LMFDB - Embedded newform 378.2.w.b.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(25,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 12]))

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

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

chi := DirichletCharacter("378.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.w (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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			121.1
Character	$\chi$	$=$	378.121
Dual form			378.2.w.b.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(-1.63077 - 0.583588i) q^{3} +(0.766044 + 0.642788i) q^{4} +(2.72763 - 0.992778i) q^{5} +(-1.33283 - 1.10615i) q^{6} +(-1.62553 - 2.08750i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.31885 + 1.90340i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(-1.63077 - 0.583588i) q^{3} +(0.766044 + 0.642788i) q^{4} +(2.72763 - 0.992778i) q^{5} +(-1.33283 - 1.10615i) q^{6} +(-1.62553 - 2.08750i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.31885 + 1.90340i) q^{9} +2.90269 q^{10} +(-0.278389 - 0.101325i) q^{11} +(-0.874122 - 1.49530i) q^{12} +(0.719192 - 4.07874i) q^{13} +(-0.813528 - 2.51757i) q^{14} +(-5.02753 + 0.0271806i) q^{15} +(0.173648 + 0.984808i) q^{16} +1.54052 q^{17} +(1.52800 + 2.58171i) q^{18} +3.28454 q^{19} +(2.72763 + 0.992778i) q^{20} +(1.43263 + 4.35288i) q^{21} +(-0.226945 - 0.190429i) q^{22} +(0.869520 - 4.93129i) q^{23} +(-0.309985 - 1.70409i) q^{24} +(2.62416 - 2.20193i) q^{25} +(2.07083 - 3.58679i) q^{26} +(-2.67072 - 4.45727i) q^{27} +(0.0965940 - 2.64399i) q^{28} +(0.827577 + 4.69342i) q^{29} +(-4.73363 - 1.69398i) q^{30} +(2.34643 + 1.96889i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(0.394857 + 0.327703i) q^{33} +(1.44761 + 0.526888i) q^{34} +(-6.50627 - 4.08015i) q^{35} +(0.552858 + 2.94862i) q^{36} +(3.73513 + 6.46944i) q^{37} +(3.08646 + 1.12338i) q^{38} +(-3.55315 + 6.23180i) q^{39} +(2.22359 + 1.86581i) q^{40} +(0.642881 - 3.64596i) q^{41} +(-0.142545 + 4.58036i) q^{42} +(-9.42283 + 7.90669i) q^{43} +(-0.148128 - 0.256564i) q^{44} +(8.21463 + 2.88968i) q^{45} +(2.50368 - 4.33651i) q^{46} +(0.901727 - 0.756639i) q^{47} +(0.291541 - 1.70734i) q^{48} +(-1.71532 + 6.78658i) q^{49} +(3.21901 - 1.17162i) q^{50} +(-2.51224 - 0.899028i) q^{51} +(3.17270 - 2.66221i) q^{52} +(-5.61189 - 9.72008i) q^{53} +(-0.985176 - 5.10190i) q^{54} -0.859936 q^{55} +(0.995066 - 2.45150i) q^{56} +(-5.35634 - 1.91682i) q^{57} +(-0.827577 + 4.69342i) q^{58} +(-0.00828236 + 0.0469716i) q^{59} +(-3.86878 - 3.21081i) q^{60} +(-1.46930 + 1.23289i) q^{61} +(1.53152 + 2.65268i) q^{62} +(0.204001 - 7.93463i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.08759 - 11.8393i) q^{65} +(0.258963 + 0.442989i) q^{66} +(-9.72699 + 3.54034i) q^{67} +(1.18010 + 0.990226i) q^{68} +(-4.29584 + 7.53439i) q^{69} +(-4.71840 - 6.05937i) q^{70} +(-5.64455 + 9.77665i) q^{71} +(-0.488970 + 2.95988i) q^{72} +(-6.10013 + 10.5657i) q^{73} +(1.29720 + 7.35678i) q^{74} +(-5.56444 + 2.05943i) q^{75} +(2.51610 + 2.11126i) q^{76} +(0.241012 + 0.745844i) q^{77} +(-5.47027 + 4.64073i) q^{78} +(4.21601 + 1.53450i) q^{79} +(1.45134 + 2.51380i) q^{80} +(1.75412 + 8.82740i) q^{81} +(1.85110 - 3.20621i) q^{82} +(1.53826 + 8.72391i) q^{83} +(-1.70052 + 4.25538i) q^{84} +(4.20197 - 1.52939i) q^{85} +(-11.5588 + 4.20706i) q^{86} +(1.38944 - 8.13688i) q^{87} +(-0.0514442 - 0.291754i) q^{88} -9.93441 q^{89} +(6.73090 + 5.52498i) q^{90} +(-9.68345 + 5.12879i) q^{91} +(3.83587 - 3.21867i) q^{92} +(-2.67748 - 4.58016i) q^{93} +(1.10613 - 0.402599i) q^{94} +(8.95902 - 3.26082i) q^{95} +(0.857903 - 1.50466i) q^{96} +(-1.39847 + 1.17345i) q^{97} +(-3.93302 + 5.79062i) q^{98} +(-0.452679 - 0.764843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8}+O(q^{10}) $ 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8	$ 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8} - 12 q^{10} - 6 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} - 36 q^{19} + 18 q^{21} + 6 q^{22} - 6 q^{23} + 30 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} + 9 q^{35} - 3 q^{36} + 51 q^{39} - 6 q^{41} - 27 q^{42} - 24 q^{43} + 18 q^{45} + 27 q^{47} + 6 q^{48} - 69 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{52} - 15 q^{53} + 45 q^{54} - 72 q^{55} + 6 q^{56} + 57 q^{57} - 3 q^{58} + 15 q^{59} - 33 q^{60} - 18 q^{61} - 24 q^{62} - 12 q^{63} - 36 q^{64} - 90 q^{65} - 36 q^{66} - 66 q^{67} - 18 q^{68} - 39 q^{69} - 12 q^{70} + 12 q^{71} + 30 q^{73} + 9 q^{74} - 21 q^{75} - 87 q^{77} + 6 q^{78} - 45 q^{79} - 6 q^{80} - 24 q^{81} + 33 q^{82} + 18 q^{83} + 6 q^{84} + 51 q^{85} - 12 q^{86} - 18 q^{87} - 12 q^{88} + 72 q^{89} - 69 q^{90} - 30 q^{91} + 12 q^{92} - 48 q^{93} + 21 q^{95} + 48 q^{97} + 6 q^{98} + 90 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8 - 12 * q^10 - 6 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 - 36 * q^19 + 18 * q^21 + 6 * q^22 - 6 * q^23 + 30 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 + 9 * q^35 - 3 * q^36 + 51 * q^39 - 6 * q^41 - 27 * q^42 - 24 * q^43 + 18 * q^45 + 27 * q^47 + 6 * q^48 - 69 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^52 - 15 * q^53 + 45 * q^54 - 72 * q^55 + 6 * q^56 + 57 * q^57 - 3 * q^58 + 15 * q^59 - 33 * q^60 - 18 * q^61 - 24 * q^62 - 12 * q^63 - 36 * q^64 - 90 * q^65 - 36 * q^66 - 66 * q^67 - 18 * q^68 - 39 * q^69 - 12 * q^70 + 12 * q^71 + 30 * q^73 + 9 * q^74 - 21 * q^75 - 87 * q^77 + 6 * q^78 - 45 * q^79 - 6 * q^80 - 24 * q^81 + 33 * q^82 + 18 * q^83 + 6 * q^84 + 51 * q^85 - 12 * q^86 - 18 * q^87 - 12 * q^88 + 72 * q^89 - 69 * q^90 - 30 * q^91 + 12 * q^92 - 48 * q^93 + 21 * q^95 + 48 * q^97 + 6 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	−1.63077	−	0.583588i	−0.941528	−	0.336935i
$3$	−1.63077	−	0.583588i	−0.941528	−	0.336935i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	2.72763	−	0.992778i	1.21984	−	0.443984i	0.349731	−	0.936850i	$-0.386273\pi$
$5$	2.72763	−	0.992778i	1.21984	−	0.443984i	0.870105	+	0.492867i	$0.164051\pi$
$6$	−1.33283	−	1.10615i	−0.544125	−	0.451584i
$7$	−1.62553	−	2.08750i	−0.614391	−	0.789001i
$7$	−1.62553	−	2.08750i	−0.614391	−	0.789001i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	2.31885	+	1.90340i	0.772950	+	0.634467i
$10$	2.90269			0.917911
$11$	−0.278389	−	0.101325i	−0.0839374	−	0.0305507i	0.299710	−	0.954030i	$-0.403110\pi$
$11$	−0.278389	−	0.101325i	−0.0839374	−	0.0305507i	−0.383648	+	0.923480i	$0.625332\pi$
$12$	−0.874122	−	1.49530i	−0.252337	−	0.431655i
$13$	0.719192	−	4.07874i	0.199468	−	1.13124i	−0.706442	−	0.707771i	$-0.749701\pi$
$13$	0.719192	−	4.07874i	0.199468	−	1.13124i	0.905910	−	0.423469i	$-0.139188\pi$
$14$	−0.813528	−	2.51757i	−0.217425	−	0.672850i
$15$	−5.02753	+	0.0271806i	−1.29810	+	0.00701801i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	1.54052			0.373630			0.186815	−	0.982395i	$-0.440183\pi$
$17$	1.54052			0.373630			0.186815	+	0.982395i	$0.440183\pi$
$18$	1.52800	+	2.58171i	0.360154	+	0.608514i
$19$	3.28454			0.753525			0.376762	−	0.926310i	$-0.377037\pi$
$19$	3.28454			0.753525			0.376762	+	0.926310i	$0.377037\pi$
$20$	2.72763	+	0.992778i	0.609918	+	0.221992i
$21$	1.43263	+	4.35288i	0.312625	+	0.949877i
$22$	−0.226945	−	0.190429i	−0.0483847	−	0.0405996i
$23$	0.869520	−	4.93129i	0.181308	−	1.02825i	−0.749301	−	0.662230i	$-0.769610\pi$
$23$	0.869520	−	4.93129i	0.181308	−	1.02825i	0.930608	−	0.366016i	$-0.119279\pi$
$24$	−0.309985	−	1.70409i	−0.0632754	−	0.347845i
$25$	2.62416	−	2.20193i	0.524832	−	0.440387i
$26$	2.07083	−	3.58679i	0.406124	−	0.703427i
$27$	−2.67072	−	4.45727i	−0.513980	−	0.857802i
$28$	0.0965940	−	2.64399i	0.0182545	−	0.499667i
$29$	0.827577	+	4.69342i	0.153677	+	0.871547i	0.959985	+	0.280051i	$0.0903513\pi$
$29$	0.827577	+	4.69342i	0.153677	+	0.871547i	−0.806308	+	0.591496i	$0.798538\pi$
$30$	−4.73363	−	1.69398i	−0.864239	−	0.309276i
$31$	2.34643	+	1.96889i	0.421431	+	0.353623i	0.828707	−	0.559682i	$-0.189077\pi$
$31$	2.34643	+	1.96889i	0.421431	+	0.353623i	−0.407276	+	0.913305i	$0.633521\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	0.394857	+	0.327703i	0.0687358	+	0.0570458i
$34$	1.44761	+	0.526888i	0.248264	+	0.0903606i
$35$	−6.50627	−	4.08015i	−1.09976	−	0.689672i
$36$	0.552858	+	2.94862i	0.0921431	+	0.491436i
$37$	3.73513	+	6.46944i	0.614052	+	1.06357i	0.990550	+	0.137152i	$0.0437950\pi$
$37$	3.73513	+	6.46944i	0.614052	+	1.06357i	−0.376498	+	0.926418i	$0.622872\pi$
$38$	3.08646	+	1.12338i	0.500689	+	0.182236i
$39$	−3.55315	+	6.23180i	−0.568959	+	0.997886i
$40$	2.22359	+	1.86581i	0.351580	+	0.295011i
$41$	0.642881	−	3.64596i	0.100401	−	0.569404i	−0.892557	−	0.450935i	$-0.851091\pi$
$41$	0.642881	−	3.64596i	0.100401	−	0.569404i	0.992958	−	0.118468i	$-0.0377984\pi$
$42$	−0.142545	+	4.58036i	−0.0219952	+	0.706765i
$43$	−9.42283	+	7.90669i	−1.43697	+	1.20576i	−0.495522	+	0.868596i	$0.665023\pi$
$43$	−9.42283	+	7.90669i	−1.43697	+	1.20576i	−0.941446	+	0.337163i	$0.890532\pi$
$44$	−0.148128	−	0.256564i	−0.0223311	−	0.0386785i
$45$	8.21463	+	2.88968i	1.22456	+	0.430768i
$46$	2.50368	−	4.33651i	0.369148	−	0.639383i
$47$	0.901727	−	0.756639i	0.131530	−	0.110367i	−0.574649	−	0.818400i	$-0.694862\pi$
$47$	0.901727	−	0.756639i	0.131530	−	0.110367i	0.706180	+	0.708033i	$0.250417\pi$
$48$	0.291541	−	1.70734i	0.0420804	−	0.246433i
$49$	−1.71532	+	6.78658i	−0.245046	+	0.969511i
$50$	3.21901	−	1.17162i	0.455237	−	0.165693i
$51$	−2.51224	−	0.899028i	−0.351783	−	0.125889i
$52$	3.17270	−	2.66221i	0.439974	−	0.369182i
$53$	−5.61189	−	9.72008i	−0.770853	−	1.33516i	−0.937096	−	0.349072i	$-0.886497\pi$
$53$	−5.61189	−	9.72008i	−0.770853	−	1.33516i	0.166243	−	0.986085i	$-0.446836\pi$
$54$	−0.985176	−	5.10190i	−0.134065	−	0.694281i
