LMFDB - Embedded newform 1638.2.m.k.289.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(289,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

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

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

chi := DirichletCharacter("1638.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.m (of order $3$, degree $2$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 15x^{8} + 14x^{7} + 110x^{6} + 36x^{5} + 233x^{4} + 164x^{3} + 345x^{2} + 76x + 16 $ x^10 - 2x^9 + 15x^8 + 14x^7 + 110x^6 + 36x^5 + 233x^4 + 164x^3 + 345x^2 + 76*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.5
Root			$2.07085 + 3.58682i$ of defining polynomial
Character	$\chi$	$=$	1638.289
Dual form			1638.2.m.k.1621.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(2.07085 - 3.58682i) q^{5} +(0.321703 - 2.62612i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(2.07085 - 3.58682i) q^{5} +(0.321703 - 2.62612i) q^{7} +1.00000 q^{8} +(2.07085 - 3.58682i) q^{10} +(0.261547 - 0.453013i) q^{11} +(-3.28981 + 1.47551i) q^{13} +(0.321703 - 2.62612i) q^{14} +1.00000 q^{16} +2.52309 q^{17} +(2.84997 + 4.93629i) q^{19} +(2.07085 - 3.58682i) q^{20} +(0.261547 - 0.453013i) q^{22} +7.39337 q^{23} +(-6.07684 - 10.5254i) q^{25} +(-3.28981 + 1.47551i) q^{26} +(0.321703 - 2.62612i) q^{28} +(1.54066 + 2.66851i) q^{29} +(-2.17638 - 3.76959i) q^{31} +1.00000 q^{32} +2.52309 q^{34} +(-8.75321 - 6.59219i) q^{35} -5.66479 q^{37} +(2.84997 + 4.93629i) q^{38} +(2.07085 - 3.58682i) q^{40} +(-2.33240 - 4.03983i) q^{41} +(-4.81529 + 8.34033i) q^{43} +(0.261547 - 0.453013i) q^{44} +7.39337 q^{46} +(5.58154 - 9.66752i) q^{47} +(-6.79301 - 1.68966i) q^{49} +(-6.07684 - 10.5254i) q^{50} +(-3.28981 + 1.47551i) q^{52} +(0.00192073 + 0.00332680i) q^{53} +(-1.08325 - 1.87624i) q^{55} +(0.321703 - 2.62612i) q^{56} +(1.54066 + 2.66851i) q^{58} -8.10749 q^{59} +(-3.00599 - 5.20652i) q^{61} +(-2.17638 - 3.76959i) q^{62} +1.00000 q^{64} +(-1.52031 + 14.8555i) q^{65} +(-1.61622 + 2.79938i) q^{67} +2.52309 q^{68} +(-8.75321 - 6.59219i) q^{70} +(-3.98568 + 6.90340i) q^{71} +(5.99080 + 10.3764i) q^{73} -5.66479 q^{74} +(2.84997 + 4.93629i) q^{76} +(-1.10553 - 0.832590i) q^{77} +(1.15602 - 2.00229i) q^{79} +(2.07085 - 3.58682i) q^{80} +(-2.33240 - 4.03983i) q^{82} -3.08133 q^{83} +(5.22495 - 9.04988i) q^{85} +(-4.81529 + 8.34033i) q^{86} +(0.261547 - 0.453013i) q^{88} +10.8520 q^{89} +(2.81653 + 9.11412i) q^{91} +7.39337 q^{92} +(5.58154 - 9.66752i) q^{94} +23.6074 q^{95} +(-1.31892 + 2.28443i) q^{97} +(-6.79301 - 1.68966i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 10 q^{4} + 2 q^{5} - 2 q^{7} + 10 q^{8}+O(q^{10}) $ 10 * q + 10 * q^2 + 10 * q^4 + 2 * q^5 - 2 * q^7 + 10 * q^8	$ 10 q + 10 q^{2} + 10 q^{4} + 2 q^{5} - 2 q^{7} + 10 q^{8} + 2 q^{10} - 6 q^{11} - 4 q^{13} - 2 q^{14} + 10 q^{16} + 8 q^{17} + 3 q^{19} + 2 q^{20} - 6 q^{22} + 12 q^{23} - q^{25} - 4 q^{26} - 2 q^{28} - 10 q^{31} + 10 q^{32} + 8 q^{34} - 16 q^{35} - 2 q^{37} + 3 q^{38} + 2 q^{40} + 4 q^{41} + 3 q^{43} - 6 q^{44} + 12 q^{46} + 15 q^{47} + 4 q^{49} - q^{50} - 4 q^{52} + 17 q^{53} + 3 q^{55} - 2 q^{56} + 4 q^{59} + 11 q^{61} - 10 q^{62} + 10 q^{64} + 4 q^{65} - q^{67} + 8 q^{68} - 16 q^{70} - 18 q^{71} + 12 q^{73} - 2 q^{74} + 3 q^{76} - 18 q^{77} - 4 q^{79} + 2 q^{80} + 4 q^{82} + q^{85} + 3 q^{86} - 6 q^{88} + 14 q^{89} + 26 q^{91} + 12 q^{92} + 15 q^{94} + 48 q^{95} - 6 q^{97} + 4 q^{98}+O(q^{100}) $ 10 * q + 10 * q^2 + 10 * q^4 + 2 * q^5 - 2 * q^7 + 10 * q^8 + 2 * q^10 - 6 * q^11 - 4 * q^13 - 2 * q^14 + 10 * q^16 + 8 * q^17 + 3 * q^19 + 2 * q^20 - 6 * q^22 + 12 * q^23 - q^25 - 4 * q^26 - 2 * q^28 - 10 * q^31 + 10 * q^32 + 8 * q^34 - 16 * q^35 - 2 * q^37 + 3 * q^38 + 2 * q^40 + 4 * q^41 + 3 * q^43 - 6 * q^44 + 12 * q^46 + 15 * q^47 + 4 * q^49 - q^50 - 4 * q^52 + 17 * q^53 + 3 * q^55 - 2 * q^56 + 4 * q^59 + 11 * q^61 - 10 * q^62 + 10 * q^64 + 4 * q^65 - q^67 + 8 * q^68 - 16 * q^70 - 18 * q^71 + 12 * q^73 - 2 * q^74 + 3 * q^76 - 18 * q^77 - 4 * q^79 + 2 * q^80 + 4 * q^82 + q^85 + 3 * q^86 - 6 * q^88 + 14 * q^89 + 26 * q^91 + 12 * q^92 + 15 * q^94 + 48 * q^95 - 6 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	2.07085	−	3.58682i	0.926112	−	1.60407i	0.136350	−	0.990661i	$-0.456463\pi$
$5$	2.07085	−	3.58682i	0.926112	−	1.60407i	0.789763	−	0.613413i	$-0.210204\pi$
$6$		0			0
$7$	0.321703	−	2.62612i	0.121592	−	0.992580i
$7$	0.321703	−	2.62612i	0.121592	−	0.992580i
$8$	1.00000			0.353553
$9$		0			0
$10$	2.07085	−	3.58682i	0.654860	−	1.13425i
$11$	0.261547	−	0.453013i	0.0788595	−	0.136589i	−0.823899	−	0.566737i	$-0.808205\pi$
$11$	0.261547	−	0.453013i	0.0788595	−	0.136589i	0.902758	+	0.430149i	$0.141539\pi$
$12$		0			0
$13$	−3.28981	+	1.47551i	−0.912430	+	0.409234i
$13$	−3.28981	+	1.47551i	−0.912430	+	0.409234i
$14$	0.321703	−	2.62612i	0.0859787	−	0.701860i
$15$		0			0
$16$	1.00000			0.250000
$17$	2.52309			0.611940			0.305970	−	0.952041i	$-0.401019\pi$
$17$	2.52309			0.611940			0.305970	+	0.952041i	$0.401019\pi$
$18$		0			0
$19$	2.84997	+	4.93629i	0.653827	+	1.13246i	0.982186	+	0.187909i	$0.0601711\pi$
$19$	2.84997	+	4.93629i	0.653827	+	1.13246i	−0.328359	+	0.944553i	$0.606496\pi$
$20$	2.07085	−	3.58682i	0.463056	−	0.802037i
$21$		0			0
$22$	0.261547	−	0.453013i	0.0557621	−	0.0965827i
$23$	7.39337			1.54162			0.770812	−	0.637062i	$-0.219851\pi$
$23$	7.39337			1.54162			0.770812	+	0.637062i	$0.219851\pi$
$24$		0			0
$25$	−6.07684	−	10.5254i	−1.21537	−	2.10508i
$26$	−3.28981	+	1.47551i	−0.645185	+	0.289372i
$27$		0			0
$28$	0.321703	−	2.62612i	0.0607961	−	0.496290i
$29$	1.54066	+	2.66851i	0.286094	+	0.495530i	0.972874	−	0.231336i	$-0.0743096\pi$
$29$	1.54066	+	2.66851i	0.286094	+	0.495530i	−0.686780	+	0.726866i	$0.740976\pi$
$30$		0			0
$31$	−2.17638	−	3.76959i	−0.390889	−	0.677039i	0.601678	−	0.798739i	$-0.294499\pi$
$31$	−2.17638	−	3.76959i	−0.390889	−	0.677039i	−0.992567	+	0.121699i	$0.961166\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	2.52309			0.432707
$35$	−8.75321	−	6.59219i	−1.47956	−	1.11428i
$36$		0			0
$37$	−5.66479			−0.931286			−0.465643	−	0.884973i	$-0.654177\pi$
$37$	−5.66479			−0.931286			−0.465643	+	0.884973i	$0.654177\pi$
$38$	2.84997	+	4.93629i	0.462326	+	0.800772i
$39$		0			0
$40$	2.07085	−	3.58682i	0.327430	−	0.567126i
$41$	−2.33240	−	4.03983i	−0.364259	−	0.630915i	0.624398	−	0.781107i	$-0.285344\pi$
$41$	−2.33240	−	4.03983i	−0.364259	−	0.630915i	−0.988657	+	0.150191i	$0.952011\pi$
$42$		0			0
$43$	−4.81529	+	8.34033i	−0.734325	+	1.27189i	0.220694	+	0.975343i	$0.429168\pi$
$43$	−4.81529	+	8.34033i	−0.734325	+	1.27189i	−0.955019	+	0.296545i	$0.904166\pi$
$44$	0.261547	−	0.453013i	0.0394297	−	0.0682943i
$45$		0			0
$46$	7.39337			1.09009
$47$	5.58154	−	9.66752i	0.814152	−	1.41015i	−0.0957835	−	0.995402i	$-0.530536\pi$
$47$	5.58154	−	9.66752i	0.814152	−	1.41015i	0.909935	−	0.414750i	$-0.136131\pi$
$48$		0			0
$49$	−6.79301	−	1.68966i	−0.970431	−	0.241380i
$50$	−6.07684	−	10.5254i	−0.859395	−	1.48852i
$51$		0			0
$52$	−3.28981	+	1.47551i	−0.456215	+	0.204617i
$53$	0.00192073	+	0.00332680i	0.000263832	+	0.000456971i	0.866157	−	0.499771i	$-0.166583\pi$
$53$	0.00192073	+	0.00332680i	0.000263832	+	0.000456971i	−0.865893	+	0.500228i	$0.833249\pi$
$54$		0			0
$55$	−1.08325	−	1.87624i	−0.146065	−	0.252993i
$56$	0.321703	−	2.62612i	0.0429894	−	0.350930i
$57$		0			0
$58$	1.54066	+	2.66851i	0.202299	+	0.350392i
$59$	−8.10749			−1.05550			−0.527752	−	0.849398i	$-0.676965\pi$
