LMFDB - Embedded newform 561.2.m.d.256.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [561,2,Mod(103,561)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(561, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("561.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 561 = 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	561.m (of order $5$, degree $4$, 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:	$4.47960755339$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			256.6
Character	$\chi$	$=$	561.256
Dual form			561.2.m.d.103.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.15962 - 1.56905i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.58398 - 4.87500i) q^{4} +(2.54481 + 1.84891i) q^{5} +(2.15962 + 1.56905i) q^{6} +(0.625170 - 1.92407i) q^{7} +(-2.57854 - 7.93593i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(2.15962 - 1.56905i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.58398 - 4.87500i) q^{4} +(2.54481 + 1.84891i) q^{5} +(2.15962 + 1.56905i) q^{6} +(0.625170 - 1.92407i) q^{7} +(-2.57854 - 7.93593i) q^{8} +(-0.809017 + 0.587785i) q^{9} +8.39687 q^{10} +(-2.35506 + 2.33531i) q^{11} +5.12588 q^{12} +(-2.41016 + 1.75109i) q^{13} +(-1.66885 - 5.13619i) q^{14} +(-0.972032 + 2.99161i) q^{15} +(-9.72672 - 7.06688i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(-0.824901 + 2.53878i) q^{18} +(1.55790 + 4.79473i) q^{19} +(13.0444 - 9.47731i) q^{20} +2.02309 q^{21} +(-1.42181 + 8.73860i) q^{22} -8.03082 q^{23} +(6.75071 - 4.90468i) q^{24} +(1.51250 + 4.65499i) q^{25} +(-2.45748 + 7.56336i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-8.38960 - 6.09540i) q^{28} +(2.81003 - 8.64837i) q^{29} +(2.59477 + 7.98589i) q^{30} +(5.74246 - 4.17214i) q^{31} -15.4056 q^{32} +(-2.94877 - 1.51815i) q^{33} -2.66943 q^{34} +(5.14839 - 3.74052i) q^{35} +(1.58398 + 4.87500i) q^{36} +(-0.519337 + 1.59835i) q^{37} +(10.8877 + 7.91035i) q^{38} +(-2.41016 - 1.75109i) q^{39} +(8.11095 - 24.9629i) q^{40} +(-1.90826 - 5.87302i) q^{41} +(4.36910 - 3.17434i) q^{42} -10.9401 q^{43} +(7.65426 + 15.1800i) q^{44} -3.14556 q^{45} +(-17.3435 + 12.6008i) q^{46} +(1.69099 + 5.20432i) q^{47} +(3.71528 - 11.4344i) q^{48} +(2.35190 + 1.70875i) q^{49} +(10.5704 + 7.67981i) q^{50} +(0.309017 - 0.951057i) q^{51} +(4.71889 + 14.5232i) q^{52} +(-1.44713 + 1.05140i) q^{53} -2.66943 q^{54} +(-10.3110 + 1.58862i) q^{55} -16.8813 q^{56} +(-4.07864 + 2.96331i) q^{57} +(-7.50118 - 23.0863i) q^{58} +(-3.18060 + 9.78887i) q^{59} +(13.0444 + 9.47731i) q^{60} +(8.98670 + 6.52922i) q^{61} +(5.85520 - 18.0205i) q^{62} +(0.625170 + 1.92407i) q^{63} +(-13.8169 + 10.0385i) q^{64} -9.37102 q^{65} +(-8.75027 + 1.34816i) q^{66} +3.69383 q^{67} +(-4.14692 + 3.01292i) q^{68} +(-2.48166 - 7.63777i) q^{69} +(5.24947 - 16.1562i) q^{70} +(-3.34686 - 2.43164i) q^{71} +(6.75071 + 4.90468i) q^{72} +(1.75764 - 5.40946i) q^{73} +(1.38634 + 4.26670i) q^{74} +(-3.95977 + 2.87694i) q^{75} +25.8420 q^{76} +(3.02100 + 5.99128i) q^{77} -7.95258 q^{78} +(8.12157 - 5.90067i) q^{79} +(-11.6866 - 35.9677i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-13.3362 - 9.68931i) q^{82} +(0.164504 + 0.119519i) q^{83} +(3.20454 - 9.86257i) q^{84} +(-0.972032 - 2.99161i) q^{85} +(-23.6265 + 17.1657i) q^{86} +9.09343 q^{87} +(24.6055 + 12.6679i) q^{88} -5.85329 q^{89} +(-6.79321 + 4.93555i) q^{90} +(1.86246 + 5.73206i) q^{91} +(-12.7207 + 39.1503i) q^{92} +(5.74246 + 4.17214i) q^{93} +(11.8177 + 8.58609i) q^{94} +(-4.90047 + 15.0821i) q^{95} +(-4.76061 - 14.6516i) q^{96} +(-0.913551 + 0.663733i) q^{97} +7.76032 q^{98} +(0.532625 - 3.27358i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9	\( 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9} + 16 q^{10} - 7 q^{11} + 18 q^{12} + 6 q^{13} - 6 q^{14} + 7 q^{15} - 23 q^{16} - 6 q^{17} - 2 q^{18} + 6 q^{19} + 3 q^{20} - 10 q^{21} + 23 q^{22} - 78 q^{23} + 10 q^{24} + q^{25} + 10 q^{26} - 6 q^{27} - 13 q^{28} + 20 q^{29} + 11 q^{30} + 5 q^{31} - 22 q^{32} - 2 q^{33} - 2 q^{34} + 29 q^{35} - 7 q^{36} - 10 q^{37} + 2 q^{38} + 6 q^{39} + 44 q^{40} - 16 q^{41} + 19 q^{42} - 36 q^{43} + 3 q^{44} - 28 q^{45} + 23 q^{46} + 19 q^{47} + 12 q^{48} - 15 q^{49} + 34 q^{50} - 6 q^{51} - 6 q^{52} - 5 q^{53} - 2 q^{54} + 24 q^{55} - 50 q^{56} - 9 q^{57} - 79 q^{58} + 34 q^{59} + 3 q^{60} - 14 q^{61} + 36 q^{62} + 5 q^{63} - 20 q^{64} + 6 q^{65} + 3 q^{66} - 18 q^{67} - 2 q^{68} + 7 q^{69} + 46 q^{70} - 8 q^{71} + 10 q^{72} + 7 q^{73} + 47 q^{74} - 9 q^{75} + 58 q^{76} + 43 q^{77} - 50 q^{78} + 14 q^{79} - 51 q^{80} - 6 q^{81} - 88 q^{82} - 47 q^{83} + 22 q^{84} + 7 q^{85} - 13 q^{86} + 20 q^{87} + 115 q^{88} - 124 q^{89} - 19 q^{90} + 10 q^{91} - 19 q^{92} + 5 q^{93} + 28 q^{94} - 13 q^{95} - 27 q^{96} - 30 q^{97} - 14 q^{98} - 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9 + 16 * q^10 - 7 * q^11 + 18 * q^12 + 6 * q^13 - 6 * q^14 + 7 * q^15 - 23 * q^16 - 6 * q^17 - 2 * q^18 + 6 * q^19 + 3 * q^20 - 10 * q^21 + 23 * q^22 - 78 * q^23 + 10 * q^24 + q^25 + 10 * q^26 - 6 * q^27 - 13 * q^28 + 20 * q^29 + 11 * q^30 + 5 * q^31 - 22 * q^32 - 2 * q^33 - 2 * q^34 + 29 * q^35 - 7 * q^36 - 10 * q^37 + 2 * q^38 + 6 * q^39 + 44 * q^40 - 16 * q^41 + 19 * q^42 - 36 * q^43 + 3 * q^44 - 28 * q^45 + 23 * q^46 + 19 * q^47 + 12 * q^48 - 15 * q^49 + 34 * q^50 - 6 * q^51 - 6 * q^52 - 5 * q^53 - 2 * q^54 + 24 * q^55 - 50 * q^56 - 9 * q^57 - 79 * q^58 + 34 * q^59 + 3 * q^60 - 14 * q^61 + 36 * q^62 + 5 * q^63 - 20 * q^64 + 6 * q^65 + 3 * q^66 - 18 * q^67 - 2 * q^68 + 7 * q^69 + 46 * q^70 - 8 * q^71 + 10 * q^72 + 7 * q^73 + 47 * q^74 - 9 * q^75 + 58 * q^76 + 43 * q^77 - 50 * q^78 + 14 * q^79 - 51 * q^80 - 6 * q^81 - 88 * q^82 - 47 * q^83 + 22 * q^84 + 7 * q^85 - 13 * q^86 + 20 * q^87 + 115 * q^88 - 124 * q^89 - 19 * q^90 + 10 * q^91 - 19 * q^92 + 5 * q^93 + 28 * q^94 - 13 * q^95 - 27 * q^96 - 30 * q^97 - 14 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/561\mathbb{Z}\right)^\times$.

$n$	$188$	$409$	$496$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	2.15962	−	1.56905i	1.52708	−	1.10949i	0.569246	−	0.822167i	$-0.307235\pi$
$2$	2.15962	−	1.56905i	1.52708	−	1.10949i	0.957834	−	0.287322i	$-0.0927649\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	1.58398	−	4.87500i	0.791992	−	2.43750i
$5$	2.54481	+	1.84891i	1.13807	+	0.826859i	0.986850	−	0.161640i	$-0.0516783\pi$
$5$	2.54481	+	1.84891i	1.13807	+	0.826859i	0.151225	+	0.988499i	$0.451678\pi$
$6$	2.15962	+	1.56905i	0.881660	+	0.640564i
$7$	0.625170	−	1.92407i	0.236292	−	0.727232i	−0.760656	−	0.649156i	$-0.775122\pi$
$7$	0.625170	−	1.92407i	0.236292	−	0.727232i	0.996947	−	0.0780759i	$-0.0248776\pi$
$8$	−2.57854	−	7.93593i	−0.911652	−	2.80578i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	8.39687			2.65532
$11$	−2.35506	+	2.33531i	−0.710078	+	0.704123i
$11$	−2.35506	+	2.33531i	−0.710078	+	0.704123i
$12$	5.12588			1.47971
$13$	−2.41016	+	1.75109i	−0.668459	+	0.485664i	−0.869509	−	0.493917i	$-0.835565\pi$
$13$	−2.41016	+	1.75109i	−0.668459	+	0.485664i	0.201050	+	0.979581i	$0.435565\pi$
$14$	−1.66885	−	5.13619i	−0.446019	−	1.37270i
$15$	−0.972032	+	2.99161i	−0.250977	+	0.772429i
$16$	−9.72672	−	7.06688i	−2.43168	−	1.76672i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$18$	−0.824901	+	2.53878i	−0.194431	+	0.598397i
$19$	1.55790	+	4.79473i	0.357407	+	1.09999i	0.954601	+	0.297889i	$0.0962825\pi$
$19$	1.55790	+	4.79473i	0.357407	+	1.09999i	−0.597193	+	0.802097i	$0.703717\pi$
$20$	13.0444	−	9.47731i	2.91682	−	2.11919i
$21$	2.02309			0.441475
$22$	−1.42181	+	8.73860i	−0.303130	+	1.86308i
$23$	−8.03082			−1.67454			−0.837271	−	0.546788i	$-0.815850\pi$
$23$	−8.03082			−1.67454			−0.837271	+	0.546788i	$0.815850\pi$
$24$	6.75071	−	4.90468i	1.37798	−	1.00116i
$25$	1.51250	+	4.65499i	0.302500	+	0.930999i
$26$	−2.45748	+	7.56336i	−0.481952	+	1.48330i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−8.38960	−	6.09540i	−1.58549	−	1.15192i
$29$	2.81003	−	8.64837i	0.521809	−	1.60596i	−0.248733	−	0.968572i	$-0.580014\pi$
$29$	2.81003	−	8.64837i	0.521809	−	1.60596i	0.770542	−	0.637390i	$-0.219986\pi$
$30$	2.59477	+	7.98589i	0.473739	+	1.45802i
$31$	5.74246	−	4.17214i	1.03138	−	0.749339i	0.0627927	−	0.998027i	$-0.479999\pi$
$31$	5.74246	−	4.17214i	1.03138	−	0.749339i	0.968584	+	0.248688i	$0.0799993\pi$
$32$	−15.4056			−2.72336
$33$	−2.94877	−	1.51815i	−0.513315	−	0.264276i
$34$	−2.66943			−0.457804
$35$	5.14839	−	3.74052i	0.870236	−	0.632263i
$36$	1.58398	+	4.87500i	0.263997	+	0.812500i
$37$	−0.519337	+	1.59835i	−0.0853785	+	0.262768i	−0.984627	−	0.174670i	$-0.944114\pi$
$37$	−0.519337	+	1.59835i	−0.0853785	+	0.262768i	0.899249	+	0.437438i	$0.144114\pi$
$38$	10.8877	+	7.91035i	1.76621	+	1.28323i
$39$	−2.41016	−	1.75109i	−0.385935	−	0.280398i
$40$	8.11095	−	24.9629i	1.28245	−	3.94699i
$41$	−1.90826	−	5.87302i	−0.298020	−	0.917211i	−0.982190	−	0.187889i	$-0.939836\pi$
$41$	−1.90826	−	5.87302i	−0.298020	−	0.917211i	0.684170	−	0.729322i	$-0.260164\pi$
$42$	4.36910	−	3.17434i	0.674167	−	0.489811i
$43$	−10.9401			−1.66836			−0.834178	−	0.551495i	$-0.814058\pi$
$43$	−10.9401			−1.66836			−0.834178	+	0.551495i	$0.814058\pi$
$44$	7.65426	+	15.1800i	1.15392	+	2.28848i
$45$	−3.14556			−0.468912
$46$	−17.3435	+	12.6008i	−2.55716	+	1.85789i
$47$	1.69099	+	5.20432i	0.246656	+	0.759128i	0.995360	+	0.0962235i	$0.0306764\pi$
