LMFDB - Embedded newform 297.2.n.b.91.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(37,297)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([10, 6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("297.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			91.5
Character	$\chi$	$=$	297.91
Dual form			297.2.n.b.235.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.448089 + 0.199502i) q^{2} +(-1.17728 - 1.30750i) q^{4} +(-1.56050 + 0.694778i) q^{5} +(-3.33599 + 0.709088i) q^{7} +(-0.569818 - 1.75372i) q^{8} -0.837851 q^{10} +(-3.25533 + 0.634703i) q^{11} +(0.417897 + 3.97602i) q^{13} +(-1.63629 - 0.347803i) q^{14} +(-0.273277 + 2.60005i) q^{16} +(-2.67346 - 1.94238i) q^{17} +(-1.36513 - 4.20144i) q^{19} +(2.74556 + 1.22240i) q^{20} +(-1.58530 - 0.365040i) q^{22} +(3.74601 - 6.48827i) q^{23} +(-1.39322 + 1.54733i) q^{25} +(-0.605969 + 1.86498i) q^{26} +(4.85453 + 3.52702i) q^{28} +(1.65433 - 0.351639i) q^{29} +(0.407506 + 3.87716i) q^{31} +(-2.48514 + 4.30439i) q^{32} +(-0.810437 - 1.40372i) q^{34} +(4.71315 - 3.42431i) q^{35} +(0.947300 - 2.91549i) q^{37} +(0.226496 - 2.15496i) q^{38} +(2.10765 + 2.34078i) q^{40} +(0.382333 + 0.0812674i) q^{41} +(-4.80634 - 8.32483i) q^{43} +(4.66230 + 3.50912i) q^{44} +(2.97296 - 2.15999i) q^{46} +(0.722834 - 0.802788i) q^{47} +(4.23124 - 1.88387i) q^{49} +(-0.932979 + 0.415389i) q^{50} +(4.70667 - 5.22729i) q^{52} +(-10.1643 + 7.38480i) q^{53} +(4.63895 - 3.25218i) q^{55} +(3.14445 + 5.44635i) q^{56} +(0.811439 + 0.172477i) q^{58} +(2.44670 + 2.71734i) q^{59} +(0.402767 - 3.83207i) q^{61} +(-0.590902 + 1.81861i) q^{62} +(2.25785 - 1.64043i) q^{64} +(-3.41458 - 5.91423i) q^{65} +(-1.55060 + 2.68572i) q^{67} +(0.607741 + 5.78227i) q^{68} +(2.79506 - 0.594109i) q^{70} +(5.67699 + 4.12458i) q^{71} +(-4.64842 + 14.3064i) q^{73} +(1.00612 - 1.11741i) q^{74} +(-3.88624 + 6.73117i) q^{76} +(10.4097 - 4.42568i) q^{77} +(-3.65339 - 1.62659i) q^{79} +(-1.38001 - 4.24724i) q^{80} +(0.155106 + 0.112691i) q^{82} +(-0.0130625 + 0.124281i) q^{83} +(5.52145 + 1.17362i) q^{85} +(-0.492848 - 4.68913i) q^{86} +(2.96804 + 5.34727i) q^{88} +7.93327 q^{89} +(-4.21345 - 12.9677i) q^{91} +(-12.8935 + 2.74060i) q^{92} +(0.484051 - 0.215514i) q^{94} +(5.04935 + 5.60787i) q^{95} +(0.313492 + 0.139576i) q^{97} +2.27180 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) $ 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.448089	+	0.199502i	0.316846	+	0.141069i	0.558997	−	0.829169i	$-0.311186\pi$
$2$	0.448089	+	0.199502i	0.316846	+	0.141069i	−0.242151	+	0.970239i	$0.577853\pi$
$3$		0			0
$3$		0			0
$4$	−1.17728	−	1.30750i	−0.588639	−	0.653750i
$5$	−1.56050	+	0.694778i	−0.697876	+	0.310714i	−0.724835	−	0.688922i	$-0.758084\pi$
$5$	−1.56050	+	0.694778i	−0.697876	+	0.310714i	0.0269596	+	0.999637i	$0.491417\pi$
$6$		0			0
$7$	−3.33599	+	0.709088i	−1.26089	+	0.268010i	−0.789409	−	0.613868i	$-0.789613\pi$
$7$	−3.33599	+	0.709088i	−1.26089	+	0.268010i	−0.471478	+	0.881878i	$0.656280\pi$
$8$	−0.569818	−	1.75372i	−0.201461	−	0.620034i
$9$		0			0
$10$	−0.837851			−0.264952
$11$	−3.25533	+	0.634703i	−0.981518	+	0.191370i
$11$	−3.25533	+	0.634703i	−0.981518	+	0.191370i
$12$		0			0
$13$	0.417897	+	3.97602i	0.115904	+	1.10275i	0.885635	+	0.464382i	$0.153724\pi$
$13$	0.417897	+	3.97602i	0.115904	+	1.10275i	−0.769731	+	0.638368i	$0.779610\pi$
$14$	−1.63629	−	0.347803i	−0.437316	−	0.0929543i
$15$		0			0
$16$	−0.273277	+	2.60005i	−0.0683191	+	0.650013i
$17$	−2.67346	−	1.94238i	−0.648409	−	0.471097i	0.214320	−	0.976763i	$-0.431246\pi$
$17$	−2.67346	−	1.94238i	−0.648409	−	0.471097i	−0.862729	+	0.505667i	$0.831246\pi$
$18$		0			0
$19$	−1.36513	−	4.20144i	−0.313182	−	0.963875i	−0.976496	−	0.215534i	$-0.930851\pi$
$19$	−1.36513	−	4.20144i	−0.313182	−	0.963875i	0.663314	−	0.748341i	$-0.269149\pi$
$20$	2.74556	+	1.22240i	0.613927	+	0.273338i
$21$		0			0
$22$	−1.58530	−	0.365040i	−0.337987	−	0.0778269i
$23$	3.74601	−	6.48827i	0.781096	−	1.35290i	−0.150208	−	0.988654i	$-0.547994\pi$
$23$	3.74601	−	6.48827i	0.781096	−	1.35290i	0.931304	−	0.364244i	$-0.118672\pi$
$24$		0			0
$25$	−1.39322	+	1.54733i	−0.278644	+	0.309465i
$26$	−0.605969	+	1.86498i	−0.118840	+	0.365753i
$27$		0			0
$28$	4.85453	+	3.52702i	0.917420	+	0.666544i
$29$	1.65433	−	0.351639i	0.307201	−	0.0652977i	−0.0517316	−	0.998661i	$-0.516474\pi$
$29$	1.65433	−	0.351639i	0.307201	−	0.0652977i	0.358933	+	0.933363i	$0.383141\pi$
$30$		0			0
$31$	0.407506	+	3.87716i	0.0731902	+	0.696358i	0.968177	+	0.250266i	$0.0805181\pi$
$31$	0.407506	+	3.87716i	0.0731902	+	0.696358i	−0.894987	+	0.446092i	$0.852815\pi$
$32$	−2.48514	+	4.30439i	−0.439315	+	0.760915i
$33$		0			0
$34$	−0.810437	−	1.40372i	−0.138989	−	0.240736i
$35$	4.71315	−	3.42431i	0.796668	−	0.578813i
$36$		0			0
$37$	0.947300	−	2.91549i	0.155735	−	0.479304i	−0.842499	−	0.538697i	$-0.818917\pi$
$37$	0.947300	−	2.91549i	0.155735	−	0.479304i	0.998235	+	0.0593935i	$0.0189167\pi$
$38$	0.226496	−	2.15496i	0.0367424	−	0.349581i
$39$		0			0
$40$	2.10765	+	2.34078i	0.333248	+	0.370110i
$41$	0.382333	+	0.0812674i	0.0597104	+	0.0126918i	0.237670	−	0.971346i	$-0.423616\pi$
$41$	0.382333	+	0.0812674i	0.0597104	+	0.0126918i	−0.177960	+	0.984038i	$0.556950\pi$
$42$		0			0
$43$	−4.80634	−	8.32483i	−0.732960	−	1.26952i	−0.955613	−	0.294626i	$-0.904805\pi$
$43$	−4.80634	−	8.32483i	−0.732960	−	1.26952i	0.222652	−	0.974898i	$-0.428529\pi$
$44$	4.66230	+	3.50912i	0.702869	+	0.529020i
$45$		0			0
$46$	2.97296	−	2.15999i	0.438340	−	0.318472i
$47$	0.722834	−	0.802788i	0.105436	−	0.117099i	−0.688117	−	0.725600i	$-0.741562\pi$
$47$	0.722834	−	0.802788i	0.105436	−	0.117099i	0.793553	+	0.608501i	$0.208229\pi$
$48$		0			0
$49$	4.23124	−	1.88387i	0.604462	−	0.269124i
$50$	−0.932979	+	0.415389i	−0.131943	+	0.0587449i
$51$		0			0
$52$	4.70667	−	5.22729i	0.652698	−	0.724894i
$53$	−10.1643	+	7.38480i	−1.39618	+	1.01438i	−0.401020	+	0.916069i	$0.631344\pi$
$53$	−10.1643	+	7.38480i	−1.39618	+	1.01438i	−0.995156	+	0.0983117i	$0.968656\pi$
$54$		0			0
$55$	4.63895	−	3.25218i	0.625516	−	0.438524i
$56$	3.14445	+	5.44635i	0.420195	+	0.727799i
$57$		0			0
$58$	0.811439	+	0.172477i	0.106547	+	0.0226473i
$59$	2.44670	+	2.71734i	0.318534	+	0.353768i	0.881054	−	0.473016i	$-0.156835\pi$
$59$	2.44670	+	2.71734i	0.318534	+	0.353768i	−0.562520	+	0.826784i	$0.690168\pi$
$60$		0			0
$61$	0.402767	−	3.83207i	0.0515690	−	0.490646i	−0.938005	−	0.346621i	$-0.887329\pi$
$61$	0.402767	−	3.83207i	0.0515690	−	0.490646i	0.989574	−	0.144025i	$-0.0460045\pi$
$62$	−0.590902	+	1.81861i	−0.0750446	+	0.230964i
$63$		0			0
$64$	2.25785	−	1.64043i	0.282232	−	0.205053i
$65$	−3.41458	−	5.91423i	−0.423527	−	0.733570i
$66$		0			0
$67$	−1.55060	+	2.68572i	−0.189436	+	0.328113i	−0.945062	−	0.326890i	$-0.893999\pi$
$67$	−1.55060	+	2.68572i	−0.189436	+	0.328113i	0.755626	+	0.655003i	$0.227333\pi$
$68$	0.607741	+	5.78227i	0.0736994	+	0.701203i
$69$		0			0
$70$	2.79506	−	0.594109i	0.334074	−	0.0710097i
$71$	5.67699	+	4.12458i	0.673735	+	0.489497i	0.871273	−	0.490798i	$-0.163295\pi$
$71$	5.67699	+	4.12458i	0.673735	+	0.489497i	−0.197538	+	0.980295i	$0.563295\pi$
$72$		0			0
$73$	−4.64842	+	14.3064i	−0.544057	+	1.67443i	0.179165	+	0.983819i	$0.442660\pi$
$73$	−4.64842	+	14.3064i	−0.544057	+	1.67443i	−0.723222	+	0.690615i	$0.757340\pi$
$74$	1.00612	−	1.11741i	0.116959	−	0.129896i
$75$		0			0
$76$	−3.88624	+	6.73117i	−0.445783	+	0.772118i
$77$	10.4097	−	4.42568i	1.18629	−	0.504353i
$78$		0			0
$79$	−3.65339	−	1.62659i	−0.411038	−	0.183006i	0.190791	−	0.981631i	$-0.438895\pi$
$79$	−3.65339	−	1.62659i	−0.411038	−	0.183006i	−0.601829	+	0.798625i	$0.705561\pi$
$80$	−1.38001	−	4.24724i	−0.154290	−	0.474856i
$81$		0			0
