LMFDB - Embedded newform 1110.2.bb.e.1009.10

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			1009.10
Character	$\chi$	$=$	1110.1009
Dual form			1110.2.bb.e.1099.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.833642 + 2.07486i) q^{5} -1.00000 q^{6} +(3.97576 - 2.29541i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.833642 + 2.07486i) 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} +(1.75939 + 1.38006i) 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} +(-1.38006 + 1.75939i) q^{20} +(2.29541 - 3.97576i) q^{21} +(-4.81750 - 2.78139i) q^{22} +6.31668i q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.61008 + 3.45938i) q^{25} -4.08416 q^{26} -1.00000i q^{27} +(3.97576 + 2.29541i) q^{28} -6.64978 q^{29} +(-0.833642 - 2.07486i) q^{30} -9.30784 q^{31} +(0.866025 - 0.500000i) q^{32} +(4.81750 - 2.78139i) q^{33} +(2.46340 + 4.26674i) q^{34} +(8.07701 + 6.33560i) q^{35} +1.00000 q^{36} +(5.45808 - 2.68502i) q^{37} +0.344607i q^{38} +(2.04208 - 3.53699i) q^{39} +(2.07486 - 0.833642i) 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} +(4.85611 - 1.19087i) q^{50} -4.92681 q^{51} +(3.53699 + 2.04208i) q^{52} +(-7.59038 - 4.38231i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(4.63737 + 11.5420i) 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} +(7.18561 + 5.63639i) q^{65} -5.56277 q^{66} +(-7.44037 + 4.29570i) q^{67} -4.92681i q^{68} +(3.15834 + 5.47041i) q^{69} +(-3.82710 - 9.52530i) 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} +(-1.75939 - 1.38006i) 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} +(0.475578 - 0.606296i) 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
$5$	0.833642	+	2.07486i	0.372816	+	0.927905i
$5$	0.833642	+	2.07486i	0.372816	+	0.927905i
$6$	−1.00000			−0.408248
$7$	3.97576	−	2.29541i	1.50270	−	0.867583i	0.502702	−	0.864460i	$-0.332339\pi$
$7$	3.97576	−	2.29541i	1.50270	−	0.867583i	0.999995	−	0.00312296i	$-0.000994071\pi$
$8$		−	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	0.0784168	−	0.996921i	$-0.475014\pi$
$13$	3.53699	−	2.04208i	0.980984	−	0.566371i	0.902567	+	0.430549i	$0.141680\pi$
$14$	−4.59082			−1.22695
$15$	1.75939	+	1.38006i	0.454271	+	0.356330i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.26674	−	2.46340i	−1.03484	−	0.597463i	−0.116470	−	0.993194i	$-0.537158\pi$
$17$	−4.26674	−	2.46340i	−1.03484	−	0.597463i	−0.918366	+	0.395731i	$0.870491\pi$
$18$	−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	$0.845919\pi$
$20$	−1.38006	+	1.75939i	−0.308591	+	0.393410i
$21$	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	$0.228834\pi$
$23$			6.31668i			1.31712i	−0.752529	+	0.658560i	$0.771166\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−3.61008	+	3.45938i	−0.722016	+	0.691876i
$26$	−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	$0.711821\pi$
$30$	−0.833642	−	2.07486i	−0.152202	−	0.378816i
$31$	−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
$35$	8.07701	+	6.33560i	1.36526	+	1.07091i
$36$	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
$40$	2.07486	−	0.833642i	0.328064	−	0.131810i
$41$	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	$-0.930622\pi$
$43$		−	2.83589i		−	0.432470i	0.976341	−	0.216235i	$-0.0693777\pi$
$44$	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	$0.0183705\pi$
$47$			0.790878i			0.115361i	−0.998335	+	0.0576807i	$0.981629\pi$
$48$			1.00000i			0.144338i
$49$	7.03780	−	12.1898i	1.00540	−	1.74140i
$50$	4.85611	−	1.19087i	0.686758	−	0.168415i
$51$	−4.92681			−0.689891
$52$	3.53699	+	2.04208i	0.490492	+	0.283186i
$53$	−7.59038	−	4.38231i	−1.04262	−	0.601956i	−0.122045	−	0.992525i	$-0.538945\pi$
$53$	−7.59038	−	4.38231i	−1.04262	−	0.601956i	−0.920574	+	0.390568i	$0.872279\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	4.63737	+	11.5420i	0.625302	+	1.55632i
$56$	−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
$65$	7.18561	+	5.63639i	0.891265	+	0.699108i
$66$	−5.56277			−0.684730
$67$	−7.44037	+	4.29570i	−0.908986	+	0.524804i	−0.880105	−	0.474779i	$-0.842528\pi$
$67$	−7.44037	+	4.29570i	−0.908986	+	0.524804i	−0.0288815	+	0.999583i	$0.509195\pi$
$68$		−	4.92681i		−	0.597463i
$69$	3.15834	+	5.47041i	0.380220	+	0.658560i
$70$	−3.82710	−	9.52530i	−0.457426	−	1.13849i
$71$	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	$0.0846937\pi$
$73$			4.49320i			0.525889i	−0.964811	+	0.262945i	$0.915306\pi$