$47$	1.69099	+	5.20432i	0.246656	+	0.759128i	−0.748704	+	0.662904i	$0.769324\pi$
$48$	3.71528	−	11.4344i	0.536254	−	1.65042i
$49$	2.35190	+	1.70875i	0.335985	+	0.244107i
$50$	10.5704	+	7.67981i	1.49487	+	1.08609i
$51$	0.309017	−	0.951057i	0.0432710	−	0.133175i
$52$	4.71889	+	14.5232i	0.654392	+	2.01401i
$53$	−1.44713	+	1.05140i	−0.198778	+	0.144421i	−0.682722	−	0.730678i	$-0.739204\pi$
$53$	−1.44713	+	1.05140i	−0.198778	+	0.144421i	0.483944	+	0.875099i	$0.339204\pi$
$54$	−2.66943			−0.363264
$55$	−10.3110	+	1.58862i	−1.39033	+	0.214209i
$56$	−16.8813			−2.25586
$57$	−4.07864	+	2.96331i	−0.540229	+	0.392499i
$58$	−7.50118	−	23.0863i	−0.984953	−	3.03137i
$59$	−3.18060	+	9.78887i	−0.414079	+	1.27440i	0.498994	+	0.866605i	$0.333703\pi$
$59$	−3.18060	+	9.78887i	−0.414079	+	1.27440i	−0.913073	+	0.407797i	$0.866297\pi$
$60$	13.0444	+	9.47731i	1.68402	+	1.22352i
$61$	8.98670	+	6.52922i	1.15063	+	0.835981i	0.988564	−	0.150799i	$-0.0481846\pi$
$61$	8.98670	+	6.52922i	1.15063	+	0.835981i	0.162065	+	0.986780i	$0.448185\pi$
$62$	5.85520	−	18.0205i	0.743612	−	2.28860i
$63$	0.625170	+	1.92407i	0.0787640	+	0.242411i
$64$	−13.8169	+	10.0385i	−1.72711	+	1.25482i
$65$	−9.37102			−1.16233
$66$	−8.75027	+	1.34816i	−1.07708	+	0.165947i
$67$	3.69383			0.451274			0.225637	−	0.974211i	$-0.427554\pi$
$67$	3.69383			0.451274			0.225637	+	0.974211i	$0.427554\pi$
$68$	−4.14692	+	3.01292i	−0.502888	+	0.365370i
$69$	−2.48166	−	7.63777i	−0.298757	−	0.919479i
$70$	5.24947	−	16.1562i	0.627431	−	1.93103i
$71$	−3.34686	−	2.43164i	−0.397199	−	0.288582i	0.371200	−	0.928553i	$-0.378946\pi$
$71$	−3.34686	−	2.43164i	−0.397199	−	0.288582i	−0.768399	+	0.639971i	$0.778946\pi$
$72$	6.75071	+	4.90468i	0.795578	+	0.578022i
$73$	1.75764	−	5.40946i	0.205716	−	0.633129i	−0.793967	−	0.607961i	$-0.791988\pi$
$73$	1.75764	−	5.40946i	0.205716	−	0.633129i	0.999683	−	0.0251682i	$-0.00801214\pi$
$74$	1.38634	+	4.26670i	0.161158	+	0.495994i
$75$	−3.95977	+	2.87694i	−0.457235	+	0.332201i
$76$	25.8420			2.96428
$77$	3.02100	+	5.99128i	0.344275	+	0.682770i
$78$	−7.95258			−0.900453
$79$	8.12157	−	5.90067i	0.913748	−	0.663877i	−0.0282116	−	0.999602i	$-0.508981\pi$
$79$	8.12157	−	5.90067i	0.913748	−	0.663877i	0.941960	+	0.335725i	$0.108981\pi$
$80$	−11.6866	−	35.9677i	−1.30660	−	4.02131i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−13.3362	−	9.68931i	−1.47274	−	1.07001i
$83$	0.164504	+	0.119519i	0.0180567	+	0.0131190i	0.596777	−	0.802407i	$-0.296448\pi$
$83$	0.164504	+	0.119519i	0.0180567	+	0.0131190i	−0.578720	+	0.815526i	$0.696448\pi$
$84$	3.20454	−	9.86257i	0.349644	−	1.07609i
$85$	−0.972032	−	2.99161i	−0.105432	−	0.324485i
$86$	−23.6265	+	17.1657i	−2.54771	+	1.85102i
$87$	9.09343			0.974918
$88$	24.6055	+	12.6679i	2.62295	+	1.35041i
$89$	−5.85329			−0.620448			−0.310224	−	0.950664i	$-0.600404\pi$
$89$	−5.85329			−0.620448			−0.310224	+	0.950664i	$0.600404\pi$
$90$	−6.79321	+	4.93555i	−0.716067	+	0.520253i
$91$	1.86246	+	5.73206i	0.195239	+	0.600883i
$92$	−12.7207	+	39.1503i	−1.32622	+	4.08170i
$93$	5.74246	+	4.17214i	0.595465	+	0.432631i
$94$	11.8177	+	8.58609i	1.21891	+	0.885588i
$95$	−4.90047	+	15.0821i	−0.502778	+	1.54739i
$96$	−4.76061	−	14.6516i	−0.485877	−	1.49538i
$97$	−0.913551	+	0.663733i	−0.0927570	+	0.0673919i	−0.633197	−	0.773991i	$-0.718258\pi$
$97$	−0.913551	+	0.663733i	−0.0927570	+	0.0673919i	0.540440	+	0.841382i	$0.318258\pi$
$98$	7.76032			0.783911
$99$	0.532625	−	3.27358i	0.0535308	−	0.329007i
$100$	25.0889			2.50889
$101$	4.85259	−	3.52561i	0.482851	−	0.350812i	−0.319578	−	0.947560i	$-0.603541\pi$
$101$	4.85259	−	3.52561i	0.482851	−	0.350812i	0.802428	+	0.596749i	$0.203541\pi$
$102$	−0.824901	−	2.53878i	−0.0816773	−	0.251377i
$103$	−1.29676	+	3.99102i	−0.127774	+	0.393247i	−0.994396	−	0.105717i	$-0.966286\pi$
$103$	−1.29676	+	3.99102i	−0.127774	+	0.393247i	0.866622	+	0.498964i	$0.166286\pi$
$104$	20.1112	+	14.6116i	1.97207	+	1.43279i
$105$	5.14839	+	3.74052i	0.502431	+	0.365037i
$106$	−1.47554	+	4.54124i	−0.143317	+	0.441084i
$107$	6.19022	+	19.0515i	0.598431	+	1.84178i	0.536846	+	0.843680i	$0.319615\pi$
$107$	6.19022	+	19.0515i	0.598431	+	1.84178i	0.0615848	+	0.998102i	$0.480385\pi$
$108$	−4.14692	+	3.01292i	−0.399038	+	0.289918i
$109$	4.32451			0.414213			0.207106	−	0.978318i	$-0.433595\pi$
$109$	4.32451			0.414213			0.207106	+	0.978318i	$0.433595\pi$
$110$	−19.7752	+	19.6093i	−1.88549	+	1.86967i
$111$	−1.68061			−0.159516
$112$	−19.6780	+	14.2969i	−1.85940	+	1.35093i
$113$	0.820132	+	2.52411i	0.0771515	+	0.237448i	0.982193	−	0.187876i	$-0.0601602\pi$
$113$	0.820132	+	2.52411i	0.0771515	+	0.237448i	−0.905041	+	0.425324i	$0.860160\pi$
$114$	−4.15872	+	12.7992i	−0.389500	+	1.19876i
$115$	−20.4369	−	14.8483i	−1.90575	−	1.38461i
$116$	−37.7098	−	27.3978i	−3.50126	−	2.54382i
$117$	0.920601	−	2.83332i	0.0851096	−	0.261940i
$118$	8.49040	+	26.1308i	0.781604	+	2.40553i
$119$	−1.63672	+	1.18914i	−0.150037	+	0.109009i
$120$	26.2476			2.39607
$121$	0.0926445	−	10.9996i	0.00842223	−	0.999965i
$122$	29.6526			2.68462
$123$	4.99589	−	3.62972i	0.450464	−	0.327281i
$124$	−11.2432	−	34.6031i	−1.00967	−	3.10745i
$125$	0.102501	−	0.315466i	0.00916797	−	0.0282161i
$126$	4.36910	+	3.17434i	0.389231	+	0.282793i
$127$	4.37943	+	3.18184i	0.388611	+	0.282343i	0.764886	−	0.644165i	$-0.222795\pi$
$127$	4.37943	+	3.18184i	0.388611	+	0.282343i	−0.376275	+	0.926508i	$0.622795\pi$
$128$	−4.56692	+	14.0555i	−0.403663	+	1.24235i
$129$	−3.38069	−	10.4047i	−0.297653	−	0.916082i
$130$	−20.2378	+	14.7036i	−1.77497	+	1.28959i
$131$	−1.47527			−0.128895			−0.0644477	−	0.997921i	$-0.520529\pi$
$131$	−1.47527			−0.128895			−0.0644477	+	0.997921i	$0.520529\pi$
$132$	−12.0718	+	11.9705i	−1.05071	+	1.04190i
$133$	10.1994			0.884397
$134$	7.97727	−	5.79582i	0.689131	−	0.500683i
$135$	−0.972032	−	2.99161i	−0.0836592	−	0.257476i
$136$	−2.57854	+	7.93593i	−0.221108	+	0.680500i
$137$	−2.40125	−	1.74461i	−0.205153	−	0.149052i	0.480465	−	0.877014i	$-0.340468\pi$
$137$	−2.40125	−	1.74461i	−0.205153	−	0.149052i	−0.685618	+	0.727962i	$0.740468\pi$
$138$	−17.3435	−	12.6008i	−1.47638	−	1.07265i
$139$	5.70501	−	17.5582i	0.483893	−	1.48927i	−0.349685	−	0.936867i	$-0.613712\pi$
$139$	5.70501	−	17.5582i	0.483893	−	1.48927i	0.833578	−	0.552402i	$-0.186288\pi$
$140$	−10.0801	−	31.0233i	−0.851923	−	2.62195i
$141$	−4.42706	+	3.21645i	−0.372825	+	0.270874i
$142$	−11.0433			−0.926734
$143$	1.58676	−	9.75240i	0.132691	−	0.815537i
$144$	12.0229			1.00191
$145$	23.1411	−	16.8130i	1.92176	−	1.39624i
$146$	−4.69190	−	14.4402i	−0.388304	−	1.19508i
$147$	−0.898344	+	2.76482i	−0.0740942	+	0.228038i
$148$	6.96936	+	5.06354i	0.572878	+	0.416220i
$149$	−4.94350	−	3.59166i	−0.404987	−	0.294240i	0.366582	−	0.930386i	$-0.380528\pi$
$149$	−4.94350	−	3.59166i	−0.404987	−	0.294240i	−0.771569	+	0.636145i	$0.780528\pi$
$150$	−4.03752	+	12.4262i	−0.329662	+	1.01459i
$151$	−2.70273	−	8.31815i	−0.219945	−	0.676921i	−0.998765	−	0.0496743i	$-0.984182\pi$
$151$	−2.70273	−	8.31815i	−0.219945	−	0.676921i	0.778820	−	0.627247i	$-0.215818\pi$
$152$	34.0335	−	24.7268i	2.76048	−	2.00561i
$153$	1.00000			0.0808452
$154$	15.9248	+	8.19877i	1.28326	+	0.660676i
$155$	22.3274			1.79338
$156$	−12.3542	+	8.97586i	−0.989129	+	0.718644i
$157$	−2.38552	−	7.34187i	−0.190385	−	0.585945i	0.809614	−	0.586962i	$-0.199676\pi$
$157$	−2.38552	−	7.34187i	−0.190385	−	0.585945i	−0.999999	+	0.00101723i	$0.999676\pi$
$158$	8.28103	−	25.4864i	0.658803	−	2.02759i
$159$	−1.44713	−	1.05140i	−0.114765	−	0.0833813i
$160$	−39.2045	−	28.4837i	−3.09938	−	2.25183i
$161$	−5.02063	+	15.4519i	−0.395681	+	1.21778i
$162$	−0.824901	−	2.53878i	−0.0648103	−	0.199466i
$163$	−2.80576	+	2.03851i	−0.219764	+	0.159668i	−0.692221	−	0.721686i	$-0.743367\pi$
$163$	−2.80576	+	2.03851i	−0.219764	+	0.159668i	0.472456	+	0.881354i	$0.343367\pi$
$164$	−31.6536			−2.47173
$165$	−4.69713	−	9.31542i	−0.365671	−	0.725204i
$166$	0.542799			0.0421293
$167$	−14.2223	+	10.3331i	−1.10055	+	0.799597i	−0.981150	−	0.193249i	$-0.938098\pi$
$167$	−14.2223	+	10.3331i	−1.10055	+	0.799597i	−0.119402	+	0.992846i	$0.538098\pi$
$168$	−5.21662	−	16.0551i	−0.402471	−	1.23868i
$169$	−1.27464	+	3.92292i	−0.0980489	+	0.301763i
$170$	−6.79321	−	4.93555i	−0.521015	−	0.378540i
$171$	−4.07864	−	2.96331i	−0.311901	−	0.226610i
$172$	−17.3290	+	53.3332i	−1.32132	+	4.06662i
$173$	−5.68376	−	17.4928i	−0.432129	−	1.32995i	−0.896001	−	0.444053i	$-0.853540\pi$
$173$	−5.68376	−	17.4928i	−0.432129	−	1.32995i	0.463872	−	0.885902i	$-0.346460\pi$
$174$	19.6383	−	14.2681i	1.48878	−	1.08166i
$175$	9.90212			0.748530
$176$	39.4104	−	6.07198i	2.97067	−	0.457693i
$177$	−10.2926			−0.773641
$178$	−12.6409	+	9.18413i	−0.947474	+	0.688380i
$179$	−0.348170	−	1.07156i	−0.0260234	−	0.0800919i	0.937201	−	0.348789i	$-0.113407\pi$
$179$	−0.348170	−	1.07156i	−0.0260234	−	0.0800919i	−0.963225	+	0.268697i	$0.913407\pi$
$180$	−4.98252	+	15.3346i	−0.371375	+	1.14297i
$181$	9.37787	+	6.81342i	0.697051	+	0.506437i	0.878971	−	0.476876i	$-0.158231\pi$
$181$	9.37787	+	6.81342i	0.697051	+	0.506437i	−0.181919	+	0.983313i	$0.558231\pi$
$182$	13.0161	+	9.45676i	0.964818	+	0.700982i
$183$	−3.43262	+	10.5645i	−0.253746	+	0.780951i
$184$	20.7078	+	63.7321i	1.52660	+	4.69839i
$185$	−4.27683	+	3.10730i	−0.314439	+	0.228453i
$186$	18.9478			1.38932
$187$	3.27795	−	0.505035i	0.239707	−	0.0369318i