$82$	0.155106	+	0.112691i	0.0171286	+	0.0124447i
$83$	−0.0130625	+	0.124281i	−0.00143379	+	0.0136416i	−0.995215	−	0.0977052i	$-0.968850\pi$
$83$	−0.0130625	+	0.124281i	−0.00143379	+	0.0136416i	0.993782	+	0.111347i	$0.0355164\pi$
$84$		0			0
$85$	5.52145	+	1.17362i	0.598885	+	0.127297i
$86$	−0.492848	−	4.68913i	−0.0531451	−	0.505642i
$87$		0			0
$88$	2.96804	+	5.34727i	0.316394	+	0.570021i
$89$	7.93327			0.840925			0.420462	−	0.907310i	$-0.361868\pi$
$89$	7.93327			0.840925			0.420462	+	0.907310i	$0.361868\pi$
$90$		0			0
$91$	−4.21345	−	12.9677i	−0.441690	−	1.35938i
$92$	−12.8935	+	2.74060i	−1.34424	+	0.285727i
$93$		0			0
$94$	0.484051	−	0.215514i	0.0499261	−	0.0222285i
$95$	5.04935	+	5.60787i	0.518052	+	0.575355i
$96$		0			0
$97$	0.313492	+	0.139576i	0.0318303	+	0.0141718i	0.422590	−	0.906321i	$-0.361121\pi$
$97$	0.313492	+	0.139576i	0.0318303	+	0.0141718i	−0.390760	+	0.920493i	$0.627788\pi$
$98$	2.27180			0.229487
$99$		0			0
$100$	3.66333			0.366333
$101$	−6.50041	−	2.89417i	−0.646815	−	0.287981i	0.0569891	−	0.998375i	$-0.481850\pi$
$101$	−6.50041	−	2.89417i	−0.646815	−	0.287981i	−0.703804	+	0.710394i	$0.748517\pi$
$102$		0			0
$103$	−1.10693	−	1.22938i	−0.109069	−	0.121134i	0.686138	−	0.727472i	$-0.259305\pi$
$103$	−1.10693	−	1.22938i	−0.109069	−	0.121134i	−0.795207	+	0.606338i	$0.792638\pi$
$104$	6.73471	−	2.99848i	0.660392	−	0.294026i
$105$		0			0
$106$	−6.02779	+	1.28125i	−0.585471	+	0.124446i
$107$	−1.02187	−	3.14498i	−0.0987876	−	0.304037i	0.889435	−	0.457062i	$-0.151098\pi$
$107$	−1.02187	−	3.14498i	−0.0987876	−	0.304037i	−0.988222	+	0.153025i	$0.951098\pi$
$108$		0			0
$109$	−5.50709			−0.527484			−0.263742	−	0.964593i	$-0.584957\pi$
$109$	−5.50709			−0.527484			−0.263742	+	0.964593i	$0.584957\pi$
$110$	2.72748	−	0.531787i	0.260055	−	0.0507039i
$111$		0			0
$112$	−0.932016	−	8.86754i	−0.0880672	−	0.837904i
$113$	−16.0506	−	3.41167i	−1.50992	−	0.320943i	−0.622761	−	0.782412i	$-0.713989\pi$
$113$	−16.0506	−	3.41167i	−1.50992	−	0.320943i	−0.887156	+	0.461469i	$0.847323\pi$
$114$		0			0
$115$	−1.33772	+	12.7276i	−0.124743	+	1.18685i
$116$	−2.40738	−	1.74906i	−0.223519	−	0.162396i
$117$		0			0
$118$	0.554226	+	1.70573i	0.0510206	+	0.157025i
$119$	10.2960	+	4.58406i	0.943829	+	0.420220i
$120$		0			0
$121$	10.1943	−	4.13233i	0.926755	−	0.375667i
$122$	0.944980	−	1.63675i	0.0855545	−	0.148185i
$123$		0			0
$124$	4.58964	−	5.09731i	0.412162	−	0.457752i
$125$	3.73834	−	11.5054i	0.334368	−	1.02908i
$126$		0			0
$127$	−8.73327	−	6.34509i	−0.774952	−	0.563036i	0.128508	−	0.991709i	$-0.458981\pi$
$127$	−8.73327	−	6.34509i	−0.774952	−	0.563036i	−0.903460	+	0.428673i	$0.858981\pi$
$128$	11.0623	−	2.35137i	0.977780	−	0.207833i
$129$		0			0
$130$	−0.350135	−	3.33131i	−0.0307089	−	0.292175i
$131$	−10.5778	+	18.3213i	−0.924189	+	1.60074i	−0.131329	+	0.991339i	$0.541925\pi$
$131$	−10.5778	+	18.3213i	−0.924189	+	1.60074i	−0.792860	+	0.609404i	$0.791409\pi$
$132$		0			0
$133$	7.53325	+	13.0480i	0.653216	+	1.13140i
$134$	−1.23061	+	0.894092i	−0.106309	+	0.0772378i
$135$		0			0
$136$	−1.88301	+	5.79530i	−0.161467	+	0.496943i
$137$	0.334546	−	3.18299i	0.0285822	−	0.271941i	−0.970892	−	0.239518i	$-0.923011\pi$
$137$	0.334546	−	3.18299i	0.0285822	−	0.271941i	0.999474	−	0.0324237i	$-0.0103226\pi$
$138$		0			0
$139$	−10.0327	−	11.1425i	−0.850963	−	0.945090i	0.148073	−	0.988976i	$-0.452693\pi$
$139$	−10.0327	−	11.1425i	−0.850963	−	0.945090i	−0.999037	+	0.0438860i	$0.986026\pi$
$140$	−10.0260	−	2.13109i	−0.847350	−	0.180110i
$141$		0			0
$142$	1.72094	+	2.98075i	0.144418	+	0.250139i
$143$	−3.88399	−	12.6780i	−0.324795	−	1.06019i
$144$		0			0
$145$	−2.33727	+	1.69812i	−0.194099	+	0.141021i
$146$	−4.93705	+	5.48315i	−0.408593	+	0.453789i
$147$		0			0
$148$	−4.92724	+	2.19375i	−0.405017	+	0.180325i
$149$	−3.70089	+	1.64774i	−0.303188	+	0.134988i	−0.552692	−	0.833386i	$-0.686399\pi$
$149$	−3.70089	+	1.64774i	−0.303188	+	0.134988i	0.249503	+	0.968374i	$0.419733\pi$
$150$		0			0
$151$	−5.21519	+	5.79206i	−0.424406	+	0.471351i	−0.916988	−	0.398915i	$-0.869387\pi$
$151$	−5.21519	+	5.79206i	−0.424406	+	0.471351i	0.492581	+	0.870266i	$0.336053\pi$
$152$	−6.59027	+	4.78811i	−0.534541	+	0.388367i
$153$		0			0
$154$	5.54740	+	0.0936570i	0.447022	+	0.00754709i
$155$	−3.32968	−	5.76717i	−0.267446	−	0.463230i
$156$		0			0
$157$	−0.302396	−	0.0642763i	−0.0241339	−	0.00512981i	0.195829	−	0.980638i	$-0.437260\pi$
$157$	−0.302396	−	0.0642763i	−0.0241339	−	0.00512981i	−0.219963	+	0.975508i	$0.570594\pi$
$158$	−1.31253	−	1.45772i	−0.104419	−	0.115970i
$159$		0			0
$160$	0.887458	−	8.44360i	0.0701597	−	0.667525i
$161$	−7.89590	+	24.3011i	−0.622284	+	1.91519i
$162$		0			0
$163$	−8.89442	+	6.46217i	−0.696665	+	0.506157i	−0.878844	−	0.477109i	$-0.841685\pi$
$163$	−8.89442	+	6.46217i	−0.696665	+	0.506157i	0.182179	+	0.983265i	$0.441685\pi$
$164$	−0.343855	−	0.595575i	−0.0268506	−	0.0465066i
$165$		0			0
$166$	−0.0306475	+	0.0530830i	−0.00237871	+	0.00412004i
$167$	−1.83697	−	17.4776i	−0.142149	−	1.35246i	−0.800313	−	0.599582i	$-0.795333\pi$
$167$	−1.83697	−	17.4776i	−0.142149	−	1.35246i	0.658164	−	0.752874i	$-0.271333\pi$
$168$		0			0
$169$	−2.91820	+	0.620282i	−0.224477	+	0.0477140i
$170$	2.23996	+	1.62742i	0.171797	+	0.124818i
$171$		0			0
$172$	−5.22631	+	16.0849i	−0.398503	+	1.22646i
$173$	−8.27429	+	9.18953i	−0.629083	+	0.698667i	−0.970461	−	0.241259i	$-0.922440\pi$
$173$	−8.27429	+	9.18953i	−0.629083	+	0.698667i	0.341378	+	0.939926i	$0.389106\pi$
$174$		0			0
$175$	3.55058	−	6.14978i	0.268398	−	0.464880i
$176$	−0.760658	−	8.63747i	−0.0573368	−	0.651074i
$177$		0			0
$178$	3.55481	+	1.58270i	0.266444	+	0.118628i
$179$	−6.76200	−	20.8113i	−0.505416	−	1.55551i	−0.800071	−	0.599906i	$-0.795205\pi$
$179$	−6.76200	−	20.8113i	−0.505416	−	1.55551i	0.294655	−	0.955604i	$-0.404795\pi$
$180$		0			0
$181$	3.54364	+	2.57460i	0.263396	+	0.191369i	0.711643	−	0.702541i	$-0.247951\pi$
$181$	3.54364	+	2.57460i	0.263396	+	0.191369i	−0.448247	+	0.893910i	$0.647951\pi$
$182$	0.699075	−	6.65125i	0.0518189	−	0.493024i
$183$		0			0
$184$	−13.5132	−	2.87231i	−0.996203	−	0.211750i
$185$	0.547360	+	5.20778i	0.0402427	+	0.382884i
$186$		0			0
$187$	9.93581	+	4.62623i	0.726579	+	0.338304i
$188$	−1.90062			−0.138617
$189$		0			0
$190$	1.14377	+	3.52018i	0.0829781	+	0.255380i
$191$	12.2413	−	2.60196i	0.885746	−	0.188271i	0.257493	−	0.966280i	$-0.417104\pi$
$191$	12.2413	−	2.60196i	0.885746	−	0.188271i	0.628253	+	0.778009i	$0.283770\pi$
$192$		0			0
$193$	−11.4794	+	5.11094i	−0.826302	+	0.367893i	−0.775916	−	0.630837i	$-0.782712\pi$
$193$	−11.4794	+	5.11094i	−0.826302	+	0.367893i	−0.0503860	+	0.998730i	$0.516045\pi$
$194$	0.112627	+	0.125084i	0.00808611	+	0.00898054i
$195$		0			0
$196$	−7.44450	−	3.31451i	−0.531750	−	0.236750i
$197$	10.3453			0.737075			0.368538	−	0.929613i	$-0.379859\pi$
$197$	10.3453			0.737075			0.368538	+	0.929613i	$0.379859\pi$
$198$		0			0
$199$	26.4773			1.87693			0.938464	−	0.345376i	$-0.112249\pi$
$199$	26.4773			1.87693			0.938464	+	0.345376i	$0.112249\pi$
$200$	3.50746	+	1.56162i	0.248015	+	0.110423i
$201$		0			0
$202$	−2.33537	−	2.59369i	−0.164316	−	0.182491i
$203$	−5.26949	+	2.34613i	−0.369846	+	0.164666i
$204$		0			0
$205$	−0.653093	+	0.138819i	−0.0456140	+	0.00969555i
$206$	−0.250742	−	0.771705i	−0.0174700	−	0.0537672i
$207$		0			0
$208$	−10.4521			−0.724721
$209$	7.11061	+	12.8106i	0.491851	+	0.886127i
$210$		0			0
$211$	0.761375	+	7.24400i	0.0524152	+	0.498698i	0.988964	+	0.148159i	$0.0473347\pi$
$211$	0.761375	+	7.24400i	0.0524152	+	0.498698i	−0.936548	+	0.350538i	$0.885999\pi$
$212$	21.6219	+	4.59587i	1.48500	+	0.315646i
$213$		0			0
$214$	0.169543	−	1.61310i	0.0115897	−	0.110269i
