LMFDB - Embedded newform 387.2.y.c.253.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(10,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("387.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.y (of order $21$, degree $12$, 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:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 43)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			253.3
Character	$\chi$	$=$	387.253
Dual form			387.2.y.c.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.515822 - 2.25996i) q^{2} +(-3.03942 - 1.46371i) q^{4} +(1.48781 + 3.79089i) q^{5} +(1.38920 + 2.40617i) q^{7} +(-1.98513 + 2.48927i) q^{8} +O(q^{10})$	\(q+(0.515822 - 2.25996i) q^{2} +(-3.03942 - 1.46371i) q^{4} +(1.48781 + 3.79089i) q^{5} +(1.38920 + 2.40617i) q^{7} +(-1.98513 + 2.48927i) q^{8} +(9.33472 - 1.40698i) q^{10} +(0.678323 - 0.326663i) q^{11} +(1.70167 + 0.256486i) q^{13} +(6.15444 - 1.89839i) q^{14} +(0.394993 + 0.495306i) q^{16} +(1.18750 - 3.02571i) q^{17} +(-0.0395049 + 0.0269340i) q^{19} +(1.02666 - 13.6998i) q^{20} +(-0.388353 - 1.70148i) q^{22} +(-0.152371 + 2.03326i) q^{23} +(-8.49199 + 7.87942i) q^{25} +(1.45741 - 3.71341i) q^{26} +(-0.700443 - 9.34676i) q^{28} +(-0.714324 + 0.220340i) q^{29} +(2.52247 + 2.34051i) q^{31} +(-4.41406 + 2.12570i) q^{32} +(-6.22544 - 4.24444i) q^{34} +(-7.05465 + 8.84626i) q^{35} +(3.91502 - 6.78101i) q^{37} +(0.0404923 + 0.103173i) q^{38} +(-12.3900 - 3.82182i) q^{40} +(1.86928 - 8.18985i) q^{41} +(-4.39142 + 4.86985i) q^{43} -2.53985 q^{44} +(4.51649 + 1.39315i) q^{46} +(-7.05780 - 3.39886i) q^{47} +(-0.359777 + 0.623151i) q^{49} +(13.4268 + 23.2560i) q^{50} +(-4.79668 - 3.27032i) q^{52} +(1.76849 - 0.266557i) q^{53} +(2.24756 + 2.08543i) q^{55} +(-8.74735 - 1.31845i) q^{56} +(0.129496 + 1.72800i) q^{58} +(-3.60798 - 4.52427i) q^{59} +(2.15836 - 2.00266i) q^{61} +(6.59062 - 4.49341i) q^{62} +(2.80908 + 12.3074i) q^{64} +(1.55946 + 6.83245i) q^{65} +(4.62708 - 3.15469i) q^{67} +(-8.03807 + 7.45824i) q^{68} +(16.3533 + 20.5063i) q^{70} +(0.543672 + 7.25480i) q^{71} +(-10.0746 - 1.51850i) q^{73} +(-13.3054 - 12.3456i) q^{74} +(0.159495 - 0.0240401i) q^{76} +(1.72834 + 1.17836i) q^{77} +(-6.70519 - 11.6137i) q^{79} +(-1.28997 + 2.23430i) q^{80} +(-17.5445 - 8.44900i) q^{82} +(-5.42706 - 1.67402i) q^{83} +13.2369 q^{85} +(8.74049 + 12.4364i) q^{86} +(-0.533404 + 2.33699i) q^{88} +(11.7786 + 3.63323i) q^{89} +(1.74682 + 4.45083i) q^{91} +(3.43922 - 5.95690i) q^{92} +(-11.3219 + 14.1972i) q^{94} +(-0.160880 - 0.109686i) q^{95} +(9.41101 - 4.53210i) q^{97} +(1.22272 + 1.13452i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{2}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	0.515822	−	2.25996i	0.364741	−	1.59803i	−0.376249	−	0.926519i	$-0.622786\pi$
$2$	0.515822	−	2.25996i	0.364741	−	1.59803i	0.740990	−	0.671516i	$-0.234357\pi$
$3$		0			0
$3$		0			0
$4$	−3.03942	−	1.46371i	−1.51971	−	0.731854i
$5$	1.48781	+	3.79089i	0.665371	+	1.69534i	0.717372	+	0.696690i	$0.245345\pi$
$5$	1.48781	+	3.79089i	0.665371	+	1.69534i	−0.0520012	+	0.998647i	$0.516560\pi$
$6$		0			0
$7$	1.38920	+	2.40617i	0.525070	+	0.909448i	0.999574	+	0.0291942i	$0.00929413\pi$
$7$	1.38920	+	2.40617i	0.525070	+	0.909448i	−0.474504	+	0.880253i	$0.657373\pi$
$8$	−1.98513	+	2.48927i	−0.701848	+	0.880089i
$9$		0			0
$10$	9.33472	−	1.40698i	2.95190	−	0.444927i
$11$	0.678323	−	0.326663i	0.204522	−	0.0984926i	−0.328819	−	0.944393i	$-0.606651\pi$
$11$	0.678323	−	0.326663i	0.204522	−	0.0984926i	0.533341	+	0.845900i	$0.320936\pi$
$12$		0			0
$13$	1.70167	+	0.256486i	0.471959	+	0.0711364i	0.380715	−	0.924692i	$-0.375678\pi$
$13$	1.70167	+	0.256486i	0.471959	+	0.0711364i	0.0912435	+	0.995829i	$0.470916\pi$
$14$	6.15444	−	1.89839i	1.64484	−	0.507367i
$15$		0			0
$16$	0.394993	+	0.495306i	0.0987483	+	0.123826i
$17$	1.18750	−	3.02571i	0.288012	−	0.733842i	−0.711503	−	0.702683i	$-0.751985\pi$
$17$	1.18750	−	3.02571i	0.288012	−	0.733842i	0.999514	−	0.0311584i	$-0.00991962\pi$
$18$		0			0
$19$	−0.0395049	+	0.0269340i	−0.00906304	+	0.00617908i	−0.567843	−	0.823137i	$-0.692222\pi$
$19$	−0.0395049	+	0.0269340i	−0.00906304	+	0.00617908i	0.558780	+	0.829316i	$0.311270\pi$
$20$	1.02666	−	13.6998i	0.229568	−	3.06338i
$21$		0			0
$22$	−0.388353	−	1.70148i	−0.0827971	−	0.362758i
$23$	−0.152371	+	2.03326i	−0.0317717	+	0.423963i	0.958526	+	0.285004i	$0.0919948\pi$
$23$	−0.152371	+	2.03326i	−0.0317717	+	0.423963i	−0.990298	+	0.138960i	$0.955624\pi$
$24$		0			0
$25$	−8.49199	+	7.87942i	−1.69840	+	1.57588i
$26$	1.45741	−	3.71341i	0.285821	−	0.728260i
$27$		0			0
$28$	−0.700443	−	9.34676i	−0.132371	−	1.76637i
$29$	−0.714324	+	0.220340i	−0.132647	+	0.0409161i	−0.360368	−	0.932810i	$-0.617349\pi$
$29$	−0.714324	+	0.220340i	−0.132647	+	0.0409161i	0.227721	+	0.973726i	$0.426873\pi$
$30$		0			0
$31$	2.52247	+	2.34051i	0.453050	+	0.420369i	0.873408	−	0.486990i	$-0.161905\pi$
$31$	2.52247	+	2.34051i	0.453050	+	0.420369i	−0.420358	+	0.907358i	$0.638096\pi$
$32$	−4.41406	+	2.12570i	−0.780303	+	0.375774i
$33$		0			0
$34$	−6.22544	−	4.24444i	−1.06765	−	0.727915i
$35$	−7.05465	+	8.84626i	−1.19245	+	1.49529i
$36$		0			0
$37$	3.91502	−	6.78101i	0.643625	−	1.11479i	−0.340992	−	0.940066i	$-0.610763\pi$
$37$	3.91502	−	6.78101i	0.643625	−	1.11479i	0.984617	−	0.174725i	$-0.0559037\pi$
$38$	0.0404923	+	0.103173i	0.00656872	+	0.0167368i
$39$		0			0
$40$	−12.3900	−	3.82182i	−1.95904	−	0.604283i
$41$	1.86928	−	8.18985i	0.291932	−	1.27904i	−0.589900	−	0.807476i	$-0.700833\pi$
$41$	1.86928	−	8.18985i	0.291932	−	1.27904i	0.881832	−	0.471563i	$-0.156310\pi$
$42$		0			0
$43$	−4.39142	+	4.86985i	−0.669685	+	0.742645i
$43$	−4.39142	+	4.86985i	−0.669685	+	0.742645i
$44$	−2.53985			−0.382897
$45$		0			0
$46$	4.51649	+	1.39315i	0.665920	+	0.205409i
$47$	−7.05780	−	3.39886i	−1.02949	−	0.495775i	−0.158644	−	0.987336i	$-0.550712\pi$
$47$	−7.05780	−	3.39886i	−1.02949	−	0.495775i	−0.870843	+	0.491561i	$0.836426\pi$
$48$		0			0
$49$	−0.359777	+	0.623151i	−0.0513966	+	0.0890216i
$50$	13.4268	+	23.2560i	1.89884	+	3.28889i
$51$		0			0
$52$	−4.79668	−	3.27032i	−0.665180	−	0.453512i
$53$	1.76849	−	0.266557i	0.242920	−	0.0366144i	−0.0264535	−	0.999650i	$-0.508421\pi$
$53$	1.76849	−	0.266557i	0.242920	−	0.0366144i	0.269374	+	0.963036i	$0.413183\pi$
$54$		0			0
$55$	2.24756	+	2.08543i	0.303061	+	0.281200i
$56$	−8.74735	−	1.31845i	−1.16891	−	0.176185i
$57$		0			0
$58$	0.129496	+	1.72800i	0.0170036	+	0.226898i
$59$	−3.60798	−	4.52427i	−0.469719	−	0.589009i	0.489383	−	0.872069i	$-0.337222\pi$
$59$	−3.60798	−	4.52427i	−0.469719	−	0.589009i	−0.959102	+	0.283060i	$0.908651\pi$
$60$		0			0
$61$	2.15836	−	2.00266i	0.276349	−	0.256415i	−0.529806	−	0.848119i	$-0.677735\pi$
$61$	2.15836	−	2.00266i	0.276349	−	0.256415i	0.806155	+	0.591704i	$0.201545\pi$
$62$	6.59062	−	4.49341i	0.837010	−	0.570663i
$63$		0			0
$64$	2.80908	+	12.3074i	0.351134	+	1.53842i
$65$	1.55946	+	6.83245i	0.193428	+	0.847462i
$66$		0			0
$67$	4.62708	−	3.15469i	0.565288	−	0.385407i	−0.246691	−	0.969094i	$-0.579343\pi$
$67$	4.62708	−	3.15469i	0.565288	−	0.385407i	0.811978	+	0.583688i	$0.198391\pi$
$68$	−8.03807	+	7.45824i	−0.974759	+	0.904445i
$69$		0			0
$70$	16.3533	+	20.5063i	1.95459	+	2.45098i
$71$	0.543672	+	7.25480i	0.0645220	+	0.860987i	0.931756	+	0.363086i	$0.118277\pi$
$71$	0.543672	+	7.25480i	0.0645220	+	0.860987i	−0.867234	+	0.497901i	$0.834104\pi$
$72$		0			0
$73$	−10.0746	−	1.51850i	−1.17914	−	0.177727i	−0.469918	−	0.882710i	$-0.655716\pi$
$73$	−10.0746	−	1.51850i	−1.17914	−	0.177727i	−0.709224	+	0.704983i	$0.750955\pi$
$74$	−13.3054	−	12.3456i	−1.54672	−	1.43515i
$75$		0			0
