LMFDB - Embedded newform 1110.2.bb.e.1009.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(1009,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1110.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.bb (of order $6$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1009.11
Character	$\chi$	$=$	1110.1009
Dual form			1110.2.bb.e.1099.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.38006 + 1.75939i) q^{5} -1.00000 q^{6} +(-3.97576 + 2.29541i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.38006 + 1.75939i) q^{5} -1.00000 q^{6} +(-3.97576 + 2.29541i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.315474 + 2.21370i) q^{10} +5.56277 q^{11} +(-0.866025 - 0.500000i) q^{12} +(-3.53699 + 2.04208i) q^{13} -4.59082 q^{14} +(-2.07486 - 0.833642i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.26674 + 2.46340i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-0.172303 - 0.298438i) q^{19} +(-0.833642 + 2.07486i) q^{20} +(2.29541 - 3.97576i) q^{21} +(4.81750 + 2.78139i) q^{22} -6.31668i q^{23} +(-0.500000 - 0.866025i) q^{24} +(-1.19087 + 4.85611i) q^{25} -4.08416 q^{26} +1.00000i q^{27} +(-3.97576 - 2.29541i) q^{28} -6.64978 q^{29} +(-1.38006 - 1.75939i) q^{30} -9.30784 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-4.81750 + 2.78139i) q^{33} +(2.46340 + 4.26674i) q^{34} +(-9.52530 - 3.82710i) q^{35} +1.00000 q^{36} +(-5.45808 + 2.68502i) q^{37} -0.344607i q^{38} +(2.04208 - 3.53699i) q^{39} +(-1.75939 + 1.38006i) q^{40} +(1.51747 + 2.62834i) q^{41} +(3.97576 - 2.29541i) q^{42} +2.83589i q^{43} +(2.78139 + 4.81750i) q^{44} +(2.21370 - 0.315474i) q^{45} +(3.15834 - 5.47041i) q^{46} -0.790878i q^{47} -1.00000i q^{48} +(7.03780 - 12.1898i) q^{49} +(-3.45938 + 3.61008i) q^{50} -4.92681 q^{51} +(-3.53699 - 2.04208i) q^{52} +(7.59038 + 4.38231i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(7.67696 + 9.78706i) q^{55} +(-2.29541 - 3.97576i) q^{56} +(0.298438 + 0.172303i) q^{57} +(-5.75888 - 3.32489i) q^{58} +(2.46374 - 4.26732i) q^{59} +(-0.315474 - 2.21370i) q^{60} +(1.03641 + 1.79512i) q^{61} +(-8.06082 - 4.65392i) q^{62} +4.59082i q^{63} -1.00000 q^{64} +(-8.47406 - 3.40473i) q^{65} -5.56277 q^{66} +(7.44037 - 4.29570i) q^{67} +4.92681i q^{68} +(3.15834 + 5.47041i) q^{69} +(-6.33560 - 8.07701i) q^{70} +(5.76273 + 9.98134i) q^{71} +(0.866025 + 0.500000i) q^{72} -4.49320i q^{73} +(-6.06935 - 0.403742i) q^{74} +(-1.39673 - 4.80095i) q^{75} +(0.172303 - 0.298438i) q^{76} +(-22.1163 + 12.7688i) q^{77} +(3.53699 - 2.04208i) q^{78} +(-4.03949 - 6.99660i) q^{79} +(-2.21370 + 0.315474i) q^{80} +(-0.500000 - 0.866025i) q^{81} +3.03495i q^{82} +(-8.26772 - 4.77337i) q^{83} +4.59082 q^{84} +(1.55428 + 10.9065i) q^{85} +(-1.41795 + 2.45596i) q^{86} +(5.75888 - 3.32489i) q^{87} +5.56277i q^{88} +(-7.77936 + 13.4742i) q^{89} +(2.07486 + 0.833642i) q^{90} +(9.37482 - 16.2377i) q^{91} +(5.47041 - 3.15834i) q^{92} +(8.06082 - 4.65392i) q^{93} +(0.395439 - 0.684920i) q^{94} +(0.287279 - 0.715011i) q^{95} +(0.500000 - 0.866025i) q^{96} +10.8823i q^{97} +(12.1898 - 7.03780i) q^{98} +(2.78139 - 4.81750i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9}+O(q^{10}) $ 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9	$ 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9} + 24 q^{14} - 20 q^{16} - 14 q^{19} - 2 q^{20} - 12 q^{21} - 20 q^{24} - 2 q^{25} - 24 q^{26} + 12 q^{29} - 2 q^{30} - 40 q^{31} + 10 q^{34} - 2 q^{35} + 40 q^{36} + 12 q^{39} + 20 q^{41} + 4 q^{45} + 2 q^{46} + 28 q^{49} + 12 q^{50} - 20 q^{51} - 20 q^{54} + 32 q^{55} + 12 q^{56} - 40 q^{59} + 12 q^{61} - 40 q^{64} + 2 q^{65} + 2 q^{69} - 22 q^{70} + 12 q^{71} - 30 q^{74} - 24 q^{75} + 14 q^{76} - 24 q^{79} - 4 q^{80} - 20 q^{81} - 24 q^{84} + 40 q^{85} - 4 q^{86} - 34 q^{89} - 4 q^{91} - 8 q^{94} + 6 q^{95} + 20 q^{96}+O(q^{100}) $ 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9 + 24 * q^14 - 20 * q^16 - 14 * q^19 - 2 * q^20 - 12 * q^21 - 20 * q^24 - 2 * q^25 - 24 * q^26 + 12 * q^29 - 2 * q^30 - 40 * q^31 + 10 * q^34 - 2 * q^35 + 40 * q^36 + 12 * q^39 + 20 * q^41 + 4 * q^45 + 2 * q^46 + 28 * q^49 + 12 * q^50 - 20 * q^51 - 20 * q^54 + 32 * q^55 + 12 * q^56 - 40 * q^59 + 12 * q^61 - 40 * q^64 + 2 * q^65 + 2 * q^69 - 22 * q^70 + 12 * q^71 - 30 * q^74 - 24 * q^75 + 14 * q^76 - 24 * q^79 - 4 * q^80 - 20 * q^81 - 24 * q^84 + 40 * q^85 - 4 * q^86 - 34 * q^89 - 4 * q^91 - 8 * q^94 + 6 * q^95 + 20 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.38006	+	1.75939i	0.617181	+	0.786821i
$5$	1.38006	+	1.75939i	0.617181	+	0.786821i
$6$	−1.00000			−0.408248
$7$	−3.97576	+	2.29541i	−1.50270	+	0.867583i	−0.502702	+	0.864460i	$0.667661\pi$
$7$	−3.97576	+	2.29541i	−1.50270	+	0.867583i	−0.999995	+	0.00312296i	$0.999006\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.315474	+	2.21370i	0.0997617	+	0.700034i
$11$	5.56277			1.67724			0.838620	−	0.544717i	$-0.183363\pi$
$11$	5.56277			1.67724			0.838620	+	0.544717i	$0.183363\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	−3.53699	+	2.04208i	−0.980984	+	0.566371i	−0.902567	−	0.430549i	$-0.858320\pi$
$13$	−3.53699	+	2.04208i	−0.980984	+	0.566371i	−0.0784168	+	0.996921i	$0.524986\pi$
$14$	−4.59082			−1.22695
$15$	−2.07486	−	0.833642i	−0.535726	−	0.215246i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.26674	+	2.46340i	1.03484	+	0.597463i	0.918366	−	0.395731i	$-0.129509\pi$
$17$	4.26674	+	2.46340i	1.03484	+	0.597463i	0.116470	+	0.993194i	$0.462842\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−0.172303	−	0.298438i	−0.0395291	−	0.0684664i	0.845584	−	0.533842i	$-0.179252\pi$
$19$	−0.172303	−	0.298438i	−0.0395291	−	0.0684664i	−0.885113	+	0.465376i	$0.845919\pi$
$20$	−0.833642	+	2.07486i	−0.186408	+	0.463953i
$21$	2.29541	−	3.97576i	0.500899	−	0.867583i
$22$	4.81750	+	2.78139i	1.02710	+	0.592994i
$23$		−	6.31668i		−	1.31712i	−0.752529	−	0.658560i	$-0.771166\pi$
$23$		−	6.31668i		−	1.31712i	0.752529	−	0.658560i	$-0.228834\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−1.19087	+	4.85611i	−0.238174	+	0.971222i
$26$	−4.08416			−0.800970
$27$			1.00000i			0.192450i
$28$	−3.97576	−	2.29541i	−0.751349	−	0.433791i
$29$	−6.64978			−1.23483			−0.617416	−	0.786636i	$-0.711821\pi$
$29$	−6.64978			−1.23483			−0.617416	+	0.786636i	$0.711821\pi$
$30$	−1.38006	−	1.75939i	−0.251963	−	0.321218i
$31$	−9.30784			−1.67174			−0.835868	−	0.548930i	$-0.815035\pi$
$31$	−9.30784			−1.67174			−0.835868	+	0.548930i	$0.815035\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−4.81750	+	2.78139i	−0.838620	+	0.484177i
$34$	2.46340	+	4.26674i	0.422470	+	0.731740i
$35$	−9.52530	−	3.82710i	−1.61007	−	0.646898i
$36$	1.00000			0.166667
$37$	−5.45808	+	2.68502i	−0.897303	+	0.441415i
$37$	−5.45808	+	2.68502i	−0.897303	+	0.441415i
$38$		−	0.344607i		−	0.0559026i
$39$	2.04208	−	3.53699i	0.326995	−	0.566371i
$40$	−1.75939	+	1.38006i	−0.278183	+	0.218207i
$41$	1.51747	+	2.62834i	0.236989	+	0.410478i	0.959849	−	0.280517i	$-0.0905060\pi$
$41$	1.51747	+	2.62834i	0.236989	+	0.410478i	−0.722860	+	0.690995i	$0.757173\pi$
$42$	3.97576	−	2.29541i	0.613474	−	0.354189i
$43$			2.83589i			0.432470i	0.976341	+	0.216235i	$0.0693777\pi$
$43$			2.83589i			0.432470i	−0.976341	+	0.216235i	$0.930622\pi$
$44$	2.78139	+	4.81750i	0.419310	+	0.726266i
$45$	2.21370	−	0.315474i	0.329999	−	0.0470281i
$46$	3.15834	−	5.47041i	0.465672	−	0.806567i
$47$		−	0.790878i		−	0.115361i	−0.998335	−	0.0576807i	$-0.981629\pi$
$47$		−	0.790878i		−	0.115361i	0.998335	−	0.0576807i	$-0.0183705\pi$
$48$		−	1.00000i		−	0.144338i
$49$	7.03780	−	12.1898i	1.00540	−	1.74140i
$50$	−3.45938	+	3.61008i	−0.489230	+	0.510543i
$51$	−4.92681			−0.689891
$52$	−3.53699	−	2.04208i	−0.490492	−	0.283186i
$53$	7.59038	+	4.38231i	1.04262	+	0.601956i	0.920574	−	0.390568i	$-0.127721\pi$
$53$	7.59038	+	4.38231i	1.04262	+	0.601956i	0.122045	+	0.992525i	$0.461055\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	7.67696	+	9.78706i	1.03516	+	1.31969i
$56$	−2.29541	−	3.97576i	−0.306737	−	0.531284i
$57$	0.298438	+	0.172303i	0.0395291	+	0.0228221i
$58$	−5.75888	−	3.32489i	−0.756178	−	0.436579i
$59$	2.46374	−	4.26732i	0.320751	−	0.555558i	−0.659892	−	0.751361i	$-0.729398\pi$
$59$	2.46374	−	4.26732i	0.320751	−	0.555558i	0.980643	+	0.195803i	$0.0627312\pi$
$60$	−0.315474	−	2.21370i	−0.0407275	−	0.285788i
$61$	1.03641	+	1.79512i	0.132699	+	0.229841i	0.924716	−	0.380658i	$-0.124302\pi$
$61$	1.03641	+	1.79512i	0.132699	+	0.229841i	−0.792017	+	0.610499i	$0.790969\pi$
$62$	−8.06082	−	4.65392i	−1.02373	−	0.591048i
$63$			4.59082i			0.578388i
$64$	−1.00000			−0.125000
$65$	−8.47406	−	3.40473i	−1.05108	−	0.422305i
$66$	−5.56277			−0.684730
$67$	7.44037	−	4.29570i	0.908986	−	0.524804i	0.0288815	−	0.999583i	$-0.490805\pi$
$67$	7.44037	−	4.29570i	0.908986	−	0.524804i	0.880105	+	0.474779i	$0.157472\pi$
