LMFDB - Embedded newform 855.2.bs.b.541.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(226,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 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("855.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.bs (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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 12 x^{16} - 8 x^{15} + 96 x^{14} - 75 x^{13} + 448 x^{12} - 405 x^{11} + 1521 x^{10} + \cdots + 361 $ x^18 + 12x^16 - 8x^15 + 96x^14 - 75x^13 + 448x^12 - 405x^11 + 1521x^10 - 1294x^9 + 3333x^8 - 2616x^7 + 5113x^6 - 3126x^5 + 4032x^4 - 1359x^3 + 1698x^2 - 513x + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			541.2
Root			$-0.359728 - 0.623068i$ of defining polynomial
Character	$\chi$	$=$	855.541
Dual form			855.2.bs.b.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.124932 - 0.708527i) q^{2} +(1.39298 - 0.507004i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(-0.645970 + 1.11885i) q^{7} +(-1.25271 - 2.16976i) q^{8} +O(q^{10})$	\(q+(-0.124932 - 0.708527i) q^{2} +(1.39298 - 0.507004i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(-0.645970 + 1.11885i) q^{7} +(-1.25271 - 2.16976i) q^{8} +(-0.124932 + 0.708527i) q^{10} +(2.88381 + 4.99491i) q^{11} +(1.80125 + 1.51143i) q^{13} +(0.873439 + 0.317906i) q^{14} +(0.890312 - 0.747060i) q^{16} +(1.18948 + 6.74589i) q^{17} +(2.40586 - 3.63481i) q^{19} -1.48238 q^{20} +(3.17874 - 2.66728i) q^{22} +(5.32803 - 1.93925i) q^{23} +(0.766044 + 0.642788i) q^{25} +(0.845852 - 1.46506i) q^{26} +(-0.332562 + 1.88605i) q^{28} +(1.04556 - 5.92966i) q^{29} +(1.19445 - 2.06885i) q^{31} +(-4.47907 - 3.75839i) q^{32} +(4.63104 - 1.68556i) q^{34} +(0.989683 - 0.830443i) q^{35} -4.53121 q^{37} +(-2.87593 - 1.25051i) q^{38} +(0.435062 + 2.46736i) q^{40} +(3.51177 - 2.94672i) q^{41} +(-0.260318 - 0.0947480i) q^{43} +(6.54954 + 5.49572i) q^{44} +(-2.03965 - 3.53278i) q^{46} +(-0.0880430 + 0.499316i) q^{47} +(2.66545 + 4.61669i) q^{49} +(0.359728 - 0.623068i) q^{50} +(3.27541 + 1.19215i) q^{52} +(-6.75604 + 2.45900i) q^{53} +(-1.00154 - 5.68000i) q^{55} +3.23685 q^{56} -4.33194 q^{58} +(-1.00094 - 5.67662i) q^{59} +(6.77273 - 2.46507i) q^{61} +(-1.61506 - 0.587833i) q^{62} +(-0.941117 + 1.63006i) q^{64} +(-1.17568 - 2.03634i) q^{65} +(-1.77501 + 10.0666i) q^{67} +(5.07713 + 8.79384i) q^{68} +(-0.712034 - 0.597468i) q^{70} +(-1.05207 - 0.382923i) q^{71} +(1.83298 - 1.53805i) q^{73} +(0.566094 + 3.21048i) q^{74} +(1.50845 - 6.28301i) q^{76} -7.45142 q^{77} +(-10.7969 + 9.05969i) q^{79} +(-1.09213 + 0.397503i) q^{80} +(-2.52657 - 2.12004i) q^{82} +(0.608609 - 1.05414i) q^{83} +(1.18948 - 6.74589i) q^{85} +(-0.0346093 + 0.196279i) q^{86} +(7.22517 - 12.5144i) q^{88} +(6.85239 + 5.74984i) q^{89} +(-2.85461 + 1.03899i) q^{91} +(6.43866 - 5.40267i) q^{92} +0.364778 q^{94} +(-3.50395 + 2.59275i) q^{95} +(-1.83977 - 10.4339i) q^{97} +(2.93805 - 2.46531i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8}+O(q^{10}) $ 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8	$ 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8} - 3 q^{10} - 3 q^{13} - 24 q^{14} + 21 q^{16} + 24 q^{17} - 12 q^{19} + 12 q^{20} + 15 q^{22} - 21 q^{23} + 21 q^{26} - 24 q^{28} + 9 q^{29} + 30 q^{31} - 45 q^{32} + 24 q^{34} + 6 q^{35} - 60 q^{37} + 15 q^{38} - 6 q^{40} + 6 q^{41} - 6 q^{43} + 30 q^{44} + 21 q^{46} - 33 q^{47} - 3 q^{49} + 9 q^{52} - 24 q^{53} - 3 q^{55} + 72 q^{56} + 36 q^{58} - 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{64} - 3 q^{65} - 24 q^{67} + 3 q^{68} + 39 q^{70} - 24 q^{71} + 6 q^{73} + 39 q^{74} + 27 q^{76} - 24 q^{77} + 9 q^{79} - 33 q^{80} - 57 q^{82} + 24 q^{85} + 33 q^{86} + 39 q^{88} + 6 q^{89} - 6 q^{91} + 66 q^{92} - 66 q^{94} + 15 q^{95} - 87 q^{97} - 39 q^{98}+O(q^{100}) $ 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8 - 3 * q^10 - 3 * q^13 - 24 * q^14 + 21 * q^16 + 24 * q^17 - 12 * q^19 + 12 * q^20 + 15 * q^22 - 21 * q^23 + 21 * q^26 - 24 * q^28 + 9 * q^29 + 30 * q^31 - 45 * q^32 + 24 * q^34 + 6 * q^35 - 60 * q^37 + 15 * q^38 - 6 * q^40 + 6 * q^41 - 6 * q^43 + 30 * q^44 + 21 * q^46 - 33 * q^47 - 3 * q^49 + 9 * q^52 - 24 * q^53 - 3 * q^55 + 72 * q^56 + 36 * q^58 - 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^64 - 3 * q^65 - 24 * q^67 + 3 * q^68 + 39 * q^70 - 24 * q^71 + 6 * q^73 + 39 * q^74 + 27 * q^76 - 24 * q^77 + 9 * q^79 - 33 * q^80 - 57 * q^82 + 24 * q^85 + 33 * q^86 + 39 * q^88 + 6 * q^89 - 6 * q^91 + 66 * q^92 - 66 * q^94 + 15 * q^95 - 87 * q^97 - 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	−0.124932	−	0.708527i	−0.0883405	−	0.501004i	−0.996586	−	0.0825655i	$-0.973689\pi$
$2$	−0.124932	−	0.708527i	−0.0883405	−	0.501004i	0.908245	−	0.418439i	$-0.137422\pi$
$3$		0			0
$3$		0			0
$4$	1.39298	−	0.507004i	0.696492	−	0.253502i
$5$	−0.939693	−	0.342020i	−0.420243	−	0.152956i
$5$	−0.939693	−	0.342020i	−0.420243	−	0.152956i
$6$		0			0
$7$	−0.645970	+	1.11885i	−0.244154	+	0.422886i	−0.961893	−	0.273425i	$-0.911843\pi$
$7$	−0.645970	+	1.11885i	−0.244154	+	0.422886i	0.717740	+	0.696311i	$0.245177\pi$
$8$	−1.25271	−	2.16976i	−0.442900	−	0.767126i
$9$		0			0
$10$	−0.124932	+	0.708527i	−0.0395071	+	0.224056i
$11$	2.88381	+	4.99491i	0.869502	+	1.50602i	0.862506	+	0.506046i	$0.168893\pi$
$11$	2.88381	+	4.99491i	0.869502	+	1.50602i	0.00699554	+	0.999976i	$0.497773\pi$
$12$		0			0
$13$	1.80125	+	1.51143i	0.499576	+	0.419194i	0.857443	−	0.514578i	$-0.172051\pi$
$13$	1.80125	+	1.51143i	0.499576	+	0.419194i	−0.357867	+	0.933773i	$0.616496\pi$
$14$	0.873439	+	0.317906i	0.233436	+	0.0849639i
$15$		0			0
$16$	0.890312	−	0.747060i	0.222578	−	0.186765i
$17$	1.18948	+	6.74589i	0.288492	+	1.63612i	0.692539	+	0.721381i	$0.256492\pi$
$17$	1.18948	+	6.74589i	0.288492	+	1.63612i	−0.404047	+	0.914738i	$0.632397\pi$
$18$		0			0
$19$	2.40586	−	3.63481i	0.551942	−	0.833883i
$19$	2.40586	−	3.63481i	0.551942	−	0.833883i
$20$	−1.48238			−0.331471
$21$		0			0
$22$	3.17874	−	2.66728i	0.677711	−	0.568667i
$23$	5.32803	−	1.93925i	1.11097	−	0.404361i	0.279622	−	0.960110i	$-0.409791\pi$
$23$	5.32803	−	1.93925i	1.11097	−	0.404361i	0.831350	+	0.555749i	$0.187569\pi$
$24$		0			0
$25$	0.766044	+	0.642788i	0.153209	+	0.128558i
$26$	0.845852	−	1.46506i	0.165885	−	0.287322i
$27$		0			0
$28$	−0.332562	+	1.88605i	−0.0628483	+	0.356430i
$29$	1.04556	−	5.92966i	0.194155	−	1.10111i	−0.719461	−	0.694533i	$-0.755611\pi$
$29$	1.04556	−	5.92966i	0.194155	−	1.10111i	0.913617	−	0.406577i	$-0.133278\pi$
$30$		0			0
$31$	1.19445	−	2.06885i	0.214529	−	0.371576i	−0.738598	−	0.674147i	$-0.764512\pi$
$31$	1.19445	−	2.06885i	0.214529	−	0.371576i	0.953127	+	0.302571i	$0.0978449\pi$
$32$	−4.47907	−	3.75839i	−0.791796	−	0.664395i
$33$		0			0
$34$	4.63104	−	1.68556i	0.794217	−	0.289071i
$35$	0.989683	−	0.830443i	0.167287	−	0.140370i
$36$		0			0
$37$	−4.53121			−0.744926			−0.372463	−	0.928047i	$-0.621487\pi$
$37$	−4.53121			−0.744926			−0.372463	+	0.928047i	$0.621487\pi$
$38$	−2.87593	−	1.25051i	−0.466537	−	0.202859i
$39$		0			0
$40$	0.435062	+	2.46736i	0.0687894	+	0.390124i
$41$	3.51177	−	2.94672i	0.548446	−	0.460201i	−0.325968	−	0.945381i	$-0.605690\pi$
$41$	3.51177	−	2.94672i	0.548446	−	0.460201i	0.874414	+	0.485180i	$0.161246\pi$
$42$		0			0
$43$	−0.260318	−	0.0947480i	−0.0396981	−	0.0144489i	0.322095	−	0.946707i	$-0.395613\pi$
$43$	−0.260318	−	0.0947480i	−0.0396981	−	0.0144489i	−0.361793	+	0.932258i	$0.617835\pi$
$44$	6.54954	+	5.49572i	0.987381	+	0.828511i
$45$		0			0
$46$	−2.03965	−	3.53278i	−0.300730	−	0.520880i
$47$	−0.0880430	+	0.499316i	−0.0128424	+	0.0728328i	−0.990555	−	0.137113i	$-0.956218\pi$
$47$	−0.0880430	+	0.499316i	−0.0128424	+	0.0728328i	0.977713	+	0.209946i	$0.0673288\pi$
$48$		0			0
$49$	2.66545	+	4.61669i	0.380778	+	0.659527i
$50$	0.359728	−	0.623068i	0.0508733	−	0.0881151i
$51$		0			0
$52$	3.27541	+	1.19215i	0.454217	+	0.165322i
$53$	−6.75604	+	2.45900i	−0.928013	+	0.337769i	−0.761422	−	0.648257i	$-0.775498\pi$
$53$	−6.75604	+	2.45900i	−0.928013	+	0.337769i	−0.166591	+	0.986026i	$0.553276\pi$
