LMFDB - Embedded newform 666.2.x.g.379.1

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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 24x^{10} + 264x^{8} - 1687x^{6} + 6600x^{4} - 15000x^{2} + 15625 $ x^12 - 24x^10 + 264x^8 - 1687x^6 + 6600x^4 - 15000*x^2 + 15625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			379.1
Root			$-2.14169 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	666.379
Dual form			666.2.x.g.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.266044 - 0.223238i) q^{5} +(-0.365982 - 0.307095i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.266044 - 0.223238i) q^{5} +(-0.365982 - 0.307095i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.173648 + 0.300767i) q^{10} +(1.29268 + 2.23899i) q^{11} +(4.21288 - 1.53336i) q^{13} +(-0.238878 + 0.413749i) q^{14} +(0.766044 - 0.642788i) q^{16} +(1.88864 + 0.687407i) q^{17} +(0.611631 - 3.46873i) q^{19} +(0.326352 + 0.118782i) q^{20} +(1.98050 - 1.66184i) q^{22} +(2.60486 - 4.51175i) q^{23} +(-0.847296 - 4.80526i) q^{25} +(-2.24162 - 3.88261i) q^{26} +(0.448944 + 0.163402i) q^{28} +(0.114111 + 0.197646i) q^{29} -6.74658 q^{31} +(-0.766044 - 0.642788i) q^{32} +(0.349006 - 1.97931i) q^{34} +(0.0288122 + 0.163402i) q^{35} +(2.42322 + 5.57925i) q^{37} -3.52224 q^{38} +(0.0603074 - 0.342020i) q^{40} +(10.0701 - 3.66521i) q^{41} +8.85889 q^{43} +(-1.98050 - 1.66184i) q^{44} +(-4.89554 - 1.78183i) q^{46} +(3.72890 - 6.45864i) q^{47} +(-1.17590 - 6.66887i) q^{49} +(-4.58512 + 1.66885i) q^{50} +(-3.43437 + 2.88178i) q^{52} +(-3.35194 + 2.81261i) q^{53} +(0.155916 - 0.884246i) q^{55} +(0.0829614 - 0.470498i) q^{56} +(0.174828 - 0.146698i) q^{58} +(-3.43016 + 2.87825i) q^{59} +(1.35175 - 0.491998i) q^{61} +(1.17153 + 6.64409i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-1.46312 - 0.532531i) q^{65} +(-8.06111 - 6.76408i) q^{67} -2.00984 q^{68} +(0.155916 - 0.0567489i) q^{70} +(-1.54193 + 8.74474i) q^{71} +7.18667 q^{73} +(5.07370 - 3.35524i) q^{74} +(0.611631 + 3.46873i) q^{76} +(0.214485 - 1.21641i) q^{77} +(2.70857 + 2.27276i) q^{79} -0.347296 q^{80} +(-5.35818 - 9.28064i) q^{82} +(1.32932 + 0.483834i) q^{83} +(-0.349006 - 0.604496i) q^{85} +(-1.53833 - 8.72431i) q^{86} +(-1.29268 + 2.23899i) q^{88} +(-2.92954 + 2.45818i) q^{89} +(-2.01273 - 0.732572i) q^{91} +(-0.904658 + 5.13057i) q^{92} +(-7.00804 - 2.55072i) q^{94} +(-0.937074 + 0.786298i) q^{95} +(-9.24175 + 16.0072i) q^{97} +(-6.36336 + 2.31607i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 6 * q^5 + 6 * q^7 + 6 * q^8	$ 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8} - 3 q^{11} - 6 q^{13} - 3 q^{14} + 3 q^{17} - 3 q^{19} + 6 q^{20} - 3 q^{22} + 21 q^{23} - 6 q^{25} - 3 q^{28} - 6 q^{29} + 42 q^{31} - 3 q^{34} + 9 q^{35} - 3 q^{37} - 42 q^{38} + 12 q^{40} + 21 q^{41} + 36 q^{43} + 3 q^{44} + 3 q^{46} - 9 q^{47} - 12 q^{49} - 12 q^{50} + 3 q^{52} + 6 q^{53} + 3 q^{56} - 3 q^{58} + 6 q^{59} - 18 q^{61} + 33 q^{62} - 6 q^{64} - 3 q^{65} - 27 q^{67} - 6 q^{68} + 18 q^{71} + 54 q^{73} - 3 q^{74} - 3 q^{76} - 51 q^{77} - 12 q^{79} - 18 q^{82} + 6 q^{83} + 3 q^{85} + 3 q^{88} + 15 q^{89} - 51 q^{91} + 6 q^{92} - 12 q^{94} + 15 q^{95} - 42 q^{97} - 51 q^{98}+O(q^{100}) $ 12 * q + 6 * q^5 + 6 * q^7 + 6 * q^8 - 3 * q^11 - 6 * q^13 - 3 * q^14 + 3 * q^17 - 3 * q^19 + 6 * q^20 - 3 * q^22 + 21 * q^23 - 6 * q^25 - 3 * q^28 - 6 * q^29 + 42 * q^31 - 3 * q^34 + 9 * q^35 - 3 * q^37 - 42 * q^38 + 12 * q^40 + 21 * q^41 + 36 * q^43 + 3 * q^44 + 3 * q^46 - 9 * q^47 - 12 * q^49 - 12 * q^50 + 3 * q^52 + 6 * q^53 + 3 * q^56 - 3 * q^58 + 6 * q^59 - 18 * q^61 + 33 * q^62 - 6 * q^64 - 3 * q^65 - 27 * q^67 - 6 * q^68 + 18 * q^71 + 54 * q^73 - 3 * q^74 - 3 * q^76 - 51 * q^77 - 12 * q^79 - 18 * q^82 + 6 * q^83 + 3 * q^85 + 3 * q^88 + 15 * q^89 - 51 * q^91 + 6 * q^92 - 12 * q^94 + 15 * q^95 - 42 * q^97 - 51 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.173648	−	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
$5$	−0.266044	−	0.223238i	−0.118979	−	0.0998350i	0.581357	−	0.813649i	$-0.302522\pi$
$5$	−0.266044	−	0.223238i	−0.118979	−	0.0998350i	−0.700336	+	0.713814i	$0.746966\pi$
$6$		0			0
$7$	−0.365982	−	0.307095i	−0.138328	−	0.116071i	0.570998	−	0.820951i	$-0.306556\pi$
$7$	−0.365982	−	0.307095i	−0.138328	−	0.116071i	−0.709326	+	0.704880i	$0.751001\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$		0			0
$10$	−0.173648	+	0.300767i	−0.0549124	+	0.0951110i
$11$	1.29268	+	2.23899i	0.389758	+	0.675081i	0.992417	−	0.122918i	$-0.0392253\pi$
$11$	1.29268	+	2.23899i	0.389758	+	0.675081i	−0.602659	+	0.797999i	$0.705892\pi$
$12$		0			0
$13$	4.21288	−	1.53336i	1.16844	−	0.425278i	0.316336	−	0.948647i	$-0.397547\pi$
$13$	4.21288	−	1.53336i	1.16844	−	0.425278i	0.852106	+	0.523369i	$0.175325\pi$
$14$	−0.238878	+	0.413749i	−0.0638428	+	0.110579i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	1.88864	+	0.687407i	0.458062	+	0.166721i	0.560737	−	0.827994i	$-0.310518\pi$
$17$	1.88864	+	0.687407i	0.458062	+	0.166721i	−0.102675	+	0.994715i	$0.532740\pi$
$18$		0			0
$19$	0.611631	−	3.46873i	0.140318	−	0.795782i	−0.830690	−	0.556735i	$-0.812054\pi$
$19$	0.611631	−	3.46873i	0.140318	−	0.795782i	0.971008	−	0.239047i	$-0.0768350\pi$
$20$	0.326352	+	0.118782i	0.0729745	+	0.0265605i
$21$		0			0
$22$	1.98050	−	1.66184i	0.422245	−	0.354305i
$23$	2.60486	−	4.51175i	0.543151	−	0.940765i	−0.455570	−	0.890200i	$-0.650565\pi$
$23$	2.60486	−	4.51175i	0.543151	−	0.940765i	0.998721	−	0.0505649i	$-0.0161022\pi$
$24$		0			0
$25$	−0.847296	−	4.80526i	−0.169459	−	0.961051i
$26$	−2.24162	−	3.88261i	−0.439619	−	0.761442i
$27$		0			0
$28$	0.448944	+	0.163402i	0.0848424	+	0.0308801i
$29$	0.114111	+	0.197646i	0.0211899	+	0.0367019i	0.876426	−	0.481537i	$-0.159921\pi$
$29$	0.114111	+	0.197646i	0.0211899	+	0.0367019i	−0.855236	+	0.518239i	$0.826588\pi$
$30$		0			0
$31$	−6.74658			−1.21172			−0.605861	−	0.795571i	$-0.707171\pi$
$31$	−6.74658			−1.21172			−0.605861	+	0.795571i	$0.707171\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$		0			0
$34$	0.349006	−	1.97931i	0.0598540	−	0.339449i
$35$	0.0288122	+	0.163402i	0.00487015	+	0.0276200i
$36$		0			0
$37$	2.42322	+	5.57925i	0.398376	+	0.917222i
$37$	2.42322	+	5.57925i	0.398376	+	0.917222i
$38$	−3.52224			−0.571383
$39$		0			0
$40$	0.0603074	−	0.342020i	0.00953543	−	0.0540781i
$41$	10.0701	−	3.66521i	1.57268	−	0.572410i	0.599086	−	0.800685i	$-0.295531\pi$
$41$	10.0701	−	3.66521i	1.57268	−	0.572410i	0.973597	+	0.228275i	$0.0733086\pi$
$42$		0			0
$43$	8.85889			1.35097			0.675484	−	0.737374i	$-0.263935\pi$
$43$	8.85889			1.35097			0.675484	+	0.737374i	$0.263935\pi$
$44$	−1.98050	−	1.66184i	−0.298572	−	0.250532i
$45$		0			0
$46$	−4.89554	−	1.78183i	−0.721807	−	0.262716i
$47$	3.72890	−	6.45864i	0.543916	−	0.942090i	−0.454758	−	0.890615i	$-0.650274\pi$
$47$	3.72890	−	6.45864i	0.543916	−	0.942090i	0.998674	−	0.0514750i	$-0.0163923\pi$
$48$		0			0
$49$	−1.17590	−	6.66887i	−0.167986	−	0.952696i
$50$	−4.58512	+	1.66885i	−0.648434	+	0.236011i
$51$		0			0
$52$	−3.43437	+	2.88178i	−0.476261	+	0.399631i
$53$	−3.35194	+	2.81261i	−0.460424	+	0.386342i	−0.843287	−	0.537464i	$-0.819383\pi$
$53$	−3.35194	+	2.81261i	−0.460424	+	0.386342i	0.382863	+	0.923805i	$0.374938\pi$
$54$		0			0
$55$	0.155916	−	0.884246i	0.0210238	−	0.119232i
$56$	0.0829614	−	0.470498i	0.0110862	−	0.0628729i
$57$		0			0
$58$	0.174828	−	0.146698i	0.0229560	−	0.0192624i
$59$	−3.43016	+	2.87825i	−0.446569	+	0.374716i	−0.838161	−	0.545423i	$-0.816369\pi$
$59$	−3.43016	+	2.87825i	−0.446569	+	0.374716i	0.391592	+	0.920139i	$0.371924\pi$
$60$		0			0
$61$	1.35175	−	0.491998i	0.173074	−	0.0629939i	−0.254030	−	0.967196i	$-0.581756\pi$
$61$	1.35175	−	0.491998i	0.173074	−	0.0629939i	0.427104	+	0.904203i	$0.359534\pi$
$62$	1.17153	+	6.64409i	0.148785	+	0.843800i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−1.46312	−	0.532531i	−0.181477	−	0.0660523i
