LMFDB - Embedded newform 666.2.x.c.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(127,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("666.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.x (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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			181.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	666.181
Dual form			666.2.x.c.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(1.79813 - 1.50881i) q^{5} +(1.93969 - 1.62760i) q^{7} +(-0.500000 + 0.866025i) q^{8} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(1.79813 - 1.50881i) q^{5} +(1.93969 - 1.62760i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-1.17365 - 2.03282i) q^{10} +(0.560307 - 0.970481i) q^{11} +(1.70574 + 0.620838i) q^{13} +(-1.26604 - 2.19285i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-2.81908 + 1.02606i) q^{17} +(-0.971782 - 5.51125i) q^{19} +(-2.20574 + 0.802823i) q^{20} +(-0.858441 - 0.720317i) q^{22} +(4.55303 + 7.88609i) q^{23} +(0.0885259 - 0.502055i) q^{25} +(0.907604 - 1.57202i) q^{26} +(-2.37939 + 0.866025i) q^{28} +(4.52481 - 7.83721i) q^{29} -4.53209 q^{31} +(0.766044 - 0.642788i) q^{32} +(0.520945 + 2.95442i) q^{34} +(1.03209 - 5.85327i) q^{35} +(2.33750 - 5.61570i) q^{37} -5.59627 q^{38} +(0.407604 + 2.31164i) q^{40} +(-6.98545 - 2.54250i) q^{41} -8.92902 q^{43} +(-0.858441 + 0.720317i) q^{44} +(8.55690 - 3.11446i) q^{46} +(-0.194593 - 0.337044i) q^{47} +(-0.102196 + 0.579585i) q^{49} +(-0.479055 - 0.174362i) q^{50} +(-1.39053 - 1.16679i) q^{52} +(9.23055 + 7.74535i) q^{53} +(-0.456767 - 2.59045i) q^{55} +(0.439693 + 2.49362i) q^{56} +(-6.93242 - 5.81699i) q^{58} +(-6.41534 - 5.38311i) q^{59} +(2.45336 + 0.892951i) q^{61} +(-0.786989 + 4.46324i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(4.00387 - 1.45729i) q^{65} +(5.62836 - 4.72275i) q^{67} +3.00000 q^{68} +(-5.58512 - 2.03282i) q^{70} +(0.448311 + 2.54250i) q^{71} -0.709141 q^{73} +(-5.12449 - 3.27714i) q^{74} +(-0.971782 + 5.51125i) q^{76} +(-0.492726 - 2.79439i) q^{77} +(3.39646 - 2.84997i) q^{79} +2.34730 q^{80} +(-3.71688 + 6.43783i) q^{82} +(-6.81180 + 2.47929i) q^{83} +(-3.52094 + 6.09845i) q^{85} +(-1.55051 + 8.79336i) q^{86} +(0.560307 + 0.970481i) q^{88} +(9.95336 + 8.35186i) q^{89} +(4.31908 - 1.57202i) q^{91} +(-1.58125 - 8.96773i) q^{92} +(-0.365715 + 0.133109i) q^{94} +(-10.0628 - 8.44372i) q^{95} +(7.34730 + 12.7259i) q^{97} +(0.553033 + 0.201288i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} + 6 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q - 3 * q^5 + 6 * q^7 - 3 * q^8	$ 6 q - 3 q^{5} + 6 q^{7} - 3 q^{8} - 6 q^{10} + 9 q^{11} - 3 q^{14} + 9 q^{19} - 3 q^{20} + 3 q^{22} + 15 q^{23} + 21 q^{25} + 9 q^{26} - 3 q^{28} - 18 q^{31} - 3 q^{35} + 9 q^{37} - 6 q^{38} + 6 q^{40} - 6 q^{41} + 12 q^{43} + 3 q^{44} + 15 q^{46} + 3 q^{47} - 6 q^{50} + 9 q^{52} + 18 q^{53} - 18 q^{55} - 3 q^{56} - 18 q^{58} + 6 q^{59} - 12 q^{61} + 3 q^{62} - 3 q^{64} - 3 q^{67} + 18 q^{68} - 12 q^{70} + 6 q^{71} - 36 q^{73} - 18 q^{74} + 9 q^{76} + 15 q^{77} + 30 q^{79} + 12 q^{80} - 6 q^{82} - 6 q^{83} - 18 q^{85} - 12 q^{86} + 9 q^{88} + 33 q^{89} + 9 q^{91} - 12 q^{92} - 12 q^{94} - 51 q^{95} + 42 q^{97} - 9 q^{98}+O(q^{100}) $ 6 * q - 3 * q^5 + 6 * q^7 - 3 * q^8 - 6 * q^10 + 9 * q^11 - 3 * q^14 + 9 * q^19 - 3 * q^20 + 3 * q^22 + 15 * q^23 + 21 * q^25 + 9 * q^26 - 3 * q^28 - 18 * q^31 - 3 * q^35 + 9 * q^37 - 6 * q^38 + 6 * q^40 - 6 * q^41 + 12 * q^43 + 3 * q^44 + 15 * q^46 + 3 * q^47 - 6 * q^50 + 9 * q^52 + 18 * q^53 - 18 * q^55 - 3 * q^56 - 18 * q^58 + 6 * q^59 - 12 * q^61 + 3 * q^62 - 3 * q^64 - 3 * q^67 + 18 * q^68 - 12 * q^70 + 6 * q^71 - 36 * q^73 - 18 * q^74 + 9 * q^76 + 15 * q^77 + 30 * q^79 + 12 * q^80 - 6 * q^82 - 6 * q^83 - 18 * q^85 - 12 * q^86 + 9 * q^88 + 33 * q^89 + 9 * q^91 - 12 * q^92 - 12 * q^94 - 51 * q^95 + 42 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$		0			0
$3$		0			0
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	1.79813	−	1.50881i	0.804150	−	0.674762i	−0.145054	−	0.989424i	$-0.546336\pi$
$5$	1.79813	−	1.50881i	0.804150	−	0.674762i	0.949204	+	0.314662i	$0.101891\pi$
$6$		0			0
$7$	1.93969	−	1.62760i	0.733135	−	0.615173i	−0.197849	−	0.980232i	$-0.563396\pi$
$7$	1.93969	−	1.62760i	0.733135	−	0.615173i	0.930984	+	0.365059i	$0.118951\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$		0			0
$10$	−1.17365	−	2.03282i	−0.371140	−	0.642834i
$11$	0.560307	−	0.970481i	0.168939	−	0.292611i	−0.769108	−	0.639119i	$-0.779299\pi$
$11$	0.560307	−	0.970481i	0.168939	−	0.292611i	0.938047	+	0.346508i	$0.112633\pi$
$12$		0			0
$13$	1.70574	+	0.620838i	0.473086	+	0.172189i	0.567550	−	0.823339i	$-0.307891\pi$
$13$	1.70574	+	0.620838i	0.473086	+	0.172189i	−0.0944636	+	0.995528i	$0.530114\pi$
$14$	−1.26604	−	2.19285i	−0.338365	−	0.586065i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−2.81908	+	1.02606i	−0.683727	+	0.248856i	−0.660447	−	0.750873i	$-0.729633\pi$
$17$	−2.81908	+	1.02606i	−0.683727	+	0.248856i	−0.0232799	+	0.999729i	$0.507411\pi$
$18$		0			0
$19$	−0.971782	−	5.51125i	−0.222942	−	1.26437i	−0.866581	−	0.499037i	$-0.833687\pi$
$19$	−0.971782	−	5.51125i	−0.222942	−	1.26437i	0.643639	−	0.765330i	$-0.277424\pi$
$20$	−2.20574	+	0.802823i	−0.493218	+	0.179517i
$21$		0			0
$22$	−0.858441	−	0.720317i	−0.183020	−	0.153572i
$23$	4.55303	+	7.88609i	0.949373	+	1.64436i	0.746749	+	0.665106i	$0.231614\pi$
$23$	4.55303	+	7.88609i	0.949373	+	1.64436i	0.202624	+	0.979257i	$0.435053\pi$
$24$		0			0
$25$	0.0885259	−	0.502055i	0.0177052	−	0.100411i
$26$	0.907604	−	1.57202i	0.177996	−	0.308298i
$27$		0			0
$28$	−2.37939	+	0.866025i	−0.449662	+	0.163663i
$29$	4.52481	−	7.83721i	0.840237	−	1.45533i	−0.0494571	−	0.998776i	$-0.515749\pi$
$29$	4.52481	−	7.83721i	0.840237	−	1.45533i	0.889694	−	0.456557i	$-0.150918\pi$
$30$		0			0
$31$	−4.53209			−0.813987			−0.406994	−	0.913431i	$-0.633423\pi$
$31$	−4.53209			−0.813987			−0.406994	+	0.913431i	$0.633423\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$		0			0
$34$	0.520945	+	2.95442i	0.0893413	+	0.506679i
$35$	1.03209	−	5.85327i	0.174455	−	0.989383i
$36$		0			0
$37$	2.33750	−	5.61570i	0.384282	−	0.923216i
$37$	2.33750	−	5.61570i	0.384282	−	0.923216i
$38$	−5.59627			−0.907834
$39$		0			0
$40$	0.407604	+	2.31164i	0.0644478	+	0.365502i
$41$	−6.98545	−	2.54250i	−1.09094	−	0.397071i	−0.266974	−	0.963704i	$-0.586024\pi$
$41$	−6.98545	−	2.54250i	−1.09094	−	0.397071i	−0.823971	+	0.566633i	$0.808246\pi$
$42$		0			0
$43$	−8.92902			−1.36166			−0.680831	−	0.732441i	$-0.738381\pi$
$43$	−8.92902			−1.36166			−0.680831	+	0.732441i	$0.738381\pi$
$44$	−0.858441	+	0.720317i	−0.129415	+	0.108592i
$45$		0			0
$46$	8.55690	−	3.11446i	1.26165	−	0.459202i
$47$	−0.194593	−	0.337044i	−0.0283843	−	0.0491630i	0.851484	−	0.524380i	$-0.175703\pi$
$47$	−0.194593	−	0.337044i	−0.0283843	−	0.0491630i	−0.879869	+	0.475217i	$0.842370\pi$
$48$		0			0
$49$	−0.102196	+	0.579585i	−0.0145995	+	0.0827978i
$50$	−0.479055	−	0.174362i	−0.0677487	−	0.0246585i
$51$		0			0
$52$	−1.39053	−	1.16679i	−0.192832	−	0.161805i
$53$	9.23055	+	7.74535i	1.26791	+	1.06391i	0.994792	+	0.101927i	$0.0325007\pi$
$53$	9.23055	+	7.74535i	1.26791	+	1.06391i	0.273122	+	0.961979i	$0.411944\pi$
$54$		0			0
$55$	−0.456767	−	2.59045i	−0.0615904	−	0.349297i
$56$	0.439693	+	2.49362i	0.0587564	+	0.333224i
$57$		0			0
$58$	−6.93242	−	5.81699i	−0.910271	−	0.763808i
$59$	−6.41534	−	5.38311i	−0.835207	−	0.700822i	0.121273	−	0.992619i	$-0.461302\pi$
$59$	−6.41534	−	5.38311i	−0.835207	−	0.700822i	−0.956480	+	0.291797i	$0.905747\pi$
$60$		0			0
$61$	2.45336	+	0.892951i	0.314121	+	0.114331i	0.494269	−	0.869309i	$-0.335436\pi$
$61$	2.45336	+	0.892951i	0.314121	+	0.114331i	−0.180149	+	0.983639i	$0.557658\pi$