$74$	−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	0.879626	−	0.475666i	$-0.157793\pi$
$83$	8.26772	+	4.77337i	0.907500	+	0.523946i	0.0278744	+	0.999611i	$0.491126\pi$
$84$	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	$0.858061\pi$
$90$	−1.75939	−	1.38006i	−0.185455	−	0.145471i
$91$	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
$95$	0.475578	−	0.606296i	0.0487933	−	0.0622047i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$		−	10.8823i		−	1.10493i	−0.833536	−	0.552465i	$-0.813687\pi$
$97$		−	10.8823i		−	1.10493i	0.833536	−	0.552465i	$-0.186313\pi$
$98$	−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	$-0.890637\pi$
$103$		−	6.83740i		−	0.673709i	0.941557	−	0.336854i	$-0.109363\pi$
$104$	−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	−0.976549	−	0.215296i	$-0.930928\pi$
$107$	−13.2236	+	7.63464i	−1.27837	+	0.738068i	−0.301823	+	0.953364i	$0.597595\pi$
$108$	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	0.384847	−	0.922981i	$-0.374254\pi$
$113$	−2.36047	−	1.36282i	−0.222055	−	0.128203i	−0.606901	+	0.794777i	$0.707588\pi$
$114$	0.172303	+	0.298438i	0.0161377	+	0.0279513i
$115$	−13.1062	+	5.26585i	−1.22216	+	0.491043i
$116$	−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
$120$	1.38006	−	1.75939i	0.125982	−	0.160609i
$121$	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	0.0964214	−	0.995341i	$-0.469260\pi$
$127$	−8.08422	−	4.66742i	−0.717358	−	0.414167i	−0.813780	+	0.581174i	$0.802594\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−1.41795	−	2.45596i	−0.124843	−	0.216235i
$130$	−3.40473	−	8.47406i	−0.298615	−	0.743224i
$131$	−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
$135$	2.07486	−	0.833642i	0.178575	−	0.0717485i
$136$	−2.46340	+	4.26674i	−0.211235	+	0.365870i
$137$		−	1.57437i		−	0.134507i	−0.997736	−	0.0672536i	$-0.978576\pi$
$137$		−	1.57437i		−	0.134507i	0.997736	−	0.0672536i	$-0.0214237\pi$
$138$		−	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
$145$	−5.54354	−	13.7974i	−0.460366	−	1.14581i
$146$	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	$0.106980\pi$
$150$	3.61008	−	3.45938i	0.294762	−	0.282457i
$151$	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
$155$	−7.75941	−	19.3125i	−0.623251	−	1.55121i
$156$	4.08416			0.326995
$157$	−4.12722	−	2.38285i	−0.329388	−	0.190172i	0.326181	−	0.945307i	$-0.394238\pi$
$157$	−4.12722	−	2.38285i	−0.329388	−	0.190172i	−0.655569	+	0.755135i	$0.727571\pi$
$158$			8.07898i			0.642729i
$159$	−8.76462			−0.695079
$160$	1.75939	+	1.38006i	0.139092	+	0.109103i
$161$	14.4994	+	25.1136i	1.14271	+	1.97923i
$162$			1.00000i			0.0785674i
$163$	16.6484	+	9.61195i	1.30400	+	0.752866i	0.981088	−	0.193562i	$-0.0620042\pi$
$163$	16.6484	+	9.61195i	1.30400	+	0.752866i	0.322914	+	0.946428i	$0.395338\pi$
$164$	−1.51747	+	2.62834i	−0.118495	+	0.205239i
$165$	9.78706	+	7.67696i	0.761922	+	0.597651i
$166$	−4.77337	−	8.26772i	−0.370486	−	0.641700i
$167$	−1.87508	+	1.08258i	−0.145098	+	0.0837723i	−0.570791	−	0.821095i	$-0.693363\pi$
$167$	−1.87508	+	1.08258i	−0.145098	+	0.0837723i	0.425694	+	0.904867i	$0.360030\pi$
$168$	−3.97576	−	2.29541i	−0.306737	−	0.177095i
$169$	1.84019	−	3.18730i	0.141553	−	0.245177i
$170$	−6.79929	+	8.66815i	−0.521482	+	0.664817i
$171$	−0.344607			−0.0263527
$172$	2.45596	−	1.41795i	0.187265	−	0.108117i
$173$	−12.2258	−	7.05859i	−0.929512	−	0.536654i	−0.0428551	−	0.999081i	$-0.513645\pi$
$173$	−12.2258	−	7.05859i	−0.929512	−	0.536654i	−0.886657	+	0.462427i	$0.846979\pi$
$174$	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	$0.505214\pi$
$180$	0.833642	+	2.07486i	0.0621360	+	0.154651i
$181$	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
$185$	10.1211	+	9.08640i	0.744121	+	0.668045i
$186$	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
$190$	−0.715011	+	0.287279i	−0.0518723	+	0.0208414i
$191$	−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	$0.308590\pi$
$193$			22.9110i			1.64917i	−0.565740	+	0.824583i	$0.691410\pi$
$194$	−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	0.320355	−	0.947298i	$-0.396198\pi$
$197$	−4.77005	−	2.75399i	−0.339852	−	0.196214i	−0.660207	+	0.751084i	$0.729531\pi$
$198$	−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	$0.477918\pi$
$200$	3.45938	+	3.61008i	0.244615	+	0.255271i
$201$	−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
$205$	−4.18841	+	5.33964i	−0.292531	+	0.372936i