$66$		0			0
$67$	−8.06111	−	6.76408i	−0.984822	−	0.826363i	−1.18267e−5	−	1.00000i	$-0.500004\pi$
$67$	−8.06111	−	6.76408i	−0.984822	−	0.826363i	−0.984810	+	0.173637i	$0.944448\pi$
$68$	−2.00984			−0.243729
$69$		0			0
$70$	0.155916	−	0.0567489i	0.0186356	−	0.00678280i
$71$	−1.54193	+	8.74474i	−0.182994	+	1.03781i	0.745512	+	0.666492i	$0.232205\pi$
$71$	−1.54193	+	8.74474i	−0.182994	+	1.03781i	−0.928506	+	0.371318i	$0.878906\pi$
$72$		0			0
$73$	7.18667			0.841136			0.420568	−	0.907261i	$-0.361831\pi$
$73$	7.18667			0.841136			0.420568	+	0.907261i	$0.361831\pi$
$74$	5.07370	−	3.35524i	0.589805	−	0.390038i
$75$		0			0
$76$	0.611631	+	3.46873i	0.0701589	+	0.397891i
$77$	0.214485	−	1.21641i	0.0244429	−	0.138622i
$78$		0			0
$79$	2.70857	+	2.27276i	0.304738	+	0.255705i	0.782313	−	0.622885i	$-0.214040\pi$
$79$	2.70857	+	2.27276i	0.304738	+	0.255705i	−0.477575	+	0.878591i	$0.658484\pi$
$80$	−0.347296			−0.0388289
$81$		0			0
$82$	−5.35818	−	9.28064i	−0.591712	−	1.02487i
$83$	1.32932	+	0.483834i	0.145912	+	0.0531077i	0.413944	−	0.910302i	$-0.364151\pi$
$83$	1.32932	+	0.483834i	0.145912	+	0.0531077i	−0.268032	+	0.963410i	$0.586373\pi$
$84$		0			0
$85$	−0.349006	−	0.604496i	−0.0378550	−	0.0655668i
$86$	−1.53833	−	8.72431i	−0.165882	−	0.940766i
$87$		0			0
$88$	−1.29268	+	2.23899i	−0.137800	+	0.238677i
$89$	−2.92954	+	2.45818i	−0.310531	+	0.260567i	−0.784711	−	0.619861i	$-0.787189\pi$
$89$	−2.92954	+	2.45818i	−0.310531	+	0.260567i	0.474180	+	0.880428i	$0.342744\pi$
$90$		0			0
$91$	−2.01273	−	0.732572i	−0.210991	−	0.0767944i
$92$	−0.904658	+	5.13057i	−0.0943172	+	0.534899i
$93$		0			0
$94$	−7.00804	−	2.55072i	−0.722824	−	0.263086i
$95$	−0.937074	+	0.786298i	−0.0961417	+	0.0806725i
$96$		0			0
$97$	−9.24175	+	16.0072i	−0.938358	+	1.62528i	−0.169824	+	0.985474i	$0.554320\pi$
$97$	−9.24175	+	16.0072i	−0.938358	+	1.62528i	−0.768534	+	0.639809i	$0.779013\pi$
$98$	−6.36336	+	2.31607i	−0.642797	+	0.233959i
$99$		0			0
$100$	2.43969	+	4.22567i	0.243969	+	0.422567i
$101$	8.56431	−	14.8338i	0.852180	−	1.47602i	−0.0270562	−	0.999634i	$-0.508613\pi$
$101$	8.56431	−	14.8338i	0.852180	−	1.47602i	0.879236	−	0.476386i	$-0.158053\pi$
$102$		0			0
$103$	6.71012	+	11.6223i	0.661167	+	1.14518i	0.980309	+	0.197468i	$0.0632720\pi$
$103$	6.71012	+	11.6223i	0.661167	+	1.14518i	−0.319142	+	0.947707i	$0.603395\pi$
$104$	3.43437	+	2.88178i	0.336768	+	0.282582i
$105$		0			0
$106$	3.35194	+	2.81261i	0.325569	+	0.273185i
$107$	−19.2261	+	6.99774i	−1.85866	+	0.676497i	−0.878676	+	0.477418i	$0.841573\pi$
$107$	−19.2261	+	6.99774i	−1.85866	+	0.676497i	−0.979984	+	0.199079i	$0.936205\pi$
$108$		0			0
$109$	1.85087	+	10.4968i	0.177281	+	1.00541i	0.935478	+	0.353385i	$0.114970\pi$
$109$	1.85087	+	10.4968i	0.177281	+	1.00541i	−0.758197	+	0.652026i	$0.773919\pi$
$110$	−0.897887			−0.0856102
$111$		0			0
$112$	−0.477756			−0.0451437
$113$	−2.12063	−	12.0267i	−0.199492	−	1.13138i	−0.905875	−	0.423546i	$-0.860785\pi$
$113$	−2.12063	−	12.0267i	−0.199492	−	1.13138i	0.706383	−	0.707830i	$-0.250326\pi$
$114$		0			0
$115$	−1.70020	+	0.618823i	−0.158545	+	0.0577055i
$116$	−0.174828	−	0.146698i	−0.0162324	−	0.0136206i
$117$		0			0
$118$	3.43016	+	2.87825i	0.315772	+	0.264964i
$119$	−0.480107	−	0.831570i	−0.0440114	−	0.0762299i
$120$		0			0
$121$	2.15795	−	3.73768i	0.196177	−	0.339789i
$122$	−0.719253	−	1.24578i	−0.0651181	−	0.112788i
$123$		0			0
$124$	6.33971	−	2.30747i	0.569323	−	0.207217i
$125$	−1.71554	+	2.97140i	−0.153442	+	0.265770i
$126$		0			0
$127$	−5.40029	+	4.53138i	−0.479198	+	0.402095i	−0.850136	−	0.526563i	$-0.823481\pi$
$127$	−5.40029	+	4.53138i	−0.479198	+	0.402095i	0.370938	+	0.928658i	$0.379036\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$		0			0
$130$	−0.270373	+	1.53336i	−0.0237133	+	0.134485i
$131$	1.86532	+	0.678920i	0.162974	+	0.0593175i	0.422219	−	0.906494i	$-0.361251\pi$
$131$	1.86532	+	0.678920i	0.162974	+	0.0593175i	−0.259245	+	0.965812i	$0.583474\pi$
$132$		0			0
$133$	−1.28908	+	1.08167i	−0.111777	+	0.0937923i
$134$	−5.26152	+	9.11322i	−0.454526	+	0.787262i
$135$		0			0
$136$	0.349006	+	1.97931i	0.0299270	+	0.169724i
$137$	8.69897	+	15.0671i	0.743203	+	1.28727i	0.951029	+	0.309100i	$0.100028\pi$
$137$	8.69897	+	15.0671i	0.743203	+	1.28727i	−0.207826	+	0.978166i	$0.566639\pi$
$138$		0			0
$139$	−0.692602	−	0.252086i	−0.0587457	−	0.0213817i	0.312480	−	0.949924i	$-0.398840\pi$
$139$	−0.692602	−	0.252086i	−0.0587457	−	0.0213817i	−0.371226	+	0.928543i	$0.621062\pi$
$140$	−0.0829614	−	0.143693i	−0.00701152	−	0.0121443i
$141$		0			0
$142$	8.87964			0.745163
$143$	8.87909	+	7.45044i	0.742507	+	0.623037i
$144$		0			0
$145$	0.0137635	−	0.0780564i	0.00114299	−	0.00648223i
$146$	−1.24795	−	7.07749i	−0.103281	−	0.585737i
$147$		0			0
$148$	−4.18530	−	4.41398i	−0.344030	−	0.362827i
$149$	19.0346			1.55938			0.779689	−	0.626167i	$-0.215377\pi$
$149$	19.0346			1.55938			0.779689	+	0.626167i	$0.215377\pi$
$150$		0			0
$151$	−1.12385	+	6.37365i	−0.0914574	+	0.518681i	0.904318	+	0.426859i	$0.140380\pi$
$151$	−1.12385	+	6.37365i	−0.0914574	+	0.518681i	−0.995775	+	0.0918214i	$0.970731\pi$
$152$	3.30983	−	1.20468i	0.268462	−	0.0977123i
$153$		0			0
$154$	−1.23517			−0.0995330
$155$	1.79489	+	1.50609i	0.144169	+	0.120972i
$156$		0			0
$157$	−11.3628	−	4.13571i	−0.906847	−	0.330065i	−0.153854	−	0.988094i	$-0.549169\pi$
$157$	−11.3628	−	4.13571i	−0.906847	−	0.330065i	−0.752993	+	0.658028i	$0.771391\pi$
$158$	1.76789	−	3.06208i	0.140646	−	0.243606i
$159$		0			0
$160$	0.0603074	+	0.342020i	0.00476772	+	0.0270391i
$161$	−2.33887	+	0.851279i	−0.184329	+	0.0670902i
$162$		0			0
$163$	11.2965	−	9.47892i	0.884813	−	0.742446i	−0.0823498	−	0.996603i	$-0.526242\pi$
$163$	11.2965	−	9.47892i	0.884813	−	0.742446i	0.967163	+	0.254157i	$0.0817980\pi$
$164$	−8.20921	+	6.88834i	−0.641031	+	0.537889i
$165$		0			0
$166$	0.245649	−	1.39315i	0.0190661	−	0.108129i
$167$	−1.44239	+	8.18020i	−0.111616	+	0.633003i	0.876755	+	0.480937i	$0.159704\pi$
$167$	−1.44239	+	8.18020i	−0.111616	+	0.633003i	−0.988370	+	0.152066i	$0.951408\pi$
$168$		0			0
$169$	5.43855	−	4.56349i	0.418350	−	0.351038i
$170$	−0.534708	+	0.448673i	−0.0410102	+	0.0344117i
$171$		0			0
$172$	−8.32464	+	3.02992i	−0.634748	+	0.231029i
$173$	1.14829	+	6.51227i	0.0873028	+	0.495119i	0.996836	+	0.0794872i	$0.0253283\pi$
$173$	1.14829	+	6.51227i	0.0873028	+	0.495119i	−0.909533	+	0.415632i	$0.863561\pi$
$174$		0			0
$175$	−1.16558	+	2.01884i	−0.0881093	+	0.152610i
$176$	2.42945	+	0.884246i	0.183126	+	0.0666526i
$177$		0			0
$178$	2.92954	+	2.45818i	0.219579	+	0.184248i
$179$	−4.53985			−0.339325			−0.169662	−	0.985502i	$-0.554268\pi$
$179$	−4.53985			−0.339325			−0.169662	+	0.985502i	$0.554268\pi$
$180$		0			0
$181$	1.46942	−	0.534826i	0.109221	−	0.0397533i	−0.286831	−	0.957981i	$-0.592602\pi$
$181$	1.46942	−	0.534826i	0.109221	−	0.0397533i	0.396053	+	0.918228i	$0.370380\pi$
$182$	−0.371937	+	2.10936i	−0.0275698	+	0.156356i
$183$		0			0
$184$	5.20972			0.384066
$185$	0.600813	−	2.02528i	0.0441727	−	0.148902i
$186$		0			0
$187$	0.902307	+	5.11724i	0.0659832	+	0.374209i
$188$	−1.29503	+	7.34450i	−0.0944500	+	0.535653i
$189$		0			0
$190$	0.937074	+	0.786298i	0.0679825	+	0.0570441i
$191$	−23.0183			−1.66555			−0.832773	−	0.553615i	$-0.813248\pi$
$191$	−23.0183			−1.66555			−0.832773	+	0.553615i	$0.813248\pi$
$192$		0			0
$193$	5.27705	+	9.14013i	0.379851	+	0.657921i	0.991040	−	0.133564i	$-0.0426420\pi$
$193$	5.27705	+	9.14013i	0.379851	+	0.657921i	−0.611190	+	0.791484i	$0.709309\pi$
$194$	17.3688	+	6.32173i	1.24701	+	0.453874i
$195$		0			0
$196$	3.38587	+	5.86451i	0.241848	+	0.418893i
$197$	−0.838489	−	4.75531i	−0.0597399	−	0.338802i	0.940259	−	0.340461i	$-0.110583\pi$
$197$	−0.838489	−	4.75531i	−0.0597399	−	0.338802i	−0.999999	+	0.00165899i	$0.999472\pi$
$198$		0			0
