LMFDB - Embedded newform 138.2.e.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(13,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("138.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.e (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:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			13.1
Root			$0.654861 + 0.755750i$ of defining polynomial
Character	$\chi$	$=$	138.13
Dual form			138.2.e.a.85.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 - 0.755750i) q^{2} +(0.841254 + 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-0.614354 + 1.34525i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(3.07385 + 0.902563i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.654861 - 0.755750i) q^{2} +(0.841254 + 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-0.614354 + 1.34525i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(3.07385 + 0.902563i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +(1.41899 - 0.416652i) q^{10} +(-0.0362090 + 0.0417874i) q^{11} +(-0.654861 + 0.755750i) q^{12} +(0.773100 - 0.227003i) q^{13} +(-1.33083 - 2.91411i) q^{14} +(-1.24412 + 0.799549i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(-0.293103 - 2.03857i) q^{17} +(0.415415 - 0.909632i) q^{18} +(0.523231 - 3.63915i) q^{19} +(-1.24412 - 0.799549i) q^{20} +(2.09792 + 2.42113i) q^{21} +0.0552927 q^{22} +(-4.62936 + 1.25259i) q^{23} +1.00000 q^{24} +(1.84204 + 2.12583i) q^{25} +(-0.677830 - 0.435615i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(-1.33083 + 2.91411i) q^{28} +(-1.04541 - 7.27098i) q^{29} +(1.41899 + 0.416652i) q^{30} +(-6.69256 + 4.30105i) q^{31} +(0.415415 + 0.909632i) q^{32} +(-0.0530529 + 0.0155777i) q^{33} +(-1.34871 + 1.55649i) q^{34} +(-3.10260 + 3.58059i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-1.28287 - 2.80909i) q^{37} +(-3.09293 + 1.98771i) q^{38} +(0.773100 + 0.227003i) q^{39} +(0.210468 + 1.46384i) q^{40} +(-0.606395 + 1.32782i) q^{41} +(0.455922 - 3.17101i) q^{42} +(-10.5428 - 6.77544i) q^{43} +(-0.0362090 - 0.0417874i) q^{44} -1.47889 q^{45} +(3.97823 + 2.67837i) q^{46} -1.27459 q^{47} +(-0.654861 - 0.755750i) q^{48} +(2.74514 + 1.76419i) q^{49} +(0.400315 - 2.78425i) q^{50} +(0.855563 - 1.87342i) q^{51} +(0.114669 + 0.797537i) q^{52} +(10.5975 + 3.11170i) q^{53} +(0.841254 - 0.540641i) q^{54} +(-0.0339693 - 0.0743823i) q^{55} +(3.07385 - 0.902563i) q^{56} +(2.40764 - 2.77857i) q^{57} +(-4.81044 + 5.55155i) q^{58} +(5.14362 - 1.51030i) q^{59} +(-0.614354 - 1.34525i) q^{60} +(10.2645 - 6.59662i) q^{61} +(7.63321 + 2.24131i) q^{62} +(0.455922 + 3.17101i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.169582 + 1.17947i) q^{65} +(0.0465151 + 0.0298935i) q^{66} +(-2.96073 - 3.41687i) q^{67} +2.05954 q^{68} +(-4.57167 - 1.44908i) q^{69} +4.73780 q^{70} +(9.56286 + 11.0361i) q^{71} +(0.841254 + 0.540641i) q^{72} +(1.40345 - 9.76122i) q^{73} +(-1.28287 + 2.80909i) q^{74} +(0.400315 + 2.78425i) q^{75} +(3.52765 + 1.03581i) q^{76} +(-0.149017 + 0.0957672i) q^{77} +(-0.334716 - 0.732925i) q^{78} +(-3.47320 + 1.01982i) q^{79} +(0.968468 - 1.11767i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(1.40060 - 0.411254i) q^{82} +(-4.16838 - 9.12749i) q^{83} +(-2.69505 + 1.73201i) q^{84} +(2.92245 + 0.858110i) q^{85} +(1.78352 + 12.4047i) q^{86} +(3.05153 - 6.68193i) q^{87} +(-0.00786897 + 0.0547299i) q^{88} +(-6.94243 - 4.46163i) q^{89} +(0.968468 + 1.11767i) q^{90} +2.58128 q^{91} +(-0.581014 - 4.76051i) q^{92} -7.95546 q^{93} +(0.834679 + 0.963271i) q^{94} +(4.57411 + 2.93960i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(2.91463 - 6.38215i) q^{97} +(-0.464395 - 3.22994i) q^{98} +(-0.0530529 - 0.0155777i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{3} - q^{4} + 8 q^{5} - q^{6} + 8 q^{7} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 - q^3 - q^4 + 8 * q^5 - q^6 + 8 * q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} + 8 q^{5} - q^{6} + 8 q^{7} - q^{8} - q^{9} - 3 q^{10} + 7 q^{11} - q^{12} + 3 q^{13} - 3 q^{14} - 3 q^{15} - q^{16} + 4 q^{17} - q^{18} - 3 q^{20} - 3 q^{21} - 26 q^{22} - 12 q^{23} + 10 q^{24} - 15 q^{25} + 3 q^{26} - q^{27} - 3 q^{28} - 25 q^{29} - 3 q^{30} + 6 q^{31} - q^{32} - 4 q^{33} - 7 q^{34} + 2 q^{35} - q^{36} + 9 q^{37} + 11 q^{38} + 3 q^{39} - 3 q^{40} + 24 q^{41} + 8 q^{42} - 30 q^{43} + 7 q^{44} - 14 q^{45} + 21 q^{46} - 48 q^{47} - q^{48} + 9 q^{49} + 7 q^{50} + 15 q^{51} + 14 q^{52} + 15 q^{53} - q^{54} - 23 q^{55} + 8 q^{56} - 11 q^{57} - 3 q^{58} + 5 q^{59} + 8 q^{60} + 12 q^{61} + 28 q^{62} + 8 q^{63} - q^{64} - 13 q^{65} + 18 q^{66} + 18 q^{67} - 18 q^{68} - q^{69} + 2 q^{70} + 28 q^{71} - q^{72} + 19 q^{73} + 9 q^{74} + 7 q^{75} + 22 q^{76} - 12 q^{77} - 8 q^{78} - 52 q^{79} + 8 q^{80} - q^{81} - 20 q^{82} + 7 q^{83} - 3 q^{84} + 23 q^{85} + 14 q^{86} + 30 q^{87} - 4 q^{88} + 3 q^{89} + 8 q^{90} + 42 q^{91} - 23 q^{92} - 16 q^{93} + 29 q^{94} + 22 q^{95} - q^{96} + 51 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 + 8 * q^5 - q^6 + 8 * q^7 - q^8 - q^9 - 3 * q^10 + 7 * q^11 - q^12 + 3 * q^13 - 3 * q^14 - 3 * q^15 - q^16 + 4 * q^17 - q^18 - 3 * q^20 - 3 * q^21 - 26 * q^22 - 12 * q^23 + 10 * q^24 - 15 * q^25 + 3 * q^26 - q^27 - 3 * q^28 - 25 * q^29 - 3 * q^30 + 6 * q^31 - q^32 - 4 * q^33 - 7 * q^34 + 2 * q^35 - q^36 + 9 * q^37 + 11 * q^38 + 3 * q^39 - 3 * q^40 + 24 * q^41 + 8 * q^42 - 30 * q^43 + 7 * q^44 - 14 * q^45 + 21 * q^46 - 48 * q^47 - q^48 + 9 * q^49 + 7 * q^50 + 15 * q^51 + 14 * q^52 + 15 * q^53 - q^54 - 23 * q^55 + 8 * q^56 - 11 * q^57 - 3 * q^58 + 5 * q^59 + 8 * q^60 + 12 * q^61 + 28 * q^62 + 8 * q^63 - q^64 - 13 * q^65 + 18 * q^66 + 18 * q^67 - 18 * q^68 - q^69 + 2 * q^70 + 28 * q^71 - q^72 + 19 * q^73 + 9 * q^74 + 7 * q^75 + 22 * q^76 - 12 * q^77 - 8 * q^78 - 52 * q^79 + 8 * q^80 - q^81 - 20 * q^82 + 7 * q^83 - 3 * q^84 + 23 * q^85 + 14 * q^86 + 30 * q^87 - 4 * q^88 + 3 * q^89 + 8 * q^90 + 42 * q^91 - 23 * q^92 - 16 * q^93 + 29 * q^94 + 22 * q^95 - q^96 + 51 * q^97 - 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{7}{11}\right)$

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 $

$2$	−0.654861	−	0.755750i	−0.463056	−	0.534396i
$2$	−0.654861	−	0.755750i	−0.463056	−	0.534396i
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$4$	−0.142315	+	0.989821i	−0.0711574	+	0.494911i
$5$	−0.614354	+	1.34525i	−0.274747	+	0.601613i	−0.995829	−	0.0912371i	$-0.970918\pi$
$5$	−0.614354	+	1.34525i	−0.274747	+	0.601613i	0.721082	+	0.692850i	$0.243645\pi$
$6$	−0.142315	−	0.989821i	−0.0580998	−	0.404093i
$7$	3.07385	+	0.902563i	1.16180	+	0.341137i	0.805134	−	0.593093i	$-0.202093\pi$
$7$	3.07385	+	0.902563i	1.16180	+	0.341137i	0.356671	+	0.934230i	$0.383912\pi$
$8$	0.841254	−	0.540641i	0.297428	−	0.191145i
$9$	0.415415	+	0.909632i	0.138472	+	0.303211i
$10$	1.41899	−	0.416652i	0.448723	−	0.131757i
$11$	−0.0362090	+	0.0417874i	−0.0109174	+	0.0125994i	−0.761182	−	0.648538i	$-0.775381\pi$
$11$	−0.0362090	+	0.0417874i	−0.0109174	+	0.0125994i	0.750265	+	0.661138i	$0.229926\pi$
$12$	−0.654861	+	0.755750i	−0.189042	+	0.218166i
$13$	0.773100	−	0.227003i	0.214419	−	0.0629592i	−0.172759	−	0.984964i	$-0.555268\pi$
$13$	0.773100	−	0.227003i	0.214419	−	0.0629592i	0.387178	+	0.922005i	$0.373450\pi$
$14$	−1.33083	−	2.91411i	−0.355679	−	0.778829i
$15$	−1.24412	+	0.799549i	−0.321231	+	0.206443i
$16$	−0.959493	−	0.281733i	−0.239873	−	0.0704331i
$17$	−0.293103	−	2.03857i	−0.0710879	−	0.494427i	−0.993997	−	0.109409i	$-0.965104\pi$
$17$	−0.293103	−	2.03857i	−0.0710879	−	0.494427i	0.922909	−	0.385018i	$-0.125805\pi$
$18$	0.415415	−	0.909632i	0.0979143	−	0.214402i
$19$	0.523231	−	3.63915i	0.120037	−	0.834879i	−0.837473	−	0.546479i	$-0.815968\pi$
$19$	0.523231	−	3.63915i	0.120037	−	0.834879i	0.957510	−	0.288399i	$-0.0931231\pi$
$20$	−1.24412	−	0.799549i	−0.278194	−	0.178785i
$21$	2.09792	+	2.42113i	0.457804	+	0.528334i
$22$	0.0552927			0.0117884
$23$	−4.62936	+	1.25259i	−0.965289	+	0.261183i