$55$	−0.859936			−0.115954
$56$	0.995066	−	2.45150i	0.132971	−	0.327595i
$57$	−5.35634	−	1.91682i	−0.709465	−	0.253889i
$58$	−0.827577	+	4.69342i	−0.108666	+	0.616277i
$59$	−0.00828236	+	0.0469716i	−0.00107827	+	0.00611518i	−0.985342	−	0.170590i	$-0.945433\pi$
$59$	−0.00828236	+	0.0469716i	−0.00107827	+	0.00611518i	0.984264	+	0.176705i	$0.0565438\pi$
$60$	−3.86878	−	3.21081i	−0.499458	−	0.414514i
$61$	−1.46930	+	1.23289i	−0.188125	+	0.157856i	−0.731986	−	0.681320i	$-0.761406\pi$
$61$	−1.46930	+	1.23289i	−0.188125	+	0.157856i	0.543861	+	0.839175i	$0.316962\pi$
$62$	1.53152	+	2.65268i	0.194504	+	0.336890i
$63$	0.204001	−	7.93463i	0.0257018	−	0.999670i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−2.08759	−	11.8393i	−0.258934	−	1.46849i
$66$	0.258963	+	0.442989i	0.0318762	+	0.0545282i
$67$	−9.72699	+	3.54034i	−1.18834	+	0.432521i	−0.859141	−	0.511739i	$-0.829001\pi$
$67$	−9.72699	+	3.54034i	−1.18834	+	0.432521i	−0.329200	+	0.944260i	$0.606779\pi$
$68$	1.18010	+	0.990226i	0.143109	+	0.120082i
$69$	−4.29584	+	7.53439i	−0.517158	+	0.907034i
$70$	−4.71840	−	6.05937i	−0.563957	−	0.724233i
$71$	−5.64455	+	9.77665i	−0.669885	+	1.16028i	0.308051	+	0.951370i	$0.400323\pi$
$71$	−5.64455	+	9.77665i	−0.669885	+	1.16028i	−0.977936	+	0.208905i	$0.933010\pi$
$72$	−0.488970	+	2.95988i	−0.0576256	+	0.348826i
$73$	−6.10013	+	10.5657i	−0.713966	+	1.23663i	0.249391	+	0.968403i	$0.419770\pi$
$73$	−6.10013	+	10.5657i	−0.713966	+	1.23663i	−0.963357	+	0.268222i	$0.913564\pi$
$74$	1.29720	+	7.35678i	0.150796	+	0.855208i
$75$	−5.56444	+	2.05943i	−0.642526	+	0.237802i
$76$	2.51610	+	2.11126i	0.288617	+	0.242178i
$77$	0.241012	+	0.745844i	0.0274659	+	0.0849968i
$78$	−5.47027	+	4.64073i	−0.619386	+	0.525459i
$79$	4.21601	+	1.53450i	0.474338	+	0.172645i	0.568116	−	0.822948i	$-0.307672\pi$
$79$	4.21601	+	1.53450i	0.474338	+	0.172645i	−0.0937786	+	0.995593i	$0.529895\pi$
$80$	1.45134	+	2.51380i	0.162265	+	0.281052i
$81$	1.75412	+	8.82740i	0.194903	+	0.980823i
$82$	1.85110	−	3.20621i	0.204420	−	0.354066i
$83$	1.53826	+	8.72391i	0.168846	+	0.957574i	0.945010	+	0.327042i	$0.106052\pi$
$83$	1.53826	+	8.72391i	0.168846	+	0.957574i	−0.776164	+	0.630531i	$0.782837\pi$
$84$	−1.70052	+	4.25538i	−0.185542	+	0.464300i
$85$	4.20197	−	1.52939i	0.455768	−	0.165886i
$86$	−11.5588	+	4.20706i	−1.24642	+	0.453659i
$87$	1.38944	−	8.13688i	0.148963	−	0.872365i
$88$	−0.0514442	−	0.291754i	−0.00548397	−	0.0311011i
$89$	−9.93441			−1.05304			−0.526522	−	0.850161i	$-0.676504\pi$
$89$	−9.93441			−1.05304			−0.526522	+	0.850161i	$0.676504\pi$
$90$	6.73090	+	5.52498i	0.709499	+	0.582384i
$91$	−9.68345	+	5.12879i	−1.01510	+	0.537644i
$92$	3.83587	−	3.21867i	0.399917	−	0.335570i
$93$	−2.67748	−	4.58016i	−0.277641	−	0.474941i
$94$	1.10613	−	0.402599i	0.114089	−	0.0415249i
$95$	8.95902	−	3.26082i	0.919176	−	0.334553i
$96$	0.857903	−	1.50466i	0.0875594	−	0.153569i
$97$	−1.39847	+	1.17345i	−0.141993	+	0.119146i	−0.711018	−	0.703174i	$-0.751765\pi$
$97$	−1.39847	+	1.17345i	−0.141993	+	0.119146i	0.569025	+	0.822321i	$0.307321\pi$
$98$	−3.93302	+	5.79062i	−0.397295	+	0.584941i
$99$	−0.452679	−	0.764843i	−0.0454959	−	0.0768697i
$100$	3.42560			0.342560
$101$	−1.50632	−	8.54277i	−0.149884	−	0.850037i	−0.963315	−	0.268374i	$-0.913514\pi$
$101$	−1.50632	−	8.54277i	−0.149884	−	0.850037i	0.813430	−	0.581663i	$-0.197598\pi$
$102$	−2.05324	−	1.70405i	−0.203301	−	0.168726i
$103$	10.6911	−	3.89124i	1.05343	−	0.383415i	0.243471	−	0.969908i	$-0.421714\pi$
$103$	10.6911	−	3.89124i	1.05343	−	0.383415i	0.809954	+	0.586493i	$0.199492\pi$
$104$	3.89189	−	1.41653i	0.381631	−	0.138902i
$105$	8.22913	+	10.4508i	0.803081	+	1.01989i
$106$	−1.94899	−	11.0533i	−0.189303	−	1.07359i
$107$	8.39124	−	14.5341i	0.811212	−	1.40506i	−0.100804	−	0.994906i	$-0.532142\pi$
$107$	8.39124	−	14.5341i	0.811212	−	1.40506i	0.912016	−	0.410154i	$-0.134525\pi$
$108$	0.819192	−	5.13117i	0.0788268	−	0.493747i
$109$	9.34891	+	16.1928i	0.895463	+	1.55099i	0.833231	+	0.552926i	$0.186489\pi$
$109$	9.34891	+	16.1928i	0.895463	+	1.55099i	0.0622322	+	0.998062i	$0.480178\pi$
$110$	−0.808076	−	0.294115i	−0.0770470	−	0.0280428i
$111$	−2.31567	−	12.7300i	−0.219794	−	1.20828i
$112$	1.77352	−	1.96332i	0.167582	−	0.185517i
$113$	8.71837	+	7.31558i	0.820155	+	0.688192i	0.953008	−	0.302944i	$-0.0979695\pi$
$113$	8.71837	+	7.31558i	0.820155	+	0.688192i	−0.132853	+	0.991136i	$0.542414\pi$
$114$	−4.37772	−	3.63320i	−0.410011	−	0.340280i
$115$	−2.52395	−	14.3140i	−0.235359	−	1.33479i
$116$	−2.38291	+	4.12733i	−0.221248	+	0.383213i
$117$	9.43119	−	8.08908i	0.871913	−	0.747836i
$118$	−0.0238481	+	0.0413061i	−0.00219540	+	0.00380254i
$119$	−2.50415	−	3.21583i	−0.229555	−	0.294795i
$120$	−2.53730	−	4.34038i	−0.231623	−	0.396221i
$121$	−8.35926	−	7.01425i	−0.759932	−	0.637659i
$122$	−1.80237	+	0.656009i	−0.163179	+	0.0593922i
$123$	−3.17614	+	5.57056i	−0.286382	+	0.502281i
$124$	0.531893	+	3.01651i	0.0477654	+	0.270891i
$125$	−2.28500	+	3.95773i	−0.204376	+	0.353990i
$126$	2.90550	−	7.38634i	0.258843	−	0.658028i
$127$	5.06958	+	8.78078i	0.449853	+	0.779168i	0.998376	−	0.0569675i	$-0.0181431\pi$
$127$	5.06958	+	8.78078i	0.449853	+	0.779168i	−0.548523	+	0.836135i	$0.684810\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	19.9808	−	7.39498i	1.75921	−	0.651091i
$130$	2.08759	−	11.8393i	0.183094	−	1.03838i
$131$	−1.41480	+	8.02370i	−0.123611	+	0.701034i	0.858512	+	0.512794i	$0.171390\pi$
$131$	−1.41480	+	8.02370i	−0.123611	+	0.701034i	−0.982123	+	0.188240i	$0.939722\pi$
$132$	0.0918346	+	0.504844i	0.00799317	+	0.0439410i
$133$	−5.33911	−	6.85648i	−0.462959	−	0.594532i
$134$	−10.3512			−0.894212
$135$	−11.7098	−	9.50638i	−1.00782	−	0.818179i
$136$	0.770259	+	1.33413i	0.0660491	+	0.114400i
$137$	14.3730	−	12.0604i	1.22797	−	1.03039i	0.229598	−	0.973286i	$-0.426259\pi$
$137$	14.3730	−	12.0604i	1.22797	−	1.03039i	0.998368	−	0.0571001i	$-0.0181854\pi$
$138$	−6.61368	+	5.61074i	−0.562994	+	0.477618i
$139$	20.4185	−	7.43173i	1.73188	−	0.630351i	0.733115	−	0.680105i	$-0.238066\pi$
$139$	20.4185	−	7.43173i	1.73188	−	0.630351i	0.998762	+	0.0497539i	$0.0158437\pi$
$140$	−2.36142	−	7.30773i	−0.199576	−	0.617616i
$141$	−1.91208	+	0.707670i	−0.161026	+	0.0595965i
$142$	−8.64796	+	7.25650i	−0.725720	+	0.608952i
$143$	−0.613495	+	1.06260i	−0.0513030	+	0.0888594i
$144$	−1.47182	+	2.61414i	−0.122652	+	0.217845i
$145$	6.91685	+	11.9803i	0.574413	+	0.994913i
$146$	−9.34594	+	7.84217i	−0.773475	+	0.649023i
$147$	6.75787	−	10.0663i	0.557380	−	0.830257i
$148$	−1.29720	+	7.35678i	−0.106629	+	0.604723i
$149$	−9.59534	−	8.05145i	−0.786081	−	0.659600i	0.158691	−	0.987328i	$-0.449273\pi$
$149$	−9.59534	−	8.05145i	−0.786081	−	0.659600i	−0.944772	+	0.327728i	$0.893717\pi$
$150$	−5.93323	+	0.0320771i	−0.484446	+	0.00261909i
$151$	17.5782	+	6.39793i	1.43049	+	0.520656i	0.937072	−	0.349135i	$-0.113525\pi$
$151$	17.5782	+	6.39793i	1.43049	+	0.520656i	0.493419	+	0.869792i	$0.335747\pi$
$152$	1.64227	+	2.84449i	0.133206	+	0.230719i
$153$	3.57223	+	2.93222i	0.288798	+	0.237056i
$154$	−0.0286165	+	0.783295i	−0.00230598	+	0.0631197i
$155$	8.35487	+	3.04093i	0.671080	+	0.244253i
$156$	−6.72759	+	2.48991i	−0.538638	+	0.199353i
$157$	2.18176	−	12.3734i	0.174124	−	0.987505i	−0.765027	−	0.643999i	$-0.777274\pi$
$157$	2.18176	−	12.3734i	0.174124	−	0.987505i	0.939150	−	0.343506i	$-0.111615\pi$
$158$	3.43692	+	2.88392i	0.273427	+	0.229432i
$159$	3.47920	+	19.1263i	0.275919	+	1.51681i
$160$	0.504047	+	2.85859i	0.0398484	+	0.225991i
$161$	−11.7075	+	6.20083i	−0.922681	+	0.488694i
$162$	−1.37081	+	8.89499i	−0.107701	+	0.698857i
$163$	−4.67949	+	8.10512i	−0.366526	+	0.634842i	−0.989020	−	0.147783i	$-0.952786\pi$
$163$	−4.67949	+	8.10512i	−0.366526	+	0.634842i	0.622494	+	0.782625i	$0.286120\pi$
$164$	2.83605	−	2.37973i	0.221459	−	0.185826i
$165$	1.40236	+	0.501849i	0.109174	+	0.0390689i
$166$	−1.53826	+	8.72391i	−0.119392	+	0.677107i
$167$	−12.8573	−	10.7885i	−0.994925	−	0.834841i	−0.00865161	−	0.999963i	$-0.502754\pi$
$167$	−12.8573	−	10.7885i	−0.994925	−	0.834841i	−0.986273	+	0.165122i	$0.947198\pi$
$168$	−3.05339	+	3.41713i	−0.235574	+	0.263637i
$169$	−3.90290	−	1.42054i	−0.300223	−	0.109272i
$170$	4.47164			0.342959
$171$	7.61635	+	6.25180i	0.582437	+	0.478087i
$172$	−12.3006			−0.937914
$173$	−1.26987	−	7.20180i	−0.0965466	−	0.547543i	−0.994262	−	0.106968i	$-0.965886\pi$
$173$	−1.26987	−	7.20180i	−0.0965466	−	0.547543i	0.897716	−	0.440575i	$-0.145225\pi$
$174$	4.08862	−	7.17095i	0.309957	−	0.543628i
$175$	−8.86219	−	1.89864i	−0.669918	−	0.143524i
$176$	0.0514442	−	0.291754i	0.00387775	−	0.0219918i
$177$	0.0409187	−	0.0717666i	0.00307564	−	0.00539431i
$178$	−9.33529	−	3.39777i	−0.699709	−	0.254673i
$179$	−16.9189			−1.26458			−0.632289	−	0.774732i	$-0.717885\pi$
$179$	−16.9189			−1.26458			−0.632289	+	0.774732i	$0.717885\pi$
$180$	4.43532	+	7.49389i	0.330589	+	0.558561i
$181$	−5.09029	−	8.81664i	−0.378358	−	0.655335i	0.612465	−	0.790497i	$-0.290178\pi$
$181$	−5.09029	−	8.81664i	−0.378358	−	0.655335i	−0.990824	+	0.135162i	$0.956845\pi$
$182$	−10.8536	+	1.50755i	−0.804523	+	0.111747i
$183$	3.11561	−	1.15310i	0.230312	−	0.0852397i
$184$	4.70539	−	1.71262i	0.346886	−	0.126256i
$185$	16.6108	+	13.9381i	1.22125	+	1.02475i
$186$	−0.949498	−	5.21970i	−0.0696206	−	0.382727i
$187$	−0.428863	−	0.156093i	−0.0313615	−	0.0114147i
$188$	1.17712			0.0858504
$189$	−4.96324	+	12.8205i	−0.361023	+	0.932557i
$190$	9.53399			0.691668
$191$	15.7868	+	5.74593i	1.14229	+	0.415761i	0.842741	−	0.538319i	$-0.180941\pi$
$191$	15.7868	+	5.74593i	1.14229	+	0.415761i	0.299552	+	0.954080i	$0.403163\pi$
$192$	1.32079	−	1.12050i	0.0953198	−	0.0808650i
$193$	5.97073	+	5.01004i	0.429783	+	0.360630i	0.831870	−	0.554971i	$-0.187271\pi$
