0.592626\pi$
$599$	12.2377	−	8.34352i	0.500019	−	0.340907i	0.786922	+	0.617053i	$0.211673\pi$
$600$	1.08333	−	0.521703i	0.0442266	−	0.0212984i
$601$	21.9268			0.894414			0.447207	−	0.894431i	$-0.352419\pi$
$601$	21.9268			0.894414			0.447207	+	0.894431i	$0.352419\pi$
$602$	−10.5708	−	5.11723i	−0.430832	−	0.208563i
$603$	21.2180			0.864063
$604$	−4.07833	+	1.96402i	−0.165945	+	0.0799148i
$605$	6.91794	−	4.71657i	0.281254	−	0.191756i
$606$	−0.848330	+	1.06377i	−0.0344610	+	0.0432128i
$607$	17.8853	+	16.5951i	0.725941	+	0.673575i	0.953910	−	0.300094i	$-0.0970179\pi$
$607$	17.8853	+	16.5951i	0.725941	+	0.673575i	−0.227969	+	0.973668i	$0.573208\pi$
$608$	−2.25248	+	3.90141i	−0.0913502	+	0.158223i
$609$	6.57478	+	11.3878i	0.266423	+	0.461459i
$610$	2.50275	−	10.9653i	0.101334	−	0.443971i
$611$	−17.0735	+	43.5026i	−0.690720	+	1.75993i
$612$	−9.40921	−	2.90236i	−0.380345	−	0.117321i
$613$	−7.47776	−	9.37682i	−0.302024	−	0.378726i	0.607541	−	0.794289i	$-0.292156\pi$
$613$	−7.47776	−	9.37682i	−0.302024	−	0.378726i	−0.909565	+	0.415563i	$0.863585\pi$
$614$	1.85364	−	24.7351i	0.0748069	−	0.998229i
$615$	7.41770	−	2.28806i	0.299110	−	0.0922634i
$616$	2.39851	+	1.63528i	0.0966387	+	0.0658871i
$617$	−2.96641	−	0.447114i	−0.119423	−	0.0180001i	0.0890588	−	0.996026i	$-0.471614\pi$
$617$	−2.96641	−	0.447114i	−0.119423	−	0.0180001i	−0.208482	+	0.978026i	$0.566852\pi$
$618$	−4.39872	−	19.2721i	−0.176943	−	0.775236i
$619$	11.8408	−	10.9866i	0.475920	−	0.441590i	−0.405379	−	0.914149i	$-0.632860\pi$
$619$	11.8408	−	10.9866i	0.475920	−	0.441590i	0.881299	+	0.472559i	$0.156670\pi$
$620$	0.0732282	+	0.977162i	0.00294091	+	0.0392438i
$621$	9.57483	+	24.3963i	0.384225	+	0.978988i
$622$	−19.7604	+	2.97840i	−0.792319	+	0.119423i
$623$	−6.28590	−	3.02713i	−0.251839	−	0.121279i
$624$	4.39253	+	2.11533i	0.175842	+	0.0846811i
$625$	−0.988831	+	0.149042i	−0.0395532	+	0.00596169i
$626$	−3.50068	−	8.91959i	−0.139915	−	0.356498i
$627$	−0.656118	−	8.75529i	−0.0262028	−	0.349653i
$628$	−4.93123	+	4.57551i	−0.196777	+	0.182583i
$629$	−12.8305	−	56.2141i	−0.511586	−	2.24140i
$630$	−2.75250	−	0.414873i	−0.109662	−	0.0165289i
$631$	28.7297	+	19.5875i	1.14371	+	0.779768i	0.978450	−	0.206482i	$-0.0662016\pi$
$631$	28.7297	+	19.5875i	1.14371	+	0.779768i	0.165259	+	0.986250i	$0.447154\pi$
$632$	6.03013	−	1.86005i	0.239866	−	0.0739888i
$633$	−0.508511	+	6.78561i	−0.0202115	+	0.269704i
$634$	7.89438	+	9.89924i	0.313526	+	0.393149i
$635$	6.29721	+	1.94243i	0.249897	+	0.0770831i
$636$	−3.40202	+	8.66821i	−0.134899	+	0.343717i
$637$	3.42168	−	14.9914i	0.135572	−	0.593980i
$638$	−4.94864	−	8.57130i	−0.195919	−	0.339341i
$639$	−9.77980	+	16.9391i	−0.386883	+	0.670101i
$640$	0.733052	+	0.680173i	0.0289764	+	0.0268862i
$641$	−21.9552	+	27.5309i	−0.867178	+	1.08741i	0.128236	+	0.991744i	$0.459069\pi$
$641$	−21.9552	+	27.5309i	−0.867178	+	1.08741i	−0.995414	+	0.0956629i	$0.969503\pi$
$642$	8.90769	−	6.07316i	0.351558	−	0.239689i
$643$	−17.5658	+	8.45923i	−0.692726	+	0.333599i	−0.746904	−	0.664932i	$-0.768461\pi$
$643$	−17.5658	+	8.45923i	−0.692726	+	0.333599i	0.0541778	+	0.998531i	$0.482746\pi$
$644$	8.57153			0.337766
$645$	7.88466	+	0.0161049i	0.310458	+	0.000634128i
$646$	28.5408			1.12292
$647$	17.9803	−	8.65884i	0.706877	−	0.340414i	−0.0456663	−	0.998957i	$-0.514541\pi$
$647$	17.9803	−	8.65884i	0.706877	−	0.340414i	0.752543	+	0.658543i	$0.228827\pi$
$648$	−1.58777	+	1.08253i	−0.0623736	+	0.0425256i
$649$	1.55136	−	1.94535i	0.0608963	−	0.0763615i
$650$	−2.97228	−	2.75788i	−0.116583	−	0.108173i
$651$	−1.05510	+	1.82748i	−0.0413526	+	0.0716248i
$652$	5.04904	+	8.74520i	0.197736	+	0.342488i
$653$	6.84769	−	30.0017i	0.267971	−	1.17406i	−0.644399	−	0.764690i	$-0.722892\pi$
$653$	6.84769	−	30.0017i	0.267971	−	1.17406i	0.912370	−	0.409368i	$-0.134251\pi$
$654$	−3.14612	+	8.01617i	−0.123023	+	0.313457i
$655$	−1.55533	−	0.479757i	−0.0607719	−	0.0187457i
$656$	4.02518	+	5.04741i	0.157157	+	0.197068i
