LMFDB - Embedded newform 650.2.m.d.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(101,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("650.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.m (of order $6$, degree $2$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.3
Root			$0.665665 + 1.24775i$ of defining polynomial
Character	$\chi$	$=$	650.101
Dual form			650.2.m.d.251.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.747754 - 1.29515i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.29515 - 0.747754i) q^{6} +(1.21306 + 0.700360i) q^{7} -1.00000i q^{8} +(0.381728 - 0.661173i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.747754 - 1.29515i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.29515 - 0.747754i) q^{6} +(1.21306 + 0.700360i) q^{7} -1.00000i q^{8} +(0.381728 - 0.661173i) q^{9} +(1.99700 - 1.15297i) q^{11} -1.49551 q^{12} +(-2.08209 - 2.94362i) q^{13} +1.40072 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.286941 + 0.496996i) q^{17} -0.763457i q^{18} +(2.38802 + 1.37872i) q^{19} -2.09479i q^{21} +(1.15297 - 1.99700i) q^{22} +(-3.72756 - 6.45632i) q^{23} +(-1.29515 + 0.747754i) q^{24} +(-3.27495 - 1.50821i) q^{26} -5.62828 q^{27} +(1.21306 - 0.700360i) q^{28} +(2.65668 + 4.60151i) q^{29} -3.52691i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.98652 - 1.72427i) q^{33} +0.573882i q^{34} +(-0.381728 - 0.661173i) q^{36} +(2.24326 - 1.29515i) q^{37} +2.75745 q^{38} +(-2.25553 + 4.89772i) q^{39} +(-1.21564 + 0.701848i) q^{41} +(-1.04739 - 1.81414i) q^{42} +(0.570878 - 0.988789i) q^{43} -2.30593i q^{44} +(-6.45632 - 3.72756i) q^{46} +4.78645i q^{47} +(-0.747754 + 1.29515i) q^{48} +(-2.51899 - 4.36302i) q^{49} +0.858244 q^{51} +(-3.59030 + 0.331331i) q^{52} -0.889650 q^{53} +(-4.87423 + 2.81414i) q^{54} +(0.700360 - 1.21306i) q^{56} -4.12379i q^{57} +(4.60151 + 2.65668i) q^{58} +(2.04411 + 1.18016i) q^{59} +(-4.67238 + 8.09281i) q^{61} +(-1.76346 - 3.05440i) q^{62} +(0.926118 - 0.534695i) q^{63} -1.00000 q^{64} -3.44854 q^{66} +(3.87454 - 2.23697i) q^{67} +(0.286941 + 0.496996i) q^{68} +(-5.57459 + 9.65548i) q^{69} +(7.77089 + 4.48652i) q^{71} +(-0.661173 - 0.381728i) q^{72} +9.79246i q^{73} +(1.29515 - 2.24326i) q^{74} +(2.38802 - 1.37872i) q^{76} +3.22997 q^{77} +(0.495508 + 5.36931i) q^{78} +15.9990 q^{79} +(3.06338 + 5.30593i) q^{81} +(-0.701848 + 1.21564i) q^{82} -8.36033i q^{83} +(-1.81414 - 1.04739i) q^{84} -1.14176i q^{86} +(3.97309 - 6.88159i) q^{87} +(-1.15297 - 1.99700i) q^{88} +(-1.93556 + 1.11749i) q^{89} +(-0.464102 - 5.02900i) q^{91} -7.45512 q^{92} +(-4.56787 + 2.63726i) q^{93} +(2.39322 + 4.14519i) q^{94} +1.49551i q^{96} +(13.9636 + 8.06189i) q^{97} +(-4.36302 - 2.51899i) q^{98} -1.76048i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 4 q^{4} + 6 q^{7} + 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 + 4 * q^4 + 6 * q^7 + 2 * q^9	$ 8 q + 2 q^{3} + 4 q^{4} + 6 q^{7} + 2 q^{9} + 12 q^{11} + 4 q^{12} - 10 q^{13} - 4 q^{16} - 6 q^{17} + 6 q^{19} + 6 q^{22} + 6 q^{26} - 4 q^{27} + 6 q^{28} - 12 q^{29} + 24 q^{33} - 2 q^{36} - 6 q^{37} + 12 q^{38} - 10 q^{39} - 24 q^{41} - 6 q^{42} + 8 q^{43} - 24 q^{46} + 2 q^{48} - 10 q^{49} - 8 q^{52} - 12 q^{53} - 18 q^{54} + 6 q^{58} + 30 q^{59} - 10 q^{61} - 12 q^{62} - 8 q^{64} - 30 q^{67} + 6 q^{68} - 18 q^{69} + 12 q^{72} + 6 q^{76} + 60 q^{77} - 12 q^{78} - 4 q^{79} + 8 q^{81} - 12 q^{82} + 6 q^{84} + 36 q^{87} - 6 q^{88} - 6 q^{89} + 24 q^{91} - 36 q^{93} - 12 q^{94} + 18 q^{97} - 24 q^{98}+O(q^{100}) $ 8 * q + 2 * q^3 + 4 * q^4 + 6 * q^7 + 2 * q^9 + 12 * q^11 + 4 * q^12 - 10 * q^13 - 4 * q^16 - 6 * q^17 + 6 * q^19 + 6 * q^22 + 6 * q^26 - 4 * q^27 + 6 * q^28 - 12 * q^29 + 24 * q^33 - 2 * q^36 - 6 * q^37 + 12 * q^38 - 10 * q^39 - 24 * q^41 - 6 * q^42 + 8 * q^43 - 24 * q^46 + 2 * q^48 - 10 * q^49 - 8 * q^52 - 12 * q^53 - 18 * q^54 + 6 * q^58 + 30 * q^59 - 10 * q^61 - 12 * q^62 - 8 * q^64 - 30 * q^67 + 6 * q^68 - 18 * q^69 + 12 * q^72 + 6 * q^76 + 60 * q^77 - 12 * q^78 - 4 * q^79 + 8 * q^81 - 12 * q^82 + 6 * q^84 + 36 * q^87 - 6 * q^88 - 6 * q^89 + 24 * q^91 - 36 * q^93 - 12 * q^94 + 18 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.747754	−	1.29515i	−0.431716	−	0.747754i	0.565305	−	0.824882i	$-0.308758\pi$
$3$	−0.747754	−	1.29515i	−0.431716	−	0.747754i	−0.997021	+	0.0771279i	$0.975425\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.29515	−	0.747754i	−0.528742	−	0.305269i
$7$	1.21306	+	0.700360i	0.458493	+	0.264711i	0.711410	−	0.702777i	$-0.248057\pi$
$7$	1.21306	+	0.700360i	0.458493	+	0.264711i	−0.252917	+	0.967488i	$0.581390\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.381728	−	0.661173i	0.127243	−	0.220391i
$10$		0			0
$11$	1.99700	−	1.15297i	0.602117	−	0.347632i	−0.167757	−	0.985828i	$-0.553652\pi$
$11$	1.99700	−	1.15297i	0.602117	−	0.347632i	0.769874	+	0.638196i	$0.220319\pi$
$12$	−1.49551			−0.431716
$13$	−2.08209	−	2.94362i	−0.577467	−	0.816414i
$13$	−2.08209	−	2.94362i	−0.577467	−	0.816414i
$14$	1.40072			0.374358
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.286941	+	0.496996i	−0.0695934	+	0.120539i	−0.898722	−	0.438518i	$-0.855504\pi$
$17$	−0.286941	+	0.496996i	−0.0695934	+	0.120539i	0.829129	+	0.559057i	$0.188837\pi$
$18$		−	0.763457i		−	0.179949i
$19$	2.38802	+	1.37872i	0.547850	+	0.316301i	0.748254	−	0.663412i	$-0.230892\pi$
$19$	2.38802	+	1.37872i	0.547850	+	0.316301i	−0.200405	+	0.979713i	$0.564226\pi$
$20$		0			0
$21$		−	2.09479i		−	0.457120i
$22$	1.15297	−	1.99700i	0.245813	−	0.425761i
$23$	−3.72756	−	6.45632i	−0.777250	−	1.34624i	−0.933521	−	0.358522i	$-0.883281\pi$
$23$	−3.72756	−	6.45632i	−0.777250	−	1.34624i	0.156272	−	0.987714i	$-0.450052\pi$
$24$	−1.29515	+	0.747754i	−0.264371	+	0.152635i
$25$		0			0
$26$	−3.27495	−	1.50821i	−0.642271	−	0.295784i
$27$	−5.62828			−1.08316
$28$	1.21306	−	0.700360i	0.229247	−	0.132356i
$29$	2.65668	+	4.60151i	0.493333	+	0.854478i	0.999970	−	0.00768111i	$-0.00244500\pi$
$29$	2.65668	+	4.60151i	0.493333	+	0.854478i	−0.506637	+	0.862159i	$0.669112\pi$
$30$		0			0
$31$		−	3.52691i		−	0.633452i	−0.948517	−	0.316726i	$-0.897416\pi$
$31$		−	3.52691i		−	0.633452i	0.948517	−	0.316726i	$-0.102584\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−2.98652	−	1.72427i	−0.519887	−	0.300157i
$34$			0.573882i			0.0984199i
$35$		0			0
$36$	−0.381728	−	0.661173i	−0.0636214	−	0.110196i
$37$	2.24326	−	1.29515i	0.368790	−	0.212921i	−0.304140	−	0.952627i	$-0.598369\pi$
$37$	2.24326	−	1.29515i	0.368790	−	0.212921i	0.672930	+	0.739706i	$0.265036\pi$
$38$	2.75745			0.447317
$39$	−2.25553	+	4.89772i	−0.361175	+	0.784262i
$40$		0			0
$41$	−1.21564	+	0.701848i	−0.189851	+	0.109610i	−0.591913	−	0.806002i	$-0.701627\pi$
$41$	−1.21564	+	0.701848i	−0.189851	+	0.109610i	0.402062	+	0.915612i	$0.368294\pi$
$42$	−1.04739	−	1.81414i	−0.161616	−	0.279928i
$43$	0.570878	−	0.988789i	0.0870580	−	0.150789i	−0.819208	−	0.573496i	$-0.805587\pi$
$43$	0.570878	−	0.988789i	0.0870580	−	0.150789i	0.906266	+	0.422707i	$0.138920\pi$
$44$		−	2.30593i		−	0.347632i
$45$		0			0
$46$	−6.45632	−	3.72756i	−0.951933	−	0.549599i
$47$			4.78645i			0.698175i	0.937090	+	0.349088i	$0.113508\pi$
$47$			4.78645i			0.698175i	−0.937090	+	0.349088i	$0.886492\pi$
$48$	−0.747754	+	1.29515i	−0.107929	+	0.186938i
$49$	−2.51899	−	4.36302i	−0.359856	−	0.623289i
$50$		0			0
$51$	0.858244			0.120178
$52$	−3.59030	+	0.331331i	−0.497884	+	0.0459473i
$53$	−0.889650			−0.122203			−0.0611014	−	0.998132i	$-0.519461\pi$
$53$	−0.889650			−0.122203			−0.0611014	+	0.998132i	$0.519461\pi$
$54$	−4.87423	+	2.81414i	−0.663299	+	0.382956i
$55$		0			0
$56$	0.700360	−	1.21306i	0.0935895	−	0.162102i
$57$		−	4.12379i		−	0.546209i
$58$	4.60151	+	2.65668i	0.604207	+	0.348839i
$59$	2.04411	+	1.18016i	0.266120	+	0.153644i	0.627123	−	0.778920i	$-0.284232\pi$
$59$	2.04411	+	1.18016i	0.266120	+	0.153644i	−0.361003	+	0.932565i	$0.617566\pi$
$60$		0			0
$61$	−4.67238	+	8.09281i	−0.598237	+	1.03618i	0.394844	+	0.918748i	$0.370799\pi$