$76$	0.159495	−	0.0240401i	0.0182954	−	0.00275759i
$77$	1.72834	+	1.17836i	0.196962	+	0.134287i
$78$		0			0
$79$	−6.70519	−	11.6137i	−0.754393	−	1.30665i	−0.945676	−	0.325112i	$-0.894598\pi$
$79$	−6.70519	−	11.6137i	−0.754393	−	1.30665i	0.191283	−	0.981535i	$-0.438735\pi$
$80$	−1.28997	+	2.23430i	−0.144223	+	0.249802i
$81$		0			0
$82$	−17.5445	−	8.44900i	−1.93747	−	0.933036i
$83$	−5.42706	−	1.67402i	−0.595697	−	0.183748i	−0.0177773	−	0.999842i	$-0.505659\pi$
$83$	−5.42706	−	1.67402i	−0.595697	−	0.183748i	−0.577919	+	0.816094i	$0.696135\pi$
$84$		0			0
$85$	13.2369			1.43574
$86$	8.74049	+	12.4364i	0.942511	+	1.34105i
$87$		0			0
$88$	−0.533404	+	2.33699i	−0.0568610	+	0.249124i
$89$	11.7786	+	3.63323i	1.24853	+	0.385121i	0.847428	−	0.530911i	$-0.178150\pi$
$89$	11.7786	+	3.63323i	1.24853	+	0.385121i	0.401105	+	0.916032i	$0.368626\pi$
$90$		0			0
$91$	1.74682	+	4.45083i	0.183117	+	0.466573i
$92$	3.43922	−	5.95690i	0.358563	−	0.621049i
$93$		0			0
$94$	−11.3219	+	14.1972i	−1.16776	+	1.46433i
$95$	−0.160880	−	0.109686i	−0.0165059	−	0.0112535i
$96$		0			0
$97$	9.41101	−	4.53210i	0.955543	−	0.460165i	0.109917	−	0.993941i	$-0.464941\pi$
$97$	9.41101	−	4.53210i	0.955543	−	0.460165i	0.845626	+	0.533775i	$0.179227\pi$
$98$	1.22272	+	1.13452i	0.123513	+	0.114603i
$99$		0			0
$100$	37.3439	−	11.5191i	3.73439	−	1.15191i
$101$	−0.171298	−	2.28582i	−0.0170448	−	0.227447i	−0.999220	−	0.0394811i	$-0.987429\pi$
$101$	−0.171298	−	2.28582i	−0.0170448	−	0.227447i	0.982175	−	0.187966i	$-0.0601895\pi$
$102$		0			0
$103$	−1.94001	+	4.94307i	−0.191155	+	0.487056i	−0.994032	−	0.109090i	$-0.965206\pi$
$103$	−1.94001	+	4.94307i	−0.191155	+	0.487056i	0.802877	+	0.596145i	$0.203302\pi$
$104$	−4.01649	+	3.72676i	−0.393850	+	0.365439i
$105$		0			0
$106$	0.309816	−	4.13421i	0.0300920	−	0.401550i
$107$	−0.800089	−	3.50542i	−0.0773475	−	0.338882i	0.921417	−	0.388575i	$-0.127033\pi$
$107$	−0.800089	−	3.50542i	−0.0773475	−	0.338882i	−0.998765	+	0.0496936i	$0.984176\pi$
$108$		0			0
$109$	0.415847	−	5.54910i	0.0398310	−	0.531507i	−0.941225	−	0.337781i	$-0.890324\pi$
$109$	0.415847	−	5.54910i	0.0398310	−	0.531507i	0.981056	−	0.193726i	$-0.0620573\pi$
$110$	5.87234	−	4.00369i	0.559906	−	0.381737i
$111$		0			0
$112$	−0.643065	+	1.63850i	−0.0607639	+	0.154824i
$113$	−0.0874119	−	0.109611i	−0.00822302	−	0.0103113i	0.777703	−	0.628632i	$-0.216385\pi$
$113$	−0.0874119	−	0.109611i	−0.00822302	−	0.0103113i	−0.785926	+	0.618321i	$0.787813\pi$
$114$		0			0
$115$	−7.93455	+	2.44748i	−0.739901	+	0.228229i
$116$	2.49365	+	0.375857i	0.231529	+	0.0348974i
$117$		0			0
$118$	−12.0857	+	5.82019i	−1.11258	+	0.535792i
$119$	8.93005	−	1.34599i	0.818617	−	0.123387i
$120$		0			0
$121$	−6.50497	+	8.15698i	−0.591361	+	0.741544i
$122$	−3.41262	−	5.91082i	−0.308964	−	0.535141i
$123$		0			0
$124$	−4.24103	−	10.8060i	−0.380856	−	0.970405i
$125$	−24.1590	−	11.6344i	−2.16084	−	1.04061i
$126$		0			0
$127$	−0.384858	+	1.68617i	−0.0341507	+	0.149624i	−0.989129	−	0.147053i	$-0.953021\pi$
$127$	−0.384858	+	1.68617i	−0.0341507	+	0.149624i	0.954978	+	0.296677i	$0.0958784\pi$
$128$	19.4647			1.72045
$129$		0			0
$130$	16.2455			1.42482
$131$	−4.87229	+	21.3469i	−0.425694	+	1.86509i	0.0714858	+	0.997442i	$0.477226\pi$
$131$	−4.87229	+	21.3469i	−0.425694	+	1.86509i	−0.497180	+	0.867647i	$0.665631\pi$
$132$		0			0
$133$	−0.119688	−	0.0576388i	−0.0103783	−	0.00499791i
$134$	−4.74273	−	12.0843i	−0.409710	−	1.04392i
$135$		0			0
$136$	5.17445	+	8.96242i	0.443706	+	0.768521i
$137$	−13.3197	+	16.7024i	−1.13798	+	1.42698i	−0.249314	+	0.968423i	$0.580205\pi$
$137$	−13.3197	+	16.7024i	−1.13798	+	1.42698i	−0.888665	+	0.458557i	$0.848366\pi$
$138$		0			0
$139$	−12.0494	+	1.81616i	−1.02202	+	0.154044i	−0.638606	−	0.769534i	$-0.720489\pi$
$139$	−12.0494	+	1.81616i	−1.02202	+	0.154044i	−0.383411	+	0.923578i	$0.625251\pi$
$140$	34.3904	−	16.5615i	2.90652	−	1.39971i
$141$		0			0
$142$	16.6760	+	2.51351i	1.39942	+	0.210929i
$143$	1.23807	−	0.381893i	0.103532	−	0.0319355i
$144$		0			0
$145$	−1.89807	−	2.38010i	−0.157626	−	0.197656i
$146$	−8.62845	+	21.9849i	−0.714095	+	1.81949i
$147$		0			0
$148$	−21.8248	+	14.8799i	−1.79399	+	1.22312i
$149$	0.617820	−	8.24424i	0.0506138	−	0.675395i	−0.912977	−	0.408012i	$-0.866222\pi$
$149$	0.617820	−	8.24424i	0.0506138	−	0.675395i	0.963590	−	0.267383i	$-0.0861588\pi$
$150$		0			0
$151$	1.01707	+	4.45608i	0.0827681	+	0.362631i	0.999303	−	0.0373233i	$-0.0118831\pi$
$151$	1.01707	+	4.45608i	0.0827681	+	0.362631i	−0.916535	+	0.399954i	$0.869026\pi$
$152$	0.0113763	−	0.151806i	0.000922736	−	0.0123131i
$153$		0			0
$154$	3.55456	−	3.29815i	0.286435	−	0.265773i
$155$	−5.11966	+	13.0447i	−0.411221	+	1.04777i
$156$		0			0
$157$	−0.748623	−	9.98968i	−0.0597466	−	0.797263i	−0.943935	−	0.330132i	$-0.892907\pi$
$157$	−0.748623	−	9.98968i	−0.0597466	−	0.797263i	0.884188	−	0.467131i	$-0.154712\pi$
$158$	−29.7053	+	9.16287i	−2.36323	+	0.728959i
$159$		0			0
$160$	−14.6256	−	13.5706i	−1.15625	−	1.07285i
$161$	−5.10404	+	2.45798i	−0.402255	+	0.193716i
$162$		0			0
$163$	17.6610	+	12.0410i	1.38331	+	0.943128i	0.999808	+	0.0195896i	$0.00623595\pi$
$163$	17.6610	+	12.0410i	1.38331	+	0.943128i	0.383506	+	0.923538i	$0.374716\pi$
$164$	−17.6691	+	22.1563i	−1.37972	+	1.73012i
$165$		0			0
$166$	−6.58263	+	11.4014i	−0.510911	+	0.884924i
$167$	−8.02372	−	20.4441i	−0.620894	−	1.58201i	−0.801197	−	0.598401i	$-0.795803\pi$
$167$	−8.02372	−	20.4441i	−0.620894	−	1.58201i	0.180302	−	0.983611i	$-0.442292\pi$
$168$		0			0
$169$	−9.59254	−	2.95891i	−0.737888	−	0.227608i
$170$	6.82788	−	29.9149i	0.523675	−	2.29437i
$171$		0			0
$172$	20.4754	−	8.37377i	1.56124	−	0.638494i
$173$	15.5770			1.18430			0.592151	−	0.805827i	$-0.298279\pi$
$173$	15.5770			1.18430			0.592151	+	0.805827i	$0.298279\pi$
$174$		0			0
$175$	−30.7563	−	9.48708i	−2.32496	−	0.717155i
$176$	0.429731	+	0.206948i	0.0323922	+	0.0155993i
$177$		0			0
$178$	14.2866	−	24.7452i	1.07083	−	1.85473i
$179$	−3.49011	−	6.04505i	−0.260863	−	0.451828i	0.705608	−	0.708602i	$-0.250674\pi$
$179$	−3.49011	−	6.04505i	−0.260863	−	0.451828i	−0.966472	+	0.256774i	$0.917340\pi$
$180$		0			0
$181$	−4.54803	−	3.10080i	−0.338053	−	0.230480i	0.382380	−	0.924005i	$-0.375104\pi$
$181$	−4.54803	−	3.10080i	−0.338053	−	0.230480i	−0.720433	+	0.693525i	$0.756057\pi$
$182$	10.9598	−	1.65192i	0.812391	−	0.122448i
$183$		0			0
$184$	−4.75884	−	4.41556i	−0.350827	−	0.325520i
$185$	31.5309	+	4.75252i	2.31820	+	0.349412i
$186$		0			0
$187$	−0.182877	−	2.44032i	−0.0133733	−	0.178454i
$188$	16.4767	+	20.6611i	1.20169	+	1.50687i
$189$		0			0
$190$	−0.330871	+	0.307004i	−0.0240039	+	0.0222724i
$191$	15.7034	−	10.7064i	1.13626	−	0.774689i	0.159115	−	0.987260i	$-0.449136\pi$
$191$	15.7034	−	10.7064i	1.13626	−	0.774689i	0.977146	+	0.212571i	$0.0681837\pi$
$192$		0			0
$193$	0.685255	+	3.00230i	0.0493257	+	0.216110i	0.993584	−	0.113095i	$-0.0360764\pi$
$193$	0.685255	+	3.00230i	0.0493257	+	0.216110i	−0.944258	+	0.329205i	$0.893219\pi$
$194$	−5.38798	−	23.6063i	−0.386835	−	1.69483i
$195$		0			0
$196$	2.00562	−	1.36741i	0.143259	−	0.0976722i
$197$	8.60862	−	7.98763i	0.613339	−	0.569095i	−0.311123	−	0.950370i	$-0.600705\pi$
$197$	8.60862	−	7.98763i	0.613339	−	0.569095i	0.924462	+	0.381274i	$0.124515\pi$
$198$		0			0
$199$	0.166901	+	0.209287i	0.0118313	+	0.0148360i	0.787712	−	0.616044i	$-0.211266\pi$
$199$	0.166901	+	0.209287i	0.0118313	+	0.0148360i	−0.775881	+	0.630880i	$0.782694\pi$
$200$	−2.75632	−	36.7805i	−0.194901	−	2.60077i
$201$		0			0
$202$	−5.25422	−	0.791947i	−0.369686	−	0.0557212i
$203$	−1.52252	−	1.41269i	−0.106860	−	0.0991514i
$204$		0			0
$205$	33.8280	−	5.09874i	2.36265	−	0.356112i
