LMFDB - Embedded newform 1323.2.o.c.881.5

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			881.5
Root			$0.827154 - 1.43267i$ of defining polynomial
Character	$\chi$	$=$	1323.881
Dual form			1323.2.o.c.440.5

$q$-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 $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.81474	−	1.04774i	1.28321	−	0.740865i	0.305780	−	0.952102i	$-0.401083\pi$
$2$	1.81474	−	1.04774i	1.28321	−	0.740865i	0.977435	+	0.211238i	$0.0677494\pi$
$3$		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	$-0.678560\pi$
$5$	1.04492	−	1.80985i	0.467300	−	0.809388i	0.999302	+	0.0373553i	$0.0118933\pi$
$6$		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	−0.0152257	−	0.999884i	$-0.504847\pi$
$11$	2.79620	−	1.61439i	0.843086	−	0.486756i	0.858312	+	0.513128i	$0.171513\pi$
$12$		0			0
$13$	−2.68740	−	1.55157i	−0.745350	−	0.430328i	0.0786612	−	0.996901i	$-0.474935\pi$
$13$	−2.68740	−	1.55157i	−0.745350	−	0.430328i	−0.824011	+	0.566573i	$0.808269\pi$
$14$		0			0
$15$		0			0
$16$	1.53250	+	2.65437i	0.383125	+	0.663593i
$17$	1.63261			0.395966			0.197983	−	0.980206i	$-0.436561\pi$
$17$	1.63261			0.395966			0.197983	+	0.980206i	$0.436561\pi$
$18$		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	0.391519	−	0.920170i	$-0.371950\pi$
$23$	−1.00527	−	0.580391i	−0.209612	−	0.121020i	−0.601131	+	0.799150i	$0.705283\pi$
$24$		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	0.328357	−	0.944554i	$-0.393505\pi$
$29$	7.05749	−	4.07464i	1.31054	−	0.756643i	0.982186	+	0.187911i	$0.0601717\pi$
$30$		0			0
$31$	−5.16886	−	2.98424i	−0.928355	−	0.535986i	−0.0420638	−	0.999115i	$-0.513393\pi$
$31$	−5.16886	−	2.98424i	−0.928355	−	0.535986i	−0.886291	+	0.463129i	$0.846727\pi$
$32$	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	$-0.901139\pi$
$41$	−1.35369	+	2.34465i	−0.211410	+	0.366173i	0.740746	+	0.671785i	$0.234472\pi$
$42$		0			0
$43$	−0.974903	−	1.68858i	−0.148671	−	0.257506i	0.782065	−	0.623196i	$-0.214166\pi$
$43$	−0.974903	−	1.68858i	−0.148671	−	0.257506i	−0.930737	+	0.365690i	$0.880833\pi$
$44$		−	7.72014i		−	1.16385i
$45$		0			0
$46$	−2.43240			−0.358637
$47$	4.06759	+	7.04527i	0.593319	+	1.02766i	0.993782	+	0.111346i	$0.0355161\pi$
$47$	4.06759	+	7.04527i	0.593319	+	1.02766i	−0.400463	+	0.916313i	$0.631151\pi$
$48$		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	$0.137460\pi$
$53$			6.09412i			0.837092i	−0.908196	+	0.418546i	$0.862540\pi$
$54$		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	$-0.916366\pi$
$59$	−1.98103	+	3.43124i	−0.257908	+	0.446709i	0.707773	+	0.706439i	$0.249700\pi$
$60$		0			0
$61$	−4.15016	+	2.39609i	−0.531373	+	0.306788i	−0.741575	−	0.670869i	$-0.765921\pi$
$61$	−4.15016	+	2.39609i	−0.531373	+	0.306788i	0.210202	+	0.977658i	$0.432588\pi$
$62$	−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	−0.844707	−	0.535229i	$-0.820225\pi$
$67$	0.336981	−	0.583668i	0.0411687	−	0.0713063i	0.885876	+	0.463923i	$0.153559\pi$
$68$	1.95182	−	3.38065i	0.236693	−	0.409963i
$69$		0			0
$70$		0			0
$71$		−	7.01535i		−	0.832568i	−0.909235	−	0.416284i	$-0.863332\pi$
$71$		−	7.01535i		−	0.832568i	0.909235	−	0.416284i	$-0.136668\pi$
$72$		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	0.921862	+	0.387519i	$0.126668\pi$
$79$	7.07973	+	12.2625i	0.796532	+	1.37963i	−0.125330	+	0.992115i	$0.539999\pi$
$80$	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	$-0.112411\pi$