$61$	−4.67238	+	8.09281i	−0.598237	+	1.03618i	−0.993081	+	0.117429i	$0.962535\pi$
$62$	−1.76346	−	3.05440i	−0.223959	−	0.387909i
$63$	0.926118	−	0.534695i	0.116680	−	0.0673652i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−3.44854			−0.424486
$67$	3.87454	−	2.23697i	0.473351	−	0.273289i	−0.244291	−	0.969702i	$-0.578555\pi$
$67$	3.87454	−	2.23697i	0.473351	−	0.273289i	0.717641	+	0.696413i	$0.245222\pi$
$68$	0.286941	+	0.496996i	0.0347967	+	0.0602696i
$69$	−5.57459	+	9.65548i	−0.671102	+	1.16238i
$70$		0			0
$71$	7.77089	+	4.48652i	0.922234	+	0.532452i	0.884347	−	0.466830i	$-0.154604\pi$
$71$	7.77089	+	4.48652i	0.922234	+	0.532452i	0.0378872	+	0.999282i	$0.487937\pi$
$72$	−0.661173	−	0.381728i	−0.0779200	−	0.0449871i
$73$			9.79246i			1.14612i	0.819513	+	0.573060i	$0.194244\pi$
$73$			9.79246i			1.14612i	−0.819513	+	0.573060i	$0.805756\pi$
$74$	1.29515	−	2.24326i	0.150558	−	0.260774i
$75$		0			0
$76$	2.38802	−	1.37872i	0.273925	−	0.158151i
$77$	3.22997			0.368089
$78$	0.495508	+	5.36931i	0.0561052	+	0.607955i
$79$	15.9990			1.80003			0.900015	−	0.435859i	$-0.143555\pi$
$79$	15.9990			1.80003			0.900015	+	0.435859i	$0.143555\pi$
$80$		0			0
$81$	3.06338	+	5.30593i	0.340376	+	0.589548i
$82$	−0.701848	+	1.21564i	−0.0775062	+	0.134245i
$83$		−	8.36033i		−	0.917665i	−0.888523	−	0.458833i	$-0.848268\pi$
$83$		−	8.36033i		−	0.917665i	0.888523	−	0.458833i	$-0.151732\pi$
$84$	−1.81414	−	1.04739i	−0.197939	−	0.114280i
$85$		0			0
$86$		−	1.14176i		−	0.123119i
$87$	3.97309	−	6.88159i	0.425960	−	0.737784i
$88$	−1.15297	−	1.99700i	−0.122907	−	0.212881i
$89$	−1.93556	+	1.11749i	−0.205169	+	0.118454i	−0.599064	−	0.800701i	$-0.704461\pi$
$89$	−1.93556	+	1.11749i	−0.205169	+	0.118454i	0.393896	+	0.919155i	$0.371127\pi$
$90$		0			0
$91$	−0.464102	−	5.02900i	−0.0486511	−	0.527182i
$92$	−7.45512			−0.777250
$93$	−4.56787	+	2.63726i	−0.473666	+	0.273471i
$94$	2.39322	+	4.14519i	0.246842	+	0.427543i
$95$		0			0
$96$			1.49551i			0.152635i
$97$	13.9636	+	8.06189i	1.41779	+	0.818561i	0.996104	−	0.0881811i	$-0.0281054\pi$
$97$	13.9636	+	8.06189i	1.41779	+	0.818561i	0.421685	+	0.906742i	$0.361439\pi$
$98$	−4.36302	−	2.51899i	−0.440732	−	0.254457i
$99$		−	1.76048i		−	0.176935i
$100$		0			0
$101$	6.21486	+	10.7645i	0.618402	+	1.07110i	0.989777	+	0.142620i	$0.0455528\pi$
$101$	6.21486	+	10.7645i	0.618402	+	1.07110i	−0.371376	+	0.928483i	$0.621114\pi$
$102$	0.743261	−	0.429122i	0.0735939	−	0.0424894i
$103$	16.3014			1.60622			0.803112	−	0.595828i	$-0.203176\pi$
$103$	16.3014			1.60622			0.803112	+	0.595828i	$0.203176\pi$
$104$	−2.94362	+	2.08209i	−0.288646	+	0.204166i
$105$		0			0
$106$	−0.770460	+	0.444825i	−0.0748337	+	0.0432052i
$107$	−5.22756	−	9.05440i	−0.505367	−	0.875322i	−0.999981	−	0.00620858i	$-0.998024\pi$
$107$	−5.22756	−	9.05440i	−0.505367	−	0.875322i	0.494614	−	0.869113i	$-0.335310\pi$
$108$	−2.81414	+	4.87423i	−0.270791	+	0.469023i
$109$		−	14.7574i		−	1.41351i	−0.707460	−	0.706754i	$-0.750159\pi$
$109$		−	14.7574i		−	1.41351i	0.707460	−	0.706754i	$-0.249841\pi$
$110$		0			0
$111$	−3.35481	−	1.93690i	−0.318425	−	0.183843i
$112$		−	1.40072i		−	0.132356i
$113$	−8.95254	+	15.5063i	−0.842184	+	1.45871i	0.0458604	+	0.998948i	$0.485397\pi$
$113$	−8.95254	+	15.5063i	−0.842184	+	1.45871i	−0.888044	+	0.459758i	$0.847936\pi$
$114$	−2.06189	−	3.57130i	−0.193114	−	0.334483i
$115$		0			0
$116$	5.31336			0.493333
$117$	−2.74104	+	0.252957i	−0.253409	+	0.0233859i
$118$	2.36033			0.217286
$119$	−0.696152	+	0.401924i	−0.0638162	+	0.0368443i
$120$		0			0
$121$	−2.84134	+	4.92134i	−0.258303	+	0.447395i
$122$			9.34477i			0.846035i
$123$	1.81799	+	1.04962i	0.163923	+	0.0946410i
$124$	−3.05440	−	1.76346i	−0.274293	−	0.158363i
$125$		0			0
$126$	0.534695	−	0.926118i	0.0476344	−	0.0825052i
$127$	6.49951	+	11.2575i	0.576738	+	0.998939i	0.995850	+	0.0910051i	$0.0290080\pi$
$127$	6.49951	+	11.2575i	0.576738	+	0.998939i	−0.419112	+	0.907934i	$0.637659\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−1.70750			−0.150337
$130$		0			0
$131$	14.0834			1.23047			0.615236	−	0.788343i	$-0.289061\pi$
$131$	14.0834			1.23047			0.615236	+	0.788343i	$0.289061\pi$
$132$	−2.98652	+	1.72427i	−0.259943	+	0.150078i
$133$	1.93121	+	3.34495i	0.167457	+	0.290044i
$134$	2.23697	−	3.87454i	0.193245	−	0.334710i
$135$		0			0
$136$	0.496996	+	0.286941i	0.0426171	+	0.0246050i
$137$	16.2022	+	9.35432i	1.38424	+	0.799194i	0.992659	−	0.120948i	$-0.0385935\pi$
$137$	16.2022	+	9.35432i	1.38424	+	0.799194i	0.391585	+	0.920142i	$0.371927\pi$
$138$			11.1492i			0.949082i
$139$	8.44854	−	14.6333i	0.716596	−	1.24118i	−0.245745	−	0.969335i	$-0.579033\pi$
$139$	8.44854	−	14.6333i	0.716596	−	1.24118i	0.962341	−	0.271846i	$-0.0876341\pi$
$140$		0			0
$141$	6.19916	−	3.57908i	0.522063	−	0.301413i
$142$	8.97305			0.753001
$143$	−7.55182	−	3.47782i	−0.631515	−	0.290830i
$144$	−0.763457			−0.0636214
$145$		0			0
$146$	4.89623	+	8.48052i	0.405215	+	0.701852i
$147$	−3.76717	+	6.52493i	−0.310711	+	0.538167i
$148$		−	2.59030i		−	0.212921i
$149$	−19.1281	−	11.0436i	−1.56703	−	0.904728i	−0.996512	−	0.0834460i	$-0.973407\pi$
$149$	−19.1281	−	11.0436i	−1.56703	−	0.904728i	−0.570522	−	0.821282i	$-0.693259\pi$
$150$		0			0
$151$			7.38516i			0.600996i	0.953783	+	0.300498i	$0.0971528\pi$
$151$			7.38516i			0.600996i	−0.953783	+	0.300498i	$0.902847\pi$
$152$	1.37872	−	2.38802i	0.111829	−	0.193694i
$153$	0.219067	+	0.379435i	0.0177105	+	0.0306755i
$154$	2.79723	−	1.61498i	0.225407	−	0.130139i
$155$		0			0
$156$	3.11378	+	4.40221i	0.249302	+	0.352459i
$157$	−13.4521			−1.07359			−0.536797	−	0.843712i	$-0.680366\pi$
$157$	−13.4521			−1.07359			−0.536797	+	0.843712i	$0.680366\pi$
$158$	13.8556	−	7.99951i	1.10229	−	0.636407i
$159$	0.665240	+	1.15223i	0.0527569	+	0.0913777i
$160$		0			0
$161$		−	10.4425i		−	0.822987i
$162$	5.30593	+	3.06338i	0.416873	+	0.240682i
$163$	13.0574	+	7.53869i	1.02273	+	0.590476i	0.914895	−	0.403692i	$-0.132273\pi$
$163$	13.0574	+	7.53869i	1.02273	+	0.590476i	0.107840	+	0.994168i	$0.465607\pi$
$164$			1.40370i			0.109610i
$165$		0			0
$166$	−4.18016	−	7.24026i	−0.324444	−	0.561953i
$167$	−20.1827	+	11.6525i	−1.56178	+	0.901695i	−0.564705	+	0.825293i	$0.691010\pi$
$167$	−20.1827	+	11.6525i	−1.56178	+	0.901695i	−0.997077	+	0.0764028i	$0.975657\pi$
$168$	−2.09479			−0.161616
$169$	−4.32982	+	12.2578i	−0.333063	+	0.942905i
$170$		0			0
$171$	1.82315	−	1.05260i	0.139420	−	0.0804941i
$172$	−0.570878	−	0.988789i	−0.0435290	−	0.0753945i
$173$	−6.81114	+	11.7972i	−0.517841	+	0.896927i	0.481944	+	0.876202i	$0.339931\pi$
$173$	−6.81114	+	11.7972i	−0.517841	+	0.896927i	−0.999785	+	0.0207251i	$0.993403\pi$
$174$		−	7.94617i		−	0.602398i
$175$		0			0
$176$	−1.99700	−	1.15297i	−0.150529	−	0.0869081i
$177$		−	3.52989i		−	0.265323i
$178$	−1.11749	+	1.93556i	−0.0837597	+	0.145076i
$179$	−6.22155	−	10.7760i	−0.465021	−	0.805439i	0.534182	−	0.845370i	$-0.320620\pi$
$179$	−6.22155	−	10.7760i	−0.465021	−	0.805439i	−0.999202	+	0.0399304i	$0.987286\pi$
$180$		0			0
$181$	−13.5029			−1.00367			−0.501833	−	0.864965i	$-0.667341\pi$
$181$	−13.5029			−1.00367			−0.501833	+	0.864965i	$0.667341\pi$
$182$	−2.91642	−	4.12319i	−0.216180	−	0.305631i
$183$	13.9752			1.03307
$184$	−6.45632	+	3.72756i	−0.475966	+	0.274799i
$185$		0			0
$186$	−2.63726	+	4.56787i	−0.193374	+	0.334933i
$187$			1.32333i			0.0967716i
$188$	4.14519	+	2.39322i	0.302319	+	0.174544i
$189$	−6.82743	−	3.94182i	−0.496623	−	0.286725i
$190$		0			0
$191$	−8.32684	+	14.4225i	−0.602509	+	1.04358i	0.389931	+	0.920844i	$0.372499\pi$
$191$	−8.32684	+	14.4225i	−0.602509	+	1.04358i	−0.992440	+	0.122732i	$0.960834\pi$
$192$	0.747754	+	1.29515i	0.0539645	+	0.0934692i
$193$	12.8883	−	7.44104i	0.927718	−	0.535618i	0.0416286	−	0.999133i	$-0.486745\pi$
$193$	12.8883	−	7.44104i	0.927718	−	0.535618i	0.886089	+	0.463515i	$0.153412\pi$
$194$	16.1238			1.15762
$195$		0			0
$196$	−5.03798			−0.359856
$197$	−0.680544	+	0.392912i	−0.0484867	+	0.0279938i	−0.524047	−	0.851689i	$-0.675579\pi$
$197$	−0.680544	+	0.392912i	−0.0484867	+	0.0279938i	0.475561	+	0.879683i	$0.342245\pi$
