LMFDB - Embedded newform 1950.2.z.m.1699.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(1699,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1950.1699");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.z (of order $6$, degree $2$, not 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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1731891456.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 $ x^8 - 9x^6 + 65x^4 - 144*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1699.1
Root			$-2.21837 + 1.28078i$ of defining polynomial
Character	$\chi$	$=$	1950.1699
Dual form			1950.2.z.m.1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(-3.08440 + 1.78078i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(-3.08440 + 1.78078i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.280776 - 0.486319i) q^{11} +1.00000i q^{12} +(2.21837 - 2.84233i) q^{13} +3.56155 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.70469 + 1.56155i) q^{17} -1.00000i q^{18} +(-1.21922 - 2.11176i) q^{19} -3.56155 q^{21} +(-0.486319 + 0.280776i) q^{22} +(-6.65511 - 3.84233i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-3.34233 + 1.35234i) q^{26} +1.00000i q^{27} +(-3.08440 - 1.78078i) q^{28} +(0.561553 - 0.972638i) q^{29} +4.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(0.486319 - 0.280776i) q^{33} +3.12311 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-0.486319 - 0.280776i) q^{37} +2.43845i q^{38} +(3.34233 - 1.35234i) q^{39} +(1.56155 - 2.70469i) q^{41} +(3.08440 + 1.78078i) q^{42} +(-0.379706 + 0.219224i) q^{43} +0.561553 q^{44} +(3.84233 + 6.65511i) q^{46} +4.00000i q^{47} +(-0.866025 + 0.500000i) q^{48} +(2.84233 - 4.92306i) q^{49} -3.12311 q^{51} +(3.57071 + 0.500000i) q^{52} -4.24621i q^{53} +(0.500000 - 0.866025i) q^{54} +(1.78078 + 3.08440i) q^{56} -2.43845i q^{57} +(-0.972638 + 0.561553i) q^{58} +(-5.12311 - 8.87348i) q^{59} +(0.842329 + 1.45896i) q^{61} +(-3.46410 - 2.00000i) q^{62} +(-3.08440 - 1.78078i) q^{63} -1.00000 q^{64} -0.561553 q^{66} +(-10.2258 - 5.90388i) q^{67} +(-2.70469 - 1.56155i) q^{68} +(-3.84233 - 6.65511i) q^{69} +(-6.28078 - 10.8786i) q^{71} +(0.866025 - 0.500000i) q^{72} -9.00000i q^{73} +(0.280776 + 0.486319i) q^{74} +(1.21922 - 2.11176i) q^{76} +2.00000i q^{77} +(-3.57071 - 0.500000i) q^{78} +15.8078 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-2.70469 + 1.56155i) q^{82} -6.56155i q^{83} +(-1.78078 - 3.08440i) q^{84} +0.438447 q^{86} +(0.972638 - 0.561553i) q^{87} +(-0.486319 - 0.280776i) q^{88} +(5.12311 - 8.87348i) q^{89} +(-1.78078 + 12.7173i) q^{91} -7.68466i q^{92} +(3.46410 + 2.00000i) q^{93} +(2.00000 - 3.46410i) q^{94} +1.00000 q^{96} +(-2.43160 + 1.40388i) q^{97} +(-4.92306 + 2.84233i) q^{98} +0.561553 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 4 q^{6} + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 - 4 * q^6 + 4 * q^9	$ 8 q + 4 q^{4} - 4 q^{6} + 4 q^{9} - 6 q^{11} + 12 q^{14} - 4 q^{16} - 18 q^{19} - 12 q^{21} + 4 q^{24} - 2 q^{26} - 12 q^{29} + 32 q^{31} - 8 q^{34} - 4 q^{36} + 2 q^{39} - 4 q^{41} - 12 q^{44} + 6 q^{46} - 2 q^{49} + 8 q^{51} + 4 q^{54} + 6 q^{56} - 8 q^{59} - 18 q^{61} - 8 q^{64} + 12 q^{66} - 6 q^{69} - 42 q^{71} - 6 q^{74} + 18 q^{76} + 44 q^{79} - 4 q^{81} - 6 q^{84} + 20 q^{86} + 8 q^{89} - 6 q^{91} + 16 q^{94} + 8 q^{96} - 12 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^6 + 4 * q^9 - 6 * q^11 + 12 * q^14 - 4 * q^16 - 18 * q^19 - 12 * q^21 + 4 * q^24 - 2 * q^26 - 12 * q^29 + 32 * q^31 - 8 * q^34 - 4 * q^36 + 2 * q^39 - 4 * q^41 - 12 * q^44 + 6 * q^46 - 2 * q^49 + 8 * q^51 + 4 * q^54 + 6 * q^56 - 8 * q^59 - 18 * q^61 - 8 * q^64 + 12 * q^66 - 6 * q^69 - 42 * q^71 - 6 * q^74 + 18 * q^76 + 44 * q^79 - 4 * q^81 - 6 * q^84 + 20 * q^86 + 8 * q^89 - 6 * q^91 + 16 * q^94 + 8 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−3.08440	+	1.78078i	−1.16579	+	0.673070i	−0.952685	−	0.303959i	$-0.901692\pi$
$7$	−3.08440	+	1.78078i	−1.16579	+	0.673070i	−0.213107	+	0.977029i	$0.568358\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	0.280776	−	0.486319i	0.0846573	−	0.146631i	−0.820588	−	0.571520i	$-0.806354\pi$
$11$	0.280776	−	0.486319i	0.0846573	−	0.146631i	0.905245	+	0.424890i	$0.139687\pi$
$12$			1.00000i			0.288675i
$13$	2.21837	−	2.84233i	0.615265	−	0.788320i
$13$	2.21837	−	2.84233i	0.615265	−	0.788320i
$14$	3.56155			0.951865
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.70469	+	1.56155i	−0.655983	+	0.378732i	−0.790745	−	0.612146i	$-0.790307\pi$
$17$	−2.70469	+	1.56155i	−0.655983	+	0.378732i	0.134761	+	0.990878i	$0.456973\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−1.21922	−	2.11176i	−0.279709	−	0.484470i	0.691603	−	0.722278i	$-0.256905\pi$
$19$	−1.21922	−	2.11176i	−0.279709	−	0.484470i	−0.971312	+	0.237807i	$0.923571\pi$
$20$		0			0
$21$	−3.56155			−0.777195
$22$	−0.486319	+	0.280776i	−0.103684	+	0.0598617i
$23$	−6.65511	−	3.84233i	−1.38769	−	0.801181i	−0.394632	−	0.918839i	$-0.629128\pi$
$23$	−6.65511	−	3.84233i	−1.38769	−	0.801181i	−0.993054	+	0.117658i	$0.962461\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$		0			0
$26$	−3.34233	+	1.35234i	−0.655485	+	0.265217i
$27$			1.00000i			0.192450i
$28$	−3.08440	−	1.78078i	−0.582896	−	0.336535i
$29$	0.561553	−	0.972638i	0.104278	−	0.180614i	−0.809165	−	0.587581i	$-0.800080\pi$
$29$	0.561553	−	0.972638i	0.104278	−	0.180614i	0.913443	+	0.406967i	$0.133414\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	0.486319	−	0.280776i	0.0846573	−	0.0488769i
$34$	3.12311			0.535608
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−0.486319	−	0.280776i	−0.0799504	−	0.0461594i	0.459492	−	0.888182i	$-0.348032\pi$
$37$	−0.486319	−	0.280776i	−0.0799504	−	0.0461594i	−0.539442	+	0.842023i	$0.681365\pi$
$38$			2.43845i			0.395568i
$39$	3.34233	−	1.35234i	0.535201	−	0.216548i
$40$		0			0
$41$	1.56155	−	2.70469i	0.243874	−	0.422401i	−0.717941	−	0.696104i	$-0.754915\pi$
$41$	1.56155	−	2.70469i	0.243874	−	0.422401i	0.961814	+	0.273703i	$0.0882485\pi$
$42$	3.08440	+	1.78078i	0.475933	+	0.274780i
$43$	−0.379706	+	0.219224i	−0.0579047	+	0.0334313i	−0.528673	−	0.848826i	$-0.677310\pi$
$43$	−0.379706	+	0.219224i	−0.0579047	+	0.0334313i	0.470768	+	0.882257i	$0.343977\pi$
$44$	0.561553			0.0846573
$45$		0			0
$46$	3.84233	+	6.65511i	0.566521	+	0.981242i
$47$			4.00000i			0.583460i	0.956501	+	0.291730i	$0.0942309\pi$
$47$			4.00000i			0.583460i	−0.956501	+	0.291730i	$0.905769\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	2.84233	−	4.92306i	0.406047	−	0.703294i
$50$		0			0
$51$	−3.12311			−0.437322
$52$	3.57071	+	0.500000i	0.495169	+	0.0693375i
$53$		−	4.24621i		−	0.583262i	−0.956531	−	0.291631i	$-0.905802\pi$
$53$		−	4.24621i		−	0.583262i	0.956531	−	0.291631i	$-0.0941979\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	1.78078	+	3.08440i	0.237966	+	0.412170i
$57$		−	2.43845i		−	0.322980i
$58$	−0.972638	+	0.561553i	−0.127714	+	0.0737355i
$59$	−5.12311	−	8.87348i	−0.666972	−	1.15523i	−0.978747	−	0.205073i	$-0.934257\pi$
$59$	−5.12311	−	8.87348i	−0.666972	−	1.15523i	0.311775	−	0.950156i	$-0.399076\pi$
$60$		0			0
$61$	0.842329	+	1.45896i	0.107849	+	0.186800i	0.914899	−	0.403683i	$-0.132270\pi$
$61$	0.842329	+	1.45896i	0.107849	+	0.186800i	−0.807050	+	0.590484i	$0.798937\pi$
$62$	−3.46410	−	2.00000i	−0.439941	−	0.254000i
$63$	−3.08440	−	1.78078i	−0.388597	−	0.224357i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−0.561553			−0.0691224
$67$	−10.2258	−	5.90388i	−1.24928	−	0.721274i	−0.278317	−	0.960489i	$-0.589776\pi$
$67$	−10.2258	−	5.90388i	−1.24928	−	0.721274i	−0.970967	+	0.239215i	$0.923110\pi$
$68$	−2.70469	−	1.56155i	−0.327992	−	0.189366i
$69$	−3.84233	−	6.65511i	−0.462562	−	0.801181i
$70$		0			0
$71$	−6.28078	−	10.8786i	−0.745391	−	1.29106i	−0.950012	−	0.312214i	$-0.898929\pi$
