LMFDB - Embedded newform 650.2.m.b.101.2

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			101.2
Root			$1.20036 - 0.747754i$ of defining polynomial
Character	$\chi$	$=$	650.101
Dual form			650.2.m.b.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 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} + 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}+ \cdots + 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

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	0.997021	−	0.0771279i	$-0.0245750\pi$
$3$	0.747754	+	1.29515i	0.431716	+	0.747754i	−0.565305	+	0.824882i	$0.691242\pi$
$4$	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	0.252917	−	0.967488i	$-0.418610\pi$
$7$	−1.21306	−	0.700360i	−0.458493	−	0.264711i	−0.711410	+	0.702777i	$0.751943\pi$
$8$			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	−0.829129	−	0.559057i	$-0.811163\pi$
$17$	0.286941	−	0.496996i	0.0695934	−	0.120539i	0.898722	+	0.438518i	$0.144496\pi$
$18$			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	$0.116719\pi$
$23$	3.72756	+	6.45632i	0.777250	+	1.34624i	−0.156272	+	0.987714i	$0.549948\pi$
$24$	−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	−0.672930	−	0.739706i	$-0.734964\pi$
$37$	−2.24326	+	1.29515i	−0.368790	+	0.212921i	0.304140	+	0.952627i	$0.401631\pi$
$38$	−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	−0.906266	−	0.422707i	$-0.861080\pi$
$43$	−0.570878	+	0.988789i	−0.0870580	+	0.150789i	0.819208	+	0.573496i	$0.194413\pi$
$44$		−	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	$-0.886492\pi$
$47$		−	4.78645i		−	0.698175i	0.937090	−	0.349088i	$-0.113508\pi$
$48$	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	$-0.480539\pi$
$53$	0.889650			0.122203			0.0611014	+	0.998132i	$0.480539\pi$
$54$	−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	−0.717641	−	0.696413i	$-0.754778\pi$
$67$	−3.87454	+	2.23697i	−0.473351	+	0.273289i	0.244291	+	0.969702i	$0.421445\pi$
$68$	−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	$-0.805756\pi$
$73$		−	9.79246i		−	1.14612i	0.819513	−	0.573060i	$-0.194244\pi$
$74$	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	$0.151732\pi$
$83$			8.36033i			0.917665i	−0.888523	+	0.458833i	$0.848268\pi$
$84$	−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	−0.421685	−	0.906742i	$-0.638561\pi$
$97$	−13.9636	−	8.06189i	−1.41779	−	0.818561i	−0.996104	+	0.0881811i	$0.971895\pi$
$98$	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	$-0.796824\pi$
$103$	−16.3014			−1.60622			−0.803112	+	0.595828i	$0.796824\pi$
$104$	−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	$0.00197627\pi$
$107$	5.22756	+	9.05440i	0.505367	+	0.875322i	−0.494614	+	0.869113i	$0.664690\pi$
$108$	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	$-0.514603\pi$
$113$	8.95254	−	15.5063i	0.842184	−	1.45871i	0.888044	−	0.459758i	$-0.152064\pi$
$114$	−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	$-0.970992\pi$
$127$	−6.49951	−	11.2575i	−0.576738	−	0.998939i	0.419112	−	0.907934i	$-0.362341\pi$
$128$	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	−0.391585	−	0.920142i	$-0.628073\pi$
$137$	−16.2022	−	9.35432i	−1.38424	−	0.799194i	−0.992659	+	0.120948i	$0.961406\pi$
$138$		−	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	$-0.319634\pi$
$157$	13.4521			1.07359			0.536797	+	0.843712i	$0.319634\pi$
$158$	−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	−0.107840	−	0.994168i	$-0.534393\pi$
$163$	−13.0574	−	7.53869i	−1.02273	−	0.590476i	−0.914895	+	0.403692i	$0.867727\pi$
$164$			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	$-0.308990\pi$
$167$	20.1827	−	11.6525i	1.56178	−	0.901695i	0.997077	−	0.0764028i	$-0.0243435\pi$
$168$	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	$-0.660069\pi$
$173$	6.81114	−	11.7972i	0.517841	−	0.896927i	0.999785	−	0.0207251i	$-0.00659746\pi$
$174$		−	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	−0.886089	−	0.463515i	$-0.846588\pi$
$193$	−12.8883	+	7.44104i	−0.927718	+	0.535618i	−0.0416286	+	0.999133i	$0.513255\pi$