$62$	−0.786989	+	4.46324i	−0.0999477	+	0.566832i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	4.00387	−	1.45729i	0.496619	−	0.180755i
$66$		0			0
$67$	5.62836	−	4.72275i	0.687613	−	0.576976i	−0.230607	−	0.973047i	$-0.574071\pi$
$67$	5.62836	−	4.72275i	0.687613	−	0.576976i	0.918220	+	0.396071i	$0.129627\pi$
$68$	3.00000			0.363803
$69$		0			0
$70$	−5.58512	−	2.03282i	−0.667550	−	0.242968i
$71$	0.448311	+	2.54250i	0.0532047	+	0.301739i	0.999785	−	0.0207290i	$-0.00659871\pi$
$71$	0.448311	+	2.54250i	0.0532047	+	0.301739i	−0.946580	+	0.322468i	$0.895488\pi$
$72$		0			0
$73$	−0.709141			−0.0829986			−0.0414993	−	0.999139i	$-0.513213\pi$
$73$	−0.709141			−0.0829986			−0.0414993	+	0.999139i	$0.513213\pi$
$74$	−5.12449	−	3.27714i	−0.595709	−	0.380960i
$75$		0			0
$76$	−0.971782	+	5.51125i	−0.111471	+	0.632183i
$77$	−0.492726	−	2.79439i	−0.0561513	−	0.318450i
$78$		0			0
$79$	3.39646	−	2.84997i	0.382132	−	0.320646i	−0.431407	−	0.902157i	$-0.641983\pi$
$79$	3.39646	−	2.84997i	0.382132	−	0.320646i	0.813539	+	0.581511i	$0.197538\pi$
$80$	2.34730			0.262436
$81$		0			0
$82$	−3.71688	+	6.43783i	−0.410461	+	0.710939i
$83$	−6.81180	+	2.47929i	−0.747693	+	0.272138i	−0.687634	−	0.726057i	$-0.741351\pi$
$83$	−6.81180	+	2.47929i	−0.747693	+	0.272138i	−0.0600581	+	0.998195i	$0.519129\pi$
$84$		0			0
$85$	−3.52094	+	6.09845i	−0.381900	+	0.661470i
$86$	−1.55051	+	8.79336i	−0.167195	+	0.948213i
$87$		0			0
$88$	0.560307	+	0.970481i	0.0597290	+	0.103454i
$89$	9.95336	+	8.35186i	1.05505	+	0.885296i	0.993616	−	0.112815i	$-0.0359868\pi$
$89$	9.95336	+	8.35186i	1.05505	+	0.885296i	0.0614384	+	0.998111i	$0.480431\pi$
$90$		0			0
$91$	4.31908	−	1.57202i	0.452762	−	0.164792i
$92$	−1.58125	−	8.96773i	−0.164857	−	0.934950i
$93$		0			0
$94$	−0.365715	+	0.133109i	−0.0377206	+	0.0137292i
$95$	−10.0628	−	8.44372i	−1.03242	−	0.866307i
$96$		0			0
$97$	7.34730	+	12.7259i	0.746005	+	1.29212i	0.949724	+	0.313089i	$0.101364\pi$
$97$	7.34730	+	12.7259i	0.746005	+	1.29212i	−0.203719	+	0.979029i	$0.565303\pi$
$98$	0.553033	+	0.201288i	0.0558648	+	0.0203331i
$99$		0			0
$100$	−0.254900	+	0.441500i	−0.0254900	+	0.0441500i
$101$	1.51367	+	2.62175i	0.150616	+	0.260874i	0.931454	−	0.363859i	$-0.118541\pi$
$101$	1.51367	+	2.62175i	0.150616	+	0.260874i	−0.780838	+	0.624733i	$0.785208\pi$
$102$		0			0
$103$	−4.20826	+	7.28893i	−0.414653	+	0.718199i	−0.995392	−	0.0958903i	$-0.969430\pi$
$103$	−4.20826	+	7.28893i	−0.414653	+	0.718199i	0.580739	+	0.814090i	$0.302764\pi$
$104$	−1.39053	+	1.16679i	−0.136353	+	0.114413i
$105$		0			0
$106$	9.23055	−	7.74535i	0.896550	−	0.752295i
$107$	5.67752	+	2.06645i	0.548866	+	0.199771i	0.601543	−	0.798841i	$-0.294553\pi$
$107$	5.67752	+	2.06645i	0.548866	+	0.199771i	−0.0526763	+	0.998612i	$0.516775\pi$
$108$		0			0
$109$	−3.47906	+	19.7307i	−0.333233	+	1.88986i	0.110791	+	0.993844i	$0.464662\pi$
$109$	−3.47906	+	19.7307i	−0.333233	+	1.88986i	−0.444024	+	0.896015i	$0.646449\pi$
$110$	−2.63041			−0.250800
$111$		0			0
$112$	2.53209			0.239260
$113$	0.442219	−	2.50795i	0.0416004	−	0.235928i	−0.956917	−	0.290362i	$-0.906224\pi$
$113$	0.442219	−	2.50795i	0.0416004	−	0.235928i	0.998517	+	0.0544340i	$0.0173354\pi$
$114$		0			0
$115$	20.0856	+	7.31056i	1.87299	+	0.681713i
$116$	−6.93242	+	5.81699i	−0.643659	+	0.540094i
$117$		0			0
$118$	−6.41534	+	5.38311i	−0.590580	+	0.495556i
$119$	−3.79813	+	6.57856i	−0.348174	+	0.603056i
$120$		0			0
$121$	4.87211	+	8.43874i	0.442919	+	0.767159i
$122$	1.30541	−	2.26103i	0.118186	−	0.204704i
$123$		0			0
$124$	4.25877	+	1.55007i	0.382449	+	0.139200i
$125$	5.26991	+	9.12776i	0.471356	+	0.816412i
$126$		0			0
$127$	−5.38326	−	4.51709i	−0.477687	−	0.400827i	0.371902	−	0.928272i	$-0.378706\pi$
$127$	−5.38326	−	4.51709i	−0.477687	−	0.400827i	−0.849589	+	0.527445i	$0.823150\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$		0			0
$130$	−0.739885	−	4.19610i	−0.0648922	−	0.368022i
$131$	−0.852044	+	0.310119i	−0.0744434	+	0.0270952i	−0.378973	−	0.925408i	$-0.623723\pi$
$131$	−0.852044	+	0.310119i	−0.0744434	+	0.0270952i	0.304530	+	0.952503i	$0.401501\pi$
$132$		0			0
$133$	−10.8550	−	9.10846i	−0.941251	−	0.789803i
$134$	−3.67365	−	6.36295i	−0.317355	−	0.549675i
$135$		0			0
$136$	0.520945	−	2.95442i	0.0446706	−	0.253340i
$137$	0.979055	−	1.69577i	0.0836464	−	0.144880i	−0.821167	−	0.570688i	$-0.806677\pi$
$137$	0.979055	−	1.69577i	0.0836464	−	0.144880i	0.904814	+	0.425808i	$0.140010\pi$
$138$		0			0
$139$	−12.7811	+	4.65193i	−1.08408	+	0.394571i	−0.821423	−	0.570319i	$-0.806819\pi$
$139$	−12.7811	+	4.65193i	−1.08408	+	0.394571i	−0.262652	+	0.964891i	$0.584597\pi$
$140$	−2.97178	+	5.14728i	−0.251161	+	0.435024i
$141$		0			0
$142$	2.58172			0.216653
$143$	1.55825	−	1.30753i	0.130307	−	0.109341i
$144$		0			0
$145$	−3.68866	−	20.9194i	−0.306327	−	1.73727i
$146$	−0.123141	+	0.698367i	−0.0101912	+	0.0577973i
$147$		0			0
$148$	−4.11721	+	4.47756i	−0.338433	+	0.368053i
$149$	6.73648			0.551874			0.275937	−	0.961176i	$-0.411012\pi$
$149$	6.73648			0.551874			0.275937	+	0.961176i	$0.411012\pi$
$150$		0			0
$151$	0.832748	+	4.72275i	0.0677681	+	0.384332i	0.999761	+	0.0218558i	$0.00695748\pi$
$151$	0.832748	+	4.72275i	0.0677681	+	0.384332i	−0.931993	+	0.362476i	$0.881931\pi$
$152$	5.25877	+	1.91404i	0.426543	+	0.155249i
$153$		0			0
$154$	−2.83750			−0.228652
$155$	−8.14930	+	6.83807i	−0.654568	+	0.549247i
$156$		0			0
$157$	13.5954	−	4.94832i	1.08503	−	0.394919i	0.263253	−	0.964727i	$-0.415205\pi$
$157$	13.5954	−	4.94832i	1.08503	−	0.394919i	0.821778	+	0.569808i	$0.192983\pi$
$158$	−2.21688	−	3.83975i	−0.176366	−	0.305474i
$159$		0			0
$160$	0.407604	−	2.31164i	0.0322239	−	0.182751i
$161$	21.6668	+	7.88609i	1.70759	+	0.621511i
$162$		0			0
$163$	7.69846	+	6.45978i	0.602990	+	0.505969i	0.892405	−	0.451235i	$-0.149016\pi$
$163$	7.69846	+	6.45978i	0.602990	+	0.505969i	−0.289415	+	0.957204i	$0.593461\pi$
$164$	5.69459	+	4.77833i	0.444673	+	0.373125i
$165$		0			0
$166$	1.25877	+	7.13884i	0.0976995	+	0.554082i
$167$	−1.81315	−	10.2829i	−0.140306	−	0.795713i	−0.971017	−	0.239010i	$-0.923177\pi$
$167$	−1.81315	−	10.2829i	−0.140306	−	0.795713i	0.830712	−	0.556703i	$-0.187934\pi$
$168$		0			0
$169$	−7.43448	−	6.23827i	−0.571883	−	0.479867i
$170$	5.39440	+	4.52644i	0.413732	+	0.347162i
$171$		0			0
$172$	8.39053	+	3.05390i	0.639772	+	0.232858i
$173$	−0.182266	+	1.03368i	−0.0138575	+	0.0785895i	−0.990952	−	0.134215i	$-0.957149\pi$
$173$	−0.182266	+	1.03368i	−0.0138575	+	0.0785895i	0.977095	+	0.212805i	$0.0682598\pi$
$174$		0			0
$175$	−0.645430	−	1.11792i	−0.0487899	−	0.0845066i
$176$	1.05303	−	0.383273i	0.0793754	−	0.0288903i
$177$		0			0
$178$	9.95336	−	8.35186i	0.746036	−	0.625999i
$179$	−9.15570			−0.684329			−0.342164	−	0.939640i	$-0.611160\pi$
$179$	−9.15570			−0.684329			−0.342164	+	0.939640i	$0.611160\pi$
$180$		0			0
$181$	21.2408	+	7.73103i	1.57882	+	0.574643i	0.974947	−	0.222439i	$-0.0714019\pi$
$181$	21.2408	+	7.73103i	1.57882	+	0.574643i	0.603871	+	0.797082i	$0.293624\pi$
$182$	−0.798133	−	4.52644i	−0.0591616	−	0.335522i
$183$		0			0
$184$	−9.10607			−0.671308
$185$	−4.26991	−	13.6246i	−0.313930	−	1.00170i
$186$		0			0
$187$	−0.583778	+	3.31077i	−0.0426901	+	0.242108i
$188$	0.0675813	+	0.383273i	0.00492888	+	0.0279530i
$189$		0			0
$190$	−10.0628	+	8.44372i	−0.730035	+	0.612572i
$191$	19.1334			1.38444			0.692222	−	0.721684i	$-0.256632\pi$
$191$	19.1334			1.38444			0.692222	+	0.721684i	$0.256632\pi$
$192$		0			0
$193$	9.50640	−	16.4656i	0.684285	−	1.18522i	−0.289375	−	0.957216i	$-0.593448\pi$
$193$	9.50640	−	16.4656i	0.684285	−	1.18522i	0.973661	−	0.228001i	$-0.0732191\pi$
$194$	13.8084	−	5.02585i	0.991385	−	0.360835i
$195$		0			0
$196$	0.294263	−	0.509678i	0.0210188	−	0.0364056i
$197$	−3.20914	+	18.1999i	−0.228642	+	1.29669i	0.626958	+	0.779053i	$0.284300\pi$
$197$	−3.20914	+	18.1999i	−0.228642	+	1.29669i	−0.855599	+	0.517639i	$0.826811\pi$