$71$	−6.28078	−	10.8786i	−0.745391	−	1.29106i	0.204621	−	0.978841i	$-0.434404\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$		−	9.00000i		−	1.05337i	−0.850060	−	0.526685i	$-0.823435\pi$
$73$		−	9.00000i		−	1.05337i	0.850060	−	0.526685i	$-0.176565\pi$
$74$	0.280776	+	0.486319i	0.0326396	+	0.0565334i
$75$		0			0
$76$	1.21922	−	2.11176i	0.139855	−	0.242235i
$77$			2.00000i			0.227921i
$78$	−3.57071	−	0.500000i	−0.404304	−	0.0566139i
$79$	15.8078			1.77851			0.889256	−	0.457409i	$-0.151223\pi$
$79$	15.8078			1.77851			0.889256	+	0.457409i	$0.151223\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.70469	+	1.56155i	−0.298683	+	0.172445i
$83$		−	6.56155i		−	0.720224i	−0.932909	−	0.360112i	$-0.882738\pi$
$83$		−	6.56155i		−	0.720224i	0.932909	−	0.360112i	$-0.117262\pi$
$84$	−1.78078	−	3.08440i	−0.194299	−	0.336535i
$85$		0			0
$86$	0.438447			0.0472790
$87$	0.972638	−	0.561553i	0.104278	−	0.0602048i
$88$	−0.486319	−	0.280776i	−0.0518418	−	0.0299309i
$89$	5.12311	−	8.87348i	0.543048	−	0.940587i	−0.455679	−	0.890144i	$-0.650603\pi$
$89$	5.12311	−	8.87348i	0.543048	−	0.940587i	0.998727	−	0.0504427i	$-0.0160632\pi$
$90$		0			0
$91$	−1.78078	+	12.7173i	−0.186676	+	1.33313i
$92$		−	7.68466i		−	0.801181i
$93$	3.46410	+	2.00000i	0.359211	+	0.207390i
$94$	2.00000	−	3.46410i	0.206284	−	0.357295i
$95$		0			0
$96$	1.00000			0.102062
$97$	−2.43160	+	1.40388i	−0.246891	+	0.142543i	−0.618340	−	0.785911i	$-0.712194\pi$
$97$	−2.43160	+	1.40388i	−0.246891	+	0.142543i	0.371449	+	0.928453i	$0.378861\pi$
$98$	−4.92306	+	2.84233i	−0.497304	+	0.287119i
$99$	0.561553			0.0564382
$100$		0			0
$101$	3.12311	−	5.40938i	0.310761	−	0.538253i	−0.667767	−	0.744371i	$-0.732750\pi$
$101$	3.12311	−	5.40938i	0.310761	−	0.538253i	0.978527	+	0.206118i	$0.0660829\pi$
$102$	2.70469	+	1.56155i	0.267804	+	0.154617i
$103$			4.43845i			0.437333i	0.975800	+	0.218667i	$0.0701707\pi$
$103$			4.43845i			0.437333i	−0.975800	+	0.218667i	$0.929829\pi$
$104$	−2.84233	−	2.21837i	−0.278713	−	0.217529i
$105$		0			0
$106$	−2.12311	+	3.67733i	−0.206214	+	0.357174i
$107$	−4.64996	−	2.68466i	−0.449529	−	0.259536i	0.258102	−	0.966118i	$-0.416903\pi$
$107$	−4.64996	−	2.68466i	−0.449529	−	0.259536i	−0.707631	+	0.706582i	$0.750236\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	2.80776			0.268935			0.134468	−	0.990918i	$-0.457068\pi$
$109$	2.80776			0.268935			0.134468	+	0.990918i	$0.457068\pi$
$110$		0			0
$111$	−0.280776	−	0.486319i	−0.0266501	−	0.0461594i
$112$		−	3.56155i		−	0.336535i
$113$	−3.46410	+	2.00000i	−0.325875	+	0.188144i	−0.654008	−	0.756487i	$-0.726914\pi$
$113$	−3.46410	+	2.00000i	−0.325875	+	0.188144i	0.328133	+	0.944632i	$0.393581\pi$
$114$	−1.21922	+	2.11176i	−0.114191	+	0.197784i
$115$		0			0
$116$	1.12311			0.104278
$117$	3.57071	+	0.500000i	0.330113	+	0.0462250i
$118$			10.2462i			0.943240i
$119$	5.56155	−	9.63289i	0.509827	−	0.883046i
$120$		0			0
$121$	5.34233	+	9.25319i	0.485666	+	0.841199i
$122$		−	1.68466i		−	0.152522i
$123$	2.70469	−	1.56155i	0.243874	−	0.140800i
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$		0			0
$126$	1.78078	+	3.08440i	0.158644	+	0.274780i
$127$	−18.8861	−	10.9039i	−1.67587	−	0.967563i	−0.964249	−	0.264998i	$-0.914629\pi$
$127$	−18.8861	−	10.9039i	−1.67587	−	0.967563i	−0.711619	−	0.702565i	$-0.752038\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−0.438447			−0.0386031
$130$		0			0
$131$	0.876894			0.0766146			0.0383073	−	0.999266i	$-0.487803\pi$
$131$	0.876894			0.0766146			0.0383073	+	0.999266i	$0.487803\pi$
$132$	0.486319	+	0.280776i	0.0423286	+	0.0244384i
$133$	7.52113	+	4.34233i	0.652165	+	0.376528i
$134$	5.90388	+	10.2258i	0.510018	+	0.883377i
$135$		0			0
$136$	1.56155	+	2.70469i	0.133902	+	0.231925i
$137$	14.2829	−	8.24621i	1.22027	−	0.704521i	0.255292	−	0.966864i	$-0.417828\pi$
$137$	14.2829	−	8.24621i	1.22027	−	0.704521i	0.964975	+	0.262343i	$0.0844951\pi$
$138$			7.68466i			0.654162i
$139$	10.7808	+	18.6729i	0.914414	+	1.58381i	0.807758	+	0.589515i	$0.200681\pi$
$139$	10.7808	+	18.6729i	0.914414	+	1.58381i	0.106656	+	0.994296i	$0.465986\pi$
$140$		0			0
$141$	−2.00000	+	3.46410i	−0.168430	+	0.291730i
$142$			12.5616i			1.05414i
$143$	−0.759413	−	1.87689i	−0.0635053	−	0.156954i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	−4.50000	+	7.79423i	−0.372423	+	0.645055i
$147$	4.92306	−	2.84233i	0.406047	−	0.234431i
$148$		−	0.561553i		−	0.0461594i
$149$	−5.12311	−	8.87348i	−0.419701	−	0.726944i	0.576208	−	0.817303i	$-0.304532\pi$
$149$	−5.12311	−	8.87348i	−0.419701	−	0.726944i	−0.995909	+	0.0903593i	$0.971198\pi$
$150$		0			0
$151$	−16.6847			−1.35778			−0.678889	−	0.734241i	$-0.737538\pi$
$151$	−16.6847			−1.35778			−0.678889	+	0.734241i	$0.737538\pi$
$152$	−2.11176	+	1.21922i	−0.171286	+	0.0988921i
$153$	−2.70469	−	1.56155i	−0.218661	−	0.126244i
$154$	1.00000	−	1.73205i	0.0805823	−	0.139573i
$155$		0			0
$156$	2.84233	+	2.21837i	0.227568	+	0.177612i
$157$			17.2462i			1.37640i	0.725522	+	0.688199i	$0.241598\pi$
$157$			17.2462i			1.37640i	−0.725522	+	0.688199i	$0.758402\pi$
$158$	−13.6899	−	7.90388i	−1.08911	−	0.628799i
$159$	2.12311	−	3.67733i	0.168373	−	0.291631i
$160$		0			0
$161$	27.3693			2.15700
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	14.2829	−	8.24621i	1.11872	−	0.645893i	0.177646	−	0.984094i	$-0.443152\pi$
$163$	14.2829	−	8.24621i	1.11872	−	0.645893i	0.941074	+	0.338201i	$0.109818\pi$
$164$	3.12311			0.243874
$165$		0			0
$166$	−3.28078	+	5.68247i	−0.254638	+	0.441045i
$167$	−20.5115	−	11.8423i	−1.58723	−	0.916387i	−0.993761	−	0.111529i	$-0.964425\pi$
$167$	−20.5115	−	11.8423i	−1.58723	−	0.916387i	−0.593468	−	0.804858i	$-0.702241\pi$
$168$			3.56155i			0.274780i
$169$	−3.15767	−	12.6107i	−0.242898	−	0.970052i
$170$		0			0
$171$	1.21922	−	2.11176i	0.0932364	−	0.161490i
$172$	−0.379706	−	0.219224i	−0.0289523	−	0.0167156i
$173$	7.68762	−	4.43845i	0.584479	−	0.337449i	−0.178433	−	0.983952i	$-0.557103\pi$
$173$	7.68762	−	4.43845i	0.584479	−	0.337449i	0.762911	+	0.646503i	$0.223769\pi$
$174$	−1.12311			−0.0851424
$175$		0			0
$176$	0.280776	+	0.486319i	0.0211643	+	0.0366577i
$177$		−	10.2462i		−	0.770152i
$178$	−8.87348	+	5.12311i	−0.665095	+	0.383993i
$179$	−7.84233	+	13.5833i	−0.586163	+	1.01526i	0.408566	+	0.912729i	$0.366029\pi$
$179$	−7.84233	+	13.5833i	−0.586163	+	1.01526i	−0.994729	+	0.102536i	$0.967304\pi$
$180$		0			0
$181$	−15.4924			−1.15154			−0.575771	−	0.817611i	$-0.695298\pi$
$181$	−15.4924			−1.15154			−0.575771	+	0.817611i	$0.695298\pi$
$182$	7.90084	−	10.1231i	0.585649	−	0.750375i
$183$			1.68466i			0.124534i
$184$	−3.84233	+	6.65511i	−0.283260	+	0.490621i
$185$		0			0
$186$	−2.00000	−	3.46410i	−0.146647	−	0.254000i
$187$			1.75379i			0.128250i
$188$	−3.46410	+	2.00000i	−0.252646	+	0.145865i
$189$	−1.78078	−	3.08440i	−0.129532	−	0.224357i
$190$		0			0
$191$	−7.96543	−	13.7965i	−0.576359	−	0.998282i	−0.995893	−	0.0905428i	$-0.971140\pi$
$191$	−7.96543	−	13.7965i	−0.576359	−	0.998282i	0.419534	−	0.907740i	$-0.362194\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	2.59808	+	1.50000i	0.187014	+	0.107972i	0.590584	−	0.806976i	$-0.298898\pi$
$193$	2.59808	+	1.50000i	0.187014	+	0.107972i	−0.403570	+	0.914949i	$0.632231\pi$
$194$	2.80776			0.201586
$195$		0			0
$196$	5.68466			0.406047
$197$	−4.43674	−	2.56155i	−0.316105	−	0.182503i	0.333550	−	0.942732i	$-0.391753\pi$
$197$	−4.43674	−	2.56155i	−0.316105	−	0.182503i	−0.649655	+	0.760229i	$0.725087\pi$
$198$	−0.486319	−	0.280776i	−0.0345612	−	0.0199539i
$199$	−2.21922	−	3.84381i	−0.157317	−	0.272480i	0.776584	−	0.630014i	$-0.216951\pi$
$199$	−2.21922	−	3.84381i	−0.157317	−	0.272480i	−0.933900	+	0.357534i	$0.883618\pi$
$200$		0			0
$201$	−5.90388	−	10.2258i	−0.416428	−	0.721274i
$202$	−5.40938	+	3.12311i	−0.380602	+	0.219741i
$203$			4.00000i			0.280745i
$204$	−1.56155	−	2.70469i	−0.109331	−	0.189366i