$54$		0			0
$55$	−1.00154	−	5.68000i	−0.135047	−	0.765891i
$56$	3.23685			0.432543
$57$		0			0
$58$	−4.33194			−0.568812
$59$	−1.00094	−	5.67662i	−0.130312	−	0.739034i	−0.978010	−	0.208556i	$-0.933124\pi$
$59$	−1.00094	−	5.67662i	−0.130312	−	0.739034i	0.847699	−	0.530478i	$-0.177987\pi$
$60$		0			0
$61$	6.77273	−	2.46507i	0.867160	−	0.315620i	0.130143	−	0.991495i	$-0.458456\pi$
$61$	6.77273	−	2.46507i	0.867160	−	0.315620i	0.737016	+	0.675875i	$0.236234\pi$
$62$	−1.61506	−	0.587833i	−0.205113	−	0.0746549i
$63$		0			0
$64$	−0.941117	+	1.63006i	−0.117640	+	0.203758i
$65$	−1.17568	−	2.03634i	−0.145825	−	0.252577i
$66$		0			0
$67$	−1.77501	+	10.0666i	−0.216852	+	1.22983i	0.660811	+	0.750552i	$0.270212\pi$
$67$	−1.77501	+	10.0666i	−0.216852	+	1.22983i	−0.877663	+	0.479278i	$0.840899\pi$
$68$	5.07713	+	8.79384i	0.615692	+	1.06641i
$69$		0			0
$70$	−0.712034	−	0.597468i	−0.0851044	−	0.0714110i
$71$	−1.05207	−	0.382923i	−0.124858	−	0.0454446i	0.278836	−	0.960339i	$-0.410052\pi$
$71$	−1.05207	−	0.382923i	−0.124858	−	0.0454446i	−0.403694	+	0.914894i	$0.632274\pi$
$72$		0			0
$73$	1.83298	−	1.53805i	0.214534	−	0.180016i	−0.529188	−	0.848505i	$-0.677503\pi$
$73$	1.83298	−	1.53805i	0.214534	−	0.180016i	0.743722	+	0.668489i	$0.233059\pi$
$74$	0.566094	+	3.21048i	0.0658071	+	0.373211i
$75$		0			0
$76$	1.50845	−	6.28301i	0.173032	−	0.720711i
$77$	−7.45142			−0.849168
$78$		0			0
$79$	−10.7969	+	9.05969i	−1.21475	+	1.01929i	−0.215666	+	0.976467i	$0.569192\pi$
$79$	−10.7969	+	9.05969i	−1.21475	+	1.01929i	−0.999082	+	0.0428275i	$0.986363\pi$
$80$	−1.09213	+	0.397503i	−0.122104	+	0.0444421i
$81$		0			0
$82$	−2.52657	−	2.12004i	−0.279012	−	0.234119i
$83$	0.608609	−	1.05414i	0.0668035	−	0.115707i	−0.830689	−	0.556737i	$-0.812053\pi$
$83$	0.608609	−	1.05414i	0.0668035	−	0.115707i	0.897493	+	0.441030i	$0.145387\pi$
$84$		0			0
$85$	1.18948	−	6.74589i	0.129018	−	0.731695i
$86$	−0.0346093	+	0.196279i	−0.00373202	+	0.0211653i
$87$		0			0
$88$	7.22517	−	12.5144i	0.770206	−	1.33404i
$89$	6.85239	+	5.74984i	0.726352	+	0.609482i	0.929135	−	0.369742i	$-0.120554\pi$
$89$	6.85239	+	5.74984i	0.726352	+	0.609482i	−0.202782	+	0.979224i	$0.564998\pi$
$90$		0			0
$91$	−2.85461	+	1.03899i	−0.299245	+	0.108916i
$92$	6.43866	−	5.40267i	0.671276	−	0.563268i
$93$		0			0
$94$	0.364778			0.0376240
$95$	−3.50395	+	2.59275i	−0.359497	+	0.266011i
$96$		0			0
$97$	−1.83977	−	10.4339i	−0.186801	−	1.05940i	−0.923620	−	0.383309i	$-0.874784\pi$
$97$	−1.83977	−	10.4339i	−0.186801	−	1.05940i	0.736819	−	0.676090i	$-0.236327\pi$
$98$	2.93805	−	2.46531i	0.296788	−	0.249034i
$99$		0			0
$100$	1.39298	+	0.507004i	0.139298	+	0.0507004i
$101$	−1.65550	−	1.38913i	−0.164728	−	0.138223i	0.556697	−	0.830715i	$-0.312068\pi$
$101$	−1.65550	−	1.38913i	−0.164728	−	0.138223i	−0.721426	+	0.692492i	$0.756513\pi$
$102$		0			0
$103$	−4.54154	−	7.86618i	−0.447491	−	0.775078i	0.550731	−	0.834683i	$-0.314349\pi$
$103$	−4.54154	−	7.86618i	−0.447491	−	0.775078i	−0.998222	+	0.0596051i	$0.981016\pi$
$104$	1.02299	−	5.80166i	0.100312	−	0.568899i
$105$		0			0
$106$	2.58631	+	4.47962i	0.251205	+	0.435099i
$107$	−1.93432	+	3.35035i	−0.186998	+	0.323890i	−0.944248	−	0.329235i	$-0.893209\pi$
$107$	−1.93432	+	3.35035i	−0.186998	+	0.323890i	0.757250	+	0.653125i	$0.226543\pi$
$108$		0			0
$109$	15.6852	+	5.70895i	1.50237	+	0.546818i	0.956673	−	0.291165i	$-0.0940429\pi$
$109$	15.6852	+	5.70895i	1.50237	+	0.546818i	0.545697	+	0.837983i	$0.316265\pi$
$110$	−3.89931	+	1.41923i	−0.371784	+	0.135318i
$111$		0			0
$112$	0.260736	+	1.47871i	0.0246372	+	0.139725i
$113$	18.0822			1.70103			0.850515	−	0.525951i	$-0.176291\pi$
$113$	18.0822			1.70103			0.850515	+	0.525951i	$0.176291\pi$
$114$		0			0
$115$	−5.66998			−0.528728
$116$	−1.54992	−	8.79002i	−0.143906	−	0.816133i
$117$		0			0
$118$	−3.89699	+	1.41839i	−0.358747	+	0.130573i
$119$	−8.31603	−	3.02679i	−0.762329	−	0.277465i
$120$		0			0
$121$	−11.1327	+	19.2825i	−1.01207	+	1.75295i
$122$	−2.59270	−	4.49070i	−0.234732	−	0.406568i
$123$		0			0
$124$	0.614933	−	3.48746i	0.0552226	−	0.313183i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$		0			0
$127$	8.26770	+	6.93743i	0.733640	+	0.615597i	0.931121	−	0.364710i	$-0.118832\pi$
$127$	8.26770	+	6.93743i	0.733640	+	0.615597i	−0.197481	+	0.980307i	$0.563276\pi$
$128$	−9.71627	−	3.53643i	−0.858805	−	0.312580i
$129$		0			0
$130$	−1.29592	+	1.08741i	−0.113660	+	0.0953718i
$131$	−2.19238	−	12.4336i	−0.191549	−	1.08633i	−0.917248	−	0.398317i	$-0.869594\pi$
$131$	−2.19238	−	12.4336i	−0.191549	−	1.08633i	0.725699	−	0.688013i	$-0.241517\pi$
$132$		0			0
$133$	2.51270	+	5.03978i	0.217879	+	0.437004i
$134$	7.35421			0.635307
$135$		0			0
$136$	13.1469	−	11.0316i	1.12734	−	0.945948i
$137$	−8.64939	+	3.14812i	−0.738967	+	0.268962i	−0.683956	−	0.729524i	$-0.739742\pi$
$137$	−8.64939	+	3.14812i	−0.738967	+	0.268962i	−0.0550118	+	0.998486i	$0.517520\pi$
$138$		0			0
$139$	3.63122	+	3.04696i	0.307996	+	0.258440i	0.783663	−	0.621186i	$-0.213349\pi$
$139$	3.63122	+	3.04696i	0.307996	+	0.258440i	−0.475667	+	0.879625i	$0.657793\pi$
$140$	0.957574	−	1.65857i	0.0809297	−	0.140174i
$141$		0			0
$142$	−0.139873	+	0.793261i	−0.0117379	+	0.0665690i
$143$	−2.35498	+	13.3557i	−0.196933	+	1.11686i
$144$		0			0
$145$	−3.01057	+	5.21445i	−0.250014	+	0.433037i
$146$	−1.31875	−	1.10656i	−0.109141	−	0.0915798i
$147$		0			0
$148$	−6.31189	+	2.29734i	−0.518835	+	0.188840i
$149$	−7.46788	+	6.26629i	−0.611792	+	0.513355i	−0.895212	−	0.445641i	$-0.852976\pi$
$149$	−7.46788	+	6.26629i	−0.611792	+	0.513355i	0.283419	+	0.958996i	$0.408531\pi$
$150$		0			0
$151$	−13.0214			−1.05967			−0.529834	−	0.848101i	$-0.677746\pi$
$151$	−13.0214			−1.05967			−0.529834	+	0.848101i	$0.677746\pi$
$152$	−10.9005	−	0.666765i	−0.884148	−	0.0540818i
$153$		0			0
$154$	0.930923	+	5.27953i	0.0750160	+	0.425437i
$155$	−1.83000	+	1.53555i	−0.146989	+	0.123339i
$156$		0			0
$157$	−17.4944	−	6.36745i	−1.39621	−	0.508178i	−0.469156	−	0.883115i	$-0.655442\pi$
$157$	−17.4944	−	6.36745i	−1.39621	−	0.508178i	−0.927050	+	0.374938i	$0.877664\pi$
$158$	7.76792	+	6.51806i	0.617982	+	0.518549i
$159$		0			0
$160$	2.92351	+	5.06366i	0.231124	+	0.400318i
$161$	−1.27202	+	7.21398i	−0.100249	+	0.568541i
$162$		0			0
$163$	4.94380	+	8.56291i	0.387228	+	0.670699i	0.992076	−	0.125642i	$-0.0400992\pi$
$163$	4.94380	+	8.56291i	0.387228	+	0.670699i	−0.604847	+	0.796341i	$0.706766\pi$
$164$	3.39783	−	5.88522i	0.265326	−	0.459558i
$165$		0			0
$166$	−0.822923	−	0.299519i	−0.0638712	−	0.0232472i
$167$	−11.2804	+	4.10574i	−0.872905	+	0.317711i	−0.739343	−	0.673329i	$-0.764864\pi$
$167$	−11.2804	+	4.10574i	−0.872905	+	0.317711i	−0.133562	+	0.991040i	$0.542642\pi$
$168$		0			0
$169$	−1.29734	−	7.35759i	−0.0997956	−	0.565969i
$170$	−4.92825			−0.377980
$171$		0			0
$172$	−0.410656			−0.0313122
$173$	−2.86662	−	16.2574i	−0.217945	−	1.23603i	−0.875722	−	0.482815i	$-0.839614\pi$
$173$	−2.86662	−	16.2574i	−0.217945	−	1.23603i	0.657777	−	0.753213i	$-0.271497\pi$
$174$		0			0
$175$	−1.21403	+	0.441869i	−0.0917717	+	0.0334022i
$176$	6.29899	+	2.29265i	0.474804	+	0.172815i
$177$		0			0
$178$	3.21783	−	5.57345i	0.241187	−	0.417747i
$179$	10.1073	+	17.5064i	0.755458	+	1.30849i	0.945146	+	0.326647i	$0.105919\pi$
$179$	10.1073	+	17.5064i	0.755458	+	1.30849i	−0.189688	+	0.981844i	$0.560748\pi$
$180$		0			0
$181$	0.0414421	−	0.235030i	0.00308037	−	0.0174696i	−0.983229	−	0.182376i	$-0.941621\pi$
$181$	0.0414421	−	0.235030i	0.00308037	−	0.0174696i	0.986309	+	0.164907i	$0.0527322\pi$
$182$	1.09279	+	1.89277i	0.0810029	+	0.140301i
$183$		0			0
$184$	−10.8822	−	9.13124i	−0.802246	−	0.673164i
$185$	4.25794	+	1.54976i	0.313050	+	0.113941i
$186$		0			0
$187$	−30.2649	+	25.3952i	−2.21319	+	1.85708i
$188$	0.130513	+	0.740178i	0.00951866	+	0.0539830i
$189$		0			0
$190$	2.27479	+	2.15872i	0.165031	+	0.156610i
$191$	0.323227			0.0233879			0.0116939	−	0.999932i	$-0.496278\pi$
$191$	0.323227			0.0233879			0.0116939	+	0.999932i	$0.496278\pi$
$192$		0			0