$657$	−1.72580	+	23.0292i	−0.0673300	+	0.898456i
$658$	−19.7253	+	6.08444i	−0.768971	+	0.237196i
$659$	−8.30791	−	5.66424i	−0.323630	−	0.220647i	0.390596	−	0.920562i	$-0.372269\pi$
$659$	−8.30791	−	5.66424i	−0.323630	−	0.220647i	−0.714226	+	0.699915i	$0.753221\pi$
$660$	−1.92716	−	0.290472i	−0.0750145	−	0.0113066i
$661$	3.56518	+	15.6201i	0.138669	+	0.607550i	0.995728	+	0.0923316i	$0.0294320\pi$
$661$	3.56518	+	15.6201i	0.138669	+	0.607550i	−0.857059	+	0.515218i	$0.827711\pi$
$662$	−2.93252	+	2.72098i	−0.113975	+	0.105754i
$663$	−2.30821	−	30.8009i	−0.0896434	−	1.19621i
$664$	4.19582	+	10.6908i	0.162829	+	0.414883i
$665$	7.97818	−	1.20252i	0.309381	−	0.0466316i
$666$	12.7445	+	6.13743i	0.493840	+	0.237821i
$667$	−26.3298	−	12.6798i	−1.01950	−	0.490963i
$668$	−5.58993	+	0.842546i	−0.216281	+	0.0325991i
$669$	−5.87499	−	14.9692i	−0.227140	−	0.578744i
$670$	1.02020	+	13.6136i	0.0394137	+	0.525939i
$671$	−13.3637	+	12.3997i	−0.515901	+	0.478686i
$672$	0.479194	+	2.09949i	0.0184853	+	0.0809894i
$673$	26.4120	+	3.98097i	1.01811	+	0.153455i	0.636829	−	0.771005i	$-0.280246\pi$
$673$	26.4120	+	3.98097i	1.01811	+	0.153455i	0.381278	+	0.924460i	$0.375484\pi$
$674$	13.8283	+	9.42797i	0.532646	+	0.363152i
$675$	5.23273	−	1.61408i	0.201408	−	0.0621261i
$676$	0.257097	−	3.43073i	0.00988836	−	0.131951i
$677$	20.8143	+	26.1003i	0.799960	+	1.00312i	0.999729	+	0.0232748i	$0.00740927\pi$
$677$	20.8143	+	26.1003i	0.799960	+	1.00312i	−0.199769	+	0.979843i	$0.564019\pi$
$678$	17.7042	+	5.46103i	0.679927	+	0.209730i
$679$	−0.170249	+	0.433789i	−0.00653358	+	0.0166473i
$680$	1.40976	−	6.17656i	0.0540618	−	0.236860i
$681$	−7.07617	−	12.2563i	−0.271159	−	0.469662i
$682$	0.794142	−	1.37549i	0.0304093	−	0.0526704i
$683$	32.8905	+	30.5179i	1.25852	+	1.16774i	0.978163	+	0.207840i	$0.0666435\pi$
$683$	32.8905	+	30.5179i	1.25852	+	1.16774i	0.280357	+	0.959896i	$0.409547\pi$
$684$	−4.36552	+	5.47419i	−0.166920	+	0.209311i
$685$	−5.37338	+	3.66351i	−0.205306	+	0.139975i
$686$	17.4148	−	8.38652i	0.664900	−	0.320199i
$687$	−11.6551			−0.444670
$688$	2.38323	+	6.10903i	0.0908597	+	0.232905i
$689$	31.4011			1.19629
$690$	−5.18475	+	2.49684i	−0.197380	+	0.0950531i
$691$	23.3452	−	15.9165i	0.888093	−	0.605492i	−0.0310056	−	0.999519i	$-0.509871\pi$
$691$	23.3452	−	15.9165i	0.888093	−	0.605492i	0.919099	+	0.394028i	$0.128919\pi$
$692$	−9.20207	+	11.5390i	−0.349810	+	0.438648i
$693$	3.30739	+	3.06881i	0.125637	+	0.116574i
$694$	−9.50524	+	16.4636i	−0.360814	+	0.624948i
$695$	−4.64216	−	8.04046i	−0.176087	−	0.304992i
$696$	1.63377	−	7.15802i	0.0619279	−	0.271324i
$697$	14.9427	−	38.0733i	0.565994	−	1.44213i
$698$	−13.6857	−	4.22148i	−0.518012	−	0.159786i
$699$	6.28318	+	7.87886i	0.237652	+	0.298006i
$700$	0.133840	−	1.78597i	0.00505868	−	0.0675034i
$701$	−30.5711	+	9.42995i	−1.15466	+	0.356164i	−0.812205	−	0.583371i	$-0.801733\pi$
$701$	−30.5711	+	9.42995i	−1.15466	+	0.356164i	−0.342451	+	0.939536i	$0.611257\pi$
$702$	18.3453	+	12.5076i	0.692400	+	0.472070i
$703$	−40.5426	−	6.11082i	−1.52909	−	0.230474i
$704$	−0.360675	−	1.58022i	−0.0135935	−	0.0595568i
$705$	10.1591	−	9.42622i	0.382612	−	0.355012i
$706$	0.340656	+	4.54573i	0.0128207	+	0.171081i
$707$	0.740414	+	1.88654i	0.0278461	+	0.0709508i
$708$	1.82520	−	0.275104i	0.0685952	−	0.0103391i
$709$	29.7775	+	14.3401i	1.11832	+	0.538554i	0.899372	−	0.437183i	$-0.144024\pi$
$709$	29.7775	+	14.3401i	1.11832	+	0.538554i	0.218946	+	0.975737i	$0.429738\pi$
$710$	−11.3385	−	5.46033i	−0.425526	−	0.204922i
$711$	9.69839	−	1.46180i	0.363718	−	0.0548217i
$712$	1.42320	+	3.62625i	0.0533366	+	0.135899i
$713$	−0.350466	−	4.67665i	−0.0131251	−	0.175142i
$714$	10.0011	−	9.27970i	0.374283	−	0.347284i
$715$	1.46242	+	6.40727i	0.0546913	+	0.239618i
$716$	−10.5556	−	1.59100i	−0.394481	−	0.0594585i
$717$	6.71632	+	4.57911i	0.250825	+	0.171010i
$718$	13.2597	−	4.09008i	0.494848	−	0.152640i
$719$	−0.616496	+	8.22657i	−0.0229914	+	0.306799i	0.973839	+	0.227240i	$0.0729703\pi$