$59$	−8.10749			−1.05550			−0.527752	+	0.849398i	$0.676965\pi$
$60$		0			0
$61$	−3.00599	−	5.20652i	−0.384877	−	0.666627i	0.606875	−	0.794797i	$-0.292423\pi$
$61$	−3.00599	−	5.20652i	−0.384877	−	0.666627i	−0.991752	+	0.128170i	$0.959090\pi$
$62$	−2.17638	−	3.76959i	−0.276400	−	0.478739i
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.52031	+	14.8555i	−0.188571	+	1.84260i
$66$		0			0
$67$	−1.61622	+	2.79938i	−0.197453	+	0.341998i	−0.947702	−	0.319157i	$-0.896600\pi$
$67$	−1.61622	+	2.79938i	−0.197453	+	0.341998i	0.750249	+	0.661155i	$0.229934\pi$
$68$	2.52309			0.305970
$69$		0			0
$70$	−8.75321	−	6.59219i	−1.04621	−	0.787917i
$71$	−3.98568	+	6.90340i	−0.473013	+	0.819283i	−0.999523	−	0.0308864i	$-0.990167\pi$
$71$	−3.98568	+	6.90340i	−0.473013	+	0.819283i	0.526510	+	0.850169i	$0.323500\pi$
$72$		0			0
$73$	5.99080	+	10.3764i	0.701170	+	1.21446i	0.968056	+	0.250734i	$0.0806721\pi$
$73$	5.99080	+	10.3764i	0.701170	+	1.21446i	−0.266886	+	0.963728i	$0.585995\pi$
$74$	−5.66479			−0.658519
$75$		0			0
$76$	2.84997	+	4.93629i	0.326914	+	0.566231i
$77$	−1.10553	−	0.832590i	−0.125986	−	0.0948825i
$78$		0			0
$79$	1.15602	−	2.00229i	0.130063	−	0.225275i	−0.793638	−	0.608390i	$-0.791816\pi$
$79$	1.15602	−	2.00229i	0.130063	−	0.225275i	0.923700	+	0.383115i	$0.125149\pi$
$80$	2.07085	−	3.58682i	0.231528	−	0.401018i
$81$		0			0
$82$	−2.33240	−	4.03983i	−0.257570	−	0.446125i
$83$	−3.08133			−0.338220			−0.169110	−	0.985597i	$-0.554089\pi$
$83$	−3.08133			−0.338220			−0.169110	+	0.985597i	$0.554089\pi$
$84$		0			0
$85$	5.22495	−	9.04988i	0.566725	−	0.981597i
$86$	−4.81529	+	8.34033i	−0.519246	+	0.899361i
$87$		0			0
$88$	0.261547	−	0.453013i	0.0278810	−	0.0482914i
$89$	10.8520			1.15031			0.575153	−	0.818046i	$-0.304942\pi$
$89$	10.8520			1.15031			0.575153	+	0.818046i	$0.304942\pi$
$90$		0			0
$91$	2.81653	+	9.11412i	0.295253	+	0.955419i
$92$	7.39337			0.770812
$93$		0			0
$94$	5.58154	−	9.66752i	0.575692	−	0.997128i
$95$	23.6074			2.42207
$96$		0			0
$97$	−1.31892	+	2.28443i	−0.133916	+	0.231949i	−0.925183	−	0.379522i	$-0.876089\pi$
$97$	−1.31892	+	2.28443i	−0.133916	+	0.231949i	0.791267	+	0.611471i	$0.209422\pi$
$98$	−6.79301	−	1.68966i	−0.686198	−	0.170682i
$99$		0			0
$100$	−6.07684	−	10.5254i	−0.607684	−	1.05254i
$101$	−6.09224	+	10.5521i	−0.606200	+	1.04997i	0.385660	+	0.922641i	$0.373974\pi$
$101$	−6.09224	+	10.5521i	−0.606200	+	1.04997i	−0.991861	+	0.127329i	$0.959360\pi$
$102$		0			0
$103$	6.81529	−	11.8044i	0.671531	−	1.16313i	−0.305940	−	0.952051i	$-0.598971\pi$
$103$	6.81529	−	11.8044i	0.671531	−	1.16313i	0.977470	−	0.211074i	$-0.0676961\pi$
$104$	−3.28981	+	1.47551i	−0.322593	+	0.144686i
$105$		0			0
$106$	0.00192073	+	0.00332680i	0.000186558	+	0.000323127i
$107$	−5.39721			−0.521768			−0.260884	−	0.965370i	$-0.584014\pi$
$107$	−5.39721			−0.521768			−0.260884	+	0.965370i	$0.584014\pi$
$108$		0			0
$109$	5.58133	+	9.66715i	0.534594	+	0.925945i	0.999183	+	0.0404180i	$0.0128689\pi$
$109$	5.58133	+	9.66715i	0.534594	+	0.925945i	−0.464588	+	0.885527i	$0.653798\pi$
$110$	−1.08325	−	1.87624i	−0.103284	−	0.178893i
$111$		0			0
$112$	0.321703	−	2.62612i	0.0303981	−	0.248145i
$113$	−2.03617	+	3.52676i	−0.191547	+	0.331769i	−0.945763	−	0.324857i	$-0.894684\pi$
$113$	−2.03617	+	3.52676i	−0.191547	+	0.331769i	0.754216	+	0.656626i	$0.228017\pi$
$114$		0			0
$115$	15.3106	−	26.5187i	1.42772	−	2.47288i
$116$	1.54066	+	2.66851i	0.143047	+	0.247765i
$117$		0			0
$118$	−8.10749			−0.746355
$119$	0.811687	−	6.62595i	0.0744072	−	0.607400i
$120$		0			0
$121$	5.36319	+	9.28931i	0.487562	+	0.844483i
$122$	−3.00599	−	5.20652i	−0.272149	−	0.471377i
$123$		0			0
$124$	−2.17638	−	3.76959i	−0.195444	−	0.338520i
$125$	−29.6284			−2.65004
$126$		0			0
$127$	−3.83432	−	6.64123i	−0.340241	−	0.589314i	0.644237	−	0.764826i	$-0.277175\pi$
$127$	−3.83432	−	6.64123i	−0.340241	−	0.589314i	−0.984477	+	0.175512i	$0.943842\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−1.52031	+	14.8555i	−0.133340	+	1.30292i
$131$	5.62392	−	9.74091i	0.491364	−	0.851067i	−0.508587	−	0.861011i	$-0.669832\pi$
$131$	5.62392	−	9.74091i	0.491364	−	0.851067i	0.999951	+	0.00994375i	$0.00316525\pi$
$132$		0			0
$133$	13.8801	−	5.89634i	1.20356	−	0.511277i
$134$	−1.61622	+	2.79938i	−0.139620	+	0.241829i
$135$		0			0
$136$	2.52309			0.216354
$137$	7.02232			0.599957			0.299978	−	0.953946i	$-0.403021\pi$
$137$	7.02232			0.599957			0.299978	+	0.953946i	$0.403021\pi$
$138$		0			0
$139$	6.59202	−	11.4177i	0.559128	−	0.968438i	−0.438441	−	0.898760i	$-0.644469\pi$
$139$	6.59202	−	11.4177i	0.559128	−	0.968438i	0.997569	−	0.0696786i	$-0.0221974\pi$
$140$	−8.75321	−	6.59219i	−0.739782	−	0.557142i
$141$		0			0
$142$	−3.98568	+	6.90340i	−0.334471	+	0.579320i
$143$	−0.192014	+	1.87624i	−0.0160570	+	0.156899i
$144$		0			0
$145$	12.7619			1.05982
$146$	5.99080	+	10.3764i	0.495802	+	0.858755i
$147$		0			0
$148$	−5.66479			−0.465643
$149$	9.06612	+	15.7030i	0.742726	+	1.28644i	0.951250	+	0.308421i	$0.0998006\pi$
$149$	9.06612	+	15.7030i	0.742726	+	1.28644i	−0.208524	+	0.978017i	$0.566866\pi$
$150$		0			0
$151$	−2.53343	−	4.38804i	−0.206168	−	0.357093i	0.744336	−	0.667805i	$-0.232766\pi$
$151$	−2.53343	−	4.38804i	−0.206168	−	0.357093i	−0.950504	+	0.310712i	$0.899433\pi$
$152$	2.84997	+	4.93629i	0.231163	+	0.400386i
$153$		0			0
$154$	−1.10553	−	0.832590i	−0.0890859	−	0.0670920i
$155$	−18.0278			−1.44803
$156$		0			0
$157$	5.80481	+	10.0542i	0.463274	+	0.802415i	0.999122	−	0.0419001i	$-0.0133411\pi$
$157$	5.80481	+	10.0542i	0.463274	+	0.802415i	−0.535847	+	0.844315i	$0.680008\pi$
$158$	1.15602	−	2.00229i	0.0919681	−	0.159293i
$159$		0			0
$160$	2.07085	−	3.58682i	0.163715	−	0.283563i
$161$	2.37847	−	19.4159i	0.187450	−	1.53019i
$162$		0			0
$163$	9.99637	+	17.3142i	0.782976	+	1.35615i	0.930201	+	0.367052i	$0.119633\pi$
$163$	9.99637	+	17.3142i	0.782976	+	1.35615i	−0.147224	+	0.989103i	$0.547034\pi$
$164$	−2.33240	−	4.03983i	−0.182130	−	0.315458i
$165$		0			0
$166$	−3.08133			−0.239158
$167$	8.82851	+	15.2914i	0.683171	+	1.18329i	0.974008	+	0.226514i	$0.0727328\pi$
$167$	8.82851	+	15.2914i	0.683171	+	1.18329i	−0.290837	+	0.956772i	$0.593934\pi$
$168$		0			0
$169$	8.64572	−	9.70832i	0.665055	−	0.746794i
$170$	5.22495	−	9.04988i	0.400735	−	0.694094i
$171$		0			0
$172$	−4.81529	+	8.34033i	−0.367162	+	0.635944i
$173$	−1.93492	−	3.35139i	−0.147110	−	0.254801i	0.783048	−	0.621961i	$-0.213664\pi$
$173$	−1.93492	−	3.35139i	−0.147110	−	0.254801i	−0.930158	+	0.367160i	$0.880330\pi$
$174$		0			0
$175$	−29.5959	+	12.5725i	−2.23724	+	0.950388i
$176$	0.261547	−	0.453013i	0.0197149	−	0.0341472i
$177$		0			0
$178$	10.8520			0.813390
$179$	−1.75984	+	3.04813i	−0.131537	+	0.227828i	−0.924269	−	0.381742i	$-0.875324\pi$
$179$	−1.75984	+	3.04813i	−0.131537	+	0.227828i	0.792732	+	0.609570i	$0.208658\pi$
$180$		0			0
$181$	8.47129			0.629666			0.314833	−	0.949147i	$-0.398052\pi$
$181$	8.47129			0.629666			0.314833	+	0.949147i	$0.398052\pi$
$182$	2.81653	+	9.11412i	0.208775	+	0.675583i
$183$		0			0
$184$	7.39337			0.545047
$185$	−11.7309	+	20.3186i	−0.862476	+	1.49385i
$186$		0			0
$187$	0.659909	−	1.14300i	0.0482573	−	0.0835841i
$188$	5.58154	−	9.66752i	0.407076	−	0.705076i
$189$		0			0
$190$	23.6074			1.71266
$191$	−10.9754	−	19.0099i	−0.794151	−	1.37551i	−0.923377	−	0.383894i	$-0.874583\pi$
$191$	−10.9754	−	19.0099i	−0.794151	−	1.37551i	0.129227	−	0.991615i	$-0.458751\pi$
$192$		0			0
