LMFDB - Embedded newform 441.2.i.b.68.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(68,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 5]))

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

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

chi := DirichletCharacter("441.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.i (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:	$3.52140272914$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.1
Root			$0.827154 - 1.43267i$ of defining polynomial
Character	$\chi$	$=$	441.68
Dual form			441.2.i.b.227.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.09548i q^{2} +(1.72861 + 0.109097i) q^{3} -2.39104 q^{4} +(1.04492 + 1.80985i) q^{5} +(0.228612 - 3.62227i) q^{6} +0.819421i q^{8} +(2.97620 + 0.377174i) q^{9} +O(q^{10})$	\(q-2.09548i q^{2} +(1.72861 + 0.109097i) q^{3} -2.39104 q^{4} +(1.04492 + 1.80985i) q^{5} +(0.228612 - 3.62227i) q^{6} +0.819421i q^{8} +(2.97620 + 0.377174i) q^{9} +(3.79250 - 2.18960i) q^{10} +(2.79620 + 1.61439i) q^{11} +(-4.13318 - 0.260856i) q^{12} +(2.68740 + 1.55157i) q^{13} +(1.60880 + 3.24252i) q^{15} -3.06500 q^{16} +(-0.816304 - 1.41388i) q^{17} +(0.790361 - 6.23656i) q^{18} +(-4.79094 - 2.76605i) q^{19} +(-2.49844 - 4.32742i) q^{20} +(3.38292 - 5.85939i) q^{22} +(-1.00527 + 0.580391i) q^{23} +(-0.0893966 + 1.41646i) q^{24} +(0.316304 - 0.547854i) q^{25} +(3.25129 - 5.63139i) q^{26} +(5.10354 + 0.976682i) q^{27} +(-7.05749 + 4.07464i) q^{29} +(6.79464 - 3.37122i) q^{30} -5.96849i q^{31} +8.06150i q^{32} +(4.65742 + 3.09571i) q^{33} +(-2.96276 + 1.71055i) q^{34} +(-7.11621 - 0.901839i) q^{36} +(2.82656 - 4.89575i) q^{37} +(-5.79620 + 10.0393i) q^{38} +(4.47620 + 2.97525i) q^{39} +(-1.48303 + 0.856225i) q^{40} +(-1.35369 + 2.34465i) q^{41} +(-0.974903 - 1.68858i) q^{43} +(-6.68583 - 3.86007i) q^{44} +(2.42725 + 5.78057i) q^{45} +(1.21620 + 2.10652i) q^{46} -8.13518 q^{47} +(-5.29820 - 0.334384i) q^{48} +(-1.14802 - 0.662809i) q^{50} +(-1.25682 - 2.53311i) q^{51} +(-6.42568 - 3.70987i) q^{52} +(-5.27766 + 3.04706i) q^{53} +(2.04662 - 10.6944i) q^{54} +6.74759i q^{55} +(-7.97990 - 5.30410i) q^{57} +(8.53834 + 14.7888i) q^{58} +3.96206 q^{59} +(-3.84672 - 7.75300i) q^{60} +4.79219i q^{61} -12.5068 q^{62} +10.7627 q^{64} +6.48504i q^{65} +(6.48700 - 9.75954i) q^{66} -0.673961 q^{67} +(1.95182 + 3.38065i) q^{68} +(-1.80103 + 0.893598i) q^{69} +7.01535i q^{71} +(-0.309064 + 2.43876i) q^{72} +(2.96276 - 1.71055i) q^{73} +(-10.2590 - 5.92301i) q^{74} +(0.606536 - 0.912519i) q^{75} +(11.4553 + 6.61374i) q^{76} +(6.23458 - 9.37978i) q^{78} -14.1595 q^{79} +(-3.20267 - 5.54718i) q^{80} +(8.71548 + 2.24509i) q^{81} +(4.91318 + 2.83662i) q^{82} +(1.54535 + 2.67662i) q^{83} +(1.70594 - 2.95477i) q^{85} +(-3.53839 + 2.04289i) q^{86} +(-12.6442 + 6.27352i) q^{87} +(-1.32286 + 2.29127i) q^{88} +(-2.45766 + 4.25679i) q^{89} +(12.1131 - 5.08625i) q^{90} +(2.40363 - 1.38774i) q^{92} +(0.651146 - 10.3172i) q^{93} +17.0471i q^{94} -11.5611i q^{95} +(-0.879488 + 13.9352i) q^{96} +(2.07939 - 1.20054i) q^{97} +(7.71314 + 5.85939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{3} - 8 q^{4} - 12 q^{6} + 3 q^{9}+O(q^{10}) $ 10 * q + 3 * q^3 - 8 * q^4 - 12 * q^6 + 3 * q^9	$ 10 q + 3 q^{3} - 8 q^{4} - 12 q^{6} + 3 q^{9} + 15 q^{10} - 12 q^{11} + 12 q^{12} + 6 q^{13} - 3 q^{15} + 12 q^{16} - 12 q^{17} + 24 q^{18} - 3 q^{19} - 3 q^{20} + 5 q^{22} - 15 q^{23} + 7 q^{25} + 3 q^{26} + 27 q^{27} - 15 q^{29} + 6 q^{30} + 3 q^{34} - 18 q^{36} + 6 q^{37} - 18 q^{38} + 18 q^{39} - 15 q^{40} - 9 q^{41} + 3 q^{43} - 24 q^{44} - 30 q^{45} - 13 q^{46} - 30 q^{47} - 15 q^{48} + 3 q^{50} + 21 q^{51} + 12 q^{52} + 9 q^{53} - 9 q^{54} - 36 q^{57} + 8 q^{58} + 36 q^{59} - 48 q^{60} + 12 q^{62} + 6 q^{64} + 39 q^{66} + 20 q^{67} + 27 q^{68} - 3 q^{69} - 30 q^{72} - 3 q^{73} - 30 q^{74} - 6 q^{75} + 9 q^{76} + 24 q^{78} - 40 q^{79} - 30 q^{80} + 15 q^{81} - 9 q^{82} - 15 q^{83} + 18 q^{85} + 54 q^{86} - 6 q^{87} - 8 q^{88} + 24 q^{89} + 24 q^{90} + 39 q^{92} + 36 q^{93} - 33 q^{96} + 6 q^{97} + 21 q^{99}+O(q^{100}) $ 10 * q + 3 * q^3 - 8 * q^4 - 12 * q^6 + 3 * q^9 + 15 * q^10 - 12 * q^11 + 12 * q^12 + 6 * q^13 - 3 * q^15 + 12 * q^16 - 12 * q^17 + 24 * q^18 - 3 * q^19 - 3 * q^20 + 5 * q^22 - 15 * q^23 + 7 * q^25 + 3 * q^26 + 27 * q^27 - 15 * q^29 + 6 * q^30 + 3 * q^34 - 18 * q^36 + 6 * q^37 - 18 * q^38 + 18 * q^39 - 15 * q^40 - 9 * q^41 + 3 * q^43 - 24 * q^44 - 30 * q^45 - 13 * q^46 - 30 * q^47 - 15 * q^48 + 3 * q^50 + 21 * q^51 + 12 * q^52 + 9 * q^53 - 9 * q^54 - 36 * q^57 + 8 * q^58 + 36 * q^59 - 48 * q^60 + 12 * q^62 + 6 * q^64 + 39 * q^66 + 20 * q^67 + 27 * q^68 - 3 * q^69 - 30 * q^72 - 3 * q^73 - 30 * q^74 - 6 * q^75 + 9 * q^76 + 24 * q^78 - 40 * q^79 - 30 * q^80 + 15 * q^81 - 9 * q^82 - 15 * q^83 + 18 * q^85 + 54 * q^86 - 6 * q^87 - 8 * q^88 + 24 * q^89 + 24 * q^90 + 39 * q^92 + 36 * q^93 - 33 * q^96 + 6 * q^97 + 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	2.09548i		−	1.48173i	−0.671655	−	0.740865i	$-0.734416\pi$
$2$		−	2.09548i		−	1.48173i	0.671655	−	0.740865i	$-0.265584\pi$
$3$	1.72861	+	0.109097i	0.998014	+	0.0629874i
$3$	1.72861	+	0.109097i	0.998014	+	0.0629874i
$4$	−2.39104			−1.19552
$5$	1.04492	+	1.80985i	0.467300	+	0.809388i	0.999302	−	0.0373553i	$-0.0118933\pi$
$5$	1.04492	+	1.80985i	0.467300	+	0.809388i	−0.532002	+	0.846743i	$0.678560\pi$
$6$	0.228612	−	3.62227i	0.0933303	−	1.47879i
$7$		0			0
$7$		0			0
$8$			0.819421i			0.289709i
$9$	2.97620	+	0.377174i	0.992065	+	0.125725i
$10$	3.79250	−	2.18960i	1.19929	−	0.692412i
$11$	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	$0.504847\pi$
$12$	−4.13318	−	0.260856i	−1.19315	−	0.0753028i
$13$	2.68740	+	1.55157i	0.745350	+	0.430328i	0.824011	−	0.566573i	$-0.191731\pi$
$13$	2.68740	+	1.55157i	0.745350	+	0.430328i	−0.0786612	+	0.996901i	$0.525065\pi$
$14$		0			0
$15$	1.60880	+	3.24252i	0.415391	+	0.837215i
$16$	−3.06500			−0.766251
$17$	−0.816304	−	1.41388i	−0.197983	−	0.342916i	0.749891	−	0.661561i	$-0.230106\pi$
$17$	−0.816304	−	1.41388i	−0.197983	−	0.342916i	−0.947874	+	0.318645i	$0.896772\pi$
$18$	0.790361	−	6.23656i	0.186290	−	1.46997i
$19$	−4.79094	−	2.76605i	−1.09912	−	0.634575i	−0.163127	−	0.986605i	$-0.552158\pi$
$19$	−4.79094	−	2.76605i	−1.09912	−	0.634575i	−0.935989	+	0.352030i	$0.885491\pi$
$20$	−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	$0.371950\pi$
$24$	−0.0893966	+	1.41646i	−0.0182480	+	0.289134i
$25$	0.316304	−	0.547854i	0.0632608	−	0.109571i
$26$	3.25129	−	5.63139i	0.637630	−	1.10441i
$27$	5.10354	+	0.976682i	0.982176	+	0.187963i
$28$		0			0
$29$	−7.05749	+	4.07464i	−1.31054	+	0.756643i	−0.982186	−	0.187911i	$-0.939828\pi$
$29$	−7.05749	+	4.07464i	−1.31054	+	0.756643i	−0.328357	+	0.944554i	$0.606495\pi$
$30$	6.79464	−	3.37122i	1.24053	−	0.615497i
$31$		−	5.96849i		−	1.07197i	−0.844227	−	0.535986i	$-0.819940\pi$
$31$		−	5.96849i		−	1.07197i	0.844227	−	0.535986i	$-0.180060\pi$
$32$			8.06150i			1.42508i
$33$	4.65742	+	3.09571i	0.810753	+	0.538893i
$34$	−2.96276	+	1.71055i	−0.508109	+	0.293357i
$35$		0			0
$36$	−7.11621	−	0.901839i	−1.18603	−	0.150306i
$37$	2.82656	−	4.89575i	0.464684	−	0.804857i	−0.534503	−	0.845167i	$-0.679501\pi$
$37$	2.82656	−	4.89575i	0.464684	−	0.804857i	0.999187	+	0.0403097i	$0.0128345\pi$
$38$	−5.79620	+	10.0393i	−0.940268	+	1.62859i
$39$	4.47620	+	2.97525i	0.716765	+	0.476421i
$40$	−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	$0.880833\pi$
$44$	−6.68583	−	3.86007i	−1.00793	−	0.581927i
$45$	2.42725	+	5.78057i	0.361832	+	0.861717i
$46$	1.21620	+	2.10652i	0.179319	+	0.310589i
$47$	−8.13518			−1.18664			−0.593319	−	0.804967i	$-0.702183\pi$
$47$	−8.13518			−1.18664			−0.593319	+	0.804967i	$0.702183\pi$