$199$	−5.14608	+	8.91327i	−0.364796	+	0.631845i	−0.988743	−	0.149621i	$-0.952195\pi$
$199$	−5.14608	+	8.91327i	−0.364796	+	0.631845i	0.623947	+	0.781466i	$0.285528\pi$
$200$	3.73783	−	3.13641i	0.264304	−	0.221778i
$201$		0			0
$202$	−16.0956	−	5.85833i	−1.13248	−	0.412191i
$203$	0.0189336	−	0.107378i	0.00132888	−	0.00753644i
$204$		0			0
$205$	−3.49730	−	1.27291i	−0.244262	−	0.0889042i
$206$	10.2805	−	8.62636i	0.716276	−	0.601027i
$207$		0			0
$208$	2.24162	−	3.88261i	0.155429	−	0.269210i
$209$	8.55710	−	3.11453i	0.591907	−	0.215437i
$210$		0			0
$211$	−0.685470	−	1.18727i	−0.0471897	−	0.0817349i	0.841466	−	0.540310i	$-0.181693\pi$
$211$	−0.685470	−	1.18727i	−0.0471897	−	0.0817349i	−0.888655	+	0.458576i	$0.848360\pi$
$212$	2.18782	−	3.78942i	0.150260	−	0.260258i
$213$		0			0
$214$	10.2300	+	17.7189i	0.699309	+	1.21124i
$215$	−2.35686	−	1.97764i	−0.160736	−	0.134874i
$216$		0			0
$217$	2.46913	+	2.07184i	0.167615	+	0.140646i
$218$	10.0159	−	3.64550i	0.678365	−	0.246904i
$219$		0			0
$220$	0.155916	+	0.884246i	0.0105119	+	0.0596159i
$221$	9.01064			0.606121
$222$		0			0
$223$	−29.2612			−1.95947			−0.979736	−	0.200292i	$-0.935811\pi$
$223$	−29.2612			−1.95947			−0.979736	+	0.200292i	$0.935811\pi$
$224$	0.0829614	+	0.470498i	0.00554309	+	0.0314364i
$225$		0			0
$226$	−11.4757	+	4.17683i	−0.763355	+	0.277838i
$227$	−7.89376	−	6.62365i	−0.523927	−	0.439627i	0.342071	−	0.939674i	$-0.388872\pi$
$227$	−7.89376	−	6.62365i	−0.523927	−	0.439627i	−0.865998	+	0.500047i	$0.833316\pi$
$228$		0			0
$229$	12.0022	+	10.0711i	0.793128	+	0.665514i	0.946518	−	0.322652i	$-0.104574\pi$
$229$	12.0022	+	10.0711i	0.793128	+	0.665514i	−0.153389	+	0.988166i	$0.549019\pi$
$230$	0.904658	+	1.56691i	0.0596514	+	0.103319i
$231$		0			0
$232$	−0.114111	+	0.197646i	−0.00749175	+	0.0129761i
$233$	3.60202	+	6.23888i	0.235976	+	0.408723i	0.959556	−	0.281518i	$-0.0908379\pi$
$233$	3.60202	+	6.23888i	0.235976	+	0.408723i	−0.723580	+	0.690241i	$0.757505\pi$
$234$		0			0
$235$	−2.43387	+	0.885855i	−0.158768	+	0.0577868i
$236$	2.23888	−	3.87785i	0.145739	−	0.252427i
$237$		0			0
$238$	−0.735567	+	0.617214i	−0.0476797	+	0.0400081i
$239$	−20.6291	−	7.50838i	−1.33439	−	0.485677i	−0.426346	−	0.904560i	$-0.640199\pi$
$239$	−20.6291	−	7.50838i	−1.33439	−	0.485677i	−0.908040	+	0.418884i	$0.862421\pi$
$240$		0			0
$241$	2.57180	−	14.5854i	0.165664	−	0.939527i	−0.782713	−	0.622383i	$-0.786165\pi$
$241$	2.57180	−	14.5854i	0.165664	−	0.939527i	0.948377	−	0.317145i	$-0.102724\pi$
$242$	−4.05562	−	1.47612i	−0.260705	−	0.0948889i
$243$		0			0
$244$	−1.10196	+	0.924653i	−0.0705457	+	0.0591949i
$245$	−1.17590	+	2.03672i	−0.0751256	+	0.130121i
$246$		0			0
$247$	−2.74210	−	15.5512i	−0.174475	−	0.989499i
$248$	−3.37329	−	5.84271i	−0.214204	−	0.371013i
$249$		0			0
$250$	3.22416	+	1.17350i	0.203913	+	0.0742184i
$251$	6.64493	+	11.5094i	0.419424	+	0.726464i	0.995882	−	0.0906631i	$-0.0288986\pi$
$251$	6.64493	+	11.5094i	0.419424	+	0.726464i	−0.576457	+	0.817127i	$0.695565\pi$
$252$		0			0
$253$	13.4690			0.846790
$254$	5.40029	+	4.53138i	0.338844	+	0.284324i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−3.03928	−	17.2366i	−0.189585	−	1.07519i	−0.919921	−	0.392104i	$-0.871747\pi$
$257$	−3.03928	−	17.2366i	−0.189585	−	1.07519i	0.730336	−	0.683088i	$-0.239364\pi$
$258$		0			0
$259$	0.826504	−	2.78607i	0.0513565	−	0.173118i
$260$	1.55702			0.0965621
$261$		0			0
$262$	0.344697	−	1.95487i	0.0212954	−	0.120772i
$263$	−13.2811	+	4.83392i	−0.818947	+	0.298072i	−0.717314	−	0.696750i	$-0.754629\pi$
$263$	−13.2811	+	4.83392i	−0.818947	+	0.298072i	−0.101633	+	0.994822i	$0.532407\pi$
$264$		0			0
$265$	1.51964			0.0933510
$266$	1.28908	+	1.08167i	0.0790385	+	0.0663211i
$267$		0			0
$268$	9.88842	+	3.59909i	0.604031	+	0.219849i
$269$	−13.4051	+	23.2183i	−0.817324	+	1.41565i	0.0903238	+	0.995912i	$0.471210\pi$
$269$	−13.4051	+	23.2183i	−0.817324	+	1.41565i	−0.907647	+	0.419734i	$0.862124\pi$
$270$		0			0
$271$	−1.89500	−	10.7471i	−0.115113	−	0.652838i	−0.986694	−	0.162587i	$-0.948016\pi$
$271$	−1.89500	−	10.7471i	−0.115113	−	0.652838i	0.871581	−	0.490251i	$-0.163095\pi$
$272$	1.88864	−	0.687407i	0.114515	−	0.0416802i
$273$		0			0
$274$	13.3276	−	11.1832i	0.805150	−	0.675601i
$275$	9.66364	−	8.10875i	0.582739	−	0.488976i
$276$		0			0
$277$	1.06680	−	6.05012i	0.0640978	−	0.363517i	−0.935841	−	0.352423i	$-0.885358\pi$
$277$	1.06680	−	6.05012i	0.0640978	−	0.363517i	0.999938	−	0.0110932i	$-0.00353116\pi$
$278$	−0.127988	+	0.725854i	−0.00767619	+	0.0435338i
$279$		0			0
$280$	−0.127104	+	0.106653i	−0.00759593	+	0.00637374i
$281$	−2.26215	+	1.89817i	−0.134948	+	0.113235i	−0.707763	−	0.706449i	$-0.750296\pi$
$281$	−2.26215	+	1.89817i	−0.134948	+	0.113235i	0.572815	+	0.819685i	$0.305851\pi$
$282$		0			0
$283$	−13.6016	+	4.95056i	−0.808529	+	0.294280i	−0.713016	−	0.701148i	$-0.752671\pi$
$283$	−13.6016	+	4.95056i	−0.808529	+	0.294280i	−0.0955129	+	0.995428i	$0.530449\pi$
$284$	−1.54193	−	8.74474i	−0.0914969	−	0.518905i
$285$		0			0
$286$	5.79541	−	10.0380i	0.342690	−	0.593556i
$287$	−4.81104	−	1.75108i	−0.283987	−	0.103363i
$288$		0			0
$289$	−9.92834	−	8.33086i	−0.584020	−	0.490051i
$290$	−0.0792606			−0.00465434
$291$		0			0
$292$	−6.75326	+	2.45799i	−0.395205	+	0.143843i
$293$	2.18486	−	12.3910i	0.127641	−	0.723888i	−0.852063	−	0.523439i	$-0.824649\pi$
$293$	2.18486	−	12.3910i	0.127641	−	0.723888i	0.979704	−	0.200449i	$-0.0642401\pi$
$294$		0			0
$295$	1.55511			0.0905419
$296$	−3.62016	+	4.88820i	−0.210417	+	0.284121i
$297$		0			0
$298$	−3.30533	−	18.7455i	−0.191473	−	1.08589i
$299$	4.05581	−	23.0016i	0.234554	−	1.33022i
$300$		0			0
$301$	−3.24220	−	2.72053i	−0.186877	−	0.156808i
$302$	6.47198			0.372420
$303$		0			0
$304$	−1.76112	−	3.05035i	−0.101007	−	0.174950i
$305$	−0.469459	−	0.170869i	−0.0268811	−	0.00978393i
$306$		0			0
$307$	9.44985	+	16.3676i	0.539331	+	0.934149i	0.998940	+	0.0460279i	$0.0146563\pi$
$307$	9.44985	+	16.3676i	0.539331	+	0.934149i	−0.459609	+	0.888121i	$0.652010\pi$
$308$	0.214485	+	1.21641i	0.0122214	+	0.0693112i
$309$		0			0
$310$	1.17153	−	2.02915i	0.0665385	−	0.115248i
$311$	0.0868584	−	0.0728829i	0.00492529	−	0.00413281i	−0.640322	−	0.768107i	$-0.721199\pi$
$311$	0.0868584	−	0.0728829i	0.00492529	−	0.00413281i	0.645247	+	0.763974i	$0.276754\pi$
$312$		0			0
$313$	−8.62740	−	3.14012i	−0.487650	−	0.177490i	0.0864813	−	0.996253i	$-0.472438\pi$
$313$	−8.62740	−	3.14012i	−0.487650	−	0.177490i	−0.574131	+	0.818764i	$0.694660\pi$
$314$	−2.09975	+	11.9083i	−0.118496	+	0.672024i
$315$		0			0
$316$	−3.32255	−	1.20931i	−0.186908	−	0.0680290i
$317$	−20.1198	+	16.8826i	−1.13004	+	0.948219i	−0.999068	−	0.0431670i	$-0.986255\pi$
$317$	−20.1198	+	16.8826i	−1.13004	+	0.948219i	−0.130975	+	0.991386i	$0.541811\pi$
$318$		0			0
$319$	−0.295018	+	0.510986i	−0.0165178	+	0.0286097i
$320$	0.326352	−	0.118782i	0.0182436	−	0.00664014i
$321$		0			0
$322$	1.24449	+	2.15551i	0.0693525	+	0.120122i
$323$	3.53958	−	6.13074i	0.196948	−	0.341123i
$324$		0			0
$325$	−10.9378	−	18.9447i	−0.606717	−	1.05087i
$326$	−11.2965	−	9.47892i	−0.625657	−	0.524989i
$327$		0			0
$328$	8.20921	+	6.88834i	0.453278	+	0.380345i
$329$	−3.34813	+	1.21862i	−0.184588	+	0.0671847i
$330$		0			0
$331$	−4.96254	−	28.1439i	−0.272766	−	1.54693i	−0.745971	−	0.665979i	$-0.768014\pi$
$331$	−4.96254	−	28.1439i	−0.272766	−	1.54693i	0.473205	−	0.880952i	$-0.343097\pi$
$332$	−1.41464			−0.0776383
$333$		0			0
$334$	8.30639			0.454506
$335$	0.634617	+	3.59909i	0.0346728	+	0.196639i
$336$		0			0
$337$	9.18348	−	3.34251i	0.500256	−	0.182078i	−0.0795532	−	0.996831i	$-0.525349\pi$
$337$	9.18348	−	3.34251i	0.500256	−	0.182078i	0.579809	+	0.814752i	$0.303127\pi$
$338$	−5.43855	−	4.56349i	−0.295818	−	0.248221i
$339$		0			0
$340$	0.534708	+	0.448673i	0.0289986	+	0.0243327i
$341$	−8.72118	−	15.1055i	−0.472278	−	0.818010i
$342$		0			0
