LMFDB - Embedded newform 464.2.u.h.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [464,2,Mod(49,464)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(464, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("464.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	464.u (of order $7$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.70505865379$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 9 x^{9} - 5 x^{8} + 35 x^{7} + 197 x^{6} - 140 x^{5} - 80 x^{4} + \cdots + 4096 $ x^12 - 3x^11 + 13x^10 - 9x^9 - 5x^8 + 35x^7 + 197x^6 - 140x^5 - 80x^4 + 576x^3 + 3328x^2 + 3072*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 58)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			49.1
Root			$-1.02179 + 1.28129i$ of defining polynomial
Character	$\chi$	$=$	464.49
Dual form			464.2.u.h.161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02179 - 1.28129i) q^{3} +(-1.07557 + 0.517965i) q^{5} +(-1.27416 - 1.59774i) q^{7} +(0.0699247 - 0.306360i) q^{9} +O(q^{10})$	\(q+(-1.02179 - 1.28129i) q^{3} +(-1.07557 + 0.517965i) q^{5} +(-1.27416 - 1.59774i) q^{7} +(0.0699247 - 0.306360i) q^{9} +(0.819415 + 3.59009i) q^{11} +(-0.479858 - 2.10239i) q^{13} +(1.76267 + 0.848856i) q^{15} -6.53517 q^{17} +(-3.31337 + 4.15484i) q^{19} +(-0.745242 + 3.26512i) q^{21} +(-5.30987 - 2.55710i) q^{23} +(-2.22890 + 2.79495i) q^{25} +(-4.89359 + 2.35663i) q^{27} +(1.75040 + 5.09275i) q^{29} +(8.10571 - 3.90350i) q^{31} +(3.76267 - 4.71824i) q^{33} +(2.19801 + 1.05851i) q^{35} +(-0.406764 + 1.78215i) q^{37} +(-2.20346 + 2.76305i) q^{39} -8.32895 q^{41} +(-3.31774 - 1.59774i) q^{43} +(0.0834753 + 0.365729i) q^{45} +(-0.220911 - 0.967876i) q^{47} +(0.628344 - 2.75296i) q^{49} +(6.67760 + 8.37344i) q^{51} +(5.10353 - 2.45773i) q^{53} +(-2.74087 - 3.43695i) q^{55} +8.70913 q^{57} -2.94918 q^{59} +(-1.12786 - 1.41429i) q^{61} +(-0.578579 + 0.278629i) q^{63} +(1.60508 + 2.01271i) q^{65} +(1.34482 - 5.89206i) q^{67} +(2.14921 + 9.41630i) q^{69} +(0.836003 + 3.66277i) q^{71} +(-11.4647 - 5.52110i) q^{73} +5.85860 q^{75} +(4.69197 - 5.88354i) q^{77} +(3.14487 - 13.7786i) q^{79} +(7.17039 + 3.45308i) q^{81} +(-1.27960 + 1.60457i) q^{83} +(7.02900 - 3.38499i) q^{85} +(4.73674 - 7.44650i) q^{87} +(14.8768 - 7.16429i) q^{89} +(-2.74767 + 3.44546i) q^{91} +(-13.2839 - 6.39717i) q^{93} +(1.41169 - 6.18501i) q^{95} +(-2.86572 + 3.59350i) q^{97} +1.15716 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - q^{7} - 11 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - q^7 - 11 * q^9	$ 12 q + 3 q^{3} - q^{7} - 11 q^{9} + 2 q^{11} + q^{13} + 9 q^{15} - 12 q^{17} + 6 q^{19} - 13 q^{21} - 35 q^{23} - 6 q^{25} - 39 q^{27} - 14 q^{29} + 8 q^{31} + 33 q^{33} + 18 q^{35} + 31 q^{37} + 22 q^{39} - 30 q^{41} + 5 q^{43} - 20 q^{45} + 33 q^{47} + 37 q^{49} + 15 q^{51} + 13 q^{53} - 36 q^{55} - 38 q^{57} - 38 q^{59} - 5 q^{61} - 4 q^{63} - 20 q^{65} + 7 q^{67} + 20 q^{69} - 3 q^{71} - 22 q^{73} + 2 q^{75} + 10 q^{77} + 60 q^{79} + 88 q^{81} + 39 q^{83} + 38 q^{85} - 9 q^{87} + 39 q^{89} - 61 q^{91} - 54 q^{93} - 55 q^{95} - 19 q^{97} + 8 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - q^7 - 11 * q^9 + 2 * q^11 + q^13 + 9 * q^15 - 12 * q^17 + 6 * q^19 - 13 * q^21 - 35 * q^23 - 6 * q^25 - 39 * q^27 - 14 * q^29 + 8 * q^31 + 33 * q^33 + 18 * q^35 + 31 * q^37 + 22 * q^39 - 30 * q^41 + 5 * q^43 - 20 * q^45 + 33 * q^47 + 37 * q^49 + 15 * q^51 + 13 * q^53 - 36 * q^55 - 38 * q^57 - 38 * q^59 - 5 * q^61 - 4 * q^63 - 20 * q^65 + 7 * q^67 + 20 * q^69 - 3 * q^71 - 22 * q^73 + 2 * q^75 + 10 * q^77 + 60 * q^79 + 88 * q^81 + 39 * q^83 + 38 * q^85 - 9 * q^87 + 39 * q^89 - 61 * q^91 - 54 * q^93 - 55 * q^95 - 19 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{7}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.02179	−	1.28129i	−0.589933	−	0.739752i	0.393839	−	0.919180i	$-0.371147\pi$
$3$	−1.02179	−	1.28129i	−0.589933	−	0.739752i	−0.983771	+	0.179428i	$0.942575\pi$
$4$		0			0
$5$	−1.07557	+	0.517965i	−0.481007	+	0.231641i	−0.658643	−	0.752455i	$-0.728869\pi$
$5$	−1.07557	+	0.517965i	−0.481007	+	0.231641i	0.177636	+	0.984096i	$0.443155\pi$
$6$		0			0
$7$	−1.27416	−	1.59774i	−0.481585	−	0.603889i	0.480380	−	0.877061i	$-0.340499\pi$
$7$	−1.27416	−	1.59774i	−0.481585	−	0.603889i	−0.961965	+	0.273171i	$0.911927\pi$
$8$		0			0
$9$	0.0699247	−	0.306360i	0.0233082	−	0.102120i
$10$		0			0
$11$	0.819415	+	3.59009i	0.247063	+	1.08245i	0.934431	+	0.356144i	$0.115909\pi$
$11$	0.819415	+	3.59009i	0.247063	+	1.08245i	−0.687368	+	0.726309i	$0.741234\pi$
$12$		0			0
$13$	−0.479858	−	2.10239i	−0.133089	−	0.583099i	−0.996858	−	0.0792116i	$-0.974760\pi$
$13$	−0.479858	−	2.10239i	−0.133089	−	0.583099i	0.863769	−	0.503888i	$-0.168097\pi$
$14$		0			0
$15$	1.76267	+	0.848856i	0.455119	+	0.219174i
$16$		0			0
$17$	−6.53517			−1.58501			−0.792506	−	0.609864i	$-0.791224\pi$
$17$	−6.53517			−1.58501			−0.792506	+	0.609864i	$0.791224\pi$
$18$		0			0
$19$	−3.31337	+	4.15484i	−0.760140	+	0.953186i	−0.999844	−	0.0176605i	$-0.994378\pi$
$19$	−3.31337	+	4.15484i	−0.760140	+	0.953186i	0.239704	+	0.970846i	$0.422950\pi$
$20$		0			0
$21$	−0.745242	+	3.26512i	−0.162625	+	0.712508i
$22$		0			0
$23$	−5.30987	−	2.55710i	−1.10718	−	0.533192i	−0.211274	−	0.977427i	$-0.567761\pi$
$23$	−5.30987	−	2.55710i	−1.10718	−	0.533192i	−0.895910	+	0.444235i	$0.853476\pi$
$24$		0			0
$25$	−2.22890	+	2.79495i	−0.445779	+	0.558989i
$26$		0			0
$27$	−4.89359	+	2.35663i	−0.941771	+	0.453533i
$28$		0			0
$29$	1.75040	+	5.09275i	0.325040	+	0.945700i
$29$	1.75040	+	5.09275i	0.325040	+	0.945700i
$30$		0			0
$31$	8.10571	−	3.90350i	1.45583	−	0.701090i	0.472232	−	0.881475i	$-0.343449\pi$
$31$	8.10571	−	3.90350i	1.45583	−	0.701090i	0.983596	+	0.180385i	$0.0577343\pi$
$32$		0			0
$33$	3.76267	−	4.71824i	0.654996	−	0.821339i
$34$		0			0
$35$	2.19801	+	1.05851i	0.371532	+	0.178920i
$36$		0			0
$37$	−0.406764	+	1.78215i	−0.0668717	+	0.292984i	−0.997295	−	0.0735026i	$-0.976582\pi$
$37$	−0.406764	+	1.78215i	−0.0668717	+	0.292984i	0.930423	+	0.366487i	$0.119439\pi$
$38$		0			0
$39$	−2.20346	+	2.76305i	−0.352836	+	0.442442i
$40$		0			0
$41$	−8.32895			−1.30076			−0.650382	−	0.759608i	$-0.725391\pi$
$41$	−8.32895			−1.30076			−0.650382	+	0.759608i	$0.725391\pi$
$42$		0			0
$43$	−3.31774	−	1.59774i	−0.505951	−	0.243653i	0.163454	−	0.986551i	$-0.447737\pi$
$43$	−3.31774	−	1.59774i	−0.505951	−	0.243653i	−0.669405	+	0.742898i	$0.733451\pi$
$44$		0			0
$45$	0.0834753	+	0.365729i	0.0124438	+	0.0545197i
$46$		0			0
$47$	−0.220911	−	0.967876i	−0.0322232	−	0.141179i	0.956257	−	0.292526i	$-0.0944960\pi$
$47$	−0.220911	−	0.967876i	−0.0322232	−	0.141179i	−0.988481	+	0.151347i	$0.951639\pi$
$48$		0			0
$49$	0.628344	−	2.75296i	0.0897635	−	0.393280i
$50$		0			0
$51$	6.67760	+	8.37344i	0.935050	+	1.17252i
$52$		0			0
$53$	5.10353	−	2.45773i	0.701023	−	0.337595i	−0.0491913	−	0.998789i	$-0.515664\pi$
$53$	5.10353	−	2.45773i	0.701023	−	0.337595i	0.750215	+	0.661194i	$0.229950\pi$
$54$		0			0
$55$	−2.74087	−	3.43695i	−0.369579	−	0.463438i
$56$		0			0