$215$	13.2842	+	9.65153i	0.905974	+	0.658229i
$216$		0			0
$217$	−4.10868	−	12.6452i	−0.278916	−	0.858414i
$218$	−2.46767	−	1.09868i	−0.167131	−	0.0744117i
$219$		0			0
$220$	−9.71357	−	2.23670i	−0.654889	−	0.150799i
$221$	6.60572	−	11.4414i	0.444349	−	0.769635i
$222$		0			0
$223$	15.7313	−	17.4714i	1.05345	−	1.16997i	0.0684035	−	0.997658i	$-0.478209\pi$
$223$	15.7313	−	17.4714i	1.05345	−	1.16997i	0.985042	−	0.172312i	$-0.0551239\pi$
$224$	5.23822	−	16.1216i	0.349993	−	1.07717i
$225$		0			0
$226$	−6.51148	−	4.73086i	−0.433137	−	0.314692i
$227$	−11.6617	+	2.47876i	−0.774012	+	0.164521i	−0.577952	−	0.816071i	$-0.696148\pi$
$227$	−11.6617	+	2.47876i	−0.774012	+	0.164521i	−0.196060	+	0.980592i	$0.562815\pi$
$228$		0			0
$229$	−0.319603	−	3.04082i	−0.0211200	−	0.200943i	0.978874	−	0.204465i	$-0.0655455\pi$
$229$	−0.319603	−	3.04082i	−0.0211200	−	0.200943i	−0.999994	+	0.00352213i	$0.998879\pi$
$230$	−3.13859	+	5.43620i	−0.206953	+	0.358453i
$231$		0			0
$232$	−1.55934	−	2.70086i	−0.102376	−	0.177320i
$233$	−19.8463	+	14.4192i	−1.30017	+	0.944632i	−0.999957	−	0.00923938i	$-0.997059\pi$
$233$	−19.8463	+	14.4192i	−1.30017	+	0.944632i	−0.300217	+	0.953871i	$0.597059\pi$
$234$		0			0
$235$	−0.570221	+	1.75496i	−0.0371971	+	0.114481i
$236$	0.672471	−	6.39814i	0.0437741	−	0.416483i
$237$		0			0
$238$	3.69897	+	4.10813i	0.239769	+	0.266290i
$239$	−6.79874	−	1.44512i	−0.439774	−	0.0934768i	−0.0172968	−	0.999850i	$-0.505506\pi$
$239$	−6.79874	−	1.44512i	−0.439774	−	0.0934768i	−0.422477	+	0.906374i	$0.638839\pi$
$240$		0			0
$241$	3.88529	+	6.72952i	0.250274	+	0.433487i	0.963601	−	0.267344i	$-0.0861461\pi$
$241$	3.88529	+	6.72952i	0.250274	+	0.433487i	−0.713327	+	0.700831i	$0.752813\pi$
$242$	5.39236	+	0.182131i	0.346634	+	0.0117078i
$243$		0			0
$244$	−5.48460	+	3.98480i	−0.351116	+	0.255100i
$245$	−5.29396	+	5.87954i	−0.338219	+	0.375630i
$246$		0			0
$247$	16.1345	−	7.18355i	1.02661	−	0.457078i
$248$	6.56725	−	2.92393i	0.417021	−	0.185670i
$249$		0			0
$250$	3.97047	−	4.40965i	0.251114	−	0.278891i
$251$	0.264684	−	0.192304i	0.0167067	−	0.0121381i	−0.579401	−	0.815043i	$-0.696713\pi$
$251$	0.264684	−	0.192304i	0.0167067	−	0.0121381i	0.596107	+	0.802905i	$0.296713\pi$
$252$		0			0
$253$	−8.07634	+	23.4990i	−0.507755	+	1.47737i
$254$	−2.64742	−	4.58547i	−0.166114	−	0.287718i
$255$		0			0
$256$	−0.0337447	−	0.00717266i	−0.00210904	−	0.000448291i
$257$	9.18661	+	10.2028i	0.573045	+	0.636431i	0.958090	−	0.286467i	$-0.0924809\pi$
$257$	9.18661	+	10.2028i	0.573045	+	0.636431i	−0.385045	+	0.922898i	$0.625814\pi$
$258$		0			0
$259$	−1.09285	+	10.3978i	−0.0679064	+	0.646087i
$260$	−3.71294	+	11.4273i	−0.230267	+	0.708689i
$261$		0			0
$262$	−8.39495	+	6.09928i	−0.518641	+	0.376815i
$263$	−8.42709	−	14.5961i	−0.519637	−	0.900037i	−0.999739	−	0.0228249i	$-0.992734\pi$
$263$	−8.42709	−	14.5961i	−0.519637	−	0.900037i	0.480103	−	0.877212i	$-0.340599\pi$
$264$		0			0
$265$	10.7306	−	18.5859i	0.659174	−	1.14172i
$266$	0.772468	+	7.34954i	0.0473631	+	0.450629i
$267$		0			0
$268$	5.33707	−	1.13443i	0.326013	−	0.0692963i
$269$	10.0297	+	7.28700i	0.611522	+	0.444296i	0.849950	−	0.526864i	$-0.176632\pi$
$269$	10.0297	+	7.28700i	0.611522	+	0.444296i	−0.238428	+	0.971160i	$0.576632\pi$
$270$		0			0
$271$	5.95460	−	18.3264i	0.361716	−	1.11325i	−0.590296	−	0.807187i	$-0.700989\pi$
$271$	5.95460	−	18.3264i	0.361716	−	1.11325i	0.952012	−	0.306061i	$-0.0990112\pi$
$272$	5.78089	−	6.42032i	0.350518	−	0.389289i
$273$		0			0
$274$	0.784919	−	1.35952i	0.0474187	−	0.0821316i
$275$	3.55329	−	5.92133i	0.214271	−	0.357070i
$276$		0			0
$277$	9.45618	+	4.21016i	0.568167	+	0.252964i	0.670654	−	0.741770i	$-0.266013\pi$
$277$	9.45618	+	4.21016i	0.568167	+	0.252964i	−0.102487	+	0.994734i	$0.532680\pi$
$278$	−2.27260	−	6.99435i	−0.136302	−	0.419493i
$279$		0			0
$280$	−8.69092	−	6.31432i	−0.519382	−	0.377353i
$281$	−1.71801	+	16.3458i	−0.102488	+	0.975106i	0.815570	+	0.578659i	$0.196424\pi$
$281$	−1.71801	+	16.3458i	−0.102488	+	0.975106i	−0.918057	+	0.396447i	$0.870243\pi$
$282$		0			0
$283$	1.23731	+	0.262999i	0.0735505	+	0.0156336i	0.244540	−	0.969639i	$-0.421363\pi$
$283$	1.23731	+	0.262999i	0.0735505	+	0.0156336i	−0.170989	+	0.985273i	$0.554696\pi$
$284$	−1.29052	−	12.2785i	−0.0765781	−	0.728592i
$285$		0			0
$286$	0.788917	−	6.45573i	0.0466497	−	0.381736i
$287$	−1.33309			−0.0786896
$288$		0			0
$289$	−1.87876	−	5.78222i	−0.110515	−	0.340130i
$290$	−1.38608	+	0.294621i	−0.0813935	+	0.0173007i
$291$		0			0
$292$	24.1781	−	10.7648i	1.41492	−	0.629961i
$293$	16.1176	+	17.9004i	0.941602	+	1.04575i	0.998876	+	0.0473960i	$0.0150923\pi$
$293$	16.1176	+	17.9004i	0.941602	+	1.04575i	−0.0572746	+	0.998358i	$0.518241\pi$
$294$		0			0
$295$	−5.70603	−	2.54049i	−0.332218	−	0.147913i
$296$	−5.65274			−0.328559
$297$		0			0
$298$	−1.98705			−0.115107
$299$	27.3630	+	12.1828i	1.58244	+	0.704548i
$300$		0			0
$301$	21.9370	+	24.3635i	1.26443	+	1.40429i
$302$	−3.49240	+	1.55491i	−0.200965	+	0.0894753i
$303$		0			0
$304$	11.2970	−	2.40125i	0.647928	−	0.137721i
$305$	2.03392	+	6.25977i	0.116462	+	0.358433i
$306$		0			0
$307$	16.2949			0.930001			0.465001	−	0.885310i	$-0.346054\pi$
$307$	16.2949			0.930001			0.465001	+	0.885310i	$0.346054\pi$
$308$	−18.0417	−	8.40042i	−1.02802	−	0.478658i
$309$		0			0
$310$	−0.341429	−	3.24848i	−0.0193919	−	0.184501i
$311$	20.9042	+	4.44333i	1.18537	+	0.251958i	0.758083	−	0.652158i	$-0.226136\pi$
$311$	20.9042	+	4.44333i	1.18537	+	0.251958i	0.427287	+	0.904116i	$0.359469\pi$
$312$		0			0
$313$	−0.325724	+	3.09905i	−0.0184110	+	0.175169i	−0.999863	−	0.0165379i	$-0.994736\pi$
$313$	−0.325724	+	3.09905i	−0.0184110	+	0.175169i	0.981452	+	0.191707i	$0.0614023\pi$
$314$	−0.122677	−	0.0891301i	−0.00692307	−	0.00502990i
$315$		0			0
$316$	2.17428	+	6.69176i	0.122313	+	0.376441i
$317$	16.6858	+	7.42898i	0.937166	+	0.417253i	0.817739	−	0.575590i	$-0.195227\pi$
$317$	16.6858	+	7.42898i	0.937166	+	0.417253i	0.119428	+	0.992843i	$0.461894\pi$
$318$		0			0
$319$	−5.16220	+	2.19471i	−0.289028	+	0.122880i
$320$	−2.38364	+	4.12859i	−0.133250	+	0.230795i
$321$		0			0
$322$	−8.38617	+	9.31379i	−0.467343	+	0.519037i
$323$	−4.51117	+	13.8840i	−0.251008	+	0.772524i
$324$		0			0
$325$	−6.73442	−	4.89284i	−0.373558	−	0.271406i
$326$	−5.27470	+	1.12117i	−0.292139	+	0.0620960i
$327$		0			0
$328$	−0.0753401	−	0.716813i	−0.00415996	−	0.0395794i
$329$	−1.84212	+	3.19065i	−0.101560	+	0.175906i
$330$		0			0
$331$	−1.88308	−	3.26159i	−0.103503	−	0.179273i	0.809622	−	0.586951i	$-0.199672\pi$
$331$	−1.88308	−	3.26159i	−0.103503	−	0.179273i	−0.913126	+	0.407678i	$0.866339\pi$
$332$	0.177876	−	0.129235i	0.00976222	−	0.00709267i
$333$		0			0
$334$	2.66369	−	8.19799i	0.145751	−	0.448574i
$335$	0.553729	−	5.26838i	0.0302534	−	0.287842i
$336$		0			0
$337$	3.99215	+	4.43373i	0.217466	+	0.241521i	0.842001	−	0.539477i	$-0.181378\pi$
$337$	3.99215	+	4.43373i	0.217466	+	0.241521i	−0.624534	+	0.780997i	$0.714711\pi$
$338$	−1.43136	−	0.304245i	−0.0778556	−	0.0165487i
$339$		0			0
$340$	−4.96577	−	8.60097i	−0.269307	−	0.466453i
$341$	−3.78741	−	12.3628i	−0.205100	−	0.669482i
$342$		0			0
$343$	6.53464	−	4.74769i	0.352837	−	0.256351i
$344$	−11.8607	+	13.1726i	−0.639485	+	0.710220i
$345$		0			0
$346$	−5.54095	+	2.46699i	−0.297883	+	0.132626i
$347$	−22.2442	+	9.90376i	−1.19413	+	0.531662i	−0.904911	−	0.425600i	$-0.860063\pi$
$347$	−22.2442	+	9.90376i	−1.19413	+	0.531662i	−0.289221	+	0.957262i	$0.593396\pi$
$348$		0			0
$349$	11.2024	−	12.4416i	0.599652	−	0.665981i	−0.364539	−	0.931188i	$-0.618773\pi$
$349$	11.2024	−	12.4416i	0.599652	−	0.665981i	0.964192	+	0.265207i	$0.0854402\pi$
$350$	2.81787	−	2.04730i	0.150621	−	0.109433i
$351$		0			0
