LMFDB - Embedded newform 297.2.n.b.289.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(37,297)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			289.5
Character	$\chi$	$=$	297.289
Dual form			297.2.n.b.37.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0512706 - 0.487807i) q^{2} +(1.72097 - 0.365803i) q^{4} +(0.178553 - 1.69882i) q^{5} +(2.28209 + 2.53451i) q^{7} +(-0.569818 - 1.75372i) q^{8} -0.837851 q^{10} +(2.17733 + 2.50184i) q^{11} +(-3.65228 - 1.62610i) q^{13} +(1.11935 - 1.24316i) q^{14} +(2.38835 - 1.06336i) q^{16} +(-2.67346 - 1.94238i) q^{17} +(-1.36513 - 4.20144i) q^{19} +(-0.314149 - 2.98893i) q^{20} +(1.10878 - 1.19039i) q^{22} +(3.74601 + 6.48827i) q^{23} +(2.03663 + 0.432899i) q^{25} +(-0.605969 + 1.86498i) q^{26} +(4.85453 + 3.52702i) q^{28} +(-1.13169 - 1.25687i) q^{29} +(-3.56147 - 1.58567i) q^{31} +(-2.48514 - 4.30439i) q^{32} +(-0.810437 + 1.40372i) q^{34} +(4.71315 - 3.42431i) q^{35} +(0.947300 - 2.91549i) q^{37} +(-1.97950 + 0.881330i) q^{38} +(-3.08100 + 0.654886i) q^{40} +(-0.261546 + 0.290476i) q^{41} +(-4.80634 + 8.32483i) q^{43} +(4.66230 + 3.50912i) q^{44} +(2.97296 - 2.15999i) q^{46} +(-1.05665 - 0.224598i) q^{47} +(-0.484141 + 4.60629i) q^{49} +(0.106752 - 1.01568i) q^{50} +(-6.88030 - 1.46245i) q^{52} +(-10.1643 + 7.38480i) q^{53} +(4.63895 - 3.25218i) q^{55} +(3.14445 - 5.44635i) q^{56} +(-0.555089 + 0.616488i) q^{58} +(-3.57664 + 0.760238i) q^{59} +(-3.52005 + 1.56723i) q^{61} +(-0.590902 + 1.81861i) q^{62} +(2.25785 - 1.64043i) q^{64} +(-3.41458 + 5.91423i) q^{65} +(-1.55060 - 2.68572i) q^{67} +(-5.31146 - 2.36482i) q^{68} +(-1.91205 - 2.12354i) q^{70} +(5.67699 + 4.12458i) q^{71} +(-4.64842 + 14.3064i) q^{73} +(-1.47077 - 0.312621i) q^{74} +(-3.88624 - 6.73117i) q^{76} +(-1.37210 + 11.2279i) q^{77} +(0.418023 + 3.97722i) q^{79} +(-1.38001 - 4.24724i) q^{80} +(0.155106 + 0.112691i) q^{82} +(0.114162 - 0.0508282i) q^{83} +(-3.77711 + 4.19490i) q^{85} +(4.30733 + 1.91775i) q^{86} +(3.14685 - 5.24403i) q^{88} +7.93327 q^{89} +(-4.21345 - 12.9677i) q^{91} +(8.82019 + 9.79581i) q^{92} +(-0.0553855 + 0.526958i) q^{94} +(-7.38123 + 1.56893i) q^{95} +(-0.0358699 - 0.341280i) q^{97} +2.27180 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.0512706	−	0.487807i	−0.0362538	−	0.344932i	−0.997580	−	0.0695211i	$-0.977853\pi$
$2$	−0.0512706	−	0.487807i	−0.0362538	−	0.344932i	0.961327	−	0.275411i	$-0.0888138\pi$
$3$		0			0
$3$		0			0
$4$	1.72097	−	0.365803i	0.860484	−	0.182902i
$5$	0.178553	−	1.69882i	0.0798514	−	0.759735i	−0.879190	−	0.476471i	$-0.841916\pi$
$5$	0.178553	−	1.69882i	0.0798514	−	0.759735i	0.959042	−	0.283265i	$-0.0914175\pi$
$6$		0			0
$7$	2.28209	+	2.53451i	0.862547	+	0.957956i	0.999468	−	0.0326264i	$-0.0103872\pi$
$7$	2.28209	+	2.53451i	0.862547	+	0.957956i	−0.136921	+	0.990582i	$0.543720\pi$
$8$	−0.569818	−	1.75372i	−0.201461	−	0.620034i
$9$		0			0
$10$	−0.837851			−0.264952
$11$	2.17733	+	2.50184i	0.656490	+	0.754334i
$11$	2.17733	+	2.50184i	0.656490	+	0.754334i
$12$		0			0
$13$	−3.65228	−	1.62610i	−1.01296	−	0.451000i	−0.167977	−	0.985791i	$-0.553724\pi$
$13$	−3.65228	−	1.62610i	−1.01296	−	0.451000i	−0.844984	+	0.534791i	$0.820390\pi$
$14$	1.11935	−	1.24316i	0.299159	−	0.332249i
$15$		0			0
$16$	2.38835	−	1.06336i	0.597088	−	0.265840i
$17$	−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	$-0.269149\pi$
$20$	−0.314149	−	2.98893i	−0.0702459	−	0.668345i
$21$		0			0
$22$	1.10878	−	1.19039i	0.236394	−	0.253792i
$23$	3.74601	+	6.48827i	0.781096	+	1.35290i	0.931304	+	0.364244i	$0.118672\pi$
$23$	3.74601	+	6.48827i	0.781096	+	1.35290i	−0.150208	+	0.988654i	$0.547994\pi$
$24$		0			0
$25$	2.03663	+	0.432899i	0.407326	+	0.0865799i
$26$	−0.605969	+	1.86498i	−0.118840	+	0.365753i
$27$		0			0
$28$	4.85453	+	3.52702i	0.917420	+	0.666544i
$29$	−1.13169	−	1.25687i	−0.210150	−	0.233395i	0.628850	−	0.777527i	$-0.283526\pi$
$29$	−1.13169	−	1.25687i	−0.210150	−	0.233395i	−0.839000	+	0.544131i	$0.816859\pi$
$30$		0			0
$31$	−3.56147	−	1.58567i	−0.639659	−	0.284795i	0.0611661	−	0.998128i	$-0.480518\pi$
$31$	−3.56147	−	1.58567i	−0.639659	−	0.284795i	−0.700825	+	0.713333i	$0.747185\pi$
$32$	−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	$0.0189167\pi$
$38$	−1.97950	+	0.881330i	−0.321117	+	0.142971i
$39$		0			0
$40$	−3.08100	+	0.654886i	−0.487148	+	0.103547i
$41$	−0.261546	+	0.290476i	−0.0408467	+	0.0453648i	−0.763222	−	0.646136i	$-0.776384\pi$
$41$	−0.261546	+	0.290476i	−0.0408467	+	0.0453648i	0.722375	+	0.691501i	$0.243050\pi$
$42$		0			0
$43$	−4.80634	+	8.32483i	−0.732960	+	1.26952i	0.222652	+	0.974898i	$0.428529\pi$
$43$	−4.80634	+	8.32483i	−0.732960	+	1.26952i	−0.955613	+	0.294626i	$0.904805\pi$
$44$	4.66230	+	3.50912i	0.702869	+	0.529020i
$45$		0			0
$46$	2.97296	−	2.15999i	0.438340	−	0.318472i
$47$	−1.05665	−	0.224598i	−0.154129	−	0.0327610i	0.130201	−	0.991488i	$-0.458438\pi$
$47$	−1.05665	−	0.224598i	−0.154129	−	0.0327610i	−0.284330	+	0.958727i	$0.591771\pi$
$48$		0			0
$49$	−0.484141	+	4.60629i	−0.0691630	+	0.658042i
$50$	0.106752	−	1.01568i	0.0150970	−	0.143639i
$51$		0			0
$52$	−6.88030	−	1.46245i	−0.954126	−	0.202806i
$53$	−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
$58$	−0.555089	+	0.616488i	−0.0728867	+	0.0809489i
$59$	−3.57664	+	0.760238i	−0.465639	+	0.0989746i	−0.434756	−	0.900548i	$-0.643165\pi$
$59$	−3.57664	+	0.760238i	−0.465639	+	0.0989746i	−0.0308830	+	0.999523i	$0.509832\pi$
$60$		0			0
$61$	−3.52005	+	1.56723i	−0.450696	+	0.200663i	−0.619516	−	0.784984i	$-0.712671\pi$
$61$	−3.52005	+	1.56723i	−0.450696	+	0.200663i	0.168820	+	0.985647i	$0.446004\pi$
$62$	−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	0.755626	−	0.655003i	$-0.227333\pi$
$67$	−1.55060	−	2.68572i	−0.189436	−	0.328113i	−0.945062	+	0.326890i	$0.893999\pi$
$68$	−5.31146	−	2.36482i	−0.644110	−	0.286776i
$69$		0			0
$70$	−1.91205	−	2.12354i	−0.228533	−	0.253812i
$71$	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	$0.757340\pi$
$74$	−1.47077	−	0.312621i	−0.170973	−	0.0363414i
$75$		0			0
$76$	−3.88624	−	6.73117i	−0.445783	−	0.772118i
$77$	−1.37210	+	11.2279i	−0.156365	+	1.27954i
$78$		0			0
$79$	0.418023	+	3.97722i	0.0470313	+	0.447473i	0.992544	+	0.121887i	$0.0388946\pi$