$188$	28.0496			2.04572
$189$	−1.63672	+	1.18914i	−0.119054	+	0.0864974i
$190$	13.0815	+	40.2607i	0.949031	+	2.92082i
$191$	2.11725	−	6.51621i	0.153199	−	0.471497i	−0.844775	−	0.535121i	$-0.820266\pi$
$191$	2.11725	−	6.51621i	0.153199	−	0.471497i	0.997974	+	0.0636244i	$0.0202660\pi$
$192$	−13.8169	−	10.0385i	−0.997146	−	0.724469i
$193$	11.4154	+	8.29380i	0.821701	+	0.597001i	0.917199	−	0.398429i	$-0.130444\pi$
$193$	11.4154	+	8.29380i	0.821701	+	0.597001i	−0.0954980	+	0.995430i	$0.530444\pi$
$194$	−0.931486	+	2.86682i	−0.0668768	+	0.205826i
$195$	−2.89580	−	8.91237i	−0.207373	−	0.638228i
$196$	12.0555	−	8.75886i	0.861110	−	0.625633i
$197$	24.3296			1.73341			0.866706	−	0.498820i	$-0.166233\pi$
$197$	24.3296			1.73341			0.866706	+	0.498820i	$0.166233\pi$
$198$	−3.98616	−	7.90539i	−0.283284	−	0.561812i
$199$	−24.1689			−1.71329			−0.856643	−	0.515910i	$-0.827454\pi$
$199$	−24.1689			−1.71329			−0.856643	+	0.515910i	$0.827454\pi$
$200$	33.0417	−	24.0062i	2.33640	−	1.69749i
$201$	1.14146	+	3.51304i	0.0805122	+	0.247791i
$202$	4.94786	−	15.2280i	0.348130	−	1.07143i
$203$	−14.8834	−	10.8134i	−1.04461	−	0.758951i
$204$	−4.14692	−	3.01292i	−0.290343	−	0.210946i
$205$	6.00254	−	18.4739i	0.419236	−	1.29027i
$206$	3.46162	+	10.6538i	0.241183	+	0.742284i
$207$	6.49707	−	4.72040i	0.451578	−	0.328090i
$208$	35.8177			2.48351
$209$	−14.8661	−	7.65370i	−1.02831	−	0.529418i
$210$	16.9876			1.17226
$211$	7.04392	−	5.11771i	0.484924	−	0.352318i	−0.318305	−	0.947988i	$-0.603114\pi$
$211$	7.04392	−	5.11771i	0.484924	−	0.352318i	0.803229	+	0.595671i	$0.203114\pi$
$212$	2.83335	+	8.72014i	0.194595	+	0.598902i
$213$	1.27839	−	3.93447i	0.0875937	−	0.269586i
$214$	43.2614	+	31.4313i	2.95729	+	2.14860i
$215$	−27.8406	−	20.2274i	−1.89871	−	1.37950i
$216$	−2.57854	+	7.93593i	−0.175447	+	0.539972i
$217$	−4.43750	−	13.6572i	−0.301237	−	0.927112i
$218$	9.33929	−	6.78539i	0.632536	−	0.459565i
$219$	5.68784			0.384348
$220$	−8.58792	+	52.7824i	−0.578997	+	3.55859i
$221$	2.97913			0.200398
$222$	−3.62947	+	2.63697i	−0.243594	+	0.176982i
$223$	0.925794	+	2.84930i	0.0619957	+	0.190803i	0.977257	−	0.212057i	$-0.0680162\pi$
$223$	0.925794	+	2.84930i	0.0619957	+	0.190803i	−0.915262	+	0.402860i	$0.868016\pi$
$224$	−9.63114	+	29.6416i	−0.643507	+	1.98051i
$225$	−3.95977	−	2.87694i	−0.263985	−	0.191796i
$226$	5.73163	+	4.16428i	0.381263	+	0.277003i
$227$	−4.85737	+	14.9494i	−0.322395	+	0.992229i	0.650208	+	0.759756i	$0.274682\pi$
$227$	−4.85737	+	14.9494i	−0.322395	+	0.992229i	−0.972603	+	0.232473i	$0.925318\pi$
$228$	7.98562	+	24.5772i	0.528860	+	1.62767i
$229$	4.40188	−	3.19816i	0.290885	−	0.211340i	−0.432766	−	0.901506i	$-0.642463\pi$
$229$	4.40188	−	3.19816i	0.290885	−	0.211340i	0.723651	+	0.690166i	$0.242463\pi$
$230$	−67.4337			−4.44645
$231$	−4.76451	+	4.72455i	−0.313482	+	0.310852i
$232$	−75.8786			−4.98168
$233$	13.2281	−	9.61079i	0.866603	−	0.629624i	−0.0630703	−	0.998009i	$-0.520089\pi$
$233$	13.2281	−	9.61079i	0.866603	−	0.629624i	0.929673	+	0.368385i	$0.120089\pi$
$234$	−2.45748	−	7.56336i	−0.160651	−	0.494432i
$235$	−5.31910	+	16.3705i	−0.346980	+	1.06789i
$236$	42.6828	+	31.0108i	2.77841	+	2.01863i
$237$	8.12157	+	5.90067i	0.527553	+	0.383290i
$238$	−1.66885	+	5.13619i	−0.108175	+	0.332930i
$239$	−6.02761	−	18.5511i	−0.389894	−	1.19997i	−0.932867	−	0.360220i	$-0.882702\pi$
$239$	−6.02761	−	18.5511i	−0.389894	−	1.19997i	0.542974	−	0.839750i	$-0.317298\pi$
$240$	30.5960	−	22.2293i	1.97496	−	1.43489i
$241$	−3.71228			−0.239129			−0.119565	−	0.992826i	$-0.538150\pi$
$241$	−3.71228			−0.239129			−0.119565	+	0.992826i	$0.538150\pi$
$242$	−17.0589	−	23.9003i	−1.09659	−	1.53637i
$243$	1.00000			0.0641500
$244$	46.0648	−	33.4680i	2.94899	−	2.14257i
$245$	2.82580	+	8.69690i	0.180533	+	0.555625i
$246$	5.09397	−	15.6776i	0.324780	−	0.999569i
$247$	−12.1508	−	8.82806i	−0.773136	−	0.561716i
$248$	−47.9170	−	34.8137i	−3.04273	−	2.21067i
$249$	−0.0628350	+	0.193386i	−0.00398201	+	0.0122554i
$250$	−0.273620	−	0.842115i	−0.0173052	−	0.0532601i
$251$	−16.0985	+	11.6963i	−1.01613	+	0.738262i	−0.965486	−	0.260455i	$-0.916127\pi$
$251$	−16.0985	+	11.6963i	−1.01613	+	0.738262i	−0.0506439	+	0.998717i	$0.516127\pi$
$252$	10.3701			0.653256
$253$	18.9131	−	18.7545i	1.18906	−	1.17908i
$254$	14.4504			0.906697
$255$	2.54481	−	1.84891i	0.159362	−	0.115783i
$256$	1.63595	+	5.03494i	0.102247	+	0.314684i
$257$	−8.28756	+	25.5065i	−0.516964	+	1.59105i	0.262716	+	0.964873i	$0.415382\pi$
$257$	−8.28756	+	25.5065i	−0.516964	+	1.59105i	−0.779680	+	0.626178i	$0.784618\pi$
$258$	−23.6265	−	17.1657i	−1.47092	−	1.06869i
$259$	2.75068	+	1.99849i	0.170919	+	0.124180i
$260$	−14.8435	+	45.6837i	−0.920558	+	2.83319i
$261$	2.81003	+	8.64837i	0.173936	+	0.535321i
$262$	−3.18603	+	2.31479i	−0.196834	+	0.143008i
$263$	−7.87858			−0.485814			−0.242907	−	0.970050i	$-0.578101\pi$
$263$	−7.87858			−0.485814			−0.242907	+	0.970050i	$0.578101\pi$
$264$	−4.44440	+	27.3158i	−0.273534	+	1.68117i
$265$	−5.62661			−0.345640
$266$	22.0267	−	16.0034i	1.35055	−	0.981229i
$267$	−1.80877	−	5.56681i	−0.110695	−	0.340683i
$268$	5.85097	−	18.0074i	0.357405	−	1.09998i
$269$	10.1381	+	7.36578i	0.618132	+	0.449099i	0.852269	−	0.523104i	$-0.175226\pi$
$269$	10.1381	+	7.36578i	0.618132	+	0.449099i	−0.234136	+	0.972204i	$0.575226\pi$
$270$	−6.79321	−	4.93555i	−0.413421	−	0.300368i
$271$	6.00261	−	18.4741i	0.364633	−	1.12222i	−0.585578	−	0.810616i	$-0.699132\pi$
$271$	6.00261	−	18.4741i	0.364633	−	1.12222i	0.950211	−	0.311608i	$-0.100868\pi$
$272$	3.71528	+	11.4344i	0.225272	+	0.693315i
$273$	−4.87598	+	3.54261i	−0.295108	+	0.214408i
$274$	−7.92317			−0.478656
$275$	−14.4329	−	7.43065i	−0.870336	−	0.448085i
$276$	−41.1650			−2.47784
$277$	−14.9848	+	10.8871i	−0.900350	+	0.654143i	−0.938556	−	0.345127i	$-0.887836\pi$
$277$	−14.9848	+	10.8871i	−0.900350	+	0.654143i	0.0382057	+	0.999270i	$0.487836\pi$
$278$	−15.2292	−	46.8705i	−0.913384	−	2.81111i
$279$	−2.19342	+	6.75067i	−0.131317	+	0.404152i
$280$	−42.9598	−	31.2122i	−2.56734	−	1.86528i
$281$	5.57577	+	4.05103i	0.332622	+	0.241664i	0.741542	−	0.670906i	$-0.234095\pi$
$281$	5.57577	+	4.05103i	0.332622	+	0.241664i	−0.408920	+	0.912570i	$0.634095\pi$
$282$	−4.51397	+	13.8926i	−0.268803	+	0.827291i
$283$	−1.13014	−	3.47823i	−0.0671801	−	0.206759i	0.911831	−	0.410566i	$-0.134669\pi$
$283$	−1.13014	−	3.47823i	−0.0671801	−	0.206759i	−0.979011	+	0.203806i	$0.934669\pi$
$284$	−17.1556	+	12.4643i	−1.01800	+	0.739619i
$285$	−15.8583			−0.939363
$286$	−11.8753	−	23.5512i	−0.702199	−	1.39261i
$287$	−12.4931			−0.737444
$288$	12.4634	−	9.05521i	0.734414	−	0.533583i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	23.5954	−	72.6192i	1.38557	−	4.26435i
$291$	−0.913551	−	0.663733i	−0.0535533	−	0.0389087i
$292$	−23.5870	−	17.1370i	−1.38033	−	1.00287i
$293$	2.70383	−	8.32152i	0.157959	−	0.486149i	−0.840489	−	0.541828i	$-0.817732\pi$
$293$	2.70383	−	8.32152i	0.157959	−	0.486149i	0.998449	+	0.0556793i	$0.0177325\pi$
$294$	2.39807	+	7.38050i	0.139858	+	0.430440i
$295$	−26.1928	+	19.0302i	−1.52500	+	1.10798i
$296$	14.0236			0.815103
$297$	3.27795	−	0.505035i	0.190206	−	0.0293051i
$298$	−16.3116			−0.944905
$299$	19.3556	−	14.0627i	1.11936	−	0.813265i
$300$	7.75289	+	23.8609i	0.447613	+	1.37761i
$301$	−6.83944	+	21.0496i	−0.394219	+	1.21328i
$302$	−18.8885	−	13.7233i	−1.08691	−	0.789687i
$303$	4.85259	+	3.52561i	0.278774	+	0.202541i
$304$	18.7305	−	57.6465i	1.07427	−	3.30625i
$305$	10.7975	+	33.2313i	0.618263	+	1.90282i
$306$	2.15962	−	1.56905i	0.123457	−	0.0896969i
$307$	13.1786			0.752142			0.376071	−	0.926591i	$-0.377275\pi$
$307$	13.1786			0.752142			0.376071	+	0.926591i	$0.377275\pi$
$308$	33.9927	−	5.23727i	1.93691	−	0.298421i
$309$	−4.19641			−0.238725
$310$	48.2187	−	35.0329i	2.73864	−	1.98974i
$311$	−5.75576	−	17.7144i	−0.326379	−	1.00449i	−0.970814	−	0.239833i	$-0.922907\pi$
$311$	−5.75576	−	17.7144i	−0.326379	−	1.00449i	0.644435	−	0.764659i	$-0.277093\pi$
$312$	−7.68180	+	23.6421i	−0.434896	+	1.33847i
$313$	5.99937	+	4.35879i	0.339104	+	0.246374i	0.744284	−	0.667864i	$-0.232791\pi$
$313$	5.99937	+	4.35879i	0.339104	+	0.246374i	−0.405180	+	0.914237i	$0.632791\pi$
$314$	−16.6716	−	12.1126i	−0.940832	−	0.683555i
$315$	−1.96651	+	6.05229i	−0.110800	+	0.341008i
$316$	−15.9013	−	48.9393i	−0.894520	−	2.75305i
$317$	22.1371	−	16.0835i	1.24334	−	0.903340i	0.245525	−	0.969390i	$-0.421040\pi$
$317$	22.1371	−	16.0835i	1.24334	−	0.903340i	0.997816	+	0.0660497i	$0.0210396\pi$
$318$	−4.77494			−0.267765
$319$	13.5788	+	26.9297i	0.760269	+	1.50778i
$320$	−53.7217			−3.00313
$321$	−16.2062	+	11.7745i	−0.904542	+	0.657188i
$322$	13.4022	+	41.2478i	0.746877	+	2.29865i
$323$	1.55790	−	4.79473i	0.0866840	−	0.266786i
$324$	−4.14692	−	3.01292i	−0.230385	−	0.167384i
$325$	−11.7967	−	8.57078i	−0.654361	−	0.475421i
$326$	−2.86085	+	8.80479i	−0.158448	+	0.487652i
$327$	1.33635	+	4.11285i	0.0739001	+	0.227441i
$328$	−41.6873	+	30.2876i	−2.30180	+	1.67235i
$329$	11.0706			0.610344
$330$	−24.7604	−	12.7477i	−1.36302	−	0.701737i
$331$	16.7386			0.920035			0.460018	−	0.887910i	$-0.347843\pi$
$331$	16.7386			0.920035			0.460018	+	0.887910i	$0.347843\pi$
$332$	0.843229	−	0.612642i	0.0462782	−	0.0336231i
$333$	−0.519337	−	1.59835i	−0.0284595	−	0.0875893i
$334$	−14.5015	+	44.6310i	−0.793486	+	2.44210i
