LMFDB - Embedded newform 990.2.ba.h.829.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [990,2,Mod(289,990)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(990, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 8]))

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

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

chi := DirichletCharacter("990.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.ba (of order $10$, degree $4$, 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:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} + 10 x^{13} - 109 x^{12} + 280 x^{11} - 198 x^{10} - 1168 x^{9} + \cdots + 390625 $ x^16 - 4x^15 + 8x^14 + 10x^13 - 109x^12 + 280x^11 - 198x^10 - 1168x^9 + 4281x^8 - 5840x^7 - 4950x^6 + 35000x^5 - 68125x^4 + 31250x^3 + 125000x^2 - 312500*x + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			829.3
Root			$-2.23122 - 0.147217i$ of defining polynomial
Character	$\chi$	$=$	990.829
Dual form			990.2.ba.h.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(0.829496 + 2.07652i) q^{5} +(4.76878 - 1.54947i) q^{7} +(-0.951057 - 0.309017i) q^{8} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(0.829496 + 2.07652i) q^{5} +(4.76878 - 1.54947i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(2.16751 + 0.549472i) q^{10} +(0.969425 + 3.17178i) q^{11} +(-1.37249 + 1.88906i) q^{13} +(1.54947 - 4.76878i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.0359433 + 0.0494717i) q^{17} +(0.636930 - 1.96027i) q^{19} +(1.71856 - 1.43058i) q^{20} +(3.13584 + 1.08005i) q^{22} +3.91525i q^{23} +(-3.62387 + 3.44493i) q^{25} +(0.721558 + 2.22073i) q^{26} +(-2.94727 - 4.05657i) q^{28} +(-1.27844 - 3.93464i) q^{29} +(7.18170 + 5.21781i) q^{31} +1.00000i q^{32} +0.0611504 q^{34} +(7.17320 + 8.61720i) q^{35} +(-4.33385 + 1.40815i) q^{37} +(-1.21151 - 1.66751i) q^{38} +(-0.147217 - 2.23122i) q^{40} +(1.41525 - 4.35570i) q^{41} -3.61803i q^{43} +(2.71698 - 1.90211i) q^{44} +(3.16751 + 2.30133i) q^{46} +(-8.44260 - 2.74317i) q^{47} +(14.6773 - 10.6637i) q^{49} +(0.656948 + 4.95665i) q^{50} +(2.22073 + 0.721558i) q^{52} +(1.30598 - 1.79753i) q^{53} +(-5.78214 + 4.64401i) q^{55} -5.01420 q^{56} +(-3.93464 - 1.27844i) q^{58} +(0.599137 + 1.84396i) q^{59} +(7.84211 - 5.69763i) q^{61} +(8.44260 - 2.74317i) q^{62} +(0.809017 + 0.587785i) q^{64} +(-5.06115 - 1.28302i) q^{65} +2.49573i q^{67} +(0.0359433 - 0.0494717i) q^{68} +(11.1878 - 0.738177i) q^{70} +(7.13254 - 5.18210i) q^{71} +(5.13205 - 1.66751i) q^{73} +(-1.40815 + 4.33385i) q^{74} -2.06115 q^{76} +(9.53757 + 13.6235i) q^{77} +(-5.38417 - 3.91183i) q^{79} +(-1.89162 - 1.19237i) q^{80} +(-2.69197 - 3.70518i) q^{82} +(-6.49620 - 8.94125i) q^{83} +(-0.0729142 + 0.115674i) q^{85} +(-2.92705 - 2.12663i) q^{86} +(0.0581575 - 3.31611i) q^{88} +6.09017 q^{89} +(-3.61803 + 11.1352i) q^{91} +(3.72363 - 1.20988i) q^{92} +(-7.18170 + 5.21781i) q^{94} +(4.59887 - 0.303437i) q^{95} +(-4.29216 + 5.90765i) q^{97} -18.1422i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 6 q^{5}+O(q^{10}) $ 16 * q + 4 * q^4 + 6 * q^5	$ 16 q + 4 q^{4} + 6 q^{5} + 4 q^{10} + 20 q^{11} + 12 q^{14} - 4 q^{16} - 16 q^{19} - 6 q^{20} + 16 q^{26} - 16 q^{29} - 4 q^{31} - 8 q^{34} + 48 q^{35} - 4 q^{40} - 40 q^{41} + 20 q^{46} + 84 q^{49} - 4 q^{50} + 32 q^{55} + 8 q^{56} + 20 q^{61} + 4 q^{64} - 72 q^{65} + 36 q^{70} + 56 q^{71} - 4 q^{74} - 24 q^{76} + 36 q^{79} - 4 q^{80} - 54 q^{85} - 20 q^{86} + 8 q^{89} - 40 q^{91} + 4 q^{94} + 50 q^{95}+O(q^{100}) $ 16 * q + 4 * q^4 + 6 * q^5 + 4 * q^10 + 20 * q^11 + 12 * q^14 - 4 * q^16 - 16 * q^19 - 6 * q^20 + 16 * q^26 - 16 * q^29 - 4 * q^31 - 8 * q^34 + 48 * q^35 - 4 * q^40 - 40 * q^41 + 20 * q^46 + 84 * q^49 - 4 * q^50 + 32 * q^55 + 8 * q^56 + 20 * q^61 + 4 * q^64 - 72 * q^65 + 36 * q^70 + 56 * q^71 - 4 * q^74 - 24 * q^76 + 36 * q^79 - 4 * q^80 - 54 * q^85 - 20 * q^86 + 8 * q^89 - 40 * q^91 + 4 * q^94 + 50 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$		0			0
$3$		0			0
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	0.829496	+	2.07652i	0.370962	+	0.928648i
$5$	0.829496	+	2.07652i	0.370962	+	0.928648i
$6$		0			0
$7$	4.76878	−	1.54947i	1.80243	−	0.585645i	0.802491	−	0.596664i	$-0.203507\pi$
$7$	4.76878	−	1.54947i	1.80243	−	0.585645i	0.999939	+	0.0110184i	$0.00350733\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$		0			0
$10$	2.16751	+	0.549472i	0.685425	+	0.173758i
$11$	0.969425	+	3.17178i	0.292293	+	0.956329i
$11$	0.969425	+	3.17178i	0.292293	+	0.956329i
$12$		0			0
$13$	−1.37249	+	1.88906i	−0.380659	+	0.523932i	−0.955759	−	0.294151i	$-0.904963\pi$
$13$	−1.37249	+	1.88906i	−0.380659	+	0.523932i	0.575100	+	0.818083i	$0.304963\pi$
$14$	1.54947	−	4.76878i	0.414114	−	1.27451i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.0359433	+	0.0494717i	0.00871753	+	0.0119986i	0.813354	−	0.581770i	$-0.197640\pi$
$17$	0.0359433	+	0.0494717i	0.00871753	+	0.0119986i	−0.804636	+	0.593768i	$0.797640\pi$
$18$		0			0
$19$	0.636930	−	1.96027i	0.146122	−	0.449717i	−0.851032	−	0.525114i	$-0.824023\pi$
$19$	0.636930	−	1.96027i	0.146122	−	0.449717i	0.997154	+	0.0753974i	$0.0240226\pi$
$20$	1.71856	−	1.43058i	0.384282	−	0.319887i
$21$		0			0
$22$	3.13584	+	1.08005i	0.668564	+	0.230267i
$23$			3.91525i			0.816387i	0.912896	+	0.408193i	$0.133841\pi$
$23$			3.91525i			0.816387i	−0.912896	+	0.408193i	$0.866159\pi$
$24$		0			0
$25$	−3.62387	+	3.44493i	−0.724775	+	0.688986i
$26$	0.721558	+	2.22073i	0.141509	+	0.435521i
$27$		0			0
$28$	−2.94727	−	4.05657i	−0.556982	−	0.766620i
$29$	−1.27844	−	3.93464i	−0.237401	−	0.730644i	−0.996794	−	0.0800122i	$-0.974504\pi$
$29$	−1.27844	−	3.93464i	−0.237401	−	0.730644i	0.759393	−	0.650632i	$-0.225496\pi$
$30$		0			0
$31$	7.18170	+	5.21781i	1.28987	+	0.937147i	0.999803	−	0.0198592i	$-0.00632179\pi$
$31$	7.18170	+	5.21781i	1.28987	+	0.937147i	0.290069	+	0.957006i	$0.406322\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	0.0611504			0.0104872
$35$	7.17320	+	8.61720i	1.21249	+	1.45657i
$36$		0			0
$37$	−4.33385	+	1.40815i	−0.712481	+	0.231499i	−0.642760	−	0.766067i	$-0.722211\pi$
$37$	−4.33385	+	1.40815i	−0.712481	+	0.231499i	−0.0697209	+	0.997567i	$0.522211\pi$
$38$	−1.21151	−	1.66751i	−0.196533	−	0.270505i
$39$		0			0
$40$	−0.147217	−	2.23122i	−0.0232771	−	0.352786i
$41$	1.41525	−	4.35570i	0.221025	−	0.680246i	−0.777646	−	0.628703i	$-0.783586\pi$
$41$	1.41525	−	4.35570i	0.221025	−	0.680246i	0.998671	−	0.0515429i	$-0.0164139\pi$
$42$		0			0
$43$		−	3.61803i		−	0.551745i	−0.961194	−	0.275873i	$-0.911033\pi$
$43$		−	3.61803i		−	0.551745i	0.961194	−	0.275873i	$-0.0889668\pi$
$44$	2.71698	−	1.90211i	0.409600	−	0.286754i
$45$		0			0
$46$	3.16751	+	2.30133i	0.467023	+	0.339312i
$47$	−8.44260	−	2.74317i	−1.23148	−	0.400132i	−0.380229	−	0.924892i	$-0.624155\pi$
$47$	−8.44260	−	2.74317i	−1.23148	−	0.400132i	−0.851250	+	0.524760i	$0.824155\pi$
$48$		0			0
$49$	14.6773	−	10.6637i	2.09676	−	1.52338i
$50$	0.656948	+	4.95665i	0.0929065	+	0.700977i
$51$		0			0
$52$	2.22073	+	0.721558i	0.307960	+	0.100062i
$53$	1.30598	−	1.79753i	0.179391	−	0.246910i	−0.709847	−	0.704356i	$-0.751236\pi$
$53$	1.30598	−	1.79753i	0.179391	−	0.246910i	0.889237	+	0.457446i	$0.151236\pi$
$54$		0			0
$55$	−5.78214	+	4.64401i	−0.779664	+	0.626199i
$56$	−5.01420			−0.670050
$57$		0			0
$58$	−3.93464	−	1.27844i	−0.516643	−	0.167868i
$59$	0.599137	+	1.84396i	0.0780011	+	0.240063i	0.982452	−	0.186515i	$-0.0597192\pi$
$59$	0.599137	+	1.84396i	0.0780011	+	0.240063i	−0.904451	+	0.426577i	$0.859719\pi$
$60$		0			0
$61$	7.84211	−	5.69763i	1.00408	−	0.729506i	0.0411202	−	0.999154i	$-0.486907\pi$
$61$	7.84211	−	5.69763i	1.00408	−	0.729506i	0.962959	+	0.269648i	$0.0869073\pi$
$62$	8.44260	−	2.74317i	1.07221	−	0.348382i
$63$		0			0
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−5.06115	−	1.28302i	−0.627758	−	0.159139i