$719$	−0.616496	+	8.22657i	−0.0229914	+	0.306799i	−0.996830	+	0.0795590i	$0.974649\pi$
$720$	0.969046	+	1.21514i	0.0361142	+	0.0452858i
$721$	−28.1359	−	8.67876i	−1.04783	−	0.323214i
$722$	0.473013	−	1.20522i	0.0176037	−	0.0448536i
$723$	−5.40777	+	23.6930i	−0.201117	+	0.881152i
$724$	−6.08058	−	10.5319i	−0.225983	−	0.391414i
$725$	−3.05310	+	5.28812i	−0.113389	+	0.196396i
$726$	−7.38000	−	6.84763i	−0.273897	−	0.254140i
$727$	−2.86162	+	3.58836i	−0.106132	+	0.133085i	−0.832060	−	0.554685i	$-0.812839\pi$
$727$	−2.86162	+	3.58836i	−0.106132	+	0.133085i	0.725929	+	0.687770i	$0.241410\pi$
$728$	6.00000	−	4.09073i	0.222375	−	0.151613i
$729$	−20.4879	+	9.86646i	−0.758812	+	0.365424i
$730$	−14.8587			−0.549945
$731$	25.9686	−	32.4275i	0.960482	−	1.19937i
$732$	−13.5238			−0.499852
$733$	−12.5511	+	6.04427i	−0.463584	+	0.223250i	−0.651071	−	0.759017i	$-0.725680\pi$
$733$	−12.5511	+	6.04427i	−0.463584	+	0.223250i	0.187487	+	0.982267i	$0.439966\pi$
$734$	−29.1887	+	19.9005i	−1.07737	+	0.734542i
$735$	−2.84310	+	3.56514i	−0.104869	+	0.131502i
$736$	−3.50835	−	3.25527i	−0.129319	−	0.119991i
$737$	11.0638	−	19.1631i	0.407540	−	0.705881i
$738$	5.01696	+	8.68962i	0.184677	+	0.319870i
$739$	0.214312	−	0.938963i	0.00788360	−	0.0345403i	−0.970833	−	0.239756i	$-0.922933\pi$
$739$	0.214312	−	0.938963i	0.00788360	−	0.0345403i	0.978717	+	0.205216i	$0.0657896\pi$
$740$	−3.32504	+	8.47206i	−0.122231	+	0.311439i
$741$	−20.9875	−	6.47378i	−0.770995	−	0.237820i
$742$	8.64786	+	10.8441i	0.317473	+	0.398099i
$743$	2.26405	−	30.2116i	0.0830598	−	1.10836i	−0.787507	−	0.616306i	$-0.788629\pi$
$743$	2.26405	−	30.2116i	0.0830598	−	1.10836i	0.870567	−	0.492050i	$-0.163752\pi$
$744$	1.12589	−	0.347291i	0.0412772	−	0.0127323i
$745$	4.75691	+	3.24321i	0.174280	+	0.118822i
$746$	−8.67525	−	1.30758i	−0.317623	−	0.0478740i
$747$	3.97195	+	17.4023i	0.145326	+	0.636716i
$748$	−7.52756	+	6.98456i	−0.275235	+	0.255381i
$749$	−1.20004	−	16.0134i	−0.0438485	−	0.585118i
$750$	0.439287	+	1.11928i	0.0160405	+	0.0408705i
$751$	−26.3259	+	3.96799i	−0.960646	+	0.144794i	−0.610601	−	0.791939i	$-0.709072\pi$
$751$	−26.3259	+	3.96799i	−0.960646	+	0.144794i	−0.350045	+	0.936733i	$0.613834\pi$
$752$	10.3843	+	5.00083i	0.378678	+	0.182361i
$753$	−1.82679	−	0.879736i	−0.0665720	−	0.0320594i
$754$	−24.4821	+	3.69008i	−0.891584	+	0.134385i
$755$	−1.65375	−	4.21370i	−0.0601863	−	0.153352i
$756$	0.732910	+	9.78001i	0.0266557	+	0.355695i
$757$	8.97690	−	8.32935i	0.326271	−	0.302735i	−0.499980	−	0.866037i	$-0.666659\pi$
$757$	8.97690	−	8.32935i	0.326271	−	0.302735i	0.826251	+	0.563301i	$0.190469\pi$
$758$	5.53552	+	24.2527i	0.201059	+	0.880898i
$759$	9.22327	+	1.39018i	0.334784	+	0.0504605i
$760$	−3.72218	−	2.53774i	−0.135018	−	0.0920534i
$761$	1.66225	−	0.512736i	0.0602565	−	0.0185867i	−0.264480	−	0.964391i	$-0.585200\pi$
$761$	1.66225	−	0.512736i	0.0602565	−	0.0185867i	0.324737	+	0.945804i	$0.394724\pi$
$762$	0.592148	−	7.90166i	0.0214512	−	0.286247i
$763$	7.99735	+	10.0284i	0.289524	+	0.363051i
$764$	−3.56048	−	1.09826i	−0.128814	−	0.0397338i
$765$	3.59739	−	9.16601i	0.130064	−	0.331398i
$766$	5.96376	−	26.1289i	0.215479	−	0.944076i
$767$	−3.11217	−	5.39044i	−0.112374	−	0.194638i
$768$	0.601201	−	1.04131i	0.0216940	−	0.0375751i
$769$	15.9148	+	14.7668i	0.573902	+	0.532503i	0.912846	−	0.408303i	$-0.133879\pi$
$769$	15.9148	+	14.7668i	0.573902	+	0.532503i	−0.338944	+	0.940806i	$0.610070\pi$
$770$	−1.80994	+	2.26960i	−0.0652259	+	0.0817906i
$771$	−21.4689	+	14.6372i	−0.773182	+	0.527147i
$772$	24.0458	−	11.5799i	0.865428	−	0.416768i
$773$	−28.4689			−1.02395			−0.511977	−	0.858999i	$-0.671087\pi$
$773$	−28.4689			−1.02395			−0.511977	+	0.858999i	$0.671087\pi$
$774$	2.24758	+	9.94084i	0.0807876	+	0.357316i
$775$	−0.979902			−0.0351991
$776$	0.234426	−	0.112894i	0.00841542	−	0.00405265i
$777$	−16.1936	+	11.0406i	−0.580943	+	0.396081i
$778$	9.37927	−	11.7612i	0.336263	−	0.421660i
$779$	−21.3197	−	19.7818i	−0.763859	−	0.708757i