$193$	1.12114	−	0.940747i	0.0807013	−	0.0677164i	−0.601545	−	0.798839i	$-0.705448\pi$
$193$	1.12114	−	0.940747i	0.0807013	−	0.0677164i	0.682246	+	0.731123i	$0.261003\pi$
$194$	−7.16283	+	2.60706i	−0.514261	+	0.187176i
$195$		0			0
$196$	6.05360	+	5.07958i	0.432400	+	0.362827i
$197$	−4.77502	+	8.27058i	−0.340206	+	0.589255i	−0.984471	−	0.175548i	$-0.943830\pi$
$197$	−4.77502	+	8.27058i	−0.340206	+	0.589255i	0.644265	+	0.764803i	$0.277164\pi$
$198$		0			0
$199$	0.242795	−	1.37696i	0.0172113	−	0.0976101i	−0.974992	−	0.222240i	$-0.928663\pi$
$199$	0.242795	−	1.37696i	0.0172113	−	0.0976101i	0.992203	+	0.124630i	$0.0397743\pi$
$200$	0.435062	−	2.46736i	0.0307635	−	0.174469i
$201$		0			0
$202$	−0.777409	+	1.34651i	−0.0546983	+	0.0947402i
$203$	5.95901	+	5.00020i	0.418241	+	0.350946i
$204$		0			0
$205$	−4.30782	+	1.56792i	−0.300871	+	0.109508i
$206$	−5.00601	+	4.20054i	−0.348786	+	0.292666i
$207$		0			0
$208$	2.73280			0.189486
$209$	25.0936	+	1.53493i	1.73576	+	0.106173i
$210$		0			0
$211$	−2.95007	−	16.7307i	−0.203091	−	1.15179i	−0.900415	−	0.435031i	$-0.856737\pi$
$211$	−2.95007	−	16.7307i	−0.203091	−	1.15179i	0.697324	−	0.716756i	$-0.254374\pi$
$212$	−8.16432	+	6.85068i	−0.560728	+	0.470507i
$213$		0			0
$214$	2.61547	+	0.951954i	0.178790	+	0.0650742i
$215$	0.212213	+	0.178068i	0.0144728	+	0.0121441i
$216$		0			0
$217$	1.54316	+	2.67282i	0.104756	+	0.181443i
$218$	2.08535	−	11.8266i	0.141238	−	0.800999i
$219$		0			0
$220$	−4.27491	−	7.40436i	−0.288214	−	0.499202i
$221$	−8.05337	+	13.9488i	−0.541728	+	0.938301i
$222$		0			0
$223$	−11.0581	−	4.02483i	−0.740507	−	0.269523i	−0.0559018	−	0.998436i	$-0.517803\pi$
$223$	−11.0581	−	4.02483i	−0.740507	−	0.269523i	−0.684606	+	0.728914i	$0.740026\pi$
$224$	7.09843	−	2.58362i	0.474283	−	0.172625i
$225$		0			0
$226$	−2.25905	−	12.8117i	−0.150270	−	0.852223i
$227$	−27.5106			−1.82594			−0.912971	−	0.408025i	$-0.866218\pi$
$227$	−27.5106			−1.82594			−0.912971	+	0.408025i	$0.866218\pi$
$228$		0			0
$229$	−9.40958			−0.621802			−0.310901	−	0.950442i	$-0.600631\pi$
$229$	−9.40958			−0.621802			−0.310901	+	0.950442i	$0.600631\pi$
$230$	0.708363	+	4.01733i	0.0467081	+	0.264895i
$231$		0			0
$232$	−14.1757	+	5.15954i	−0.930681	+	0.338740i
$233$	1.04994	+	0.382148i	0.0687841	+	0.0250354i	0.376183	−	0.926545i	$-0.377236\pi$
$233$	1.04994	+	0.382148i	0.0687841	+	0.0250354i	−0.307399	+	0.951581i	$0.599459\pi$
$234$		0			0
$235$	0.253510	−	0.439092i	0.0165371	−	0.0286432i
$236$	−4.27237	−	7.39996i	−0.278108	−	0.481696i
$237$		0			0
$238$	−1.10562	+	6.27027i	−0.0716666	+	0.406441i
$239$	−6.48276	−	11.2285i	−0.419335	−	0.726310i	0.576538	−	0.817071i	$-0.304403\pi$
$239$	−6.48276	−	11.2285i	−0.419335	−	0.726310i	−0.995873	+	0.0907608i	$0.971070\pi$
$240$		0			0
$241$	−15.6540	−	13.1353i	−1.00836	−	0.846118i	−0.0202435	−	0.999795i	$-0.506444\pi$
$241$	−15.6540	−	13.1353i	−1.00836	−	0.846118i	−0.988121	+	0.153677i	$0.950889\pi$
$242$	15.0530	+	5.47884i	0.967643	+	0.352193i
$243$		0			0
$244$	8.18450	−	6.86761i	0.523959	−	0.439654i
$245$	−0.925700	−	5.24990i	−0.0591408	−	0.335404i
$246$		0			0
$247$	9.82729	−	2.91092i	0.625296	−	0.185217i
$248$	−5.98520			−0.380061
$249$		0			0
$250$	−0.551136	+	0.462458i	−0.0348569	+	0.0292484i
$251$	−15.5328	+	5.65348i	−0.980422	+	0.356844i	−0.782004	−	0.623273i	$-0.785802\pi$
$251$	−15.5328	+	5.65348i	−0.980422	+	0.356844i	−0.198418	+	0.980118i	$0.563580\pi$
$252$		0			0
$253$	25.0514	+	21.0206i	1.57497	+	1.32156i
$254$	3.88245	−	6.72460i	0.243606	−	0.421939i
$255$		0			0
$256$	−1.94547	+	11.0333i	−0.121592	+	0.689583i
$257$	2.02701	−	11.4958i	0.126442	−	0.717087i	−0.853999	−	0.520274i	$-0.825830\pi$
$257$	2.02701	−	11.4958i	0.126442	−	0.717087i	0.980441	−	0.196813i	$-0.0630591\pi$
$258$		0			0
$259$	2.92702	−	5.06975i	0.181876	−	0.315019i
$260$	−2.67014	−	2.24051i	−0.165595	−	0.138951i
$261$		0			0
$262$	−8.53564	+	3.10672i	−0.527334	+	0.191934i
$263$	5.34724	−	4.48687i	0.329725	−	0.276672i	−0.462863	−	0.886430i	$-0.653178\pi$
$263$	5.34724	−	4.48687i	0.329725	−	0.276672i	0.792588	+	0.609758i	$0.208733\pi$
$264$		0			0
$265$	7.18962			0.441655
$266$	3.25690	−	2.40995i	0.199693	−	0.147763i
$267$		0			0
$268$	2.63125	+	14.9225i	0.160729	+	0.911539i
$269$	3.94311	−	3.30866i	0.240416	−	0.201733i	−0.514617	−	0.857420i	$-0.672066\pi$
$269$	3.94311	−	3.30866i	0.240416	−	0.201733i	0.755032	+	0.655688i	$0.227621\pi$
$270$		0			0
$271$	3.24655	+	1.18165i	0.197214	+	0.0717801i	0.438739	−	0.898615i	$-0.355425\pi$
$271$	3.24655	+	1.18165i	0.197214	+	0.0717801i	−0.241525	+	0.970395i	$0.577648\pi$
$272$	6.09860	+	5.11733i	0.369782	+	0.310284i
$273$		0			0
$274$	3.31112	+	5.73502i	0.200032	+	0.346465i
$275$	−1.00154	+	5.68000i	−0.0603950	+	0.342517i
$276$		0			0
$277$	−4.09007	−	7.08421i	−0.245749	−	0.425649i	0.716593	−	0.697491i	$-0.245700\pi$
$277$	−4.09007	−	7.08421i	−0.245749	−	0.425649i	−0.962342	+	0.271842i	$0.912367\pi$
$278$	1.70519	−	2.95348i	0.102271	−	0.177138i
$279$		0			0
$280$	−3.04165	−	1.10707i	−0.181773	−	0.0661601i
$281$	10.5082	−	3.82467i	0.626866	−	0.228160i	−0.00900091	−	0.999959i	$-0.502865\pi$
$281$	10.5082	−	3.82467i	0.626866	−	0.228160i	0.635866	+	0.771799i	$0.280643\pi$
$282$		0			0
$283$	3.01728	+	17.1119i	0.179359	+	1.01719i	0.932992	+	0.359898i	$0.117189\pi$
$283$	3.01728	+	17.1119i	0.179359	+	1.01719i	−0.753633	+	0.657296i	$0.771700\pi$
$284$	−1.65966			−0.0984829
$285$		0			0
$286$	9.75711			0.576950
$287$	1.02845	+	5.83264i	0.0607076	+	0.344290i
$288$		0			0
$289$	−28.1174	+	10.2339i	−1.65397	+	0.601994i
$290$	4.07070	+	1.48161i	0.239040	+	0.0870033i
$291$		0			0
$292$	1.77351	−	3.07181i	0.103787	−	0.179764i
$293$	1.43049	+	2.47768i	0.0835699	+	0.144747i	0.904781	−	0.425877i	$-0.140034\pi$
$293$	1.43049	+	2.47768i	0.0835699	+	0.144747i	−0.821211	+	0.570625i	$0.806701\pi$
$294$		0			0
$295$	−1.00094	+	5.67662i	−0.0582771	+	0.330506i
$296$	5.67630	+	9.83163i	0.329928	+	0.571452i
$297$		0			0
$298$	5.37282	+	4.50833i	0.311239	+	0.261160i
$299$	12.5281	+	4.55987i	0.724521	+	0.263704i
$300$		0			0
$301$	0.274166	−	0.230053i	0.0158027	−	0.0132600i
$302$	1.62680	+	9.22602i	0.0936116	+	0.530898i
$303$		0			0
$304$	−0.573459	−	5.03344i	−0.0328901	−	0.288687i
$305$	−7.20739			−0.412694
$306$		0			0
$307$	21.4527	−	18.0009i	1.22437	−	1.02737i	0.225784	−	0.974177i	$-0.427506\pi$
$307$	21.4527	−	18.0009i	1.22437	−	1.02737i	0.998584	−	0.0531897i	$-0.0169388\pi$
$308$	−10.3797	+	3.77790i	−0.591438	+	0.215266i
$309$		0			0
$310$	1.31661	+	1.10476i	0.0747783	+	0.0627464i
$311$	−10.9646	+	18.9912i	−0.621744	+	1.07689i	0.367417	+	0.930056i	$0.380242\pi$
$311$	−10.9646	+	18.9912i	−0.621744	+	1.07689i	−0.989161	+	0.146836i	$0.953091\pi$
$312$		0			0
$313$	0.204904	−	1.16207i	0.0115819	−	0.0656841i	−0.978469	−	0.206394i	$-0.933827\pi$
$313$	0.204904	−	1.16207i	0.0115819	−	0.0656841i	0.990051	+	0.140710i	$0.0449384\pi$
$314$	−2.32589	+	13.1908i	−0.131257	+	0.744398i
$315$		0			0
$316$	−10.4466	+	18.0941i	−0.587668	+	1.01787i
$317$	−22.7839	−	19.1180i	−1.27967	−	1.07377i	−0.993289	−	0.115660i	$-0.963102\pi$
$317$	−22.7839	−	19.1180i	−1.27967	−	1.07377i	−0.286385	−	0.958115i	$-0.592454\pi$
$318$		0			0
$319$	32.6333	−	11.8775i	1.82711	−	0.665015i
$320$	1.44188	−	1.20988i	0.0806033	−	0.0676342i
$321$		0			0
$322$	5.27021			0.293697
$323$	27.3818	+	11.9061i	1.52356	+	0.662474i
$324$		0			0
$325$	0.408310	+	2.31564i	0.0226489	+	0.128449i
$326$	5.44941	−	4.57260i	0.301815	−	0.253253i
$327$		0			0
$328$	−10.7929	−	3.92830i	−0.595939	−	0.216904i
$329$	−0.501788	−	0.421050i	−0.0276645	−	0.0232133i
$330$		0			0
$331$	12.7192	+	22.0304i	0.699113	+	1.21090i	0.968774	+	0.247944i	$0.0797549\pi$
$331$	12.7192	+	22.0304i	0.699113	+	1.21090i	−0.269662	+	0.962955i	$0.586912\pi$
$332$	0.313328	−	1.77697i	0.0171961	−	0.0975239i
$333$		0			0
$334$	4.31831	+	7.47954i	0.236288	+	0.409262i
$335$	5.11094	−	8.85241i	0.279241	−	0.483659i
$336$		0			0
$337$	−11.0931	−	4.03756i	−0.604280	−	0.219940i	0.0217189	−	0.999764i	$-0.493086\pi$