$194$	16.1238			1.15762
$195$		0			0
$196$	−5.03798			−0.359856
$197$	0.680544	−	0.392912i	0.0484867	−	0.0279938i	−0.475561	−	0.879683i	$-0.657755\pi$
$197$	0.680544	−	0.392912i	0.0484867	−	0.0279938i	0.524047	+	0.851689i	$0.324421\pi$
$198$	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	−0.225055	−	0.974346i	$-0.572256\pi$
$223$	7.55955	−	4.36451i	0.506225	−	0.292269i	0.731281	+	0.682077i	$0.238923\pi$
$224$	−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	0.588594	−	0.808429i	$-0.299682\pi$
$227$	2.75373	+	1.58987i	0.182772	+	0.105523i	−0.405823	+	0.913952i	$0.633015\pi$
$228$	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	$-0.635901\pi$
$233$	−12.6417			−0.828183			−0.414091	+	0.910235i	$0.635901\pi$
$234$	−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	0.832559	−	0.553936i	$-0.186875\pi$
$257$	−1.01708	−	1.76163i	−0.0634435	−	0.109887i	−0.896003	+	0.444049i	$0.853542\pi$
$258$	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	0.874737	−	0.484599i	$-0.161034\pi$
$263$	0.286941	+	0.496996i	0.0176935	+	0.0306461i	−0.857043	+	0.515245i	$0.827701\pi$
$264$	−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	−0.946857	−	0.321653i	$-0.895761\pi$
$277$	−3.24326	+	5.61749i	−0.194869	+	0.337522i	0.751989	+	0.659176i	$0.229095\pi$
$278$			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	0.792814	−	0.609463i	$-0.208615\pi$
$283$	−2.21055	−	3.82878i	−0.131403	−	0.227597i	−0.924218	+	0.381866i	$0.875282\pi$
$284$	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	0.776386	−	0.630258i	$-0.217051\pi$
$293$	10.5915	+	6.11498i	0.618760	+	0.357241i	−0.157626	+	0.987499i	$0.550384\pi$
$294$			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	$0.0539047\pi$
$307$			5.90606i			0.337077i	−0.985695	+	0.168538i	$0.946095\pi$
$308$	−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	$-0.609698\pi$
$313$	−11.9542			−0.675690			−0.337845	+	0.941202i	$0.609698\pi$
$314$	−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	$0.183138\pi$
$317$			19.3758i			1.08825i	−0.839004	+	0.544125i	$0.816862\pi$
$318$	−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	$-0.680029\pi$
$337$	−19.6758			−1.07181			−0.535905	+	0.844278i	$0.680029\pi$
$338$	−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	−0.970483	−	0.241169i	$-0.922469\pi$
$347$	−5.14845	+	8.91737i	−0.276383	+	0.478710i	0.694100	+	0.719879i	$0.255803\pi$
$348$	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	0.284567	−	0.958656i	$-0.408150\pi$
$353$	23.6182	−	13.6360i	1.25707	−	0.725771i	0.972504	+	0.232885i	$0.0748167\pi$
$354$	−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	0.938909	−	0.344166i	$-0.111838\pi$
$367$	3.28351	+	5.68721i	0.171398	+	0.296870i	−0.767511	+	0.641036i	$0.778505\pi$
$368$	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	−0.901806	−	0.432141i	$-0.857758\pi$
$373$	−1.48052	+	2.56433i	−0.0766582	+	0.132776i	0.825148	+	0.564917i	$0.191092\pi$
$374$	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	0.788938	−	0.614472i	$-0.210631\pi$
$383$	12.7454	+	7.35856i	0.651259	+	0.376005i	−0.137679	+	0.990477i	$0.543964\pi$
$384$	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	−0.100547	−	0.994932i	$-0.532059\pi$
$397$	−20.1731	−	11.6469i	−1.01246	−	0.584542i	−0.911910	+	0.410390i	$0.865392\pi$
$398$			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	$0.354162\pi$
$433$	−11.5604	+	20.0232i	−0.555558	+	0.962254i	−0.997860	+	0.0653880i	$0.979172\pi$
$434$		−	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	$-0.720455\pi$
$443$	−26.8788			−1.27705			−0.638526	+	0.769600i	$0.720455\pi$
$444$	−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	−0.894446	−	0.447175i	$-0.852430\pi$
$457$	−20.4028	+	11.7796i	−0.954405	+	0.551026i	−0.0599582	+	0.998201i	$0.519097\pi$
$458$	−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	$0.0215201\pi$
$463$			2.90726i			0.135112i	−0.997715	+	0.0675558i	$0.978480\pi$
$464$	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	$-0.279335\pi$
