LMFDB - Embedded newform 207.2.i.b.82.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(55,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("207.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 69)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			82.1
Root			$-0.841254 + 0.540641i$ of defining polynomial
Character	$\chi$	$=$	207.82
Dual form			207.2.i.b.154.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.44306 - 1.66538i) q^{2} +(-0.406440 + 2.82685i) q^{4} +(-0.246902 + 0.540641i) q^{5} +(-2.76921 - 0.813115i) q^{7} +(1.58671 - 1.01971i) q^{8} +O(q^{10})$	\(q+(-1.44306 - 1.66538i) q^{2} +(-0.406440 + 2.82685i) q^{4} +(-0.246902 + 0.540641i) q^{5} +(-2.76921 - 0.813115i) q^{7} +(1.58671 - 1.01971i) q^{8} +(1.25667 - 0.368991i) q^{10} +(-2.88000 + 3.32369i) q^{11} +(-5.22659 + 1.53466i) q^{13} +(2.64200 + 5.78517i) q^{14} +(1.49254 + 0.438250i) q^{16} +(-0.543234 - 3.77827i) q^{17} +(0.0164316 - 0.114284i) q^{19} +(-1.42796 - 0.917695i) q^{20} +9.69123 q^{22} +(2.38594 + 4.16021i) q^{23} +(3.04297 + 3.51178i) q^{25} +(10.0981 + 6.48964i) q^{26} +(3.42408 - 7.49768i) q^{28} +(-0.782192 - 5.44027i) q^{29} +(-5.64226 + 3.62606i) q^{31} +(-2.99103 - 6.54943i) q^{32} +(-5.50835 + 6.35697i) q^{34} +(1.12333 - 1.29639i) q^{35} +(-3.82214 - 8.36932i) q^{37} +(-0.214039 + 0.137555i) q^{38} +(0.159538 + 1.10961i) q^{40} +(-1.77098 + 3.87790i) q^{41} +(2.64955 + 1.70277i) q^{43} +(-8.22505 - 9.49221i) q^{44} +(3.48528 - 9.97693i) q^{46} -3.51213 q^{47} +(1.11862 + 0.718892i) q^{49} +(1.45725 - 10.1354i) q^{50} +(-2.21398 - 15.3985i) q^{52} +(-9.41982 - 2.76591i) q^{53} +(-1.08585 - 2.37767i) q^{55} +(-5.22308 + 1.53363i) q^{56} +(-7.93137 + 9.15329i) q^{58} +(-3.89315 + 1.14313i) q^{59} +(9.95056 - 6.39484i) q^{61} +(14.1809 + 4.16389i) q^{62} +(-5.29867 + 11.6025i) q^{64} +(0.460754 - 3.20462i) q^{65} +(-4.70908 - 5.43457i) q^{67} +10.9014 q^{68} -3.78002 q^{70} +(5.28262 + 6.09647i) q^{71} +(0.543351 - 3.77909i) q^{73} +(-8.42253 + 18.4428i) q^{74} +(0.316387 + 0.0928996i) q^{76} +(10.6779 - 6.86225i) q^{77} +(-0.375512 + 0.110260i) q^{79} +(-0.605448 + 0.698725i) q^{80} +(9.01381 - 2.64669i) q^{82} +(0.397033 + 0.869381i) q^{83} +(2.17681 + 0.639170i) q^{85} +(-0.987716 - 6.86971i) q^{86} +(-1.18049 + 8.21051i) q^{88} +(5.05368 + 3.24780i) q^{89} +15.7214 q^{91} +(-12.7300 + 5.05381i) q^{92} +(5.06822 + 5.84903i) q^{94} +(0.0577299 + 0.0371007i) q^{95} +(-6.52719 + 14.2925i) q^{97} +(-0.417005 - 2.90033i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 8 q^{4} - 5 q^{5} - 8 q^{7} + 15 q^{8}+O(q^{10}) $ 10 * q + 4 * q^2 + 8 * q^4 - 5 * q^5 - 8 * q^7 + 15 * q^8	$ 10 q + 4 q^{2} + 8 q^{4} - 5 q^{5} - 8 q^{7} + 15 q^{8} - 2 q^{10} - 7 q^{11} - 30 q^{13} - q^{14} + 12 q^{16} + 2 q^{17} + 10 q^{19} - 4 q^{20} + 6 q^{22} + q^{23} + 24 q^{25} - q^{26} + 9 q^{28} + 14 q^{29} - 28 q^{31} - 23 q^{32} - 8 q^{34} + 4 q^{35} + 19 q^{37} + 15 q^{38} - 13 q^{40} - 19 q^{41} - 24 q^{43} - 54 q^{44} + 18 q^{46} - 26 q^{47} - 13 q^{49} + 36 q^{50} - 57 q^{52} + q^{53} - 24 q^{55} + 10 q^{56} + 10 q^{58} - 2 q^{59} + 30 q^{61} + 24 q^{62} + 13 q^{64} + 4 q^{65} + 4 q^{67} + 50 q^{68} + 6 q^{70} + 14 q^{71} - 26 q^{73} + 12 q^{74} + 19 q^{76} + 43 q^{77} + 20 q^{79} + 5 q^{80} + 10 q^{82} - 18 q^{83} + 21 q^{85} - 14 q^{86} - 38 q^{88} + 5 q^{89} + 46 q^{91} - 52 q^{92} - 6 q^{94} - 5 q^{95} + 15 q^{97} - 58 q^{98}+O(q^{100}) $ 10 * q + 4 * q^2 + 8 * q^4 - 5 * q^5 - 8 * q^7 + 15 * q^8 - 2 * q^10 - 7 * q^11 - 30 * q^13 - q^14 + 12 * q^16 + 2 * q^17 + 10 * q^19 - 4 * q^20 + 6 * q^22 + q^23 + 24 * q^25 - q^26 + 9 * q^28 + 14 * q^29 - 28 * q^31 - 23 * q^32 - 8 * q^34 + 4 * q^35 + 19 * q^37 + 15 * q^38 - 13 * q^40 - 19 * q^41 - 24 * q^43 - 54 * q^44 + 18 * q^46 - 26 * q^47 - 13 * q^49 + 36 * q^50 - 57 * q^52 + q^53 - 24 * q^55 + 10 * q^56 + 10 * q^58 - 2 * q^59 + 30 * q^61 + 24 * q^62 + 13 * q^64 + 4 * q^65 + 4 * q^67 + 50 * q^68 + 6 * q^70 + 14 * q^71 - 26 * q^73 + 12 * q^74 + 19 * q^76 + 43 * q^77 + 20 * q^79 + 5 * q^80 + 10 * q^82 - 18 * q^83 + 21 * q^85 - 14 * q^86 - 38 * q^88 + 5 * q^89 + 46 * q^91 - 52 * q^92 - 6 * q^94 - 5 * q^95 + 15 * q^97 - 58 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.44306	−	1.66538i	−1.02040	−	1.17760i	−0.983982	−	0.178266i	$-0.942951\pi$
$2$	−1.44306	−	1.66538i	−1.02040	−	1.17760i	−0.0364161	−	0.999337i	$-0.511594\pi$
$3$		0			0
$3$		0			0
$4$	−0.406440	+	2.82685i	−0.203220	+	1.41343i
$5$	−0.246902	+	0.540641i	−0.110418	+	0.241782i	−0.956772	−	0.290839i	$-0.906066\pi$
$5$	−0.246902	+	0.540641i	−0.110418	+	0.241782i	0.846354	+	0.532621i	$0.178793\pi$
$6$		0			0
$7$	−2.76921	−	0.813115i	−1.04666	−	0.307328i	−0.287196	−	0.957872i	$-0.592723\pi$
$7$	−2.76921	−	0.813115i	−1.04666	−	0.307328i	−0.759469	+	0.650543i	$0.774541\pi$
$8$	1.58671	−	1.01971i	0.560986	−	0.360524i
$9$		0			0
$10$	1.25667	−	0.368991i	0.397393	−	0.116685i
$11$	−2.88000	+	3.32369i	−0.868352	+	1.00213i	0.131590	+	0.991304i	$0.457992\pi$
$11$	−2.88000	+	3.32369i	−0.868352	+	1.00213i	−0.999941	+	0.0108271i	$0.996554\pi$
$12$		0			0
$13$	−5.22659	+	1.53466i	−1.44959	+	0.425639i	−0.909407	−	0.415906i	$-0.863464\pi$
$13$	−5.22659	+	1.53466i	−1.44959	+	0.425639i	−0.540186	+	0.841545i	$0.681646\pi$
$14$	2.64200	+	5.78517i	0.706104	+	1.54615i
$15$		0			0
$16$	1.49254	+	0.438250i	0.373136	+	0.109563i
$17$	−0.543234	−	3.77827i	−0.131753	−	0.916366i	−0.943268	−	0.332033i	$-0.892265\pi$
$17$	−0.543234	−	3.77827i	−0.131753	−	0.916366i	0.811514	−	0.584333i	$-0.198644\pi$
$18$		0			0
$19$	0.0164316	−	0.114284i	0.00376967	−	0.0262187i	−0.987850	−	0.155412i	$-0.950330\pi$
$19$	0.0164316	−	0.114284i	0.00376967	−	0.0262187i	0.991619	+	0.129193i	$0.0412387\pi$
$20$	−1.42796	−	0.917695i	−0.319302	−	0.205203i
$21$		0			0
$22$	9.69123			2.06618
$23$	2.38594	+	4.16021i	0.497502	+	0.867463i
$23$	2.38594	+	4.16021i	0.497502	+	0.867463i
$24$		0			0
$25$	3.04297	+	3.51178i	0.608594	+	0.702355i
$26$	10.0981	+	6.48964i	1.98040	+	1.27272i
$27$		0			0
$28$	3.42408	−	7.49768i	0.647089	−	1.41693i
$29$	−0.782192	−	5.44027i	−0.145249	−	1.01023i	−0.923862	−	0.382727i	$-0.874985\pi$
$29$	−0.782192	−	5.44027i	−0.145249	−	1.01023i	0.778612	−	0.627506i	$-0.215924\pi$
$30$		0			0
$31$	−5.64226	+	3.62606i	−1.01338	+	0.651260i	−0.938266	−	0.345915i	$-0.887569\pi$
$31$	−5.64226	+	3.62606i	−1.01338	+	0.651260i	−0.0751143	+	0.997175i	$0.523932\pi$
$32$	−2.99103	−	6.54943i	−0.528744	−	1.15779i
$33$		0			0
$34$	−5.50835	+	6.35697i	−0.944673	+	1.09021i
$35$	1.12333	−	1.29639i	0.189877	−	0.219130i
$36$		0			0
$37$	−3.82214	−	8.36932i	−0.628356	−	1.37591i	−0.909283	−	0.416178i	$-0.863369\pi$
$37$	−3.82214	−	8.36932i	−0.628356	−	1.37591i	0.280927	−	0.959729i	$-0.409358\pi$
$38$	−0.214039	+	0.137555i	−0.0347217	+	0.0223143i
$39$		0			0
$40$	0.159538	+	1.10961i	0.0252251	+	0.175445i
$41$	−1.77098	+	3.87790i	−0.276580	+	0.605626i	−0.996040	−	0.0889080i	$-0.971662\pi$
$41$	−1.77098	+	3.87790i	−0.276580	+	0.605626i	0.719460	+	0.694534i	$0.244390\pi$
$42$		0			0
$43$	2.64955	+	1.70277i	0.404053	+	0.259669i	0.726846	−	0.686800i	$-0.240985\pi$
$43$	2.64955	+	1.70277i	0.404053	+	0.259669i	−0.322793	+	0.946470i	$0.604622\pi$
$44$	−8.22505	−	9.49221i	−1.23997	−	1.43100i
$45$		0			0
$46$	3.48528	−	9.97693i	0.513876	−	1.47102i
$47$	−3.51213			−0.512297			−0.256148	−	0.966637i	$-0.582454\pi$
$47$	−3.51213			−0.512297			−0.256148	+	0.966637i	$0.582454\pi$
$48$		0			0
$49$	1.11862	+	0.718892i	0.159803	+	0.102699i
$50$	1.45725	−	10.1354i	0.206087	−	1.43336i
$51$		0			0
$52$	−2.21398	−	15.3985i	−0.307023	−	2.13539i
$53$	−9.41982	−	2.76591i	−1.29391	−	0.379927i	−0.438900	−	0.898536i	$-0.644632\pi$
$53$	−9.41982	−	2.76591i	−1.29391	−	0.379927i	−0.855012	+	0.518609i	$0.826450\pi$
$54$		0			0
$55$	−1.08585	−	2.37767i	−0.146416	−	0.320605i
$56$	−5.22308	+	1.53363i	−0.697963	+	0.204940i
$57$		0			0
$58$	−7.93137	+	9.15329i	−1.04144	+	1.20189i
