LMFDB - Embedded newform 1323.2.o.c.881.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(440,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("1323.440");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.o (of order $6$, degree $2$, 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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.3
Root			$-0.539982 + 0.935277i$ of defining polynomial
Character	$\chi$	$=$	1323.881
Dual form			1323.2.o.c.440.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.254498 + 0.146935i) q^{2} +(-0.956820 + 1.65726i) q^{4} +(-1.53014 + 2.65027i) q^{5} -1.15010i q^{8} +O(q^{10})$	\(q+(-0.254498 + 0.146935i) q^{2} +(-0.956820 + 1.65726i) q^{4} +(-1.53014 + 2.65027i) q^{5} -1.15010i q^{8} -0.899320i q^{10} +(-3.37445 + 1.94824i) q^{11} +(-2.02935 - 1.17164i) q^{13} +(-1.74465 - 3.02182i) q^{16} -3.36525 q^{17} -2.54838i q^{19} +(-2.92813 - 5.07167i) q^{20} +(0.572527 - 0.991647i) q^{22} +(2.58141 + 1.49038i) q^{23} +(-2.18263 - 3.78042i) q^{25} +0.688621 q^{26} +(3.67241 - 2.12027i) q^{29} +(-0.409400 - 0.236367i) q^{31} +(2.88005 + 1.66280i) q^{32} +(0.856452 - 0.494473i) q^{34} +7.78789 q^{37} +(0.374446 + 0.648559i) q^{38} +(3.04808 + 1.75981i) q^{40} +(-3.12737 + 5.41676i) q^{41} +(2.06191 + 3.57133i) q^{43} -7.45645i q^{44} -0.875953 q^{46} +(-2.02694 - 3.51076i) q^{47} +(1.11095 + 0.641408i) q^{50} +(3.88344 - 2.24211i) q^{52} -5.76703i q^{53} -11.9243i q^{55} +(-0.623082 + 1.07921i) q^{58} +(-2.34352 + 4.05910i) q^{59} +(-1.38580 + 0.800092i) q^{61} +0.138922 q^{62} +6.00131 q^{64} +(6.21035 - 3.58555i) q^{65} +(-0.787831 + 1.36456i) q^{67} +(3.21994 - 5.57711i) q^{68} -13.6132i q^{71} -0.988946i q^{73} +(-1.98201 + 1.14431i) q^{74} +(4.22333 + 2.43834i) q^{76} +(4.63908 + 8.03512i) q^{79} +10.6782 q^{80} -1.83808i q^{82} +(-5.49361 - 9.51520i) q^{83} +(5.14930 - 8.91884i) q^{85} +(-1.04950 - 0.605932i) q^{86} +(2.24067 + 3.88095i) q^{88} -4.31697 q^{89} +(-4.93989 + 2.85205i) q^{92} +(1.03171 + 0.595655i) q^{94} +(6.75390 + 3.89937i) q^{95} +(4.98797 - 2.87980i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4}+O(q^{10}) $ 10 * q + 4 * q^4	$ 10 q + 4 q^{4} - 12 q^{11} - 6 q^{13} - 6 q^{16} + 24 q^{17} - 3 q^{20} + 5 q^{22} - 15 q^{23} + 7 q^{25} - 6 q^{26} + 15 q^{29} - 9 q^{31} + 48 q^{32} - 3 q^{34} - 12 q^{37} - 18 q^{38} - 15 q^{40} - 9 q^{41} + 3 q^{43} + 26 q^{46} + 15 q^{47} - 3 q^{50} + 12 q^{52} + 8 q^{58} - 18 q^{59} + 12 q^{61} + 12 q^{62} + 6 q^{64} - 3 q^{65} - 10 q^{67} + 27 q^{68} - 30 q^{74} - 9 q^{76} + 20 q^{79} + 60 q^{80} - 15 q^{83} + 18 q^{85} + 54 q^{86} - 8 q^{88} - 48 q^{89} - 39 q^{92} - 3 q^{94} - 6 q^{97}+O(q^{100}) $ 10 * q + 4 * q^4 - 12 * q^11 - 6 * q^13 - 6 * q^16 + 24 * q^17 - 3 * q^20 + 5 * q^22 - 15 * q^23 + 7 * q^25 - 6 * q^26 + 15 * q^29 - 9 * q^31 + 48 * q^32 - 3 * q^34 - 12 * q^37 - 18 * q^38 - 15 * q^40 - 9 * q^41 + 3 * q^43 + 26 * q^46 + 15 * q^47 - 3 * q^50 + 12 * q^52 + 8 * q^58 - 18 * q^59 + 12 * q^61 + 12 * q^62 + 6 * q^64 - 3 * q^65 - 10 * q^67 + 27 * q^68 - 30 * q^74 - 9 * q^76 + 20 * q^79 + 60 * q^80 - 15 * q^83 + 18 * q^85 + 54 * q^86 - 8 * q^88 - 48 * q^89 - 39 * q^92 - 3 * q^94 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.254498	+	0.146935i	−0.179958	+	0.103899i	−0.587273	−	0.809389i	$-0.699798\pi$
$2$	−0.254498	+	0.146935i	−0.179958	+	0.103899i	0.407315	+	0.913288i	$0.366465\pi$
$3$		0			0
$3$		0			0
$4$	−0.956820	+	1.65726i	−0.478410	+	0.828631i
$5$	−1.53014	+	2.65027i	−0.684297	+	1.18524i	0.289360	+	0.957220i	$0.406558\pi$
$5$	−1.53014	+	2.65027i	−0.684297	+	1.18524i	−0.973657	+	0.228017i	$0.926776\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.15010i		−	0.406622i
$9$		0			0
$10$		−	0.899320i		−	0.284390i
$11$	−3.37445	+	1.94824i	−1.01743	+	0.587416i	−0.913360	−	0.407154i	$-0.866521\pi$
$11$	−3.37445	+	1.94824i	−1.01743	+	0.587416i	−0.104074	+	0.994570i	$0.533188\pi$
$12$		0			0
$13$	−2.02935	−	1.17164i	−0.562840	−	0.324956i	0.191445	−	0.981503i	$-0.438683\pi$
$13$	−2.02935	−	1.17164i	−0.562840	−	0.324956i	−0.754285	+	0.656548i	$0.772016\pi$
$14$		0			0
$15$		0			0
$16$	−1.74465	−	3.02182i	−0.436163	−	0.755456i
$17$	−3.36525			−0.816194			−0.408097	−	0.912939i	$-0.633808\pi$
$17$	−3.36525			−0.816194			−0.408097	+	0.912939i	$0.633808\pi$
$18$		0			0
$19$		−	2.54838i		−	0.584639i	−0.956321	−	0.292319i	$-0.905573\pi$
$19$		−	2.54838i		−	0.584639i	0.956321	−	0.292319i	$-0.0944270\pi$
$20$	−2.92813	−	5.07167i	−0.654750	−	1.13406i
$21$		0			0
$22$	0.572527	−	0.991647i	0.122063	−	0.211420i
$23$	2.58141	+	1.49038i	0.538261	+	0.310765i	0.744374	−	0.667763i	$-0.232748\pi$
$23$	2.58141	+	1.49038i	0.538261	+	0.310765i	−0.206113	+	0.978528i	$0.566081\pi$
$24$		0			0
$25$	−2.18263	−	3.78042i	−0.436525	−	0.756084i
$26$	0.688621			0.135050
$27$		0			0
$28$		0			0
$29$	3.67241	−	2.12027i	0.681949	−	0.393724i	−0.118640	−	0.992937i	$-0.537853\pi$
$29$	3.67241	−	2.12027i	0.681949	−	0.393724i	0.800589	+	0.599214i	$0.204520\pi$
$30$		0			0
$31$	−0.409400	−	0.236367i	−0.0735305	−	0.0424528i	0.462784	−	0.886471i	$-0.346851\pi$
$31$	−0.409400	−	0.236367i	−0.0735305	−	0.0424528i	−0.536314	+	0.844018i	$0.680184\pi$
$32$	2.88005	+	1.66280i	0.509126	+	0.293944i
$33$		0			0
$34$	0.856452	−	0.494473i	0.146880	−	0.0848014i
$35$		0			0
$36$		0			0
$37$	7.78789			1.28032			0.640161	−	0.768241i	$-0.278868\pi$
$37$	7.78789			1.28032			0.640161	+	0.768241i	$0.278868\pi$
$38$	0.374446	+	0.648559i	0.0607431	+	0.105210i
$39$		0			0
$40$	3.04808	+	1.75981i	0.481943	+	0.278250i
$41$	−3.12737	+	5.41676i	−0.488413	+	0.845956i	−0.999911	−	0.0133282i	$-0.995757\pi$
$41$	−3.12737	+	5.41676i	−0.488413	+	0.845956i	0.511498	+	0.859284i	$0.329091\pi$
$42$		0			0
$43$	2.06191	+	3.57133i	0.314438	+	0.544623i	0.979318	−	0.202328i	$-0.0648506\pi$
$43$	2.06191	+	3.57133i	0.314438	+	0.544623i	−0.664880	+	0.746950i	$0.731517\pi$
$44$		−	7.45645i		−	1.12410i
$45$		0			0
$46$	−0.875953			−0.129152
$47$	−2.02694	−	3.51076i	−0.295659	−	0.512097i	0.679479	−	0.733695i	$-0.262206\pi$
$47$	−2.02694	−	3.51076i	−0.295659	−	0.512097i	−0.975138	+	0.221598i	$0.928873\pi$
$48$		0			0
$49$		0			0
$50$	1.11095	+	0.641408i	0.157112	+	0.0907087i
$51$		0			0
$52$	3.88344	−	2.24211i	0.538537	−	0.310924i
$53$		−	5.76703i		−	0.792162i	−0.918216	−	0.396081i	$-0.870370\pi$
$53$		−	5.76703i		−	0.792162i	0.918216	−	0.396081i	$-0.129630\pi$
$54$		0			0
$55$		−	11.9243i		−	1.60787i
$56$		0			0
$57$		0			0
$58$	−0.623082	+	1.07921i	−0.0818146	+	0.141707i
$59$	−2.34352	+	4.05910i	−0.305101	+	0.528450i	−0.977284	−	0.211935i	$-0.932023\pi$
$59$	−2.34352	+	4.05910i	−0.305101	+	0.528450i	0.672183	+	0.740385i	$0.265357\pi$
$60$		0			0
$61$	−1.38580	+	0.800092i	−0.177433	+	0.102441i	−0.586086	−	0.810249i	$-0.699332\pi$
$61$	−1.38580	+	0.800092i	−0.177433	+	0.102441i	0.408653	+	0.912690i	$0.365999\pi$
$62$	0.138922			0.0176432
$63$		0			0
$64$	6.00131			0.750164
$65$	6.21035	−	3.58555i	0.770299	−	0.444733i
$66$		0			0
$67$	−0.787831	+	1.36456i	−0.0962489	+	0.166708i	−0.910129	−	0.414325i	$-0.864018\pi$
$67$	−0.787831	+	1.36456i	−0.0962489	+	0.166708i	0.813880	+	0.581033i	$0.197351\pi$