$467$	27.6192			1.27806			0.639031	+	0.769181i	$0.279335\pi$
$468$	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	0.427846	−	0.903852i	$-0.359273\pi$
$487$	−3.11137	−	1.79635i	−0.140990	−	0.0814004i	−0.568836	+	0.822451i	$0.692606\pi$
$488$	−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	−0.960632	−	0.277826i	$-0.910386\pi$
$503$	−5.37617	+	9.31181i	−0.239712	+	0.415193i	0.720920	+	0.693018i	$0.243720\pi$
$504$	−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	$-0.860622\pi$
$523$	−18.7535	−	32.4820i	−0.820033	−	1.42034i	0.0856245	−	0.996327i	$-0.472711\pi$
$524$	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	$-0.587302\pi$
$547$	−12.6690			−0.541685			−0.270843	+	0.962624i	$0.587302\pi$
$548$	−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	−0.363713	−	0.931511i	$-0.618491\pi$
$557$	6.16319	−	3.55832i	0.261143	−	0.150771i	0.624856	+	0.780740i	$0.285158\pi$
$558$	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	$-0.634099\pi$
$563$	13.9005	−	24.0764i	0.585838	−	1.01470i	0.994770	−	0.102136i	$-0.0325678\pi$
$564$		−	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	$-0.846903\pi$
$577$		−	22.2259i		−	0.925278i	0.886547	−	0.462639i	$-0.153097\pi$
$578$	−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	−0.917366	−	0.398045i	$-0.869689\pi$
$587$	−24.9872	+	14.4264i	−1.03133	+	0.595440i	−0.113966	+	0.993485i	$0.536355\pi$
$588$	−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	$0.185964\pi$
$593$			26.8623i			1.10310i	−0.834141	+	0.551551i	$0.814036\pi$
$594$	−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	$-0.653619\pi$
$607$	13.1827	−	22.8331i	0.535068	−	0.926765i	0.999160	−	0.0409783i	$-0.0130475\pi$
$608$	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	$-0.225821\pi$
$613$	42.1452	−	24.3325i	1.70223	−	0.982781i	0.943500	−	0.331373i	$-0.107512\pi$
$614$	−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	0.536984	−	0.843593i	$-0.319564\pi$
$617$	1.86056	+	1.07419i	0.0749032	+	0.0432454i	−0.462081	+	0.886838i	$0.652897\pi$
$618$	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	0.999987	−	0.00513351i	$-0.00163405\pi$
$643$	37.9229	+	21.8948i	1.49553	+	0.863447i	0.495548	+	0.868581i	$0.334967\pi$
$644$	−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	$-0.949092\pi$
$647$	−16.0638	−	27.8234i	−0.631534	−	1.09385i	0.355704	−	0.934599i	$-0.384241\pi$
$648$	−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	$-0.876346\pi$
$653$	−20.2073	−	35.0001i	−0.790773	−	1.36966i	0.134717	−	0.990884i	$-0.456988\pi$
$654$	−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	0.818366	−	0.574697i	$-0.194880\pi$
$673$	−2.29638	−	3.97744i	−0.0885189	−	0.153319i	−0.906885	+	0.421378i	$0.861547\pi$
$674$	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	$-0.501963\pi$
$677$	−0.320925			−0.0123341			−0.00616707	+	0.999981i	$0.501963\pi$
$678$	−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	0.677413	−	0.735603i	$-0.263101\pi$
$683$	9.90665	+	5.71961i	0.379068	+	0.218855i	−0.298345	+	0.954458i	$0.596435\pi$
$684$		−	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	$-0.462754\pi$
$727$	6.29553			0.233488			0.116744	+	0.993162i	$0.462754\pi$
$728$	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	$-0.997235\pi$
$733$		−	0.470338i		−	0.0173723i	0.999962	−	0.00868616i	$-0.00276492\pi$
$734$	−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	−0.180173	−	0.983635i	$-0.557666\pi$
$743$	15.8531	−	9.15278i	0.581593	−	0.335783i	0.761766	+	0.647852i	$0.224332\pi$
$744$	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	0.822077	−	0.569376i	$-0.192815\pi$
$757$	−2.25766	−	3.91038i	−0.0820560	−	0.142125i	−0.904133	+	0.427251i	$0.859482\pi$
$758$	−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	0.222862	−	0.974850i	$-0.428460\pi$
$773$	−14.1781	−	8.18575i	−0.509952	−	0.294421i	−0.732814	+	0.680429i	$0.761793\pi$
$774$	−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	0.997973	−	0.0636403i	$-0.0202710\pi$
$787$	40.4488	+	23.3531i	1.44185	+	0.832450i	0.443872	+	0.896090i	$0.353604\pi$