$68$			4.92681i			0.597463i
$69$	3.15834	+	5.47041i	0.380220	+	0.658560i
$70$	−6.33560	−	8.07701i	−0.757249	−	0.965388i
$71$	5.76273	+	9.98134i	0.683910	+	1.18457i	0.973778	+	0.227501i	$0.0730555\pi$
$71$	5.76273	+	9.98134i	0.683910	+	1.18457i	−0.289867	+	0.957067i	$0.593611\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$		−	4.49320i		−	0.525889i	−0.964811	−	0.262945i	$-0.915306\pi$
$73$		−	4.49320i		−	0.525889i	0.964811	−	0.262945i	$-0.0846937\pi$
$74$	−6.06935	−	0.403742i	−0.705547	−	0.0469340i
$75$	−1.39673	−	4.80095i	−0.161281	−	0.554366i
$76$	0.172303	−	0.298438i	0.0197646	−	0.0342332i
$77$	−22.1163	+	12.7688i	−2.52038	+	1.45514i
$78$	3.53699	−	2.04208i	0.400485	−	0.231220i
$79$	−4.03949	−	6.99660i	−0.454478	−	0.787179i	0.544180	−	0.838969i	$-0.316841\pi$
$79$	−4.03949	−	6.99660i	−0.454478	−	0.787179i	−0.998658	+	0.0517893i	$0.983508\pi$
$80$	−2.21370	+	0.315474i	−0.247499	+	0.0352711i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$			3.03495i			0.335154i
$83$	−8.26772	−	4.77337i	−0.907500	−	0.523946i	−0.0278744	−	0.999611i	$-0.508874\pi$
$83$	−8.26772	−	4.77337i	−0.907500	−	0.523946i	−0.879626	+	0.475666i	$0.842207\pi$
$84$	4.59082			0.500899
$85$	1.55428	+	10.9065i	0.168585	+	1.18297i
$86$	−1.41795	+	2.45596i	−0.152901	+	0.264833i
$87$	5.75888	−	3.32489i	0.617416	−	0.356466i
$88$			5.56277i			0.592994i
$89$	−7.77936	+	13.4742i	−0.824611	+	1.42827i	0.0776059	+	0.996984i	$0.475272\pi$
$89$	−7.77936	+	13.4742i	−0.824611	+	1.42827i	−0.902217	+	0.431283i	$0.858061\pi$
$90$	2.07486	+	0.833642i	0.218709	+	0.0878736i
$91$	9.37482	−	16.2377i	0.982748	−	1.70217i
$92$	5.47041	−	3.15834i	0.570329	−	0.329280i
$93$	8.06082	−	4.65392i	0.835868	−	0.482589i
$94$	0.395439	−	0.684920i	0.0407864	−	0.0706441i
$95$	0.287279	−	0.715011i	0.0294742	−	0.0733585i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$			10.8823i			1.10493i	0.833536	+	0.552465i	$0.186313\pi$
$97$			10.8823i			1.10493i	−0.833536	+	0.552465i	$0.813687\pi$
$98$	12.1898	−	7.03780i	1.23136	−	0.710925i
$99$	2.78139	−	4.81750i	0.279540	−	0.484177i
$100$	−4.80095	+	1.39673i	−0.480095	+	0.139673i
$101$	9.76114			0.971270			0.485635	−	0.874162i	$-0.338588\pi$
$101$	9.76114			0.971270			0.485635	+	0.874162i	$0.338588\pi$
$102$	−4.26674	−	2.46340i	−0.422470	−	0.243913i
$103$			6.83740i			0.673709i	0.941557	+	0.336854i	$0.109363\pi$
$103$			6.83740i			0.673709i	−0.941557	+	0.336854i	$0.890637\pi$
$104$	−2.04208	−	3.53699i	−0.200242	−	0.346830i
$105$	10.1627	−	1.44828i	0.991778	−	0.141338i
$106$	4.38231	+	7.59038i	0.425647	+	0.737243i
$107$	13.2236	−	7.63464i	1.27837	−	0.738068i	0.301823	−	0.953364i	$-0.402405\pi$
$107$	13.2236	−	7.63464i	1.27837	−	0.738068i	0.976549	+	0.215296i	$0.0690715\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	−1.82982	+	3.16934i	−0.175265	+	0.303568i	−0.940253	−	0.340477i	$-0.889411\pi$
$109$	−1.82982	+	3.16934i	−0.175265	+	0.303568i	0.764988	+	0.644044i	$0.222745\pi$
$110$	1.75491	+	12.3143i	0.167324	+	1.17412i
$111$	3.38432	−	5.05434i	0.321226	−	0.479737i
$112$		−	4.59082i		−	0.433791i
$113$	2.36047	+	1.36282i	0.222055	+	0.128203i	0.606901	−	0.794777i	$-0.292412\pi$
$113$	2.36047	+	1.36282i	0.222055	+	0.128203i	−0.384847	+	0.922981i	$0.625746\pi$
$114$	0.172303	+	0.298438i	0.0161377	+	0.0279513i
$115$	11.1135	−	8.71740i	1.03634	−	0.812901i
$116$	−3.32489	−	5.75888i	−0.308708	−	0.534698i
$117$			4.08416i			0.377581i
$118$	4.26732	−	2.46374i	0.392839	−	0.226806i
$119$	−22.6181			−2.07339
$120$	0.833642	−	2.07486i	0.0761008	−	0.189408i
$121$	19.9445			1.81313
$122$			2.07282i			0.187665i
$123$	−2.62834	−	1.51747i	−0.236989	−	0.136826i
$124$	−4.65392	−	8.06082i	−0.417934	−	0.723883i
$125$	−10.1872	+	4.60652i	−0.911175	+	0.412020i
$126$	−2.29541	+	3.97576i	−0.204491	+	0.354189i
$127$	8.08422	+	4.66742i	0.717358	+	0.414167i	0.813780	−	0.581174i	$-0.197406\pi$
$127$	8.08422	+	4.66742i	0.717358	+	0.414167i	−0.0964214	+	0.995341i	$0.530740\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−1.41795	−	2.45596i	−0.124843	−	0.216235i
$130$	−5.63639	−	7.18561i	−0.494344	−	0.630220i
$131$	−0.651740	+	1.12885i	−0.0569428	+	0.0986278i	−0.893092	−	0.449875i	$-0.851469\pi$
$131$	−0.651740	+	1.12885i	−0.0569428	+	0.0986278i	0.836149	+	0.548503i	$0.184802\pi$
$132$	−4.81750	−	2.78139i	−0.419310	−	0.242089i
$133$	1.37008	+	0.791013i	0.118801	+	0.0685895i
$134$	8.59140			0.742184
$135$	−1.75939	+	1.38006i	−0.151424	+	0.118777i
$136$	−2.46340	+	4.26674i	−0.211235	+	0.365870i
$137$			1.57437i			0.134507i	0.997736	+	0.0672536i	$0.0214237\pi$
$137$			1.57437i			0.134507i	−0.997736	+	0.0672536i	$0.978576\pi$
$138$			6.31668i			0.537712i
$139$	1.68295	−	2.91495i	0.142746	−	0.247243i	−0.785784	−	0.618501i	$-0.787740\pi$
$139$	1.68295	−	2.91495i	0.142746	−	0.247243i	0.928530	+	0.371258i	$0.121074\pi$
$140$	−1.44828	−	10.1627i	−0.122402	−	0.858905i
$141$	0.395439	+	0.684920i	0.0333020	+	0.0576807i
$142$			11.5255i			0.967195i
$143$	−19.6755	+	11.3596i	−1.64534	+	0.949940i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−9.17709	−	11.6995i	−0.762116	−	0.971592i
$146$	2.24660	−	3.89123i	0.185930	−	0.322040i
$147$			14.0756i			1.16094i
$148$	−5.05434	−	3.38432i	−0.415464	−	0.278190i
$149$	23.0472			1.88810			0.944052	−	0.329797i	$-0.106980\pi$
$149$	23.0472			1.88810			0.944052	+	0.329797i	$0.106980\pi$
$150$	1.19087	−	4.85611i	0.0972343	−	0.396500i
$151$	5.89291	+	10.2068i	0.479559	+	0.830620i	0.999725	−	0.0234450i	$-0.00746345\pi$
$151$	5.89291	+	10.2068i	0.479559	+	0.830620i	−0.520167	+	0.854065i	$0.674130\pi$
$152$	0.298438	−	0.172303i	0.0242065	−	0.0139757i
$153$	4.26674	−	2.46340i	0.344946	−	0.199154i
$154$	−25.5377			−2.05788
$155$	−12.8454	−	16.3761i	−1.03176	−	1.31536i
$156$	4.08416			0.326995
$157$	4.12722	+	2.38285i	0.329388	+	0.190172i	0.655569	−	0.755135i	$-0.272429\pi$
$157$	4.12722	+	2.38285i	0.329388	+	0.190172i	−0.326181	+	0.945307i	$0.605762\pi$
$158$		−	8.07898i		−	0.642729i
$159$	−8.76462			−0.695079
$160$	−2.07486	−	0.833642i	−0.164032	−	0.0659052i
$161$	14.4994	+	25.1136i	1.14271	+	1.97923i
$162$		−	1.00000i		−	0.0785674i
$163$	−16.6484	−	9.61195i	−1.30400	−	0.752866i	−0.322914	−	0.946428i	$-0.604662\pi$
$163$	−16.6484	−	9.61195i	−1.30400	−	0.752866i	−0.981088	+	0.193562i	$0.937996\pi$
$164$	−1.51747	+	2.62834i	−0.118495	+	0.205239i
$165$	−11.5420	−	4.63737i	−0.898541	−	0.361018i
$166$	−4.77337	−	8.26772i	−0.370486	−	0.641700i
$167$	1.87508	−	1.08258i	0.145098	−	0.0837723i	−0.425694	−	0.904867i	$-0.639970\pi$
$167$	1.87508	−	1.08258i	0.145098	−	0.0837723i	0.570791	+	0.821095i	$0.306637\pi$
$168$	3.97576	+	2.29541i	0.306737	+	0.177095i
$169$	1.84019	−	3.18730i	0.141553	−	0.245177i
$170$	−4.10720	+	10.2224i	−0.315008	+	0.784025i
$171$	−0.344607			−0.0263527
$172$	−2.45596	+	1.41795i	−0.187265	+	0.108117i
$173$	12.2258	+	7.05859i	0.929512	+	0.536654i	0.886657	−	0.462427i	$-0.153021\pi$
$173$	12.2258	+	7.05859i	0.929512	+	0.536654i	0.0428551	+	0.999081i	$0.486355\pi$
$174$	6.64978			0.504118
$175$	−6.41214	−	22.0403i	−0.484712	−	1.66609i
$176$	−2.78139	+	4.81750i	−0.209655	+	0.363133i
$177$			4.92748i			0.370372i
$178$	−13.4742	+	7.77936i	−1.00994	+	0.583088i
$179$	−0.438270			−0.0327579			−0.0163789	−	0.999866i	$-0.505214\pi$
$179$	−0.438270			−0.0327579			−0.0163789	+	0.999866i	$0.505214\pi$
$180$	1.38006	+	1.75939i	0.102864	+	0.131137i
$181$	2.99121	+	5.18092i	0.222335	+	0.385095i	0.955516	−	0.294938i	$-0.0952989\pi$
$181$	2.99121	+	5.18092i	0.222335	+	0.385095i	−0.733182	+	0.680033i	$0.761966\pi$
$182$	16.2377	−	9.37482i	1.20362	−	0.694908i
$183$	−1.79512	−	1.03641i	−0.132699	−	0.0766138i
$184$	6.31668			0.465672
$185$	−12.2565	−	5.89737i	−0.901113	−	0.433584i
$186$	9.30784			0.682484
$187$	23.7349	+	13.7034i	1.73567	+	1.00209i
$188$	0.684920	−	0.395439i	0.0499529	−	0.0288403i
$189$	−2.29541	−	3.97576i	−0.166966	−	0.289194i
$190$	0.606296	−	0.475578i	0.0439853	−	0.0345020i
$191$	−6.53274			−0.472692			−0.236346	−	0.971669i	$-0.575950\pi$
$191$	−6.53274			−0.472692			−0.236346	+	0.971669i	$0.575950\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$		−	22.9110i		−	1.64917i	−0.565740	−	0.824583i	$-0.691410\pi$
$193$		−	22.9110i		−	1.64917i	0.565740	−	0.824583i	$-0.308590\pi$
$194$	−5.44115	+	9.42435i	−0.390652	+	0.676629i
$195$	9.04112	−	1.28845i	0.647448	−	0.0922676i
$196$	14.0756			1.00540
$197$	4.77005	+	2.75399i	0.339852	+	0.196214i	0.660207	−	0.751084i	$-0.270469\pi$
$197$	4.77005	+	2.75399i	0.339852	+	0.196214i	−0.320355	+	0.947298i	$0.603802\pi$
$198$	4.81750	−	2.78139i	0.342365	−	0.197665i
$199$	1.95566			0.138633			0.0693165	−	0.997595i	$-0.477918\pi$
$199$	1.95566			0.138633			0.0693165	+	0.997595i	$0.477918\pi$
$200$	−4.85611	−	1.19087i	−0.343379	−	0.0842073i
$201$	−4.29570	+	7.44037i	−0.302995	+	0.524804i