$205$		0			0
$206$	2.21922	−	3.84381i	0.154621	−	0.267811i
$207$		−	7.68466i		−	0.534121i
$208$	1.35234	+	3.34233i	0.0937682	+	0.231749i
$209$	−1.36932			−0.0947176
$210$		0			0
$211$	−0.561553	+	0.972638i	−0.0386589	+	0.0669592i	−0.884707	−	0.466147i	$-0.845642\pi$
$211$	−0.561553	+	0.972638i	−0.0386589	+	0.0669592i	0.846049	+	0.533106i	$0.178975\pi$
$212$	3.67733	−	2.12311i	0.252560	−	0.145815i
$213$		−	12.5616i		−	0.860703i
$214$	2.68466	+	4.64996i	0.183519	+	0.317865i
$215$		0			0
$216$	1.00000			0.0680414
$217$	−12.3376	+	7.12311i	−0.837530	+	0.483548i
$218$	−2.43160	−	1.40388i	−0.164688	−	0.0950829i
$219$	4.50000	−	7.79423i	0.304082	−	0.526685i
$220$		0			0
$221$	−1.56155	+	11.1517i	−0.105041	+	0.750146i
$222$			0.561553i			0.0376890i
$223$	−0.379706	−	0.219224i	−0.0254270	−	0.0146803i	0.487233	−	0.873272i	$-0.338006\pi$
$223$	−0.379706	−	0.219224i	−0.0254270	−	0.0146803i	−0.512660	+	0.858592i	$0.671340\pi$
$224$	−1.78078	+	3.08440i	−0.118983	+	0.206085i
$225$		0			0
$226$	4.00000			0.266076
$227$	25.7077	−	14.8423i	1.70628	−	0.985120i	0.767205	−	0.641402i	$-0.221647\pi$
$227$	25.7077	−	14.8423i	1.70628	−	0.985120i	0.939073	−	0.343718i	$-0.111686\pi$
$228$	2.11176	−	1.21922i	0.139855	−	0.0807451i
$229$	−9.49242			−0.627277			−0.313638	−	0.949542i	$-0.601548\pi$
$229$	−9.49242			−0.627277			−0.313638	+	0.949542i	$0.601548\pi$
$230$		0			0
$231$	−1.00000	+	1.73205i	−0.0657952	+	0.113961i
$232$	−0.972638	−	0.561553i	−0.0638568	−	0.0368677i
$233$			25.3693i			1.66200i	0.556273	+	0.831000i	$0.312231\pi$
$233$			25.3693i			1.66200i	−0.556273	+	0.831000i	$0.687769\pi$
$234$	−2.84233	−	2.21837i	−0.185809	−	0.145019i
$235$		0			0
$236$	5.12311	−	8.87348i	0.333486	−	0.577614i
$237$	13.6899	+	7.90388i	0.889256	+	0.513412i
$238$	−9.63289	+	5.56155i	−0.624408	+	0.360502i
$239$	−27.0540			−1.74998			−0.874988	−	0.484144i	$-0.839131\pi$
$239$	−27.0540			−1.74998			−0.874988	+	0.484144i	$0.839131\pi$
$240$		0			0
$241$	−7.78078	−	13.4767i	−0.501204	−	0.868111i	−0.999999	−	0.00139067i	$-0.999557\pi$
$241$	−7.78078	−	13.4767i	−0.501204	−	0.868111i	0.498795	−	0.866720i	$-0.333776\pi$
$242$		−	10.6847i		−	0.686836i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−0.842329	+	1.45896i	−0.0539246	+	0.0934002i
$245$		0			0
$246$	−3.12311			−0.199122
$247$	−8.70700	−	1.21922i	−0.554013	−	0.0775773i
$248$		−	4.00000i		−	0.254000i
$249$	3.28078	−	5.68247i	0.207911	−	0.360112i
$250$		0			0
$251$	−11.9654	−	20.7247i	−0.755252	−	1.30813i	−0.945249	−	0.326350i	$-0.894181\pi$
$251$	−11.9654	−	20.7247i	−0.755252	−	1.30813i	0.189998	−	0.981785i	$-0.439152\pi$
$252$		−	3.56155i		−	0.224357i
$253$	−3.73720	+	2.15767i	−0.234955	+	0.135652i
$254$	10.9039	+	18.8861i	0.684170	+	1.18502i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.7914	+	6.80776i	0.735527	+	0.424657i	0.820441	−	0.571732i	$-0.193728\pi$
$257$	11.7914	+	6.80776i	0.735527	+	0.424657i	−0.0849138	+	0.996388i	$0.527061\pi$
$258$	0.379706	+	0.219224i	0.0236395	+	0.0136483i
$259$	2.00000			0.124274
$260$		0			0
$261$	1.12311			0.0695185
$262$	−0.759413	−	0.438447i	−0.0469167	−	0.0270874i
$263$	5.46925	+	3.15767i	0.337248	+	0.194710i	0.659054	−	0.752095i	$-0.270957\pi$
$263$	5.46925	+	3.15767i	0.337248	+	0.194710i	−0.321806	+	0.946806i	$0.604290\pi$
$264$	−0.280776	−	0.486319i	−0.0172806	−	0.0299309i
$265$		0			0
$266$	−4.34233	−	7.52113i	−0.266245	−	0.461150i
$267$	8.87348	−	5.12311i	0.543048	−	0.313529i
$268$		−	11.8078i		−	0.721274i
$269$	−1.68466	−	2.91791i	−0.102715	−	0.177908i	0.810087	−	0.586310i	$-0.199420\pi$
$269$	−1.68466	−	2.91791i	−0.102715	−	0.177908i	−0.912803	+	0.408401i	$0.866086\pi$
$270$		0			0
$271$	−4.46543	+	7.73436i	−0.271256	+	0.469829i	−0.969184	−	0.246339i	$-0.920772\pi$
$271$	−4.46543	+	7.73436i	−0.271256	+	0.469829i	0.697928	+	0.716168i	$0.254106\pi$
$272$		−	3.12311i		−	0.189366i
$273$	−7.90084	+	10.1231i	−0.478181	+	0.612678i
$274$	−16.4924			−0.996344
$275$		0			0
$276$	3.84233	−	6.65511i	0.231281	−	0.400591i
$277$	4.33013	−	2.50000i	0.260172	−	0.150210i	−0.364241	−	0.931305i	$-0.618672\pi$
$277$	4.33013	−	2.50000i	0.260172	−	0.150210i	0.624413	+	0.781094i	$0.285338\pi$
$278$		−	21.5616i		−	1.29318i
$279$	2.00000	+	3.46410i	0.119737	+	0.207390i
$280$		0			0
$281$	−1.75379			−0.104622			−0.0523111	−	0.998631i	$-0.516659\pi$
$281$	−1.75379			−0.104622			−0.0523111	+	0.998631i	$0.516659\pi$
$282$	3.46410	−	2.00000i	0.206284	−	0.119098i
$283$	25.6478	+	14.8078i	1.52460	+	0.880230i	0.999575	+	0.0291454i	$0.00927859\pi$
$283$	25.6478	+	14.8078i	1.52460	+	0.880230i	0.525028	+	0.851085i	$0.324055\pi$
$284$	6.28078	−	10.8786i	0.372696	−	0.645528i
$285$		0			0
$286$	−0.280776	+	2.00514i	−0.0166027	+	0.118567i
$287$			11.1231i			0.656576i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	−3.62311	+	6.27540i	−0.213124	+	0.369141i
$290$		0			0
$291$	−2.80776			−0.164594
$292$	7.79423	−	4.50000i	0.456123	−	0.263343i
$293$	−17.5337	+	10.1231i	−1.02433	+	0.591398i	−0.915356	−	0.402646i	$-0.868090\pi$
$293$	−17.5337	+	10.1231i	−1.02433	+	0.591398i	−0.108976	+	0.994044i	$0.534757\pi$
$294$	−5.68466			−0.331536
$295$		0			0
$296$	−0.280776	+	0.486319i	−0.0163198	+	0.0282667i
$297$	0.486319	+	0.280776i	0.0282191	+	0.0162923i
$298$			10.2462i			0.593547i
$299$	−25.6847	+	10.3923i	−1.48538	+	0.601003i
$300$		0			0
$301$	0.780776	−	1.35234i	0.0450032	−	0.0779478i
$302$	14.4493	+	8.34233i	0.831466	+	0.480047i
$303$	5.40938	−	3.12311i	0.310761	−	0.179418i
$304$	2.43845			0.139855
$305$		0			0
$306$	1.56155	+	2.70469i	0.0892680	+	0.154617i
$307$			22.2462i			1.26966i	0.772653	+	0.634829i	$0.218930\pi$
$307$			22.2462i			1.26966i	−0.772653	+	0.634829i	$0.781070\pi$
$308$	−1.73205	+	1.00000i	−0.0986928	+	0.0569803i
$309$	−2.21922	+	3.84381i	−0.126247	+	0.218667i
$310$		0			0
$311$	−10.3153			−0.584929			−0.292465	−	0.956276i	$-0.594475\pi$
$311$	−10.3153			−0.584929			−0.292465	+	0.956276i	$0.594475\pi$
$312$	−1.35234	−	3.34233i	−0.0765614	−	0.189222i
$313$		−	31.0000i		−	1.75222i	−0.482108	−	0.876112i	$-0.660129\pi$
$313$		−	31.0000i		−	1.75222i	0.482108	−	0.876112i	$-0.339871\pi$
$314$	8.62311	−	14.9357i	0.486630	−	0.842868i
$315$		0			0
$316$	7.90388	+	13.6899i	0.444628	+	0.770118i
$317$			16.2462i			0.912478i	0.889857	+	0.456239i	$0.150804\pi$
$317$			16.2462i			0.912478i	−0.889857	+	0.456239i	$0.849196\pi$
$318$	−3.67733	+	2.12311i	−0.206214	+	0.119058i
$319$	−0.315342	−	0.546188i	−0.0176557	−	0.0305806i
$320$		0			0
$321$	−2.68466	−	4.64996i	−0.149843	−	0.259536i
$322$	−23.7025	−	13.6847i	−1.32089	−	0.762616i
$323$	6.59524	+	3.80776i	0.366969	+	0.211870i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−16.4924			−0.913431
$327$	2.43160	+	1.40388i	0.134468	+	0.0776349i
$328$	−2.70469	−	1.56155i	−0.149341	−	0.0862223i
$329$	−7.12311	−	12.3376i	−0.392710	−	0.680193i
$330$		0			0
$331$	8.34233	+	14.4493i	0.458536	+	0.794207i	0.998884	−	0.0472342i	$-0.0150407\pi$
$331$	8.34233	+	14.4493i	0.458536	+	0.794207i	−0.540348	+	0.841442i	$0.681707\pi$
$332$	5.68247	−	3.28078i	0.311866	−	0.180056i
$333$		−	0.561553i		−	0.0307729i
$334$	11.8423	+	20.5115i	0.647983	+	1.12234i
$335$		0			0
$336$	1.78078	−	3.08440i	0.0971493	−	0.168268i
$337$			8.05398i			0.438728i	0.975643	+	0.219364i	$0.0703982\pi$
$337$			8.05398i			0.438728i	−0.975643	+	0.219364i	$0.929602\pi$
$338$	−3.57071	+	12.5000i	−0.194221	+	0.679910i
$339$	−4.00000			−0.217250
$340$		0			0
$341$	1.12311	−	1.94528i	0.0608196	−	0.105343i
$342$	−2.11176	+	1.21922i	−0.114191	+	0.0659281i
$343$		−	4.68466i		−	0.252948i
$344$	0.219224	+	0.379706i	0.0118197	+	0.0204724i
$345$		0			0
$346$	−8.87689			−0.477225
$347$	−21.4842	+	12.4039i	−1.15333	+	0.665875i	−0.949696	−	0.313172i	$-0.898608\pi$
$347$	−21.4842	+	12.4039i	−1.15333	+	0.665875i	−0.203633	+	0.979047i	$0.565275\pi$
