LMFDB - Embedded newform 900.2.bj.f.127.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(127,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 1]))

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

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

chi := DirichletCharacter("900.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.bj (of order $20$, degree $8$, 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			127.11
Character	$\chi$	$=$	900.127
Dual form			900.2.bj.f.163.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.510631 + 1.31881i) q^{2} +(-1.47851 - 1.34685i) q^{4} +(1.27726 + 1.83538i) q^{5} +(-3.58459 + 3.58459i) q^{7} +(2.53121 - 1.26213i) q^{8} +O(q^{10})$	\(q+(-0.510631 + 1.31881i) q^{2} +(-1.47851 - 1.34685i) q^{4} +(1.27726 + 1.83538i) q^{5} +(-3.58459 + 3.58459i) q^{7} +(2.53121 - 1.26213i) q^{8} +(-3.07272 + 0.747264i) q^{10} +(-2.14789 - 2.95632i) q^{11} +(-2.29513 + 0.363512i) q^{13} +(-2.89699 - 6.55779i) q^{14} +(0.372000 + 3.98266i) q^{16} +(-0.0789506 + 0.154949i) q^{17} +(-2.48237 - 7.63995i) q^{19} +(0.583526 - 4.43390i) q^{20} +(4.99559 - 1.32307i) q^{22} +(3.36266 + 0.532593i) q^{23} +(-1.73721 + 4.68851i) q^{25} +(0.692558 - 3.21245i) q^{26} +(10.1278 - 0.471963i) q^{28} +(3.85226 + 1.25167i) q^{29} +(-6.48919 + 2.10846i) q^{31} +(-5.44233 - 1.54307i) q^{32} +(-0.164034 - 0.183243i) q^{34} +(-11.1575 - 2.00061i) q^{35} +(-0.376041 - 2.37423i) q^{37} +(11.3432 + 0.627421i) q^{38} +(5.54950 + 3.03365i) q^{40} +(1.04472 + 0.759030i) q^{41} +(-1.11142 - 1.11142i) q^{43} +(-0.806027 + 7.26383i) q^{44} +(-2.41947 + 4.16275i) q^{46} +(2.44309 + 4.79484i) q^{47} -18.6986i q^{49} +(-5.29617 - 4.68514i) q^{50} +(3.88297 + 2.55373i) q^{52} +(-5.47602 - 10.7473i) q^{53} +(2.68254 - 7.71817i) q^{55} +(-4.54912 + 13.5976i) q^{56} +(-3.61780 + 4.44125i) q^{58} +(-8.45350 - 6.14182i) q^{59} +(3.26236 - 2.37025i) q^{61} +(0.532916 - 9.63464i) q^{62} +(4.81404 - 6.38945i) q^{64} +(-3.59866 - 3.74812i) q^{65} +(-6.44454 - 3.28366i) q^{67} +(0.325423 - 0.122760i) q^{68} +(8.33581 - 13.6931i) q^{70} +(2.21118 + 0.718455i) q^{71} +(-0.489747 + 3.09214i) q^{73} +(3.32318 + 0.716429i) q^{74} +(-6.61964 + 14.6391i) q^{76} +(18.2965 + 2.89788i) q^{77} +(-1.57257 + 4.83988i) q^{79} +(-6.83455 + 5.76966i) q^{80} +(-1.53448 + 0.990196i) q^{82} +(-4.71681 + 9.25727i) q^{83} +(-0.385231 + 0.0530066i) q^{85} +(2.03328 - 0.898229i) q^{86} +(-9.16802 - 4.77213i) q^{88} +(0.271710 + 0.373976i) q^{89} +(6.92404 - 9.53013i) q^{91} +(-4.25442 - 5.31644i) q^{92} +(-7.57099 + 0.773580i) q^{94} +(10.8515 - 14.3143i) q^{95} +(-7.98438 + 4.06824i) q^{97} +(24.6599 + 9.54808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{8}+O(q^{10}) $ 240 * q - 12 * q^8	$ 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) $ 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{20}\right)$

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 $

$2$	−0.510631	+	1.31881i	−0.361070	+	0.932539i
$2$	−0.510631	+	1.31881i	−0.361070	+	0.932539i
$3$		0			0
$3$		0			0
$4$	−1.47851	−	1.34685i	−0.739256	−	0.673424i
$5$	1.27726	+	1.83538i	0.571208	+	0.820805i
$5$	1.27726	+	1.83538i	0.571208	+	0.820805i
$6$		0			0
$7$	−3.58459	+	3.58459i	−1.35485	+	1.35485i	−0.474702	+	0.880147i	$0.657444\pi$
$7$	−3.58459	+	3.58459i	−1.35485	+	1.35485i	−0.880147	+	0.474702i	$0.842556\pi$
$8$	2.53121	−	1.26213i	0.894918	−	0.446232i
$9$		0			0
$10$	−3.07272	+	0.747264i	−0.971679	+	0.236306i
$11$	−2.14789	−	2.95632i	−0.647613	−	0.891363i	0.351380	−	0.936233i	$-0.385713\pi$
$11$	−2.14789	−	2.95632i	−0.647613	−	0.891363i	−0.998993	+	0.0448703i	$0.985713\pi$
$12$		0			0
$13$	−2.29513	+	0.363512i	−0.636553	+	0.100820i	−0.466366	−	0.884592i	$-0.654437\pi$
$13$	−2.29513	+	0.363512i	−0.636553	+	0.100820i	−0.170187	+	0.985412i	$0.554437\pi$
$14$	−2.89699	−	6.55779i	−0.774253	−	1.75264i
$15$		0			0
$16$	0.372000	+	3.98266i	0.0929999	+	0.995666i
$17$	−0.0789506	+	0.154949i	−0.0191483	+	0.0375807i	−0.900383	−	0.435099i	$-0.856713\pi$
$17$	−0.0789506	+	0.154949i	−0.0191483	+	0.0375807i	0.881234	+	0.472680i	$0.156713\pi$
$18$		0			0
$19$	−2.48237	−	7.63995i	−0.569495	−	1.75272i	−0.654203	−	0.756319i	$-0.726996\pi$
$19$	−2.48237	−	7.63995i	−0.569495	−	1.75272i	0.0847083	−	0.996406i	$-0.473004\pi$
$20$	0.583526	−	4.43390i	0.130480	−	0.991451i
$21$		0			0
$22$	4.99559	−	1.32307i	1.06506	−	0.282079i
$23$	3.36266	+	0.532593i	0.701164	+	0.111053i	0.496830	−	0.867848i	$-0.334497\pi$
$23$	3.36266	+	0.532593i	0.701164	+	0.111053i	0.204334	+	0.978901i	$0.434497\pi$
$24$		0			0
$25$	−1.73721	+	4.68851i	−0.347442	+	0.937702i
$26$	0.692558	−	3.21245i	0.135822	−	0.630014i
$27$		0			0
$28$	10.1278	−	0.471963i	1.91397	−	0.0891927i
$29$	3.85226	+	1.25167i	0.715346	+	0.232430i	0.644004	−	0.765022i	$-0.277272\pi$
$29$	3.85226	+	1.25167i	0.715346	+	0.232430i	0.0713420	+	0.997452i	$0.477272\pi$
$30$		0			0
$31$	−6.48919	+	2.10846i	−1.16549	+	0.378691i	−0.826959	−	0.562263i	$-0.809931\pi$
$31$	−6.48919	+	2.10846i	−1.16549	+	0.378691i	−0.338534	+	0.940954i	$0.609931\pi$
$32$	−5.44233	−	1.54307i	−0.962077	−	0.272780i
$33$		0			0
$34$	−0.164034	−	0.183243i	−0.0281316	−	0.0314258i
$35$	−11.1575	−	2.00061i	−1.88597	−	0.338166i
$36$		0			0
$37$	−0.376041	−	2.37423i	−0.0618208	−	0.390321i	−0.999126	−	0.0418104i	$-0.986687\pi$
$37$	−0.376041	−	2.37423i	−0.0618208	−	0.390321i	0.937305	−	0.348511i	$-0.113313\pi$
$38$	11.3432	+	0.627421i	1.84011	+	0.101781i
$39$		0			0
$40$	5.54950	+	3.03365i	0.877454	+	0.479662i
$41$	1.04472	+	0.759030i	0.163157	+	0.118541i	0.666368	−	0.745623i	$-0.267848\pi$
$41$	1.04472	+	0.759030i	0.163157	+	0.118541i	−0.503211	+	0.864164i	$0.667848\pi$
$42$		0			0
$43$	−1.11142	−	1.11142i	−0.169491	−	0.169491i	0.617265	−	0.786755i	$-0.288241\pi$
$43$	−1.11142	−	1.11142i	−0.169491	−	0.169491i	−0.786755	+	0.617265i	$0.788241\pi$
$44$	−0.806027	+	7.26383i	−0.121513	+	1.09506i
$45$		0			0
$46$	−2.41947	+	4.16275i	−0.356731	+	0.613764i
$47$	2.44309	+	4.79484i	0.356362	+	0.699399i	0.997695	−	0.0678636i	$-0.0216183\pi$
$47$	2.44309	+	4.79484i	0.356362	+	0.699399i	−0.641333	+	0.767263i	$0.721618\pi$
$48$		0			0
$49$		−	18.6986i		−	2.67123i
$50$	−5.29617	−	4.68514i	−0.748992	−	0.662579i
$51$		0			0
$52$	3.88297	+	2.55373i	0.538471	+	0.354138i
$53$	−5.47602	−	10.7473i	−0.752189	−	1.47625i	−0.875155	−	0.483842i	$-0.839241\pi$
$53$	−5.47602	−	10.7473i	−0.752189	−	1.47625i	0.122966	−	0.992411i	$-0.460759\pi$
$54$		0			0
$55$	2.68254	−	7.71817i	0.361713	−	1.04072i
$56$	−4.54912	+	13.5976i	−0.607901	+	1.81705i
$57$		0			0
$58$	−3.61780	+	4.44125i	−0.475040	+	0.583164i
$59$	−8.45350	−	6.14182i	−1.10055	−	0.799597i	−0.119402	−	0.992846i	$-0.538098\pi$
$59$	−8.45350	−	6.14182i	−1.10055	−	0.799597i	−0.981150	+	0.193249i	$0.938098\pi$
$60$		0			0
$61$	3.26236	−	2.37025i	0.417703	−	0.303479i	−0.359010	−	0.933334i	$-0.616886\pi$
$61$	3.26236	−	2.37025i	0.417703	−	0.303479i	0.776713	+	0.629855i	$0.216886\pi$
$62$	0.532916	−	9.63464i	0.0676804	−	1.22360i
$63$		0			0
$64$	4.81404	−	6.38945i	0.601755	−	0.798681i
$65$	−3.59866	−	3.74812i	−0.446358	−	0.464897i
$66$		0			0
$67$	−6.44454	−	3.28366i	−0.787326	−	0.401163i	0.0136140	−	0.999907i	$-0.495666\pi$
$67$	−6.44454	−	3.28366i	−0.787326	−	0.401163i	−0.800940	+	0.598745i	$0.795666\pi$
$68$	0.325423	−	0.122760i	0.0394633	−	0.0148868i
$69$		0			0
$70$	8.33581	−	13.6931i	0.996319	−	1.63664i
$71$	2.21118	+	0.718455i	0.262419	+	0.0852650i	0.437271	−	0.899330i	$-0.355945\pi$
$71$	2.21118	+	0.718455i	0.262419	+	0.0852650i	−0.174853	+	0.984595i	$0.555945\pi$
$72$		0			0
$73$	−0.489747	+	3.09214i	−0.0573205	+	0.361908i	0.942310	+	0.334740i	$0.108649\pi$