$352$	5.35793	−	15.5895i	0.285579	−	0.830924i
$353$	−4.01566	−	6.95533i	−0.213732	−	0.370195i	0.739148	−	0.673544i	$-0.235229\pi$
$353$	−4.01566	−	6.95533i	−0.213732	−	0.370195i	−0.952880	+	0.303349i	$0.901895\pi$
$354$		0			0
$355$	−11.7246	−	2.49214i	−0.622277	−	0.132269i
$356$	−9.33967	−	10.3728i	−0.495001	−	0.549755i
$357$		0			0
$358$	1.12192	−	10.6743i	0.0592952	−	0.564156i
$359$	8.90742	−	27.4142i	0.470116	−	1.44687i	−0.382317	−	0.924031i	$-0.624874\pi$
$359$	8.90742	−	27.4142i	0.470116	−	1.44687i	0.852433	−	0.522836i	$-0.175126\pi$
$360$		0			0
$361$	−0.417162	+	0.303086i	−0.0219559	+	0.0159519i
$362$	1.07422	+	1.86061i	0.0564600	+	0.0977916i
$363$		0			0
$364$	−11.9948	+	20.7756i	−0.628700	+	1.08894i
$365$	−2.68591	−	25.5547i	−0.140587	−	1.33759i
$366$		0			0
$367$	−21.8551	+	4.64545i	−1.14083	+	0.242491i	−0.739313	−	0.673362i	$-0.764850\pi$
$367$	−21.8551	+	4.64545i	−1.14083	+	0.242491i	−0.401515	+	0.915852i	$0.631516\pi$
$368$	15.8462	+	11.5129i	0.826038	+	0.600152i
$369$		0			0
$370$	−0.793696	+	2.44275i	−0.0412623	+	0.126992i
$371$	28.6716	−	31.8431i	1.48856	−	1.65321i
$372$		0			0
$373$	−3.53936	+	6.13036i	−0.183261	+	0.317418i	−0.942989	−	0.332823i	$-0.891999\pi$
$373$	−3.53936	+	6.13036i	−0.183261	+	0.317418i	0.759728	+	0.650241i	$0.225332\pi$
$374$	3.52918	+	4.05517i	0.182490	+	0.209688i
$375$		0			0
$376$	−1.81975	−	0.810205i	−0.0938465	−	0.0417831i
$377$	2.08946	+	6.43070i	0.107613	+	0.331198i
$378$		0			0
$379$	19.6964	+	14.3103i	1.01174	+	0.735070i	0.964573	−	0.263818i	$-0.0849817\pi$
$379$	19.6964	+	14.3103i	1.01174	+	0.735070i	0.0471638	+	0.998887i	$0.484982\pi$
$380$	1.38780	−	13.2040i	0.0711927	−	0.677353i
$381$		0			0
$382$	6.00426	+	1.27625i	0.307205	+	0.0652984i
$383$	−1.84366	−	17.5413i	−0.0942067	−	0.896317i	−0.934925	−	0.354845i	$-0.884534\pi$
$383$	−1.84366	−	17.5413i	−0.0942067	−	0.896317i	0.840719	−	0.541472i	$-0.182133\pi$
$384$		0			0
$385$	−13.1694	+	14.1387i	−0.671176	+	0.720574i
$386$	−6.16341			−0.313709
$387$		0			0
$388$	−0.186572	−	0.574210i	−0.00947177	−	0.0291511i
$389$	−17.4922	+	3.71808i	−0.886890	+	0.188514i	−0.628763	−	0.777597i	$-0.716439\pi$
$389$	−17.4922	+	3.71808i	−0.886890	+	0.188514i	−0.258127	+	0.966111i	$0.583105\pi$
$390$		0			0
$391$	−22.6175	+	10.0700i	−1.14382	+	0.509259i
$392$	−5.71481	−	6.34694i	−0.288642	−	0.320569i
$393$		0			0
$394$	4.63563	+	2.06392i	0.233540	+	0.103979i
$395$	6.83122			0.343716
$396$		0			0
$397$	−21.9395			−1.10111			−0.550556	−	0.834798i	$-0.685584\pi$
$397$	−21.9395			−1.10111			−0.550556	+	0.834798i	$0.685584\pi$
$398$	11.8642	+	5.28228i	0.594698	+	0.264777i
$399$		0			0
$400$	−3.64239	−	4.04529i	−0.182120	−	0.202264i
$401$	−4.94005	+	2.19945i	−0.246694	+	0.109835i	−0.526359	−	0.850262i	$-0.676443\pi$
$401$	−4.94005	+	2.19945i	−0.246694	+	0.109835i	0.279665	+	0.960098i	$0.409777\pi$
$402$		0			0
$403$	−15.2454	+	3.24051i	−0.759426	+	0.161421i
$404$	3.86867	+	11.9065i	0.192473	+	0.592372i
$405$		0			0
$406$	−2.82926			−0.140414
$407$	−1.23330	+	10.0921i	−0.0611324	+	0.500248i
$408$		0			0
$409$	−2.46898	−	23.4907i	−0.122083	−	1.16154i	−0.868369	−	0.495918i	$-0.834832\pi$
$409$	−2.46898	−	23.4907i	−0.122083	−	1.16154i	0.746286	−	0.665625i	$-0.231835\pi$
$410$	−0.320338	−	0.0680899i	−0.0158204	−	0.00336272i
$411$		0			0
$412$	−0.304238	+	2.89464i	−0.0149888	+	0.142608i
$413$	−10.0890	−	7.33011i	−0.496449	−	0.360691i
$414$		0			0
$415$	−0.0659639	−	0.203016i	−0.00323804	−	0.00996567i
$416$	−18.1529	−	8.08218i	−0.890017	−	0.396261i
$417$		0			0
$418$	0.630444	+	7.15886i	0.0308360	+	0.350151i
$419$	−9.06566	+	15.7022i	−0.442886	+	0.767102i	−0.997902	−	0.0647380i	$-0.979379\pi$
$419$	−9.06566	+	15.7022i	−0.442886	+	0.767102i	0.555016	+	0.831840i	$0.312712\pi$
$420$		0			0
$421$	−8.57303	+	9.52132i	−0.417824	+	0.464041i	−0.914908	−	0.403662i	$-0.867737\pi$
$421$	−8.57303	+	9.52132i	−0.417824	+	0.464041i	0.497084	+	0.867702i	$0.334404\pi$
$422$	−1.10403	+	3.39785i	−0.0537432	+	0.165405i
$423$		0			0
$424$	18.7427	+	13.6174i	0.910226	+	0.661318i
$425$	6.73020	−	1.43055i	0.326463	−	0.0693918i
$426$		0			0
$427$	1.37364	+	13.0694i	0.0664753	+	0.632470i
$428$	−2.90904	+	5.03861i	−0.140614	+	0.243551i
$429$		0			0
$430$	4.02700	+	6.97496i	0.194199	+	0.336362i
$431$	−5.32265	+	3.86713i	−0.256383	+	0.186273i	−0.708551	−	0.705660i	$-0.750651\pi$
$431$	−5.32265	+	3.86713i	−0.256383	+	0.186273i	0.452168	+	0.891933i	$0.350651\pi$
$432$		0			0
$433$	4.32555	−	13.3127i	0.207873	−	0.639767i	−0.791710	−	0.610897i	$-0.790809\pi$
$433$	4.32555	−	13.3127i	0.207873	−	0.639767i	0.999583	−	0.0288700i	$-0.00919089\pi$
$434$	0.681693	−	6.48587i	0.0327223	−	0.311332i
$435$		0			0
$436$	6.48339	+	7.20053i	0.310498	+	0.344843i
$437$	−32.3738	−	6.88127i	−1.54865	−	0.329176i
$438$		0			0
$439$	−12.5891	−	21.8050i	−0.600846	−	1.04070i	−0.992693	−	0.120665i	$-0.961497\pi$
$439$	−12.5891	−	21.8050i	−0.600846	−	1.04070i	0.391848	−	0.920030i	$-0.371836\pi$
$440$	−8.34678	−	6.28227i	−0.397917	−	0.299495i
$441$		0			0
$442$	5.24254	−	3.80893i	0.249362	−	0.181172i
$443$	−17.9477	+	19.9330i	−0.852723	+	0.947045i	−0.999110	−	0.0421828i	$-0.986569\pi$
$443$	−17.9477	+	19.9330i	−0.852723	+	0.947045i	0.146387	+	0.989227i	$0.453235\pi$
$444$		0			0
$445$	−12.3798	+	5.51186i	−0.586861	+	0.261287i
$446$	10.5346	−	4.69030i	0.498827	−	0.222092i
$447$		0			0
$448$	−6.36898	+	7.07347i	−0.300906	+	0.334190i
$449$	11.4685	−	8.33234i	0.541231	−	0.393228i	−0.283311	−	0.959028i	$-0.591433\pi$
$449$	11.4685	−	8.33234i	0.541231	−	0.393228i	0.824542	+	0.565801i	$0.191433\pi$
$450$		0			0
$451$	−1.29620	−	0.0218838i	−0.0610357	−	0.00103047i
$452$	14.4353	+	25.0027i	0.678981	+	1.17603i
$453$		0			0
$454$	−5.71997	−	1.21582i	−0.268452	−	0.0570612i
$455$	15.5847	+	17.3086i	0.730623	+	0.811439i
$456$		0			0
$457$	−2.57572	+	24.5063i	−0.120487	+	1.14636i	0.752493	+	0.658600i	$0.228851\pi$
$457$	−2.57572	+	24.5063i	−0.120487	+	1.14636i	−0.872980	+	0.487756i	$0.837816\pi$
$458$	0.463439	−	1.42632i	0.0216551	−	0.0666475i
$459$		0			0
$460$	18.2162	−	13.2348i	0.849334	−	0.617077i
$461$	−13.1227	−	22.7292i	−0.611185	−	1.05860i	−0.991041	−	0.133558i	$-0.957360\pi$
$461$	−13.1227	−	22.7292i	−0.611185	−	1.05860i	0.379856	−	0.925046i	$-0.375973\pi$
$462$		0			0
$463$	−6.34609	+	10.9917i	−0.294928	+	0.510830i	−0.974968	−	0.222345i	$-0.928629\pi$
$463$	−6.34609	+	10.9917i	−0.294928	+	0.510830i	0.680040	+	0.733175i	$0.261962\pi$
$464$	0.462189	+	4.39744i	0.0214566	+	0.204146i
$465$		0			0
$466$	−11.7696	+	2.50170i	−0.545214	+	0.115889i
$467$	−22.4130	−	16.2840i	−1.03715	−	0.753534i	−0.0674235	−	0.997724i	$-0.521478\pi$
$467$	−22.4130	−	16.2840i	−1.03715	−	0.753534i	−0.969727	+	0.244190i	$0.921478\pi$
$468$		0			0
$469$	3.26838	−	10.0591i	0.150920	−	0.464484i
$470$	−0.605627	+	0.672617i	−0.0279355	+	0.0310255i
$471$		0			0
$472$	3.37128	−	5.83923i	0.155176	−	0.268772i
$473$	20.9300	+	24.0494i	0.962363	+	1.10579i
$474$		0			0
$475$	8.40291	+	3.74122i	0.385552	+	0.171659i
$476$	−6.12756	−	18.8587i	−0.280856	−	0.864386i
$477$		0			0
$478$	−2.75813	−	2.00390i	−0.126154	−	0.0916563i
$479$	−1.63297	+	15.5366i	−0.0746121	+	0.709886i	0.891720	+	0.452588i	$0.149499\pi$
$479$	−1.63297	+	15.5366i	−0.0746121	+	0.709886i	−0.966332	+	0.257299i	$0.917168\pi$
$480$		0			0
$481$	11.9879	+	2.54811i	0.546603	+	0.116184i
$482$	0.398402	+	3.79055i	0.0181467	+	0.172655i
$483$		0			0
$484$	−17.4046	−	8.46415i	−0.791117	−	0.384734i
$485$	−0.586177			−0.0266169
$486$		0			0
$487$	8.32090	+	25.6091i	0.377056	+	1.16046i	0.942081	+	0.335386i	$0.108867\pi$
$487$	8.32090	+	25.6091i	0.377056	+	1.16046i	−0.565025	+	0.825074i	$0.691133\pi$
$488$	−6.94988	+	1.47724i	−0.314606	+	0.0668716i