$343$	−3.28977	+	5.69804i	−0.177631	+	0.307665i
$344$	4.42945	+	7.67203i	0.238820	+	0.413648i
$345$		0			0
$346$	6.21394	−	2.26169i	0.334063	−	0.121589i
$347$	8.28817	−	14.3555i	0.444932	−	0.770645i	−0.553115	−	0.833105i	$-0.686561\pi$
$347$	8.28817	−	14.3555i	0.444932	−	0.770645i	0.998047	+	0.0624595i	$0.0198944\pi$
$348$		0			0
$349$	14.3165	−	12.0129i	0.766342	−	0.643038i	−0.173427	−	0.984847i	$-0.555484\pi$
$349$	14.3165	−	12.0129i	0.766342	−	0.643038i	0.939769	+	0.341809i	$0.111040\pi$
$350$	2.19057	+	0.797302i	0.117091	+	0.0426176i
$351$		0			0
$352$	0.448944	−	2.54609i	0.0239288	−	0.135707i
$353$	5.07813	+	1.84829i	0.270282	+	0.0983745i	0.473606	−	0.880737i	$-0.342952\pi$
$353$	5.07813	+	1.84829i	0.270282	+	0.0983745i	−0.203324	+	0.979112i	$0.565174\pi$
$354$		0			0
$355$	2.36238	−	1.98227i	0.125382	−	0.105208i
$356$	1.91212	−	3.31190i	0.101342	−	0.175530i
$357$		0			0
$358$	0.788337	+	4.47088i	0.0416649	+	0.236294i
$359$	−5.28319	−	9.15075i	−0.278836	−	0.482958i	0.692260	−	0.721649i	$-0.256615\pi$
$359$	−5.28319	−	9.15075i	−0.278836	−	0.482958i	−0.971096	+	0.238690i	$0.923282\pi$
$360$		0			0
$361$	6.19614	+	2.25521i	0.326113	+	0.118695i
$362$	−0.781863	−	1.35423i	−0.0410938	−	0.0711766i
$363$		0			0
$364$	2.14190			0.112266
$365$	−1.91197	−	1.60434i	−0.100077	−	0.0839748i
$366$		0			0
$367$	−0.0374864	+	0.212596i	−0.00195677	+	0.0110974i	−0.985771	−	0.168097i	$-0.946238\pi$
$367$	−0.0374864	+	0.212596i	−0.00195677	+	0.0110974i	0.983814	+	0.179194i	$0.0573490\pi$
$368$	−0.904658	−	5.13057i	−0.0471586	−	0.267450i
$369$		0			0
$370$	−2.09884	−	0.239999i	−0.109114	−	0.0124769i
$371$	2.09049			0.108533
$372$		0			0
$373$	−3.43905	+	19.5038i	−0.178067	+	1.00987i	0.756476	+	0.654021i	$0.226919\pi$
$373$	−3.43905	+	19.5038i	−0.178067	+	1.00987i	−0.934543	+	0.355849i	$0.884192\pi$
$374$	4.88281	−	1.77720i	0.252484	−	0.0918967i
$375$		0			0
$376$	7.45780			0.384607
$377$	0.783798	+	0.657684i	0.0403676	+	0.0338725i
$378$		0			0
$379$	21.7031	+	7.89927i	1.11481	+	0.405758i	0.832756	−	0.553640i	$-0.186761\pi$
$379$	21.7031	+	7.89927i	1.11481	+	0.405758i	0.282056	+	0.959398i	$0.408984\pi$
$380$	0.611631	−	1.05938i	0.0313760	−	0.0543449i
$381$		0			0
$382$	3.99708	+	22.6686i	0.204509	+	1.15983i
$383$	−4.77929	+	1.73952i	−0.244210	+	0.0888853i	−0.461226	−	0.887283i	$-0.652590\pi$
$383$	−4.77929	+	1.73952i	−0.244210	+	0.0888853i	0.217015	+	0.976168i	$0.430368\pi$
$384$		0			0
$385$	−0.328611	+	0.275737i	−0.0167475	+	0.0140529i
$386$	8.08492	−	6.78405i	0.411511	−	0.345299i
$387$		0			0
$388$	3.20963	−	18.2027i	0.162944	−	0.924102i
$389$	5.06138	−	28.7045i	0.256622	−	1.45538i	−0.535252	−	0.844692i	$-0.679783\pi$
$389$	5.06138	−	28.7045i	0.256622	−	1.45538i	0.791874	−	0.610684i	$-0.209105\pi$
$390$		0			0
$391$	8.02104	−	6.73045i	0.405642	−	0.340374i
$392$	5.18746	−	4.35280i	0.262006	−	0.219849i
$393$		0			0
$394$	−4.53746	+	1.65150i	−0.228594	+	0.0832014i
$395$	−0.213234	−	1.20931i	−0.0107290	−	0.0608470i
$396$		0			0
$397$	7.99625	−	13.8499i	0.401320	−	0.695107i	−0.592565	−	0.805522i	$-0.701885\pi$
$397$	7.99625	−	13.8499i	0.401320	−	0.695107i	0.993886	+	0.110416i	$0.0352182\pi$
$398$	9.67147	+	3.52013i	0.484787	+	0.176448i
$399$		0			0
$400$	−3.73783	−	3.13641i	−0.186891	−	0.156820i
$401$	5.43983			0.271652			0.135826	−	0.990733i	$-0.456631\pi$
$401$	5.43983			0.271652			0.135826	+	0.990733i	$0.456631\pi$
$402$		0			0
$403$	−28.4225	+	10.3450i	−1.41583	+	0.515319i
$404$	−2.97435	+	16.8684i	−0.147980	+	0.839234i
$405$		0			0
$406$	−0.109034			−0.00541128
$407$	−9.35942	+	12.6378i	−0.463929	+	0.626431i
$408$		0			0
$409$	−6.55076	−	37.1512i	−0.323914	−	1.83701i	−0.517198	−	0.855866i	$-0.673025\pi$
$409$	−6.55076	−	37.1512i	−0.323914	−	1.83701i	0.193283	−	0.981143i	$-0.438086\pi$
$410$	−0.646275	+	3.66521i	−0.0319173	+	0.181012i
$411$		0			0
$412$	−10.2805	−	8.62636i	−0.506484	−	0.424990i
$413$	2.13927			0.105267
$414$		0			0
$415$	−0.245649	−	0.425477i	−0.0120584	−	0.0208858i
$416$	−4.21288	−	1.53336i	−0.206553	−	0.0751792i
$417$		0			0
$418$	−4.55314	−	7.88627i	−0.222701	−	0.385730i
$419$	−1.07518	−	6.09766i	−0.0525261	−	0.297890i	0.947216	−	0.320596i	$-0.103883\pi$
$419$	−1.07518	−	6.09766i	−0.0525261	−	0.297890i	−0.999742	+	0.0227055i	$0.992772\pi$
$420$		0			0
$421$	5.05431	−	8.75433i	0.246332	−	0.426660i	−0.716173	−	0.697923i	$-0.754108\pi$
$421$	5.05431	−	8.75433i	0.246332	−	0.426660i	0.962505	+	0.271263i	$0.0874412\pi$
$422$	−1.05020	+	0.881223i	−0.0511230	+	0.0428973i
$423$		0			0
$424$	−4.11176	−	1.49656i	−0.199685	−	0.0726793i
$425$	1.70293	−	9.65782i	0.0826044	−	0.468473i
$426$		0			0
$427$	−0.645808	−	0.235055i	−0.0312528	−	0.0113751i
$428$	15.6733	−	13.1514i	0.757597	−	0.635699i
$429$		0			0
$430$	−1.53833	+	2.66447i	−0.0741849	+	0.128492i
$431$	−32.1170	+	11.6896i	−1.54702	+	0.563070i	−0.967716	−	0.252042i	$-0.918898\pi$
$431$	−32.1170	+	11.6896i	−1.54702	+	0.563070i	−0.579304	+	0.815111i	$0.696676\pi$
$432$		0			0
$433$	0.343160	+	0.594370i	0.0164912	+	0.0285636i	0.874153	−	0.485650i	$-0.161417\pi$
$433$	0.343160	+	0.594370i	0.0164912	+	0.0285636i	−0.857662	+	0.514214i	$0.828084\pi$
$434$	1.61161	−	2.79139i	0.0773597	−	0.133991i
$435$		0			0
$436$	−5.32937	−	9.23073i	−0.255230	−	0.442072i
$437$	−14.0568	−	11.7951i	−0.672430	−	0.564236i
$438$		0			0
$439$	16.4768	+	13.8257i	0.786393	+	0.659862i	0.944850	−	0.327503i	$-0.106207\pi$
$439$	16.4768	+	13.8257i	0.786393	+	0.659862i	−0.158456	+	0.987366i	$0.550652\pi$
$440$	0.843738	−	0.307095i	0.0402236	−	0.0146402i
$441$		0			0
$442$	−1.56468	−	8.87374i	−0.0744243	−	0.422081i
$443$	28.5971			1.35869			0.679344	−	0.733820i	$-0.262264\pi$
$443$	28.5971			1.35869			0.679344	+	0.733820i	$0.262264\pi$
$444$		0			0
$445$	1.32815			0.0629602
$446$	5.08115	+	28.8166i	0.240599	+	1.36451i
$447$		0			0
$448$	0.448944	−	0.163402i	0.0212106	−	0.00772002i
$449$	26.4813	+	22.2204i	1.24973	+	1.04865i	0.996699	+	0.0811896i	$0.0258719\pi$
$449$	26.4813	+	22.2204i	1.24973	+	1.04865i	0.253031	+	0.967458i	$0.418573\pi$
$450$		0			0
$451$	21.2238	+	17.8089i	0.999388	+	0.838587i
$452$	6.10611	+	10.5761i	0.287207	+	0.497458i
$453$		0			0
$454$	−5.15229	+	8.92402i	−0.241809	+	0.418825i
$455$	0.371937	+	0.644213i	0.0174367	+	0.0302012i
$456$		0			0
$457$	−30.9238	+	11.2553i	−1.44655	+	0.526503i	−0.941627	−	0.336659i	$-0.890703\pi$
$457$	−30.9238	+	11.2553i	−1.44655	+	0.526503i	−0.504928	+	0.863162i	$0.668481\pi$
$458$	7.83389	−	13.5687i	0.366053	−	0.634023i
$459$		0			0
$460$	1.38602	−	1.16301i	0.0646234	−	0.0542255i
$461$	−17.0455	−	6.20405i	−0.793888	−	0.288952i	−0.0869368	−	0.996214i	$-0.527708\pi$
$461$	−17.0455	−	6.20405i	−0.793888	−	0.288952i	−0.706951	+	0.707262i	$0.749930\pi$
$462$		0			0
$463$	0.0589368	−	0.334247i	0.00273903	−	0.0155338i	−0.983408	−	0.181410i	$-0.941934\pi$
$463$	0.0589368	−	0.334247i	0.00273903	−	0.0155338i	0.986147	+	0.165876i	$0.0530451\pi$
$464$	0.214458	+	0.0780564i	0.00995598	+	0.00362368i
$465$		0			0
$466$	5.51861	−	4.63067i	0.255645	−	0.214512i
$467$	−7.10101	+	12.2993i	−0.328596	+	0.569144i	−0.982233	−	0.187663i	$-0.939909\pi$
$467$	−7.10101	+	12.2993i	−0.328596	+	0.569144i	0.653638	+	0.756808i	$0.273242\pi$
$468$		0			0
$469$	0.873006	+	4.95106i	0.0403117	+	0.228619i
$470$	1.29503	+	2.24306i	0.0597354	+	0.103465i
$471$		0			0
$472$	−4.20771	−	1.53148i	−0.193676	−	0.0704922i
$473$	11.4517	+	19.8350i	0.526551	+	0.912013i
$474$		0			0
$475$	−17.1864			−0.788566
$476$	0.735567	+	0.617214i	0.0337147	+	0.0282900i
$477$		0			0
$478$	−3.81210	+	21.6195i	−0.174362	+	0.988853i
$479$	5.90065	+	33.4642i	0.269608	+	1.52902i	0.755586	+	0.655049i	$0.227352\pi$
$479$	5.90065	+	33.4642i	0.269608	+	1.52902i	−0.485979	+	0.873971i	$0.661537\pi$
$480$		0			0
$481$	18.7637	+	19.7890i	0.855553	+	0.902301i
$482$	−14.8104			−0.674595
$483$		0			0
