LMFDB - Embedded newform 990.2.ba.h.289.3

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			289.3
Root			$-2.23122 + 0.147217i$ of defining polynomial
Character	$\chi$	$=$	990.289
Dual form			990.2.ba.h.829.3

$q$-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 $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$	$1$

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	0.999939	−	0.0110184i	$-0.00350733\pi$
$7$	4.76878	+	1.54947i	1.80243	+	0.585645i	0.802491	+	0.596664i	$0.203507\pi$
$8$	−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	0.575100	−	0.818083i	$-0.304963\pi$
$13$	−1.37249	−	1.88906i	−0.380659	−	0.523932i	−0.955759	+	0.294151i	$0.904963\pi$
$14$	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	−0.804636	−	0.593768i	$-0.797640\pi$
$17$	0.0359433	−	0.0494717i	0.00871753	−	0.0119986i	0.813354	+	0.581770i	$0.197640\pi$
$18$		0			0
$19$	0.636930	+	1.96027i	0.146122	+	0.449717i	0.997154	−	0.0753974i	$-0.0240226\pi$
$19$	0.636930	+	1.96027i	0.146122	+	0.449717i	−0.851032	+	0.525114i	$0.824023\pi$
$20$	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	$-0.866159\pi$
$23$		−	3.91525i		−	0.816387i	0.912896	−	0.408193i	$-0.133841\pi$
$24$		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	0.759393	+	0.650632i	$0.225496\pi$
$29$	−1.27844	+	3.93464i	−0.237401	+	0.730644i	−0.996794	+	0.0800122i	$0.974504\pi$
$30$		0			0
$31$	7.18170	−	5.21781i	1.28987	−	0.937147i	0.290069	−	0.957006i	$-0.406322\pi$
$31$	7.18170	−	5.21781i	1.28987	−	0.937147i	0.999803	+	0.0198592i	$0.00632179\pi$
$32$		−	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	−0.0697209	−	0.997567i	$-0.522211\pi$
$37$	−4.33385	−	1.40815i	−0.712481	−	0.231499i	−0.642760	+	0.766067i	$0.722211\pi$
$38$	−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	0.998671	+	0.0515429i	$0.0164139\pi$
$41$	1.41525	+	4.35570i	0.221025	+	0.680246i	−0.777646	+	0.628703i	$0.783586\pi$
$42$		0			0
$43$			3.61803i			0.551745i	0.961194	+	0.275873i	$0.0889668\pi$
$43$			3.61803i			0.551745i	−0.961194	+	0.275873i	$0.911033\pi$
$44$	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	−0.851250	−	0.524760i	$-0.824155\pi$
$47$	−8.44260	+	2.74317i	−1.23148	+	0.400132i	−0.380229	+	0.924892i	$0.624155\pi$
$48$		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	0.889237	−	0.457446i	$-0.151236\pi$
$53$	1.30598	+	1.79753i	0.179391	+	0.246910i	−0.709847	+	0.704356i	$0.751236\pi$
$54$		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	−0.904451	−	0.426577i	$-0.859719\pi$
$59$	0.599137	−	1.84396i	0.0780011	−	0.240063i	0.982452	+	0.186515i	$0.0597192\pi$
$60$		0			0
$61$	7.84211	+	5.69763i	1.00408	+	0.729506i	0.962959	−	0.269648i	$-0.0869073\pi$
$61$	7.84211	+	5.69763i	1.00408	+	0.729506i	0.0411202	+	0.999154i	$0.486907\pi$
$62$	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	$-0.951283\pi$
$67$		−	2.49573i		−	0.304902i	0.988311	−	0.152451i	$-0.0487167\pi$
$68$	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	0.924172	−	0.381975i	$-0.124756\pi$
$71$	7.13254	+	5.18210i	0.846477	+	0.615002i	−0.0776953	+	0.996977i	$0.524756\pi$
$72$		0			0
$73$	5.13205	+	1.66751i	0.600662	+	0.195167i	0.593535	−	0.804808i	$-0.297732\pi$
$73$	5.13205	+	1.66751i	0.600662	+	0.195167i	0.00712611	+	0.999975i	$0.497732\pi$
$74$	−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	−0.847921	−	0.530123i	$-0.822146\pi$
$79$	−5.38417	+	3.91183i	−0.605766	+	0.440115i	0.242155	+	0.970238i	$0.422146\pi$
$80$	−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	0.286676	+	0.958028i	$0.407450\pi$