$23$	−4.62936	+	1.25259i	−0.965289	+	0.261183i
$24$	1.00000			0.204124
$25$	1.84204	+	2.12583i	0.368409	+	0.425167i
$26$	−0.677830	−	0.435615i	−0.132933	−	0.0854311i
$27$	−0.142315	+	0.989821i	−0.0273885	+	0.190491i
$28$	−1.33083	+	2.91411i	−0.251503	+	0.550715i
$29$	−1.04541	−	7.27098i	−0.194128	−	1.35019i	−0.820939	−	0.571016i	$-0.806549\pi$
$29$	−1.04541	−	7.27098i	−0.194128	−	1.35019i	0.626811	−	0.779171i	$-0.284360\pi$
$30$	1.41899	+	0.416652i	0.259070	+	0.0760699i
$31$	−6.69256	+	4.30105i	−1.20202	+	0.772491i	−0.979305	−	0.202392i	$-0.935128\pi$
$31$	−6.69256	+	4.30105i	−1.20202	+	0.772491i	−0.222715	+	0.974884i	$0.571492\pi$
$32$	0.415415	+	0.909632i	0.0734357	+	0.160802i
$33$	−0.0530529	+	0.0155777i	−0.00923533	+	0.00271174i
$34$	−1.34871	+	1.55649i	−0.231302	+	0.266937i
$35$	−3.10260	+	3.58059i	−0.524435	+	0.605230i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	−1.28287	−	2.80909i	−0.210902	−	0.461811i	0.774386	−	0.632713i	$-0.218059\pi$
$37$	−1.28287	−	2.80909i	−0.210902	−	0.461811i	−0.985288	+	0.170903i	$0.945332\pi$
$38$	−3.09293	+	1.98771i	−0.501740	+	0.322448i
$39$	0.773100	+	0.227003i	0.123795	+	0.0363495i
$40$	0.210468	+	1.46384i	0.0332779	+	0.231453i
$41$	−0.606395	+	1.32782i	−0.0947030	+	0.207371i	−0.951055	−	0.309022i	$-0.899998\pi$
$41$	−0.606395	+	1.32782i	−0.0947030	+	0.207371i	0.856352	+	0.516393i	$0.172726\pi$
$42$	0.455922	−	3.17101i	0.0703503	−	0.489297i
$43$	−10.5428	−	6.77544i	−1.60776	−	1.03324i	−0.963234	−	0.268663i	$-0.913418\pi$
$43$	−10.5428	−	6.77544i	−1.60776	−	1.03324i	−0.644526	−	0.764582i	$-0.722945\pi$
$44$	−0.0362090	−	0.0417874i	−0.00545871	−	0.00629969i
$45$	−1.47889			−0.220460
$46$	3.97823	+	2.67837i	0.586559	+	0.394904i
$47$	−1.27459			−0.185918			−0.0929591	−	0.995670i	$-0.529633\pi$
$47$	−1.27459			−0.185918			−0.0929591	+	0.995670i	$0.529633\pi$
$48$	−0.654861	−	0.755750i	−0.0945210	−	0.109083i
$49$	2.74514	+	1.76419i	0.392163	+	0.252028i
$50$	0.400315	−	2.78425i	0.0566130	−	0.393752i
$51$	0.855563	−	1.87342i	0.119803	−	0.262331i
$52$	0.114669	+	0.797537i	0.0159017	+	0.110598i
$53$	10.5975	+	3.11170i	1.45567	+	0.427424i	0.911413	−	0.411492i	$-0.134992\pi$
$53$	10.5975	+	3.11170i	1.45567	+	0.427424i	0.544260	+	0.838916i	$0.316810\pi$
$54$	0.841254	−	0.540641i	0.114480	−	0.0735719i
$55$	−0.0339693	−	0.0743823i	−0.00458041	−	0.0100297i
$56$	3.07385	−	0.902563i	0.410760	−	0.120610i
$57$	2.40764	−	2.77857i	0.318900	−	0.368030i
$58$	−4.81044	+	5.55155i	−0.631642	+	0.728954i
$59$	5.14362	−	1.51030i	0.669642	−	0.196625i	0.0707986	−	0.997491i	$-0.477445\pi$
$59$	5.14362	−	1.51030i	0.669642	−	0.196625i	0.598844	+	0.800866i	$0.295627\pi$
$60$	−0.614354	−	1.34525i	−0.0793127	−	0.173671i
$61$	10.2645	−	6.59662i	1.31424	−	0.844611i	0.319555	−	0.947568i	$-0.396467\pi$
$61$	10.2645	−	6.59662i	1.31424	−	0.844611i	0.994686	+	0.102957i	$0.0328303\pi$
$62$	7.63321	+	2.24131i	0.969419	+	0.284647i
$63$	0.455922	+	3.17101i	0.0574408	+	0.399509i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	−0.169582	+	1.17947i	−0.0210341	+	0.146295i
$66$	0.0465151	+	0.0298935i	0.00572562	+	0.00367963i
$67$	−2.96073	−	3.41687i	−0.361711	−	0.417437i	0.545501	−	0.838110i	$-0.316339\pi$
$67$	−2.96073	−	3.41687i	−0.361711	−	0.417437i	−0.907212	+	0.420673i	$0.861794\pi$
$68$	2.05954			0.249756
$69$	−4.57167	−	1.44908i	−0.550365	−	0.174448i
$70$	4.73780			0.566275
$71$	9.56286	+	11.0361i	1.13490	+	1.30975i	0.944675	+	0.328008i	$0.106377\pi$
$71$	9.56286	+	11.0361i	1.13490	+	1.30975i	0.190228	+	0.981740i	$0.439077\pi$
$72$	0.841254	+	0.540641i	0.0991427	+	0.0637151i
$73$	1.40345	−	9.76122i	0.164262	−	1.14246i	−0.726226	−	0.687456i	$-0.758727\pi$
$73$	1.40345	−	9.76122i	0.164262	−	1.14246i	0.890487	−	0.455008i	$-0.150364\pi$
$74$	−1.28287	+	2.80909i	−0.149130	+	0.326550i
$75$	0.400315	+	2.78425i	0.0462243	+	0.321497i
$76$	3.52765	+	1.03581i	0.404649	+	0.118816i
$77$	−0.149017	+	0.0957672i	−0.0169820	+	0.0109137i
$78$	−0.334716	−	0.732925i	−0.0378991	−	0.0829874i
$79$	−3.47320	+	1.01982i	−0.390765	+	0.114739i	−0.471212	−	0.882020i	$-0.656183\pi$
$79$	−3.47320	+	1.01982i	−0.390765	+	0.114739i	0.0804469	+	0.996759i	$0.474365\pi$
$80$	0.968468	−	1.11767i	0.108278	−	0.124959i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	1.40060	−	0.411254i	0.154671	−	0.0454155i
$83$	−4.16838	−	9.12749i	−0.457540	−	1.00187i	−0.988041	−	0.154188i	$-0.950724\pi$
$83$	−4.16838	−	9.12749i	−0.457540	−	1.00187i	0.530502	−	0.847684i	$-0.322004\pi$
$84$	−2.69505	+	1.73201i	−0.294054	+	0.188977i
$85$	2.92245	+	0.858110i	0.316985	+	0.0930751i
$86$	1.78352	+	12.4047i	0.192322	+	1.33763i
$87$	3.05153	−	6.68193i	0.327159	−	0.716378i
$88$	−0.00786897	+	0.0547299i	−0.000838835	+	0.00583422i
$89$	−6.94243	−	4.46163i	−0.735896	−	0.472932i	0.118237	−	0.992985i	$-0.462276\pi$
$89$	−6.94243	−	4.46163i	−0.735896	−	0.472932i	−0.854134	+	0.520054i	$0.825912\pi$
$90$	0.968468	+	1.11767i	0.102085	+	0.117813i
$91$	2.58128			0.270591
$92$	−0.581014	−	4.76051i	−0.0605749	−	0.496317i
$93$	−7.95546			−0.824943
$94$	0.834679	+	0.963271i	0.0860906	+	0.0993539i
$95$	4.57411	+	2.93960i	0.469294	+	0.301597i
$96$	−0.142315	+	0.989821i	−0.0145249	+	0.101023i
$97$	2.91463	−	6.38215i	0.295936	−	0.648009i	−0.702004	−	0.712173i	$-0.747711\pi$
$97$	2.91463	−	6.38215i	0.295936	−	0.648009i	0.997939	+	0.0641646i	$0.0204383\pi$
$98$	−0.464395	−	3.22994i	−0.0469110	−	0.326273i
$99$	−0.0530529	−	0.0155777i	−0.00533202	−	0.00156562i
$100$	−2.36635	+	1.52076i	−0.236635	+	0.152076i
$101$	6.37690	+	13.9635i	0.634526	+	1.38942i	0.904468	+	0.426541i	$0.140268\pi$
$101$	6.37690	+	13.9635i	0.634526	+	1.38942i	−0.269943	+	0.962876i	$0.587005\pi$
$102$	−1.97611	+	0.580239i	−0.195664	+	0.0574522i
$103$	−10.0337	+	11.5795i	−0.988648	+	1.14096i	0.00136697	+	0.999999i	$0.499565\pi$
$103$	−10.0337	+	11.5795i	−0.988648	+	1.14096i	−0.990015	+	0.140962i	$0.954981\pi$
$104$	0.527646	−	0.608936i	0.0517400	−	0.0597111i
$105$	−4.54589	+	1.33479i	−0.443633	+	0.130262i
$106$	−4.58820	−	10.0468i	−0.445645	−	0.975827i
$107$	−8.13948	+	5.23093i	−0.786873	+	0.505693i	−0.871308	−	0.490736i	$-0.836728\pi$
$107$	−8.13948	+	5.23093i	−0.786873	+	0.505693i	0.0844348	+	0.996429i	$0.473092\pi$
$108$	−0.959493	−	0.281733i	−0.0923273	−	0.0271097i
$109$	1.90704	+	13.2638i	0.182662	+	1.27044i	0.850437	+	0.526077i	$0.176338\pi$
$109$	1.90704	+	13.2638i	0.182662	+	1.27044i	−0.667775	+	0.744363i	$0.732753\pi$
$110$	−0.0339693	+	0.0743823i	−0.00323884	+	0.00709207i
$111$	0.439490	−	3.05672i	0.0417146	−	0.290131i
$112$	−2.69505	−	1.73201i	−0.254659	−	0.163659i
$113$	−5.38879	−	6.21899i	−0.506934	−	0.585033i	0.443377	−	0.896335i	$-0.353780\pi$
$113$	−5.38879	−	6.21899i	−0.506934	−	0.585033i	−0.950311	+	0.311302i	$0.899235\pi$
$114$	−3.67657			−0.344343
$115$	1.15902	−	6.99717i	0.108079	−	0.652490i
$116$	7.34575			0.682036
$117$	0.527646	+	0.608936i	0.0487809	+	0.0562962i
$118$	−4.50977	−	2.89825i	−0.415158	−	0.266806i
$119$	0.938989	−	6.53081i	0.0860769	−	0.598678i
$120$	−0.614354	+	1.34525i	−0.0560826	+	0.122804i
$121$	1.56503	+	10.8850i	0.142275	+	0.989546i
$122$	−11.7072	−	3.43756i	−1.05992	−	0.311222i
$123$	−1.22801	+	0.789191i	−0.110726	+	0.0711590i
$124$	−3.30482	−	7.23654i	−0.296782	−	0.649861i
$125$	−11.0864	+	3.25525i	−0.991595	+	0.291159i
$126$	2.09792	−	2.42113i	0.186898	−	0.215692i
$127$	−12.6731	+	14.6256i	−1.12456	+	1.29781i	−0.174877	+	0.984590i	$0.555953\pi$
$127$	−12.6731	+	14.6256i	−1.12456	+	1.29781i	−0.949681	+	0.313219i	$0.898593\pi$
$128$	−0.959493	+	0.281733i	−0.0848080	+	0.0249019i
$129$	−5.20608	−	11.3997i	−0.458370	−	1.00369i
$130$	1.00244	−	0.644227i	0.0879196	−	0.0565025i
$131$	20.0561	+	5.88899i	1.75231	+	0.514523i	0.990999	−	0.133869i	$-0.0427401\pi$
$131$	20.0561	+	5.88899i	1.75231	+	0.514523i	0.761306	+	0.648392i	$0.224558\pi$
$132$	−0.00786897	−	0.0547299i	−0.000684906	−	0.00476362i
$133$	4.89289	−	10.7139i	0.424268	−	0.929017i
$134$	−0.643429	+	4.47515i	−0.0555838	+	0.386594i
