LMFDB - Embedded newform 966.2.q.d.547.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, degree $10$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 10 x^{18} - 14 x^{17} + 77 x^{16} + 12 x^{15} - 226 x^{14} - 793 x^{13} + \cdots + 1849 $ x^20 - 6x^19 + 10x^18 - 14x^17 + 77x^16 + 12x^15 - 226x^14 - 793x^13 + 690x^12 + 6105x^11 + 13883x^10 + 24365x^9 + 36461x^8 + 41912x^7 + 45709x^6 + 33023x^5 + 25949x^4 + 12217x^3 + 2895x^2 - 172*x + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			547.2
Root			$-0.370938 - 2.57993i$ of defining polynomial
Character	$\chi$	$=$	966.547
Dual form			966.2.q.d.883.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.411445 - 2.86166i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(0.415415 + 0.909632i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.411445 - 2.86166i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(0.415415 + 0.909632i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-1.20100 + 2.62983i) q^{10} +(0.803230 - 0.235849i) q^{11} +(0.959493 - 0.281733i) q^{12} +(-0.152616 + 0.334182i) q^{13} +(-0.142315 - 0.989821i) q^{14} +(-1.89326 - 2.18494i) q^{15} +(0.415415 + 0.909632i) q^{16} +(4.13930 - 2.66017i) q^{17} +(-0.142315 + 0.989821i) q^{18} +(-5.60899 - 3.60468i) q^{19} +(1.89326 - 2.18494i) q^{20} +(0.959493 + 0.281733i) q^{21} -0.837140 q^{22} +(4.61192 - 1.31538i) q^{23} -1.00000 q^{24} +(-3.22236 - 0.946169i) q^{25} +(0.240584 - 0.277649i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(-0.142315 + 0.989821i) q^{28} +(0.968242 - 0.622251i) q^{29} +(1.20100 + 2.62983i) q^{30} +(0.454331 + 0.524326i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(0.347760 - 0.761489i) q^{33} +(-4.72109 + 1.38624i) q^{34} +(2.77398 - 0.814514i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-1.06362 - 7.39764i) q^{37} +(4.36623 + 5.03890i) q^{38} +(0.152616 + 0.334182i) q^{39} +(-2.43214 + 1.56304i) q^{40} +(0.696844 - 4.84665i) q^{41} +(-0.841254 - 0.540641i) q^{42} +(-3.87504 + 4.47203i) q^{43} +(0.803230 + 0.235849i) q^{44} -2.89109 q^{45} +(-4.79569 - 0.0372286i) q^{46} -13.1345 q^{47} +(0.959493 + 0.281733i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(2.82526 + 1.81569i) q^{50} +(0.700246 - 4.87032i) q^{51} +(-0.309061 + 0.198622i) q^{52} +(3.90231 + 8.54486i) q^{53} +(0.654861 + 0.755750i) q^{54} +(-0.344437 - 2.39561i) q^{55} +(0.415415 - 0.909632i) q^{56} +(-6.39734 + 1.87843i) q^{57} +(-1.10433 + 0.324260i) q^{58} +(-0.451958 + 0.989651i) q^{59} +(-0.411445 - 2.86166i) q^{60} +(2.54671 + 2.93905i) q^{61} +(-0.288208 - 0.631087i) q^{62} +(0.841254 - 0.540641i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(0.893523 + 0.574233i) q^{65} +(-0.548210 + 0.632668i) q^{66} +(3.47995 + 1.02181i) q^{67} +4.92040 q^{68} +(2.02606 - 4.34685i) q^{69} -2.89109 q^{70} +(-0.514307 - 0.151014i) q^{71} +(-0.654861 + 0.755750i) q^{72} +(-3.30895 - 2.12653i) q^{73} +(-1.06362 + 7.39764i) q^{74} +(-2.82526 + 1.81569i) q^{75} +(-2.76974 - 6.06489i) q^{76} +(0.548210 + 0.632668i) q^{77} +(-0.0522839 - 0.363642i) q^{78} +(3.69618 - 8.09350i) q^{79} +(2.77398 - 0.814514i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-2.03408 + 4.45401i) q^{82} +(-1.62379 - 11.2937i) q^{83} +(0.654861 + 0.755750i) q^{84} +(-5.90941 - 12.9398i) q^{85} +(4.97799 - 3.19916i) q^{86} +(0.163797 - 1.13924i) q^{87} +(-0.704247 - 0.452592i) q^{88} +(4.70531 - 5.43021i) q^{89} +(2.77398 + 0.814514i) q^{90} -0.367382 q^{91} +(4.59094 + 1.38682i) q^{92} +0.693783 q^{93} +(12.6024 + 3.70040i) q^{94} +(-12.6232 + 14.5679i) q^{95} +(-0.841254 - 0.540641i) q^{96} +(-1.00635 + 6.99932i) q^{97} +(0.841254 - 0.540641i) q^{98} +(-0.347760 - 0.761489i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} - 10 q^{10} - 7 q^{11} + 2 q^{12} - 8 q^{13} - 2 q^{14} - q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} + 2 q^{21} + 4 q^{22} - 20 q^{24} + 16 q^{25} - 8 q^{26} + 2 q^{27} - 2 q^{28} + 3 q^{29} + 10 q^{30} + 9 q^{31} - 2 q^{32} - 4 q^{33} - 9 q^{34} + q^{35} - 2 q^{36} - q^{37} + 3 q^{38} + 8 q^{39} + q^{40} + 10 q^{41} + 2 q^{42} - 15 q^{43} - 7 q^{44} - 10 q^{45} - 28 q^{47} + 2 q^{48} - 2 q^{49} + 5 q^{50} - 2 q^{51} + 3 q^{52} + 38 q^{53} + 2 q^{54} - 8 q^{55} - 2 q^{56} - 14 q^{57} - 19 q^{58} - 10 q^{59} - 12 q^{60} - 6 q^{61} + 20 q^{62} - 2 q^{63} - 2 q^{64} - 36 q^{65} - 4 q^{66} + 36 q^{67} - 20 q^{68} + 11 q^{69} - 10 q^{70} - q^{71} - 2 q^{72} + 65 q^{73} - q^{74} - 5 q^{75} + 14 q^{76} + 4 q^{77} - 14 q^{78} + 10 q^{79} + q^{80} - 2 q^{81} + 10 q^{82} - 14 q^{83} + 2 q^{84} - 5 q^{85} + 51 q^{86} - 3 q^{87} - 7 q^{88} - 18 q^{89} + q^{90} - 30 q^{91} - 11 q^{92} + 2 q^{93} + 38 q^{94} - 73 q^{95} + 2 q^{96} - 20 q^{97} - 2 q^{98} + 4 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 - 10 * q^10 - 7 * q^11 + 2 * q^12 - 8 * q^13 - 2 * q^14 - q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 8 * q^19 + q^20 + 2 * q^21 + 4 * q^22 - 20 * q^24 + 16 * q^25 - 8 * q^26 + 2 * q^27 - 2 * q^28 + 3 * q^29 + 10 * q^30 + 9 * q^31 - 2 * q^32 - 4 * q^33 - 9 * q^34 + q^35 - 2 * q^36 - q^37 + 3 * q^38 + 8 * q^39 + q^40 + 10 * q^41 + 2 * q^42 - 15 * q^43 - 7 * q^44 - 10 * q^45 - 28 * q^47 + 2 * q^48 - 2 * q^49 + 5 * q^50 - 2 * q^51 + 3 * q^52 + 38 * q^53 + 2 * q^54 - 8 * q^55 - 2 * q^56 - 14 * q^57 - 19 * q^58 - 10 * q^59 - 12 * q^60 - 6 * q^61 + 20 * q^62 - 2 * q^63 - 2 * q^64 - 36 * q^65 - 4 * q^66 + 36 * q^67 - 20 * q^68 + 11 * q^69 - 10 * q^70 - q^71 - 2 * q^72 + 65 * q^73 - q^74 - 5 * q^75 + 14 * q^76 + 4 * q^77 - 14 * q^78 + 10 * q^79 + q^80 - 2 * q^81 + 10 * q^82 - 14 * q^83 + 2 * q^84 - 5 * q^85 + 51 * q^86 - 3 * q^87 - 7 * q^88 - 18 * q^89 + q^90 - 30 * q^91 - 11 * q^92 + 2 * q^93 + 38 * q^94 - 73 * q^95 + 2 * q^96 - 20 * q^97 - 2 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	0.411445	−	2.86166i	0.184004	−	1.27977i	−0.663174	−	0.748465i	$-0.730791\pi$
$5$	0.411445	−	2.86166i	0.184004	−	1.27977i	0.847178	−	0.531309i	$-0.178300\pi$
$6$	−0.841254	+	0.540641i	−0.343440	+	0.220716i
$7$	0.415415	+	0.909632i	0.157012	+	0.343809i
$7$	0.415415	+	0.909632i	0.157012	+	0.343809i
$8$	−0.654861	−	0.755750i	−0.231528	−	0.267198i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	−1.20100	+	2.62983i	−0.379790	+	0.831624i
$11$	0.803230	−	0.235849i	0.242183	−	0.0711113i	−0.158389	−	0.987377i	$-0.550630\pi$
$11$	0.803230	−	0.235849i	0.242183	−	0.0711113i	0.400571	+	0.916266i	$0.368812\pi$
$12$	0.959493	−	0.281733i	0.276982	−	0.0813292i
$13$	−0.152616	+	0.334182i	−0.0423280	+	0.0926855i	−0.929615	−	0.368533i	$-0.879860\pi$
$13$	−0.152616	+	0.334182i	−0.0423280	+	0.0926855i	0.887287	+	0.461218i	$0.152587\pi$
$14$	−0.142315	−	0.989821i	−0.0380352	−	0.264541i
$15$	−1.89326	−	2.18494i	−0.488838	−	0.564149i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	4.13930	−	2.66017i	1.00393	−	0.645186i	0.0681135	−	0.997678i	$-0.478302\pi$
$17$	4.13930	−	2.66017i	1.00393	−	0.645186i	0.935815	+	0.352492i	$0.114666\pi$
$18$	−0.142315	+	0.989821i	−0.0335439	+	0.233303i
$19$	−5.60899	−	3.60468i	−1.28679	−	0.826970i	−0.295081	−	0.955472i	$-0.595347\pi$
$19$	−5.60899	−	3.60468i	−1.28679	−	0.826970i	−0.991709	+	0.128503i	$0.958983\pi$
$20$	1.89326	−	2.18494i	0.423346	−	0.488567i
$21$	0.959493	+	0.281733i	0.209379	+	0.0614791i
$22$	−0.837140			−0.178479
$23$	4.61192	−	1.31538i	0.961651	−	0.274276i
$23$	4.61192	−	1.31538i	0.961651	−	0.274276i
$24$	−1.00000			−0.204124
$25$	−3.22236	−	0.946169i	−0.644471	−	0.189234i
$26$	0.240584	−	0.277649i	0.0471824	−	0.0544514i
$27$	−0.841254	−	0.540641i	−0.161899	−	0.104046i
$28$	−0.142315	+	0.989821i	−0.0268950	+	0.187059i
$29$	0.968242	−	0.622251i	0.179798	−	0.115549i	−0.447646	−	0.894211i	$-0.647738\pi$
$29$	0.968242	−	0.622251i	0.179798	−	0.115549i	0.627444	+	0.778662i	$0.284101\pi$
$30$	1.20100	+	2.62983i	0.219272	+	0.480138i
$31$	0.454331	+	0.524326i	0.0816003	+	0.0941717i	0.795081	−	0.606503i	$-0.207428\pi$
$31$	0.454331	+	0.524326i	0.0816003	+	0.0941717i	−0.713481	+	0.700674i	$0.752883\pi$
$32$	−0.142315	−	0.989821i	−0.0251579	−	0.174977i
$33$	0.347760	−	0.761489i	0.0605373	−	0.132558i
$34$	−4.72109	+	1.38624i	−0.809660	+	0.237738i
$35$	2.77398	−	0.814514i	0.468888	−	0.137678i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	−1.06362	−	7.39764i	−0.174858	−	1.21616i	−0.868443	−	0.495789i	$-0.834879\pi$
$37$	−1.06362	−	7.39764i	−0.174858	−	1.21616i	0.693585	−	0.720375i	$-0.256030\pi$
$38$	4.36623	+	5.03890i	0.708296	+	0.817417i
$39$	0.152616	+	0.334182i	0.0244381	+	0.0535120i
$40$	−2.43214	+	1.56304i	−0.384555	+	0.247138i
$41$	0.696844	−	4.84665i	0.108829	−	0.756920i	−0.860197	−	0.509961i	$-0.829660\pi$
$41$	0.696844	−	4.84665i	0.108829	−	0.756920i	0.969026	−	0.246959i	$-0.0794312\pi$
$42$	−0.841254	−	0.540641i	−0.129808	−	0.0834227i
$43$	−3.87504	+	4.47203i	−0.590938	+	0.681979i	−0.969920	−	0.243425i	$-0.921729\pi$
$43$	−3.87504	+	4.47203i	−0.590938	+	0.681979i	0.378982	+	0.925404i	$0.376274\pi$
$44$	0.803230	+	0.235849i	0.121091	+	0.0355556i
$45$	−2.89109			−0.430978
$46$	−4.79569	−	0.0372286i	−0.707085	−	0.00548905i
$47$	−13.1345			−1.91586			−0.957929	−	0.287006i	$-0.907340\pi$
$47$	−13.1345			−1.91586			−0.957929	+	0.287006i	$0.907340\pi$
$48$	0.959493	+	0.281733i	0.138491	+	0.0406646i
$49$	−0.654861	+	0.755750i	−0.0935515	+	0.107964i
$50$	2.82526	+	1.81569i	0.399552	+	0.256777i
$51$	0.700246	−	4.87032i	0.0980540	−	0.681981i
$52$	−0.309061	+	0.198622i	−0.0428591	+	0.0275439i
$53$	3.90231	+	8.54486i	0.536023	+	1.17373i	0.963009	+	0.269469i	$0.0868480\pi$
$53$	3.90231	+	8.54486i	0.536023	+	1.17373i	−0.426986	+	0.904258i	$0.640425\pi$
$54$	0.654861	+	0.755750i	0.0891153	+	0.102844i
$55$	−0.344437	−	2.39561i	−0.0464438	−	0.323024i