$198$	−0.880240	−	1.52462i	−0.0625559	−	0.108350i
$199$	0.0713036	−	0.123501i	0.00505458	−	0.00875479i	−0.863487	−	0.504371i	$-0.831724\pi$
$199$	0.0713036	−	0.123501i	0.00505458	−	0.00875479i	0.868542	+	0.495616i	$0.165058\pi$
$200$		0			0
$201$	−5.79441	−	3.34540i	−0.408706	−	0.235967i
$202$	10.7645	+	6.21486i	0.757384	+	0.437276i
$203$			7.44253i			0.522363i
$204$	0.429122	−	0.743261i	0.0300446	−	0.0520387i
$205$		0			0
$206$	14.1174	−	8.15070i	0.983608	−	0.567886i
$207$	−5.69166			−0.395598
$208$	−1.50821	+	3.27495i	−0.104575	+	0.227077i
$209$	6.35849			0.439826
$210$		0			0
$211$	−7.84697	−	13.5913i	−0.540207	−	0.935667i	−0.998892	−	0.0470674i	$-0.985012\pi$
$211$	−7.84697	−	13.5913i	−0.540207	−	0.935667i	0.458684	−	0.888599i	$-0.348321\pi$
$212$	−0.444825	+	0.770460i	−0.0305507	+	0.0529154i
$213$		−	13.4193i		−	0.919472i
$214$	−9.05440	−	5.22756i	−0.618946	−	0.357349i
$215$		0			0
$216$			5.62828i			0.382956i
$217$	2.47011	−	4.27835i	0.167682	−	0.290434i
$218$	−7.37872	−	12.7803i	−0.499750	−	0.865593i
$219$	12.6827	−	7.32235i	0.857016	−	0.494798i
$220$		0			0
$221$	2.06040	−	0.190145i	0.138598	−	0.0127905i
$222$	−3.87381			−0.259993
$223$	−7.55955	+	4.36451i	−0.506225	+	0.292269i	−0.731281	−	0.682077i	$-0.761077\pi$
$223$	−7.55955	+	4.36451i	−0.506225	+	0.292269i	0.225055	+	0.974346i	$0.427744\pi$
$224$	−0.700360	−	1.21306i	−0.0467948	−	0.0810509i
$225$		0			0
$226$			17.9051i			1.19103i
$227$	−2.75373	−	1.58987i	−0.182772	−	0.105523i	0.405823	−	0.913952i	$-0.366985\pi$
$227$	−2.75373	−	1.58987i	−0.182772	−	0.105523i	−0.588594	+	0.808429i	$0.700318\pi$
$228$	−3.57130	−	2.06189i	−0.236515	−	0.136552i
$229$			17.5485i			1.15964i	0.814746	+	0.579818i	$0.196876\pi$
$229$			17.5485i			1.15964i	−0.814746	+	0.579818i	$0.803124\pi$
$230$		0			0
$231$	−2.41522	−	4.18328i	−0.158910	−	0.275240i
$232$	4.60151	−	2.65668i	0.302104	−	0.174420i
$233$	12.6417			0.828183			0.414091	−	0.910235i	$-0.364099\pi$
$233$	12.6417			0.828183			0.414091	+	0.910235i	$0.364099\pi$
$234$	−2.24733	+	1.58958i	−0.146912	+	0.103914i
$235$		0			0
$236$	2.04411	−	1.18016i	0.133060	−	0.0768222i
$237$	−11.9633	−	20.7211i	−0.777101	−	1.34598i
$238$	−0.401924	+	0.696152i	−0.0260528	+	0.0451249i
$239$		−	21.4485i		−	1.38739i	−0.720269	−	0.693695i	$-0.755981\pi$
$239$		−	21.4485i		−	1.38739i	0.720269	−	0.693695i	$-0.244019\pi$
$240$		0			0
$241$	−16.2431	−	9.37795i	−1.04631	−	0.604087i	−0.124695	−	0.992195i	$-0.539795\pi$
$241$	−16.2431	−	9.37795i	−1.04631	−	0.604087i	−0.921614	+	0.388108i	$0.873129\pi$
$242$			5.68268i			0.365296i
$243$	−3.86111	+	6.68763i	−0.247690	+	0.429012i
$244$	4.67238	+	8.09281i	0.299119	+	0.518089i
$245$		0			0
$246$	2.09924			0.133843
$247$	−0.913628	−	9.90006i	−0.0581327	−	0.629925i
$248$	−3.52691			−0.223959
$249$	−10.8279	+	6.25147i	−0.686188	+	0.396171i
$250$		0			0
$251$	−1.66938	+	2.89145i	−0.105370	+	0.182507i	−0.913889	−	0.405963i	$-0.866936\pi$
$251$	−1.66938	+	2.89145i	−0.105370	+	0.182507i	0.808519	+	0.588470i	$0.200269\pi$
$252$		−	1.06939i		−	0.0673652i
$253$	−14.8878	−	8.59550i	−0.935990	−	0.540394i
$254$	11.2575	+	6.49951i	0.706357	+	0.407815i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.01708	+	1.76163i	0.0634435	+	0.109887i	0.896003	−	0.444049i	$-0.146458\pi$
$257$	1.01708	+	1.76163i	0.0634435	+	0.109887i	−0.832559	+	0.553936i	$0.813125\pi$
$258$	−1.47874	+	0.853752i	−0.0920625	+	0.0531523i
$259$	3.62828			0.225450
$260$		0			0
$261$	4.05652			0.251092
$262$	12.1966	−	7.04170i	0.753507	−	0.435038i
$263$	−0.286941	−	0.496996i	−0.0176935	−	0.0306461i	0.857043	−	0.515245i	$-0.172299\pi$
$263$	−0.286941	−	0.496996i	−0.0176935	−	0.0306461i	−0.874737	+	0.484599i	$0.838966\pi$
$264$	−1.72427	+	2.98652i	−0.106121	+	0.183808i
$265$		0			0
$266$	3.34495	+	1.93121i	0.205092	+	0.118410i
$267$	2.89464	+	1.67122i	0.177149	+	0.102277i
$268$		−	4.47394i		−	0.273289i
$269$	−14.7498	+	25.5474i	−0.899309	+	1.55765i	−0.0709307	+	0.997481i	$0.522597\pi$
$269$	−14.7498	+	25.5474i	−0.899309	+	1.55765i	−0.828379	+	0.560168i	$0.810736\pi$
$270$		0			0
$271$	4.70362	−	2.71564i	0.285725	−	0.164963i	−0.350288	−	0.936642i	$-0.613916\pi$
$271$	4.70362	−	2.71564i	0.285725	−	0.164963i	0.636012	+	0.771679i	$0.280583\pi$
$272$	0.573882			0.0347967
$273$	−6.16626	+	4.36153i	−0.373199	+	0.263972i
$274$	18.7086			1.13023
$275$		0			0
$276$	5.57459	+	9.65548i	0.335551	+	0.581191i
$277$	3.24326	−	5.61749i	0.194869	−	0.337522i	−0.751989	−	0.659176i	$-0.770905\pi$
$277$	3.24326	−	5.61749i	0.194869	−	0.337522i	0.946857	+	0.321653i	$0.104239\pi$
$278$		−	16.8971i		−	1.01342i
$279$	−2.33190	−	1.34632i	−0.139607	−	0.0806023i
$280$		0			0
$281$		−	7.33791i		−	0.437743i	−0.975754	−	0.218871i	$-0.929762\pi$
$281$		−	7.33791i		−	0.437743i	0.975754	−	0.218871i	$-0.0702375\pi$
$282$	3.57908	−	6.19916i	0.213131	−	0.369154i
$283$	2.21055	+	3.82878i	0.131403	+	0.227597i	0.924218	−	0.381866i	$-0.124718\pi$
$283$	2.21055	+	3.82878i	0.131403	+	0.227597i	−0.792814	+	0.609463i	$0.791385\pi$
$284$	7.77089	−	4.48652i	0.461117	−	0.266226i
$285$		0			0
$286$	−8.27898	+	0.764026i	−0.489546	+	0.0451778i
$287$	−1.96619			−0.116060
$288$	−0.661173	+	0.381728i	−0.0389600	+	0.0224936i
$289$	8.33533	+	14.4372i	0.490314	+	0.849248i
$290$		0			0
$291$		−	24.1132i		−	1.41354i
$292$	8.48052	+	4.89623i	0.496285	+	0.286530i
$293$	−10.5915	−	6.11498i	−0.618760	−	0.357241i	0.157626	−	0.987499i	$-0.449616\pi$
$293$	−10.5915	−	6.11498i	−0.618760	−	0.357241i	−0.776386	+	0.630258i	$0.782949\pi$
$294$			7.53434i			0.439412i
$295$		0			0
$296$	−1.29515	−	2.24326i	−0.0752789	−	0.130387i
$297$	−11.2397	+	6.48922i	−0.652191	+	0.376542i
$298$	−22.0872			−1.27948
$299$	−11.2439	+	24.4152i	−0.650249	+	1.41196i
$300$		0			0
$301$	1.38502	−	0.799640i	0.0798311	−	0.0460905i
$302$	3.69258	+	6.39573i	0.212484	+	0.368033i
$303$	9.29437	−	16.0983i	0.533948	−	0.924824i
$304$		−	2.75745i		−	0.158151i
$305$		0			0
$306$	0.379435	+	0.219067i	0.0216909	+	0.0125232i
$307$		−	5.90606i		−	0.337077i	−0.985695	−	0.168538i	$-0.946095\pi$
$307$		−	5.90606i		−	0.337077i	0.985695	−	0.168538i	$-0.0539047\pi$
$308$	1.61498	−	2.79723i	0.0920222	−	0.159387i
$309$	−12.1894	−	21.1127i	−0.693433	−	1.20106i
$310$		0			0
$311$	4.24250			0.240570			0.120285	−	0.992739i	$-0.461619\pi$
$311$	4.24250			0.240570			0.120285	+	0.992739i	$0.461619\pi$
$312$	4.89772	+	2.25553i	0.277279	+	0.127695i
$313$	11.9542			0.675690			0.337845	−	0.941202i	$-0.390302\pi$
$313$	11.9542			0.675690			0.337845	+	0.941202i	$0.390302\pi$
$314$	−11.6498	+	6.72604i	−0.657439	+	0.379573i
$315$		0			0
$316$	7.99951	−	13.8556i	0.450007	−	0.779436i
$317$		−	19.3758i		−	1.08825i	−0.839004	−	0.544125i	$-0.816862\pi$
$317$		−	19.3758i		−	1.08825i	0.839004	−	0.544125i	$-0.183138\pi$
$318$	1.15223	+	0.665240i	0.0646138	+	0.0373048i
$319$	10.6108	+	6.12613i	0.594089	+	0.342997i
$320$		0			0
$321$	−7.81785	+	13.5409i	−0.436350	+	0.755780i
$322$	−5.22127	−	9.04350i	−0.290970	−	0.503974i
$323$	−1.37044	+	0.791225i	−0.0762534	+	0.0440249i
$324$	6.12676			0.340376
$325$		0			0
$326$	15.0774			0.835059
$327$	−19.1131	+	11.0349i	−1.05696	+	0.610234i
$328$	0.701848	+	1.21564i	0.0387531	+	0.0671223i
$329$	−3.35224	+	5.80624i	−0.184815	+	0.320109i
$330$		0			0
$331$	−10.0141	−	5.78167i	−0.550427	−	0.317789i	0.198867	−	0.980026i	$-0.436274\pi$
$331$	−10.0141	−	5.78167i	−0.550427	−	0.317789i	−0.749294	+	0.662237i	$0.769607\pi$
$332$	−7.24026	−	4.18016i	−0.397361	−	0.229416i
$333$		−	1.97758i		−	0.108371i
$334$	−11.6525	+	20.1827i	−0.637595	+	1.10435i
$335$		0			0
$336$	−1.81414	+	1.04739i	−0.0989694	+	0.0571400i
$337$	19.6758			1.07181			0.535905	−	0.844278i	$-0.319971\pi$
$337$	19.6758			1.07181			0.535905	+	0.844278i	$0.319971\pi$
$338$	2.37915	+	12.7804i	0.129409	+	0.695164i
$339$	26.7772			1.45434
$340$		0			0
$341$	−4.06641	−	7.04323i	−0.220209	−	0.381412i
$342$	1.05260	−	1.82315i	0.0569179	−	0.0985847i
$343$		−	16.8618i		−	0.910454i
$344$	−0.988789	−	0.570878i	−0.0533119	−	0.0307797i