$484$	−0.749448	+	4.25033i	−0.0340658	+	0.193197i
$485$	6.03213	−	2.19551i	0.273905	−	0.0996932i
$486$		0			0
$487$	−25.3330			−1.14795			−0.573974	−	0.818874i	$-0.694599\pi$
$487$	−25.3330			−1.14795			−0.573974	+	0.818874i	$0.694599\pi$
$488$	1.10196	+	0.924653i	0.0498833	+	0.0418571i
$489$		0			0
$490$	2.20997	+	0.804364i	0.0998364	+	0.0363375i
$491$	10.6344	−	18.4193i	0.479922	−	0.831249i	−0.519813	−	0.854280i	$-0.673998\pi$
$491$	10.6344	−	18.4193i	0.479922	−	0.831249i	0.999735	+	0.0230308i	$0.00733158\pi$
$492$		0			0
$493$	0.0796507	+	0.451722i	0.00358729	+	0.0203445i
$494$	−14.8388	+	5.40087i	−0.667628	+	0.242997i
$495$		0			0
$496$	−5.16818	+	4.33662i	−0.232058	+	0.194720i
$497$	3.24979	−	2.72690i	0.145773	−	0.122318i
$498$		0			0
$499$	2.85314	−	16.1810i	0.127724	−	0.724359i	−0.851928	−	0.523658i	$-0.824567\pi$
$499$	2.85314	−	16.1810i	0.127724	−	0.724359i	0.979653	−	0.200701i	$-0.0643220\pi$
$500$	0.595800	−	3.37895i	0.0266450	−	0.151111i
$501$		0			0
$502$	10.1806	−	8.54256i	0.454383	−	0.381273i
$503$	−15.9979	+	13.4238i	−0.713311	+	0.598539i	−0.925526	−	0.378684i	$-0.876377\pi$
$503$	−15.9979	+	13.4238i	−0.713311	+	0.598539i	0.212215	+	0.977223i	$0.431932\pi$
$504$		0			0
$505$	−5.58995	+	2.03458i	−0.248750	+	0.0905375i
$506$	−2.33887	−	13.2644i	−0.103975	−	0.589674i
$507$		0			0
$508$	3.52479	−	6.10511i	0.156387	−	0.270871i
$509$	37.6746	+	13.7124i	1.66990	+	0.607793i	0.991871	−	0.127245i	$-0.0406135\pi$
$509$	37.6746	+	13.7124i	1.66990	+	0.607793i	0.678026	+	0.735038i	$0.262836\pi$
$510$		0			0
$511$	−2.63019	−	2.20699i	−0.116353	−	0.0976317i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−16.4470	+	5.98622i	−0.725447	+	0.264041i
$515$	0.809339	−	4.58999i	0.0356637	−	0.202259i
$516$		0			0
$517$	19.2811			0.847982
$518$	−2.88726	−	0.330153i	−0.126859	−	0.0145061i
$519$		0			0
$520$	−0.270373	−	1.53336i	−0.0118566	−	0.0672424i
$521$	−1.59181	+	9.02760i	−0.0697384	+	0.395506i	0.929879	+	0.367864i	$0.119911\pi$
$521$	−1.59181	+	9.02760i	−0.0697384	+	0.395506i	−0.999618	+	0.0276419i	$0.991200\pi$
$522$		0			0
$523$	22.7091	+	19.0552i	0.993000	+	0.833226i	0.985999	−	0.166749i	$-0.0533270\pi$
$523$	22.7091	+	19.0552i	0.993000	+	0.833226i	0.00700102	+	0.999975i	$0.497771\pi$
$524$	−1.98503			−0.0867164
$525$		0			0
$526$	7.06672	+	12.2399i	0.308124	+	0.533686i
$527$	−12.7418	−	4.63765i	−0.555043	−	0.202019i
$528$		0			0
$529$	−2.07059	−	3.58637i	−0.0900257	−	0.155929i
$530$	−0.263884	−	1.49656i	−0.0114624	−	0.0650063i
$531$		0			0
$532$	0.841386	−	1.45732i	0.0364787	−	0.0631830i
$533$	36.8039	−	30.8822i	1.59415	−	1.33765i
$534$		0			0
$535$	6.67716	+	2.43029i	0.288679	+	0.105071i
$536$	1.82731	−	10.3632i	0.0789276	−	0.447621i
$537$		0			0
$538$	25.1934	+	9.16963i	1.08616	+	0.395331i
$539$	13.4115	−	11.2536i	0.577673	−	0.484725i
$540$		0			0
$541$	−14.4930	+	25.1027i	−0.623104	+	1.07925i	0.365800	+	0.930693i	$0.380795\pi$
$541$	−14.4930	+	25.1027i	−0.623104	+	1.07925i	−0.988904	+	0.148554i	$0.952538\pi$
$542$	−10.2547	+	3.73242i	−0.440478	+	0.160321i
$543$		0			0
$544$	−1.00492	−	1.74058i	−0.0430857	−	0.0746266i
$545$	1.85087	−	3.20580i	0.0792825	−	0.137321i
$546$		0			0
$547$	−2.68304	−	4.64717i	−0.114719	−	0.198699i	0.802949	−	0.596048i	$-0.203263\pi$
$547$	−2.68304	−	4.64717i	−0.114719	−	0.198699i	−0.917667	+	0.397350i	$0.869930\pi$
$548$	−13.3276	−	11.1832i	−0.569327	−	0.477722i
$549$		0			0
$550$	−9.66364	−	8.10875i	−0.412059	−	0.345758i
$551$	0.755374	−	0.274934i	0.0321800	−	0.0117126i
$552$		0			0
$553$	−0.293334	−	1.66358i	−0.0124738	−	0.0707426i
$554$	−6.14345			−0.261010
$555$		0			0
$556$	0.737051			0.0312579
$557$	2.03774	+	11.5566i	0.0863416	+	0.489668i	0.997059	+	0.0766376i	$0.0244184\pi$
$557$	2.03774	+	11.5566i	0.0863416	+	0.489668i	−0.910717	+	0.413030i	$0.864470\pi$
$558$		0			0
$559$	37.3214	−	13.5839i	1.57853	−	0.574537i
$560$	0.127104	+	0.106653i	0.00537114	+	0.00450692i
$561$		0			0
$562$	2.26215	+	1.89817i	0.0954229	+	0.0800693i
$563$	9.45929	+	16.3840i	0.398662	+	0.690502i	0.993561	−	0.113298i	$-0.0361415\pi$
$563$	9.45929	+	16.3840i	0.398662	+	0.690502i	−0.594899	+	0.803800i	$0.702808\pi$
$564$		0			0
$565$	−2.12063	+	3.67304i	−0.0892156	+	0.154526i
$566$	7.23724	+	12.5353i	0.304204	+	0.526897i
$567$		0			0
$568$	−8.34413	+	3.03702i	−0.350112	+	0.127430i
$569$	−10.8074	+	18.7189i	−0.453068	+	0.784737i	−0.998575	−	0.0533694i	$-0.983004\pi$
$569$	−10.8074	+	18.7189i	−0.453068	+	0.784737i	0.545507	+	0.838107i	$0.316337\pi$
$570$		0			0
$571$	−26.8881	+	22.5618i	−1.12523	+	0.944181i	−0.998857	−	0.0478018i	$-0.984778\pi$
$571$	−26.8881	+	22.5618i	−1.12523	+	0.944181i	−0.126374	+	0.991983i	$0.540334\pi$
$572$	−10.8918	−	3.96430i	−0.455410	−	0.165756i
$573$		0			0
$574$	−0.889044	+	5.04202i	−0.0371080	+	0.210450i
$575$	−23.8872	−	8.69423i	−0.996165	−	0.362574i
$576$		0			0
$577$	−33.0040	+	27.6937i	−1.37398	+	1.15290i	−0.402593	+	0.915379i	$0.631891\pi$
$577$	−33.0040	+	27.6937i	−1.37398	+	1.15290i	−0.971382	+	0.237523i	$0.923664\pi$
$578$	−6.48026	+	11.2241i	−0.269543	+	0.466863i
$579$		0			0
$580$	0.0137635	+	0.0780564i	0.000571496	+	0.00324112i
$581$	−0.337926	−	0.585304i	−0.0140195	−	0.0242825i
$582$		0			0
$583$	−10.6304	−	3.86915i	−0.440266	−	0.160244i
$584$	3.59334	+	6.22384i	0.148693	+	0.257544i
$585$		0			0
$586$	−12.5821			−0.519762
$587$	15.6463	+	13.1288i	0.645790	+	0.541882i	0.905790	−	0.423726i	$-0.139278\pi$
$587$	15.6463	+	13.1288i	0.645790	+	0.541882i	−0.260000	+	0.965609i	$0.583723\pi$
$588$		0			0
$589$	−4.12642	+	23.4021i	−0.170026	+	0.964267i
$590$	−0.270042	−	1.53148i	−0.0111174	−	0.0630501i
$591$		0			0
$592$	5.44257	+	2.71633i	0.223688	+	0.111641i
$593$	0.908005			0.0372873			0.0186436	−	0.999826i	$-0.494065\pi$
$593$	0.908005			0.0372873			0.0186436	+	0.999826i	$0.494065\pi$
$594$		0			0
$595$	−0.0579080	+	0.328413i	−0.00237400	+	0.0134636i
$596$	−17.8867	+	6.51023i	−0.732668	+	0.266669i
$597$		0			0
$598$	−23.3565			−0.955117
$599$	9.44037	+	7.92141i	0.385723	+	0.323660i	0.814944	−	0.579539i	$-0.196767\pi$
$599$	9.44037	+	7.92141i	0.385723	+	0.323660i	−0.429221	+	0.903199i	$0.641212\pi$
$600$		0			0
$601$	32.2492	+	11.7377i	1.31547	+	0.478792i	0.902004	−	0.431727i	$-0.142095\pi$
$601$	32.2492	+	11.7377i	1.31547	+	0.478792i	0.413467	+	0.910519i	$0.364318\pi$
$602$	−2.11619	+	3.66535i	−0.0862496	+	0.149389i
$603$		0			0
$604$	−1.12385	−	6.37365i	−0.0457287	−	0.259340i
$605$	−1.40850	+	0.512653i	−0.0572637	+	0.0208423i
$606$		0			0
$607$	−3.12973	+	2.62616i	−0.127032	+	0.106593i	−0.704090	−	0.710110i	$-0.748645\pi$
$607$	−3.12973	+	2.62616i	−0.127032	+	0.106593i	0.577058	+	0.816703i	$0.304201\pi$
$608$	−2.69820	+	2.26405i	−0.109426	+	0.0918196i
$609$		0			0
$610$	−0.0867525	+	0.491998i	−0.00351251	+	0.0199204i
$611$	5.80596	−	32.9272i	0.234884	−	1.33209i
$612$		0			0
$613$	15.2276	−	12.7775i	0.615036	−	0.516077i	−0.281202	−	0.959648i	$-0.590733\pi$
$613$	15.2276	−	12.7775i	0.615036	−	0.516077i	0.896239	+	0.443572i	$0.146289\pi$
$614$	14.4780	−	12.1485i	0.584285	−	0.490273i
$615$		0			0
$616$	1.16068	−	0.422454i	0.0467652	−	0.0170211i
$617$	−0.664267	−	3.76724i	−0.0267424	−	0.151664i	0.968513	−	0.248964i	$-0.0800902\pi$
$617$	−0.664267	−	3.76724i	−0.0267424	−	0.151664i	−0.995255	+	0.0973009i	$0.968979\pi$
$618$		0			0
$619$	5.97516	−	10.3493i	0.240162	−	0.415973i	−0.720598	−	0.693353i	$-0.756133\pi$
$619$	5.97516	−	10.3493i	0.240162	−	0.415973i	0.960760	+	0.277380i	$0.0894661\pi$
$620$	−2.20176	−	0.801375i	−0.0884248	−	0.0321840i
$621$		0			0
$622$	−0.0868584	−	0.0728829i	−0.00348271	−	0.00292234i
$623$	1.82706			0.0731995
$624$		0			0
$625$	−21.8059	+	7.93669i	−0.872235	+	0.317468i
$626$	−1.59428	+	9.04161i	−0.0637202	+	0.361375i
$627$		0			0
$628$	12.0920			0.482523
$629$	0.741374	+	12.2029i	0.0295605	+	0.486562i
$630$		0			0
$631$	−3.49888	−	19.8431i	−0.139288	−	0.789942i	−0.971777	−	0.235901i	$-0.924196\pi$