$83$	1.54535	+	2.67662i	0.169624	+	0.293798i	−0.768664	+	0.639653i	$0.779078\pi$
$84$		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	$-0.416109\pi$
$89$	4.91531			0.521022			0.260511	+	0.965471i	$0.416109\pi$
$90$		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	$-0.705564\pi$
$97$	−2.07939	+	1.20054i	−0.211130	+	0.121896i	0.390706	+	0.920515i	$0.372231\pi$
$98$		0			0
$99$		0			0
$100$	1.51259			0.151259
$101$	1.76025	+	3.04885i	0.175152	+	0.303372i	0.940214	−	0.340585i	$-0.110625\pi$
$101$	1.76025	+	3.04885i	0.175152	+	0.303372i	−0.765062	+	0.643957i	$0.777292\pi$
$102$		0			0
$103$	13.5832	+	7.84228i	1.33840	+	0.772723i	0.986569	−	0.163342i	$-0.0522275\pi$
$103$	13.5832	+	7.84228i	1.33840	+	0.772723i	0.351826	+	0.936065i	$0.385561\pi$
$104$	−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	$0.0252518\pi$
$107$			1.63949i			0.158496i	−0.996855	+	0.0792478i	$0.974748\pi$
$108$		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	−0.333222	−	0.942848i	$-0.608136\pi$
$113$	−13.9931	−	8.07894i	−1.31636	−	0.760003i	−0.983142	+	0.182845i	$0.941469\pi$
$114$		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	$-0.867624\pi$
$131$	−1.23061	+	2.13148i	−0.107519	+	0.186228i	0.807246	+	0.590216i	$0.200957\pi$
$132$		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	−0.978013	−	0.208545i	$-0.933127\pi$
$137$	−15.0571	+	8.69322i	−1.28641	+	0.742712i	−0.308401	+	0.951256i	$0.599794\pi$
$138$		0			0
$139$	8.61174	+	4.97199i	0.730438	+	0.421719i	0.818582	−	0.574389i	$-0.194760\pi$
$139$	8.61174	+	4.97199i	0.730438	+	0.421719i	−0.0881443	+	0.996108i	$0.528094\pi$
$140$		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	0.791047	−	0.611756i	$-0.209536\pi$
$149$	8.01695	+	4.62859i	0.656774	+	0.379189i	−0.134273	+	0.990944i	$0.542870\pi$
$150$		0			0
$151$	5.98489	+	10.3661i	0.487044	+	0.843584i	0.999889	−	0.0148966i	$-0.00474192\pi$
$151$	5.98489	+	10.3661i	0.487044	+	0.843584i	−0.512845	+	0.858481i	$0.671409\pi$
$152$	−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	$-0.0809651\pi$
$157$	15.4598	+	8.92569i	1.23382	+	0.712348i	0.265998	+	0.963974i	$0.414298\pi$
$158$	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	$-0.991743\pi$
$167$	−6.16899	+	10.6850i	−0.477371	+	0.826830i	0.522293	+	0.852766i	$0.325077\pi$
$168$		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	$-0.0546509\pi$
$173$	4.53368	+	7.85256i	0.344689	+	0.597019i	−0.640608	+	0.767868i	$0.721318\pi$
$174$		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	$-0.810278\pi$
$179$		−	15.0210i		−	1.12272i	0.827571	−	0.561362i	$-0.189722\pi$
$180$		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	−0.189395	−	0.981901i	$-0.560653\pi$
$191$	7.82585	−	4.51825i	0.566258	−	0.326929i	0.755654	+	0.654972i	$0.227319\pi$
$192$		0			0
$193$	2.74134	−	4.74815i	0.197326	−	0.341779i	−0.750334	−	0.661058i	$-0.770108\pi$
$193$	2.74134	−	4.74815i	0.197326	−	0.341779i	0.947661	+	0.319279i	$0.103441\pi$
$194$	−2.51570	+	4.35733i	−0.180617	+	0.312838i
$195$		0			0
$196$		0			0
$197$			2.88946i			0.205865i	0.994688	+	0.102933i	$0.0328226\pi$
$197$			2.88946i			0.205865i	−0.994688	+	0.102933i	$0.967177\pi$
$198$		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	−0.452460	−	0.891785i	$-0.649454\pi$
$211$	7.93224	−	13.7390i	0.546078	−	0.945835i	0.998538	−	0.0540502i	$-0.0172131\pi$