$206$	−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
$210$	−8.07701	−	6.33560i	−0.557367	−	0.437198i
$211$	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
$215$	5.88408	−	2.36412i	0.401291	−	0.161232i
$216$	−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
$220$	−7.67696	+	9.78706i	−0.517581	+	0.659844i
$221$	−20.1219			−1.35354
$222$	−5.45808	+	2.68502i	−0.366322	+	0.180207i
$223$		−	15.4197i		−	1.03258i	−0.856415	−	0.516288i	$-0.827313\pi$
$223$		−	15.4197i		−	1.03258i	0.856415	−	0.516288i	$-0.172687\pi$
$224$	2.29541	−	3.97576i	0.153368	−	0.265642i
$225$	1.19087	+	4.85611i	0.0793914	+	0.323741i
$226$	1.36282	+	2.36047i	0.0906534	+	0.157016i
$227$	−18.1508	+	10.4794i	−1.20471	+	0.695540i	−0.961599	−	0.274458i	$-0.911502\pi$
$227$	−18.1508	+	10.4794i	−1.20471	+	0.695540i	−0.243112	+	0.969998i	$0.578168\pi$
$228$		−	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	$-0.970868\pi$
$233$		−	2.79011i		−	0.182786i	0.995815	−	0.0913929i	$-0.0291319\pi$
$234$	−2.04208	+	3.53699i	−0.133495	+	0.231220i
$235$	−1.64096	+	0.659309i	−0.107044	+	0.0430086i
$236$	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	$-0.0989599\pi$
$240$	−2.07486	+	0.833642i	−0.133932	+	0.0538114i
$241$	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
$250$	6.51915	+	9.08299i	0.412307	+	0.574459i
$251$	−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
$255$	−4.10720	−	10.2224i	−0.257203	−	0.640154i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−15.3651	−	8.87105i	−0.958449	−	0.553361i	−0.0627536	−	0.998029i	$-0.519988\pi$
$257$	−15.3651	−	8.87105i	−0.958449	−	0.553361i	−0.895695	+	0.444668i	$0.853322\pi$
$258$			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	−0.701364	−	0.712803i	$-0.747425\pi$
$263$	−7.05032	+	4.07050i	−0.434741	+	0.250998i	0.266623	+	0.963801i	$0.414092\pi$
$264$	−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
$275$	−20.0821	+	19.2438i	−1.21099	+	1.16044i
$276$	−3.15834	+	5.47041i	−0.190110	+	0.329280i
$277$	−7.76350	+	4.48226i	−0.466463	+	0.269313i	−0.714758	−	0.699372i	$-0.753463\pi$
$277$	−7.76350	+	4.48226i	−0.466463	+	0.269313i	0.248295	+	0.968685i	$0.420130\pi$
$278$	−2.91495	+	1.68295i	−0.174827	+	0.100936i
$279$	−4.65392	+	8.06082i	−0.278623	+	0.482589i
$280$	6.33560	−	8.07701i	0.378624	−	0.482694i
$281$	−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	0.0179852	−	0.999838i	$-0.494275\pi$
$283$	15.0203	−	8.67196i	0.892863	−	0.515495i	0.874878	+	0.484343i	$0.160941\pi$
$284$	−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	−0.392535	−	0.919737i	$-0.628402\pi$
$293$	3.55547	−	2.05275i	0.207713	−	0.119923i	0.600248	+	0.799814i	$0.295069\pi$
$294$	−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
$300$	−4.85611	+	1.19087i	−0.280368	+	0.0687550i
$301$	−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
$305$	−2.86062	+	3.64689i	−0.163799	+	0.208821i
$306$	4.92681			0.281647
$307$		−	11.3448i		−	0.647483i	−0.946146	−	0.323741i	$-0.895059\pi$
$307$		−	11.3448i		−	0.647483i	0.946146	−	0.323741i	$-0.104941\pi$
$308$	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	0.177138	−	0.984186i	$-0.443316\pi$
$313$	−10.3784	−	5.99199i	−0.586624	−	0.338687i	−0.763761	+	0.645499i	$0.776650\pi$
$314$	2.38285	+	4.12722i	0.134472	+	0.232912i
$315$	9.52530	−	3.82710i	0.536690	−	0.215633i
$316$	4.03949	−	6.99660i	0.227239	−	0.393590i
$317$	14.7696	+	8.52724i	0.829544	+	0.478937i	0.853696	−	0.520771i	$-0.174355\pi$
$317$	14.7696	+	8.52724i	0.829544	+	0.478937i	−0.0241526	+	0.999708i	$0.507689\pi$
$318$	7.59038	+	4.38231i	0.425647	+	0.245748i
$319$	−36.9912			−2.07111
$320$	−0.833642	−	2.07486i	−0.0466020	−	0.115988i
$321$	−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
$330$	−4.63737	−	11.5420i	−0.255279	−	0.635365i
$331$	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
$335$	−15.1156	−	11.8566i	−0.825853	−	0.647798i
$336$	2.29541	+	3.97576i	0.125225	+	0.216896i
$337$	5.89288	−	3.40225i	0.321005	−	0.185333i	−0.330835	−	0.943689i	$-0.607330\pi$
$337$	5.89288	−	3.40225i	0.321005	−	0.185333i	0.651841	+	0.758356i	$0.273997\pi$
$338$	−3.18730	+	1.84019i	−0.173366	+	0.100093i
$339$	−2.72564			−0.148036
$340$	10.2224	−	4.10720i	0.554389	−	0.222744i
$341$	−51.7774			−2.80390
$342$	0.298438	+	0.172303i	0.0161377	+	0.00931710i
$343$		−	32.4827i		−	1.75390i
$344$	−2.83589			−0.152901
$345$	−8.71740	+	11.1135i	−0.469329	+	0.598329i
$346$	7.05859	+	12.2258i	0.379472	+	0.657265i
