LMFDB - Embedded newform 1323.2.o.d.440.5

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			440.5
Root			$0.827154 + 1.43267i$ of defining polynomial
Character	$\chi$	$=$	1323.440
Dual form			1323.2.o.d.881.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.81474 + 1.04774i) q^{2} +(1.19552 + 2.07070i) q^{4} +(-1.04492 - 1.80985i) q^{5} +0.819421i q^{8} +O(q^{10})$	\(q+(1.81474 + 1.04774i) q^{2} +(1.19552 + 2.07070i) q^{4} +(-1.04492 - 1.80985i) q^{5} +0.819421i q^{8} -4.37920i q^{10} +(2.79620 + 1.61439i) q^{11} +(2.68740 - 1.55157i) q^{13} +(1.53250 - 2.65437i) q^{16} -1.63261 q^{17} -5.53210i q^{19} +(2.49844 - 4.32742i) q^{20} +(3.38292 + 5.85939i) q^{22} +(-1.00527 + 0.580391i) q^{23} +(0.316304 - 0.547854i) q^{25} +6.50257 q^{26} +(7.05749 + 4.07464i) q^{29} +(5.16886 - 2.98424i) q^{31} +(6.98146 - 4.03075i) q^{32} +(-2.96276 - 1.71055i) q^{34} -5.65313 q^{37} +(5.79620 - 10.0393i) q^{38} +(1.48303 - 0.856225i) q^{40} +(1.35369 + 2.34465i) q^{41} +(-0.974903 + 1.68858i) q^{43} +7.72014i q^{44} -2.43240 q^{46} +(-4.06759 + 7.04527i) q^{47} +(1.14802 - 0.662809i) q^{50} +(6.42568 + 3.70987i) q^{52} -6.09412i q^{53} -6.74759i q^{55} +(8.53834 + 14.7888i) q^{58} +(1.98103 + 3.43124i) q^{59} +(4.15016 + 2.39609i) q^{61} +12.5068 q^{62} +10.7627 q^{64} +(-5.61621 - 3.24252i) q^{65} +(0.336981 + 0.583668i) q^{67} +(-1.95182 - 3.38065i) q^{68} +7.01535i q^{71} -3.42110i q^{73} +(-10.2590 - 5.92301i) q^{74} +(11.4553 - 6.61374i) q^{76} +(7.07973 - 12.2625i) q^{79} -6.40534 q^{80} +5.67325i q^{82} +(-1.54535 + 2.67662i) q^{83} +(1.70594 + 2.95477i) q^{85} +(-3.53839 + 2.04289i) q^{86} +(-1.32286 + 2.29127i) q^{88} -4.91531 q^{89} +(-2.40363 - 1.38774i) q^{92} +(-14.7632 + 8.52356i) q^{94} +(-10.0122 + 5.78057i) q^{95} +(2.07939 + 1.20054i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.81474	+	1.04774i	1.28321	+	0.740865i	0.977435	−	0.211238i	$-0.0677494\pi$
$2$	1.81474	+	1.04774i	1.28321	+	0.740865i	0.305780	+	0.952102i	$0.401083\pi$
$3$		0			0
$3$		0			0
$4$	1.19552	+	2.07070i	0.597760	+	1.03535i
$5$	−1.04492	−	1.80985i	−0.467300	−	0.809388i	0.532002	−	0.846743i	$-0.321440\pi$
$5$	−1.04492	−	1.80985i	−0.467300	−	0.809388i	−0.999302	+	0.0373553i	$0.988107\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			0.819421i			0.289709i
$9$		0			0
$10$		−	4.37920i		−	1.38482i
$11$	2.79620	+	1.61439i	0.843086	+	0.486756i	0.858312	−	0.513128i	$-0.171513\pi$
$11$	2.79620	+	1.61439i	0.843086	+	0.486756i	−0.0152257	+	0.999884i	$0.504847\pi$
$12$		0			0
$13$	2.68740	−	1.55157i	0.745350	−	0.430328i	−0.0786612	−	0.996901i	$-0.525065\pi$
$13$	2.68740	−	1.55157i	0.745350	−	0.430328i	0.824011	+	0.566573i	$0.191731\pi$
$14$		0			0
$15$		0			0
$16$	1.53250	−	2.65437i	0.383125	−	0.663593i
$17$	−1.63261			−0.395966			−0.197983	−	0.980206i	$-0.563439\pi$
$17$	−1.63261			−0.395966			−0.197983	+	0.980206i	$0.563439\pi$
$18$		0			0
$19$		−	5.53210i		−	1.26915i	−0.772861	−	0.634575i	$-0.781175\pi$
$19$		−	5.53210i		−	1.26915i	0.772861	−	0.634575i	$-0.218825\pi$
$20$	2.49844	−	4.32742i	0.558667	−	0.967640i
$21$		0			0
$22$	3.38292	+	5.85939i	0.721241	+	1.24923i
$23$	−1.00527	+	0.580391i	−0.209612	+	0.121020i	−0.601131	−	0.799150i	$-0.705283\pi$
$23$	−1.00527	+	0.580391i	−0.209612	+	0.121020i	0.391519	+	0.920170i	$0.371950\pi$
$24$		0			0
$25$	0.316304	−	0.547854i	0.0632608	−	0.109571i
$26$	6.50257			1.27526
$27$		0			0
$28$		0			0
$29$	7.05749	+	4.07464i	1.31054	+	0.756643i	0.982186	−	0.187911i	$-0.0601717\pi$
$29$	7.05749	+	4.07464i	1.31054	+	0.756643i	0.328357	+	0.944554i	$0.393505\pi$
$30$		0			0
$31$	5.16886	−	2.98424i	0.928355	−	0.535986i	0.0420638	−	0.999115i	$-0.486607\pi$
$31$	5.16886	−	2.98424i	0.928355	−	0.535986i	0.886291	+	0.463129i	$0.153273\pi$
$32$	6.98146	−	4.03075i	1.23416	−	0.712542i
$33$		0			0
$34$	−2.96276	−	1.71055i	−0.508109	−	0.293357i
$35$		0			0
$36$		0			0
$37$	−5.65313			−0.929369			−0.464684	−	0.885476i	$-0.653832\pi$
$37$	−5.65313			−0.929369			−0.464684	+	0.885476i	$0.653832\pi$
$38$	5.79620	−	10.0393i	0.940268	−	1.62859i
$39$		0			0
$40$	1.48303	−	0.856225i	0.234487	−	0.135381i
$41$	1.35369	+	2.34465i	0.211410	+	0.366173i	0.952156	−	0.305612i	$-0.0988611\pi$
$41$	1.35369	+	2.34465i	0.211410	+	0.366173i	−0.740746	+	0.671785i	$0.765528\pi$
$42$		0			0
$43$	−0.974903	+	1.68858i	−0.148671	+	0.257506i	−0.930737	−	0.365690i	$-0.880833\pi$
$43$	−0.974903	+	1.68858i	−0.148671	+	0.257506i	0.782065	+	0.623196i	$0.214166\pi$
$44$			7.72014i			1.16385i
$45$		0			0
$46$	−2.43240			−0.358637
$47$	−4.06759	+	7.04527i	−0.593319	+	1.02766i	0.400463	+	0.916313i	$0.368849\pi$
$47$	−4.06759	+	7.04527i	−0.593319	+	1.02766i	−0.993782	+	0.111346i	$0.964484\pi$
$48$		0			0
$49$		0			0
$50$	1.14802	−	0.662809i	0.162354	−	0.0937353i
$51$		0			0
$52$	6.42568	+	3.70987i	0.891082	+	0.514466i
$53$		−	6.09412i		−	0.837092i	−0.908196	−	0.418546i	$-0.862540\pi$
$53$		−	6.09412i		−	0.837092i	0.908196	−	0.418546i	$-0.137460\pi$
$54$		0			0
$55$		−	6.74759i		−	0.909845i
$56$		0			0
$57$		0			0
$58$	8.53834	+	14.7888i	1.12114	+	1.94187i
$59$	1.98103	+	3.43124i	0.257908	+	0.446709i	0.965681	−	0.259730i	$-0.0836336\pi$
$59$	1.98103	+	3.43124i	0.257908	+	0.446709i	−0.707773	+	0.706439i	$0.750300\pi$
$60$		0			0
$61$	4.15016	+	2.39609i	0.531373	+	0.306788i	0.741575	−	0.670869i	$-0.234079\pi$
$61$	4.15016	+	2.39609i	0.531373	+	0.306788i	−0.210202	+	0.977658i	$0.567412\pi$
$62$	12.5068			1.58837
$63$		0			0
$64$	10.7627			1.34534
$65$	−5.61621	−	3.24252i	−0.696605	−	0.402185i
$66$		0			0
$67$	0.336981	+	0.583668i	0.0411687	+	0.0713063i	0.885876	−	0.463923i	$-0.153559\pi$
$67$	0.336981	+	0.583668i	0.0411687	+	0.0713063i	−0.844707	+	0.535229i	$0.820225\pi$
$68$	−1.95182	−	3.38065i	−0.236693	−	0.409963i
$69$		0			0
$70$		0			0
$71$			7.01535i			0.832568i	0.909235	+	0.416284i	$0.136668\pi$
$71$			7.01535i			0.832568i	−0.909235	+	0.416284i	$0.863332\pi$
$72$		0			0
$73$		−	3.42110i		−	0.400409i	−0.979754	−	0.200205i	$-0.935839\pi$
$73$		−	3.42110i		−	0.400409i	0.979754	−	0.200205i	$-0.0641607\pi$
$74$	−10.2590	−	5.92301i	−1.19258	−	0.688536i
$75$		0			0
$76$	11.4553	−	6.61374i	1.31402	−	0.758648i
$77$		0			0
$78$		0			0
$79$	7.07973	−	12.2625i	0.796532	−	1.37963i	−0.125330	−	0.992115i	$-0.539999\pi$
$79$	7.07973	−	12.2625i	0.796532	−	1.37963i	0.921862	−	0.387519i	$-0.126668\pi$
$80$	−6.40534			−0.716138
$81$		0			0
$82$			5.67325i			0.626505i
$83$	−1.54535	+	2.67662i	−0.169624	+	0.293798i	−0.938288	−	0.345856i	$-0.887589\pi$
$83$	−1.54535	+	2.67662i	−0.169624	+	0.293798i	0.768664	+	0.639653i	$0.220922\pi$
$84$		0			0
$85$	1.70594	+	2.95477i	0.185035	+	0.320490i
$86$	−3.53839	+	2.04289i	−0.381554	+	0.220291i
$87$		0			0
$88$	−1.32286	+	2.29127i	−0.141018	+	0.244250i