$68$	3.21994	−	5.57711i	0.390476	−	0.676324i
$69$		0			0
$70$		0			0
$71$		−	13.6132i		−	1.61559i	−0.589462	−	0.807796i	$-0.700660\pi$
$71$		−	13.6132i		−	1.61559i	0.589462	−	0.807796i	$-0.299340\pi$
$72$		0			0
$73$		−	0.988946i		−	0.115747i	−0.998324	−	0.0578737i	$-0.981568\pi$
$73$		−	0.988946i		−	0.115747i	0.998324	−	0.0578737i	$-0.0184321\pi$
$74$	−1.98201	+	1.14431i	−0.230404	+	0.133024i
$75$		0			0
$76$	4.22333	+	2.43834i	0.484450	+	0.279697i
$77$		0			0
$78$		0			0
$79$	4.63908	+	8.03512i	0.521937	+	0.904021i	0.999674	+	0.0255186i	$0.00812370\pi$
$79$	4.63908	+	8.03512i	0.521937	+	0.904021i	−0.477737	+	0.878503i	$0.658543\pi$
$80$	10.6782			1.19386
$81$		0			0
$82$		−	1.83808i		−	0.202982i
$83$	−5.49361	−	9.51520i	−0.603002	−	1.04443i	−0.992364	−	0.123345i	$-0.960638\pi$
$83$	−5.49361	−	9.51520i	−0.603002	−	1.04443i	0.389362	−	0.921085i	$-0.372695\pi$
$84$		0			0
$85$	5.14930	−	8.91884i	0.558519	−	0.967384i
$86$	−1.04950	−	0.605932i	−0.113171	−	0.0653393i
$87$		0			0
$88$	2.24067	+	3.88095i	0.238856	+	0.413710i
$89$	−4.31697			−0.457598			−0.228799	−	0.973474i	$-0.573480\pi$
$89$	−4.31697			−0.457598			−0.228799	+	0.973474i	$0.573480\pi$
$90$		0			0
$91$		0			0
$92$	−4.93989	+	2.85205i	−0.515019	+	0.297346i
$93$		0			0
$94$	1.03171	+	0.595655i	0.106412	+	0.0614371i
$95$	6.75390	+	3.89937i	0.692936	+	0.400067i
$96$		0			0
$97$	4.98797	−	2.87980i	0.506451	−	0.292400i	−0.224923	−	0.974377i	$-0.572213\pi$
$97$	4.98797	−	2.87980i	0.506451	−	0.292400i	0.731374	+	0.681977i	$0.238880\pi$
$98$		0			0
$99$		0			0
$100$	8.35353			0.835353
$101$	−8.57900	−	14.8593i	−0.853642	−	1.47855i	−0.877899	−	0.478846i	$-0.841055\pi$
$101$	−8.57900	−	14.8593i	−0.853642	−	1.47855i	0.0242566	−	0.999706i	$-0.492278\pi$
$102$		0			0
$103$	−8.50422	−	4.90992i	−0.837946	−	0.483788i	0.0186195	−	0.999827i	$-0.494073\pi$
$103$	−8.50422	−	4.90992i	−0.837946	−	0.483788i	−0.856566	+	0.516038i	$0.827406\pi$
$104$	−1.34751	+	2.33395i	−0.132134	+	0.228863i
$105$		0			0
$106$	0.847377	+	1.46770i	0.0823045	+	0.142556i
$107$		−	3.46989i		−	0.335447i	−0.985834	−	0.167723i	$-0.946358\pi$
$107$		−	3.46989i		−	0.335447i	0.985834	−	0.167723i	$-0.0536416\pi$
$108$		0			0
$109$	−1.22213			−0.117059			−0.0585295	−	0.998286i	$-0.518641\pi$
$109$	−1.22213			−0.117059			−0.0585295	+	0.998286i	$0.518641\pi$
$110$	1.75209	+	3.03471i	0.167055	+	0.289348i
$111$		0			0
$112$		0			0
$113$	1.87681	+	1.08358i	0.176555	+	0.101934i	0.585673	−	0.810547i	$-0.300830\pi$
$113$	1.87681	+	1.08358i	0.176555	+	0.101934i	−0.409118	+	0.912482i	$0.634164\pi$
$114$		0			0
$115$	−7.89981	+	4.56096i	−0.736661	+	0.425311i
$116$			8.11486i			0.753445i
$117$		0			0
$118$		−	1.37738i		−	0.126798i
$119$		0			0
$120$		0			0
$121$	2.09126	−	3.62216i	0.190114	−	0.329287i
$122$	0.235123	−	0.407244i	0.0212870	−	0.0368702i
$123$		0			0
$124$	0.783445	−	0.452322i	0.0703555	−	0.0406198i
$125$	−1.94249			−0.173742
$126$		0			0
$127$	2.74889			0.243925			0.121962	−	0.992535i	$-0.461081\pi$
$127$	2.74889			0.243925			0.121962	+	0.992535i	$0.461081\pi$
$128$	−7.28743	+	4.20740i	−0.644124	+	0.371885i
$129$		0			0
$130$	−1.05368	+	1.82503i	−0.0924141	+	0.160066i
$131$	3.73911	−	6.47632i	0.326687	−	0.565839i	−0.655165	−	0.755486i	$-0.727401\pi$
$131$	3.73911	−	6.47632i	0.326687	−	0.565839i	0.981852	+	0.189647i	$0.0607343\pi$
$132$		0			0
$133$		0			0
$134$		−	0.463039i		−	0.0400005i
$135$		0			0
$136$			3.87038i			0.331882i
$137$	−10.5731	+	6.10439i	−0.903321	+	0.521533i	−0.878276	−	0.478153i	$-0.841306\pi$
$137$	−10.5731	+	6.10439i	−0.903321	+	0.521533i	−0.0250451	+	0.999686i	$0.507973\pi$
$138$		0			0
$139$	−11.5501	−	6.66842i	−0.979663	−	0.565608i	−0.0774943	−	0.996993i	$-0.524692\pi$
$139$	−11.5501	−	6.66842i	−0.979663	−	0.565608i	−0.902168	+	0.431384i	$0.858025\pi$
$140$		0			0
$141$		0			0
$142$	2.00026	+	3.46454i	0.167858	+	0.290738i
$143$	9.13057			0.763536
$144$		0			0
$145$			12.9772i			1.07770i
$146$	0.145310	+	0.251685i	0.0120260	+	0.0208296i
$147$		0			0
$148$	−7.45161	+	12.9066i	−0.612519	+	1.06091i
$149$	−7.33827	−	4.23675i	−0.601174	−	0.347088i	0.168329	−	0.985731i	$-0.446163\pi$
$149$	−7.33827	−	4.23675i	−0.601174	−	0.347088i	−0.769503	+	0.638643i	$0.779496\pi$
$150$		0			0
$151$	1.67827	+	2.90685i	0.136576	+	0.236556i	0.926198	−	0.377037i	$-0.123057\pi$
$151$	1.67827	+	2.90685i	0.136576	+	0.236556i	−0.789623	+	0.613593i	$0.789724\pi$
$152$	−2.93089			−0.237727
$153$		0			0
$154$		0			0
$155$	1.25288	−	0.723348i	0.100633	−	0.0581007i
$156$		0			0
$157$	−14.4700	−	8.35426i	−1.15483	−	0.666743i	−0.204772	−	0.978810i	$-0.565645\pi$
$157$	−14.4700	−	8.35426i	−1.15483	−	0.666743i	−0.950060	+	0.312067i	$0.898979\pi$
$158$	−2.36128	−	1.36328i	−0.187853	−	0.108457i
$159$		0			0
$160$	−8.81374	+	5.08862i	−0.696787	+	0.402290i
$161$		0			0
$162$		0			0
$163$	−25.3324			−1.98419			−0.992094	−	0.125498i	$-0.959947\pi$
$163$	−25.3324			−1.98419			−0.992094	+	0.125498i	$0.959947\pi$
$164$	−5.98466	−	10.3657i	−0.467324	−	0.809428i
$165$		0			0
$166$	2.79623	+	1.61440i	0.217029	+	0.125302i
$167$	−0.875828	+	1.51698i	−0.0677736	+	0.117387i	−0.897921	−	0.440157i	$-0.854923\pi$
$167$	−0.875828	+	1.51698i	−0.0677736	+	0.117387i	0.830147	+	0.557544i	$0.188256\pi$
$168$		0			0
$169$	−3.75450	−	6.50298i	−0.288808	−	0.500229i
$170$			3.02644i			0.232117i
$171$		0			0
$172$	−7.89150			−0.601721
$173$	11.9633	+	20.7210i	0.909551	+	1.57539i	0.814689	+	0.579898i	$0.196908\pi$
$173$	11.9633	+	20.7210i	0.909551	+	1.57539i	0.0948622	+	0.995490i	$0.469759\pi$
$174$		0			0
$175$		0			0
$176$	11.7745	+	6.79799i	0.887533	+	0.512418i
$177$		0			0
$178$	1.09866	−	0.634313i	0.0823482	−	0.0475438i
$179$		−	25.3869i		−	1.89751i	−0.316013	−	0.948755i	$-0.602344\pi$
$179$		−	25.3869i		−	1.89751i	0.316013	−	0.948755i	$-0.397656\pi$
$180$		0			0
$181$			22.4032i			1.66522i	0.553859	+	0.832610i	$0.313155\pi$
$181$			22.4032i			1.66522i	−0.553859	+	0.832610i	$0.686845\pi$
$182$		0			0
$183$		0			0
$184$	1.71408	−	2.96888i	0.126364	−	0.218869i
$185$	−11.9165	+	20.6400i	−0.876121	+	1.51749i
$186$		0			0
$187$	11.3559	−	6.55631i	0.830423	−	0.479445i
$188$	7.75766			0.565786
$189$		0			0
$190$	−2.29181			−0.166265
$191$	−3.71434	+	2.14447i	−0.268760	+	0.155169i	−0.628324	−	0.777952i	$-0.716259\pi$
$191$	−3.71434	+	2.14447i	−0.268760	+	0.155169i	0.359564	+	0.933120i	$0.382925\pi$
$192$		0			0
$193$	11.6725	−	20.2173i	0.840203	−	1.45527i	−0.0495201	−	0.998773i	$-0.515769\pi$
$193$	11.6725	−	20.2173i	0.840203	−	1.45527i	0.889723	−	0.456501i	$-0.150897\pi$
$194$	−0.846286	+	1.46581i	−0.0607598	+	0.105239i
$195$		0			0
$196$		0			0
$197$			18.7811i			1.33809i	0.743220	+	0.669047i	$0.233298\pi$
$197$			18.7811i			1.33809i	−0.743220	+	0.669047i	$0.766702\pi$
$198$		0			0
$199$		−	4.53713i		−	0.321629i	−0.986985	−	0.160814i	$-0.948588\pi$
$199$		−	4.53713i		−	0.321629i	0.986985	−	0.160814i	$-0.0514120\pi$
$200$	−4.34786	+	2.51024i	−0.307440	+	0.177501i
$201$		0			0
$202$	4.36668	+	2.52111i	0.307239	+	0.177384i
$203$		0			0
$204$		0			0
$205$	−9.57060	−	16.5768i	−0.668439	−	1.15777i