$66$		0			0
$67$			2.49573i			0.304902i	0.988311	+	0.152451i	$0.0487167\pi$
$67$			2.49573i			0.304902i	−0.988311	+	0.152451i	$0.951283\pi$
$68$	0.0359433	−	0.0494717i	0.00435876	−	0.00599932i
$69$		0			0
$70$	11.1878	−	0.738177i	1.33719	−	0.0882290i
$71$	7.13254	−	5.18210i	0.846477	−	0.615002i	−0.0776953	−	0.996977i	$-0.524756\pi$
$71$	7.13254	−	5.18210i	0.846477	−	0.615002i	0.924172	+	0.381975i	$0.124756\pi$
$72$		0			0
$73$	5.13205	−	1.66751i	0.600662	−	0.195167i	0.00712611	−	0.999975i	$-0.497732\pi$
$73$	5.13205	−	1.66751i	0.600662	−	0.195167i	0.593535	+	0.804808i	$0.297732\pi$
$74$	−1.40815	+	4.33385i	−0.163695	+	0.503800i
$75$		0			0
$76$	−2.06115			−0.236430
$77$	9.53757	+	13.6235i	1.08691	+	1.55254i
$78$		0			0
$79$	−5.38417	−	3.91183i	−0.605766	−	0.440115i	0.242155	−	0.970238i	$-0.422146\pi$
$79$	−5.38417	−	3.91183i	−0.605766	−	0.440115i	−0.847921	+	0.530123i	$0.822146\pi$
$80$	−1.89162	−	1.19237i	−0.211490	−	0.133312i
$81$		0			0
$82$	−2.69197	−	3.70518i	−0.297278	−	0.409169i
$83$	−6.49620	−	8.94125i	−0.713050	−	0.981429i	−0.999726	−	0.0234017i	$-0.992550\pi$
$83$	−6.49620	−	8.94125i	−0.713050	−	0.981429i	0.286676	−	0.958028i	$-0.407450\pi$
$84$		0			0
$85$	−0.0729142	+	0.115674i	−0.00790865	+	0.0125466i
$86$	−2.92705	−	2.12663i	−0.315632	−	0.229320i
$87$		0			0
$88$	0.0581575	−	3.31611i	0.00619961	−	0.353499i
$89$	6.09017			0.645557			0.322778	−	0.946475i	$-0.395383\pi$
$89$	6.09017			0.645557			0.322778	+	0.946475i	$0.395383\pi$
$90$		0			0
$91$	−3.61803	+	11.1352i	−0.379273	+	1.16728i
$92$	3.72363	−	1.20988i	0.388215	−	0.126139i
$93$		0			0
$94$	−7.18170	+	5.21781i	−0.740736	+	0.538176i
$95$	4.59887	−	0.303437i	0.471834	−	0.0311320i
$96$		0			0
$97$	−4.29216	+	5.90765i	−0.435802	+	0.599831i	−0.969273	−	0.245988i	$-0.920888\pi$
$97$	−4.29216	+	5.90765i	−0.435802	+	0.599831i	0.533470	+	0.845819i	$0.320888\pi$
$98$		−	18.1422i		−	1.83263i
$99$		0			0
$100$	4.39616	+	2.38197i	0.439616	+	0.238197i
$101$	−0.179498	−	0.130413i	−0.0178608	−	0.0129766i	0.578819	−	0.815456i	$-0.303514\pi$
$101$	−0.179498	−	0.130413i	−0.0178608	−	0.0129766i	−0.596680	+	0.802479i	$0.703514\pi$
$102$		0			0
$103$	0.538341	−	0.174918i	0.0530443	−	0.0172351i	−0.282375	−	0.959304i	$-0.591122\pi$
$103$	0.538341	−	0.174918i	0.0530443	−	0.0172351i	0.335419	+	0.942069i	$0.391122\pi$
$104$	1.88906	−	1.37249i	0.185238	−	0.134583i
$105$		0			0
$106$	−0.686596	−	2.11313i	−0.0666881	−	0.205245i
$107$	2.12087	+	0.689113i	0.205033	+	0.0666191i	0.409733	−	0.912206i	$-0.365622\pi$
$107$	2.12087	+	0.689113i	0.205033	+	0.0666191i	−0.204700	+	0.978825i	$0.565622\pi$
$108$		0			0
$109$	−7.86288			−0.753127			−0.376563	−	0.926391i	$-0.622894\pi$
$109$	−7.86288			−0.753127			−0.376563	+	0.926391i	$0.622894\pi$
$110$	0.358428	+	7.40753i	0.0341748	+	0.706280i
$111$		0			0
$112$	−2.94727	+	4.05657i	−0.278491	+	0.383310i
$113$	−11.9469	−	3.88177i	−1.12387	−	0.365166i	−0.312624	−	0.949877i	$-0.601208\pi$
$113$	−11.9469	−	3.88177i	−1.12387	−	0.365166i	−0.811242	+	0.584710i	$0.801208\pi$
$114$		0			0
$115$	−8.13010	+	3.24769i	−0.758136	+	0.302848i
$116$	−3.34700	+	2.43174i	−0.310762	+	0.225781i
$117$		0			0
$118$	1.84396	+	0.599137i	0.169750	+	0.0551551i
$119$	0.248061	+	0.180227i	0.0227397	+	0.0165214i
$120$		0			0
$121$	−9.12043	+	6.14961i	−0.829130	+	0.559056i
$122$		−	9.69338i		−	0.877597i
$123$		0			0
$124$	2.74317	−	8.44260i	0.246344	−	0.758168i
$125$	−10.1595	−	4.66749i	−0.908689	−	0.417473i
$126$		0			0
$127$	−8.50112	−	11.7008i	−0.754353	−	1.03828i	−0.997663	−	0.0683289i	$-0.978233\pi$
$127$	−8.50112	−	11.7008i	−0.754353	−	1.03828i	0.243310	−	0.969949i	$-0.421767\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$		0			0
$130$	−4.01286	+	3.34041i	−0.351951	+	0.292974i
$131$	−15.3256			−1.33900			−0.669502	−	0.742810i	$-0.733493\pi$
$131$	−15.3256			−1.33900			−0.669502	+	0.742810i	$0.733493\pi$
$132$		0			0
$133$		−	10.3350i		−	0.896159i
$134$	2.01909	+	1.46696i	0.174423	+	0.126726i
$135$		0			0
$136$	−0.0188965	−	0.0581575i	−0.00162036	−	0.00498696i
$137$	−0.649130	−	0.893451i	−0.0554589	−	0.0763326i	0.780387	−	0.625297i	$-0.215022\pi$
$137$	−0.649130	−	0.893451i	−0.0554589	−	0.0763326i	−0.835846	+	0.548964i	$0.815022\pi$
$138$		0			0
$139$	3.06115	+	9.42125i	0.259643	+	0.799100i	0.992879	+	0.119126i	$0.0380092\pi$
$139$	3.06115	+	9.42125i	0.259643	+	0.799100i	−0.733236	+	0.679974i	$0.761991\pi$
$140$	5.97880	−	9.48497i	0.505301	−	0.801627i
$141$		0			0
$142$		−	8.81631i		−	0.739848i
$143$	−7.32222	−	2.52192i	−0.612315	−	0.210894i
$144$		0			0
$145$	7.10990	−	5.91848i	0.590445	−	0.491503i
$146$	1.66751	−	5.13205i	0.138004	−	0.424732i
$147$		0			0
$148$	2.67847	+	3.68660i	0.220169	+	0.303036i
$149$	−7.11314	+	5.16800i	−0.582731	+	0.423379i	−0.839708	−	0.543039i	$-0.817274\pi$
$149$	−7.11314	+	5.16800i	−0.582731	+	0.423379i	0.256977	+	0.966418i	$0.417274\pi$
$150$		0			0
$151$	6.67177	−	20.5336i	0.542941	−	1.67100i	−0.182894	−	0.983133i	$-0.558547\pi$
$151$	6.67177	−	20.5336i	0.542941	−	1.67100i	0.725835	−	0.687868i	$-0.241453\pi$
$152$	−1.21151	+	1.66751i	−0.0982667	+	0.135253i
$153$		0			0
$154$	16.6276	+	0.291613i	1.33989	+	0.0234988i
$155$	−4.87770	+	19.2411i	−0.391786	+	1.54548i
$156$		0			0
$157$	3.24760	+	1.05521i	0.259186	+	0.0842148i	0.435728	−	0.900078i	$-0.356491\pi$
$157$	3.24760	+	1.05521i	0.259186	+	0.0842148i	−0.176542	+	0.984293i	$0.556491\pi$
$158$	−6.32947	+	2.05657i	−0.503546	+	0.163612i
$159$		0			0
$160$	−2.07652	+	0.829496i	−0.164163	+	0.0655774i
$161$	6.06657	+	18.6710i	0.478113	+	1.47148i
$162$		0			0
$163$	−10.2336	+	14.0853i	−0.801554	+	1.10324i	0.191019	+	0.981586i	$0.438821\pi$
$163$	−10.2336	+	14.0853i	−0.801554	+	1.10324i	−0.992572	+	0.121657i	$0.961179\pi$
$164$	−4.57985			−0.357626
$165$		0			0
$166$	−11.0520			−0.857801
$167$	−1.94321	+	2.67460i	−0.150370	+	0.206967i	−0.877556	−	0.479473i	$-0.840828\pi$
$167$	−1.94321	+	2.67460i	−0.150370	+	0.206967i	0.727186	+	0.686440i	$0.240828\pi$
$168$		0			0
$169$	2.33237	+	7.17831i	0.179413	+	0.552178i
$170$	0.0507240	+	0.126980i	0.00389035	+	0.00973892i
$171$		0			0
$172$	−3.44095	+	1.11803i	−0.262370	+	0.0852493i
$173$	4.87758	+	1.58482i	0.370836	+	0.120492i	0.488505	−	0.872561i	$-0.337542\pi$
$173$	4.87758	+	1.58482i	0.370836	+	0.120492i	−0.117670	+	0.993053i	$0.537542\pi$
$174$		0			0
$175$	−11.9436	+	22.0432i	−0.902855	+	1.66631i
$176$	−2.64861	−	1.99621i	−0.199646	−	0.150470i
$177$		0			0
$178$	3.57971	−	4.92705i	0.268311	−	0.369298i
$179$	−4.46201	+	13.7327i	−0.333507	+	1.02643i	0.633947	+	0.773377i	$0.281434\pi$
$179$	−4.46201	+	13.7327i	−0.333507	+	1.02643i	−0.967453	+	0.253051i	$0.918566\pi$
$180$		0			0
$181$	−9.63223	+	6.99822i	−0.715958	+	0.520174i	−0.885090	−	0.465419i	$-0.845903\pi$
$181$	−9.63223	+	6.99822i	−0.715958	+	0.520174i	0.169132	+	0.985593i	$0.445903\pi$
$182$	6.88191	+	9.47214i	0.510121	+	0.702121i
$183$		0			0
$184$	1.20988	−	3.72363i	0.0891935	−	0.274509i
$185$	−6.51898	−	7.83128i	−0.479285	−	0.575767i
$186$		0			0
$187$	−0.122069	+	0.161963i	−0.00892658	+	0.0118439i
$188$			8.87707i			0.647427i
$189$		0			0
$190$	2.45766	−	3.89892i	0.178298	−	0.282858i
$191$	−3.25026	−	10.0033i	−0.235181	−	0.723812i	−0.997097	−	0.0761369i	$-0.975741\pi$
$191$	−3.25026	−	10.0033i	−0.235181	−	0.723812i	0.761917	−	0.647675i	$-0.224259\pi$
$192$		0			0
$193$	2.86174	+	3.93885i	0.205993	+	0.283525i	0.899496	−	0.436929i	$-0.143934\pi$
$193$	2.86174	+	3.93885i	0.205993	+	0.283525i	−0.693503	+	0.720453i	$0.743934\pi$
$194$	2.25652	+	6.94485i	0.162009	+	0.498612i
$195$		0			0
$196$	−14.6773	−	10.6637i	−1.04838	−	0.761692i
$197$			15.9760i			1.13824i	0.822253	+	0.569122i	$0.192717\pi$
$197$			15.9760i			1.13824i	−0.822253	+	0.569122i	$0.807283\pi$
$198$		0			0