$489$		0			0
$490$	−3.54514	+	1.57840i	−0.160153	+	0.0713048i
$491$	−26.0959	−	28.9825i	−1.17769	−	1.30796i	−0.941797	−	0.336182i	$-0.890864\pi$
$491$	−26.0959	−	28.9825i	−1.17769	−	1.30796i	−0.235895	−	0.971778i	$-0.575802\pi$
$492$		0			0
$493$	−5.10580	−	2.27325i	−0.229954	−	0.102382i
$494$	8.66283			0.389759
$495$		0			0
$496$	−10.1922			−0.457642
$497$	−21.8631	−	9.73408i	−0.980694	−	0.436633i
$498$		0			0
$499$	−16.0826	−	17.8616i	−0.719958	−	0.799594i	0.266461	−	0.963846i	$-0.414146\pi$
$499$	−16.0826	−	17.8616i	−0.719958	−	0.799594i	−0.986418	+	0.164252i	$0.947479\pi$
$500$	−19.4444	+	8.65722i	−0.869582	+	0.387163i
$501$		0			0
$502$	0.156967	−	0.0333644i	0.00700578	−	0.00148912i
$503$	7.41223	+	22.8125i	0.330495	+	1.01716i	0.968899	+	0.247457i	$0.0795949\pi$
$503$	7.41223	+	22.8125i	0.330495	+	1.01716i	−0.638404	+	0.769701i	$0.720405\pi$
$504$		0			0
$505$	12.1547			0.540876
$506$	−8.30702	+	8.91841i	−0.369292	+	0.396472i
$507$		0			0
$508$	1.98528	+	18.8887i	0.0880827	+	0.838050i
$509$	3.61803	+	0.769037i	0.160367	+	0.0340870i	0.287395	−	0.957812i	$-0.407211\pi$
$509$	3.61803	+	0.769037i	0.160367	+	0.0340870i	−0.127029	+	0.991899i	$0.540544\pi$
$510$		0			0
$511$	5.36264	−	51.0221i	0.237229	−	2.25709i
$512$	−18.3128	−	13.3050i	−0.809318	−	0.588004i
$513$		0			0
$514$	2.08094	+	6.40449i	0.0917865	+	0.282490i
$515$	2.58151	+	1.14936i	0.113755	+	0.0506470i
$516$		0			0
$517$	−1.84353	+	3.07212i	−0.0810783	+	0.135112i
$518$	−2.56407	+	4.44110i	−0.112659	+	0.195131i
$519$		0			0
$520$	−8.42621	+	9.35825i	−0.369514	+	0.410387i
$521$	1.98178	−	6.09929i	0.0868234	−	0.267215i	−0.898213	−	0.439560i	$-0.855134\pi$
$521$	1.98178	−	6.09929i	0.0868234	−	0.267215i	0.985037	+	0.172345i	$0.0551344\pi$
$522$		0			0
$523$	2.21554	+	1.60969i	0.0968790	+	0.0703867i	0.635170	−	0.772372i	$-0.280930\pi$
$523$	2.21554	+	1.60969i	0.0968790	+	0.0703867i	−0.538291	+	0.842759i	$0.680930\pi$
$524$	36.4082	−	7.73880i	1.59050	−	0.338071i
$525$		0			0
$526$	−0.864124	−	8.22159i	−0.0376776	−	0.358478i
$527$	6.44147	−	11.1570i	0.280595	−	0.486005i
$528$		0			0
$529$	−16.5651	−	28.6916i	−0.720222	−	1.24746i
$530$	8.51617	−	6.18736i	0.369919	−	0.268762i
$531$		0			0
$532$	8.19149	−	25.2108i	0.355146	−	1.09303i
$533$	−0.163345	+	1.55413i	−0.00707527	+	0.0673167i
$534$		0			0
$535$	3.77969	+	4.19777i	0.163410	+	0.181485i
$536$	5.59356	+	1.18895i	0.241605	+	0.0513547i
$537$		0			0
$538$	3.04042	+	5.26617i	0.131082	+	0.227041i
$539$	−12.5784	+	8.81819i	−0.541788	+	0.379826i
$540$		0			0
$541$	−16.9114	+	12.2869i	−0.727079	+	0.528254i	−0.888638	−	0.458609i	$-0.848348\pi$
$541$	−16.9114	+	12.2869i	−0.727079	+	0.528254i	0.161559	+	0.986863i	$0.448348\pi$
$542$	6.32434	−	7.02389i	0.271654	−	0.301702i
$543$		0			0
$544$	15.0047	−	6.68051i	0.643320	−	0.286424i
$545$	8.59381	−	3.82621i	0.368118	−	0.163897i
$546$		0			0
$547$	−28.0208	+	31.1202i	−1.19808	+	1.33060i	−0.267925	+	0.963440i	$0.586338\pi$
$547$	−28.0208	+	31.1202i	−1.19808	+	1.33060i	−0.930156	+	0.367164i	$0.880329\pi$
$548$	−4.55562	+	3.30985i	−0.194606	+	0.141390i
$549$		0			0
$550$	2.77350	−	1.94439i	0.118263	−	0.0829092i
$551$	−3.73576	−	6.47053i	−0.159149	−	0.275654i
$552$		0			0
$553$	13.3411	+	2.83573i	0.567320	+	0.120588i
$554$	3.39727	+	3.77305i	0.144336	+	0.160302i
$555$		0			0
$556$	−2.75747	+	26.2355i	−0.116943	+	1.11263i
$557$	3.87025	−	11.9114i	0.163988	−	0.504702i	−0.834973	−	0.550291i	$-0.814517\pi$
$557$	3.87025	−	11.9114i	0.163988	−	0.504702i	0.998960	+	0.0455895i	$0.0145166\pi$
$558$		0			0
$559$	31.0911	−	22.5890i	1.31502	−	0.955415i
$560$	7.61538	+	13.1902i	0.321809	+	0.557389i
$561$		0			0
$562$	−4.03083	+	6.98160i	−0.170030	+	0.294501i
$563$	−1.51658	−	14.4293i	−0.0639161	−	0.608121i	−0.978859	−	0.204537i	$-0.934431\pi$
$563$	−1.51658	−	14.4293i	−0.0639161	−	0.608121i	0.914943	−	0.403584i	$-0.132236\pi$
$564$		0			0
$565$	27.4173	−	5.82774i	1.15346	−	0.245175i
$566$	0.501956	+	0.364693i	0.0210988	+	0.0153292i
$567$		0			0
$568$	3.99850	−	12.3061i	0.167773	−	0.516353i
$569$	18.7172	−	20.7876i	0.784666	−	0.871460i	−0.209667	−	0.977773i	$-0.567238\pi$
$569$	18.7172	−	20.7876i	0.784666	−	0.871460i	0.994333	+	0.106313i	$0.0339046\pi$
$570$		0			0
$571$	−4.52443	+	7.83654i	−0.189341	+	0.327949i	−0.945031	−	0.326981i	$-0.893969\pi$
$571$	−4.52443	+	7.83654i	−0.189341	+	0.327949i	0.755689	+	0.654930i	$0.227302\pi$
$572$	−12.0040	+	20.0039i	−0.501911	+	0.836404i
$573$		0			0
$574$	−0.597341	−	0.265953i	−0.0249325	−	0.0111007i
$575$	4.82046	+	14.8359i	0.201027	+	0.618698i
$576$		0			0
$577$	−31.0234	−	22.5398i	−1.29152	−	0.938346i	−0.291687	−	0.956514i	$-0.594217\pi$
$577$	−31.0234	−	22.5398i	−1.29152	−	0.938346i	−0.999835	+	0.0181683i	$0.994217\pi$
$578$	0.311714	−	2.96576i	0.0129656	−	0.123359i
$579$		0			0
$580$	4.97191	+	1.05681i	0.206447	+	0.0438817i
$581$	−0.0445499	−	0.423864i	−0.00184824	−	0.0175848i
$582$		0			0
$583$	28.4010	−	30.4913i	1.17625	−	1.26282i
$584$	27.7381			1.14781
$585$		0			0
$586$	3.65095	+	11.2365i	0.150819	+	0.464175i
$587$	−0.706826	+	0.150241i	−0.0291738	+	0.00620109i	−0.222475	−	0.974938i	$-0.571414\pi$
$587$	−0.706826	+	0.150241i	−0.0291738	+	0.00620109i	0.193302	+	0.981139i	$0.438080\pi$
$588$		0			0
$589$	15.7333	−	7.00493i	0.648281	−	0.288633i
$590$	−2.04997	−	2.27673i	−0.0843961	−	0.0937313i
$591$		0			0
$592$	7.32155	+	3.25977i	0.300914	+	0.133976i
$593$	39.6596			1.62863			0.814313	−	0.580426i	$-0.197114\pi$
$593$	39.6596			1.62863			0.814313	+	0.580426i	$0.197114\pi$
$594$		0			0
$595$	−19.2517			−0.789244
$596$	6.51139	+	2.89906i	0.266717	+	0.118750i
$597$		0			0
$598$	9.83054	+	10.9179i	0.402001	+	0.446467i
$599$	18.6151	−	8.28799i	0.760594	−	0.338638i	0.0104783	−	0.999945i	$-0.496665\pi$
$599$	18.6151	−	8.28799i	0.760594	−	0.338638i	0.750115	+	0.661307i	$0.229998\pi$
$600$		0			0
$601$	47.3147	−	10.0570i	1.93001	−	0.410235i	0.931032	−	0.364936i	$-0.118909\pi$
$601$	47.3147	−	10.0570i	1.93001	−	0.410235i	0.998973	−	0.0452991i	$-0.0144241\pi$
$602$	4.96914	+	15.2935i	0.202527	+	0.623315i
$603$		0			0
$604$	13.7129			0.557968
$605$	−13.0371	+	13.5313i	−0.530035	+	0.550125i
$606$		0			0
$607$	2.05945	+	19.5944i	0.0835905	+	0.795310i	0.953357	+	0.301846i	$0.0976029\pi$
$607$	2.05945	+	19.5944i	0.0835905	+	0.795310i	−0.869766	+	0.493464i	$0.835730\pi$
$608$	21.4771	+	4.56511i	0.871013	+	0.185140i
$609$		0			0
$610$	−0.337458	+	3.21070i	−0.0136633	+	0.129997i
$611$	3.49397	+	2.53852i	0.141351	+	0.102698i
$612$		0			0
$613$	1.76690	+	5.43796i	0.0713644	+	0.219637i	0.980377	−	0.197131i	$-0.0631626\pi$
$613$	1.76690	+	5.43796i	0.0713644	+	0.219637i	−0.909013	+	0.416768i	$0.863163\pi$
$614$	7.30158	+	3.25087i	0.294668	+	0.131194i
$615$		0			0
$616$	−13.6930	−	15.7339i	−0.551708	−	0.633935i
$617$	3.05346	−	5.28875i	0.122928	−	0.212917i	−0.797993	−	0.602666i	$-0.794105\pi$
$617$	3.05346	−	5.28875i	0.122928	−	0.212917i	0.920921	+	0.389749i	$0.127438\pi$
$618$		0			0
$619$	−1.19087	+	1.32260i	−0.0478653	+	0.0531598i	−0.766602	−	0.642123i	$-0.778054\pi$
$619$	−1.19087	+	1.32260i	−0.0478653	+	0.0531598i	0.718737	+	0.695282i	$0.244721\pi$
$620$	−3.62062	+	11.1431i	−0.145408	+	0.447519i
$621$		0			0
$622$	8.48050	+	6.16144i	0.340037	+	0.247051i
$623$	−26.4653	+	5.62538i	−1.06031	+	0.225376i
$624$		0			0
$625$	1.07184	+	10.1979i	0.0428737	+	0.407916i
$626$	−0.764220	+	1.32367i	−0.0305444	+	0.0529044i
$627$		0			0
$628$	0.271963	+	0.471055i	0.0108525	+	0.0187971i
$629$	−8.19556	+	5.95442i	−0.326778	+	0.237418i
$630$		0			0
$631$	−13.8566	+	42.6461i	−0.551621	+	1.69771i	0.153084	+	0.988213i	$0.451079\pi$
$631$	−13.8566	+	42.6461i	−0.551621	+	1.69771i	−0.704705	+	0.709501i	$0.748921\pi$