$48$	−5.29820	−	0.334384i	−0.764729	−	0.0482641i
$49$		0			0
$50$	−1.14802	−	0.662809i	−0.162354	−	0.0937353i
$51$	−1.25682	−	2.53311i	−0.175990	−	0.354706i
$52$	−6.42568	−	3.70987i	−0.891082	−	0.514466i
$53$	−5.27766	+	3.04706i	−0.724943	+	0.418546i	−0.816569	−	0.577248i	$-0.804127\pi$
$53$	−5.27766	+	3.04706i	−0.724943	+	0.418546i	0.0916264	+	0.995793i	$0.470793\pi$
$54$	2.04662	−	10.6944i	0.278510	−	1.45532i
$55$			6.74759i			0.909845i
$56$		0			0
$57$	−7.97990	−	5.30410i	−1.05696	−	0.702545i
$58$	8.53834	+	14.7888i	1.12114	+	1.94187i
$59$	3.96206			0.515816			0.257908	−	0.966170i	$-0.416967\pi$
$59$	3.96206			0.515816			0.257908	+	0.966170i	$0.416967\pi$
$60$	−3.84672	−	7.75300i	−0.496609	−	1.00091i
$61$			4.79219i			0.613577i	0.951778	+	0.306788i	$0.0992544\pi$
$61$			4.79219i			0.613577i	−0.951778	+	0.306788i	$0.900746\pi$
$62$	−12.5068			−1.58837
$63$		0			0
$64$	10.7627			1.34534
$65$			6.48504i			0.804370i
$66$	6.48700	−	9.75954i	0.798494	−	1.20132i
$67$	−0.673961			−0.0823375			−0.0411687	−	0.999152i	$-0.513108\pi$
$67$	−0.673961			−0.0823375			−0.0411687	+	0.999152i	$0.513108\pi$
$68$	1.95182	+	3.38065i	0.236693	+	0.409963i
$69$	−1.80103	+	0.893598i	−0.216819	+	0.107577i
$70$		0			0
$71$			7.01535i			0.832568i	0.909235	+	0.416284i	$0.136668\pi$
$71$			7.01535i			0.832568i	−0.909235	+	0.416284i	$0.863332\pi$
$72$	−0.309064	+	2.43876i	−0.0364236	+	0.287410i
$73$	2.96276	−	1.71055i	0.346765	−	0.200205i	−0.316495	−	0.948594i	$-0.602506\pi$
$73$	2.96276	−	1.71055i	0.346765	−	0.200205i	0.663259	+	0.748390i	$0.269173\pi$
$74$	−10.2590	−	5.92301i	−1.19258	−	0.688536i
$75$	0.606536	−	0.912519i	0.0700367	−	0.105369i
$76$	11.4553	+	6.61374i	1.31402	+	0.758648i
$77$		0			0
$78$	6.23458	−	9.37978i	0.705927	−	1.06205i
$79$	−14.1595			−1.59306			−0.796532	−	0.604596i	$-0.793335\pi$
$79$	−14.1595			−1.59306			−0.796532	+	0.604596i	$0.793335\pi$
$80$	−3.20267	−	5.54718i	−0.358069	−	0.620194i
$81$	8.71548	+	2.24509i	0.968387	+	0.249454i
$82$	4.91318	+	2.83662i	0.542570	+	0.313253i
$83$	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
$87$	−12.6442	+	6.27352i	−1.35560	+	0.672592i
$88$	−1.32286	+	2.29127i	−0.141018	+	0.244250i
$89$	−2.45766	+	4.25679i	−0.260511	+	0.451219i	−0.966378	−	0.257126i	$-0.917224\pi$
$89$	−2.45766	+	4.25679i	−0.260511	+	0.451219i	0.705867	+	0.708345i	$0.250558\pi$
$90$	12.1131	−	5.08625i	1.27683	−	0.536138i
$91$		0			0
$92$	2.40363	−	1.38774i	0.250596	−	0.144682i
$93$	0.651146	−	10.3172i	0.0675207	−	1.06984i
$94$			17.0471i			1.75828i
$95$		−	11.5611i		−	1.18615i
$96$	−0.879488	+	13.9352i	−0.0897624	+	1.42226i
$97$	2.07939	−	1.20054i	0.211130	−	0.121896i	−0.390706	−	0.920515i	$-0.627769\pi$
$97$	2.07939	−	1.20054i	0.211130	−	0.121896i	0.601837	+	0.798619i	$0.294436\pi$
$98$		0			0
$99$	7.71314	+	5.85939i	0.775199	+	0.588891i
$100$	−0.756296	+	1.30994i	−0.0756296	+	0.130994i
$101$	1.76025	−	3.04885i	0.175152	−	0.303372i	−0.765062	−	0.643957i	$-0.777292\pi$
$101$	1.76025	−	3.04885i	0.175152	−	0.303372i	0.940214	+	0.340585i	$0.110625\pi$
$102$	−5.30807	+	2.63365i	−0.525578	+	0.260770i
$103$	13.5832	−	7.84228i	1.33840	−	0.772723i	0.351826	−	0.936065i	$-0.385561\pi$
$103$	13.5832	−	7.84228i	1.33840	−	0.772723i	0.986569	+	0.163342i	$0.0522275\pi$
$104$	−1.27139	+	2.20211i	−0.124670	+	0.215935i
$105$		0			0
$106$	6.38506	+	11.0592i	0.620172	+	1.07417i
$107$	1.41984	+	0.819746i	0.137261	+	0.0792478i	0.567058	−	0.823678i	$-0.308081\pi$
$107$	1.41984	+	0.819746i	0.137261	+	0.0792478i	−0.429797	+	0.902926i	$0.641415\pi$
$108$	−12.2028	−	2.33529i	−1.17421	−	0.224713i
$109$	2.90672	+	5.03459i	0.278414	+	0.482227i	0.970991	−	0.239117i	$-0.0768581\pi$
$109$	2.90672	+	5.03459i	0.278414	+	0.482227i	−0.692577	+	0.721344i	$0.743525\pi$
$110$	14.1395			1.34814
$111$	5.42015	−	8.15449i	0.514458	−	0.773989i
$112$		0			0
$113$	13.9931	+	8.07894i	1.31636	+	0.760003i	0.983142	−	0.182845i	$-0.0585307\pi$
$113$	13.9931	+	8.07894i	1.31636	+	0.760003i	0.333222	+	0.942848i	$0.391864\pi$
$114$	−11.1146	+	16.7217i	−1.04098	+	1.56613i
$115$	−2.10084	−	1.21292i	−0.195904	−	0.113105i
$116$	16.8748	−	9.74265i	1.56678	−	0.904582i
$117$	7.41301	+	5.63139i	0.685333	+	0.520622i
$118$		−	8.30241i		−	0.764299i
$119$		0			0
$120$	−2.65699	+	1.31829i	−0.242549	+	0.120343i
$121$	−0.287505	−	0.497972i	−0.0261368	−	0.0452702i
$122$	10.0419			0.909155
$123$	−2.59579	+	3.90531i	−0.234055	+	0.352130i
$124$			14.2709i			1.28156i
$125$	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	$0.639935\pi$
$128$		−	6.43006i		−	0.568343i
$129$	−1.50101	−	3.02526i	−0.132156	−	0.266359i
$130$	13.5893			1.19186
$131$	−1.23061	−	2.13148i	−0.107519	−	0.186228i	0.807246	−	0.590216i	$-0.200957\pi$
$131$	−1.23061	−	2.13148i	−0.107519	−	0.186228i	−0.914765	+	0.403987i	$0.867624\pi$
$132$	−11.1361	−	7.40197i	−0.969272	−	0.644258i
$133$		0			0
$134$			1.41227i			0.122002i
$135$	3.56512	+	10.2572i	0.306837	+	0.882797i
$136$	1.15856	−	0.668896i	0.0993459	−	0.0573574i
$137$	−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	$0.933127\pi$
$138$	1.87252	+	3.77403i	0.159399	+	0.321267i
$139$	−8.61174	−	4.97199i	−0.730438	−	0.421719i	0.0881443	−	0.996108i	$-0.471906\pi$
$139$	−8.61174	−	4.97199i	−0.730438	−	0.421719i	−0.818582	+	0.574389i	$0.805240\pi$
$140$		0			0
$141$	−14.0626	−	0.887527i	−1.18428	−	0.0747432i
$142$	14.7005			1.23364
$143$	5.00967	+	8.67701i	0.418930	+	0.725608i
$144$	−9.12205	−	1.15604i	−0.760171	−	0.0963366i
$145$	−14.7490	−	8.51532i	−1.22483	−	0.707159i
$146$	−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	$0.209536\pi$
$150$	−1.91217	−	1.27098i	−0.156128	−	0.103775i
$151$	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	$0.00474192\pi$
$152$	2.26656	−	3.92579i	0.183842	−	0.318424i
$153$	−1.89620	−	4.51587i	−0.153299	−	0.365087i
$154$		0			0
$155$	10.8020	−	6.23656i	0.867641	−	0.500933i
$156$	−10.7028	−	7.11395i	−0.856907	−	0.569572i
$157$			17.8514i			1.42470i	0.701826	+	0.712348i	$0.252368\pi$
$157$			17.8514i			1.42470i	−0.701826	+	0.712348i	$0.747632\pi$
$158$			29.6709i			2.36049i
$159$	−9.45546	+	4.69140i	−0.749866	+	0.372053i
$160$	−14.5901	+	8.42358i	−1.15345	+	0.665943i
$161$		0			0
$162$	4.70454	−	18.2631i	0.369623	−	1.43489i
$163$	−8.91768	+	15.4459i	−0.698486	+	1.20981i	0.270505	+	0.962719i	$0.412809\pi$
$163$	−8.91768	+	15.4459i	−0.698486	+	1.20981i	−0.968991	+	0.247095i	$0.920524\pi$
$164$	3.23672	−	5.60616i	0.252745	−	0.437768i
$165$	−0.736145	+	11.6640i	−0.0573088	+	0.908039i
$166$	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
$170$	−6.19166	−	3.57476i	−0.474879	−	0.274171i
$171$	−13.2155	−	10.0393i	−1.01061	−	0.767726i
$172$	2.33103	+	4.03747i	0.177740	+	0.307854i
$173$	−9.06736			−0.689379			−0.344689	−	0.938717i	$-0.612016\pi$
$173$	−9.06736			−0.689379			−0.344689	+	0.938717i	$0.612016\pi$
$174$	13.1461	+	26.4957i	0.996600	+	2.00863i
$175$		0			0
$176$	−8.57037	−	4.94810i	−0.646016	−	0.372977i
$177$	6.84885	+	0.432250i	0.514791	+	0.0324899i
$178$	8.92002	+	5.14997i	0.668584	+	0.386007i
$179$	13.0086	−	7.51051i	0.972307	−	0.561362i	0.0723682	−	0.997378i	$-0.476944\pi$
$179$	13.0086	−	7.51051i	0.972307	−	0.561362i	0.899939	+	0.436016i	$0.143611\pi$
$180$	−5.80364	−	13.8216i	−0.432578	−	1.03020i
$181$			2.34159i			0.174049i	0.996206	+	0.0870246i	$0.0277359\pi$
$181$			2.34159i			0.174049i	−0.996206	+	0.0870246i	$0.972264\pi$
$182$		0			0
$183$	−0.522815	+	8.28383i	−0.0386476	+	0.612358i
$184$	−0.475584	−	0.823736i	−0.0350605	−	0.0607266i
$185$	11.8141			0.868589
$186$	−21.6195	−	1.36446i	−1.58522	−	0.100047i
$187$		−	5.27132i		−	0.385477i
$188$	19.4516			1.41865
$189$		0			0
$190$	−24.2262			−1.75755
$191$		−	9.03651i		−	0.653859i	−0.945049	−	0.326929i	$-0.893986\pi$