$348$	0.972638	+	0.561553i	0.0521389	+	0.0301024i
$349$	−9.62311	+	16.6677i	−0.515113	+	0.892202i	0.484733	+	0.874662i	$0.338917\pi$
$349$	−9.62311	+	16.6677i	−0.515113	+	0.892202i	−0.999846	+	0.0175398i	$0.994417\pi$
$350$		0			0
$351$	2.84233	+	2.21837i	0.151712	+	0.118408i
$352$		−	0.561553i		−	0.0299309i
$353$	1.94528	+	1.12311i	0.103537	+	0.0597769i	0.550874	−	0.834588i	$-0.314294\pi$
$353$	1.94528	+	1.12311i	0.103537	+	0.0597769i	−0.447338	+	0.894365i	$0.647628\pi$
$354$	−5.12311	+	8.87348i	−0.272290	+	0.471620i
$355$		0			0
$356$	10.2462			0.543048
$357$	9.63289	−	5.56155i	0.509827	−	0.294349i
$358$	13.5833	−	7.84233i	0.717900	−	0.414480i
$359$	4.87689			0.257393			0.128696	−	0.991684i	$-0.458921\pi$
$359$	4.87689			0.257393			0.128696	+	0.991684i	$0.458921\pi$
$360$		0			0
$361$	6.52699	−	11.3051i	0.343526	−	0.595004i
$362$	13.4168	+	7.74621i	0.705173	+	0.407132i
$363$			10.6847i			0.560799i
$364$	−11.9039	+	4.81645i	−0.623933	+	0.252450i
$365$		0			0
$366$	0.842329	−	1.45896i	0.0440293	−	0.0762609i
$367$	8.82674	+	5.09612i	0.460752	+	0.266015i	0.712360	−	0.701814i	$-0.247626\pi$
$367$	8.82674	+	5.09612i	0.460752	+	0.266015i	−0.251609	+	0.967829i	$0.580960\pi$
$368$	6.65511	−	3.84233i	0.346922	−	0.200295i
$369$	3.12311			0.162582
$370$		0			0
$371$	7.56155	+	13.0970i	0.392576	+	0.679962i
$372$			4.00000i			0.207390i
$373$	8.22068	−	4.74621i	0.425651	−	0.245750i	−0.271841	−	0.962342i	$-0.587633\pi$
$373$	8.22068	−	4.74621i	0.425651	−	0.245750i	0.697492	+	0.716593i	$0.254299\pi$
$374$	0.876894	−	1.51883i	0.0453431	−	0.0785366i
$375$		0			0
$376$	4.00000			0.206284
$377$	−1.51883	−	3.75379i	−0.0782235	−	0.193330i
$378$			3.56155i			0.183187i
$379$	−12.0270	+	20.8314i	−0.617785	+	1.07003i	0.372104	+	0.928191i	$0.378636\pi$
$379$	−12.0270	+	20.8314i	−0.617785	+	1.07003i	−0.989889	+	0.141844i	$0.954697\pi$
$380$		0			0
$381$	−10.9039	−	18.8861i	−0.558623	−	0.967563i
$382$			15.9309i			0.815094i
$383$	4.70983	−	2.71922i	0.240661	−	0.138946i	−0.374819	−	0.927098i	$-0.622295\pi$
$383$	4.70983	−	2.71922i	0.240661	−	0.138946i	0.615481	+	0.788152i	$0.288962\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$		0			0
$386$	−1.50000	−	2.59808i	−0.0763480	−	0.132239i
$387$	−0.379706	−	0.219224i	−0.0193016	−	0.0111438i
$388$	−2.43160	−	1.40388i	−0.123446	−	0.0712713i
$389$	−11.3693			−0.576447			−0.288224	−	0.957563i	$-0.593065\pi$
$389$	−11.3693			−0.576447			−0.288224	+	0.957563i	$0.593065\pi$
$390$		0			0
$391$	24.0000			1.21373
$392$	−4.92306	−	2.84233i	−0.248652	−	0.143559i
$393$	0.759413	+	0.438447i	0.0383073	+	0.0221167i
$394$	2.56155	+	4.43674i	0.129049	+	0.223520i
$395$		0			0
$396$	0.280776	+	0.486319i	0.0141095	+	0.0244384i
$397$	−8.49377	+	4.90388i	−0.426290	+	0.246119i	−0.697765	−	0.716327i	$-0.745822\pi$
$397$	−8.49377	+	4.90388i	−0.426290	+	0.246119i	0.271475	+	0.962446i	$0.412489\pi$
$398$			4.43845i			0.222479i
$399$	4.34233	+	7.52113i	0.217388	+	0.376528i
$400$		0			0
$401$	6.31534	−	10.9385i	0.315373	−	0.546242i	−0.664144	−	0.747605i	$-0.731204\pi$
$401$	6.31534	−	10.9385i	0.315373	−	0.546242i	0.979517	+	0.201363i	$0.0645370\pi$
$402$			11.8078i			0.588918i
$403$	8.87348	−	11.3693i	0.442019	−	0.566346i
$404$	6.24621			0.310761
$405$		0			0
$406$	2.00000	−	3.46410i	0.0992583	−	0.171920i
$407$	−0.273094	+	0.157671i	−0.0135368	+	0.00781545i
$408$			3.12311i			0.154617i
$409$	8.12311	+	14.0696i	0.401662	+	0.695699i	0.993927	−	0.110045i	$-0.0350994\pi$
$409$	8.12311	+	14.0696i	0.401662	+	0.695699i	−0.592265	+	0.805743i	$0.701766\pi$
$410$		0			0
$411$	16.4924			0.813511
$412$	−3.84381	+	2.21922i	−0.189371	+	0.109333i
$413$	31.6034	+	18.2462i	1.55510	+	0.897837i
$414$	−3.84233	+	6.65511i	−0.188840	+	0.327081i
$415$		0			0
$416$	0.500000	−	3.57071i	0.0245145	−	0.175069i
$417$			21.5616i			1.05587i
$418$	1.18586	+	0.684658i	0.0580025	+	0.0334877i
$419$	−5.96543	+	10.3324i	−0.291431	+	0.504773i	−0.974148	−	0.225910i	$-0.927465\pi$
$419$	−5.96543	+	10.3324i	−0.291431	+	0.504773i	0.682718	+	0.730682i	$0.260798\pi$
$420$		0			0
$421$	31.2462			1.52285			0.761424	−	0.648255i	$-0.224501\pi$
$421$	31.2462			1.52285			0.761424	+	0.648255i	$0.224501\pi$
$422$	0.972638	−	0.561553i	0.0473473	−	0.0273360i
$423$	−3.46410	+	2.00000i	−0.168430	+	0.0972433i
$424$	−4.24621			−0.206214
$425$		0			0
$426$	−6.28078	+	10.8786i	−0.304305	+	0.527071i
$427$	−5.19615	−	3.00000i	−0.251459	−	0.145180i
$428$		−	5.36932i		−	0.259536i
$429$	0.280776	−	2.00514i	0.0135560	−	0.0968093i
$430$		0			0
$431$	−9.15767	+	15.8616i	−0.441109	+	0.764024i	−0.997772	−	0.0667146i	$-0.978748\pi$
$431$	−9.15767	+	15.8616i	−0.441109	+	0.764024i	0.556663	+	0.830739i	$0.312082\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	11.8513	−	6.84233i	0.569535	−	0.328821i	−0.187428	−	0.982278i	$-0.560015\pi$
$433$	11.8513	−	6.84233i	0.569535	−	0.328821i	0.756964	+	0.653457i	$0.226682\pi$
$434$	14.2462			0.683840
$435$		0			0
$436$	1.40388	+	2.43160i	0.0672338	+	0.116452i
$437$			18.7386i			0.896390i
$438$	−7.79423	+	4.50000i	−0.372423	+	0.215018i
$439$	−3.46543	+	6.00231i	−0.165396	+	0.286475i	−0.936796	−	0.349876i	$-0.886224\pi$
$439$	−3.46543	+	6.00231i	−0.165396	+	0.286475i	0.771400	+	0.636351i	$0.219557\pi$
$440$		0			0
$441$	5.68466			0.270698
$442$	6.92820	−	8.87689i	0.329541	−	0.422231i
$443$			2.80776i			0.133401i	0.997773	+	0.0667004i	$0.0212472\pi$
$443$			2.80776i			0.133401i	−0.997773	+	0.0667004i	$0.978753\pi$
$444$	0.280776	−	0.486319i	0.0133251	−	0.0230797i
$445$		0			0
$446$	0.219224	+	0.379706i	0.0103805	+	0.0179796i
$447$		−	10.2462i		−	0.484629i
$448$	3.08440	−	1.78078i	0.145724	−	0.0841338i
$449$	−1.56155	−	2.70469i	−0.0736942	−	0.127642i	0.826823	−	0.562462i	$-0.190146\pi$
$449$	−1.56155	−	2.70469i	−0.0736942	−	0.127642i	−0.900518	+	0.434819i	$0.856812\pi$
$450$		0			0
$451$	−0.876894	−	1.51883i	−0.0412913	−	0.0715187i
$452$	−3.46410	−	2.00000i	−0.162938	−	0.0940721i
$453$	−14.4493	−	8.34233i	−0.678889	−	0.391957i
$454$	−29.6847			−1.39317
$455$		0			0
$456$	−2.43845			−0.114191
$457$	−3.90368	−	2.25379i	−0.182606	−	0.105428i	0.405910	−	0.913913i	$-0.366955\pi$
$457$	−3.90368	−	2.25379i	−0.182606	−	0.105428i	−0.588517	+	0.808485i	$0.700288\pi$
$458$	8.22068	+	4.74621i	0.384127	+	0.221776i
$459$	−1.56155	−	2.70469i	−0.0728870	−	0.126244i
$460$		0			0
$461$	−5.31534	−	9.20644i	−0.247560	−	0.428787i	0.715288	−	0.698830i	$-0.246295\pi$
$461$	−5.31534	−	9.20644i	−0.247560	−	0.428787i	−0.962848	+	0.270043i	$0.912962\pi$
$462$	1.73205	−	1.00000i	0.0805823	−	0.0465242i
$463$		−	27.8078i		−	1.29234i	−0.763195	−	0.646168i	$-0.776370\pi$
$463$		−	27.8078i		−	1.29234i	0.763195	−	0.646168i	$-0.223630\pi$
$464$	0.561553	+	0.972638i	0.0260694	+	0.0451536i
$465$		0			0
$466$	12.6847	−	21.9705i	0.587605	−	1.01776i
$467$		−	3.43845i		−	0.159112i	−0.996830	−	0.0795562i	$-0.974650\pi$
$467$		−	3.43845i		−	0.159112i	0.996830	−	0.0795562i	$-0.0253503\pi$
$468$	1.35234	+	3.34233i	0.0625121	+	0.154499i
$469$	42.0540			1.94187
$470$		0			0
$471$	−8.62311	+	14.9357i	−0.397332	+	0.688199i
$472$	−8.87348	+	5.12311i	−0.408435	+	0.235810i
$473$			0.246211i			0.0113208i
$474$	−7.90388	−	13.6899i	−0.363037	−	0.628799i
$475$		0			0
$476$	11.1231			0.509827
$477$	3.67733	−	2.12311i	0.168373	−	0.0972103i
$478$	23.4294	+	13.5270i	1.07164	+	0.618710i
$479$	−5.80776	+	10.0593i	−0.265364	+	0.459623i	−0.967659	−	0.252263i	$-0.918825\pi$
$479$	−5.80776	+	10.0593i	−0.265364	+	0.459623i	0.702295	+	0.711886i	$0.252159\pi$
$480$		0			0
$481$	−1.87689	+	0.759413i	−0.0855790	+	0.0346262i
$482$			15.5616i			0.708809i
$483$	23.7025	+	13.6847i	1.07850	+	0.622674i
$484$	−5.34233	+	9.25319i	−0.242833	+	0.420599i
$485$		0			0
$486$	1.00000			0.0453609
$487$	36.9660	−	21.3423i	1.67509	−	0.967113i	0.710372	−	0.703827i	$-0.248527\pi$