$193$	5.97073	+	5.01004i	0.429783	+	0.360630i	−0.402087	+	0.915601i	$0.631715\pi$
$194$	−1.71548	+	0.624382i	−0.123164	+	0.0448280i
$195$	−3.50490	+	20.5256i	−0.250991	+	1.46987i
$196$	−5.67634	+	4.09623i	−0.405453	+	0.292588i
$197$	−5.77393	−	10.0007i	−0.411376	−	0.712524i	0.583665	−	0.811995i	$-0.301618\pi$
$197$	−5.77393	−	10.0007i	−0.411376	−	0.712524i	−0.995040	+	0.0994711i	$0.968285\pi$
$198$	−0.163787	−	0.873543i	−0.0116398	−	0.0620800i
$199$	−23.0719			−1.63552			−0.817760	−	0.575559i	$-0.804784\pi$
$199$	−23.0719			−1.63552			−0.817760	+	0.575559i	$0.804784\pi$
$200$	3.21901	+	1.17162i	0.227618	+	0.0828464i
$201$	17.9286	−	0.0969285i	1.26459	−	0.00683681i
$202$	1.50632	−	8.54277i	0.105984	−	0.601067i
$203$	8.45228	−	9.35685i	0.593234	−	0.656722i
$204$	−1.34660	−	2.30353i	−0.0942809	−	0.161279i
$205$	−1.86608	−	10.5831i	−0.130333	−	0.739155i
$206$	11.3772			0.792689
$207$	11.4025	−	9.77988i	0.792530	−	0.679749i
$208$	4.14166			0.287173
$209$	−0.914378	−	0.332807i	−0.0632489	−	0.0230207i
$210$	4.15847	+	12.6351i	0.286962	+	0.871902i
$211$	−2.08041	−	1.74567i	−0.143221	−	0.120177i	0.568362	−	0.822778i	$-0.307577\pi$
$211$	−2.08041	−	1.74567i	−0.143221	−	0.120177i	−0.711583	+	0.702602i	$0.752022\pi$
$212$	1.94899	−	11.0533i	0.133857	−	0.759142i
$213$	14.9105	−	12.6494i	1.02165	−	0.866724i
$214$	12.8561	−	10.7876i	0.878827	−	0.737423i
$215$	−17.8524	+	30.9213i	−1.21753	+	2.10882i
$216$	2.52475	−	4.54154i	0.171788	−	0.309013i
$217$	0.295872	−	8.09866i	0.0200851	−	0.549773i
$218$	3.24684	+	18.4138i	0.219904	+	1.24714i
$219$	16.1140	−	13.6704i	1.08888	−	0.923757i
$220$	−0.658749	−	0.552756i	−0.0444129	−	0.0372668i
$221$	1.10793	−	6.28338i	0.0745273	−	0.422666i
$222$	2.17789	−	12.7543i	0.146171	−	0.856011i
$223$	−4.67914	−	1.70307i	−0.313339	−	0.114046i	0.180564	−	0.983563i	$-0.442208\pi$
$223$	−4.67914	−	1.70307i	−0.313339	−	0.114046i	−0.493902	+	0.869517i	$0.664430\pi$
$224$	2.33806	−	1.23834i	0.156218	−	0.0827401i
$225$	10.2762	−	0.111117i	0.685080	−	0.00740779i
$226$	5.69051	+	9.85625i	0.378527	+	0.655628i
$227$	1.44817	+	0.527091i	0.0961184	+	0.0349842i	0.389632	−	0.920971i	$-0.372602\pi$
$227$	1.44817	+	0.527091i	0.0961184	+	0.0349842i	−0.293513	+	0.955955i	$0.594825\pi$
$228$	−2.87109	−	4.91136i	−0.190142	−	0.325263i
$229$	−3.13679	−	2.63208i	−0.207285	−	0.173933i	0.533235	−	0.845967i	$-0.320976\pi$
$229$	−3.13679	−	2.63208i	−0.207285	−	0.173933i	−0.740520	+	0.672035i	$0.765421\pi$
$230$	2.52395	−	14.3140i	0.166424	−	0.943838i
$231$	0.0422297	−	1.35695i	0.00277851	−	0.0892810i
$232$	−3.65083	+	3.06341i	−0.239689	+	0.201123i
$233$	9.75353	+	16.8936i	0.638975	+	1.10674i	0.985658	+	0.168755i	$0.0539747\pi$
$233$	9.75353	+	16.8936i	0.638975	+	1.10674i	−0.346683	+	0.937982i	$0.612692\pi$
$234$	11.6290	−	4.37559i	0.760214	−	0.286041i
$235$	1.70841	−	2.95905i	0.111444	−	0.193027i
$236$	−0.0365374	+	0.0306585i	−0.00237838	+	0.00199570i
$237$	−5.97984	−	4.96284i	−0.388432	−	0.322371i
$238$	−1.25325	−	3.87836i	−0.0812364	−	0.251397i
$239$	−4.28912	+	1.56111i	−0.277440	+	0.100980i	−0.476993	−	0.878907i	$-0.658273\pi$
$239$	−4.28912	+	1.56111i	−0.277440	+	0.100980i	0.199553	+	0.979887i	$0.436051\pi$
$240$	−0.899789	−	4.94643i	−0.0580811	−	0.319291i
$241$	−21.4132	+	17.9678i	−1.37935	+	1.15741i	−0.409893	+	0.912134i	$0.634434\pi$
$241$	−21.4132	+	17.9678i	−1.37935	+	1.15741i	−0.969453	+	0.245276i	$0.921122\pi$
$242$	−5.45612	−	9.45027i	−0.350732	−	0.607486i
$243$	2.29099	−	15.4192i	0.146967	−	0.989141i
$244$	−1.91804			−0.122790
$245$	2.05879	+	20.2142i	0.131531	+	1.29144i
$246$	−4.88984	+	4.14831i	−0.311765	+	0.264487i
$247$	2.36222	−	13.3968i	0.150304	−	0.852417i
$248$	−0.531893	+	3.01651i	−0.0337752	+	0.191549i
$249$	2.58262	−	15.1244i	0.163667	−	0.958472i
$250$	−3.50082	+	2.93753i	−0.221411	+	0.185786i
$251$	−5.70251	−	9.87703i	−0.359939	−	0.623433i	0.628011	−	0.778204i	$-0.283869\pi$
$251$	−5.70251	−	9.87703i	−0.359939	−	0.623433i	−0.987950	+	0.154772i	$0.950536\pi$
$252$	5.25656	−	5.94715i	0.331132	−	0.374635i
$253$	−0.741729	+	1.28471i	−0.0466321	+	0.0807692i
$254$	1.76065	+	9.98513i	0.110473	+	0.626523i
$255$	−7.74500	+	0.0418722i	−0.485011	+	0.00262214i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	2.93379	+	2.46174i	0.183005	+	0.153559i	0.729688	−	0.683780i	$-0.239665\pi$
$257$	2.93379	+	2.46174i	0.183005	+	0.153559i	−0.546683	+	0.837339i	$0.684110\pi$
$258$	21.3050	−	0.115182i	1.32639	−	0.00717095i
$259$	7.43341	−	18.3134i	0.461889	−	1.13794i
$260$	6.01098	−	10.4113i	0.372785	−	0.645683i
$261$	−7.01444	+	12.4586i	−0.434183	+	0.771165i
$262$	−4.07374	+	7.05593i	−0.251677	+	0.435917i
$263$	4.88282	+	27.6919i	0.301088	+	1.70755i	0.641371	+	0.767231i	$0.278366\pi$
$263$	4.88282	+	27.6919i	0.301088	+	1.70755i	−0.340283	+	0.940323i	$0.610523\pi$
$264$	−0.0863706	+	0.505808i	−0.00531574	+	0.0311303i
$265$	−24.9571	−	20.9415i	−1.53310	−	1.28642i
$266$	−2.67207	−	8.26906i	−0.163835	−	0.507009i
$267$	16.2008	+	5.79760i	0.991471	+	0.354808i
$268$	−9.72699	−	3.54034i	−0.594171	−	0.216260i
$269$	6.44483	+	11.1628i	0.392948	+	0.680606i	0.992837	−	0.119477i	$-0.0381219\pi$
$269$	6.44483	+	11.1628i	0.392948	+	0.680606i	−0.599889	+	0.800083i	$0.704789\pi$
$270$	−7.75226	−	12.9381i	−0.471787	−	0.787386i
$271$	3.15205	−	5.45951i	0.191473	−	0.331642i	−0.754265	−	0.656570i	$-0.772007\pi$
$271$	3.15205	−	5.45951i	0.191473	−	0.331642i	0.945739	+	0.324928i	$0.105340\pi$
$272$	0.267508	+	1.51711i	0.0162201	+	0.0919885i
$273$	18.7846	−	2.71275i	1.13690	−	0.164183i
$274$	17.6311	−	6.41718i	1.06513	−	0.387676i
$275$	−0.953648	+	0.347100i	−0.0575072	+	0.0209309i
$276$	−8.13381	+	3.01036i	−0.489598	+	0.181203i
$277$	−1.65106	−	9.36365i	−0.0992029	−	0.562607i	−0.993378	−	0.114890i	$-0.963348\pi$
$277$	−1.65106	−	9.36365i	−0.0992029	−	0.562607i	0.894175	−	0.447717i	$-0.147763\pi$
$278$	21.7289			1.30321
$279$	1.69343	+	9.03176i	0.101383	+	0.540717i
$280$	0.280382	−	7.67467i	0.0167560	−	0.458649i
$281$	24.5846	−	20.6289i	1.46660	−	1.23062i	0.547369	−	0.836892i	$-0.315630\pi$
$281$	24.5846	−	20.6289i	1.46660	−	1.23062i	0.919227	−	0.393728i	$-0.128815\pi$
$282$	−2.03880	+	0.0110225i	−0.121409	+	0.000656380i
$283$	−19.8753	+	7.23401i	−1.18146	+	0.430017i	−0.856718	−	0.515785i	$-0.827500\pi$
$283$	−19.8753	+	7.23401i	−1.18146	+	0.430017i	−0.324744	+	0.945802i	$0.605278\pi$
$284$	−10.6083	+	3.86110i	−0.629486	+	0.229114i
$285$	−16.5131	+	0.0892758i	−0.978153	+	0.00528824i
$286$	−0.939928	+	0.788693i	−0.0555791	+	0.0466364i
$287$	−8.65597	+	4.58459i	−0.510946	+	0.270620i
$288$	−2.27715	+	1.95310i	−0.134182	+	0.115087i
$289$	−14.6268			−0.860400
$290$	2.40220	+	13.6235i	0.141062	+	0.800002i
$291$	2.96540	−	1.09751i	0.173835	−	0.0643371i
$292$	−11.4645	+	4.17273i	−0.670909	+	0.244191i
$293$	−7.49941	+	2.72956i	−0.438120	+	0.159463i	−0.551657	−	0.834071i	$-0.686004\pi$
$293$	−7.49941	+	2.72956i	−0.438120	+	0.159463i	0.113537	+	0.993534i	$0.463782\pi$
$294$	9.79321	−	7.14793i	0.571152	−	0.416876i
$295$	0.0240411	+	0.136344i	0.00139973	+	0.00793825i
$296$	−3.73513	+	6.46944i	−0.217100	+	0.376029i
$297$	0.291863	+	1.51147i	0.0169356	+	0.0877041i
$298$	−6.26291	−	10.8477i	−0.362801	−	0.628390i
$299$	−19.4881	−	7.09310i	−1.12703	−	0.410205i
$300$	−5.58638	−	1.99914i	−0.322530	−	0.115420i
$301$	31.8223	+	6.81762i	1.83421	+	0.392961i
$302$	14.3299	+	12.0242i	0.824591	+	0.691914i
$303$	−2.52899	+	14.8104i	−0.145287	+	0.850835i
$304$	0.570354	+	3.23464i	0.0327121	+	0.185519i
$305$	−2.78374	+	4.82158i	−0.159396	+	0.276083i
$306$	2.35392	+	3.97716i	0.134564	+	0.227359i
$307$	17.0773	−	29.5787i	0.974652	−	1.68815i	0.293572	−	0.955937i	$-0.405156\pi$
$307$	17.0773	−	29.5787i	0.974652	−	1.68815i	0.681080	−	0.732209i	$-0.261511\pi$
$308$	−0.294793	+	0.726269i	−0.0167974	+	0.0413830i
$309$	−19.7056	+	0.106536i	−1.12102	+	0.00606061i
$310$	6.81096	+	5.71507i	0.386836	+	0.324594i
$311$	8.39009	−	3.05374i	0.475758	−	0.173162i	−0.0930007	−	0.995666i	$-0.529646\pi$
$311$	8.39009	−	3.05374i	0.475758	−	0.173162i	0.568759	+	0.822504i	$0.307424\pi$
$312$	−7.17347	+	0.0387823i	−0.406118	+	0.00219562i
$313$	2.42859	+	13.7732i	0.137272	+	0.778509i	0.973250	+	0.229747i	$0.0737898\pi$
$313$	2.42859	+	13.7732i	0.137272	+	0.778509i	−0.835978	+	0.548763i	$0.815099\pi$
$314$	6.28214	−	10.8810i	0.354522	−	0.614049i
$315$	−7.32089	−	21.8453i	−0.412485	−	1.23084i
$316$	2.24329	+	3.88549i	0.126195	+	0.218576i
$317$	16.1837	−	13.5797i	0.908965	−	0.762712i	−0.0629566	−	0.998016i	$-0.520053\pi$
$317$	16.1837	−	13.5797i	0.908965	−	0.762712i	0.971922	+	0.235304i	$0.0756085\pi$
$318$	−3.27220	+	19.1628i	−0.183496	+	1.07460i
$319$	0.245174	−	1.39045i	0.0137271	−	0.0778503i
$320$	−0.504047	+	2.85859i	−0.0281771	+	0.159800i
$321$	−22.1661	+	18.8047i	−1.23719	+	1.04958i
$322$	−13.1223	+	1.82267i	−0.731276	+	0.101573i
$323$	5.05989			0.281540
$324$	−4.33041	+	7.88971i	−0.240578	+	0.438317i
$325$	−7.09384	−	12.2869i	−0.393496	−	0.681554i
$326$	−7.16940	+	6.01584i	−0.397076	+	0.333186i
$327$	−5.79604	−	31.8627i	−0.320522	−	1.76201i
$328$	3.47894	−	1.26623i	0.192092	−	0.0699158i
$329$	−3.04527	−	0.652420i	−0.167891	−	0.0359691i
$330$	1.14615	+	0.951220i	0.0630933	+	0.0523629i
$331$	9.12790	−	7.65922i	0.501715	−	0.420989i	−0.356488	−	0.934300i	$-0.616026\pi$
$331$	9.12790	−	7.65922i	0.501715	−	0.420989i	0.858203	+	0.513311i	$0.171581\pi$
$332$	−4.42925	+	7.67168i	−0.243086	+	0.421038i
$333$	−3.65273	+	22.1111i	−0.200169	+	1.21168i
$334$	−8.39198	−	14.5353i	−0.459189	−	0.795338i
$335$	−23.0169	+	19.3135i	−1.25755	+	1.05521i
$336$	−4.03798	+	2.16673i	−0.220290	+	0.118205i
$337$	1.19041	−	6.75113i	0.0648456	−	0.367757i	−0.935066	−	0.354473i	$-0.884660\pi$