$347$		−	30.8025i		−	1.65357i	−0.562522	−	0.826783i	$-0.690169\pi$
$347$		−	30.8025i		−	1.65357i	0.562522	−	0.826783i	$-0.309831\pi$
$348$	−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	$0.981810\pi$
$350$	16.5732	−	15.8814i	0.885876	−	0.848896i
$351$	−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	0.925777	−	0.378070i	$-0.123412\pi$
$353$	19.9390	+	11.5118i	1.06125	+	0.612712i	0.135471	+	0.990781i	$0.456745\pi$
$354$	−2.46374	+	4.26732i	−0.130946	+	0.226806i
$355$	−15.9058	+	20.2777i	−0.844194	+	1.07623i
$356$	−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
$365$	−9.32276	+	3.74572i	−0.487976	+	0.196060i
$366$	−1.03641	−	1.79512i	−0.0541741	−	0.0938323i
$367$	−20.6183	+	11.9040i	−1.07627	+	0.621383i	−0.929887	−	0.367845i	$-0.880096\pi$
$367$	−20.6183	+	11.9040i	−1.07627	+	0.621383i	−0.146380	+	0.989228i	$0.546762\pi$
$368$	−5.47041	−	3.15834i	−0.285165	−	0.164640i
$369$	3.03495			0.157993
$370$	−4.22196	−	12.9296i	−0.219489	−	0.672179i
$371$	−40.2367			−2.08899
$372$	−8.06082	−	4.65392i	−0.417934	−	0.241294i
$373$	−21.2928	+	12.2934i	−1.10250	+	0.636529i	−0.936877	−	0.349660i	$-0.886297\pi$
$373$	−21.2928	+	12.2934i	−1.10250	+	0.636529i	−0.165624	+	0.986189i	$0.552964\pi$
$374$	13.7034	+	23.7349i	0.708584	+	1.22730i
$375$	−11.1257	+	1.10426i	−0.574527	+	0.0570236i
$376$	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	−0.559732	−	0.828674i	$-0.689096\pi$
$383$	−2.38651	+	1.37785i	−0.121945	+	0.0704050i	0.437787	+	0.899079i	$0.355763\pi$
$384$	1.00000			0.0510310
$385$	44.9306	+	35.2435i	2.28988	+	1.79618i
$386$	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	$0.668739\pi$
$390$	−7.18561	−	5.63639i	−0.363858	−	0.285409i
$391$	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
$395$	11.1495	−	14.2140i	0.560991	−	0.715186i
$396$	5.56277			0.279540
$397$			33.8847i			1.70063i	0.526278	+	0.850313i	$0.323587\pi$
$397$			33.8847i			1.70063i	−0.526278	+	0.850313i	$0.676413\pi$
$398$	−1.69365	−	0.977829i	−0.0848950	−	0.0490142i
$399$	−1.58203			−0.0792004
$400$	−1.19087	−	4.85611i	−0.0595436	−	0.242806i
$401$	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
$405$	1.38006	−	1.75939i	0.0685757	−	0.0874245i
$406$	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	$-0.0719188\pi$
$410$	6.29708	−	2.53006i	0.310991	−	0.124951i
$411$	−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	$-0.0604042\pi$
$420$	3.82710	+	9.52530i	0.186743	+	0.464787i
$421$	−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
$425$	23.9251	−	5.86720i	1.16054	−	0.284601i
$426$	−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	$-0.868594\pi$
$433$		−	16.6967i		−	0.802394i	0.915992	−	0.401197i	$-0.131406\pi$
$434$	42.7306			2.05113
$435$	−11.6995	−	9.17709i	−0.560949	−	0.440008i
$436$	−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	$0.745584\pi$
$440$	11.5420	−	4.63737i	0.550242	−	0.221078i
$441$	−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	$-0.952848\pi$
$443$		−	6.21290i		−	0.295184i	0.989048	−	0.147592i	$-0.0471522\pi$
$444$	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	0.397313	−	0.917683i	$-0.369943\pi$
$457$	29.7299	−	17.1646i	1.39071	−	0.802925i	0.993393	+	0.114759i	$0.0366095\pi$
$458$			6.08773i			0.284461i
$459$	−2.46340	+	4.26674i	−0.114982	+	0.199154i
$460$	−11.1135	−	8.71740i	−0.518168	−	0.406451i
$461$	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	−0.222775	−	0.974870i	$-0.571512\pi$
$463$	10.9760	−	6.33701i	0.510099	−	0.294506i	0.732874	+	0.680364i	$0.238178\pi$
$464$	3.32489	−	5.75888i	0.154354	−	0.267349i
$465$	−16.3761	−	12.8454i	−0.759422	−	0.595690i
$466$	−1.39505	+	2.41630i	−0.0646246	+	0.111933i
$467$		−	27.9225i		−	1.29210i	−0.763296	−	0.646049i	$-0.776420\pi$
$467$		−	27.9225i		−	1.29210i	0.763296	−	0.646049i	$-0.223580\pi$
$468$	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
$485$	22.5792	−	9.07195i	1.02527	−	0.411936i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$			33.4835i			1.51728i	0.651509	+	0.758641i	$0.274136\pi$
$487$			33.4835i			1.51728i	−0.651509	+	0.758641i	$0.725864\pi$
$488$	1.79512	−	1.03641i	0.0812612	−	0.0469162i
$489$	19.2239			0.869335
$490$	−24.7644	−	19.4252i	−1.11874	−	0.877539i
$491$	−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	$-0.398825\pi$
$500$	−1.10426	−	11.1257i	−0.0493839	−	0.497555i
$501$	−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	0.756482	−	0.654014i	$-0.226916\pi$
