LMFDB - Embedded newform 111.2.k.a.46.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [111,2,Mod(7,111)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(111, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("111.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 111 = 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	111.k (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:	$0.886339462436$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 18 x^{16} - 33 x^{15} + 150 x^{14} - 231 x^{13} + 796 x^{12} - 801 x^{11} + \cdots + 361 $ x^18 - 3x^17 + 18x^16 - 33x^15 + 150x^14 - 231x^13 + 796x^12 - 801x^11 + 2382x^10 - 1621x^9 + 5184x^8 - 2001x^7 + 6622x^6 - 1269x^5 + 5964x^4 - 347x^3 + 1662x^2 - 57*x + 361
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			46.2
Root			$0.662500 - 1.14748i$ of defining polynomial
Character	$\chi$	$=$	111.46
Dual form			111.2.k.a.70.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.230084 + 1.30487i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.229637 - 0.0835811i) q^{4} +(1.21929 + 1.02311i) q^{5} -1.32500 q^{6} +(-2.25942 - 1.89588i) q^{7} +(1.48690 + 2.57538i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})$	\(q+(0.230084 + 1.30487i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.229637 - 0.0835811i) q^{4} +(1.21929 + 1.02311i) q^{5} -1.32500 q^{6} +(-2.25942 - 1.89588i) q^{7} +(1.48690 + 2.57538i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(-1.05448 + 1.82642i) q^{10} +(-1.22577 - 2.12309i) q^{11} +(0.0424353 + 0.240662i) q^{12} +(-1.07313 + 0.390586i) q^{13} +(1.95402 - 3.38446i) q^{14} +(-1.21929 + 1.02311i) q^{15} +(-2.64403 + 2.21860i) q^{16} +(3.07519 + 1.11928i) q^{17} +(0.230084 - 1.30487i) q^{18} +(1.00236 - 5.68469i) q^{19} +(0.365507 + 0.133034i) q^{20} +(2.25942 - 1.89588i) q^{21} +(2.48833 - 2.08795i) q^{22} +(0.230355 - 0.398987i) q^{23} +(-2.79445 + 1.01710i) q^{24} +(-0.428318 - 2.42911i) q^{25} +(-0.756572 - 1.31042i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-0.677306 - 0.246519i) q^{28} +(-0.100499 - 0.174069i) q^{29} +(-1.61556 - 1.35562i) q^{30} +5.10690 q^{31} +(1.05279 + 0.883392i) q^{32} +(2.30369 - 0.838473i) q^{33} +(-0.752960 + 4.27025i) q^{34} +(-0.815204 - 4.62325i) q^{35} -0.244375 q^{36} +(0.749148 + 6.03645i) q^{37} +7.64842 q^{38} +(-0.198306 - 1.12465i) q^{39} +(-0.821930 + 4.66140i) q^{40} +(-9.28407 + 3.37912i) q^{41} +(2.99373 + 2.51204i) q^{42} -10.5286 q^{43} +(-0.458932 - 0.385089i) q^{44} +(-0.795836 - 1.37843i) q^{45} +(0.573627 + 0.208783i) q^{46} +(3.00362 - 5.20243i) q^{47} +(-1.72577 - 2.98911i) q^{48} +(0.295083 + 1.67350i) q^{49} +(3.07112 - 1.11780i) q^{50} +(-1.63627 + 2.83411i) q^{51} +(-0.213784 + 0.179386i) q^{52} +(-9.57587 + 8.03511i) q^{53} +(1.24509 + 0.453177i) q^{54} +(0.677581 - 3.84275i) q^{55} +(1.52308 - 8.63784i) q^{56} +(5.42427 + 1.97427i) q^{57} +(0.204014 - 0.171188i) q^{58} +(-10.8723 + 9.12298i) q^{59} +(-0.194482 + 0.336853i) q^{60} +(9.52397 - 3.46644i) q^{61} +(1.17502 + 6.66384i) q^{62} +(1.47473 + 2.55431i) q^{63} +(-4.36201 + 7.55523i) q^{64} +(-1.70806 - 0.621684i) q^{65} +(1.62414 + 2.81309i) q^{66} +(8.33279 + 6.99204i) q^{67} +0.799728 q^{68} +(0.352925 + 0.296139i) q^{69} +(5.84518 - 2.12747i) q^{70} +(0.536681 - 3.04367i) q^{71} +(-0.516394 - 2.92862i) q^{72} +3.91627 q^{73} +(-7.70442 + 2.36643i) q^{74} +2.46658 q^{75} +(-0.244953 - 1.38920i) q^{76} +(-1.25560 + 7.12084i) q^{77} +(1.42189 - 0.517526i) q^{78} +(-8.04725 - 6.75245i) q^{79} -5.49370 q^{80} +(0.766044 + 0.642788i) q^{81} +(-6.54543 - 11.3370i) q^{82} +(6.08352 + 2.21422i) q^{83} +(0.360387 - 0.624209i) q^{84} +(2.60441 + 4.51097i) q^{85} +(-2.42246 - 13.7384i) q^{86} +(0.188876 - 0.0687451i) q^{87} +(3.64518 - 6.31363i) q^{88} +(-5.11880 + 4.29518i) q^{89} +(1.61556 - 1.35562i) q^{90} +(3.16514 + 1.15202i) q^{91} +(0.0195504 - 0.110876i) q^{92} +(-0.886804 + 5.02932i) q^{93} +(7.47958 + 2.72234i) q^{94} +(7.03822 - 5.90577i) q^{95} +(-1.05279 + 0.883392i) q^{96} +(4.01549 - 6.95504i) q^{97} +(-2.11580 + 0.770090i) q^{98} +(0.425704 + 2.41429i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8}+O(q^{10}) $ 18 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8	\( 18 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8} + 12 q^{10} + 6 q^{11} - 6 q^{12} + 18 q^{13} - 9 q^{14} + 6 q^{15} - 9 q^{16} - 21 q^{17} - 3 q^{18} + 12 q^{19} - 6 q^{21} - 51 q^{22} + 6 q^{24} + 6 q^{25} + 15 q^{26} + 9 q^{27} - 39 q^{28} - 3 q^{29} + 15 q^{30} - 24 q^{31} + 21 q^{32} - 18 q^{34} - 12 q^{35} + 18 q^{36} + 27 q^{37} + 24 q^{38} + 18 q^{39} + 39 q^{40} + 9 q^{41} + 6 q^{42} - 72 q^{43} - 21 q^{44} + 21 q^{46} + 21 q^{47} - 3 q^{48} - 18 q^{49} + 24 q^{50} - 3 q^{51} - 30 q^{52} - 18 q^{53} + 3 q^{54} + 9 q^{55} + 54 q^{56} - 3 q^{57} - 66 q^{59} - 36 q^{60} + 33 q^{61} + 69 q^{62} + 18 q^{64} - 63 q^{65} + 42 q^{67} + 48 q^{68} - 12 q^{69} + 63 q^{70} + 15 q^{71} - 6 q^{72} - 24 q^{73} - 51 q^{74} - 6 q^{75} + 12 q^{76} + 39 q^{77} - 27 q^{78} - 6 q^{79} - 12 q^{80} + 15 q^{82} + 33 q^{83} - 6 q^{84} + 30 q^{85} - 60 q^{86} - 9 q^{87} - 3 q^{88} + 45 q^{89} - 15 q^{90} + 21 q^{91} - 24 q^{92} - 6 q^{93} + 18 q^{94} - 24 q^{95} - 21 q^{96} - 24 q^{97} - 36 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8 + 12 * q^10 + 6 * q^11 - 6 * q^12 + 18 * q^13 - 9 * q^14 + 6 * q^15 - 9 * q^16 - 21 * q^17 - 3 * q^18 + 12 * q^19 - 6 * q^21 - 51 * q^22 + 6 * q^24 + 6 * q^25 + 15 * q^26 + 9 * q^27 - 39 * q^28 - 3 * q^29 + 15 * q^30 - 24 * q^31 + 21 * q^32 - 18 * q^34 - 12 * q^35 + 18 * q^36 + 27 * q^37 + 24 * q^38 + 18 * q^39 + 39 * q^40 + 9 * q^41 + 6 * q^42 - 72 * q^43 - 21 * q^44 + 21 * q^46 + 21 * q^47 - 3 * q^48 - 18 * q^49 + 24 * q^50 - 3 * q^51 - 30 * q^52 - 18 * q^53 + 3 * q^54 + 9 * q^55 + 54 * q^56 - 3 * q^57 - 66 * q^59 - 36 * q^60 + 33 * q^61 + 69 * q^62 + 18 * q^64 - 63 * q^65 + 42 * q^67 + 48 * q^68 - 12 * q^69 + 63 * q^70 + 15 * q^71 - 6 * q^72 - 24 * q^73 - 51 * q^74 - 6 * q^75 + 12 * q^76 + 39 * q^77 - 27 * q^78 - 6 * q^79 - 12 * q^80 + 15 * q^82 + 33 * q^83 - 6 * q^84 + 30 * q^85 - 60 * q^86 - 9 * q^87 - 3 * q^88 + 45 * q^89 - 15 * q^90 + 21 * q^91 - 24 * q^92 - 6 * q^93 + 18 * q^94 - 24 * q^95 - 21 * q^96 - 24 * q^97 - 36 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/111\mathbb{Z}\right)^\times$.

$n$	$38$	$76$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.230084	+	1.30487i	0.162694	+	0.922683i	0.951410	+	0.307926i	$0.0996348\pi$
$2$	0.230084	+	1.30487i	0.162694	+	0.922683i	−0.788717	+	0.614757i	$0.789254\pi$
$3$	−0.173648	+	0.984808i	−0.100256	+	0.568579i
$3$	−0.173648	+	0.984808i	−0.100256	+	0.568579i
$4$	0.229637	−	0.0835811i	0.114819	−	0.0417906i
$5$	1.21929	+	1.02311i	0.545283	+	0.457547i	0.873340	−	0.487111i	$-0.161949\pi$
$5$	1.21929	+	1.02311i	0.545283	+	0.457547i	−0.328057	+	0.944658i	$0.606394\pi$
$6$	−1.32500			−0.540929
$7$	−2.25942	−	1.89588i	−0.853980	−	0.716574i	0.106683	−	0.994293i	$-0.465977\pi$
$7$	−2.25942	−	1.89588i	−0.853980	−	0.716574i	−0.960662	+	0.277719i	$0.910422\pi$
$8$	1.48690	+	2.57538i	0.525698	+	0.910536i
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$	−1.05448	+	1.82642i	−0.333457	+	0.577564i
$11$	−1.22577	−	2.12309i	−0.369582	−	0.640135i	0.619918	−	0.784667i	$-0.287166\pi$
$11$	−1.22577	−	2.12309i	−0.369582	−	0.640135i	−0.989500	+	0.144531i	$0.953833\pi$
$12$	0.0424353	+	0.240662i	0.0122500	+	0.0694732i
$13$	−1.07313	+	0.390586i	−0.297631	+	0.108329i	−0.486520	−	0.873670i	$-0.661734\pi$
$13$	−1.07313	+	0.390586i	−0.297631	+	0.108329i	0.188888	+	0.981999i	$0.439512\pi$
$14$	1.95402	−	3.38446i	0.522233	−	0.904534i
$15$	−1.21929	+	1.02311i	−0.314820	+	0.264165i
$16$	−2.64403	+	2.21860i	−0.661007	+	0.554650i
$17$	3.07519	+	1.11928i	0.745843	+	0.271464i	0.686855	−	0.726794i	$-0.258991\pi$
$17$	3.07519	+	1.11928i	0.745843	+	0.271464i	0.0589873	+	0.998259i	$0.481213\pi$
$18$	0.230084	−	1.30487i	0.0542313	−	0.307561i
$19$	1.00236	−	5.68469i	0.229958	−	1.30416i	−0.623018	−	0.782208i	$-0.714094\pi$
$19$	1.00236	−	5.68469i	0.229958	−	1.30416i	0.852976	−	0.521950i	$-0.174795\pi$
$20$	0.365507	+	0.133034i	0.0817299	+	0.0297472i
$21$	2.25942	−	1.89588i	0.493045	−	0.413714i
$22$	2.48833	−	2.08795i	0.530513	−	0.445153i
$23$	0.230355	−	0.398987i	0.0480324	−	0.0831945i	−0.841010	−	0.541020i	$-0.818038\pi$
$23$	0.230355	−	0.398987i	0.0480324	−	0.0831945i	0.889042	+	0.457826i	$0.151372\pi$
$24$	−2.79445	+	1.01710i	−0.570416	+	0.207614i
$25$	−0.428318	−	2.42911i	−0.0856635	−	0.485822i
$26$	−0.756572	−	1.31042i	−0.148376	−	0.256995i
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$	−0.677306	−	0.246519i	−0.127999	−	0.0465878i
$29$	−0.100499	−	0.174069i	−0.0186621	−	0.0323237i	0.856544	−	0.516075i	$-0.172607\pi$
$29$	−0.100499	−	0.174069i	−0.0186621	−	0.0323237i	−0.875206	+	0.483751i	$0.839274\pi$
$30$	−1.61556	−	1.35562i	−0.294960	−	0.247501i
$31$	5.10690			0.917227			0.458613	−	0.888636i	$-0.348346\pi$
$31$	5.10690			0.917227			0.458613	+	0.888636i	$0.348346\pi$
$32$	1.05279	+	0.883392i	0.186108	+	0.156163i
$33$	2.30369	−	0.838473i	0.401020	−	0.145959i
$34$	−0.752960	+	4.27025i	−0.129132	+	0.732342i
$35$	−0.815204	−	4.62325i	−0.137795	−	0.781472i
$36$	−0.244375			−0.0407291
$37$	0.749148	+	6.03645i	0.123159	+	0.992387i
$37$	0.749148	+	6.03645i	0.123159	+	0.992387i
$38$	7.64842			1.24074
$39$	−0.198306	−	1.12465i	−0.0317543	−	0.180088i
$40$	−0.821930	+	4.66140i	−0.129959	+	0.737032i
$41$	−9.28407	+	3.37912i	−1.44993	+	0.527730i	−0.942571	−	0.334006i	$-0.891599\pi$
$41$	−9.28407	+	3.37912i	−1.44993	+	0.527730i	−0.507356	+	0.861736i	$0.669377\pi$
$42$	2.99373	+	2.51204i	0.461942	+	0.387616i
$43$	−10.5286			−1.60559			−0.802796	−	0.596253i	$-0.796655\pi$
$43$	−10.5286			−1.60559			−0.802796	+	0.596253i	$0.796655\pi$