$191$		−	9.03651i		−	0.653859i	0.945049	−	0.326929i	$-0.106014\pi$
$192$	18.6045	+	1.17418i	1.34267	+	0.0847394i
$193$	−5.48269			−0.394652			−0.197326	−	0.980338i	$-0.563226\pi$
$193$	−5.48269			−0.394652			−0.197326	+	0.980338i	$0.563226\pi$
$194$	−2.51570	−	4.35733i	−0.180617	−	0.312838i
$195$	−0.707501	+	11.2101i	−0.0506652	+	0.802773i
$196$		0			0
$197$		−	2.88946i		−	0.205865i	−0.994688	−	0.102933i	$-0.967177\pi$
$197$		−	2.88946i		−	0.205865i	0.994688	−	0.102933i	$-0.0328226\pi$
$198$	12.2782	−	16.1627i	0.872576	−	1.14864i
$199$	−4.45419	+	2.57163i	−0.315749	+	0.182298i	−0.649496	−	0.760365i	$-0.725020\pi$
$199$	−4.45419	+	2.57163i	−0.315749	+	0.182298i	0.333747	+	0.942663i	$0.391687\pi$
$200$	0.448923	+	0.259186i	0.0317437	+	0.0183272i
$201$	−1.16502	−	0.0735274i	−0.0821740	−	0.00518622i
$202$	−6.38881	−	3.68858i	−0.449515	−	0.259528i
$203$		0			0
$204$	3.00511	+	6.05676i	0.210400	+	0.424058i
$205$	−5.65795			−0.395168
$206$	−16.4334	−	28.4634i	−1.14497	−	1.98314i
$207$	−3.21078	+	1.34820i	−0.223164	+	0.0937061i
$208$	−8.23688	−	4.75557i	−0.571125	−	0.329739i
$209$	−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
$213$	−0.765356	+	12.1268i	−0.0524413	+	0.830915i
$214$	1.71776	−	2.97525i	0.117424	−	0.203384i
$215$	2.03738	−	3.52885i	0.138948	−	0.240666i
$216$	−0.800314	+	4.18194i	−0.0544544	+	0.284545i
$217$		0			0
$218$	10.5499	−	6.09099i	0.714529	−	0.412534i
$219$	5.30807	−	2.63365i	0.358686	−	0.177965i
$220$		−	16.1338i		−	1.08774i
$221$		−	5.06621i		−	0.340790i
$222$	−17.0876	−	11.3578i	−1.14684	−	0.762287i
$223$	13.5288	−	7.81085i	0.905955	−	0.523053i	0.0268275	−	0.999640i	$-0.491460\pi$
$223$	13.5288	−	7.81085i	0.905955	−	0.523053i	0.879127	+	0.476587i	$0.158126\pi$
$224$		0			0
$225$	1.14802	−	1.51122i	0.0765346	−	0.100748i
$226$	16.9293	−	29.3224i	1.12612	−	1.95049i
$227$	−1.04045	+	1.80211i	−0.0690569	+	0.119610i	−0.898486	−	0.439001i	$-0.855332\pi$
$227$	−1.04045	+	1.80211i	−0.0690569	+	0.119610i	0.829430	+	0.558611i	$0.188666\pi$
$228$	19.0803	+	12.6823i	1.26362	+	0.839908i
$229$	−5.57233	+	3.21719i	−0.368230	+	0.212598i	−0.672685	−	0.739929i	$-0.734859\pi$
$229$	−5.57233	+	3.21719i	−0.368230	+	0.212598i	0.304455	+	0.952527i	$0.401526\pi$
$230$	−2.54165	+	4.40226i	−0.167591	+	0.290277i
$231$		0			0
$232$	−3.33885	−	5.78305i	−0.219206	−	0.379676i
$233$	13.5222	+	7.80704i	0.885868	+	0.511456i	0.872589	−	0.488456i	$-0.162440\pi$
$233$	13.5222	+	7.80704i	0.885868	+	0.511456i	0.0132791	+	0.999912i	$0.495773\pi$
$234$	11.8005	−	15.5338i	0.771421	−	1.01548i
$235$	−8.50057	−	14.7234i	−0.554516	−	0.960450i
$236$	−9.47344			−0.616668
$237$	−24.4762	−	1.54476i	−1.58990	−	0.100343i
$238$		0			0
$239$	−14.8777	−	8.58964i	−0.962358	−	0.555618i	−0.0654600	−	0.997855i	$-0.520851\pi$
$239$	−14.8777	−	8.58964i	−0.962358	−	0.555618i	−0.896898	+	0.442238i	$0.854185\pi$
$240$	−4.93099	−	9.93833i	−0.318294	−	0.641516i
$241$	−9.71544	−	5.60921i	−0.625827	−	0.361321i	0.153307	−	0.988179i	$-0.451008\pi$
$241$	−9.71544	−	5.60921i	−0.625827	−	0.361321i	−0.779134	+	0.626857i	$0.784341\pi$
$242$	−1.04349	+	0.602460i	−0.0670782	+	0.0387276i
$243$	14.8207	+	4.83172i	0.950751	+	0.309955i
$244$		−	11.4583i		−	0.733544i
$245$		0			0
$246$	8.18350	+	5.43943i	0.521761	+	0.346806i
$247$	−8.58343	−	14.8669i	−0.546151	−	0.945961i
$248$	4.89070			0.310560
$249$	2.37930	+	4.79544i	0.150782	+	0.303898i
$250$		−	24.6663i		−	1.56004i
$251$	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
$254$			20.1007i			1.26123i
$255$	3.27126	−	4.92153i	0.204854	−	0.308198i
$256$	8.05134			0.503209
$257$	−4.69024	−	8.12373i	−0.292569	−	0.506745i	0.681847	−	0.731494i	$-0.261177\pi$
$257$	−4.69024	−	8.12373i	−0.292569	−	0.506745i	−0.974416	+	0.224750i	$0.927843\pi$
$258$	−6.33938	+	3.14534i	−0.394672	+	0.195820i
$259$		0			0
$260$		−	15.5060i		−	0.961641i
$261$	−22.5413	+	9.46504i	−1.39527	+	0.585871i
$262$	−4.46647	+	2.57872i	−0.275940	+	0.159314i
$263$	−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	$0.754157\pi$
$264$	−2.53669	+	3.81639i	−0.156122	+	0.234882i
$265$	−11.0294	−	6.36784i	−0.677532	−	0.391173i
$266$		0			0
$267$	−4.71274	+	7.09021i	−0.288415	+	0.433914i
$268$	1.61147			0.0984362
$269$	8.16473	+	14.1417i	0.497812	+	0.862236i	0.999997	−	0.00252412i	$-0.000803452\pi$
$269$	8.16473	+	14.1417i	0.497812	+	0.862236i	−0.502184	+	0.864761i	$0.667470\pi$
$270$	21.4937	−	7.47064i	1.30807	−	0.454649i
$271$	12.6186	+	7.28538i	0.766528	+	0.442555i	0.831635	−	0.555323i	$-0.187405\pi$
$271$	12.6186	+	7.28538i	0.766528	+	0.442555i	−0.0651065	+	0.997878i	$0.520739\pi$
$272$	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
$276$	4.30635	−	2.13663i	0.259212	−	0.128610i
$277$	−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	$0.835490\pi$
$278$	−10.4187	+	18.0457i	−0.624873	+	1.08231i
$279$	2.25116	−	17.7634i	0.134773	−	1.06347i
$280$		0			0
$281$	−4.76893	+	2.75334i	−0.284490	+	0.164251i	−0.635455	−	0.772138i	$-0.719187\pi$
$281$	−4.76893	+	2.75334i	−0.284490	+	0.164251i	0.350964	+	0.936389i	$0.385854\pi$
$282$	−1.85980	+	29.4678i	−0.110749	+	1.75478i
$283$		−	30.2829i		−	1.80013i	−0.435756	−	0.900065i	$-0.643519\pi$
$283$		−	30.2829i		−	1.80013i	0.435756	−	0.900065i	$-0.356481\pi$
$284$		−	16.7740i		−	0.995353i
$285$	1.26129	−	19.9847i	0.0747124	−	1.18379i
$286$	18.1825	−	10.4977i	1.07515	−	0.620740i
$287$		0			0
$288$	−3.04059	+	23.9926i	−0.179168	+	1.41378i
$289$	7.16730	−	12.4141i	0.421606	−	0.730242i
$290$	−17.8437	+	30.9062i	−1.04782	+	1.81487i
$291$	3.72544	−	1.84841i	0.218389	−	0.108356i
$292$	−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
$296$	4.01168	+	2.31615i	0.233174	+	0.134623i
$297$	12.6938	+	10.9701i	0.736568	+	0.636549i
$298$	−9.69912	−	16.7994i	−0.561855	−	0.973161i
$299$	−3.60207			−0.208313
$300$	−1.45025	+	2.18187i	−0.0837304	+	0.125970i
$301$		0			0
$302$	−21.7220	−	12.5412i	−1.24996	−	0.721667i
$303$	3.37542	−	5.07824i	0.193913	−	0.291737i
$304$	14.6842	+	8.47795i	0.842198	+	0.486244i
$305$	−8.67313	+	5.00743i	−0.496622	+	0.286725i
$306$	−9.46292	+	3.97345i	−0.540959	+	0.227147i
$307$		−	3.11346i		−	0.177695i	−0.996045	−	0.0888473i	$-0.971682\pi$
$307$		−	3.11346i		−	0.177695i	0.996045	−	0.0888473i	$-0.0283183\pi$
$308$		0			0
$309$	24.3357	−	12.0744i	1.38441	−	0.686887i
$310$	−13.0686	−	22.6355i	−0.742247	−	1.28561i
$311$	−19.4521			−1.10303			−0.551514	−	0.834166i	$-0.685949\pi$
$311$	−19.4521			−1.10303			−0.551514	+	0.834166i	$0.685949\pi$
$312$	−2.43798	+	3.66789i	−0.138024	+	0.207653i
$313$			25.5447i			1.44387i	0.691959	+	0.721937i	$0.256748\pi$
$313$			25.5447i			1.44387i	−0.691959	+	0.721937i	$0.743252\pi$
$314$	37.4073			2.11101
$315$		0			0
$316$	33.8559			1.90454
$317$			16.2274i			0.911424i	0.890127	+	0.455712i	$0.150615\pi$
$317$			16.2274i			0.911424i	−0.890127	+	0.455712i	$0.849385\pi$
$318$	9.83075	+	19.8137i	0.551281	+	1.11110i
$319$	−26.3122			−1.47320
$320$	11.2461	+	19.4789i	0.628677	+	1.08890i
$321$	2.36492	+	1.57192i	0.131997	+	0.0877362i
$322$		0			0
$323$			9.03174i			0.502540i
$324$	−20.8391	−	5.36810i	−1.15773	−	0.298228i
$325$	1.70007	−	0.981535i	0.0943029	−	0.0544458i
$326$	32.3665	+	18.6868i	1.79262	+	1.03497i
$327$	4.47534	+	9.01997i	0.247487	+	0.498806i
$328$	−1.92126	−	1.10924i	−0.106084	−	0.0612474i
$329$		0			0
$330$	24.4416	+	1.54258i	1.34547	+	0.0849161i
$331$	23.3117			1.28132			0.640662	−	0.767823i	$-0.278660\pi$
$331$	23.3117			1.28132			0.640662	+	0.767823i	$0.278660\pi$
$332$	−3.69499	−	6.39992i	−0.202789	−	0.351241i
$333$	10.2590	−	13.5046i	0.562188	−	0.740048i
$334$	22.3902	+	12.9270i	1.22514	+	0.707334i
$335$	−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
$339$	23.3073	+	15.4920i	1.26588	+	0.841408i
$340$	−4.07897	+	7.06498i	−0.221213	+	0.383152i