$337$	1.19041	−	6.75113i	0.0648456	−	0.367757i	0.999912	−	0.0132843i	$-0.00422865\pi$
$338$	−3.18168	−	2.66974i	−0.173060	−	0.145215i
$339$	−9.94840	−	17.0180i	−0.540323	−	0.924291i
$340$	4.20197	+	1.52939i	0.227884	+	0.0829429i
$341$	−0.453722	−	0.785869i	−0.0245704	−	0.0425572i
$342$	5.01879	+	8.47971i	0.271385	+	0.458530i
$343$	16.9553	−	7.45103i	0.915500	−	0.402318i
$344$	−11.5588	−	4.20706i	−0.623209	−	0.226830i
$345$	−4.23750	+	24.8159i	−0.228140	+	1.33604i
$346$	1.26987	−	7.20180i	0.0682687	−	0.387171i
$347$	−16.6266	−	13.9514i	−0.892565	−	0.748951i	0.0761582	−	0.997096i	$-0.475735\pi$
$347$	−16.6266	−	13.9514i	−0.892565	−	0.748951i	−0.968723	+	0.248145i	$0.920179\pi$
$348$	6.29465	−	5.34010i	0.337429	−	0.286259i
$349$	3.07425	+	17.4349i	0.164561	+	0.933271i	0.949516	+	0.313718i	$0.101575\pi$
$349$	3.07425	+	17.4349i	0.164561	+	0.933271i	−0.784955	+	0.619553i	$0.787314\pi$
$350$	−7.67836	−	4.81518i	−0.410425	−	0.257382i
$351$	−20.1008	+	7.68753i	−1.07290	+	0.410330i
$352$	0.148128	−	0.256564i	0.00789522	−	0.0136749i
$353$	−20.0031	+	16.7846i	−1.06466	+	0.893356i	−0.994558	−	0.104184i	$-0.966777\pi$
$353$	−20.0031	+	16.7846i	−1.06466	+	0.893356i	−0.0701022	+	0.997540i	$0.522333\pi$
$354$	0.0629967	−	0.0534435i	0.00334823	−	0.00284049i
$355$	−5.69023	+	32.2709i	−0.302006	+	1.71276i
$356$	−7.61020	−	6.38571i	−0.403340	−	0.338442i
$357$	2.20699	+	6.70569i	0.116806	+	0.354903i
$358$	−15.8986	−	5.78661i	−0.840266	−	0.305832i
$359$	21.6232			1.14123			0.570614	−	0.821219i	$-0.306705\pi$
$359$	21.6232			1.14123			0.570614	+	0.821219i	$0.306705\pi$
$360$	1.60478	+	8.55892i	0.0845791	+	0.451095i
$361$	−8.21181			−0.432200
$362$	−1.76784	−	10.0259i	−0.0929155	−	0.526950i
$363$	9.53862	+	16.3170i	0.500648	+	0.856421i
$364$	−10.7147	−	2.29552i	−0.561602	−	0.120318i
$365$	−6.14950	+	34.8755i	−0.321879	+	1.82547i
$366$	3.32210	−	0.0179604i	0.173649	−	0.000938807i
$367$	13.4581	+	4.89835i	0.702507	+	0.255692i	0.668481	−	0.743729i	$-0.266945\pi$
$367$	13.4581	+	4.89835i	0.702507	+	0.255692i	0.0340261	+	0.999421i	$0.489167\pi$
$368$	5.00737			0.261027
$369$	8.43048	−	7.23077i	0.438873	−	0.376419i
$370$	10.8419	+	18.7788i	0.563645	+	0.976262i
$371$	−11.1684	+	27.5151i	−0.579835	+	1.42851i
$372$	0.893005	−	5.22966i	0.0463002	−	0.271145i
$373$	15.1586	−	5.51727i	0.784881	−	0.285673i	0.0816747	−	0.996659i	$-0.473973\pi$
$373$	15.1586	−	5.51727i	0.784881	−	0.285673i	0.703207	+	0.710986i	$0.251751\pi$
$374$	−0.349612	−	0.293359i	−0.0180780	−	0.0151693i
$375$	6.03600	−	5.12067i	0.311698	−	0.264430i
$376$	1.10613	+	0.402599i	0.0570444	+	0.0207625i
$377$	19.7385			1.01658
$378$	−9.04880	+	10.3498i	−0.465420	+	0.532338i
$379$	−7.89841			−0.405714			−0.202857	−	0.979208i	$-0.565023\pi$
$379$	−7.89841			−0.405714			−0.202857	+	0.979208i	$0.565023\pi$
$380$	8.95902	+	3.26082i	0.459588	+	0.167276i
$381$	−3.14299	−	17.2780i	−0.161020	−	0.885179i
$382$	12.8695	+	10.7988i	0.658462	+	0.552515i
$383$	7.33019	−	2.66797i	0.374555	−	0.136327i	−0.147881	−	0.989005i	$-0.547245\pi$
$383$	7.33019	−	2.66797i	0.374555	−	0.136327i	0.522437	+	0.852678i	$0.325023\pi$
$384$	1.62437	−	0.601187i	0.0828932	−	0.0306792i
$385$	1.39785	+	1.79512i	0.0712410	+	0.0914877i
$386$	3.89712	+	6.75000i	0.198358	+	0.343566i
$387$	−36.8997	+	0.398998i	−1.87572	+	0.0202822i
$388$	−1.82557			−0.0926793
$389$	−15.0945	−	5.49396i	−0.765322	−	0.278555i	−0.0702839	−	0.997527i	$-0.522391\pi$
$389$	−15.0945	−	5.49396i	−0.765322	−	0.278555i	−0.695039	+	0.718972i	$0.744613\pi$
$390$	−10.3137	+	18.0890i	−0.522254	+	0.915970i
$391$	1.33951	−	7.59675i	0.0677420	−	0.384184i
$392$	−6.73501	+	1.90778i	−0.340169	+	0.0963573i
$393$	6.98975	−	12.2592i	0.352586	−	0.618394i
$394$	−2.00527	−	11.3724i	−0.101024	−	0.572935i
$395$	13.0231			0.655265
$396$	0.144860	−	0.876880i	0.00727948	−	0.0440649i
$397$	−20.4150			−1.02460			−0.512300	−	0.858807i	$-0.671206\pi$
$397$	−20.4150			−1.02460			−0.512300	+	0.858807i	$0.671206\pi$
$398$	−21.6805	−	7.89104i	−1.08674	−	0.395542i
$399$	4.70552	+	14.2972i	0.235570	+	0.715756i
$400$	2.62416	+	2.20193i	0.131208	+	0.110097i
$401$	0.435730	−	2.47115i	0.0217593	−	0.123403i	−0.971993	−	0.235009i	$-0.924488\pi$
$401$	0.435730	−	2.47115i	0.0217593	−	0.123403i	0.993753	+	0.111605i	$0.0355993\pi$
$402$	16.8805	+	6.04087i	0.841925	+	0.301291i
$403$	9.71813	−	8.15448i	0.484094	−	0.406203i
$404$	4.33728	−	7.51238i	0.215788	−	0.373755i
$405$	13.5483	+	22.3365i	0.673218	+	1.10991i
$406$	11.1428	−	5.90172i	0.553007	−	0.292897i
$407$	−0.384302	−	2.17948i	−0.0190491	−	0.108033i
$408$	−0.477537	−	2.62517i	−0.0236416	−	0.129966i
$409$	−4.39952	−	3.69164i	−0.217542	−	0.182540i	0.527504	−	0.849553i	$-0.323128\pi$
$409$	−4.39952	−	3.69164i	−0.217542	−	0.182540i	−0.745046	+	0.667013i	$0.767573\pi$
$410$	1.86608	−	10.5831i	0.0921593	−	0.522662i
$411$	−30.4774	+	11.2798i	−1.50334	+	0.556392i
$412$	10.6911	+	3.89124i	0.526713	+	0.191708i
$413$	0.111516	−	0.0590642i	0.00548737	−	0.00290636i
$414$	14.0598	−	5.29019i	0.691001	−	0.259999i
$415$	12.8567	+	22.2685i	0.631112	+	1.09312i
$416$	3.89189	+	1.41653i	0.190816	+	0.0694512i
$417$	−37.6351	+	0.203469i	−1.84300	+	0.00996390i
$418$	−0.745408	−	0.625472i	−0.0364591	−	0.0305928i
$419$	−2.00536	+	11.3730i	−0.0979683	+	0.555606i	0.895829	+	0.444399i	$0.146583\pi$
$419$	−2.00536	+	11.3730i	−0.0979683	+	0.555606i	−0.993797	+	0.111207i	$0.964528\pi$
$420$	−0.413764	+	13.2954i	−0.0201896	+	0.648747i
$421$	−21.2715	+	17.8489i	−1.03671	+	0.869901i	−0.991634	−	0.129083i	$-0.958797\pi$
$421$	−21.2715	+	17.8489i	−1.03671	+	0.869901i	−0.0450738	+	0.998984i	$0.514352\pi$
$422$	−1.35789	−	2.35193i	−0.0661010	−	0.114490i
$423$	3.53116	−	0.0381825i	0.171691	−	0.00185650i
$424$	5.61189	−	9.72008i	0.272538	−	0.472049i
$425$	4.04257	−	3.39212i	0.196093	−	0.164542i
$426$	18.3377	−	6.78686i	0.888463	−	0.328824i
$427$	4.96206	+	1.06307i	0.240131	+	0.0514458i
$428$	15.7704	−	5.73995i	0.762290	−	0.277451i
$429$	1.62059	−	1.37484i	0.0782430	−	0.0663778i
$430$	−27.3515	+	22.9507i	−1.31901	+	1.10678i
$431$	6.92449	+	11.9936i	0.333541	+	0.577710i	0.983203	−	0.182513i	$-0.0584232\pi$
$431$	6.92449	+	11.9936i	0.333541	+	0.577710i	−0.649663	+	0.760223i	$0.725090\pi$
$432$	3.92579	−	3.40414i	0.188880	−	0.163782i
$433$	−30.2784			−1.45509			−0.727543	−	0.686062i	$-0.759338\pi$
$433$	−30.2784			−1.45509			−0.727543	+	0.686062i	$0.759338\pi$
$434$	3.04793	−	7.50906i	0.146305	−	0.360446i
$435$	−4.28824	−	23.5738i	−0.205605	−	1.13028i
$436$	−3.24684	+	18.4138i	−0.155495	+	0.881859i
$437$	2.85597	−	16.1970i	0.136620	−	0.774809i
$438$	19.8177	−	7.33463i	0.946927	−	0.350462i
$439$	−2.65341	+	2.22648i	−0.126641	+	0.106264i	−0.703908	−	0.710291i	$-0.748563\pi$
$439$	−2.65341	+	2.22648i	−0.126641	+	0.106264i	0.577268	+	0.816555i	$0.304119\pi$
$440$	−0.429968	−	0.744727i	−0.0204979	−	0.0355034i
$441$	−16.8952	+	12.4721i	−0.804532	+	0.593910i
$442$	3.19015	−	5.52551i	0.151740	−	0.262822i
$443$	−3.21332	−	18.2237i	−0.152670	−	0.865832i	−0.960886	−	0.276946i	$-0.910678\pi$
$443$	−3.21332	−	18.2237i	−0.152670	−	0.865832i	0.808216	−	0.588886i	$-0.200433\pi$
$444$	6.40877	−	11.2402i	0.304147	−	0.533437i
$445$	−27.0974	+	9.86266i	−1.28454	+	0.467535i
$446$	−3.81447	−	3.20072i	−0.180620	−	0.151559i
$447$	10.9491	+	18.7298i	0.517875	+	0.885890i
$448$	2.62059	−	0.363997i	0.123811	−	0.0171972i
$449$	10.3958	−	18.0061i	0.490609	−	0.849759i	−0.509333	−	0.860570i	$-0.670108\pi$
$449$	10.3958	−	18.0061i	0.490609	−	0.849759i	0.999942	+	0.0108104i	$0.00344112\pi$
$450$	9.69447	+	3.41025i	0.457002	+	0.160761i
$451$	−0.548399	+	0.949855i	−0.0258231	+	0.0447269i
$452$	1.97629	+	11.2081i	0.0929570	+	0.527185i
$453$	−24.9323	−	20.6920i	−1.17142	−	0.972195i
$454$	1.18056	+	0.990607i	0.0554064	+	0.0464915i
$455$	−21.3212	+	23.6030i	−0.999551	+	1.10653i
$456$	−1.01816	−	5.59714i	−0.0476796	−	0.262110i
$457$	−1.04401	−	0.379989i	−0.0488367	−	0.0177751i	0.317486	−	0.948263i	$-0.397161\pi$
$457$	−1.04401	−	0.379989i	−0.0488367	−	0.0177751i	−0.366323	+	0.930488i	$0.619383\pi$
$458$	−2.04739	−	3.54619i	−0.0956684	−	0.165703i
$459$	−4.11429	−	6.86651i	−0.192038	−	0.320501i
$460$	7.26741	−	12.5875i	0.338845	−	0.586897i
$461$	−4.81360	−	27.2993i	−0.224192	−	1.27145i	−0.864225	−	0.503106i	$-0.832190\pi$
$461$	−4.81360	−	27.2993i	−0.224192	−	1.27145i	0.640033	−	0.768347i	$-0.278921\pi$
$462$	0.503789	−	1.26068i	0.0234384	−	0.0586520i
$463$	−16.8063	+	6.11699i	−0.781054	+	0.284281i	−0.701612	−	0.712559i	$-0.747536\pi$
$463$	−16.8063	+	6.11699i	−0.781054	+	0.284281i	−0.0794421	+	0.996839i	$0.525314\pi$
$464$	−4.47841	+	1.63001i	−0.207905	+	0.0756712i
$465$	−11.8503	−	9.83487i	−0.549543	−	0.456081i
$466$	3.38737	+	19.2107i	0.156917	+	0.889919i
$467$	−17.9954			−0.832726			−0.416363	−	0.909199i	$-0.636695\pi$
$467$	−17.9954			−0.832726			−0.416363	+	0.909199i	$0.636695\pi$
$468$	12.4243	−	0.134344i	0.574312	−	0.00621005i
$469$	23.2019	+	14.5502i	1.07137	+	0.671866i
$470$	2.61743	−	2.19629i	0.120733	−	0.101307i
$471$	−10.7789	+	18.9050i	−0.496667	+	0.871095i
$472$	−0.0448198	+	0.0163131i	−0.00206300	+	0.000750870i
$473$	3.42436	−	1.24636i	0.157452	−	0.0573079i
$474$	−3.92182	−	6.70877i	−0.180135	−	0.308144i
$475$	8.61916	−	7.23234i	0.395474	−	0.331842i
$476$	0.148805	−	4.07311i	0.00682045	−	0.186691i
$477$	5.48809	−	33.2211i	0.251282	−	1.52109i
$478$	−4.56439			−0.208770
$479$	0.831982	+	4.71840i	0.0380142	+	0.215589i	0.997898	−	0.0648101i	$-0.0206442\pi$
$479$	0.831982	+	4.71840i	0.0380142	+	0.215589i	−0.959883	+	0.280399i	$0.909533\pi$
$480$	0.846254	−	4.95587i	0.0386260	−	0.226204i
$481$	29.0735	−	10.5819i	1.32564	−	0.482492i
$482$	−26.2672	+	9.56048i	−1.19644	+	0.435468i
$483$	22.7110	−	3.27978i	1.03339	−	0.149235i
