LMFDB - Embedded newform 462.2.y.a.247.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(25,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 24]))

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

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

chi := DirichletCharacter("462.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.y (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			247.2
Character	$\chi$	$=$	462.247
Dual form			462.2.y.a.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.978148 + 0.207912i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.00883 + 1.12042i) q^{5} +(0.309017 - 0.951057i) q^{6} +(0.191063 - 2.63884i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(0.978148 + 0.207912i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.00883 + 1.12042i) q^{5} +(0.309017 - 0.951057i) q^{6} +(0.191063 - 2.63884i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(0.753838 + 1.30569i) q^{10} +(1.15632 - 3.10853i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.02968 + 3.16903i) q^{13} +(0.735534 - 2.54145i) q^{14} +(1.21974 - 0.886190i) q^{15} +(0.669131 + 0.743145i) q^{16} +(0.990369 - 0.210509i) q^{17} +(-0.913545 - 0.406737i) q^{18} +(3.90700 - 1.73951i) q^{19} +(0.465898 + 1.43389i) q^{20} +(-2.60442 - 0.465851i) q^{21} +(1.77735 - 2.80019i) q^{22} +(-2.00031 + 3.46463i) q^{23} +(0.669131 - 0.743145i) q^{24} +(0.285040 - 2.71197i) q^{25} +(0.348301 + 3.31387i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.24786 - 2.33299i) q^{28} +(-7.79896 + 5.66628i) q^{29} +(1.37733 - 0.613227i) q^{30} +(2.09214 - 2.32356i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.97063 - 1.47491i) q^{33} +1.01249 q^{34} +(3.14937 - 2.44808i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(0.333372 + 3.17182i) q^{37} +(4.18328 - 0.889184i) q^{38} +(3.25931 - 0.692787i) q^{39} +(0.157595 + 1.49942i) q^{40} +(3.91586 + 2.84504i) q^{41} +(-2.45065 - 0.997159i) q^{42} -8.86848 q^{43} +(2.32070 - 2.36946i) q^{44} +(-0.753838 - 1.30569i) q^{45} +(-2.67693 + 2.97303i) q^{46} +(2.24405 - 0.999117i) q^{47} +(0.809017 - 0.587785i) q^{48} +(-6.92699 - 1.00837i) q^{49} +(0.842662 - 2.59345i) q^{50} +(-0.105834 - 1.00695i) q^{51} +(-0.348301 + 3.31387i) q^{52} +(-0.537502 + 0.596956i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(4.64939 - 1.84042i) q^{55} +(1.70565 - 2.02257i) q^{56} +(-1.32159 - 4.06742i) q^{57} +(-8.80662 + 3.92096i) q^{58} +(3.83960 + 1.70950i) q^{59} +(1.47473 - 0.313464i) q^{60} +(-3.49506 - 3.88165i) q^{61} +(2.52952 - 1.83780i) q^{62} +(-0.735534 + 2.54145i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-2.51188 + 4.35070i) q^{65} +(-2.59906 - 2.06031i) q^{66} +(-0.962822 - 1.66766i) q^{67} +(0.990369 + 0.210509i) q^{68} +(3.23656 + 2.35150i) q^{69} +(3.58953 - 1.73979i) q^{70} +(-3.87630 + 11.9300i) q^{71} +(-0.669131 - 0.743145i) q^{72} +(-4.88516 - 2.17501i) q^{73} +(-0.333372 + 3.17182i) q^{74} +(-2.66732 - 0.566957i) q^{75} +4.27674 q^{76} +(-7.98198 - 3.64526i) q^{77} +3.33212 q^{78} +(-13.8458 - 2.94302i) q^{79} +(-0.157595 + 1.49942i) q^{80} +(0.913545 + 0.406737i) q^{81} +(3.23878 + 3.59703i) q^{82} +(-3.24141 + 9.97604i) q^{83} +(-2.18977 - 1.48489i) q^{84} +(1.23498 + 0.897262i) q^{85} +(-8.67468 - 1.84386i) q^{86} +(4.82002 + 8.34852i) q^{87} +(2.76262 - 1.83519i) q^{88} +(2.34316 - 4.05847i) q^{89} +(-0.465898 - 1.43389i) q^{90} +(8.55932 - 2.11168i) q^{91} +(-3.23656 + 2.35150i) q^{92} +(-2.09214 - 2.32356i) q^{93} +(2.40274 - 0.510719i) q^{94} +(5.89049 + 2.62261i) q^{95} +(0.913545 - 0.406737i) q^{96} +(0.904571 + 2.78398i) q^{97} +(-6.56597 - 2.42654i) q^{98} +(-1.77735 + 2.80019i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9} + 10 q^{10} + 6 q^{11} + 12 q^{12} - 2 q^{13} - 5 q^{14} + 3 q^{16} - 2 q^{17} - 3 q^{18} + 7 q^{19} - 10 q^{20} - 4 q^{21} + 2 q^{22} + 24 q^{23} + 3 q^{24} + 4 q^{25} + 4 q^{26} + 6 q^{27} + 14 q^{28} - 6 q^{29} - 7 q^{31} + 12 q^{32} - q^{33} - 24 q^{34} + 4 q^{35} - 6 q^{36} - q^{37} + 8 q^{38} - q^{39} + 16 q^{41} - 4 q^{42} + 52 q^{43} - 4 q^{44} - 10 q^{45} - 4 q^{46} + 27 q^{47} + 6 q^{48} - 33 q^{49} - 22 q^{50} - 8 q^{51} - 4 q^{52} + 13 q^{53} - 12 q^{54} + 30 q^{55} + 14 q^{56} - 16 q^{57} - 3 q^{58} + 14 q^{59} - 5 q^{60} + 9 q^{61} - 4 q^{62} + 5 q^{63} - 6 q^{64} - 50 q^{65} - 4 q^{66} - 20 q^{67} - 2 q^{68} - 32 q^{69} - 17 q^{70} - 18 q^{71} - 3 q^{72} + 7 q^{73} + q^{74} + 11 q^{75} - 4 q^{76} - 34 q^{77} - 12 q^{78} + q^{79} + 3 q^{81} - 2 q^{82} - 68 q^{83} - 5 q^{84} - 19 q^{86} - 8 q^{87} - q^{88} - 42 q^{89} + 10 q^{90} - 16 q^{91} + 32 q^{92} + 7 q^{93} + 8 q^{94} + 38 q^{95} + 3 q^{96} - 80 q^{97} - 2 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 11 * q^7 + 6 * q^8 + 3 * q^9 + 10 * q^10 + 6 * q^11 + 12 * q^12 - 2 * q^13 - 5 * q^14 + 3 * q^16 - 2 * q^17 - 3 * q^18 + 7 * q^19 - 10 * q^20 - 4 * q^21 + 2 * q^22 + 24 * q^23 + 3 * q^24 + 4 * q^25 + 4 * q^26 + 6 * q^27 + 14 * q^28 - 6 * q^29 - 7 * q^31 + 12 * q^32 - q^33 - 24 * q^34 + 4 * q^35 - 6 * q^36 - q^37 + 8 * q^38 - q^39 + 16 * q^41 - 4 * q^42 + 52 * q^43 - 4 * q^44 - 10 * q^45 - 4 * q^46 + 27 * q^47 + 6 * q^48 - 33 * q^49 - 22 * q^50 - 8 * q^51 - 4 * q^52 + 13 * q^53 - 12 * q^54 + 30 * q^55 + 14 * q^56 - 16 * q^57 - 3 * q^58 + 14 * q^59 - 5 * q^60 + 9 * q^61 - 4 * q^62 + 5 * q^63 - 6 * q^64 - 50 * q^65 - 4 * q^66 - 20 * q^67 - 2 * q^68 - 32 * q^69 - 17 * q^70 - 18 * q^71 - 3 * q^72 + 7 * q^73 + q^74 + 11 * q^75 - 4 * q^76 - 34 * q^77 - 12 * q^78 + q^79 + 3 * q^81 - 2 * q^82 - 68 * q^83 - 5 * q^84 - 19 * q^86 - 8 * q^87 - q^88 - 42 * q^89 + 10 * q^90 - 16 * q^91 + 32 * q^92 + 7 * q^93 + 8 * q^94 + 38 * q^95 + 3 * q^96 - 80 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	1.00883	+	1.12042i	0.451164	+	0.501068i	0.925222	−	0.379425i	$-0.123878\pi$
$5$	1.00883	+	1.12042i	0.451164	+	0.501068i	−0.474059	+	0.880493i	$0.657212\pi$
$6$	0.309017	−	0.951057i	0.126156	−	0.388267i
$7$	0.191063	−	2.63884i	0.0722150	−	0.997389i
$7$	0.191063	−	2.63884i	0.0722150	−	0.997389i
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	0.753838	+	1.30569i	0.238385	+	0.412894i
$11$	1.15632	−	3.10853i	0.348642	−	0.937256i
$11$	1.15632	−	3.10853i	0.348642	−	0.937256i
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	1.02968	+	3.16903i	0.285582	+	0.878932i	0.986224	+	0.165418i	$0.0528974\pi$
$13$	1.02968	+	3.16903i	0.285582	+	0.878932i	−0.700641	+	0.713514i	$0.747103\pi$
$14$	0.735534	−	2.54145i	0.196580	−	0.679232i
$15$	1.21974	−	0.886190i	0.314934	−	0.228813i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	0.990369	−	0.210509i	0.240200	−	0.0510560i	−0.0862387	−	0.996275i	$-0.527485\pi$
$17$	0.990369	−	0.210509i	0.240200	−	0.0510560i	0.326438	+	0.945218i	$0.394151\pi$
$18$	−0.913545	−	0.406737i	−0.215325	−	0.0958687i
$19$	3.90700	−	1.73951i	0.896327	−	0.399070i	0.0937336	−	0.995597i	$-0.470120\pi$
$19$	3.90700	−	1.73951i	0.896327	−	0.399070i	0.802593	+	0.596527i	$0.203453\pi$
$20$	0.465898	+	1.43389i	0.104178	+	0.320627i
$21$	−2.60442	−	0.465851i	−0.568330	−	0.101657i
$22$	1.77735	−	2.80019i	0.378931	−	0.597002i
$23$	−2.00031	+	3.46463i	−0.417093	+	0.722426i	−0.995646	−	0.0932192i	$-0.970284\pi$
$23$	−2.00031	+	3.46463i	−0.417093	+	0.722426i	0.578553	+	0.815645i	$0.303618\pi$
$24$	0.669131	−	0.743145i	0.136586	−	0.151694i
$25$	0.285040	−	2.71197i	0.0570080	−	0.542395i
$26$	0.348301	+	3.31387i	0.0683075	+	0.649903i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	1.24786	−	2.33299i	0.235823	−	0.440894i
$29$	−7.79896	+	5.66628i	−1.44823	+	1.05220i	−0.461990	+	0.886885i	$0.652864\pi$
$29$	−7.79896	+	5.66628i	−1.44823	+	1.05220i	−0.986241	+	0.165316i	$0.947136\pi$
$30$	1.37733	−	0.613227i	0.251465	−	0.111959i
$31$	2.09214	−	2.32356i	0.375759	−	0.417323i	−0.525370	−	0.850874i	$-0.676073\pi$
$31$	2.09214	−	2.32356i	0.375759	−	0.417323i	0.901129	+	0.433551i	$0.142740\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−2.97063	−	1.47491i	−0.517120	−	0.256749i
$34$	1.01249			0.173641
$35$	3.14937	−	2.44808i	0.532340	−	0.413801i
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	0.333372	+	3.17182i	0.0548059	+	0.521444i	0.987141	+	0.159849i	$0.0511008\pi$
$37$	0.333372	+	3.17182i	0.0548059	+	0.521444i	−0.932335	+	0.361594i	$0.882233\pi$
$38$	4.18328	−	0.889184i	0.678618	−	0.144245i
$39$	3.25931	−	0.692787i	0.521906	−	0.110935i
$40$	0.157595	+	1.49942i	0.0249180	+	0.237079i
$41$	3.91586	+	2.84504i	0.611555	+	0.444321i	0.849962	−	0.526845i	$-0.176625\pi$
$41$	3.91586	+	2.84504i	0.611555	+	0.444321i	−0.238406	+	0.971165i	$0.576625\pi$
$42$	−2.45065	−	0.997159i	−0.378143	−	0.153865i
$43$	−8.86848			−1.35243			−0.676215	−	0.736704i	$-0.736381\pi$
$43$	−8.86848			−1.35243			−0.676215	+	0.736704i	$0.736381\pi$
$44$	2.32070	−	2.36946i	0.349858	−	0.357210i
$45$	−0.753838	−	1.30569i	−0.112376	−	0.194640i
$46$	−2.67693	+	2.97303i	−0.394692	+	0.438350i
$47$	2.24405	−	0.999117i	0.327329	−	0.145736i	−0.236492	−	0.971634i	$-0.575998\pi$
$47$	2.24405	−	0.999117i	0.327329	−	0.145736i	0.563821	+	0.825897i	$0.309331\pi$
$48$	0.809017	−	0.587785i	0.116772	−	0.0848395i
$49$	−6.92699	−	1.00837i	−0.989570	−	0.144053i
$50$	0.842662	−	2.59345i	0.119170	−	0.366769i
$51$	−0.105834	−	1.00695i	−0.0148198	−	0.141001i
$52$	−0.348301	+	3.31387i	−0.0483007	+	0.459551i
$53$	−0.537502	+	0.596956i	−0.0738316	+	0.0819983i	−0.778929	−	0.627112i	$-0.784237\pi$
$53$	−0.537502	+	0.596956i	−0.0738316	+	0.0819983i	0.705097	+	0.709111i	$0.250903\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	4.64939	−	1.84042i	0.626924	−	0.248162i
$56$	1.70565	−	2.02257i	0.227927	−	0.270277i
$57$	−1.32159	−	4.06742i	−0.175048	−	0.538743i
$58$	−8.80662	+	3.92096i	−1.15637	+	0.514847i
$59$	3.83960	+	1.70950i	0.499874	+	0.222558i	0.641155	−	0.767411i	$-0.278456\pi$