$56$	0.415415	−	0.909632i	0.0555122	−	0.121555i
$57$	−6.39734	+	1.87843i	−0.847348	+	0.248804i
$58$	−1.10433	+	0.324260i	−0.145006	+	0.0425775i
$59$	−0.451958	+	0.989651i	−0.0588400	+	0.128842i	−0.936768	−	0.349951i	$-0.886198\pi$
$59$	−0.451958	+	0.989651i	−0.0588400	+	0.128842i	0.877928	+	0.478793i	$0.158925\pi$
$60$	−0.411445	−	2.86166i	−0.0531173	−	0.369439i
$61$	2.54671	+	2.93905i	0.326072	+	0.376307i	0.894989	−	0.446087i	$-0.147183\pi$
$61$	2.54671	+	2.93905i	0.326072	+	0.376307i	−0.568917	+	0.822395i	$0.692638\pi$
$62$	−0.288208	−	0.631087i	−0.0366024	−	0.0801481i
$63$	0.841254	−	0.540641i	0.105988	−	0.0681143i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	0.893523	+	0.574233i	0.110828	+	0.0712248i
$66$	−0.548210	+	0.632668i	−0.0674800	+	0.0778760i
$67$	3.47995	+	1.02181i	0.425144	+	0.124834i	0.487303	−	0.873233i	$-0.337981\pi$
$67$	3.47995	+	1.02181i	0.425144	+	0.124834i	−0.0621595	+	0.998066i	$0.519799\pi$
$68$	4.92040			0.596686
$69$	2.02606	−	4.34685i	0.243910	−	0.523299i
$70$	−2.89109			−0.345551
$71$	−0.514307	−	0.151014i	−0.0610370	−	0.0179221i	0.251072	−	0.967969i	$-0.419217\pi$
$71$	−0.514307	−	0.151014i	−0.0610370	−	0.0179221i	−0.312109	+	0.950046i	$0.601035\pi$
$72$	−0.654861	+	0.755750i	−0.0771761	+	0.0890659i
$73$	−3.30895	−	2.12653i	−0.387283	−	0.248892i	0.332482	−	0.943110i	$-0.392114\pi$
$73$	−3.30895	−	2.12653i	−0.387283	−	0.248892i	−0.719765	+	0.694218i	$0.755750\pi$
$74$	−1.06362	+	7.39764i	−0.123643	+	0.859958i
$75$	−2.82526	+	1.81569i	−0.326233	+	0.209657i
$76$	−2.76974	−	6.06489i	−0.317712	−	0.695691i
$77$	0.548210	+	0.632668i	0.0624743	+	0.0720992i
$78$	−0.0522839	−	0.363642i	−0.00591998	−	0.0411744i
$79$	3.69618	−	8.09350i	0.415853	−	0.910590i	−0.579561	−	0.814929i	$-0.696776\pi$
$79$	3.69618	−	8.09350i	0.415853	−	0.910590i	0.995414	−	0.0956614i	$-0.0304966\pi$
$80$	2.77398	−	0.814514i	0.310140	−	0.0910654i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	−2.03408	+	4.45401i	−0.224626	+	0.491863i
$83$	−1.62379	−	11.2937i	−0.178235	−	1.23965i	−0.860845	−	0.508867i	$-0.830065\pi$
$83$	−1.62379	−	11.2937i	−0.178235	−	1.23965i	0.682611	−	0.730782i	$-0.260844\pi$
$84$	0.654861	+	0.755750i	0.0714512	+	0.0824590i
$85$	−5.90941	−	12.9398i	−0.640965	−	1.40352i
$86$	4.97799	−	3.19916i	0.536790	−	0.344974i
$87$	0.163797	−	1.13924i	0.0175609	−	0.122139i
$88$	−0.704247	−	0.452592i	−0.0750729	−	0.0482465i
$89$	4.70531	−	5.43021i	0.498762	−	0.575601i	−0.449424	−	0.893319i	$-0.648371\pi$
$89$	4.70531	−	5.43021i	0.498762	−	0.575601i	0.948186	+	0.317717i	$0.102916\pi$
$90$	2.77398	+	0.814514i	0.292403	+	0.0858573i
$91$	−0.367382			−0.0385121
$92$	4.59094	+	1.38682i	0.478639	+	0.144586i
$93$	0.693783			0.0719419
$94$	12.6024	+	3.70040i	1.29984	+	0.381668i
$95$	−12.6232	+	14.5679i	−1.29511	+	1.49463i
$96$	−0.841254	−	0.540641i	−0.0858601	−	0.0551789i
$97$	−1.00635	+	6.99932i	−0.102179	+	0.710674i	0.872751	+	0.488165i	$0.162334\pi$
$97$	−1.00635	+	6.99932i	−0.102179	+	0.710674i	−0.974931	+	0.222508i	$0.928575\pi$
$98$	0.841254	−	0.540641i	0.0849794	−	0.0546130i
$99$	−0.347760	−	0.761489i	−0.0349512	−	0.0765325i
$100$	−2.19928	−	2.53811i	−0.219928	−	0.253811i
$101$	−0.266828	−	1.85583i	−0.0265504	−	0.184662i	0.972231	−	0.234025i	$-0.0751898\pi$
$101$	−0.266828	−	1.85583i	−0.0265504	−	0.184662i	−0.998781	+	0.0493634i	$0.984281\pi$
$102$	−2.04401	+	4.47575i	−0.202387	+	0.443165i
$103$	−11.5152	+	3.38117i	−1.13463	+	0.333157i	−0.794525	−	0.607231i	$-0.792280\pi$
$103$	−11.5152	+	3.38117i	−1.13463	+	0.333157i	−0.340103	+	0.940388i	$0.610462\pi$
$104$	0.352500	−	0.103503i	0.0345655	−	0.0101493i
$105$	1.20100	−	2.62983i	0.117206	−	0.256645i
$106$	−1.33687	−	9.29814i	−0.129848	−	0.903115i
$107$	−1.94941	−	2.24974i	−0.188457	−	0.217491i	0.653657	−	0.756791i	$-0.273234\pi$
$107$	−1.94941	−	2.24974i	−0.188457	−	0.217491i	−0.842113	+	0.539301i	$0.818689\pi$
$108$	−0.415415	−	0.909632i	−0.0399733	−	0.0875294i
$109$	1.49249	−	0.959168i	0.142955	−	0.0918716i	−0.467208	−	0.884147i	$-0.654740\pi$
$109$	1.49249	−	0.959168i	0.142955	−	0.0918716i	0.610163	+	0.792276i	$0.291104\pi$
$110$	−0.344437	+	2.39561i	−0.0328408	+	0.228412i
$111$	−6.28728	−	4.04059i	−0.596762	−	0.383516i
$112$	−0.654861	+	0.755750i	−0.0618785	+	0.0714116i
$113$	8.72614	+	2.56223i	0.820886	+	0.241034i	0.665098	−	0.746756i	$-0.268390\pi$
$113$	8.72614	+	2.56223i	0.820886	+	0.241034i	0.155789	+	0.987790i	$0.450208\pi$
$114$	6.66742			0.624461
$115$	−1.86663	−	13.7390i	−0.174064	−	1.28116i
$116$	1.15095			0.106863
$117$	0.352500	+	0.103503i	0.0325887	+	0.00956889i
$118$	0.712468	−	0.822232i	0.0655880	−	0.0756925i
$119$	4.13930	+	2.66017i	0.379449	+	0.243857i
$120$	−0.411445	+	2.86166i	−0.0375596	+	0.261233i
$121$	−8.66424	+	5.56817i	−0.787658	+	0.506197i
$122$	−1.61552	−	3.53749i	−0.146262	−	0.320270i
$123$	−3.20652	−	3.70052i	−0.289122	−	0.333665i
$124$	0.0987356	+	0.686721i	0.00886672	+	0.0616694i
$125$	1.97157	−	4.31714i	0.176343	−	0.386137i
$126$	−0.959493	+	0.281733i	−0.0854784	+	0.0250987i
$127$	12.4786	−	3.66404i	1.10729	−	0.325131i	0.323548	−	0.946212i	$-0.395124\pi$
$127$	12.4786	−	3.66404i	1.10729	−	0.325131i	0.783746	+	0.621081i	$0.213306\pi$
$128$	0.415415	−	0.909632i	0.0367178	−	0.0804009i
$129$	0.842126	+	5.85712i	0.0741451	+	0.515690i
$130$	−0.695549	−	0.802707i	−0.0610037	−	0.0704020i
$131$	−0.357108	−	0.781957i	−0.0312006	−	0.0683199i	0.893390	−	0.449282i	$-0.148320\pi$
$131$	−0.357108	−	0.781957i	−0.0312006	−	0.0683199i	−0.924591	+	0.380962i	$0.875593\pi$
$132$	0.704247	−	0.452592i	0.0612968	−	0.0393931i
$133$	0.948872	−	6.59955i	0.0822777	−	0.572254i
$134$	−3.05111	−	1.96083i	−0.263576	−	0.169390i
$135$	−1.89326	+	2.18494i	−0.162946	+	0.188050i
$136$	−4.72109	−	1.38624i	−0.404830	−	0.118869i
$137$	0.487925			0.0416863			0.0208431	−	0.999783i	$-0.493365\pi$
$137$	0.487925			0.0416863			0.0208431	+	0.999783i	$0.493365\pi$
$138$	−3.16864	+	3.59996i	−0.269733	+	0.306449i
$139$	−11.3141			−0.959652			−0.479826	−	0.877364i	$-0.659300\pi$
$139$	−11.3141			−0.959652			−0.479826	+	0.877364i	$0.659300\pi$
$140$	2.77398	+	0.814514i	0.234444	+	0.0688390i
$141$	−8.60124	+	9.92636i	−0.724355	+	0.835950i
$142$	0.450928	+	0.289794i	0.0378411	+	0.0243190i
$143$	−0.0437689	+	0.304419i	−0.00366014	+	0.0254568i
$144$	0.841254	−	0.540641i	0.0701045	−	0.0450534i
$145$	−1.38229	−	3.02680i	−0.114793	−	0.251362i
$146$	2.57580	+	2.97263i	0.213175	+	0.246017i
$147$	0.142315	+	0.989821i	0.0117379	+	0.0816391i
$148$	3.10469	−	6.79832i	0.255204	−	0.558819i
$149$	14.5518	−	4.27280i	1.19213	−	0.350042i	0.375292	−	0.926906i	$-0.377542\pi$
$149$	14.5518	−	4.27280i	1.19213	−	0.350042i	0.816840	+	0.576865i	$0.195724\pi$
$150$	3.22236	−	0.946169i	0.263104	−	0.0772544i
$151$	−4.51350	+	9.88318i	−0.367303	+	0.804281i	0.632261	+	0.774755i	$0.282127\pi$
$151$	−4.51350	+	9.88318i	−0.367303	+	0.804281i	−0.999564	+	0.0295260i	$0.990600\pi$
$152$	0.948872	+	6.59955i	0.0769637	+	0.535294i
$153$	−3.22218	−	3.71859i	−0.260497	−	0.300630i
$154$	−0.347760	−	0.761489i	−0.0280233	−	0.0613625i
$155$	1.68738	−	1.08441i	0.135533	−	0.0871020i
$156$	−0.0522839	+	0.363642i	−0.00418606	+	0.0291147i
$157$	−5.98126	−	3.84392i	−0.477357	−	0.306779i	0.279746	−	0.960074i	$-0.409750\pi$
$157$	−5.98126	−	3.84392i	−0.477357	−	0.306779i	−0.757103	+	0.653295i	$0.773386\pi$
$158$	−5.82666	+	6.72432i	−0.463544	+	0.534958i
$159$	9.01324	+	2.64653i	0.714797	+	0.209883i
$160$	−2.89109			−0.228561
$161$	3.11237	+	3.64872i	0.245289	+	0.287559i
$162$	1.00000			0.0785674
$163$	8.18953	+	2.40466i	0.641454	+	0.188348i	0.586254	−	0.810127i	$-0.300602\pi$
$163$	8.18953	+	2.40466i	0.641454	+	0.188348i	0.0552000	+	0.998475i	$0.482420\pi$
$164$	3.20652	−	3.70052i	0.250387	−	0.288962i
$165$	−2.03604	−	1.30848i	−0.158505	−	0.101865i
$166$	−1.62379	+	11.2937i	−0.126031	+	0.876564i
$167$	18.1786	−	11.6827i	1.40670	−	0.904033i	0.406747	−	0.913541i	$-0.366663\pi$
$167$	18.1786	−	11.6827i	1.40670	−	0.904033i	0.999955	+	0.00950804i	$0.00302655\pi$
$168$	−0.415415	−	0.909632i	−0.0320500	−	0.0701796i
$169$	8.42480	+	9.72274i	0.648062	+	0.747903i
$170$	2.02447	+	14.0805i	0.155270	+	1.07993i
$171$	−2.76974	+	6.06489i	−0.211808	+	0.463794i
$172$	−5.67765	+	1.66711i	−0.432917	+	0.127116i
$173$	−2.24295	+	0.658588i	−0.170528	+	0.0500715i	−0.365882	−	0.930661i	$-0.619233\pi$
$173$	−2.24295	+	0.658588i	−0.170528	+	0.0500715i	0.195354	+	0.980733i	$0.437414\pi$
$174$	−0.478122	+	1.04694i	−0.0362464	+	0.0793685i
$175$	−0.477949	−	3.32421i	−0.0361296	−	0.251287i
$176$	0.548210	+	0.632668i	0.0413229	+	0.0476891i
$177$	0.451958	+	0.989651i	0.0339713	+	0.0743867i
$178$	−6.04458	+	3.88461i	−0.453060	+	0.291164i
$179$	−2.39727	+	16.6734i	−0.179180	+	1.24623i	0.679485	+	0.733689i	$0.262203\pi$
$179$	−2.39727	+	16.6734i	−0.179180	+	1.24623i	−0.858666	+	0.512536i	$0.828706\pi$
$180$	−2.43214	−	1.56304i	−0.181281	−	0.116502i
$181$	2.32664	−	2.68509i	0.172938	−	0.199581i	−0.662663	−	0.748917i	$-0.730574\pi$
$181$	2.32664	−	2.68509i	0.172938	−	0.199581i	0.835601	+	0.549336i	$0.185119\pi$
$182$	0.352500	+	0.103503i	0.0261291	+	0.00767218i
$183$	3.88893			0.287478
$184$	−4.01426	−	2.62406i	−0.295935	−	0.193448i
$185$	−21.6071			−1.58859
$186$	−0.665680	−	0.195461i	−0.0488100	−	0.0143319i
$187$	2.69741	−	3.11298i	0.197254	−	0.227643i
$188$	−11.0494	−	7.10102i	−0.805861	−	0.517895i
$189$	0.142315	−	0.989821i	0.0103519	−	0.0719989i
$190$	16.2161	−	10.4214i	1.17644	−	0.756051i
$191$	6.88106	+	15.0674i	0.497896	+	1.09024i	0.977148	+	0.212562i	$0.0681808\pi$
$191$	6.88106	+	15.0674i	0.497896	+	1.09024i	−0.479252	+	0.877677i	$0.659092\pi$
$192$	0.654861	+	0.755750i	0.0472605	+	0.0545415i