$484$	−1.89489	−	10.7465i	−0.0861313	−	0.488475i
$485$	−2.64953	+	4.58912i	−0.120309	+	0.208381i
$486$	7.42650	−	13.7057i	0.336873	−	0.621705i
$487$	1.98528	+	3.43861i	0.0899616	+	0.155818i	0.907495	−	0.420064i	$-0.137992\pi$
$487$	1.98528	+	3.43861i	0.0899616	+	0.155818i	−0.817533	+	0.575882i	$0.804659\pi$
$488$	−1.80237	−	0.656009i	−0.0815894	−	0.0296961i
$489$	12.3612	−	10.4867i	0.558995	−	0.474226i
$490$	−4.97905	+	19.6993i	−0.224931	+	0.889925i
$491$	−13.9317	−	11.6901i	−0.628728	−	0.527565i	0.271806	−	0.962352i	$-0.412379\pi$
$491$	−13.9317	−	11.6901i	−0.628728	−	0.527565i	−0.900533	+	0.434787i	$0.856824\pi$
$492$	−6.01375	+	2.22572i	−0.271121	+	0.100343i
$493$	1.27490	+	7.23030i	0.0574185	+	0.325636i
$494$	6.80173	−	11.7809i	0.306024	−	0.530049i
$495$	−1.99406	−	1.63680i	−0.0896264	−	0.0735689i
$496$	−1.53152	+	2.65268i	−0.0687674	+	0.119109i
$497$	29.5841	−	4.10920i	1.32703	−	0.184323i
$498$	7.59973	−	13.3290i	0.340552	−	0.597288i
$499$	14.7769	+	12.3993i	0.661505	+	0.555068i	0.910537	−	0.413427i	$-0.135668\pi$
$499$	14.7769	+	12.3993i	0.661505	+	0.555068i	−0.249033	+	0.968495i	$0.580113\pi$
$500$	−4.29439	+	1.56303i	−0.192051	+	0.0699008i
$501$	14.6712	+	25.0970i	0.655462	+	1.12125i
$502$	−1.98046	−	11.2317i	−0.0883922	−	0.501297i
$503$	10.2088	−	17.6822i	0.455190	−	0.788412i	−0.543509	−	0.839403i	$-0.682905\pi$
$503$	10.2088	−	17.6822i	0.455190	−	0.788412i	0.998699	+	0.0509915i	$0.0162381\pi$
$504$	6.97359	−	3.79065i	0.310629	−	0.168849i
$505$	−12.5898	−	21.8061i	−0.560237	−	0.970359i
$506$	−1.13639	+	0.953548i	−0.0505189	+	0.0423904i
$507$	5.53574	+	4.59427i	0.245851	+	0.204039i
$508$	−1.76065	+	9.98513i	−0.0781161	+	0.443018i
$509$	7.57638	−	42.9678i	0.335817	−	1.90451i	−0.0831940	−	0.996533i	$-0.526512\pi$
$509$	7.57638	−	42.9678i	0.335817	−	1.90451i	0.419011	−	0.907981i	$-0.362377\pi$
$510$	−7.29224	−	2.60960i	−0.322906	−	0.115555i
$511$	31.9719	−	4.44086i	1.41435	−	0.196452i
$512$	−1.00000			−0.0441942
$513$	−8.77207	−	14.6401i	−0.387296	−	0.646375i
$514$	1.91489	+	3.31669i	0.0844623	+	0.146293i
$515$	25.2983	−	21.2278i	1.11478	−	0.935407i
$516$	20.0595	+	7.17850i	0.883072	+	0.316016i
$517$	−0.327697	+	0.119272i	−0.0144121	+	0.00524558i
$518$	13.2487	−	14.6665i	0.582112	−	0.644411i
$519$	−2.13201	+	12.4856i	−0.0935850	+	0.548057i
$520$	9.20936	−	7.72757i	0.403857	−	0.338876i
$521$	7.61050	−	13.1818i	0.333422	−	0.577504i	−0.649758	−	0.760141i	$-0.725130\pi$
$521$	7.61050	−	13.1818i	0.333422	−	0.577504i	0.983180	+	0.182637i	$0.0584633\pi$
$522$	−10.8525	+	9.30813i	−0.475001	+	0.407406i
$523$	−5.33094	−	9.23345i	−0.233106	−	0.403751i	0.725615	−	0.688101i	$-0.241555\pi$
$523$	−5.33094	−	9.23345i	−0.233106	−	0.403751i	−0.958720	+	0.284350i	$0.908222\pi$
$524$	−6.24133	+	5.23710i	−0.272654	+	0.228784i
$525$	13.3442	+	8.26812i	0.582389	+	0.360850i
$526$	−4.88282	+	27.6919i	−0.212901	+	1.20742i
$527$	3.61472	+	3.03311i	0.157460	+	0.132124i
$528$	−0.254158	+	0.445763i	−0.0110608	+	0.0193994i
$529$	−1.94867	−	0.709258i	−0.0847248	−	0.0308373i
$530$	−16.2896	−	28.2144i	−0.707574	−	1.22555i
$531$	−0.108611	+	0.0931554i	−0.00471333	+	0.00404260i
$532$	0.317267	−	8.68428i	0.0137553	−	0.376511i
$533$	−14.4086	−	5.24430i	−0.624105	−	0.227156i
$534$	13.2409	+	10.9890i	0.572988	+	0.475539i
$535$	8.45915	−	47.9742i	0.365721	−	2.07411i
$536$	−7.92952	−	6.65365i	−0.342503	−	0.287394i
$537$	27.5909	+	9.87368i	1.19064	+	0.426081i
$538$	2.23826	+	12.6938i	0.0964984	+	0.547270i
$539$	1.16518	−	1.71550i	0.0501878	−	0.0738919i
$540$	−2.85966	−	14.8092i	−0.123060	−	0.637288i
$541$	−11.1950	+	19.3903i	−0.481311	+	0.833654i	−0.999770	−	0.0214478i	$-0.993172\pi$
$541$	−11.1950	+	19.3903i	−0.481311	+	0.833654i	0.518459	+	0.855102i	$0.326506\pi$
$542$	4.82922	−	4.05220i	0.207433	−	0.174057i
$543$	3.15582	+	17.3486i	0.135429	+	0.744499i
$544$	−0.267508	+	1.51711i	−0.0114693	+	0.0650457i
$545$	41.5762	+	34.8866i	1.78093	+	1.49438i
$546$	18.5796	+	3.87556i	0.795133	+	0.165859i
$547$	28.0019	+	10.1918i	1.19727	+	0.435772i	0.862272	−	0.506445i	$-0.169041\pi$
$547$	28.0019	+	10.1918i	1.19727	+	0.435772i	0.335002	+	0.942217i	$0.391263\pi$
$548$	18.7626			0.801498
$549$	−5.75379	+	0.0622159i	−0.245566	+	0.00265531i
$550$	−1.01485			−0.0432734
$551$	2.71821	+	15.4157i	0.115800	+	0.656732i
$552$	−8.67289	+	0.0468887i	−0.369143	+	0.00199572i
$553$	−3.64996	−	11.2953i	−0.155212	−	0.480325i
$554$	1.65106	−	9.36365i	0.0701470	−	0.397823i
$555$	−18.9543	−	32.4238i	−0.804567	−	1.37631i
$556$	20.4185	+	7.43173i	0.865938	+	0.315176i
$557$	−27.4303			−1.16226			−0.581129	−	0.813811i	$-0.697389\pi$
$557$	−27.4303			−1.16226			−0.581129	+	0.813811i	$0.697389\pi$
$558$	−1.49774	+	9.06626i	−0.0634043	+	0.383805i
$559$	25.4725	+	44.1197i	1.07737	+	1.86607i
$560$	2.88837	−	7.11594i	0.122056	−	0.300703i
$561$	0.608284	+	0.504832i	0.0256818	+	0.0213140i
$562$	30.1575	−	10.9764i	1.27212	−	0.463013i
$563$	20.8031	+	17.4558i	0.876744	+	0.735676i	0.965507	−	0.260377i	$-0.0838468\pi$
$563$	20.8031	+	17.4558i	0.876744	+	0.735676i	−0.0887626	+	0.996053i	$0.528291\pi$
$564$	−1.91962	−	0.686954i	−0.0808305	−	0.0289260i
$565$	31.0433	+	11.2988i	1.30600	+	0.475345i
$566$	−21.1508			−0.889035
$567$	15.5758	−	18.0109i	0.654124	−	0.756387i
$568$	−11.2891			−0.473680
$569$	−10.4978	−	3.82088i	−0.440090	−	0.160180i	0.112466	−	0.993656i	$-0.464125\pi$
$569$	−10.4978	−	3.82088i	−0.440090	−	0.160180i	−0.552556	+	0.833476i	$0.686347\pi$
$570$	−15.5478	−	5.56393i	−0.651225	−	0.233047i
$571$	−4.35132	−	3.65119i	−0.182097	−	0.152797i	0.547183	−	0.837013i	$-0.315700\pi$
$571$	−4.35132	−	3.65119i	−0.182097	−	0.152797i	−0.729280	+	0.684216i	$0.760145\pi$
$572$	−1.15299	+	0.419655i	−0.0482090	+	0.0175467i
$573$	−22.3915	−	18.5833i	−0.935416	−	0.776329i
$574$	−9.70198	+	1.34759i	−0.404953	+	0.0562474i
$575$	−8.57662	−	14.8551i	−0.357670	−	0.619502i
$576$	−2.80782	+	1.05648i	−0.116992	+	0.0440201i
$577$	−13.0773			−0.544417			−0.272209	−	0.962238i	$-0.587754\pi$
$577$	−13.0773			−0.544417			−0.272209	+	0.962238i	$0.587754\pi$
$578$	−13.7447	−	5.00266i	−0.571704	−	0.208083i
$579$	−6.81311	−	11.6547i	−0.283143	−	0.484352i
$580$	−2.40220	+	13.6235i	−0.0997459	+	0.565687i
$581$	15.7107	−	17.3921i	0.651789	−	0.721545i
$582$	3.16194	−	0.0170946i	0.131066	−	0.000708592i
$583$	0.577398	+	3.27459i	0.0239134	+	0.135620i
$584$	−12.2003			−0.504850
$585$	17.6942	−	31.4271i	0.731564	−	1.29935i
$586$	−7.98070			−0.329680
$587$	−31.4510	−	11.4472i	−1.29812	−	0.472478i	−0.401738	−	0.915755i	$-0.631594\pi$
$587$	−31.4510	−	11.4472i	−1.29812	−	0.472478i	−0.896385	+	0.443276i	$0.853816\pi$
$588$	11.6473	−	3.36738i	0.480329	−	0.138869i
$589$	7.70694	+	6.46689i	0.317559	+	0.266464i
$590$	−0.0240411	+	0.136344i	−0.000989757	+	0.00561319i
$591$	3.57966	+	19.6786i	0.147248	+	0.809468i
$592$	−5.72256	+	4.80180i	−0.235196	+	0.197353i
$593$	13.9689	−	24.1948i	0.573633	−	0.993561i	−0.422556	−	0.906337i	$-0.638867\pi$
$593$	13.9689	−	24.1948i	0.573633	−	0.993561i	0.996189	−	0.0872245i	$-0.0277997\pi$
$594$	−0.242690	+	1.52014i	−0.00995768	+	0.0623719i
$595$	−10.0230	−	6.28555i	−0.410904	−	0.257682i
$596$	−2.17509	−	12.3355i	−0.0890950	−	0.505283i
$597$	37.6250	+	13.4645i	1.53989	+	0.551064i
$598$	−15.8869	−	13.3307i	−0.649662	−	0.545132i
$599$	−0.435976	+	2.47254i	−0.0178135	+	0.101025i	−0.992418	−	0.122907i	$-0.960778\pi$
$599$	−0.435976	+	2.47254i	−0.0178135	+	0.101025i	0.974605	+	0.223932i	$0.0718894\pi$
$600$	−4.56573	−	3.78923i	−0.186395	−	0.154695i
$601$	13.4389	+	4.89138i	0.548186	+	0.199523i	0.601240	−	0.799068i	$-0.294673\pi$
$601$	13.4389	+	4.89138i	0.548186	+	0.199523i	−0.0530544	+	0.998592i	$0.516896\pi$
$602$	27.5714	+	17.2903i	1.12373	+	0.704701i
$603$	−29.2941	−	10.3049i	−1.19295	−	0.419647i
$604$	9.35315	+	16.2001i	0.380574	+	0.659174i
$605$	−29.7646	−	10.8334i	−1.21010	−	0.440441i
$606$	−7.44193	+	13.0523i	−0.302308	+	0.530211i
$607$	14.4417	+	12.1180i	0.586170	+	0.491855i	0.886967	−	0.461833i	$-0.152808\pi$
$607$	14.4417	+	12.1180i	0.586170	+	0.491855i	−0.300797	+	0.953688i	$0.597253\pi$
$608$	−0.570354	+	3.23464i	−0.0231309	+	0.131182i
$609$	−19.2443	+	10.3263i	−0.779819	+	0.418441i
$610$	−4.26493	+	3.57870i	−0.172682	+	0.144897i
$611$	−2.43762	−	4.22208i	−0.0986156	−	0.170807i
$612$	0.851688	+	4.54240i	0.0344275	+	0.183616i
$613$	6.52722	−	11.3055i	0.263632	−	0.456624i	−0.703572	−	0.710624i	$-0.748413\pi$
$613$	6.52722	−	11.3055i	0.263632	−	0.456624i	0.967204	+	0.254000i	$0.0817463\pi$
$614$	26.1639	−	21.9541i	1.05589	−	0.885996i
$615$	−3.13301	+	18.3477i	−0.126335	+	0.739849i
$616$	−0.525414	+	0.581644i	−0.0211695	+	0.0234351i
$617$	19.2687	−	7.01323i	0.775729	−	0.282342i	0.0763383	−	0.997082i	$-0.475677\pi$
$617$	19.2687	−	7.01323i	0.775729	−	0.282342i	0.699390	+	0.714740i	$0.253455\pi$
$618$	−18.5537	−	6.63962i	−0.746339	−	0.267085i
$619$	19.8068	−	16.6199i	0.796101	−	0.668008i	−0.151146	−	0.988511i	$-0.548296\pi$
$619$	19.8068	−	16.6199i	0.796101	−	0.668008i	0.947247	+	0.320503i	$0.103852\pi$
$620$	4.44554	+	7.69989i	0.178537	+	0.309235i
$621$	−24.3024	+	9.29440i	−0.975220	+	0.372971i
$622$	8.92855			0.358002
$623$	16.1486	+	20.7381i	0.646982	+	0.830854i
$624$	−6.75412	−	2.41703i	−0.270381	−	0.0967585i
$625$	−5.27773	+	29.9315i	−0.211109	+	1.19726i
$626$	−2.42859	+	13.7732i	−0.0970661	+	0.550489i
$627$	1.29692	+	1.07635i	0.0517941	+	0.0429854i
$628$	9.62479	−	8.07616i	0.384071	−	0.322274i
$629$	5.75404	+	9.96629i	0.229429	+	0.397382i
$630$	0.592153	−	23.0318i	0.0235919	−	0.917607i
$631$	9.27214	−	16.0598i	0.369118	−	0.639331i	−0.620310	−	0.784357i	$-0.712993\pi$
$631$	9.27214	−	16.0598i	0.369118	−	0.639331i	0.989428	+	0.145026i	$0.0463265\pi$
$632$	0.779086	+	4.41842i	0.0309904	+	0.175755i
