LMFDB - Embedded newform 63.2.f.b.22.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,2,Mod(22,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("63.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.503057532734$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.1
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	63.22
Dual form			63.2.f.b.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.849814 - 1.47192i) q^{2} +(0.349814 + 1.69636i) q^{3} +(-0.444368 + 0.769668i) q^{4} +(1.79418 - 3.10761i) q^{5} +(2.19963 - 1.95649i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.88874 q^{8} +(-2.75526 + 1.18682i) q^{9} -6.09888 q^{10} +(1.40545 + 2.43430i) q^{11} +(-1.46108 - 0.484566i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(0.849814 - 1.47192i) q^{14} +(5.89926 + 1.95649i) q^{15} +(2.49381 + 4.31941i) q^{16} -4.11126 q^{17} +(4.08836 + 3.04695i) q^{18} -0.888736 q^{19} +(1.59455 + 2.76185i) q^{20} +(-1.29418 + 1.15113i) q^{21} +(2.38874 - 4.13741i) q^{22} +(-2.93818 + 5.08907i) q^{23} +(-0.660706 - 3.20397i) q^{24} +(-3.93818 - 6.82112i) q^{25} +1.69963 q^{26} +(-2.97710 - 4.25874i) q^{27} -0.888736 q^{28} +(0.849814 + 1.47192i) q^{29} +(-2.13348 - 10.3459i) q^{30} +(3.49381 - 6.05146i) q^{31} +(2.34981 - 4.07000i) q^{32} +(-3.63781 + 3.23569i) q^{33} +(3.49381 + 6.05146i) q^{34} +3.58836 q^{35} +(0.310892 - 2.64802i) q^{36} +4.76509 q^{37} +(0.755260 + 1.30815i) q^{38} +(-1.64400 - 0.545231i) q^{39} +(-3.38874 + 5.86946i) q^{40} +(2.70582 - 4.68661i) q^{41} +(2.79418 + 0.926690i) q^{42} +(-2.60507 - 4.51212i) q^{43} -2.49814 q^{44} +(-1.25526 + 10.6917i) q^{45} +9.98762 q^{46} +(1.33310 + 2.30900i) q^{47} +(-6.45489 + 5.74138i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-6.69344 + 11.5934i) q^{50} +(-1.43818 - 6.97418i) q^{51} +(-0.444368 - 0.769668i) q^{52} -0.123644 q^{53} +(-3.73855 + 8.00119i) q^{54} +10.0865 q^{55} +(-0.944368 - 1.63569i) q^{56} +(-0.310892 - 1.50761i) q^{57} +(1.44437 - 2.50172i) q^{58} +(4.43818 - 7.68715i) q^{59} +(-4.12729 + 3.67107i) q^{60} +(-1.93818 - 3.35702i) q^{61} -11.8764 q^{62} +(-2.40545 - 1.79272i) q^{63} +1.98762 q^{64} +(1.79418 + 3.10761i) q^{65} +(7.85414 + 2.60483i) q^{66} +(-6.15452 + 10.6599i) q^{67} +(1.82691 - 3.16431i) q^{68} +(-9.66071 - 3.20397i) q^{69} +(-3.04944 - 5.28179i) q^{70} -2.87636 q^{71} +(5.20396 - 2.24159i) q^{72} -10.6414 q^{73} +(-4.04944 - 7.01384i) q^{74} +(10.1934 - 9.06668i) q^{75} +(0.394926 - 0.684031i) q^{76} +(-1.40545 + 2.43430i) q^{77} +(0.594554 + 2.88318i) q^{78} +(3.54325 + 6.13709i) q^{79} +17.8974 q^{80} +(6.18292 - 6.53999i) q^{81} -9.19777 q^{82} +(2.05563 + 3.56046i) q^{83} +(-0.310892 - 1.50761i) q^{84} +(-7.37636 + 12.7762i) q^{85} +(-4.42766 + 7.66893i) q^{86} +(-2.19963 + 1.95649i) q^{87} +(-2.65452 - 4.59776i) q^{88} +9.60940 q^{89} +(16.8040 - 7.23828i) q^{90} -1.00000 q^{91} +(-2.61126 - 4.52284i) q^{92} +(11.4876 + 3.80987i) q^{93} +(2.26578 - 3.92445i) q^{94} +(-1.59455 + 2.76185i) q^{95} +(7.72617 + 2.56238i) q^{96} +(-3.66071 - 6.34053i) q^{97} +1.69963 q^{98} +(-6.76145 - 5.03913i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 4 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 3 q^{7} - 12 q^{8} - 4 q^{9} + 2 q^{11} - 2 q^{12} - 3 q^{13} - q^{14} + 11 q^{15} - 3 q^{16} - 24 q^{17} + 13 q^{18} - 6 q^{19} + 16 q^{20} - 2 q^{21}+ \cdots - 46 q^{99}+O(q^{100}) $ 6 * q + q^2 - 4 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 3 * q^7 - 12 * q^8 - 4 * q^9 + 2 * q^11 - 2 * q^12 - 3 * q^13 - q^14 + 11 * q^15 - 3 * q^16 - 24 * q^17 + 13 * q^18 - 6 * q^19 + 16 * q^20 - 2 * q^21 + 15 * q^22 + 15 * q^24 - 6 * q^25 - 2 * q^26 - 7 * q^27 - 6 * q^28 - q^29 - 26 * q^30 + 3 * q^31 + 8 * q^32 + 8 * q^33 + 3 * q^34 + 10 * q^35 - 11 * q^36 - 6 * q^37 - 8 * q^38 + 2 * q^39 - 21 * q^40 + 22 * q^41 + 11 * q^42 + 3 * q^43 + 46 * q^44 + 5 * q^45 + 24 * q^46 + 9 * q^47 - 14 * q^48 - 3 * q^49 - 10 * q^50 + 9 * q^51 - 3 * q^52 - 36 * q^53 - 17 * q^54 - 12 * q^55 - 6 * q^56 + 11 * q^57 + 9 * q^58 + 9 * q^59 - 20 * q^60 + 6 * q^61 - 36 * q^62 - 8 * q^63 - 24 * q^64 + 5 * q^65 - 2 * q^66 - 6 * q^68 - 39 * q^69 + 18 * q^71 - 24 * q^72 + 6 * q^73 - 6 * q^74 + 31 * q^75 + 21 * q^76 - 2 * q^77 + 10 * q^78 - 15 * q^79 + 22 * q^80 + 32 * q^81 + 18 * q^82 + 12 * q^83 + 11 * q^84 - 9 * q^85 - 34 * q^86 - q^87 + 21 * q^88 - 4 * q^89 + 73 * q^90 - 6 * q^91 - 15 * q^92 + 33 * q^93 - 24 * q^94 - 16 * q^95 + 5 * q^96 - 3 * q^97 - 2 * q^98 - 46 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.849814	−	1.47192i	−0.600909	−	1.04081i	−0.992684	−	0.120744i	$-0.961472\pi$
$2$	−0.849814	−	1.47192i	−0.600909	−	1.04081i	0.391774	−	0.920061i	$-0.371861\pi$
$3$	0.349814	+	1.69636i	0.201965	+	0.979393i
$3$	0.349814	+	1.69636i	0.201965	+	0.979393i
$4$	−0.444368	+	0.769668i	−0.222184	+	0.384834i
$5$	1.79418	−	3.10761i	0.802383	−	1.38977i	−0.115661	−	0.993289i	$-0.536899\pi$
$5$	1.79418	−	3.10761i	0.802383	−	1.38977i	0.918044	−	0.396479i	$-0.129768\pi$
$6$	2.19963	−	1.95649i	0.897994	−	0.798733i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	−1.88874			−0.667769
$9$	−2.75526	+	1.18682i	−0.918420	+	0.395607i
$10$	−6.09888			−1.92864
$11$	1.40545	+	2.43430i	0.423758	+	0.733970i	0.996304	−	0.0859026i	$-0.0273774\pi$
$11$	1.40545	+	2.43430i	0.423758	+	0.733970i	−0.572546	+	0.819873i	$0.694044\pi$
$12$	−1.46108	−	0.484566i	−0.421777	−	0.139882i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	−0.926995	−	0.375073i	$-0.877618\pi$
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	0.788320	+	0.615265i	$0.210951\pi$
$14$	0.849814	−	1.47192i	0.227122	−	0.393387i
$15$	5.89926	+	1.95649i	1.52318	+	0.505163i
$16$	2.49381	+	4.31941i	0.623453	+	1.07985i
$17$	−4.11126			−0.997128			−0.498564	−	0.866853i	$-0.666139\pi$
$17$	−4.11126			−0.997128			−0.498564	+	0.866853i	$0.666139\pi$
$18$	4.08836	+	3.04695i	0.963637	+	0.718173i
$19$	−0.888736			−0.203890			−0.101945	−	0.994790i	$-0.532507\pi$
$19$	−0.888736			−0.203890			−0.101945	+	0.994790i	$0.532507\pi$
$20$	1.59455	+	2.76185i	0.356553	+	0.617568i
$21$	−1.29418	+	1.15113i	−0.282414	+	0.251196i
$22$	2.38874	−	4.13741i	0.509280	−	0.882099i
$23$	−2.93818	+	5.08907i	−0.612652	+	1.06115i	0.378139	+	0.925749i	$0.376564\pi$
$23$	−2.93818	+	5.08907i	−0.612652	+	1.06115i	−0.990792	+	0.135396i	$0.956769\pi$
$24$	−0.660706	−	3.20397i	−0.134866	−	0.654008i
$25$	−3.93818	−	6.82112i	−0.787636	−	1.36422i
$26$	1.69963			0.333325
$27$	−2.97710	−	4.25874i	−0.572943	−	0.819595i
$28$	−0.888736			−0.167955
$29$	0.849814	+	1.47192i	0.157807	+	0.273329i	0.934077	−	0.357071i	$-0.116224\pi$
$29$	0.849814	+	1.47192i	0.157807	+	0.273329i	−0.776271	+	0.630399i	$0.782891\pi$
$30$	−2.13348	−	10.3459i	−0.389518	−	1.88889i
$31$	3.49381	−	6.05146i	0.627507	−	1.08687i	−0.360544	−	0.932742i	$-0.617409\pi$
$31$	3.49381	−	6.05146i	0.627507	−	1.08687i	0.988050	−	0.154131i	$-0.0492579\pi$
$32$	2.34981	−	4.07000i	0.415392	−	0.719481i
$33$	−3.63781	+	3.23569i	−0.633261	+	0.563262i
$34$	3.49381	+	6.05146i	0.599183	+	1.03782i
$35$	3.58836			0.606544
$36$	0.310892	−	2.64802i	0.0518154	−	0.441337i
$37$	4.76509			0.783376			0.391688	−	0.920098i	$-0.371891\pi$