$212$	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	$-0.841874\pi$
$223$	−13.5288	+	7.81085i	−0.905955	+	0.523053i	−0.0268275	+	0.999640i	$0.508540\pi$
$224$		0			0
$225$		0			0
$226$	−33.8586			−2.25224
$227$	−1.04045	−	1.80211i	−0.0690569	−	0.119610i	0.829430	−	0.558611i	$-0.188666\pi$
$227$	−1.04045	−	1.80211i	−0.0690569	−	0.119610i	−0.898486	+	0.439001i	$0.855332\pi$
$228$		0			0
$229$	−5.57233	−	3.21719i	−0.368230	−	0.212598i	0.304455	−	0.952527i	$-0.401526\pi$
$229$	−5.57233	−	3.21719i	−0.368230	−	0.212598i	−0.672685	+	0.739929i	$0.734859\pi$
$230$	−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	$0.170894\pi$
$233$			15.6141i			1.02291i	−0.859310	+	0.511456i	$0.829106\pi$
$234$		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	0.896898	−	0.442238i	$-0.145815\pi$
$239$	14.8777	+	8.58964i	0.962358	+	0.555618i	0.0654600	+	0.997855i	$0.479149\pi$
$240$		0			0
$241$	−9.71544	+	5.60921i	−0.625827	+	0.361321i	−0.779134	−	0.626857i	$-0.784341\pi$
$241$	−9.71544	+	5.60921i	−0.625827	+	0.361321i	0.153307	+	0.988179i	$0.451008\pi$
$242$			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	$-0.383027\pi$
$251$	11.3837			0.718535			0.359267	+	0.933235i	$0.383027\pi$
$252$		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	$-0.927843\pi$
$257$	−4.69024	+	8.12373i	−0.292569	+	0.506745i	0.681847	+	0.731494i	$0.261177\pi$
$258$		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	−0.716280	−	0.697813i	$-0.754157\pi$
$263$	−7.62367	+	4.40153i	−0.470096	+	0.271410i	0.246184	+	0.969223i	$0.420823\pi$
$264$		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	$-0.665863\pi$
$269$	−16.3295			−0.995625			−0.497812	+	0.867285i	$0.665863\pi$
$270$		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	−0.869393	−	0.494122i	$-0.835490\pi$
$277$	−14.3568	−	24.8668i	−0.862618	−	1.49410i	0.00677410	−	0.999977i	$-0.497844\pi$
$278$	20.8374			1.24975
$279$		0			0
$280$		0			0
$281$	4.76893	−	2.75334i	0.284490	−	0.164251i	−0.350964	−	0.936389i	$-0.614146\pi$
$281$	4.76893	−	2.75334i	0.284490	−	0.164251i	0.635455	+	0.772138i	$0.280813\pi$
$282$		0			0
$283$	−26.2257	−	15.1414i	−1.55896	−	0.900065i	−0.997357	−	0.0726567i	$-0.976852\pi$
$283$	−26.2257	−	15.1414i	−1.55896	−	0.900065i	−0.561601	−	0.827408i	$-0.689814\pi$
$284$	−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	$-0.899710\pi$
$293$	−3.54362	+	6.13773i	−0.207021	+	0.358570i	0.743754	+	0.668453i	$0.233043\pi$
$294$		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	−0.446652	−	0.894708i	$-0.647384\pi$
$311$	9.72605	−	16.8460i	0.551514	−	0.955249i	0.998166	−	0.0605417i	$-0.0192828\pi$
$312$		0			0
$313$	−22.1224	+	12.7724i	−1.25043	+	0.721937i	−0.971195	−	0.238285i	$-0.923415\pi$
$313$	−22.1224	+	12.7724i	−1.25043	+	0.721937i	−0.279237	+	0.960222i	$0.590081\pi$
$314$	37.4073			2.11101
$315$		0			0
$316$	33.8559			1.90454
$317$	−14.0534	+	8.11372i	−0.789316	+	0.455712i	−0.839722	−	0.543017i	$-0.817282\pi$
$317$	−14.0534	+	8.11372i	−0.789316	+	0.455712i	0.0504056	+	0.998729i	$0.483949\pi$
$318$		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	−0.985285	−	0.170919i	$-0.945326\pi$
$331$	−11.6558	−	20.1885i	−0.640662	−	1.10966i	0.344623	−	0.938741i	$-0.388007\pi$
$332$	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	−0.657860	−	0.753140i	$-0.728538\pi$
$337$	5.93515	−	10.2800i	0.323308	−	0.559986i	0.981168	+	0.193154i	$0.0618717\pi$