$345$		0			0
$346$			13.6223i			0.732338i
$347$	5.14845	−	8.91737i	0.276383	−	0.478710i	−0.694100	−	0.719879i	$-0.744197\pi$
$347$	5.14845	−	8.91737i	0.276383	−	0.478710i	0.970483	+	0.241169i	$0.0775308\pi$
$348$	−3.97309	−	6.88159i	−0.212980	−	0.368892i
$349$	15.0780	−	8.70528i	0.807106	−	0.465983i	−0.0388439	−	0.999245i	$-0.512368\pi$
$349$	15.0780	−	8.70528i	0.807106	−	0.465983i	0.845950	+	0.533262i	$0.179034\pi$
$350$		0			0
$351$	11.7186	+	16.5675i	0.625491	+	0.884309i
$352$	−2.30593			−0.122907
$353$	−23.6182	+	13.6360i	−1.25707	+	0.725771i	−0.972504	−	0.232885i	$-0.925183\pi$
$353$	−23.6182	+	13.6360i	−1.25707	+	0.725771i	−0.284567	+	0.958656i	$0.591850\pi$
$354$	−1.76495	−	3.05697i	−0.0938058	−	0.162476i
$355$		0			0
$356$			2.23499i			0.118454i
$357$	1.04110	+	0.601080i	0.0551009	+	0.0318125i
$358$	−10.7760	−	6.22155i	−0.569532	−	0.328819i
$359$			27.8199i			1.46828i	0.678999	+	0.734139i	$0.262414\pi$
$359$			27.8199i			1.46828i	−0.678999	+	0.734139i	$0.737586\pi$
$360$		0			0
$361$	−5.69824	−	9.86964i	−0.299907	−	0.519455i
$362$	−11.6939	+	6.75147i	−0.614617	+	0.354849i
$363$	8.49848			0.446055
$364$	−4.58729	−	2.11258i	−0.240439	−	0.110729i
$365$		0			0
$366$	12.1029	−	6.98759i	0.632626	−	0.365247i
$367$	−3.28351	−	5.68721i	−0.171398	−	0.296870i	0.767511	−	0.641036i	$-0.221495\pi$
$367$	−3.28351	−	5.68721i	−0.171398	−	0.296870i	−0.938909	+	0.344166i	$0.888162\pi$
$368$	−3.72756	+	6.45632i	−0.194312	+	0.336559i
$369$			1.07166i			0.0557885i
$370$		0			0
$371$	−1.07920	−	0.623076i	−0.0560292	−	0.0323485i
$372$			5.27453i			0.273471i
$373$	1.48052	−	2.56433i	0.0766582	−	0.132776i	−0.825148	−	0.564917i	$-0.808908\pi$
$373$	1.48052	−	2.56433i	0.0766582	−	0.132776i	0.901806	+	0.432141i	$0.142242\pi$
$374$	0.661666	+	1.14604i	0.0342139	+	0.0592603i
$375$		0			0
$376$	4.78645			0.246842
$377$	8.01365	−	17.4010i	0.412724	−	0.896197i
$378$	−7.88364			−0.405491
$379$	9.25913	−	5.34576i	0.475610	−	0.274593i	−0.242975	−	0.970032i	$-0.578123\pi$
$379$	9.25913	−	5.34576i	0.475610	−	0.274593i	0.718585	+	0.695439i	$0.244790\pi$
$380$		0			0
$381$	9.72006	−	16.8356i	0.497974	−	0.862516i
$382$			16.6537i			0.852076i
$383$	−12.7454	−	7.35856i	−0.651259	−	0.376005i	0.137679	−	0.990477i	$-0.456036\pi$
$383$	−12.7454	−	7.35856i	−0.651259	−	0.376005i	−0.788938	+	0.614472i	$0.789369\pi$
$384$	1.29515	+	0.747754i	0.0660927	+	0.0381587i
$385$		0			0
$386$	7.44104	−	12.8883i	0.378739	−	0.655995i
$387$	−0.435841	−	0.754898i	−0.0221550	−	0.0383736i
$388$	13.9636	−	8.06189i	0.708895	−	0.409281i
$389$	−12.2344			−0.620310			−0.310155	−	0.950686i	$-0.600381\pi$
$389$	−12.2344			−0.620310			−0.310155	+	0.950686i	$0.600381\pi$
$390$		0			0
$391$	4.27835			0.216366
$392$	−4.36302	+	2.51899i	−0.220366	+	0.127228i
$393$	−10.5309	−	18.2401i	−0.531214	−	0.920090i
$394$	−0.392912	+	0.680544i	−0.0197946	+	0.0342853i
$395$		0			0
$396$	−1.52462	−	0.880240i	−0.0766151	−	0.0442337i
$397$	20.1731	+	11.6469i	1.01246	+	0.584542i	0.911910	−	0.410390i	$-0.134608\pi$
$397$	20.1731	+	11.6469i	1.01246	+	0.584542i	0.100547	+	0.994932i	$0.467941\pi$
$398$		−	0.142607i		−	0.00714825i
$399$	2.88814	−	5.00240i	0.144588	−	0.250433i
$400$		0			0
$401$	−25.8098	+	14.9013i	−1.28888	+	0.744136i	−0.978455	−	0.206461i	$-0.933805\pi$
$401$	−25.8098	+	14.9013i	−1.28888	+	0.744136i	−0.310427	+	0.950597i	$0.600472\pi$
$402$	−6.69081			−0.333707
$403$	−10.3819	+	7.34335i	−0.517159	+	0.365798i
$404$	12.4297			0.618402
$405$		0			0
$406$	3.72127	+	6.44542i	0.184683	+	0.319881i
$407$	2.98652	−	5.17281i	0.148036	−	0.256407i
$408$		−	0.858244i		−	0.0424894i
$409$	21.5604	+	12.4479i	1.06609	+	0.615509i	0.927112	−	0.374786i	$-0.122284\pi$
$409$	21.5604	+	12.4479i	1.06609	+	0.615509i	0.138982	+	0.990295i	$0.455617\pi$
$410$		0			0
$411$		−	27.9789i		−	1.38010i
$412$	8.15070	−	14.1174i	0.401556	−	0.695516i
$413$	1.65308	+	2.86322i	0.0813428	+	0.140890i
$414$	−4.92912	+	2.84583i	−0.242253	+	0.139865i
$415$		0			0
$416$	0.331331	+	3.59030i	0.0162448	+	0.176029i
$417$	−25.2697			−1.23746
$418$	5.50662	−	3.17925i	0.269337	−	0.155502i
$419$	−1.06582	−	1.84605i	−0.0520685	−	0.0901853i	0.838816	−	0.544414i	$-0.183248\pi$
$419$	−1.06582	−	1.84605i	−0.0520685	−	0.0901853i	−0.890885	+	0.454229i	$0.849915\pi$
$420$		0			0
$421$		−	8.63429i		−	0.420809i	−0.977614	−	0.210405i	$-0.932522\pi$
$421$		−	8.63429i		−	0.420809i	0.977614	−	0.210405i	$-0.0674782\pi$
$422$	−13.5913	−	7.84697i	−0.661616	−	0.381984i
$423$	3.16467	+	1.82712i	0.153872	+	0.0888378i
$424$			0.889650i			0.0432052i
$425$		0			0
$426$	−6.70963	−	11.6214i	−0.325083	−	0.563060i
$427$	−11.3358	+	6.54470i	−0.548576	+	0.316720i
$428$	−10.4551			−0.505367
$429$	1.14261	+	12.3813i	0.0551656	+	0.597774i
$430$		0			0
$431$	−24.8608	+	14.3534i	−1.19750	+	0.691379i	−0.959998	−	0.280007i	$-0.909663\pi$
$431$	−24.8608	+	14.3534i	−1.19750	+	0.691379i	−0.237506	+	0.971386i	$0.576330\pi$
$432$	2.81414	+	4.87423i	0.135395	+	0.234512i
$433$	11.5604	−	20.0232i	0.555558	−	0.962254i	−0.442302	−	0.896866i	$-0.645838\pi$
$433$	11.5604	−	20.0232i	0.555558	−	0.962254i	0.997860	−	0.0653880i	$-0.0208285\pi$
$434$		−	4.94022i		−	0.237138i
$435$		0			0
$436$	−12.7803	−	7.37872i	−0.612067	−	0.353377i
$437$		−	20.5571i		−	0.983380i
$438$	7.32235	−	12.6827i	0.349875	−	0.606002i
$439$	−12.1304	−	21.0104i	−0.578951	−	1.00277i	−0.995600	−	0.0937047i	$-0.970129\pi$
$439$	−12.1304	−	21.0104i	−0.578951	−	1.00277i	0.416649	−	0.909067i	$-0.363204\pi$
$440$		0			0
$441$	−3.84628			−0.183156
$442$	1.68929	−	1.19487i	0.0803514	−	0.0568343i
$443$	26.8788			1.27705			0.638526	−	0.769600i	$-0.279545\pi$
$443$	26.8788			1.27705			0.638526	+	0.769600i	$0.279545\pi$
$444$	−3.35481	+	1.93690i	−0.159212	+	0.0919214i
$445$		0			0
$446$	−4.36451	+	7.55955i	−0.206666	+	0.357955i
$447$			33.0316i			1.56234i
$448$	−1.21306	−	0.700360i	−0.0573117	−	0.0330889i
$449$	−31.5658	−	18.2245i	−1.48968	−	0.860068i	−0.489751	−	0.871862i	$-0.662912\pi$
$449$	−31.5658	−	18.2245i	−1.48968	−	0.860068i	−0.999930	+	0.0117943i	$0.996246\pi$
$450$		0			0
$451$	−1.61842	+	2.80318i	−0.0762082	+	0.131996i
$452$	8.95254	+	15.5063i	0.421092	+	0.729353i
$453$	9.56487	−	5.52228i	0.449397	−	0.259459i
$454$	−3.17974			−0.149233
$455$		0			0
$456$	−4.12379			−0.193114
$457$	20.4028	−	11.7796i	0.954405	−	0.551026i	0.0599582	−	0.998201i	$-0.480903\pi$
$457$	20.4028	−	11.7796i	0.954405	−	0.551026i	0.894446	+	0.447175i	$0.147570\pi$
$458$	8.77424	+	15.1974i	0.409993	+	0.710129i
$459$	1.61498	−	2.79723i	0.0753809	−	0.130564i
$460$		0			0
$461$	−30.8930	−	17.8361i	−1.43883	−	0.830708i	−0.441061	−	0.897477i	$-0.645398\pi$
$461$	−30.8930	−	17.8361i	−1.43883	−	0.830708i	−0.997768	+	0.0667687i	$0.978731\pi$
$462$	−4.18328	−	2.41522i	−0.194624	−	0.112366i
$463$		−	2.90726i		−	0.135112i	−0.997715	−	0.0675558i	$-0.978480\pi$
$463$		−	2.90726i		−	0.135112i	0.997715	−	0.0675558i	$-0.0215201\pi$
$464$	2.65668	−	4.60151i	0.123333	−	0.213620i
$465$		0			0
$466$	10.9480	−	6.32083i	0.507156	−	0.292807i
$467$	−27.6192			−1.27806			−0.639031	−	0.769181i	$-0.720665\pi$
$467$	−27.6192			−1.27806			−0.639031	+	0.769181i	$0.720665\pi$
$468$	−1.15145	+	2.50028i	−0.0532258	+	0.115576i
$469$	6.26673			0.289371
$470$		0			0
$471$	10.0588	+	17.4224i	0.463487	+	0.802784i
$472$	1.18016	−	2.04411i	0.0543215	−	0.0940876i
$473$		−	2.63281i		−	0.121057i
$474$	−20.7211	−	11.9633i	−0.951751	−	0.549494i
$475$		0			0
$476$			0.803848i			0.0368443i
$477$	−0.339605	+	0.588213i	−0.0155494	+	0.0269324i
$478$	−10.7243	−	18.5750i	−0.490517	−	0.849600i
$479$	3.35481	−	1.93690i	0.153285	−	0.0884994i	−0.421395	−	0.906877i	$-0.638460\pi$
$479$	3.35481	−	1.93690i	0.153285	−	0.0884994i	0.574681	+	0.818378i	$0.305126\pi$
$480$		0			0
$481$	−8.48309	−	3.90670i	−0.386796	−	0.178130i
$482$	−18.7559			−0.854308
$483$	−13.5246	+	7.80844i	−0.615392	+	0.355296i
$484$	2.84134	+	4.92134i	0.129152	+	0.223697i
$485$		0			0
$486$			7.72221i			0.350287i
$487$	3.11137	+	1.79635i	0.140990	+	0.0814004i	0.568836	−	0.822451i	$-0.307394\pi$