$73$	−0.489747	+	3.09214i	−0.0573205	+	0.361908i	−0.999631	+	0.0271671i	$0.991351\pi$
$74$	3.32318	+	0.716429i	0.386311	+	0.0832831i
$75$		0			0
$76$	−6.61964	+	14.6391i	−0.759324	+	1.67922i
$77$	18.2965	+	2.89788i	2.08508	+	0.330244i
$78$		0			0
$79$	−1.57257	+	4.83988i	−0.176928	+	0.544529i	−0.999716	−	0.0238193i	$-0.992417\pi$
$79$	−1.57257	+	4.83988i	−0.176928	+	0.544529i	0.822788	+	0.568348i	$0.192417\pi$
$80$	−6.83455	+	5.76966i	−0.764125	+	0.645068i
$81$		0			0
$82$	−1.53448	+	0.990196i	−0.169455	+	0.109349i
$83$	−4.71681	+	9.25727i	−0.517738	+	1.01612i	0.473094	+	0.881012i	$0.343137\pi$
$83$	−4.71681	+	9.25727i	−0.517738	+	1.01612i	−0.990831	+	0.135105i	$0.956863\pi$
$84$		0			0
$85$	−0.385231	+	0.0530066i	−0.0417841	+	0.00574938i
$86$	2.03328	−	0.898229i	0.219255	−	0.0968585i
$87$		0			0
$88$	−9.16802	−	4.77213i	−0.977314	−	0.508711i
$89$	0.271710	+	0.373976i	0.0288012	+	0.0396414i	0.823175	−	0.567788i	$-0.192201\pi$
$89$	0.271710	+	0.373976i	0.0288012	+	0.0396414i	−0.794374	+	0.607430i	$0.792201\pi$
$90$		0			0
$91$	6.92404	−	9.53013i	0.725837	−	0.999029i
$92$	−4.25442	−	5.31644i	−0.443554	−	0.554277i
$93$		0			0
$94$	−7.57099	+	0.773580i	−0.780888	+	0.0797887i
$95$	10.8515	−	14.3143i	1.11335	−	1.46862i
$96$		0			0
$97$	−7.98438	+	4.06824i	−0.810691	+	0.413067i	−0.809636	−	0.586932i	$-0.800336\pi$
$97$	−7.98438	+	4.06824i	−0.810691	+	0.413067i	−0.00105434	+	0.999999i	$0.500336\pi$
$98$	24.6599	+	9.54808i	2.49102	+	0.964501i
$99$		0			0
$100$	8.88319	−	4.59226i	0.888319	−	0.459226i
$101$	−13.9581			−1.38889			−0.694443	−	0.719548i	$-0.744349\pi$
$101$	−13.9581			−1.38889			−0.694443	+	0.719548i	$0.744349\pi$
$102$		0			0
$103$	1.74857	−	0.890942i	0.172292	−	0.0877872i	−0.365718	−	0.930726i	$-0.619176\pi$
$103$	1.74857	−	0.890942i	0.172292	−	0.0877872i	0.538010	+	0.842939i	$0.319176\pi$
$104$	−5.35064	+	3.81688i	−0.524674	+	0.374276i
$105$		0			0
$106$	16.9698	−	1.73392i	1.64826	−	0.168414i
$107$	1.69891	−	1.69891i	0.164239	−	0.164239i	−0.620202	−	0.784442i	$-0.712950\pi$
$107$	1.69891	−	1.69891i	0.164239	−	0.164239i	0.784442	+	0.620202i	$0.212950\pi$
$108$		0			0
$109$	−7.28790	+	10.0309i	−0.698054	+	0.960790i	0.301918	+	0.953334i	$0.402373\pi$
$109$	−7.28790	+	10.0309i	−0.698054	+	0.960790i	−0.999972	+	0.00745557i	$0.997627\pi$
$110$	8.80900	+	7.47888i	0.839906	+	0.713084i
$111$		0			0
$112$	−15.6097	−	12.9428i	−1.47498	−	1.22298i
$113$	2.53451	−	0.401427i	0.238427	−	0.0377631i	−0.0360775	−	0.999349i	$-0.511486\pi$
$113$	2.53451	−	0.401427i	0.238427	−	0.0377631i	0.274504	+	0.961586i	$0.411486\pi$
$114$		0			0
$115$	3.31749	+	6.85201i	0.309357	+	0.638953i
$116$	−4.00980	−	7.03902i	−0.372300	−	0.653557i
$117$		0			0
$118$	12.4165	−	8.01234i	1.14303	−	0.737596i
$119$	−0.272424	−	0.838435i	−0.0249731	−	0.0768593i
$120$		0			0
$121$	−0.727187	+	2.23805i	−0.0661079	+	0.203459i
$122$	1.46004	+	5.51276i	0.132186	+	0.499101i
$123$		0			0
$124$	12.4341	+	5.62256i	1.11662	+	0.504921i
$125$	−10.8240	+	2.80002i	−0.968132	+	0.250441i
$126$		0			0
$127$	−0.925072	+	5.84068i	−0.0820869	+	0.518276i	0.912044	+	0.410092i	$0.134504\pi$
$127$	−0.925072	+	5.84068i	−0.0820869	+	0.518276i	−0.994131	+	0.108184i	$0.965496\pi$
$128$	5.96826	+	9.61144i	0.527525	+	0.849540i
$129$		0			0
$130$	6.78063	−	2.83203i	0.594701	−	0.248386i
$131$	7.60143	−	2.46985i	0.664140	−	0.215792i	0.0425014	−	0.999096i	$-0.486467\pi$
$131$	7.60143	−	2.46985i	0.664140	−	0.215792i	0.621639	+	0.783304i	$0.286467\pi$
$132$		0			0
$133$	36.2844	+	18.4878i	3.14626	+	1.60310i
$134$	7.62130	−	6.82238i	0.658380	−	0.589364i
$135$		0			0
$136$	−0.00427381	+	0.491855i	−0.000366476	+	0.0421762i
$137$	−1.34244	−	8.47586i	−0.114693	−	0.724141i	−0.976277	−	0.216526i	$-0.930527\pi$
$137$	−1.34244	−	8.47586i	−0.114693	−	0.724141i	0.861584	−	0.507615i	$-0.169473\pi$
$138$		0			0
$139$	−6.00917	+	4.36592i	−0.509691	+	0.370312i	−0.812706	−	0.582674i	$-0.802007\pi$
$139$	−6.00917	+	4.36592i	−0.509691	+	0.370312i	0.303015	+	0.952986i	$0.402007\pi$
$140$	13.8020	+	17.9854i	1.16648	+	1.52005i
$141$		0			0
$142$	−2.07660	+	2.54926i	−0.174264	+	0.213929i
$143$	6.00433	+	6.00433i	0.502107	+	0.502107i
$144$		0			0
$145$	2.62305	+	8.66906i	0.217832	+	0.719926i
$146$	−3.82786	−	2.22482i	−0.316796	−	0.184128i
$147$		0			0
$148$	−2.64175	+	4.01680i	−0.217150	+	0.330179i
$149$		−	2.32631i		−	0.190579i	−0.995450	−	0.0952895i	$-0.969622\pi$
$149$		−	2.32631i		−	0.190579i	0.995450	−	0.0952895i	$-0.0303777\pi$
$150$		0			0
$151$		−	0.484681i		−	0.0394428i	−0.999806	−	0.0197214i	$-0.993722\pi$
$151$		−	0.484681i		−	0.0394428i	0.999806	−	0.0197214i	$-0.00627792\pi$
$152$	−15.9260	−	16.2052i	−1.29177	−	1.31442i
$153$		0			0
$154$	−13.1645	+	22.6498i	−1.06083	+	1.82517i
$155$	−12.1582	−	9.21704i	−0.976571	−	0.740330i
$156$		0			0
$157$	−0.830154	−	0.830154i	−0.0662535	−	0.0662535i	0.673204	−	0.739457i	$-0.264918\pi$
$157$	−0.830154	−	0.830154i	−0.0662535	−	0.0662535i	−0.739457	+	0.673204i	$0.764918\pi$
$158$	−5.57987	−	4.54531i	−0.443911	−	0.361606i
$159$		0			0
$160$	−4.11915	−	11.9596i	−0.325647	−	0.945491i
$161$	−13.9629	+	10.1446i	−1.10043	+	0.799510i
$162$		0			0
$163$	−0.817862	−	5.16378i	−0.0640599	−	0.404458i	−0.998793	−	0.0491088i	$-0.984362\pi$
$163$	−0.817862	−	5.16378i	−0.0640599	−	0.404458i	0.934734	−	0.355349i	$-0.115638\pi$
$164$	−0.522327	−	2.52931i	−0.0407869	−	0.197506i
$165$		0			0
$166$	−9.80002	−	10.9476i	−0.760629	−	0.849700i
$167$	4.98818	+	2.54161i	0.385997	+	0.196675i	0.636211	−	0.771515i	$-0.280501\pi$
$167$	4.98818	+	2.54161i	0.385997	+	0.196675i	−0.250214	+	0.968191i	$0.580501\pi$
$168$		0			0
$169$	−7.22828	+	2.34861i	−0.556021	+	0.180662i
$170$	0.126805	−	0.535112i	0.00972550	−	0.0410412i
$171$		0			0
$172$	0.146335	+	3.14018i	0.0111579	+	0.239436i
$173$	−1.74772	+	11.0347i	−0.132877	+	0.838951i	0.827748	+	0.561101i	$0.189622\pi$
$173$	−1.74772	+	11.0347i	−0.132877	+	0.838951i	−0.960624	+	0.277850i	$0.910378\pi$
$174$		0			0
$175$	−10.5792	−	23.0336i	−0.799712	−	1.74117i
$176$	10.9750	−	9.65407i	0.827272	−	0.727703i
$177$		0			0
$178$	−0.631946	+	0.167369i	−0.0473664	+	0.0125449i
$179$	−4.77193	+	14.6865i	−0.356671	+	1.09772i	0.598364	+	0.801224i	$0.295818\pi$
$179$	−4.77193	+	14.6865i	−0.356671	+	1.09772i	−0.955035	+	0.296495i	$0.904182\pi$
$180$		0			0
$181$	4.03056	+	12.4048i	0.299589	+	0.922040i	0.981641	+	0.190737i	$0.0610877\pi$
$181$	4.03056	+	12.4048i	0.299589	+	0.922040i	−0.682052	+	0.731303i	$0.738912\pi$
$182$	9.03279	+	13.9979i	0.669555	+	1.03759i
$183$		0			0
$184$	9.18381	−	2.89602i	0.677039	−	0.213498i
$185$	3.87730	−	3.72269i	0.285065	−	0.273698i
$186$		0			0
$187$	0.627656	−	0.0994109i	0.0458987	−	0.00726965i
$188$	2.84578	−	10.3797i	0.207550	−	0.757018i
$189$		0			0
$190$	13.3367	+	21.6204i	0.967545	+	1.56851i
$191$	−3.56464	+	4.90630i	−0.257928	+	0.355007i	−0.918268	−	0.395959i	$-0.870412\pi$
$191$	−3.56464	+	4.90630i	−0.257928	+	0.355007i	0.660340	+	0.750967i	$0.270412\pi$
$192$		0			0
$193$	−15.5167	+	15.5167i	−1.11692	+	1.11692i	−0.124726	+	0.992191i	$0.539805\pi$
$193$	−15.5167	+	15.5167i	−1.11692	+	1.11692i	−0.992191	+	0.124726i	$0.960195\pi$
$194$	−1.28817	−	12.6072i	−0.0924850	−	0.905147i
$195$		0			0
$196$	−25.1842	+	27.6461i	−1.79887	+	1.97472i
$197$	5.39911	−	2.75099i	0.384671	−	0.196000i	−0.250952	−	0.968000i	$-0.580744\pi$
$197$	5.39911	−	2.75099i	0.384671	−	0.196000i	0.635623	+	0.772000i	$0.280744\pi$
$198$		0			0
$199$	−8.50614			−0.602984			−0.301492	−	0.953469i	$-0.597485\pi$
$199$	−8.50614			−0.602984			−0.301492	+	0.953469i	$0.597485\pi$
$200$	1.52028	+	14.0602i	0.107500	+	0.994205i
$201$		0			0
$202$	7.12745	−	18.4081i	0.501486	−	1.29519i
$203$	−18.2955	+	9.32203i	−1.28409	+	0.654278i
$204$		0			0