$193$	0.646102	+	4.49374i	0.0465075	+	0.323466i	0.999772	+	0.0213310i	$0.00679039\pi$
$193$	0.646102	+	4.49374i	0.0465075	+	0.323466i	−0.953265	+	0.302135i	$0.902301\pi$
$194$	2.93752	−	6.43228i	0.210902	−	0.461811i
$195$	1.01911	−	0.299237i	0.0729799	−	0.0214288i
$196$	−0.959493	+	0.281733i	−0.0685352	+	0.0201238i
$197$	6.91653	−	15.1451i	0.492782	−	1.07904i	−0.485966	−	0.873978i	$-0.661532\pi$
$197$	6.91653	−	15.1451i	0.492782	−	1.07904i	0.978748	−	0.205065i	$-0.0657406\pi$
$198$	0.119137	+	0.828619i	0.00846673	+	0.0588874i
$199$	15.9765	+	18.4379i	1.13255	+	1.30703i	0.945847	+	0.324612i	$0.105234\pi$
$199$	15.9765	+	18.4379i	1.13255	+	1.30703i	0.186700	+	0.982417i	$0.440221\pi$
$200$	1.39513	+	3.05490i	0.0986504	+	0.216014i
$201$	3.05111	−	1.96083i	0.215209	−	0.138306i
$202$	−0.266828	+	1.85583i	−0.0187739	+	0.130576i
$203$	0.968242	+	0.622251i	0.0679572	+	0.0436735i
$204$	3.22218	−	3.71859i	0.225597	−	0.260353i
$205$	−13.5828	−	3.98826i	−0.948662	−	0.278552i
$206$	12.0014			0.836175
$207$	−1.95834	−	4.37778i	−0.136114	−	0.304276i
$208$	−0.367382			−0.0254733
$209$	−5.35547	−	1.57251i	−0.370445	−	0.108773i
$210$	−1.89326	+	2.18494i	−0.130647	+	0.150775i
$211$	20.6405	+	13.2648i	1.42095	+	0.913188i	0.999981	+	0.00611215i	$0.00194557\pi$
$211$	20.6405	+	13.2648i	1.42095	+	0.913188i	0.420967	+	0.907076i	$0.361691\pi$
$212$	−1.33687	+	9.29814i	−0.0918167	+	0.638599i
$213$	−0.450928	+	0.289794i	−0.0308971	+	0.0198564i
$214$	1.23662	+	2.70782i	0.0845337	+	0.185103i
$215$	11.2031	+	12.9290i	0.764044	+	0.881754i
$216$	0.142315	+	0.989821i	0.00968330	+	0.0673488i
$217$	−0.288208	+	0.631087i	−0.0195648	+	0.0428410i
$218$	−1.70227	+	0.499831i	−0.115292	+	0.0338528i
$219$	−3.77402	+	1.10815i	−0.255025	+	0.0748821i
$220$	1.00541	−	2.20153i	0.0677845	−	0.148427i
$221$	0.257257	+	1.78926i	0.0173050	+	0.120359i
$222$	4.89424	+	5.64825i	0.328480	+	0.379086i
$223$	5.34847	+	11.7115i	0.358160	+	0.784261i	0.999850	+	0.0172971i	$0.00550612\pi$
$223$	5.34847	+	11.7115i	0.358160	+	0.784261i	−0.641690	+	0.766964i	$0.721767\pi$
$224$	0.841254	−	0.540641i	0.0562086	−	0.0361231i
$225$	−0.477949	+	3.32421i	−0.0318633	+	0.221614i
$226$	−7.65081	−	4.91688i	−0.508924	−	0.327066i
$227$	−15.4755	+	17.8597i	−1.02714	+	1.18539i	−0.0446682	+	0.999002i	$0.514223\pi$
$227$	−15.4755	+	17.8597i	−1.02714	+	1.18539i	−0.982477	+	0.186386i	$0.940322\pi$
$228$	−6.39734	−	1.87843i	−0.423674	−	0.124402i
$229$	10.7947			0.713332			0.356666	−	0.934232i	$-0.383913\pi$
$229$	10.7947			0.713332			0.356666	+	0.934232i	$0.383913\pi$
$230$	−2.07970	+	13.7083i	−0.137131	+	0.903900i
$231$	0.837140			0.0550797
$232$	−1.10433	−	0.324260i	−0.0725028	−	0.0212887i
$233$	11.8628	−	13.6904i	0.777159	−	0.896889i	−0.219742	−	0.975558i	$-0.570522\pi$
$233$	11.8628	−	13.6904i	0.777159	−	0.896889i	0.996901	+	0.0786692i	$0.0250671\pi$
$234$	−0.309061	−	0.198622i	−0.0202040	−	0.0129843i
$235$	−5.40410	+	37.5864i	−0.352525	+	2.45186i
$236$	−0.915257	+	0.588200i	−0.0595782	+	0.0382886i
$237$	−3.69618	−	8.09350i	−0.240093	−	0.525729i
$238$	−3.22218	−	3.71859i	−0.208863	−	0.241040i
$239$	−1.69934	−	11.8191i	−0.109921	−	0.764516i	−0.967991	−	0.250984i	$-0.919246\pi$
$239$	−1.69934	−	11.8191i	−0.109921	−	0.764516i	0.858070	−	0.513532i	$-0.171663\pi$
$240$	1.20100	−	2.62983i	0.0775243	−	0.169755i
$241$	19.7053	−	5.78599i	1.26933	−	0.372708i	0.423369	−	0.905957i	$-0.360847\pi$
$241$	19.7053	−	5.78599i	1.26933	−	0.372708i	0.845958	+	0.533249i	$0.179029\pi$
$242$	9.88201	−	2.90162i	0.635239	−	0.186523i
$243$	−0.415415	+	0.909632i	−0.0266489	+	0.0583529i
$244$	0.553452	+	3.84934i	0.0354311	+	0.246429i
$245$	1.89326	+	2.18494i	0.120956	+	0.139591i
$246$	2.03408	+	4.45401i	0.129688	+	0.283977i
$247$	2.06064	−	1.32429i	0.131115	−	0.0842627i
$248$	0.0987356	−	0.686721i	0.00626972	−	0.0436068i
$249$	−9.59860	−	6.16864i	−0.608286	−	0.390922i
$250$	−3.10799	+	3.58681i	−0.196566	+	0.226850i
$251$	22.0130	+	6.46359i	1.38945	+	0.407978i	0.889047	−	0.457816i	$-0.151368\pi$
$251$	22.0130	+	6.46359i	1.38945	+	0.407978i	0.500400	+	0.865794i	$0.333186\pi$
$252$	1.00000			0.0629941
$253$	3.39420	−	2.14427i	0.213391	−	0.134809i
$254$	−13.0054			−0.816030
$255$	−13.6491	−	4.00773i	−0.854739	−	0.250974i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	−2.06554	−	1.32744i	−0.128845	−	0.0828034i	0.474631	−	0.880185i	$-0.342582\pi$
$257$	−2.06554	−	1.32744i	−0.128845	−	0.0828034i	−0.603476	+	0.797381i	$0.706218\pi$
$258$	0.842126	−	5.85712i	0.0524285	−	0.364648i
$259$	6.28728	−	4.04059i	0.390673	−	0.251070i
$260$	0.441226	+	0.966150i	0.0273637	+	0.0599181i
$261$	−0.753713	−	0.869831i	−0.0466536	−	0.0538412i
$262$	0.122340	+	0.850891i	0.00755817	+	0.0525682i
$263$	−4.38837	+	9.60919i	−0.270598	+	0.592528i	−0.995333	−	0.0965003i	$-0.969235\pi$
$263$	−4.38837	+	9.60919i	−0.270598	+	0.592528i	0.724735	+	0.689028i	$0.241962\pi$
$264$	−0.803230	+	0.235849i	−0.0494354	+	0.0145155i
$265$	26.0581	−	7.65134i	1.60074	−	0.470018i
$266$	−2.76974	+	6.06489i	−0.169824	+	0.371863i
$267$	−1.02256	−	7.11207i	−0.0625797	−	0.435251i
$268$	2.37509	+	2.74100i	0.145082	+	0.167433i
$269$	−4.04549	−	8.85839i	−0.246658	−	0.540105i	0.745292	−	0.666738i	$-0.232310\pi$
$269$	−4.04549	−	8.85839i	−0.246658	−	0.540105i	−0.991950	+	0.126633i	$0.959583\pi$
$270$	2.43214	−	1.56304i	0.148015	−	0.0951236i
$271$	−3.08399	+	21.4496i	−0.187339	+	1.30297i	0.651523	+	0.758629i	$0.274130\pi$
$271$	−3.08399	+	21.4496i	−0.187339	+	1.30297i	−0.838862	+	0.544344i	$0.816779\pi$
$272$	4.13930	+	2.66017i	0.250982	+	0.161296i
$273$	−0.240584	+	0.277649i	−0.0145608	+	0.0168041i
$274$	−0.468161	−	0.137464i	−0.0282826	−	0.00830453i
$275$	−2.81144			−0.169537
$276$	4.05452	−	2.56143i	0.244053	−	0.154180i
$277$	−8.20272			−0.492854			−0.246427	−	0.969161i	$-0.579256\pi$
$277$	−8.20272			−0.492854			−0.246427	+	0.969161i	$0.579256\pi$
$278$	10.8558	+	3.18756i	0.651089	+	0.191177i
$279$	0.454331	−	0.524326i	0.0272001	−	0.0313906i
$280$	−2.43214	−	1.56304i	−0.145348	−	0.0934095i
$281$	−3.47849	+	24.1934i	−0.207509	+	1.44326i	0.573739	+	0.819038i	$0.305492\pi$
$281$	−3.47849	+	24.1934i	−0.207509	+	1.44326i	−0.781248	+	0.624220i	$0.785417\pi$
$282$	11.0494	−	7.10102i	0.657983	−	0.422860i
$283$	0.356818	+	0.781322i	0.0212106	+	0.0464448i	0.919941	−	0.392057i	$-0.128236\pi$
$283$	0.356818	+	0.781322i	0.0212106	+	0.0464448i	−0.898730	+	0.438502i	$0.855509\pi$
$284$	−0.351018	−	0.405097i	−0.0208291	−	0.0240381i
$285$	2.74327	+	19.0799i	0.162498	+	1.13020i
$286$	0.127761	−	0.279757i	0.00755465	−	0.0165424i
$287$	4.69815	−	1.37950i	0.277323	−	0.0814294i
$288$	−0.959493	+	0.281733i	−0.0565387	+	0.0166013i
$289$	2.99527	−	6.55874i	0.176193	−	0.385808i
$290$	0.473553	+	3.29363i	0.0278080	+	0.193409i
$291$	4.63072	+	5.34413i	0.271457	+	0.313278i
$292$	−1.63397	−	3.57790i	−0.0956211	−	0.209381i
$293$	18.6806	−	12.0053i	1.09133	−	0.701355i	0.134182	−	0.990957i	$-0.457159\pi$
$293$	18.6806	−	12.0053i	1.09133	−	0.701355i	0.957147	+	0.289602i	$0.0935228\pi$
$294$	0.142315	−	0.989821i	0.00829997	−	0.0577276i
$295$	2.64609	+	1.70054i	0.154061	+	0.0990092i
$296$	−4.89424	+	5.64825i	−0.284472	+	0.328298i
$297$	−0.803230	−	0.235849i	−0.0466081	−	0.0136854i
$298$	−15.1662			−0.878552
$299$	−0.264275	+	1.74197i	−0.0152834	+	0.100741i
$300$	−3.35839			−0.193897
$301$	−5.67765	−	1.66711i	−0.327255	−	0.0960906i
$302$	7.11508	−	8.21124i	0.409427	−	0.472504i
$303$	−1.57728	−	1.01365i	−0.0906122	−	0.0582329i
$304$	0.948872	−	6.59955i	0.0544216	−	0.378510i
$305$	9.45841	−	6.07855i	0.541587	−	0.348057i
$306$	2.04401	+	4.47575i	0.116848	+	0.255862i
$307$	6.43348	+	7.42463i	0.367178	+	0.423746i	0.909032	−	0.416727i	$-0.136823\pi$
$307$	6.43348	+	7.42463i	0.367178	+	0.423746i	−0.541854	+	0.840473i	$0.682277\pi$
$308$	0.119137	+	0.828619i	0.00678848	+	0.0472149i
$309$	−4.98555	+	10.9168i	−0.283618	+	0.621036i
$310$	−1.92454	+	0.565096i	−0.109306	+	0.0320953i
$311$	24.1213	−	7.08265i	1.36779	−	0.401620i	0.486289	−	0.873798i	$-0.338350\pi$
$311$	24.1213	−	7.08265i	1.36779	−	0.401620i	0.881503	+	0.472178i	$0.156532\pi$
$312$	0.152616	−	0.334182i	0.00864017	−	0.0189193i
$313$	4.97309	+	34.5886i	0.281096	+	1.95506i	0.296044	+	0.955174i	$0.404332\pi$
$313$	4.97309	+	34.5886i	0.281096	+	1.95506i	−0.0149487	+	0.999888i	$0.504758\pi$
$314$	4.65602	+	5.37333i	0.262754	+	0.303235i
$315$	−1.20100	−	2.62983i	−0.0676688	−	0.148174i
$316$	7.48510	−	4.81038i	0.421070	−	0.270605i
$317$	2.52666	−	17.5733i	0.141912	−	0.987016i	−0.787063	−	0.616873i	$-0.788399\pi$
$317$	2.52666	−	17.5733i	0.141912	−	0.987016i	0.928975	−	0.370144i	$-0.120692\pi$
$318$	−7.90253	−	5.07865i	−0.443152	−	0.284796i
$319$	0.630963	−	0.728170i	0.0353271	−	0.0407697i
$320$	2.77398	+	0.814514i	0.155070	+	0.0455327i
$321$	−2.97683			−0.166151
$322$	−1.95834	−	4.37778i	−0.109134	−	0.243964i
$323$	−32.8063			−1.82539
$324$	−0.959493	−	0.281733i	−0.0533052	−	0.0156518i
$325$	0.807975	−	0.932453i	0.0448184	−	0.0517232i
$326$	−7.18033	−	4.61452i	−0.397682	−	0.255574i
$327$	0.252485	−	1.75607i	0.0139625	−	0.0971111i
$328$	−4.11919	+	2.64724i	−0.227444	+	0.146170i
$329$	−5.45625	−	11.9475i	−0.300813	−	0.658688i
$330$	1.58492	+	1.82910i	0.0872472	+	0.100689i
$331$	1.10891	+	7.71265i	0.0609513	+	0.423926i	0.997336	+	0.0729494i	$0.0232412\pi$
$331$	1.10891	+	7.71265i	0.0609513	+	0.423926i	−0.936384	+	0.350976i	$0.885850\pi$
$332$	4.73983	−	10.3788i	0.260132	−	0.569610i
$333$	−7.17097	+	2.10559i	−0.392967	+	0.115385i
$334$	−20.7336	+	6.08794i	−1.13449	+	0.333117i
$335$	4.35587	−	9.53803i	0.237987	−	0.521118i
$336$	0.142315	+	0.989821i	0.00776391	+	0.0539992i
$337$	−11.8821	−	13.7127i	−0.647261	−	0.746979i	0.333380	−	0.942792i	$-0.391811\pi$