$206$	10.1705	+	6.93410i	0.708610	+	0.483122i
$207$		0			0
$208$	0.545110	+	0.944158i	0.0377966	+	0.0654656i
$209$	−0.0179987	+	0.0311747i	−0.00124500	+	0.00215640i
$210$		0			0
$211$	−14.7666	−	7.11124i	−1.01658	−	0.489558i	−0.150045	−	0.988679i	$-0.547942\pi$
$211$	−14.7666	−	7.11124i	−1.01658	−	0.489558i	−0.866532	+	0.499122i	$0.833656\pi$
$212$	−5.76534	−	1.77837i	−0.395965	−	0.122139i
$213$		0			0
$214$	−8.33482			−0.569757
$215$	−24.9947	−	9.40196i	−1.70462	−	0.641208i
$216$		0			0
$217$	−2.12745	+	9.32096i	−0.144421	+	0.632748i
$218$	−12.3263	−	3.80215i	−0.834839	−	0.257514i
$219$		0			0
$220$	−3.77882	−	9.62828i	−0.254768	−	0.649139i
$221$	2.79679	−	4.84418i	0.188132	−	0.325855i
$222$		0			0
$223$	3.03608	−	3.80712i	0.203311	−	0.254944i	−0.669714	−	0.742619i	$-0.733583\pi$
$223$	3.03608	−	3.80712i	0.203311	−	0.254944i	0.873025	+	0.487675i	$0.162155\pi$
$224$	−11.2468	−	7.66796i	−0.751460	−	0.512337i
$225$		0			0
$226$	−0.292806	+	0.141008i	−0.0194772	+	0.00937971i
$227$	−14.1316	−	13.1122i	−0.937947	−	0.870288i	0.0537930	−	0.998552i	$-0.482869\pi$
$227$	−14.1316	−	13.1122i	−0.937947	−	0.870288i	−0.991740	+	0.128265i	$0.959059\pi$
$228$		0			0
$229$	−6.90123	+	2.12875i	−0.456046	+	0.140672i	−0.514263	−	0.857632i	$-0.671935\pi$
$229$	−6.90123	+	2.12875i	−0.456046	+	0.140672i	0.0582171	+	0.998304i	$0.481458\pi$
$230$	1.43841	+	19.1943i	0.0948460	+	1.26563i
$231$		0			0
$232$	0.869538	−	2.21555i	0.0570880	−	0.145458i
$233$	6.45459	−	5.98898i	0.422854	−	0.392351i	−0.439841	−	0.898076i	$-0.644965\pi$
$233$	6.45459	−	5.98898i	0.422854	−	0.392351i	0.862695	+	0.505724i	$0.168775\pi$
$234$		0			0
$235$	2.38400	−	31.8122i	0.155515	−	2.07520i
$236$	4.34397	+	19.0322i	0.282768	+	1.23889i
$237$		0			0
$238$	1.56443	−	20.8759i	0.101407	−	1.35318i
$239$	−4.97430	+	3.39142i	−0.321761	+	0.219373i	−0.713418	−	0.700738i	$-0.752854\pi$
$239$	−4.97430	+	3.39142i	−0.321761	+	0.219373i	0.391658	+	0.920111i	$0.371902\pi$
$240$		0			0
$241$	−6.42983	+	16.3830i	−0.414182	+	1.05532i	0.559787	+	0.828637i	$0.310883\pi$
$241$	−6.42983	+	16.3830i	−0.414182	+	1.05532i	−0.973969	+	0.226682i	$0.927212\pi$
$242$	15.0791	+	18.9085i	0.969319	+	1.21549i
$243$		0			0
$244$	−9.49147	+	2.92773i	−0.607629	+	0.187429i
$245$	−2.89758	−	0.436740i	−0.185119	−	0.0279023i
$246$		0			0
$247$	−0.0741325	+	0.0357003i	−0.00471694	+	0.00227156i
$248$	−10.8336	+	1.63290i	−0.687934	+	0.103689i
$249$		0			0
$250$	−38.7549	+	48.5971i	−2.45108	+	3.07355i
$251$	−8.69184	−	15.0547i	−0.548624	−	0.950245i	−0.998369	−	0.0570882i	$-0.981818\pi$
$251$	−8.69184	−	15.0547i	−0.548624	−	0.950245i	0.449745	−	0.893157i	$-0.351515\pi$
$252$		0			0
$253$	0.560833	+	1.42898i	0.0352592	+	0.0898391i
$254$	3.61217	+	1.73953i	0.226648	+	0.109148i
$255$		0			0
$256$	4.42216	−	19.3748i	0.276385	−	1.21092i
$257$	24.3517			1.51902			0.759508	−	0.650498i	$-0.225440\pi$
$257$	24.3517			1.51902			0.759508	+	0.650498i	$0.225440\pi$
$258$		0			0
$259$	21.7550			1.35179
$260$	5.26085	−	23.0493i	0.326264	−	1.42946i
$261$		0			0
$262$	45.7300	+	22.0224i	2.82521	+	1.36055i
$263$	7.49599	+	19.0995i	0.462223	+	1.17772i	0.952060	+	0.305910i	$0.0989608\pi$
$263$	7.49599	+	19.0995i	0.462223	+	1.17772i	−0.489838	+	0.871814i	$0.662944\pi$
$264$		0			0
$265$	3.64167	+	6.30755i	0.223706	+	0.387470i
$266$	−0.191999	+	0.240759i	−0.0117722	+	0.0147619i
$267$		0			0
$268$	−18.6812	+	2.81574i	−1.14114	+	0.171999i
$269$	−15.3360	+	7.38545i	−0.935055	+	0.450299i	−0.838422	−	0.545021i	$-0.816522\pi$
$269$	−15.3360	+	7.38545i	−0.935055	+	0.450299i	−0.0966331	+	0.995320i	$0.530807\pi$
$270$		0			0
$271$	−3.41724	−	0.515067i	−0.207583	−	0.0312881i	0.0444275	−	0.999013i	$-0.485854\pi$
$271$	−3.41724	−	0.515067i	−0.207583	−	0.0312881i	−0.252010	+	0.967725i	$0.581092\pi$
$272$	1.96771	−	0.606957i	0.119310	−	0.0368022i
$273$		0			0
$274$	30.8761	+	38.7175i	1.86530	+	2.33901i
$275$	−3.18640	+	8.11881i	−0.192147	+	0.489582i
$276$		0			0
$277$	19.9087	−	13.5735i	1.19619	−	0.815552i	0.209448	−	0.977820i	$-0.432833\pi$
$277$	19.9087	−	13.5735i	1.19619	−	0.815552i	0.986747	+	0.162268i	$0.0518809\pi$
$278$	−2.11090	+	28.1680i	−0.126603	+	1.68941i
$279$		0			0
$280$	−8.01634	−	35.1219i	−0.479068	−	2.09893i
$281$	−0.429939	+	5.73714i	−0.0256480	+	0.342249i	0.969587	+	0.244746i	$0.0787046\pi$
$281$	−0.429939	+	5.73714i	−0.0256480	+	0.342249i	−0.995235	+	0.0975031i	$0.968914\pi$
$282$		0			0
$283$	11.6970	−	10.8533i	0.695317	−	0.645160i	−0.251154	−	0.967947i	$-0.580810\pi$
$283$	11.6970	−	10.8533i	0.695317	−	0.645160i	0.946472	+	0.322787i	$0.104620\pi$
$284$	8.96647	−	22.8462i	0.532062	−	1.35567i
$285$		0			0
$286$	−0.224442	−	2.99497i	−0.0132716	−	0.177097i
$287$	22.3030	−	6.87956i	1.31650	−	0.406088i
$288$		0			0
$289$	4.71715	+	4.37687i	0.277479	+	0.257463i
$290$	−6.35800	+	3.06185i	−0.373355	+	0.179798i
$291$		0			0
$292$	28.3983	+	19.3616i	1.66188	+	1.13305i
$293$	3.77347	−	4.73178i	0.220449	−	0.276434i	−0.659293	−	0.751886i	$-0.729144\pi$
$293$	3.77347	−	4.73178i	0.220449	−	0.276434i	0.879741	+	0.475453i	$0.157716\pi$
$294$		0			0
$295$	11.7830	−	20.4087i	0.686032	−	1.18824i
$296$	9.10795	+	23.2067i	0.529389	+	1.34886i
$297$		0			0
$298$	−18.3130	−	5.64881i	−1.06084	−	0.327227i
$299$	−0.780788	+	3.42085i	−0.0451541	+	0.197833i
$300$		0			0
$301$	−17.8183	−	3.80130i	−1.02703	−	0.219103i
$302$	10.5952			0.609686
$303$		0			0
$304$	−0.0289447	−	0.00892826i	−0.00166009	−	0.000512071i
$305$	10.8031	+	5.20250i	0.618584	+	0.297894i
$306$		0			0
$307$	−11.7476	+	20.3475i	−0.670472	+	1.16129i	0.307298	+	0.951613i	$0.400575\pi$
$307$	−11.7476	+	20.3475i	−0.670472	+	1.16129i	−0.977770	+	0.209679i	$0.932758\pi$
$308$	−3.52837	−	6.11131i	−0.201047	−	0.348224i
$309$		0			0
$310$	26.8396	+	18.2990i	1.52439	+	1.03931i
$311$	−1.16489	+	0.175579i	−0.0660550	+	0.00995619i	−0.181987	−	0.983301i	$-0.558253\pi$
$311$	−1.16489	+	0.175579i	−0.0660550	+	0.00995619i	0.115932	+	0.993257i	$0.463015\pi$
$312$		0			0
$313$	21.8138	+	20.2403i	1.23299	+	1.14405i	0.984495	+	0.175415i	$0.0561268\pi$
$313$	21.8138	+	20.2403i	1.23299	+	1.14405i	0.248496	+	0.968633i	$0.420064\pi$
$314$	−22.9625	−	3.46103i	−1.29585	−	0.195317i
$315$		0			0
$316$	3.38079	+	45.1135i	0.190184	+	2.53783i
$317$	16.7284	+	20.9767i	0.939560	+	1.17817i	0.983822	+	0.179151i	$0.0573350\pi$
$317$	16.7284	+	20.9767i	0.939560	+	1.17817i	−0.0442619	+	0.999020i	$0.514094\pi$
$318$		0			0
$319$	−0.412565	+	0.382805i	−0.0230992	+	0.0214330i
$320$	−42.4765	+	28.9600i	−2.37451	+	1.61891i
$321$		0			0
$322$	2.92216	+	12.8028i	0.162846	+	0.713473i
$323$	0.0345821	+	0.151514i	0.00192420	+	0.00843048i
$324$		0			0
$325$	−16.4715	+	11.2301i	−0.913677	+	0.622934i
$326$	36.3222	−	33.7021i	2.01170	−	1.86659i
$327$		0			0
$328$	16.6760	+	20.9110i	0.920777	+	1.15462i
$329$	−1.62649	−	21.7040i	−0.0896713	−	1.19658i
$330$		0			0
$331$	2.75598	+	0.415397i	0.151482	+	0.0228323i	0.224346	−	0.974510i	$-0.427976\pi$
$331$	2.75598	+	0.415397i	0.151482	+	0.0228323i	−0.0728632	+	0.997342i	$0.523214\pi$
$332$	14.0448	+	13.0317i	0.770810	+	0.715207i
$333$		0			0
$334$	−50.3417	+	7.58779i	−2.75458	+	0.415186i
$335$	18.8433	+	12.8472i	1.02952	+	0.701915i
$336$		0			0
$337$	−4.52447	−	7.83661i	−0.246463	−	0.426887i	0.716079	−	0.698020i	$-0.245935\pi$
$337$	−4.52447	−	7.83661i	−0.246463	−	0.426887i	−0.962542	+	0.271132i	$0.912602\pi$
$338$	−11.6351	+	20.1525i	−0.632864	+	1.09615i
$339$		0			0
$340$	−40.2325	−	19.3750i	−2.18191	−	1.05075i
$341$	2.47561	+	0.763625i	0.134062	+	0.0413526i
$342$		0			0
$343$	17.4496			0.942192
$344$	−3.40484	−	20.5987i	−0.183577	−	1.11061i
$345$		0			0
$346$	8.03498	−	35.2036i	0.431963	−	1.89255i