$89$	−4.91531			−0.521022			−0.260511	−	0.965471i	$-0.583891\pi$
$89$	−4.91531			−0.521022			−0.260511	+	0.965471i	$0.583891\pi$
$90$		0			0
$91$		0			0
$92$	−2.40363	−	1.38774i	−0.250596	−	0.144682i
$93$		0			0
$94$	−14.7632	+	8.52356i	−1.52271	+	0.879138i
$95$	−10.0122	+	5.78057i	−1.02723	+	0.593074i
$96$		0			0
$97$	2.07939	+	1.20054i	0.211130	+	0.121896i	0.601837	−	0.798619i	$-0.294436\pi$
$97$	2.07939	+	1.20054i	0.211130	+	0.121896i	−0.390706	+	0.920515i	$0.627769\pi$
$98$		0			0
$99$		0			0
$100$	1.51259			0.151259
$101$	−1.76025	+	3.04885i	−0.175152	+	0.303372i	−0.940214	−	0.340585i	$-0.889375\pi$
$101$	−1.76025	+	3.04885i	−0.175152	+	0.303372i	0.765062	+	0.643957i	$0.222708\pi$
$102$		0			0
$103$	−13.5832	+	7.84228i	−1.33840	+	0.772723i	−0.986569	−	0.163342i	$-0.947772\pi$
$103$	−13.5832	+	7.84228i	−1.33840	+	0.772723i	−0.351826	+	0.936065i	$0.614439\pi$
$104$	1.27139	+	2.20211i	0.124670	+	0.215935i
$105$		0			0
$106$	6.38506	−	11.0592i	0.620172	−	1.07417i
$107$		−	1.63949i		−	0.158496i	−0.996855	−	0.0792478i	$-0.974748\pi$
$107$		−	1.63949i		−	0.158496i	0.996855	−	0.0792478i	$-0.0252518\pi$
$108$		0			0
$109$	−5.81345			−0.556827			−0.278414	−	0.960461i	$-0.589809\pi$
$109$	−5.81345			−0.556827			−0.278414	+	0.960461i	$0.589809\pi$
$110$	7.06973	−	12.2451i	0.674072	−	1.16753i
$111$		0			0
$112$		0			0
$113$	−13.9931	+	8.07894i	−1.31636	+	0.760003i	−0.983142	−	0.182845i	$-0.941469\pi$
$113$	−13.9931	+	8.07894i	−1.31636	+	0.760003i	−0.333222	+	0.942848i	$0.608136\pi$
$114$		0			0
$115$	2.10084	+	1.21292i	0.195904	+	0.113105i
$116$			19.4853i			1.80916i
$117$		0			0
$118$			8.30241i			0.764299i
$119$		0			0
$120$		0			0
$121$	−0.287505	−	0.497972i	−0.0261368	−	0.0452702i
$122$	5.02097	+	8.69658i	0.454577	+	0.787351i
$123$		0			0
$124$	12.3590	+	7.13545i	1.10987	+	0.640782i
$125$	−11.7712			−1.05285
$126$		0			0
$127$	−9.59240			−0.851188			−0.425594	−	0.904914i	$-0.639935\pi$
$127$	−9.59240			−0.851188			−0.425594	+	0.904914i	$0.639935\pi$
$128$	5.56860	+	3.21503i	0.492199	+	0.284171i
$129$		0			0
$130$	−6.79464	−	11.7687i	−0.595929	−	1.03218i
$131$	1.23061	+	2.13148i	0.107519	+	0.186228i	0.914765	−	0.403987i	$-0.132376\pi$
$131$	1.23061	+	2.13148i	0.107519	+	0.186228i	−0.807246	+	0.590216i	$0.799043\pi$
$132$		0			0
$133$		0			0
$134$			1.41227i			0.122002i
$135$		0			0
$136$		−	1.33779i		−	0.114715i
$137$	−15.0571	−	8.69322i	−1.28641	−	0.742712i	−0.308401	−	0.951256i	$-0.599794\pi$
$137$	−15.0571	−	8.69322i	−1.28641	−	0.742712i	−0.978013	+	0.208545i	$0.933127\pi$
$138$		0			0
$139$	−8.61174	+	4.97199i	−0.730438	+	0.421719i	−0.818582	−	0.574389i	$-0.805240\pi$
$139$	−8.61174	+	4.97199i	−0.730438	+	0.421719i	0.0881443	+	0.996108i	$0.471906\pi$
$140$		0			0
$141$		0			0
$142$	−7.35026	+	12.7310i	−0.616820	+	1.06836i
$143$	10.0193			0.837860
$144$		0			0
$145$		−	17.0306i		−	1.41432i
$146$	3.58442	−	6.20840i	0.296649	−	0.513811i
$147$		0			0
$148$	−6.75843	−	11.7060i	−0.555540	−	0.962223i
$149$	8.01695	−	4.62859i	0.656774	−	0.379189i	−0.134273	−	0.990944i	$-0.542870\pi$
$149$	8.01695	−	4.62859i	0.656774	−	0.379189i	0.791047	+	0.611756i	$0.209536\pi$
$150$		0			0
$151$	5.98489	−	10.3661i	0.487044	−	0.843584i	−0.512845	−	0.858481i	$-0.671409\pi$
$151$	5.98489	−	10.3661i	0.487044	−	0.843584i	0.999889	+	0.0148966i	$0.00474192\pi$
$152$	4.53311			0.367684
$153$		0			0
$154$		0			0
$155$	−10.8020	−	6.23656i	−0.867641	−	0.500933i
$156$		0			0
$157$	−15.4598	+	8.92569i	−1.23382	+	0.712348i	−0.967825	−	0.251626i	$-0.919035\pi$
$157$	−15.4598	+	8.92569i	−1.23382	+	0.712348i	−0.265998	+	0.963974i	$0.585702\pi$
$158$	25.6957	−	14.8354i	2.04424	−	1.18024i
$159$		0			0
$160$	−14.5901	−	8.42358i	−1.15345	−	0.665943i
$161$		0			0
$162$		0			0
$163$	17.8354			1.39697			0.698486	−	0.715623i	$-0.253857\pi$
$163$	17.8354			1.39697			0.698486	+	0.715623i	$0.253857\pi$
$164$	−3.23672	+	5.60616i	−0.252745	+	0.437768i
$165$		0			0
$166$	−5.60881	+	3.23825i	−0.435328	+	0.251337i
$167$	6.16899	+	10.6850i	0.477371	+	0.826830i	0.999664	−	0.0259359i	$-0.00825657\pi$
$167$	6.16899	+	10.6850i	0.477371	+	0.826830i	−0.522293	+	0.852766i	$0.674923\pi$
$168$		0			0
$169$	−1.68526	+	2.91896i	−0.129635	+	0.224535i
$170$			7.14952i			0.548343i
$171$		0			0
$172$	−4.66207			−0.355479
$173$	−4.53368	+	7.85256i	−0.344689	+	0.597019i	−0.985297	−	0.170849i	$-0.945349\pi$
$173$	−4.53368	+	7.85256i	−0.344689	+	0.597019i	0.640608	+	0.767868i	$0.278682\pi$
$174$		0			0
$175$		0			0
$176$	8.57037	−	4.94810i	0.646016	−	0.372977i
$177$		0			0
$178$	−8.92002	−	5.14997i	−0.668584	−	0.386007i
$179$			15.0210i			1.12272i	0.827571	+	0.561362i	$0.189722\pi$
$179$			15.0210i			1.12272i	−0.827571	+	0.561362i	$0.810278\pi$
$180$		0			0
$181$		−	2.34159i		−	0.174049i	−0.996206	−	0.0870246i	$-0.972264\pi$
$181$		−	2.34159i		−	0.174049i	0.996206	−	0.0870246i	$-0.0277359\pi$
$182$		0			0
$183$		0			0
$184$	−0.475584	−	0.823736i	−0.0350605	−	0.0607266i
$185$	5.90704	+	10.2313i	0.434294	+	0.752220i
$186$		0			0
$187$	−4.56510	−	2.63566i	−0.333833	−	0.192739i
$188$	−19.4516			−1.41865
$189$		0			0
$190$	−24.2262			−1.75755
$191$	7.82585	+	4.51825i	0.566258	+	0.326929i	0.755654	−	0.654972i	$-0.227319\pi$
$191$	7.82585	+	4.51825i	0.566258	+	0.326929i	−0.189395	+	0.981901i	$0.560653\pi$
$192$		0			0
$193$	2.74134	+	4.74815i	0.197326	+	0.341779i	0.947661	−	0.319279i	$-0.103441\pi$
$193$	2.74134	+	4.74815i	0.197326	+	0.341779i	−0.750334	+	0.661058i	$0.770108\pi$
$194$	2.51570	+	4.35733i	0.180617	+	0.312838i
$195$		0			0
$196$		0			0
$197$		−	2.88946i		−	0.205865i	−0.994688	−	0.102933i	$-0.967177\pi$
$197$		−	2.88946i		−	0.205865i	0.994688	−	0.102933i	$-0.0328226\pi$
$198$		0			0
$199$			5.14325i			0.364596i	0.983243	+	0.182298i	$0.0583535\pi$
$199$			5.14325i			0.364596i	−0.983243	+	0.182298i	$0.941646\pi$
$200$	0.448923	+	0.259186i	0.0317437	+	0.0183272i
$201$		0			0
$202$	−6.38881	+	3.68858i	−0.449515	+	0.259528i
$203$		0			0
$204$		0			0
$205$	2.82897	−	4.89993i	0.197584	−	0.342226i
$206$	−32.8667			−2.28993
$207$		0			0
$208$		−	9.51113i		−	0.659479i
$209$	8.93095	−	15.4689i	0.617767	−	1.07000i
$210$		0			0
$211$	7.93224	+	13.7390i	0.546078	+	0.945835i	0.998538	+	0.0540502i	$0.0172131\pi$
$211$	7.93224	+	13.7390i	0.546078	+	0.945835i	−0.452460	+	0.891785i	$0.649454\pi$
$212$	12.6191	−	7.28565i	0.866684	−	0.500380i
$213$		0			0
$214$	1.71776	−	2.97525i	0.117424	−	0.203384i
$215$	4.07476			0.277897
$216$		0			0
$217$		0			0
$218$	−10.5499	−	6.09099i	−0.714529	−	0.412534i
$219$		0			0
$220$	13.9723	−	8.06689i	0.942010	−	0.543870i
$221$	−4.38747	+	2.53311i	−0.295133	+	0.170395i
$222$		0			0
$223$	13.5288	+	7.81085i	0.905955	+	0.523053i	0.879127	−	0.476587i	$-0.158126\pi$
$223$	13.5288	+	7.81085i	0.905955	+	0.523053i	0.0268275	+	0.999640i	$0.491460\pi$
$224$		0			0