$780$	−2.43767	+	4.22217i	−0.0872827	+	0.151178i
$781$	10.1991	+	17.6653i	0.364951	+	0.632114i
$782$	−6.74704	+	29.5607i	−0.241274	+	1.05709i
$783$	12.2161	−	31.1262i	0.436569	−	1.11236i
$784$	−3.62391	−	1.11783i	−0.129425	−	0.0399224i
$785$	−4.19421	−	5.25937i	−0.149698	−	0.187715i
$786$	−0.146253	+	1.95161i	−0.00521668	+	0.0696117i
$787$	31.0866	−	9.58895i	1.10812	−	0.341809i	0.313908	−	0.949453i	$-0.398362\pi$
$787$	31.0866	−	9.58895i	1.10812	−	0.341809i	0.794209	+	0.607644i	$0.207885\pi$
$788$	−11.9997	−	8.18124i	−0.427471	−	0.291444i
$789$	2.19201	+	0.330392i	0.0780376	+	0.0117623i
$790$	1.40422	+	6.15227i	0.0499598	+	0.218888i
$791$	20.2297	−	18.7704i	0.719284	−	0.667398i
$792$	−0.188259	−	2.51214i	−0.00668949	−	0.0892651i
$793$	16.6610	+	42.4516i	0.591650	+	1.50750i
$794$	−33.1693	+	4.99947i	−1.17714	+	0.177425i
$795$	−8.38974	−	4.04029i	−0.297553	−	0.143294i
$796$	12.3872	+	5.96534i	0.439051	+	0.211436i
$797$	−50.9974	+	7.68662i	−1.80642	+	0.272274i	−0.963876	−	0.266352i	$-0.914182\pi$
$797$	−50.9974	+	7.68662i	−1.80642	+	0.272274i	−0.842545	+	0.538626i	$0.818944\pi$
$798$	−3.54430	−	9.03073i	−0.125467	−	0.319684i
$799$	−5.45681	−	72.8160i	−0.193048	−	2.57605i
$800$	−0.733052	+	0.680173i	−0.0259173	+	0.0240477i
$801$	1.34726	+	5.90275i	0.0476032	+	0.208563i
$802$	−32.3408	−	4.87459i	−1.14199	−	0.172128i
$803$	19.8990	+	13.5669i	0.702221	+	0.478766i
$804$	15.6857	−	4.83839i	0.553191	−	0.170637i
$805$	−0.640551	+	8.54756i	−0.0225765	+	0.301262i
$806$	−2.47724	−	3.10636i	−0.0872570	−	0.109417i
$807$	15.6406	+	4.82448i	0.550574	+	0.169830i
$808$	0.413413	−	1.05336i	0.0145438	−	0.0370570i
$809$	2.06218	−	9.03499i	0.0725023	−	0.317653i	−0.925652	−	0.378375i	$-0.876483\pi$
$809$	2.06218	−	9.03499i	0.0725023	−	0.317653i	0.998155	+	0.0607215i	$0.0193402\pi$
$810$	−0.960844	−	1.66423i	−0.0337606	−	0.0584751i
$811$	5.75661	−	9.97073i	0.202142	−	0.350120i	−0.747077	−	0.664738i	$-0.768543\pi$
$811$	5.75661	−	9.97073i	0.202142	−	0.350120i	0.949218	+	0.314618i	$0.101876\pi$
$812$	−8.01670	−	7.43841i	−0.281331	−	0.261037i
$813$	15.0324	−	18.8500i	0.527209	−	0.661099i
$814$	12.1885	−	8.30996i	0.427206	−	0.291264i
$815$	−9.09806	+	4.38139i	−0.318691	+	0.153474i
$816$	−7.61771			−0.266673
$817$	−14.7182	−	25.6134i	−0.514926	−	0.896100i
$818$	19.3643			0.677057
$819$	10.1688	−	4.89705i	0.355327	−	0.171117i
$820$	−5.33410	+	3.63673i	−0.186275	+	0.127000i
$821$	16.9720	−	21.2822i	0.592326	−	0.742754i	−0.391834	−	0.920036i	$-0.628159\pi$
$821$	16.9720	−	21.2822i	0.592326	−	0.742754i	0.984160	+	0.177282i	$0.0567306\pi$
$822$	5.73227	+	5.31877i	0.199936	+	0.185513i
$823$	−18.0420	+	31.2497i	−0.628905	+	1.08930i	0.358867	+	0.933389i	$0.383163\pi$
$823$	−18.0420	+	31.2497i	−0.628905	+	1.08930i	−0.987772	+	0.155906i	$0.950170\pi$
$824$	8.22008	+	14.2376i	0.286360	+	0.495990i
$825$	0.433677	−	1.90006i	0.0150987	−	0.0661516i
$826$	1.00445	−	2.55929i	0.0349492	−	0.0890491i
$827$	−9.39367	−	2.89756i	−0.326650	−	0.100758i	0.127093	−	0.991891i	$-0.459435\pi$
$827$	−9.39367	−	2.89756i	−0.326650	−	0.100758i	−0.453743	+	0.891133i	$0.649912\pi$
$828$	−4.63780	−	5.81562i	−0.161175	−	0.202107i
$829$	−1.47077	+	19.6260i	−0.0510819	+	0.681640i	0.911613	+	0.411050i	$0.134838\pi$
$829$	−1.47077	+	19.6260i	−0.0510819	+	0.681640i	−0.962695	+	0.270590i	$0.912781\pi$
$830$	−10.9744	+	3.38517i	−0.380928	+	0.117501i
$831$	16.9551	+	11.5598i	0.588165	+	0.401004i
$832$	−4.00938	−	0.604317i	−0.139000	−	0.0209509i
$833$	5.34637	+	23.4240i	0.185241	+	0.811592i
$834$	−8.18342	+	7.59310i	−0.283369	+	0.262928i
$835$	−0.422454	−	5.63726i	−0.0146196	−	0.195085i
$836$	2.66769	+	6.79716i	0.0922640	+	0.235085i
$837$	5.30603	−	0.799755i	0.183403	−	0.0276436i
$838$	−32.5637	−	15.6818i	−1.12489	−	0.541720i
$839$	−19.1029	−	9.19948i	−0.659506	−	0.317601i	0.0740260	−	0.997256i	$-0.476415\pi$
$839$	−19.1029	−	9.19948i	−0.659506	−	0.317601i	−0.733532	+	0.679655i	$0.762129\pi$
$840$	−2.12943	+	0.320959i	−0.0734721	+	0.0110741i