$206$	2.88575			0.201060
$207$		0			0
$208$			8.17644i			0.566934i
$209$	4.96485	+	8.59937i	0.343426	+	0.594831i
$210$		0			0
$211$	−3.44148	+	5.96082i	−0.236921	+	0.410360i	−0.959829	−	0.280584i	$-0.909472\pi$
$211$	−3.44148	+	5.96082i	−0.236921	+	0.410360i	0.722908	+	0.690944i	$0.242805\pi$
$212$	9.55747	+	5.51801i	0.656410	+	0.378978i
$213$		0			0
$214$	0.509847	+	0.883081i	0.0348524	+	0.0603662i
$215$	−12.6200			−0.860676
$216$		0			0
$217$		0			0
$218$	0.311031	−	0.179574i	0.0210657	−	0.0121623i
$219$		0			0
$220$	19.7616	+	11.4094i	1.33233	+	0.769220i
$221$	6.82927	+	3.94288i	0.459387	+	0.265227i
$222$		0			0
$223$	5.57176	−	3.21686i	0.373113	−	0.215417i	−0.301705	−	0.953401i	$-0.597556\pi$
$223$	5.57176	−	3.21686i	0.373113	−	0.215417i	0.674818	+	0.737985i	$0.264222\pi$
$224$		0			0
$225$		0			0
$226$	−0.636860			−0.0423633
$227$	9.86983	+	17.0951i	0.655084	+	1.13464i	0.981873	+	0.189541i	$0.0607000\pi$
$227$	9.86983	+	17.0951i	0.655084	+	1.13464i	−0.326789	+	0.945097i	$0.605967\pi$
$228$		0			0
$229$	−9.44564	−	5.45344i	−0.624185	−	0.360373i	0.154311	−	0.988022i	$-0.450684\pi$
$229$	−9.44564	−	5.45344i	−0.624185	−	0.360373i	−0.778497	+	0.627649i	$0.784017\pi$
$230$	1.34033	−	2.32151i	0.0883785	−	0.153076i
$231$		0			0
$232$	−2.43852	−	4.22364i	−0.160097	−	0.277295i
$233$			20.7782i			1.36122i	0.732645	+	0.680611i	$0.238286\pi$
$233$			20.7782i			1.36122i	−0.732645	+	0.680611i	$0.761714\pi$
$234$		0			0
$235$	12.4060			0.809275
$236$	−4.48466	−	7.76766i	−0.291927	−	0.505632i
$237$		0			0
$238$		0			0
$239$	−23.6739	−	13.6681i	−1.53134	−	0.884119i	−0.999300	−	0.0373991i	$-0.988093\pi$
$239$	−23.6739	−	13.6681i	−1.53134	−	0.884119i	−0.532039	−	0.846720i	$-0.678574\pi$
$240$		0			0
$241$	18.4688	−	10.6630i	1.18968	−	0.686861i	0.231445	−	0.972848i	$-0.425655\pi$
$241$	18.4688	−	10.6630i	1.18968	−	0.686861i	0.958234	+	0.285987i	$0.0923213\pi$
$242$			1.22911i			0.0790103i
$243$		0			0
$244$		−	3.06218i		−	0.196036i
$245$		0			0
$246$		0			0
$247$	−2.98580	+	5.17155i	−0.189982	+	0.329058i
$248$	−0.271846	+	0.470851i	−0.0172622	+	0.0298991i
$249$		0			0
$250$	0.494361	−	0.285419i	0.0312661	−	0.0180515i
$251$	26.7381			1.68769			0.843847	−	0.536584i	$-0.180286\pi$
$251$	26.7381			1.68769			0.843847	+	0.536584i	$0.180286\pi$
$252$		0			0
$253$	−11.6144			−0.730193
$254$	−0.699589	+	0.403908i	−0.0438961	+	0.0253434i
$255$		0			0
$256$	−4.76489	+	8.25303i	−0.297805	+	0.515814i
$257$	1.52640	−	2.64380i	0.0952140	−	0.164916i	−0.814484	−	0.580186i	$-0.802980\pi$
$257$	1.52640	−	2.64380i	0.0952140	−	0.164916i	0.909698	+	0.415271i	$0.136313\pi$
$258$		0			0
$259$		0			0
$260$			13.7229i			0.851058i
$261$		0			0
$262$			2.19762i			0.135769i
$263$	14.0447	−	8.10868i	0.866030	−	0.500003i	3.24009e−6	−	1.00000i	$-0.499999\pi$
$263$	14.0447	−	8.10868i	0.866030	−	0.500003i	0.866027	+	0.499997i	$0.166666\pi$
$264$		0			0
$265$	15.2842	+	8.82433i	0.938901	+	0.542074i
$266$		0			0
$267$		0			0
$268$	−1.50763	−	2.61128i	−0.0920929	−	0.159510i
$269$	0.606511			0.0369796			0.0184898	−	0.999829i	$-0.494114\pi$
$269$	0.606511			0.0369796			0.0184898	+	0.999829i	$0.494114\pi$
$270$		0			0
$271$		−	22.9726i		−	1.39548i	−0.716349	−	0.697742i	$-0.754188\pi$
$271$		−	22.9726i		−	1.39548i	0.716349	−	0.697742i	$-0.245812\pi$
$272$	5.87120	+	10.1692i	0.355994	+	0.616599i
$273$		0			0
$274$	1.79389	−	3.10711i	0.108373	−	0.187708i
$275$	14.7303	+	8.50455i	0.888271	+	0.512844i
$276$		0			0
$277$	−6.64173	−	11.5038i	−0.399063	−	0.691197i	0.594548	−	0.804060i	$-0.297331\pi$
$277$	−6.64173	−	11.5038i	−0.399063	−	0.691197i	−0.993611	+	0.112863i	$0.963998\pi$
$278$	3.91929			0.235064
$279$		0			0
$280$		0			0
$281$	−5.68377	+	3.28153i	−0.339065	+	0.195759i	−0.659859	−	0.751390i	$-0.729384\pi$
$281$	−5.68377	+	3.28153i	−0.339065	+	0.195759i	0.320793	+	0.947149i	$0.396050\pi$
$282$		0			0
$283$	2.57413	+	1.48617i	0.153016	+	0.0883437i	0.574553	−	0.818467i	$-0.305176\pi$
$283$	2.57413	+	1.48617i	0.153016	+	0.0883437i	−0.421537	+	0.906811i	$0.638509\pi$
$284$	22.5607	+	13.0254i	1.33873	+	0.772916i
$285$		0			0
$286$	−2.32371	+	1.34160i	−0.137404	+	0.0793303i
$287$		0			0
$288$		0			0
$289$	−5.67506			−0.333827
$290$	−1.90680	−	3.30267i	−0.111971	−	0.193940i
$291$		0			0
$292$	1.63894	+	0.946243i	0.0959118	+	0.0553747i
$293$	−3.03087	+	5.24962i	−0.177065	+	0.306686i	−0.940874	−	0.338756i	$-0.889994\pi$
$293$	−3.03087	+	5.24962i	−0.177065	+	0.306686i	0.763809	+	0.645443i	$0.223327\pi$
$294$		0			0
$295$	−7.17181	−	12.4219i	−0.417559	−	0.723234i
$296$		−	8.95685i		−	0.520606i
$297$		0			0
$298$	2.49010			0.144248
$299$	−3.49238	−	6.04899i	−0.201970	−	0.349822i
$300$		0			0
$301$		0			0
$302$	−0.854235	−	0.493193i	−0.0491557	−	0.0283801i
$303$		0			0
$304$	−7.70076	+	4.44604i	−0.441669	+	0.254998i
$305$		−	4.89700i		−	0.280401i
$306$		0			0
$307$			21.6030i			1.23295i	0.787375	+	0.616474i	$0.211439\pi$
$307$			21.6030i			1.23295i	−0.787375	+	0.616474i	$0.788561\pi$
$308$		0			0
$309$		0			0
$310$	−0.212570	+	0.368182i	−0.0120732	+	0.0209113i
$311$	5.51171	−	9.54656i	0.312540	−	0.541336i	−0.666371	−	0.745620i	$-0.732153\pi$
$311$	5.51171	−	9.54656i	0.312540	−	0.541336i	0.978912	+	0.204284i	$0.0654868\pi$
$312$		0			0
$313$	−11.7383	+	6.77710i	−0.663487	+	0.383064i	−0.793604	−	0.608434i	$-0.791798\pi$
$313$	−11.7383	+	6.77710i	−0.663487	+	0.383064i	0.130117	+	0.991499i	$0.458465\pi$
$314$	4.91012			0.277094
$315$		0			0
$316$	−17.7551			−0.998800
$317$	−9.65977	+	5.57707i	−0.542547	+	0.313240i	−0.746111	−	0.665822i	$-0.768081\pi$
$317$	−9.65977	+	5.57707i	−0.542547	+	0.313240i	0.203564	+	0.979062i	$0.434748\pi$
$318$		0			0
$319$	−8.26156	+	14.3094i	−0.462559	+	0.801175i
$320$	−9.18282	+	15.9051i	−0.513335	+	0.889123i
$321$		0			0
$322$		0			0
$323$			8.57595i			0.477179i
$324$		0			0
$325$			10.2291i			0.567406i
$326$	6.44706	−	3.72221i	0.357070	−	0.206154i
$327$		0			0
$328$	6.22982	+	3.59679i	0.343984	+	0.198599i
$329$		0			0
$330$		0			0
$331$	9.51009	+	16.4720i	0.522722	+	0.905380i	0.999650	+	0.0264385i	$0.00841661\pi$
$331$	9.51009	+	16.4720i	0.522722	+	0.905380i	−0.476929	+	0.878942i	$0.658250\pi$
$332$	21.0256			1.15393
$333$		0			0
$334$		−	0.514758i		−	0.0281663i
$335$	−2.41098	−	4.17593i	−0.131726	−	0.228156i
$336$		0			0
$337$	3.32635	−	5.76140i	0.181198	−	0.313843i	−0.761091	−	0.648645i	$-0.775336\pi$
$337$	3.32635	−	5.76140i	0.181198	−	0.313843i	0.942289	+	0.334802i	$0.108669\pi$
$338$	1.91103	+	1.10333i	0.103946	+	0.0600134i
$339$		0			0
$340$	9.85390	+	17.0675i	0.534403	+	0.925613i
$341$	1.84200			0.0997499
$342$		0			0
$343$		0			0
$344$	4.10738	−	2.37140i	0.221455	−	0.127857i
$345$		0			0
$346$	−6.08927	−	3.51564i	−0.327361	−	0.189002i
$347$	−23.0796	−	13.3250i	−1.23898	−	0.715325i	−0.270094	−	0.962834i	$-0.587055\pi$
$347$	−23.0796	−	13.3250i	−1.23898	−	0.715325i	−0.968886	+	0.247509i	$0.920388\pi$
$348$		0			0
$349$	−20.5135	+	11.8435i	−1.09806	+	0.633966i	−0.935711	−	0.352768i	$-0.885241\pi$
$349$	−20.5135	+	11.8435i	−1.09806	+	0.633966i	−0.162350	+	0.986733i	$0.551907\pi$
$350$		0			0
$351$		0			0