$205$	−0.0587314	+	2.88692i	−0.00410198	+	0.201632i
$206$	0.282108	+	2.76098i	0.0196554	+	0.192366i
$207$		0			0
$208$	−2.30153	−	9.00549i	−0.159583	−	0.624418i
$209$	−17.2542	+	23.7484i	−1.19350	+	1.64271i
$210$		0			0
$211$	14.0641	+	19.3576i	0.968216	+	1.33263i	0.942943	+	0.332954i	$0.108046\pi$
$211$	14.0641	+	19.3576i	0.968216	+	1.33263i	0.0252730	+	0.999681i	$0.491954\pi$
$212$	−6.37860	+	23.2654i	−0.438084	+	1.59787i
$213$		0			0
$214$	1.37302	+	3.10804i	0.0938576	+	0.212462i
$215$	0.620303	−	3.45946i	0.0423043	−	0.235933i
$216$		0			0
$217$	15.7031	−	30.8191i	1.06600	−	2.09214i
$218$	−9.50746	−	14.7335i	−0.643927	−	0.997875i
$219$		0			0
$220$	−14.3614	+	7.79844i	−0.968243	+	0.525771i
$221$	0.124876	−	0.384327i	0.00840004	−	0.0258527i
$222$		0			0
$223$	−12.2020	−	1.93261i	−0.817106	−	0.129417i	−0.266129	−	0.963937i	$-0.585745\pi$
$223$	−12.2020	−	1.93261i	−0.817106	−	0.129417i	−0.550977	+	0.834520i	$0.685745\pi$
$224$	25.0398	−	13.9772i	1.67304	−	0.933893i
$225$		0			0
$226$	−0.764793	+	3.54751i	−0.0508733	+	0.235977i
$227$	−1.66272	+	10.4980i	−0.110358	+	0.696776i	0.869025	+	0.494768i	$0.164747\pi$
$227$	−1.66272	+	10.4980i	−0.110358	+	0.696776i	−0.979384	+	0.202008i	$0.935253\pi$
$228$		0			0
$229$	−27.1390	−	8.81799i	−1.79339	−	0.582709i	−0.793721	−	0.608282i	$-0.791859\pi$
$229$	−27.1390	−	8.81799i	−1.79339	−	0.582709i	−0.999673	+	0.0255728i	$0.991859\pi$
$230$	−10.7305	+	0.876286i	−0.707548	+	0.0577806i
$231$		0			0
$232$	11.3307	−	1.69381i	0.743894	−	0.111204i
$233$	12.6044	+	6.42226i	0.825741	+	0.420736i	0.815180	−	0.579208i	$-0.196638\pi$
$233$	12.6044	+	6.42226i	0.825741	+	0.420736i	0.0105616	+	0.999944i	$0.496638\pi$
$234$		0			0
$235$	−5.67986	+	10.6083i	−0.370513	+	0.692006i
$236$	4.22650	+	20.4663i	0.275121	+	1.33225i
$237$		0			0
$238$	1.24484	+	0.0688554i	0.0806913	+	0.00446324i
$239$	11.1088	−	8.07104i	0.718571	−	0.522072i	−0.167356	−	0.985896i	$-0.553523\pi$
$239$	11.1088	−	8.07104i	0.718571	−	0.522072i	0.885927	+	0.463824i	$0.153523\pi$
$240$		0			0
$241$	−11.3875	−	8.27348i	−0.733531	−	0.532942i	0.157147	−	0.987575i	$-0.449770\pi$
$241$	−11.3875	−	8.27348i	−0.733531	−	0.532942i	−0.890679	+	0.454634i	$0.849770\pi$
$242$	−2.58024	−	2.10184i	−0.165864	−	0.135111i
$243$		0			0
$244$	−8.01581	−	0.889470i	−0.513160	−	0.0569425i
$245$	34.3190	−	23.8830i	2.19256	−	1.52583i
$246$		0			0
$247$	8.47457	+	16.6323i	0.539224	+	1.05829i
$248$	−13.7643	+	13.5272i	−0.874036	+	0.858977i
$249$		0			0
$250$	1.83440	−	15.7046i	0.116018	−	0.993247i
$251$		−	23.3921i		−	1.47650i	−0.674529	−	0.738248i	$-0.735653\pi$
$251$		−	23.3921i		−	1.47650i	0.674529	−	0.738248i	$-0.264347\pi$
$252$		0			0
$253$	−5.64811	−	11.0850i	−0.355094	−	0.696911i
$254$	−7.23037	−	4.20242i	−0.453673	−	0.263683i
$255$		0			0
$256$	−15.7232	+	2.96310i	−0.982702	+	0.185194i
$257$	−1.62654	−	1.62654i	−0.101461	−	0.101461i	0.654554	−	0.756015i	$-0.272856\pi$
$257$	−1.62654	−	1.62654i	−0.101461	−	0.101461i	−0.756015	+	0.654554i	$0.772856\pi$
$258$		0			0
$259$	9.85860	+	7.16270i	0.612584	+	0.445068i
$260$	0.272512	+	10.3885i	0.0169005	+	0.644266i
$261$		0			0
$262$	−0.624258	+	11.2860i	−0.0385668	+	0.697252i
$263$	0.459613	+	2.90188i	0.0283409	+	0.178938i	0.997798	−	0.0663225i	$-0.0211266\pi$
$263$	0.459613	+	2.90188i	0.0283409	+	0.178938i	−0.969457	+	0.245260i	$0.921127\pi$
$264$		0			0
$265$	12.7310	−	23.7776i	0.782060	−	1.46065i
$266$	−42.9098	+	38.4117i	−2.63097	+	2.35517i
$267$		0			0
$268$	5.10575	+	13.5347i	0.311883	+	0.826766i
$269$	−6.22594	+	2.02293i	−0.379602	+	0.123340i	−0.492602	−	0.870255i	$-0.663954\pi$
$269$	−6.22594	+	2.02293i	−0.379602	+	0.123340i	0.113000	+	0.993595i	$0.463954\pi$
$270$		0			0
$271$	−8.56017	−	2.78137i	−0.519993	−	0.168956i	0.0372489	−	0.999306i	$-0.488141\pi$
$271$	−8.56017	−	2.78137i	−0.519993	−	0.168956i	−0.557242	+	0.830350i	$0.688141\pi$
$272$	−0.646480	−	0.256793i	−0.0391986	−	0.0155703i
$273$		0			0
$274$	11.8635	+	2.55761i	0.716702	+	0.154511i
$275$	17.5920	−	4.93466i	1.06084	−	0.297571i
$276$		0			0
$277$	−23.4349	−	3.71172i	−1.40807	−	0.223016i	−0.594317	−	0.804231i	$-0.702577\pi$
$277$	−23.4349	−	3.71172i	−1.40807	−	0.223016i	−0.813750	+	0.581215i	$0.802577\pi$
$278$	−2.68934	−	10.1543i	−0.161296	−	0.609015i
$279$		0			0
$280$	−30.7671	+	9.01832i	−1.83869	+	0.538948i
$281$	3.61430	+	11.1237i	0.215611	+	0.663582i	0.999110	+	0.0421887i	$0.0134331\pi$
$281$	3.61430	+	11.1237i	0.215611	+	0.663582i	−0.783499	+	0.621393i	$0.786567\pi$
$282$		0			0
$283$	−2.51629	+	4.93851i	−0.149578	+	0.293564i	−0.953622	−	0.301006i	$-0.902678\pi$
$283$	−2.51629	+	4.93851i	−0.149578	+	0.293564i	0.804044	+	0.594570i	$0.202678\pi$
$284$	−2.30160	−	4.04037i	−0.136575	−	0.239752i
$285$		0			0
$286$	−10.9846	+	4.85257i	−0.649531	+	0.286938i
$287$	−6.46569	+	1.02406i	−0.381658	+	0.0604486i
$288$		0			0
$289$	9.97457	+	13.7288i	0.586740	+	0.807578i
$290$	−12.7722	−	0.967390i	−0.750011	−	0.0568071i
$291$		0			0
$292$	4.88874	−	3.91215i	0.286092	−	0.228941i
$293$	−12.6498	+	12.6498i	−0.739007	+	0.739007i	−0.972386	−	0.233379i	$-0.925022\pi$
$293$	−12.6498	+	12.6498i	−0.739007	+	0.739007i	0.233379	+	0.972386i	$0.425022\pi$
$294$		0			0
$295$	0.475236	−	23.3601i	0.0276693	−	1.36007i
$296$	−3.94844	−	5.53506i	−0.229498	−	0.321719i
$297$		0			0
$298$	3.06796	+	1.18789i	0.177722	+	0.0688124i
$299$	−7.91134			−0.457524
$300$		0			0
$301$	7.96801			0.459268
$302$	0.639201	+	0.247493i	0.0367819	+	0.0142416i
$303$		0			0
$304$	29.5039	−	12.7285i	1.69217	−	0.730030i
$305$	8.51718	+	2.96024i	0.487693	+	0.169503i
$306$		0			0
$307$	19.3582	−	19.3582i	1.10483	−	1.10483i	0.111010	−	0.993819i	$-0.464591\pi$
$307$	19.3582	−	19.3582i	1.10483	−	1.10483i	0.993819	−	0.111010i	$-0.0354086\pi$
$308$	−23.1486	−	28.9271i	−1.31901	−	1.64828i
$309$		0			0
$310$	18.3639	−	11.3279i	1.04300	−	0.643379i
$311$	19.4921	+	26.8285i	1.10529	+	1.52131i	0.828175	+	0.560470i	$0.189379\pi$
$311$	19.4921	+	26.8285i	1.10529	+	1.52131i	0.277118	+	0.960836i	$0.410621\pi$
$312$		0			0
$313$	16.1010	−	2.55014i	0.910080	−	0.144143i	0.316197	−	0.948694i	$-0.397594\pi$
$313$	16.1010	−	2.55014i	0.910080	−	0.144143i	0.593883	+	0.804551i	$0.297594\pi$
$314$	1.51872	−	0.670912i	0.0857061	−	0.0378618i
$315$		0			0
$316$	8.84365	−	5.03781i	0.497494	−	0.283399i
$317$	−0.737751	+	1.44792i	−0.0414362	+	0.0813232i	−0.910796	−	0.412856i	$-0.864531\pi$
$317$	−0.737751	+	1.44792i	−0.0414362	+	0.0813232i	0.869360	+	0.494179i	$0.164531\pi$
$318$		0			0
$319$	−4.57388	−	14.0769i	−0.256088	−	0.788158i
$320$	17.8758	+	0.674578i	0.999289	+	0.0377101i
$321$		0			0
$322$	−6.24896	−	23.5946i	−0.348241	−	1.31487i
$323$	1.37979	+	0.218537i	0.0767735	+	0.0121597i
$324$		0			0
$325$	2.28278	−	11.3922i	0.126626	−	0.631926i
$326$	7.22766	+	1.55818i	0.400303	+	0.0862996i
$327$		0			0
$328$	3.60239	+	0.602694i	0.198909	+	0.0332782i
$329$	−25.9450	−	8.43005i	−1.43040	−	0.464764i
$330$		0			0
$331$	28.9649	−	9.41126i	1.59205	−	0.517290i	0.626928	−	0.779077i	$-0.284312\pi$
$331$	28.9649	−	9.41126i	1.59205	−	0.517290i	0.965126	+	0.261787i	$0.0843118\pi$
$332$	19.4420	−	7.33416i	1.06702	−	0.402514i
$333$		0			0
$334$	−5.89901	+	5.28064i	−0.322780	+	0.288944i
$335$	−2.20461	−	16.0222i	−0.120451	−	0.875389i
$336$		0			0
$337$	0.338783	+	2.13899i	0.0184547	+	0.116518i	0.995196	−	0.0979030i	$-0.0312135\pi$
$337$	0.338783	+	2.13899i	0.0184547	+	0.116518i	−0.976741	+	0.214421i	$0.931213\pi$
$338$	0.593613	−	10.7320i	0.0322883	−	0.583743i
$339$		0			0
$340$	0.640960	+	0.440476i	0.0347609	+	0.0238882i
$341$	20.1713	+	14.6553i	1.09234	+	0.793631i
$342$		0			0
$343$	41.9347	+	41.9347i	2.26426	+	2.26426i
$344$	−4.21601	−	1.41048i	−0.227312	−	0.0760481i
$345$		0			0