$44$	−0.458932	−	0.385089i	−0.0691865	−	0.0580544i
$45$	−0.795836	−	1.37843i	−0.118636	−	0.205484i
$46$	0.573627	+	0.208783i	0.0845767	+	0.0307834i
$47$	3.00362	−	5.20243i	0.438123	−	0.758852i	−0.559421	−	0.828883i	$-0.688977\pi$
$47$	3.00362	−	5.20243i	0.438123	−	0.758852i	0.997545	+	0.0700314i	$0.0223099\pi$
$48$	−1.72577	−	2.98911i	−0.249093	−	0.431441i
$49$	0.295083	+	1.67350i	0.0421547	+	0.239071i
$50$	3.07112	−	1.11780i	0.434323	−	0.158080i
$51$	−1.63627	+	2.83411i	−0.229124	+	0.396855i
$52$	−0.213784	+	0.179386i	−0.0296465	+	0.0248764i
$53$	−9.57587	+	8.03511i	−1.31535	+	1.10371i	−0.328077	+	0.944651i	$0.606401\pi$
$53$	−9.57587	+	8.03511i	−1.31535	+	1.10371i	−0.987270	+	0.159056i	$0.949155\pi$
$54$	1.24509	+	0.453177i	0.169436	+	0.0616695i
$55$	0.677581	−	3.84275i	0.0913650	−	0.518156i
$56$	1.52308	−	8.63784i	0.203531	−	1.15428i
$57$	5.42427	+	1.97427i	0.718462	+	0.261499i
$58$	0.204014	−	0.171188i	0.0267883	−	0.0224781i
$59$	−10.8723	+	9.12298i	−1.41546	+	1.18771i	−0.461737	+	0.887017i	$0.652774\pi$
$59$	−10.8723	+	9.12298i	−1.41546	+	1.18771i	−0.953721	+	0.300693i	$0.902782\pi$
$60$	−0.194482	+	0.336853i	−0.0251075	+	0.0434876i
$61$	9.52397	−	3.46644i	1.21942	−	0.443832i	0.349458	−	0.936952i	$-0.386366\pi$
$61$	9.52397	−	3.46644i	1.21942	−	0.443832i	0.869961	+	0.493120i	$0.164144\pi$
$62$	1.17502	+	6.66384i	0.149227	+	0.846309i
$63$	1.47473	+	2.55431i	0.185799	+	0.321812i
$64$	−4.36201	+	7.55523i	−0.545252	+	0.944404i
$65$	−1.70806	−	0.621684i	−0.211859	−	0.0771104i
$66$	1.62414	+	2.81309i	0.199918	+	0.346268i
$67$	8.33279	+	6.99204i	1.01801	+	0.854214i	0.989376	−	0.145376i	$-0.0464393\pi$
$67$	8.33279	+	6.99204i	1.01801	+	0.854214i	0.0286356	+	0.999590i	$0.490884\pi$
$68$	0.799728			0.0969813
$69$	0.352925	+	0.296139i	0.0424871	+	0.0356509i
$70$	5.84518	−	2.12747i	0.698632	−	0.254281i
$71$	0.536681	−	3.04367i	0.0636923	−	0.361217i	−0.936259	−	0.351311i	$-0.885736\pi$
$71$	0.536681	−	3.04367i	0.0636923	−	0.361217i	0.999951	−	0.00990538i	$-0.00315303\pi$
$72$	−0.516394	−	2.92862i	−0.0608577	−	0.345141i
$73$	3.91627			0.458364			0.229182	−	0.973384i	$-0.426395\pi$
$73$	3.91627			0.458364			0.229182	+	0.973384i	$0.426395\pi$
$74$	−7.70442	+	2.36643i	−0.895621	+	0.275092i
$75$	2.46658			0.284816
$76$	−0.244953	−	1.38920i	−0.0280980	−	0.159352i
$77$	−1.25560	+	7.12084i	−0.143089	+	0.811495i
$78$	1.42189	−	0.517526i	0.160997	−	0.0585983i
$79$	−8.04725	−	6.75245i	−0.905387	−	0.759710i	0.0658491	−	0.997830i	$-0.479024\pi$
$79$	−8.04725	−	6.75245i	−0.905387	−	0.759710i	−0.971236	+	0.238120i	$0.923469\pi$
$80$	−5.49370			−0.614215
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$	−6.54543	−	11.3370i	−0.722822	−	1.25196i
$83$	6.08352	+	2.21422i	0.667753	+	0.243042i	0.653580	−	0.756857i	$-0.273266\pi$
$83$	6.08352	+	2.21422i	0.667753	+	0.243042i	0.0141729	+	0.999900i	$0.495488\pi$
$84$	0.360387	−	0.624209i	0.0393214	−	0.0681067i
$85$	2.60441	+	4.51097i	0.282488	+	0.489283i
$86$	−2.42246	−	13.7384i	−0.261220	−	1.48145i
$87$	0.188876	−	0.0687451i	0.0202496	−	0.00737024i
$88$	3.64518	−	6.31363i	0.388577	−	0.673036i
$89$	−5.11880	+	4.29518i	−0.542592	+	0.455288i	−0.872423	−	0.488751i	$-0.837452\pi$
$89$	−5.11880	+	4.29518i	−0.542592	+	0.455288i	0.329832	+	0.944040i	$0.393008\pi$
$90$	1.61556	−	1.35562i	0.170295	−	0.142894i
$91$	3.16514	+	1.15202i	0.331797	+	0.120764i
$92$	0.0195504	−	0.110876i	0.00203827	−	0.0115596i
$93$	−0.886804	+	5.02932i	−0.0919573	+	0.521516i
$94$	7.47958	+	2.72234i	0.771460	+	0.280788i
$95$	7.03822	−	5.90577i	0.722106	−	0.605919i
$96$	−1.05279	+	0.883392i	−0.107450	+	0.0901609i
$97$	4.01549	−	6.95504i	0.407712	−	0.706177i	−0.586921	−	0.809644i	$-0.699660\pi$
$97$	4.01549	−	6.95504i	0.407712	−	0.706177i	0.994633	+	0.103467i	$0.0329936\pi$
$98$	−2.11580	+	0.770090i	−0.213729	+	0.0777908i
$99$	0.425704	+	2.41429i	0.0427849	+	0.242645i
$100$	−0.301385	−	0.522015i	−0.0301385	−	0.0522015i
$101$	6.71188	−	11.6253i	0.667857	−	1.15676i	−0.310645	−	0.950526i	$-0.600545\pi$
$101$	6.71188	−	11.6253i	0.667857	−	1.15676i	0.978502	−	0.206237i	$-0.0661217\pi$
$102$	−4.07462	−	1.48304i	−0.403448	−	0.146843i
$103$	3.09286	+	5.35700i	0.304749	+	0.527841i	0.977205	−	0.212296i	$-0.0680941\pi$
$103$	3.09286	+	5.35700i	0.304749	+	0.527841i	−0.672457	+	0.740137i	$0.734761\pi$
$104$	−2.60154	−	2.18295i	−0.255102	−	0.214056i
$105$	4.69457			0.458143
$106$	−12.6880	−	10.6465i	−1.23237	−	1.03408i
$107$	−7.21581	+	2.62634i	−0.697579	+	0.253898i	−0.666377	−	0.745615i	$-0.732156\pi$
$107$	−7.21581	+	2.62634i	−0.697579	+	0.253898i	−0.0312020	+	0.999513i	$0.509934\pi$
$108$	0.0424353	−	0.240662i	0.00408333	−	0.0231577i
$109$	1.00751	+	5.71388i	0.0965021	+	0.547291i	0.994277	+	0.106835i	$0.0340718\pi$
$109$	1.00751	+	5.71388i	0.0965021	+	0.547291i	−0.897775	+	0.440455i	$0.854817\pi$
$110$	5.17019			0.492958
$111$	−6.07483	−	0.310452i	−0.576598	−	0.0294668i
$112$	10.1802			0.961934
$113$	0.592434	+	3.35986i	0.0557315	+	0.316069i	0.999911	−	0.0133633i	$-0.00425380\pi$
$113$	0.592434	+	3.35986i	0.0557315	+	0.316069i	−0.944179	+	0.329432i	$0.893143\pi$
$114$	−1.32813	+	7.53222i	−0.124391	+	0.705457i
$115$	0.689076	−	0.250803i	0.0642567	−	0.0233875i
$116$	−0.0376271	−	0.0315729i	−0.00349359	−	0.00293147i
$117$	1.14200			0.105578
$118$	−14.4058	−	12.0879i	−1.32617	−	1.11279i
$119$	−4.82612	−	8.35909i	−0.442410	−	0.766276i
$120$	−4.44785	−	1.61889i	−0.406032	−	0.147783i
$121$	2.49500	−	4.32146i	0.226818	−	0.392860i
$122$	6.71457	+	11.6300i	0.607908	+	1.05293i
$123$	−1.71563	−	9.72980i	−0.154693	−	0.877306i
$124$	1.17274	−	0.426841i	0.105315	−	0.0383314i
$125$	5.94217	−	10.2921i	0.531484	−	0.920557i
$126$	−2.99373	+	2.51204i	−0.266703	+	0.223790i
$127$	0.594127	−	0.498532i	0.0527203	−	0.0442376i	−0.616047	−	0.787710i	$-0.711267\pi$
$127$	0.594127	−	0.498532i	0.0527203	−	0.0442376i	0.668767	+	0.743472i	$0.266822\pi$
$128$	−8.27936	−	3.01344i	−0.731799	−	0.266353i
$129$	1.82827	−	10.3686i	0.160970	−	0.912906i
$130$	0.418219	−	2.37184i	0.0366803	−	0.208024i
$131$	−3.93693	−	1.43293i	−0.343971	−	0.125195i	0.164257	−	0.986418i	$-0.447477\pi$
$131$	−3.93693	−	1.43293i	−0.343971	−	0.125195i	−0.508229	+	0.861222i	$0.669699\pi$
$132$	0.458932	−	0.385089i	0.0399449	−	0.0335177i
$133$	−13.0422	+	10.9437i	−1.13091	+	0.948942i
$134$	−7.20646	+	12.4820i	−0.622544	+	1.07828i
$135$	1.49568	−	0.544384i	0.128728	−	0.0468531i
$136$	1.68992	+	9.58404i	0.144910	+	0.821825i
$137$	5.39249	+	9.34007i	0.460712	+	0.797976i	0.998997	−	0.0447869i	$-0.0142609\pi$
$137$	5.39249	+	9.34007i	0.460712	+	0.797976i	−0.538285	+	0.842763i	$0.680928\pi$
$138$	−0.305221	+	0.528658i	−0.0259821	+	0.0450023i
$139$	−14.3999	−	5.24114i	−1.22139	−	0.444548i	−0.350747	−	0.936470i	$-0.614072\pi$
$139$	−14.3999	−	5.24114i	−1.22139	−	0.444548i	−0.870639	+	0.491922i	$0.836294\pi$
$140$	−0.573618	−	0.993535i	−0.0484795	−	0.0839690i
$141$	4.60182	+	3.86138i	0.387543	+	0.325187i
$142$	4.09507			0.343651
$143$	2.14465	+	1.79957i	0.179344	+	0.150488i
$144$	3.24338	−	1.18049i	0.270282	−	0.0983744i
$145$	0.0555538	−	0.315061i	0.00461349	−	0.0261644i
$146$	0.901069	+	5.11022i	0.0745730	+	0.422925i
$147$	−1.69931			−0.140157
$148$	0.676566	+	1.32358i	0.0556134	+	0.108798i
$149$	11.0009			0.901230			0.450615	−	0.892718i	$-0.351205\pi$
$149$	11.0009			0.901230			0.450615	+	0.892718i	$0.351205\pi$
$150$	0.567521	+	3.21857i	0.0463379	+	0.262795i
$151$	−3.98983	+	22.6274i	−0.324687	+	1.84139i	0.187176	+	0.982326i	$0.440067\pi$
$151$	−3.98983	+	22.6274i	−0.324687	+	1.84139i	−0.511863	+	0.859067i	$0.671044\pi$
$152$	16.1307	−	5.87109i	1.30837	−	0.476208i
$153$	−2.50692	−	2.10355i	−0.202672	−	0.170062i
$154$	−9.58067			−0.772032
$155$	6.22680	+	5.22491i	0.500149	+	0.419674i
$156$	−0.139538	−	0.241686i	−0.0111719	−	0.0193504i
$157$	21.4656	+	7.81285i	1.71314	+	0.623533i	0.997211	−	0.0746355i	$-0.0237793\pi$
$157$	21.4656	+	7.81285i	1.71314	+	0.623533i	0.715933	+	0.698169i	$0.246002\pi$
$158$	6.95952	−	12.0542i	0.553670	−	0.958985i
$159$	−6.25021	−	10.8257i	−0.495674	−	0.858532i
$160$	0.379848	+	2.15422i	0.0300296	+	0.170306i
$161$	−1.27690	+	0.464753i	−0.100634	+	0.0366277i
$162$	−0.662500	+	1.14748i	−0.0520509	+	0.0901548i
$163$	−9.35759	+	7.85195i	−0.732943	+	0.615012i	−0.930932	−	0.365192i	$-0.881003\pi$
$163$	−9.35759	+	7.85195i	−0.732943	+	0.615012i	0.197989	+	0.980204i	$0.436559\pi$
$164$	−1.84954	+	1.55195i	−0.144425	+	0.121187i
$165$	3.66671	+	1.33457i	0.285453	+	0.103896i
$166$	−1.48955	+	8.44766i	−0.115612	+	0.655666i
$167$	1.70910	−	9.69277i	0.132254	−	0.750049i	−0.844479	−	0.535589i	$-0.820090\pi$
$167$	1.70910	−	9.69277i	0.132254	−	0.750049i	0.976733	−	0.214460i	$-0.0687992\pi$
$168$	8.24213	+	2.99989i	0.635894	+	0.231447i
$169$	−8.95954	+	7.51794i	−0.689195	+	0.578303i
$170$	−5.28700	+	4.43632i	−0.405494	+	0.340250i
$171$	−2.88619	+	4.99904i	−0.220713	+	0.382286i
$172$	−2.41775	+	0.879990i	−0.184352	+	0.0670986i
$173$	1.39902	+	7.93423i	0.106365	+	0.603228i	0.990666	+	0.136310i	$0.0435244\pi$
$173$	1.39902	+	7.93423i	0.106365	+	0.603228i	−0.884301	+	0.466918i	$0.845364\pi$
$174$	0.133161	+	0.230641i	0.0100949	+	0.0174848i
$175$	−3.63754	+	6.30041i	−0.274972	+	0.476266i
$176$	7.95124	+	2.89402i	0.599347	+	0.218145i
$177$	−7.09642	−	12.2914i	−0.533399	−	0.923875i
$178$	−6.78241	−	5.69112i	−0.508363	−	0.426567i
$179$	24.5275			1.83327			0.916635	−	0.399725i	$-0.130894\pi$
$179$	24.5275			1.83327			0.916635	+	0.399725i	$0.130894\pi$
$180$	−0.297964	−	0.250022i	−0.0222089	−	0.0186355i
$181$	16.4598	−	5.99087i	1.22344	−	0.445298i	0.352097	−	0.935963i	$-0.385469\pi$
$181$	16.4598	−	5.99087i	1.22344	−	0.445298i	0.871348	+	0.490666i	$0.163246\pi$
$182$	−0.774985	+	4.39516i	−0.0574457	+	0.325791i
$183$	1.75996	+	9.98122i	0.130100	+	0.737833i
$184$	1.37006			0.101002