$83$	−6.49620	+	8.94125i	−0.713050	+	0.981429i	−0.999726	+	0.0234017i	$0.992550\pi$
$84$		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	0.533470	−	0.845819i	$-0.320888\pi$
$97$	−4.29216	−	5.90765i	−0.435802	−	0.599831i	−0.969273	+	0.245988i	$0.920888\pi$
$98$			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	−0.596680	−	0.802479i	$-0.703514\pi$
$101$	−0.179498	+	0.130413i	−0.0178608	+	0.0129766i	0.578819	+	0.815456i	$0.303514\pi$
$102$		0			0
$103$	0.538341	+	0.174918i	0.0530443	+	0.0172351i	0.335419	−	0.942069i	$-0.391122\pi$
$103$	0.538341	+	0.174918i	0.0530443	+	0.0172351i	−0.282375	+	0.959304i	$0.591122\pi$
$104$	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	−0.204700	−	0.978825i	$-0.565622\pi$
$107$	2.12087	−	0.689113i	0.205033	−	0.0666191i	0.409733	+	0.912206i	$0.365622\pi$
$108$		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	−0.811242	−	0.584710i	$-0.801208\pi$
$113$	−11.9469	+	3.88177i	−1.12387	+	0.365166i	−0.312624	+	0.949877i	$0.601208\pi$
$114$		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	0.243310	+	0.969949i	$0.421767\pi$
$127$	−8.50112	+	11.7008i	−0.754353	+	1.03828i	−0.997663	+	0.0683289i	$0.978233\pi$
$128$	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	−0.835846	−	0.548964i	$-0.815022\pi$
$137$	−0.649130	+	0.893451i	−0.0554589	+	0.0763326i	0.780387	+	0.625297i	$0.215022\pi$
$138$		0			0
$139$	3.06115	−	9.42125i	0.259643	−	0.799100i	−0.733236	−	0.679974i	$-0.761991\pi$
$139$	3.06115	−	9.42125i	0.259643	−	0.799100i	0.992879	−	0.119126i	$-0.0380092\pi$
$140$	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	0.256977	−	0.966418i	$-0.417274\pi$
$149$	−7.11314	−	5.16800i	−0.582731	−	0.423379i	−0.839708	+	0.543039i	$0.817274\pi$
$150$		0			0
$151$	6.67177	+	20.5336i	0.542941	+	1.67100i	0.725835	+	0.687868i	$0.241453\pi$
$151$	6.67177	+	20.5336i	0.542941	+	1.67100i	−0.182894	+	0.983133i	$0.558547\pi$
$152$	−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	−0.176542	−	0.984293i	$-0.556491\pi$
$157$	3.24760	−	1.05521i	0.259186	−	0.0842148i	0.435728	+	0.900078i	$0.356491\pi$
$158$	−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	−0.992572	−	0.121657i	$-0.961179\pi$
$163$	−10.2336	−	14.0853i	−0.801554	−	1.10324i	0.191019	−	0.981586i	$-0.438821\pi$
$164$	−4.57985			−0.357626
$165$		0			0
$166$	−11.0520			−0.857801
$167$	−1.94321	−	2.67460i	−0.150370	−	0.206967i	0.727186	−	0.686440i	$-0.240828\pi$
$167$	−1.94321	−	2.67460i	−0.150370	−	0.206967i	−0.877556	+	0.479473i	$0.840828\pi$
$168$		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	−0.117670	−	0.993053i	$-0.537542\pi$
$173$	4.87758	−	1.58482i	0.370836	−	0.120492i	0.488505	+	0.872561i	$0.337542\pi$
$174$		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	−0.967453	−	0.253051i	$-0.918566\pi$
$179$	−4.46201	−	13.7327i	−0.333507	−	1.02643i	0.633947	−	0.773377i	$-0.281434\pi$
$180$		0			0
$181$	−9.63223	−	6.99822i	−0.715958	−	0.520174i	0.169132	−	0.985593i	$-0.445903\pi$
$181$	−9.63223	−	6.99822i	−0.715958	−	0.520174i	−0.885090	+	0.465419i	$0.845903\pi$
$182$	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	0.761917	+	0.647675i	$0.224259\pi$
$191$	−3.25026	+	10.0033i	−0.235181	+	0.723812i	−0.997097	+	0.0761369i	$0.975741\pi$
$192$		0			0
$193$	2.86174	−	3.93885i	0.205993	−	0.283525i	−0.693503	−	0.720453i	$-0.743934\pi$
$193$	2.86174	−	3.93885i	0.205993	−	0.283525i	0.899496	+	0.436929i	$0.143934\pi$
$194$	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	$-0.807283\pi$
$197$		−	15.9760i		−	1.13824i	0.822253	−	0.569122i	$-0.192717\pi$