$487$	36.9660	−	21.3423i	1.67509	−	0.967113i	0.964718	−	0.263286i	$-0.0848064\pi$
$488$	1.45896	−	0.842329i	0.0660439	−	0.0381305i
$489$	16.4924			0.745813
$490$		0			0
$491$	−15.6501	+	27.1068i	−0.706279	+	1.22331i	0.259949	+	0.965622i	$0.416294\pi$
$491$	−15.6501	+	27.1068i	−0.706279	+	1.22331i	−0.966228	+	0.257689i	$0.917039\pi$
$492$	2.70469	+	1.56155i	0.121937	+	0.0704002i
$493$			3.50758i			0.157973i
$494$	6.93087	+	5.40938i	0.311835	+	0.243379i
$495$		0			0
$496$	−2.00000	+	3.46410i	−0.0898027	+	0.155543i
$497$	38.7448	+	22.3693i	1.73794	+	1.00340i
$498$	−5.68247	+	3.28078i	−0.254638	+	0.147015i
$499$	−6.05398			−0.271013			−0.135507	−	0.990776i	$-0.543266\pi$
$499$	−6.05398			−0.271013			−0.135507	+	0.990776i	$0.543266\pi$
$500$		0			0
$501$	−11.8423	−	20.5115i	−0.529076	−	0.916387i
$502$			23.9309i			1.06809i
$503$	21.0577	−	12.1577i	0.938917	−	0.542084i	0.0492961	−	0.998784i	$-0.484302\pi$
$503$	21.0577	−	12.1577i	0.938917	−	0.542084i	0.889621	+	0.456700i	$0.150969\pi$
$504$	−1.78078	+	3.08440i	−0.0793221	+	0.137390i
$505$		0			0
$506$	4.31534			0.191840
$507$	3.57071	−	12.5000i	0.158581	−	0.555144i
$508$		−	21.8078i		−	0.967563i
$509$	−8.12311	+	14.0696i	−0.360050	+	0.623625i	−0.987969	−	0.154654i	$-0.950574\pi$
$509$	−8.12311	+	14.0696i	−0.360050	+	0.623625i	0.627918	+	0.778279i	$0.283907\pi$
$510$		0			0
$511$	16.0270	+	27.7596i	0.708992	+	1.22801i
$512$			1.00000i			0.0441942i
$513$	2.11176	−	1.21922i	0.0932364	−	0.0538300i
$514$	−6.80776	−	11.7914i	−0.300278	−	0.520096i
$515$		0			0
$516$	−0.219224	−	0.379706i	−0.00965078	−	0.0167156i
$517$	1.94528	+	1.12311i	0.0855531	+	0.0493941i
$518$	−1.73205	−	1.00000i	−0.0761019	−	0.0439375i
$519$	8.87689			0.389652
$520$		0			0
$521$	34.7386			1.52193			0.760964	−	0.648795i	$-0.224727\pi$
$521$	34.7386			1.52193			0.760964	+	0.648795i	$0.224727\pi$
$522$	−0.972638	−	0.561553i	−0.0425712	−	0.0245785i
$523$	21.5908	+	12.4654i	0.944098	+	0.545075i	0.891243	−	0.453527i	$-0.149834\pi$
$523$	21.5908	+	12.4654i	0.944098	+	0.545075i	0.0528556	+	0.998602i	$0.483168\pi$
$524$	0.438447	+	0.759413i	0.0191537	+	0.0331751i
$525$		0			0
$526$	−3.15767	−	5.46925i	−0.137681	−	0.238470i
$527$	−10.8188	+	6.24621i	−0.471272	+	0.272089i
$528$			0.561553i			0.0244384i
$529$	18.0270	+	31.2237i	0.783782	+	1.35755i
$530$		0			0
$531$	5.12311	−	8.87348i	0.222324	−	0.385076i
$532$			8.68466i			0.376528i
$533$	−4.22351	−	10.4384i	−0.182941	−	0.452139i
$534$	−10.2462			−0.443397
$535$		0			0
$536$	−5.90388	+	10.2258i	−0.255009	+	0.441688i
$537$	−13.5833	+	7.84233i	−0.586163	+	0.338421i
$538$			3.36932i			0.145262i
$539$	−1.59612	−	2.76456i	−0.0687497	−	0.119078i
$540$		0			0
$541$	−22.3153			−0.959411			−0.479706	−	0.877429i	$-0.659257\pi$
$541$	−22.3153			−0.959411			−0.479706	+	0.877429i	$0.659257\pi$
$542$	7.73436	−	4.46543i	0.332219	−	0.191807i
$543$	−13.4168	−	7.74621i	−0.575771	−	0.332422i
$544$	−1.56155	+	2.70469i	−0.0669510	+	0.115963i
$545$		0			0
$546$	11.9039	−	4.81645i	0.509439	−	0.206125i
$547$		−	30.9309i		−	1.32251i	−0.750162	−	0.661254i	$-0.770024\pi$
$547$		−	30.9309i		−	1.32251i	0.750162	−	0.661254i	$-0.229976\pi$
$548$	14.2829	+	8.24621i	0.610133	+	0.352261i
$549$	−0.842329	+	1.45896i	−0.0359497	+	0.0622668i
$550$		0			0
$551$	−2.73863			−0.116670
$552$	−6.65511	+	3.84233i	−0.283260	+	0.163540i
$553$	−48.7574	+	28.1501i	−2.07338	+	1.19706i
$554$	−5.00000			−0.212430
$555$		0			0
$556$	−10.7808	+	18.6729i	−0.457207	+	0.791905i
$557$	27.3799	+	15.8078i	1.16012	+	0.669796i	0.951333	−	0.308164i	$-0.0997147\pi$
$557$	27.3799	+	15.8078i	1.16012	+	0.669796i	0.208788	+	0.977961i	$0.433048\pi$
$558$		−	4.00000i		−	0.169334i
$559$	−0.219224	+	1.56557i	−0.00927217	+	0.0662165i
$560$		0			0
$561$	−0.876894	+	1.51883i	−0.0370225	+	0.0641249i
$562$	1.51883	+	0.876894i	0.0640678	+	0.0369896i
$563$	−18.0201	+	10.4039i	−0.759455	+	0.438471i	−0.829100	−	0.559100i	$-0.811147\pi$
$563$	−18.0201	+	10.4039i	−0.759455	+	0.438471i	0.0696453	+	0.997572i	$0.477813\pi$
$564$	−4.00000			−0.168430
$565$		0			0
$566$	−14.8078	−	25.6478i	−0.622417	−	1.07806i
$567$		−	3.56155i		−	0.149571i
$568$	−10.8786	+	6.28078i	−0.456457	+	0.263536i
$569$	−5.75379	+	9.96585i	−0.241211	+	0.417790i	−0.961060	−	0.276341i	$-0.910878\pi$
$569$	−5.75379	+	9.96585i	−0.241211	+	0.417790i	0.719848	+	0.694131i	$0.244211\pi$
$570$		0			0
$571$	21.4233			0.896537			0.448268	−	0.893899i	$-0.352041\pi$
$571$	21.4233			0.896537			0.448268	+	0.893899i	$0.352041\pi$
$572$	1.24573	−	1.59612i	0.0520867	−	0.0667370i
$573$		−	15.9309i		−	0.665522i
$574$	5.56155	−	9.63289i	0.232135	−	0.402069i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$			23.0000i			0.957503i	0.877951	+	0.478751i	$0.158910\pi$
$577$			23.0000i			0.957503i	−0.877951	+	0.478751i	$0.841090\pi$
$578$	6.27540	−	3.62311i	0.261022	−	0.150701i
$579$	1.50000	+	2.59808i	0.0623379	+	0.107972i
$580$		0			0
$581$	11.6847	+	20.2384i	0.484761	+	0.839631i
$582$	2.43160	+	1.40388i	0.100793	+	0.0581928i
$583$	−2.06501	−	1.19224i	−0.0855241	−	0.0493774i
$584$	−9.00000			−0.372423
$585$		0			0
$586$	20.2462			0.836363
$587$	15.5286	+	8.96543i	0.640933	+	0.370043i	0.784974	−	0.619529i	$-0.212676\pi$
$587$	15.5286	+	8.96543i	0.640933	+	0.370043i	−0.144041	+	0.989572i	$0.546010\pi$
$588$	4.92306	+	2.84233i	0.203024	+	0.117216i
$589$	−4.87689	−	8.44703i	−0.200949	−	0.348054i
$590$		0			0
$591$	−2.56155	−	4.43674i	−0.105368	−	0.182503i
$592$	0.486319	−	0.280776i	0.0199876	−	0.0115398i
$593$			38.9848i			1.60092i	0.599389	+	0.800458i	$0.295410\pi$
$593$			38.9848i			1.60092i	−0.599389	+	0.800458i	$0.704590\pi$
$594$	−0.280776	−	0.486319i	−0.0115204	−	0.0199539i
$595$		0			0
$596$	5.12311	−	8.87348i	0.209851	−	0.363472i
$597$		−	4.43845i		−	0.181654i
$598$	27.4397	+	3.84233i	1.12209	+	0.157125i
$599$	18.3153			0.748345			0.374172	−	0.927359i	$-0.377927\pi$
$599$	18.3153			0.748345			0.374172	+	0.927359i	$0.377927\pi$
$600$		0			0
$601$	2.90388	−	5.02967i	0.118452	−	0.205165i	−0.800703	−	0.599062i	$-0.795540\pi$
$601$	2.90388	−	5.02967i	0.118452	−	0.205165i	0.919154	+	0.393898i	$0.128874\pi$
$602$	−1.35234	+	0.780776i	−0.0551174	+	0.0318221i
$603$		−	11.8078i		−	0.480849i
$604$	−8.34233	−	14.4493i	−0.339445	−	0.587935i
$605$		0			0
$606$	−6.24621			−0.253735
$607$	−34.0948	+	19.6847i	−1.38387	+	0.798976i	−0.992615	−	0.121308i	$-0.961291\pi$
$607$	−34.0948	+	19.6847i	−1.38387	+	0.798976i	−0.391252	+	0.920284i	$0.627958\pi$
$608$	−2.11176	−	1.21922i	−0.0856431	−	0.0494460i
$609$	−2.00000	+	3.46410i	−0.0810441	+	0.140372i
$610$		0			0
$611$	11.3693	+	8.87348i	0.459953	+	0.358983i
$612$		−	3.12311i		−	0.126244i
$613$	−31.6501	−	18.2732i	−1.27834	−	0.738048i	−0.301794	−	0.953373i	$-0.597585\pi$
$613$	−31.6501	−	18.2732i	−1.27834	−	0.738048i	−0.976542	+	0.215326i	$0.930919\pi$
$614$	11.1231	−	19.2658i	0.448892	−	0.777504i
$615$		0			0
$616$	2.00000			0.0805823
$617$	41.0230	−	23.6847i	1.65153	−	0.953508i	0.675079	−	0.737745i	$-0.264109\pi$
$617$	41.0230	−	23.6847i	1.65153	−	0.953508i	0.976446	−	0.215763i	$-0.0692240\pi$
$618$	3.84381	−	2.21922i	0.154621	−	0.0892703i
$619$	12.3002			0.494386			0.247193	−	0.968966i	$-0.420492\pi$
$619$	12.3002			0.494386			0.247193	+	0.968966i	$0.420492\pi$
$620$		0			0
$621$	3.84233	−	6.65511i	0.154187	−	0.267060i
$622$	8.93335	+	5.15767i	0.358195	+	0.206804i
$623$			36.4924i			1.46204i
$624$	−0.500000	+	3.57071i	−0.0200160	+	0.142943i
$625$		0			0
$626$	−15.5000	+	26.8468i	−0.619505	+	1.07301i
$627$	−1.18586	−	0.684658i	−0.0473588	−	0.0273426i
$628$	−14.9357	+	8.62311i	−0.595998	+	0.344099i
$629$	1.75379			0.0699281
$630$		0			0
$631$	−16.4654	−	28.5190i	−0.655479	−	1.13532i	−0.981774	−	0.190054i	$-0.939134\pi$
$631$	−16.4654	−	28.5190i	−0.655479	−	1.13532i	0.326295	−	0.945268i	$-0.394200\pi$
$632$		−	15.8078i		−	0.628799i
$633$	−0.972638	+	0.561553i	−0.0386589	+	0.0223197i