$193$	−6.42959	+	11.1364i	−0.462812	+	0.801614i	−0.999100	−	0.0424212i	$-0.986493\pi$
$193$	−6.42959	+	11.1364i	−0.462812	+	0.801614i	0.536288	+	0.844035i	$0.319826\pi$
$194$	−1.31892	+	2.28443i	−0.0946928	+	0.164013i
$195$		0			0
$196$	−6.79301	−	1.68966i	−0.485215	−	0.120690i
$197$	5.27054	+	9.12883i	0.375510	+	0.650403i	0.990403	−	0.138208i	$-0.0441342\pi$
$197$	5.27054	+	9.12883i	0.375510	+	0.650403i	−0.614893	+	0.788610i	$0.710801\pi$
$198$		0			0
$199$	13.1036			0.928893			0.464446	−	0.885601i	$-0.346253\pi$
$199$	13.1036			0.928893			0.464446	+	0.885601i	$0.346253\pi$
$200$	−6.07684	−	10.5254i	−0.429697	−	0.744258i
$201$		0			0
$202$	−6.09224	+	10.5521i	−0.428648	+	0.742441i
$203$	7.50346	−	3.18750i	0.526640	−	0.223719i
$204$		0			0
$205$	−19.3202			−1.34938
$206$	6.81529	−	11.8044i	0.474844	−	0.822454i
$207$		0			0
$208$	−3.28981	+	1.47551i	−0.228107	+	0.102308i
$209$	2.98160			0.206242
$210$		0			0
$211$	−0.979430	−	1.69642i	−0.0674267	−	0.116787i	0.830341	−	0.557255i	$-0.188146\pi$
$211$	−0.979430	−	1.69642i	−0.0674267	−	0.116787i	−0.897768	+	0.440469i	$0.854812\pi$
$212$	0.00192073	+	0.00332680i	0.000131916	+	0.000228485i
$213$		0			0
$214$	−5.39721			−0.368946
$215$	19.9435	+	34.5431i	1.36013	+	2.35582i
$216$		0			0
$217$	−10.5996	+	4.50274i	−0.719545	+	0.305666i
$218$	5.58133	+	9.66715i	0.378015	+	0.654742i
$219$		0			0
$220$	−1.08325	−	1.87624i	−0.0730327	−	0.126496i
$221$	−8.30051	+	3.72286i	−0.558352	+	0.250427i
$222$		0			0
$223$	6.26821	+	10.8569i	0.419751	+	0.727029i	0.995914	−	0.0903050i	$-0.0287842\pi$
$223$	6.26821	+	10.8569i	0.419751	+	0.727029i	−0.576164	+	0.817334i	$0.695451\pi$
$224$	0.321703	−	2.62612i	0.0214947	−	0.175465i
$225$		0			0
$226$	−2.03617	+	3.52676i	−0.135444	+	0.234596i
$227$	21.7299			1.44226			0.721132	−	0.692798i	$-0.243622\pi$
$227$	21.7299			1.44226			0.721132	+	0.692798i	$0.243622\pi$
$228$		0			0
$229$	−7.77570	+	13.4679i	−0.513833	+	0.889985i	0.486038	+	0.873938i	$0.338442\pi$
$229$	−7.77570	+	13.4679i	−0.513833	+	0.889985i	−0.999871	+	0.0160474i	$0.994892\pi$
$230$	15.3106	−	26.5187i	1.00955	−	1.74859i
$231$		0			0
$232$	1.54066	+	2.66851i	0.101150	+	0.175196i
$233$	−10.3320	+	17.8955i	−0.676870	+	1.17237i	0.299048	+	0.954238i	$0.403331\pi$
$233$	−10.3320	+	17.8955i	−0.676870	+	1.17237i	−0.975919	+	0.218135i	$0.930003\pi$
$234$		0			0
$235$	−23.1171	−	40.0400i	−1.50799	−	2.61192i
$236$	−8.10749			−0.527752
$237$		0			0
$238$	0.811687	−	6.62595i	0.0526139	−	0.429497i
$239$	30.0971			1.94682			0.973410	−	0.229071i	$-0.0735687\pi$
$239$	30.0971			1.94682			0.973410	+	0.229071i	$0.0735687\pi$
$240$		0			0
$241$	2.05219			0.132193			0.0660965	−	0.997813i	$-0.478945\pi$
$241$	2.05219			0.132193			0.0660965	+	0.997813i	$0.478945\pi$
$242$	5.36319	+	9.28931i	0.344759	+	0.597140i
$243$		0			0
$244$	−3.00599	−	5.20652i	−0.192439	−	0.333314i
$245$	−20.1278	+	20.8663i	−1.28592	+	1.33310i
$246$		0			0
$247$	−16.6594	−	12.0343i	−1.06001	−	0.765724i
$248$	−2.17638	−	3.76959i	−0.138200	−	0.239369i
$249$		0			0
$250$	−29.6284			−1.87386
$251$	8.23457	−	14.2627i	0.519761	−	0.900253i	−0.479975	−	0.877282i	$-0.659354\pi$
$251$	8.23457	−	14.2627i	0.519761	−	0.900253i	0.999736	−	0.0229705i	$-0.00731239\pi$
$252$		0			0
$253$	1.93372	−	3.34929i	0.121572	−	0.210568i
$254$	−3.83432	−	6.64123i	−0.240586	−	0.416708i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−11.8742			−0.740693			−0.370346	−	0.928894i	$-0.620761\pi$
$257$	−11.8742			−0.740693			−0.370346	+	0.928894i	$0.620761\pi$
$258$		0			0
$259$	−1.82238	+	14.8764i	−0.113237	+	0.924376i
$260$	−1.52031	+	14.8555i	−0.0942856	+	0.921300i
$261$		0			0
$262$	5.62392	−	9.74091i	0.347447	−	0.601795i
$263$	12.5158	−	21.6781i	0.771760	−	1.33673i	−0.164838	−	0.986321i	$-0.552710\pi$
$263$	12.5158	−	21.6781i	0.771760	−	1.33673i	0.936598	−	0.350406i	$-0.113957\pi$
$264$		0			0
$265$	0.0159101			0.000977353
$266$	13.8801	−	5.89634i	0.851045	−	0.361528i
$267$		0			0
$268$	−1.61622	+	2.79938i	−0.0987264	+	0.170999i
$269$	15.5300			0.946882			0.473441	−	0.880826i	$-0.343012\pi$
$269$	15.5300			0.946882			0.473441	+	0.880826i	$0.343012\pi$
$270$		0			0
$271$	−5.27690			−0.320549			−0.160274	−	0.987072i	$-0.551238\pi$
$271$	−5.27690			−0.320549			−0.160274	+	0.987072i	$0.551238\pi$
$272$	2.52309			0.152985
$273$		0			0
$274$	7.02232			0.424234
$275$	−6.35752			−0.383373
$276$		0			0
$277$	−11.1319			−0.668850			−0.334425	−	0.942422i	$-0.608542\pi$
$277$	−11.1319			−0.668850			−0.334425	+	0.942422i	$0.608542\pi$
$278$	6.59202	−	11.4177i	0.395363	−	0.684789i
$279$		0			0
$280$	−8.75321	−	6.59219i	−0.523105	−	0.393959i
$281$	−19.3908			−1.15676			−0.578379	−	0.815768i	$-0.696314\pi$
$281$	−19.3908			−1.15676			−0.578379	+	0.815768i	$0.696314\pi$
$282$		0			0
$283$	−13.0180	+	22.5478i	−0.773838	+	1.34033i	0.161608	+	0.986855i	$0.448332\pi$
$283$	−13.0180	+	22.5478i	−0.773838	+	1.34033i	−0.935445	+	0.353471i	$0.885001\pi$
$284$	−3.98568	+	6.90340i	−0.236507	+	0.409641i
$285$		0			0
$286$	−0.192014	+	1.87624i	−0.0113540	+	0.110945i
$287$	−11.3594	+	4.82553i	−0.670525	+	0.284842i
$288$		0			0
$289$	−10.6340			−0.625529
$290$	12.7619			0.749407
$291$		0			0
$292$	5.99080	+	10.3764i	0.350585	+	0.607231i
$293$	6.46216	−	11.1928i	0.377523	−	0.653890i	−0.613178	−	0.789945i	$-0.710109\pi$
$293$	6.46216	−	11.1928i	0.377523	−	0.653890i	0.990701	+	0.136055i	$0.0434424\pi$
$294$		0			0
$295$	−16.7894	+	29.0801i	−0.977516	+	1.69311i
$296$	−5.66479			−0.329259
$297$		0			0
$298$	9.06612	+	15.7030i	0.525186	+	0.909649i
$299$	−24.3228	+	10.9090i	−1.40662	+	0.630885i
$300$		0			0
$301$	20.3536	+	15.3286i	1.17316	+	0.883528i
$302$	−2.53343	−	4.38804i	−0.145783	−	0.252503i
$303$		0			0
$304$	2.84997	+	4.93629i	0.163457	+	0.283116i
$305$	−24.8998			−1.42576
$306$		0			0
$307$	20.0771			1.14586			0.572931	−	0.819604i	$-0.305806\pi$
$307$	20.0771			1.14586			0.572931	+	0.819604i	$0.305806\pi$
$308$	−1.10553	−	0.832590i	−0.0629932	−	0.0474412i
$309$		0			0
$310$	−18.0278			−1.02391
$311$	−10.4837	−	18.1583i	−0.594475	−	1.02966i	−0.993621	−	0.112774i	$-0.964026\pi$
$311$	−10.4837	−	18.1583i	−0.594475	−	1.02966i	0.399145	−	0.916888i	$-0.369307\pi$
$312$		0			0
$313$	9.55610	−	16.5517i	0.540143	−	0.935555i	−0.458752	−	0.888564i	$-0.651703\pi$
$313$	9.55610	−	16.5517i	0.540143	−	0.935555i	0.998895	−	0.0469909i	$-0.0149632\pi$
$314$	5.80481	+	10.0542i	0.327584	+	0.567393i
$315$		0			0
$316$	1.15602	−	2.00229i	0.0650313	−	0.112637i
$317$	−9.13122	+	15.8157i	−0.512860	+	0.888300i	0.487028	+	0.873386i	$0.338081\pi$
$317$	−9.13122	+	15.8157i	−0.512860	+	0.888300i	−0.999889	+	0.0149141i	$0.995253\pi$
$318$		0			0
$319$	1.61183			0.0902450
$320$	2.07085	−	3.58682i	0.115764	−	0.200509i
$321$		0			0
$322$	2.37847	−	19.4159i	0.132547	−	1.08200i
$323$	7.19074	+	12.4547i	0.400103	+	0.692999i
$324$		0			0
$325$	35.5220	+	25.6601i	1.97041	+	1.42337i
$326$	9.99637	+	17.3142i	0.553648	+	0.958946i
$327$		0			0
$328$	−2.33240	−	4.03983i	−0.128785	−	0.223062i
$329$	−23.5925	−	17.7679i	−1.30069	−	0.979575i
$330$		0			0
$331$	5.12199	+	8.87155i	0.281530	+	0.487625i	0.971762	−	0.235964i	$-0.0758247\pi$
$331$	5.12199	+	8.87155i	0.281530	+	0.487625i	−0.690232	+	0.723589i	$0.742491\pi$
$332$	−3.08133			−0.169110
$333$		0			0
$334$	8.82851	+	15.2914i	0.483075	+	0.836710i
$335$	6.69390	+	11.5942i	0.365727	+	0.633457i
$336$		0			0
$337$	−32.6266			−1.77728			−0.888642	−	0.458601i	$-0.848351\pi$
$337$	−32.6266			−1.77728			−0.888642	+	0.458601i	$0.848351\pi$
