LMFDB - Embedded newform 378.2.w.b.25.7

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			25.7
Character	$\chi$	$=$	378.25
Dual form			378.2.w.b.121.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(-0.0864462 - 1.72989i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.47620 + 0.537294i) q^{5} +(-0.672891 - 1.59600i) q^{6} +(0.815021 - 2.51709i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.98505 + 0.299085i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(-0.0864462 - 1.72989i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.47620 + 0.537294i) q^{5} +(-0.672891 - 1.59600i) q^{6} +(0.815021 - 2.51709i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.98505 + 0.299085i) q^{9} +1.57094 q^{10} +(-0.143165 + 0.0521079i) q^{11} +(-1.17817 - 1.26961i) q^{12} +(0.449644 + 2.55006i) q^{13} +(-0.0950264 - 2.64404i) q^{14} +(0.801849 - 2.60012i) q^{15} +(0.173648 - 0.984808i) q^{16} -2.00680 q^{17} +(-2.70274 + 1.30200i) q^{18} +2.65186 q^{19} +(1.47620 - 0.537294i) q^{20} +(-4.42475 - 1.19231i) q^{21} +(-0.116709 + 0.0979308i) q^{22} +(0.312253 + 1.77087i) q^{23} +(-1.54135 - 0.790081i) q^{24} +(-1.93973 - 1.62763i) q^{25} +(1.29470 + 2.24248i) q^{26} +(0.775432 + 5.13797i) q^{27} +(-0.993612 - 2.45209i) q^{28} +(-0.108810 + 0.617093i) q^{29} +(-0.135802 - 2.71756i) q^{30} +(3.09560 - 2.59751i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.102517 + 0.243156i) q^{33} +(-1.88578 + 0.686368i) q^{34} +(2.55556 - 3.27783i) q^{35} +(-2.09444 + 2.14787i) q^{36} +(-1.17849 + 2.04121i) q^{37} +(2.49193 - 0.906988i) q^{38} +(4.37245 - 0.998278i) q^{39} +(1.20341 - 1.00978i) q^{40} +(1.02299 + 5.80168i) q^{41} +(-4.56570 + 0.392953i) q^{42} +(-6.52340 - 5.47378i) q^{43} +(-0.0761766 + 0.131942i) q^{44} +(-4.56725 - 1.16234i) q^{45} +(0.899097 + 1.55728i) q^{46} +(7.86746 + 6.60158i) q^{47} +(-1.71862 - 0.215260i) q^{48} +(-5.67148 - 4.10296i) q^{49} +(-2.37943 - 0.866042i) q^{50} +(0.173481 + 3.47156i) q^{51} +(1.98359 + 1.66443i) q^{52} +(-0.736320 + 1.27534i) q^{53} +(2.48596 + 4.56290i) q^{54} -0.239338 q^{55} +(-1.77235 - 1.96437i) q^{56} +(-0.229243 - 4.58742i) q^{57} +(0.108810 + 0.617093i) q^{58} +(2.04376 + 11.5907i) q^{59} +(-1.05707 - 2.50723i) q^{60} +(3.33891 + 2.80168i) q^{61} +(2.02051 - 3.49962i) q^{62} +(-1.68006 + 7.75741i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.706365 + 4.00600i) q^{65} +(0.179499 + 0.193429i) q^{66} +(7.82126 + 2.84670i) q^{67} +(-1.53730 + 1.28995i) q^{68} +(3.03643 - 0.693250i) q^{69} +(1.28035 - 3.95421i) q^{70} +(-0.592726 - 1.02663i) q^{71} +(-1.23351 + 2.73468i) q^{72} +(2.75235 + 4.76721i) q^{73} +(-0.409286 + 2.32118i) q^{74} +(-2.64794 + 3.49622i) q^{75} +(2.03144 - 1.70458i) q^{76} +(0.0144776 + 0.402829i) q^{77} +(3.76733 - 2.43354i) q^{78} +(5.26374 - 1.91584i) q^{79} +(0.785472 - 1.36048i) q^{80} +(8.82110 - 1.78557i) q^{81} +(2.94559 + 5.10191i) q^{82} +(-1.77041 + 10.0405i) q^{83} +(-4.15595 + 1.93082i) q^{84} +(-2.96245 - 1.07824i) q^{85} +(-8.00213 - 2.91254i) q^{86} +(1.07691 + 0.134884i) q^{87} +(-0.0264559 + 0.150039i) q^{88} +13.3191 q^{89} +(-4.68935 + 0.469846i) q^{90} +(6.78519 + 0.946556i) q^{91} +(1.37750 + 1.15586i) q^{92} +(-4.76102 - 5.13050i) q^{93} +(9.65087 + 3.51263i) q^{94} +(3.91468 + 1.42483i) q^{95} +(-1.68860 + 0.385526i) q^{96} +(-13.5643 - 11.3818i) q^{97} +(-6.73275 - 1.91576i) q^{98} +(0.411771 - 0.198363i) 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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.0864462	−	1.72989i	−0.0499098	−	0.998754i
$3$	−0.0864462	−	1.72989i	−0.0499098	−	0.998754i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	1.47620	+	0.537294i	0.660179	+	0.240285i	0.650313	−	0.759666i	$-0.274638\pi$
$5$	1.47620	+	0.537294i	0.660179	+	0.240285i	0.00986509	+	0.999951i	$0.496860\pi$
$6$	−0.672891	−	1.59600i	−0.274707	−	0.651565i
$7$	0.815021	−	2.51709i	0.308049	−	0.951371i
$7$	0.815021	−	2.51709i	0.308049	−	0.951371i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−2.98505	+	0.299085i	−0.995018	+	0.0996951i
$10$	1.57094			0.496776
$11$	−0.143165	+	0.0521079i	−0.0431659	+	0.0157111i	−0.363513	−	0.931589i	$-0.618423\pi$
$11$	−0.143165	+	0.0521079i	−0.0431659	+	0.0157111i	0.320347	+	0.947300i	$0.396201\pi$
$12$	−1.17817	−	1.26961i	−0.340110	−	0.366504i
$13$	0.449644	+	2.55006i	0.124709	+	0.707259i	0.981480	+	0.191563i	$0.0613555\pi$
$13$	0.449644	+	2.55006i	0.124709	+	0.707259i	−0.856772	+	0.515696i	$0.827533\pi$
$14$	−0.0950264	−	2.64404i	−0.0253969	−	0.706651i
$15$	0.801849	−	2.60012i	0.207037	−	0.671348i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−2.00680			−0.486722			−0.243361	−	0.969936i	$-0.578250\pi$
$17$	−2.00680			−0.486722			−0.243361	+	0.969936i	$0.578250\pi$
$18$	−2.70274	+	1.30200i	−0.637042	+	0.306884i
$19$	2.65186			0.608377			0.304189	−	0.952612i	$-0.401615\pi$
$19$	2.65186			0.608377			0.304189	+	0.952612i	$0.401615\pi$
$20$	1.47620	−	0.537294i	0.330089	−	0.120143i
$21$	−4.42475	−	1.19231i	−0.965560	−	0.260182i
$22$	−0.116709	+	0.0979308i	−0.0248825	+	0.0208789i
$23$	0.312253	+	1.77087i	0.0651093	+	0.369253i	0.999901	+	0.0140572i	$0.00447469\pi$
$23$	0.312253	+	1.77087i	0.0651093	+	0.369253i	−0.934792	+	0.355196i	$0.884414\pi$
$24$	−1.54135	−	0.790081i	−0.314628	−	0.161275i
$25$	−1.93973	−	1.62763i	−0.387946	−	0.325525i
$26$	1.29470	+	2.24248i	0.253911	+	0.439787i
$27$	0.775432	+	5.13797i	0.149232	+	0.988802i
$28$	−0.993612	−	2.45209i	−0.187775	−	0.463401i
$29$	−0.108810	+	0.617093i	−0.0202055	+	0.114591i	−0.993242	−	0.116058i	$-0.962974\pi$
$29$	−0.108810	+	0.617093i	−0.0202055	+	0.114591i	0.973037	+	0.230650i	$0.0740851\pi$
$30$	−0.135802	−	2.71756i	−0.0247940	−	0.496157i
$31$	3.09560	−	2.59751i	0.555986	−	0.466527i	−0.320976	−	0.947087i	$-0.604011\pi$
$31$	3.09560	−	2.59751i	0.555986	−	0.466527i	0.876962	+	0.480560i	$0.159567\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	0.102517	+	0.243156i	0.0178459	+	0.0423280i
$34$	−1.88578	+	0.686368i	−0.323409	+	0.117711i
$35$	2.55556	−	3.27783i	0.431968	−	0.554055i
$36$	−2.09444	+	2.14787i	−0.349073	+	0.357978i
$37$	−1.17849	+	2.04121i	−0.193743	+	0.335572i	−0.946488	−	0.322740i	$-0.895396\pi$
$37$	−1.17849	+	2.04121i	−0.193743	+	0.335572i	0.752745	+	0.658312i	$0.228729\pi$
$38$	2.49193	−	0.906988i	0.404244	−	0.147133i
$39$	4.37245	−	0.998278i	0.700153	−	0.159852i
$40$	1.20341	−	1.00978i	0.190276	−	0.159661i
$41$	1.02299	+	5.80168i	0.159765	+	0.906070i	0.954300	+	0.298852i	$0.0966036\pi$
$41$	1.02299	+	5.80168i	0.159765	+	0.906070i	−0.794535	+	0.607218i	$0.792285\pi$
$42$	−4.56570	+	0.392953i	−0.704502	+	0.0606340i
$43$	−6.52340	−	5.47378i	−0.994809	−	0.834744i	−0.00855234	−	0.999963i	$-0.502722\pi$
$43$	−6.52340	−	5.47378i	−0.994809	−	0.834744i	−0.986257	+	0.165219i	$0.947167\pi$
$44$	−0.0761766	+	0.131942i	−0.0114841	+	0.0198910i
$45$	−4.56725	−	1.16234i	−0.680845	−	0.173272i
$46$	0.899097	+	1.55728i	0.132565	+	0.229609i
$47$	7.86746	+	6.60158i	1.14759	+	0.962940i	0.999660	−	0.0260585i	$-0.00829562\pi$
$47$	7.86746	+	6.60158i	1.14759	+	0.962940i	0.147927	+	0.988998i	$0.452740\pi$
$48$	−1.71862	−	0.215260i	−0.248062	−	0.0310701i
$49$	−5.67148	−	4.10296i	−0.810212	−	0.586137i
$50$	−2.37943	−	0.866042i	−0.336502	−	0.122477i
$51$	0.173481	+	3.47156i	0.0242922	+	0.486115i
$52$	1.98359	+	1.66443i	0.275075	+	0.230815i
$53$	−0.736320	+	1.27534i	−0.101141	+	0.175182i	−0.912155	−	0.409845i	$-0.865583\pi$
$53$	−0.736320	+	1.27534i	−0.101141	+	0.175182i	0.811014	+	0.585027i	$0.198916\pi$
$54$	2.48596	+	4.56290i	0.338296	+	0.620932i
$55$	−0.239338			−0.0322724
$56$	−1.77235	−	1.96437i	−0.236841	−	0.262500i
$57$	−0.229243	−	4.58742i	−0.0303640	−	0.607619i
$58$	0.108810	+	0.617093i	0.0142875	+	0.0810282i
$59$	2.04376	+	11.5907i	0.266075	+	1.50898i	0.765957	+	0.642891i	$0.222265\pi$
$59$	2.04376	+	11.5907i	0.266075	+	1.50898i	−0.499883	+	0.866093i	$0.666624\pi$
$60$	−1.05707	−	2.50723i	−0.136468	−	0.323682i
$61$	3.33891	+	2.80168i	0.427504	+	0.358718i	0.831009	−	0.556259i	$-0.187764\pi$
$61$	3.33891	+	2.80168i	0.427504	+	0.358718i	−0.403505	+	0.914977i	$0.632208\pi$
$62$	2.02051	−	3.49962i	0.256605	−	0.444452i
$63$	−1.68006	+	7.75741i	−0.211667	+	0.977342i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.706365	+	4.00600i	−0.0876138	+	0.496883i
$66$	0.179499	+	0.193429i	0.0220948	+	0.0238094i
$67$	7.82126	+	2.84670i	0.955519	+	0.347780i	0.772276	−	0.635287i	$-0.219118\pi$
$67$	7.82126	+	2.84670i	0.955519	+	0.347780i	0.183243	+	0.983068i	$0.441341\pi$
$68$	−1.53730	+	1.28995i	−0.186425	+	0.156429i
$69$	3.03643	−	0.693250i	0.365543	−	0.0834574i
$70$	1.28035	−	3.95421i	0.153031	−	0.472618i
$71$	−0.592726	−	1.02663i	−0.0703437	−	0.121839i	0.828708	−	0.559681i	$-0.189076\pi$
$71$	−0.592726	−	1.02663i	−0.0703437	−	0.121839i	−0.899052	+	0.437842i	$0.855743\pi$
$72$	−1.23351	+	2.73468i	−0.145371	+	0.322285i
$73$	2.75235	+	4.76721i	0.322138	+	0.557960i	0.980929	−	0.194366i	$-0.0622650\pi$
$73$	2.75235	+	4.76721i	0.322138	+	0.557960i	−0.658791	+	0.752326i	$0.728932\pi$
$74$	−0.409286	+	2.32118i	−0.0475785	+	0.269831i
$75$	−2.64794	+	3.49622i	−0.305757	+	0.403709i
$76$	2.03144	−	1.70458i	0.233022	−	0.195529i
$77$	0.0144776	+	0.402829i	0.00164987	+	0.0459066i