$198$		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	−0.0554754	−	0.998460i	$-0.517667\pi$
$211$	12.7388	−	9.25526i	0.876974	−	0.637159i	0.932449	+	0.361301i	$0.117667\pi$
$212$	−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	−0.733340	−	0.679862i	$-0.762039\pi$
$223$	−13.8432	+	4.49794i	−0.927011	+	0.301204i	−0.193671	+	0.981067i	$0.562039\pi$
$224$	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	−0.0183719	−	0.999831i	$-0.505848\pi$
$227$	−9.35512	−	3.03966i	−0.620921	−	0.201749i	−0.602549	+	0.798082i	$0.705848\pi$
$228$		0			0
$229$	−12.5785	+	9.13881i	−0.831210	+	0.603909i	−0.919901	−	0.392150i	$-0.871732\pi$
$229$	−12.5785	+	9.13881i	−0.831210	+	0.603909i	0.0886913	+	0.996059i	$0.471732\pi$
$230$	−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	0.927024	+	0.375002i	$0.122358\pi$
$233$	15.2217	+	20.9509i	0.997206	+	1.37254i	0.0701824	+	0.997534i	$0.477642\pi$
$234$		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	0.925246	+	0.379369i	$0.123859\pi$
$239$	6.17911	+	19.0173i	0.399693	+	1.23013i	−0.525552	+	0.850761i	$0.676141\pi$
$240$		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	−0.553792	−	0.832655i	$-0.686820\pi$
$251$	1.06115	−	0.770971i	0.0669792	−	0.0486632i	0.620771	+	0.783992i	$0.286820\pi$
$252$		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	0.438421	−	0.898770i	$-0.355538\pi$
$257$	4.24551	+	1.37945i	0.264827	+	0.0860477i	−0.173594	+	0.984817i	$0.555538\pi$
$258$		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	$-0.855984\pi$
$263$		−	14.1791i		−	0.874320i	0.899384	−	0.437160i	$-0.144016\pi$
$264$		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	0.918702	+	0.394952i	$0.129239\pi$
$269$	25.8847	+	18.8063i	1.57822	+	1.14664i	0.659516	+	0.751691i	$0.270761\pi$
$270$		0			0
$271$	0.327988	−	1.00944i	0.0199238	−	0.0613192i	−0.940600	−	0.339516i	$-0.889737\pi$
$271$	0.327988	−	1.00944i	0.0199238	−	0.0613192i	0.960524	+	0.278197i	$0.0897367\pi$
$272$	−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	0.675659	−	0.737214i	$-0.263859\pi$
$277$	−3.89892	−	5.36641i	−0.234264	−	0.322436i	−0.909923	+	0.414778i	$0.863859\pi$
$278$	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	0.897412	−	0.441194i	$-0.145445\pi$
$281$	12.6582	+	9.19674i	0.755126	+	0.548631i	−0.142285	+	0.989826i	$0.545445\pi$
$282$		0			0
$283$	−21.3993	+	6.95305i	−1.27205	+	0.413316i	−0.865775	−	0.500433i	$-0.833174\pi$
$283$	−21.3993	+	6.95305i	−1.27205	+	0.413316i	−0.406280	+	0.913749i	$0.633174\pi$
$284$	−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	−0.243500	−	0.969901i	$-0.578296\pi$
$293$	−17.2985	−	5.62063i	−1.01059	−	0.328360i	−0.767089	+	0.641540i	$0.778296\pi$
$294$		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	$0.114953\pi$
$307$			12.3820i			0.706676i	−0.935496	+	0.353338i	$0.885047\pi$
$308$	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	0.834140	−	0.551553i	$-0.185965\pi$
$311$	−2.90784	−	8.94941i	−0.164889	−	0.507475i	−0.999028	+	0.0440788i	$0.985965\pi$
$312$		0			0
$313$	−8.95297	+	12.3227i	−0.506052	+	0.696520i	−0.983247	−	0.182277i	$-0.941653\pi$
$313$	−8.95297	+	12.3227i	−0.506052	+	0.696520i	0.477196	+	0.878797i	$0.341653\pi$
$314$	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	0.526900	−	0.849927i	$-0.323354\pi$
$317$	−7.90964	−	10.8867i	−0.444250	−	0.611457i	−0.971150	+	0.238470i	$0.923354\pi$
$318$		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	0.0533455	−	0.998576i	$-0.483012\pi$
$337$	−9.00338	−	2.92538i	−0.490445	−	0.159355i	−0.543791	+	0.839221i	$0.683012\pi$