$346$	−13.6602	−	7.93955i	−0.734376	−	0.426833i
$347$	9.21046	+	18.0766i	0.494444	+	0.970400i	0.994533	+	0.104426i	$0.0333006\pi$
$347$	9.21046	+	18.0766i	0.494444	+	0.970400i	−0.500089	+	0.865974i	$0.666699\pi$
$348$		0			0
$349$		−	14.1136i		−	0.755485i	−0.925911	−	0.377742i	$-0.876701\pi$
$349$		−	14.1136i		−	0.755485i	0.925911	−	0.377742i	$-0.123299\pi$
$350$	35.7789	−	2.19030i	1.91246	−	0.117076i
$351$		0			0
$352$	7.12770	+	19.4036i	0.379908	+	1.03421i
$353$	−2.65081	−	5.20251i	−0.141088	−	0.276901i	0.809640	−	0.586927i	$-0.199662\pi$
$353$	−2.65081	−	5.20251i	−0.141088	−	0.276901i	−0.950728	+	0.310025i	$0.899662\pi$
$354$		0			0
$355$	1.50562	+	4.97600i	0.0799098	+	0.264099i
$356$	0.101963	−	0.918880i	0.00540403	−	0.0487006i
$357$		0			0
$358$	−16.9320	−	13.7926i	−0.894882	−	0.728963i
$359$	−11.6169	−	8.44018i	−0.613117	−	0.445456i	0.237393	−	0.971414i	$-0.423707\pi$
$359$	−11.6169	−	8.44018i	−0.613117	−	0.445456i	−0.850511	+	0.525958i	$0.823707\pi$
$360$		0			0
$361$	−36.8354	+	26.7624i	−1.93870	+	1.40855i
$362$	−18.4177	−	1.01873i	−0.968011	−	0.0535431i
$363$		0			0
$364$	−23.0729	+	4.76478i	−1.20935	+	0.249742i
$365$	−6.30077	+	3.05060i	−0.329797	+	0.159676i
$366$		0			0
$367$	11.4013	+	5.80923i	0.595141	+	0.303239i	0.725494	−	0.688228i	$-0.241611\pi$
$367$	11.4013	+	5.80923i	0.595141	+	0.303239i	−0.130354	+	0.991468i	$0.541611\pi$
$368$	−0.870232	+	13.5905i	−0.0453640	+	0.708453i
$369$		0			0
$370$	2.92965	+	7.01434i	0.152305	+	0.364658i
$371$	58.1539	+	18.8954i	3.01920	+	0.980998i
$372$		0			0
$373$	1.82551	−	11.5258i	0.0945215	−	0.596785i	−0.894275	−	0.447517i	$-0.852308\pi$
$373$	1.82551	−	11.5258i	0.0945215	−	0.596785i	0.988797	−	0.149268i	$-0.0476917\pi$
$374$	−0.189396	+	0.878520i	−0.00979345	+	0.0454272i
$375$		0			0
$376$	12.2357	+	9.05323i	0.631008	+	0.466885i
$377$	−9.29641	−	1.47241i	−0.478790	−	0.0758328i
$378$		0			0
$379$	−6.06211	+	18.6573i	−0.311390	+	0.958359i	0.665825	+	0.746108i	$0.268080\pi$
$379$	−6.06211	+	18.6573i	−0.311390	+	0.958359i	−0.977215	+	0.212251i	$0.931920\pi$
$380$	−35.3233	+	6.54848i	−1.81205	+	0.335930i
$381$		0			0
$382$	−4.65026	−	7.20638i	−0.237928	−	0.368710i
$383$	6.04626	−	11.8664i	0.308949	−	0.606347i	−0.683367	−	0.730075i	$-0.739485\pi$
$383$	6.04626	−	11.8664i	0.308949	−	0.606347i	0.992316	+	0.123728i	$0.0394851\pi$
$384$		0			0
$385$	18.0507	+	37.2823i	0.919949	+	1.90008i
$386$	−12.5403	−	28.3869i	−0.638283	−	1.44485i
$387$		0			0
$388$	17.2843	+	4.73879i	0.877478	+	0.240576i
$389$	14.6739	+	20.1969i	0.743995	+	1.02402i	0.998379	+	0.0569179i	$0.0181273\pi$
$389$	14.6739	+	20.1969i	0.743995	+	1.02402i	−0.254384	+	0.967103i	$0.581873\pi$
$390$		0			0
$391$	−0.348009	+	0.478994i	−0.0175996	+	0.0242237i
$392$	−23.6001	−	47.3301i	−1.19199	−	2.39053i
$393$		0			0
$394$	0.871071	+	8.52514i	0.0438839	+	0.429490i
$395$	−10.8916	+	3.29553i	−0.548015	+	0.165816i
$396$		0			0
$397$	9.79542	−	4.99102i	0.491618	−	0.250492i	−0.190563	−	0.981675i	$-0.561031\pi$
$397$	9.79542	−	4.99102i	0.491618	−	0.250492i	0.682181	+	0.731183i	$0.261031\pi$
$398$	4.34349	−	11.2180i	0.217720	−	0.562306i
$399$		0			0
$400$	−19.3190	−	5.17460i	−0.965950	−	0.258730i
$401$	−17.4413			−0.870979			−0.435490	−	0.900194i	$-0.643425\pi$
$401$	−17.4413			−0.870979			−0.435490	+	0.900194i	$0.643425\pi$
$402$		0			0
$403$	14.1270	−	7.19809i	0.703718	−	0.358562i
$404$	20.6373	+	18.7995i	1.02674	+	0.935309i
$405$		0			0
$406$	−2.95172	−	28.8884i	−0.146492	−	1.43371i
$407$	−6.21128	+	6.21128i	−0.307882	+	0.307882i
$408$		0			0
$409$	0.170633	−	0.234856i	0.00843724	−	0.0116129i	−0.804778	−	0.593577i	$-0.797715\pi$
$409$	0.170633	−	0.234856i	0.00843724	−	0.0116129i	0.813215	+	0.581964i	$0.197715\pi$
$410$	−3.77731	−	1.55161i	−0.186548	−	0.0766284i
$411$		0			0
$412$	−3.78525	−	1.03779i	−0.186486	−	0.0511284i
$413$	52.3183	−	8.28640i	2.57441	−	0.407747i
$414$		0			0
$415$	−23.0152	+	3.16682i	−1.12977	+	0.155453i
$416$	13.0517	+	1.56320i	0.639915	+	0.0766420i
$417$		0			0
$418$	−22.5091	−	34.8817i	−1.10096	−	1.70612i
$419$	−7.74771	−	23.8450i	−0.378500	−	1.16490i	−0.941087	−	0.338166i	$-0.890194\pi$
$419$	−7.74771	−	23.8450i	−0.378500	−	1.16490i	0.562586	−	0.826739i	$-0.309806\pi$
$420$		0			0
$421$	8.37229	−	25.7672i	0.408040	−	1.25582i	−0.510289	−	0.860003i	$-0.670462\pi$
$421$	8.37229	−	25.7672i	0.408040	−	1.25582i	0.918330	−	0.395816i	$-0.129538\pi$
$422$	−32.7106	+	8.66332i	−1.59233	+	0.421724i
$423$		0			0
$424$	−27.4255	−	20.2922i	−1.33190	−	0.985475i
$425$	−0.589327	−	0.639340i	−0.0285866	−	0.0310125i
$426$		0			0
$427$	−3.19788	+	20.1906i	−0.154756	+	0.977092i
$428$	−4.80002	+	0.223685i	−0.232018	+	0.0108122i
$429$		0			0
$430$	4.24562	+	2.58457i	0.204742	+	0.124639i
$431$	−16.1967	+	5.26263i	−0.780168	+	0.253492i	−0.671912	−	0.740631i	$-0.734527\pi$
$431$	−16.1967	+	5.26263i	−0.780168	+	0.253492i	−0.108256	+	0.994123i	$0.534527\pi$
$432$		0			0
$433$	−3.15400	−	1.60704i	−0.151571	−	0.0772295i	0.376560	−	0.926392i	$-0.377107\pi$
$433$	−3.15400	−	1.60704i	−0.151571	−	0.0772295i	−0.528131	+	0.849163i	$0.677107\pi$
$434$	32.6260	+	36.4466i	1.56610	+	1.74949i
$435$		0			0
$436$	24.2854	−	5.01517i	1.16306	−	0.240183i
$437$	−4.27839	−	27.0127i	−0.204663	−	1.29219i
$438$		0			0
$439$	−22.6963	+	16.4898i	−1.08324	+	0.787016i	−0.978244	−	0.207457i	$-0.933481\pi$
$439$	−22.6963	+	16.4898i	−1.08324	+	0.787016i	−0.104991	+	0.994473i	$0.533481\pi$
$440$	−2.95130	−	22.9220i	−0.140698	−	1.09276i
$441$		0			0
$442$	0.443089	+	0.360936i	0.0210756	+	0.0171680i
$443$	−14.4728	−	14.4728i	−0.687624	−	0.687624i	0.274082	−	0.961706i	$-0.411626\pi$
$443$	−14.4728	−	14.4728i	−0.687624	−	0.687624i	−0.961706	+	0.274082i	$0.911626\pi$
$444$		0			0
$445$	−0.339343	+	0.976355i	−0.0160864	+	0.0462836i
$446$	8.77945	−	15.1052i	0.415719	−	0.715254i
$447$		0			0
$448$	5.64720	+	40.1599i	0.266805	+	1.89738i
$449$		−	31.4725i		−	1.48528i	−0.669692	−	0.742639i	$-0.733574\pi$
$449$		−	31.4725i		−	1.48528i	0.669692	−	0.742639i	$-0.266426\pi$
$450$		0			0
$451$		−	4.71882i		−	0.222201i
$452$	−4.28796	−	2.82008i	−0.201689	−	0.132646i
$453$		0			0
$454$	−12.9958	−	7.55340i	−0.609923	−	0.354499i
$455$	26.3352	+	0.535761i	1.23461	+	0.0251169i
$456$		0			0
$457$	11.4538	+	11.4538i	0.535787	+	0.535787i	0.922289	−	0.386502i	$-0.126317\pi$
$457$	11.4538	+	11.4538i	0.535787	+	0.535787i	−0.386502	+	0.922289i	$0.626317\pi$
$458$	25.4872	−	31.2884i	1.19094	−	1.46201i
$459$		0			0
$460$	4.32367	−	14.5989i	0.201592	−	0.680679i
$461$	27.0478	−	19.6514i	1.25974	−	0.915257i	0.260998	−	0.965339i	$-0.415949\pi$
$461$	27.0478	−	19.6514i	1.25974	−	0.915257i	0.998745	+	0.0500827i	$0.0159485\pi$
$462$		0			0
$463$	−0.528273	−	3.33538i	−0.0245509	−	0.155008i	0.972367	−	0.233456i	$-0.0750036\pi$
$463$	−0.528273	−	3.33538i	−0.0245509	−	0.155008i	−0.996918	+	0.0784479i	$0.975004\pi$
$464$	−3.55196	+	15.8079i	−0.164896	+	0.733862i
$465$		0			0
$466$	−14.9059	+	13.3434i	−0.690504	+	0.618120i
$467$	21.4459	+	10.9272i	0.992398	+	0.505652i	0.873275	−	0.487228i	$-0.161992\pi$
$467$	21.4459	+	10.9272i	0.992398	+	0.505652i	0.119123	+	0.992880i	$0.461992\pi$
$468$		0			0
$469$	34.8716	−	11.3305i	1.61022	−	0.523193i
$470$	−11.0899	−	12.9076i	−0.511541	−	0.595381i
$471$		0			0
$472$	−29.1494	−	4.87680i	−1.34171	−	0.224473i
$473$	−0.898505	+	5.67294i	−0.0413133	+	0.260842i
$474$		0			0
$475$	40.1324	+	1.63358i	1.84140	+	0.0749537i
$476$	−0.726463	+	1.60655i	−0.0332974	+	0.0736362i
$477$		0			0
$478$	4.97165	+	18.7718i	0.227398	+	0.858600i
$479$	0.487335	−	1.49986i	0.0222669	−	0.0685305i	−0.939306	−	0.343082i	$-0.888529\pi$
$479$	0.487335	−	1.49986i	0.0222669	−	0.0685305i	0.961572	+	0.274551i	$0.0885293\pi$
$480$		0			0