$78$	3.76733	−	2.43354i	0.426566	−	0.275544i
$79$	5.26374	−	1.91584i	0.592217	−	0.215549i	−0.0284874	−	0.999594i	$-0.509069\pi$
$79$	5.26374	−	1.91584i	0.592217	−	0.215549i	0.620704	+	0.784045i	$0.286847\pi$
$80$	0.785472	−	1.36048i	0.0878184	−	0.152106i
$81$	8.82110	−	1.78557i	0.980122	−	0.198397i
$82$	2.94559	+	5.10191i	0.325286	+	0.563412i
$83$	−1.77041	+	10.0405i	−0.194327	+	1.10208i	0.719046	+	0.694962i	$0.244579\pi$
$83$	−1.77041	+	10.0405i	−0.194327	+	1.10208i	−0.913374	+	0.407123i	$0.866532\pi$
$84$	−4.15595	+	1.93082i	−0.453452	+	0.210669i
$85$	−2.96245	−	1.07824i	−0.321323	−	0.116952i
$86$	−8.00213	−	2.91254i	−0.862892	−	0.314067i
$87$	1.07691	+	0.134884i	0.115457	+	0.0144611i
$88$	−0.0264559	+	0.150039i	−0.00282020	+	0.0159942i
$89$	13.3191			1.41182			0.705911	−	0.708300i	$-0.250538\pi$
$89$	13.3191			1.41182			0.705911	+	0.708300i	$0.250538\pi$
$90$	−4.68935	+	0.469846i	−0.494301	+	0.0495261i
$91$	6.78519	+	0.946556i	0.711281	+	0.0992260i
$92$	1.37750	+	1.15586i	0.143614	+	0.120506i
$93$	−4.76102	−	5.13050i	−0.493695	−	0.532008i
$94$	9.65087	+	3.51263i	0.995411	+	0.362300i
$95$	3.91468	+	1.42483i	0.401638	+	0.146184i
$96$	−1.68860	+	0.385526i	−0.172342	+	0.0393475i
$97$	−13.5643	−	11.3818i	−1.37724	−	1.15564i	−0.970220	−	0.242226i	$-0.922122\pi$
$97$	−13.5643	−	11.3818i	−1.37724	−	1.15564i	−0.407023	−	0.913418i	$-0.633433\pi$
$98$	−6.73275	−	1.91576i	−0.680110	−	0.193521i
$99$	0.411771	−	0.198363i	0.0413846	−	0.0199363i
$100$	−2.53214			−0.253214
$101$	−2.42066	+	13.7283i	−0.240865	+	1.36601i	0.589038	+	0.808105i	$0.299507\pi$
$101$	−2.42066	+	13.7283i	−0.240865	+	1.36601i	−0.829903	+	0.557908i	$0.811604\pi$
$102$	1.35036	+	3.20286i	0.133706	+	0.317131i
$103$	−10.9881	−	3.99935i	−1.08269	−	0.394068i	−0.261784	−	0.965127i	$-0.584311\pi$
$103$	−10.9881	−	3.99935i	−1.08269	−	0.394068i	−0.820909	+	0.571059i	$0.806533\pi$
$104$	2.43324	+	0.885626i	0.238598	+	0.0868427i
$105$	−5.89121	−	4.13748i	−0.574924	−	0.403777i
$106$	−0.255721	+	1.45027i	−0.0248378	+	0.140862i
$107$	−8.91437	−	15.4401i	−0.861785	−	1.49266i	−0.870205	−	0.492691i	$-0.836013\pi$
$107$	−8.91437	−	15.4401i	−0.861785	−	1.49266i	0.00841969	−	0.999965i	$-0.497320\pi$
$108$	3.89664	+	3.43747i	0.374954	+	0.330771i
$109$	2.58960	−	4.48532i	0.248039	−	0.429615i	−0.714943	−	0.699183i	$-0.753547\pi$
$109$	2.58960	−	4.48532i	0.248039	−	0.429615i	0.962982	+	0.269567i	$0.0868807\pi$
$110$	−0.224904	+	0.0818585i	−0.0214438	+	0.00780490i
$111$	3.63295	+	1.86221i	0.344824	+	0.176753i
$112$	−2.33732	−	1.23973i	−0.220856	−	0.117143i
$113$	−10.0890	+	8.46568i	−0.949094	+	0.796385i	−0.979145	−	0.203164i	$-0.934878\pi$
$113$	−10.0890	+	8.46568i	−0.949094	+	0.796385i	0.0300505	+	0.999548i	$0.490433\pi$
$114$	−1.78441	−	4.23236i	−0.167125	−	0.396397i
$115$	−0.490532	+	2.78194i	−0.0457423	+	0.259418i
$116$	0.313306	+	0.542662i	0.0290897	+	0.0503849i
$117$	−2.10490	−	7.47758i	−0.194598	−	0.691302i
$118$	5.88477	+	10.1927i	0.541737	+	0.938316i
$119$	−1.63559	+	5.05131i	−0.149934	+	0.463053i
$120$	−1.85085	−	1.99448i	−0.168958	−	0.182070i
$121$	−8.40871	+	7.05574i	−0.764428	+	0.641431i
$122$	4.09578	+	1.49074i	0.370814	+	0.134965i
$123$	9.94784	−	2.27120i	0.896967	−	0.204787i
$124$	0.701715	−	3.97962i	0.0630159	−	0.357381i
$125$	−5.91628	−	10.2473i	−0.529168	−	0.916546i
$126$	1.07445	+	7.86419i	0.0957200	+	0.700598i
$127$	8.64820	−	14.9791i	0.767404	−	1.32918i	−0.171563	−	0.985173i	$-0.554882\pi$
$127$	8.64820	−	14.9791i	0.767404	−	1.32918i	0.938966	−	0.344009i	$-0.111785\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	−8.90513	+	11.7580i	−0.784053	+	1.03523i
$130$	0.706365	+	4.00600i	0.0619523	+	0.351349i
$131$	−2.11053	−	11.9694i	−0.184398	−	1.04577i	−0.926727	−	0.375736i	$-0.877390\pi$
$131$	−2.11053	−	11.9694i	−0.184398	−	1.04577i	0.742329	−	0.670036i	$-0.233721\pi$
$132$	0.234830	+	0.120371i	0.0204393	+	0.0104770i
$133$	2.16132	−	6.67496i	0.187410	−	0.578792i
$134$	8.32321			0.719016
$135$	−1.61590	+	8.00132i	−0.139075	+	0.688644i
$136$	−1.00340	+	1.73794i	−0.0860410	+	0.149027i
$137$	−9.39966	−	7.88725i	−0.803067	−	0.673854i	0.145875	−	0.989303i	$-0.453400\pi$
$137$	−9.39966	−	7.88725i	−0.803067	−	0.673854i	−0.948942	+	0.315449i	$0.897845\pi$
$138$	2.61621	−	1.68996i	0.222706	−	0.143859i
$139$	−8.84226	−	3.21832i	−0.749991	−	0.272974i	−0.0613890	−	0.998114i	$-0.519553\pi$
$139$	−8.84226	−	3.21832i	−0.749991	−	0.272974i	−0.688602	+	0.725140i	$0.741775\pi$
$140$	−0.149281	−	4.15364i	−0.0126166	−	0.351047i
$141$	10.7399	−	14.1805i	0.904464	−	1.19422i
$142$	−0.908109	−	0.761994i	−0.0762069	−	0.0639451i
$143$	−0.197251	−	0.341649i	−0.0164950	−	0.0285702i
$144$	−0.223808	+	2.99164i	−0.0186506	+	0.249303i
$145$	−0.492186	+	0.852492i	−0.0408738	+	0.0707956i
$146$	4.21685	+	3.53835i	0.348989	+	0.292836i
$147$	−6.60740	+	10.1657i	−0.544969	+	0.838456i
$148$	0.409286	+	2.32118i	0.0336431	+	0.190799i
$149$	−6.68294	+	5.60765i	−0.547488	+	0.459397i	−0.874089	−	0.485765i	$-0.838541\pi$
$149$	−6.68294	+	5.60765i	−0.547488	+	0.459397i	0.326602	+	0.945162i	$0.394096\pi$
$150$	−1.29247	+	4.19102i	−0.105529	+	0.342196i
$151$	−8.15758	+	2.96912i	−0.663855	+	0.241623i	−0.651900	−	0.758305i	$-0.726028\pi$
$151$	−8.15758	+	2.96912i	−0.663855	+	0.241623i	−0.0119549	+	0.999929i	$0.503805\pi$
$152$	1.32593	−	2.29657i	0.107547	−	0.186277i
$153$	5.99042	−	0.600206i	0.484297	−	0.0485238i
$154$	0.151380	+	0.373583i	0.0121985	+	0.0301042i
$155$	5.96536	−	2.17121i	0.479149	−	0.174396i
$156$	2.70781	−	3.57528i	0.216799	−	0.286252i
$157$	−3.05461	−	17.3236i	−0.243785	−	1.38257i	−0.823298	−	0.567609i	$-0.807868\pi$
$157$	−3.05461	−	17.3236i	−0.243785	−	1.38257i	0.579513	−	0.814963i	$-0.303243\pi$
$158$	4.29104	−	3.60061i	0.341377	−	0.286449i
$159$	2.26986	+	1.16351i	0.180012	+	0.0922720i
$160$	0.272791	−	1.54708i	0.0215661	−	0.122307i
$161$	4.71194	+	0.657331i	0.371353	+	0.0518049i
$162$	7.67842	−	4.69488i	0.603273	−	0.368865i
$163$	5.67681	+	9.83252i	0.444642	+	0.770143i	0.998027	−	0.0627828i	$-0.0199975\pi$
$163$	5.67681	+	9.83252i	0.444642	+	0.770143i	−0.553385	+	0.832926i	$0.686664\pi$
$164$	4.51290	+	3.78678i	0.352399	+	0.295698i
$165$	0.0206899	+	0.414029i	0.00161071	+	0.0322321i
$166$	1.77041	+	10.0405i	0.137410	+	0.779292i
$167$	−2.71446	+	2.27771i	−0.210052	+	0.176254i	−0.741744	−	0.670684i	$-0.766001\pi$
$167$	−2.71446	+	2.27771i	−0.210052	+	0.176254i	0.531692	+	0.846938i	$0.321556\pi$
$168$	−3.24494	+	3.23579i	−0.250353	+	0.249647i
$169$	5.91539	−	2.15303i	0.455030	−	0.165617i
$170$	−3.15258			−0.241792
$171$	−7.91593	+	0.793131i	−0.605346	+	0.0606523i
$172$	−8.51569			−0.649316
$173$	0.725547	−	4.11478i	0.0551623	−	0.312841i	−0.944725	−	0.327864i	$-0.893671\pi$
$173$	0.725547	−	4.11478i	0.0551623	−	0.312841i	0.999887	+	0.0150233i	$0.00478224\pi$
$174$	1.05810	−	0.241575i	0.0802142	−	0.0183138i
$175$	−5.67780	+	3.55592i	−0.429201	+	0.268803i
$176$	0.0264559	+	0.150039i	0.00199419	+	0.0113096i
$177$	19.8740	−	4.53746i	1.49382	−	0.341056i
$178$	12.5159	−	4.55540i	0.938104	−	0.341442i
$179$	9.61881			0.718944			0.359472	−	0.933156i	$-0.382957\pi$
$179$	9.61881			0.718944			0.359472	+	0.933156i	$0.382957\pi$
$180$	−4.24585	+	2.04536i	−0.316467	+	0.152452i
$181$	9.15825	−	15.8625i	0.680727	−	1.17905i	−0.294032	−	0.955796i	$-0.594997\pi$
$181$	9.15825	−	15.8625i	0.680727	−	1.17905i	0.974759	−	0.223259i	$-0.0716694\pi$
$182$	6.69974	−	1.43120i	0.496617	−	0.106088i
$183$	4.55796	−	6.01815i	0.336934	−	0.444874i
$184$	1.68975	+	0.615018i	0.124570	+	0.0453398i
$185$	−2.83642	+	2.38004i	−0.208538	+	0.174984i
$186$	−6.22863	−	3.19273i	−0.456706	−	0.234102i
$187$	0.287305	−	0.104570i	0.0210098	−	0.00764694i
$188$	10.2702			0.749034
$189$	13.5647	+	2.23572i	0.986688	+	0.162625i
$190$	4.16591			0.302227
$191$	−24.6811	+	8.98318i	−1.78586	+	0.650000i	−0.786380	+	0.617743i	$0.788047\pi$
$191$	−24.6811	+	8.98318i	−1.78586	+	0.650000i	−0.999480	+	0.0322573i	$0.989730\pi$
$192$	−1.45491	+	0.939811i	−0.104999	+	0.0678250i
$193$	−18.0523	+	15.1477i	−1.29943	+	1.09035i	−0.309192	+	0.951000i	$0.600058\pi$
$193$	−18.0523	+	15.1477i	−1.29943	+	1.09035i	−0.990242	+	0.139355i	$0.955497\pi$
$194$	−16.6390	−	6.05611i	−1.19461	−	0.434804i
$195$	6.99100	+	0.875632i	0.500636	+	0.0627053i
$196$	−6.98194	+	0.502508i	−0.498710	+	0.0358934i
$197$	3.70639	−	6.41965i	0.264069	−	0.457381i	−0.703250	−	0.710942i	$-0.748269\pi$
$197$	3.70639	−	6.41965i	0.264069	−	0.457381i	0.967319	+	0.253561i	$0.0816020\pi$
$198$	0.319094	−	0.327235i	0.0226770	−	0.0232556i
$199$	12.5281			0.888096			0.444048	−	0.896003i	$-0.353542\pi$
$199$	12.5281			0.888096			0.444048	+	0.896003i	$0.353542\pi$
$200$	−2.37943	+	0.866042i	−0.168251	+	0.0612384i
$201$	4.24837	−	13.7760i	0.299657	−	0.971685i
$202$	2.42066	+	13.7283i	0.170317	+	0.965917i
$203$	1.46460	+	0.776828i	0.102794	+	0.0545227i
$204$	2.36437	+	2.54785i	0.165539	+	0.178386i
$205$	−1.60706	+	9.11411i	−0.112242	+	0.636557i
$206$	−11.6933			−0.814713
$207$	−1.46173	−	5.19277i	−0.101598	−	0.360922i
$208$	2.58940			0.179542
$209$	−0.379653	+	0.138183i	−0.0262612	+	0.00955828i
$210$	−6.95103	−	1.87304i	−0.479667	−	0.129252i
$211$	10.6769	−	8.95899i	0.735028	−	0.616762i	−0.196469	−	0.980510i	$-0.562947\pi$