$338$	−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	0.910936	−	0.412549i	$-0.135361\pi$
$347$	18.7979	+	10.8530i	1.00913	+	0.582619i	0.0981903	+	0.995168i	$0.468695\pi$
$348$		0			0
$349$	−2.20868	+	1.27518i	−0.118228	+	0.0682588i	−0.557948	−	0.829876i	$-0.688411\pi$
$349$	−2.20868	+	1.27518i	−0.118228	+	0.0682588i	0.439720	+	0.898135i	$0.355078\pi$
$350$		0			0
$351$		0			0
$352$	26.0288			1.38734
$353$	12.6873	+	21.9751i	0.675279	+	1.16962i	0.976387	+	0.216027i	$0.0693100\pi$
$353$	12.6873	+	21.9751i	0.675279	+	1.16962i	−0.301109	+	0.953590i	$0.597357\pi$
$354$		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	$0.0958897\pi$
$359$			11.2437i			0.593421i	−0.954967	+	0.296711i	$0.904110\pi$
$360$		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	$-0.694215\pi$
$367$	−2.86810	+	1.65590i	−0.149714	+	0.0864372i	0.423272	+	0.906003i	$0.360882\pi$
$368$		−	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	−0.767091	−	0.641539i	$-0.778296\pi$
$373$	3.32271	−	5.75510i	0.172043	−	0.297988i	0.939134	+	0.343551i	$0.111630\pi$
$374$	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	0.0168739	−	0.999858i	$-0.494629\pi$
$383$	17.1112	−	29.6374i	0.874339	−	1.51440i	0.857465	−	0.514542i	$-0.172038\pi$
$384$		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	−0.173960	−	0.984753i	$-0.555656\pi$
$389$	11.6737	−	6.73982i	0.591881	−	0.341723i	0.765841	+	0.643030i	$0.222323\pi$
$390$		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	−0.283786	−	0.958888i	$-0.591590\pi$
$401$	−25.1534	−	14.5223i	−1.25610	−	0.725209i	−0.972314	+	0.233678i	$0.924924\pi$
$402$		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	$-0.602565\pi$
$409$	−26.2193	−	15.1377i	−1.29646	−	0.748513i	−0.979791	+	0.200023i	$0.935898\pi$
$410$	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	0.0579246	−	0.998321i	$-0.481552\pi$
$419$	18.2902	−	31.6795i	0.893534	−	1.54765i	0.835609	−	0.549325i	$-0.185115\pi$
$420$		0			0
$421$	3.85999	+	6.68570i	0.188124	+	0.325841i	0.944625	−	0.328152i	$-0.106426\pi$
$421$	3.85999	+	6.68570i	0.188124	+	0.325841i	−0.756501	+	0.653993i	$0.773093\pi$
$422$		−	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	$-0.811927\pi$
$431$		−	23.1299i		−	1.11413i	0.830469	−	0.557065i	$-0.188073\pi$
$432$		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	0.617770	−	0.786359i	$-0.288036\pi$
$439$	33.6842	−	19.4476i	1.60766	−	0.928184i	0.989892	−	0.141824i	$-0.0452969\pi$
$440$	−5.52912			−0.263590
$441$		0			0
$442$	−10.6161			−0.504959
$443$	32.3277	−	18.6644i	1.53594	−	0.886774i	0.536867	−	0.843667i	$-0.319608\pi$
$443$	32.3277	−	18.6644i	1.53594	−	0.886774i	0.999070	−	0.0431065i	$-0.0137255\pi$
$444$		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	$0.190924\pi$
$449$			23.9224i			1.12897i	−0.825445	+	0.564483i	$0.809076\pi$
$450$		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	0.725380	−	0.688348i	$-0.241664\pi$
$457$	−4.99031	−	8.64348i	−0.233437	−	0.404325i	−0.958817	+	0.284024i	$0.908331\pi$
$458$	−13.4831			−0.630024
$459$		0			0
$460$			5.80028i			0.270439i
$461$	16.7279	+	28.9735i	0.779094	+	1.34943i	0.932465	+	0.361261i	$0.117654\pi$
$461$	16.7279	+	28.9735i	0.779094	+	1.34943i	−0.153371	+	0.988169i	$0.549013\pi$
$462$		0			0
$463$	11.5353	−	19.9798i	0.536092	−	0.928538i	−0.463018	−	0.886349i	$-0.653233\pi$
$463$	11.5353	−	19.9798i	0.536092	−	0.928538i	0.999110	−	0.0421893i	$-0.0134333\pi$