$59$	−3.89315	+	1.14313i	−0.506845	+	0.148823i	−0.525150	−	0.851009i	$-0.675991\pi$
$59$	−3.89315	+	1.14313i	−0.506845	+	0.148823i	0.0183058	+	0.999832i	$0.494173\pi$
$60$		0			0
$61$	9.95056	−	6.39484i	1.27404	−	0.818775i	0.283899	−	0.958854i	$-0.408372\pi$
$61$	9.95056	−	6.39484i	1.27404	−	0.818775i	0.990140	+	0.140079i	$0.0447357\pi$
$62$	14.1809	+	4.16389i	1.80098	+	0.528814i
$63$		0			0
$64$	−5.29867	+	11.6025i	−0.662334	+	1.45031i
$65$	0.460754	−	3.20462i	0.0571496	−	0.397484i
$66$		0			0
$67$	−4.70908	−	5.43457i	−0.575306	−	0.663939i	0.391283	−	0.920271i	$-0.372031\pi$
$67$	−4.70908	−	5.43457i	−0.575306	−	0.663939i	−0.966589	+	0.256332i	$0.917486\pi$
$68$	10.9014			1.32199
$69$		0			0
$70$	−3.78002			−0.451798
$71$	5.28262	+	6.09647i	0.626932	+	0.723518i	0.977008	−	0.213203i	$-0.0683897\pi$
$71$	5.28262	+	6.09647i	0.626932	+	0.723518i	−0.350076	+	0.936721i	$0.613844\pi$
$72$		0			0
$73$	0.543351	−	3.77909i	0.0635944	−	0.442309i	−0.933002	−	0.359872i	$-0.882821\pi$
$73$	0.543351	−	3.77909i	0.0635944	−	0.442309i	0.996596	−	0.0824373i	$-0.0262704\pi$
$74$	−8.42253	+	18.4428i	−0.979099	+	2.14393i
$75$		0			0
$76$	0.316387	+	0.0928996i	0.0362921	+	0.0106563i
$77$	10.6779	−	6.86225i	1.21686	−	0.782026i
$78$		0			0
$79$	−0.375512	+	0.110260i	−0.0422484	+	0.0124053i	−0.302788	−	0.953058i	$-0.597918\pi$
$79$	−0.375512	+	0.110260i	−0.0422484	+	0.0124053i	0.260540	+	0.965463i	$0.416099\pi$
$80$	−0.605448	+	0.698725i	−0.0676912	+	0.0781198i
$81$		0			0
$82$	9.01381	−	2.64669i	0.995409	−	0.292279i
$83$	0.397033	+	0.869381i	0.0435800	+	0.0954269i	0.930170	−	0.367130i	$-0.119659\pi$
$83$	0.397033	+	0.869381i	0.0435800	+	0.0954269i	−0.886590	+	0.462557i	$0.846932\pi$
$84$		0			0
$85$	2.17681	+	0.639170i	0.236109	+	0.0693277i
$86$	−0.987716	−	6.86971i	−0.106508	−	0.740780i
$87$		0			0
$88$	−1.18049	+	8.21051i	−0.125841	+	0.875243i
$89$	5.05368	+	3.24780i	0.535689	+	0.344266i	0.780351	−	0.625342i	$-0.215041\pi$
$89$	5.05368	+	3.24780i	0.535689	+	0.344266i	−0.244662	+	0.969608i	$0.578677\pi$
$90$		0			0
$91$	15.7214			1.64805
$92$	−12.7300	+	5.05381i	−1.32720	+	0.526897i
$93$		0			0
$94$	5.06822	+	5.84903i	0.522747	+	0.603282i
$95$	0.0577299	+	0.0371007i	0.00592296	+	0.00380645i
$96$		0			0
$97$	−6.52719	+	14.2925i	−0.662736	+	1.45119i	0.217215	+	0.976124i	$0.430303\pi$
$97$	−6.52719	+	14.2925i	−0.662736	+	1.45119i	−0.879951	+	0.475065i	$0.842425\pi$
$98$	−0.417005	−	2.90033i	−0.0421238	−	0.292978i
$99$		0			0
$100$	−11.1641	+	7.17471i	−1.11641	+	0.717471i
$101$	−0.479451	−	1.04985i	−0.0477072	−	0.104464i	0.884278	−	0.466962i	$-0.154651\pi$
$101$	−0.479451	−	1.04985i	−0.0477072	−	0.104464i	−0.931985	+	0.362498i	$0.881924\pi$
$102$		0			0
$103$	−0.355200	+	0.409923i	−0.0349989	+	0.0403909i	−0.772979	−	0.634431i	$-0.781234\pi$
$103$	−0.355200	+	0.409923i	−0.0349989	+	0.0403909i	0.737980	+	0.674822i	$0.235780\pi$
$104$	−6.72814	+	7.76469i	−0.659749	+	0.761390i
$105$		0			0
$106$	8.98709	+	19.6790i	0.872903	+	1.91139i
$107$	9.59037	−	6.16335i	0.927136	−	0.595834i	0.0124160	−	0.999923i	$-0.496048\pi$
$107$	9.59037	−	6.16335i	0.927136	−	0.595834i	0.914720	+	0.404089i	$0.132411\pi$
$108$		0			0
$109$	0.800747	+	5.56931i	0.0766976	+	0.533444i	0.991557	+	0.129671i	$0.0413922\pi$
$109$	0.800747	+	5.56931i	0.0766976	+	0.533444i	−0.914859	+	0.403772i	$0.867699\pi$
$110$	−2.39279	+	5.23948i	−0.228143	+	0.499564i
$111$		0			0
$112$	−3.77682	−	2.42722i	−0.356876	−	0.229351i
$113$	3.17081	+	3.65931i	0.298285	+	0.344239i	0.885031	−	0.465532i	$-0.154137\pi$
$113$	3.17081	+	3.65931i	0.298285	+	0.344239i	−0.586746	+	0.809771i	$0.699591\pi$
$114$		0			0
$115$	−2.83827	+	0.262769i	−0.264670	+	0.0245034i
$116$	15.6968			1.45741
$117$		0			0
$118$	7.52180	+	4.83397i	0.692438	+	0.445003i
$119$	−1.56784	+	10.9046i	−0.143724	+	0.999619i
$120$		0			0
$121$	−1.18709	−	8.25642i	−0.107918	−	0.750584i
$122$	−25.0091	−	7.34334i	−2.26422	−	0.664835i
$123$		0			0
$124$	−7.95710	−	17.4236i	−0.714569	−	1.56469i
$125$	−5.50131	+	1.61533i	−0.492052	+	0.144479i
$126$		0			0
$127$	−10.4009	+	12.0033i	−0.922933	+	1.06512i	0.0747580	+	0.997202i	$0.476182\pi$
$127$	−10.4009	+	12.0033i	−0.922933	+	1.06512i	−0.997691	+	0.0679196i	$0.978364\pi$
$128$	13.1520	−	3.86177i	1.16248	−	0.341335i
$129$		0			0
$130$	−6.00181	+	3.85713i	−0.526393	+	0.338292i
$131$	−15.2762	−	4.48550i	−1.33469	−	0.391900i	−0.464918	−	0.885354i	$-0.653916\pi$
$131$	−15.2762	−	4.48550i	−1.33469	−	0.391900i	−0.869772	+	0.493454i	$0.835734\pi$
$132$		0			0
$133$	−0.138429	+	0.303117i	−0.0120033	+	0.0262836i
$134$	−2.25514	+	15.6848i	−0.194814	+	1.35496i
$135$		0			0
$136$	−4.71471	−	5.44107i	−0.404283	−	0.466568i
$137$	19.3249			1.65104			0.825519	−	0.564374i	$-0.190883\pi$
$137$	19.3249			1.65104			0.825519	+	0.564374i	$0.190883\pi$
$138$		0			0
$139$	0.855237			0.0725402			0.0362701	−	0.999342i	$-0.488452\pi$
$139$	0.855237			0.0725402			0.0362701	+	0.999342i	$0.488452\pi$
$140$	3.20814	+	3.70239i	0.271137	+	0.312909i
$141$		0			0
$142$	2.52980	−	17.5952i	0.212296	−	1.47655i
$143$	9.95180	−	21.7914i	0.832211	−	1.82229i
$144$		0			0
$145$	3.13436	+	0.920330i	0.260294	+	0.0764292i
$146$	−7.07771	+	4.54857i	−0.585756	+	0.376442i
$147$		0			0
$148$	25.2123	−	7.40300i	2.07244	−	0.608523i
$149$	3.51997	−	4.06226i	0.288367	−	0.332793i	−0.593020	−	0.805187i	$-0.702065\pi$
$149$	3.51997	−	4.06226i	0.288367	−	0.332793i	0.881387	+	0.472394i	$0.156610\pi$
$150$		0			0
$151$	−11.2904	+	3.31516i	−0.918798	+	0.269784i	−0.706740	−	0.707473i	$-0.749835\pi$
$151$	−11.2904	+	3.31516i	−0.918798	+	0.269784i	−0.212058	+	0.977257i	$0.568017\pi$
$152$	−0.0904654	−	0.198092i	−0.00733771	−	0.0160674i
$153$		0			0
$154$	−26.8371	−	7.88008i	−2.16259	−	0.634995i
$155$	−0.567309	−	3.94572i	−0.0455673	−	0.316928i
$156$		0			0
$157$	2.62494	−	18.2569i	0.209493	−	1.45706i	−0.565323	−	0.824870i	$-0.691248\pi$
$157$	2.62494	−	18.2569i	0.209493	−	1.45706i	0.774816	−	0.632187i	$-0.217843\pi$
$158$	0.725512	+	0.466259i	0.0577187	+	0.0370935i
$159$		0			0
$160$	4.27938			0.338315
$161$	−3.22444	−	13.4605i	−0.254122	−	1.06084i
$162$		0			0
$163$	13.6532	+	15.7566i	1.06940	+	1.23415i	0.971019	+	0.239003i	$0.0768205\pi$
$163$	13.6532	+	15.7566i	1.06940	+	1.23415i	0.0983798	+	0.995149i	$0.468634\pi$
$164$	−10.2425	−	6.58243i	−0.799802	−	0.514001i
$165$		0			0
$166$	0.874908	−	1.91578i	0.0679060	−	0.148693i
$167$	0.869105	+	6.04476i	0.0672534	+	0.467758i	0.995420	+	0.0955937i	$0.0304750\pi$
$167$	0.869105	+	6.04476i	0.0672534	+	0.467758i	−0.928167	+	0.372164i	$0.878616\pi$
$168$		0			0
$169$	14.0257	−	9.01377i	1.07890	−	0.693367i
$170$	−2.07681	−	4.54759i	−0.159284	−	0.348784i
$171$		0			0
$172$	−5.89035	+	6.79783i	−0.449135	+	0.518329i
$173$	−9.42476	+	10.8767i	−0.716551	+	0.826944i	−0.990888	−	0.134690i	$-0.956996\pi$
$173$	−9.42476	+	10.8767i	−0.716551	+	0.826944i	0.274337	+	0.961634i	$0.411542\pi$
$174$		0			0
$175$	−5.57116	−	12.1991i	−0.421140	−	0.922169i
$176$	−5.75513	+	3.69860i	−0.433809	+	0.278792i
$177$		0			0
$178$	−1.88394	−	13.1031i	−0.141207	−	0.982118i
$179$	−7.85312	+	17.1959i	−0.586969	+	1.28528i	0.350287	+	0.936643i	$0.386084\pi$
$179$	−7.85312	+	17.1959i	−0.586969	+	1.28528i	−0.937256	+	0.348641i	$0.886643\pi$
$180$		0			0
$181$	−1.75153	−	1.12564i	−0.130190	−	0.0836680i	0.473925	−	0.880565i	$-0.342837\pi$
$181$	−1.75153	−	1.12564i	−0.130190	−	0.0836680i	−0.604115	+	0.796897i	$0.706473\pi$
$182$	−22.6869	−	26.1821i	−1.68167	−	1.94075i
$183$		0			0
$184$	8.02801	+	4.16805i	0.591832	+	0.307273i
$185$	5.46849			0.402051
$186$		0			0
$187$	14.1223	+	9.07587i	1.03273	+	0.663693i
$188$	1.42747	−	9.92827i	0.104109	−	0.724094i
$189$		0			0
$190$	−0.0215209	−	0.149681i	−0.00156129	−	0.0108590i
$191$	−0.844106	−	0.247852i	−0.0610774	−	0.0179339i	0.251051	−	0.967974i	$-0.419224\pi$
$191$	−0.844106	−	0.247852i	−0.0610774	−	0.0179339i	−0.312129	+	0.950040i	$0.601042\pi$
$192$		0			0
$193$	−1.12815	−	2.47030i	−0.0812059	−	0.177816i	0.864674	−	0.502334i	$-0.167525\pi$