$211$	10.6769	−	8.95899i	0.735028	−	0.616762i	0.931497	+	0.363748i	$0.118503\pi$
$212$	0.255721	+	1.45027i	0.0175630	+	0.0996048i
$213$	−1.72472	+	1.11410i	−0.118176	+	0.0763370i
$214$	−13.6576	−	11.4601i	−0.933615	−	0.783396i
$215$	−6.68884	−	11.5854i	−0.456175	−	0.790118i
$216$	4.83733	+	1.89744i	0.329138	+	0.129104i
$217$	−4.01520	−	9.90892i	−0.272570	−	0.672662i
$218$	0.899358	−	5.10051i	0.0609122	−	0.345450i
$219$	8.00883	−	5.17338i	0.541187	−	0.349585i
$220$	−0.183344	+	0.153844i	−0.0123610	+	0.0103721i
$221$	−0.902347	−	5.11747i	−0.0606985	−	0.344238i
$222$	4.05076	+	0.507364i	0.271870	+	0.0340520i
$223$	−22.1372	+	8.05727i	−1.48241	+	0.539555i	−0.951440	−	0.307833i	$-0.900396\pi$
$223$	−22.1372	+	8.05727i	−1.48241	+	0.539555i	−0.530974	+	0.847388i	$0.678174\pi$
$224$	−2.62038	−	0.365551i	−0.175081	−	0.0244244i
$225$	6.27700	+	4.27841i	0.418466	+	0.285227i
$226$	−6.58513	+	11.4058i	−0.438037	+	0.758702i
$227$	14.9277	−	5.43323i	0.990785	−	0.360616i	0.204761	−	0.978812i	$-0.434358\pi$
$227$	14.9277	−	5.43323i	0.990785	−	0.360616i	0.786024	+	0.618196i	$0.212136\pi$
$228$	−3.12435	−	3.36682i	−0.206915	−	0.222973i
$229$	−13.6567	+	11.4593i	−0.902459	+	0.757253i	−0.970670	−	0.240418i	$-0.922716\pi$
$229$	−13.6567	+	11.4593i	−0.902459	+	0.757253i	0.0682101	+	0.997671i	$0.478271\pi$
$230$	0.490532	+	2.78194i	0.0323447	+	0.183436i
$231$	0.695599	−	0.0598677i	0.0457670	−	0.00393900i
$232$	0.480013	+	0.402779i	0.0315144	+	0.0264437i
$233$	1.77572	−	3.07563i	0.116331	−	0.201491i	−0.801980	−	0.597351i	$-0.796220\pi$
$233$	1.77572	−	3.07563i	0.116331	−	0.201491i	0.918311	+	0.395860i	$0.129553\pi$
$234$	−4.53544	−	6.30671i	−0.296491	−	0.412282i
$235$	8.06698	+	13.9724i	0.526232	+	0.911461i
$236$	9.01599	+	7.56531i	0.586891	+	0.492460i
$237$	−3.76923	−	8.94008i	−0.244838	−	0.580721i
$238$	0.190699	+	5.30608i	0.0123612	+	0.343942i
$239$	−16.6278	−	6.05203i	−1.07556	−	0.391473i	−0.257309	−	0.966329i	$-0.582836\pi$
$239$	−16.6278	−	6.05203i	−1.07556	−	0.391473i	−0.818255	+	0.574856i	$0.805058\pi$
$240$	−2.42138	−	1.24117i	−0.156299	−	0.0801174i
$241$	−3.93935	−	3.30551i	−0.253756	−	0.212926i	0.507032	−	0.861927i	$-0.330743\pi$
$241$	−3.93935	−	3.30551i	−0.253756	−	0.212926i	−0.760788	+	0.649001i	$0.775187\pi$
$242$	−5.48839	+	9.50618i	−0.352807	+	0.611080i
$243$	−3.85140	−	15.1052i	−0.247067	−	0.968998i
$244$	4.35864			0.279033
$245$	−6.16777	−	9.10406i	−0.394044	−	0.581637i
$246$	8.57112	−	5.53659i	0.546475	−	0.353000i
$247$	1.19239	+	6.76238i	0.0758700	+	0.430280i
$248$	−0.701715	−	3.97962i	−0.0445589	−	0.252706i
$249$	17.5220	+	2.19465i	1.11041	+	0.139080i
$250$	−9.06427	−	7.60582i	−0.573275	−	0.481035i
$251$	8.62412	−	14.9374i	0.544350	−	0.942841i	−0.454298	−	0.890850i	$-0.650110\pi$
$251$	8.62412	−	14.9374i	0.544350	−	0.942841i	0.998648	−	0.0519915i	$-0.0165569\pi$
$252$	3.69937	+	7.02244i	0.233038	+	0.442372i
$253$	−0.136980	−	0.237257i	−0.00861188	−	0.0149162i
$254$	3.00349	−	17.0336i	0.188456	−	1.06878i
$255$	−1.60915	+	5.21793i	−0.100769	+	0.326760i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	9.72730	−	8.16217i	0.606772	−	0.509142i	−0.286842	−	0.957978i	$-0.592606\pi$
$257$	9.72730	−	8.16217i	0.606772	−	0.509142i	0.893614	+	0.448835i	$0.148161\pi$
$258$	−4.34662	+	14.0946i	−0.270609	+	0.877492i
$259$	4.17741	+	4.63000i	0.259571	+	0.287694i
$260$	2.03390	+	3.52281i	0.126137	+	0.218476i
$261$	0.140241	−	1.87460i	0.00868068	−	0.116035i
$262$	−6.07703	−	10.5257i	−0.375440	−	0.650281i
$263$	5.06464	−	28.7230i	0.312299	−	1.77114i	−0.274682	−	0.961535i	$-0.588572\pi$
$263$	5.06464	−	28.7230i	0.312299	−	1.77114i	0.586981	−	0.809601i	$-0.300316\pi$
$264$	0.261838	+	0.0327955i	0.0161150	+	0.00201842i
$265$	−1.77219	+	1.48705i	−0.108865	+	0.0913486i
$266$	−0.251996	−	7.01162i	−0.0154509	−	0.429910i
$267$	−1.15139	−	23.0406i	−0.0704637	−	1.41006i
$268$	7.82126	−	2.84670i	0.477759	−	0.173890i
$269$	−4.75658	+	8.23864i	−0.290014	+	0.502319i	−0.973813	−	0.227352i	$-0.926993\pi$
$269$	−4.75658	+	8.23864i	−0.290014	+	0.502319i	0.683799	+	0.729671i	$0.260327\pi$
$270$	1.21816	+	8.07146i	0.0741349	+	0.491213i
$271$	9.56173	+	16.5614i	0.580833	+	1.00603i	0.995381	+	0.0960053i	$0.0306066\pi$
$271$	9.56173	+	16.5614i	0.580833	+	1.00603i	−0.414547	+	0.910028i	$0.636060\pi$
$272$	−0.348478	+	1.97632i	−0.0211296	+	0.119832i
$273$	1.05088	−	11.8195i	0.0636024	−	0.715347i
$274$	−11.5304	−	4.19672i	−0.696577	−	0.253533i
$275$	0.362514	+	0.131944i	0.0218604	+	0.00795654i
$276$	1.88043	−	2.48284i	0.113188	−	0.149449i
$277$	2.07245	−	11.7534i	0.124521	−	0.706196i	−0.857070	−	0.515201i	$-0.827717\pi$
$277$	2.07245	−	11.7534i	0.124521	−	0.706196i	0.981591	−	0.190995i	$-0.0611715\pi$
$278$	−9.40974			−0.564359
$279$	−8.46365	+	8.67957i	−0.506705	+	0.519632i
$280$	−1.56091	−	3.85209i	−0.0932821	−	0.230207i
$281$	9.34298	+	7.83969i	0.557355	+	0.467677i	0.877423	−	0.479718i	$-0.159261\pi$
$281$	9.34298	+	7.83969i	0.557355	+	0.467677i	−0.320067	+	0.947395i	$0.603706\pi$
$282$	5.24219	−	16.9986i	0.312168	−	1.01225i
$283$	27.2122	+	9.90445i	1.61760	+	0.588758i	0.982923	−	0.184019i	$-0.0589108\pi$
$283$	27.2122	+	9.90445i	1.61760	+	0.588758i	0.634677	+	0.772777i	$0.281133\pi$
$284$	−1.11396	−	0.405449i	−0.0661014	−	0.0240590i
$285$	2.12639	−	6.89514i	0.125956	−	0.408433i
$286$	−0.302207	−	0.253581i	−0.0178699	−	0.0149946i
$287$	15.4371	+	2.15352i	0.911224	+	0.127119i
$288$	0.812891	+	2.88777i	0.0479001	+	0.170163i
$289$	−12.9727			−0.763102
$290$	−0.170935	+	0.969418i	−0.0100376	+	0.0569262i
$291$	−18.5167	+	24.4486i	−1.08547	+	1.43320i
$292$	5.17273	+	1.88272i	0.302711	+	0.110178i
$293$	−8.39310	−	3.05484i	−0.490330	−	0.178466i	0.0850096	−	0.996380i	$-0.472908\pi$
$293$	−8.39310	−	3.05484i	−0.490330	−	0.178466i	−0.575340	+	0.817915i	$0.695130\pi$
$294$	−2.73204	+	11.8125i	−0.159336	+	0.688921i
$295$	−3.21063	+	18.2084i	−0.186930	+	1.06013i
$296$	1.17849	+	2.04121i	0.0684984	+	0.118643i
$297$	−0.378743	−	0.695172i	−0.0219769	−	0.0403380i
$298$	−4.36198	+	7.55517i	−0.252683	+	0.437659i
$299$	−4.37543	+	1.59253i	−0.253038	+	0.0920982i
$300$	0.218894	+	4.38032i	0.0126378	+	0.252898i
$301$	−19.0947	+	11.9587i	−1.10060	+	0.689290i
$302$	−6.65012	+	5.58011i	−0.382672	+	0.321100i
$303$	23.9577	+	3.00073i	1.37633	+	0.172387i
$304$	0.460490	−	2.61157i	0.0264109	−	0.149784i
$305$	3.42359	+	5.92983i	0.196034	+	0.339541i
$306$	5.42387	−	2.61285i	0.310062	−	0.149367i
$307$	−5.81110	−	10.0651i	−0.331657	−	0.574447i	0.651180	−	0.758923i	$-0.274274\pi$
$307$	−5.81110	−	10.0651i	−0.331657	−	0.574447i	−0.982837	+	0.184477i	$0.940941\pi$
$308$	0.270024	+	0.299279i	0.0153860	+	0.0170530i
$309$	−5.96857	+	19.3540i	−0.339540	+	1.10101i
$310$	4.86301	−	4.08055i	0.276200	−	0.231760i
$311$	−15.7751	−	5.74167i	−0.894524	−	0.325580i	−0.146468	−	0.989215i	$-0.546790\pi$
$311$	−15.7751	−	5.74167i	−0.894524	−	0.325580i	−0.748056	+	0.663636i	$0.769013\pi$
$312$	1.32169	−	4.28580i	0.0748261	−	0.242635i
$313$	−4.06391	+	23.0476i	−0.229706	+	1.30273i	0.623775	+	0.781604i	$0.285598\pi$
$313$	−4.06391	+	23.0476i	−0.229706	+	1.30273i	−0.853481	+	0.521123i	$0.825513\pi$
$314$	−8.79541	−	15.2341i	−0.496354	−	0.859710i
$315$	−6.64812	+	10.5488i	−0.374579	+	0.594360i
$316$	2.80078	−	4.85109i	0.157556	−	0.272895i
$317$	−4.02133	−	3.37430i	−0.225861	−	0.189520i	0.522834	−	0.852434i	$-0.324875\pi$
$317$	−4.02133	−	3.37430i	−0.225861	−	0.189520i	−0.748695	+	0.662915i	$0.769319\pi$
$318$	2.53091	+	0.317000i	0.141927	+	0.0177765i
$319$	−0.0165776	−	0.0940161i	−0.000928166	−	0.00526389i
$320$	−0.272791	−	1.54708i	−0.0152495	−	0.0864843i
$321$	−25.9392	+	16.7556i	−1.44778	+	0.935209i
$322$	4.65260	−	0.993891i	0.259279	−	0.0553874i
$323$	−5.32176			−0.296110
$324$	5.60961	−	7.03792i	0.311645	−	0.390995i
$325$	3.27835	−	5.67827i	0.181850	−	0.314974i
$326$	8.69738	+	7.29797i	0.481703	+	0.404197i
$327$	−7.98297	−	4.09199i	−0.441459	−	0.226287i
$328$	5.53590	+	2.01490i	0.305669	+	0.111254i
$329$	23.0289	−	14.4227i	1.26963	−	0.795148i
$330$	0.161049	+	0.381984i	0.00886543	+	0.0210275i
$331$	19.1221	+	16.0454i	1.05105	+	0.881933i	0.993203	−	0.116393i	$-0.0371331\pi$
$331$	19.1221	+	16.0454i	1.05105	+	0.881933i	0.0578435	+	0.998326i	$0.481578\pi$
$332$	5.09768	+	8.82944i	0.279772	+	0.484579i
$333$	2.90737	−	6.44558i	0.159323	−	0.353216i
$334$	−1.77174	+	3.06875i	−0.0969454	+	0.167914i
$335$	10.0163	+	8.40463i	0.547246	+	0.459194i
$336$	−1.94254	+	4.15049i	−0.105974	+	0.226428i
$337$	5.35647	+	30.3780i	0.291785	+	1.65480i	0.679988	+	0.733223i	$0.261985\pi$
$337$	5.35647	+	30.3780i	0.291785	+	1.65480i	−0.388202	+	0.921574i	$0.626904\pi$
$338$	4.82227	−	4.04637i	0.262297	−	0.220093i
$339$	15.5169	+	16.7211i	0.842761	+	0.908164i
$340$	−2.96245	+	1.07824i	−0.160662	+	0.0584760i
$341$	−0.307831	+	0.533179i	−0.0166700	+	0.0288732i
$342$	−7.16728	+	3.45271i	−0.387562	+	0.186701i
$343$	−14.9499	+	10.9316i	−0.807219	+	0.590253i
$344$	−8.00213	+	2.91254i	−0.431446	+	0.157034i
$345$	4.85487	+	0.608079i	0.261377	+	0.0327379i
$346$	−0.725547	−	4.11478i	−0.0390056	−	0.221212i
$347$	3.88739	−	3.26191i	0.208686	−	0.175108i	−0.532454	−	0.846459i	$-0.678730\pi$
$347$	3.88739	−	3.26191i	0.208686	−	0.175108i	0.741140	+	0.671351i	$0.234286\pi$