$57$	8.70913			1.15355
$58$		0			0
$59$	−2.94918			−0.383951			−0.191975	−	0.981400i	$-0.561489\pi$
$59$	−2.94918			−0.383951			−0.191975	+	0.981400i	$0.561489\pi$
$60$		0			0
$61$	−1.12786	−	1.41429i	−0.144407	−	0.181081i	0.704368	−	0.709835i	$-0.251231\pi$
$61$	−1.12786	−	1.41429i	−0.144407	−	0.181081i	−0.848775	+	0.528754i	$0.822659\pi$
$62$		0			0
$63$	−0.578579	+	0.278629i	−0.0728941	+	0.0351040i
$64$		0			0
$65$	1.60508	+	2.01271i	0.199086	+	0.249646i
$66$		0			0
$67$	1.34482	−	5.89206i	0.164296	−	0.719830i	−0.823912	−	0.566717i	$-0.808213\pi$
$67$	1.34482	−	5.89206i	0.164296	−	0.719830i	0.988209	−	0.153113i	$-0.0489297\pi$
$68$		0			0
$69$	2.14921	+	9.41630i	0.258734	+	1.13359i
$70$		0			0
$71$	0.836003	+	3.66277i	0.0992153	+	0.434691i	1.00000		0.000424562i	$0.000135142\pi$
$71$	0.836003	+	3.66277i	0.0992153	+	0.434691i	−0.900785	+	0.434266i	$0.857008\pi$
$72$		0			0
$73$	−11.4647	−	5.52110i	−1.34184	−	0.646196i	−0.381329	−	0.924439i	$-0.624534\pi$
$73$	−11.4647	−	5.52110i	−1.34184	−	0.646196i	−0.960511	+	0.278243i	$0.910248\pi$
$74$		0			0
$75$	5.85860			0.676493
$76$		0			0
$77$	4.69197	−	5.88354i	0.534700	−	0.670492i
$78$		0			0
$79$	3.14487	−	13.7786i	0.353826	−	1.55021i	−0.414438	−	0.910077i	$-0.636022\pi$
$79$	3.14487	−	13.7786i	0.353826	−	1.55021i	0.768264	−	0.640133i	$-0.221121\pi$
$80$		0			0
$81$	7.17039	+	3.45308i	0.796710	+	0.383676i
$82$		0			0
$83$	−1.27960	+	1.60457i	−0.140455	+	0.176125i	−0.847083	−	0.531460i	$-0.821644\pi$
$83$	−1.27960	+	1.60457i	−0.140455	+	0.176125i	0.706629	+	0.707584i	$0.250215\pi$
$84$		0			0
$85$	7.02900	−	3.38499i	0.762403	−	0.367154i
$86$		0			0
$87$	4.73674	−	7.44650i	0.507832	−	0.798349i
$88$		0			0
$89$	14.8768	−	7.16429i	1.57694	−	0.759413i	0.578521	−	0.815668i	$-0.303630\pi$
$89$	14.8768	−	7.16429i	1.57694	−	0.759413i	0.998416	+	0.0562548i	$0.0179159\pi$
$90$		0			0
$91$	−2.74767	+	3.44546i	−0.288034	+	0.361183i
$92$		0			0
$93$	−13.2839	−	6.39717i	−1.37747	−	0.663356i
$94$		0			0
$95$	1.41169	−	6.18501i	0.144836	−	0.634569i
$96$		0			0
$97$	−2.86572	+	3.59350i	−0.290970	+	0.364864i	−0.905734	−	0.423846i	$-0.860680\pi$
$97$	−2.86572	+	3.59350i	−0.290970	+	0.364864i	0.614764	+	0.788711i	$0.289251\pi$
$98$		0			0
$99$	1.15716			0.116299
$100$		0			0
$101$	−0.188984	−	0.0910101i	−0.0188047	−	0.00905584i	0.424458	−	0.905448i	$-0.360465\pi$
$101$	−0.188984	−	0.0910101i	−0.0188047	−	0.00905584i	−0.443262	+	0.896392i	$0.646179\pi$
$102$		0			0
$103$	−2.47612	−	10.8486i	−0.243979	−	1.06894i	−0.937357	−	0.348369i	$-0.886735\pi$
$103$	−2.47612	−	10.8486i	−0.243979	−	1.06894i	0.693378	−	0.720574i	$-0.256122\pi$
$104$		0			0
$105$	−0.889661	−	3.89786i	−0.0868220	−	0.380392i
$106$		0			0
$107$	−0.900276	+	3.94436i	−0.0870329	+	0.381316i	−0.999620	−	0.0275663i	$-0.991224\pi$
$107$	−0.900276	+	3.94436i	−0.0870329	+	0.381316i	0.912587	+	0.408882i	$0.134081\pi$
$108$		0			0
$109$	−9.74736	−	12.2228i	−0.933628	−	1.17073i	−0.985087	−	0.172057i	$-0.944959\pi$
$109$	−9.74736	−	12.2228i	−0.933628	−	1.17073i	0.0514595	−	0.998675i	$-0.483613\pi$
$110$		0			0
$111$	2.69908	−	1.29981i	0.256185	−	0.123372i
$112$		0			0
$113$	11.5102	+	14.4333i	1.08278	+	1.35777i	0.929176	+	0.369638i	$0.120518\pi$
$113$	11.5102	+	14.4333i	1.08278	+	1.35777i	0.153609	+	0.988132i	$0.450910\pi$
$114$		0			0
$115$	7.03560			0.656073
$116$		0			0
$117$	−0.677644			−0.0626482
$118$		0			0
$119$	8.32683	+	10.4415i	0.763319	+	0.957172i
$120$		0			0
$121$	−2.30665	+	1.11082i	−0.209695	+	0.100984i
$122$		0			0
$123$	8.51046	+	10.6718i	0.767363	+	0.962242i
$124$		0			0
$125$	2.27785	−	9.97992i	0.203737	−	0.892631i
$126$		0			0
$127$	4.20519	+	18.4241i	0.373150	+	1.63488i	0.717874	+	0.696173i	$0.245115\pi$
$127$	4.20519	+	18.4241i	0.373150	+	1.63488i	−0.344724	+	0.938704i	$0.612027\pi$
$128$		0			0
$129$	1.34288	+	5.88354i	0.118234	+	0.518017i
$130$		0			0
$131$	4.42173	+	2.12939i	0.386328	+	0.186046i	0.616959	−	0.786995i	$-0.288365\pi$
$131$	4.42173	+	2.12939i	0.386328	+	0.186046i	−0.230630	+	0.973041i	$0.574079\pi$
$132$		0			0
$133$	10.8601			0.941691
$134$		0			0
$135$	4.04272	−	5.06941i	0.347942	−	0.436306i
$136$		0			0
$137$	−0.849284	+	3.72096i	−0.0725592	+	0.317903i	−0.998163	−	0.0605922i	$-0.980701\pi$
$137$	−0.849284	+	3.72096i	−0.0725592	+	0.317903i	0.925603	+	0.378495i	$0.123558\pi$
$138$		0			0
$139$	−10.9299	−	5.26355i	−0.927060	−	0.446448i	−0.0914734	−	0.995808i	$-0.529158\pi$
$139$	−10.9299	−	5.26355i	−0.927060	−	0.446448i	−0.835586	+	0.549359i	$0.814872\pi$
$140$		0			0
$141$	−1.01440	+	1.27202i	−0.0854281	+	0.107123i
$142$		0			0
$143$	7.15458	−	3.44546i	0.598296	−	0.288124i
$144$		0			0
$145$	−4.52053	−	4.57094i	−0.375410	−	0.379596i
$146$		0			0
$147$	−4.16937	+	2.00786i	−0.343884	+	0.165606i
$148$		0			0
$149$	−4.48771	+	5.62741i	−0.367648	+	0.461016i	−0.930903	−	0.365268i	$-0.880977\pi$
$149$	−4.48771	+	5.62741i	−0.367648	+	0.461016i	0.563255	+	0.826283i	$0.309549\pi$
$150$		0			0
$151$	−8.36320	−	4.02750i	−0.680587	−	0.327754i	0.0614519	−	0.998110i	$-0.480427\pi$
$151$	−8.36320	−	4.02750i	−0.680587	−	0.327754i	−0.742039	+	0.670356i	$0.766141\pi$
$152$		0			0
$153$	−0.456970	+	2.00212i	−0.0369439	+	0.161862i
$154$		0			0
$155$	−6.69634	+	8.39694i	−0.537863	+	0.674459i
$156$		0			0
$157$	−1.99480			−0.159202			−0.0796011	−	0.996827i	$-0.525365\pi$
$157$	−1.99480			−0.159202			−0.0796011	+	0.996827i	$0.525365\pi$
$158$		0			0
$159$	−8.36381	−	4.02780i	−0.663293	−	0.319425i
$160$		0			0
$161$	2.68002	+	11.7419i	0.211215	+	0.925394i
$162$		0			0
$163$	−0.910347	−	3.98849i	−0.0713039	−	0.312403i	0.926681	−	0.375848i	$-0.122648\pi$
$163$	−0.910347	−	3.98849i	−0.0713039	−	0.312403i	−0.997985	+	0.0634450i	$0.979791\pi$
$164$		0			0
$165$	−1.60311	+	7.02370i	−0.124802	+	0.546794i
$166$		0			0
$167$	−4.59082	−	5.75670i	−0.355248	−	0.445467i	0.571809	−	0.820387i	$-0.306242\pi$
$167$	−4.59082	−	5.75670i	−0.355248	−	0.445467i	−0.927057	+	0.374920i	$0.877670\pi$
$168$		0			0
$169$	7.52280	−	3.62279i	0.578677	−	0.278676i
$170$		0			0
$171$	1.04119	+	1.30561i	0.0796219	+	0.0998427i
$172$		0			0
$173$	−9.85163			−0.749005			−0.374503	−	0.927226i	$-0.622187\pi$
$173$	−9.85163			−0.749005			−0.374503	+	0.927226i	$0.622187\pi$
$174$		0			0
$175$	7.30556			0.552248
$176$		0			0
$177$	3.01345	+	3.77875i	0.226505	+	0.284028i
$178$		0			0
$179$	−11.0708	+	5.33143i	−0.827472	+	0.398490i	−0.799167	−	0.601110i	$-0.794726\pi$
$179$	−11.0708	+	5.33143i	−0.827472	+	0.398490i	−0.0283058	+	0.999599i	$0.509011\pi$
$180$		0			0
$181$	8.59415	+	10.7767i	0.638799	+	0.801028i	0.990852	−	0.134952i	$-0.0430880\pi$
$181$	8.59415	+	10.7767i	0.638799	+	0.801028i	−0.352054	+	0.935980i	$0.614517\pi$
$182$		0			0
$183$	−0.659674	+	2.89022i	−0.0487645	+	0.213651i
$184$		0			0
$185$	−0.485590	−	2.12751i	−0.0357013	−	0.156418i
$186$		0			0
$187$	−5.35502	−	23.4619i	−0.391598	−	1.71570i
$188$		0			0
$189$	10.0005	+	4.81597i	0.727427	+	0.350310i
$190$		0			0
$191$	−15.8384			−1.14603			−0.573015	−	0.819545i	$-0.694226\pi$