$79$	0.418023	+	3.97722i	0.0470313	+	0.447473i	−0.945513	+	0.325585i	$0.894439\pi$
$80$	−1.38001	−	4.24724i	−0.154290	−	0.474856i
$81$		0			0
$82$	0.155106	+	0.112691i	0.0171286	+	0.0124447i
$83$	0.114162	−	0.0508282i	0.0125309	−	0.00557912i	−0.400462	−	0.916314i	$-0.631150\pi$
$83$	0.114162	−	0.0508282i	0.0125309	−	0.00557912i	0.412993	+	0.910734i	$0.364484\pi$
$84$		0			0
$85$	−3.77711	+	4.19490i	−0.409685	+	0.455001i
$86$	4.30733	+	1.91775i	0.464472	+	0.206796i
$87$		0			0
$88$	3.14685	−	5.24403i	0.335455	−	0.559015i
$89$	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
$92$	8.82019	+	9.79581i	0.919568	+	1.02128i
$93$		0			0
$94$	−0.0553855	+	0.526958i	−0.00571258	+	0.0543515i
$95$	−7.38123	+	1.56893i	−0.757298	+	0.160969i
$96$		0			0
$97$	−0.0358699	−	0.341280i	−0.00364204	−	0.0346517i	0.992550	−	0.121838i	$-0.0388790\pi$
$97$	−0.0358699	−	0.341280i	−0.00364204	−	0.0346517i	−0.996192	+	0.0871867i	$0.972212\pi$
$98$	2.27180			0.229487
$99$		0			0
$100$	3.66333			0.366333
$101$	0.743781	+	7.07660i	0.0740090	+	0.704148i	0.967121	+	0.254315i	$0.0818500\pi$
$101$	0.743781	+	7.07660i	0.0740090	+	0.704148i	−0.893112	+	0.449833i	$0.851483\pi$
$102$		0			0
$103$	1.61814	−	0.343946i	0.159440	−	0.0338900i	−0.127500	−	0.991839i	$-0.540695\pi$
$103$	1.61814	−	0.343946i	0.159440	−	0.0338900i	0.286940	+	0.957949i	$0.407362\pi$
$104$	−0.770589	+	7.33167i	−0.0755625	+	0.718929i
$105$		0			0
$106$	4.12349	+	4.57960i	0.400509	+	0.444810i
$107$	−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	$0.584957\pi$
$110$	−1.82428	−	2.09617i	−0.173938	−	0.199862i
$111$		0			0
$112$	8.14552	+	3.62662i	0.769680	+	0.342683i
$113$	10.9799	−	12.1944i	1.03290	−	1.14716i	0.0439343	−	0.999034i	$-0.486011\pi$
$113$	10.9799	−	12.1944i	1.03290	−	1.14716i	0.988969	−	0.148121i	$-0.0473225\pi$
$114$		0			0
$115$	11.6913	−	5.20529i	1.09022	−	0.485395i
$116$	−2.40738	−	1.74906i	−0.223519	−	0.162396i
$117$		0			0
$118$	0.554226	+	1.70573i	0.0510206	+	0.157025i
$119$	−1.17807	−	11.2086i	−0.107994	−	1.02749i
$120$		0			0
$121$	−1.51845	+	10.8947i	−0.138040	+	0.990427i
$122$	0.944980	+	1.63675i	0.0855545	+	0.148185i
$123$		0			0
$124$	−6.70922	−	1.42609i	−0.602506	−	0.128067i
$125$	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	$0.858981\pi$
$128$	−7.56750	−	8.40456i	−0.668879	−	0.742865i
$129$		0			0
$130$	3.06007	+	1.36243i	0.268386	+	0.119493i
$131$	−10.5778	−	18.3213i	−0.924189	−	1.60074i	−0.792860	−	0.609404i	$-0.791409\pi$
$131$	−10.5778	−	18.3213i	−0.924189	−	1.60074i	−0.131329	−	0.991339i	$-0.541925\pi$
$132$		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
$137$	−2.92382	+	1.30177i	−0.249799	+	0.111218i	−0.527817	−	0.849358i	$-0.676989\pi$
$137$	−2.92382	+	1.30177i	−0.249799	+	0.111218i	0.278018	+	0.960576i	$0.410323\pi$
$138$		0			0
$139$	14.6660	−	3.11735i	1.24395	−	0.264411i	0.461512	−	0.887134i	$-0.347307\pi$
$139$	14.6660	−	3.11735i	1.24395	−	0.264411i	0.782442	+	0.622723i	$0.213974\pi$
$140$	6.85856	−	7.61721i	0.579654	−	0.643771i
$141$		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
$146$	7.21708	+	1.53404i	0.597290	+	0.126958i
$147$		0			0
$148$	0.563778	−	5.36399i	0.0463423	−	0.440917i
$149$	0.423458	−	4.02893i	0.0346910	−	0.330063i	−0.963388	−	0.268111i	$-0.913601\pi$
$149$	0.423458	−	4.02893i	0.0346910	−	0.330063i	0.998079	−	0.0619522i	$-0.0197326\pi$
$150$		0			0
$151$	7.62367	+	1.62046i	0.620405	+	0.131871i	0.507382	−	0.861721i	$-0.330613\pi$
$151$	7.62367	+	1.62046i	0.620405	+	0.131871i	0.113023	+	0.993592i	$0.463947\pi$
$152$	−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
$157$	0.206863	−	0.229745i	0.0165095	−	0.0183356i	−0.734834	−	0.678248i	$-0.762740\pi$
$157$	0.206863	−	0.229745i	0.0165095	−	0.0183356i	0.751343	+	0.659912i	$0.229406\pi$
$158$	1.91868	−	0.407829i	0.152642	−	0.0324451i
$159$		0			0
$160$	−7.75610	+	3.45324i	−0.613174	+	0.273003i
$161$	−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
$167$	16.0545	+	7.14793i	1.24234	+	0.553124i	0.919410	−	0.393300i	$-0.128667\pi$
$167$	16.0545	+	7.14793i	1.24234	+	0.553124i	0.322926	+	0.946424i	$0.395333\pi$
$168$		0			0
$169$	1.99628	+	2.21709i	0.153560	+	0.170546i
$170$	2.23996	+	1.62742i	0.171797	+	0.124818i
$171$		0			0
$172$	−5.22631	+	16.0849i	−0.398503	+	1.22646i
$173$	12.0955	+	2.57098i	0.919605	+	0.195468i	0.643311	−	0.765605i	$-0.277560\pi$
$173$	12.0955	+	2.57098i	0.919605	+	0.195468i	0.276294	+	0.961073i	$0.410894\pi$
$174$		0			0
$175$	3.55058	+	6.14978i	0.268398	+	0.464880i
$176$	7.86060	+	3.65999i	0.592515	+	0.275882i
$177$		0			0
$178$	−0.406743	−	3.86990i	−0.0304867	−	0.290061i
$179$	−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	$0.647951\pi$
$182$	−6.10969	+	2.72021i	−0.452880	+	0.201635i
$183$		0			0
$184$	9.24407	−	10.2666i	0.681482	−	0.756862i
$185$	−4.78375	−	2.12986i	−0.351708	−	0.156591i
$186$		0			0
$187$	−0.961474	−	10.9178i	−0.0703099	−	0.798387i
$188$	−1.90062			−0.138617
$189$		0			0
$190$	1.14377	+	3.52018i	0.0829781	+	0.255380i
$191$	−8.37399	−	9.30026i	−0.605921	−	0.672943i	0.359649	−	0.933088i	$-0.382896\pi$
$191$	−8.37399	−	9.30026i	−0.605921	−	0.672943i	−0.965570	+	0.260144i	$0.916230\pi$
$192$		0			0
$193$	1.31347	−	12.4969i	0.0945460	−	0.899545i	−0.839732	−	0.543000i	$-0.817288\pi$
$193$	1.31347	−	12.4969i	0.0945460	−	0.899545i	0.934278	−	0.356544i	$-0.116045\pi$
$194$	−0.164640	+	0.0349952i	−0.0118204	+	0.00251251i
$195$		0			0
$196$	0.851805	+	8.10438i	0.0608432	+	0.578885i
$197$	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	$0.112249\pi$
$200$	−0.401325	−	3.81836i	−0.0283780	−	0.269999i
$201$		0			0
$202$	3.41388	−	0.725643i	0.240200	−	0.0510561i
$203$	0.602939	−	5.73658i	0.0423180	−	0.402629i
$204$		0			0
$205$	0.446767	+	0.496185i	0.0312036	+	0.0346551i
$206$	−0.250742	−	0.771705i	−0.0174700	−	0.0537672i
$207$		0			0
$208$	−10.4521			−0.724721
$209$	7.53900	−	12.5633i	0.521483	−	0.869019i
$210$		0			0
$211$	−6.65418	−	2.96263i	−0.458092	−	0.203956i	0.164699	−	0.986344i	$-0.447335\pi$
$211$	−6.65418	−	2.96263i	−0.458092	−	0.203956i	−0.622791	+	0.782388i	$0.714001\pi$
$212$	−14.7911	+	16.4272i	−1.01586	+	1.12822i
$213$		0			0
$214$	−1.48175	+	0.659719i	−0.101291	+	0.0450975i