$347$	−10.0705	−	3.10634i	−0.540613	−	0.166757i	0.0124100	−	0.999923i	$-0.496050\pi$
$347$	−10.0705	−	3.10634i	−0.540613	−	0.166757i	−0.553023	+	0.833166i	$0.686526\pi$
$348$		0			0
$349$	−4.48874	−	11.4371i	−0.240277	−	0.612215i	0.758966	−	0.651130i	$-0.225705\pi$
$349$	−4.48874	−	11.4371i	−0.240277	−	0.612215i	−0.999242	+	0.0389157i	$0.987610\pi$
$350$	−37.3052	+	64.6145i	−1.99405	+	3.45379i
$351$		0			0
$352$	−2.29977	+	2.88382i	−0.122578	+	0.153708i
$353$	−3.53890	−	2.41278i	−0.188356	−	0.128419i	0.465470	−	0.885063i	$-0.345885\pi$
$353$	−3.53890	−	2.41278i	−0.188356	−	0.128419i	−0.653827	+	0.756644i	$0.726838\pi$
$354$		0			0
$355$	−26.6933	+	12.8548i	−1.41673	+	0.682262i
$356$	−30.4822	−	28.2834i	−1.61556	−	1.49902i
$357$		0			0
$358$	−15.4619	+	4.76935i	−0.817184	+	0.252068i
$359$	2.55838	+	34.1392i	0.135026	+	1.80180i	0.495062	+	0.868858i	$0.335145\pi$
$359$	2.55838	+	34.1392i	0.135026	+	1.80180i	−0.360036	+	0.932938i	$0.617236\pi$
$360$		0			0
$361$	−6.94064	+	17.6845i	−0.365297	+	0.930762i
$362$	−9.35366	+	8.67893i	−0.491617	+	0.456154i
$363$		0			0
$364$	1.20539	−	16.0848i	0.0631795	−	0.843071i
$365$	−9.23266	−	40.4509i	−0.483259	−	2.11730i
$366$		0			0
$367$	−2.31138	+	30.8433i	−0.120653	+	1.61000i	0.528219	+	0.849108i	$0.322860\pi$
$367$	−2.31138	+	30.8433i	−0.120653	+	1.61000i	−0.648873	+	0.760897i	$0.724759\pi$
$368$	−1.06727	+	0.727652i	−0.0556353	+	0.0379315i
$369$		0			0
$370$	27.0048	−	68.8072i	1.40391	−	3.57711i
$371$	3.09817	+	3.88498i	0.160849	+	0.201698i
$372$		0			0
$373$	7.58815	−	2.34063i	0.392900	−	0.121193i	−0.0920093	−	0.995758i	$-0.529329\pi$
$373$	7.58815	−	2.34063i	0.392900	−	0.121193i	0.484909	+	0.874565i	$0.338853\pi$
$374$	−5.60936	−	0.845475i	−0.290053	−	0.0437185i
$375$		0			0
$376$	22.4713	−	10.8216i	1.15887	−	0.558082i
$377$	−1.27206	+	0.191732i	−0.0655144	+	0.00987471i
$378$		0			0
$379$	13.9219	−	17.4576i	0.715122	−	0.896735i	−0.282929	−	0.959141i	$-0.591306\pi$
$379$	13.9219	−	17.4576i	0.715122	−	0.896735i	0.998051	+	0.0624060i	$0.0198774\pi$
$380$	0.328433	+	0.568862i	0.0168483	+	0.0291820i
$381$		0			0
$382$	−16.0959	−	41.0118i	−0.823539	−	2.09834i
$383$	−22.6340	−	10.8999i	−1.15654	−	0.556961i	−0.245549	−	0.969384i	$-0.578968\pi$
$383$	−22.6340	−	10.8999i	−1.15654	−	0.556961i	−0.910992	+	0.412423i	$0.864682\pi$
$384$		0			0
$385$	−1.89559	+	8.30511i	−0.0966081	+	0.423268i
$386$	7.13855			0.363343
$387$		0			0
$388$	−35.2377			−1.78892
$389$	−3.91826	+	17.1670i	−0.198664	+	0.870403i	0.773070	+	0.634321i	$0.218720\pi$
$389$	−3.91826	+	17.1670i	−0.198664	+	0.870403i	−0.971733	+	0.236081i	$0.924137\pi$
$390$		0			0
$391$	5.97109	+	2.87553i	0.301971	+	0.145422i
$392$	−0.836989	−	2.13261i	−0.0422743	−	0.107713i
$393$		0			0
$394$	−13.6112	−	23.5753i	−0.685724	−	1.18771i
$395$	34.0503	−	42.6977i	1.71326	−	2.14836i
$396$		0			0
$397$	−1.43147	+	0.215759i	−0.0718434	+	0.0108287i	−0.184866	−	0.982764i	$-0.559185\pi$
$397$	−1.43147	+	0.215759i	−0.0718434	+	0.0108287i	0.113022	+	0.993592i	$0.463947\pi$
$398$	0.559072	−	0.269235i	0.0280238	−	0.0134955i
$399$		0			0
$400$	−7.25700	−	1.09382i	−0.362850	−	0.0546908i
$401$	−7.37812	+	2.27585i	−0.368446	+	0.113650i	−0.473448	−	0.880822i	$-0.656991\pi$
$401$	−7.37812	+	2.27585i	−0.368446	+	0.113650i	0.105003	+	0.994472i	$0.466515\pi$
$402$		0			0
$403$	3.69211	+	4.62976i	0.183917	+	0.230625i
$404$	−2.82512	+	7.19829i	−0.140555	+	0.358129i
$405$		0			0
$406$	−3.97797	+	2.71214i	−0.197424	+	0.134601i
$407$	0.440541	−	5.87861i	0.0218368	−	0.291392i
$408$		0			0
$409$	−7.12781	−	31.2290i	−0.352448	−	1.54417i	−0.771511	−	0.636216i	$-0.780499\pi$
$409$	−7.12781	−	31.2290i	−0.352448	−	1.54417i	0.419063	−	0.907957i	$-0.362359\pi$
$410$	5.92622	−	79.0800i	0.292675	−	3.90548i
$411$		0			0
$412$	13.1317	−	12.1845i	0.646954	−	0.600286i
$413$	5.87394	−	14.9666i	0.289038	−	0.736456i
$414$		0			0
$415$	−1.72841	−	23.0640i	−0.0848442	−	1.13217i
$416$	−8.05649	+	2.48510i	−0.395002	+	0.121842i
$417$		0			0
$418$	0.0611695	+	0.0567570i	0.00299190	+	0.00277608i
$419$	−19.9028	+	9.58467i	−0.972314	+	0.468242i	−0.851455	−	0.524428i	$-0.824279\pi$
$419$	−19.9028	+	9.58467i	−0.972314	+	0.468242i	−0.120859	+	0.992670i	$0.538565\pi$
$420$		0			0
$421$	−12.5748	−	8.57335i	−0.612858	−	0.417840i	0.216717	−	0.976234i	$-0.430465\pi$
$421$	−12.5748	−	8.57335i	−0.612858	−	0.417840i	−0.829575	+	0.558395i	$0.811417\pi$
$422$	−23.6881	+	29.7039i	−1.15312	+	1.44596i
$423$		0			0
$424$	−2.84714	+	4.93139i	−0.138269	+	0.239489i
$425$	13.7565	+	35.0511i	0.667290	+	1.70023i
$426$		0			0
$427$	7.81715	+	2.41127i	0.378298	+	0.116690i
$428$	−2.69910	+	11.8255i	−0.130466	+	0.571609i
$429$		0			0
$430$	−34.1409	+	51.6373i	−1.64642	+	2.49017i
$431$	−16.5109			−0.795301			−0.397651	−	0.917537i	$-0.630174\pi$
$431$	−16.5109			−0.795301			−0.397651	+	0.917537i	$0.630174\pi$
$432$		0			0
$433$	24.1153	+	7.43859i	1.15891	+	0.357476i	0.813833	−	0.581099i	$-0.197377\pi$
$433$	24.1153	+	7.43859i	1.15891	+	0.357476i	0.345075	+	0.938575i	$0.387853\pi$
$434$	19.9676	+	9.61591i	0.958477	+	0.461578i
$435$		0			0
$436$	−9.38620	+	16.2574i	−0.449517	+	0.778587i
$437$	−0.0487442	−	0.0844275i	−0.00233175	−	0.00403872i
$438$		0			0
$439$	15.6707	+	10.6841i	0.747922	+	0.509924i	0.876279	−	0.481804i	$-0.160018\pi$
$439$	15.6707	+	10.6841i	0.747922	+	0.509924i	−0.128358	+	0.991728i	$0.540971\pi$
$440$	−9.65289	+	1.45494i	−0.460184	+	0.0693615i
$441$		0			0
$442$	−9.50503	−	8.81938i	−0.452108	−	0.419495i
$443$	37.0756	+	5.58825i	1.76152	+	0.265506i	0.948510	−	0.316748i	$-0.102591\pi$
$443$	37.0756	+	5.58825i	1.76152	+	0.265506i	0.813007	+	0.582254i	$0.197829\pi$
$444$		0			0
$445$	3.75126	+	50.0571i	0.177827	+	2.37293i
$446$	−7.03788	−	8.82523i	−0.333253	−	0.417887i
$447$		0			0
$448$	−25.7113	+	23.8566i	−1.21474	+	1.12712i
$449$	14.9462	−	10.1902i	0.705357	−	0.480904i	−0.156745	−	0.987639i	$-0.550100\pi$
$449$	14.9462	−	10.1902i	0.705357	−	0.480904i	0.862102	+	0.506735i	$0.169148\pi$
$450$		0			0
$451$	−1.40735	−	6.16599i	−0.0662693	−	0.290345i
$452$	0.105243	+	0.461100i	0.00495022	+	0.0216883i
$453$		0			0
$454$	−36.9225	+	25.1733i	−1.73286	+	1.18144i
$455$	−14.2736	+	13.2440i	−0.669159	+	0.620889i
$456$		0			0
$457$	4.42658	+	5.55075i	0.207067	+	0.259653i	0.874510	−	0.485007i	$-0.161183\pi$
$457$	4.42658	+	5.55075i	0.207067	+	0.259653i	−0.667444	+	0.744660i	$0.732612\pi$
$458$	1.25109	+	16.6946i	0.0584594	+	0.780087i
$459$		0			0
$460$	27.6988	+	4.17493i	1.29147	+	0.194657i
$461$	−1.48177	−	1.37488i	−0.0690130	−	0.0640347i	0.644912	−	0.764257i	$-0.276894\pi$
$461$	−1.48177	−	1.37488i	−0.0690130	−	0.0640347i	−0.713925	+	0.700222i	$0.753084\pi$
$462$		0			0
$463$	−23.5610	+	3.55125i	−1.09497	+	0.165041i	−0.671600	−	0.740914i	$-0.734392\pi$
$463$	−23.5610	+	3.55125i	−1.09497	+	0.165041i	−0.423374	+	0.905955i	$0.639154\pi$
$464$	−0.391289	−	0.266776i	−0.0181651	−	0.0123848i
$465$		0			0
$466$	−10.2055	−	17.6764i	−0.472759	−	0.818842i
$467$	8.68583	−	15.0443i	0.401932	−	0.696167i	−0.592027	−	0.805918i	$-0.701672\pi$
$467$	8.68583	−	15.0443i	0.401932	−	0.696167i	0.993959	+	0.109751i	$0.0350054\pi$
$468$		0			0
$469$	14.0187	+	6.75104i	0.647323	+	0.311734i
$470$	−70.6647	−	21.7972i	−3.25952	−	1.00543i
$471$		0			0
$472$	18.4244			0.848052
$473$	−1.38800	+	4.73784i	−0.0638203	+	0.217846i
$474$		0			0
$475$	0.123251	−	0.539998i	0.00565515	−	0.0247768i
$476$	−29.1123	−	8.97997i	−1.33436	−	0.411596i
$477$		0			0
$478$	5.09863	+	12.9911i	0.233206	+	0.594199i
$479$	3.86370	−	6.69213i	0.176537	−	0.305771i	−0.764155	−	0.645033i	$-0.776844\pi$
$479$	3.86370	−	6.69213i	0.176537	−	0.305771i	0.940692	+	0.339261i	$0.110177\pi$
$480$		0			0