$202$	8.45340	+	4.88057i	0.594779	+	0.343396i
$203$	26.4379	−	15.2640i	1.85558	−	1.07132i
$204$	−2.46340	−	4.26674i	−0.172473	−	0.298732i
$205$	−2.53006	+	6.29708i	−0.176707	+	0.439807i
$206$	−3.41870	+	5.92136i	−0.238192	+	0.412561i
$207$	−5.47041	−	3.15834i	−0.380220	−	0.219520i
$208$		−	4.08416i		−	0.283186i
$209$	−0.958485	−	1.66014i	−0.0662998	−	0.114835i
$210$	9.52530	+	3.82710i	0.657308	+	0.264095i
$211$	17.4309			1.19999			0.599997	−	0.800002i	$-0.295168\pi$
$211$	17.4309			1.19999			0.599997	+	0.800002i	$0.295168\pi$
$212$			8.76462i			0.601956i
$213$	−9.98134	−	5.76273i	−0.683910	−	0.394856i
$214$	15.2693			1.04379
$215$	−4.98943	+	3.91370i	−0.340276	+	0.266912i
$216$	−1.00000			−0.0680414
$217$	37.0058	−	21.3653i	2.51211	−	1.45037i
$218$	−3.16934	+	1.82982i	−0.214655	+	0.123931i
$219$	2.24660	+	3.89123i	0.151811	+	0.262945i
$220$	−4.63737	+	11.5420i	−0.312651	+	0.778160i
$221$	−20.1219			−1.35354
$222$	5.45808	−	2.68502i	0.366322	−	0.180207i
$223$			15.4197i			1.03258i	0.856415	+	0.516288i	$0.172687\pi$
$223$			15.4197i			1.03258i	−0.856415	+	0.516288i	$0.827313\pi$
$224$	2.29541	−	3.97576i	0.153368	−	0.265642i
$225$	3.61008	+	3.45938i	0.240672	+	0.230625i
$226$	1.36282	+	2.36047i	0.0906534	+	0.157016i
$227$	18.1508	−	10.4794i	1.20471	−	0.695540i	0.243112	−	0.969998i	$-0.421832\pi$
$227$	18.1508	−	10.4794i	1.20471	−	0.695540i	0.961599	+	0.274458i	$0.0884983\pi$
$228$			0.344607i			0.0228221i
$229$	−3.04386	−	5.27213i	−0.201144	−	0.348392i	0.747753	−	0.663977i	$-0.231133\pi$
$229$	−3.04386	−	5.27213i	−0.201144	−	0.348392i	−0.948897	+	0.315585i	$0.897799\pi$
$230$	13.9832	−	1.99275i	0.922028	−	0.131398i
$231$	12.7688	−	22.1163i	0.840128	−	1.45514i
$232$		−	6.64978i		−	0.436579i
$233$			2.79011i			0.182786i	0.995815	+	0.0913929i	$0.0291319\pi$
$233$			2.79011i			0.182786i	−0.995815	+	0.0913929i	$0.970868\pi$
$234$	−2.04208	+	3.53699i	−0.133495	+	0.231220i
$235$	1.39146	−	1.09146i	0.0907687	−	0.0711989i
$236$	4.92748			0.320751
$237$	6.99660	+	4.03949i	0.454478	+	0.262393i
$238$	−19.5878	−	11.3090i	−1.26969	−	0.733056i
$239$	11.4549	−	19.8404i	0.740954	−	1.28337i	−0.211107	−	0.977463i	$-0.567707\pi$
$239$	11.4549	−	19.8404i	0.740954	−	1.28337i	0.952061	−	0.305908i	$-0.0989599\pi$
$240$	1.75939	−	1.38006i	0.113568	−	0.0890825i
$241$	14.8775	+	25.7686i	0.958343	+	1.65990i	0.726525	+	0.687140i	$0.241134\pi$
$241$	14.8775	+	25.7686i	0.958343	+	1.65990i	0.231818	+	0.972759i	$0.425532\pi$
$242$	17.2724	+	9.97223i	1.11031	+	0.641039i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−1.03641	+	1.79512i	−0.0663495	+	0.114921i
$245$	31.1592	−	4.44048i	1.99069	−	0.283692i
$246$	−1.51747	−	2.62834i	−0.0967505	−	0.167577i
$247$	1.21887	+	0.703715i	0.0775548	+	0.0447763i
$248$		−	9.30784i		−	0.591048i
$249$	9.54674			0.605000
$250$	−11.1257	−	1.10426i	−0.703649	−	0.0698394i
$251$	−17.2782			−1.09059			−0.545295	−	0.838244i	$-0.683582\pi$
$251$	−17.2782			−1.09059			−0.545295	+	0.838244i	$0.683582\pi$
$252$	−3.97576	+	2.29541i	−0.250450	+	0.144597i
$253$		−	35.1383i		−	2.20912i
$254$	4.66742	+	8.08422i	0.292860	+	0.507249i
$255$	−6.79929	−	8.66815i	−0.425788	−	0.542821i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.3651	+	8.87105i	0.958449	+	0.553361i	0.895695	−	0.444668i	$-0.146678\pi$
$257$	15.3651	+	8.87105i	0.958449	+	0.553361i	0.0627536	+	0.998029i	$0.480012\pi$
$258$		−	2.83589i		−	0.176555i
$259$	15.5368	−	23.2035i	0.965411	−	1.44180i
$260$	−1.28845	−	9.04112i	−0.0799061	−	0.560706i
$261$	−3.32489	+	5.75888i	−0.205805	+	0.356466i
$262$	−1.12885	+	0.651740i	−0.0697404	+	0.0402646i
$263$	7.05032	−	4.07050i	0.434741	−	0.250998i	−0.266623	−	0.963801i	$-0.585908\pi$
$263$	7.05032	−	4.07050i	0.434741	−	0.250998i	0.701364	+	0.712803i	$0.252575\pi$
$264$	−2.78139	−	4.81750i	−0.171183	−	0.296497i
$265$	2.76501	+	19.4022i	0.169853	+	1.19187i
$266$	0.791013	+	1.37008i	0.0485001	+	0.0840047i
$267$		−	15.5587i		−	0.952178i
$268$	7.44037	+	4.29570i	0.454493	+	0.262402i
$269$	−18.8248			−1.14777			−0.573885	−	0.818936i	$-0.694564\pi$
$269$	−18.8248			−1.14777			−0.573885	+	0.818936i	$0.694564\pi$
$270$	−2.21370	+	0.315474i	−0.134722	+	0.0191991i
$271$	−4.41811	+	7.65239i	−0.268381	+	0.464849i	−0.968444	−	0.249232i	$-0.919822\pi$
$271$	−4.41811	+	7.65239i	−0.268381	+	0.464849i	0.700063	+	0.714081i	$0.253155\pi$
$272$	−4.26674	+	2.46340i	−0.258709	+	0.149366i
$273$			18.7496i			1.13478i
$274$	−0.787183	+	1.36344i	−0.0475555	+	0.0823685i
$275$	−6.62455	+	27.0135i	−0.399475	+	1.62897i
$276$	−3.15834	+	5.47041i	−0.190110	+	0.329280i
$277$	7.76350	−	4.48226i	0.466463	−	0.269313i	−0.248295	−	0.968685i	$-0.579870\pi$
$277$	7.76350	−	4.48226i	0.466463	−	0.269313i	0.714758	+	0.699372i	$0.246537\pi$
$278$	2.91495	−	1.68295i	0.174827	−	0.100936i
$279$	−4.65392	+	8.06082i	−0.278623	+	0.482589i
$280$	3.82710	−	9.52530i	0.228713	−	0.569245i
$281$	−4.07767	+	7.06272i	−0.243253	+	0.421327i	−0.961639	−	0.274318i	$-0.911548\pi$
$281$	−4.07767	+	7.06272i	−0.243253	+	0.421327i	0.718386	+	0.695645i	$0.244881\pi$
$282$			0.790878i			0.0470961i
$283$	−15.0203	+	8.67196i	−0.892863	+	0.515495i	−0.874878	−	0.484343i	$-0.839059\pi$
$283$	−15.0203	+	8.67196i	−0.892863	+	0.515495i	−0.0179852	+	0.999838i	$0.505725\pi$
$284$	−5.76273	+	9.98134i	−0.341955	+	0.592284i
$285$	0.108715	+	0.762857i	0.00643969	+	0.0451877i
$286$	−22.7193			−1.34342
$287$	−12.0662	−	6.96644i	−0.712247	−	0.411216i
$288$			1.00000i			0.0589256i
$289$	3.63672	+	6.29898i	0.213925	+	0.370528i
$290$	−2.09783	−	14.7206i	−0.123189	−	0.864425i
$291$	−5.44115	−	9.42435i	−0.318966	−	0.552465i
$292$	3.89123	−	2.24660i	0.227717	−	0.131472i
$293$	−3.55547	+	2.05275i	−0.207713	+	0.119923i	−0.600248	−	0.799814i	$-0.704931\pi$
$293$	−3.55547	+	2.05275i	−0.207713	+	0.119923i	0.392535	+	0.919737i	$0.371598\pi$
$294$	−7.03780	+	12.1898i	−0.410453	+	0.710925i
$295$	10.9080	−	1.55449i	0.635086	−	0.0905060i
$296$	−2.68502	−	5.45808i	−0.156064	−	0.317245i
$297$			5.56277i			0.322785i
$298$	19.9595	+	11.5236i	1.15622	+	0.667546i
$299$	12.8992	+	22.3420i	0.745978	+	1.29207i
$300$	3.45938	−	3.61008i	0.199727	−	0.208428i
$301$	−6.50953	−	11.2748i	−0.375203	−	0.649871i
$302$			11.7858i			0.678198i
$303$	−8.45340	+	4.88057i	−0.485635	+	0.280381i
$304$	0.344607			0.0197646
$305$	−1.72799	+	4.30082i	−0.0989446	+	0.246264i
$306$	4.92681			0.281647
$307$			11.3448i			0.647483i	0.946146	+	0.323741i	$0.104941\pi$
$307$			11.3448i			0.647483i	−0.946146	+	0.323741i	$0.895059\pi$
$308$	−22.1163	−	12.7688i	−1.26019	−	0.727572i
$309$	−3.41870	−	5.92136i	−0.194483	−	0.336854i
$310$	−2.93638	−	20.6048i	−0.166775	−	1.17027i
$311$	6.22248	−	10.7777i	0.352845	−	0.611145i	−0.633902	−	0.773413i	$-0.718548\pi$
$311$	6.22248	−	10.7777i	0.352845	−	0.611145i	0.986747	+	0.162269i	$0.0518811\pi$
$312$	3.53699	+	2.04208i	0.200242	+	0.115610i
$313$	10.3784	+	5.99199i	0.586624	+	0.338687i	0.763761	−	0.645499i	$-0.223350\pi$
$313$	10.3784	+	5.99199i	0.586624	+	0.338687i	−0.177138	+	0.984186i	$0.556684\pi$
$314$	2.38285	+	4.12722i	0.134472	+	0.232912i
$315$	−8.07701	+	6.33560i	−0.455088	+	0.356971i
$316$	4.03949	−	6.99660i	0.227239	−	0.393590i
$317$	−14.7696	−	8.52724i	−0.829544	−	0.478937i	0.0241526	−	0.999708i	$-0.492311\pi$
$317$	−14.7696	−	8.52724i	−0.829544	−	0.478937i	−0.853696	+	0.520771i	$0.825645\pi$
$318$	−7.59038	−	4.38231i	−0.425647	−	0.245748i
$319$	−36.9912			−2.07111
$320$	−1.38006	−	1.75939i	−0.0771477	−	0.0983526i
$321$	−7.63464	+	13.2236i	−0.426124	+	0.738068i
$322$			28.9987i			1.61604i
$323$		−	1.69781i		−	0.0944688i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−5.70447	−	19.6079i	−0.316427	−	1.08765i
$326$	−9.61195	−	16.6484i	−0.532357	−	0.922069i
$327$		−	3.65964i		−	0.202378i
$328$	−2.62834	+	1.51747i	−0.145126	+	0.0837884i
$329$	1.81539	+	3.14434i	0.100085	+	0.173353i
$330$	−7.67696	−	9.78706i	−0.422603	−	0.538760i
$331$	3.27461	−	5.67178i	0.179989	−	0.311749i	−0.761888	−	0.647709i	$-0.775727\pi$
$331$	3.27461	−	5.67178i	0.179989	−	0.311749i	0.941876	+	0.335960i	$0.109061\pi$
$332$		−	9.54674i		−	0.523946i
$333$	−0.403742	+	6.06935i	−0.0221249	+	0.332598i
$334$	2.16515			0.118472
$335$	17.8260	+	7.16216i	0.973936	+	0.391311i
$336$	2.29541	+	3.97576i	0.125225	+	0.216896i
$337$	−5.89288	+	3.40225i	−0.321005	+	0.185333i	−0.651841	−	0.758356i	$-0.726003\pi$
$337$	−5.89288	+	3.40225i	−0.321005	+	0.185333i	0.330835	+	0.943689i	$0.392670\pi$
$338$	3.18730	−	1.84019i	0.173366	−	0.100093i
$339$	−2.72564			−0.148036
$340$	−8.66815	+	6.79929i	−0.470097	+	0.368743i
$341$	−51.7774			−2.80390
$342$	−0.298438	−	0.172303i	−0.0161377	−	0.00931710i
$343$			32.4827i			1.75390i
$344$	−2.83589			−0.152901
$345$	−5.26585	+	13.1062i	−0.283504	+	0.705615i
$346$	7.05859	+	12.2258i	0.379472	+	0.657265i
$347$			30.8025i			1.65357i	0.562522	+	0.826783i	$0.309831\pi$