$59$	3.83960	+	1.70950i	0.499874	+	0.222558i	−0.141281	+	0.989969i	$0.545122\pi$
$60$	1.47473	−	0.313464i	0.190387	−	0.0404680i
$61$	−3.49506	−	3.88165i	−0.447496	−	0.496995i	0.476619	−	0.879110i	$-0.341862\pi$
$61$	−3.49506	−	3.88165i	−0.447496	−	0.496995i	−0.924115	+	0.382116i	$0.875196\pi$
$62$	2.52952	−	1.83780i	0.321249	−	0.233401i
$63$	−0.735534	+	2.54145i	−0.0926686	+	0.320193i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−2.51188	+	4.35070i	−0.311560	+	0.539638i
$66$	−2.59906	−	2.06031i	−0.319923	−	0.253606i
$67$	−0.962822	−	1.66766i	−0.117627	−	0.203737i	0.801200	−	0.598397i	$-0.204196\pi$
$67$	−0.962822	−	1.66766i	−0.117627	−	0.203737i	−0.918827	+	0.394661i	$0.870862\pi$
$68$	0.990369	+	0.210509i	0.120100	+	0.0255280i
$69$	3.23656	+	2.35150i	0.389636	+	0.283087i
$70$	3.58953	−	1.73979i	0.429031	−	0.207945i
$71$	−3.87630	+	11.9300i	−0.460032	+	1.41583i	0.405093	+	0.914275i	$0.367239\pi$
$71$	−3.87630	+	11.9300i	−0.460032	+	1.41583i	−0.865125	+	0.501557i	$0.832761\pi$
$72$	−0.669131	−	0.743145i	−0.0788578	−	0.0875805i
$73$	−4.88516	−	2.17501i	−0.571765	−	0.254566i	0.100425	−	0.994945i	$-0.467980\pi$
$73$	−4.88516	−	2.17501i	−0.571765	−	0.254566i	−0.672190	+	0.740379i	$0.734646\pi$
$74$	−0.333372	+	3.17182i	−0.0387537	+	0.368716i
$75$	−2.66732	−	0.566957i	−0.307996	−	0.0654665i
$76$	4.27674			0.490576
$77$	−7.98198	−	3.64526i	−0.909632	−	0.415416i
$78$	3.33212			0.377288
$79$	−13.8458	−	2.94302i	−1.55778	−	0.331116i	−0.653120	−	0.757254i	$-0.726540\pi$
$79$	−13.8458	−	2.94302i	−1.55778	−	0.331116i	−0.904658	+	0.426139i	$0.859874\pi$
$80$	−0.157595	+	1.49942i	−0.0176197	+	0.167640i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	3.23878	+	3.59703i	0.357663	+	0.397225i
$83$	−3.24141	+	9.97604i	−0.355791	+	1.09501i	0.599758	+	0.800181i	$0.295264\pi$
$83$	−3.24141	+	9.97604i	−0.355791	+	1.09501i	−0.955549	+	0.294832i	$0.904736\pi$
$84$	−2.18977	−	1.48489i	−0.238924	−	0.162014i
$85$	1.23498	+	0.897262i	0.133952	+	0.0973218i
$86$	−8.67468	−	1.84386i	−0.935415	−	0.198829i
$87$	4.82002	+	8.34852i	0.516761	+	0.895056i
$88$	2.76262	−	1.83519i	0.294497	−	0.195631i
$89$	2.34316	−	4.05847i	0.248374	−	0.430197i	−0.714701	−	0.699430i	$-0.753437\pi$
$89$	2.34316	−	4.05847i	0.248374	−	0.430197i	0.963075	+	0.269234i	$0.0867704\pi$
$90$	−0.465898	−	1.43389i	−0.0491099	−	0.151145i
$91$	8.55932	−	2.11168i	0.897260	−	0.221365i
$92$	−3.23656	+	2.35150i	−0.337435	+	0.245161i
$93$	−2.09214	−	2.32356i	−0.216945	−	0.240942i
$94$	2.40274	−	0.510719i	0.247824	−	0.0526766i
$95$	5.89049	+	2.62261i	0.604351	+	0.269075i
$96$	0.913545	−	0.406737i	0.0932383	−	0.0415124i
$97$	0.904571	+	2.78398i	0.0918452	+	0.282671i	0.986419	−	0.164250i	$-0.0525205\pi$
$97$	0.904571	+	2.78398i	0.0918452	+	0.282671i	−0.894573	+	0.446921i	$0.852521\pi$
$98$	−6.56597	−	2.42654i	−0.663263	−	0.245117i
$99$	−1.77735	+	2.80019i	−0.178630	+	0.281429i
$100$	1.36346	−	2.36157i	0.136346	−	0.236157i
$101$	−12.5492	+	13.9373i	−1.24869	+	1.38681i	−0.357040	+	0.934089i	$0.616214\pi$
$101$	−12.5492	+	13.9373i	−1.24869	+	1.38681i	−0.891651	+	0.452723i	$0.850453\pi$
$102$	0.105834	−	1.00695i	0.0104792	−	0.0997027i
$103$	1.18653	+	11.2890i	0.116912	+	1.11234i	0.882924	+	0.469516i	$0.155572\pi$
$103$	1.18653	+	11.2890i	0.116912	+	1.11234i	−0.766012	+	0.642826i	$0.777762\pi$
$104$	−1.02968	+	3.16903i	−0.100969	+	0.310749i
$105$	−2.10547	−	3.38801i	−0.205473	−	0.330636i
$106$	−0.649871	+	0.472159i	−0.0631210	+	0.0458601i
$107$	−1.26321	+	0.562419i	−0.122120	+	0.0543711i	−0.466887	−	0.884317i	$-0.654624\pi$
$107$	−1.26321	+	0.562419i	−0.122120	+	0.0543711i	0.344767	+	0.938688i	$0.387958\pi$
$108$	−0.669131	+	0.743145i	−0.0643871	+	0.0715091i
$109$	−0.724913	−	1.25559i	−0.0694341	−	0.120263i	0.829218	−	0.558925i	$-0.188786\pi$
$109$	−0.724913	−	1.25559i	−0.0694341	−	0.120263i	−0.898652	+	0.438662i	$0.855453\pi$
$110$	4.93043	−	0.833540i	0.470098	−	0.0794750i
$111$	3.18929			0.302714
$112$	2.08889	−	1.62374i	0.197381	−	0.153429i
$113$	9.71078	+	7.05529i	0.913513	+	0.663706i	0.941901	−	0.335891i	$-0.109037\pi$
$113$	9.71078	+	7.05529i	0.913513	+	0.663706i	−0.0283878	+	0.999597i	$0.509037\pi$
$114$	−0.447041	−	4.25331i	−0.0418692	−	0.398359i
$115$	−5.89982	+	1.25405i	−0.550161	+	0.116940i
$116$	−9.42939	+	2.00428i	−0.875497	+	0.186093i
$117$	−0.348301	−	3.31387i	−0.0322005	−	0.306367i
$118$	3.40027	+	2.47044i	0.313020	+	0.227423i
$119$	−0.366279	−	2.65365i	−0.0335767	−	0.243260i
$120$	1.50768			0.137631
$121$	−8.32587	−	7.18887i	−0.756897	−	0.653534i
$122$	−2.61164	−	4.52349i	−0.236447	−	0.409538i
$123$	3.23878	−	3.59703i	0.292031	−	0.324333i
$124$	2.85634	−	1.27172i	0.256507	−	0.114204i
$125$	9.42479	−	6.84751i	0.842979	−	0.612460i
$126$	−1.24786	+	2.33299i	−0.111168	+	0.207839i
$127$	3.10501	−	9.55625i	0.275525	−	0.847980i	−0.713555	−	0.700600i	$-0.752916\pi$
$127$	3.10501	−	9.55625i	0.275525	−	0.847980i	0.989080	−	0.147380i	$-0.0470841\pi$
$128$	0.104528	+	0.994522i	0.00923910	+	0.0879041i
$129$	−0.927009	+	8.81990i	−0.0816186	+	0.776549i
$130$	−3.36155	+	3.73338i	−0.294827	+	0.327439i
$131$	−3.61343	+	6.25865i	−0.315707	+	0.546821i	−0.979588	−	0.201018i	$-0.935575\pi$
$131$	−3.61343	+	6.25865i	−0.315707	+	0.546821i	0.663880	+	0.747839i	$0.268908\pi$
$132$	−2.11390	−	2.55566i	−0.183992	−	0.222442i
$133$	−3.84381	−	10.6423i	−0.333300	−	0.922805i
$134$	−0.595057	−	1.83140i	−0.0514051	−	0.158209i
$135$	−1.37733	+	0.613227i	−0.118542	+	0.0527782i
$136$	0.924960	+	0.411819i	0.0793146	+	0.0353131i
$137$	−2.14792	+	0.456554i	−0.183509	+	0.0390060i	−0.298749	−	0.954332i	$-0.596569\pi$
$137$	−2.14792	+	0.456554i	−0.183509	+	0.0390060i	0.115240	+	0.993338i	$0.463236\pi$
$138$	2.67693	+	2.97303i	0.227876	+	0.253081i
$139$	15.6388	−	11.3622i	1.32646	−	0.963732i	0.326637	−	0.945150i	$-0.394085\pi$
$139$	15.6388	−	11.3622i	1.32646	−	0.963732i	0.999827	−	0.0185824i	$-0.00591529\pi$
$140$	3.87282	−	0.955469i	0.327313	−	0.0807518i
$141$	−0.759076	−	2.33620i	−0.0639258	−	0.196743i
$142$	−6.27198	+	10.8634i	−0.526333	+	0.911635i
$143$	11.0417	+	0.463612i	0.923350	+	0.0387692i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−14.2165	−	3.02180i	−1.18061	−	0.250947i
$146$	−4.32620	−	3.14317i	−0.358039	−	0.260130i
$147$	−1.72691	+	6.78364i	−0.142433	+	0.559505i
$148$	−0.985545	+	3.03319i	−0.0810113	+	0.249327i
$149$	−10.1875	−	11.3143i	−0.834591	−	0.926907i	0.163630	−	0.986522i	$-0.447680\pi$
$149$	−10.1875	−	11.3143i	−0.834591	−	0.926907i	−0.998221	+	0.0596145i	$0.981013\pi$
$150$	−2.49116	−	1.10913i	−0.203402	−	0.0905605i
$151$	2.29811	−	21.8651i	0.187018	−	1.77936i	−0.350954	−	0.936393i	$-0.614143\pi$
$151$	2.29811	−	21.8651i	0.187018	−	1.77936i	0.537972	−	0.842963i	$-0.319191\pi$
$152$	4.18328	+	0.889184i	0.339309	+	0.0721224i
$153$	−1.01249			−0.0818553
$154$	−7.04967	−	5.22515i	−0.568078	−	0.421055i
$155$	4.71398			0.378636
$156$	3.25931	+	0.692787i	0.260953	+	0.0554673i
$157$	−0.270177	+	2.57056i	−0.0215625	+	0.205153i	−0.999999	−	0.00139441i	$-0.999556\pi$
$157$	−0.270177	+	2.57056i	−0.0215625	+	0.205153i	0.978437	+	0.206548i	$0.0662228\pi$
$158$	−12.9314	−	5.75742i	−1.02877	−	0.458036i
$159$	0.537502	+	0.596956i	0.0426267	+	0.0473417i
$160$	−0.465898	+	1.43389i	−0.0368324	+	0.113359i
$161$	8.76043	+	5.94046i	0.690419	+	0.468174i
$162$	0.809017	+	0.587785i	0.0635624	+	0.0461808i
$163$	12.4039	+	2.63653i	0.971548	+	0.206509i	0.666234	−	0.745743i	$-0.267905\pi$
$163$	12.4039	+	2.63653i	0.971548	+	0.206509i	0.305314	+	0.952252i	$0.401239\pi$
$164$	2.42014	+	4.19180i	0.188981	+	0.327325i
$165$	−1.34434	−	4.81630i	−0.104657	−	0.374948i
$166$	−5.24472	+	9.08412i	−0.407069	+	0.705064i
$167$	−6.50788	−	20.0292i	−0.503595	−	1.54991i	−0.803120	−	0.595817i	$-0.796828\pi$
$167$	−6.50788	−	20.0292i	−0.503595	−	1.54991i	0.299525	−	0.954088i	$-0.403172\pi$
$168$	−1.83320	−	1.90772i	−0.141434	−	0.147184i
$169$	1.53469	−	1.11502i	0.118053	−	0.0857704i
$170$	1.02144	+	1.13442i	0.0783406	+	0.0870061i
$171$	−4.18328	+	0.889184i	−0.319904	+	0.0679976i
$172$	−8.10176	−	3.60714i	−0.617754	−	0.275042i
$173$	20.3804	−	9.07393i	1.54949	−	0.689878i	0.559219	−	0.829020i	$-0.311101\pi$
$173$	20.3804	−	9.07393i	1.54949	−	0.689878i	0.990272	+	0.139142i	$0.0444344\pi$
$174$	2.97894	+	9.16823i	0.225833	+	0.695042i
$175$	−7.10201	−	1.27033i	−0.536862	−	0.0960282i
$176$	3.08381	−	1.22070i	0.232451	−	0.0920137i
$177$	2.10148	−	3.63988i	0.157957	−	0.273590i
$178$	3.13576	−	3.48261i	0.235035	−	0.261033i
$179$	0.446336	−	4.24660i	0.0333607	−	0.317406i	−0.965097	−	0.261892i	$-0.915654\pi$
$179$	0.446336	−	4.24660i	0.0333607	−	0.317406i	0.998458	−	0.0555141i	$-0.0176798\pi$
$180$	−0.157595	−	1.49942i	−0.0117464	−	0.111760i
$181$	−6.23341	+	19.1845i	−0.463326	+	1.42597i	0.397750	+	0.917494i	$0.369791\pi$
$181$	−6.23341	+	19.1845i	−0.463326	+	1.42597i	−0.861076	+	0.508476i	$0.830209\pi$
$182$	8.81132	−	0.285956i	0.653139	−	0.0211965i
$183$	−4.22572	+	3.07017i	−0.312374	+	0.226953i
$184$	−3.65474	+	1.62720i	−0.269431	+	0.119958i
$185$	−3.21746	+	3.57335i	−0.236552	+	0.262718i
$186$	−1.56333	−	2.70776i	−0.114629	−	0.198543i
$187$	0.490805	−	3.32200i	0.0358912	−	0.242929i
$188$	2.45642			0.179153
$189$	2.45065	+	0.997159i	0.178258	+	0.0725327i
$190$	5.21649	+	3.79001i	0.378444	+	0.274956i
$191$	1.51372	+	14.4021i	0.109529	+	1.04210i	0.901867	+	0.432014i	$0.142197\pi$
$191$	1.51372	+	14.4021i	0.109529	+	1.04210i	−0.792338	+	0.610082i	$0.791136\pi$
$192$	0.978148	−	0.207912i	0.0705917	−	0.0150047i
$193$	26.2489	−	5.57938i	1.88944	−	0.401612i	0.890829	−	0.454338i	$-0.150124\pi$
$193$	26.2489	−	5.57938i	1.88944	−	0.401612i	0.998609	+	0.0527260i	$0.0167910\pi$
$194$	0.305981	+	2.91122i	0.0219682	+	0.209013i
$195$	4.06431	+	2.95289i	0.291051	+	0.211461i