$481$	1.72612	+	5.31246i	0.0787045	+	0.242227i
$482$	16.7259	−	10.7932i	0.761845	−	0.491617i
$483$		0			0
$484$	4.08947	−	2.32958i	0.185885	−	0.105890i
$485$	−17.6649	−	9.45812i	−0.802121	−	0.429471i
$486$		0			0
$487$	10.1551	−	1.60842i	0.460173	−	0.0728843i	0.0779561	−	0.996957i	$-0.475161\pi$
$487$	10.1551	−	1.60842i	0.460173	−	0.0728843i	0.382217	+	0.924073i	$0.375161\pi$
$488$	5.26616	−	10.1171i	0.238388	−	0.457981i
$489$		0			0
$490$	13.9728	+	57.4555i	0.631226	+	2.59558i
$491$	17.6012	−	24.2260i	0.794333	−	1.09331i	−0.199222	−	0.979954i	$-0.563842\pi$
$491$	17.6012	−	24.2260i	0.794333	−	1.09331i	0.993555	−	0.113351i	$-0.0361585\pi$
$492$		0			0
$493$	−0.498084	+	0.498084i	−0.0224326	+	0.0224326i
$494$	−26.2622	+	2.68338i	−1.18159	+	0.120731i
$495$		0			0
$496$	−10.8113	−	25.0599i	−0.485441	−	1.12522i
$497$	−10.5015	+	5.35080i	−0.471059	+	0.240016i
$498$		0			0
$499$	11.8477			0.530374			0.265187	−	0.964197i	$-0.414566\pi$
$499$	11.8477			0.530374			0.265187	+	0.964197i	$0.414566\pi$
$500$	19.7747	+	10.4385i	0.884351	+	0.466823i
$501$		0			0
$502$	30.8497	+	11.9447i	1.37689	+	0.533119i
$503$	−30.3925	+	15.4858i	−1.35514	+	0.690477i	−0.972387	−	0.233375i	$-0.925023\pi$
$503$	−30.3925	+	15.4858i	−1.35514	+	0.690477i	−0.382750	+	0.923852i	$0.625023\pi$
$504$		0			0
$505$	−17.8282	−	25.6184i	−0.793343	−	1.14000i
$506$	17.5032	−	1.78842i	0.778110	−	0.0795048i
$507$		0			0
$508$	9.23424	−	7.38958i	0.409703	−	0.327860i
$509$	15.7134	−	21.6276i	0.696482	−	0.958626i	−0.303501	−	0.952831i	$-0.598156\pi$
$509$	15.7134	−	21.6276i	0.696482	−	0.958626i	0.999983	−	0.00579453i	$-0.00184447\pi$
$510$		0			0
$511$	−9.32851	−	12.8396i	−0.412669	−	0.567990i
$512$	4.12100	−	22.2490i	0.182124	−	0.983276i
$513$		0			0
$514$	2.97565	−	1.31453i	0.131250	−	0.0579815i
$515$	3.86860	+	2.07132i	0.170471	+	0.0912734i
$516$		0			0
$517$	8.92756	−	17.5213i	0.392634	−	0.770587i
$518$	−14.4803	+	9.34412i	−0.636229	+	0.410557i
$519$		0			0
$520$	−13.8396	−	4.94529i	−0.606905	−	0.216865i
$521$	8.01289	−	24.6611i	0.351051	−	1.08042i	−0.607213	−	0.794539i	$-0.707712\pi$
$521$	8.01289	−	24.6611i	0.351051	−	1.08042i	0.958264	−	0.285885i	$-0.0922876\pi$
$522$		0			0
$523$	−39.6455	−	6.27924i	−1.73358	−	0.274572i	−0.791793	−	0.610789i	$-0.790852\pi$
$523$	−39.6455	−	6.27924i	−1.73358	−	0.274572i	−0.941785	+	0.336217i	$0.890852\pi$
$524$	−14.5653	−	6.58626i	−0.636289	−	0.287722i
$525$		0			0
$526$	−4.06172	−	0.875648i	−0.177099	−	0.0381801i
$527$	0.185620	−	1.17196i	0.00808574	−	0.0510514i
$528$		0			0
$529$	−10.8505	−	3.52553i	−0.471759	−	0.153284i
$530$	24.8573	+	28.9314i	1.07973	+	1.25670i
$531$		0			0
$532$	−28.7466	−	76.2040i	−1.24632	−	3.30386i
$533$	−2.67367	−	1.36230i	−0.115809	−	0.0590079i
$534$		0			0
$535$	5.28807	+	0.948184i	0.228623	+	0.0409936i
$536$	−20.4569	−	0.177753i	−0.883603	−	0.00767777i
$537$		0			0
$538$	0.511297	−	9.24379i	0.0220436	−	0.398528i
$539$	−55.2790	+	40.1625i	−2.38103	+	1.72992i
$540$		0			0
$541$	−13.8700	−	10.0772i	−0.596319	−	0.433251i	0.248252	−	0.968696i	$-0.420144\pi$
$541$	−13.8700	−	10.0772i	−0.596319	−	0.433251i	−0.844570	+	0.535445i	$0.820144\pi$
$542$	8.03918	−	9.86898i	0.345312	−	0.423909i
$543$		0			0
$544$	0.668773	−	0.721458i	0.0286734	−	0.0309323i
$545$	−27.7191	−	0.563916i	−1.18736	−	0.0241555i
$546$		0			0
$547$	−12.6963	−	24.9180i	−0.542857	−	1.06542i	−0.985652	−	0.168793i	$-0.946013\pi$
$547$	−12.6963	−	24.9180i	−0.542857	−	1.06542i	0.442795	−	0.896623i	$-0.353987\pi$
$548$	−9.43087	+	14.3397i	−0.402867	+	0.612563i
$549$		0			0
$550$	−2.47517	+	25.7203i	−0.105541	+	1.09672i
$551$		−	32.5382i		−	1.38617i
$552$		0			0
$553$	−11.7120	−	22.9860i	−0.498043	−	0.977465i
$554$	16.8616	−	29.0108i	0.716382	−	1.23255i
$555$		0			0
$556$	14.7649	+	1.63837i	0.626169	+	0.0694826i
$557$	−21.2811	−	21.2811i	−0.901710	−	0.901710i	0.0938737	−	0.995584i	$-0.470075\pi$
$557$	−21.2811	−	21.2811i	−0.901710	−	0.901710i	−0.995584	+	0.0938737i	$0.970075\pi$
$558$		0			0
$559$	2.95487	+	2.14684i	0.124978	+	0.0908018i
$560$	3.81718	−	45.1809i	0.161305	−	1.90924i
$561$		0			0
$562$	−16.5156	−	0.913516i	−0.696666	−	0.0385344i
$563$	3.04270	+	19.2108i	0.128234	+	0.809640i	0.965033	+	0.262129i	$0.0844247\pi$
$563$	3.04270	+	19.2108i	0.128234	+	0.809640i	−0.836798	+	0.547511i	$0.815575\pi$
$564$		0			0
$565$	3.97400	+	4.13905i	0.167187	+	0.174131i
$566$	−5.22805	−	5.84026i	−0.219751	−	0.245485i
$567$		0			0
$568$	6.50374	−	0.972241i	0.272891	−	0.0407943i
$569$	30.0678	−	9.76960i	1.26051	−	0.409563i	0.398831	−	0.917024i	$-0.369416\pi$
$569$	30.0678	−	9.76960i	1.26051	−	0.409563i	0.861675	+	0.507461i	$0.169416\pi$
$570$		0			0
$571$	24.6115	+	7.99676i	1.02996	+	0.334654i	0.774774	−	0.632238i	$-0.217864\pi$
$571$	24.6115	+	7.99676i	1.02996	+	0.334654i	0.255185	+	0.966892i	$0.417864\pi$
$572$	−0.790557	−	16.9644i	−0.0330548	−	0.709317i
$573$		0			0
$574$	1.95103	−	9.04993i	0.0814346	−	0.377737i
$575$	−8.33872	+	14.8406i	−0.347749	+	0.618898i
$576$		0			0
$577$	−3.74572	−	0.593263i	−0.155936	−	0.0246979i	0.0779781	−	0.996955i	$-0.475154\pi$
$577$	−3.74572	−	0.593263i	−0.155936	−	0.0246979i	−0.233914	+	0.972257i	$0.575154\pi$
$578$	−23.1990	+	6.14420i	−0.964952	+	0.255565i
$579$		0			0
$580$	7.79770	−	16.3502i	0.323782	−	0.678903i
$581$	−16.2757	−	50.0914i	−0.675229	−	2.07814i
$582$		0			0
$583$	−20.0105	+	39.2728i	−0.828750	+	1.62651i
$584$	2.66304	+	8.44498i	0.110197	+	0.349456i
$585$		0			0
$586$	−10.2233	−	23.1420i	−0.422319	−	0.955986i
$587$	8.90911	−	1.41106i	0.367718	−	0.0582409i	0.0301590	−	0.999545i	$-0.490399\pi$
$587$	8.90911	−	1.41106i	0.367718	−	0.0582409i	0.337559	+	0.941304i	$0.390399\pi$
$588$		0			0
$589$	32.2171	+	44.3431i	1.32748	+	1.82712i
$590$	30.5648	+	12.5551i	1.25833	+	0.516885i
$591$		0			0
$592$	9.31588	−	2.38086i	0.382880	−	0.0978527i
$593$	−32.7211	+	32.7211i	−1.34370	+	1.34370i	−0.451349	+	0.892348i	$0.649057\pi$
$593$	−32.7211	+	32.7211i	−1.34370	+	1.34370i	−0.892348	+	0.451349i	$0.850943\pi$
$594$		0			0
$595$	1.19089	−	1.57090i	0.0488216	−	0.0644007i
$596$	−3.13319	+	3.43948i	−0.128341	+	0.140887i
$597$		0			0
$598$	4.03977	−	10.4335i	0.165199	−	0.426659i
$599$	−29.9007			−1.22171			−0.610854	−	0.791743i	$-0.709174\pi$
$599$	−29.9007			−1.22171			−0.610854	+	0.791743i	$0.709174\pi$
$600$		0			0
$601$	21.0255			0.857649			0.428825	−	0.903388i	$-0.358928\pi$
$601$	21.0255			0.857649			0.428825	+	0.903388i	$0.358928\pi$
$602$	−4.06871	+	10.5083i	−0.165828	+	0.428285i
$603$		0			0
$604$	−0.652791	+	0.716607i	−0.0265617	+	0.0291583i
$605$	−5.03647	+	1.52391i	−0.204762	+	0.0619559i
$606$		0			0
$607$	−8.79927	+	8.79927i	−0.357151	+	0.357151i	−0.862762	−	0.505611i	$-0.831267\pi$
$607$	−8.79927	+	8.79927i	−0.357151	+	0.357151i	0.505611	+	0.862762i	$0.331267\pi$
$608$	1.72086	+	45.4096i	0.0697902	+	1.84160i
$609$		0			0
$610$	−8.25313	+	9.72095i	−0.334159	+	0.393590i
$611$	−7.35018	−	10.1167i	−0.297357	−	0.409276i
$612$		0			0
$613$	−17.2679	+	2.73497i	−0.697445	+	0.110464i	−0.495082	−	0.868846i	$-0.664862\pi$
$613$	−17.2679	+	2.73497i	−0.697445	+	0.110464i	−0.202363	+	0.979311i	$0.564862\pi$
$614$	15.6449	+	35.4146i	0.631375	+	1.42922i
$615$		0			0
$616$	49.9697	−	15.7575i	2.01334	−	0.634887i
$617$	−14.0284	+	27.5323i	−0.564763	+	1.10841i	0.415293	+	0.909688i	$0.363679\pi$
$617$	−14.0284	+	27.5323i	−0.564763	+	1.10841i	−0.980056	+	0.198722i	$0.936321\pi$
$618$		0			0
$619$	−4.97483	−	15.3110i	−0.199955	−	0.615399i	−0.999883	−	0.0153026i	$-0.995129\pi$
$619$	−4.97483	−	15.3110i	−0.199955	−	0.615399i	0.799928	−	0.600097i	$-0.204871\pi$
$620$	5.56212	+	30.0028i	0.223380	+	1.20494i
$621$		0			0
$622$	−45.3349	+	12.0068i	−1.81776	+	0.481430i