$347$			30.8025i			1.65357i	−0.562522	+	0.826783i	$0.690169\pi$
$348$	5.75888	+	3.32489i	0.308708	+	0.178233i
$349$	−10.2495	+	17.7527i	−0.548645	+	0.950282i	0.449722	+	0.893168i	$0.351523\pi$
$349$	−10.2495	+	17.7527i	−0.548645	+	0.950282i	−0.998368	+	0.0571133i	$0.981810\pi$
$350$	5.46707	−	22.2935i	0.292227	−	1.19164i
$351$	−2.04208	−	3.53699i	−0.108998	−	0.188790i
$352$	−4.81750	+	2.78139i	−0.256774	+	0.148248i
$353$	−19.9390	−	11.5118i	−1.06125	−	0.612712i	−0.135471	−	0.990781i	$-0.543255\pi$
$353$	−19.9390	−	11.5118i	−1.06125	−	0.612712i	−0.925777	+	0.378070i	$0.876588\pi$
$354$	−2.46374	+	4.26732i	−0.130946	+	0.226806i
$355$	−9.60812	+	23.9137i	−0.509946	+	1.26921i
$356$	−15.5587			−0.824611
$357$	19.5878	−	11.3090i	1.03670	−	0.598538i
$358$	−0.379553	−	0.219135i	−0.0200600	−	0.0115817i
$359$	−17.6881			−0.933543			−0.466772	−	0.884378i	$-0.654583\pi$
$359$	−17.6881			−0.933543			−0.466772	+	0.884378i	$0.654583\pi$
$360$	0.315474	+	2.21370i	0.0166269	+	0.116672i
$361$	9.44062	−	16.3516i	0.496875	−	0.860613i
$362$			5.98241i			0.314429i
$363$	−17.2724	+	9.97223i	−0.906567	+	0.523406i
$364$	18.7496			0.982748
$365$	7.90527	−	6.20088i	0.413781	−	0.324569i
$366$	−1.03641	−	1.79512i	−0.0541741	−	0.0938323i
$367$	20.6183	−	11.9040i	1.07627	−	0.621383i	0.146380	−	0.989228i	$-0.453238\pi$
$367$	20.6183	−	11.9040i	1.07627	−	0.621383i	0.929887	+	0.367845i	$0.119904\pi$
$368$	5.47041	+	3.15834i	0.285165	+	0.164640i
$369$	3.03495			0.157993
$370$	−7.66572	−	11.2355i	−0.398522	−	0.584106i
$371$	−40.2367			−2.08899
$372$	8.06082	+	4.65392i	0.417934	+	0.241294i
$373$	21.2928	−	12.2934i	1.10250	−	0.636529i	0.165624	−	0.986189i	$-0.447036\pi$
$373$	21.2928	−	12.2934i	1.10250	−	0.636529i	0.936877	+	0.349660i	$0.113703\pi$
$374$	13.7034	+	23.7349i	0.708584	+	1.22730i
$375$	6.51915	−	9.08299i	0.336648	−	0.469043i
$376$	0.790878			0.0407864
$377$	23.5202	−	13.5794i	1.21135	−	0.699374i
$378$		−	4.59082i		−	0.236126i
$379$	−15.8775	+	27.5006i	−0.815571	+	1.41261i	0.0933462	+	0.995634i	$0.470244\pi$
$379$	−15.8775	+	27.5006i	−0.815571	+	1.41261i	−0.908917	+	0.416977i	$0.863090\pi$
$380$	0.762857	−	0.108715i	0.0391337	−	0.00557694i
$381$	−9.33485			−0.478239
$382$	−5.65752	−	3.26637i	−0.289464	−	0.167122i
$383$	2.38651	−	1.37785i	0.121945	−	0.0704050i	−0.437787	−	0.899079i	$-0.644237\pi$
$383$	2.38651	−	1.37785i	0.121945	−	0.0704050i	0.559732	+	0.828674i	$0.310904\pi$
$384$	1.00000			0.0510310
$385$	−52.9871	−	21.2893i	−2.70047	−	1.08500i
$386$	11.4555	−	19.8415i	0.583069	−	1.00990i
$387$	2.45596	+	1.41795i	0.124843	+	0.0720783i
$388$	−9.42435	+	5.44115i	−0.478449	+	0.276233i
$389$	9.75014	+	16.8877i	0.494351	+	0.856242i	0.999979	−	0.00651011i	$-0.00207225\pi$
$389$	9.75014	+	16.8877i	0.494351	+	0.856242i	−0.505627	+	0.862752i	$0.668739\pi$
$390$	8.47406	+	3.40473i	0.429101	+	0.172405i
$391$	15.5605	−	26.9516i	0.786930	−	1.36300i
$392$	12.1898	+	7.03780i	0.615679	+	0.355462i
$393$		−	1.30348i		−	0.0657518i
$394$	2.75399	+	4.77005i	0.138744	+	0.240312i
$395$	6.73498	−	16.7627i	0.338874	−	0.843425i
$396$	5.56277			0.279540
$397$		−	33.8847i		−	1.70063i	−0.526278	−	0.850313i	$-0.676413\pi$
$397$		−	33.8847i		−	1.70063i	0.526278	−	0.850313i	$-0.323587\pi$
$398$	1.69365	+	0.977829i	0.0848950	+	0.0490142i
$399$	−1.58203			−0.0792004
$400$	−3.61008	−	3.45938i	−0.180504	−	0.172969i
$401$	29.9329			1.49478			0.747388	−	0.664388i	$-0.231308\pi$
$401$	29.9329			1.49478			0.747388	+	0.664388i	$0.231308\pi$
$402$	−7.44037	+	4.29570i	−0.371092	+	0.214250i
$403$	32.9217	−	19.0074i	1.63995	−	0.946824i
$404$	4.88057	+	8.45340i	0.242817	+	0.420572i
$405$	0.833642	−	2.07486i	0.0414240	−	0.103101i
$406$	30.5279			1.51507
$407$	−30.3621	+	14.9362i	−1.50499	+	0.740359i
$408$		−	4.92681i		−	0.243913i
$409$	13.7785	−	23.8650i	0.681301	−	1.18005i	−0.293283	−	0.956026i	$-0.594748\pi$
$409$	13.7785	−	23.8650i	0.681301	−	1.18005i	0.974584	−	0.224022i	$-0.0719188\pi$
$410$	−5.33964	+	4.18841i	−0.263706	+	0.206851i
$411$	−0.787183	−	1.36344i	−0.0388289	−	0.0672536i
$412$	−5.92136	+	3.41870i	−0.291724	+	0.168427i
$413$			22.6211i			1.11311i
$414$	−3.15834	−	5.47041i	−0.155224	−	0.268856i
$415$	−3.01175	−	21.1336i	−0.147841	−	1.03741i
$416$	2.04208	−	3.53699i	0.100121	−	0.173415i
$417$			3.36589i			0.164829i
$418$		−	1.91697i		−	0.0937621i
$419$	13.3949	−	23.2006i	0.654381	−	1.13342i	−0.327667	−	0.944793i	$-0.606262\pi$
$419$	13.3949	−	23.2006i	0.654381	−	1.13342i	0.982049	−	0.188629i	$-0.0604042\pi$
$420$	6.33560	+	8.07701i	0.309146	+	0.394118i
$421$	−22.0943			−1.07681			−0.538405	−	0.842686i	$-0.680973\pi$
$421$	−22.0943			−1.07681			−0.538405	+	0.842686i	$0.680973\pi$
$422$	15.0956	+	8.71546i	0.734844	+	0.424262i
$423$	−0.684920	−	0.395439i	−0.0333020	−	0.0192269i
$424$	−4.38231	+	7.59038i	−0.212824	+	0.368621i
$425$	−17.0437	+	17.7862i	−0.826741	+	0.862756i
$426$	−5.76273	−	9.98134i	−0.279205	−	0.483598i
$427$	−8.24106	−	4.75798i	−0.398813	−	0.230255i
$428$	13.2236	+	7.63464i	0.639186	+	0.369034i
$429$	11.3596	−	19.6755i	0.548448	−	0.949940i
$430$	−6.27782	+	0.894651i	−0.302743	+	0.0431439i
$431$	9.67487	+	16.7574i	0.466022	+	0.807174i	0.999247	−	0.0387993i	$-0.0123533\pi$
$431$	9.67487	+	16.7574i	0.466022	+	0.807174i	−0.533225	+	0.845974i	$0.679020\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$			16.6967i			0.802394i	0.915992	+	0.401197i	$0.131406\pi$
$433$			16.6967i			0.802394i	−0.915992	+	0.401197i	$0.868594\pi$
$434$	42.7306			2.05113
$435$	13.7974	+	5.54354i	0.661532	+	0.265792i
$436$	−3.65964			−0.175265
$437$	−1.88514	+	1.08839i	−0.0901784	+	0.0520645i
$438$			4.49320i			0.214693i
$439$	5.70310	+	9.87807i	0.272194	+	0.471454i	0.969423	−	0.245394i	$-0.0789173\pi$
$439$	5.70310	+	9.87807i	0.272194	+	0.471454i	−0.697229	+	0.716848i	$0.745584\pi$
$440$	−9.78706	+	7.67696i	−0.466580	+	0.365985i
$441$	−7.03780	−	12.1898i	−0.335133	−	0.580468i
$442$	−17.4261	−	10.0609i	−0.828873	−	0.478550i
$443$			6.21290i			0.295184i	0.989048	+	0.147592i	$0.0471522\pi$
$443$			6.21290i			0.295184i	−0.989048	+	0.147592i	$0.952848\pi$
$444$	6.06935	+	0.403742i	0.288039	+	0.0191607i
$445$	−34.4424	+	4.90837i	−1.63273	+	0.232679i
$446$	−7.70983	+	13.3538i	−0.365071	+	0.632321i
$447$	−19.9595	+	11.5236i	−0.944052	+	0.545049i
$448$	3.97576	−	2.29541i	0.187837	−	0.108448i
$449$	−12.4576	−	21.5772i	−0.587910	−	1.01829i	−0.994506	−	0.104682i	$-0.966618\pi$
$449$	−12.4576	−	21.5772i	−0.587910	−	1.01829i	0.406596	−	0.913608i	$-0.366716\pi$
$450$	1.39673	+	4.80095i	0.0658425	+	0.226319i
$451$	8.44136	+	14.6209i	0.397488	+	0.688470i
$452$			2.72564i			0.128203i
$453$	−10.2068	−	5.89291i	−0.479559	−	0.276873i
$454$	20.9587			0.983643
$455$	41.5061	−	5.91502i	1.94584	−	0.277301i
$456$	−0.172303	+	0.298438i	−0.00806885	+	0.0139757i
$457$	−29.7299	+	17.1646i	−1.39071	+	0.802925i	−0.993393	−	0.114759i	$-0.963391\pi$
$457$	−29.7299	+	17.1646i	−1.39071	+	0.802925i	−0.397313	+	0.917683i	$0.630057\pi$
$458$		−	6.08773i		−	0.284461i
$459$	−2.46340	+	4.26674i	−0.114982	+	0.199154i
$460$	13.1062	+	5.26585i	0.611081	+	0.245522i
$461$	8.74147	−	15.1407i	0.407131	−	0.705171i	−0.587436	−	0.809271i	$-0.699863\pi$
$461$	8.74147	−	15.1407i	0.407131	−	0.705171i	0.994567	+	0.104099i	$0.0331960\pi$
$462$	22.1163	−	12.7688i	1.02894	−	0.594060i
$463$	−10.9760	+	6.33701i	−0.510099	+	0.294506i	−0.732874	−	0.680364i	$-0.761822\pi$
$463$	−10.9760	+	6.33701i	−0.510099	+	0.294506i	0.222775	+	0.974870i	$0.428488\pi$
$464$	3.32489	−	5.75888i	0.154354	−	0.267349i
$465$	19.3125	+	7.75941i	0.895593	+	0.359834i
$466$	−1.39505	+	2.41630i	−0.0646246	+	0.111933i
$467$			27.9225i			1.29210i	0.763296	+	0.646049i	$0.223580\pi$
$467$			27.9225i			1.29210i	−0.763296	+	0.646049i	$0.776420\pi$
$468$	−3.53699	+	2.04208i	−0.163497	+	0.0943952i
$469$	−19.7208	+	34.1574i	−0.910621	+	1.57724i
$470$	1.75077	−	0.249501i	0.0807569	−	0.0115086i
$471$	−4.76570			−0.219592
$472$	4.26732	+	2.46374i	0.196419	+	0.113403i
$473$			15.7754i			0.725355i
$474$	4.03949	+	6.99660i	0.185540	+	0.321365i
$475$	1.65444	−	0.481323i	0.0759109	−	0.0220846i
$476$	−11.3090	−	19.5878i	−0.518349	−	0.897806i
$477$	7.59038	−	4.38231i	0.347540	−	0.200652i
$478$	19.8404	−	11.4549i	0.907480	−	0.523934i
$479$	−2.64819	+	4.58680i	−0.120999	+	0.209576i	−0.920162	−	0.391538i	$-0.871943\pi$
$479$	−2.64819	+	4.58680i	−0.120999	+	0.209576i	0.799163	+	0.601114i	$0.205276\pi$
$480$	2.21370	−	0.315474i	0.101041	−	0.0143994i
$481$	13.8221	−	20.6427i	0.630235	−	0.941228i
$482$			29.7550i			1.35530i
$483$	−25.1136	−	14.4994i	−1.14271	−	0.659744i
$484$	9.97223	+	17.2724i	0.453283	+	0.785110i
$485$	−19.1462	+	15.0182i	−0.869382	+	0.681942i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$		−	33.4835i		−	1.51728i	−0.651509	−	0.758641i	$-0.725864\pi$