$337$	−11.8821	−	13.7127i	−0.647261	−	0.746979i	−0.980641	+	0.195814i	$0.937265\pi$
$338$	−5.34433	−	11.7024i	−0.290693	−	0.636529i
$339$	7.65081	−	4.91688i	0.415535	−	0.267048i
$340$	2.02447	−	14.0805i	0.109792	−	0.763623i
$341$	0.488594	+	0.314000i	0.0264589	+	0.0170041i
$342$	4.36623	−	5.03890i	0.236099	−	0.272472i
$343$	−0.959493	−	0.281733i	−0.0518078	−	0.0152121i
$344$	5.91735			0.319042
$345$	−11.6056	−	7.58640i	−0.624824	−	0.408438i
$346$	2.33764			0.125672
$347$	−15.7942	−	4.63760i	−0.847877	−	0.248959i	−0.171197	−	0.985237i	$-0.554764\pi$
$347$	−15.7942	−	4.63760i	−0.847877	−	0.248959i	−0.676680	+	0.736278i	$0.736582\pi$
$348$	0.753713	−	0.869831i	0.0404032	−	0.0466278i
$349$	6.22536	+	4.00079i	0.333236	+	0.214158i	0.696549	−	0.717510i	$-0.254718\pi$
$349$	6.22536	+	4.00079i	0.333236	+	0.214158i	−0.363313	+	0.931667i	$0.618354\pi$
$350$	−0.477949	+	3.32421i	−0.0255475	+	0.177687i
$351$	0.309061	−	0.198622i	0.0164965	−	0.0106016i
$352$	−0.347760	−	0.761489i	−0.0185357	−	0.0405875i
$353$	0.497384	+	0.574012i	0.0264731	+	0.0305516i	0.768832	−	0.639451i	$-0.220838\pi$
$353$	0.497384	+	0.574012i	0.0264731	+	0.0305516i	−0.742359	+	0.670003i	$0.766293\pi$
$354$	−0.154834	−	1.07689i	−0.00822934	−	0.0572363i
$355$	−0.643760	+	1.40964i	−0.0341673	+	0.0748158i
$356$	6.89415	−	2.02431i	0.365389	−	0.107288i
$357$	4.72109	−	1.38624i	0.249866	−	0.0733674i
$358$	6.99759	−	15.3226i	0.369834	−	0.809824i
$359$	3.02493	+	21.0388i	0.159649	+	1.11039i	0.899280	+	0.437373i	$0.144091\pi$
$359$	3.02493	+	21.0388i	0.159649	+	1.11039i	−0.739631	+	0.673013i	$0.765000\pi$
$360$	1.89326	+	2.18494i	0.0997836	+	0.115156i
$361$	10.5742	+	23.1542i	0.556534	+	1.21864i
$362$	−2.98888	+	1.92083i	−0.157092	+	0.100957i
$363$	−1.46573	+	10.1944i	−0.0769308	+	0.535065i
$364$	−0.309061	−	0.198622i	−0.0161992	−	0.0104106i
$365$	−7.44686	+	8.59413i	−0.389786	+	0.449838i
$366$	−3.73140	−	1.09564i	−0.195043	−	0.0572699i
$367$	24.6347			1.28592			0.642961	−	0.765899i	$-0.277706\pi$
$367$	24.6347			1.28592			0.642961	+	0.765899i	$0.277706\pi$
$368$	3.11237	+	3.64872i	0.162244	+	0.190203i
$369$	−4.89649			−0.254901
$370$	20.7319	+	6.08744i	1.07780	+	0.316471i
$371$	−6.15160	+	7.09933i	−0.319375	+	0.368579i
$372$	0.583647	+	0.375087i	0.0302607	+	0.0194474i
$373$	2.85682	−	19.8696i	0.147920	−	1.02881i	−0.771696	−	0.635992i	$-0.780591\pi$
$373$	2.85682	−	19.8696i	0.147920	−	1.02881i	0.919616	−	0.392818i	$-0.128500\pi$
$374$	−3.46517	+	2.22693i	−0.179180	+	0.115152i
$375$	−1.97157	−	4.31714i	−0.101811	−	0.222936i
$376$	8.60124	+	9.92636i	0.443575	+	0.511913i
$377$	0.0601762	+	0.418535i	0.00309923	+	0.0215556i
$378$	−0.415415	+	0.909632i	−0.0213666	+	0.0467864i
$379$	−9.77019	+	2.86879i	−0.501861	+	0.147360i	−0.522858	−	0.852420i	$-0.675134\pi$
$379$	−9.77019	+	2.86879i	−0.501861	+	0.147360i	0.0209970	+	0.999780i	$0.493316\pi$
$380$	−18.4953	+	5.43070i	−0.948788	+	0.278589i
$381$	5.40263	−	11.8301i	0.276785	−	0.606075i
$382$	−2.35734	−	16.3957i	−0.120612	−	0.838877i
$383$	−14.8866	−	17.1800i	−0.760668	−	0.877857i	0.234889	−	0.972022i	$-0.424527\pi$
$383$	−14.8866	−	17.1800i	−0.760668	−	0.877857i	−0.995557	+	0.0941649i	$0.969982\pi$
$384$	−0.415415	−	0.909632i	−0.0211991	−	0.0464195i
$385$	2.03604	−	1.30848i	0.103766	−	0.0666865i
$386$	0.646102	−	4.49374i	0.0328857	−	0.228725i
$387$	4.97799	+	3.19916i	0.253045	+	0.162622i
$388$	−4.63072	+	5.34413i	−0.235089	+	0.271307i
$389$	−5.44619	−	1.59914i	−0.276133	−	0.0810798i	0.140734	−	0.990047i	$-0.455054\pi$
$389$	−5.44619	−	1.59914i	−0.276133	−	0.0810798i	−0.416867	+	0.908968i	$0.636872\pi$
$390$	−1.06213			−0.0537832
$391$	15.5910	−	17.7132i	0.788470	−	0.895797i
$392$	1.00000			0.0505076
$393$	−0.824819	−	0.242189i	−0.0416066	−	0.0122168i
$394$	−10.9032	+	12.5830i	−0.549297	+	0.633922i
$395$	−21.6401	−	13.9072i	−1.08883	−	0.699749i
$396$	0.119137	−	0.828619i	0.00598688	−	0.0416397i
$397$	−9.97710	+	6.41189i	−0.500736	+	0.321804i	−0.766511	−	0.642232i	$-0.778009\pi$
$397$	−9.97710	+	6.41189i	−0.500736	+	0.321804i	0.265774	+	0.964035i	$0.414372\pi$
$398$	−10.1348	−	22.1922i	−0.508013	−	1.11239i
$399$	−4.36623	−	5.03890i	−0.218585	−	0.252260i
$400$	−0.477949	−	3.32421i	−0.0238975	−	0.166211i
$401$	−15.4803	+	33.8972i	−0.773052	+	1.69275i	−0.0532358	+	0.998582i	$0.516954\pi$
$401$	−15.4803	+	33.8972i	−0.773052	+	1.69275i	−0.719816	+	0.694165i	$0.755774\pi$
$402$	−3.47995	+	1.02181i	−0.173564	+	0.0509631i
$403$	−0.244559	+	0.0718089i	−0.0121823	+	0.00357705i
$404$	0.778867	−	1.70548i	0.0387501	−	0.0848508i
$405$	0.411445	+	2.86166i	0.0204449	+	0.142197i
$406$	−0.753713	−	0.869831i	−0.0374061	−	0.0431690i
$407$	−2.59906	−	5.69115i	−0.128831	−	0.282100i
$408$	−4.13930	+	2.66017i	−0.204926	+	0.131698i
$409$	4.36674	−	30.3713i	0.215921	−	1.50177i	−0.536959	−	0.843608i	$-0.680427\pi$
$409$	4.36674	−	30.3713i	0.215921	−	1.50177i	0.752881	−	0.658157i	$-0.228664\pi$
$410$	11.9089	+	7.65342i	0.588141	+	0.377975i
$411$	0.319523	−	0.368749i	0.0157609	−	0.0181891i
$412$	−11.5152	−	3.38117i	−0.567314	−	0.166579i
$413$	−1.08797			−0.0535354
$414$	0.645648	+	4.75217i	0.0317319	+	0.233557i
$415$	−32.9870			−1.61927
$416$	0.352500	+	0.103503i	0.0172827	+	0.00507467i
$417$	−7.40918	+	8.55065i	−0.362829	+	0.418727i
$418$	4.69551	+	3.01762i	0.229665	+	0.147597i
$419$	1.28620	−	8.94571i	0.0628349	−	0.437026i	−0.933983	−	0.357317i	$-0.883692\pi$
$419$	1.28620	−	8.94571i	0.0628349	−	0.437026i	0.996818	−	0.0797095i	$-0.0253993\pi$
$420$	2.43214	−	1.56304i	0.118676	−	0.0762686i
$421$	−10.8044	−	23.6583i	−0.526573	−	1.15303i	−0.966890	−	0.255192i	$-0.917861\pi$
$421$	−10.8044	−	23.6583i	−0.526573	−	1.15303i	0.440317	−	0.897842i	$-0.354866\pi$
$422$	−16.0673	−	18.5426i	−0.782142	−	0.902639i
$423$	1.86923	+	13.0008i	0.0908850	+	0.632119i
$424$	3.90231	−	8.54486i	0.189513	−	0.414975i
$425$	−15.8553	+	4.65553i	−0.769094	+	0.225826i
$426$	0.514307	−	0.151014i	0.0249183	−	0.00731666i
$427$	−1.61552	+	3.53749i	−0.0781804	+	0.171191i
$428$	−0.423648	−	2.94653i	−0.0204778	−	0.142426i
$429$	0.201402	+	0.232431i	0.00972379	+	0.0112219i
$430$	−7.10674	−	15.5616i	−0.342718	−	0.750447i
$431$	−7.69145	+	4.94300i	−0.370484	+	0.238096i	−0.712613	−	0.701557i	$-0.752488\pi$
$431$	−7.69145	+	4.94300i	−0.370484	+	0.238096i	0.342129	+	0.939653i	$0.388852\pi$
$432$	0.142315	−	0.989821i	0.00684713	−	0.0476228i
$433$	−5.01968	−	3.22595i	−0.241230	−	0.155029i	0.414440	−	0.910077i	$-0.363977\pi$
$433$	−5.01968	−	3.22595i	−0.241230	−	0.155029i	−0.655670	+	0.755047i	$0.727614\pi$
$434$	0.454331	−	0.524326i	0.0218086	−	0.0251685i
$435$	−3.19271	−	0.937466i	−0.153079	−	0.0449480i
$436$	1.77413			0.0849655
$437$	−30.6097	−	9.24652i	−1.46426	−	0.442321i
$438$	3.93335			0.187943
$439$	16.1737	+	4.74902i	0.771928	+	0.226658i	0.643897	−	0.765112i	$-0.277316\pi$
$439$	16.1737	+	4.74902i	0.771928	+	0.226658i	0.128030	+	0.991770i	$0.459135\pi$
$440$	−1.58492	+	1.82910i	−0.0755583	+	0.0871989i
$441$	0.841254	+	0.540641i	0.0400597	+	0.0257448i
$442$	0.257257	−	1.78926i	0.0122365	−	0.0851067i
$443$	−12.4780	+	8.01914i	−0.592849	+	0.381001i	−0.802391	−	0.596799i	$-0.796439\pi$
$443$	−12.4780	+	8.01914i	−0.592849	+	0.381001i	0.209542	+	0.977800i	$0.432803\pi$
$444$	−3.10469	−	6.79832i	−0.147342	−	0.322634i
$445$	−13.6035	−	15.6992i	−0.644866	−	0.744215i
$446$	−1.83230	−	12.7440i	−0.0867621	−	0.603444i
$447$	6.30025	−	13.7956i	0.297992	−	0.652511i
$448$	−0.959493	+	0.281733i	−0.0453318	+	0.0133106i
$449$	6.49307	−	1.90654i	0.306427	−	0.0899751i	−0.124904	−	0.992169i	$-0.539862\pi$
$449$	6.49307	−	1.90654i	0.306427	−	0.0899751i	0.431331	+	0.902194i	$0.358044\pi$
$450$	1.39513	−	3.05490i	0.0657669	−	0.144010i
$451$	−0.583355	−	4.05733i	−0.0274691	−	0.191052i
$452$	5.95565	+	6.87319i	0.280130	+	0.323288i
$453$	4.51350	+	9.88318i	0.212063	+	0.464352i
$454$	19.8803	−	12.7763i	0.933028	−	0.599621i
$455$	−0.151157	+	1.05132i	−0.00708636	+	0.0492867i
$456$	5.60899	+	3.60468i	0.262665	+	0.168804i
$457$	−16.4968	+	19.0383i	−0.771688	+	0.890576i	−0.996480	−	0.0838310i	$-0.973284\pi$
$457$	−16.4968	+	19.0383i	−0.771688	+	0.890576i	0.224792	+	0.974407i	$0.427830\pi$
$458$	−10.3574	−	3.04121i	−0.483970	−	0.142106i
$459$	−4.92040			−0.229665
$460$	5.85753	−	12.5671i	0.273109	−	0.585945i
$461$	−35.0173			−1.63092			−0.815458	−	0.578816i	$-0.803515\pi$
$461$	−35.0173			−1.63092			−0.815458	+	0.578816i	$0.803515\pi$
$462$	−0.803230	−	0.235849i	−0.0373696	−	0.0109727i
$463$	−17.2289	+	19.8832i	−0.800693	+	0.924049i	−0.998419	−	0.0562082i	$-0.982099\pi$
$463$	−17.2289	+	19.8832i	−0.800693	+	0.924049i	0.197726	+	0.980257i	$0.436644\pi$
$464$	0.968242	+	0.622251i	0.0449495	+	0.0288873i
$465$	0.285453	−	1.98537i	0.0132376	−	0.0920694i
$466$	−15.2393	+	9.79371i	−0.705948	+	0.453685i
$467$	−17.0739	−	37.3866i	−0.790086	−	1.73005i	−0.676405	−	0.736530i	$-0.736463\pi$
$467$	−17.0739	−	37.3866i	−0.790086	−	1.73005i	−0.113681	−	0.993517i	$-0.536264\pi$
$468$	0.240584	+	0.277649i	0.0111210	+	0.0128343i
$469$	0.516157	+	3.58995i	0.0238339	+	0.165768i
$470$	15.7745	−	34.5413i	0.727624	−	1.59327i
$471$	−6.82194	+	2.00310i	−0.314338	+	0.0922981i
$472$	1.04390	−	0.306516i	0.0480493	−	0.0141085i
$473$	−2.05782	+	4.50600i	−0.0946186	+	0.207186i
$474$	1.26625	+	8.80699i	0.0581610	+	0.404519i
$475$	14.6635	+	16.9226i	0.672808	+	0.776462i
$476$	2.04401	+	4.47575i	0.0936869	+	0.205146i
$477$	7.90253	−	5.07865i	0.361832	−	0.232535i
$478$	−1.69934	+	11.8191i	−0.0777258	+	0.540595i
$479$	21.9487	+	14.1056i	1.00286	+	0.644501i	0.935537	−	0.353229i	$-0.114917\pi$
$479$	21.9487	+	14.1056i	1.00286	+	0.644501i	0.0673272	+	0.997731i	$0.478553\pi$
$480$	−1.89326	+	2.18494i	−0.0864151	+	0.0997284i
$481$	2.63448	+	0.773554i	0.120122	+	0.0352710i