$464$	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	$-0.881890\pi$
$467$	−40.2791			−1.86389			−0.931946	+	0.362597i	$0.881890\pi$
$468$		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	$-0.165536\pi$
$479$	0.0777513	+	0.134669i	0.00355255	+	0.00615319i	−0.864244	+	0.503073i	$0.832203\pi$
$480$		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	0.305963	−	0.952043i	$-0.401022\pi$
$491$	−8.10003	−	4.67655i	−0.365549	−	0.211050i	−0.671512	+	0.740993i	$0.734355\pi$
$492$		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	−0.887501	−	0.460805i	$-0.847561\pi$
$499$	−0.998116	+	1.72879i	−0.0446818	+	0.0773912i	0.842820	+	0.538196i	$0.180894\pi$
$500$	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	$-0.613829\pi$
$503$	−15.7008			−0.700063			−0.350032	+	0.936738i	$0.613829\pi$
$504$		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	$-0.723983\pi$
$509$	7.59893	−	13.1617i	0.336817	−	0.583383i	0.983832	+	0.179093i	$0.0573164\pi$
$510$		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	$-0.858792\pi$
$521$	−41.2320			−1.80641			−0.903204	+	0.429211i	$0.858792\pi$
$522$		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	0.710636	−	0.703560i	$-0.248407\pi$
$547$	−5.94015	−	10.2886i	−0.253982	−	0.439910i	−0.964619	+	0.263649i	$0.915074\pi$
$548$			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	$-0.776507\pi$
$557$		−	30.4848i		−	1.29168i	0.763472	−	0.645841i	$-0.223493\pi$
$558$		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	$-0.990854\pi$
$563$	−11.2686	+	19.5177i	−0.474914	+	0.822575i	0.524673	+	0.851304i	$0.324187\pi$
$564$		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	0.630465	−	0.776218i	$-0.282864\pi$
$569$	38.5935	−	22.2819i	1.61792	−	0.934108i	0.987457	−	0.157890i	$-0.0504691\pi$
$570$		0			0
$571$	−17.6415	+	30.5560i	−0.738274	+	1.27873i	0.214998	+	0.976614i	$0.431025\pi$
$571$	−17.6415	+	30.5560i	−0.738274	+	1.27873i	−0.953272	+	0.302113i	$0.902308\pi$
$572$	−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	−0.982583	−	0.185826i	$-0.940504\pi$
$587$	−15.8021	−	27.3700i	−0.652222	−	1.12968i	0.330361	−	0.943855i	$-0.392829\pi$
$588$		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	$-0.224159\pi$
$593$	37.1177			1.52424			0.762120	+	0.647436i	$0.224159\pi$
$594$		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	−0.0930277	−	0.995664i	$-0.529655\pi$
$599$	−24.5188	−	14.1559i	−1.00181	−	0.578396i	−0.908784	+	0.417267i	$0.862988\pi$
$600$		0			0
$601$	−20.8341	+	12.0286i	−0.849840	+	0.490655i	−0.860597	−	0.509287i	$-0.829909\pi$
$601$	−20.8341	+	12.0286i	−0.849840	+	0.490655i	0.0107568	+	0.999942i	$0.496576\pi$
$602$		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	$-0.395224\pi$
$607$	−8.24496	−	4.76023i	−0.334653	−	0.193212i	−0.657905	+	0.753101i	$0.728557\pi$
$608$	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	0.0719831	−	0.997406i	$-0.477067\pi$
$617$	−18.7738	−	10.8390i	−0.755804	−	0.436364i	−0.827787	+	0.561042i	$0.810401\pi$
$618$		0			0
$619$	20.8767	−	12.0532i	0.839105	−	0.484457i	−0.0178550	−	0.999841i	$-0.505684\pi$
$619$	20.8767	−	12.0532i	0.839105	−	0.484457i	0.856960	+	0.515383i	$0.172350\pi$
$620$			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	−0.965148	−	0.261706i	$-0.915715\pi$
$641$	−30.9152	+	17.8489i	−1.22108	+	0.704989i	−0.255930	+	0.966695i	$0.582382\pi$
$642$		0			0