$225$		0			0
$226$	−33.8586			−2.25224
$227$	1.04045	−	1.80211i	0.0690569	−	0.119610i	−0.829430	−	0.558611i	$-0.811334\pi$
$227$	1.04045	−	1.80211i	0.0690569	−	0.119610i	0.898486	+	0.439001i	$0.144668\pi$
$228$		0			0
$229$	5.57233	−	3.21719i	0.368230	−	0.212598i	−0.304455	−	0.952527i	$-0.598474\pi$
$229$	5.57233	−	3.21719i	0.368230	−	0.212598i	0.672685	+	0.739929i	$0.265141\pi$
$230$	2.54165	+	4.40226i	0.167591	+	0.290277i
$231$		0			0
$232$	−3.33885	+	5.78305i	−0.219206	+	0.379676i
$233$		−	15.6141i		−	1.02291i	−0.859310	−	0.511456i	$-0.829106\pi$
$233$		−	15.6141i		−	1.02291i	0.859310	−	0.511456i	$-0.170894\pi$
$234$		0			0
$235$	17.0011			1.10903
$236$	−4.73672	+	8.20424i	−0.308334	+	0.534050i
$237$		0			0
$238$		0			0
$239$	14.8777	−	8.58964i	0.962358	−	0.555618i	0.0654600	−	0.997855i	$-0.479149\pi$
$239$	14.8777	−	8.58964i	0.962358	−	0.555618i	0.896898	+	0.442238i	$0.145815\pi$
$240$		0			0
$241$	9.71544	+	5.60921i	0.625827	+	0.361321i	0.779134	−	0.626857i	$-0.215659\pi$
$241$	9.71544	+	5.60921i	0.625827	+	0.361321i	−0.153307	+	0.988179i	$0.548992\pi$
$242$		−	1.20492i		−	0.0774552i
$243$		0			0
$244$			11.4583i			0.733544i
$245$		0			0
$246$		0			0
$247$	−8.58343	−	14.8669i	−0.546151	−	0.945961i
$248$	2.44535	+	4.23547i	0.155280	+	0.268953i
$249$		0			0
$250$	−21.3617	−	12.3332i	−1.35103	−	0.780018i
$251$	−11.3837			−0.718535			−0.359267	−	0.933235i	$-0.616973\pi$
$251$	−11.3837			−0.718535			−0.359267	+	0.933235i	$0.616973\pi$
$252$		0			0
$253$	−3.74790			−0.235629
$254$	−17.4077	−	10.0504i	−1.09226	−	0.630615i
$255$		0			0
$256$	−4.02567	−	6.97267i	−0.251604	−	0.435792i
$257$	4.69024	+	8.12373i	0.292569	+	0.506745i	0.974416	−	0.224750i	$-0.0721565\pi$
$257$	4.69024	+	8.12373i	0.292569	+	0.506745i	−0.681847	+	0.731494i	$0.738823\pi$
$258$		0			0
$259$		0			0
$260$		−	15.5060i		−	0.961641i
$261$		0			0
$262$			5.15744i			0.318628i
$263$	−7.62367	−	4.40153i	−0.470096	−	0.271410i	0.246184	−	0.969223i	$-0.420823\pi$
$263$	−7.62367	−	4.40153i	−0.470096	−	0.271410i	−0.716280	+	0.697813i	$0.754157\pi$
$264$		0			0
$265$	−11.0294	+	6.36784i	−0.677532	+	0.391173i
$266$		0			0
$267$		0			0
$268$	−0.805735	+	1.39557i	−0.0492181	+	0.0852482i
$269$	16.3295			0.995625			0.497812	−	0.867285i	$-0.334137\pi$
$269$	16.3295			0.995625			0.497812	+	0.867285i	$0.334137\pi$
$270$		0			0
$271$			14.5708i			0.885111i	0.896741	+	0.442555i	$0.145928\pi$
$271$			14.5708i			0.885111i	−0.896741	+	0.442555i	$0.854072\pi$
$272$	−2.50197	+	4.33355i	−0.151704	+	0.262760i
$273$		0			0
$274$	−18.2165	−	31.5519i	−1.10050	−	1.90612i
$275$	1.76890	−	1.02127i	0.106669	−	0.0615851i
$276$		0			0
$277$	−14.3568	+	24.8668i	−0.862618	+	1.49410i	0.00677410	+	0.999977i	$0.497844\pi$
$277$	−14.3568	+	24.8668i	−0.862618	+	1.49410i	−0.869393	+	0.494122i	$0.835490\pi$
$278$	−20.8374			−1.24975
$279$		0			0
$280$		0			0
$281$	4.76893	+	2.75334i	0.284490	+	0.164251i	0.635455	−	0.772138i	$-0.280813\pi$
$281$	4.76893	+	2.75334i	0.284490	+	0.164251i	−0.350964	+	0.936389i	$0.614146\pi$
$282$		0			0
$283$	26.2257	−	15.1414i	1.55896	−	0.900065i	0.561601	−	0.827408i	$-0.310186\pi$
$283$	26.2257	−	15.1414i	1.55896	−	0.900065i	0.997357	−	0.0726567i	$-0.0231477\pi$
$284$	−14.5267	+	8.38699i	−0.862001	+	0.497676i
$285$		0			0
$286$	18.1825	+	10.4977i	1.07515	+	0.620740i
$287$		0			0
$288$		0			0
$289$	−14.3346			−0.843211
$290$	17.8437	−	30.9062i	1.04782	−	1.81487i
$291$		0			0
$292$	7.08408	−	4.08999i	0.414564	−	0.239349i
$293$	3.54362	+	6.13773i	0.207021	+	0.358570i	0.950775	−	0.309883i	$-0.100290\pi$
$293$	3.54362	+	6.13773i	0.207021	+	0.358570i	−0.743754	+	0.668453i	$0.766957\pi$
$294$		0			0
$295$	4.14001	−	7.17071i	0.241041	−	0.417495i
$296$		−	4.63229i		−	0.269246i
$297$		0			0
$298$	19.3982			1.12371
$299$	−1.80103	+	3.11948i	−0.104156	+	0.180404i
$300$		0			0
$301$		0			0
$302$	21.7220	−	12.5412i	1.24996	−	0.721667i
$303$		0			0
$304$	−14.6842	−	8.47795i	−0.842198	−	0.486244i
$305$		−	10.0149i		−	0.573449i
$306$		0			0
$307$			3.11346i			0.177695i	0.996045	+	0.0888473i	$0.0283183\pi$
$307$			3.11346i			0.177695i	−0.996045	+	0.0888473i	$0.971682\pi$
$308$		0			0
$309$		0			0
$310$	−13.0686	−	22.6355i	−0.742247	−	1.28561i
$311$	−9.72605	−	16.8460i	−0.551514	−	0.955249i	−0.998166	−	0.0605417i	$-0.980717\pi$
$311$	−9.72605	−	16.8460i	−0.551514	−	0.955249i	0.446652	−	0.894708i	$-0.352616\pi$
$312$		0			0
$313$	22.1224	+	12.7724i	1.25043	+	0.721937i	0.971195	−	0.238285i	$-0.0765852\pi$
$313$	22.1224	+	12.7724i	1.25043	+	0.721937i	0.279237	+	0.960222i	$0.409919\pi$
$314$	−37.4073			−2.11101
$315$		0			0
$316$	33.8559			1.90454
$317$	−14.0534	−	8.11372i	−0.789316	−	0.455712i	0.0504056	−	0.998729i	$-0.483949\pi$
$317$	−14.0534	−	8.11372i	−0.789316	−	0.455712i	−0.839722	+	0.543017i	$0.817282\pi$
$318$		0			0
$319$	13.1561	+	22.7871i	0.736601	+	1.27583i
$320$	−11.2461	−	19.4789i	−0.628677	−	1.08890i
$321$		0			0
$322$		0			0
$323$			9.03174i			0.502540i
$324$		0			0
$325$		−	1.96307i		−	0.108892i
$326$	32.3665	+	18.6868i	1.79262	+	1.03497i
$327$		0			0
$328$	−1.92126	+	1.10924i	−0.106084	+	0.0612474i
$329$		0			0
$330$		0			0
$331$	−11.6558	+	20.1885i	−0.640662	+	1.10966i	0.344623	+	0.938741i	$0.388007\pi$
$331$	−11.6558	+	20.1885i	−0.640662	+	1.10966i	−0.985285	+	0.170919i	$0.945326\pi$
$332$	−7.38999			−0.405578
$333$		0			0
$334$			25.8540i			1.41467i
$335$	0.704232	−	1.21977i	0.0384763	−	0.0666430i
$336$		0			0
$337$	5.93515	+	10.2800i	0.323308	+	0.559986i	0.981168	−	0.193154i	$-0.0618717\pi$
$337$	5.93515	+	10.2800i	0.323308	+	0.559986i	−0.657860	+	0.753140i	$0.728538\pi$
$338$	−6.11662	+	3.53143i	−0.332700	+	0.192085i
$339$		0			0
$340$	−4.07897	+	7.06498i	−0.221213	+	0.383152i
$341$	19.2709			1.04358
$342$		0			0
$343$		0			0
$344$	−1.38366	−	0.798855i	−0.0746019	−	0.0430714i
$345$		0			0
$346$	−16.4549	+	9.50024i	−0.884621	+	0.510736i
$347$	18.7979	−	10.8530i	1.00913	−	0.582619i	0.0981903	−	0.995168i	$-0.468695\pi$
$347$	18.7979	−	10.8530i	1.00913	−	0.582619i	0.910936	+	0.412549i	$0.135361\pi$
$348$		0			0
$349$	2.20868	+	1.27518i	0.118228	+	0.0682588i	0.557948	−	0.829876i	$-0.311589\pi$
$349$	2.20868	+	1.27518i	0.118228	+	0.0682588i	−0.439720	+	0.898135i	$0.644922\pi$
$350$		0			0
$351$		0			0
$352$	26.0288			1.38734
$353$	−12.6873	+	21.9751i	−0.675279	+	1.16962i	0.301109	+	0.953590i	$0.402643\pi$
$353$	−12.6873	+	21.9751i	−0.675279	+	1.16962i	−0.976387	+	0.216027i	$0.930690\pi$
$354$		0			0
$355$	12.6967	−	7.33044i	0.673871	−	0.389059i
$356$	−5.87636	−	10.1782i	−0.311446	−	0.539441i
$357$		0			0
$358$	−15.7381	+	27.2592i	−0.831786	+	1.44070i
$359$		−	11.2437i		−	0.593421i	−0.954967	−	0.296711i	$-0.904110\pi$
$359$		−	11.2437i		−	0.593421i	0.954967	−	0.296711i	$-0.0958897\pi$
$360$		0			0
$361$	−11.6041			−0.610741