$487$		−	33.4835i		−	1.51728i	0.651509	−	0.758641i	$-0.274136\pi$
$488$	−1.79512	+	1.03641i	−0.0812612	+	0.0469162i
$489$	19.2239			0.869335
$490$	29.2049	+	11.7340i	1.31934	+	0.530089i
$491$	−32.5795			−1.47029			−0.735146	−	0.677908i	$-0.762887\pi$
$491$	−32.5795			−1.47029			−0.735146	+	0.677908i	$0.762887\pi$
$492$		−	3.03495i		−	0.136826i
$493$	−28.3729	−	16.3811i	−1.27785	−	0.737767i
$494$	0.703715	+	1.21887i	0.0316616	+	0.0548395i
$495$	12.3143	−	1.75491i	0.553488	−	0.0788774i
$496$	4.65392	−	8.06082i	0.208967	−	0.361942i
$497$	−45.8225	−	26.4556i	−2.05542	−	1.18670i
$498$	8.26772	+	4.77337i	0.370486	+	0.213900i
$499$	−14.8859	−	25.7831i	−0.666384	−	1.15421i	−0.978908	−	0.204301i	$-0.934508\pi$
$499$	−14.8859	−	25.7831i	−0.666384	−	1.15421i	0.312524	−	0.949910i	$-0.398825\pi$
$500$	−9.08299	−	6.51915i	−0.406204	−	0.291545i
$501$	−1.08258	+	1.87508i	−0.0483659	+	0.0837723i
$502$	−14.9634	−	8.63909i	−0.667847	−	0.385582i
$503$	−12.7463	−	7.35909i	−0.568330	−	0.328126i	0.188152	−	0.982140i	$-0.439750\pi$
$503$	−12.7463	−	7.35909i	−0.568330	−	0.328126i	−0.756482	+	0.654014i	$0.773084\pi$
$504$	−4.59082			−0.204491
$505$	13.4710	+	17.1736i	0.599450	+	0.764215i
$506$	17.5691	−	30.4306i	0.781043	−	1.35281i
$507$			3.68037i			0.163451i
$508$			9.33485i			0.414167i
$509$	−4.55207	+	7.88442i	−0.201767	+	0.349471i	−0.949098	−	0.314981i	$-0.898002\pi$
$509$	−4.55207	+	7.88442i	−0.201767	+	0.349471i	0.747331	+	0.664452i	$0.231335\pi$
$510$	−1.55428	−	10.9065i	−0.0688247	−	0.482947i
$511$	10.3137	+	17.8639i	0.456253	+	0.790253i
$512$		−	1.00000i		−	0.0441942i
$513$	0.298438	−	0.172303i	0.0131764	−	0.00760738i
$514$	8.87105	+	15.3651i	0.391285	+	0.677726i
$515$	−12.0296	+	9.43601i	−0.530088	+	0.415800i
$516$	1.41795	−	2.45596i	0.0624216	−	0.108117i
$517$		−	4.39947i		−	0.193489i
$518$	25.0570	−	12.3264i	1.10094	−	0.541593i
$519$	−14.1172			−0.619675
$520$	3.40473	−	8.47406i	0.149307	−	0.371612i
$521$	−15.4746	−	26.8028i	−0.677954	−	1.17425i	−0.975596	−	0.219574i	$-0.929533\pi$
$521$	−15.4746	−	26.8028i	−0.677954	−	1.17425i	0.297642	−	0.954678i	$-0.403800\pi$
$522$	−5.75888	+	3.32489i	−0.252059	+	0.145526i
$523$	−27.5574	+	15.9103i	−1.20500	+	0.695708i	−0.961663	−	0.274234i	$-0.911576\pi$
$523$	−27.5574	+	15.9103i	−1.20500	+	0.695708i	−0.243338	+	0.969942i	$0.578242\pi$
$524$	−1.30348			−0.0569428
$525$	16.5732	+	15.8814i	0.723314	+	0.693120i
$526$	8.14101			0.354965
$527$	−39.7141	−	22.9290i	−1.72997	−	0.998801i
$528$		−	5.56277i		−	0.242089i
$529$	−16.9005			−0.734803
$530$	−7.30656	+	18.1853i	−0.317376	+	0.789921i
$531$	−2.46374	−	4.26732i	−0.106917	−	0.185186i
$532$			1.58203i			0.0685895i
$533$	−10.7346	−	6.19760i	−0.464966	−	0.268448i
$534$	7.77936	−	13.4742i	0.336646	−	0.583088i
$535$	31.6816	+	12.7291i	1.36971	+	0.550328i
$536$	4.29570	+	7.44037i	0.185546	+	0.321375i
$537$	0.379553	−	0.219135i	0.0163789	−	0.00945638i
$538$	−16.3028	−	9.41241i	−0.702862	−	0.405798i
$539$	39.1497	−	67.8092i	1.68630	−	2.92075i
$540$	−2.07486	−	0.833642i	−0.0892877	−	0.0358743i
$541$	−6.69515			−0.287847			−0.143923	−	0.989589i	$-0.545972\pi$
$541$	−6.69515			−0.287847			−0.143923	+	0.989589i	$0.545972\pi$
$542$	−7.65239	+	4.41811i	−0.328698	+	0.189774i
$543$	−5.18092	−	2.99121i	−0.222335	−	0.128365i
$544$	−4.92681			−0.211235
$545$	−8.10134	+	1.15452i	−0.347023	+	0.0494542i
$546$	−9.37482	+	16.2377i	−0.401205	+	0.694908i
$547$		−	35.7120i		−	1.52693i	−0.645846	−	0.763467i	$-0.723495\pi$
$547$		−	35.7120i		−	1.52693i	0.645846	−	0.763467i	$-0.276505\pi$
$548$	−1.36344	+	0.787183i	−0.0582433	+	0.0336268i
$549$	2.07282			0.0884660
$550$	−19.2438	+	20.0821i	−0.820557	+	0.856302i
$551$	1.14578	+	1.98455i	0.0488118	+	0.0845446i
$552$	−5.47041	+	3.15834i	−0.232836	+	0.134428i
$553$	32.1201	+	18.5446i	1.36589	+	0.788595i
$554$	8.96452			0.380866
$555$	13.5631	−	1.02096i	0.575721	−	0.0433373i
$556$	3.36589			0.142746
$557$	30.1476	+	17.4057i	1.27739	+	0.737504i	0.976369	−	0.216112i	$-0.0693377\pi$
$557$	30.1476	+	17.4057i	1.27739	+	0.737504i	0.301026	+	0.953616i	$0.402671\pi$
$558$	−8.06082	+	4.65392i	−0.341242	+	0.197016i
$559$	−5.79112	−	10.0305i	−0.244938	−	0.424246i
$560$	8.07701	−	6.33560i	0.341316	−	0.267728i
$561$	−27.4067			−1.15711
$562$	−7.06272	+	4.07767i	−0.297923	+	0.172006i
$563$			9.82543i			0.414093i	0.978331	+	0.207046i	$0.0663851\pi$
$563$			9.82543i			0.414093i	−0.978331	+	0.207046i	$0.933615\pi$
$564$	−0.395439	+	0.684920i	−0.0166510	+	0.0288403i
$565$	0.859869	+	6.03375i	0.0361749	+	0.253842i
$566$	−17.3439			−0.729020
$567$	3.97576	+	2.29541i	0.166966	+	0.0963981i
$568$	−9.98134	+	5.76273i	−0.418808	+	0.241799i
$569$	31.6650			1.32746			0.663732	−	0.747970i	$-0.268971\pi$
$569$	31.6650			1.32746			0.663732	+	0.747970i	$0.268971\pi$
$570$	−0.287279	+	0.715011i	−0.0120328	+	0.0299485i
$571$	−4.57376	+	7.92198i	−0.191406	+	0.331525i	−0.945716	−	0.324993i	$-0.894638\pi$
$571$	−4.57376	+	7.92198i	−0.191406	+	0.331525i	0.754311	+	0.656518i	$0.227971\pi$
$572$	−19.6755	−	11.3596i	−0.822672	−	0.474970i
$573$	5.65752	−	3.26637i	0.236346	−	0.136455i
$574$	−6.96644	−	12.0662i	−0.290774	−	0.503634i
$575$	30.6745	+	7.52236i	1.27922	+	0.313704i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	2.80185	+	1.61765i	0.116642	+	0.0673435i	0.557186	−	0.830388i	$-0.311881\pi$
$577$	2.80185	+	1.61765i	0.116642	+	0.0673435i	−0.440544	+	0.897731i	$0.645214\pi$
$578$			7.27343i			0.302535i
$579$	11.4555	+	19.8415i	0.476073	+	0.824583i
$580$	5.54354	−	13.7974i	0.230183	−	0.572904i
$581$	43.8273			1.81826
$582$		−	10.8823i		−	0.451086i
$583$	42.2236	+	24.3778i	1.74872	+	1.00962i
$584$	4.49320			0.185930
$585$	−7.18561	+	5.63639i	−0.297088	+	0.233036i
$586$	−4.10550			−0.169597
$587$	−7.63234	+	4.40653i	−0.315020	+	0.181877i	−0.649171	−	0.760643i	$-0.724884\pi$
$587$	−7.63234	+	4.40653i	−0.315020	+	0.181877i	0.334150	+	0.942520i	$0.391551\pi$
$588$	−12.1898	+	7.03780i	−0.502700	+	0.290234i
$589$	1.60377	+	2.77781i	0.0660823	+	0.114458i
$590$	10.2238	+	4.10775i	0.420908	+	0.169114i
$591$	−5.50798			−0.226568
$592$	0.403742	−	6.06935i	0.0165937	−	0.249449i
$593$		−	26.1287i		−	1.07298i	−0.843908	−	0.536488i	$-0.819751\pi$
$593$		−	26.1287i		−	1.07298i	0.843908	−	0.536488i	$-0.180249\pi$
$594$	−2.78139	+	4.81750i	−0.114122	+	0.197665i
$595$	−31.2143	−	39.7939i	−1.27966	−	1.63139i
$596$	11.5236	+	19.9595i	0.472026	+	0.817573i
$597$	−1.69365	+	0.977829i	−0.0693165	+	0.0400199i
$598$			25.7983i			1.05497i
$599$	−15.0582	−	26.0816i	−0.615263	−	1.06567i	−0.990338	−	0.138673i	$-0.955716\pi$
$599$	−15.0582	−	26.0816i	−0.615263	−	1.06567i	0.375075	−	0.926994i	$-0.377617\pi$
$600$	4.80095	−	1.39673i	0.195998	−	0.0570213i
$601$	0.722599	−	1.25158i	0.0294754	−	0.0510529i	−0.850911	−	0.525309i	$-0.823950\pi$
$601$	0.722599	−	1.25158i	0.0294754	−	0.0510529i	0.880387	+	0.474256i	$0.157283\pi$
$602$		−	13.0191i		−	0.530617i
$603$		−	8.59140i		−	0.349869i
$604$	−5.89291	+	10.2068i	−0.239779	+	0.415310i
$605$	27.5245	+	35.0900i	1.11903	+	1.42661i
$606$	−9.76114			−0.396519
$607$	30.7389	+	17.7471i	1.24765	+	0.720333i	0.970641	−	0.240533i	$-0.0773221\pi$
$607$	30.7389	+	17.7471i	1.24765	+	0.720333i	0.277013	+	0.960866i	$0.410655\pi$
$608$	0.298438	+	0.172303i	0.0121033	+	0.00698783i
$609$	−15.2640	+	26.4379i	−0.618527	+	1.07132i
$610$	−3.64689	+	2.86062i	−0.147658	+	0.115823i
$611$	1.61504	+	2.79732i	0.0653373	+	0.113168i
$612$	4.26674	+	2.46340i	0.172473	+	0.0995772i
$613$	−24.7958	−	14.3159i	−1.00149	−	0.578212i	−0.0928029	−	0.995685i	$-0.529583\pi$
$613$	−24.7958	−	14.3159i	−1.00149	−	0.578212i	−0.908690	+	0.417473i	$0.862916\pi$
$614$	−5.67241	+	9.82490i	−0.228920	+	0.396501i
$615$	−0.957447	−	6.71846i	−0.0386080	−	0.270915i
$616$	−12.7688	−	22.1163i	−0.514471	−	0.891090i
$617$	−0.156726	−	0.0904860i	−0.00630956	−	0.00364283i	0.496842	−	0.867841i	$-0.334493\pi$
$617$	−0.156726	−	0.0904860i	−0.00630956	−	0.00364283i	−0.503151	+	0.864198i	$0.667826\pi$
$618$		−	6.83740i		−	0.275040i
$619$	2.98990			0.120174			0.0600871	−	0.998193i	$-0.480862\pi$
$619$	2.98990			0.120174			0.0600871	+	0.998193i	$0.480862\pi$
$620$	7.75941	−	19.3125i	0.311625	−	0.775607i
$621$	6.31668			0.253480
$622$	10.7777	−	6.22248i	0.432145	−	0.249499i
$623$		−	71.4272i		−	2.86167i
$624$	2.04208	+	3.53699i	0.0817486	+	0.141593i
$625$	−22.1636	−	11.5660i	−0.886546	−	0.462640i
$626$	5.99199	+	10.3784i	0.239488	+	0.414805i
$627$	1.66014	+	0.958485i	0.0662998	+	0.0382782i
$628$			4.76570i			0.190172i
$629$	−29.9025	−	1.98916i	−1.19229	−	0.0793129i
$630$	−10.1627	+	1.44828i	−0.404892	+	0.0577010i
$631$	−6.44703	+	11.1666i	−0.256652	+	0.444535i	−0.965343	−	0.260985i	$-0.915953\pi$
$631$	−6.44703	+	11.1666i	−0.256652	+	0.444535i	0.708691	+	0.705519i	$0.249286\pi$
$632$	6.99660	−	4.03949i	0.278310	−	0.160682i
$633$	−15.0956	+	8.71546i	−0.599997	+	0.346409i