$198$		0			0
$199$	2.78699	+	4.82721i	0.197564	+	0.342192i	0.947738	−	0.319049i	$-0.103364\pi$
$199$	2.78699	+	4.82721i	0.197564	+	0.342192i	−0.750174	+	0.661241i	$0.770030\pi$
$200$	0.390530	+	0.327693i	0.0276146	+	0.0231714i
$201$		0			0
$202$	2.84477	−	1.03541i	0.200157	−	0.0728513i
$203$	−3.97906	−	22.5663i	−0.279275	−	1.58385i
$204$		0			0
$205$	−16.3969	+	5.96799i	−1.14521	+	0.416823i
$206$	6.44743	+	5.41004i	0.449214	+	0.376935i
$207$		0			0
$208$	0.907604	+	1.57202i	0.0629310	+	0.109000i
$209$	−5.89306	−	2.14490i	−0.407631	−	0.148366i
$210$		0			0
$211$	−10.8550	+	18.8015i	−0.747292	+	1.29435i	0.201825	+	0.979422i	$0.435313\pi$
$211$	−10.8550	+	18.8015i	−0.747292	+	1.29435i	−0.949116	+	0.314925i	$0.898021\pi$
$212$	−6.02481	−	10.4353i	−0.413786	−	0.716698i
$213$		0			0
$214$	3.02094	−	5.23243i	0.206508	−	0.357682i
$215$	−16.0556	+	13.4722i	−1.09498	+	0.918797i
$216$		0			0
$217$	−8.79086	+	7.37641i	−0.596762	+	0.500743i
$218$	18.8268	+	6.85240i	1.27511	+	0.464103i
$219$		0			0
$220$	−0.456767	+	2.59045i	−0.0307952	+	0.174648i
$221$	−5.44562			−0.366312
$222$		0			0
$223$	−10.1429			−0.679219			−0.339610	−	0.940567i	$-0.610295\pi$
$223$	−10.1429			−0.679219			−0.339610	+	0.940567i	$0.610295\pi$
$224$	0.439693	−	2.49362i	0.0293782	−	0.166612i
$225$		0			0
$226$	−2.39306	−	0.871001i	−0.159184	−	0.0579381i
$227$	3.34524	−	2.80699i	0.222031	−	0.186306i	−0.524986	−	0.851111i	$-0.675930\pi$
$227$	3.34524	−	2.80699i	0.222031	−	0.186306i	0.747017	+	0.664804i	$0.231485\pi$
$228$		0			0
$229$	−9.01889	+	7.56774i	−0.595985	+	0.500091i	−0.890152	−	0.455663i	$-0.849402\pi$
$229$	−9.01889	+	7.56774i	−0.595985	+	0.500091i	0.294167	+	0.955754i	$0.404958\pi$
$230$	10.6873	−	18.5110i	0.704701	−	1.22058i
$231$		0			0
$232$	4.52481	+	7.83721i	0.297069	+	0.514538i
$233$	8.13816	−	14.0957i	0.533148	−	0.923440i	−0.466102	−	0.884731i	$-0.654342\pi$
$233$	8.13816	−	14.0957i	0.533148	−	0.923440i	0.999251	−	0.0387091i	$-0.0123246\pi$
$234$		0			0
$235$	−0.858441	−	0.312447i	−0.0559985	−	0.0203818i
$236$	4.18732	+	7.25265i	0.272571	+	0.472107i
$237$		0			0
$238$	5.81908	+	4.88279i	0.377195	+	0.316504i
$239$	−14.6493	+	5.33191i	−0.947584	+	0.344893i	−0.769157	−	0.639060i	$-0.779323\pi$
$239$	−14.6493	+	5.33191i	−0.947584	+	0.344893i	−0.178428	+	0.983953i	$0.557101\pi$
$240$		0			0
$241$	−0.151826	−	0.861050i	−0.00977999	−	0.0554651i	0.979527	−	0.201312i	$-0.0645205\pi$
$241$	−0.151826	−	0.861050i	−0.00977999	−	0.0554651i	−0.989307	+	0.145847i	$0.953409\pi$
$242$	9.15657	−	3.33272i	0.588607	−	0.214235i
$243$		0			0
$244$	−2.00000	−	1.67820i	−0.128037	−	0.107436i
$245$	0.690722	+	1.19637i	0.0441286	+	0.0764330i
$246$		0			0
$247$	1.76399	−	10.0041i	0.112240	−	0.636543i
$248$	2.26604	−	3.92490i	0.143894	−	0.249232i
$249$		0			0
$250$	9.90420	−	3.60483i	0.626397	−	0.227990i
$251$	−1.26991	+	2.19956i	−0.0801563	+	0.138835i	−0.903317	−	0.428974i	$-0.858875\pi$
$251$	−1.26991	+	2.19956i	−0.0801563	+	0.138835i	0.823161	+	0.567809i	$0.192209\pi$
$252$		0			0
$253$	10.2044			0.641545
$254$	−5.38326	+	4.51709i	−0.337775	+	0.283427i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−2.89187	+	16.4006i	−0.180390	+	1.02304i	0.751346	+	0.659908i	$0.229405\pi$
$257$	−2.89187	+	16.4006i	−0.180390	+	1.02304i	−0.931736	+	0.363135i	$0.881706\pi$
$258$		0			0
$259$	−4.60607	−	14.6972i	−0.286207	−	0.913242i
$260$	−4.26083			−0.264245
$261$		0			0
$262$	0.157451	+	0.892951i	0.00972738	+	0.0551667i
$263$	−6.14068	−	2.23503i	−0.378651	−	0.137818i	0.145681	−	0.989332i	$-0.453463\pi$
$263$	−6.14068	−	2.23503i	−0.378651	−	0.137818i	−0.524332	+	0.851514i	$0.675685\pi$
$264$		0			0
$265$	28.2841			1.73748
$266$	−10.8550	+	9.10846i	−0.665565	+	0.558475i
$267$		0			0
$268$	−6.90420	+	2.51292i	−0.421741	+	0.153501i
$269$	−4.42902	−	7.67128i	−0.270042	−	0.467726i	0.698830	−	0.715287i	$-0.253704\pi$
$269$	−4.42902	−	7.67128i	−0.270042	−	0.467726i	−0.968872	+	0.247561i	$0.920371\pi$
$270$		0			0
$271$	1.64930	−	9.35365i	0.100188	−	0.568194i	−0.892846	−	0.450362i	$-0.851295\pi$
$271$	1.64930	−	9.35365i	0.100188	−	0.568194i	0.993034	−	0.117831i	$-0.0375941\pi$
$272$	−2.81908	−	1.02606i	−0.170932	−	0.0622141i
$273$		0			0
$274$	−1.50000	−	1.25865i	−0.0906183	−	0.0760378i
$275$	−0.437633	−	0.367218i	−0.0263903	−	0.0221441i
$276$		0			0
$277$	−5.11040	−	28.9825i	−0.307054	−	1.74139i	−0.613674	−	0.789560i	$-0.710309\pi$
$277$	−5.11040	−	28.9825i	−0.307054	−	1.74139i	0.306619	−	0.951832i	$-0.400802\pi$
$278$	2.36184	+	13.3947i	0.141654	+	0.803360i
$279$		0			0
$280$	4.55303	+	3.82045i	0.272096	+	0.228315i
$281$	−4.54323	−	3.81223i	−0.271027	−	0.227418i	0.497137	−	0.867672i	$-0.334385\pi$
$281$	−4.54323	−	3.81223i	−0.271027	−	0.227418i	−0.768163	+	0.640254i	$0.778829\pi$
$282$		0			0
$283$	−21.2062	−	7.71843i	−1.26058	−	0.458813i	−0.376615	−	0.926370i	$-0.622912\pi$
$283$	−21.2062	−	7.71843i	−1.26058	−	0.458813i	−0.883963	+	0.467557i	$0.845134\pi$
$284$	0.448311	−	2.54250i	0.0266023	−	0.150869i
$285$		0			0
$286$	−1.01707	−	1.76162i	−0.0601409	−	0.104167i
$287$	−17.6878	+	6.43783i	−1.04408	+	0.380013i
$288$		0			0
$289$	−6.12836	+	5.14230i	−0.360492	+	0.302488i
$290$	−21.2422			−1.24738
$291$		0			0
$292$	0.666374	+	0.242540i	0.0389966	+	0.0141936i
$293$	0.705737	+	4.00243i	0.0412296	+	0.233825i	0.998458	−	0.0555078i	$-0.0176778\pi$
$293$	0.705737	+	4.00243i	0.0412296	+	0.233825i	−0.957229	+	0.289333i	$0.906567\pi$
$294$		0			0
$295$	−19.6578			−1.14452
$296$	3.69459	+	4.83218i	0.214744	+	0.280865i
$297$		0			0
$298$	1.16978	−	6.63414i	0.0677634	−	0.384305i
$299$	2.87030	+	16.2783i	0.165994	+	0.941397i
$300$		0			0
$301$	−17.3195	+	14.5328i	−0.998282	+	0.837658i
$302$	4.79561			0.275956
$303$		0			0
$304$	2.79813	−	4.84651i	0.160484	−	0.277966i
$305$	5.75877	−	2.09602i	0.329746	−	0.120018i
$306$		0			0
$307$	5.59240	−	9.68631i	0.319175	−	0.552827i	−0.661141	−	0.750261i	$-0.729928\pi$
$307$	5.59240	−	9.68631i	0.319175	−	0.552827i	0.980316	+	0.197434i	$0.0632609\pi$
$308$	−0.492726	+	2.79439i	−0.0280757	+	0.159225i
$309$		0			0
$310$	5.31908	+	9.21291i	0.302103	+	0.523258i
$311$	−6.32501	−	5.30731i	−0.358658	−	0.300950i	0.445597	−	0.895233i	$-0.352991\pi$
$311$	−6.32501	−	5.30731i	−0.358658	−	0.300950i	−0.804256	+	0.594283i	$0.797436\pi$
$312$		0			0
$313$	11.0633	−	4.02671i	0.625335	−	0.227603i	−0.00986477	−	0.999951i	$-0.503140\pi$
$313$	11.0633	−	4.02671i	0.625335	−	0.227603i	0.635199	+	0.772348i	$0.280918\pi$
$314$	−2.51233	−	14.2481i	−0.141779	−	0.804067i
$315$		0			0
$316$	−4.16637	+	1.51644i	−0.234377	+	0.0853062i
$317$	−10.1441	−	8.51190i	−0.569749	−	0.478076i	0.311814	−	0.950143i	$-0.399063\pi$
$317$	−10.1441	−	8.51190i	−0.569749	−	0.478076i	−0.881562	+	0.472067i	$0.843508\pi$
$318$		0			0
$319$	−5.07057	−	8.78249i	−0.283898	−	0.491725i
$320$	−2.20574	−	0.802823i	−0.123304	−	0.0448791i
$321$		0			0
$322$	11.5287	−	19.9683i	0.642469	−	1.11279i
$323$	8.39440	+	14.5395i	0.467077	+	0.809001i
$324$		0			0
$325$	0.462697	−	0.801414i	0.0256658	−	0.0444544i
$326$	7.69846	−	6.45978i	0.426378	−	0.357774i
$327$		0			0
$328$	5.69459	−	4.77833i	0.314431	−	0.263839i
$329$	−0.926022	−	0.337044i	−0.0510532	−	0.0185819i
$330$		0			0
$331$	4.26217	−	24.1720i	0.234270	−	1.32861i	−0.609875	−	0.792498i	$-0.708780\pi$
$331$	4.26217	−	24.1720i	0.234270	−	1.32861i	0.844145	−	0.536115i	$-0.180109\pi$
$332$	7.24897			0.397839
$333$		0			0
$334$	−10.4415			−0.571334
$335$	2.99479	−	16.9843i	0.163623	−	0.927950i
$336$		0			0
$337$	−11.3576	−	4.13381i	−0.618686	−	0.225183i	0.0136136	−	0.999907i	$-0.495667\pi$
$337$	−11.3576	−	4.13381i	−0.618686	−	0.225183i	−0.632299	+	0.774724i	$0.717889\pi$
$338$	−7.43448	+	6.23827i	−0.404382	+	0.339317i
$339$		0			0
$340$	5.39440	−	4.52644i	0.292552	−	0.245481i
$341$	−2.53936	+	4.39831i	−0.137514	+	0.238182i
$342$		0			0
$343$	9.60741	+	16.6405i	0.518751	+	0.898504i