$199$	−16.7076			−1.18437			−0.592184	−	0.805803i	$-0.701734\pi$
$199$	−16.7076			−1.18437			−0.592184	+	0.805803i	$0.701734\pi$
$200$	4.51105	−	2.15649i	0.318979	−	0.152487i
$201$		0			0
$202$	−0.211013	+	0.0685623i	−0.0148468	+	0.00482403i
$203$	−12.1932	−	16.7825i	−0.855797	−	1.17790i
$204$		0			0
$205$	10.2186	−	0.674234i	0.713701	−	0.0470906i
$206$	0.174918	−	0.538341i	0.0121871	−	0.0375080i
$207$		0			0
$208$		−	2.33501i		−	0.161904i
$209$	6.83501	+	0.119871i	0.472788	+	0.00829167i
$210$		0			0
$211$	12.7388	+	9.25526i	0.876974	+	0.637159i	0.932449	−	0.361301i	$-0.117667\pi$
$211$	12.7388	+	9.25526i	0.876974	+	0.637159i	−0.0554754	+	0.998460i	$0.517667\pi$
$212$	−2.11313	−	0.686596i	−0.145130	−	0.0471556i
$213$		0			0
$214$	1.80412	−	1.31077i	0.123327	−	0.0896025i
$215$	7.51292	−	3.00114i	0.512377	−	0.204676i
$216$		0			0
$217$	42.3328	+	13.7548i	2.87374	+	0.933735i
$218$	−4.62168	+	6.36120i	−0.313020	+	0.430835i
$219$		0			0
$220$	6.20350	+	4.06406i	0.418240	+	0.273999i
$221$	−0.142787			−0.00960488
$222$		0			0
$223$	−13.8432	−	4.49794i	−0.927011	−	0.301204i	−0.193671	−	0.981067i	$-0.562039\pi$
$223$	−13.8432	−	4.49794i	−0.927011	−	0.301204i	−0.733340	+	0.679862i	$0.762039\pi$
$224$	1.54947	+	4.76878i	0.103528	+	0.318628i
$225$		0			0
$226$	−10.1626	+	7.38357i	−0.676007	+	0.491148i
$227$	−9.35512	+	3.03966i	−0.620921	+	0.201749i	−0.602549	−	0.798082i	$-0.705848\pi$
$227$	−9.35512	+	3.03966i	−0.620921	+	0.201749i	−0.0183719	+	0.999831i	$0.505848\pi$
$228$		0			0
$229$	−12.5785	−	9.13881i	−0.831210	−	0.603909i	0.0886913	−	0.996059i	$-0.471732\pi$
$229$	−12.5785	−	9.13881i	−0.831210	−	0.603909i	−0.919901	+	0.392150i	$0.871732\pi$
$230$	−2.15132	+	8.48633i	−0.141854	+	0.559572i
$231$		0			0
$232$			4.13712i			0.271616i
$233$	15.2217	−	20.9509i	0.997206	−	1.37254i	0.0701824	−	0.997534i	$-0.477642\pi$
$233$	15.2217	−	20.9509i	0.997206	−	1.37254i	0.927024	−	0.375002i	$-0.122358\pi$
$234$		0			0
$235$	−1.30686	−	19.8067i	−0.0852501	−	1.29204i
$236$	1.56856	−	1.13963i	0.102105	−	0.0741834i
$237$		0			0
$238$	0.291613	−	0.0947508i	0.0189025	−	0.00614178i
$239$	6.17911	−	19.0173i	0.399693	−	1.23013i	−0.525552	−	0.850761i	$-0.676141\pi$
$239$	6.17911	−	19.0173i	0.399693	−	1.23013i	0.925246	−	0.379369i	$-0.123859\pi$
$240$		0			0
$241$	9.01381			0.580630			0.290315	−	0.956931i	$-0.406240\pi$
$241$	9.01381			0.580630			0.290315	+	0.956931i	$0.406240\pi$
$242$	−0.385714	+	10.9932i	−0.0247946	+	0.706672i
$243$		0			0
$244$	−7.84211	−	5.69763i	−0.502040	−	0.364753i
$245$	34.3181	+	21.6323i	2.19251	+	1.38203i
$246$		0			0
$247$	2.82890	+	3.89364i	0.179998	+	0.247747i
$248$	−5.21781	−	7.18170i	−0.331331	−	0.456038i
$249$		0			0
$250$	−9.74766	+	5.47569i	−0.616496	+	0.346313i
$251$	1.06115	+	0.770971i	0.0669792	+	0.0486632i	0.620771	−	0.783992i	$-0.286820\pi$
$251$	1.06115	+	0.770971i	0.0669792	+	0.0486632i	−0.553792	+	0.832655i	$0.686820\pi$
$252$		0			0
$253$	−12.4183	+	3.79554i	−0.780734	+	0.238624i
$254$	−14.4630			−0.907488
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	4.24551	−	1.37945i	0.264827	−	0.0860477i	−0.173594	−	0.984817i	$-0.555538\pi$
$257$	4.24551	−	1.37945i	0.264827	−	0.0860477i	0.438421	+	0.898770i	$0.355538\pi$
$258$		0			0
$259$	−18.4853	+	13.4304i	−1.14862	+	0.834522i
$260$	0.343754	+	5.20992i	0.0213187	+	0.323105i
$261$		0			0
$262$	−9.00817	+	12.3987i	−0.556526	+	0.765993i
$263$			14.1791i			0.874320i	0.899384	+	0.437160i	$0.144016\pi$
$263$			14.1791i			0.874320i	−0.899384	+	0.437160i	$0.855984\pi$
$264$		0			0
$265$	4.81592	+	1.22086i	0.295840	+	0.0749966i
$266$	−8.36120	−	6.07477i	−0.512658	−	0.372468i
$267$		0			0
$268$	2.37358	−	0.771224i	0.144990	−	0.0471100i
$269$	25.8847	−	18.8063i	1.57822	−	1.14664i	0.659516	−	0.751691i	$-0.270761\pi$
$269$	25.8847	−	18.8063i	1.57822	−	1.14664i	0.918702	−	0.394952i	$-0.129239\pi$
$270$		0			0
$271$	0.327988	+	1.00944i	0.0199238	+	0.0613192i	0.960524	−	0.278197i	$-0.0897367\pi$
$271$	0.327988	+	1.00944i	0.0199238	+	0.0613192i	−0.940600	+	0.339516i	$0.889737\pi$
$272$	−0.0581575	−	0.0188965i	−0.00352631	−	0.00114577i
$273$		0			0
$274$	−1.10437			−0.0667172
$275$	−14.4396	−	8.15454i	−0.870744	−	0.491737i
$276$		0			0
$277$	−3.89892	+	5.36641i	−0.234264	+	0.322436i	−0.909923	−	0.414778i	$-0.863859\pi$
$277$	−3.89892	+	5.36641i	−0.234264	+	0.322436i	0.675659	+	0.737214i	$0.263859\pi$
$278$	9.42125	+	3.06115i	0.565049	+	0.183596i
$279$		0			0
$280$	−4.15925	−	10.4121i	−0.248563	−	0.622241i
$281$	12.6582	−	9.19674i	0.755126	−	0.548631i	−0.142285	−	0.989826i	$-0.545445\pi$
$281$	12.6582	−	9.19674i	0.755126	−	0.548631i	0.897412	+	0.441194i	$0.145445\pi$
$282$		0			0
$283$	−21.3993	−	6.95305i	−1.27205	−	0.413316i	−0.406280	−	0.913749i	$-0.633174\pi$
$283$	−21.3993	−	6.95305i	−1.27205	−	0.413316i	−0.865775	+	0.500433i	$0.833174\pi$
$284$	−7.13254	−	5.18210i	−0.423239	−	0.307501i
$285$		0			0
$286$	−6.34417	+	4.44146i	−0.375139	+	0.262629i
$287$		−	22.9643i		−	1.35554i
$288$		0			0
$289$	5.25213	−	16.1644i	0.308949	−	0.950847i
$290$	−0.609057	−	9.23082i	−0.0357651	−	0.542052i
$291$		0			0
$292$	−3.17178	−	4.36559i	−0.185615	−	0.255477i
$293$	−17.2985	+	5.62063i	−1.01059	+	0.328360i	−0.767089	−	0.641540i	$-0.778296\pi$
$293$	−17.2985	+	5.62063i	−1.01059	+	0.328360i	−0.243500	+	0.969901i	$0.578296\pi$
$294$		0			0
$295$	−3.33203	+	2.77367i	−0.193998	+	0.161490i
$296$	4.55688			0.264863
$297$		0			0
$298$			8.79232i			0.509326i
$299$	−7.39616	−	5.37363i	−0.427731	−	0.310765i
$300$		0			0
$301$	−5.60604	−	17.2536i	−0.323127	−	0.994482i
$302$	−12.6905	−	17.4669i	−0.730254	−	1.00511i
$303$		0			0
$304$	0.636930	+	1.96027i	0.0365305	+	0.112429i
$305$	18.3362	+	11.5581i	1.04993	+	0.661817i
$306$		0			0
$307$		−	12.3820i		−	0.706676i	−0.935496	−	0.353338i	$-0.885047\pi$
$307$		−	12.3820i		−	0.706676i	0.935496	−	0.353338i	$-0.114953\pi$
$308$	10.0094	−	13.2806i	0.570339	−	0.756735i
$309$		0			0
$310$	12.6993	+	15.2558i	0.721274	+	0.866470i
$311$	−2.90784	+	8.94941i	−0.164889	+	0.507475i	−0.999028	−	0.0440788i	$-0.985965\pi$
$311$	−2.90784	+	8.94941i	−0.164889	+	0.507475i	0.834140	+	0.551553i	$0.185965\pi$
$312$		0			0
$313$	−8.95297	−	12.3227i	−0.506052	−	0.696520i	0.477196	−	0.878797i	$-0.341653\pi$
$313$	−8.95297	−	12.3227i	−0.506052	−	0.696520i	−0.983247	+	0.182277i	$0.941653\pi$
$314$	2.76257	−	2.00712i	0.155901	−	0.113269i
$315$		0			0
$316$	−2.05657	+	6.32947i	−0.115691	+	0.356061i
$317$	−7.90964	+	10.8867i	−0.444250	+	0.611457i	−0.971150	−	0.238470i	$-0.923354\pi$
$317$	−7.90964	+	10.8867i	−0.444250	+	0.611457i	0.526900	+	0.849927i	$0.323354\pi$
$318$		0			0
$319$	11.2405	−	7.86928i	0.629346	−	0.440595i
$320$	−0.549472	+	2.16751i	−0.0307164	+	0.121167i
$321$		0			0
$322$	18.6710	+	6.06657i	1.04049	+	0.338077i
$323$	0.119871	−	0.0389485i	0.00666982	−	0.00216715i
$324$		0			0
$325$	−1.53398	−	11.5738i	−0.0850900	−	0.642001i
$326$	5.38010	+	16.5582i	0.297976	+	0.917076i
$327$		0			0
$328$	−2.69197	+	3.70518i	−0.148639	+	0.204584i
$329$	−44.5114			−2.45399
$330$		0			0
$331$	−3.82236			−0.210096			−0.105048	−	0.994467i	$-0.533500\pi$
$331$	−3.82236			−0.210096			−0.105048	+	0.994467i	$0.533500\pi$
$332$	−6.49620	+	8.94125i	−0.356525	+	0.490715i
$333$		0			0
$334$	1.02161	+	3.14419i	0.0558999	+	0.172042i
$335$	−5.18244	+	2.07020i	−0.283147	+	0.113107i
$336$		0			0
$337$	−9.00338	+	2.92538i	−0.490445	+	0.159355i	−0.543791	−	0.839221i	$-0.683012\pi$
$337$	−9.00338	+	2.92538i	−0.490445	+	0.159355i	0.0533455	+	0.998576i	$0.483012\pi$
$338$	7.17831	+	2.33237i	0.390449	+	0.126864i
$339$		0			0
$340$	0.132544	+	0.0336004i	0.00718820	+	0.00182224i
$341$	−9.58765	+	27.8371i	−0.519201	+	1.50746i
$342$		0			0
$343$	32.8390	−	45.1989i	1.77314	−	2.44051i
$344$	−1.11803	+	3.44095i	−0.0602804	+	0.185524i
$345$		0			0
$346$	4.14912	−	3.01451i	0.223058	−	0.162061i