$487$	3.11137	+	1.79635i	0.140990	+	0.0814004i	−0.427846	+	0.903852i	$0.640727\pi$
$488$	8.09281	+	4.67238i	0.366344	+	0.211509i
$489$		−	22.5483i		−	1.01967i
$490$		0			0
$491$	−3.00669	−	5.20774i	−0.135690	−	0.235022i	0.790171	−	0.612887i	$-0.209992\pi$
$491$	−3.00669	−	5.20774i	−0.135690	−	0.235022i	−0.925861	+	0.377865i	$0.876658\pi$
$492$	1.81799	−	1.04962i	0.0819615	−	0.0473205i
$493$	−3.04924			−0.137331
$494$	−5.74125	−	8.11689i	−0.258311	−	0.365196i
$495$		0			0
$496$	−3.05440	+	1.76346i	−0.137146	+	0.0791815i
$497$	6.28436	+	10.8848i	0.281892	+	0.488252i
$498$	−6.25147	+	10.8279i	−0.280135	+	0.485208i
$499$		−	44.0098i		−	1.97015i	−0.172134	−	0.985074i	$-0.555066\pi$
$499$		−	44.0098i		−	1.97015i	0.172134	−	0.985074i	$-0.444934\pi$
$500$		0			0
$501$	30.1833	+	17.4264i	1.34849	+	0.778552i
$502$			3.33876i			0.149016i
$503$	5.37617	−	9.31181i	0.239712	−	0.415193i	−0.720920	−	0.693018i	$-0.756280\pi$
$503$	5.37617	−	9.31181i	0.239712	−	0.415193i	0.960632	+	0.277826i	$0.0896137\pi$
$504$	−0.534695	−	0.926118i	−0.0238172	−	0.0412526i
$505$		0			0
$506$	−17.1910			−0.764233
$507$	19.1132	−	3.55804i	0.848849	−	0.158018i
$508$	12.9990			0.576738
$509$	6.28436	−	3.62828i	0.278549	−	0.160821i	−0.354217	−	0.935163i	$-0.615253\pi$
$509$	6.28436	−	3.62828i	0.278549	−	0.160821i	0.632767	+	0.774343i	$0.281919\pi$
$510$		0			0
$511$	−6.85824	+	11.8788i	−0.303391	+	0.525488i
$512$			1.00000i			0.0441942i
$513$	−13.4404	−	7.75985i	−0.593410	−	0.342606i
$514$	1.76163	+	1.01708i	0.0777022	+	0.0448614i
$515$		0			0
$516$	−0.853752	+	1.47874i	−0.0375843	+	0.0650980i
$517$	5.51861	+	9.55852i	0.242708	+	0.420383i
$518$	3.14218	−	1.81414i	0.138060	−	0.0797087i
$519$	20.3722			0.894241
$520$		0			0
$521$	42.5711			1.86507			0.932537	−	0.361074i	$-0.117590\pi$
$521$	42.5711			1.86507			0.932537	+	0.361074i	$0.117590\pi$
$522$	3.51305	−	2.02826i	0.153762	−	0.0887746i
$523$	18.7535	+	32.4820i	0.820033	+	1.42034i	0.905657	+	0.424011i	$0.139378\pi$
$523$	18.7535	+	32.4820i	0.820033	+	1.42034i	−0.0856245	+	0.996327i	$0.527289\pi$
$524$	7.04170	−	12.1966i	0.307618	−	0.532810i
$525$		0			0
$526$	−0.496996	−	0.286941i	−0.0216701	−	0.0125112i
$527$	1.75286	+	1.01202i	0.0763559	+	0.0440841i
$528$			3.44854i			0.150078i
$529$	−16.2894	+	28.2140i	−0.708234	+	1.22670i
$530$		0			0
$531$	1.56059	−	0.901005i	0.0677237	−	0.0391003i
$532$	3.86241			0.167457
$533$	4.59704	+	2.11707i	0.199120	+	0.0917003i
$534$	3.34244			0.144642
$535$		0			0
$536$	−2.23697	−	3.87454i	−0.0966223	−	0.167355i
$537$	−9.30438	+	16.1157i	−0.401513	+	0.695442i
$538$			29.4995i			1.27182i
$539$	−10.0608	−	5.80862i	−0.433351	−	0.250195i
$540$		0			0
$541$			33.0878i			1.42256i	0.702911	+	0.711278i	$0.251883\pi$
$541$			33.0878i			1.42256i	−0.702911	+	0.711278i	$0.748117\pi$
$542$	2.71564	−	4.70362i	0.116647	−	0.202038i
$543$	10.0969	+	17.4883i	0.433298	+	0.750495i
$544$	0.496996	−	0.286941i	0.0213085	−	0.0123025i
$545$		0			0
$546$	−3.15937	+	6.86033i	−0.135209	+	0.293595i
$547$	12.6690			0.541685			0.270843	−	0.962624i	$-0.412698\pi$
$547$	12.6690			0.541685			0.270843	+	0.962624i	$0.412698\pi$
$548$	16.2022	−	9.35432i	0.692122	−	0.399597i
$549$	3.56716	+	6.17851i	0.152243	+	0.263692i
$550$		0			0
$551$			14.6513i			0.624167i
$552$	9.65548	+	5.57459i	0.410964	+	0.237270i
$553$	19.4078	+	11.2051i	0.825301	+	0.476488i
$554$		−	6.48652i		−	0.275586i
$555$		0			0
$556$	−8.44854	−	14.6333i	−0.358298	−	0.620590i
$557$	−6.16319	+	3.55832i	−0.261143	+	0.150771i	−0.624856	−	0.780740i	$-0.714842\pi$
$557$	−6.16319	+	3.55832i	−0.261143	+	0.150771i	0.363713	+	0.931511i	$0.381509\pi$
$558$	−2.69265			−0.113989
$559$	−4.09924	+	0.378299i	−0.173379	+	0.0160003i
$560$		0			0
$561$	1.71391	−	0.989527i	0.0723614	−	0.0417779i
$562$	−3.66895	−	6.35481i	−0.154765	−	0.268062i
$563$	−13.9005	+	24.0764i	−0.585838	+	1.01470i	0.408933	+	0.912565i	$0.365901\pi$
$563$	−13.9005	+	24.0764i	−0.585838	+	1.01470i	−0.994770	+	0.102136i	$0.967432\pi$
$564$		−	7.15817i		−	0.301413i
$565$		0			0
$566$	3.82878	+	2.21055i	0.160936	+	0.0929163i
$567$			8.58188i			0.360405i
$568$	4.48652	−	7.77089i	0.188250	−	0.326059i
$569$	−1.58838	−	2.75116i	−0.0665884	−	0.115334i	0.830809	−	0.556558i	$-0.187878\pi$
$569$	−1.58838	−	2.75116i	−0.0665884	−	0.115334i	−0.897397	+	0.441223i	$0.854545\pi$
$570$		0			0
$571$	32.6833			1.36775			0.683877	−	0.729598i	$-0.260293\pi$
$571$	32.6833			1.36775			0.683877	+	0.729598i	$0.260293\pi$
$572$	−6.78779	+	4.80116i	−0.283812	+	0.200746i
$573$	24.9057			1.04045
$574$	−1.70277	+	0.983093i	−0.0710721	+	0.0410335i
$575$		0			0
$576$	−0.381728	+	0.661173i	−0.0159054	+	0.0275489i
$577$			22.2259i			0.925278i	0.886547	+	0.462639i	$0.153097\pi$
$577$			22.2259i			0.925278i	−0.886547	+	0.462639i	$0.846903\pi$
$578$	14.4372	+	8.33533i	0.600509	+	0.346704i
$579$	−19.2745	−	11.1281i	−0.801021	−	0.462470i
$580$		0			0
$581$	5.85524	−	10.1416i	0.242916	−	0.420743i
$582$	−12.0566	−	20.8827i	−0.499763	−	0.865615i
$583$	−1.77663	+	1.02574i	−0.0735804	+	0.0424817i
$584$	9.79246			0.405215
$585$		0			0
$586$	−12.2300			−0.505215
$587$	24.9872	−	14.4264i	1.03133	−	0.595440i	0.113966	−	0.993485i	$-0.463645\pi$
$587$	24.9872	−	14.4264i	1.03133	−	0.595440i	0.917366	+	0.398045i	$0.130311\pi$
$588$	3.76717	+	6.52493i	0.155356	+	0.269084i
$589$	4.86264	−	8.42234i	0.200362	−	0.347037i
$590$		0			0
$591$	1.01776	+	0.587603i	0.0418650	+	0.0241708i
$592$	−2.24326	−	1.29515i	−0.0921975	−	0.0532302i
$593$		−	26.8623i		−	1.10310i	−0.834141	−	0.551551i	$-0.814036\pi$
$593$		−	26.8623i		−	1.10310i	0.834141	−	0.551551i	$-0.185964\pi$
$594$	−6.48922	+	11.2397i	−0.266256	+	0.461168i
$595$		0			0
$596$	−19.1281	+	11.0436i	−0.783517	+	0.452364i
$597$	−0.213270			−0.00872857
$598$	2.47011	+	26.7661i	0.101010	+	1.09455i
$599$	−10.1107			−0.413111			−0.206556	−	0.978435i	$-0.566225\pi$
$599$	−10.1107			−0.413111			−0.206556	+	0.978435i	$0.566225\pi$
$600$		0			0
$601$	5.47305	+	9.47959i	0.223250	+	0.386681i	0.955793	−	0.294040i	$-0.0950000\pi$
$601$	5.47305	+	9.47959i	0.223250	+	0.386681i	−0.732543	+	0.680721i	$0.761667\pi$
$602$	0.799640	−	1.38502i	0.0325909	−	0.0564491i
$603$		−	3.41566i		−	0.139096i
$604$	6.39573	+	3.69258i	0.260239	+	0.150249i
$605$		0			0
$606$		−	18.5887i		−	0.755116i
$607$	−13.1827	+	22.8331i	−0.535068	+	0.926765i	0.464092	+	0.885787i	$0.346381\pi$
$607$	−13.1827	+	22.8331i	−0.535068	+	0.926765i	−0.999160	+	0.0409783i	$0.986953\pi$
$608$	−1.37872	−	2.38802i	−0.0559147	−	0.0968470i
$609$	9.63918	−	5.56518i	0.390599	−	0.225513i
$610$		0			0
$611$	14.0895	−	9.96581i	0.570000	−	0.403173i
$612$	0.438134			0.0177105
$613$	−42.1452	+	24.3325i	−1.70223	+	0.982781i	−0.758728	+	0.651408i	$0.774179\pi$
$613$	−42.1452	+	24.3325i	−1.70223	+	0.982781i	−0.943500	+	0.331373i	$0.892488\pi$
$614$	−2.95303	−	5.11480i	−0.119175	−	0.206417i
$615$		0			0
$616$		−	3.22997i		−	0.130139i
$617$	−1.86056	−	1.07419i	−0.0749032	−	0.0432454i	0.462081	−	0.886838i	$-0.347103\pi$
$617$	−1.86056	−	1.07419i	−0.0749032	−	0.0432454i	−0.536984	+	0.843593i	$0.680436\pi$
$618$	−21.1127	−	12.1894i	−0.849278	−	0.490331i
$619$			35.4125i			1.42335i	0.702509	+	0.711675i	$0.252063\pi$
$619$			35.4125i			1.42335i	−0.702509	+	0.711675i	$0.747937\pi$
$620$		0			0
$621$	20.9797	+	36.3380i	0.841888	+	1.45819i
$622$	3.67411	−	2.12125i	0.147318	−	0.0850543i
$623$	−3.13059			−0.125425
$624$	5.36931	−	0.495508i	0.214945	−	0.0198362i
$625$		0			0
$626$	10.3526	−	5.97709i	0.413774	−	0.238892i
$627$	−4.75459	−	8.23518i	−0.189880	−	0.328882i
$628$	−6.72604	+	11.6498i	−0.268398	+	0.464880i
$629$			1.48652i			0.0592716i
$630$		0			0
$631$	30.7743	+	17.7676i	1.22511	+	0.707315i	0.966002	−	0.258534i	$-0.0832394\pi$
$631$	30.7743	+	17.7676i	1.22511	+	0.707315i	0.259104	+	0.965849i	$0.416573\pi$
$632$		−	15.9990i		−	0.636407i
$633$	−11.7352	+	20.3260i	−0.466432	+	0.807884i
$634$	−9.68788	−	16.7799i	−0.384755	−	0.666415i
$635$		0			0
$636$	1.33048			0.0527569
$637$	−7.59832	+	16.4992i	−0.301056	+	0.653720i