$338$	8.64572	−	9.70832i	0.470265	−	0.528063i
$339$		0			0
$340$	5.22495	−	9.04988i	0.283363	−	0.490799i
$341$	−2.27690			−0.123301
$342$		0			0
$343$	−6.62259	+	17.2957i	−0.357586	+	0.933880i
$344$	−4.81529	+	8.34033i	−0.259623	+	0.449680i
$345$		0			0
$346$	−1.93492	−	3.35139i	−0.104022	−	0.180172i
$347$	−8.43192			−0.452649			−0.226325	−	0.974052i	$-0.572671\pi$
$347$	−8.43192			−0.452649			−0.226325	+	0.974052i	$0.572671\pi$
$348$		0			0
$349$	18.3077	+	31.7099i	0.979990	+	1.69739i	0.662373	+	0.749174i	$0.269549\pi$
$349$	18.3077	+	31.7099i	0.979990	+	1.69739i	0.317617	+	0.948219i	$0.397117\pi$
$350$	−29.5959	+	12.5725i	−1.58197	+	0.672026i
$351$		0			0
$352$	0.261547	−	0.453013i	0.0139405	−	0.0241457i
$353$	−2.61947	+	4.53705i	−0.139420	+	0.241483i	−0.927277	−	0.374375i	$-0.877857\pi$
$353$	−2.61947	+	4.53705i	−0.139420	+	0.241483i	0.787857	+	0.615858i	$0.211191\pi$
$354$		0			0
$355$	16.5075	+	28.5918i	0.876126	+	1.51750i
$356$	10.8520			0.575153
$357$		0			0
$358$	−1.75984	+	3.04813i	−0.0930105	+	0.161099i
$359$	2.54006	−	4.39951i	0.134059	−	0.232197i	−0.791178	−	0.611585i	$-0.790532\pi$
$359$	2.54006	−	4.39951i	0.134059	−	0.232197i	0.925238	+	0.379388i	$0.123865\pi$
$360$		0			0
$361$	−6.74463	+	11.6820i	−0.354980	+	0.614844i
$362$	8.47129			0.445241
$363$		0			0
$364$	2.81653	+	9.11412i	0.147626	+	0.477710i
$365$	49.6242			2.59745
$366$		0			0
$367$	−2.43151	+	4.21150i	−0.126924	+	0.219839i	−0.922483	−	0.386037i	$-0.873844\pi$
$367$	−2.43151	+	4.21150i	−0.126924	+	0.219839i	0.795559	+	0.605876i	$0.207177\pi$
$368$	7.39337			0.385406
$369$		0			0
$370$	−11.7309	+	20.3186i	−0.609862	+	1.05631i
$371$	0.00935447	−	0.00397382i	0.000485660	−	0.000206310i
$372$		0			0
$373$	−14.4061	−	24.9521i	−0.745919	−	1.29197i	−0.949764	−	0.312967i	$-0.898677\pi$
$373$	−14.4061	−	24.9521i	−0.745919	−	1.29197i	0.203845	−	0.979003i	$-0.434656\pi$
$374$	0.659909	−	1.14300i	0.0341231	−	0.0591029i
$375$		0			0
$376$	5.58154	−	9.66752i	0.287846	−	0.498564i
$377$	−9.00592	−	6.50562i	−0.463828	−	0.335057i
$378$		0			0
$379$	−14.1550	−	24.5172i	−0.727094	−	1.25936i	−0.958106	−	0.286413i	$-0.907537\pi$
$379$	−14.1550	−	24.5172i	−0.727094	−	1.25936i	0.231013	−	0.972951i	$-0.425796\pi$
$380$	23.6074			1.21103
$381$		0			0
$382$	−10.9754	−	19.0099i	−0.561549	−	0.972632i
$383$	−9.36815	−	16.2261i	−0.478690	−	0.829115i	0.521012	−	0.853550i	$-0.325555\pi$
$383$	−9.36815	−	16.2261i	−0.478690	−	0.829115i	−0.999701	+	0.0244344i	$0.992222\pi$
$384$		0			0
$385$	−5.27573	+	2.24115i	−0.268876	+	0.114220i
$386$	−6.42959	+	11.1364i	−0.327258	+	0.566827i
$387$		0			0
$388$	−1.31892	+	2.28443i	−0.0669579	+	0.115974i
$389$	−3.55307	−	6.15409i	−0.180148	−	0.312025i	0.761783	−	0.647832i	$-0.224324\pi$
$389$	−3.55307	−	6.15409i	−0.180148	−	0.312025i	−0.941931	+	0.335807i	$0.890991\pi$
$390$		0			0
$391$	18.6542			0.943382
$392$	−6.79301	−	1.68966i	−0.343099	−	0.0853408i
$393$		0			0
$394$	5.27054	+	9.12883i	0.265526	+	0.459904i
$395$	−4.78789	−	8.29287i	−0.240905	−	0.417260i
$396$		0			0
$397$	−19.6633	−	34.0578i	−0.986872	−	1.70931i	−0.633302	−	0.773905i	$-0.718301\pi$
$397$	−19.6633	−	34.0578i	−0.986872	−	1.70931i	−0.353571	−	0.935408i	$-0.615033\pi$
$398$	13.1036			0.656826
$399$		0			0
$400$	−6.07684	−	10.5254i	−0.303842	−	0.526270i
$401$	8.60307			0.429617			0.214808	−	0.976656i	$-0.431087\pi$
$401$	8.60307			0.429617			0.214808	+	0.976656i	$0.431087\pi$
$402$		0			0
$403$	12.7220	+	9.18998i	0.633726	+	0.457786i
$404$	−6.09224	+	10.5521i	−0.303100	+	0.524985i
$405$		0			0
$406$	7.50346	−	3.18750i	0.372391	−	0.158193i
$407$	−1.48161	+	2.56623i	−0.0734408	+	0.127203i
$408$		0			0
$409$	−36.5325			−1.80642			−0.903208	−	0.429204i	$-0.858794\pi$
$409$	−36.5325			−1.80642			−0.903208	+	0.429204i	$0.858794\pi$
$410$	−19.3202			−0.954155
$411$		0			0
$412$	6.81529	−	11.8044i	0.335765	−	0.581563i
$413$	−2.60820	+	21.2912i	−0.128341	+	1.04767i
$414$		0			0
$415$	−6.38097	+	11.0522i	−0.313230	+	0.542529i
$416$	−3.28981	+	1.47551i	−0.161296	+	0.0723430i
$417$		0			0
$418$	2.98160			0.145835
$419$	−6.77818	−	11.7402i	−0.331136	−	0.573544i	0.651599	−	0.758564i	$-0.274099\pi$
$419$	−6.77818	−	11.7402i	−0.331136	−	0.573544i	−0.982735	+	0.185019i	$0.940765\pi$
$420$		0			0
$421$	4.50209			0.219418			0.109709	−	0.993964i	$-0.465008\pi$
$421$	4.50209			0.219418			0.109709	+	0.993964i	$0.465008\pi$
$422$	−0.979430	−	1.69642i	−0.0476779	−	0.0825806i
$423$		0			0
$424$	0.00192073	+	0.00332680i	9.32788e−5	+	0.000161564i
$425$	−15.3324	−	26.5566i	−0.743732	−	1.28818i
$426$		0			0
$427$	−14.6400	+	6.21913i	−0.708479	+	0.300965i
$428$	−5.39721			−0.260884
$429$		0			0
$430$	19.9435	+	34.5431i	0.961760	+	1.66582i
$431$	−0.253853	+	0.439686i	−0.0122277	+	0.0211789i	−0.872074	−	0.489373i	$-0.837226\pi$
$431$	−0.253853	+	0.439686i	−0.0122277	+	0.0211789i	0.859847	+	0.510552i	$0.170559\pi$
$432$		0			0
$433$	−6.41093	+	11.1041i	−0.308090	+	0.533627i	−0.977944	−	0.208865i	$-0.933023\pi$
$433$	−6.41093	+	11.1041i	−0.308090	+	0.533627i	0.669855	+	0.742492i	$0.266356\pi$
$434$	−10.5996	+	4.50274i	−0.508795	+	0.216138i
$435$		0			0
$436$	5.58133	+	9.66715i	0.267297	+	0.462972i
$437$	21.0709	+	36.4958i	1.00796	+	1.74583i
$438$		0			0
$439$	−0.433280			−0.0206793			−0.0103397	−	0.999947i	$-0.503291\pi$
$439$	−0.433280			−0.0206793			−0.0103397	+	0.999947i	$0.503291\pi$
$440$	−1.08325	−	1.87624i	−0.0516419	−	0.0894464i
$441$		0			0
$442$	−8.30051	+	3.72286i	−0.394815	+	0.177078i
$443$	7.03339	−	12.1822i	0.334166	−	0.578793i	−0.649158	−	0.760654i	$-0.724879\pi$
$443$	7.03339	−	12.1822i	0.334166	−	0.578793i	0.983324	+	0.181861i	$0.0582119\pi$
$444$		0			0
$445$	22.4728	−	38.9240i	1.06531	−	1.84518i
$446$	6.26821	+	10.8569i	0.296809	+	0.514087i
$447$		0			0
$448$	0.321703	−	2.62612i	0.0151990	−	0.124073i
$449$	−15.2892	+	26.4817i	−0.721542	+	1.24975i	0.238840	+	0.971059i	$0.423233\pi$
$449$	−15.2892	+	26.4817i	−0.721542	+	1.24975i	−0.960382	+	0.278688i	$0.910100\pi$
$450$		0			0
$451$	−2.44013			−0.114901
$452$	−2.03617	+	3.52676i	−0.0957735	+	0.165885i
$453$		0			0
$454$	21.7299			1.01983
$455$	38.5233	+	8.77158i	1.80600	+	0.411218i
$456$		0			0
$457$	2.31026			0.108069			0.0540346	−	0.998539i	$-0.482792\pi$
$457$	2.31026			0.108069			0.0540346	+	0.998539i	$0.482792\pi$
$458$	−7.77570	+	13.4679i	−0.363335	+	0.629314i
$459$		0			0
$460$	15.3106	−	26.5187i	0.713859	−	1.23644i
$461$	15.0409	−	26.0516i	0.700524	−	1.21334i	−0.267759	−	0.963486i	$-0.586283\pi$
$461$	15.0409	−	26.0516i	0.700524	−	1.21334i	0.968283	−	0.249857i	$-0.0803835\pi$
$462$		0			0
$463$	29.4727			1.36971			0.684856	−	0.728679i	$-0.259865\pi$
$463$	29.4727			1.36971			0.684856	+	0.728679i	$0.259865\pi$
$464$	1.54066	+	2.66851i	0.0715236	+	0.123882i
$465$		0			0
$466$	−10.3320	+	17.8955i	−0.478619	+	0.828993i
$467$	−2.92442	+	5.06525i	−0.135326	+	0.234392i	−0.925722	−	0.378205i	$-0.876542\pi$
$467$	−2.92442	+	5.06525i	−0.135326	+	0.234392i	0.790396	+	0.612596i	$0.209875\pi$
$468$		0			0
$469$	6.83156	+	5.14496i	0.315452	+	0.237572i
$470$	−23.1171	−	40.0400i	−1.06631	−	1.84691i
$471$		0			0
$472$	−8.10749			−0.373177
$473$	2.51885	+	4.36278i	0.115817	+	0.200601i
$474$		0			0
$475$	34.6376	−	59.9940i	1.58928	−	2.75272i
$476$	0.811687	−	6.62595i	0.0372036	−	0.303700i
$477$		0			0
$478$	30.0971			1.37661
$479$	8.66374	−	15.0060i	0.395856	−	0.685643i	−0.597354	−	0.801978i	$-0.703781\pi$
$479$	8.66374	−	15.0060i	0.395856	−	0.685643i	0.993210	+	0.116335i	$0.0371145\pi$