$338$	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	−0.463902	−	0.885887i	$-0.653551\pi$
$347$	9.72341	−	13.3831i	0.521980	−	0.718444i	0.985882	+	0.167443i	$0.0535510\pi$
$348$		0			0
$349$	−9.03161	−	27.7964i	−0.483451	−	1.48791i	−0.834212	−	0.551444i	$-0.814077\pi$
$349$	−9.03161	−	27.7964i	−0.483451	−	1.48791i	0.350761	−	0.936465i	$-0.385923\pi$
$350$	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	$0.266606\pi$
$353$			27.9200i			1.48603i	−0.669272	+	0.743017i	$0.733394\pi$
$354$		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	−0.711060	−	0.703131i	$-0.751785\pi$
$359$	5.25768	−	16.1815i	0.277490	−	0.854025i	0.988550	−	0.150894i	$-0.0482152\pi$
$360$		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	−0.532971	−	0.846133i	$-0.678925\pi$
$367$	−27.9983	−	9.09719i	−1.46150	−	0.474870i	−0.928527	+	0.371264i	$0.878925\pi$
$368$	−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	$-0.863380\pi$
$373$		−	16.0743i		−	0.832297i	0.909297	−	0.416149i	$-0.136620\pi$
$374$	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	0.896794	−	0.442448i	$-0.145890\pi$
$379$	14.6618	+	10.6524i	0.753125	+	0.547178i	−0.143669	+	0.989626i	$0.545890\pi$
$380$	−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	0.959942	−	0.280200i	$-0.0904008\pi$
$383$	7.76587	+	10.6888i	0.396817	+	0.546172i	−0.563124	+	0.826372i	$0.690401\pi$
$384$		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	0.496150	+	0.868237i	$0.334746\pi$
$389$	−8.19653	+	25.2263i	−0.415580	+	1.27902i	−0.911731	+	0.410788i	$0.865254\pi$
$390$		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	$-0.724722\pi$
$397$		−	30.3246i		−	1.52195i	0.648783	−	0.760974i	$-0.275278\pi$
$398$	−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	0.907025	−	0.421076i	$-0.138348\pi$
$401$	15.7565	+	11.4478i	0.786844	+	0.571676i	−0.120181	+	0.992752i	$0.538348\pi$
$402$		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	−0.986172	−	0.165723i	$-0.947004\pi$
$409$	−22.9197	+	16.6521i	−1.13330	+	0.823394i	−0.147132	+	0.989117i	$0.547004\pi$
$410$	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	0.972070	+	0.234690i	$0.0754076\pi$
$421$	6.63964	+	20.4347i	0.323596	+	0.995927i	−0.648474	+	0.761237i	$0.724592\pi$
$422$	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	0.0619316	−	0.998080i	$-0.480274\pi$
$431$	21.3896	−	15.5404i	1.03030	−	0.748557i	0.968369	+	0.249523i	$0.0802739\pi$
$432$		0			0
$433$	31.2725	+	10.1611i	1.50286	+	0.488309i	0.940851	−	0.338821i	$-0.110028\pi$
$433$	31.2725	+	10.1611i	1.50286	+	0.488309i	0.562010	+	0.827130i	$0.310028\pi$
$434$	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	−0.659195	−	0.751972i	$-0.729103\pi$
$443$	−15.7961	+	5.13247i	−0.750496	+	0.243851i	−0.0913015	+	0.995823i	$0.529103\pi$
$444$		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	−0.480667	−	0.876903i	$-0.659605\pi$
$449$	4.33928	−	3.15267i	0.204783	−	0.148784i	0.685450	+	0.728119i	$0.259605\pi$
$450$		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	−0.756462	−	0.654037i	$-0.773074\pi$
$457$	2.12330	−	2.92247i	0.0993237	−	0.136707i	0.855786	+	0.517330i	$0.173074\pi$
$458$	−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	$-0.984322\pi$
$463$		−	2.11880i		−	0.0984690i	0.998787	−	0.0492345i	$-0.0156782\pi$
$464$	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	−0.954017	−	0.299754i	$-0.903095\pi$
$467$	−8.08494	+	11.1280i	−0.374126	+	0.514941i	0.579890	+	0.814695i	$0.303095\pi$
$468$		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	−0.171180	−	0.985240i	$-0.554758\pi$