$185$	−5.26251	+	8.12665i	−0.386907	+	0.597483i
$186$	−6.76665			−0.496155
$187$	−1.39314	−	7.90087i	−0.101876	−	0.577769i
$188$	0.254919	−	1.44572i	0.0185919	−	0.105440i
$189$	−2.77159	+	1.00877i	−0.201603	+	0.0733776i
$190$	9.32564	+	7.82514i	0.676553	+	0.567696i
$191$	1.24545			0.0901177			0.0450589	−	0.998984i	$-0.485652\pi$
$191$	1.24545			0.0901177			0.0450589	+	0.998984i	$0.485652\pi$
$192$	−6.68299	−	5.60770i	−0.482304	−	0.404701i
$193$	−5.05734	−	8.75957i	−0.364035	−	0.630527i	0.624586	−	0.780956i	$-0.285268\pi$
$193$	−5.05734	−	8.75957i	−0.364035	−	0.630527i	−0.988621	+	0.150429i	$0.951935\pi$
$194$	9.99932	+	3.63946i	0.717909	+	0.261298i
$195$	0.908841	−	1.57416i	0.0650835	−	0.112728i
$196$	0.207635	+	0.359634i	0.0148311	+	0.0256882i
$197$	−1.38359	−	7.84672i	−0.0985765	−	0.559055i	−0.993593	−	0.113021i	$-0.963947\pi$
$197$	−1.38359	−	7.84672i	−0.0985765	−	0.559055i	0.895016	−	0.446034i	$-0.147164\pi$
$198$	−3.05238	+	1.11098i	−0.216923	+	0.0789537i
$199$	7.15761	−	12.3973i	0.507390	−	0.878824i	−0.492574	−	0.870271i	$-0.663944\pi$
$199$	7.15761	−	12.3973i	0.507390	−	0.878824i	0.999963	−	0.00855379i	$-0.00272279\pi$
$200$	5.61902	−	4.71492i	0.397325	−	0.333395i
$201$	−8.33279	+	6.99204i	−0.587750	+	0.493180i
$202$	16.7138	+	6.08334i	1.17598	+	0.428022i
$203$	−0.102944	+	0.583827i	−0.00722528	+	0.0409766i
$204$	−0.138871	+	0.787578i	−0.00972294	+	0.0551415i
$205$	−14.7772	−	5.37845i	−1.03208	−	0.375647i
$206$	−6.27857	+	5.26834i	−0.437449	+	0.367063i
$207$	−0.352925	+	0.296139i	−0.0245300	+	0.0205831i
$208$	1.97082	−	3.41356i	0.136652	−	0.236688i
$209$	−13.2978	+	4.83999i	−0.919826	+	0.334789i
$210$	1.08014	+	6.12581i	0.0745371	+	0.422721i
$211$	−5.14044	−	8.90351i	−0.353883	−	0.612943i	0.633043	−	0.774116i	$-0.281805\pi$
$211$	−5.14044	−	8.90351i	−0.353883	−	0.612943i	−0.986926	+	0.161174i	$0.948472\pi$
$212$	−1.52739	+	2.64552i	−0.104902	+	0.181695i
$213$	2.90423	+	1.05705i	0.198995	+	0.0724282i
$214$	−5.08728	−	8.81142i	−0.347759	−	0.602336i
$215$	−12.8374	−	10.7719i	−0.875503	−	0.734634i
$216$	2.97380			0.202341
$217$	−11.5386	−	9.68206i	−0.783293	−	0.657261i
$218$	−7.22406	+	2.62934i	−0.489275	+	0.178082i
$219$	−0.680052	+	3.85677i	−0.0459537	+	0.260616i
$220$	−0.165584	−	0.939072i	−0.0111637	−	0.0633122i
$221$	−3.73724			−0.251394
$222$	−0.992622	−	7.99830i	−0.0666204	−	0.536811i
$223$	−19.2496			−1.28905			−0.644526	−	0.764582i	$-0.722945\pi$
$223$	−19.2496			−1.28905			−0.644526	+	0.764582i	$0.722945\pi$
$224$	−0.703881	−	3.99190i	−0.0470300	−	0.266720i
$225$	−0.428318	+	2.42911i	−0.0285545	+	0.161941i
$226$	−4.24787	+	1.54610i	−0.282564	+	0.102845i
$227$	−3.05773	−	2.56574i	−0.202949	−	0.170294i	0.535649	−	0.844441i	$-0.320067\pi$
$227$	−3.05773	−	2.56574i	−0.202949	−	0.170294i	−0.738598	+	0.674147i	$0.764512\pi$
$228$	1.41063			0.0934211
$229$	5.16991	+	4.33807i	0.341637	+	0.286668i	0.797422	−	0.603422i	$-0.206197\pi$
$229$	5.16991	+	4.33807i	0.341637	+	0.286668i	−0.455784	+	0.890090i	$0.650641\pi$
$230$	0.485811	+	0.841449i	0.0320334	+	0.0554835i
$231$	−6.79463	−	2.47304i	−0.447054	−	0.162714i
$232$	0.298862	−	0.517645i	0.0196213	−	0.0339850i
$233$	−9.25046	−	16.0223i	−0.606018	−	1.04965i	−0.991890	−	0.127102i	$-0.959433\pi$
$233$	−9.25046	−	16.0223i	−0.606018	−	1.04965i	0.385872	−	0.922552i	$-0.373901\pi$
$234$	0.262755	+	1.49016i	0.0171768	+	0.0974146i
$235$	8.98493	−	3.27025i	0.586112	−	0.213327i
$236$	−1.73419	+	3.00370i	−0.112886	+	0.195524i
$237$	8.04725	−	6.75245i	0.522725	−	0.438619i
$238$	9.79711	−	8.22076i	0.635053	−	0.532872i
$239$	9.75427	+	3.55026i	0.630951	+	0.229647i	0.637645	−	0.770330i	$-0.279909\pi$
$239$	9.75427	+	3.55026i	0.630951	+	0.229647i	−0.00669404	+	0.999978i	$0.502131\pi$
$240$	0.953971	−	5.41024i	0.0615786	−	0.349230i
$241$	1.88258	−	10.6766i	0.121267	−	0.687742i	−0.862188	−	0.506589i	$-0.830906\pi$
$241$	1.88258	−	10.6766i	0.121267	−	0.687742i	0.983455	−	0.181152i	$-0.0579827\pi$
$242$	6.21301	+	2.26135i	0.399387	+	0.145365i
$243$	−0.766044	+	0.642788i	−0.0491418	+	0.0412348i
$244$	1.89733	−	1.59205i	0.121464	−	0.101920i
$245$	−1.35238	+	2.34238i	−0.0864001	+	0.149649i
$246$	12.3014	−	4.47734i	0.784308	−	0.285465i
$247$	1.14470	+	6.49190i	0.0728353	+	0.413070i
$248$	7.59344	+	13.1522i	0.482184	+	0.835168i
$249$	−3.23697	+	5.60660i	−0.205135	+	0.355304i
$250$	14.7971	+	5.38571i	0.935852	+	0.340622i
$251$	4.24249	+	7.34821i	0.267784	+	0.463815i	0.968289	−	0.249832i	$-0.0803754\pi$
$251$	4.24249	+	7.34821i	0.267784	+	0.463815i	−0.700505	+	0.713647i	$0.747042\pi$
$252$	0.552145	+	0.463305i	0.0347819	+	0.0291854i
$253$	−1.12945			−0.0710076
$254$	0.787219	+	0.660555i	0.0493945	+	0.0414469i
$255$	−4.89469	+	1.78152i	−0.306517	+	0.111563i
$256$	−1.00262	+	5.68615i	−0.0626639	+	0.355384i
$257$	−4.01532	−	22.7720i	−0.250469	−	1.42048i	−0.807442	−	0.589947i	$-0.799148\pi$
$257$	−4.01532	−	22.7720i	−0.250469	−	1.42048i	0.556973	−	0.830531i	$-0.311963\pi$
$258$	13.9504			0.868512
$259$	9.75173	−	15.0592i	0.605943	−	0.935731i
$260$	−0.444196			−0.0275479
$261$	0.0349028	+	0.197944i	0.00216043	+	0.0122524i
$262$	0.963958	−	5.46688i	0.0595535	−	0.337745i
$263$	4.60338	−	1.67549i	0.283857	−	0.103315i	−0.196168	−	0.980570i	$-0.562850\pi$
$263$	4.60338	−	1.67549i	0.283857	−	0.103315i	0.480025	+	0.877255i	$0.340628\pi$
$264$	5.58474	+	4.68615i	0.343717	+	0.288413i
$265$	−19.8965			−1.22224
$266$	−17.2810	−	14.5005i	−1.05956	−	0.889080i
$267$	−3.34106	−	5.78688i	−0.204469	−	0.354151i
$268$	2.49792	+	0.909169i	0.152585	+	0.0555363i
$269$	3.74448	−	6.48564i	0.228305	−	0.395436i	−0.729001	−	0.684513i	$-0.760015\pi$
$269$	3.74448	−	6.48564i	0.228305	−	0.395436i	0.957306	+	0.289077i	$0.0933483\pi$
$270$	1.05448	+	1.82642i	0.0641737	+	0.111152i
$271$	3.45930	+	19.6187i	0.210137	+	1.19175i	0.889148	+	0.457620i	$0.151298\pi$
$271$	3.45930	+	19.6187i	0.210137	+	1.19175i	−0.679010	+	0.734129i	$0.737591\pi$
$272$	−10.6141	+	3.86322i	−0.643575	+	0.234242i
$273$	−1.68414	+	2.91701i	−0.101929	+	0.176545i
$274$	−10.9469	+	9.18550i	−0.661324	+	0.554916i
$275$	−4.63220	+	3.88688i	−0.279332	+	0.234387i
$276$	0.105796	+	0.0385067i	0.00636819	+	0.00231783i
$277$	5.48051	−	31.0815i	0.329292	−	1.86751i	−0.148326	−	0.988938i	$-0.547389\pi$
$277$	5.48051	−	31.0815i	0.329292	−	1.86751i	0.477618	−	0.878568i	$-0.341500\pi$
$278$	3.52582	−	19.9959i	0.211465	−	1.19928i
$279$	−4.79892	−	1.74666i	−0.287304	−	0.104570i
$280$	10.6945	−	8.97376i	0.639120	−	0.536285i
$281$	−3.13467	+	2.63030i	−0.186999	+	0.156910i	−0.731481	−	0.681862i	$-0.761171\pi$
$281$	−3.13467	+	2.63030i	−0.186999	+	0.156910i	0.544482	+	0.838772i	$0.316726\pi$
$282$	−3.97980	+	6.89322i	−0.236994	+	0.410485i
$283$	27.7551	−	10.1020i	1.64987	−	0.600503i	0.661146	−	0.750257i	$-0.270070\pi$
$283$	27.7551	−	10.1020i	1.64987	−	0.600503i	0.988723	+	0.149754i	$0.0478481\pi$
$284$	−0.131151	−	0.743796i	−0.00778239	−	0.0441362i
$285$	4.59387	+	7.95682i	0.272118	+	0.471321i
$286$	−1.85476	+	3.21254i	−0.109674	+	0.189961i
$287$	27.3830	+	9.96659i	1.61637	+	0.588309i
$288$	−0.687157	−	1.19019i	−0.0404911	−	0.0701327i
$289$	−4.81876	−	4.04342i	−0.283456	−	0.237848i
$290$	0.423896			0.0248920
$291$	6.15209	+	5.16222i	0.360642	+	0.302615i
$292$	0.899321	−	0.327326i	0.0526288	−	0.0191553i
$293$	−3.00728	+	17.0551i	−0.175687	+	0.996370i	0.761661	+	0.647976i	$0.224384\pi$
$293$	−3.00728	+	17.0551i	−0.175687	+	0.996370i	−0.937348	+	0.348394i	$0.886727\pi$
$294$	−0.390985	−	2.21739i	−0.0228027	−	0.129321i
$295$	−22.5903			−1.31526
$296$	−14.4323	+	10.9049i	−0.838859	+	0.633837i
$297$	−2.45153			−0.142252
$298$	2.53113	+	14.3548i	0.146625	+	0.831550i
$299$	−0.0913614	+	0.518136i	−0.00528357	+	0.0299646i
$300$	0.566419	−	0.206160i	0.0327022	−	0.0119026i
$301$	23.7885	+	19.9609i	1.37114	+	1.15053i
$302$	−30.4438			−1.75185
$303$	10.2832	+	8.62863i	0.590754	+	0.495702i
$304$	9.96179	+	17.2543i	0.571348	+	0.989604i
$305$	15.1590	+	5.51743i	0.868003	+	0.315927i
$306$	2.16806	−	3.75519i	0.123940	−	0.214670i
$307$	−0.0205345	−	0.0355668i	−0.00117196	−	0.00202990i	0.865439	−	0.501015i	$-0.167040\pi$
$307$	−0.0205345	−	0.0355668i	−0.00117196	−	0.00202990i	−0.866611	+	0.498985i	$0.833706\pi$
$308$	0.306836	+	1.74016i	0.0174836	+	0.0991545i
$309$	−5.81268	+	2.11564i	−0.330672	+	0.120355i
$310$	−5.38514	+	9.32733i	−0.305855	+	0.529757i
$311$	25.7424	−	21.6004i	1.45972	−	1.22485i	0.534632	−	0.845085i	$-0.320450\pi$
$311$	25.7424	−	21.6004i	1.45972	−	1.22485i	0.925084	−	0.379762i	$-0.123994\pi$
$312$	2.60154	−	2.18295i	0.147283	−	0.123585i
$313$	3.34056	+	1.21586i	0.188819	+	0.0687247i	0.434699	−	0.900576i	$-0.356855\pi$
$313$	3.34056	+	1.21586i	0.188819	+	0.0687247i	−0.245880	+	0.969300i	$0.579077\pi$
$314$	−5.25586	+	29.8075i	−0.296605	+	1.68213i
$315$	−0.815204	+	4.62325i	−0.0459315	+	0.260491i
$316$	−2.41233	−	0.878015i	−0.135704	−	0.0493922i
$317$	−19.0127	+	15.9535i	−1.06786	+	0.896040i	−0.994857	−	0.101292i	$-0.967702\pi$
$317$	−19.0127	+	15.9535i	−1.06786	+	0.896040i	−0.0730022	+	0.997332i	$0.523258\pi$
$318$	12.6880	−	10.6465i	0.711509	−	0.597027i
$319$	−0.246375	+	0.426735i	−0.0137944	+	0.0238926i
$320$	−13.0484	+	4.74922i	−0.729426	+	0.265489i
$321$	−1.33343	−	7.56225i	−0.0744247	−	0.422083i
$322$	−0.900236	−	1.55925i	−0.0501682	−	0.0868938i
$323$	9.44521	−	16.3596i	0.525545	−	0.910271i
$324$	0.229637	+	0.0835811i	0.0127576	+	0.00464340i
$325$	1.40841	+	2.43944i	0.0781247	+	0.135316i
$326$	−12.3988	−	10.4038i	−0.686706	−	0.576215i
$327$	−5.80203			−0.320853
$328$	−22.5070	−	18.8856i	−1.24274	−	1.04278i
$329$	−16.6496	+	6.05996i	−0.917922	+	0.334096i
$330$	−0.897794	+	5.09165i	−0.0494220	+	0.280286i
$331$	4.50126	+	25.5279i	0.247412	+	1.40314i	0.814825	+	0.579707i	$0.196833\pi$
$331$	4.50126	+	25.5279i	0.247412	+	1.40314i	−0.567413	+	0.823433i	$0.692056\pi$
