LMFDB - Embedded newform 57.2.e.b.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,2,Mod(7,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("57.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	57.e (of order $3$, degree $2$, 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:	$0.455147291521$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.3
Root			$0.403374 - 1.68443i$ of defining polynomial
Character	$\chi$	$=$	57.49
Dual form			57.2.e.b.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25707 - 2.17731i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.16044 - 3.74200i) q^{4} +(-1.66044 + 2.87597i) q^{5} +(1.25707 + 2.17731i) q^{6} +2.32088 q^{7} -5.83502 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.25707 - 2.17731i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.16044 - 3.74200i) q^{4} +(-1.66044 + 2.87597i) q^{5} +(1.25707 + 2.17731i) q^{6} +2.32088 q^{7} -5.83502 q^{8} +(-0.500000 - 0.866025i) q^{9} +(4.17458 + 7.23058i) q^{10} -1.70739 q^{11} +4.32088 q^{12} +(-2.01414 - 3.48859i) q^{13} +(2.91751 - 5.05328i) q^{14} +(-1.66044 - 2.87597i) q^{15} +(-3.01414 + 5.22064i) q^{16} -2.51414 q^{18} +(0.193252 + 4.35461i) q^{19} +14.3492 q^{20} +(-1.16044 + 2.00994i) q^{21} +(-2.14631 + 3.71751i) q^{22} +(1.17458 + 2.03443i) q^{23} +(2.91751 - 5.05328i) q^{24} +(-3.01414 - 5.22064i) q^{25} -10.1276 q^{26} +1.00000 q^{27} +(-5.01414 - 8.68474i) q^{28} +(-3.32088 - 5.75194i) q^{29} -8.34916 q^{30} +6.70739 q^{31} +(1.74293 + 3.01885i) q^{32} +(0.853695 - 1.47864i) q^{33} +(-3.85369 + 6.67479i) q^{35} +(-2.16044 + 3.74200i) q^{36} -1.00000 q^{37} +(9.72426 + 5.05328i) q^{38} +4.02827 q^{39} +(9.68872 - 16.7813i) q^{40} +(3.32088 - 5.75194i) q^{41} +(2.91751 + 5.05328i) q^{42} +(-0.353695 + 0.612617i) q^{43} +(3.68872 + 6.38904i) q^{44} +3.32088 q^{45} +5.90611 q^{46} +(3.00000 + 5.19615i) q^{47} +(-3.01414 - 5.22064i) q^{48} -1.61350 q^{49} -15.1559 q^{50} +(-8.70285 + 15.0738i) q^{52} +(4.98133 + 8.62791i) q^{53} +(1.25707 - 2.17731i) q^{54} +(2.83502 - 4.91040i) q^{55} -13.5424 q^{56} +(-3.86783 - 2.00994i) q^{57} -16.6983 q^{58} +(-0.853695 + 1.47864i) q^{59} +(-7.17458 + 12.4267i) q^{60} +(-1.69325 - 2.93280i) q^{61} +(8.43165 - 14.6040i) q^{62} +(-1.16044 - 2.00994i) q^{63} -3.29261 q^{64} +13.3774 q^{65} +(-2.14631 - 3.71751i) q^{66} +(4.18872 + 7.25507i) q^{67} -2.34916 q^{69} +(9.68872 + 16.7813i) q^{70} +(4.70739 - 8.15344i) q^{71} +(2.91751 + 5.05328i) q^{72} +(-5.82088 + 10.0821i) q^{73} +(-1.25707 + 2.17731i) q^{74} +6.02827 q^{75} +(15.8774 - 10.1310i) q^{76} -3.96265 q^{77} +(5.06382 - 8.77079i) q^{78} +(1.67458 - 2.90046i) q^{79} +(-10.0096 - 17.3371i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-8.34916 - 14.4612i) q^{82} -10.0565 q^{83} +10.0283 q^{84} +(0.889237 + 1.54020i) q^{86} +6.64177 q^{87} +9.96265 q^{88} +(1.33956 + 2.32018i) q^{89} +(4.17458 - 7.23058i) q^{90} +(-4.67458 - 8.09661i) q^{91} +(5.07522 - 8.79054i) q^{92} +(-3.35369 + 5.80877i) q^{93} +15.0848 q^{94} +(-12.8446 - 6.67479i) q^{95} -3.48586 q^{96} +(-8.86330 + 15.3517i) q^{97} +(-2.02827 + 3.51307i) q^{98} +(0.853695 + 1.47864i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 3 q^{3} - 5 q^{4} - 2 q^{5} + q^{6} - 2 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + q^2 - 3 * q^3 - 5 * q^4 - 2 * q^5 + q^6 - 2 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q + q^{2} - 3 q^{3} - 5 q^{4} - 2 q^{5} + q^{6} - 2 q^{7} - 6 q^{8} - 3 q^{9} + 4 q^{10} + 10 q^{12} + q^{13} + 3 q^{14} - 2 q^{15} - 5 q^{16} - 2 q^{18} + 4 q^{19} + 44 q^{20} + q^{21} - 18 q^{22} - 14 q^{23} + 3 q^{24} - 5 q^{25} - 42 q^{26} + 6 q^{27} - 17 q^{28} - 4 q^{29} - 8 q^{30} + 30 q^{31} + 17 q^{32} - 18 q^{35} - 5 q^{36} - 6 q^{37} + 41 q^{38} - 2 q^{39} + 24 q^{40} + 4 q^{41} + 3 q^{42} + 3 q^{43} - 12 q^{44} + 4 q^{45} + 40 q^{46} + 18 q^{47} - 5 q^{48} - 4 q^{49} - 46 q^{50} - 5 q^{52} + 6 q^{53} + q^{54} - 12 q^{55} - 42 q^{56} - 5 q^{57} - 16 q^{58} - 22 q^{60} - 13 q^{61} + 23 q^{62} + q^{63} - 30 q^{64} + 12 q^{65} - 18 q^{66} - 9 q^{67} + 28 q^{69} + 24 q^{70} + 18 q^{71} + 3 q^{72} - 19 q^{73} - q^{74} + 10 q^{75} + 27 q^{76} + 24 q^{77} + 21 q^{78} - 11 q^{79} - 10 q^{80} - 3 q^{81} - 8 q^{82} - 8 q^{83} + 34 q^{84} + 17 q^{86} + 8 q^{87} + 12 q^{88} + 16 q^{89} + 4 q^{90} - 7 q^{91} + 2 q^{92} - 15 q^{93} + 12 q^{94} + 2 q^{95} - 34 q^{96} + 2 q^{97} + 14 q^{98}+O(q^{100}) $ 6 * q + q^2 - 3 * q^3 - 5 * q^4 - 2 * q^5 + q^6 - 2 * q^7 - 6 * q^8 - 3 * q^9 + 4 * q^10 + 10 * q^12 + q^13 + 3 * q^14 - 2 * q^15 - 5 * q^16 - 2 * q^18 + 4 * q^19 + 44 * q^20 + q^21 - 18 * q^22 - 14 * q^23 + 3 * q^24 - 5 * q^25 - 42 * q^26 + 6 * q^27 - 17 * q^28 - 4 * q^29 - 8 * q^30 + 30 * q^31 + 17 * q^32 - 18 * q^35 - 5 * q^36 - 6 * q^37 + 41 * q^38 - 2 * q^39 + 24 * q^40 + 4 * q^41 + 3 * q^42 + 3 * q^43 - 12 * q^44 + 4 * q^45 + 40 * q^46 + 18 * q^47 - 5 * q^48 - 4 * q^49 - 46 * q^50 - 5 * q^52 + 6 * q^53 + q^54 - 12 * q^55 - 42 * q^56 - 5 * q^57 - 16 * q^58 - 22 * q^60 - 13 * q^61 + 23 * q^62 + q^63 - 30 * q^64 + 12 * q^65 - 18 * q^66 - 9 * q^67 + 28 * q^69 + 24 * q^70 + 18 * q^71 + 3 * q^72 - 19 * q^73 - q^74 + 10 * q^75 + 27 * q^76 + 24 * q^77 + 21 * q^78 - 11 * q^79 - 10 * q^80 - 3 * q^81 - 8 * q^82 - 8 * q^83 + 34 * q^84 + 17 * q^86 + 8 * q^87 + 12 * q^88 + 16 * q^89 + 4 * q^90 - 7 * q^91 + 2 * q^92 - 15 * q^93 + 12 * q^94 + 2 * q^95 - 34 * q^96 + 2 * q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.25707	−	2.17731i	0.888882	−	1.53959i	0.0476826	−	0.998863i	$-0.484816\pi$
$2$	1.25707	−	2.17731i	0.888882	−	1.53959i	0.841199	−	0.540726i	$-0.181850\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−2.16044	−	3.74200i	−1.08022	−	1.87100i
$5$	−1.66044	+	2.87597i	−0.742572	+	1.28617i	0.208748	+	0.977969i	$0.433061\pi$
$5$	−1.66044	+	2.87597i	−0.742572	+	1.28617i	−0.951320	+	0.308204i	$0.900272\pi$
$6$	1.25707	+	2.17731i	0.513196	+	0.888882i
$7$	2.32088			0.877212			0.438606	−	0.898679i	$-0.355472\pi$
$7$	2.32088			0.877212			0.438606	+	0.898679i	$0.355472\pi$
$8$	−5.83502			−2.06299
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	4.17458	+	7.23058i	1.32012	+	2.28651i
$11$	−1.70739			−0.514797			−0.257399	−	0.966305i	$-0.582865\pi$
$11$	−1.70739			−0.514797			−0.257399	+	0.966305i	$0.582865\pi$
$12$	4.32088			1.24733
$13$	−2.01414	−	3.48859i	−0.558621	−	0.967560i	−0.997612	−	0.0690685i	$-0.977997\pi$
$13$	−2.01414	−	3.48859i	−0.558621	−	0.967560i	0.438991	−	0.898492i	$-0.355336\pi$
$14$	2.91751	−	5.05328i	0.779738	−	1.35055i
$15$	−1.66044	−	2.87597i	−0.428724	−	0.742572i
$16$	−3.01414	+	5.22064i	−0.753534	+	1.30516i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	−2.51414			−0.592588
$19$	0.193252	+	4.35461i	0.0443351	+	0.999017i
$19$	0.193252	+	4.35461i	0.0443351	+	0.999017i
$20$	14.3492			3.20857
$21$	−1.16044	+	2.00994i	−0.253229	+	0.438606i
$22$	−2.14631	+	3.71751i	−0.457594	+	0.792576i
$23$	1.17458	+	2.03443i	0.244917	+	0.424208i	0.962108	−	0.272668i	$-0.0879061\pi$
$23$	1.17458	+	2.03443i	0.244917	+	0.424208i	−0.717191	+	0.696876i	$0.754573\pi$
$24$	2.91751	−	5.05328i	0.595534	−	1.03150i
$25$	−3.01414	−	5.22064i	−0.602827	−	1.04413i
$26$	−10.1276			−1.98619
$27$	1.00000			0.192450
$28$	−5.01414	−	8.68474i	−0.947583	−	1.64126i
$29$	−3.32088	−	5.75194i	−0.616673	−	1.06811i	−0.990089	−	0.140444i	$-0.955147\pi$
$29$	−3.32088	−	5.75194i	−0.616673	−	1.06811i	0.373416	−	0.927664i	$-0.378186\pi$
$30$	−8.34916			−1.52434
$31$	6.70739			1.20468			0.602341	−	0.798239i	$-0.294235\pi$
$31$	6.70739			1.20468			0.602341	+	0.798239i	$0.294235\pi$
$32$	1.74293	+	3.01885i	0.308110	+	0.533662i
$33$	0.853695	−	1.47864i	0.148609	−	0.257399i
$34$		0			0
$35$	−3.85369	+	6.67479i	−0.651393	+	1.12825i
$36$	−2.16044	+	3.74200i	−0.360074	+	0.623666i
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	9.72426	+	5.05328i	1.57748	+	0.819750i
$39$	4.02827			0.645040
$40$	9.68872	−	16.7813i	1.53192	−	2.65336i
$41$	3.32088	−	5.75194i	0.518635	−	0.898302i	−0.481131	−	0.876649i	$-0.659774\pi$
$41$	3.32088	−	5.75194i	0.518635	−	0.898302i	0.999766	−	0.0216532i	$-0.00689298\pi$
$42$	2.91751	+	5.05328i	0.450182	+	0.779738i
$43$	−0.353695	+	0.612617i	−0.0539379	+	0.0934232i	−0.891734	−	0.452561i	$-0.850511\pi$
$43$	−0.353695	+	0.612617i	−0.0539379	+	0.0934232i	0.837796	+	0.545984i	$0.183844\pi$
$44$	3.68872	+	6.38904i	0.556095	+	0.963185i
$45$	3.32088			0.495048
$46$	5.90611			0.870808
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$	−3.01414	−	5.22064i	−0.435053	−	0.753534i
$49$	−1.61350			−0.230499
$50$	−15.1559			−2.14337
$51$		0			0
$52$	−8.70285	+	15.0738i	−1.20687	+	2.09036i