$196$	−5.91798	−	3.73865i	−0.422713	−	0.267047i
$197$	6.49016			0.462405			0.231202	−	0.972906i	$-0.425734\pi$
$197$	6.49016			0.462405			0.231202	+	0.972906i	$0.425734\pi$
$198$	−2.32070	+	2.36946i	−0.164925	+	0.168390i
$199$	−0.882429	−	1.52841i	−0.0625537	−	0.108346i	0.833053	−	0.553194i	$-0.186591\pi$
$199$	−0.882429	−	1.52841i	−0.0625537	−	0.108346i	−0.895606	+	0.444848i	$0.853258\pi$
$200$	1.82466	−	2.02649i	0.129023	−	0.143295i
$201$	−1.75916	+	0.783230i	−0.124082	+	0.0552448i
$202$	−15.1727	+	11.0236i	−1.06755	+	0.775618i
$203$	13.4623	+	21.6629i	0.944870	+	1.52043i
$204$	0.312878	−	0.962939i	0.0219058	−	0.0674192i
$205$	0.762804	+	7.25759i	0.0532765	+	0.506892i
$206$	−1.18653	+	11.2890i	−0.0826692	+	0.786545i
$207$	2.67693	−	2.97303i	0.186060	−	0.206640i
$208$	−1.66606	+	2.88570i	−0.115520	+	0.200087i
$209$	−0.889582	−	14.1564i	−0.0615336	−	0.979220i
$210$	−1.35505	−	3.75173i	−0.0935076	−	0.258894i
$211$	−1.21389	−	3.73597i	−0.0835677	−	0.257195i	0.900538	−	0.434776i	$-0.143173\pi$
$211$	−1.21389	−	3.73597i	−0.0835677	−	0.257195i	−0.984106	+	0.177582i	$0.943173\pi$
$212$	−0.733837	+	0.326725i	−0.0504001	+	0.0224396i
$213$	11.4595	+	5.10209i	0.785190	+	0.349589i
$214$	−1.35254	+	0.287492i	−0.0924580	+	0.0196526i
$215$	−8.94681	−	9.93644i	−0.610168	−	0.677660i
$216$	−0.809017	+	0.587785i	−0.0550466	+	0.0399937i
$217$	−5.73177	−	5.96477i	−0.389098	−	0.404915i
$218$	−0.448021	−	1.37887i	−0.0303438	−	0.0933886i
$219$	−2.67374	+	4.63105i	−0.180674	+	0.312937i
$220$	4.99600	+	0.209769i	0.336830	+	0.0141426i
$221$	1.68688	+	2.92176i	0.113472	+	0.196539i
$222$	3.11960	+	0.663091i	0.209374	+	0.0445037i
$223$	19.5341	+	14.1924i	1.30810	+	0.950392i	1.00000		0.000961469i	$-0.000306045\pi$
$223$	19.5341	+	14.1924i	1.30810	+	0.950392i	0.308102	+	0.951353i	$0.400306\pi$
$224$	2.38084	−	1.15396i	0.159076	−	0.0771020i
$225$	−0.842662	+	2.59345i	−0.0561775	+	0.172896i
$226$	8.03170	+	8.92010i	0.534260	+	0.593356i
$227$	14.6857	+	6.53851i	0.974727	+	0.433976i	0.831385	−	0.555697i	$-0.187548\pi$
$227$	14.6857	+	6.53851i	0.974727	+	0.433976i	0.143342	+	0.989673i	$0.454215\pi$
$228$	0.447041	−	4.25331i	0.0296060	−	0.281683i
$229$	3.94428	+	0.838382i	0.260645	+	0.0554019i	0.336381	−	0.941726i	$-0.390797\pi$
$229$	3.94428	+	0.838382i	0.260645	+	0.0554019i	−0.0757355	+	0.997128i	$0.524130\pi$
$230$	−6.03163			−0.397714
$231$	−4.45964	+	7.55723i	−0.293422	+	0.497229i
$232$	−9.64005			−0.632900
$233$	−26.6317	−	5.66075i	−1.74470	−	0.370848i	−0.778303	−	0.627889i	$-0.783919\pi$
$233$	−26.6317	−	5.66075i	−1.74470	−	0.370848i	−0.966401	+	0.257040i	$0.917253\pi$
$234$	0.348301	−	3.31387i	0.0227692	−	0.216634i
$235$	3.38331	+	1.50635i	0.220703	+	0.0982631i
$236$	2.81233	+	3.12341i	0.183067	+	0.203317i
$237$	−4.37418	+	13.4624i	−0.284134	+	0.874474i
$238$	0.193450	−	2.67181i	0.0125395	−	0.173188i
$239$	10.4462	+	7.58962i	0.675710	+	0.490932i	0.871932	−	0.489628i	$-0.162867\pi$
$239$	10.4462	+	7.58962i	0.675710	+	0.490932i	−0.196222	+	0.980560i	$0.562867\pi$
$240$	1.47473	+	0.313464i	0.0951934	+	0.0202340i
$241$	−12.5800	−	21.7892i	−0.810350	−	1.40357i	−0.912619	−	0.408811i	$-0.865943\pi$
$241$	−12.5800	−	21.7892i	−0.810350	−	1.40357i	0.102269	−	0.994757i	$-0.467390\pi$
$242$	−6.64928	−	8.76283i	−0.427432	−	0.563296i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−1.61408	−	4.96763i	−0.103331	−	0.318020i
$245$	−5.85837	−	8.77843i	−0.374278	−	0.560833i
$246$	3.91586	−	2.84504i	0.249666	−	0.181393i
$247$	9.53552	+	10.5903i	0.606731	+	0.673843i
$248$	3.05833	−	0.650068i	0.194204	−	0.0412793i
$249$	9.58257	+	4.26644i	0.607271	+	0.270374i
$250$	10.6425	−	4.73835i	0.673092	−	0.299680i
$251$	−4.65546	−	14.3280i	−0.293850	−	0.904377i	−0.983605	−	0.180335i	$-0.942282\pi$
$251$	−4.65546	−	14.3280i	−0.293850	−	0.904377i	0.689755	−	0.724042i	$-0.257718\pi$
$252$	−1.70565	+	2.02257i	−0.107446	+	0.127410i
$253$	8.45691	+	10.2242i	0.531681	+	0.642791i
$254$	5.02402	−	8.70185i	0.315235	−	0.546003i
$255$	1.02144	−	1.13442i	0.0639649	−	0.0710402i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−1.44923	−	13.7885i	−0.0904006	−	0.860105i	−0.941933	−	0.335802i	$-0.890993\pi$
$257$	−1.44923	−	13.7885i	−0.0904006	−	0.860105i	0.851532	−	0.524303i	$-0.175674\pi$
$258$	−2.74051	+	8.43443i	−0.170617	+	0.525105i
$259$	8.43363	−	0.273698i	0.524040	−	0.0170068i
$260$	−4.06431	+	2.95289i	−0.252058	+	0.183131i
$261$	8.80662	−	3.92096i	0.545116	−	0.242701i
$262$	−4.83572	+	5.37061i	−0.298752	+	0.331797i
$263$	0.501795	+	0.869135i	0.0309420	+	0.0535931i	0.881082	−	0.472964i	$-0.156816\pi$
$263$	0.501795	+	0.869135i	0.0309420	+	0.0535931i	−0.850140	+	0.526557i	$0.823483\pi$
$264$	−1.53636	−	2.93932i	−0.0945564	−	0.180903i
$265$	−1.21109			−0.0743968
$266$	−1.54715	−	11.2089i	−0.0948617	−	0.687263i
$267$	−3.79131	−	2.75455i	−0.232024	−	0.168575i
$268$	−0.201285	−	1.91510i	−0.0122954	−	0.116983i
$269$	−7.22426	+	1.53556i	−0.440471	+	0.0936250i	−0.422808	−	0.906219i	$-0.638956\pi$
$269$	−7.22426	+	1.53556i	−0.440471	+	0.0936250i	−0.0176623	+	0.999844i	$0.505622\pi$
$270$	−1.47473	+	0.313464i	−0.0897492	+	0.0190768i
$271$	−0.607491	−	5.77989i	−0.0369024	−	0.351103i	−0.997356	−	0.0726645i	$-0.976850\pi$
$271$	−0.607491	−	5.77989i	−0.0369024	−	0.351103i	0.960454	−	0.278439i	$-0.0898169\pi$
$272$	0.819125	+	0.595129i	0.0496668	+	0.0360850i
$273$	−1.20542	−	8.73316i	−0.0729555	−	0.528555i
$274$	−2.19590			−0.132659
$275$	−8.10064	−	4.02195i	−0.488487	−	0.242533i
$276$	2.00031	+	3.46463i	0.120404	+	0.208546i
$277$	11.1115	−	12.3405i	0.667624	−	0.741471i	−0.310253	−	0.950654i	$-0.600414\pi$
$277$	11.1115	−	12.3405i	0.667624	−	0.741471i	0.977877	+	0.209183i	$0.0670804\pi$
$278$	17.6594	−	7.86246i	1.05914	−	0.471559i
$279$	−2.52952	+	1.83780i	−0.151438	+	0.110026i
$280$	3.98684	−	0.129386i	0.238259	−	0.00773228i
$281$	0.0421440	−	0.129706i	0.00251410	−	0.00773761i	−0.949792	−	0.312883i	$-0.898705\pi$
$281$	0.0421440	−	0.129706i	0.00251410	−	0.00773761i	0.952306	+	0.305146i	$0.0987051\pi$
$282$	−0.256766	−	2.44297i	−0.0152902	−	0.145477i
$283$	−0.165240	+	1.57215i	−0.00982249	+	0.0934547i	−0.998335	−	0.0576857i	$-0.981628\pi$
$283$	−0.165240	+	1.57215i	−0.00982249	+	0.0934547i	0.988512	+	0.151140i	$0.0482946\pi$
$284$	−8.39355	+	9.32198i	−0.498065	+	0.553158i
$285$	3.22397	−	5.58408i	0.190972	−	0.330772i
$286$	10.7040	+	2.74917i	0.632940	+	0.162562i
$287$	8.25580	−	9.78977i	0.487324	−	0.577872i
$288$	−0.309017	−	0.951057i	−0.0182090	−	0.0560415i
$289$	−14.5938	+	6.49756i	−0.858456	+	0.382209i
$290$	−13.2775	−	5.91154i	−0.779684	−	0.347137i
$291$	2.86328	−	0.608610i	0.167849	−	0.0356773i
$292$	−3.57816	−	3.97395i	−0.209396	−	0.232558i
$293$	−1.56135	+	1.13439i	−0.0912153	+	0.0662718i	−0.632458	−	0.774595i	$-0.717954\pi$
$293$	−1.56135	+	1.13439i	−0.0912153	+	0.0662718i	0.541243	+	0.840866i	$0.317954\pi$
$294$	−3.09957	+	6.27636i	−0.180771	+	0.366044i
$295$	1.95815	+	6.02657i	0.114008	+	0.350881i
$296$	−1.59464	+	2.76201i	−0.0926869	+	0.160538i
$297$	2.59906	+	2.06031i	0.150813	+	0.119551i
$298$	−7.61248	−	13.1852i	−0.440979	−	0.763798i
$299$	−13.0392	−	2.77157i	−0.754077	−	0.160284i
$300$	−2.20612	−	1.60284i	−0.127370	−	0.0925399i
$301$	−1.69444	+	23.4025i	−0.0976658	+	1.34890i
$302$	6.79390	−	20.9095i	0.390945	−	1.20320i
$303$	12.5492	+	13.9373i	0.720932	+	0.800676i
$304$	3.90700	+	1.73951i	0.224082	+	0.0997676i
$305$	0.823163	−	7.83187i	0.0471342	−	0.448452i
$306$	−0.990369	−	0.210509i	−0.0566156	−	0.0120340i
$307$	12.8003			0.730552			0.365276	−	0.930899i	$-0.380975\pi$
$307$	12.8003			0.730552			0.365276	+	0.930899i	$0.380975\pi$
$308$	−5.80924	−	6.57668i	−0.331012	−	0.374741i
$309$	11.3512			0.645749
$310$	4.61097	+	0.980092i	0.261885	+	0.0556655i
$311$	1.75137	−	16.6632i	0.0993111	−	0.944882i	−0.825486	−	0.564422i	$-0.809099\pi$
$311$	1.75137	−	16.6632i	0.0993111	−	0.944882i	0.924797	−	0.380460i	$-0.124234\pi$
$312$	3.04404	+	1.35530i	0.172335	+	0.0767285i
$313$	6.65522	+	7.39137i	0.376175	+	0.417785i	0.901269	−	0.433259i	$-0.142637\pi$
$313$	6.65522	+	7.39137i	0.376175	+	0.417785i	−0.525094	+	0.851044i	$0.675970\pi$
$314$	−0.798723	+	2.45822i	−0.0450745	+	0.138725i
$315$	−3.58953	+	1.73979i	−0.202247	+	0.0980262i
$316$	−11.4518	−	8.32019i	−0.644212	−	0.468047i
$317$	16.5295	+	3.51345i	0.928389	+	0.197335i	0.647203	−	0.762318i	$-0.275939\pi$
$317$	16.5295	+	3.51345i	0.928389	+	0.197335i	0.281186	+	0.959653i	$0.409272\pi$
$318$	0.401642	+	0.695665i	0.0225230	+	0.0390109i
$319$	8.59571	+	30.7953i	0.481267	+	1.72420i
$320$	−0.753838	+	1.30569i	−0.0421408	+	0.0729901i
$321$	0.427296	+	1.31508i	0.0238494	+	0.0734008i
$322$	7.33391	+	7.63204i	0.408703	+	0.425317i
$323$	3.50319	−	2.54521i	0.194922	−	0.141619i
$324$	0.669131	+	0.743145i	0.0371739	+	0.0412858i
$325$	8.88784	−	1.88917i	0.493009	−	0.104792i
$326$	11.5847	+	5.15783i	0.641616	+	0.285666i
$327$	−1.32448	+	0.589697i	−0.0732440	+	0.0326103i
$328$	1.49573	+	4.60338i	0.0825877	+	0.254179i
$329$	−2.20776	−	6.11260i	−0.121718	−	0.336999i
$330$	−0.313604	−	4.99055i	−0.0172633	−	0.274721i
$331$	16.5112	−	28.5983i	0.907538	−	1.57190i	0.0900652	−	0.995936i	$-0.471292\pi$
$331$	16.5112	−	28.5983i	0.907538	−	1.57190i	0.817473	−	0.575967i	$-0.195374\pi$
$332$	−7.01880	+	7.79517i	−0.385207	+	0.427815i
$333$	0.333372	−	3.17182i	0.0182686	−	0.173815i
$334$	−2.20136	−	20.9446i	−0.120453	−	1.14604i
$335$	0.897153	−	2.76115i	0.0490167	−	0.150858i
$336$	−1.39650	−	2.24717i	−0.0761853	−	0.122593i
$337$	−15.3305	+	11.1383i	−0.835105	+	0.606740i	−0.920999	−	0.389565i	$-0.872625\pi$
$337$	−15.3305	+	11.1383i	−0.835105	+	0.606740i	0.0858937	+	0.996304i	$0.472625\pi$
$338$	1.73298	−	0.771570i	0.0942614	−	0.0419679i
$339$	8.03170	−	8.92010i	0.436222	−	0.484473i