$332$	1.58207			0.0868274
$333$	1.36062	−	5.92864i	0.0745615	−	0.324887i
$334$	13.0410			0.713574
$335$	3.00649	+	17.0507i	0.164262	+	0.931577i
$336$	−1.76777	+	10.0255i	−0.0964395	+	0.546936i
$337$	0.344450	−	0.125370i	0.0187634	−	0.00682932i	−0.332621	−	0.943060i	$-0.607933\pi$
$337$	0.344450	−	0.125370i	0.0187634	−	0.00682932i	0.351385	+	0.936231i	$0.385711\pi$
$338$	−11.8714	−	9.96128i	−0.645718	−	0.541822i
$339$	−3.41169			−0.185298
$340$	0.975101	+	0.818207i	0.0528823	+	0.0443735i
$341$	−6.25986	−	10.8424i	−0.338991	−	0.587149i
$342$	−7.18716	−	2.61591i	−0.388637	−	0.141452i
$343$	−7.81708	+	13.5396i	−0.422083	+	0.731069i
$344$	−15.6549	−	27.1151i	−0.844057	−	1.46195i
$345$	0.127336	+	0.722159i	0.00685554	+	0.0388797i
$346$	−10.0312	+	3.65107i	−0.539283	+	0.196283i
$347$	−10.5030	+	18.1918i	−0.563833	+	0.976588i	0.433324	+	0.901238i	$0.357341\pi$
$347$	−10.5030	+	18.1918i	−0.563833	+	0.976588i	−0.997157	+	0.0753496i	$0.975993\pi$
$348$	0.0376271	−	0.0315729i	0.00201702	−	0.00169248i
$349$	8.63908	−	7.24905i	0.462439	−	0.388032i	−0.381588	−	0.924332i	$-0.624623\pi$
$349$	8.63908	−	7.24905i	0.462439	−	0.388032i	0.844028	+	0.536300i	$0.180178\pi$
$350$	−9.05816	−	3.29690i	−0.484179	−	0.176227i
$351$	−0.198306	+	1.12465i	−0.0105848	+	0.0600292i
$352$	0.585051	−	3.31799i	0.0311833	−	0.176849i
$353$	−25.3287	−	9.21889i	−1.34811	−	0.490672i	−0.435753	−	0.900066i	$-0.643518\pi$
$353$	−25.3287	−	9.21889i	−1.34811	−	0.490672i	−0.912358	+	0.409394i	$0.865740\pi$
$354$	14.4058	−	12.0879i	0.765662	−	0.642467i
$355$	3.76836	−	3.16203i	0.200004	−	0.167823i
$356$	−0.816471	+	1.41417i	−0.0432729	+	0.0749508i
$357$	9.07014	−	3.30126i	0.480043	−	0.174721i
$358$	5.64338	+	32.0052i	0.298262	+	1.69153i
$359$	−11.5699	−	20.0396i	−0.610634	−	1.05765i	−0.991134	−	0.132868i	$-0.957581\pi$
$359$	−11.5699	−	20.0396i	−0.610634	−	1.05765i	0.380500	−	0.924781i	$-0.375752\pi$
$360$	2.36665	−	4.09916i	0.124734	−	0.216045i
$361$	−13.4568	−	4.89789i	−0.708255	−	0.257784i
$362$	11.6044	+	20.0995i	0.609915	+	1.05640i
$363$	3.82256	+	3.20751i	0.200632	+	0.168350i
$364$	0.823121			0.0431433
$365$	4.77507	+	4.00676i	0.249938	+	0.209723i
$366$	−12.6193	+	4.59303i	−0.659619	+	0.240082i
$367$	−1.14399	+	6.48788i	−0.0597157	+	0.338664i	−0.999999	−	0.00172982i	$-0.999449\pi$
$367$	−1.14399	+	6.48788i	−0.0597157	+	0.338664i	0.940283	+	0.340394i	$0.110560\pi$
$368$	0.276128	+	1.56600i	0.0143942	+	0.0816333i
$369$	9.87990			0.514327
$370$	−11.8150	−	4.99708i	−0.614235	−	0.259786i
$371$	36.8695			1.91417
$372$	0.216713	+	1.22904i	0.0112360	+	0.0637227i
$373$	0.750629	−	4.25703i	0.0388661	−	0.220420i	−0.959188	−	0.282768i	$-0.908747\pi$
$373$	0.750629	−	4.25703i	0.0388661	−	0.220420i	0.998055	+	0.0623471i	$0.0198586\pi$
$374$	9.98907	−	3.63572i	0.516522	−	0.187999i
$375$	9.10394	+	7.63911i	0.470125	+	0.394482i
$376$	17.8643			0.921282
$377$	0.175836	+	0.147544i	0.00905603	+	0.00759891i
$378$	−1.95402	−	3.38446i	−0.100504	−	0.174078i
$379$	4.91716	+	1.78970i	0.252578	+	0.0919307i	0.465206	−	0.885202i	$-0.345980\pi$
$379$	4.91716	+	1.78970i	0.252578	+	0.0919307i	−0.212629	+	0.977133i	$0.568202\pi$
$380$	1.12263	−	1.94445i	0.0575896	−	0.0997480i
$381$	0.387789	+	0.671670i	0.0198670	+	0.0344107i
$382$	0.286558	+	1.62515i	0.0146616	+	0.0831501i
$383$	7.31682	−	2.66310i	0.373872	−	0.136078i	−0.148248	−	0.988950i	$-0.547363\pi$
$383$	7.31682	−	2.66310i	0.373872	−	0.136078i	0.522120	+	0.852872i	$0.325141\pi$
$384$	4.40535	−	7.63030i	0.224810	−	0.389382i
$385$	−8.81632	+	7.39777i	−0.449321	+	0.377025i
$386$	10.2665	−	8.61461i	0.522550	−	0.438472i
$387$	9.89363	+	3.60099i	0.502921	+	0.183048i
$388$	0.340797	−	1.93276i	0.0173013	−	0.0981208i
$389$	−5.87960	+	33.3449i	−0.298108	+	1.69065i	0.356189	+	0.934414i	$0.384076\pi$
$389$	−5.87960	+	33.3449i	−0.298108	+	1.69065i	−0.654297	+	0.756238i	$0.727035\pi$
$390$	2.26318	+	0.823731i	0.114601	+	0.0417113i
$391$	1.15496	−	0.969128i	0.0584089	−	0.0490109i
$392$	−3.87114	+	3.24827i	−0.195522	+	0.164063i
$393$	2.09480	−	3.62829i	0.105669	−	0.183023i
$394$	9.92061	−	3.61081i	0.499793	−	0.181910i
$395$	−2.90347	−	16.4664i	−0.146089	−	0.828514i
$396$	0.299546	+	0.518829i	0.0150528	+	0.0260722i
$397$	−5.10209	+	8.83708i	−0.256067	+	0.443520i	−0.965185	−	0.261569i	$-0.915760\pi$
$397$	−5.10209	+	8.83708i	−0.256067	+	0.443520i	0.709118	+	0.705090i	$0.249093\pi$
$398$	17.8238	+	6.48732i	0.893425	+	0.325180i
$399$	−8.51272	−	14.7445i	−0.426169	−	0.738146i
$400$	6.52171	+	5.47236i	0.326085	+	0.273618i
$401$	−6.85679			−0.342412			−0.171206	−	0.985235i	$-0.554766\pi$
$401$	−6.85679			−0.342412			−0.171206	+	0.985235i	$0.554766\pi$
$402$	−11.0409	−	9.26445i	−0.550672	−	0.462069i
$403$	−5.48035	+	1.99468i	−0.272995	+	0.0993622i
$404$	0.569641	−	3.23059i	0.0283407	−	0.160728i
$405$	0.276391	+	1.56749i	0.0137340	+	0.0778892i
$406$	−0.785504			−0.0389839
$407$	11.8976	−	8.98979i	0.589744	−	0.445607i
$408$	−9.73189			−0.481800
$409$	−2.36721	−	13.4251i	−0.117051	−	0.663830i	−0.985714	−	0.168427i	$-0.946131\pi$
$409$	−2.36721	−	13.4251i	−0.117051	−	0.663830i	0.868663	−	0.495403i	$-0.164980\pi$
$410$	3.61819	−	20.5198i	0.178690	−	1.01340i
$411$	−10.1346	+	3.68868i	−0.499901	+	0.181949i
$412$	1.15798	+	0.971661i	0.0570496	+	0.0478703i
$413$	41.8612			2.05985
$414$	−0.467625	−	0.392384i	−0.0229825	−	0.0192846i
$415$	5.15220	+	8.92387i	0.252911	+	0.438055i
$416$	−1.47481	−	0.536788i	−0.0723086	−	0.0263182i
$417$	7.66204	−	13.2710i	0.375212	−	0.649886i
$418$	−9.37516	−	16.2383i	−0.458554	−	0.794239i
$419$	2.87541	+	16.3073i	0.140473	+	0.796663i	0.970891	+	0.239522i	$0.0769907\pi$
$419$	2.87541	+	16.3073i	0.140473	+	0.796663i	−0.830418	+	0.557141i	$0.811898\pi$
$420$	1.07805	−	0.392378i	0.0526034	−	0.0191461i
$421$	4.98312	−	8.63102i	0.242862	−	0.420650i	−0.718666	−	0.695355i	$-0.755247\pi$
$421$	4.98312	−	8.63102i	0.242862	−	0.420650i	0.961528	+	0.274705i	$0.0885803\pi$
$422$	10.4352	−	8.75616i	0.507977	−	0.426243i
$423$	−4.60182	+	3.86138i	−0.223748	+	0.187747i
$424$	−34.9318	−	12.7141i	−1.69644	−	0.617454i
$425$	1.40169	−	7.94937i	0.0679919	−	0.385601i
$426$	−0.711102	+	4.03286i	−0.0344530	+	0.195393i
$427$	−28.0906	−	10.2241i	−1.35940	−	0.494780i
$428$	−1.43751	+	1.20621i	−0.0694845	+	0.0583044i
$429$	−2.14465	+	1.79957i	−0.103545	+	0.0868842i
$430$	11.1022	−	19.2296i	0.535395	−	0.927332i
$431$	6.21543	−	2.26223i	0.299387	−	0.108968i	−0.187959	−	0.982177i	$-0.560187\pi$
$431$	6.21543	−	2.26223i	0.299387	−	0.108968i	0.487346	+	0.873209i	$0.337965\pi$
$432$	0.599352	+	3.39909i	0.0288363	+	0.163539i
$433$	0.786742	+	1.36268i	0.0378084	+	0.0654861i	0.884310	−	0.466899i	$-0.154629\pi$
$433$	0.786742	+	1.36268i	0.0378084	+	0.0654861i	−0.846502	+	0.532386i	$0.821296\pi$
$434$	9.97898	−	17.2841i	0.479006	−	0.829663i
$435$	0.300628	+	0.109420i	0.0144140	+	0.00524627i
$436$	0.708935	+	1.22791i	0.0339518	+	0.0588063i
$437$	−2.03722	−	1.70943i	−0.0974533	−	0.0817731i
$438$	−5.18905			−0.247942
$439$	17.1792	+	14.4150i	0.819917	+	0.687992i	0.952953	−	0.303119i	$-0.0980280\pi$
$439$	17.1792	+	14.4150i	0.819917	+	0.687992i	−0.133035	+	0.991111i	$0.542472\pi$
$440$	10.9041	−	3.96875i	0.519830	−	0.189203i
$441$	0.295083	−	1.67350i	0.0140516	−	0.0796904i
$442$	−0.859877	−	4.87661i	−0.0409002	−	0.231957i
$443$	−37.5819			−1.78557			−0.892785	−	0.450482i	$-0.851252\pi$
$443$	−37.5819			−1.78557			−0.892785	+	0.450482i	$0.851252\pi$
$444$	−1.42096	+	0.436450i	−0.0674356	+	0.0207130i
$445$	−10.6357			−0.504182
$446$	−4.42903	−	25.1183i	−0.209721	−	1.18939i
$447$	−1.91029	+	10.8338i	−0.0903536	+	0.512421i
$448$	24.1794	−	8.80058i	1.14237	−	0.415788i
$449$	−1.76168	−	1.47822i	−0.0831386	−	0.0697616i	0.600271	−	0.799797i	$-0.295059\pi$
$449$	−1.76168	−	1.47822i	−0.0831386	−	0.0697616i	−0.683410	+	0.730035i	$0.739504\pi$
$450$	−3.26822			−0.154065
$451$	18.5543	+	15.5689i	0.873686	+	0.733110i
$452$	0.416866	+	0.722032i	0.0196077	+	0.0339615i
$453$	−21.5908	−	7.85842i	−1.01443	−	0.369221i
$454$	2.64443	−	4.58028i	0.124109	−	0.214963i
$455$	2.68059	+	4.64292i	0.125668	+	0.217663i
$456$	2.98083	+	16.9051i	0.139590	+	0.791655i
$457$	−3.08395	+	1.12247i	−0.144261	+	0.0525068i	−0.413142	−	0.910667i	$-0.635569\pi$
$457$	−3.08395	+	1.12247i	−0.144261	+	0.0525068i	0.268880	+	0.963174i	$0.413346\pi$
$458$	−4.47111	+	7.74418i	−0.208921	+	0.361862i
$459$	2.50692	−	2.10355i	0.117013	−	0.0981854i
$460$	0.137275	−	0.115188i	0.00640049	−	0.00537065i
$461$	−23.2997	−	8.48040i	−1.08518	−	0.394972i	−0.263344	−	0.964702i	$-0.584825\pi$
$461$	−23.2997	−	8.48040i	−1.08518	−	0.394972i	−0.821832	+	0.569730i	$0.807048\pi$
$462$	1.66367	−	9.43512i	0.0774007	−	0.438961i
$463$	1.28064	−	7.26288i	0.0595164	−	0.337534i	−0.940481	−	0.339847i	$-0.889625\pi$
$463$	1.28064	−	7.26288i	0.0595164	−	0.337534i	0.999997	+	0.00231212i	$0.000735970\pi$
$464$	0.651910	+	0.237276i	0.0302641	+	0.0110152i
$465$	−6.22680	+	5.22491i	−0.288761	+	0.242299i
$466$	18.7786	−	15.7571i	0.869902	−	0.729935i
$467$	−15.7245	+	27.2357i	−0.727645	+	1.26032i	0.230231	+	0.973136i	$0.426052\pi$
$467$	−15.7245	+	27.2357i	−0.727645	+	1.26032i	−0.957876	+	0.287182i	$0.907282\pi$
$468$	0.262245	−	0.0954493i	0.0121223	−	0.00441215i
$469$	−5.57120	−	31.5959i	−0.257254	−	1.45896i
$470$	6.33453	+	10.9717i	0.292190	+	0.506088i
$471$	−11.4216	+	19.7828i	−0.526281	+	0.911545i
$472$	−39.6612	−	14.4355i	−1.82556	−	0.664448i
$473$	12.9056	+	22.3531i	0.593399	+	1.02780i
$474$	10.6626	+	8.94699i	0.489750	+	0.410949i
$475$	−14.2381			−0.653288
$476$	−1.80692	−	1.51619i	−0.0828200	−	0.0694943i
$477$	11.7465	−	4.27539i	0.537837	−	0.195757i
$478$	−2.38833	+	13.5449i	−0.109240	+	0.619530i
$479$	0.560958	+	3.18135i	0.0256308	+	0.145360i	0.994938	−	0.100495i	$-0.0320426\pi$
$479$	0.560958	+	3.18135i	0.0256308	+	0.145360i	−0.969307	+	0.245854i	$0.920931\pi$