$362$	2.45338	−	4.24938i	0.128947	−	0.223342i
$363$		0			0
$364$		0			0
$365$	−6.19166	+	3.57476i	−0.324086	+	0.187111i
$366$		0			0
$367$	2.86810	+	1.65590i	0.149714	+	0.0864372i	0.572985	−	0.819566i	$-0.305785\pi$
$367$	2.86810	+	1.65590i	0.149714	+	0.0864372i	−0.423272	+	0.906003i	$0.639118\pi$
$368$			3.55780i			0.185463i
$369$		0			0
$370$			24.7562i			1.28701i
$371$		0			0
$372$		0			0
$373$	3.32271	+	5.75510i	0.172043	+	0.297988i	0.939134	−	0.343551i	$-0.111630\pi$
$373$	3.32271	+	5.75510i	0.172043	+	0.297988i	−0.767091	+	0.641539i	$0.778296\pi$
$374$	−5.52298	−	9.56608i	−0.285586	−	0.494650i
$375$		0			0
$376$	−5.77304	−	3.33307i	−0.297722	−	0.171890i
$377$	25.2884			1.30242
$378$		0			0
$379$	−3.84940			−0.197730			−0.0988652	−	0.995101i	$-0.531521\pi$
$379$	−3.84940			−0.197730			−0.0988652	+	0.995101i	$0.531521\pi$
$380$	−23.9397	−	13.8216i	−1.22808	−	0.709033i
$381$		0			0
$382$	9.46792	+	16.3989i	0.484421	+	0.839041i
$383$	−17.1112	−	29.6374i	−0.874339	−	1.51440i	−0.857465	−	0.514542i	$-0.827962\pi$
$383$	−17.1112	−	29.6374i	−0.874339	−	1.51440i	−0.0168739	−	0.999858i	$-0.505371\pi$
$384$		0			0
$385$		0			0
$386$			11.4889i			0.584768i
$387$		0			0
$388$			5.74107i			0.291459i
$389$	11.6737	+	6.73982i	0.591881	+	0.341723i	0.765841	−	0.643030i	$-0.222323\pi$
$389$	11.6737	+	6.73982i	0.591881	+	0.341723i	−0.173960	+	0.984753i	$0.555656\pi$
$390$		0			0
$391$	1.64121	−	0.947550i	0.0829993	−	0.0479197i
$392$		0			0
$393$		0			0
$394$	3.02740	−	5.24361i	0.152518	−	0.264169i
$395$	−29.5909			−1.48888
$396$		0			0
$397$			29.5027i			1.48070i	0.672223	+	0.740349i	$0.265340\pi$
$397$			29.5027i			1.48070i	−0.672223	+	0.740349i	$0.734660\pi$
$398$	−5.38880	+	9.33367i	−0.270116	+	0.467855i
$399$		0			0
$400$	−0.969472	−	1.67918i	−0.0484736	−	0.0839588i
$401$	−25.1534	+	14.5223i	−1.25610	+	0.725209i	−0.972314	−	0.233678i	$-0.924924\pi$
$401$	−25.1534	+	14.5223i	−1.25610	+	0.725209i	−0.283786	+	0.958888i	$0.591590\pi$
$402$		0			0
$403$	9.26052	−	16.0397i	0.461300	−	0.798994i
$404$	−8.41768			−0.418795
$405$		0			0
$406$		0			0
$407$	−15.8073	−	9.12634i	−0.783538	−	0.452376i
$408$		0			0
$409$	26.2193	−	15.1377i	1.29646	−	0.748513i	0.316671	−	0.948536i	$-0.397435\pi$
$409$	26.2193	−	15.1377i	1.29646	−	0.748513i	0.979791	+	0.200023i	$0.0641017\pi$
$410$	10.2677	−	5.92806i	0.507086	−	0.292766i
$411$		0			0
$412$	−32.4781	−	18.7512i	−1.60008	−	0.923806i
$413$		0			0
$414$		0			0
$415$	6.45904			0.317062
$416$	12.5080	−	21.6645i	0.613254	−	1.06219i
$417$		0			0
$418$	32.4147	−	18.7146i	1.58545	−	0.915363i
$419$	−18.2902	−	31.6795i	−0.893534	−	1.54765i	−0.835609	−	0.549325i	$-0.814885\pi$
$419$	−18.2902	−	31.6795i	−0.893534	−	1.54765i	−0.0579246	−	0.998321i	$-0.518448\pi$
$420$		0			0
$421$	3.85999	−	6.68570i	0.188124	−	0.325841i	−0.756501	−	0.653993i	$-0.773093\pi$
$421$	3.85999	−	6.68570i	0.188124	−	0.325841i	0.944625	+	0.328152i	$0.106426\pi$
$422$			33.2437i			1.61828i
$423$		0			0
$424$	4.99365			0.242513
$425$	−0.516400	+	0.894431i	−0.0250491	+	0.0433863i
$426$		0			0
$427$		0			0
$428$	3.39490	−	1.96005i	0.164099	−	0.0947424i
$429$		0			0
$430$	7.39464	+	4.26930i	0.356601	+	0.205884i
$431$			23.1299i			1.11413i	0.830469	+	0.557065i	$0.188073\pi$
$431$			23.1299i			1.11413i	−0.830469	+	0.557065i	$0.811927\pi$
$432$		0			0
$433$		−	34.9265i		−	1.67846i	−0.543776	−	0.839230i	$-0.683006\pi$
$433$		−	34.9265i		−	1.67846i	0.543776	−	0.839230i	$-0.316994\pi$
$434$		0			0
$435$		0			0
$436$	−6.95010	−	12.0379i	−0.332849	−	0.576512i
$437$	3.21078	+	5.56123i	0.153592	+	0.266030i
$438$		0			0
$439$	−33.6842	−	19.4476i	−1.60766	−	0.928184i	−0.989892	−	0.141824i	$-0.954703\pi$
$439$	−33.6842	−	19.4476i	−1.60766	−	0.928184i	−0.617770	−	0.786359i	$-0.711964\pi$
$440$	5.52912			0.263590
$441$		0			0
$442$	−10.6161			−0.504959
$443$	32.3277	+	18.6644i	1.53594	+	0.886774i	0.999070	+	0.0431065i	$0.0137255\pi$
$443$	32.3277	+	18.6644i	1.53594	+	0.886774i	0.536867	+	0.843667i	$0.319608\pi$
$444$		0			0
$445$	5.13609	+	8.89596i	0.243474	+	0.421709i
$446$	16.3675	+	28.3493i	0.775023	+	1.34238i
$447$		0			0
$448$		0			0
$449$		−	23.9224i		−	1.12897i	−0.825445	−	0.564483i	$-0.809076\pi$
$449$		−	23.9224i		−	1.12897i	0.825445	−	0.564483i	$-0.190924\pi$
$450$		0			0
$451$			8.74150i			0.411621i
$452$	−33.4582	−	19.3171i	−1.57374	−	0.908600i
$453$		0			0
$454$	3.77628	−	2.18024i	0.177230	−	0.102324i
$455$		0			0
$456$		0			0
$457$	−4.99031	+	8.64348i	−0.233437	+	0.404325i	−0.958817	−	0.284024i	$-0.908331\pi$
$457$	−4.99031	+	8.64348i	−0.233437	+	0.404325i	0.725380	+	0.688348i	$0.241664\pi$
$458$	13.4831			0.630024
$459$		0			0
$460$			5.80028i			0.270439i
$461$	−16.7279	+	28.9735i	−0.779094	+	1.34943i	0.153371	+	0.988169i	$0.450987\pi$
$461$	−16.7279	+	28.9735i	−0.779094	+	1.34943i	−0.932465	+	0.361261i	$0.882346\pi$
$462$		0			0
$463$	11.5353	+	19.9798i	0.536092	+	0.928538i	0.999110	+	0.0421893i	$0.0134333\pi$
$463$	11.5353	+	19.9798i	0.536092	+	0.928538i	−0.463018	+	0.886349i	$0.653233\pi$
$464$	21.6312	−	12.4888i	1.00420	−	0.579778i
$465$		0			0
$466$	16.3595	−	28.3355i	0.757839	−	1.31262i
$467$	40.2791			1.86389			0.931946	−	0.362597i	$-0.118110\pi$
$467$	40.2791			1.86389			0.931946	+	0.362597i	$0.118110\pi$
$468$		0			0
$469$		0			0
$470$	30.8527	+	17.8128i	1.42313	+	0.821643i
$471$		0			0
$472$	−2.81163	+	1.62329i	−0.129416	+	0.0747182i
$473$	−5.45205	+	3.14774i	−0.250686	+	0.144733i
$474$		0			0
$475$	−3.03078	−	1.74982i	−0.139062	−	0.0802874i
$476$		0			0
$477$		0			0
$478$	35.9989			1.64655
$479$	−0.0777513	+	0.134669i	−0.00355255	+	0.00615319i	−0.867796	−	0.496920i	$-0.834464\pi$
$479$	−0.0777513	+	0.134669i	−0.00355255	+	0.00615319i	0.864244	+	0.503073i	$0.167797\pi$
$480$		0			0
$481$	−15.1922	+	8.77123i	−0.692705	+	0.399934i
$482$	11.7540	+	20.3585i	0.535380	+	0.927305i
$483$		0			0
$484$	0.687435	−	1.19067i	0.0312471	−	0.0541215i
$485$		−	5.01784i		−	0.227848i
$486$		0			0
$487$	−16.5022			−0.747787			−0.373893	−	0.927472i	$-0.621977\pi$
$487$	−16.5022			−0.747787			−0.373893	+	0.927472i	$0.621977\pi$
$488$	−1.96341	+	3.40072i	−0.0888793	+	0.153944i
$489$		0			0
$490$		0			0
$491$	−8.10003	+	4.67655i	−0.365549	+	0.211050i	−0.671512	−	0.740993i	$-0.734355\pi$
$491$	−8.10003	+	4.67655i	−0.365549	+	0.211050i	0.305963	+	0.952043i	$0.401022\pi$
$492$		0			0
$493$	−11.5221	−	6.65230i	−0.518930	−	0.299604i
$494$		−	35.9729i		−	1.61850i
$495$		0			0
$496$		−	18.2934i		−	0.821399i
$497$		0			0
$498$		0			0
$499$	−0.998116	−	1.72879i	−0.0446818	−	0.0773912i	0.842820	−	0.538196i	$-0.180894\pi$
$499$	−0.998116	−	1.72879i	−0.0446818	−	0.0773912i	−0.887501	+	0.460805i	$0.847561\pi$
$500$	−14.0727	−	24.3746i	−0.629351	−	1.09007i
$501$		0			0
$502$	−20.6585	−	11.9272i	−0.922035	−	0.532337i