$191$	−15.8384			−1.14603			−0.573015	+	0.819545i	$0.694226\pi$
$192$		0			0
$193$	10.2409	−	12.8416i	0.737153	−	0.924360i	−0.262018	−	0.965063i	$-0.584388\pi$
$193$	10.2409	−	12.8416i	0.737153	−	0.924360i	0.999171	+	0.0407024i	$0.0129596\pi$
$194$		0			0
$195$	0.938800	−	4.11315i	0.0672289	−	0.294549i
$196$		0			0
$197$	−13.1902	−	6.35208i	−0.939764	−	0.452567i	−0.0996782	−	0.995020i	$-0.531781\pi$
$197$	−13.1902	−	6.35208i	−0.939764	−	0.452567i	−0.840086	+	0.542453i	$0.817496\pi$
$198$		0			0
$199$	−0.884637	+	1.10930i	−0.0627102	+	0.0786362i	−0.812197	−	0.583383i	$-0.801729\pi$
$199$	−0.884637	+	1.10930i	−0.0627102	+	0.0786362i	0.749487	+	0.662019i	$0.230300\pi$
$200$		0			0
$201$	−8.92356	+	4.29736i	−0.629419	+	0.303112i
$202$		0			0
$203$	5.90662	−	9.28563i	0.414563	−	0.651724i
$204$		0			0
$205$	8.95833	−	4.31410i	0.625677	−	0.301310i
$206$		0			0
$207$	−1.15469	+	1.44793i	−0.0802562	+	0.100638i
$208$		0			0
$209$	−17.6313	−	8.49077i	−1.21958	−	0.587319i
$210$		0			0
$211$	−5.73403	+	25.1224i	−0.394747	+	1.72950i	0.252842	+	0.967508i	$0.418635\pi$
$211$	−5.73403	+	25.1224i	−0.394747	+	1.72950i	−0.647588	+	0.761990i	$0.724222\pi$
$212$		0			0
$213$	3.83884	−	4.81375i	0.263033	−	0.329833i
$214$		0			0
$215$	4.39602			0.299806
$216$		0			0
$217$	−16.5647	−	7.97714i	−1.12449	−	0.541524i
$218$		0			0
$219$	4.64042	+	20.3310i	0.313570	+	1.37384i
$220$		0			0
$221$	3.13595	+	13.7395i	0.210947	+	0.924219i
$222$		0			0
$223$	−0.528048	+	2.31353i	−0.0353607	+	0.154925i	−0.989526	−	0.144355i	$-0.953889\pi$
$223$	−0.528048	+	2.31353i	−0.0353607	+	0.154925i	0.954165	+	0.299280i	$0.0967465\pi$
$224$		0			0
$225$	0.700406	+	0.878281i	0.0466937	+	0.0585521i
$226$		0			0
$227$	11.6966	−	5.63281i	0.776334	−	0.373863i	−0.00338357	−	0.999994i	$-0.501077\pi$
$227$	11.6966	−	5.63281i	0.776334	−	0.373863i	0.779717	+	0.626132i	$0.215363\pi$
$228$		0			0
$229$	−16.0288	−	20.0995i	−1.05921	−	1.32821i	−0.942189	−	0.335081i	$-0.891236\pi$
$229$	−16.0288	−	20.0995i	−1.05921	−	1.32821i	−0.117023	−	0.993129i	$-0.537335\pi$
$230$		0			0
$231$	−12.3327			−0.811435
$232$		0			0
$233$	−7.05047			−0.461891			−0.230946	−	0.972967i	$-0.574182\pi$
$233$	−7.05047			−0.461891			−0.230946	+	0.972967i	$0.574182\pi$
$234$		0			0
$235$	0.738930	+	0.926589i	0.0482025	+	0.0604440i
$236$		0			0
$237$	−20.8677	+	10.0494i	−1.35550	+	0.652777i
$238$		0			0
$239$	2.19867	+	2.75704i	0.142220	+	0.178338i	0.847840	−	0.530252i	$-0.177903\pi$
$239$	2.19867	+	2.75704i	0.142220	+	0.178338i	−0.705620	+	0.708591i	$0.749331\pi$
$240$		0			0
$241$	−2.64178	+	11.5744i	−0.170172	+	0.745573i	0.815755	+	0.578397i	$0.196322\pi$
$241$	−2.64178	+	11.5744i	−0.170172	+	0.745573i	−0.985927	+	0.167175i	$0.946535\pi$
$242$		0			0
$243$	0.723578	+	3.17020i	0.0464176	+	0.203369i
$244$		0			0
$245$	0.750110	+	3.28644i	0.0479227	+	0.209963i
$246$		0			0
$247$	10.3251	+	4.97229i	0.656968	+	0.316379i
$248$		0			0
$249$	3.36341			0.213147
$250$		0			0
$251$	5.80625	−	7.28081i	0.366488	−	0.459561i	−0.564059	−	0.825734i	$-0.690761\pi$
$251$	5.80625	−	7.28081i	0.366488	−	0.459561i	0.930547	+	0.366174i	$0.119332\pi$
$252$		0			0
$253$	4.82923	−	21.1582i	0.303611	−	1.33021i
$254$		0			0
$255$	−11.5193	−	5.54742i	−0.721369	−	0.347393i
$256$		0			0
$257$	−7.18322	+	9.00748i	−0.448077	+	0.561871i	−0.953652	−	0.300912i	$-0.902709\pi$
$257$	−7.18322	+	9.00748i	−0.448077	+	0.561871i	0.505575	+	0.862783i	$0.331280\pi$
$258$		0			0
$259$	3.36570	−	1.62083i	0.209134	−	0.100714i
$260$		0			0
$261$	1.68261	−	0.180143i	0.104151	−	0.0111506i
$262$		0			0
$263$	9.06859	−	4.36720i	0.559193	−	0.269293i	−0.132866	−	0.991134i	$-0.542418\pi$
$263$	9.06859	−	4.36720i	0.559193	−	0.269293i	0.692059	+	0.721841i	$0.256704\pi$
$264$		0			0
$265$	−4.21616	+	5.28690i	−0.258997	+	0.324771i
$266$		0			0
$267$	−24.3805	−	11.7410i	−1.49206	−	0.718540i
$268$		0			0
$269$	1.87086	−	8.19676i	0.114068	−	0.499765i	−0.885326	−	0.464970i	$-0.846065\pi$
$269$	1.87086	−	8.19676i	0.114068	−	0.499765i	0.999394	−	0.0347951i	$-0.0110779\pi$
$270$		0			0
$271$	−5.40055	+	6.77207i	−0.328060	+	0.411374i	−0.918320	−	0.395839i	$-0.870454\pi$
$271$	−5.40055	+	6.77207i	−0.328060	+	0.411374i	0.590260	+	0.807213i	$0.299025\pi$
$272$		0			0
$273$	7.22218			0.437106
$274$		0			0
$275$	−11.8605	−	5.71172i	−0.715215	−	0.344429i
$276$		0			0
$277$	4.30577	+	18.8648i	0.258709	+	1.13348i	0.922634	+	0.385678i	$0.126032\pi$
$277$	4.30577	+	18.8648i	0.258709	+	1.13348i	−0.663925	+	0.747799i	$0.731110\pi$
$278$		0			0
$279$	−0.629089	−	2.75622i	−0.0376626	−	0.165010i
$280$		0			0
$281$	3.38217	−	14.8182i	0.201763	−	0.883982i	−0.768100	−	0.640330i	$-0.778798\pi$
$281$	3.38217	−	14.8182i	0.201763	−	0.883982i	0.969863	−	0.243652i	$-0.0783454\pi$
$282$		0			0
$283$	−9.37454	−	11.7553i	−0.557259	−	0.698780i	0.420790	−	0.907158i	$-0.361753\pi$
$283$	−9.37454	−	11.7553i	−0.557259	−	0.698780i	−0.978048	+	0.208378i	$0.933182\pi$
$284$		0			0
$285$	−9.36724	+	4.51102i	−0.554867	+	0.267210i
$286$		0			0
$287$	10.6124	+	13.3075i	0.626429	+	0.785517i
$288$		0			0
$289$	25.7085			1.51226
$290$		0			0
$291$	7.53248			0.441562
$292$		0			0
$293$	18.3708	+	23.0362i	1.07323	+	1.34579i	0.934702	+	0.355432i	$0.115666\pi$
$293$	18.3708	+	23.0362i	1.07323	+	1.34579i	0.138530	+	0.990358i	$0.455762\pi$
$294$		0			0
$295$	3.17204	−	1.52757i	0.184683	−	0.0889387i
$296$		0			0
$297$	−12.4704	−	15.6374i	−0.723605	−	0.907372i
$298$		0			0
$299$	−2.82805	+	12.3905i	−0.163550	+	0.716560i
$300$		0			0
$301$	1.67454	+	7.33666i	0.0965191	+	0.422878i
$302$		0			0
$303$	0.0764928	+	0.335137i	0.00439440	+	0.0192531i
$304$		0			0
$305$	1.94564	+	0.936969i	0.111407	+	0.0536507i
$306$		0			0
$307$	5.88515			0.335883			0.167942	−	0.985797i	$-0.446288\pi$
$307$	5.88515			0.335883			0.167942	+	0.985797i	$0.446288\pi$
$308$		0			0
$309$	−11.3701	+	14.2576i	−0.646822	+	0.811089i
$310$		0			0
$311$	−5.11730	+	22.4204i	−0.290175	+	1.27134i	0.594106	+	0.804387i	$0.297506\pi$
$311$	−5.11730	+	22.4204i	−0.290175	+	1.27134i	−0.884281	+	0.466955i	$0.845351\pi$
$312$		0			0
$313$	−18.5136	−	8.91566i	−1.04645	−	0.503943i	−0.170003	−	0.985444i	$-0.554378\pi$
$313$	−18.5136	−	8.91566i	−1.04645	−	0.503943i	−0.876446	+	0.481501i	$0.840092\pi$
$314$		0			0
$315$	0.477980	−	0.599367i	0.0269311	−	0.0337705i
$316$		0			0
$317$	−6.35119	+	3.05857i	−0.356718	+	0.171786i	−0.603656	−	0.797245i	$-0.706290\pi$
$317$	−6.35119	+	3.05857i	−0.356718	+	0.171786i	0.246938	+	0.969031i	$0.420576\pi$
$318$		0			0
$319$	−16.8491	+	10.4572i	−0.943370	+	0.585488i
$320$		0			0
$321$	5.97376	−	2.87681i	0.333423	−	0.160568i
$322$		0			0
$323$	21.6535	−	27.1526i	1.20483	−	1.51081i
$324$		0			0
$325$	6.94563	+	3.34484i	0.385274	+	0.185538i
$326$		0			0
$327$	−5.70115	+	24.9783i	−0.315274	+	1.38131i
$328$		0			0
$329$	−1.26494	+	1.58618i	−0.0697383	+	0.0874491i
$330$		0			0
$331$	−20.4930			−1.12640			−0.563200	−	0.826321i	$-0.690430\pi$
$331$	−20.4930			−1.12640			−0.563200	+	0.826321i	$0.690430\pi$
$332$		0			0
$333$	0.517538	+	0.249233i	0.0283609	+	0.0136579i