$480$	−2.18746			−0.0998433
$481$	−3.16168	−	6.18526i	−0.144160	−	0.282024i
$482$	14.3648			0.654297
$483$	−0.235961	−	1.33820i	−0.0107366	−	0.0608903i
$484$	0.211752	−	1.20090i	0.00962508	−	0.0545865i
$485$	12.0118	−	4.37194i	0.545428	−	0.198519i
$486$	−1.01501	−	0.851694i	−0.0460417	−	0.0386336i
$487$	9.64976			0.437273			0.218636	−	0.975806i	$-0.429839\pi$
$487$	9.64976			0.437273			0.218636	+	0.975806i	$0.429839\pi$
$488$	23.0886	+	19.3736i	1.04517	+	0.877003i
$489$	−6.10773	−	10.5789i	−0.276201	−	0.478395i
$490$	−3.36767	−	1.22573i	−0.152136	−	0.0553728i
$491$	7.71811	−	13.3682i	0.348313	−	0.603296i	−0.637637	−	0.770337i	$-0.720088\pi$
$491$	7.71811	−	13.3682i	0.348313	−	0.603296i	0.985950	+	0.167041i	$0.0534212\pi$
$492$	−1.20720	−	2.09093i	−0.0544247	−	0.0942664i
$493$	−0.114221	−	0.647779i	−0.00514425	−	0.0291745i
$494$	−8.20771	+	2.98736i	−0.369282	+	0.134408i
$495$	−1.95102	+	3.37926i	−0.0876916	+	0.151886i
$496$	−13.5028	+	11.3302i	−0.606293	+	0.508740i
$497$	−6.98300	+	5.85943i	−0.313230	+	0.262832i
$498$	−8.06066	−	2.93384i	−0.361207	−	0.131469i
$499$	0.249611	−	1.41561i	0.0111741	−	0.0633716i	−0.978711	−	0.205244i	$-0.934201\pi$
$499$	0.249611	−	1.41561i	0.0111741	−	0.0633716i	0.989885	+	0.141872i	$0.0453123\pi$
$500$	0.504315	−	2.86011i	0.0225537	−	0.127908i
$501$	9.24873	+	3.36626i	0.413203	+	0.150394i
$502$	−8.61234	+	7.22661i	−0.384387	+	0.322539i
$503$	−18.5983	+	15.6058i	−0.829256	+	0.695828i	−0.955120	−	0.296219i	$-0.904274\pi$
$503$	−18.5983	+	15.6058i	−0.829256	+	0.695828i	0.125864	+	0.992047i	$0.459830\pi$
$504$	−4.38555	+	7.59599i	−0.195348	+	0.338352i
$505$	20.0777	−	7.30768i	0.893445	−	0.325187i
$506$	−0.259867	−	1.47378i	−0.0115525	−	0.0655175i
$507$	−5.84792	−	10.1289i	−0.259715	−	0.449840i
$508$	0.0947659	−	0.164139i	0.00420456	−	0.00728251i
$509$	20.8236	+	7.57915i	0.922988	+	0.335940i	0.759427	−	0.650593i	$-0.225480\pi$
$509$	20.8236	+	7.57915i	0.922988	+	0.335940i	0.163561	+	0.986533i	$0.447702\pi$
$510$	−3.45084	−	5.97703i	−0.152806	−	0.264667i
$511$	−8.84848	−	7.42475i	−0.391434	−	0.328452i
$512$	−25.2718			−1.11687
$513$	−4.42191	−	3.71042i	−0.195232	−	0.163819i
$514$	28.7906	−	10.4789i	1.26990	−	0.462206i
$515$	−1.70968	+	9.69607i	−0.0753374	+	0.427260i
$516$	−0.446783	−	2.53383i	−0.0196685	−	0.111546i
$517$	−14.7270			−0.647691
$518$	21.8940	+	9.25988i	0.961966	+	0.406856i
$519$	−8.05662			−0.353647
$520$	−0.938641	−	5.32330i	−0.0411621	−	0.233442i
$521$	2.84763	−	16.1497i	0.124757	−	0.707532i	−0.856695	−	0.515823i	$-0.827486\pi$
$521$	2.84763	−	16.1497i	0.124757	−	0.707532i	0.981452	−	0.191708i	$-0.0614028\pi$
$522$	−0.250260	+	0.0910872i	−0.0109536	+	0.00398678i
$523$	1.39289	+	1.16878i	0.0609069	+	0.0511070i	0.672733	−	0.739885i	$-0.265120\pi$
$523$	1.39289	+	1.16878i	0.0609069	+	0.0511070i	−0.611826	+	0.790992i	$0.709565\pi$
$524$	−1.02383			−0.0447263
$525$	−5.57304	−	4.67634i	−0.243227	−	0.204092i
$526$	3.24547	+	5.62131i	0.141509	+	0.245101i
$527$	15.7047	+	5.71604i	0.684107	+	0.248994i
$528$	−4.23077	+	7.32791i	−0.184121	+	0.318906i
$529$	11.3939	+	19.7348i	0.495386	+	0.858033i
$530$	−4.57787	−	25.9624i	−0.198850	−	1.12774i
$531$	13.3369	−	4.85423i	0.578772	−	0.210656i
$532$	−2.08029	+	3.60317i	−0.0901922	+	0.156217i
$533$	8.64313	−	7.25245i	0.374375	−	0.314138i
$534$	6.78241	−	5.69112i	0.293504	−	0.246279i
$535$	−11.4852	−	4.18027i	−0.496548	−	0.180729i
$536$	−5.61717	+	31.8566i	−0.242625	+	1.37599i
$537$	−4.25915	+	24.1549i	−0.183796	+	1.04236i
$538$	9.32446	+	3.39383i	0.402006	+	0.146318i
$539$	3.19128	−	2.67780i	0.137458	−	0.115341i
$540$	0.297964	−	0.250022i	0.0128223	−	0.0107592i
$541$	−15.4079	+	26.6873i	−0.662437	+	1.14738i	0.317536	+	0.948246i	$0.397145\pi$
$541$	−15.4079	+	26.6873i	−0.662437	+	1.14738i	−0.979973	+	0.199129i	$0.936189\pi$
$542$	−24.8039	+	9.02787i	−1.06542	+	0.387780i
$543$	3.04164	+	17.2500i	0.130529	+	0.740269i
$544$	2.24875	+	3.89496i	0.0964145	+	0.166995i
$545$	−4.61746	+	7.99768i	−0.197790	+	0.342583i
$546$	−4.19381	−	1.52642i	−0.179479	−	0.0653248i
$547$	−6.85280	−	11.8694i	−0.293005	−	0.507499i	0.681514	−	0.731805i	$-0.261322\pi$
$547$	−6.85280	−	11.8694i	−0.293005	−	0.507499i	−0.974519	+	0.224306i	$0.927989\pi$
$548$	2.01897	+	1.69412i	0.0862462	+	0.0723691i
$549$	−10.1352			−0.432560
$550$	−6.13766	−	5.15011i	−0.261711	−	0.219601i
$551$	−1.09026	+	0.396823i	−0.0464468	+	0.0169052i
$552$	−0.237908	+	1.34924i	−0.0101260	+	0.0574277i
$553$	5.38030	+	30.5132i	0.228794	+	1.29755i
$554$	41.8183			1.77669
$555$	−7.08937	−	6.59373i	−0.300927	−	0.279888i
$556$	−3.74482			−0.158816
$557$	1.22089	+	6.92399i	0.0517306	+	0.293379i	0.999687	−	0.0250216i	$-0.00796546\pi$
$557$	1.22089	+	6.92399i	0.0517306	+	0.293379i	−0.947956	+	0.318400i	$0.896854\pi$
$558$	1.17502	−	6.66384i	0.0497424	−	0.282103i
$559$	11.2985	−	4.11231i	0.477875	−	0.173932i
$560$	12.4126	+	10.4154i	0.524527	+	0.440130i
$561$	8.02275			0.338721
$562$	−4.15343	−	3.48514i	−0.175202	−	0.147012i
$563$	−2.81914	−	4.88290i	−0.118813	−	0.205790i	0.800485	−	0.599353i	$-0.204575\pi$
$563$	−2.81914	−	4.88290i	−0.118813	−	0.205790i	−0.919297	+	0.393563i	$0.871242\pi$
$564$	1.37949	+	0.502092i	0.0580869	+	0.0211419i
$565$	−2.71514	+	4.70277i	−0.114227	+	0.197847i
$566$	19.5678	+	33.8925i	0.822498	+	1.42461i
$567$	−0.512168	−	2.90465i	−0.0215090	−	0.121984i
$568$	8.63660	−	3.14346i	0.362384	−	0.131897i
$569$	17.6996	−	30.6565i	0.742004	−	1.28519i	−0.209577	−	0.977792i	$-0.567209\pi$
$569$	17.6996	−	30.6565i	0.742004	−	1.28519i	0.951581	−	0.307397i	$-0.0994580\pi$
$570$	−9.32564	+	7.82514i	−0.390608	+	0.327759i
$571$	−0.624413	+	0.523944i	−0.0261309	+	0.0219264i	−0.655760	−	0.754970i	$-0.727651\pi$
$571$	−0.624413	+	0.523944i	−0.0261309	+	0.0219264i	0.629629	+	0.776896i	$0.283207\pi$
$572$	0.642901	+	0.233997i	0.0268811	+	0.00978391i
$573$	−0.216270	+	1.22653i	−0.00903483	+	0.0512390i
$574$	−6.70473	+	38.0244i	−0.279850	+	1.58711i
$575$	−1.06785	−	0.388665i	−0.0445323	−	0.0162084i
$576$	6.68299	−	5.60770i	0.278458	−	0.233654i
$577$	2.15318	−	1.80673i	0.0896381	−	0.0752153i	−0.596867	−	0.802340i	$-0.703588\pi$
$577$	2.15318	−	1.80673i	0.0896381	−	0.0752153i	0.686506	+	0.727125i	$0.259144\pi$
$578$	4.16742	−	7.21818i	0.173342	−	0.300237i
$579$	9.50469	−	3.45942i	0.395001	−	0.143769i
$580$	−0.0135759	−	0.0769930i	−0.000563710	−	0.00319696i
$581$	−9.54732	−	16.5365i	−0.396090	−	0.686048i
$582$	−5.32053	+	9.21542i	−0.220543	+	0.381992i
$583$	28.7970	+	10.4813i	1.19265	+	0.434089i
$584$	5.82309	+	10.0859i	0.240961	+	0.417357i
$585$	1.39243	+	1.16838i	0.0575697	+	0.0483067i
$586$	−22.9466			−0.947916
$587$	22.5654	+	18.9346i	0.931373	+	0.781515i	0.976063	−	0.217486i	$-0.0697858\pi$
$587$	22.5654	+	18.9346i	0.931373	+	0.781515i	−0.0446906	+	0.999001i	$0.514230\pi$
$588$	−0.390226	+	0.142031i	−0.0160927	+	0.00585725i
$589$	5.11898	−	29.0312i	0.210924	−	1.19621i
$590$	−5.19767	−	29.4774i	−0.213985	−	1.21357i
$591$	7.96776			0.327750
$592$	−15.3733	−	14.2985i	−0.631837	−	0.587664i
$593$	−46.5729			−1.91252			−0.956260	−	0.292520i	$-0.905506\pi$
$593$	−46.5729			−1.91252			−0.956260	+	0.292520i	$0.905506\pi$
$594$	−0.564058	−	3.19893i	−0.0231436	−	0.131254i
$595$	2.66779	−	15.1298i	0.109369	−	0.620261i
$596$	2.52622	−	0.919469i	0.103478	−	0.0376629i
$597$	10.9661	+	9.20165i	0.448812	+	0.376598i
$598$	−0.697121			−0.0285074
$599$	−1.73561	−	1.45635i	−0.0709150	−	0.0595047i	0.606641	−	0.794976i	$-0.292516\pi$
$599$	−1.73561	−	1.45635i	−0.0709150	−	0.0595047i	−0.677556	+	0.735471i	$0.736961\pi$
$600$	3.66756	+	6.35240i	0.149727	+	0.259336i
$601$	−10.3265	−	3.75854i	−0.421227	−	0.153314i	0.122705	−	0.992443i	$-0.460843\pi$
$601$	−10.3265	−	3.75854i	−0.421227	−	0.153314i	−0.543932	+	0.839129i	$0.683065\pi$
$602$	−20.5730	+	35.6335i	−0.838494	+	1.45231i
$603$	−5.43884	−	9.42035i	−0.221487	−	0.383626i
$604$	0.975013	+	5.52957i	0.0396727	+	0.224995i
$605$	7.46344	−	2.71647i	0.303432	−	0.110440i
$606$	−8.89324	+	15.4036i	−0.361263	+	0.625727i
$607$	7.44402	−	6.24628i	0.302144	−	0.253529i	−0.479092	−	0.877765i	$-0.659034\pi$
$607$	7.44402	−	6.24628i	0.302144	−	0.253529i	0.781236	+	0.624236i	$0.214590\pi$
$608$	6.07709	−	5.09929i	0.246459	−	0.206803i
$609$	−0.557081	−	0.202761i	−0.0225741	−	0.00821628i
$610$	−3.71169	+	21.0500i	−0.150282	+	0.852291i
$611$	−1.19127	+	6.75603i	−0.0481936	+	0.273320i
$612$	−0.751499	−	0.273523i	−0.0303775	−	0.0110565i
$613$	−5.84691	+	4.90614i	−0.236155	+	0.198157i	−0.753183	−	0.657811i	$-0.771483\pi$
$613$	−5.84691	+	4.90614i	−0.236155	+	0.198157i	0.517028	+	0.855968i	$0.327038\pi$
$614$	0.0416854	−	0.0349782i	0.00168228	−	0.00141160i
$615$	7.86277	−	13.6187i	0.317058	−	0.549160i
$616$	−20.2058	+	7.35433i	−0.814117	+	0.296314i
$617$	−7.75646	−	43.9891i	−0.312263	−	1.77093i	−0.587171	−	0.809463i	$-0.699758\pi$
$617$	−7.75646	−	43.9891i	−0.312263	−	1.77093i	0.274907	−	0.961471i	$-0.411353\pi$
$618$	−4.09804	−	7.09802i	−0.164848	−	0.285524i
$619$	−10.7813	+	18.6737i	−0.433336	+	0.750560i	−0.997158	−	0.0753365i	$-0.975997\pi$
$619$	−10.7813	+	18.6737i	−0.433336	+	0.750560i	0.563822	+	0.825896i	$0.309330\pi$
$620$	1.86661	+	0.679390i	0.0749648	+	0.0272850i
$621$	−0.230355	−	0.398987i	−0.00924383	−	0.0160108i
$622$	34.1086	+	28.6205i	1.36763	+	1.14758i
$623$	19.7086			0.789610
$624$	3.01947	+	2.53363i	0.120875	+	0.101427i
$625$	6.18605	−	2.25154i	0.247442	−	0.0900615i
$626$	−0.817936	+	4.63874i	−0.0326913	+	0.185402i
$627$	−2.45733	−	13.9362i	−0.0981363	−	0.556558i
$628$	5.58232			0.222759
$629$	−4.45269	+	19.4017i	−0.177540	+	0.773598i
$630$	−6.22031			−0.247823
$631$	−0.164572	−	0.933335i	−0.00655152	−	0.0371555i	0.981357	−	0.192195i	$-0.0615606\pi$
$631$	−0.164572	−	0.933335i	−0.00655152	−	0.0371555i	−0.987908	+	0.155040i	$0.950450\pi$