$337$	−11.0931	−	4.03756i	−0.604280	−	0.219940i	−0.625998	+	0.779824i	$0.715308\pi$
$338$	−5.05097	+	1.83840i	−0.274737	+	0.0999960i
$339$		0			0
$340$	−1.76327	−	9.99999i	−0.0956266	−	0.542326i
$341$	13.7783			0.746135
$342$		0			0
$343$	−15.9308			−0.860180
$344$	0.120523	+	0.683519i	0.00649816	+	0.0368529i
$345$		0			0
$346$	−11.1607	+	4.06215i	−0.600001	+	0.218383i
$347$	−4.62279	−	1.68256i	−0.248164	−	0.0903244i	0.214943	−	0.976627i	$-0.431043\pi$
$347$	−4.62279	−	1.68256i	−0.248164	−	0.0903244i	−0.463107	+	0.886302i	$0.653266\pi$
$348$		0			0
$349$	18.1158	−	31.3775i	0.969717	−	1.67960i	0.273349	−	0.961915i	$-0.411869\pi$
$349$	18.1158	−	31.3775i	0.969717	−	1.67960i	0.696368	−	0.717685i	$-0.254798\pi$
$350$	0.464747	+	0.804966i	0.0248418	+	0.0430272i
$351$		0			0
$352$	5.85600	−	33.2110i	0.312126	−	1.77015i
$353$	−12.7952	−	22.1620i	−0.681022	−	1.17957i	−0.974669	−	0.223651i	$-0.928202\pi$
$353$	−12.7952	−	22.1620i	−0.681022	−	1.17957i	0.293647	−	0.955914i	$-0.405131\pi$
$354$		0			0
$355$	0.857657	+	0.719660i	0.0455197	+	0.0381956i
$356$	12.4605	+	4.53524i	0.660403	+	0.240367i
$357$		0			0
$358$	11.1410	−	9.34844i	0.588822	−	0.494080i
$359$	−5.34835	−	30.3320i	−0.282275	−	1.60086i	−0.714859	−	0.699269i	$-0.753509\pi$
$359$	−5.34835	−	30.3320i	−0.282275	−	1.60086i	0.432583	−	0.901594i	$-0.357602\pi$
$360$		0			0
$361$	−7.42369	−	17.4897i	−0.390721	−	0.920509i
$362$	−0.171702			−0.00902447
$363$		0			0
$364$	−3.44965	+	2.89460i	−0.180811	+	0.151718i
$365$	−2.24848	+	0.818381i	−0.117691	+	0.0428360i
$366$		0			0
$367$	23.0842	+	19.3699i	1.20499	+	1.01110i	0.999473	+	0.0324481i	$0.0103304\pi$
$367$	23.0842	+	19.3699i	1.20499	+	1.01110i	0.205512	+	0.978655i	$0.434114\pi$
$368$	3.29488	−	5.70690i	0.171757	−	0.297493i
$369$		0			0
$370$	0.566094	−	3.21048i	0.0294298	−	0.166905i
$371$	1.61294	−	9.14744i	0.0837397	−	0.474912i
$372$		0			0
$373$	14.0122	−	24.2699i	0.725526	−	1.25665i	−0.233231	−	0.972421i	$-0.574930\pi$
$373$	14.0122	−	24.2699i	0.725526	−	1.25665i	0.958757	−	0.284227i	$-0.0917369\pi$
$374$	21.7743	+	18.2708i	1.12592	+	0.944760i
$375$		0			0
$376$	1.19369	−	0.434467i	0.0615598	−	0.0224059i
$377$	10.8456	−	9.10050i	0.558574	−	0.468699i
$378$		0			0
$379$	−22.6159			−1.16170			−0.580851	−	0.814010i	$-0.697280\pi$
$379$	−22.6159			−1.16170			−0.580851	+	0.814010i	$0.697280\pi$
$380$	−3.56640	+	5.38818i	−0.182952	+	0.276408i
$381$		0			0
$382$	−0.0403815	−	0.229015i	−0.00206610	−	0.0117174i
$383$	−7.67822	+	6.44279i	−0.392339	+	0.329211i	−0.817523	−	0.575895i	$-0.804654\pi$
$383$	−7.67822	+	6.44279i	−0.392339	+	0.329211i	0.425185	+	0.905107i	$0.360209\pi$
$384$		0			0
$385$	7.00204	+	2.54854i	0.356857	+	0.129885i
$386$	−0.806611	−	0.676827i	−0.0410554	−	0.0344496i
$387$		0			0
$388$	−7.85279	−	13.6014i	−0.398665	−	0.690508i
$389$	1.26793	−	7.19077i	0.0642865	−	0.364587i	−0.935646	−	0.352941i	$-0.885182\pi$
$389$	1.26793	−	7.19077i	0.0642865	−	0.364587i	0.999932	−	0.0116460i	$-0.00370714\pi$
$390$		0			0
$391$	19.4195	+	33.6356i	0.982089	+	1.70103i
$392$	6.67807	−	11.5668i	0.337294	−	0.584210i
$393$		0			0
$394$	6.45648	+	2.34997i	0.325273	+	0.118390i
$395$	13.2444	−	4.82056i	0.666397	−	0.242549i
$396$		0			0
$397$	−6.31493	−	35.8137i	−0.316937	−	1.79744i	−0.561145	−	0.827717i	$-0.689639\pi$
$397$	−6.31493	−	35.8137i	−0.316937	−	1.79744i	0.244208	−	0.969723i	$-0.421472\pi$
$398$	−1.00595			−0.0504235
$399$		0			0
$400$	1.16222			0.0581110
$401$	−1.58822	−	9.00726i	−0.0793121	−	0.449801i	−0.998440	−	0.0558411i	$-0.982216\pi$
$401$	−1.58822	−	9.00726i	−0.0793121	−	0.449801i	0.919128	−	0.393960i	$-0.128895\pi$
$402$		0			0
$403$	5.27841	−	1.92118i	0.262936	−	0.0957009i
$404$	−3.01038	−	1.09569i	−0.149772	−	0.0545125i
$405$		0			0
$406$	2.79830	−	4.84681i	0.138878	−	0.240543i
$407$	−13.0671	−	22.6330i	−0.647714	−	1.12187i
$408$		0			0
$409$	−0.814898	+	4.62152i	−0.0402941	+	0.228519i	−0.998304	−	0.0582158i	$-0.981459\pi$
$409$	−0.814898	+	4.62152i	−0.0402941	+	0.228519i	0.958010	+	0.286735i	$0.0925700\pi$
$410$	1.64910	+	2.85632i	0.0814432	+	0.141064i
$411$		0			0
$412$	−10.3145	−	8.65488i	−0.508158	−	0.426395i
$413$	6.99788	+	2.54702i	0.344343	+	0.125331i
$414$		0			0
$415$	−0.932443	+	0.782413i	−0.0457718	+	0.0384071i
$416$	−2.38739	−	13.5396i	−0.117052	−	0.663832i
$417$		0			0
$418$	−2.04746	−	17.9712i	−0.100145	−	0.879002i
$419$	0.588477			0.0287490			0.0143745	−	0.999897i	$-0.495424\pi$
$419$	0.588477			0.0287490			0.0143745	+	0.999897i	$0.495424\pi$
$420$		0			0
$421$	−4.71306	+	3.95473i	−0.229701	+	0.192742i	−0.750373	−	0.661015i	$-0.770126\pi$
$421$	−4.71306	+	3.95473i	−0.229701	+	0.192742i	0.520672	+	0.853757i	$0.325681\pi$
$422$	−11.4856	+	4.18040i	−0.559109	+	0.203499i
$423$		0			0
$424$	13.7988	+	11.5786i	0.670129	+	0.562305i
$425$	−3.42498	+	5.93224i	−0.166136	+	0.287756i
$426$		0			0
$427$	−1.61693	+	9.17005i	−0.0782486	+	0.443770i
$428$	−0.995840	+	5.64769i	−0.0481358	+	0.272991i
$429$		0			0
$430$	0.0996536	−	0.172605i	0.00480572	−	0.00832376i
$431$	0.241775	+	0.202873i	0.0116459	+	0.00977207i	0.648592	−	0.761136i	$-0.275358\pi$
$431$	0.241775	+	0.202873i	0.0116459	+	0.00977207i	−0.636946	+	0.770908i	$0.719803\pi$
$432$		0			0
$433$	−32.1844	+	11.7142i	−1.54668	+	0.562947i	−0.967637	−	0.252348i	$-0.918797\pi$
$433$	−32.1844	+	11.7142i	−1.54668	+	0.562947i	−0.579046	+	0.815295i	$0.696575\pi$
$434$	1.70098	−	1.42729i	0.0816495	−	0.0685121i
$435$		0			0
$436$	24.7437			1.18501
$437$	5.76970	−	24.0319i	0.276002	−	1.14960i
$438$		0			0
$439$	−0.363229	−	2.05997i	−0.0173360	−	0.0983172i	0.974912	−	0.222590i	$-0.0714512\pi$
$439$	−0.363229	−	2.05997i	−0.0173360	−	0.0983172i	−0.992248	+	0.124273i	$0.960340\pi$
$440$	−11.0696	+	9.28850i	−0.527723	+	0.442812i
$441$		0			0
$442$	10.8893	+	3.96336i	0.517949	+	0.188518i
$443$	6.51336	+	5.46536i	0.309459	+	0.259667i	0.784268	−	0.620422i	$-0.213039\pi$
$443$	6.51336	+	5.46536i	0.309459	+	0.259667i	−0.474809	+	0.880089i	$0.657483\pi$
$444$		0			0
$445$	−4.47258	−	7.74674i	−0.212021	−	0.367231i
$446$	−1.47018	+	8.33782i	−0.0696151	+	0.394807i
$447$		0			0
$448$	−1.21587	−	2.10594i	−0.0574443	−	0.0994964i
$449$	−7.75850	+	13.4381i	−0.366146	+	0.634184i	−0.988959	−	0.148187i	$-0.952656\pi$
$449$	−7.75850	+	13.4381i	−0.366146	+	0.634184i	0.622813	+	0.782371i	$0.285990\pi$
$450$		0			0
$451$	24.8459	+	9.04316i	1.16995	+	0.425826i
$452$	25.1882	−	9.16775i	1.18475	−	0.431215i
$453$		0			0
$454$	3.43696	+	19.4920i	0.161305	+	0.914804i
$455$	3.03782			0.142415
$456$		0			0
$457$	37.2930			1.74449			0.872247	−	0.489065i	$-0.162662\pi$
$457$	37.2930			1.74449			0.872247	+	0.489065i	$0.162662\pi$
$458$	1.17556	+	6.66694i	0.0549303	+	0.311525i
$459$		0			0
$460$	−7.89818	+	2.87470i	−0.368255	+	0.134034i
$461$	−16.4663	−	5.99324i	−0.766912	−	0.279133i	−0.0712079	−	0.997461i	$-0.522685\pi$
$461$	−16.4663	−	5.99324i	−0.766912	−	0.279133i	−0.695704	+	0.718328i	$0.744908\pi$
$462$		0			0
$463$	16.7188	−	28.9578i	0.776987	−	1.34578i	−0.156683	−	0.987649i	$-0.550080\pi$
$463$	16.7188	−	28.9578i	0.776987	−	1.34578i	0.933671	−	0.358133i	$-0.116586\pi$
$464$	−3.49894	−	6.06034i	−0.162434	−	0.281344i
$465$		0			0
$466$	0.139590	−	0.791656i	0.00646640	−	0.0366728i
$467$	7.48091	+	12.9573i	0.346175	+	0.599593i	0.985567	−	0.169288i	$-0.0541469\pi$
$467$	7.48091	+	12.9573i	0.346175	+	0.599593i	−0.639391	+	0.768882i	$0.720814\pi$
$468$		0			0
$469$	−10.1164	−	8.48869i	−0.467133	−	0.391971i
$470$	−0.342780	−	0.124762i	−0.0158112	−	0.00575482i
$471$		0			0
$472$	−11.0630	+	9.28298i	−0.509217	+	0.427284i
$473$	−0.277450	−	1.57350i	−0.0127572	−	0.0723496i
$474$		0			0
$475$	4.17941	−	1.23797i	0.191764	−	0.0568020i
$476$	−13.1187			−0.601294
$477$		0			0
$478$	−7.14577	+	5.99601i	−0.326840	+	0.274251i
$479$	−14.8807	+	5.41612i	−0.679915	+	0.247469i	−0.658811	−	0.752309i	$-0.728940\pi$
$479$	−14.8807	+	5.41612i	−0.679915	+	0.247469i	−0.0211037	+	0.999777i	$0.506718\pi$
$480$		0			0
$481$	−8.16183	−	6.84858i	−0.372147	−	0.312269i
$482$	−7.35101	+	12.7323i	−0.334829	+	0.579941i