$482$	−20.5372			−0.935442
$483$	4.79569	+	0.0372286i	0.218211	+	0.00169396i
$484$	−10.2992			−0.468145
$485$	19.6156	+	5.75967i	0.890700	+	0.261533i
$486$	0.654861	−	0.755750i	0.0297051	−	0.0342815i
$487$	16.5736	+	10.6512i	0.751022	+	0.482652i	0.859302	−	0.511468i	$-0.170898\pi$
$487$	16.5736	+	10.6512i	0.751022	+	0.482652i	−0.108281	+	0.994120i	$0.534535\pi$
$488$	0.553452	−	3.84934i	0.0250536	−	0.174252i
$489$	7.18033	−	4.61452i	0.324706	−	0.208676i
$490$	−1.20100	−	2.62983i	−0.0542557	−	0.118803i
$491$	−13.1093	−	15.1289i	−0.591614	−	0.682759i	0.378446	−	0.925623i	$-0.376458\pi$
$491$	−13.1093	−	15.1289i	−0.591614	−	0.682759i	−0.970060	+	0.242864i	$0.921913\pi$
$492$	−0.696844	−	4.84665i	−0.0314161	−	0.218504i
$493$	2.35255	−	5.15137i	0.105954	−	0.232006i
$494$	−2.35027	+	0.690100i	−0.105743	+	0.0310491i
$495$	−2.32221	+	0.681862i	−0.104375	+	0.0306474i
$496$	−0.288208	+	0.631087i	−0.0129409	+	0.0283366i
$497$	−0.0762835	−	0.530564i	−0.00342178	−	0.0237990i
$498$	7.47188	+	8.62301i	0.334823	+	0.386406i
$499$	−10.1325	−	22.1870i	−0.453592	−	0.993228i	−0.988902	−	0.148572i	$-0.952532\pi$
$499$	−10.1325	−	22.1870i	−0.453592	−	0.993228i	0.535310	−	0.844656i	$-0.320195\pi$
$500$	3.99261	−	2.56590i	0.178555	−	0.114750i
$501$	3.07527	−	21.3890i	0.137393	−	0.955590i
$502$	−19.3003	−	12.4035i	−0.861414	−	0.553597i
$503$	7.06012	−	8.14782i	0.314795	−	0.363293i	−0.576198	−	0.817310i	$-0.695464\pi$
$503$	7.06012	−	8.14782i	0.314795	−	0.363293i	0.890993	+	0.454017i	$0.150010\pi$
$504$	−0.959493	−	0.281733i	−0.0427392	−	0.0125494i
$505$	−5.42054			−0.241211
$506$	−3.86082	+	1.10116i	−0.171634	+	0.0489524i
$507$	12.8650			0.571356
$508$	12.4786	+	3.66404i	0.553647	+	0.162565i
$509$	20.6321	−	23.8107i	0.914500	−	1.05539i	−0.0837633	−	0.996486i	$-0.526694\pi$
$509$	20.6321	−	23.8107i	0.914500	−	1.05539i	0.998264	−	0.0589040i	$-0.0187606\pi$
$510$	11.9671	+	7.69078i	0.529912	+	0.340554i
$511$	0.559774	−	3.89332i	0.0247630	−	0.172230i
$512$	0.841254	−	0.540641i	0.0371785	−	0.0238932i
$513$	2.76974	+	6.06489i	0.122287	+	0.267772i
$514$	1.60789	+	1.85560i	0.0709208	+	0.0818469i
$515$	4.93790	+	34.3438i	0.217590	+	1.51337i
$516$	−2.45816	+	5.38261i	−0.108214	+	0.236956i
$517$	−10.5500	+	3.09775i	−0.463988	+	0.136239i
$518$	−7.17097	+	2.10559i	−0.315074	+	0.0925142i
$519$	−0.971089	+	2.12639i	−0.0426261	+	0.0933381i
$520$	−0.151157	−	1.05132i	−0.00662869	−	0.0461035i
$521$	22.9363	+	26.4699i	1.00486	+	1.15967i	0.987145	+	0.159825i	$0.0510931\pi$
$521$	22.9363	+	26.4699i	1.00486	+	1.15967i	0.0177130	+	0.999843i	$0.494361\pi$
$522$	0.478122	+	1.04694i	0.0209268	+	0.0458234i
$523$	8.11314	−	5.21400i	0.354763	−	0.227992i	−0.351105	−	0.936336i	$-0.614194\pi$
$523$	8.11314	−	5.21400i	0.354763	−	0.227992i	0.705867	+	0.708344i	$0.250557\pi$
$524$	0.122340	−	0.850891i	0.00534443	−	0.0371713i
$525$	−2.82526	−	1.81569i	−0.123305	−	0.0792430i
$526$	6.91783	−	7.98360i	0.301632	−	0.348102i
$527$	3.27541	+	0.961747i	0.142679	+	0.0418944i
$528$	0.837140			0.0364318
$529$	19.5395	−	12.1329i	0.849546	−	0.527515i
$530$	−27.1582			−1.17968
$531$	1.04390	+	0.306516i	0.0453013	+	0.0133017i
$532$	4.36623	−	5.03890i	0.189300	−	0.218464i
$533$	1.51332	+	0.972549i	0.0655490	+	0.0421258i
$534$	−1.02256	+	7.11207i	−0.0442505	+	0.307769i
$535$	−7.24007	+	4.65291i	−0.313016	+	0.201163i
$536$	−1.50665	−	3.29911i	−0.0650776	−	0.142500i
$537$	11.0310	+	12.7305i	0.476023	+	0.549360i
$538$	1.38592	+	9.63930i	0.0597514	+	0.415580i
$539$	−0.347760	+	0.761489i	−0.0149791	+	0.0327997i
$540$	−2.77398	+	0.814514i	−0.119373	+	0.0350511i
$541$	42.3138	−	12.4245i	1.81921	−	0.534169i	0.819945	−	0.572442i	$-0.194004\pi$
$541$	42.3138	−	12.4245i	1.81921	−	0.534169i	0.999267	+	0.0382727i	$0.0121855\pi$
$542$	9.00213	−	19.7119i	0.386675	−	0.846699i
$543$	−0.505628	−	3.51672i	−0.0216986	−	0.150917i
$544$	−3.22218	−	3.71859i	−0.138150	−	0.159433i
$545$	−2.13074	−	4.66566i	−0.0912707	−	0.199855i
$546$	0.309061	−	0.198622i	0.0132266	−	0.00850022i
$547$	3.75566	−	26.1212i	0.160580	−	1.11686i	−0.736962	−	0.675934i	$-0.763741\pi$
$547$	3.75566	−	26.1212i	0.160580	−	1.11686i	0.897543	−	0.440927i	$-0.145350\pi$
$548$	0.410469	+	0.263792i	0.0175344	+	0.0112686i
$549$	2.54671	−	2.93905i	0.108691	−	0.125436i
$550$	2.69756	+	0.792076i	0.115024	+	0.0337742i
$551$	−7.67387			−0.326918
$552$	−4.61192	+	1.31538i	−0.196296	+	0.0559863i
$553$	8.89756			0.378363
$554$	7.87045	+	2.31097i	0.334383	+	0.0981838i
$555$	−14.1497	+	16.3296i	−0.600620	+	0.693153i
$556$	−9.51805	−	6.11688i	−0.403655	−	0.259413i
$557$	2.90329	−	20.1929i	0.123016	−	0.855599i	−0.831091	−	0.556136i	$-0.812283\pi$
$557$	2.90329	−	20.1929i	0.123016	−	0.855599i	0.954108	−	0.299463i	$-0.0968074\pi$
$558$	−0.583647	+	0.375087i	−0.0247078	+	0.0158787i
$559$	−0.903081	−	1.97747i	−0.0381963	−	0.0836382i
$560$	1.89326	+	2.18494i	0.0800049	+	0.0923305i
$561$	−0.586203	−	4.07713i	−0.0247495	−	0.172137i
$562$	10.1537	−	22.2334i	0.428306	−	0.937860i
$563$	−10.3256	+	3.03188i	−0.435173	+	0.127778i	−0.491980	−	0.870607i	$-0.663727\pi$
$563$	−10.3256	+	3.03188i	−0.435173	+	0.127778i	0.0568061	+	0.998385i	$0.481908\pi$
$564$	−12.6024	+	3.70040i	−0.530658	+	0.155815i
$565$	10.9226	−	23.9170i	0.459515	−	1.00620i
$566$	−0.122240	−	0.850201i	−0.00513815	−	0.0357366i
$567$	−0.654861	−	0.755750i	−0.0275016	−	0.0317385i
$568$	0.222671	+	0.487581i	0.00934305	+	0.0204584i
$569$	22.3652	−	14.3732i	0.937597	−	0.602557i	0.0198844	−	0.999802i	$-0.493670\pi$
$569$	22.3652	−	14.3732i	0.937597	−	0.602557i	0.917712	+	0.397245i	$0.130034\pi$
$570$	2.74327	−	19.0799i	0.114903	−	0.799169i
$571$	4.14901	+	2.66641i	0.173631	+	0.111586i	0.624570	−	0.780969i	$-0.285274\pi$
$571$	4.14901	+	2.66641i	0.173631	+	0.111586i	−0.450939	+	0.892555i	$0.648911\pi$
$572$	−0.201402	+	0.232431i	−0.00842105	+	0.00971841i
$573$	15.8933	+	4.66670i	0.663953	+	0.194954i
$574$	−4.89649			−0.204376
$575$	−16.1058	−	0.125028i	−0.671659	−	0.00521404i
$576$	1.00000			0.0416667
$577$	−10.3595	−	3.04182i	−0.431271	−	0.126633i	0.0588900	−	0.998264i	$-0.481244\pi$
$577$	−10.3595	−	3.04182i	−0.431271	−	0.126633i	−0.490161	+	0.871632i	$0.663062\pi$
$578$	−4.72176	+	5.44920i	−0.196399	+	0.226657i
$579$	3.81925	+	2.45448i	0.158723	+	0.102005i
$580$	0.473553	−	3.29363i	0.0196632	−	0.136761i
$581$	9.59860	−	6.16864i	0.398217	−	0.255918i
$582$	−2.93752	−	6.43228i	−0.121764	−	0.266627i
$583$	5.14975	+	5.94313i	0.213281	+	0.246139i
$584$	0.559774	+	3.89332i	0.0231636	+	0.161107i
$585$	0.441226	−	0.966150i	0.0182425	−	0.0399454i
$586$	−21.3061	+	6.25605i	−0.880148	+	0.258435i
$587$	−36.6493	+	10.7612i	−1.51268	+	0.444163i	−0.929698	−	0.368323i	$-0.879932\pi$
$587$	−36.6493	+	10.7612i	−1.51268	+	0.444163i	−0.582981	+	0.812485i	$0.698114\pi$
$588$	−0.415415	+	0.909632i	−0.0171314	+	0.0375126i
$589$	−0.658311	−	4.57865i	−0.0271252	−	0.188660i
$590$	−2.05981	−	2.37714i	−0.0848009	−	0.0978655i
$591$	−6.91653	−	15.1451i	−0.284508	−	0.622986i
$592$	6.28728	−	4.04059i	0.258406	−	0.166067i
$593$	0.296441	−	2.06179i	0.0121734	−	0.0846677i	−0.982829	−	0.184518i	$-0.940927\pi$
$593$	0.296441	−	2.06179i	0.0121734	−	0.0846677i	0.995002	+	0.0998508i	$0.0318365\pi$
$594$	0.704247	+	0.452592i	0.0288956	+	0.0185701i
$595$	9.31560	−	10.7508i	0.381902	−	0.440739i
$596$	14.5518	+	4.27280i	0.596066	+	0.175021i
$597$	24.3969			0.998497
$598$	0.744339	−	1.59695i	0.0304383	−	0.0653042i
$599$	−34.6326			−1.41505			−0.707525	−	0.706688i	$-0.750188\pi$
$599$	−34.6326			−1.41505			−0.707525	+	0.706688i	$0.750188\pi$
$600$	3.22236	+	0.946169i	0.131552	+	0.0386272i
$601$	13.3726	−	15.4328i	0.545480	−	0.629518i	−0.414344	−	0.910121i	$-0.635989\pi$
$601$	13.3726	−	15.4328i	0.545480	−	0.629518i	0.959824	+	0.280602i	$0.0905343\pi$
$602$	4.97799	+	3.19916i	0.202888	+	0.130388i
$603$	0.516157	−	3.58995i	0.0210195	−	0.146194i
$604$	−9.14024	+	5.87408i	−0.371911	+	0.239013i
$605$	12.3694	+	27.0851i	0.502886	+	1.10117i
$606$	1.22781	+	1.41696i	0.0498762	+	0.0575602i
$607$	−5.32252	−	37.0189i	−0.216034	−	1.50255i	−0.752479	−	0.658616i	$-0.771142\pi$
$607$	−5.32252	−	37.0189i	−0.216034	−	1.50255i	0.536445	−	0.843935i	$-0.319767\pi$
$608$	−2.76974	+	6.06489i	−0.112328	+	0.245964i
$609$	1.10433	−	0.324260i	0.0447497	−	0.0131397i
$610$	−10.7878	+	3.16758i	−0.436785	+	0.128252i
$611$	2.00453	−	4.38930i	0.0810945	−	0.177572i
$612$	−0.700246	−	4.87032i	−0.0283058	−	0.196871i
$613$	−15.5788	−	17.9788i	−0.629220	−	0.726159i	0.348210	−	0.937416i	$-0.386790\pi$
$613$	−15.5788	−	17.9788i	−0.629220	−	0.726159i	−0.977430	+	0.211258i	$0.932244\pi$
$614$	−4.08112	−	8.93640i	−0.164700	−	0.360644i
$615$	−11.9089	+	7.65342i	−0.480215	+	0.308616i
$616$	0.119137	−	0.828619i	0.00480018	−	0.0333860i
$617$	10.3593	+	6.65749i	0.417048	+	0.268020i	0.732293	−	0.680990i	$-0.238450\pi$
$617$	10.3593	+	6.65749i	0.417048	+	0.268020i	−0.315245	+	0.949010i	$0.602087\pi$
$618$	7.85922	−	9.07003i	0.316144	−	0.364850i
$619$	28.3561	+	8.32609i	1.13973	+	0.334654i	0.796523	−	0.604608i	$-0.206670\pi$
$619$	28.3561	+	8.32609i	1.13973	+	0.334654i	0.343203	+	0.939261i	$0.388488\pi$
$620$	2.00579			0.0805544
$621$	−4.59094	−	1.38682i	−0.184228	−	0.0556512i
$622$	−25.1396			−1.00801
$623$	6.89415	+	2.02431i	0.276208	+	0.0811021i
$624$	−0.240584	+	0.277649i	−0.00963106	+	0.0111148i
$625$	−25.6693	−	16.4967i	−1.02677	−	0.659866i
$626$	4.97309	−	34.5886i	0.198765	−	1.38244i
$627$	−4.69551	+	3.01762i	−0.187520	+	0.120512i
$628$	−2.95358	−	6.46743i	−0.117861	−	0.258079i
$629$	−24.0816	−	27.7916i	−0.960196	−	1.10813i
$630$	0.411445	+	2.86166i	0.0163924	+	0.114011i
$631$	−18.8579	+	41.2930i	−0.750721	+	1.64385i	0.0143454	+	0.999897i	$0.495434\pi$