$193$	−1.12815	−	2.47030i	−0.0812059	−	0.177816i	−0.945880	+	0.324518i	$0.894798\pi$
$194$	33.2217	−	9.75477i	2.38518	−	0.700351i
$195$		0			0
$196$	−2.48685	+	2.86998i	−0.177632	+	0.204999i
$197$	−1.85721	+	0.545328i	−0.132321	+	0.0388530i	−0.347223	−	0.937783i	$-0.612875\pi$
$197$	−1.85721	+	0.545328i	−0.132321	+	0.0388530i	0.214901	+	0.976636i	$0.431057\pi$
$198$		0			0
$199$	−18.2312	+	11.7165i	−1.29237	+	0.830558i	−0.992360	−	0.123377i	$-0.960627\pi$
$199$	−18.2312	+	11.7165i	−1.29237	+	0.830558i	−0.300013	+	0.953935i	$0.596991\pi$
$200$	8.40932	+	2.46920i	0.594629	+	0.174599i
$201$		0			0
$202$	−1.05653	+	2.31347i	−0.0743369	+	0.162775i
$203$	−2.25750	+	15.7013i	−0.158446	+	1.10201i
$204$		0			0
$205$	−1.65929	−	1.91493i	−0.115890	−	0.133744i
$206$	1.19525			0.0832773
$207$		0			0
$208$	−8.47347			−0.587530
$209$	0.332524	+	0.383753i	0.0230011	+	0.0265447i
$210$		0			0
$211$	−1.12464	+	7.82203i	−0.0774233	+	0.538491i	0.913787	+	0.406194i	$0.133144\pi$
$211$	−1.12464	+	7.82203i	−0.0774233	+	0.538491i	−0.991210	+	0.132297i	$0.957765\pi$
$212$	11.6474	−	25.5043i	0.799947	−	1.75164i
$213$		0			0
$214$	−24.1038	−	7.07752i	−1.64770	−	0.483809i
$215$	−1.57477	+	1.01204i	−0.107398	+	0.0690206i
$216$		0			0
$217$	18.5730	−	5.45354i	1.26082	−	0.370210i
$218$	8.11951	−	9.37041i	0.549922	−	0.634644i
$219$		0			0
$220$	7.16266	−	2.10315i	0.482906	−	0.141794i
$221$	8.63763	+	18.9138i	0.581030	+	1.27228i
$222$		0			0
$223$	11.5298	+	3.38544i	0.772090	+	0.226706i	0.643968	−	0.765052i	$-0.277287\pi$
$223$	11.5298	+	3.38544i	0.772090	+	0.226706i	0.128122	+	0.991758i	$0.459105\pi$
$224$	2.95735	+	20.5688i	0.197596	+	1.37431i
$225$		0			0
$226$	1.51847	−	10.5612i	0.101007	−	0.702522i
$227$	−0.113005	−	0.0726240i	−0.00750041	−	0.00482022i	0.536885	−	0.843655i	$-0.319601\pi$
$227$	−0.113005	−	0.0726240i	−0.00750041	−	0.00482022i	−0.544386	+	0.838835i	$0.683237\pi$
$228$		0			0
$229$	−9.04483			−0.597699			−0.298850	−	0.954300i	$-0.596603\pi$
$229$	−9.04483			−0.597699			−0.298850	+	0.954300i	$0.596603\pi$
$230$	4.53341	+	4.34761i	0.298924	+	0.286673i
$231$		0			0
$232$	−6.78863	−	7.83450i	−0.445696	−	0.514360i
$233$	−20.9710	−	13.4772i	−1.37386	−	0.882924i	−0.374832	−	0.927093i	$-0.622300\pi$
$233$	−20.9710	−	13.4772i	−1.37386	−	0.882924i	−0.999024	+	0.0441690i	$0.985936\pi$
$234$		0			0
$235$	0.867153	−	1.89880i	0.0565668	−	0.123864i
$236$	−1.64913	−	11.4700i	−0.107349	−	0.746631i
$237$		0			0
$238$	20.4227	−	13.1249i	1.32381	−	0.850761i
$239$	1.83094	+	4.00919i	0.118433	+	0.259333i	0.959559	−	0.281506i	$-0.0908340\pi$
$239$	1.83094	+	4.00919i	0.118433	+	0.259333i	−0.841126	+	0.540839i	$0.818107\pi$
$240$		0			0
$241$	10.7042	−	12.3533i	0.689517	−	0.795746i	−0.297779	−	0.954635i	$-0.596246\pi$
$241$	10.7042	−	12.3533i	0.689517	−	0.795746i	0.987296	+	0.158889i	$0.0507913\pi$
$242$	−12.0370	+	13.8915i	−0.773771	+	0.892979i
$243$		0			0
$244$	14.0330	+	30.7279i	0.898368	+	1.96715i
$245$	−0.664852	+	0.427274i	−0.0424758	+	0.0272976i
$246$		0			0
$247$	0.0895070	+	0.622535i	0.00569519	+	0.0396109i
$248$	−5.25507	+	11.5070i	−0.333697	+	0.730695i
$249$		0			0
$250$	10.6289	+	6.83075i	0.672228	+	0.432015i
$251$	0.871654	+	1.00594i	0.0550183	+	0.0634945i	0.782592	−	0.622535i	$-0.213897\pi$
$251$	0.871654	+	1.00594i	0.0550183	+	0.0634945i	−0.727573	+	0.686030i	$0.759352\pi$
$252$		0			0
$253$	−20.6987	−	4.05126i	−1.30132	−	0.254701i
$254$	34.9993			2.19605
$255$		0			0
$256$	−3.94983	−	2.53840i	−0.246864	−	0.158650i
$257$	−2.61706	+	18.2020i	−0.163248	+	1.13541i	0.729213	+	0.684287i	$0.239886\pi$
$257$	−2.61706	+	18.2020i	−0.163248	+	1.13541i	−0.892461	+	0.451125i	$0.851023\pi$
$258$		0			0
$259$	3.77911	+	26.2843i	0.234822	+	1.63323i
$260$	8.87171	+	2.60497i	0.550200	+	0.161553i
$261$		0			0
$262$	14.5744	+	31.9136i	0.900412	+	1.97163i
$263$	4.50044	−	1.32145i	0.277509	−	0.0814841i	−0.140016	−	0.990149i	$-0.544716\pi$
$263$	4.50044	−	1.32145i	0.277509	−	0.0814841i	0.417526	+	0.908665i	$0.362897\pi$
$264$		0			0
$265$	3.82114	−	4.40983i	0.234731	−	0.270894i
$266$	0.704568	−	0.206880i	0.0431998	−	0.0126846i
$267$		0			0
$268$	17.2767	−	11.1031i	1.05534	−	0.678227i
$269$	1.62088	+	0.475933i	0.0988267	+	0.0290181i	0.330772	−	0.943711i	$-0.392691\pi$
$269$	1.62088	+	0.475933i	0.0988267	+	0.0290181i	−0.231945	+	0.972729i	$0.574509\pi$
$270$		0			0
$271$	0.718471	−	1.57323i	0.0436440	−	0.0955670i	−0.886554	−	0.462625i	$-0.846908\pi$
$271$	0.718471	−	1.57323i	0.0436440	−	0.0955670i	0.930198	+	0.367058i	$0.119635\pi$
$272$	0.845029	−	5.87731i	0.0512374	−	0.356364i
$273$		0			0
$274$	−27.8870	−	32.1833i	−1.68472	−	1.94427i
$275$	−20.4358			−1.23233
$276$		0			0
$277$	20.8841			1.25481			0.627403	−	0.778695i	$-0.284118\pi$
$277$	20.8841			1.25481			0.627403	+	0.778695i	$0.284118\pi$
$278$	−1.23416	−	1.42430i	−0.0740199	−	0.0854236i
$279$		0			0
$280$	0.460445	−	3.20247i	0.0275169	−	0.191384i
$281$	−4.00713	+	8.77439i	−0.239045	+	0.523436i	−0.990691	−	0.136131i	$-0.956533\pi$
$281$	−4.00713	+	8.77439i	−0.239045	+	0.523436i	0.751646	+	0.659567i	$0.229260\pi$
$282$		0			0
$283$	−10.2541	−	3.01086i	−0.609540	−	0.178977i	−0.0376277	−	0.999292i	$-0.511980\pi$
$283$	−10.2541	−	3.01086i	−0.609540	−	0.178977i	−0.571912	+	0.820315i	$0.693798\pi$
$284$	−19.3809	+	12.4553i	−1.15004	+	0.739089i
$285$		0			0
$286$	−50.6520	+	14.8728i	−2.99512	+	0.879446i
$287$	8.05740	−	9.29873i	0.475613	−	0.548887i
$288$		0			0
$289$	2.33114	−	0.684485i	0.137126	−	0.0402639i
$290$	−2.99037	−	6.54799i	−0.175600	−	0.384511i
$291$		0			0
$292$	10.4621	+	3.07195i	0.612247	+	0.179772i
$293$	−2.71284	−	18.8682i	−0.158486	−	1.10229i	−0.901425	−	0.432935i	$-0.857478\pi$
$293$	−2.71284	−	18.8682i	−0.158486	−	1.10229i	0.742940	−	0.669359i	$-0.233431\pi$
$294$		0			0
$295$	0.343204	−	2.38704i	0.0199821	−	0.138979i
$296$	−14.5989	−	9.38217i	−0.848546	−	0.545327i
$297$		0			0
$298$	−11.8447			−0.686148
$299$	−18.8548	−	18.0821i	−1.09040	−	1.04571i
$300$		0			0
$301$	−5.95264	−	6.86971i	−0.343104	−	0.395964i
$302$	21.8137	+	14.0188i	1.25524	+	0.806693i
$303$		0			0
$304$	0.0746101	−	0.163373i	0.00427918	−	0.00937011i
$305$	1.00049	+	6.95858i	0.0572881	+	0.398447i
$306$		0			0
$307$	−14.1535	+	9.09593i	−0.807786	+	0.519132i	−0.878148	−	0.478389i	$-0.841221\pi$
$307$	−14.1535	+	9.09593i	−0.807786	+	0.519132i	0.0703624	+	0.997521i	$0.477584\pi$
$308$	15.0587	+	32.9739i	0.858047	+	1.87886i
$309$		0			0
$310$	−5.75247	+	6.63870i	−0.326718	+	0.377053i
$311$	18.4911	−	21.3399i	1.04854	−	1.21008i	0.0714034	−	0.997448i	$-0.477252\pi$
$311$	18.4911	−	21.3399i	1.04854	−	1.21008i	0.977133	−	0.212628i	$-0.0682023\pi$
$312$		0			0
$313$	−4.08653	−	8.94825i	−0.230984	−	0.505785i	0.758279	−	0.651930i	$-0.226041\pi$
$313$	−4.08653	−	8.94825i	−0.230984	−	0.505785i	−0.989263	+	0.146145i	$0.953313\pi$
$314$	−34.1926	+	21.9743i	−1.92960	+	1.24008i
$315$		0			0
$316$	−0.159066	−	1.10633i	−0.00894819	−	0.0622360i
$317$	−0.922840	+	2.02074i	−0.0518319	+	0.113496i	−0.933776	−	0.357858i	$-0.883507\pi$
$317$	−0.922840	+	2.02074i	−0.0518319	+	0.113496i	0.881944	+	0.471354i	$0.156235\pi$
$318$		0			0
$319$	20.3345	+	13.0682i	1.13851	+	0.731678i
$320$	−4.96451	−	5.72935i	−0.277525	−	0.320281i
$321$		0			0
$322$	−17.7639	+	24.7943i	−0.989942	+	1.38173i
$323$	−0.440724			−0.0245225
$324$		0			0
$325$	−21.2937	−	13.6847i	−1.18116	−	0.759088i
$326$	6.53839	−	45.4755i	0.362128	−	2.51865i
$327$		0			0
$328$	1.14433	+	7.95899i	0.0631850	+	0.439461i
$329$	9.72584	+	2.85576i	0.536203	+	0.157443i
$330$		0			0
$331$	−8.39589	−	18.3844i	−0.461480	−	1.01050i	−0.987148	−	0.159810i	$-0.948912\pi$
$331$	−8.39589	−	18.3844i	−0.461480	−	1.01050i	0.525668	−	0.850690i	$-0.323815\pi$
$332$	−2.61898	+	0.769002i	−0.143735	+	0.0422045i
$333$		0			0
$334$	8.81266	−	10.1704i	0.482207	−	0.556497i
$335$	4.10084	−	1.20411i	0.224053	−	0.0657878i
$336$		0			0
$337$	−17.5013	+	11.2474i	−0.953356	+	0.612685i	−0.922152	−	0.386828i	$-0.873571\pi$