$334$		0			0
$335$	1.60543	+	7.03387i	0.0877143	+	0.384301i
$336$		0			0
$337$	1.65202	+	7.23799i	0.0899914	+	0.394278i	0.999784	−	0.0207851i	$-0.00661657\pi$
$337$	1.65202	+	7.23799i	0.0899914	+	0.394278i	−0.909793	+	0.415063i	$0.863759\pi$
$338$		0			0
$339$	6.73219	−	29.4957i	0.365643	−	1.60198i
$340$		0			0
$341$	20.6559	+	25.9016i	1.11858	+	1.40265i
$342$		0			0
$343$	−18.0876	+	8.71052i	−0.976637	+	0.470324i
$344$		0			0
$345$	−7.18893	−	9.01463i	−0.387039	−	0.485331i
$346$		0			0
$347$	20.9493			1.12462			0.562308	−	0.826928i	$-0.309913\pi$
$347$	20.9493			1.12462			0.562308	+	0.826928i	$0.309913\pi$
$348$		0			0
$349$	−13.5931			−0.727620			−0.363810	−	0.931473i	$-0.618524\pi$
$349$	−13.5931			−0.727620			−0.363810	+	0.931473i	$0.618524\pi$
$350$		0			0
$351$	7.30278	+	9.15740i	0.389794	+	0.488786i
$352$		0			0
$353$	−16.4612	+	7.92731i	−0.876142	+	0.421928i	−0.817214	−	0.576334i	$-0.804483\pi$
$353$	−16.4612	+	7.92731i	−0.876142	+	0.421928i	−0.0589283	+	0.998262i	$0.518768\pi$
$354$		0			0
$355$	−2.79636	−	3.50653i	−0.148415	−	0.186107i
$356$		0			0
$357$	4.87029	−	21.3381i	0.257763	−	1.12933i
$358$		0			0
$359$	−1.94398	−	8.51711i	−0.102599	−	0.449516i	−0.999966	−	0.00823107i	$-0.997380\pi$
$359$	−1.94398	−	8.51711i	−0.102599	−	0.449516i	0.897367	−	0.441285i	$-0.145477\pi$
$360$		0			0
$361$	−2.05635	−	9.00944i	−0.108229	−	0.474181i
$362$		0			0
$363$	3.78020	+	1.82045i	0.198409	+	0.0955488i
$364$		0			0
$365$	15.1908			0.795121
$366$		0			0
$367$	9.32017	−	11.6871i	0.486509	−	0.610063i	−0.476618	−	0.879110i	$-0.658138\pi$
$367$	9.32017	−	11.6871i	0.486509	−	0.610063i	0.963127	+	0.269048i	$0.0867090\pi$
$368$		0			0
$369$	−0.582400	+	2.55166i	−0.0303185	+	0.132834i
$370$		0			0
$371$	−10.4295	−	5.02258i	−0.541473	−	0.260759i
$372$		0			0
$373$	21.8812	−	27.4381i	1.13296	−	1.42069i	0.239881	−	0.970802i	$-0.422891\pi$
$373$	21.8812	−	27.4381i	1.13296	−	1.42069i	0.893084	−	0.449891i	$-0.148537\pi$
$374$		0			0
$375$	−15.1146	+	7.27883i	−0.780517	+	0.375877i
$376$		0			0
$377$	9.86703	−	6.12382i	0.508178	−	0.315393i
$378$		0			0
$379$	29.8111	−	14.3563i	1.53129	−	0.737432i	0.536948	−	0.843616i	$-0.319577\pi$
$379$	29.8111	−	14.3563i	1.53129	−	0.737432i	0.994347	+	0.106183i	$0.0338630\pi$
$380$		0			0
$381$	19.3098	−	24.2137i	0.989271	−	1.24051i
$382$		0			0
$383$	−7.70600	−	3.71101i	−0.393758	−	0.189624i	0.226519	−	0.974007i	$-0.427265\pi$
$383$	−7.70600	−	3.71101i	−0.393758	−	0.189624i	−0.620277	+	0.784383i	$0.712980\pi$
$384$		0			0
$385$	−1.99905	+	8.75841i	−0.101881	+	0.446370i
$386$		0			0
$387$	−0.721476	+	0.904703i	−0.0366747	+	0.0459886i
$388$		0			0
$389$	−25.7864			−1.30742			−0.653710	−	0.756745i	$-0.726788\pi$
$389$	−25.7864			−1.30742			−0.653710	+	0.756745i	$0.726788\pi$
$390$		0			0
$391$	34.7009	+	16.7111i	1.75490	+	0.845116i
$392$		0			0
$393$	−1.78973	−	7.84131i	−0.0902798	−	0.395542i
$394$		0			0
$395$	3.75431	+	16.4487i	0.188900	+	0.827623i
$396$		0			0
$397$	−1.89709	+	8.31170i	−0.0952123	+	0.417152i	−0.999961	−	0.00879271i	$-0.997201\pi$
$397$	−1.89709	+	8.31170i	−0.0952123	+	0.417152i	0.904749	+	0.425945i	$0.140058\pi$
$398$		0			0
$399$	−11.0968	−	13.9149i	−0.555534	−	0.696618i
$400$		0			0
$401$	−14.2012	+	6.83892i	−0.709173	+	0.341520i	−0.753455	−	0.657499i	$-0.771614\pi$
$401$	−14.2012	+	6.83892i	−0.709173	+	0.341520i	0.0442823	+	0.999019i	$0.485900\pi$
$402$		0			0
$403$	−12.0963	−	15.1683i	−0.602559	−	0.755585i
$404$		0			0
$405$	−9.50080			−0.472099
$406$		0			0
$407$	−6.73139			−0.333663
$408$		0			0
$409$	14.2564	+	17.8769i	0.704931	+	0.883956i	0.997381	−	0.0723249i	$-0.0230419\pi$
$409$	14.2564	+	17.8769i	0.704931	+	0.883956i	−0.292450	+	0.956281i	$0.594470\pi$
$410$		0			0
$411$	5.63541	−	2.71387i	0.277974	−	0.133865i
$412$		0			0
$413$	3.75771	+	4.71202i	0.184905	+	0.231864i
$414$		0			0
$415$	0.545184	−	2.38861i	0.0267621	−	0.117252i
$416$		0			0
$417$	4.42395	+	19.3826i	0.216642	+	0.949169i
$418$		0			0
$419$	4.52733	+	19.8355i	0.221175	+	0.969030i	0.956595	+	0.291419i	$0.0941274\pi$
$419$	4.52733	+	19.8355i	0.221175	+	0.969030i	−0.735421	+	0.677611i	$0.763015\pi$
$420$		0			0
$421$	17.4411	+	8.39918i	0.850026	+	0.409351i	0.807587	−	0.589748i	$-0.200773\pi$
$421$	17.4411	+	8.39918i	0.850026	+	0.409351i	0.0424390	+	0.999099i	$0.486487\pi$
$422$		0			0
$423$	−0.311966			−0.0151683
$424$		0			0
$425$	14.5662	−	18.2655i	0.706566	−	0.886005i
$426$		0			0
$427$	−0.822600	+	3.60405i	−0.0398084	+	0.174412i
$428$		0			0
$429$	−11.7251	−	5.64653i	−0.566095	−	0.272617i
$430$		0			0
$431$	−2.84252	+	3.56441i	−0.136920	+	0.171692i	−0.845564	−	0.533874i	$-0.820736\pi$
$431$	−2.84252	+	3.56441i	−0.136920	+	0.171692i	0.708644	+	0.705566i	$0.249307\pi$
$432$		0			0
$433$	16.5499	−	7.97003i	0.795340	−	0.383015i	0.00833722	−	0.999965i	$-0.497346\pi$
$433$	16.5499	−	7.97003i	0.795340	−	0.383015i	0.787002	+	0.616950i	$0.211632\pi$
$434$		0			0
$435$	−1.23764	+	10.4627i	−0.0593405	+	0.501646i
$436$		0			0
$437$	28.2179	−	13.5890i	1.34985	−	0.650052i
$438$		0			0
$439$	11.9493	−	14.9840i	0.570310	−	0.715146i	−0.410116	−	0.912033i	$-0.634512\pi$
$439$	11.9493	−	14.9840i	0.570310	−	0.715146i	0.980426	+	0.196887i	$0.0630832\pi$
$440$		0			0
$441$	−0.799460	−	0.385000i	−0.0380695	−	0.0183333i
$442$		0			0
$443$	0.504155	−	2.20885i	0.0239531	−	0.104945i	−0.961538	−	0.274671i	$-0.911431\pi$
$443$	0.504155	−	2.20885i	0.0239531	−	0.104945i	0.985491	+	0.169726i	$0.0542882\pi$
$444$		0			0
$445$	−12.2901	+	15.4113i	−0.582607	+	0.730566i
$446$		0			0
$447$	11.7959			0.557925
$448$		0			0
$449$	21.9677	+	10.5791i	1.03672	+	0.499258i	0.873241	−	0.487289i	$-0.162014\pi$
$449$	21.9677	+	10.5791i	1.03672	+	0.499258i	0.163479	+	0.986547i	$0.447729\pi$
$450$		0			0
$451$	−6.82486	−	29.9017i	−0.321370	−	1.40801i
$452$		0			0
$453$	3.38507	+	14.8309i	0.159044	+	0.696818i
$454$		0			0
$455$	1.17066	−	5.12902i	0.0548816	−	0.240452i
$456$		0			0
$457$	−16.2192	−	20.3383i	−0.758704	−	0.951385i	0.241114	−	0.970497i	$-0.422487\pi$
$457$	−16.2192	−	20.3383i	−0.758704	−	0.951385i	−0.999817	+	0.0191124i	$0.993916\pi$
$458$		0			0
$459$	31.9804	−	15.4010i	1.49272	−	0.718856i
$460$		0			0
$461$	−16.3101	−	20.4522i	−0.759636	−	0.952553i	0.240199	−	0.970724i	$-0.422787\pi$
$461$	−16.3101	−	20.4522i	−0.759636	−	0.952553i	−0.999835	+	0.0181704i	$0.994216\pi$
$462$		0			0
$463$	28.3236			1.31631			0.658155	−	0.752882i	$-0.271337\pi$
$463$	28.3236			1.31631			0.658155	+	0.752882i	$0.271337\pi$
$464$		0			0
$465$	17.6012			0.816235
$466$		0			0
$467$	0.102786	+	0.128890i	0.00475638	+	0.00596432i	0.784204	−	0.620503i	$-0.213072\pi$
$467$	0.102786	+	0.128890i	0.00475638	+	0.00596432i	−0.779448	+	0.626467i	$0.784500\pi$
$468$		0			0
$469$	−11.1275	+	5.35872i	−0.513820	+	0.247443i
$470$		0			0
$471$	2.03827	+	2.55591i	0.0939186	+	0.117770i
$472$		0			0
$473$	3.01743	−	13.2202i	0.138741	−	0.607866i
$474$		0			0
$475$	−4.22739	−	18.5214i	−0.193966	−	0.849821i
$476$		0			0
$477$	−0.396088	−	1.73537i	−0.0181356	−	0.0794573i
$478$		0			0