$631$	−3.49888	−	19.8431i	−0.139288	−	0.789942i	0.832489	−	0.554041i	$-0.186915\pi$
$632$	−0.613983	+	3.48207i	−0.0244229	+	0.138509i
$633$		0			0
$634$	20.1198	+	16.8826i	0.799061	+	0.670492i
$635$	2.44829			0.0971575
$636$		0			0
$637$	−15.1797	−	26.2920i	−0.601442	−	1.04173i
$638$	0.554452	+	0.201804i	0.0219510	+	0.00798950i
$639$		0			0
$640$	−0.173648	−	0.300767i	−0.00686405	−	0.0118889i
$641$	−5.23531	−	29.6909i	−0.206782	−	1.17272i	−0.894610	−	0.446848i	$-0.852547\pi$
$641$	−5.23531	−	29.6909i	−0.206782	−	1.17272i	0.687828	−	0.725874i	$-0.258565\pi$
$642$		0			0
$643$	6.52757	−	11.3061i	0.257422	−	0.445868i	−0.708128	−	0.706084i	$-0.750460\pi$
$643$	6.52757	−	11.3061i	0.257422	−	0.445868i	0.965551	+	0.260215i	$0.0837936\pi$
$644$	1.90666	−	1.59988i	0.0751331	−	0.0630442i
$645$		0			0
$646$	−6.65224	−	2.42122i	−0.261729	−	0.0952615i
$647$	−8.16883	+	46.3278i	−0.321150	+	1.82133i	0.214303	+	0.976767i	$0.431252\pi$
$647$	−8.16883	+	46.3278i	−0.321150	+	1.82133i	−0.535453	+	0.844565i	$0.679859\pi$
$648$		0			0
$649$	−10.8785	−	3.95944i	−0.427017	−	0.155422i
$650$	−16.7576	+	14.0613i	−0.657287	+	0.551530i
$651$		0			0
$652$	−7.37329	+	12.7709i	−0.288760	+	0.500148i
$653$	−25.9534	+	9.44628i	−1.01564	+	0.369661i	−0.795595	−	0.605829i	$-0.792842\pi$
$653$	−25.9534	+	9.44628i	−1.01564	+	0.369661i	−0.220042	+	0.975491i	$0.570619\pi$
$654$		0			0
$655$	−0.344697	−	0.597032i	−0.0134684	−	0.0233280i
$656$	5.35818	−	9.28064i	0.209202	−	0.362348i
$657$		0			0
$658$	1.78150	+	3.08565i	0.0694502	+	0.120291i
$659$	−27.5226	−	23.0942i	−1.07213	−	0.899624i	−0.0768864	−	0.997040i	$-0.524498\pi$
$659$	−27.5226	−	23.0942i	−1.07213	−	0.899624i	−0.995244	+	0.0974158i	$0.968942\pi$
$660$		0			0
$661$	30.2001	+	25.3409i	1.17465	+	0.985645i	0.999999	+	0.00101438i	$0.000322887\pi$
$661$	30.2001	+	25.3409i	1.17465	+	0.985645i	0.174647	+	0.984631i	$0.444122\pi$
$662$	−26.8546	+	9.77429i	−1.04373	+	0.379888i
$663$		0			0
$664$	0.245649	+	1.39315i	0.00953304	+	0.0540645i
$665$	0.584421			0.0226629
$666$		0			0
$667$	1.18897			0.0460372
$668$	−1.44239	−	8.18020i	−0.0558078	−	0.316501i
$669$		0			0
$670$	3.43421	−	1.24995i	0.132675	−	0.0482898i
$671$	2.84896	+	2.39056i	0.109983	+	0.0922867i
$672$		0			0
$673$	11.6863	+	9.80600i	0.450475	+	0.377994i	0.839612	−	0.543186i	$-0.182782\pi$
$673$	11.6863	+	9.80600i	0.450475	+	0.377994i	−0.389137	+	0.921180i	$0.627227\pi$
$674$	−4.88643	−	8.46354i	−0.188218	−	0.326003i
$675$		0			0
$676$	−3.54976	+	6.14837i	−0.136529	+	0.236476i
$677$	10.7029	+	18.5379i	0.411345	+	0.712471i	0.995037	−	0.0995043i	$-0.0317257\pi$
$677$	10.7029	+	18.5379i	0.411345	+	0.712471i	−0.583692	+	0.811975i	$0.698392\pi$
$678$		0			0
$679$	8.29805	−	3.02024i	0.318450	−	0.115906i
$680$	0.349006	−	0.604496i	0.0133838	−	0.0231814i
$681$		0			0
$682$	−13.3616	+	11.2117i	−0.511643	+	0.429319i
$683$	11.8657	+	4.31877i	0.454029	+	0.165253i	0.558904	−	0.829232i	$-0.311222\pi$
$683$	11.8657	+	4.31877i	0.454029	+	0.165253i	−0.104875	+	0.994485i	$0.533444\pi$
$684$		0			0
$685$	1.04922	−	5.95045i	0.0400888	−	0.227355i
$686$	6.18274	+	2.25033i	0.236058	+	0.0859181i
$687$		0			0
$688$	6.78631	−	5.69439i	0.258725	−	0.217096i
$689$	−9.80855	+	16.9889i	−0.373676	+	0.647226i
$690$		0			0
$691$	−0.596082	−	3.38055i	−0.0226760	−	0.128602i	0.971368	−	0.237579i	$-0.0763538\pi$
$691$	−0.596082	−	3.38055i	−0.0226760	−	0.128602i	−0.994044	+	0.108977i	$0.965243\pi$
$692$	−3.30637	−	5.72679i	−0.125689	−	0.217700i
$693$		0			0
$694$	−15.5767	−	5.66944i	−0.591282	−	0.215209i
$695$	0.127988	+	0.221681i	0.00485485	+	0.00840884i
$696$		0			0
$697$	21.5382			0.815818
$698$	−14.3165	−	12.0129i	−0.541886	−	0.454696i
$699$		0			0
$700$	0.404801	−	2.29574i	0.0153000	−	0.0867708i
$701$	−0.0325577	−	0.184644i	−0.00122969	−	0.00697390i	0.984187	−	0.177134i	$-0.0566826\pi$
$701$	−0.0325577	−	0.184644i	−0.00122969	−	0.00697390i	−0.985416	+	0.170160i	$0.945571\pi$
$702$		0			0
$703$	20.8350	−	4.99308i	0.785808	−	0.188317i
$704$	−2.58536			−0.0974395
$705$		0			0
$706$	0.938401	−	5.32193i	0.0353172	−	0.200294i
$707$	−7.68978	+	2.79885i	−0.289204	+	0.105262i
$708$		0			0
$709$	−48.4114			−1.81813			−0.909064	−	0.416656i	$-0.863202\pi$
$709$	−48.4114			−1.81813			−0.909064	+	0.416656i	$0.863202\pi$
$710$	−2.36238	−	1.98227i	−0.0886585	−	0.0743933i
$711$		0			0
$712$	−3.59362	−	1.30797i	−0.134677	−	0.0490182i
$713$	−17.5739	+	30.4389i	−0.658148	+	1.13995i
$714$		0			0
$715$	−0.699012	−	3.96430i	−0.0261416	−	0.148256i
$716$	4.26607	−	1.55272i	0.159430	−	0.0580279i
$717$		0			0
$718$	−8.09432	+	6.79194i	−0.302077	+	0.253473i
$719$	34.9152	−	29.2973i	1.30212	−	1.09261i	0.312341	−	0.949970i	$-0.398887\pi$
$719$	34.9152	−	29.2973i	1.30212	−	1.09261i	0.989775	−	0.142635i	$-0.0455575\pi$
$720$		0			0
$721$	1.11336	−	6.31419i	0.0414637	−	0.235153i
$722$	1.14500	−	6.49362i	0.0426125	−	0.241668i
$723$		0			0
$724$	−1.19788	+	1.00514i	−0.0445190	+	0.0373559i
$725$	0.853053	−	0.715797i	0.0316816	−	0.0265840i
$726$		0			0
$727$	−39.4113	+	14.3445i	−1.46168	+	0.532009i	−0.945828	−	0.324667i	$-0.894748\pi$
$727$	−39.4113	+	14.3445i	−1.46168	+	0.532009i	−0.515854	+	0.856676i	$0.672525\pi$
$728$	−0.371937	−	2.10936i	−0.0137849	−	0.0781780i
$729$		0			0
$730$	−1.24795	+	2.16152i	−0.0461888	+	0.0800013i
$731$	16.7312	+	6.08967i	0.618827	+	0.225234i
$732$		0			0
$733$	13.4938	+	11.3227i	0.498406	+	0.418212i	0.857027	−	0.515271i	$-0.172309\pi$
$733$	13.4938	+	11.3227i	0.498406	+	0.418212i	−0.358622	+	0.933483i	$0.616753\pi$
$734$	0.215875			0.00796811
$735$		0			0
$736$	−4.89554	+	1.78183i	−0.180452	+	0.0656791i
$737$	4.72425	−	26.7925i	0.174020	−	0.986916i
$738$		0			0
$739$	39.4393			1.45080			0.725400	−	0.688328i	$-0.241655\pi$
$739$	39.4393			1.45080			0.725400	+	0.688328i	$0.241655\pi$
$740$	0.128108	+	2.10863i	0.00470933	+	0.0775149i
$741$		0			0
$742$	−0.363009	−	2.05873i	−0.0133265	−	0.0755783i
$743$	−2.27755	+	12.9167i	−0.0835554	+	0.473866i	0.914104	+	0.405481i	$0.132896\pi$
$743$	−2.27755	+	12.9167i	−0.0835554	+	0.473866i	−0.997659	+	0.0683854i	$0.978215\pi$
$744$		0			0
$745$	−5.06406	−	4.24925i	−0.185533	−	0.155680i
$746$	19.8047			0.725102
$747$		0			0
$748$	−2.59809	−	4.50002i	−0.0949955	−	0.164537i
$749$	9.18539	+	3.34321i	0.335627	+	0.122158i
$750$		0			0
$751$	19.9893	+	34.6226i	0.729421	+	1.26340i	0.957128	+	0.289665i	$0.0935440\pi$
$751$	19.9893	+	34.6226i	0.729421	+	1.26340i	−0.227707	+	0.973730i	$0.573123\pi$
$752$	−1.29503	−	7.34450i	−0.0472250	−	0.267826i
$753$		0			0
$754$	0.511588	−	0.886096i	0.0186309	−	0.0322697i
$755$	1.72183	−	1.44479i	0.0626639	−	0.0525813i
$756$		0			0
$757$	−26.2852	−	9.56703i	−0.955352	−	0.347720i	−0.183141	−	0.983087i	$-0.558627\pi$
$757$	−26.2852	−	9.56703i	−0.955352	−	0.347720i	−0.772210	+	0.635367i	$0.780849\pi$
$758$	4.01057	−	22.7451i	0.145670	−	0.826137i
$759$		0			0
$760$	−1.14949	−	0.418380i	−0.0416964	−	0.0151763i
$761$	1.66744	−	1.39915i	0.0604447	−	0.0507191i	−0.612065	−	0.790808i	$-0.709661\pi$
$761$	1.66744	−	1.39915i	0.0604447	−	0.0507191i	0.672510	+	0.740088i	$0.265216\pi$
$762$		0			0
$763$	2.54614	−	4.41004i	0.0921763	−	0.159654i
$764$	21.6301	−	7.87272i	0.782550	−	0.284825i
$765$		0			0
$766$	2.54301	+	4.40462i	0.0918826	+	0.159145i
$767$	−10.0374	+	17.3854i	−0.362431	+	0.627749i
$768$		0			0
$769$	20.6905	+	35.8370i	0.746118	+	1.29231i	0.949671	+	0.313250i	$0.101418\pi$
$769$	20.6905	+	35.8370i	0.746118	+	1.29231i	−0.203553	+	0.979064i	$0.565249\pi$
$770$	0.328611	+	0.275737i	0.0118423	+	0.00993687i
$771$		0			0
$772$	−8.08492	−	6.78405i	−0.290983	−	0.244163i
$773$	−11.5459	+	4.20237i	−0.415278	+	0.151149i	−0.541205	−	0.840891i	$-0.682032\pi$
$773$	−11.5459	+	4.20237i	−0.415278	+	0.151149i	0.125927	+	0.992040i	$0.459809\pi$
$774$		0			0
$775$	5.71635	+	32.4191i	0.205338	+	1.16453i