$481$	8.40131	−	10.5349i	0.383067	−	0.480350i
$482$	33.7082	+	22.9819i	1.53537	+	1.04680i
$483$		0			0
$484$	31.7108	−	15.2711i	1.44140	−	0.694142i
$485$	31.1825	+	28.9332i	1.41593	+	1.31379i
$486$		0			0
$487$	16.7051	−	5.15285i	0.756982	−	0.233498i	0.107843	−	0.994168i	$-0.465606\pi$
$487$	16.7051	−	5.15285i	0.756982	−	0.233498i	0.649139	+	0.760670i	$0.275129\pi$
$488$	0.700556	+	9.34827i	0.0317127	+	0.423176i
$489$		0			0
$490$	−2.48165	+	6.32314i	−0.112109	+	0.285650i
$491$	−15.9175	+	14.7693i	−0.718346	+	0.666528i	−0.952107	−	0.305766i	$-0.901087\pi$
$491$	−15.9175	+	14.7693i	−0.718346	+	0.666528i	0.233760	+	0.972294i	$0.424897\pi$
$492$		0			0
$493$	−0.181578	+	2.42299i	−0.00817786	+	0.109126i
$494$	0.0424423	+	0.185952i	0.00190957	+	0.00836636i
$495$		0			0
$496$	−0.162910	+	2.17388i	−0.00731487	+	0.0976102i
$497$	−16.7010	+	11.3866i	−0.749144	+	0.510758i
$498$		0			0
$499$	−13.1125	+	33.4100i	−0.586995	+	1.49564i	0.260842	+	0.965382i	$0.416000\pi$
$499$	−13.1125	+	33.4100i	−0.586995	+	1.49564i	−0.847837	+	0.530257i	$0.822095\pi$
$500$	56.4000	+	70.7234i	2.52229	+	3.16285i
$501$		0			0
$502$	−38.5065	+	11.8777i	−1.71863	+	0.530127i
$503$	−0.0899578	−	0.0135590i	−0.00401102	−	0.000604564i	0.147036	−	0.989131i	$-0.453027\pi$
$503$	−0.0899578	−	0.0135590i	−0.00401102	−	0.000604564i	−0.151047	+	0.988527i	$0.548265\pi$
$504$		0			0
$505$	8.41042	−	4.05025i	0.374259	−	0.180234i
$506$	3.51873	−	0.530363i	0.156426	−	0.0235775i
$507$		0			0
$508$	3.63781	−	4.56168i	0.161402	−	0.202392i
$509$	11.3425	+	19.6459i	0.502749	+	0.870787i	0.999995	+	0.00317746i	$0.00101142\pi$
$509$	11.3425	+	19.6459i	0.502749	+	0.870787i	−0.497246	+	0.867610i	$0.665655\pi$
$510$		0			0
$511$	−10.3419	−	26.3507i	−0.457498	−	1.16569i
$512$	−6.43101	−	3.09701i	−0.284213	−	0.136870i
$513$		0			0
$514$	12.5611	−	55.0339i	0.554048	−	2.42744i
$515$	−21.6250			−0.952913
$516$		0			0
$517$	−5.89775			−0.259383
$518$	11.2217	−	49.1656i	0.493054	−	2.16021i
$519$		0			0
$520$	−20.1035	−	9.68136i	−0.881599	−	0.424556i
$521$	−1.72346	−	4.39129i	−0.0755060	−	0.192386i	0.888137	−	0.459578i	$-0.151999\pi$
$521$	−1.72346	−	4.39129i	−0.0755060	−	0.192386i	−0.963643	+	0.267192i	$0.913904\pi$
$522$		0			0
$523$	−0.853098	−	1.47761i	−0.0373034	−	0.0646113i	0.846771	−	0.531958i	$-0.178543\pi$
$523$	−0.853098	−	1.47761i	−0.0373034	−	0.0646113i	−0.884074	+	0.467346i	$0.845210\pi$
$524$	46.0546	−	57.7507i	2.01191	−	2.52285i
$525$		0			0
$526$	47.0307	−	7.08874i	2.05064	−	0.309084i
$527$	10.0771	−	4.85290i	0.438968	−	0.211396i
$528$		0			0
$529$	18.6322	+	2.80835i	0.810095	+	0.122102i
$530$	16.1333	−	4.97646i	0.700785	−	0.216164i
$531$		0			0
$532$	0.279416	+	0.350377i	0.0121142	+	0.0151908i
$533$	5.28148	−	13.4570i	0.228766	−	0.582887i
$534$		0			0
$535$	12.0983	−	8.24846i	0.523054	−	0.356612i
$536$	−1.33246	+	17.7805i	−0.0575537	+	0.768001i
$537$		0			0
$538$	8.78018	+	38.4685i	0.378540	+	1.65849i
$539$	−0.0404841	+	0.540223i	−0.00174378	+	0.0232691i
$540$		0			0
$541$	−8.33253	+	7.73145i	−0.358243	+	0.332401i	−0.838676	−	0.544630i	$-0.816670\pi$
$541$	−8.33253	+	7.73145i	−0.358243	+	0.332401i	0.480433	+	0.877031i	$0.340480\pi$
$542$	−2.92672	+	7.45716i	−0.125713	+	0.320313i
$543$		0			0
$544$	1.19004	+	15.8799i	0.0510224	+	0.680846i
$545$	21.6547	−	6.67960i	0.927586	−	0.286123i
$546$		0			0
$547$	−17.1076	−	15.8735i	−0.731467	−	0.678703i	0.223737	−	0.974650i	$-0.428174\pi$
$547$	−17.1076	−	15.8735i	−0.731467	−	0.678703i	−0.955204	+	0.295947i	$0.904365\pi$
$548$	64.9316	−	31.2694i	2.77374	−	1.33576i
$549$		0			0
$550$	16.7046	+	11.3890i	0.712286	+	0.485628i
$551$	0.0222847	−	0.0279441i	0.000949358	−	0.00119046i
$552$		0			0
$553$	18.6298	−	32.2677i	0.792218	−	1.37216i
$554$	−20.4063	−	51.9943i	−0.866979	−	2.20903i
$555$		0			0
$556$	39.2815	+	12.1167i	1.66591	+	0.513865i
$557$	1.28534	−	5.63146i	0.0544618	−	0.238613i	−0.940369	−	0.340155i	$-0.889521\pi$
$557$	1.28534	−	5.63146i	0.0544618	−	0.238613i	0.994831	+	0.101542i	$0.0323777\pi$
$558$		0			0
$559$	−8.72180	+	7.16055i	−0.368893	+	0.302859i
$560$	−7.16814			−0.302909
$561$		0			0
$562$	12.7440	+	3.93099i	0.537571	+	0.165819i
$563$	3.42474	+	1.64927i	0.144336	+	0.0695084i	0.504657	−	0.863320i	$-0.331619\pi$
$563$	3.42474	+	1.64927i	0.144336	+	0.0695084i	−0.360322	+	0.932828i	$0.617333\pi$
$564$		0			0
$565$	0.285471	−	0.494450i	0.0120098	−	0.0208017i
$566$	−18.4944	−	32.0333i	−0.777378	−	1.34646i
$567$		0			0
$568$	−19.1384	−	13.0483i	−0.803030	−	0.547497i
$569$	−35.8718	+	5.40680i	−1.50382	+	0.226665i	−0.848707	−	0.528863i	$-0.822619\pi$
$569$	−35.8718	+	5.40680i	−1.50382	+	0.226665i	−0.655116	+	0.755528i	$0.727380\pi$
$570$		0			0
$571$	−19.4633	−	18.0593i	−0.814514	−	0.755758i	0.158289	−	0.987393i	$-0.449402\pi$
$571$	−19.4633	−	18.0593i	−0.814514	−	0.755758i	−0.972803	+	0.231635i	$0.925593\pi$
$572$	−4.32199	−	0.651435i	−0.180711	−	0.0272379i
$573$		0			0
$574$	−4.04319	−	53.9526i	−0.168759	−	2.25194i
$575$	−14.7269	−	18.4670i	−0.614156	−	0.770127i
$576$		0			0
$577$	9.54816	−	8.85940i	0.397495	−	0.368821i	−0.455949	−	0.890006i	$-0.650700\pi$
$577$	9.54816	−	8.85940i	0.397495	−	0.368821i	0.853444	+	0.521184i	$0.174510\pi$
$578$	12.3248	−	8.40289i	0.512643	−	0.349514i
$579$		0			0
$580$	2.28525	+	10.0123i	0.0948899	+	0.415740i
$581$	−3.51130	−	15.3840i	−0.145673	−	0.638236i
$582$		0			0
$583$	1.11253	−	0.758511i	0.0460763	−	0.0314143i
$584$	23.7793	−	22.0639i	0.983994	−	0.913013i
$585$		0			0
$586$	−8.74722	−	10.9687i	−0.361344	−	0.453111i
$587$	0.430770	+	5.74822i	0.0177798	+	0.237255i	0.999013	+	0.0444278i	$0.0141465\pi$
$587$	0.430770	+	5.74822i	0.0177798	+	0.237255i	−0.981233	+	0.192827i	$0.938234\pi$
$588$		0			0
$589$	−0.162689	−	0.0245215i	−0.00670350	−	0.00101039i
$590$	−40.0450	−	37.1564i	−1.64863	−	1.52970i
$591$		0			0
$592$	4.90508	−	0.739322i	0.201598	−	0.0303859i
$593$	−6.69370	−	4.56369i	−0.274877	−	0.187408i	0.418033	−	0.908432i	$-0.362720\pi$
$593$	−6.69370	−	4.56369i	−0.274877	−	0.187408i	−0.692911	+	0.721024i	$0.743672\pi$
$594$		0			0
$595$	18.3888	+	31.8503i	0.753866	+	1.30573i
$596$	−13.9450	+	24.1534i	−0.571209	+	0.989362i
$597$		0			0
$598$	7.32826	+	3.52910i	0.299675	+	0.144316i
$599$	8.12129	+	2.50509i	0.331827	+	0.102355i	0.456192	−	0.889882i	$-0.349213\pi$
$599$	8.12129	+	2.50509i	0.331827	+	0.102355i	−0.124365	+	0.992237i	$0.539689\pi$
$600$		0			0
$601$	35.6791			1.45538			0.727691	−	0.685905i	$-0.240594\pi$
$601$	35.6791			1.45538			0.727691	+	0.685905i	$0.240594\pi$
$602$	−17.7818	+	38.3078i	−0.724734	+	1.56131i
$603$		0			0
$604$	3.43110	−	15.0326i	0.139609	−	0.611668i
$605$	−40.6004	−	12.5236i	−1.65064	−	0.509155i
$606$		0			0
$607$	12.0041	+	30.5861i	0.487233	+	1.24145i	0.937321	+	0.348466i	$0.113297\pi$
$607$	12.0041	+	30.5861i	0.487233	+	1.24145i	−0.450088	+	0.892984i	$0.648607\pi$
$608$	0.117123	−	0.202864i	0.00474998	−	0.00822721i
$609$		0			0
$610$	17.3299	−	21.7311i	0.701669	−	0.879865i
$611$	−11.1383	−	7.59397i	−0.450608	−	0.307219i
$612$		0			0
$613$	2.01111	−	0.968499i	0.0812280	−	0.0391173i	−0.392829	−	0.919612i	$-0.628503\pi$
$613$	2.01111	−	0.968499i	0.0812280	−	0.0391173i	0.474057	+	0.880494i	$0.342789\pi$
$614$	39.9249	+	37.0449i	1.61124	+	1.49501i
$615$		0			0
$616$	−6.36422	+	1.96310i	−0.256422	+	0.0790956i
$617$	0.983300	+	13.1212i	0.0395862	+	0.528241i	0.981383	+	0.192059i	$0.0615166\pi$
$617$	0.983300	+	13.1212i	0.0395862	+	0.528241i	−0.941797	+	0.336182i	$0.890864\pi$
$618$		0			0
$619$	−5.06713	+	12.9108i	−0.203665	+	0.518930i	−0.995815	−	0.0913968i	$-0.970867\pi$
$619$	−5.06713	+	12.9108i	−0.203665	+	0.518930i	0.792149	+	0.610327i	$0.208962\pi$