$479$	−10.3200	−	4.96986i	−0.471534	−	0.227079i	0.182998	−	0.983113i	$-0.441420\pi$
$479$	−10.3200	−	4.96986i	−0.471534	−	0.227079i	−0.654532	+	0.756034i	$0.727134\pi$
$480$		0			0
$481$	3.94197			0.179739
$482$		0			0
$483$	12.3064	−	15.4317i	0.559960	−	0.702167i
$484$		0			0
$485$	1.22096	−	5.34938i	0.0554410	−	0.242903i
$486$		0			0
$487$	20.9047	+	10.0672i	0.947284	+	0.456188i	0.842733	−	0.538332i	$-0.180945\pi$
$487$	20.9047	+	10.0672i	0.947284	+	0.456188i	0.104551	+	0.994520i	$0.466659\pi$
$488$		0			0
$489$	−4.18022	+	5.24183i	−0.189036	+	0.237044i
$490$		0			0
$491$	12.7203	−	6.12578i	0.574060	−	0.276453i	−0.124247	−	0.992251i	$-0.539651\pi$
$491$	12.7203	−	6.12578i	0.574060	−	0.276453i	0.698307	+	0.715799i	$0.253937\pi$
$492$		0			0
$493$	−11.4391	−	33.2820i	−0.515193	−	1.49895i
$494$		0			0
$495$	−1.24460	+	0.599367i	−0.0559406	+	0.0269396i
$496$		0			0
$497$	4.78696	−	6.00265i	0.214724	−	0.269256i
$498$		0			0
$499$	−6.84483	−	3.29630i	−0.306417	−	0.147563i	0.274356	−	0.961628i	$-0.411535\pi$
$499$	−6.84483	−	3.29630i	−0.306417	−	0.147563i	−0.580773	+	0.814066i	$0.697250\pi$
$500$		0			0
$501$	−2.68513	+	11.7643i	−0.119963	+	0.525591i
$502$		0			0
$503$	1.05159	−	1.31865i	0.0468882	−	0.0587959i	−0.757835	−	0.652447i	$-0.773743\pi$
$503$	1.05159	−	1.31865i	0.0468882	−	0.0587959i	0.804723	+	0.593651i	$0.202314\pi$
$504$		0			0
$505$	0.250405			0.0111429
$506$		0			0
$507$	−12.3286	−	5.93713i	−0.547531	−	0.263677i
$508$		0			0
$509$	−9.21187	−	40.3599i	−0.408309	−	1.78892i	−0.592003	−	0.805936i	$-0.701663\pi$
$509$	−9.21187	−	40.3599i	−0.408309	−	1.78892i	0.183694	−	0.982983i	$-0.441194\pi$
$510$		0			0
$511$	5.78651	+	25.3523i	0.255980	+	1.12152i
$512$		0			0
$513$	6.42287	−	28.1405i	0.283577	−	1.24243i
$514$		0			0
$515$	8.28242	+	10.3858i	0.364967	+	0.457654i
$516$		0			0
$517$	3.29374	−	1.58618i	0.144859	−	0.0697603i
$518$		0			0
$519$	10.0663	+	12.6228i	0.441863	+	0.554078i
$520$		0			0
$521$	−5.78621			−0.253498			−0.126749	−	0.991935i	$-0.540454\pi$
$521$	−5.78621			−0.253498			−0.126749	+	0.991935i	$0.540454\pi$
$522$		0			0
$523$	14.4968			0.633899			0.316949	−	0.948442i	$-0.397341\pi$
$523$	14.4968			0.633899			0.316949	+	0.948442i	$0.397341\pi$
$524$		0			0
$525$	−7.46477	−	9.36053i	−0.325789	−	0.408527i
$526$		0			0
$527$	−52.9722	+	25.5101i	−2.30750	+	1.11124i
$528$		0			0
$529$	7.31571	+	9.17361i	0.318074	+	0.398852i
$530$		0			0
$531$	−0.206221	+	0.903512i	−0.00894921	+	0.0392091i
$532$		0			0
$533$	3.99671	+	17.5107i	0.173117	+	0.758474i
$534$		0			0
$535$	−1.07474	−	4.70873i	−0.0464650	−	0.203576i
$536$		0			0
$537$	18.1432	+	8.73730i	0.782937	+	0.377042i
$538$		0			0
$539$	10.3982			0.447884
$540$		0			0
$541$	−1.39658	+	1.75125i	−0.0600435	+	0.0752921i	−0.810946	−	0.585121i	$-0.801047\pi$
$541$	−1.39658	+	1.75125i	−0.0600435	+	0.0752921i	0.750903	+	0.660413i	$0.229619\pi$
$542$		0			0
$543$	5.02665	−	22.0232i	0.215714	−	0.945105i
$544$		0			0
$545$	16.8149	+	8.09763i	0.720271	+	0.346864i
$546$		0			0
$547$	−26.0264	+	32.6361i	−1.11281	+	1.39542i	−0.203612	+	0.979052i	$0.565268\pi$
$547$	−26.0264	+	32.6361i	−1.11281	+	1.39542i	−0.909197	+	0.416366i	$0.863303\pi$
$548$		0			0
$549$	−0.512147	+	0.246637i	−0.0218579	+	0.0105262i
$550$		0			0
$551$	−26.9593	−	9.60157i	−1.14850	−	0.409041i
$552$		0			0
$553$	−26.0216	+	12.5314i	−1.10655	+	0.532888i
$554$		0			0
$555$	−2.22978	+	2.79606i	−0.0946489	+	0.118686i
$556$		0			0
$557$	18.4842	+	8.90152i	0.783201	+	0.377170i	0.782357	−	0.622830i	$-0.214017\pi$
$557$	18.4842	+	8.90152i	0.783201	+	0.377170i	0.000843646		1.00000i	$0.499731\pi$
$558$		0			0
$559$	−1.76704	+	7.74189i	−0.0747376	+	0.327447i
$560$		0			0
$561$	−24.5897	+	30.8345i	−1.03818	+	1.30183i
$562$		0			0
$563$	−19.9670			−0.841511			−0.420755	−	0.907174i	$-0.638235\pi$
$563$	−19.9670			−0.841511			−0.420755	+	0.907174i	$0.638235\pi$
$564$		0			0
$565$	−19.8559	−	9.56208i	−0.835343	−	0.402280i
$566$		0			0
$567$	−3.61907	−	15.8562i	−0.151987	−	0.665897i
$568$		0			0
$569$	1.35962	+	5.95688i	0.0569982	+	0.249726i	0.995398	−	0.0958256i	$-0.0305491\pi$
$569$	1.35962	+	5.95688i	0.0569982	+	0.249726i	−0.938400	+	0.345551i	$0.887692\pi$
$570$		0			0
$571$	4.79370	−	21.0026i	0.200610	−	0.878931i	−0.769956	−	0.638097i	$-0.779722\pi$
$571$	4.79370	−	21.0026i	0.200610	−	0.878931i	0.970566	−	0.240834i	$-0.0774210\pi$
$572$		0			0
$573$	16.1836	+	20.2936i	0.676080	+	0.847778i
$574$		0			0
$575$	18.9821	−	9.14130i	0.791609	−	0.381219i
$576$		0			0
$577$	8.43341	+	10.5752i	0.351087	+	0.440250i	0.925747	−	0.378143i	$-0.123437\pi$
$577$	8.43341	+	10.5752i	0.351087	+	0.440250i	−0.574660	+	0.818392i	$0.694866\pi$
$578$		0			0
$579$	−26.9179			−1.11867
$580$		0			0
$581$	4.19410			0.174001
$582$		0			0
$583$	13.0054	+	16.3082i	0.538627	+	0.675418i
$584$		0			0
$585$	0.728850	−	0.350996i	0.0301343	−	0.0145119i
$586$		0			0
$587$	3.59029	+	4.50208i	0.148187	+	0.185821i	0.850385	−	0.526161i	$-0.176369\pi$
$587$	3.59029	+	4.50208i	0.148187	+	0.185821i	−0.702198	+	0.711982i	$0.747798\pi$
$588$		0			0
$589$	−10.6388	+	46.6117i	−0.438364	+	1.92060i
$590$		0			0
$591$	5.33884	+	23.3910i	0.219611	+	0.962176i
$592$		0			0
$593$	−4.14764	−	18.1720i	−0.170323	−	0.746235i	−0.985866	−	0.167538i	$-0.946418\pi$
$593$	−4.14764	−	18.1720i	−0.170323	−	0.746235i	0.815542	−	0.578697i	$-0.196439\pi$
$594$		0			0
$595$	−14.3644	−	6.91752i	−0.588882	−	0.283591i
$596$		0			0
$597$	2.32525			0.0951661
$598$		0			0
$599$	−4.23604	+	5.31183i	−0.173080	+	0.217036i	−0.860804	−	0.508937i	$-0.830039\pi$
$599$	−4.23604	+	5.31183i	−0.173080	+	0.217036i	0.687724	+	0.725973i	$0.258610\pi$
$600$		0			0
$601$	−7.16071	+	31.3731i	−0.292091	+	1.27974i	0.589517	+	0.807756i	$0.299318\pi$
$601$	−7.16071	+	31.3731i	−0.292091	+	1.27974i	−0.881609	+	0.471981i	$0.843539\pi$
$602$		0			0
$603$	−1.71106	−	0.824002i	−0.0696796	−	0.0335559i
$604$		0			0
$605$	1.90558	−	2.38952i	0.0774729	−	0.0971480i
$606$		0			0
$607$	−7.04607	+	3.39321i	−0.285991	+	0.137726i	−0.571380	−	0.820686i	$-0.693592\pi$
$607$	−7.04607	+	3.39321i	−0.285991	+	0.137726i	0.285389	+	0.958412i	$0.407877\pi$
$608$		0			0
$609$	−17.9329	+	1.91992i	−0.726678	+	0.0777991i
$610$		0			0
$611$	−1.92885	+	0.928886i	−0.0780329	+	0.0375787i
$612$		0			0
$613$	−8.06459	+	10.1127i	−0.325726	+	0.408447i	−0.917550	−	0.397620i	$-0.869836\pi$
$613$	−8.06459	+	10.1127i	−0.325726	+	0.408447i	0.591825	+	0.806067i	$0.298408\pi$
$614$		0			0
$615$	−14.6812	−	7.07008i	−0.592002	−	0.285093i
$616$		0			0
$617$	−8.86499	+	38.8401i	−0.356891	+	1.56364i	0.403998	+	0.914760i	$0.367620\pi$
$617$	−8.86499	+	38.8401i	−0.356891	+	1.56364i	−0.760889	+	0.648882i	$0.775237\pi$
$618$		0			0
$619$	−3.34154	+	4.19015i	−0.134308	+	0.168416i	−0.844437	−	0.535655i	$-0.820065\pi$
$619$	−3.34154	+	4.19015i	−0.134308	+	0.168416i	0.710130	+	0.704071i	$0.248636\pi$
$620$		0			0
$621$	32.0104			1.28453
$622$		0			0
$623$	−30.4020	−	14.6408i	−1.21803	−	0.586573i
$624$		0			0
$625$	−1.25815	−	5.51231i	−0.0503259	−	0.220492i
$626$		0			0