$348$	0.911663	−	0.588897i	0.0488703	−	0.0315682i
$349$	1.30426	−	7.39685i	0.0698157	−	0.395945i	−0.929796	−	0.368076i	$-0.880017\pi$
$349$	1.30426	−	7.39685i	0.0698157	−	0.395945i	0.999612	−	0.0278690i	$-0.00887211\pi$
$350$	−4.11919	+	5.28340i	−0.220180	+	0.282409i
$351$	−12.7534	+	4.28765i	−0.680728	+	0.228858i
$352$	0.0761766	+	0.131942i	0.00406023	+	0.00703252i
$353$	3.57113	+	2.99654i	0.190072	+	0.159490i	0.732858	−	0.680382i	$-0.238186\pi$
$353$	3.57113	+	2.99654i	0.190072	+	0.159490i	−0.542786	+	0.839871i	$0.682630\pi$
$354$	17.1236	−	11.0611i	0.910108	−	0.587893i
$355$	−0.323381	−	1.83399i	−0.0171633	−	0.0973379i
$356$	10.2030	−	8.56136i	0.540759	−	0.453751i
$357$	8.87961	+	2.39272i	0.469959	+	0.126636i
$358$	9.03873	−	3.28983i	0.477712	−	0.173873i
$359$	−27.3759			−1.44484			−0.722421	−	0.691453i	$-0.756971\pi$
$359$	−27.3759			−1.44484			−0.722421	+	0.691453i	$0.756971\pi$
$360$	−3.29024	+	3.37418i	−0.173411	+	0.177835i
$361$	−11.9677			−0.629877
$362$	3.18063	−	18.0382i	0.167170	−	0.948068i
$363$	12.9326	+	13.9362i	0.678784	+	0.731462i
$364$	5.80619	−	3.63633i	0.304327	−	0.190596i
$365$	1.50164	+	8.51620i	0.0785992	+	0.445758i
$366$	2.22476	−	7.21413i	0.116290	−	0.377088i
$367$	16.3222	−	5.94079i	0.852011	−	0.310107i	0.121151	−	0.992634i	$-0.461341\pi$
$367$	16.3222	−	5.94079i	0.852011	−	0.310107i	0.730860	+	0.682527i	$0.239119\pi$
$368$	1.79819			0.0937373
$369$	−4.78889	−	17.0124i	−0.249299	−	0.885628i
$370$	−1.85134	+	3.20662i	−0.0962468	+	0.166704i
$371$	2.61004	+	2.89282i	0.135506	+	0.150188i
$372$	−6.94498	−	0.869868i	−0.360080	−	0.0451005i
$373$	−19.0218	−	6.92338i	−0.984913	−	0.358479i	−0.201164	−	0.979557i	$-0.564473\pi$
$373$	−19.0218	−	6.92338i	−0.984913	−	0.358479i	−0.783748	+	0.621079i	$0.786695\pi$
$374$	0.234213	−	0.196528i	0.0121109	−	0.0101622i
$375$	−17.2153	+	11.1204i	−0.888993	+	0.574253i
$376$	9.65087	−	3.51263i	0.497706	−	0.181150i
$377$	−1.62255			−0.0835655
$378$	13.5113	−	2.53852i	0.694948	−	0.130567i
$379$	15.7102			0.806981			0.403490	−	0.914984i	$-0.367797\pi$
$379$	15.7102			0.806981			0.403490	+	0.914984i	$0.367797\pi$
$380$	3.91468	−	1.42483i	0.200819	−	0.0730921i
$381$	−26.6599	−	13.6656i	−1.36583	−	0.700108i
$382$	−20.1202	+	16.8829i	−1.02944	+	0.863802i
$383$	0.798805	+	0.290741i	0.0408170	+	0.0148562i	0.362348	−	0.932043i	$-0.381975\pi$
$383$	0.798805	+	0.290741i	0.0408170	+	0.0148562i	−0.321531	+	0.946899i	$0.604197\pi$
$384$	−1.04573	+	1.38074i	−0.0533648	+	0.0704606i
$385$	−0.195066	+	0.602436i	−0.00994147	+	0.0307030i
$386$	−11.7828	+	20.4084i	−0.599729	+	1.03876i
$387$	21.1098	+	14.3885i	1.07307	+	0.731408i
$388$	−17.7069			−0.898931
$389$	−7.25010	+	2.63882i	−0.367595	+	0.133793i	−0.519211	−	0.854646i	$-0.673774\pi$
$389$	−7.25010	+	2.63882i	−0.367595	+	0.133793i	0.151617	+	0.988439i	$0.451552\pi$
$390$	6.86888	−	1.56824i	0.347819	−	0.0794109i
$391$	−0.626631	−	3.55380i	−0.0316901	−	0.179723i
$392$	−6.38901	+	2.86017i	−0.322694	+	0.144460i
$393$	−20.5233	+	4.68570i	−1.03527	+	0.236362i
$394$	1.28721	−	7.30016i	0.0648489	−	0.367777i
$395$	8.79972			0.442762
$396$	0.187929	−	0.416637i	0.00944381	−	0.0209368i
$397$	9.44714			0.474138			0.237069	−	0.971493i	$-0.423813\pi$
$397$	9.44714			0.474138			0.237069	+	0.971493i	$0.423813\pi$
$398$	11.7726	−	4.28488i	0.590107	−	0.214781i
$399$	−11.7338	−	3.16182i	−0.587425	−	0.158289i
$400$	−1.93973	+	1.62763i	−0.0969865	+	0.0813813i
$401$	6.38018	+	36.1838i	0.318611	+	1.80693i	0.551217	+	0.834362i	$0.314164\pi$
$401$	6.38018	+	36.1838i	0.318611	+	1.80693i	−0.232606	+	0.972571i	$0.574725\pi$
$402$	−0.719510	−	14.3983i	−0.0358859	−	0.718120i
$403$	8.01573	+	6.72599i	0.399292	+	0.335046i
$404$	6.97002	+	12.0724i	0.346771	+	0.600626i
$405$	13.9811	+	2.10366i	0.694727	+	0.104532i
$406$	1.64196	+	0.229059i	0.0814891	+	0.0113680i
$407$	0.0623560	−	0.353639i	0.00309087	−	0.0175292i
$408$	3.09320	+	1.58554i	0.153136	+	0.0784959i
$409$	13.9216	−	11.6816i	0.688380	−	0.577619i	−0.230062	−	0.973176i	$-0.573893\pi$
$409$	13.9216	−	11.6816i	0.688380	−	0.577619i	0.918442	+	0.395557i	$0.129448\pi$
$410$	1.60706	+	9.11411i	0.0793672	+	0.450114i
$411$	−12.8315	+	16.9422i	−0.632933	+	0.835698i
$412$	−10.9881	+	3.99935i	−0.541346	+	0.197034i
$413$	30.8406	+	4.30236i	1.51757	+	0.211705i
$414$	−3.14961	−	4.37966i	−0.154795	−	0.215249i
$415$	−8.00817	+	13.8706i	−0.393105	+	0.680879i
$416$	2.43324	−	0.885626i	0.119299	−	0.0434214i
$417$	−4.80297	+	15.5744i	−0.235202	+	0.762680i
$418$	−0.309496	+	0.259698i	−0.0151380	+	0.0127023i
$419$	−4.31602	−	24.4774i	−0.210851	−	1.19580i	−0.887962	−	0.459916i	$-0.847879\pi$
$419$	−4.31602	−	24.4774i	−0.210851	−	1.19580i	0.677111	−	0.735881i	$-0.263232\pi$
$420$	−7.17245	+	0.617307i	−0.349980	+	0.0301215i
$421$	19.2335	+	16.1388i	0.937384	+	0.786558i	0.977128	−	0.212651i	$-0.0682099\pi$
$421$	19.2335	+	16.1388i	0.937384	+	0.786558i	−0.0397443	+	0.999210i	$0.512654\pi$
$422$	6.96886	−	12.0704i	0.339239	−	0.587578i
$423$	−25.4592	−	17.3530i	−1.23787	−	0.843734i
$424$	0.736320	+	1.27534i	0.0357589	+	0.0619362i
$425$	3.89266	+	3.26633i	0.188822	+	0.158440i
$426$	−1.23967	+	1.63680i	−0.0600620	+	0.0793034i
$427$	9.77336	−	6.12091i	0.472966	−	0.296212i
$428$	−16.7535	−	6.09779i	−0.809813	−	0.294748i
$429$	−0.573965	+	0.370758i	−0.0277113	+	0.0179004i
$430$	−10.2479	−	8.59900i	−0.494197	−	0.414681i
$431$	−6.06335	+	10.5020i	−0.292061	+	0.505865i	−0.974297	−	0.225267i	$-0.927674\pi$
$431$	−6.06335	+	10.5020i	−0.292061	+	0.505865i	0.682236	+	0.731132i	$0.261008\pi$
$432$	5.19456	+	0.128547i	0.249923	+	0.00618472i
$433$	−33.6394			−1.61660			−0.808302	−	0.588768i	$-0.799613\pi$
$433$	−33.6394			−1.61660			−0.808302	+	0.588768i	$0.799613\pi$
$434$	−7.16211	−	7.93806i	−0.343792	−	0.381039i
$435$	1.51727	+	0.777735i	0.0727474	+	0.0372895i
$436$	−0.899358	−	5.10051i	−0.0430714	−	0.244270i
$437$	0.828050	+	4.69610i	0.0396110	+	0.224645i
$438$	5.75644	−	7.60057i	0.275053	−	0.363169i
$439$	1.83966	+	1.54366i	0.0878022	+	0.0736748i	0.685632	−	0.727948i	$-0.259526\pi$
$439$	1.83966	+	1.54366i	0.0878022	+	0.0736748i	−0.597830	+	0.801623i	$0.703970\pi$
$440$	−0.119669	+	0.207273i	−0.00570500	+	0.00988135i
$441$	18.1568	+	10.5513i	0.864610	+	0.502443i
$442$	−2.59821	−	4.50022i	−0.123584	−	0.214054i
$443$	3.04937	−	17.2938i	0.144880	−	0.821655i	−0.822584	−	0.568644i	$-0.807468\pi$
$443$	3.04937	−	17.2938i	0.144880	−	0.821655i	0.967463	−	0.253011i	$-0.0814208\pi$
$444$	3.98000	−	0.908677i	0.188883	−	0.0431239i
$445$	19.6617	+	7.15628i	0.932055	+	0.339240i
$446$	−18.0464	+	15.1427i	−0.854521	+	0.717028i
$447$	10.2783	+	11.0760i	0.486149	+	0.523877i
$448$	−2.58737	+	0.552716i	−0.122242	+	0.0261134i
$449$	13.2766	+	22.9958i	0.626563	+	1.08524i	0.988236	+	0.152935i	$0.0488724\pi$
$449$	13.2766	+	22.9958i	0.626563	+	1.08524i	−0.361673	+	0.932305i	$0.617794\pi$
$450$	7.36175	+	1.87353i	0.347036	+	0.0883190i
$451$	−0.448770	−	0.777292i	−0.0211318	−	0.0366013i
$452$	−2.28699	+	12.9702i	−0.107571	+	0.610066i
$453$	5.84145	+	13.8551i	0.274455	+	0.650968i
$454$	12.1692	−	10.2111i	0.571127	−	0.479232i
$455$	9.50775	+	5.04295i	0.445730	+	0.236417i
$456$	−4.08745	−	2.09518i	−0.191412	−	0.0981159i
$457$	18.5148	−	6.73883i	0.866085	−	0.315229i	0.129504	−	0.991579i	$-0.458661\pi$
$457$	18.5148	−	6.73883i	0.866085	−	0.315229i	0.736581	+	0.676350i	$0.236439\pi$
$458$	−8.91377	+	15.4391i	−0.416513	+	0.721422i
$459$	−1.55614	−	10.3109i	−0.0726344	−	0.481271i
$460$	1.41243	+	2.44640i	0.0658549	+	0.114064i
$461$	−2.01136	+	11.4070i	−0.0936783	+	0.531276i	0.901466	+	0.432850i	$0.142492\pi$
$461$	−2.01136	+	11.4070i	−0.0936783	+	0.531276i	−0.995144	+	0.0984263i	$0.968619\pi$
$462$	0.633173	−	0.294166i	0.0294579	−	0.0136858i
$463$	−23.2800	−	8.47323i	−1.08191	−	0.393784i	−0.261294	−	0.965259i	$-0.584149\pi$
$463$	−23.2800	−	8.47323i	−1.08191	−	0.393784i	−0.820619	+	0.571475i	$0.806371\pi$
$464$	0.588823	+	0.214314i	0.0273354	+	0.00994928i
$465$	−4.27165	−	10.1317i	−0.198093	−	0.469848i
$466$	0.616700	−	3.49748i	0.0285681	−	0.162018i
$467$	−19.1950			−0.888237			−0.444118	−	0.895968i	$-0.646483\pi$
$467$	−19.1950			−0.888237			−0.444118	+	0.895968i	$0.646483\pi$
$468$	−6.41894	−	4.37515i	−0.296716	−	0.202242i
$469$	13.5399	−	17.3667i	0.625214	−	0.801919i
$470$	12.3593	+	10.3707i	0.570094	+	0.478365i
$471$	−29.7039	+	6.78171i	−1.36868	+	0.312485i
$472$	11.0597	+	4.02542i	0.509066	+	0.185285i
$473$	1.21915	+	0.443735i	0.0560566	+	0.0204029i
$474$	−6.59961	−	7.11177i	−0.303130	−	0.326655i
$475$	−5.14388	−	4.31623i	−0.236017	−	0.198042i
$476$	1.99399	+	4.92086i	0.0913942	+	0.225547i
$477$	1.81652	−	4.02719i	0.0831727	−	0.184392i
$478$	−17.6950			−0.809348
$479$	−4.42645	+	25.1037i	−0.202250	+	1.14702i	0.699460	+	0.714672i	$0.253424\pi$
$479$	−4.42645	+	25.1037i	−0.202250	+	1.14702i	−0.901709	+	0.432343i	$0.857687\pi$
$480$	−2.69986	−	0.338161i	−0.123231	−	0.0154349i
$481$	−5.73510	−	2.08740i	−0.261498	−	0.0951775i
$482$	−4.83233	−	1.75882i	−0.220106	−	0.0801122i
$483$	0.729782	−	8.20798i	0.0332062	−	0.373476i
$484$	−1.90610	+	10.8100i	−0.0866409	+	0.491365i
$485$	−13.9083	−	24.0898i	−0.631542	−	1.09386i
$486$	−8.78541	−	12.8770i	−0.398514	−	0.584112i