$335$	9.40011	+	6.82958i	0.513583	+	0.373140i
$336$	−19.6780	−	14.2969i	−1.07353	−	0.779962i
$337$	6.61577	−	20.3612i	0.360384	−	1.10915i	−0.592438	−	0.805616i	$-0.701834\pi$
$337$	6.61577	−	20.3612i	0.360384	−	1.10915i	0.952822	−	0.303531i	$-0.0981656\pi$
$338$	3.40255	+	10.4720i	0.185075	+	0.569601i
$339$	−2.14713	+	1.55998i	−0.116616	+	0.0847267i
$340$	−16.1238			−0.874434
$341$	−3.78061	+	23.2361i	−0.204731	+	1.25830i
$342$	−13.4579			−0.727719
$343$	16.2151	−	11.7810i	0.875533	−	0.636112i
$344$	28.2096	+	86.8202i	1.52096	+	4.68103i
$345$	7.80621	−	24.0251i	0.420272	−	1.29347i
$346$	−39.7219	−	28.8597i	−2.13547	−	1.55151i
$347$	−5.55492	−	4.03589i	−0.298204	−	0.216658i	0.428615	−	0.903487i	$-0.359002\pi$
$347$	−5.55492	−	4.03589i	−0.298204	−	0.216658i	−0.726818	+	0.686830i	$0.759002\pi$
$348$	14.4039	−	44.3305i	0.772128	−	2.37636i
$349$	−0.0163293	−	0.0502564i	−0.000874087	−	0.00269016i	0.950619	−	0.310362i	$-0.100450\pi$
$349$	−0.0163293	−	0.0502564i	−0.000874087	−	0.00269016i	−0.951493	+	0.307672i	$0.900450\pi$
$350$	21.3848	−	15.5370i	1.14307	−	0.830486i
$351$	2.97913			0.159014
$352$	36.2813	−	35.9770i	1.93380	−	1.91758i
$353$	−14.9076			−0.793449			−0.396724	−	0.917938i	$-0.629853\pi$
$353$	−14.9076			−0.793449			−0.396724	+	0.917938i	$0.629853\pi$
$354$	−22.2281	+	16.1497i	−1.18141	+	0.858347i
$355$	−4.02124	−	12.3761i	−0.213425	−	0.656856i
$356$	−9.27152	+	28.5348i	−0.491390	+	1.51234i
$357$	−1.63672	−	1.18914i	−0.0866241	−	0.0629361i
$358$	−2.43324	−	1.76785i	−0.128601	−	0.0934340i
$359$	−9.41684	+	28.9821i	−0.497002	+	1.52961i	0.316812	+	0.948489i	$0.397388\pi$
$359$	−9.41684	+	28.9821i	−0.497002	+	1.52961i	−0.813813	+	0.581126i	$0.802612\pi$
$360$	8.11095	+	24.9629i	0.427485	+	1.31566i
$361$	−5.19104	+	3.77151i	−0.273213	+	0.198501i
$362$	30.9432			1.62634
$363$	10.4899	−	3.31096i	0.550576	−	0.173780i
$364$	30.8939			1.61928
$365$	14.4745	−	10.5163i	0.757629	−	0.550449i
$366$	9.16314	+	28.2013i	0.478965	+	1.47410i
$367$	8.44071	−	25.9778i	0.440601	−	1.35603i	−0.446635	−	0.894716i	$-0.647378\pi$
$367$	8.44071	−	25.9778i	0.440601	−	1.35603i	0.887236	−	0.461315i	$-0.152622\pi$
$368$	78.1136	+	56.7528i	4.07195	+	2.95845i
$369$	4.99589	+	3.62972i	0.260075	+	0.188956i
$370$	−4.36080	+	13.4212i	−0.226707	+	0.697733i
$371$	1.11827	+	3.44168i	0.0580577	+	0.178683i
$372$	29.4352	−	21.3859i	1.52614	−	1.10881i
$373$	−26.6279			−1.37874			−0.689370	−	0.724410i	$-0.742112\pi$
$373$	−26.6279			−1.37874			−0.689370	+	0.724410i	$0.742112\pi$
$374$	6.28669	−	6.23396i	0.325077	−	0.322350i
$375$	0.331700			0.0171289
$376$	36.9408	−	26.8391i	1.90508	−	1.38412i
$377$	8.37142	+	25.7646i	0.431150	+	1.32694i
$378$	−1.66885	+	5.13619i	−0.0858363	+	0.264177i
$379$	−29.2147	−	21.2257i	−1.50066	−	1.09029i	−0.970119	−	0.242631i	$-0.921990\pi$
$379$	−29.2147	−	21.2257i	−1.50066	−	1.09029i	−0.530539	−	0.847661i	$-0.678010\pi$
$380$	65.7630	+	47.7796i	3.37357	+	2.45104i
$381$	−1.67279	+	5.14833i	−0.0856998	+	0.263757i
$382$	−5.65185	−	17.3946i	−0.289174	−	0.889985i
$383$	−7.03413	+	5.11059i	−0.359427	+	0.261139i	−0.752813	−	0.658234i	$-0.771304\pi$
$383$	−7.03413	+	5.11059i	−0.359427	+	0.261139i	0.393386	+	0.919373i	$0.371304\pi$
$384$	−14.7789			−0.754181
$385$	−3.38949	+	20.8322i	−0.172745	+	1.06171i
$386$	37.6664			1.91717
$387$	8.85076	−	6.43046i	0.449910	−	0.326878i
$388$	1.78865	+	5.50490i	0.0908050	+	0.279469i
$389$	−8.59407	+	26.4498i	−0.435736	+	1.34106i	0.456594	+	0.889675i	$0.349069\pi$
$389$	−8.59407	+	26.4498i	−0.435736	+	1.34106i	−0.892330	+	0.451383i	$0.850931\pi$
$390$	−20.2378	−	14.7036i	−1.02478	−	0.744548i
$391$	6.49707	+	4.72040i	0.328571	+	0.238721i
$392$	7.49608	−	23.0706i	0.378609	−	1.16524i
$393$	−0.455885	−	1.40307i	−0.0229964	−	0.0707755i
$394$	52.5426	−	38.1744i	2.64706	−	1.92320i
$395$	31.5777			1.58885
$396$	−15.1150	−	7.78184i	−0.759559	−	0.391052i
$397$	32.7625			1.64430			0.822150	−	0.569270i	$-0.192774\pi$
$397$	32.7625			1.64430			0.822150	+	0.569270i	$0.192774\pi$
$398$	−52.1955	+	37.9223i	−2.61633	+	1.90087i
$399$	3.15178	+	9.70017i	0.157786	+	0.485616i
$400$	18.1846	−	55.9665i	0.909230	−	2.79832i
$401$	−23.0029	−	16.7126i	−1.14871	−	0.834587i	−0.160401	−	0.987052i	$-0.551279\pi$
$401$	−23.0029	−	16.7126i	−1.14871	−	0.834587i	−0.988309	+	0.152465i	$0.951279\pi$
$402$	7.97727	+	5.79582i	0.397870	+	0.289069i
$403$	−6.53449	+	20.1111i	−0.325506	+	1.00180i
$404$	−9.50094	−	29.2409i	−0.472690	−	1.45479i
$405$	2.54481	−	1.84891i	0.126453	−	0.0918733i
$406$	−49.1092			−2.43725
$407$	−2.50958	−	4.97704i	−0.124395	−	0.246703i
$408$	−8.34433			−0.413106
$409$	15.6124	−	11.3430i	0.771981	−	0.560877i	−0.130581	−	0.991438i	$-0.541684\pi$
$409$	15.6124	−	11.3430i	0.771981	−	0.560877i	0.902562	+	0.430561i	$0.141684\pi$
$410$	−16.0234	−	49.3149i	−0.791339	−	2.43549i
$411$	0.917196	−	2.82284i	0.0452420	−	0.139240i
$412$	17.4022	+	12.6434i	0.857345	+	0.622897i
$413$	16.8461	+	12.2394i	0.828942	+	0.602262i
$414$	6.62463	−	20.3885i	0.325583	−	1.00204i
$415$	0.197651	+	0.608308i	0.00970232	+	0.0298607i
$416$	37.1301	−	26.9766i	1.82045	−	1.32264i
$417$	18.4618			0.904078
$418$	−44.1143	+	6.79671i	−2.15770	+	0.332438i
$419$	1.21745			0.0594764			0.0297382	−	0.999558i	$-0.490533\pi$
$419$	1.21745			0.0594764			0.0297382	+	0.999558i	$0.490533\pi$
$420$	26.3900	−	19.1735i	1.28770	−	0.935569i
$421$	2.41698	+	7.43870i	0.117796	+	0.362540i	0.992520	−	0.122082i	$-0.0389571\pi$
$421$	2.41698	+	7.43870i	0.117796	+	0.362540i	−0.874724	+	0.484622i	$0.838957\pi$
$422$	7.18222	−	22.1046i	0.349625	−	1.07604i
$423$	−4.42706	−	3.21645i	−0.215251	−	0.156389i
$424$	12.0753	+	8.77322i	0.586428	+	0.426065i
$425$	1.51250	−	4.65499i	0.0733670	−	0.225800i
$426$	−3.41257	−	10.5028i	−0.165340	−	0.508863i
$427$	18.1809	−	13.2092i	0.879836	−	0.639239i
$428$	102.681			4.96330
$429$	9.76542	−	1.50456i	0.471479	−	0.0726410i
$430$	−91.8629			−4.43002
$431$	−3.80490	+	2.76442i	−0.183276	+	0.133157i	−0.675640	−	0.737232i	$-0.736133\pi$
$431$	−3.80490	+	2.76442i	−0.183276	+	0.133157i	0.492365	+	0.870389i	$0.336133\pi$
$432$	3.71528	+	11.4344i	0.178751	+	0.550140i
$433$	−4.20395	+	12.9384i	−0.202029	+	0.621781i	0.797793	+	0.602931i	$0.206001\pi$
$433$	−4.20395	+	12.9384i	−0.202029	+	0.621781i	−0.999822	+	0.0188503i	$0.993999\pi$
$434$	−31.0122	−	22.5317i	−1.48863	−	1.08156i
$435$	23.1411	+	16.8130i	1.10953	+	0.806120i
$436$	6.84995	−	21.0820i	0.328053	−	1.00964i
$437$	−12.5112	−	38.5056i	−0.598493	−	1.84197i
$438$	12.2836	−	8.92453i	0.586931	−	0.426430i
$439$	−3.51500			−0.167762			−0.0838809	−	0.996476i	$-0.526732\pi$
$439$	−3.51500			−0.167762			−0.0838809	+	0.996476i	$0.526732\pi$
$440$	39.1944	+	77.7309i	1.86852	+	3.70568i
$441$	−2.90710			−0.138433
$442$	6.43377	−	4.67441i	0.306023	−	0.222339i
$443$	−6.84781	−	21.0754i	−0.325349	−	1.00132i	−0.971283	−	0.237928i	$-0.923532\pi$
$443$	−6.84781	−	21.0754i	−0.325349	−	1.00132i	0.645934	−	0.763394i	$-0.276468\pi$
$444$	−2.66206	+	8.19297i	−0.126336	+	0.388821i
$445$	−14.8955	−	10.8222i	−0.706116	−	0.513023i
$446$	6.47007	+	4.70078i	0.306367	+	0.222588i
$447$	1.88825	−	5.81143i	0.0893111	−	0.274871i
$448$	10.6770	+	32.8604i	0.504441	+	1.55251i
$449$	−24.2728	+	17.6352i	−1.14551	+	0.832258i	−0.987877	−	0.155240i	$-0.950385\pi$
$449$	−24.2728	+	17.6352i	−1.14551	+	0.832258i	−0.157628	+	0.987498i	$0.550385\pi$
$450$	−13.0657			−0.615922
$451$	18.2094	+	9.37494i	0.857447	+	0.441449i
$452$	13.6041			0.639883
$453$	7.07584	−	5.14090i	0.332452	−	0.241540i
$454$	12.9664	+	39.9066i	0.608544	+	1.87291i
$455$	−5.85848	+	18.0305i	−0.274650	+	0.845285i
$456$	34.0335	+	24.7268i	1.59377	+	1.15794i
$457$	1.05311	+	0.765127i	0.0492623	+	0.0357911i	0.612144	−	0.790746i	$-0.290307\pi$
$457$	1.05311	+	0.765127i	0.0492623	+	0.0357911i	−0.562882	+	0.826538i	$0.690307\pi$
$458$	4.48831	−	13.8136i	0.209725	−	0.645467i
$459$	0.309017	+	0.951057i	0.0144237	+	0.0443915i
$460$	−104.757	+	76.1106i	−4.88433	+	3.54868i
$461$	18.3589			0.855061			0.427530	−	0.904001i	$-0.359384\pi$
$461$	18.3589			0.855061			0.427530	+	0.904001i	$0.359384\pi$
$462$	−2.87644	+	17.6790i	−0.133824	+	0.822501i
$463$	−26.4569			−1.22956			−0.614778	−	0.788700i	$-0.710754\pi$
$463$	−26.4569			−1.22956			−0.614778	+	0.788700i	$0.710754\pi$
$464$	−88.4493	+	64.2622i	−4.10615	+	2.98330i
$465$	6.89955	+	21.2346i	0.319959	+	0.984732i
$466$	13.4878	−	41.5113i	0.624812	−	1.92297i
$467$	22.6163	+	16.4317i	1.04656	+	0.760368i	0.971555	−	0.236816i	$-0.0761038\pi$
$467$	22.6163	+	16.4317i	1.04656	+	0.760368i	0.0750017	+	0.997183i	$0.476104\pi$
$468$	−12.3542	−	8.97586i	−0.571074	−	0.414909i
$469$	2.30927	−	7.10721i	0.106632	−	0.328180i
$470$	14.1990	+	43.7000i	0.654950	+	2.01573i
$471$	6.24536	−	4.53752i	0.287771	−	0.209078i
$472$	85.8851			3.95318
$473$	25.7647	−	25.5486i	1.18466	−	1.17473i
$474$	26.7980			1.23087
$475$	−19.9631	+	14.5040i	−0.915970	+	0.665491i
$476$	3.20454	+	9.86257i	0.146880	+	0.452050i
$477$	0.552753	−	1.70120i	0.0253088	−	0.0778925i
$478$	−42.1250	−	30.6056i	−1.92675	−	1.39987i
$479$	−12.8183	−	9.31304i	−0.585683	−	0.425524i	0.255085	−	0.966919i	$-0.417896\pi$
$479$	−12.8183	−	9.31304i	−0.585683	−	0.425524i	−0.840768	+	0.541395i	$0.817896\pi$
$480$	14.9748	−	46.0876i	0.683502	−	2.10360i
$481$	−1.54717	−	4.76170i	−0.0705449	−	0.217115i
$482$	−8.01712	+	5.82478i	−0.365170	+	0.265311i