$776$	−18.4835			−0.663519
$777$		0			0
$778$	−29.1473			−1.04498
$779$	−6.55446	−	37.1722i	−0.234838	−	1.33183i
$780$		0			0
$781$	−21.5726	+	7.85179i	−0.771929	+	0.280959i
$782$	−8.02104	−	6.73045i	−0.286832	−	0.240681i
$783$		0			0
$784$	−5.18746	−	4.35280i	−0.185266	−	0.155457i
$785$	2.09975	+	3.63688i	0.0749434	+	0.129806i
$786$		0			0
$787$	−12.0763	+	20.9167i	−0.430473	+	0.745601i	−0.996914	−	0.0785015i	$-0.974986\pi$
$787$	−12.0763	+	20.9167i	−0.430473	+	0.745601i	0.566441	+	0.824102i	$0.308320\pi$
$788$	2.41433	+	4.18175i	0.0860071	+	0.148969i
$789$		0			0
$790$	−1.15391	+	0.419989i	−0.0410543	+	0.0149425i
$791$	−2.91723	+	5.05279i	−0.103725	+	0.179657i
$792$		0			0
$793$	4.94036	−	4.14545i	0.175437	−	0.147209i
$794$	−15.0280	−	5.46975i	−0.533325	−	0.194114i
$795$		0			0
$796$	1.78721	−	10.1358i	0.0633461	−	0.359254i
$797$	−30.9648	−	11.2703i	−1.09683	−	0.399214i	−0.270684	−	0.962668i	$-0.587250\pi$
$797$	−30.9648	−	11.2703i	−1.09683	−	0.399214i	−0.826147	+	0.563455i	$0.809472\pi$
$798$		0			0
$799$	11.4823	−	9.63475i	0.406213	−	0.340853i
$800$	−2.43969	+	4.22567i	−0.0862562	+	0.149400i
$801$		0			0
$802$	−0.944617	−	5.35719i	−0.0333556	−	0.189169i
$803$	9.29008	+	16.0909i	0.327840	+	0.567835i
$804$		0			0
$805$	0.812281	+	0.295646i	0.0286291	+	0.0104202i
$806$	15.1233	+	26.1943i	0.532696	+	0.922656i
$807$		0			0
$808$	17.1286			0.602582
$809$	−27.3400	−	22.9410i	−0.961224	−	0.806563i	0.0199275	−	0.999801i	$-0.493656\pi$
$809$	−27.3400	−	22.9410i	−0.961224	−	0.806563i	−0.981152	+	0.193238i	$0.938101\pi$
$810$		0			0
$811$	5.88324	−	33.3655i	0.206589	−	1.17162i	−0.688332	−	0.725396i	$-0.741657\pi$
$811$	5.88324	−	33.3655i	0.206589	−	1.17162i	0.894920	−	0.446226i	$-0.147232\pi$
$812$	0.0189336	+	0.107378i	0.000664439	+	0.00376822i
$813$		0			0
$814$	14.0710	+	7.02270i	0.493189	+	0.246146i
$815$	−5.12143			−0.179396
$816$		0			0
$817$	5.41838	−	30.7291i	0.189565	−	1.07508i
$818$	−35.4493	+	12.9025i	−1.23945	+	0.451125i
$819$		0			0
$820$	3.72175			0.129969
$821$	18.1645	+	15.2418i	0.633945	+	0.531943i	0.902152	−	0.431418i	$-0.141987\pi$
$821$	18.1645	+	15.2418i	0.633945	+	0.531943i	−0.268207	+	0.963361i	$0.586431\pi$
$822$		0			0
$823$	−23.3126	−	8.48508i	−0.812625	−	0.295771i	−0.0979172	−	0.995195i	$-0.531218\pi$
$823$	−23.3126	−	8.48508i	−0.812625	−	0.295771i	−0.714708	+	0.699423i	$0.753440\pi$
$824$	−6.71012	+	11.6223i	−0.233758	+	0.404881i
$825$		0			0
$826$	−0.371481	−	2.10677i	−0.0129255	−	0.0733040i
$827$	49.8660	−	18.1497i	1.73401	−	0.631129i	0.735108	−	0.677950i	$-0.237131\pi$
$827$	49.8660	−	18.1497i	1.73401	−	0.631129i	0.998903	+	0.0468213i	$0.0149091\pi$
$828$		0			0
$829$	−4.78684	+	4.01663i	−0.166254	+	0.139503i	−0.722119	−	0.691769i	$-0.756832\pi$
$829$	−4.78684	+	4.01663i	−0.166254	+	0.139503i	0.555865	+	0.831273i	$0.312387\pi$
$830$	−0.376356	+	0.315801i	−0.0130635	+	0.0109616i
$831$		0			0
$832$	−0.778508	+	4.41514i	−0.0269899	+	0.153067i
$833$	2.36338	−	13.4034i	0.0818863	−	0.464400i
$834$		0			0
$835$	2.20987	−	1.85430i	0.0764757	−	0.0641707i
$836$	−6.97581	+	5.85340i	−0.241264	+	0.202444i
$837$		0			0
$838$	−5.81832	+	2.11770i	−0.200991	+	0.0731546i
$839$	−1.97545	−	11.2033i	−0.0682002	−	0.386783i	−0.999733	−	0.0231242i	$-0.992639\pi$
$839$	−1.97545	−	11.2033i	−0.0682002	−	0.386783i	0.931532	−	0.363658i	$-0.118472\pi$
$840$		0			0
$841$	14.4740	−	25.0696i	0.499102	−	0.864470i
$842$	−9.49900	−	3.45735i	−0.327357	−	0.119148i
$843$		0			0
$844$	1.05020	+	0.881223i	0.0361494	+	0.0303329i
$845$	−2.46564			−0.0848206
$846$		0			0
$847$	−1.93760	+	0.705227i	−0.0665766	+	0.0242319i
$848$	−0.759822	+	4.30917i	−0.0260924	+	0.147977i
$849$		0			0
$850$	−9.80681			−0.336371
$851$	31.4843	+	3.60017i	1.07927	+	0.123412i
$852$		0			0
$853$	−0.162161	−	0.919663i	−0.00555230	−	0.0314886i	0.981906	−	0.189370i	$-0.0606447\pi$
$853$	−0.162161	−	0.919663i	−0.00555230	−	0.0314886i	−0.987458	+	0.157882i	$0.949534\pi$
$854$	−0.119340	+	0.676813i	−0.00408375	+	0.0231601i
$855$		0			0
$856$	−15.6733	−	13.1514i	−0.535702	−	0.449507i
$857$	−34.2745			−1.17080			−0.585398	−	0.810746i	$-0.699062\pi$
$857$	−34.2745			−1.17080			−0.585398	+	0.810746i	$0.699062\pi$
$858$		0			0
$859$	8.03105	+	13.9102i	0.274016	+	0.474609i	0.969886	−	0.243558i	$-0.0783146\pi$
$859$	8.03105	+	13.9102i	0.274016	+	0.474609i	−0.695871	+	0.718167i	$0.744981\pi$
$860$	2.89112	+	1.05228i	0.0985862	+	0.0358825i
$861$		0			0
$862$	17.0891	+	29.5992i	0.582057	+	1.00815i
$863$	1.11602	+	6.32926i	0.0379898	+	0.215451i	0.997893	−	0.0648808i	$-0.0206667\pi$
$863$	1.11602	+	6.32926i	0.0379898	+	0.215451i	−0.959903	+	0.280331i	$0.909556\pi$
$864$		0			0
$865$	1.14829	−	1.98889i	0.0390430	−	0.0676245i
$866$	0.525751	−	0.441157i	0.0178657	−	0.0149911i
$867$		0			0
$868$	−3.02883	−	1.10241i	−0.102805	−	0.0374181i
$869$	−1.58737	+	9.00241i	−0.0538478	+	0.305386i
$870$		0			0
$871$	−44.3322	−	16.1356i	−1.50214	−	0.546735i
$872$	−8.16506	+	6.85130i	−0.276504	+	0.232014i
$873$		0			0
$874$	−9.17495	+	15.8915i	−0.310347	+	0.537537i
$875$	1.54036	−	0.560645i	0.0520736	−	0.0189533i
$876$		0			0
$877$	−21.9328	−	37.9888i	−0.740619	−	1.28279i	−0.952214	−	0.305432i	$-0.901199\pi$
$877$	−21.9328	−	37.9888i	−0.740619	−	1.28279i	0.211595	−	0.977357i	$-0.432134\pi$
$878$	10.7545	−	18.6273i	0.362945	−	0.628639i
$879$		0			0
$880$	−0.448944	−	0.777593i	−0.0151339	−	0.0262127i
$881$	18.2452	+	15.3095i	0.614696	+	0.515791i	0.896131	−	0.443789i	$-0.146366\pi$
$881$	18.2452	+	15.3095i	0.614696	+	0.515791i	−0.281436	+	0.959580i	$0.590811\pi$
$882$		0			0
$883$	5.99963	+	5.03429i	0.201904	+	0.169417i	0.738133	−	0.674655i	$-0.235708\pi$
$883$	5.99963	+	5.03429i	0.201904	+	0.169417i	−0.536230	+	0.844072i	$0.680152\pi$
$884$	−8.46723	+	3.08182i	−0.284784	+	0.103653i
$885$		0			0
$886$	−4.96583	−	28.1626i	−0.166830	−	0.946142i
$887$	37.5492			1.26078			0.630389	−	0.776280i	$-0.282896\pi$
$887$	37.5492			1.26078			0.630389	+	0.776280i	$0.282896\pi$
$888$		0			0
$889$	3.36798			0.112958
$890$	−0.230630	−	1.30797i	−0.00773075	−	0.0438433i
$891$		0			0
$892$	27.4965	−	10.0079i	0.920651	−	0.335090i
$893$	−20.1226	−	16.8849i	−0.673377	−	0.565030i
$894$		0			0
$895$	1.20780	+	1.01347i	0.0403724	+	0.0338765i
$896$	−0.238878	−	0.413749i	−0.00798035	−	0.0138224i
$897$		0			0
$898$	17.2844	−	29.9375i	0.576789	−	0.999028i
$899$	−0.769858	−	1.33343i	−0.0256762	−	0.0444725i
$900$		0			0
$901$	−8.26400	+	3.00785i	−0.275314	+	0.100206i
$902$	13.8528	−	23.9938i	0.461249	−	0.798907i
$903$		0			0
$904$	9.35511	−	7.84987i	0.311146	−	0.261083i
$905$	−0.510325	−	0.185743i	−0.0169638	−	0.00617431i
$906$		0			0
$907$	5.69564	−	32.3016i	0.189120	−	1.07256i	−0.731426	−	0.681921i	$-0.761145\pi$
$907$	5.69564	−	32.3016i	0.189120	−	1.07256i	0.920546	−	0.390634i	$-0.127744\pi$
$908$	9.68313	+	3.52437i	0.321346	+	0.116960i
$909$		0			0
$910$	0.569840	−	0.478153i	0.0188900	−	0.0158506i
$911$	16.8114	−	29.1181i	0.556985	−	0.964727i	−0.440761	−	0.897625i	$-0.645291\pi$
$911$	16.8114	−	29.1181i	0.556985	−	0.964727i	0.997746	−	0.0671021i	$-0.0213753\pi$
$912$		0			0
$913$	0.635092	+	3.60179i	0.0210185	+	0.119202i
$914$	16.4542	+	28.4995i	0.544257	+	0.942680i
$915$		0			0
$916$	−14.7229	−	5.35869i	−0.486458	−	0.177056i
$917$	−0.474180	−	0.821303i	−0.0156588	−	0.0271218i
$918$		0			0
$919$	−29.1313			−0.960954			−0.480477	−	0.877007i	$-0.659536\pi$
$919$	−29.1313			−0.960954			−0.480477	+	0.877007i	$0.659536\pi$
$920$	−1.38602	−	1.16301i	−0.0456956	−	0.0383432i
$921$		0			0
$922$	−3.14988	+	17.8639i	−0.103736	+	0.588315i
$923$	6.91287	+	39.2049i	0.227540	+	1.29044i
$924$		0			0
$925$	24.7565	−	16.3715i	0.813989	−	0.538291i
$926$	−0.339403			−0.0111535
$927$		0			0
$928$	0.0396303	−	0.224755i	0.00130093	−	0.00737793i
$929$	28.9996	−	10.5550i	0.951446	−	0.346298i	0.180770	−	0.983525i	$-0.442141\pi$