$135$	−1.24412	−	0.799549i	−0.107077	−	0.0688142i
$136$	−1.34871	−	1.55649i	−0.115651	−	0.133468i
$137$	5.89909			0.503993			0.251997	−	0.967728i	$-0.418913\pi$
$137$	5.89909			0.503993			0.251997	+	0.967728i	$0.418913\pi$
$138$	1.89867	+	4.40398i	0.161625	+	0.374892i
$139$	−4.04356			−0.342971			−0.171485	−	0.985187i	$-0.554857\pi$
$139$	−4.04356			−0.342971			−0.171485	+	0.985187i	$0.554857\pi$
$140$	−3.10260	−	3.58059i	−0.262217	−	0.302615i
$141$	−1.07225	−	0.689096i	−0.0903001	−	0.0580323i
$142$	2.07821	−	14.4543i	0.174399	−	1.21297i
$143$	−0.0185073	+	0.0405254i	−0.00154766	+	0.00338890i
$144$	−0.142315	−	0.989821i	−0.0118596	−	0.0824851i
$145$	10.4235	+	3.06062i	0.865626	+	0.254171i
$146$	−8.29611	+	5.33158i	−0.686591	+	0.441245i
$147$	1.35556	+	2.96827i	0.111805	+	0.244819i
$148$	2.96306	−	0.870034i	0.243562	−	0.0715164i
$149$	5.37873	−	6.20739i	0.440643	−	0.508529i	−0.491372	−	0.870950i	$-0.663504\pi$
$149$	5.37873	−	6.20739i	0.440643	−	0.508529i	0.932014	+	0.362421i	$0.118050\pi$
$150$	1.84204	−	2.12583i	0.150402	−	0.173574i
$151$	12.3286	−	3.62000i	1.00328	−	0.294591i	0.261482	−	0.965208i	$-0.415789\pi$
$151$	12.3286	−	3.62000i	1.00328	−	0.294591i	0.741803	+	0.670617i	$0.233971\pi$
$152$	−1.52730	−	3.34433i	−0.123881	−	0.271261i
$153$	1.73259	−	1.11347i	0.140072	−	0.0900187i
$154$	0.169961	+	0.0499051i	0.0136959	+	0.00402147i
$155$	−1.67437	−	11.6455i	−0.134489	−	0.935390i
$156$	−0.334716	+	0.732925i	−0.0267987	+	0.0586810i
$157$	−0.557702	+	3.87890i	−0.0445095	+	0.309570i	0.955389	+	0.295349i	$0.0954360\pi$
$157$	−0.557702	+	3.87890i	−0.0445095	+	0.309570i	−0.999899	+	0.0142211i	$0.995473\pi$
$158$	3.04519	+	1.95703i	0.242262	+	0.155693i
$159$	7.23284	+	8.34715i	0.573602	+	0.661972i
$160$	−1.47889			−0.116917
$161$	−15.3605	−	0.328020i	−1.21058	−	0.0258516i
$162$	1.00000			0.0785674
$163$	−10.2975	−	11.8839i	−0.806560	−	0.930820i	0.192162	−	0.981363i	$-0.438450\pi$
$163$	−10.2975	−	11.8839i	−0.806560	−	0.930820i	−0.998722	+	0.0505437i	$0.983905\pi$
$164$	−1.22801	−	0.789191i	−0.0958911	−	0.0616255i
$165$	0.0116373	−	0.0809395i	0.000905966	−	0.00630113i
$166$	−4.16838	+	9.12749i	−0.323529	+	0.708431i
$167$	0.572056	+	3.97873i	0.0442670	+	0.307884i	0.999911	+	0.0133587i	$0.00425233\pi$
$167$	0.572056	+	3.97873i	0.0442670	+	0.307884i	−0.955644	+	0.294525i	$0.904839\pi$
$168$	3.07385	+	0.902563i	0.237152	+	0.0696342i
$169$	−10.3901	+	6.67734i	−0.799242	+	0.513641i
$170$	−1.26528	−	2.77059i	−0.0970429	−	0.212494i
$171$	3.52765	−	1.03581i	0.269766	−	0.0792104i
$172$	8.20687	−	9.47123i	0.625768	−	0.722175i
$173$	−3.44095	+	3.97106i	−0.261610	+	0.301914i	−0.871325	−	0.490707i	$-0.836739\pi$
$173$	−3.44095	+	3.97106i	−0.261610	+	0.301914i	0.609715	+	0.792621i	$0.291284\pi$
$174$	−7.04820	+	2.06954i	−0.534322	+	0.156891i
$175$	3.74347	+	8.19705i	0.282979	+	0.619638i
$176$	0.0465151	−	0.0298935i	0.00350621	−	0.00225331i
$177$	5.14362	+	1.51030i	0.386618	+	0.113521i
$178$	1.17445	+	8.16849i	0.0880288	+	0.612254i
$179$	−0.877732	+	1.92196i	−0.0656048	+	0.143654i	−0.939594	−	0.342291i	$-0.888797\pi$
$179$	−0.877732	+	1.92196i	−0.0656048	+	0.143654i	0.873989	+	0.485945i	$0.161525\pi$
$180$	0.210468	−	1.46384i	0.0156874	−	0.109108i
$181$	−0.194228	−	0.124823i	−0.0144369	−	0.00927802i	0.533402	−	0.845862i	$-0.320913\pi$
$181$	−0.194228	−	0.124823i	−0.0144369	−	0.00927802i	−0.547839	+	0.836584i	$0.684549\pi$
$182$	−1.69038	−	1.95080i	−0.125299	−	0.144603i
$183$	12.2015			0.901960
$184$	−3.21727	+	3.55657i	−0.237180	+	0.262194i
$185$	4.56705			0.335776
$186$	5.20972	+	6.01234i	0.381995	+	0.440846i
$187$	0.0957997	+	0.0615667i	0.00700557	+	0.00450220i
$188$	0.181393	−	1.26162i	0.0132295	−	0.0920129i
$189$	−1.33083	+	2.91411i	−0.0968036	+	0.211970i
$190$	−0.773802	−	5.38191i	−0.0561375	−	0.390445i
$191$	−4.22482	−	1.24052i	−0.305697	−	0.0897608i	0.125286	−	0.992121i	$-0.460015\pi$
$191$	−4.22482	−	1.24052i	−0.305697	−	0.0897608i	−0.430984	+	0.902360i	$0.641833\pi$
$192$	0.841254	−	0.540641i	0.0607122	−	0.0390174i
$193$	8.93029	+	19.5546i	0.642817	+	1.40757i	0.897703	+	0.440601i	$0.145235\pi$
$193$	8.93029	+	19.5546i	0.642817	+	1.40757i	−0.254886	+	0.966971i	$0.582038\pi$
$194$	−6.73198	+	1.97669i	−0.483328	+	0.141918i
$195$	−0.780332	+	0.900551i	−0.0558807	+	0.0644898i
$196$	−2.13691	+	2.46613i	−0.152636	+	0.176152i
$197$	−8.53190	+	2.50519i	−0.607873	+	0.178487i	−0.571160	−	0.820838i	$-0.693507\pi$
$197$	−8.53190	+	2.50519i	−0.607873	+	0.178487i	−0.0367120	+	0.999326i	$0.511688\pi$
$198$	0.0229694	+	0.0502960i	0.00163236	+	0.00357438i
$199$	15.2730	−	9.81535i	1.08267	−	0.695792i	0.127500	−	0.991839i	$-0.459305\pi$
$199$	15.2730	−	9.81535i	1.08267	−	0.695792i	0.955173	+	0.296047i	$0.0956685\pi$
$200$	2.69894	+	0.792480i	0.190844	+	0.0560368i
$201$	−0.643429	−	4.47515i	−0.0453840	−	0.315652i
$202$	6.37690	−	13.9635i	0.448677	−	0.982466i
$203$	3.34909	−	23.2934i	0.235060	−	1.63488i
$204$	1.73259	+	1.11347i	0.121306	+	0.0779585i
$205$	−1.41370	−	1.63150i	−0.0987374	−	0.113949i
$206$	15.3219			1.06752
$207$	−3.06250	−	3.69067i	−0.212859	−	0.256520i
$208$	−0.805738			−0.0558679
$209$	0.133125	+	0.153634i	0.00920845	+	0.0106271i
$210$	3.98569	+	2.56145i	0.275039	+	0.176757i
$211$	−2.44839	+	17.0289i	−0.168554	+	1.17232i	0.713322	+	0.700836i	$0.247190\pi$
$211$	−2.44839	+	17.0289i	−0.168554	+	1.17232i	−0.881876	+	0.471482i	$0.843719\pi$
$212$	−4.58820	+	10.0468i	−0.315119	+	0.690014i
$213$	2.07821	+	14.4543i	0.142397	+	0.990390i
$214$	9.28350	+	2.72588i	0.634607	+	0.186337i
$215$	15.5916	−	10.0201i	1.06334	−	0.683368i
$216$	0.415415	+	0.909632i	0.0282654	+	0.0618926i
$217$	−24.4539	+	7.18031i	−1.66004	+	0.487431i
$218$	8.77525	−	10.1272i	0.594335	−	0.685899i
$219$	6.45797	−	7.45290i	0.436389	−	0.503620i
$220$	0.0784595	−	0.0230378i	0.00528974	−	0.00155321i
$221$	−0.689360	−	1.50949i	−0.0463713	−	0.101539i
$222$	−2.59792	+	1.66958i	−0.174361	+	0.112055i
$223$	9.25505	+	2.71753i	0.619764	+	0.181979i	0.576517	−	0.817085i	$-0.304411\pi$
$223$	9.25505	+	2.71753i	0.619764	+	0.181979i	0.0432473	+	0.999064i	$0.486230\pi$
$224$	0.455922	+	3.17101i	0.0304626	+	0.211872i
$225$	−1.16851	+	2.55869i	−0.0779008	+	0.170579i
$226$	−1.17109	+	8.14514i	−0.0779001	+	0.541807i
$227$	−11.1785	−	7.18400i	−0.741944	−	0.476819i	0.114263	−	0.993450i	$-0.463549\pi$
$227$	−11.1785	−	7.18400i	−0.741944	−	0.476819i	−0.856208	+	0.516632i	$0.827186\pi$
$228$	2.40764	+	2.77857i	0.159450	+	0.184015i
$229$	10.3343			0.682912			0.341456	−	0.939898i	$-0.389080\pi$
$229$	10.3343			0.682912			0.341456	+	0.939898i	$0.389080\pi$
$230$	−6.04711	+	3.70624i	−0.398735	+	0.244382i
$231$	−0.177136			−0.0116547
$232$	−4.81044	−	5.55155i	−0.315821	−	0.364477i
$233$	−0.186234	−	0.119685i	−0.0122006	−	0.00784085i	0.534526	−	0.845152i	$-0.320490\pi$
$233$	−0.186234	−	0.119685i	−0.0122006	−	0.00784085i	−0.546727	+	0.837311i	$0.684126\pi$
$234$	0.114669	−	0.797537i	0.00749611	−	0.0521366i
$235$	0.783050	−	1.71464i	0.0510805	−	0.111851i
$236$	0.762917	+	5.30620i	0.0496617	+	0.345404i
$237$	−3.47320	−	1.01982i	−0.225608	−	0.0662446i
$238$	−5.55056	+	3.56713i	−0.359790	+	0.231223i
$239$	4.19290	+	9.18117i	0.271216	+	0.593881i	0.995409	−	0.0957174i	$-0.0305145\pi$
$239$	4.19290	+	9.18117i	0.271216	+	0.593881i	−0.724192	+	0.689598i	$0.757787\pi$
$240$	1.41899	−	0.416652i	0.0915951	−	0.0268948i
$241$	1.63492	−	1.88680i	0.105315	−	0.121540i	−0.700645	−	0.713510i	$-0.747104\pi$
$241$	1.63492	−	1.88680i	0.105315	−	0.121540i	0.805960	+	0.591970i	$0.201650\pi$
$242$	7.20147	−	8.31093i	0.462928	−	0.534247i
$243$	−0.959493	+	0.281733i	−0.0615515	+	0.0180732i
$244$	5.06868	+	11.0989i	0.324489	+	0.710532i
$245$	−4.05976	+	2.60905i	−0.259369	+	0.166686i
$246$	1.40060	+	0.411254i	0.0892992	+	0.0262206i
$247$	−0.421587	−	2.93220i	−0.0268249	−	0.186572i
$248$	−3.30482	+	7.23654i	−0.209856	+	0.459521i
$249$	1.42803	−	9.93213i	0.0904974	−	0.629423i