$632$	−0.770822	+	7.33388i	−0.0306617	+	0.291726i
$633$		0			0
$634$	5.99461	+	6.65768i	0.238076	+	0.264410i
$635$	18.0367	+	3.83381i	0.715764	+	0.152140i
$636$		0			0
$637$	9.25852	+	16.0362i	0.366836	+	0.635379i
$638$	−2.75097	−	0.0464448i	−0.108912	−	0.00183877i
$639$		0			0
$640$	−15.6290	+	11.3552i	−0.617792	+	0.448852i
$641$	18.0729	−	20.0720i	0.713837	−	0.792797i	−0.271677	−	0.962389i	$-0.587578\pi$
$641$	18.0729	−	20.0720i	0.713837	−	0.792797i	0.985514	+	0.169592i	$0.0542449\pi$
$642$		0			0
$643$	−29.7427	+	13.2423i	−1.17294	+	0.522225i	−0.898325	−	0.439331i	$-0.855216\pi$
$643$	−29.7427	+	13.2423i	−1.17294	+	0.522225i	−0.274610	+	0.961556i	$0.588549\pi$
$644$	41.0694	−	18.2853i	1.61836	−	0.720540i
$645$		0			0
$646$	−4.79128	+	5.32126i	−0.188510	+	0.209362i
$647$	−25.4705	+	18.5054i	−1.00135	+	0.727523i	−0.962377	−	0.271717i	$-0.912408\pi$
$647$	−25.4705	+	18.5054i	−1.00135	+	0.727523i	−0.0389724	+	0.999240i	$0.512408\pi$
$648$		0			0
$649$	−9.68953	−	7.29290i	−0.380347	−	0.286271i
$650$	−2.04149	−	3.53596i	−0.0800736	−	0.138692i
$651$		0			0
$652$	18.9205	+	4.02168i	0.740984	+	0.157501i
$653$	3.11800	+	3.46289i	0.122017	+	0.135513i	0.801058	−	0.598587i	$-0.204271\pi$
$653$	3.11800	+	3.46289i	0.122017	+	0.135513i	−0.679041	+	0.734100i	$0.737604\pi$
$654$		0			0
$655$	3.77741	−	35.9396i	0.147596	−	1.40428i
$656$	−0.315782	+	0.971878i	−0.0123292	+	0.0379455i
$657$		0			0
$658$	−1.46197	+	1.06219i	−0.0569937	+	0.0414084i
$659$	−16.0209	−	27.7490i	−0.624086	−	1.08095i	−0.988717	−	0.149797i	$-0.952138\pi$
$659$	−16.0209	−	27.7490i	−0.624086	−	1.08095i	0.364631	−	0.931152i	$-0.381195\pi$
$660$		0			0
$661$	20.3527	−	35.2519i	0.791627	−	1.37114i	−0.133331	−	0.991072i	$-0.542567\pi$
$661$	20.3527	−	35.2519i	0.791627	−	1.37114i	0.924959	−	0.380067i	$-0.124099\pi$
$662$	−0.193093	−	1.83716i	−0.00750478	−	0.0714032i
$663$		0			0
$664$	0.225398	−	0.0479098i	0.00874713	−	0.00185926i
$665$	−20.8211	−	15.1274i	−0.807406	−	0.586615i
$666$		0			0
$667$	3.91560	−	12.0510i	0.151613	−	0.466616i
$668$	−20.6893	+	22.9778i	−0.800495	+	0.889039i
$669$		0			0
$670$	1.29917	−	2.25023i	0.0501914	−	0.0869340i
$671$	1.12109	+	12.7303i	0.0432792	+	0.491447i
$672$		0			0
$673$	−34.4987	−	15.3598i	−1.32983	−	0.592077i	−0.385994	−	0.922501i	$-0.626142\pi$
$673$	−34.4987	−	15.3598i	−1.32983	−	0.592077i	−0.943833	+	0.330424i	$0.892808\pi$
$674$	0.904299	+	2.78315i	0.0348323	+	0.107203i
$675$		0			0
$676$	4.24655	+	3.08530i	0.163329	+	0.118665i
$677$	1.97566	−	18.7971i	0.0759307	−	0.722432i	−0.888640	−	0.458606i	$-0.848349\pi$
$677$	1.97566	−	18.7971i	0.0759307	−	0.722432i	0.964570	−	0.263826i	$-0.0849845\pi$
$678$		0			0
$679$	−1.14478	−	0.243330i	−0.0439326	−	0.00933815i
$680$	−1.08802	−	10.3518i	−0.0417237	−	0.396974i
$681$		0			0
$682$	0.769301	−	6.29521i	0.0294581	−	0.241056i
$683$	−31.1053			−1.19021			−0.595105	−	0.803648i	$-0.702890\pi$
$683$	−31.1053			−1.19021			−0.595105	+	0.803648i	$0.702890\pi$
$684$		0			0
$685$	1.68941	+	5.19948i	0.0645492	+	0.198662i
$686$	3.87527	−	0.823714i	0.147959	−	0.0314496i
$687$		0			0
$688$	22.9585	−	10.2218i	0.875283	−	0.389701i
$689$	−33.6098	−	37.3274i	−1.28043	−	1.42206i
$690$		0			0
$691$	20.2911	+	9.03419i	0.771911	+	0.343677i	0.754610	−	0.656173i	$-0.227826\pi$
$691$	20.2911	+	9.03419i	0.771911	+	0.343677i	0.0173008	+	0.999850i	$0.494493\pi$
$692$	21.7565			0.827057
$693$		0			0
$694$	−11.9432			−0.453358
$695$	23.3975	+	10.4173i	0.887520	+	0.395149i
$696$		0			0
$697$	−0.864299	−	0.959901i	−0.0327377	−	0.0363589i
$698$	7.50180	−	3.34001i	0.283947	−	0.126421i
$699$		0			0
$700$	−12.2209	+	2.59762i	−0.461905	+	0.0981810i
$701$	9.25374	+	28.4801i	0.349509	+	1.07568i	0.959125	+	0.282981i	$0.0913235\pi$
$701$	9.25374	+	28.4801i	0.349509	+	1.07568i	−0.609616	+	0.792697i	$0.708677\pi$
$702$		0			0
$703$	−13.5424			−0.510763
$704$	−6.30886	+	6.77319i	−0.237774	+	0.255274i
$705$		0			0
$706$	−0.411770	−	3.91773i	−0.0154972	−	0.147446i
$707$	23.7375	+	5.04557i	0.892742	+	0.189758i
$708$		0			0
$709$	−1.79849	+	17.1115i	−0.0675436	+	0.642635i	0.907413	+	0.420240i	$0.138054\pi$
$709$	−1.79849	+	17.1115i	−0.0675436	+	0.642635i	−0.974957	+	0.222395i	$0.928613\pi$
$710$	−4.75647	−	3.45578i	−0.178507	−	0.129693i
$711$		0			0
$712$	−4.52052	−	13.9127i	−0.169414	−	0.521402i
$713$	26.6826	+	11.8799i	0.999271	+	0.444904i
$714$		0			0
$715$	14.8694	+	17.0855i	0.556082	+	0.638961i
$716$	−19.2500	+	33.3420i	−0.719407	+	1.24605i
$717$		0			0
$718$	9.46050	−	10.5070i	0.353063	−	0.392116i
$719$	−1.46013	+	4.49382i	−0.0544537	+	0.167591i	−0.974585	−	0.224020i	$-0.928082\pi$
$719$	−1.46013	+	4.49382i	−0.0544537	+	0.167591i	0.920131	+	0.391611i	$0.128082\pi$
$720$		0			0
$721$	4.56446	+	3.31628i	0.169989	+	0.123505i
$722$	−0.247392	+	0.0525847i	−0.00920696	+	0.00195700i
$723$		0			0
$724$	−0.805554	−	7.66433i	−0.0299382	−	0.284843i
$725$	−1.76074	+	3.04969i	−0.0653923	+	0.113263i
$726$		0			0
$727$	−2.60044	−	4.50410i	−0.0964450	−	0.167048i	0.813766	−	0.581193i	$-0.197414\pi$
$727$	−2.60044	−	4.50410i	−0.0964450	−	0.167048i	−0.910211	+	0.414145i	$0.864081\pi$
$728$	−20.3408	+	14.7784i	−0.753879	+	0.547725i
$729$		0			0
$730$	3.89468	−	11.9866i	0.144149	−	0.443644i
$731$	−3.32043	+	31.5918i	−0.122811	+	1.16847i
$732$		0			0
$733$	−32.8297	−	36.4610i	−1.21259	−	1.34672i	−0.920702	−	0.390267i	$-0.872383\pi$
$733$	−32.8297	−	36.4610i	−1.21259	−	1.34672i	−0.291890	−	0.956452i	$-0.594284\pi$
$734$	−10.7198	−	2.27857i	−0.395676	−	0.0841034i
$735$		0			0
$736$	18.6187	+	32.2485i	0.686294	+	1.18870i
$737$	3.34308	−	9.72706i	0.123144	−	0.358301i
$738$		0			0
$739$	12.6160	−	9.16603i	0.464086	−	0.337178i	−0.331046	−	0.943615i	$-0.607402\pi$
$739$	12.6160	−	9.16603i	0.464086	−	0.337178i	0.795132	+	0.606437i	$0.207402\pi$
$740$	6.16478	−	6.84668i	0.226622	−	0.251689i
$741$		0			0
$742$	19.2002	−	8.54847i	0.704861	−	0.313824i
$743$	−10.1718	+	4.52879i	−0.373168	+	0.166145i	−0.584747	−	0.811216i	$-0.698806\pi$
$743$	−10.1718	+	4.52879i	−0.373168	+	0.166145i	0.211579	+	0.977361i	$0.432139\pi$
$744$		0			0
$745$	4.63041	−	5.14259i	0.169645	−	0.188410i
$746$	−2.80897	+	2.04083i	−0.102844	+	0.0747202i
$747$		0			0
$748$	−5.64842	−	18.4374i	−0.206527	−	0.674140i
$749$	5.63901	+	9.76705i	0.206045	+	0.356880i
$750$		0			0
$751$	7.90852	+	1.68101i	0.288586	+	0.0613409i	0.349930	−	0.936776i	$-0.386205\pi$
$751$	7.90852	+	1.68101i	0.288586	+	0.0613409i	−0.0613440	+	0.998117i	$0.519539\pi$
$752$	1.88976	+	2.09879i	0.0689124	+	0.0765350i
$753$		0			0
$754$	−0.346673	+	3.29838i	−0.0126251	+	0.120120i
$755$	4.11410	−	12.6619i	0.149727	−	0.460814i
$756$		0			0
$757$	−24.1585	+	17.5522i	−0.878056	+	0.637945i	−0.932737	−	0.360559i	$-0.882586\pi$
$757$	−24.1585	+	17.5522i	−0.878056	+	0.637945i	0.0546803	+	0.998504i	$0.482586\pi$
$758$	5.97081	+	10.3417i	0.216869	+	0.375629i
$759$		0			0
$760$	6.95742	−	12.0506i	0.252372	−	0.437121i
$761$	3.64727	+	34.7014i	0.132213	+	1.25793i	0.836483	+	0.547993i	$0.184608\pi$
$761$	3.64727	+	34.7014i	0.132213	+	1.25793i	−0.704269	+	0.709933i	$0.748725\pi$
$762$		0			0
$763$	18.3716	−	3.90501i	0.665098	−	0.141371i
$764$	−17.8134	−	12.9422i	−0.644468	−	0.468233i
$765$		0			0
$766$	2.67339	−	8.22786i	0.0965936	−	0.297284i
$767$	−9.78174	+	10.8637i	−0.353198	+	0.392266i
$768$		0			0
$769$	2.80362	−	4.85600i	0.101101	−	0.175112i	−0.811038	−	0.584994i	$-0.801097\pi$
$769$	2.80362	−	4.85600i	0.101101	−	0.175112i	0.912139	+	0.409882i	$0.134430\pi$
$770$	−8.72177	+	3.70806i	−0.314311	+	0.133629i
$771$		0			0
$772$	20.1969	+	8.99226i	0.726904	+	0.323639i
$773$	3.34979	+	10.3096i	0.120483	+	0.370810i	0.993051	−	0.117683i	$-0.0375467\pi$
