LMFDB - Embedded newform 209.2.j.a.100.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(23,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("209.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.j (of order $9$, degree $6$, 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:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			100.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	209.100
Dual form			209.2.j.a.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26604 - 0.460802i) q^{2} +(-0.347296 + 1.96962i) q^{3} +(-0.141559 + 0.118782i) q^{4} +(-0.358441 - 0.300767i) q^{5} +(0.467911 + 2.65366i) q^{6} +(1.17365 + 2.03282i) q^{7} +(-1.47178 + 2.54920i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})$	\(q+(1.26604 - 0.460802i) q^{2} +(-0.347296 + 1.96962i) q^{3} +(-0.141559 + 0.118782i) q^{4} +(-0.358441 - 0.300767i) q^{5} +(0.467911 + 2.65366i) q^{6} +(1.17365 + 2.03282i) q^{7} +(-1.47178 + 2.54920i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(-0.592396 - 0.215615i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.184793 - 0.320070i) q^{12} +(-0.819078 - 4.64522i) q^{13} +(2.42262 + 2.03282i) q^{14} +(0.716881 - 0.601535i) q^{15} +(-0.624485 + 3.54163i) q^{16} +(4.37211 - 1.59132i) q^{17} -1.34730 q^{18} +(4.34002 + 0.405223i) q^{19} +0.0864665 q^{20} +(-4.41147 + 1.60565i) q^{21} +(-0.233956 + 1.32683i) q^{22} +(0.315207 - 0.264490i) q^{23} +(-4.50980 - 3.78417i) q^{24} +(-0.830222 - 4.70842i) q^{25} +(-3.17752 - 5.50362i) q^{26} +(-2.00000 + 3.46410i) q^{27} +(-0.407604 - 0.148356i) q^{28} +(3.10607 + 1.13052i) q^{29} +(0.630415 - 1.09191i) q^{30} +(-1.96064 - 3.39592i) q^{31} +(-0.180922 - 1.02606i) q^{32} +(-1.53209 - 1.28558i) q^{33} +(4.80200 - 4.02936i) q^{34} +(0.190722 - 1.08164i) q^{35} +(0.173648 - 0.0632028i) q^{36} -4.87939 q^{37} +(5.68139 - 1.48686i) q^{38} +9.43376 q^{39} +(1.29426 - 0.471073i) q^{40} +(0.205737 - 1.16679i) q^{41} +(-4.84524 + 4.06564i) q^{42} +(-5.23783 - 4.39506i) q^{43} +(-0.0320889 - 0.181985i) q^{44} +(0.233956 + 0.405223i) q^{45} +(0.277189 - 0.480105i) q^{46} +(9.09627 + 3.31077i) q^{47} +(-6.75877 - 2.45999i) q^{48} +(0.745100 - 1.29055i) q^{49} +(-3.22075 - 5.57851i) q^{50} +(1.61587 + 9.16404i) q^{51} +(0.667718 + 0.560282i) q^{52} +(6.34002 - 5.31991i) q^{53} +(-0.935822 + 5.30731i) q^{54} +(0.439693 - 0.160035i) q^{55} -6.90941 q^{56} +(-2.30541 + 8.40744i) q^{57} +4.45336 q^{58} +(-4.16637 + 1.51644i) q^{59} +(-0.0300295 + 0.170306i) q^{60} +(-7.85117 + 6.58791i) q^{61} +(-4.04710 - 3.39592i) q^{62} +(-0.407604 - 2.31164i) q^{63} +(-4.29813 - 7.44459i) q^{64} +(-1.10354 + 1.91139i) q^{65} +(-2.53209 - 0.921605i) q^{66} +(4.89053 + 1.78001i) q^{67} +(-0.429892 + 0.744596i) q^{68} +(0.411474 + 0.712694i) q^{69} +(-0.256959 - 1.45729i) q^{70} +(-6.68345 - 5.60808i) q^{71} +(2.25490 - 1.89209i) q^{72} +(-2.35710 + 13.3678i) q^{73} +(-6.17752 + 2.24843i) q^{74} +9.56212 q^{75} +(-0.662504 + 0.458155i) q^{76} -2.34730 q^{77} +(11.9436 - 4.34710i) q^{78} +(0.103541 - 0.587208i) q^{79} +(1.28905 - 1.08164i) q^{80} +(-8.42649 - 7.07066i) q^{81} +(-0.277189 - 1.57202i) q^{82} +(7.05690 + 12.2229i) q^{83} +(0.433763 - 0.751299i) q^{84} +(-2.04576 - 0.744596i) q^{85} +(-8.65657 - 3.15074i) q^{86} +(-3.30541 + 5.72513i) q^{87} +(-1.47178 - 2.54920i) q^{88} +(1.51842 + 8.61138i) q^{89} +(0.482926 + 0.405223i) q^{90} +(8.48158 - 7.11689i) q^{91} +(-0.0132037 + 0.0748822i) q^{92} +(7.36959 - 2.68231i) q^{93} +13.0419 q^{94} +(-1.43376 - 1.45059i) q^{95} +2.08378 q^{96} +(7.73783 - 2.81634i) q^{97} +(0.348641 - 1.97724i) q^{98} +(0.766044 - 0.642788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 12 q^{6} + 6 q^{7} + 6 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 12 * q^6 + 6 * q^7 + 6 * q^8	\( 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 12 q^{6} + 6 q^{7} + 6 q^{8} - 3 q^{11} + 6 q^{12} + 12 q^{13} - 12 q^{14} - 12 q^{15} + 9 q^{16} - 3 q^{17} - 6 q^{18} + 6 q^{19} - 30 q^{20} - 6 q^{21} - 6 q^{22} + 9 q^{23} - 30 q^{24} + 18 q^{25} + 6 q^{26} - 12 q^{27} - 6 q^{28} - 6 q^{29} + 18 q^{30} - 3 q^{31} - 18 q^{32} - 9 q^{34} + 21 q^{35} - 18 q^{37} - 15 q^{38} + 24 q^{39} + 18 q^{40} - 9 q^{41} + 24 q^{42} - 12 q^{43} + 9 q^{44} + 6 q^{45} - 9 q^{46} + 27 q^{47} - 18 q^{48} + 3 q^{49} + 21 q^{50} - 12 q^{51} - 24 q^{52} + 18 q^{53} - 24 q^{54} - 3 q^{55} + 30 q^{56} - 18 q^{57} - 6 q^{59} + 60 q^{60} - 21 q^{61} + 15 q^{62} - 6 q^{63} - 12 q^{64} + 3 q^{65} - 6 q^{66} + 12 q^{67} + 6 q^{68} - 18 q^{69} - 54 q^{70} - 42 q^{71} + 15 q^{72} - 15 q^{73} - 12 q^{74} - 12 q^{75} - 9 q^{76} - 12 q^{77} + 42 q^{78} - 9 q^{79} + 51 q^{80} + 9 q^{82} + 6 q^{83} - 30 q^{84} + 18 q^{85} - 30 q^{86} - 24 q^{87} + 6 q^{88} + 21 q^{89} - 18 q^{90} + 39 q^{91} - 45 q^{92} + 30 q^{93} + 72 q^{94} + 24 q^{95} + 27 q^{97} - 9 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 12 * q^6 + 6 * q^7 + 6 * q^8 - 3 * q^11 + 6 * q^12 + 12 * q^13 - 12 * q^14 - 12 * q^15 + 9 * q^16 - 3 * q^17 - 6 * q^18 + 6 * q^19 - 30 * q^20 - 6 * q^21 - 6 * q^22 + 9 * q^23 - 30 * q^24 + 18 * q^25 + 6 * q^26 - 12 * q^27 - 6 * q^28 - 6 * q^29 + 18 * q^30 - 3 * q^31 - 18 * q^32 - 9 * q^34 + 21 * q^35 - 18 * q^37 - 15 * q^38 + 24 * q^39 + 18 * q^40 - 9 * q^41 + 24 * q^42 - 12 * q^43 + 9 * q^44 + 6 * q^45 - 9 * q^46 + 27 * q^47 - 18 * q^48 + 3 * q^49 + 21 * q^50 - 12 * q^51 - 24 * q^52 + 18 * q^53 - 24 * q^54 - 3 * q^55 + 30 * q^56 - 18 * q^57 - 6 * q^59 + 60 * q^60 - 21 * q^61 + 15 * q^62 - 6 * q^63 - 12 * q^64 + 3 * q^65 - 6 * q^66 + 12 * q^67 + 6 * q^68 - 18 * q^69 - 54 * q^70 - 42 * q^71 + 15 * q^72 - 15 * q^73 - 12 * q^74 - 12 * q^75 - 9 * q^76 - 12 * q^77 + 42 * q^78 - 9 * q^79 + 51 * q^80 + 9 * q^82 + 6 * q^83 - 30 * q^84 + 18 * q^85 - 30 * q^86 - 24 * q^87 + 6 * q^88 + 21 * q^89 - 18 * q^90 + 39 * q^91 - 45 * q^92 + 30 * q^93 + 72 * q^94 + 24 * q^95 + 27 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	1.26604	−	0.460802i	0.895229	−	0.325837i	0.146889	−	0.989153i	$-0.453074\pi$
$2$	1.26604	−	0.460802i	0.895229	−	0.325837i	0.748339	+	0.663316i	$0.230852\pi$
$3$	−0.347296	+	1.96962i	−0.200512	+	1.13716i	0.703836	+	0.710362i	$0.251469\pi$
$3$	−0.347296	+	1.96962i	−0.200512	+	1.13716i	−0.904348	+	0.426796i	$0.859642\pi$
$4$	−0.141559	+	0.118782i	−0.0707796	+	0.0593912i
$5$	−0.358441	−	0.300767i	−0.160300	−	0.134507i	0.559110	−	0.829094i	$-0.311143\pi$
$5$	−0.358441	−	0.300767i	−0.160300	−	0.134507i	−0.719409	+	0.694586i	$0.755587\pi$
$6$	0.467911	+	2.65366i	0.191024	+	1.08335i
$7$	1.17365	+	2.03282i	0.443597	+	0.768333i	0.997953	−	0.0639466i	$-0.0203687\pi$
$7$	1.17365	+	2.03282i	0.443597	+	0.768333i	−0.554356	+	0.832280i	$0.687035\pi$
$8$	−1.47178	+	2.54920i	−0.520353	+	0.901278i
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$	−0.592396	−	0.215615i	−0.187332	−	0.0681833i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−0.184793	−	0.320070i	−0.0533450	−	0.0923963i
$13$	−0.819078	−	4.64522i	−0.227171	−	1.28835i	−0.858490	−	0.512829i	$-0.828597\pi$
$13$	−0.819078	−	4.64522i	−0.227171	−	1.28835i	0.631319	−	0.775523i	$-0.282514\pi$
$14$	2.42262	+	2.03282i	0.647472	+	0.543294i
$15$	0.716881	−	0.601535i	0.185098	−	0.155316i
$16$	−0.624485	+	3.54163i	−0.156121	+	0.885408i
$17$	4.37211	−	1.59132i	1.06039	−	0.385951i	0.247817	−	0.968807i	$-0.420287\pi$
$17$	4.37211	−	1.59132i	1.06039	−	0.385951i	0.812576	+	0.582855i	$0.198065\pi$
$18$	−1.34730			−0.317561
$19$	4.34002	+	0.405223i	0.995669	+	0.0929645i
$19$	4.34002	+	0.405223i	0.995669	+	0.0929645i
$20$	0.0864665			0.0193345
$21$	−4.41147	+	1.60565i	−0.962663	+	0.350381i
$22$	−0.233956	+	1.32683i	−0.0498795	+	0.282881i
$23$	0.315207	−	0.264490i	0.0657253	−	0.0551501i	−0.609333	−	0.792914i	$-0.708563\pi$
$23$	0.315207	−	0.264490i	0.0657253	−	0.0551501i	0.675059	+	0.737764i	$0.264118\pi$