$483$		0			0
$484$	−5.73142	+	32.5045i	−0.260519	+	1.47748i
$485$	−1.83977	+	10.4339i	−0.0835398	+	0.473778i
$486$		0			0
$487$	−3.24767	+	5.62514i	−0.147166	+	0.254899i	−0.930179	−	0.367106i	$-0.880349\pi$
$487$	−3.24767	+	5.62514i	−0.147166	+	0.254899i	0.783013	+	0.622006i	$0.213682\pi$
$488$	−13.8329	−	11.6072i	−0.626186	−	0.525433i
$489$		0			0
$490$	−3.60405	+	1.31177i	−0.162814	+	0.0592596i
$491$	1.28942	−	1.08195i	0.0581905	−	0.0488277i	−0.613229	−	0.789906i	$-0.710130\pi$
$491$	1.28942	−	1.08195i	0.0581905	−	0.0488277i	0.671419	+	0.741078i	$0.265685\pi$
$492$		0			0
$493$	41.2445			1.85756
$494$	−3.29021	−	6.59923i	−0.148034	−	0.296914i
$495$		0			0
$496$	−0.482121	−	2.73424i	−0.0216479	−	0.122771i
$497$	1.10804	−	0.929757i	0.0497024	−	0.0417053i
$498$		0			0
$499$	−12.5320	−	4.56129i	−0.561011	−	0.204191i	0.0459208	−	0.998945i	$-0.485378\pi$
$499$	−12.5320	−	4.56129i	−0.561011	−	0.204191i	−0.606932	+	0.794754i	$0.707600\pi$
$500$	−1.13557	−	0.952857i	−0.0507843	−	0.0426130i
$501$		0			0
$502$	5.94619	+	10.2991i	0.265391	+	0.459672i
$503$	−1.32303	+	7.50329i	−0.0589911	+	0.334555i	−0.999993	−	0.00384718i	$-0.998775\pi$
$503$	−1.32303	+	7.50329i	−0.0589911	+	0.334555i	0.941001	+	0.338402i	$0.109887\pi$
$504$		0			0
$505$	1.08055	+	1.87157i	0.0480838	+	0.0832836i
$506$	11.7639	−	20.3757i	0.522971	−	0.905812i
$507$		0			0
$508$	15.0341	+	5.47196i	0.667029	+	0.242779i
$509$	17.8484	−	6.49628i	0.791116	−	0.287943i	0.0853161	−	0.996354i	$-0.472810\pi$
$509$	17.8484	−	6.49628i	0.791116	−	0.287943i	0.705800	+	0.708411i	$0.250588\pi$
$510$		0			0
$511$	0.536805	+	3.04437i	0.0237468	+	0.134675i
$512$	−12.6192			−0.557696
$513$		0			0
$514$	−8.39830			−0.370433
$515$	1.57726	+	8.94509i	0.0695024	+	0.394168i
$516$		0			0
$517$	−2.74794	+	1.00017i	−0.120854	+	0.0439873i
$518$	−3.95773	−	1.44050i	−0.173893	−	0.0632918i
$519$		0			0
$520$	−2.94558	+	5.10189i	−0.129172	+	0.223733i
$521$	10.1510	+	17.5821i	0.444724	+	0.770285i	0.998033	−	0.0626910i	$-0.0199683\pi$
$521$	10.1510	+	17.5821i	0.444724	+	0.770285i	−0.553308	+	0.832976i	$0.686635\pi$
$522$		0			0
$523$	−2.66928	+	15.1382i	−0.116719	+	0.661948i	0.869165	+	0.494522i	$0.164657\pi$
$523$	−2.66928	+	15.1382i	−0.116719	+	0.661948i	−0.985885	+	0.167426i	$0.946454\pi$
$524$	−9.35784	−	16.2083i	−0.408799	−	0.708061i
$525$		0			0
$526$	−3.84711	−	3.22811i	−0.167742	−	0.140752i
$527$	15.3770	+	5.59677i	0.669832	+	0.243799i
$528$		0			0
$529$	7.00825	−	5.88062i	0.304706	−	0.255679i
$530$	−0.898217	−	5.09404i	−0.0390160	−	0.221271i
$531$		0			0
$532$	6.05534	+	5.74637i	0.262532	+	0.249137i
$533$	10.7793			0.466904
$534$		0			0
$535$	2.96356	−	2.48672i	0.128126	−	0.107510i
$536$	24.0657	−	8.75919i	1.03948	−	0.378339i
$537$		0			0
$538$	−2.83690	−	2.38044i	−0.122307	−	0.102628i
$539$	−15.3733	+	26.6273i	−0.662175	+	1.14692i
$540$		0			0
$541$	2.26414	−	12.8406i	0.0973431	−	0.552060i	−0.896661	−	0.442718i	$-0.854014\pi$
$541$	2.26414	−	12.8406i	0.0973431	−	0.552060i	0.994004	−	0.109342i	$-0.0348745\pi$
$542$	0.431630	−	2.44790i	0.0185401	−	0.105146i
$543$		0			0
$544$	20.0259	−	34.6859i	0.858603	−	1.48714i
$545$	−12.7867	−	10.7293i	−0.547722	−	0.459593i
$546$		0			0
$547$	−13.7727	+	5.01285i	−0.588878	+	0.214334i	−0.619236	−	0.785205i	$-0.712557\pi$
$547$	−13.7727	+	5.01285i	−0.588878	+	0.214334i	0.0303580	+	0.999539i	$0.490335\pi$
$548$	−10.4523	+	8.77056i	−0.446502	+	0.374660i
$549$		0			0
$550$	4.14956			0.176938
$551$	−19.0377	−	18.0663i	−0.811034	−	0.769651i
$552$		0			0
$553$	−3.16197	−	17.9324i	−0.134461	−	0.762565i
$554$	−4.50837	+	3.78297i	−0.191542	+	0.160723i
$555$		0			0
$556$	6.60306	+	2.40332i	0.280032	+	0.101923i
$557$	23.1541	+	19.4286i	0.981071	+	0.823216i	0.984251	−	0.176779i	$-0.0565677\pi$
$557$	23.1541	+	19.4286i	0.981071	+	0.823216i	−0.00317970	+	0.999995i	$0.501012\pi$
$558$		0			0
$559$	−0.325692	−	0.564116i	−0.0137753	−	0.0238596i
$560$	0.260736	−	1.47871i	0.0110181	−	0.0624867i
$561$		0			0
$562$	−4.02269	−	6.96750i	−0.169687	−	0.293906i
$563$	9.01300	−	15.6110i	0.379853	−	0.657924i	−0.611188	−	0.791486i	$-0.709308\pi$
$563$	9.01300	−	15.6110i	0.379853	−	0.657924i	0.991041	+	0.133561i	$0.0426413\pi$
$564$		0			0
$565$	−16.9917	−	6.18447i	−0.714846	−	0.260183i
$566$	11.7472	−	4.27565i	0.493774	−	0.179719i
$567$		0			0
$568$	0.487092	+	2.76244i	0.0204379	+	0.115909i
$569$	39.6582			1.66256			0.831280	−	0.555854i	$-0.187609\pi$
$569$	39.6582			1.66256			0.831280	+	0.555854i	$0.187609\pi$
$570$		0			0
$571$	−31.2303			−1.30695			−0.653473	−	0.756950i	$-0.726689\pi$
$571$	−31.2303			−1.30695			−0.653473	+	0.756950i	$0.726689\pi$
$572$	3.49097	+	19.7983i	0.145965	+	0.827809i
$573$		0			0
$574$	4.00410	−	1.45737i	0.167128	−	0.0608295i
$575$	5.32803	+	1.93925i	0.222194	+	0.0808721i
$576$		0			0
$577$	−8.82708	+	15.2890i	−0.367476	+	0.636488i	−0.989170	−	0.146773i	$-0.953111\pi$
$577$	−8.82708	+	15.2890i	−0.367476	+	0.636488i	0.621694	+	0.783260i	$0.286445\pi$
$578$	10.7638	+	18.6434i	0.447714	+	0.775463i
$579$		0			0
$580$	−1.54992	+	8.79002i	−0.0643568	+	0.364986i
$581$	0.786286	+	1.36189i	0.0326206	+	0.0565006i
$582$		0			0
$583$	−31.7656	−	26.6545i	−1.31560	−	1.10392i
$584$	−5.63340	−	2.05039i	−0.233112	−	0.0848458i
$585$		0			0
$586$	1.57679	−	1.32308i	0.0651364	−	0.0546559i
$587$	−0.824684	−	4.67702i	−0.0340384	−	0.193041i	0.963047	−	0.269333i	$-0.0868031\pi$
$587$	−0.824684	−	4.67702i	−0.0340384	−	0.193041i	−0.997086	+	0.0762916i	$0.975692\pi$
$588$		0			0
$589$	−4.64619	−	9.31895i	−0.191443	−	0.383980i
$590$	4.14709			0.170733
$591$		0			0
$592$	−4.03419	+	3.38509i	−0.165804	+	0.139126i
$593$	4.38739	−	1.59688i	0.180168	−	0.0655760i	−0.250361	−	0.968153i	$-0.580549\pi$
$593$	4.38739	−	1.59688i	0.180168	−	0.0655760i	0.430529	+	0.902577i	$0.358327\pi$
$594$		0			0
$595$	6.77929	+	5.68850i	0.277924	+	0.233206i
$596$	−7.22559	+	12.5151i	−0.295972	+	0.512638i
$597$		0			0
$598$	1.66562	−	9.44619i	0.0681122	−	0.386284i
$599$	−5.76250	+	32.6807i	−0.235449	+	1.33530i	0.606216	+	0.795300i	$0.292687\pi$
$599$	−5.76250	+	32.6807i	−0.235449	+	1.33530i	−0.841666	+	0.539999i	$0.818425\pi$
$600$		0			0
$601$	9.35026	−	16.1951i	0.381405	−	0.660613i	−0.609858	−	0.792510i	$-0.708774\pi$
$601$	9.35026	−	16.1951i	0.381405	−	0.660613i	0.991263	+	0.131898i	$0.0421070\pi$
$602$	−0.197251	−	0.165513i	−0.00803935	−	0.00674581i
$603$		0			0
$604$	−18.1386	+	6.60192i	−0.738050	+	0.268628i
$605$	17.0563	−	14.3120i	0.693439	−	0.581865i
$606$		0			0
$607$	8.41685			0.341629			0.170815	−	0.985303i	$-0.445360\pi$
$607$	8.41685			0.341629			0.170815	+	0.985303i	$0.445360\pi$
$608$	−24.4370	+	7.23843i	−0.991053	+	0.293557i
$609$		0			0
$610$	0.900437	+	5.10663i	0.0364576	+	0.206761i
$611$	−0.913267	+	0.766322i	−0.0369468	+	0.0310021i
$612$		0			0
$613$	32.7815	+	11.9315i	1.32403	+	0.481908i	0.904748	−	0.425947i	$-0.140059\pi$
$613$	32.7815	+	11.9315i	1.32403	+	0.481908i	0.419283	+	0.907855i	$0.362281\pi$
$614$	−15.4343	−	12.9509i	−0.622876	−	0.522655i
$615$		0			0
$616$	9.33448	+	16.1678i	0.376097	+	0.651419i
$617$	−7.14999	+	40.5496i	−0.287848	+	1.63247i	0.407084	+	0.913391i	$0.366546\pi$
$617$	−7.14999	+	40.5496i	−0.287848	+	1.63247i	−0.694932	+	0.719076i	$0.744565\pi$
$618$		0			0
$619$	−8.59148	−	14.8809i	−0.345321	−	0.598113i	0.640091	−	0.768299i	$-0.278897\pi$
$619$	−8.59148	−	14.8809i	−0.345321	−	0.598113i	−0.985412	+	0.170186i	$0.945563\pi$
$620$	−1.77063	+	3.06682i	−0.0711102	+	0.123166i
$621$		0			0
$622$	14.8256	+	5.39608i	0.594453	+	0.216363i
$623$	−10.8597	+	3.95259i	−0.435083	+	0.158357i
$624$		0			0
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	−0.848957			−0.0339311
$627$		0			0
$628$	−27.5978			−1.10127
$629$	−5.38979	−	30.5670i	−0.214905	−	1.21879i
$630$		0			0
$631$	−9.86061	+	3.58897i	−0.392545	+	0.142875i	−0.530749	−	0.847529i	$-0.678089\pi$
$631$	−9.86061	+	3.58897i	−0.392545	+	0.142875i	0.138204	+	0.990404i	$0.455867\pi$
$632$	33.1828	+	12.0775i	1.31994	+	0.480419i
$633$		0			0
$634$	−10.6992	+	18.5315i	−0.424918	+	0.735980i