$503$	12.7463	+	7.35909i	0.568330	+	0.328126i	−0.188152	+	0.982140i	$0.560250\pi$
$504$	−4.59082			−0.204491
$505$	8.13730	+	20.2530i	0.362105	+	0.901246i
$506$	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
$515$	14.1866	−	5.69994i	0.625138	−	0.251169i
$516$	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
$520$	5.63639	−	7.18561i	0.247172	−	0.315110i
$521$	−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	0.243338	−	0.969942i	$-0.421758\pi$
$523$	27.5574	−	15.9103i	1.20500	−	0.695708i	0.961663	+	0.274234i	$0.0884243\pi$
$524$	−1.30348			−0.0569428
$525$	5.46707	+	22.2935i	0.238603	+	0.972969i
$526$	8.14101			0.354965
$527$	39.7141	+	22.9290i	1.72997	+	0.998801i
$528$			5.56277i			0.242089i
$529$	−16.9005			−0.734803
$530$	−12.0957	+	15.4203i	−0.525403	+	0.669816i
$531$	−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
$535$	−26.8645	−	21.0725i	−1.16146	−	0.911044i
$536$	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
$540$	1.75939	+	1.38006i	0.0757119	+	0.0593883i
$541$	−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	$0.276505\pi$
$547$			35.7120i			1.52693i	−0.645846	+	0.763467i	$0.723495\pi$
$548$	1.36344	−	0.787183i	0.0582433	−	0.0336268i
$549$	2.07282			0.0884660
$550$	27.0135	−	6.62455i	1.15186	−	0.282472i
$551$	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
$555$	13.3084	+	2.80849i	0.564908	+	0.119214i
$556$	3.36589			0.142746
$557$	−30.1476	−	17.4057i	−1.27739	−	0.737504i	−0.301026	−	0.953616i	$-0.597329\pi$
$557$	−30.1476	−	17.4057i	−1.27739	−	0.737504i	−0.976369	+	0.216112i	$0.930662\pi$
$558$	8.06082	−	4.65392i	0.341242	−	0.197016i
$559$	−5.79112	−	10.0305i	−0.244938	−	0.424246i
$560$	−9.52530	+	3.82710i	−0.402517	+	0.161724i
$561$	−27.4067			−1.15711
$562$	7.06272	−	4.07767i	0.297923	−	0.172006i
$563$		−	9.82543i		−	0.414093i	−0.978331	−	0.207046i	$-0.933615\pi$
$563$		−	9.82543i		−	0.414093i	0.978331	−	0.207046i	$-0.0663851\pi$
$564$	−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	$0.268971\pi$
$570$	−0.475578	+	0.606296i	−0.0199198	+	0.0253949i
$571$	−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
$575$	−21.8518	−	22.8037i	−0.911283	−	0.950981i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−2.80185	−	1.61765i	−0.116642	−	0.0673435i	0.440544	−	0.897731i	$-0.354786\pi$
$577$	−2.80185	−	1.61765i	−0.116642	−	0.0673435i	−0.557186	+	0.830388i	$0.688119\pi$
$578$		−	7.27343i		−	0.302535i
$579$	11.4555	+	19.8415i	0.476073	+	0.824583i
$580$	9.17709	−	11.6995i	0.381058	−	0.485796i
$581$	43.8273			1.81826
$582$			10.8823i			0.451086i
$583$	−42.2236	−	24.3778i	−1.74872	−	1.00962i
$584$	4.49320			0.185930
$585$	8.47406	−	3.40473i	0.350359	−	0.140768i
$586$	−4.10550			−0.169597
$587$	7.63234	−	4.40653i	0.315020	−	0.181877i	−0.334150	−	0.942520i	$-0.608449\pi$
$587$	7.63234	−	4.40653i	0.315020	−	0.181877i	0.649171	+	0.760643i	$0.275116\pi$
$588$	12.1898	−	7.03780i	0.502700	−	0.290234i
$589$	1.60377	+	2.77781i	0.0660823	+	0.114458i
$590$	−8.66933	−	6.80021i	−0.356911	−	0.279960i
$591$	−5.50798			−0.226568
$592$	−0.403742	+	6.06935i	−0.0165937	+	0.249449i
$593$			26.1287i			1.07298i	0.843908	+	0.536488i	$0.180249\pi$
$593$			26.1287i			1.07298i	−0.843908	+	0.536488i	$0.819751\pi$
$594$	−2.78139	+	4.81750i	−0.114122	+	0.197665i
$595$	−18.8554	−	46.9293i	−0.772995	−	1.92391i
$596$	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
$605$	16.6266	+	41.3820i	0.675965	+	1.68242i
$606$	−9.76114			−0.396519
$607$	−30.7389	−	17.7471i	−1.24765	−	0.720333i	−0.277013	−	0.960866i	$-0.589345\pi$
$607$	−30.7389	−	17.7471i	−1.24765	−	0.720333i	−0.970641	+	0.240533i	$0.922678\pi$
$608$	−0.298438	−	0.172303i	−0.0121033	−	0.00698783i
$609$	−15.2640	+	26.4379i	−0.618527	+	1.07132i
$610$	4.30082	−	1.72799i	0.174135	−	0.0699644i
$611$	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	0.908690	−	0.417473i	$-0.137084\pi$
$613$	24.7958	+	14.3159i	1.00149	+	0.578212i	0.0928029	+	0.995685i	$0.470417\pi$
$614$	−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	0.503151	−	0.864198i	$-0.332174\pi$
$617$	0.156726	+	0.0904860i	0.00630956	+	0.00364283i	−0.496842	+	0.867841i	$0.665507\pi$
$618$			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	$0.480862\pi$
$620$	12.8454	−	16.3761i	0.515882	−	0.657679i
$621$	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
$625$	1.06536	−	24.9773i	0.0426146	−	0.999092i