$344$	4.46451	−	7.73275i	0.240710	−	0.416922i
$345$		0			0
$346$	0.986329	+	0.358995i	0.0530254	+	0.0192997i
$347$	−0.904200	−	1.56612i	−0.0485400	−	0.0840738i	0.840735	−	0.541447i	$-0.182124\pi$
$347$	−0.904200	−	1.56612i	−0.0485400	−	0.0840738i	−0.889275	+	0.457374i	$0.848790\pi$
$348$		0			0
$349$	3.95677	+	3.32012i	0.211801	+	0.177722i	0.742516	−	0.669828i	$-0.233632\pi$
$349$	3.95677	+	3.32012i	0.211801	+	0.177722i	−0.530715	+	0.847550i	$0.678077\pi$
$350$	−1.21301	+	0.441500i	−0.0648382	+	0.0235992i
$351$		0			0
$352$	−0.194593	−	1.10359i	−0.0103718	−	0.0588216i
$353$	−29.1570	+	10.6123i	−1.55187	+	0.564835i	−0.968856	−	0.247625i	$-0.920350\pi$
$353$	−29.1570	+	10.6123i	−1.55187	+	0.564835i	−0.583017	+	0.812460i	$0.698128\pi$
$354$		0			0
$355$	4.64227	+	3.89533i	0.246386	+	0.206743i
$356$	−6.49660	−	11.2524i	−0.344319	−	0.596378i
$357$		0			0
$358$	−1.58987	+	9.01660i	−0.0840272	+	0.476542i
$359$	1.51367	−	2.62175i	0.0798885	−	0.138371i	−0.823313	−	0.567587i	$-0.807877\pi$
$359$	1.51367	−	2.62175i	0.0798885	−	0.138371i	0.903202	+	0.429216i	$0.141210\pi$
$360$		0			0
$361$	−11.5753	+	4.21307i	−0.609227	+	0.221741i
$362$	11.3020	−	19.5756i	0.594020	−	1.02887i
$363$		0			0
$364$	−4.59627			−0.240910
$365$	−1.27513	+	1.06996i	−0.0667433	+	0.0560043i
$366$		0			0
$367$	4.82651	+	27.3725i	0.251942	+	1.42883i	0.803802	+	0.594897i	$0.202807\pi$
$367$	4.82651	+	27.3725i	0.251942	+	1.42883i	−0.551860	+	0.833937i	$0.686082\pi$
$368$	−1.58125	+	8.96773i	−0.0824285	+	0.467475i
$369$		0			0
$370$	−14.1591	+	1.83915i	−0.736097	+	0.0956131i
$371$	30.5107			1.58404
$372$		0			0
$373$	0.898681	+	5.09667i	0.0465319	+	0.263896i	0.999194	−	0.0401346i	$-0.0127787\pi$
$373$	0.898681	+	5.09667i	0.0465319	+	0.263896i	−0.952662	+	0.304030i	$0.901668\pi$
$374$	3.15910	+	1.14982i	0.163353	+	0.0594557i
$375$		0			0
$376$	0.389185			0.0200707
$377$	12.5838	−	10.5590i	0.648098	−	0.543818i
$378$		0			0
$379$	19.8195	−	7.21372i	1.01806	−	0.370544i	0.221538	−	0.975152i	$-0.428892\pi$
$379$	19.8195	−	7.21372i	1.01806	−	0.370544i	0.796523	+	0.604608i	$0.206670\pi$
$380$	6.56805	+	11.3762i	0.336934	+	0.583586i
$381$		0			0
$382$	3.32248	−	18.8427i	0.169993	−	0.964078i
$383$	−36.6771	−	13.3494i	−1.87411	−	0.682121i	−0.962658	−	0.270721i	$-0.912738\pi$
$383$	−36.6771	−	13.3494i	−1.87411	−	0.682121i	−0.911455	−	0.411400i	$-0.865040\pi$
$384$		0			0
$385$	−5.10220	−	4.28125i	−0.260032	−	0.218193i
$386$	−14.5646	−	12.2212i	−0.741321	−	0.622042i
$387$		0			0
$388$	−2.55169	−	14.4713i	−0.129542	−	0.734671i
$389$	−2.78312	−	15.7838i	−0.141110	−	0.800273i	−0.970409	−	0.241468i	$-0.922371\pi$
$389$	−2.78312	−	15.7838i	−0.141110	−	0.800273i	0.829299	−	0.558805i	$-0.188740\pi$
$390$		0			0
$391$	−20.9270	−	17.5598i	−1.05832	−	0.888037i
$392$	−0.450837	−	0.378297i	−0.0227707	−	0.0191069i
$393$		0			0
$394$	17.3662	+	6.32077i	0.874896	+	0.318436i
$395$	1.80722	−	10.2492i	0.0909310	−	0.515695i
$396$		0			0
$397$	−7.32042	−	12.6793i	−0.367401	−	0.636358i	0.621757	−	0.783210i	$-0.286419\pi$
$397$	−7.32042	−	12.6793i	−0.367401	−	0.636358i	−0.989158	+	0.146852i	$0.953086\pi$
$398$	5.23783	−	1.90641i	0.262548	−	0.0955598i
$399$		0			0
$400$	0.390530	−	0.327693i	0.0195265	−	0.0163847i
$401$	−11.8075			−0.589637			−0.294818	−	0.955553i	$-0.595259\pi$
$401$	−11.8075			−0.589637			−0.294818	+	0.955553i	$0.595259\pi$
$402$		0			0
$403$	−7.73055	−	2.81369i	−0.385086	−	0.140160i
$404$	−0.525692	−	2.98135i	−0.0261542	−	0.148328i
$405$		0			0
$406$	−22.9145			−1.13723
$407$	−4.14022	−	5.41501i	−0.205223	−	0.268412i
$408$		0			0
$409$	0.975652	−	5.53320i	0.0482429	−	0.273599i	−0.951139	−	0.308764i	$-0.900085\pi$
$409$	0.975652	−	5.53320i	0.0482429	−	0.273599i	0.999382	+	0.0351652i	$0.0111957\pi$
$410$	3.03003	+	17.1842i	0.149642	+	0.848665i
$411$		0			0
$412$	6.44743	−	5.41004i	0.317642	−	0.266533i
$413$	−21.2053			−1.04345
$414$		0			0
$415$	−8.50774	+	14.7358i	−0.417629	+	0.723354i
$416$	1.70574	−	0.620838i	0.0836306	−	0.0304391i
$417$		0			0
$418$	−3.13563	+	5.43107i	−0.153369	+	0.265642i
$419$	1.76171	−	9.99114i	0.0860650	−	0.488099i	−0.911057	−	0.412281i	$-0.864732\pi$
$419$	1.76171	−	9.99114i	0.0860650	−	0.488099i	0.997122	−	0.0758179i	$-0.0241568\pi$
$420$		0			0
$421$	−5.48158	−	9.49438i	−0.267156	−	0.462728i	0.700970	−	0.713190i	$-0.252751\pi$
$421$	−5.48158	−	9.49438i	−0.267156	−	0.462728i	−0.968126	+	0.250463i	$0.919417\pi$
$422$	16.6309	+	13.9550i	0.809579	+	0.679317i
$423$		0			0
$424$	−11.3229	+	4.12122i	−0.549891	+	0.200144i
$425$	0.265578	+	1.50617i	0.0128824	+	0.0730598i
$426$		0			0
$427$	6.21213	−	2.26103i	0.300626	−	0.109419i
$428$	−4.62836	−	3.88365i	−0.223720	−	0.187723i
$429$		0			0
$430$	10.4795	+	18.1511i	0.505367	+	0.875322i
$431$	4.80066	+	1.74730i	0.231240	+	0.0841643i	0.455041	−	0.890470i	$-0.349625\pi$
$431$	4.80066	+	1.74730i	0.231240	+	0.0841643i	−0.223802	+	0.974635i	$0.571847\pi$
$432$		0			0
$433$	13.8712	−	24.0257i	0.666609	−	1.15460i	−0.312237	−	0.950004i	$-0.601078\pi$
$433$	13.8712	−	24.0257i	0.666609	−	1.15460i	0.978846	−	0.204596i	$-0.0655882\pi$
$434$	5.73783	+	9.93821i	0.275424	+	0.477049i
$435$		0			0
$436$	10.0175	−	17.3509i	0.479753	−	0.830957i
$437$	39.0376	−	32.7564i	1.86742	−	1.56695i
$438$		0			0
$439$	−22.3214	+	18.7298i	−1.06534	+	0.893927i	−0.994622	−	0.103570i	$-0.966973\pi$
$439$	−22.3214	+	18.7298i	−1.06534	+	0.893927i	−0.0707180	+	0.997496i	$0.522529\pi$
$440$	2.47178	+	0.899655i	0.117838	+	0.0428894i
$441$		0			0
$442$	−0.945622	+	5.36289i	−0.0449787	+	0.255087i
$443$	−6.97864			−0.331565			−0.165783	−	0.986162i	$-0.553015\pi$
$443$	−6.97864			−0.331565			−0.165783	+	0.986162i	$0.553015\pi$
$444$		0			0
$445$	30.4989			1.44579
$446$	−1.76130	+	9.98881i	−0.0833998	+	0.472984i
$447$		0			0
$448$	−2.37939	−	0.866025i	−0.112415	−	0.0409159i
$449$	−13.9834	+	11.7335i	−0.659917	+	0.553736i	−0.910062	−	0.414472i	$-0.863966\pi$
$449$	−13.9834	+	11.7335i	−0.659917	+	0.553736i	0.250145	+	0.968208i	$0.419522\pi$
$450$		0			0
$451$	−6.38144	+	5.35467i	−0.300490	+	0.252141i
$452$	−1.27332	+	2.20545i	−0.0598919	+	0.103736i
$453$		0			0
$454$	−2.18345	−	3.78184i	−0.102474	−	0.177491i
$455$	5.39440	−	9.34337i	0.252893	−	0.438024i
$456$		0			0
$457$	21.4209	+	7.79656i	1.00203	+	0.364708i	0.790365	−	0.612636i	$-0.209891\pi$
$457$	21.4209	+	7.79656i	1.00203	+	0.364708i	0.211660	+	0.977343i	$0.432113\pi$
$458$	5.88666	+	10.1960i	0.275066	+	0.476427i
$459$		0			0
$460$	−16.3739	−	13.7394i	−0.763438	−	0.640601i
$461$	8.17277	−	2.97465i	0.380644	−	0.138543i	−0.144610	−	0.989489i	$-0.546193\pi$
$461$	8.17277	−	2.97465i	0.380644	−	0.138543i	0.525254	+	0.850946i	$0.323970\pi$
$462$		0			0
$463$	0.592701	+	3.36137i	0.0275451	+	0.156216i	0.995478	−	0.0949930i	$-0.0302829\pi$
$463$	0.592701	+	3.36137i	0.0275451	+	0.156216i	−0.967933	+	0.251209i	$0.919172\pi$
$464$	8.50387	−	3.09516i	0.394782	−	0.143689i
$465$		0			0
$466$	−12.4684	−	10.4622i	−0.577586	−	0.484653i
$467$	18.3170	+	31.7260i	0.847611	+	1.46810i	0.883335	+	0.468743i	$0.155293\pi$
$467$	18.3170	+	31.7260i	0.847611	+	1.46810i	−0.0357242	+	0.999362i	$0.511374\pi$
$468$		0			0
$469$	3.23055	−	18.3214i	0.149173	−	0.846002i
$470$	−0.456767	+	0.791143i	−0.0210691	+	0.0364927i
$471$		0			0
$472$	7.86959	−	2.86429i	0.362227	−	0.131840i
$473$	−5.00299	+	8.66544i	−0.230038	+	0.398437i
$474$		0			0
$475$	−2.85298			−0.130904
$476$	5.81908	−	4.88279i	0.266717	−	0.223802i
$477$		0			0
$478$	2.70708	+	15.3526i	0.123819	+	0.702213i
$479$	3.57832	−	20.2936i	0.163497	−	0.927240i	−0.787103	−	0.616822i	$-0.788420\pi$
$479$	3.57832	−	20.2936i	0.163497	−	0.927240i	0.950600	−	0.310418i	$-0.100469\pi$
$480$		0			0
$481$	7.47359	−	8.12771i	0.340766	−	0.370592i
$482$	−0.874333			−0.0398248
$483$		0			0
$484$	−1.69207	−	9.59619i	−0.0769121	−	0.436190i