$634$	−8.52724	−	14.7696i	−0.338660	−	0.586576i
$635$	2.94490	+	20.6646i	0.116865	+	0.820048i
$636$	−4.38231	−	7.59038i	−0.173770	−	0.300978i
$637$			57.4870i			2.27772i
$638$	−32.0353	−	18.4956i	−1.26829	−	0.732248i
$639$	11.5255			0.455940
$640$	−0.315474	−	2.21370i	−0.0124702	−	0.0875043i
$641$	−3.88882	+	6.73563i	−0.153599	+	0.266041i	−0.932548	−	0.361046i	$-0.882420\pi$
$641$	−3.88882	+	6.73563i	−0.153599	+	0.266041i	0.778949	+	0.627087i	$0.215753\pi$
$642$	−13.2236	+	7.63464i	−0.521893	+	0.301315i
$643$		−	10.4182i		−	0.410854i	−0.978672	−	0.205427i	$-0.934142\pi$
$643$		−	10.4182i		−	0.410854i	0.978672	−	0.205427i	$-0.0658583\pi$
$644$	−14.4994	+	25.1136i	−0.571355	+	0.989616i
$645$	2.36412	−	5.88408i	0.0930872	−	0.231685i
$646$	0.848906	−	1.47035i	0.0333997	−	0.0578501i
$647$	19.3832	−	11.1909i	0.762032	−	0.439959i	−0.0679927	−	0.997686i	$-0.521659\pi$
$647$	19.3832	−	11.1909i	0.762032	−	0.439959i	0.830025	+	0.557726i	$0.188326\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	13.7052	−	23.7381i	0.537977	−	0.931804i
$650$	4.86371	−	19.8331i	0.190770	−	0.777920i
$651$	−21.3653	+	37.0058i	−0.837372	+	1.45037i
$652$		−	19.2239i		−	0.752866i
$653$	19.8211	−	11.4437i	0.775660	−	0.447827i	−0.0592300	−	0.998244i	$-0.518865\pi$
$653$	19.8211	−	11.4437i	0.775660	−	0.447827i	0.834890	+	0.550417i	$0.185531\pi$
$654$	1.82982	−	3.16934i	0.0715516	−	0.123931i
$655$	−2.88552	+	0.411214i	−0.112746	+	0.0160675i
$656$	−3.03495			−0.118495
$657$	−3.89123	−	2.24660i	−0.151811	−	0.0876482i
$658$			3.63077i			0.141542i
$659$	−12.6990	−	21.9954i	−0.494684	−	0.856818i	0.505297	−	0.862945i	$-0.331383\pi$
$659$	−12.6990	−	21.9954i	−0.494684	−	0.856818i	−0.999981	+	0.00612736i	$0.998050\pi$
$660$	−1.75491	−	12.3143i	−0.0683098	−	0.479334i
$661$	18.2220	+	31.5614i	0.708754	+	1.22760i	0.965320	+	0.261070i	$0.0840755\pi$
$661$	18.2220	+	31.5614i	0.708754	+	1.22760i	−0.256566	+	0.966527i	$0.582591\pi$
$662$	5.67178	−	3.27461i	0.220440	−	0.127271i
$663$	17.4261	−	10.0609i	0.676772	−	0.390734i
$664$	4.77337	−	8.26772i	0.185243	−	0.320850i
$665$	0.499088	+	3.50213i	0.0193538	+	0.135807i
$666$	−3.38432	+	5.05434i	−0.131140	+	0.195852i
$667$			42.0045i			1.62642i
$668$	1.87508	+	1.08258i	0.0725489	+	0.0418861i
$669$	−7.70983	−	13.3538i	−0.298079	−	0.516288i
$670$	11.8566	+	15.1156i	0.458062	+	0.583966i
$671$	5.76533	+	9.98584i	0.222568	+	0.385499i
$672$			4.59082i			0.177095i
$673$	−19.2569	+	11.1180i	−0.742299	+	0.428567i	−0.822905	−	0.568180i	$-0.807648\pi$
$673$	−19.2569	+	11.1180i	−0.742299	+	0.428567i	0.0806056	+	0.996746i	$0.474315\pi$
$674$	−6.80451			−0.262100
$675$	−4.85611	−	1.19087i	−0.186912	−	0.0458367i
$676$	3.68037			0.141553
$677$			18.6984i			0.718637i	0.933215	+	0.359318i	$0.116991\pi$
$677$			18.6984i			0.718637i	−0.933215	+	0.359318i	$0.883009\pi$
$678$	−2.36047	−	1.36282i	−0.0906534	−	0.0523388i
$679$	−24.9793	−	43.2655i	−0.958618	−	1.66038i
$680$	−10.9065	+	1.55428i	−0.418245	+	0.0596039i
$681$	−10.4794	+	18.1508i	−0.401570	+	0.695540i
$682$	−44.8405	−	25.8887i	−1.71703	−	0.991330i
$683$	22.2375	+	12.8388i	0.850893	+	0.491264i	0.860952	−	0.508686i	$-0.169869\pi$
$683$	22.2375	+	12.8388i	0.850893	+	0.491264i	−0.0100588	+	0.999949i	$0.503202\pi$
$684$	−0.172303	−	0.298438i	−0.00658819	−	0.0114111i
$685$	−2.76992	+	2.17272i	−0.105833	+	0.0830153i
$686$	−16.2414	+	28.1309i	−0.620098	+	1.07404i
$687$	5.27213	+	3.04386i	0.201144	+	0.116131i
$688$	−2.45596	−	1.41795i	−0.0936324	−	0.0540587i
$689$	−35.7961			−1.36372
$690$	−11.1135	+	8.71740i	−0.423083	+	0.331866i
$691$	−1.65593	+	2.86815i	−0.0629945	+	0.109110i	−0.895803	−	0.444452i	$-0.853398\pi$
$691$	−1.65593	+	2.86815i	−0.0629945	+	0.109110i	0.832808	+	0.553562i	$0.186732\pi$
$692$			14.1172i			0.536654i
$693$			25.5377i			0.970096i
$694$	−15.4013	+	26.6758i	−0.584624	+	1.01260i
$695$	7.45109	−	1.06185i	0.282636	−	0.0402784i
$696$	3.32489	+	5.75888i	0.126030	+	0.218290i
$697$			14.9526i			0.566370i
$698$	−17.7527	+	10.2495i	−0.671951	+	0.387951i
$699$	−1.39505	−	2.41630i	−0.0527657	−	0.0913929i
$700$	15.8814	−	16.5732i	0.600260	−	0.626409i
$701$	23.3852	−	40.5044i	0.883248	−	1.52983i	0.0355404	−	0.999368i	$-0.488685\pi$
$701$	23.3852	−	40.5044i	0.883248	−	1.52983i	0.847708	−	0.530463i	$-0.177982\pi$
$702$		−	4.08416i		−	0.154147i
$703$	1.74176	+	1.16626i	0.0656917	+	0.0439864i
$704$	−5.56277			−0.209655
$705$	−0.659309	+	1.64096i	−0.0248310	+	0.0618021i
$706$	−11.5118	−	19.9390i	−0.433253	−	0.750416i
$707$	−38.8080	+	22.4058i	−1.45952	+	0.842657i
$708$	−4.26732	+	2.46374i	−0.160376	+	0.0925930i
$709$	15.5695			0.584726			0.292363	−	0.956307i	$-0.405559\pi$
$709$	15.5695			0.584726			0.292363	+	0.956307i	$0.405559\pi$
$710$	−20.2777	+	15.9058i	−0.761010	+	0.596935i
$711$	−8.07898			−0.302985
$712$	−13.4742	−	7.77936i	−0.504969	−	0.291544i
$713$			58.7946i			2.20188i
$714$	22.6181			0.846460
$715$	−47.1393	−	18.9397i	−1.76291	−	0.708306i
$716$	−0.219135	−	0.379553i	−0.00818947	−	0.0141846i
$717$			22.9098i			0.855580i
$718$	−15.3184	−	8.84406i	−0.571676	−	0.330057i
$719$	13.8700	−	24.0236i	0.517264	−	0.895928i	−0.482535	−	0.875877i	$-0.660284\pi$
$719$	13.8700	−	24.0236i	0.517264	−	0.895928i	0.999799	−	0.0200510i	$-0.00638286\pi$
$720$	−0.833642	+	2.07486i	−0.0310680	+	0.0773254i
$721$	−15.6946	−	27.1839i	−0.584498	−	1.01238i
$722$	16.3516	−	9.44062i	0.608545	−	0.351344i
$723$	−25.7686	−	14.8775i	−0.958343	−	0.553300i
$724$	−2.99121	+	5.18092i	−0.111167	+	0.192547i
$725$	7.91903	−	32.2921i	0.294105	−	1.19930i
$726$	−19.9445			−0.740209
$727$	−10.1585	+	5.86501i	−0.376758	+	0.217521i	−0.676407	−	0.736528i	$-0.736464\pi$
$727$	−10.1585	+	5.86501i	−0.376758	+	0.217521i	0.299649	+	0.954050i	$0.403131\pi$
$728$	16.2377	+	9.37482i	0.601808	+	0.347454i
$729$	−1.00000			−0.0370370
$730$	9.94661	−	1.41749i	0.368140	−	0.0524636i
$731$	−6.98595	+	12.1000i	−0.258385	+	0.447535i
$732$		−	2.07282i		−	0.0766138i
$733$	3.89937	−	2.25130i	0.144026	−	0.0831537i	−0.426255	−	0.904603i	$-0.640167\pi$
$733$	3.89937	−	2.25130i	0.144026	−	0.0831537i	0.570282	+	0.821449i	$0.306834\pi$
$734$	23.8080			0.878769
$735$	−24.7644	+	19.4252i	−0.913448	+	0.716508i
$736$	3.15834	+	5.47041i	0.116418	+	0.201642i
$737$	41.3891	−	23.8960i	1.52459	−	0.880221i
$738$	2.62834	+	1.51747i	0.0967505	+	0.0558589i
$739$	−21.0628			−0.774807			−0.387404	−	0.921910i	$-0.626628\pi$
$739$	−21.0628			−0.774807			−0.387404	+	0.921910i	$0.626628\pi$
$740$	−1.02096	−	13.5631i	−0.0375312	−	0.498589i
$741$	−1.40743			−0.0517032
$742$	−34.8460	−	20.1184i	−1.27924	−	0.738569i
$743$	26.0896	−	15.0628i	0.957135	−	0.552602i	0.0618450	−	0.998086i	$-0.480302\pi$
$743$	26.0896	−	15.0628i	0.957135	−	0.552602i	0.895290	+	0.445484i	$0.146968\pi$
$744$	4.65392	+	8.06082i	0.170621	+	0.295524i
$745$	31.8066	+	40.5490i	1.16530	+	1.48560i
$746$	24.5868			0.900188
$747$	−8.26772	+	4.77337i	−0.302500	+	0.174649i
$748$			27.4067i			1.00209i
$749$	−35.0492	+	60.7070i	−1.28067	+	2.21819i
$750$	10.1872	−	4.60652i	0.371986	−	0.168206i
$751$	−40.9512			−1.49433			−0.747165	−	0.664639i	$-0.768585\pi$
$751$	−40.9512			−1.49433			−0.747165	+	0.664639i	$0.768585\pi$
$752$	0.684920	+	0.395439i	0.0249765	+	0.0144202i
$753$	14.9634	−	8.63909i	0.545295	−	0.314826i
$754$	27.1588			0.989064
$755$	−9.82517	+	24.4539i	−0.357574	+	0.889970i
$756$	2.29541	−	3.97576i	0.0834832	−	0.144597i
$757$	9.54210	+	5.50913i	0.346814	+	0.200233i	0.663281	−	0.748371i	$-0.269163\pi$
$757$	9.54210	+	5.50913i	0.346814	+	0.200233i	−0.316467	+	0.948603i	$0.602497\pi$
$758$	−27.5006	+	15.8775i	−0.998866	+	0.576696i
$759$	17.5691	+	30.4306i	0.637719	+	1.10456i
$760$	0.715011	+	0.287279i	0.0259362	+	0.0104207i
$761$	24.9539	−	43.2215i	0.904579	−	1.56678i	0.0830983	−	0.996541i	$-0.473518\pi$
$761$	24.9539	−	43.2215i	0.904579	−	1.56678i	0.821481	−	0.570236i	$-0.193148\pi$
$762$	−8.08422	−	4.66742i	−0.292860	−	0.169083i
$763$		−	16.8007i		−	0.608227i
$764$	−3.26637	−	5.65752i	−0.118173	−	0.204682i
$765$	10.2224	+	4.10720i	0.369593	+	0.148496i
$766$	2.75571			0.0995678
$767$			20.1246i			0.726658i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	3.34221			0.120523			0.0602616	−	0.998183i	$-0.480807\pi$
$769$	3.34221			0.120523			0.0602616	+	0.998183i	$0.480807\pi$
$770$	−35.2435	−	44.9306i	−1.27009	−	1.61919i
$771$	−17.7421			−0.638966
$772$	19.8415	−	11.4555i	0.714110	−	0.412292i
$773$	−23.3383	+	13.4744i	−0.839420	+	0.484639i	−0.857067	−	0.515205i	$-0.827716\pi$
$773$	−23.3383	+	13.4744i	−0.839420	+	0.484639i	0.0176471	+	0.999844i	$0.494382\pi$
$774$	1.41795	+	2.45596i	0.0509670	+	0.0882775i
$775$	11.0844	−	45.1999i	0.398165	−	1.62363i
$776$	−10.8823			−0.390652
$777$	−1.85350	+	27.8633i	−0.0664941	+	0.999589i
$778$			19.5003i			0.699119i
$779$	0.522931	−	0.905744i	0.0187360	−	0.0324516i