$841$	3.02707	+	7.71285i	0.104382	+	0.265960i
$842$	2.21187	+	29.5154i	0.0762262	+	1.01717i
$843$	15.2647	−	14.1636i	0.525745	−	0.487820i
$844$	−1.25929	−	5.51731i	−0.0433466	−	0.189914i
$845$	3.40192	+	0.512757i	0.117030	+	0.0176394i
$846$	14.8009	+	10.0911i	0.508867	+	0.346939i
$847$	−14.3293	+	4.42001i	−0.492362	+	0.151873i
$848$	0.578741	−	7.72277i	0.0198741	−	0.265201i
$849$	−0.450066	−	0.564365i	−0.0154462	−	0.0193690i
$850$	6.05394	+	1.86739i	0.207648	+	0.0640511i
$851$	15.9135	−	40.5468i	0.545506	−	1.38993i
$852$	−3.36718	+	14.7526i	−0.115358	+	0.505415i
$853$	−20.4507	−	35.4217i	−0.700220	−	1.21282i	−0.968389	−	0.249445i	$-0.919752\pi$
$853$	−20.4507	−	35.4217i	−0.700220	−	1.21282i	0.268169	−	0.963372i	$-0.413581\pi$
$854$	−10.0718	+	17.4449i	−0.344651	+	0.596952i
$855$	−5.13264	−	4.76240i	−0.175533	−	0.162871i
$856$	−5.59035	+	7.01008i	−0.191074	+	0.239600i
$857$	18.1548	−	12.3777i	0.620155	−	0.422814i	−0.212069	−	0.977255i	$-0.568020\pi$
$857$	18.1548	−	12.3777i	0.620155	−	0.422814i	0.832223	+	0.554441i	$0.187068\pi$
$858$	7.11968	−	3.42866i	0.243062	−	0.117052i
$859$	45.2753			1.54477			0.772387	−	0.635152i	$-0.219063\pi$
$859$	45.2753			1.54477			0.772387	+	0.635152i	$0.219063\pi$
$860$	−6.27004	+	1.92004i	−0.213807	+	0.0654727i
$861$	−13.9026			−0.473799
$862$	7.31402	−	3.52225i	0.249116	−	0.119968i
$863$	−8.72114	+	5.94597i	−0.296871	+	0.202403i	−0.702590	−	0.711594i	$-0.747973\pi$
$863$	−8.72114	+	5.94597i	−0.296871	+	0.202403i	0.405719	+	0.913998i	$0.367021\pi$
$864$	3.41424	−	4.28132i	0.116155	−	0.145654i
$865$	−10.8191	−	10.0387i	−0.367860	−	0.341324i
$866$	4.53209	−	7.84980i	0.154007	−	0.266747i
$867$	13.9102	+	24.0932i	0.472416	+	0.818248i
$868$	0.390521	−	1.71098i	0.0132551	−	0.0580746i
$869$	3.73686	−	9.52136i	0.126764	−	0.322990i
$870$	7.01591	+	2.16412i	0.237862	+	0.0733706i
$871$	−34.5123	−	43.2771i	−1.16941	−	1.46639i
$872$	0.535207	−	7.14184i	0.0181244	−	0.241853i
$873$	0.386434	−	0.119199i	0.0130788	−	0.00403428i
$874$	17.8141	+	12.1455i	0.602572	+	0.410827i
$875$	1.77098	+	0.266932i	0.0598699	+	0.00902393i
$876$	3.97559	+	17.4182i	0.134323	+	0.588506i
$877$	−8.66844	+	8.04314i	−0.292712	+	0.271597i	−0.812835	−	0.582494i	$-0.802077\pi$
$877$	−8.66844	+	8.04314i	−0.292712	+	0.271597i	0.520122	+	0.854092i	$0.325886\pi$
$878$	−2.35518	−	31.4277i	−0.0794835	−	1.06063i
$879$	9.01531	+	22.9706i	0.304079	+	0.774781i
$880$	1.60276	−	0.241577i	0.0540289	−	0.00814354i
$881$	13.8688	+	6.67886i	0.467252	+	0.225017i	0.652669	−	0.757643i	$-0.273649\pi$
$881$	13.8688	+	6.67886i	0.467252	+	0.225017i	−0.185417	+	0.982660i	$0.559364\pi$
$882$	−5.31053	−	2.55742i	−0.178815	−	0.0861127i
$883$	7.21507	−	1.08750i	0.242807	−	0.0365972i	−0.0265114	−	0.999649i	$-0.508440\pi$
$883$	7.21507	−	1.08750i	0.242807	−	0.0365972i	0.269318	+	0.963051i	$0.413202\pi$
$884$	9.38487	+	23.9123i	0.315647	+	0.804257i
$885$	0.137938	+	1.84065i	0.00463673	+	0.0618729i
$886$	−8.05608	+	7.47495i	−0.270649	+	0.251126i
$887$	6.47376	+	28.3634i	0.217368	+	0.952350i	0.959414	+	0.282001i	$0.0909982\pi$
$887$	6.47376	+	28.3634i	0.217368	+	0.952350i	−0.742047	+	0.670348i	$0.766145\pi$
$888$	10.8211	+	1.63101i	0.363131	+	0.0547332i
$889$	−9.75171	−	6.64860i	−0.327062	−	0.222987i
$890$	−3.72247	+	1.14823i	−0.124777	+	0.0384887i
$891$	−0.232768	+	3.10608i	−0.00779803	+	0.104058i
$892$	8.33850	+	10.4562i	0.279194	+	0.350098i
$893$	−49.6163	−	15.3046i	−1.66034	−	0.512148i
$894$	2.52911	−	6.44407i	0.0845861	−	0.215522i
$895$	2.37537	−	10.4072i	0.0794000	−	0.347874i
$896$	−0.895490	−	1.55103i	−0.0299162	−	0.0518164i
$897$	11.6666	−	20.2071i	0.389535	−	0.674695i
$898$	28.7305	+	26.6580i	0.958750	+	0.889590i
$899$	−3.73063	+	4.67807i	−0.124424	+	0.156022i
$900$	−1.28416	+	0.875528i	−0.0428055	+	0.0291843i
$901$	−44.2052	+	21.2881i	−1.47269	+	0.709209i
$902$	10.4641			0.348416
$903$	−13.4854	−	4.18988i	−0.448766	−	0.139430i
$904$	−15.4086			−0.512483