$635$	−5.39636	−	9.34677i	−0.214148	−	0.370915i
$636$		0			0
$637$	−2.17666	+	12.3444i	−0.0862422	+	0.489104i
$638$	−12.4925	−	21.6377i	−0.494583	−	0.856643i
$639$		0			0
$640$	7.92078	+	6.64632i	0.313096	+	0.262719i
$641$	−3.51394	−	1.27897i	−0.138792	−	0.0505163i	0.271690	−	0.962385i	$-0.412417\pi$
$641$	−3.51394	−	1.27897i	−0.138792	−	0.0505163i	−0.410482	+	0.911869i	$0.634640\pi$
$642$		0			0
$643$	−10.8122	+	9.07254i	−0.426393	+	0.357786i	−0.830589	−	0.556886i	$-0.811996\pi$
$643$	−10.8122	+	9.07254i	−0.426393	+	0.357786i	0.404196	+	0.914672i	$0.367551\pi$
$644$	1.88562	+	10.6939i	0.0743037	+	0.421397i
$645$		0			0
$646$	5.01493	−	20.8882i	0.197310	−	0.821834i
$647$	41.4758			1.63058			0.815291	−	0.579052i	$-0.196577\pi$
$647$	41.4758			1.63058			0.815291	+	0.579052i	$0.196577\pi$
$648$		0			0
$649$	25.4677	−	21.3699i	0.999694	−	0.838843i
$650$	1.58968	−	0.578597i	0.0623524	−	0.0226944i
$651$		0			0
$652$	11.2281	+	9.42146i	0.439725	+	0.368973i
$653$	18.2540	−	31.6169i	0.714334	−	1.23726i	−0.248882	−	0.968534i	$-0.580063\pi$
$653$	18.2540	−	31.6169i	0.714334	−	1.23726i	0.963216	−	0.268729i	$-0.0866037\pi$
$654$		0			0
$655$	−2.19238	+	12.4336i	−0.0856634	+	0.485821i
$656$	0.925189	−	5.24700i	0.0361225	−	0.204861i
$657$		0			0
$658$	−0.235636	+	0.408133i	−0.00918604	+	0.0159107i
$659$	−12.7965	−	10.7376i	−0.498482	−	0.418276i	0.358572	−	0.933502i	$-0.383264\pi$
$659$	−12.7965	−	10.7376i	−0.498482	−	0.418276i	−0.857055	+	0.515226i	$0.827708\pi$
$660$		0			0
$661$	4.02830	−	1.46618i	0.156683	−	0.0570278i	−0.262488	−	0.964935i	$-0.584543\pi$
$661$	4.02830	−	1.46618i	0.156683	−	0.0570278i	0.419171	+	0.907907i	$0.362321\pi$
$662$	14.0201	−	11.7642i	0.544905	−	0.457230i
$663$		0			0
$664$	−3.04965			−0.118349
$665$	−0.637465	−	5.59524i	−0.0247198	−	0.216974i
$666$		0			0
$667$	−5.92829	−	33.6210i	−0.229544	−	1.30181i
$668$	−13.6318	+	11.4384i	−0.527430	+	0.442567i
$669$		0			0
$670$	−6.91069	−	2.51529i	−0.266983	−	0.0971740i
$671$	31.8441	+	26.7204i	1.22933	+	1.03153i
$672$		0			0
$673$	11.8988	+	20.6094i	0.458666	+	0.794434i	0.998891	−	0.0470875i	$-0.0149940\pi$
$673$	11.8988	+	20.6094i	0.458666	+	0.794434i	−0.540224	+	0.841521i	$0.681661\pi$
$674$	−1.47483	+	8.36418i	−0.0568083	+	0.322176i
$675$		0			0
$676$	−5.53751	−	9.59125i	−0.212981	−	0.368894i
$677$	8.95247	−	15.5061i	0.344072	−	0.595949i	−0.641113	−	0.767446i	$-0.721527\pi$
$677$	8.95247	−	15.5061i	0.344072	−	0.595949i	0.985185	+	0.171497i	$0.0548604\pi$
$678$		0			0
$679$	12.8624	+	4.68153i	0.493613	+	0.179661i
$680$	−16.1270	+	5.86977i	−0.618444	+	0.225095i
$681$		0			0
$682$	−1.72135	−	9.76227i	−0.0659139	−	0.373817i
$683$	−8.10967			−0.310308			−0.155154	−	0.987890i	$-0.549587\pi$
$683$	−8.10967			−0.310308			−0.155154	+	0.987890i	$0.549587\pi$
$684$		0			0
$685$	9.20449			0.351686
$686$	1.99027	+	11.2874i	0.0759888	+	0.430954i
$687$		0			0
$688$	−0.302547	+	0.110118i	−0.0115345	+	0.00419821i
$689$	−15.8859	−	5.78199i	−0.605204	−	0.220276i
$690$		0			0
$691$	−4.61817	+	7.99890i	−0.175683	+	0.304293i	−0.940398	−	0.340077i	$-0.889547\pi$
$691$	−4.61817	+	7.99890i	−0.175683	+	0.304293i	0.764714	+	0.644370i	$0.222880\pi$
$692$	−12.2357	−	21.1929i	−0.465133	−	0.805633i
$693$		0			0
$694$	−0.614601	+	3.48557i	−0.0233299	+	0.132311i
$695$	−2.37011	−	4.10516i	−0.0899035	−	0.155717i
$696$		0			0
$697$	24.0555	+	20.1849i	0.911166	+	0.764559i
$698$	−24.4951	−	8.91547i	−0.927151	−	0.337456i
$699$		0			0
$700$	−1.46709	+	1.23103i	−0.0554507	+	0.0465287i
$701$	7.42346	+	42.1005i	0.280380	+	1.59011i	0.721336	+	0.692586i	$0.243529\pi$
$701$	7.42346	+	42.1005i	0.280380	+	1.59011i	−0.440955	+	0.897529i	$0.645360\pi$
$702$		0			0
$703$	−10.9014	+	16.4701i	−0.411156	+	0.621181i
$704$	−10.8560			−0.409152
$705$		0			0
$706$	−14.1038	+	11.8345i	−0.530805	+	0.445398i
$707$	2.62363	−	0.954923i	0.0986718	−	0.0359136i
$708$		0			0
$709$	17.4610	+	14.6515i	0.655762	+	0.550250i	0.908813	−	0.417203i	$-0.136990\pi$
$709$	17.4610	+	14.6515i	0.655762	+	0.550250i	−0.253051	+	0.967453i	$0.581434\pi$
$710$	0.402749	−	0.697582i	0.0151149	−	0.0261798i
$711$		0			0
$712$	3.89170	−	22.0709i	0.145848	−	0.827144i
$713$	2.35206	−	13.3392i	0.0880855	−	0.499557i
$714$		0			0
$715$	6.78089	−	11.7448i	0.253591	−	0.439232i
$716$	22.9552	+	19.2617i	0.857876	+	0.719843i
$717$		0			0
$718$	−20.8229	+	7.57890i	−0.777102	+	0.282842i
$719$	−21.6987	+	18.2073i	−0.809224	+	0.679019i	−0.950422	−	0.310962i	$-0.899349\pi$
$719$	−21.6987	+	18.2073i	−0.809224	+	0.679019i	0.141199	+	0.989981i	$0.454904\pi$
$720$		0			0
$721$	11.7348			0.437027
$722$	−11.4644	+	7.44491i	−0.426662	+	0.277071i
$723$		0			0
$724$	−0.0614330	−	0.348404i	−0.00228314	−	0.0129483i
$725$	4.61245	−	3.87031i	0.171302	−	0.143740i
$726$		0			0
$727$	−27.2512	−	9.91861i	−1.01069	−	0.367861i	−0.216992	−	0.976173i	$-0.569625\pi$
$727$	−27.2512	−	9.91861i	−1.01069	−	0.367861i	−0.793698	+	0.608312i	$0.791847\pi$
$728$	5.83038	+	4.89227i	0.216088	+	0.181320i
$729$		0			0
$730$	0.860753	+	1.49087i	0.0318579	+	0.0551795i
$731$	0.329516	−	1.86878i	0.0121876	−	0.0691192i
$732$		0			0
$733$	−8.37714	−	14.5096i	−0.309417	−	0.535925i	0.668818	−	0.743426i	$-0.266800\pi$
$733$	−8.37714	−	14.5096i	−0.309417	−	0.535925i	−0.978235	+	0.207501i	$0.933467\pi$
$734$	10.8402	−	18.7757i	0.400117	−	0.693024i
$735$		0			0
$736$	−31.1531	−	11.3388i	−1.14832	−	0.417954i
$737$	−55.4005	+	20.1641i	−2.04070	+	0.742756i
$738$		0			0
$739$	0.254943	+	1.44586i	0.00937824	+	0.0531866i	0.989138	−	0.146992i	$-0.0469590\pi$
$739$	0.254943	+	1.44586i	0.00937824	+	0.0531866i	−0.979760	+	0.200178i	$0.935848\pi$
$740$	6.71698			0.246921
$741$		0			0
$742$	−6.68271			−0.245330
$743$	−4.98854	−	28.2914i	−0.183012	−	1.03791i	−0.928483	−	0.371374i	$-0.878887\pi$
$743$	−4.98854	−	28.2914i	−0.183012	−	1.03791i	0.745472	−	0.666537i	$-0.232224\pi$
$744$		0			0
$745$	9.16071	−	3.33423i	0.335622	−	0.122157i
$746$	−18.9465	−	6.89595i	−0.693679	−	0.252479i
$747$		0			0
$748$	−29.2830	+	50.7196i	−1.07069	+	1.85449i
$749$	−2.49903	−	4.32845i	−0.0913126	−	0.158158i
$750$		0			0
$751$	−8.78054	+	49.7969i	−0.320406	+	1.81712i	0.219757	+	0.975555i	$0.429474\pi$
$751$	−8.78054	+	49.7969i	−0.320406	+	1.81712i	−0.540163	+	0.841560i	$0.681637\pi$
$752$	0.294634	+	0.510321i	0.0107442	+	0.0186095i
$753$		0			0
$754$	−7.80291	−	6.54741i	−0.284165	−	0.238443i
$755$	12.2361	+	4.45359i	0.445318	+	0.162083i
$756$		0			0
$757$	5.88606	−	4.93899i	0.213932	−	0.179511i	−0.529524	−	0.848295i	$-0.677629\pi$
$757$	5.88606	−	4.93899i	0.213932	−	0.179511i	0.743456	+	0.668784i	$0.233185\pi$
$758$	2.82546	+	16.0240i	0.102625	+	0.582017i
$759$		0			0
$760$	10.0151	+	4.35475i	0.363285	+	0.157963i
$761$	−39.1347			−1.41863			−0.709315	−	0.704891i	$-0.750996\pi$
$761$	−39.1347			−1.41863			−0.709315	+	0.704891i	$0.750996\pi$
$762$		0			0
$763$	−16.5196	+	13.8616i	−0.598051	+	0.501824i
$764$	0.450250	−	0.163878i	0.0162895	−	0.00592888i
$765$		0			0
$766$	5.52415	+	4.63531i	0.199596	+	0.167481i
$767$	6.77686	−	11.7379i	0.244698	−	0.423829i
$768$		0			0
$769$	−5.81543	+	32.9809i	−0.209710	+	1.18932i	0.680145	+	0.733078i	$0.261917\pi$
$769$	−5.81543	+	32.9809i	−0.209710	+	1.18932i	−0.889854	+	0.456245i	$0.849194\pi$
$770$	0.930923	−	5.27953i	0.0335482	−	0.190261i
$771$		0			0
$772$	1.08476	−	1.87887i	0.0390415	−	0.0676219i
$773$	−0.361162	−	0.303051i	−0.0129901	−	0.0109000i	0.636269	−	0.771467i	$-0.280477\pi$
$773$	−0.361162	−	0.303051i	−0.0129901	−	0.0109000i	−0.649260	+	0.760567i	$0.724921\pi$
$774$		0			0
$775$	2.24483	−	0.817051i	0.0806367	−	0.0293493i
$776$	−20.3343	+	17.0625i	−0.729959	+	0.612508i
$777$		0			0
$778$	−5.25326			−0.188338
$779$	−2.26197	−	19.8540i	−0.0810433	−	0.711344i
$780$		0			0
$781$	−1.12131	−	6.35928i	−0.0401237	−	0.227553i
$782$	21.4056	−	17.9614i	0.765463	−	0.642300i
$783$		0			0
$784$	5.82202	+	2.11904i	0.207929	+	0.0756801i
$785$	14.2616	+	11.9669i	0.509018	+	0.427116i
$786$		0			0
$787$	0.935856	+	1.62095i	0.0333596	+	0.0577806i	0.882223	−	0.470831i	$-0.156046\pi$