$487$	11.8852	−	20.5857i	0.538569	−	0.932828i	−0.460413	−	0.887705i	$-0.652299\pi$
$487$	11.8852	−	20.5857i	0.538569	−	0.932828i	0.998981	−	0.0451233i	$-0.0143681\pi$
$488$	4.09578	−	1.49074i	0.185407	−	0.0674827i
$489$	16.5185	−	10.6703i	0.746991	−	0.482526i
$490$	−8.90958	−	6.44552i	−0.402494	−	0.291179i
$491$	−14.9640	+	12.5563i	−0.675317	+	0.566658i	−0.914634	−	0.404283i	$-0.867521\pi$
$491$	−14.9640	+	12.5563i	−0.675317	+	0.566658i	0.239317	+	0.970941i	$0.423076\pi$
$492$	6.16059	−	8.13419i	0.277741	−	0.366718i
$493$	0.218361	−	1.23838i	0.00983447	−	0.0557740i
$494$	3.43335	+	5.94674i	0.154474	+	0.267556i
$495$	0.714438	−	0.0715826i	0.0321116	−	0.00321740i
$496$	−2.02051	−	3.49962i	−0.0907235	−	0.157138i
$497$	−3.06721	+	0.655219i	−0.137583	+	0.0293906i
$498$	17.2159	−	3.93057i	0.771462	−	0.176133i
$499$	27.5793	−	23.1418i	1.23462	−	1.03597i	0.236694	−	0.971584i	$-0.423936\pi$
$499$	27.5793	−	23.1418i	1.23462	−	1.03597i	0.997925	−	0.0643842i	$-0.0205083\pi$
$500$	−11.1190	−	4.04697i	−0.497255	−	0.180986i
$501$	4.17484	+	4.49883i	0.186518	+	0.200993i
$502$	2.99513	−	16.9862i	0.133679	−	0.758131i
$503$	−1.27576	−	2.20968i	−0.0568833	−	0.0985248i	0.836181	−	0.548453i	$-0.184783\pi$
$503$	−1.27576	−	2.20968i	−0.0568833	−	0.0985248i	−0.893065	+	0.449928i	$0.851450\pi$
$504$	5.87809	+	5.33368i	0.261831	+	0.237581i
$505$	−10.9495	+	18.9651i	−0.487247	+	0.843936i
$506$	−0.209866	−	0.176098i	−0.00932968	−	0.00782853i
$507$	−4.23587	−	10.0469i	−0.188121	−	0.446197i
$508$	−3.00349	−	17.0336i	−0.133258	−	0.755745i
$509$	2.92151	+	16.5687i	0.129494	+	0.734395i	0.978537	+	0.206072i	$0.0660680\pi$
$509$	2.92151	+	16.5687i	0.129494	+	0.734395i	−0.849043	+	0.528323i	$0.822821\pi$
$510$	0.272528	+	5.45362i	0.0120678	+	0.241490i
$511$	14.2427	−	3.04254i	0.630061	−	0.134594i
$512$	−1.00000			−0.0441942
$513$	2.05633	+	13.6251i	0.0907894	+	0.601565i
$514$	6.34904	−	10.9969i	0.280044	−	0.485051i
$515$	−14.0719	−	11.8077i	−0.620082	−	0.520310i
$516$	0.736150	+	14.7312i	0.0324072	+	0.648506i
$517$	−1.47034	−	0.535160i	−0.0646655	−	0.0235363i
$518$	5.50903	+	2.92202i	0.242053	+	0.128386i
$519$	−7.18085	−	0.899411i	−0.315204	−	0.0394797i
$520$	3.11611	+	2.61473i	0.136651	+	0.114663i
$521$	−10.4887	−	18.1669i	−0.459517	−	0.795907i	0.539418	−	0.842038i	$-0.318644\pi$
$521$	−10.4887	−	18.1669i	−0.459517	−	0.795907i	−0.998935	+	0.0461309i	$0.985311\pi$
$522$	−0.509367	−	1.80951i	−0.0222944	−	0.0792002i
$523$	13.4118	−	23.2300i	0.586459	−	1.01578i	−0.408233	−	0.912878i	$-0.633855\pi$
$523$	13.4118	−	23.2300i	0.586459	−	1.01578i	0.994692	−	0.102898i	$-0.0328116\pi$
$524$	−9.31055	−	7.81248i	−0.406733	−	0.341290i
$525$	6.64219	+	9.51459i	0.289889	+	0.415251i
$526$	−5.06464	−	28.7230i	−0.220829	−	1.25238i
$527$	−6.21226	+	5.21270i	−0.270610	+	0.227069i
$528$	0.257264	−	0.0587361i	0.0111960	−	0.00255616i
$529$	18.5744	−	6.76054i	0.807584	−	0.293937i
$530$	−1.15672	+	2.00349i	−0.0502446	+	0.0870262i
$531$	−9.56735	−	33.9877i	−0.415188	−	1.47494i
$532$	−2.63492	−	6.50258i	−0.114238	−	0.281923i
$533$	−14.3346	+	5.21738i	−0.620902	+	0.225990i
$534$	−8.96231	−	21.2573i	−0.387837	−	0.919893i
$535$	−4.86353	−	27.5824i	−0.210269	−	1.19249i
$536$	6.37595	−	5.35005i	0.275399	−	0.231087i
$537$	−0.831510	−	16.6395i	−0.0358823	−	0.718048i
$538$	−1.65194	+	9.36863i	−0.0712203	+	0.403911i
$539$	1.02576	+	0.291872i	0.0441824	+	0.0125718i
$540$	3.90530	+	7.16805i	0.168057	+	0.308464i
$541$	−9.41676	−	16.3103i	−0.404858	−	0.701235i	0.589447	−	0.807807i	$-0.299346\pi$
$541$	−9.41676	−	16.3103i	−0.404858	−	0.701235i	−0.994305	+	0.106572i	$0.966012\pi$
$542$	14.6494	+	12.2923i	0.629246	+	0.528000i
$543$	−28.2322	−	14.4715i	−1.21156	−	0.621032i
$544$	0.348478	+	1.97632i	0.0149409	+	0.0847339i
$545$	6.23271	−	5.22987i	0.266980	−	0.224023i
$546$	−3.05499	−	11.4661i	−0.130742	−	0.490704i
$547$	−12.8549	+	4.67879i	−0.549634	+	0.200050i	−0.601884	−	0.798584i	$-0.705583\pi$
$547$	−12.8549	+	4.67879i	−0.549634	+	0.200050i	0.0522499	+	0.998634i	$0.483361\pi$
$548$	−12.2704			−0.524165
$549$	−10.8048	−	7.36454i	−0.461136	−	0.314311i
$550$	0.385779			0.0164497
$551$	−0.288549	+	1.63644i	−0.0122926	+	0.0697147i
$552$	0.917843	−	2.97625i	0.0390660	−	0.126678i
$553$	−0.532295	−	14.8108i	−0.0226355	−	0.629817i
$554$	−2.07245	−	11.7534i	−0.0880499	−	0.499356i
$555$	4.36241	+	4.70096i	0.185174	+	0.199545i
$556$	−8.84226	+	3.21832i	−0.374995	+	0.136487i
$557$	3.98127			0.168692			0.0843460	−	0.996437i	$-0.473120\pi$
$557$	3.98127			0.168692			0.0843460	+	0.996437i	$0.473120\pi$
$558$	−4.98464	+	11.0509i	−0.211017	+	0.467820i
$559$	11.0253	−	19.0963i	0.466318	−	0.807687i
$560$	−2.78427	−	3.08592i	−0.117657	−	0.130404i
$561$	−0.205732	−	0.487966i	−0.00868600	−	0.0206019i
$562$	11.4609	+	4.17141i	0.483447	+	0.175960i
$563$	6.87739	−	5.77082i	0.289848	−	0.243211i	−0.486256	−	0.873816i	$-0.661638\pi$
$563$	6.87739	−	5.77082i	0.289848	−	0.243211i	0.776104	+	0.630605i	$0.217193\pi$
$564$	−0.887824	−	17.7664i	−0.0373841	−	0.748101i
$565$	−19.4420	+	7.07631i	−0.817931	+	0.297703i
$566$	28.9587			1.21722
$567$	2.69493	−	23.6588i	0.113176	−	0.993575i
$568$	−1.18545			−0.0497405
$569$	22.6685	−	8.25064i	0.950311	−	0.345885i	0.180081	−	0.983652i	$-0.442364\pi$
$569$	22.6685	−	8.25064i	0.950311	−	0.345885i	0.770230	+	0.637767i	$0.220142\pi$
$570$	−0.360128	−	7.20658i	−0.0150841	−	0.301851i
$571$	−1.77212	+	1.48699i	−0.0741610	+	0.0622284i	−0.679115	−	0.734032i	$-0.737636\pi$
$571$	−1.77212	+	1.48699i	−0.0741610	+	0.0622284i	0.604954	+	0.796261i	$0.293192\pi$
$572$	−0.370711	−	0.134928i	−0.0155002	−	0.00564162i
$573$	17.6735	+	41.9190i	0.738322	+	1.75119i
$574$	15.2427	−	3.25615i	0.636217	−	0.135909i
$575$	2.27664	−	3.94325i	0.0949423	−	0.164445i
$576$	1.75154	+	2.43559i	0.0729809	+	0.101483i
$577$	5.24734			0.218449			0.109225	−	0.994017i	$-0.465163\pi$
$577$	5.24734			0.218449			0.109225	+	0.994017i	$0.465163\pi$
$578$	−12.1904	+	4.43694i	−0.507053	+	0.184552i
$579$	27.7644	+	29.9191i	1.15385	+	1.24340i
$580$	0.170935	+	0.969418i	0.00709767	+	0.0402529i
$581$	23.8298	+	12.6395i	0.988629	+	0.524373i
$582$	−9.03804	+	29.3073i	−0.374639	+	1.21483i
$583$	0.0389600	−	0.220953i	0.00161356	−	0.00915093i
$584$	5.50470			0.227786
$585$	0.910403	−	12.1694i	0.0376405	−	0.503142i
$586$	−8.93175			−0.368967
$587$	25.0371	−	9.11274i	1.03339	−	0.376123i	0.231019	−	0.972949i	$-0.425794\pi$
$587$	25.0371	−	9.11274i	1.03339	−	0.376123i	0.802371	+	0.596826i	$0.203572\pi$
$588$	1.47285	+	12.0346i	0.0607392	+	0.496297i
$589$	8.20907	−	6.88823i	0.338249	−	0.283825i
$590$	3.21063	+	18.2084i	0.132180	+	0.749627i
$591$	−11.4257	−	5.85669i	−0.469991	−	0.240912i
$592$	1.80555	+	1.51504i	0.0742078	+	0.0622677i
$593$	6.75739	+	11.7041i	0.277493	+	0.480632i	0.970761	−	0.240048i	$-0.0771632\pi$
$593$	6.75739	+	11.7041i	0.277493	+	0.480632i	−0.693268	+	0.720680i	$0.743830\pi$
$594$	−0.593665	−	0.523710i	−0.0243584	−	0.0214881i
$595$	−5.12850	+	6.57797i	−0.210248	+	0.269670i
$596$	−1.51490	+	8.59142i	−0.0620527	+	0.351918i
$597$	−1.08301	−	21.6723i	−0.0443247	−	0.886989i
$598$	−3.56688	+	2.99297i	−0.145861	+	0.122392i
$599$	−7.22264	−	40.9616i	−0.295109	−	1.67365i	−0.666759	−	0.745274i	$-0.732319\pi$
$599$	−7.22264	−	40.9616i	−0.295109	−	1.67365i	0.371650	−	0.928373i	$-0.378792\pi$
$600$	1.70385	+	4.04129i	0.0695594	+	0.164985i
$601$	7.66563	−	2.79006i	0.312688	−	0.113809i	−0.180909	−	0.983500i	$-0.557904\pi$
$601$	7.66563	−	2.79006i	0.312688	−	0.113809i	0.493597	+	0.869691i	$0.335682\pi$
$602$	−13.8530	+	17.7683i	−0.564607	+	0.724182i
$603$	−24.1983	−	6.15834i	−0.985430	−	0.250787i
$604$	−4.34056	+	7.51807i	−0.176615	+	0.305906i
$605$	−16.2040	+	5.89777i	−0.658785	+	0.239778i
$606$	23.5392	−	5.37424i	0.956213	−	0.218314i
$607$	10.8391	−	9.09507i	0.439945	−	0.369157i	−0.395744	−	0.918361i	$-0.629513\pi$
$607$	10.8391	−	9.09507i	0.439945	−	0.369157i	0.835689	+	0.549204i	$0.185069\pi$
$608$	−0.460490	−	2.61157i	−0.0186753	−	0.105913i
$609$	1.21722	−	2.60075i	0.0493243	−	0.105388i
$610$	5.24524	+	4.40128i	0.212374	+	0.178203i
$611$	−13.2969	+	23.0308i	−0.537933	+	0.931728i
$612$	4.20312	−	4.31035i	0.169901	−	0.174236i
$613$	6.92814	+	11.9999i	0.279825	+	0.484671i	0.971341	−	0.237690i	$-0.0763902\pi$
$613$	6.92814	+	11.9999i	0.279825	+	0.484671i	−0.691516	+	0.722361i	$0.743057\pi$
$614$	−8.90312	−	7.47061i	−0.359301	−	0.301489i
$615$	15.9054	+	1.99217i	0.641366	+	0.0803319i
$616$	0.356099	+	0.188876i	0.0143476	+	0.00761005i
$617$	22.0077	+	8.01016i	0.885998	+	0.322477i	0.744628	−	0.667480i	$-0.232627\pi$
$617$	22.0077	+	8.01016i	0.885998	+	0.322477i	0.141370	+	0.989957i	$0.454849\pi$
$618$	1.01084	+	20.2282i	0.0406621	+	0.813697i
$619$	−12.3944	−	10.4001i	−0.498173	−	0.418017i	0.358772	−	0.933425i	$-0.383196\pi$
$619$	−12.3944	−	10.4001i	−0.498173	−	0.418017i	−0.856945	+	0.515409i	$0.827640\pi$
$620$	3.17410	−	5.49771i	0.127475	−	0.220793i
$621$	−8.85657	+	2.97754i	−0.355402	+	0.119485i
$622$	−16.7875			−0.673118
$623$	10.8553	−	33.5254i	0.434910	−	1.34317i
$624$	−0.223844	−	4.47938i	−0.00896091	−	0.179319i
$625$	−1.02932	−	5.83755i	−0.0411727	−	0.233502i
$626$	4.06391	+	23.0476i	0.162427	+	0.921167i
$627$	0.271860	+	0.644814i	0.0108571	+	0.0257514i