$905$	10.9568	−	5.27653i	0.364217	−	0.175398i
$906$	−4.49705	+	3.06604i	−0.149405	+	0.101862i
$907$	−27.3391	+	34.2822i	−0.907781	+	1.13832i	0.0821289	+	0.996622i	$0.473828\pi$
$907$	−27.3391	+	34.2822i	−0.907781	+	1.13832i	−0.989910	+	0.141699i	$0.954743\pi$
$908$	8.62806	+	8.00567i	0.286332	+	0.265678i
$909$	0.879367	−	1.52311i	0.0291668	−	0.0505183i
$910$	3.63091	+	6.28893i	0.120364	+	0.208476i
$911$	−8.44325	+	36.9923i	−0.279737	+	1.22561i	0.618389	+	0.785872i	$0.287786\pi$
$911$	−8.44325	+	36.9923i	−0.279737	+	1.22561i	−0.898126	+	0.439737i	$0.855072\pi$
$912$	−1.97897	+	5.04234i	−0.0655303	+	0.166969i
$913$	17.7880	+	5.48688i	0.588698	+	0.181589i
$914$	−9.97098	−	12.5032i	−0.329811	−	0.413570i
$915$	1.01063	−	13.4859i	0.0334104	−	0.445831i
$916$	9.26255	−	2.85712i	0.306043	−	0.0944018i
$917$	2.40855	+	1.64212i	0.0795374	+	0.0542277i
$918$	−34.3053	−	5.17069i	−1.13224	−	0.170658i
$919$	5.66122	+	24.8034i	0.186747	+	0.818190i	0.978317	+	0.207112i	$0.0664065\pi$
$919$	5.66122	+	24.8034i	0.186747	+	0.818190i	−0.791571	+	0.611078i	$0.790736\pi$
$920$	3.50835	−	3.25527i	0.115667	−	0.107323i
$921$	−2.22882	−	29.7416i	−0.0734422	−	0.980019i
$922$	−11.9412	−	30.4256i	−0.393262	−	1.00201i
$923$	50.4572	−	7.60519i	1.66082	−	0.250328i
$924$	3.14482	+	1.51446i	0.103457	+	0.0498222i
$925$	−8.19989	−	3.94886i	−0.269611	−	0.129838i
$926$	−17.8616	+	2.69221i	−0.586970	+	0.0884715i
$927$	9.33511	+	23.7855i	0.306605	+	0.781217i
$928$	0.456316	+	6.08912i	0.0149793	+	0.199885i
$929$	21.7321	−	20.1644i	0.713007	−	0.661573i	−0.237816	−	0.971310i	$-0.576431\pi$
$929$	21.7321	−	20.1644i	0.713007	−	0.661573i	0.950822	+	0.309737i	$0.100241\pi$
$930$	0.262182	+	1.14870i	0.00859730	+	0.0376672i
$931$	16.8938	+	2.54633i	0.553671	+	0.0834525i
$932$	−6.92478	−	4.72123i	−0.226829	−	0.154649i
$933$	−22.9608	+	7.08247i	−0.751703	+	0.231870i
$934$	−0.298833	+	3.98766i	−0.00977813	+	0.130480i
$935$	−6.40249	−	8.02847i	−0.209384	−	0.262559i
$936$	−6.02191	−	1.85751i	−0.196832	−	0.0607147i
$937$	17.7328	−	45.1824i	0.579305	−	1.47605i	−0.277664	−	0.960678i	$-0.589560\pi$
$937$	17.7328	−	45.1824i	0.579305	−	1.47605i	0.856969	−	0.515368i	$-0.172345\pi$
$938$	5.44065	−	23.8370i	0.177643	−	0.778307i
$939$	−5.76068	−	9.97779i	−0.187993	−	0.325613i
$940$	−5.76287	+	9.98158i	−0.187964	+	0.325563i
$941$	−21.6931	−	20.1283i	−0.707176	−	0.656163i	0.242229	−	0.970219i	$-0.422122\pi$
$941$	−21.6931	−	20.1283i	−0.707176	−	0.656163i	−0.949404	+	0.314056i	$0.898312\pi$
$942$	−5.04312	+	6.32388i	−0.164314	+	0.206043i
$943$	25.5287	−	17.4052i	0.831329	−	0.566791i
$944$	−1.38308	+	0.666057i	−0.0450155	+	0.0216783i
$945$	−9.80743			−0.319036
$946$	10.1501	+	3.15360i	0.330007	+	0.102532i
$947$	−30.1457			−0.979603			−0.489802	−	0.871834i	$-0.662931\pi$
$947$	−30.1457			−0.979603			−0.489802	+	0.871834i	$0.662931\pi$
$948$	6.83632	−	3.29220i	0.222033	−	0.106926i
$949$	49.7785	−	33.9384i	1.61588	−	1.10169i
$950$	2.80880	−	3.52212i	0.0911295	−	0.114273i
$951$	11.1602	+	10.3552i	0.361895	+	0.335790i
$952$	−5.67329	+	9.82643i	−0.183872	+	0.318476i
$953$	−29.6906	−	51.4257i	−0.961774	−	1.66584i	−0.718043	−	0.695999i	$-0.754962\pi$
$953$	−29.6906	−	51.4257i	−0.961774	−	1.66584i	−0.243732	−	0.969843i	$-0.578372\pi$
$954$	2.67840	−	11.7348i	0.0867162	−	0.379929i
$955$	1.36127	−	3.46845i	0.0440496	−	0.112236i
$956$	−6.46010	−	1.99268i	−0.208935	−	0.0644478i
$957$	−7.41985	−	9.30420i	−0.239850	−	0.300762i
$958$	−0.861401	+	11.4946i	−0.0278306	+	0.371374i
$959$	11.1300	−	3.43316i	0.359407	−	0.110862i
$960$	0.993471	+	0.677337i	0.0320642	+	0.0218610i
$961$	29.7043	+	4.47720i	0.958202	+	0.144426i
$962$	−8.21154	−	35.9771i	−0.264751	−	1.15995i
$963$	−10.2155	+	9.47859i	−0.329190	+	0.305443i
$964$	−1.51040	−	20.1549i	−0.0486468	−	0.649147i
$965$	9.75053	+	24.8440i	0.313881	+	0.799755i
$966$	10.1913	−	1.53609i	0.327900	−	0.0494230i
$967$	4.55348	+	2.19284i	0.146430	+	0.0705170i	0.505664	−	0.862731i	$-0.331248\pi$