$485$	32.4124	+	11.7972i	1.47177	+	0.535681i
$486$		0			0
$487$	42.2867			1.91620			0.958098	−	0.286442i	$-0.0924726\pi$
$487$	42.2867			1.91620			0.958098	+	0.286442i	$0.0924726\pi$
$488$	−2.00000	+	1.67820i	−0.0905357	+	0.0759685i
$489$		0			0
$490$	1.29813	−	0.472482i	0.0586437	−	0.0213446i
$491$	16.5560	+	28.6759i	0.747163	+	1.29412i	0.949177	+	0.314742i	$0.101918\pi$
$491$	16.5560	+	28.6759i	0.747163	+	1.29412i	−0.202014	+	0.979383i	$0.564749\pi$
$492$		0			0
$493$	−4.71436	+	26.7364i	−0.212324	+	1.20415i
$494$	−9.54576	−	3.47437i	−0.429484	−	0.156319i
$495$		0			0
$496$	−3.47178	−	2.91317i	−0.155888	−	0.130805i
$497$	5.00774	+	4.20199i	0.224628	+	0.188485i
$498$		0			0
$499$	−1.73577	−	9.84402i	−0.0777036	−	0.440679i	−0.998694	−	0.0510934i	$-0.983729\pi$
$499$	−1.73577	−	9.84402i	−0.0777036	−	0.440679i	0.920990	−	0.389586i	$-0.127382\pi$
$500$	−1.83022	−	10.3797i	−0.0818500	−	0.464195i
$501$		0			0
$502$	1.94562	+	1.63257i	0.0868374	+	0.0728652i
$503$	−25.5023	−	21.3990i	−1.13709	−	0.954132i	−0.137751	−	0.990467i	$-0.543987\pi$
$503$	−25.5023	−	21.3990i	−1.13709	−	0.954132i	−0.999340	+	0.0363348i	$0.988432\pi$
$504$		0			0
$505$	6.67752	+	2.43042i	0.297146	+	0.108152i
$506$	1.77197	−	10.0494i	0.0787739	−	0.446749i
$507$		0			0
$508$	3.51367	+	6.08586i	0.155894	+	0.270016i
$509$	19.3751	−	7.05196i	0.858786	−	0.312573i	0.125169	−	0.992135i	$-0.460053\pi$
$509$	19.3751	−	7.05196i	0.858786	−	0.312573i	0.733617	+	0.679563i	$0.237830\pi$
$510$		0			0
$511$	−1.37551	+	1.15419i	−0.0608492	+	0.0510585i
$512$	1.00000			0.0441942
$513$		0			0
$514$	15.6493	+	5.69588i	0.690261	+	0.251234i
$515$	3.43061	+	19.4559i	0.151171	+	0.857331i
$516$		0			0
$517$	−0.436127			−0.0191808
$518$	−15.2738	+	1.98394i	−0.671092	+	0.0871694i
$519$		0			0
$520$	−0.739885	+	4.19610i	−0.0324461	+	0.184011i
$521$	4.53121	+	25.6978i	0.198516	+	1.12584i	0.907322	+	0.420437i	$0.138123\pi$
$521$	4.53121	+	25.6978i	0.198516	+	1.12584i	−0.708806	+	0.705404i	$0.750766\pi$
$522$		0			0
$523$	1.10535	−	0.927500i	0.0483337	−	0.0405567i	−0.618301	−	0.785942i	$-0.712179\pi$
$523$	1.10535	−	0.927500i	0.0483337	−	0.0405567i	0.666634	+	0.745385i	$0.267734\pi$
$524$	0.906726			0.0396105
$525$		0			0
$526$	−3.26739	+	5.65928i	−0.142465	+	0.246756i
$527$	12.7763	−	4.65020i	0.556545	−	0.202566i
$528$		0			0
$529$	−29.9602	+	51.8926i	−1.30262	+	2.25620i
$530$	4.91147	−	27.8544i	0.213341	−	1.20992i
$531$		0			0
$532$	7.08512	+	12.2718i	0.307179	+	0.532050i
$533$	−10.3369	−	8.67366i	−0.447739	−	0.375698i
$534$		0			0
$535$	13.3268	−	4.85057i	0.576169	−	0.209708i
$536$	1.27584	+	7.23567i	0.0551081	+	0.312534i
$537$		0			0
$538$	−8.32383	+	3.02962i	−0.358866	+	0.130616i
$539$	0.505215	+	0.423925i	0.0217611	+	0.0182598i
$540$		0			0
$541$	2.72921	+	4.72713i	0.117338	+	0.203235i	0.918712	−	0.394929i	$-0.129231\pi$
$541$	2.72921	+	4.72713i	0.117338	+	0.203235i	−0.801374	+	0.598164i	$0.795897\pi$
$542$	−8.92514	−	3.24849i	−0.383368	−	0.139534i
$543$		0			0
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$	23.5141	+	40.7277i	1.00723	+	1.74458i
$546$		0			0
$547$	−20.1086	+	34.8291i	−0.859781	+	1.48918i	0.0123559	+	0.999924i	$0.496067\pi$
$547$	−20.1086	+	34.8291i	−0.859781	+	1.48918i	−0.872137	+	0.489261i	$0.837266\pi$
$548$	−1.50000	+	1.25865i	−0.0640768	+	0.0537668i
$549$		0			0
$550$	−0.437633	+	0.367218i	−0.0186607	+	0.0156582i
$551$	−47.5899	−	17.3213i	−2.02740	−	0.737913i
$552$		0			0
$553$	1.94949	−	11.0561i	0.0829009	−	0.470154i
$554$	−29.4296			−1.25035
$555$		0			0
$556$	13.6013			0.576824
$557$	3.06640	−	17.3904i	0.129928	−	0.736856i	−0.848331	−	0.529466i	$-0.822392\pi$
$557$	3.06640	−	17.3904i	0.129928	−	0.736856i	0.978259	−	0.207389i	$-0.0664967\pi$
$558$		0			0
$559$	−15.2306	−	5.54347i	−0.644184	−	0.234464i
$560$	4.55303	−	3.82045i	0.192401	−	0.161443i
$561$		0			0
$562$	−4.54323	+	3.81223i	−0.191645	+	0.160809i
$563$	1.15523	−	2.00092i	0.0486871	−	0.0843286i	−0.840655	−	0.541571i	$-0.817830\pi$
$563$	1.15523	−	2.00092i	0.0486871	−	0.0843286i	0.889342	+	0.457243i	$0.151163\pi$
$564$		0			0
$565$	−2.98886	−	5.17685i	−0.125742	−	0.217792i
$566$	−11.2836	+	19.5437i	−0.474284	+	0.821485i
$567$		0			0
$568$	−2.42602	−	0.883000i	−0.101794	−	0.0370498i
$569$	−0.141559	−	0.245188i	−0.00593447	−	0.0102788i	0.863043	−	0.505131i	$-0.168556\pi$
$569$	−0.141559	−	0.245188i	−0.00593447	−	0.0102788i	−0.868977	+	0.494852i	$0.835222\pi$
$570$		0			0
$571$	−8.40420	−	7.05196i	−0.351705	−	0.295115i	0.449769	−	0.893145i	$-0.351506\pi$
$571$	−8.40420	−	7.05196i	−0.351705	−	0.295115i	−0.801474	+	0.598029i	$0.795951\pi$
$572$	−1.91147	+	0.695720i	−0.0799227	+	0.0290895i
$573$		0			0
$574$	3.26857	+	18.5370i	0.136428	+	0.773719i
$575$	4.36231	−	1.58775i	0.181921	−	0.0662138i
$576$		0			0
$577$	−12.1382	−	10.1851i	−0.505318	−	0.424012i	0.354160	−	0.935185i	$-0.384767\pi$
$577$	−12.1382	−	10.1851i	−0.505318	−	0.424012i	−0.859478	+	0.511173i	$0.829211\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$		0			0
$580$	−3.68866	+	20.9194i	−0.153163	+	0.868633i
$581$	−9.17752	+	15.8959i	−0.380748	+	0.659474i
$582$		0			0
$583$	12.6887	−	4.61830i	0.525511	−	0.191270i
$584$	0.354570	−	0.614134i	0.0146722	−	0.0254130i
$585$		0			0
$586$	4.06418			0.167890
$587$	14.2947	−	11.9947i	0.590007	−	0.495074i	−0.298209	−	0.954500i	$-0.596389\pi$
$587$	14.2947	−	11.9947i	0.590007	−	0.495074i	0.888216	+	0.459426i	$0.151945\pi$
$588$		0			0
$589$	4.40420	+	24.9775i	0.181472	+	1.02918i
$590$	−3.41353	+	19.3591i	−0.140533	+	0.797002i
$591$		0			0
$592$	5.40033	−	2.79936i	0.221952	−	0.115053i
$593$	39.4329			1.61932			0.809658	−	0.586901i	$-0.199652\pi$
$593$	39.4329			1.61932			0.809658	+	0.586901i	$0.199652\pi$
$594$		0			0
$595$	3.09627	+	17.5598i	0.126935	+	0.719882i
$596$	−6.33022	−	2.30401i	−0.259296	−	0.0943760i
$597$		0			0
$598$	16.5294			0.675937
$599$	−5.35710	+	4.49514i	−0.218885	+	0.183666i	−0.745636	−	0.666353i	$-0.767854\pi$
$599$	−5.35710	+	4.49514i	−0.218885	+	0.183666i	0.526751	+	0.850019i	$0.323410\pi$
$600$		0			0
$601$	−33.7301	+	12.2768i	−1.37588	+	0.500780i	−0.920927	−	0.389735i	$-0.872567\pi$
$601$	−33.7301	+	12.2768i	−1.37588	+	0.500780i	−0.454954	+	0.890515i	$0.650344\pi$
$602$	11.3045	+	19.5800i	0.460738	+	0.798022i
$603$		0			0
$604$	0.832748	−	4.72275i	0.0338841	−	0.192166i
$605$	21.4932	+	7.82288i	0.873823	+	0.318045i
$606$		0			0
$607$	8.60788	+	7.22287i	0.349383	+	0.293167i	0.800542	−	0.599276i	$-0.204545\pi$
$607$	8.60788	+	7.22287i	0.349383	+	0.293167i	−0.451159	+	0.892443i	$0.648989\pi$
$608$	−4.28699	−	3.59721i	−0.173860	−	0.145886i
$609$		0			0
$610$	−1.06418	−	6.03525i	−0.0430873	−	0.244360i
$611$	−0.122674	−	0.695720i	−0.00496286	−	0.0281458i
$612$		0			0
$613$	0.735767	+	0.617381i	0.0297173	+	0.0249358i	0.657525	−	0.753432i	$-0.271603\pi$
$613$	0.735767	+	0.617381i	0.0297173	+	0.0249358i	−0.627808	+	0.778368i	$0.716048\pi$
$614$	−8.56805	−	7.18945i	−0.345778	−	0.290142i
$615$		0			0
$616$	2.66637	+	0.970481i	0.107431	+	0.0391018i
$617$	3.71641	−	21.0768i	0.149617	−	0.848521i	−0.813926	−	0.580969i	$-0.802674\pi$
$617$	3.71641	−	21.0768i	0.149617	−	0.848521i	0.963543	−	0.267553i	$-0.0862150\pi$
$618$		0			0
$619$	−5.72550	−	9.91686i	−0.230127	−	0.398592i	0.727718	−	0.685876i	$-0.240581\pi$
$619$	−5.72550	−	9.91686i	−0.230127	−	0.398592i	−0.957845	+	0.287284i	$0.907248\pi$
$620$	9.99660	−	3.63846i	0.401473	−	0.146124i
$621$		0			0
$622$	−6.32501	+	5.30731i	−0.253610	+	0.212804i
$623$	32.8999			1.31811
$624$		0			0
$625$	25.6434	+	9.33342i	1.02573	+	0.373337i
$626$	−2.04442	−	11.5945i	−0.0817113	−	0.463408i
$627$		0			0
$628$	−14.4679			−0.577333
$629$	−0.827534	+	18.2295i	−0.0329959	+	0.726858i
$630$		0			0
$631$	8.35710	−	47.3954i	0.332691	−	1.88678i	−0.116247	−	0.993220i	$-0.537087\pi$
$631$	8.35710	−	47.3954i	0.332691	−	1.88678i	0.448938	−	0.893563i	$-0.351802\pi$