$638$	12.2523			0.485071
$639$	5.93274	−	3.42527i	0.234695	−	0.135501i
$640$		0			0
$641$	11.2929	−	19.5598i	0.446041	−	0.772566i	−0.552083	−	0.833789i	$-0.686167\pi$
$641$	11.2929	−	19.5598i	0.446041	−	0.772566i	0.998124	+	0.0612235i	$0.0195002\pi$
$642$			15.6357i			0.617092i
$643$	−37.9229	−	21.8948i	−1.49553	−	0.863447i	−0.495548	−	0.868581i	$-0.665033\pi$
$643$	−37.9229	−	21.8948i	−1.49553	−	0.863447i	−0.999987	+	0.00513351i	$0.998366\pi$
$644$	−9.04350	−	5.22127i	−0.356364	−	0.205747i
$645$		0			0
$646$	−0.791225	+	1.37044i	−0.0311303	+	0.0539193i
$647$	16.0638	+	27.8234i	0.631534	+	1.09385i	0.987238	+	0.159251i	$0.0509079\pi$
$647$	16.0638	+	27.8234i	0.631534	+	1.09385i	−0.355704	+	0.934599i	$0.615759\pi$
$648$	5.30593	−	3.06338i	0.208437	−	0.120341i
$649$	5.44276			0.213647
$650$		0			0
$651$	−7.38814			−0.289564
$652$	13.0574	−	7.53869i	0.511367	−	0.295238i
$653$	20.2073	+	35.0001i	0.790773	+	1.36966i	0.925489	+	0.378774i	$0.123654\pi$
$653$	20.2073	+	35.0001i	0.790773	+	1.36966i	−0.134717	+	0.990884i	$0.543012\pi$
$654$	−11.0349	+	19.1131i	−0.431500	+	0.747380i
$655$		0			0
$656$	1.21564	+	0.701848i	0.0474627	+	0.0274026i
$657$	6.47451	+	3.73806i	0.252595	+	0.145836i
$658$			6.70447i			0.261368i
$659$	1.00360	−	1.73829i	0.0390947	−	0.0677140i	−0.845816	−	0.533475i	$-0.820886\pi$
$659$	1.00360	−	1.73829i	0.0390947	−	0.0677140i	0.884911	+	0.465761i	$0.154219\pi$
$660$		0			0
$661$	10.7058	−	6.18097i	0.416406	−	0.240412i	−0.277133	−	0.960832i	$-0.589384\pi$
$661$	10.7058	−	6.18097i	0.416406	−	0.240412i	0.693538	+	0.720420i	$0.256051\pi$
$662$	−11.5633			−0.449422
$663$	−1.78694	−	2.52635i	−0.0693990	−	0.0981152i
$664$	−8.36033			−0.324444
$665$		0			0
$666$	−0.988789	−	1.71263i	−0.0383148	−	0.0663632i
$667$	19.8059	−	34.3048i	0.766886	−	1.32829i
$668$			23.3049i			0.901695i
$669$	11.3054	+	6.52716i	0.437091	+	0.252355i
$670$		0			0
$671$			21.5484i			0.831867i
$672$	−1.04739	+	1.81414i	−0.0404041	+	0.0699819i
$673$	2.29638	+	3.97744i	0.0885189	+	0.153319i	0.906885	−	0.421378i	$-0.138453\pi$
$673$	2.29638	+	3.97744i	0.0885189	+	0.153319i	−0.818366	+	0.574697i	$0.805120\pi$
$674$	17.0398	−	9.83791i	0.656347	−	0.378942i
$675$		0			0
$676$	8.45062	+	9.87861i	0.325024	+	0.379947i
$677$	0.320925			0.0123341			0.00616707	−	0.999981i	$-0.498037\pi$
$677$	0.320925			0.0123341			0.00616707	+	0.999981i	$0.498037\pi$
$678$	23.1897	−	13.3886i	0.890596	−	0.514186i
$679$	11.2925	+	19.5591i	0.433365	+	0.750610i
$680$		0			0
$681$			4.75532i			0.182224i
$682$	−7.04323	−	4.06641i	−0.269699	−	0.155711i
$683$	−9.90665	−	5.71961i	−0.379068	−	0.218855i	0.298345	−	0.954458i	$-0.403565\pi$
$683$	−9.90665	−	5.71961i	−0.379068	−	0.218855i	−0.677413	+	0.735603i	$0.736899\pi$
$684$		−	2.10519i		−	0.0804941i
$685$		0			0
$686$	−8.43092	−	14.6028i	−0.321894	−	0.557537i
$687$	22.7279	−	13.1219i	0.867123	−	0.500633i
$688$	−1.14176			−0.0435290
$689$	1.85233	+	2.61879i	0.0705682	+	0.0997681i
$690$		0			0
$691$	−19.0613	+	11.0050i	−0.725124	+	0.418651i	−0.816636	−	0.577153i	$-0.804164\pi$
$691$	−19.0613	+	11.0050i	−0.725124	+	0.418651i	0.0915115	+	0.995804i	$0.470830\pi$
$692$	6.81114	+	11.7972i	0.258921	+	0.448463i
$693$	1.23297	−	2.13557i	0.0468366	−	0.0811235i
$694$		−	10.2969i		−	0.390865i
$695$		0			0
$696$	−6.88159	−	3.97309i	−0.260846	−	0.150599i
$697$		−	0.805556i		−	0.0305126i
$698$	8.70528	−	15.0780i	0.329500	−	0.570710i
$699$	−9.45285	−	16.3728i	−0.357540	−	0.619277i
$700$		0			0
$701$	6.84486			0.258527			0.129263	−	0.991610i	$-0.458739\pi$
$701$	6.84486			0.258527			0.129263	+	0.991610i	$0.458739\pi$
$702$	18.4323	+	8.48861i	0.695684	+	0.320382i
$703$	7.14261			0.269389
$704$	−1.99700	+	1.15297i	−0.0752646	+	0.0434541i
$705$		0			0
$706$	−13.6360	+	23.6182i	−0.513197	+	0.888884i
$707$			17.4106i			0.654791i
$708$	−3.05697	−	1.76495i	−0.114888	−	0.0663307i
$709$	−30.9654	−	17.8779i	−1.16293	−	0.671418i	−0.210925	−	0.977502i	$-0.567648\pi$
$709$	−30.9654	−	17.8779i	−1.16293	−	0.671418i	−0.952004	+	0.306084i	$0.900981\pi$
$710$		0			0
$711$	6.10728	−	10.5781i	0.229041	−	0.396710i
$712$	1.11749	+	1.93556i	0.0418798	+	0.0725380i
$713$	−22.7709	+	13.1468i	−0.852776	+	0.492351i
$714$	1.20216			0.0449897
$715$		0			0
$716$	−12.4431			−0.465021
$717$	−27.7790	+	16.0382i	−1.03743	+	0.598959i
$718$	13.9099	+	24.0927i	0.519115	+	0.899133i
$719$	−22.1412	+	38.3497i	−0.825728	+	1.43020i	0.0756332	+	0.997136i	$0.475902\pi$
$719$	−22.1412	+	38.3497i	−0.825728	+	1.43020i	−0.901361	+	0.433068i	$0.857431\pi$
$720$		0			0
$721$	19.7746	+	11.4168i	0.736443	+	0.425186i
$722$	−9.86964	−	5.69824i	−0.367310	−	0.212066i
$723$			28.0496i			1.04318i
$724$	−6.75147	+	11.6939i	−0.250916	+	0.434600i
$725$		0			0
$726$	7.35990	−	4.24924i	0.273152	−	0.157704i
$727$	−6.29553			−0.233488			−0.116744	−	0.993162i	$-0.537246\pi$
$727$	−6.29553			−0.233488			−0.116744	+	0.993162i	$0.537246\pi$
$728$	−5.02900	+	0.464102i	−0.186387	+	0.0172008i
$729$	29.9289			1.10848
$730$		0			0
$731$	0.327616	+	0.567448i	0.0121173	+	0.0209878i
$732$	6.98759	−	12.1029i	0.258269	−	0.447334i
$733$			0.470338i			0.0173723i	0.999962	+	0.00868616i	$0.00276492\pi$
$733$			0.470338i			0.0173723i	−0.999962	+	0.00868616i	$0.997235\pi$
$734$	−5.68721	−	3.28351i	−0.209919	−	0.121197i
$735$		0			0
$736$			7.45512i			0.274799i
$737$	5.15830	−	8.93444i	0.190008	−	0.329104i
$738$	0.535831	+	0.928087i	0.0197242	+	0.0341633i
$739$	−15.2283	+	8.79208i	−0.560183	+	0.323422i	−0.753219	−	0.657770i	$-0.771500\pi$
$739$	−15.2283	+	8.79208i	−0.560183	+	0.323422i	0.193036	+	0.981192i	$0.438167\pi$
$740$		0			0
$741$	−12.1389	+	8.58609i	−0.445932	+	0.315418i
$742$	−1.24615			−0.0457477
$743$	−15.8531	+	9.15278i	−0.581593	+	0.335783i	−0.761766	−	0.647852i	$-0.775668\pi$
$743$	−15.8531	+	9.15278i	−0.581593	+	0.335783i	0.180173	+	0.983635i	$0.442334\pi$
$744$	2.63726	+	4.56787i	0.0966868	+	0.167466i
$745$		0			0
$746$		−	2.96103i		−	0.108411i
$747$	−5.52762	−	3.19138i	−0.202245	−	0.116766i
$748$	1.14604	+	0.661666i	0.0419034	+	0.0241929i
$749$		−	14.6447i		−	0.535105i
$750$		0			0
$751$	11.1507	+	19.3136i	0.406895	+	0.704762i	0.994540	−	0.104356i	$-0.0332782\pi$
$751$	11.1507	+	19.3136i	0.406895	+	0.704762i	−0.587645	+	0.809119i	$0.699945\pi$
$752$	4.14519	−	2.39322i	0.151159	−	0.0872719i
$753$	4.99314			0.181960
$754$	−1.76048	−	19.0765i	−0.0641129	−	0.694726i
$755$		0			0
$756$	−6.82743	+	3.94182i	−0.248311	+	0.143363i
$757$	2.25766	+	3.91038i	0.0820560	+	0.142125i	0.904133	−	0.427251i	$-0.140518\pi$
$757$	2.25766	+	3.91038i	0.0820560	+	0.142125i	−0.822077	+	0.569376i	$0.807185\pi$
$758$	5.34576	−	9.25913i	0.194167	−	0.336307i
$759$			25.7093i			0.933187i
$760$		0			0
$761$	−11.3639	−	6.56094i	−0.411941	−	0.237834i	0.279683	−	0.960093i	$-0.409771\pi$
$761$	−11.3639	−	6.56094i	−0.411941	−	0.237834i	−0.691623	+	0.722258i	$0.743104\pi$
$762$		−	19.4401i		−	0.704241i
$763$	10.3355	−	17.9017i	0.374171	−	0.648084i
$764$	8.32684	+	14.4225i	0.301254	+	0.521788i
$765$		0			0
$766$	−14.7171			−0.531751
$767$	−0.782050	−	8.47428i	−0.0282382	−	0.305988i
$768$	1.49551			0.0539645
$769$	28.6082	−	16.5169i	1.03164	−	0.595616i	0.114184	−	0.993460i	$-0.463575\pi$
$769$	28.6082	−	16.5169i	1.03164	−	0.595616i	0.917453	+	0.397843i	$0.130241\pi$
$770$		0			0
$771$	1.52105	−	2.63453i	0.0547792	−	0.0948803i
$772$		−	14.8821i		−	0.535618i
$773$	14.1781	+	8.18575i	0.509952	+	0.294421i	0.732814	−	0.680429i	$-0.238207\pi$
$773$	14.1781	+	8.18575i	0.509952	+	0.294421i	−0.222862	+	0.974850i	$0.571540\pi$
$774$	−0.754898	−	0.435841i	−0.0271342	−	0.0156660i
$775$		0			0
$776$	8.06189	−	13.9636i	0.289405	−	0.501264i
$777$	−2.71306	−	4.69916i	−0.0973305	−	0.168581i
$778$	−10.5953	+	6.11721i	−0.379861	+	0.219313i
$779$	−3.87062			−0.138679
$780$		0			0
$781$	20.6912			0.740391
$782$	3.70516	−	2.13918i	0.132496	−	0.0764968i
$783$	−14.9525	−	25.8986i	−0.534360	−	0.925539i
$784$	−2.51899	+	4.36302i	−0.0899640	+	0.155822i
$785$		0			0
$786$	−18.2401	−	10.5309i	−0.650602	−	0.375625i