$632$	5.42469	−	30.7650i	0.215783	−	1.22376i
$633$	9.66087	−	3.51627i	0.383985	−	0.139759i
$634$	−25.1918	−	21.1384i	−1.00049	−	0.839515i
$635$	1.23447			0.0489883
$636$	−2.34010	−	1.96358i	−0.0927911	−	0.0778610i
$637$	−0.970305	−	1.68062i	−0.0384449	−	0.0665885i
$638$	−0.613520	−	0.223303i	−0.0242895	−	0.00884066i
$639$	−1.54531	+	2.67656i	−0.0611315	+	0.105883i
$640$	−7.01188	−	12.1449i	−0.277169	−	0.480070i
$641$	−5.09261	−	28.8816i	−0.201146	−	1.14076i	−0.903390	−	0.428820i	$-0.858930\pi$
$641$	−5.09261	−	28.8816i	−0.201146	−	1.14076i	0.702244	−	0.711936i	$-0.252182\pi$
$642$	9.56095	−	3.47990i	0.377341	−	0.137341i
$643$	3.99411	−	6.91800i	0.157512	−	0.272819i	−0.776459	−	0.630168i	$-0.782986\pi$
$643$	3.99411	−	6.91800i	0.157512	−	0.272819i	0.933971	+	0.357349i	$0.116319\pi$
$644$	−0.254379	+	0.213449i	−0.0100239	+	0.00841108i
$645$	12.8374	−	10.7719i	0.505472	−	0.424141i
$646$	23.5203	+	8.56069i	0.925394	+	0.336816i
$647$	−2.35179	+	13.3377i	−0.0924584	+	0.524357i	0.903038	+	0.429560i	$0.141331\pi$
$647$	−2.35179	+	13.3377i	−0.0924584	+	0.524357i	−0.995497	+	0.0947973i	$0.969780\pi$
$648$	−0.516394	+	2.92862i	−0.0202859	+	0.115047i
$649$	32.6958	+	11.9003i	1.28342	+	0.467128i
$650$	−2.85911	+	2.39907i	−0.112143	+	0.0940994i
$651$	11.5386	−	9.68206i	0.452234	−	0.379470i
$652$	−1.49258	+	2.58522i	−0.0584538	+	0.101245i
$653$	−4.41904	+	1.60840i	−0.172930	+	0.0629415i	−0.427034	−	0.904235i	$-0.640442\pi$
$653$	−4.41904	+	1.60840i	−0.172930	+	0.0629415i	0.254104	+	0.967177i	$0.418219\pi$
$654$	−1.33495	−	7.57089i	−0.0522008	−	0.296045i
$655$	−3.33423	−	5.77505i	−0.130279	−	0.225650i
$656$	17.0504	−	29.5321i	0.665706	−	1.15304i
$657$	−3.68009	−	1.33944i	−0.143574	−	0.0522566i
$658$	−11.7383	−	20.3313i	−0.457605	−	0.792595i
$659$	−36.3168	−	30.4734i	−1.41470	−	1.18708i	−0.954107	−	0.299467i	$-0.903191\pi$
$659$	−36.3168	−	30.4734i	−1.41470	−	1.18708i	−0.460596	−	0.887610i	$-0.652364\pi$
$660$	0.953559			0.0371172
$661$	11.8697	+	9.95983i	0.461676	+	0.387393i	0.843747	−	0.536740i	$-0.180345\pi$
$661$	11.8697	+	9.95983i	0.461676	+	0.387393i	−0.382071	+	0.924133i	$0.624789\pi$
$662$	−32.2749	+	11.7471i	−1.25440	+	0.456565i
$663$	0.648964	−	3.68046i	0.0252037	−	0.142937i
$664$	3.34311	+	18.9597i	0.129738	+	0.735780i
$665$	−27.0989			−1.05085
$666$	8.04916	+	0.411349i	0.311898	+	0.0159395i
$667$	−0.0926014			−0.00358554
$668$	−0.417660	−	2.36867i	−0.0161598	−	0.0916466i
$669$	3.34267	−	18.9572i	0.129235	−	0.732928i
$670$	−21.5572	+	7.84616i	−0.832826	+	0.303124i
$671$	−19.0337	−	15.9712i	−0.734788	−	0.616561i
$672$	4.05349			0.156367
$673$	−6.45032	−	5.41246i	−0.248641	−	0.208635i	0.509946	−	0.860207i	$-0.329666\pi$
$673$	−6.45032	−	5.41246i	−0.248641	−	0.208635i	−0.758587	+	0.651572i	$0.774110\pi$
$674$	0.242844	+	0.420617i	0.00935398	+	0.0162016i
$675$	−2.31783	−	0.843621i	−0.0892133	−	0.0324710i
$676$	−1.42909	+	2.47525i	−0.0549648	+	0.0952019i
$677$	18.1875	+	31.5017i	0.699004	+	1.21071i	0.968812	+	0.247796i	$0.0797063\pi$
$677$	18.1875	+	31.5017i	0.699004	+	1.21071i	−0.269808	+	0.962914i	$0.586960\pi$
$678$	−0.784975	−	4.45181i	−0.0301468	−	0.170971i
$679$	−22.2586	+	8.10146i	−0.854205	+	0.310905i
$680$	−7.74498	+	13.4147i	−0.297007	+	0.514430i
$681$	3.05773	−	2.56574i	0.117173	−	0.0983195i
$682$	12.7076	−	10.6630i	0.486601	−	0.408306i
$683$	−13.0158	−	4.73736i	−0.498035	−	0.181270i	0.0807748	−	0.996732i	$-0.474261\pi$
$683$	−13.0158	−	4.73736i	−0.498035	−	0.181270i	−0.578810	+	0.815462i	$0.696483\pi$
$684$	−0.244953	+	1.38920i	−0.00936600	+	0.0531173i
$685$	−2.98087	+	16.9054i	−0.113893	+	0.645920i
$686$	−19.4660	−	7.08504i	−0.743215	−	0.270508i
$687$	−5.16991	+	4.33807i	−0.197244	+	0.165508i
$688$	27.8378	−	23.3587i	1.06131	−	0.890543i
$689$	7.13771	−	12.3629i	0.271925	−	0.470988i
$690$	−0.913026	+	0.332314i	−0.0347583	+	0.0126510i
$691$	−2.55632	−	14.4976i	−0.0972469	−	0.551515i	−0.994036	−	0.109056i	$-0.965217\pi$
$691$	−2.55632	−	14.4976i	−0.0972469	−	0.551515i	0.896789	−	0.442459i	$-0.145894\pi$
$692$	0.984418	+	1.70506i	0.0374220	+	0.0648168i
$693$	3.61535	−	6.26196i	0.137336	−	0.237872i
$694$	−26.1545	−	9.51947i	−0.992813	−	0.361354i
$695$	−12.1954	−	21.1231i	−0.462600	−	0.801246i
$696$	0.457884	+	0.384210i	0.0173560	+	0.0145634i
$697$	−32.3324			−1.22468
$698$	11.4468	+	9.60499i	0.433267	+	0.363554i
$699$	17.3852	−	6.32769i	0.657568	−	0.239335i
$700$	−0.308720	+	1.75084i	−0.0116685	+	0.0661755i
$701$	−4.12120	−	23.3725i	−0.155656	−	0.882767i	−0.958184	−	0.286153i	$-0.907623\pi$
$701$	−4.12120	−	23.3725i	−0.155656	−	0.882767i	0.802528	−	0.596614i	$-0.203488\pi$
$702$	−1.51314			−0.0571100
$703$	35.0663	+	1.79205i	1.32255	+	0.0675885i
$704$	21.3872			0.806062
$705$	1.66035	+	9.41630i	0.0625323	+	0.354638i
$706$	6.20173	−	35.1718i	0.233405	−	1.32371i
$707$	−37.2051	+	13.5416i	−1.39924	+	0.509283i
$708$	−2.65693	−	2.22943i	−0.0998534	−	0.0837870i
$709$	27.3708			1.02793			0.513966	−	0.857810i	$-0.328176\pi$
$709$	27.3708			1.02793			0.513966	+	0.857810i	$0.328176\pi$
$710$	4.99308	+	4.18969i	0.187387	+	0.157236i
$711$	5.25247	+	9.09755i	0.196983	+	0.341185i
$712$	−18.6729	−	6.79637i	−0.699796	−	0.254705i
$713$	1.17640	−	2.03759i	0.0440566	−	0.0763082i
$714$	6.39461	+	11.0758i	0.239312	+	0.414501i
$715$	0.773794	+	4.38841i	0.0289383	+	0.164117i
$716$	5.63243	−	2.05004i	0.210494	−	0.0766134i
$717$	−5.19014	+	8.98958i	−0.193829	+	0.335722i
$718$	23.4870	−	19.7079i	0.876528	−	0.735494i
$719$	−5.37076	+	4.50661i	−0.200296	+	0.168068i	−0.737419	−	0.675436i	$-0.763956\pi$
$719$	−5.37076	+	4.50661i	−0.200296	+	0.168068i	0.537123	+	0.843504i	$0.319511\pi$
$720$	5.16239	+	1.87896i	0.192391	+	0.0700246i
$721$	3.16813	−	17.9674i	0.117987	−	0.669140i
$722$	3.29491	−	18.6864i	0.122624	−	0.695434i
$723$	10.1875	+	3.70795i	0.378878	+	0.137900i
$724$	3.27905	−	2.75145i	0.121865	−	0.102257i
$725$	−0.379786	+	0.318679i	−0.0141049	+	0.0118354i
$726$	−3.30587	+	5.72594i	−0.122692	+	0.212509i
$727$	−30.0378	+	10.9329i	−1.11404	+	0.405478i	−0.832475	−	0.554063i	$-0.813077\pi$
$727$	−30.0378	+	10.9329i	−1.11404	+	0.405478i	−0.281567	+	0.959541i	$0.590854\pi$
$728$	1.73936	+	9.86438i	0.0644648	+	0.365598i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−4.12963	+	7.15273i	−0.152845	+	0.264735i
$731$	−32.3773	−	11.7844i	−1.19752	−	0.435861i
$732$	1.23839	+	2.14496i	0.0457723	+	0.0792800i
$733$	10.6827	+	8.96387i	0.394575	+	0.331088i	0.818392	−	0.574660i	$-0.194866\pi$
$733$	10.6827	+	8.96387i	0.394575	+	0.331088i	−0.423817	+	0.905748i	$0.639310\pi$
$734$	−8.72905			−0.322195
$735$	−2.07196	−	1.73858i	−0.0764254	−	0.0641285i
$736$	0.594977	−	0.216554i	0.0219311	−	0.00798228i
$737$	4.63067	−	26.2618i	0.170573	−	0.967367i
$738$	2.27320	+	12.8920i	0.0836778	+	0.474560i
$739$	52.1143			1.91705			0.958527	−	0.285000i	$-0.0919937\pi$
$739$	52.1143			1.91705			0.958527	+	0.285000i	$0.0919937\pi$
$740$	−0.529233	+	2.30603i	−0.0194550	+	0.0847713i
$741$	−6.59205			−0.242165
$742$	8.48307	+	48.1099i	0.311423	+	1.76617i
$743$	1.59418	−	9.04104i	0.0584848	−	0.331684i	−0.941501	−	0.337010i	$-0.890584\pi$
$743$	1.59418	−	9.04104i	0.0584848	−	0.331684i	0.999986	+	0.00532647i	$0.00169548\pi$
$744$	−14.2710	+	5.19422i	−0.523201	+	0.190429i
$745$	13.4133	+	11.2551i	0.491426	+	0.412355i
$746$	5.72757			0.209701
$747$	−4.95933	−	4.16137i	−0.181452	−	0.152257i
$748$	−0.980279	−	1.69789i	−0.0358426	−	0.0620811i
$749$	21.2827	+	7.74629i	0.777655	+	0.283043i
$750$	−7.87338	+	13.6371i	−0.287495	+	0.497956i
$751$	−19.0288	−	32.9589i	−0.694371	−	1.20269i	−0.970392	−	0.241535i	$-0.922349\pi$
$751$	−19.0288	−	32.9589i	−0.694371	−	1.20269i	0.276021	−	0.961152i	$-0.410984\pi$
$752$	3.60046	+	20.4192i	0.131295	+	0.744612i
$753$	−7.97328	+	2.90204i	−0.290562	+	0.105756i
$754$	−0.152069	+	0.263391i	−0.00553802	+	0.00959214i
$755$	−28.0150	+	23.5074i	−1.01957	+	0.855522i
$756$	−0.552145	+	0.463305i	−0.0200813	+	0.0168502i
$757$	11.6352	+	4.23487i	0.422889	+	0.153919i	0.544694	−	0.838635i	$-0.316646\pi$
$757$	11.6352	+	4.23487i	0.422889	+	0.153919i	−0.121805	+	0.992554i	$0.538868\pi$
$758$	−1.20397	+	6.82804i	−0.0437301	+	0.248005i
$759$	0.196126	−	1.11229i	0.00711893	−	0.0403735i
$760$	25.6747	+	9.34484i	0.931321	+	0.338973i
$761$	9.41139	−	7.89709i	0.341163	−	0.286269i	−0.456067	−	0.889945i	$-0.650742\pi$
$761$	9.41139	−	7.89709i	0.341163	−	0.286269i	0.797230	+	0.603676i	$0.206298\pi$
$762$	−0.787219	+	0.660555i	−0.0285179	+	0.0239294i
$763$	8.55642	−	14.8202i	0.309763	−	0.536526i
$764$	0.286002	−	0.104096i	0.0103472	−	0.00376607i
$765$	−0.904502	−	5.12968i	−0.0327023	−	0.185464i
$766$	5.15849	+	8.93476i	0.186384	+	0.322826i
$767$	8.10408	−	14.0367i	0.292621	−	0.506835i
$768$	−5.42566	−	1.97478i	−0.195782	−	0.0712587i
$769$	6.35491	+	11.0070i	0.229164	+	0.396924i	0.957561	−	0.288232i	$-0.0930675\pi$
$769$	6.35491	+	11.0070i	0.229164	+	0.396924i	−0.728397	+	0.685156i	$0.759734\pi$
$770$	−11.6816	−	9.80205i	−0.420976	−	0.353241i
$771$	23.1233			0.832765
$772$	−1.89349	−	1.58883i	−0.0681481	−	0.0571831i
$773$	−19.7231	+	7.17863i	−0.709392	+	0.258197i	−0.671415	−	0.741081i	$-0.734313\pi$
$773$	−19.7231	+	7.17863i	−0.709392	+	0.258197i	−0.0379762	+	0.999279i	$0.512091\pi$
$774$	−2.42246	+	13.7384i	−0.0870734	+	0.493818i
$775$	−2.18738	−	12.4052i	−0.0785729	−	0.445609i
$776$	23.8825			0.857332
$777$	13.1370	+	12.2186i	0.471288	+	0.438339i
$778$	−44.8635			−1.60844
$779$	9.90326	+	56.1642i	0.354821	+	2.01229i
$780$	0.0771338	−	0.437448i	0.00276183	−	0.0156631i
$781$	−7.11982	+	2.59140i	−0.254767	+	0.0927276i
$782$	1.53032	+	1.28409i	0.0547243	+	0.0459191i
$783$	−0.200997			−0.00718305
$784$	−4.49303	−	3.77010i	−0.160465	−	0.134647i
$785$	18.1795	+	31.4878i	0.648853	+	1.12385i
$786$	5.21643	+	1.89863i	0.186064	+	0.0677218i