$483$	−16.2471			−0.739268
$484$	−53.4764	−	17.8748i	−2.43074	−	0.812493i
$485$	−3.55200			−0.161288
$486$	2.15962	−	1.56905i	0.0979623	−	0.0711737i
$487$	2.09776	+	6.45623i	0.0950584	+	0.292560i	0.987269	−	0.159060i	$-0.0508463\pi$
$487$	2.09776	+	6.45623i	0.0950584	+	0.292560i	−0.892210	+	0.451620i	$0.850846\pi$
$488$	28.6429	−	88.1537i	1.29660	−	3.99053i
$489$	−2.80576	−	2.03851i	−0.126881	−	0.0921844i
$490$	19.7486	+	14.3482i	0.892149	+	0.648184i
$491$	−2.61180	+	8.03830i	−0.117869	+	0.362763i	−0.992535	−	0.121963i	$-0.961081\pi$
$491$	−2.61180	+	8.03830i	−0.117869	+	0.362763i	0.874666	+	0.484727i	$0.161081\pi$
$492$	−9.78150	−	30.1044i	−0.440984	−	1.35721i
$493$	−7.35674	+	5.34499i	−0.331331	+	0.240726i
$494$	−40.0928			−1.80386
$495$	7.40799	−	7.34586i	0.332965	−	0.330172i
$496$	−85.3393			−3.83185
$497$	−6.77101	+	4.91942i	−0.303721	+	0.220666i
$498$	0.167734	+	0.516232i	0.00751634	+	0.0231329i
$499$	−0.951253	+	2.92766i	−0.0425839	+	0.131060i	−0.970088	−	0.242753i	$-0.921950\pi$
$499$	−0.951253	+	2.92766i	−0.0425839	+	0.131060i	0.927504	+	0.373813i	$0.121950\pi$
$500$	−1.37554	−	0.999386i	−0.0615159	−	0.0446939i
$501$	−14.2223	−	10.3331i	−0.635404	−	0.461648i
$502$	−16.4146	+	50.5189i	−0.732619	+	2.25477i
$503$	9.40972	+	28.9601i	0.419559	+	1.29127i	0.908109	+	0.418733i	$0.137526\pi$
$503$	9.40972	+	28.9601i	0.419559	+	1.29127i	−0.488550	+	0.872536i	$0.662474\pi$
$504$	13.6573	−	9.92260i	0.608344	−	0.441988i
$505$	18.8675			0.839592
$506$	11.4183	−	70.1782i	0.507604	−	3.11980i
$507$	−4.12481			−0.183189
$508$	22.4484	−	16.3097i	0.995988	−	0.723627i
$509$	−3.48245	−	10.7179i	−0.154357	−	0.475061i	0.843738	−	0.536755i	$-0.180350\pi$
$509$	−3.48245	−	10.7179i	−0.154357	−	0.475061i	−0.998095	+	0.0616932i	$0.980350\pi$
$510$	2.59477	−	7.98589i	0.114899	−	0.353621i
$511$	−9.30937	−	6.76365i	−0.411822	−	0.299206i
$512$	−12.4796	−	9.06695i	−0.551525	−	0.400706i
$513$	1.55790	−	4.79473i	0.0687830	−	0.211692i
$514$	22.1231	+	68.0879i	0.975808	+	3.00323i
$515$	−10.6791	+	7.75880i	−0.470576	+	0.341894i
$516$	−56.0779			−2.46869
$517$	−16.1361	−	8.30752i	−0.709664	−	0.365364i
$518$	9.07615			0.398783
$519$	14.8803	−	10.8112i	0.653172	−	0.474557i
$520$	24.1636	+	74.3678i	1.05964	+	3.26124i
$521$	−6.72723	+	20.7043i	−0.294725	+	0.907071i	0.688588	+	0.725153i	$0.258231\pi$
$521$	−6.72723	+	20.7043i	−0.294725	+	0.907071i	−0.983314	+	0.181919i	$0.941769\pi$
$522$	19.6383	+	14.2681i	0.859547	+	0.624497i
$523$	26.6731	+	19.3792i	1.16633	+	0.847392i	0.990566	−	0.137040i	$-0.0437589\pi$
$523$	26.6731	+	19.3792i	1.16633	+	0.847392i	0.175769	+	0.984431i	$0.443759\pi$
$524$	−2.33681	+	7.19197i	−0.102084	+	0.314182i
$525$	3.05992	+	9.41748i	0.133546	+	0.411012i
$526$	−17.0147	+	12.3619i	−0.741877	+	0.539005i
$527$	−7.09807			−0.309197
$528$	17.9533	+	35.6052i	0.781316	+	1.54952i
$529$	41.4941			1.80409
$530$	−12.1513	+	8.82845i	−0.527820	+	0.383484i
$531$	−3.18060	−	9.78887i	−0.138026	−	0.424801i
$532$	16.1556	−	49.7219i	0.700435	−	2.15572i
$533$	14.8834	+	10.8134i	0.644670	+	0.468381i
$534$	−12.6409	−	9.18413i	−0.547024	−	0.397436i
$535$	−19.4717	+	59.9278i	−0.841836	+	2.59090i
$536$	−9.52470	−	29.3140i	−0.411404	−	1.26617i
$537$	0.911520	−	0.662258i	0.0393350	−	0.0285785i
$538$	33.4518			1.44221
$539$	−9.52933	+	1.46819i	−0.410457	+	0.0632394i
$540$	−16.1238			−0.693856
$541$	20.4844	−	14.8828i	0.880695	−	0.639862i	−0.0527401	−	0.998608i	$-0.516795\pi$
$541$	20.4844	−	14.8828i	0.880695	−	0.639862i	0.933435	+	0.358746i	$0.116795\pi$
$542$	−16.0236	−	49.3155i	−0.688272	−	2.11828i
$543$	−3.58203	+	11.0243i	−0.153719	+	0.473100i
$544$	12.4634	+	9.05521i	0.534365	+	0.388239i
$545$	11.0051	+	7.99565i	0.471405	+	0.342496i
$546$	−4.97171	+	15.3014i	−0.212770	+	0.654838i
$547$	0.239216	+	0.736231i	0.0102281	+	0.0314790i	0.956040	−	0.293235i	$-0.0947319\pi$
$547$	0.239216	+	0.736231i	0.0102281	+	0.0314790i	−0.945812	+	0.324714i	$0.894732\pi$
$548$	−12.3085	+	8.94267i	−0.525794	+	0.382012i
$549$	−11.1082			−0.474085
$550$	−42.8286	+	6.59862i	−1.82622	+	0.281366i
$551$	45.8443			1.95303
$552$	−54.2137	+	39.3886i	−2.30749	+	1.67649i
$553$	−6.27596	−	19.3154i	−0.266881	−	0.821375i
$554$	−15.2790	+	47.0240i	−0.649143	+	1.99786i
$555$	−4.27683	−	3.10730i	−0.181542	−	0.131898i
$556$	−76.5597	−	55.6239i	−3.24685	−	2.35898i
$557$	−8.25226	+	25.3979i	−0.349660	+	1.07614i	0.609382	+	0.792877i	$0.291418\pi$
$557$	−8.25226	+	25.3979i	−0.349660	+	1.07614i	−0.959042	+	0.283265i	$0.908582\pi$
$558$	5.85520	+	18.0205i	0.247871	+	0.762867i
$559$	26.3675	−	19.1571i	1.11523	−	0.810261i
$560$	−76.5107			−3.23317
$561$	1.49326	+	2.96145i	0.0630454	+	0.125032i
$562$	18.3978			0.776065
$563$	−23.7247	+	17.2370i	−0.999879	+	0.726454i	−0.962062	−	0.272830i	$-0.912040\pi$
$563$	−23.7247	+	17.2370i	−0.999879	+	0.726454i	−0.0378166	+	0.999285i	$0.512040\pi$
$564$	8.66779	+	26.6767i	0.364980	+	1.12329i
$565$	−2.57978	+	7.93973i	−0.108532	+	0.334027i
$566$	−7.89821	−	5.73838i	−0.331986	−	0.241202i
$567$	−1.63672	−	1.18914i	−0.0687356	−	0.0499393i
$568$	−10.6673	+	32.8305i	−0.447589	+	1.37754i
$569$	−4.52299	−	13.9203i	−0.189614	−	0.583571i	0.810384	−	0.585899i	$-0.199259\pi$
$569$	−4.52299	−	13.9203i	−0.189614	−	0.583571i	−0.999997	+	0.00232896i	$0.999259\pi$
$570$	−34.2478	+	24.8825i	−1.43448	+	1.04221i
$571$	−38.8875			−1.62739			−0.813696	−	0.581290i	$-0.802548\pi$
$571$	−38.8875			−1.62739			−0.813696	+	0.581290i	$0.802548\pi$
$572$	−45.0296	−	23.1831i	−1.88278	−	0.969334i
$573$	6.85155			0.286228
$574$	−26.9803	+	19.6024i	−1.12614	+	0.818186i
$575$	−12.1466	−	37.3834i	−0.506549	−	1.55900i
$576$	5.27757	−	16.2427i	0.219899	−	0.676779i
$577$	−15.3378	−	11.1436i	−0.638522	−	0.463914i	0.220820	−	0.975315i	$-0.429127\pi$
$577$	−15.3378	−	11.1436i	−0.638522	−	0.463914i	−0.859342	+	0.511401i	$0.829127\pi$
$578$	2.15962	+	1.56905i	0.0898283	+	0.0652640i
$579$	−4.36031	+	13.4197i	−0.181208	+	0.557702i
$580$	−45.3082	−	139.444i	−1.88132	−	5.79011i
$581$	0.332807	−	0.241798i	0.0138072	−	0.0100315i
$582$	−3.01435			−0.124949
$583$	0.952730	−	5.85560i	0.0394581	−	0.242514i
$584$	−47.4612			−1.96396
$585$	7.58132	−	5.50815i	0.313449	−	0.227734i
$586$	−7.21769	−	22.2138i	−0.298160	−	0.917642i
$587$	−0.755488	+	2.32515i	−0.0311823	+	0.0959693i	−0.965436	−	0.260639i	$-0.916067\pi$
$587$	−0.755488	+	2.32515i	−0.0311823	+	0.0959693i	0.934254	+	0.356608i	$0.116067\pi$
$588$	12.0555	+	8.75886i	0.497162	+	0.361209i
$589$	28.9505	+	21.0338i	1.19288	+	0.866681i
$590$	−26.7071	+	82.1959i	−1.09951	+	3.38395i
$591$	7.51826	+	23.1388i	0.309260	+	0.951804i
$592$	16.3468	−	11.8767i	0.671850	−	0.488128i
$593$	−9.34416			−0.383719			−0.191859	−	0.981422i	$-0.561452\pi$
$593$	−9.34416			−0.383719			−0.191859	+	0.981422i	$0.561452\pi$
$594$	6.28669	−	6.23396i	0.257946	−	0.255782i
$595$	−6.36375			−0.260889
$596$	−25.3398	+	18.4104i	−1.03796	+	0.754121i
$597$	−7.46859	−	22.9860i	−0.305669	−	0.940753i
$598$	19.7356	−	60.7400i	0.807049	−	2.48384i
$599$	38.4571	+	27.9407i	1.57132	+	1.14163i	0.925883	+	0.377810i	$0.123323\pi$
$599$	38.4571	+	27.9407i	1.57132	+	1.14163i	0.645432	+	0.763818i	$0.276677\pi$
$600$	33.0417	+	24.0062i	1.34892	+	0.980048i
$601$	−2.20088	+	6.77363i	−0.0897760	+	0.276302i	−0.985857	−	0.167588i	$-0.946402\pi$
$601$	−2.20088	+	6.77363i	−0.0897760	+	0.276302i	0.896081	+	0.443890i	$0.146402\pi$
$602$	18.2574	+	56.1907i	0.744118	+	2.29016i
$603$	−2.98837	+	2.17118i	−0.121696	+	0.0884173i
$604$	−44.8321			−1.82419
$605$	20.5731	−	27.8206i	0.836415	−	1.13107i
$606$	16.0116			0.650427
$607$	−31.8664	+	23.1523i	−1.29342	+	0.939724i	−0.999868	−	0.0162194i	$-0.994837\pi$
$607$	−31.8664	+	23.1523i	−1.29342	+	0.939724i	−0.293551	+	0.955943i	$0.594837\pi$
$608$	−24.0005	−	73.8659i	−0.973348	−	2.99566i
$609$	5.68494	−	17.4964i	0.230365	−	0.708991i
$610$	75.4602	+	54.8250i	3.05529	+	2.21980i
$611$	−13.1888	−	9.58220i	−0.533560	−	0.387654i
$612$	1.58398	−	4.87500i	0.0640288	−	0.197060i
$613$	9.85387	+	30.3271i	0.397994	+	1.22490i	0.926605	+	0.376036i	$0.122713\pi$
$613$	9.85387	+	30.3271i	0.397994	+	1.22490i	−0.528611	+	0.848864i	$0.677287\pi$
$614$	28.4607	−	20.6779i	1.14858	−	0.834493i
$615$	19.4246			0.783277
$616$	39.7566	−	39.4232i	1.60184	−	1.58841i
$617$	28.6421			1.15309			0.576543	−	0.817067i	$-0.304401\pi$
$617$	28.6421			1.15309			0.576543	+	0.817067i	$0.304401\pi$
$618$	−9.06264	+	6.58440i	−0.364553	+	0.264863i
$619$	7.01272	+	21.5829i	0.281865	+	0.867492i	0.987321	+	0.158738i	$0.0507424\pi$
$619$	7.01272	+	21.5829i	0.281865	+	0.867492i	−0.705456	+	0.708754i	$0.749258\pi$
$620$	35.3663	−	108.846i	1.42034	−	4.37137i
$621$	6.49707	+	4.72040i	0.260719	+	0.189423i
$622$	−40.2251	−	29.2253i	−1.61288	−	1.17183i
$623$	−3.65930	+	11.2622i	−0.146607	+	0.451209i
$624$	11.0683	+	34.0647i	0.443086	+	1.36368i
$625$	20.6430	−	14.9980i	0.825719	−	0.599920i
$626$	19.7955			0.791188
$627$	2.68521	−	16.5037i	0.107237	−	0.659093i
$628$	−39.5702			−1.57902
$629$	1.35964	−	0.987837i	0.0542125	−	0.0393877i
$630$	5.24947	+	16.1562i	0.209144	+	0.643678i
$631$	−9.75578	+	30.0252i	−0.388372	+	1.19528i	0.545633	+	0.838024i	$0.316289\pi$
$631$	−9.75578	+	30.0252i	−0.388372	+	1.19528i	−0.934005	+	0.357261i	$0.883711\pi$
$632$	−67.7691	−	49.2371i	−2.69571	−	1.95855i
$633$	7.04392	+	5.11771i	0.279971	+	0.203411i
$634$	22.5717	−	69.4685i	0.896436	−	2.75895i