$627$	7.13639	+	31.2666i	0.285000	+	1.24867i
$628$		0			0
$629$	2.65828	−	11.6467i	0.105992	−	0.464383i
$630$		0			0
$631$	13.8533	+	17.3715i	0.551493	+	0.691550i	0.976960	−	0.213424i	$-0.0684615\pi$
$631$	13.8533	+	17.3715i	0.551493	+	0.691550i	−0.425467	+	0.904974i	$0.639890\pi$
$632$		0			0
$633$	38.0480	−	18.3230i	1.51227	−	0.728273i
$634$		0			0
$635$	−14.0660	−	17.6382i	−0.558192	−	0.699951i
$636$		0			0
$637$	−6.08932			−0.241267
$638$		0			0
$639$	1.18058			0.0467032
$640$		0			0
$641$	−11.7556	−	14.7411i	−0.464319	−	0.582237i	0.493451	−	0.869774i	$-0.335735\pi$
$641$	−11.7556	−	14.7411i	−0.464319	−	0.582237i	−0.957770	+	0.287536i	$0.907164\pi$
$642$		0			0
$643$	−6.79428	+	3.27195i	−0.267940	+	0.129033i	−0.563030	−	0.826436i	$-0.690365\pi$
$643$	−6.79428	+	3.27195i	−0.267940	+	0.129033i	0.295090	+	0.955469i	$0.404650\pi$
$644$		0			0
$645$	−4.49182	−	5.63257i	−0.176865	−	0.221782i
$646$		0			0
$647$	7.61765	−	33.3751i	0.299481	−	1.31211i	−0.571422	−	0.820656i	$-0.693608\pi$
$647$	7.61765	−	33.3751i	0.299481	−	1.31211i	0.870903	−	0.491455i	$-0.163535\pi$
$648$		0			0
$649$	−2.41660	−	10.5878i	−0.0948599	−	0.415608i
$650$		0			0
$651$	6.70469	+	29.3752i	0.262777	+	1.15130i
$652$		0			0
$653$	−23.9395	−	11.5287i	−0.936827	−	0.451152i	−0.0977780	−	0.995208i	$-0.531174\pi$
$653$	−23.9395	−	11.5287i	−0.936827	−	0.451152i	−0.839049	+	0.544056i	$0.816888\pi$
$654$		0			0
$655$	−5.85881			−0.228923
$656$		0			0
$657$	−2.49311	+	3.12626i	−0.0972656	+	0.121967i
$658$		0			0
$659$	−4.15512	+	18.2048i	−0.161860	+	0.709156i	0.827232	+	0.561860i	$0.189914\pi$
$659$	−4.15512	+	18.2048i	−0.161860	+	0.709156i	−0.989092	+	0.147296i	$0.952943\pi$
$660$		0			0
$661$	−20.0943	−	9.67691i	−0.781578	−	0.376388i	0.000156121	−	1.00000i	$-0.499950\pi$
$661$	−20.0943	−	9.67691i	−0.781578	−	0.376388i	−0.781734	+	0.623612i	$0.785665\pi$
$662$		0			0
$663$	14.4000	−	18.0570i	0.559249	−	0.701276i
$664$		0			0
$665$	−11.6808	+	5.62515i	−0.452960	+	0.218134i
$666$		0			0
$667$	3.72829	−	31.5178i	0.144360	−	1.22037i
$668$		0			0
$669$	3.50385	−	1.68737i	0.135467	−	0.0652374i
$670$		0			0
$671$	4.15324	−	5.20800i	0.160334	−	0.201053i
$672$		0			0
$673$	−27.9494	−	13.4597i	−1.07737	−	0.518835i	−0.190896	−	0.981610i	$-0.561139\pi$
$673$	−27.9494	−	13.4597i	−1.07737	−	0.518835i	−0.886475	+	0.462776i	$0.846854\pi$
$674$		0			0
$675$	4.32065	−	18.9300i	0.166302	−	0.728616i
$676$		0			0
$677$	7.98459	−	10.0124i	0.306873	−	0.384806i	−0.604351	−	0.796718i	$-0.706567\pi$
$677$	7.98459	−	10.0124i	0.306873	−	0.384806i	0.911224	+	0.411912i	$0.135139\pi$
$678$		0			0
$679$	9.39285			0.360464
$680$		0			0
$681$	−19.1688	−	9.23121i	−0.734550	−	0.353741i
$682$		0			0
$683$	9.57228	+	41.9389i	0.366273	+	1.60475i	0.736924	+	0.675975i	$0.236277\pi$
$683$	9.57228	+	41.9389i	0.366273	+	1.60475i	−0.370651	+	0.928772i	$0.620865\pi$
$684$		0			0
$685$	−1.01386	−	4.44203i	−0.0387378	−	0.169721i
$686$		0			0
$687$	−9.37510	+	41.0750i	−0.357682	+	1.56711i
$688$		0			0
$689$	−7.61608	−	9.55026i	−0.290150	−	0.363836i
$690$		0			0
$691$	−38.7258	+	18.6494i	−1.47320	+	0.709456i	−0.986447	−	0.164083i	$-0.947533\pi$
$691$	−38.7258	+	18.6494i	−1.47320	+	0.709456i	−0.486754	+	0.873539i	$0.661819\pi$
$692$		0			0
$693$	−1.47440	−	1.84884i	−0.0560078	−	0.0702316i
$694$		0			0
$695$	14.4821			0.549338
$696$		0			0
$697$	54.4311			2.06173
$698$		0			0
$699$	7.20412	+	9.03368i	0.272485	+	0.341685i
$700$		0			0
$701$	−36.5596	+	17.6062i	−1.38084	+	0.664976i	−0.969178	−	0.246362i	$-0.920765\pi$
$701$	−36.5596	+	17.6062i	−1.38084	+	0.664976i	−0.411659	+	0.911338i	$0.635051\pi$
$702$		0			0
$703$	−6.05679	−	7.59498i	−0.228436	−	0.286450i
$704$		0			0
$705$	0.432194	−	1.89357i	0.0162774	−	0.0713158i
$706$		0			0
$707$	0.0953850	+	0.417909i	0.00358732	+	0.0157171i
$708$		0			0
$709$	7.69612	+	33.7189i	0.289034	+	1.26634i	0.885854	+	0.463965i	$0.153574\pi$
$709$	7.69612	+	33.7189i	0.289034	+	1.26634i	−0.596820	+	0.802375i	$0.703569\pi$
$710$		0			0
$711$	−4.00130	−	1.92693i	−0.150061	−	0.0722654i
$712$		0			0
$713$	−53.0219			−1.98569
$714$		0			0
$715$	−5.91059	+	7.41164i	−0.221043	+	0.277180i
$716$		0			0
$717$	1.28598	−	5.63425i	0.0480258	−	0.210415i
$718$		0			0
$719$	5.57889	+	2.68665i	0.208057	+	0.100195i	0.535010	−	0.844845i	$-0.320308\pi$
$719$	5.57889	+	2.68665i	0.208057	+	0.100195i	−0.326953	+	0.945041i	$0.606022\pi$
$720$		0			0
$721$	−14.1783	+	17.7790i	−0.528026	+	0.662124i
$722$		0			0
$723$	17.5295	−	8.44176i	0.651929	−	0.313952i
$724$		0			0
$725$	−18.1354	−	6.45895i	−0.673533	−	0.239879i
$726$		0			0
$727$	18.1287	−	8.73032i	0.672356	−	0.323790i	−0.0663703	−	0.997795i	$-0.521142\pi$
$727$	18.1287	−	8.73032i	0.672356	−	0.323790i	0.738726	+	0.674005i	$0.235428\pi$
$728$		0			0
$729$	18.2088	−	22.8331i	0.674400	−	0.845671i
$730$		0			0
$731$	21.6820	+	10.4415i	0.801938	+	0.386193i
$732$		0			0
$733$	3.27267	−	14.3385i	0.120879	−	0.529604i	−0.877838	−	0.478958i	$-0.841015\pi$
$733$	3.27267	−	14.3385i	0.120879	−	0.529604i	0.998717	−	0.0506464i	$-0.0161282\pi$
$734$		0			0
$735$	3.44443	−	4.31917i	0.127050	−	0.159315i
$736$		0			0
$737$	22.2550			0.819773
$738$		0			0
$739$	−12.7546	−	6.14231i	−0.469187	−	0.225949i	0.184324	−	0.982866i	$-0.440990\pi$
$739$	−12.7546	−	6.14231i	−0.469187	−	0.225949i	−0.653511	+	0.756917i	$0.726705\pi$
$740$		0			0
$741$	−4.17914	−	18.3100i	−0.153525	−	0.672636i
$742$		0			0
$743$	−5.91234	−	25.9037i	−0.216903	−	0.950313i	−0.959751	−	0.280853i	$-0.909383\pi$
$743$	−5.91234	−	25.9037i	−0.216903	−	0.950313i	0.742848	−	0.669460i	$-0.233474\pi$
$744$		0			0
$745$	1.91202	−	8.37713i	0.0700512	−	0.306914i
$746$		0			0
$747$	0.402101	+	0.504219i	0.0147121	+	0.0184484i
$748$		0			0
$749$	7.44916	−	3.58733i	0.272186	−	0.131078i
$750$		0			0
$751$	−23.2027	−	29.0953i	−0.846678	−	1.06170i	−0.997324	−	0.0731132i	$-0.976707\pi$
$751$	−23.2027	−	29.0953i	−0.846678	−	1.06170i	0.150645	−	0.988588i	$-0.451865\pi$
$752$		0			0
$753$	−15.2616			−0.556164
$754$		0			0
$755$	11.0813			0.403289
$756$		0			0
$757$	14.2931	+	17.9230i	0.519492	+	0.651423i	0.970501	−	0.241097i	$-0.0775071\pi$
$757$	14.2931	+	17.9230i	0.519492	+	0.651423i	−0.451009	+	0.892520i	$0.648936\pi$
$758$		0			0
$759$	−32.0443	+	15.4317i	−1.16313	+	0.560136i
$760$		0			0
$761$	19.2173	+	24.0977i	0.696626	+	0.873542i	0.996766	−	0.0803533i	$-0.0256049\pi$
$761$	19.2173	+	24.0977i	0.696626	+	0.873542i	−0.300140	+	0.953895i	$0.597033\pi$
$762$		0			0
$763$	−7.10921	+	31.1475i	−0.257371	+	1.12761i
$764$		0			0
$765$	−0.545525	−	2.39010i	−0.0197235	−	0.0864144i
$766$		0			0
$767$	1.41519	+	6.20034i	0.0510994	+	0.223881i
$768$		0			0
$769$	11.8596	+	5.71126i	0.427667	+	0.205953i	0.635320	−	0.772249i	$-0.280868\pi$
$769$	11.8596	+	5.71126i	0.427667	+	0.205953i	−0.207653	+	0.978203i	$0.566583\pi$
$770$		0			0
$771$	18.8809			0.679980
$772$		0			0
$773$	−0.659056	+	0.826430i	−0.0237046	+	0.0297246i	−0.793543	−	0.608515i	$-0.791766\pi$
$773$	−0.659056	+	0.826430i	−0.0237046	+	0.0297246i	0.769838	+	0.638239i	$0.220337\pi$