$37$	4.76509			0.783376			0.391688	+	0.920098i	$0.371891\pi$
$38$	0.755260	+	1.30815i	0.122519	+	0.212210i
$39$	−1.64400	−	0.545231i	−0.263250	−	0.0873068i
$40$	−3.38874	+	5.86946i	−0.535806	+	0.928044i
$41$	2.70582	−	4.68661i	0.422578	−	0.731926i	−0.573613	−	0.819126i	$-0.694459\pi$
$41$	2.70582	−	4.68661i	0.422578	−	0.731926i	0.996191	+	0.0872002i	$0.0277920\pi$
$42$	2.79418	+	0.926690i	0.431152	+	0.142991i
$43$	−2.60507	−	4.51212i	−0.397270	−	0.688092i	0.596118	−	0.802897i	$-0.296709\pi$
$43$	−2.60507	−	4.51212i	−0.397270	−	0.688092i	−0.993388	+	0.114805i	$0.963376\pi$
$44$	−2.49814			−0.376609
$45$	−1.25526	+	10.6917i	−0.187123	+	1.59382i
$46$	9.98762			1.47259
$47$	1.33310	+	2.30900i	0.194453	+	0.336803i	0.946721	−	0.322055i	$-0.104373\pi$
$47$	1.33310	+	2.30900i	0.194453	+	0.336803i	−0.752268	+	0.658857i	$0.771040\pi$
$48$	−6.45489	+	5.74138i	−0.931683	+	0.828697i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−6.69344	+	11.5934i	−0.946595	+	1.63955i
$51$	−1.43818	−	6.97418i	−0.201385	−	0.976580i
$52$	−0.444368	−	0.769668i	−0.0616227	−	0.106734i
$53$	−0.123644			−0.0169838			−0.00849190	−	0.999964i	$-0.502703\pi$
$53$	−0.123644			−0.0169838			−0.00849190	+	0.999964i	$0.502703\pi$
$54$	−3.73855	+	8.00119i	−0.508752	+	1.08882i
$55$	10.0865			1.36006
$56$	−0.944368	−	1.63569i	−0.126196	−	0.218579i
$57$	−0.310892	−	1.50761i	−0.0411787	−	0.199688i
$58$	1.44437	−	2.50172i	0.189655	−	0.328492i
$59$	4.43818	−	7.68715i	0.577802	−	1.00078i	−0.417929	−	0.908479i	$-0.637244\pi$
$59$	4.43818	−	7.68715i	0.577802	−	1.00078i	0.995731	−	0.0923022i	$-0.0294226\pi$
$60$	−4.12729	+	3.67107i	−0.532830	+	0.473933i
$61$	−1.93818	−	3.35702i	−0.248158	−	0.429823i	0.714857	−	0.699271i	$-0.246492\pi$
$61$	−1.93818	−	3.35702i	−0.248158	−	0.429823i	−0.963015	+	0.269448i	$0.913159\pi$
$62$	−11.8764			−1.50830
$63$	−2.40545	−	1.79272i	−0.303058	−	0.225861i
$64$	1.98762			0.248453
$65$	1.79418	+	3.10761i	0.222541	+	0.385452i
$66$	7.85414	+	2.60483i	0.966778	+	0.320632i
$67$	−6.15452	+	10.6599i	−0.751894	+	1.30232i	0.195010	+	0.980801i	$0.437526\pi$
$67$	−6.15452	+	10.6599i	−0.751894	+	1.30232i	−0.946904	+	0.321517i	$0.895807\pi$
$68$	1.82691	−	3.16431i	0.221546	−	0.383729i
$69$	−9.66071	−	3.20397i	−1.16301	−	0.385713i
$70$	−3.04944	−	5.28179i	−0.364478	−	0.631295i
$71$	−2.87636			−0.341361			−0.170680	−	0.985326i	$-0.554597\pi$
$71$	−2.87636			−0.341361			−0.170680	+	0.985326i	$0.554597\pi$
$72$	5.20396	−	2.24159i	0.613292	−	0.264174i
$73$	−10.6414			−1.24549			−0.622744	−	0.782426i	$-0.713982\pi$
$73$	−10.6414			−1.24549			−0.622744	+	0.782426i	$0.713982\pi$
$74$	−4.04944	−	7.01384i	−0.470738	−	0.815342i
$75$	10.1934	−	9.06668i	1.17704	−	1.04693i
$76$	0.394926	−	0.684031i	0.0453011	−	0.0784638i
$77$	−1.40545	+	2.43430i	−0.160165	+	0.277415i
$78$	0.594554	+	2.88318i	0.0673200	+	0.326456i
$79$	3.54325	+	6.13709i	0.398647	+	0.690477i	0.993559	−	0.113314i	$-0.0361465\pi$
$79$	3.54325	+	6.13709i	0.398647	+	0.690477i	−0.594912	+	0.803791i	$0.702813\pi$
$80$	17.8974			2.00099
$81$	6.18292	−	6.53999i	0.686991	−	0.726666i
$82$	−9.19777			−1.01572
$83$	2.05563	+	3.56046i	0.225635	+	0.390811i	0.956510	−	0.291700i	$-0.0942210\pi$
$83$	2.05563	+	3.56046i	0.225635	+	0.390811i	−0.730875	+	0.682512i	$0.760888\pi$
$84$	−0.310892	−	1.50761i	−0.0339211	−	0.164494i
$85$	−7.37636	+	12.7762i	−0.800078	+	1.38578i
$86$	−4.42766	+	7.66893i	−0.477447	+	0.826962i
$87$	−2.19963	+	1.95649i	−0.235825	+	0.209757i
$88$	−2.65452	−	4.59776i	−0.282972	−	0.490123i
$89$	9.60940			1.01859			0.509297	−	0.860591i	$-0.329905\pi$