$773$	3.34979	+	10.3096i	0.120483	+	0.370810i	−0.872568	+	0.488493i	$0.837547\pi$
$774$		0			0
$775$	−6.56697	−	4.77118i	−0.235893	−	0.171386i
$776$	0.0661431	−	0.629310i	0.00237440	−	0.0225909i
$777$		0			0
$778$	−8.57982	−	1.82370i	−0.307601	−	0.0653827i
$779$	−0.180494	−	1.71729i	−0.00646688	−	0.0615282i
$780$		0			0
$781$	−21.0984	−	9.82364i	−0.754958	−	0.351517i
$782$	−12.1436			−0.434255
$783$		0			0
$784$	3.74186	+	11.5163i	0.133638	+	0.411295i
$785$	0.516546	−	0.109795i	0.0184363	−	0.00391876i
$786$		0			0
$787$	−2.26233	+	1.00726i	−0.0806434	+	0.0359048i	−0.446662	−	0.894703i	$-0.647387\pi$
$787$	−2.26233	+	1.00726i	−0.0806434	+	0.0359048i	0.366019	+	0.930608i	$0.380721\pi$
$788$	−12.1794	−	13.5265i	−0.433872	−	0.481863i
$789$		0			0
$790$	3.06099	+	1.36284i	0.108905	+	0.0484877i
$791$	55.9640			1.98985
$792$		0			0
$793$	15.4047			0.547037
$794$	−9.83084	−	4.37697i	−0.348883	−	0.155333i
$795$		0			0
$796$	−31.1712	−	34.6191i	−1.10483	−	1.22704i
$797$	8.84284	−	3.93708i	0.313229	−	0.139459i	−0.244100	−	0.969750i	$-0.578493\pi$
$797$	8.84284	−	3.93708i	0.313229	−	0.139459i	0.557330	+	0.830291i	$0.311826\pi$
$798$		0			0
$799$	−3.49179	+	0.742202i	−0.123531	+	0.0262572i
$800$	−3.19795	−	9.84226i	−0.113064	−	0.347977i
$801$		0			0
$802$	−2.65237			−0.0936586
$803$	6.05183	−	49.5223i	0.213564	−	1.74760i
$804$		0			0
$805$	−4.56233	−	43.4077i	−0.160801	−	1.52992i
$806$	−7.47777	−	1.58945i	−0.263393	−	0.0559859i
$807$		0			0
$808$	−1.37151	+	13.0491i	−0.0482496	+	0.459064i
$809$	−6.36318	−	4.62312i	−0.223717	−	0.162540i	0.470281	−	0.882517i	$-0.344153\pi$
$809$	−6.36318	−	4.62312i	−0.223717	−	0.162540i	−0.693998	+	0.719976i	$0.744153\pi$
$810$		0			0
$811$	12.2076	+	37.5712i	0.428668	+	1.31930i	0.899438	+	0.437048i	$0.143976\pi$
$811$	12.2076	+	37.5712i	0.428668	+	1.31930i	−0.470770	+	0.882256i	$0.656024\pi$
$812$	9.27123	+	4.12782i	0.325356	+	0.144858i
$813$		0			0
$814$	−2.56603	+	4.27612i	−0.0899392	+	0.149878i
$815$	9.38994	−	16.2639i	0.328915	−	0.569698i
$816$		0			0
$817$	−28.4149	+	31.5580i	−0.994113	+	1.10407i
$818$	3.58013	−	11.0185i	0.125176	−	0.385253i
$819$		0			0
$820$	0.950378	+	0.690490i	0.0331886	+	0.0241130i
$821$	−3.28033	+	0.697257i	−0.114484	+	0.0243344i	−0.264798	−	0.964304i	$-0.585305\pi$
$821$	−3.28033	+	0.697257i	−0.114484	+	0.0243344i	0.150313	+	0.988638i	$0.451972\pi$
$822$		0			0
$823$	−1.68310	−	16.0136i	−0.0586691	−	0.558199i	−0.983891	−	0.178772i	$-0.942788\pi$
$823$	−1.68310	−	16.0136i	−0.0586691	−	0.558199i	0.925221	−	0.379428i	$-0.123879\pi$
$824$	−1.52523	+	2.64177i	−0.0531339	+	0.0920306i
$825$		0			0
$826$	−3.05841	−	5.29732i	−0.106416	−	0.184317i
$827$	12.3703	−	8.98751i	0.430156	−	0.312526i	−0.351555	−	0.936167i	$-0.614347\pi$
$827$	12.3703	−	8.98751i	0.430156	−	0.312526i	0.781711	+	0.623641i	$0.214347\pi$
$828$		0			0
$829$	−13.0239	+	40.0835i	−0.452340	+	1.39216i	0.421890	+	0.906647i	$0.361367\pi$
$829$	−13.0239	+	40.0835i	−0.452340	+	1.39216i	−0.874230	+	0.485512i	$0.838633\pi$
$830$	0.0109444	−	0.104129i	0.000379886	−	0.00361438i
$831$		0			0
$832$	7.46592	+	8.29174i	0.258834	+	0.287464i
$833$	−14.9712	−	3.18223i	−0.518722	−	0.110258i
$834$		0			0
$835$	15.0096	+	25.9975i	0.519430	+	0.899679i
$836$	8.37869	−	24.3788i	0.289783	−	0.843157i
$837$		0			0
$838$	−7.19483	+	5.22735i	−0.248541	+	0.180576i
$839$	−1.77145	+	1.96739i	−0.0611573	+	0.0679220i	−0.772947	−	0.634471i	$-0.781218\pi$
$839$	−1.77145	+	1.96739i	−0.0611573	+	0.0679220i	0.711790	+	0.702393i	$0.247885\pi$
$840$		0			0
$841$	−23.8797	+	10.6319i	−0.823437	+	0.366618i
$842$	−5.74100	+	2.55606i	−0.197848	+	0.0880876i
$843$		0			0
$844$	8.57518	−	9.52371i	0.295170	−	0.327819i
$845$	4.12288	−	2.99545i	0.141831	−	0.103047i
$846$		0			0
$847$	−31.0780	+	21.0141i	−1.06785	+	0.722053i
$848$	−16.4232	−	28.4458i	−0.563976	−	0.976834i
$849$		0			0
$850$	3.30112	+	0.701676i	0.113228	+	0.0240673i
$851$	−15.3679	−	17.0678i	−0.526805	−	0.585076i
$852$		0			0
$853$	−0.969018	+	9.21959i	−0.0331785	+	0.315673i	0.965328	+	0.261040i	$0.0840654\pi$
$853$	−0.969018	+	9.21959i	−0.0331785	+	0.315673i	−0.998507	+	0.0546327i	$0.982601\pi$
$854$	−1.99185	+	6.13027i	−0.0681596	+	0.209774i
$855$		0			0
$856$	−4.93314	+	3.58414i	−0.168611	+	0.122503i
$857$	−10.2678	−	17.7844i	−0.350742	−	0.607502i	0.635638	−	0.771987i	$-0.280737\pi$
$857$	−10.2678	−	17.7844i	−0.350742	−	0.607502i	−0.986380	+	0.164485i	$0.947404\pi$
$858$		0			0
$859$	−18.0139	+	31.2010i	−0.614626	+	1.06456i	0.375824	+	0.926691i	$0.377360\pi$
$859$	−18.0139	+	31.2010i	−0.614626	+	1.06456i	−0.990450	+	0.137872i	$0.955974\pi$
$860$	−3.01982	−	28.7316i	−0.102975	−	0.979740i
$861$		0			0
$862$	−3.15652	+	0.670939i	−0.107511	+	0.0228523i
$863$	3.49209	+	2.53715i	0.118872	+	0.0863656i	0.645633	−	0.763648i	$-0.276594\pi$
$863$	3.49209	+	2.53715i	0.118872	+	0.0863656i	−0.526761	+	0.850014i	$0.676594\pi$
$864$		0			0
$865$	6.52733	−	20.0890i	0.221936	−	0.683048i
$866$	4.59414	−	5.10230i	0.156115	−	0.173383i
$867$		0			0
$868$	−11.6966	+	20.2591i	−0.397008	+	0.687637i
$869$	12.9254	+	2.97627i	0.438463	+	0.100963i
$870$		0			0
$871$	−11.3265	−	5.04287i	−0.383783	−	0.170871i
$872$	3.13804	+	9.65790i	0.106268	+	0.327058i
$873$		0			0
$874$	−13.1335	−	9.54206i	−0.444248	−	0.322765i
$875$	−4.31273	+	41.0329i	−0.145797	+	1.38716i
$876$		0			0
$877$	−30.4360	−	6.46938i	−1.02775	−	0.218455i	−0.336968	−	0.941516i	$-0.609401\pi$
$877$	−30.4360	−	6.46938i	−1.02775	−	0.218455i	−0.690785	+	0.723061i	$0.742735\pi$
$878$	−1.29090	−	12.2821i	−0.0435658	−	0.414501i
$879$		0			0
$880$	7.18813	+	12.9503i	0.242312	+	0.436553i
$881$	−43.9267			−1.47993			−0.739964	−	0.672647i	$-0.765157\pi$
$881$	−43.9267			−1.47993			−0.739964	+	0.672647i	$0.765157\pi$
$882$		0			0
$883$	−1.81685	−	5.59170i	−0.0611420	−	0.188176i	0.915820	−	0.401589i	$-0.131542\pi$
$883$	−1.81685	−	5.59170i	−0.0611420	−	0.188176i	−0.976962	+	0.213413i	$0.931542\pi$
$884$	−22.7365	+	4.83279i	−0.764710	+	0.162544i
$885$		0			0
$886$	−12.0188	+	5.35113i	−0.403781	+	0.179775i
$887$	5.14903	+	5.71858i	0.172887	+	0.192011i	0.823361	−	0.567518i	$-0.192096\pi$
$887$	5.14903	+	5.71858i	0.172887	+	0.192011i	−0.650474	+	0.759529i	$0.725430\pi$
$888$		0			0
$889$	33.6334	+	14.9745i	1.12803	+	0.502230i
$890$	−6.64689			−0.222804
$891$		0			0
$892$	−41.3640			−1.38497
$893$	−4.35963	−	1.94103i	−0.145889	−	0.0649541i
$894$		0			0
$895$	25.0113	+	27.7779i	0.836036	+	0.928512i
$896$	−35.2365	+	15.6883i	−1.17717	+	0.524109i
$897$		0			0
$898$	6.80121	−	1.44564i	0.226959	−	0.0482417i
$899$	2.03751	+	6.27081i	0.0679547	+	0.209143i
$900$		0			0
$901$	41.5180			1.38316
$902$	−0.576446	−	0.268400i	−0.0191936	−	0.00893675i
$903$		0			0
$904$	3.16284	+	30.0924i	0.105194	+	1.00086i
$905$	−7.31861	−	1.55562i	−0.243279	−	0.0517105i
$906$		0			0
$907$	1.98505	−	18.8865i	0.0659126	−	0.627117i	−0.910842	−	0.412756i	$-0.864566\pi$
$907$	1.98505	−	18.8865i	0.0659126	−	0.627117i	0.976754	−	0.214361i	$-0.0687669\pi$
$908$	16.9700	+	12.3294i	0.563170	+	0.409167i
$909$		0			0
$910$	3.53024	+	10.8650i	0.117026	+	0.360170i
$911$	−45.7095	−	20.3512i	−1.51442	−	0.674265i	−0.529667	−	0.848206i	$-0.677683\pi$
$911$	−45.7095	−	20.3512i	−1.51442	−	0.674265i	−0.984756	+	0.173941i	$0.944350\pi$
$912$		0			0
$913$	−0.0363591	−	0.412867i	−0.00120331	−	0.0136639i
$914$	−6.04320	+	10.4671i	−0.199891	+	0.346222i
$915$		0			0
$916$	−3.59961	+	3.99778i	−0.118935	+	0.132090i
$917$	22.2961	−	68.6205i	0.736284	−	2.26605i
$918$		0			0
$919$	−2.48708	−	1.80697i	−0.0820411	−	0.0596063i	0.546009	−	0.837780i	$-0.316147\pi$
$919$	−2.48708	−	1.80697i	−0.0820411	−	0.0596063i	−0.628050	+	0.778173i	$0.716147\pi$
$920$	23.0829	−	4.90641i	0.761019	−	0.161760i
$921$		0			0