$337$	−17.5013	+	11.2474i	−0.953356	+	0.612685i	−0.0312041	+	0.999513i	$0.509934\pi$
$338$	−35.2513	−	10.3507i	−1.91742	−	0.563005i
$339$		0			0
$340$	−2.69158	+	5.89375i	−0.145972	+	0.319633i
$341$	4.19778	−	29.1962i	0.227323	−	1.58106i
$342$		0			0
$343$	10.7169	+	12.3680i	0.578659	+	0.667808i
$344$	5.94040			0.320285
$345$		0			0
$346$	31.7144			1.70498
$347$	6.82813	+	7.88009i	0.366553	+	0.423025i	0.908825	−	0.417178i	$-0.136981\pi$
$347$	6.82813	+	7.88009i	0.366553	+	0.423025i	−0.542271	+	0.840203i	$0.682435\pi$
$348$		0			0
$349$	−3.31808	+	23.0778i	−0.177613	+	1.23533i	0.684653	+	0.728869i	$0.259954\pi$
$349$	−3.31808	+	23.0778i	−0.177613	+	1.23533i	−0.862266	+	0.506456i	$0.830955\pi$
$350$	−12.2767	+	26.8822i	−0.656217	+	1.43692i
$351$		0			0
$352$	30.3824	+	8.92109i	1.61939	+	0.475496i
$353$	−6.88478	+	4.42458i	−0.366440	+	0.235497i	−0.710883	−	0.703311i	$-0.751704\pi$
$353$	−6.88478	+	4.42458i	−0.366440	+	0.235497i	0.344443	+	0.938807i	$0.388068\pi$
$354$		0			0
$355$	−4.60029	+	1.35077i	−0.244158	+	0.0716913i
$356$	−11.2351	+	12.9660i	−0.595458	+	0.687195i
$357$		0			0
$358$	39.9703	−	11.7363i	2.11250	−	0.620285i
$359$	−11.1044	−	24.3152i	−0.586067	−	1.28331i	−0.937790	−	0.347203i	$-0.887131\pi$
$359$	−11.1044	−	24.3152i	−0.586067	−	1.28331i	0.351723	−	0.936104i	$-0.385596\pi$
$360$		0			0
$361$	18.2176	+	5.34916i	0.958820	+	0.281535i
$362$	0.652944	+	4.54132i	0.0343180	+	0.238687i
$363$		0			0
$364$	−6.38980	+	44.4421i	−0.334917	+	2.32940i
$365$	1.90897	+	1.22682i	0.0999203	+	0.0642149i
$366$		0			0
$367$	−6.47075			−0.337770			−0.168885	−	0.985636i	$-0.554017\pi$
$367$	−6.47075			−0.337770			−0.168885	+	0.985636i	$0.554017\pi$
$368$	1.73790	+	7.25492i	0.0905944	+	0.378189i
$369$		0			0
$370$	−7.89137	−	9.10712i	−0.410253	−	0.473457i
$371$	23.8365	+	15.3188i	1.23753	+	0.795312i
$372$		0			0
$373$	−4.35363	+	9.53313i	−0.225423	+	0.493607i	−0.988222	−	0.153029i	$-0.951097\pi$
$373$	−4.35363	+	9.53313i	−0.225423	+	0.493607i	0.762799	+	0.646636i	$0.223825\pi$
$374$	−5.26460	−	36.6161i	−0.272226	−	1.89337i
$375$		0			0
$376$	−5.57272	+	3.58137i	−0.287391	+	0.184695i
$377$	12.4372	+	27.2336i	0.640547	+	1.40260i
$378$		0			0
$379$	16.3889	−	18.9138i	0.841843	−	0.971539i	−0.158031	−	0.987434i	$-0.550514\pi$
$379$	16.3889	−	18.9138i	0.841843	−	0.971539i	0.999874	+	0.0158956i	$0.00505993\pi$
$380$	−0.128342	+	0.148115i	−0.00658381	+	0.00759812i
$381$		0			0
$382$	0.805329	+	1.76342i	0.0412042	+	0.0902247i
$383$	−29.0472	+	18.6675i	−1.48424	+	0.953865i	−0.487508	+	0.873119i	$0.662094\pi$
$383$	−29.0472	+	18.6675i	−1.48424	+	0.953865i	−0.996735	+	0.0807462i	$0.974270\pi$
$384$		0			0
$385$	1.07362	+	7.46720i	0.0547168	+	0.380564i
$386$	−2.48601	+	5.44359i	−0.126534	+	0.277072i
$387$		0			0
$388$	−37.7500	−	24.2605i	−1.91647	−	1.23164i
$389$	0.416126	+	0.480235i	0.0210984	+	0.0243489i	0.766201	−	0.642601i	$-0.222145\pi$
$389$	0.416126	+	0.480235i	0.0210984	+	0.0243489i	−0.745102	+	0.666950i	$0.767599\pi$
$390$		0			0
$391$	14.4223	−	11.2747i	0.729365	−	0.570185i
$392$	2.50799			0.126672
$393$		0			0
$394$	3.58825	+	2.30603i	0.180774	+	0.116176i
$395$	0.0331036	−	0.230241i	0.00166562	−	0.0115847i
$396$		0			0
$397$	−3.68158	−	25.6060i	−0.184773	−	1.28513i	−0.845287	−	0.534313i	$-0.820570\pi$
$397$	−3.68158	−	25.6060i	−0.184773	−	1.28513i	0.660513	−	0.750814i	$-0.270339\pi$
$398$	45.8211	+	13.4543i	2.29680	+	0.674402i
$399$		0			0
$400$	3.00273	+	6.57506i	0.150137	+	0.328753i
$401$	3.90835	−	1.14760i	0.195174	−	0.0573082i	−0.182685	−	0.983172i	$-0.558479\pi$
$401$	3.90835	−	1.14760i	0.195174	−	0.0573082i	0.377859	+	0.925863i	$0.376661\pi$
$402$		0			0
$403$	23.9250	−	27.6109i	1.19179	−	1.37540i
$404$	3.16264	−	0.928636i	0.157347	−	0.0462014i
$405$		0			0
$406$	29.4063	−	18.8983i	1.45941	−	0.937907i
$407$	38.8248	+	11.4000i	1.92447	+	0.565077i
$408$		0			0
$409$	1.96355	−	4.29957i	0.0970912	−	0.212600i	−0.854854	−	0.518869i	$-0.826353\pi$
$409$	1.96355	−	4.29957i	0.0970912	−	0.212600i	0.951945	+	0.306269i	$0.0990806\pi$
$410$	−0.794621	+	5.52671i	−0.0392435	+	0.272945i
$411$		0			0
$412$	−1.01442	−	1.17071i	−0.0499771	−	0.0576767i
$413$	11.7105			0.576234
$414$		0			0
$415$	−0.568051			−0.0278845
$416$	25.6840	+	29.6409i	1.25926	+	1.45327i
$417$		0			0
$418$	0.159243	−	1.10756i	0.00778882	−	0.0541724i
$419$	12.4436	−	27.2476i	0.607908	−	1.33113i	−0.316088	−	0.948730i	$-0.602369\pi$
$419$	12.4436	−	27.2476i	0.607908	−	1.33113i	0.923996	−	0.382403i	$-0.124903\pi$
$420$		0			0
$421$	−33.7401	−	9.90698i	−1.64439	−	0.482837i	−0.676970	−	0.736011i	$-0.736707\pi$
$421$	−33.7401	−	9.90698i	−1.64439	−	0.482837i	−0.967421	+	0.253174i	$0.918526\pi$
$422$	14.6496	−	9.41472i	0.713131	−	0.458301i
$423$		0			0
$424$	−17.7669	+	5.21684i	−0.862839	+	0.253352i
$425$	11.6154	−	13.4049i	0.563430	−	0.650233i
$426$		0			0
$427$	−32.7550	+	9.61773i	−1.58512	+	0.465435i
$428$	13.5250	+	29.6156i	0.653755	+	1.43152i
$429$		0			0
$430$	3.95792	+	1.16215i	0.190868	+	0.0560438i
$431$	−0.314633	−	2.18832i	−0.0151553	−	0.105408i	0.980840	−	0.194817i	$-0.0624112\pi$
$431$	−0.314633	−	2.18832i	−0.0151553	−	0.105408i	−0.995995	+	0.0894092i	$0.971502\pi$
$432$		0			0
$433$	−3.23760	+	22.5180i	−0.155589	+	1.08214i	0.751052	+	0.660242i	$0.229546\pi$
$433$	−3.23760	+	22.5180i	−0.155589	+	1.08214i	−0.906641	+	0.421902i	$0.861363\pi$
$434$	−35.8842	−	23.0614i	−1.72250	−	1.10698i
$435$		0			0
$436$	−16.0691			−0.769570
$437$	0.514652	−	0.204316i	0.0246191	−	0.00977378i
$438$		0			0
$439$	−16.7396	−	19.3185i	−0.798937	−	0.922022i	0.199386	−	0.979921i	$-0.436105\pi$
$439$	−16.7396	−	19.3185i	−0.798937	−	0.922022i	−0.998322	+	0.0578988i	$0.981560\pi$
$440$	−4.14747	−	2.66542i	−0.197723	−	0.127069i
$441$		0			0
$442$	19.0340	−	41.6787i	0.905356	−	1.98245i
$443$	0.228356	+	1.58825i	0.0108495	+	0.0754602i	0.994527	−	0.104481i	$-0.0333182\pi$
$443$	0.228356	+	1.58825i	0.0108495	+	0.0754602i	−0.983677	+	0.179941i	$0.942409\pi$
$444$		0			0
$445$	−3.00366	+	1.93034i	−0.142387	+	0.0915067i
$446$	−11.0001	−	24.0868i	−0.520870	−	1.14055i
$447$		0			0
$448$	24.1073	−	27.8213i	1.13896	−	1.31443i
$449$	−6.93413	+	8.00242i	−0.327242	+	0.377657i	−0.895400	−	0.445262i	$-0.853111\pi$
$449$	−6.93413	+	8.00242i	−0.327242	+	0.377657i	0.568158	+	0.822919i	$0.307656\pi$
$450$		0			0
$451$	−7.78854	−	17.0545i	−0.366748	−	0.803066i
$452$	−11.6331	+	7.47612i	−0.547174	+	0.351647i
$453$		0			0
$454$	0.0421267	+	0.292997i	0.00197710	+	0.0137511i
$455$	−3.88165	+	8.49963i	−0.181975	+	0.398469i
$456$		0			0
$457$	0.398167	+	0.255886i	0.0186255	+	0.0119699i	0.549920	−	0.835217i	$-0.314658\pi$
$457$	0.398167	+	0.255886i	0.0186255	+	0.0119699i	−0.531295	+	0.847187i	$0.678294\pi$
$458$	13.0522	+	15.0631i	0.609891	+	0.703852i
$459$		0			0
$460$	0.410776	−	8.13017i	0.0191525	−	0.379071i
$461$	−20.7268			−0.965342			−0.482671	−	0.875802i	$-0.660333\pi$
$461$	−20.7268			−0.965342			−0.482671	+	0.875802i	$0.660333\pi$
$462$		0			0
$463$	−17.5452	−	11.2756i	−0.815395	−	0.524023i	0.0652109	−	0.997872i	$-0.479228\pi$
$463$	−17.5452	−	11.2756i	−0.815395	−	0.524023i	−0.880606	+	0.473849i	$0.842864\pi$
$464$	1.21674	−	8.46263i	0.0564859	−	0.392868i
$465$		0			0
$466$	7.81769	+	54.3732i	0.362147	+	2.51879i
$467$	−33.5318	−	9.84582i	−1.55167	−	0.455610i	−0.610067	−	0.792349i	$-0.708858\pi$
$467$	−33.5318	−	9.84582i	−1.55167	−	0.455610i	−0.941598	+	0.336739i	$0.890676\pi$
$468$		0			0
$469$	8.62153	+	18.8785i	0.398105	+	0.871729i
$470$	−4.41358	+	1.29594i	−0.203583	+	0.0597775i
$471$		0			0
$472$	−5.01162	+	5.78371i	−0.230678	+	0.266217i
$473$	−13.2902	+	3.90235i	−0.611083	+	0.179430i
$474$		0			0
$475$	0.451343	−	0.290060i	0.0207090	−	0.0133089i
$476$	−30.1883	−	8.86410i	−1.38368	−	0.406285i
$477$		0			0
$478$	4.03468	−	8.83472i	0.184542	−	0.404090i
$479$	−1.19808	+	8.33285i	−0.0547418	+	0.380738i	0.943972	+	0.330027i	$0.107058\pi$