$632$	0.769915	+	4.36640i	0.0306256	+	0.173686i
$633$		0			0
$634$	−10.1441	+	8.51190i	−0.402873	+	0.338051i
$635$	−16.4953			−0.654594
$636$		0			0
$637$	−0.534148	+	0.925172i	−0.0211637	+	0.0366566i
$638$	−9.52956	+	3.46848i	−0.377279	+	0.137318i
$639$		0			0
$640$	−1.17365	+	2.03282i	−0.0463925	+	0.0803542i
$641$	−5.53121	+	31.3691i	−0.218470	+	1.23900i	0.656313	+	0.754488i	$0.272115\pi$
$641$	−5.53121	+	31.3691i	−0.218470	+	1.23900i	−0.874783	+	0.484515i	$0.838996\pi$
$642$		0			0
$643$	−11.2897	−	19.5543i	−0.445221	−	0.771146i	0.552846	−	0.833283i	$-0.313542\pi$
$643$	−11.2897	−	19.5543i	−0.445221	−	0.771146i	−0.998068	+	0.0621372i	$0.980208\pi$
$644$	−17.6630	−	14.8210i	−0.696019	−	0.584029i
$645$		0			0
$646$	15.7763	−	5.74211i	0.620711	−	0.225920i
$647$	−5.12954	−	29.0911i	−0.201663	−	1.14369i	−0.902605	−	0.430469i	$-0.858348\pi$
$647$	−5.12954	−	29.0911i	−0.201663	−	1.14369i	0.700942	−	0.713218i	$-0.252763\pi$
$648$		0			0
$649$	−8.81877	+	3.20977i	−0.346167	+	0.125995i
$650$	−0.708892	−	0.594831i	−0.0278050	−	0.0233312i
$651$		0			0
$652$	−5.02481	−	8.70323i	−0.196787	−	0.340845i
$653$	−8.71600	−	3.17237i	−0.341084	−	0.124144i	0.165799	−	0.986160i	$-0.446980\pi$
$653$	−8.71600	−	3.17237i	−0.341084	−	0.124144i	−0.506882	+	0.862015i	$0.669202\pi$
$654$		0			0
$655$	−1.06418	+	1.84321i	−0.0415809	+	0.0720202i
$656$	−3.71688	−	6.43783i	−0.145120	−	0.251355i
$657$		0			0
$658$	−0.492726	+	0.853427i	−0.0192085	+	0.0332700i
$659$	−20.8418	+	17.4884i	−0.811883	+	0.681250i	−0.951056	−	0.309018i	$-0.900000\pi$
$659$	−20.8418	+	17.4884i	−0.811883	+	0.681250i	0.139174	+	0.990268i	$0.455555\pi$
$660$		0			0
$661$	8.43763	−	7.08001i	0.328186	−	0.275381i	−0.463774	−	0.885953i	$-0.653505\pi$
$661$	8.43763	−	7.08001i	0.328186	−	0.275381i	0.791960	+	0.610573i	$0.209061\pi$
$662$	−23.0646	−	8.39484i	−0.896433	−	0.326275i
$663$		0			0
$664$	1.25877	−	7.13884i	0.0488498	−	0.277041i
$665$	−33.2618			−1.28984
$666$		0			0
$667$	82.4065			3.19079
$668$	−1.81315	+	10.2829i	−0.0701528	+	0.397856i
$669$		0			0
$670$	−16.2062	−	5.89858i	−0.626100	−	0.227882i
$671$	2.24123	−	1.88061i	0.0865217	−	0.0726003i
$672$		0			0
$673$	10.1141	−	8.48670i	0.389868	−	0.327138i	−0.426694	−	0.904396i	$-0.640322\pi$
$673$	10.1141	−	8.48670i	0.389868	−	0.327138i	0.816562	+	0.577258i	$0.195877\pi$
$674$	−6.04323	+	10.4672i	−0.232777	+	0.403181i
$675$		0			0
$676$	4.85251	+	8.40480i	0.186635	+	0.323261i
$677$	−17.7763	+	30.7895i	−0.683199	+	1.18334i	0.290800	+	0.956784i	$0.406079\pi$
$677$	−17.7763	+	30.7895i	−0.683199	+	1.18334i	−0.973999	+	0.226552i	$0.927255\pi$
$678$		0			0
$679$	34.9641	+	12.7259i	1.34180	+	0.488375i
$680$	−3.52094	−	6.09845i	−0.135022	−	0.233865i
$681$		0			0
$682$	3.89053	+	3.26454i	0.148976	+	0.125006i
$683$	30.8756	−	11.2378i	1.18142	−	0.430002i	0.324717	−	0.945811i	$-0.394731\pi$
$683$	30.8756	−	11.2378i	1.18142	−	0.430002i	0.856704	+	0.515809i	$0.172509\pi$
$684$		0			0
$685$	−0.798133	−	4.52644i	−0.0304951	−	0.172946i
$686$	18.0560	−	6.57186i	0.689382	−	0.250915i
$687$		0			0
$688$	−6.84002	−	5.73946i	−0.260773	−	0.218815i
$689$	10.9363	+	18.9422i	0.416639	+	0.721641i
$690$		0			0
$691$	−7.38089	+	41.8591i	−0.280782	+	1.59240i	0.439191	+	0.898394i	$0.355265\pi$
$691$	−7.38089	+	41.8591i	−0.280782	+	1.59240i	−0.719973	+	0.694002i	$0.755846\pi$
$692$	0.524815	−	0.909006i	0.0199505	−	0.0345552i
$693$		0			0
$694$	−1.69934	+	0.618509i	−0.0645061	+	0.0234783i
$695$	−15.9632	+	27.6490i	−0.605517	+	1.04879i
$696$		0			0
$697$	22.3013			0.844722
$698$	3.95677	−	3.32012i	0.149766	−	0.125668i
$699$		0			0
$700$	0.224155	+	1.27125i	0.00847228	+	0.0480487i
$701$	2.88161	−	16.3424i	0.108837	−	0.617244i	−0.880781	−	0.473523i	$-0.842982\pi$
$701$	2.88161	−	16.3424i	0.108837	−	0.617244i	0.989618	−	0.143721i	$-0.0459068\pi$
$702$		0			0
$703$	−33.2211	−	7.42528i	−1.25296	−	0.280050i
$704$	−1.12061			−0.0422348
$705$		0			0
$706$	5.38800	+	30.5569i	0.202780	+	1.15002i
$707$	7.20321	+	2.62175i	0.270905	+	0.0986012i
$708$		0			0
$709$	5.68779			0.213609			0.106805	−	0.994280i	$-0.465938\pi$
$709$	5.68779			0.213609			0.106805	+	0.994280i	$0.465938\pi$
$710$	4.64227	−	3.89533i	0.174221	−	0.146189i
$711$		0			0
$712$	−12.2096	+	4.44393i	−0.457574	+	0.166543i
$713$	−20.6348	−	35.7404i	−0.772778	−	1.33849i
$714$		0			0
$715$	0.829126	−	4.70221i	0.0310076	−	0.175853i
$716$	8.60354	+	3.13143i	0.321529	+	0.117027i
$717$		0			0
$718$	−2.31908	−	1.94594i	−0.0865472	−	0.0726217i
$719$	−9.21735	−	7.73427i	−0.343749	−	0.288440i	0.454525	−	0.890734i	$-0.349809\pi$
$719$	−9.21735	−	7.73427i	−0.343749	−	0.288440i	−0.798274	+	0.602294i	$0.794253\pi$
$720$		0			0
$721$	3.70068	+	20.9876i	0.137821	+	0.781620i
$722$	2.13903	+	12.1311i	0.0796066	+	0.451471i
$723$		0			0
$724$	−17.3157	−	14.5296i	−0.643532	−	0.539987i
$725$	−3.53415	−	2.96550i	−0.131255	−	0.110136i
$726$		0			0
$727$	−25.5898	−	9.31391i	−0.949072	−	0.345434i	−0.179330	−	0.983789i	$-0.557393\pi$
$727$	−25.5898	−	9.31391i	−0.949072	−	0.345434i	−0.769742	+	0.638355i	$0.779615\pi$
$728$	−0.798133	+	4.52644i	−0.0295808	+	0.167761i
$729$		0			0
$730$	0.832282	+	1.44155i	0.0308041	+	0.0533543i
$731$	25.1716	−	9.16171i	0.931005	−	0.338858i
$732$		0			0
$733$	−16.2324	+	13.6206i	−0.599556	+	0.503087i	−0.891303	−	0.453408i	$-0.850208\pi$
$733$	−16.2324	+	13.6206i	−0.599556	+	0.503087i	0.291747	+	0.956496i	$0.405764\pi$
$734$	27.7948			1.02592
$735$		0			0
$736$	8.55690	+	3.11446i	0.315412	+	0.114800i
$737$	−1.42973	−	8.10840i	−0.0526648	−	0.298677i
$738$		0			0
$739$	−30.6195			−1.12636			−0.563178	−	0.826336i	$-0.690421\pi$
$739$	−30.6195			−1.12636			−0.563178	+	0.826336i	$0.690421\pi$
$740$	−0.647489	+	14.2634i	−0.0238022	+	0.524331i
$741$		0			0
$742$	5.29813	−	30.0472i	0.194501	−	1.10307i
$743$	2.98798	+	16.9457i	0.109618	+	0.621676i	0.989275	+	0.146067i	$0.0466614\pi$
$743$	2.98798	+	16.9457i	0.109618	+	0.621676i	−0.879656	+	0.475610i	$0.842228\pi$
$744$		0			0
$745$	12.1131	−	10.1641i	0.443789	−	0.372383i
$746$	5.17530			0.189481
$747$		0			0
$748$	1.68092	−	2.91144i	0.0614606	−	0.106453i
$749$	14.3760	−	5.23243i	0.525287	−	0.191189i
$750$		0			0
$751$	13.7506	−	23.8168i	0.501767	−	0.869086i	−0.498231	−	0.867045i	$-0.666017\pi$
$751$	13.7506	−	23.8168i	0.501767	−	0.869086i	0.999998	−	0.00204181i	$-0.000649930\pi$
$752$	0.0675813	−	0.383273i	0.00246444	−	0.0139765i
$753$		0			0
$754$	−8.21348	−	14.2262i	−0.299117	−	0.518086i
$755$	8.62314	+	7.23567i	0.313828	+	0.263333i
$756$		0			0
$757$	−18.0753	+	6.57888i	−0.656959	+	0.239113i	−0.648923	−	0.760854i	$-0.724780\pi$
$757$	−18.0753	+	6.57888i	−0.656959	+	0.239113i	−0.00803598	+	0.999968i	$0.502558\pi$
$758$	−3.66250	−	20.7711i	−0.133028	−	0.754440i
$759$		0			0
$760$	12.3439	−	4.49281i	0.447760	−	0.162971i
$761$	−30.1313	−	25.2832i	−1.09226	−	0.916515i	−0.0953800	−	0.995441i	$-0.530407\pi$
$761$	−30.1313	−	25.2832i	−1.09226	−	0.916515i	−0.996881	+	0.0789255i	$0.974851\pi$
$762$		0			0
$763$	25.3653	+	43.9340i	0.918286	+	1.59052i
$764$	−17.9795	−	6.54401i	−0.650476	−	0.236754i
$765$		0			0
$766$	−19.5155	+	33.8018i	−0.705123	+	1.22131i
$767$	−7.60085	−	13.1651i	−0.274451	−	0.475363i
$768$		0			0
$769$	−6.48087	+	11.2252i	−0.233706	+	0.404791i	−0.958896	−	0.283758i	$-0.908419\pi$
$769$	−6.48087	+	11.2252i	−0.233706	+	0.404791i	0.725190	+	0.688549i	$0.241752\pi$
$770$	−5.10220	+	4.28125i	−0.183870	+	0.154286i
$771$		0			0
$772$	−14.5646	+	12.2212i	−0.524193	+	0.439850i
$773$	11.1878	+	4.07202i	0.402397	+	0.146460i	0.535287	−	0.844670i	$-0.320204\pi$
$773$	11.1878	+	4.07202i	0.402397	+	0.146460i	−0.132890	+	0.991131i	$0.542426\pi$
$774$		0			0
$775$	−0.401207	+	2.27536i	−0.0144118	+	0.0817333i
$776$	−14.6946			−0.527505
$777$		0			0
$778$	−16.0273			−0.574608
$779$	−7.22399	+	40.9693i	−0.258826	+	1.46788i
$780$		0			0