$922$	−1.34562	−	12.8027i	−0.0443155	−	0.421634i
$923$	−14.0270	+	24.2955i	−0.461705	+	0.799696i
$924$		0			0
$925$	3.19142	+	5.52769i	0.104933	+	0.181749i
$926$	−5.03648	+	3.65922i	−0.165509	+	0.120249i
$927$		0			0
$928$	−2.59765	+	7.99474i	−0.0852720	+	0.262440i
$929$	−0.0946583	+	0.900613i	−0.00310564	+	0.0295482i	−0.995965	−	0.0897428i	$-0.971395\pi$
$929$	−0.0946583	+	0.900613i	−0.00310564	+	0.0295482i	0.992859	+	0.119291i	$0.0380621\pi$
$930$		0			0
$931$	−13.6911	−	15.2055i	−0.448709	−	0.498342i
$932$	42.2177	+	8.97365i	1.38289	+	0.293942i
$933$		0			0
$934$	−6.79433	−	11.7681i	−0.222317	−	0.385065i
$935$	−18.7190	−	0.316034i	−0.612177	−	0.0103354i
$936$		0			0
$937$	17.8423	−	12.9632i	0.582881	−	0.423488i	−0.256881	−	0.966443i	$-0.582695\pi$
$937$	17.8423	−	12.9632i	0.582881	−	0.423488i	0.839762	+	0.542955i	$0.182695\pi$
$938$	3.47133	−	3.85530i	0.113343	−	0.125880i
$939$		0			0
$940$	2.96592	−	1.32051i	0.0967376	−	0.0430703i
$941$	−4.98880	+	2.22116i	−0.162630	+	0.0724077i	−0.486437	−	0.873715i	$-0.661704\pi$
$941$	−4.98880	+	2.22116i	−0.162630	+	0.0724077i	0.323807	+	0.946123i	$0.395037\pi$
$942$		0			0
$943$	1.95951	−	2.17625i	0.0638103	−	0.0708685i
$944$	−7.73386	+	5.61898i	−0.251716	+	0.182882i
$945$		0			0
$946$	4.58059	+	14.9519i	0.148928	+	0.486127i
$947$	16.2203	+	28.0944i	0.527089	+	0.912945i	0.999502	+	0.0315677i	$0.0100500\pi$
$947$	16.2203	+	28.0944i	0.527089	+	0.912945i	−0.472412	+	0.881378i	$0.656617\pi$
$948$		0			0
$949$	−58.8250	−	12.5036i	−1.90954	−	0.405885i
$950$	3.01887	+	3.35279i	0.0979450	+	0.108779i
$951$		0			0
$952$	2.17233	−	20.6683i	0.0704055	−	0.669864i
$953$	16.6278	−	51.1752i	0.538628	−	1.65773i	−0.197049	−	0.980394i	$-0.563136\pi$
$953$	16.6278	−	51.1752i	0.538628	−	1.65773i	0.735677	−	0.677333i	$-0.236864\pi$
$954$		0			0
$955$	−17.2947	+	12.5653i	−0.559642	+	0.406604i
$956$	6.11452	+	10.5907i	0.197758	+	0.342527i
$957$		0			0
$958$	−3.83130	+	6.63600i	−0.123784	+	0.214400i
$959$	1.14098	+	10.8557i	0.0368440	+	0.350548i
$960$		0			0
$961$	15.4563	−	3.28533i	0.498589	−	0.105978i
$962$	4.86330	+	3.53339i	0.156799	+	0.113921i
$963$		0			0
$964$	4.22478	−	13.0025i	0.136071	−	0.418784i
$965$	14.3625	−	15.9512i	0.462346	−	0.513487i
$966$		0			0
$967$	14.4075	−	24.9546i	0.463315	−	0.802486i	−0.535809	−	0.844340i	$-0.679993\pi$
$967$	14.4075	−	24.9546i	0.463315	−	0.802486i	0.999124	+	0.0418540i	$0.0133264\pi$
$968$	−13.0559	−	15.5233i	−0.419631	−	0.498937i
$969$		0			0
$970$	−0.262659	−	0.116943i	−0.00843348	−	0.00375483i
$971$	−1.66685	−	5.13005i	−0.0534919	−	0.164631i	0.920742	−	0.390173i	$-0.127585\pi$
$971$	−1.66685	−	5.13005i	−0.0534919	−	0.164631i	−0.974233	+	0.225542i	$0.927585\pi$
$972$		0			0
$973$	41.3700	+	30.0571i	1.32626	+	0.963586i
$974$	−1.38056	+	13.1352i	−0.0442361	+	0.420878i
$975$		0			0
$976$	9.85351	+	2.09443i	0.315403	+	0.0670410i
$977$	−0.346236	−	3.29421i	−0.0110771	−	0.105391i	0.987586	−	0.157077i	$-0.0502072\pi$
$977$	−0.346236	−	3.29421i	−0.0110771	−	0.105391i	−0.998663	+	0.0516860i	$0.983540\pi$
$978$		0			0
$979$	−25.8254	+	5.03527i	−0.825383	+	0.160928i
$980$	13.9200			0.444657
$981$		0			0
$982$	−5.91123	−	18.1929i	−0.188635	−	0.580559i
$983$	33.1319	−	7.04241i	1.05674	−	0.224618i	0.353404	−	0.935471i	$-0.385024\pi$
$983$	33.1319	−	7.04241i	1.05674	−	0.224618i	0.703341	+	0.710853i	$0.251691\pi$
$984$		0			0
$985$	−16.1439	+	7.18772i	−0.514387	+	0.229020i
$986$	−1.83433	−	2.03723i	−0.0584170	−	0.0648787i
$987$		0			0
$988$	−28.3873	−	12.6389i	−0.903121	−	0.402095i
$989$	−72.0183			−2.29005
$990$		0			0
$991$	8.66640			0.275297			0.137649	−	0.990481i	$-0.456046\pi$
$991$	8.66640			0.275297			0.137649	+	0.990481i	$0.456046\pi$
$992$	−17.7015	−	7.88122i	−0.562023	−	0.250229i
$993$		0			0
$994$	−7.85464	−	8.72346i	−0.249134	−	0.276691i
$995$	−41.3178	+	18.3959i	−1.30986	+	0.583189i
$996$		0			0
$997$	29.6040	−	6.29253i	0.937569	−	0.199286i	0.286306	−	0.958138i	$-0.407573\pi$
$997$	29.6040	−	6.29253i	0.937569	−	0.199286i	0.651263	+	0.758852i	$0.274239\pi$
$998$	−3.64303	−	11.2121i	−0.115318	−	0.354912i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.n.b.91.5		72
3.2	odd	2		99.2.m.b.58.5	yes	72
9.2	odd	6		99.2.m.b.25.5	yes	72
9.4	even	3		891.2.f.e.487.5		36
9.5	odd	6		891.2.f.f.487.5		36
9.7	even	3	inner	297.2.n.b.289.5		72
11.4	even	5	inner	297.2.n.b.37.5		72
33.2	even	10		1089.2.e.o.364.9		36
33.20	odd	10		1089.2.e.p.364.10		36
33.26	odd	10		99.2.m.b.4.5	✓	72
99.2	even	30		1089.2.e.o.727.9		36
99.4	even	15		891.2.f.e.730.5		36
99.13	odd	30		9801.2.a.cn.1.9		18
99.20	odd	30		1089.2.e.p.727.10		36
99.31	even	15		9801.2.a.cp.1.10		18
99.59	odd	30		891.2.f.f.730.5		36
99.68	even	30		9801.2.a.co.1.10		18
99.70	even	15	inner	297.2.n.b.235.5		72
99.86	odd	30		9801.2.a.cm.1.9		18
99.92	odd	30		99.2.m.b.70.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.5	✓	72	33.26	odd	10
99.2.m.b.25.5	yes	72	9.2	odd	6
99.2.m.b.58.5	yes	72	3.2	odd	2
99.2.m.b.70.5	yes	72	99.92	odd	30
297.2.n.b.37.5		72	11.4	even	5	inner
297.2.n.b.91.5		72	1.1	even	1	trivial
297.2.n.b.235.5		72	99.70	even	15	inner
297.2.n.b.289.5		72	9.7	even	3	inner
891.2.f.e.487.5		36	9.4	even	3
891.2.f.e.730.5		36	99.4	even	15
891.2.f.f.487.5		36	9.5	odd	6
891.2.f.f.730.5		36	99.59	odd	30
1089.2.e.o.364.9		36	33.2	even	10
1089.2.e.o.727.9		36	99.2	even	30
1089.2.e.p.364.10		36	33.20	odd	10
1089.2.e.p.727.10		36	99.20	odd	30
9801.2.a.cm.1.9		18	99.86	odd	30
9801.2.a.cn.1.9		18	99.13	odd	30
9801.2.a.co.1.10		18	99.68	even	30
9801.2.a.cp.1.10		18	99.31	even	15

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.448089 + 0.199502i) q^{2} +(-1.17728 - 1.30750i) q^{4} +(-1.56050 + 0.694778i) q^{5} +(-3.33599 + 0.709088i) q^{7} +(-0.569818 - 1.75372i) q^{8} -0.837851 q^{10} +(-3.25533 + 0.634703i) q^{11} +(0.417897 + 3.97602i) q^{13} +(-1.63629 - 0.347803i) q^{14} +(-0.273277 + 2.60005i) q^{16} +(-2.67346 - 1.94238i) q^{17} +(-1.36513 - 4.20144i) q^{19} +(2.74556 + 1.22240i) q^{20} +(-1.58530 - 0.365040i) q^{22} +(3.74601 - 6.48827i) q^{23} +(-1.39322 + 1.54733i) q^{25} +(-0.605969 + 1.86498i) q^{26} +(4.85453 + 3.52702i) q^{28} +(1.65433 - 0.351639i) q^{29} +(0.407506 + 3.87716i) q^{31} +(-2.48514 + 4.30439i) q^{32} +(-0.810437 - 1.40372i) q^{34} +(4.71315 - 3.42431i) q^{35} +(0.947300 - 2.91549i) q^{37} +(0.226496 - 2.15496i) q^{38} +(2.10765 + 2.34078i) q^{40} +(0.382333 + 0.0812674i) q^{41} +(-4.80634 - 8.32483i) q^{43} +(4.66230 + 3.50912i) q^{44} +(2.97296 - 2.15999i) q^{46} +(0.722834 - 0.802788i) q^{47} +(4.23124 - 1.88387i) q^{49} +(-0.932979 + 0.415389i) q^{50} +(4.70667 - 5.22729i) q^{52} +(-10.1643 + 7.38480i) q^{53} +(4.63895 - 3.25218i) q^{55} +(3.14445 + 5.44635i) q^{56} +(0.811439 + 0.172477i) q^{58} +(2.44670 + 2.71734i) q^{59} +(0.402767 - 3.83207i) q^{61} +(-0.590902 + 1.81861i) q^{62} +(2.25785 - 1.64043i) q^{64} +(-3.41458 - 5.91423i) q^{65} +(-1.55060 + 2.68572i) q^{67} +(0.607741 + 5.78227i) q^{68} +(2.79506 - 0.594109i) q^{70} +(5.67699 + 4.12458i) q^{71} +(-4.64842 + 14.3064i) q^{73} +(1.00612 - 1.11741i) q^{74} +(-3.88624 + 6.73117i) q^{76} +(10.4097 - 4.42568i) q^{77} +(-3.65339 - 1.62659i) q^{79} +(-1.38001 - 4.24724i) q^{80} +(0.155106 + 0.112691i) q^{82} +(-0.0130625 + 0.124281i) q^{83} +(5.52145 + 1.17362i) q^{85} +(-0.492848 - 4.68913i) q^{86} +(2.96804 + 5.34727i) q^{88} +7.93327 q^{89} +(-4.21345 - 12.9677i) q^{91} +(-12.8935 + 2.74060i) q^{92} +(0.484051 - 0.215514i) q^{94} +(5.04935 + 5.60787i) q^{95} +(0.313492 + 0.139576i) q^{97} +2.27180 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) \) 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Introduction

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