$341$	9.63545	−	16.6891i	0.521789	−	0.903765i
$342$	−21.0372	+	27.6928i	−1.13756	+	1.49745i
$343$		0			0
$344$	1.38366	−	0.798855i	0.0746019	−	0.0430714i
$345$	−3.49920	−	2.32586i	−0.188391	−	0.125220i
$346$			19.0005i			1.02147i
$347$			21.7060i			1.16524i	0.812745	+	0.582619i	$0.197972\pi$
$347$			21.7060i			1.16524i	−0.812745	+	0.582619i	$0.802028\pi$
$348$	30.2328	−	15.0003i	1.62065	−	0.804098i
$349$	2.20868	−	1.27518i	0.118228	−	0.0682588i	−0.439720	−	0.898135i	$-0.644922\pi$
$349$	2.20868	−	1.27518i	0.118228	−	0.0682588i	0.557948	+	0.829876i	$0.311589\pi$
$350$		0			0
$351$	12.1998	+	10.5432i	0.651180	+	0.562756i
$352$	−13.0144	+	22.5416i	−0.693669	+	1.20147i
$353$	12.6873	−	21.9751i	0.675279	−	1.16962i	−0.301109	−	0.953590i	$-0.597357\pi$
$353$	12.6873	−	21.9751i	0.675279	−	1.16962i	0.976387	−	0.216027i	$-0.0693100\pi$
$354$	0.905771	−	14.3516i	0.0481412	−	0.762781i
$355$	−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
$359$	9.73735	+	5.62186i	0.513918	+	0.296711i	0.734443	−	0.678671i	$-0.237444\pi$
$359$	9.73735	+	5.62186i	0.513918	+	0.296711i	−0.220525	+	0.975381i	$0.570777\pi$
$360$	−4.73672	+	1.98893i	−0.249647	+	0.104826i
$361$	5.80204	+	10.0494i	0.305371	+	0.528917i
$362$	4.90676			0.257894
$363$	−0.442656	−	0.892167i	−0.0232334	−	0.0468266i
$364$		0			0
$365$	6.19166	+	3.57476i	0.324086	+	0.187111i
$366$	17.3586	+	1.09555i	0.907349	+	0.0572653i
$367$	−2.86810	−	1.65590i	−0.149714	−	0.0864372i	0.423272	−	0.906003i	$-0.360882\pi$
$367$	−2.86810	−	1.65590i	−0.149714	−	0.0864372i	−0.572985	+	0.819566i	$0.694215\pi$
$368$	3.08114	−	1.77890i	0.160616	−	0.0927315i
$369$	−4.91318	+	6.46757i	−0.255770	+	0.336688i
$370$		−	24.7562i		−	1.28701i
$371$		0			0
$372$	−1.55692	+	24.6688i	−0.0807224	+	1.27902i
$373$	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	$0.778296\pi$
$374$	−11.0460			−0.571173
$375$	20.3478	+	1.28421i	1.05076	+	0.0663161i
$376$		−	6.66613i		−	0.343780i
$377$	−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	$0.531521\pi$
$380$			27.6432i			1.41807i
$381$	−16.5815	−	1.04651i	−0.849498	−	0.0536141i
$382$	−18.9358			−0.968842
$383$	17.1112	+	29.6374i	0.874339	+	1.51440i	0.857465	+	0.514542i	$0.172038\pi$
$383$	17.1112	+	29.6374i	0.874339	+	1.51440i	0.0168739	+	0.999858i	$0.494629\pi$
$384$	0.701503	−	11.1151i	0.0357984	−	0.567214i
$385$		0			0
$386$			11.4889i			0.584768i
$387$	−2.26461	−	5.39326i	−0.115117	−	0.274155i
$388$	−4.97191	+	2.87054i	−0.252411	+	0.145729i
$389$	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	$0.555656\pi$
$390$	23.4906	+	1.48255i	1.18949	+	0.0750721i
$391$	1.64121	+	0.947550i	0.0829993	+	0.0479197i
$392$		0			0
$393$	−1.89471	−	3.81875i	−0.0955753	−	0.192631i
$394$	−6.05480			−0.305036
$395$	−14.7954	−	25.6265i	−0.744440	−	1.28941i
$396$	−18.4424	−	14.0100i	−0.926767	−	0.704031i
$397$	25.5501	+	14.7513i	1.28232	+	0.740349i	0.977272	−	0.211988i	$-0.0679938\pi$
$397$	25.5501	+	14.7513i	1.28232	+	0.740349i	0.305049	+	0.952337i	$0.401327\pi$
$398$	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	$0.591590\pi$
$402$	−0.154075	+	2.44127i	−0.00768458	+	0.121760i
$403$	9.26052	−	16.0397i	0.461300	−	0.798994i
$404$	−4.20884	+	7.28993i	−0.209398	+	0.362687i
$405$	5.04368	+	18.1196i	0.250622	+	0.900370i
$406$		0			0
$407$	15.8073	−	9.12634i	0.783538	−	0.452376i
$408$	2.07568	−	1.02987i	0.102761	−	0.0509859i
$409$		−	30.2755i		−	1.49703i	−0.663121	−	0.748513i	$-0.730768\pi$
$409$		−	30.2755i		−	1.49703i	0.663121	−	0.748513i	$-0.269232\pi$
$410$			11.8561i			0.585532i
$411$	−25.0795	−	16.6699i	−1.23708	−	0.822265i
$412$	−32.4781	+	18.7512i	−1.60008	+	0.923806i
$413$		0			0
$414$	2.82512	+	6.72812i	0.138847	+	0.330669i
$415$	−3.22952	+	5.59369i	−0.158531	+	0.274583i
$416$	−12.5080	+	21.6645i	−0.613254	+	1.06219i
$417$	−14.3439	−	9.53416i	−0.702425	−	0.466890i
$418$	−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	$0.773093\pi$
$422$	−28.7899	−	16.6219i	−1.40147	−	0.809140i
$423$	−24.2119	−	3.06838i	−1.17722	−	0.149190i
$424$	−2.49682	−	4.32463i	−0.121256	−	0.210022i
$425$	−1.03280			−0.0500982
$426$	25.4115	+	1.60379i	1.23119	+	0.0777038i
$427$		0			0
$428$	−3.39490	−	1.96005i	−0.164099	−	0.0947424i
$429$	7.71314	+	15.5457i	0.372394	+	0.750554i
$430$	−7.39464	−	4.26930i	−0.356601	−	0.205884i
$431$	20.0311	−	11.5650i	0.964865	−	0.557065i	0.0671983	−	0.997740i	$-0.478594\pi$
$431$	20.0311	−	11.5650i	0.964865	−	0.557065i	0.897667	+	0.440674i	$0.145261\pi$
$432$	−15.6424	−	2.99353i	−0.752593	−	0.144026i
$433$			34.9265i			1.67846i	0.543776	+	0.839230i	$0.316994\pi$
$433$			34.9265i			1.67846i	−0.543776	+	0.839230i	$0.683006\pi$
$434$		0			0
$435$	−24.5662	−	16.3288i	−1.17786	−	0.782904i
$436$	−6.95010	−	12.0379i	−0.332849	−	0.576512i
$437$	6.42155			0.307185
$438$	−5.51876	−	11.1230i	−0.263696	−	0.531476i
$439$		−	38.8952i		−	1.85637i	−0.372122	−	0.928184i	$-0.621370\pi$
$439$		−	38.8952i		−	1.85637i	0.372122	−	0.928184i	$-0.378630\pi$
$440$	−5.52912			−0.263590
$441$		0			0
$442$	−10.6161			−0.504959
$443$		−	37.3289i		−	1.77355i	−0.462204	−	0.886774i	$-0.652941\pi$
$443$		−	37.3289i		−	1.77355i	0.462204	−	0.886774i	$-0.347059\pi$
$444$	−12.9598	+	19.4977i	−0.615045	+	0.925321i
$445$	−10.2722			−0.486948
$446$	−16.3675	−	28.3493i	−0.775023	−	1.34238i
$447$	14.3632	−	7.12640i	0.679354	−	0.337067i
$448$		0			0
$449$		−	23.9224i		−	1.12897i	−0.825445	−	0.564483i	$-0.809076\pi$
$449$		−	23.9224i		−	1.12897i	0.825445	−	0.564483i	$-0.190924\pi$
$450$	−3.16673	−	2.40565i	−0.149281	−	0.113403i
$451$	−7.57036	+	4.37075i	−0.356474	+	0.205810i
$452$	−33.4582	−	19.3171i	−1.57374	−	0.908600i
$453$	11.4765	−	17.2661i	0.539212	−	0.811232i
$454$	3.77628	+	2.18024i	0.177230	+	0.102324i
$455$		0			0
$456$	4.34629	−	6.53889i	0.203534	−	0.306212i
$457$	9.98063			0.466874			0.233437	−	0.972372i	$-0.425003\pi$
$457$	9.98063			0.466874			0.233437	+	0.972372i	$0.425003\pi$
$458$	6.74155	+	11.6767i	0.315012	+	0.545617i
$459$	−2.78513	−	8.01306i	−0.129999	−	0.374017i
$460$	5.02319	+	2.90014i	0.234207	+	0.135220i
$461$	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
$465$	19.3529	−	9.60212i	0.897470	−	0.445288i
$466$	16.3595	−	28.3355i	0.757839	−	1.31262i
$467$	20.1395	−	34.8827i	0.931946	−	1.61418i	0.151955	−	0.988387i	$-0.451443\pi$
$467$	20.1395	−	34.8827i	0.931946	−	1.61418i	0.779991	−	0.625791i	$-0.215224\pi$
$468$	−17.7248	−	13.4649i	−0.819330	−	0.622415i
$469$		0			0
$470$	−30.8527	+	17.8128i	−1.42313	+	0.821643i
$471$	−1.94754	+	30.8581i	−0.0897379	+	1.42187i
$472$			3.24659i			0.149436i
$473$		−	6.29549i		−	0.289467i
$474$	−3.23702	+	51.2894i	−0.148681	+	2.35580i
$475$	−3.03078	+	1.74982i	−0.139062	+	0.0802874i
$476$		0			0
$477$	−16.8566	+	7.07805i	−0.771812	+	0.324082i
$478$	−17.9994	+	31.1759i	−0.823275	+	1.42595i
$479$	0.0777513	−	0.134669i	0.00355255	−	0.00615319i	−0.864244	−	0.503073i	$-0.832203\pi$
$479$	0.0777513	−	0.134669i	0.00355255	−	0.00615319i	0.867796	+	0.496920i	$0.165536\pi$
$480$	−26.1396	+	12.9694i	−1.19310	+	0.591968i
$481$	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
$485$	4.34558	+	2.50892i	0.197323	+	0.113924i
$486$	10.1248	−	31.0566i	0.459269	−	1.40876i
$487$	8.25111	+	14.2913i	0.373893	+	0.647602i	0.990161	−	0.139935i	$-0.0446892\pi$
$487$	8.25111	+	14.2913i	0.373893	+	0.647602i	−0.616267	+	0.787537i	$0.711356\pi$
$488$	−3.92682			−0.177759
$489$	−17.1003	+	25.7270i	−0.773302	+	1.16342i
$490$		0			0
$491$	8.10003	+	4.67655i	0.365549	+	0.211050i	0.671512	−	0.740993i	$-0.265645\pi$
$491$	8.10003	+	4.67655i	0.365549	+	0.211050i	−0.305963	+	0.952043i	$0.598978\pi$
$492$	6.20665	−	9.33776i	0.279817	−	0.420979i
$493$	11.5221	+	6.65230i	0.518930	+	0.299604i
$494$	−31.1534	+	17.9864i	−1.40166	+	0.809248i