$479$	−1.19808	+	8.33285i	−0.0547418	+	0.380738i	−0.998713	+	0.0507108i	$0.983851\pi$
$480$		0			0
$481$	32.8208	+	37.8773i	1.49650	+	1.72705i
$482$	−36.0197			−1.64065
$483$		0			0
$484$	23.8222			1.08283
$485$	−6.11556	−	7.05773i	−0.277693	−	0.320475i
$486$		0			0
$487$	2.06033	−	14.3299i	0.0933622	−	0.649349i	−0.888377	−	0.459115i	$-0.848166\pi$
$487$	2.06033	−	14.3299i	0.0933622	−	0.649349i	0.981739	−	0.190233i	$-0.0609244\pi$
$488$	9.26772	−	20.2935i	0.419530	−	0.918642i
$489$		0			0
$490$	1.67100	+	0.490649i	0.0754880	+	0.0221653i
$491$	14.3714	−	9.23594i	0.648572	−	0.416812i	−0.174572	−	0.984644i	$-0.555854\pi$
$491$	14.3714	−	9.23594i	0.648572	−	0.416812i	0.823144	+	0.567832i	$0.192218\pi$
$492$		0			0
$493$	−20.1299	+	5.91067i	−0.906605	+	0.266203i
$494$	0.907594	−	1.04742i	0.0408346	−	0.0471256i
$495$		0			0
$496$	−10.0104	+	2.93933i	−0.449482	+	0.131980i
$497$	−9.67158	−	21.1778i	−0.433830	−	0.949955i
$498$		0			0
$499$	0.848637	+	0.249182i	0.0379902	+	0.0111549i	0.300672	−	0.953727i	$-0.402789\pi$
$499$	0.848637	+	0.249182i	0.0379902	+	0.0111549i	−0.262682	+	0.964882i	$0.584607\pi$
$500$	−2.33035	−	16.2079i	−0.104216	−	0.724840i
$501$		0			0
$502$	0.417427	−	2.90327i	0.0186307	−	0.129579i
$503$	−10.3791	−	6.67027i	−0.462783	−	0.297413i	0.288396	−	0.957511i	$-0.406878\pi$
$503$	−10.3791	−	6.67027i	−0.462783	−	0.297413i	−0.751179	+	0.660099i	$0.770514\pi$
$504$		0			0
$505$	0.685970			0.0305253
$506$	23.1227	+	40.3175i	1.02793	+	1.79233i
$507$		0			0
$508$	−29.7042	−	34.2805i	−1.31791	−	1.52095i
$509$	−14.1847	−	9.11596i	−0.628727	−	0.404058i	0.187111	−	0.982339i	$-0.440087\pi$
$509$	−14.1847	−	9.11596i	−0.628727	−	0.404058i	−0.815838	+	0.578281i	$0.803724\pi$
$510$		0			0
$511$	−4.57749	+	10.0233i	−0.202496	+	0.443405i
$512$	−2.42904	−	16.8943i	−0.107349	−	0.746631i
$513$		0			0
$514$	34.0899	−	21.9083i	1.50364	−	0.966332i
$515$	−0.133921	−	0.293247i	−0.00590128	−	0.0129220i
$516$		0			0
$517$	10.1149	−	11.6732i	0.444854	−	0.513389i
$518$	38.3199	−	44.2235i	1.68368	−	1.94307i
$519$		0			0
$520$	−2.53671	−	5.55463i	−0.111242	−	0.243587i
$521$	25.8894	−	16.6381i	1.13424	−	0.728929i	0.167796	−	0.985822i	$-0.446335\pi$
$521$	25.8894	−	16.6381i	1.13424	−	0.728929i	0.966440	+	0.256892i	$0.0826986\pi$
$522$		0			0
$523$	−4.83716	−	33.6432i	−0.211514	−	1.47111i	−0.768103	−	0.640326i	$-0.778799\pi$
$523$	−4.83716	−	33.6432i	−0.211514	−	1.47111i	0.556589	−	0.830788i	$-0.312110\pi$
$524$	18.8887	−	41.3605i	0.825158	−	1.80684i
$525$		0			0
$526$	−8.69513	−	5.58802i	−0.379126	−	0.243649i
$527$	16.7653	+	19.3482i	0.730308	+	0.842821i
$528$		0			0
$529$	−11.6146	+	19.8520i	−0.504984	+	0.863129i
$530$	−12.8582			−0.558524
$531$		0			0
$532$	−0.800605	−	0.514518i	−0.0347106	−	0.0223072i
$533$	3.30489	−	22.9860i	0.143151	−	0.995636i
$534$		0			0
$535$	0.964276	+	6.70669i	0.0416893	+	0.289955i
$536$	−13.0137	−	3.82115i	−0.562104	−	0.165049i
$537$		0			0
$538$	−1.54642	−	3.38618i	−0.0666708	−	0.145989i
$539$	−5.61100	+	1.64754i	−0.241683	+	0.0709644i
$540$		0			0
$541$	8.89394	−	10.2642i	0.382380	−	0.441290i	−0.531633	−	0.846975i	$-0.678421\pi$
$541$	8.89394	−	10.2642i	0.382380	−	0.441290i	0.914013	+	0.405685i	$0.132967\pi$
$542$	−3.65683	+	1.07374i	−0.157074	+	0.0461212i
$543$		0			0
$544$	−23.1207	+	14.8588i	−0.991292	+	0.637065i
$545$	−3.20870	−	0.942161i	−0.137446	−	0.0403577i
$546$		0			0
$547$	−13.0508	+	28.5773i	−0.558012	+	1.22188i	0.394927	+	0.918713i	$0.370770\pi$
$547$	−13.0508	+	28.5773i	−0.558012	+	1.22188i	−0.952939	+	0.303163i	$0.901957\pi$
$548$	−7.85441	+	54.6287i	−0.335524	+	2.33362i
$549$		0			0
$550$	29.4901	+	34.0334i	1.25746	+	1.45119i
$551$	−0.634591			−0.0270345
$552$		0			0
$553$	1.12953			0.0480324
$554$	−30.1371	−	34.7801i	−1.28040	−	1.47766i
$555$		0			0
$556$	−0.347602	+	2.41763i	−0.0147416	+	0.102530i
$557$	−9.54082	+	20.8915i	−0.404257	+	0.885200i	0.592563	+	0.805524i	$0.298116\pi$
$557$	−9.54082	+	20.8915i	−0.404257	+	0.885200i	−0.996821	+	0.0796763i	$0.974611\pi$
$558$		0			0
$559$	−16.4613	−	4.83347i	−0.696238	−	0.204434i
$560$	2.24476	−	1.44262i	0.0948584	−	0.0609618i
$561$		0			0
$562$	20.3952	−	5.98858i	0.860321	−	0.252613i
$563$	−20.2740	+	23.3974i	−0.854447	+	0.986084i	−0.999995	−	0.00326733i	$-0.998960\pi$
$563$	−20.2740	+	23.3974i	−0.854447	+	0.986084i	0.145548	+	0.989351i	$0.453505\pi$
$564$		0			0
$565$	−2.76125	+	0.810777i	−0.116167	+	0.0341096i
$566$	9.78299	+	21.4218i	0.411210	+	0.900424i
$567$		0			0
$568$	14.5986	+	4.28655i	0.612545	+	0.179859i
$569$	3.49368	+	24.2991i	0.146463	+	1.01867i	0.921950	+	0.387308i	$0.126595\pi$
$569$	3.49368	+	24.2991i	0.146463	+	1.01867i	−0.775487	+	0.631363i	$0.782496\pi$
$570$		0			0
$571$	0.483445	−	3.36243i	0.0202315	−	0.140713i	−0.977202	−	0.212312i	$-0.931901\pi$
$571$	0.483445	−	3.36243i	0.0202315	−	0.140713i	0.997434	+	0.0715981i	$0.0228099\pi$
$572$	57.5563	+	36.9892i	2.40655	+	1.54659i
$573$		0			0
$574$	−27.1132			−1.13169
$575$	−7.34938	+	21.0383i	−0.306490	+	0.877356i
$576$		0			0
$577$	25.1811	+	29.0606i	1.04830	+	1.20981i	0.977196	+	0.212339i	$0.0681082\pi$
$577$	25.1811	+	29.0606i	1.04830	+	1.20981i	0.0711086	+	0.997469i	$0.477346\pi$
$578$	−4.50391	−	2.89449i	−0.187338	−	0.120395i
$579$		0			0
$580$	−3.87557	+	8.48630i	−0.160924	+	0.352375i
$581$	−0.392563	−	2.73034i	−0.0162863	−	0.113273i
$582$		0			0
$583$	36.3221	−	23.3428i	1.50431	−	0.966760i
$584$	−2.99145	−	6.55037i	−0.123787	−	0.271056i
$585$		0			0
$586$	−27.5080	+	31.7459i	−1.13634	+	1.31141i
$587$	−9.12735	+	10.5335i	−0.376726	+	0.434765i	−0.912174	−	0.409803i	$-0.865597\pi$
$587$	−9.12735	+	10.5335i	−0.376726	+	0.434765i	0.535448	+	0.844568i	$0.320143\pi$
$588$		0			0
$589$	0.321691	+	0.704405i	0.0132550	+	0.0290245i
$590$	−4.47059	+	2.87307i	−0.184051	+	0.118283i
$591$		0			0
$592$	−2.03685	−	14.1666i	−0.0837141	−	0.582245i
$593$	11.8614	−	25.9727i	0.487087	−	1.06657i	−0.493366	−	0.869822i	$-0.664234\pi$
$593$	11.8614	−	25.9727i	0.487087	−	1.06657i	0.980453	−	0.196751i	$-0.0630390\pi$
$594$		0			0
$595$	−5.50835	−	3.54000i	−0.225820	−	0.145126i
$596$	10.0528	+	11.6015i	0.411777	+	0.475216i
$597$		0			0
$598$	−2.90488	+	57.4940i	−0.118789	+	2.35110i
$599$	1.09226			0.0446286			0.0223143	−	0.999751i	$-0.492897\pi$
$599$	1.09226			0.0446286			0.0223143	+	0.999751i	$0.492897\pi$
$600$		0			0
$601$	−6.85228	−	4.40370i	−0.279511	−	0.179630i	0.393373	−	0.919379i	$-0.371308\pi$
$601$	−6.85228	−	4.40370i	−0.279511	−	0.179630i	−0.672883	+	0.739748i	$0.734944\pi$
$602$	−2.85067	+	19.8268i	−0.116185	+	0.808081i
$603$		0			0
$604$	−4.78259	−	33.2637i	−0.194601	−	1.35348i
$605$	4.75686	+	1.39674i	0.193394	+	0.0567855i
$606$		0			0
$607$	12.3636	+	27.0726i	0.501824	+	1.09884i	0.975872	+	0.218342i	$0.0700650\pi$
$607$	12.3636	+	27.0726i	0.501824	+	1.09884i	−0.474048	+	0.880499i	$0.657208\pi$
$608$	−0.797646	+	0.234210i	−0.0323488	+	0.00949847i
$609$		0			0
$610$	10.1449	−	11.7079i	0.410756	−	0.474037i
$611$	18.3564	−	5.38994i	0.742622	−	0.218054i
$612$		0			0
$613$	−20.8492	+	13.3989i	−0.842090	+	0.541178i	−0.889098	−	0.457716i	$-0.848668\pi$
$613$	−20.8492	+	13.3989i	−0.842090	+	0.541178i	0.0470085	+	0.998894i	$0.485031\pi$
$614$	35.5726	+	10.4451i	1.43559	+	0.421529i
$615$		0			0
$616$	9.94512	−	21.7768i	0.400700	−	0.877411i
$617$	−4.28821	+	29.8252i	−0.172637	+	1.20072i	0.700649	+	0.713506i	$0.252894\pi$
$617$	−4.28821	+	29.8252i	−0.172637	+	1.20072i	−0.873285	+	0.487209i	$0.838015\pi$
$618$		0			0
$619$	−9.85640	−	11.3749i	−0.396162	−	0.457195i	0.522267	−	0.852782i	$-0.325087\pi$
$619$	−9.85640	−	11.3749i	−0.396162	−	0.457195i	−0.918428	+	0.395587i	$0.870541\pi$
$620$	11.3845			0.457214
$621$		0			0
$622$	−62.2230			−2.49491
$623$	−11.3539	−	13.1031i	−0.454884	−	0.524964i
$624$		0			0
$625$	−2.82153	+	19.6242i	−0.112861	+	0.784968i
$626$	−9.00514	+	19.7185i	−0.359918	+	0.788110i
$627$		0			0
$628$	50.5426	+	14.8406i	2.01687	+	0.592206i
$629$	−29.5452	+	18.9876i	−1.17805	+	0.757084i
$630$		0			0