$503$	15.7008			0.700063			0.350032	−	0.936738i	$-0.386171\pi$
$503$	15.7008			0.700063			0.350032	+	0.936738i	$0.386171\pi$
$504$		0			0
$505$	7.35727			0.327394
$506$	−6.80147	−	3.92683i	−0.302362	−	0.174569i
$507$		0			0
$508$	−11.4679	−	19.8630i	−0.508807	−	0.881279i
$509$	−7.59893	−	13.1617i	−0.336817	−	0.583383i	0.647016	−	0.762477i	$-0.276017\pi$
$509$	−7.59893	−	13.1617i	−0.336817	−	0.583383i	−0.983832	+	0.179093i	$0.942684\pi$
$510$		0			0
$511$		0			0
$512$		−	29.7316i		−	1.31396i
$513$		0			0
$514$			19.6566i			0.867016i
$515$	28.3867	+	16.3890i	1.25087	+	0.722187i
$516$		0			0
$517$	−22.7476	+	13.1333i	−1.00044	+	0.577603i
$518$		0			0
$519$		0			0
$520$	2.65699	−	4.60204i	0.116517	−	0.201813i
$521$	41.2320			1.80641			0.903204	−	0.429211i	$-0.141208\pi$
$521$	41.2320			1.80641			0.903204	+	0.429211i	$0.141208\pi$
$522$		0			0
$523$		−	42.7598i		−	1.86976i	−0.354970	−	0.934878i	$-0.615509\pi$
$523$		−	42.7598i		−	1.86976i	0.354970	−	0.934878i	$-0.384491\pi$
$524$	−2.94244	+	5.09645i	−0.128541	+	0.222640i
$525$		0			0
$526$	−9.22332	−	15.9753i	−0.402156	−	0.696554i
$527$	−8.43872	+	4.87210i	−0.367596	+	0.212232i
$528$		0			0
$529$	−10.8263	+	18.7517i	−0.470708	+	0.815291i
$530$	−26.6874			−1.15923
$531$		0			0
$532$		0			0
$533$	7.27579	+	4.20068i	0.315149	+	0.181952i
$534$		0			0
$535$	−2.96723	+	1.71313i	−0.128284	+	0.0740650i
$536$	−0.478269	+	0.276129i	−0.0206581	+	0.0119270i
$537$		0			0
$538$	29.6337	+	17.1090i	1.27760	+	0.737623i
$539$		0			0
$540$		0			0
$541$	−16.0862			−0.691599			−0.345800	−	0.938308i	$-0.612392\pi$
$541$	−16.0862			−0.691599			−0.345800	+	0.938308i	$0.612392\pi$
$542$	−15.2664	+	26.4421i	−0.655747	+	1.13579i
$543$		0			0
$544$	−11.3980	+	6.58063i	−0.488685	+	0.282142i
$545$	6.07456	+	10.5214i	0.260206	+	0.450689i
$546$		0			0
$547$	−5.94015	+	10.2886i	−0.253982	+	0.439910i	−0.964619	−	0.263649i	$-0.915074\pi$
$547$	−5.94015	+	10.2886i	−0.253982	+	0.439910i	0.710636	+	0.703560i	$0.248407\pi$
$548$		−	41.5717i		−	1.77585i
$549$		0			0
$550$	4.28012			0.182505
$551$	22.5413	−	39.0427i	0.960293	−	1.66328i
$552$		0			0
$553$		0			0
$554$	−52.1078	+	30.0845i	−2.21385	+	1.27817i
$555$		0			0
$556$	−20.5910	−	11.8882i	−0.873254	−	0.504173i
$557$			30.4848i			1.29168i	0.763472	+	0.645841i	$0.223493\pi$
$557$			30.4848i			1.29168i	−0.763472	+	0.645841i	$0.776507\pi$
$558$		0			0
$559$			6.05052i			0.255910i
$560$		0			0
$561$		0			0
$562$	5.76958	+	9.99320i	0.243375	+	0.421538i
$563$	11.2686	+	19.5177i	0.474914	+	0.822575i	0.999587	−	0.0287288i	$-0.00914592\pi$
$563$	11.2686	+	19.5177i	0.474914	+	0.822575i	−0.524673	+	0.851304i	$0.675813\pi$
$564$		0			0
$565$	29.2433	+	16.8836i	1.23027	+	0.710300i
$566$	63.4572			2.66730
$567$		0			0
$568$	−5.74852			−0.241202
$569$	38.5935	+	22.2819i	1.61792	+	0.934108i	0.987457	+	0.157890i	$0.0504691\pi$
$569$	38.5935	+	22.2819i	1.61792	+	0.934108i	0.630465	+	0.776218i	$0.282864\pi$
$570$		0			0
$571$	−17.6415	−	30.5560i	−0.738274	−	1.27873i	−0.953272	−	0.302113i	$-0.902308\pi$
$571$	−17.6415	−	30.5560i	−0.738274	−	1.27873i	0.214998	−	0.976614i	$-0.431025\pi$
$572$	11.9783	+	20.7471i	0.500839	+	0.867479i
$573$		0			0
$574$		0			0
$575$			0.734319i			0.0306232i
$576$		0			0
$577$			3.75461i			0.156306i	0.996941	+	0.0781531i	$0.0249023\pi$
$577$			3.75461i			0.156306i	−0.996941	+	0.0781531i	$0.975098\pi$
$578$	−26.0136	−	15.0189i	−1.08202	−	0.624705i
$579$		0			0
$580$	35.2654	−	20.3605i	1.46432	−	0.845423i
$581$		0			0
$582$		0			0
$583$	9.83827	−	17.0404i	0.407460	−	0.705741i
$584$	2.80332			0.116002
$585$		0			0
$586$			14.8512i			0.613497i
$587$	15.8021	−	27.3700i	0.652222	−	1.12968i	−0.330361	−	0.943855i	$-0.607171\pi$
$587$	15.8021	−	27.3700i	0.652222	−	1.12968i	0.982583	−	0.185826i	$-0.0594961\pi$
$588$		0			0
$589$	−16.5091	−	28.5946i	−0.680246	−	1.17822i
$590$	15.0261	−	8.67532i	0.618614	−	0.357157i
$591$		0			0
$592$	−8.66343	+	15.0055i	−0.356065	+	0.616722i
$593$	−37.1177			−1.52424			−0.762120	−	0.647436i	$-0.775841\pi$
$593$	−37.1177			−1.52424			−0.762120	+	0.647436i	$0.775841\pi$
$594$		0			0
$595$		0			0
$596$	19.1689	+	11.0671i	0.785187	+	0.453328i
$597$		0			0
$598$	−6.53682	+	3.77403i	−0.267310	+	0.154332i
$599$	−24.5188	+	14.1559i	−1.00181	+	0.578396i	−0.908784	−	0.417267i	$-0.862988\pi$
$599$	−24.5188	+	14.1559i	−1.00181	+	0.578396i	−0.0930277	+	0.995664i	$0.529655\pi$
$600$		0			0
$601$	20.8341	+	12.0286i	0.849840	+	0.490655i	0.860597	−	0.509287i	$-0.170091\pi$
$601$	20.8341	+	12.0286i	0.849840	+	0.490655i	−0.0107568	+	0.999942i	$0.503424\pi$
$602$		0			0
$603$		0			0
$604$	28.6203			1.16454
$605$	−0.600836	+	1.04068i	−0.0244274	+	0.0423096i
$606$		0			0
$607$	8.24496	−	4.76023i	0.334653	−	0.193212i	−0.323252	−	0.946313i	$-0.604776\pi$
$607$	8.24496	−	4.76023i	0.334653	−	0.193212i	0.657905	+	0.753101i	$0.271443\pi$
$608$	−22.2985	−	38.6221i	−0.904323	−	1.56633i
$609$		0			0
$610$	10.4930	−	18.1744i	0.424848	−	0.735859i
$611$			25.2446i			1.02129i
$612$		0			0
$613$	−2.46216			−0.0994459			−0.0497230	−	0.998763i	$-0.515834\pi$
$613$	−2.46216			−0.0994459			−0.0497230	+	0.998763i	$0.515834\pi$
$614$	−3.26210	+	5.65012i	−0.131648	+	0.228020i
$615$		0			0
$616$		0			0
$617$	−18.7738	+	10.8390i	−0.755804	+	0.436364i	−0.827787	−	0.561042i	$-0.810401\pi$
$617$	−18.7738	+	10.8390i	−0.755804	+	0.436364i	0.0719831	+	0.997406i	$0.477067\pi$
$618$		0			0
$619$	−20.8767	−	12.0532i	−0.839105	−	0.484457i	0.0178550	−	0.999841i	$-0.494316\pi$
$619$	−20.8767	−	12.0532i	−0.839105	−	0.484457i	−0.856960	+	0.515383i	$0.827650\pi$
$620$		−	29.8238i		−	1.19775i
$621$		0			0
$622$		−	40.7615i		−	1.63439i
$623$		0			0
$624$		0			0
$625$	10.7184	+	18.5648i	0.428735	+	0.742591i
$626$	26.7643	+	46.3571i	1.06972	+	1.85280i
$627$		0			0
$628$	−36.9649	−	21.3417i	−1.47506	−	0.851627i
$629$	9.22934			0.367998
$630$		0			0
$631$	3.37520			0.134365			0.0671824	−	0.997741i	$-0.478599\pi$
$631$	3.37520			0.134365			0.0671824	+	0.997741i	$0.478599\pi$
$632$	10.0481	+	5.80128i	0.399692	+	0.230762i
$633$		0			0
$634$	−17.0021	−	29.4486i	−0.675242	−	1.16955i
$635$	10.0232	+	17.3608i	0.397761	+	0.688941i
$636$		0			0
$637$		0			0
$638$			55.1368i			2.18289i
$639$		0			0
$640$		−	13.4377i		−	0.531174i
$641$	−30.9152	−	17.8489i	−1.22108	−	0.704989i	−0.255930	−	0.966695i	$-0.582382\pi$
$641$	−30.9152	−	17.8489i	−1.22108	−	0.704989i	−0.965148	+	0.261706i	$0.915715\pi$
$642$		0			0
$643$	3.03956	−	1.75489i	0.119868	−	0.0692060i	−0.438867	−	0.898552i	$-0.644620\pi$
$643$	3.03956	−	1.75489i	0.119868	−	0.0692060i	0.558735	+	0.829346i	$0.311287\pi$
$644$		0			0
$645$		0			0
$646$	−9.46292	+	16.3903i	−0.372314	+	0.644866i
$647$	−14.0599			−0.552752			−0.276376	−	0.961050i	$-0.589134\pi$
$647$	−14.0599			−0.552752			−0.276376	+	0.961050i	$0.589134\pi$