$635$	5.26187	+	16.1944i	0.208811	+	0.642654i
$636$	−7.41780	+	5.38934i	−0.294135	+	0.213701i
$637$	−8.66063			−0.343147
$638$	71.5793	+	36.8520i	2.83385	+	1.45898i
$639$	4.13695			0.163655
$640$	−37.6094	+	27.3248i	−1.48664	+	1.08011i
$641$	−3.14107	−	9.66722i	−0.124065	−	0.381832i	0.869665	−	0.493643i	$-0.164335\pi$
$641$	−3.14107	−	9.66722i	−0.124065	−	0.381832i	−0.993730	+	0.111811i	$0.964335\pi$
$642$	−16.5244	+	50.8568i	−0.652166	+	2.00716i
$643$	4.25624	+	3.09234i	0.167850	+	0.121950i	0.668539	−	0.743677i	$-0.266920\pi$
$643$	4.25624	+	3.09234i	0.167850	+	0.121950i	−0.500689	+	0.865627i	$0.666920\pi$
$644$	67.3754	+	48.9511i	2.65496	+	1.92894i
$645$	10.6342	−	32.7286i	0.418720	−	1.28869i
$646$	−4.15872	−	12.7992i	−0.163623	−	0.503578i
$647$	15.2502	−	11.0799i	0.599545	−	0.435595i	−0.246172	−	0.969226i	$-0.579173\pi$
$647$	15.2502	−	11.0799i	0.599545	−	0.435595i	0.845717	+	0.533631i	$0.179173\pi$
$648$	−8.34433			−0.327796
$649$	−15.3696	−	30.4811i	−0.603308	−	1.19649i
$650$	−38.9243			−1.52674
$651$	11.6175	−	8.44062i	0.455327	−	0.330814i
$652$	5.49344	+	16.9071i	0.215140	+	0.662132i
$653$	−11.3455	+	34.9178i	−0.443983	+	1.36644i	0.439613	+	0.898187i	$0.355116\pi$
$653$	−11.3455	+	34.9178i	−0.443983	+	1.36644i	−0.883595	+	0.468251i	$0.844884\pi$
$654$	9.33929	+	6.78539i	0.365195	+	0.265330i
$655$	−3.75430	−	2.72766i	−0.146692	−	0.106578i
$656$	−22.9428	+	70.6106i	−0.895765	+	2.75688i
$657$	1.75764	+	5.40946i	0.0685720	+	0.211043i
$658$	23.9084	−	17.3704i	0.932045	−	0.677170i
$659$	−34.9395			−1.36105			−0.680524	−	0.732725i	$-0.738248\pi$
$659$	−34.9395			−1.36105			−0.680524	+	0.732725i	$0.738248\pi$
$660$	−52.8529	+	8.14307i	−2.05729	+	0.316968i
$661$	−16.4031			−0.638007			−0.319003	−	0.947754i	$-0.603348\pi$
$661$	−16.4031			−0.638007			−0.319003	+	0.947754i	$0.603348\pi$
$662$	36.1489	−	26.2637i	1.40497	−	1.02077i
$663$	0.920601	+	2.83332i	0.0357532	+	0.110037i
$664$	0.524316	−	1.61368i	0.0203474	−	0.0626229i
$665$	25.9555	+	18.8577i	1.00651	+	0.731272i
$666$	−3.62947	−	2.63697i	−0.140639	−	0.102180i
$667$	−22.5668	+	69.4535i	−0.873791	+	2.68925i
$668$	27.8459	+	85.7010i	1.07739	+	3.31587i
$669$	−2.42376	+	1.76096i	−0.0937080	+	0.0680828i
$670$	31.0166			1.19828
$671$	−36.4120	+	5.61002i	−1.40567	+	0.216572i
$672$	−31.1670			−1.20229
$673$	−21.3719	+	15.5276i	−0.823825	+	0.598544i	−0.917805	−	0.397030i	$-0.870041\pi$
$673$	−21.3719	+	15.5276i	−0.823825	+	0.598544i	0.0939809	+	0.995574i	$0.470041\pi$
$674$	−17.6604	−	54.3530i	−0.680252	−	2.09360i
$675$	1.51250	−	4.65499i	0.0582161	−	0.179171i
$676$	17.1053	+	12.4277i	0.657894	+	0.477988i
$677$	7.65145	+	5.55910i	0.294069	+	0.213654i	0.725031	−	0.688717i	$-0.241826\pi$
$677$	7.65145	+	5.55910i	0.294069	+	0.213654i	−0.430962	+	0.902370i	$0.641826\pi$
$678$	−2.18929	+	6.73794i	−0.0840791	+	0.258769i
$679$	0.705948	+	2.17268i	0.0270918	+	0.0833800i
$680$	−21.2348	+	15.4280i	−0.814316	+	0.591635i
$681$	−15.7188			−0.602345
$682$	28.2940	+	56.1131i	1.08343	+	2.14868i
$683$	−36.5061			−1.39687			−0.698434	−	0.715674i	$-0.746119\pi$
$683$	−36.5061			−1.39687			−0.698434	+	0.715674i	$0.746119\pi$
$684$	−20.9066	+	15.1895i	−0.799385	+	0.580787i
$685$	−2.88510	−	8.87941i	−0.110234	−	0.339265i
$686$	16.5335	−	50.8848i	0.631250	−	1.94279i
$687$	4.40188	+	3.19816i	0.167942	+	0.122017i
$688$	106.412	+	77.3126i	4.05691	+	2.94752i
$689$	1.64672	−	5.06809i	0.0627351	−	0.193079i
$690$	−20.8382	−	64.1333i	−0.793296	−	2.44151i
$691$	25.4175	−	18.4669i	0.966926	−	0.702513i	0.0121769	−	0.999926i	$-0.496124\pi$
$691$	25.4175	−	18.4669i	0.966926	−	0.702513i	0.954749	+	0.297413i	$0.0961239\pi$
$692$	−94.2805			−3.58401
$693$	−5.96562	−	3.07135i	−0.226615	−	0.116671i
$694$	−18.3290			−0.695760
$695$	46.9818	−	34.1343i	1.78212	−	1.29479i
$696$	−23.4478	−	72.1649i	−0.888786	−	2.73540i
$697$	−1.90826	+	5.87302i	−0.0722804	+	0.222456i
$698$	−0.114120	−	0.0829131i	−0.00431951	−	0.00313831i
$699$	13.2281	+	9.61079i	0.500333	+	0.363514i
$700$	15.6848	−	48.2728i	0.592830	−	1.82454i
$701$	1.19554	+	3.67950i	0.0451550	+	0.138973i	0.971092	−	0.238705i	$-0.0767228\pi$
$701$	1.19554	+	3.67950i	0.0451550	+	0.138973i	−0.925937	+	0.377678i	$0.876723\pi$
$702$	6.43377	−	4.67441i	0.242827	−	0.176424i
$703$	−8.47275			−0.319556
$704$	9.09647	−	55.9081i	0.342836	−	2.10711i
$705$	−17.2130			−0.648278
$706$	−32.1946	+	23.3908i	−1.21166	+	0.880323i
$707$	−3.74985	−	11.5408i	−0.141028	−	0.434038i
$708$	−16.3034	+	50.1766i	−0.612718	+	1.88575i
$709$	25.1842	+	18.2974i	0.945814	+	0.687174i	0.949813	−	0.312818i	$-0.101273\pi$
$709$	25.1842	+	18.2974i	0.945814	+	0.687174i	−0.00399896	+	0.999992i	$0.501273\pi$
$710$	−28.1031	−	20.4181i	−1.05469	−	0.766279i
$711$	−3.10217	+	9.54748i	−0.116340	+	0.358059i
$712$	15.0930	+	46.4513i	0.565632	+	1.74084i
$713$	−46.1167	+	33.5057i	−1.72708	+	1.25480i
$714$	−5.40051			−0.202109
$715$	22.0693	−	21.8843i	0.825347	−	0.818425i
$716$	−5.77533			−0.215834
$717$	15.7805	−	11.4652i	0.589333	−	0.428176i
$718$	25.1376	+	77.3657i	0.938128	+	2.88726i
$719$	−4.20725	+	12.9486i	−0.156904	+	0.482901i	−0.998349	−	0.0574423i	$-0.981705\pi$
$719$	−4.20725	+	12.9486i	−0.156904	+	0.482901i	0.841445	+	0.540343i	$0.181705\pi$
$720$	30.5960	+	22.2293i	1.14024	+	0.828436i
$721$	6.86833	+	4.99013i	0.255790	+	0.185842i
$722$	−5.29296	+	16.2901i	−0.196984	+	0.606253i
$723$	−1.14716	−	3.53059i	−0.0426633	−	0.131304i
$724$	48.0698	−	34.9248i	1.78650	−	1.29797i
$725$	44.5083			1.65300
$726$	17.4591	−	23.6096i	0.647967	−	0.876234i
$727$	4.28782			0.159026			0.0795132	−	0.996834i	$-0.474663\pi$
$727$	4.28782			0.159026			0.0795132	+	0.996834i	$0.474663\pi$
$728$	40.6868	−	29.5607i	1.50795	−	1.09559i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	14.7587	−	45.4225i	0.546242	−	1.68116i
$731$	8.85076	+	6.43046i	0.327357	+	0.237839i
$732$	46.0648	+	33.4680i	1.70260	+	1.23701i
$733$	−12.6334	+	38.8815i	−0.466624	+	1.43612i	0.390304	+	0.920686i	$0.372370\pi$
$733$	−12.6334	+	38.8815i	−0.466624	+	1.43612i	−0.856928	+	0.515436i	$0.827630\pi$
$734$	−22.5319	−	69.3461i	−0.831668	−	2.55961i
$735$	−7.39803	+	5.37498i	−0.272880	+	0.198259i
$736$	123.720			4.56038
$737$	−8.69921	+	8.62625i	−0.320440	+	0.317752i
$738$	16.4844			0.606800
$739$	15.9153	−	11.5631i	0.585453	−	0.425357i	−0.255233	−	0.966880i	$-0.582152\pi$
$739$	15.9153	−	11.5631i	0.585453	−	0.425357i	0.840686	+	0.541523i	$0.182152\pi$
$740$	8.37367	+	25.7715i	0.307822	+	0.947379i
$741$	4.64119	−	14.2841i	0.170498	−	0.524740i
$742$	7.81522	+	5.67809i	0.286906	+	0.208449i
$743$	5.57280	+	4.04888i	0.204446	+	0.148539i	0.685297	−	0.728263i	$-0.259672\pi$
$743$	5.57280	+	4.04888i	0.204446	+	0.148539i	−0.480851	+	0.876802i	$0.659672\pi$
$744$	18.3027	−	56.3298i	0.671008	−	2.06515i
$745$	−5.93960	−	18.2802i	−0.217610	−	0.669735i
$746$	−57.5060	+	41.7806i	−2.10545	+	1.52970i
$747$	−0.203338			−0.00743976
$748$	2.73017	−	16.7800i	0.0998249	−	0.613536i
$749$	40.5265			1.48081
$750$	0.716346	−	0.520456i	0.0261573	−	0.0190044i
$751$	12.4847	+	38.4239i	0.455572	+	1.40211i	0.870462	+	0.492236i	$0.163820\pi$
$751$	12.4847	+	38.4239i	0.455572	+	1.40211i	−0.414889	+	0.909872i	$0.636180\pi$
$752$	20.3305	−	62.5709i	0.741378	−	2.28173i
$753$	−16.0985	−	11.6963i	−0.586663	−	0.426236i
$754$	58.5051	+	42.5064i	2.13063	+	1.54799i
$755$	8.50160	−	26.1652i	0.309405	−	0.952250i
$756$	3.20454	+	9.86257i	0.116548	+	0.358698i
$757$	−31.6738	+	23.0124i	−1.15120	+	0.836399i	−0.988641	−	0.150299i	$-0.951976\pi$
$757$	−31.6738	+	23.0124i	−1.15120	+	0.836399i	−0.162564	+	0.986698i	$0.551976\pi$
$758$	−96.3968			−3.50129
$759$	23.6810	+	12.1920i	0.859567	+	0.442541i
$760$	132.327			4.79999
$761$	18.6798	−	13.5717i	0.677143	−	0.491973i	−0.195266	−	0.980750i	$-0.562557\pi$
$761$	18.6798	−	13.5717i	0.677143	−	0.491973i	0.872409	+	0.488777i	$0.162557\pi$
$762$	4.46541	+	13.7431i	0.161765	+	0.497861i
$763$	2.70355	−	8.32067i	0.0978751	−	0.301229i
$764$	−28.4129	−	20.6432i	−1.02794	−	0.746843i
$765$	2.54481	+	1.84891i	0.0920079	+	0.0668476i
$766$	−7.17223	+	22.0739i	−0.259143	+	0.797561i
$767$	−9.47540	−	29.1623i	−0.342137	−	1.05299i
$768$	−4.28297	+	3.11176i	−0.154549	+	0.112286i
$769$	−22.4095			−0.808106			−0.404053	−	0.914736i	$-0.632399\pi$
$769$	−22.4095			−0.808106			−0.404053	+	0.914736i	$0.632399\pi$
$770$	25.3669	+	50.3080i	0.914160	+	1.81297i
$771$	−26.8191			−0.965867
$772$	58.5142	−	42.5130i	2.10597	−	1.53008i
$773$	−9.11989	−	28.0681i	−0.328020	−	1.00954i	−0.970059	−	0.242869i	$-0.921911\pi$
$773$	−9.11989	−	28.0681i	−0.328020	−	1.00954i	0.642039	−	0.766672i	$-0.278089\pi$
$774$	9.02453	−	27.7747i	0.324380	−	0.998339i
$775$	28.1068	+	20.4208i	1.00962	+	0.733535i
$776$	7.62297	+	5.53841i	0.273649	+	0.198817i
$777$	−1.05067	+	3.23362i	−0.0376924	+	0.116005i
$778$	22.9413	+	70.6060i	0.822485	+	2.53135i
$779$	25.1866	−	18.2992i	0.902405	−	0.655636i
$780$	−48.0347			−1.71992
$781$	13.5607	−	2.08930i	0.485240	−	0.0747612i
$782$	21.4378			0.766612
$783$	−7.35674	+	5.34499i	−0.262909	+	0.191014i
$784$	−10.8007	−	33.2411i	−0.385739	−	1.18718i
$785$	7.50379	−	23.0943i	0.267822	−	0.824270i
$786$	−3.18603	−	2.31479i	−0.113642	−	0.0825657i
$787$	34.5247	+	25.0837i	1.23067	+	0.894136i	0.996940	−	0.0781652i	$-0.0249062\pi$
$787$	34.5247	+	25.0837i	1.23067	+	0.894136i	0.233732	+	0.972301i	$0.424906\pi$