$215$	13.2842	+	9.65153i	0.905974	+	0.658229i
$216$		0			0
$217$	−4.10868	−	12.6452i	−0.278916	−	0.858414i
$218$	0.282352	+	2.68640i	0.0191233	+	0.181946i
$219$		0			0
$220$	6.79383	−	7.29385i	0.458040	−	0.491751i
$221$	6.60572	+	11.4414i	0.444349	+	0.769635i
$222$		0			0
$223$	−22.9963	−	4.88802i	−1.53995	−	0.327326i	−0.641748	−	0.766915i	$-0.721791\pi$
$223$	−22.9963	−	4.88802i	−1.53995	−	0.327326i	−0.898199	+	0.439590i	$0.855124\pi$
$224$	5.23822	−	16.1216i	0.349993	−	1.07717i
$225$		0			0
$226$	−6.51148	−	4.73086i	−0.433137	−	0.314692i
$227$	7.97750	+	8.85991i	0.529485	+	0.588053i	0.947247	−	0.320503i	$-0.103852\pi$
$227$	7.97750	+	8.85991i	0.529485	+	0.588053i	−0.417762	+	0.908557i	$0.637185\pi$
$228$		0			0
$229$	2.79323	+	1.24363i	0.184582	+	0.0821811i	0.496947	−	0.867781i	$-0.334454\pi$
$229$	2.79323	+	1.24363i	0.184582	+	0.0821811i	−0.312365	+	0.949962i	$0.601121\pi$
$230$	−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
$236$	−5.87718	+	2.61669i	−0.382572	+	0.170332i
$237$		0			0
$238$	−5.40723	+	1.14934i	−0.350499	+	0.0745008i
$239$	4.65088	−	5.16532i	0.300840	−	0.334117i	−0.573704	−	0.819063i	$-0.694494\pi$
$239$	4.65088	−	5.16532i	0.300840	−	0.334117i	0.874544	+	0.484946i	$0.161161\pi$
$240$		0			0
$241$	3.88529	−	6.72952i	0.250274	−	0.433487i	−0.713327	−	0.700831i	$-0.752813\pi$
$241$	3.88529	−	6.72952i	0.250274	−	0.433487i	0.963601	+	0.267344i	$0.0861461\pi$
$242$	5.39236	+	0.182131i	0.346634	+	0.0117078i
$243$		0			0
$244$	−5.48460	+	3.98480i	−0.351116	+	0.255100i
$245$	7.73881	+	1.64494i	0.494415	+	0.105091i
$246$		0			0
$247$	−1.84612	+	17.5647i	−0.117466	+	1.11761i
$248$	−0.751429	+	7.14937i	−0.0477158	+	0.453985i
$249$		0			0
$250$	−5.80410	−	1.23370i	−0.367084	−	0.0780260i
$251$	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
$256$	0.0230840	−	0.0256374i	0.00144275	−	0.00160234i
$257$	−13.4292	+	2.85445i	−0.837688	+	0.178056i	−0.606730	−	0.794908i	$-0.707519\pi$
$257$	−13.4292	+	2.85445i	−0.837688	+	0.178056i	−0.230957	+	0.972964i	$0.574186\pi$
$258$		0			0
$259$	9.55117	−	4.25245i	0.593481	−	0.264235i
$260$	−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	0.480103	+	0.877212i	$0.340599\pi$
$263$	−8.42709	+	14.5961i	−0.519637	+	0.900037i	−0.999739	+	0.0228249i	$0.992734\pi$
$264$		0			0
$265$	10.7306	+	18.5859i	0.659174	+	1.14172i
$266$	−6.75113	−	3.00579i	−0.413938	−	0.184297i
$267$		0			0
$268$	−3.65098	−	4.05482i	−0.223019	−	0.247688i
$269$	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	$-0.0990112\pi$
$272$	−8.45061	−	1.79623i	−0.512393	−	0.108913i
$273$		0			0
$274$	0.784919	+	1.35952i	0.0474187	+	0.0821316i
$275$	3.35138	+	6.03790i	0.202096	+	0.364099i
$276$		0			0
$277$	−1.08198	−	10.2944i	−0.0650100	−	0.618529i	−0.977719	−	0.209919i	$-0.932680\pi$
$277$	−1.08198	−	10.2944i	−0.0650100	−	0.618529i	0.912709	−	0.408611i	$-0.133987\pi$
$278$	−2.27260	−	6.99435i	−0.136302	−	0.419493i
$279$		0			0
$280$	−8.69092	−	6.31432i	−0.519382	−	0.377353i
$281$	15.0149	−	6.68504i	0.895711	−	0.398796i	0.0933486	−	0.995633i	$-0.470243\pi$
$281$	15.0149	−	6.68504i	0.895711	−	0.398796i	0.802362	+	0.596837i	$0.203576\pi$
$282$		0			0
$283$	−0.846419	+	0.940044i	−0.0503144	+	0.0558798i	−0.767777	−	0.640718i	$-0.778637\pi$
$283$	−0.846419	+	0.940044i	−0.0503144	+	0.0558798i	0.717462	+	0.696597i	$0.245304\pi$
$284$	11.2787	+	5.02160i	0.669268	+	0.297977i
$285$		0			0
$286$	−5.98529	+	2.54464i	−0.353918	+	0.150468i
$287$	−1.33309			−0.0786896
$288$		0			0
$289$	−1.87876	−	5.78222i	−0.110515	−	0.340130i
$290$	0.948189	+	1.05307i	0.0556796	+	0.0618385i
$291$		0			0
$292$	−2.76647	+	26.3212i	−0.161896	+	1.54033i
$293$	−23.5610	+	5.00805i	−1.37645	+	0.292574i	−0.835966	−	0.548780i	$-0.815092\pi$
$293$	−23.5610	+	5.00805i	−1.37645	+	0.292574i	−0.540484	+	0.841354i	$0.681759\pi$
$294$		0			0
$295$	0.652887	+	6.21181i	0.0380126	+	0.361665i
$296$	−5.65274			−0.328559
$297$		0			0
$298$	−1.98705			−0.115107
$299$	−3.13089	−	29.7884i	−0.181064	−	1.72271i
$300$		0			0
$301$	−32.0679	+	6.81623i	−1.84836	+	0.392881i
$302$	0.399602	−	3.80196i	0.0229945	−	0.218778i
$303$		0			0
$304$	−7.72805	−	8.58287i	−0.443234	−	0.492262i
$305$	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	$0.346054\pi$
$308$	1.74587	+	19.8248i	0.0994800	+	1.12962i
$309$		0			0
$310$	2.98398	+	1.32855i	0.169479	+	0.0754568i
$311$	−14.3002	+	15.8819i	−0.810888	+	0.900582i	−0.996631	−	0.0820162i	$-0.973864\pi$
$311$	−14.3002	+	15.8819i	−0.810888	+	0.900582i	0.185743	+	0.982598i	$0.440531\pi$
$312$		0			0
$313$	2.84672	−	1.26744i	0.160906	−	0.0716401i	−0.324703	−	0.945816i	$-0.605264\pi$
$313$	2.84672	−	1.26744i	0.160906	−	0.0716401i	0.485609	+	0.874176i	$0.338598\pi$
$314$	−0.122677	−	0.0891301i	−0.00692307	−	0.00502990i
$315$		0			0
$316$	2.17428	+	6.69176i	0.122313	+	0.376441i
$317$	−1.90920	−	18.1648i	−0.107231	−	1.02024i	−0.907345	−	0.420388i	$-0.861894\pi$
$317$	−1.90920	−	18.1648i	−0.107231	−	1.02024i	0.800113	−	0.599849i	$-0.204773\pi$
$318$		0			0
$319$	0.680426	−	5.56795i	0.0380966	−	0.311745i
$320$	−2.38364	−	4.12859i	−0.133250	−	0.230795i
$321$		0			0
$322$	12.2591	+	2.60575i	0.683171	+	0.145212i
$323$	−4.51117	+	13.8840i	−0.251008	+	0.772524i
$324$		0			0
$325$	−6.73442	−	4.89284i	−0.373558	−	0.271406i
$326$	3.60832	+	4.00744i	0.199846	+	0.221952i
$327$		0			0
$328$	0.658448	+	0.293160i	0.0363567	+	0.0161871i
$329$	−1.84212	−	3.19065i	−0.101560	−	0.175906i
$330$		0			0
$331$	−1.88308	+	3.26159i	−0.103503	+	0.179273i	−0.913126	−	0.407678i	$-0.866339\pi$
$331$	−1.88308	+	3.26159i	−0.103503	+	0.179273i	0.809622	+	0.586951i	$0.199672\pi$
$332$	0.177876	−	0.129235i	0.00976222	−	0.00709267i
$333$		0			0
$334$	2.66369	−	8.19799i	0.145751	−	0.448574i
$335$	−4.83941	+	2.15465i	−0.264405	+	0.117721i
$336$		0			0
$337$	−5.83580	+	1.24044i	−0.317896	+	0.0675710i	−0.364096	−	0.931361i	$-0.618622\pi$
$337$	−5.83580	+	1.24044i	−0.317896	+	0.0675710i	0.0462001	+	0.998932i	$0.485289\pi$
$338$	0.979163	−	1.08747i	0.0532594	−	0.0591506i
$339$		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
$344$	17.3382	+	3.68534i	0.934811	+	0.198700i
$345$		0			0
$346$	0.633999	−	6.03209i	0.0340840	−	0.324287i
$347$	2.54520	−	24.2159i	0.136633	−	1.29998i	−0.684403	−	0.729104i	$-0.739937\pi$