$648$		0			0
$649$			12.7926i			0.502153i
$650$	2.05679	−	3.56246i	0.0806739	−	0.139731i
$651$		0			0
$652$	21.3225	+	36.9317i	0.835055	+	1.44636i
$653$	−10.2675	+	5.92792i	−0.401797	+	0.231978i	−0.687259	−	0.726412i	$-0.741186\pi$
$653$	−10.2675	+	5.92792i	−0.401797	+	0.231978i	0.285462	+	0.958390i	$0.407853\pi$
$654$		0			0
$655$	2.57177	−	4.45443i	0.100487	−	0.174049i
$656$	8.29810			0.323986
$657$		0			0
$658$		0			0
$659$	−5.03144	−	2.90491i	−0.195997	−	0.113159i	0.398790	−	0.917042i	$-0.369430\pi$
$659$	−5.03144	−	2.90491i	−0.195997	−	0.113159i	−0.594787	+	0.803883i	$0.702764\pi$
$660$		0			0
$661$	−8.41592	+	4.85893i	−0.327341	+	0.188991i	−0.654660	−	0.755923i	$-0.727188\pi$
$661$	−8.41592	+	4.85893i	−0.327341	+	0.188991i	0.327319	+	0.944914i	$0.393855\pi$
$662$	−42.3046	+	24.4246i	−1.64422	+	0.949288i
$663$		0			0
$664$	−2.19328	−	1.26629i	−0.0851158	−	0.0491416i
$665$		0			0
$666$		0			0
$667$	−9.45954			−0.366275
$668$	−14.7503	+	25.5483i	−0.570707	+	0.988493i
$669$		0			0
$670$	2.55600	−	1.47571i	0.0987468	−	0.0570115i
$671$	7.73645	+	13.3999i	0.298662	+	0.517298i
$672$		0			0
$673$	13.4646	−	23.3214i	0.519023	−	0.898975i	−0.480732	−	0.876867i	$-0.659629\pi$
$673$	13.4646	−	23.3214i	0.519023	−	0.898975i	0.999756	−	0.0221072i	$-0.00703750\pi$
$674$			24.8740i			0.958110i
$675$		0			0
$676$	−8.05905			−0.309964
$677$	−22.7056	+	39.3273i	−0.872648	+	1.51147i	−0.0134007	+	0.999910i	$0.504266\pi$
$677$	−22.7056	+	39.3273i	−0.872648	+	1.51147i	−0.859247	+	0.511560i	$0.829068\pi$
$678$		0			0
$679$		0			0
$680$	−2.42120	+	1.39788i	−0.0928487	+	0.0536062i
$681$		0			0
$682$	34.9717	+	20.1909i	1.33913	+	0.773150i
$683$		−	43.4795i		−	1.66370i	−0.555003	−	0.831848i	$-0.687283\pi$
$683$		−	43.4795i		−	1.66370i	0.555003	−	0.831848i	$-0.312717\pi$
$684$		0			0
$685$			36.3347i			1.38828i
$686$		0			0
$687$		0			0
$688$	2.98808	+	5.17551i	0.113919	+	0.197314i
$689$	−9.45546	−	16.3773i	−0.360224	−	0.623927i
$690$		0			0
$691$	23.6991	+	13.6827i	0.901557	+	0.520514i	0.877705	−	0.479201i	$-0.159074\pi$
$691$	23.6991	+	13.6827i	0.901557	+	0.520514i	0.0238522	+	0.999715i	$0.492407\pi$
$692$	−21.6804			−0.824166
$693$		0			0
$694$	45.4845			1.72657
$695$	17.9971	+	10.3906i	0.682668	+	0.394139i
$696$		0			0
$697$	−2.21004	−	3.82790i	−0.0837112	−	0.144992i
$698$	2.67212	+	4.62824i	0.101141	+	0.175182i
$699$		0			0
$700$		0			0
$701$		−	8.26437i		−	0.312141i	−0.987746	−	0.156070i	$-0.950117\pi$
$701$		−	8.26437i		−	0.312141i	0.987746	−	0.156070i	$-0.0498827\pi$
$702$		0			0
$703$			31.2737i			1.17951i
$704$	30.0947	+	17.3752i	1.13424	+	0.654852i
$705$		0			0
$706$	−46.0484	+	26.5861i	−1.73306	+	1.00058i
$707$		0			0
$708$		0			0
$709$	−21.4086	+	37.0807i	−0.804015	+	1.39260i	0.112938	+	0.993602i	$0.463974\pi$
$709$	−21.4086	+	37.0807i	−0.804015	+	1.39260i	−0.916954	+	0.398994i	$0.869360\pi$
$710$	30.7216			1.15296
$711$		0			0
$712$		−	4.02771i		−	0.150945i
$713$	−3.46405	+	5.99992i	−0.129730	+	0.224699i
$714$		0			0
$715$	−10.4694	−	18.1335i	−0.391532	−	0.678153i
$716$	−31.1041	+	17.9579i	−1.16241	+	0.671120i
$717$		0			0
$718$	11.7805	−	20.4044i	0.439645	−	0.761487i
$719$	23.1451			0.863165			0.431583	−	0.902073i	$-0.357955\pi$
$719$	23.1451			0.863165			0.431583	+	0.902073i	$0.357955\pi$
$720$		0			0
$721$		0			0
$722$	−21.0584	−	12.1581i	−0.783712	−	0.452477i
$723$		0			0
$724$	4.84874	−	2.79942i	0.180202	−	0.104040i
$725$	4.46462	−	2.57765i	0.165812	−	0.0957316i
$726$		0			0
$727$	4.76878	+	2.75326i	0.176864	+	0.102113i	0.585819	−	0.810442i	$-0.300773\pi$
$727$	4.76878	+	2.75326i	0.176864	+	0.102113i	−0.408954	+	0.912555i	$0.634106\pi$
$728$		0			0
$729$		0			0
$730$	−14.9817			−0.554497
$731$	1.59163	−	2.75679i	0.0588687	−	0.101964i
$732$		0			0
$733$	−3.45543	+	1.99499i	−0.127629	+	0.0736867i	−0.562455	−	0.826828i	$-0.690143\pi$
$733$	−3.45543	+	1.99499i	−0.127629	+	0.0736867i	0.434826	+	0.900514i	$0.356810\pi$
$734$	3.46991	+	6.01005i	0.128077	+	0.221835i
$735$		0			0
$736$	−4.67882	+	8.10395i	−0.172463	+	0.298716i
$737$			2.17607i			0.0801566i
$738$		0			0
$739$	−1.74331			−0.0641289			−0.0320644	−	0.999486i	$-0.510208\pi$
$739$	−1.74331			−0.0641289			−0.0320644	+	0.999486i	$0.510208\pi$
$740$	−14.1240	+	24.4635i	−0.519208	+	0.899295i
$741$		0			0
$742$		0			0
$743$	−8.70204	+	5.02413i	−0.319247	+	0.184317i	−0.651057	−	0.759029i	$-0.725674\pi$
$743$	−8.70204	+	5.02413i	−0.319247	+	0.184317i	0.331810	+	0.943346i	$0.392341\pi$
$744$		0			0
$745$	−16.7541	−	9.67296i	−0.613821	−	0.354390i
$746$			13.9253i			0.509843i
$747$		0			0
$748$		−	12.6040i		−	0.460846i
$749$		0			0
$750$		0			0
$751$	11.6725	+	20.2174i	0.425936	+	0.737743i	0.996507	−	0.0835052i	$-0.0266115\pi$
$751$	11.6725	+	20.2174i	0.425936	+	0.737743i	−0.570571	+	0.821248i	$0.693278\pi$
$752$	12.4672	+	21.5938i	0.454631	+	0.787444i
$753$		0			0
$754$	45.8919	+	26.4957i	1.67128	+	0.964916i
$755$	−25.0148			−0.910383
$756$		0			0
$757$	−14.3334			−0.520957			−0.260479	−	0.965480i	$-0.583880\pi$
$757$	−14.3334			−0.520957			−0.260479	+	0.965480i	$0.583880\pi$
$758$	−6.98566	−	4.03317i	−0.253730	−	0.146491i
$759$		0			0
$760$	−4.73672	−	8.20424i	−0.171819	−	0.297599i
$761$	11.3178	+	19.6029i	0.410268	+	0.710606i	0.994919	−	0.100680i	$-0.0321017\pi$
$761$	11.3178	+	19.6029i	0.410268	+	0.710606i	−0.584650	+	0.811285i	$0.698768\pi$
$762$		0			0
$763$		0			0
$764$			21.6067i			0.781702i
$765$		0			0
$766$		−	71.7122i		−	2.59107i
$767$	10.6476	+	6.14741i	0.384463	+	0.221970i
$768$		0			0
$769$	42.6873	−	24.6455i	1.53934	−	0.888741i	0.540468	−	0.841365i	$-0.318247\pi$
$769$	42.6873	−	24.6455i	1.53934	−	0.888741i	0.998877	−	0.0473762i	$-0.0150860\pi$
$770$		0			0
$771$		0			0
$772$	−6.55467	+	11.3530i	−0.235908	+	0.408604i
$773$	−22.0167			−0.791886			−0.395943	−	0.918275i	$-0.629582\pi$
$773$	−22.0167			−0.791886			−0.395943	+	0.918275i	$0.629582\pi$
$774$		0			0
$775$		−	3.77571i		−	0.135627i
$776$	−0.983745	+	1.70390i	−0.0353144	+	0.0611663i
$777$		0			0
$778$	14.1232	+	24.4621i	0.506340	+	0.877007i
$779$	12.9708	−	7.48872i	0.464729	−	0.268311i
$780$		0			0
$781$	−11.3255	+	19.6163i	−0.405258	+	0.701927i
$782$	3.97115			0.142008
$783$		0			0
$784$		0			0
$785$	32.3083	+	18.6532i	1.15313	+	0.665761i
$786$		0			0
$787$	−9.40107	+	5.42771i	−0.335112	+	0.193477i	−0.658108	−	0.752923i	$-0.728643\pi$
$787$	−9.40107	+	5.42771i	−0.335112	+	0.193477i	0.322996	+	0.946400i	$0.395310\pi$
$788$	5.98320	−	3.45440i	0.213143	−	0.123058i
$789$		0			0
$790$	−53.6998	−	31.0036i	−1.91055	−	1.10306i
$791$		0			0
$792$		0			0
$793$	14.8708			0.528079
$794$	−30.9112	+	53.5397i	−1.09700	+	1.90005i
$795$		0			0
$796$	−10.6502	+	6.14887i	−0.377485	+	0.217941i
$797$	−1.98299	−	3.43465i	−0.0702412	−	0.121661i	0.828766	−	0.559596i	$-0.189044\pi$