$53$	4.98133	+	8.62791i	0.684238	+	1.18513i	0.973676	+	0.227938i	$0.0731983\pi$
$53$	4.98133	+	8.62791i	0.684238	+	1.18513i	−0.289438	+	0.957197i	$0.593468\pi$
$54$	1.25707	−	2.17731i	0.171065	−	0.296294i
$55$	2.83502	−	4.91040i	0.382274	−	0.662118i
$56$	−13.5424			−1.80968
$57$	−3.86783	−	2.00994i	−0.512307	−	0.266224i
$58$	−16.6983			−2.19260
$59$	−0.853695	+	1.47864i	−0.111142	+	0.192503i	−0.916231	−	0.400651i	$-0.868784\pi$
$59$	−0.853695	+	1.47864i	−0.111142	+	0.192503i	0.805089	+	0.593154i	$0.202117\pi$
$60$	−7.17458	+	12.4267i	−0.926234	+	1.60428i
$61$	−1.69325	−	2.93280i	−0.216799	−	0.375506i	0.737029	−	0.675861i	$-0.236228\pi$
$61$	−1.69325	−	2.93280i	−0.216799	−	0.375506i	−0.953828	+	0.300355i	$0.902895\pi$
$62$	8.43165	−	14.6040i	1.07082	−	1.85472i
$63$	−1.16044	−	2.00994i	−0.146202	−	0.253229i
$64$	−3.29261			−0.411576
$65$	13.3774			1.65927
$66$	−2.14631	−	3.71751i	−0.264192	−	0.457594i
$67$	4.18872	+	7.25507i	0.511733	+	0.886348i	0.999907	+	0.0136016i	$0.00432967\pi$
$67$	4.18872	+	7.25507i	0.511733	+	0.886348i	−0.488174	+	0.872746i	$0.662337\pi$
$68$		0			0
$69$	−2.34916			−0.282805
$70$	9.68872	+	16.7813i	1.15802	+	2.00575i
$71$	4.70739	−	8.15344i	0.558664	−	0.967635i	−0.438944	−	0.898514i	$-0.644647\pi$
$71$	4.70739	−	8.15344i	0.558664	−	0.967635i	0.997608	−	0.0691206i	$-0.0220193\pi$
$72$	2.91751	+	5.05328i	0.343832	+	0.595534i
$73$	−5.82088	+	10.0821i	−0.681283	+	1.18002i	0.293307	+	0.956018i	$0.405244\pi$
$73$	−5.82088	+	10.0821i	−0.681283	+	1.18002i	−0.974590	+	0.223998i	$0.928089\pi$
$74$	−1.25707	+	2.17731i	−0.146131	+	0.253107i
$75$	6.02827			0.696085
$76$	15.8774	−	10.1310i	1.82127	−	1.16211i
$77$	−3.96265			−0.451586
$78$	5.06382	−	8.77079i	0.573364	−	0.993096i
$79$	1.67458	−	2.90046i	0.188405	−	0.326327i	−0.756314	−	0.654209i	$-0.773002\pi$
$79$	1.67458	−	2.90046i	0.188405	−	0.326327i	0.944719	+	0.327882i	$0.106335\pi$
$80$	−10.0096	−	17.3371i	−1.11911	−	1.93835i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−8.34916	−	14.4612i	−0.922010	−	1.59697i
$83$	−10.0565			−1.10385			−0.551925	−	0.833894i	$-0.686106\pi$
$83$	−10.0565			−1.10385			−0.551925	+	0.833894i	$0.686106\pi$
$84$	10.0283			1.09417
$85$		0			0
$86$	0.889237	+	1.54020i	0.0958889	+	0.166084i
$87$	6.64177			0.712072
$88$	9.96265			1.06202
$89$	1.33956	+	2.32018i	0.141993	+	0.245939i	0.928247	−	0.371964i	$-0.121316\pi$
$89$	1.33956	+	2.32018i	0.141993	+	0.245939i	−0.786254	+	0.617903i	$0.787982\pi$
$90$	4.17458	−	7.23058i	0.440039	−	0.762170i
$91$	−4.67458	−	8.09661i	−0.490029	−	0.848755i
$92$	5.07522	−	8.79054i	0.529128	−	0.916477i
$93$	−3.35369	+	5.80877i	−0.347762	+	0.602341i
$94$	15.0848			1.55588
$95$	−12.8446	−	6.67479i	−1.31783	−	0.684820i
$96$	−3.48586			−0.355774
$97$	−8.86330	+	15.3517i	−0.899931	+	1.55873i	−0.0723511	+	0.997379i	$0.523050\pi$
$97$	−8.86330	+	15.3517i	−0.899931	+	1.55873i	−0.827580	+	0.561347i	$0.810283\pi$
$98$	−2.02827	+	3.51307i	−0.204887	+	0.354874i
$99$	0.853695	+	1.47864i	0.0857995	+	0.148609i
$100$	−13.0237	+	22.5578i	−1.30237	+	2.25578i
$101$	−8.02827	−	13.9054i	−0.798843	−	1.38364i	−0.920370	−	0.391049i	$-0.872112\pi$
$101$	−8.02827	−	13.9054i	−0.798843	−	1.38364i	0.121527	−	0.992588i	$-0.461221\pi$
$102$		0			0
$103$	−7.54787			−0.743714			−0.371857	−	0.928290i	$-0.621279\pi$
$103$	−7.54787			−0.743714			−0.371857	+	0.928290i	$0.621279\pi$
$104$	11.7525	+	20.3560i	1.15243	+	1.99607i
$105$	−3.85369	−	6.67479i	−0.376082	−	0.651393i
$106$	25.0475			2.43283
$107$	7.28354			0.704126			0.352063	−	0.935976i	$-0.385480\pi$
$107$	7.28354			0.704126			0.352063	+	0.935976i	$0.385480\pi$
$108$	−2.16044	−	3.74200i	−0.207889	−	0.360074i
$109$	6.12763	−	10.6134i	0.586921	−	1.01658i	−0.407712	−	0.913110i	$-0.633673\pi$
$109$	6.12763	−	10.6134i	0.586921	−	1.01658i	0.994633	−	0.103466i	$-0.0329933\pi$
$110$	−7.12763	−	12.3454i	−0.679593	−	1.17709i
$111$	0.500000	−	0.866025i	0.0474579	−	0.0821995i
$112$	−6.99546	+	12.1165i	−0.661009	+	1.14490i
$113$	7.37743			0.694010			0.347005	−	0.937863i	$-0.387199\pi$
$113$	7.37743			0.694010			0.347005	+	0.937863i	$0.387199\pi$
$114$	−9.23840	+	5.89482i	−0.865255	+	0.552100i
$115$	−7.80128			−0.727473
$116$	−14.3492	+	24.8535i	−1.33229	+	2.30759i
$117$	−2.01414	+	3.48859i	−0.186207	+	0.322520i
$118$	2.14631	+	3.71751i	0.197583	+	0.342225i
$119$		0			0
$120$	9.68872	+	16.7813i	0.884455	+	1.53192i
$121$	−8.08482			−0.734984
$122$	−8.51414			−0.770834
$123$	3.32088	+	5.75194i	0.299434	+	0.518635i
$124$	−14.4909	−	25.0990i	−1.30132	−	2.25396i
$125$	3.41478			0.305427
$126$	−5.83502			−0.519825
$127$	−7.32088	−	12.6801i	−0.649623	−	1.12518i	−0.983213	−	0.182462i	$-0.941593\pi$
$127$	−7.32088	−	12.6801i	−0.649623	−	1.12518i	0.333589	−	0.942718i	$-0.391740\pi$
$128$	−7.62490	+	13.2067i	−0.673952	+	1.16732i
$129$	−0.353695	−	0.612617i	−0.0311411	−	0.0539379i
$130$	16.8163	−	29.1268i	1.47489	−	2.55459i
$131$	−0.320884	+	0.555788i	−0.0280358	+	0.0485594i	−0.879703	−	0.475524i	$-0.842259\pi$
$131$	−0.320884	+	0.555788i	−0.0280358	+	0.0485594i	0.851667	+	0.524083i	$0.175592\pi$
$132$	−7.37743			−0.642123
$133$	0.448517	+	10.1066i	0.0388913	+	0.876349i
$134$	21.0620			1.81948
$135$	−1.66044	+	2.87597i	−0.142908	+	0.247524i
$136$		0			0
$137$	−1.29261	−	2.23887i	−0.110435	−	0.191279i	0.805511	−	0.592581i	$-0.201891\pi$
$137$	−1.29261	−	2.23887i	−0.110435	−	0.191279i	−0.915946	+	0.401302i	$0.868558\pi$
$138$	−2.95305	+	5.11484i	−0.251381	+	0.435404i
$139$	9.28807	+	16.0874i	0.787804	+	1.36452i	0.927309	+	0.374296i	$0.122115\pi$
$139$	9.28807	+	16.0874i	0.787804	+	1.36452i	−0.139505	+	0.990221i	$0.544551\pi$
$140$	33.3027			2.81460
$141$	−6.00000			−0.505291
$142$	−11.8350	−	20.4989i	−0.993173	−	1.72023i
$143$	3.43892	+	5.95638i	0.287577	+	0.498097i
$144$	6.02827			0.502356
$145$	22.0565			1.83170
$146$	14.6345	+	25.3477i	1.21116	+	2.09779i
$147$	0.806748	−	1.39733i	0.0665394	−	0.115250i
$148$	2.16044	+	3.74200i	0.177587	+	0.307590i
$149$	1.98133	−	3.43176i	0.162317	−	0.281141i	−0.773382	−	0.633940i	$-0.781437\pi$
$149$	1.98133	−	3.43176i	0.162317	−	0.281141i	0.935699	+	0.352799i	$0.114770\pi$
$150$	7.57795	−	13.1254i	0.618737	−	1.07168i
$151$	−8.69832			−0.707859			−0.353929	−	0.935272i	$-0.615155\pi$
$151$	−8.69832			−0.707859			−0.353929	+	0.935272i	$0.615155\pi$
$152$	−1.12763	−	25.4093i	−0.0914630	−	2.06096i
$153$		0			0
$154$	−4.98133	+	8.62791i	−0.401407	+	0.695257i
$155$	−11.1372	+	19.2903i	−0.894564	+	1.54943i
$156$	−8.70285	−	15.0738i	−0.696786	−	1.20687i
$157$	2.84916	−	4.93489i	0.227388	−	0.393847i	−0.729645	−	0.683826i	$-0.760315\pi$
$157$	2.84916	−	4.93489i	0.227388	−	0.393847i	0.957033	+	0.289979i	$0.0936482\pi$
$158$	−4.21012	−	7.29214i	−0.334939	−	0.580132i
$159$	−9.96265			−0.790090
$160$	−11.5761			−0.915175
$161$	2.72606	+	4.72168i	0.214844	+	0.372120i
$162$	1.25707	+	2.17731i	0.0987646	+	0.171065i
$163$	18.3774			1.43943			0.719716	−	0.694269i	$-0.244272\pi$
$163$	18.3774			1.43943			0.719716	+	0.694269i	$0.244272\pi$
$164$	−28.6983			−2.24096
$165$	2.83502	+	4.91040i	0.220706	+	0.382274i
$166$	−12.6418	+	21.8962i	−0.981192	+	1.69947i
$167$	−10.8163	−	18.7345i	−0.836994	−	1.44972i	−0.892396	−	0.451252i	$-0.850977\pi$
$167$	−10.8163	−	18.7345i	−0.836994	−	1.44972i	0.0554023	−	0.998464i	$-0.482356\pi$
$168$	6.77121	−	11.7281i	0.522410	−	0.904840i
$169$	−1.61350	+	2.79466i	−0.124115	+	0.214974i
$170$		0			0
$171$	3.67458	−	2.34467i	0.281002	−	0.179301i
$172$	3.05655			0.233060
$173$	2.34916	−	4.06886i	0.178603	−	0.309350i	−0.762799	−	0.646636i	$-0.776175\pi$
$173$	2.34916	−	4.06886i	0.178603	−	0.309350i	0.941402	+	0.337286i	$0.109509\pi$
$174$	8.34916	−	14.4612i	0.632948	−	1.09630i
$175$	−6.99546	−	12.1165i	−0.528807	−	0.915921i
$176$	5.14631	−	8.91366i	0.387917	−	0.671893i
$177$	−0.853695	−	1.47864i	−0.0641676	−	0.111142i
$178$	6.73566			0.504859
$179$	−1.06562			−0.0796482			−0.0398241	−	0.999207i	$-0.512680\pi$
$179$	−1.06562			−0.0796482			−0.0398241	+	0.999207i	$0.512680\pi$
$180$	−7.17458	−	12.4267i	−0.534762	−	0.926234i
$181$	1.83502	+	3.17835i	0.136396	+	0.236245i	0.926130	−	0.377205i	$-0.123115\pi$
$181$	1.83502	+	3.17835i	0.136396	+	0.236245i	−0.789734	+	0.613450i	$0.789781\pi$
$182$	−23.5051			−1.74231
$183$	3.38650			0.250338
$184$	−6.85369	−	11.8709i	−0.505261	−	0.875138i
$185$	1.66044	−	2.87597i	0.122078	−	0.211446i
$186$	8.43165	+	14.6040i	0.618238	+	1.07082i
$187$		0			0
$188$	12.9627	−	22.4520i	0.945399	−	1.63748i
$189$	2.32088			0.168820
$190$	−30.6796	+	19.5760i	−2.22574	+	1.42019i
$191$	−0.877832			−0.0635177			−0.0317588	−	0.999496i	$-0.510111\pi$
$191$	−0.877832			−0.0635177			−0.0317588	+	0.999496i	$0.510111\pi$