$340$	0.763257	+	1.32200i	0.0413934	+	0.0716955i
$341$	−4.80366	−	9.19023i	−0.260133	−	0.497679i
$342$	−4.27674			−0.231260
$343$	−3.98442	+	18.0866i	−0.215139	+	0.976584i
$344$	−7.17475	−	5.21276i	−0.386837	−	0.281053i
$345$	0.630477	+	5.99859i	0.0339437	+	0.322953i
$346$	21.8216	−	4.63832i	1.17314	−	0.249358i
$347$	−20.5257	+	4.36288i	−1.10188	+	0.234212i	−0.722734	−	0.691126i	$-0.757115\pi$
$347$	−20.5257	+	4.36288i	−1.10188	+	0.234212i	−0.379145	+	0.925337i	$0.623782\pi$
$348$	1.00766	+	9.58724i	0.0540162	+	0.513930i
$349$	7.29469	+	5.29990i	0.390476	+	0.283697i	0.765650	−	0.643257i	$-0.222417\pi$
$349$	7.29469	+	5.29990i	0.390476	+	0.283697i	−0.375175	+	0.926954i	$0.622417\pi$
$350$	−6.68270	−	2.71916i	−0.357205	−	0.145345i
$351$	−3.33212			−0.177855
$352$	3.27022	−	0.552864i	0.174303	−	0.0294678i
$353$	7.60863	+	13.1785i	0.404967	+	0.701423i	0.994318	−	0.106454i	$-0.0339498\pi$
$353$	7.60863	+	13.1785i	0.404967	+	0.701423i	−0.589351	+	0.807877i	$0.700616\pi$
$354$	2.81233	−	3.12341i	0.149474	−	0.166008i
$355$	−17.2772	+	7.69230i	−0.916978	+	0.408265i
$356$	3.79131	−	2.75455i	0.200939	−	0.145991i
$357$	−2.67740	+	0.0868902i	−0.141703	+	0.00459872i
$358$	1.31950	−	4.06101i	0.0697378	−	0.214631i
$359$	−1.03944	−	9.88957i	−0.0548593	−	0.521952i	−0.987099	−	0.160110i	$-0.948815\pi$
$359$	−1.03944	−	9.88957i	−0.0548593	−	0.521952i	0.932240	−	0.361841i	$-0.117852\pi$
$360$	0.157595	−	1.49942i	0.00830599	−	0.0790262i
$361$	−0.474739	+	0.527251i	−0.0249863	+	0.0277500i
$362$	−10.0859	+	17.4692i	−0.530102	+	0.918163i
$363$	−8.01978	+	7.52882i	−0.420929	+	0.395160i
$364$	8.67823	+	1.55227i	0.454863	+	0.0813610i
$365$	−2.49137	−	7.66766i	−0.130405	−	0.401344i
$366$	−4.77170	+	2.12450i	−0.249421	+	0.111049i
$367$	−32.2034	−	14.3379i	−1.68100	−	0.748431i	−0.999868	−	0.0162746i	$-0.994819\pi$
$367$	−32.2034	−	14.3379i	−1.68100	−	0.748431i	−0.681136	−	0.732157i	$-0.738514\pi$
$368$	−3.91319	+	0.831774i	−0.203989	+	0.0433592i
$369$	−3.23878	−	3.59703i	−0.168604	−	0.187254i
$370$	−3.89009	+	2.82632i	−0.202236	+	0.146933i
$371$	1.47258	+	1.53244i	0.0764524	+	0.0795603i
$372$	−0.966189	−	2.97362i	−0.0500946	−	0.154175i
$373$	−12.8988	+	22.3413i	−0.667872	+	1.15679i	0.310626	+	0.950532i	$0.399461\pi$
$373$	−12.8988	+	22.3413i	−0.667872	+	1.15679i	−0.978498	+	0.206256i	$0.933872\pi$
$374$	1.17076	−	3.14736i	0.0605387	−	0.162746i
$375$	−5.82484	−	10.0889i	−0.300794	−	0.520990i
$376$	2.40274	+	0.510719i	0.123912	+	0.0263383i
$377$	−25.9871	−	18.8807i	−1.33840	−	0.972406i
$378$	2.18977	+	1.48489i	0.112630	+	0.0763744i
$379$	9.20215	−	28.3213i	0.472683	−	1.45477i	−0.376375	−	0.926467i	$-0.622830\pi$
$379$	9.20215	−	28.3213i	0.472683	−	1.45477i	0.849058	−	0.528300i	$-0.177170\pi$
$380$	4.31452	+	4.79175i	0.221330	+	0.245812i
$381$	−9.17934	−	4.08690i	−0.470272	−	0.209378i
$382$	−1.51372	+	14.4021i	−0.0774485	+	0.736873i
$383$	20.1225	+	4.27716i	1.02821	+	0.218553i	0.690983	−	0.722871i	$-0.257178\pi$
$383$	20.1225	+	4.27716i	1.02821	+	0.218553i	0.337227	+	0.941423i	$0.390511\pi$
$384$	1.00000			0.0510310
$385$	−3.96826	−	12.6206i	−0.202241	−	0.643208i
$386$	26.8353			1.36588
$387$	8.67468	+	1.84386i	0.440959	+	0.0937287i
$388$	−0.305981	+	2.91122i	−0.0155338	+	0.147795i
$389$	−4.36161	−	1.94191i	−0.221142	−	0.0984590i	0.293175	−	0.956059i	$-0.405288\pi$
$389$	−4.36161	−	1.94191i	−0.221142	−	0.0984590i	−0.514318	+	0.857600i	$0.671955\pi$
$390$	3.36155	+	3.73338i	0.170219	+	0.189047i
$391$	−1.25170	+	3.85235i	−0.0633013	+	0.194821i
$392$	−5.01135	−	4.88737i	−0.253111	−	0.246850i
$393$	5.84666	+	4.24785i	0.294925	+	0.214275i
$394$	6.34833	+	1.34938i	0.319824	+	0.0679808i
$395$	−10.6707	−	18.4822i	−0.536901	−	0.929940i
$396$	−2.76262	+	1.83519i	−0.138827	+	0.0922215i
$397$	−6.26693	+	10.8546i	−0.314528	+	0.544779i	−0.979337	−	0.202235i	$-0.935180\pi$
$397$	−6.26693	+	10.8546i	−0.314528	+	0.544779i	0.664809	+	0.747013i	$0.268513\pi$
$398$	−0.545371	−	1.67848i	−0.0273370	−	0.0841346i
$399$	−10.9858	+	2.71032i	−0.549978	+	0.135686i
$400$	2.20612	−	1.60284i	0.110306	−	0.0801419i
$401$	−19.2117	−	21.3368i	−0.959389	−	1.06551i	−0.997803	−	0.0662474i	$-0.978897\pi$
$401$	−19.2117	−	21.3368i	−0.959389	−	1.06551i	0.0384143	−	0.999262i	$-0.487769\pi$
$402$	−1.88356	+	0.400364i	−0.0939436	+	0.0199683i
$403$	9.51767	+	4.23754i	0.474109	+	0.211087i
$404$	−17.1331	+	7.62813i	−0.852402	+	0.379514i
$405$	0.465898	+	1.43389i	0.0231506	+	0.0712503i
$406$	8.66418	+	23.9884i	0.429996	+	1.19053i
$407$	10.2452	+	2.63133i	0.507834	+	0.130430i
$408$	0.506247	−	0.876846i	0.0250630	−	0.0434103i
$409$	−23.9473	+	26.5962i	−1.18412	+	1.31510i	−0.245801	+	0.969320i	$0.579051\pi$
$409$	−23.9473	+	26.5962i	−1.18412	+	1.31510i	−0.938317	+	0.345776i	$0.887616\pi$
$410$	−0.762804	+	7.25759i	−0.0376722	+	0.358427i
$411$	0.229534	+	2.18387i	0.0113221	+	0.107723i
$412$	−3.50772	+	10.7957i	−0.172813	+	0.531864i
$413$	5.24471	−	9.80549i	0.258075	−	0.482496i
$414$	3.23656	−	2.35150i	0.159068	−	0.115570i
$415$	−14.4474	+	6.43241i	−0.709196	+	0.315754i
$416$	−2.22962	+	2.47625i	−0.109316	+	0.121408i
$417$	−9.66530	−	16.7408i	−0.473312	−	0.819800i
$418$	2.07314	−	14.0320i	0.101401	−	0.686329i
$419$	10.6538			0.520471			0.260235	−	0.965545i	$-0.416200\pi$
$419$	10.6538			0.520471			0.260235	+	0.965545i	$0.416200\pi$
$420$	−0.545415	−	3.95147i	−0.0266135	−	0.192812i
$421$	25.9800	+	18.8756i	1.26619	+	0.919940i	0.999044	−	0.0437162i	$-0.0139197\pi$
$421$	25.9800	+	18.8756i	1.26619	+	0.919940i	0.267145	+	0.963656i	$0.413920\pi$
$422$	−0.410612	−	3.90671i	−0.0199883	−	0.190176i
$423$	−2.40274	+	0.510719i	−0.116825	+	0.0248320i
$424$	−0.785731	+	0.167012i	−0.0381584	+	0.00811083i
$425$	−0.288601	−	2.74586i	−0.0139992	−	0.133194i
$426$	10.1483	+	7.37315i	0.491686	+	0.357230i
$427$	−10.9108	+	8.48126i	−0.528013	+	0.410437i
$428$	−1.38276			−0.0668382
$429$	1.61524	−	10.9327i	0.0779845	−	0.527836i
$430$	−6.68540	−	11.5795i	−0.322399	−	0.558411i
$431$	−13.8152	+	15.3433i	−0.665453	+	0.739061i	−0.977484	−	0.211012i	$-0.932324\pi$
$431$	−13.8152	+	15.3433i	−0.665453	+	0.739061i	0.312030	+	0.950072i	$0.398991\pi$
$432$	−0.913545	+	0.406737i	−0.0439530	+	0.0195691i
$433$	−23.7210	+	17.2343i	−1.13996	+	0.828229i	−0.987114	−	0.160021i	$-0.948844\pi$
$433$	−23.7210	+	17.2343i	−1.13996	+	0.828229i	−0.152846	+	0.988250i	$0.548844\pi$
$434$	−4.36637	−	7.02613i	−0.209593	−	0.337265i
$435$	−4.49127	+	13.8227i	−0.215340	+	0.662749i
$436$	−0.151548	−	1.44188i	−0.00725784	−	0.0690537i
$437$	−1.78844	+	17.0159i	−0.0855526	+	0.813979i
$438$	−3.57816	+	3.97395i	−0.170971	+	0.189883i
$439$	9.30560	−	16.1178i	0.444132	−	0.769259i	−0.553859	−	0.832610i	$-0.686845\pi$
$439$	9.30560	−	16.1178i	0.444132	−	0.769259i	0.997991	+	0.0633509i	$0.0201787\pi$
$440$	4.84321	+	1.24391i	0.230891	+	0.0593011i
$441$	6.56597	+	2.42654i	0.312665	+	0.115549i
$442$	1.04255	+	3.20863i	0.0495889	+	0.152619i
$443$	−4.25773	+	1.89567i	−0.202291	+	0.0900658i	−0.505382	−	0.862896i	$-0.668648\pi$
$443$	−4.25773	+	1.89567i	−0.202291	+	0.0900658i	0.303090	+	0.952962i	$0.401982\pi$
$444$	2.91356	+	1.29720i	0.138271	+	0.0615624i
$445$	6.91105	−	1.46899i	0.327615	−	0.0696367i
$446$	16.1565	+	17.9436i	0.765032	+	0.849655i
$447$	−12.3172	+	8.94900i	−0.582586	+	0.423273i
$448$	2.56873	−	0.633736i	0.121361	−	0.0299412i
$449$	−8.61738	−	26.5216i	−0.406679	−	1.25163i	−0.919485	−	0.393125i	$-0.871394\pi$
$449$	−8.61738	−	26.5216i	−0.406679	−	1.25163i	0.512806	−	0.858505i	$-0.328606\pi$
$450$	−1.36346	+	2.36157i	−0.0642739	+	0.111326i
$451$	13.3719	−	8.88280i	0.629656	−	0.418275i
$452$	6.00159	+	10.3951i	0.282291	+	0.488942i
$453$	−21.5051	−	4.57105i	−1.01040	−	0.214767i
$454$	13.0054	+	9.44897i	0.610373	+	0.443462i
$455$	11.0009	+	7.45971i	0.515730	+	0.349717i
$456$	1.32159	−	4.06742i	0.0618889	−	0.190475i
$457$	−4.16302	−	4.62351i	−0.194738	−	0.216278i	0.637866	−	0.770148i	$-0.279817\pi$
$457$	−4.16302	−	4.62351i	−0.194738	−	0.216278i	−0.832604	+	0.553869i	$0.813151\pi$
$458$	3.68378	+	1.64012i	0.172132	+	0.0766379i
$459$	−0.105834	+	1.00695i	−0.00493993	+	0.0470003i
$460$	−5.89982	−	1.25405i	−0.275081	−	0.0584702i
$461$	−3.82714			−0.178248			−0.0891239	−	0.996021i	$-0.528407\pi$
$461$	−3.82714			−0.178248			−0.0891239	+	0.996021i	$0.528407\pi$
$462$	−5.93342	+	6.46487i	−0.276048	+	0.300773i
$463$	11.4623			0.532699			0.266350	−	0.963876i	$-0.414182\pi$
$463$	11.4623			0.532699			0.266350	+	0.963876i	$0.414182\pi$
$464$	−9.42939	−	2.00428i	−0.437748	−	0.0930463i
$465$	0.492745	−	4.68816i	0.0228505	−	0.217408i
$466$	−24.8728	−	11.0741i	−1.15221	−	0.512998i
$467$	11.2689	+	12.5154i	0.521461	+	0.579142i	0.945138	−	0.326672i	$-0.105927\pi$
$467$	11.2689	+	12.5154i	0.521461	+	0.579142i	−0.423676	+	0.905814i	$0.639261\pi$
$468$	1.02968	−	3.16903i	0.0475971	−	0.146489i
$469$	−4.58464	+	2.22211i	−0.211699	+	0.102607i
$470$	2.99619	+	2.17686i	0.138204	+	0.100411i
$471$	2.52824	+	0.537394i	0.116495	+	0.0247618i
$472$	2.10148	+	3.63988i	0.0967286	+	0.167539i
$473$	−10.2548	+	27.5679i	−0.471515	+	1.26757i
$474$	−7.07758	+	12.2587i	−0.325084	+	0.563062i
$475$	−3.60385	−	11.0915i	−0.165356	−	0.508913i
$476$	0.744724	−	2.57321i	0.0341344	−	0.117943i
$477$	0.649871	−	0.472159i	0.0297555	−	0.0216187i
$478$	8.63997	+	9.59566i	0.395183	+	0.438895i
$479$	−37.8795	+	8.05153i	−1.73076	+	0.367884i	−0.962294	−	0.272011i	$-0.912311\pi$
$479$	−37.8795	+	8.05153i	−1.73076	+	0.367884i	−0.768463	+	0.639895i	$0.778978\pi$
$480$	1.37733	+	0.613227i	0.0628663	+	0.0279899i
$481$	−9.70834	+	4.32243i	−0.442662	+	0.197086i
$482$	−7.77488	−	23.9286i	−0.354136	−	1.08992i
$483$	6.82363	−	8.09150i	0.310486	−	0.368176i
$484$	−4.68208	−	9.95380i	−0.212822	−	0.452445i
$485$	−2.20667	+	3.82207i	−0.100200	+	0.173551i
$486$	0.669131	−	0.743145i	0.0303524	−	0.0337097i