$628$	−13.4754	−	11.3072i	−0.537725	−	0.451205i
$629$	2.36500	−	4.09630i	0.0942988	−	0.163330i
$630$	−2.63927	+	12.1865i	−0.105151	+	0.485520i
$631$	−4.42151	−	7.65828i	−0.176018	−	0.304871i	0.764495	−	0.644629i	$-0.222988\pi$
$631$	−4.42151	−	7.65828i	−0.176018	−	0.304871i	−0.940513	+	0.339758i	$0.889655\pi$
$632$	0.972699	−	5.51645i	0.0386919	−	0.219433i
$633$	−16.4211	−	17.6954i	−0.652679	−	0.703330i
$634$	−4.93290	−	1.79543i	−0.195910	−	0.0713055i
$635$	20.8147	−	17.4656i	0.826006	−	0.693102i
$636$	2.48670	−	0.567740i	0.0986041	−	0.0225124i
$637$	7.91264	−	16.3075i	0.313510	−	0.646126i
$638$	−0.0477332	−	0.0826763i	−0.00188978	−	0.00327319i
$639$	2.07637	+	2.88728i	0.0821400	+	0.114219i
$640$	−0.785472	−	1.36048i	−0.0310485	−	0.0537776i
$641$	1.99370	−	11.3069i	0.0787466	−	0.446594i	−0.919785	−	0.392423i	$-0.871637\pi$
$641$	1.99370	−	11.3069i	0.0787466	−	0.446594i	0.998532	−	0.0541715i	$-0.0172518\pi$
$642$	−18.6441	+	24.6169i	−0.735823	+	0.971551i
$643$	22.8634	−	19.1847i	0.901644	−	0.756570i	−0.0688666	−	0.997626i	$-0.521938\pi$
$643$	22.8634	−	19.1847i	0.901644	−	0.756570i	0.970511	+	0.241056i	$0.0774939\pi$
$644$	4.03208	−	2.52523i	0.158886	−	0.0995082i
$645$	−19.4633	+	12.5725i	−0.766366	+	0.495041i
$646$	−5.00081	+	1.82015i	−0.196754	+	0.0716127i
$647$	5.26944	−	9.12693i	0.207163	−	0.358817i	−0.743657	−	0.668562i	$-0.766910\pi$
$647$	5.26944	−	9.12693i	0.207163	−	0.358817i	0.950820	+	0.309745i	$0.100244\pi$
$648$	2.86420	−	8.53208i	0.112516	−	0.335172i
$649$	−0.896563	−	1.55289i	−0.0351932	−	0.0609564i
$650$	1.13856	−	6.45709i	0.0446580	−	0.253268i
$651$	−16.7943	+	7.80245i	−0.658219	+	0.305802i
$652$	10.6689	+	3.88317i	0.417827	+	0.152077i
$653$	33.4984	+	12.1924i	1.31089	+	0.477126i	0.900529	−	0.434796i	$-0.143180\pi$
$653$	33.4984	+	12.1924i	1.31089	+	0.477126i	0.410364	+	0.911922i	$0.365402\pi$
$654$	−8.90108	−	1.11487i	−0.348060	−	0.0435950i
$655$	3.31552	−	18.8033i	0.129548	−	0.734704i
$656$	5.89118			0.230012
$657$	−9.64172	−	13.4072i	−0.376159	−	0.523065i
$658$	16.7073	−	21.4292i	0.651317	−	0.835399i
$659$	−34.0992	−	28.6127i	−1.32832	−	1.11459i	−0.984468	−	0.175566i	$-0.943824\pi$
$659$	−34.0992	−	28.6127i	−1.32832	−	1.11459i	−0.343850	−	0.939025i	$-0.611731\pi$
$660$	0.281982	+	0.303866i	0.0109761	+	0.0118280i
$661$	9.18298	+	3.34233i	0.357176	+	0.130002i	0.514375	−	0.857565i	$-0.328024\pi$
$661$	9.18298	+	3.34233i	0.357176	+	0.130002i	−0.157198	+	0.987567i	$0.550246\pi$
$662$	23.4568	+	8.53756i	0.911673	+	0.331822i
$663$	−8.77466	+	2.00335i	−0.340780	+	0.0778037i
$664$	7.81010	+	6.55345i	0.303091	+	0.254323i
$665$	6.77696	−	8.69234i	0.262799	−	0.337074i
$666$	0.527511	−	7.05125i	0.0204406	−	0.273230i
$667$	−1.12677			−0.0436287
$668$	−0.615319	+	3.48965i	−0.0238074	+	0.135019i
$669$	15.8519	+	37.5984i	0.612869	+	1.45364i
$670$	12.2868	+	4.47201i	0.474679	+	0.172769i
$671$	−0.624005	−	0.227119i	−0.0240895	−	0.00876784i
$672$	−0.405842	+	4.56457i	−0.0156557	+	0.176082i
$673$	−6.91074	+	39.1928i	−0.266390	+	1.51077i	0.498659	+	0.866798i	$0.333826\pi$
$673$	−6.91074	+	39.1928i	−0.266390	+	1.51077i	−0.765049	+	0.643972i	$0.777285\pi$
$674$	15.4233	+	26.7140i	0.594085	+	1.02898i
$675$	6.85856	−	11.2284i	0.263986	−	0.432180i
$676$	3.14751	−	5.45165i	0.121058	−	0.209679i
$677$	−23.4151	+	8.52238i	−0.899914	+	0.327542i	−0.750218	−	0.661190i	$-0.770052\pi$
$677$	−23.4151	+	8.52238i	−0.899914	+	0.327542i	−0.149696	+	0.988732i	$0.547829\pi$
$678$	20.3000	+	10.4056i	0.779618	+	0.399624i
$679$	−39.7041	+	24.8661i	−1.52370	+	0.954273i
$680$	−2.41501	+	2.02644i	−0.0926116	+	0.0777103i
$681$	−10.6893	−	25.3536i	−0.409617	−	0.971552i
$682$	−0.106909	+	0.606308i	−0.00409374	+	0.0232167i
$683$	0.382129	+	0.661867i	0.0146218	+	0.0253256i	0.873244	−	0.487284i	$-0.162012\pi$
$683$	0.382129	+	0.661867i	0.0146218	+	0.0253256i	−0.858622	+	0.512609i	$0.828679\pi$
$684$	−5.55414	+	5.69584i	−0.212368	+	0.217786i
$685$	−9.63804	−	16.6936i	−0.368251	−	0.637829i
$686$	−10.3095	+	15.3855i	−0.393617	+	0.587423i
$687$	21.0040	+	22.6340i	0.801351	+	0.863540i
$688$	−6.52340	+	5.47378i	−0.248702	+	0.208686i
$689$	−3.58328	−	1.30421i	−0.136512	−	0.0496864i
$690$	4.77006	−	1.08906i	0.181593	−	0.0414597i
$691$	−2.72450	+	15.4514i	−0.103645	+	0.587800i	0.888108	+	0.459635i	$0.152020\pi$
$691$	−2.72450	+	15.4514i	−0.103645	+	0.587800i	−0.991753	+	0.128165i	$0.959091\pi$
$692$	−2.08913	−	3.61848i	−0.0794168	−	0.137554i
$693$	−0.163696	−	1.19814i	−0.00621832	−	0.0455134i
$694$	2.53731	−	4.39476i	0.0963151	−	0.166823i
$695$	−11.3238	−	9.50180i	−0.429536	−	0.360424i
$696$	0.655268	−	0.865189i	0.0248379	−	0.0327949i
$697$	−2.05295	−	11.6428i	−0.0777609	−	0.441004i
$698$	−1.30426	−	7.39685i	−0.0493672	−	0.279975i
$699$	−5.47402	−	2.80592i	−0.207046	−	0.106130i
$700$	−2.06374	+	6.37361i	−0.0780022	+	0.240900i
$701$	8.05593			0.304268			0.152134	−	0.988360i	$-0.451385\pi$
$701$	8.05593			0.304268			0.152134	+	0.988360i	$0.451385\pi$
$702$	−10.5179	+	8.39101i	−0.396971	+	0.316698i
$703$	−3.12519	+	5.41299i	−0.117869	+	0.204155i
$704$	0.116709	+	0.0979308i	0.00439865	+	0.00369090i
$705$	23.4734	−	15.1629i	0.884060	−	0.571067i
$706$	4.38064	+	1.59442i	0.164868	+	0.0600069i
$707$	32.5824	+	17.2818i	1.22539	+	0.649951i
$708$	12.3078	−	16.2507i	0.462555	−	0.610738i
$709$	39.2685	+	32.9502i	1.47476	+	1.23747i	0.911573	+	0.411139i	$0.134869\pi$
$709$	39.2685	+	32.9502i	1.47476	+	1.23747i	0.563186	+	0.826330i	$0.309576\pi$
$710$	−0.931140	−	1.61278i	−0.0349450	−	0.0605266i
$711$	−15.1395	+	7.29320i	−0.567777	+	0.273517i
$712$	6.65955	−	11.5347i	0.249577	−	0.432281i
$713$	5.56648	+	4.67083i	0.208466	+	0.174924i
$714$	9.16246	−	0.788580i	0.342897	−	0.0295119i
$715$	−0.107617	−	0.610326i	−0.00402465	−	0.0228249i
$716$	7.36844	−	6.18285i	0.275371	−	0.231064i
$717$	−9.03195	+	29.2875i	−0.337304	+	1.09376i
$718$	−25.7249	+	9.36309i	−0.960044	+	0.349428i
$719$	−19.1886	+	33.2357i	−0.715616	+	1.23948i	0.247106	+	0.968989i	$0.420520\pi$
$719$	−19.1886	+	33.2357i	−0.715616	+	1.23948i	−0.962722	+	0.270494i	$0.912813\pi$
$720$	−1.93778	+	4.29602i	−0.0722167	+	0.160103i
$721$	−19.0223	+	24.3986i	−0.708427	+	0.908650i
$722$	−11.2459	+	4.09318i	−0.418530	+	0.152332i
$723$	−5.37763	+	7.10040i	−0.199996	+	0.264067i
$724$	−3.18063	−	18.0382i	−0.118207	−	0.670385i
$725$	1.21546	−	1.01989i	0.0451410	−	0.0378778i
$726$	16.9191	+	8.67256i	0.627927	+	0.321869i
$727$	−4.09252	+	23.2098i	−0.151783	+	0.860805i	0.809885	+	0.586589i	$0.199529\pi$
$727$	−4.09252	+	23.2098i	−0.151783	+	0.860805i	−0.961668	+	0.274216i	$0.911582\pi$
$728$	4.21234	−	5.40287i	0.156120	−	0.200244i
$729$	−25.7974	+	7.96829i	−0.955460	+	0.295122i
$730$	4.32379	+	7.48902i	0.160031	+	0.277181i
$731$	13.0912	+	10.9848i	0.484195	+	0.406288i
$732$	−0.376788	−	7.53997i	−0.0139265	−	0.278685i
$733$	−1.75312	−	9.94246i	−0.0647531	−	0.367233i	−0.999915	−	0.0130134i	$-0.995858\pi$
$733$	−1.75312	−	9.94246i	−0.0647531	−	0.367233i	0.935162	−	0.354220i	$-0.115254\pi$
$734$	13.3060	−	11.1650i	0.491132	−	0.412109i
$735$	−15.2159	+	11.4566i	−0.561246	+	0.422582i
$736$	1.68975	−	0.615018i	0.0622850	−	0.0226699i
$737$	−1.26807			−0.0467099
$738$	−10.3187	−	14.3485i	−0.379835	−	0.528175i
$739$	46.0792			1.69505			0.847526	−	0.530754i	$-0.178091\pi$
$739$	46.0792			1.69505			0.847526	+	0.530754i	$0.178091\pi$
$740$	−0.642965	+	3.64644i	−0.0236359	+	0.134046i
$741$	11.5951	−	2.64729i	0.425957	−	0.0972506i
$742$	3.44204	+	1.82567i	0.126361	+	0.0670225i
$743$	−6.26738	−	35.5441i	−0.229928	−	1.30399i	−0.853037	−	0.521851i	$-0.825242\pi$
$743$	−6.26738	−	35.5441i	−0.229928	−	1.30399i	0.623109	−	0.782135i	$-0.285869\pi$
$744$	−6.82366	+	1.55791i	−0.250167	+	0.0571159i
$745$	−12.8783	+	4.68733i	−0.471826	+	0.171731i
$746$	−20.2426			−0.741134
$747$	2.28180	−	30.5008i	0.0834867	−	1.11597i
$748$	0.152872	−	0.264781i	0.00558954	−	0.00968136i
$749$	−46.1296	+	9.85424i	−1.68554	+	0.360066i
$750$	−12.3737	+	16.3377i	−0.451823	+	0.596568i
$751$	18.9667	+	6.90332i	0.692105	+	0.251906i	0.664036	−	0.747700i	$-0.268842\pi$
$751$	18.9667	+	6.90332i	0.692105	+	0.251906i	0.0280686	+	0.999606i	$0.491064\pi$
$752$	7.86746	−	6.60158i	0.286897	−	0.240735i
$753$	−26.5856	−	13.6275i	−0.968835	−	0.496614i
$754$	−1.52470	+	0.554944i	−0.0555262	+	0.0202099i
$755$	−13.6375			−0.496321
$756$	11.8283	−	7.00657i	0.430190	−	0.254827i
$757$	9.27001			0.336924			0.168462	−	0.985708i	$-0.446120\pi$
$757$	9.27001			0.336924			0.168462	+	0.985708i	$0.446120\pi$
$758$	14.7628	−	5.37322i	0.536209	−	0.195164i
$759$	−0.398587	+	0.257471i	−0.0144678	+	0.00934561i
$760$	3.19128	−	2.67780i	0.115760	−	0.0971340i
$761$	−3.02722	−	1.10182i	−0.109737	−	0.0399408i	0.286568	−	0.958060i	$-0.407485\pi$
$761$	−3.02722	−	1.10182i	−0.109737	−	0.0399408i	−0.396305	+	0.918119i	$0.629708\pi$
$762$	−29.7260	−	3.72322i	−1.07686	−	0.134878i
$763$	−9.17937	−	10.1739i	−0.332315	−	0.368319i
$764$	−13.1325	+	22.7462i	−0.475118	+	0.822929i
$765$	9.16557	+	2.33259i	0.331382	+	0.0843351i
$766$	0.850070			0.0307143
$767$	−28.6381	+	10.4234i	−1.03406	+	0.376367i
$768$	−0.510425	+	1.65513i	−0.0184184	+	0.0597245i
$769$	5.35413	+	30.3648i	0.193075	+	1.09498i	0.915134	+	0.403151i	$0.132085\pi$