$192$	1.64631	−	2.85148i	0.118812	−	0.205788i
$193$	4.30675	−	7.45951i	0.310006	−	0.536947i	−0.668357	−	0.743841i	$-0.733002\pi$
$193$	4.30675	−	7.45951i	0.310006	−	0.536947i	0.978363	+	0.206894i	$0.0663354\pi$
$194$	22.2835	+	38.5962i	1.59986	+	2.77105i
$195$	−6.68872	+	11.5852i	−0.478989	+	0.829633i
$196$	3.48586	+	6.03769i	0.248990	+	0.431264i
$197$	24.7357			1.76234			0.881172	−	0.472797i	$-0.156756\pi$
$197$	24.7357			1.76234			0.881172	+	0.472797i	$0.156756\pi$
$198$	4.29261			0.305063
$199$	10.9955	+	19.0447i	0.779448	+	1.35004i	0.932260	+	0.361788i	$0.117834\pi$
$199$	10.9955	+	19.0447i	0.779448	+	1.35004i	−0.152813	+	0.988255i	$0.548833\pi$
$200$	17.5876	+	30.4625i	1.24363	+	2.15403i
$201$	−8.37743			−0.590899
$202$	−40.3684			−2.84031
$203$	−7.70739	−	13.3496i	−0.540953	−	0.936958i
$204$		0			0
$205$	11.0283	+	19.1015i	0.770248	+	1.33411i
$206$	−9.48820	+	16.4340i	−0.661074	+	1.14501i
$207$	1.17458	−	2.03443i	0.0816389	−	0.141403i
$208$	24.2835			1.68376
$209$	−0.329957	−	7.43502i	−0.0228236	−	0.514291i
$210$	−19.3774			−1.33717
$211$	6.60896	−	11.4471i	0.454979	−	0.788048i	−0.543708	−	0.839275i	$-0.682980\pi$
$211$	6.60896	−	11.4471i	0.454979	−	0.788048i	0.998687	+	0.0512272i	$0.0163133\pi$
$212$	21.5237	−	37.2802i	1.47826	−	2.56042i
$213$	4.70739	+	8.15344i	0.322545	+	0.558664i
$214$	9.15591	−	15.8585i	0.625885	−	1.08406i
$215$	−1.17458	−	2.03443i	−0.0801056	−	0.138747i
$216$	−5.83502			−0.397023
$217$	15.5671			1.05676
$218$	−15.4057	−	26.6835i	−1.04341	−	1.80723i
$219$	−5.82088	−	10.0821i	−0.393339	−	0.681283i
$220$	−24.4996			−1.65176
$221$		0			0
$222$	−1.25707	−	2.17731i	−0.0843689	−	0.146131i
$223$	2.74020	−	4.74616i	0.183497	−	0.317827i	−0.759572	−	0.650423i	$-0.774591\pi$
$223$	2.74020	−	4.74616i	0.183497	−	0.317827i	0.943069	+	0.332597i	$0.107925\pi$
$224$	4.04514	+	7.00639i	0.270277	+	0.468134i
$225$	−3.01414	+	5.22064i	−0.200942	+	0.348043i
$226$	9.27394	−	16.0629i	0.616893	−	1.06849i
$227$	7.70739			0.511557			0.255779	−	0.966735i	$-0.417668\pi$
$227$	7.70739			0.511557			0.255779	+	0.966735i	$0.417668\pi$
$228$	0.835021	+	18.8158i	0.0553006	+	1.24611i
$229$	4.02827			0.266196			0.133098	−	0.991103i	$-0.457508\pi$
$229$	4.02827			0.266196			0.133098	+	0.991103i	$0.457508\pi$
$230$	−9.80675	+	16.9858i	−0.646638	+	1.12001i
$231$	1.98133	−	3.43176i	0.130362	−	0.225793i
$232$	19.3774	+	33.5627i	1.27219	+	2.20350i
$233$	−13.0565	+	22.6146i	−0.855363	+	1.48153i	0.0209451	+	0.999781i	$0.493332\pi$
$233$	−13.0565	+	22.6146i	−0.855363	+	1.48153i	−0.876308	+	0.481751i	$0.840001\pi$
$234$	5.06382	+	8.77079i	0.331032	+	0.573364i
$235$	−19.9253			−1.29978
$236$	7.37743			0.480230
$237$	1.67458	+	2.90046i	0.108776	+	0.188405i
$238$		0			0
$239$	−7.70739			−0.498550			−0.249275	−	0.968433i	$-0.580192\pi$
$239$	−7.70739			−0.498550			−0.249275	+	0.968433i	$0.580192\pi$
$240$	20.0192			1.29223
$241$	−10.8492	−	18.7913i	−0.698856	−	1.21045i	−0.968863	−	0.247595i	$-0.920360\pi$
$241$	−10.8492	−	18.7913i	−0.698856	−	1.21045i	0.270008	−	0.962858i	$-0.412974\pi$
$242$	−10.1632	+	17.6031i	−0.653314	+	1.13157i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−7.31635	+	12.6723i	−0.468381	+	0.811260i
$245$	2.67912	−	4.64036i	0.171162	−	0.296462i
$246$	16.6983			1.06465
$247$	14.8022	−	9.44496i	0.941842	−	0.600969i
$248$	−39.1378			−2.48525
$249$	5.02827	−	8.70923i	0.318654	−	0.551925i
$250$	4.29261	−	7.43502i	0.271489	−	0.470232i
$251$	−4.70739	−	8.15344i	−0.297128	−	0.514640i	0.678350	−	0.734739i	$-0.262695\pi$
$251$	−4.70739	−	8.15344i	−0.297128	−	0.514640i	−0.975478	+	0.220099i	$0.929362\pi$
$252$	−5.01414	+	8.68474i	−0.315861	+	0.547087i
$253$	−2.00546	−	3.47357i	−0.126082	−	0.218381i
$254$	−36.8114			−2.30975
$255$		0			0
$256$	15.8774	+	27.5005i	0.992340	+	1.71878i
$257$	5.07522	+	8.79054i	0.316584	+	0.548339i	0.979773	−	0.200113i	$-0.0641309\pi$
$257$	5.07522	+	8.79054i	0.316584	+	0.548339i	−0.663189	+	0.748452i	$0.730798\pi$
$258$	−1.77847			−0.110723
$259$	−2.32088			−0.144213
$260$	−28.9012	−	50.0583i	−1.79237	−	3.10448i
$261$	−3.32088	+	5.75194i	−0.205558	+	0.356036i
$262$	0.806748	+	1.39733i	0.0498410	+	0.0863272i
$263$	−1.29261	+	2.23887i	−0.0797058	+	0.138054i	−0.903123	−	0.429382i	$-0.858731\pi$
$263$	−1.29261	+	2.23887i	−0.0797058	+	0.138054i	0.823417	+	0.567436i	$0.192065\pi$
$264$	−4.98133	+	8.62791i	−0.306579	+	0.531011i
$265$	−33.0848			−2.03238
$266$	22.5689	+	11.7281i	1.38379	+	0.719094i
$267$	−2.67912			−0.163959
$268$	18.0990	−	31.3483i	1.10557	−	1.91490i
$269$	−0.273937	+	0.474473i	−0.0167023	+	0.0289292i	−0.874256	−	0.485466i	$-0.838650\pi$
$269$	−0.273937	+	0.474473i	−0.0167023	+	0.0289292i	0.857553	+	0.514395i	$0.171983\pi$
$270$	4.17458	+	7.23058i	0.254057	+	0.440039i
$271$	10.4431	−	18.0879i	0.634370	−	1.09876i	−0.352278	−	0.935895i	$-0.614593\pi$
$271$	10.4431	−	18.0879i	0.634370	−	1.09876i	0.986648	−	0.162866i	$-0.0520739\pi$
$272$		0			0
$273$	9.34916			0.565837
$274$	−6.49960			−0.392655
$275$	5.14631	+	8.91366i	0.310334	+	0.537514i
$276$	5.07522	+	8.79054i	0.305492	+	0.529128i
$277$	−23.7831			−1.42899			−0.714495	−	0.699640i	$-0.753344\pi$
$277$	−23.7831			−1.42899			−0.714495	+	0.699640i	$0.753344\pi$
$278$	46.7030			2.80106
$279$	−3.35369	−	5.80877i	−0.200780	−	0.347762i
$280$	22.4864	−	38.9476i	1.34382	−	2.32756i
$281$	5.95305	+	10.3110i	0.355129	+	0.615102i	0.987140	−	0.159858i	$-0.0511035\pi$
$281$	5.95305	+	10.3110i	0.355129	+	0.615102i	−0.632011	+	0.774960i	$0.717770\pi$
$282$	−7.54241	+	13.0638i	−0.449144	+	0.777940i
$283$	−9.02827	+	15.6374i	−0.536675	+	0.929549i	0.462405	+	0.886669i	$0.346987\pi$
$283$	−9.02827	+	15.6374i	−0.536675	+	0.929549i	−0.999080	+	0.0428799i	$0.986347\pi$
$284$	−40.6802			−2.41392
$285$	12.2029	−	7.78637i	0.722835	−	0.461225i
$286$	17.2918			1.02249
$287$	7.70739	−	13.3496i	0.454953	−	0.788001i
$288$	1.74293	−	3.01885i	0.102703	−	0.177887i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	27.7266	−	48.0239i	1.62816	−	2.82006i
$291$	−8.86330	−	15.3517i	−0.519576	−	0.899931i
$292$	50.3027			2.94375
$293$	−27.3966			−1.60053			−0.800264	−	0.599648i	$-0.795307\pi$
$293$	−27.3966			−1.60053			−0.800264	+	0.599648i	$0.795307\pi$
$294$	−2.02827	−	3.51307i	−0.118291	−	0.204887i
$295$	−2.83502	−	4.91040i	−0.165061	−	0.285895i
$296$	5.83502			0.339154
$297$	−1.70739			−0.0990728
$298$	−4.98133	−	8.62791i	−0.288561	−	0.499801i
$299$	4.73153	−	8.19524i	0.273631	−	0.473943i
$300$	−13.0237	−	22.5578i	−0.751926	−	1.30237i
$301$	−0.820884	+	1.42181i	−0.0473150	+	0.0819520i
$302$	−10.9344	+	18.9389i	−0.629203	+	1.08981i
$303$	16.0565			0.922425
$304$	−23.3163	−	12.1165i	−1.33728	−	0.694929i
$305$	11.2462			0.643955
$306$		0			0
$307$	−1.80675	+	3.12938i	−0.103117	+	0.178603i	−0.912967	−	0.408033i	$-0.866215\pi$
$307$	−1.80675	+	3.12938i	−0.103117	+	0.178603i	0.809851	+	0.586636i	$0.199548\pi$
$308$	8.56108	+	14.8282i	0.487813	+	0.844917i
$309$	3.77394	−	6.53665i	0.214692	−	0.371857i
$310$	28.0005	+	48.4983i	1.59032	+	2.75452i
$311$	18.4057			1.04369			0.521846	−	0.853040i	$-0.325244\pi$
$311$	18.4057			1.04369			0.521846	+	0.853040i	$0.325244\pi$
$312$	−23.5051			−1.33071
$313$	−11.5424	−	19.9920i	−0.652416	−	1.13002i	−0.982535	−	0.186078i	$-0.940422\pi$
$313$	−11.5424	−	19.9920i	−0.652416	−	1.13002i	0.330119	−	0.943939i	$-0.392911\pi$
$314$	−7.16317	−	12.4070i	−0.404241	−	0.700166i
$315$	7.70739			0.434262
$316$	−14.4713			−0.814076
$317$	12.6887	+	21.9775i	0.712669	+	1.23438i	0.963852	+	0.266440i	$0.0858473\pi$
$317$	12.6887	+	21.9775i	0.712669	+	1.23438i	−0.251182	+	0.967940i	$0.580819\pi$
$318$	−12.5237	+	21.6917i	−0.702296	+	1.21641i
$319$	5.67004	+	9.82080i	0.317461	+	0.549859i
$320$	5.46719	−	9.46945i	0.305625	−	0.529358i
$321$	−3.64177	+	6.30773i	−0.203264	+	0.352063i
$322$	13.7074			0.763883
$323$		0			0
$324$	4.32088			0.240049
$325$	−12.1418	+	21.0302i	−0.673504	+	1.16654i
$326$	23.1017	−	40.0133i	1.27948	−	2.21613i
$327$	6.12763	+	10.6134i	0.338859	+	0.586921i
$328$	−19.3774	+	33.5627i	−1.06994	+	1.85319i
$329$	6.96265	+	12.0597i	0.383864	+	0.664871i
$330$	14.2553			0.784726
$331$	−21.3492			−1.17346			−0.586728	−	0.809784i	$-0.699584\pi$
$331$	−21.3492			−1.17346			−0.586728	+	0.809784i	$0.699584\pi$
$332$	21.7266	+	37.6316i	1.19240	+	2.06530i
$333$	0.500000	+	0.866025i	0.0273998	+	0.0474579i
$334$	−54.3876			−2.97595
$335$	−27.8205			−1.52000
$336$	−6.99546	−	12.1165i	−0.381634	−	0.661009i
$337$	2.04241	−	3.53756i	0.111257	−	0.192703i	−0.805020	−	0.593247i	$-0.797846\pi$
$337$	2.04241	−	3.53756i	0.111257	−	0.192703i	0.916277	+	0.400544i	$0.131179\pi$
$338$	4.05655	+	7.02615i	0.220647	+	0.382172i