$626$	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	$0.0658583\pi$
$643$			10.4182i			0.410854i	−0.978672	+	0.205427i	$0.934142\pi$
$644$	−14.4994	+	25.1136i	−0.571355	+	0.989616i
$645$	3.91370	−	4.98943i	0.154102	−	0.196459i
$646$	0.848906	−	1.47035i	0.0333997	−	0.0578501i
$647$	−19.3832	+	11.1909i	−0.762032	+	0.439959i	−0.830025	−	0.557726i	$-0.811674\pi$
$647$	−19.3832	+	11.1909i	−0.762032	+	0.439959i	0.0679927	+	0.997686i	$0.478341\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	13.7052	−	23.7381i	0.537977	−	0.931804i
$650$	14.7442	−	14.1287i	0.578313	−	0.554172i
$651$	−21.3653	+	37.0058i	−0.837372	+	1.45037i
$652$			19.2239i			0.752866i
$653$	−19.8211	+	11.4437i	−0.775660	+	0.447827i	−0.834890	−	0.550417i	$-0.814469\pi$
$653$	−19.8211	+	11.4437i	−0.775660	+	0.447827i	0.0592300	+	0.998244i	$0.481135\pi$
$654$	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
$670$	7.16216	+	17.8260i	0.276698	+	0.688677i
$671$	5.76533	+	9.98584i	0.222568	+	0.385499i
$672$		−	4.59082i		−	0.177095i
$673$	19.2569	−	11.1180i	0.742299	−	0.428567i	−0.0806056	−	0.996746i	$-0.525685\pi$
$673$	19.2569	−	11.1180i	0.742299	−	0.428567i	0.822905	+	0.568180i	$0.192352\pi$
$674$	−6.80451			−0.262100
$675$	3.45938	+	3.61008i	0.133152	+	0.138952i
$676$	3.68037			0.141553
$677$		−	18.6984i		−	0.718637i	−0.933215	−	0.359318i	$-0.883009\pi$
$677$		−	18.6984i		−	0.718637i	0.933215	−	0.359318i	$-0.116991\pi$
$678$	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	0.0100588	−	0.999949i	$-0.496798\pi$
$683$	−22.2375	−	12.8388i	−0.850893	−	0.491264i	−0.860952	+	0.508686i	$0.830131\pi$
$684$	−0.172303	−	0.298438i	−0.00658819	−	0.0114111i
$685$	3.26659	−	1.31246i	0.124810	−	0.0501465i
$686$	−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
$690$	13.1062	−	5.26585i	0.498945	−	0.200468i
$691$	−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
$700$	−22.2935	+	5.46707i	−0.842616	+	0.206636i
$701$	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
$705$	−1.09146	+	1.39146i	−0.0411067	+	0.0524053i
$706$	−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	$0.405559\pi$
$710$	23.9137	−	9.60812i	0.897466	−	0.360586i
$711$	−8.07898			−0.302985
$712$	13.4742	+	7.77936i	0.504969	+	0.291544i
$713$		−	58.7946i		−	2.20188i
$714$	22.6181			0.846460
$715$	39.9719	+	31.3539i	1.49487	+	1.17257i
$716$	−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	$-0.00638286\pi$
$720$	−1.38006	+	1.75939i	−0.0514318	+	0.0655684i
$721$	−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
$725$	24.0062	−	23.0041i	0.891569	−	0.854351i
$726$	−19.9445			−0.740209
$727$	10.1585	−	5.86501i	0.376758	−	0.217521i	−0.299649	−	0.954050i	$-0.596869\pi$
$727$	10.1585	−	5.86501i	0.376758	−	0.217521i	0.676407	+	0.736528i	$0.263536\pi$
$728$	−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	−0.570282	−	0.821449i	$-0.693166\pi$
$733$	−3.89937	+	2.25130i	−0.144026	+	0.0831537i	0.426255	+	0.904603i	$0.359833\pi$
$734$	23.8080			0.878769
$735$	29.2049	−	11.7340i	1.07724	−	0.432815i
$736$	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	$0.626628\pi$
$740$	−2.80849	+	13.3084i	−0.103242	+	0.489225i
$741$	−1.40743			−0.0517032
$742$	34.8460	+	20.1184i	1.27924	+	0.738569i
$743$	−26.0896	+	15.0628i	−0.957135	+	0.552602i	−0.895290	−	0.445484i	$-0.853032\pi$
$743$	−26.0896	+	15.0628i	−0.957135	+	0.552602i	−0.0618450	+	0.998086i	$0.519698\pi$
$744$	4.65392	+	8.06082i	0.170621	+	0.295524i
$745$	19.2132	+	47.8198i	0.703916	+	1.75198i
$746$	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
$755$	−16.2651	+	20.7358i	−0.591949	+	0.754653i
$756$	2.29541	−	3.97576i	0.0834832	−	0.144597i
$757$	−9.54210	−	5.50913i	−0.346814	−	0.200233i	0.316467	−	0.948603i	$-0.397503\pi$
$757$	−9.54210	−	5.50913i	−0.346814	−	0.200233i	−0.663281	+	0.748371i	$0.730837\pi$
$758$	27.5006	−	15.8775i	0.998866	−	0.576696i
$759$	17.5691	+	30.4306i	0.637719	+	1.10456i
$760$	−0.606296	−	0.475578i	−0.0219927	−	0.0172510i
$761$	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
$765$	−8.66815	−	6.79929i	−0.313398	−	0.245829i
$766$	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	$0.480807\pi$
$770$	−21.2893	−	52.9871i	−0.767213	−	1.90952i
$771$	−17.7421			−0.638966
$772$	−19.8415	+	11.4555i	−0.714110	+	0.412292i
$773$	23.3383	−	13.4744i	0.839420	−	0.484639i	−0.0176471	−	0.999844i	$-0.505618\pi$
$773$	23.3383	−	13.4744i	0.839420	−	0.484639i	0.857067	+	0.515205i	$0.172284\pi$