$250$	9.72018	+	6.24678i	0.614758	+	0.395081i
$251$	−9.41401	−	10.8643i	−0.594207	−	0.685752i	0.376390	−	0.926461i	$-0.377165\pi$
$251$	−9.41401	−	10.8643i	−0.594207	−	0.685752i	−0.970597	+	0.240710i	$0.922620\pi$
$252$	−3.20362			−0.201809
$253$	0.115282	−	0.238804i	0.00724772	−	0.0150135i
$254$	19.3524			1.21428
$255$	1.99460	+	2.30189i	0.124906	+	0.144150i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	2.43482	−	16.9346i	0.151880	−	1.05635i	−0.761185	−	0.648535i	$-0.775382\pi$
$257$	2.43482	−	16.9346i	0.151880	−	1.05635i	0.913065	−	0.407814i	$-0.133709\pi$
$258$	−5.20608	+	11.3997i	−0.324116	+	0.709716i
$259$	−1.40796	−	9.79257i	−0.0874863	−	0.608480i
$260$	−1.14333	−	0.335712i	−0.0709064	−	0.0208200i
$261$	6.17964	−	3.97141i	0.382510	−	0.245824i
$262$	−8.68332	−	19.0138i	−0.536457	−	1.17468i
$263$	9.43152	−	2.76934i	0.581573	−	0.170765i	0.0223034	−	0.999751i	$-0.492900\pi$
$263$	9.43152	−	2.76934i	0.581573	−	0.170765i	0.559269	+	0.828986i	$0.311082\pi$
$264$	−0.0362090	+	0.0417874i	−0.00222851	+	0.00257184i
$265$	−10.6966	+	12.3445i	−0.657086	+	0.758318i
$266$	−11.3012	+	3.31834i	−0.692922	+	0.203460i
$267$	−3.42821	−	7.50672i	−0.209803	−	0.459404i
$268$	3.80345	−	2.44433i	0.232332	−	0.149311i
$269$	−25.9470	−	7.61874i	−1.58202	−	0.464523i	−0.631548	−	0.775337i	$-0.717580\pi$
$269$	−25.9470	−	7.61874i	−1.58202	−	0.464523i	−0.950471	+	0.310814i	$0.899398\pi$
$270$	0.210468	+	1.46384i	0.0128087	+	0.0890864i
$271$	5.82097	−	12.7462i	0.353599	−	0.774274i	−0.646338	−	0.763051i	$-0.723700\pi$
$271$	5.82097	−	12.7462i	0.353599	−	0.774274i	0.999937	−	0.0112226i	$-0.00357233\pi$
$272$	−0.293103	+	2.03857i	−0.0177720	+	0.123607i
$273$	2.17151	+	1.39554i	0.131426	+	0.0844621i
$274$	−3.86308	−	4.45824i	−0.233377	−	0.269332i
$275$	−0.155532			−0.00937891
$276$	2.08494	−	4.31891i	0.125499	−	0.259968i
$277$	−6.65528			−0.399877			−0.199938	−	0.979808i	$-0.564074\pi$
$277$	−6.65528			−0.399877			−0.199938	+	0.979808i	$0.564074\pi$
$278$	2.64797	+	3.05592i	0.158815	+	0.183282i
$279$	−6.69256	−	4.30105i	−0.400673	−	0.257497i
$280$	−0.674259	+	4.68958i	−0.0402947	+	0.280256i
$281$	−6.11673	+	13.3938i	−0.364894	+	0.799006i	0.634760	+	0.772709i	$0.281099\pi$
$281$	−6.11673	+	13.3938i	−0.364894	+	0.799006i	−0.999654	+	0.0262969i	$0.991628\pi$
$282$	0.181393	+	1.26162i	0.0108018	+	0.0751282i
$283$	13.1361	+	3.85711i	0.780861	+	0.229282i	0.647784	−	0.761824i	$-0.275696\pi$
$283$	13.1361	+	3.85711i	0.780861	+	0.229282i	0.133077	+	0.991106i	$0.457514\pi$
$284$	−12.2847	+	7.89492i	−0.728965	+	0.468477i
$285$	2.25872	+	4.94590i	0.133795	+	0.292970i
$286$	0.0427468	−	0.0125516i	0.00252767	−	0.000742191i
$287$	−3.06241	+	3.53421i	−0.180768	+	0.208618i
$288$	−0.654861	+	0.755750i	−0.0385880	+	0.0445330i
$289$	12.2415	−	3.59443i	0.720089	−	0.211437i
$290$	−4.51289	−	9.88185i	−0.265006	−	0.580282i
$291$	5.90239	−	3.79324i	0.346004	−	0.222363i
$292$	9.46214	+	2.77833i	0.553730	+	0.162590i
$293$	−4.21529	−	29.3180i	−0.246260	−	1.71278i	−0.619463	−	0.785026i	$-0.712650\pi$
$293$	−4.21529	−	29.3180i	−0.246260	−	1.71278i	0.373203	−	0.927750i	$-0.378260\pi$
$294$	1.35556	−	2.96827i	0.0790580	−	0.173113i
$295$	−1.12827	+	7.84730i	−0.0656905	+	0.456887i
$296$	−2.59792	−	1.66958i	−0.151001	−	0.0970425i
$297$	−0.0362090	−	0.0417874i	−0.00210106	−	0.00242475i
$298$	−8.21355			−0.475798
$299$	−3.29462	+	2.01926i	−0.190533	+	0.116777i
$300$	−2.81288			−0.162402
$301$	−26.2917	−	30.3422i	−1.51543	−	1.74890i
$302$	−10.8093	−	6.94672i	−0.622006	−	0.399739i
$303$	−2.18463	+	15.1944i	−0.125504	+	0.872897i
$304$	−1.52730	+	3.34433i	−0.0875969	+	0.191810i
$305$	2.56803	+	17.8610i	0.147045	+	1.02272i
$306$	−1.97611	−	0.580239i	−0.112967	−	0.0331700i
$307$	7.67787	−	4.93427i	0.438199	−	0.281613i	−0.302883	−	0.953028i	$-0.597949\pi$
$307$	7.67787	−	4.93427i	0.438199	−	0.281613i	0.741082	+	0.671414i	$0.234313\pi$
$308$	−0.0735851	−	0.161129i	−0.00419290	−	0.00918118i
$309$	−14.7012	+	4.31667i	−0.836323	+	0.245567i
$310$	−7.70461	+	8.89160i	−0.437593	+	0.505009i
$311$	−15.0457	+	17.3636i	−0.853162	+	0.984602i	−0.999990	−	0.00456050i	$-0.998548\pi$
$311$	−15.0457	+	17.3636i	−0.853162	+	0.984602i	0.146827	+	0.989162i	$0.453094\pi$
$312$	0.773100	−	0.227003i	0.0437682	−	0.0128515i
$313$	8.20118	+	17.9581i	0.463558	+	1.01505i	0.986662	+	0.162782i	$0.0520466\pi$
$313$	8.20118	+	17.9581i	0.463558	+	1.01505i	−0.523104	+	0.852269i	$0.675226\pi$
$314$	3.29670	−	2.11866i	0.186043	−	0.119563i
$315$	−4.54589	−	1.33479i	−0.256132	−	0.0752070i
$316$	−0.515155	−	3.58298i	−0.0289797	−	0.201558i
$317$	−8.65385	+	18.9493i	−0.486049	+	1.06430i	0.494707	+	0.869060i	$0.335275\pi$
$317$	−8.65385	+	18.9493i	−0.486049	+	1.06430i	−0.980756	+	0.195238i	$0.937452\pi$
$318$	1.57185	−	10.9324i	0.0881448	−	0.613061i
$319$	0.341689	+	0.219590i	0.0191309	+	0.0122947i
$320$	0.968468	+	1.11767i	0.0541390	+	0.0624797i
$321$	−9.67542			−0.540029
$322$	9.81109	+	11.8235i	0.546750	+	0.658898i
$323$	−7.57204			−0.421320
$324$	−0.654861	−	0.755750i	−0.0363812	−	0.0419861i
$325$	1.90665	+	1.22533i	0.105762	+	0.0679692i
$326$	−2.23785	+	15.5646i	−0.123943	+	0.862044i
$327$	−5.56664	+	12.1892i	−0.307836	+	0.674066i
$328$	0.207742	+	1.44488i	0.0114706	+	0.0797799i
$329$	−3.91790	−	1.15040i	−0.216001	−	0.0634235i
$330$	−0.0687909	+	0.0442092i	−0.00378681	+	0.00243364i
$331$	−6.45836	−	14.1418i	−0.354983	−	0.777305i	−0.999915	−	0.0130646i	$-0.995841\pi$
$331$	−6.45836	−	14.1418i	−0.354983	−	0.777305i	0.644931	−	0.764241i	$-0.276886\pi$
$332$	9.62781	−	2.82698i	0.528395	−	0.155151i
$333$	2.02231	−	2.33387i	0.110822	−	0.127895i
$334$	2.63231	−	3.03785i	0.144034	−	0.166224i
$335$	6.41547	−	1.88375i	0.350514	−	0.102920i
$336$	−1.33083	−	2.91411i	−0.0726027	−	0.158978i
$337$	5.95413	−	3.82649i	0.324342	−	0.208442i	−0.368329	−	0.929695i	$-0.620070\pi$
$337$	5.95413	−	3.82649i	0.324342	−	0.208442i	0.692671	+	0.721253i	$0.256434\pi$
$338$	11.8505	+	3.47962i	0.644582	+	0.189266i
$339$	−1.17109	−	8.14514i	−0.0636051	−	0.442384i
$340$	−1.26528	+	2.77059i	−0.0686197	+	0.150256i
$341$	0.0626013	−	0.435401i	0.00339005	−	0.0235783i
$342$	−3.09293	−	1.98771i	−0.167247	−	0.107483i
$343$	−7.83961	−	9.04740i	−0.423299	−	0.488513i
$344$	−12.5322			−0.675693
$345$	4.75799	−	5.25978i	0.256162	−	0.283177i
$346$	5.25447			0.282482
$347$	16.6438	+	19.2080i	0.893486	+	1.03114i	0.999324	+	0.0367541i	$0.0117018\pi$
$347$	16.6438	+	19.2080i	0.893486	+	1.03114i	−0.105839	+	0.994383i	$0.533753\pi$
$348$	6.17964	+	3.97141i	0.331263	+	0.212890i
$349$	3.29197	−	22.8962i	0.176215	−	1.22560i	−0.689208	−	0.724563i	$-0.742041\pi$
$349$	3.29197	−	22.8962i	0.176215	−	1.22560i	0.865423	−	0.501041i	$-0.167049\pi$
$350$	3.74347	−	8.19705i	0.200097	−	0.438151i
$351$	0.114669	+	0.797537i	0.00612055	+	0.0425694i
$352$	−0.0530529	−	0.0155777i	−0.00282773	−	0.000830297i
$353$	20.2471	−	13.0120i	1.07765	−	0.692561i	0.123634	−	0.992328i	$-0.460545\pi$
$353$	20.2471	−	13.0120i	1.07765	−	0.692561i	0.954013	+	0.299767i	$0.0969088\pi$
$354$	−2.22694	−	4.87633i	−0.118361	−	0.259174i
$355$	−20.7213	+	6.08432i	−1.09977	+	0.322922i
$356$	5.40423	−	6.23681i	0.286424	−	0.330550i
$357$	4.32075	−	4.98641i	0.228678	−	0.263909i
$358$	2.02732	−	0.595274i	0.107147	−	0.0314612i
$359$	7.96450	+	17.4398i	0.420350	+	0.920438i	0.994795	+	0.101895i	$0.0324907\pi$
$359$	7.96450	+	17.4398i	0.420350	+	0.920438i	−0.574445	+	0.818543i	$0.694782\pi$
$360$	−1.24412	+	0.799549i	−0.0655710	+	0.0421399i
$361$	5.26072	+	1.54469i	0.276880	+	0.0812992i
$362$	0.0328576	+	0.228530i	0.00172696	+	0.0120113i
$363$	−4.56830	+	10.0032i	−0.239773	+	0.525030i
$364$	−0.367354	+	2.55500i	−0.0192546	+	0.133918i
$365$	12.2690	+	7.88483i	0.642191	+	0.412711i
$366$	−7.99028	−	9.22127i	−0.417659	−	0.482004i
$367$	−26.2686			−1.37121			−0.685606	−	0.727973i	$-0.740463\pi$
$367$	−26.2686			−1.37121			−0.685606	+	0.727973i	$0.740463\pi$
$368$	4.79474	+	0.102391i	0.249943	+	0.00533748i
$369$	−1.45973			−0.0759907