$339$	−3.68872	+	6.38904i	−0.200344	+	0.347005i
$340$		0			0
$341$	−11.4521			−0.620167
$342$	−0.485863	−	10.9481i	−0.0262725	−	0.592005i
$343$	−19.9909			−1.07941
$344$	2.06382	−	3.57463i	0.111274	−	0.192731i
$345$	3.90064	−	6.75611i	0.210003	−	0.363737i
$346$	−5.90611	−	10.2297i	−0.317514	−	0.549951i
$347$	−9.85369	+	17.0671i	−0.528974	+	0.916210i	0.470455	+	0.882424i	$0.344090\pi$
$347$	−9.85369	+	17.0671i	−0.528974	+	0.916210i	−0.999429	+	0.0337860i	$0.989244\pi$
$348$	−14.3492	−	24.8535i	−0.769196	−	1.33229i
$349$	23.3118			1.24785			0.623926	−	0.781483i	$-0.285537\pi$
$349$	23.3118			1.24785			0.623926	+	0.781483i	$0.285537\pi$
$350$	−35.1751			−1.88019
$351$	−2.01414	−	3.48859i	−0.107507	−	0.186207i
$352$	−2.97586	−	5.15435i	−0.158614	−	0.274728i
$353$	25.1896			1.34071			0.670355	−	0.742041i	$-0.266142\pi$
$353$	25.1896			1.34071			0.670355	+	0.742041i	$0.266142\pi$
$354$	−4.29261			−0.228150
$355$	15.6327	+	27.0766i	0.829697	+	1.43708i
$356$	5.78807	−	10.0252i	0.306767	−	0.531337i
$357$		0			0
$358$	−1.33956	+	2.32018i	−0.0707978	+	0.122625i
$359$	1.61350	−	2.79466i	0.0851570	−	0.147496i	−0.820301	−	0.571932i	$-0.806194\pi$
$359$	1.61350	−	2.79466i	0.0851570	−	0.147496i	0.905458	+	0.424436i	$0.139527\pi$
$360$	−19.3774			−1.02128
$361$	−18.9253	+	1.68308i	−0.996069	+	0.0885831i
$362$	9.22699			0.484960
$363$	4.04241	−	7.00166i	0.212172	−	0.367492i
$364$	−20.1983	+	34.9845i	−1.05868	+	1.83369i
$365$	−19.3305	−	33.4814i	−1.01180	−	1.75250i
$366$	4.25707	−	7.37346i	0.222521	−	0.385417i
$367$	14.7311	+	25.5151i	0.768959	+	1.33188i	0.938128	+	0.346288i	$0.112558\pi$
$367$	14.7311	+	25.5151i	0.768959	+	1.33188i	−0.169170	+	0.985587i	$0.554109\pi$
$368$	−14.1614			−0.738212
$369$	−6.64177			−0.345757
$370$	−4.17458	−	7.23058i	−0.217026	−	0.375900i
$371$	11.5611	+	20.0244i	0.600222	+	1.03961i
$372$	28.9819			1.50264
$373$	19.6700			1.01848			0.509238	−	0.860626i	$-0.329927\pi$
$373$	19.6700			1.01848			0.509238	+	0.860626i	$0.329927\pi$
$374$		0			0
$375$	−1.70739	+	2.95729i	−0.0881692	+	0.152714i
$376$	−17.5051	−	30.3197i	−0.902755	−	1.56362i
$377$	−13.3774	+	23.1704i	−0.688973	+	1.19334i
$378$	2.91751	−	5.05328i	0.150061	−	0.259913i
$379$	−0.763937			−0.0392408			−0.0196204	−	0.999808i	$-0.506246\pi$
$379$	−0.763937			−0.0392408			−0.0196204	+	0.999808i	$0.506246\pi$
$380$	2.77301	+	62.4850i	0.142252	+	3.20541i
$381$	14.6418			0.750121
$382$	−1.10349	+	1.91131i	−0.0564597	+	0.0977911i
$383$	−1.91932	+	3.32435i	−0.0980724	+	0.169866i	−0.910887	−	0.412656i	$-0.864601\pi$
$383$	−1.91932	+	3.32435i	−0.0980724	+	0.169866i	0.812814	+	0.582523i	$0.197934\pi$
$384$	−7.62490	−	13.2067i	−0.389107	−	0.673952i
$385$	6.57976	−	11.3965i	0.335335	−	0.580818i
$386$	−10.8278	−	18.7542i	−0.551118	−	0.954565i
$387$	0.707389			0.0359586
$388$	76.5946			3.88850
$389$	−16.1035	−	27.8921i	−0.816480	−	1.41418i	−0.908261	−	0.418405i	$-0.862589\pi$
$389$	−16.1035	−	27.8921i	−0.816480	−	1.41418i	0.0917810	−	0.995779i	$-0.470744\pi$
$390$	16.8163	+	29.1268i	0.851529	+	1.47489i
$391$		0			0
$392$	9.41478			0.475518
$393$	−0.320884	−	0.555788i	−0.0161865	−	0.0280358i
$394$	31.0944	−	53.8571i	1.56651	−	2.71328i
$395$	5.56108	+	9.63208i	0.279809	+	0.484643i
$396$	3.68872	−	6.38904i	0.185365	−	0.321062i
$397$	13.2977	−	23.0322i	0.667391	−	1.15596i	−0.311240	−	0.950331i	$-0.600744\pi$
$397$	13.2977	−	23.0322i	0.667391	−	1.15596i	0.978631	−	0.205624i	$-0.0659224\pi$
$398$	55.2882			2.77135
$399$	−8.97679	−	4.66485i	−0.449402	−	0.233535i
$400$	36.3401			1.81700
$401$	4.66044	−	8.07212i	0.232731	−	0.403103i	−0.725880	−	0.687822i	$-0.758567\pi$
$401$	4.66044	−	8.07212i	0.232731	−	0.403103i	0.958611	+	0.284719i	$0.0919004\pi$
$402$	−10.5310	+	18.2402i	−0.525239	+	0.909740i
$403$	−13.5096	−	23.3993i	−0.672961	−	1.16560i
$404$	−34.6892	+	60.0835i	−1.72585	+	2.98927i
$405$	−1.66044	−	2.87597i	−0.0825080	−	0.142908i
$406$	−38.7549			−1.92337
$407$	1.70739			0.0846321
$408$		0			0
$409$	−10.9006	−	18.8805i	−0.539002	−	0.933579i	−0.998958	−	0.0456372i	$-0.985468\pi$
$409$	−10.9006	−	18.8805i	−0.539002	−	0.933579i	0.459956	−	0.887942i	$-0.347865\pi$
$410$	55.4532			2.73864
$411$	2.58522			0.127520
$412$	16.3067	+	28.2441i	0.803376	+	1.39149i
$413$	−1.98133	+	3.43176i	−0.0974947	+	0.168866i
$414$	−2.95305	−	5.11484i	−0.145135	−	0.251381i
$415$	16.6983	−	28.9223i	0.819688	−	1.41974i
$416$	7.02101	−	12.1607i	0.344233	−	0.596229i
$417$	−18.5761			−0.909678
$418$	−16.6031	−	8.62791i	−0.812084	−	0.422005i
$419$	4.93438			0.241060			0.120530	−	0.992710i	$-0.461541\pi$
$419$	4.93438			0.241060			0.120530	+	0.992710i	$0.461541\pi$
$420$	−16.6514	+	28.8410i	−0.812504	+	1.40730i
$421$	−2.12763	+	3.68517i	−0.103694	+	0.179604i	−0.913204	−	0.407503i	$-0.866400\pi$
$421$	−2.12763	+	3.68517i	−0.103694	+	0.179604i	0.809510	+	0.587107i	$0.199733\pi$
$422$	−16.6158	−	28.7795i	−0.808846	−	1.40096i
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$	−29.0661	−	50.3440i	−1.41158	−	2.44492i
$425$		0			0
$426$	23.6700			1.14682
$427$	−3.92984	−	6.80669i	−0.190178	−	0.329399i
$428$	−15.7357	−	27.2550i	−0.760612	−	1.31742i
$429$	−6.87783			−0.332065
$430$	−5.90611			−0.284818
$431$	0.414779	+	0.718418i	0.0199792	+	0.0346050i	0.875842	−	0.482598i	$-0.160307\pi$
$431$	0.414779	+	0.718418i	0.0199792	+	0.0346050i	−0.855863	+	0.517203i	$0.826973\pi$
$432$	−3.01414	+	5.22064i	−0.145018	+	0.251178i
$433$	−8.24113	−	14.2741i	−0.396043	−	0.685967i	0.597190	−	0.802099i	$-0.296284\pi$
$433$	−8.24113	−	14.2741i	−0.396043	−	0.685967i	−0.993234	+	0.116132i	$0.962950\pi$
$434$	19.5689	−	33.8943i	0.939336	−	1.62698i
$435$	−11.0283	+	19.1015i	−0.528765	+	0.915848i
$436$	−52.9536			−2.53602
$437$	−8.63217	+	5.50800i	−0.412933	+	0.263483i
$438$	−29.2690			−1.39853
$439$	−14.2170	+	24.6245i	−0.678540	+	1.17527i	0.296881	+	0.954915i	$0.404054\pi$
$439$	−14.2170	+	24.6245i	−0.678540	+	1.17527i	−0.975421	+	0.220351i	$0.929280\pi$
$440$	−16.5424	+	28.6523i	−0.788628	+	1.36594i
$441$	0.806748	+	1.39733i	0.0384166	+	0.0665394i
$442$		0			0
$443$	7.70739	+	13.3496i	0.366189	+	0.634258i	0.988966	−	0.148141i	$-0.0473290\pi$
$443$	7.70739	+	13.3496i	0.366189	+	0.634258i	−0.622777	+	0.782399i	$0.713996\pi$
$444$	−4.32088			−0.205060
$445$	−8.89703			−0.421760
$446$	−6.88924	−	11.9325i	−0.326215	−	0.565021i
$447$	1.98133	+	3.43176i	0.0937135	+	0.162317i
$448$	−7.64177			−0.361040
$449$	−23.1523			−1.09262			−0.546312	−	0.837582i	$-0.683969\pi$
$449$	−23.1523			−1.09262			−0.546312	+	0.837582i	$0.683969\pi$
$450$	7.57795	+	13.1254i	0.357228	+	0.618737i
$451$	−5.67004	+	9.82080i	−0.266992	+	0.462444i
$452$	−15.9385	−	27.6063i	−0.749685	−	1.29849i
$453$	4.34916	−	7.53296i	0.204341	−	0.353929i
$454$	9.68872	−	16.7813i	0.454714	−	0.787588i
$455$	31.0475			1.45553
$456$	22.5689	+	11.7281i	1.05688	+	0.549217i
$457$	4.68819			0.219304			0.109652	−	0.993970i	$-0.465026\pi$
$457$	4.68819			0.219304			0.109652	+	0.993970i	$0.465026\pi$
$458$	5.06382	−	8.77079i	0.236617	−	0.409832i
$459$		0			0
$460$	16.8542	+	29.1924i	0.785832	+	1.36110i
$461$	−6.27394	+	10.8668i	−0.292206	+	0.506116i	−0.974331	−	0.225119i	$-0.927723\pi$
$461$	−6.27394	+	10.8668i	−0.292206	+	0.506116i	0.682125	+	0.731236i	$0.261056\pi$
$462$	−4.98133	−	8.62791i	−0.231752	−	0.401407i
$463$	22.8880			1.06369			0.531847	−	0.846841i	$-0.321498\pi$
$463$	22.8880			1.06369			0.531847	+	0.846841i	$0.321498\pi$
$464$	40.0384			1.85874
$465$	−11.1372	−	19.2903i	−0.516477	−	0.894564i
$466$	32.8259	+	56.8562i	1.52063	+	2.63381i
$467$	−11.8122			−0.546604			−0.273302	−	0.961928i	$-0.588116\pi$
$467$	−11.8122			−0.546604			−0.273302	+	0.961928i	$0.588116\pi$
$468$	17.4057			0.804579
$469$	9.72153	+	16.8382i	0.448898	+	0.777515i
$470$	−25.0475	+	43.3835i	−1.15535	+	2.00113i
$471$	2.84916	+	4.93489i	0.131282	+	0.227388i
$472$	4.98133	−	8.62791i	0.229284	−	0.397132i
$473$	0.603895	−	1.04598i	0.0277671	−	0.0480940i
$474$	8.42024			0.386755
$475$	22.1514	−	14.1343i	1.01637	−	0.648526i
$476$		0			0
$477$	4.98133	−	8.62791i	0.228079	−	0.395045i
$478$	−9.68872	+	16.7813i	−0.443152	+	0.767561i
$479$	17.0192	+	29.4781i	0.777627	+	1.34689i	0.933306	+	0.359082i	$0.116910\pi$
$479$	17.0192	+	29.4781i	0.777627	+	1.34689i	−0.155679	+	0.987808i	$0.549756\pi$
$480$	5.78807	−	10.0252i	0.264188	−	0.457587i
$481$	2.01414	+	3.48859i	0.0918367	+	0.159066i
$482$	−54.5525			−2.48480
$483$	−5.45213			−0.248080
$484$	17.4668	+	30.2534i	0.793945	+	1.37515i
$485$	−29.4340	−	50.9811i	−1.33653	−	2.31493i
$486$	−2.51414			−0.114044
$487$	−7.41478			−0.335996			−0.167998	−	0.985787i	$-0.553730\pi$
$487$	−7.41478			−0.335996			−0.167998	+	0.985787i	$0.553730\pi$