$480$		0			0
$481$	18.6361	−	8.35848i	0.849733	−	0.381114i
$482$	2.05219			0.0934746
$483$		0			0
$484$	5.36319	+	9.28931i	0.243781	+	0.422241i
$485$	5.46256	+	9.46143i	0.248042	+	0.429622i
$486$		0			0
$487$	−38.0645			−1.72487			−0.862434	−	0.506169i	$-0.831061\pi$
$487$	−38.0645			−1.72487			−0.862434	+	0.506169i	$0.831061\pi$
$488$	−3.00599	−	5.20652i	−0.136075	−	0.235688i
$489$		0			0
$490$	−20.1278	+	20.8663i	−0.909282	+	0.942642i
$491$	8.22130	+	14.2397i	0.371022	+	0.642629i	0.989723	−	0.142997i	$-0.0456741\pi$
$491$	8.22130	+	14.2397i	0.371022	+	0.642629i	−0.618701	+	0.785627i	$0.712341\pi$
$492$		0			0
$493$	3.88724	+	6.73290i	0.175073	+	0.303235i
$494$	−16.6594	−	12.0343i	−0.749542	−	0.541448i
$495$		0			0
$496$	−2.17638	−	3.76959i	−0.0977222	−	0.169260i
$497$	16.8469	+	12.6877i	0.755689	+	0.569122i
$498$		0			0
$499$	−3.74298	+	6.48304i	−0.167559	+	0.290221i	−0.937561	−	0.347821i	$-0.886922\pi$
$499$	−3.74298	+	6.48304i	−0.167559	+	0.290221i	0.770002	+	0.638041i	$0.220255\pi$
$500$	−29.6284			−1.32502
$501$		0			0
$502$	8.23457	−	14.2627i	0.367527	−	0.636575i
$503$	−1.27275	+	2.20447i	−0.0567492	+	0.0982925i	−0.893004	−	0.450048i	$-0.851407\pi$
$503$	−1.27275	+	2.20447i	−0.0567492	+	0.0982925i	0.836255	+	0.548340i	$0.184740\pi$
$504$		0			0
$505$	25.2322	+	43.7035i	1.12282	+	1.94478i
$506$	1.93372	−	3.34929i	0.0859642	−	0.148894i
$507$		0			0
$508$	−3.83432	−	6.64123i	−0.170120	−	0.294657i
$509$	34.4426			1.52664			0.763320	−	0.646021i	$-0.223568\pi$
$509$	34.4426			1.52664			0.763320	+	0.646021i	$0.223568\pi$
$510$		0			0
$511$	29.1769	−	12.3945i	1.29071	−	0.548298i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−11.8742			−0.523749
$515$	−28.2269	−	48.8904i	−1.24383	−	2.15437i
$516$		0			0
$517$	−2.91968	−	5.05703i	−0.128407	−	0.222408i
$518$	−1.82238	+	14.8764i	−0.0800708	+	0.653633i
$519$		0			0
$520$	−1.52031	+	14.8555i	−0.0666700	+	0.651458i
$521$	−21.9782	−	38.0673i	−0.962881	−	1.66776i	−0.715204	−	0.698916i	$-0.753666\pi$
$521$	−21.9782	−	38.0673i	−0.962881	−	1.66776i	−0.247677	−	0.968843i	$-0.579667\pi$
$522$		0			0
$523$	−28.4937			−1.24594			−0.622971	−	0.782245i	$-0.714075\pi$
$523$	−28.4937			−1.24594			−0.622971	+	0.782245i	$0.714075\pi$
$524$	5.62392	−	9.74091i	0.245682	−	0.425533i
$525$		0			0
$526$	12.5158	−	21.6781i	0.545717	−	0.945209i
$527$	−5.49120	−	9.51104i	−0.239201	−	0.414308i
$528$		0			0
$529$	31.6619			1.37661
$530$	0.0159101			0.000691093
$531$		0			0
$532$	13.8801	−	5.89634i	0.601780	−	0.255639i
$533$	13.6340	+	9.84880i	0.590553	+	0.426599i
$534$		0			0
$535$	−11.1768	+	19.3588i	−0.483216	+	0.836955i
$536$	−1.61622	+	2.79938i	−0.0698101	+	0.120915i
$537$		0			0
$538$	15.5300			0.669547
$539$	−2.54213	+	2.63540i	−0.109497	+	0.113515i
$540$		0			0
$541$	0.327013	−	0.566403i	0.0140594	−	0.0243516i	−0.858910	−	0.512126i	$-0.828858\pi$
$541$	0.327013	−	0.566403i	0.0140594	−	0.0243516i	0.872969	+	0.487775i	$0.162191\pi$
$542$	−5.27690			−0.226662
$543$		0			0
$544$	2.52309			0.108177
$545$	46.2324			1.98038
$546$		0			0
$547$	4.52174			0.193336			0.0966678	−	0.995317i	$-0.469182\pi$
$547$	4.52174			0.193336			0.0966678	+	0.995317i	$0.469182\pi$
$548$	7.02232			0.299978
$549$		0			0
$550$	−6.35752			−0.271086
$551$	−8.78169	+	15.2103i	−0.374113	+	0.647982i
$552$		0			0
$553$	−4.88635	−	3.67999i	−0.207789	−	0.156489i
$554$	−11.1319			−0.472948
$555$		0			0
$556$	6.59202	−	11.4177i	0.279564	−	0.484219i
$557$	−1.09711	+	1.90025i	−0.0464859	+	0.0805160i	−0.888332	−	0.459201i	$-0.848136\pi$
$557$	−1.09711	+	1.90025i	−0.0464859	+	0.0805160i	0.841846	+	0.539717i	$0.181469\pi$
$558$		0			0
$559$	3.53513	−	34.5431i	0.149520	−	1.46102i
$560$	−8.75321	−	6.59219i	−0.369891	−	0.278571i
$561$		0			0
$562$	−19.3908			−0.817951
$563$	15.0368			0.633725			0.316862	−	0.948472i	$-0.397371\pi$
$563$	15.0368			0.633725			0.316862	+	0.948472i	$0.397371\pi$
$564$		0			0
$565$	8.43322	+	14.6068i	0.354788	+	0.614511i
$566$	−13.0180	+	22.5478i	−0.547186	+	0.947754i
$567$		0			0
$568$	−3.98568	+	6.90340i	−0.167235	+	0.289660i
$569$	18.1733			0.761863			0.380932	−	0.924603i	$-0.375603\pi$
$569$	18.1733			0.761863			0.380932	+	0.924603i	$0.375603\pi$
$570$		0			0
$571$	−18.3240	−	31.7382i	−0.766837	−	1.32820i	−0.939270	−	0.343180i	$-0.888496\pi$
$571$	−18.3240	−	31.7382i	−0.766837	−	1.32820i	0.172433	−	0.985021i	$-0.444837\pi$
$572$	−0.192014	+	1.87624i	−0.00802852	+	0.0784497i
$573$		0			0
$574$	−11.3594	+	4.82553i	−0.474133	+	0.201414i
$575$	−44.9283	−	77.8181i	−1.87364	−	3.24524i
$576$		0			0
$577$	−14.3809	−	24.9085i	−0.598686	−	1.03695i	−0.993015	−	0.117985i	$-0.962357\pi$
$577$	−14.3809	−	24.9085i	−0.598686	−	1.03695i	0.394330	−	0.918969i	$-0.370977\pi$
$578$	−10.6340			−0.442316
$579$		0			0
$580$	12.7619			0.529911
$581$	−0.991273	+	8.09194i	−0.0411249	+	0.335710i
$582$		0			0
$583$	0.00200944			8.32227e−5
$584$	5.99080	+	10.3764i	0.247901	+	0.429377i
$585$		0			0
$586$	6.46216	−	11.1928i	0.266949	−	0.462370i
$587$	7.20528	+	12.4799i	0.297394	+	0.515101i	0.975539	−	0.219827i	$-0.0705493\pi$
$587$	7.20528	+	12.4799i	0.297394	+	0.515101i	−0.678145	+	0.734928i	$0.737216\pi$
$588$		0			0
$589$	12.4052	−	21.4864i	0.511147	−	0.885333i
$590$	−16.7894	+	29.0801i	−0.691208	+	1.19721i
$591$		0			0
$592$	−5.66479			−0.232822
$593$	−9.75838	+	16.9020i	−0.400729	+	0.694083i	−0.993814	−	0.111057i	$-0.964576\pi$
$593$	−9.75838	+	16.9020i	−0.400729	+	0.694083i	0.593085	+	0.805140i	$0.297910\pi$
$594$		0			0
$595$	−22.0852	−	16.6327i	−0.905404	−	0.681875i
$596$	9.06612	+	15.7030i	0.371363	+	0.643219i
$597$		0			0
$598$	−24.3228	+	10.9090i	−0.994633	+	0.446103i
$599$	−0.837961	−	1.45139i	−0.0342382	−	0.0593022i	0.848399	−	0.529358i	$-0.177567\pi$
$599$	−0.837961	−	1.45139i	−0.0342382	−	0.0593022i	−0.882637	+	0.470056i	$0.844234\pi$
$600$		0			0
$601$	−7.12111	−	12.3341i	−0.290476	−	0.503119i	0.683446	−	0.730001i	$-0.260480\pi$
$601$	−7.12111	−	12.3341i	−0.290476	−	0.503119i	−0.973922	+	0.226882i	$0.927147\pi$
$602$	20.3536	+	15.3286i	0.829551	+	0.624749i
$603$		0			0
$604$	−2.53343	−	4.38804i	−0.103084	−	0.178547i
$605$	44.4254			1.80615
$606$		0			0
$607$	17.1509	+	29.7063i	0.696135	+	1.20574i	0.969797	+	0.243915i	$0.0784319\pi$
$607$	17.1509	+	29.7063i	0.696135	+	1.20574i	−0.273662	+	0.961826i	$0.588235\pi$
$608$	2.84997	+	4.93629i	0.115581	+	0.200193i
$609$		0			0
$610$	−24.8998			−1.00816
$611$	−4.09768	+	40.0400i	−0.165774	+	1.61984i
$612$		0			0
$613$	1.82769	−	3.16565i	0.0738197	−	0.127860i	−0.826753	−	0.562566i	$-0.809814\pi$
$613$	1.82769	−	3.16565i	0.0738197	−	0.127860i	0.900572	+	0.434706i	$0.143148\pi$
$614$	20.0771			0.810246
$615$		0			0
$616$	−1.10553	−	0.832590i	−0.0445429	−	0.0335460i
$617$	−2.31545	+	4.01048i	−0.0932167	+	0.161456i	−0.908863	−	0.417095i	$-0.863048\pi$
$617$	−2.31545	+	4.01048i	−0.0932167	+	0.161456i	0.815646	+	0.578551i	$0.196382\pi$
$618$		0			0
$619$	−0.674947	−	1.16904i	−0.0271284	−	0.0469878i	0.852142	−	0.523310i	$-0.175303\pi$
$619$	−0.674947	−	1.16904i	−0.0271284	−	0.0469878i	−0.879271	+	0.476322i	$0.841970\pi$
$620$	−18.0278			−0.724014
$621$		0			0
$622$	−10.4837	−	18.1583i	−0.420358	−	0.728081i
$623$	3.49111	−	28.4986i	0.139868	−	1.14177i
$624$		0			0
$625$	−30.9717	+	53.6446i	−1.23887	+	2.14578i
$626$	9.55610	−	16.5517i	0.381939	−	0.661537i
$627$		0			0
$628$	5.80481	+	10.0542i	0.231637	+	0.401207i
$629$	−14.2928			−0.569892
$630$		0			0