$370$	−2.99078	−	3.45154i	−0.155483	−	0.179437i
$371$	29.7665	+	19.1298i	1.54540	+	0.993167i
$372$	1.13218	−	7.87449i	0.0587008	−	0.408273i
$373$	8.47650	−	18.5609i	0.438896	−	0.961049i	−0.552903	−	0.833246i	$-0.686480\pi$
$373$	8.47650	−	18.5609i	0.438896	−	0.961049i	0.991800	−	0.127803i	$-0.0407927\pi$
$374$	−0.0162064	−	0.112718i	−0.000838015	−	0.00582852i
$375$	−11.0864	−	3.25525i	−0.572498	−	0.168100i
$376$	−1.07225	+	0.689096i	−0.0552973	+	0.0355374i
$377$	−2.45874	−	5.38389i	−0.126631	−	0.277284i
$378$	3.07385	−	0.902563i	0.158102	−	0.0464228i
$379$	−2.61309	+	3.01566i	−0.134225	+	0.154904i	−0.818883	−	0.573961i	$-0.805406\pi$
$379$	−2.61309	+	3.01566i	−0.134225	+	0.154904i	0.684658	+	0.728865i	$0.259952\pi$
$380$	−3.56064	+	4.10920i	−0.182657	+	0.210798i
$381$	−18.5685	+	5.45220i	−0.951293	+	0.279325i
$382$	1.82915	+	4.00527i	0.0935873	+	0.204928i
$383$	5.31857	−	3.41804i	0.271766	−	0.174654i	−0.397658	−	0.917534i	$-0.630177\pi$
$383$	5.31857	−	3.41804i	0.271766	−	0.174654i	0.669425	+	0.742880i	$0.266541\pi$
$384$	−0.959493	−	0.281733i	−0.0489639	−	0.0143771i
$385$	−0.0372816	−	0.259299i	−0.00190005	−	0.0132151i
$386$	8.93029	−	19.5546i	0.454540	−	0.995304i
$387$	1.78352	−	12.4047i	0.0906616	−	0.630565i
$388$	5.90239	+	3.79324i	0.299648	+	0.192572i
$389$	16.6443	+	19.2085i	0.843900	+	0.973912i	0.999904	−	0.0138443i	$-0.00440693\pi$
$389$	16.6443	+	19.2085i	0.843900	+	0.973912i	−0.156005	+	0.987756i	$0.549861\pi$
$390$	1.19160			0.0603390
$391$	3.91038	+	9.07017i	0.197756	+	0.458698i
$392$	3.26315			0.164814
$393$	13.6884	+	15.7973i	0.690488	+	0.796866i
$394$	7.48050	+	4.80743i	0.376862	+	0.242195i
$395$	0.761858	−	5.29884i	0.0383333	−	0.266614i
$396$	0.0229694	−	0.0502960i	0.00115426	−	0.00252747i
$397$	0.488864	+	3.40012i	0.0245354	+	0.170647i	0.998405	−	0.0564614i	$-0.0179818\pi$
$397$	0.488864	+	3.40012i	0.0245354	+	0.170647i	−0.973869	+	0.227109i	$0.927073\pi$
$398$	−17.4196	−	5.11486i	−0.873167	−	0.256385i
$399$	9.90856	−	6.36784i	0.496048	−	0.318791i
$400$	−1.16851	−	2.55869i	−0.0584256	−	0.127934i
$401$	8.01654	−	2.35387i	0.400327	−	0.117547i	−0.0753705	−	0.997156i	$-0.524014\pi$
$401$	8.01654	−	2.35387i	0.400327	−	0.117547i	0.475697	+	0.879609i	$0.342196\pi$
$402$	−2.96073	+	3.41687i	−0.147668	+	0.170418i
$403$	−4.19767	+	4.84437i	−0.209101	+	0.241315i
$404$	−14.7289	+	4.32479i	−0.732789	+	0.215166i
$405$	−0.614354	−	1.34525i	−0.0305275	−	0.0668459i
$406$	−19.7972	+	12.7229i	−0.982518	+	0.631426i
$407$	0.163836	+	0.0481065i	0.00812103	+	0.00238455i
$408$	−0.293103	−	2.03857i	−0.0145107	−	0.100924i
$409$	−1.73917	+	3.80824i	−0.0859962	+	0.188305i	−0.947744	−	0.319031i	$-0.896643\pi$
$409$	−1.73917	+	3.80824i	−0.0859962	+	0.188305i	0.861748	+	0.507336i	$0.169370\pi$
$410$	−0.307227	+	2.13681i	−0.0151729	+	0.105530i
$411$	4.96263	+	3.18929i	0.244789	+	0.157316i
$412$	−10.0337	−	11.5795i	−0.494324	−	0.570480i
$413$	17.1738			0.845070
$414$	−0.783711	+	4.73136i	−0.0385173	+	0.232534i
$415$	14.8396			0.728447
$416$	0.527646	+	0.608936i	0.0258700	+	0.0298556i
$417$	−3.40166	−	2.18612i	−0.166580	−	0.107055i
$418$	0.0289308	−	0.201218i	0.00141505	−	0.00984191i
$419$	3.73254	−	8.17311i	0.182346	−	0.399283i	−0.796280	−	0.604928i	$-0.793202\pi$
$419$	3.73254	−	8.17311i	0.182346	−	0.399283i	0.978627	+	0.205645i	$0.0659293\pi$
$420$	−0.674259	−	4.68958i	−0.0329005	−	0.228828i
$421$	6.48508	+	1.90419i	0.316063	+	0.0928046i	0.435917	−	0.899987i	$-0.356424\pi$
$421$	6.48508	+	1.90419i	0.316063	+	0.0928046i	−0.119853	+	0.992792i	$0.538242\pi$
$422$	14.4729	−	9.30119i	0.704532	−	0.452775i
$423$	−0.529484	−	1.15941i	−0.0257444	−	0.0563724i
$424$	10.5975	−	3.11170i	0.514658	−	0.151117i
$425$	3.79376	−	4.37823i	0.184024	−	0.212375i
$426$	9.56286	−	11.0361i	0.463322	−	0.534702i
$427$	37.5055	−	11.0126i	1.81502	−	0.532938i
$428$	−4.01932	−	8.80107i	−0.194281	−	0.425416i
$429$	−0.0374790	+	0.0240863i	−0.00180950	+	0.00116290i
$430$	−17.7831	−	5.22158i	−0.857576	−	0.251807i
$431$	3.22681	+	22.4430i	0.155430	+	1.08104i	0.906922	+	0.421298i	$0.138425\pi$
$431$	3.22681	+	22.4430i	0.155430	+	1.08104i	−0.751492	+	0.659742i	$0.770666\pi$
$432$	0.415415	−	0.909632i	0.0199867	−	0.0437647i
$433$	−4.26292	+	29.6492i	−0.204863	+	1.42485i	0.584734	+	0.811225i	$0.301199\pi$
$433$	−4.26292	+	29.6492i	−0.204863	+	1.42485i	−0.789596	+	0.613627i	$0.789710\pi$
$434$	21.4404	+	13.7789i	1.02917	+	0.661409i
$435$	7.11412	+	8.21014i	0.341096	+	0.393646i
$436$	−13.4002			−0.641752
$437$	2.13614	+	17.5024i	0.102185	+	0.837251i
$438$	−9.86160			−0.471205
$439$	0.983215	+	1.13469i	0.0469263	+	0.0541559i	0.778727	−	0.627362i	$-0.215865\pi$
$439$	0.983215	+	1.13469i	0.0469263	+	0.0541559i	−0.731801	+	0.681518i	$0.761320\pi$
$440$	−0.0687909	−	0.0442092i	−0.00327948	−	0.00210759i
$441$	−0.464395	+	3.22994i	−0.0221141	+	0.153807i
$442$	−0.689360	+	1.50949i	−0.0327895	+	0.0717990i
$443$	0.838999	+	5.83536i	0.0398620	+	0.277246i	0.999997	−	0.00228902i	$-0.000728619\pi$
$443$	0.838999	+	5.83536i	0.0398620	+	0.277246i	−0.960135	+	0.279536i	$0.909820\pi$
$444$	2.96306	+	0.870034i	0.140621	+	0.0412900i
$445$	10.2671	−	6.59827i	0.486707	−	0.312788i
$446$	−4.00700	−	8.77411i	−0.189737	−	0.415466i
$447$	7.88084	−	2.31402i	0.372751	−	0.109450i
$448$	2.09792	−	2.42113i	0.0991175	−	0.114388i
$449$	24.1373	−	27.8559i	1.13911	−	1.31460i	0.196577	−	0.980488i	$-0.437017\pi$
$449$	24.1373	−	27.8559i	1.13911	−	1.31460i	0.942533	−	0.334114i	$-0.108437\pi$
$450$	2.69894	−	0.792480i	0.127229	−	0.0373579i
$451$	−0.0335292	−	0.0734187i	−0.00157883	−	0.00345715i
$452$	6.92259	−	4.44888i	0.325611	−	0.209258i
$453$	12.3286	+	3.62000i	0.579247	+	0.170082i
$454$	1.89107	+	13.1527i	0.0887523	+	0.617286i
$455$	−1.58582	+	3.47245i	−0.0743442	+	0.162791i
$456$	0.523231	−	3.63915i	0.0245025	−	0.170419i
$457$	−4.87731	−	3.13445i	−0.228151	−	0.146624i	0.421572	−	0.906795i	$-0.361479\pi$
$457$	−4.87731	−	3.13445i	−0.228151	−	0.146624i	−0.649723	+	0.760171i	$0.725115\pi$
$458$	−6.76755	−	7.81017i	−0.316227	−	0.364945i
$459$	2.05954			0.0961310
$460$	6.76101	+	2.14303i	0.315233	+	0.0999192i
$461$	−19.1277			−0.890864			−0.445432	−	0.895316i	$-0.646950\pi$
$461$	−19.1277			−0.890864			−0.445432	+	0.895316i	$0.646950\pi$
$462$	0.116000	+	0.133871i	0.00539679	+	0.00622823i
$463$	−17.1083	−	10.9948i	−0.795091	−	0.510974i	0.0789197	−	0.996881i	$-0.474853\pi$
$463$	−17.1083	−	10.9948i	−0.795091	−	0.510974i	−0.874010	+	0.485907i	$0.838489\pi$
$464$	−1.04541	+	7.27098i	−0.0485319	+	0.337547i
$465$	4.88747	−	10.7021i	0.226651	−	0.496296i
$466$	0.0315052	+	0.219124i	0.00145945	+	0.0101507i
$467$	−26.0471	−	7.64812i	−1.20532	−	0.353913i	−0.383433	−	0.923569i	$-0.625258\pi$
$467$	−26.0471	−	7.64812i	−1.20532	−	0.353913i	−0.821883	+	0.569656i	$0.807076\pi$
$468$	−0.677830	+	0.435615i	−0.0313327	+	0.0201363i
$469$	−6.01690	−	13.1752i	−0.277835	−	0.608373i
$470$	−1.80863	+	0.531061i	−0.0834257	+	0.0244960i
$471$	−2.56626	+	2.96162i	−0.118247	+	0.136464i
$472$	3.51056	−	4.05140i	0.161586	−	0.186481i
$473$	0.664872	−	0.195224i	0.0305708	−	0.00897641i
$474$	1.50373	+	3.29271i	0.0690686	+	0.151239i
$475$	8.70004	−	5.59118i	0.399185	−	0.256541i
$476$	6.33070	+	1.85886i	0.290167	+	0.0852008i
$477$	1.57185	+	10.9324i	0.0719699	+	0.500562i
$478$	4.19290	−	9.18117i	0.191779	−	0.419937i
$479$	0.531346	−	3.69559i	0.0242778	−	0.168856i	−0.974075	−	0.226224i	$-0.927362\pi$
$479$	0.531346	−	3.69559i	0.0242778	−	0.168856i	0.998353	+	0.0573682i	$0.0182709\pi$
$480$	−1.24412	−	0.799549i	−0.0567862	−	0.0364943i
$481$	−1.62945	−	1.88049i	−0.0742967	−	0.0857430i
$482$	−2.49660			−0.113717
$483$	−12.7447	−	8.58046i	−0.579905	−	0.390424i
$484$	−10.9969			−0.499861
$485$	6.79495	+	7.84179i	0.308543	+	0.356077i
$486$	0.841254	+	0.540641i	0.0381600	+	0.0245240i
$487$	−3.28140	+	22.8226i	−0.148694	+	1.03419i	0.769666	+	0.638446i	$0.220423\pi$
$487$	−3.28140	+	22.8226i	−0.148694	+	1.03419i	−0.918360	+	0.395745i	$0.870486\pi$