$352$	−12.9581			−0.690670
$353$	−2.29422	−	3.97371i	−0.122109	−	0.211499i	0.798490	−	0.602008i	$-0.205632\pi$
$353$	−2.29422	−	3.97371i	−0.122109	−	0.211499i	−0.920599	+	0.390509i	$0.872299\pi$
$354$		0			0
$355$	36.0788	+	20.8301i	1.91486	+	1.10555i
$356$	4.13057	−	7.15435i	0.218920	−	0.379180i
$357$		0			0
$358$	3.73022	+	6.46094i	0.197148	+	0.341471i
$359$		−	6.13079i		−	0.323571i	−0.986826	−	0.161785i	$-0.948275\pi$
$359$		−	6.13079i		−	0.323571i	0.986826	−	0.161785i	$-0.0517252\pi$
$360$		0			0
$361$	12.5058			0.658197
$362$	−3.29182	−	5.70159i	−0.173014	−	0.299669i
$363$		0			0
$364$		0			0
$365$	2.62097	+	1.51322i	0.137188	+	0.0792056i
$366$		0			0
$367$	−22.8860	+	13.2132i	−1.19464	+	0.689725i	−0.959355	−	0.282202i	$-0.908935\pi$
$367$	−22.8860	+	13.2132i	−1.19464	+	0.689725i	−0.235283	+	0.971927i	$0.575602\pi$
$368$		−	10.4008i		−	0.542177i
$369$		0			0
$370$		−	7.00381i		−	0.364111i
$371$		0			0
$372$		0			0
$373$	−10.0581	+	17.4211i	−0.520789	+	0.902033i	0.478919	+	0.877859i	$0.341029\pi$
$373$	−10.0581	+	17.4211i	−0.520789	+	0.902033i	−0.999708	+	0.0241735i	$0.992305\pi$
$374$	−1.92670	+	3.33714i	−0.0996273	+	0.172560i
$375$		0			0
$376$	−4.03772	+	2.33118i	−0.208230	+	0.120221i
$377$	−9.93679			−0.511771
$378$		0			0
$379$	−17.4561			−0.896660			−0.448330	−	0.893868i	$-0.647981\pi$
$379$	−17.4561			−0.896660			−0.448330	+	0.893868i	$0.647981\pi$
$380$	−12.9245	+	7.46199i	−0.663015	+	0.382792i
$381$		0			0
$382$	0.630195	−	1.09153i	0.0322436	−	0.0558476i
$383$	14.0317	−	24.3036i	0.716985	−	1.24185i	−0.245204	−	0.969471i	$-0.578855\pi$
$383$	14.0317	−	24.3036i	0.716985	−	1.24185i	0.962189	−	0.272383i	$-0.0878117\pi$
$384$		0			0
$385$		0			0
$386$			6.86037i			0.349183i
$387$		0			0
$388$			11.0218i			0.559548i
$389$	−29.6520	+	17.1196i	−1.50342	+	0.867999i	−0.503426	+	0.864038i	$0.667928\pi$
$389$	−29.6520	+	17.1196i	−1.50342	+	0.867999i	−0.999992	+	0.00396103i	$0.998739\pi$
$390$		0			0
$391$	−8.68710	−	5.01550i	−0.439325	−	0.253645i
$392$		0			0
$393$		0			0
$394$	−2.75959	−	4.77975i	−0.139026	−	0.240800i
$395$	−28.3937			−1.42864
$396$		0			0
$397$			13.0396i			0.654440i	0.944948	+	0.327220i	$0.106112\pi$
$397$			13.0396i			0.654440i	−0.944948	+	0.327220i	$0.893888\pi$
$398$	0.666662	+	1.15469i	0.0334167	+	0.0578795i
$399$		0			0
$400$	−7.61585	+	13.1910i	−0.380792	+	0.659552i
$401$	−15.8943	−	9.17659i	−0.793725	−	0.458257i	0.0475475	−	0.998869i	$-0.484859\pi$
$401$	−15.8943	−	9.17659i	−0.793725	−	0.458257i	−0.841272	+	0.540612i	$0.818193\pi$
$402$		0			0
$403$	0.553877	+	0.959344i	0.0275906	+	0.0477883i
$404$	32.8342			1.63356
$405$		0			0
$406$		0			0
$407$	−26.2798	+	15.1727i	−1.30264	+	0.752081i
$408$		0			0
$409$	−5.60133	−	3.23393i	−0.276968	−	0.159907i	0.355082	−	0.934835i	$-0.384453\pi$
$409$	−5.60133	−	3.23393i	−0.276968	−	0.159907i	−0.632050	+	0.774928i	$0.717786\pi$
$410$	4.87140	+	2.81251i	0.240581	+	0.138900i
$411$		0			0
$412$	16.2740	−	9.39581i	0.801764	−	0.462899i
$413$		0			0
$414$		0			0
$415$	33.6238			1.65053
$416$	−3.89642	−	6.74880i	−0.191038	−	0.330887i
$417$		0			0
$418$	−2.52709	−	1.45902i	−0.123604	−	0.0713629i
$419$	−7.11542	+	12.3243i	−0.347611	+	0.602080i	−0.985825	−	0.167779i	$-0.946340\pi$
$419$	−7.11542	+	12.3243i	−0.347611	+	0.602080i	0.638214	+	0.769859i	$0.279674\pi$
$420$		0			0
$421$	15.1718	+	26.2784i	0.739429	+	1.28073i	0.952753	+	0.303747i	$0.0982378\pi$
$421$	15.1718	+	26.2784i	0.739429	+	1.28073i	−0.213324	+	0.976982i	$0.568429\pi$
$422$		−	2.02269i		−	0.0984631i
$423$		0			0
$424$	−6.63266			−0.322110
$425$	7.34510	+	12.7221i	0.356290	+	0.617112i
$426$		0			0
$427$		0			0
$428$	5.75051	+	3.32006i	0.277962	+	0.160481i
$429$		0			0
$430$	3.21177	−	1.85432i	0.154885	−	0.0894230i
$431$			2.45562i			0.118283i	0.998250	+	0.0591415i	$0.0188363\pi$
$431$			2.45562i			0.118283i	−0.998250	+	0.0591415i	$0.981164\pi$
$432$		0			0
$433$		−	12.4545i		−	0.598525i	−0.954171	−	0.299262i	$-0.903259\pi$
$433$		−	12.4545i		−	0.598525i	0.954171	−	0.299262i	$-0.0967406\pi$
$434$		0			0
$435$		0			0
$436$	1.16936	−	2.02539i	0.0560022	−	0.0969987i
$437$	3.79805	−	6.57841i	0.181685	−	0.314688i
$438$		0			0
$439$	−15.1815	+	8.76502i	−0.724571	+	0.418331i	−0.816433	−	0.577440i	$-0.804052\pi$
$439$	−15.1815	+	8.76502i	−0.724571	+	0.418331i	0.0918615	+	0.995772i	$0.470718\pi$
$440$	−13.7141			−0.653794
$441$		0			0
$442$	−2.31739			−0.110227
$443$	7.79825	−	4.50232i	0.370506	−	0.213912i	−0.303173	−	0.952935i	$-0.598046\pi$
$443$	7.79825	−	4.50232i	0.370506	−	0.213912i	0.673680	+	0.739024i	$0.264713\pi$
$444$		0			0
$445$	6.60555	−	11.4411i	0.313133	−	0.542362i
$446$	−0.945337	+	1.63737i	−0.0447630	+	0.0775318i
$447$		0			0
$448$		0			0
$449$		−	30.8120i		−	1.45411i	−0.686581	−	0.727054i	$-0.740889\pi$
$449$		−	30.8120i		−	1.45411i	0.686581	−	0.727054i	$-0.259111\pi$
$450$		0			0
$451$		−	24.3714i		−	1.14761i
$452$	−3.59154	+	2.07357i	−0.168932	+	0.0975327i
$453$		0			0
$454$	−5.02371	−	2.90044i	−0.235775	−	0.136125i
$455$		0			0
$456$		0			0
$457$	−6.91430	−	11.9759i	−0.323437	−	0.560210i	0.657758	−	0.753230i	$-0.271505\pi$
$457$	−6.91430	−	11.9759i	−0.323437	−	0.560210i	−0.981195	+	0.193020i	$0.938172\pi$
$458$	3.20520			0.149769
$459$		0			0
$460$		−	17.4561i		−	0.813893i
$461$	−6.16989	−	10.6866i	−0.287360	−	0.497723i	0.685818	−	0.727773i	$-0.259444\pi$
$461$	−6.16989	−	10.6866i	−0.287360	−	0.497723i	−0.973179	+	0.230050i	$0.926111\pi$
$462$		0			0
$463$	6.37802	−	11.0471i	0.296412	−	0.513401i	−0.678900	−	0.734230i	$-0.737543\pi$
$463$	6.37802	−	11.0471i	0.296412	−	0.513401i	0.975312	+	0.220830i	$0.0708765\pi$
$464$	−12.8141	−	7.39825i	−0.594882	−	0.343455i
$465$		0			0
$466$	−3.05303	−	5.28801i	−0.141429	−	0.244962i
$467$	−10.9800			−0.508093			−0.254046	−	0.967192i	$-0.581762\pi$
$467$	−10.9800			−0.508093			−0.254046	+	0.967192i	$0.581762\pi$
$468$		0			0
$469$		0			0
$470$	−3.15730	+	1.82287i	−0.145635	+	0.0840825i
$471$		0			0
$472$	4.66837	+	2.69528i	0.214879	+	0.124061i
$473$	−13.9156	−	8.03417i	−0.639840	−	0.369412i
$474$		0			0
$475$	−9.63396	+	5.56217i	−0.442036	+	0.255210i
$476$		0			0
$477$		0			0
$478$	8.03330			0.367435
$479$	5.59729	+	9.69478i	0.255747	+	0.442966i	0.965098	−	0.261889i	$-0.0843454\pi$
$479$	5.59729	+	9.69478i	0.255747	+	0.442966i	−0.709351	+	0.704855i	$0.751012\pi$
$480$		0			0
$481$	−15.8043	−	9.12464i	−0.720616	−	0.416048i
$482$	−3.13352	+	5.42741i	−0.142728	+	0.247212i
$483$		0			0
$484$	4.00191	+	6.93152i	0.181905	+	0.315069i
$485$			17.6260i			0.800353i
$486$		0			0
$487$	2.96665			0.134432			0.0672158	−	0.997738i	$-0.478588\pi$
$487$	2.96665			0.134432			0.0672158	+	0.997738i	$0.478588\pi$
$488$	0.920185	+	1.59381i	0.0416548	+	0.0721483i
$489$		0			0
$490$		0			0
$491$	20.1795	+	11.6507i	0.910690	+	0.525787i	0.880653	−	0.473762i	$-0.157104\pi$
$491$	20.1795	+	11.6507i	0.910690	+	0.525787i	0.0300367	+	0.999549i	$0.490438\pi$
$492$		0			0
$493$	−12.3586	+	7.13524i	−0.556603	+	0.321355i
$494$		−	1.75487i		−	0.0789553i
$495$		0			0
$496$			1.64952i			0.0740654i
$497$		0			0
$498$		0			0