$487$	−1.01393	+	9.64693i	−0.0459457	+	0.437144i	0.947233	+	0.320545i	$0.103866\pi$
$487$	−1.01393	+	9.64693i	−0.0459457	+	0.437144i	−0.993179	+	0.116599i	$0.962801\pi$
$488$	−0.545981	−	5.19466i	−0.0247154	−	0.235151i
$489$	3.91865	−	12.0604i	0.177207	−	0.545388i
$490$	−3.90521	−	9.80462i	−0.176420	−	0.442928i
$491$	−27.4516	+	19.9448i	−1.23888	+	0.900096i	−0.997523	−	0.0703417i	$-0.977591\pi$
$491$	−27.4516	+	19.9448i	−1.23888	+	0.900096i	−0.241353	+	0.970437i	$0.577591\pi$
$492$	4.42181	−	1.96872i	0.199351	−	0.0887566i
$493$	−6.53104	+	7.25346i	−0.294143	+	0.326679i
$494$	7.12531	+	12.3414i	0.320583	+	0.555266i
$495$	−4.93043	+	0.833540i	−0.221607	+	0.0374649i
$496$	3.12665			0.140391
$497$	30.7408	+	12.5083i	1.37891	+	0.561075i
$498$	8.48613	+	6.16553i	0.380273	+	0.276284i
$499$	0.865580	+	8.23545i	0.0387487	+	0.368669i	0.996664	+	0.0816174i	$0.0260086\pi$
$499$	0.865580	+	8.23545i	0.0387487	+	0.368669i	−0.957915	+	0.287052i	$0.907325\pi$
$500$	11.3951	−	2.42211i	0.509605	−	0.108320i
$501$	−20.5997	+	4.37861i	−0.920328	+	0.195622i
$502$	−1.57476	−	14.9828i	−0.0702850	−	0.668717i
$503$	−25.0909	−	18.2296i	−1.11875	−	0.812817i	−0.134728	−	0.990883i	$-0.543016\pi$
$503$	−25.0909	−	18.2296i	−1.11875	−	0.812817i	−0.984019	+	0.178066i	$0.943016\pi$
$504$	−2.08889	+	1.62374i	−0.0930465	+	0.0723273i
$505$	−28.2757			−1.25825
$506$	6.14637	+	11.7591i	0.273240	+	0.522755i
$507$	−0.948489	−	1.64283i	−0.0421239	−	0.0729607i
$508$	6.72345	−	7.46715i	0.298305	−	0.331301i
$509$	30.2910	−	13.4864i	1.34263	−	0.597776i	0.395450	−	0.918487i	$-0.370589\pi$
$509$	30.2910	−	13.4864i	1.34263	−	0.597776i	0.947177	+	0.320711i	$0.103922\pi$
$510$	1.23498	−	0.897262i	0.0546856	−	0.0397314i
$511$	−6.67289	+	12.4756i	−0.295191	+	0.551888i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	0.447041	+	4.25331i	0.0197373	+	0.187788i
$514$	1.44923	−	13.7885i	0.0639229	−	0.608186i
$515$	−11.4515	+	12.7182i	−0.504613	+	0.560429i
$516$	−4.43424	+	7.68033i	−0.195207	+	0.338108i
$517$	−0.510947	−	8.13100i	−0.0224714	−	0.357601i
$518$	8.30624	+	1.48573i	0.364955	+	0.0652793i
$519$	−6.89389	−	21.2172i	−0.302608	−	0.931332i
$520$	−4.58943	+	2.04335i	−0.201260	+	0.0896067i
$521$	−1.09813	−	0.488919i	−0.0481100	−	0.0214199i	0.382541	−	0.923939i	$-0.375049\pi$
$521$	−1.09813	−	0.488919i	−0.0481100	−	0.0214199i	−0.430651	+	0.902519i	$0.641716\pi$
$522$	9.42939	−	2.00428i	0.412713	−	0.0877249i
$523$	−10.6349	−	11.8112i	−0.465031	−	0.516469i	0.464320	−	0.885668i	$-0.346299\pi$
$523$	−10.6349	−	11.8112i	−0.465031	−	0.516469i	−0.929351	+	0.369199i	$0.879632\pi$
$524$	−5.84666	+	4.24785i	−0.255412	+	0.185568i
$525$	−2.00574	+	6.93032i	−0.0875375	+	0.302464i
$526$	0.310126	+	0.954471i	0.0135222	+	0.0416169i
$527$	1.58286	−	2.74159i	0.0689504	−	0.119426i
$528$	−0.891667	−	3.19452i	−0.0388048	−	0.139023i
$529$	3.49755	+	6.05794i	0.152068	+	0.263389i
$530$	−1.18463	−	0.251800i	−0.0514569	−	0.0109375i
$531$	−3.40027	−	2.47044i	−0.147559	−	0.107208i
$532$	0.817127	−	11.2857i	0.0354269	−	0.489295i
$533$	−4.98394	+	15.3390i	−0.215879	+	0.664406i
$534$	−3.13576	−	3.48261i	−0.135697	−	0.150707i
$535$	−1.90452	−	0.847946i	−0.0823395	−	0.0366599i
$536$	0.201285	−	1.91510i	0.00869417	−	0.0827195i
$537$	−4.17669	−	0.887782i	−0.180237	−	0.0383106i
$538$	−7.38565			−0.318418
$539$	−11.1443	+	20.3667i	−0.480020	+	0.877257i
$540$	−1.50768			−0.0648801
$541$	44.5532	+	9.47008i	1.91549	+	0.407151i	0.999988	+	0.00484440i	$0.00154202\pi$
$541$	44.5532	+	9.47008i	1.91549	+	0.407151i	0.915505	+	0.402306i	$0.131791\pi$
$542$	0.607491	−	5.77989i	0.0260940	−	0.248268i
$543$	18.4278	+	8.20459i	0.790813	+	0.352092i
$544$	0.677491	+	0.752430i	0.0290472	+	0.0322602i
$545$	0.675470	−	2.07888i	0.0289340	−	0.0890496i
$546$	0.636645	−	8.79294i	0.0272459	−	0.376303i
$547$	−25.3787	−	18.4387i	−1.08512	−	0.788382i	−0.106547	−	0.994308i	$-0.533980\pi$
$547$	−25.3787	−	18.4387i	−1.08512	−	0.788382i	−0.978568	+	0.205925i	$0.933980\pi$
$548$	−2.14792	−	0.456554i	−0.0917544	−	0.0195030i
$549$	2.61164	+	4.52349i	0.111462	+	0.193058i
$550$	−7.08741	−	5.61828i	−0.302208	−	0.239564i
$551$	−20.6140	+	35.7045i	−0.878185	+	1.52106i
$552$	1.23626	+	3.80481i	0.0526186	+	0.161943i
$553$	−10.4116	+	35.9747i	−0.442746	+	1.52980i
$554$	13.4344	−	9.76067i	0.570773	−	0.414691i
$555$	3.21746	+	3.57335i	0.136574	+	0.151680i
$556$	18.9082	−	4.01906i	0.801885	−	0.170446i
$557$	11.5129	+	5.12587i	0.487816	+	0.217190i	0.635880	−	0.771788i	$-0.280637\pi$
$557$	11.5129	+	5.12587i	0.487816	+	0.217190i	−0.148063	+	0.988978i	$0.547304\pi$
$558$	−2.85634	+	1.27172i	−0.120919	+	0.0538364i
$559$	−9.13171	−	28.1045i	−0.386230	−	1.18869i
$560$	3.92662	+	0.702352i	0.165930	+	0.0296798i
$561$	−3.25250	−	0.835360i	−0.137321	−	0.0352689i
$562$	0.0681905	−	0.118109i	0.00287644	−	0.00498214i
$563$	−3.87163	+	4.29988i	−0.163170	+	0.181218i	−0.819185	−	0.573529i	$-0.805574\pi$
$563$	−3.87163	+	4.29988i	−0.163170	+	0.181218i	0.656015	+	0.754748i	$0.272241\pi$
$564$	0.256766	−	2.44297i	0.0108118	−	0.102867i
$565$	1.89164	+	17.9978i	0.0795820	+	0.757172i
$566$	−0.488498	+	1.50344i	−0.0205331	+	0.0631943i
$567$	1.24786	−	2.33299i	0.0524052	−	0.0979764i
$568$	−10.1483	+	7.37315i	−0.425812	+	0.309371i
$569$	24.5074	−	10.9114i	1.02740	−	0.457429i	0.177362	−	0.984146i	$-0.443244\pi$
$569$	24.5074	−	10.9114i	1.02740	−	0.457429i	0.850041	+	0.526717i	$0.176577\pi$
$570$	4.31452	−	4.79175i	0.180715	−	0.200705i
$571$	9.83960	+	17.0427i	0.411774	+	0.713214i	0.995084	−	0.0990359i	$-0.0315759\pi$
$571$	9.83960	+	17.0427i	0.411774	+	0.713214i	−0.583310	+	0.812250i	$0.698243\pi$
$572$	9.89849	+	4.91458i	0.413877	+	0.205489i
$573$	14.4814			0.604968
$574$	10.1108	−	7.85937i	0.422017	−	0.328044i
$575$	8.82582	+	6.41233i	0.368062	+	0.267413i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	8.79238	−	1.86888i	0.366032	−	0.0778024i	−0.0212242	−	0.999775i	$-0.506756\pi$
$577$	8.79238	−	1.86888i	0.366032	−	0.0778024i	0.387256	+	0.921972i	$0.373423\pi$
$578$	−15.6258	+	3.32136i	−0.649946	+	0.138150i
$579$	−2.80506	−	26.6883i	−0.116574	−	1.10913i
$580$	−11.7583	−	8.54291i	−0.488237	−	0.354725i
$581$	25.7059	+	10.4596i	1.06646	+	0.433939i
$582$	2.92725			0.121338
$583$	1.23413	+	2.36111i	0.0511126	+	0.0977872i
$584$	−2.67374	−	4.63105i	−0.110640	−	0.191634i
$585$	3.36155	−	3.73338i	0.138983	−	0.154356i
$586$	−1.76309	+	0.784977i	−0.0728325	+	0.0324271i
$587$	13.2582	−	9.63263i	0.547224	−	0.397581i	−0.279537	−	0.960135i	$-0.590181\pi$
$587$	13.2582	−	9.63263i	0.547224	−	0.397581i	0.826761	+	0.562554i	$0.190181\pi$
$588$	−4.33677	+	5.49476i	−0.178845	+	0.226600i
$589$	4.13214	−	12.7174i	0.170262	−	0.524012i
$590$	0.662367	+	6.30200i	0.0272692	+	0.259449i
$591$	0.678406	−	6.45460i	0.0279059	−	0.265507i
$592$	−2.13405	+	2.37010i	−0.0877090	+	0.0974107i
$593$	−0.971088	+	1.68197i	−0.0398778	+	0.0690704i	−0.885275	−	0.465067i	$-0.846030\pi$
$593$	−0.971088	+	1.68197i	−0.0398778	+	0.0690704i	0.845398	+	0.534137i	$0.179364\pi$
$594$	2.11390	+	2.55566i	0.0867346	+	0.104860i
$595$	2.60369	−	3.08747i	0.106741	−	0.126574i
$596$	−4.70477	−	14.4798i	−0.192715	−	0.593115i
$597$	−1.61228	+	0.717832i	−0.0659861	+	0.0293789i
$598$	−12.1780	−	5.42201i	−0.497997	−	0.221722i
$599$	−17.5152	+	3.72298i	−0.715653	+	0.152117i	−0.551327	−	0.834289i	$-0.685878\pi$
$599$	−17.5152	+	3.72298i	−0.715653	+	0.152117i	−0.164326	+	0.986406i	$0.552545\pi$
$600$	−1.82466	−	2.02649i	−0.0744914	−	0.0827311i
$601$	1.72048	−	1.25000i	0.0701797	−	0.0509885i	−0.552142	−	0.833750i	$-0.686189\pi$
$601$	1.72048	−	1.25000i	0.0701797	−	0.0509885i	0.622322	+	0.782761i	$0.286189\pi$
$602$	−6.52307	+	22.5388i	−0.265861	+	0.918615i
$603$	0.595057	+	1.83140i	0.0242326	+	0.0745802i
$604$	10.9928	−	19.0400i	0.447289	−	0.774727i
$605$	−0.344833	−	16.5809i	−0.0140195	−	0.674108i
$606$	9.37724	+	16.2419i	0.380924	+	0.659780i
$607$	−19.0183	−	4.04247i	−0.771930	−	0.164079i	−0.194924	−	0.980818i	$-0.562446\pi$
$607$	−19.0183	−	4.04247i	−0.771930	−	0.164079i	−0.577006	+	0.816740i	$0.695779\pi$
$608$	3.45996	+	2.51381i	0.140320	+	0.101948i
$609$	22.9514	−	11.1242i	0.930037	−	0.450775i
$610$	2.43351	−	7.48958i	0.0985301	−	0.303244i
$611$	5.47690	+	6.08271i	0.221572	+	0.246080i
$612$	−0.924960	−	0.411819i	−0.0373893	−	0.0166468i
$613$	3.33663	−	31.7460i	0.134765	−	1.28221i	−0.692920	−	0.721014i	$-0.743676\pi$
$613$	3.33663	−	31.7460i	0.134765	−	1.28221i	0.827685	−	0.561192i	$-0.189657\pi$
$614$	12.5206	+	2.66133i	0.505290	+	0.107403i
$615$	7.29757			0.294266
$616$	−4.31493	−	7.64077i	−0.173854	−	0.307855i
$617$	−17.1429			−0.690149			−0.345074	−	0.938575i	$-0.612146\pi$
$617$	−17.1429			−0.690149			−0.345074	+	0.938575i	$0.612146\pi$
$618$	11.1032	+	2.36005i	0.446635	+	0.0949352i
$619$	3.62683	−	34.5070i	0.145775	−	1.38695i	−0.639970	−	0.768400i	$-0.721053\pi$
$619$	3.62683	−	34.5070i	0.145775	−	1.38695i	0.785744	−	0.618552i	$-0.212280\pi$
$620$	4.30644	+	1.91735i	0.172951	+	0.0770026i
$621$	−2.67693	−	2.97303i	−0.107422	−	0.119304i
$622$	5.17757	−	15.9349i	0.207602	−	0.638932i
$623$	−10.2620	−	6.95865i	−0.411137	−	0.278792i
$624$	2.69574	+	1.95857i	0.107916	+	0.0784056i
$625$	3.84353	+	0.816967i	0.153741	+	0.0326787i
$626$	4.97304	+	8.61355i	0.198763	+	0.344267i
$627$	−14.1719	−	0.595041i	−0.565970	−	0.0237636i
$628$	−1.29236	+	2.23843i	−0.0515708	+	0.0893232i
$629$	0.997858	+	3.07109i	0.0397872	+	0.122452i
$630$	−3.87282	+	0.955469i	−0.154297	+	0.0380668i
$631$	−13.0403	+	9.47434i	−0.519127	+	0.377167i	−0.816275	−	0.577664i	$-0.803964\pi$
$631$	−13.0403	+	9.47434i	−0.519127	+	0.377167i	0.297148	+	0.954831i	$0.403964\pi$
$632$	−9.47165	−	10.5193i	−0.376762	−	0.418437i
$633$	−3.84239	+	0.816725i	−0.152721	+	0.0324619i
$634$	15.4378	+	6.87335i	0.613113	+	0.272976i