$347$	2.54520	−	24.2159i	0.136633	−	1.29998i	0.821036	−	0.570876i	$-0.193396\pi$
$348$		0			0
$349$	−16.3759	−	3.48081i	−0.876583	−	0.186323i	−0.252420	−	0.967618i	$-0.581227\pi$
$349$	−16.3759	−	3.48081i	−0.876583	−	0.186323i	−0.624163	+	0.781294i	$0.714560\pi$
$350$	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	−0.952880	−	0.303349i	$-0.901895\pi$
$353$	−4.01566	+	6.95533i	−0.213732	+	0.370195i	0.739148	+	0.673544i	$0.235229\pi$
$354$		0			0
$355$	8.02056	−	8.90773i	0.425687	−	0.472773i
$356$	13.6529	−	2.90201i	0.723602	−	0.153806i
$357$		0			0
$358$	−9.80521	+	4.36556i	−0.518221	+	0.230727i
$359$	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
$365$	23.4740	+	10.4513i	1.22868	+	0.547045i
$366$		0			0
$367$	14.9506	+	16.6044i	0.780417	+	0.866741i	0.993909	−	0.110204i	$-0.0351503\pi$
$367$	14.9506	+	16.6044i	0.780417	+	0.866741i	−0.213492	+	0.976945i	$0.568484\pi$
$368$	15.8462	+	11.5129i	0.826038	+	0.600152i
$369$		0			0
$370$	−0.793696	+	2.44275i	−0.0412623	+	0.126992i
$371$	−41.9127	−	8.90882i	−2.17600	−	0.462523i
$372$		0			0
$373$	−3.53936	−	6.13036i	−0.183261	−	0.317418i	0.759728	−	0.650241i	$-0.225332\pi$
$373$	−3.53936	−	6.13036i	−0.183261	−	0.317418i	−0.942989	+	0.332823i	$0.891999\pi$
$374$	−5.27648	+	1.02877i	−0.272840	+	0.0531967i
$375$		0			0
$376$	0.208217	+	1.98105i	0.0107380	+	0.102165i
$377$	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	$0.484982\pi$
$380$	−12.1289	+	5.40015i	−0.622202	+	0.277022i
$381$		0			0
$382$	−4.10739	+	4.56172i	−0.210153	+	0.233398i
$383$	16.1130	+	7.17398i	0.823337	+	0.366573i	0.774767	−	0.632247i	$-0.217867\pi$
$383$	16.1130	+	7.17398i	0.823337	+	0.366573i	0.0485695	+	0.998820i	$0.484534\pi$
$384$		0			0
$385$	18.8292	+	4.33572i	0.959624	+	0.220969i
$386$	−6.16341			−0.313709
$387$		0			0
$388$	−0.186572	−	0.574210i	−0.00947177	−	0.0291511i
$389$	11.9661	+	13.2897i	0.606703	+	0.673812i	0.965740	−	0.259511i	$-0.0835615\pi$
$389$	11.9661	+	13.2897i	0.606703	+	0.673812i	−0.359037	+	0.933323i	$0.616895\pi$
$390$		0			0
$391$	2.58791	−	24.6223i	0.130876	−	1.24520i
$392$	8.35402	−	1.77570i	0.421942	−	0.0896865i
$393$		0			0
$394$	−0.530412	−	5.04653i	−0.0267218	−	0.254241i
$395$	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	$0.685584\pi$
$398$	−1.35751	−	12.9158i	−0.0680458	−	0.647412i
$399$		0			0
$400$	5.32452	−	1.13176i	0.266226	−	0.0565881i
$401$	0.565244	−	5.37793i	0.0282269	−	0.268561i	−0.971301	−	0.237852i	$-0.923557\pi$
$401$	0.565244	−	5.37793i	0.0282269	−	0.268561i	0.999528	−	0.0307093i	$-0.00977662\pi$
$402$		0			0
$403$	10.4290	+	11.5826i	0.519508	+	0.576972i
$404$	3.86867	+	11.9065i	0.192473	+	0.592372i
$405$		0			0
$406$	−2.82926			−0.140414
$407$	9.35669	−	3.97800i	0.463794	−	0.197182i
$408$		0			0
$409$	21.5781	+	9.60718i	1.06697	+	0.475044i	0.863662	−	0.504071i	$-0.168165\pi$
$409$	21.5781	+	9.60718i	1.06697	+	0.475044i	0.203305	+	0.979115i	$0.434832\pi$
$410$	0.219137	−	0.243376i	0.0108224	−	0.0120195i
$411$		0			0
$412$	2.65895	−	1.18384i	0.130997	−	0.0583236i
$413$	−10.0890	−	7.33011i	−0.496449	−	0.360691i
$414$		0			0
$415$	−0.0659639	−	0.203016i	−0.00323804	−	0.00996567i
$416$	2.07706	+	19.7619i	0.101836	+	0.968908i
$417$		0			0
$418$	−6.51498	−	3.03345i	−0.318658	−	0.148371i
$419$	−9.06566	−	15.7022i	−0.442886	−	0.767102i	0.555016	−	0.831840i	$-0.312712\pi$
$419$	−9.06566	−	15.7022i	−0.442886	−	0.767102i	−0.997902	+	0.0647380i	$0.979379\pi$
$420$		0			0
$421$	12.5322	+	2.66381i	0.610783	+	0.129826i	0.502910	−	0.864339i	$-0.332263\pi$
$421$	12.5322	+	2.66381i	0.610783	+	0.129826i	0.107873	+	0.994165i	$0.465596\pi$
$422$	−1.10403	+	3.39785i	−0.0537432	+	0.165405i
$423$		0			0
$424$	18.7427	+	13.6174i	0.910226	+	0.661318i
$425$	−4.60399	−	5.11325i	−0.223326	−	0.248029i
$426$		0			0
$427$	−12.0052	−	5.34507i	−0.580973	−	0.258666i
$428$	−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	$-0.00919089\pi$
$434$	−5.95778	+	2.65257i	−0.285982	+	0.127328i
$435$		0			0
$436$	−9.47753	+	2.01451i	−0.453892	+	0.0964776i
$437$	22.1463	−	24.5959i	1.05940	−	1.17658i
$438$		0			0
$439$	−12.5891	+	21.8050i	−0.600846	+	1.04070i	0.391848	+	0.920030i	$0.371836\pi$
$439$	−12.5891	+	21.8050i	−0.600846	+	1.04070i	−0.992693	+	0.120665i	$0.961497\pi$
$440$	−8.34678	−	6.28227i	−0.397917	−	0.299495i
$441$		0			0
$442$	5.24254	−	3.80893i	0.249362	−	0.181172i
$443$	26.2363	+	5.57671i	1.24653	+	0.264957i	0.783502	−	0.621389i	$-0.213431\pi$
$443$	26.2363	+	5.57671i	1.24653	+	0.264957i	0.463024	+	0.886346i	$0.346765\pi$
$444$		0			0
$445$	1.41651	−	13.4772i	0.0671490	−	0.638880i
$446$	−1.20537	+	11.4684i	−0.0570761	+	0.543043i
$447$		0			0
$448$	9.31029	+	1.97896i	0.439870	+	0.0934972i
$449$	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
$454$	3.91292	−	4.34573i	0.183642	−	0.203955i
$455$	−22.7820	+	4.84247i	−1.06804	+	0.227019i
$456$		0			0
$457$	22.5109	−	10.0225i	1.05302	−	0.468833i	0.194118	−	0.980978i	$-0.437816\pi$
$457$	22.5109	−	10.0225i	1.05302	−	0.468833i	0.858899	+	0.512145i	$0.171149\pi$
$458$	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	0.379856	+	0.925046i	$0.375973\pi$
$461$	−13.1227	+	22.7292i	−0.611185	+	1.05860i	−0.991041	+	0.133558i	$0.957360\pi$
$462$		0			0
$463$	−6.34609	−	10.9917i	−0.294928	−	0.510830i	0.680040	−	0.733175i	$-0.261962\pi$
$463$	−6.34609	−	10.9917i	−0.294928	−	0.510830i	−0.974968	+	0.222345i	$0.928629\pi$
$464$	−4.03939	−	1.79845i	−0.187524	−	0.0834910i
$465$		0			0
$466$	8.05131	+	8.94188i	0.372970	+	0.414225i
$467$	−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
$470$	0.885317	+	0.188180i	0.0408366	+	0.00868009i
$471$		0			0
$472$	3.37128	+	5.83923i	0.155176	+	0.268772i
$473$	−31.2924	+	6.10120i	−1.43883	+	0.280534i
$474$		0			0
$475$	−0.961466	−	9.14774i	−0.0441151	−	0.419727i
$476$	−6.12756	−	18.8587i	−0.280856	−	0.864386i
$477$		0			0
$478$	−2.75813	−	2.00390i	−0.126154	−	0.0916563i
$479$	14.2716	−	6.35412i	0.652086	−	0.290327i	−0.0539074	−	0.998546i	$-0.517168\pi$
$479$	14.2716	−	6.35412i	0.652086	−	0.290327i	0.705993	+	0.708219i	$0.250501\pi$
$480$		0			0
$481$	−8.20070	+	9.10780i	−0.373920	+	0.415280i
$482$	−3.48191	−	1.55025i	−0.158597	−	0.0706118i
$483$		0			0