$499$	2.29296	−	3.97152i	0.102647	−	0.177790i	−0.810127	−	0.586254i	$-0.800602\pi$
$499$	2.29296	−	3.97152i	0.102647	−	0.177790i	0.912774	+	0.408464i	$0.133935\pi$
$500$	1.85862	−	3.21922i	0.0831198	−	0.143968i
$501$		0			0
$502$	−6.80480	+	3.92875i	−0.303713	+	0.175349i
$503$	23.1383			1.03169			0.515844	−	0.856683i	$-0.327479\pi$
$503$	23.1383			1.03169			0.515844	+	0.856683i	$0.327479\pi$
$504$		0			0
$505$	52.5081			2.33658
$506$	2.95585	−	1.70656i	0.131404	−	0.0758660i
$507$		0			0
$508$	−2.63020	+	4.55563i	−0.116696	+	0.202123i
$509$	−4.82853	+	8.36326i	−0.214021	+	0.370695i	−0.952969	−	0.303067i	$-0.901989\pi$
$509$	−4.82853	+	8.36326i	−0.214021	+	0.370695i	0.738948	+	0.673762i	$0.235323\pi$
$510$		0			0
$511$		0			0
$512$		−	19.6301i		−	0.867536i
$513$		0			0
$514$			0.897123i			0.0395704i
$515$	26.0252	−	15.0257i	1.14681	−	0.662110i
$516$		0			0
$517$	13.6796	+	7.89791i	0.601627	+	0.347350i
$518$		0			0
$519$		0			0
$520$	−4.12374	−	7.14252i	−0.180838	−	0.313220i
$521$	10.0007			0.438139			0.219069	−	0.975709i	$-0.429698\pi$
$521$	10.0007			0.438139			0.219069	+	0.975709i	$0.429698\pi$
$522$		0			0
$523$			12.4472i			0.544279i	0.962258	+	0.272139i	$0.0877312\pi$
$523$			12.4472i			0.544279i	−0.962258	+	0.272139i	$0.912269\pi$
$524$	7.15531	+	12.3934i	0.312581	+	0.541406i
$525$		0			0
$526$	−2.38289	+	4.12729i	−0.103899	+	0.179959i
$527$	1.37774	+	0.795437i	0.0600152	+	0.0346498i
$528$		0			0
$529$	−7.05755	−	12.2240i	−0.306850	−	0.531480i
$530$	−5.18640			−0.225283
$531$		0			0
$532$		0			0
$533$	12.6930	−	7.32833i	0.549797	−	0.317425i
$534$		0			0
$535$	9.19615	+	5.30940i	0.397584	+	0.229545i
$536$	1.56938	+	0.906084i	0.0677870	+	0.0391369i
$537$		0			0
$538$	−0.154356	+	0.0891175i	−0.00665476	+	0.00384213i
$539$		0			0
$540$		0			0
$541$	−13.9303			−0.598909			−0.299455	−	0.954111i	$-0.596805\pi$
$541$	−13.9303			−0.598909			−0.299455	+	0.954111i	$0.596805\pi$
$542$	3.37547	+	5.84648i	0.144989	+	0.251128i
$543$		0			0
$544$	−9.69211	−	5.59574i	−0.415546	−	0.239916i
$545$	1.87003	−	3.23898i	0.0801032	−	0.138743i
$546$		0			0
$547$	−21.6768	−	37.5454i	−0.926834	−	1.60532i	−0.788584	−	0.614926i	$-0.789186\pi$
$547$	−21.6768	−	37.5454i	−0.926834	−	1.60532i	−0.138250	−	0.990397i	$-0.544148\pi$
$548$		−	23.3632i		−	0.998026i
$549$		0			0
$550$	−4.99846			−0.213135
$551$	−5.40325	−	9.35870i	−0.230186	−	0.398694i
$552$		0			0
$553$		0			0
$554$	3.38062	+	1.95180i	0.143629	+	0.0829241i
$555$		0			0
$556$	22.1026	−	12.7610i	0.937361	−	0.541186i
$557$			35.9503i			1.52326i	0.648010	+	0.761632i	$0.275602\pi$
$557$			35.9503i			1.52326i	−0.648010	+	0.761632i	$0.724398\pi$
$558$		0			0
$559$		−	9.66329i		−	0.408714i
$560$		0			0
$561$		0			0
$562$	0.964340	−	1.67029i	0.0406782	−	0.0704568i
$563$	3.05554	−	5.29235i	0.128776	−	0.223046i	−0.794427	−	0.607360i	$-0.792229\pi$
$563$	3.05554	−	5.29235i	0.128776	−	0.223046i	0.923202	+	0.384314i	$0.125562\pi$
$564$		0			0
$565$	−5.74354	+	3.31603i	−0.241633	+	0.139507i
$566$	−0.873481			−0.0367151
$567$		0			0
$568$	−15.6566			−0.656935
$569$	16.7182	−	9.65223i	0.700861	−	0.404642i	−0.106807	−	0.994280i	$-0.534063\pi$
$569$	16.7182	−	9.65223i	0.700861	−	0.404642i	0.807668	+	0.589637i	$0.200729\pi$
$570$		0			0
$571$	−6.36118	+	11.0179i	−0.266207	+	0.461085i	−0.967879	−	0.251416i	$-0.919104\pi$
$571$	−6.36118	+	11.0179i	−0.266207	+	0.461085i	0.701672	+	0.712500i	$0.252437\pi$
$572$	−8.73631	+	15.1317i	−0.365284	+	0.632690i
$573$		0			0
$574$		0			0
$575$		−	13.0118i		−	0.542628i
$576$		0			0
$577$			8.14664i			0.339149i	0.985517	+	0.169575i	$0.0542393\pi$
$577$			8.14664i			0.339149i	−0.985517	+	0.169575i	$0.945761\pi$
$578$	1.44429	−	0.833863i	0.0600747	−	0.0346841i
$579$		0			0
$580$	−21.5066	−	12.4168i	−0.893012	−	0.515581i
$581$		0			0
$582$		0			0
$583$	11.2355	+	19.4605i	0.465328	+	0.805973i
$584$	−1.13739			−0.0470654
$585$		0			0
$586$		−	1.78136i		−	0.0735873i
$587$	−12.3041	−	21.3113i	−0.507843	−	0.879610i	−0.999959	−	0.00908019i	$-0.997110\pi$
$587$	−12.3041	−	21.3113i	−0.507843	−	0.879610i	0.492116	−	0.870530i	$-0.336224\pi$
$588$		0			0
$589$	−0.602354	+	1.04331i	−0.0248196	+	0.0429888i
$590$	3.65043	+	2.10758i	0.150286	+	0.0867676i
$591$		0			0
$592$	−13.5872	−	23.5336i	−0.558429	−	0.967227i
$593$	−37.8641			−1.55489			−0.777447	−	0.628949i	$-0.783486\pi$
$593$	−37.8641			−1.55489			−0.777447	+	0.628949i	$0.783486\pi$
$594$		0			0
$595$		0			0
$596$	14.0428	−	8.10762i	0.575216	−	0.332101i
$597$		0			0
$598$	1.77761	+	1.02631i	0.0726920	+	0.0419687i
$599$	9.22572	+	5.32647i	0.376953	+	0.217634i	0.676492	−	0.736450i	$-0.263499\pi$
$599$	9.22572	+	5.32647i	0.376953	+	0.217634i	−0.299539	+	0.954084i	$0.596833\pi$
$600$		0			0
$601$	39.8636	−	23.0153i	1.62607	−	0.938812i	0.640821	−	0.767691i	$-0.278594\pi$
$601$	39.8636	−	23.0153i	1.62607	−	0.938812i	0.985250	−	0.171122i	$-0.0547391\pi$
$602$		0			0
$603$		0			0
$604$	−6.42322			−0.261357
$605$	6.39981	+	11.0848i	0.260189	+	0.450661i
$606$		0			0
$607$	−3.74063	−	2.15965i	−0.151827	−	0.0876576i	0.422162	−	0.906521i	$-0.361271\pi$
$607$	−3.74063	−	2.15965i	−0.151827	−	0.0876576i	−0.573989	+	0.818863i	$0.694605\pi$
$608$	4.23745	−	7.33947i	0.171851	−	0.297655i
$609$		0			0
$610$	0.719539	+	1.24628i	0.0291333	+	0.0504603i
$611$			9.49940i			0.384305i
$612$		0			0
$613$	−28.7676			−1.16191			−0.580956	−	0.813935i	$-0.697321\pi$
$613$	−28.7676			−1.16191			−0.580956	+	0.813935i	$0.697321\pi$
$614$	−3.17423	−	5.49793i	−0.128102	−	0.221878i
$615$		0			0
$616$		0			0
$617$	−0.935498	−	0.540110i	−0.0376617	−	0.0217440i	0.481051	−	0.876693i	$-0.340255\pi$
$617$	−0.935498	−	0.540110i	−0.0376617	−	0.0217440i	−0.518713	+	0.854949i	$0.673589\pi$
$618$		0			0
$619$	6.57128	−	3.79393i	0.264122	−	0.152491i	−0.362091	−	0.932143i	$-0.617937\pi$
$619$	6.57128	−	3.79393i	0.264122	−	0.152491i	0.626214	+	0.779652i	$0.284604\pi$
$620$			2.76846i			0.111184i
$621$		0			0
$622$			3.23944i			0.129890i
$623$		0			0
$624$		0			0
$625$	13.8854	−	24.0502i	0.555416	−	0.962010i
$626$	1.99158	−	3.44952i	0.0795996	−	0.137871i
$627$		0			0
$628$	27.6904	−	15.9871i	1.10497	−	0.637953i
$629$	−26.2082			−1.04499
$630$		0			0
$631$	35.0387			1.39487			0.697435	−	0.716648i	$-0.254325\pi$
$631$	35.0387			1.39487			0.697435	+	0.716648i	$0.254325\pi$
$632$	9.24118	−	5.33540i	0.367595	−	0.212231i
$633$		0			0
$634$	1.63893	−	2.83871i	0.0650903	−	0.112740i
$635$	−4.20618	+	7.28531i	−0.166917	+	0.289109i
$636$		0			0
$637$		0			0
$638$		−	4.85564i		−	0.192237i
$639$		0			0
$640$		−	25.7516i		−	1.01792i
$641$	26.9229	−	15.5439i	1.06339	−	0.613949i	0.137023	−	0.990568i	$-0.456247\pi$
$641$	26.9229	−	15.5439i	1.06339	−	0.613949i	0.926368	+	0.376619i	$0.122913\pi$
$642$		0			0
$643$	0.977928	+	0.564607i	0.0385657	+	0.0222659i	0.519159	−	0.854678i	$-0.326245\pi$
$643$	0.977928	+	0.564607i	0.0385657	+	0.0222659i	−0.480593	+	0.876944i	$0.659579\pi$
$644$		0			0
$645$		0			0
$646$	−1.26011	−	2.18257i	−0.0495782	−	0.0858719i
$647$	−27.1984			−1.06928			−0.534640	−	0.845080i	$-0.679553\pi$
$647$	−27.1984			−1.06928			−0.534640	+	0.845080i	$0.679553\pi$
$648$		0			0