$488$	5.06868	−	11.0989i	0.229448	−	0.502422i
$489$	−2.23785	−	15.5646i	−0.101199	−	0.703856i
$490$	4.63037	+	1.35960i	0.209179	+	0.0614204i
$491$	−0.944131	+	0.606756i	−0.0426080	+	0.0273825i	−0.561771	−	0.827292i	$-0.689880\pi$
$491$	−0.944131	+	0.606756i	−0.0426080	+	0.0273825i	0.519163	+	0.854675i	$0.326244\pi$
$492$	−0.606395	−	1.32782i	−0.0273384	−	0.0598628i
$493$	−14.5160	+	4.26229i	−0.653769	+	0.191964i
$494$	−1.93993	+	2.23880i	−0.0872816	+	0.100728i
$495$	0.0535492	−	0.0617990i	0.00240686	−	0.00277766i
$496$	7.63321	−	2.24131i	0.342741	−	0.100638i
$497$	19.4340	+	42.5545i	0.871733	+	1.90883i
$498$	−8.44136	+	5.42493i	−0.378266	+	0.243097i
$499$	−38.0512	−	11.1728i	−1.70340	−	0.500165i	−0.721964	−	0.691931i	$-0.756760\pi$
$499$	−38.0512	−	11.1728i	−1.70340	−	0.500165i	−0.981441	+	0.191766i	$0.938579\pi$
$500$	−1.64436	−	11.4368i	−0.0735381	−	0.511469i
$501$	−1.66982	+	3.65640i	−0.0746022	+	0.163356i
$502$	−2.04586	+	14.2293i	−0.0913112	+	0.635083i
$503$	−28.6350	−	18.4026i	−1.27677	−	0.820530i	−0.286284	−	0.958145i	$-0.592420\pi$
$503$	−28.6350	−	18.4026i	−1.27677	−	0.820530i	−0.990486	+	0.137614i	$0.956057\pi$
$504$	2.09792	+	2.42113i	0.0934489	+	0.107846i
$505$	−22.7020			−1.01023
$506$	−0.255970	+	0.0692591i	−0.0113792	+	0.00307894i
$507$	−12.3508			−0.548518
$508$	−12.6731	−	14.6256i	−0.562279	−	0.648905i
$509$	0.791310	+	0.508544i	0.0350742	+	0.0225408i	0.558060	−	0.829800i	$-0.311546\pi$
$509$	0.791310	+	0.508544i	0.0350742	+	0.0225408i	−0.522986	+	0.852341i	$0.675182\pi$
$510$	0.433467	−	3.01483i	0.0191942	−	0.133499i
$511$	13.1241	−	28.7378i	0.580577	−	1.27129i
$512$	−0.142315	−	0.989821i	−0.00628949	−	0.0437443i
$513$	3.52765	+	1.03581i	0.155749	+	0.0457321i
$514$	−14.3928	+	9.24967i	−0.634838	+	0.407985i
$515$	−9.41304	−	20.6117i	−0.414788	−	0.908259i
$516$	12.0246	−	3.53074i	0.529353	−	0.155432i
$517$	0.0461516	−	0.0532618i	0.00202975	−	0.00234245i
$518$	−6.47871	+	7.47683i	−0.284658	+	0.328513i
$519$	−5.04163	+	1.48035i	−0.221303	+	0.0649804i
$520$	0.495008	+	1.08392i	0.0217075	+	0.0475329i
$521$	−33.9920	+	21.8454i	−1.48922	+	0.957062i	−0.493014	+	0.870022i	$0.664105\pi$
$521$	−33.9920	+	21.8454i	−1.48922	+	0.957062i	−0.996205	+	0.0870408i	$0.972259\pi$
$522$	−7.04820	−	2.06954i	−0.308491	−	0.0905812i
$523$	2.00533	+	13.9473i	0.0876868	+	0.609875i	0.985523	+	0.169544i	$0.0542296\pi$
$523$	2.00533	+	13.9473i	0.0876868	+	0.609875i	−0.897836	+	0.440330i	$0.854861\pi$
$524$	−8.68332	+	19.0138i	−0.379333	+	0.830623i
$525$	−1.28245	+	8.91966i	−0.0559709	+	0.389286i
$526$	−8.26927	−	5.31433i	−0.360557	−	0.231716i
$527$	10.7296	+	12.3826i	0.467389	+	0.539396i
$528$	0.0552927			0.00240630
$529$	19.8620	−	11.5974i	0.863567	−	0.504235i
$530$	16.3341			0.709510
$531$	3.51056	+	4.05140i	0.152345	+	0.175816i
$532$	9.90856	+	6.36784i	0.429591	+	0.276081i
$533$	−0.167385	+	1.16419i	−0.00725027	+	0.0504267i
$534$	−3.42821	+	7.50672i	−0.148353	+	0.324848i
$535$	−2.03637	−	14.1633i	−0.0880399	−	0.612331i
$536$	−4.33803	−	1.27376i	−0.187374	−	0.0550180i
$537$	−1.77749	+	1.14232i	−0.0767043	+	0.0492948i
$538$	11.2338	+	24.5987i	0.484325	+	1.06052i
$539$	−0.173120	+	0.0508326i	−0.00745680	+	0.00218951i
$540$	0.968468	−	1.11767i	0.0416762	−	0.0480969i
$541$	20.9730	−	24.2042i	0.901701	−	1.04062i	−0.0972695	−	0.995258i	$-0.531011\pi$
$541$	20.9730	−	24.2042i	0.901701	−	1.04062i	0.998971	−	0.0453605i	$-0.0144437\pi$
$542$	−13.4448	+	3.94776i	−0.577505	+	0.169571i
$543$	−0.0959109	−	0.210016i	−0.00411593	−	0.00901263i
$544$	1.73259	−	1.11347i	0.0742843	−	0.0477396i
$545$	−19.0147	−	5.58321i	−0.814499	−	0.239158i
$546$	−0.367354	−	2.55500i	−0.0157213	−	0.109344i
$547$	−14.2184	+	31.1339i	−0.607934	+	1.33119i	0.316045	+	0.948744i	$0.397645\pi$
$547$	−14.2184	+	31.1339i	−0.607934	+	1.33119i	−0.923978	+	0.382445i	$0.875082\pi$
$548$	−0.839528	+	5.83905i	−0.0358629	+	0.249432i
$549$	10.2645	+	6.59662i	0.438080	+	0.281537i
$550$	0.101852	+	0.117543i	0.00434297	+	0.00501205i
$551$	−27.0072			−1.15054
$552$	−4.62936	+	1.25259i	−0.197039	+	0.0533138i
$553$	−11.5965			−0.493135
$554$	4.35828	+	5.02972i	0.185166	+	0.213692i
$555$	3.84204	+	2.46913i	0.163086	+	0.104809i
$556$	0.575459	−	4.00241i	0.0244049	−	0.169740i
$557$	−4.69734	+	10.2857i	−0.199033	+	0.435820i	−0.982661	−	0.185409i	$-0.940639\pi$
$557$	−4.69734	+	10.2857i	−0.199033	+	0.435820i	0.783629	+	0.621229i	$0.213366\pi$
$558$	1.13218	+	7.87449i	0.0479290	+	0.333354i
$559$	−9.68868	−	2.84485i	−0.409787	−	0.120324i
$560$	3.98569	−	2.56145i	0.168426	−	0.108241i
$561$	0.0473063	+	0.103586i	0.00199728	+	0.00437342i
$562$	14.1280	−	4.14834i	0.595952	−	0.174987i
$563$	−11.3275	+	13.0726i	−0.477397	+	0.550946i	−0.942454	−	0.334335i	$-0.891488\pi$
$563$	−11.3275	+	13.0726i	−0.477397	+	0.550946i	0.465057	+	0.885281i	$0.346034\pi$
$564$	0.834679	−	0.963271i	0.0351463	−	0.0405610i
$565$	11.6767	−	3.42859i	0.491242	−	0.144242i
$566$	−5.68732	−	12.4535i	−0.239056	−	0.523459i
$567$	−2.69505	+	1.73201i	−0.113182	+	0.0727374i
$568$	14.0114	+	4.11411i	0.587904	+	0.172624i
$569$	−4.13566	−	28.7642i	−0.173376	−	1.20586i	−0.871687	−	0.490063i	$-0.836974\pi$
$569$	−4.13566	−	28.7642i	−0.173376	−	1.20586i	0.698311	−	0.715794i	$-0.253935\pi$
$570$	2.25872	−	4.94590i	0.0946072	−	0.207161i
$571$	−0.447773	+	3.11433i	−0.0187387	+	0.130331i	−0.997043	−	0.0768408i	$-0.975517\pi$
$571$	−0.447773	+	3.11433i	−0.0187387	+	0.130331i	0.978305	+	0.207171i	$0.0664258\pi$
$572$	−0.0374790	−	0.0240863i	−0.00156708	−	0.00100710i
$573$	−2.88347	−	3.32770i	−0.120459	−	0.139017i
$574$	4.67642			0.195190
$575$	−11.1903	−	7.53393i	−0.466668	−	0.314186i
$576$	1.00000			0.0416667
$577$	−7.10693	−	8.20184i	−0.295866	−	0.341447i	0.588281	−	0.808656i	$-0.299805\pi$
$577$	−7.10693	−	8.20184i	−0.295866	−	0.341447i	−0.884147	+	0.467209i	$0.845259\pi$
$578$	−10.7330	−	6.89766i	−0.446433	−	0.286905i
$579$	−3.05938	+	21.2785i	−0.127144	+	0.884303i
$580$	−4.51289	+	9.88185i	−0.187387	+	0.410321i
$581$	−4.57484	−	31.8187i	−0.189796	−	1.32006i
$582$	−6.73198	−	1.97669i	−0.279050	−	0.0819363i
$583$	−0.513753	+	0.330169i	−0.0212775	+	0.0136742i
$584$	−4.09666	−	8.97043i	−0.169521	−	0.371199i
$585$	−1.14333	+	0.335712i	−0.0472709	+	0.0138800i
$586$	−19.3966	+	22.3849i	−0.801268	+	0.924712i
$587$	21.1402	−	24.3971i	0.872549	−	1.00698i	−0.127336	−	0.991860i	$-0.540643\pi$
$587$	21.1402	−	24.3971i	0.872549	−	1.00698i	0.999886	−	0.0151162i	$-0.00481181\pi$
$588$	−3.13097	+	0.919336i	−0.129119	+	0.0379128i
$589$	12.1504	+	26.6057i	0.500649	+	1.09627i
$590$	6.66945	−	4.28620i	0.274577	−	0.176460i
$591$	−8.53190	−	2.50519i	−0.350955	−	0.103050i
$592$	0.439490	+	3.05672i	0.0180629	+	0.125631i
$593$	14.5904	−	31.9486i	0.599157	−	1.31197i	−0.330591	−	0.943774i	$-0.607248\pi$
$593$	14.5904	−	31.9486i	0.599157	−	1.31197i	0.929748	−	0.368196i	$-0.120025\pi$
$594$	−0.00786897	+	0.0547299i	−0.000322868	+	0.00224559i
$595$	8.20868	+	5.27540i	0.336523	+	0.216270i
$596$	5.37873	+	6.20739i	0.220321	+	0.254264i
$597$	18.1550			0.743036
$598$	3.68357	+	1.16758i	0.150632	+	0.0477458i
$599$	−33.0831			−1.35174			−0.675870	−	0.737021i	$-0.736232\pi$
$599$	−33.0831			−1.35174			−0.675870	+	0.737021i	$0.736232\pi$
$600$	1.84204	+	2.12583i	0.0752012	+	0.0867868i
$601$	−34.4280	−	22.1256i	−1.40435	−	0.902521i	−0.404422	−	0.914573i	$-0.632527\pi$
$601$	−34.4280	−	22.1256i	−1.40435	−	0.902521i	−0.999927	+	0.0120520i	$0.996164\pi$
$602$	−5.71372	+	39.7398i	−0.232874	+	1.61967i
$603$	1.87816	−	4.11260i	0.0764846	−	0.167478i
$604$	1.82861	+	12.7183i	0.0744051	+	0.517499i
$605$	−15.6045	−	4.58190i	−0.634413	−	0.186281i
$606$	12.9138	−	8.29920i	0.524588	−	0.337132i
$607$	0.360269	+	0.788879i	0.0146229	+	0.0320196i	0.916803	−	0.399341i	$-0.130761\pi$
$607$	0.360269	+	0.788879i	0.0146229	+	0.0320196i	−0.902180	+	0.431360i	$0.858034\pi$
$608$	3.52765	−	1.03581i	0.143065	−	0.0420077i
$609$	15.4108	−	17.7850i	0.624478	−	0.720685i