$484$	1.37212	+	19.3049i	0.0623689	+	0.877494i
$485$	−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	$0.691133\pi$
$488$	4.75427	+	5.28015i	0.215216	+	0.239021i
$489$		0			0
$490$	0.405638	−	3.85938i	0.0183248	−	0.174349i
$491$	38.1475	−	8.10850i	1.72157	−	0.365932i	0.762040	−	0.647529i	$-0.224198\pi$
$491$	38.1475	−	8.10850i	1.72157	−	0.365932i	0.959533	+	0.281598i	$0.0908644\pi$
$492$		0			0
$493$	0.584209	+	5.55837i	0.0263114	+	0.250337i
$494$	8.66283			0.389759
$495$		0			0
$496$	−10.1922			−0.457642
$497$	2.50159	+	23.8010i	0.112212	+	1.06762i
$498$		0			0
$499$	23.5099	−	4.99718i	1.05245	−	0.223705i	0.350963	−	0.936389i	$-0.385854\pi$
$499$	23.5099	−	4.99718i	1.05245	−	0.223705i	0.701485	+	0.712685i	$0.252521\pi$
$500$	2.22485	−	21.1680i	0.0994981	−	0.946661i
$501$		0			0
$502$	−0.107378	−	0.119255i	−0.00479251	−	0.00532262i
$503$	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
$506$	11.8771	+	2.73489i	0.528001	+	0.121581i
$507$		0			0
$508$	−17.3507	−	7.72504i	−0.769814	−	0.342743i
$509$	−2.47502	+	2.74879i	−0.109703	+	0.121838i	−0.795495	−	0.605960i	$-0.792789\pi$
$509$	−2.47502	+	2.74879i	−0.109703	+	0.121838i	0.685792	+	0.727798i	$0.259456\pi$
$510$		0			0
$511$	−46.8678	+	20.8669i	−2.07331	+	0.923096i
$512$	−18.3128	−	13.3050i	−0.809318	−	0.588004i
$513$		0			0
$514$	2.08094	+	6.40449i	0.0917865	+	0.282490i
$515$	−0.295378	−	2.81034i	−0.0130159	−	0.123838i
$516$		0			0
$517$	−1.73877	−	3.13260i	−0.0764712	−	0.137772i
$518$	−2.56407	−	4.44110i	−0.112659	−	0.195131i
$519$		0			0
$520$	12.3176	+	2.61818i	0.540162	+	0.114815i
$521$	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	$0.680930\pi$
$524$	−24.9061	−	27.6610i	−1.08803	−	1.20838i
$525$		0			0
$526$	7.55217	+	3.36244i	0.329290	+	0.146609i
$527$	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
$533$	1.42759	−	0.635602i	0.0618356	−	0.0275310i
$534$		0			0
$535$	−5.52522	+	1.17442i	−0.238876	+	0.0507746i
$536$	−3.82644	+	4.24969i	−0.165277	+	0.183559i
$537$		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	$0.448348\pi$
$542$	−9.24503	−	1.96509i	−0.397108	−	0.0844080i
$543$		0			0
$544$	−1.71684	+	16.3347i	−0.0736091	+	0.700344i
$545$	−0.983309	+	9.35556i	−0.0421203	+	0.400748i
$546$		0			0
$547$	40.9613	+	8.70658i	1.75138	+	0.372267i	0.968326	−	0.249690i	$-0.0803288\pi$
$547$	40.9613	+	8.70658i	1.75138	+	0.372267i	0.783051	+	0.621957i	$0.213662\pi$
$548$	−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
$553$	−9.12636	+	10.1358i	−0.388092	+	0.431020i
$554$	−4.96620	+	1.05560i	−0.210993	+	0.0448480i
$555$		0			0
$556$	24.0994	−	10.7297i	1.02204	−	0.455042i
$557$	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
$563$	13.2544	+	5.90124i	0.558606	+	0.248707i	0.666564	−	0.745448i	$-0.267764\pi$
$563$	13.2544	+	5.90124i	0.558606	+	0.248707i	−0.107958	+	0.994155i	$0.534431\pi$
$564$		0			0
$565$	−18.7556	−	20.8302i	−0.789056	−	0.876335i
$566$	0.501956	+	0.364693i	0.0210988	+	0.0153292i
$567$		0			0
$568$	3.99850	−	12.3061i	0.167773	−	0.516353i
$569$	−27.3612	−	5.81579i	−1.14704	−	0.243811i	−0.405096	−	0.914274i	$-0.632762\pi$
$569$	−27.3612	−	5.81579i	−1.14704	−	0.243811i	−0.741943	+	0.670463i	$0.766095\pi$
$570$		0			0
$571$	−4.52443	−	7.83654i	−0.189341	−	0.327949i	0.755689	−	0.654930i	$-0.227302\pi$
$571$	−4.52443	−	7.83654i	−0.189341	−	0.327949i	−0.945031	+	0.326981i	$0.893969\pi$
$572$	−11.3219	−	20.3977i	−0.473391	−	0.852870i
$573$		0			0
$574$	0.0683481	+	0.650289i	0.00285280	+	0.0271425i
$575$	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	$0.994217\pi$
$578$	−2.72428	+	1.21293i	−0.113315	+	0.0504511i
$579$		0			0
$580$	−3.40118	+	3.77740i	−0.141226	+	0.156848i
$581$	0.389352	+	0.173351i	0.0161530	+	0.00719180i
$582$		0			0
$583$	−40.6067	−	9.35034i	−1.68176	−	0.387252i
$584$	27.7381			1.14781
$585$		0			0
$586$	3.65095	+	11.2365i	0.150819	+	0.464175i
$587$	0.483525	+	0.537009i	0.0199572	+	0.0221647i	0.753041	−	0.657974i	$-0.228586\pi$
$587$	0.483525	+	0.537009i	0.0199572	+	0.0221647i	−0.733084	+	0.680139i	$0.761920\pi$
$588$		0			0
$589$	−1.80022	+	17.1279i	−0.0741767	+	0.705744i
$590$	2.99669	−	0.636966i	0.123372	−	0.0262235i
$591$		0			0
$592$	−0.837737	−	7.97054i	−0.0344308	−	0.327587i
$593$	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
$596$	−0.745038	−	7.08856i	−0.0305179	−	0.290359i
$597$		0			0
$598$	−14.3705	+	3.05454i	−0.587652	+	0.124909i
$599$	−2.12996	+	20.2652i	−0.0870276	+	0.828013i	0.860739	+	0.509047i	$0.170002\pi$
$599$	−2.12996	+	20.2652i	−0.0870276	+	0.828013i	−0.947766	+	0.318965i	$0.896665\pi$
$600$		0			0
$601$	−32.3670	−	35.9472i	−1.32028	−	1.46632i	−0.781560	−	0.623830i	$-0.785576\pi$
$601$	−32.3670	−	35.9472i	−1.32028	−	1.46632i	−0.538717	−	0.842487i	$-0.681091\pi$
$602$	4.96914	+	15.2935i	0.202527	+	0.623315i
$603$		0			0
$604$	13.7129			0.557968
$605$	18.2370	+	4.52485i	0.741439	+	0.183961i
$606$		0			0
$607$	−17.9989	−	8.01364i	−0.730554	−	0.325264i	0.00753068	−	0.999972i	$-0.497603\pi$
$607$	−17.9989	−	8.01364i	−0.730554	−	0.325264i	−0.738085	+	0.674708i	$0.764270\pi$
$608$	−14.6921	+	16.3172i	−0.595842	+	0.661750i
$609$		0			0
$610$	2.94928	−	1.31310i	0.119413	−	0.0531660i
$611$	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	$0.863163\pi$
$614$	−0.835451	−	7.94879i	−0.0337161	−	0.320787i
$615$		0			0
$616$	20.4724	−	3.99159i	0.824858	−	0.160826i
$617$	3.05346	+	5.28875i	0.122928	+	0.212917i	0.920921	−	0.389749i	$-0.127438\pi$
$617$	3.05346	+	5.28875i	0.122928	+	0.212917i	−0.797993	+	0.602666i	$0.794105\pi$
$618$		0			0
$619$	1.74084	+	0.370027i	0.0699704	+	0.0148727i	0.242764	−	0.970085i	$-0.421946\pi$
$619$	1.74084	+	0.370027i	0.0699704	+	0.0148727i	−0.172793	+	0.984958i	$0.555279\pi$
$620$	−3.62062	+	11.1431i	−0.145408	+	0.447519i
$621$		0			0
$622$	8.48050	+	6.16144i	0.340037	+	0.247051i
$623$	18.1044	+	20.1070i	0.725337	+	0.805568i
$624$		0			0
$625$	−9.36756	−	4.17071i	−0.374702	−	0.166828i
$626$	−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	$0.748921\pi$
$632$	6.73674	−	2.99939i	0.267973	−	0.119309i
$633$		0			0
$634$	−8.76303	+	1.86264i	−0.348024	+	0.0739748i
$635$	−12.3385	+	13.7033i	−0.489639	+	0.543799i
$636$		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