$788$	38.5377	−	118.607i	1.37285	−	4.22519i
$789$	−2.43461	−	7.49297i	−0.0866746	−	0.266757i
$790$	68.1958	−	49.5471i	2.42630	−	1.76281i
$791$	5.36929			0.190910
$792$	−27.3523	+	4.21418i	−0.971921	+	0.149744i
$793$	−33.0927			−1.17515
$794$	70.7544	−	51.4061i	2.51098	−	1.82433i
$795$	−1.73872	−	5.35122i	−0.0616660	−	0.189788i
$796$	−38.2831	+	117.823i	−1.35691	+	4.17614i
$797$	−14.7719	−	10.7324i	−0.523247	−	0.380161i	0.294579	−	0.955627i	$-0.404821\pi$
$797$	−14.7719	−	10.7324i	−0.523247	−	0.380161i	−0.817826	+	0.575466i	$0.804821\pi$
$798$	22.0267	+	16.0034i	0.779738	+	0.566513i
$799$	1.69099	−	5.20432i	0.0598228	−	0.184116i
$800$	−23.3010	−	71.7132i	−0.823815	−	2.53544i
$801$	4.73541	−	3.44048i	0.167318	−	0.121563i
$802$	−75.9004			−2.68014
$803$	8.49341	+	16.8442i	0.299726	+	0.594420i
$804$	18.9341			0.667756
$805$	−41.3458	+	30.0395i	−1.45725	+	1.05875i
$806$	17.4434	+	53.6852i	0.614417	+	1.89098i
$807$	−3.87242	+	11.9181i	−0.136316	+	0.419536i
$808$	−40.4916	−	29.4189i	−1.42449	−	1.03495i
$809$	8.17078	+	5.93642i	0.287269	+	0.208713i	0.722082	−	0.691808i	$-0.243185\pi$
$809$	8.17078	+	5.93642i	0.287269	+	0.208713i	−0.434812	+	0.900521i	$0.643185\pi$
$810$	2.59477	−	7.98589i	0.0911711	−	0.280596i
$811$	−3.91755	−	12.0570i	−0.137564	−	0.423378i	0.858416	−	0.512954i	$-0.171449\pi$
$811$	−3.91755	−	12.0570i	−0.137564	−	0.423378i	−0.995980	+	0.0895760i	$0.971449\pi$
$812$	−76.2903	+	55.4282i	−2.67727	+	1.94515i
$813$	19.4249			0.681260
$814$	−13.2290	−	6.81083i	−0.463676	−	0.238719i
$815$	−10.9092			−0.382131
$816$	−9.72672	+	7.06688i	−0.340503	+	0.247390i
$817$	−17.0437	−	52.4550i	−0.596283	−	1.83517i
$818$	15.9189	−	48.9933i	0.556590	−	1.71301i
$819$	−4.87598	−	3.54261i	−0.170381	−	0.123789i
$820$	−80.5525	−	58.5248i	−2.81301	−	2.04377i
$821$	6.75404	−	20.7868i	0.235718	−	0.725465i	−0.761308	−	0.648391i	$-0.775442\pi$
$821$	6.75404	−	20.7868i	0.235718	−	0.725465i	0.997025	−	0.0770738i	$-0.0245577\pi$
$822$	−2.44840	−	7.53539i	−0.0853976	−	0.262827i
$823$	−32.9573	+	23.9449i	−1.14882	+	0.834666i	−0.988323	−	0.152371i	$-0.951309\pi$
$823$	−32.9573	+	23.9449i	−1.14882	+	0.834666i	−0.160496	+	0.987037i	$0.551309\pi$
$824$	35.0162			1.21985
$825$	2.60696	−	16.0227i	0.0907626	−	0.557838i
$826$	55.5854			1.93406
$827$	−34.7076	+	25.2165i	−1.20690	+	0.876865i	−0.994946	−	0.100415i	$-0.967983\pi$
$827$	−34.7076	+	25.2165i	−1.20690	+	0.876865i	−0.211955	+	0.977279i	$0.567983\pi$
$828$	−12.7207	−	39.1503i	−0.442075	−	1.36057i
$829$	−6.50079	+	20.0074i	−0.225782	+	0.694885i	0.772429	+	0.635101i	$0.219041\pi$
$829$	−6.50079	+	20.0074i	−0.225782	+	0.694885i	−0.998211	+	0.0597846i	$0.980959\pi$
$830$	1.38132	+	1.00359i	0.0479463	+	0.0348350i
$831$	−14.9848	−	10.8871i	−0.519817	−	0.377669i
$832$	15.7226	−	48.3890i	0.545081	−	1.67759i
$833$	−0.898344	−	2.76482i	−0.0311258	−	0.0957953i
$834$	39.8704	−	28.9676i	1.38060	−	1.00306i
$835$	−55.2979			−1.91366
$836$	−60.8595	+	60.3491i	−2.10487	+	2.08722i
$837$	−7.09807			−0.245345
$838$	2.62923	−	1.91025i	0.0908253	−	0.0659884i
$839$	−16.9555	−	52.1836i	−0.585368	−	1.80158i	−0.597787	−	0.801655i	$-0.703953\pi$
$839$	−16.9555	−	52.1836i	−0.585368	−	1.80158i	0.0124194	−	0.999923i	$-0.496047\pi$
$840$	16.4092	−	50.5023i	0.566171	−	1.74250i
$841$	−43.4366	−	31.5585i	−1.49781	−	1.08822i
$842$	16.8915	+	12.2724i	0.582119	+	0.422934i
$843$	−2.12975	+	6.55471i	−0.0733526	+	0.225756i
$844$	−13.7914	−	42.4455i	−0.474719	−	1.46103i
$845$	−10.4969	+	7.62641i	−0.361103	+	0.262357i
$846$	−14.6075			−0.502217
$847$	−21.1061	−	7.05488i	−0.725216	−	0.242408i
$848$	21.5059			0.738515
$849$	2.95876	−	2.14966i	0.101544	−	0.0737762i
$850$	−4.03752	−	12.4262i	−0.138486	−	0.426215i
$851$	4.17070	−	12.8361i	0.142970	−	0.440016i
$852$	−17.1556	−	12.4643i	−0.587742	−	0.427019i
$853$	−6.02472	−	4.37722i	−0.206283	−	0.149873i	0.479848	−	0.877352i	$-0.340692\pi$
$853$	−6.02472	−	4.37722i	−0.206283	−	0.149873i	−0.686130	+	0.727479i	$0.740692\pi$
$854$	18.5379	−	57.0537i	0.634353	−	1.95234i
$855$	−4.90047	−	15.0821i	−0.167593	−	0.515797i
$856$	135.230	−	98.2503i	4.62207	−	3.35813i
$857$	−24.2942			−0.829873			−0.414936	−	0.909850i	$-0.636196\pi$
$857$	−24.2942			−0.829873			−0.414936	+	0.909850i	$0.636196\pi$
$858$	18.7288	−	18.5718i	0.639392	−	0.634029i
$859$	27.2765			0.930661			0.465330	−	0.885137i	$-0.345936\pi$
$859$	27.2765			0.930661			0.465330	+	0.885137i	$0.345936\pi$
$860$	−142.708	+	103.683i	−4.86629	+	3.53557i
$861$	−3.86058	−	11.8816i	−0.131568	−	0.404925i
$862$	−3.87960	+	11.9402i	−0.132140	+	0.406684i
$863$	19.5371	+	14.1945i	0.665051	+	0.483188i	0.868365	−	0.495926i	$-0.165171\pi$
$863$	19.5371	+	14.1945i	0.665051	+	0.483188i	−0.203314	+	0.979114i	$0.565171\pi$
$864$	12.4634	+	9.05521i	0.424014	+	0.308064i
$865$	17.8786	−	55.0247i	0.607891	−	1.87090i
$866$	11.2222	+	34.5383i	0.381345	+	1.17366i
$867$	−0.809017	+	0.587785i	−0.0274757	+	0.0199622i
$868$	−73.6079			−2.49841
$869$	−5.34692	+	32.8628i	−0.181382	+	1.11480i
$870$	76.3564			2.58872
$871$	−8.90274	+	6.46822i	−0.301658	+	0.219167i
$872$	−11.1509	−	34.3190i	−0.377618	−	1.16219i
$873$	0.348945	−	1.07394i	0.0118100	−	0.0363475i
$874$	−87.4369	−	63.5266i	−2.95760	−	2.14882i
$875$	−0.542899	−	0.394439i	−0.0183533	−	0.0133345i
$876$	9.00944	−	27.7282i	0.304401	−	0.936850i
$877$	−4.33776	−	13.3503i	−0.146476	−	0.450807i	0.850722	−	0.525616i	$-0.176165\pi$
$877$	−4.33776	−	13.3503i	−0.146476	−	0.450807i	−0.997198	+	0.0748095i	$0.976165\pi$
$878$	−7.59106	+	5.51523i	−0.256186	+	0.186130i
$879$	8.74977			0.295122
$880$	111.519	+	57.4144i	3.75929	+	1.93544i
$881$	17.8403			0.601057			0.300528	−	0.953773i	$-0.402837\pi$
$881$	17.8403			0.601057			0.300528	+	0.953773i	$0.402837\pi$
$882$	−6.27823	+	4.56140i	−0.211399	+	0.153590i
$883$	−5.86687	−	18.0564i	−0.197436	−	0.607645i	−0.999940	−	0.0109979i	$-0.996499\pi$
$883$	−5.86687	−	18.0564i	−0.197436	−	0.607645i	0.802504	−	0.596647i	$-0.203501\pi$
$884$	4.71889	−	14.5232i	0.158713	−	0.488470i
$885$	−26.1928	−	19.0302i	−0.880461	−	0.639693i
$886$	−47.8571	−	34.7702i	−1.60779	−	1.16813i
$887$	3.96221	−	12.1944i	0.133038	−	0.409449i	−0.862242	−	0.506497i	$-0.830940\pi$
$887$	3.96221	−	12.1944i	0.133038	−	0.409449i	0.995280	+	0.0970481i	$0.0309401\pi$
$888$	4.33352	+	13.3372i	0.145423	+	0.447567i
$889$	8.85998	−	6.43715i	0.297154	−	0.215895i
$890$	−49.1493			−1.64749
$891$	1.49326	+	2.96145i	0.0500260	+	0.0992123i
$892$	15.3568			0.514183
$893$	−22.3189	+	16.2156i	−0.746874	+	0.542635i
$894$	−5.04056	−	15.5132i	−0.168581	−	0.518840i
$895$	1.09519	−	3.37064i	0.0366081	−	0.112668i
$896$	24.1888	+	17.5742i	0.808091	+	0.587112i
$897$	19.3556	+	14.0627i	0.646265	+	0.469539i
$898$	−24.7494	+	76.1707i	−0.825897	+	2.54185i
$899$	−19.9458	−	61.3867i	−0.665228	−	2.04736i
$900$	−20.2973	+	14.7469i	−0.676578	+	0.491562i
$901$	1.78875			0.0595918
$902$	54.0351	−	8.32522i	1.79917	−	0.277199i
$903$	−22.1329			−0.736537
$904$	17.9164	−	13.0170i	0.595891	−	0.432940i
$905$	11.2675	+	34.6777i	0.374544	+	1.15273i
$906$	7.21476	−	22.2047i	0.239694	−	0.737703i
$907$	3.61141	+	2.62384i	0.119915	+	0.0871232i	0.646126	−	0.763231i	$-0.276388\pi$
$907$	3.61141	+	2.62384i	0.119915	+	0.0871232i	−0.526211	+	0.850354i	$0.676388\pi$
$908$	65.1846	+	47.3594i	2.16323	+	1.57168i
$909$	−1.85352	+	5.70456i	−0.0614775	+	0.189208i
$910$	15.6388	+	48.1313i	0.518422	+	1.59554i
$911$	40.6313	−	29.5204i	1.34618	−	0.978054i	0.346983	−	0.937871i	$-0.387206\pi$
$911$	40.6313	−	29.5204i	1.34618	−	0.978054i	0.999192	−	0.0401821i	$-0.0127938\pi$
$912$	60.6131			2.00710
$913$	−0.666533	+	0.102693i	−0.0220590	+	0.00339864i
$914$	3.47484			0.114937
$915$	−28.2682	+	20.5381i	−0.934519	+	0.678967i
$916$	−8.61850	−	26.5250i	−0.284763	−	0.876411i
$917$	−0.922297	+	2.83854i	−0.0304569	+	0.0937368i
$918$	2.15962	+	1.56905i	0.0712780	+	0.0517865i
$919$	−6.26381	−	4.55092i	−0.206624	−	0.150121i	0.479661	−	0.877454i	$-0.340760\pi$
$919$	−6.26381	−	4.55092i	−0.206624	−	0.150121i	−0.686285	+	0.727333i	$0.740760\pi$
$920$	−65.1376	+	200.473i	−2.14752	+	6.60940i
$921$	4.07241	+	12.5336i	0.134190	+	0.412996i
$922$	39.6483	−	28.8062i	1.30575	−	0.948681i
$923$	12.3245			0.405666
$924$	15.4853	+	30.7106i	0.509428	+	1.01030i
$925$	−8.22583			−0.270463
$926$	−57.1367	+	41.5123i	−1.87763	+	1.36418i
$927$	−1.29676	−	3.99102i	−0.0425913	−	0.131082i
$928$	−43.2902	+	133.234i	−1.42107	+	4.37361i
$929$	−42.8331	−	31.1201i	−1.40531	−	1.02102i	−0.993984	−	0.109529i	$-0.965066\pi$
$929$	−42.8331	−	31.1201i	−1.40531	−	1.02102i	−0.411326	−	0.911488i	$-0.634934\pi$
$930$	48.2187	+	35.0329i	1.58115	+	1.14877i
$931$	−4.52898	+	13.9388i	−0.148431	+	0.456825i
$932$	−25.8995	−	79.7105i	−0.848366	−	2.61100i
$933$	15.0688	−	10.9481i	0.493330	−	0.358425i
$934$	74.6247			2.44179
$935$	9.27553	+	4.77542i	0.303342	+	0.156173i
$936$	−24.8588			−0.812536
$937$	12.8756	−	9.35470i	0.420629	−	0.305605i	−0.357262	−	0.934004i	$-0.616290\pi$
$937$	12.8756	−	9.35470i	0.420629	−	0.305605i	0.777891	+	0.628400i	$0.216290\pi$
$938$	−6.16445	−	18.9722i	−0.201276	−	0.619465i
$939$	−2.29155	+	7.05268i	−0.0747820	+	0.230155i
$940$	71.3808	+	51.8612i	2.32819	+	1.69153i
$941$	0.486353	+	0.353356i	0.0158547	+	0.0115191i	0.595684	−	0.803219i	$-0.296881\pi$
$941$	0.486353	+	0.353356i	0.0158547	+	0.0115191i	−0.579830	+	0.814738i	$0.696881\pi$