$89$	9.60940			1.01859			0.509297	+	0.860591i	$0.329905\pi$
$90$	16.8040	−	7.23828i	1.77130	−	0.762981i
$91$	−1.00000			−0.104828
$92$	−2.61126	−	4.52284i	−0.272243	−	0.471539i
$93$	11.4876	+	3.80987i	1.19121	+	0.395065i
$94$	2.26578	−	3.92445i	0.233697	−	0.404776i
$95$	−1.59455	+	2.76185i	−0.163598	+	0.283360i
$96$	7.72617	+	2.56238i	0.788549	+	0.261522i
$97$	−3.66071	−	6.34053i	−0.371688	−	0.643783i	0.618137	−	0.786070i	$-0.287888\pi$
$97$	−3.66071	−	6.34053i	−0.371688	−	0.643783i	−0.989825	+	0.142287i	$0.954554\pi$
$98$	1.69963			0.171688
$99$	−6.76145	−	5.03913i	−0.679551	−	0.506452i
$100$	7.00000			0.700000
$101$	−1.73236	−	3.00054i	−0.172376	−	0.298564i	0.766874	−	0.641798i	$-0.221811\pi$
$101$	−1.73236	−	3.00054i	−0.172376	−	0.298564i	−0.939250	+	0.343233i	$0.888478\pi$
$102$	−9.04325	+	8.04364i	−0.895415	+	0.796439i
$103$	7.93818	−	13.7493i	0.782172	−	1.35476i	−0.148502	−	0.988912i	$-0.547445\pi$
$103$	7.93818	−	13.7493i	0.782172	−	1.35476i	0.930674	−	0.365849i	$-0.119221\pi$
$104$	0.944368	−	1.63569i	0.0926029	−	0.160393i
$105$	1.25526	+	6.08715i	0.122501	+	0.594045i
$106$	0.105074	+	0.181994i	0.0102057	+	0.0176768i
$107$	−5.35346			−0.517538			−0.258769	−	0.965939i	$-0.583317\pi$
$107$	−5.35346			−0.517538			−0.258769	+	0.965939i	$0.583317\pi$
$108$	4.60074	−	0.398930i	0.442707	−	0.0383871i
$109$	−18.8640			−1.80684			−0.903421	−	0.428755i	$-0.858952\pi$
$109$	−18.8640			−1.80684			−0.903421	+	0.428755i	$0.858952\pi$
$110$	−8.57165	−	14.8465i	−0.817275	−	1.41556i
$111$	1.66690	+	8.08330i	0.158215	+	0.767233i
$112$	−2.49381	+	4.31941i	−0.235643	+	0.408145i
$113$	9.27561	−	16.0658i	0.872576	−	1.51135i	0.0132538	−	0.999912i	$-0.495781\pi$
$113$	9.27561	−	16.0658i	0.872576	−	1.51135i	0.859322	−	0.511434i	$-0.170886\pi$
$114$	−1.95489	+	1.73880i	−0.183092	+	0.162854i
$115$	10.5433	+	18.2614i	0.983163	+	1.70289i
$116$	−1.51052			−0.140248
$117$	0.349814	−	2.97954i	0.0323403	−	0.275458i
$118$	−15.0865			−1.38883
$119$	−2.05563	−	3.56046i	−0.188439	−	0.326387i
$120$	−11.1421	−	3.69529i	−1.01713	−	0.337332i
$121$	1.54944	−	2.68371i	0.140858	−	0.243974i
$122$	−3.29418	+	5.70569i	−0.298241	+	0.516569i
$123$	8.89671	+	2.95059i	0.802189	+	0.266046i
$124$	3.10507	+	5.37815i	0.278844	+	0.482972i
$125$	−10.3214			−0.923175
$126$	−0.594554	+	5.06410i	−0.0529671	+	0.451146i
$127$	9.98762			0.886258			0.443129	−	0.896458i	$-0.353868\pi$
$127$	9.98762			0.886258			0.443129	+	0.896458i	$0.353868\pi$
$128$	−6.38874	−	11.0656i	−0.564690	−	0.978071i
$129$	6.74288	−	5.99754i	0.593678	−	0.528054i
$130$	3.04944	−	5.28179i	0.267454	−	0.463244i
$131$	−8.02654	+	13.9024i	−0.701282	+	1.21466i	0.266734	+	0.963770i	$0.414055\pi$
$131$	−8.02654	+	13.9024i	−0.701282	+	1.21466i	−0.968017	+	0.250886i	$0.919278\pi$
$132$	−0.873885	−	4.23774i	−0.0760619	−	0.368848i
$133$	−0.444368	−	0.769668i	−0.0385316	−	0.0667387i
$134$	20.9208			1.80728
$135$	−18.5760	+	1.61072i	−1.59877	+	0.138629i
$136$	7.76509			0.665851
$137$	6.49381	+	11.2476i	0.554804	+	0.960948i	0.997919	+	0.0644834i	$0.0205400\pi$
$137$	6.49381	+	11.2476i	0.554804	+	0.960948i	−0.443115	+	0.896465i	$0.646127\pi$
$138$	3.49381	+	16.9426i	0.297413	+	1.44225i
$139$	−0.555632	+	0.962383i	−0.0471281	+	0.0816283i	−0.888627	−	0.458630i	$-0.848340\pi$
$139$	−0.555632	+	0.962383i	−0.0471281	+	0.0816283i	0.841499	+	0.540259i	$0.181674\pi$
$140$	−1.59455	+	2.76185i	−0.134764	+	0.233419i
$141$	−3.45056	+	3.06914i	−0.290589	+	0.258468i
$142$	2.44437	+	4.23377i	0.205127	+	0.355290i
$143$	−2.81089			−0.235059