$495$	−2.54502	+	20.0822i	−0.114390	+	0.902626i
$496$			18.2934i			0.821399i
$497$		0			0
$498$	10.0487	−	4.98577i	0.450295	−	0.223418i
$499$	−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	$0.847561\pi$
$500$	−28.1454			−1.25870
$501$	−11.8295	+	17.7972i	−0.528503	+	0.795120i
$502$		−	23.8544i		−	1.06467i
$503$	−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
$506$			7.85366i			0.349138i
$507$	−2.59471	−	5.22960i	−0.115235	−	0.232255i
$508$	22.9358			1.01761
$509$	7.59893	+	13.1617i	0.336817	+	0.583383i	0.983832	−	0.179093i	$-0.0573164\pi$
$509$	7.59893	+	13.1617i	0.336817	+	0.583383i	−0.647016	+	0.762477i	$0.723983\pi$
$510$	−10.3130	−	6.85486i	−0.456667	−	0.303538i
$511$		0			0
$512$		−	29.7316i		−	1.31396i
$513$	−21.7492	−	18.7959i	−0.960249	−	0.829857i
$514$	−17.0231	+	9.82831i	−0.750858	+	0.433508i
$515$	28.3867	+	16.3890i	1.25087	+	0.722187i
$516$	3.58897	+	7.23352i	0.157996	+	0.318438i
$517$	−22.7476	−	13.1333i	−1.00044	−	0.577603i
$518$		0			0
$519$	−15.6739	−	0.989225i	−0.688010	−	0.0434222i
$520$	−5.31397			−0.233033
$521$	20.6160	+	35.7080i	0.903204	+	1.56440i	0.823310	+	0.567592i	$0.192125\pi$
$521$	20.6160	+	35.7080i	0.903204	+	1.56440i	0.0798940	+	0.996803i	$0.474542\pi$
$522$	19.8338	+	47.2349i	0.868102	+	2.06742i
$523$	−37.0311	−	21.3799i	−1.61926	−	0.934878i	−0.987113	−	0.160026i	$-0.948842\pi$
$523$	−37.0311	−	21.3799i	−1.61926	−	0.934878i	−0.632143	−	0.774852i	$-0.717824\pi$
$524$	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
$528$	−14.2750	−	9.48835i	−0.621240	−	0.412928i
$529$	−10.8263	+	18.7517i	−0.470708	+	0.815291i
$530$	−13.3437	+	23.1119i	−0.579613	+	1.00392i
$531$	11.7919	+	1.49438i	0.511723	+	0.0648507i
$532$		0			0
$533$	−7.27579	+	4.20068i	−0.315149	+	0.181952i
$534$	14.8574	+	9.87546i	0.642942	+	0.427353i
$535$			3.42626i			0.148130i
$536$		−	0.552258i		−	0.0238539i
$537$	23.3062	−	11.5635i	1.00574	−	0.499004i
$538$	29.6337	−	17.1090i	1.27760	−	0.737623i
$539$		0			0
$540$	−8.52435	−	24.5253i	−0.366830	−	1.05540i
$541$	8.04309	−	13.9310i	0.345800	−	0.598942i	−0.639699	−	0.768625i	$-0.720941\pi$
$541$	8.04309	−	13.9310i	0.345800	−	0.598942i	0.985499	+	0.169683i	$0.0542744\pi$
$542$	15.2664	−	26.4421i	0.655747	−	1.13579i
$543$	−0.255461	+	4.04770i	−0.0109629	+	0.173704i
$544$	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	$0.915074\pi$
$548$	36.0021	+	20.7858i	1.53794	+	0.887927i
$549$	−1.80749	+	14.2625i	−0.0771417	+	0.608708i
$550$	−2.14006	−	3.70669i	−0.0912525	−	0.158054i
$551$	45.0827			1.92059
$552$	−0.732233	−	1.47580i	−0.0311659	−	0.0628144i
$553$		0			0
$554$	52.1078	+	30.0845i	2.21385	+	1.27817i
$555$	20.4220	+	1.28889i	0.866864	+	0.0547101i
$556$	20.5910	+	11.8882i	0.873254	+	0.504173i
$557$	26.4006	−	15.2424i	1.11863	−	0.645841i	0.177579	−	0.984107i	$-0.443173\pi$
$557$	26.4006	−	15.2424i	1.11863	−	0.645841i	0.941051	+	0.338265i	$0.109840\pi$
$558$	−37.2228	−	4.71726i	−1.57577	−	0.199697i
$559$		−	6.05052i		−	0.255910i
$560$		0			0
$561$	0.575088	−	9.11207i	0.0242802	−	0.384712i
$562$	5.76958	+	9.99320i	0.243375	+	0.421538i
$563$	22.5371			0.949828			0.474914	−	0.880032i	$-0.342479\pi$
$563$	22.5371			0.949828			0.474914	+	0.880032i	$0.342479\pi$
$564$	33.6242	+	2.12211i	1.41583	+	0.0893571i
$565$			33.7673i			1.42060i
$566$	−63.4572			−2.66730
$567$		0			0
$568$	−5.74852			−0.241202
$569$		−	44.5639i		−	1.86822i	−0.356992	−	0.934108i	$-0.616198\pi$
$569$		−	44.5639i		−	1.86822i	0.356992	−	0.934108i	$-0.383802\pi$
$570$	−41.8776	−	2.64301i	−1.75406	−	0.110704i
$571$	35.2830			1.47655			0.738274	−	0.674501i	$-0.235641\pi$
$571$	35.2830			1.47655			0.738274	+	0.674501i	$0.235641\pi$
$572$	−11.9783	−	20.7471i	−0.500839	−	0.867479i
$573$	0.985859	−	15.6206i	0.0411849	−	0.652561i
$574$		0			0
$575$			0.734319i			0.0306232i
$576$	32.0319	+	4.05941i	1.33466	+	0.169142i
$577$	−3.25158	+	1.87730i	−0.135365	+	0.0781531i	−0.566153	−	0.824300i	$-0.691569\pi$
$577$	−3.25158	+	1.87730i	−0.135365	+	0.0781531i	0.430788	+	0.902453i	$0.358236\pi$
$578$	−26.0136	−	15.0189i	−1.08202	−	0.624705i
$579$	−9.47744	−	0.598147i	−0.393869	−	0.0248581i
$580$	35.2654	+	20.3605i	1.46432	+	0.845423i
$581$		0			0
$582$	−3.87330	−	7.80658i	−0.160554	−	0.323593i
$583$	−19.6765			−0.814919
$584$	1.40166	+	2.42775i	0.0580011	+	0.100461i
$585$	−2.44599	+	19.3007i	−0.101129	+	0.797987i
$586$	12.8615	+	7.42559i	0.531304	+	0.306748i
$587$	−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
$591$	0.315232	−	4.99475i	0.0129669	−	0.205456i
$592$	−8.66343	+	15.0055i	−0.356065	+	0.616722i
$593$	−18.5588	+	32.1448i	−0.762120	+	1.32003i	0.179636	+	0.983733i	$0.442508\pi$
$593$	−18.5588	+	32.1448i	−0.762120	+	1.32003i	−0.941756	+	0.336297i	$0.890825\pi$
$594$	22.9876	−	26.5996i	0.943193	−	1.09139i
$595$		0			0
$596$	−19.1689	+	11.0671i	−0.785187	+	0.453328i
$597$	−7.98012	+	3.95940i	−0.326605	+	0.162048i
$598$			7.54806i			0.308663i
$599$		−	28.3119i		−	1.15679i	−0.815756	−	0.578396i	$-0.803679\pi$
$599$		−	28.3119i		−	1.15679i	0.815756	−	0.578396i	$-0.196321\pi$
$600$	0.747737	+	0.497008i	0.0305262	+	0.0202903i
$601$	20.8341	−	12.0286i	0.849840	−	0.490655i	−0.0107568	−	0.999942i	$-0.503424\pi$
$601$	20.8341	−	12.0286i	0.849840	−	0.490655i	0.860597	+	0.509287i	$0.170091\pi$
$602$		0			0
$603$	−2.00584	−	0.254201i	−0.0816841	−	0.0103519i
$604$	−14.3101	+	24.7859i	−0.582271	+	1.00852i
$605$	0.600836	−	1.04068i	0.0244274	−	0.0423096i
$606$	−10.6414	−	7.07312i	−0.432275	−	0.287326i
$607$	−8.24496	+	4.76023i	−0.334653	+	0.193212i	−0.657905	−	0.753101i	$-0.728557\pi$
$607$	−8.24496	+	4.76023i	−0.334653	+	0.193212i	0.323252	+	0.946313i	$0.395224\pi$
$608$	22.2985	−	38.6221i	0.904323	−	1.56633i
$609$		0			0
$610$	10.4930	+	18.1744i	0.424848	+	0.735859i
$611$	−21.8625	−	12.6223i	−0.884461	−	0.510644i
$612$	4.53390	+	10.7976i	0.183272	+	0.436469i
$613$	1.23108	+	2.13230i	0.0497230	+	0.0861227i	0.889816	−	0.456320i	$-0.150833\pi$
$613$	1.23108	+	2.13230i	0.0497230	+	0.0861227i	−0.840093	+	0.542443i	$0.817499\pi$
$614$	−6.52420			−0.263295
$615$	−9.78040	−	0.617267i	−0.394384	−	0.0248906i
$616$		0			0
$617$	18.7738	+	10.8390i	0.755804	+	0.436364i	0.827787	−	0.561042i	$-0.189599\pi$
$617$	18.7738	+	10.8390i	0.755804	+	0.436364i	−0.0719831	+	0.997406i	$0.522933\pi$
$618$	−25.3016	−	50.9950i	−1.01778	−	2.05132i
$619$	20.8767	+	12.0532i	0.839105	+	0.484457i	0.856960	−	0.515383i	$-0.172350\pi$
$619$	20.8767	+	12.0532i	0.839105	+	0.484457i	−0.0178550	+	0.999841i	$0.505684\pi$
$620$	−25.8281	+	14.9119i	−1.03728	+	0.598875i
$621$	−5.69727	+	1.98022i	−0.228624	+	0.0794635i
$622$			40.7615i			1.63439i
$623$		0			0
$624$	−13.7196	−	9.11915i	−0.549222	−	0.365058i
$625$	10.7184	+	18.5648i	0.428735	+	0.742591i
$626$	53.5285			2.13943
$627$	−13.7505	−	27.7140i	−0.549143	−	1.10679i
$628$		−	42.6834i		−	1.70325i
$629$	−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	$0.478599\pi$
$632$		−	11.6026i		−	0.461525i
$633$	15.2107	−	22.8841i	0.604569	−	0.909561i
$634$	34.0043			1.35048
$635$	−10.0232	−	17.3608i	−0.397761	−	0.688941i
$636$	22.6084	−	11.2173i	0.896481	−	0.444797i
$637$		0			0
$638$			55.1368i			2.18289i
$639$	−2.64601	+	20.8790i	−0.104674	+	0.825962i
$640$	11.6374	−	6.71887i	0.460010	−	0.265587i
$641$	−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	$0.915715\pi$
$642$	3.29393	−	4.95565i	0.130001	−	0.195584i
$643$	3.03956	+	1.75489i	0.119868	+	0.0692060i	0.558735	−	0.829346i	$-0.311287\pi$
$643$	3.03956	+	1.75489i	0.119868	+	0.0692060i	−0.438867	+	0.898552i	$0.644620\pi$
$644$		0			0
$645$	3.90683	−	5.87774i	0.153831	−	0.231436i
$646$	18.9258			0.744627
$647$	−7.02996	−	12.1762i	−0.276376	−	0.478698i	0.694105	−	0.719874i	$-0.255800\pi$
$647$	−7.02996	−	12.1762i	−0.276376	−	0.478698i	−0.970481	+	0.241176i	$0.922467\pi$