$24$	−4.50980	−	3.78417i	−0.920559	−	0.772441i
$25$	−0.830222	−	4.70842i	−0.166044	−	0.941685i
$26$	−3.17752	−	5.50362i	−0.623163	−	1.07935i
$27$	−2.00000	+	3.46410i	−0.384900	+	0.666667i
$28$	−0.407604	−	0.148356i	−0.0770299	−	0.0280366i
$29$	3.10607	+	1.13052i	0.576782	+	0.209932i	0.613906	−	0.789379i	$-0.289597\pi$
$29$	3.10607	+	1.13052i	0.576782	+	0.209932i	−0.0371239	+	0.999311i	$0.511820\pi$
$30$	0.630415	−	1.09191i	0.115097	−	0.199355i
$31$	−1.96064	−	3.39592i	−0.352141	−	0.609926i	0.634483	−	0.772936i	$-0.281213\pi$
$31$	−1.96064	−	3.39592i	−0.352141	−	0.609926i	−0.986624	+	0.163011i	$0.947880\pi$
$32$	−0.180922	−	1.02606i	−0.0319828	−	0.181384i
$33$	−1.53209	−	1.28558i	−0.266702	−	0.223790i
$34$	4.80200	−	4.02936i	0.823537	−	0.691029i
$35$	0.190722	−	1.08164i	0.0322380	−	0.182831i
$36$	0.173648	−	0.0632028i	0.0289414	−	0.0105338i
$37$	−4.87939			−0.802166			−0.401083	−	0.916042i	$-0.631366\pi$
$37$	−4.87939			−0.802166			−0.401083	+	0.916042i	$0.631366\pi$
$38$	5.68139	−	1.48686i	0.921643	−	0.241201i
$39$	9.43376			1.51061
$40$	1.29426	−	0.471073i	0.204641	−	0.0744832i
$41$	0.205737	−	1.16679i	0.0321307	−	0.182222i	−0.964519	−	0.264015i	$-0.914953\pi$
$41$	0.205737	−	1.16679i	0.0321307	−	0.182222i	0.996649	+	0.0817922i	$0.0260644\pi$
$42$	−4.84524	+	4.06564i	−0.747636	+	0.627341i
$43$	−5.23783	−	4.39506i	−0.798761	−	0.670240i	0.149136	−	0.988817i	$-0.452351\pi$
$43$	−5.23783	−	4.39506i	−0.798761	−	0.670240i	−0.947897	+	0.318577i	$0.896795\pi$
$44$	−0.0320889	−	0.181985i	−0.00483758	−	0.0274353i
$45$	0.233956	+	0.405223i	0.0348760	+	0.0604071i
$46$	0.277189	−	0.480105i	0.0408693	−	0.0707876i
$47$	9.09627	+	3.31077i	1.32683	+	0.482925i	0.905640	−	0.424048i	$-0.139391\pi$
$47$	9.09627	+	3.31077i	1.32683	+	0.482925i	0.421187	+	0.906974i	$0.361614\pi$
$48$	−6.75877	−	2.45999i	−0.975544	−	0.355069i
$49$	0.745100	−	1.29055i	0.106443	−	0.184364i
$50$	−3.22075	−	5.57851i	−0.455483	−	0.788920i
$51$	1.61587	+	9.16404i	0.226267	+	1.28322i
$52$	0.667718	+	0.560282i	0.0925959	+	0.0776972i
$53$	6.34002	−	5.31991i	0.870869	−	0.730746i	−0.0934119	−	0.995628i	$-0.529777\pi$
$53$	6.34002	−	5.31991i	0.870869	−	0.730746i	0.964281	+	0.264882i	$0.0853329\pi$
$54$	−0.935822	+	5.30731i	−0.127349	+	0.722234i
$55$	0.439693	−	0.160035i	0.0592881	−	0.0215791i
$56$	−6.90941			−0.923309
$57$	−2.30541	+	8.40744i	−0.305359	+	1.11359i
$58$	4.45336			0.584755
$59$	−4.16637	+	1.51644i	−0.542416	+	0.197423i	−0.598674	−	0.800993i	$-0.704305\pi$
$59$	−4.16637	+	1.51644i	−0.542416	+	0.197423i	0.0562579	+	0.998416i	$0.482083\pi$
$60$	−0.0300295	+	0.170306i	−0.00387679	+	0.0219864i
$61$	−7.85117	+	6.58791i	−1.00524	+	0.843496i	−0.987702	−	0.156351i	$-0.950027\pi$
$61$	−7.85117	+	6.58791i	−1.00524	+	0.843496i	−0.0175373	+	0.999846i	$0.505583\pi$
$62$	−4.04710	−	3.39592i	−0.513983	−	0.431283i
$63$	−0.407604	−	2.31164i	−0.0513532	−	0.291239i
$64$	−4.29813	−	7.44459i	−0.537267	−	0.930573i
$65$	−1.10354	+	1.91139i	−0.136877	+	0.237079i
$66$	−2.53209	−	0.921605i	−0.311679	−	0.113442i
$67$	4.89053	+	1.78001i	0.597473	+	0.217462i	0.623013	−	0.782211i	$-0.285908\pi$
$67$	4.89053	+	1.78001i	0.597473	+	0.217462i	−0.0255399	+	0.999674i	$0.508130\pi$
$68$	−0.429892	+	0.744596i	−0.0521321	+	0.0902955i
$69$	0.411474	+	0.712694i	0.0495357	+	0.0857983i
$70$	−0.256959	−	1.45729i	−0.0307125	−	0.174179i
$71$	−6.68345	−	5.60808i	−0.793179	−	0.665557i	0.153351	−	0.988172i	$-0.450994\pi$
$71$	−6.68345	−	5.60808i	−0.793179	−	0.665557i	−0.946530	+	0.322615i	$0.895438\pi$
$72$	2.25490	−	1.89209i	0.265743	−	0.222984i
$73$	−2.35710	+	13.3678i	−0.275877	+	1.56458i	0.460284	+	0.887772i	$0.347748\pi$
$73$	−2.35710	+	13.3678i	−0.275877	+	1.56458i	−0.736161	+	0.676806i	$0.763364\pi$
$74$	−6.17752	+	2.24843i	−0.718122	+	0.261375i
$75$	9.56212			1.10414
$76$	−0.662504	+	0.458155i	−0.0759944	+	0.0525540i
$77$	−2.34730			−0.267499
$78$	11.9436	−	4.34710i	1.35234	−	0.492212i
$79$	0.103541	−	0.587208i	0.0116492	−	0.0660661i	−0.978429	−	0.206583i	$-0.933765\pi$
$79$	0.103541	−	0.587208i	0.0116492	−	0.0660661i	0.990078	+	0.140517i	$0.0448766\pi$
$80$	1.28905	−	1.08164i	0.144120	−	0.120931i
$81$	−8.42649	−	7.07066i	−0.936277	−	0.785629i
$82$	−0.277189	−	1.57202i	−0.0306104	−	0.173600i
$83$	7.05690	+	12.2229i	0.774596	+	1.34164i	0.935021	+	0.354591i	$0.115380\pi$
$83$	7.05690	+	12.2229i	0.774596	+	1.34164i	−0.160426	+	0.987048i	$0.551287\pi$
$84$	0.433763	−	0.751299i	0.0473274	−	0.0819735i
$85$	−2.04576	−	0.744596i	−0.221894	−	0.0807627i
$86$	−8.65657	−	3.15074i	−0.933462	−	0.339753i
$87$	−3.30541	+	5.72513i	−0.354377	+	0.613799i
$88$	−1.47178	−	2.54920i	−0.156892	−	0.271746i
$89$	1.51842	+	8.61138i	0.160952	+	0.912804i	0.953141	+	0.302528i	$0.0978305\pi$
$89$	1.51842	+	8.61138i	0.160952	+	0.912804i	−0.792189	+	0.610276i	$0.791058\pi$
$90$	0.482926	+	0.405223i	0.0509049	+	0.0427142i
$91$	8.48158	−	7.11689i	0.889111	−	0.746053i
$92$	−0.0132037	+	0.0748822i	−0.00137659	+	0.00780701i
$93$	7.36959	−	2.68231i	0.764190	−	0.278143i
$94$	13.0419			1.34517
$95$	−1.43376	−	1.45059i	−0.147101	−	0.148827i
$96$	2.08378			0.212675
$97$	7.73783	−	2.81634i	0.785657	−	0.285956i	0.0821276	−	0.996622i	$-0.473828\pi$
$97$	7.73783	−	2.81634i	0.785657	−	0.285956i	0.703530	+	0.710666i	$0.251606\pi$
$98$	0.348641	−	1.97724i	0.0352180	−	0.199731i
$99$	0.766044	−	0.642788i	0.0769904	−	0.0646026i
$100$	0.676803	+	0.567905i	0.0676803	+	0.0567905i
$101$	−0.243756	−	1.38241i	−0.0242546	−	0.137555i	0.970276	−	0.242002i	$-0.0778039\pi$
$101$	−0.243756	−	1.38241i	−0.0242546	−	0.137555i	−0.994530	+	0.104447i	$0.966693\pi$
$102$	6.26857	+	10.8575i	0.620681	+	1.07505i
$103$	1.76604	−	3.05888i	0.174014	−	0.301400i	−0.765806	−	0.643072i	$-0.777660\pi$
$103$	1.76604	−	3.05888i	0.174014	−	0.301400i	0.939819	+	0.341671i	$0.110993\pi$
$104$	13.0471	+	4.74876i	1.27937	+	0.465654i
$105$	2.06418	+	0.751299i	0.201443	+	0.0733193i
$106$	5.57532	−	9.65674i	0.541523	−	0.937946i
$107$	3.31521	+	5.74211i	0.320493	+	0.555111i	0.980590	−	0.196070i	$-0.0628180\pi$
$107$	3.31521	+	5.74211i	0.320493	+	0.555111i	−0.660097	+	0.751181i	$0.729485\pi$
$108$	−0.128356	−	0.727940i	−0.0123510	−	0.0700461i
$109$	−14.3157	−	12.0123i	−1.37119	−	1.15057i	−0.972345	−	0.233551i	$-0.924966\pi$
$109$	−14.3157	−	12.0123i	−1.37119	−	1.15057i	−0.398848	−	0.917017i	$-0.630590\pi$
$110$	0.482926	−	0.405223i	0.0460452	−	0.0386365i
$111$	1.69459	−	9.61051i	0.160844	−	0.912190i
$112$	−7.93242	+	2.88716i	−0.749543	+	0.272811i
$113$	−13.6655			−1.28554			−0.642771	−	0.766058i	$-0.722215\pi$
$113$	−13.6655			−1.28554			−0.642771	+	0.766058i	$0.722215\pi$
$114$	0.955423	+	11.7065i	0.0894835	+	1.09642i
$115$	−0.192533			−0.0179538
$116$	−0.573978	+	0.208911i	−0.0532925	+	0.0193969i
$117$	−0.819078	+	4.64522i	−0.0757238	+	0.429451i
$118$	−4.57604	+	3.83975i	−0.421258	+	0.353478i
$119$	8.36618	+	7.02006i	0.766927	+	0.643528i
$120$	0.478340	+	2.71280i	0.0436663	+	0.247644i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−6.90420	+	11.9584i	−0.625077	+	1.08266i
$123$	2.22668	+	0.810446i	0.200773	+	0.0730754i
$124$	0.680922	+	0.247835i	0.0611486	+	0.0222563i
$125$	−2.28833	+	3.96351i	−0.204675	+	0.354507i
$126$	−1.58125	−	2.73881i	−0.140869	−	0.243992i
$127$	−1.79174	−	10.1614i	−0.158991	−	0.901682i	−0.955046	−	0.296458i	$-0.904195\pi$
$127$	−1.79174	−	10.1614i	−0.158991	−	0.901682i	0.796055	−	0.605224i	$-0.206917\pi$
$128$	−7.27584	−	6.10516i	−0.643100	−	0.539625i
$129$	10.4757	−	8.79012i	0.922330	−	0.773927i
$130$	−0.516359	+	2.92842i	−0.0452877	+	0.256839i
$131$	−7.23783	+	2.63435i	−0.632372	+	0.230165i	−0.638263	−	0.769818i	$-0.720347\pi$
$131$	−7.23783	+	2.63435i	−0.632372	+	0.230165i	0.00589151	+	0.999983i	$0.498125\pi$
$132$	0.369585			0.0321683
$133$	4.26991	+	9.29807i	0.370249	+	0.806245i
$134$	7.01186			0.605732