$144$	−11.9975	−	8.94138i	−0.999788	−	0.745115i
$145$	6.09888			0.506485
$146$	9.04325	+	15.6634i	0.748425	+	1.29631i
$147$	−1.64400	−	0.545231i	−0.135595	−	0.0449699i
$148$	−2.11745	+	3.66754i	−0.174054	+	0.301470i
$149$	−4.21634	+	7.30291i	−0.345416	+	0.598278i	−0.985429	−	0.170086i	$-0.945595\pi$
$149$	−4.21634	+	7.30291i	−0.345416	+	0.598278i	0.640013	+	0.768364i	$0.278929\pi$
$150$	−22.0080	−	7.29894i	−1.79694	−	0.595956i
$151$	7.42580	+	12.8619i	0.604303	+	1.04668i	0.992161	+	0.124964i	$0.0398816\pi$
$151$	7.42580	+	12.8619i	0.604303	+	1.04668i	−0.387858	+	0.921719i	$0.626785\pi$
$152$	1.67859			0.136151
$153$	11.3276	−	4.87933i	0.915782	−	0.394470i
$154$	4.77747			0.384980
$155$	−12.5371	−	21.7148i	−1.00700	−	1.74418i
$156$	1.15019	−	1.02305i	0.0920886	−	0.0819094i
$157$	−1.44437	+	2.50172i	−0.115273	+	0.199659i	−0.917889	−	0.396837i	$-0.870108\pi$
$157$	−1.44437	+	2.50172i	−0.115273	+	0.199659i	0.802616	+	0.596496i	$0.203441\pi$
$158$	6.02221	−	10.4308i	0.479101	−	0.829828i
$159$	−0.0432524	−	0.209744i	−0.00343014	−	0.0166338i
$160$	−8.43199	−	14.6046i	−0.666607	−	1.15460i
$161$	−5.87636			−0.463122
$162$	−14.8807	−	3.54299i	−1.16914	−	0.278363i
$163$	−10.3090			−0.807466			−0.403733	−	0.914877i	$-0.632287\pi$
$163$	−10.3090			−0.807466			−0.403733	+	0.914877i	$0.632287\pi$
$164$	2.40476	+	4.16516i	0.187780	+	0.325245i
$165$	3.52840	+	17.1103i	0.274686	+	1.33204i
$166$	3.49381	−	6.05146i	0.271172	−	0.469684i
$167$	−6.07598	+	10.5239i	−0.470174	+	0.814365i	−0.999418	−	0.0341045i	$-0.989142\pi$
$167$	−6.07598	+	10.5239i	−0.470174	+	0.814365i	0.529244	+	0.848469i	$0.322475\pi$
$168$	2.44437	−	2.17417i	0.188587	−	0.167741i
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	25.0741			1.92310
$171$	2.44870	−	1.05477i	0.187257	−	0.0806602i
$172$	4.63045			0.353068
$173$	3.30470	+	5.72391i	0.251252	+	0.435181i	0.963871	−	0.266370i	$-0.0858244\pi$
$173$	3.30470	+	5.72391i	0.251252	+	0.435181i	−0.712619	+	0.701551i	$0.752491\pi$
$174$	4.74907	+	1.57503i	0.360026	+	0.119403i
$175$	3.93818	−	6.82112i	0.297698	−	0.515629i
$176$	−7.00983	+	12.1414i	−0.528386	+	0.915191i
$177$	14.5927	+	4.83967i	1.09685	+	0.363772i
$178$	−8.16621	−	14.1443i	−0.612083	−	1.06016i
$179$	−3.84294			−0.287234			−0.143617	−	0.989633i	$-0.545873\pi$
$179$	−3.84294			−0.287234			−0.143617	+	0.989633i	$0.545873\pi$
$180$	−7.67123	−	5.71716i	−0.571779	−	0.426132i
$181$	18.5426			1.37826			0.689129	−	0.724639i	$-0.257993\pi$
$181$	18.5426			1.37826			0.689129	+	0.724639i	$0.257993\pi$
$182$	0.849814	+	1.47192i	0.0629924	+	0.109106i
$183$	5.01671	−	4.46218i	0.370846	−	0.329854i
$184$	5.54944	−	9.61192i	0.409110	−	0.708600i
$185$	8.54944	−	14.8081i	0.628567	−	1.08871i
$186$	−4.15452	−	20.1466i	−0.304624	−	1.47722i
$187$	−5.77816	−	10.0081i	−0.422541	−	0.731862i
$188$	−2.36955			−0.172818
$189$	2.19963	−	4.70761i	0.159999	−	0.342429i
$190$	5.42030			0.393230
$191$	−2.31708	−	4.01330i	−0.167658	−	0.290392i	0.769938	−	0.638119i	$-0.220287\pi$
$191$	−2.31708	−	4.01330i	−0.167658	−	0.290392i	−0.937596	+	0.347726i	$0.886954\pi$
$192$	0.695298	+	3.37172i	0.0501788	+	0.243333i
$193$	12.6483	−	21.9075i	0.910446	−	1.57694i	0.0970118	−	0.995283i	$-0.469072\pi$
$193$	12.6483	−	21.9075i	0.910446	−	1.57694i	0.813435	−	0.581656i	$-0.197595\pi$
$194$	−6.22184	+	10.7765i	−0.446702	+	0.773711i
$195$	−4.64400	+	4.13066i	−0.332563	+	0.295803i
$196$	−0.444368	−	0.769668i	−0.0317406	−	0.0549763i
$197$	10.7207			0.763816			0.381908	−	0.924200i	$-0.375267\pi$
$197$	10.7207			0.763816			0.381908	+	0.924200i	$0.375267\pi$