$648$	−1.83967	+	7.14164i	−0.0722691	+	0.280550i
$649$	11.0787	+	6.39629i	0.434877	+	0.251076i
$650$	−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	$0.407853\pi$
$654$	18.9012	−	9.37798i	0.739095	−	0.366708i
$655$	2.57177	−	4.45443i	0.100487	−	0.174049i
$656$	4.14905	−	7.18637i	0.161993	−	0.280581i
$657$	9.46292	−	3.97345i	0.369184	−	0.155019i
$658$		0			0
$659$	5.03144	−	2.90491i	0.195997	−	0.113159i	−0.398790	−	0.917042i	$-0.630570\pi$
$659$	5.03144	−	2.90491i	0.195997	−	0.113159i	0.594787	+	0.803883i	$0.297236\pi$
$660$	1.76015	−	27.8890i	0.0685139	−	1.08558i
$661$			9.71786i			0.377981i	0.981979	+	0.188991i	$0.0605215\pi$
$661$			9.71786i			0.377981i	−0.981979	+	0.188991i	$0.939478\pi$
$662$		−	48.8491i		−	1.89858i
$663$	0.552710	−	8.75751i	0.0214655	−	0.340114i
$664$	−2.19328	+	1.26629i	−0.0851158	+	0.0491416i
$665$		0			0
$666$	−28.2987	−	21.4975i	−1.09655	−	0.833010i
$667$	4.72977	−	8.19220i	0.183137	−	0.317203i
$668$	14.7503	−	25.5483i	0.570707	−	0.988493i
$669$	24.2382	−	12.0260i	0.937102	−	0.464951i
$670$	−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	$0.659629\pi$
$674$	−21.5415	−	12.4370i	−0.829747	−	0.479055i
$675$	2.14935	−	2.48707i	0.0827284	−	0.0957272i
$676$	4.02953	+	6.97935i	0.154982	+	0.268436i
$677$	−45.4112			−1.74530			−0.872648	−	0.488350i	$-0.837599\pi$
$677$	−45.4112			−1.74530			−0.872648	+	0.488350i	$0.837599\pi$
$678$	32.4631	−	48.8400i	1.24674	−	1.87569i
$679$		0			0
$680$	2.42120	+	1.39788i	0.0928487	+	0.0536062i
$681$	−1.99513	+	3.00163i	−0.0764537	+	0.115023i
$682$	−34.9717	−	20.1909i	−1.33913	−	0.773150i
$683$	−37.6543	+	21.7397i	−1.44080	+	0.831848i	−0.997903	−	0.0647226i	$-0.979384\pi$
$683$	−37.6543	+	21.7397i	−1.44080	+	0.831848i	−0.442900	+	0.896571i	$0.646050\pi$
$684$	31.5988	+	24.0044i	1.20821	+	0.917832i
$685$		−	36.3347i		−	1.38828i
$686$		0			0
$687$	−9.98338	+	4.95334i	−0.380890	+	0.188982i
$688$	2.98808	+	5.17551i	0.113919	+	0.197314i
$689$	−18.9109			−0.720448
$690$	−4.87380	+	7.33251i	−0.185542	+	0.279144i
$691$			27.3654i			1.04103i	0.853853	+	0.520514i	$0.174260\pi$
$691$			27.3654i			1.04103i	−0.853853	+	0.520514i	$0.825740\pi$
$692$	21.6804			0.824166
$693$		0			0
$694$	45.4845			1.72657
$695$		−	20.7812i		−	0.788277i
$696$	−5.14065	−	10.3609i	−0.194856	−	0.392729i
$697$	4.42008			0.167422
$698$	−2.67212	−	4.62824i	−0.101141	−	0.175182i
$699$	22.5229	+	14.9706i	0.851893	+	0.566239i
$700$		0			0
$701$		−	8.26437i		−	0.312141i	−0.987746	−	0.156070i	$-0.950117\pi$
$701$		−	8.26437i		−	0.312141i	0.987746	−	0.156070i	$-0.0498827\pi$
$702$	22.0931	−	25.5645i	0.833852	−	0.964872i
$703$	−27.0838	+	15.6368i	−1.02148	+	0.589754i
$704$	30.0947	+	17.3752i	1.13424	+	0.654852i
$705$	−13.0879	−	26.3785i	−0.492919	−	0.993471i
$706$	−46.0484	−	26.5861i	−1.73306	−	1.00058i
$707$		0			0
$708$	−16.3759	−	1.03353i	−0.615444	−	0.0388423i
$709$	42.8171			1.60803			0.804015	−	0.594608i	$-0.202693\pi$
$709$	42.8171			1.60803			0.804015	+	0.594608i	$0.202693\pi$
$710$	15.3608	+	26.6057i	0.576481	+	0.998494i
$711$	−42.1413	−	5.34058i	−1.58042	−	0.200287i
$712$	−3.48810	−	2.01385i	−0.130722	−	0.0754724i
$713$	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
$717$	−24.7806	−	16.4713i	−0.925450	−	0.615131i
$718$	11.7805	−	20.4044i	0.439645	−	0.761487i
$719$	11.5725	−	20.0442i	0.431583	−	0.747523i	−0.565427	−	0.824798i	$-0.691289\pi$
$719$	11.5725	−	20.0442i	0.431583	−	0.747523i	0.997010	+	0.0772751i	$0.0246220\pi$
$720$	−7.43951	−	17.7175i	−0.277254	−	0.660291i
$721$		0			0
$722$	21.0584	−	12.1581i	0.783712	−	0.452477i
$723$	−16.1823	−	10.7561i	−0.601825	−	0.400023i
$724$		−	5.59884i		−	0.208079i
$725$			5.15530i			0.191463i
$726$	−1.86952	+	0.927578i	−0.0693844	+	0.0344256i
$727$	4.76878	−	2.75326i	0.176864	−	0.102113i	−0.408954	−	0.912555i	$-0.634106\pi$
$727$	4.76878	−	2.75326i	0.176864	−	0.102113i	0.585819	+	0.810442i	$0.300773\pi$
$728$		0			0
$729$	25.0922	+	9.96907i	0.929340	+	0.369225i
$730$	7.49084	−	12.9745i	0.277248	−	0.480208i
$731$	−1.59163	+	2.75679i	−0.0588687	+	0.101964i
$732$	1.25007	−	19.8070i	0.0462040	−	0.732087i
$733$	3.45543	−	1.99499i	0.127629	−	0.0736867i	−0.434826	−	0.900514i	$-0.643190\pi$
$733$	3.45543	−	1.99499i	0.127629	−	0.0736867i	0.562455	+	0.826828i	$0.309857\pi$
$734$	−3.46991	+	6.01005i	−0.128077	+	0.221835i
$735$		0			0
$736$	−4.67882	−	8.10395i	−0.172463	−	0.298716i
$737$	−1.88453	−	1.08803i	−0.0694176	−	0.0400783i
$738$	13.5527	+	10.2955i	0.498881	+	0.378981i
$739$	0.871657	+	1.50976i	0.0320644	+	0.0555372i	0.881612	−	0.471974i	$-0.156458\pi$
$739$	0.871657	+	1.50976i	0.0320644	+	0.0555372i	−0.849548	+	0.527512i	$0.823125\pi$
$740$	−28.2480			−1.03842
$741$	−13.2155	−	26.6356i	−0.485483	−	0.978483i
$742$		0			0
$743$	8.70204	+	5.02413i	0.319247	+	0.184317i	0.651057	−	0.759029i	$-0.274326\pi$
$743$	8.70204	+	5.02413i	0.319247	+	0.184317i	−0.331810	+	0.943346i	$0.607659\pi$
$744$	8.45412	+	0.533563i	0.309943	+	0.0195614i
$745$	16.7541	+	9.67296i	0.613821	+	0.354390i
$746$	12.0597	−	6.96267i	0.441537	−	0.254921i
$747$	3.58971	+	8.54902i	0.131341	+	0.312792i
$748$			12.6040i			0.460846i
$749$		0			0
$750$	2.69103	−	42.6385i	0.0982626	−	1.55694i
$751$	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	$0.693278\pi$
$752$	24.9344			0.909262
$753$	19.6781	+	1.24194i	0.717108	+	0.0452586i
$754$			52.9913i			1.92983i
$755$	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	$0.583880\pi$
$758$			8.06634i			0.292983i
$759$	−6.47867	−	0.408886i	−0.235161	−	0.0148416i
$760$	9.47344			0.343638
$761$	−11.3178	−	19.6029i	−0.410268	−	0.710606i	0.584650	−	0.811285i	$-0.301232\pi$
$761$	−11.3178	−	19.6029i	−0.410268	−	0.710606i	−0.994919	+	0.100680i	$0.967898\pi$
$762$	−2.19293	+	34.7463i	−0.0794416	+	1.25873i
$763$		0			0
$764$			21.6067i			0.781702i
$765$	6.19166	−	8.15054i	0.223860	−	0.294683i
$766$	62.1046	−	35.8561i	2.24393	−	1.29553i
$767$	10.6476	+	6.14741i	0.384463	+	0.221970i
$768$	13.9176	+	0.878380i	0.502210	+	0.0316958i
$769$	42.6873	+	24.6455i	1.53934	+	0.888741i	0.998877	+	0.0473762i	$0.0150860\pi$
$769$	42.6873	+	24.6455i	1.53934	+	0.888741i	0.540468	+	0.841365i	$0.318247\pi$
$770$		0			0
$771$	−7.22133	−	14.5545i	−0.260070	−	0.524167i
$772$	13.1093			0.471815
$773$	−11.0083	−	19.0670i	−0.395943	−	0.685793i	0.597278	−	0.802034i	$-0.296249\pi$
$773$	−11.0083	−	19.0670i	−0.395943	−	0.685793i	−0.993221	+	0.116241i	$0.962915\pi$
$774$	−11.3015	+	4.74545i	−0.406223	+	0.170572i
$775$	−3.26986	−	1.88785i	−0.117457	−	0.0678137i
$776$	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
$780$	1.69166	−	26.8038i	0.0605713	−	0.959732i
$781$	−11.3255	+	19.6163i	−0.405258	+	0.701927i
$782$	1.98557	−	3.43911i	0.0710040	−	0.122982i
$783$	−39.9978	+	13.9022i	−1.42941	+	0.496823i
$784$		0			0
$785$	−32.3083	+	18.6532i	−1.15313	+	0.665761i
$786$	−8.00213	+	3.97032i	−0.285426	+	0.141617i
$787$			10.8554i			0.386954i	0.981105	+	0.193477i	$0.0619765\pi$
$787$			10.8554i			0.386954i	−0.981105	+	0.193477i	$0.938024\pi$
$788$			6.90881i			0.246116i
$789$	−12.6982	−	8.44025i	−0.452067	−	0.300481i
$790$	−53.6998	+	31.0036i	−1.91055	+	1.10306i
$791$		0			0
$792$	−4.80130	+	6.32030i	−0.170607	+	0.224582i
$793$	−7.43542	+	12.8785i	−0.264039	+	0.457330i
$794$	30.9112	−	53.5397i	1.09700	−	1.90005i
$795$	−18.3709	−	12.2108i	−0.651548	−	0.433073i
$796$	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
$800$	4.41653	+	2.54988i	0.156148	+	0.0901520i
$801$	−8.92002	+	11.7421i	−0.315173	+	0.414886i
$802$	30.4312	+	52.7084i	1.07456	+	1.86120i
$803$	11.0460			0.389803
$804$	2.78560	+	0.175807i	0.0982407	+	0.00620024i
$805$		0			0
$806$	−33.6109	−	19.4053i	−1.18389	−	0.683521i
$807$	12.5708	+	25.3363i	0.442514	+	0.891880i