$488$	9.88016	+	17.1129i	0.447254	+	0.774667i
$489$	−9.18872	+	15.9153i	−0.415528	+	0.719716i
$490$	−6.73566	−	11.6665i	−0.304286	−	0.527039i
$491$	−1.93438	+	3.35044i	−0.0872973	+	0.151203i	−0.906368	−	0.422489i	$-0.861156\pi$
$491$	−1.93438	+	3.35044i	−0.0872973	+	0.151203i	0.819071	+	0.573693i	$0.194490\pi$
$492$	14.3492	−	24.8535i	0.646910	−	1.12048i
$493$		0			0
$494$	−1.95719	−	44.1019i	−0.0880581	−	1.98424i
$495$	−5.67004			−0.254849
$496$	−20.2170	+	35.0169i	−0.907770	+	1.57230i
$497$	10.9253	−	18.9232i	0.490067	−	0.848821i
$498$	−12.6418	−	21.8962i	−0.566491	−	0.981192i
$499$	17.7931	−	30.8186i	0.796530	−	1.37963i	−0.125333	−	0.992115i	$-0.540000\pi$
$499$	17.7931	−	30.8186i	0.796530	−	1.37963i	0.921863	−	0.387516i	$-0.126667\pi$
$500$	−7.37743	−	12.7781i	−0.329929	−	0.571453i
$501$	21.6327			0.966478
$502$	−23.6700			−1.05645
$503$	−4.29261	−	7.43502i	−0.191398	−	0.331511i	0.754316	−	0.656512i	$-0.227969\pi$
$503$	−4.29261	−	7.43502i	−0.191398	−	0.331511i	−0.945714	+	0.325001i	$0.894635\pi$
$504$	6.77121	+	11.7281i	0.301613	+	0.522410i
$505$	53.3219			2.37280
$506$	−10.0840			−0.448289
$507$	−1.61350	−	2.79466i	−0.0716578	−	0.124115i
$508$	−31.6327	+	54.7894i	−1.40347	+	2.43089i
$509$	3.97173	+	6.87923i	0.176044	+	0.304917i	0.940522	−	0.339733i	$-0.110337\pi$
$509$	3.97173	+	6.87923i	0.176044	+	0.304917i	−0.764478	+	0.644649i	$0.777003\pi$
$510$		0			0
$511$	−13.5096	+	23.3993i	−0.597630	+	1.03512i
$512$	49.3365			2.18038
$513$	0.193252	+	4.35461i	0.00853230	+	0.192261i
$514$	25.5196			1.12562
$515$	12.5328	−	21.7075i	0.552262	−	0.956545i
$516$	−1.52827	+	2.64705i	−0.0672785	+	0.116530i
$517$	−5.12217	−	8.87186i	−0.225273	−	0.390184i
$518$	−2.91751	+	5.05328i	−0.128188	+	0.222028i
$519$	2.34916	+	4.06886i	0.103117	+	0.178603i
$520$	−78.0576			−3.42305
$521$	−0.0757489			−0.00331862			−0.00165931	−	0.999999i	$-0.500528\pi$
$521$	−0.0757489			−0.00331862			−0.00165931	+	0.999999i	$0.500528\pi$
$522$	8.34916	+	14.4612i	0.365433	+	0.632948i
$523$	−10.1514	−	17.5827i	−0.443888	−	0.768837i	0.554086	−	0.832460i	$-0.313068\pi$
$523$	−10.1514	−	17.5827i	−0.443888	−	0.768837i	−0.997974	+	0.0636224i	$0.979735\pi$
$524$	2.77301			0.121139
$525$	13.9909			0.610614
$526$	3.24980	+	5.62882i	0.141698	+	0.245428i
$527$		0			0
$528$	5.14631	+	8.91366i	0.223964	+	0.387917i
$529$	8.74073	−	15.1394i	0.380032	−	0.658234i
$530$	−41.5899	+	72.0358i	−1.80655	+	3.12904i
$531$	1.70739			0.0740944
$532$	36.8497	−	23.5130i	1.59764	−	1.01942i
$533$	−26.7549			−1.15888
$534$	−3.36783	+	5.83326i	−0.145740	+	0.252430i
$535$	−12.0939	+	20.9472i	−0.522865	+	0.905628i
$536$	−24.4412	−	42.3335i	−1.05570	−	1.82853i
$537$	0.532810	−	0.922854i	0.0229925	−	0.0398241i
$538$	0.688716	+	1.19289i	0.0296927	+	0.0514292i
$539$	2.75486			0.118660
$540$	14.3492			0.617489
$541$	16.5475	+	28.6611i	0.711432	+	1.23224i	0.964320	+	0.264740i	$0.0852862\pi$
$541$	16.5475	+	28.6611i	0.711432	+	1.23224i	−0.252888	+	0.967495i	$0.581381\pi$
$542$	−26.2553	−	45.4755i	−1.12776	−	1.95334i
$543$	−3.67004			−0.157497
$544$		0			0
$545$	20.3492	+	35.2458i	0.871662	+	1.50976i
$546$	11.7525	−	20.3560i	0.502962	−	0.871156i
$547$	17.9581	+	31.1044i	0.767834	+	1.32993i	0.938735	+	0.344639i	$0.111999\pi$
$547$	17.9581	+	31.1044i	0.767834	+	1.32993i	−0.170902	+	0.985288i	$0.554668\pi$
$548$	−5.58522	+	9.67389i	−0.238589	+	0.413248i
$549$	−1.69325	+	2.93280i	−0.0722663	+	0.125169i
$550$	25.8770			1.10340
$551$	24.4057	−	15.5727i	1.03972	−	0.663421i
$552$	13.7074			0.583425
$553$	3.88650	−	6.73162i	0.165271	−	0.286258i
$554$	−29.8970	+	51.7832i	−1.27020	+	2.20006i
$555$	1.66044	+	2.87597i	0.0704818	+	0.122078i
$556$	40.1327	−	69.5119i	1.70201	−	2.94796i
$557$	0.962653	+	1.66736i	0.0407889	+	0.0706485i	0.885699	−	0.464260i	$-0.153680\pi$
$557$	0.962653	+	1.66736i	0.0407889	+	0.0706485i	−0.844910	+	0.534908i	$0.820346\pi$
$558$	−16.8633			−0.713880
$559$	2.84956			0.120523
$560$	−23.2311	−	40.2375i	−0.981694	−	1.70034i
$561$		0			0
$562$	29.9336			1.26267
$563$	10.8861			0.458795			0.229397	−	0.973333i	$-0.426324\pi$
$563$	10.8861			0.458795			0.229397	+	0.973333i	$0.426324\pi$
$564$	12.9627	+	22.4520i	0.545826	+	0.945399i
$565$	−12.2498	+	21.2173i	−0.515353	+	0.892618i
$566$	22.6983	+	39.3146i	0.954081	+	1.65252i
$567$	−1.16044	+	2.00994i	−0.0487340	+	0.0844098i
$568$	−27.4677	+	47.5755i	−1.15252	+	1.99622i
$569$	−36.4358			−1.52747			−0.763735	−	0.645530i	$-0.776636\pi$
$569$	−36.4358			−1.52747			−0.763735	+	0.645530i	$0.776636\pi$
$570$	−1.61350	−	36.3574i	−0.0675819	−	1.52284i
$571$	−7.54787			−0.315869			−0.157934	−	0.987450i	$-0.550483\pi$
$571$	−7.54787			−0.315869			−0.157934	+	0.987450i	$0.550483\pi$
$572$	14.8592	−	25.7368i	0.621293	−	1.07611i
$573$	0.438916	−	0.760225i	0.0183360	−	0.0317588i
$574$	−19.3774	−	33.5627i	−0.808798	−	1.40088i
$575$	7.08068	−	12.2641i	0.295285	−	0.511449i
$576$	1.64631	+	2.85148i	0.0685961	+	0.118812i
$577$	−15.4823			−0.644535			−0.322267	−	0.946649i	$-0.604445\pi$
$577$	−15.4823			−0.644535			−0.322267	+	0.946649i	$0.604445\pi$
$578$	42.7403			1.77776
$579$	4.30675	+	7.45951i	0.178982	+	0.310006i
$580$	−47.6519	−	82.5355i	−1.97864	−	3.42710i
$581$	−23.3401			−0.968310
$582$	−44.5671			−1.84736
$583$	−8.50506	−	14.7312i	−0.352244	−	0.610104i
$584$	33.9650	−	58.8291i	1.40548	−	2.43436i
$585$	−6.68872	−	11.5852i	−0.276544	−	0.478989i
$586$	−34.4394	+	59.6509i	−1.42268	+	2.46415i
$587$	14.8729	−	25.7606i	0.613870	−	1.06325i	−0.376712	−	0.926331i	$-0.622945\pi$
$587$	14.8729	−	25.7606i	0.613870	−	1.06325i	0.990582	−	0.136924i	$-0.0437215\pi$
$588$	−6.97173			−0.287509
$589$	1.29622	+	29.2081i	0.0534098	+	1.20350i
$590$	−14.2553			−0.586880
$591$	−12.3678	+	21.4217i	−0.508745	+	0.881172i
$592$	3.01414	−	5.22064i	0.123880	−	0.214567i
$593$	0.273937	+	0.474473i	0.0112493	+	0.0194843i	0.871595	−	0.490226i	$-0.163086\pi$
$593$	0.273937	+	0.474473i	0.0112493	+	0.0194843i	−0.860346	+	0.509711i	$0.829753\pi$
$594$	−2.14631	+	3.71751i	−0.0880640	+	0.152531i
$595$		0			0
$596$	−17.1222			−0.701351
$597$	−21.9909			−0.900029
$598$	−11.8957	−	20.6040i	−0.486452	−	0.842559i
$599$	22.8163	+	39.5191i	0.932251	+	1.61471i	0.779465	+	0.626446i	$0.215491\pi$
$599$	22.8163	+	39.5191i	0.932251	+	1.61471i	0.152786	+	0.988259i	$0.451175\pi$
$600$	−35.1751			−1.43602
$601$	−6.85783			−0.279737			−0.139868	−	0.990170i	$-0.544668\pi$
$601$	−6.85783			−0.279737			−0.139868	+	0.990170i	$0.544668\pi$
$602$	2.06382	+	3.57463i	0.0841149	+	0.145691i
$603$	4.18872	−	7.25507i	0.170578	−	0.295449i
$604$	18.7922	+	32.5491i	0.764644	+	1.32440i
$605$	13.4244	−	23.2517i	0.545779	−	0.945316i
$606$	20.1842	−	34.9600i	0.819926	−	1.42015i
$607$	−6.76394			−0.274540			−0.137270	−	0.990534i	$-0.543833\pi$
$607$	−6.76394			−0.274540			−0.137270	+	0.990534i	$0.543833\pi$
$608$	−12.8091	+	8.17319i	−0.519477	+	0.331467i
$609$	15.4148			0.624638
$610$	14.1372	−	24.4864i	0.572400	−	0.991426i
$611$	12.0848	−	20.9315i	0.488900	−	0.846799i
$612$		0			0
$613$	−2.22153	+	3.84780i	−0.0897266	+	0.155411i	−0.907396	−	0.420278i	$-0.861933\pi$
$613$	−2.22153	+	3.84780i	−0.0897266	+	0.155411i	0.817669	+	0.575689i	$0.195266\pi$
$614$	4.54241	+	7.86769i	0.183317	+	0.317514i
$615$	−22.0565			−0.889406
$616$	23.1222			0.931619
$617$	16.0005	+	27.7137i	0.644157	+	1.11571i	0.984496	+	0.175410i	$0.0561250\pi$
$617$	16.0005	+	27.7137i	0.644157	+	1.11571i	−0.340339	+	0.940303i	$0.610542\pi$
$618$	−9.48820	−	16.4340i	−0.381671	−	0.661074i
$619$	−14.3774			−0.577878			−0.288939	−	0.957348i	$-0.593302\pi$
$619$	−14.3774			−0.577878			−0.288939	+	0.957348i	$0.593302\pi$
$620$	96.2454			3.86531
$621$	1.17458	+	2.03443i	0.0471342	+	0.0816389i
$622$	23.1372	−	40.0749i	0.927719	−	1.60686i
$623$	3.10896	+	5.38487i	0.124558	+	0.215740i
$624$	−12.1418	+	21.0302i	−0.486060	+	0.841880i
$625$	9.40064	−	16.2824i	0.376026	−	0.651296i
$626$	−58.0384			−2.31968
$627$	6.60389	+	3.43176i	0.263734	+	0.137051i
$628$	−24.6218			−0.982516
$629$		0			0
$630$	9.68872	−	16.7813i	0.386008	−	0.668585i
$631$	−5.54695	−	9.60759i	−0.220820	−	0.382472i	0.734237	−	0.678893i	$-0.237540\pi$
$631$	−5.54695	−	9.60759i	−0.220820	−	0.382472i	−0.955057	+	0.296421i	$0.904207\pi$
$632$	−9.77121	+	16.9242i	−0.388678	+	0.673209i
$633$	6.60896	+	11.4471i	0.262683	+	0.454979i
$634$	63.8023			2.53391
$635$	48.6236			1.92957
$636$	21.5237	+	37.2802i	0.853472	+	1.47826i
$637$	3.24980	+	5.62882i	0.128762	+	0.223022i
$638$	28.5105			1.12874
$639$	−9.41478			−0.372443
$640$	−25.3214	−	43.8580i	−1.00092	−	1.73364i
$641$	−21.7357	+	37.6473i	−0.858507	+	1.48698i	0.0148458	+	0.999890i	$0.495274\pi$