$633$	2.37392	+	4.06089i	0.0943550	+	0.161406i
$634$	19.8522	−	7.22561i	0.788432	−	0.286966i
$635$	22.5453	+	18.9178i	0.894684	+	0.750729i
$636$	−9.62892	+	16.8880i	−0.381812	+	0.669652i
$637$	26.4471	+	11.8772i	1.04787	+	0.470593i
$638$	0.705950	−	1.22274i	0.0279488	−	0.0484088i
$639$	−31.6978	+	11.9267i	−1.25394	+	0.471814i
$640$	−1.45134	+	2.51380i	−0.0573694	+	0.0993667i
$641$	−2.13677	−	12.1183i	−0.0843975	−	0.478642i	−0.997485	−	0.0708784i	$-0.977420\pi$
$641$	−2.13677	−	12.1183i	−0.0843975	−	0.478642i	0.913087	−	0.407764i	$-0.133691\pi$
$642$	−27.2609	+	10.0894i	−1.07590	+	0.398197i
$643$	−29.8571	−	25.0531i	−1.17745	−	0.987998i	−0.999993	−	0.00386972i	$-0.998768\pi$
$643$	−29.8571	−	25.0531i	−1.17745	−	0.987998i	−0.177458	−	0.984128i	$-0.556787\pi$
$644$	−12.9543	−	2.77533i	−0.510471	−	0.109363i
$645$	47.1586	−	40.0072i	1.85687	−	1.57528i
$646$	4.75474	+	1.73058i	0.187073	+	0.0680889i
$647$	23.5544	+	40.7974i	0.926019	+	1.60391i	0.789914	+	0.613218i	$0.210125\pi$
$647$	23.5544	+	40.7974i	0.926019	+	1.60391i	0.136106	+	0.990694i	$0.456541\pi$
$648$	−6.76769	+	5.93282i	−0.265860	+	0.233063i
$649$	0.00706512	−	0.0122372i	0.000277330	−	0.000480350i
$650$	−2.46367	−	13.9721i	−0.0966329	−	0.548033i
$651$	−5.20878	+	13.0344i	−0.204148	+	0.510859i
$652$	−8.79457	+	3.20096i	−0.344422	+	0.125359i
$653$	−24.7165	+	8.99607i	−0.967231	+	0.352043i	−0.776863	−	0.629669i	$-0.783190\pi$
$653$	−24.7165	+	8.99607i	−0.967231	+	0.352043i	−0.190368	+	0.981713i	$0.560968\pi$
$654$	5.45119	−	31.9235i	0.213158	−	1.24831i
$655$	4.10671	+	23.2903i	0.160462	+	0.910028i
$656$	3.70221			0.144547
$657$	−34.2561	+	12.8893i	−1.33646	+	0.502861i
$658$	−2.63847	−	1.65462i	−0.102858	−	0.0645037i
$659$	−4.00501	+	3.36060i	−0.156013	+	0.130910i	−0.717453	−	0.696607i	$-0.754692\pi$
$659$	−4.00501	+	3.36060i	−0.156013	+	0.130910i	0.561440	+	0.827518i	$0.310248\pi$
$660$	0.751689	+	1.28586i	0.0292595	+	0.0500520i
$661$	−38.1146	+	13.8726i	−1.48249	+	0.539581i	−0.951459	−	0.307774i	$-0.900416\pi$
$661$	−38.1146	+	13.8726i	−1.48249	+	0.539581i	−0.531027	+	0.847355i	$0.678194\pi$
$662$	11.1970	−	4.07539i	0.435185	−	0.158394i
$663$	−5.47369	+	9.60019i	−0.212580	+	0.372841i
$664$	−6.78600	+	5.69413i	−0.263348	+	0.220975i
$665$	−21.3701	−	13.4014i	−0.828697	−	0.519685i
$666$	−10.9949	+	19.5284i	−0.426044	+	0.756708i
$667$	23.8642			0.924027
$668$	−2.91450	−	16.5290i	−0.112766	−	0.639525i
$669$	6.63673	+	5.50801i	0.256591	+	0.212952i
$670$	−28.2344	+	10.2765i	−1.09079	+	0.397015i
$671$	0.533961	−	0.194346i	0.0206133	−	0.00750264i
$672$	−4.53552	+	0.654991i	−0.174962	+	0.0252668i
$673$	2.47474	+	14.0350i	0.0953943	+	0.541008i	0.994626	+	0.103535i	$0.0330154\pi$
$673$	2.47474	+	14.0350i	0.0953943	+	0.541008i	−0.899231	+	0.437473i	$0.855874\pi$
$674$	3.42764	−	5.93684i	0.132028	−	0.228679i
$675$	−16.8230	−	5.81586i	−0.647518	−	0.223853i
$676$	−2.07669	−	3.59693i	−0.0798727	−	0.138344i
$677$	−4.67276	−	1.70075i	−0.179589	−	0.0653650i	0.250661	−	0.968075i	$-0.419352\pi$
$677$	−4.67276	−	1.70075i	−0.179589	−	0.0653650i	−0.430249	+	0.902710i	$0.641574\pi$
$678$	−3.52794	−	19.3942i	−0.135490	−	0.744831i
$679$	4.72284	+	1.01182i	0.181246	+	0.0388302i
$680$	3.42548	+	2.87432i	0.131361	+	0.110225i
$681$	−2.05403	−	1.70470i	−0.0787108	−	0.0653243i
$682$	−0.157576	−	0.893657i	−0.00603389	−	0.0342199i
$683$	−9.65780	+	16.7278i	−0.369545	+	0.640071i	−0.989494	−	0.144571i	$-0.953820\pi$
$683$	−9.65780	+	16.7278i	−0.369545	+	0.640071i	0.619949	+	0.784642i	$0.287153\pi$
$684$	1.81588	+	9.68485i	0.0694321	+	0.370309i
$685$	27.2310	−	47.1654i	1.04044	−	1.80210i
$686$	18.4812	−	1.20262i	0.705614	−	0.0459164i
$687$	3.57934	+	6.12292i	0.136560	+	0.233604i
$688$	−9.42283	−	7.90669i	−0.359242	−	0.301440i
$689$	−43.6818	+	15.8989i	−1.66414	+	0.605698i
$690$	−12.4695	+	21.8700i	−0.474705	+	0.832576i
$691$	−2.06397	−	11.7054i	−0.0785171	−	0.445293i	−0.998568	−	0.0534942i	$-0.982964\pi$
$691$	−2.06397	−	11.7054i	−0.0785171	−	0.445293i	0.920051	−	0.391799i	$-0.128147\pi$
$692$	3.65645	−	6.33316i	0.138997	−	0.240751i
$693$	−0.860770	+	2.18824i	−0.0326979	+	0.0831244i
$694$	−10.8523	−	18.7967i	−0.411946	−	0.713512i
$695$	48.3162	−	40.5421i	1.83274	−	1.53785i
$696$	7.74146	−	2.86515i	0.293439	−	0.108603i
$697$	0.990370	−	5.61667i	0.0375129	−	0.212746i
$698$	−3.07425	+	17.4349i	−0.116362	+	0.659922i
$699$	−6.04689	−	33.2417i	−0.228714	−	1.25732i
$700$	−5.56841	−	7.15095i	−0.210466	−	0.270280i
$701$	1.66339			0.0628253			0.0314126	−	0.999507i	$-0.489999\pi$
$701$	1.66339			0.0628253			0.0314126	+	0.999507i	$0.489999\pi$
$702$	−21.5179	+	0.349027i	−0.812140	+	0.0131732i
$703$	12.2682	+	21.2491i	0.462704	+	0.801426i
$704$	0.226945	−	0.190429i	0.00855329	−	0.00717707i
$705$	−4.51289	+	3.82853i	−0.169965	+	0.144191i
$706$	−24.5375	+	8.93092i	−0.923481	+	0.336120i
$707$	−15.3845	+	17.0309i	−0.578593	+	0.640515i
$708$	0.0774762	−	0.0286743i	0.00291174	−	0.00107765i
$709$	2.94595	−	2.47195i	0.110638	−	0.0928360i	−0.585791	−	0.810462i	$-0.699216\pi$
$709$	2.94595	−	2.47195i	0.110638	−	0.0928360i	0.696428	+	0.717626i	$0.254771\pi$
$710$	−16.3844	+	28.3786i	−0.614895	+	1.06503i
$711$	6.85551	+	11.5830i	0.257102	+	0.434398i
$712$	−4.96720	−	8.60345i	−0.186154	−	0.322428i
$713$	11.7494	−	9.85895i	0.440020	−	0.369221i
$714$	−0.219593	+	7.05612i	−0.00821807	+	0.264069i
$715$	−0.618460	+	3.50746i	−0.0231291	+	0.131172i
$716$	−12.9606	−	10.8753i	−0.484362	−	0.406428i
$717$	7.90563	−	0.0427407i	0.295241	−	0.00159618i
$718$	20.3191	+	7.39556i	0.758304	+	0.276000i
$719$	7.88105	+	13.6504i	0.293914	+	0.509073i	0.974732	−	0.223379i	$-0.0717089\pi$
$719$	7.88105	+	13.6504i	0.293914	+	0.509073i	−0.680818	+	0.732453i	$0.738376\pi$
$720$	−1.41933	+	8.59162i	−0.0528952	+	0.320191i
$721$	−25.5016	−	15.9924i	−0.949731	−	0.595587i
$722$	−7.71657	−	2.80860i	−0.287181	−	0.104525i
$723$	45.4059	−	16.8050i	1.68866	−	0.624983i
$724$	1.76784	−	10.0259i	0.0657012	−	0.372610i
$725$	12.5063	+	10.4940i	0.464472	+	0.389739i
$726$	3.38263	+	18.5954i	0.125541	+	0.690139i
$727$	−2.04939	−	11.6227i	−0.0760077	−	0.431061i	−0.998937	−	0.0460921i	$-0.985323\pi$
$727$	−2.04939	−	11.6227i	−0.0760077	−	0.431061i	0.922929	−	0.384969i	$-0.125788\pi$
$728$	−9.28339	−	5.82172i	−0.344065	−	0.215767i
$729$	−12.7345	+	23.8082i	−0.471650	+	0.881786i
$730$	−17.7068	+	30.6690i	−0.655357	+	1.13511i
$731$	−14.5160	+	12.1804i	−0.536895	+	0.450508i
$732$	3.12789	+	1.11935i	0.115610	+	0.0413722i
$733$	5.14377	−	29.1717i	0.189989	−	1.07748i	−0.729386	−	0.684102i	$-0.760194\pi$
$733$	5.14377	−	29.1717i	0.189989	−	1.07748i	0.919376	−	0.393381i	$-0.128695\pi$
$734$	10.9711	+	9.20588i	0.404952	+	0.339795i
$735$	8.43938	−	34.1664i	0.311291	−	1.26025i
$736$	4.70539	+	1.71262i	0.173443	+	0.0631280i
$737$	3.06661			0.112960
$738$	10.3951	−	3.91131i	0.382650	−	0.143977i
$739$	−25.1747			−0.926065			−0.463032	−	0.886341i	$-0.653239\pi$
$739$	−25.1747			−0.926065			−0.463032	+	0.886341i	$0.653239\pi$
$740$	3.76536	+	21.3544i	0.138418	+	0.785005i
$741$	−11.6704	+	20.4686i	−0.428725	+	0.751932i
$742$	−19.9056	+	22.0359i	−0.730757	+	0.808964i
$743$	−2.42758	+	13.7675i	−0.0890591	+	0.505079i	0.907348	+	0.420381i	$0.138104\pi$
$743$	−2.42758	+	13.7675i	−0.0890591	+	0.505079i	−0.996407	+	0.0846981i	$0.973007\pi$
$744$	2.62780	−	4.60884i	0.0963398	−	0.168968i
$745$	−34.1659	−	12.4354i	−1.25174	−	0.455597i
$746$	16.1314			0.590613
$747$	−13.0381	+	23.1574i	−0.477040	+	0.847283i
$748$	−0.228193	−	0.395242i	−0.00834357	−	0.0144515i
$749$	−43.9801	+	6.10878i	−1.60700	+	0.223210i
$750$	7.42335	−	2.74742i	0.271062	−	0.100322i
$751$	5.98765	−	2.17933i	0.218492	−	0.0795248i	−0.230455	−	0.973083i	$-0.574021\pi$
$751$	5.98765	−	2.17933i	0.218492	−	0.0795248i	0.448947	+	0.893558i	$0.351799\pi$
$752$	0.901727	+	0.756639i	0.0328826	+	0.0275918i
$753$	3.53538	+	19.4351i	0.128836	+	0.708255i
$754$	18.5481	+	6.75095i	0.675481	+	0.245855i
$755$	54.2986			1.97613
$756$	−12.0429	+	6.63080i	−0.437998	+	0.241160i
$757$	40.1257			1.45839			0.729196	−	0.684305i	$-0.239894\pi$
$757$	40.1257			1.45839			0.729196	+	0.684305i	$0.239894\pi$
$758$	−7.42208	−	2.70142i	−0.269582	−	0.0981198i
$759$	1.95934	−	1.66221i	0.0711194	−	0.0603345i
$760$	7.30346	+	6.12833i	0.264924	+	0.222298i
$761$	17.1857	−	6.25508i	0.622981	−	0.226746i	−0.0111927	−	0.999937i	$-0.503563\pi$
$761$	17.1857	−	6.25508i	0.622981	−	0.226746i	0.634173	+	0.773191i	$0.281341\pi$
$762$	2.95599	−	17.3110i	0.107084	−	0.627111i
$763$	18.6056	−	45.8377i	0.673566	−	1.65943i
$764$	8.39998	+	14.5492i	0.303901	+	0.526371i
$765$	12.6548	+	4.45161i	0.457535	+	0.160948i
$766$	7.80063			0.281848
$767$	0.185628	+	0.0675632i	0.00670266	+	0.00243957i
$768$	1.73203	−	0.00936395i	0.0624991	−	0.000337892i
$769$	1.55869	−	8.83975i	0.0562077	−	0.318770i	−0.943721	−	0.330744i	$-0.892700\pi$
$769$	1.55869	−	8.83975i	0.0562077	−	0.318770i	0.999928	+	0.0119740i	$0.00381155\pi$
$770$	0.699582	+	2.16495i	0.0252112	+	0.0780194i
$771$	−3.34770	−	5.72666i	−0.120565	−	0.206241i
$772$	1.35345	+	7.67582i	0.0487119	+	0.276259i
$773$	−12.0616			−0.433824			−0.216912	−	0.976191i	$-0.569598\pi$
$773$	−12.0616			−0.433824			−0.216912	+	0.976191i	$0.569598\pi$
$774$	−34.8109	−	12.2455i	−1.25125	−	0.440156i
$775$	10.4928			0.376912
$776$	−1.71548	−	0.624382i	−0.0615820	−	0.0224140i
$777$	−22.8097	+	25.5269i	−0.818292	+	0.915772i
$778$	−12.3052	−	10.3253i	−0.441162	−	0.370178i
$779$	2.11157	−	11.9753i	0.0756548	−	0.429060i
$780$	−15.8785	+	13.4706i	−0.568541	+	0.482324i
$781$	2.56200	−	2.14977i	0.0916756	−	0.0769250i
$782$	3.85697	−	6.68047i	0.137925	−	0.238893i
$783$	18.7096	−	16.2235i	0.668628	−	0.579782i
$784$	−6.98134	−	0.510786i	−0.249334	−	0.0182424i