$781$	2.71864	+	0.989503i	0.0972804	+	0.0354072i
$782$	−20.9270	+	17.5598i	−0.748346	+	0.627937i
$783$		0			0
$784$	−0.450837	+	0.378297i	−0.0161013	+	0.0135106i
$785$	16.9802	−	29.4106i	0.606051	−	1.04971i
$786$		0			0
$787$	−10.4618	−	18.1204i	−0.372924	−	0.645923i	0.617090	−	0.786892i	$-0.288311\pi$
$787$	−10.4618	−	18.1204i	−0.372924	−	0.645923i	−0.990014	+	0.140970i	$0.954978\pi$
$788$	9.24035	−	16.0048i	0.329174	−	0.570146i
$789$		0			0
$790$	−9.77972	−	3.55953i	−0.347947	−	0.126642i
$791$	−3.22416	−	5.58440i	−0.114638	−	0.198558i
$792$		0			0
$793$	3.63041	+	3.04628i	0.128920	+	0.108177i
$794$	−13.7579	+	5.00746i	−0.488249	+	0.177708i
$795$		0			0
$796$	−0.967911	−	5.48930i	−0.0343067	−	0.194563i
$797$	−3.67752	+	1.33851i	−0.130264	+	0.0474124i	−0.406330	−	0.913726i	$-0.633192\pi$
$797$	−3.67752	+	1.33851i	−0.130264	+	0.0474124i	0.276065	+	0.961139i	$0.410969\pi$
$798$		0			0
$799$	0.894400	+	0.750491i	0.0316416	+	0.0265505i
$800$	−0.254900	−	0.441500i	−0.00901208	−	0.0156094i
$801$		0			0
$802$	−2.05035	+	11.6281i	−0.0724002	+	0.410602i
$803$	−0.397337	+	0.688207i	−0.0140217	+	0.0242863i
$804$		0			0
$805$	50.8585	−	18.5110i	1.79253	−	0.652426i
$806$	−4.11334	+	7.12452i	−0.144886	+	0.250950i
$807$		0			0
$808$	−3.02734			−0.106501
$809$	−11.5921	+	9.72697i	−0.407558	+	0.341982i	−0.823406	−	0.567452i	$-0.807929\pi$
$809$	−11.5921	+	9.72697i	−0.407558	+	0.341982i	0.415848	+	0.909434i	$0.363485\pi$
$810$		0			0
$811$	6.99629	+	39.6779i	0.245673	+	1.39328i	0.818924	+	0.573901i	$0.194571\pi$
$811$	6.99629	+	39.6779i	0.245673	+	1.39328i	−0.573251	+	0.819380i	$0.694318\pi$
$812$	−3.97906	+	22.5663i	−0.139637	+	0.791923i
$813$		0			0
$814$	−6.05169	+	3.13701i	−0.212112	+	0.109952i
$815$	23.5895			0.826303
$816$		0			0
$817$	8.67705	+	49.2100i	0.303572	+	1.72164i
$818$	−5.27972	−	1.92166i	−0.184601	−	0.0671892i
$819$		0			0
$820$	17.4492			0.609354
$821$	−19.4008	+	16.2792i	−0.677092	+	0.568148i	−0.915155	−	0.403102i	$-0.867932\pi$
$821$	−19.4008	+	16.2792i	−0.677092	+	0.568148i	0.238063	+	0.971250i	$0.423488\pi$
$822$		0			0
$823$	−26.7212	+	9.72573i	−0.931443	+	0.339018i	−0.762781	−	0.646656i	$-0.776167\pi$
$823$	−26.7212	+	9.72573i	−0.931443	+	0.339018i	−0.168662	+	0.985674i	$0.553945\pi$
$824$	−4.20826	−	7.28893i	−0.146602	−	0.253922i
$825$		0			0
$826$	−3.68227	+	20.8832i	−0.128122	+	0.726618i
$827$	2.64068	+	0.961130i	0.0918255	+	0.0334218i	0.387524	−	0.921859i	$-0.373330\pi$
$827$	2.64068	+	0.961130i	0.0918255	+	0.0334218i	−0.295699	+	0.955281i	$0.595553\pi$
$828$		0			0
$829$	−15.2585	−	12.8034i	−0.529950	−	0.444681i	0.338134	−	0.941098i	$-0.390204\pi$
$829$	−15.2585	−	12.8034i	−0.529950	−	0.444681i	−0.868084	+	0.496417i	$0.834649\pi$
$830$	13.0346	+	10.9373i	0.452438	+	0.379641i
$831$		0			0
$832$	−0.315207	−	1.78763i	−0.0109279	−	0.0619749i
$833$	−0.306589	−	1.73875i	−0.0106227	−	0.0602443i
$834$		0			0
$835$	−18.7752	−	15.7543i	−0.649743	−	0.545199i
$836$	4.80406	+	4.03109i	0.166152	+	0.139418i
$837$		0			0
$838$	−9.53343	−	3.46989i	−0.329327	−	0.119865i
$839$	−6.48726	+	36.7911i	−0.223965	+	1.27017i	0.640688	+	0.767801i	$0.278649\pi$
$839$	−6.48726	+	36.7911i	−0.223965	+	1.27017i	−0.864654	+	0.502369i	$0.832462\pi$
$840$		0			0
$841$	−26.4479	−	45.8091i	−0.911997	−	1.57962i
$842$	−10.3020	+	3.74962i	−0.355030	+	0.129221i
$843$		0			0
$844$	16.6309	−	13.9550i	0.572459	−	0.480350i
$845$	−22.7806			−0.783675
$846$		0			0
$847$	23.1853	+	8.43874i	0.796655	+	0.289959i
$848$	2.09240	+	11.8666i	0.0718532	+	0.407500i
$849$		0			0
$850$	1.52940			0.0524580
$851$	54.9286	−	7.13479i	1.88293	−	0.244577i
$852$		0			0
$853$	3.87227	−	21.9608i	0.132584	−	0.751922i	−0.843928	−	0.536457i	$-0.819762\pi$
$853$	3.87227	−	21.9608i	0.132584	−	0.751922i	0.976512	−	0.215465i	$-0.0691266\pi$
$854$	−1.14796	−	6.51038i	−0.0392822	−	0.222781i
$855$		0			0
$856$	−4.62836	+	3.88365i	−0.158194	+	0.132740i
$857$	18.2817			0.624491			0.312245	−	0.950002i	$-0.398919\pi$
$857$	18.2817			0.624491			0.312245	+	0.950002i	$0.398919\pi$
$858$		0			0
$859$	7.59358	−	13.1525i	0.259090	−	0.448756i	−0.706909	−	0.707305i	$-0.749911\pi$
$859$	7.59358	−	13.1525i	0.259090	−	0.448756i	0.965998	+	0.258549i	$0.0832442\pi$
$860$	19.6951	−	7.16842i	0.671596	−	0.244441i
$861$		0			0
$862$	2.55438	−	4.42431i	0.0870024	−	0.150693i
$863$	−0.353855	+	2.00681i	−0.0120454	+	0.0683127i	−0.990238	−	0.139387i	$-0.955487\pi$
$863$	−0.353855	+	2.00681i	−0.0120454	+	0.0683127i	0.978193	+	0.207700i	$0.0665978\pi$
$864$		0			0
$865$	1.23190	+	2.13371i	0.0418857	+	0.0725482i
$866$	−21.2520	−	17.8325i	−0.722171	−	0.605974i
$867$		0			0
$868$	10.7836	−	3.92490i	0.366019	−	0.133220i
$869$	−0.862778	−	4.89306i	−0.0292677	−	0.165986i
$870$		0			0
$871$	12.5326	−	4.56148i	0.424649	−	0.154560i
$872$	−15.3478	−	12.8783i	−0.519741	−	0.436114i
$873$		0			0
$874$	−25.4800	−	44.1326i	−0.861873	−	1.49281i
$875$	25.0783	+	9.12776i	0.847802	+	0.308575i
$876$		0			0
$877$	−1.13445	+	1.96492i	−0.0383076	+	0.0663507i	−0.884544	−	0.466458i	$-0.845530\pi$
$877$	−1.13445	+	1.96492i	−0.0383076	+	0.0663507i	0.846236	+	0.532808i	$0.178863\pi$
$878$	14.5692	+	25.2346i	0.491688	+	0.851628i
$879$		0			0
$880$	1.31521	−	2.27801i	0.0443356	−	0.0767916i
$881$	−23.1616	+	19.4349i	−0.780335	+	0.654779i	−0.943333	−	0.331848i	$-0.892328\pi$
$881$	−23.1616	+	19.4349i	−0.780335	+	0.654779i	0.162998	+	0.986626i	$0.447884\pi$
$882$		0			0
$883$	−1.65136	+	1.38566i	−0.0555727	+	0.0466310i	−0.670151	−	0.742225i	$-0.733771\pi$
$883$	−1.65136	+	1.38566i	−0.0555727	+	0.0466310i	0.614578	+	0.788856i	$0.289326\pi$
$884$	5.11721	+	1.86251i	0.172110	+	0.0626431i
$885$		0			0
$886$	−1.21183	+	6.87262i	−0.0407122	+	0.230890i
$887$	30.0387			1.00860			0.504300	−	0.863528i	$-0.331750\pi$
$887$	30.0387			1.00860			0.504300	+	0.863528i	$0.331750\pi$
$888$		0			0
$889$	−17.7939			−0.596787
$890$	5.29607	−	30.0355i	0.177525	−	1.00679i
$891$		0			0
$892$	9.53121	+	3.46908i	0.319129	+	0.116153i
$893$	−1.66843	+	1.39998i	−0.0558320	+	0.0468486i
$894$		0			0
$895$	−16.4632	+	13.8142i	−0.550303	+	0.461759i
$896$	−1.26604	+	2.19285i	−0.0422956	+	0.0732581i
$897$		0			0
$898$	9.12701	+	15.8084i	0.304572	+	0.527535i
$899$	−20.5069	+	35.5189i	−0.683942	+	1.18462i
$900$		0			0
$901$	−33.9688	−	12.3636i	−1.13167	−	0.411893i
$902$	4.16519	+	7.21432i	0.138686	+	0.240211i
$903$		0			0
$904$	1.95084	+	1.63695i	0.0648839	+	0.0544440i
$905$	49.8585	−	18.1470i	1.65735	−	0.603227i
$906$		0			0
$907$	−0.218474	−	1.23903i	−0.00725431	−	0.0411412i	0.980966	−	0.194181i	$-0.0622049\pi$
$907$	−0.218474	−	1.23903i	−0.00725431	−	0.0411412i	−0.988220	+	0.153040i	$0.951094\pi$
$908$	−4.10354	+	1.49357i	−0.136181	+	0.0495657i
$909$		0			0
$910$	−8.26470	−	6.93491i	−0.273972	−	0.229890i
$911$	−22.8371	−	39.5550i	−0.756626	−	1.31052i	−0.944562	−	0.328334i	$-0.893513\pi$
$911$	−22.8371	−	39.5550i	−0.756626	−	1.31052i	0.187935	−	0.982181i	$-0.439820\pi$
$912$		0			0
$913$	−1.41060	+	7.99989i	−0.0466839	+	0.264758i
$914$	11.3978	−	19.7416i	0.377006	−	0.652993i
$915$		0			0
$916$	11.0633	−	4.02671i	0.365542	−	0.133046i
$917$	−1.14796	+	1.98832i	−0.0379088	+	0.0656600i
$918$		0			0
$919$	−12.5006			−0.412358			−0.206179	−	0.978514i	$-0.566103\pi$
$919$	−12.5006			−0.412358			−0.206179	+	0.978514i	$0.566103\pi$
$920$	−16.3739	+	13.7394i	−0.539832	+	0.452973i
$921$		0			0
$922$	−1.51027	−	8.56515i	−0.0497380	−	0.282078i
$923$	−0.813777	+	4.61516i	−0.0267858	+	0.151910i
$924$		0			0
$925$	−2.61246	−	1.67069i	−0.0858973	−	0.0549318i
$926$	3.41323			0.112166
$927$		0			0
$928$	−1.57145	−	8.91215i	−0.0515854	−	0.292556i
$929$	14.8769	+	5.41473i	0.488094	+	0.177652i	0.574331	−	0.818623i	$-0.305262\pi$
$929$	14.8769	+	5.41473i	0.488094	+	0.177652i	−0.0862374	+	0.996275i	$0.527484\pi$
$930$		0			0
$931$	3.29355			0.107942