$641$	−21.7357	+	37.6473i	−0.858507	+	1.48698i	−0.873353	+	0.487088i	$0.838059\pi$
$642$	9.15591	+	15.8585i	0.361355	+	0.625885i
$643$	11.8113	−	20.4577i	0.465792	−	0.806775i	−0.533445	−	0.845835i	$-0.679103\pi$
$643$	11.8113	−	20.4577i	0.465792	−	0.806775i	0.999237	+	0.0390599i	$0.0124363\pi$
$644$	11.7790	−	20.4018i	0.464158	−	0.803945i
$645$	2.34916			0.0924980
$646$		0			0
$647$	−19.9253			−0.783345			−0.391672	−	0.920105i	$-0.628103\pi$
$647$	−19.9253			−0.783345			−0.391672	+	0.920105i	$0.628103\pi$
$648$	2.91751	−	5.05328i	0.114611	−	0.198511i
$649$	1.45759	−	2.52462i	0.0572154	−	0.0990999i
$650$	30.5261	+	52.8727i	1.19733	+	2.07384i
$651$	−7.78354	+	13.4815i	−0.305061	+	0.528381i
$652$	−39.7034	−	68.7683i	−1.55490	−	2.69317i
$653$	−2.11310			−0.0826918			−0.0413459	−	0.999145i	$-0.513165\pi$
$653$	−2.11310			−0.0826918			−0.0413459	+	0.999145i	$0.513165\pi$
$654$	30.8114			1.20482
$655$	−1.06562	−	1.84571i	−0.0416372	−	0.0721178i
$656$	20.0192	+	34.6743i	0.781618	+	1.35380i
$657$	11.6418			0.454189
$658$	35.0101			1.36484
$659$	−21.7507	−	37.6734i	−0.847288	−	1.46755i	−0.883619	−	0.468206i	$-0.844900\pi$
$659$	−21.7507	−	37.6734i	−0.847288	−	1.46755i	0.0363312	−	0.999340i	$-0.488433\pi$
$660$	12.2498	−	21.2173i	0.476823	−	0.825881i
$661$	−11.0565	−	19.1505i	−0.430050	−	0.744868i	0.566827	−	0.823837i	$-0.308171\pi$
$661$	−11.0565	−	19.1505i	−0.430050	−	0.744868i	−0.996877	+	0.0789685i	$0.974837\pi$
$662$	−26.8374	+	46.4837i	−1.04306	+	1.80664i
$663$		0			0
$664$	58.6802			2.27723
$665$	−29.8109	−	15.4914i	−1.15602	−	0.600732i
$666$	2.51414			0.0974208
$667$	7.80128	−	13.5122i	0.302067	−	0.523195i
$668$	−46.7362	+	80.9495i	−1.80828	+	3.13203i
$669$	2.74020	+	4.74616i	0.105942	+	0.183497i
$670$	−34.9723	+	60.5737i	−1.35110	+	2.34017i
$671$	2.89104	+	5.00743i	0.111607	+	0.193310i
$672$	−8.09029			−0.312090
$673$	12.5953			0.485515			0.242758	−	0.970087i	$-0.421948\pi$
$673$	12.5953			0.485515			0.242758	+	0.970087i	$0.421948\pi$
$674$	−5.13490	−	8.89391i	−0.197789	−	0.342581i
$675$	−3.01414	−	5.22064i	−0.116014	−	0.200942i
$676$	13.9435			0.536287
$677$	−32.9427			−1.26609			−0.633045	−	0.774115i	$-0.718195\pi$
$677$	−32.9427			−1.26609			−0.633045	+	0.774115i	$0.718195\pi$
$678$	9.27394	+	16.0629i	0.356163	+	0.616893i
$679$	−20.5707	+	35.6295i	−0.789430	+	1.36733i
$680$		0			0
$681$	−3.85369	+	6.67479i	−0.147674	+	0.255779i
$682$	−14.3961	+	24.9348i	−0.551255	+	0.954802i
$683$	−18.3876			−0.703580			−0.351790	−	0.936079i	$-0.614427\pi$
$683$	−18.3876			−0.703580			−0.351790	+	0.936079i	$0.614427\pi$
$684$	−16.7125	−	8.68474i	−0.639017	−	0.332069i
$685$	8.58522			0.328024
$686$	−25.1300	+	43.5264i	−0.959466	+	1.66184i
$687$	−2.01414	+	3.48859i	−0.0768441	+	0.133098i
$688$	−2.13217	−	3.69302i	−0.0812882	−	0.140795i
$689$	20.0661	−	34.7556i	0.764459	−	1.32408i
$690$	−9.80675	−	16.9858i	−0.373336	−	0.646638i
$691$	−16.6599			−0.633773			−0.316887	−	0.948463i	$-0.602637\pi$
$691$	−16.6599			−0.633773			−0.316887	+	0.948463i	$0.602637\pi$
$692$	−20.3009			−0.771724
$693$	1.98133	+	3.43176i	0.0752644	+	0.130362i
$694$	24.7735	+	42.9090i	0.940391	+	1.62880i
$695$	−61.6892			−2.34001
$696$	−38.7549			−1.46900
$697$		0			0
$698$	29.3045	−	50.7570i	1.10919	−	1.92118i
$699$	−13.0565	−	22.6146i	−0.493844	−	0.855363i
$700$	−30.2266	+	52.3540i	−1.14246	+	1.97879i
$701$	24.3588	−	42.1906i	0.920018	−	1.59352i	0.120633	−	0.992697i	$-0.461507\pi$
$701$	24.3588	−	42.1906i	0.920018	−	1.59352i	0.799384	−	0.600820i	$-0.205159\pi$
$702$	−10.1276			−0.382243
$703$	−0.193252	−	4.35461i	−0.00728865	−	0.164237i
$704$	5.62177			0.211878
$705$	9.96265	−	17.2558i	0.375215	−	0.649892i
$706$	31.6651	−	54.8456i	1.19173	−	2.06414i
$707$	−18.6327	−	32.2728i	−0.700755	−	1.21374i
$708$	−3.68872	+	6.38904i	−0.138630	+	0.240115i
$709$	−14.7498	−	25.5474i	−0.553940	−	0.959453i	−0.997985	−	0.0634483i	$-0.979790\pi$
$709$	−14.7498	−	25.5474i	−0.553940	−	0.959453i	0.444045	−	0.896005i	$-0.353543\pi$
$710$	78.6055			2.95001
$711$	−3.34916			−0.125603
$712$	−7.81635	−	13.5383i	−0.292930	−	0.507370i
$713$	7.87836	+	13.6457i	0.295047	+	0.511036i
$714$		0			0
$715$	−22.8405			−0.854186
$716$	2.30221	+	3.98755i	0.0860377	+	0.149022i
$717$	3.85369	−	6.67479i	0.143919	−	0.249275i
$718$	−4.05655	−	7.02615i	−0.151389	−	0.262213i
$719$	−11.3250	+	19.6155i	−0.422352	+	0.731535i	−0.996169	−	0.0874484i	$-0.972129\pi$
$719$	−11.3250	+	19.6155i	−0.422352	+	0.731535i	0.573817	+	0.818984i	$0.305462\pi$
$720$	−10.0096	+	17.3371i	−0.373036	+	0.646117i
$721$	−17.5177			−0.652395
$722$	−20.1258	+	43.3219i	−0.749006	+	1.61228i
$723$	21.6983			0.806969
$724$	7.92892	−	13.7333i	0.294676	−	0.510394i
$725$	−20.0192	+	34.6743i	−0.743494	+	1.28777i
$726$	−10.1632	−	17.6031i	−0.377191	−	0.653314i
$727$	−26.3638	+	45.6635i	−0.977780	+	1.69356i	−0.307342	+	0.951599i	$0.599440\pi$
$727$	−26.3638	+	45.6635i	−0.977780	+	1.69356i	−0.670438	+	0.741966i	$0.733894\pi$
$728$	27.2763	+	47.2439i	1.01093	+	1.75097i
$729$	1.00000			0.0370370
$730$	−97.1990			−3.59750
$731$		0			0
$732$	−7.31635	−	12.6723i	−0.270420	−	0.468381i
$733$	5.72659			0.211516			0.105758	−	0.994392i	$-0.466273\pi$
$733$	5.72659			0.211516			0.105758	+	0.994392i	$0.466273\pi$
$734$	74.0721			2.73405
$735$	2.67912	+	4.64036i	0.0988207	+	0.171162i
$736$	−4.09442	+	7.09175i	−0.150922	+	0.261405i
$737$	−7.15177	−	12.3872i	−0.263439	−	0.456289i
$738$	−8.34916	+	14.4612i	−0.307337	+	0.532323i
$739$	−16.7083	+	28.9397i	−0.614625	+	1.06456i	0.375825	+	0.926691i	$0.377359\pi$
$739$	−16.7083	+	28.9397i	−0.614625	+	1.06456i	−0.990450	+	0.137872i	$0.955974\pi$
$740$	−14.3492			−0.527486
$741$	0.778474	+	17.5416i	0.0285979	+	0.644406i
$742$	58.1323			2.13410
$743$	17.9759	−	31.1351i	0.659470	−	1.14224i	−0.321282	−	0.946983i	$-0.604114\pi$
$743$	17.9759	−	31.1351i	0.659470	−	1.14224i	0.980753	−	0.195253i	$-0.0625528\pi$
$744$	19.5689	−	33.8943i	0.717430	−	1.24263i
$745$	6.57976	+	11.3965i	0.241064	+	0.417534i
$746$	24.7266	−	42.8277i	0.905305	−	1.56803i
$747$	5.02827	+	8.70923i	0.183975	+	0.318654i
$748$		0			0
$749$	16.9043			0.617668
$750$	4.29261	+	7.43502i	0.156744	+	0.271489i
$751$	11.5752	+	20.0489i	0.422386	+	0.731594i	0.996172	−	0.0874112i	$-0.0278594\pi$
$751$	11.5752	+	20.0489i	0.422386	+	0.731594i	−0.573787	+	0.819005i	$0.694526\pi$
$752$	−36.1696			−1.31897
$753$	9.41478			0.343094
$754$	33.6327	+	58.2535i	1.22483	+	2.12147i
$755$	14.4431	−	25.0161i	0.525637	−	0.910429i
$756$	−5.01414	−	8.68474i	−0.182362	−	0.315861i
$757$	−6.49454	+	11.2489i	−0.236048	+	0.408847i	−0.959577	−	0.281447i	$-0.909186\pi$
$757$	−6.49454	+	11.2489i	−0.236048	+	0.408847i	0.723529	+	0.690294i	$0.242519\pi$
$758$	−0.960321	+	1.66333i	−0.0348804	+	0.0604147i
$759$	4.01093			0.145587
$760$	74.9486	+	38.9476i	2.71867	+	1.41278i
$761$	13.3593			0.484274			0.242137	−	0.970242i	$-0.422152\pi$
$761$	13.3593			0.484274			0.242137	+	0.970242i	$0.422152\pi$
$762$	18.4057	−	31.8796i	0.666768	−	1.15488i
$763$	14.2215	−	24.6324i	0.514854	−	0.891753i
$764$	1.89651	+	3.28484i	0.0686131	+	0.118841i
$765$		0			0
$766$	4.82542	+	8.35787i	0.174350	+	0.301982i
$767$	6.87783			0.248344
$768$	−31.7549			−1.14585
$769$	−5.81181	−	10.0664i	−0.209579	−	0.363002i	0.742003	−	0.670397i	$-0.233876\pi$
$769$	−5.81181	−	10.0664i	−0.209579	−	0.363002i	−0.951582	+	0.307395i	$0.900543\pi$
$770$	−16.5424	−	28.6523i	−0.596147	−	1.03256i
$771$	−10.1504			−0.365559
$772$	−37.2179			−1.33950
$773$	3.87783	+	6.71660i	0.139476	+	0.241579i	0.927298	−	0.374323i	$-0.122125\pi$
$773$	3.87783	+	6.71660i	0.139476	+	0.241579i	−0.787822	+	0.615902i	$0.788792\pi$
$774$	0.889237	−	1.54020i	0.0319630	−	0.0553615i
$775$	−20.2170	−	35.0169i	−0.726216	−	1.25784i
$776$	51.7175	−	89.5774i	1.85655	−	3.21564i
$777$	1.16044	−	2.00994i	0.0416306	−	0.0721064i
$778$	−80.9728			−2.90301
$779$	25.6892	+	13.3496i	0.920413	+	0.478299i
$780$	57.8023			2.06966
$781$	−8.03735	+	13.9211i	−0.287599	+	0.498136i
$782$		0			0
$783$	−3.32088	−	5.75194i	−0.118679	−	0.205558i
$784$	4.86330	−	8.42347i	0.173689	−	0.300838i
$785$	9.46173	+	16.3882i	0.337703	+	0.584920i
$786$	−1.61350			−0.0575515
$787$	−18.8880			−0.673283			−0.336642	−	0.941633i	$-0.609291\pi$
$787$	−18.8880			−0.673283			−0.336642	+	0.941633i	$0.609291\pi$
$788$	−53.4400	−	92.5607i	−1.90372	−	3.29734i
$789$	−1.29261	−	2.23887i	−0.0460182	−	0.0797058i
$790$	27.9627			0.994867
$791$	17.1222			0.608794
$792$	−4.98133	−	8.62791i	−0.177004	−	0.306579i
$793$	−6.82088	+	11.8141i	−0.242217	+	0.419532i
$794$	−33.4322	−	57.9062i	−1.18646	−	2.05502i
$795$	16.5424	−	28.6523i	0.586699	−	1.01619i
$796$	47.5101	−	82.2900i	1.68395	−	2.91669i