$479$	−25.4118	−	18.4628i	−1.16110	−	0.843586i	−0.989916	+	0.141654i	$0.954758\pi$
$480$		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	−0.466344	−	0.884603i	$-0.654429\pi$
$487$	−7.14274	+	2.32082i	−0.323668	+	0.105166i	0.142676	+	0.989769i	$0.454429\pi$
$488$	−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	−0.998363	−	0.0571923i	$-0.981785\pi$
$491$	−3.48008	+	10.7106i	−0.157054	+	0.483361i	0.841310	+	0.540554i	$0.181785\pi$
$492$		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	−0.571420	−	0.820658i	$-0.693607\pi$
$499$	8.33753	−	25.6603i	0.373239	−	1.14871i	0.944659	−	0.328054i	$-0.106393\pi$
$500$	−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	−0.897235	−	0.441554i	$-0.854427\pi$
$503$	−30.5818	+	9.93662i	−1.36357	+	0.443052i	−0.466339	+	0.884606i	$0.654427\pi$
$504$		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	0.998750	−	0.0499888i	$-0.0159186\pi$
$509$	3.64048	+	11.2043i	0.161362	+	0.496620i	−0.837388	+	0.546609i	$0.815919\pi$
$510$		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	−0.965568	−	0.260152i	$-0.916227\pi$
$521$	−0.718847	+	2.21238i	−0.0314933	+	0.0969263i	0.934074	+	0.357079i	$0.116227\pi$
$522$		0			0
$523$	0.901612	−	1.24096i	0.0394248	−	0.0542635i	−0.788850	−	0.614586i	$-0.789323\pi$
$523$	0.901612	−	1.24096i	0.0394248	−	0.0542635i	0.828274	+	0.560323i	$0.189323\pi$
$524$	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	−0.285904	−	0.958258i	$-0.592294\pi$
$541$	12.4927	−	9.07650i	0.537104	−	0.390229i	0.823008	+	0.568029i	$0.192294\pi$
$542$	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	−0.517385	−	0.855752i	$-0.673095\pi$
$547$	−10.1261	+	3.29017i	−0.432960	+	0.140677i	0.0844251	+	0.996430i	$0.473095\pi$
$548$	−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	0.898334	−	0.439313i	$-0.144778\pi$
$557$	32.2595	+	10.4818i	1.36688	+	0.444126i	0.468545	+	0.883439i	$0.344778\pi$
$558$		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	0.825337	−	0.564641i	$-0.190985\pi$
$563$	0.789857	+	1.08714i	0.0332885	+	0.0458177i	−0.792048	+	0.610458i	$0.790985\pi$
$564$		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	−0.919303	−	0.393550i	$-0.871247\pi$
$569$	−9.70595	−	29.8718i	−0.406894	−	1.25229i	0.512409	−	0.858742i	$-0.328753\pi$
$570$		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	−0.183244	+	0.983068i	$0.558660\pi$
$577$	−25.4998	+	35.0975i	−1.06157	+	1.46113i	−0.878327	+	0.478060i	$0.841340\pi$
$578$	−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	0.245285	−	0.969451i	$-0.421118\pi$
$587$	−3.05524	−	0.992708i	−0.126103	−	0.0409734i	−0.371389	+	0.928477i	$0.621118\pi$
$588$		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	$-0.999794\pi$
$593$		−	0.0315027i		−	0.00129366i	1.00000		0.000646829i	$-0.000205892\pi$
$594$		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	0.747906	−	0.663804i	$-0.231059\pi$
$599$	8.50993	+	6.18283i	0.347706	+	0.252623i	−0.400200	+	0.916428i	$0.631059\pi$
$600$		0			0
$601$	7.45305	−	22.9381i	0.304016	−	0.935665i	−0.676026	−	0.736877i	$-0.736300\pi$
$601$	7.45305	−	22.9381i	0.304016	−	0.935665i	0.980043	−	0.198788i	$-0.0637005\pi$
$602$	−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	0.837682	−	0.546158i	$-0.183910\pi$
$607$	1.46340	+	2.01420i	0.0593975	+	0.0817537i	−0.778285	+	0.627911i	$0.783910\pi$
$608$	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	0.520359	−	0.853948i	$-0.325798\pi$
$613$	35.7338	−	11.6106i	1.44328	−	0.468949i	0.922917	+	0.384999i	$0.125798\pi$
$614$	−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	$-0.630207\pi$