$787$	−15.9066	+	27.5510i	−0.567009	+	0.982089i	0.429851	+	0.902900i	$0.358566\pi$
$787$	−15.9066	+	27.5510i	−0.567009	+	0.982089i	−0.996860	+	0.0791885i	$0.974767\pi$
$788$	−0.973561	−	1.68626i	−0.0346817	−	0.0600704i
$789$	0.850671	+	4.82439i	0.0302847	+	0.171753i
$790$	20.8185	−	7.57730i	0.740688	−	0.269588i
$791$	5.03132	−	8.71450i	0.178893	−	0.309852i
$792$	−5.58474	+	4.68615i	−0.198445	+	0.166515i
$793$	−8.86647	+	7.43985i	−0.314858	+	0.264197i
$794$	−12.7052	−	4.62430i	−0.450889	−	0.164110i
$795$	3.45500	−	19.5943i	0.122536	−	0.694937i
$796$	0.607470	−	3.44513i	0.0215312	−	0.122110i
$797$	−30.5604	−	11.1231i	−1.08250	−	0.393999i	−0.261665	−	0.965159i	$-0.584272\pi$
$797$	−30.5604	−	11.1231i	−1.08250	−	0.393999i	−0.820839	+	0.571160i	$0.806494\pi$
$798$	17.2810	−	14.5005i	0.611740	−	0.513310i
$799$	15.0597	−	12.6366i	0.532773	−	0.447049i
$800$	1.69493	−	2.93571i	0.0599248	−	0.103793i
$801$	6.27914	−	2.28542i	0.221862	−	0.0807513i
$802$	−1.57764	−	8.94722i	−0.0557083	−	0.315937i
$803$	−4.80042	−	8.31458i	−0.169403	−	0.293415i
$804$	−1.32912	+	2.30210i	−0.0468743	+	0.0811887i
$805$	−2.03240	−	0.739734i	−0.0716328	−	0.0260722i
$806$	−3.86374	−	6.69220i	−0.136094	−	0.235723i
$807$	5.73688	+	4.81382i	0.201948	+	0.169454i
$808$	39.9196			1.40436
$809$	35.0991	+	29.4516i	1.23402	+	1.03546i	0.997968	+	0.0637221i	$0.0202971\pi$
$809$	35.0991	+	29.4516i	1.23402	+	1.03546i	0.236049	+	0.971741i	$0.424147\pi$
$810$	−1.98178	+	0.721308i	−0.0696326	+	0.0253442i
$811$	6.89899	−	39.1261i	0.242256	−	1.37390i	−0.584523	−	0.811377i	$-0.698718\pi$
$811$	6.89899	−	39.1261i	0.242256	−	1.37390i	0.826779	−	0.562526i	$-0.190170\pi$
$812$	0.0251570	+	0.142673i	0.000882838	+	0.00500682i
$813$	−19.9213			−0.698671
$814$	14.4680	+	13.4565i	0.507102	+	0.471649i
$815$	−19.4430			−0.681059
$816$	−1.96141	−	11.1237i	−0.0686630	−	0.389407i
$817$	−10.5535	+	59.8517i	−0.369219	+	2.09395i
$818$	16.9734	−	6.17781i	0.593461	−	0.216002i
$819$	−2.58025	−	2.16508i	−0.0901611	−	0.0756541i
$820$	−3.84293			−0.134201
$821$	19.4366	+	16.3092i	0.678342	+	0.569197i	0.915521	−	0.402269i	$-0.131778\pi$
$821$	19.4366	+	16.3092i	0.678342	+	0.569197i	−0.237179	+	0.971466i	$0.576223\pi$
$822$	−7.14505	−	12.3756i	−0.249212	−	0.431648i
$823$	−43.0520	−	15.6696i	−1.50070	−	0.546209i	−0.544457	−	0.838789i	$-0.683264\pi$
$823$	−43.0520	−	15.6696i	−1.50070	−	0.546209i	−0.956241	+	0.292579i	$0.905486\pi$
$824$	−9.19755	+	15.9306i	−0.320412	+	0.554969i
$825$	−3.02345	−	5.23677i	−0.105263	−	0.182321i
$826$	9.63158	+	54.6234i	0.335126	+	1.90059i
$827$	−13.1792	+	4.79684i	−0.458286	+	0.166802i	−0.560839	−	0.827925i	$-0.689521\pi$
$827$	−13.1792	+	4.79684i	−0.458286	+	0.166802i	0.102553	+	0.994728i	$0.467299\pi$
$828$	−0.0562930	+	0.0975024i	−0.00195632	+	0.00338844i
$829$	−13.8578	+	11.6281i	−0.481301	+	0.403860i	−0.850897	−	0.525333i	$-0.823941\pi$
$829$	−13.8578	+	11.6281i	−0.481301	+	0.403860i	0.369595	+	0.929193i	$0.379496\pi$
$830$	−10.4591	+	8.77619i	−0.363039	+	0.304626i
$831$	29.6576	+	10.7945i	1.02881	+	0.374457i
$832$	1.73002	−	9.81145i	0.0599778	−	0.340151i
$833$	−0.965673	+	5.47660i	−0.0334586	+	0.189753i
$834$	19.0799	+	6.94452i	0.660683	+	0.240469i
$835$	12.0006	−	10.0697i	0.415299	−	0.348477i
$836$	−2.64913	+	2.22289i	−0.0916221	+	0.0768801i
$837$	2.55345	−	4.42271i	0.0882602	−	0.152871i
$838$	−20.6173	+	7.50409i	−0.712213	+	0.259224i
$839$	1.83553	+	10.4098i	0.0633696	+	0.359387i	0.999960	+	0.00896038i	$0.00285222\pi$
$839$	1.83553	+	10.4098i	0.0633696	+	0.359387i	−0.936590	+	0.350426i	$0.886037\pi$
$840$	6.98035	+	12.0903i	0.240845	+	0.417156i
$841$	14.4798	−	25.0797i	0.499303	−	0.864819i
$842$	12.4089	+	4.51647i	0.427639	+	0.155648i
$843$	−2.04601	−	3.54379i	−0.0704683	−	0.122055i
$844$	−1.92460	−	1.61493i	−0.0662475	−	0.0555883i
$845$	−18.6159			−0.640408
$846$	−6.09741	−	5.11633i	−0.209633	−	0.175903i
$847$	−13.8302	+	5.03378i	−0.475211	+	0.172963i
$848$	7.49215	−	42.4901i	0.257281	−	1.45912i
$849$	5.12894	+	29.0876i	0.176025	+	0.998285i
$850$	10.6954			0.366849
$851$	2.58104	+	1.09163i	0.0884768	+	0.0374205i
$852$	0.755270			0.0258751
$853$	−7.14538	−	40.5235i	−0.244653	−	1.38750i	−0.821297	−	0.570501i	$-0.806749\pi$
$853$	−7.14538	−	40.5235i	−0.244653	−	1.38750i	0.576644	−	0.816996i	$-0.304362\pi$
$854$	6.87798	−	39.0069i	0.235360	−	1.33479i
$855$	−8.63366	+	3.14239i	−0.295265	+	0.107468i
$856$	−17.4930	−	14.6784i	−0.597899	−	0.501697i
$857$	32.3109			1.10372			0.551860	−	0.833937i	$-0.313918\pi$
$857$	32.3109			1.10372			0.551860	+	0.833937i	$0.313918\pi$
$858$	−2.84166	−	2.38443i	−0.0970126	−	0.0814033i
$859$	−13.3544	−	23.1304i	−0.455645	−	0.789201i	0.543080	−	0.839681i	$-0.317258\pi$
$859$	−13.3544	−	23.1304i	−0.455645	−	0.789201i	−0.998725	+	0.0504804i	$0.983925\pi$
$860$	−3.84827	−	1.40066i	−0.131225	−	0.0477620i
$861$	−14.5702	+	25.2363i	−0.496550	+	0.860050i
$862$	4.38199	+	7.58983i	0.149251	+	0.258510i
$863$	2.39053	+	13.5574i	0.0813745	+	0.461498i	0.998080	+	0.0619346i	$0.0197270\pi$
$863$	2.39053	+	13.5574i	0.0813745	+	0.461498i	−0.916706	+	0.399563i	$0.869162\pi$
$864$	1.29143	−	0.470043i	0.0439355	−	0.0159912i
$865$	−6.41175	+	11.1055i	−0.218006	+	0.377597i
$866$	−1.59710	+	1.34013i	−0.0542717	+	0.0455394i
$867$	4.81876	−	4.04342i	0.163654	−	0.137322i
$868$	−3.45894	−	1.25895i	−0.117404	−	0.0427315i
$869$	−4.47199	+	25.3619i	−0.151702	+	0.860345i
$870$	−0.0736087	+	0.417456i	−0.00249557	+	0.0141531i
$871$	−11.6731	−	4.24867i	−0.395528	−	0.143961i
$872$	−13.2174	+	11.0907i	−0.447597	+	0.375578i
$873$	−6.15209	+	5.16222i	−0.208217	+	0.174715i
$874$	1.76185	−	3.05162i	0.0595955	−	0.103222i
$875$	−32.9385	+	11.9886i	−1.11352	+	0.405290i
$876$	0.166188	+	0.942497i	0.00561496	+	0.0318440i
$877$	9.37046	+	16.2301i	0.316418	+	0.548052i	0.979738	−	0.200284i	$-0.0641865\pi$
$877$	9.37046	+	16.2301i	0.316418	+	0.548052i	−0.663320	+	0.748336i	$0.730853\pi$
$878$	−14.8571	+	25.7333i	−0.501403	+	0.868456i
$879$	−16.2738	−	5.92318i	−0.548901	−	0.199784i
$880$	6.73399	+	11.6636i	0.227003	+	0.393180i
$881$	38.2767	+	32.1180i	1.28958	+	1.08208i	0.991847	+	0.127431i	$0.0406732\pi$
$881$	38.2767	+	32.1180i	1.28958	+	1.08208i	0.297728	+	0.954651i	$0.403771\pi$
$882$	2.25159			0.0758151
$883$	40.4326	+	33.9270i	1.36066	+	1.14173i	0.975777	+	0.218769i	$0.0702042\pi$
$883$	40.4326	+	33.9270i	1.36066	+	1.14173i	0.384888	+	0.922963i	$0.374240\pi$
$884$	−0.858208	+	0.312362i	−0.0288647	+	0.0105059i
$885$	3.92277	−	22.2471i	0.131862	−	0.747829i
$886$	−8.64699	−	49.0395i	−0.290501	−	1.64752i
$887$	−28.0602			−0.942171			−0.471085	−	0.882088i	$-0.656138\pi$
$887$	−28.0602			−0.942171			−0.471085	+	0.882088i	$0.656138\pi$
$888$	−8.23313	−	16.1066i	−0.276286	−	0.540503i
$889$	−2.28754			−0.0767215
$890$	−2.44711	−	13.8783i	−0.0820273	−	0.465200i
$891$	0.425704	−	2.41429i	0.0142616	−	0.0808817i
$892$	−4.42044	+	1.60891i	−0.148007	+	0.0538702i
$893$	−26.5635	−	22.2894i	−0.888913	−	0.745887i
$894$	−14.5762			−0.487502
$895$	29.9061	+	25.0942i	0.999652	+	0.838808i
$896$	12.9934	+	22.5053i	0.434080	+	0.751848i
$897$	−0.494400	−	0.179947i	−0.0165075	−	0.00600825i
$898$	1.52355	−	2.63887i	0.0508416	−	0.0880603i
$899$	−0.513236	−	0.888951i	−0.0171174	−	0.0296482i
$900$	0.104670	+	0.593613i	0.00348900	+	0.0197871i
$901$	−38.4411	+	13.9914i	−1.28066	+	0.466122i
$902$	−16.0463	+	27.7931i	−0.534284	+	0.925408i
$903$	−23.7885	+	19.9609i	−0.791630	+	0.664256i
$904$	−7.77204	+	6.52151i	−0.258494	+	0.216902i
$905$	26.1985	+	9.53549i	0.870869	+	0.316970i
$906$	5.28652	−	29.9813i	0.175633	−	0.996063i
$907$	2.67837	−	15.1898i	0.0889340	−	0.504370i	−0.907504	−	0.420043i	$-0.862015\pi$
$907$	2.67837	−	15.1898i	0.0889340	−	0.504370i	0.996438	−	0.0843265i	$-0.0268739\pi$
$908$	−0.916617	−	0.333621i	−0.0304190	−	0.0110716i
$909$	−10.2832	+	8.62863i	−0.341072	+	0.286194i
$910$	−5.44165	+	4.56608i	−0.180389	+	0.151364i
$911$	24.8245	−	42.9973i	0.822473	−	1.42457i	−0.0813617	−	0.996685i	$-0.525927\pi$
$911$	24.8245	−	42.9973i	0.822473	−	1.42457i	0.903835	−	0.427881i	$-0.140740\pi$
$912$	−18.7220	+	6.81427i	−0.619949	+	0.225643i
$913$	−2.75598	−	15.6300i	−0.0912098	−	0.517276i
$914$	−2.17424	−	3.76590i	−0.0719175	−	0.124565i
$915$	−8.06595	+	13.9706i	−0.266652	+	0.461855i
$916$	1.54979	+	0.564076i	0.0512063	+	0.0186376i
$917$	6.17852	+	10.7015i	0.204033	+	0.353395i
$918$	3.32166	+	2.78721i	0.109631	+	0.0919915i
$919$	2.18727			0.0721515			0.0360757	−	0.999349i	$-0.488514\pi$
$919$	2.18727			0.0721515			0.0360757	+	0.999349i	$0.488514\pi$
$920$	1.67050	+	1.40172i	0.0550748	+	0.0462132i
$921$	0.0385922	−	0.0140464i	0.00127166	−	0.000462845i
$922$	5.70494	−	32.3543i	0.187882	−	1.06553i
$923$	0.612887	+	3.47586i	0.0201734	+	0.114409i
$924$	−1.76700			−0.0581300
$925$	14.3423	−	4.40528i	0.471573	−	0.144845i
$926$	9.77176			0.321120
$927$	−1.07414	−	6.09175i	−0.0352794	−	0.200079i
$928$	0.0479674	−	0.272037i	0.00157461	−	0.00893004i
$929$	−44.1246	+	16.0600i	−1.44768	+	0.526913i	−0.941943	−	0.335773i	$-0.891002\pi$
$929$	−44.1246	+	16.0600i	−1.44768	+	0.526913i	−0.505739	+	0.862687i	$0.668780\pi$
$930$	−8.25051	−	6.92300i	−0.270545	−	0.227014i
$931$	9.80911			0.321480
$932$	−3.46341	−	2.90615i	−0.113448	−	0.0951940i
$933$	16.8021	+	29.1022i	0.550077	+	0.952762i
$934$	−39.1570	−	14.2520i	−1.28126	−	0.466339i
$935$	6.38479	−	11.0588i	0.208805	−	0.361661i
$936$	1.69803	+	2.94108i	0.0555019	+	0.0961321i
$937$	−7.80638	−	44.2722i	−0.255023	−	1.44631i	−0.796012	−	0.605280i	$-0.793061\pi$
$937$	−7.80638	−	44.2722i	−0.255023	−	1.44631i	0.540989	−	0.841030i	$-0.318050\pi$
$938$	39.9467	−	14.5394i	1.30431	−	0.474728i
$939$	−1.77747	+	3.07867i	−0.0580056	+	0.100469i
$940$	1.78994	−	1.50194i	0.0583815	−	0.0489879i
$941$	−0.583016	+	0.489209i	−0.0190058	+	0.0159478i	−0.652241	−	0.758012i	$-0.726171\pi$