$631$	−20.8686	+	36.1455i	−0.830766	+	1.43893i	0.0666652	+	0.997775i	$0.478764\pi$
$631$	−20.8686	+	36.1455i	−0.830766	+	1.43893i	−0.897431	+	0.441154i	$0.854569\pi$
$632$	1.15602	−	2.00229i	0.0459840	−	0.0796467i
$633$		0			0
$634$	−9.13122	+	15.8157i	−0.362647	+	0.628123i
$635$	−31.7612			−1.26040
$636$		0			0
$637$	24.8409	−	4.46452i	0.984231	−	0.176891i
$638$	1.61183			0.0638128
$639$		0			0
$640$	2.07085	−	3.58682i	0.0818575	−	0.141781i
$641$	15.8022			0.624149			0.312075	−	0.950058i	$-0.398976\pi$
$641$	15.8022			0.624149			0.312075	+	0.950058i	$0.398976\pi$
$642$		0			0
$643$	17.7586	−	30.7588i	0.700330	−	1.21301i	−0.268021	−	0.963413i	$-0.586370\pi$
$643$	17.7586	−	30.7588i	0.700330	−	1.21301i	0.968351	−	0.249594i	$-0.0802971\pi$
$644$	2.37847	−	19.4159i	0.0937248	−	0.765093i
$645$		0			0
$646$	7.19074	+	12.4547i	0.282916	+	0.490024i
$647$	−3.99546	+	6.92034i	−0.157078	+	0.272067i	−0.933814	−	0.357760i	$-0.883541\pi$
$647$	−3.99546	+	6.92034i	−0.157078	+	0.272067i	0.776736	+	0.629827i	$0.216874\pi$
$648$		0			0
$649$	−2.12049	+	3.67280i	−0.0832366	+	0.144170i
$650$	35.5220	+	25.6601i	1.39329	+	1.00647i
$651$		0			0
$652$	9.99637	+	17.3142i	0.391488	+	0.678077i
$653$	−43.4971			−1.70217			−0.851086	−	0.525026i	$-0.824056\pi$
$653$	−43.4971			−1.70217			−0.851086	+	0.525026i	$0.824056\pi$
$654$		0			0
$655$	−23.2926	−	40.3439i	−0.910116	−	1.57637i
$656$	−2.33240	−	4.03983i	−0.0910648	−	0.157729i
$657$		0			0
$658$	−23.5925	−	17.7679i	−0.919730	−	0.692664i
$659$	−2.30892	+	3.99917i	−0.0899429	+	0.155786i	−0.907487	−	0.420081i	$-0.862002\pi$
$659$	−2.30892	+	3.99917i	−0.0899429	+	0.155786i	0.817544	+	0.575866i	$0.195335\pi$
$660$		0			0
$661$	−12.9276	+	22.3912i	−0.502824	+	0.870918i	0.497170	+	0.867653i	$0.334372\pi$
$661$	−12.9276	+	22.3912i	−0.502824	+	0.870918i	−0.999995	+	0.00326450i	$0.998961\pi$
$662$	5.12199	+	8.87155i	0.199072	+	0.344803i
$663$		0			0
$664$	−3.08133			−0.119579
$665$	7.59458	−	61.9959i	0.294505	−	2.40410i
$666$		0			0
$667$	11.3907	+	19.7293i	0.441050	+	0.763921i
$668$	8.82851	+	15.2914i	0.341585	+	0.591643i
$669$		0			0
$670$	6.69390	+	11.5942i	0.258608	+	0.447922i
$671$	−3.14483			−0.121405
$672$		0			0
$673$	6.36967	+	11.0326i	0.245533	+	0.425275i	0.962281	−	0.272056i	$-0.0877038\pi$
$673$	6.36967	+	11.0326i	0.245533	+	0.425275i	−0.716748	+	0.697332i	$0.754370\pi$
$674$	−32.6266			−1.25673
$675$		0			0
$676$	8.64572	−	9.70832i	0.332528	−	0.373397i
$677$	−12.1455	+	21.0367i	−0.466791	+	0.808505i	−0.999280	−	0.0379314i	$-0.987923\pi$
$677$	−12.1455	+	21.0367i	−0.466791	+	0.808505i	0.532490	+	0.846436i	$0.321256\pi$
$678$		0			0
$679$	5.57489	+	4.19855i	0.213945	+	0.161125i
$680$	5.22495	−	9.04988i	0.200368	−	0.347047i
$681$		0			0
$682$	−2.27690			−0.0871871
$683$	−9.96097			−0.381146			−0.190573	−	0.981673i	$-0.561035\pi$
$683$	−9.96097			−0.381146			−0.190573	+	0.981673i	$0.561035\pi$
$684$		0			0
$685$	14.5422	−	25.1878i	0.555627	−	0.962375i
$686$	−6.62259	+	17.2957i	−0.252852	+	0.660353i
$687$		0			0
$688$	−4.81529	+	8.34033i	−0.183581	+	0.317972i
$689$	−0.0112276	−	0.00811048i	−0.000427736	−	0.000308985i
$690$		0			0
$691$	−28.2230			−1.07365			−0.536827	−	0.843692i	$-0.680377\pi$
$691$	−28.2230			−1.07365			−0.536827	+	0.843692i	$0.680377\pi$
$692$	−1.93492	−	3.35139i	−0.0735548	−	0.127401i
$693$		0			0
$694$	−8.43192			−0.320071
$695$	−27.3022	−	47.2888i	−1.03563	−	1.79377i
$696$		0			0
$697$	−5.88486	−	10.1929i	−0.222905	−	0.386083i
$698$	18.3077	+	31.7099i	0.692958	+	1.20024i
$699$		0			0
$700$	−29.5959	+	12.5725i	−1.11862	+	0.475194i
$701$	1.33647			0.0504778			0.0252389	−	0.999681i	$-0.491965\pi$
$701$	1.33647			0.0504778			0.0252389	+	0.999681i	$0.491965\pi$
$702$		0			0
$703$	−16.1445	−	27.9631i	−0.608901	−	1.05465i
$704$	0.261547	−	0.453013i	0.00985743	−	0.0170736i
$705$		0			0
$706$	−2.61947	+	4.53705i	−0.0985850	+	0.170754i
$707$	25.7511	+	19.3936i	0.968470	+	0.729371i
$708$		0			0
$709$	16.7552	+	29.0208i	0.629254	+	1.08990i	0.987702	+	0.156350i	$0.0499728\pi$
$709$	16.7552	+	29.0208i	0.629254	+	1.08990i	−0.358448	+	0.933550i	$0.616694\pi$
$710$	16.5075	+	28.5918i	0.619515	+	1.07303i
$711$		0			0
$712$	10.8520			0.406695
$713$	−16.0908	−	27.8700i	−0.602604	−	1.04374i
$714$		0			0
$715$	6.33211	+	4.57414i	0.236808	+	0.171063i
$716$	−1.75984	+	3.04813i	−0.0657683	+	0.113914i
$717$		0			0
$718$	2.54006	−	4.39951i	0.0947942	−	0.164188i
$719$	−3.53164	−	6.11698i	−0.131708	−	0.228125i	0.792627	−	0.609707i	$-0.208713\pi$
$719$	−3.53164	−	6.11698i	−0.131708	−	0.228125i	−0.924335	+	0.381582i	$0.875379\pi$
$720$		0			0
$721$	−28.8074	−	21.6953i	−1.07284	−	0.807975i
$722$	−6.74463	+	11.6820i	−0.251009	+	0.434760i
$723$		0			0
$724$	8.47129			0.314833
$725$	18.7247	−	32.4322i	0.695419	−	1.20450i
$726$		0			0
$727$	−22.2264			−0.824331			−0.412166	−	0.911109i	$-0.635228\pi$
$727$	−22.2264			−0.824331			−0.412166	+	0.911109i	$0.635228\pi$
$728$	2.81653	+	9.11412i	0.104388	+	0.337792i
$729$		0			0
$730$	49.6242			1.83667
$731$	−12.1494	+	21.0434i	−0.449363	+	0.778320i
$732$		0			0
$733$	7.77847	−	13.4727i	0.287304	−	0.497626i	−0.685861	−	0.727732i	$-0.740574\pi$
$733$	7.77847	−	13.4727i	0.287304	−	0.497626i	0.973165	+	0.230107i	$0.0739076\pi$
$734$	−2.43151	+	4.21150i	−0.0897487	+	0.155449i
$735$		0			0
$736$	7.39337			0.272523
$737$	0.845436	+	1.46434i	0.0311420	+	0.0539396i
$738$		0			0
$739$	3.19399	−	5.53216i	0.117493	−	0.203504i	−0.801281	−	0.598289i	$-0.795848\pi$
$739$	3.19399	−	5.53216i	0.117493	−	0.203504i	0.918774	+	0.394785i	$0.129181\pi$
$740$	−11.7309	+	20.3186i	−0.431238	+	0.746926i
$741$		0			0
$742$	0.00935447	−	0.00397382i	0.000343413	−	0.000145884i
$743$	5.24875	+	9.09109i	0.192558	+	0.333520i	0.946097	−	0.323883i	$-0.104988\pi$
$743$	5.24875	+	9.09109i	0.192558	+	0.333520i	−0.753539	+	0.657403i	$0.771655\pi$
$744$		0			0
$745$	75.0983			2.75139
$746$	−14.4061	−	24.9521i	−0.527445	−	0.913561i
$747$		0			0
$748$	0.659909	−	1.14300i	0.0241286	−	0.0417920i
$749$	−1.73630	+	14.1737i	−0.0634430	+	0.517897i
$750$		0			0
$751$	16.5633			0.604404			0.302202	−	0.953244i	$-0.402278\pi$
$751$	16.5633			0.604404			0.302202	+	0.953244i	$0.402278\pi$
$752$	5.58154	−	9.66752i	0.203538	−	0.352538i
$753$		0			0
$754$	−9.00592	−	6.50562i	−0.327976	−	0.236921i
$755$	−20.9854			−0.763739
$756$		0			0
$757$	−13.5475	−	23.4649i	−0.492391	−	0.852847i	0.507570	−	0.861610i	$-0.330544\pi$
$757$	−13.5475	−	23.4649i	−0.492391	−	0.852847i	−0.999962	+	0.00876370i	$0.997210\pi$
$758$	−14.1550	−	24.5172i	−0.514133	−	0.890504i
$759$		0			0
$760$	23.6074			0.856331
$761$	−1.40179	−	2.42797i	−0.0508148	−	0.0880139i	0.839499	−	0.543361i	$-0.182849\pi$
$761$	−1.40179	−	2.42797i	−0.0508148	−	0.0880139i	−0.890314	+	0.455347i	$0.849515\pi$
$762$		0			0
$763$	27.1826	−	11.5473i	0.984077	−	0.418040i
$764$	−10.9754	−	19.0099i	−0.397075	−	0.687755i
$765$		0			0
$766$	−9.36815	−	16.2261i	−0.338485	−	0.586273i
$767$	26.6721	−	11.9627i	0.963074	−	0.431948i
$768$		0			0
$769$	−4.67209	−	8.09231i	−0.168480	−	0.291816i	0.769406	−	0.638761i	$-0.220553\pi$
$769$	−4.67209	−	8.09231i	−0.168480	−	0.291816i	−0.937886	+	0.346945i	$0.887219\pi$
$770$	−5.27573	+	2.24115i	−0.190124	+	0.0807655i
$771$		0			0
$772$	−6.42959	+	11.1364i	−0.231406	+	0.400807i
$773$	−50.5572			−1.81841			−0.909207	−	0.416344i	$-0.863311\pi$
$773$	−50.5572			−1.81841			−0.909207	+	0.416344i	$0.863311\pi$
$774$		0			0
$775$	−26.4510	+	45.8144i	−0.950147	+	1.64570i