$780$	5.63639	+	7.18561i	0.201815	+	0.257286i
$781$	32.0568	+	55.5240i	1.14708	+	1.98680i
$782$	26.9516	−	15.5605i	0.963789	−	0.556444i
$783$		−	6.64978i		−	0.237644i
$784$	7.03780	+	12.1898i	0.251350	+	0.435351i
$785$	1.50346	+	10.5498i	0.0536606	+	0.376540i
$786$	0.651740	−	1.12885i	0.0232468	−	0.0402646i
$787$			15.2711i			0.544357i	0.962247	+	0.272179i	$0.0877442\pi$
$787$			15.2711i			0.544357i	−0.962247	+	0.272179i	$0.912256\pi$
$788$			5.50798i			0.196214i
$789$	−4.07050	+	7.05032i	−0.144914	+	0.250998i
$790$	14.2140	−	11.1495i	0.505713	−	0.396681i
$791$	−12.5129			−0.444908
$792$	4.81750	+	2.78139i	0.171183	+	0.0988323i
$793$	−7.33155	−	4.23287i	−0.260351	−	0.150314i
$794$	16.9424	−	29.3450i	0.601262	−	1.04142i
$795$	−12.0957	−	15.4203i	−0.428990	−	0.546903i
$796$	0.977829	+	1.69365i	0.0346582	+	0.0600298i
$797$	−14.9279	−	8.61864i	−0.528774	−	0.305288i	0.211743	−	0.977325i	$-0.432086\pi$
$797$	−14.9279	−	8.61864i	−0.528774	−	0.305288i	−0.740517	+	0.672038i	$0.765419\pi$
$798$	−1.37008	−	0.791013i	−0.0485001	−	0.0280016i
$799$	1.94825	−	3.37447i	0.0689242	−	0.119380i
$800$	−1.39673	−	4.80095i	−0.0493819	−	0.169739i
$801$	7.77936	+	13.4742i	0.274870	+	0.476089i
$802$	25.9226	+	14.9664i	0.915360	+	0.528483i
$803$		−	24.9947i		−	0.882043i
$804$	−8.59140			−0.302995
$805$	−24.1746	+	60.1683i	−0.852041	+	2.12065i
$806$	38.0147			1.33901
$807$	16.3028	−	9.41241i	0.573885	−	0.331333i
$808$			9.76114i			0.343396i
$809$	23.1544	+	40.1046i	0.814065	+	1.41000i	0.909998	+	0.414614i	$0.136083\pi$
$809$	23.1544	+	40.1046i	0.814065	+	1.41000i	−0.0959329	+	0.995388i	$0.530583\pi$
$810$	1.75939	−	1.38006i	0.0618185	−	0.0484903i
$811$	−4.17444	−	7.23034i	−0.146584	−	0.253892i	0.783379	−	0.621545i	$-0.213495\pi$
$811$	−4.17444	−	7.23034i	−0.146584	−	0.253892i	−0.929963	+	0.367653i	$0.880161\pi$
$812$	26.4379	+	15.2640i	0.927790	+	0.535660i
$813$		−	8.83621i		−	0.309900i
$814$	−33.7624	−	2.24592i	−1.18337	−	0.0787196i
$815$	−6.06464	−	42.5560i	−0.212435	−	1.49067i
$816$	2.46340	−	4.26674i	0.0862364	−	0.149366i
$817$	0.846339	−	0.488634i	0.0296097	−	0.0170951i
$818$	23.8650	−	13.7785i	0.834420	−	0.481753i
$819$	−9.37482	−	16.2377i	−0.327583	−	0.567390i
$820$	−6.71846	+	0.957447i	−0.234619	+	0.0334355i
$821$	−4.78626	−	8.29004i	−0.167041	−	0.289324i	0.770337	−	0.637637i	$-0.220088\pi$
$821$	−4.78626	−	8.29004i	−0.167041	−	0.289324i	−0.937378	+	0.348313i	$0.886755\pi$
$822$		−	1.57437i		−	0.0549123i
$823$	25.7377	+	14.8597i	0.897161	+	0.517976i	0.876278	−	0.481806i	$-0.160019\pi$
$823$	25.7377	+	14.8597i	0.897161	+	0.517976i	0.0208828	+	0.999782i	$0.493352\pi$
$824$	−6.83740			−0.238192
$825$	−7.76970	−	26.7066i	−0.270506	−	0.929805i
$826$	−11.3106	+	19.5905i	−0.393545	+	0.681640i
$827$	21.0017	−	12.1253i	0.730299	−	0.421638i	−0.0882326	−	0.996100i	$-0.528122\pi$
$827$	21.0017	−	12.1253i	0.730299	−	0.421638i	0.818532	+	0.574462i	$0.194789\pi$
$828$		−	6.31668i		−	0.219520i
$829$	−7.72686	+	13.3833i	−0.268365	+	0.464822i	−0.968440	−	0.249248i	$-0.919817\pi$
$829$	−7.72686	+	13.3833i	−0.268365	+	0.464822i	0.700075	+	0.714070i	$0.253150\pi$
$830$	7.95857	−	19.8081i	0.276246	−	0.687551i
$831$	−4.48226	+	7.76350i	−0.155488	+	0.269313i
$832$	3.53699	−	2.04208i	0.122623	−	0.0707964i
$833$	60.0569	−	34.6739i	2.08085	−	1.20138i
$834$	−1.68295	+	2.91495i	−0.0582757	+	0.100936i
$835$	4.49239	+	1.80496i	0.155465	+	0.0624633i
$836$	0.958485	−	1.66014i	0.0331499	−	0.0574173i
$837$		−	9.30784i		−	0.321726i
$838$	23.2006	−	13.3949i	0.801450	−	0.462718i
$839$	22.7055	−	39.3271i	0.783882	−	1.35772i	−0.145783	−	0.989317i	$-0.546570\pi$
$839$	22.7055	−	39.3271i	0.783882	−	1.35772i	0.929665	−	0.368407i	$-0.120097\pi$
$840$	1.44828	+	10.1627i	0.0499705	+	0.350646i
$841$	15.2196			0.524812
$842$	−19.1342	−	11.0471i	−0.659408	−	0.380710i
$843$		−	8.15533i		−	0.280885i
$844$	8.71546	+	15.0956i	0.299999	+	0.519613i
$845$	8.14725	−	1.16106i	0.280274	−	0.0399417i
$846$	−0.395439	−	0.684920i	−0.0135955	−	0.0235480i
$847$	−79.2945	+	45.7807i	−2.72459	+	1.57304i
$848$	−7.59038	+	4.38231i	−0.260655	+	0.150489i
$849$	8.67196	−	15.0203i	0.297621	−	0.515495i
$850$	−23.6534	+	6.88143i	−0.811304	+	0.236031i
$851$	16.9604	+	34.4770i	0.581396	+	1.18185i
$852$		−	11.5255i		−	0.394856i
$853$	−11.3994	−	6.58143i	−0.390307	−	0.225344i	0.291986	−	0.956423i	$-0.405684\pi$
$853$	−11.3994	−	6.58143i	−0.390307	−	0.225344i	−0.682293	+	0.731079i	$0.739017\pi$
$854$	−4.75798	−	8.24106i	−0.162815	−	0.282003i
$855$	−0.475578	−	0.606296i	−0.0162644	−	0.0207349i
$856$	7.63464	+	13.2236i	0.260947	+	0.451973i
$857$		−	24.1318i		−	0.824326i	−0.911110	−	0.412163i	$-0.864773\pi$
$857$		−	24.1318i		−	0.824326i	0.911110	−	0.412163i	$-0.135227\pi$
$858$	19.6755	−	11.3596i	0.671709	−	0.387812i
$859$	38.0261			1.29743			0.648716	−	0.761030i	$-0.275306\pi$
$859$	38.0261			1.29743			0.648716	+	0.761030i	$0.275306\pi$
$860$	−5.88408	−	2.36412i	−0.200645	−	0.0806159i
$861$	13.9329			0.474831
$862$			19.3497i			0.659055i
$863$	23.1420	+	13.3611i	0.787765	+	0.454816i	0.839175	−	0.543862i	$-0.183038\pi$
$863$	23.1420	+	13.3611i	0.787765	+	0.454816i	−0.0514104	+	0.998678i	$0.516372\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	4.45360	+	31.2512i	0.151427	+	1.06257i
$866$	−8.34837	+	14.4598i	−0.283689	+	0.491364i
$867$	−6.29898	−	3.63672i	−0.213925	−	0.123509i
$868$	37.0058	+	21.3653i	1.25606	+	0.725185i
$869$	−22.4708	−	38.9205i	−0.762269	−	1.32029i
$870$	9.17709	+	11.6995i	0.311132	+	0.396651i
$871$	−17.5443	+	30.3877i	−0.594467	+	1.02965i
$872$	−3.16934	−	1.82982i	−0.107327	−	0.0619655i
$873$	9.42435	+	5.44115i	0.318966	+	0.184155i
$874$	−2.17677			−0.0736304
$875$	29.9282	−	41.6983i	1.01176	−	1.40966i
$876$	−2.24660	+	3.89123i	−0.0759056	+	0.131472i
$877$		−	41.2325i		−	1.39232i	−0.717885	−	0.696161i	$-0.754890\pi$
$877$		−	41.2325i		−	1.39232i	0.717885	−	0.696161i	$-0.245110\pi$
$878$			11.4062i			0.384941i
$879$	2.05275	−	3.55547i	0.0692376	−	0.119923i
$880$	−12.3143	+	1.75491i	−0.415116	+	0.0591580i
$881$	−0.661986	−	1.14659i	−0.0223029	−	0.0386297i	0.854659	−	0.519190i	$-0.173766\pi$
$881$	−0.661986	−	1.14659i	−0.0223029	−	0.0386297i	−0.876961	+	0.480561i	$0.840433\pi$
$882$		−	14.0756i		−	0.473950i
$883$	32.5928	−	18.8174i	1.09683	−	0.633257i	0.161446	−	0.986881i	$-0.448384\pi$
$883$	32.5928	−	18.8174i	1.09683	−	0.633257i	0.935388	+	0.353624i	$0.115051\pi$
$884$	−10.0609	−	17.4261i	−0.338386	−	0.586102i
$885$	−8.66933	+	6.80021i	−0.291416	+	0.228587i
$886$	−3.10645	+	5.38053i	−0.104363	+	0.180762i
$887$		−	52.7455i		−	1.77102i	−0.464619	−	0.885511i	$-0.653809\pi$
$887$		−	52.7455i		−	1.77102i	0.464619	−	0.885511i	$-0.346191\pi$
$888$	5.05434	+	3.38432i	0.169613	+	0.113571i
$889$	−42.8546			−1.43730
$890$	−32.2822	−	12.9704i	−1.08210	−	0.434769i
$891$	−2.78139	−	4.81750i	−0.0931800	−	0.161392i
$892$	−13.3538	+	7.70983i	−0.447119	+	0.258144i
$893$	−0.236028	+	0.136271i	−0.00789838	+	0.00456013i
$894$	−23.0472			−0.770815
$895$	−0.604839	−	0.771086i	−0.0202175	−	0.0257746i
$896$	4.59082			0.153368
$897$	−22.3420	−	12.8992i	−0.745978	−	0.430691i
$898$		−	24.9152i		−	0.831430i
$899$	61.8951			2.06432
$900$	−1.19087	+	4.85611i	−0.0396957	+	0.161870i
$901$	21.5908	+	37.3963i	0.719293	+	1.24585i
$902$			16.8827i			0.562133i
$903$	11.2748	+	6.50953i	0.375203	+	0.216624i
$904$	−1.36282	+	2.36047i	−0.0453267	+	0.0785082i
$905$	−4.98719	+	12.4127i	−0.165780	+	0.412611i
$906$	−5.89291	−	10.2068i	−0.195779	−	0.339099i
$907$	−7.47988	+	4.31851i	−0.248365	+	0.143394i	−0.619016	−	0.785379i	$-0.712468\pi$
$907$	−7.47988	+	4.31851i	−0.248365	+	0.143394i	0.370650	+	0.928773i	$0.379135\pi$
$908$	18.1508	+	10.4794i	0.602356	+	0.347770i
$909$	4.88057	−	8.45340i	0.161878	−	0.280381i
$910$	38.9028	+	15.6305i	1.28962	+	0.518146i
$911$	−35.0148			−1.16009			−0.580046	−	0.814584i	$-0.696965\pi$
$911$	−35.0148			−1.16009			−0.580046	+	0.814584i	$0.696965\pi$
$912$	−0.298438	+	0.172303i	−0.00988228	+	0.00570554i
$913$	−45.9915	−	26.5532i	−1.52210	−	0.878782i
$914$	−34.3291			−1.13551
$915$	−0.653922	−	4.58861i	−0.0216180	−	0.151695i
$916$	3.04386	−	5.27213i	0.100572	−	0.174196i
$917$		−	5.98403i		−	0.197610i
$918$	−4.26674	+	2.46340i	−0.140823	+	0.0813044i
$919$	−13.6549			−0.450433			−0.225216	−	0.974309i	$-0.572309\pi$
$919$	−13.6549			−0.450433			−0.225216	+	0.974309i	$0.572309\pi$
$920$	8.71740	+	11.1135i	0.287404	+	0.366400i
$921$	−5.67241	−	9.82490i	−0.186912	−	0.323741i
$922$	15.1407	−	8.74147i	0.498631	−	0.287885i
$923$	−40.7654	−	23.5359i	−1.34181	−	0.774694i
$924$	25.5377			0.840128
$925$	−6.53890	−	29.7026i	−0.214998	−	0.976615i
$926$	−12.6740			−0.416494
$927$	5.92136	+	3.41870i	0.194483	+	0.112285i
$928$	5.75888	−	3.32489i	0.189044	−	0.109145i
$929$	−16.3016	−	28.2353i	−0.534839	−	0.926369i	−0.999171	−	0.0407076i	$-0.987039\pi$