$941$	−0.583016	+	0.489209i	−0.0190058	+	0.0159478i	0.633235	+	0.773959i	$0.281727\pi$
$942$	−28.4420	−	10.3520i	−0.926689	−	0.337287i
$943$	−0.790407	+	4.48262i	−0.0257392	+	0.145974i
$944$	8.50650	−	48.2428i	0.276863	−	1.57017i
$945$	−4.41145	−	1.60564i	−0.143505	−	0.0522314i
$946$	−26.1985	+	21.9832i	−0.851788	+	0.714735i
$947$	45.1313	−	37.8696i	1.46657	−	1.23060i	0.547318	−	0.836925i	$-0.315649\pi$
$947$	45.1313	−	37.8696i	1.46657	−	1.23060i	0.919251	−	0.393672i	$-0.128796\pi$
$948$	1.28357	−	2.22321i	0.0416885	−	0.0722066i
$949$	−4.20264	+	1.52964i	−0.136424	+	0.0496541i
$950$	−3.27595	−	18.5788i	−0.106286	−	0.602777i
$951$	−12.4097	−	21.4941i	−0.402411	−	0.696995i
$952$	14.3519	−	24.8582i	0.465148	−	0.805660i
$953$	5.93152	+	2.15890i	0.192141	+	0.0699336i	0.436298	−	0.899802i	$-0.356289\pi$
$953$	5.93152	+	2.15890i	0.192141	+	0.0699336i	−0.244158	+	0.969736i	$0.578511\pi$
$954$	8.28152	+	14.3440i	0.268124	+	0.464405i
$955$	1.51857	+	1.27423i	0.0491397	+	0.0412331i
$956$	2.53668			0.0820421
$957$	−0.377469	−	0.316734i	−0.0122018	−	0.0102386i
$958$	−4.02218	+	1.46395i	−0.129951	+	0.0472982i
$959$	5.52373	−	31.3266i	0.178370	−	1.01159i
$960$	−2.41124	−	13.6748i	−0.0778225	−	0.441353i
$961$	−4.91955			−0.158695
$962$	7.34352	−	5.54871i	0.236764	−	0.178898i
$963$	7.67891			0.247449
$964$	−0.460054	−	2.60910i	−0.0148174	−	0.0840334i
$965$	2.79560	−	15.8547i	0.0899937	−	0.510379i
$966$	1.69189	−	0.615798i	0.0544357	−	0.0198130i
$967$	−16.8643	−	14.1508i	−0.542318	−	0.455059i	0.330012	−	0.943977i	$-0.392947\pi$
$967$	−16.8643	−	14.1508i	−0.542318	−	0.455059i	−0.872330	+	0.488918i	$0.837392\pi$
$968$	14.8392			0.476951
$969$	14.4709	+	12.1425i	0.464872	+	0.390074i
$970$	8.46853	+	14.6679i	0.271908	+	0.470959i
$971$	−0.695704	−	0.253216i	−0.0223262	−	0.00812608i	0.330833	−	0.943689i	$-0.392670\pi$
$971$	−0.695704	−	0.253216i	−0.0223262	−	0.00812608i	−0.353159	+	0.935563i	$0.614893\pi$
$972$	−0.122187	+	0.211635i	−0.00391916	+	0.00678819i
$973$	22.5989	+	39.1424i	0.724487	+	1.25485i
$974$	2.22025	+	12.5917i	0.0711415	+	0.403464i
$975$	−2.64695	+	0.963412i	−0.0847703	+	0.0308539i
$976$	−17.4910	+	30.2952i	−0.559872	+	0.969727i
$977$	27.4541	−	23.0367i	0.878334	−	0.737010i	−0.0875018	−	0.996164i	$-0.527888\pi$
$977$	27.4541	−	23.0367i	0.878334	−	0.737010i	0.965836	+	0.259155i	$0.0834439\pi$
$978$	12.3988	−	10.4038i	0.396470	−	0.332678i
$979$	15.3935	+	5.60277i	0.491978	+	0.179065i
$980$	−0.114777	+	0.650931i	−0.00366641	+	0.0207932i
$981$	1.00751	−	5.71388i	0.0321674	−	0.182430i
$982$	19.2195	+	6.99533i	0.613320	+	0.223230i
$983$	−13.0988	+	10.9912i	−0.417788	+	0.350566i	−0.827321	−	0.561730i	$-0.810136\pi$
$983$	−13.0988	+	10.9912i	−0.417788	+	0.350566i	0.409533	+	0.912295i	$0.365692\pi$
$984$	22.5070	−	18.8856i	0.717497	−	0.602051i
$985$	6.34103	−	10.9830i	0.202042	−	0.349947i
$986$	0.818988	−	0.298087i	0.0260819	−	0.00949303i
$987$	−3.07672	−	17.4490i	−0.0979331	−	0.555406i
$988$	0.805465	+	1.39511i	0.0256253	+	0.0443843i
$989$	−2.42531	+	4.20076i	−0.0771204	+	0.133577i
$990$	−4.85839	−	1.76831i	−0.154410	−	0.0562006i
$991$	−5.03451	−	8.72003i	−0.159926	−	0.277001i	0.774916	−	0.632065i	$-0.217792\pi$
$991$	−5.03451	−	8.72003i	−0.159926	−	0.277001i	−0.934842	+	0.355064i	$0.884459\pi$
$992$	5.37648	+	4.51140i	0.170703	+	0.143237i
$993$	−25.9217			−0.822601
$994$	−9.25248	−	7.76375i	−0.293471	−	0.246251i
$995$	21.4110	−	7.79297i	0.678775	−	0.247054i
$996$	−0.274724	+	1.55803i	−0.00870495	+	0.0493682i
$997$	−2.38066	−	13.5014i	−0.0753964	−	0.427594i	−0.999019	−	0.0442902i	$-0.985897\pi$
$997$	−2.38066	−	13.5014i	−0.0753964	−	0.427594i	0.923622	−	0.383304i	$-0.125214\pi$
$998$	1.90462			0.0602898
$999$	5.60230	+	2.36945i	0.177249	+	0.0749659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	111.2.k.a.46.2	✓	18
3.2	odd	2		333.2.x.d.46.2		18
37.12	even	9		4107.2.a.n.1.6		9
37.25	even	18		4107.2.a.m.1.4		9
37.33	even	9	inner	111.2.k.a.70.2	yes	18
111.107	odd	18		333.2.x.d.181.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.2.k.a.46.2	✓	18	1.1	even	1	trivial
111.2.k.a.70.2	yes	18	37.33	even	9	inner
333.2.x.d.46.2		18	3.2	odd	2
333.2.x.d.181.2		18	111.107	odd	18
4107.2.a.m.1.4		9	37.25	even	18
4107.2.a.n.1.6		9	37.12	even	9

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:	\( N \)	\(=\)	\( 111 = 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	111.k (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.230084 + 1.30487i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.229637 - 0.0835811i) q^{4} +(1.21929 + 1.02311i) q^{5} -1.32500 q^{6} +(-2.25942 - 1.89588i) q^{7} +(1.48690 + 2.57538i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})\)	\(q+(0.230084 + 1.30487i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.229637 - 0.0835811i) q^{4} +(1.21929 + 1.02311i) q^{5} -1.32500 q^{6} +(-2.25942 - 1.89588i) q^{7} +(1.48690 + 2.57538i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(-1.05448 + 1.82642i) q^{10} +(-1.22577 - 2.12309i) q^{11} +(0.0424353 + 0.240662i) q^{12} +(-1.07313 + 0.390586i) q^{13} +(1.95402 - 3.38446i) q^{14} +(-1.21929 + 1.02311i) q^{15} +(-2.64403 + 2.21860i) q^{16} +(3.07519 + 1.11928i) q^{17} +(0.230084 - 1.30487i) q^{18} +(1.00236 - 5.68469i) q^{19} +(0.365507 + 0.133034i) q^{20} +(2.25942 - 1.89588i) q^{21} +(2.48833 - 2.08795i) q^{22} +(0.230355 - 0.398987i) q^{23} +(-2.79445 + 1.01710i) q^{24} +(-0.428318 - 2.42911i) q^{25} +(-0.756572 - 1.31042i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-0.677306 - 0.246519i) q^{28} +(-0.100499 - 0.174069i) q^{29} +(-1.61556 - 1.35562i) q^{30} +5.10690 q^{31} +(1.05279 + 0.883392i) q^{32} +(2.30369 - 0.838473i) q^{33} +(-0.752960 + 4.27025i) q^{34} +(-0.815204 - 4.62325i) q^{35} -0.244375 q^{36} +(0.749148 + 6.03645i) q^{37} +7.64842 q^{38} +(-0.198306 - 1.12465i) q^{39} +(-0.821930 + 4.66140i) q^{40} +(-9.28407 + 3.37912i) q^{41} +(2.99373 + 2.51204i) q^{42} -10.5286 q^{43} +(-0.458932 - 0.385089i) q^{44} +(-0.795836 - 1.37843i) q^{45} +(0.573627 + 0.208783i) q^{46} +(3.00362 - 5.20243i) q^{47} +(-1.72577 - 2.98911i) q^{48} +(0.295083 + 1.67350i) q^{49} +(3.07112 - 1.11780i) q^{50} +(-1.63627 + 2.83411i) q^{51} +(-0.213784 + 0.179386i) q^{52} +(-9.57587 + 8.03511i) q^{53} +(1.24509 + 0.453177i) q^{54} +(0.677581 - 3.84275i) q^{55} +(1.52308 - 8.63784i) q^{56} +(5.42427 + 1.97427i) q^{57} +(0.204014 - 0.171188i) q^{58} +(-10.8723 + 9.12298i) q^{59} +(-0.194482 + 0.336853i) q^{60} +(9.52397 - 3.46644i) q^{61} +(1.17502 + 6.66384i) q^{62} +(1.47473 + 2.55431i) q^{63} +(-4.36201 + 7.55523i) q^{64} +(-1.70806 - 0.621684i) q^{65} +(1.62414 + 2.81309i) q^{66} +(8.33279 + 6.99204i) q^{67} +0.799728 q^{68} +(0.352925 + 0.296139i) q^{69} +(5.84518 - 2.12747i) q^{70} +(0.536681 - 3.04367i) q^{71} +(-0.516394 - 2.92862i) q^{72} +3.91627 q^{73} +(-7.70442 + 2.36643i) q^{74} +2.46658 q^{75} +(-0.244953 - 1.38920i) q^{76} +(-1.25560 + 7.12084i) q^{77} +(1.42189 - 0.517526i) q^{78} +(-8.04725 - 6.75245i) q^{79} -5.49370 q^{80} +(0.766044 + 0.642788i) q^{81} +(-6.54543 - 11.3370i) q^{82} +(6.08352 + 2.21422i) q^{83} +(0.360387 - 0.624209i) q^{84} +(2.60441 + 4.51097i) q^{85} +(-2.42246 - 13.7384i) q^{86} +(0.188876 - 0.0687451i) q^{87} +(3.64518 - 6.31363i) q^{88} +(-5.11880 + 4.29518i) q^{89} +(1.61556 - 1.35562i) q^{90} +(3.16514 + 1.15202i) q^{91} +(0.0195504 - 0.110876i) q^{92} +(-0.886804 + 5.02932i) q^{93} +(7.47958 + 2.72234i) q^{94} +(7.03822 - 5.90577i) q^{95} +(-1.05279 + 0.883392i) q^{96} +(4.01549 - 6.95504i) q^{97} +(-2.11580 + 0.770090i) q^{98} +(0.425704 + 2.41429i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8}+O(q^{10}) \) 18 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8	\( 18 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8} + 12 q^{10} + 6 q^{11} - 6 q^{12} + 18 q^{13} - 9 q^{14} + 6 q^{15} - 9 q^{16} - 21 q^{17} - 3 q^{18} + 12 q^{19} - 6 q^{21} - 51 q^{22} + 6 q^{24} + 6 q^{25} + 15 q^{26} + 9 q^{27} - 39 q^{28} - 3 q^{29} + 15 q^{30} - 24 q^{31} + 21 q^{32} - 18 q^{34} - 12 q^{35} + 18 q^{36} + 27 q^{37} + 24 q^{38} + 18 q^{39} + 39 q^{40} + 9 q^{41} + 6 q^{42} - 72 q^{43} - 21 q^{44} + 21 q^{46} + 21 q^{47} - 3 q^{48} - 18 q^{49} + 24 q^{50} - 3 q^{51} - 30 q^{52} - 18 q^{53} + 3 q^{54} + 9 q^{55} + 54 q^{56} - 3 q^{57} - 66 q^{59} - 36 q^{60} + 33 q^{61} + 69 q^{62} + 18 q^{64} - 63 q^{65} + 42 q^{67} + 48 q^{68} - 12 q^{69} + 63 q^{70} + 15 q^{71} - 6 q^{72} - 24 q^{73} - 51 q^{74} - 6 q^{75} + 12 q^{76} + 39 q^{77} - 27 q^{78} - 6 q^{79} - 12 q^{80} + 15 q^{82} + 33 q^{83} - 6 q^{84} + 30 q^{85} - 60 q^{86} - 9 q^{87} - 3 q^{88} + 45 q^{89} - 15 q^{90} + 21 q^{91} - 24 q^{92} - 6 q^{93} + 18 q^{94} - 24 q^{95} - 21 q^{96} - 24 q^{97} - 36 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8 + 12 * q^10 + 6 * q^11 - 6 * q^12 + 18 * q^13 - 9 * q^14 + 6 * q^15 - 9 * q^16 - 21 * q^17 - 3 * q^18 + 12 * q^19 - 6 * q^21 - 51 * q^22 + 6 * q^24 + 6 * q^25 + 15 * q^26 + 9 * q^27 - 39 * q^28 - 3 * q^29 + 15 * q^30 - 24 * q^31 + 21 * q^32 - 18 * q^34 - 12 * q^35 + 18 * q^36 + 27 * q^37 + 24 * q^38 + 18 * q^39 + 39 * q^40 + 9 * q^41 + 6 * q^42 - 72 * q^43 - 21 * q^44 + 21 * q^46 + 21 * q^47 - 3 * q^48 - 18 * q^49 + 24 * q^50 - 3 * q^51 - 30 * q^52 - 18 * q^53 + 3 * q^54 + 9 * q^55 + 54 * q^56 - 3 * q^57 - 66 * q^59 - 36 * q^60 + 33 * q^61 + 69 * q^62 + 18 * q^64 - 63 * q^65 + 42 * q^67 + 48 * q^68 - 12 * q^69 + 63 * q^70 + 15 * q^71 - 6 * q^72 - 24 * q^73 - 51 * q^74 - 6 * q^75 + 12 * q^76 + 39 * q^77 - 27 * q^78 - 6 * q^79 - 12 * q^80 + 15 * q^82 + 33 * q^83 - 6 * q^84 + 30 * q^85 - 60 * q^86 - 9 * q^87 - 3 * q^88 + 45 * q^89 - 15 * q^90 + 21 * q^91 - 24 * q^92 - 6 * q^93 + 18 * q^94 - 24 * q^95 - 21 * q^96 - 24 * q^97 - 36 * q^98 - 9 * q^99

Introduction

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