$808$	2.49829	+	1.44239i	0.0878896	+	0.0507431i
$809$	−36.0199	+	20.7961i	−1.26639	+	0.731152i	−0.974303	−	0.225240i	$-0.927683\pi$
$809$	−36.0199	+	20.7961i	−1.26639	+	0.731152i	−0.292088	+	0.956391i	$0.594350\pi$
$810$	37.9693	−	10.5689i	1.33411	−	0.371354i
$811$			13.3293i			0.468056i	0.972230	+	0.234028i	$0.0751907\pi$
$811$			13.3293i			0.468056i	−0.972230	+	0.234028i	$0.924809\pi$
$812$		0			0
$813$	21.0179	+	13.9703i	0.737131	+	0.489958i
$814$	−19.1241	−	33.1239i	−0.670299	−	1.16099i
$815$	−37.2729			−1.30561
$816$	3.85216	+	7.76398i	0.134853	+	0.271794i
$817$			10.7865i			0.377372i
$818$	−63.4417			−2.21819
$819$		0			0
$820$	13.5284			0.472432
$821$			38.6054i			1.34734i	0.739034	+	0.673668i	$0.235282\pi$
$821$			38.6054i			1.34734i	−0.739034	+	0.673668i	$0.764718\pi$
$822$	−34.9314	+	52.5535i	−1.21837	+	1.83302i
$823$	−10.6976			−0.372896			−0.186448	−	0.982465i	$-0.559698\pi$
$823$	−10.6976			−0.372896			−0.186448	+	0.982465i	$0.559698\pi$
$824$	6.42613	+	11.1304i	0.223865	+	0.387745i
$825$	3.16916	−	1.57240i	0.110336	−	0.0547441i
$826$		0			0
$827$			11.7079i			0.407125i	0.979062	+	0.203562i	$0.0652520\pi$
$827$			11.7079i			0.407125i	−0.979062	+	0.203562i	$0.934748\pi$
$828$	7.67710	−	3.22359i	0.266798	−	0.112028i
$829$	15.0948	−	8.71498i	0.524263	−	0.302684i	−0.214414	−	0.976743i	$-0.568784\pi$
$829$	15.0948	−	8.71498i	0.524263	−	0.302684i	0.738677	+	0.674059i	$0.235451\pi$
$830$	11.7215	+	6.76740i	0.406858	+	0.234900i
$831$	−27.5303	+	41.4187i	−0.955015	+	1.43680i
$832$	28.9237	+	16.6991i	1.00275	+	0.578937i
$833$		0			0
$834$	−19.9786	+	30.0574i	−0.691804	+	1.04080i
$835$	−25.7843			−0.892302
$836$	21.3543	+	36.9867i	0.738553	+	1.27921i
$837$	5.82931	−	30.4604i	0.201491	−	1.05286i
$838$	−66.3838	−	38.3267i	−2.29319	−	1.32397i
$839$	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
$843$	−8.54401	+	4.23918i	−0.294271	+	0.146005i
$844$	−18.9663	+	32.8506i	−0.652848	+	1.13077i
$845$	3.52191	−	6.10012i	0.121157	−	0.209851i
$846$	−6.42973	+	50.7356i	−0.221059	+	1.74432i
$847$		0			0
$848$	16.1761	−	9.33925i	0.555488	−	0.320711i
$849$	3.30378	−	52.3473i	0.113385	−	1.79656i
$850$			2.16421i			0.0742319i
$851$			6.56205i			0.224944i
$852$	1.83000	−	28.9957i	0.0626947	−	0.993376i
$853$	−28.0716	+	16.2071i	−0.961153	+	0.554922i	−0.896528	−	0.442987i	$-0.853919\pi$
$853$	−28.0716	+	16.2071i	−0.961153	+	0.554922i	−0.0646255	+	0.997910i	$0.520585\pi$
$854$		0			0
$855$	4.36056	−	34.4082i	0.149128	−	1.17674i
$856$	−0.671716	+	1.16345i	−0.0229588	+	0.0397658i
$857$	−22.2270	+	38.4982i	−0.759258	+	1.31507i	0.183971	+	0.982932i	$0.441105\pi$
$857$	−22.2270	+	38.4982i	−0.759258	+	1.31507i	−0.943229	+	0.332142i	$0.892229\pi$
$858$	32.5758	−	16.1627i	1.11212	−	0.551787i
$859$	−13.5528	+	7.82472i	−0.462416	+	0.266976i	−0.713060	−	0.701103i	$-0.752691\pi$
$859$	−13.5528	+	7.82472i	−0.462416	+	0.266976i	0.250644	+	0.968079i	$0.419358\pi$
$860$	−4.87147	+	8.43763i	−0.166116	+	0.287721i
$861$		0			0
$862$	−24.2342	−	41.9748i	−0.825420	−	1.42967i
$863$	15.6911	+	9.05927i	0.534132	+	0.308381i	0.742697	−	0.669627i	$-0.233546\pi$
$863$	15.6911	+	9.05927i	0.534132	+	0.308381i	−0.208565	+	0.978008i	$0.566879\pi$
$864$	−7.87352	+	41.1422i	−0.267863	+	1.39968i
$865$	−9.47462	−	16.4105i	−0.322147	−	0.557975i
$866$	73.1878			2.48702
$867$	13.7438	−	20.6773i	0.466765	−	0.702237i
$868$		0			0
$869$	−39.5927	−	22.8589i	−1.34309	−	0.775434i
$870$	−34.2166	+	51.4781i	−1.16005	+	1.74527i
$871$	−1.81120	−	1.04570i	−0.0613703	−	0.0354321i
$872$	−4.12545	+	2.38183i	−0.139705	+	0.0806589i
$873$	6.64149	−	2.78874i	0.224780	−	0.0943846i
$874$		−	13.4562i		−	0.455164i
$875$		0			0
$876$	−12.6918	+	6.29716i	−0.428817	+	0.212761i
$877$	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	$0.818395\pi$
$878$	−81.5042			−2.75063
$879$	−6.79515	+	10.2232i	−0.229195	+	0.344818i
$880$		−	20.6814i		−	0.697170i
$881$	−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	$0.713679\pi$
$884$			12.1135i			0.407422i
$885$	6.37417	+	12.8470i	0.214265	+	0.431848i
$886$	−78.2219			−2.62792
$887$	11.2584	+	19.5001i	0.378020	+	0.654750i	0.990774	−	0.135524i	$-0.0432716\pi$
$887$	11.2584	+	19.5001i	0.378020	+	0.654750i	−0.612754	+	0.790274i	$0.709938\pi$
$888$	6.68195	+	4.44138i	0.224232	+	0.149043i
$889$		0			0
$890$			21.5251i			0.721525i
$891$	20.7458	+	20.3479i	0.695010	+	0.681680i
$892$	−32.3479	+	18.6761i	−1.08309	+	0.625321i
$893$	38.9751	+	22.5023i	1.30425	+	0.753011i
$894$	−14.9332	−	30.0977i	−0.499442	−	1.00662i
$895$	27.1857	+	15.6957i	0.908719	+	0.524649i
$896$		0			0
$897$	−6.22657	−	0.392976i	−0.207899	−	0.0131211i
$898$	−50.1289			−1.67282
$899$	24.3195	+	42.1225i	0.811099	+	1.40487i
$900$	−2.74496	+	3.61339i	−0.0914987	+	0.120446i
$901$	8.61635	+	4.97465i	0.287052	+	0.165730i
$902$	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
$906$	−36.1808	−	24.0487i	−1.20203	−	0.798966i
$907$	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	$0.0638473\pi$
$908$	2.48775	−	4.30891i	0.0825589	−	0.142996i
$909$	6.38881	−	8.41005i	0.211903	−	0.278944i
$910$		0			0
$911$	4.92610	−	2.84408i	0.163209	−	0.0942287i	−0.416171	−	0.909286i	$-0.636628\pi$
$911$	4.92610	−	2.84408i	0.163209	−	0.0942287i	0.579380	+	0.815058i	$0.303295\pi$
$912$	24.4584	+	16.2571i	0.809899	+	0.538326i
$913$			9.97917i			0.330262i
$914$		−	20.9142i		−	0.691781i
$915$	−15.5388	+	7.70969i	−0.513696	+	0.254874i
$916$	13.3237	−	7.69242i	0.440226	−	0.254165i
$917$		0			0
$918$	−16.7912	+	5.83618i	−0.554193	+	0.192623i
$919$	−10.9255	+	18.9235i	−0.360399	+	0.624230i	−0.988027	−	0.154284i	$-0.950693\pi$
$919$	−10.9255	+	18.9235i	−0.360399	+	0.624230i	0.627627	+	0.778514i	$0.284026\pi$
$920$	0.993890	−	1.72147i	0.0327676	−	0.0567551i
$921$	0.339670	−	5.38196i	0.0111925	−	0.177342i
$922$	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
$926$	−41.8672	−	24.1720i	−1.37584	−	0.794343i
$927$	43.3843	−	18.2169i	1.42493	−	0.598322i
$928$	−32.8477	−	56.8940i	−1.07828	−	1.86764i
$929$	−16.1761			−0.530721			−0.265361	−	0.964149i	$-0.585491\pi$
$929$	−16.1761			−0.530721			−0.265361	+	0.964149i	$0.585491\pi$
$930$	−20.1211	−	40.5537i	−0.659796	−	1.32981i
$931$		0			0
$932$	−32.3321	−	18.6669i	−1.05907	−	0.611456i
$933$	−33.6251	−	2.12217i	−1.10084	−	0.0694768i
$934$	−73.0960	−	42.2020i	−2.39177	−	1.38089i
$935$	9.54029	−	5.50809i	0.312001	−	0.180134i
$936$	−4.61448	+	6.07437i	−0.150829	+	0.198547i
$937$		−	14.0440i		−	0.458799i	−0.973332	−	0.229400i	$-0.926324\pi$
$937$		−	14.0440i		−	0.458799i	0.973332	−	0.229400i	$-0.0736762\pi$
$938$		0			0
$939$	−2.78686	+	44.1569i	−0.0909459	+	1.44101i
$940$	20.3252	+	35.2043i	0.662936	+	1.14824i
$941$	−43.1868			−1.40785			−0.703924	−	0.710275i	$-0.748571\pi$
$941$	−43.1868			−1.40785			−0.703924	+	0.710275i	$0.748571\pi$
$942$	64.6626	+	4.08103i	2.10682	+	0.132967i
$943$		−	3.14267i		−	0.102339i
$944$	−12.1437			−0.395244
$945$		0			0
$946$	−13.1921			−0.428911
$947$		−	19.1952i		−	0.623759i	−0.950122	−	0.311879i	$-0.899041\pi$
$947$		−	19.1952i		−	0.623759i	0.950122	−	0.311879i	$-0.100959\pi$
$948$	58.5237	+	3.69359i	1.90076	+	0.119962i
$949$	10.6161			0.344615
$950$	3.66672	+	6.35095i	0.118964	+	0.206052i
$951$	−1.77037	+	28.0509i	−0.0574082	+	0.909614i
$952$		0			0
$953$		−	5.62718i		−	0.182282i	−0.995838	−	0.0911411i	$-0.970949\pi$
$953$		−	5.62718i		−	0.182282i	0.995838	−	0.0911411i	$-0.0290514\pi$
$954$	14.8319	+	35.3228i	0.480201	+	1.14362i
$955$	16.3547	−	9.44239i	0.529225	−	0.305548i
$956$	35.5732	+	20.5382i	1.15052	+	0.664252i
$957$	−45.4836	−	2.87060i	−1.47028	−	0.0927932i
$958$	−0.282197	−	0.162926i	−0.00911736	−	0.00526391i
$959$		0			0
$960$	17.3151	+	34.8983i	0.558842	+	1.12634i
$961$	−4.62282			−0.149123