$135$	1.75877	−	0.640140i	0.151371	−	0.0550945i
$136$	−2.37820	+	13.4875i	−0.203929	+	1.15654i
$137$	11.9251	−	10.0064i	1.01883	−	0.854903i	0.0293533	−	0.999569i	$-0.490655\pi$
$137$	11.9251	−	10.0064i	1.01883	−	0.854903i	0.989481	+	0.144666i	$0.0462108\pi$
$138$	0.849356	+	0.712694i	0.0723020	+	0.0606686i
$139$	−3.23648	−	18.3550i	−0.274515	−	1.55685i	−0.740499	−	0.672058i	$-0.765411\pi$
$139$	−3.23648	−	18.3550i	−0.274515	−	1.55685i	0.465984	−	0.884793i	$-0.345700\pi$
$140$	0.101481	+	0.175771i	0.00857673	+	0.0148553i
$141$	−9.68004	+	16.7663i	−0.815207	+	1.41198i
$142$	−11.0458	−	4.02033i	−0.926940	−	0.337378i
$143$	4.43242	+	1.61327i	0.370657	+	0.134908i
$144$	1.79813	−	3.11446i	0.149844	−	0.259538i
$145$	−0.773318	−	1.33943i	−0.0642206	−	0.111233i
$146$	3.17571	+	18.0103i	0.262823	+	1.49055i
$147$	2.28312	+	1.91576i	0.188308	+	0.158010i
$148$	0.690722	−	0.579585i	0.0567770	−	0.0476416i
$149$	−2.60354	+	14.7654i	−0.213290	+	1.20963i	0.670558	+	0.741857i	$0.266055\pi$
$149$	−2.60354	+	14.7654i	−0.213290	+	1.20963i	−0.883849	+	0.467773i	$0.845057\pi$
$150$	12.1061	−	4.40625i	0.988456	−	0.359769i
$151$	−7.68004			−0.624993			−0.312497	−	0.949919i	$-0.601165\pi$
$151$	−7.68004			−0.624993			−0.312497	+	0.949919i	$0.601165\pi$
$152$	−7.42056	+	10.4672i	−0.601887	+	0.849001i
$153$	−4.65270			−0.376149
$154$	−2.97178	+	1.08164i	−0.239473	+	0.0871610i
$155$	−0.318611	+	1.80693i	−0.0255915	+	0.145136i
$156$	−1.33544	+	1.12056i	−0.106921	+	0.0897170i
$157$	−10.2738	−	8.62073i	−0.819937	−	0.688009i	0.133020	−	0.991113i	$-0.457533\pi$
$157$	−10.2738	−	8.62073i	−0.819937	−	0.688009i	−0.952957	+	0.303104i	$0.901977\pi$
$158$	−0.139500	−	0.791143i	−0.0110980	−	0.0629400i
$159$	8.27631	+	14.3350i	0.656354	+	1.13684i
$160$	−0.243756	+	0.422197i	−0.0192706	+	0.0333776i
$161$	0.907604	+	0.330341i	0.0715292	+	0.0260345i
$162$	−13.9265	−	5.06883i	−1.09417	−	0.398245i
$163$	2.26857	−	3.92928i	0.177688	−	0.307765i	−0.763400	−	0.645926i	$-0.776471\pi$
$163$	2.26857	−	3.92928i	0.177688	−	0.307765i	0.941088	+	0.338161i	$0.109805\pi$
$164$	0.109470	+	0.189608i	0.00854820	+	0.0148059i
$165$	0.162504	+	0.921605i	0.0126509	+	0.0717469i
$166$	14.5667	+	12.2229i	1.13060	+	0.948682i
$167$	5.94356	−	4.98724i	0.459927	−	0.385924i	−0.383177	−	0.923675i	$-0.625170\pi$
$167$	5.94356	−	4.98724i	0.459927	−	0.385924i	0.843104	+	0.537750i	$0.180726\pi$
$168$	2.39961	−	13.6089i	0.185134	−	1.04995i
$169$	−8.69119	+	3.16333i	−0.668553	+	0.243333i
$170$	−2.93313			−0.224961
$171$	−3.93969	−	1.86516i	−0.301276	−	0.142632i
$172$	1.26352			0.0963424
$173$	−12.2306	+	4.45156i	−0.929872	+	0.338446i	−0.762159	−	0.647390i	$-0.775860\pi$
$173$	−12.2306	+	4.45156i	−0.929872	+	0.338446i	−0.167713	+	0.985836i	$0.553638\pi$
$174$	−1.54664	+	8.77141i	−0.117250	+	0.664959i
$175$	8.59698	−	7.21372i	0.649871	−	0.545306i
$176$	−2.75490	−	2.31164i	−0.207658	−	0.174246i
$177$	−1.53983	−	8.73281i	−0.115741	−	0.656398i
$178$	5.89053	+	10.2027i	0.441514	+	0.764724i
$179$	5.41400	−	9.37732i	0.404661	−	0.700894i	−0.589621	−	0.807680i	$-0.700723\pi$
$179$	5.41400	−	9.37732i	0.404661	−	0.700894i	0.994282	+	0.106786i	$0.0340561\pi$
$180$	−0.0812519	−	0.0295733i	−0.00605616	−	0.00220426i
$181$	−13.8109	−	5.02677i	−1.02656	−	0.373637i	−0.226789	−	0.973944i	$-0.572823\pi$
$181$	−13.8109	−	5.02677i	−1.02656	−	0.373637i	−0.799769	+	0.600307i	$0.795045\pi$
$182$	7.45858	−	12.9186i	0.552867	−	0.957593i
$183$	−10.2490	−	17.7517i	−0.757626	−	1.31225i
$184$	0.210323	+	1.19280i	0.0155052	+	0.0879343i
$185$	1.74897	+	1.46756i	0.128587	+	0.107897i
$186$	8.09421	−	6.79185i	0.593496	−	0.498002i
$187$	−0.807934	+	4.58202i	−0.0590819	+	0.335070i
$188$	−1.68092	+	0.611806i	−0.122594	+	0.0446205i
$189$	−9.38919			−0.682963
$190$	−2.48364	−	1.17582i	−0.180182	−	0.0853033i
$191$	−2.95037			−0.213481			−0.106741	−	0.994287i	$-0.534041\pi$
$191$	−2.95037			−0.213481			−0.106741	+	0.994287i	$0.534041\pi$
$192$	16.1557	−	5.88019i	1.16594	−	0.424366i
$193$	4.01455	−	22.7676i	0.288973	−	1.63885i	−0.401763	−	0.915744i	$-0.631602\pi$
$193$	4.01455	−	22.7676i	0.288973	−	1.63885i	0.690737	−	0.723106i	$-0.257286\pi$
$194$	8.49866	−	7.13122i	0.610168	−	0.511992i
$195$	−3.38144	−	2.83737i	−0.242150	−	0.203188i
$196$	0.0478189	+	0.271194i	0.00341563	+	0.0193710i
$197$	−4.55303	−	7.88609i	−0.324390	−	0.561860i	0.656999	−	0.753892i	$-0.271826\pi$
$197$	−4.55303	−	7.88609i	−0.324390	−	0.561860i	−0.981389	+	0.192032i	$0.938492\pi$
$198$	0.673648	−	1.16679i	0.0478741	−	0.0829204i
$199$	−3.19207	−	1.16182i	−0.226280	−	0.0823590i	0.226392	−	0.974036i	$-0.427307\pi$
$199$	−3.19207	−	1.16182i	−0.226280	−	0.0823590i	−0.452672	+	0.891677i	$0.649529\pi$
$200$	13.2246	+	4.81337i	0.935122	+	0.340357i
$201$	−5.20439	+	9.01427i	−0.367090	+	0.635818i
$202$	−0.945622	−	1.63787i	−0.0665338	−	0.115240i
$203$	1.34730	+	7.64090i	0.0945617	+	0.536286i
$204$	−1.31727	−	1.10532i	−0.0922271	−	0.0773877i
$205$	−0.424678	+	0.356347i	−0.0296608	+	0.0248884i
$206$	0.826352	−	4.68647i	0.0575747	−	0.326522i
$207$	−0.386659	+	0.140732i	−0.0268747	+	0.00978158i
$208$	16.9632			1.17618
$209$	−2.52094	+	3.55596i	−0.174377	+	0.245971i
$210$	2.95954			0.204228
$211$	5.10607	−	1.85846i	0.351516	−	0.127941i	−0.160226	−	0.987080i	$-0.551222\pi$
$211$	5.10607	−	1.85846i	0.351516	−	0.127941i	0.511742	+	0.859139i	$0.329000\pi$
$212$	−0.265578	+	1.50617i	−0.0182399	+	0.103444i
$213$	13.3669	−	11.2162i	0.915885	−	0.768518i
$214$	6.84318	+	5.74211i	0.467790	+	0.392522i
$215$	0.555560	+	3.15074i	0.0378889	+	0.214878i
$216$	−5.88713	−	10.1968i	−0.400568	−	0.693804i
$217$	4.60220	−	7.97124i	0.312417	−	0.541123i
$218$	−23.6596	−	8.61138i	−1.60243	−	0.583236i
$219$	−25.5107	−	9.28515i	−1.72386	−	0.627432i
$220$	−0.0432332	+	0.0748822i	−0.00291478	+	0.00504855i
$221$	−10.9731	−	19.0060i	−0.738132	−	1.27848i
$222$	−2.28312	−	12.9482i	−0.153233	−	0.869027i
$223$	0.718941	+	0.603263i	0.0481438	+	0.0403975i	0.666542	−	0.745467i	$-0.267774\pi$
$223$	0.718941	+	0.603263i	0.0481438	+	0.0403975i	−0.618398	+	0.785865i	$0.712218\pi$
$224$	1.87346	−	1.57202i	0.125176	−	0.105035i
$225$	−0.830222	+	4.70842i	−0.0553481	+	0.313895i
$226$	−17.3011	+	6.29710i	−1.15085	+	0.418877i
$227$	−19.9017			−1.32092			−0.660460	−	0.750861i	$-0.729639\pi$
$227$	−19.9017			−1.32092			−0.660460	+	0.750861i	$0.729639\pi$
$228$	−0.672304	−	1.46399i	−0.0445244	−	0.0969553i
$229$	22.1438			1.46331			0.731653	−	0.681677i	$-0.238749\pi$
$229$	22.1438			1.46331			0.731653	+	0.681677i	$0.238749\pi$
$230$	−0.243756	+	0.0887198i	−0.0160728	+	0.00585001i
$231$	0.815207	−	4.62327i	0.0536367	−	0.304189i
$232$	−7.45336	+	6.25411i	−0.489337	+	0.410603i
$233$	14.9349	+	12.5319i	0.978421	+	0.820993i	0.983850	−	0.178993i	$-0.0572839\pi$
$233$	14.9349	+	12.5319i	0.978421	+	0.820993i	−0.00542962	+	0.999985i	$0.501728\pi$
$234$	1.10354	+	6.25849i	0.0721407	+	0.409130i
$235$	−2.26470	−	3.92258i	−0.147733	−	0.255881i
$236$	0.409663	−	0.709557i	0.0266668	−	0.0461882i
$237$	1.12061	+	0.407870i	0.0727918	+	0.0264940i
$238$	13.8268	+	5.03255i	0.896260	+	0.326212i
$239$	0.0564370	−	0.0977517i	0.00365061	−	0.00632303i	−0.864194	−	0.503158i	$-0.832171\pi$
$239$	0.0564370	−	0.0977517i	0.00365061	−	0.00632303i	0.867845	+	0.496835i	$0.165505\pi$
$240$	1.68273	+	2.91458i	0.108620	+	0.188135i
$241$	3.29204	+	18.6701i	0.212059	+	1.20265i	0.885938	+	0.463804i	$0.153516\pi$
$241$	3.29204	+	18.6701i	0.212059	+	1.20265i	−0.673879	+	0.738842i	$0.735373\pi$
$242$	−1.03209	−	0.866025i	−0.0663452	−	0.0556702i
$243$	7.66044	−	6.42788i	0.491418	−	0.412348i
$244$	0.328878	−	1.86516i	0.0210543	−	0.119405i
$245$	−0.655230	+	0.238484i	−0.0418611	+	0.0152362i
$246$	3.19253			0.203548
$247$	−1.67247	−	20.4923i	−0.106416	−	1.30389i
$248$	11.5425			0.732951
$249$	−26.5253	+	9.65441i	−1.68097	+	0.611824i