$788$		−	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	−0.929821	−	0.368011i	$-0.880039\pi$
$797$	−4.12750	+	7.14904i	−0.146204	+	0.253232i	0.783618	+	0.621243i	$0.213372\pi$
$798$			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	$0.349171\pi$
$823$	−15.5619	+	26.9539i	−0.542453	+	0.939555i	−0.998762	+	0.0497345i	$0.984162\pi$
$824$		−	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	$0.0868437\pi$
$827$			15.4978i			0.538911i	−0.963013	+	0.269455i	$0.913156\pi$
$828$	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	$0.163060\pi$
$853$			28.6312i			0.980313i	−0.871635	+	0.490156i	$0.836940\pi$
$854$	−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	$-0.427499\pi$
$857$	13.2207			0.451610			0.225805	+	0.974172i	$0.427499\pi$
$858$	−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	$0.349925\pi$
$863$			52.3436i			1.78180i	−0.454201	+	0.890899i	$0.650075\pi$
$864$	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	0.846490	−	0.532404i	$-0.178711\pi$
$877$	23.9478	+	13.8263i	0.808660	+	0.466880i	−0.0378301	+	0.999284i	$0.512045\pi$
$878$	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	$-0.348836\pi$
$883$	27.1744			0.914490			0.457245	+	0.889341i	$0.348836\pi$
$884$	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	0.646199	−	0.763169i	$-0.276358\pi$
$887$	−10.0613	−	17.4266i	−0.337824	−	0.585128i	−0.984023	+	0.178041i	$0.943024\pi$
$888$	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	0.576218	−	0.817296i	$-0.304528\pi$
$907$	−12.6396	−	21.8924i	−0.419690	−	0.726924i	−0.995908	+	0.0903720i	$0.971194\pi$
$908$	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	$-0.201512\pi$
$937$	49.3573			1.61243			0.806216	+	0.591621i	$0.201512\pi$
$938$	−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	−0.704456	−	0.709747i	$-0.748809\pi$
$947$	−13.6026	+	7.85347i	−0.442025	+	0.255203i	0.262431	+	0.964951i	$0.415476\pi$
$948$	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	−0.954940	−	0.296800i	$-0.904081\pi$
$953$	−6.80495	+	11.7865i	−0.220434	+	0.381803i	0.734506	+	0.678602i	$0.237414\pi$
$954$			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	$0.0445590\pi$
$967$			8.67779i			0.279059i	−0.990218	+	0.139529i	$0.955441\pi$
$968$	−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	0.0712213	−	0.997461i	$-0.477310\pi$
$977$	30.3399	−	17.5167i	0.970658	−	0.560410i	0.899437	+	0.437051i	$0.143977\pi$
$978$	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	$0.165507\pi$
$983$			31.1547i			0.993681i	−0.867842	+	0.496841i	$0.834493\pi$
$984$	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	$-0.586610\pi$
$997$	22.0961	−	38.2716i	0.699791	−	1.21207i	0.968539	−	0.248863i	$-0.0800570\pi$
$998$	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.b.101.2	✓	8
5.2	odd	4		650.2.n.c.49.4		8
5.3	odd	4		650.2.n.f.49.1		8
5.4	even	2		650.2.m.d.101.3	yes	8
13.2	odd	12		8450.2.a.ck.1.1		4
13.4	even	6	inner	650.2.m.b.251.2	yes	8
13.11	odd	12		8450.2.a.co.1.1		4
65.4	even	6		650.2.m.d.251.3	yes	8
65.17	odd	12		650.2.n.f.199.1		8
65.24	odd	12		8450.2.a.ch.1.4		4
65.43	odd	12		650.2.n.c.199.4		8
65.54	odd	12		8450.2.a.cl.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.m.b.101.2	✓	8	1.1	even	1	trivial
650.2.m.b.251.2	yes	8	13.4	even	6	inner
650.2.m.d.101.3	yes	8	5.4	even	2
650.2.m.d.251.3	yes	8	65.4	even	6
650.2.n.c.49.4		8	5.2	odd	4
650.2.n.c.199.4		8	65.43	odd	12
650.2.n.f.49.1		8	5.3	odd	4
650.2.n.f.199.1		8	65.17	odd	12
8450.2.a.ch.1.4		4	65.24	odd	12
8450.2.a.ck.1.1		4	13.2	odd	12
8450.2.a.cl.1.4		4	65.54	odd	12
8450.2.a.co.1.1		4	13.11	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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 4 q^{4} - 6 q^{7} + 2 q^{9} + 12 q^{11} - 4 q^{12} + 10 q^{13} - 4 q^{16} + 6 q^{17} + 6 q^{19} - 6 q^{22} + 6 q^{26} + 4 q^{27} - 6 q^{28} - 12 q^{29} - 24 q^{33} - 2 q^{36} + 6 q^{37}+ \cdots + 24 q^{98}+O(q^{100}) \) 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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