$620$	34.6544	−	32.1546i	1.39175	−	1.29136i
$621$		0			0
$622$	−0.204074	+	2.72318i	−0.00818263	+	0.109190i
$623$	7.62076	+	33.3887i	0.305319	+	1.33769i
$624$		0			0
$625$	3.83193	−	51.1336i	0.153277	−	2.04534i
$626$	56.9943	−	38.8581i	2.27795	−	1.55308i
$627$		0			0
$628$	−12.3466	+	31.4586i	−0.492683	+	1.25534i
$629$	−15.8683	−	19.8982i	−0.632709	−	0.793392i
$630$		0			0
$631$	−5.11794	+	1.57867i	−0.203742	+	0.0628461i	−0.394946	−	0.918704i	$-0.629237\pi$
$631$	−5.11794	+	1.57867i	−0.203742	+	0.0628461i	0.191204	+	0.981550i	$0.438761\pi$
$632$	42.2203	+	6.36369i	1.67944	+	0.253134i
$633$		0			0
$634$	56.0355	−	26.9853i	2.22545	−	1.07172i
$635$	−6.96470	+	1.04976i	−0.276386	+	0.0416584i
$636$		0			0
$637$	−0.772051	+	0.968121i	−0.0305898	+	0.0383584i
$638$	0.652314	+	1.12984i	0.0258254	+	0.0447309i
$639$		0			0
$640$	28.9599	+	73.7885i	1.14474	+	2.91675i
$641$	4.56273	+	2.19729i	0.180217	+	0.0867879i	0.521817	−	0.853058i	$-0.325254\pi$
$641$	4.56273	+	2.19729i	0.180217	+	0.0867879i	−0.341600	+	0.939845i	$0.610969\pi$
$642$		0			0
$643$	−4.59652	+	20.1387i	−0.181269	+	0.794191i	0.799758	+	0.600322i	$0.204961\pi$
$643$	−4.59652	+	20.1387i	−0.181269	+	0.794191i	−0.981027	+	0.193869i	$0.937896\pi$
$644$	19.1111			0.753082
$645$		0			0
$646$	0.360255			0.0141740
$647$	6.78518	−	29.7278i	0.266753	−	1.16872i	−0.647013	−	0.762479i	$-0.723982\pi$
$647$	6.78518	−	29.7278i	0.266753	−	1.16872i	0.913766	−	0.406242i	$-0.133161\pi$
$648$		0			0
$649$	−3.92529	−	1.89032i	−0.154081	−	0.0742015i
$650$	16.8832	+	43.0178i	0.662215	+	1.68730i
$651$		0			0
$652$	−36.0546	−	62.4483i	−1.41201	−	2.44567i
$653$	−25.9574	+	32.5496i	−1.01579	+	1.27376i	−0.0544173	+	0.998518i	$0.517330\pi$
$653$	−25.9574	+	32.5496i	−1.01579	+	1.27376i	−0.961374	+	0.275244i	$0.911241\pi$
$654$		0			0
$655$	−88.1729	+	13.2899i	−3.44520	+	0.519280i
$656$	4.79483	−	2.30907i	0.187207	−	0.0901540i
$657$		0			0
$658$	−49.8892	−	7.51959i	−1.94488	−	0.293144i
$659$	20.9158	−	6.45166i	0.814762	−	0.251321i	0.140754	−	0.990045i	$-0.455047\pi$
$659$	20.9158	−	6.45166i	0.814762	−	0.251321i	0.674008	+	0.738724i	$0.264571\pi$
$660$		0			0
$661$	−3.40742	−	4.27277i	−0.132533	−	0.166191i	0.711136	−	0.703054i	$-0.248181\pi$
$661$	−3.40742	−	4.27277i	−0.132533	−	0.166191i	−0.843670	+	0.536863i	$0.819609\pi$
$662$	2.36038	−	6.01414i	0.0917386	−	0.233746i
$663$		0			0
$664$	14.9405	−	10.1862i	0.579803	−	0.395303i
$665$	0.0404284	−	0.539480i	0.00156775	−	0.0209201i
$666$		0			0
$667$	−0.339165	−	1.48598i	−0.0131325	−	0.0575373i
$668$	−5.53674	+	73.8826i	−0.214223	+	2.85861i
$669$		0			0
$670$	38.7539	−	35.9584i	1.49719	−	1.38919i
$671$	0.809867	−	2.06351i	0.0312646	−	0.0796608i
$672$		0			0
$673$	0.265593	+	3.54410i	0.0102379	+	0.136615i	0.999980	−	0.00624712i	$-0.00198853\pi$
$673$	0.265593	+	3.54410i	0.0102379	+	0.136615i	−0.989743	+	0.142862i	$0.954369\pi$
$674$	−20.0443	+	6.18284i	−0.772076	+	0.238154i
$675$		0			0
$676$	24.8248	+	23.0341i	0.954800	+	0.885925i
$677$	8.78571	−	4.23097i	0.337662	−	0.162610i	−0.257367	−	0.966314i	$-0.582855\pi$
$677$	8.78571	−	4.23097i	0.337662	−	0.162610i	0.595029	+	0.803704i	$0.297141\pi$
$678$		0			0
$679$	23.9788	+	16.3485i	0.920223	+	0.627398i
$680$	−26.2769	+	32.9502i	−1.00767	+	1.26358i
$681$		0			0
$682$	3.00274	−	5.20089i	0.114981	−	0.199152i
$683$	7.66440	+	19.5286i	0.293270	+	0.747240i	0.999239	+	0.0389974i	$0.0124164\pi$
$683$	7.66440	+	19.5286i	0.293270	+	0.747240i	−0.705969	+	0.708242i	$0.749488\pi$
$684$		0			0
$685$	−83.1341	−	25.6435i	−3.17639	−	0.979787i
$686$	9.00091	−	39.4356i	0.343656	−	1.50566i
$687$		0			0
$688$	−4.14665	−	0.251538i	−0.158089	−	0.00958981i
$689$	3.07775			0.117253
$690$		0			0
$691$	8.48595	+	2.61757i	0.322821	+	0.0995770i	0.451930	−	0.892053i	$-0.350736\pi$
$691$	8.48595	+	2.61757i	0.322821	+	0.0995770i	−0.129109	+	0.991630i	$0.541212\pi$
$692$	−47.3452	−	22.8003i	−1.79980	−	0.866736i
$693$		0			0
$694$	−12.2148	+	21.1566i	−0.463667	+	0.803095i
$695$	−24.8121	−	42.9758i	−0.941177	−	1.63017i
$696$		0			0
$697$	−22.5603	−	15.3814i	−0.854532	−	0.582610i
$698$	−28.1628	+	4.24486i	−1.06598	+	0.160671i
$699$		0			0
$700$	79.5952	+	73.8535i	3.00842	+	2.79140i
$701$	−24.8182	−	3.74074i	−0.937370	−	0.141286i	−0.337448	−	0.941344i	$-0.609564\pi$
$701$	−24.8182	−	3.74074i	−0.937370	−	0.141286i	−0.599922	+	0.800058i	$0.704802\pi$
$702$		0			0
$703$	0.0279772	+	0.373330i	0.00105518	+	0.0140804i
$704$	5.92582	+	7.43074i	0.223338	+	0.280057i
$705$		0			0
$706$	−7.27823	+	6.75321i	−0.273920	+	0.254160i
$707$	5.26210	−	3.58764i	0.197902	−	0.134927i
$708$		0			0
$709$	−11.1254	−	48.7436i	−0.417824	−	1.83060i	−0.544629	−	0.838677i	$-0.683330\pi$
$709$	−11.1254	−	48.7436i	−0.417824	−	1.83060i	0.126806	−	0.991928i	$-0.459528\pi$
$710$	15.2824	+	66.9566i	0.573538	+	2.51284i
$711$		0			0
$712$	−32.4261	+	22.1078i	−1.21522	+	0.828524i
$713$	−5.14322	+	4.77221i	−0.192615	+	0.178721i
$714$		0			0
$715$	3.28973	+	4.12519i	0.123029	+	0.154273i
$716$	1.75973	+	23.4820i	0.0657642	+	0.877562i
$717$		0			0
$718$	78.4729	+	11.8279i	2.92858	+	0.441413i
$719$	8.04392	+	7.46367i	0.299988	+	0.278348i	0.815776	−	0.578368i	$-0.196310\pi$
$719$	8.04392	+	7.46367i	0.299988	+	0.278348i	−0.515788	+	0.856716i	$0.672501\pi$
$720$		0			0
$721$	−14.5890	+	2.19893i	−0.543321	+	0.0818925i
$722$	36.3861	+	24.8076i	1.35415	+	0.923245i
$723$		0			0
$724$	9.28473	+	16.0816i	0.345064	+	0.597669i
$725$	4.32989	−	7.49958i	0.160808	−	0.278527i
$726$		0			0
$727$	−21.2553	−	10.2360i	−0.788316	−	0.379633i	−0.00399815	−	0.999992i	$-0.501273\pi$
$727$	−21.2553	−	10.2360i	−0.788316	−	0.379633i	−0.784318	+	0.620359i	$0.786987\pi$
$728$	−14.5470	−	4.48714i	−0.539146	−	0.166305i
$729$		0			0
$730$	−96.1799			−3.55978
$731$	9.51991	+	19.0701i	0.352107	+	0.705333i
$732$		0			0
$733$	7.85287	−	34.4057i	0.290052	−	1.27080i	−0.594399	−	0.804170i	$-0.702610\pi$
$733$	7.85287	−	34.4057i	0.290052	−	1.27080i	0.884451	−	0.466633i	$-0.154533\pi$
$734$	68.5124	+	21.1333i	2.52884	+	0.780043i
$735$		0			0
$736$	−3.64951	−	9.29881i	−0.134523	−	0.342759i
$737$	2.10813	−	3.65139i	0.0776541	−	0.134501i
$738$		0			0
$739$	−13.7042	+	17.1846i	−0.504119	+	0.632145i	−0.967153	−	0.254196i	$-0.918189\pi$
$739$	−13.7042	+	17.1846i	−0.504119	+	0.632145i	0.463034	+	0.886340i	$0.346761\pi$
$740$	−88.8794	−	60.5969i	−3.26727	−	2.22759i
$741$		0			0
$742$	10.3780	−	4.99779i	0.380989	−	0.183475i
$743$	1.34948	+	1.25213i	0.0495075	+	0.0459362i	0.704539	−	0.709666i	$-0.251154\pi$
$743$	1.34948	+	1.25213i	0.0495075	+	0.0459362i	−0.655031	+	0.755602i	$0.727344\pi$
$744$		0			0
$745$	32.1722	−	9.92381i	1.17870	−	0.363580i
$746$	−1.37561	−	18.3563i	−0.0503648	−	0.672071i
$747$		0			0
$748$	−3.01608	+	7.68483i	−0.110279	+	0.280985i
$749$	7.32316	−	6.79490i	0.267582	−	0.248280i
$750$		0			0
$751$	−2.39276	+	31.9291i	−0.0873129	+	1.16511i	0.765692	+	0.643207i	$0.222397\pi$
$751$	−2.39276	+	31.9291i	−0.0873129	+	1.16511i	−0.853005	+	0.521903i	$0.825222\pi$
$752$	−1.10431	−	4.83830i	−0.0402700	−	0.176435i
$753$		0			0
$754$	−0.222848	+	2.97371i	−0.00811566	+	0.108296i
$755$	−15.3793	+	10.4854i	−0.559710	+	0.381604i
$756$		0			0
$757$	6.22743	−	15.8672i	0.226340	−	0.576704i	−0.771917	−	0.635723i	$-0.780702\pi$
$757$	6.22743	−	15.8672i	0.226340	−	0.576704i	0.998257	+	0.0590188i	$0.0187972\pi$
$758$	−32.2722	−	40.4681i	−1.17218	−	1.46987i
$759$		0			0
$760$	0.592404	−	0.182732i	0.0214887	−	0.00662840i
$761$	2.81970	+	0.425001i	0.102214	+	0.0154063i	0.199950	−	0.979806i	$-0.435922\pi$
$761$	2.81970	+	0.425001i	0.102214	+	0.0154063i	−0.0977361	+	0.995212i	$0.531160\pi$
$762$		0			0
$763$	13.9298	−	6.70823i	0.504292	−	0.242854i