$787$	−40.4488	−	23.3531i	−1.44185	−	0.832450i	−0.443872	−	0.896090i	$-0.646396\pi$
$787$	−40.4488	−	23.3531i	−1.44185	−	0.832450i	−0.997973	+	0.0636403i	$0.979729\pi$
$788$			0.785824i			0.0279938i
$789$	−0.429122	+	0.743261i	−0.0152772	+	0.0264608i
$790$		0			0
$791$	−21.7199	+	12.5400i	−0.772271	+	0.445871i
$792$	−1.76048			−0.0625559
$793$	33.5505	−	3.09621i	1.19141	−	0.109950i
$794$	23.2938			0.826667
$795$		0			0
$796$	−0.0713036	−	0.123501i	−0.00252729	−	0.00437739i
$797$	4.12750	−	7.14904i	0.146204	−	0.253232i	−0.783618	−	0.621243i	$-0.786628\pi$
$797$	4.12750	−	7.14904i	0.146204	−	0.253232i	0.929821	+	0.368011i	$0.119961\pi$
$798$		−	5.77627i		−	0.204478i
$799$	−2.37885	−	1.37343i	−0.0841575	−	0.0485884i
$800$		0			0
$801$			1.70632i			0.0602897i
$802$	−14.9013	+	25.8098i	−0.526184	+	0.911377i
$803$	11.2904	+	19.5555i	0.398429	+	0.690098i
$804$	−5.79441	+	3.34540i	−0.204353	+	0.117983i
$805$		0			0
$806$	−5.31932	+	11.5505i	−0.187365	+	0.406848i
$807$	44.1168			1.55298
$808$	10.7645	−	6.21486i	0.378692	−	0.218638i
$809$	13.0395	+	22.5850i	0.458443	+	0.794046i	0.998879	−	0.0473387i	$-0.0150740\pi$
$809$	13.0395	+	22.5850i	0.458443	+	0.794046i	−0.540436	+	0.841385i	$0.681741\pi$
$810$		0			0
$811$		−	37.2793i		−	1.30905i	−0.756039	−	0.654526i	$-0.772868\pi$
$811$		−	37.2793i		−	1.30905i	0.756039	−	0.654526i	$-0.227132\pi$
$812$	6.44542	+	3.72127i	0.226190	+	0.130591i
$813$	−7.03430	−	4.06126i	−0.246704	−	0.142434i
$814$		−	5.97305i		−	0.209355i
$815$		0			0
$816$	−0.429122	−	0.743261i	−0.0150223	−	0.0260194i
$817$	2.72654	−	1.57417i	0.0953894	−	0.0550731i
$818$	24.8958			0.870462
$819$	−3.50220	−	1.61286i	−0.122377	−	0.0563579i
$820$		0			0
$821$	−24.4587	+	14.1212i	−0.853614	+	0.492835i	−0.861869	−	0.507131i	$-0.830706\pi$
$821$	−24.4587	+	14.1212i	−0.853614	+	0.492835i	0.00825433	+	0.999966i	$0.497373\pi$
$822$	−13.9895	−	24.2305i	−0.487938	−	0.845134i
$823$	15.5619	−	26.9539i	0.542453	−	0.939555i	−0.456310	−	0.889821i	$-0.650829\pi$
$823$	15.5619	−	26.9539i	0.542453	−	0.939555i	0.998762	−	0.0497345i	$-0.0158375\pi$
$824$		−	16.3014i		−	0.567886i
$825$		0			0
$826$	2.86322	+	1.65308i	0.0996241	+	0.0575180i
$827$		−	15.4978i		−	0.538911i	−0.963013	−	0.269455i	$-0.913156\pi$
$827$		−	15.4978i		−	0.538911i	0.963013	−	0.269455i	$-0.0868437\pi$
$828$	−2.84583	+	4.92912i	−0.0988994	+	0.171299i
$829$	−3.70674	−	6.42026i	−0.128740	−	0.222985i	0.794448	−	0.607332i	$-0.207760\pi$
$829$	−3.70674	−	6.42026i	−0.128740	−	0.222985i	−0.923189	+	0.384347i	$0.874427\pi$
$830$		0			0
$831$	−9.70064			−0.336512
$832$	2.08209	+	2.94362i	0.0721834	+	0.102052i
$833$	2.89121			0.100174
$834$	−21.8842	+	12.6349i	−0.757788	+	0.437509i
$835$		0			0
$836$	3.17925	−	5.50662i	0.109957	−	0.190450i
$837$			19.8505i			0.686132i
$838$	−1.84605	−	1.06582i	−0.0637706	−	0.0368180i
$839$	−8.38778	−	4.84269i	−0.289578	−	0.167188i	0.348173	−	0.937430i	$-0.386802\pi$
$839$	−8.38778	−	4.84269i	−0.289578	−	0.167188i	−0.637752	+	0.770242i	$0.720135\pi$
$840$		0			0
$841$	0.384096	−	0.665273i	0.0132447	−	0.0229404i
$842$	−4.31714	−	7.47751i	−0.148779	−	0.257692i
$843$	−9.50367	+	5.48695i	−0.327324	+	0.188981i
$844$	−15.6939			−0.540207
$845$		0			0
$846$	3.65425			0.125636
$847$	−6.89342	+	3.97992i	−0.236861	+	0.136752i
$848$	0.444825	+	0.770460i	0.0152754	+	0.0264577i
$849$	3.30589	−	5.72597i	0.113458	−	0.196515i
$850$		0			0
$851$	−16.7238	−	9.65548i	−0.573284	−	0.330985i
$852$	−11.6214	−	6.70963i	−0.398143	−	0.229868i
$853$		−	28.6312i		−	0.980313i	−0.871635	−	0.490156i	$-0.836940\pi$
$853$		−	28.6312i		−	0.980313i	0.871635	−	0.490156i	$-0.163060\pi$
$854$	−6.54470	+	11.3358i	−0.223955	+	0.387902i
$855$		0			0
$856$	−9.05440	+	5.22756i	−0.309473	+	0.178674i
$857$	−13.2207			−0.451610			−0.225805	−	0.974172i	$-0.572501\pi$
$857$	−13.2207			−0.451610			−0.225805	+	0.974172i	$0.572501\pi$
$858$	7.18016	+	10.1512i	0.245127	+	0.346556i
$859$	−15.9161			−0.543049			−0.271524	−	0.962432i	$-0.587528\pi$
$859$	−15.9161			−0.543049			−0.271524	+	0.962432i	$0.587528\pi$
$860$		0			0
$861$	1.47022	+	2.54650i	0.0501051	+	0.0867845i
$862$	−14.3534	+	24.8608i	−0.488879	+	0.846763i
$863$		−	52.3436i		−	1.78180i	−0.454201	−	0.890899i	$-0.650075\pi$
$863$		−	52.3436i		−	1.78180i	0.454201	−	0.890899i	$-0.349925\pi$
$864$	4.87423	+	2.81414i	0.165825	+	0.0957390i
$865$		0			0
$866$		−	23.1208i		−	0.785677i
$867$	12.4655	−	21.5910i	0.423352	−	0.733268i
$868$	−2.47011	−	4.27835i	−0.0838410	−	0.145217i
$869$	31.9500	−	18.4463i	1.08383	−	0.625749i
$870$		0			0
$871$	−14.6519	−	6.74762i	−0.496462	−	0.228635i
$872$	−14.7574			−0.499750
$873$	10.6606	−	6.15491i	0.360807	−	0.208312i
$874$	−10.2786	−	17.8030i	−0.347677	−	0.602195i
$875$		0			0
$876$		−	14.6447i		−	0.494798i
$877$	−23.9478	−	13.8263i	−0.808660	−	0.466880i	0.0378301	−	0.999284i	$-0.487955\pi$
$877$	−23.9478	−	13.8263i	−0.808660	−	0.466880i	−0.846490	+	0.532404i	$0.821289\pi$
$878$	−21.0104	−	12.1304i	−0.709067	−	0.409380i
$879$			18.2900i			0.616907i
$880$		0			0
$881$	−15.6436	−	27.0956i	−0.527047	−	0.912873i	−0.999503	−	0.0315183i	$-0.989966\pi$
$881$	−15.6436	−	27.0956i	−0.527047	−	0.912873i	0.472456	−	0.881354i	$-0.343368\pi$
$882$	−3.33098	+	1.92314i	−0.112160	+	0.0647555i
$883$	−27.1744			−0.914490			−0.457245	−	0.889341i	$-0.651164\pi$
$883$	−27.1744			−0.914490			−0.457245	+	0.889341i	$0.651164\pi$
$884$	0.865532	−	1.87944i	0.0291110	−	0.0632122i
$885$		0			0
$886$	23.2777	−	13.4394i	0.782031	−	0.451506i
$887$	10.0613	+	17.4266i	0.337824	+	0.585128i	0.984023	−	0.178041i	$-0.0569758\pi$
$887$	10.0613	+	17.4266i	0.337824	+	0.585128i	−0.646199	+	0.763169i	$0.723642\pi$
$888$	−1.93690	+	3.35481i	−0.0649982	+	0.112580i
$889$			18.2080i			0.610676i
$890$		0			0
$891$	12.2351	+	7.06395i	0.409892	+	0.236651i
$892$			8.72902i			0.292269i
$893$	−6.59919	+	11.4301i	−0.220834	+	0.382495i
$894$	16.5158	+	28.6062i	0.552371	+	0.956735i
$895$		0			0
$896$	−1.40072			−0.0467948
$897$	40.0289	−	3.69407i	1.33652	−	0.123341i
$898$	−36.4490			−1.21632
$899$	16.2291	−	9.36988i	0.541271	−	0.312503i
$900$		0			0
$901$	0.255277	−	0.442153i	0.00850451	−	0.0147302i
$902$			3.23683i			0.107775i
$903$	−2.07130	−	1.19587i	−0.0689287	−	0.0397960i
$904$	15.5063	+	8.95254i	0.515730	+	0.297757i
$905$		0			0
$906$	5.52228	−	9.56487i	0.183465	−	0.317772i
$907$	12.6396	+	21.8924i	0.419690	+	0.726924i	0.995908	−	0.0903720i	$-0.0288056\pi$
$907$	12.6396	+	21.8924i	0.419690	+	0.726924i	−0.576218	+	0.817296i	$0.695472\pi$
$908$	−2.75373	+	1.58987i	−0.0913859	+	0.0527617i
$909$	9.48955			0.314749
$910$		0			0
$911$	−13.3655			−0.442820			−0.221410	−	0.975181i	$-0.571066\pi$
$911$	−13.3655			−0.442820			−0.221410	+	0.975181i	$0.571066\pi$
$912$	−3.57130	+	2.06189i	−0.118258	+	0.0682761i
$913$	−9.63918	−	16.6955i	−0.319010	−	0.552542i
$914$	11.7796	−	20.4028i	0.389634	−	0.674866i
$915$		0			0
$916$	15.1974	+	8.77424i	0.502137	+	0.289909i
$917$	17.0840	+	9.86345i	0.564163	+	0.325720i
$918$		−	3.22997i		−	0.106605i
$919$	0.454547	−	0.787299i	0.0149941	−	0.0259706i	−0.858431	−	0.512929i	$-0.828560\pi$
$919$	0.454547	−	0.787299i	0.0149941	−	0.0259706i	0.873425	+	0.486958i	$0.161894\pi$
$920$		0			0
$921$	−7.64922	+	4.41628i	−0.252051	+	0.145521i
$922$	−35.6721			−1.17480
$923$	−2.97305	−	32.2159i	−0.0978590	−	1.06040i
$924$	−4.83044			−0.158910
$925$		0			0
$926$	−1.45363	−	2.51776i	−0.0477692	−	0.0827387i
$927$	6.22271	−	10.7780i	0.204381	−	0.353997i
$928$		−	5.31336i		−	0.174420i
$929$	−5.65093	−	3.26256i	−0.185401	−	0.107041i	0.404427	−	0.914570i	$-0.367471\pi$
$929$	−5.65093	−	3.26256i	−0.185401	−	0.107041i	−0.589828	+	0.807529i	$0.700804\pi$
$930$		0			0
$931$		−	13.8920i		−	0.455291i
$932$	6.32083	−	10.9480i	0.207046	−	0.358614i
$933$	−3.17234	−	5.49466i	−0.103858	−	0.179887i
$934$	−23.9189	+	13.8096i	−0.782650	+	0.451863i
$935$		0			0
$936$	0.252957	+	2.74104i	0.00826815	+	0.0895935i
$937$	−49.3573			−1.61243			−0.806216	−	0.591621i	$-0.798488\pi$
$937$	−49.3573			−1.61243			−0.806216	+	0.591621i	$0.798488\pi$