$250$	−1.07074	+	6.07245i	−0.0677193	+	0.384055i
$251$	3.81315	−	3.19961i	0.240684	−	0.201958i	−0.514465	−	0.857512i	$-0.672009\pi$
$251$	3.81315	−	3.19961i	0.240684	−	0.201958i	0.755148	+	0.655554i	$0.227565\pi$
$252$	0.332282	+	0.278817i	0.0209318	+	0.0175638i
$253$	0.0714517	+	0.405223i	0.00449213	+	0.0254761i
$254$	−6.95084	−	12.0392i	−0.436134	−	0.755407i
$255$	2.17705	−	3.77076i	0.136332	−	0.236134i
$256$	4.13088	+	1.50352i	0.258180	+	0.0939699i
$257$	13.8020	+	5.02352i	0.860945	+	0.313358i	0.734495	−	0.678614i	$-0.237419\pi$
$257$	13.8020	+	5.02352i	0.860945	+	0.313358i	0.126451	+	0.991973i	$0.459641\pi$
$258$	9.21213	−	15.9559i	0.573522	−	0.993370i
$259$	−5.72668	−	9.91890i	−0.355839	−	0.616331i
$260$	−0.0708228	−	0.401656i	−0.00439224	−	0.0249096i
$261$	−2.53209	−	2.12467i	−0.156732	−	0.131514i
$262$	−7.94949	+	6.67042i	−0.491121	+	0.412100i
$263$	−1.64749	+	9.34337i	−0.101589	+	0.576137i	0.890940	+	0.454122i	$0.150047\pi$
$263$	−1.64749	+	9.34337i	−0.101589	+	0.576137i	−0.992528	+	0.122015i	$0.961064\pi$
$264$	5.53209	−	2.01352i	0.340477	−	0.123923i
$265$	−3.87258			−0.237891
$266$	9.69047	+	9.80418i	0.594161	+	0.601133i
$267$	−17.4884			−1.07028
$268$	−0.903733	+	0.328932i	−0.0552043	+	0.0200927i
$269$	−2.63697	+	14.9550i	−0.160779	+	0.911824i	0.792531	+	0.609831i	$0.208763\pi$
$269$	−2.63697	+	14.9550i	−0.160779	+	0.911824i	−0.953310	+	0.301992i	$0.902348\pi$
$270$	1.93170	−	1.62089i	0.117560	−	0.0986443i
$271$	10.8007	+	9.06283i	0.656093	+	0.550528i	0.908913	−	0.416986i	$-0.136913\pi$
$271$	10.8007	+	9.06283i	0.656093	+	0.550528i	−0.252820	+	0.967513i	$0.581358\pi$
$272$	2.90554	+	16.4782i	0.176175	+	0.999135i
$273$	11.0719	+	19.1771i	0.670103	+	1.16065i
$274$	10.4868	−	18.1637i	0.633531	−	1.09731i
$275$	4.49273	+	1.63522i	0.270922	+	0.0986074i
$276$	−0.142903	−	0.0520126i	−0.00860178	−	0.00313079i
$277$	−3.47044	+	6.01097i	−0.208518	+	0.361164i	−0.951248	−	0.308427i	$-0.900197\pi$
$277$	−3.47044	+	6.01097i	−0.208518	+	0.361164i	0.742730	+	0.669591i	$0.233531\pi$
$278$	−12.5556	−	21.7469i	−0.753032	−	1.30429i
$279$	0.680922	+	3.86170i	0.0407657	+	0.231194i
$280$	2.47662	+	2.07813i	0.148006	+	0.124192i
$281$	−21.9158	+	18.3895i	−1.30739	+	1.09703i	−0.318570	+	0.947899i	$0.603203\pi$
$281$	−21.9158	+	18.3895i	−1.30739	+	1.09703i	−0.988818	+	0.149129i	$0.952353\pi$
$282$	−4.52940	+	25.6875i	−0.269722	+	1.52967i
$283$	−26.6177	+	9.68804i	−1.58226	+	0.575894i	−0.975693	−	0.219141i	$-0.929675\pi$
$283$	−26.6177	+	9.68804i	−1.58226	+	0.575894i	−0.606563	+	0.795035i	$0.707452\pi$
$284$	1.61225			0.0956691
$285$	3.35504	−	2.32018i	0.198735	−	0.137436i
$286$	6.35504			0.375781
$287$	2.61334	−	0.951178i	0.154261	−	0.0561463i
$288$	−0.180922	+	1.02606i	−0.0106609	+	0.0604612i
$289$	3.56031	−	2.98745i	0.209430	−	0.175733i
$290$	−1.59627	−	1.33943i	−0.0937360	−	0.0786538i
$291$	2.85978	+	16.2186i	0.167644	+	0.950754i
$292$	−1.25418	−	2.17231i	−0.0733956	−	0.127125i
$293$	1.35070	−	2.33948i	0.0789087	−	0.136674i	−0.823871	−	0.566778i	$-0.808190\pi$
$293$	1.35070	−	2.33948i	0.0789087	−	0.136674i	0.902779	+	0.430104i	$0.141523\pi$
$294$	3.77332	+	1.37338i	0.220064	+	0.0800969i
$295$	1.94949	+	0.709557i	0.113504	+	0.0413120i
$296$	7.18139	−	12.4385i	0.417410	−	0.722975i
$297$	−2.00000	−	3.46410i	−0.116052	−	0.201008i
$298$	3.50774	+	19.8934i	0.203198	+	1.15239i
$299$	−1.48680	−	1.24757i	−0.0859836	−	0.0721488i
$300$	−1.35361	+	1.13581i	−0.0781505	+	0.0655761i
$301$	2.78699	−	15.8058i	0.160639	−	0.911031i
$302$	−9.72328	+	3.53898i	−0.559512	+	0.203646i
$303$	2.80747			0.161285
$304$	−4.14543	+	15.1177i	−0.237757	+	0.867060i
$305$	4.79561			0.274596
$306$	−5.89053	+	2.14398i	−0.336739	+	0.122563i
$307$	−3.79086	+	21.4990i	−0.216356	+	1.22701i	0.662183	+	0.749343i	$0.269630\pi$
$307$	−3.79086	+	21.4990i	−0.216356	+	1.22701i	−0.878538	+	0.477672i	$0.841481\pi$
$308$	0.332282	−	0.278817i	0.0189335	−	0.0158871i
$309$	5.41147	+	4.54077i	0.307848	+	0.258315i
$310$	0.429263	+	2.43447i	0.0243805	+	0.138269i
$311$	6.17412	+	10.6939i	0.350102	+	0.606394i	0.986267	−	0.165159i	$-0.0528136\pi$
$311$	6.17412	+	10.6939i	0.350102	+	0.606394i	−0.636165	+	0.771553i	$0.719480\pi$
$312$	−13.8844	+	24.0486i	−0.786051	+	1.36148i
$313$	25.9466	+	9.44377i	1.46659	+	0.533794i	0.947171	−	0.320729i	$-0.103928\pi$
$313$	25.9466	+	9.44377i	1.46659	+	0.533794i	0.519415	+	0.854522i	$0.326150\pi$
$314$	−16.9795	−	6.18004i	−0.958210	−	0.348760i
$315$	−0.549163	+	0.951178i	−0.0309418	+	0.0535928i
$316$	0.0550928	+	0.0954236i	0.00309921	+	0.00536799i
$317$	−3.16890	−	17.9717i	−0.177983	−	1.00939i	−0.934644	−	0.355585i	$-0.884282\pi$
$317$	−3.16890	−	17.9717i	−0.177983	−	1.00939i	0.756661	−	0.653808i	$-0.226829\pi$
$318$	17.0838	+	14.3350i	0.958011	+	0.803866i
$319$	−2.53209	+	2.12467i	−0.141770	+	0.118959i
$320$	−0.698463	+	3.96118i	−0.0390453	+	0.221437i
$321$	−12.4611	+	4.53547i	−0.695511	+	0.253145i
$322$	1.30129			0.0725180
$323$	19.6199	−	5.13468i	1.09168	−	0.285701i
$324$	2.03272			0.112929
$325$	−21.1917	+	7.71313i	−1.17550	+	0.427848i
$326$	1.06149	−	6.02001i	0.0587905	−	0.333417i
$327$	28.6313	−	24.0246i	1.58332	−	1.32856i
$328$	2.67159	+	2.24173i	0.147514	+	0.123779i
$329$	3.94562	+	22.3767i	0.217529	+	1.23367i
$330$	0.630415	+	1.09191i	0.0347032	+	0.0601077i
$331$	−14.6211	+	25.3245i	−0.803647	+	1.39196i	0.113553	+	0.993532i	$0.463777\pi$
$331$	−14.6211	+	25.3245i	−0.803647	+	1.39196i	−0.917200	+	0.398426i	$0.869557\pi$
$332$	−2.45084	−	0.892032i	−0.134507	−	0.0489566i
$333$	4.58512	+	1.66885i	0.251263	+	0.0914523i
$334$	5.22668	−	9.05288i	0.285991	−	0.495351i
$335$	−1.21760	−	2.10894i	−0.0665244	−	0.115224i
$336$	−2.93170	−	16.6265i	−0.159938	−	0.907051i
$337$	9.90807	+	8.31386i	0.539727	+	0.452885i	0.871445	−	0.490494i	$-0.163184\pi$
$337$	9.90807	+	8.31386i	0.539727	+	0.452885i	−0.331718	+	0.943379i	$0.607628\pi$
$338$	−9.54576	+	8.00984i	−0.519221	+	0.435678i
$339$	4.74598	−	26.9158i	0.257766	−	1.46186i
$340$	0.378041	−	0.137596i	0.0205022	−	0.00746217i
$341$	3.92127			0.212349
$342$	−5.84730	−	0.545955i	−0.316186	−	0.0295219i
$343$	19.9290			1.07607
$344$	18.9128	−	6.88370i	1.01971	−	0.371144i
$345$	0.0668661	−	0.379217i	0.00359995	−	0.0204163i
$346$	−13.4331	+	11.2717i	−0.722170	+	0.605972i
$347$	25.0069	+	20.9832i	1.34244	+	1.12644i	0.980992	+	0.194047i	$0.0621614\pi$
$347$	25.0069	+	20.9832i	1.34244	+	1.12644i	0.361447	+	0.932393i	$0.382283\pi$
$348$	−0.212134	−	1.20307i	−0.0113716	−	0.0644913i
$349$	−9.17365	−	15.8892i	−0.491054	−	0.850531i	0.508893	−	0.860830i	$-0.330055\pi$
$349$	−9.17365	−	15.8892i	−0.491054	−	0.850531i	−0.999947	+	0.0102992i	$0.996722\pi$
$350$	7.56006	−	13.0944i	0.404102	−	0.699925i
$351$	17.7297	+	6.45307i	0.946340	+	0.344440i
$352$	0.979055	+	0.356347i	0.0521838	+	0.0189934i
$353$	5.18227	−	8.97595i	0.275824	−	0.477742i	−0.694519	−	0.719475i	$-0.744383\pi$
$353$	5.18227	−	8.97595i	0.275824	−	0.477742i	0.970343	+	0.241733i	$0.0777159\pi$
$354$	−5.97359	−	10.3466i	−0.317493	−	0.549914i
$355$	0.708892	+	4.02033i	0.0376241	+	0.213377i
$356$	−1.23783	−	1.03866i	−0.0656046	−	0.0550488i
$357$	−16.7324	+	14.0401i	−0.885571	+	0.743082i
$358$	2.53327	−	14.3669i	0.133888	−	0.759314i
$359$	11.7811	−	4.28795i	0.621781	−	0.226310i	−0.0118694	−	0.999930i	$-0.503778\pi$
$359$	11.7811	−	4.28795i	0.621781	−	0.226310i	0.633650	+	0.773620i	$0.281556\pi$
$360$	−1.37733			−0.0725914
$361$	18.6716	+	3.51735i	0.982715	+	0.185124i
$362$	−19.8016			−1.04075
$363$	1.87939	−	0.684040i	0.0986421	−	0.0359028i
$364$	−0.355286	+	2.01492i	−0.0186220	+	0.105611i
$365$	4.86547	−	4.08261i	0.254670	−	0.213694i
$366$	−21.1557	−	17.7517i	−1.10583	−	0.927898i
$367$	0.399148	+	2.26368i	0.0208353	+	0.118163i	0.993452	−	0.114254i	$-0.0364477\pi$
$367$	0.399148	+	2.26368i	0.0208353	+	0.118163i	−0.972616	+	0.232417i	$0.925337\pi$