$641$	−26.4193	−	5.61560i	−1.04350	−	0.221803i	−0.345887	−	0.938276i	$-0.612422\pi$
$641$	−26.4193	−	5.61560i	−1.04350	−	0.221803i	−0.697614	+	0.716473i	$0.745755\pi$
$642$		0			0
$643$	3.40317	−	32.3790i	0.134208	−	1.27690i	−0.695426	−	0.718597i	$-0.744784\pi$
$643$	3.40317	−	32.3790i	0.134208	−	1.27690i	0.829634	−	0.558307i	$-0.188549\pi$
$644$	−4.69918	+	44.7097i	−0.185174	+	1.76181i
$645$		0			0
$646$	7.00398	+	1.48874i	0.275568	+	0.0585738i
$647$	−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
$652$	−12.9431	+	14.3748i	−0.506892	+	0.562961i
$653$	−4.55794	+	0.968821i	−0.178366	+	0.0379129i	−0.296229	−	0.955117i	$-0.595729\pi$
$653$	−4.55794	+	0.968821i	−0.178366	+	0.0379129i	0.117863	+	0.993030i	$0.462396\pi$
$654$		0			0
$655$	−33.0133	+	14.6985i	−1.28994	+	0.574318i
$656$	−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	0.364631	+	0.931152i	$0.381195\pi$
$659$	−16.0209	+	27.7490i	−0.624086	+	1.08095i	−0.988717	+	0.149797i	$0.952138\pi$
$660$		0			0
$661$	20.3527	+	35.2519i	0.791627	+	1.37114i	0.924959	+	0.380067i	$0.124099\pi$
$661$	20.3527	+	35.2519i	0.791627	+	1.37114i	−0.133331	+	0.991072i	$0.542567\pi$
$662$	1.68757	+	0.751356i	0.0655894	+	0.0292023i
$663$		0			0
$664$	−0.154190	−	0.171245i	−0.00598373	−	0.00664561i
$665$	−20.8211	−	15.1274i	−0.807406	−	0.586615i
$666$		0			0
$667$	3.91560	−	12.0510i	0.151613	−	0.466616i
$668$	30.2441	+	6.42857i	1.17018	+	0.248729i
$669$		0			0
$670$	1.29917	+	2.25023i	0.0501914	+	0.0869340i
$671$	−11.5853	−	5.39424i	−0.447245	−	0.208242i
$672$		0			0
$673$	3.94736	+	37.5567i	0.152160	+	1.44770i	0.758072	+	0.652171i	$0.226142\pi$
$673$	3.94736	+	37.5567i	0.152160	+	1.44770i	−0.605912	+	0.795532i	$0.707192\pi$
$674$	0.904299	+	2.78315i	0.0348323	+	0.107203i
$675$		0			0
$676$	4.24655	+	3.08530i	0.163329	+	0.118665i
$677$	−17.2666	+	7.68759i	−0.663610	+	0.295458i	−0.710765	−	0.703429i	$-0.751651\pi$
$677$	−17.2666	+	7.68759i	−0.663610	+	0.295458i	0.0471552	+	0.998888i	$0.484984\pi$
$678$		0			0
$679$	0.783119	−	0.869742i	0.0300534	−	0.0333776i
$680$	9.50895	+	4.23366i	0.364652	+	0.162353i
$681$		0			0
$682$	−5.83647	+	2.48137i	−0.223490	+	0.0950167i
$683$	−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
$686$	−2.65099	−	2.94423i	−0.101215	−	0.112411i
$687$		0			0
$688$	−2.62692	+	24.9935i	−0.100150	+	0.952868i
$689$	49.1314	−	10.4432i	1.87176	−	0.397854i
$690$		0			0
$691$	−2.32172	−	22.0897i	−0.0883225	−	0.840333i	−0.945568	−	0.325425i	$-0.894493\pi$
$691$	−2.32172	−	22.0897i	−0.0883225	−	0.840333i	0.857245	−	0.514908i	$-0.172174\pi$
$692$	21.7565			0.827057
$693$		0			0
$694$	−11.9432			−0.453358
$695$	−2.67716	−	25.4715i	−0.101551	−	0.966189i
$696$		0			0
$697$	1.26345	−	0.268554i	0.0478565	−	0.0101722i
$698$	−0.858360	+	8.16675i	−0.0324894	+	0.309116i
$699$		0			0
$700$	8.36004	+	9.28477i	0.315980	+	0.350931i
$701$	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
$704$	9.02018	+	2.07704i	0.339961	+	0.0782814i
$705$		0			0
$706$	3.59874	+	1.60226i	0.135440	+	0.0603020i
$707$	−16.2384	+	18.0345i	−0.610707	+	0.678258i
$708$		0			0
$709$	15.7182	−	6.99820i	0.590310	−	0.262823i	−0.0897681	−	0.995963i	$-0.528613\pi$
$709$	15.7182	−	6.99820i	0.590310	−	0.262823i	0.680078	+	0.733140i	$0.261946\pi$
$710$	−4.75647	−	3.45578i	−0.178507	−	0.129693i
$711$		0			0
$712$	−4.52052	−	13.9127i	−0.169414	−	0.521402i
$713$	−3.05304	−	29.0477i	−0.114337	−	1.08785i
$714$		0			0
$715$	−22.2311	+	4.33449i	−0.831398	+	0.162101i
$716$	−19.2500	−	33.3420i	−0.719407	−	1.24605i
$717$		0			0
$718$	−13.8295	−	2.93956i	−0.516114	−	0.109703i
$719$	−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
$722$	0.169236	+	0.187955i	0.00629829	+	0.00699496i
$723$		0			0
$724$	7.04028	+	3.13454i	0.261650	+	0.116494i
$725$	−1.76074	−	3.04969i	−0.0653923	−	0.113263i
$726$		0			0
$727$	−2.60044	+	4.50410i	−0.0964450	+	0.167048i	−0.910211	−	0.414145i	$-0.864081\pi$
$727$	−2.60044	+	4.50410i	−0.0964450	+	0.167048i	0.813766	+	0.581193i	$0.197414\pi$
$728$	−20.3408	+	14.7784i	−0.753879	+	0.547725i
$729$		0			0
$730$	3.89468	−	11.9866i	0.144149	−	0.443644i
$731$	29.0195	−	12.9203i	1.07333	−	0.477876i
$732$		0			0
$733$	47.9910	−	10.2008i	1.77259	−	0.376775i	0.798332	−	0.602217i	$-0.205716\pi$
$733$	47.9910	−	10.2008i	1.77259	−	0.376775i	0.974257	+	0.225442i	$0.0723826\pi$
$734$	7.33320	−	8.14435i	0.270673	−	0.300613i
$735$		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	$0.207402\pi$
$740$	−9.01179	−	1.91552i	−0.331280	−	0.0704157i
$741$		0			0
$742$	−2.19690	+	20.9021i	−0.0806506	+	0.767339i
$743$	1.16387	−	11.0734i	0.0426981	−	0.406245i	−0.952209	−	0.305448i	$-0.901194\pi$
$743$	1.16387	−	11.0734i	0.0426981	−	0.406245i	0.994907	−	0.100798i	$-0.0321395\pi$
$744$		0			0
$745$	−6.76882	−	1.43876i	−0.247990	−	0.0527119i
$746$	−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
$751$	−5.41006	+	6.00848i	−0.197416	+	0.219252i	−0.833722	−	0.552184i	$-0.813795\pi$
$751$	−5.41006	+	6.00848i	−0.197416	+	0.219252i	0.636307	+	0.771436i	$0.280461\pi$
$752$	−2.76248	+	0.587184i	−0.100737	+	0.0214124i
$753$		0			0
$754$	3.02981	−	1.34896i	0.110339	−	0.0491262i
$755$	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
$761$	−31.8760	−	14.1921i	−1.15550	−	0.514463i	−0.262685	−	0.964882i	$-0.584608\pi$
$761$	−31.8760	−	14.1921i	−1.15550	−	0.514463i	−0.892817	+	0.450419i	$0.851275\pi$
$762$		0			0
$763$	−12.5677	−	13.9578i	−0.454980	−	0.505306i
$764$	−17.8134	−	12.9422i	−0.644468	−	0.468233i
$765$		0			0
$766$	2.67339	−	8.22786i	0.0965936	−	0.297284i
$767$	14.2991	+	3.03937i	0.516312	+	0.109745i
$768$		0			0
$769$	2.80362	+	4.85600i	0.101101	+	0.175112i	0.912139	−	0.409882i	$-0.134430\pi$
$769$	2.80362	+	4.85600i	0.101101	+	0.175112i	−0.811038	+	0.584994i	$0.801097\pi$
$770$	1.14961	−	9.40730i	0.0414291	−	0.339016i
$771$		0			0
$772$	−2.31095	−	21.9872i	−0.0831728	−	0.791337i
$773$	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
$776$	−0.578070	+	0.257373i	−0.0207515	+	0.00923916i
$777$		0			0
$778$	5.86928	−	6.51849i	0.210424	−	0.233699i
$779$	1.57746	+	0.702332i	0.0565185	+	0.0251636i
$780$		0			0
$781$	2.04166	+	23.1835i	0.0730562	+	0.829572i
$782$	−12.1436			−0.434255