$769$	5.35413	+	30.3648i	0.193075	+	1.09498i	−0.722059	+	0.691832i	$0.756804\pi$
$770$	0.0227435	+	0.632821i	0.000819617	+	0.0228053i
$771$	−14.9606	−	16.1216i	−0.538792	−	0.580605i
$772$	−4.09213	+	23.2076i	−0.147279	+	0.835260i
$773$	−18.1850			−0.654070			−0.327035	−	0.945012i	$-0.606049\pi$
$773$	−18.1850			−0.654070			−0.327035	+	0.945012i	$0.606049\pi$
$774$	24.7579	+	6.30076i	0.889904	+	0.226476i
$775$	−10.2324			−0.367559
$776$	−16.6390	+	6.05611i	−0.597307	+	0.217402i
$777$	7.64827	−	7.62671i	0.274380	−	0.273607i
$778$	−5.91033	+	4.95936i	−0.211896	+	0.177802i
$779$	2.71283	+	15.3852i	0.0971972	+	0.551232i
$780$	5.91827	−	3.82296i	0.211908	−	0.136884i
$781$	0.138353	+	0.116092i	0.00495067	+	0.00415411i
$782$	−1.80431	−	3.12516i	−0.0645220	−	0.111755i
$783$	−3.25498	−	0.0805491i	−0.116323	−	0.00287859i
$784$	−5.02547	+	4.87285i	−0.179481	+	0.174030i
$785$	4.79863	−	27.2144i	0.171270	−	0.971322i
$786$	−17.6830	+	11.4225i	−0.630733	+	0.407428i
$787$	2.75271	−	2.30979i	0.0981234	−	0.0823353i	−0.592406	−	0.805639i	$-0.701822\pi$
$787$	2.75271	−	2.30979i	0.0981234	−	0.0823353i	0.690530	+	0.723304i	$0.257378\pi$
$788$	−1.28721	−	7.30016i	−0.0458551	−	0.260057i
$789$	−50.1255	−	6.27829i	−1.78452	−	0.223513i
$790$	8.26903	−	3.00968i	0.294199	−	0.107080i
$791$	13.0861	+	32.2947i	0.465289	+	1.14827i
$792$	0.0340978	−	0.455786i	0.00121161	−	0.0161956i
$793$	−5.64312	+	9.77417i	−0.200393	+	0.347091i
$794$	8.87741	−	3.23111i	0.315047	−	0.114668i
$795$	2.72563	+	2.93715i	0.0966682	+	0.104170i
$796$	9.59711	−	8.05293i	0.340161	−	0.285429i
$797$	6.35445	+	36.0379i	0.225086	+	1.27653i	0.862521	+	0.506022i	$0.168885\pi$
$797$	6.35445	+	36.0379i	0.225086	+	1.27653i	−0.637435	+	0.770504i	$0.720004\pi$
$798$	−12.1076	+	1.04205i	−0.428603	+	0.0368883i
$799$	−15.7885	−	13.2481i	−0.558555	−	0.468684i
$800$	−1.26607	+	2.19289i	−0.0447623	+	0.0775305i
$801$	−39.7583	+	3.98355i	−1.40479	+	0.140752i
$802$	18.3710	+	31.8195i	0.648703	+	1.12359i
$803$	−0.642450	−	0.539080i	−0.0226716	−	0.0190237i
$804$	−5.60061	−	13.2838i	−0.197518	−	0.468485i
$805$	6.60261	+	3.50206i	0.232711	+	0.123431i
$806$	9.83274	+	3.57883i	0.346344	+	0.126059i
$807$	14.6631	+	7.51617i	0.516167	+	0.264582i
$808$	10.6787	+	8.96049i	0.375675	+	0.315229i
$809$	−4.17719	+	7.23511i	−0.146862	+	0.254373i	−0.930066	−	0.367392i	$-0.880251\pi$
$809$	−4.17719	+	7.23511i	−0.146862	+	0.254373i	0.783204	+	0.621765i	$0.213584\pi$
$810$	13.8574	−	2.80503i	0.486901	−	0.0985588i
$811$	−39.1589			−1.37505			−0.687527	−	0.726159i	$-0.741304\pi$
$811$	−39.1589			−1.37505			−0.687527	+	0.726159i	$0.741304\pi$
$812$	1.62128	−	0.346339i	0.0568958	−	0.0121541i
$813$	27.8229	−	17.9724i	0.975790	−	0.630320i
$814$	−0.0623560	−	0.353639i	−0.00218558	−	0.0123950i
$815$	3.09717	+	17.5649i	0.108489	+	0.615273i
$816$	3.44894	+	0.431984i	0.120737	+	0.0151225i
$817$	−17.2991	−	14.5157i	−0.605219	−	0.507839i
$818$	9.08669	−	15.7386i	0.317709	−	0.550288i
$819$	−20.5373	−	0.796168i	−0.717630	−	0.0278204i
$820$	4.62735	+	8.01481i	0.161594	+	0.279889i
$821$	8.42976	−	47.8075i	0.294201	−	1.66849i	−0.376233	−	0.926525i	$-0.622781\pi$
$821$	8.42976	−	47.8075i	0.294201	−	1.66849i	0.670434	−	0.741969i	$-0.266108\pi$
$822$	−6.26311	+	20.3091i	−0.218451	+	0.708362i
$823$	−22.2324	−	8.09193i	−0.774973	−	0.282067i	−0.0758980	−	0.997116i	$-0.524182\pi$
$823$	−22.2324	−	8.09193i	−0.774973	−	0.282067i	−0.699075	+	0.715049i	$0.746405\pi$
$824$	−8.95761	+	7.51633i	−0.312053	+	0.261844i
$825$	0.196911	−	0.638516i	0.00685557	−	0.0222303i
$826$	30.4522	−	6.50521i	1.05957	−	0.226345i
$827$	10.7534	+	18.6254i	0.373931	+	0.647667i	0.990166	−	0.139895i	$-0.0446764\pi$
$827$	10.7534	+	18.6254i	0.373931	+	0.647667i	−0.616236	+	0.787562i	$0.711343\pi$
$828$	−4.45760	−	3.03831i	−0.154912	−	0.105588i
$829$	6.70362	+	11.6110i	0.232826	+	0.403267i	0.958639	−	0.284626i	$-0.0918693\pi$
$829$	6.70362	+	11.6110i	0.232826	+	0.403267i	−0.725812	+	0.687893i	$0.758536\pi$
$830$	−2.78121	+	15.7730i	−0.0965371	+	0.547489i
$831$	−20.5113	−	2.56907i	−0.711531	−	0.0891201i
$832$	1.98359	−	1.66443i	0.0687687	−	0.0577038i
$833$	11.3816	+	8.23384i	0.394348	+	0.285286i
$834$	0.813437	+	16.2778i	0.0281670	+	0.563655i
$835$	−5.23090	+	1.90389i	−0.181023	+	0.0658869i
$836$	−0.202009	+	0.349890i	−0.00698664	+	0.0121012i
$837$	15.7464	+	13.8909i	0.544274	+	0.480139i
$838$	−12.4275	−	21.5250i	−0.429300	−	0.743570i
$839$	−4.79363	+	27.1860i	−0.165495	+	0.938566i	0.783058	+	0.621948i	$0.213659\pi$
$839$	−4.79363	+	27.1860i	−0.165495	+	0.938566i	−0.948553	+	0.316618i	$0.897453\pi$
$840$	−6.52877	+	3.03320i	−0.225264	+	0.104655i
$841$	26.8821	+	9.78429i	0.926970	+	0.337389i
$842$	23.5934	+	8.58729i	0.813082	+	0.295938i
$843$	12.7542	−	16.8401i	0.439276	−	0.580002i
$844$	2.42026	−	13.7260i	0.0833087	−	0.472467i
$845$	9.88913			0.340197
$846$	−29.8589	−	7.59895i	−1.02657	−	0.261257i
$847$	10.9067	+	26.9161i	0.374758	+	0.924846i
$848$	1.12811	+	0.946595i	0.0387394	+	0.0325062i
$849$	14.7812	−	47.9305i	0.507290	−	1.64497i
$850$	4.77505	+	1.73798i	0.163783	+	0.0596121i
$851$	−3.98271	−	1.44959i	−0.136526	−	0.0496912i
$852$	−0.605085	+	1.96208i	−0.0207299	+	0.0672198i
$853$	−2.90805	−	2.44014i	−0.0995696	−	0.0835489i	0.591644	−	0.806199i	$-0.298479\pi$
$853$	−2.90805	−	2.44014i	−0.0995696	−	0.0835489i	−0.691214	+	0.722651i	$0.742924\pi$
$854$	7.09048	−	9.09446i	0.242631	−	0.311206i
$855$	−12.1117	−	3.08236i	−0.414211	−	0.105415i
$856$	−17.8287			−0.609374
$857$	0.460387	−	2.61099i	0.0157265	−	0.0891896i	−0.975934	−	0.218065i	$-0.930026\pi$
$857$	0.460387	−	2.61099i	0.0157265	−	0.0891896i	0.991661	+	0.128875i	$0.0411367\pi$
$858$	−0.412544	+	0.544706i	−0.0140840	+	0.0185960i
$859$	6.69714	+	2.43756i	0.228504	+	0.0831685i	0.453735	−	0.891137i	$-0.350091\pi$
$859$	6.69714	+	2.43756i	0.228504	+	0.0831685i	−0.225231	+	0.974305i	$0.572314\pi$
$860$	−12.5709	−	4.57543i	−0.428664	−	0.156021i
$861$	2.39089	−	26.8907i	0.0814812	−	0.916432i
$862$	−2.10578	+	11.9425i	−0.0717231	+	0.406762i
$863$	−10.9851	−	19.0268i	−0.373939	−	0.647680i	0.616229	−	0.787567i	$-0.288660\pi$
$863$	−10.9851	−	19.0268i	−0.373939	−	0.647680i	−0.990168	+	0.139887i	$0.955326\pi$
$864$	4.92526	−	1.65585i	0.167561	−	0.0563332i
$865$	3.28190	−	5.68442i	0.111588	−	0.193276i
$866$	−31.6107	+	11.5053i	−1.07417	+	0.390967i
$867$	1.12144	+	22.4414i	0.0380862	+	0.762151i
$868$	−9.44516	−	5.00975i	−0.320589	−	0.170042i
$869$	−0.653753	+	0.548564i	−0.0221771	+	0.0186088i
$870$	1.69176	+	0.211896i	0.0573562	+	0.00718394i
$871$	−3.74248	+	21.2247i	−0.126809	+	0.719170i
$872$	−2.58960	−	4.48532i	−0.0876949	−	0.151892i
$873$	43.8942	+	29.9183i	1.48559	+	1.01258i
$874$	2.38427	+	4.12968i	0.0806493	+	0.139689i
$875$	−30.6153	+	6.54005i	−1.03498	+	0.221094i
$876$	2.80974	−	9.11102i	0.0949323	−	0.307833i
$877$	11.7653	−	9.87226i	0.397286	−	0.333362i	−0.422158	−	0.906522i	$-0.638727\pi$
$877$	11.7653	−	9.87226i	0.397286	−	0.333362i	0.819443	+	0.573160i	$0.194283\pi$
$878$	2.25668	+	0.821363i	0.0761592	+	0.0277197i
$879$	−4.55899	+	14.7832i	−0.153771	+	0.498626i
$880$	−0.0415607	+	0.235702i	−0.00140101	+	0.00794552i
$881$	21.0821	+	36.5153i	0.710274	+	1.23023i	0.964754	+	0.263153i	$0.0847623\pi$
$881$	21.0821	+	36.5153i	0.710274	+	1.23023i	−0.254480	+	0.967078i	$0.581904\pi$
$882$	20.6706	+	3.70498i	0.696015	+	0.124753i
$883$	−17.7835	+	30.8019i	−0.598463	+	1.03657i	0.394585	+	0.918859i	$0.370888\pi$
$883$	−17.7835	+	30.8019i	−0.598463	+	1.03657i	−0.993048	+	0.117709i	$0.962445\pi$
$884$	−3.98068	−	3.34019i	−0.133885	−	0.112343i
$885$	31.7761	+	3.98000i	1.06814	+	0.133786i
$886$	−3.04937	−	17.2938i	−0.102446	−	0.580998i
$887$	−5.46247	−	30.9792i	−0.183412	−	1.04018i	−0.927979	−	0.372633i	$-0.878455\pi$
$887$	−5.46247	−	30.9792i	−0.183412	−	1.04018i	0.744567	−	0.667548i	$-0.232656\pi$
$888$	3.42919	−	2.21512i	0.115076	−	0.0743345i
$889$	−30.6553	−	33.9766i	−1.02815	−	1.13954i
$890$	20.9236			0.701360
$891$	−1.16983	+	0.715280i	−0.0391908	+	0.0239628i
$892$	−11.7789	+	20.4017i	−0.394388	+	0.683100i
$893$	20.8634	+	17.5064i	0.698166	+	0.585831i
$894$	13.4467	+	6.89264i	0.449725	+	0.230524i
$895$	14.1993	+	5.16813i	0.474631	+	0.172752i
$896$	−2.24230	+	1.40432i	−0.0749099	+	0.0469150i
$897$	3.13314	+	7.43135i	0.104612	+	0.248126i
$898$	20.3410	+	17.0681i	0.678788	+	0.569571i
$899$	1.26607	+	2.19291i	0.0422260	+	0.0731375i
$900$	7.55856	−	0.757325i	0.251952	−	0.0252442i
$901$	1.47765	−	2.55937i	0.0492277	−	0.0852648i
$902$	−0.687556	−	0.576928i	−0.0228931	−	0.0192096i
$903$	22.3380	+	31.9980i	0.743362	+	1.06483i
$904$	2.28699	+	12.9702i	0.0760643	+	0.431382i
$905$	22.0423	−	18.4957i	0.732711	−	0.614817i
$906$	10.2279	+	11.0216i	0.339798	+	0.366169i
$907$	15.2400	−	5.54689i	0.506034	−	0.184181i	−0.0763718	−	0.997079i	$-0.524334\pi$
$907$	15.2400	−	5.54689i	0.506034	−	0.184181i	0.582406	+	0.812898i	$0.302111\pi$
$908$	7.94285	−	13.7574i	0.263593	−	0.456556i
$909$	3.11989	−	41.7036i	0.103480	−	1.38322i
$910$	10.6592	+	1.48699i	0.353348	+	0.0492931i
$911$	18.9350	−	6.89179i	0.627346	−	0.228335i	−0.00872984	−	0.999962i	$-0.502779\pi$
$911$	18.9350	−	6.89179i	0.627346	−	0.228335i	0.636076	+	0.771627i	$0.280557\pi$
$912$	−4.55754	−	0.570838i	−0.150915	−	0.0189023i