$198$	−1.67123	+	14.2346i	−0.118769	+	1.01161i
$199$	−8.76647			−0.621439			−0.310719	−	0.950502i	$-0.600570\pi$
$199$	−8.76647			−0.621439			−0.310719	+	0.950502i	$0.600570\pi$
$200$	7.43818	+	12.8833i	0.525959	+	0.910987i
$201$	−20.2360	−	6.71127i	−1.42734	−	0.473376i
$202$	−2.94437	+	5.09979i	−0.207165	+	0.358820i
$203$	−0.849814	+	1.47192i	−0.0596453	+	0.103309i
$204$	6.00688	+	1.99218i	0.420566	+	0.139481i
$205$	−9.70946	−	16.8173i	−0.678138	−	1.17457i
$206$	−26.9839			−1.88006
$207$	2.05563	−	17.5088i	0.142876	−	1.21695i
$208$	−4.98762			−0.345829
$209$	−1.24907	−	2.16345i	−0.0864000	−	0.149649i
$210$	7.89307	−	7.02059i	0.544673	−	0.484467i
$211$	−5.26509	+	9.11941i	−0.362464	+	0.627806i	−0.988366	−	0.152096i	$-0.951398\pi$
$211$	−5.26509	+	9.11941i	−0.362464	+	0.627806i	0.625902	+	0.779902i	$0.284731\pi$
$212$	0.0549434	−	0.0951647i	0.00377353	−	0.00653594i
$213$	−1.00619	−	4.87933i	−0.0689430	−	0.334326i
$214$	4.54944	+	7.87987i	0.310993	+	0.538656i
$215$	−18.6959			−1.27505
$216$	5.62296	+	8.04364i	0.382594	+	0.547300i
$217$	6.98762			0.474351
$218$	16.0309	+	27.7663i	1.08575	+	1.88057i
$219$	−3.72253	−	18.0517i	−0.251545	−	1.21982i
$220$	−4.48212	+	7.76326i	−0.302184	+	0.523399i
$221$	2.05563	−	3.56046i	0.138277	−	0.239502i
$222$	10.4814	−	9.32284i	0.703468	−	0.625708i
$223$	2.83379	+	4.90827i	0.189765	+	0.328682i	0.945172	−	0.326574i	$-0.105894\pi$
$223$	2.83379	+	4.90827i	0.189765	+	0.328682i	−0.755407	+	0.655256i	$0.772561\pi$
$224$	4.69963			0.314007
$225$	18.9462	+	14.1201i	1.26308	+	0.941338i
$226$	−31.5302			−2.09736
$227$	5.54944	+	9.61192i	0.368329	+	0.637965i	0.989304	−	0.145865i	$-0.0465965\pi$
$227$	5.54944	+	9.61192i	0.368329	+	0.637965i	−0.620975	+	0.783830i	$0.713263\pi$
$228$	1.29851	+	0.430652i	0.0859961	+	0.0285206i
$229$	−9.82141	+	17.0112i	−0.649017	+	1.12413i	0.334341	+	0.942452i	$0.391486\pi$
$229$	−9.82141	+	17.0112i	−0.649017	+	1.12413i	−0.983358	+	0.181679i	$0.941847\pi$
$230$	17.9196	−	31.0377i	1.18158	−	2.04656i
$231$	−4.62110	−	1.53259i	−0.304046	−	0.100837i
$232$	−1.60507	−	2.78007i	−0.105378	−	0.182521i
$233$	8.96286			0.587177			0.293588	−	0.955932i	$-0.405151\pi$
$233$	8.96286			0.587177			0.293588	+	0.955932i	$0.405151\pi$
$234$	−4.68292	+	2.01715i	−0.306132	+	0.131865i
$235$	9.56732			0.624103
$236$	3.94437	+	6.83185i	0.256756	+	0.444715i
$237$	−9.17123	+	8.15747i	−0.595735	+	0.529884i
$238$	−3.49381	+	6.05146i	−0.226470	+	0.392258i
$239$	−5.61126	+	9.71899i	−0.362963	+	0.628670i	−0.988447	−	0.151567i	$-0.951568\pi$
$239$	−5.61126	+	9.71899i	−0.362963	+	0.628670i	0.625484	+	0.780237i	$0.284901\pi$
$240$	6.26076	+	30.3604i	0.404130	+	1.95975i
$241$	3.49312	+	6.05026i	0.225012	+	0.389732i	0.956323	−	0.292312i	$-0.0944246\pi$
$241$	3.49312	+	6.05026i	0.225012	+	0.389732i	−0.731311	+	0.682044i	$0.761091\pi$
$242$	−5.26695			−0.338572
$243$	13.2570	+	8.20066i	0.850440	+	0.526073i
$244$	3.44506			0.220547
$245$	1.79418	+	3.10761i	0.114626	+	0.198538i
$246$	−3.21751	−	15.6027i	−0.205141	−	0.994792i
$247$	0.444368	−	0.769668i	0.0282745	−	0.0489728i
$248$	−6.59888	+	11.4296i	−0.419030	+	0.725781i
$249$	−5.32072	+	4.73259i	−0.337187	+	0.299915i
$250$	8.77128	+	15.1923i	0.554745	+	0.960846i
$251$	4.62041			0.291638			0.145819	−	0.989311i	$-0.453418\pi$
$251$	4.62041			0.291638			0.145819	+	0.989311i	$0.453418\pi$
$252$	2.44870	−	1.05477i	0.154254	−	0.0664442i
$253$	−16.5178			−1.03847
$254$	−8.48762	−	14.7010i	−0.532561	−	0.922422i
$255$	−24.2534	−	8.04364i	−1.51881	−	0.503712i
$256$	−8.87085	+	15.3648i	−0.554428	+	0.960298i