$967$	4.55348	+	2.19284i	0.146430	+	0.0705170i	−0.359234	+	0.933248i	$0.616962\pi$
$968$	7.54365	+	3.63283i	0.242462	+	0.116764i
$969$	33.9342	−	5.11476i	1.09012	−	0.164310i
$970$	0.0950594	+	0.242208i	0.00305217	+	0.00777681i
$971$	0.807638	+	10.7772i	0.0259183	+	0.345856i	0.995055	+	0.0993301i	$0.0316700\pi$
$971$	0.807638	+	10.7772i	0.0259183	+	0.345856i	−0.969136	+	0.246526i	$0.920711\pi$
$972$	10.3488	−	9.60227i	0.331938	−	0.307993i
$973$	3.70008	+	16.2111i	0.118619	+	0.519705i
$974$	−18.0097	−	2.71453i	−0.577069	−	0.0869792i
$975$	−4.02820	−	2.74638i	−0.129006	−	0.0879545i
$976$	10.7476	−	3.31519i	0.344022	−	0.106117i
$977$	1.79224	−	23.9158i	0.0573388	−	0.765133i	−0.892231	−	0.451579i	$-0.850861\pi$
$977$	1.79224	−	23.9158i	0.0573388	−	0.765133i	0.949570	−	0.313555i	$-0.101520\pi$
$978$	7.57039	+	9.49297i	0.242074	+	0.303552i
$979$	6.03359	+	1.86112i	0.192834	+	0.0594815i
$980$	1.38552	−	3.53024i	0.0442587	−	0.112769i
$981$	2.47692	−	10.8521i	0.0790820	−	0.346481i
$982$	10.1425	+	17.5673i	0.323660	+	0.560596i
$983$	24.3296	−	42.1401i	0.775993	−	1.34406i	−0.158242	−	0.987400i	$-0.550583\pi$
$983$	24.3296	−	42.1401i	0.775993	−	1.34406i	0.934235	−	0.356659i	$-0.116084\pi$
$984$	5.69036	+	5.27989i	0.181402	+	0.168317i
$985$	9.05510	−	11.3547i	0.288519	−	0.361792i
$986$	31.9632	−	21.7922i	1.01792	−	0.694004i
$987$	−22.3624	+	10.7692i	−0.711804	+	0.342787i
$988$	18.2661			0.581124
$989$	30.0081	−	9.18919i	0.954202	−	0.292199i
$990$	2.51919			0.0800650
$991$	−26.0349	+	12.5377i	−0.827026	+	0.398274i	−0.798999	−	0.601333i	$-0.794637\pi$
$991$	−26.0349	+	12.5377i	−0.827026	+	0.398274i	−0.0280268	+	0.999607i	$0.508922\pi$
$992$	−0.809633	+	0.551999i	−0.0257059	+	0.0175260i
$993$	−2.99906	+	3.76070i	−0.0951722	+	0.119342i
$994$	16.5223	+	15.3305i	0.524056	+	0.486252i
$995$	−6.87435	+	11.9067i	−0.217932	+	0.377469i
$996$	6.90460	+	11.9591i	0.218781	+	0.378939i
$997$	−2.38693	+	10.4578i	−0.0755949	+	0.331203i	−0.998558	−	0.0536859i	$-0.982903\pi$
$997$	−2.38693	+	10.4578i	−0.0755949	+	0.331203i	0.922963	+	0.384889i	$0.125760\pi$
$998$	6.19021	−	15.7724i	0.195948	−	0.499267i
$999$	47.6241	+	14.6901i	1.50676	+	0.464774i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.b.31.2	✓	48
43.25	even	21	inner	430.2.q.b.111.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.b.31.2	✓	48	1.1	even	1	trivial
430.2.q.b.111.2	yes	48	43.25	even	21	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.900969 + 0.433884i) q^{2} +(-0.993471 + 0.677337i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(0.601201 - 1.04131i) q^{6} +(-0.895490 - 1.55103i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-0.567823 + 1.44679i) q^{9} +O(q^{10})\)	\(q+(-0.900969 + 0.433884i) q^{2} +(-0.993471 + 0.677337i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(0.601201 - 1.04131i) q^{6} +(-0.895490 - 1.55103i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-0.567823 + 1.44679i) q^{9} +(-0.955573 - 0.294755i) q^{10} +(1.01059 + 1.26724i) q^{11} +(-0.0898556 + 1.19904i) q^{12} +(3.87453 - 1.19513i) q^{13} +(1.47978 + 1.00889i) q^{14} +(-1.18897 - 0.179209i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-4.64418 + 4.30917i) q^{17} +(-0.116148 - 1.54988i) q^{18} +(1.64585 + 4.19355i) q^{19} +(0.988831 - 0.149042i) q^{20} +(1.94022 + 0.934359i) q^{21} +(-1.46034 - 0.703264i) q^{22} +(-4.73249 + 0.713308i) q^{23} +(-0.439287 - 1.11928i) q^{24} +(0.0747301 + 0.997204i) q^{25} +(-2.97228 + 2.75788i) q^{26} +(-1.21853 - 5.33872i) q^{27} +(-1.77098 - 0.266932i) q^{28} +(5.04517 + 3.43974i) q^{29} +(1.14898 - 0.354414i) q^{30} +(-0.0732282 + 0.977162i) q^{31} +(0.623490 + 0.781831i) q^{32} +(-1.86234 - 0.574456i) q^{33} +(2.31458 - 5.89746i) q^{34} +(0.398530 - 1.74608i) q^{35} +(0.777114 + 1.34600i) q^{36} +(-4.55060 + 7.88187i) q^{37} +(-3.30237 - 3.06415i) q^{38} +(-3.03973 + 3.81170i) q^{39} +(-0.826239 + 0.563320i) q^{40} +(-5.81655 + 2.80110i) q^{41} -2.15348 q^{42} +(-6.48618 + 0.964089i) q^{43} +1.62086 