$610$	11.8168	−	13.6373i	0.478446	−	0.552157i
$611$	−0.985386	+	0.289336i	−0.0398645	+	0.0117053i
$612$	0.855563	+	1.87342i	0.0345841	+	0.0757286i
$613$	11.4396	−	7.35175i	0.462039	−	0.296935i	−0.288836	−	0.957379i	$-0.593268\pi$
$613$	11.4396	−	7.35175i	0.462039	−	0.296935i	0.750875	+	0.660444i	$0.229632\pi$
$614$	−8.75700	−	2.57129i	−0.353404	−	0.103769i
$615$	−0.307227	−	2.13681i	−0.0123886	−	0.0861646i
$616$	−0.0735851	+	0.161129i	−0.00296483	+	0.00649207i
$617$	6.07169	−	42.2295i	0.244437	−	1.70010i	−0.384895	−	0.922960i	$-0.625762\pi$
$617$	6.07169	−	42.2295i	0.244437	−	1.70010i	0.629332	−	0.777137i	$-0.283329\pi$
$618$	12.8896	+	8.28362i	0.518494	+	0.333216i
$619$	20.6446	+	23.8251i	0.829775	+	0.957612i	0.999612	−	0.0278606i	$-0.00886945\pi$
$619$	20.6446	+	23.8251i	0.829775	+	0.957612i	−0.169837	+	0.985472i	$0.554324\pi$
$620$	11.7653			0.472505
$621$	−0.581014	−	4.76051i	−0.0233153	−	0.191033i
$622$	22.9754			0.921229
$623$	−17.3131	−	19.9803i	−0.693633	−	0.800496i
$624$	−0.677830	−	0.435615i	−0.0271349	−	0.0174386i
$625$	0.430261	−	2.99253i	0.0172104	−	0.119701i
$626$	8.20118	−	17.9581i	0.327785	−	0.717749i
$627$	0.0289308	+	0.201218i	0.00115539	+	0.00803589i
$628$	−3.76005	−	1.10405i	−0.150042	−	0.0440564i
$629$	−5.35052	+	3.43857i	−0.213339	+	0.137105i
$630$	1.96815	+	4.30965i	0.0784131	+	0.171701i
$631$	46.7584	−	13.7295i	1.86142	−	0.546563i	0.862224	−	0.506528i	$-0.169071\pi$
$631$	46.7584	−	13.7295i	1.86142	−	0.546563i	0.999198	−	0.0400350i	$-0.0127469\pi$
$632$	−2.37048	+	2.73568i	−0.0942927	+	0.108820i
$633$	−11.2662	+	13.0019i	−0.447793	+	0.516780i
$634$	19.9880	−	5.86900i	0.793824	−	0.233088i
$635$	−11.8892	−	26.0338i	−0.471809	−	1.03312i
$636$	−9.29153	+	5.97130i	−0.368433	+	0.236778i
$637$	2.52274	+	0.740745i	0.0999548	+	0.0293494i
$638$	−0.0578035	−	0.402032i	−0.00228846	−	0.0159166i
$639$	−6.06626	+	13.2833i	−0.239978	+	0.525478i
$640$	0.210468	−	1.46384i	0.00831949	−	0.0578633i
$641$	25.3919	+	16.3184i	1.00292	+	0.644537i	0.935551	−	0.353191i	$-0.114903\pi$
$641$	25.3919	+	16.3184i	1.00292	+	0.644537i	0.0673684	+	0.997728i	$0.478540\pi$
$642$	6.33605	+	7.31220i	0.250064	+	0.288589i
$643$	34.4723			1.35946			0.679728	−	0.733464i	$-0.262098\pi$
$643$	34.4723			1.35946			0.679728	+	0.733464i	$0.262098\pi$
$644$	2.51071	−	15.1575i	0.0989358	−	0.597288i
$645$	18.5338			0.729769
$646$	4.95863	+	5.72257i	0.195095	+	0.225151i
$647$	11.7496	+	7.55102i	0.461925	+	0.296861i	0.750829	−	0.660497i	$-0.229654\pi$
$647$	11.7496	+	7.55102i	0.461925	+	0.296861i	−0.288903	+	0.957358i	$0.593291\pi$
$648$	−0.142315	+	0.989821i	−0.00559065	+	0.0388839i
$649$	−0.123134	+	0.269625i	−0.00483342	+	0.0105837i
$650$	−0.322549	−	2.24338i	−0.0126514	−	0.0879924i
$651$	−24.4539	−	7.18031i	−0.958423	−	0.281418i
$652$	13.2284	−	8.50140i	0.518065	−	0.332940i
$653$	15.3401	+	33.5902i	0.600306	+	1.31449i	0.929011	+	0.370053i	$0.120661\pi$
$653$	15.3401	+	33.5902i	0.600306	+	1.31449i	−0.328705	+	0.944433i	$0.606612\pi$
$654$	12.8574	−	3.77527i	0.502763	−	0.147625i
$655$	−20.2437	+	23.3624i	−0.790985	+	0.912845i
$656$	0.955922	−	1.10319i	0.0373225	−	0.0430724i
$657$	9.46214	−	2.77833i	0.369153	−	0.108393i
$658$	1.69626	+	3.71430i	0.0661272	+	0.144798i
$659$	−9.28343	+	5.96610i	−0.361631	+	0.232406i	−0.708821	−	0.705389i	$-0.750772\pi$
$659$	−9.28343	+	5.96610i	−0.361631	+	0.232406i	0.347189	+	0.937795i	$0.387136\pi$
$660$	0.0784595	+	0.0230378i	0.00305403	+	0.000896745i
$661$	−4.83516	−	33.6292i	−0.188066	−	1.30803i	−0.837009	−	0.547189i	$-0.815698\pi$
$661$	−4.83516	−	33.6292i	−0.188066	−	1.30803i	0.648943	−	0.760837i	$-0.275211\pi$
$662$	−6.45836	+	14.1418i	−0.251011	+	0.549638i
$663$	0.236164	−	1.64256i	0.00917185	−	0.0637916i
$664$	−8.44136	−	5.42493i	−0.327588	−	0.210528i
$665$	11.4069	+	13.1643i	0.442342	+	0.510490i
$666$	−3.08816			−0.119664
$667$	13.9471	+	32.3505i	0.540036	+	1.25262i
$668$	−4.01965			−0.155525
$669$	6.31664	+	7.28979i	0.244215	+	0.281840i
$670$	−5.62488	−	3.61489i	−0.217308	−	0.139655i
$671$	−0.0960131	+	0.667786i	−0.00370655	+	0.0257796i
$672$	−1.33083	+	2.91411i	−0.0513379	+	0.112414i
$673$	4.46767	+	31.0733i	0.172216	+	1.19779i	0.874190	+	0.485585i	$0.161393\pi$
$673$	4.46767	+	31.0733i	0.172216	+	1.19779i	−0.701974	+	0.712203i	$0.747698\pi$
$674$	−6.79099	−	1.99402i	−0.261579	−	0.0768066i
$675$	−2.36635	+	1.52076i	−0.0910807	+	0.0585340i
$676$	−5.13070	−	11.2347i	−0.197335	−	0.432103i
$677$	37.7447	−	11.0828i	1.45065	−	0.425948i	0.540891	−	0.841093i	$-0.318087\pi$
$677$	37.7447	−	11.0828i	1.45065	−	0.425948i	0.909756	+	0.415144i	$0.136269\pi$
$678$	−5.38879	+	6.21899i	−0.206955	+	0.238839i
$679$	14.7194	−	16.9871i	0.564879	−	0.651905i
$680$	2.92245	−	0.858110i	0.112071	−	0.0329070i
$681$	−5.52000	−	12.0871i	−0.211527	−	0.463180i
$682$	−0.370050	+	0.237816i	−0.0141699	+	0.00910646i
$683$	−30.3414	−	8.90905i	−1.16098	−	0.340895i	−0.356168	−	0.934422i	$-0.615917\pi$
$683$	−30.3414	−	8.90905i	−1.16098	−	0.340895i	−0.804814	+	0.593527i	$0.797735\pi$
$684$	0.523231	+	3.63915i	0.0200062	+	0.139146i
$685$	−3.62413	+	7.93574i	−0.138471	+	0.303209i
$686$	−1.70371	+	11.8496i	−0.0650480	+	0.452419i
$687$	8.69379	+	5.58716i	0.331689	+	0.213164i
$688$	8.20687	+	9.47123i	0.312884	+	0.361087i
$689$	8.89927			0.339035
$690$	−7.09090	−	0.151425i	−0.269946	−	0.00576463i
$691$	22.2620			0.846886			0.423443	−	0.905923i	$-0.360821\pi$
$691$	22.2620			0.846886			0.423443	+	0.905923i	$0.360821\pi$
$692$	−3.44095	−	3.97106i	−0.130805	−	0.150957i
$693$	−0.149017	−	0.0957672i	−0.00566067	−	0.00363789i
$694$	3.61704	−	25.1571i	0.137301	−	0.954950i
$695$	2.48418	−	5.43959i	0.0942303	−	0.206336i
$696$	−1.04541	−	7.27098i	−0.0396261	−	0.275606i
$697$	2.88460	+	0.846994i	0.109262	+	0.0320822i
$698$	−19.4596	+	12.5059i	−0.736555	+	0.473355i
$699$	−0.0919633	−	0.201372i	−0.00347837	−	0.00761657i
$700$	−8.64636	+	2.53880i	−0.326802	+	0.0959577i
$701$	−9.06733	+	10.4643i	−0.342468	+	0.395230i	−0.900690	−	0.434462i	$-0.856938\pi$
$701$	−9.06733	+	10.4643i	−0.342468	+	0.395230i	0.558222	+	0.829692i	$0.311484\pi$
$702$	0.527646	−	0.608936i	0.0199147	−	0.0229828i
$703$	−10.8939	+	3.19874i	−0.410872	+	0.120643i
$704$	0.0229694	+	0.0502960i	0.000865692	+	0.00189560i
$705$	1.58575	−	1.01910i	0.0597227	−	0.0383814i
$706$	−23.0929	−	6.78069i	−0.869113	−	0.255195i
$707$	6.99871	+	48.6771i	0.263214	+	1.83069i
$708$	−2.22694	+	4.87633i	−0.0836937	+	0.183264i
$709$	−6.98803	+	48.6028i	−0.262441	+	1.82532i	0.251926	+	0.967746i	$0.418936\pi$
$709$	−6.98803	+	48.6028i	−0.262441	+	1.82532i	−0.514367	+	0.857570i	$0.671973\pi$
$710$	18.1678	+	11.6757i	0.681825	+	0.438182i
$711$	−2.37048	−	2.73568i	−0.0889000	−	0.102596i
$712$	−8.25248			−0.309275
$713$	25.5949	−	28.2942i	0.958535	−	1.05962i
$714$	−6.59797			−0.246923
$715$	−0.0431466	−	0.0497938i	−0.00161359	−	0.00186218i
$716$	−1.77749	−	1.14232i	−0.0664278	−	0.0426906i
$717$	−1.43642	+	9.99055i	−0.0536442	+	0.373104i
$718$	7.96450	−	17.4398i	0.297232	−	0.650848i
$719$	−5.20770	−	36.2204i	−0.194214	−	1.35079i	−0.820701	−	0.571359i	$-0.806417\pi$
$719$	−5.20770	−	36.2204i	−0.194214	−	1.35079i	0.626486	−	0.779433i	$-0.284493\pi$
$720$	1.41899	+	0.416652i	0.0528825	+	0.0155277i
$721$	−41.2932	+	26.5375i	−1.53784	+	0.988310i
$722$	−2.27764	−	4.98734i	−0.0847650	−	0.185609i
$723$	2.39547	−	0.703372i	0.0890883	−	0.0261587i
$724$	0.151194	−	0.174487i	0.00561908	−	0.00648477i
$725$	13.5312	−	15.6158i	0.502536	−	0.579958i
$726$	10.5515	−	3.09820i	0.391602	−	0.114985i
$727$	7.73116	+	16.9289i	0.286733	+	0.627857i	0.997111	−	0.0759632i	$-0.0242032\pi$
$727$	7.73116	+	16.9289i	0.286733	+	0.627857i	−0.710378	+	0.703821i	$0.751476\pi$
$728$	2.17151	−	1.39554i	0.0804814	−	0.0517223i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	−2.07555	−	14.4358i	−0.0768197	−	0.534293i
$731$	−10.7221	+	23.4782i	−0.396572	+	0.868371i
$732$	−1.73645	+	12.0773i	−0.0641812	+	0.446390i