$257$	0.712008	−	1.23323i	0.0444138	−	0.0769270i	−0.842964	−	0.537970i	$-0.819191\pi$
$257$	0.712008	−	1.23323i	0.0444138	−	0.0769270i	0.887378	+	0.461043i	$0.152525\pi$
$258$	−14.5581	−	4.82819i	−0.906348	−	0.300590i
$259$	2.38255	+	4.12669i	0.148044	+	0.256420i
$260$	−3.18911			−0.197780
$261$	−4.08836	−	3.04695i	−0.253063	−	0.188601i
$262$	27.2843			1.68563
$263$	−8.13162	−	14.0844i	−0.501417	−	0.868480i	−0.999999	−	0.00163692i	$-0.999479\pi$
$263$	−8.13162	−	14.0844i	−0.501417	−	0.868480i	0.498582	−	0.866843i	$-0.333854\pi$
$264$	6.87085	−	6.11137i	0.422872	−	0.376129i
$265$	−0.221840	+	0.384237i	−0.0136275	+	0.0236035i
$266$	−0.755260	+	1.30815i	−0.0463080	+	0.0802078i
$267$	3.36151	+	16.3010i	0.205721	+	0.997604i
$268$	−5.46974	−	9.47387i	−0.334118	−	0.578709i
$269$	−18.6538			−1.13734			−0.568672	−	0.822564i	$-0.692543\pi$
$269$	−18.6538			−1.13734			−0.568672	+	0.822564i	$0.692543\pi$
$270$	18.1570	+	25.9736i	1.10500	+	1.58070i
$271$	3.96286			0.240727			0.120363	−	0.992730i	$-0.461594\pi$
$271$	3.96286			0.240727			0.120363	+	0.992730i	$0.461594\pi$
$272$	−10.2527	−	17.7582i	−0.621662	−	1.07675i
$273$	−0.349814	−	1.69636i	−0.0211717	−	0.102668i
$274$	11.0371	−	19.1168i	0.666773	−	1.15489i
$275$	11.0698	−	19.1734i	0.667534	−	1.15620i
$276$	6.75890	−	6.01179i	0.406838	−	0.361867i
$277$	1.16690	+	2.02112i	0.0701120	+	0.121438i	0.898950	−	0.438051i	$-0.144331\pi$
$277$	1.16690	+	2.02112i	0.0701120	+	0.121438i	−0.828838	+	0.559488i	$0.810998\pi$
$278$	1.88874			0.113279
$279$	−2.44437	+	20.8199i	−0.146340	+	1.24645i
$280$	−6.77747			−0.405031
$281$	−13.9975	−	24.2443i	−0.835018	−	1.44629i	−0.894016	−	0.448035i	$-0.852124\pi$
$281$	−13.9975	−	24.2443i	−0.835018	−	1.44629i	0.0589978	−	0.998258i	$-0.481210\pi$
$282$	7.44987	+	2.47075i	0.443633	+	0.147131i
$283$	−5.16002	+	8.93741i	−0.306731	+	0.531274i	−0.977645	−	0.210261i	$-0.932569\pi$
$283$	−5.16002	+	8.93741i	−0.306731	+	0.531274i	0.670914	+	0.741535i	$0.265902\pi$
$284$	1.27816	−	2.21384i	0.0758449	−	0.131367i
$285$	−5.24288	−	1.73880i	−0.310561	−	0.102998i
$286$	2.38874	+	4.13741i	0.141249	+	0.244650i
$287$	5.41164			0.319439
$288$	−1.64400	+	14.0027i	−0.0968734	+	0.825117i
$289$	−0.0975070			−0.00573571
$290$	−5.18292	−	8.97708i	−0.304351	−	0.527152i
$291$	9.47524	−	8.42787i	0.555448	−	0.494051i
$292$	4.72872	−	8.19038i	0.276727	−	0.479306i
$293$	15.3480	−	26.5834i	0.896637	−	1.55302i	0.0648718	−	0.997894i	$-0.479336\pi$
$293$	15.3480	−	26.5834i	0.896637	−	1.55302i	0.831765	−	0.555127i	$-0.187330\pi$
$294$	0.594554	+	2.88318i	0.0346751	+	0.168150i
$295$	−15.9258	−	27.5843i	−0.927236	−	1.60602i
$296$	−9.00000			−0.523114
$297$	6.18292	−	13.2326i	0.358769	−	0.767833i
$298$	14.3324			0.830255
$299$	−2.93818	−	5.08907i	−0.169919	−	0.294309i
$300$	2.44870	+	11.8745i	0.141376	+	0.685575i
$301$	2.60507	−	4.51212i	0.150154	−	0.260074i
$302$	12.6211	−	21.8604i	0.726262	−	1.25792i
$303$	4.48398	−	3.98833i	0.257598	−	0.229124i
$304$	−2.21634	−	3.83881i	−0.127116	−	0.220171i
$305$	−13.9098			−0.796471
$306$	−16.8083	−	12.5268i	−0.960869	−	0.716110i
$307$	−11.4437			−0.653125			−0.326563	−	0.945176i	$-0.605890\pi$
$307$	−11.4437			−0.653125			−0.326563	+	0.945176i	$0.605890\pi$
$308$	−1.24907	−	2.16345i	−0.0711724	−	0.123274i
$309$	26.1007	+	8.65628i	1.48482	+	0.492439i
$310$	−21.3083	+	36.9071i	−1.21023	+	2.09618i
$311$	−5.98143	+	10.3601i	−0.339176	+	0.587470i	−0.984278	−	0.176627i	$-0.943481\pi$
$311$	−5.98143	+	10.3601i	−0.339176	+	0.587470i	0.645102	+	0.764096i	$0.276815\pi$
$312$	3.10507	+	1.02980i	0.175790	+	0.0583008i