$635$	13.8395	−	6.16173i	0.549203	−	0.244521i
$636$	0.248228	+	0.763969i	0.00984290	+	0.0302933i
$637$	−3.93703	−	22.9902i	−0.155991	−	0.910904i
$638$	2.00517	+	31.9095i	0.0793856	+	1.26331i
$639$	6.27198	−	10.8634i	0.248116	−	0.429749i
$640$	−1.00883	+	1.12042i	−0.0398776	+	0.0442886i
$641$	3.47507	−	33.0631i	0.137257	−	1.30591i	−0.681518	−	0.731801i	$-0.738680\pi$
$641$	3.47507	−	33.0631i	0.137257	−	1.30591i	0.818775	−	0.574114i	$-0.194653\pi$
$642$	0.144538	+	1.37519i	0.00570445	+	0.0542742i
$643$	9.68045	−	29.7934i	0.381760	−	1.17494i	−0.557044	−	0.830483i	$-0.688064\pi$
$643$	9.68045	−	29.7934i	0.381760	−	1.17494i	0.938804	−	0.344453i	$-0.111936\pi$
$644$	5.58685	+	8.99007i	0.220153	+	0.354258i
$645$	−10.8172	+	7.85916i	−0.425927	+	0.309454i
$646$	3.95581	−	1.76124i	0.155639	−	0.0692951i
$647$	29.4213	−	32.6756i	1.15667	−	1.28461i	0.204560	−	0.978854i	$-0.434424\pi$
$647$	29.4213	−	32.6756i	1.15667	−	1.28461i	0.952110	−	0.305757i	$-0.0989095\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	9.75382	−	9.95878i	0.382871	−	0.390916i
$650$	9.08640			0.356398
$651$	−6.53123	+	5.07688i	−0.255979	+	0.198979i
$652$	10.2591	+	7.45371i	0.401779	+	0.291910i
$653$	1.51009	+	14.3676i	0.0590944	+	0.562246i	0.983509	+	0.180858i	$0.0578873\pi$
$653$	1.51009	+	14.3676i	0.0590944	+	0.562246i	−0.924415	+	0.381388i	$0.875446\pi$
$654$	−1.41814	+	0.301436i	−0.0554538	+	0.0117871i
$655$	−10.6577	+	2.26536i	−0.416430	+	0.0885149i
$656$	0.505947	+	4.81376i	0.0197539	+	0.187946i
$657$	4.32620	+	3.14317i	0.168781	+	0.122627i
$658$	−0.888632	−	6.43805i	−0.0346425	−	0.250981i
$659$	−11.8379			−0.461137			−0.230569	−	0.973056i	$-0.574059\pi$
$659$	−11.8379			−0.461137			−0.230569	+	0.973056i	$0.574059\pi$
$660$	0.730844	−	4.94670i	0.0284481	−	0.192550i
$661$	9.16905	+	15.8813i	0.356635	+	0.617709i	0.987396	−	0.158267i	$-0.0505907\pi$
$661$	9.16905	+	15.8813i	0.356635	+	0.617709i	−0.630762	+	0.775977i	$0.717257\pi$
$662$	22.0963	−	24.5404i	0.858798	−	0.953792i
$663$	3.08208	−	1.37223i	0.119698	−	0.0532929i
$664$	−8.48613	+	6.16553i	−0.329326	+	0.239269i
$665$	8.04612	−	15.0430i	0.312015	−	0.583342i
$666$	0.985545	−	3.03319i	0.0381891	−	0.117534i
$667$	−4.03125	−	38.3548i	−0.156091	−	1.48510i
$668$	2.20136	−	20.9446i	0.0851733	−	0.810370i
$669$	16.1565	−	17.9436i	0.624646	−	0.693740i
$670$	1.45162	−	2.51429i	0.0560811	−	0.0971354i
$671$	−16.1076	+	6.37605i	−0.621827	+	0.246145i
$672$	−0.898770	−	2.48842i	−0.0346708	−	0.0959927i
$673$	−1.02569	−	3.15674i	−0.0395373	−	0.121683i	0.929340	−	0.369226i	$-0.120377\pi$
$673$	−1.02569	−	3.15674i	−0.0395373	−	0.121683i	−0.968877	+	0.247542i	$0.920377\pi$
$674$	−17.3113	+	7.70747i	−0.666805	+	0.296881i
$675$	2.49116	+	1.10913i	0.0958847	+	0.0426906i
$676$	1.85552	−	0.394404i	0.0713663	−	0.0151694i
$677$	25.6729	+	28.5127i	0.986690	+	1.09583i	0.995394	+	0.0958685i	$0.0305628\pi$
$677$	25.6729	+	28.5127i	0.986690	+	1.09583i	−0.00870368	+	0.999962i	$0.502771\pi$
$678$	9.71078	−	7.05529i	0.372940	−	0.270957i
$679$	7.51932	−	1.85510i	0.288565	−	0.0711924i
$680$	0.471719	+	1.45180i	0.0180896	+	0.0556740i
$681$	8.03777	−	13.9218i	0.308008	−	0.533486i
$682$	−2.78793	−	9.98814i	−0.106755	−	0.382466i
$683$	3.46045	+	5.99367i	0.132410	+	0.229341i	0.924605	−	0.380927i	$-0.124395\pi$
$683$	3.46045	+	5.99367i	0.132410	+	0.229341i	−0.792195	+	0.610268i	$0.791062\pi$
$684$	−4.18328	−	0.889184i	−0.159952	−	0.0339988i
$685$	−2.67842	−	1.94599i	−0.102337	−	0.0743523i
$686$	−7.65776	+	16.8629i	−0.292375	+	0.643830i
$687$	1.24608	−	3.83504i	0.0475409	−	0.146316i
$688$	−5.93417	−	6.59057i	−0.226238	−	0.251263i
$689$	−2.44523	−	1.08869i	−0.0931559	−	0.0414757i
$690$	−0.630477	+	5.99859i	−0.0240018	+	0.228362i
$691$	10.4277	+	2.21647i	0.396687	+	0.0843184i	0.401936	−	0.915668i	$-0.368338\pi$
$691$	10.4277	+	2.21647i	0.396687	+	0.0843184i	−0.00524906	+	0.999986i	$0.501671\pi$
$692$	22.3091			0.848065
$693$	7.04967	+	5.22515i	0.267795	+	0.198487i
$694$	−20.9843			−0.796553
$695$	28.5074	+	6.05944i	1.08135	+	0.229848i
$696$	−1.00766	+	9.58724i	−0.0381952	+	0.363403i
$697$	4.47706	+	1.99331i	0.169581	+	0.0755022i
$698$	6.03337	+	6.70074i	0.228366	+	0.253627i
$699$	−8.41352	+	25.8941i	−0.318228	+	0.979407i
$700$	−5.97132	−	4.04916i	−0.225695	−	0.153044i
$701$	26.5866	+	19.3163i	1.00416	+	0.729566i	0.962977	−	0.269585i	$-0.0868866\pi$
$701$	26.5866	+	19.3163i	1.00416	+	0.729566i	0.0411853	+	0.999152i	$0.486887\pi$
$702$	−3.25931	−	0.692787i	−0.123015	−	0.0261475i
$703$	6.81988	+	11.8124i	0.257217	+	0.445513i
$704$	3.31371	+	0.139134i	0.124890	+	0.00524382i
$705$	1.85175	−	3.20732i	0.0697408	−	0.120795i
$706$	4.70239	+	14.4725i	0.176977	+	0.544679i
$707$	34.3806	+	35.7783i	1.29302	+	1.34558i
$708$	3.40027	−	2.47044i	0.127790	−	0.0928449i
$709$	−12.3759	−	13.7449i	−0.464788	−	0.516199i	0.464491	−	0.885578i	$-0.346237\pi$
$709$	−12.3759	−	13.7449i	−0.464788	−	0.516199i	−0.929279	+	0.369379i	$0.879571\pi$
$710$	−18.4990	+	3.93207i	−0.694253	+	0.147568i
$711$	12.9314	+	5.75742i	0.484965	+	0.215920i
$712$	4.28116	−	1.90610i	0.160443	−	0.0714339i
$713$	3.86535	+	11.8963i	0.144758	+	0.445520i
$714$	−2.63696	−	0.471671i	−0.0986856	−	0.0176518i
$715$	10.6197	+	12.8390i	0.397156	+	0.480152i
$716$	2.13500	−	3.69793i	0.0797886	−	0.138198i
$717$	8.63997	−	9.59566i	0.322666	−	0.358356i
$718$	1.03944	−	9.88957i	0.0387914	−	0.369075i
$719$	−2.23205	−	21.2366i	−0.0832416	−	0.791991i	−0.953904	−	0.300110i	$-0.902976\pi$
$719$	−2.23205	−	21.2366i	−0.0832416	−	0.791991i	0.870663	−	0.491880i	$-0.163690\pi$
$720$	0.465898	−	1.43389i	0.0173630	−	0.0534378i
$721$	30.0167	−	0.974139i	1.11788	−	0.0362788i
$722$	−0.573986	+	0.417025i	−0.0213616	+	0.0155201i
$723$	−22.9848	+	10.2335i	−0.854815	+	0.380588i
$724$	−13.4975	+	14.9905i	−0.501632	+	0.557118i
$725$	13.1438	+	22.7657i	0.488148	+	0.845496i
$726$	−9.40986	+	5.69689i	−0.349233	+	0.211431i
$727$	−4.37419			−0.162230			−0.0811148	−	0.996705i	$-0.525848\pi$
$727$	−4.37419			−0.162230			−0.0811148	+	0.996705i	$0.525848\pi$
$728$	8.16585	+	3.32265i	0.302647	+	0.123146i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−0.842735	−	8.01809i	−0.0311910	−	0.296763i
$731$	−8.78307	+	1.86690i	−0.324854	+	0.0690497i
$732$	−5.10914	+	1.08598i	−0.188839	+	0.0401390i
$733$	5.37383	+	51.1285i	0.198487	+	1.88848i	0.411476	+	0.911421i	$0.365014\pi$
$733$	5.37383	+	51.1285i	0.198487	+	1.88848i	−0.212989	+	0.977055i	$0.568320\pi$
$734$	−28.5187	−	20.7200i	−1.05264	−	0.764790i
$735$	−9.34271	+	4.90868i	−0.344611	+	0.181060i
$736$	−4.00061			−0.147464
$737$	−6.29728	+	1.06462i	−0.231963	+	0.0392158i
$738$	−2.42014	−	4.19180i	−0.0890865	−	0.154302i
$739$	−17.9604	+	19.9470i	−0.660683	+	0.733762i	−0.976609	−	0.215021i	$-0.931018\pi$
$739$	−17.9604	+	19.9470i	−0.660683	+	0.733762i	0.315927	+	0.948784i	$0.397685\pi$
$740$	−4.39271	+	1.95576i	−0.161479	+	0.0718951i
$741$	11.5290	−	8.37630i	0.423528	−	0.307711i
$742$	1.12179	+	1.80512i	0.0411821	+	0.0662680i
$743$	−4.01206	+	12.3479i	−0.147188	+	0.452999i	−0.997286	−	0.0736263i	$-0.976543\pi$
$743$	−4.01206	+	12.3479i	−0.147188	+	0.452999i	0.850098	+	0.526625i	$0.176543\pi$
$744$	−0.326824	−	3.10953i	−0.0119820	−	0.114001i
$745$	2.39938	−	22.8286i	0.0879064	−	0.836374i
$746$	−17.2619	+	19.1713i	−0.632003	+	0.701911i
$747$	5.24472	−	9.08412i	0.191894	−	0.332370i
$748$	1.79955	−	2.83517i	0.0657982	−	0.103664i
$749$	1.24278	+	3.44088i	0.0454103	+	0.125727i
$750$	−3.59995	−	11.0795i	−0.131452	−	0.404566i
$751$	28.7120	−	12.7834i	1.04772	−	0.466473i	0.190638	−	0.981660i	$-0.438944\pi$
$751$	28.7120	−	12.7834i	1.04772	−	0.466473i	0.857078	+	0.515187i	$0.172278\pi$
$752$	2.24405	+	0.999117i	0.0818322	+	0.0364341i
$753$	−14.7362	+	3.13227i	−0.537016	+	0.114146i
$754$	−21.4937	−	23.8711i	−0.782753	−	0.869336i
$755$	26.8165	−	19.4833i	0.975953	−	0.709072i
$756$	1.83320	+	1.90772i	0.0666727	+	0.0693830i
$757$	2.61420	+	8.04567i	0.0950146	+	0.292425i	0.987257	−	0.159131i	$-0.0508692\pi$
$757$	2.61420	+	8.04567i	0.0950146	+	0.292425i	−0.892243	+	0.451556i	$0.850869\pi$
$758$	14.8894	−	25.7892i	0.540807	−	0.936705i
$759$	11.0522	−	7.34186i	0.401169	−	0.266493i
$760$	3.22397	+	5.58408i	0.116946	+	0.202556i
$761$	5.25848	+	1.11773i	0.190620	+	0.0405175i	0.302232	−	0.953234i	$-0.402268\pi$
$761$	5.25848	+	1.11773i	0.190620	+	0.0405175i	−0.111612	+	0.993752i	$0.535602\pi$
$762$	−8.12903	−	5.90609i	−0.294484	−	0.213955i
$763$	−3.45180	+	1.67304i	−0.124964	+	0.0605680i
$764$	−4.47499	+	13.7726i	−0.161900	+	0.498276i
$765$	−1.02144	−	1.13442i	−0.0369301	−	0.0410151i
$766$	18.7935	+	8.36739i	0.679036	+	0.302326i
$767$	−1.46390	+	13.9281i	−0.0528583	+	0.502914i
$768$	0.978148	+	0.207912i	0.0352959	+	0.00750237i
$769$	8.08465			0.291540			0.145770	−	0.989319i	$-0.453434\pi$
$769$	8.08465			0.291540			0.145770	+	0.989319i	$0.453434\pi$
$770$	−1.25756	−	13.1699i	−0.0453193	−	0.474610i
$771$	−13.8645			−0.499317
$772$	26.2489	+	5.57938i	0.944719	+	0.200806i
$773$	3.94800	−	37.5627i	0.142000	−	1.35104i	−0.658896	−	0.752234i	$-0.728976\pi$
$773$	3.94800	−	37.5627i	0.142000	−	1.35104i	0.800896	−	0.598804i	$-0.204357\pi$
$774$	8.10176	+	3.60714i	0.291212	+	0.129656i
$775$	−5.70508	−	6.33613i	−0.204933	−	0.227601i
$776$	−0.904571	+	2.78398i	−0.0324722	+	0.0999391i
$777$	0.609355	−	8.41604i	0.0218605	−	0.301924i
$778$	−3.86255	−	2.80631i	−0.138479	−	0.100611i
$779$	20.2482	+	4.30390i	0.725469	+	0.154203i
$780$	2.51188	+	4.35070i	0.0899397	+	0.155780i
$781$	32.6025	+	25.8444i	1.16661	+	0.924786i
$782$	−2.02530	+	3.50792i	−0.0724245	+	0.125443i
$783$	−2.97894	−	9.16823i	−0.106459	−	0.327646i
$784$	−3.88570	−	5.82249i	−0.138775	−	0.207946i
$785$	−3.15268	+	2.29055i	−0.112524	+	0.0817534i
$786$	4.83572	+	5.37061i	0.172484	+	0.191563i