$929$	28.9996	−	10.5550i	0.951446	−	0.346298i	0.770676	+	0.637228i	$0.219919\pi$
$930$		0			0
$931$	−23.8518			−0.781710
$932$	−5.51861	−	4.63067i	−0.180768	−	0.151683i
$933$		0			0
$934$	13.3455	+	4.85738i	0.436679	+	0.158938i
$935$	0.902307	−	1.56284i	0.0295086	−	0.0511104i
$936$		0			0
$937$	1.27251	+	7.21677i	0.0415711	+	0.235762i	0.998513	−	0.0545189i	$-0.0173625\pi$
$937$	1.27251	+	7.21677i	0.0415711	+	0.235762i	−0.956942	+	0.290281i	$0.906251\pi$
$938$	4.72425	−	1.71949i	0.154252	−	0.0561432i
$939$		0			0
$940$	1.98411	−	1.66486i	0.0647144	−	0.0543018i
$941$	−32.3208	+	27.1204i	−1.05363	+	0.884098i	−0.993470	−	0.114090i	$-0.963605\pi$
$941$	−32.3208	+	27.1204i	−1.05363	+	0.884098i	−0.0601572	+	0.998189i	$0.519160\pi$
$942$		0			0
$943$	9.69464	−	54.9810i	0.315701	−	1.79043i
$944$	−0.777554	+	4.40973i	−0.0253072	+	0.143524i
$945$		0			0
$946$	17.5451	−	14.7221i	0.570439	−	0.478655i
$947$	29.9494	−	25.1305i	0.973224	−	0.816632i	−0.00982951	−	0.999952i	$-0.503129\pi$
$947$	29.9494	−	25.1305i	0.973224	−	0.816632i	0.983053	+	0.183320i	$0.0586844\pi$
$948$		0			0
$949$	30.2766	−	11.0198i	0.982819	−	0.357717i
$950$	2.98438	+	16.9253i	0.0968262	+	0.549129i
$951$		0			0
$952$	0.480107	−	0.831570i	0.0155604	−	0.0269514i
$953$	−1.14509	−	0.416780i	−0.0370932	−	0.0135008i	0.323407	−	0.946260i	$-0.395172\pi$
$953$	−1.14509	−	0.416780i	−0.0370932	−	0.0135008i	−0.360500	+	0.932759i	$0.617394\pi$
$954$		0			0
$955$	6.12389	+	5.13855i	0.198164	+	0.166280i
$956$	21.9530			0.710012
$957$		0			0
$958$	31.9312	−	11.6220i	1.03165	−	0.375490i
$959$	1.44336	−	8.18569i	0.0466085	−	0.264330i
$960$		0			0
$961$	14.5164			0.468270
$962$	16.2301	−	21.9150i	0.523278	−	0.706568i
$963$		0			0
$964$	2.57180	+	14.5854i	0.0828320	+	0.469764i
$965$	0.636491	−	3.60972i	0.0204894	−	0.116201i
$966$		0			0
$967$	9.72067	+	8.15661i	0.312596	+	0.262299i	0.785564	−	0.618781i	$-0.212373\pi$
$967$	9.72067	+	8.15661i	0.312596	+	0.262299i	−0.472968	+	0.881080i	$0.656817\pi$
$968$	4.31590			0.138718
$969$		0			0
$970$	−3.20963	−	5.55924i	−0.103055	−	0.178496i
$971$	0.827436	+	0.301162i	0.0265537	+	0.00966475i	0.355263	−	0.934766i	$-0.384391\pi$
$971$	0.827436	+	0.301162i	0.0265537	+	0.00966475i	−0.328709	+	0.944431i	$0.606614\pi$
$972$		0			0
$973$	0.176065	+	0.304954i	0.00564439	+	0.00977638i
$974$	4.39903	+	24.9481i	0.140954	+	0.799389i
$975$		0			0
$976$	0.719253	−	1.24578i	0.0230227	−	0.0398765i
$977$	−35.8592	+	30.0895i	−1.14724	+	0.962647i	−0.999651	−	0.0264023i	$-0.991595\pi$
$977$	−35.8592	+	30.0895i	−1.14724	+	0.962647i	−0.147586	+	0.989049i	$0.547150\pi$
$978$		0			0
$979$	−9.29081	−	3.38158i	−0.296935	−	0.108076i
$980$	0.408386	−	2.31607i	0.0130454	−	0.0739843i
$981$		0			0
$982$	−19.9861	−	7.27433i	−0.637781	−	0.232133i
$983$	26.4449	−	22.1899i	0.843460	−	0.707747i	−0.114879	−	0.993379i	$-0.536648\pi$
$983$	26.4449	−	22.1899i	0.843460	−	0.707747i	0.958339	+	0.285633i	$0.0922037\pi$
$984$		0			0
$985$	−0.838489	+	1.45231i	−0.0267165	+	0.0462743i
$986$	0.431028	−	0.156881i	0.0137267	−	0.00499612i
$987$		0			0
$988$	7.89555	+	13.6755i	0.251191	+	0.435075i
$989$	23.0762	−	39.9691i	0.733780	−	1.27094i
$990$		0			0
$991$	23.7701	+	41.1711i	0.755083	+	1.30784i	0.945333	+	0.326107i	$0.105737\pi$
$991$	23.7701	+	41.1711i	0.755083	+	1.30784i	−0.190249	+	0.981736i	$0.560930\pi$
$992$	5.16818	+	4.33662i	0.164090	+	0.137688i
$993$		0			0
$994$	−3.24979	−	2.72690i	−0.103077	−	0.0864919i
$995$	3.35887	−	1.22253i	0.106483	−	0.0387567i
$996$		0			0
$997$	9.31464	+	52.8259i	0.294998	+	1.67301i	0.667212	+	0.744868i	$0.267487\pi$
$997$	9.31464	+	52.8259i	0.294998	+	1.67301i	−0.372215	+	0.928147i	$0.621401\pi$
$998$	−16.4306			−0.520101
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.x.g.379.1		12
3.2	odd	2		74.2.f.b.9.1	✓	12
12.11	even	2		592.2.bc.d.305.2		12
37.33	even	9	inner	666.2.x.g.181.1		12
111.62	odd	18		2738.2.a.q.1.3		6
111.86	odd	18		2738.2.a.t.1.3		6
111.107	odd	18		74.2.f.b.33.1	yes	12
444.107	even	18		592.2.bc.d.33.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.9.1	✓	12	3.2	odd	2
74.2.f.b.33.1	yes	12	111.107	odd	18
592.2.bc.d.33.2		12	444.107	even	18
592.2.bc.d.305.2		12	12.11	even	2
666.2.x.g.181.1		12	37.33	even	9	inner
666.2.x.g.379.1		12	1.1	even	1	trivial
2738.2.a.q.1.3		6	111.62	odd	18
2738.2.a.t.1.3		6	111.86	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)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.266044 - 0.223238i) q^{5} +(-0.365982 - 0.307095i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.266044 - 0.223238i) q^{5} +(-0.365982 - 0.307095i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.173648 + 0.300767i) q^{10} +(1.29268 + 2.23899i) q^{11} +(4.21288 - 1.53336i) q^{13} +(-0.238878 + 0.413749i) q^{14} +(0.766044 - 0.642788i) q^{16} +(1.88864 + 0.687407i) q^{17} +(0.611631 - 3.46873i) q^{19} +(0.326352 + 0.118782i) q^{20} +(1.98050 - 1.66184i) q^{22} +(2.60486 - 4.51175i) q^{23} +(-0.847296 - 4.80526i) q^{25} +(-2.24162 - 3.88261i) q^{26} +(0.448944 + 0.163402i) q^{28} +(0.114111 + 0.197646i) q^{29} -6.74658 q^{31} +(-0.766044 - 0.642788i) q^{32} +(0.349006 - 1.97931i) q^{34} +(0.0288122 + 0.163402i) q^{35} +(2.42322 + 5.57925i) q^{37} -3.52224 q^{38} +(0.0603074 - 0.342020i) q^{40} +(10.0701 - 3.66521i) q^{41} +8.85889 q^{43} +(-1.98050 - 1.66184i) q^{44} +(-4.89554 - 1.78183i) q^{46} +(3.72890 - 6.45864i) q^{47} +(-1.17590 - 6.66887i) q^{49} +(-4.58512 + 1.66885i) q^{50} +(-3.43437 + 2.88178i) q^{52} +(-3.35194 + 2.81261i) q^{53} +(0.155916 - 0.884246i) q^{55} +(0.0829614 - 0.470498i) q^{56} +(0.174828 - 0.146698i) q^{58} +(-3.43016 + 2.87825i) q^{59} +(1.35175 - 0.491998i) q^{61} +(1.17153 + 6.64409i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-1.46312 - 0.532531i) q^{65} +(-8.06111 - 6.76408i) q^{67} -2.00984 q^{68} +(0.155916 - 0.0567489i) q^{70} +(-1.54193 + 8.74474i) q^{71} +7.18667 q^{73} +(5.07370 - 3.35524i) q^{74} +(0.611631 + 3.46873i) q^{76} +(0.214485 - 1.21641i) q^{77} +(2.70857 + 2.27276i) q^{79} -0.347296 q^{80} +(-5.35818 - 9.28064i) q^{82} +(1.32932 + 0.483834i) q^{83} +(-0.349006 - 0.604496i) q^{85} +(-1.53833 - 8.72431i) q^{86} +(-1.29268 + 2.23899i) q^{88} +(-2.92954 + 2.45818i) q^{89} +(-2.01273 - 0.732572i) q^{91} +(-0.904658 + 5.13057i) q^{92} +(-7.00804 - 2.55072i) q^{94} +(-0.937074 + 0.786298i) q^{95} +(-9.24175 + 16.0072i) q^{97} +(-6.36336 + 2.31607i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 6 * q^5 + 6 * q^7 + 6 * q^8	\( 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8} - 3 q^{11} - 6 q^{13} - 3 q^{14} + 3 q^{17} - 3 q^{19} + 6 q^{20} - 3 q^{22} + 21 q^{23} - 6 q^{25} - 3 q^{28} - 6 q^{29} + 42 q^{31} - 3 q^{34} + 9 q^{35} - 3 q^{37} - 42 q^{38} + 12 q^{40} + 21 q^{41} + 36 q^{43} + 3 q^{44} + 3 q^{46} - 9 q^{47} - 12 q^{49} - 12 q^{50} + 3 q^{52} + 6 q^{53} + 3 q^{56} - 3 q^{58} + 6 q^{59} - 18 q^{61} + 33 q^{62} - 6 q^{64} - 3 q^{65} - 27 q^{67} - 6 q^{68} + 18 q^{71} + 54 q^{73} - 3 q^{74} - 3 q^{76} - 51 q^{77} - 12 q^{79} - 18 q^{82} + 6 q^{83} + 3 q^{85} + 3 q^{88} + 15 q^{89} - 51 q^{91} + 6 q^{92} - 12 q^{94} + 15 q^{95} - 42 q^{97} - 51 q^{98}+O(q^{100}) \) 12 * q + 6 * q^5 + 6 * q^7 + 6 * q^8 - 3 * q^11 - 6 * q^13 - 3 * q^14 + 3 * q^17 - 3 * q^19 + 6 * q^20 - 3 * q^22 + 21 * q^23 - 6 * q^25 - 3 * q^28 - 6 * q^29 + 42 * q^31 - 3 * q^34 + 9 * q^35 - 3 * q^37 - 42 * q^38 + 12 * q^40 + 21 * q^41 + 36 * q^43 + 3 * q^44 + 3 * q^46 - 9 * q^47 - 12 * q^49 - 12 * q^50 + 3 * q^52 + 6 * q^53 + 3 * q^56 - 3 * q^58 + 6 * q^59 - 18 * q^61 + 33 * q^62 - 6 * q^64 - 3 * q^65 - 27 * q^67 - 6 * q^68 + 18 * q^71 + 54 * q^73 - 3 * q^74 - 3 * q^76 - 51 * q^77 - 12 * q^79 - 18 * q^82 + 6 * q^83 + 3 * q^85 + 3 * q^88 + 15 * q^89 - 51 * q^91 + 6 * q^92 - 12 * q^94 + 15 * q^95 - 42 * q^97 - 51 * q^98

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