$623$	−2.31452	−	0.366584i	−0.0927293	−	0.0146869i
$624$		0			0
$625$	−18.9642	−	16.2898i	−0.758568	−	0.651593i
$626$	−4.85849	+	22.5363i	−0.194185	+	0.900730i
$627$		0			0
$628$	0.109302	+	2.34548i	0.00436162	+	0.0935950i
$629$	0.397574	+	0.129180i	0.0158523	+	0.00515073i
$630$		0			0
$631$	19.9039	−	6.46717i	0.792362	−	0.257454i	0.115253	−	0.993336i	$-0.463232\pi$
$631$	19.9039	−	6.46717i	0.792362	−	0.257454i	0.677110	+	0.735882i	$0.263232\pi$
$632$	2.12806	+	14.2355i	0.0846499	+	0.566259i
$633$		0			0
$634$	−1.53281	−	1.71230i	−0.0608756	−	0.0680043i
$635$	−11.9014	+	5.76221i	−0.472293	+	0.228666i
$636$		0			0
$637$	6.79717	+	42.9156i	0.269314	+	1.70038i
$638$	20.9004	+	1.15605i	0.827453	+	0.0457685i
$639$		0			0
$640$	−10.0176	+	23.2303i	−0.395980	+	0.918259i
$641$	−20.7955	−	15.1088i	−0.821375	−	0.596764i	0.0957313	−	0.995407i	$-0.469481\pi$
$641$	−20.7955	−	15.1088i	−0.821375	−	0.596764i	−0.917106	+	0.398644i	$0.869481\pi$
$642$		0			0
$643$	−21.3854	−	21.3854i	−0.843357	−	0.843357i	0.145937	−	0.989294i	$-0.453380\pi$
$643$	−21.3854	−	21.3854i	−0.843357	−	0.843357i	−0.989294	+	0.145937i	$0.953380\pi$
$644$	34.3076	+	3.80693i	1.35191	+	0.150014i
$645$		0			0
$646$	−0.992771	+	1.70809i	−0.0390601	+	0.0672037i
$647$	−3.69522	−	7.25227i	−0.145274	−	0.285116i	0.806891	−	0.590700i	$-0.201148\pi$
$647$	−3.69522	−	7.25227i	−0.145274	−	0.285116i	−0.952165	+	0.305584i	$0.901148\pi$
$648$		0			0
$649$			38.1832i			1.49882i
$650$	13.8585	+	8.82776i	0.543575	+	0.346253i
$651$		0			0
$652$	−5.74560	+	8.73625i	−0.225015	+	0.342138i
$653$	−7.89301	−	15.4909i	−0.308878	−	0.606206i	0.683428	−	0.730018i	$-0.260488\pi$
$653$	−7.89301	−	15.4909i	−0.308878	−	0.606206i	−0.992306	+	0.123811i	$0.960488\pi$
$654$		0			0
$655$	14.2421	+	10.7968i	0.556486	+	0.421867i
$656$	−2.63433	+	4.44311i	−0.102853	+	0.173474i
$657$		0			0
$658$	24.3659	−	29.9119i	0.949884	−	1.16609i
$659$	23.0988	+	16.7822i	0.899800	+	0.653743i	0.938415	−	0.345511i	$-0.112294\pi$
$659$	23.0988	+	16.7822i	0.899800	+	0.653743i	−0.0386145	+	0.999254i	$0.512294\pi$
$660$		0			0
$661$	13.1962	−	9.58763i	0.513274	−	0.372916i	−0.300790	−	0.953690i	$-0.597250\pi$
$661$	13.1962	−	9.58763i	0.513274	−	0.372916i	0.814064	+	0.580775i	$0.197250\pi$
$662$	−2.37870	+	43.0048i	−0.0924510	+	1.67143i
$663$		0			0
$664$	−0.255334	+	29.3853i	−0.00990887	+	1.14037i
$665$	12.4125	+	90.2093i	0.481337	+	3.49816i
$666$		0			0
$667$	12.2872	+	6.26065i	0.475763	+	0.242413i
$668$	−3.95194	−	10.4761i	−0.152905	−	0.405333i
$669$		0			0
$670$	22.2560	+	5.27398i	0.859825	+	0.203752i
$671$	−14.0144	−	4.55355i	−0.541020	−	0.175788i
$672$		0			0
$673$	−6.95002	+	43.8807i	−0.267903	+	1.69148i	0.376201	+	0.926538i	$0.377230\pi$
$673$	−6.95002	+	43.8807i	−0.267903	+	1.69148i	−0.644104	+	0.764938i	$0.722770\pi$
$674$	−2.99391	−	0.645444i	−0.115321	−	0.0248616i
$675$		0			0
$676$	13.8503	+	6.26294i	0.532705	+	0.240882i
$677$	43.8185	+	6.94016i	1.68408	+	0.266732i	0.923804	−	0.382867i	$-0.125063\pi$
$677$	43.8185	+	6.94016i	1.68408	+	0.266732i	0.760277	+	0.649599i	$0.225063\pi$
$678$		0			0
$679$	14.0377	−	43.2037i	0.538719	−	1.65801i
$680$	−0.908198	+	0.620383i	−0.0348278	+	0.0237906i
$681$		0			0
$682$	−29.6277	+	19.1187i	−1.13450	+	0.732092i
$683$	−10.0493	+	19.7229i	−0.384527	+	0.754676i	−0.999424	−	0.0339308i	$-0.989197\pi$
$683$	−10.0493	+	19.7229i	−0.384527	+	0.754676i	0.614897	+	0.788607i	$0.289197\pi$
$684$		0			0
$685$	13.8417	−	13.2898i	0.528865	−	0.507776i
$686$	−76.7170	+	33.8907i	−2.92907	+	1.29395i
$687$		0			0
$688$	4.01298	−	4.83988i	0.152993	−	0.184519i
$689$	16.4749	+	22.6758i	0.627644	+	0.863878i
$690$		0			0
$691$	−8.55773	+	11.7787i	−0.325551	+	0.448083i	−0.940152	−	0.340755i	$-0.889317\pi$
$691$	−8.55773	+	11.7787i	−0.325551	+	0.448083i	0.614601	+	0.788838i	$0.289317\pi$
$692$	17.4461	−	13.9610i	0.663200	−	0.530717i
$693$		0			0
$694$	−28.5427	+	2.91640i	−1.08346	+	0.110705i
$695$	−15.6884	−	5.45267i	−0.595094	−	0.206831i
$696$		0			0
$697$	−0.200092	+	0.101952i	−0.00757903	+	0.00386171i
$698$	18.6132	+	7.20685i	0.704519	+	0.272783i
$699$		0			0
$700$	−15.3812	+	48.3040i	−0.581356	+	1.82572i
$701$	25.3484			0.957396			0.478698	−	0.877980i	$-0.341109\pi$
$701$	25.3484			0.957396			0.478698	+	0.877980i	$0.341109\pi$
$702$		0			0
$703$	−17.2055	+	8.76666i	−0.648919	+	0.330641i
$704$	−29.2292	−	0.507993i	−1.10162	−	0.0191457i
$705$		0			0
$706$	8.21469	−	0.839351i	0.309164	−	0.0315894i
$707$	50.0342	−	50.0342i	1.88173	−	1.88173i
$708$		0			0
$709$	1.90556	−	2.62277i	0.0715646	−	0.0985003i	−0.771734	−	0.635945i	$-0.780610\pi$
$709$	1.90556	−	2.62277i	0.0715646	−	0.0985003i	0.843299	+	0.537445i	$0.180610\pi$
$710$	−7.33120	−	0.555278i	−0.275135	−	0.0208392i
$711$		0			0
$712$	1.15976	+	0.603678i	0.0434639	+	0.0226238i
$713$	−22.9439	+	3.63396i	−0.859256	+	0.136093i
$714$		0			0
$715$	−3.35111	+	18.6893i	−0.125324	+	0.698940i
$716$	26.8358	−	15.2871i	1.00290	−	0.571305i
$717$		0			0
$718$	17.0629	−	11.0107i	0.636783	−	0.410915i
$719$	−5.03398	−	15.4930i	−0.187736	−	0.577792i	0.812249	−	0.583311i	$-0.198243\pi$
$719$	−5.03398	−	15.4930i	−0.187736	−	0.577792i	−0.999985	+	0.00551941i	$0.998243\pi$
$720$		0			0
$721$	−3.07426	+	9.46159i	−0.114491	+	0.352368i
$722$	−16.4853	−	62.2445i	−0.613519	−	2.31650i
$723$		0			0
$724$	10.7481	−	23.7692i	0.399451	−	0.883375i
$725$	−12.5607	+	15.8869i	−0.466491	+	0.590025i
$726$		0			0
$727$	−1.01165	+	6.38733i	−0.0375201	+	0.236893i	−0.999320	−	0.0368591i	$-0.988265\pi$
$727$	−1.01165	+	6.38733i	−0.0375201	+	0.236893i	0.961800	+	0.273752i	$0.0882647\pi$
$728$	5.49791	−	32.8618i	0.203766	−	1.21794i
$729$		0			0
$730$	−0.805790	−	9.86724i	−0.0298236	−	0.365203i
$731$	0.259962	−	0.0844668i	0.00961504	−	0.00312412i
$732$		0			0
$733$	−32.8807	−	16.7535i	−1.21447	−	0.618806i	−0.275007	−	0.961442i	$-0.588680\pi$
$733$	−32.8807	−	16.7535i	−1.21447	−	0.618806i	−0.939468	+	0.342637i	$0.888680\pi$
$734$	−13.4831	+	12.0697i	−0.497670	+	0.445501i
$735$		0			0
$736$	−17.4789	−	8.08739i	−0.644280	−	0.298105i
$737$	4.13463	+	26.1050i	0.152301	+	0.961591i
$738$		0			0
$739$	−7.37894	+	5.36112i	−0.271439	+	0.197212i	−0.715175	−	0.698946i	$-0.753653\pi$
$739$	−7.37894	+	5.36112i	−0.271439	+	0.197212i	0.443736	+	0.896158i	$0.353653\pi$
$740$	−10.7465	+	0.281905i	−0.395051	+	0.0103630i
$741$		0			0
$742$	−54.6145	+	67.0453i	−2.00496	+	2.46131i
$743$	30.2418	+	30.2418i	1.10946	+	1.10946i	0.993221	+	0.116243i	$0.0370853\pi$
$743$	30.2418	+	30.2418i	1.10946	+	1.10946i	0.116243	+	0.993221i	$0.462915\pi$
$744$		0			0
$745$	4.26966	−	2.97131i	0.156428	−	0.108860i
$746$	14.2682	+	8.29295i	0.522396	+	0.303626i
$747$		0			0
$748$	−1.06189	−	0.698377i	−0.0388265	−	0.0255352i
$749$			12.1798i			0.445039i
$750$		0			0
$751$		−	30.4435i		−	1.11090i	−0.831550	−	0.555450i	$-0.812546\pi$
$751$		−	30.4435i		−	1.11090i	0.831550	−	0.555450i	$-0.187454\pi$
$752$	−18.1874	+	11.5137i	−0.663226	+	0.419861i
$753$		0			0
$754$	6.68886	−	11.5083i	0.243594	−	0.419109i
$755$	0.889571	−	0.619064i	0.0323748	−	0.0225300i
$756$		0			0
$757$	21.7586	+	21.7586i	0.790830	+	0.790830i	0.981629	−	0.190799i	$-0.0611080\pi$
$757$	21.7586	+	21.7586i	0.790830	+	0.790830i	−0.190799	+	0.981629i	$0.561108\pi$
$758$	−21.5099	−	17.5217i	−0.781273	−	0.636418i
$759$		0			0
$760$	9.40098	−	49.9286i	0.341009	−	1.81110i
$761$	43.4573	−	31.5736i	1.57533	−	1.14454i	0.653505	−	0.756922i	$-0.273298\pi$
$761$	43.4573	−	31.5736i	1.57533	−	1.14454i	0.921820	−	0.387619i	$-0.126702\pi$
$762$		0			0
$763$	−9.83266	−	62.0810i	−0.355966	−	2.24748i
$764$	11.8784	−	2.45300i	0.429745	−	0.0887466i
$765$		0			0
$766$	12.5622	+	14.0332i	0.453890	+	0.507041i
$767$	21.6345	+	11.0233i	0.781175	+	0.398029i