$617$		−	45.5803i		−	1.83499i	0.397744	−	0.917496i	$-0.369793\pi$
$618$		0			0
$619$	−1.77382	−	5.45924i	−0.0712957	−	0.219425i	0.909059	−	0.416667i	$-0.136802\pi$
$619$	−1.77382	−	5.45924i	−0.0712957	−	0.219425i	−0.980355	+	0.197241i	$0.936802\pi$
$620$	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	−0.849968	−	0.526834i	$-0.823379\pi$
$631$	3.70103	−	11.3906i	0.147336	−	0.453453i	0.997304	+	0.0733811i	$0.0233790\pi$
$632$	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	0.899455	+	0.437013i	$0.143964\pi$
$641$	10.8526	+	33.4007i	0.428650	+	1.31925i	−0.470805	+	0.882237i	$0.656036\pi$
$642$		0			0
$643$	20.9529	−	28.8392i	0.826302	−	1.13731i	−0.162298	−	0.986742i	$-0.551891\pi$
$643$	20.9529	−	28.8392i	0.826302	−	1.13731i	0.988600	−	0.150565i	$-0.0481093\pi$
$644$	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	0.975694	−	0.219136i	$-0.0703238\pi$
$647$	11.8476	+	16.3068i	0.465778	+	0.641088i	−0.509917	+	0.860224i	$0.670324\pi$
$648$		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	0.725334	−	0.688397i	$-0.241685\pi$
$653$	23.1905	+	7.53504i	0.907513	+	0.294869i	0.182178	+	0.983266i	$0.441685\pi$
$654$		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	0.889692	−	0.456562i	$-0.150919\pi$
$673$	4.68377	+	6.44665i	0.180546	+	0.248500i	−0.709146	+	0.705062i	$0.750919\pi$
$674$	−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	−0.940312	−	0.340313i	$-0.889467\pi$
$677$	−8.48443	+	11.6778i	−0.326083	+	0.448815i	0.614229	+	0.789128i	$0.289467\pi$
$678$		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	$-0.807837\pi$
$683$		−	29.6723i		−	1.13538i	0.823242	−	0.567690i	$-0.192163\pi$
$684$		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	−0.961223	−	0.275774i	$-0.911066\pi$
$691$	−26.1812	+	19.0218i	−0.995980	+	0.723622i	−0.0347577	+	0.999396i	$0.511066\pi$
$692$			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	−0.998640	−	0.0521266i	$-0.983400\pi$
$701$	−5.86089	−	18.0380i	−0.221363	−	0.681284i	0.777278	−	0.629157i	$-0.216600\pi$
$702$		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	0.707878	−	0.706335i	$-0.249653\pi$
$709$	6.78617	+	4.93044i	0.254860	+	0.185167i	−0.453018	+	0.891501i	$0.649653\pi$
$710$	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	−0.898104	−	0.439783i	$-0.855055\pi$
$719$	2.33218	−	7.17771i	0.0869756	−	0.267684i	0.985079	+	0.172100i	$0.0550552\pi$
$720$		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	$-0.851318\pi$
$727$		−	24.2826i		−	0.900593i	0.892879	−	0.450297i	$-0.148682\pi$
$728$	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	0.659754	−	0.751482i	$-0.270660\pi$
$733$	20.3541	+	6.61345i	0.751796	+	0.244273i	0.0920424	+	0.995755i	$0.470660\pi$
$734$	−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	0.0747558	−	0.997202i	$-0.476182\pi$
$739$	28.4419	−	20.6642i	1.04625	−	0.760147i	0.971496	+	0.237055i	$0.0761823\pi$
$740$	−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	−0.263550	−	0.964646i	$-0.584893\pi$
$743$	20.0435	−	27.5875i	0.735324	−	1.01209i	0.998874	−	0.0474407i	$-0.0151065\pi$
$744$		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	−0.921799	−	0.387669i	$-0.873280\pi$
$751$	−11.0690	−	34.0669i	−0.403914	−	1.24312i	0.517884	−	0.855451i	$-0.326720\pi$
$752$	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	0.985176	−	0.171544i	$-0.0548756\pi$
$757$	14.2408	+	19.6008i	0.517592	+	0.712404i	−0.467584	+	0.883948i	$0.654876\pi$
$758$			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	−0.420443	−	0.907319i	$-0.638125\pi$