$797$	−1.98299	−	3.43465i	−0.0702412	−	0.121661i	−0.899007	+	0.437934i	$0.855710\pi$
$798$		0			0
$799$	6.64078	−	11.5022i	0.234934	−	0.406917i
$800$		−	5.09977i		−	0.180304i
$801$		0			0
$802$	−60.8624			−2.14913
$803$	5.52298	−	9.56608i	0.194902	−	0.337580i
$804$		0			0
$805$		0			0
$806$	33.6109	−	19.4053i	1.18389	−	0.683521i
$807$		0			0
$808$	−2.49829	−	1.44239i	−0.0878896	−	0.0507431i
$809$		−	41.5922i		−	1.46230i	−0.682215	−	0.731152i	$-0.738983\pi$
$809$		−	41.5922i		−	1.46230i	0.682215	−	0.731152i	$-0.261017\pi$
$810$		0			0
$811$		−	13.3293i		−	0.468056i	−0.972230	−	0.234028i	$-0.924809\pi$
$811$		−	13.3293i		−	0.468056i	0.972230	−	0.234028i	$-0.0751907\pi$
$812$		0			0
$813$		0			0
$814$	−19.1241	−	33.1239i	−0.670299	−	1.16099i
$815$	−18.6364	−	32.2792i	−0.652806	−	1.13069i
$816$		0			0
$817$	9.34139	+	5.39326i	0.326814	+	0.188686i
$818$	63.4417			2.21819
$819$		0			0
$820$	13.5284			0.472432
$821$	−33.4332	−	19.3027i	−1.16683	−	0.673668i	−0.213897	−	0.976856i	$-0.568616\pi$
$821$	−33.4332	−	19.3027i	−1.16683	−	0.673668i	−0.952931	+	0.303188i	$0.901949\pi$
$822$		0			0
$823$	5.34881	+	9.26442i	0.186448	+	0.322937i	0.944063	−	0.329764i	$-0.106969\pi$
$823$	5.34881	+	9.26442i	0.186448	+	0.322937i	−0.757616	+	0.652701i	$0.773636\pi$
$824$	−6.42613	−	11.1304i	−0.223865	−	0.387745i
$825$		0			0
$826$		0			0
$827$			11.7079i			0.407125i	0.979062	+	0.203562i	$0.0652520\pi$
$827$			11.7079i			0.407125i	−0.979062	+	0.203562i	$0.934748\pi$
$828$		0			0
$829$		−	17.4300i		−	0.605367i	−0.953091	−	0.302684i	$-0.902117\pi$
$829$		−	17.4300i		−	0.605367i	0.953091	−	0.302684i	$-0.0978826\pi$
$830$	11.7215	+	6.76740i	0.406858	+	0.234900i
$831$		0			0
$832$	28.9237	−	16.6991i	1.00275	−	0.578937i
$833$		0			0
$834$		0			0
$835$	12.8921	−	22.3298i	0.446151	−	0.772756i
$836$	42.7085			1.47711
$837$		0			0
$838$		−	76.6534i		−	2.64795i
$839$	−0.704502	+	1.22023i	−0.0243221	+	0.0421271i	−0.877930	−	0.478789i	$-0.841076\pi$
$839$	−0.704502	+	1.22023i	−0.0243221	+	0.0421271i	0.853608	+	0.520916i	$0.174409\pi$
$840$		0			0
$841$	18.7055	+	32.3988i	0.645016	+	1.11720i
$842$	14.0097	−	8.08853i	0.482808	−	0.278749i
$843$		0			0
$844$	−18.9663	+	32.8506i	−0.652848	+	1.13077i
$845$	7.04382			0.242315
$846$		0			0
$847$		0			0
$848$	−16.1761	−	9.33925i	−0.555488	−	0.320711i
$849$		0			0
$850$	−1.87426	+	1.08211i	−0.0642867	+	0.0371160i
$851$	5.68290	−	3.28102i	0.194807	−	0.112472i
$852$		0			0
$853$	−28.0716	−	16.2071i	−0.961153	−	0.554922i	−0.0646255	−	0.997910i	$-0.520585\pi$
$853$	−28.0716	−	16.2071i	−0.961153	−	0.554922i	−0.896528	+	0.442987i	$0.853919\pi$
$854$		0			0
$855$		0			0
$856$	1.34343			0.0459176
$857$	22.2270	−	38.4982i	0.759258	−	1.31507i	−0.183971	−	0.982932i	$-0.558895\pi$
$857$	22.2270	−	38.4982i	0.759258	−	1.31507i	0.943229	−	0.332142i	$-0.107771\pi$
$858$		0			0
$859$	13.5528	−	7.82472i	0.462416	−	0.266976i	−0.250644	−	0.968079i	$-0.580642\pi$
$859$	13.5528	−	7.82472i	0.462416	−	0.266976i	0.713060	+	0.701103i	$0.247309\pi$
$860$	4.87147	+	8.43763i	0.166116	+	0.287721i
$861$		0			0
$862$	−24.2342	+	41.9748i	−0.825420	+	1.42967i
$863$		−	18.1185i		−	0.616762i	−0.951263	−	0.308381i	$-0.900213\pi$
$863$		−	18.1185i		−	0.616762i	0.951263	−	0.308381i	$-0.0997872\pi$
$864$		0			0
$865$	18.9492			0.644294
$866$	36.5939	−	63.3825i	1.24351	−	2.15383i
$867$		0			0
$868$		0			0
$869$	39.5927	−	22.8589i	1.34309	−	0.775434i
$870$		0			0
$871$	1.81120	+	1.04570i	0.0613703	+	0.0354321i
$872$		−	4.76366i		−	0.161318i
$873$		0			0
$874$			13.4562i			0.455164i
$875$		0			0
$876$		0			0
$877$	1.38926	+	2.40628i	0.0469121	+	0.0812542i	0.888528	−	0.458822i	$-0.151729\pi$
$877$	1.38926	+	2.40628i	0.0469121	+	0.0812542i	−0.841616	+	0.540077i	$0.818395\pi$
$878$	−40.7521	−	70.5847i	−1.37532	−	2.38212i
$879$		0			0
$880$	−17.9106	−	10.3407i	−0.603767	−	0.348585i
$881$	1.96106			0.0660696			0.0330348	−	0.999454i	$-0.489483\pi$
$881$	1.96106			0.0660696			0.0330348	+	0.999454i	$0.489483\pi$
$882$		0			0
$883$	−36.9657			−1.24400			−0.621998	−	0.783019i	$-0.713679\pi$
$883$	−36.9657			−1.24400			−0.621998	+	0.783019i	$0.713679\pi$
$884$	−10.4906	−	6.05676i	−0.352838	−	0.203711i
$885$		0			0
$886$	39.1110	+	67.7422i	1.31396	+	2.27584i
$887$	−11.2584	−	19.5001i	−0.378020	−	0.654750i	0.612754	−	0.790274i	$-0.290062\pi$
$887$	−11.2584	−	19.5001i	−0.378020	−	0.654750i	−0.990774	+	0.135524i	$0.956728\pi$
$888$		0			0
$889$		0			0
$890$			21.5251i			0.721525i
$891$		0			0
$892$			37.3521i			1.25064i
$893$	38.9751	+	22.5023i	1.30425	+	0.753011i
$894$		0			0
$895$	27.1857	−	15.6957i	0.908719	−	0.524649i
$896$		0			0
$897$		0			0
$898$	25.0644	−	43.4129i	0.836411	−	1.44871i
$899$	48.6389			1.62220
$900$		0			0
$901$			9.94931i			0.331459i
$902$	−9.15882	+	15.8635i	−0.304955	+	0.528198i
$903$		0			0
$904$	−6.62005	−	11.4663i	−0.220180	−	0.381362i
$905$	−4.23792	+	2.44676i	−0.140873	+	0.0813332i
$906$		0			0
$907$	9.55982	−	16.5581i	0.317428	−	0.549802i	−0.662522	−	0.749042i	$-0.730514\pi$
$907$	9.55982	−	16.5581i	0.317428	−	0.549802i	0.979951	+	0.199240i	$0.0638473\pi$
$908$	4.97550			0.165118
$909$		0			0
$910$		0			0
$911$	−4.92610	−	2.84408i	−0.163209	−	0.0942287i	0.416171	−	0.909286i	$-0.363372\pi$
$911$	−4.92610	−	2.84408i	−0.163209	−	0.0942287i	−0.579380	+	0.815058i	$0.696705\pi$
$912$		0			0
$913$	−8.64222	+	4.98959i	−0.286016	+	0.165131i
$914$	−18.1122	+	10.4571i	−0.599100	+	0.345890i
$915$		0			0
$916$	13.3237	+	7.69242i	0.440226	+	0.254165i
$917$		0			0
$918$		0			0
$919$	21.8510			0.720798			0.360399	−	0.932798i	$-0.382640\pi$
$919$	21.8510			0.720798			0.360399	+	0.932798i	$0.382640\pi$
$920$	−0.993890	+	1.72147i	−0.0327676	+	0.0567551i
$921$		0			0
$922$	−60.7134	+	35.0529i	−1.99949	+	1.15441i
$923$	10.8848	+	18.8530i	0.358278	+	0.620555i
$924$		0			0
$925$	−1.78811	+	3.09709i	−0.0587926	+	0.101832i
$926$			48.3441i			1.58869i
$927$		0			0
$928$	65.6955			2.15656
$929$	−8.08806	+	14.0089i	−0.265361	+	0.459618i	−0.967658	−	0.252266i	$-0.918824\pi$
$929$	−8.08806	+	14.0089i	−0.265361	+	0.459618i	0.702297	+	0.711884i	$0.252158\pi$
$930$		0			0
$931$		0			0
$932$	32.3321	−	18.6669i	1.05907	−	0.611456i
$933$		0			0
$934$	73.0960	+	42.2020i	2.39177	+	1.38089i
$935$			11.0162i			0.360267i
$936$		0			0
$937$			14.0440i			0.458799i	0.973332	+	0.229400i	$0.0736762\pi$
$937$			14.0440i			0.458799i	−0.973332	+	0.229400i	$0.926324\pi$
$938$		0			0
$939$		0			0
$940$	20.3252	+	35.2043i	0.662936	+	1.14824i
$941$	−21.5934	−	37.4009i	−0.703924	−	1.21923i	−0.967078	−	0.254479i	$-0.918096\pi$
$941$	−21.5934	−	37.4009i	−0.703924	−	1.21923i	0.263154	−	0.964754i	$-0.415237\pi$
$942$		0			0
$943$	−2.72163	−	1.57133i	−0.0886284	−	0.0511696i
$944$	12.1437			0.395244
$945$		0			0