$643$	−3.03956	−	1.75489i	−0.119868	−	0.0692060i	0.438867	−	0.898552i	$-0.355380\pi$
$643$	−3.03956	−	1.75489i	−0.119868	−	0.0692060i	−0.558735	+	0.829346i	$0.688713\pi$
$644$		0			0
$645$		0			0
$646$	−9.46292	−	16.3903i	−0.372314	−	0.644866i
$647$	14.0599			0.552752			0.276376	−	0.961050i	$-0.410866\pi$
$647$	14.0599			0.552752			0.276376	+	0.961050i	$0.410866\pi$
$648$		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	0.285462	−	0.958390i	$-0.407853\pi$
$653$	−10.2675	−	5.92792i	−0.401797	−	0.231978i	−0.687259	+	0.726412i	$0.741186\pi$
$654$		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	−0.594787	−	0.803883i	$-0.702764\pi$
$659$	−5.03144	+	2.90491i	−0.195997	+	0.113159i	0.398790	+	0.917042i	$0.369430\pi$
$660$		0			0
$661$	8.41592	+	4.85893i	0.327341	+	0.188991i	0.654660	−	0.755923i	$-0.272812\pi$
$661$	8.41592	+	4.85893i	0.327341	+	0.188991i	−0.327319	+	0.944914i	$0.606145\pi$
$662$	−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	0.999756	+	0.0221072i	$0.00703750\pi$
$673$	13.4646	+	23.3214i	0.519023	+	0.898975i	−0.480732	+	0.876867i	$0.659629\pi$
$674$		−	24.8740i		−	0.958110i
$675$		0			0
$676$	−8.05905			−0.309964
$677$	22.7056	+	39.3273i	0.872648	+	1.51147i	0.859247	+	0.511560i	$0.170932\pi$
$677$	22.7056	+	39.3273i	0.872648	+	1.51147i	0.0134007	+	0.999910i	$0.495734\pi$
$678$		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	$0.312717\pi$
$683$			43.4795i			1.66370i	−0.555003	+	0.831848i	$0.687283\pi$
$684$		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	$-0.840926\pi$
$691$	−23.6991	+	13.6827i	−0.901557	+	0.520514i	−0.0238522	+	0.999715i	$0.507593\pi$
$692$	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	$0.0498827\pi$
$701$			8.26437i			0.312141i	−0.987746	+	0.156070i	$0.950117\pi$
$702$		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	−0.916954	−	0.398994i	$-0.869360\pi$
$709$	−21.4086	−	37.0807i	−0.804015	−	1.39260i	0.112938	−	0.993602i	$-0.463974\pi$
$710$	−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	$-0.642045\pi$
$719$	−23.1451			−0.863165			−0.431583	+	0.902073i	$0.642045\pi$
$720$		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	$-0.699227\pi$
$727$	−4.76878	+	2.75326i	−0.176864	+	0.102113i	0.408954	+	0.912555i	$0.365894\pi$
$728$		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	$-0.309857\pi$
$733$	3.45543	+	1.99499i	0.127629	+	0.0736867i	−0.434826	+	0.900514i	$0.643190\pi$
$734$	−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	0.331810	−	0.943346i	$-0.392341\pi$
$743$	−8.70204	−	5.02413i	−0.319247	−	0.184317i	−0.651057	+	0.759029i	$0.725674\pi$
$744$		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	−0.570571	−	0.821248i	$-0.693278\pi$
$751$	11.6725	−	20.2174i	0.425936	−	0.737743i	0.996507	+	0.0835052i	$0.0266115\pi$
$752$	−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	$-0.967898\pi$
$761$	−11.3178	+	19.6029i	−0.410268	+	0.710606i	0.584650	+	0.811285i	$0.301232\pi$
$762$		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	−0.998877	−	0.0473762i	$-0.984914\pi$
$769$	−42.6873	−	24.6455i	−1.53934	−	0.888741i	−0.540468	−	0.841365i	$-0.681753\pi$
$770$		0			0
$771$		0			0
$772$	−6.55467	−	11.3530i	−0.235908	−	0.408604i
$773$	22.0167			0.791886			0.395943	−	0.918275i	$-0.370418\pi$
$773$	22.0167			0.791886			0.395943	+	0.918275i	$0.370418\pi$
$774$		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	$-0.271357\pi$