$368$	0.739885	+	1.28152i	0.0385692	+	0.0668038i
$369$	−0.592396	+	1.02606i	−0.0308389	+	0.0534146i
$370$	2.89053	+	1.05207i	0.150271	+	0.0546943i
$371$	18.2554	+	6.64441i	0.947771	+	0.344961i
$372$	−0.724622	+	1.25508i	−0.0375699	+	0.0650730i
$373$	−0.940159	−	1.62840i	−0.0486796	−	0.0843156i	0.840659	−	0.541565i	$-0.182168\pi$
$373$	−0.940159	−	1.62840i	−0.0486796	−	0.0843156i	−0.889338	+	0.457249i	$0.848835\pi$
$374$	1.08853	+	6.17334i	0.0562863	+	0.319216i
$375$	−7.01186	−	5.88365i	−0.362091	−	0.303830i
$376$	−21.8275	+	18.3155i	−1.12567	+	0.944549i
$377$	2.70739	−	15.3543i	0.139437	−	0.790789i
$378$	−11.8871	+	4.32656i	−0.611408	+	0.222534i
$379$	−8.83244			−0.453692			−0.226846	−	0.973931i	$-0.572841\pi$
$379$	−8.83244			−0.453692			−0.226846	+	0.973931i	$0.572841\pi$
$380$	0.375266	+	0.0350382i	0.0192508	+	0.00179742i
$381$	20.6364			1.05723
$382$	−3.73530	+	1.35954i	−0.191115	+	0.0695600i
$383$	6.65863	−	37.7630i	0.340240	−	1.92960i	−0.0273862	−	0.999625i	$-0.508718\pi$
$383$	6.65863	−	37.7630i	0.340240	−	1.92960i	0.367626	−	0.929974i	$-0.380171\pi$
$384$	14.5517	−	12.2103i	0.742588	−	0.623105i
$385$	0.841367	+	0.705990i	0.0428800	+	0.0359806i
$386$	−5.40879	−	30.6747i	−0.275300	−	1.56130i
$387$	3.41875	+	5.92145i	0.173785	+	0.301004i
$388$	−0.760830	+	1.31780i	−0.0386253	+	0.0669010i
$389$	−14.6099	−	5.31758i	−0.740753	−	0.269612i	−0.0560438	−	0.998428i	$-0.517849\pi$
$389$	−14.6099	−	5.31758i	−0.740753	−	0.269612i	−0.684709	+	0.728816i	$0.740071\pi$
$390$	−5.58853	−	2.03406i	−0.282986	−	0.102998i
$391$	0.957234	−	1.65798i	0.0484094	−	0.0838475i
$392$	2.19325	+	3.79882i	0.110776	+	0.191869i
$393$	−2.67499	−	15.1706i	−0.134936	−	0.765257i
$394$	−9.39827	−	7.88609i	−0.473478	−	0.397295i
$395$	−0.213726	+	0.179338i	−0.0107537	+	0.00902345i
$396$	−0.0320889	+	0.181985i	−0.00161253	+	0.00914510i
$397$	33.6361	−	12.2425i	1.68815	−	0.614435i	0.693757	−	0.720209i	$-0.255954\pi$
$397$	33.6361	−	12.2425i	1.68815	−	0.614435i	0.994390	+	0.105774i	$0.0337319\pi$
$398$	−4.57667			−0.229408
$399$	−19.7965	+	5.18091i	−0.991067	+	0.259370i
$400$	17.1940			0.859698
$401$	−30.5043	+	11.1027i	−1.52331	+	0.554441i	−0.961973	−	0.273144i	$-0.911936\pi$
$401$	−30.5043	+	11.1027i	−1.52331	+	0.554441i	−0.561341	+	0.827585i	$0.689714\pi$
$402$	−2.43519	+	13.8107i	−0.121456	+	0.688813i
$403$	−14.1689	+	11.8891i	−0.705803	+	0.592239i
$404$	0.198711	+	0.166739i	0.00988627	+	0.00829556i
$405$	0.893771	+	5.06883i	0.0444118	+	0.251872i
$406$	5.22668	+	9.05288i	0.259396	+	0.449287i
$407$	2.43969	−	4.22567i	0.120931	−	0.209459i
$408$	−25.7392	−	9.36829i	−1.27428	−	0.463800i
$409$	−2.51842	−	0.916629i	−0.124528	−	0.0453244i	0.279005	−	0.960290i	$-0.409996\pi$
$409$	−2.51842	−	0.916629i	−0.124528	−	0.0453244i	−0.403532	+	0.914965i	$0.632218\pi$
$410$	−0.373455	+	0.646844i	−0.0184437	+	0.0319453i
$411$	15.5672	+	26.9631i	0.767872	+	1.32999i
$412$	0.113341	+	0.642788i	0.00558390	+	0.0316679i
$413$	−7.97250	−	6.68972i	−0.392301	−	0.329180i
$414$	−0.424678	+	0.356347i	−0.0208718	+	0.0175135i
$415$	1.14677	−	6.50368i	0.0562929	−	0.319253i
$416$	−4.61809	+	1.68085i	−0.226420	+	0.0824103i
$417$	37.2763			1.82543
$418$	−1.55303	+	5.66366i	−0.0759613	+	0.277019i
$419$	−33.4415			−1.63372			−0.816862	−	0.576833i	$-0.804288\pi$
$419$	−33.4415			−1.63372			−0.816862	+	0.576833i	$0.804288\pi$
$420$	−0.381445	+	0.138834i	−0.0186126	+	0.00677443i
$421$	−1.16994	+	6.63506i	−0.0570194	+	0.323373i	−0.999954	−	0.00960533i	$-0.996942\pi$
$421$	−1.16994	+	6.63506i	−0.0570194	+	0.323373i	0.942934	+	0.332978i	$0.108054\pi$
$422$	5.60813	−	4.70578i	0.272999	−	0.229074i
$423$	−7.41534	−	6.22221i	−0.360546	−	0.302534i
$424$	4.23039	+	23.9917i	0.205446	+	1.16514i
$425$	−11.1224	−	19.2646i	−0.539517	−	0.934471i
$426$	11.7547	−	20.3597i	0.569515	−	0.986428i
$427$	−22.6065	−	8.22811i	−1.09401	−	0.398186i
$428$	−1.15136	−	0.419061i	−0.0556531	−	0.0202561i
$429$	−4.71688	+	8.16988i	−0.227733	+	0.394445i
$430$	2.15523	+	3.73297i	0.103934	+	0.180020i
$431$	−1.28224	−	7.27195i	−0.0617634	−	0.350278i	−0.999991	−	0.00425868i	$-0.998644\pi$
$431$	−1.28224	−	7.27195i	−0.0617634	−	0.350278i	0.938228	−	0.346019i	$-0.112467\pi$
$432$	−11.0196	−	9.24654i	−0.530181	−	0.444874i
$433$	20.9971	−	17.6186i	1.00905	−	0.846697i	0.0208415	−	0.999783i	$-0.493365\pi$
$433$	20.9971	−	17.6186i	1.00905	−	0.846697i	0.988213	+	0.153086i	$0.0489210\pi$
$434$	2.15342	−	12.2126i	0.103367	−	0.586226i
$435$	2.90673	−	1.05796i	0.139367	−	0.0507254i
$436$	3.45336			0.165386
$437$	1.47519	−	1.02017i	0.0705677	−	0.0488011i
$438$	−36.5763			−1.74769
$439$	−8.39053	+	3.05390i	−0.400458	+	0.145755i	−0.534395	−	0.845235i	$-0.679460\pi$
$439$	−8.39053	+	3.05390i	−0.400458	+	0.145755i	0.133937	+	0.990990i	$0.457238\pi$
$440$	−0.239170	+	1.35640i	−0.0114020	+	0.0646639i
$441$	−1.14156	+	0.957882i	−0.0543600	+	0.0456134i
$442$	−22.6505	−	19.0060i	−1.07737	−	0.904024i
$443$	2.52569	+	14.3239i	0.119999	+	0.680550i	0.984153	+	0.177322i	$0.0567433\pi$
$443$	2.52569	+	14.3239i	0.119999	+	0.680550i	−0.864154	+	0.503228i	$0.832146\pi$
$444$	0.901674	+	1.56175i	0.0427916	+	0.0741171i
$445$	2.04576	−	3.54336i	0.0969783	−	0.167971i
$446$	1.18820	+	0.432468i	0.0562627	+	0.0204780i
$447$	−28.1780	−	10.2559i	−1.33277	−	0.485090i
$448$	10.0890	−	17.4746i	0.476660	−	0.825600i
$449$	−8.43242	−	14.6054i	−0.397950	−	0.689270i	0.595522	−	0.803339i	$-0.296945\pi$
$449$	−8.43242	−	14.6054i	−0.397950	−	0.689270i	−0.993473	+	0.114068i	$0.963612\pi$
$450$	1.11856	+	6.34364i	0.0527292	+	0.299042i
$451$	0.907604	+	0.761570i	0.0427374	+	0.0358609i
$452$	1.93448	−	1.62322i	0.0909902	−	0.0763498i
$453$	2.66725	−	15.1267i	0.125318	−	0.710716i
$454$	−25.1964	+	9.17074i	−1.18253	+	0.430404i
$455$	−5.18067			−0.242874
$456$	−18.0392	−	18.2509i	−0.844763	−	0.854675i
$457$	−15.6186			−0.730605			−0.365303	−	0.930889i	$-0.619034\pi$
$457$	−15.6186			−0.730605			−0.365303	+	0.930889i	$0.619034\pi$
$458$	28.0351	−	10.2039i	1.30999	−	0.476799i
$459$	−3.23173	+	18.3281i	−0.150844	+	0.855481i
$460$	0.0272549	−	0.0228696i	0.00127077	−	0.00106630i
$461$	15.6322	+	13.1170i	0.728065	+	0.610919i	0.929603	−	0.368561i	$-0.120150\pi$
$461$	15.6322	+	13.1170i	0.728065	+	0.610919i	−0.201538	+	0.979481i	$0.564594\pi$
$462$	−1.09833	−	6.22892i	−0.0510988	−	0.289795i
$463$	5.64425	+	9.77612i	0.262310	+	0.454335i	0.966855	−	0.255324i	$-0.0821822\pi$
$463$	5.64425	+	9.77612i	0.262310	+	0.454335i	−0.704545	+	0.709659i	$0.748849\pi$
$464$	−5.94356	+	10.2946i	−0.275923	+	0.477913i
$465$	−3.44831	−	1.25508i	−0.159912	−	0.0582031i
$466$	24.6830	+	8.98389i	1.14342	+	0.416171i
$467$	6.12748	−	10.6131i	0.283546	−	0.491116i	−0.688710	−	0.725037i	$-0.741823\pi$
$467$	6.12748	−	10.6131i	0.283546	−	0.491116i	0.972256	+	0.233921i	$0.0751558\pi$
$468$	−0.435822	−	0.754866i	−0.0201459	−	0.0348937i
$469$	2.12133	+	12.0307i	0.0979539	+	0.555524i
$470$	−4.67474	−	3.92258i	−0.215630	−	0.180935i
$471$	20.5476	−	17.2415i	0.946782	−	0.794444i
$472$	2.26629	−	12.8528i	0.104315	−	0.591597i
$473$	6.42514	−	2.33856i	0.295428	−	0.107527i
$474$	1.60670			0.0737980
$475$	−1.69522	−	20.7711i	−0.0777821	−	0.953043i
$476$	−2.01817			−0.0925027
$477$	−7.77719	+	2.83067i	−0.356093	+	0.129607i
$478$	0.0264075	−	0.149764i	0.00120785	−	0.00685006i
$479$	7.02687	−	5.89625i	0.321066	−	0.269406i	−0.467982	−	0.883738i	$-0.655019\pi$
$479$	7.02687	−	5.89625i	0.321066	−	0.269406i	0.789048	+	0.614332i	$0.210574\pi$
$480$	−0.746911	−	0.626733i	−0.0340917	−	0.0286063i
$481$	3.99660	+	22.6658i	0.182229	+	1.03347i
$482$	12.7711	+	22.1202i	0.581708	+	1.00755i
$483$	−0.965852	+	1.67290i	−0.0439478	+	0.0761198i
$484$	0.173648	+	0.0632028i	0.00789310	+	0.00287285i
$485$	−3.62061	−	1.31780i	−0.164404	−	0.0598380i
$486$	6.73648	−	11.6679i	0.305573	−	0.529268i