$774$		0			0
$775$	−7.15669	+	31.3555i	−0.257076	+	1.12632i
$776$		0			0
$777$	−5.51580	−	2.65627i	−0.197878	−	0.0952932i
$778$		0			0
$779$	27.5969	−	34.6054i	0.988762	−	1.23987i
$780$		0			0
$781$	−12.4646	+	6.00265i	−0.446020	+	0.214792i
$782$		0			0
$783$	−20.5674	−	20.7968i	−0.735020	−	0.743217i
$784$		0			0
$785$	2.14554	−	1.03324i	0.0765774	−	0.0368778i
$786$		0			0
$787$	−13.1805	+	16.5279i	−0.469835	+	0.589155i	−0.959131	−	0.282963i	$-0.908683\pi$
$787$	−13.1805	+	16.5279i	−0.469835	+	0.589155i	0.489295	+	0.872118i	$0.337254\pi$
$788$		0			0
$789$	−14.8619	−	7.15710i	−0.529097	−	0.254799i
$790$		0			0
$791$	8.39491	−	36.7805i	0.298489	−	1.30776i
$792$		0			0
$793$	−2.43218	+	3.04986i	−0.0863693	+	0.108304i
$794$		0			0
$795$	11.0821			0.393041
$796$		0			0
$797$	−25.4835	−	12.2722i	−0.902672	−	0.434704i	−0.0758186	−	0.997122i	$-0.524157\pi$
$797$	−25.4835	−	12.2722i	−0.902672	−	0.434704i	−0.826853	+	0.562418i	$0.809871\pi$
$798$		0			0
$799$	1.44369	+	6.32524i	0.0510742	+	0.223771i
$800$		0			0
$801$	−1.15460	−	5.05862i	−0.0407957	−	0.178738i
$802$		0			0
$803$	10.4269	−	45.6833i	0.367958	−	1.61213i
$804$		0			0
$805$	−8.96445	−	11.2411i	−0.315955	−	0.396195i
$806$		0			0
$807$	−12.4140	+	5.97829i	−0.436995	+	0.210446i
$808$		0			0
$809$	9.21710	+	11.5579i	0.324056	+	0.406353i	0.916998	−	0.398892i	$-0.130605\pi$
$809$	9.21710	+	11.5579i	0.324056	+	0.406353i	−0.592942	+	0.805245i	$0.702034\pi$
$810$		0			0
$811$	−36.6892			−1.28833			−0.644166	−	0.764886i	$-0.722795\pi$
$811$	−36.6892			−1.28833			−0.644166	+	0.764886i	$0.722795\pi$
$812$		0			0
$813$	14.1952			0.497848
$814$		0			0
$815$	3.04503	+	3.81835i	0.106663	+	0.133751i
$816$		0			0
$817$	17.6313	−	8.49077i	0.616840	−	0.297055i
$818$		0			0
$819$	0.863424	+	1.08270i	0.0301705	+	0.0378326i
$820$		0			0
$821$	2.53522	−	11.1075i	0.0884800	−	0.387656i	−0.911226	−	0.411907i	$-0.864863\pi$
$821$	2.53522	−	11.1075i	0.0884800	−	0.387656i	0.999706	+	0.0242509i	$0.00772004\pi$
$822$		0			0
$823$	9.09064	+	39.8287i	0.316880	+	1.38834i	0.842992	+	0.537926i	$0.180792\pi$
$823$	9.09064	+	39.8287i	0.316880	+	1.38834i	−0.526112	+	0.850415i	$0.676351\pi$
$824$		0			0
$825$	4.80063	+	21.0329i	0.167136	+	0.732272i
$826$		0			0
$827$	−32.4791	−	15.6411i	−1.12941	−	0.543895i	−0.226622	−	0.973983i	$-0.572768\pi$
$827$	−32.4791	−	15.6411i	−1.12941	−	0.543895i	−0.902787	+	0.430088i	$0.858483\pi$
$828$		0			0
$829$	23.8361			0.827862			0.413931	−	0.910308i	$-0.364155\pi$
$829$	23.8361			0.827862			0.413931	+	0.910308i	$0.364155\pi$
$830$		0			0
$831$	19.7717	−	24.7929i	0.685871	−	0.860056i
$832$		0			0
$833$	−4.10634	+	17.9910i	−0.142276	+	0.623353i
$834$		0			0
$835$	7.91950	+	3.81383i	0.274065	+	0.131983i
$836$		0			0
$837$	−30.4669	+	38.2043i	−1.05309	+	1.32053i
$838$		0			0
$839$	−37.5826	+	18.0988i	−1.29750	+	0.624841i	−0.949827	−	0.312776i	$-0.898741\pi$
$839$	−37.5826	+	18.0988i	−1.29750	+	0.624841i	−0.347669	+	0.937617i	$0.613027\pi$
$840$		0			0
$841$	−22.8722	+	17.8287i	−0.788697	+	0.614782i
$842$		0			0
$843$	−22.4423	+	10.8076i	−0.772954	+	0.372235i
$844$		0			0
$845$	−6.21478	+	7.79309i	−0.213795	+	0.268090i
$846$		0			0
$847$	4.71383	+	2.27006i	0.161969	+	0.0780003i
$848$		0			0
$849$	−5.48309	+	24.0230i	−0.188179	+	0.824467i
$850$		0			0
$851$	6.71700	−	8.42286i	0.230256	−	0.288732i
$852$		0			0
$853$	46.4024			1.58879			0.794395	−	0.607402i	$-0.207788\pi$
$853$	46.4024			1.58879			0.794395	+	0.607402i	$0.207788\pi$
$854$		0			0
$855$	−1.79613	−	0.864971i	−0.0614264	−	0.0295814i
$856$		0			0
$857$	−4.49342	−	19.6870i	−0.153492	−	0.672494i	−0.991854	−	0.127379i	$-0.959343\pi$
$857$	−4.49342	−	19.6870i	−0.153492	−	0.672494i	0.838362	−	0.545114i	$-0.183514\pi$
$858$		0			0
$859$	2.39482	+	10.4924i	0.0817102	+	0.357996i	0.999210	−	0.0397403i	$-0.0126531\pi$
$859$	2.39482	+	10.4924i	0.0817102	+	0.357996i	−0.917500	+	0.397736i	$0.869796\pi$
$860$		0			0
$861$	6.20709	−	27.1950i	0.211537	−	0.926804i
$862$		0			0
$863$	−13.1334	−	16.4688i	−0.447066	−	0.560603i	0.506324	−	0.862343i	$-0.331004\pi$
$863$	−13.1334	−	16.4688i	−0.447066	−	0.560603i	−0.953390	+	0.301740i	$0.902433\pi$
$864$		0			0
$865$	10.5961	−	5.10280i	0.360277	−	0.173500i
$866$		0			0
$867$	−26.2688	−	32.9400i	−0.892134	−	1.11870i
$868$		0			0
$869$	52.0433			1.76545
$870$		0			0
$871$	−13.0328			−0.441598
$872$		0			0
$873$	0.900520	+	1.12922i	0.0304780	+	0.0382182i
$874$		0			0
$875$	−18.8477	+	9.07655i	−0.637167	+	0.306844i
$876$		0			0
$877$	11.8492	+	14.8584i	0.400119	+	0.501733i	0.940550	−	0.339655i	$-0.110310\pi$
$877$	11.8492	+	14.8584i	0.400119	+	0.501733i	−0.540431	+	0.841388i	$0.681739\pi$
$878$		0			0
$879$	10.7449	−	47.0765i	0.362417	−	1.58785i
$880$		0			0
$881$	−7.18429	−	31.4764i	−0.242045	−	1.06047i	−0.939152	−	0.343501i	$-0.888387\pi$
$881$	−7.18429	−	31.4764i	−0.242045	−	1.06047i	0.697108	−	0.716966i	$-0.254470\pi$
$882$		0			0
$883$	5.15306	+	22.5770i	0.173414	+	0.759778i	0.984576	+	0.174956i	$0.0559784\pi$
$883$	5.15306	+	22.5770i	0.173414	+	0.759778i	−0.811162	+	0.584822i	$0.801164\pi$
$884$		0			0
$885$	−5.19842	−	2.50343i	−0.174743	−	0.0841519i
$886$		0			0
$887$	46.3944			1.55777			0.778886	−	0.627165i	$-0.215785\pi$
$887$	46.3944			1.55777			0.778886	+	0.627165i	$0.215785\pi$
$888$		0			0
$889$	24.0789	−	30.1940i	0.807581	−	1.01267i
$890$		0			0
$891$	−6.52134	+	28.5719i	−0.218473	+	0.957193i
$892$		0			0
$893$	4.75333	+	2.28908i	0.159064	+	0.0766013i
$894$		0			0
$895$	9.14590	−	11.4686i	0.305714	−	0.383353i
$896$		0			0
$897$	18.7655	−	9.03697i	0.626561	−	0.301736i
$898$		0			0
$899$	34.0678	+	34.4477i	1.13622	+	1.14889i
$900$		0			0
$901$	−33.3524	+	16.0617i	−1.11113	+	0.535092i
$902$		0			0
$903$	7.68934	−	9.64212i	0.255885	−	0.320870i
$904$		0			0
$905$	−14.8255	−	7.13960i	−0.492818	−	0.237328i
$906$		0			0
$907$	−4.83478	+	21.1826i	−0.160536	+	0.703356i	0.829021	+	0.559217i	$0.188898\pi$
$907$	−4.83478	+	21.1826i	−0.160536	+	0.703356i	−0.989558	+	0.144138i	$0.953959\pi$
$908$		0			0
$909$	−0.0410966	+	0.0515335i	−0.00136309	+	0.00170926i
$910$		0			0
$911$	28.1482			0.932591			0.466295	−	0.884629i	$-0.345588\pi$
$911$	28.1482			0.932591			0.466295	+	0.884629i	$0.345588\pi$
$912$		0			0
$913$	−6.80908	−	3.27908i	−0.225348	−	0.108522i
$914$		0			0
$915$	−0.787511	−	3.45031i	−0.0260343	−	0.114064i
$916$		0			0
$917$	−2.23175	−	9.77796i	−0.0736990	−	0.322897i
$918$		0			0
$919$	10.5313	−	46.1407i	0.347396	−	1.52204i	−0.435671	−	0.900106i	$-0.643489\pi$
$919$	10.5313	−	46.1407i	0.347396	−	1.52204i	0.783067	−	0.621937i	$-0.213654\pi$
$920$		0			0
$921$	−6.01341	−	7.54057i	−0.198148	−	0.248470i
$922$		0			0
$923$	7.29942	−	3.51522i	0.240263	−	0.115705i
$924$		0			0
$925$	−4.07438	−	5.10912i	−0.133965	−	0.167987i
$926$		0			0
$927$	−3.49672			−0.114847
$928$		0			0
$929$	−14.6578			−0.480908			−0.240454	−	0.970661i	$-0.577296\pi$
$929$	−14.6578			−0.480908			−0.240454	+	0.970661i	$0.577296\pi$
$930$		0			0
$931$	9.35615	+	11.7322i	0.306636	+	0.384509i
$932$		0			0