$774$	1.41795	+	2.45596i	0.0509670	+	0.0882775i
$775$	33.6020	−	32.1994i	1.20702	−	1.15664i
$776$	−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
$780$	3.40473	+	8.47406i	0.121909	+	0.303420i
$781$	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	$-0.912256\pi$
$787$		−	15.2711i		−	0.544357i	0.962247	−	0.272179i	$-0.0877442\pi$
$788$		−	5.50798i		−	0.196214i
$789$	−4.07050	+	7.05032i	−0.144914	+	0.250998i
$790$	−16.7627	+	6.73498i	−0.596392	+	0.239620i
$791$	−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
$795$	−7.30656	−	18.1853i	−0.259137	−	0.644968i
$796$	0.977829	+	1.69365i	0.0346582	+	0.0600298i
$797$	14.9279	+	8.61864i	0.528774	+	0.305288i	0.740517	−	0.672038i	$-0.234581\pi$
$797$	14.9279	+	8.61864i	0.528774	+	0.305288i	−0.211743	+	0.977325i	$0.567914\pi$
$798$	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
$805$	−40.0200	+	51.0199i	−1.41052	+	1.79822i
$806$	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	$0.530583\pi$
$810$	−2.07486	+	0.833642i	−0.0729031	+	0.0292912i
$811$	−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	−0.0208828	−	0.999782i	$-0.506648\pi$
$823$	−25.7377	−	14.8597i	−0.897161	−	0.517976i	−0.876278	+	0.481806i	$0.839981\pi$
$824$	−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	−0.818532	−	0.574462i	$-0.805211\pi$
$827$	−21.0017	+	12.1253i	−0.730299	+	0.421638i	0.0882326	+	0.996100i	$0.471878\pi$
$828$			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	$0.253150\pi$
$830$	13.1751	−	16.7964i	0.457314	−	0.583011i
$831$	−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
$835$	−3.80934	−	2.98804i	−0.131828	−	0.103405i
$836$	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	0.682293	−	0.731079i	$-0.260983\pi$
$853$	11.3994	+	6.58143i	0.390307	+	0.225344i	−0.291986	+	0.956423i	$0.594316\pi$
$854$	−4.75798	−	8.24106i	−0.162815	−	0.282003i
$855$	−0.287279	−	0.715011i	−0.00982473	−	0.0244528i
$856$	7.63464	+	13.2236i	0.260947	+	0.451973i
$857$			24.1318i			0.824326i	0.911110	+	0.412163i	$0.135227\pi$
$857$			24.1318i			0.824326i	−0.911110	+	0.412163i	$0.864773\pi$
$858$	−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	$0.275306\pi$
$860$	4.98943	+	3.91370i	0.170138	+	0.133456i
$861$	13.9329			0.474831
$862$		−	19.3497i		−	0.659055i
$863$	−23.1420	−	13.3611i	−0.787765	−	0.454816i	0.0514104	−	0.998678i	$-0.483628\pi$
$863$	−23.1420	−	13.3611i	−0.787765	−	0.454816i	−0.839175	+	0.543862i	$0.816962\pi$
$864$	−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
$870$	5.54354	+	13.7974i	0.187944	+	0.467774i
$871$	−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
$875$	−51.0759	+	5.06944i	−1.72668	+	0.171378i
$876$	−2.24660	+	3.89123i	−0.0759056	+	0.131472i
$877$			41.2325i			1.39232i	0.717885	+	0.696161i	$0.245110\pi$
$877$			41.2325i			1.39232i	−0.717885	+	0.696161i	$0.754890\pi$
$878$		−	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	−0.935388	−	0.353624i	$-0.884949\pi$
$883$	−32.5928	+	18.8174i	−1.09683	+	0.633257i	−0.161446	+	0.986881i	$0.551616\pi$
$884$	−10.0609	−	17.4261i	−0.338386	−	0.586102i
$885$	10.2238	−	4.10775i	0.343670	−	0.138081i
$886$	−3.10645	+	5.38053i	−0.104363	+	0.180762i
$887$			52.7455i			1.77102i	0.464619	+	0.885511i	$0.346191\pi$
$887$			52.7455i			1.77102i	−0.464619	+	0.885511i	$0.653809\pi$
$888$	−5.05434	−	3.38432i	−0.169613	−	0.113571i
$889$	−42.8546			−1.43730
$890$	27.3738	+	21.4720i	0.917571	+	0.719742i
$891$	−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
$895$	−0.365361	−	0.909349i	−0.0122127	−	0.0303962i
$896$	4.59082			0.153368
$897$	22.3420	+	12.8992i	0.745978	+	0.430691i
$898$			24.9152i			0.831430i
$899$	61.8951			2.06432
$900$	−3.61008	+	3.45938i	−0.120336	+	0.115313i
$901$	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
$905$	−8.25609	+	10.5254i	−0.274442	+	0.349875i
$906$	−5.89291	−	10.2068i	−0.195779	−	0.339099i
$907$	7.47988	−	4.31851i	0.248365	−	0.143394i	−0.370650	−	0.928773i	$-0.620865\pi$
$907$	7.47988	−	4.31851i	0.248365	−	0.143394i	0.619016	+	0.785379i	$0.287532\pi$
$908$	−18.1508	−	10.4794i	−0.602356	−	0.347770i
$909$	4.88057	−	8.45340i	0.161878	−	0.280381i
$910$	−32.9878	−	25.8756i	−1.09354	−	0.857768i
$911$	−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	$0.572309\pi$
$920$	5.26585	+	13.1062i	0.173610	+	0.432099i
$921$	−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
$925$	−10.4156	+	28.5747i	−0.342463	+	0.939531i