q^{44} +(-1.40031 + 0.674354i) q^{45} +(3.95433 - 2.69602i) q^{46} +(-7.18618 + 9.01118i) q^{47} +(0.881423 + 0.817841i) q^{48} +(1.89620 - 3.28431i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(1.69510 - 7.42672i) q^{51} +(1.48134 - 3.77439i) q^{52} +(7.40036 + 2.28271i) q^{53} +(3.41424 + 4.28132i) q^{54} +(-0.121127 + 1.61633i) q^{55} +(1.71141 - 0.527900i) q^{56} +(-4.47556 - 3.05138i) q^{57} +(-6.03799 - 0.910081i) q^{58} +(-0.341593 - 1.49662i) q^{59} +(-0.881423 + 0.817841i) q^{60} +(0.840510 + 11.2158i) q^{61} +(-0.357998 - 0.912165i) q^{62} +(2.75250 - 0.414873i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(3.65313 + 1.75926i) q^{65} +(1.92716 - 0.290472i) q^{66} +(-4.98755 - 12.7081i) q^{67} +(0.473445 + 6.31769i) q^{68} +(4.21844 - 3.91414i) q^{69} +(0.398530 + 1.74608i) q^{70} +(12.4442 + 1.87566i) q^{71} +(-1.28416 - 0.875528i) q^{72} +(14.1986 - 4.37968i) q^{73} +(0.680133 - 9.07575i) q^{74} +(-0.749686 - 0.940076i) q^{75} +(4.30482 + 1.32786i) q^{76} +(1.06056 - 2.70226i) q^{77} +(1.08487 - 4.75311i) q^{78} +(-3.15524 - 5.46504i) q^{79} +(0.500000 - 0.866025i) q^{80} +(1.40870 + 1.30708i) q^{81} +(4.02518 - 5.04741i) q^{82} +(9.48908 - 6.46955i) q^{83} +(1.94022 - 0.934359i) q^{84} -6.33541 q^{85} +(5.42554 - 3.68286i) q^{86} -7.34210 q^{87} +(-1.46034 + 0.703264i) q^{88} +(3.21864 - 2.19443i) q^{89} +(0.969046 - 1.21514i) q^{90} +(-5.32330 - 4.93930i) q^{91} +(-2.39297 + 4.14475i) q^{92} +(-0.589118 - 1.02038i) q^{93} +(2.56472 - 11.2368i) q^{94} +(-1.64585 + 4.19355i) q^{95} +(-1.14898 - 0.354414i) q^{96} +(-0.162228 - 0.203428i) q^{97} +(-0.283406 + 3.78179i) q^{98} +(-2.40727 + 0.742543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9}+O(q^{10}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9} - 4 q^{10} - 9 q^{11} - q^{12} - 11 q^{13} + 7 q^{14} - 6 q^{15} - 8 q^{16} - 11 q^{17} - 15 q^{18} + 31 q^{19} - 4 q^{20} + 4 q^{21} + 12 q^{22} + 4 q^{23} + 6 q^{24} + 4 q^{25} + 31 q^{26} + 44 q^{27} + 13 q^{29} + q^{30} - q^{31} - 8 q^{32} - 30 q^{33} - 25 q^{34} + 14 q^{35} - 36 q^{36} - 27 q^{37} - 4 q^{38} + 4 q^{39} - 4 q^{40} + 16 q^{41} + 4 q^{42} - 7 q^{43} - 30 q^{44} + 12 q^{45} - 52 q^{46} - 43 q^{47} - q^{48} - 23 q^{49} - 24 q^{50} - 7 q^{51} - 25 q^{52} + 73 q^{53} - 61 q^{54} + 27 q^{55} + 7 q^{56} + 136 q^{57} - 36 q^{58} + 58 q^{59} + q^{60} - 61 q^{61} + 27 q^{62} + 32 q^{63} - 8 q^{64} - q^{65} + 12 q^{66} + 39 q^{67} + 17 q^{68} - 34 q^{69} + 14 q^{70} + 60 q^{71} + 27 q^{72} + 3 q^{73} + 29 q^{74} - 12 q^{75} + 17 q^{76} - 27 q^{77} - 17 q^{78} - 2 q^{79} + 24 q^{80} - 165 q^{81} + 2 q^{82} + 74 q^{83} + 4 q^{84} - 8 q^{85} + 14 q^{86} + 88 q^{87} + 12 q^{88} + 23 q^{89} - 2 q^{90} - 39 q^{91} + 4 q^{92} - 46 q^{93} + 55 q^{94} - 31 q^{95} - q^{96} - 85 q^{97} + 33 q^{98} - 168 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9 - 4 * q^10 - 9 * q^11 - q^12 - 11 * q^13 + 7 * q^14 - 6 * q^15 - 8 * q^16 - 11 * q^17 - 15 * q^18 + 31 * q^19 - 4 * q^20 + 4 * q^21 + 12 * q^22 + 4 * q^23 + 6 * q^24 + 4 * q^25 + 31 * q^26 + 44 * q^27 + 13 * q^29 + q^30 - q^31 - 8 * q^32 - 30 * q^33 - 25 * q^34 + 14 * q^35 - 36 * q^36 - 27 * q^37 - 4 * q^38 + 4 * q^39 - 4 * q^40 + 16 * q^41 + 4 * q^42 - 7 * q^43 - 30 * q^44 + 12 * q^45 - 52 * q^46 - 43 * q^47 - q^48 - 23 * q^49 - 24 * q^50 - 7 * q^51 - 25 * q^52 + 73 * q^53 - 61 * q^54 + 27 * q^55 + 7 * q^56 + 136 * q^57 - 36 * q^58 + 58 * q^59 + q^60 - 61 * q^61 + 27 * q^62 + 32 * q^63 - 8 * q^64 - q^65 + 12 * q^66 + 39 * q^67 + 17 * q^68 - 34 * q^69 + 14 * q^70 + 60 * q^71 + 27 * q^72 + 3 * q^73 + 29 * q^74 - 12 * q^75 + 17 * q^76 - 27 * q^77 - 17 * q^78 - 2 * q^79 + 24 * q^80 - 165 * q^81 + 2 * q^82 + 74 * q^83 + 4 * q^84 - 8 * q^85 + 14 * q^86 + 88 * q^87 + 12 * q^88 + 23 * q^89 - 2 * q^90 - 39 * q^91 + 4 * q^92 - 46 * q^93 + 55 * q^94 - 31 * q^95 - q^96 - 85 * q^97 + 33 * q^98 - 168 * q^99

Introduction

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