$933$	33.9558	−	16.3522i	1.11166	−	0.535348i
$934$		0			0
$935$	17.9121	+	22.4610i	0.585788	+	0.734555i
$936$		0			0
$937$	−3.32974	+	14.5885i	−0.108778	+	0.476586i	0.890969	+	0.454065i	$0.150027\pi$
$937$	−3.32974	+	14.5885i	−0.108778	+	0.476586i	−0.999746	+	0.0225215i	$0.992831\pi$
$938$		0			0
$939$	7.49350	+	32.8312i	0.244541	+	1.07140i
$940$		0			0
$941$	−1.43120	−	6.27052i	−0.0466559	−	0.204413i	0.946228	−	0.323501i	$-0.104860\pi$
$941$	−1.43120	−	6.27052i	−0.0466559	−	0.204413i	−0.992884	+	0.119088i	$0.962003\pi$
$942$		0			0
$943$	44.2256	+	21.2979i	1.44018	+	0.693557i
$944$		0			0
$945$	−13.2507			−0.431044
$946$		0			0
$947$	−4.57843	+	5.74117i	−0.148779	+	0.186563i	−0.850636	−	0.525755i	$-0.823783\pi$
$947$	−4.57843	+	5.74117i	−0.148779	+	0.186563i	0.701857	+	0.712318i	$0.252354\pi$
$948$		0			0
$949$	−6.10611	+	26.7526i	−0.198213	+	0.868427i
$950$		0			0
$951$	10.4085	+	5.01247i	0.337519	+	0.162541i
$952$		0			0
$953$	9.94995	−	12.4768i	0.322311	−	0.404165i	−0.594108	−	0.804385i	$-0.702495\pi$
$953$	9.94995	−	12.4768i	0.322311	−	0.404165i	0.916419	+	0.400220i	$0.131066\pi$
$954$		0			0
$955$	17.0353	−	8.20376i	0.551249	−	0.265467i
$956$		0			0
$957$	30.6150	+	10.9035i	0.989641	+	0.352462i
$958$		0			0
$959$	7.02724	−	3.38414i	0.226921	−	0.109280i
$960$		0			0
$961$	31.1370	−	39.0445i	1.00442	−	1.25950i
$962$		0			0
$963$	1.14545	+	0.551617i	0.0369115	+	0.0177756i
$964$		0			0
$965$	−4.36320	+	19.1164i	−0.140456	+	0.615379i
$966$		0			0
$967$	−10.0093	+	12.5512i	−0.321876	+	0.403620i	−0.916274	−	0.400551i	$-0.868819\pi$
$967$	−10.0093	+	12.5512i	−0.321876	+	0.403620i	0.594399	+	0.804171i	$0.297390\pi$
$968$		0			0
$969$	−56.9157			−1.82839
$970$		0			0
$971$	−30.2279	−	14.5570i	−0.970059	−	0.467156i	−0.119384	−	0.992848i	$-0.538092\pi$
$971$	−30.2279	−	14.5570i	−0.970059	−	0.467156i	−0.850675	+	0.525692i	$0.823806\pi$
$972$		0			0
$973$	5.51657	+	24.1697i	0.176853	+	0.774844i
$974$		0			0
$975$	−2.81130	−	12.3171i	−0.0900336	−	0.394463i
$976$		0			0
$977$	1.77592	−	7.78082i	0.0568168	−	0.248931i	−0.938542	−	0.345165i	$-0.887823\pi$
$977$	1.77592	−	7.78082i	0.0568168	−	0.248931i	0.995359	+	0.0962348i	$0.0306800\pi$
$978$		0			0
$979$	37.9107	+	47.5385i	1.21163	+	1.51934i
$980$		0			0
$981$	−4.42616	+	2.13153i	−0.141316	+	0.0680544i
$982$		0			0
$983$	−33.8360	−	42.4290i	−1.07920	−	1.35327i	−0.931292	−	0.364274i	$-0.881317\pi$
$983$	−33.8360	−	42.4290i	−1.07920	−	1.35327i	−0.147909	−	0.989001i	$-0.547254\pi$
$984$		0			0
$985$	17.4771			0.556867
$986$		0			0
$987$	3.32486			0.105832
$988$		0			0
$989$	13.5312	+	16.9676i	0.430267	+	0.539538i
$990$		0			0
$991$	3.14619	−	1.51512i	0.0999420	−	0.0481295i	−0.383245	−	0.923647i	$-0.625193\pi$
$991$	3.14619	−	1.51512i	0.0999420	−	0.0481295i	0.483187	+	0.875517i	$0.339479\pi$
$992$		0			0
$993$	20.9396	+	26.2575i	0.664500	+	0.833256i
$994$		0			0
$995$	0.376906	−	1.65133i	0.0119487	−	0.0523508i
$996$		0			0
$997$	2.94547	+	12.9049i	0.0932838	+	0.408703i	0.999913	−	0.0132262i	$-0.00421016\pi$
$997$	2.94547	+	12.9049i	0.0932838	+	0.408703i	−0.906629	+	0.421929i	$0.861353\pi$
$998$		0			0
$999$	−2.20933	−	9.67971i	−0.0699001	−	0.306252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.2.u.h.49.1		12
4.3	odd	2		58.2.d.b.49.2	yes	12
12.11	even	2		522.2.k.h.397.2		12
29.16	even	7	inner	464.2.u.h.161.1		12
116.19	even	28		1682.2.b.i.1681.3		12
116.39	even	28		1682.2.b.i.1681.10		12
116.83	odd	14		1682.2.a.t.1.4		6
116.91	odd	14		1682.2.a.q.1.3		6
116.103	odd	14		58.2.d.b.45.2	✓	12
348.335	even	14		522.2.k.h.451.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.2.d.b.45.2	✓	12	116.103	odd	14
58.2.d.b.49.2	yes	12	4.3	odd	2
464.2.u.h.49.1		12	1.1	even	1	trivial
464.2.u.h.161.1		12	29.16	even	7	inner
522.2.k.h.397.2		12	12.11	even	2
522.2.k.h.451.2		12	348.335	even	14
1682.2.a.q.1.3		6	116.91	odd	14
1682.2.a.t.1.4		6	116.83	odd	14
1682.2.b.i.1681.3		12	116.19	even	28
1682.2.b.i.1681.10		12	116.39	even	28

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:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.u (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.02179 - 1.28129i) q^{3} +(-1.07557 + 0.517965i) q^{5} +(-1.27416 - 1.59774i) q^{7} +(0.0699247 - 0.306360i) q^{9} +O(q^{10})\)	\(q+(-1.02179 - 1.28129i) q^{3} +(-1.07557 + 0.517965i) q^{5} +(-1.27416 - 1.59774i) q^{7} +(0.0699247 - 0.306360i) q^{9} +(0.819415 + 3.59009i) q^{11} +(-0.479858 - 2.10239i) q^{13} +(1.76267 + 0.848856i) q^{15} -6.53517 q^{17} +(-3.31337 + 4.15484i) q^{19} +(-0.745242 + 3.26512i) q^{21} +(-5.30987 - 2.55710i) q^{23} +(-2.22890 + 2.79495i) q^{25} +(-4.89359 + 2.35663i) q^{27} +(1.75040 + 5.09275i) q^{29} +(8.10571 - 3.90350i) q^{31} +(3.76267 - 4.71824i) q^{33} +(2.19801 + 1.05851i) q^{35} +(-0.406764 + 1.78215i) q^{37} +(-2.20346 + 2.76305i) q^{39} -8.32895 q^{41} +(-3.31774 - 1.59774i) q^{43} +(0.0834753 + 0.365729i) q^{45} +(-0.220911 - 0.967876i) q^{47} +(0.628344 - 2.75296i) q^{49} +(6.67760 + 8.37344i) q^{51} +(5.10353 - 2.45773i) q^{53} +(-2.74087 - 3.43695i) q^{55} +8.70913 q^{57} -2.94918 q^{59} +(-1.12786 - 1.41429i) q^{61} +(-0.578579 + 0.278629i) q^{63} +(1.60508 + 2.01271i) q^{65} +(1.34482 - 5.89206i) q^{67} +(2.14921 + 9.41630i) q^{69} +(0.836003 + 3.66277i) q^{71} +(-11.4647 - 5.52110i) q^{73} +5.85860 q^{75} +(4.69197 - 5.88354i) q^{77} +(3.14487 - 13.7786i) q^{79} +(7.17039 + 3.45308i) q^{81} +(-1.27960 + 1.60457i) q^{83} +(7.02900 - 3.38499i) q^{85} +(4.73674 - 7.44650i) q^{87} +(14.8768 - 7.16429i) q^{89} +(-2.74767 + 3.44546i) q^{91} +(-13.2839 - 6.39717i) q^{93} +(1.41169 - 6.18501i) q^{95} +(-2.86572 + 3.59350i) q^{97} +1.15716 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - q^{7} - 11 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - q^7 - 11 * q^9	\( 12 q + 3 q^{3} - q^{7} - 11 q^{9} + 2 q^{11} + q^{13} + 9 q^{15} - 12 q^{17} + 6 q^{19} - 13 q^{21} - 35 q^{23} - 6 q^{25} - 39 q^{27} - 14 q^{29} + 8 q^{31} + 33 q^{33} + 18 q^{35} + 31 q^{37} + 22 q^{39} - 30 q^{41} + 5 q^{43} - 20 q^{45} + 33 q^{47} + 37 q^{49} + 15 q^{51} + 13 q^{53} - 36 q^{55} - 38 q^{57} - 38 q^{59} - 5 q^{61} - 4 q^{63} - 20 q^{65} + 7 q^{67} + 20 q^{69} - 3 q^{71} - 22 q^{73} + 2 q^{75} + 10 q^{77} + 60 q^{79} + 88 q^{81} + 39 q^{83} + 38 q^{85} - 9 q^{87} + 39 q^{89} - 61 q^{91} - 54 q^{93} - 55 q^{95} - 19 q^{97} + 8 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - q^7 - 11 * q^9 + 2 * q^11 + q^13 + 9 * q^15 - 12 * q^17 + 6 * q^19 - 13 * q^21 - 35 * q^23 - 6 * q^25 - 39 * q^27 - 14 * q^29 + 8 * q^31 + 33 * q^33 + 18 * q^35 + 31 * q^37 + 22 * q^39 - 30 * q^41 + 5 * q^43 - 20 * q^45 + 33 * q^47 + 37 * q^49 + 15 * q^51 + 13 * q^53 - 36 * q^55 - 38 * q^57 - 38 * q^59 - 5 * q^61 - 4 * q^63 - 20 * q^65 + 7 * q^67 + 20 * q^69 - 3 * q^71 - 22 * q^73 + 2 * q^75 + 10 * q^77 + 60 * q^79 + 88 * q^81 + 39 * q^83 + 38 * q^85 - 9 * q^87 + 39 * q^89 - 61 * q^91 - 54 * q^93 - 55 * q^95 - 19 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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