$787$	32.8511	−	6.98272i	1.17102	−	0.248907i	0.418959	−	0.908005i	$-0.362395\pi$
$787$	32.8511	−	6.98272i	1.17102	−	0.248907i	0.752057	+	0.659098i	$0.229062\pi$
$788$	5.92905	+	2.63979i	0.211214	+	0.0940385i
$789$	0.916825	−	0.408197i	0.0326398	−	0.0145322i
$790$	−6.59485	−	20.2969i	−0.234634	−	0.722130i
$791$	20.4732	−	24.2772i	0.727943	−	0.863198i
$792$	−3.08381	+	1.22070i	−0.109578	+	0.0433757i
$793$	8.70229	−	15.0728i	0.309028	−	0.535251i
$794$	−8.38679	+	9.31447i	−0.297636	+	0.330558i
$795$	−0.126594	+	1.20446i	−0.00448981	+	0.0427177i
$796$	−0.184478	−	1.75519i	−0.00653864	−	0.0622110i
$797$	6.22274	−	19.1516i	0.220421	−	0.678385i	−0.778304	−	0.627888i	$-0.783920\pi$
$797$	6.22274	−	19.1516i	0.220421	−	0.678385i	0.998724	−	0.0504969i	$-0.0160805\pi$
$798$	−11.3092	+	0.367021i	−0.400343	+	0.0129924i
$799$	2.01212	−	1.46189i	0.0711836	−	0.0517179i
$800$	2.49116	−	1.10913i	0.0880757	−	0.0392138i
$801$	−3.13576	+	3.48261i	−0.110796	+	0.123052i
$802$	−14.3558	−	24.8649i	−0.506919	−	0.878010i
$803$	−12.4099	+	12.6706i	−0.437935	+	0.447137i
$804$	−1.92564			−0.0679122
$805$	2.18199	+	15.8083i	0.0769052	+	0.557170i
$806$	8.42865	+	6.12377i	0.296887	+	0.215701i
$807$	0.772011	+	7.34519i	0.0271761	+	0.258563i
$808$	−18.3446	+	3.89927i	−0.645362	+	0.137176i
$809$	15.4440	−	3.28271i	0.542981	−	0.115414i	0.0717476	−	0.997423i	$-0.477142\pi$
$809$	15.4440	−	3.28271i	0.542981	−	0.115414i	0.471233	+	0.882009i	$0.343809\pi$
$810$	0.157595	+	1.49942i	0.00553733	+	0.0526842i
$811$	−42.2704	−	30.7113i	−1.48431	−	1.07842i	−0.976134	−	0.217167i	$-0.930318\pi$
$811$	−42.2704	−	30.7113i	−1.48431	−	1.07842i	−0.508180	−	0.861251i	$-0.669682\pi$
$812$	3.48737	+	25.2656i	0.122383	+	0.886649i
$813$	−5.81173			−0.203826
$814$	9.47420	+	4.70392i	0.332070	+	0.164872i
$815$	9.55943	+	16.5574i	0.334852	+	0.579981i
$816$	0.677491	−	0.752430i	0.0237169	−	0.0263403i
$817$	−34.6491	+	15.4268i	−1.21222	+	0.539715i
$818$	−28.9536	+	21.0361i	−1.01234	+	0.735509i
$819$	−8.81132	+	0.285956i	−0.307892	+	0.00999210i
$820$	−2.25507	+	6.94040i	−0.0787506	+	0.242369i
$821$	−1.76344	−	16.7780i	−0.0615444	−	0.585555i	−0.981222	−	0.192881i	$-0.938217\pi$
$821$	−1.76344	−	16.7780i	−0.0615444	−	0.585555i	0.919678	−	0.392674i	$-0.128450\pi$
$822$	−0.229534	+	2.18387i	−0.00800593	+	0.0761713i
$823$	−11.2650	+	12.5111i	−0.392675	+	0.436109i	−0.906771	−	0.421623i	$-0.861461\pi$
$823$	−11.2650	+	12.5111i	−0.392675	+	0.436109i	0.514097	+	0.857732i	$0.328127\pi$
$824$	−5.67561	+	9.83045i	−0.197719	+	0.342460i
$825$	−4.84667	+	7.63586i	−0.168739	+	0.265847i
$826$	7.16878	−	8.50078i	0.249434	−	0.295780i
$827$	−5.65424	−	17.4020i	−0.196617	−	0.605126i	−0.999954	−	0.00960049i	$-0.996944\pi$
$827$	−5.65424	−	17.4020i	−0.196617	−	0.605126i	0.803337	−	0.595525i	$-0.203056\pi$
$828$	3.65474	−	1.62720i	0.127011	−	0.0565489i
$829$	17.5400	+	7.80930i	0.609188	+	0.271228i	0.688057	−	0.725657i	$-0.258464\pi$
$829$	17.5400	+	7.80930i	0.609188	+	0.271228i	−0.0788683	+	0.996885i	$0.525131\pi$
$830$	−15.4691	+	3.28805i	−0.536940	+	0.114130i
$831$	−11.1115	−	12.3405i	−0.385453	−	0.428089i
$832$	−2.69574	+	1.95857i	−0.0934580	+	0.0679012i
$833$	−7.07255	+	0.459538i	−0.245049	+	0.0159220i
$834$	−5.97348	−	18.3845i	−0.206845	−	0.636603i
$835$	15.8758	−	27.4977i	0.549404	−	0.951596i
$836$	4.94526	−	13.2944i	0.171035	−	0.459795i
$837$	1.56333	+	2.70776i	0.0540365	+	0.0935939i
$838$	10.4210	+	2.21504i	0.359986	+	0.0765174i
$839$	−35.7419	−	25.9680i	−1.23395	−	0.896515i	−0.236768	−	0.971566i	$-0.576088\pi$
$839$	−35.7419	−	25.9680i	−1.23395	−	0.896515i	−0.997180	+	0.0750511i	$0.976088\pi$
$840$	0.288061	−	3.97852i	0.00993905	−	0.137272i
$841$	19.7556	−	60.8015i	0.681228	−	2.09660i
$842$	21.4878	+	23.8647i	0.740520	+	0.822431i
$843$	−0.124590	−	0.0554711i	−0.00429111	−	0.00191053i
$844$	0.410612	−	3.90671i	0.0141338	−	0.134475i
$845$	2.79753	+	0.594633i	0.0962380	+	0.0204560i
$846$	−2.45642			−0.0844536
$847$	−20.5611	+	20.5971i	−0.706487	+	0.707726i
$848$	−0.803284			−0.0275849
$849$	1.54627	+	0.328669i	0.0530677	+	0.0112799i
$850$	0.288601	−	2.74586i	0.00989894	−	0.0941821i
$851$	−11.6560	−	5.18960i	−0.399563	−	0.177897i
$852$	8.39355	+	9.32198i	0.287558	+	0.319366i
$853$	−8.43569	+	25.9624i	−0.288833	+	0.888935i	0.696391	+	0.717663i	$0.254788\pi$
$853$	−8.43569	+	25.9624i	−0.288833	+	0.888935i	−0.985224	+	0.171273i	$0.945212\pi$
$854$	−12.4358	+	6.02743i	−0.425543	+	0.206255i
$855$	−5.21649	−	3.79001i	−0.178400	−	0.129615i
$856$	−1.35254	−	0.287492i	−0.0462290	−	0.00982628i
$857$	25.4210	+	44.0304i	0.868364	+	1.50405i	0.863668	+	0.504062i	$0.168162\pi$
$857$	25.4210	+	44.0304i	0.868364	+	1.50405i	0.00469635	+	0.999989i	$0.498505\pi$
$858$	3.85298	−	10.3580i	0.131539	−	0.353616i
$859$	−19.7826	+	34.2645i	−0.674975	+	1.16909i	0.301502	+	0.953466i	$0.402512\pi$
$859$	−19.7826	+	34.2645i	−0.674975	+	1.16909i	−0.976476	+	0.215625i	$0.930821\pi$
$860$	−4.13180	−	12.7164i	−0.140893	−	0.433625i
$861$	−8.87318	−	9.23388i	−0.302397	−	0.314690i
$862$	−16.7033	+	12.1357i	−0.568917	+	0.413343i
$863$	23.1857	+	25.7503i	0.789250	+	0.876551i	0.994774	−	0.102101i	$-0.0325564\pi$
$863$	23.1857	+	25.7503i	0.789250	+	0.876551i	−0.205524	+	0.978652i	$0.565890\pi$
$864$	−0.978148	+	0.207912i	−0.0332773	+	0.00707330i
$865$	30.7270	+	13.6805i	1.04475	+	0.465153i
$866$	−26.7859	+	11.9258i	−0.910221	+	0.405256i
$867$	4.93650	+	15.1930i	0.167652	+	0.515981i
$868$	−2.81014	−	7.78041i	−0.0953824	−	0.264084i
$869$	−25.1586	+	39.6371i	−0.853448	+	1.34460i
$870$	−7.26703	+	12.5869i	−0.246376	+	0.426735i
$871$	4.29346	−	4.76837i	0.145478	−	0.161570i
$872$	0.151548	−	1.44188i	0.00513207	−	0.0488283i
$873$	−0.305981	−	2.91122i	−0.0103559	−	0.0985297i
$874$	−5.28715	+	16.2722i	−0.178841	+	0.550415i
$875$	−16.2688	−	26.1789i	−0.549985	−	0.885007i
$876$	−4.32620	+	3.14317i	−0.146169	+	0.106198i
$877$	−5.22514	+	2.32638i	−0.176440	+	0.0785564i	−0.493056	−	0.869998i	$-0.664120\pi$
$877$	−5.22514	+	2.32638i	−0.176440	+	0.0785564i	0.316615	+	0.948554i	$0.397454\pi$
$878$	12.4533	−	13.8308i	0.420279	−	0.466768i
$879$	0.964970	+	1.67138i	0.0325476	+	0.0563742i
$880$	4.47875	+	2.22369i	0.150979	+	0.0749605i
$881$	−40.5590			−1.36647			−0.683233	−	0.730200i	$-0.739427\pi$
$881$	−40.5590			−1.36647			−0.683233	+	0.730200i	$0.739427\pi$
$882$	5.91798	+	3.73865i	0.199269	+	0.125887i
$883$	34.4233	+	25.0100i	1.15844	+	0.841652i	0.989579	−	0.143988i	$-0.0459928\pi$
$883$	34.4233	+	25.0100i	1.15844	+	0.841652i	0.168856	+	0.985641i	$0.445993\pi$
$884$	0.352653	+	3.35527i	0.0118610	+	0.112850i
$885$	6.19824	−	1.31748i	0.208352	−	0.0442865i
$886$	−4.55882	+	0.969008i	−0.153157	+	0.0325545i
$887$	−4.79505	−	45.6219i	−0.161002	−	1.53183i	−0.714888	−	0.699239i	$-0.753522\pi$
$887$	−4.79505	−	45.6219i	−0.161002	−	1.53183i	0.553886	−	0.832593i	$-0.313144\pi$
$888$	2.58019	+	1.87462i	0.0865855	+	0.0629080i
$889$	−24.6242	−	10.0195i	−0.825869	−	0.336043i
$890$	7.06544			0.236834
$891$	2.32070	−	2.36946i	0.0777463	−	0.0793800i
$892$	12.0728	+	20.9106i	0.404226	+	0.700140i
$893$	7.02954	−	7.80710i	0.235235	−	0.261255i
$894$	−13.9087	+	6.19255i	−0.465176	+	0.207110i
$895$	5.20827	−	3.78403i	0.174093	−	0.126486i
$896$	2.64436	−	0.0858180i	0.0883418	−	0.00286698i
$897$	−4.11936	+	12.6781i	−0.137541	+	0.423309i
$898$	−2.91493	−	27.7337i	−0.0972723	−	0.925484i
$899$	−3.15060	+	29.9760i	−0.105078	+	0.999754i
$900$	−1.82466	+	2.02649i	−0.0608220	+	0.0675497i
$901$	−0.406660	+	0.704356i	−0.0135478	+	0.0234655i
$902$	14.9265	−	5.90852i	0.496998	−	0.196732i
$903$	23.0972	+	4.13139i	0.768627	+	0.137484i
$904$	3.70919	+	11.4157i	0.123366	+	0.379681i
$905$	−27.7832	+	12.3699i	−0.923544	+	0.411188i
$906$	−20.0848	−	8.94232i	−0.667272	−	0.297089i
$907$	−22.9893	+	4.88652i	−0.763346	+	0.162254i	−0.573104	−	0.819483i	$-0.694261\pi$
$907$	−22.9893	+	4.88652i	−0.763346	+	0.162254i	−0.190243	+	0.981737i	$0.560927\pi$
$908$	10.7566	+	11.9465i	0.356972	+	0.396457i
$909$	15.1727	−	11.0236i	0.503246	−	0.365630i
$910$	9.20954	+	9.58392i	0.305293	+	0.317704i
$911$	−9.54374	−	29.3726i	−0.316198	−	0.973158i	−0.975258	−	0.221068i	$-0.929046\pi$
$911$	−9.54374	−	29.3726i	−0.316198	−	0.973158i	0.659060	−	0.752090i	$-0.270954\pi$
$912$	2.13837	−	3.70377i	0.0708085	−	0.122644i
$913$	27.2627	+	21.6115i	0.902263	+	0.715235i
$914$	−3.11077	−	5.38801i	−0.102895	−	0.178220i
$915$	−7.70292	−	1.63731i	−0.254651	−	0.0541277i
$916$	3.26228	+	2.37018i	0.107789	+	0.0783130i
$917$	15.8252	+	10.7311i	0.522594	+	0.354372i
$918$	−0.312878	+	0.962939i	−0.0103265	+	0.0317817i
$919$	−15.0454	−	16.7096i	−0.496300	−	0.551197i	0.442002	−	0.897014i	$-0.354269\pi$
$919$	−15.0454	−	16.7096i	−0.496300	−	0.551197i	−0.938302	+	0.345817i	$0.887602\pi$
$920$	−5.51017	−	2.45328i	−0.181665	−	0.0808824i
$921$	1.33800	−	12.7302i	0.0440885	−	0.419474i
$922$	−3.74351	−	0.795708i	−0.123286	−	0.0262052i
$923$	−41.7980			−1.37580
$924$	−7.14788	+	5.08997i	−0.235148	+	0.167448i
$925$	8.69691			0.285953
$926$	11.2118	+	2.38315i	0.368444	+	0.0783152i
$927$	1.18653	−	11.2890i	0.0389706	−	0.370781i
$928$	−8.80662	−	3.92096i	−0.289091	−	0.128712i
$929$	−15.6759	−	17.4099i	−0.514310	−	0.571199i	0.428919	−	0.903343i	$-0.358895\pi$
$929$	−15.6759	−	17.4099i	−0.514310	−	0.571199i	−0.943229	+	0.332144i	$0.892228\pi$
$930$	1.45670	−	4.48326i	0.0477671	−	0.147012i
$931$	−28.8178	+	8.10985i	−0.944465	+	0.265790i
$932$	−22.0269	−	16.0035i	−0.721514	−	0.524211i
$933$	−16.3888	−	3.48355i	−0.536546	−	0.114046i
$934$	8.42054	+	14.5848i	0.275528	+	0.477229i
$935$	4.21718	−	2.80144i	0.137917	−	0.0916167i
$936$	1.66606	−	2.88570i	0.0544569	−	0.0943221i
$937$	11.3958	+	35.0727i	0.372285	+	1.14578i	0.945292	+	0.326226i	$0.105777\pi$
$937$	11.3958	+	35.0727i	0.372285	+	1.14578i	−0.573007	+	0.819551i	$0.694223\pi$