$913$	−0.269727	−	1.52970i	−0.00892666	−	0.0506256i
$914$	15.0934	−	12.6649i	0.499245	−	0.418916i
$915$	9.96200	−	6.43505i	0.329334	−	0.212736i
$916$	−3.09572	+	17.5567i	−0.102285	+	0.580090i
$917$	−31.8482	−	4.44292i	−1.05172	−	0.146718i
$918$	−4.98883	−	9.15684i	−0.164656	−	0.302221i
$919$	−2.97492	−	5.15271i	−0.0981335	−	0.169972i	0.812779	−	0.582573i	$-0.197954\pi$
$919$	−2.97492	−	5.15271i	−0.0981335	−	0.169972i	−0.910912	+	0.412601i	$0.864621\pi$
$920$	2.16397	+	1.81579i	0.0713439	+	0.0598647i
$921$	−16.9092	+	10.9227i	−0.557178	+	0.359914i
$922$	2.01136	+	11.4070i	0.0662406	+	0.375669i
$923$	2.35145	−	1.97310i	0.0773991	−	0.0649455i
$924$	0.494377	−	0.492983i	0.0162638	−	0.0162180i
$925$	5.60828	−	2.04125i	0.184399	−	0.0671157i
$926$	−24.7741			−0.814126
$927$	33.9963	+	8.65190i	1.11659	+	0.284166i
$928$	0.626612			0.0205696
$929$	−5.01283	+	28.4292i	−0.164466	+	0.932731i	0.785148	+	0.619308i	$0.212587\pi$
$929$	−5.01283	+	28.4292i	−0.164466	+	0.932731i	−0.949614	+	0.313423i	$0.898524\pi$
$930$	−7.47930	−	8.05973i	−0.245256	−	0.264289i
$931$	−15.0399	−	10.8805i	−0.492914	−	0.356593i
$932$	−0.616700	−	3.49748i	−0.0202007	−	0.114564i
$933$	−8.56876	+	27.7856i	−0.280529	+	0.909658i
$934$	−18.0374	+	6.56506i	−0.590200	+	0.214815i
$935$	0.480305			0.0157077
$936$	−7.52822	−	1.91589i	−0.246068	−	0.0626230i
$937$	20.9444	−	36.2767i	0.684222	−	1.18511i	−0.289458	−	0.957191i	$-0.593475\pi$
$937$	20.9444	−	36.2767i	0.684222	−	1.18511i	0.973681	−	0.227917i	$-0.0731914\pi$
$938$	6.78359	−	20.9503i	0.221492	−	0.684050i
$939$	40.2212	+	5.03775i	1.31257	+	0.164401i
$940$	15.1610	+	5.51814i	0.494496	+	0.179982i
$941$	11.1086	−	9.32120i	0.362129	−	0.303862i	−0.443510	−	0.896270i	$-0.646267\pi$
$941$	11.1086	−	9.32120i	0.362129	−	0.303862i	0.805639	+	0.592407i	$0.201822\pi$
$942$	−25.5930	+	16.5320i	−0.833866	+	0.538643i
$943$	−9.95461	+	3.62318i	−0.324167	+	0.117987i
$944$	11.7695			0.383066
$945$	18.8231	+	10.5886i	0.612314	+	0.344448i
$946$	1.29739			0.0421819
$947$	38.8662	−	14.1462i	1.26298	−	0.459688i	0.378214	−	0.925718i	$-0.376538\pi$
$947$	38.8662	−	14.1462i	1.26298	−	0.459688i	0.884769	+	0.466030i	$0.154316\pi$
$948$	−8.63397	−	4.42568i	−0.280418	−	0.143739i
$949$	−10.9191	+	9.16220i	−0.354449	+	0.297418i
$950$	−6.30990	−	2.29662i	−0.204720	−	0.0745121i
$951$	−5.48954	+	7.24817i	−0.178011	+	0.235038i
$952$	3.55677	+	3.94211i	0.115275	+	0.127765i
$953$	25.2418	−	43.7201i	0.817662	−	1.41623i	−0.0897391	−	0.995965i	$-0.528603\pi$
$953$	25.2418	−	43.7201i	0.817662	−	1.41623i	0.907401	−	0.420266i	$-0.138063\pi$
$954$	0.329588	−	4.40561i	0.0106708	−	0.142637i
$955$	−41.2609			−1.33517
$956$	−16.6278	+	6.05203i	−0.537782	+	0.195737i
$957$	−0.161205	+	0.0368047i	−0.00521100	+	0.00118973i
$958$	4.42645	+	25.1037i	0.143012	+	0.811062i
$959$	−27.5138	+	17.2315i	−0.888468	+	0.556435i
$960$	−2.65270	+	0.605639i	−0.0856154	+	0.0195469i
$961$	−2.54745	+	14.4473i	−0.0821759	+	0.466043i
$962$	−6.10316			−0.196774
$963$	31.2278	+	43.4235i	1.00630	+	1.39930i
$964$	−5.14245			−0.165627
$965$	−34.7877	+	12.6617i	−1.11985	+	0.407594i
$966$	−2.12152	−	7.96258i	−0.0682589	−	0.256192i
$967$	28.8985	−	24.2488i	0.929314	−	0.779787i	−0.0463799	−	0.998924i	$-0.514768\pi$
$967$	28.8985	−	24.2488i	0.929314	−	0.779787i	0.975694	+	0.219137i	$0.0703240\pi$
$968$	1.90610	+	10.8100i	0.0612644	+	0.347447i
$969$	0.460046	+	9.20606i	0.0147788	+	0.295741i
$970$	−21.3087	−	17.8801i	−0.684181	−	0.574096i
$971$	−4.61657	−	7.99613i	−0.148153	−	0.256608i	0.782392	−	0.622786i	$-0.213999\pi$
$971$	−4.61657	−	7.99613i	−0.148153	−	0.256608i	−0.930545	+	0.366178i	$0.880666\pi$
$972$	−12.6598	−	9.09562i	−0.406062	−	0.291742i
$973$	−15.3074	+	19.6338i	−0.490734	+	0.629430i
$974$	4.12768	−	23.4092i	0.132259	−	0.750080i
$975$	−10.1062	−	5.18033i	−0.323657	−	0.165903i
$976$	3.33891	−	2.80168i	0.106876	−	0.0896795i
$977$	−6.58710	−	37.3573i	−0.210740	−	1.19517i	−0.888147	−	0.459559i	$-0.848008\pi$
$977$	−6.58710	−	37.3573i	−0.210740	−	1.19517i	0.677407	−	0.735608i	$-0.263104\pi$
$978$	11.8728	−	15.6764i	0.379652	−	0.501276i
$979$	−1.90683	+	0.694030i	−0.0609426	+	0.0221813i
$980$	−10.5768	−	3.00955i	−0.337862	−	0.0961366i
$981$	−6.38860	+	14.1634i	−0.203972	+	0.452203i
$982$	−9.76707	+	16.9171i	−0.311680	+	0.539845i
$983$	28.2811	−	10.2935i	0.902028	−	0.328311i	0.150963	−	0.988539i	$-0.451763\pi$
$983$	28.2811	−	10.2935i	0.902028	−	0.328311i	0.751065	+	0.660228i	$0.229540\pi$
$984$	3.00701	−	9.75069i	0.0958598	−	0.310841i
$985$	8.92062	−	7.48529i	0.284235	−	0.238501i
$986$	−0.218361	−	1.23838i	−0.00695402	−	0.0394382i
$987$	−26.9404	−	38.5908i	−0.857524	−	1.22836i
$988$	5.26020	+	4.41383i	0.167349	+	0.140423i
$989$	7.65643	−	13.2613i	0.243460	−	0.421686i
$990$	0.646869	−	0.311618i	0.0205589	−	0.00990386i
$991$	3.36568	+	5.82952i	0.106914	+	0.185181i	0.914519	−	0.404544i	$-0.132570\pi$
$991$	3.36568	+	5.82952i	0.106914	+	0.185181i	−0.807604	+	0.589725i	$0.799236\pi$
$992$	−3.09560	−	2.59751i	−0.0982853	−	0.0824712i
$993$	26.1037	−	34.4663i	0.828376	−	1.09375i
$994$	−2.65814	+	1.66475i	−0.0843110	+	0.0528027i
$995$	18.4941	+	6.73130i	0.586302	+	0.213397i
$996$	14.8333	−	9.58171i	0.470011	−	0.303608i
$997$	0.907844	+	0.761771i	0.0287517	+	0.0241255i	0.657050	−	0.753847i	$-0.271804\pi$
$997$	0.907844	+	0.761771i	0.0287517	+	0.0241255i	−0.628299	+	0.777972i	$0.716248\pi$
$998$	18.0011	−	31.1788i	0.569815	−	0.986949i
$999$	−11.4015	−	4.47223i	−0.360727	−	0.141495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.w.b.25.7	yes	72
7.2	even	3		378.2.v.a.79.10	yes	72
27.13	even	9		378.2.v.a.67.10	✓	72
189.121	even	9	inner	378.2.w.b.121.7	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.67.10	✓	72	27.13	even	9
378.2.v.a.79.10	yes	72	7.2	even	3
378.2.w.b.25.7	yes	72	1.1	even	1	trivial
378.2.w.b.121.7	yes	72	189.121	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(-0.0864462 - 1.72989i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.47620 + 0.537294i) q^{5} +(-0.672891 - 1.59600i) q^{6} +(0.815021 - 2.51709i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.98505 + 0.299085i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(-0.0864462 - 1.72989i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.47620 + 0.537294i) q^{5} +(-0.672891 - 1.59600i) q^{6} +(0.815021 - 2.51709i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.98505 + 0.299085i) q^{9} +1.57094 q^{10} +(-0.143165 + 0.0521079i) q^{11} +(-1.17817 - 1.26961i) q^{12} +(0.449644 + 2.55006i) q^{13} +(-0.0950264 - 2.64404i) q^{14} +(0.801849 - 2.60012i) q^{15} +(0.173648 - 0.984808i) q^{16} -2.00680 q^{17} +(-2.70274 + 1.30200i) q^{18} +2.65186 q^{19} +(1.47620 - 0.537294i) q^{20} +(-4.42475 - 1.19231i) q^{21} +(-0.116709 + 0.0979308i) q^{22} +(0.312253 + 1.77087i) q^{23} +(-1.54135 - 0.790081i) q^{24} +(-1.93973 - 1.62763i) q^{25} +(1.29470 + 2.24248i) q^{26} +(0.775432 + 5.13797i) q^{27} +(-0.993612 - 2.45209i) q^{28} +(-0.108810 + 0.617093i) q^{29} +(-0.135802 - 2.71756i) q^{30} +(3.09560 - 2.59751i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.102517 + 0.243156i) q^{33} +(-1.88578 + 0.686368i) q^{34} +(2.55556 - 3.27783i) q^{35} +(-2.09444 + 2.14787i) q^{36} +(-1.17849 + 2.04121i) q^{37} +(2.49193 - 0.906988i) q^{38} +(4.37245 - 0.998278i) q^{39} +(1.20341 - 1.00978i) q^{40} +(1.02299 + 5.80168i) q^{41} +(-4.56570 + 0.392953i) q^{42} +(-6.52340 - 5.47378i) q^{43} +(-0.0761766 + 0.131942i) q^{44} +(-4.56725 - 1.16234i) q^{45} +(0.899097 + 1.55728i) q^{46} +(7.86746 + 6.60158i) q^{47} +(-1.71862 - 0.215260i) q^{48} +(-5.67148 - 4.10296i) q^{49} +(-2.37943 - 0.866042i) q^{50} +(0.173481 + 3.47156i) q^{51} +(1.98359 + 1.66443i) q^{52} +(-0.736320 + 1.27534i) q^{53} +(2.48596 + 4.56290i) q^{54} -0.239338 q^{55} +(-1.77235 - 1.96437i) q^{56} +(-0.229243 - 4.58742i) q^{57} +(0.108810 + 0.617093i) q^{58} +(2.04376 + 11.5907i) q^{59} +(-1.05707 - 2.50723i) q^{60} +(3.33891 + 2.80168i) q^{61} +(2.02051 - 3.49962i) q^{62} +(-1.68006 + 7.75741i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.706365 + 4.00600i) q^{65} +(0.179499 + 0.193429i) q^{66} +(7.82126 + 2.84670i) q^{67} +(-1.53730 + 1.28995i) q^{68} +(3.03643 - 0.693250i) q^{69} +(1.28035 - 3.95421i) q^{70} +(-0.592726 - 1.02663i) q^{71} +(-1.23351 + 2.73468i) q^{72} +(2.75235 + 4.76721i) q^{73} +(-0.409286 + 2.32118i) q^{74} +(-2.64794 + 3.49622i) q^{75} +(2.03144 - 1.70458i) q^{76} +(0.0144776 + 0.402829i) q^{77} +(3.76733 - 2.43354i) q^{78} +(5.26374 - 1.91584i) q^{79} +(0.785472 - 1.36048i) q^{80} +(8.82110 - 1.78557i) q^{81} +(2.94559 + 5.10191i) q^{82} +(-1.77041 + 10.0405i) q^{83} +(-4.15595 + 1.93082i) q^{84} +(-2.96245 - 1.07824i) q^{85} +(-8.00213 - 2.91254i) q^{86} +(1.07691 + 0.134884i) q^{87} +(-0.0264559 + 0.150039i) q^{88} +13.3191 q^{89} +(-4.68935 + 0.469846i) q^{90} +(6.78519 + 0.946556i) q^{91} +(1.37750 + 1.15586i) q^{92} +(-4.76102 - 5.13050i) q^{93} +(9.65087 + 3.51263i) q^{94} +(3.91468 + 1.42483i) q^{95} +(-1.68860 + 0.385526i) q^{96} +(-13.5643 - 11.3818i) q^{97} +(-6.73275 - 1.91576i) q^{98} +(0.411771 - 0.198363i) 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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