$733$	−19.0255	−	12.2269i	−0.702722	−	0.451612i	0.139866	−	0.990170i	$-0.455333\pi$
$733$	−19.0255	−	12.2269i	−0.702722	−	0.451612i	−0.842588	+	0.538558i	$0.818969\pi$
$734$	17.2023	+	19.8525i	0.634948	+	0.732769i
$735$	−4.82585			−0.178004
$736$	−3.06250	−	3.69067i	−0.112885	−	0.136040i
$737$	0.249987			0.00920840
$738$	0.955922	+	1.10319i	0.0351880	+	0.0406091i
$739$	−15.0475	−	9.67041i	−0.553530	−	0.355732i	0.233780	−	0.972289i	$-0.424890\pi$
$739$	−15.0475	−	9.67041i	−0.553530	−	0.355732i	−0.787310	+	0.616558i	$0.788527\pi$
$740$	−0.649959	+	4.52056i	−0.0238930	+	0.166179i
$741$	1.23061	−	2.69465i	0.0452075	−	0.0989906i
$742$	−5.03559	−	35.0233i	−0.184862	−	1.28575i
$743$	21.5290	+	6.32150i	0.789824	+	0.231913i	0.651675	−	0.758498i	$-0.274067\pi$
$743$	21.5290	+	6.32150i	0.789824	+	0.231913i	0.138149	+	0.990411i	$0.455885\pi$
$744$	−6.69256	+	4.30105i	−0.245361	+	0.157684i
$745$	5.04602	+	11.0493i	0.184872	+	0.404813i
$746$	−19.5783	+	5.74872i	−0.716814	+	0.210476i
$747$	6.57105	−	7.58339i	0.240422	−	0.277462i
$748$	−0.0745738	+	0.0860627i	−0.00272669	+	0.00314677i
$749$	−29.7408	+	8.73267i	−1.08670	+	0.319085i
$750$	4.79987	+	10.5103i	0.175267	+	0.383780i
$751$	39.5260	−	25.4018i	1.44232	−	0.926924i	0.442781	−	0.896630i	$-0.353992\pi$
$751$	39.5260	−	25.4018i	1.44232	−	0.926924i	0.999541	−	0.0302948i	$-0.00964461\pi$
$752$	1.22296	+	0.359094i	0.0445968	+	0.0130948i
$753$	−2.04586	−	14.2293i	−0.0745553	−	0.518543i
$754$	−2.45874	+	5.38389i	−0.0895420	+	0.196070i
$755$	−2.70432	+	18.8089i	−0.0984201	+	0.684527i
$756$	−2.69505	−	1.73201i	−0.0980181	−	0.0629924i
$757$	−18.8145	−	21.7131i	−0.683825	−	0.789176i	0.302647	−	0.953103i	$-0.402130\pi$
$757$	−18.8145	−	21.7131i	−0.683825	−	0.789176i	−0.986473	+	0.163926i	$0.947584\pi$
$758$	3.99029			0.144934
$759$	0.226089	−	0.138569i	0.00820650	−	0.00502972i
$760$	5.43725			0.197230
$761$	−10.2728	−	11.8554i	−0.372387	−	0.429758i	0.538364	−	0.842712i	$-0.319042\pi$
$761$	−10.2728	−	11.8554i	−0.372387	−	0.429758i	−0.910752	+	0.412954i	$0.864497\pi$
$762$	16.2803	+	10.4627i	0.589772	+	0.379024i
$763$	−6.10944	+	42.4921i	−0.221176	+	1.53832i
$764$	1.82915	−	4.00527i	0.0661762	−	0.144906i
$765$	0.433467	+	3.01483i	0.0156720	+	0.109001i
$766$	−6.06611	−	1.78117i	−0.219177	−	0.0643563i

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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 - 0.755750i) q^{2} +(0.841254 + 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-0.614354 + 1.34525i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(3.07385 + 0.902563i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.654861 - 0.755750i) q^{2} +(0.841254 + 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-0.614354 + 1.34525i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(3.07385 + 0.902563i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +(1.41899 - 0.416652i) q^{10} +(-0.0362090 + 0.0417874i) q^{11} +(-0.654861 + 0.755750i) q^{12} +(0.773100 - 0.227003i) q^{13} +(-1.33083 - 2.91411i) q^{14} +(-1.24412 + 0.799549i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(-0.293103 - 2.03857i) q^{17} +(0.415415 - 0.909632i) q^{18} +(0.523231 - 3.63915i) q^{19} +(-1.24412 - 0.799549i) q^{20} +(2.09792 + 2.42113i) q^{21} +0.0552927 q^{22} +(-4.62936 + 1.25259i) q^{23} +1.00000 q^{24} +(1.84204 + 2.12583i) q^{25} +(-0.677830 - 0.435615i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(-1.33083 + 2.91411i) q^{28} +(-1.04541 - 7.27098i) q^{29} +(1.41899 + 0.416652i) q^{30} +(-6.69256 + 4.30105i) q^{31} +(0.415415 + 0.909632i) q^{32} +(-0.0530529 + 0.0155777i) q^{33} +(-1.34871 + 1.55649i) q^{34} +(-3.10260 + 3.58059i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-1.28287 - 2.80909i) q^{37} +(-3.09293 + 1.98771i) q^{38} +(0.773100 + 0.227003i) q^{39} +(0.210468 + 1.46384i) q^{40} +(-0.606395 + 1.32782i) q^{41} +(0.455922 - 3.17101i) q^{42} +(-10.5428 - 6.77544i) q^{43} +(-0.0362090 - 0.0417874i) q^{44} -1.47889 q^{45} +(3.97823 + 2.67837i) q^{46} -1.27459 q^{47} +(-0.654861 - 0.755750i) q^{48} +(2.74514 + 1.76419i) q^{49} +(0.400315 - 2.78425i) q^{50} +(0.855563 - 1.87342i) q^{51} +(0.114669 + 0.797537i) q^{52} +(10.5975 + 3.11170i) q^{53} +(0.841254 - 0.540641i) q^{54} +(-0.0339693 - 0.0743823i) q^{55} +(3.07385 - 0.902563i) q^{56} +(2.40764 - 2.77857i) q^{57} +(-4.81044 + 5.55155i) q^{58} +(5.14362 - 1.51030i) q^{59} +(-0.614354 - 1.34525i) q^{60} +(10.2645 - 6.59662i) q^{61} +(7.63321 + 2.24131i) q^{62} +(0.455922 + 3.17101i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.169582 + 1.17947i) q^{65} +(0.0465151 + 0.0298935i) q^{66} +(-2.96073 - 3.41687i) q^{67} +2.05954 q^{68} +(-4.57167 - 1.44908i) q^{69} +4.73780 q^{70} +(9.56286 + 11.0361i) q^{71} +(0.841254 + 0.540641i) q^{72} +(1.40345 - 9.76122i) q^{73} +(-1.28287 + 2.80909i) q^{74} +(0.400315 + 2.78425i) q^{75} +(3.52765 + 1.03581i) q^{76} +(-0.149017 + 0.0957672i) q^{77} +(-0.334716 - 0.732925i) q^{78} +(-3.47320 + 1.01982i) q^{79} +(0.968468 - 1.11767i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(1.40060 - 0.411254i) q^{82} +(-4.16838 - 9.12749i) q^{83} +(-2.69505 + 1.73201i) q^{84} +(2.92245 + 0.858110i) q^{85} +(1.78352 + 12.4047i) q^{86} +(3.05153 - 6.68193i) q^{87} +(-0.00786897 + 0.0547299i) q^{88} +(-6.94243 - 4.46163i) q^{89} +(0.968468 + 1.11767i) q^{90} +2.58128 q^{91} +(-0.581014 - 4.76051i) q^{92} -7.95546 q^{93} +(0.834679 + 0.963271i) q^{94} +(4.57411 + 2.93960i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(2.91463 - 6.38215i) q^{97} +(-0.464395 - 3.22994i) q^{98} +(-0.0530529 - 0.0155777i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{3} - q^{4} + 8 q^{5} - q^{6} + 8 q^{7} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 - q^3 - q^4 + 8 * q^5 - q^6 + 8 * q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} + 8 q^{5} - q^{6} + 8 q^{7} - q^{8} - q^{9} - 3 q^{10} + 7 q^{11} - q^{12} + 3 q^{13} - 3 q^{14} - 3 q^{15} - q^{16} + 4 q^{17} - q^{18} - 3 q^{20} - 3 q^{21} - 26 q^{22} - 12 q^{23} + 10 q^{24} - 15 q^{25} + 3 q^{26} - q^{27} - 3 q^{28} - 25 q^{29} - 3 q^{30} + 6 q^{31} - q^{32} - 4 q^{33} - 7 q^{34} + 2 q^{35} - q^{36} + 9 q^{37} + 11 q^{38} + 3 q^{39} - 3 q^{40} + 24 q^{41} + 8 q^{42} - 30 q^{43} + 7 q^{44} - 14 q^{45} + 21 q^{46} - 48 q^{47} - q^{48} + 9 q^{49} + 7 q^{50} + 15 q^{51} + 14 q^{52} + 15 q^{53} - q^{54} - 23 q^{55} + 8 q^{56} - 11 q^{57} - 3 q^{58} + 5 q^{59} + 8 q^{60} + 12 q^{61} + 28 q^{62} + 8 q^{63} - q^{64} - 13 q^{65} + 18 q^{66} + 18 q^{67} - 18 q^{68} - q^{69} + 2 q^{70} + 28 q^{71} - q^{72} + 19 q^{73} + 9 q^{74} + 7 q^{75} + 22 q^{76} - 12 q^{77} - 8 q^{78} - 52 q^{79} + 8 q^{80} - q^{81} - 20 q^{82} + 7 q^{83} - 3 q^{84} + 23 q^{85} + 14 q^{86} + 30 q^{87} - 4 q^{88} + 3 q^{89} + 8 q^{90} + 42 q^{91} - 23 q^{92} - 16 q^{93} + 29 q^{94} + 22 q^{95} - q^{96} + 51 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 + 8 * q^5 - q^6 + 8 * q^7 - q^8 - q^9 - 3 * q^10 + 7 * q^11 - q^12 + 3 * q^13 - 3 * q^14 - 3 * q^15 - q^16 + 4 * q^17 - q^18 - 3 * q^20 - 3 * q^21 - 26 * q^22 - 12 * q^23 + 10 * q^24 - 15 * q^25 + 3 * q^26 - q^27 - 3 * q^28 - 25 * q^29 - 3 * q^30 + 6 * q^31 - q^32 - 4 * q^33 - 7 * q^34 + 2 * q^35 - q^36 + 9 * q^37 + 11 * q^38 + 3 * q^39 - 3 * q^40 + 24 * q^41 + 8 * q^42 - 30 * q^43 + 7 * q^44 - 14 * q^45 + 21 * q^46 - 48 * q^47 - q^48 + 9 * q^49 + 7 * q^50 + 15 * q^51 + 14 * q^52 + 15 * q^53 - q^54 - 23 * q^55 + 8 * q^56 - 11 * q^57 - 3 * q^58 + 5 * q^59 + 8 * q^60 + 12 * q^61 + 28 * q^62 + 8 * q^63 - q^64 - 13 * q^65 + 18 * q^66 + 18 * q^67 - 18 * q^68 - q^69 + 2 * q^70 + 28 * q^71 - q^72 + 19 * q^73 + 9 * q^74 + 7 * q^75 + 22 * q^76 - 12 * q^77 - 8 * q^78 - 52 * q^79 + 8 * q^80 - q^81 - 20 * q^82 + 7 * q^83 - 3 * q^84 + 23 * q^85 + 14 * q^86 + 30 * q^87 - 4 * q^88 + 3 * q^89 + 8 * q^90 + 42 * q^91 - 23 * q^92 - 16 * q^93 + 29 * q^94 + 22 * q^95 - q^96 + 51 * q^97 - 2 * q^98 - 4 * q^99

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