$783$		0			0
$784$	3.74186	+	11.5163i	0.133638	+	0.411295i
$785$	−0.353359	−	0.392445i	−0.0126119	−	0.0140070i
$786$		0			0
$787$	0.258858	−	2.46286i	0.00922727	−	0.0877916i	−0.988939	−	0.148322i	$-0.952613\pi$
$787$	0.258858	−	2.46286i	0.00922727	−	0.0877916i	0.998166	+	0.0605308i	$0.0192793\pi$
$788$	17.8040	−	3.78436i	0.634242	−	0.134812i
$789$		0			0
$790$	−0.350241	−	3.33232i	−0.0124610	−	0.118559i
$791$	55.9640			1.98985
$792$		0			0
$793$	15.4047			0.547037
$794$	1.12485	+	10.7022i	0.0399195	+	0.379808i
$795$		0			0
$796$	45.5667	−	9.68549i	1.61507	−	0.343293i
$797$	−1.01180	+	9.62666i	−0.0358399	+	0.340994i	0.961878	+	0.273478i	$0.0881740\pi$
$797$	−1.01180	+	9.62666i	−0.0358399	+	0.340994i	−0.997718	+	0.0675160i	$0.978493\pi$
$798$		0			0
$799$	2.38866	+	2.65287i	0.0845047	+	0.0938520i
$800$	−3.19795	−	9.84226i	−0.113064	−	0.347977i
$801$		0			0
$802$	−2.65237			−0.0936586
$803$	−45.9135	+	19.5201i	−1.62025	+	0.688850i
$804$		0			0
$805$	39.8733	+	17.7527i	1.40535	+	0.625702i
$806$	5.11539	−	5.68121i	0.180182	−	0.200112i
$807$		0			0
$808$	11.9866	−	5.33676i	0.421686	−	0.187747i
$809$	−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	$0.656024\pi$
$812$	−1.06082	−	10.0930i	−0.0372275	−	0.354196i
$813$		0			0
$814$	−2.42022	−	4.36030i	−0.0848286	−	0.152829i
$815$	9.38994	+	16.2639i	0.328915	+	0.569698i
$816$		0			0
$817$	41.5375	+	8.82907i	1.45321	+	0.308890i
$818$	3.58013	−	11.0185i	0.125176	−	0.385253i
$819$		0			0
$820$	0.950378	+	0.690490i	0.0331886	+	0.0241130i
$821$	2.24401	+	2.49222i	0.0783165	+	0.0869792i	0.781029	−	0.624494i	$-0.214695\pi$
$821$	2.24401	+	2.49222i	0.0783165	+	0.0869792i	−0.702713	+	0.711473i	$0.748028\pi$
$822$		0			0
$823$	14.7097	+	6.54920i	0.512749	+	0.228291i	0.646766	−	0.762688i	$-0.276121\pi$
$823$	14.7097	+	6.54920i	0.512749	+	0.228291i	−0.134017	+	0.990979i	$0.542788\pi$
$824$	−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	$0.838633\pi$
$830$	−0.0956507	+	0.0425864i	−0.00332008	+	0.00147820i
$831$		0			0
$832$	−10.9138	+	2.31980i	−0.378369	+	0.0804247i
$833$	10.2415	−	11.3743i	0.354847	−	0.394098i
$834$		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
$839$	2.58954	+	0.550423i	0.0894008	+	0.0190027i	0.252395	−	0.967624i	$-0.418782\pi$
$839$	2.58954	+	0.550423i	0.0894008	+	0.0190027i	−0.162994	+	0.986627i	$0.552115\pi$
$840$		0			0
$841$	2.73233	−	25.9963i	0.0942181	−	0.896426i
$842$	0.656889	−	6.24988i	0.0226379	−	0.215385i
$843$		0			0
$844$	−12.5354	−	2.66447i	−0.431485	−	0.0917150i
$845$	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
$850$	−2.25823	+	2.50802i	−0.0774567	+	0.0860244i
$851$	22.4651	−	4.77510i	0.770093	−	0.163688i
$852$		0			0
$853$	8.46891	−	3.77060i	0.289970	−	0.129103i	−0.256597	−	0.966519i	$-0.582601\pi$
$853$	8.46891	−	3.77060i	0.289970	−	0.129103i	0.546567	+	0.837416i	$0.315935\pi$
$854$	−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	−0.986380	−	0.164485i	$-0.947404\pi$
$857$	−10.2678	+	17.7844i	−0.350742	+	0.607502i	0.635638	+	0.771987i	$0.280737\pi$
$858$		0			0
$859$	−18.0139	−	31.2010i	−0.614626	−	1.06456i	−0.990450	−	0.137872i	$-0.955974\pi$
$859$	−18.0139	−	31.2010i	−0.614626	−	1.06456i	0.375824	−	0.926691i	$-0.377360\pi$
$860$	26.3922	+	11.7506i	0.899968	+	0.400691i
$861$		0			0
$862$	2.15931	+	2.39816i	0.0735464	+	0.0816815i
$863$	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
$866$	−6.71579	−	1.42749i	−0.228212	−	0.0485079i
$867$		0			0
$868$	−11.6966	−	20.2591i	−0.397008	−	0.687637i
$869$	−9.04022	+	9.70557i	−0.306668	+	0.329239i
$870$		0			0
$871$	1.29598	+	12.3304i	0.0439127	+	0.417801i
$872$	3.13804	+	9.65790i	0.106268	+	0.327058i
$873$		0			0
$874$	−13.1335	−	9.54206i	−0.444248	−	0.322765i
$875$	37.6919	−	16.7815i	1.27422	−	0.567319i
$876$		0			0
$877$	20.8207	−	23.1237i	0.703064	−	0.780832i	−0.280797	−	0.959767i	$-0.590599\pi$
$877$	20.8207	−	23.1237i	0.703064	−	0.780832i	0.983861	+	0.178935i	$0.0572653\pi$
$878$	11.2821	+	5.02310i	0.380752	+	0.169522i
$879$		0			0
$880$	7.62119	−	12.7002i	0.256910	−	0.428125i
$881$	−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	$0.931542\pi$
$884$	15.5535	+	17.2740i	0.523122	+	0.580986i
$885$		0			0
$886$	1.37520	−	13.0842i	0.0462009	−	0.439572i
$887$	−7.52695	+	1.59990i	−0.252730	+	0.0537195i	−0.332534	−	0.943091i	$-0.607904\pi$
$887$	−7.52695	+	1.59990i	−0.252730	+	0.0537195i	0.0798043	+	0.996811i	$0.474570\pi$
$888$		0			0
$889$	−3.84835	−	36.6146i	−0.129070	−	1.22801i
$890$	−6.64689			−0.222804
$891$		0			0
$892$	−41.3640			−1.38497
$893$	0.498831	+	4.74606i	0.0166927	+	0.158821i
$894$		0			0
$895$	−36.5620	+	7.77150i	−1.22213	+	0.259773i
$896$	4.03178	−	38.3598i	0.134692	−	1.28151i
$897$		0			0
$898$	−4.65257	−	5.16720i	−0.155258	−	0.172432i
$899$	2.03751	+	6.27081i	0.0679547	+	0.209143i
$900$		0			0
$901$	41.5180			1.38316
$902$	0.0557818	+	0.633417i	0.00185733	+	0.0210905i
$903$		0			0
$904$	−27.6422	−	12.3071i	−0.919365	−	0.409328i
$905$	5.00651	−	5.56030i	0.166422	−	0.184830i
$906$		0			0
$907$	−17.3487	+	7.72415i	−0.576055	+	0.256476i	−0.674019	−	0.738714i	$-0.735434\pi$
$907$	−17.3487	+	7.72415i	−0.576055	+	0.256476i	0.0979642	+	0.995190i	$0.468767\pi$
$908$	16.9700	+	12.3294i	0.563170	+	0.409167i
$909$		0			0
$910$	3.53024	+	10.8650i	0.117026	+	0.360170i
$911$	5.23011	+	49.7612i	0.173281	+	1.64866i	0.643015	+	0.765853i	$0.277683\pi$
$911$	5.23011	+	49.7612i	0.173281	+	1.64866i	−0.469734	+	0.882808i	$0.655650\pi$
$912$		0			0
$913$	0.375733	+	0.174946i	0.0124349	+	0.00578985i
$914$	−6.04320	−	10.4671i	−0.199891	−	0.346222i
$915$		0			0
$916$	5.26198	+	1.11847i	0.173861	+	0.0369552i
$917$	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	$0.716147\pi$
$920$	−15.7905	−	17.5371i	−0.520598	−	0.578182i
$921$		0			0
$922$	11.7603	+	5.23600i	0.387303	+	0.172439i
$923$	−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
$929$	0.827283	−	0.368330i	0.0271423	−	0.0120845i	−0.393121	−	0.919487i	$-0.628605\pi$
$929$	0.827283	−	0.368330i	0.0271423	−	0.0120845i	0.420263	+	0.907402i	$0.361938\pi$
$930$		0			0
$931$	20.0140	−	4.25410i	0.655931	−	0.139422i
$932$	−28.8803	+	32.0748i	−0.946004	+	1.05064i
$933$		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	$0.182695\pi$