$347$	9.72341	+	13.3831i	0.521980	+	0.718444i	0.985882	−	0.167443i	$-0.0535510\pi$
$347$	9.72341	+	13.3831i	0.521980	+	0.718444i	−0.463902	+	0.885887i	$0.653551\pi$
$348$		0			0
$349$	−9.03161	+	27.7964i	−0.483451	+	1.48791i	0.350761	+	0.936465i	$0.385923\pi$
$349$	−9.03161	+	27.7964i	−0.483451	+	1.48791i	−0.834212	+	0.551444i	$0.814077\pi$
$350$	10.8130	+	22.6193i	0.577981	+	1.20905i
$351$		0			0
$352$	−3.17178	+	0.969425i	−0.169057	+	0.0516705i
$353$		−	27.9200i		−	1.48603i	−0.669272	−	0.743017i	$-0.733394\pi$
$353$		−	27.9200i		−	1.48603i	0.669272	−	0.743017i	$-0.266606\pi$
$354$		0			0
$355$	16.6771	+	10.5123i	0.885131	+	0.557937i
$356$	−1.88197	−	5.79210i	−0.0997440	−	0.306980i
$357$		0			0
$358$	8.48725	+	11.6817i	0.448565	+	0.617397i
$359$	5.25768	+	16.1815i	0.277490	+	0.854025i	0.988550	+	0.150894i	$0.0482152\pi$
$359$	5.25768	+	16.1815i	0.277490	+	0.854025i	−0.711060	+	0.703131i	$0.751785\pi$
$360$		0			0
$361$	11.9343	+	8.67081i	0.628123	+	0.456358i
$362$			11.9061i			0.625770i
$363$		0			0
$364$	11.7082			0.613677
$365$	7.71963	+	9.27363i	0.404064	+	0.485404i
$366$		0			0
$367$	−27.9983	+	9.09719i	−1.46150	+	0.474870i	−0.928527	−	0.371264i	$-0.878925\pi$
$367$	−27.9983	+	9.09719i	−1.46150	+	0.474870i	−0.532971	+	0.846133i	$0.678925\pi$
$368$	−2.30133	−	3.16751i	−0.119965	−	0.165118i
$369$		0			0
$370$	−10.1674	+	0.670853i	−0.528578	+	0.0348760i
$371$	3.44273	−	10.5956i	0.178738	−	0.550098i
$372$		0			0
$373$			16.0743i			0.832297i	0.909297	+	0.416149i	$0.136620\pi$
$373$			16.0743i			0.832297i	−0.909297	+	0.416149i	$0.863380\pi$
$374$	0.0592807	+	0.193956i	0.00306533	+	0.0100292i
$375$		0			0
$376$	7.18170	+	5.21781i	0.370368	+	0.269088i
$377$	9.18743	+	2.98518i	0.473177	+	0.153744i
$378$		0			0
$379$	14.6618	−	10.6524i	0.753125	−	0.547178i	−0.143669	−	0.989626i	$-0.545890\pi$
$379$	14.6618	−	10.6524i	0.753125	−	0.547178i	0.896794	+	0.442448i	$0.145890\pi$
$380$	−1.70972	−	4.28002i	−0.0877066	−	0.219560i
$381$		0			0
$382$	−10.0033	−	3.25026i	−0.511812	−	0.166298i
$383$	7.76587	−	10.6888i	0.396817	−	0.546172i	−0.563124	−	0.826372i	$-0.690401\pi$
$383$	7.76587	−	10.6888i	0.396817	−	0.546172i	0.959942	+	0.280200i	$0.0904008\pi$
$384$		0			0
$385$	−20.3780	+	31.1056i	−1.03856	+	1.58529i
$386$	4.86869			0.247810
$387$		0			0
$388$	6.94485	+	2.25652i	0.352572	+	0.114557i
$389$	−8.19653	−	25.2263i	−0.415580	−	1.27902i	−0.911731	−	0.410788i	$-0.865254\pi$
$389$	−8.19653	−	25.2263i	−0.415580	−	1.27902i	0.496150	−	0.868237i	$-0.334746\pi$
$390$		0			0
$391$	−0.193694	+	0.140727i	−0.00979553	+	0.00711687i
$392$	−17.2542	+	5.60624i	−0.871470	+	0.283158i
$393$		0			0
$394$	12.9249	+	9.39047i	0.651145	+	0.473085i
$395$	3.65684	−	14.4252i	0.183996	−	0.725810i
$396$		0			0
$397$			30.3246i			1.52195i	0.648783	+	0.760974i	$0.275278\pi$
$397$			30.3246i			1.52195i	−0.648783	+	0.760974i	$0.724722\pi$
$398$	−9.82047	+	13.5167i	−0.492256	+	0.677532i
$399$		0			0
$400$	0.906896	−	4.91707i	0.0453448	−	0.245853i
$401$	15.7565	−	11.4478i	0.786844	−	0.571676i	−0.120181	−	0.992752i	$-0.538348\pi$
$401$	15.7565	−	11.4478i	0.786844	−	0.571676i	0.907025	+	0.421076i	$0.138348\pi$
$402$		0			0
$403$	−19.7136	+	6.40532i	−0.982002	+	0.319072i
$404$	−0.0685623	+	0.211013i	−0.00341110	+	0.0104983i
$405$		0			0
$406$	−20.7444			−1.02952
$407$	−8.66771	−	12.3809i	−0.429642	−	0.613701i
$408$		0			0
$409$	−22.9197	−	16.6521i	−1.13330	−	0.823394i	−0.147132	−	0.989117i	$-0.547004\pi$
$409$	−22.9197	−	16.6521i	−1.13330	−	0.823394i	−0.986172	+	0.165723i	$0.947004\pi$
$410$	5.46090	−	8.66336i	0.269695	−	0.427853i
$411$		0			0
$412$	−0.332713	−	0.457940i	−0.0163916	−	0.0225611i
$413$	5.71431	+	7.86508i	0.281183	+	0.387015i
$414$		0			0
$415$	13.1781	−	20.9062i	0.646888	−	1.02625i
$416$	−1.88906	−	1.37249i	−0.0926190	−	0.0672916i
$417$		0			0
$418$	4.11450	−	5.45918i	0.201247	−	0.267017i
$419$	−15.4826			−0.756374			−0.378187	−	0.925729i	$-0.623452\pi$
$419$	−15.4826			−0.756374			−0.378187	+	0.925729i	$0.623452\pi$
$420$		0			0
$421$	6.63964	−	20.4347i	0.323596	−	0.995927i	−0.648474	−	0.761237i	$-0.724592\pi$
$421$	6.63964	−	20.4347i	0.323596	−	0.995927i	0.972070	−	0.234690i	$-0.0754076\pi$
$422$	14.9753	−	4.86578i	0.728988	−	0.236862i
$423$		0			0
$424$	−1.79753	+	1.30598i	−0.0872959	+	0.0634242i
$425$	−0.300680	−	0.0554570i	−0.0145851	−	0.00269006i
$426$		0			0
$427$	28.5690	−	39.3219i	1.38255	−	1.90292i
$428$		−	2.23002i		−	0.107792i
$429$		0			0
$430$	1.98801	−	7.84211i	0.0958702	−	0.378180i
$431$	21.3896	+	15.5404i	1.03030	+	0.748557i	0.968369	−	0.249523i	$-0.0802739\pi$
$431$	21.3896	+	15.5404i	1.03030	+	0.748557i	0.0619316	+	0.998080i	$0.480274\pi$
$432$		0			0
$433$	31.2725	−	10.1611i	1.50286	−	0.488309i	0.562010	−	0.827130i	$-0.310028\pi$
$433$	31.2725	−	10.1611i	1.50286	−	0.488309i	0.940851	+	0.338821i	$0.110028\pi$
$434$	36.0105	−	26.1631i	1.72856	−	1.25587i
$435$		0			0
$436$	2.42976	+	7.47804i	0.116365	+	0.358133i
$437$	7.67495	+	2.49374i	0.367143	+	0.119292i
$438$		0			0
$439$	12.1796			0.581299			0.290649	−	0.956830i	$-0.406129\pi$
$439$	12.1796			0.581299			0.290649	+	0.956830i	$0.406129\pi$
$440$	6.93422	−	2.62994i	0.330576	−	0.125377i
$441$		0			0
$442$	−0.0839280	+	0.115517i	−0.00399205	+	0.00549458i
$443$	−15.7961	−	5.13247i	−0.750496	−	0.243851i	−0.0913015	−	0.995823i	$-0.529103\pi$
$443$	−15.7961	−	5.13247i	−0.750496	−	0.243851i	−0.659195	+	0.751972i	$0.729103\pi$
$444$		0			0
$445$	5.05177	+	12.6464i	0.239477	+	0.599495i
$446$	−11.7757	+	8.55558i	−0.557598	+	0.405119i
$447$		0			0
$448$	4.76878	+	1.54947i	0.225304	+	0.0732057i
$449$	4.33928	+	3.15267i	0.204783	+	0.148784i	0.685450	−	0.728119i	$-0.259605\pi$
$449$	4.33928	+	3.15267i	0.204783	+	0.148784i	−0.480667	+	0.876903i	$0.659605\pi$
$450$		0			0
$451$	15.1873	+	0.266353i	0.715143	+	0.0125421i
$452$			12.5617i			0.590852i
$453$		0			0
$454$	−3.03966	+	9.35512i	−0.142658	+	0.439058i
$455$	−26.1235	+	1.72365i	−1.22469	+	0.0808061i
$456$		0			0
$457$	2.12330	+	2.92247i	0.0993237	+	0.136707i	0.855786	−	0.517330i	$-0.173074\pi$
$457$	2.12330	+	2.92247i	0.0993237	+	0.136707i	−0.756462	+	0.654037i	$0.773074\pi$
$458$	−14.7869	+	4.80456i	−0.690947	+	0.224502i
$459$		0			0
$460$	5.60107	+	6.72860i	0.261151	+	0.313722i
$461$	40.6625			1.89384			0.946922	−	0.321464i	$-0.104175\pi$
$461$	40.6625			1.89384			0.946922	+	0.321464i	$0.104175\pi$
$462$		0			0
$463$			2.11880i			0.0984690i	0.998787	+	0.0492345i	$0.0156782\pi$
$463$			2.11880i			0.0984690i	−0.998787	+	0.0492345i	$0.984322\pi$
$464$	3.34700	+	2.43174i	0.155381	+	0.112891i
$465$		0			0
$466$	−8.00252	−	24.6292i	−0.370709	−	1.14093i
$467$	−8.08494	−	11.1280i	−0.374126	−	0.514941i	0.579890	−	0.814695i	$-0.303095\pi$
$467$	−8.08494	−	11.1280i	−0.374126	−	0.514941i	−0.954017	+	0.299754i	$0.903095\pi$
$468$		0			0
$469$	3.86707	+	11.9016i	0.178565	+	0.549565i
$470$	−16.7921	−	10.5848i	−0.774561	−	0.488240i
$471$		0			0
$472$		−	1.93885i		−	0.0892428i
$473$	11.4756	−	3.50741i	0.527650	−	0.161271i
$474$		0			0
$475$	4.44484	+	9.29795i	0.203943	+	0.426619i
$476$	0.0947508	−	0.291613i	0.00434289	−	0.0133661i
$477$		0			0
$478$	−11.7534	−	16.1771i	−0.537586	−	0.739924i
$479$	−25.4118	+	18.4628i	−1.16110	+	0.843586i	−0.989916	−	0.141654i	$-0.954758\pi$
$479$	−25.4118	+	18.4628i	−1.16110	+	0.843586i	−0.171180	+	0.985240i	$0.554758\pi$
$480$		0			0
$481$	3.28806	−	10.1196i	0.149922	−	0.461414i
$482$	5.29818	−	7.29232i	0.241326	−	0.332156i
$483$		0			0
$484$	8.66700	+	6.77371i	0.393954	+	0.307896i
$485$	−15.8277	−	4.01238i	−0.718698	−	0.182193i
$486$		0			0
$487$	−7.14274	−	2.32082i	−0.323668	−	0.105166i	0.142676	−	0.989769i	$-0.454429\pi$
$487$	−7.14274	−	2.32082i	−0.323668	−	0.105166i	−0.466344	+	0.884603i	$0.654429\pi$
$488$	−9.21895	+	2.99542i	−0.417322	+	0.135596i
$489$		0			0