$932$	−12.4684	+	10.4622i	−0.408415	+	0.342701i
$933$		0			0
$934$	34.4247	−	12.5296i	1.12641	−	0.409980i
$935$	3.94562	+	6.83402i	0.129036	+	0.223496i
$936$		0			0
$937$	7.32454	−	41.5395i	0.239282	−	1.35704i	−0.594123	−	0.804375i	$-0.702501\pi$
$937$	7.32454	−	41.5395i	0.239282	−	1.35704i	0.833405	−	0.552663i	$-0.186388\pi$
$938$	−17.4820	−	6.36295i	−0.570809	−	0.207758i
$939$		0			0
$940$	0.699807	+	0.587208i	0.0228252	+	0.0191526i
$941$	−40.3469	−	33.8551i	−1.31527	−	1.10364i	−0.987285	−	0.158961i	$-0.949186\pi$
$941$	−40.3469	−	33.8551i	−1.31527	−	1.10364i	−0.327986	−	0.944683i	$-0.606370\pi$
$942$		0			0
$943$	−11.7547	−	66.6639i	−0.382784	−	2.17088i
$944$	−1.45424	−	8.24741i	−0.0473315	−	0.268430i
$945$		0			0
$946$	7.66503	+	6.43172i	0.249212	+	0.209113i
$947$	−3.45929	−	2.90269i	−0.112412	−	0.0943248i	0.584849	−	0.811142i	$-0.301154\pi$
$947$	−3.45929	−	2.90269i	−0.112412	−	0.0943248i	−0.697261	+	0.716817i	$0.745598\pi$
$948$		0			0
$949$	−1.20961	−	0.440261i	−0.0392655	−	0.0142915i
$950$	−0.495414	+	2.80963i	−0.0160734	+	0.0911566i
$951$		0			0
$952$	−3.79813	−	6.57856i	−0.123098	−	0.213212i
$953$	44.1715	−	16.0771i	1.43085	−	0.520789i	0.493678	−	0.869645i	$-0.335652\pi$
$953$	44.1715	−	16.0771i	1.43085	−	0.520789i	0.937176	+	0.348856i	$0.113430\pi$
$954$		0			0
$955$	34.4044	−	28.8687i	1.11330	−	0.934170i
$956$	15.5895			0.504199
$957$		0			0
$958$	−19.3640	−	7.04791i	−0.625621	−	0.227707i
$959$	−0.860967	−	4.88279i	−0.0278021	−	0.157673i
$960$		0			0
$961$	−10.4602			−0.337425
$962$	−6.70645	−	8.77141i	−0.216225	−	0.282802i
$963$		0			0
$964$	−0.151826	+	0.861050i	−0.00489000	+	0.0277325i
$965$	−7.74969	−	43.9507i	−0.249471	−	1.41482i
$966$		0			0
$967$	0.149548	−	0.125486i	0.00480915	−	0.00403536i	−0.640380	−	0.768058i	$-0.721223\pi$
$967$	0.149548	−	0.125486i	0.00480915	−	0.00403536i	0.645189	+	0.764023i	$0.276779\pi$
$968$	−9.74422			−0.313191
$969$		0			0
$970$	17.2463	−	29.8714i	0.553745	−	0.959114i
$971$	0.752679	−	0.273953i	0.0241546	−	0.00879156i	−0.329915	−	0.944011i	$-0.607020\pi$
$971$	0.752679	−	0.273953i	0.0241546	−	0.00879156i	0.354069	+	0.935219i	$0.384798\pi$
$972$		0			0
$973$	−17.2199	+	29.8257i	−0.552044	+	0.956168i
$974$	7.34302	−	41.6443i	0.235285	−	1.33437i
$975$		0			0
$976$	1.30541	+	2.26103i	0.0417851	+	0.0723739i
$977$	12.6438	+	10.6094i	0.404512	+	0.339426i	0.822235	−	0.569149i	$-0.192727\pi$
$977$	12.6438	+	10.6094i	0.404512	+	0.339426i	−0.417722	+	0.908575i	$0.637172\pi$
$978$		0			0
$979$	13.6823	−	4.97994i	0.437287	−	0.159159i
$980$	−0.239885	−	1.36046i	−0.00766286	−	0.0434582i
$981$		0			0
$982$	31.1152	−	11.3250i	0.992924	−	0.361395i
$983$	22.4466	+	18.8349i	0.715934	+	0.600740i	0.926257	−	0.376892i	$-0.123007\pi$
$983$	22.4466	+	18.8349i	0.715934	+	0.600740i	−0.210323	+	0.977632i	$0.567452\pi$
$984$		0			0
$985$	21.6898	+	37.5679i	0.691096	+	1.19701i
$986$	25.5116	+	9.28547i	0.812455	+	0.295710i
$987$		0			0
$988$	−5.07919	+	8.79742i	−0.161591	+	0.279883i
$989$	−40.6541	−	70.4150i	−1.29273	−	2.23907i
$990$		0			0
$991$	6.89393	−	11.9406i	0.218993	−	0.379307i	−0.735507	−	0.677517i	$-0.763056\pi$
$991$	6.89393	−	11.9406i	0.218993	−	0.379307i	0.954500	+	0.298210i	$0.0963895\pi$
$992$	−3.47178	+	2.91317i	−0.110229	+	0.0924933i
$993$		0			0
$994$	5.00774	−	4.20199i	0.158836	−	0.133279i
$995$	12.2947	+	4.47492i	0.389769	+	0.141864i
$996$		0			0
$997$	3.43170	−	19.4622i	0.108683	−	0.616373i	−0.881002	−	0.473113i	$-0.843130\pi$
$997$	3.43170	−	19.4622i	0.108683	−	0.616373i	0.989685	−	0.143260i	$-0.0457585\pi$
$998$	−9.99588			−0.316414
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.x.c.181.1		6
3.2	odd	2		74.2.f.a.33.1	yes	6
12.11	even	2		592.2.bc.b.33.1		6
37.9	even	9	inner	666.2.x.c.379.1		6
111.71	odd	18		2738.2.a.m.1.3		3
111.77	odd	18		2738.2.a.p.1.3		3
111.83	odd	18		74.2.f.a.9.1	✓	6
444.83	even	18		592.2.bc.b.305.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.a.9.1	✓	6	111.83	odd	18
74.2.f.a.33.1	yes	6	3.2	odd	2
592.2.bc.b.33.1		6	12.11	even	2
592.2.bc.b.305.1		6	444.83	even	18
666.2.x.c.181.1		6	1.1	even	1	trivial
666.2.x.c.379.1		6	37.9	even	9	inner
2738.2.a.m.1.3		3	111.71	odd	18
2738.2.a.p.1.3		3	111.77	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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.x (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(1.79813 - 1.50881i) q^{5} +(1.93969 - 1.62760i) q^{7} +(-0.500000 + 0.866025i) q^{8} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(1.79813 - 1.50881i) q^{5} +(1.93969 - 1.62760i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-1.17365 - 2.03282i) q^{10} +(0.560307 - 0.970481i) q^{11} +(1.70574 + 0.620838i) q^{13} +(-1.26604 - 2.19285i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-2.81908 + 1.02606i) q^{17} +(-0.971782 - 5.51125i) q^{19} +(-2.20574 + 0.802823i) q^{20} +(-0.858441 - 0.720317i) q^{22} +(4.55303 + 7.88609i) q^{23} +(0.0885259 - 0.502055i) q^{25} +(0.907604 - 1.57202i) q^{26} +(-2.37939 + 0.866025i) q^{28} +(4.52481 - 7.83721i) q^{29} -4.53209 q^{31} +(0.766044 - 0.642788i) q^{32} +(0.520945 + 2.95442i) q^{34} +(1.03209 - 5.85327i) q^{35} +(2.33750 - 5.61570i) q^{37} -5.59627 q^{38} +(0.407604 + 2.31164i) q^{40} +(-6.98545 - 2.54250i) q^{41} -8.92902 q^{43} +(-0.858441 + 0.720317i) q^{44} +(8.55690 - 3.11446i) q^{46} +(-0.194593 - 0.337044i) q^{47} +(-0.102196 + 0.579585i) q^{49} +(-0.479055 - 0.174362i) q^{50} +(-1.39053 - 1.16679i) q^{52} +(9.23055 + 7.74535i) q^{53} +(-0.456767 - 2.59045i) q^{55} +(0.439693 + 2.49362i) q^{56} +(-6.93242 - 5.81699i) q^{58} +(-6.41534 - 5.38311i) q^{59} +(2.45336 + 0.892951i) q^{61} +(-0.786989 + 4.46324i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(4.00387 - 1.45729i) q^{65} +(5.62836 - 4.72275i) q^{67} +3.00000 q^{68} +(-5.58512 - 2.03282i) q^{70} +(0.448311 + 2.54250i) q^{71} -0.709141 q^{73} +(-5.12449 - 3.27714i) q^{74} +(-0.971782 + 5.51125i) q^{76} +(-0.492726 - 2.79439i) q^{77} +(3.39646 - 2.84997i) q^{79} +2.34730 q^{80} +(-3.71688 + 6.43783i) q^{82} +(-6.81180 + 2.47929i) q^{83} +(-3.52094 + 6.09845i) q^{85} +(-1.55051 + 8.79336i) q^{86} +(0.560307 + 0.970481i) q^{88} +(9.95336 + 8.35186i) q^{89} +(4.31908 - 1.57202i) q^{91} +(-1.58125 - 8.96773i) q^{92} +(-0.365715 + 0.133109i) q^{94} +(-10.0628 - 8.44372i) q^{95} +(7.34730 + 12.7259i) q^{97} +(0.553033 + 0.201288i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} + 6 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q - 3 * q^5 + 6 * q^7 - 3 * q^8	\( 6 q - 3 q^{5} + 6 q^{7} - 3 q^{8} - 6 q^{10} + 9 q^{11} - 3 q^{14} + 9 q^{19} - 3 q^{20} + 3 q^{22} + 15 q^{23} + 21 q^{25} + 9 q^{26} - 3 q^{28} - 18 q^{31} - 3 q^{35} + 9 q^{37} - 6 q^{38} + 6 q^{40} - 6 q^{41} + 12 q^{43} + 3 q^{44} + 15 q^{46} + 3 q^{47} - 6 q^{50} + 9 q^{52} + 18 q^{53} - 18 q^{55} - 3 q^{56} - 18 q^{58} + 6 q^{59} - 12 q^{61} + 3 q^{62} - 3 q^{64} - 3 q^{67} + 18 q^{68} - 12 q^{70} + 6 q^{71} - 36 q^{73} - 18 q^{74} + 9 q^{76} + 15 q^{77} + 30 q^{79} + 12 q^{80} - 6 q^{82} - 6 q^{83} - 18 q^{85} - 12 q^{86} + 9 q^{88} + 33 q^{89} + 9 q^{91} - 12 q^{92} - 12 q^{94} - 51 q^{95} + 42 q^{97} - 9 q^{98}+O(q^{100}) \) 6 * q - 3 * q^5 + 6 * q^7 - 3 * q^8 - 6 * q^10 + 9 * q^11 - 3 * q^14 + 9 * q^19 - 3 * q^20 + 3 * q^22 + 15 * q^23 + 21 * q^25 + 9 * q^26 - 3 * q^28 - 18 * q^31 - 3 * q^35 + 9 * q^37 - 6 * q^38 + 6 * q^40 - 6 * q^41 + 12 * q^43 + 3 * q^44 + 15 * q^46 + 3 * q^47 - 6 * q^50 + 9 * q^52 + 18 * q^53 - 18 * q^55 - 3 * q^56 - 18 * q^58 + 6 * q^59 - 12 * q^61 + 3 * q^62 - 3 * q^64 - 3 * q^67 + 18 * q^68 - 12 * q^70 + 6 * q^71 - 36 * q^73 - 18 * q^74 + 9 * q^76 + 15 * q^77 + 30 * q^79 + 12 * q^80 - 6 * q^82 - 6 * q^83 - 18 * q^85 - 12 * q^86 + 9 * q^88 + 33 * q^89 + 9 * q^91 - 12 * q^92 - 12 * q^94 - 51 * q^95 + 42 * q^97 - 9 * q^98

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