$938$	−5.07445	−	1.07861i	−0.165687	−	0.0352178i
$939$		0			0
$940$	−0.339362	+	3.22882i	−0.0110688	+	0.105312i
$941$	0.570822	−	5.43101i	0.0186083	−	0.177046i	−0.981270	−	0.192636i	$-0.938296\pi$
$941$	0.570822	−	5.43101i	0.0186083	−	0.177046i	0.999878	+	0.0155906i	$0.00496286\pi$
$942$		0			0
$943$	−2.86444	−	0.608856i	−0.0932791	−	0.0198271i
$944$	−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	−0.472412	−	0.881378i	$-0.656617\pi$
$947$	16.2203	−	28.0944i	0.527089	−	0.912945i	0.999502	−	0.0315677i	$-0.0100500\pi$
$948$		0			0
$949$	40.2410	−	44.6921i	1.30628	−	1.45077i
$950$	−4.41304	+	0.938020i	−0.143178	+	0.0304334i
$951$		0			0
$952$	−18.9854	+	8.45287i	−0.615322	+	0.273959i
$953$	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
$959$	−9.97177	−	4.43972i	−0.322005	−	0.143366i
$960$		0			0
$961$	−10.5733	−	11.7429i	−0.341075	−	0.378802i
$962$	4.86330	+	3.53339i	0.156799	+	0.113921i
$963$		0			0
$964$	4.22478	−	13.0025i	0.136071	−	0.418784i
$965$	−20.9954	−	4.46271i	−0.675866	−	0.143660i
$966$		0			0
$967$	14.4075	+	24.9546i	0.463315	+	0.802486i	0.999124	−	0.0418540i	$-0.0133264\pi$
$967$	14.4075	+	24.9546i	0.463315	+	0.802486i	−0.535809	+	0.844340i	$0.679993\pi$
$968$	19.9715	−	3.54507i	0.641908	−	0.113943i
$969$		0			0
$970$	0.0300537	+	0.285941i	0.000964965	+	0.00918102i
$971$	−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
$974$	12.0657	−	5.37199i	0.386609	−	0.172130i
$975$		0			0
$976$	−6.74058	+	7.48618i	−0.215761	+	0.239627i
$977$	3.02599	+	1.34726i	0.0968100	+	0.0431026i	0.454570	−	0.890711i	$-0.349793\pi$
$977$	3.02599	+	1.34726i	0.0968100	+	0.0431026i	−0.357760	+	0.933813i	$0.616460\pi$
$978$		0			0
$979$	17.2734	+	19.8478i	0.552059	+	0.634338i
$980$	13.9200			0.444657
$981$		0			0
$982$	−5.91123	−	18.1929i	−0.188635	−	0.580559i
$983$	−22.6649	−	25.1719i	−0.722897	−	0.802859i	0.263946	−	0.964537i	$-0.414976\pi$
$983$	−22.6649	−	25.1719i	−0.722897	−	0.802859i	−0.986843	+	0.161679i	$0.948309\pi$
$984$		0			0
$985$	1.84719	−	17.5749i	0.0588565	−	0.559982i
$986$	2.68146	−	0.569962i	0.0853951	−	0.0181513i
$987$		0			0
$988$	3.24810	+	30.9036i	0.103336	+	0.983174i
$989$	−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	$0.456046\pi$
$992$	2.02542	+	19.2706i	0.0643071	+	0.611841i
$993$		0			0
$994$	11.4821	−	2.44059i	0.364189	−	0.0774107i
$995$	4.72761	−	44.9802i	0.149875	−	1.42597i
$996$		0			0
$997$	−20.2515	−	22.4916i	−0.641372	−	0.712316i	0.331553	−	0.943437i	$-0.392427\pi$
$997$	−20.2515	−	22.4916i	−0.641372	−	0.712316i	−0.972925	+	0.231121i	$0.925761\pi$
$998$	−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.289.5		72
3.2	odd	2		99.2.m.b.25.5	yes	72
9.2	odd	6		891.2.f.f.487.5		36
9.4	even	3	inner	297.2.n.b.91.5		72
9.5	odd	6		99.2.m.b.58.5	yes	72
9.7	even	3		891.2.f.e.487.5		36
11.4	even	5	inner	297.2.n.b.235.5		72
33.2	even	10		1089.2.e.o.727.9		36
33.20	odd	10		1089.2.e.p.727.10		36
33.26	odd	10		99.2.m.b.70.5	yes	72
99.2	even	30		9801.2.a.co.1.10		18
99.4	even	15	inner	297.2.n.b.37.5		72
99.20	odd	30		9801.2.a.cm.1.9		18
99.59	odd	30		99.2.m.b.4.5	✓	72
99.68	even	30		1089.2.e.o.364.9		36
99.70	even	15		891.2.f.e.730.5		36
99.79	odd	30		9801.2.a.cn.1.9		18
99.86	odd	30		1089.2.e.p.364.10		36
99.92	odd	30		891.2.f.f.730.5		36
99.97	even	15		9801.2.a.cp.1.10		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.5	✓	72	99.59	odd	30
99.2.m.b.25.5	yes	72	3.2	odd	2
99.2.m.b.58.5	yes	72	9.5	odd	6
99.2.m.b.70.5	yes	72	33.26	odd	10
297.2.n.b.37.5		72	99.4	even	15	inner
297.2.n.b.91.5		72	9.4	even	3	inner
297.2.n.b.235.5		72	11.4	even	5	inner
297.2.n.b.289.5		72	1.1	even	1	trivial
891.2.f.e.487.5		36	9.7	even	3
891.2.f.e.730.5		36	99.70	even	15
891.2.f.f.487.5		36	9.2	odd	6
891.2.f.f.730.5		36	99.92	odd	30
1089.2.e.o.364.9		36	99.68	even	30
1089.2.e.o.727.9		36	33.2	even	10
1089.2.e.p.364.10		36	99.86	odd	30
1089.2.e.p.727.10		36	33.20	odd	10
9801.2.a.cm.1.9		18	99.20	odd	30
9801.2.a.cn.1.9		18	99.79	odd	30
9801.2.a.co.1.10		18	99.2	even	30
9801.2.a.cp.1.10		18	99.97	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)

\(f(q)\)	\(=\)	\(q+(-0.0512706 - 0.487807i) q^{2} +(1.72097 - 0.365803i) q^{4} +(0.178553 - 1.69882i) q^{5} +(2.28209 + 2.53451i) q^{7} +(-0.569818 - 1.75372i) q^{8} -0.837851 q^{10} +(2.17733 + 2.50184i) q^{11} +(-3.65228 - 1.62610i) q^{13} +(1.11935 - 1.24316i) q^{14} +(2.38835 - 1.06336i) q^{16} +(-2.67346 - 1.94238i) q^{17} +(-1.36513 - 4.20144i) q^{19} +(-0.314149 - 2.98893i) q^{20} +(1.10878 - 1.19039i) q^{22} +(3.74601 + 6.48827i) q^{23} +(2.03663 + 0.432899i) q^{25} +(-0.605969 + 1.86498i) q^{26} +(4.85453 + 3.52702i) q^{28} +(-1.13169 - 1.25687i) q^{29} +(-3.56147 - 1.58567i) q^{31} +(-2.48514 - 4.30439i) q^{32} +(-0.810437 + 1.40372i) q^{34} +(4.71315 - 3.42431i) q^{35} +(0.947300 - 2.91549i) q^{37} +(-1.97950 + 0.881330i) q^{38} +(-3.08100 + 0.654886i) q^{40} +(-0.261546 + 0.290476i) q^{41} +(-4.80634 + 8.32483i) q^{43} +(4.66230 + 3.50912i) q^{44} +(2.97296 - 2.15999i) q^{46} +(-1.05665 - 0.224598i) q^{47} +(-0.484141 + 4.60629i) q^{49} +(0.106752 - 1.01568i) q^{50} +(-6.88030 - 1.46245i) q^{52} +(-10.1643 + 7.38480i) q^{53} +(4.63895 - 3.25218i) q^{55} +(3.14445 - 5.44635i) q^{56} +(-0.555089 + 0.616488i) q^{58} +(-3.57664 + 0.760238i) q^{59} +(-3.52005 + 1.56723i) q^{61} +(-0.590902 + 1.81861i) q^{62} +(2.25785 - 1.64043i) q^{64} +(-3.41458 + 5.91423i) q^{65} +(-1.55060 - 2.68572i) q^{67} +(-5.31146 - 2.36482i) q^{68} +(-1.91205 - 2.12354i) q^{70} +(5.67699 + 4.12458i) q^{71} +(-4.64842 + 14.3064i) q^{73} +(-1.47077 - 0.312621i) q^{74} +(-3.88624 - 6.73117i) q^{76} +(-1.37210 + 11.2279i) q^{77} +(0.418023 + 3.97722i) q^{79} +(-1.38001 - 4.24724i) q^{80} +(0.155106 + 0.112691i) q^{82} +(0.114162 - 0.0508282i) q^{83} +(-3.77711 + 4.19490i) q^{85} +(4.30733 + 1.91775i) q^{86} +(3.14685 - 5.24403i) q^{88} +7.93327 q^{89} +(-4.21345 - 12.9677i) q^{91} +(8.82019 + 9.79581i) q^{92} +(-0.0553855 + 0.526958i) q^{94} +(-7.38123 + 1.56893i) q^{95} +(-0.0358699 - 0.341280i) q^{97} +2.27180 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) \) 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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