$490$	37.6726	−	15.0488i	1.70187	−	0.679838i
$491$	−3.48008	−	10.7106i	−0.157054	−	0.483361i	0.841310	−	0.540554i	$-0.181785\pi$
$491$	−3.48008	−	10.7106i	−0.157054	−	0.483361i	−0.998363	+	0.0571923i	$0.981785\pi$
$492$		0			0
$493$	0.148702	−	0.204671i	0.00669719	−	0.00921790i
$494$	4.81281			0.216539
$495$		0			0
$496$	−8.87707			−0.398592
$497$	25.9840	−	35.7640i	1.16554	−	1.60423i
$498$		0			0
$499$	8.33753	+	25.6603i	0.373239	+	1.14871i	0.944659	+	0.328054i	$0.106393\pi$
$499$	8.33753	+	25.6603i	0.373239	+	1.14871i	−0.571420	+	0.820658i	$0.693607\pi$
$500$	−1.29960	+	11.1046i	−0.0581200	+	0.496611i
$501$		0			0
$502$	1.24746	−	0.405323i	0.0556767	−	0.0180905i
$503$	−30.5818	−	9.93662i	−1.36357	−	0.443052i	−0.466339	−	0.884606i	$-0.654427\pi$
$503$	−30.5818	−	9.93662i	−1.36357	−	0.443052i	−0.897235	+	0.441554i	$0.854427\pi$
$504$		0			0
$505$	0.121913	−	0.480909i	0.00542504	−	0.0214002i
$506$	−4.22866	+	12.2776i	−0.187987	+	0.545806i
$507$		0			0
$508$	−8.50112	+	11.7008i	−0.377176	+	0.519139i
$509$	3.64048	−	11.2043i	0.161362	−	0.496620i	−0.837388	−	0.546609i	$-0.815919\pi$
$509$	3.64048	−	11.2043i	0.161362	−	0.496620i	0.998750	+	0.0499888i	$0.0159186\pi$
$510$		0			0
$511$	21.8899	−	15.9039i	0.968352	−	0.703549i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$		0			0
$514$	1.37945	−	4.24551i	0.0608449	−	0.187261i
$515$	0.809772	+	0.972783i	0.0356828	+	0.0428659i
$516$		0			0
$517$	0.516268	−	29.4374i	0.0227054	−	1.29465i
$518$			22.8491i			1.00393i
$519$		0			0
$520$	4.41696	+	2.78421i	0.193697	+	0.122096i
$521$	−0.718847	−	2.21238i	−0.0314933	−	0.0969263i	0.934074	−	0.357079i	$-0.116227\pi$
$521$	−0.718847	−	2.21238i	−0.0314933	−	0.0969263i	−0.965568	+	0.260152i	$0.916227\pi$
$522$		0			0
$523$	0.901612	+	1.24096i	0.0394248	+	0.0542635i	0.828274	−	0.560323i	$-0.189323\pi$
$523$	0.901612	+	1.24096i	0.0394248	+	0.0542635i	−0.788850	+	0.614586i	$0.789323\pi$
$524$	4.73587	+	14.5755i	0.206888	+	0.636735i
$525$		0			0
$526$	11.4711	+	8.33426i	0.500165	+	0.363391i
$527$			0.542836i			0.0236463i
$528$		0			0
$529$	7.67080			0.333513
$530$	3.81842	−	3.17856i	0.165862	−	0.138068i
$531$		0			0
$532$	−9.82918	+	3.19369i	−0.426149	+	0.138464i
$533$	6.28578	+	8.65163i	0.272267	+	0.374744i
$534$		0			0
$535$	0.328298	+	4.97565i	0.0141935	+	0.215116i
$536$	0.771224	−	2.37358i	0.0333118	−	0.102523i
$537$		0			0
$538$		−	31.9952i		−	1.37941i
$539$	48.0515	+	36.2156i	2.06972	+	1.55992i
$540$		0			0
$541$	12.4927	+	9.07650i	0.537104	+	0.390229i	0.823008	−	0.568029i	$-0.192294\pi$
$541$	12.4927	+	9.07650i	0.537104	+	0.390229i	−0.285904	+	0.958258i	$0.592294\pi$
$542$	1.00944	+	0.327988i	0.0433593	+	0.0140883i
$543$		0			0
$544$	−0.0494717	+	0.0359433i	−0.00212108	+	0.00154106i
$545$	−6.52222	−	16.3274i	−0.279381	−	0.699390i
$546$		0			0
$547$	−10.1261	−	3.29017i	−0.432960	−	0.140677i	0.0844251	−	0.996430i	$-0.473095\pi$
$547$	−10.1261	−	3.29017i	−0.432960	−	0.140677i	−0.517385	+	0.855752i	$0.673095\pi$
$548$	−0.649130	+	0.893451i	−0.0277295	+	0.0381663i
$549$		0			0
$550$	−15.0846	+	6.88880i	−0.643208	+	0.293739i
$551$	−8.52724			−0.363272
$552$		0			0
$553$	−31.7372	−	10.3120i	−1.34960	−	0.438513i
$554$	2.04979	+	6.30859i	0.0870871	+	0.268026i
$555$		0			0
$556$	8.01420	−	5.82265i	0.339878	−	0.246936i
$557$	32.2595	−	10.4818i	1.36688	−	0.444126i	0.468545	−	0.883439i	$-0.344778\pi$
$557$	32.2595	−	10.4818i	1.36688	−	0.444126i	0.898334	+	0.439313i	$0.144778\pi$
$558$		0			0
$559$	6.83470	+	4.96570i	0.289077	+	0.210027i
$560$	−10.8683	−	2.75516i	−0.459269	−	0.116427i
$561$		0			0
$562$		−	15.6464i		−	0.660005i
$563$	0.789857	−	1.08714i	0.0332885	−	0.0458177i	−0.792048	−	0.610458i	$-0.790985\pi$
$563$	0.789857	−	1.08714i	0.0332885	−	0.0458177i	0.825337	+	0.564641i	$0.190985\pi$
$564$		0			0
$565$	−1.84930	−	28.0278i	−0.0778006	−	1.17914i
$566$	−18.2033	+	13.2255i	−0.765142	+	0.555908i
$567$		0			0
$568$	−8.38481	+	2.72439i	−0.351819	+	0.114313i
$569$	−9.70595	+	29.8718i	−0.406894	+	1.25229i	0.512409	+	0.858742i	$0.328753\pi$
$569$	−9.70595	+	29.8718i	−0.406894	+	1.25229i	−0.919303	+	0.393550i	$0.871247\pi$
$570$		0			0
$571$	9.25361			0.387252			0.193626	−	0.981075i	$-0.437975\pi$
$571$	9.25361			0.387252			0.193626	+	0.981075i	$0.437975\pi$
$572$	−0.135798	+	7.74317i	−0.00567801	+	0.323758i
$573$		0			0
$574$	−18.5785	−	13.4981i	−0.775451	−	0.563398i
$575$	−13.4878	−	14.1884i	−0.562479	−	0.591696i
$576$		0			0
$577$	−25.4998	−	35.0975i	−1.06157	−	1.46113i	−0.878327	−	0.478060i	$-0.841340\pi$
$577$	−25.4998	−	35.0975i	−1.06157	−	1.46113i	−0.183244	−	0.983068i	$-0.558660\pi$
$578$	−9.99015	−	13.7503i	−0.415536	−	0.571936i
$579$		0			0
$580$	−7.82589	−	4.93300i	−0.324952	−	0.204832i
$581$	−44.8332	−	32.5732i	−1.85999	−	1.35136i
$582$		0			0
$583$	6.96744	+	2.39973i	0.288562	+	0.0993865i
$584$	−5.39616			−0.223295
$585$		0			0
$586$	−5.62063	+	17.2985i	−0.232186	+	0.714595i
$587$	−3.05524	+	0.992708i	−0.126103	+	0.0409734i	−0.371389	−	0.928477i	$-0.621118\pi$
$587$	−3.05524	+	0.992708i	−0.126103	+	0.0409734i	0.245285	+	0.969451i	$0.421118\pi$
$588$		0			0
$589$	14.8026	−	10.7547i	0.609929	−	0.443139i
$590$	0.285433	+	4.32599i	0.0117511	+	0.178098i
$591$		0			0
$592$	2.67847	−	3.68660i	0.110084	−	0.151518i
$593$			0.0315027i			0.00129366i	1.00000		0.000646829i	$0.000205892\pi$
$593$			0.0315027i			0.00129366i	−1.00000		0.000646829i	$0.999794\pi$
$594$		0			0
$595$	−0.168479	+	0.664600i	−0.00690696	+	0.0272460i
$596$	7.11314	+	5.16800i	0.291366	+	0.211689i
$597$		0			0
$598$	−8.69471	+	2.82508i	−0.355553	+	0.115526i
$599$	8.50993	−	6.18283i	0.347706	−	0.252623i	−0.400200	−	0.916428i	$-0.631059\pi$
$599$	8.50993	−	6.18283i	0.347706	−	0.252623i	0.747906	+	0.663804i	$0.231059\pi$
$600$		0			0
$601$	7.45305	+	22.9381i	0.304016	+	0.935665i	0.980043	+	0.198788i	$0.0637005\pi$
$601$	7.45305	+	22.9381i	0.304016	+	0.935665i	−0.676026	+	0.736877i	$0.736300\pi$
$602$	−17.2536	−	5.60604i	−0.703205	−	0.228485i
$603$		0			0
$604$	−21.5903			−0.878497
$605$	−20.3352	−	13.8377i	−0.826742	−	0.562582i
$606$		0			0
$607$	1.46340	−	2.01420i	0.0593975	−	0.0817537i	−0.778285	−	0.627911i	$-0.783910\pi$
$607$	1.46340	−	2.01420i	0.0593975	−	0.0817537i	0.837682	+	0.546158i	$0.183910\pi$
$608$	1.96027	+	0.636930i	0.0794995	+	0.0258309i
$609$		0			0
$610$	20.1285	−	8.04062i	0.814979	−	0.325555i
$611$	16.7694	−	12.1836i	0.678415	−	0.492898i
$612$		0			0
$613$	35.7338	+	11.6106i	1.44328	+	0.468949i	0.922917	−	0.384999i	$-0.125798\pi$
$613$	35.7338	+	11.6106i	1.44328	+	0.468949i	0.520359	+	0.853948i	$0.325798\pi$
$614$	−10.0172	−	7.27794i	−0.404262	−	0.293714i
$615$		0			0
$616$	−4.86089	−	15.9039i	−0.195851	−	0.640788i
$617$			45.5803i			1.83499i	0.397744	+	0.917496i	$0.369793\pi$
$617$			45.5803i			1.83499i	−0.397744	+	0.917496i	$0.630207\pi$
$618$		0			0
$619$	−1.77382	+	5.45924i	−0.0712957	+	0.219425i	−0.980355	−	0.197241i	$-0.936802\pi$
$619$	−1.77382	+	5.45924i	−0.0712957	+	0.219425i	0.909059	+	0.416667i	$0.136802\pi$
$620$	19.8067	−	1.30686i	0.795455	−	0.0524848i
$621$		0			0
$622$	5.53104	+	7.61283i	0.221775	+	0.305246i
$623$	29.0427	−	9.43655i	1.16357	−	0.378067i
$624$		0			0
$625$	1.26491	−	24.9680i	0.0505964	−	0.998719i
$626$	−15.2317			−0.608781
$627$		0			0
$628$		−	3.41472i		−	0.136262i
$629$	−0.225437	−	0.163789i	−0.00898875	−	0.00653071i
$630$		0			0
$631$	3.70103	+	11.3906i	0.147336	+	0.453453i	0.997304	−	0.0733811i	$-0.0233790\pi$
$631$	3.70103	+	11.3906i	0.147336	+	0.453453i	−0.849968	+	0.526834i	$0.823379\pi$
$632$	3.91183	+	5.38417i	0.155604	+	0.214171i
$633$		0			0
$634$	4.15834	+	12.7981i	0.165149	+	0.508276i
$635$	17.2453	−	27.3585i	0.684358	−	1.08569i
$636$		0			0
$637$			42.3621i			1.67845i
$638$	0.240605	−	13.7192i	0.00952563	−	0.543148i
$639$		0			0
$640$	1.43058	+	1.71856i	0.0565485	+	0.0679320i