$787$	9.40107	+	5.42771i	0.335112	+	0.193477i	−0.322996	+	0.946400i	$0.604690\pi$
$788$	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	$-0.810956\pi$
$797$	1.98299	−	3.43465i	0.0702412	−	0.121661i	0.899007	+	0.437934i	$0.144290\pi$
$798$		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	$0.261017\pi$
$809$			41.5922i			1.46230i	−0.682215	+	0.731152i	$0.738983\pi$
$810$		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	−0.952931	−	0.303188i	$-0.901949\pi$
$821$	−33.4332	+	19.3027i	−1.16683	+	0.673668i	−0.213897	+	0.976856i	$0.568616\pi$
$822$		0			0
$823$	5.34881	−	9.26442i	0.186448	−	0.322937i	−0.757616	−	0.652701i	$-0.773636\pi$
$823$	5.34881	−	9.26442i	0.186448	−	0.322937i	0.944063	+	0.329764i	$0.106969\pi$
$824$	6.42613	−	11.1304i	0.223865	−	0.387745i
$825$		0			0
$826$		0			0
$827$		−	11.7079i		−	0.407125i	−0.979062	−	0.203562i	$-0.934748\pi$
$827$		−	11.7079i		−	0.407125i	0.979062	−	0.203562i	$-0.0652520\pi$
$828$		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	$-0.158924\pi$
$839$	0.704502	+	1.22023i	0.0243221	+	0.0421271i	−0.853608	+	0.520916i	$0.825591\pi$
$840$		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	$-0.479415\pi$
$853$	28.0716	−	16.2071i	0.961153	−	0.554922i	0.896528	+	0.442987i	$0.146081\pi$
$854$		0			0
$855$		0			0
$856$	1.34343			0.0459176
$857$	−22.2270	−	38.4982i	−0.759258	−	1.31507i	−0.943229	−	0.332142i	$-0.892229\pi$
$857$	−22.2270	−	38.4982i	−0.759258	−	1.31507i	0.183971	−	0.982932i	$-0.441105\pi$
$858$		0			0
$859$	−13.5528	−	7.82472i	−0.462416	−	0.266976i	0.250644	−	0.968079i	$-0.419358\pi$
$859$	−13.5528	−	7.82472i	−0.462416	−	0.266976i	−0.713060	+	0.701103i	$0.752691\pi$
$860$	−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	$0.0997872\pi$
$863$			18.1185i			0.616762i	−0.951263	+	0.308381i	$0.900213\pi$
$864$		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	−0.841616	−	0.540077i	$-0.818395\pi$
$877$	1.38926	−	2.40628i	0.0469121	−	0.0812542i	0.888528	+	0.458822i	$0.151729\pi$
$878$	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	$-0.510517\pi$
$881$	−1.96106			−0.0660696			−0.0330348	+	0.999454i	$0.510517\pi$
$882$		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	$-0.709938\pi$
$887$	11.2584	−	19.5001i	0.378020	−	0.654750i	0.990774	+	0.135524i	$0.0432716\pi$
$888$		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	0.979951	−	0.199240i	$-0.0638473\pi$
$907$	9.55982	+	16.5581i	0.317428	+	0.549802i	−0.662522	+	0.749042i	$0.730514\pi$
$908$	−4.97550			−0.165118
$909$		0			0
$910$		0			0
$911$	−4.92610	+	2.84408i	−0.163209	+	0.0942287i	−0.579380	−	0.815058i	$-0.696705\pi$
$911$	−4.92610	+	2.84408i	−0.163209	+	0.0942287i	0.416171	+	0.909286i	$0.363372\pi$
$912$		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	$-0.0811756\pi$
$929$	8.08806	+	14.0089i	0.265361	+	0.459618i	−0.702297	+	0.711884i	$0.747842\pi$
$930$		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	−0.263154	−	0.964754i	$-0.584763\pi$
$941$	21.5934	−	37.4009i	0.703924	−	1.21923i	0.967078	−	0.254479i	$-0.0819040\pi$
$942$		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	−0.204965	−	0.978769i	$-0.565708\pi$
$947$	16.6235	−	9.59758i	0.540191	−	0.311879i	0.745156	+	0.666890i	$0.232375\pi$
$948$		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	$0.0290514\pi$
$953$			5.62718i			0.182282i	−0.995838	+	0.0911411i	$0.970949\pi$