$942$	6.36798	−	19.5986i	0.207480	−	0.638558i
$943$	15.3249	+	47.1651i	0.499047	+	1.53591i
$944$	100.114	−	72.7367i	3.25842	−	2.36738i
$945$	−6.36375			−0.207013
$946$	15.5548	−	95.6016i	0.505729	−	3.10827i
$947$	0.962379			0.0312731			0.0156366	−	0.999878i	$-0.495023\pi$
$947$	0.962379			0.0312731			0.0156366	+	0.999878i	$0.495023\pi$
$948$	41.6302	−	30.2461i	1.35209	−	0.982348i
$949$	5.23623	+	16.1155i	0.169975	+	0.523130i
$950$	−20.3550	+	62.6464i	−0.660405	+	2.03252i
$951$	22.1371	+	16.0835i	0.717844	+	0.521544i
$952$	13.6573	+	9.92260i	0.442635	+	0.321593i
$953$	8.94869	−	27.5412i	0.289877	−	0.892148i	−0.695018	−	0.718992i	$-0.744604\pi$
$953$	8.94869	−	27.5412i	0.289877	−	0.892148i	0.984894	−	0.173156i	$-0.0553964\pi$
$954$	−1.47554	−	4.54124i	−0.0477723	−	0.147028i
$955$	17.4359	−	12.6679i	0.564213	−	0.409925i
$956$	−99.9842			−3.23372
$957$	−21.4156	+	21.2360i	−0.692268	+	0.686462i
$958$	−42.2953			−1.36650
$959$	−4.85795	+	3.52951i	−0.156871	+	0.113974i
$960$	−16.6009	−	51.0924i	−0.535792	−	1.64900i
$961$	5.98956	−	18.4340i	0.193212	−	0.594644i
$962$	−10.8127	−	7.85586i	−0.348614	−	0.253283i
$963$	−16.2062	−	11.7745i	−0.522238	−	0.379428i
$964$	−5.88020	+	18.0974i	−0.189388	+	0.582878i
$965$	13.7156	+	42.2123i	0.441521	+	1.35886i
$966$	−35.0875	+	25.4926i	−1.12892	+	0.820210i
$967$	13.6451			0.438797			0.219399	−	0.975635i	$-0.429591\pi$
$967$	13.6451			0.438797			0.219399	+	0.975635i	$0.429591\pi$
$968$	−87.5310	+	27.6277i	−2.81335	+	0.887988i
$969$	5.04148			0.161956
$970$	−7.67096	+	5.57328i	−0.246300	+	0.178947i
$971$	−6.90504	−	21.2515i	−0.221593	−	0.681994i	−0.998620	−	0.0525257i	$-0.983273\pi$
$971$	−6.90504	−	21.2515i	−0.221593	−	0.681994i	0.777026	−	0.629468i	$-0.216727\pi$
$972$	1.58398	−	4.87500i	0.0508063	−	0.156366i
$973$	−30.2167	−	21.9537i	−0.968703	−	0.703804i
$974$	14.6605	+	10.6515i	0.469754	+	0.341296i
$975$	4.50593	−	13.8678i	0.144305	−	0.444125i
$976$	−41.2699	−	127.016i	−1.32102	−	4.06568i
$977$	37.1132	−	26.9643i	1.18736	−	0.862666i	0.194375	−	0.980927i	$-0.437732\pi$
$977$	37.1132	−	26.9643i	1.18736	−	0.862666i	0.992982	+	0.118262i	$0.0377322\pi$
$978$	−9.25790			−0.296035
$979$	13.7849	−	13.6693i	0.440567	−	0.436871i
$980$	46.8734			1.49732
$981$	−3.49860	+	2.54188i	−0.111702	+	0.0811561i
$982$	6.97203	+	21.4577i	0.222486	+	0.684743i
$983$	−7.60433	+	23.4037i	−0.242541	+	0.746463i	0.753491	+	0.657459i	$0.228369\pi$
$983$	−7.60433	+	23.4037i	−0.242541	+	0.746463i	−0.996031	+	0.0890044i	$0.971631\pi$
$984$	−41.6873	−	30.2876i	−1.32894	−	0.965534i
$985$	61.9142	+	44.9833i	1.97275	+	1.43329i
$986$	−7.50118	+	23.0863i	−0.238886	+	0.735216i
$987$	3.42102	+	10.5288i	0.108892	+	0.335136i
$988$	−62.2835	+	45.2516i	−1.98150	+	1.43964i
$989$	87.8584			2.79373
$990$	4.47238	−	27.4878i	0.142142	−	0.873620i
$991$	9.20888			0.292530			0.146265	−	0.989245i	$-0.453275\pi$
$991$	9.20888			0.292530			0.146265	+	0.989245i	$0.453275\pi$
$992$	−88.4663	+	64.2745i	−2.80881	+	2.04072i
$993$	5.17250	+	15.9193i	0.164144	+	0.505185i
$994$	−6.90394	+	21.2481i	−0.218980	+	0.673950i
$995$	−61.5052	−	44.6862i	−1.94985	−	1.41665i
$996$	0.843229	+	0.612642i	0.0267187	+	0.0194123i
$997$	14.4828	−	44.5736i	0.458676	−	1.41166i	−0.408089	−	0.912942i	$-0.633805\pi$
$997$	14.4828	−	44.5736i	0.458676	−	1.41166i	0.866765	−	0.498717i	$-0.166195\pi$
$998$	2.53931	+	7.81518i	0.0803804	+	0.247385i
$999$	1.35964	−	0.987837i	0.0430172	−	0.0312538i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	561.2.m.d.256.6	yes	24
11.2	odd	10		6171.2.a.bl.1.12		12
11.4	even	5	inner	561.2.m.d.103.6	✓	24
11.9	even	5		6171.2.a.bk.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
561.2.m.d.103.6	✓	24	11.4	even	5	inner
561.2.m.d.256.6	yes	24	1.1	even	1	trivial
6171.2.a.bk.1.1		12	11.9	even	5
6171.2.a.bl.1.12		12	11.2	odd	10

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:	\( N \)	\(=\)	\( 561 = 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	561.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.15962 - 1.56905i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.58398 - 4.87500i) q^{4} +(2.54481 + 1.84891i) q^{5} +(2.15962 + 1.56905i) q^{6} +(0.625170 - 1.92407i) q^{7} +(-2.57854 - 7.93593i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(2.15962 - 1.56905i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.58398 - 4.87500i) q^{4} +(2.54481 + 1.84891i) q^{5} +(2.15962 + 1.56905i) q^{6} +(0.625170 - 1.92407i) q^{7} +(-2.57854 - 7.93593i) q^{8} +(-0.809017 + 0.587785i) q^{9} +8.39687 q^{10} +(-2.35506 + 2.33531i) q^{11} +5.12588 q^{12} +(-2.41016 + 1.75109i) q^{13} +(-1.66885 - 5.13619i) q^{14} +(-0.972032 + 2.99161i) q^{15} +(-9.72672 - 7.06688i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(-0.824901 + 2.53878i) q^{18} +(1.55790 + 4.79473i) q^{19} +(13.0444 - 9.47731i) q^{20} +2.02309 q^{21} +(-1.42181 + 8.73860i) q^{22} -8.03082 q^{23} +(6.75071 - 4.90468i) q^{24} +(1.51250 + 4.65499i) q^{25} +(-2.45748 + 7.56336i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-8.38960 - 6.09540i) q^{28} +(2.81003 - 8.64837i) q^{29} +(2.59477 + 7.98589i) q^{30} +(5.74246 - 4.17214i) q^{31} -15.4056 q^{32} +(-2.94877 - 1.51815i) q^{33} -2.66943 q^{34} +(5.14839 - 3.74052i) q^{35} +(1.58398 + 4.87500i) q^{36} +(-0.519337 + 1.59835i) q^{37} +(10.8877 + 7.91035i) q^{38} +(-2.41016 - 1.75109i) q^{39} +(8.11095 - 24.9629i) q^{40} +(-1.90826 - 5.87302i) q^{41} +(4.36910 - 3.17434i) q^{42} -10.9401 q^{43} +(7.65426 + 15.1800i) q^{44} -3.14556 q^{45} +(-17.3435 + 12.6008i) q^{46} +(1.69099 + 5.20432i) q^{47} +(3.71528 - 11.4344i) q^{48} +(2.35190 + 1.70875i) q^{49} +(10.5704 + 7.67981i) q^{50} +(0.309017 - 0.951057i) q^{51} +(4.71889 + 14.5232i) q^{52} +(-1.44713 + 1.05140i) q^{53} -2.66943 q^{54} +(-10.3110 + 1.58862i) q^{55} -16.8813 q^{56} +(-4.07864 + 2.96331i) q^{57} +(-7.50118 - 23.0863i) q^{58} +(-3.18060 + 9.78887i) q^{59} +(13.0444 + 9.47731i) q^{60} +(8.98670 + 6.52922i) q^{61} +(5.85520 - 18.0205i) q^{62} +(0.625170 + 1.92407i) q^{63} +(-13.8169 + 10.0385i) q^{64} -9.37102 q^{65} +(-8.75027 + 1.34816i) q^{66} +3.69383 q^{67} +(-4.14692 + 3.01292i) q^{68} +(-2.48166 - 7.63777i) q^{69} +(5.24947 - 16.1562i) q^{70} +(-3.34686 - 2.43164i) q^{71} +(6.75071 + 4.90468i) q^{72} +(1.75764 - 5.40946i) q^{73} +(1.38634 + 4.26670i) q^{74} +(-3.95977 + 2.87694i) q^{75} +25.8420 q^{76} +(3.02100 + 5.99128i) q^{77} -7.95258 q^{78} +(8.12157 - 5.90067i) q^{79} +(-11.6866 - 35.9677i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-13.3362 - 9.68931i) q^{82} +(0.164504 + 0.119519i) q^{83} +(3.20454 - 9.86257i) q^{84} +(-0.972032 - 2.99161i) q^{85} +(-23.6265 + 17.1657i) q^{86} +9.09343 q^{87} +(24.6055 + 12.6679i) q^{88} -5.85329 q^{89} +(-6.79321 + 4.93555i) q^{90} +(1.86246 + 5.73206i) q^{91} +(-12.7207 + 39.1503i) q^{92} +(5.74246 + 4.17214i) q^{93} +(11.8177 + 8.58609i) q^{94} +(-4.90047 + 15.0821i) q^{95} +(-4.76061 - 14.6516i) q^{96} +(-0.913551 + 0.663733i) q^{97} +7.76032 q^{98} +(0.532625 - 3.27358i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9	\( 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9} + 16 q^{10} - 7 q^{11} + 18 q^{12} + 6 q^{13} - 6 q^{14} + 7 q^{15} - 23 q^{16} - 6 q^{17} - 2 q^{18} + 6 q^{19} + 3 q^{20} - 10 q^{21} + 23 q^{22} - 78 q^{23} + 10 q^{24} + q^{25} + 10 q^{26} - 6 q^{27} - 13 q^{28} + 20 q^{29} + 11 q^{30} + 5 q^{31} - 22 q^{32} - 2 q^{33} - 2 q^{34} + 29 q^{35} - 7 q^{36} - 10 q^{37} + 2 q^{38} + 6 q^{39} + 44 q^{40} - 16 q^{41} + 19 q^{42} - 36 q^{43} + 3 q^{44} - 28 q^{45} + 23 q^{46} + 19 q^{47} + 12 q^{48} - 15 q^{49} + 34 q^{50} - 6 q^{51} - 6 q^{52} - 5 q^{53} - 2 q^{54} + 24 q^{55} - 50 q^{56} - 9 q^{57} - 79 q^{58} + 34 q^{59} + 3 q^{60} - 14 q^{61} + 36 q^{62} + 5 q^{63} - 20 q^{64} + 6 q^{65} + 3 q^{66} - 18 q^{67} - 2 q^{68} + 7 q^{69} + 46 q^{70} - 8 q^{71} + 10 q^{72} + 7 q^{73} + 47 q^{74} - 9 q^{75} + 58 q^{76} + 43 q^{77} - 50 q^{78} + 14 q^{79} - 51 q^{80} - 6 q^{81} - 88 q^{82} - 47 q^{83} + 22 q^{84} + 7 q^{85} - 13 q^{86} + 20 q^{87} + 115 q^{88} - 124 q^{89} - 19 q^{90} + 10 q^{91} - 19 q^{92} + 5 q^{93} + 28 q^{94} - 13 q^{95} - 27 q^{96} - 30 q^{97} - 14 q^{98} - 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9 + 16 * q^10 - 7 * q^11 + 18 * q^12 + 6 * q^13 - 6 * q^14 + 7 * q^15 - 23 * q^16 - 6 * q^17 - 2 * q^18 + 6 * q^19 + 3 * q^20 - 10 * q^21 + 23 * q^22 - 78 * q^23 + 10 * q^24 + q^25 + 10 * q^26 - 6 * q^27 - 13 * q^28 + 20 * q^29 + 11 * q^30 + 5 * q^31 - 22 * q^32 - 2 * q^33 - 2 * q^34 + 29 * q^35 - 7 * q^36 - 10 * q^37 + 2 * q^38 + 6 * q^39 + 44 * q^40 - 16 * q^41 + 19 * q^42 - 36 * q^43 + 3 * q^44 - 28 * q^45 + 23 * q^46 + 19 * q^47 + 12 * q^48 - 15 * q^49 + 34 * q^50 - 6 * q^51 - 6 * q^52 - 5 * q^53 - 2 * q^54 + 24 * q^55 - 50 * q^56 - 9 * q^57 - 79 * q^58 + 34 * q^59 + 3 * q^60 - 14 * q^61 + 36 * q^62 + 5 * q^63 - 20 * q^64 + 6 * q^65 + 3 * q^66 - 18 * q^67 - 2 * q^68 + 7 * q^69 + 46 * q^70 - 8 * q^71 + 10 * q^72 + 7 * q^73 + 47 * q^74 - 9 * q^75 + 58 * q^76 + 43 * q^77 - 50 * q^78 + 14 * q^79 - 51 * q^80 - 6 * q^81 - 88 * q^82 - 47 * q^83 + 22 * q^84 + 7 * q^85 - 13 * q^86 + 20 * q^87 + 115 * q^88 - 124 * q^89 - 19 * q^90 + 10 * q^91 - 19 * q^92 + 5 * q^93 + 28 * q^94 - 13 * q^95 - 27 * q^96 - 30 * q^97 - 14 * q^98 - 7 * q^99

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