$787$	0.935856	+	1.62095i	0.0333596	+	0.0577806i	−0.848864	+	0.528612i	$0.822713\pi$
$788$	−2.45831	+	13.9417i	−0.0875735	+	0.496654i
$789$		0			0
$790$	−5.07015	−	8.78175i	−0.180388	−	0.312441i
$791$	−11.6805	+	20.2313i	−0.415312	+	0.719342i
$792$		0			0
$793$	15.9251	+	5.79628i	0.565519	+	0.205832i
$794$	−24.5861	+	8.94859i	−0.872526	+	0.317574i
$795$		0			0
$796$	−0.359915	−	2.04118i	−0.0127569	−	0.0723478i
$797$	38.5450			1.36533			0.682666	−	0.730730i	$-0.260820\pi$
$797$	38.5450			1.36533			0.682666	+	0.730730i	$0.260820\pi$
$798$		0			0
$799$	−3.47306			−0.122868
$800$	−1.01532	−	5.75818i	−0.0358971	−	0.203583i
$801$		0			0
$802$	−6.18346	+	2.25060i	−0.218346	+	0.0794713i
$803$	12.9684	+	4.72011i	0.457645	+	0.166569i
$804$		0			0
$805$	3.66263	−	6.34386i	0.129091	−	0.223592i
$806$	−2.02065	−	3.49987i	−0.0711745	−	0.123278i
$807$		0			0
$808$	−0.940213	+	5.33221i	−0.0330766	+	0.187587i
$809$	8.78371	+	15.2138i	0.308819	+	0.534890i	0.978104	−	0.208115i	$-0.0667330\pi$
$809$	8.78371	+	15.2138i	0.308819	+	0.534890i	−0.669285	+	0.743005i	$0.733400\pi$
$810$		0			0
$811$	−27.2855	−	22.8953i	−0.958125	−	0.803962i	0.0225221	−	0.999746i	$-0.492830\pi$
$811$	−27.2855	−	22.8953i	−0.958125	−	0.803962i	−0.980647	+	0.195784i	$0.937275\pi$
$812$	10.8359	+	3.94396i	0.380267	+	0.138406i
$813$		0			0
$814$	−14.4035	+	12.0860i	−0.504844	+	0.423614i
$815$	−1.71696	−	9.73738i	−0.0601426	−	0.341086i
$816$		0			0
$817$	−0.970679	+	0.718256i	−0.0339598	+	0.0251286i
$818$	3.37628			0.118049
$819$		0			0
$820$	−5.20578	+	4.36817i	−0.181794	+	0.152543i
$821$	−24.1772	+	8.79979i	−0.843791	+	0.307115i	−0.727506	−	0.686101i	$-0.759321\pi$
$821$	−24.1772	+	8.79979i	−0.843791	+	0.307115i	−0.116285	+	0.993216i	$0.537099\pi$
$822$		0			0
$823$	−10.2945	−	8.63812i	−0.358844	−	0.301106i	0.445486	−	0.895289i	$-0.353031\pi$
$823$	−10.2945	−	8.63812i	−0.358844	−	0.301106i	−0.804330	+	0.594183i	$0.797475\pi$
$824$	−11.3785	+	19.7081i	−0.396388	+	0.686565i
$825$		0			0
$826$	0.930370	−	5.27639i	0.0323717	−	0.183589i
$827$	1.48361	−	8.41399i	0.0515903	−	0.292583i	−0.948086	−	0.318013i	$-0.896984\pi$
$827$	1.48361	−	8.41399i	0.0515903	−	0.292583i	0.999677	+	0.0254301i	$0.00809552\pi$
$828$		0			0
$829$	6.74559	−	11.6837i	0.234284	−	0.405792i	−0.724780	−	0.688980i	$-0.758059\pi$
$829$	6.74559	−	11.6837i	0.234284	−	0.405792i	0.959064	+	0.283188i	$0.0913921\pi$
$830$	0.670853	+	0.562912i	0.0232856	+	0.0195390i
$831$		0			0
$832$	−4.15891	+	1.51372i	−0.144184	+	0.0524787i
$833$	−27.9732	+	23.4723i	−0.969213	+	0.813267i
$834$		0			0
$835$	12.0044			0.415428
$836$	35.7332	−	10.5844i	1.23586	−	0.366070i
$837$		0			0
$838$	−0.0735198	−	0.416952i	−0.00253970	−	0.0144034i
$839$	1.90844	−	1.60137i	0.0658865	−	0.0552853i	−0.609250	−	0.792978i	$-0.708529\pi$
$839$	1.90844	−	1.60137i	0.0658865	−	0.0552853i	0.675136	+	0.737693i	$0.264085\pi$
$840$		0			0
$841$	−6.81655	−	2.48102i	−0.235054	−	0.0855525i
$842$	3.39084	+	2.84526i	0.116856	+	0.0980540i
$843$		0			0
$844$	−12.5919	−	21.8098i	−0.433432	−	0.750726i
$845$	−1.29734	+	7.35759i	−0.0446299	+	0.253109i
$846$		0			0
$847$	−14.3828	−	24.9118i	−0.494200	−	0.855979i
$848$	−4.17796	+	7.23644i	−0.143472	+	0.248500i
$849$		0			0
$850$	4.63104	+	1.68556i	0.158843	+	0.0578143i
$851$	−24.1424	+	8.78712i	−0.827592	+	0.301219i
$852$		0			0
$853$	−5.82355	−	33.0270i	−0.199395	−	1.13082i	−0.906020	−	0.423235i	$-0.860894\pi$
$853$	−5.82355	−	33.0270i	−0.199395	−	1.13082i	0.706625	−	0.707588i	$-0.250217\pi$
$854$	6.69923			0.229243
$855$		0			0
$856$	9.69260			0.331286
$857$	−1.76650	−	10.0183i	−0.0603425	−	0.342219i	−1.00000		0.000102570i	$-0.999967\pi$
$857$	−1.76650	−	10.0183i	−0.0603425	−	0.342219i	0.939658	−	0.342117i	$-0.111144\pi$
$858$		0			0
$859$	−25.6251	+	9.32677i	−0.874317	+	0.318225i	−0.739914	−	0.672702i	$-0.765134\pi$
$859$	−25.6251	+	9.32677i	−0.874317	+	0.318225i	−0.134403	+	0.990927i	$0.542912\pi$
$860$	0.385891	+	0.140453i	0.0131588	+	0.00478940i
$861$		0			0
$862$	0.113536	−	0.196650i	0.00386704	−	0.00669791i
$863$	9.37937	+	16.2455i	0.319278	+	0.553005i	0.980337	−	0.197328i	$-0.0632265\pi$
$863$	9.37937	+	16.2455i	0.319278	+	0.553005i	−0.661060	+	0.750333i	$0.729893\pi$
$864$		0			0
$865$	−2.86662	+	16.2574i	−0.0974680	+	0.552768i
$866$	12.3207	+	21.3400i	0.418673	+	0.725163i
$867$		0			0
$868$	3.50472	+	2.94081i	0.118958	+	0.0998177i
$869$	−76.3886	−	27.8032i	−2.59131	−	0.943158i
$870$		0			0
$871$	−18.4122	+	15.4496i	−0.623872	+	0.523491i
$872$	−7.26199	−	41.1848i	−0.245922	−	1.39469i
$873$		0			0
$874$	−17.7481	−	1.08562i	−0.600338	−	0.0367216i
$875$	1.29194			0.0436755
$876$		0			0
$877$	17.6865	−	14.8407i	0.597230	−	0.501135i	−0.293324	−	0.956013i	$-0.594761\pi$
$877$	17.6865	−	14.8407i	0.597230	−	0.501135i	0.890554	+	0.454878i	$0.150317\pi$
$878$	−1.41417	+	0.514715i	−0.0477258	+	0.0173708i
$879$		0			0
$880$	−5.13498	−	4.30876i	−0.173100	−	0.145248i
$881$	27.3103	−	47.3029i	0.920108	−	1.59367i	0.120863	−	0.992669i	$-0.461434\pi$
$881$	27.3103	−	47.3029i	0.920108	−	1.59367i	0.799245	−	0.601005i	$-0.205233\pi$
$882$		0			0
$883$	−3.22999	+	18.3182i	−0.108698	+	0.616456i	0.880981	+	0.473152i	$0.156884\pi$
$883$	−3.22999	+	18.3182i	−0.108698	+	0.616456i	−0.989679	+	0.143304i	$0.954227\pi$
$884$	−4.14608	+	23.5136i	−0.139448	+	0.790848i
$885$		0			0
$886$	3.05862	−	5.29769i	0.102756	−	0.177979i
$887$	2.87998	+	2.41659i	0.0967001	+	0.0811410i	0.689856	−	0.723947i	$-0.257674\pi$
$887$	2.87998	+	2.41659i	0.0967001	+	0.0811410i	−0.593156	+	0.805088i	$0.702118\pi$
$888$		0			0
$889$	−13.1026	+	4.76897i	−0.439448	+	0.159946i
$890$	−4.93000	+	4.13676i	−0.165254	+	0.138665i
$891$		0			0
$892$	−17.4444			−0.584082
$893$	1.60310	+	1.52130i	0.0536458	+	0.0509085i
$894$		0			0
$895$	−3.51024	−	19.9076i	−0.117334	−	0.665437i
$896$	10.2332	−	8.58664i	0.341866	−	0.286860i
$897$		0			0
$898$	10.4905	+	3.81825i	0.350074	+	0.127417i
$899$	−11.0187	−	9.24577i	−0.367494	−	0.308364i
$900$		0			0
$901$	−24.6243	−	42.6506i	−0.820355	−	1.42090i
$902$	3.30327	−	18.7338i	0.109987	−	0.623766i
$903$		0			0
$904$	−22.6518	−	39.2340i	−0.753387	−	1.30490i
$905$	−0.119328	+	0.206682i	−0.00396659	+	0.00687033i
$906$		0			0
$907$	22.7463	+	8.27896i	0.755277	+	0.274898i	0.690825	−	0.723022i	$-0.257248\pi$
$907$	22.7463	+	8.27896i	0.755277	+	0.274898i	0.0644525	+	0.997921i	$0.479470\pi$
$908$	−38.3218	+	13.9480i	−1.27175	+	0.462880i
$909$		0			0
$910$	−0.379522	−	2.15237i	−0.0125810	−	0.0713505i
$911$	−29.7647			−0.986148			−0.493074	−	0.869987i	$-0.664127\pi$
$911$	−29.7647			−0.986148			−0.493074	+	0.869987i	$0.664127\pi$
$912$		0			0
$913$	7.02046			0.232343
$914$	−4.65911	−	26.4231i	−0.154110	−	0.873999i
$915$		0			0
$916$	−13.1074	+	4.77070i	−0.433080	+	0.157628i
$917$	15.3276	+	5.57878i	0.506161	+	0.184228i
$918$		0			0
$919$	−22.8174	+	39.5210i	−0.752678	+	1.30368i	0.193842	+	0.981033i	$0.437905\pi$
$919$	−22.8174	+	39.5210i	−0.752678	+	1.30368i	−0.946520	+	0.322644i	$0.895428\pi$
$920$	7.10284	+	12.3025i	0.234174	+	0.405601i
$921$		0			0
$922$	−2.18920	+	12.4156i	−0.0720974	+	0.408885i
$923$	−1.31628	−	2.27987i	−0.0433260	−	0.0750428i
$924$		0			0
$925$	−3.47111	−	2.91260i	−0.114129	−	0.0957658i
$926$	−22.6061	−	8.22793i	−0.742881	−	0.270387i
$927$		0			0
$928$	−26.9691	+	22.6297i	−0.885304	+	0.742858i
$929$	4.73685	+	26.8640i	0.155411	+	0.881380i	0.958409	+	0.285398i	$0.0921259\pi$
$929$	4.73685	+	26.8640i	0.155411	+	0.881380i	−0.802998	+	0.595982i	$0.796763\pi$
$930$		0			0
$931$	23.1935	+	1.41870i	0.760135	+	0.0464962i
$932$	1.65631			0.0542541
$933$		0			0
$934$	8.24600	−	6.91922i	0.269817	−	0.226404i
$935$	37.1254	−	13.5125i	1.21413	−	0.441907i
$936$		0			0
$937$	33.5860	+	28.1820i	1.09721	+	0.920666i	0.997234	−	0.0743247i	$-0.0236801\pi$
$937$	33.5860	+	28.1820i	1.09721	+	0.920666i	0.0999724	+	0.994990i	$0.468125\pi$
$938$	−4.75059	+	8.22827i	−0.155112	+	0.268663i
$939$		0			0
$940$	0.130513	−	0.740178i	0.00425687	−	0.0241419i