$938$	5.42715	−	3.13337i	0.177203	−	0.102308i
$939$	−8.93878	−	15.4824i	−0.291706	−	0.505250i
$940$		0			0
$941$		−	4.46988i		−	0.145714i	−0.997342	−	0.0728570i	$-0.976788\pi$
$941$		−	4.46988i		−	0.145714i	0.997342	−	0.0728570i	$-0.0232117\pi$
$942$	17.4224	+	10.0588i	0.567654	+	0.327735i
$943$	9.06272	+	5.23236i	0.295123	+	0.170389i
$944$		−	2.36033i		−	0.0768222i
$945$		0			0
$946$	−1.31641	−	2.28008i	−0.0428000	−	0.0741318i
$947$	13.6026	−	7.85347i	0.442025	−	0.255203i	−0.262431	−	0.964951i	$-0.584524\pi$
$947$	13.6026	−	7.85347i	0.442025	−	0.255203i	0.704456	+	0.709747i	$0.251191\pi$
$948$	−23.9266			−0.777101
$949$	28.8253	−	20.3888i	0.935708	−	0.661847i
$950$		0			0
$951$	−25.0945	+	14.4883i	−0.813744	+	0.469815i
$952$	0.401924	+	0.696152i	0.0130264	+	0.0225624i
$953$	6.80495	−	11.7865i	0.220434	−	0.381803i	−0.734506	−	0.678602i	$-0.762586\pi$
$953$	6.80495	−	11.7865i	0.220434	−	0.381803i	0.954940	+	0.296800i	$0.0959194\pi$
$954$			0.679210i			0.0219902i
$955$		0			0
$956$	−18.5750	−	10.7243i	−0.600758	−	0.346848i
$957$		−	18.3233i		−	0.592309i
$958$	1.93690	−	3.35481i	0.0625785	−	0.108389i
$959$	13.1028	+	22.6947i	0.423111	+	0.732850i
$960$		0			0
$961$	18.5609			0.598738
$962$	−9.29992	+	0.858244i	−0.299842	+	0.0276709i
$963$	−7.98203			−0.257217
$964$	−16.2431	+	9.37795i	−0.523154	+	0.302043i
$965$		0			0
$966$	−7.80844	+	13.5246i	−0.251233	+	0.435148i
$967$		−	8.67779i		−	0.279059i	−0.990218	−	0.139529i	$-0.955441\pi$
$967$		−	8.67779i		−	0.279059i	0.990218	−	0.139529i	$-0.0445590\pi$
$968$	4.92134	+	2.84134i	0.158178	+	0.0913241i
$969$	2.04951	+	1.18328i	0.0658396	+	0.0380125i
$970$		0			0
$971$	24.8891	−	43.1092i	0.798730	−	1.38344i	−0.121714	−	0.992565i	$-0.538839\pi$
$971$	24.8891	−	43.1092i	0.798730	−	1.38344i	0.920444	−	0.390875i	$-0.127828\pi$
$972$	3.86111	+	6.68763i	0.123845	+	0.214506i
$973$	20.4972	−	11.8340i	0.657109	−	0.379382i
$974$	3.59270			0.115118
$975$		0			0
$976$	9.34477			0.299119
$977$	−30.3399	+	17.5167i	−0.970658	+	0.560410i	−0.899437	−	0.437051i	$-0.856023\pi$
$977$	−30.3399	+	17.5167i	−0.970658	+	0.560410i	−0.0712213	+	0.997461i	$0.522690\pi$
$978$	−11.2742	−	19.5274i	−0.360508	−	0.624419i
$979$	−2.57686	+	4.46326i	−0.0823570	+	0.142646i
$980$		0			0
$981$	−9.75723	−	5.63334i	−0.311524	−	0.179859i
$982$	−5.20774	−	3.00669i	−0.166186	−	0.0959474i
$983$		−	31.1547i		−	0.993681i	−0.867842	−	0.496841i	$-0.834493\pi$
$983$		−	31.1547i		−	0.993681i	0.867842	−	0.496841i	$-0.165507\pi$
$984$	1.04962	−	1.81799i	0.0334607	−	0.0579556i
$985$		0			0
$986$	−2.64072	+	1.52462i	−0.0840977	+	0.0485538i
$987$	10.0266			0.319150
$988$	−9.03051	−	4.15880i	−0.287299	−	0.132309i
$989$	−8.51192			−0.270663
$990$		0			0
$991$	−18.6073	−	32.2288i	−0.591081	−	1.02378i	−0.994087	−	0.108586i	$-0.965368\pi$
$991$	−18.6073	−	32.2288i	−0.591081	−	1.02378i	0.403006	−	0.915197i	$-0.367965\pi$
$992$	−1.76346	+	3.05440i	−0.0559898	+	0.0969772i
$993$			17.2931i			0.548779i
$994$	10.8848	+	6.28436i	0.345246	+	0.199328i
$995$		0			0
$996$			12.5029i			0.396171i
$997$	−22.0961	+	38.2716i	−0.699791	+	1.21207i	0.268747	+	0.963211i	$0.413390\pi$
$997$	−22.0961	+	38.2716i	−0.699791	+	1.21207i	−0.968539	+	0.248863i	$0.919943\pi$
$998$	−22.0049	−	38.1136i	−0.696552	−	1.20646i
$999$	−12.6257	+	7.28945i	−0.399459	+	0.230628i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.m.d.101.3	yes	8
5.2	odd	4		650.2.n.f.49.1		8
5.3	odd	4		650.2.n.c.49.4		8
5.4	even	2		650.2.m.b.101.2	✓	8
13.2	odd	12		8450.2.a.cl.1.4		4
13.4	even	6	inner	650.2.m.d.251.3	yes	8
13.11	odd	12		8450.2.a.ch.1.4		4
65.4	even	6		650.2.m.b.251.2	yes	8
65.17	odd	12		650.2.n.c.199.4		8
65.24	odd	12		8450.2.a.co.1.1		4
65.43	odd	12		650.2.n.f.199.1		8
65.54	odd	12		8450.2.a.ck.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.m.b.101.2	✓	8	5.4	even	2
650.2.m.b.251.2	yes	8	65.4	even	6
650.2.m.d.101.3	yes	8	1.1	even	1	trivial
650.2.m.d.251.3	yes	8	13.4	even	6	inner
650.2.n.c.49.4		8	5.3	odd	4
650.2.n.c.199.4		8	65.17	odd	12
650.2.n.f.49.1		8	5.2	odd	4
650.2.n.f.199.1		8	65.43	odd	12
8450.2.a.ch.1.4		4	13.11	odd	12
8450.2.a.ck.1.1		4	65.54	odd	12
8450.2.a.cl.1.4		4	13.2	odd	12
8450.2.a.co.1.1		4	65.24	odd	12

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.747754 - 1.29515i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.29515 - 0.747754i) q^{6} +(1.21306 + 0.700360i) q^{7} -1.00000i q^{8} +(0.381728 - 0.661173i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.747754 - 1.29515i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.29515 - 0.747754i) q^{6} +(1.21306 + 0.700360i) q^{7} -1.00000i q^{8} +(0.381728 - 0.661173i) q^{9} +(1.99700 - 1.15297i) q^{11} -1.49551 q^{12} +(-2.08209 - 2.94362i) q^{13} +1.40072 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.286941 + 0.496996i) q^{17} -0.763457i q^{18} +(2.38802 + 1.37872i) q^{19} -2.09479i q^{21} +(1.15297 - 1.99700i) q^{22} +(-3.72756 - 6.45632i) q^{23} +(-1.29515 + 0.747754i) q^{24} +(-3.27495 - 1.50821i) q^{26} -5.62828 q^{27} +(1.21306 - 0.700360i) q^{28} +(2.65668 + 4.60151i) q^{29} -3.52691i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.98652 - 1.72427i) q^{33} +0.573882i q^{34} +(-0.381728 - 0.661173i) q^{36} +(2.24326 - 1.29515i) q^{37} +2.75745 q^{38} +(-2.25553 + 4.89772i) q^{39} +(-1.21564 + 0.701848i) q^{41} +(-1.04739 - 1.81414i) q^{42} +(0.570878 - 0.988789i) q^{43} -2.30593i q^{44} +(-6.45632 - 3.72756i) q^{46} +4.78645i q^{47} +(-0.747754 + 1.29515i) q^{48} +(-2.51899 - 4.36302i) q^{49} +0.858244 q^{51} +(-3.59030 + 0.331331i) q^{52} -0.889650 q^{53} +(-4.87423 + 2.81414i) q^{54} +(0.700360 - 1.21306i) q^{56} -4.12379i q^{57} +(4.60151 + 2.65668i) q^{58} +(2.04411 + 1.18016i) q^{59} +(-4.67238 + 8.09281i) q^{61} +(-1.76346 - 3.05440i) q^{62} +(0.926118 - 0.534695i) q^{63} -1.00000 q^{64} -3.44854 q^{66} +(3.87454 - 2.23697i) q^{67} +(0.286941 + 0.496996i) q^{68} +(-5.57459 + 9.65548i) q^{69} +(7.77089 + 4.48652i) q^{71} +(-0.661173 - 0.381728i) q^{72} +9.79246i q^{73} +(1.29515 - 2.24326i) q^{74} +(2.38802 - 1.37872i) q^{76} +3.22997 q^{77} +(0.495508 + 5.36931i) q^{78} +15.9990 q^{79} +(3.06338 + 5.30593i) q^{81} +(-0.701848 + 1.21564i) q^{82} -8.36033i q^{83} +(-1.81414 - 1.04739i) q^{84} -1.14176i q^{86} +(3.97309 - 6.88159i) q^{87} +(-1.15297 - 1.99700i) q^{88} +(-1.93556 + 1.11749i) q^{89} +(-0.464102 - 5.02900i) q^{91} -7.45512 q^{92} +(-4.56787 + 2.63726i) q^{93} +(2.39322 + 4.14519i) q^{94} +1.49551i q^{96} +(13.9636 + 8.06189i) q^{97} +(-4.36302 - 2.51899i) q^{98} -1.76048i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 4 q^{4} + 6 q^{7} + 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 4 * q^4 + 6 * q^7 + 2 * q^9	\( 8 q + 2 q^{3} + 4 q^{4} + 6 q^{7} + 2 q^{9} + 12 q^{11} + 4 q^{12} - 10 q^{13} - 4 q^{16} - 6 q^{17} + 6 q^{19} + 6 q^{22} + 6 q^{26} - 4 q^{27} + 6 q^{28} - 12 q^{29} + 24 q^{33} - 2 q^{36} - 6 q^{37} + 12 q^{38} - 10 q^{39} - 24 q^{41} - 6 q^{42} + 8 q^{43} - 24 q^{46} + 2 q^{48} - 10 q^{49} - 8 q^{52} - 12 q^{53} - 18 q^{54} + 6 q^{58} + 30 q^{59} - 10 q^{61} - 12 q^{62} - 8 q^{64} - 30 q^{67} + 6 q^{68} - 18 q^{69} + 12 q^{72} + 6 q^{76} + 60 q^{77} - 12 q^{78} - 4 q^{79} + 8 q^{81} - 12 q^{82} + 6 q^{84} + 36 q^{87} - 6 q^{88} - 6 q^{89} + 24 q^{91} - 36 q^{93} - 12 q^{94} + 18 q^{97} - 24 q^{98}+O(q^{100}) \) 8 * q + 2 * q^3 + 4 * q^4 + 6 * q^7 + 2 * q^9 + 12 * q^11 + 4 * q^12 - 10 * q^13 - 4 * q^16 - 6 * q^17 + 6 * q^19 + 6 * q^22 + 6 * q^26 - 4 * q^27 + 6 * q^28 - 12 * q^29 + 24 * q^33 - 2 * q^36 - 6 * q^37 + 12 * q^38 - 10 * q^39 - 24 * q^41 - 6 * q^42 + 8 * q^43 - 24 * q^46 + 2 * q^48 - 10 * q^49 - 8 * q^52 - 12 * q^53 - 18 * q^54 + 6 * q^58 + 30 * q^59 - 10 * q^61 - 12 * q^62 - 8 * q^64 - 30 * q^67 + 6 * q^68 - 18 * q^69 + 12 * q^72 + 6 * q^76 + 60 * q^77 - 12 * q^78 - 4 * q^79 + 8 * q^81 - 12 * q^82 + 6 * q^84 + 36 * q^87 - 6 * q^88 - 6 * q^89 + 24 * q^91 - 36 * q^93 - 12 * q^94 + 18 * q^97 - 24 * q^98

Introduction

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