$776$	−1.31892	+	2.28443i	−0.0473464	+	0.0820063i
$777$		0			0
$778$	−3.55307	−	6.15409i	−0.127384	−	0.220635i
$779$	13.2945	−	23.0268i	0.476325	−	0.825020i
$780$		0			0
$781$	2.08489	+	3.61113i	0.0746031	+	0.129216i
$782$	18.6542			0.667072
$783$		0			0
$784$	−6.79301	−	1.68966i	−0.242608	−	0.0603450i
$785$	48.0836			1.71618
$786$		0			0
$787$	5.54021			0.197487			0.0987436	−	0.995113i	$-0.468518\pi$
$787$	5.54021			0.197487			0.0987436	+	0.995113i	$0.468518\pi$
$788$	5.27054	+	9.12883i	0.187755	+	0.325201i
$789$		0			0
$790$	−4.78789	−	8.29287i	−0.170346	−	0.295047i
$791$	8.60664	+	6.48180i	0.306017	+	0.230466i
$792$		0			0
$793$	17.5714	+	12.6931i	0.623980	+	0.450745i
$794$	−19.6633	−	34.0578i	−0.697824	−	1.20867i
$795$		0			0
$796$	13.1036			0.464446
$797$	4.90846	−	8.50171i	0.173867	−	0.301146i	−0.765902	−	0.642958i	$-0.777707\pi$
$797$	4.90846	−	8.50171i	0.173867	−	0.301146i	0.939768	+	0.341812i	$0.111040\pi$
$798$		0			0
$799$	14.0828	−	24.3921i	0.498212	−	0.862929i
$800$	−6.07684	−	10.5254i	−0.214849	−	0.372129i
$801$		0			0
$802$	8.60307			0.303785
$803$	6.26751			0.221176
$804$		0			0
$805$	−64.7158	−	48.7385i	−2.28093	−	1.71781i
$806$	12.7220	+	9.18998i	0.448112	+	0.323703i
$807$		0			0
$808$	−6.09224	+	10.5521i	−0.214324	+	0.371220i
$809$	−20.3684	+	35.2791i	−0.716114	+	1.24035i	0.246414	+	0.969165i	$0.420748\pi$
$809$	−20.3684	+	35.2791i	−0.716114	+	1.24035i	−0.962528	+	0.271181i	$0.912586\pi$
$810$		0			0
$811$	−23.9184			−0.839887			−0.419944	−	0.907550i	$-0.637950\pi$
$811$	−23.9184			−0.839887			−0.419944	+	0.907550i	$0.637950\pi$
$812$	7.50346	−	3.18750i	0.263320	−	0.111859i
$813$		0			0
$814$	−1.48161	+	2.56623i	−0.0519305	+	0.0899462i
$815$	82.8039			2.90050
$816$		0			0
$817$	−54.8937			−1.92049
$818$	−36.5325			−1.27733
$819$		0			0
$820$	−19.3202			−0.674690
$821$	21.9250			0.765187			0.382594	−	0.923917i	$-0.375031\pi$
$821$	21.9250			0.765187			0.382594	+	0.923917i	$0.375031\pi$
$822$		0			0
$823$	−2.58998			−0.0902809			−0.0451404	−	0.998981i	$-0.514374\pi$
$823$	−2.58998			−0.0902809			−0.0451404	+	0.998981i	$0.514374\pi$
$824$	6.81529	−	11.8044i	0.237422	−	0.411227i
$825$		0			0
$826$	−2.60820	+	21.2912i	−0.0907510	+	0.740817i
$827$	−8.21658			−0.285718			−0.142859	−	0.989743i	$-0.545630\pi$
$827$	−8.21658			−0.285718			−0.142859	+	0.989743i	$0.545630\pi$
$828$		0			0
$829$	4.31494	−	7.47369i	0.149864	−	0.259572i	−0.781313	−	0.624139i	$-0.785450\pi$
$829$	4.31494	−	7.47369i	0.149864	−	0.259572i	0.931177	+	0.364567i	$0.118783\pi$
$830$	−6.38097	+	11.0522i	−0.221487	+	0.383626i
$831$		0			0
$832$	−3.28981	+	1.47551i	−0.114054	+	0.0511542i
$833$	−17.1394	−	4.26318i	−0.593846	−	0.147710i
$834$		0			0
$835$	73.1301			2.53077
$836$	2.98160			0.103121
$837$		0			0
$838$	−6.77818	−	11.7402i	−0.234148	−	0.405557i
$839$	−0.656067	+	1.13634i	−0.0226499	+	0.0392309i	−0.877128	−	0.480256i	$-0.840544\pi$
$839$	−0.656067	+	1.13634i	−0.0226499	+	0.0392309i	0.854478	+	0.519487i	$0.173877\pi$
$840$		0			0
$841$	9.75270	−	16.8922i	0.336300	−	0.582489i
$842$	4.50209			0.155152
$843$		0			0
$844$	−0.979430	−	1.69642i	−0.0337134	−	0.0583933i
$845$	−16.9180	−	51.1151i	−0.581996	−	1.75841i
$846$		0			0
$847$	26.1202	−	11.0960i	0.897501	−	0.381262i
$848$	0.00192073	+	0.00332680i	6.59580e−5	+	0.000114243i
$849$		0			0
$850$	−15.3324	−	26.5566i	−0.525898	−	0.910882i
$851$	−41.8819			−1.43569
$852$		0			0
$853$	3.91347			0.133995			0.0669974	−	0.997753i	$-0.478658\pi$
$853$	3.91347			0.133995			0.0669974	+	0.997753i	$0.478658\pi$
$854$	−14.6400	+	6.21913i	−0.500970	+	0.212814i
$855$		0			0
$856$	−5.39721			−0.184473
$857$	20.7141	+	35.8779i	0.707580	+	1.22556i	0.965752	+	0.259466i	$0.0835464\pi$
$857$	20.7141	+	35.8779i	0.707580	+	1.22556i	−0.258172	+	0.966099i	$0.583120\pi$
$858$		0			0
$859$	−6.13898	+	10.6330i	−0.209459	+	0.362794i	−0.951544	−	0.307511i	$-0.900504\pi$
$859$	−6.13898	+	10.6330i	−0.209459	+	0.362794i	0.742085	+	0.670306i	$0.233837\pi$
$860$	19.9435	+	34.5431i	0.680067	+	1.17791i
$861$		0			0
$862$	−0.253853	+	0.439686i	−0.00864626	+	0.0149758i
$863$	−18.8040	+	32.5694i	−0.640095	+	1.10868i	0.345316	+	0.938486i	$0.387772\pi$
$863$	−18.8040	+	32.5694i	−0.640095	+	1.10868i	−0.985411	+	0.170191i	$0.945562\pi$
$864$		0			0
$865$	−16.0277			−0.544960
$866$	−6.41093	+	11.1041i	−0.217852	+	0.377331i
$867$		0			0
$868$	−10.5996	+	4.50274i	−0.359772	+	0.152833i
$869$	−0.604708	−	1.04739i	−0.0205133	−	0.0355301i
$870$		0			0
$871$	1.18654	−	11.5942i	0.0402045	−	0.392854i
$872$	5.58133	+	9.66715i	0.189008	+	0.327371i
$873$		0			0
$874$	21.0709	+	36.4958i	0.712733	+	1.23449i
$875$	−9.53154	+	77.8077i	−0.322225	+	2.63038i
$876$		0			0
$877$	11.5660	+	20.0329i	0.390557	+	0.676465i	0.992523	−	0.122057i	$-0.0389491\pi$
$877$	11.5660	+	20.0329i	0.390557	+	0.676465i	−0.601966	+	0.798522i	$0.705616\pi$
$878$	−0.433280			−0.0146225
$879$		0			0
$880$	−1.08325	−	1.87624i	−0.0365164	−	0.0632482i
$881$	25.2659	+	43.7618i	0.851229	+	1.47437i	0.880100	+	0.474788i	$0.157475\pi$
$881$	25.2659	+	43.7618i	0.851229	+	1.47437i	−0.0288713	+	0.999583i	$0.509191\pi$
$882$		0			0
$883$	30.7977			1.03643			0.518213	−	0.855251i	$-0.326597\pi$
$883$	30.7977			1.03643			0.518213	+	0.855251i	$0.326597\pi$
$884$	−8.30051	+	3.72286i	−0.279176	+	0.125213i
$885$		0			0
$886$	7.03339	−	12.1822i	0.236291	−	0.409269i
$887$	−20.0317			−0.672597			−0.336299	−	0.941755i	$-0.609175\pi$
$887$	−20.0317			−0.672597			−0.336299	+	0.941755i	$0.609175\pi$
$888$		0			0
$889$	−18.6742	+	7.93287i	−0.626312	+	0.266060i
$890$	22.4728	−	38.9240i	0.753290	−	1.30474i
$891$		0			0
$892$	6.26821	+	10.8569i	0.209875	+	0.363515i
$893$	63.6289			2.12926
$894$		0			0
$895$	7.28873	+	12.6245i	0.243635	+	0.421989i
$896$	0.321703	−	2.62612i	0.0107473	−	0.0877325i
$897$		0			0
$898$	−15.2892	+	26.4817i	−0.510207	+	0.883705i
$899$	6.70613	−	11.6154i	0.223662	−	0.387394i
$900$		0			0
$901$	0.00484618	+	0.00839382i	0.000161450	+	0.000279639i
$902$	−2.44013			−0.0812474
$903$		0			0
$904$	−2.03617	+	3.52676i	−0.0677221	+	0.117298i
$905$	17.5428	−	30.3850i	0.583141	−	1.01003i
$906$		0			0
$907$	−7.83200	+	13.5654i	−0.260057	+	0.450432i	−0.966257	−	0.257580i	$-0.917075\pi$
$907$	−7.83200	+	13.5654i	−0.260057	+	0.450432i	0.706200	+	0.708013i	$0.250408\pi$
$908$	21.7299			0.721132
$909$		0			0
$910$	38.5233	+	8.77158i	1.27703	+	0.290775i
$911$	−6.84991			−0.226948			−0.113474	−	0.993541i	$-0.536198\pi$
$911$	−6.84991			−0.226948			−0.113474	+	0.993541i	$0.536198\pi$
$912$		0			0
$913$	−0.805913	+	1.39588i	−0.0266718	+	0.0461970i
$914$	2.31026			0.0764165
$915$		0			0
$916$	−7.77570	+	13.4679i	−0.256917	+	0.444992i
$917$	−23.7716	−	17.9028i	−0.785006	−	0.591201i
$918$		0			0
$919$	−4.77437	−	8.26945i	−0.157492	−	0.272784i	0.776472	−	0.630152i	$-0.217008\pi$
$919$	−4.77437	−	8.26945i	−0.157492	−	0.272784i	−0.933964	+	0.357368i	$0.883674\pi$
$920$	15.3106	−	26.5187i	0.504774	−	0.874295i
$921$		0			0
$922$	15.0409	−	26.0516i	0.495345	−	0.857963i
$923$	2.92608	−	28.5918i	0.0963130	−	0.941111i
$924$		0			0
$925$	34.4240	+	59.6242i	1.13186	+	1.96043i
$926$	29.4727			0.968532
$927$		0			0
$928$	1.54066	+	2.66851i	0.0505748	+	0.0875981i
$929$	−19.9328	−	34.5247i	−0.653975	−	1.13272i	−0.982150	−	0.188101i	$-0.939767\pi$
$929$	−19.9328	−	34.5247i	−0.653975	−	1.13272i	0.328174	−	0.944617i	$-0.393567\pi$
$930$		0			0
$931$	−11.0192	−	38.3478i	−0.361140	−	1.25680i
$932$	−10.3320	+	17.8955i	−0.338435	+	0.586187i
$933$		0			0