$962$	−18.3799	−	31.8350i	−0.592593	−	1.02640i
$963$	3.91654	+	2.97525i	0.126209	+	0.0958761i
$964$	23.2300	+	13.4119i	0.748189	+	0.431967i
$965$	−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
$969$	−0.985339	+	15.6124i	−0.0316537	+	0.501542i
$970$	5.25740	−	9.10608i	0.168805	−	0.292379i
$971$	−20.4479	+	35.4168i	−0.656205	+	1.13658i	0.325386	+	0.945581i	$0.394506\pi$
$971$	−20.4479	+	35.4168i	−0.656205	+	1.13658i	−0.981590	+	0.190998i	$0.938828\pi$
$972$	−35.4370	−	11.5528i	−1.13664	−	0.370558i
$973$		0			0
$974$	29.9472	−	17.2900i	0.959571	−	0.554009i
$975$	3.04584	−	1.51122i	0.0975450	−	0.0483978i
$976$		−	14.6881i		−	0.470154i
$977$			10.3726i			0.331850i	0.986138	+	0.165925i	$0.0530609\pi$
$977$			10.3726i			0.331850i	−0.986138	+	0.165925i	$0.946939\pi$
$978$	53.9105	+	35.8334i	1.72387	+	1.14582i
$979$	−13.7442	+	7.93522i	−0.439267	+	0.253611i
$980$		0			0
$981$	6.75206	+	16.0803i	0.215577	+	0.513404i
$982$	9.79963	−	16.9735i	0.312719	−	0.541645i
$983$	−1.05850	+	1.83338i	−0.0337609	+	0.0584756i	−0.882412	−	0.470477i	$-0.844082\pi$
$983$	−1.05850	+	1.83338i	−0.0337609	+	0.0584756i	0.848651	+	0.528953i	$0.177415\pi$
$984$	−3.20009	−	2.12705i	−0.102015	−	0.0678077i
$985$	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
$989$	1.96007	+	1.13165i	0.0623267	+	0.0359843i
$990$	42.0818	+	5.33304i	1.33745	+	0.169495i
$991$	−17.0581	−	29.5456i	−0.541870	−	0.938546i	−0.998797	−	0.0490418i	$-0.984383\pi$
$991$	−17.0581	−	29.5456i	−0.541870	−	0.938546i	0.456927	−	0.889504i	$-0.348950\pi$
$992$	48.1149			1.52765
$993$	40.2968	+	2.54324i	1.27878	+	0.0807073i
$994$		0			0
$995$	−9.30850	−	5.37427i	−0.295099	−	0.170376i
$996$	−5.68900	−	11.4661i	−0.180263	−	0.363317i
$997$	−39.6843	−	22.9118i	−1.25682	−	0.725623i	−0.284361	−	0.958717i	$-0.591782\pi$
$997$	−39.6843	−	22.9118i	−1.25682	−	0.725623i	−0.972454	+	0.233094i	$0.925115\pi$
$998$	−3.62264	+	2.09153i	−0.114673	+	0.0662064i
$999$	19.2071	−	22.2250i	0.607685	−	0.703168i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.1	✓	10	7.6	odd	2
63.2.i.b.38.5	yes	10	63.11	odd	6
63.2.s.b.47.5	yes	10	63.20	even	6
63.2.s.b.59.5	yes	10	7.4	even	3
189.2.i.b.143.1		10	63.25	even	3
189.2.i.b.152.5		10	21.20	even	2
189.2.s.b.17.1		10	21.11	odd	6
189.2.s.b.89.1		10	63.34	odd	6
441.2.i.b.68.1		10	1.1	even	1	trivial
441.2.i.b.227.5		10	63.38	even	6	inner
441.2.o.c.146.1		10	63.47	even	6
441.2.o.c.293.1		10	7.2	even	3
441.2.o.d.146.1		10	63.2	odd	6
441.2.o.d.293.1		10	7.5	odd	6
441.2.s.b.362.5		10	9.2	odd	6
441.2.s.b.374.5		10	7.3	odd	6
567.2.p.c.80.1		10	63.4	even	3
567.2.p.c.404.1		10	63.41	even	6
567.2.p.d.80.5		10	63.32	odd	6
567.2.p.d.404.5		10	63.13	odd	6
1008.2.ca.b.257.5		10	28.27	even	2
1008.2.ca.b.353.5		10	252.11	even	6
1008.2.df.b.689.3		10	28.11	odd	6
1008.2.df.b.929.3		10	252.83	odd	6
1323.2.i.b.521.1		10	63.52	odd	6
1323.2.i.b.1097.5		10	3.2	odd	2
1323.2.o.c.440.5		10	63.16	even	3
1323.2.o.c.881.5		10	21.5	even	6
1323.2.o.d.440.5		10	63.61	odd	6
1323.2.o.d.881.5		10	21.2	odd	6
1323.2.s.b.656.1		10	9.7	even	3
1323.2.s.b.962.1		10	21.17	even	6
3024.2.ca.b.2033.5		10	252.151	odd	6
3024.2.ca.b.2609.5		10	84.83	odd	2
3024.2.df.b.17.5		10	84.11	even	6
3024.2.df.b.1601.5		10	252.223	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.09548i q^{2} +(1.72861 + 0.109097i) q^{3} -2.39104 q^{4} +(1.04492 + 1.80985i) q^{5} +(0.228612 - 3.62227i) q^{6} +0.819421i q^{8} +(2.97620 + 0.377174i) q^{9} +O(q^{10})\)	\(q-2.09548i q^{2} +(1.72861 + 0.109097i) q^{3} -2.39104 q^{4} +(1.04492 + 1.80985i) q^{5} +(0.228612 - 3.62227i) q^{6} +0.819421i q^{8} +(2.97620 + 0.377174i) q^{9} +(3.79250 - 2.18960i) q^{10} +(2.79620 + 1.61439i) q^{11} +(-4.13318 - 0.260856i) q^{12} +(2.68740 + 1.55157i) q^{13} +(1.60880 + 3.24252i) q^{15} -3.06500 q^{16} +(-0.816304 - 1.41388i) q^{17} +(0.790361 - 6.23656i) q^{18} +(-4.79094 - 2.76605i) q^{19} +(-2.49844 - 4.32742i) q^{20} +(3.38292 - 5.85939i) q^{22} +(-1.00527 + 0.580391i) q^{23} +(-0.0893966 + 1.41646i) q^{24} +(0.316304 - 0.547854i) q^{25} +(3.25129 - 5.63139i) q^{26} +(5.10354 + 0.976682i) q^{27} +(-7.05749 + 4.07464i) q^{29} +(6.79464 - 3.37122i) q^{30} -5.96849i q^{31} +8.06150i q^{32} +(4.65742 + 3.09571i) q^{33} +(-2.96276 + 1.71055i) q^{34} +(-7.11621 - 0.901839i) q^{36} +(2.82656 - 4.89575i) q^{37} +(-5.79620 + 10.0393i) q^{38} +(4.47620 + 2.97525i) q^{39} +(-1.48303 + 0.856225i) q^{40} +(-1.35369 + 2.34465i) q^{41} +(-0.974903 - 1.68858i) q^{43} +(-6.68583 - 3.86007i) q^{44} +(2.42725 + 5.78057i) q^{45} +(1.21620 + 2.10652i) q^{46} -8.13518 q^{47} +(-5.29820 - 0.334384i) q^{48} +(-1.14802 - 0.662809i) q^{50} +(-1.25682 - 2.53311i) q^{51} +(-6.42568 - 3.70987i) q^{52} +(-5.27766 + 3.04706i) q^{53} +(2.04662 - 10.6944i) q^{54} +6.74759i q^{55} +(-7.97990 - 5.30410i) q^{57} +(8.53834 + 14.7888i) q^{58} +3.96206 q^{59} +(-3.84672 - 7.75300i) q^{60} +4.79219i q^{61} -12.5068 q^{62} +10.7627 q^{64} +6.48504i q^{65} +(6.48700 - 9.75954i) q^{66} -0.673961 q^{67} +(1.95182 + 3.38065i) q^{68} +(-1.80103 + 0.893598i) q^{69} +7.01535i q^{71} +(-0.309064 + 2.43876i) q^{72} +(2.96276 - 1.71055i) q^{73} +(-10.2590 - 5.92301i) q^{74} +(0.606536 - 0.912519i) q^{75} +(11.4553 + 6.61374i) q^{76} +(6.23458 - 9.37978i) q^{78} -14.1595 q^{79} +(-3.20267 - 5.54718i) q^{80} +(8.71548 + 2.24509i) q^{81} +(4.91318 + 2.83662i) q^{82} +(1.54535 + 2.67662i) q^{83} +(1.70594 - 2.95477i) q^{85} +(-3.53839 + 2.04289i) q^{86} +(-12.6442 + 6.27352i) q^{87} +(-1.32286 + 2.29127i) q^{88} +(-2.45766 + 4.25679i) q^{89} +(12.1131 - 5.08625i) q^{90} +(2.40363 - 1.38774i) q^{92} +(0.651146 - 10.3172i) q^{93} +17.0471i q^{94} -11.5611i q^{95} +(-0.879488 + 13.9352i) q^{96} +(2.07939 - 1.20054i) q^{97} +(7.71314 + 5.85939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{3} - 8 q^{4} - 12 q^{6} + 3 q^{9}+O(q^{10}) \) 10 * q + 3 * q^3 - 8 * q^4 - 12 * q^6 + 3 * q^9	\( 10 q + 3 q^{3} - 8 q^{4} - 12 q^{6} + 3 q^{9} + 15 q^{10} - 12 q^{11} + 12 q^{12} + 6 q^{13} - 3 q^{15} + 12 q^{16} - 12 q^{17} + 24 q^{18} - 3 q^{19} - 3 q^{20} + 5 q^{22} - 15 q^{23} + 7 q^{25} + 3 q^{26} + 27 q^{27} - 15 q^{29} + 6 q^{30} + 3 q^{34} - 18 q^{36} + 6 q^{37} - 18 q^{38} + 18 q^{39} - 15 q^{40} - 9 q^{41} + 3 q^{43} - 24 q^{44} - 30 q^{45} - 13 q^{46} - 30 q^{47} - 15 q^{48} + 3 q^{50} + 21 q^{51} + 12 q^{52} + 9 q^{53} - 9 q^{54} - 36 q^{57} + 8 q^{58} + 36 q^{59} - 48 q^{60} + 12 q^{62} + 6 q^{64} + 39 q^{66} + 20 q^{67} + 27 q^{68} - 3 q^{69} - 30 q^{72} - 3 q^{73} - 30 q^{74} - 6 q^{75} + 9 q^{76} + 24 q^{78} - 40 q^{79} - 30 q^{80} + 15 q^{81} - 9 q^{82} - 15 q^{83} + 18 q^{85} + 54 q^{86} - 6 q^{87} - 8 q^{88} + 24 q^{89} + 24 q^{90} + 39 q^{92} + 36 q^{93} - 33 q^{96} + 6 q^{97} + 21 q^{99}+O(q^{100}) \) 10 * q + 3 * q^3 - 8 * q^4 - 12 * q^6 + 3 * q^9 + 15 * q^10 - 12 * q^11 + 12 * q^12 + 6 * q^13 - 3 * q^15 + 12 * q^16 - 12 * q^17 + 24 * q^18 - 3 * q^19 - 3 * q^20 + 5 * q^22 - 15 * q^23 + 7 * q^25 + 3 * q^26 + 27 * q^27 - 15 * q^29 + 6 * q^30 + 3 * q^34 - 18 * q^36 + 6 * q^37 - 18 * q^38 + 18 * q^39 - 15 * q^40 - 9 * q^41 + 3 * q^43 - 24 * q^44 - 30 * q^45 - 13 * q^46 - 30 * q^47 - 15 * q^48 + 3 * q^50 + 21 * q^51 + 12 * q^52 + 9 * q^53 - 9 * q^54 - 36 * q^57 + 8 * q^58 + 36 * q^59 - 48 * q^60 + 12 * q^62 + 6 * q^64 + 39 * q^66 + 20 * q^67 + 27 * q^68 - 3 * q^69 - 30 * q^72 - 3 * q^73 - 30 * q^74 - 6 * q^75 + 9 * q^76 + 24 * q^78 - 40 * q^79 - 30 * q^80 + 15 * q^81 - 9 * q^82 - 15 * q^83 + 18 * q^85 + 54 * q^86 - 6 * q^87 - 8 * q^88 + 24 * q^89 + 24 * q^90 + 39 * q^92 + 36 * q^93 - 33 * q^96 + 6 * q^97 + 21 * q^99

Introduction

L-functions

Modular forms

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Database

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