$631$	−18.8579	+	41.2930i	−0.750721	+	1.64385i	−0.765066	+	0.643952i	$0.777294\pi$
$632$	−8.53714	+	2.50673i	−0.339589	+	0.0997124i
$633$	23.5415	−	6.91241i	0.935691	−	0.274744i
$634$	−7.37529	+	16.1496i	−0.292910	+	0.641384i
$635$	−5.35100	−	37.2170i	−0.212348	−	1.47691i
$636$	6.15160	+	7.09933i	0.243927	+	0.281507i
$637$	−0.152616	−	0.334182i	−0.00604686	−	0.0132408i
$638$	−0.810553	+	0.520911i	−0.0320901	+	0.0206231i
$639$	−0.0762835	+	0.530564i	−0.00301773	+	0.0209888i
$640$	−2.43214	−	1.56304i	−0.0961387	−	0.0617846i
$641$	1.95488	−	2.25605i	0.0772130	−	0.0891086i	−0.715829	−	0.698276i	$-0.753951\pi$
$641$	1.95488	−	2.25605i	0.0772130	−	0.0891086i	0.793042	+	0.609167i	$0.208496\pi$
$642$	2.85625	+	0.838671i	0.112727	+	0.0330997i
$643$	27.0360			1.06619			0.533097	−	0.846054i	$-0.321028\pi$
$643$	27.0360			1.06619			0.533097	+	0.846054i	$0.321028\pi$
$644$	0.645648	+	4.75217i	0.0254421	+	0.187262i
$645$	17.1076			0.673610
$646$	31.4775	+	9.24261i	1.23846	+	0.363646i
$647$	−3.89782	+	4.49833i	−0.153239	+	0.176847i	−0.827178	−	0.561939i	$-0.810055\pi$
$647$	−3.89782	+	4.49833i	−0.153239	+	0.176847i	0.673939	+	0.738787i	$0.264601\pi$
$648$	0.841254	+	0.540641i	0.0330476	+	0.0212384i
$649$	−0.129618	+	0.901511i	−0.00508794	+	0.0353874i
$650$	−1.03795	+	0.667049i	−0.0407117	+	0.0261638i
$651$	0.288208	+	0.631087i	0.0112958	+	0.0247342i
$652$	5.58941	+	6.45053i	0.218898	+	0.252622i
$653$	6.33879	+	44.0873i	0.248056	+	1.72527i	0.609424	+	0.792845i	$0.291401\pi$
$653$	6.33879	+	44.0873i	0.248056	+	1.72527i	−0.361368	+	0.932423i	$0.617690\pi$
$654$	−0.737001	+	1.61381i	−0.0288190	+	0.0631048i
$655$	−2.38463	+	0.700189i	−0.0931750	+	0.0273587i
$656$	4.69815	−	1.37950i	0.183432	−	0.0538605i
$657$	−1.63397	+	3.57790i	−0.0637474	+	0.139587i
$658$	1.86923	+	13.0008i	0.0728701	+	0.506823i
$659$	8.67193	+	10.0079i	0.337810	+	0.389854i	0.899084	−	0.437776i	$-0.144234\pi$
$659$	8.67193	+	10.0079i	0.337810	+	0.389854i	−0.561274	+	0.827630i	$0.689688\pi$
$660$	−1.00541	−	2.20153i	−0.0391354	−	0.0856945i
$661$	−6.75115	+	4.33870i	−0.262589	+	0.168756i	−0.665310	−	0.746567i	$-0.731701\pi$
$661$	−6.75115	+	4.33870i	−0.262589	+	0.168756i	0.402721	+	0.915323i	$0.368064\pi$
$662$	1.10891	−	7.71265i	0.0430991	−	0.299761i
$663$	1.52070	+	0.977297i	0.0590592	+	0.0379551i
$664$	−7.47188	+	8.62301i	−0.289965	+	0.334638i
$665$	−18.4953	−	5.43070i	−0.717216	−	0.210594i
$666$	7.47371			0.289600
$667$	3.64695	−	4.14338i	0.141211	−	0.160432i
$668$	21.6089			0.836075
$669$	12.3535	+	3.62731i	0.477613	+	0.140240i
$670$	−6.86660	+	7.92448i	−0.265280	+	0.306149i
$671$	2.73876	+	1.76010i	0.105729	+	0.0679478i
$672$	0.142315	−	0.989821i	0.00548991	−	0.0381832i
$673$	−31.3313	+	20.1354i	−1.20773	+	0.776163i	−0.980278	−	0.197625i	$-0.936677\pi$
$673$	−31.3313	+	20.1354i	−1.20773	+	0.776163i	−0.227456	+	0.973788i	$0.573041\pi$
$674$	7.53750	+	16.5048i	0.290334	+	0.635742i
$675$	2.19928	+	2.53811i	0.0846504	+	0.0976917i
$676$	1.83088	+	12.7341i	0.0704186	+	0.489772i
$677$	−3.20356	+	7.01482i	−0.123123	+	0.269601i	−0.961150	−	0.276028i	$-0.910982\pi$
$677$	−3.20356	+	7.01482i	−0.123123	+	0.269601i	0.838027	+	0.545629i	$0.183709\pi$
$678$	−8.72614	+	2.56223i	−0.335125	+	0.0984017i
$679$	−6.78486	+	1.99221i	−0.260379	+	0.0764542i
$680$	−5.90941	+	12.9398i	−0.226615	+	0.496219i
$681$	3.36315	+	23.3912i	0.128876	+	0.896353i
$682$	−0.380339	−	0.438934i	−0.0145639	−	0.0168077i
$683$	11.7878	+	25.8118i	0.451049	+	0.987660i	0.989437	+	0.144963i	$0.0463062\pi$
$683$	11.7878	+	25.8118i	0.451049	+	0.987660i	−0.538388	+	0.842697i	$0.680967\pi$
$684$	−5.60899	+	3.60468i	−0.214465	+	0.137828i
$685$	0.200754	−	1.39628i	0.00767043	−	0.0533490i
$686$	0.841254	+	0.540641i	0.0321192	+	0.0206418i
$687$	7.06901	−	8.15807i	0.269699	−	0.311250i
$688$	−5.67765	−	1.66711i	−0.216459	−	0.0635580i
$689$	−3.45109			−0.131476
$690$	8.99814	+	10.5488i	0.342553	+	0.401585i
$691$	7.70839			0.293241			0.146620	−	0.989193i	$-0.453160\pi$
$691$	7.70839			0.293241			0.146620	+	0.989193i	$0.453160\pi$
$692$	−2.24295	−	0.658588i	−0.0852640	−	0.0250358i
$693$	0.548210	−	0.632668i	0.0208248	−	0.0240331i
$694$	13.8479	+	8.89948i	0.525658	+	0.337820i
$695$	−4.65514	+	32.3772i	−0.176580	+	1.22814i
$696$	−0.968242	+	0.622251i	−0.0367011	+	0.0235864i
$697$	−10.0085	−	21.9155i	−0.379098	−	0.830108i
$698$	−4.84603	−	5.59262i	−0.183425	−	0.211684i
$699$	−2.57804	−	17.9306i	−0.0975102	−	0.678199i
$700$	1.39513	−	3.05490i	0.0527309	−	0.115464i
$701$	−6.37675	+	1.87238i	−0.240846	+	0.0707189i	−0.399928	−	0.916547i	$-0.630965\pi$
$701$	−6.37675	+	1.87238i	−0.240846	+	0.0707189i	0.159082	+	0.987265i	$0.449147\pi$
$702$	−0.352500	+	0.103503i	−0.0133043	+	0.00390648i
$703$	−20.7003	+	45.3272i	−0.780725	+	1.70955i
$704$	0.119137	+	0.828619i	0.00449016	+	0.0312297i
$705$	24.8669	+	28.6980i	0.936543	+	1.08083i
$706$	−0.315519	−	0.690890i	−0.0118747	−	0.0260020i
$707$	1.57728	−	1.01365i	0.0593196	−	0.0381224i
$708$	−0.154834	+	1.07689i	−0.00581902	+	0.0404722i
$709$	24.5439	+	15.7734i	0.921766	+	0.592383i	0.913169	−	0.407580i	$-0.133627\pi$
$709$	24.5439	+	15.7734i	0.921766	+	0.592383i	0.00859630	+	0.999963i	$0.497264\pi$
$710$	1.01482	−	1.17117i	0.0380857	−	0.0439532i
$711$	−8.53714	−	2.50673i	−0.320168	−	0.0940098i
$712$	−7.18520			−0.269277
$713$	2.78503	+	1.82053i	0.104300	+	0.0681794i
$714$	−4.92040			−0.184141
$715$	0.853137	+	0.250504i	0.0319055	+	0.00936830i
$716$	−11.0310	+	12.7305i	−0.412248	+	0.475760i
$717$	−10.0451	−	6.45562i	−0.375142	−	0.241089i
$718$	3.02493	−	21.0388i	0.112889	−	0.785162i
$719$	−27.6202	+	17.7504i	−1.03006	+	0.661978i	−0.942509	−	0.334182i	$-0.891540\pi$
$719$	−27.6202	+	17.7504i	−1.03006	+	0.661978i	−0.0875496	+	0.996160i	$0.527904\pi$
$720$	−1.20100	−	2.62983i	−0.0447587	−	0.0980079i
$721$	−7.85922	−	9.07003i	−0.292693	−	0.337785i
$722$	−3.62254	−	25.1953i	−0.134817	−	0.937674i
$723$	8.53144	−	18.6813i	0.317288	−	0.694763i
$724$	3.40897	−	1.00096i	0.126693	−	0.0372005i
$725$	−3.70877	+	1.08899i	−0.137740	+	0.0404442i
$726$	4.27844	−	9.36848i	0.158788	−	0.347697i
$727$	5.59206	+	38.8936i	0.207398	+	1.44248i	0.781605	+	0.623774i	$0.214401\pi$
$727$	5.59206	+	38.8936i	0.207398	+	1.44248i	−0.574207	+	0.818710i	$0.694689\pi$
$728$	0.240584	+	0.277649i	0.00891663	+	0.0102903i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	9.56646	−	6.14799i	0.354070	−	0.227547i
$731$	−4.14360	+	28.8194i	−0.153256	+	1.06592i
$732$	3.27157	+	2.10251i	0.120921	+	0.0777111i
$733$	−10.3868	+	11.9870i	−0.383645	+	0.442750i	−0.914422	−	0.404761i	$-0.867355\pi$
$733$	−10.3868	+	11.9870i	−0.383645	+	0.442750i	0.530777	+	0.847511i	$0.321900\pi$
$734$	−23.6368	−	6.94040i	−0.872452	−	0.256175i
$735$	2.89109			0.106639
$736$	−1.95834	−	4.37778i	−0.0721852	−	0.161367i
$737$	3.03619			0.111840
$738$	4.69815	+	1.37950i	0.172941	+	0.0507801i
$739$	−28.3432	+	32.7098i	−1.04262	+	1.20325i	−0.0639201	+	0.997955i	$0.520360\pi$
$739$	−28.3432	+	32.7098i	−1.04262	+	1.20325i	−0.978700	+	0.205293i	$0.934185\pi$
$740$	−18.1771	−	11.6817i	−0.668203	−	0.429428i
$741$	0.348598	−	2.42455i	0.0128061	−	0.0890682i
$742$	7.90253	−	5.07865i	0.290111	−	0.186443i
$743$	−10.9799	−	24.0427i	−0.402814	−	0.882040i	−0.996977	−	0.0776953i	$-0.975244\pi$
$743$	−10.9799	−	24.0427i	−0.402814	−	0.882040i	0.594163	−	0.804345i	$-0.297483\pi$
$744$	−0.454331	−	0.524326i	−0.0166566	−	0.0192227i
$745$	−6.24004	−	43.4004i	−0.228617	−	1.59007i
$746$	−8.33901	+	18.2599i	−0.305313	+	0.668542i
$747$	−10.9477	+	3.21453i	−0.400555	+	0.117614i
$748$	3.95221	−	1.16047i	0.144507	−	0.0424311i
$749$	1.23662	−	2.70782i	0.0451852	−	0.0989417i
$750$	0.675430	+	4.69772i	0.0246632	+	0.171536i
$751$	30.2444	+	34.9039i	1.10363	+	1.27366i	0.958762	+	0.284209i	$0.0917310\pi$
$751$	30.2444	+	34.9039i	1.10363	+	1.27366i	0.144870	+	0.989451i	$0.453724\pi$
$752$	−5.45625	−	11.9475i	−0.198969	−	0.435681i
$753$	19.3003	−	12.4035i	0.703342	−	0.452010i
$754$	0.0601762	−	0.418535i	0.00219149	−	0.0152421i
$755$	26.4253	+	16.9825i	0.961713	+	0.618056i
$756$	0.654861	−	0.755750i	0.0238171	−	0.0274863i
$757$	20.9678	+	6.15670i	0.762088	+	0.223769i	0.639607	−	0.768702i	$-0.279097\pi$
$757$	20.9678	+	6.15670i	0.762088	+	0.223769i	0.122480	+	0.992471i	$0.460915\pi$
$758$	10.1827			0.369851
$759$	0.602194	−	3.96936i	0.0218583	−	0.144079i
$760$	19.2761			0.699217
$761$	−20.9187	−	6.14228i	−0.758302	−	0.222658i	−0.120348	−	0.992732i	$-0.538401\pi$
$761$	−20.9187	−	6.14228i	−0.758302	−	0.222658i	−0.637954	+	0.770074i	$0.720219\pi$
$762$	−8.51671	+	9.82881i	−0.308528	+	0.356060i
$763$	1.49249	+	0.959168i	0.0540319	+	0.0347242i
$764$	−2.35734	+	16.3957i	−0.0852857	+	0.593175i
$765$	−11.9671	+	7.69078i	−0.432671	+	0.278061i
$766$	9.44338	+	20.6781i	0.341203	+	0.747131i
$767$	−0.261748	−	0.302073i	−0.00945116	−	0.0109072i
$768$	0.142315	+	0.989821i	0.00513534	+	0.0357171i
$769$	−14.9468	+	32.7289i	−0.538995	+	1.18023i	0.422739	+	0.906251i	$0.361069\pi$
$769$	−14.9468	+	32.7289i	−0.538995	+	1.18023i	−0.961734	+	0.273983i	$0.911659\pi$
$770$	−2.32221	+	0.681862i	−0.0836866	+	0.0245726i
$771$	−2.35585	+	0.691740i	−0.0848439	+	0.0249124i
$772$	−1.88596	+	4.12968i	−0.0678773	+	0.148631i
$773$	−0.165347	−	1.15001i	−0.00594712	−	0.0413631i	0.986632	−	0.162965i	$-0.0521059\pi$
$773$	−0.165347	−	1.15001i	−0.00594712	−	0.0413631i	−0.992579	+	0.121602i	$0.961197\pi$
$774$	−3.87504	−	4.47203i	−0.139285	−	0.160744i
$775$	−0.967915	−	2.11944i	−0.0347685	−	0.0761325i
$776$	5.94875	−	3.82303i	0.213548	−	0.137239i
$777$	1.06362	−	7.39764i	0.0381571	−	0.265389i
$778$	4.77505	+	3.06874i	0.171194	+	0.110020i
$779$	−21.3792	+	24.6729i	−0.765990	+	0.883999i
$780$	1.01911	+	0.299237i	0.0364900	+	0.0107144i