$487$	14.5954	+	25.2800i	0.661380	+	1.14554i	0.980253	+	0.197747i	$0.0633623\pi$
$487$	14.5954	+	25.2800i	0.661380	+	1.14554i	−0.318873	+	0.947797i	$0.603304\pi$
$488$	−5.23870	−	29.7102i	−0.237145	−	1.34492i
$489$	6.95130	+	5.83284i	0.314349	+	0.263770i
$490$	−0.719656	+	0.603863i	−0.0325107	+	0.0272798i
$491$	−6.27038	+	35.5611i	−0.282978	+	1.60485i	0.429440	+	0.903095i	$0.358711\pi$
$491$	−6.27038	+	35.5611i	−0.282978	+	1.60485i	−0.712419	+	0.701755i	$0.752400\pi$
$492$	−0.411474	+	0.149764i	−0.0185507	+	0.00675190i
$493$	15.3791			0.692639
$494$	−11.5603	−	25.1735i	−0.520123	−	1.13261i
$495$	−0.467911			−0.0210310
$496$	13.2515	−	4.82315i	0.595010	−	0.216566i
$497$	3.55619	−	20.1681i	0.159517	−	0.904665i
$498$	−29.1334	+	24.4458i	−1.30550	+	1.09544i
$499$	15.4402	+	12.9558i	0.691196	+	0.579983i	0.919254	−	0.393665i	$-0.128793\pi$
$499$	15.4402	+	12.9558i	0.691196	+	0.579983i	−0.228058	+	0.973648i	$0.573237\pi$
$500$	−0.146860	−	0.832885i	−0.00656778	−	0.0372478i
$501$	7.75877	+	13.4386i	0.346636	+	0.600392i
$502$	3.35323	−	5.80796i	0.149662	−	0.259222i
$503$	40.4702	+	14.7299i	1.80448	+	0.656776i	0.997837	+	0.0657316i	$0.0209381\pi$
$503$	40.4702	+	14.7299i	1.80448	+	0.656776i	0.806639	+	0.591044i	$0.201284\pi$
$504$	6.49273	+	2.36316i	0.289209	+	0.105263i
$505$	−0.328411	+	0.568825i	−0.0146141	+	0.0253124i
$506$	0.277189	+	0.480105i	0.0123225	+	0.0213433i
$507$	−3.21213	−	18.2169i	−0.142656	−	0.809042i
$508$	1.46064	+	1.22562i	0.0648053	+	0.0543781i
$509$	24.3384	−	20.4224i	1.07878	−	0.905206i	0.0829628	−	0.996553i	$-0.473562\pi$
$509$	24.3384	−	20.4224i	1.07878	−	0.905206i	0.995819	+	0.0913471i	$0.0291173\pi$
$510$	1.01867	−	5.77715i	0.0451073	−	0.255816i
$511$	−29.9406	+	10.8975i	−1.32450	+	0.482077i
$512$	24.9186			1.10126
$513$	−10.0838	+	14.2238i	−0.445210	+	0.627998i
$514$	19.7888			0.872847
$515$	−1.55303	+	0.565258i	−0.0684348	+	0.0249082i
$516$	−0.438815	+	2.48865i	−0.0193178	+	0.109556i
$517$	−7.41534	+	6.22221i	−0.326126	+	0.273653i
$518$	−11.8209	−	9.91890i	−0.519380	−	0.435812i
$519$	−4.52023	−	25.6355i	−0.198416	−	1.12527i
$520$	−3.24834	−	5.62629i	−0.142449	−	0.246729i
$521$	11.6814	−	20.2328i	0.511771	−	0.886413i	−0.488136	−	0.872768i	$-0.662323\pi$
$521$	11.6814	−	20.2328i	0.511771	−	0.886413i	0.999907	−	0.0136457i	$-0.00434369\pi$
$522$	−4.18479	−	1.52314i	−0.183163	−	0.0666660i
$523$	−41.0629	−	14.9457i	−1.79555	−	0.653529i	−0.998787	−	0.0492432i	$-0.984319\pi$
$523$	−41.0629	−	14.9457i	−1.79555	−	0.653529i	−0.796768	−	0.604285i	$-0.793459\pi$
$524$	0.711667	−	1.23264i	0.0310893	−	0.0538483i
$525$	11.2226	+	19.4380i	0.489793	+	0.848346i
$526$	2.21966	+	12.5883i	0.0967816	+	0.548876i
$527$	−13.9761	−	11.7274i	−0.608809	−	0.510852i
$528$	5.50980	−	4.62327i	0.239783	−	0.201202i
$529$	−3.96451	+	22.4838i	−0.172370	+	0.977558i
$530$	−4.90286	+	1.78449i	−0.212966	+	0.0775135i
$531$	4.43376			0.192409
$532$	−1.70889	−	0.809037i	−0.0740899	−	0.0350762i
$533$	−5.58853			−0.242066
$534$	−22.1411	+	8.05872i	−0.958141	+	0.348735i
$535$	0.538734	−	3.05531i	0.0232915	−	0.132093i
$536$	−11.7354	+	9.84716i	−0.506891	+	0.425332i
$537$	16.5895	+	13.9202i	0.715888	+	0.600701i
$538$	3.55279	+	20.1488i	0.153171	+	0.868678i
$539$	0.745100	+	1.29055i	0.0320937	+	0.0555880i
$540$	−0.172933	+	0.299529i	−0.00744185	+	0.0128897i
$541$	−28.5574	−	10.3940i	−1.22778	−	0.446874i	−0.354942	−	0.934889i	$-0.615499\pi$
$541$	−28.5574	−	10.3940i	−1.22778	−	0.446874i	−0.872836	+	0.488014i	$0.837721\pi$
$542$	17.8503	+	6.49697i	0.766736	+	0.279069i
$543$	14.6973	−	25.4564i	0.630721	−	1.09244i
$544$	−2.42380	−	4.19815i	−0.103920	−	0.179994i
$545$	1.51842	+	8.61138i	0.0650419	+	0.368871i
$546$	22.8544	+	19.1771i	0.978078	+	0.820705i
$547$	−26.0023	+	21.8185i	−1.11178	+	0.932892i	−0.998160	−	0.0606329i	$-0.980688\pi$
$547$	−26.0023	+	21.8185i	−1.11178	+	0.932892i	−0.113617	+	0.993525i	$0.536244\pi$
$548$	−0.499533	+	2.83299i	−0.0213390	+	0.121019i
$549$	9.63088	−	3.50535i	0.411036	−	0.149605i
$550$	6.44150			0.274667
$551$	13.0223	+	6.16511i	0.554768	+	0.262643i
$552$	−2.42240			−0.103104
$553$	1.31521	−	0.478696i	0.0559283	−	0.0203562i
$554$	−1.62386	+	9.20935i	−0.0689910	+	0.391268i
$555$	−3.49794	+	2.93512i	−0.148479	+	0.124589i
$556$	2.63840	+	2.21388i	0.111893	+	0.0938896i
$557$	−5.83931	−	33.1164i	−0.247419	−	1.40319i	−0.814806	−	0.579734i	$-0.803157\pi$
$557$	−5.83931	−	33.1164i	−0.247419	−	1.40319i	0.567387	−	0.823451i	$-0.307954\pi$
$558$	2.64156	+	4.57531i	0.111826	+	0.193689i
$559$	−16.1258	+	27.9308i	−0.682050	+	1.18135i
$560$	3.71167	+	1.35094i	0.156847	+	0.0570875i
$561$	−8.74422	−	3.18264i	−0.369181	−	0.134371i
$562$	−19.2724	+	33.3808i	−0.812959	+	1.40809i
$563$	20.0988	+	34.8121i	0.847063	+	1.46716i	0.883817	+	0.467832i	$0.154965\pi$
$563$	20.0988	+	34.8121i	0.847063	+	1.46716i	−0.0367543	+	0.999324i	$0.511702\pi$
$564$	−0.621244	−	3.52325i	−0.0261591	−	0.148356i
$565$	4.89827	+	4.11014i	0.206072	+	0.172915i
$566$	−29.2349	+	24.5310i	−1.22883	+	1.03111i
$567$	4.48364	−	25.4280i	0.188295	−	1.06788i
$568$	24.1327	−	8.78358i	1.01259	−	0.368551i
$569$	13.3901			0.561343			0.280671	−	0.959804i	$-0.409443\pi$
$569$	13.3901			0.561343			0.280671	+	0.959804i	$0.409443\pi$
$570$	3.17848	−	4.48346i	0.133132	−	0.187791i
$571$	25.1242			1.05142			0.525708	−	0.850665i	$-0.323800\pi$
$571$	25.1242			1.05142			0.525708	+	0.850665i	$0.323800\pi$
$572$	−0.819078	+	0.298120i	−0.0342474	+	0.0124650i
$573$	1.02465	−	5.81109i	0.0428055	−	0.242762i
$574$	2.87030	−	2.40847i	0.119804	−	0.100528i
$575$	−1.50703	−	1.26454i	−0.0628473	−	0.0527352i
$576$	1.49273	+	8.46567i	0.0621969	+	0.352736i
$577$	−17.8764	−	30.9629i	−0.744206	−	1.28900i	−0.950565	−	0.310527i	$-0.899495\pi$
$577$	−17.8764	−	30.9629i	−0.744206	−	1.28900i	0.206358	−	0.978476i	$-0.433839\pi$
$578$	3.13088	−	5.42285i	0.130228	−	0.225561i
$579$	43.4492	+	15.8142i	1.80569	+	0.657217i
$580$	0.268571	+	0.0977517i	0.0111518	+	0.00405892i
$581$	−16.5646	+	28.6908i	−0.687217	+	1.19030i
$582$	11.0942	+	19.2157i	0.459870	+	0.796518i
$583$	1.43717	+	8.15058i	0.0595214	+	0.337562i
$584$	−30.6080	−	25.6831i	−1.26657	−	1.06278i
$585$	1.69072	−	1.41868i	0.0699028	−	0.0586554i
$586$	0.632008	−	3.58429i	0.0261080	−	0.148066i
$587$	2.14765	−	0.781681i	0.0886431	−	0.0322634i	−0.297318	−	0.954779i	$-0.596092\pi$
$587$	2.14765	−	0.781681i	0.0886431	−	0.0322634i	0.385961	+	0.922515i	$0.373870\pi$
$588$	−0.550756			−0.0227128
$589$	−7.13310	−	15.5329i	−0.293914	−	0.640021i
$590$	2.79511			0.115073
$591$	17.1138	−	6.22892i	0.703968	−	0.256223i
$592$	3.04710	−	17.2810i	0.125235	−	0.710244i
$593$	9.03462	−	7.58094i	0.371007	−	0.311312i	−0.438153	−	0.898901i	$-0.644367\pi$
$593$	9.03462	−	7.58094i	0.371007	−	0.311312i	0.809160	+	0.587589i	$0.199923\pi$
$594$	−4.12836	−	3.46410i	−0.169388	−	0.142134i
$595$	−0.887374	−	5.03255i	−0.0363788	−	0.206314i
$596$	−1.38532	−	2.39944i	−0.0567447	−	0.0982847i
$597$	3.39693	−	5.88365i	0.139027	−	0.240802i
$598$	−2.45723	−	0.894360i	−0.100484	−	0.0365731i
$599$	−43.9889	−	16.0107i	−1.79734	−	0.654178i	−0.998623	−	0.0524690i	$-0.983291\pi$
$599$	−43.9889	−	16.0107i	−1.79734	−	0.654178i	−0.798716	−	0.601709i	$-0.794487\pi$
$600$	−14.0733	+	24.3758i	−0.574542	+	0.995136i
$601$	6.92767	+	11.9991i	0.282586	+	0.489453i	0.972021	−	0.234895i	$-0.0754745\pi$
$601$	6.92767	+	11.9991i	0.282586	+	0.489453i	−0.689435	+	0.724347i	$0.742141\pi$
$602$	−3.75490	−	21.2951i	−0.153038	−	0.867923i
$603$	−3.98680	−	3.34532i	−0.162355	−	0.136232i
$604$	1.08718	−	0.912254i	0.0442368	−	0.0371191i
$605$	−0.0812519	+	0.460802i	−0.00330336	+	0.0187343i
$606$	3.55438	−	1.29369i	0.144387	−	0.0525525i
$607$	−7.68004			−0.311723			−0.155862	−	0.987779i	$-0.549815\pi$
$607$	−7.68004			−0.311723			−0.155862	+	0.987779i	$0.549815\pi$
$608$	−0.369423	−	4.52644i	−0.0149821	−	0.183571i