$929$	−16.3016	−	28.2353i	−0.534839	−	0.926369i	0.464332	−	0.885661i	$-0.346295\pi$
$930$	12.8454	+	16.3761i	0.421216	+	0.536993i
$931$	−4.85054			−0.158970
$932$	−2.41630	+	1.39505i	−0.0791486	+	0.0456965i
$933$			12.4450i			0.407430i
$934$	−13.9612	+	24.1816i	−0.456825	+	0.791245i
$935$	8.64611	+	60.6703i	0.282758	+	1.98413i
$936$	−4.08416			−0.133495
$937$	23.4871	+	13.5603i	0.767289	+	0.442994i	0.831907	−	0.554916i	$-0.187249\pi$
$937$	23.4871	+	13.5603i	0.767289	+	0.442994i	−0.0646178	+	0.997910i	$0.520583\pi$
$938$	−34.1574	+	19.7208i	−1.11528	+	0.643906i
$939$	−11.9840			−0.391082
$940$	1.64096	+	0.659309i	0.0535222	+	0.0215043i
$941$	−26.5953	+	46.0644i	−0.866982	+	1.50166i	−0.00191538	+	0.999998i	$0.500610\pi$
$941$	−26.5953	+	46.0644i	−0.866982	+	1.50166i	−0.865066	+	0.501658i	$0.832724\pi$
$942$	−4.12722	−	2.38285i	−0.134472	−	0.0776375i
$943$	16.6024	−	9.58539i	0.540648	−	0.312143i
$944$	2.46374	+	4.26732i	0.0801879	+	0.138889i
$945$	3.82710	−	9.52530i	0.124496	−	0.309858i
$946$	−7.88772	+	13.6619i	−0.256452	+	0.444188i
$947$	−38.7881	−	22.3943i	−1.26045	−	0.727719i	−0.287285	−	0.957845i	$-0.592753\pi$
$947$	−38.7881	−	22.3943i	−1.26045	−	0.727719i	−0.973161	+	0.230127i	$0.926086\pi$
$948$			8.07898i			0.262393i
$949$	9.17548	+	15.8924i	0.297849	+	0.515889i
$950$	1.67345	+	0.410382i	0.0542939	+	0.0133146i
$951$	17.0545			0.553029
$952$		−	22.6181i		−	0.733056i
$953$	20.0337	+	11.5665i	0.648955	+	0.374674i	0.788056	−	0.615604i	$-0.211088\pi$
$953$	20.0337	+	11.5665i	0.648955	+	0.374674i	−0.139101	+	0.990278i	$0.544421\pi$
$954$	8.76462			0.283765
$955$	−9.01557	−	11.4936i	−0.291737	−	0.371924i
$956$	22.9098			0.740954
$957$	32.0353	−	18.4956i	1.03556	−	0.597878i
$958$	−4.58680	+	2.64819i	−0.148193	+	0.0855591i
$959$	−3.61381	−	6.25931i	−0.116696	−	0.202124i
$960$	2.07486	+	0.833642i	0.0669658	+	0.0269057i
$961$	55.6358			1.79470
$962$	22.2917	−	10.9661i	0.718713	−	0.353560i
$963$		−	15.2693i		−	0.492046i
$964$	−14.8775	+	25.7686i	−0.479172	+	0.829950i
$965$	40.3092	−	31.6185i	1.29760	−	1.01784i
$966$	−14.4994	−	25.1136i	−0.466509	−	0.808018i
$967$	31.6057	−	18.2475i	1.01637	−	0.586801i	0.103319	−	0.994648i	$-0.467054\pi$
$967$	31.6057	−	18.2475i	1.01637	−	0.586801i	0.913050	+	0.407847i	$0.133720\pi$
$968$			19.9445i			0.641039i
$969$	0.848906	+	1.47035i	0.0272708	+	0.0472344i
$970$	−24.0902	+	3.43308i	−0.773489	+	0.110230i
$971$	−20.2731	+	35.1140i	−0.650595	+	1.12686i	0.332384	+	0.943144i	$0.392147\pi$
$971$	−20.2731	+	35.1140i	−0.650595	+	1.12686i	−0.982979	+	0.183719i	$0.941186\pi$
$972$			1.00000i			0.0320750i
$973$			15.4522i			0.495375i
$974$	16.7418	−	28.9976i	0.536440	−	0.929142i
$975$	14.7442	+	14.1287i	0.472191	+	0.452480i
$976$	−2.07282			−0.0663495
$977$	−40.6045	−	23.4430i	−1.29905	−	0.750008i	−0.318811	−	0.947818i	$-0.603284\pi$
$977$	−40.6045	−	23.4430i	−1.29905	−	0.750008i	−0.980240	+	0.197810i	$0.936617\pi$
$978$	16.6484	+	9.61195i	0.532357	+	0.307356i
$979$	−43.2748	+	74.9542i	−1.38307	+	2.39555i
$980$	19.4252	+	24.7644i	0.620514	+	0.791069i
$981$	1.82982	+	3.16934i	0.0584216	+	0.101189i
$982$	−28.2147	−	16.2898i	−0.900367	−	0.519827i
$983$	30.6587	+	17.7008i	0.977860	+	0.564568i	0.901623	−	0.432522i	$-0.142376\pi$
$983$	30.6587	+	17.7008i	0.977860	+	0.564568i	0.0762366	+	0.997090i	$0.475710\pi$
$984$	1.51747	−	2.62834i	0.0483753	−	0.0837884i
$985$	1.73762	+	12.1930i	0.0553653	+	0.388502i
$986$	−16.3811	−	28.3729i	−0.521680	−	0.903577i
$987$	−3.14434	−	1.81539i	−0.100085	−	0.0577844i
$988$			1.40743i			0.0447763i
$989$	17.9134			0.569614
$990$	11.5420	+	4.63737i	0.366828	+	0.147385i
$991$	−22.9595			−0.729332			−0.364666	−	0.931138i	$-0.618817\pi$
$991$	−22.9595			−0.729332			−0.364666	+	0.931138i	$0.618817\pi$
$992$	8.06082	−	4.65392i	0.255931	−	0.147762i
$993$			6.54921i			0.207833i
$994$	−26.4556	−	45.8225i	−0.839122	−	1.45340i
$995$	2.69893	+	3.44076i	0.0855617	+	0.109079i
$996$	4.77337	+	8.26772i	0.151250	+	0.261973i
$997$	−16.1071	−	9.29942i	−0.510116	−	0.294516i	0.222765	−	0.974872i	$-0.428492\pi$
$997$	−16.1071	−	9.29942i	−0.510116	−	0.294516i	−0.732881	+	0.680357i	$0.761825\pi$
$998$		−	29.7718i		−	0.942409i
$999$	−2.68502	−	5.45808i	−0.0849504	−	0.172686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.bb.e.1009.11	yes	40
5.4	even	2	inner	1110.2.bb.e.1009.10	✓	40
37.26	even	3	inner	1110.2.bb.e.1099.10	yes	40
185.174	even	6	inner	1110.2.bb.e.1099.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.bb.e.1009.10	✓	40	5.4	even	2	inner
1110.2.bb.e.1009.11	yes	40	1.1	even	1	trivial
1110.2.bb.e.1099.10	yes	40	37.26	even	3	inner
1110.2.bb.e.1099.11	yes	40	185.174	even	6	inner

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.38006 + 1.75939i) q^{5} -1.00000 q^{6} +(-3.97576 + 2.29541i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.38006 + 1.75939i) q^{5} -1.00000 q^{6} +(-3.97576 + 2.29541i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.315474 + 2.21370i) q^{10} +5.56277 q^{11} +(-0.866025 - 0.500000i) q^{12} +(-3.53699 + 2.04208i) q^{13} -4.59082 q^{14} +(-2.07486 - 0.833642i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.26674 + 2.46340i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-0.172303 - 0.298438i) q^{19} +(-0.833642 + 2.07486i) q^{20} +(2.29541 - 3.97576i) q^{21} +(4.81750 + 2.78139i) q^{22} -6.31668i q^{23} +(-0.500000 - 0.866025i) q^{24} +(-1.19087 + 4.85611i) q^{25} -4.08416 q^{26} +1.00000i q^{27} +(-3.97576 - 2.29541i) q^{28} -6.64978 q^{29} +(-1.38006 - 1.75939i) q^{30} -9.30784 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-4.81750 + 2.78139i) q^{33} +(2.46340 + 4.26674i) q^{34} +(-9.52530 - 3.82710i) q^{35} +1.00000 q^{36} +(-5.45808 + 2.68502i) q^{37} -0.344607i q^{38} +(2.04208 - 3.53699i) q^{39} +(-1.75939 + 1.38006i) q^{40} +(1.51747 + 2.62834i) q^{41} +(3.97576 - 2.29541i) q^{42} +2.83589i q^{43} +(2.78139 + 4.81750i) q^{44} +(2.21370 - 0.315474i) q^{45} +(3.15834 - 5.47041i) q^{46} -0.790878i q^{47} -1.00000i q^{48} +(7.03780 - 12.1898i) q^{49} +(-3.45938 + 3.61008i) q^{50} -4.92681 q^{51} +(-3.53699 - 2.04208i) q^{52} +(7.59038 + 4.38231i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(7.67696 + 9.78706i) q^{55} +(-2.29541 - 3.97576i) q^{56} +(0.298438 + 0.172303i) q^{57} +(-5.75888 - 3.32489i) q^{58} +(2.46374 - 4.26732i) q^{59} +(-0.315474 - 2.21370i) q^{60} +(1.03641 + 1.79512i) q^{61} +(-8.06082 - 4.65392i) q^{62} +4.59082i q^{63} -1.00000 q^{64} +(-8.47406 - 3.40473i) q^{65} -5.56277 q^{66} +(7.44037 - 4.29570i) q^{67} +4.92681i q^{68} +(3.15834 + 5.47041i) q^{69} +(-6.33560 - 8.07701i) q^{70} +(5.76273 + 9.98134i) q^{71} +(0.866025 + 0.500000i) q^{72} -4.49320i q^{73} +(-6.06935 - 0.403742i) q^{74} +(-1.39673 - 4.80095i) q^{75} +(0.172303 - 0.298438i) q^{76} +(-22.1163 + 12.7688i) q^{77} +(3.53699 - 2.04208i) q^{78} +(-4.03949 - 6.99660i) q^{79} +(-2.21370 + 0.315474i) q^{80} +(-0.500000 - 0.866025i) q^{81} +3.03495i q^{82} +(-8.26772 - 4.77337i) q^{83} +4.59082 q^{84} +(1.55428 + 10.9065i) q^{85} +(-1.41795 + 2.45596i) q^{86} +(5.75888 - 3.32489i) q^{87} +5.56277i q^{88} +(-7.77936 + 13.4742i) q^{89} +(2.07486 + 0.833642i) q^{90} +(9.37482 - 16.2377i) q^{91} +(5.47041 - 3.15834i) q^{92} +(8.06082 - 4.65392i) q^{93} +(0.395439 - 0.684920i) q^{94} +(0.287279 - 0.715011i) q^{95} +(0.500000 - 0.866025i) q^{96} +10.8823i q^{97} +(12.1898 - 7.03780i) q^{98} +(2.78139 - 4.81750i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9}+O(q^{10}) \) 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9	\( 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9} + 24 q^{14} - 20 q^{16} - 14 q^{19} - 2 q^{20} - 12 q^{21} - 20 q^{24} - 2 q^{25} - 24 q^{26} + 12 q^{29} - 2 q^{30} - 40 q^{31} + 10 q^{34} - 2 q^{35} + 40 q^{36} + 12 q^{39} + 20 q^{41} + 4 q^{45} + 2 q^{46} + 28 q^{49} + 12 q^{50} - 20 q^{51} - 20 q^{54} + 32 q^{55} + 12 q^{56} - 40 q^{59} + 12 q^{61} - 40 q^{64} + 2 q^{65} + 2 q^{69} - 22 q^{70} + 12 q^{71} - 30 q^{74} - 24 q^{75} + 14 q^{76} - 24 q^{79} - 4 q^{80} - 20 q^{81} - 24 q^{84} + 40 q^{85} - 4 q^{86} - 34 q^{89} - 4 q^{91} - 8 q^{94} + 6 q^{95} + 20 q^{96}+O(q^{100}) \) 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9 + 24 * q^14 - 20 * q^16 - 14 * q^19 - 2 * q^20 - 12 * q^21 - 20 * q^24 - 2 * q^25 - 24 * q^26 + 12 * q^29 - 2 * q^30 - 40 * q^31 + 10 * q^34 - 2 * q^35 + 40 * q^36 + 12 * q^39 + 20 * q^41 + 4 * q^45 + 2 * q^46 + 28 * q^49 + 12 * q^50 - 20 * q^51 - 20 * q^54 + 32 * q^55 + 12 * q^56 - 40 * q^59 + 12 * q^61 - 40 * q^64 + 2 * q^65 + 2 * q^69 - 22 * q^70 + 12 * q^71 - 30 * q^74 - 24 * q^75 + 14 * q^76 - 24 * q^79 - 4 * q^80 - 20 * q^81 - 24 * q^84 + 40 * q^85 - 4 * q^86 - 34 * q^89 - 4 * q^91 - 8 * q^94 + 6 * q^95 + 20 * q^96

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