$781$	−0.448723			−0.0160566
$782$	−19.9498	+	12.6032i	−0.713405	+	0.450691i
$783$	−1.15095			−0.0411316
$784$	−0.959493	−	0.281733i	−0.0342676	−	0.0100619i
$785$	−13.4610	+	15.5348i	−0.480443	+	0.554460i
$786$	0.723176	+	0.464757i	0.0257948	+	0.0165773i
$787$	0.399132	−	2.77602i	0.0142275	−	0.0989544i	−0.981470	−	0.191614i	$-0.938628\pi$
$787$	0.399132	−	2.77602i	0.0142275	−	0.0989544i	0.995698	+	0.0926597i	$0.0295369\pi$
$788$	14.0066	−	9.00150i	0.498965	−	0.320665i
$789$	4.38837	+	9.60919i	0.156230	+	0.342096i
$790$	16.8454	+	19.4406i	0.599332	+	0.691666i
$791$	1.29429	+	9.00196i	0.0460196	+	0.320073i
$792$	−0.347760	+	0.761489i	−0.0123571	+	0.0270583i
$793$	−1.37085	+	0.402517i	−0.0486802	+	0.0142938i
$794$	11.3794	−	3.34129i	0.403840	−	0.118578i
$795$	11.2819	−	24.7039i	0.400128	−	0.876159i
$796$	3.47203	+	24.1485i	0.123063	+	0.855922i
$797$	−26.5459	−	30.6356i	−0.940304	−	1.08517i	−0.996232	−	0.0867335i	$-0.972357\pi$
$797$	−26.5459	−	30.6356i	−0.940304	−	1.08517i	0.0559279	−	0.998435i	$-0.482188\pi$
$798$	2.76974	+	6.06489i	0.0980479	+	0.214695i
$799$	−54.3675	+	34.9399i	−1.92338	+	1.23608i
$800$	−0.477949	+	3.32421i	−0.0168981	+	0.117529i
$801$	−6.04458	−	3.88461i	−0.213575	−	0.137256i
$802$	24.4032	−	28.1628i	0.861708	−	0.994464i
$803$	−3.15938	−	0.927679i	−0.111492	−	0.0327371i
$804$	3.62687			0.127910
$805$	11.7220	−	7.40531i	0.413145	−	0.261003i
$806$	0.254883			0.00897787
$807$	−9.34395	−	2.74363i	−0.328923	−	0.0965804i
$808$	−1.22781	+	1.41696i	−0.0431941	+	0.0498486i
$809$	5.07314	+	3.26031i	0.178362	+	0.114626i	0.626775	−	0.779200i	$-0.284374\pi$
$809$	5.07314	+	3.26031i	0.178362	+	0.114626i	−0.448413	+	0.893826i	$0.648011\pi$
$810$	0.411445	−	2.86166i	0.0144567	−	0.100549i
$811$	−7.60235	+	4.88574i	−0.266955	+	0.171561i	−0.667270	−	0.744816i	$-0.732537\pi$
$811$	−7.60235	+	4.88574i	−0.266955	+	0.171561i	0.400315	+	0.916378i	$0.368901\pi$
$812$	0.478122	+	1.04694i	0.0167788	+	0.0367405i
$813$	14.1910	+	16.3773i	0.497699	+	0.574375i
$814$	0.890398	+	6.19285i	0.0312084	+	0.217059i
$815$	10.2509	−	22.4463i	0.359073	−	0.786259i
$816$	4.72109	−	1.38624i	0.165271	−	0.0485280i
$817$	37.8553	−	11.1153i	1.32439	−	0.388876i
$818$	−12.7464	+	27.9108i	−0.445669	+	0.975879i
$819$	0.0522839	+	0.363642i	0.00182695	+	0.0127067i
$820$	−9.27034	−	10.6985i	−0.323734	−	0.373609i
$821$	1.79241	+	3.92483i	0.0625556	+	0.136978i	0.938328	−	0.345747i	$-0.112374\pi$
$821$	1.79241	+	3.92483i	0.0625556	+	0.136978i	−0.875772	+	0.482725i	$0.839647\pi$
$822$	−0.410469	+	0.263792i	−0.0143167	+	0.00920081i
$823$	3.87791	−	26.9715i	0.135176	−	0.940166i	−0.803485	−	0.595325i	$-0.797023\pi$
$823$	3.87791	−	26.9715i	0.135176	−	0.940166i	0.938661	−	0.344842i	$-0.112067\pi$
$824$	10.0962	+	6.48843i	0.351717	+	0.226035i
$825$	−1.84110	+	2.12475i	−0.0640990	+	0.0739742i
$826$	1.04390	+	0.306516i	0.0363219	+	0.0106651i
$827$	−26.5834			−0.924395			−0.462197	−	0.886777i	$-0.652939\pi$
$827$	−26.5834			−0.924395			−0.462197	+	0.886777i	$0.652939\pi$
$828$	0.719347	−	4.74158i	0.0249990	−	0.164781i
$829$	−3.91646			−0.136024			−0.0680121	−	0.997684i	$-0.521666\pi$
$829$	−3.91646			−0.136024			−0.0680121	+	0.997684i	$0.521666\pi$
$830$	31.6508	+	9.29350i	1.09861	+	0.322582i
$831$	−5.37164	+	6.19920i	−0.186340	+	0.215048i
$832$	−0.309061	−	0.198622i	−0.0107148	−	0.00688596i
$833$	−0.700246	+	4.87032i	−0.0242621	+	0.168746i
$834$	9.51805	−	6.11688i	0.329583	−	0.211810i
$835$	−25.9524	−	56.8278i	−0.898119	−	1.96661i
$836$	−3.65514	−	4.21826i	−0.126416	−	0.145892i
$837$	−0.0987356	−	0.686721i	−0.00341280	−	0.0237366i
$838$	−3.75440	+	8.22098i	−0.129693	+	0.283989i
$839$	50.1497	−	14.7253i	1.73136	−	0.508373i	0.744180	−	0.667979i	$-0.232841\pi$
$839$	50.1497	−	14.7253i	1.73136	−	0.508373i	0.987181	+	0.159606i	$0.0510223\pi$
$840$	−2.77398	+	0.814514i	−0.0957114	+	0.0281034i
$841$	−11.4967	+	25.1743i	−0.396439	+	0.868081i
$842$	3.70142	+	25.7439i	0.127559	+	0.887194i
$843$	16.0062	+	18.4722i	0.551284	+	0.636216i
$844$	10.1924	+	22.3182i	0.350836	+	0.768223i
$845$	31.2895	−	20.1086i	1.07639	−	0.691756i
$846$	1.86923	−	13.0008i	0.0642654	−	0.446976i
$847$	−8.66424	−	5.56817i	−0.297707	−	0.191324i
$848$	−6.15160	+	7.09933i	−0.211247	+	0.243792i
$849$	0.824150	+	0.241992i	0.0282848	+	0.00830515i
$850$	16.5246			0.566790
$851$	−14.6360	−	32.7182i	−0.501717	−	1.12157i
$852$	−0.536020			−0.0183637
$853$	−7.22805	−	2.12235i	−0.247484	−	0.0726677i	0.155638	−	0.987814i	$-0.450257\pi$
$853$	−7.22805	−	2.12235i	−0.247484	−	0.0726677i	−0.403122	+	0.915146i	$0.632075\pi$
$854$	2.54671	−	2.93905i	0.0871465	−	0.100572i
$855$	16.2161	+	10.4214i	0.554578	+	0.356406i
$856$	−0.423648	+	2.94653i	−0.0144800	+	0.100710i
$857$	−15.8813	+	10.2063i	−0.542495	+	0.348640i	−0.783014	−	0.622004i	$-0.786319\pi$
$857$	−15.8813	+	10.2063i	−0.542495	+	0.348640i	0.240519	+	0.970644i	$0.422682\pi$
$858$	−0.127761	−	0.279757i	−0.00436168	−	0.00955075i
$859$	−1.40814	−	1.62508i	−0.0480452	−	0.0554472i	0.731218	−	0.682144i	$-0.238952\pi$
$859$	−1.40814	−	1.62508i	−0.0480452	−	0.0554472i	−0.779264	+	0.626696i	$0.784407\pi$
$860$	2.43466	+	16.9334i	0.0830213	+	0.577426i
$861$	2.03408	−	4.45401i	0.0693211	−	0.151792i
$862$	8.77250	−	2.57584i	0.298792	−	0.0877334i
$863$	9.45143	−	2.77519i	0.321731	−	0.0944686i	−0.116879	−	0.993146i	$-0.537289\pi$
$863$	9.45143	−	2.77519i	0.321731	−	0.0944686i	0.438610	+	0.898677i	$0.355471\pi$
$864$	−0.415415	+	0.909632i	−0.0141327	+	0.0309463i
$865$	0.961808	+	6.68952i	0.0327025	+	0.227451i
$866$	3.90749	+	4.50949i	0.132782	+	0.153239i
$867$	−2.99527	−	6.55874i	−0.101725	−	0.222746i
$868$	−0.583647	+	0.375087i	−0.0198103	+	0.0127313i
$869$	1.06003	−	7.37268i	0.0359591	−	0.250101i
$870$	2.79927	+	1.79898i	0.0949042	+	0.0609912i
$871$	−0.872566	+	1.00699i	−0.0295658	+	0.0341207i
$872$	−1.70227	−	0.499831i	−0.0576460	−	0.0169264i
$873$	7.07130			0.239327
$874$	26.7647	+	17.4957i	0.905331	+	0.591801i
$875$	4.74603			0.160445
$876$	−3.77402	−	1.10815i	−0.127512	−	0.0374410i
$877$	12.3983	−	14.3084i	0.418660	−	0.483159i	−0.506768	−	0.862082i	$-0.669160\pi$
$877$	12.3983	−	14.3084i	0.418660	−	0.483159i	0.925428	+	0.378923i	$0.123705\pi$
$878$	−14.1806	−	9.11330i	−0.478571	−	0.307559i
$879$	3.16019	−	21.9796i	0.106591	−	0.741353i
$880$	2.03604	−	1.30848i	0.0686349	−	0.0441090i
$881$	−12.8482	−	28.1336i	−0.432866	−	0.947845i	−0.992853	−	0.119343i	$-0.961921\pi$
$881$	−12.8482	−	28.1336i	−0.432866	−	0.947845i	0.559987	−	0.828502i	$-0.310806\pi$
$882$	−0.654861	−	0.755750i	−0.0220503	−	0.0254474i
$883$	1.59318	+	11.0808i	0.0536147	+	0.372898i	0.998910	+	0.0466820i	$0.0148647\pi$
$883$	1.59318	+	11.0808i	0.0536147	+	0.372898i	−0.945295	+	0.326216i	$0.894226\pi$
$884$	−0.750931	+	1.64431i	−0.0252565	+	0.0553041i
$885$	3.01800	−	0.886165i	0.101449	−	0.0297881i
$886$	14.2318	−	4.17884i	0.478127	−	0.140391i
$887$	21.1411	−	46.2926i	0.709850	−	1.55435i	−0.117755	−	0.993043i	$-0.537570\pi$
$887$	21.1411	−	46.2926i	0.709850	−	1.55435i	0.827605	−	0.561311i	$-0.189703\pi$
$888$	1.06362	+	7.39764i	0.0356927	+	0.248248i
$889$	8.51671	+	9.82881i	0.285641	+	0.329648i
$890$	8.62944	+	18.8958i	0.289259	+	0.633390i
$891$	−0.704247	+	0.452592i	−0.0235932	+	0.0151624i
$892$	−1.83230	+	12.7440i	−0.0613501	+	0.426699i
$893$	73.6710	+	47.3455i	2.46531	+	1.58436i
$894$	−9.93172	+	11.4618i	−0.332167	+	0.383341i
$895$	46.7272	+	13.7203i	1.56192	+	0.458620i
$896$	1.00000			0.0334077
$897$	1.14343	+	1.34047i	0.0381780	+	0.0447571i
$898$	−6.76719			−0.225824
$899$	0.766165	+	0.224966i	0.0255530	+	0.00750305i
$900$	−2.19928	+	2.53811i	−0.0733094	+	0.0846035i
$901$	38.8836	+	24.9890i	1.29540	+	0.832503i
$902$	−0.583355	+	4.05733i	−0.0194236	+	0.135094i
$903$	−4.97799	+	3.19916i	−0.165657	+	0.106461i
$904$	−3.77801	−	8.27268i	−0.125655	−	0.275145i
$905$	−6.72653	−	7.76283i	−0.223598	−	0.258045i
$906$	−1.54625	−	10.7544i	−0.0513709	−	0.357292i
$907$	−16.4364	+	35.9907i	−0.545761	+	1.19505i	0.412972	+	0.910744i	$0.364491\pi$
$907$	−16.4364	+	35.9907i	−0.545761	+	1.19505i	−0.958733	+	0.284307i	$0.908237\pi$
$908$	−22.6745	+	6.65783i	−0.752479	+	0.220948i
$909$	−1.79897	+	0.528224i	−0.0596679	+	0.0175201i
$910$	0.441226	−	0.966150i	0.0146265	−	0.0320276i
$911$	−6.67022	−	46.3924i	−0.220994	−	1.53705i	−0.734290	−	0.678836i	$-0.762485\pi$
$911$	−6.67022	−	46.3924i	−0.220994	−	1.53705i	0.513296	−	0.858212i	$-0.328424\pi$
$912$	−4.36623	−	5.03890i	−0.144580	−	0.166855i
$913$	−3.96790	−	8.68849i	−0.131318	−	0.287547i
$914$	21.1923	−	13.6195i	0.700979	−	0.450492i
$915$	1.60008	−	11.1288i	0.0528970	−	0.367907i
$916$	9.08106	+	5.83604i	0.300047	+	0.192828i
$917$	0.562945	−	0.649673i	0.0185901	−	0.0214541i
$918$	4.72109	+	1.38624i	0.155819	+	0.0457526i
$919$	−21.1198			−0.696679			−0.348339	−	0.937369i	$-0.613254\pi$
$919$	−21.1198			−0.696679			−0.348339	+	0.937369i	$0.613254\pi$
$920$	−9.16083	+	10.4078i	−0.302024	+	0.343135i
$921$	9.82419			0.323718
$922$	33.5988	+	9.86550i	1.10652	+	0.324903i
$923$	0.128958	−	0.148825i	0.00424469	−	0.00489864i
$924$	0.704247	+	0.452592i	0.0231680	+	0.0148892i
$925$	−3.57205	+	24.8442i	−0.117448	+	0.816871i
$926$	22.1327	−	14.2238i	0.727326	−	0.467424i
$927$	4.98555	+	10.9168i	0.163747	+	0.358556i
$928$	−0.753713	−	0.869831i	−0.0247418	−	0.0285536i
$929$	−3.10933	−	21.6259i	−0.102014	−	0.709522i	−0.975069	−	0.221901i	$-0.928774\pi$
$929$	−3.10933	−	21.6259i	−0.102014	−	0.709522i	0.873055	−	0.487621i	$-0.162135\pi$
$930$	−0.833234	+	1.82453i	−0.0273228	+	0.0598286i
$931$	6.39734	−	1.87843i	0.209664	−	0.0615630i
$932$	17.3812	−	5.10359i	0.569341	−	0.167174i
$933$	10.4434	−	22.8678i	0.341901	−	0.748658i
$934$	5.84926	+	40.6825i	0.191394	+	1.33117i