$926$	−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	$-0.346295\pi$
$930$	7.75941	+	19.3125i	0.254441	+	0.633280i
$931$	−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	0.0646178	−	0.997910i	$-0.479417\pi$
$937$	−23.4871	−	13.5603i	−0.767289	−	0.442994i	−0.831907	+	0.554916i	$0.812751\pi$
$938$	34.1574	−	19.7208i	1.11528	−	0.643906i
$939$	−11.9840			−0.391082
$940$	−1.39146	−	1.09146i	−0.0453844	−	0.0355994i
$941$	−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
$945$	6.33560	−	8.07701i	0.206097	−	0.262745i
$946$	−7.88772	+	13.6619i	−0.256452	+	0.444188i
$947$	38.7881	+	22.3943i	1.26045	+	0.727719i	0.973161	−	0.230127i	$-0.0739141\pi$
$947$	38.7881	+	22.3943i	1.26045	+	0.727719i	0.287285	+	0.957845i	$0.407247\pi$
$948$		−	8.07898i		−	0.262393i
$949$	9.17548	+	15.8924i	0.297849	+	0.515889i
$950$	−1.19213	−	1.24406i	−0.0386777	−	0.0403626i
$951$	17.0545			0.553029
$952$			22.6181i			0.733056i
$953$	−20.0337	−	11.5665i	−0.648955	−	0.374674i	0.139101	−	0.990278i	$-0.455579\pi$
$953$	−20.0337	−	11.5665i	−0.648955	−	0.374674i	−0.788056	+	0.615604i	$0.788912\pi$
$954$	8.76462			0.283765
$955$	−5.44597	−	13.5545i	−0.176227	−	0.438614i
$956$	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
$960$	−1.75939	−	1.38006i	−0.0567839	−	0.0445412i
$961$	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
$965$	−47.5370	+	19.0995i	−1.53027	+	0.614836i
$966$	−14.4994	−	25.1136i	−0.466509	−	0.808018i
$967$	−31.6057	+	18.2475i	−1.01637	+	0.586801i	−0.913050	−	0.407847i	$-0.866280\pi$
$967$	−31.6057	+	18.2475i	−1.01637	+	0.586801i	−0.103319	+	0.994648i	$0.532946\pi$
$968$		−	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
$975$	4.86371	+	19.8331i	0.155763	+	0.635169i
$976$	−2.07282			−0.0663495
$977$	40.6045	+	23.4430i	1.29905	+	0.750008i	0.980240	−	0.197810i	$-0.0633831\pi$
$977$	40.6045	+	23.4430i	1.29905	+	0.750008i	0.318811	+	0.947818i	$0.396716\pi$
$978$	−16.6484	−	9.61195i	−0.532357	−	0.307356i
$979$	−43.2748	+	74.9542i	−1.38307	+	2.39555i
$980$	11.7340	+	29.2049i	0.374829	+	0.932915i
$981$	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	−0.0762366	−	0.997090i	$-0.524290\pi$
$983$	−30.6587	−	17.7008i	−0.977860	−	0.564568i	−0.901623	+	0.432522i	$0.857624\pi$
$984$	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
$990$	−9.78706	−	7.67696i	−0.311053	−	0.243990i
$991$	−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
$995$	1.63032	+	4.05772i	0.0516846	+	0.128638i
$996$	4.77337	+	8.26772i	0.151250	+	0.261973i
$997$	16.1071	+	9.29942i	0.510116	+	0.294516i	0.732881	−	0.680357i	$-0.238175\pi$
$997$	16.1071	+	9.29942i	0.510116	+	0.294516i	−0.222765	+	0.974872i	$0.571508\pi$
$998$			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.1009.10	✓	40
5.4	even	2	inner	1110.2.bb.e.1009.11	yes	40
37.26	even	3	inner	1110.2.bb.e.1099.11	yes	40
185.174	even	6	inner	1110.2.bb.e.1099.10	yes	40

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.833642 + 2.07486i) q^{5} -1.00000 q^{6} +(3.97576 - 2.29541i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.833642 + 2.07486i) 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} +(1.75939 + 1.38006i) 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} +(-1.38006 + 1.75939i) q^{20} +(2.29541 - 3.97576i) q^{21} +(-4.81750 - 2.78139i) q^{22} +6.31668i q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.61008 + 3.45938i) q^{25} -4.08416 q^{26} -1.00000i q^{27} +(3.97576 + 2.29541i) q^{28} -6.64978 q^{29} +(-0.833642 - 2.07486i) q^{30} -9.30784 q^{31} +(0.866025 - 0.500000i) q^{32} +(4.81750 - 2.78139i) q^{33} +(2.46340 + 4.26674i) q^{34} +(8.07701 + 6.33560i) q^{35} +1.00000 q^{36} +(5.45808 - 2.68502i) q^{37} +0.344607i q^{38} +(2.04208 - 3.53699i) q^{39} +(2.07486 - 0.833642i) 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} +(4.85611 - 1.19087i) q^{50} -4.92681 q^{51} +(3.53699 + 2.04208i) q^{52} +(-7.59038 - 4.38231i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(4.63737 + 11.5420i) 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} +(7.18561 + 5.63639i) q^{65} -5.56277 q^{66} +(-7.44037 + 4.29570i) q^{67} -4.92681i q^{68} +(3.15834 + 5.47041i) q^{69} +(-3.82710 - 9.52530i) 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} +(-1.75939 - 1.38006i) 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} +(0.475578 - 0.606296i) 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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