$785$	−6.33298	−	35.9161i	−0.226034	−	1.28190i
$786$	10.7611	−	9.12924i	0.383836	−	0.325629i
$787$	17.2239	+	14.4526i	0.613966	+	0.515179i	0.895900	−	0.444255i	$-0.146532\pi$
$787$	17.2239	+	14.4526i	0.613966	+	0.515179i	−0.281934	+	0.959434i	$0.590976\pi$
$788$	2.00527	−	11.3724i	0.0714346	−	0.405126i
$789$	8.19787	−	48.0087i	0.291852	−	1.70916i
$790$	12.2378	+	4.45418i	0.435400	+	0.158473i
$791$	1.09934	−	30.0913i	0.0390880	−	1.06992i
$792$	0.436034	−	0.774453i	0.0154938	−	0.0275190i
$793$	3.97194	+	6.87960i	0.141048	+	0.244302i
$794$	−19.1838	−	6.98234i	−0.680808	−	0.247794i
$795$	28.4782	+	48.7155i	1.01002	+	1.72776i
$796$	−17.6741	−	14.8303i	−0.626441	−	0.525646i
$797$	−6.54790	+	37.1350i	−0.231939	+	1.31539i	0.617027	+	0.786942i	$0.288337\pi$
$797$	−6.54790	+	37.1350i	−0.231939	+	1.31539i	−0.848966	+	0.528448i	$0.822774\pi$
$798$	−0.468195	+	15.0444i	−0.0165739	+	0.532565i
$799$	1.38913	−	1.16562i	0.0491438	−	0.0412365i
$800$	1.71280	+	2.96666i	0.0605566	+	0.104887i
$801$	−23.0364	−	18.9092i	−0.813951	−	0.668123i
$802$	1.25463	−	2.17309i	0.0443027	−	0.0767345i
$803$	2.76878	−	2.32328i	0.0977082	−	0.0819869i
$804$	13.7964	+	11.4500i	0.486562	+	0.403812i
$805$	−25.7778	+	28.5366i	−0.908547	+	1.00578i
$806$	11.9210	−	4.33891i	0.419901	−	0.152831i
$807$	−3.99560	−	21.9651i	−0.140652	−	0.773207i
$808$	6.64509	−	5.57589i	0.233774	−	0.196159i
$809$	−10.8527	−	18.7975i	−0.381562	−	0.660884i	0.609724	−	0.792614i	$-0.291280\pi$
$809$	−10.8527	−	18.7975i	−0.381562	−	0.660884i	−0.991286	+	0.131730i	$0.957947\pi$
$810$	5.09167	+	25.6232i	0.178903	+	0.900308i
$811$	49.8708			1.75120			0.875600	−	0.483037i	$-0.160466\pi$
$811$	49.8708			1.75120			0.875600	+	0.483037i	$0.160466\pi$
$812$	12.4893	−	1.73475i	0.438288	−	0.0608777i
$813$	−8.32639	+	7.06373i	−0.292019	+	0.247736i
$814$	0.384302	−	2.17948i	0.0134698	−	0.0763908i
$815$	−4.71736	+	26.7535i	−0.165242	+	0.937134i
$816$	0.449125	−	2.63018i	0.0157225	−	0.0920749i
$817$	−30.9496	+	25.9698i	−1.08279	+	0.908569i
$818$	−2.87158	−	4.97373i	−0.100403	−	0.173902i
$819$	−32.2166	−	6.53860i	−1.12574	−	0.228477i
$820$	5.37318	−	9.30661i	0.187639	−	0.325001i
$821$	3.75716	+	21.3079i	0.131126	+	0.743651i	0.977480	+	0.211030i	$0.0676817\pi$
$821$	3.75716	+	21.3079i	0.131126	+	0.743651i	−0.846354	+	0.532621i	$0.821207\pi$
$822$	−32.4973	+	0.175692i	−1.13347	+	0.00612796i
$823$	−45.6493	+	16.6150i	−1.59123	+	0.579162i	−0.977608	−	0.210435i	$-0.932512\pi$
$823$	−45.6493	+	16.6150i	−1.59123	+	0.579162i	−0.613626	+	0.789597i	$0.710290\pi$
$824$	8.71546	+	7.31314i	0.303618	+	0.254765i
$825$	1.75775	−	0.00950302i	0.0611970	−	0.000330853i
$826$	0.124992	−	0.0173613i	0.00434904	−	0.000604076i
$827$	18.1270	−	31.3970i	0.630339	−	1.09178i	−0.357143	−	0.934050i	$-0.616249\pi$
$827$	18.1270	−	31.3970i	0.630339	−	1.09178i	0.987482	−	0.157730i	$-0.0504175\pi$
$828$	15.0212	−	0.162425i	0.522024	−	0.00564466i
$829$	−1.46911	+	2.54458i	−0.0510243	+	0.0883768i	−0.890409	−	0.455160i	$-0.849582\pi$
$829$	−1.46911	+	2.54458i	−0.0510243	+	0.0883768i	0.839385	+	0.543537i	$0.182915\pi$
$830$	4.46509	+	25.3228i	0.154986	+	0.878967i
$831$	−2.77201	+	16.2335i	−0.0961598	+	0.563135i
$832$	3.17270	+	2.66221i	0.109994	+	0.0922955i
$833$	−2.64249	+	10.4548i	−0.0915567	+	0.362239i
$834$	−35.4350	−	12.6808i	−1.22701	−	0.439099i
$835$	−45.7805	−	16.6627i	−1.58430	−	0.576638i
$836$	−0.486531	−	0.842696i	−0.0168270	−	0.0291452i
$837$	2.50922	−	15.7170i	0.0867314	−	0.543260i
$838$	−5.77420	+	10.0012i	−0.199467	+	0.345486i
$839$	−1.43777	−	8.15399i	−0.0496373	−	0.281507i	0.949879	−	0.312619i	$-0.101206\pi$
$839$	−1.43777	−	8.15399i	−0.0496373	−	0.281507i	−0.999516	+	0.0311119i	$0.990095\pi$
$840$	−4.93609	+	12.3520i	−0.170311	+	0.426186i
$841$	5.90775	−	2.15025i	0.203716	−	0.0741464i
$842$	−26.0933	+	9.49719i	−0.899235	+	0.327295i
$843$	−52.1308	+	19.2939i	−1.79548	+	0.664516i
$844$	−0.471590	−	2.67452i	−0.0162328	−	0.0920608i
$845$	−12.0560			−0.414738
$846$	3.33126	+	1.17185i	0.114531	+	0.0402889i
$847$	−1.05406	+	28.8518i	−0.0362178	+	0.991360i
$848$	8.59792	−	7.21451i	0.295254	−	0.247747i
$849$	36.6338	−	0.198055i	1.25727	−	0.00679724i
$850$	4.95894	−	1.80491i	0.170090	−	0.0619078i
$851$	35.1505	−	12.7937i	1.20494	−	0.438564i
$852$	19.5530	−	0.105711i	0.669875	−	0.00362159i
$853$	−18.9419	+	15.8941i	−0.648559	+	0.544205i	−0.906633	−	0.421920i	$-0.861356\pi$
$853$	−18.9419	+	15.8941i	−0.648559	+	0.544205i	0.258075	+	0.966125i	$0.416912\pi$
$854$	4.29922	+	2.69609i	0.147116	+	0.0922582i
$855$	26.9813	+	9.49127i	0.922740	+	0.324595i
$856$	16.7825			0.573613
$857$	−6.79818	−	38.5544i	−0.232221	−	1.31699i	−0.848387	−	0.529376i	$-0.822426\pi$
$857$	−6.79818	−	38.5544i	−0.232221	−	1.31699i	0.616166	−	0.787616i	$-0.288685\pi$
$858$	1.99308	−	0.737650i	0.0680427	−	0.0251829i
$859$	−4.05547	+	1.47607i	−0.138371	+	0.0503628i	−0.410277	−	0.911961i	$-0.634568\pi$
$859$	−4.05547	+	1.47607i	−0.138371	+	0.0503628i	0.271906	+	0.962324i	$0.412346\pi$
$860$	−33.5516	+	12.2118i	−1.14410	+	0.416419i
$861$	16.7915	−	2.42491i	0.572251	−	0.0826408i
$862$	2.40485	+	13.6386i	0.0819095	+	0.464532i
$863$	1.63200	−	2.82670i	0.0555538	−	0.0962220i	−0.836911	−	0.547339i	$-0.815641\pi$
$863$	1.63200	−	2.82670i	0.0555538	−	0.0962220i	0.892465	+	0.451117i	$0.148974\pi$
$864$	4.85332	−	1.85615i	0.165113	−	0.0631473i
$865$	−10.6135	−	18.3832i	−0.360871	−	0.625047i
$866$	−28.4524	−	10.3558i	−0.966851	−	0.351905i
$867$	23.8530	+	8.53603i	0.810091	+	0.289899i
$868$	5.43237	−	6.01375i	0.184387	−	0.204120i
$869$	−1.01820	−	0.854375i	−0.0345402	−	0.0289827i
$870$	4.03310	−	23.6188i	0.136735	−	0.800753i
$871$	7.44454	+	42.2201i	0.252249	+	1.43057i
$872$	−9.34891	+	16.1928i	−0.316594	+	0.548357i
$873$	−5.47639	+	0.0592164i	−0.185348	+	0.00200417i
$874$	8.22345	−	14.2434i	0.278162	−	0.481791i
$875$	11.9761	−	1.66346i	0.404866	−	0.0562353i
$876$	21.1312	−	0.114243i	0.713956	−	0.00385990i
$877$	39.1678	+	32.8657i	1.32260	+	1.10980i	0.985746	+	0.168241i	$0.0538088\pi$
$877$	39.1678	+	32.8657i	1.32260	+	1.10980i	0.336858	+	0.941555i	$0.390636\pi$
$878$	−3.25490	+	1.18468i	−0.109847	+	0.0399812i
$879$	13.8228	−	0.0747309i	0.466231	−	0.00252061i
$880$	−0.149326	−	0.846872i	−0.00503379	−	0.0285480i
$881$	−26.4607	+	45.8313i	−0.891484	+	1.54409i	−0.0533863	+	0.998574i	$0.517001\pi$
$881$	−26.4607	+	45.8313i	−0.891484	+	1.54409i	−0.838097	+	0.545521i	$0.816332\pi$
$882$	−20.1420	+	5.94146i	−0.678215	+	0.200059i
$883$	−11.5763	−	20.0507i	−0.389573	−	0.674761i	0.602819	−	0.797878i	$-0.294044\pi$
$883$	−11.5763	−	20.0507i	−0.389573	−	0.674761i	−0.992392	+	0.123117i	$0.960711\pi$
$884$	4.88760	−	4.10118i	0.164388	−	0.137938i
$885$	0.0403631	−	0.236376i	0.00135679	−	0.00794570i
$886$	3.21332	−	18.2237i	0.107954	−	0.612236i
$887$	−1.14598	+	6.49915i	−0.0384781	+	0.218220i	−0.997984	−	0.0634691i	$-0.979784\pi$
$887$	−1.14598	+	6.49915i	−0.0384781	+	0.218220i	0.959506	+	0.281689i	$0.0908947\pi$
$888$	9.86665	−	8.37042i	0.331103	−	0.280893i
$889$	10.0891	−	24.8561i	0.338379	−	0.833648i
$890$	−28.8365			−0.966601
$891$	0.406110	−	2.63519i	0.0136052	−	0.0882821i
$892$	−2.48972	−	4.31232i	−0.0833620	−	0.144387i
$893$	2.96176	−	2.48521i	0.0991114	−	0.0831644i
$894$	3.88282	+	21.3451i	0.129861	+	0.713887i
$895$	−46.1486	+	16.7967i	−1.54258	+	0.561452i
$896$	2.58705	+	0.554250i	0.0864271	+	0.0185162i
$897$	27.6413	+	22.9403i	0.922916	+	0.765954i
$898$	15.9273	−	13.3646i	0.531501	−	0.445982i
$899$	−7.29898	+	12.6422i	−0.243434	+	0.421641i
$900$	7.94345	+	6.52029i	0.264782	+	0.217343i
$901$	−8.64522	−	14.9740i	−0.288014	−	0.498855i
$902$	−0.840196	+	0.705008i	−0.0279755	+	0.0234742i
$903$	−47.9163	−	29.6891i	−1.59455	−	0.987992i
$904$	−1.97629	+	11.2081i	−0.0657305	+	0.372776i
$905$	−22.6374	−	18.9950i	−0.752493	−	0.631417i
$906$	−16.3516	−	27.9715i	−0.543245	−	0.929289i
$907$	−52.3265	−	19.0453i	−1.73747	−	0.632388i	−0.738356	−	0.674412i	$-0.764397\pi$
$907$	−52.3265	−	19.0453i	−1.73747	−	0.632388i	−0.999117	+	0.0420235i	$0.986620\pi$
$908$	0.770555	+	1.33464i	0.0255718	+	0.0442916i
$909$	12.7674	−	22.6765i	0.423467	−	0.752133i
$910$	−28.1080	+	14.8873i	−0.931772	+	0.493509i
$911$	−4.19059	−	1.52525i	−0.138840	−	0.0505338i	0.271665	−	0.962392i	$-0.412426\pi$
$911$	−4.19059	−	1.52525i	−0.138840	−	0.0505338i	−0.410506	+	0.911858i	$0.634648\pi$
$912$	0.957579	−	5.60782i	0.0317086	−	0.185693i
$913$	0.455718	−	2.58450i	0.0150820	−	0.0855346i
$914$	−0.851085	−	0.714145i	−0.0281514	−	0.0236218i
$915$	7.35346	−	6.23834i	0.243098	−	0.206233i
$916$	−0.711052	−	4.03258i	−0.0234938	−	0.133240i
$917$	19.0493	−	10.0894i	0.629063	−	0.333180i
$918$	−1.51768	−	7.85957i	−0.0500909	−	0.259405i
$919$	−23.6375	+	40.9413i	−0.779728	+	1.35053i	0.152370	+	0.988324i	$0.451310\pi$
$919$	−23.6375	+	40.9413i	−0.779728	+	1.35053i	−0.932098	+	0.362206i	$0.882024\pi$
$920$	11.1343	−	9.34281i	0.367088	−	0.308023i
$921$	−45.1110	+	38.2701i	−1.48646	+	1.26104i
$922$	4.81360	−	27.2993i	0.158527	−	0.899054i
$923$	35.8169	+	30.0540i	1.17893	+	0.989239i
$924$	0.904583	−	1.01234i	0.0297586	−	0.0333036i
$925$	24.0469	+	8.75235i	0.790657	+	0.287775i
$926$	−17.8849			−0.587733
$927$	32.1976	+	11.3263i	1.05751	+	0.372003i
$928$	−4.76583			−0.156446
$929$	8.23222	+	46.6873i	0.270090	+	1.53176i	0.754137	+	0.656717i	$0.228055\pi$
$929$	8.23222	+	46.6873i	0.270090	+	1.53176i	−0.484047	+	0.875042i	$0.660833\pi$
$930$	−7.77188	−	13.2948i	−0.254850	−	0.435953i
$931$	−5.63405	+	22.2908i	−0.184648	+	0.730551i
$932$	−3.38737	+	19.2107i	−0.110957	+	0.629268i
$933$	−15.4645	+	0.0836065i	−0.506284	+	0.00273715i
$934$	−16.9101	−	6.15477i	−0.553315	−	0.201390i
$935$	−1.32475			−0.0433239
$936$	11.7209	+	4.12311i	0.383111	+	0.134768i