$634$	8.12311	−	14.0696i	0.322610	−	0.558776i
$635$		0			0
$636$	4.24621			0.168373
$637$	−7.68762	−	19.0000i	−0.304594	−	0.752807i
$638$			0.630683i			0.0249690i
$639$	6.28078	−	10.8786i	0.248464	−	0.430352i
$640$		0			0
$641$	−19.1231	−	33.1222i	−0.755317	−	1.30825i	−0.945216	−	0.326444i	$-0.894149\pi$
$641$	−19.1231	−	33.1222i	−0.755317	−	1.30825i	0.189899	−	0.981804i	$-0.439184\pi$
$642$			5.36932i			0.211910i
$643$	−21.2578	+	12.2732i	−0.838326	+	0.484008i	−0.856695	−	0.515824i	$-0.827486\pi$
$643$	−21.2578	+	12.2732i	−0.838326	+	0.484008i	0.0183689	+	0.999831i	$0.494153\pi$
$644$	13.6847	+	23.7025i	0.539251	+	0.934010i
$645$		0			0
$646$	−3.80776	−	6.59524i	−0.149814	−	0.259486i
$647$	−28.0794	−	16.2116i	−1.10391	−	0.637346i	−0.166668	−	0.986013i	$-0.553301\pi$
$647$	−28.0794	−	16.2116i	−1.10391	−	0.637346i	−0.937247	+	0.348667i	$0.886634\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−5.75379			−0.225856
$650$		0			0
$651$	−14.2462			−0.558353
$652$	14.2829	+	8.24621i	0.559360	+	0.322947i
$653$	−32.5760	−	18.8078i	−1.27480	−	0.736005i	−0.298911	−	0.954281i	$-0.596623\pi$
$653$	−32.5760	−	18.8078i	−1.27480	−	0.736005i	−0.975887	+	0.218276i	$0.929957\pi$
$654$	−1.40388	−	2.43160i	−0.0548961	−	0.0950829i
$655$		0			0
$656$	1.56155	+	2.70469i	0.0609684	+	0.105600i
$657$	7.79423	−	4.50000i	0.304082	−	0.175562i
$658$			14.2462i			0.555375i
$659$	9.15767	+	15.8616i	0.356732	+	0.617878i	0.987413	−	0.158164i	$-0.0505575\pi$
$659$	9.15767	+	15.8616i	0.356732	+	0.617878i	−0.630681	+	0.776042i	$0.717224\pi$
$660$		0			0
$661$	24.2732	−	42.0424i	0.944118	−	1.63526i	0.186610	−	0.982434i	$-0.440250\pi$
$661$	24.2732	−	42.0424i	0.944118	−	1.63526i	0.757508	−	0.652826i	$-0.226417\pi$
$662$		−	16.6847i		−	0.648468i
$663$	−6.92820	+	8.87689i	−0.269069	+	0.344750i
$664$	−6.56155			−0.254638
$665$		0			0
$666$	−0.280776	+	0.486319i	−0.0108799	+	0.0188445i
$667$	−7.47439	+	4.31534i	−0.289410	+	0.167091i
$668$		−	23.6847i		−	0.916387i
$669$	−0.219224	−	0.379706i	−0.00847567	−	0.0146803i
$670$		0			0
$671$	0.946025			0.0365209
$672$	−3.08440	+	1.78078i	−0.118983	+	0.0686949i
$673$	24.9015	+	14.3769i	0.959883	+	0.554189i	0.896137	−	0.443778i	$-0.146362\pi$
$673$	24.9015	+	14.3769i	0.959883	+	0.554189i	0.0637458	+	0.997966i	$0.479695\pi$
$674$	4.02699	−	6.97495i	0.155114	−	0.268665i
$675$		0			0
$676$	9.34233	−	9.03996i	0.359320	−	0.347691i
$677$			11.6155i			0.446421i	0.974770	+	0.223211i	$0.0716537\pi$
$677$			11.6155i			0.446421i	−0.974770	+	0.223211i	$0.928346\pi$
$678$	3.46410	+	2.00000i	0.133038	+	0.0768095i
$679$	5.00000	−	8.66025i	0.191882	−	0.332350i
$680$		0			0
$681$	29.6847			1.13752
$682$	−1.94528	+	1.12311i	−0.0744885	+	0.0430059i
$683$	−13.3701	+	7.71922i	−0.511592	+	0.295368i	−0.733488	−	0.679703i	$-0.762109\pi$
$683$	−13.3701	+	7.71922i	−0.511592	+	0.295368i	0.221896	+	0.975070i	$0.428776\pi$
$684$	2.43845			0.0932364
$685$		0			0
$686$	−2.34233	+	4.05703i	−0.0894305	+	0.154898i
$687$	−8.22068	−	4.74621i	−0.313638	−	0.181079i
$688$		−	0.438447i		−	0.0167156i
$689$	−12.0691	−	9.41967i	−0.459797	−	0.358861i
$690$		0			0
$691$	2.41146	−	4.17677i	0.0917362	−	0.158892i	−0.816506	−	0.577338i	$-0.804092\pi$
$691$	2.41146	−	4.17677i	0.0917362	−	0.158892i	0.908242	+	0.418446i	$0.137425\pi$
$692$	7.68762	+	4.43845i	0.292239	+	0.168724i
$693$	−1.73205	+	1.00000i	−0.0657952	+	0.0379869i
$694$	24.8078			0.941690
$695$		0			0
$696$	−0.561553	−	0.972638i	−0.0212856	−	0.0368677i
$697$			9.75379i			0.369451i
$698$	16.6677	−	9.62311i	0.630882	−	0.364240i
$699$	−12.6847	+	21.9705i	−0.479778	+	0.831000i
$700$		0			0
$701$	−0.876894			−0.0331198			−0.0165599	−	0.999863i	$-0.505271\pi$
$701$	−0.876894			−0.0331198			−0.0165599	+	0.999863i	$0.505271\pi$
$702$	−1.35234	−	3.34233i	−0.0510410	−	0.126148i
$703$			1.36932i			0.0516448i
$704$	−0.280776	+	0.486319i	−0.0105822	+	0.0183288i
$705$		0			0
$706$	−1.12311	−	1.94528i	−0.0422686	−	0.0732114i
$707$			22.2462i			0.836655i
$708$	8.87348	−	5.12311i	0.333486	−	0.192538i
$709$	−14.3769	−	24.9015i	−0.539936	−	0.935196i	−0.998907	−	0.0467448i	$-0.985115\pi$
$709$	−14.3769	−	24.9015i	−0.539936	−	0.935196i	0.458971	−	0.888451i	$-0.348218\pi$
$710$		0			0
$711$	7.90388	+	13.6899i	0.296419	+	0.513412i
$712$	−8.87348	−	5.12311i	−0.332548	−	0.191997i
$713$	−26.6204	−	15.3693i	−0.996943	−	0.575585i
$714$	−11.1231			−0.416272
$715$		0			0
$716$	−15.6847			−0.586163
$717$	−23.4294	−	13.5270i	−0.874988	−	0.505175i
$718$	−4.22351	−	2.43845i	−0.157620	−	0.0910020i
$719$	−8.71922	−	15.1021i	−0.325172	−	0.563215i	0.656375	−	0.754435i	$-0.272089\pi$
$719$	−8.71922	−	15.1021i	−0.325172	−	0.563215i	−0.981547	+	0.191220i	$0.938756\pi$
$720$		0			0
$721$	−7.90388	−	13.6899i	−0.294356	−	0.509839i
$722$	−11.3051	+	6.52699i	−0.420731	+	0.242909i
$723$		−	15.5616i		−	0.578740i
$724$	−7.74621	−	13.4168i	−0.287886	−	0.498633i
$725$		0			0
$726$	5.34233	−	9.25319i	0.198272	−	0.343418i
$727$		−	50.7926i		−	1.88379i	−0.335902	−	0.941897i	$-0.609041\pi$
$727$		−	50.7926i		−	1.88379i	0.335902	−	0.941897i	$-0.390959\pi$
$728$	12.7173	+	1.78078i	0.471334	+	0.0660000i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	0.684658	−	1.18586i	0.0253230	−	0.0438607i
$732$	−1.45896	+	0.842329i	−0.0539246	+	0.0311334i
$733$			47.9848i			1.77236i	0.463340	+	0.886180i	$0.346651\pi$
$733$			47.9848i			1.77236i	−0.463340	+	0.886180i	$0.653349\pi$
$734$	−5.09612	−	8.82674i	−0.188101	−	0.325801i
$735$		0			0
$736$	−7.68466			−0.283260
$737$	−5.74234	+	3.31534i	−0.211522	+	0.122122i
$738$	−2.70469	−	1.56155i	−0.0995610	−	0.0574816i
$739$	−6.56155	+	11.3649i	−0.241371	+	0.418066i	−0.961105	−	0.276183i	$-0.910930\pi$
$739$	−6.56155	+	11.3649i	−0.241371	+	0.418066i	0.719734	+	0.694250i	$0.244264\pi$
$740$		0			0
$741$	−6.93087	−	5.40938i	−0.254612	−	0.198718i
$742$		−	15.1231i		−	0.555187i
$743$	9.63289	+	5.56155i	0.353397	+	0.204034i	0.666180	−	0.745791i	$-0.267928\pi$
$743$	9.63289	+	5.56155i	0.353397	+	0.204034i	−0.312784	+	0.949824i	$0.601261\pi$
$744$	2.00000	−	3.46410i	0.0733236	−	0.127000i
$745$		0			0
$746$	−9.49242			−0.347542
$747$	5.68247	−	3.28078i	0.207911	−	0.120037i
$748$	−1.51883	+	0.876894i	−0.0555338	+	0.0320624i
$749$	19.1231			0.698743
$750$		0			0
$751$	−25.1231	+	43.5145i	−0.916755	+	1.58787i	−0.112444	+	0.993658i	$0.535868\pi$
$751$	−25.1231	+	43.5145i	−0.916755	+	1.58787i	−0.804311	+	0.594208i	$0.797465\pi$
$752$	−3.46410	−	2.00000i	−0.126323	−	0.0729325i
$753$		−	23.9309i		−	0.872089i
$754$	−0.561553	+	4.01029i	−0.0204505	+	0.146046i
$755$		0			0
$756$	1.78078	−	3.08440i	0.0647662	−	0.112178i
$757$	26.5737	+	15.3423i	0.965837	+	0.557626i	0.897965	−	0.440068i	$-0.145046\pi$
$757$	26.5737	+	15.3423i	0.965837	+	0.557626i	0.0678727	+	0.997694i	$0.478379\pi$
$758$	20.8314	−	12.0270i	0.756629	−	0.436840i
$759$	−4.31534			−0.156637
$760$		0			0
$761$	11.4924	+	19.9055i	0.416600	+	0.721572i	0.995595	−	0.0937588i	$-0.0298882\pi$
$761$	11.4924	+	19.9055i	0.416600	+	0.721572i	−0.578995	+	0.815331i	$0.696555\pi$
$762$			21.8078i			0.790012i
$763$	−8.66025	+	5.00000i	−0.313522	+	0.181012i
$764$	7.96543	−	13.7965i	0.288179	−	0.499141i
$765$		0			0
$766$	−5.43845			−0.196499
$767$	−36.5863	−	5.12311i	−1.32105	−	0.184985i
$768$		−	1.00000i		−	0.0360844i
$769$	−4.65767	+	8.06732i	−0.167960	+	0.290915i	−0.937702	−	0.347439i	$-0.887051\pi$
$769$	−4.65767	+	8.06732i	−0.167960	+	0.290915i	0.769743	+	0.638354i	$0.220385\pi$
$770$		0			0
$771$	6.80776	+	11.7914i	0.245176	+	0.424657i
$772$			3.00000i			0.107972i
$773$	25.6478	−	14.8078i	0.922487	−	0.532598i	0.0380595	−	0.999275i	$-0.487882\pi$
$773$	25.6478	−	14.8078i	0.922487	−	0.532598i	0.884428	+	0.466677i	$0.154549\pi$
$774$	0.219224	+	0.379706i	0.00787983	+	0.0136483i
$775$		0			0
$776$	1.40388	+	2.43160i	0.0503964	+	0.0872892i