$631$	8.01736	−	2.35411i	0.319166	−	0.0937156i	−0.118225	−	0.992987i	$-0.537721\pi$
$631$	8.01736	−	2.35411i	0.319166	−	0.0937156i	0.437392	+	0.899271i	$0.355902\pi$
$632$	−0.483394	+	0.557866i	−0.0192284	+	0.0221907i
$633$		0			0
$634$	4.69701	−	1.37917i	0.186542	−	0.0547738i
$635$	−3.92146	−	8.58681i	−0.155619	−	0.340757i
$636$		0			0
$637$	−6.94981	−	2.04065i	−0.275362	−	0.0808535i
$638$	−7.58041	−	52.7229i	−0.300111	−	2.08732i
$639$		0			0
$640$	−1.15942	+	8.06397i	−0.0458302	+	0.318756i
$641$	−23.4514	−	15.0713i	−0.926273	−	0.595280i	−0.0118020	−	0.999930i	$-0.503757\pi$
$641$	−23.4514	−	15.0713i	−0.926273	−	0.595280i	−0.914471	+	0.404651i	$0.867393\pi$
$642$		0			0
$643$	23.4722			0.925651			0.462826	−	0.886449i	$-0.346836\pi$
$643$	23.4722			0.925651			0.462826	+	0.886449i	$0.346836\pi$
$644$	39.3615	−	3.64412i	1.55106	−	0.143599i
$645$		0			0
$646$	0.635992	+	0.733974i	0.0250228	+	0.0288778i
$647$	−19.1278	−	12.2927i	−0.751993	−	0.483276i	0.107639	−	0.994190i	$-0.465671\pi$
$647$	−19.1278	−	12.2927i	−0.751993	−	0.483276i	−0.859632	+	0.510914i	$0.829307\pi$
$648$		0			0
$649$	7.41283	−	16.2318i	0.290979	−	0.637156i
$650$	7.93800	+	55.2100i	0.311354	+	2.16552i
$651$		0			0
$652$	−50.0908	+	32.1914i	−1.96171	+	1.26071i
$653$	10.9352	+	23.9447i	0.427927	+	0.937030i	0.993658	+	0.112440i	$0.0358667\pi$
$653$	10.9352	+	23.9447i	0.427927	+	0.937030i	−0.565731	+	0.824590i	$0.691406\pi$
$654$		0			0
$655$	6.19678	−	7.15147i	0.242128	−	0.279431i
$656$	−4.34275	+	5.01180i	−0.169556	+	0.195678i
$657$		0			0
$658$	−9.27904	−	20.3183i	−0.361735	−	0.792089i
$659$	34.0894	−	21.9079i	1.32793	−	0.853412i	0.331982	−	0.943286i	$-0.392283\pi$
$659$	34.0894	−	21.9079i	1.32793	−	0.853412i	0.995953	+	0.0898741i	$0.0286465\pi$
$660$		0			0
$661$	1.86892	+	12.9986i	0.0726924	+	0.505587i	0.993343	+	0.115198i	$0.0367503\pi$
$661$	1.86892	+	12.9986i	0.0726924	+	0.505587i	−0.920650	+	0.390389i	$0.872341\pi$
$662$	−18.5013	+	40.5122i	−0.719074	+	1.57455i
$663$		0			0
$664$	1.51650	+	0.974593i	0.0588514	+	0.0378215i
$665$	−0.129699	−	0.149681i	−0.00502952	−	0.00580437i
$666$		0			0
$667$	20.7664	−	16.2342i	0.804077	−	0.628591i
$668$	−17.4409			−0.674808
$669$		0			0
$670$	−7.92307	−	5.09185i	−0.306095	−	0.196715i
$671$	−7.40311	+	51.4897i	−0.285794	+	1.98774i
$672$		0			0
$673$	1.32403	+	9.20880i	0.0510375	+	0.354973i	0.999297	+	0.0374784i	$0.0119325\pi$
$673$	1.32403	+	9.20880i	0.0510375	+	0.354973i	−0.948260	+	0.317495i	$0.897158\pi$
$674$	43.9866	+	12.9156i	1.69430	+	0.497492i
$675$		0			0
$676$	19.7800	+	43.3122i	0.760769	+	1.66585i
$677$	−49.6687	+	14.5840i	−1.90892	+	0.560510i	−0.925645	+	0.378394i	$0.876476\pi$
$677$	−49.6687	+	14.5840i	−1.90892	+	0.560510i	−0.983277	+	0.182116i	$0.941705\pi$
$678$		0			0
$679$	29.6967	−	34.2718i	1.13965	−	1.31523i
$680$	4.10574	−	1.20555i	0.157448	−	0.0462309i
$681$		0			0
$682$	−54.6805	+	35.1410i	−2.09382	+	1.34562i
$683$	33.2213	+	9.75466i	1.27118	+	0.373252i	0.846644	−	0.532160i	$-0.178620\pi$
$683$	33.2213	+	9.75466i	1.27118	+	0.373252i	0.424535	+	0.905412i	$0.360438\pi$
$684$		0			0
$685$	−4.77136	+	10.4478i	−0.182304	+	0.399191i
$686$	5.13223	−	35.6955i	0.195950	−	1.36286i
$687$		0			0
$688$	3.20834	+	3.70262i	0.122317	+	0.141161i
$689$	53.4782			2.03736
$690$		0			0
$691$	−36.6389			−1.39381			−0.696905	−	0.717163i	$-0.745440\pi$
$691$	−36.6389			−1.39381			−0.696905	+	0.717163i	$0.745440\pi$
$692$	−26.9164	−	31.0631i	−1.02321	−	1.18084i
$693$		0			0
$694$	3.26994	−	22.7429i	0.124125	−	0.863309i
$695$	−0.211160	+	0.462376i	−0.00800975	+	0.0175389i
$696$		0			0
$697$	15.6138	+	4.58463i	0.591416	+	0.173655i
$698$	43.2215	−	27.7768i	1.63596	−	1.05137i
$699$		0			0
$700$	36.7495	−	10.7906i	1.38900	−	0.407848i
$701$	−19.2776	+	22.2476i	−0.728106	+	0.840280i	−0.992257	−	0.124202i	$-0.960363\pi$
$701$	−19.2776	+	22.2476i	−0.728106	+	0.840280i	0.264151	+	0.964481i	$0.414908\pi$
$702$		0			0
$703$	−1.01929	+	0.299290i	−0.0384431	+	0.0112879i
$704$	−23.3029	−	51.0262i	−0.878261	−	1.92312i
$705$		0			0
$706$	17.3038	+	5.08085i	0.651237	+	0.191220i
$707$	0.474053	+	3.29711i	0.0178286	+	0.124001i
$708$		0			0
$709$	2.48348	−	17.2730i	0.0932689	−	0.648700i	−0.888536	−	0.458807i	$-0.848277\pi$
$709$	2.48348	−	17.2730i	0.0932689	−	0.648700i	0.981805	−	0.189893i	$-0.0608140\pi$
$710$	8.88805	+	5.71200i	0.333562	+	0.214368i
$711$		0			0
$712$	11.3305			0.424630
$713$	−28.5472	−	14.8214i	−1.06910	−	0.555067i
$714$		0			0
$715$	9.32420	+	10.7607i	0.348705	+	0.402427i
$716$	−45.4185	−	29.1887i	−1.69737	−	1.09083i
$717$		0			0
$718$	−24.4698	+	53.5814i	−0.913204	+	1.99964i
$719$	1.31850	+	9.17039i	0.0491719	+	0.341998i	0.999525	+	0.0308239i	$0.00981311\pi$
$719$	1.31850	+	9.17039i	0.0491719	+	0.341998i	−0.950353	+	0.311174i	$0.899278\pi$
$720$		0			0
$721$	1.31694	−	0.846346i	0.0490454	−	0.0315196i
$722$	−17.3807	−	38.0584i	−0.646842	−	1.41639i
$723$		0			0
$724$	3.89390	−	4.49380i	0.144716	−	0.167011i
$725$	16.7248	−	19.3015i	0.621144	−	0.716839i
$726$		0			0
$727$	9.25417	+	20.2638i	0.343218	+	0.751543i	0.999997	−	0.00254057i	$-0.000808688\pi$
$727$	9.25417	+	20.2638i	0.343218	+	0.751543i	−0.656779	+	0.754083i	$0.728081\pi$
$728$	24.9452	−	16.0313i	0.924532	−	0.594161i
$729$		0			0
$730$	−0.711638	−	4.94955i	−0.0263389	−	0.183191i
$731$	4.99418	−	10.9357i	0.184717	−	0.404473i
$732$		0			0
$733$	−20.3123	−	13.0539i	−0.750250	−	0.482157i	0.108790	−	0.994065i	$-0.465302\pi$
$733$	−20.3123	−	13.0539i	−0.750250	−	0.482157i	−0.859040	+	0.511908i	$0.828939\pi$
$734$	9.33768	+	10.7763i	0.344660	+	0.397759i
$735$		0			0
$736$	20.1106	−	28.0698i	0.741286	−	1.03467i
$737$	31.6250			1.16492
$738$		0			0
$739$	−0.343937	−	0.221035i	−0.0126519	−	0.00813090i	0.534300	−	0.845295i	$-0.320575\pi$
$739$	−0.343937	−	0.221035i	−0.0126519	−	0.00813090i	−0.546951	+	0.837164i	$0.684212\pi$
$740$	−2.22261	+	15.4586i	−0.0817049	+	0.568270i
$741$		0			0
$742$	−8.88591	−	61.8028i	−0.326212	−	2.26885i
$743$	−32.4863	−	9.53885i	−1.19181	−	0.349947i	−0.375093	−	0.926987i	$-0.622389\pi$
$743$	−32.4863	−	9.53885i	−1.19181	−	0.349947i	−0.816715	+	0.577041i	$0.804207\pi$
$744$		0			0
$745$	1.32714	+	2.90602i	0.0486225	+	0.106468i
$746$	22.1589	−	6.50643i	0.811294	−	0.238217i
$747$		0			0
$748$	−31.3960	+	36.2330i	−1.14795	+	1.32481i
$749$	−31.5693	+	9.26958i	−1.15352	+	0.338703i
$750$		0			0
$751$	11.2488	−	7.22919i	0.410476	−	0.263797i	−0.319066	−	0.947732i	$-0.603369\pi$
$751$	11.2488	−	7.22919i	0.410476	−	0.263797i	0.729543	+	0.683935i	$0.239733\pi$
$752$	−5.24200	−	1.53919i	−0.191156	−	0.0561285i
$753$		0			0
$754$	27.4068	−	60.0124i	0.998095	−	2.18552i
$755$	0.995314	−	6.92256i	0.0362232	−	0.251938i
$756$		0			0
$757$	5.48862	+	6.33421i	0.199487	+	0.230221i	0.846675	−	0.532110i	$-0.178601\pi$
$757$	5.48862	+	6.33421i	0.199487	+	0.230221i	−0.647188	+	0.762330i	$0.724055\pi$
$758$	−55.1490			−2.00310
$759$		0			0
$760$	0.129433			0.00469501
$761$	6.72393	+	7.75983i	0.243742	+	0.281294i	0.864418	−	0.502774i	$-0.167687\pi$
$761$	6.72393	+	7.75983i	0.243742	+	0.281294i	−0.620676	+	0.784067i	$0.713142\pi$
$762$		0			0
$763$	2.31105	−	16.0737i	0.0836657	−	0.581908i
$764$	1.04372	−	2.28543i	0.0377605	−	0.0826839i
$765$		0			0
$766$	73.0054	+	21.4363i	2.63779	+	0.774526i
$767$	18.5935	−	11.9493i	0.671374	−	0.431466i
$768$		0			0
$769$	16.8096	−	4.93575i	0.606170	−	0.177988i	0.0357777	−	0.999360i	$-0.488609\pi$
$769$	16.8096	−	4.93575i	0.606170	−	0.177988i	0.570393	+	0.821372i	$0.306791\pi$
$770$	10.8864	−	12.5636i	0.392320	−	0.452761i
$771$		0			0
$772$	7.44170	−	2.18508i	0.267833	−	0.0786428i
$773$	−16.5615	−	36.2646i	−0.595675	−	1.30435i	−0.931951	−	0.362583i	$-0.881895\pi$
$773$	−16.5615	−	36.2646i	−0.595675	−	1.30435i	0.336276	−	0.941763i	$-0.390833\pi$
$774$		0			0
$775$	−29.9032	−	8.78036i	−1.07415	−	0.315400i
$776$	4.21759	+	29.3340i	0.151403	+	1.05303i
$777$		0			0
$778$	0.199279	−	1.38602i	0.00714451	−	0.0496911i