$935$	−7.79845	−	8.99990i	−0.255037	−	0.294328i
$936$	−0.152616	−	0.334182i	−0.00498841	−	0.0109231i
$937$	−34.5519	+	22.2052i	−1.12876	+	0.725411i	−0.965301	−	0.261139i	$-0.915902\pi$
$937$	−34.5519	+	22.2052i	−1.12876	+	0.725411i	−0.163460	+	0.986550i	$0.552266\pi$
$938$	0.516157	−	3.58995i	0.0168531	−	0.117216i
$939$	29.3970	+	18.8923i	0.959334	+	0.616527i
$940$	−24.8669	+	28.6980i	−0.811070	+	0.936025i
$941$	55.4917	+	16.2938i	1.80898	+	0.531164i	0.998508	−	0.0546144i	$-0.0173930\pi$
$941$	55.4917	+	16.2938i	1.80898	+	0.531164i	0.810471	+	0.585778i	$0.199211\pi$
$942$	7.10994			0.231654
$943$	−3.16141	−	23.2690i	−0.102950	−	0.757742i
$944$	−1.08797			−0.0354103
$945$	−2.77398	−	0.814514i	−0.0902376	−	0.0264961i
$946$	3.24395	−	3.74372i	0.105470	−	0.121719i
$947$	−35.6837	−	22.9325i	−1.15956	−	0.745206i	−0.188043	−	0.982161i	$-0.560214\pi$
$947$	−35.6837	−	22.9325i	−1.15956	−	0.745206i	−0.971521	+	0.236955i	$0.923851\pi$
$948$	1.26625	−	8.80699i	0.0411260	−	0.286038i
$949$	1.21565	−	0.781248i	0.0394616	−	0.0253604i
$950$	−9.30189	−	20.3683i	−0.301793	−	0.660835i
$951$	−11.6264	−	13.4176i	−0.377013	−	0.435096i
$952$	−0.700246	−	4.87032i	−0.0226951	−	0.157848i
$953$	−15.0589	+	32.9744i	−0.487805	+	1.06814i	0.492438	+	0.870348i	$0.336106\pi$
$953$	−15.0589	+	32.9744i	−0.487805	+	1.06814i	−0.980243	+	0.197797i	$0.936621\pi$
$954$	−9.01324	+	2.64653i	−0.291814	+	0.0856845i
$955$	45.9490	−	13.4918i	1.48687	−	0.436586i
$956$	4.96034	−	10.8616i	0.160429	−	0.351290i
$957$	−0.137121	−	0.953700i	−0.00443250	−	0.0308287i
$958$	−17.0857	−	19.7179i	−0.552013	−	0.637057i
$959$	0.202691	+	0.443832i	0.00654525	+	0.0143321i
$960$	2.43214	−	1.56304i	0.0784969	−	0.0504469i
$961$	4.34326	−	30.2080i	0.140105	−	0.974453i
$962$	−2.30983	−	1.48444i	−0.0744720	−	0.0478602i
$963$	−1.94941	+	2.24974i	−0.0628189	+	0.0724969i
$964$	19.7053	+	5.78599i	0.634664	+	0.186354i
$965$	13.1254			0.422521
$966$	−4.59094	−	1.38682i	−0.147711	−	0.0446203i
$967$	−3.27958			−0.105464			−0.0527321	−	0.998609i	$-0.516793\pi$
$967$	−3.27958			−0.105464			−0.0527321	+	0.998609i	$0.516793\pi$
$968$	9.88201	+	2.90162i	0.317620	+	0.0932616i
$969$	−21.4836	+	24.7934i	−0.690152	+	0.796478i
$970$	−17.1984	−	11.0527i	−0.552207	−	0.354882i
$971$	−1.61190	+	11.2110i	−0.0517282	+	0.359777i	0.947474	+	0.319834i	$0.103627\pi$
$971$	−1.61190	+	11.2110i	−0.0517282	+	0.359777i	−0.999202	+	0.0399439i	$0.987282\pi$
$972$	−0.841254	+	0.540641i	−0.0269832	+	0.0173411i
$973$	−4.70006	−	10.2917i	−0.150677	−	0.329937i
$974$	−12.9015	−	14.8891i	−0.413390	−	0.477077i
$975$	−0.175590	−	1.22125i	−0.00562338	−	0.0391114i
$976$	−1.61552	+	3.53749i	−0.0517115	+	0.113232i
$977$	−24.6424	+	7.23566i	−0.788380	+	0.231489i	−0.651049	−	0.759036i	$-0.725671\pi$
$977$	−24.6424	+	7.23566i	−0.788380	+	0.231489i	−0.137331	+	0.990525i	$0.543852\pi$
$978$	−8.18953	+	2.40466i	−0.261872	+	0.0768927i
$979$	2.49873	−	5.47145i	0.0798597	−	0.174868i
$980$	0.411445	+	2.86166i	0.0131431	+	0.0914124i
$981$	−1.16181	−	1.34080i	−0.0370937	−	0.0428084i
$982$	8.31596	+	18.2094i	0.265373	+	0.581086i
$983$	13.3063	−	8.55146i	0.424406	−	0.272749i	−0.310955	−	0.950425i	$-0.600649\pi$
$983$	13.3063	−	8.55146i	0.424406	−	0.272749i	0.735361	+	0.677675i	$0.237013\pi$
$984$	−0.696844	+	4.84665i	−0.0222146	+	0.154506i
$985$	−40.4943	−	26.0241i	−1.29026	−	0.829198i
$986$	−3.70857	+	4.27991i	−0.118105	+	0.136300i
$987$	−12.6024	−	3.70040i	−0.401139	−	0.117785i
$988$	2.44949			0.0779286
$989$	−11.9889	+	25.7218i	−0.381226	+	0.817905i
$990$	2.42024			0.0769204
$991$	25.7863	+	7.57155i	0.819130	+	0.240518i	0.664341	−	0.747429i	$-0.268712\pi$
$991$	25.7863	+	7.57155i	0.819130	+	0.240518i	0.154789	+	0.987948i	$0.450530\pi$
$992$	0.454331	−	0.524326i	0.0144250	−	0.0166474i
$993$	6.55502	+	4.21265i	0.208017	+	0.133685i
$994$	−0.0762835	+	0.530564i	−0.00241957	+	0.0168285i
$995$	59.3365	−	38.1333i	1.88109	−	1.20891i
$996$	−4.73983	−	10.3788i	−0.150187	−	0.328864i
$997$	−18.5684	−	21.4291i	−0.588068	−	0.678667i	0.381251	−	0.924471i	$-0.375493\pi$
$997$	−18.5684	−	21.4291i	−0.588068	−	0.678667i	−0.969319	+	0.245805i	$0.920948\pi$
$998$	3.47123	+	24.1429i	0.109880	+	0.764232i
$999$	−3.10469	+	6.79832i	−0.0982280	+	0.215089i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.d.547.2	✓	20
23.9	even	11	inner	966.2.q.d.883.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.d.547.2	✓	20	1.1	even	1	trivial
966.2.q.d.883.2	yes	20	23.9	even	11	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.411445 - 2.86166i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(0.415415 + 0.909632i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.411445 - 2.86166i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(0.415415 + 0.909632i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-1.20100 + 2.62983i) q^{10} +(0.803230 - 0.235849i) q^{11} +(0.959493 - 0.281733i) q^{12} +(-0.152616 + 0.334182i) q^{13} +(-0.142315 - 0.989821i) q^{14} +(-1.89326 - 2.18494i) q^{15} +(0.415415 + 0.909632i) q^{16} +(4.13930 - 2.66017i) q^{17} +(-0.142315 + 0.989821i) q^{18} +(-5.60899 - 3.60468i) q^{19} +(1.89326 - 2.18494i) q^{20} +(0.959493 + 0.281733i) q^{21} -0.837140 q^{22} +(4.61192 - 1.31538i) q^{23} -1.00000 q^{24} +(-3.22236 - 0.946169i) q^{25} +(0.240584 - 0.277649i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(-0.142315 + 0.989821i) q^{28} +(0.968242 - 0.622251i) q^{29} +(1.20100 + 2.62983i) q^{30} +(0.454331 + 0.524326i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(0.347760 - 0.761489i) q^{33} +(-4.72109 + 1.38624i) q^{34} +(2.77398 - 0.814514i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-1.06362 - 7.39764i) q^{37} +(4.36623 + 5.03890i) q^{38} +(0.152616 + 0.334182i) q^{39} +(-2.43214 + 1.56304i) q^{40} +(0.696844 - 4.84665i) q^{41} +(-0.841254 - 0.540641i) q^{42} +(-3.87504 + 4.47203i) q^{43} +(0.803230 + 0.235849i) q^{44} -2.89109 q^{45} +(-4.79569 - 0.0372286i) q^{46} -13.1345 q^{47} +(0.959493 + 0.281733i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(2.82526 + 1.81569i) q^{50} +(0.700246 - 4.87032i) q^{51} +(-0.309061 + 0.198622i) q^{52} +(3.90231 + 8.54486i) q^{53} +(0.654861 + 0.755750i) q^{54} +(-0.344437 - 2.39561i) q^{55} +(0.415415 - 0.909632i) q^{56} +(-6.39734 + 1.87843i) q^{57} +(-1.10433 + 0.324260i) q^{58} +(-0.451958 + 0.989651i) q^{59} +(-0.411445 - 2.86166i) q^{60} +(2.54671 + 2.93905i) q^{61} +(-0.288208 - 0.631087i) q^{62} +(0.841254 - 0.540641i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(0.893523 + 0.574233i) q^{65} +(-0.548210 + 0.632668i) q^{66} +(3.47995 + 1.02181i) q^{67} +4.92040 q^{68} +(2.02606 - 4.34685i) q^{69} -2.89109 q^{70} +(-0.514307 - 0.151014i) q^{71} +(-0.654861 + 0.755750i) q^{72} +(-3.30895 - 2.12653i) q^{73} +(-1.06362 + 7.39764i) q^{74} +(-2.82526 + 1.81569i) q^{75} +(-2.76974 - 6.06489i) q^{76} +(0.548210 + 0.632668i) q^{77} +(-0.0522839 - 0.363642i) q^{78} +(3.69618 - 8.09350i) q^{79} +(2.77398 - 0.814514i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-2.03408 + 4.45401i) q^{82} +(-1.62379 - 11.2937i) q^{83} +(0.654861 + 0.755750i) q^{84} +(-5.90941 - 12.9398i) q^{85} +(4.97799 - 3.19916i) q^{86} +(0.163797 - 1.13924i) q^{87} +(-0.704247 - 0.452592i) q^{88} +(4.70531 - 5.43021i) q^{89} +(2.77398 + 0.814514i) q^{90} -0.367382 q^{91} +(4.59094 + 1.38682i) q^{92} +0.693783 q^{93} +(12.6024 + 3.70040i) q^{94} +(-12.6232 + 14.5679i) q^{95} +(-0.841254 - 0.540641i) q^{96} +(-1.00635 + 6.99932i) q^{97} +(0.841254 - 0.540641i) q^{98} +(-0.347760 - 0.761489i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} - 10 q^{10} - 7 q^{11} + 2 q^{12} - 8 q^{13} - 2 q^{14} - q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} + 2 q^{21} + 4 q^{22} - 20 q^{24} + 16 q^{25} - 8 q^{26} + 2 q^{27} - 2 q^{28} + 3 q^{29} + 10 q^{30} + 9 q^{31} - 2 q^{32} - 4 q^{33} - 9 q^{34} + q^{35} - 2 q^{36} - q^{37} + 3 q^{38} + 8 q^{39} + q^{40} + 10 q^{41} + 2 q^{42} - 15 q^{43} - 7 q^{44} - 10 q^{45} - 28 q^{47} + 2 q^{48} - 2 q^{49} + 5 q^{50} - 2 q^{51} + 3 q^{52} + 38 q^{53} + 2 q^{54} - 8 q^{55} - 2 q^{56} - 14 q^{57} - 19 q^{58} - 10 q^{59} - 12 q^{60} - 6 q^{61} + 20 q^{62} - 2 q^{63} - 2 q^{64} - 36 q^{65} - 4 q^{66} + 36 q^{67} - 20 q^{68} + 11 q^{69} - 10 q^{70} - q^{71} - 2 q^{72} + 65 q^{73} - q^{74} - 5 q^{75} + 14 q^{76} + 4 q^{77} - 14 q^{78} + 10 q^{79} + q^{80} - 2 q^{81} + 10 q^{82} - 14 q^{83} + 2 q^{84} - 5 q^{85} + 51 q^{86} - 3 q^{87} - 7 q^{88} - 18 q^{89} + q^{90} - 30 q^{91} - 11 q^{92} + 2 q^{93} + 38 q^{94} - 73 q^{95} + 2 q^{96} - 20 q^{97} - 2 q^{98} + 4 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 - 10 * q^10 - 7 * q^11 + 2 * q^12 - 8 * q^13 - 2 * q^14 - q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 8 * q^19 + q^20 + 2 * q^21 + 4 * q^22 - 20 * q^24 + 16 * q^25 - 8 * q^26 + 2 * q^27 - 2 * q^28 + 3 * q^29 + 10 * q^30 + 9 * q^31 - 2 * q^32 - 4 * q^33 - 9 * q^34 + q^35 - 2 * q^36 - q^37 + 3 * q^38 + 8 * q^39 + q^40 + 10 * q^41 + 2 * q^42 - 15 * q^43 - 7 * q^44 - 10 * q^45 - 28 * q^47 + 2 * q^48 - 2 * q^49 + 5 * q^50 - 2 * q^51 + 3 * q^52 + 38 * q^53 + 2 * q^54 - 8 * q^55 - 2 * q^56 - 14 * q^57 - 19 * q^58 - 10 * q^59 - 12 * q^60 - 6 * q^61 + 20 * q^62 - 2 * q^63 - 2 * q^64 - 36 * q^65 - 4 * q^66 + 36 * q^67 - 20 * q^68 + 11 * q^69 - 10 * q^70 - q^71 - 2 * q^72 + 65 * q^73 - q^74 - 5 * q^75 + 14 * q^76 + 4 * q^77 - 14 * q^78 + 10 * q^79 + q^80 - 2 * q^81 + 10 * q^82 - 14 * q^83 + 2 * q^84 - 5 * q^85 + 51 * q^86 - 3 * q^87 - 7 * q^88 - 18 * q^89 + q^90 - 30 * q^91 - 11 * q^92 + 2 * q^93 + 38 * q^94 - 73 * q^95 + 2 * q^96 - 20 * q^97 - 2 * q^98 + 4 * q^99

Introduction

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