$761$	8.62191	−	6.26419i	0.312544	−	0.227077i	0.732987	+	0.680242i	$0.238125\pi$
$762$		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	−0.507899	−	0.861416i	$-0.669578\pi$
$773$	−11.4679	+	3.72614i	−0.412471	+	0.134020i	0.0954286	+	0.995436i	$0.469578\pi$
$774$		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	−0.575265	−	0.817967i	$-0.695101\pi$
$787$	10.6725	−	14.6895i	0.380435	−	0.523624i	0.955700	+	0.294343i	$0.0951009\pi$
$788$	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	−0.791920	−	0.610624i	$-0.790919\pi$
$797$	0.946725	−	1.30306i	0.0335347	−	0.0461566i	0.825455	+	0.564468i	$0.190919\pi$
$798$		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	0.160429	−	0.987047i	$-0.448712\pi$
$809$	−20.7273	−	15.0593i	−0.728733	−	0.529455i	−0.889162	+	0.457592i	$0.848712\pi$
$810$		0			0
$811$	13.5506	+	41.7045i	0.475827	+	1.46444i	0.844839	+	0.535020i	$0.179696\pi$
$811$	13.5506	+	41.7045i	0.475827	+	1.46444i	−0.369012	+	0.929424i	$0.620304\pi$
$812$	−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	−0.810163	−	0.586205i	$-0.800621\pi$
$821$	5.43938	−	16.7407i	0.189836	−	0.584254i	0.999998	+	0.00195152i	$0.000621189\pi$
$822$		0			0
$823$	7.43854	+	10.2383i	0.259291	+	0.356884i	0.918738	−	0.394867i	$-0.129209\pi$
$823$	7.43854	+	10.2383i	0.259291	+	0.356884i	−0.659447	+	0.751751i	$0.729209\pi$
$824$	−0.566045			−0.0197191
$825$		0			0
$826$	9.72177			0.338264
$827$	−5.19856	−	7.15520i	−0.180772	−	0.248811i	0.709009	−	0.705200i	$-0.249143\pi$
$827$	−5.19856	−	7.15520i	−0.180772	−	0.248811i	−0.889780	+	0.456389i	$0.849143\pi$
$828$		0			0
$829$	−11.6571	+	35.8767i	−0.404866	+	1.24605i	0.516141	+	0.856504i	$0.327368\pi$
$829$	−11.6571	+	35.8767i	−0.404866	+	1.24605i	−0.921007	+	0.389546i	$0.872632\pi$
$830$	−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	−0.916123	−	0.400898i	$-0.868698\pi$
$839$	−11.8934	−	36.6041i	−0.410606	−	1.26372i	0.505517	−	0.862817i	$-0.331302\pi$
$840$		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	0.114936	−	0.993373i	$-0.463334\pi$
$853$	29.9122	−	41.1706i	1.02417	−	1.40965i	0.909237	−	0.416280i	$-0.136666\pi$
$854$	−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	$0.0630397\pi$
$857$			11.5197i			0.393506i	−0.980453	+	0.196753i	$0.936960\pi$
$858$		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	−0.192187	−	0.981358i	$-0.561558\pi$
$863$	23.5170	−	32.3684i	0.800530	−	1.10183i	0.992716	−	0.120476i	$-0.0384421\pi$
$864$		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	−0.694903	−	0.719104i	$-0.744553\pi$
$877$	−24.7104	+	8.02891i	−0.834413	+	0.271117i	−0.139510	+	0.990221i	$0.544553\pi$
$878$	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	−0.906369	−	0.422486i	$-0.861157\pi$
$883$	−41.3431	+	13.4332i	−1.39131	+	0.452063i	−0.484937	+	0.874549i	$0.661157\pi$
$884$	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	−0.185731	−	0.982601i	$-0.559465\pi$
$887$	−27.2078	−	8.84036i	−0.913549	−	0.296830i	−0.727818	+	0.685770i	$0.759465\pi$
$888$		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	−0.0282187	−	0.999602i	$-0.508983\pi$
$907$	28.0438	−	38.5990i	0.931179	−	1.28166i	0.959398	−	0.282056i	$-0.0910165\pi$
$908$	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	0.335602	−	0.942004i	$-0.391060\pi$
$911$	40.3003	−	29.2799i	1.33521	−	0.970085i	0.999606	−	0.0280809i	$-0.00893959\pi$
$912$		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	−0.157053	−	0.987590i	$-0.550199\pi$
$919$	−34.7058	−	25.2153i	−1.14484	−	0.831775i	−0.987786	+	0.155815i	$0.950199\pi$