$779$	0.414084	+	0.266116i	0.0148361	+	0.00953458i
$780$		0			0
$781$	−35.4767			−1.26946
$782$	−39.5889	−	7.74853i	−1.41569	−	0.277087i
$783$		0			0
$784$	1.35453	+	1.56321i	0.0483761	+	0.0558290i
$785$	9.22230	+	5.92681i	0.329158	+	0.211537i
$786$		0			0
$787$	3.63295	−	7.95506i	0.129501	−	0.283567i	−0.833764	−	0.552121i	$-0.813819\pi$
$787$	3.63295	−	7.95506i	0.129501	−	0.283567i	0.963265	+	0.268554i	$0.0865458\pi$
$788$	−0.786714	−	5.47172i	−0.0280255	−	0.194922i
$789$		0			0
$790$	−0.431209	+	0.277121i	−0.0153417	+	0.00985953i
$791$	−5.80521	−	12.7116i	−0.206410	−	0.451974i
$792$		0			0
$793$	−42.1935	+	48.6939i	−1.49834	+	1.72917i
$794$	−37.3310	+	43.0823i	−1.32483	+	1.52893i
$795$		0			0
$796$	−25.7108	−	56.2988i	−0.911296	−	1.99546i
$797$	23.5236	−	15.1177i	0.833248	−	0.535496i	−0.0530606	−	0.998591i	$-0.516898\pi$
$797$	23.5236	−	15.1177i	0.833248	−	0.535496i	0.886308	+	0.463095i	$0.153261\pi$
$798$		0			0
$799$	1.90791	+	13.2698i	0.0674969	+	0.469451i
$800$	13.8985	−	30.4335i	0.491387	−	1.07599i
$801$		0			0
$802$	−7.55118	−	4.85285i	−0.266641	−	0.171360i
$803$	10.9957	+	12.6897i	0.388029	+	0.447810i
$804$		0			0
$805$	8.07344	+	1.58017i	0.284551	+	0.0556938i
$806$	−80.5079			−2.83577
$807$		0			0
$808$	−1.83130	−	1.17690i	−0.0644249	−	0.0414033i
$809$	4.51144	−	31.3777i	0.158614	−	1.10318i	−0.742577	−	0.669760i	$-0.766397\pi$
$809$	4.51144	−	31.3777i	0.158614	−	1.10318i	0.901191	−	0.433422i	$-0.142694\pi$
$810$		0			0
$811$	0.428649	+	2.98132i	0.0150519	+	0.104688i	0.995962	−	0.0897716i	$-0.0286137\pi$
$811$	0.428649	+	2.98132i	0.0150519	+	0.104688i	−0.980910	+	0.194460i	$0.937705\pi$
$812$	−43.4677	−	12.7633i	−1.52542	−	0.447903i
$813$		0			0
$814$	−37.0412	−	81.1090i	−1.29829	−	2.84287i
$815$	−11.8897	+	3.49112i	−0.416477	+	0.122289i
$816$		0			0
$817$	0.238136	−	0.274824i	0.00833133	−	0.00961487i
$818$	−9.99395	+	2.93449i	−0.349430	+	0.102602i
$819$		0			0
$820$	6.08762	−	3.91227i	0.212589	−	0.136623i
$821$	46.9671	+	13.7908i	1.63916	+	0.481302i	0.966076	−	0.258259i	$-0.0831489\pi$
$821$	46.9671	+	13.7908i	1.63916	+	0.481302i	0.673089	+	0.739561i	$0.264967\pi$
$822$		0			0
$823$	12.1950	−	26.7033i	0.425090	−	0.930818i	−0.569008	−	0.822332i	$-0.692673\pi$
$823$	12.1950	−	26.7033i	0.425090	−	0.930818i	0.994098	−	0.108486i	$-0.0346002\pi$
$824$	−0.145594	+	1.01263i	−0.00507202	+	0.0352767i
$825$		0			0
$826$	−16.8989	−	19.5024i	−0.587988	−	0.678575i
$827$	−1.94586			−0.0676642			−0.0338321	−	0.999428i	$-0.510771\pi$
$827$	−1.94586			−0.0676642			−0.0338321	+	0.999428i	$0.510771\pi$
$828$		0			0
$829$	20.0800			0.697406			0.348703	−	0.937233i	$-0.386622\pi$
$829$	20.0800			0.697406			0.348703	+	0.937233i	$0.386622\pi$
$830$	0.819733	+	0.946022i	0.0284533	+	0.0328369i
$831$		0			0
$832$	9.88806	−	68.7729i	0.342807	−	2.38427i
$833$	2.10850	−	4.61697i	0.0730552	−	0.159969i
$834$		0			0
$835$	−3.48263	−	1.02259i	−0.120521	−	0.0353882i
$836$	−1.21996	+	0.784023i	−0.0421933	+	0.0271160i
$837$		0			0
$838$	−63.3345	+	18.5967i	−2.18785	+	0.642412i
$839$	29.6418	−	34.2085i	1.02335	−	1.18101i	0.0400154	−	0.999199i	$-0.487259\pi$
$839$	29.6418	−	34.2085i	1.02335	−	1.18101i	0.983334	−	0.181809i	$-0.0581952\pi$
$840$		0			0
$841$	−1.15940	+	0.340430i	−0.0399792	+	0.0117390i
$842$	32.1901	+	70.4865i	1.10934	+	2.42912i
$843$		0			0
$844$	−21.6546	−	6.35838i	−0.745383	−	0.218864i
$845$	1.41023	+	9.80839i	0.0485135	+	0.337419i
$846$		0			0
$847$	−3.42610	+	23.8290i	−0.117722	+	0.818776i
$848$	−12.8473	−	8.25648i	−0.441179	−	0.283529i
$849$		0			0
$850$	−39.0860			−1.34064
$851$	25.6987	−	35.8695i	0.880940	−	1.22959i
$852$		0			0
$853$	−5.46124	−	6.30261i	−0.186989	−	0.215797i	0.654513	−	0.756051i	$-0.272874\pi$
$853$	−5.46124	−	6.30261i	−0.186989	−	0.215797i	−0.841502	+	0.540254i	$0.818328\pi$
$854$	63.2846	+	40.6706i	2.16556	+	1.39172i
$855$		0			0
$856$	8.93224	−	19.5589i	0.305298	−	0.668509i
$857$	6.28380	+	43.7048i	0.214651	+	1.49293i	0.757355	+	0.653004i	$0.226491\pi$
$857$	6.28380	+	43.7048i	0.214651	+	1.49293i	−0.542704	+	0.839924i	$0.682599\pi$
$858$		0			0
$859$	−4.19265	+	2.69445i	−0.143051	+	0.0919335i	−0.610209	−	0.792241i	$-0.708914\pi$
$859$	−4.19265	+	2.69445i	−0.143051	+	0.0919335i	0.467157	+	0.884174i	$0.345278\pi$
$860$	−2.22084	−	4.86296i	−0.0757301	−	0.165826i
$861$		0			0
$862$	−3.19035	+	3.68186i	−0.108664	+	0.125405i
$863$	30.6584	−	35.3817i	1.04362	−	1.20441i	0.0651849	−	0.997873i	$-0.479236\pi$
$863$	30.6584	−	35.3817i	1.04362	−	1.20441i	0.978440	−	0.206534i	$-0.0662183\pi$
$864$		0			0
$865$	−3.55342	−	7.78090i	−0.120820	−	0.264559i
$866$	42.1731	−	27.1030i	1.43310	−	0.920997i
$867$		0			0
$868$	7.86752	+	54.7198i	0.267041	+	1.85731i
$869$	0.715002	−	1.56564i	0.0242548	−	0.0531106i
$870$		0			0
$871$	32.9527	+	21.1774i	1.11656	+	0.717569i
$872$	6.94966	+	8.02034i	0.235345	+	0.271603i
$873$		0			0
$874$	−1.08294	−	0.562250i	−0.0366310	−	0.0190184i
$875$	16.5477			0.559416
$876$		0			0
$877$	27.5528	+	17.7071i	0.930392	+	0.597926i	0.915655	−	0.401965i	$-0.131673\pi$
$877$	27.5528	+	17.7071i	0.930392	+	0.597926i	0.0147367	+	0.999891i	$0.495309\pi$
$878$	−8.01644	+	55.7556i	−0.270542	+	1.88166i
$879$		0			0
$880$	−0.578657	−	4.02465i	−0.0195065	−	0.135671i
$881$	19.8756	+	5.83599i	0.669625	+	0.196620i	0.598836	−	0.800872i	$-0.295630\pi$
$881$	19.8756	+	5.83599i	0.669625	+	0.196620i	0.0707889	+	0.997491i	$0.477448\pi$
$882$		0			0
$883$	8.15692	+	17.8612i	0.274502	+	0.601076i	0.995801	−	0.0915486i	$-0.0291817\pi$
$883$	8.15692	+	17.8612i	0.274502	+	0.601076i	−0.721299	+	0.692624i	$0.756454\pi$
$884$	−56.9771	+	16.7300i	−1.91635	+	0.562691i
$885$		0			0
$886$	2.31551	−	2.67225i	0.0777912	−	0.0897759i
$887$	−3.84895	+	1.13015i	−0.129235	+	0.0379469i	−0.345711	−	0.938341i	$-0.612362\pi$
$887$	−3.84895	+	1.13015i	−0.129235	+	0.0379469i	0.216475	+	0.976288i	$0.430544\pi$
$888$		0			0
$889$	38.5625	−	24.7826i	1.29334	−	0.831181i
$890$	7.54921	+	2.21665i	0.253050	+	0.0743022i
$891$		0			0
$892$	−14.2563	+	31.2169i	−0.477336	+	1.04522i
$893$	−0.0577100	+	0.401382i	−0.00193119	+	0.0134317i
$894$		0			0
$895$	−7.35787	−	8.49143i	−0.245946	−	0.283837i
$896$	−39.5607			−1.32163
$897$		0			0
$898$	23.3335			0.778648
$899$	24.1401	+	27.8591i	0.805117	+	0.929154i
$900$		0			0
$901$	−5.33319	+	37.0932i	−0.177674	+	1.23575i
$902$	−17.1630	+	37.5816i	−0.571464	+	1.25133i
$903$		0			0
$904$	8.76260	+	2.57293i	0.291440	+	0.0855744i
$905$	1.04102	−	0.669024i	0.0346047	−	0.0222391i
$906$		0			0
$907$	21.8396	−	6.41268i	0.725172	−	0.212930i	0.101744	−	0.994811i	$-0.467558\pi$
$907$	21.8396	−	6.41268i	0.725172	−	0.212930i	0.623428	+	0.781881i	$0.285740\pi$
$908$	0.251227	−	0.289931i	0.00833726	−	0.00962171i
$909$		0			0
$910$	19.7566	−	5.80106i	0.654924	−	0.192303i
$911$	−8.93317	−	19.5609i	−0.295969	−	0.648082i	0.701973	−	0.712204i	$-0.252303\pi$
$911$	−8.93317	−	19.5609i	−0.295969	−	0.648082i	−0.997942	+	0.0641216i	$0.979575\pi$
$912$		0			0
$913$	−4.03301	−	1.18420i	−0.133473	−	0.0391913i
$914$	−0.148431	−	1.03236i	−0.00490965	−	0.0341474i
$915$		0			0
$916$	3.67618	−	25.5684i	0.121464	−	0.844804i
$917$	38.6559	+	24.8426i	1.27653	+	0.820376i
$918$		0			0
$919$	21.5131			0.709653			0.354826	−	0.934932i	$-0.384540\pi$
$919$	21.5131			0.709653			0.354826	+	0.934932i	$0.384540\pi$
$920$	−4.23555	+	3.31116i	−0.139642	+	0.109166i
$921$		0			0
$922$	29.9100	+	34.5180i	0.985034	+	1.13679i
$923$	−36.9661	−	23.7567i	−1.21675	−	0.781960i
$924$		0			0
$925$	17.7605	−	38.8901i	0.583962	−	1.27870i
$926$	6.54060	+	45.4909i	0.214938	+	1.49492i
$927$		0			0
$928$	−33.2911	+	21.3949i	−1.09283	+	0.702322i
$929$	3.91788	+	8.57896i	0.128541	+	0.281467i	0.962950	−	0.269680i	$-0.0869179\pi$
$929$	3.91788	+	8.57896i	0.128541	+	0.281467i	−0.834409	+	0.551146i	$0.814191\pi$
$930$		0			0
$931$	0.100539	−	0.116028i	0.00329503	−	0.00380267i
$932$	46.6216	−	53.8042i	1.52714	−	1.76242i
$933$		0			0
$934$	31.9914	+	70.0513i	1.04679	+	2.29215i