$764$	−63.4004	+	9.55607i	−2.29375	+	0.345727i
$765$		0			0
$766$	−36.3085	+	45.5295i	−1.31188	+	1.64505i
$767$	−4.97919	−	8.62421i	−0.179788	−	0.311402i
$768$		0			0
$769$	17.5058	+	44.6040i	0.631275	+	1.60846i	0.784400	+	0.620255i	$0.212971\pi$
$769$	17.5058	+	44.6040i	0.631275	+	1.60846i	−0.153126	+	0.988207i	$0.548934\pi$
$770$	17.7915	+	8.56791i	0.641160	+	0.308766i
$771$		0			0
$772$	2.31171	−	10.1283i	0.0832003	−	0.364524i
$773$	−12.7995			−0.460366			−0.230183	−	0.973147i	$-0.573933\pi$
$773$	−12.7995			−0.460366			−0.230183	+	0.973147i	$0.573933\pi$
$774$		0			0
$775$	−39.8627			−1.43191
$776$	−7.40041	+	32.4233i	−0.265659	+	1.16393i
$777$		0			0
$778$	36.7757	+	17.7103i	1.31847	+	0.634943i
$779$	0.146739	+	0.373886i	0.00525749	+	0.0133959i
$780$		0			0
$781$	2.73866	+	4.74350i	0.0979970	+	0.169736i
$782$	9.57861	−	12.0112i	0.342530	−	0.429519i
$783$		0			0
$784$	−0.450760	+	0.0679411i	−0.0160986	+	0.00242647i
$785$	36.7559	−	17.7007i	1.31188	−	0.631766i
$786$		0			0
$787$	−13.0915	−	1.97322i	−0.466660	−	0.0703377i	−0.0884966	−	0.996076i	$-0.528206\pi$
$787$	−13.0915	−	1.97322i	−0.466660	−	0.0703377i	−0.378164	+	0.925739i	$0.623444\pi$
$788$	−37.8568	+	11.6773i	−1.34859	+	0.415986i
$789$		0			0
$790$	−78.9314	−	98.9768i	−2.80825	−	3.52144i
$791$	0.142310	−	0.362600i	0.00505997	−	0.0128926i
$792$		0			0
$793$	4.18647	−	2.85429i	0.148666	−	0.101359i
$794$	−0.250775	+	3.34636i	−0.00889968	+	0.118758i
$795$		0			0
$796$	−0.200947	−	0.880406i	−0.00712238	−	0.0312052i
$797$	−0.866491	+	11.5625i	−0.0306927	+	0.409566i	0.960604	+	0.277920i	$0.0896451\pi$
$797$	−0.866491	+	11.5625i	−0.0306927	+	0.409566i	−0.991297	+	0.131645i	$0.957974\pi$
$798$		0			0
$799$	−18.6651	+	17.3187i	−0.660324	+	0.612691i
$800$	20.7349	−	52.8316i	0.733089	−	1.86788i
$801$		0			0
$802$	1.33754	+	17.8482i	0.0472301	+	0.630242i
$803$	−7.32986	+	2.26096i	−0.258665	+	0.0797876i
$804$		0			0
$805$	−16.9118	−	15.6918i	−0.596062	−	0.553065i
$806$	12.3676	−	5.95591i	0.435629	−	0.209788i
$807$		0			0
$808$	6.03006	+	4.11123i	0.212137	+	0.144632i
$809$	15.0173	−	18.8311i	0.527980	−	0.662066i	−0.444302	−	0.895877i	$-0.646548\pi$
$809$	15.0173	−	18.8311i	0.527980	−	0.662066i	0.972282	+	0.233811i	$0.0751197\pi$
$810$		0			0
$811$	9.67307	−	16.7542i	0.339667	−	0.588321i	−0.644703	−	0.764433i	$-0.723019\pi$
$811$	9.67307	−	16.7542i	0.339667	−	0.588321i	0.984370	+	0.176112i	$0.0563522\pi$
$812$	2.55981	+	6.52228i	0.0898316	+	0.228887i
$813$		0			0
$814$	−13.0582	−	4.02792i	−0.457689	−	0.141178i
$815$	−19.3700	+	84.8657i	−0.678503	+	2.97271i
$816$		0			0
$817$	0.0423181	−	0.310661i	0.00148052	−	0.0108687i
$818$	−74.2530			−2.59620
$819$		0			0
$820$	−110.280	−	34.0170i	−3.85116	−	1.18793i
$821$	−4.68010	−	2.25382i	−0.163336	−	0.0786587i	0.350429	−	0.936589i	$-0.386036\pi$
$821$	−4.68010	−	2.25382i	−0.163336	−	0.0786587i	−0.513766	+	0.857930i	$0.671750\pi$
$822$		0			0
$823$	27.1185	−	46.9706i	0.945290	−	1.63729i	0.190122	−	0.981761i	$-0.439112\pi$
$823$	27.1185	−	46.9706i	0.945290	−	1.63729i	0.755169	−	0.655530i	$-0.227555\pi$
$824$	−8.45347	−	14.6418i	−0.294491	−	0.510073i
$825$		0			0
$826$	−30.7939	−	20.9950i	−1.07146	−	0.730508i
$827$	3.32662	−	0.501407i	0.115678	−	0.0174356i	−0.0909482	−	0.995856i	$-0.528990\pi$
$827$	3.32662	−	0.501407i	0.115678	−	0.0174356i	0.206626	+	0.978420i	$0.433752\pi$
$828$		0			0
$829$	−29.6523	−	27.5133i	−1.02987	−	0.955578i	−0.0308341	−	0.999525i	$-0.509816\pi$
$829$	−29.6523	−	27.5133i	−1.02987	−	0.955578i	−0.999034	+	0.0439467i	$0.986007\pi$
$830$	−53.0153	−	7.99078i	−1.84019	−	0.277364i
$831$		0			0
$832$	1.62346	+	21.6636i	0.0562834	+	0.751050i
$833$	1.45824	+	1.82857i	0.0505249	+	0.0633562i
$834$		0			0
$835$	65.5635	−	60.8341i	2.26892	−	2.10525i
$836$	0.100336	−	0.0684082i	0.00347021	−	0.00236595i
$837$		0			0
$838$	11.3947	+	49.9235i	0.393624	+	1.72458i
$839$	−0.0182394	−	0.0799120i	−0.000629694	−	0.00275887i	0.974612	−	0.223900i	$-0.0718790\pi$
$839$	−0.0182394	−	0.0799120i	−0.000629694	−	0.00275887i	−0.975242	+	0.221141i	$0.929022\pi$
$840$		0			0
$841$	−23.4992	+	16.0215i	−0.810318	+	0.552465i
$842$	−25.8618	+	23.9962i	−0.891257	+	0.826965i
$843$		0			0
$844$	34.4733	+	43.2281i	1.18662	+	1.48797i
$845$	−3.05503	−	40.7666i	−0.105096	−	1.40241i
$846$		0			0
$847$	−28.6638	−	4.32038i	−0.984901	−	0.148450i
$848$	0.830567	+	0.770654i	0.0285218	+	0.0264644i
$849$		0			0
$850$	86.3101	−	13.0092i	2.96041	−	0.446210i
$851$	13.1910	+	8.99347i	0.452181	+	0.308292i
$852$		0			0
$853$	12.0750	+	20.9145i	0.413441	+	0.716101i	0.995263	−	0.0972152i	$-0.0309935\pi$
$853$	12.0750	+	20.9145i	0.413441	+	0.716101i	−0.581823	+	0.813316i	$0.697660\pi$
$854$	9.48164	−	16.4227i	0.324455	−	0.561973i
$855$		0			0
$856$	10.3142	+	4.96706i	0.352532	+	0.169771i
$857$	−40.2162	−	12.4051i	−1.37376	−	0.423749i	−0.481966	−	0.876190i	$-0.660077\pi$
$857$	−40.2162	−	12.4051i	−1.37376	−	0.423749i	−0.891794	+	0.452441i	$0.850553\pi$
$858$		0			0
$859$	−2.35350			−0.0803004			−0.0401502	−	0.999194i	$-0.512784\pi$
$859$	−2.35350			−0.0803004			−0.0401502	+	0.999194i	$0.512784\pi$
$860$	62.2076	+	65.1614i	2.12126	+	2.22199i
$861$		0			0
$862$	−8.51667	+	37.3140i	−0.290079	+	1.27092i
$863$	29.2992	+	9.03761i	0.997356	+	0.307644i	0.750113	−	0.661310i	$-0.229999\pi$
$863$	29.2992	+	9.03761i	0.997356	+	0.307644i	0.247243	+	0.968953i	$0.420475\pi$
$864$		0			0
$865$	23.1758	+	59.0509i	0.787999	+	2.00779i
$866$	29.2501	−	50.6627i	0.993960	−	1.72159i
$867$		0			0
$868$	20.1094	−	25.2164i	0.682557	−	0.855899i
$869$	−8.34206	−	5.68752i	−0.282985	−	0.192936i
$870$		0			0
$871$	8.68290	−	4.18147i	0.294209	−	0.141684i
$872$	12.9877	+	12.0508i	0.439819	+	0.408092i
$873$		0			0
$874$	−0.215946	+	0.0666106i	−0.00730449	+	0.00225314i
$875$	−5.56750	−	74.2932i	−0.188216	−	2.51157i
$876$		0			0
$877$	−16.8677	+	42.9782i	−0.569582	+	1.45127i	0.298287	+	0.954476i	$0.403585\pi$
$877$	−16.8677	+	42.9782i	−0.569582	+	1.45127i	−0.867868	+	0.496794i	$0.834510\pi$
$878$	32.2290	−	29.9041i	1.08767	−	1.00921i
$879$		0			0
$880$	−0.145155	+	1.93696i	−0.00489318	+	0.0652950i
$881$	2.29329	+	10.0475i	0.0772627	+	0.338510i	0.998755	−	0.0498868i	$-0.0158861\pi$
$881$	2.29329	+	10.0475i	0.0772627	+	0.338510i	−0.921492	+	0.388397i	$0.873029\pi$
$882$		0			0
$883$	0.882701	−	11.7788i	0.0297053	−	0.396389i	−0.962457	−	0.271434i	$-0.912502\pi$
$883$	0.882701	−	11.7788i	0.0297053	−	0.396389i	0.992162	−	0.124955i	$-0.0398787\pi$
$884$	−15.5911	+	10.6298i	−0.524385	+	0.357520i
$885$		0			0
$886$	31.7537	−	80.9070i	1.06679	−	2.71812i
$887$	13.8680	+	17.3899i	0.465640	+	0.583895i	0.958098	−	0.286442i	$-0.0924726\pi$
$887$	13.8680	+	17.3899i	0.465640	+	0.583895i	−0.492457	+	0.870337i	$0.663901\pi$
$888$		0			0
$889$	−4.59187	+	1.41641i	−0.154006	+	0.0475047i
$890$	115.062	+	17.3428i	3.85689	+	0.581333i
$891$		0			0
$892$	−14.8005	+	7.12752i	−0.495556	+	0.238647i
$893$	0.370362	−	0.0558232i	0.0123937	−	0.00186805i
$894$		0			0
$895$	17.7235	−	22.2245i	0.592430	−	0.742884i
$896$	27.0404	+	46.8354i	0.903358	+	1.56466i
$897$		0			0
$898$	−15.3198	−	39.0343i	−0.511229	−	1.30259i
$899$	−2.31757	−	1.11608i	−0.0772954	−	0.0372235i
$900$		0			0
$901$	1.29356	−	5.66746i	0.0430947	−	0.188810i
$902$	−14.6608			−0.488152
$903$		0			0
$904$	0.446375			0.0148462
$905$	4.98815	−	21.8545i	0.165812	−	0.726468i
$906$		0			0
$907$	−31.5843	−	15.2102i	−1.04874	−	0.505046i	−0.171541	−	0.985177i	$-0.554875\pi$
$907$	−31.5843	−	15.2102i	−1.04874	−	0.505046i	−0.877197	+	0.480131i	$0.840589\pi$
$908$	23.7594	+	60.5381i	0.788485	+	2.00903i
$909$		0			0
$910$	22.5683	+	39.0895i	0.748132	+	1.29580i