$641$	10.8526	−	33.4007i	0.428650	−	1.31925i	−0.470805	−	0.882237i	$-0.656036\pi$
$641$	10.8526	−	33.4007i	0.428650	−	1.31925i	0.899455	−	0.437013i	$-0.143964\pi$
$642$		0			0
$643$	20.9529	+	28.8392i	0.826302	+	1.13731i	0.988600	+	0.150565i	$0.0481093\pi$
$643$	20.9529	+	28.8392i	0.826302	+	1.13731i	−0.162298	+	0.986742i	$0.551891\pi$
$644$	15.8825	−	11.5393i	0.625858	−	0.454712i
$645$		0			0
$646$	0.0389485	−	0.119871i	0.00153241	−	0.00471627i
$647$	11.8476	−	16.3068i	0.465778	−	0.641088i	−0.509917	−	0.860224i	$-0.670324\pi$
$647$	11.8476	−	16.3068i	0.465778	−	0.641088i	0.975694	+	0.219136i	$0.0703238\pi$
$648$		0			0
$649$	−5.26781	+	3.68791i	−0.206780	+	0.144763i
$650$	−10.2651	−	5.56192i	−0.402630	−	0.218156i
$651$		0			0
$652$	16.5582	+	5.38010i	0.648470	+	0.210701i
$653$	23.1905	−	7.53504i	0.907513	−	0.294869i	0.182178	−	0.983266i	$-0.441685\pi$
$653$	23.1905	−	7.53504i	0.907513	−	0.294869i	0.725334	+	0.688397i	$0.241685\pi$
$654$		0			0
$655$	−12.7125	−	31.8239i	−0.496720	−	1.24346i
$656$	1.41525	+	4.35570i	0.0552563	+	0.170061i
$657$		0			0
$658$	−26.1631	+	36.0105i	−1.01994	+	1.40383i
$659$	−6.98788			−0.272209			−0.136104	−	0.990694i	$-0.543458\pi$
$659$	−6.98788			−0.272209			−0.136104	+	0.990694i	$0.543458\pi$
$660$		0			0
$661$	−3.61827			−0.140735			−0.0703673	−	0.997521i	$-0.522417\pi$
$661$	−3.61827			−0.140735			−0.0703673	+	0.997521i	$0.522417\pi$
$662$	−2.24673	+	3.09235i	−0.0873215	+	0.120188i
$663$		0			0
$664$	3.41525	+	10.5111i	0.132537	+	0.407908i
$665$	21.4609	−	8.57285i	0.832216	−	0.332441i
$666$		0			0
$667$	15.4051	−	5.00542i	0.596488	−	0.193811i
$668$	3.14419	+	1.02161i	0.121652	+	0.0395272i
$669$		0			0
$670$	−1.37133	+	5.40952i	−0.0529793	+	0.208988i
$671$	25.6740	+	19.3501i	0.991133	+	0.747001i
$672$		0			0
$673$	4.68377	−	6.44665i	0.180546	−	0.248500i	−0.709146	−	0.705062i	$-0.750919\pi$
$673$	4.68377	−	6.44665i	0.180546	−	0.248500i	0.889692	+	0.456562i	$0.150919\pi$
$674$	−2.92538	+	9.00338i	−0.112681	+	0.346797i
$675$		0			0
$676$	6.10624	−	4.43644i	0.234855	−	0.170632i
$677$	−8.48443	−	11.6778i	−0.326083	−	0.448815i	0.614229	−	0.789128i	$-0.289467\pi$
$677$	−8.48443	−	11.6778i	−0.326083	−	0.448815i	−0.940312	+	0.340313i	$0.889467\pi$
$678$		0			0
$679$	−11.3146	+	34.8229i	−0.434216	+	1.33638i
$680$	0.105091	−	0.0874803i	0.00403004	−	0.00335472i
$681$		0			0
$682$	16.8852	+	24.1188i	0.646567	+	0.923557i
$683$			29.6723i			1.13538i	0.823242	+	0.567690i	$0.192163\pi$
$683$			29.6723i			1.13538i	−0.823242	+	0.567690i	$0.807837\pi$
$684$		0			0
$685$	1.31682	−	2.08904i	0.0503130	−	0.0798183i
$686$	−17.2645	−	53.1345i	−0.659160	−	2.02869i
$687$		0			0
$688$	2.12663	+	2.92705i	0.0810769	+	0.111593i
$689$	1.60321	+	4.93417i	0.0610774	+	0.187977i
$690$		0			0
$691$	−26.1812	−	19.0218i	−0.995980	−	0.723622i	−0.0347577	−	0.999396i	$-0.511066\pi$
$691$	−26.1812	−	19.0218i	−0.995980	−	0.723622i	−0.961223	+	0.275774i	$0.911066\pi$
$692$		−	5.12859i		−	0.194960i
$693$		0			0
$694$	16.5424			0.627943
$695$	−17.0242	+	14.1714i	−0.645765	+	0.537553i
$696$		0			0
$697$	0.266353	−	0.0865432i	0.0100888	−	0.00327806i
$698$	17.1791	+	23.6451i	0.650240	+	0.894979i
$699$		0			0
$700$	24.6551	+	4.54735i	0.931876	+	0.171874i
$701$	−5.86089	+	18.0380i	−0.221363	+	0.681284i	0.777278	+	0.629157i	$0.216600\pi$
$701$	−5.86089	+	18.0380i	−0.221363	+	0.681284i	−0.998640	+	0.0521266i	$0.983400\pi$
$702$		0			0
$703$			9.39242i			0.354242i
$704$	−1.08005	+	3.13584i	−0.0407058	+	0.118186i
$705$		0			0
$706$	−22.5878	−	16.4110i	−0.850103	−	0.617636i
$707$	−1.05806	−	0.343785i	−0.0397925	−	0.0129294i
$708$		0			0
$709$	6.78617	−	4.93044i	0.254860	−	0.185167i	−0.453018	−	0.891501i	$-0.649653\pi$
$709$	6.78617	−	4.93044i	0.254860	−	0.185167i	0.707878	+	0.706335i	$0.249653\pi$
$710$	18.3072	−	7.31309i	0.687059	−	0.274455i
$711$		0			0
$712$	−5.79210	−	1.88197i	−0.217068	−	0.0705297i
$713$	−20.4290	+	28.1182i	−0.765074	+	1.05303i
$714$		0			0
$715$	−0.836934	−	17.2967i	−0.0312995	−	0.646859i
$716$	14.4394			0.539625
$717$		0			0
$718$	16.1815	+	5.25768i	0.603887	+	0.196215i
$719$	2.33218	+	7.17771i	0.0869756	+	0.267684i	0.985079	−	0.172100i	$-0.0550552\pi$
$719$	2.33218	+	7.17771i	0.0869756	+	0.267684i	−0.898104	+	0.439783i	$0.855055\pi$
$720$		0			0
$721$	2.29620	−	1.66829i	0.0855150	−	0.0621303i
$722$	14.0297	−	4.55851i	0.522130	−	0.169650i
$723$		0			0
$724$	9.63223	+	6.99822i	0.357979	+	0.260087i
$725$	18.1875	+	9.85449i	0.675466	+	0.365987i
$726$		0			0
$727$			24.2826i			0.900593i	0.892879	+	0.450297i	$0.148682\pi$
$727$			24.2826i			0.900593i	−0.892879	+	0.450297i	$0.851318\pi$
$728$	6.88191	−	9.47214i	0.255061	−	0.351061i
$729$		0			0
$730$	12.0400	−	0.794409i	0.445621	−	0.0294024i
$731$	0.178990	−	0.130044i	0.00662019	−	0.00480985i
$732$		0			0
$733$	20.3541	−	6.61345i	0.751796	−	0.244273i	0.0920424	−	0.995755i	$-0.470660\pi$
$733$	20.3541	−	6.61345i	0.751796	−	0.244273i	0.659754	+	0.751482i	$0.270660\pi$
$734$	−9.09719	+	27.9983i	−0.335784	+	1.03344i
$735$		0			0
$736$	−3.91525			−0.144318
$737$	−7.91593	+	2.41943i	−0.291587	+	0.0891207i
$738$		0			0
$739$	28.4419	+	20.6642i	1.04625	+	0.760147i	0.971496	−	0.237055i	$-0.0761823\pi$
$739$	28.4419	+	20.6642i	1.04625	+	0.760147i	0.0747558	+	0.997202i	$0.476182\pi$
$740$	−5.43351	+	8.61991i	−0.199740	+	0.316874i
$741$		0			0
$742$	−6.54846	−	9.01318i	−0.240401	−	0.330884i
$743$	20.0435	+	27.5875i	0.735324	+	1.01209i	0.998874	+	0.0474407i	$0.0151065\pi$
$743$	20.0435	+	27.5875i	0.735324	+	1.01209i	−0.263550	+	0.964646i	$0.584893\pi$
$744$		0			0
$745$	−16.6318	−	10.4837i	−0.609341	−	0.384095i
$746$	13.0044	+	9.44825i	0.476125	+	0.345925i
$747$		0			0
$748$	0.191758	+	0.0660453i	0.00701136	+	0.00241485i
$749$	11.1817			0.408572
$750$		0			0
$751$	−11.0690	+	34.0669i	−0.403914	+	1.24312i	0.517884	+	0.855451i	$0.326720\pi$
$751$	−11.0690	+	34.0669i	−0.403914	+	1.24312i	−0.921799	+	0.387669i	$0.873280\pi$
$752$	8.44260	−	2.74317i	0.307870	−	0.100033i
$753$		0			0
$754$	7.81529	−	5.67814i	0.284616	−	0.206786i
$755$	48.1727	−	3.17847i	1.75318	−	0.115676i
$756$		0			0
$757$	14.2408	−	19.6008i	0.517592	−	0.712404i	−0.467584	−	0.883948i	$-0.654876\pi$
$757$	14.2408	−	19.6008i	0.517592	−	0.712404i	0.985176	+	0.171544i	$0.0548756\pi$
$758$		−	18.1230i		−	0.658256i
$759$		0			0
$760$	−4.46756	−	1.13254i	−0.162055	−	0.0410817i
$761$	8.62191	+	6.26419i	0.312544	+	0.227077i	0.732987	−	0.680242i	$-0.238125\pi$
$761$	8.62191	+	6.26419i	0.312544	+	0.227077i	−0.420443	+	0.907319i	$0.638125\pi$
$762$		0			0
$763$	−37.4964	+	12.1833i	−1.35746	+	0.441065i
$764$	−8.50930	+	6.18237i	−0.307856	+	0.223670i
$765$		0			0
$766$	−4.08276	−	12.5654i	−0.147516	−	0.454008i
$767$	−4.30566	−	1.39899i	−0.155468	−	0.0505147i
$768$		0			0
$769$	−25.8297			−0.931444			−0.465722	−	0.884931i	$-0.654205\pi$
$769$	−25.8297			−0.931444			−0.465722	+	0.884931i	$0.654205\pi$
$770$	13.1870	+	34.7695i	0.475227	+	1.25301i
$771$		0			0
$772$	2.86174	−	3.93885i	0.102996	−	0.141762i
$773$	−11.4679	−	3.72614i	−0.412471	−	0.134020i	0.0954286	−	0.995436i	$-0.469578\pi$
$773$	−11.4679	−	3.72614i	−0.412471	−	0.134020i	−0.507899	+	0.861416i	$0.669578\pi$
$774$		0			0
$775$	−44.0006	+	5.83177i	−1.58055	+	0.209484i
$776$	5.90765	−	4.29216i	0.212072	−	0.154079i
$777$		0			0
$778$	−25.2263	−	8.19653i	−0.904407	−	0.293860i
$779$	−7.63693	−	5.54855i	−0.273621	−	0.198798i
$780$		0			0
$781$	23.3510	+	17.5992i	0.835563	+	0.629750i
$782$			0.239419i			0.00856161i
$783$		0			0
$784$	−5.60624	+	17.2542i	−0.200223	+	0.616222i
$785$	0.502707	+	7.61899i	0.0179424	+	0.271933i
$786$		0			0
$787$	10.6725	+	14.6895i	0.380435	+	0.523624i	0.955700	−	0.294343i	$-0.0951009\pi$
$787$	10.6725	+	14.6895i	0.380435	+	0.523624i	−0.575265	+	0.817967i	$0.695101\pi$
$788$	15.1941	−	4.93686i	0.541267	−	0.175868i