$935$	−8.39362	+	5.39425i	−0.274501	+	0.176411i
$936$		0			0
$937$	−4.34317	−	30.2074i	−0.141885	−	0.986833i	−0.929014	−	0.370044i	$-0.879342\pi$
$937$	−4.34317	−	30.2074i	−0.141885	−	0.986833i	0.787129	−	0.616788i	$-0.211567\pi$
$938$	18.9985	−	41.6010i	0.620324	−	1.35832i
$939$		0			0
$940$	5.01518	+	3.22306i	0.163577	+	0.105125i
$941$	−11.2525	−	12.9861i	−0.366821	−	0.423334i	0.542093	−	0.840319i	$-0.317632\pi$
$941$	−11.2525	−	12.9861i	−0.366821	−	0.423334i	−0.908913	+	0.416985i	$0.863087\pi$
$942$		0			0
$943$	−20.3583	+	1.88479i	−0.662958	+	0.0613772i
$944$	−6.31167			−0.205427
$945$		0			0
$946$	25.6774	+	16.5019i	0.834846	+	0.536523i
$947$	−3.25806	+	22.6603i	−0.105873	+	0.736361i	0.865862	+	0.500284i	$0.166771\pi$
$947$	−3.25806	+	22.6603i	−0.105873	+	0.736361i	−0.971734	+	0.236077i	$0.924138\pi$
$948$		0			0
$949$	2.95976	+	20.5856i	0.0960779	+	0.668236i
$950$	−1.13438	−	0.333083i	−0.0368040	−	0.0108066i
$951$		0			0
$952$	8.63184	+	18.9011i	0.279759	+	0.612588i
$953$	−16.9722	+	4.98350i	−0.549784	+	0.161431i	−0.544815	−	0.838556i	$-0.683400\pi$
$953$	−16.9722	+	4.98350i	−0.549784	+	0.161431i	−0.00496960	+	0.999988i	$0.501582\pi$
$954$		0			0
$955$	0.342411	−	0.395163i	0.0110802	−	0.0127872i
$956$	−12.0776	+	3.54629i	−0.390616	+	0.114695i
$957$		0			0
$958$	15.6063	−	10.0295i	0.504216	−	0.324040i
$959$	−53.5148	−	15.7134i	−1.72808	−	0.507411i
$960$		0			0
$961$	5.80893	−	12.7198i	0.187385	−	0.410316i
$962$	15.7176	−	109.318i	0.506756	−	3.52457i
$963$		0			0
$964$	30.5703	+	35.2800i	0.984604	+	1.13629i
$965$	1.61409			0.0519593
$966$		0			0
$967$	15.3851			0.494752			0.247376	−	0.968920i	$-0.420432\pi$
$967$	15.3851			0.494752			0.247376	+	0.968920i	$0.420432\pi$
$968$	−10.3028	−	11.8900i	−0.331144	−	0.382160i
$969$		0			0
$970$	−2.92869	+	20.3695i	−0.0940345	+	0.654024i
$971$	0.934048	−	2.04528i	0.0299750	−	0.0656361i	−0.894052	−	0.447963i	$-0.852150\pi$
$971$	0.934048	−	2.04528i	0.0299750	−	0.0656361i	0.924027	+	0.382327i	$0.124877\pi$
$972$		0			0
$973$	−2.36833	−	0.695406i	−0.0759253	−	0.0222937i
$974$	−26.8379	+	17.2477i	−0.859941	+	0.552651i
$975$		0			0
$976$	17.6542	−	5.18374i	0.565097	−	0.165927i
$977$	28.8876	−	33.3380i	0.924195	−	1.06658i	−0.0734023	−	0.997302i	$-0.523386\pi$
$977$	28.8876	−	33.3380i	0.924195	−	1.06658i	0.997598	−	0.0692758i	$-0.0220688\pi$
$978$		0			0
$979$	−25.3493	+	7.44322i	−0.810167	+	0.237886i
$980$	−0.937620	−	2.05310i	−0.0299512	−	0.0655839i
$981$		0			0
$982$	−36.1202	−	10.6058i	−1.15264	−	0.338446i
$983$	6.50446	+	45.2395i	0.207460	+	1.44292i	0.781405	+	0.624024i	$0.214503\pi$
$983$	6.50446	+	45.2395i	0.207460	+	1.44292i	−0.573945	+	0.818894i	$0.694588\pi$
$984$		0			0
$985$	0.163724	−	1.13873i	0.00521670	−	0.0362829i
$986$	38.8922	+	24.9945i	1.23858	+	0.795987i
$987$		0			0
$988$	−1.79619			−0.0571445
$989$	−0.762187	+	15.0854i	−0.0242361	+	0.479687i
$990$		0			0
$991$	−7.94904	−	9.17369i	−0.252510	−	0.291412i	0.615316	−	0.788281i	$-0.289028\pi$
$991$	−7.94904	−	9.17369i	−0.252510	−	0.291412i	−0.867826	+	0.496869i	$0.834483\pi$
$992$	40.6248	+	26.1080i	1.28984	+	0.828929i
$993$		0			0
$994$	−21.3124	+	46.6678i	−0.675990	+	1.48021i
$995$	−1.83308	−	12.7493i	−0.0581125	−	0.404181i
$996$		0			0
$997$	−20.8582	+	13.4048i	−0.660586	+	0.424533i	−0.827521	−	0.561435i	$-0.810250\pi$
$997$	−20.8582	+	13.4048i	−0.660586	+	0.424533i	0.166935	+	0.985968i	$0.446613\pi$
$998$	−0.809652	−	1.77289i	−0.0256291	−	0.0561199i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.i.b.82.1		10
3.2	odd	2		69.2.e.a.13.1	✓	10
23.4	even	11		4761.2.a.br.1.5		5
23.16	even	11	inner	207.2.i.b.154.1		10
23.19	odd	22		4761.2.a.bq.1.5		5
69.50	odd	22		1587.2.a.o.1.1		5
69.62	odd	22		69.2.e.a.16.1	yes	10
69.65	even	22		1587.2.a.p.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.a.13.1	✓	10	3.2	odd	2
69.2.e.a.16.1	yes	10	69.62	odd	22
207.2.i.b.82.1		10	1.1	even	1	trivial
207.2.i.b.154.1		10	23.16	even	11	inner
1587.2.a.o.1.1		5	69.50	odd	22
1587.2.a.p.1.1		5	69.65	even	22
4761.2.a.bq.1.5		5	23.19	odd	22
4761.2.a.br.1.5		5	23.4	even	11

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.44306 - 1.66538i) q^{2} +(-0.406440 + 2.82685i) q^{4} +(-0.246902 + 0.540641i) q^{5} +(-2.76921 - 0.813115i) q^{7} +(1.58671 - 1.01971i) q^{8} +O(q^{10})\)	\(q+(-1.44306 - 1.66538i) q^{2} +(-0.406440 + 2.82685i) q^{4} +(-0.246902 + 0.540641i) q^{5} +(-2.76921 - 0.813115i) q^{7} +(1.58671 - 1.01971i) q^{8} +(1.25667 - 0.368991i) q^{10} +(-2.88000 + 3.32369i) q^{11} +(-5.22659 + 1.53466i) q^{13} +(2.64200 + 5.78517i) q^{14} +(1.49254 + 0.438250i) q^{16} +(-0.543234 - 3.77827i) q^{17} +(0.0164316 - 0.114284i) q^{19} +(-1.42796 - 0.917695i) q^{20} +9.69123 q^{22} +(2.38594 + 4.16021i) q^{23} +(3.04297 + 3.51178i) q^{25} +(10.0981 + 6.48964i) q^{26} +(3.42408 - 7.49768i) q^{28} +(-0.782192 - 5.44027i) q^{29} +(-5.64226 + 3.62606i) q^{31} +(-2.99103 - 6.54943i) q^{32} +(-5.50835 + 6.35697i) q^{34} +(1.12333 - 1.29639i) q^{35} +(-3.82214 - 8.36932i) q^{37} +(-0.214039 + 0.137555i) q^{38} +(0.159538 + 1.10961i) q^{40} +(-1.77098 + 3.87790i) q^{41} +(2.64955 + 1.70277i) q^{43} +(-8.22505 - 9.49221i) q^{44} +(3.48528 - 9.97693i) q^{46} -3.51213 q^{47} +(1.11862 + 0.718892i) q^{49} +(1.45725 - 10.1354i) q^{50} +(-2.21398 - 15.3985i) q^{52} +(-9.41982 - 2.76591i) q^{53} +(-1.08585 - 2.37767i) q^{55} +(-5.22308 + 1.53363i) q^{56} +(-7.93137 + 9.15329i) q^{58} +(-3.89315 + 1.14313i) q^{59} +(9.95056 - 6.39484i) q^{61} +(14.1809 + 4.16389i) q^{62} +(-5.29867 + 11.6025i) q^{64} +(0.460754 - 3.20462i) q^{65} +(-4.70908 - 5.43457i) q^{67} +10.9014 q^{68} -3.78002 q^{70} +(5.28262 + 6.09647i) q^{71} +(0.543351 - 3.77909i) q^{73} +(-8.42253 + 18.4428i) q^{74} +(0.316387 + 0.0928996i) q^{76} +(10.6779 - 6.86225i) q^{77} +(-0.375512 + 0.110260i) q^{79} +(-0.605448 + 0.698725i) q^{80} +(9.01381 - 2.64669i) q^{82} +(0.397033 + 0.869381i) q^{83} +(2.17681 + 0.639170i) q^{85} +(-0.987716 - 6.86971i) q^{86} +(-1.18049 + 8.21051i) q^{88} +(5.05368 + 3.24780i) q^{89} +15.7214 q^{91} +(-12.7300 + 5.05381i) q^{92} +(5.06822 + 5.84903i) q^{94} +(0.0577299 + 0.0371007i) q^{95} +(-6.52719 + 14.2925i) q^{97} +(-0.417005 - 2.90033i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 8 q^{4} - 5 q^{5} - 8 q^{7} + 15 q^{8}+O(q^{10}) \) 10 * q + 4 * q^2 + 8 * q^4 - 5 * q^5 - 8 * q^7 + 15 * q^8	\( 10 q + 4 q^{2} + 8 q^{4} - 5 q^{5} - 8 q^{7} + 15 q^{8} - 2 q^{10} - 7 q^{11} - 30 q^{13} - q^{14} + 12 q^{16} + 2 q^{17} + 10 q^{19} - 4 q^{20} + 6 q^{22} + q^{23} + 24 q^{25} - q^{26} + 9 q^{28} + 14 q^{29} - 28 q^{31} - 23 q^{32} - 8 q^{34} + 4 q^{35} + 19 q^{37} + 15 q^{38} - 13 q^{40} - 19 q^{41} - 24 q^{43} - 54 q^{44} + 18 q^{46} - 26 q^{47} - 13 q^{49} + 36 q^{50} - 57 q^{52} + q^{53} - 24 q^{55} + 10 q^{56} + 10 q^{58} - 2 q^{59} + 30 q^{61} + 24 q^{62} + 13 q^{64} + 4 q^{65} + 4 q^{67} + 50 q^{68} + 6 q^{70} + 14 q^{71} - 26 q^{73} + 12 q^{74} + 19 q^{76} + 43 q^{77} + 20 q^{79} + 5 q^{80} + 10 q^{82} - 18 q^{83} + 21 q^{85} - 14 q^{86} - 38 q^{88} + 5 q^{89} + 46 q^{91} - 52 q^{92} - 6 q^{94} - 5 q^{95} + 15 q^{97} - 58 q^{98}+O(q^{100}) \) 10 * q + 4 * q^2 + 8 * q^4 - 5 * q^5 - 8 * q^7 + 15 * q^8 - 2 * q^10 - 7 * q^11 - 30 * q^13 - q^14 + 12 * q^16 + 2 * q^17 + 10 * q^19 - 4 * q^20 + 6 * q^22 + q^23 + 24 * q^25 - q^26 + 9 * q^28 + 14 * q^29 - 28 * q^31 - 23 * q^32 - 8 * q^34 + 4 * q^35 + 19 * q^37 + 15 * q^38 - 13 * q^40 - 19 * q^41 - 24 * q^43 - 54 * q^44 + 18 * q^46 - 26 * q^47 - 13 * q^49 + 36 * q^50 - 57 * q^52 + q^53 - 24 * q^55 + 10 * q^56 + 10 * q^58 - 2 * q^59 + 30 * q^61 + 24 * q^62 + 13 * q^64 + 4 * q^65 + 4 * q^67 + 50 * q^68 + 6 * q^70 + 14 * q^71 - 26 * q^73 + 12 * q^74 + 19 * q^76 + 43 * q^77 + 20 * q^79 + 5 * q^80 + 10 * q^82 - 18 * q^83 + 21 * q^85 - 14 * q^86 - 38 * q^88 + 5 * q^89 + 46 * q^91 - 52 * q^92 - 6 * q^94 - 5 * q^95 + 15 * q^97 - 58 * q^98

Introduction

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