$946$	−13.1921			−0.428911
$947$	16.6235	+	9.59758i	0.540191	+	0.311879i	0.745156	−	0.666890i	$-0.232375\pi$
$947$	16.6235	+	9.59758i	0.540191	+	0.311879i	−0.204965	+	0.978769i	$0.565708\pi$
$948$		0			0
$949$	−5.30807	−	9.19386i	−0.172307	−	0.298445i
$950$	−3.66672	−	6.35095i	−0.118964	−	0.206052i
$951$		0			0
$952$		0			0
$953$		−	5.62718i		−	0.182282i	−0.995838	−	0.0911411i	$-0.970949\pi$
$953$		−	5.62718i		−	0.182282i	0.995838	−	0.0911411i	$-0.0290514\pi$
$954$		0			0
$955$		−	18.8848i		−	0.611097i
$956$	35.5732	+	20.5382i	1.15052	+	0.664252i
$957$		0			0
$958$	−0.282197	+	0.162926i	−0.00911736	+	0.00526391i
$959$		0			0
$960$		0			0
$961$	2.31141	−	4.00348i	0.0745616	−	0.129144i
$962$	−36.7599			−1.18519
$963$		0			0
$964$			26.8237i			0.863934i
$965$	5.72894	−	9.92282i	0.184421	−	0.319427i
$966$		0			0
$967$	−7.62091	−	13.1998i	−0.245072	−	0.424477i	0.717080	−	0.696991i	$-0.245478\pi$
$967$	−7.62091	−	13.1998i	−0.245072	−	0.424477i	−0.962152	+	0.272514i	$0.912145\pi$
$968$	0.408049	−	0.235587i	0.0131152	−	0.00757206i
$969$		0			0
$970$	5.25740	−	9.10608i	0.168805	−	0.292379i
$971$	−40.8958			−1.31241			−0.656205	−	0.754583i	$-0.727839\pi$
$971$	−40.8958			−1.31241			−0.656205	+	0.754583i	$0.727839\pi$
$972$		0			0
$973$		0			0
$974$	−29.9472	−	17.2900i	−0.959571	−	0.554009i
$975$		0			0
$976$	12.7202	−	7.34404i	0.407165	−	0.235077i
$977$	8.98296	−	5.18631i	0.287390	−	0.165925i	−0.349374	−	0.936983i	$-0.613606\pi$
$977$	8.98296	−	5.18631i	0.287390	−	0.165925i	0.636764	+	0.771058i	$0.280272\pi$
$978$		0			0
$979$	−13.7442	−	7.93522i	−0.439267	−	0.253611i
$980$		0			0
$981$		0			0
$982$	−19.5993			−0.625438
$983$	1.05850	−	1.83338i	0.0337609	−	0.0584756i	−0.848651	−	0.528953i	$-0.822585\pi$
$983$	1.05850	−	1.83338i	0.0337609	−	0.0584756i	0.882412	+	0.470477i	$0.155918\pi$
$984$		0			0
$985$	−5.22947	+	3.01924i	−0.166625	+	0.0962009i
$986$	−13.9398	−	24.1444i	−0.443932	−	0.768914i
$987$		0			0
$988$	20.5234	−	35.5475i	0.652935	−	1.13092i
$989$		−	2.26330i		−	0.0719687i
$990$		0			0
$991$	34.1163			1.08374			0.541870	−	0.840462i	$-0.317717\pi$
$991$	34.1163			1.08374			0.541870	+	0.840462i	$0.317717\pi$
$992$	24.0575	−	41.6688i	0.763825	−	1.32298i
$993$		0			0
$994$		0			0
$995$	9.30850	−	5.37427i	0.295099	−	0.170376i
$996$		0			0
$997$	39.6843	+	22.9118i	1.25682	+	0.725623i	0.972454	−	0.233094i	$-0.0748851\pi$
$997$	39.6843	+	22.9118i	1.25682	+	0.725623i	0.284361	+	0.958717i	$0.408218\pi$
$998$		−	4.18307i		−	0.132413i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.o.d.440.5		10
3.2	odd	2		441.2.o.c.146.1		10
7.2	even	3		1323.2.i.b.521.1		10
7.3	odd	6		1323.2.s.b.656.1		10
7.4	even	3		189.2.s.b.89.1		10
7.5	odd	6		189.2.i.b.143.1		10
7.6	odd	2		1323.2.o.c.440.5		10
9.4	even	3		441.2.o.d.293.1		10
9.5	odd	6		1323.2.o.c.881.5		10
21.2	odd	6		441.2.i.b.227.5		10
21.5	even	6		63.2.i.b.38.5	yes	10
21.11	odd	6		63.2.s.b.47.5	yes	10
21.17	even	6		441.2.s.b.362.5		10
21.20	even	2		441.2.o.d.146.1		10
28.11	odd	6		3024.2.df.b.1601.5		10
28.19	even	6		3024.2.ca.b.2033.5		10
63.4	even	3		63.2.i.b.5.1	✓	10
63.5	even	6		189.2.s.b.17.1		10
63.11	odd	6		567.2.p.c.404.1		10
63.13	odd	6		441.2.o.c.293.1		10
63.23	odd	6		1323.2.s.b.962.1		10
63.25	even	3		567.2.p.d.404.5		10
63.31	odd	6		441.2.i.b.68.1		10
63.32	odd	6		189.2.i.b.152.5		10
63.40	odd	6		63.2.s.b.59.5	yes	10
63.41	even	6	inner	1323.2.o.d.881.5		10
63.47	even	6		567.2.p.d.80.5		10
63.58	even	3		441.2.s.b.374.5		10
63.59	even	6		1323.2.i.b.1097.5		10
63.61	odd	6		567.2.p.c.80.1		10
84.11	even	6		1008.2.df.b.929.3		10
84.47	odd	6		1008.2.ca.b.353.5		10
252.67	odd	6		1008.2.ca.b.257.5		10
252.95	even	6		3024.2.ca.b.2609.5		10
252.103	even	6		1008.2.df.b.689.3		10
252.131	odd	6		3024.2.df.b.17.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.1	✓	10	63.4	even	3
63.2.i.b.38.5	yes	10	21.5	even	6
63.2.s.b.47.5	yes	10	21.11	odd	6
63.2.s.b.59.5	yes	10	63.40	odd	6
189.2.i.b.143.1		10	7.5	odd	6
189.2.i.b.152.5		10	63.32	odd	6
189.2.s.b.17.1		10	63.5	even	6
189.2.s.b.89.1		10	7.4	even	3
441.2.i.b.68.1		10	63.31	odd	6
441.2.i.b.227.5		10	21.2	odd	6
441.2.o.c.146.1		10	3.2	odd	2
441.2.o.c.293.1		10	63.13	odd	6
441.2.o.d.146.1		10	21.20	even	2
441.2.o.d.293.1		10	9.4	even	3
441.2.s.b.362.5		10	21.17	even	6
441.2.s.b.374.5		10	63.58	even	3
567.2.p.c.80.1		10	63.61	odd	6
567.2.p.c.404.1		10	63.11	odd	6
567.2.p.d.80.5		10	63.47	even	6
567.2.p.d.404.5		10	63.25	even	3
1008.2.ca.b.257.5		10	252.67	odd	6
1008.2.ca.b.353.5		10	84.47	odd	6
1008.2.df.b.689.3		10	252.103	even	6
1008.2.df.b.929.3		10	84.11	even	6
1323.2.i.b.521.1		10	7.2	even	3
1323.2.i.b.1097.5		10	63.59	even	6
1323.2.o.c.440.5		10	7.6	odd	2
1323.2.o.c.881.5		10	9.5	odd	6
1323.2.o.d.440.5		10	1.1	even	1	trivial
1323.2.o.d.881.5		10	63.41	even	6	inner
1323.2.s.b.656.1		10	7.3	odd	6
1323.2.s.b.962.1		10	63.23	odd	6
3024.2.ca.b.2033.5		10	28.19	even	6
3024.2.ca.b.2609.5		10	252.95	even	6
3024.2.df.b.17.5		10	252.131	odd	6
3024.2.df.b.1601.5		10	28.11	odd	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)

\(f(q)\)	\(=\)	\(q+(1.81474 + 1.04774i) q^{2} +(1.19552 + 2.07070i) q^{4} +(-1.04492 - 1.80985i) q^{5} +0.819421i q^{8} +O(q^{10})\)	\(q+(1.81474 + 1.04774i) q^{2} +(1.19552 + 2.07070i) q^{4} +(-1.04492 - 1.80985i) q^{5} +0.819421i q^{8} -4.37920i q^{10} +(2.79620 + 1.61439i) q^{11} +(2.68740 - 1.55157i) q^{13} +(1.53250 - 2.65437i) q^{16} -1.63261 q^{17} -5.53210i q^{19} +(2.49844 - 4.32742i) q^{20} +(3.38292 + 5.85939i) q^{22} +(-1.00527 + 0.580391i) q^{23} +(0.316304 - 0.547854i) q^{25} +6.50257 q^{26} +(7.05749 + 4.07464i) q^{29} +(5.16886 - 2.98424i) q^{31} +(6.98146 - 4.03075i) q^{32} +(-2.96276 - 1.71055i) q^{34} -5.65313 q^{37} +(5.79620 - 10.0393i) q^{38} +(1.48303 - 0.856225i) q^{40} +(1.35369 + 2.34465i) q^{41} +(-0.974903 + 1.68858i) q^{43} +7.72014i q^{44} -2.43240 q^{46} +(-4.06759 + 7.04527i) q^{47} +(1.14802 - 0.662809i) q^{50} +(6.42568 + 3.70987i) q^{52} -6.09412i q^{53} -6.74759i q^{55} +(8.53834 + 14.7888i) q^{58} +(1.98103 + 3.43124i) q^{59} +(4.15016 + 2.39609i) q^{61} +12.5068 q^{62} +10.7627 q^{64} +(-5.61621 - 3.24252i) q^{65} +(0.336981 + 0.583668i) q^{67} +(-1.95182 - 3.38065i) q^{68} +7.01535i q^{71} -3.42110i q^{73} +(-10.2590 - 5.92301i) q^{74} +(11.4553 - 6.61374i) q^{76} +(7.07973 - 12.2625i) q^{79} -6.40534 q^{80} +5.67325i q^{82} +(-1.54535 + 2.67662i) q^{83} +(1.70594 + 2.95477i) q^{85} +(-3.53839 + 2.04289i) q^{86} +(-1.32286 + 2.29127i) q^{88} -4.91531 q^{89} +(-2.40363 - 1.38774i) q^{92} +(-14.7632 + 8.52356i) q^{94} +(-10.0122 + 5.78057i) q^{95} +(2.07939 + 1.20054i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4}+O(q^{10}) \) 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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