$920$	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	0.639153	−	0.769079i	$-0.279285\pi$
$929$	3.20719	+	2.33016i	0.105224	+	0.0764500i	−0.533929	+	0.845529i	$0.679285\pi$
$930$		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	0.828879	−	0.559429i	$-0.188979\pi$
$937$	1.24563	+	1.71446i	0.0406929	+	0.0560090i	−0.788186	+	0.615437i	$0.788979\pi$
$938$	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	0.652316	−	0.757947i	$-0.273797\pi$
$941$	4.08118	+	2.96515i	0.133043	+	0.0966612i	−0.519274	+	0.854608i	$0.673797\pi$
$942$		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	$0.00510065\pi$
$947$			0.986192i			0.0320470i	−0.999872	+	0.0160235i	$0.994899\pi$
$948$		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	0.640562	−	0.767907i	$-0.278702\pi$
$953$	21.8386	+	7.09580i	0.707422	+	0.229855i	0.0668608	+	0.997762i	$0.478702\pi$
$954$		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	$0.104898\pi$
$967$			20.1267i			0.647231i	−0.946189	+	0.323616i	$0.895102\pi$
$968$	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	0.998964	+	0.0455060i	$0.0144900\pi$
$971$	6.77852	+	20.8621i	0.217533	+	0.669498i	−0.781431	+	0.623991i	$0.785510\pi$
$972$		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	0.820562	+	0.571557i	$0.193660\pi$
$977$	34.7133	+	47.7788i	1.11058	+	1.52858i	0.290015	+	0.957022i	$0.406340\pi$
$978$		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	0.930012	−	0.367530i	$-0.119796\pi$
$983$	45.9751	+	14.9382i	1.46638	+	0.476455i	0.536367	+	0.843985i	$0.319796\pi$
$984$		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	−0.0580799	−	0.998312i	$-0.518498\pi$
$997$	−21.8457	−	7.09810i	−0.691861	−	0.224799i	−0.633781	+	0.773513i	$0.718498\pi$
$998$	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.289.3		16
3.2	odd	2		110.2.j.b.69.2	yes	16
5.4	even	2	inner	990.2.ba.h.289.1		16
11.4	even	5	inner	990.2.ba.h.829.1		16
12.11	even	2		880.2.cd.b.289.4		16
15.2	even	4		550.2.h.n.201.1		8
15.8	even	4		550.2.h.j.201.2		8
15.14	odd	2		110.2.j.b.69.4	yes	16
33.2	even	10		1210.2.b.l.969.3		8
33.20	odd	10		1210.2.b.k.969.7		8
33.26	odd	10		110.2.j.b.59.4	yes	16
55.4	even	10	inner	990.2.ba.h.829.3		16
60.59	even	2		880.2.cd.b.289.2		16
132.59	even	10		880.2.cd.b.609.2		16
165.2	odd	20		6050.2.a.dl.1.4		4
165.53	even	20		6050.2.a.di.1.2		4
165.59	odd	10		110.2.j.b.59.2	✓	16
165.68	odd	20		6050.2.a.da.1.1		4
165.92	even	20		550.2.h.n.301.1		8
165.119	odd	10		1210.2.b.k.969.1		8
165.134	even	10		1210.2.b.l.969.5		8
165.152	even	20		6050.2.a.dd.1.3		4
165.158	even	20		550.2.h.j.301.2		8
660.59	even	10		880.2.cd.b.609.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.j.b.59.2	✓	16	165.59	odd	10
110.2.j.b.59.4	yes	16	33.26	odd	10
110.2.j.b.69.2	yes	16	3.2	odd	2
110.2.j.b.69.4	yes	16	15.14	odd	2
550.2.h.j.201.2		8	15.8	even	4
550.2.h.j.301.2		8	165.158	even	20
550.2.h.n.201.1		8	15.2	even	4
550.2.h.n.301.1		8	165.92	even	20
880.2.cd.b.289.2		16	60.59	even	2
880.2.cd.b.289.4		16	12.11	even	2
880.2.cd.b.609.2		16	132.59	even	10
880.2.cd.b.609.4		16	660.59	even	10
990.2.ba.h.289.1		16	5.4	even	2	inner
990.2.ba.h.289.3		16	1.1	even	1	trivial
990.2.ba.h.829.1		16	11.4	even	5	inner
990.2.ba.h.829.3		16	55.4	even	10	inner
1210.2.b.k.969.1		8	165.119	odd	10
1210.2.b.k.969.7		8	33.20	odd	10
1210.2.b.l.969.3		8	33.2	even	10
1210.2.b.l.969.5		8	165.134	even	10
6050.2.a.da.1.1		4	165.68	odd	20
6050.2.a.dd.1.3		4	165.152	even	20
6050.2.a.di.1.2		4	165.53	even	20
6050.2.a.dl.1.4		4	165.2	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more