$797$	34.5105			1.22243			0.611213	−	0.791466i	$-0.290682\pi$
$797$	34.5105			1.22243			0.611213	+	0.791466i	$0.290682\pi$
$798$	−21.4412	+	13.6812i	−0.759012	+	0.484309i
$799$		0			0
$800$	10.5069	−	18.1984i	0.371474	−	0.643412i
$801$	1.33956	−	2.32018i	0.0473309	−	0.0819796i
$802$	−11.7170	−	20.2944i	−0.413741	−	0.716621i
$803$	9.93852	−	17.2140i	0.350723	−	0.607469i
$804$	18.0990	+	31.3483i	0.638301	+	1.10557i
$805$	−18.1059			−0.638148
$806$	−67.9300			−2.39273
$807$	−0.273937	−	0.474473i	−0.00964305	−	0.0167023i
$808$	46.8452	+	81.1382i	1.64801	+	2.85443i
$809$	40.6044			1.42758			0.713788	−	0.700362i	$-0.246978\pi$
$809$	40.6044			1.42758			0.713788	+	0.700362i	$0.246978\pi$
$810$	−8.34916			−0.293360
$811$	8.54787	+	14.8054i	0.300156	+	0.519886i	0.976171	−	0.217002i	$-0.0696278\pi$
$811$	8.54787	+	14.8054i	0.300156	+	0.519886i	−0.676015	+	0.736888i	$0.736294\pi$
$812$	−33.3027	+	57.6820i	−1.16870	+	2.02424i
$813$	10.4431	+	18.0879i	0.366254	+	0.634370i
$814$	2.14631	−	3.71751i	0.0752280	−	0.130299i
$815$	−30.5147	+	52.8529i	−1.06888	+	1.85136i
$816$		0			0
$817$	−2.73606	−	1.42181i	−0.0957227	−	0.0497430i
$818$	−54.8114			−1.91644
$819$	−4.67458	+	8.09661i	−0.163343	+	0.282918i
$820$	47.6519	−	82.5355i	1.66408	−	2.88226i
$821$	19.0475	+	32.9912i	0.664761	+	1.15140i	0.979350	+	0.202172i	$0.0648002\pi$
$821$	19.0475	+	32.9912i	0.664761	+	1.15140i	−0.314588	+	0.949228i	$0.601867\pi$
$822$	3.24980	−	5.62882i	0.113350	−	0.196328i
$823$	6.60442	+	11.4392i	0.230216	+	0.398745i	0.957871	−	0.287197i	$-0.0927235\pi$
$823$	6.60442	+	11.4392i	0.230216	+	0.398745i	−0.727656	+	0.685942i	$0.759390\pi$
$824$	44.0420			1.53428
$825$	−10.2926			−0.358343
$826$	4.98133	+	8.62791i	0.173323	+	0.300203i
$827$	16.9344	+	29.3312i	0.588866	+	1.01995i	0.994381	+	0.105858i	$0.0337588\pi$
$827$	16.9344	+	29.3312i	0.588866	+	1.01995i	−0.405515	+	0.914088i	$0.632908\pi$
$828$	−10.1504			−0.352752
$829$	16.8397			0.584866			0.292433	−	0.956286i	$-0.405535\pi$
$829$	16.8397			0.584866			0.292433	+	0.956286i	$0.405535\pi$
$830$	−41.9819	−	72.7147i	−1.45721	−	2.52396i
$831$	11.8916	−	20.5968i	0.412514	−	0.714495i
$832$	6.63177	+	11.4866i	0.229915	+	0.398225i
$833$		0			0
$834$	−23.3515	+	40.4460i	−0.808596	+	1.40053i
$835$	71.8397			2.48611
$836$	−27.1090	+	17.2976i	−0.937583	+	0.598251i
$837$	6.70739			0.231841
$838$	6.20285	−	10.7437i	0.214274	−	0.371133i
$839$	1.26847	−	2.19706i	0.0437926	−	0.0758509i	−0.843298	−	0.537446i	$-0.819389\pi$
$839$	1.26847	−	2.19706i	0.0437926	−	0.0758509i	0.887091	+	0.461595i	$0.152723\pi$
$840$	22.4864	+	38.9476i	0.775854	+	1.34382i
$841$	−7.55655	+	13.0883i	−0.260571	+	0.451322i
$842$	5.34916	+	9.26501i	0.184344	+	0.319293i
$843$	−11.9061			−0.410068
$844$	−57.1131			−1.96591
$845$	−5.35823	−	9.28073i	−0.184329	−	0.319267i
$846$	−7.54241	−	13.0638i	−0.259313	−	0.449144i
$847$	−18.7639			−0.644737
$848$	−60.0576			−2.06239
$849$	−9.02827	−	15.6374i	−0.309850	−	0.536675i
$850$		0			0
$851$	−1.17458	−	2.03443i	−0.0402641	−	0.0697394i
$852$	20.3401	−	35.2301i	0.696840	−	1.20696i
$853$	0.312212	−	0.540766i	0.0106899	−	0.0185155i	−0.860631	−	0.509229i	$-0.829931\pi$
$853$	0.312212	−	0.540766i	0.0106899	−	0.0185155i	0.871321	+	0.490714i	$0.163264\pi$
$854$	−19.7603			−0.676185
$855$	0.641769	+	14.4612i	0.0219480	+	0.494561i
$856$	−42.4996			−1.45261
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	−0.810227	−	0.586116i	$-0.800656\pi$
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	0.912705	+	0.408619i	$0.133990\pi$
$858$	−8.64591	+	14.9751i	−0.295166	+	0.511243i
$859$	13.6035	+	23.5619i	0.464145	+	0.803923i	0.999163	−	0.0409180i	$-0.0130282\pi$
$859$	13.6035	+	23.5619i	0.464145	+	0.803923i	−0.535017	+	0.844841i	$0.679695\pi$
$860$	−5.07522	+	8.79054i	−0.173064	+	0.299755i
$861$	7.70739	+	13.3496i	0.262667	+	0.454953i
$862$	2.08562			0.0710365
$863$	−26.1131			−0.888900			−0.444450	−	0.895804i	$-0.646601\pi$
$863$	−26.1131			−0.888900			−0.444450	+	0.895804i	$0.646601\pi$
$864$	1.74293	+	3.01885i	0.0592957	+	0.102703i
$865$	7.80128	+	13.5122i	0.265252	+	0.459429i
$866$	−41.4386			−1.40814
$867$	−17.0000			−0.577350
$868$	−33.6318	−	58.2519i	−1.14154	−	1.97720i
$869$	−2.85916	+	4.95221i	−0.0969903	+	0.167992i
$870$	27.7266	+	48.0239i	0.940019	+	1.62816i
$871$	16.8733	−	29.2254i	0.571730	−	0.990265i
$872$	−35.7549	+	61.9292i	−1.21081	+	2.09719i
$873$	17.7266			0.599954
$874$	1.14137	+	25.7188i	0.0386074	+	0.869952i
$875$	7.92531			0.267924
$876$	−25.1514	+	43.5635i	−0.849786	+	1.47187i
$877$	13.3296	−	23.0875i	0.450107	−	0.779608i	−0.548285	−	0.836292i	$-0.684719\pi$
$877$	13.3296	−	23.0875i	0.450107	−	0.779608i	0.998392	+	0.0566830i	$0.0180524\pi$
$878$	35.7435	+	61.9095i	1.20628	+	2.08934i
$879$	13.6983	−	23.7262i	0.462033	−	0.800264i
$880$	17.0903	+	29.6012i	0.576113	+	0.997858i
$881$	6.73566			0.226930			0.113465	−	0.993542i	$-0.463805\pi$
$881$	6.73566			0.226930			0.113465	+	0.993542i	$0.463805\pi$
$882$	4.05655			0.136591
$883$	−16.0803	−	27.8519i	−0.541145	−	0.937290i	−0.998839	−	0.0481803i	$-0.984658\pi$
$883$	−16.0803	−	27.8519i	−0.541145	−	0.937290i	0.457694	−	0.889110i	$-0.348676\pi$
$884$		0			0
$885$	5.67004			0.190596
$886$	38.7549			1.30200
$887$	−1.91932	−	3.32435i	−0.0644443	−	0.111621i	0.832003	−	0.554771i	$-0.187194\pi$
$887$	−1.91932	−	3.32435i	−0.0644443	−	0.111621i	−0.896447	+	0.443150i	$0.853861\pi$
$888$	−2.91751	+	5.05328i	−0.0979052	+	0.169577i
$889$	−16.9909	−	29.4291i	−0.569857	−	0.987022i
$890$	−11.1842	+	19.3716i	−0.374895	+	0.649336i
$891$	0.853695	−	1.47864i	0.0285998	−	0.0495364i
$892$	−23.6802			−0.792871
$893$	−22.0475	+	14.0680i	−0.737791	+	0.470768i
$894$	9.96265			0.333201
$895$	1.76940	−	3.06469i	0.0591446	−	0.102441i
$896$	−17.6965	+	30.6513i	−0.591199	+	1.02399i
$897$	4.73153	+	8.19524i	0.157981	+	0.273631i
$898$	−29.1040	+	50.4096i	−0.971214	+	1.68219i
$899$	−22.2745	−	38.5805i	−0.742895	−	1.28673i
$900$	26.0475			0.868249
$901$		0			0
$902$	14.2553	+	24.6908i	0.474648	+	0.822115i
$903$	−0.820884	−	1.42181i	−0.0273173	−	0.0473150i
$904$	−43.0475			−1.43174
$905$	−12.1878			−0.405136
$906$	−10.9344	−	18.9389i	−0.363270	−	0.629203i
$907$	19.9819	−	34.6096i	0.663487	−	1.14919i	−0.316207	−	0.948690i	$-0.602409\pi$
$907$	19.9819	−	34.6096i	0.663487	−	1.14919i	0.979693	−	0.200502i	$-0.0642574\pi$
$908$	−16.6514	−	28.8410i	−0.552595	−	0.957123i
$909$	−8.02827	+	13.9054i	−0.266281	+	0.461212i
$910$	39.0288	−	67.5999i	1.29379	−	2.24091i
$911$	29.3219			0.971479			0.485740	−	0.874104i	$-0.338550\pi$
$911$	29.3219			0.971479			0.485740	+	0.874104i	$0.338550\pi$
$912$	22.1514	−	14.1343i	0.733505	−	0.468033i
$913$	17.1704			0.568259
$914$	5.89337	−	10.2076i	0.194935	−	0.337638i
$915$	−5.62310	+	9.73949i	−0.185894	+	0.321978i
$916$	−8.70285	−	15.0738i	−0.287550	−	0.498052i
$917$	−0.744736	+	1.28992i	−0.0245933	+	0.0425969i
$918$		0			0
$919$	−30.6218			−1.01012			−0.505059	−	0.863085i	$-0.668529\pi$
$919$	−30.6218			−1.01012			−0.505059	+	0.863085i	$0.668529\pi$
$920$	45.5207			1.50077
$921$	−1.80675	−	3.12938i	−0.0595344	−	0.103117i
$922$	15.7735	+	27.3206i	0.519474	+	0.899755i
$923$	−37.9253			−1.24833
$924$	−17.1222			−0.563278
$925$	3.01414	+	5.22064i	0.0991042	+	0.171654i
$926$	28.7717	−	49.8341i	0.945498	−	1.63765i
$927$	3.77394	+	6.53665i	0.123952	+	0.214692i
$928$	11.5761	−	20.0505i	0.380006	−	0.658189i
$929$	2.96213	−	5.13055i	0.0971842	−	0.168328i	−0.813334	−	0.581797i	$-0.802350\pi$
$929$	2.96213	−	5.13055i	0.0971842	−	0.168328i	0.910518	+	0.413469i	$0.135683\pi$
$930$	−56.0011			−1.83635
$931$	−0.311812	−	7.02615i	−0.0102192	−	0.230273i
$932$	112.832			3.69592
$933$	−9.20285	+	15.9398i	−0.301288	+	0.521846i
$934$	−14.8488	+	25.7188i	−0.485866	+	0.841545i
$935$		0			0
$936$	11.7525	−	20.3560i	0.384144	−	0.665356i
$937$	2.50546	+	4.33959i	0.0818499	+	0.141768i	0.904045	−	0.427438i	$-0.140584\pi$
$937$	2.50546	+	4.33959i	0.0818499	+	0.141768i	−0.822195	+	0.569206i	$0.807251\pi$
$938$	48.8825			1.59607
$939$	23.0848			0.753345
$940$	43.0475	+	74.5604i	1.40405	+	2.43189i
$941$	−4.19872	−	7.27239i	−0.136874	−	0.237073i	0.789438	−	0.613831i	$-0.210372\pi$
$941$	−4.19872	−	7.27239i	−0.136874	−	0.237073i	−0.926312	+	0.376758i	$0.877039\pi$
$942$	14.3263			0.466778
$943$	15.6026			0.508089
$944$	−5.14631	−	8.91366i	−0.167498	−	0.290115i
$945$	−3.85369	+	6.67479i	−0.125361	+	0.217131i
$946$	−1.51827	−	2.62973i	−0.0493633	−	0.0854998i
$947$	9.73566	−	16.8627i	0.316367	−	0.547963i	−0.663360	−	0.748300i	$-0.730870\pi$
$947$	9.73566	−	16.8627i	0.316367	−	0.547963i	0.979727	+	0.200337i	$0.0642037\pi$
$948$	7.23566	−	12.5325i	0.235003	−	0.407038i