$954$		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	−0.962152	−	0.272514i	$-0.912145\pi$
$967$	−7.62091	+	13.1998i	−0.245072	+	0.424477i	0.717080	+	0.696991i	$0.245478\pi$
$968$	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	$-0.272161\pi$
$971$	40.8958			1.31241			0.656205	+	0.754583i	$0.272161\pi$
$972$		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	0.636764	−	0.771058i	$-0.280272\pi$
$977$	8.98296	+	5.18631i	0.287390	+	0.165925i	−0.349374	+	0.936983i	$0.613606\pi$
$978$		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	$-0.177415\pi$
$983$	−1.05850	−	1.83338i	−0.0337609	−	0.0584756i	−0.882412	+	0.470477i	$0.844082\pi$
$984$		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	$-0.925115\pi$
$997$	−39.6843	+	22.9118i	−1.25682	+	0.725623i	−0.284361	+	0.958717i	$0.591782\pi$
$998$			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.c.881.5		10
3.2	odd	2		441.2.o.d.293.1		10
7.2	even	3		1323.2.s.b.962.1		10
7.3	odd	6		1323.2.i.b.1097.5		10
7.4	even	3		189.2.i.b.152.5		10
7.5	odd	6		189.2.s.b.17.1		10
7.6	odd	2		1323.2.o.d.881.5		10
9.2	odd	6		1323.2.o.d.440.5		10
9.7	even	3		441.2.o.c.146.1		10
21.2	odd	6		441.2.s.b.374.5		10
21.5	even	6		63.2.s.b.59.5	yes	10
21.11	odd	6		63.2.i.b.5.1	✓	10
21.17	even	6		441.2.i.b.68.1		10
21.20	even	2		441.2.o.c.293.1		10
28.11	odd	6		3024.2.ca.b.2609.5		10
28.19	even	6		3024.2.df.b.17.5		10
63.2	odd	6		1323.2.i.b.521.1		10
63.4	even	3		567.2.p.c.404.1		10
63.5	even	6		567.2.p.c.80.1		10
63.11	odd	6		189.2.s.b.89.1		10
63.16	even	3		441.2.i.b.227.5		10
63.20	even	6	inner	1323.2.o.c.440.5		10
63.25	even	3		63.2.s.b.47.5	yes	10
63.32	odd	6		567.2.p.d.404.5		10
63.34	odd	6		441.2.o.d.146.1		10
63.38	even	6		1323.2.s.b.656.1		10
63.40	odd	6		567.2.p.d.80.5		10
63.47	even	6		189.2.i.b.143.1		10
63.52	odd	6		441.2.s.b.362.5		10
63.61	odd	6		63.2.i.b.38.5	yes	10
84.11	even	6		1008.2.ca.b.257.5		10
84.47	odd	6		1008.2.df.b.689.3		10
252.11	even	6		3024.2.df.b.1601.5		10
252.47	odd	6		3024.2.ca.b.2033.5		10
252.151	odd	6		1008.2.df.b.929.3		10
252.187	even	6		1008.2.ca.b.353.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.1	✓	10	21.11	odd	6
63.2.i.b.38.5	yes	10	63.61	odd	6
63.2.s.b.47.5	yes	10	63.25	even	3
63.2.s.b.59.5	yes	10	21.5	even	6
189.2.i.b.143.1		10	63.47	even	6
189.2.i.b.152.5		10	7.4	even	3
189.2.s.b.17.1		10	7.5	odd	6
189.2.s.b.89.1		10	63.11	odd	6
441.2.i.b.68.1		10	21.17	even	6
441.2.i.b.227.5		10	63.16	even	3
441.2.o.c.146.1		10	9.7	even	3
441.2.o.c.293.1		10	21.20	even	2
441.2.o.d.146.1		10	63.34	odd	6
441.2.o.d.293.1		10	3.2	odd	2
441.2.s.b.362.5		10	63.52	odd	6
441.2.s.b.374.5		10	21.2	odd	6
567.2.p.c.80.1		10	63.5	even	6
567.2.p.c.404.1		10	63.4	even	3
567.2.p.d.80.5		10	63.40	odd	6
567.2.p.d.404.5		10	63.32	odd	6
1008.2.ca.b.257.5		10	84.11	even	6
1008.2.ca.b.353.5		10	252.187	even	6
1008.2.df.b.689.3		10	84.47	odd	6
1008.2.df.b.929.3		10	252.151	odd	6
1323.2.i.b.521.1		10	63.2	odd	6
1323.2.i.b.1097.5		10	7.3	odd	6
1323.2.o.c.440.5		10	63.20	even	6	inner
1323.2.o.c.881.5		10	1.1	even	1	trivial
1323.2.o.d.440.5		10	9.2	odd	6
1323.2.o.d.881.5		10	7.6	odd	2
1323.2.s.b.656.1		10	63.38	even	6
1323.2.s.b.962.1		10	7.2	even	3
3024.2.ca.b.2033.5		10	252.47	odd	6
3024.2.ca.b.2609.5		10	28.11	odd	6
3024.2.df.b.17.5		10	28.19	even	6
3024.2.df.b.1601.5		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)

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more