$609$	−15.5175			−0.628802
$610$	6.07145	−	2.20983i	0.245826	−	0.0894733i
$611$	7.92871	−	44.9660i	0.320761	−	1.81913i
$612$	0.658633	−	0.552659i	0.0266237	−	0.0223399i
$613$	13.6912	+	11.4883i	0.552982	+	0.464007i	0.875949	−	0.482403i	$-0.160236\pi$
$613$	13.6912	+	11.4883i	0.552982	+	0.464007i	−0.322967	+	0.946410i	$0.604680\pi$
$614$	5.10741	+	28.9656i	0.206118	+	1.16896i
$615$	−0.554378	−	0.960210i	−0.0223547	−	0.0387194i
$616$	3.45471	−	5.98373i	0.139194	−	0.241091i
$617$	12.8109	+	4.66280i	0.515748	+	0.187717i	0.586764	−	0.809758i	$-0.300402\pi$
$617$	12.8109	+	4.66280i	0.515748	+	0.187717i	−0.0710153	+	0.997475i	$0.522624\pi$
$618$	8.94356	+	3.25519i	0.359763	+	0.130943i
$619$	−19.8410	+	34.3655i	−0.797475	+	1.38127i	0.123780	+	0.992310i	$0.460498\pi$
$619$	−19.8410	+	34.3655i	−0.797475	+	1.38127i	−0.921255	+	0.388958i	$0.872835\pi$
$620$	−0.169529	−	0.293634i	−0.00680846	−	0.0117926i
$621$	0.285807	+	1.62089i	0.0114690	+	0.0650441i
$622$	12.7445	+	10.6939i	0.511007	+	0.428786i
$623$	−15.7233	+	13.1934i	−0.629940	+	0.528582i
$624$	−5.89124	+	33.4109i	−0.235839	+	1.33751i
$625$	−20.4513	+	7.44367i	−0.818052	+	0.297747i
$626$	37.2012			1.48686
$627$	−6.12836	−	6.20026i	−0.244743	−	0.247615i
$628$	2.47834			0.0988965
$629$	−21.3332	+	7.76466i	−0.850611	+	0.309597i
$630$	−0.256959	+	1.45729i	−0.0102375	+	0.0580598i
$631$	−19.8097	+	16.6223i	−0.788613	+	0.661725i	−0.945402	−	0.325907i	$-0.894330\pi$
$631$	−19.8097	+	16.6223i	−0.788613	+	0.661725i	0.156788	+	0.987632i	$0.449886\pi$
$632$	1.34452	+	1.12819i	0.0534822	+	0.0448769i
$633$	1.88713	+	10.7024i	0.0750065	+	0.425383i
$634$	−12.2934	−	21.2928i	−0.488233	−	0.845644i
$635$	−2.41400	+	4.18117i	−0.0957967	+	0.165925i
$636$	−2.87433	−	1.04617i	−0.113975	−	0.0414834i
$637$	−6.60519	−	2.40409i	−0.261707	−	0.0952536i
$638$	−2.22668	+	3.85673i	−0.0881552	+	0.152689i
$639$	4.36231	+	7.55574i	0.172570	+	0.298901i
$640$	0.771726	+	4.37667i	0.0305051	+	0.173003i
$641$	−2.92674	−	2.45582i	−0.115599	−	0.0969992i	0.583156	−	0.812360i	$-0.301818\pi$
$641$	−2.92674	−	2.45582i	−0.115599	−	0.0969992i	−0.698755	+	0.715361i	$0.746262\pi$
$642$	−13.6864	+	11.4842i	−0.540157	+	0.453246i
$643$	−1.80834	+	10.2556i	−0.0713141	+	0.404443i	0.928165	+	0.372169i	$0.121386\pi$
$643$	−1.80834	+	10.2556i	−0.0713141	+	0.404443i	−0.999479	+	0.0322734i	$0.989725\pi$
$644$	−0.167718	+	0.0610445i	−0.00660903	+	0.00240549i
$645$	−6.39868			−0.251948
$646$	22.4736	−	15.5416i	0.884212	−	0.611477i
$647$	−29.5725			−1.16262			−0.581308	−	0.813683i	$-0.697459\pi$
$647$	−29.5725			−1.16262			−0.581308	+	0.813683i	$0.697459\pi$
$648$	30.4265	−	11.0743i	1.19527	−	0.435041i
$649$	0.769915	−	4.36640i	0.0302218	−	0.171396i
$650$	−23.2753	+	19.5303i	−0.912934	+	0.766043i
$651$	14.1019	+	11.8329i	0.552699	+	0.463769i
$652$	0.145592	+	0.825692i	0.00570182	+	0.0323366i
$653$	3.30019	+	5.71610i	0.129147	+	0.223688i	0.923346	−	0.383969i	$-0.125443\pi$
$653$	3.30019	+	5.71610i	0.129147	+	0.223688i	−0.794200	+	0.607657i	$0.792110\pi$
$654$	25.1780	−	43.6095i	0.984537	−	1.70527i
$655$	3.38666	+	1.23264i	0.132328	+	0.0481634i
$656$	4.00387	+	1.45729i	0.156325	+	0.0568976i
$657$	6.78699	−	11.7554i	0.264786	−	0.458622i
$658$	15.3066	+	26.5118i	0.596713	+	1.03354i
$659$	0.773318	+	4.38571i	0.0301242	+	0.170843i	0.996158	−	0.0875723i	$-0.0279109\pi$
$659$	0.773318	+	4.38571i	0.0301242	+	0.170843i	−0.966034	+	0.258415i	$0.916800\pi$
$660$	−0.132474	−	0.111159i	−0.00515656	−	0.00432686i
$661$	35.1011	−	29.4533i	1.36527	−	1.14560i	0.390959	−	0.920408i	$-0.372143\pi$
$661$	35.1011	−	29.4533i	1.36527	−	1.14560i	0.974314	−	0.225192i	$-0.0723011\pi$
$662$	−6.84137	+	38.7993i	−0.265897	+	1.50798i
$663$	41.2455	−	15.0121i	1.60184	−	0.583022i
$664$	−41.5449			−1.61225
$665$	1.26604	−	4.61706i	0.0490951	−	0.179042i
$666$	6.57398			0.254736
$667$	1.27807	−	0.465178i	0.0494869	−	0.0180118i
$668$	−0.248970	+	1.41198i	−0.00963295	+	0.0546312i
$669$	−1.43788	+	1.20653i	−0.0555917	+	0.0466470i
$670$	−2.51334	−	2.10894i	−0.0970986	−	0.0814754i
$671$	−1.77972	−	10.0933i	−0.0687051	−	0.389646i
$672$	2.44562	+	4.23594i	0.0943419	+	0.163405i
$673$	−5.24644	+	9.08711i	−0.202236	+	0.350282i	−0.949248	−	0.314527i	$-0.898154\pi$
$673$	−5.24644	+	9.08711i	−0.202236	+	0.350282i	0.747013	+	0.664810i	$0.231487\pi$
$674$	16.3751	+	5.96005i	0.630745	+	0.229573i
$675$	17.9709	+	6.54087i	0.691700	+	0.251758i
$676$	0.854570	−	1.48016i	0.0328681	−	0.0569292i
$677$	3.75372	+	6.50163i	0.144267	+	0.249878i	0.929099	−	0.369830i	$-0.120584\pi$
$677$	3.75372	+	6.50163i	0.144267	+	0.249878i	−0.784832	+	0.619708i	$0.787251\pi$
$678$	−6.39424	−	36.2635i	−0.245569	−	1.39269i
$679$	14.8066	+	12.4242i	0.568225	+	0.476797i
$680$	4.90903	−	4.11917i	0.188253	−	0.157963i
$681$	6.91178	−	39.1986i	0.264860	−	1.50210i
$682$	4.96451	−	1.80693i	0.190101	−	0.0691910i
$683$	−45.0337			−1.72316			−0.861582	−	0.507618i	$-0.830526\pi$
$683$	−45.0337			−1.72316			−0.861582	+	0.507618i	$0.830526\pi$
$684$	0.779248	−	0.203935i	0.0297953	−	0.00779766i
$685$	−7.28405			−0.278309
$686$	25.2310	−	9.18334i	0.963325	−	0.350622i
$687$	−7.69047	+	43.6148i	−0.293410	+	1.66401i
$688$	18.8366	−	15.8058i	0.718139	−	0.602590i
$689$	−29.9051	−	25.0934i	−1.13929	−	0.955982i
$690$	−0.0900885	−	0.510917i	−0.00342961	−	0.0194503i
$691$	3.36113	+	5.82165i	0.127863	+	0.221466i	0.922849	−	0.385163i	$-0.125855\pi$
$691$	3.36113	+	5.82165i	0.127863	+	0.221466i	−0.794985	+	0.606629i	$0.792521\pi$
$692$	1.20258	−	2.08293i	0.0457153	−	0.0791812i
$693$	2.20574	+	0.802823i	0.0837890	+	0.0304967i
$694$	41.3289	+	15.0425i	1.56882	+	0.571006i
$695$	−4.36050	+	7.55261i	−0.165403	+	0.286487i
$696$	−9.72967	−	16.8523i	−0.368802	−	0.638784i
$697$	−0.957234	−	5.42874i	−0.0362578	−	0.205628i
$698$	−18.9360	−	15.8892i	−0.716740	−	0.601416i
$699$	−29.8699	+	25.0638i	−1.12978	+	0.948000i
$700$	−0.360120	+	2.04234i	−0.0136112	+	0.0771932i
$701$	15.3268	−	5.57851i	0.578886	−	0.210697i	−0.0359482	−	0.999354i	$-0.511445\pi$
$701$	15.3268	−	5.57851i	0.578886	−	0.210697i	0.614834	+	0.788656i	$0.289223\pi$
$702$	25.4201			0.959422
$703$	−21.1766	−	1.97724i	−0.798692	−	0.0745730i
$704$	8.59627			0.323984
$705$	8.51249	−	3.09829i	0.320599	−	0.116688i
$706$	2.42484	−	13.7520i	0.0912601	−	0.517562i
$707$	2.52410	−	2.11797i	0.0949285	−	0.0796545i
$708$	1.25528	+	1.05331i	0.0471763	+	0.0395856i
$709$	−6.93077	−	39.3063i	−0.260291	−	1.47618i	−0.782118	−	0.623130i	$-0.785861\pi$
$709$	−6.93077	−	39.3063i	−0.260291	−	1.47618i	0.521828	−	0.853051i	$-0.325250\pi$
$710$	2.75007	+	4.76325i	0.103208	+	0.178762i
$711$	−0.298133	+	0.516382i	−0.0111809	+	0.0193658i
$712$	−24.1869	−	8.80331i	−0.906443	−	0.329918i
$713$	−1.51620	−	0.551851i	−0.0567820	−	0.0206670i
$714$	−14.7142	+	25.4857i	−0.550665	+	0.953779i
$715$	−1.10354	−	1.91139i	−0.0412701	−	0.0714819i
$716$	0.347458	+	1.97053i	0.0129851	+	0.0736423i
$717$	0.172933	+	0.145108i	0.00645830	+	0.00541916i
$718$	12.9394	−	10.8575i	0.482896	−	0.405198i
$719$	−7.82501	+	44.3778i	−0.291824	+	1.65501i	0.388016	+	0.921653i	$0.373161\pi$
$719$	−7.82501	+	44.3778i	−0.291824	+	1.65501i	−0.679840	+	0.733361i	$0.737951\pi$
$720$	−1.58125	+	0.575529i	−0.0589298	+	0.0214487i
$721$	8.29086			0.308768
$722$	25.2599	−	4.15079i	0.940075	−	0.154476i
$723$	−37.9162			−1.41012
$724$	2.55216	−	0.928909i	0.0948501	−	0.0345226i
$725$	2.74422	−	15.5633i	0.101918	−	0.578005i
$726$	2.06418	−	1.73205i	0.0766088	−	0.0642824i
$727$	−27.1306	−	22.7653i	−1.00622	−	0.844318i	−0.0183856	−	0.999831i	$-0.505853\pi$
$727$	−27.1306	−	22.7653i	−1.00622	−	0.844318i	−0.987834	+	0.155513i	$0.950297\pi$
$728$	5.65935	+	32.0958i	0.209749	+	1.18955i
$729$	−6.50000	−	11.2583i	−0.240741	−	0.416975i
$730$	4.27862	−	7.41079i	0.158359	−	0.274285i
$731$	−29.8943	−	10.8806i	−1.10568	−	0.402435i