$649$		−	18.2630i		−	0.716884i
$650$	−1.50300	−	2.60328i	−0.0589526	−	0.102109i
$651$		0			0
$652$	24.2386	−	41.9824i	0.949256	−	1.64416i
$653$	−19.3030	−	11.1446i	−0.755384	−	0.436121i	0.0722517	−	0.997386i	$-0.476981\pi$
$653$	−19.3030	−	11.1446i	−0.755384	−	0.436121i	−0.827636	+	0.561265i	$0.810315\pi$
$654$		0			0
$655$	11.4427	+	19.8193i	0.447102	+	0.774404i
$656$	21.8247			0.852110
$657$		0			0
$658$		0			0
$659$	7.69208	−	4.44103i	0.299641	−	0.172998i	−0.342641	−	0.939467i	$-0.611321\pi$
$659$	7.69208	−	4.44103i	0.299641	−	0.172998i	0.642282	+	0.766469i	$0.277988\pi$
$660$		0			0
$661$	16.7724	+	9.68352i	0.652369	+	0.376645i	0.789363	−	0.613926i	$-0.210411\pi$
$661$	16.7724	+	9.68352i	0.652369	+	0.376645i	−0.136994	+	0.990572i	$0.543744\pi$
$662$	−4.84060	−	2.79472i	−0.188135	−	0.108620i
$663$		0			0
$664$	−10.9434	+	6.31819i	−0.424687	+	0.245193i
$665$		0			0
$666$		0			0
$667$	12.6400			0.489422
$668$	−1.67602	−	2.90295i	−0.0648472	−	0.112319i
$669$		0			0
$670$	1.22718	+	0.708512i	0.0474101	+	0.0273722i
$671$	3.11754	−	5.39973i	0.120351	−	0.208454i
$672$		0			0
$673$	11.5828	+	20.0620i	0.446484	+	0.773333i	0.998154	−	0.0607292i	$-0.0193426\pi$
$673$	11.5828	+	20.0620i	0.446484	+	0.773333i	−0.551670	+	0.834062i	$0.686009\pi$
$674$			1.95502i			0.0753047i
$675$		0			0
$676$	14.3695			0.552674
$677$	1.56346	+	2.70800i	0.0600887	+	0.104077i	0.894505	−	0.447058i	$-0.147528\pi$
$677$	1.56346	+	2.70800i	0.0600887	+	0.104077i	−0.834416	+	0.551135i	$0.814195\pi$
$678$		0			0
$679$		0			0
$680$	−10.2576	−	5.92220i	−0.393359	−	0.227106i
$681$		0			0
$682$	−0.468786	+	0.270654i	−0.0179507	+	0.0103639i
$683$			31.4039i			1.20164i	0.799385	+	0.600819i	$0.205159\pi$
$683$			31.4039i			1.20164i	−0.799385	+	0.600819i	$0.794841\pi$
$684$		0			0
$685$		−	37.3621i		−	1.42753i
$686$		0			0
$687$		0			0
$688$	7.19462	−	12.4614i	0.274292	−	0.475088i
$689$	−6.75691	+	11.7033i	−0.257418	+	0.445860i
$690$		0			0
$691$	38.2557	−	22.0869i	1.45532	−	0.840227i	0.456540	−	0.889703i	$-0.349088\pi$
$691$	38.2557	−	22.0869i	1.45532	−	0.840227i	0.998775	+	0.0494760i	$0.0157551\pi$
$692$	−45.7868			−1.74055
$693$		0			0
$694$	7.83164			0.297285
$695$	35.3463	−	20.4072i	1.34076	−	0.774089i
$696$		0			0
$697$	10.5244	−	18.2288i	0.398640	−	0.690465i
$698$	3.48043	−	6.02828i	0.131736	−	0.228174i
$699$		0			0
$700$		0			0
$701$			9.69906i			0.366328i	0.983082	+	0.183164i	$0.0586340\pi$
$701$			9.69906i			0.366328i	−0.983082	+	0.183164i	$0.941366\pi$
$702$		0			0
$703$		−	19.8465i		−	0.748526i
$704$	−20.2511	+	11.6920i	−0.763242	+	0.440658i
$705$		0			0
$706$	1.16775	+	0.674202i	0.0439490	+	0.0253739i
$707$		0			0
$708$		0			0
$709$	0.548932	+	0.950778i	0.0206156	+	0.0357072i	0.876149	−	0.482040i	$-0.160104\pi$
$709$	0.548932	+	0.950778i	0.0206156	+	0.0357072i	−0.855534	+	0.517747i	$0.826771\pi$
$710$	−12.2426			−0.459458
$711$		0			0
$712$			4.96495i			0.186069i
$713$	−0.704553	−	1.22032i	−0.0263857	−	0.0457014i
$714$		0			0
$715$	−13.9710	+	24.1985i	−0.522486	+	0.904972i
$716$	42.0728	+	24.2908i	1.57233	+	0.907788i
$717$		0			0
$718$	0.900826	+	1.56028i	0.0336185	+	0.0582290i
$719$	22.7295			0.847669			0.423835	−	0.905740i	$-0.360684\pi$
$719$	22.7295			0.847669			0.423835	+	0.905740i	$0.360684\pi$
$720$		0			0
$721$		0			0
$722$	−3.18269	+	1.83753i	−0.118448	+	0.0683858i
$723$		0			0
$724$	−37.1280	−	21.4359i	−1.37985	−	0.796658i
$725$	−16.0310	−	9.25550i	−0.595376	−	0.343741i
$726$		0			0
$727$	−3.47919	+	2.00871i	−0.129036	+	0.0744990i	−0.563129	−	0.826369i	$-0.690402\pi$
$727$	−3.47919	+	2.00871i	−0.129036	+	0.0744990i	0.434093	+	0.900868i	$0.357069\pi$
$728$		0			0
$729$		0			0
$730$	−0.889379			−0.0329174
$731$	−6.93885	−	12.0184i	−0.256643	−	0.444518i
$732$		0			0
$733$	7.20188	+	4.15801i	0.266008	+	0.153580i	0.627072	−	0.778961i	$-0.284253\pi$
$733$	7.20188	+	4.15801i	0.266008	+	0.153580i	−0.361064	+	0.932541i	$0.617587\pi$
$734$	3.88296	−	6.72549i	0.143323	−	0.248242i
$735$		0			0
$736$	4.95640	+	8.58473i	0.182695	+	0.316437i
$737$		−	6.13953i		−	0.226152i
$738$		0			0
$739$	4.57014			0.168115			0.0840576	−	0.996461i	$-0.473212\pi$
$739$	4.57014			0.168115			0.0840576	+	0.996461i	$0.473212\pi$
$740$	−22.8040	−	39.4976i	−0.838290	−	1.45196i
$741$		0			0
$742$		0			0
$743$	−1.51258	−	0.873286i	−0.0554910	−	0.0320378i	0.471998	−	0.881600i	$-0.343533\pi$
$743$	−1.51258	−	0.873286i	−0.0554910	−	0.0320378i	−0.527489	+	0.849562i	$0.676866\pi$
$744$		0			0
$745$	22.4571	−	12.9656i	0.822764	−	0.475023i
$746$		−	5.91154i		−	0.216437i
$747$		0			0
$748$			25.0929i			0.917486i
$749$		0			0
$750$		0			0
$751$	−2.91647	+	5.05147i	−0.106423	+	0.184331i	−0.914319	−	0.404995i	$-0.867273\pi$
$751$	−2.91647	+	5.05147i	−0.106423	+	0.184331i	0.807895	+	0.589326i	$0.200607\pi$
$752$	−7.07260	+	12.2501i	−0.257911	+	0.446715i
$753$		0			0
$754$	2.52890	−	1.46006i	0.0920970	−	0.0531723i
$755$	−10.2719			−0.373834
$756$		0			0
$757$	−42.0967			−1.53003			−0.765015	−	0.644013i	$-0.777268\pi$
$757$	−42.0967			−1.53003			−0.765015	+	0.644013i	$0.777268\pi$
$758$	4.44255	−	2.56491i	0.161361	−	0.0931617i
$759$		0			0
$760$	4.48466	−	7.76766i	0.162676	−	0.281763i
$761$	−0.293431	+	0.508238i	−0.0106369	+	0.0184236i	−0.871295	−	0.490760i	$-0.836719\pi$
$761$	−0.293431	+	0.508238i	−0.0106369	+	0.0184236i	0.860658	+	0.509184i	$0.170053\pi$
$762$		0			0
$763$		0			0
$764$		−	8.20750i		−	0.296937i
$765$		0			0
$766$			8.24696i			0.297975i
$767$	9.51165	−	5.49155i	0.343446	−	0.198288i
$768$		0			0
$769$	−45.1905	−	26.0907i	−1.62961	−	0.940856i	−0.984208	−	0.177014i	$-0.943356\pi$
$769$	−45.1905	−	26.0907i	−1.62961	−	0.940856i	−0.645403	−	0.763843i	$-0.723310\pi$
$770$		0			0
$771$		0			0
$772$	22.3369	+	38.6887i	0.803923	+	1.39244i
$773$	−32.7812			−1.17906			−0.589530	−	0.807747i	$-0.700687\pi$
$773$	−32.7812			−1.17906			−0.589530	+	0.807747i	$0.700687\pi$
$774$		0			0
$775$			2.06361i			0.0741270i
$776$	−3.31206	−	5.73666i	−0.118896	−	0.205934i
$777$		0			0
$778$	5.03093	−	8.71383i	0.180368	−	0.312406i
$779$	13.8040	+	7.96973i	0.494579	+	0.285545i
$780$		0			0
$781$	26.5218	+	45.9371i	0.949024	+	1.64376i
$782$	2.94780			0.105413
$783$		0			0
$784$		0			0
$785$	44.2821	−	25.5663i	1.58050	−	0.912500i
$786$		0			0
$787$	−35.5013	−	20.4967i	−1.26549	−	0.730628i	−0.291355	−	0.956615i	$-0.594106\pi$
$787$	−35.5013	−	20.4967i	−1.26549	−	0.730628i	−0.974130	+	0.225987i	$0.927439\pi$
$788$	−31.1251	−	17.9701i	−1.10879	−	0.640158i
$789$		0			0
$790$	7.22614	−	4.17201i	0.257095	−	0.148434i
$791$		0			0
$792$		0			0
$793$	3.74969			0.133156
$794$	−1.91597	−	3.31856i	−0.0679954	−	0.117771i
$795$		0			0
$796$	7.51921	+	4.34122i	0.266511	+	0.153870i
$797$	17.0441	−	29.5213i	0.603734	−	1.04570i	−0.388516	−	0.921442i	$-0.627012\pi$
$797$	17.0441	−	29.5213i	0.603734	−	1.04570i	0.992250	−	0.124256i	$-0.0396544\pi$
$798$		0			0
$799$	6.82116	+	11.8146i	0.241315	+	0.417971i
$800$		−	14.5171i		−	0.513256i
$801$		0			0
$802$	5.39344			0.190449
$803$	1.92670	+	3.33714i	0.0679918	+	0.117765i
$804$		0			0
$805$		0			0
$806$	−0.281922	−	0.162768i	−0.00993027	−	0.00573324i