$911$	−34.7823	+	43.6156i	−1.15239	+	1.44505i	−0.277498	+	0.960726i	$0.589505\pi$
$911$	−34.7823	+	43.6156i	−1.15239	+	1.44505i	−0.874890	+	0.484322i	$0.839066\pi$
$912$		0			0
$913$	−4.22814	+	0.637289i	−0.139931	+	0.0210912i
$914$	14.8278	−	7.14070i	0.490461	−	0.236193i
$915$		0			0
$916$	24.0916	+	3.63123i	0.796010	+	0.119979i
$917$	−58.1330	+	17.9316i	−1.91972	+	0.592155i
$918$		0			0
$919$	27.4108	+	34.3720i	0.904198	+	1.13383i	0.990494	+	0.137559i	$0.0439258\pi$
$919$	27.4108	+	34.3720i	0.904198	+	1.13383i	−0.0862951	+	0.996270i	$0.527503\pi$
$920$	9.65863	−	24.6098i	0.318436	−	0.811361i
$921$		0			0
$922$	−3.87151	+	2.63955i	−0.127502	+	0.0869291i
$923$	−0.935602	+	12.4847i	−0.0307957	+	0.410940i
$924$		0			0
$925$	20.1841	+	88.4323i	0.663649	+	2.90764i
$926$	−4.12759	+	55.0789i	−0.135641	+	1.81000i
$927$		0			0
$928$	2.68469	−	2.49103i	0.0881294	−	0.0817721i
$929$	2.10522	−	5.36400i	0.0690699	−	0.175987i	−0.892171	−	0.451699i	$-0.850818\pi$
$929$	2.10522	−	5.36400i	0.0690699	−	0.175987i	0.961240	+	0.275711i	$0.0889134\pi$
$930$		0			0
$931$	−0.00257101	−	0.0343077i	−8.42614e−5	−	0.00112439i
$932$	−28.3843	+	8.75541i	−0.929760	+	0.286793i
$933$		0			0
$934$	−29.5192	−	27.3898i	−0.965898	−	0.896222i
$935$	8.97889	−	4.32401i	0.293641	−	0.141410i
$936$		0			0
$937$	−18.1263	−	12.3583i	−0.592161	−	0.403729i	0.229828	−	0.973231i	$-0.426184\pi$
$937$	−18.1263	−	12.3583i	−0.592161	−	0.403729i	−0.821990	+	0.569503i	$0.807136\pi$
$938$	22.4882	−	28.1994i	0.734267	−	0.920742i
$939$		0			0
$940$	−53.8098	+	93.2013i	−1.75508	+	3.03989i
$941$	6.91668	+	17.6234i	0.225477	+	0.574507i	0.998183	−	0.0602578i	$-0.0191923\pi$
$941$	6.91668	+	17.6234i	0.225477	+	0.574507i	−0.772706	+	0.634765i	$0.781097\pi$
$942$		0			0
$943$	16.3672	+	5.04862i	0.532991	+	0.164406i
$944$	0.815767	−	3.57411i	0.0265510	−	0.116327i
$945$		0			0
$946$	9.99139	+	5.58071i	0.324848	+	0.181445i
$947$	−40.2434			−1.30774			−0.653868	−	0.756609i	$-0.726855\pi$
$947$	−40.2434			−1.30774			−0.653868	+	0.756609i	$0.726855\pi$
$948$		0			0
$949$	−16.7542	−	5.16798i	−0.543864	−	0.167760i
$950$	−1.15680	−	0.557086i	−0.0375316	−	0.0180743i
$951$		0			0
$952$	−14.3767	+	24.9013i	−0.465953	+	0.807054i
$953$	18.3255	+	31.7407i	0.593621	+	1.02818i	0.993740	+	0.111718i	$0.0356354\pi$
$953$	18.3255	+	31.7407i	0.593621	+	1.02818i	−0.400119	+	0.916463i	$0.631031\pi$
$954$		0			0
$955$	63.9506	+	43.6008i	2.06939	+	1.41089i
$956$	20.0830	−	3.02703i	0.649532	−	0.0979012i
$957$		0			0
$958$	−13.1310	−	12.1838i	−0.424243	−	0.393640i
$959$	−58.6926	−	8.84648i	−1.89528	−	0.285668i
$960$		0			0
$961$	−1.43176	−	19.1056i	−0.0461859	−	0.616308i
$962$	−19.4749	−	24.4208i	−0.627897	−	0.787358i
$963$		0			0
$964$	43.5228	−	40.3833i	1.40178	−	1.30066i
$965$	−10.3619	+	7.06459i	−0.333560	+	0.227417i
$966$		0			0
$967$	1.90500	+	8.34635i	0.0612607	+	0.268400i	0.996278	−	0.0862025i	$-0.0274732\pi$
$967$	1.90500	+	8.34635i	0.0612607	+	0.268400i	−0.935017	+	0.354603i	$0.884616\pi$
$968$	−7.39172	−	32.3853i	−0.237579	−	1.04090i
$969$		0			0
$970$	81.4725	−	55.5470i	2.61592	−	1.78351i
$971$	−36.2742	+	33.6575i	−1.16409	+	1.08012i	−0.168562	+	0.985691i	$0.553912\pi$
$971$	−36.2742	+	33.6575i	−1.16409	+	1.08012i	−0.995531	+	0.0944301i	$0.969897\pi$
$972$		0			0
$973$	−21.1091	−	26.4699i	−0.676725	−	0.848587i
$974$	−3.02838	−	40.4109i	−0.0970356	−	1.29485i
$975$		0			0
$976$	1.84447	+	0.278009i	0.0590400	+	0.00889884i
$977$	13.4546	+	12.4840i	0.430450	+	0.399399i	0.865421	−	0.501045i	$-0.167051\pi$
$977$	13.4546	+	12.4840i	0.430450	+	0.399399i	−0.434971	+	0.900444i	$0.643241\pi$
$978$		0			0
$979$	9.17655	−	1.38314i	0.293284	−	0.0442054i
$980$	8.16770	+	5.56865i	0.260908	+	0.177884i
$981$		0			0
$982$	25.1674	+	43.5912i	0.803124	+	1.39105i
$983$	−2.35817	+	4.08447i	−0.0752140	+	0.130274i	−0.901179	−	0.433446i	$-0.857297\pi$
$983$	−2.35817	+	4.08447i	−0.0752140	+	0.130274i	0.825965	+	0.563721i	$0.190631\pi$
$984$		0			0
$985$	43.0882	+	20.7502i	1.37291	+	0.661157i
$986$	5.38220	+	1.66019i	0.171404	+	0.0528712i
$987$		0			0
$988$	0.277575			0.00883083
$989$	−9.23252	−	9.67091i	−0.293577	−	0.307517i
$990$		0			0
$991$	−10.0778	+	44.1536i	−0.320131	+	1.40259i	0.517188	+	0.855872i	$0.326979\pi$
$991$	−10.0778	+	44.1536i	−0.320131	+	1.40259i	−0.837319	+	0.546714i	$0.815878\pi$
$992$	−16.1096	−	4.96915i	−0.511480	−	0.157771i
$993$		0			0
$994$	17.1185	+	43.6172i	0.542965	+	1.38345i
$995$	−0.545067	+	0.944083i	−0.0172798	+	0.0299295i
$996$		0			0
$997$	−18.2570	+	22.8935i	−0.578204	+	0.725045i	−0.981805	−	0.189890i	$-0.939187\pi$
$997$	−18.2570	+	22.8935i	−0.578204	+	0.725045i	0.403601	+	0.914935i	$0.367758\pi$
$998$	68.7418	+	46.8673i	2.17598	+	1.48356i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.y.c.253.3		36
3.2	odd	2		43.2.g.a.38.1	yes	36
12.11	even	2		688.2.bg.c.81.1		36
43.17	even	21	inner	387.2.y.c.361.3		36
129.17	odd	42		43.2.g.a.17.1	✓	36
129.62	even	42		1849.2.a.o.1.1		18
129.110	odd	42		1849.2.a.n.1.18		18
516.275	even	42		688.2.bg.c.17.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.17.1	✓	36	129.17	odd	42
43.2.g.a.38.1	yes	36	3.2	odd	2
387.2.y.c.253.3		36	1.1	even	1	trivial
387.2.y.c.361.3		36	43.17	even	21	inner
688.2.bg.c.17.1		36	516.275	even	42
688.2.bg.c.81.1		36	12.11	even	2
1849.2.a.n.1.18		18	129.110	odd	42
1849.2.a.o.1.1		18	129.62	even	42

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.y (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.515822 - 2.25996i) q^{2} +(-3.03942 - 1.46371i) q^{4} +(1.48781 + 3.79089i) q^{5} +(1.38920 + 2.40617i) q^{7} +(-1.98513 + 2.48927i) q^{8} +O(q^{10})\)	\(q+(0.515822 - 2.25996i) q^{2} +(-3.03942 - 1.46371i) q^{4} +(1.48781 + 3.79089i) q^{5} +(1.38920 + 2.40617i) q^{7} +(-1.98513 + 2.48927i) q^{8} +(9.33472 - 1.40698i) q^{10} +(0.678323 - 0.326663i) q^{11} +(1.70167 + 0.256486i) q^{13} +(6.15444 - 1.89839i) q^{14} +(0.394993 + 0.495306i) q^{16} +(1.18750 - 3.02571i) q^{17} +(-0.0395049 + 0.0269340i) q^{19} +(1.02666 - 13.6998i) q^{20} +(-0.388353 - 1.70148i) q^{22} +(-0.152371 + 2.03326i) q^{23} +(-8.49199 + 7.87942i) q^{25} +(1.45741 - 3.71341i) q^{26} +(-0.700443 - 9.34676i) q^{28} +(-0.714324 + 0.220340i) q^{29} +(2.52247 + 2.34051i) q^{31} +(-4.41406 + 2.12570i) q^{32} +(-6.22544 - 4.24444i) q^{34} +(-7.05465 + 8.84626i) q^{35} +(3.91502 - 6.78101i) q^{37} +(0.0404923 + 0.103173i) q^{38} +(-12.3900 - 3.82182i) q^{40} +(1.86928 - 8.18985i) q^{41} +(-4.39142 + 4.86985i) q^{43} -2.53985 q^{44} +(4.51649 + 1.39315i) q^{46} +(-7.05780 - 3.39886i) q^{47} +(-0.359777 + 0.623151i) q^{49} +(13.4268 + 23.2560i) q^{50} +(-4.79668 - 3.27032i) q^{52} +(1.76849 - 0.266557i) q^{53} +(2.24756 + 2.08543i) q^{55} +(-8.74735 - 1.31845i) q^{56} +(0.129496 + 1.72800i) q^{58} +(-3.60798 - 4.52427i) q^{59} +(2.15836 - 2.00266i) q^{61} +(6.59062 - 4.49341i) q^{62} +(2.80908 + 12.3074i) q^{64} +(1.55946 + 6.83245i) q^{65} +(4.62708 - 3.15469i) q^{67} +(-8.03807 + 7.45824i) q^{68} +(16.3533 + 20.5063i) q^{70} +(0.543672 + 7.25480i) q^{71} +(-10.0746 - 1.51850i) q^{73} +(-13.3054 - 12.3456i) q^{74} +(0.159495 - 0.0240401i) q^{76} +(1.72834 + 1.17836i) q^{77} +(-6.70519 - 11.6137i) q^{79} +(-1.28997 + 2.23430i) q^{80} +(-17.5445 - 8.44900i) q^{82} +(-5.42706 - 1.67402i) q^{83} +13.2369 q^{85} +(8.74049 + 12.4364i) q^{86} +(-0.533404 + 2.33699i) q^{88} +(11.7786 + 3.63323i) q^{89} +(1.74682 + 4.45083i) q^{91} +(3.43922 - 5.95690i) q^{92} +(-11.3219 + 14.1972i) q^{94} +(-0.160880 - 0.109686i) q^{95} +(9.41101 - 4.53210i) q^{97} +(1.22272 + 1.13452i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

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