$768$		0			0
$769$	−31.7516	+	10.3167i	−1.14499	+	0.372031i	−0.819255	−	0.573429i	$-0.805613\pi$
$769$	−31.7516	+	10.3167i	−1.14499	+	0.372031i	−0.325738	+	0.945460i	$0.605613\pi$
$770$	−58.3854	+	4.76794i	−2.10406	+	0.171824i
$771$		0			0
$772$	43.8403	−	2.04300i	1.57785	−	0.0735292i
$773$	−0.594263	+	3.75203i	−0.0213742	+	0.134951i	−0.996068	−	0.0885934i	$-0.971763\pi$
$773$	−0.594263	+	3.75203i	−0.0213742	+	0.134951i	0.974694	+	0.223545i	$0.0717628\pi$
$774$		0			0
$775$	1.38752	−	34.0875i	0.0498412	−	1.22446i
$776$	−15.0755	+	20.3749i	−0.541177	+	0.731417i
$777$		0			0
$778$	−34.1287	+	9.03890i	−1.22357	+	0.324060i
$779$	3.20558	−	9.86577i	0.114852	−	0.353478i
$780$		0			0
$781$	−2.62538	−	8.08010i	−0.0939436	−	0.289129i
$782$	−0.453997	−	0.703546i	−0.0162349	−	0.0251588i
$783$		0			0
$784$	74.4702	−	6.95587i	2.65965	−	0.248424i
$785$	0.463321	−	2.58397i	0.0165366	−	0.0922257i
$786$		0			0
$787$	−49.7140	+	7.87392i	−1.77211	+	0.280675i	−0.955173	−	0.296048i	$-0.904331\pi$
$787$	−49.7140	+	7.87392i	−1.77211	+	0.280675i	−0.816940	+	0.576723i	$0.804331\pi$
$788$	−11.6878	−	3.20442i	−0.416361	−	0.114153i
$789$		0			0
$790$	1.21540	−	16.0467i	0.0432422	−	0.570916i
$791$	−7.64623	+	10.5241i	−0.271869	+	0.374195i
$792$		0			0
$793$	−6.62592	+	6.62592i	−0.235293	+	0.235293i
$794$	1.58035	+	15.4669i	0.0560847	+	0.548898i
$795$		0			0
$796$	12.5764	+	11.4565i	0.445760	+	0.406064i
$797$	−26.4812	+	13.4929i	−0.938013	+	0.477942i	−0.855012	−	0.518608i	$-0.826450\pi$
$797$	−26.4812	+	13.4929i	−0.938013	+	0.477942i	−0.0830009	+	0.996549i	$0.526450\pi$
$798$		0			0
$799$	−0.935840			−0.0331076
$800$	16.6892	−	22.8358i	0.590051	−	0.807366i
$801$		0			0
$802$	8.90609	−	23.0018i	0.314485	−	0.812222i
$803$	10.1933	−	5.19373i	0.359712	−	0.183283i
$804$		0			0
$805$	−36.4535	−	12.6698i	−1.28482	−	0.446552i
$806$	2.27920	+	22.3064i	0.0802814	+	0.785711i
$807$		0			0
$808$	−35.3309	+	17.6170i	−1.24294	+	0.619765i
$809$	0.842151	−	1.15912i	0.0296085	−	0.0407525i	−0.793956	−	0.607975i	$-0.791982\pi$
$809$	0.842151	−	1.15912i	0.0296085	−	0.0407525i	0.823565	+	0.567223i	$0.191982\pi$
$810$		0			0
$811$	11.2040	+	15.4209i	0.393425	+	0.541503i	0.959079	−	0.283140i	$-0.0913761\pi$
$811$	11.2040	+	15.4209i	0.393425	+	0.541503i	−0.565654	+	0.824643i	$0.691376\pi$
$812$	39.6055	+	10.8585i	1.38988	+	0.381060i
$813$		0			0
$814$	−5.01982	−	11.3632i	−0.175945	−	0.398279i
$815$	8.43285	−	8.09657i	0.295390	−	0.283611i
$816$		0			0
$817$	−5.73226	+	11.2502i	−0.200546	+	0.393595i
$818$	0.222599	+	0.344956i	0.00778300	+	0.0120611i
$819$		0			0
$820$	3.97508	−	4.18925i	0.138816	−	0.146295i
$821$	−11.2314	+	34.5666i	−0.391978	+	1.20638i	0.539312	+	0.842106i	$0.318684\pi$
$821$	−11.2314	+	34.5666i	−0.391978	+	1.20638i	−0.931290	+	0.364278i	$0.881316\pi$
$822$		0			0
$823$	38.2611	+	6.05996i	1.33370	+	0.211237i	0.782246	−	0.622970i	$-0.214074\pi$
$823$	38.2611	+	6.05996i	1.33370	+	0.211237i	0.551452	+	0.834207i	$0.314074\pi$
$824$	3.30152	−	4.46209i	0.115014	−	0.155444i
$825$		0			0
$826$	−15.7871	+	73.2291i	−0.549305	+	2.54797i
$827$	−5.96468	+	37.6595i	−0.207412	+	1.30955i	0.635752	+	0.771894i	$0.280690\pi$
$827$	−5.96468	+	37.6595i	−0.207412	+	1.30955i	−0.843164	+	0.537656i	$0.819310\pi$
$828$		0			0
$829$	38.8788	+	12.6325i	1.35032	+	0.438745i	0.892799	−	0.450455i	$-0.148738\pi$
$829$	38.8788	+	12.6325i	1.35032	+	0.438745i	0.457519	+	0.889200i	$0.348738\pi$
$830$	7.57582	−	31.9697i	0.262961	−	1.10968i
$831$		0			0
$832$	−8.72618	+	16.4145i	−0.302526	+	0.569072i
$833$	2.89733	+	1.47627i	0.100387	+	0.0511496i
$834$		0			0
$835$	1.70641	+	12.4015i	0.0590527	+	0.429171i
$836$	57.4962	−	11.8735i	1.98855	−	0.410654i
$837$		0			0
$838$	35.4032	+	1.95824i	1.22298	+	0.0676463i
$839$	23.4014	−	17.0021i	0.807905	−	0.586977i	−0.105318	−	0.994439i	$-0.533586\pi$
$839$	23.4014	−	17.0021i	0.807905	−	0.586977i	0.913222	+	0.407461i	$0.133586\pi$
$840$		0			0
$841$	−10.1883	−	7.40223i	−0.351320	−	0.255249i
$842$	29.7069	+	24.1990i	1.02377	+	0.833952i
$843$		0			0
$844$	5.27778	−	47.5628i	0.181669	−	1.63718i
$845$	−13.5430	−	10.2668i	−0.465893	−	0.353189i
$846$		0			0
$847$	−5.41583	−	10.6292i	−0.186090	−	0.365223i
$848$	40.7658	−	25.8071i	1.39990	−	0.886220i
$849$		0			0
$850$	1.14410	−	0.450743i	0.0392421	−	0.0154604i
$851$		−	8.18402i		−	0.280544i
$852$		0			0
$853$	−18.8285	−	36.9530i	−0.644675	−	1.26525i	−0.949778	−	0.312926i	$-0.898691\pi$
$853$	−18.8285	−	36.9530i	−0.644675	−	1.26525i	0.305103	−	0.952319i	$-0.401309\pi$
$854$	−24.9946	−	14.5273i	−0.855298	−	0.497115i
$855$		0			0
$856$	2.15604	−	6.44453i	0.0736919	−	0.220269i
$857$	−17.7064	−	17.7064i	−0.604839	−	0.604839i	0.336754	−	0.941593i	$-0.390671\pi$
$857$	−17.7064	−	17.7064i	−0.604839	−	0.604839i	−0.941593	+	0.336754i	$0.890671\pi$
$858$		0			0
$859$	−4.27825	−	3.10833i	−0.145972	−	0.106055i	0.512402	−	0.858745i	$-0.328756\pi$
$859$	−4.27825	−	3.10833i	−0.145972	−	0.106055i	−0.658374	+	0.752691i	$0.728756\pi$
$860$	−5.57649	+	4.27940i	−0.190157	+	0.145926i
$861$		0			0
$862$	1.33013	−	24.0476i	0.0453046	−	0.819066i
$863$	−6.09322	−	38.4711i	−0.207416	−	1.30957i	−0.843156	−	0.537668i	$-0.819305\pi$
$863$	−6.09322	−	38.4711i	−0.207416	−	1.30957i	0.635741	−	0.771903i	$-0.280695\pi$
$864$		0			0
$865$	−22.4851	+	10.8864i	−0.764515	+	0.370150i
$866$	3.72991	−	3.33892i	0.126747	−	0.113461i
$867$		0			0
$868$	−64.7259	+	24.4167i	−2.19694	+	0.828757i
$869$	17.6859	−	5.74650i	0.599954	−	0.194937i
$870$		0			0
$871$	15.9847	+	5.19374i	0.541620	+	0.175983i
$872$	−5.78682	+	34.5887i	−0.195967	+	1.17132i
$873$		0			0
$874$	37.8092	+	8.15112i	1.27892	+	0.275716i
$875$	28.7629	−	48.8367i	0.972362	−	1.65098i
$876$		0			0
$877$	21.9564	+	3.47756i	0.741416	+	0.117429i	0.515706	−	0.856766i	$-0.327530\pi$
$877$	21.9564	+	3.47756i	0.741416	+	0.117429i	0.225710	+	0.974195i	$0.427530\pi$
$878$	−10.1575	−	38.3523i	−0.342799	−	1.29433i
$879$		0			0
$880$	31.7368	+	7.81248i	1.06985	+	0.263359i
$881$	−1.35026	−	4.15569i	−0.0454916	−	0.140009i	0.925731	−	0.378183i	$-0.123451\pi$
$881$	−1.35026	−	4.15569i	−0.0454916	−	0.140009i	−0.971222	+	0.238174i	$0.923451\pi$
$882$		0			0
$883$	−11.2399	+	22.0596i	−0.378254	+	0.742365i	−0.999137	−	0.0415385i	$-0.986774\pi$
$883$	−11.2399	+	22.0596i	−0.378254	+	0.742365i	0.620883	+	0.783903i	$0.286774\pi$
$884$	−0.702261	+	0.400045i	−0.0236196	+	0.0134550i
$885$		0			0
$886$	26.4771	−	11.6966i	0.889517	−	0.392955i
$887$	−23.2179	+	3.67735i	−0.779581	+	0.123473i	−0.533527	−	0.845783i	$-0.679134\pi$
$887$	−23.2179	+	3.67735i	−0.779581	+	0.123473i	−0.246053	+	0.969256i	$0.579134\pi$
$888$		0			0
$889$	−17.6204	−	24.2525i	−0.590971	−	0.813401i
$890$	−1.11435	−	0.946085i	−0.0373530	−	0.0317128i
$891$		0			0
$892$	15.4379	+	19.2916i	0.516898	+	0.645931i
$893$	30.5677	−	30.5677i	1.02291	−	1.02291i
$894$		0			0
$895$	−33.0502	+	10.0002i	−1.10475	+	0.334269i
$896$	−55.8469	−	13.0593i	−1.86571	−	0.436281i
$897$		0			0
$898$	41.5062	+	16.0708i	1.38508	+	0.536290i
$899$	−27.6371			−0.921750
$900$		0			0
$901$	2.09762			0.0698818
$902$	6.22322	+	2.40957i	0.207211	+	0.0802300i
$903$		0			0
$904$	5.90872	−	4.21498i	0.196521	−	0.140188i
$905$	−17.6194	+	23.2417i	−0.585687	+	0.772581i
$906$		0			0
$907$	17.2451	−	17.2451i	0.572613	−	0.572613i	−0.360245	−	0.932858i	$-0.617307\pi$
$907$	17.2451	−	17.2451i	0.572613	−	0.572613i	0.932858	+	0.360245i	$0.117307\pi$
$908$	16.5975	−	13.2820i	0.550809	−	0.440778i
$909$		0			0
$910$	−14.1541	+	34.4575i	−0.469204	+	1.14225i
$911$	−9.09960	−	12.5245i	−0.301483	−	0.414956i	0.631218	−	0.775605i	$-0.282555\pi$
$911$	−9.09960	−	12.5245i	−0.301483	−	0.414956i	−0.932702	+	0.360649i	$0.882555\pi$
$912$		0			0