$949$	46.8962			1.52232
$950$	−2.92892	−	65.9981i	−0.0950266	−	2.14126i
$951$	−25.3774			−0.822920
$952$		0			0
$953$	−10.7543	+	18.6271i	−0.348367	+	0.603390i	−0.985960	−	0.166984i	$-0.946597\pi$
$953$	−10.7543	+	18.6271i	−0.348367	+	0.603390i	0.637592	+	0.770374i	$0.279930\pi$
$954$	−12.5237	−	21.6917i	−0.405471	−	0.702296i
$955$	1.45759	−	2.52462i	0.0471665	−	0.0816947i
$956$	16.6514	+	28.8410i	0.538544	+	0.932785i
$957$	−11.3401			−0.366573
$958$	85.5772			2.76487
$959$	−3.00000	−	5.19615i	−0.0968751	−	0.167793i
$960$	5.46719	+	9.46945i	0.176453	+	0.305625i
$961$	13.9891			0.451260
$962$	10.1276			0.326528
$963$	−3.64177	−	6.30773i	−0.117354	−	0.203264i
$964$	−46.8780	+	81.1950i	−1.50984	+	2.61512i
$965$	14.3022	+	24.7722i	0.460404	+	0.797444i
$966$	−6.85369	+	11.8709i	−0.220514	+	0.381941i
$967$	5.41024	−	9.37081i	0.173982	−	0.301345i	−0.765827	−	0.643047i	$-0.777670\pi$
$967$	5.41024	−	9.37081i	0.173982	−	0.301345i	0.939808	+	0.341702i	$0.111003\pi$
$968$	47.1751			1.51627
$969$		0			0
$970$	−148.002			−4.75206
$971$	−15.4996	+	26.8461i	−0.497406	+	0.861532i	−0.999996	−	0.00299289i	$-0.999047\pi$
$971$	−15.4996	+	26.8461i	−0.497406	+	0.861532i	0.502590	+	0.864525i	$0.332381\pi$
$972$	−2.16044	+	3.74200i	−0.0692962	+	0.120025i
$973$	21.5565	+	37.3370i	0.691071	+	1.19697i
$974$	−9.32088	+	16.1442i	−0.298660	+	0.517295i
$975$	−12.1418	−	21.0302i	−0.388848	−	0.673504i
$976$	20.4148			0.653461
$977$	56.0950			1.79464			0.897318	−	0.441384i	$-0.145512\pi$
$977$	56.0950			1.79464			0.897318	+	0.441384i	$0.145512\pi$
$978$	23.1017	+	40.0133i	0.738711	+	1.27948i
$979$	−2.28715	−	3.96145i	−0.0730975	−	0.126609i
$980$	−23.1523			−0.739573
$981$	−12.2553			−0.391280
$982$	4.86330	+	8.42347i	0.155194	+	0.268804i
$983$	16.7225	−	28.9641i	0.533363	−	0.923813i	−0.465877	−	0.884849i	$-0.654261\pi$
$983$	16.7225	−	28.9641i	0.533363	−	0.923813i	0.999241	−	0.0389632i	$-0.0124055\pi$
$984$	−19.3774	−	33.5627i	−0.617730	−	1.06994i
$985$	−41.0721	+	71.1390i	−1.30867	+	2.26668i
$986$		0			0
$987$	−13.9253			−0.443247
$988$	−67.3223	−	34.9845i	−2.14181	−	1.11301i
$989$	−1.66177			−0.0528412
$990$	−7.12763	+	12.3454i	−0.226531	+	0.392363i
$991$	−4.22245	+	7.31350i	−0.134131	+	0.232321i	−0.925265	−	0.379321i	$-0.876158\pi$
$991$	−4.22245	+	7.31350i	−0.134131	+	0.232321i	0.791134	+	0.611642i	$0.209491\pi$
$992$	11.6905	+	20.2486i	0.371174	+	0.642893i
$993$	10.6746	−	18.4889i	0.338748	−	0.586728i
$994$	−27.4677	−	47.5755i	−0.871223	−	1.50900i
$995$	−73.0293			−2.31519
$996$	−43.4532			−1.37687
$997$	−25.2074	−	43.6605i	−0.798326	−	1.38274i	−0.920706	−	0.390258i	$-0.872386\pi$
$997$	−25.2074	−	43.6605i	−0.798326	−	1.38274i	0.122380	−	0.992483i	$-0.460947\pi$
$998$	−44.7344	−	77.4822i	−1.41604	−	2.45266i
$999$	−1.00000			−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.e.b.49.3	yes	6
3.2	odd	2		171.2.f.b.163.1		6
4.3	odd	2		912.2.q.l.49.1		6
12.11	even	2		2736.2.s.z.1873.3		6
19.7	even	3	inner	57.2.e.b.7.3	✓	6
19.8	odd	6		1083.2.a.o.1.3		3
19.11	even	3		1083.2.a.l.1.1		3
57.8	even	6		3249.2.a.t.1.1		3
57.11	odd	6		3249.2.a.y.1.3		3
57.26	odd	6		171.2.f.b.64.1		6
76.7	odd	6		912.2.q.l.577.1		6
228.83	even	6		2736.2.s.z.577.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.e.b.7.3	✓	6	19.7	even	3	inner
57.2.e.b.49.3	yes	6	1.1	even	1	trivial
171.2.f.b.64.1		6	57.26	odd	6
171.2.f.b.163.1		6	3.2	odd	2
912.2.q.l.49.1		6	4.3	odd	2
912.2.q.l.577.1		6	76.7	odd	6
1083.2.a.l.1.1		3	19.11	even	3
1083.2.a.o.1.3		3	19.8	odd	6
2736.2.s.z.577.3		6	228.83	even	6
2736.2.s.z.1873.3		6	12.11	even	2
3249.2.a.t.1.1		3	57.8	even	6
3249.2.a.y.1.3		3	57.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25707 - 2.17731i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.16044 - 3.74200i) q^{4} +(-1.66044 + 2.87597i) q^{5} +(1.25707 + 2.17731i) q^{6} +2.32088 q^{7} -5.83502 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.25707 - 2.17731i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.16044 - 3.74200i) q^{4} +(-1.66044 + 2.87597i) q^{5} +(1.25707 + 2.17731i) q^{6} +2.32088 q^{7} -5.83502 q^{8} +(-0.500000 - 0.866025i) q^{9} +(4.17458 + 7.23058i) q^{10} -1.70739 q^{11} +4.32088 q^{12} +(-2.01414 - 3.48859i) q^{13} +(2.91751 - 5.05328i) q^{14} +(-1.66044 - 2.87597i) q^{15} +(-3.01414 + 5.22064i) q^{16} -2.51414 q^{18} +(0.193252 + 4.35461i) q^{19} +14.3492 q^{20} +(-1.16044 + 2.00994i) q^{21} +(-2.14631 + 3.71751i) q^{22} +(1.17458 + 2.03443i) q^{23} +(2.91751 - 5.05328i) q^{24} +(-3.01414 - 5.22064i) q^{25} -10.1276 q^{26} +1.00000 q^{27} +(-5.01414 - 8.68474i) q^{28} +(-3.32088 - 5.75194i) q^{29} -8.34916 q^{30} +6.70739 q^{31} +(1.74293 + 3.01885i) q^{32} +(0.853695 - 1.47864i) q^{33} +(-3.85369 + 6.67479i) q^{35} +(-2.16044 + 3.74200i) q^{36} -1.00000 q^{37} +(9.72426 + 5.05328i) q^{38} +4.02827 q^{39} +(9.68872 - 16.7813i) q^{40} +(3.32088 - 5.75194i) q^{41} +(2.91751 + 5.05328i) q^{42} +(-0.353695 + 0.612617i) q^{43} +(3.68872 + 6.38904i) q^{44} +3.32088 q^{45} +5.90611 q^{46} +(3.00000 + 5.19615i) q^{47} +(-3.01414 - 5.22064i) q^{48} -1.61350 q^{49} -15.1559 q^{50} +(-8.70285 + 15.0738i) q^{52} +(4.98133 + 8.62791i) q^{53} +(1.25707 - 2.17731i) q^{54} +(2.83502 - 4.91040i) q^{55} -13.5424 q^{56} +(-3.86783 - 2.00994i) q^{57} -16.6983 q^{58} +(-0.853695 + 1.47864i) q^{59} +(-7.17458 + 12.4267i) q^{60} +(-1.69325 - 2.93280i) q^{61} +(8.43165 - 14.6040i) q^{62} +(-1.16044 - 2.00994i) q^{63} -3.29261 q^{64} +13.3774 q^{65} +(-2.14631 - 3.71751i) q^{66} +(4.18872 + 7.25507i) q^{67} -2.34916 q^{69} +(9.68872 + 16.7813i) q^{70} +(4.70739 - 8.15344i) q^{71} +(2.91751 + 5.05328i) q^{72} +(-5.82088 + 10.0821i) q^{73} +(-1.25707 + 2.17731i) q^{74} +6.02827 q^{75} +(15.8774 - 10.1310i) q^{76} -3.96265 q^{77} +(5.06382 - 8.77079i) q^{78} +(1.67458 - 2.90046i) q^{79} +(-10.0096 - 17.3371i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-8.34916 - 14.4612i) q^{82} -10.0565 q^{83} +10.0283 q^{84} +(0.889237 + 1.54020i) q^{86} +6.64177 q^{87} +9.96265 q^{88} +(1.33956 + 2.32018i) q^{89} +(4.17458 - 7.23058i) q^{90} +(-4.67458 - 8.09661i) q^{91} +(5.07522 - 8.79054i) q^{92} +(-3.35369 + 5.80877i) q^{93} +15.0848 q^{94} +(-12.8446 - 6.67479i) q^{95} -3.48586 q^{96} +(-8.86330 + 15.3517i) q^{97} +(-2.02827 + 3.51307i) q^{98} +(0.853695 + 1.47864i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 3 q^{3} - 5 q^{4} - 2 q^{5} + q^{6} - 2 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + q^2 - 3 * q^3 - 5 * q^4 - 2 * q^5 + q^6 - 2 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + q^{2} - 3 q^{3} - 5 q^{4} - 2 q^{5} + q^{6} - 2 q^{7} - 6 q^{8} - 3 q^{9} + 4 q^{10} + 10 q^{12} + q^{13} + 3 q^{14} - 2 q^{15} - 5 q^{16} - 2 q^{18} + 4 q^{19} + 44 q^{20} + q^{21} - 18 q^{22} - 14 q^{23} + 3 q^{24} - 5 q^{25} - 42 q^{26} + 6 q^{27} - 17 q^{28} - 4 q^{29} - 8 q^{30} + 30 q^{31} + 17 q^{32} - 18 q^{35} - 5 q^{36} - 6 q^{37} + 41 q^{38} - 2 q^{39} + 24 q^{40} + 4 q^{41} + 3 q^{42} + 3 q^{43} - 12 q^{44} + 4 q^{45} + 40 q^{46} + 18 q^{47} - 5 q^{48} - 4 q^{49} - 46 q^{50} - 5 q^{52} + 6 q^{53} + q^{54} - 12 q^{55} - 42 q^{56} - 5 q^{57} - 16 q^{58} - 22 q^{60} - 13 q^{61} + 23 q^{62} + q^{63} - 30 q^{64} + 12 q^{65} - 18 q^{66} - 9 q^{67} + 28 q^{69} + 24 q^{70} + 18 q^{71} + 3 q^{72} - 19 q^{73} - q^{74} + 10 q^{75} + 27 q^{76} + 24 q^{77} + 21 q^{78} - 11 q^{79} - 10 q^{80} - 3 q^{81} - 8 q^{82} - 8 q^{83} + 34 q^{84} + 17 q^{86} + 8 q^{87} + 12 q^{88} + 16 q^{89} + 4 q^{90} - 7 q^{91} + 2 q^{92} - 15 q^{93} + 12 q^{94} + 2 q^{95} - 34 q^{96} + 2 q^{97} + 14 q^{98}+O(q^{100}) \) 6 * q + q^2 - 3 * q^3 - 5 * q^4 - 2 * q^5 + q^6 - 2 * q^7 - 6 * q^8 - 3 * q^9 + 4 * q^10 + 10 * q^12 + q^13 + 3 * q^14 - 2 * q^15 - 5 * q^16 - 2 * q^18 + 4 * q^19 + 44 * q^20 + q^21 - 18 * q^22 - 14 * q^23 + 3 * q^24 - 5 * q^25 - 42 * q^26 + 6 * q^27 - 17 * q^28 - 4 * q^29 - 8 * q^30 + 30 * q^31 + 17 * q^32 - 18 * q^35 - 5 * q^36 - 6 * q^37 + 41 * q^38 - 2 * q^39 + 24 * q^40 + 4 * q^41 + 3 * q^42 + 3 * q^43 - 12 * q^44 + 4 * q^45 + 40 * q^46 + 18 * q^47 - 5 * q^48 - 4 * q^49 - 46 * q^50 - 5 * q^52 + 6 * q^53 + q^54 - 12 * q^55 - 42 * q^56 - 5 * q^57 - 16 * q^58 - 22 * q^60 - 13 * q^61 + 23 * q^62 + q^63 - 30 * q^64 + 12 * q^65 - 18 * q^66 - 9 * q^67 + 28 * q^69 + 24 * q^70 + 18 * q^71 + 3 * q^72 - 19 * q^73 - q^74 + 10 * q^75 + 27 * q^76 + 24 * q^77 + 21 * q^78 - 11 * q^79 - 10 * q^80 - 3 * q^81 - 8 * q^82 - 8 * q^83 + 34 * q^84 + 17 * q^86 + 8 * q^87 + 12 * q^88 + 16 * q^89 + 4 * q^90 - 7 * q^91 + 2 * q^92 - 15 * q^93 + 12 * q^94 + 2 * q^95 - 34 * q^96 + 2 * q^97 + 14 * q^98

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