$937$	−17.0443	−	29.5215i	−0.556812	−	0.964426i	−0.997760	−	0.0668936i	$-0.978691\pi$
$937$	−17.0443	−	29.5215i	−0.556812	−	0.964426i	0.440949	−	0.897532i	$-0.354642\pi$
$938$	16.8262	+	21.6082i	0.549396	+	0.705534i
$939$	4.07741	−	23.8783i	0.133061	−	0.779240i
$940$	3.21076	−	1.16862i	0.104723	−	0.0381162i
$941$	−7.60478	−	6.38117i	−0.247909	−	0.208020i	0.510362	−	0.859959i	$-0.329511\pi$
$941$	−7.60478	−	6.38117i	−0.247909	−	0.208020i	−0.758271	+	0.651939i	$0.773956\pi$
$942$	−16.5948	+	14.0782i	−0.540687	+	0.458694i
$943$	−17.4203	−	6.34048i	−0.567283	−	0.206474i
$944$	−0.0476962			−0.00155238
$945$	−0.809955	+	39.8971i	−0.0263478	+	1.29785i
$946$	3.64412			0.118481
$947$	−15.7234	−	5.72284i	−0.510941	−	0.185967i	0.0736675	−	0.997283i	$-0.476530\pi$
$947$	−15.7234	−	5.72284i	−0.510941	−	0.185967i	−0.584608	+	0.811316i	$0.698752\pi$
$948$	−1.39077	−	7.64552i	−0.0451702	−	0.248315i
$949$	38.7077	+	32.4796i	1.25651	+	1.05433i
$950$	10.5730	−	3.84825i	0.343032	−	0.124854i
$951$	−34.3169	+	12.7008i	−1.11280	+	0.411853i
$952$	1.53292	−	3.77658i	0.0496821	−	0.122400i
$953$	−13.3831	−	23.1802i	−0.433520	−	0.750879i	0.563653	−	0.826011i	$-0.309395\pi$
$953$	−13.3831	−	23.1802i	−0.433520	−	0.750879i	−0.997174	+	0.0751323i	$0.976062\pi$
$954$	16.5194	−	29.3406i	0.534835	−	0.949936i
$955$	48.7651			1.57800
$956$	−4.28912	−	1.56111i	−0.138720	−	0.0504900i
$957$	−1.21127	+	2.12443i	−0.0391549	+	0.0686731i
$958$	−0.831982	+	4.71840i	−0.0268801	+	0.152445i
$959$	−48.5397	−	10.3992i	−1.56743	−	0.335807i
$960$	2.49023	−	4.36756i	0.0803717	−	0.140962i
$961$	−3.75388	−	21.2893i	−0.121093	−	0.686752i
$962$	30.9393			0.997525
$963$	47.1222	−	17.7304i	1.51849	−	0.571354i
$964$	−27.9530			−0.900305
$965$	21.2598	+	7.73794i	0.684378	+	0.249093i
$966$	22.4631	+	4.68565i	0.722740	+	0.150758i
$967$	−3.99514	−	3.35232i	−0.128475	−	0.107803i	0.576286	−	0.817248i	$-0.304501\pi$
$967$	−3.99514	−	3.35232i	−0.128475	−	0.107803i	−0.704761	+	0.709445i	$0.748946\pi$
$968$	1.89489	−	10.7465i	0.0609041	−	0.345404i
$969$	−8.25154	−	2.95289i	−0.265078	−	0.0948606i
$970$	−4.05932	+	3.40617i	−0.130337	+	0.109366i
$971$	26.2108	−	45.3985i	0.841146	−	1.45691i	−0.0477809	−	0.998858i	$-0.515215\pi$
$971$	26.2108	−	45.3985i	0.841146	−	1.45691i	0.888927	−	0.458049i	$-0.151452\pi$
$972$	11.6663	−	10.3392i	0.374196	−	0.331629i
$973$	−48.7046	−	30.5432i	−1.56140	−	0.979170i
$974$	0.689481	+	3.91024i	0.0220924	+	0.125292i
$975$	4.39797	+	24.1770i	0.140848	+	0.774285i
$976$	−1.46930	−	1.23289i	−0.0470313	−	0.0394639i
$977$	4.45343	−	25.2567i	0.142478	−	0.808033i	−0.826880	−	0.562379i	$-0.809886\pi$
$977$	4.45343	−	25.2567i	0.142478	−	0.808033i	0.969358	−	0.245654i	$-0.0790026\pi$
$978$	15.2024	−	5.62650i	0.486120	−	0.179916i
$979$	2.76563	+	1.00661i	0.0883898	+	0.0321713i
$980$	−11.4163	+	16.8084i	−0.364682	+	0.536924i
$981$	−9.14266	+	55.3433i	−0.291903	+	1.76698i
$982$	−9.09325	−	15.7500i	−0.290177	−	0.502602i
$983$	28.3944	+	10.3347i	0.905640	+	0.329626i	0.752511	−	0.658580i	$-0.228843\pi$
$983$	28.3944	+	10.3347i	0.905640	+	0.329626i	0.153130	+	0.988206i	$0.451065\pi$
$984$	−6.41232	+	0.0346673i	−0.204417	+	0.00110515i
$985$	−25.6777	−	21.5462i	−0.818160	−	0.686517i
$986$	−1.27490	+	7.23030i	−0.0406010	+	0.230260i
$987$	4.58540	+	2.84113i	0.145955	+	0.0904342i
$988$	10.4209	−	8.74413i	0.331531	−	0.278188i
$989$	30.7969	+	53.3418i	0.979284	+	1.69617i
$990$	−1.31399	−	2.22010i	−0.0417612	−	0.0705595i
$991$	18.5696	−	32.1636i	0.589884	−	1.02171i	−0.404363	−	0.914599i	$-0.632507\pi$
$991$	18.5696	−	32.1636i	0.589884	−	1.02171i	0.994247	−	0.107111i	$-0.0341600\pi$
$992$	−2.34643	+	1.96889i	−0.0744992	+	0.0625123i
$993$	−19.3554	+	7.16352i	−0.614224	+	0.227327i
$994$	29.2054	+	6.25699i	0.926340	+	0.198460i
$995$	−62.9316	+	22.9052i	−1.99507	+	0.726145i
$996$	11.7002	−	9.92592i	0.370735	−	0.314515i
$997$	−20.6262	+	17.3074i	−0.653238	+	0.548132i	−0.908052	−	0.418858i	$-0.862430\pi$
$997$	−20.6262	+	17.3074i	−0.653238	+	0.548132i	0.254813	+	0.966990i	$0.417986\pi$
$998$	9.64493	+	16.7055i	0.305305	+	0.528804i
$999$	18.8606	−	33.9266i	0.596722	−	1.07339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.w.b.121.1	yes	72
7.4	even	3		378.2.v.a.67.8	✓	72
27.25	even	9		378.2.v.a.79.8	yes	72
189.25	even	9	inner	378.2.w.b.25.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.67.8	✓	72	7.4	even	3
378.2.v.a.79.8	yes	72	27.25	even	9
378.2.w.b.25.1	yes	72	189.25	even	9	inner
378.2.w.b.121.1	yes	72	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(-1.63077 - 0.583588i) q^{3} +(0.766044 + 0.642788i) q^{4} +(2.72763 - 0.992778i) q^{5} +(-1.33283 - 1.10615i) q^{6} +(-1.62553 - 2.08750i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.31885 + 1.90340i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(-1.63077 - 0.583588i) q^{3} +(0.766044 + 0.642788i) q^{4} +(2.72763 - 0.992778i) q^{5} +(-1.33283 - 1.10615i) q^{6} +(-1.62553 - 2.08750i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.31885 + 1.90340i) q^{9} +2.90269 q^{10} +(-0.278389 - 0.101325i) q^{11} +(-0.874122 - 1.49530i) q^{12} +(0.719192 - 4.07874i) q^{13} +(-0.813528 - 2.51757i) q^{14} +(-5.02753 + 0.0271806i) q^{15} +(0.173648 + 0.984808i) q^{16} +1.54052 q^{17} +(1.52800 + 2.58171i) q^{18} +3.28454 q^{19} +(2.72763 + 0.992778i) q^{20} +(1.43263 + 4.35288i) q^{21} +(-0.226945 - 0.190429i) q^{22} +(0.869520 - 4.93129i) q^{23} +(-0.309985 - 1.70409i) q^{24} +(2.62416 - 2.20193i) q^{25} +(2.07083 - 3.58679i) q^{26} +(-2.67072 - 4.45727i) q^{27} +(0.0965940 - 2.64399i) q^{28} +(0.827577 + 4.69342i) q^{29} +(-4.73363 - 1.69398i) q^{30} +(2.34643 + 1.96889i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(0.394857 + 0.327703i) q^{33} +(1.44761 + 0.526888i) q^{34} +(-6.50627 - 4.08015i) q^{35} +(0.552858 + 2.94862i) q^{36} +(3.73513 + 6.46944i) q^{37} +(3.08646 + 1.12338i) q^{38} +(-3.55315 + 6.23180i) q^{39} +(2.22359 + 1.86581i) q^{40} +(0.642881 - 3.64596i) q^{41} +(-0.142545 + 4.58036i) q^{42} +(-9.42283 + 7.90669i) q^{43} +(-0.148128 - 0.256564i) q^{44} +(8.21463 + 2.88968i) q^{45} +(2.50368 - 4.33651i) q^{46} +(0.901727 - 0.756639i) q^{47} +(0.291541 - 1.70734i) q^{48} +(-1.71532 + 6.78658i) q^{49} +(3.21901 - 1.17162i) q^{50} +(-2.51224 - 0.899028i) q^{51} +(3.17270 - 2.66221i) q^{52} +(-5.61189 - 9.72008i) q^{53} +(-0.985176 - 5.10190i) q^{54} -0.859936 q^{55} +(0.995066 - 2.45150i) q^{56} +(-5.35634 - 1.91682i) q^{57} +(-0.827577 + 4.69342i) q^{58} +(-0.00828236 + 0.0469716i) q^{59} +(-3.86878 - 3.21081i) q^{60} +(-1.46930 + 1.23289i) q^{61} +(1.53152 + 2.65268i) q^{62} +(0.204001 - 7.93463i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.08759 - 11.8393i) q^{65} +(0.258963 + 0.442989i) q^{66} +(-9.72699 + 3.54034i) q^{67} +(1.18010 + 0.990226i) q^{68} +(-4.29584 + 7.53439i) q^{69} +(-4.71840 - 6.05937i) q^{70} +(-5.64455 + 9.77665i) q^{71} +(-0.488970 + 2.95988i) q^{72} +(-6.10013 + 10.5657i) q^{73} +(1.29720 + 7.35678i) q^{74} +(-5.56444 + 2.05943i) q^{75} +(2.51610 + 2.11126i) q^{76} +(0.241012 + 0.745844i) q^{77} +(-5.47027 + 4.64073i) q^{78} +(4.21601 + 1.53450i) q^{79} +(1.45134 + 2.51380i) q^{80} +(1.75412 + 8.82740i) q^{81} +(1.85110 - 3.20621i) q^{82} +(1.53826 + 8.72391i) q^{83} +(-1.70052 + 4.25538i) q^{84} +(4.20197 - 1.52939i) q^{85} +(-11.5588 + 4.20706i) q^{86} +(1.38944 - 8.13688i) q^{87} +(-0.0514442 - 0.291754i) q^{88} -9.93441 q^{89} +(6.73090 + 5.52498i) q^{90} +(-9.68345 + 5.12879i) q^{91} +(3.83587 - 3.21867i) q^{92} +(-2.67748 - 4.58016i) q^{93} +(1.10613 - 0.402599i) q^{94} +(8.95902 - 3.26082i) q^{95} +(0.857903 - 1.50466i) q^{96} +(-1.39847 + 1.17345i) q^{97} +(-3.93302 + 5.79062i) q^{98} +(-0.452679 - 0.764843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8}+O(q^{10}) \) 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8	\( 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8} - 12 q^{10} - 6 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} - 36 q^{19} + 18 q^{21} + 6 q^{22} - 6 q^{23} + 30 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} + 9 q^{35} - 3 q^{36} + 51 q^{39} - 6 q^{41} - 27 q^{42} - 24 q^{43} + 18 q^{45} + 27 q^{47} + 6 q^{48} - 69 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{52} - 15 q^{53} + 45 q^{54} - 72 q^{55} + 6 q^{56} + 57 q^{57} - 3 q^{58} + 15 q^{59} - 33 q^{60} - 18 q^{61} - 24 q^{62} - 12 q^{63} - 36 q^{64} - 90 q^{65} - 36 q^{66} - 66 q^{67} - 18 q^{68} - 39 q^{69} - 12 q^{70} + 12 q^{71} + 30 q^{73} + 9 q^{74} - 21 q^{75} - 87 q^{77} + 6 q^{78} - 45 q^{79} - 6 q^{80} - 24 q^{81} + 33 q^{82} + 18 q^{83} + 6 q^{84} + 51 q^{85} - 12 q^{86} - 18 q^{87} - 12 q^{88} + 72 q^{89} - 69 q^{90} - 30 q^{91} + 12 q^{92} - 48 q^{93} + 21 q^{95} + 48 q^{97} + 6 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8 - 12 * q^10 - 6 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 - 36 * q^19 + 18 * q^21 + 6 * q^22 - 6 * q^23 + 30 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 + 9 * q^35 - 3 * q^36 + 51 * q^39 - 6 * q^41 - 27 * q^42 - 24 * q^43 + 18 * q^45 + 27 * q^47 + 6 * q^48 - 69 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^52 - 15 * q^53 + 45 * q^54 - 72 * q^55 + 6 * q^56 + 57 * q^57 - 3 * q^58 + 15 * q^59 - 33 * q^60 - 18 * q^61 - 24 * q^62 - 12 * q^63 - 36 * q^64 - 90 * q^65 - 36 * q^66 - 66 * q^67 - 18 * q^68 - 39 * q^69 - 12 * q^70 + 12 * q^71 + 30 * q^73 + 9 * q^74 - 21 * q^75 - 87 * q^77 + 6 * q^78 - 45 * q^79 - 6 * q^80 - 24 * q^81 + 33 * q^82 + 18 * q^83 + 6 * q^84 + 51 * q^85 - 12 * q^86 - 18 * q^87 - 12 * q^88 + 72 * q^89 - 69 * q^90 - 30 * q^91 + 12 * q^92 - 48 * q^93 + 21 * q^95 + 48 * q^97 + 6 * q^98 + 90 * q^99

Introduction

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