$807$		0			0
$808$	−17.0896	+	9.86670i	−0.601211	+	0.347109i
$809$			6.94607i			0.244211i	0.992517	+	0.122105i	$0.0389646\pi$
$809$			6.94607i			0.244211i	−0.992517	+	0.122105i	$0.961035\pi$
$810$		0			0
$811$		−	39.8573i		−	1.39958i	−0.714350	−	0.699789i	$-0.753277\pi$
$811$		−	39.8573i		−	1.39958i	0.714350	−	0.699789i	$-0.246723\pi$
$812$		0			0
$813$		0			0
$814$	4.45878	−	7.72284i	0.156280	−	0.270685i
$815$	38.7620	−	67.1378i	1.35777	−	2.35173i
$816$		0			0
$817$	9.10111	−	5.25453i	0.318408	−	0.183833i
$818$	1.90071			0.0664566
$819$		0			0
$820$	36.6294			1.27915
$821$	−36.4612	+	21.0509i	−1.27250	+	0.734680i	−0.975459	−	0.220183i	$-0.929334\pi$
$821$	−36.4612	+	21.0509i	−1.27250	+	0.734680i	−0.297045	+	0.954863i	$0.596001\pi$
$822$		0			0
$823$	−16.3411	+	28.3035i	−0.569614	+	0.986600i	0.426990	+	0.904256i	$0.359574\pi$
$823$	−16.3411	+	28.3035i	−0.569614	+	0.986600i	−0.996604	+	0.0823435i	$0.973760\pi$
$824$	−5.64689	+	9.78070i	−0.196719	+	0.340727i
$825$		0			0
$826$		0			0
$827$			31.4399i			1.09327i	0.837370	+	0.546637i	$0.184092\pi$
$827$			31.4399i			1.09327i	−0.837370	+	0.546637i	$0.815908\pi$
$828$		0			0
$829$			41.2369i			1.43222i	0.697989	+	0.716109i	$0.254079\pi$
$829$			41.2369i			1.43222i	−0.697989	+	0.716109i	$0.745921\pi$
$830$	−8.55721	+	4.94051i	−0.297025	+	0.171488i
$831$		0			0
$832$	−12.1788	−	7.03141i	−0.422222	−	0.243770i
$833$		0			0
$834$		0			0
$835$	−2.68027	−	4.64236i	−0.0927546	−	0.160656i
$836$	−19.0019			−0.657194
$837$		0			0
$838$		−	4.18201i		−	0.144465i
$839$	4.04385	+	7.00416i	0.139609	+	0.241810i	0.927349	−	0.374198i	$-0.122082\pi$
$839$	4.04385	+	7.00416i	0.139609	+	0.241810i	−0.787740	+	0.616009i	$0.788749\pi$
$840$		0			0
$841$	−5.50894	+	9.54177i	−0.189963	+	0.329026i
$842$	−7.72241	−	4.45853i	−0.266132	−	0.153651i
$843$		0			0
$844$	−6.58576	−	11.4069i	−0.226691	−	0.392641i
$845$	22.9796			0.790521
$846$		0			0
$847$		0			0
$848$	−17.4269	+	10.0615i	−0.598444	+	0.345512i
$849$		0			0
$850$	−3.73863	−	2.15850i	−0.128234	−	0.0740359i
$851$	20.1037	+	11.6069i	0.689147	+	0.397879i
$852$		0			0
$853$	−24.5887	+	14.1963i	−0.841900	+	0.486071i	−0.857910	−	0.513801i	$-0.828237\pi$
$853$	−24.5887	+	14.1963i	−0.841900	+	0.486071i	0.0160098	+	0.999872i	$0.494904\pi$
$854$		0			0
$855$		0			0
$856$	−3.99072			−0.136400
$857$	25.6587	+	44.4422i	0.876485	+	1.51812i	0.855172	+	0.518344i	$0.173451\pi$
$857$	25.6587	+	44.4422i	0.876485	+	1.51812i	0.0213132	+	0.999773i	$0.493215\pi$
$858$		0			0
$859$	−14.5234	−	8.38509i	−0.495532	−	0.286096i	0.231334	−	0.972874i	$-0.425691\pi$
$859$	−14.5234	−	8.38509i	−0.495532	−	0.286096i	−0.726867	+	0.686779i	$0.759024\pi$
$860$	12.0751	−	20.9146i	0.411756	−	0.713183i
$861$		0			0
$862$	−0.360816	−	0.624951i	−0.0122894	−	0.0212859i
$863$		−	16.4407i		−	0.559647i	−0.960051	−	0.279823i	$-0.909724\pi$
$863$		−	16.4407i		−	0.559647i	0.960051	−	0.279823i	$-0.0902759\pi$
$864$		0			0
$865$	−73.2217			−2.48961
$866$	1.83000	+	3.16965i	0.0621859	+	0.107709i
$867$		0			0
$868$		0			0
$869$	−31.3086	−	18.0760i	−1.06207	−	0.613188i
$870$		0			0
$871$	3.19757	−	1.84612i	0.108345	−	0.0625532i
$872$			1.40557i			0.0475987i
$873$		0			0
$874$			2.23226i			0.0755074i
$875$		0			0
$876$		0			0
$877$	−3.06175	+	5.30311i	−0.103388	+	0.179073i	−0.913078	−	0.407784i	$-0.866302\pi$
$877$	−3.06175	+	5.30311i	−0.103388	+	0.179073i	0.809690	+	0.586857i	$0.199635\pi$
$878$	2.57577	−	4.46137i	0.0869281	−	0.150564i
$879$		0			0
$880$	−36.0330	+	20.8037i	−1.21467	+	0.701292i
$881$	−41.3283			−1.39238			−0.696192	−	0.717855i	$-0.745124\pi$
$881$	−41.3283			−1.39238			−0.696192	+	0.717855i	$0.745124\pi$
$882$		0			0
$883$	24.2918			0.817483			0.408741	−	0.912650i	$-0.365968\pi$
$883$	24.2918			0.817483			0.408741	+	0.912650i	$0.365968\pi$
$884$	−13.0688	+	7.54526i	−0.439550	+	0.253775i
$885$		0			0
$886$	−1.32310	+	2.29167i	−0.0444502	+	0.0769901i
$887$	−3.35036	+	5.80299i	−0.112494	+	0.194845i	−0.916775	−	0.399404i	$-0.869217\pi$
$887$	−3.35036	+	5.80299i	−0.112494	+	0.194845i	0.804281	+	0.594249i	$0.202551\pi$
$888$		0			0
$889$		0			0
$890$			3.88234i			0.130136i
$891$		0			0
$892$			12.3118i			0.412230i
$893$	−8.94675	+	5.16541i	−0.299392	+	0.172854i
$894$		0			0
$895$	67.2823	+	38.8455i	2.24900	+	1.29846i
$896$		0			0
$897$		0			0
$898$	4.52735	+	7.84160i	0.151080	+	0.261678i
$899$	−2.00465			−0.0668588
$900$		0			0
$901$			19.4075i			0.646558i
$902$	3.58101	+	6.20249i	0.119235	+	0.206520i
$903$		0			0
$904$	1.24622	−	2.15852i	0.0414487	−	0.0717912i
$905$	−59.3747	−	34.2800i	−1.97368	−	1.13951i
$906$		0			0
$907$	−10.1494	−	17.5793i	−0.337005	−	0.583710i	0.646863	−	0.762606i	$-0.276081\pi$
$907$	−10.1494	−	17.5793i	−0.337005	−	0.583710i	−0.983868	+	0.178897i	$0.942747\pi$
$908$	−37.7746			−1.25360
$909$		0			0
$910$		0			0
$911$	30.3982	−	17.5504i	1.00714	−	0.581472i	0.0967861	−	0.995305i	$-0.469144\pi$
$911$	30.3982	−	17.5504i	1.00714	−	0.581472i	0.910353	+	0.413833i	$0.135810\pi$
$912$		0			0
$913$	37.0757	+	21.4057i	1.22703	+	0.708425i
$914$	3.51936	+	2.03190i	0.116410	+	0.0672093i
$915$		0			0
$916$	18.0756	−	10.4359i	0.597233	−	0.344813i
$917$		0			0
$918$		0			0
$919$	33.8265			1.11583			0.557916	−	0.829897i	$-0.311601\pi$
$919$	33.8265			1.11583			0.557916	+	0.829897i	$0.311601\pi$
$920$	5.24555	+	9.08557i	0.172941	+	0.299542i
$921$		0			0
$922$	3.14046	+	1.81314i	0.103425	+	0.0597127i
$923$	−15.9499	+	27.6260i	−0.524996	+	0.909320i
$924$		0			0
$925$	−16.9981	−	29.4415i	−0.558893	−	0.968031i
$926$			3.74861i			0.123187i
$927$		0			0
$928$	14.1023			0.462931
$929$	16.0586	+	27.8142i	0.526864	+	0.912555i	0.999510	+	0.0313029i	$0.00996565\pi$
$929$	16.0586	+	27.8142i	0.526864	+	0.912555i	−0.472646	+	0.881252i	$0.656701\pi$
$930$		0			0
$931$		0			0
$932$	−34.4348	−	19.8810i	−1.12795	−	0.651222i
$933$		0			0
$934$	2.79439	−	1.61334i	0.0914351	−	0.0527901i
$935$			40.1282i			1.31233i
$936$		0			0
$937$			13.9224i			0.454824i	0.973799	+	0.227412i	$0.0730263\pi$
$937$			13.9224i			0.454824i	−0.973799	+	0.227412i	$0.926974\pi$
$938$		0			0
$939$		0			0
$940$	−11.8703	+	20.5599i	−0.387166	+	0.670590i
$941$	28.6047	−	49.5448i	0.932487	−	1.61512i	0.153433	−	0.988159i	$-0.450967\pi$
$941$	28.6047	−	49.5448i	0.932487	−	1.61512i	0.779054	−	0.626956i	$-0.215700\pi$
$942$		0			0
$943$	−16.1460	+	9.32192i	−0.525787	+	0.303563i
$944$	16.3545			0.532294
$945$		0			0
$946$	4.72200			0.153525
$947$	29.8658	−	17.2430i	0.970509	−	0.560324i	0.0711175	−	0.997468i	$-0.477343\pi$
$947$	29.8658	−	17.2430i	0.970509	−	0.560324i	0.899391	+	0.437144i	$0.144010\pi$
$948$		0			0
$949$	−1.15869	+	2.00691i	−0.0376128	+	0.0651472i
$950$	1.63455	−	2.83113i	0.0530318	−	0.0918538i
$951$		0			0
$952$		0			0
$953$		−	2.58761i		−	0.0838209i	−0.999121	−	0.0419104i	$-0.986656\pi$
$953$		−	2.58761i		−	0.0838209i	0.999121	−	0.0419104i	$-0.0133444\pi$
$954$		0			0
$955$		−	13.1253i		−	0.424726i
$956$	45.3034	−	26.1559i	1.46522	−	0.845943i
$957$		0			0
$958$	−2.84900	−	1.64487i	−0.0920470	−	0.0531434i
$959$		0			0
$960$		0			0
$961$	−15.3883	−	26.6532i	−0.496396	−	0.859782i