$732$	3.55943	+	1.29553i	0.131560	+	0.0478840i
$733$	−8.55422	+	14.8163i	−0.315957	+	0.547254i	−0.979640	−	0.200760i	$-0.935659\pi$
$733$	−8.55422	+	14.8163i	−0.315957	+	0.547254i	0.663683	+	0.748014i	$0.268992\pi$
$734$	1.54845	+	2.68199i	0.0571543	+	0.0989941i
$735$	−0.242163	−	1.37338i	−0.00893232	−	0.0506577i
$736$	−0.328411	−	0.275570i	−0.0121054	−	0.0101576i
$737$	−3.98680	+	3.34532i	−0.146856	+	0.123226i
$738$	−0.277189	+	1.57202i	−0.0102035	+	0.0578667i
$739$	5.33244	−	1.94085i	0.196157	−	0.0713954i	−0.242074	−	0.970258i	$-0.577828\pi$
$739$	5.33244	−	1.94085i	0.196157	−	0.0713954i	0.438231	+	0.898863i	$0.355605\pi$
$740$	−0.421903			−0.0155095
$741$	40.9427	+	3.82278i	1.50407	+	0.140433i
$742$	26.1739			0.960873
$743$	30.8323	−	11.2221i	1.13113	−	0.411697i	0.292427	−	0.956288i	$-0.405537\pi$
$743$	30.8323	−	11.2221i	1.13113	−	0.411697i	0.838702	+	0.544591i	$0.183315\pi$
$744$	−4.00867	+	22.7343i	−0.146965	+	0.833481i
$745$	5.37417	−	4.50946i	0.196894	−	0.165214i
$746$	−1.94066	−	1.62840i	−0.0710525	−	0.0596201i
$747$	−2.45084	−	13.8994i	−0.0896714	−	0.508552i
$748$	−0.429892	−	0.744596i	−0.0157184	−	0.0272251i
$749$	−7.78177	+	13.4784i	−0.284340	+	0.492491i
$750$	−11.5885	−	4.21788i	−0.423153	−	0.154015i
$751$	−16.7015	−	6.07883i	−0.609445	−	0.221820i	0.0188155	−	0.999823i	$-0.494010\pi$
$751$	−16.7015	−	6.07883i	−0.609445	−	0.221820i	−0.628260	+	0.778003i	$0.716233\pi$
$752$	−17.4060	+	30.1481i	−0.634732	+	1.09939i
$753$	4.97771	+	8.62165i	0.181398	+	0.314190i
$754$	−3.64765	−	20.6869i	−0.132840	−	0.753371i
$755$	2.75284	+	2.30991i	0.100186	+	0.0840661i
$756$	1.32913	−	1.11527i	0.0483399	−	0.0405620i
$757$	5.05762	−	28.6832i	0.183822	−	1.04251i	−0.743637	−	0.668584i	$-0.766901\pi$
$757$	5.05762	−	28.6832i	0.183822	−	1.04251i	0.927459	−	0.373924i	$-0.121988\pi$
$758$	−11.1823	+	4.07001i	−0.406158	+	0.147829i
$759$	−0.822948			−0.0298711
$760$	5.80802	−	1.52000i	0.210679	−	0.0551363i
$761$	−31.9513			−1.15823			−0.579117	−	0.815244i	$-0.696603\pi$
$761$	−31.9513			−1.15823			−0.579117	+	0.815244i	$0.696603\pi$
$762$	26.1266	−	9.50931i	0.946467	−	0.344486i
$763$	7.61721	−	43.1994i	0.275762	−	1.56392i

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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.j (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26604 - 0.460802i) q^{2} +(-0.347296 + 1.96962i) q^{3} +(-0.141559 + 0.118782i) q^{4} +(-0.358441 - 0.300767i) q^{5} +(0.467911 + 2.65366i) q^{6} +(1.17365 + 2.03282i) q^{7} +(-1.47178 + 2.54920i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})\)	\(q+(1.26604 - 0.460802i) q^{2} +(-0.347296 + 1.96962i) q^{3} +(-0.141559 + 0.118782i) q^{4} +(-0.358441 - 0.300767i) q^{5} +(0.467911 + 2.65366i) q^{6} +(1.17365 + 2.03282i) q^{7} +(-1.47178 + 2.54920i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(-0.592396 - 0.215615i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.184793 - 0.320070i) q^{12} +(-0.819078 - 4.64522i) q^{13} +(2.42262 + 2.03282i) q^{14} +(0.716881 - 0.601535i) q^{15} +(-0.624485 + 3.54163i) q^{16} +(4.37211 - 1.59132i) q^{17} -1.34730 q^{18} +(4.34002 + 0.405223i) q^{19} +0.0864665 q^{20} +(-4.41147 + 1.60565i) q^{21} +(-0.233956 + 1.32683i) q^{22} +(0.315207 - 0.264490i) q^{23} +(-4.50980 - 3.78417i) q^{24} +(-0.830222 - 4.70842i) q^{25} +(-3.17752 - 5.50362i) q^{26} +(-2.00000 + 3.46410i) q^{27} +(-0.407604 - 0.148356i) q^{28} +(3.10607 + 1.13052i) q^{29} +(0.630415 - 1.09191i) q^{30} +(-1.96064 - 3.39592i) q^{31} +(-0.180922 - 1.02606i) q^{32} +(-1.53209 - 1.28558i) q^{33} +(4.80200 - 4.02936i) q^{34} +(0.190722 - 1.08164i) q^{35} +(0.173648 - 0.0632028i) q^{36} -4.87939 q^{37} +(5.68139 - 1.48686i) q^{38} +9.43376 q^{39} +(1.29426 - 0.471073i) q^{40} +(0.205737 - 1.16679i) q^{41} +(-4.84524 + 4.06564i) q^{42} +(-5.23783 - 4.39506i) q^{43} +(-0.0320889 - 0.181985i) q^{44} +(0.233956 + 0.405223i) q^{45} +(0.277189 - 0.480105i) q^{46} +(9.09627 + 3.31077i) q^{47} +(-6.75877 - 2.45999i) q^{48} +(0.745100 - 1.29055i) q^{49} +(-3.22075 - 5.57851i) q^{50} +(1.61587 + 9.16404i) q^{51} +(0.667718 + 0.560282i) q^{52} +(6.34002 - 5.31991i) q^{53} +(-0.935822 + 5.30731i) q^{54} +(0.439693 - 0.160035i) q^{55} -6.90941 q^{56} +(-2.30541 + 8.40744i) q^{57} +4.45336 q^{58} +(-4.16637 + 1.51644i) q^{59} +(-0.0300295 + 0.170306i) q^{60} +(-7.85117 + 6.58791i) q^{61} +(-4.04710 - 3.39592i) q^{62} +(-0.407604 - 2.31164i) q^{63} +(-4.29813 - 7.44459i) q^{64} +(-1.10354 + 1.91139i) q^{65} +(-2.53209 - 0.921605i) q^{66} +(4.89053 + 1.78001i) q^{67} +(-0.429892 + 0.744596i) q^{68} +(0.411474 + 0.712694i) q^{69} +(-0.256959 - 1.45729i) q^{70} +(-6.68345 - 5.60808i) q^{71} +(2.25490 - 1.89209i) q^{72} +(-2.35710 + 13.3678i) q^{73} +(-6.17752 + 2.24843i) q^{74} +9.56212 q^{75} +(-0.662504 + 0.458155i) q^{76} -2.34730 q^{77} +(11.9436 - 4.34710i) q^{78} +(0.103541 - 0.587208i) q^{79} +(1.28905 - 1.08164i) q^{80} +(-8.42649 - 7.07066i) q^{81} +(-0.277189 - 1.57202i) q^{82} +(7.05690 + 12.2229i) q^{83} +(0.433763 - 0.751299i) q^{84} +(-2.04576 - 0.744596i) q^{85} +(-8.65657 - 3.15074i) q^{86} +(-3.30541 + 5.72513i) q^{87} +(-1.47178 - 2.54920i) q^{88} +(1.51842 + 8.61138i) q^{89} +(0.482926 + 0.405223i) q^{90} +(8.48158 - 7.11689i) q^{91} +(-0.0132037 + 0.0748822i) q^{92} +(7.36959 - 2.68231i) q^{93} +13.0419 q^{94} +(-1.43376 - 1.45059i) q^{95} +2.08378 q^{96} +(7.73783 - 2.81634i) q^{97} +(0.348641 - 1.97724i) q^{98} +(0.766044 - 0.642788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 12 q^{6} + 6 q^{7} + 6 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 12 * q^6 + 6 * q^7 + 6 * q^8	\( 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 12 q^{6} + 6 q^{7} + 6 q^{8} - 3 q^{11} + 6 q^{12} + 12 q^{13} - 12 q^{14} - 12 q^{15} + 9 q^{16} - 3 q^{17} - 6 q^{18} + 6 q^{19} - 30 q^{20} - 6 q^{21} - 6 q^{22} + 9 q^{23} - 30 q^{24} + 18 q^{25} + 6 q^{26} - 12 q^{27} - 6 q^{28} - 6 q^{29} + 18 q^{30} - 3 q^{31} - 18 q^{32} - 9 q^{34} + 21 q^{35} - 18 q^{37} - 15 q^{38} + 24 q^{39} + 18 q^{40} - 9 q^{41} + 24 q^{42} - 12 q^{43} + 9 q^{44} + 6 q^{45} - 9 q^{46} + 27 q^{47} - 18 q^{48} + 3 q^{49} + 21 q^{50} - 12 q^{51} - 24 q^{52} + 18 q^{53} - 24 q^{54} - 3 q^{55} + 30 q^{56} - 18 q^{57} - 6 q^{59} + 60 q^{60} - 21 q^{61} + 15 q^{62} - 6 q^{63} - 12 q^{64} + 3 q^{65} - 6 q^{66} + 12 q^{67} + 6 q^{68} - 18 q^{69} - 54 q^{70} - 42 q^{71} + 15 q^{72} - 15 q^{73} - 12 q^{74} - 12 q^{75} - 9 q^{76} - 12 q^{77} + 42 q^{78} - 9 q^{79} + 51 q^{80} + 9 q^{82} + 6 q^{83} - 30 q^{84} + 18 q^{85} - 30 q^{86} - 24 q^{87} + 6 q^{88} + 21 q^{89} - 18 q^{90} + 39 q^{91} - 45 q^{92} + 30 q^{93} + 72 q^{94} + 24 q^{95} + 27 q^{97} - 9 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 12 * q^6 + 6 * q^7 + 6 * q^8 - 3 * q^11 + 6 * q^12 + 12 * q^13 - 12 * q^14 - 12 * q^15 + 9 * q^16 - 3 * q^17 - 6 * q^18 + 6 * q^19 - 30 * q^20 - 6 * q^21 - 6 * q^22 + 9 * q^23 - 30 * q^24 + 18 * q^25 + 6 * q^26 - 12 * q^27 - 6 * q^28 - 6 * q^29 + 18 * q^30 - 3 * q^31 - 18 * q^32 - 9 * q^34 + 21 * q^35 - 18 * q^37 - 15 * q^38 + 24 * q^39 + 18 * q^40 - 9 * q^41 + 24 * q^42 - 12 * q^43 + 9 * q^44 + 6 * q^45 - 9 * q^46 + 27 * q^47 - 18 * q^48 + 3 * q^49 + 21 * q^50 - 12 * q^51 - 24 * q^52 + 18 * q^53 - 24 * q^54 - 3 * q^55 + 30 * q^56 - 18 * q^57 - 6 * q^59 + 60 * q^60 - 21 * q^61 + 15 * q^62 - 6 * q^63 - 12 * q^64 + 3 * q^65 - 6 * q^66 + 12 * q^67 + 6 * q^68 - 18 * q^69 - 54 * q^70 - 42 * q^71 + 15 * q^72 - 15 * q^73 - 12 * q^74 - 12 * q^75 - 9 * q^76 - 12 * q^77 + 42 * q^78 - 9 * q^79 + 51 * q^80 + 9 * q^82 + 6 * q^83 - 30 * q^84 + 18 * q^85 - 30 * q^86 - 24 * q^87 + 6 * q^88 + 21 * q^89 - 18 * q^90 + 39 * q^91 - 45 * q^92 + 30 * q^93 + 72 * q^94 + 24 * q^95 + 27 * q^97 - 9 * q^98

Introduction

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