$941$	7.61144	−	43.1666i	0.248126	−	1.40719i	−0.564994	−	0.825095i	$-0.691122\pi$
$941$	7.61144	−	43.1666i	0.248126	−	1.40719i	0.813120	−	0.582096i	$-0.197767\pi$
$942$		0			0
$943$	12.9964	−	22.5104i	0.423221	−	0.733040i
$944$	−5.13193	−	4.30620i	−0.167030	−	0.140155i
$945$		0			0
$946$	−1.08020	+	0.393162i	−0.0351205	+	0.0127828i
$947$	−10.4462	+	8.76541i	−0.339456	+	0.284838i	−0.796540	−	0.604586i	$-0.793339\pi$
$947$	−10.4462	+	8.76541i	−0.339456	+	0.284838i	0.457083	+	0.889424i	$0.348894\pi$
$948$		0			0
$949$	5.62631			0.182638
$950$	−1.39928	−	2.80656i	−0.0453986	−	0.0910567i
$951$		0			0
$952$	3.85018	+	21.8355i	0.124785	+	0.707692i
$953$	−9.46945	+	7.94581i	−0.306746	+	0.257390i	−0.783145	−	0.621839i	$-0.786386\pi$
$953$	−9.46945	+	7.94581i	−0.306746	+	0.257390i	0.476400	+	0.879229i	$0.341941\pi$
$954$		0			0
$955$	−0.303734	−	0.110550i	−0.00982860	−	0.00357732i
$956$	−14.7233	−	12.3543i	−0.476185	−	0.399566i
$957$		0			0
$958$	5.69654	+	9.86669i	0.184047	+	0.318778i
$959$	2.06496	−	11.7110i	0.0666811	−	0.378167i
$960$		0			0
$961$	12.6466	+	21.9045i	0.407954	+	0.706598i
$962$	−3.83273	+	6.63848i	−0.123572	+	0.214033i
$963$		0			0
$964$	−28.4655	−	10.3606i	−0.916810	−	0.333692i
$965$	−1.37528	+	0.500561i	−0.0442718	+	0.0161136i
$966$		0			0
$967$	−2.82125	−	16.0001i	−0.0907254	−	0.514529i	−0.995974	−	0.0896462i	$-0.971426\pi$
$967$	−2.82125	−	16.0001i	−0.0907254	−	0.514529i	0.905248	−	0.424883i	$-0.139685\pi$
$968$	55.7845			1.79298
$969$		0			0
$970$	7.62252			0.244744
$971$	−5.64449	−	32.0115i	−0.181140	−	1.02730i	−0.930815	−	0.365491i	$-0.880901\pi$
$971$	−5.64449	−	32.0115i	−0.181140	−	1.02730i	0.749674	−	0.661807i	$-0.230210\pi$
$972$		0			0
$973$	−5.75476	+	2.09456i	−0.184489	+	0.0671485i
$974$	4.39130	+	1.59830i	0.140706	+	0.0512129i
$975$		0			0
$976$	4.18829	−	7.25433i	0.134064	−	0.232205i
$977$	6.29447	+	10.9023i	0.201378	+	0.348797i	0.948973	−	0.315359i	$-0.102125\pi$
$977$	6.29447	+	10.9023i	0.201378	+	0.348797i	−0.747595	+	0.664155i	$0.768791\pi$
$978$		0			0
$979$	−8.95892	+	50.8085i	−0.286328	+	1.62385i
$980$	−3.95121	−	6.84370i	−0.126217	−	0.218614i
$981$		0			0
$982$	−0.927679	−	0.778415i	−0.0296034	−	0.0248402i
$983$	29.9686	+	10.9077i	0.955850	+	0.347901i	0.772406	−	0.635129i	$-0.219053\pi$
$983$	29.9686	+	10.9077i	0.955850	+	0.347901i	0.183444	+	0.983030i	$0.441275\pi$
$984$		0			0
$985$	7.31576	−	6.13865i	0.233100	−	0.195594i
$986$	−5.15277	−	29.2228i	−0.164098	−	0.930645i
$987$		0			0
$988$	12.2134	−	9.03734i	0.388560	−	0.287516i
$989$	−1.57072			−0.0499461
$990$		0			0
$991$	6.27678	−	5.26685i	0.199389	−	0.167307i	−0.537627	−	0.843183i	$-0.680679\pi$
$991$	6.27678	−	5.26685i	0.199389	−	0.167307i	0.737015	+	0.675876i	$0.236235\pi$
$992$	−13.1255	+	4.77731i	−0.416737	+	0.151680i
$993$		0			0
$994$	−0.797188	−	0.668920i	−0.0252853	−	0.0212168i
$995$	−0.699101	+	1.21088i	−0.0221630	+	0.0383874i
$996$		0			0
$997$	−2.85615	+	16.1980i	−0.0904552	+	0.512997i	0.905590	+	0.424153i	$0.139428\pi$
$997$	−2.85615	+	16.1980i	−0.0904552	+	0.512997i	−0.996046	+	0.0888435i	$0.971683\pi$
$998$	−1.66614	+	9.44914i	−0.0527407	+	0.299107i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.bs.b.541.2		18
3.2	odd	2		95.2.k.b.66.2	yes	18
15.2	even	4		475.2.u.c.199.3		36
15.8	even	4		475.2.u.c.199.4		36
15.14	odd	2		475.2.l.b.351.2		18
19.17	even	9	inner	855.2.bs.b.226.2		18
57.17	odd	18		95.2.k.b.36.2	✓	18
57.32	even	18		1805.2.a.u.1.4		9
57.44	odd	18		1805.2.a.t.1.6		9
285.17	even	36		475.2.u.c.74.4		36
285.44	odd	18		9025.2.a.ce.1.4		9
285.74	odd	18		475.2.l.b.226.2		18
285.89	even	18		9025.2.a.cd.1.6		9
285.188	even	36		475.2.u.c.74.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.36.2	✓	18	57.17	odd	18
95.2.k.b.66.2	yes	18	3.2	odd	2
475.2.l.b.226.2		18	285.74	odd	18
475.2.l.b.351.2		18	15.14	odd	2
475.2.u.c.74.3		36	285.188	even	36
475.2.u.c.74.4		36	285.17	even	36
475.2.u.c.199.3		36	15.2	even	4
475.2.u.c.199.4		36	15.8	even	4
855.2.bs.b.226.2		18	19.17	even	9	inner
855.2.bs.b.541.2		18	1.1	even	1	trivial
1805.2.a.t.1.6		9	57.44	odd	18
1805.2.a.u.1.4		9	57.32	even	18
9025.2.a.cd.1.6		9	285.89	even	18
9025.2.a.ce.1.4		9	285.44	odd	18

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.bs (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.124932 - 0.708527i) q^{2} +(1.39298 - 0.507004i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(-0.645970 + 1.11885i) q^{7} +(-1.25271 - 2.16976i) q^{8} +O(q^{10})\)	\(q+(-0.124932 - 0.708527i) q^{2} +(1.39298 - 0.507004i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(-0.645970 + 1.11885i) q^{7} +(-1.25271 - 2.16976i) q^{8} +(-0.124932 + 0.708527i) q^{10} +(2.88381 + 4.99491i) q^{11} +(1.80125 + 1.51143i) q^{13} +(0.873439 + 0.317906i) q^{14} +(0.890312 - 0.747060i) q^{16} +(1.18948 + 6.74589i) q^{17} +(2.40586 - 3.63481i) q^{19} -1.48238 q^{20} +(3.17874 - 2.66728i) q^{22} +(5.32803 - 1.93925i) q^{23} +(0.766044 + 0.642788i) q^{25} +(0.845852 - 1.46506i) q^{26} +(-0.332562 + 1.88605i) q^{28} +(1.04556 - 5.92966i) q^{29} +(1.19445 - 2.06885i) q^{31} +(-4.47907 - 3.75839i) q^{32} +(4.63104 - 1.68556i) q^{34} +(0.989683 - 0.830443i) q^{35} -4.53121 q^{37} +(-2.87593 - 1.25051i) q^{38} +(0.435062 + 2.46736i) q^{40} +(3.51177 - 2.94672i) q^{41} +(-0.260318 - 0.0947480i) q^{43} +(6.54954 + 5.49572i) q^{44} +(-2.03965 - 3.53278i) q^{46} +(-0.0880430 + 0.499316i) q^{47} +(2.66545 + 4.61669i) q^{49} +(0.359728 - 0.623068i) q^{50} +(3.27541 + 1.19215i) q^{52} +(-6.75604 + 2.45900i) q^{53} +(-1.00154 - 5.68000i) q^{55} +3.23685 q^{56} -4.33194 q^{58} +(-1.00094 - 5.67662i) q^{59} +(6.77273 - 2.46507i) q^{61} +(-1.61506 - 0.587833i) q^{62} +(-0.941117 + 1.63006i) q^{64} +(-1.17568 - 2.03634i) q^{65} +(-1.77501 + 10.0666i) q^{67} +(5.07713 + 8.79384i) q^{68} +(-0.712034 - 0.597468i) q^{70} +(-1.05207 - 0.382923i) q^{71} +(1.83298 - 1.53805i) q^{73} +(0.566094 + 3.21048i) q^{74} +(1.50845 - 6.28301i) q^{76} -7.45142 q^{77} +(-10.7969 + 9.05969i) q^{79} +(-1.09213 + 0.397503i) q^{80} +(-2.52657 - 2.12004i) q^{82} +(0.608609 - 1.05414i) q^{83} +(1.18948 - 6.74589i) q^{85} +(-0.0346093 + 0.196279i) q^{86} +(7.22517 - 12.5144i) q^{88} +(6.85239 + 5.74984i) q^{89} +(-2.85461 + 1.03899i) q^{91} +(6.43866 - 5.40267i) q^{92} +0.364778 q^{94} +(-3.50395 + 2.59275i) q^{95} +(-1.83977 - 10.4339i) q^{97} +(2.93805 - 2.46531i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8}+O(q^{10}) \) 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8	\( 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8} - 3 q^{10} - 3 q^{13} - 24 q^{14} + 21 q^{16} + 24 q^{17} - 12 q^{19} + 12 q^{20} + 15 q^{22} - 21 q^{23} + 21 q^{26} - 24 q^{28} + 9 q^{29} + 30 q^{31} - 45 q^{32} + 24 q^{34} + 6 q^{35} - 60 q^{37} + 15 q^{38} - 6 q^{40} + 6 q^{41} - 6 q^{43} + 30 q^{44} + 21 q^{46} - 33 q^{47} - 3 q^{49} + 9 q^{52} - 24 q^{53} - 3 q^{55} + 72 q^{56} + 36 q^{58} - 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{64} - 3 q^{65} - 24 q^{67} + 3 q^{68} + 39 q^{70} - 24 q^{71} + 6 q^{73} + 39 q^{74} + 27 q^{76} - 24 q^{77} + 9 q^{79} - 33 q^{80} - 57 q^{82} + 24 q^{85} + 33 q^{86} + 39 q^{88} + 6 q^{89} - 6 q^{91} + 66 q^{92} - 66 q^{94} + 15 q^{95} - 87 q^{97} - 39 q^{98}+O(q^{100}) \) 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8 - 3 * q^10 - 3 * q^13 - 24 * q^14 + 21 * q^16 + 24 * q^17 - 12 * q^19 + 12 * q^20 + 15 * q^22 - 21 * q^23 + 21 * q^26 - 24 * q^28 + 9 * q^29 + 30 * q^31 - 45 * q^32 + 24 * q^34 + 6 * q^35 - 60 * q^37 + 15 * q^38 - 6 * q^40 + 6 * q^41 - 6 * q^43 + 30 * q^44 + 21 * q^46 - 33 * q^47 - 3 * q^49 + 9 * q^52 - 24 * q^53 - 3 * q^55 + 72 * q^56 + 36 * q^58 - 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^64 - 3 * q^65 - 24 * q^67 + 3 * q^68 + 39 * q^70 - 24 * q^71 + 6 * q^73 + 39 * q^74 + 27 * q^76 - 24 * q^77 + 9 * q^79 - 33 * q^80 - 57 * q^82 + 24 * q^85 + 33 * q^86 + 39 * q^88 + 6 * q^89 - 6 * q^91 + 66 * q^92 - 66 * q^94 + 15 * q^95 - 87 * q^97 - 39 * q^98

Introduction

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