$962$	5.36291			0.172907
$963$		0			0
$964$			40.8101i			1.31441i
$965$	35.7209	+	61.8704i	1.14990	+	1.99168i
$966$		0			0
$967$	2.79472	−	4.84059i	0.0898721	−	0.155663i	−0.817585	−	0.575808i	$-0.804688\pi$
$967$	2.79472	−	4.84059i	0.0898721	−	0.155663i	0.907457	+	0.420145i	$0.138021\pi$
$968$	−4.16585	−	2.40515i	−0.133895	−	0.0773045i
$969$		0			0
$970$	−2.58986	−	4.48578i	−0.0831555	−	0.144030i
$971$	16.0332			0.514531			0.257265	−	0.966341i	$-0.417179\pi$
$971$	16.0332			0.514531			0.257265	+	0.966341i	$0.417179\pi$
$972$		0			0
$973$		0			0
$974$	−0.755007	+	0.435904i	−0.0241920	+	0.0139673i
$975$		0			0
$976$	4.83547	+	2.79176i	0.154780	+	0.0893621i
$977$	−38.0208	−	21.9513i	−1.21639	−	0.702285i	−0.252248	−	0.967663i	$-0.581170\pi$
$977$	−38.0208	−	21.9513i	−1.21639	−	0.702285i	−0.964144	+	0.265378i	$0.914503\pi$
$978$		0			0
$979$	14.5674	−	8.41048i	0.465576	−	0.268800i
$980$		0			0
$981$		0			0
$982$	−6.84755			−0.218514
$983$	9.08808	+	15.7410i	0.289865	+	0.502061i	0.973777	−	0.227503i	$-0.0730563\pi$
$983$	9.08808	+	15.7410i	0.289865	+	0.502061i	−0.683912	+	0.729564i	$0.739723\pi$
$984$		0			0
$985$	−49.7749	−	28.7376i	−1.58596	−	0.915655i
$986$	2.09683	−	3.63181i	0.0667766	−	0.115660i
$987$		0			0
$988$	−5.71374	−	9.89649i	−0.181778	−	0.314849i
$989$			12.2921i			0.390865i
$990$		0			0
$991$	47.6292			1.51299			0.756496	−	0.653998i	$-0.226910\pi$
$991$	47.6292			1.51299			0.756496	+	0.653998i	$0.226910\pi$
$992$	−0.786063	−	1.36150i	−0.0249575	−	0.0432277i
$993$		0			0
$994$		0			0
$995$	12.0246	+	6.94242i	0.381206	+	0.220090i
$996$		0			0
$997$	−28.4838	+	16.4451i	−0.902090	+	0.520822i	−0.877878	−	0.478885i	$-0.841041\pi$
$997$	−28.4838	+	16.4451i	−0.902090	+	0.520822i	−0.0242120	+	0.999707i	$0.507708\pi$
$998$			1.34766i			0.0426595i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.o.c.881.3		10
3.2	odd	2		441.2.o.d.293.3		10
7.2	even	3		1323.2.s.b.962.3		10
7.3	odd	6		1323.2.i.b.1097.3		10
7.4	even	3		189.2.i.b.152.3		10
7.5	odd	6		189.2.s.b.17.3		10
7.6	odd	2		1323.2.o.d.881.3		10
9.2	odd	6		1323.2.o.d.440.3		10
9.7	even	3		441.2.o.c.146.3		10
21.2	odd	6		441.2.s.b.374.3		10
21.5	even	6		63.2.s.b.59.3	yes	10
21.11	odd	6		63.2.i.b.5.3	✓	10
21.17	even	6		441.2.i.b.68.3		10
21.20	even	2		441.2.o.c.293.3		10
28.11	odd	6		3024.2.ca.b.2609.1		10
28.19	even	6		3024.2.df.b.17.1		10
63.2	odd	6		1323.2.i.b.521.3		10
63.4	even	3		567.2.p.c.404.3		10
63.5	even	6		567.2.p.c.80.3		10
63.11	odd	6		189.2.s.b.89.3		10
63.16	even	3		441.2.i.b.227.3		10
63.20	even	6	inner	1323.2.o.c.440.3		10
63.25	even	3		63.2.s.b.47.3	yes	10
63.32	odd	6		567.2.p.d.404.3		10
63.34	odd	6		441.2.o.d.146.3		10
63.38	even	6		1323.2.s.b.656.3		10
63.40	odd	6		567.2.p.d.80.3		10
63.47	even	6		189.2.i.b.143.3		10
63.52	odd	6		441.2.s.b.362.3		10
63.61	odd	6		63.2.i.b.38.3	yes	10
84.11	even	6		1008.2.ca.b.257.4		10
84.47	odd	6		1008.2.df.b.689.5		10
252.11	even	6		3024.2.df.b.1601.1		10
252.47	odd	6		3024.2.ca.b.2033.1		10
252.151	odd	6		1008.2.df.b.929.5		10
252.187	even	6		1008.2.ca.b.353.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.3	✓	10	21.11	odd	6
63.2.i.b.38.3	yes	10	63.61	odd	6
63.2.s.b.47.3	yes	10	63.25	even	3
63.2.s.b.59.3	yes	10	21.5	even	6
189.2.i.b.143.3		10	63.47	even	6
189.2.i.b.152.3		10	7.4	even	3
189.2.s.b.17.3		10	7.5	odd	6
189.2.s.b.89.3		10	63.11	odd	6
441.2.i.b.68.3		10	21.17	even	6
441.2.i.b.227.3		10	63.16	even	3
441.2.o.c.146.3		10	9.7	even	3
441.2.o.c.293.3		10	21.20	even	2
441.2.o.d.146.3		10	63.34	odd	6
441.2.o.d.293.3		10	3.2	odd	2
441.2.s.b.362.3		10	63.52	odd	6
441.2.s.b.374.3		10	21.2	odd	6
567.2.p.c.80.3		10	63.5	even	6
567.2.p.c.404.3		10	63.4	even	3
567.2.p.d.80.3		10	63.40	odd	6
567.2.p.d.404.3		10	63.32	odd	6
1008.2.ca.b.257.4		10	84.11	even	6
1008.2.ca.b.353.4		10	252.187	even	6
1008.2.df.b.689.5		10	84.47	odd	6
1008.2.df.b.929.5		10	252.151	odd	6
1323.2.i.b.521.3		10	63.2	odd	6
1323.2.i.b.1097.3		10	7.3	odd	6
1323.2.o.c.440.3		10	63.20	even	6	inner
1323.2.o.c.881.3		10	1.1	even	1	trivial
1323.2.o.d.440.3		10	9.2	odd	6
1323.2.o.d.881.3		10	7.6	odd	2
1323.2.s.b.656.3		10	63.38	even	6
1323.2.s.b.962.3		10	7.2	even	3
3024.2.ca.b.2033.1		10	252.47	odd	6
3024.2.ca.b.2609.1		10	28.11	odd	6
3024.2.df.b.17.1		10	28.19	even	6
3024.2.df.b.1601.1		10	252.11	even	6

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.254498 + 0.146935i) q^{2} +(-0.956820 + 1.65726i) q^{4} +(-1.53014 + 2.65027i) q^{5} -1.15010i q^{8} +O(q^{10})\)	\(q+(-0.254498 + 0.146935i) q^{2} +(-0.956820 + 1.65726i) q^{4} +(-1.53014 + 2.65027i) q^{5} -1.15010i q^{8} -0.899320i q^{10} +(-3.37445 + 1.94824i) q^{11} +(-2.02935 - 1.17164i) q^{13} +(-1.74465 - 3.02182i) q^{16} -3.36525 q^{17} -2.54838i q^{19} +(-2.92813 - 5.07167i) q^{20} +(0.572527 - 0.991647i) q^{22} +(2.58141 + 1.49038i) q^{23} +(-2.18263 - 3.78042i) q^{25} +0.688621 q^{26} +(3.67241 - 2.12027i) q^{29} +(-0.409400 - 0.236367i) q^{31} +(2.88005 + 1.66280i) q^{32} +(0.856452 - 0.494473i) q^{34} +7.78789 q^{37} +(0.374446 + 0.648559i) q^{38} +(3.04808 + 1.75981i) q^{40} +(-3.12737 + 5.41676i) q^{41} +(2.06191 + 3.57133i) q^{43} -7.45645i q^{44} -0.875953 q^{46} +(-2.02694 - 3.51076i) q^{47} +(1.11095 + 0.641408i) q^{50} +(3.88344 - 2.24211i) q^{52} -5.76703i q^{53} -11.9243i q^{55} +(-0.623082 + 1.07921i) q^{58} +(-2.34352 + 4.05910i) q^{59} +(-1.38580 + 0.800092i) q^{61} +0.138922 q^{62} +6.00131 q^{64} +(6.21035 - 3.58555i) q^{65} +(-0.787831 + 1.36456i) q^{67} +(3.21994 - 5.57711i) q^{68} -13.6132i q^{71} -0.988946i q^{73} +(-1.98201 + 1.14431i) q^{74} +(4.22333 + 2.43834i) q^{76} +(4.63908 + 8.03512i) q^{79} +10.6782 q^{80} -1.83808i q^{82} +(-5.49361 - 9.51520i) q^{83} +(5.14930 - 8.91884i) q^{85} +(-1.04950 - 0.605932i) q^{86} +(2.24067 + 3.88095i) q^{88} -4.31697 q^{89} +(-4.93989 + 2.85205i) q^{92} +(1.03171 + 0.595655i) q^{94} +(6.75390 + 3.89937i) q^{95} +(4.98797 - 2.87980i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4}+O(q^{10}) \) 10 * q + 4 * q^4	\( 10 q + 4 q^{4} - 12 q^{11} - 6 q^{13} - 6 q^{16} + 24 q^{17} - 3 q^{20} + 5 q^{22} - 15 q^{23} + 7 q^{25} - 6 q^{26} + 15 q^{29} - 9 q^{31} + 48 q^{32} - 3 q^{34} - 12 q^{37} - 18 q^{38} - 15 q^{40} - 9 q^{41} + 3 q^{43} + 26 q^{46} + 15 q^{47} - 3 q^{50} + 12 q^{52} + 8 q^{58} - 18 q^{59} + 12 q^{61} + 12 q^{62} + 6 q^{64} - 3 q^{65} - 10 q^{67} + 27 q^{68} - 30 q^{74} - 9 q^{76} + 20 q^{79} + 60 q^{80} - 15 q^{83} + 18 q^{85} + 54 q^{86} - 8 q^{88} - 48 q^{89} - 39 q^{92} - 3 q^{94} - 6 q^{97}+O(q^{100}) \) 10 * q + 4 * q^4 - 12 * q^11 - 6 * q^13 - 6 * q^16 + 24 * q^17 - 3 * q^20 + 5 * q^22 - 15 * q^23 + 7 * q^25 - 6 * q^26 + 15 * q^29 - 9 * q^31 + 48 * q^32 - 3 * q^34 - 12 * q^37 - 18 * q^38 - 15 * q^40 - 9 * q^41 + 3 * q^43 + 26 * q^46 + 15 * q^47 - 3 * q^50 + 12 * q^52 + 8 * q^58 - 18 * q^59 + 12 * q^61 + 12 * q^62 + 6 * q^64 - 3 * q^65 - 10 * q^67 + 27 * q^68 - 30 * q^74 - 9 * q^76 + 20 * q^79 + 60 * q^80 - 15 * q^83 + 18 * q^85 + 54 * q^86 - 8 * q^88 - 48 * q^89 - 39 * q^92 - 3 * q^94 - 6 * q^97

Introduction

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