$913$	37.4986	−	5.93919i	1.24102	−	0.196559i
$914$	−20.9540	+	9.25672i	−0.693098	+	0.306185i
$915$		0			0
$916$	28.2488	+	49.5896i	0.933368	+	1.63849i
$917$	−18.3946	+	36.1014i	−0.607443	+	1.19217i
$918$		0			0
$919$	−1.20487	−	3.70821i	−0.0397450	−	0.122323i	0.929215	−	0.369539i	$-0.120484\pi$
$919$	−1.20487	−	3.70821i	−0.0397450	−	0.122323i	−0.968960	+	0.247216i	$0.920484\pi$
$920$	17.0454	+	13.1568i	0.561971	+	0.433765i
$921$		0			0
$922$	12.1050	+	45.7055i	0.398656	+	1.50523i
$923$	−5.33610	−	0.845155i	−0.175640	−	0.0278186i
$924$		0			0
$925$	11.7849	+	2.36146i	0.387484	+	0.0776444i
$926$	4.66849	+	1.00646i	0.153416	+	0.0330743i
$927$		0			0
$928$	−19.0338	−	12.7563i	−0.624816	−	0.418747i
$929$	−38.5916	−	12.5392i	−1.26615	−	0.411397i	−0.402468	−	0.915434i	$-0.631847\pi$
$929$	−38.5916	−	12.5392i	−1.26615	−	0.411397i	−0.863682	+	0.504037i	$0.831847\pi$
$930$		0			0
$931$	−142.856	+	46.4168i	−4.68193	+	1.52125i
$932$	−9.98595	−	26.4716i	−0.327101	−	0.867106i
$933$		0			0
$934$	−25.3619	+	22.7033i	−0.829866	+	0.742873i
$935$	0.984137	+	1.02501i	0.0321847	+	0.0335214i
$936$		0			0
$937$	0.186494	+	1.17748i	0.00609250	+	0.0384665i	0.990547	−	0.137172i	$-0.0438012\pi$
$937$	0.186494	+	1.17748i	0.00609250	+	0.0384665i	−0.984455	+	0.175638i	$0.943801\pi$
$938$	−2.86379	+	51.7747i	−0.0935060	+	1.69050i
$939$		0			0
$940$	22.6855	−	8.03452i	0.739918	−	0.262057i
$941$	33.0777	+	24.0323i	1.07830	+	0.783432i	0.977386	−	0.211463i	$-0.0678229\pi$
$941$	33.0777	+	24.0323i	1.07830	+	0.783432i	0.100915	+	0.994895i	$0.467823\pi$
$942$		0			0
$943$	3.10877	+	3.10877i	0.101236	+	0.101236i
$944$	21.3161	−	35.9522i	0.693781	−	1.17014i
$945$		0			0
$946$	−7.02272	−	4.08173i	−0.228328	−	0.132709i
$947$	−9.49396	−	18.6329i	−0.308512	−	0.605489i	0.683741	−	0.729725i	$-0.260352\pi$
$947$	−9.49396	−	18.6329i	−0.308512	−	0.605489i	−0.992253	+	0.124236i	$0.960352\pi$
$948$		0			0
$949$		−	7.27488i		−	0.236152i
$950$	−22.6472	+	52.0928i	−0.734772	+	1.69011i
$951$		0			0
$952$	−1.74778	−	1.77842i	−0.0566459	−	0.0576389i
$953$	15.2023	+	29.8361i	0.492450	+	0.966488i	0.994802	+	0.101825i	$0.0324680\pi$
$953$	15.2023	+	29.8361i	0.492450	+	0.966488i	−0.502352	+	0.864663i	$0.667532\pi$
$954$		0			0
$955$	−13.5579	−	0.275821i	−0.438722	−	0.00892535i
$956$	−27.2950	−	3.02878i	−0.882784	−	0.0979577i
$957$		0			0
$958$	1.72918	+	1.40858i	0.0558674	+	0.0455091i
$959$	35.1946	+	25.5704i	1.13649	+	0.825711i
$960$		0			0
$961$	12.5844	−	9.14311i	0.405949	−	0.294939i
$962$	−7.88753	−	0.436279i	−0.254304	−	0.0140662i
$963$		0			0
$964$	5.69339	+	27.5696i	0.183372	+	0.887958i
$965$	−48.2979	−	8.66011i	−1.55476	−	0.278779i
$966$		0			0
$967$	42.1959	+	21.4999i	1.35693	+	0.691390i	0.972747	−	0.231868i	$-0.0744838\pi$
$967$	42.1959	+	21.4999i	1.35693	+	0.691390i	0.384181	+	0.923258i	$0.374484\pi$
$968$	0.984057	+	6.58278i	0.0316288	+	0.211579i
$969$		0			0
$970$	21.4937	−	18.4670i	0.690121	−	0.592940i
$971$	−2.37842	−	0.772795i	−0.0763271	−	0.0248002i	0.270605	−	0.962691i	$-0.412776\pi$
$971$	−2.37842	−	0.772795i	−0.0763271	−	0.0248002i	−0.346932	+	0.937890i	$0.612776\pi$
$972$		0			0
$973$	5.89039	−	37.1904i	0.188837	−	1.19227i
$974$	−3.06433	+	14.2140i	−0.0981875	+	0.455446i
$975$		0			0
$976$	10.6535	+	12.1112i	0.341010	+	0.387669i
$977$	30.5830	+	4.84387i	0.978436	+	0.154969i	0.625114	−	0.780533i	$-0.285052\pi$
$977$	30.5830	+	4.84387i	0.978436	+	0.154969i	0.353321	+	0.935502i	$0.385052\pi$
$978$		0			0
$979$	0.521990	−	1.60652i	0.0166829	−	0.0513446i
$980$	−82.9078	−	10.9111i	−2.64839	−	0.348543i
$981$		0			0
$982$	22.9618	+	35.5832i	0.732739	+	1.13551i
$983$	−13.7947	+	27.0737i	−0.439983	+	0.863516i	0.559417	+	0.828887i	$0.311025\pi$
$983$	−13.7947	+	27.0737i	−0.439983	+	0.863516i	−0.999400	+	0.0346297i	$0.988975\pi$
$984$		0			0
$985$	11.9452	+	6.39568i	0.380605	+	0.203783i
$986$	−0.402541	−	0.911215i	−0.0128195	−	0.0290190i
$987$		0			0
$988$	9.87139	−	36.0050i	0.314051	−	1.14547i
$989$	−3.14541	−	4.32928i	−0.100018	−	0.137663i
$990$		0			0
$991$	2.41083	−	3.31822i	0.0765826	−	0.105407i	−0.769007	−	0.639240i	$-0.779249\pi$
$991$	2.41083	−	3.31822i	0.0765826	−	0.105407i	0.845590	+	0.533833i	$0.179249\pi$
$992$	38.5698	−	1.46166i	1.22459	−	0.0464077i
$993$		0			0
$994$	−1.69428	−	16.5818i	−0.0537392	−	0.525943i
$995$	−10.8646	−	15.6120i	−0.344430	−	0.494932i
$996$		0			0
$997$	−22.2908	+	11.3577i	−0.705957	+	0.359703i	−0.769825	−	0.638255i	$-0.779656\pi$
$997$	−22.2908	+	11.3577i	−0.705957	+	0.359703i	0.0638675	+	0.997958i	$0.479656\pi$
$998$	−6.04978	+	15.6248i	−0.191502	+	0.494594i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.f.127.11		240
3.2	odd	2		300.2.w.a.127.20	yes	240
4.3	odd	2	inner	900.2.bj.f.127.15		240
12.11	even	2		300.2.w.a.127.16	✓	240
25.13	odd	20	inner	900.2.bj.f.163.15		240
75.38	even	20		300.2.w.a.163.16	yes	240
100.63	even	20	inner	900.2.bj.f.163.11		240
300.263	odd	20		300.2.w.a.163.20	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.16	✓	240	12.11	even	2
300.2.w.a.127.20	yes	240	3.2	odd	2
300.2.w.a.163.16	yes	240	75.38	even	20
300.2.w.a.163.20	yes	240	300.263	odd	20
900.2.bj.f.127.11		240	1.1	even	1	trivial
900.2.bj.f.127.15		240	4.3	odd	2	inner
900.2.bj.f.163.11		240	100.63	even	20	inner
900.2.bj.f.163.15		240	25.13	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.510631 + 1.31881i) q^{2} +(-1.47851 - 1.34685i) q^{4} +(1.27726 + 1.83538i) q^{5} +(-3.58459 + 3.58459i) q^{7} +(2.53121 - 1.26213i) q^{8} +O(q^{10})\)	\(q+(-0.510631 + 1.31881i) q^{2} +(-1.47851 - 1.34685i) q^{4} +(1.27726 + 1.83538i) q^{5} +(-3.58459 + 3.58459i) q^{7} +(2.53121 - 1.26213i) q^{8} +(-3.07272 + 0.747264i) q^{10} +(-2.14789 - 2.95632i) q^{11} +(-2.29513 + 0.363512i) q^{13} +(-2.89699 - 6.55779i) q^{14} +(0.372000 + 3.98266i) q^{16} +(-0.0789506 + 0.154949i) q^{17} +(-2.48237 - 7.63995i) q^{19} +(0.583526 - 4.43390i) q^{20} +(4.99559 - 1.32307i) q^{22} +(3.36266 + 0.532593i) q^{23} +(-1.73721 + 4.68851i) q^{25} +(0.692558 - 3.21245i) q^{26} +(10.1278 - 0.471963i) q^{28} +(3.85226 + 1.25167i) q^{29} +(-6.48919 + 2.10846i) q^{31} +(-5.44233 - 1.54307i) q^{32} +(-0.164034 - 0.183243i) q^{34} +(-11.1575 - 2.00061i) q^{35} +(-0.376041 - 2.37423i) q^{37} +(11.3432 + 0.627421i) q^{38} +(5.54950 + 3.03365i) q^{40} +(1.04472 + 0.759030i) q^{41} +(-1.11142 - 1.11142i) q^{43} +(-0.806027 + 7.26383i) q^{44} +(-2.41947 + 4.16275i) q^{46} +(2.44309 + 4.79484i) q^{47} -18.6986i q^{49} +(-5.29617 - 4.68514i) q^{50} +(3.88297 + 2.55373i) q^{52} +(-5.47602 - 10.7473i) q^{53} +(2.68254 - 7.71817i) q^{55} +(-4.54912 + 13.5976i) q^{56} +(-3.61780 + 4.44125i) q^{58} +(-8.45350 - 6.14182i) q^{59} +(3.26236 - 2.37025i) q^{61} +(0.532916 - 9.63464i) q^{62} +(4.81404 - 6.38945i) q^{64} +(-3.59866 - 3.74812i) q^{65} +(-6.44454 - 3.28366i) q^{67} +(0.325423 - 0.122760i) q^{68} +(8.33581 - 13.6931i) q^{70} +(2.21118 + 0.718455i) q^{71} +(-0.489747 + 3.09214i) q^{73} +(3.32318 + 0.716429i) q^{74} +(-6.61964 + 14.6391i) q^{76} +(18.2965 + 2.89788i) q^{77} +(-1.57257 + 4.83988i) q^{79} +(-6.83455 + 5.76966i) q^{80} +(-1.53448 + 0.990196i) q^{82} +(-4.71681 + 9.25727i) q^{83} +(-0.385231 + 0.0530066i) q^{85} +(2.03328 - 0.898229i) q^{86} +(-9.16802 - 4.77213i) q^{88} +(0.271710 + 0.373976i) q^{89} +(6.92404 - 9.53013i) q^{91} +(-4.25442 - 5.31644i) q^{92} +(-7.57099 + 0.773580i) q^{94} +(10.8515 - 14.3143i) q^{95} +(-7.98438 + 4.06824i) q^{97} +(24.6599 + 9.54808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8}+O(q^{10}) \) 240 * q - 12 * q^8	\( 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) \) 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

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