$934$	−2.92442	+	5.06525i	−0.0956900	+	0.165740i
$935$	−2.73314	−	4.73394i	−0.0893833	−	0.154816i
$936$		0			0
$937$	−11.4259			−0.373268			−0.186634	−	0.982430i	$-0.559758\pi$
$937$	−11.4259			−0.373268			−0.186634	+	0.982430i	$0.559758\pi$
$938$	6.83156	+	5.14496i	0.223058	+	0.167989i
$939$		0			0
$940$	−23.1171	−	40.0400i	−0.753996	−	1.30596i
$941$	−19.0547	−	33.0037i	−0.621165	−	1.07589i	−0.989269	−	0.146104i	$-0.953326\pi$
$941$	−19.0547	−	33.0037i	−0.621165	−	1.07589i	0.368105	−	0.929784i	$-0.380007\pi$
$942$		0			0
$943$	−17.2443	−	29.8680i	−0.561551	−	0.972635i
$944$	−8.10749			−0.263876
$945$		0			0
$946$	2.51885	+	4.36278i	0.0818950	+	0.141846i
$947$	8.09255			0.262973			0.131486	−	0.991318i	$-0.458025\pi$
$947$	8.09255			0.262973			0.131486	+	0.991318i	$0.458025\pi$
$948$		0			0
$949$	−35.0191	−	25.2968i	−1.13677	−	0.821169i
$950$	34.6376	−	59.9940i	1.12379	−	1.94646i
$951$		0			0
$952$	0.811687	−	6.62595i	0.0263069	−	0.214748i
$953$	2.17357	−	3.76473i	0.0704088	−	0.121952i	−0.828672	−	0.559735i	$-0.810903\pi$
$953$	2.17357	−	3.76473i	0.0704088	−	0.121952i	0.899081	+	0.437783i	$0.144236\pi$
$954$		0			0
$955$	−90.9134			−2.94189
$956$	30.0971			0.973410
$957$		0			0
$958$	8.66374	−	15.0060i	0.279913	−	0.484823i
$959$	2.25910	−	18.4414i	0.0729501	−	0.595505i
$960$		0			0
$961$	6.02677	−	10.4387i	0.194412	−	0.336731i
$962$	18.6361	−	8.35848i	0.600852	−	0.269488i
$963$		0			0
$964$	2.05219			0.0660965
$965$	26.6294	+	46.1235i	0.857232	+	1.48477i
$966$		0			0
$967$	−6.10945			−0.196467			−0.0982333	−	0.995163i	$-0.531319\pi$
$967$	−6.10945			−0.196467			−0.0982333	+	0.995163i	$0.531319\pi$
$968$	5.36319	+	9.28931i	0.172379	+	0.298570i
$969$		0			0
$970$	5.46256	+	9.46143i	0.175392	+	0.303788i
$971$	3.52129	+	6.09906i	0.113004	+	0.195728i	0.916980	−	0.398933i	$-0.130619\pi$
$971$	3.52129	+	6.09906i	0.113004	+	0.195728i	−0.803976	+	0.594661i	$0.797286\pi$
$972$		0			0
$973$	−27.8636	−	20.9846i	−0.893267	−	0.672734i
$974$	−38.0645			−1.21967
$975$		0			0
$976$	−3.00599	−	5.20652i	−0.0962193	−	0.166657i
$977$	15.4653	−	26.7867i	0.494779	−	0.856982i	−0.505203	−	0.863000i	$-0.668583\pi$
$977$	15.4653	−	26.7867i	0.494779	−	0.856982i	0.999982	+	0.00601874i	$0.00191584\pi$
$978$		0			0
$979$	2.83830	−	4.91609i	0.0907126	−	0.157119i
$980$	−20.1278	+	20.8663i	−0.642960	+	0.666548i
$981$		0			0
$982$	8.22130	+	14.2397i	0.262352	+	0.454407i
$983$	−14.5237	−	25.1559i	−0.463235	−	0.802347i	0.535885	−	0.844291i	$-0.319978\pi$
$983$	−14.5237	−	25.1559i	−0.463235	−	0.802347i	−0.999120	+	0.0419441i	$0.986645\pi$
$984$		0			0
$985$	43.6579			1.39106
$986$	3.88724	+	6.73290i	0.123795	+	0.214419i
$987$		0			0
$988$	−16.6594	−	12.0343i	−0.530007	−	0.382862i
$989$	−35.6012	+	61.6631i	−1.13205	+	1.96077i
$990$		0			0
$991$	6.96955	−	12.0716i	0.221395	−	0.383468i	−0.733837	−	0.679326i	$-0.762272\pi$
$991$	6.96955	−	12.0716i	0.221395	−	0.383468i	0.955232	+	0.295858i	$0.0956056\pi$
$992$	−2.17638	−	3.76959i	−0.0691000	−	0.119685i
$993$		0			0
$994$	16.8469	+	12.6877i	0.534353	+	0.402430i
$995$	27.1357	−	47.0004i	0.860259	−	1.49001i
$996$		0			0
$997$	−36.8250			−1.16626			−0.583129	−	0.812379i	$-0.698172\pi$
$997$	−36.8250			−1.16626			−0.583129	+	0.812379i	$0.698172\pi$
$998$	−3.74298	+	6.48304i	−0.118482	+	0.205217i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.m.k.289.5		10
3.2	odd	2		546.2.j.e.289.1	✓	10
7.4	even	3		1638.2.p.j.991.5		10
13.9	even	3		1638.2.p.j.919.5		10
21.11	odd	6		546.2.k.e.445.1	yes	10
39.35	odd	6		546.2.k.e.373.1	yes	10
91.74	even	3	inner	1638.2.m.k.1621.5		10
273.74	odd	6		546.2.j.e.529.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.e.289.1	✓	10	3.2	odd	2
546.2.j.e.529.1	yes	10	273.74	odd	6
546.2.k.e.373.1	yes	10	39.35	odd	6
546.2.k.e.445.1	yes	10	21.11	odd	6
1638.2.m.k.289.5		10	1.1	even	1	trivial
1638.2.m.k.1621.5		10	91.74	even	3	inner
1638.2.p.j.919.5		10	13.9	even	3
1638.2.p.j.991.5		10	7.4	even	3

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.m (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(2.07085 - 3.58682i) q^{5} +(0.321703 - 2.62612i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(2.07085 - 3.58682i) q^{5} +(0.321703 - 2.62612i) q^{7} +1.00000 q^{8} +(2.07085 - 3.58682i) q^{10} +(0.261547 - 0.453013i) q^{11} +(-3.28981 + 1.47551i) q^{13} +(0.321703 - 2.62612i) q^{14} +1.00000 q^{16} +2.52309 q^{17} +(2.84997 + 4.93629i) q^{19} +(2.07085 - 3.58682i) q^{20} +(0.261547 - 0.453013i) q^{22} +7.39337 q^{23} +(-6.07684 - 10.5254i) q^{25} +(-3.28981 + 1.47551i) q^{26} +(0.321703 - 2.62612i) q^{28} +(1.54066 + 2.66851i) q^{29} +(-2.17638 - 3.76959i) q^{31} +1.00000 q^{32} +2.52309 q^{34} +(-8.75321 - 6.59219i) q^{35} -5.66479 q^{37} +(2.84997 + 4.93629i) q^{38} +(2.07085 - 3.58682i) q^{40} +(-2.33240 - 4.03983i) q^{41} +(-4.81529 + 8.34033i) q^{43} +(0.261547 - 0.453013i) q^{44} +7.39337 q^{46} +(5.58154 - 9.66752i) q^{47} +(-6.79301 - 1.68966i) q^{49} +(-6.07684 - 10.5254i) q^{50} +(-3.28981 + 1.47551i) q^{52} +(0.00192073 + 0.00332680i) q^{53} +(-1.08325 - 1.87624i) q^{55} +(0.321703 - 2.62612i) q^{56} +(1.54066 + 2.66851i) q^{58} -8.10749 q^{59} +(-3.00599 - 5.20652i) q^{61} +(-2.17638 - 3.76959i) q^{62} +1.00000 q^{64} +(-1.52031 + 14.8555i) q^{65} +(-1.61622 + 2.79938i) q^{67} +2.52309 q^{68} +(-8.75321 - 6.59219i) q^{70} +(-3.98568 + 6.90340i) q^{71} +(5.99080 + 10.3764i) q^{73} -5.66479 q^{74} +(2.84997 + 4.93629i) q^{76} +(-1.10553 - 0.832590i) q^{77} +(1.15602 - 2.00229i) q^{79} +(2.07085 - 3.58682i) q^{80} +(-2.33240 - 4.03983i) q^{82} -3.08133 q^{83} +(5.22495 - 9.04988i) q^{85} +(-4.81529 + 8.34033i) q^{86} +(0.261547 - 0.453013i) q^{88} +10.8520 q^{89} +(2.81653 + 9.11412i) q^{91} +7.39337 q^{92} +(5.58154 - 9.66752i) q^{94} +23.6074 q^{95} +(-1.31892 + 2.28443i) q^{97} +(-6.79301 - 1.68966i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 10 q^{4} + 2 q^{5} - 2 q^{7} + 10 q^{8}+O(q^{10}) \) 10 * q + 10 * q^2 + 10 * q^4 + 2 * q^5 - 2 * q^7 + 10 * q^8	\( 10 q + 10 q^{2} + 10 q^{4} + 2 q^{5} - 2 q^{7} + 10 q^{8} + 2 q^{10} - 6 q^{11} - 4 q^{13} - 2 q^{14} + 10 q^{16} + 8 q^{17} + 3 q^{19} + 2 q^{20} - 6 q^{22} + 12 q^{23} - q^{25} - 4 q^{26} - 2 q^{28} - 10 q^{31} + 10 q^{32} + 8 q^{34} - 16 q^{35} - 2 q^{37} + 3 q^{38} + 2 q^{40} + 4 q^{41} + 3 q^{43} - 6 q^{44} + 12 q^{46} + 15 q^{47} + 4 q^{49} - q^{50} - 4 q^{52} + 17 q^{53} + 3 q^{55} - 2 q^{56} + 4 q^{59} + 11 q^{61} - 10 q^{62} + 10 q^{64} + 4 q^{65} - q^{67} + 8 q^{68} - 16 q^{70} - 18 q^{71} + 12 q^{73} - 2 q^{74} + 3 q^{76} - 18 q^{77} - 4 q^{79} + 2 q^{80} + 4 q^{82} + q^{85} + 3 q^{86} - 6 q^{88} + 14 q^{89} + 26 q^{91} + 12 q^{92} + 15 q^{94} + 48 q^{95} - 6 q^{97} + 4 q^{98}+O(q^{100}) \) 10 * q + 10 * q^2 + 10 * q^4 + 2 * q^5 - 2 * q^7 + 10 * q^8 + 2 * q^10 - 6 * q^11 - 4 * q^13 - 2 * q^14 + 10 * q^16 + 8 * q^17 + 3 * q^19 + 2 * q^20 - 6 * q^22 + 12 * q^23 - q^25 - 4 * q^26 - 2 * q^28 - 10 * q^31 + 10 * q^32 + 8 * q^34 - 16 * q^35 - 2 * q^37 + 3 * q^38 + 2 * q^40 + 4 * q^41 + 3 * q^43 - 6 * q^44 + 12 * q^46 + 15 * q^47 + 4 * q^49 - q^50 - 4 * q^52 + 17 * q^53 + 3 * q^55 - 2 * q^56 + 4 * q^59 + 11 * q^61 - 10 * q^62 + 10 * q^64 + 4 * q^65 - q^67 + 8 * q^68 - 16 * q^70 - 18 * q^71 + 12 * q^73 - 2 * q^74 + 3 * q^76 - 18 * q^77 - 4 * q^79 + 2 * q^80 + 4 * q^82 + q^85 + 3 * q^86 - 6 * q^88 + 14 * q^89 + 26 * q^91 + 12 * q^92 + 15 * q^94 + 48 * q^95 - 6 * q^97 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more