$938$	−4.94646	+	1.22035i	−0.161508	+	0.0398458i
$939$	8.04654	−	5.84616i	0.262589	−	0.190782i
$940$	2.47812	+	2.75223i	0.0808273	+	0.0897678i
$941$	−26.3829	+	5.60786i	−0.860059	+	0.182811i	−0.616771	−	0.787143i	$-0.711559\pi$
$941$	−26.3829	+	5.60786i	−0.860059	+	0.182811i	−0.243288	+	0.969954i	$0.578226\pi$
$942$	2.36126	+	1.05130i	0.0769340	+	0.0342532i
$943$	−17.6899	+	7.87607i	−0.576064	+	0.256480i
$944$	1.29879	+	3.99726i	0.0422720	+	0.130100i
$945$	1.35505	+	3.75173i	0.0440799	+	0.122044i
$946$	−15.7624	+	24.8334i	−0.512479	+	0.807403i
$947$	4.06656	−	7.04349i	0.132145	−	0.228883i	−0.792358	−	0.610056i	$-0.791147\pi$
$947$	4.06656	−	7.04349i	0.132145	−	0.228883i	0.924503	+	0.381174i	$0.124480\pi$
$948$	−9.47165	+	10.5193i	−0.307625	+	0.341652i
$949$	1.86253	−	17.7208i	0.0604603	−	0.575242i
$950$	−1.21904	−	11.5984i	−0.0395509	−	0.376302i
$951$	5.22201	−	16.0717i	0.169335	−	0.521160i
$952$	1.26345	−	2.36214i	0.0409487	−	0.0765574i
$953$	−26.1448	+	18.9953i	−0.846914	+	0.615319i	−0.924293	−	0.381683i	$-0.875345\pi$
$953$	−26.1448	+	18.9953i	−0.846914	+	0.615319i	0.0773795	+	0.997002i	$0.475345\pi$
$954$	0.733837	−	0.326725i	0.0237588	−	0.0105781i
$955$	−14.6093	+	16.2253i	−0.472746	+	0.525037i
$956$	6.45612	+	11.1823i	0.208806	+	0.361662i
$957$	31.5251	−	5.32964i	1.01906	−	0.172283i
$958$	−38.7257			−1.25117
$959$	0.794387	+	5.75525i	0.0256521	+	0.185847i
$960$	1.21974	+	0.886190i	0.0393668	+	0.0286017i
$961$	2.21852	+	21.1078i	0.0715650	+	0.680896i
$962$	−10.3949	+	2.20950i	−0.335144	+	0.0712371i
$963$	1.35254	−	0.287492i	0.0435851	−	0.00926430i
$964$	−2.62994	−	25.0222i	−0.0847047	−	0.805911i
$965$	32.7320	+	23.7812i	1.05368	+	0.765544i
$966$	8.35683	−	6.49597i	0.268877	−	0.209004i
$967$	33.5357			1.07844			0.539218	−	0.842166i	$-0.318720\pi$
$967$	33.5357			1.07844			0.539218	+	0.842166i	$0.318720\pi$
$968$	−2.51025	−	10.7097i	−0.0806826	−	0.344224i
$969$	−2.16509	−	3.75004i	−0.0695526	−	0.120469i
$970$	−2.95311	+	3.27976i	−0.0948185	+	0.105307i
$971$	−5.01020	+	2.23068i	−0.160785	+	0.0715861i	−0.485551	−	0.874208i	$-0.661381\pi$
$971$	−5.01020	+	2.23068i	−0.160785	+	0.0715861i	0.324766	+	0.945794i	$0.394714\pi$
$972$	0.809017	−	0.587785i	0.0259492	−	0.0188532i
$973$	−26.9952	−	43.4392i	−0.865426	−	1.39260i
$974$	−2.99749	+	9.22532i	−0.0960457	+	0.295598i
$975$	−0.949787	−	9.03662i	−0.0304175	−	0.289403i
$976$	0.545981	−	5.19466i	0.0174764	−	0.166277i
$977$	−22.5560	+	25.0510i	−0.721632	+	0.801453i	−0.986661	−	0.162787i	$-0.947952\pi$
$977$	−22.5560	+	25.0510i	−0.721632	+	0.801453i	0.265029	+	0.964240i	$0.414618\pi$
$978$	6.34050	−	10.9821i	0.202747	−	0.351168i
$979$	−9.90642	−	11.9766i	−0.316611	−	0.382775i
$980$	−1.78138	−	10.4023i	−0.0569041	−	0.332290i
$981$	0.448021	+	1.37887i	0.0143042	+	0.0440238i
$982$	−30.9985	+	13.8014i	−0.989203	+	0.440421i
$983$	14.3917	+	6.40760i	0.459024	+	0.204371i	0.623203	−	0.782060i	$-0.285831\pi$
$983$	14.3917	+	6.40760i	0.459024	+	0.204371i	−0.164179	+	0.986431i	$0.552498\pi$
$984$	4.73450	−	1.00635i	0.150930	−	0.0320813i
$985$	6.54748	+	7.27172i	0.208620	+	0.231696i
$986$	−7.89640	+	5.73707i	−0.251473	+	0.182706i
$987$	−6.30989	+	1.55672i	−0.200846	+	0.0495510i
$988$	4.40368	+	13.5531i	0.140100	+	0.431183i
$989$	17.7397	−	30.7260i	0.564089	−	0.977031i
$990$	−4.99600	−	0.209769i	−0.158783	−	0.00666691i
$991$	−25.5245	−	44.2098i	−0.810814	−	1.40437i	−0.912295	−	0.409533i	$-0.865692\pi$
$991$	−25.5245	−	44.2098i	−0.810814	−	1.40437i	0.101482	−	0.994837i	$-0.467642\pi$
$992$	3.05833	+	0.650068i	0.0971020	+	0.0206397i
$993$	−26.7157	−	19.4101i	−0.847797	−	0.615961i
$994$	27.4684	+	18.6264i	0.871246	+	0.590792i
$995$	0.822243	−	2.53060i	0.0260669	−	0.0802255i
$996$	7.01880	+	7.79517i	0.222399	+	0.246999i
$997$	−0.797693	−	0.355156i	−0.0252632	−	0.0112479i	0.394066	−	0.919082i	$-0.371068\pi$
$997$	−0.797693	−	0.355156i	−0.0252632	−	0.0112479i	−0.419329	+	0.907834i	$0.637735\pi$
$998$	−0.865580	+	8.23545i	−0.0273995	+	0.260689i
$999$	−3.11960	−	0.663091i	−0.0986997	−	0.0209793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.a.247.2	yes	24
7.4	even	3	inner	462.2.y.a.445.2	yes	24
11.9	even	5	inner	462.2.y.a.163.2	✓	24
77.53	even	15	inner	462.2.y.a.361.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.a.163.2	✓	24	11.9	even	5	inner
462.2.y.a.247.2	yes	24	1.1	even	1	trivial
462.2.y.a.361.2	yes	24	77.53	even	15	inner
462.2.y.a.445.2	yes	24	7.4	even	3	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.978148 + 0.207912i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.00883 + 1.12042i) q^{5} +(0.309017 - 0.951057i) q^{6} +(0.191063 - 2.63884i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(0.978148 + 0.207912i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.00883 + 1.12042i) q^{5} +(0.309017 - 0.951057i) q^{6} +(0.191063 - 2.63884i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(0.753838 + 1.30569i) q^{10} +(1.15632 - 3.10853i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.02968 + 3.16903i) q^{13} +(0.735534 - 2.54145i) q^{14} +(1.21974 - 0.886190i) q^{15} +(0.669131 + 0.743145i) q^{16} +(0.990369 - 0.210509i) q^{17} +(-0.913545 - 0.406737i) q^{18} +(3.90700 - 1.73951i) q^{19} +(0.465898 + 1.43389i) q^{20} +(-2.60442 - 0.465851i) q^{21} +(1.77735 - 2.80019i) q^{22} +(-2.00031 + 3.46463i) q^{23} +(0.669131 - 0.743145i) q^{24} +(0.285040 - 2.71197i) q^{25} +(0.348301 + 3.31387i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.24786 - 2.33299i) q^{28} +(-7.79896 + 5.66628i) q^{29} +(1.37733 - 0.613227i) q^{30} +(2.09214 - 2.32356i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.97063 - 1.47491i) q^{33} +1.01249 q^{34} +(3.14937 - 2.44808i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(0.333372 + 3.17182i) q^{37} +(4.18328 - 0.889184i) q^{38} +(3.25931 - 0.692787i) q^{39} +(0.157595 + 1.49942i) q^{40} +(3.91586 + 2.84504i) q^{41} +(-2.45065 - 0.997159i) q^{42} -8.86848 q^{43} +(2.32070 - 2.36946i) q^{44} +(-0.753838 - 1.30569i) q^{45} +(-2.67693 + 2.97303i) q^{46} +(2.24405 - 0.999117i) q^{47} +(0.809017 - 0.587785i) q^{48} +(-6.92699 - 1.00837i) q^{49} +(0.842662 - 2.59345i) q^{50} +(-0.105834 - 1.00695i) q^{51} +(-0.348301 + 3.31387i) q^{52} +(-0.537502 + 0.596956i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(4.64939 - 1.84042i) q^{55} +(1.70565 - 2.02257i) q^{56} +(-1.32159 - 4.06742i) q^{57} +(-8.80662 + 3.92096i) q^{58} +(3.83960 + 1.70950i) q^{59} +(1.47473 - 0.313464i) q^{60} +(-3.49506 - 3.88165i) q^{61} +(2.52952 - 1.83780i) q^{62} +(-0.735534 + 2.54145i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-2.51188 + 4.35070i) q^{65} +(-2.59906 - 2.06031i) q^{66} +(-0.962822 - 1.66766i) q^{67} +(0.990369 + 0.210509i) q^{68} +(3.23656 + 2.35150i) q^{69} +(3.58953 - 1.73979i) q^{70} +(-3.87630 + 11.9300i) q^{71} +(-0.669131 - 0.743145i) q^{72} +(-4.88516 - 2.17501i) q^{73} +(-0.333372 + 3.17182i) q^{74} +(-2.66732 - 0.566957i) q^{75} +4.27674 q^{76} +(-7.98198 - 3.64526i) q^{77} +3.33212 q^{78} +(-13.8458 - 2.94302i) q^{79} +(-0.157595 + 1.49942i) q^{80} +(0.913545 + 0.406737i) q^{81} +(3.23878 + 3.59703i) q^{82} +(-3.24141 + 9.97604i) q^{83} +(-2.18977 - 1.48489i) q^{84} +(1.23498 + 0.897262i) q^{85} +(-8.67468 - 1.84386i) q^{86} +(4.82002 + 8.34852i) q^{87} +(2.76262 - 1.83519i) q^{88} +(2.34316 - 4.05847i) q^{89} +(-0.465898 - 1.43389i) q^{90} +(8.55932 - 2.11168i) q^{91} +(-3.23656 + 2.35150i) q^{92} +(-2.09214 - 2.32356i) q^{93} +(2.40274 - 0.510719i) q^{94} +(5.89049 + 2.62261i) q^{95} +(0.913545 - 0.406737i) q^{96} +(0.904571 + 2.78398i) q^{97} +(-6.56597 - 2.42654i) q^{98} +(-1.77735 + 2.80019i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9} + 10 q^{10} + 6 q^{11} + 12 q^{12} - 2 q^{13} - 5 q^{14} + 3 q^{16} - 2 q^{17} - 3 q^{18} + 7 q^{19} - 10 q^{20} - 4 q^{21} + 2 q^{22} + 24 q^{23} + 3 q^{24} + 4 q^{25} + 4 q^{26} + 6 q^{27} + 14 q^{28} - 6 q^{29} - 7 q^{31} + 12 q^{32} - q^{33} - 24 q^{34} + 4 q^{35} - 6 q^{36} - q^{37} + 8 q^{38} - q^{39} + 16 q^{41} - 4 q^{42} + 52 q^{43} - 4 q^{44} - 10 q^{45} - 4 q^{46} + 27 q^{47} + 6 q^{48} - 33 q^{49} - 22 q^{50} - 8 q^{51} - 4 q^{52} + 13 q^{53} - 12 q^{54} + 30 q^{55} + 14 q^{56} - 16 q^{57} - 3 q^{58} + 14 q^{59} - 5 q^{60} + 9 q^{61} - 4 q^{62} + 5 q^{63} - 6 q^{64} - 50 q^{65} - 4 q^{66} - 20 q^{67} - 2 q^{68} - 32 q^{69} - 17 q^{70} - 18 q^{71} - 3 q^{72} + 7 q^{73} + q^{74} + 11 q^{75} - 4 q^{76} - 34 q^{77} - 12 q^{78} + q^{79} + 3 q^{81} - 2 q^{82} - 68 q^{83} - 5 q^{84} - 19 q^{86} - 8 q^{87} - q^{88} - 42 q^{89} + 10 q^{90} - 16 q^{91} + 32 q^{92} + 7 q^{93} + 8 q^{94} + 38 q^{95} + 3 q^{96} - 80 q^{97} - 2 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 11 * q^7 + 6 * q^8 + 3 * q^9 + 10 * q^10 + 6 * q^11 + 12 * q^12 - 2 * q^13 - 5 * q^14 + 3 * q^16 - 2 * q^17 - 3 * q^18 + 7 * q^19 - 10 * q^20 - 4 * q^21 + 2 * q^22 + 24 * q^23 + 3 * q^24 + 4 * q^25 + 4 * q^26 + 6 * q^27 + 14 * q^28 - 6 * q^29 - 7 * q^31 + 12 * q^32 - q^33 - 24 * q^34 + 4 * q^35 - 6 * q^36 - q^37 + 8 * q^38 - q^39 + 16 * q^41 - 4 * q^42 + 52 * q^43 - 4 * q^44 - 10 * q^45 - 4 * q^46 + 27 * q^47 + 6 * q^48 - 33 * q^49 - 22 * q^50 - 8 * q^51 - 4 * q^52 + 13 * q^53 - 12 * q^54 + 30 * q^55 + 14 * q^56 - 16 * q^57 - 3 * q^58 + 14 * q^59 - 5 * q^60 + 9 * q^61 - 4 * q^62 + 5 * q^63 - 6 * q^64 - 50 * q^65 - 4 * q^66 - 20 * q^67 - 2 * q^68 - 32 * q^69 - 17 * q^70 - 18 * q^71 - 3 * q^72 + 7 * q^73 + q^74 + 11 * q^75 - 4 * q^76 - 34 * q^77 - 12 * q^78 + q^79 + 3 * q^81 - 2 * q^82 - 68 * q^83 - 5 * q^84 - 19 * q^86 - 8 * q^87 - q^88 - 42 * q^89 + 10 * q^90 - 16 * q^91 + 32 * q^92 + 7 * q^93 + 8 * q^94 + 38 * q^95 + 3 * q^96 - 80 * q^97 - 2 * q^99

Introduction

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