$777$	1.73205	+	1.00000i	0.0621370	+	0.0358748i
$778$	9.84612	+	5.68466i	0.353000	+	0.203805i
$779$	−7.61553			−0.272855
$780$		0			0
$781$	−7.05398			−0.252411
$782$	−20.7846	−	12.0000i	−0.743256	−	0.429119i
$783$	0.972638	+	0.561553i	0.0347592	+	0.0200683i
$784$	2.84233	+	4.92306i	0.101512	+	0.175824i
$785$		0			0
$786$	−0.438447	−	0.759413i	−0.0156389	−	0.0270874i
$787$	−10.3923	+	6.00000i	−0.370446	+	0.213877i	−0.673653	−	0.739048i	$-0.735276\pi$
$787$	−10.3923	+	6.00000i	−0.370446	+	0.213877i	0.303207	+	0.952925i	$0.401942\pi$
$788$		−	5.12311i		−	0.182503i
$789$	3.15767	+	5.46925i	0.112416	+	0.194710i
$790$		0			0
$791$	7.12311	−	12.3376i	0.253268	−	0.438674i
$792$		−	0.561553i		−	0.0199539i
$793$	6.01543	+	0.842329i	0.213614	+	0.0299120i
$794$	9.80776			0.348065
$795$		0			0
$796$	2.21922	−	3.84381i	0.0786583	−	0.136240i
$797$	−22.7299	+	13.1231i	−0.805134	+	0.464844i	−0.845263	−	0.534350i	$-0.820556\pi$
$797$	−22.7299	+	13.1231i	−0.805134	+	0.464844i	0.0401293	+	0.999194i	$0.487223\pi$
$798$		−	8.68466i		−	0.307434i
$799$	−6.24621	−	10.8188i	−0.220975	−	0.382740i
$800$		0			0
$801$	10.2462			0.362032
$802$	−10.9385	+	6.31534i	−0.386252	+	0.223002i
$803$	−4.37687	−	2.52699i	−0.154456	−	0.0891755i
$804$	5.90388	−	10.2258i	0.208214	−	0.360637i
$805$		0			0
$806$	−13.3693	+	5.40938i	−0.470914	+	0.190537i
$807$		−	3.36932i		−	0.118606i
$808$	−5.40938	−	3.12311i	−0.190301	−	0.109870i
$809$	15.8078	−	27.3799i	0.555771	−	0.962624i	−0.442072	−	0.896980i	$-0.645756\pi$
$809$	15.8078	−	27.3799i	0.555771	−	0.962624i	0.997843	−	0.0656446i	$-0.0209103\pi$
$810$		0			0
$811$	−16.9309			−0.594523			−0.297262	−	0.954796i	$-0.596073\pi$
$811$	−16.9309			−0.594523			−0.297262	+	0.954796i	$0.596073\pi$
$812$	−3.46410	+	2.00000i	−0.121566	+	0.0701862i
$813$	−7.73436	+	4.46543i	−0.271256	+	0.156610i
$814$	0.315342			0.0110527
$815$		0			0
$816$	1.56155	−	2.70469i	0.0546653	−	0.0946830i
$817$	0.925894	+	0.534565i	0.0323929	+	0.0187021i
$818$		−	16.2462i		−	0.568035i
$819$	−11.9039	+	4.81645i	−0.415955	+	0.168300i
$820$		0			0
$821$	−19.4924	+	33.7619i	−0.680290	+	1.17830i	0.294602	+	0.955620i	$0.404813\pi$
$821$	−19.4924	+	33.7619i	−0.680290	+	1.17830i	−0.974892	+	0.222677i	$0.928520\pi$
$822$	−14.2829	−	8.24621i	−0.498172	−	0.287620i
$823$	−43.9877	+	25.3963i	−1.53331	+	0.885260i	−0.534109	+	0.845416i	$0.679353\pi$
$823$	−43.9877	+	25.3963i	−1.53331	+	0.885260i	−0.999206	+	0.0398436i	$0.987314\pi$
$824$	4.43845			0.154621
$825$		0			0
$826$	−18.2462	−	31.6034i	−0.634867	−	1.09962i
$827$			6.06913i			0.211044i	0.994417	+	0.105522i	$0.0336514\pi$
$827$			6.06913i			0.211044i	−0.994417	+	0.105522i	$0.966349\pi$
$828$	6.65511	−	3.84233i	0.231281	−	0.133530i
$829$	6.27320	−	10.8655i	0.217877	−	0.377374i	−0.736282	−	0.676675i	$-0.763420\pi$
$829$	6.27320	−	10.8655i	0.217877	−	0.377374i	0.954159	+	0.299301i	$0.0967534\pi$
$830$		0			0
$831$	5.00000			0.173448
$832$	−2.21837	+	2.84233i	−0.0769081	+	0.0985400i
$833$			17.7538i			0.615132i
$834$	10.7808	−	18.6729i	0.373308	−	0.646588i
$835$		0			0
$836$	−0.684658	−	1.18586i	−0.0236794	−	0.0410139i
$837$			4.00000i			0.138260i
$838$	10.3324	−	5.96543i	0.356928	−	0.206073i
$839$	6.84233	+	11.8513i	0.236223	+	0.409151i	0.959628	−	0.281274i	$-0.0907569\pi$
$839$	6.84233	+	11.8513i	0.236223	+	0.409151i	−0.723404	+	0.690425i	$0.757424\pi$
$840$		0			0
$841$	13.8693	+	24.0224i	0.478252	+	0.828357i
$842$	−27.0600	−	15.6231i	−0.932550	−	0.538408i
$843$	−1.51883	−	0.876894i	−0.0523111	−	0.0302018i
$844$	−1.12311			−0.0386589
$845$		0			0
$846$	4.00000			0.137523
$847$	−32.9557	−	19.0270i	−1.13237	−	0.653775i
$848$	3.67733	+	2.12311i	0.126280	+	0.0729077i
$849$	14.8078	+	25.6478i	0.508201	+	0.880230i
$850$		0			0
$851$	2.15767	+	3.73720i	0.0739640	+	0.128109i
$852$	10.8786	−	6.28078i	0.372696	−	0.215176i
$853$		−	18.9848i		−	0.650029i	−0.945709	−	0.325014i	$-0.894631\pi$
$853$		−	18.9848i		−	0.650029i	0.945709	−	0.325014i	$-0.105369\pi$
$854$	3.00000	+	5.19615i	0.102658	+	0.177809i
$855$		0			0
$856$	−2.68466	+	4.64996i	−0.0917597	+	0.158933i
$857$		−	56.2462i		−	1.92133i	−0.277703	−	0.960667i	$-0.589573\pi$
$857$		−	56.2462i		−	1.92133i	0.277703	−	0.960667i	$-0.410427\pi$
$858$	−1.24573	+	1.59612i	−0.0425286	+	0.0544906i
$859$	−27.4233			−0.935671			−0.467835	−	0.883816i	$-0.654966\pi$
$859$	−27.4233			−0.935671			−0.467835	+	0.883816i	$0.654966\pi$
$860$		0			0
$861$	−5.56155	+	9.63289i	−0.189537	+	0.328288i
$862$	15.8616	−	9.15767i	0.540247	−	0.311912i
$863$		−	2.06913i		−	0.0704340i	−0.999380	−	0.0352170i	$-0.988788\pi$
$863$		−	2.06913i		−	0.0704340i	0.999380	−	0.0352170i	$-0.0112122\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$		0			0
$866$	−13.6847			−0.465024
$867$	−6.27540	+	3.62311i	−0.213124	+	0.123047i
$868$	−12.3376	−	7.12311i	−0.418765	−	0.241774i
$869$	4.43845	−	7.68762i	0.150564	−	0.260785i
$870$		0			0
$871$	−39.4654	+	15.9682i	−1.33724	+	0.541061i
$872$		−	2.80776i		−	0.0950829i
$873$	−2.43160	−	1.40388i	−0.0822970	−	0.0475142i
$874$	9.36932	−	16.2281i	0.316922	−	0.548925i
$875$		0			0
$876$	9.00000			0.304082
$877$	37.6655	−	21.7462i	1.27188	−	0.734317i	0.296534	−	0.955022i	$-0.404169\pi$
$877$	37.6655	−	21.7462i	1.27188	−	0.734317i	0.975341	+	0.220705i	$0.0708357\pi$
$878$	6.00231	−	3.46543i	0.202568	−	0.116953i
$879$	−20.2462			−0.682888
$880$		0			0
$881$	−24.5616	+	42.5419i	−0.827500	+	1.43327i	0.0724940	+	0.997369i	$0.476904\pi$
$881$	−24.5616	+	42.5419i	−0.827500	+	1.43327i	−0.899994	+	0.435903i	$0.856429\pi$
$882$	−4.92306	−	2.84233i	−0.165768	−	0.0957062i
$883$		−	34.2462i		−	1.15248i	−0.817282	−	0.576238i	$-0.804520\pi$
$883$		−	34.2462i		−	1.15248i	0.817282	−	0.576238i	$-0.195480\pi$
$884$	−10.4384	+	4.22351i	−0.351083	+	0.142052i
$885$		0			0
$886$	1.40388	−	2.43160i	0.0471643	−	0.0816910i
$887$	35.8269	+	20.6847i	1.20295	+	0.694523i	0.961210	−	0.275818i	$-0.0889488\pi$
$887$	35.8269	+	20.6847i	1.20295	+	0.694523i	0.241739	+	0.970341i	$0.422282\pi$
$888$	−0.486319	+	0.280776i	−0.0163198	+	0.00942224i
$889$	77.6695			2.60495
$890$		0			0
$891$	0.280776	+	0.486319i	0.00940636	+	0.0162923i
$892$		−	0.438447i		−	0.0146803i
$893$	8.44703	−	4.87689i	0.282669	−	0.163199i
$894$	−5.12311	+	8.87348i	−0.171342	+	0.296774i
$895$		0			0
$896$	−3.56155			−0.118983
$897$	−27.4397	−	3.84233i	−0.916186	−	0.128292i
$898$			3.12311i			0.104219i
$899$	2.24621	−	3.89055i	0.0749153	−	0.129757i
$900$		0			0
$901$	6.63068	+	11.4847i	0.220900	+	0.382610i
$902$			1.75379i			0.0583948i
$903$	1.35234	−	0.780776i	0.0450032	−	0.0259826i
$904$	2.00000	+	3.46410i	0.0665190	+	0.115214i
$905$		0			0
$906$	8.34233	+	14.4493i	0.277155	+	0.480047i
$907$	3.34436	+	1.93087i	0.111048	+	0.0641135i	0.554495	−	0.832187i	$-0.312911\pi$
$907$	3.34436	+	1.93087i	0.111048	+	0.0641135i	−0.443447	+	0.896300i	$0.646245\pi$
$908$	25.7077	+	14.8423i	0.853139	+	0.492560i
$909$	6.24621			0.207174
$910$		0			0
$911$	39.6847			1.31481			0.657406	−	0.753537i	$-0.271654\pi$
$911$	39.6847			1.31481			0.657406	+	0.753537i	$0.271654\pi$
$912$	2.11176	+	1.21922i	0.0699273	+	0.0403725i
$913$	−3.19101	−	1.84233i	−0.105607	−	0.0609722i
$914$	2.25379	+	3.90368i	0.0745487	+	0.129122i
$915$		0			0
$916$	−4.74621	−	8.22068i	−0.156819	−	0.271619i
$917$	−2.70469	+	1.56155i	−0.0893167	+	0.0515670i
$918$			3.12311i			0.103078i
$919$	13.6577	+	23.6558i	0.450525	+	0.780332i	0.998419	−	0.0562158i	$-0.0179035\pi$
$919$	13.6577	+	23.6558i	0.450525	+	0.780332i	−0.547894	+	0.836548i	$0.684570\pi$
$920$		0			0
$921$	−11.1231	+	19.2658i	−0.366519	+	0.634829i
$922$			10.6307i			0.350103i
$923$	−44.8537	−	6.28078i	−1.47638	−	0.206734i
$924$	−2.00000			−0.0657952
$925$		0			0
$926$	−13.9039	+	24.0822i	−0.456910	+	0.791391i
$927$	−3.84381	+	2.21922i	−0.126247	+	0.0728889i
$928$		−	1.12311i		−	0.0368677i