$789$		0			0
$790$	−9.52078	−	11.4374i	−0.338734	−	0.406923i
$791$	−62.9867			−2.23955
$792$		0			0
$793$			22.6342i			0.803762i
$794$	24.5331	+	17.8243i	0.870648	+	0.632562i
$795$		0			0
$796$	5.16292	+	15.8898i	0.182995	+	0.563201i
$797$	0.946725	+	1.30306i	0.0335347	+	0.0461566i	0.825455	−	0.564468i	$-0.190919\pi$
$797$	0.946725	+	1.30306i	0.0335347	+	0.0461566i	−0.791920	+	0.610624i	$0.790919\pi$
$798$		0			0
$799$	−0.167746	−	0.516268i	−0.00593441	−	0.0182642i
$800$	−3.44493	−	3.62387i	−0.121797	−	0.128123i
$801$		0			0
$802$		−	19.4762i		−	0.687727i
$803$	10.2641	+	14.6612i	0.362213	+	0.517384i
$804$		0			0
$805$	−33.7385	+	28.0849i	−1.18913	+	0.989862i
$806$	−6.40532	+	19.7136i	−0.225618	+	0.694380i
$807$		0			0
$808$	0.130413	+	0.179498i	0.00458792	+	0.00631473i
$809$	−20.7273	+	15.0593i	−0.728733	+	0.529455i	−0.889162	−	0.457592i	$-0.848712\pi$
$809$	−20.7273	+	15.0593i	−0.728733	+	0.529455i	0.160429	+	0.987047i	$0.448712\pi$
$810$		0			0
$811$	13.5506	−	41.7045i	0.475827	−	1.46444i	−0.369012	−	0.929424i	$-0.620304\pi$
$811$	13.5506	−	41.7045i	0.475827	−	1.46444i	0.844839	−	0.535020i	$-0.179696\pi$
$812$	−12.1932	+	16.7825i	−0.427898	+	0.588951i
$813$		0			0
$814$	−15.1111	−	0.265017i	−0.529646	−	0.00928883i
$815$	−37.7370	−	9.56650i	−1.32187	−	0.335100i
$816$		0			0
$817$	−7.09233	−	2.30444i	−0.248129	−	0.0806220i
$818$	−26.9437	+	8.75453i	−0.942063	+	0.306095i
$819$		0			0
$820$	−3.79897	−	9.51016i	−0.132666	−	0.332109i
$821$	5.43938	+	16.7407i	0.189836	+	0.584254i	0.999998	−	0.00195152i	$-0.000621189\pi$
$821$	5.43938	+	16.7407i	0.189836	+	0.584254i	−0.810163	+	0.586205i	$0.800621\pi$
$822$		0			0
$823$	7.43854	−	10.2383i	0.259291	−	0.356884i	−0.659447	−	0.751751i	$-0.729209\pi$
$823$	7.43854	−	10.2383i	0.259291	−	0.356884i	0.918738	+	0.394867i	$0.129209\pi$
$824$	−0.566045			−0.0197191
$825$		0			0
$826$	9.72177			0.338264
$827$	−5.19856	+	7.15520i	−0.180772	+	0.248811i	−0.889780	−	0.456389i	$-0.849143\pi$
$827$	−5.19856	+	7.15520i	−0.180772	+	0.248811i	0.709009	+	0.705200i	$0.249143\pi$
$828$		0			0
$829$	−11.6571	−	35.8767i	−0.404866	−	1.24605i	−0.921007	−	0.389546i	$-0.872632\pi$
$829$	−11.6571	−	35.8767i	−0.404866	−	1.24605i	0.516141	−	0.856504i	$-0.327368\pi$
$830$	−9.16758	−	22.9497i	−0.318211	−	0.796595i
$831$		0			0
$832$	−2.22073	+	0.721558i	−0.0769899	+	0.0250155i
$833$	1.05510	+	0.342823i	0.0365571	+	0.0118781i
$834$		0			0
$835$	−7.16576	−	1.81655i	−0.247981	−	0.0628643i
$836$	−1.99813	−	6.53752i	−0.0691068	−	0.226105i
$837$		0			0
$838$	−9.10044	+	12.5257i	−0.314369	+	0.432692i
$839$	−11.8934	+	36.6041i	−0.410606	+	1.26372i	0.505517	+	0.862817i	$0.331302\pi$
$839$	−11.8934	+	36.6041i	−0.410606	+	1.26372i	−0.916123	+	0.400898i	$0.868698\pi$
$840$		0			0
$841$	9.61452	−	6.98536i	0.331535	−	0.240874i
$842$	−12.6293	−	17.3828i	−0.435236	−	0.599051i
$843$		0			0
$844$	4.86578	−	14.9753i	0.167487	−	0.515472i
$845$	−12.9712	+	10.7976i	−0.446223	+	0.371449i
$846$		0			0
$847$	−33.9647	+	43.4580i	−1.16704	+	1.49324i
$848$			2.22187i			0.0762994i
$849$		0			0
$850$	−0.221601	+	0.210659i	−0.00760086	+	0.00722554i
$851$	−5.51328	−	16.9681i	−0.188993	−	0.581660i
$852$		0			0
$853$	29.9122	+	41.1706i	1.02417	+	1.40965i	0.909237	+	0.416280i	$0.136666\pi$
$853$	29.9122	+	41.1706i	1.02417	+	1.40965i	0.114936	+	0.993373i	$0.463334\pi$
$854$	−15.0196	−	46.2256i	−0.513961	−	1.58181i
$855$		0			0
$856$	−1.80412	−	1.31077i	−0.0616636	−	0.0448012i
$857$		−	11.5197i		−	0.393506i	−0.980453	−	0.196753i	$-0.936960\pi$
$857$		−	11.5197i		−	0.393506i	0.980453	−	0.196753i	$-0.0630397\pi$
$858$		0			0
$859$	−23.9497			−0.817153			−0.408577	−	0.912724i	$-0.633975\pi$
$859$	−23.9497			−0.817153			−0.408577	+	0.912724i	$0.633975\pi$
$860$	−5.17588	−	6.21781i	−0.176496	−	0.212025i
$861$		0			0
$862$	25.1450	−	8.17010i	0.856441	−	0.278275i
$863$	23.5170	+	32.3684i	0.800530	+	1.10183i	0.992716	+	0.120476i	$0.0384421\pi$
$863$	23.5170	+	32.3684i	0.800530	+	1.10183i	−0.192187	+	0.981358i	$0.561558\pi$
$864$		0			0
$865$	0.755018	+	11.4430i	0.0256714	+	0.389074i
$866$	10.1611	−	31.2725i	0.345287	−	1.06268i
$867$		0			0
$868$		−	44.5114i		−	1.51081i
$869$	7.18793	−	20.8696i	0.243834	−	0.707954i
$870$		0			0
$871$	−4.71460	−	3.42536i	−0.159748	−	0.116064i
$872$	7.47804	+	2.42976i	0.253238	+	0.0822821i
$873$		0			0
$874$	6.52871	−	4.74338i	0.220837	−	0.160447i
$875$	−55.6804	−	6.51646i	−1.88234	−	0.220297i
$876$		0			0
$877$	−24.7104	−	8.02891i	−0.834413	−	0.271117i	−0.139510	−	0.990221i	$-0.544553\pi$
$877$	−24.7104	−	8.02891i	−0.834413	−	0.271117i	−0.694903	+	0.719104i	$0.744553\pi$
$878$	7.15897	−	9.85347i	0.241603	−	0.332539i
$879$		0			0
$880$	1.94817	−	7.15574i	0.0656727	−	0.241220i
$881$	−25.1372			−0.846893			−0.423446	−	0.905921i	$-0.639180\pi$
$881$	−25.1372			−0.846893			−0.423446	+	0.905921i	$0.639180\pi$
$882$		0			0
$883$	−41.3431	−	13.4332i	−1.39131	−	0.452063i	−0.484937	−	0.874549i	$-0.661157\pi$
$883$	−41.3431	−	13.4332i	−1.39131	−	0.452063i	−0.906369	+	0.422486i	$0.861157\pi$
$884$	0.0441236	+	0.135798i	0.00148404	+	0.00456739i
$885$		0			0
$886$	−13.4370	+	9.76254i	−0.451424	+	0.327979i
$887$	−27.2078	+	8.84036i	−0.913549	+	0.296830i	−0.727818	−	0.685770i	$-0.759465\pi$
$887$	−27.2078	+	8.84036i	−0.913549	+	0.296830i	−0.185731	+	0.982601i	$0.559465\pi$
$888$		0			0
$889$	−58.6701	−	42.6263i	−1.96773	−	1.42964i
$890$	13.2005	+	3.34638i	0.442481	+	0.112171i
$891$		0			0
$892$			14.5556i			0.487358i
$893$	−10.7547	+	14.8026i	−0.359892	+	0.495349i
$894$		0			0
$895$	−32.2174	+	2.12573i	−1.07691	+	0.0710553i
$896$	4.05657	−	2.94727i	0.135520	−	0.0984614i
$897$		0			0
$898$	5.10113	−	1.65746i	0.170227	−	0.0553100i
$899$	11.3488	−	34.9281i	0.378504	−	1.16492i
$900$		0			0
$901$	0.135868			0.00452643
$902$	9.14237	−	12.1302i	0.304407	−	0.403893i
$903$		0			0
$904$	10.1626	+	7.38357i	0.338003	+	0.245574i
$905$	−22.5219	−	14.1965i	−0.748652	−	0.471908i
$906$		0			0
$907$	28.0438	+	38.5990i	0.931179	+	1.28166i	0.959398	+	0.282056i	$0.0910165\pi$
$907$	28.0438	+	38.5990i	0.931179	+	1.28166i	−0.0282187	+	0.999602i	$0.508983\pi$
$908$	5.78178	+	7.95794i	0.191875	+	0.264094i
$909$		0			0
$910$	−13.9606	+	22.1475i	−0.462788	+	0.734183i
$911$	40.3003	+	29.2799i	1.33521	+	0.970085i	0.999606	+	0.0280809i	$0.00893959\pi$
$911$	40.3003	+	29.2799i	1.33521	+	0.970085i	0.335602	+	0.942004i	$0.391060\pi$
$912$		0			0
$913$	22.0621	−	29.2724i	0.730150	−	0.968775i
$914$	3.61237			0.119487
$915$		0			0
$916$	−4.80456	+	14.7869i	−0.158747	+	0.488573i
$917$	−73.0845	+	23.7466i	−2.41346	+	0.784182i
$918$		0			0
$919$	−34.7058	+	25.2153i	−1.14484	+	0.831775i	−0.987786	−	0.155815i	$-0.950199\pi$
$919$	−34.7058	+	25.2153i	−1.14484	+	0.831775i	−0.157053	+	0.987590i	$0.550199\pi$
$920$	8.73578	−	0.576394i	0.288010	−	0.0190031i
$921$		0			0
$922$	23.9008	−	32.8967i	0.787132	−	1.08339i
$923$			20.5862i			0.677602i
$924$		0			0
$925$	10.8543	−	20.0328i	0.356889	−	0.658674i
$926$	1.71415	+	1.24540i	0.0563303	+	0.0409264i
$927$		0			0
$928$	3.93464	−	1.27844i	0.129161	−	0.0419669i
$929$	3.20719	−	2.33016i	0.105224	−	0.0764500i	−0.533929	−	0.845529i	$-0.679285\pi$
$929$	3.20719	−	2.33016i	0.105224	−	0.0764500i	0.639153	+	0.769079i	$0.279285\pi$
$930$		0			0
$931$	−11.5553	−	35.5635i	−0.378709	−	1.16555i
$932$	−24.6292	−	8.00252i	−0.806757	−	0.262131i
$933$		0			0
$934$	−13.7549			−0.450075
$935$	−0.437576	−	0.119131i	−0.0143103	−	0.00389601i
$936$		0			0
$937$	1.24563	−	1.71446i	0.0406929	−	0.0560090i	−0.788186	−	0.615437i	$-0.788979\pi$
$937$	1.24563	−	1.71446i	0.0406929	−	0.0560090i	0.828879	+	0.559429i	$0.188979\pi$
$938$	11.9016	+	3.86707i	0.388601	+	0.126264i
$939$		0			0
$940$	−18.4334	+	7.36349i	−0.601232	+	0.240171i
$941$	4.08118	−	2.96515i	0.133043	−	0.0966612i	−0.519274	−	0.854608i	$-0.673797\pi$