$929$	−24.9309	−	43.1815i	−0.817955	−	1.41674i	−0.907186	−	0.420729i	$-0.861774\pi$
$929$	−24.9309	−	43.1815i	−0.817955	−	1.41674i	0.0892310	−	0.996011i	$-0.471559\pi$
$930$		0			0
$931$	−13.8617			−0.454300
$932$	−21.9705	+	12.6847i	−0.719667	+	0.415500i
$933$	−8.93335	−	5.15767i	−0.292465	−	0.168855i
$934$	−1.71922	+	2.97778i	−0.0562547	+	0.0974360i
$935$		0			0
$936$	0.500000	−	3.57071i	0.0163430	−	0.116712i
$937$		−	11.2462i		−	0.367398i	−0.982983	−	0.183699i	$-0.941193\pi$
$937$		−	11.2462i		−	0.367398i	0.982983	−	0.183699i	$-0.0588071\pi$
$938$	−36.4198	−	21.0270i	−1.18915	−	0.686555i
$939$	15.5000	−	26.8468i	0.505823	−	0.876112i
$940$		0			0
$941$	34.6307			1.12893			0.564464	−	0.825458i	$-0.309083\pi$
$941$	34.6307			1.12893			0.564464	+	0.825458i	$0.309083\pi$
$942$	14.9357	−	8.62311i	0.486630	−	0.280956i
$943$	−20.7846	+	12.0000i	−0.676840	+	0.390774i
$944$	10.2462			0.333486
$945$		0			0
$946$	0.123106	−	0.213225i	0.00400251	−	0.00693255i
$947$	−40.4170	−	23.3348i	−1.31338	−	0.758278i	−0.330722	−	0.943728i	$-0.607292\pi$
$947$	−40.4170	−	23.3348i	−1.31338	−	0.758278i	−0.982654	+	0.185451i	$0.940625\pi$
$948$			15.8078i			0.513412i
$949$	−25.5810	−	19.9653i	−0.830393	−	0.648102i
$950$		0			0
$951$	−8.12311	+	14.0696i	−0.263410	+	0.456239i
$952$	−9.63289	−	5.56155i	−0.312204	−	0.180251i
$953$	7.14143	−	4.12311i	0.231334	−	0.133560i	−0.379854	−	0.925047i	$-0.624026\pi$
$953$	7.14143	−	4.12311i	0.231334	−	0.133560i	0.611187	+	0.791486i	$0.290692\pi$
$954$	−4.24621			−0.137476
$955$		0			0
$956$	−13.5270	−	23.4294i	−0.437494	−	0.757762i
$957$		−	0.630683i		−	0.0203871i
$958$	10.0593	−	5.80776i	0.325003	−	0.187640i
$959$	−29.3693	+	50.8691i	−0.948385	+	1.64265i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	2.00514	+	0.280776i	0.0646485	+	0.00905259i
$963$		−	5.36932i		−	0.173024i
$964$	7.78078	−	13.4767i	0.250602	−	0.434055i
$965$		0			0
$966$	−13.6847	−	23.7025i	−0.440297	−	0.762616i
$967$			16.6307i			0.534807i	0.963585	+	0.267403i	$0.0861656\pi$
$967$			16.6307i			0.534807i	−0.963585	+	0.267403i	$0.913834\pi$
$968$	9.25319	−	5.34233i	0.297409	−	0.171709i
$969$	3.80776	+	6.59524i	0.122323	+	0.211870i
$970$		0			0
$971$	−7.31534	−	12.6705i	−0.234760	−	0.406617i	0.724443	−	0.689335i	$-0.242097\pi$
$971$	−7.31534	−	12.6705i	−0.234760	−	0.406617i	−0.959203	+	0.282718i	$0.908764\pi$
$972$	−0.866025	−	0.500000i	−0.0277778	−	0.0160375i
$973$	−66.5044	−	38.3963i	−2.13203	−	1.23093i
$974$	−42.6847			−1.36770
$975$		0			0
$976$	−1.68466			−0.0539246
$977$	40.0504	+	23.1231i	1.28133	+	0.739774i	0.977091	−	0.212823i	$-0.0682659\pi$
$977$	40.0504	+	23.1231i	1.28133	+	0.739774i	0.304235	+	0.952597i	$0.401599\pi$
$978$	−14.2829	−	8.24621i	−0.456715	−	0.263685i
$979$	−2.87689	−	4.98293i	−0.0919459	−	0.159255i
$980$		0			0
$981$	1.40388	+	2.43160i	0.0448225	+	0.0776349i
$982$	27.1068	−	15.6501i	0.865011	−	0.499415i
$983$			22.2462i			0.709544i	0.934953	+	0.354772i	$0.115441\pi$
$983$			22.2462i			0.709544i	−0.934953	+	0.354772i	$0.884559\pi$
$984$	−1.56155	−	2.70469i	−0.0497805	−	0.0862223i
$985$		0			0
$986$	1.75379	−	3.03765i	0.0558520	−	0.0967385i
$987$		−	14.2462i		−	0.453462i
$988$	−3.29762	−	8.15009i	−0.104911	−	0.259289i
$989$	3.36932			0.107138
$990$		0			0
$991$	9.97301	−	17.2738i	0.316803	−	0.548719i	−0.663016	−	0.748605i	$-0.730724\pi$
$991$	9.97301	−	17.2738i	0.316803	−	0.548719i	0.979819	+	0.199886i	$0.0640572\pi$
$992$	3.46410	−	2.00000i	0.109985	−	0.0635001i
$993$			16.6847i			0.529472i
$994$	−22.3693	−	38.7448i	−0.709512	−	1.22891i
$995$		0			0
$996$	6.56155			0.207911
$997$	23.9625	−	13.8348i	0.758900	−	0.438151i	−0.0700008	−	0.997547i	$-0.522300\pi$
$997$	23.9625	−	13.8348i	0.758900	−	0.438151i	0.828901	+	0.559396i	$0.188967\pi$
$998$	5.24290	+	3.02699i	0.165961	+	0.0958176i
$999$	0.280776	−	0.486319i	0.00888337	−	0.0153865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.z.m.1699.1		8
5.2	odd	4		1950.2.i.bg.451.1	yes	4
5.3	odd	4		1950.2.i.z.451.2	✓	4
5.4	even	2	inner	1950.2.z.m.1699.4		8
13.3	even	3	inner	1950.2.z.m.1849.4		8
65.3	odd	12		1950.2.i.z.601.2	yes	4
65.29	even	6	inner	1950.2.z.m.1849.1		8
65.42	odd	12		1950.2.i.bg.601.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.i.z.451.2	✓	4	5.3	odd	4
1950.2.i.z.601.2	yes	4	65.3	odd	12
1950.2.i.bg.451.1	yes	4	5.2	odd	4
1950.2.i.bg.601.1	yes	4	65.42	odd	12
1950.2.z.m.1699.1		8	1.1	even	1	trivial
1950.2.z.m.1699.4		8	5.4	even	2	inner
1950.2.z.m.1849.1		8	65.29	even	6	inner
1950.2.z.m.1849.4		8	13.3	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.z (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(-3.08440 + 1.78078i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(-3.08440 + 1.78078i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.280776 - 0.486319i) q^{11} +1.00000i q^{12} +(2.21837 - 2.84233i) q^{13} +3.56155 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.70469 + 1.56155i) q^{17} -1.00000i q^{18} +(-1.21922 - 2.11176i) q^{19} -3.56155 q^{21} +(-0.486319 + 0.280776i) q^{22} +(-6.65511 - 3.84233i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-3.34233 + 1.35234i) q^{26} +1.00000i q^{27} +(-3.08440 - 1.78078i) q^{28} +(0.561553 - 0.972638i) q^{29} +4.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(0.486319 - 0.280776i) q^{33} +3.12311 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-0.486319 - 0.280776i) q^{37} +2.43845i q^{38} +(3.34233 - 1.35234i) q^{39} +(1.56155 - 2.70469i) q^{41} +(3.08440 + 1.78078i) q^{42} +(-0.379706 + 0.219224i) q^{43} +0.561553 q^{44} +(3.84233 + 6.65511i) q^{46} +4.00000i q^{47} +(-0.866025 + 0.500000i) q^{48} +(2.84233 - 4.92306i) q^{49} -3.12311 q^{51} +(3.57071 + 0.500000i) q^{52} -4.24621i q^{53} +(0.500000 - 0.866025i) q^{54} +(1.78078 + 3.08440i) q^{56} -2.43845i q^{57} +(-0.972638 + 0.561553i) q^{58} +(-5.12311 - 8.87348i) q^{59} +(0.842329 + 1.45896i) q^{61} +(-3.46410 - 2.00000i) q^{62} +(-3.08440 - 1.78078i) q^{63} -1.00000 q^{64} -0.561553 q^{66} +(-10.2258 - 5.90388i) q^{67} +(-2.70469 - 1.56155i) q^{68} +(-3.84233 - 6.65511i) q^{69} +(-6.28078 - 10.8786i) q^{71} +(0.866025 - 0.500000i) q^{72} -9.00000i q^{73} +(0.280776 + 0.486319i) q^{74} +(1.21922 - 2.11176i) q^{76} +2.00000i q^{77} +(-3.57071 - 0.500000i) q^{78} +15.8078 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-2.70469 + 1.56155i) q^{82} -6.56155i q^{83} +(-1.78078 - 3.08440i) q^{84} +0.438447 q^{86} +(0.972638 - 0.561553i) q^{87} +(-0.486319 - 0.280776i) q^{88} +(5.12311 - 8.87348i) q^{89} +(-1.78078 + 12.7173i) q^{91} -7.68466i q^{92} +(3.46410 + 2.00000i) q^{93} +(2.00000 - 3.46410i) q^{94} +1.00000 q^{96} +(-2.43160 + 1.40388i) q^{97} +(-4.92306 + 2.84233i) q^{98} +0.561553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 4 q^{6} + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 - 4 * q^6 + 4 * q^9	\( 8 q + 4 q^{4} - 4 q^{6} + 4 q^{9} - 6 q^{11} + 12 q^{14} - 4 q^{16} - 18 q^{19} - 12 q^{21} + 4 q^{24} - 2 q^{26} - 12 q^{29} + 32 q^{31} - 8 q^{34} - 4 q^{36} + 2 q^{39} - 4 q^{41} - 12 q^{44} + 6 q^{46} - 2 q^{49} + 8 q^{51} + 4 q^{54} + 6 q^{56} - 8 q^{59} - 18 q^{61} - 8 q^{64} + 12 q^{66} - 6 q^{69} - 42 q^{71} - 6 q^{74} + 18 q^{76} + 44 q^{79} - 4 q^{81} - 6 q^{84} + 20 q^{86} + 8 q^{89} - 6 q^{91} + 16 q^{94} + 8 q^{96} - 12 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^6 + 4 * q^9 - 6 * q^11 + 12 * q^14 - 4 * q^16 - 18 * q^19 - 12 * q^21 + 4 * q^24 - 2 * q^26 - 12 * q^29 + 32 * q^31 - 8 * q^34 - 4 * q^36 + 2 * q^39 - 4 * q^41 - 12 * q^44 + 6 * q^46 - 2 * q^49 + 8 * q^51 + 4 * q^54 + 6 * q^56 - 8 * q^59 - 18 * q^61 - 8 * q^64 + 12 * q^66 - 6 * q^69 - 42 * q^71 - 6 * q^74 + 18 * q^76 + 44 * q^79 - 4 * q^81 - 6 * q^84 + 20 * q^86 + 8 * q^89 - 6 * q^91 + 16 * q^94 + 8 * q^96 - 12 * q^99

Introduction

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