$941$	4.08118	−	2.96515i	0.133043	−	0.0966612i	0.652316	+	0.757947i	$0.273797\pi$
$942$		0			0
$943$	17.0537	+	5.54107i	0.555344	+	0.180442i
$944$	−1.56856	−	1.13963i	−0.0510524	−	0.0370917i
$945$		0			0
$946$	3.90765	−	11.3456i	0.127049	−	0.368877i
$947$		−	0.986192i		−	0.0320470i	−0.999872	−	0.0160235i	$-0.994899\pi$
$947$		−	0.986192i		−	0.0320470i	0.999872	−	0.0160235i	$-0.00510065\pi$
$948$		0			0
$949$	−3.89364	+	11.9834i	−0.126393	+	0.388998i
$950$	10.1348	+	1.86925i	0.328817	+	0.0606464i
$951$		0			0
$952$	−0.180227	−	0.248061i	−0.00584118	−	0.00803969i
$953$	21.8386	−	7.09580i	0.707422	−	0.229855i	0.0668608	−	0.997762i	$-0.478702\pi$
$953$	21.8386	−	7.09580i	0.707422	−	0.229855i	0.640562	+	0.767907i	$0.278702\pi$
$954$		0			0
$955$	18.0759	−	15.0469i	0.584924	−	0.486907i
$956$	−19.9960			−0.646718
$957$		0			0
$958$			31.4107i			1.01484i
$959$	−4.47994	−	3.25486i	−0.144665	−	0.105105i
$960$		0			0
$961$	14.7718	+	45.4628i	0.476508	+	1.46654i
$962$	−6.25426	−	8.60824i	−0.201645	−	0.277541i
$963$		0			0
$964$	−2.78542	−	8.57264i	−0.0897123	−	0.276106i
$965$	−5.80530	+	9.20972i	−0.186879	+	0.296472i
$966$		0			0
$967$		−	20.1267i		−	0.647231i	−0.946189	−	0.323616i	$-0.895102\pi$
$967$		−	20.1267i		−	0.647231i	0.946189	−	0.323616i	$-0.104898\pi$
$968$	10.5744	−	3.03026i	0.339873	−	0.0973963i
$969$		0			0
$970$	−12.5494	+	10.4464i	−0.402936	+	0.335415i
$971$	6.77852	−	20.8621i	0.217533	−	0.669498i	−0.781431	−	0.623991i	$-0.785510\pi$
$971$	6.77852	−	20.8621i	0.217533	−	0.669498i	0.998964	−	0.0455060i	$-0.0144900\pi$
$972$		0			0
$973$	29.1959	+	40.1847i	0.935978	+	1.28826i
$974$	−6.07597	+	4.41445i	−0.194687	+	0.141448i
$975$		0			0
$976$	−2.99542	+	9.21895i	−0.0958810	+	0.295091i
$977$	34.7133	−	47.7788i	1.11058	−	1.52858i	0.290015	−	0.957022i	$-0.406340\pi$
$977$	34.7133	−	47.7788i	1.11058	−	1.52858i	0.820562	−	0.571557i	$-0.193660\pi$
$978$		0			0
$979$	5.90396	+	19.3167i	0.188691	+	0.617365i
$980$	9.96860	−	39.3232i	0.318435	−	1.25613i
$981$		0			0
$982$	−10.7106	−	3.48008i	−0.341788	−	0.111054i
$983$	45.9751	−	14.9382i	1.46638	−	0.476455i	0.536367	−	0.843985i	$-0.319796\pi$
$983$	45.9751	−	14.9382i	1.46638	−	0.476455i	0.930012	+	0.367530i	$0.119796\pi$
$984$		0			0
$985$	−33.1745	+	13.2520i	−1.05703	+	0.422245i
$986$	−0.0781772	−	0.240605i	−0.00248967	−	0.00766241i
$987$		0			0
$988$	2.82890	−	3.89364i	0.0899992	−	0.123873i
$989$	14.1655			0.450437
$990$		0			0
$991$	−55.0154			−1.74762			−0.873811	−	0.486266i	$-0.838359\pi$
$991$	−55.0154			−1.74762			−0.873811	+	0.486266i	$0.838359\pi$
$992$	−5.21781	+	7.18170i	−0.165666	+	0.228019i
$993$		0			0
$994$	−13.6606	−	42.0431i	−0.433289	−	1.33353i
$995$	−13.8589	−	34.6936i	−0.439356	−	1.09986i
$996$		0			0
$997$	−21.8457	+	7.09810i	−0.691861	+	0.224799i	−0.633781	−	0.773513i	$-0.718498\pi$
$997$	−21.8457	+	7.09810i	−0.691861	+	0.224799i	−0.0580799	+	0.998312i	$0.518498\pi$
$998$	25.6603	+	8.33753i	0.812262	+	0.263920i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.ba.h.829.3		16
3.2	odd	2		110.2.j.b.59.2	✓	16
5.4	even	2	inner	990.2.ba.h.829.1		16
11.3	even	5	inner	990.2.ba.h.289.1		16
12.11	even	2		880.2.cd.b.609.4		16
15.2	even	4		550.2.h.j.301.2		8
15.8	even	4		550.2.h.n.301.1		8
15.14	odd	2		110.2.j.b.59.4	yes	16
33.5	odd	10		1210.2.b.k.969.1		8
33.14	odd	10		110.2.j.b.69.4	yes	16
33.17	even	10		1210.2.b.l.969.5		8
55.14	even	10	inner	990.2.ba.h.289.3		16
60.59	even	2		880.2.cd.b.609.2		16
132.47	even	10		880.2.cd.b.289.2		16
165.14	odd	10		110.2.j.b.69.2	yes	16
165.17	odd	20		6050.2.a.da.1.1		4
165.38	even	20		6050.2.a.dd.1.3		4
165.47	even	20		550.2.h.j.201.2		8
165.83	odd	20		6050.2.a.dl.1.4		4
165.104	odd	10		1210.2.b.k.969.7		8
165.113	even	20		550.2.h.n.201.1		8
165.137	even	20		6050.2.a.di.1.2		4
165.149	even	10		1210.2.b.l.969.3		8
660.179	even	10		880.2.cd.b.289.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.j.b.59.2	✓	16	3.2	odd	2
110.2.j.b.59.4	yes	16	15.14	odd	2
110.2.j.b.69.2	yes	16	165.14	odd	10
110.2.j.b.69.4	yes	16	33.14	odd	10
550.2.h.j.201.2		8	165.47	even	20
550.2.h.j.301.2		8	15.2	even	4
550.2.h.n.201.1		8	165.113	even	20
550.2.h.n.301.1		8	15.8	even	4
880.2.cd.b.289.2		16	132.47	even	10
880.2.cd.b.289.4		16	660.179	even	10
880.2.cd.b.609.2		16	60.59	even	2
880.2.cd.b.609.4		16	12.11	even	2
990.2.ba.h.289.1		16	11.3	even	5	inner
990.2.ba.h.289.3		16	55.14	even	10	inner
990.2.ba.h.829.1		16	5.4	even	2	inner
990.2.ba.h.829.3		16	1.1	even	1	trivial
1210.2.b.k.969.1		8	33.5	odd	10
1210.2.b.k.969.7		8	165.104	odd	10
1210.2.b.l.969.3		8	165.149	even	10
1210.2.b.l.969.5		8	33.17	even	10
6050.2.a.da.1.1		4	165.17	odd	20
6050.2.a.dd.1.3		4	165.38	even	20
6050.2.a.di.1.2		4	165.137	even	20
6050.2.a.dl.1.4		4	165.83	odd	20

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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(0.829496 + 2.07652i) q^{5} +(4.76878 - 1.54947i) q^{7} +(-0.951057 - 0.309017i) q^{8} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(0.829496 + 2.07652i) q^{5} +(4.76878 - 1.54947i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(2.16751 + 0.549472i) q^{10} +(0.969425 + 3.17178i) q^{11} +(-1.37249 + 1.88906i) q^{13} +(1.54947 - 4.76878i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.0359433 + 0.0494717i) q^{17} +(0.636930 - 1.96027i) q^{19} +(1.71856 - 1.43058i) q^{20} +(3.13584 + 1.08005i) q^{22} +3.91525i q^{23} +(-3.62387 + 3.44493i) q^{25} +(0.721558 + 2.22073i) q^{26} +(-2.94727 - 4.05657i) q^{28} +(-1.27844 - 3.93464i) q^{29} +(7.18170 + 5.21781i) q^{31} +1.00000i q^{32} +0.0611504 q^{34} +(7.17320 + 8.61720i) q^{35} +(-4.33385 + 1.40815i) q^{37} +(-1.21151 - 1.66751i) q^{38} +(-0.147217 - 2.23122i) q^{40} +(1.41525 - 4.35570i) q^{41} -3.61803i q^{43} +(2.71698 - 1.90211i) q^{44} +(3.16751 + 2.30133i) q^{46} +(-8.44260 - 2.74317i) q^{47} +(14.6773 - 10.6637i) q^{49} +(0.656948 + 4.95665i) q^{50} +(2.22073 + 0.721558i) q^{52} +(1.30598 - 1.79753i) q^{53} +(-5.78214 + 4.64401i) q^{55} -5.01420 q^{56} +(-3.93464 - 1.27844i) q^{58} +(0.599137 + 1.84396i) q^{59} +(7.84211 - 5.69763i) q^{61} +(8.44260 - 2.74317i) q^{62} +(0.809017 + 0.587785i) q^{64} +(-5.06115 - 1.28302i) q^{65} +2.49573i q^{67} +(0.0359433 - 0.0494717i) q^{68} +(11.1878 - 0.738177i) q^{70} +(7.13254 - 5.18210i) q^{71} +(5.13205 - 1.66751i) q^{73} +(-1.40815 + 4.33385i) q^{74} -2.06115 q^{76} +(9.53757 + 13.6235i) q^{77} +(-5.38417 - 3.91183i) q^{79} +(-1.89162 - 1.19237i) q^{80} +(-2.69197 - 3.70518i) q^{82} +(-6.49620 - 8.94125i) q^{83} +(-0.0729142 + 0.115674i) q^{85} +(-2.92705 - 2.12663i) q^{86} +(0.0581575 - 3.31611i) q^{88} +6.09017 q^{89} +(-3.61803 + 11.1352i) q^{91} +(3.72363 - 1.20988i) q^{92} +(-7.18170 + 5.21781i) q^{94} +(4.59887 - 0.303437i) q^{95} +(-4.29216 + 5.90765i) q^{97} -18.1422i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 6 q^{5}+O(q^{10}) \) 16 * q + 4 * q^4 + 6 * q^5	\( 16 q + 4 q^{4} + 6 q^{5} + 4 q^{10} + 20 q^{11} + 12 q^{14} - 4 q^{16} - 16 q^{19} - 6 q^{20} + 16 q^{26} - 16 q^{29} - 4 q^{31} - 8 q^{34} + 48 q^{35} - 4 q^{40} - 40 q^{41} + 20 q^{46} + 84 q^{49} - 4 q^{50} + 32 q^{55} + 8 q^{56} + 20 q^{61} + 4 q^{64} - 72 q^{65} + 36 q^{70} + 56 q^{71} - 4 q^{74} - 24 q^{76} + 36 q^{79} - 4 q^{80} - 54 q^{85} - 20 q^{86} + 8 q^{89} - 40 q^{91} + 4 q^{94} + 50 q^{95}+O(q^{100}) \) 16 * q + 4 * q^4 + 6 * q^5 + 4 * q^10 + 20 * q^11 + 12 * q^14 - 4 * q^16 - 16 * q^19 - 6 * q^20 + 16 * q^26 - 16 * q^29 - 4 * q^31 - 8 * q^34 + 48 * q^35 - 4 * q^40 - 40 * q^41 + 20 * q^46 + 84 * q^49 - 4 * q^50 + 32 * q^55 + 8 * q^56 + 20 * q^61 + 4 * q^64 - 72 * q^65 + 36 * q^70 + 56 * q^71 - 4 * q^74 - 24 * q^76 + 36 * q^79 - 4 * q^80 - 54 * q^85 - 20 * q^86 + 8 * q^89 - 40 * q^91 + 4 * q^94 + 50 * q^95

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