$313$	6.77197	+	11.7294i	0.382774	+	0.662985i	0.991458	−	0.130429i	$-0.0416353\pi$
$313$	6.77197	+	11.7294i	0.382774	+	0.662985i	−0.608683	+	0.793413i	$0.708302\pi$
$314$	4.90978			0.277075
$315$	−9.88688	+	4.25874i	−0.557062	+	0.239953i
$316$	−6.29803			−0.354292
$317$	14.9814	+	25.9486i	0.841441	+	1.45742i	0.888676	+	0.458535i	$0.151626\pi$
$317$	14.9814	+	25.9486i	0.841441	+	1.45742i	−0.0472355	+	0.998884i	$0.515041\pi$
$318$	−0.271971	+	0.241908i	−0.0152514	+	0.0135655i
$319$	−2.38874	+	4.13741i	−0.133744	+	0.231651i
$320$	3.56615	−	6.17676i	0.199354	−	0.345291i
$321$	−1.87271	−	9.08138i	−0.104525	−	0.506873i
$322$	4.99381	+	8.64953i	0.278294	+	0.482020i
$323$	3.65383			0.203304
$324$	2.28613	+	7.66496i	0.127007	+	0.425831i
$325$	7.87636			0.436902
$326$	8.76076	+	15.1741i	0.485214	+	0.840415i
$327$	−6.59888	−	32.0001i	−0.364919	−	1.76961i
$328$	−5.11058	+	8.85178i	−0.282184	+	0.488758i
$329$	−1.33310	+	2.30900i	−0.0734964	+	0.127299i
$330$	22.1866	−	19.7341i	1.22133	−	1.08633i
$331$	−1.04325	−	1.80697i	−0.0573423	−	0.0993198i	0.835929	−	0.548837i	$-0.184929\pi$
$331$	−1.04325	−	1.80697i	−0.0573423	−	0.0993198i	−0.893272	+	0.449517i	$0.851596\pi$
$332$	−3.65383			−0.200530
$333$	−13.1291	+	5.65531i	−0.719469	+	0.309909i
$334$	20.6538			1.13013
$335$	22.0846	+	38.2517i	1.20661	+	2.08992i
$336$	−8.19963	−	2.71941i	−0.447326	−	0.148356i
$337$	8.10439	−	14.0372i	0.441474	−	0.764655i	−0.556325	−	0.830965i	$-0.687789\pi$
$337$	8.10439	−	14.0372i	0.441474	−	0.764655i	0.997799	+	0.0663093i	$0.0211224\pi$
$338$	10.1978	−	17.6631i	0.554686	−	0.960743i
$339$	30.4981	+	10.1147i	1.65643	+	0.549355i
$340$	−6.55563	−	11.3547i	−0.355529	−	0.615794i
$341$	19.6414			1.06364
$342$	−3.63348	−	2.70793i	−0.196476	−	0.146428i
$343$	−1.00000			−0.0539949
$344$	4.92030	+	8.52220i	0.265285	+	0.459486i
$345$	−27.2898	+	24.2732i	−1.46923	+	1.30683i
$346$	5.61677	−	9.72852i	0.301959	−	0.523009i
$347$	−5.63348	+	9.75747i	−0.302421	+	0.523808i	−0.976684	−	0.214683i	$-0.931128\pi$
$347$	−5.63348	+	9.75747i	−0.302421	+	0.523808i	0.674263	+	0.738491i	$0.264461\pi$
$348$	−0.528401	−	2.56238i	−0.0283253	−	0.137358i
$349$	0.0988844	+	0.171273i	0.00529316	+	0.00916803i	0.868660	−	0.495409i	$-0.164982\pi$
$349$	0.0988844	+	0.171273i	0.00529316	+	0.00916803i	−0.863367	+	0.504577i	$0.831648\pi$
$350$	−13.3869			−0.715559
$351$	5.17673	−	0.448873i	0.276313	−	0.0239591i
$352$	13.2101			0.704103
$353$	6.25093	+	10.8269i	0.332703	+	0.576259i	0.983041	−	0.183386i	$-0.0587059\pi$
$353$	6.25093	+	10.8269i	0.332703	+	0.576259i	−0.650338	+	0.759645i	$0.725373\pi$
$354$	−5.27747	−	25.5921i	−0.280494	−	1.36021i
$355$	−5.16071	+	8.93861i	−0.273902	+	0.474412i
$356$	−4.27011	+	7.39605i	−0.226315	+	0.391990i
$357$	5.32072	−	4.73259i	0.281603	−	0.250475i
$358$	3.26578	+	5.65650i	0.172602	+	0.298955i
$359$	20.0197			1.05660			0.528299	−	0.849059i	$-0.322830\pi$
$359$	20.0197			1.05660			0.528299	+	0.849059i	$0.322830\pi$
$360$	2.37085	−	20.1937i	0.124955	−	1.06430i
$361$	−18.2101			−0.958429
$362$	−15.7577	−	27.2932i	−0.828208	−	1.43450i
$363$	5.09455	+	1.68961i	0.267395	+	0.0886814i
$364$	0.444368	−	0.769668i	0.0232912	−	0.0403416i
$365$	−19.0927	+	33.0695i	−0.999357	+	1.73094i
$366$	−10.8312	−	3.59218i	−0.566158	−	0.187766i
$367$	−15.0364	−	26.0438i	−0.784892	−	1.35947i	−0.929063	−	0.369921i	$-0.879385\pi$
$367$	−15.0364	−	26.0438i	−0.784892	−	1.35947i	0.144171	−	0.989553i	$-0.453948\pi$
$368$	−29.3090			−1.52784
$369$	−1.89307	+	16.1242i	−0.0985491	+	0.839390i
$370$	−29.0617			−1.51085
$371$	−0.0618219	−	0.107079i	−0.00320963	−	0.00555925i
$372$	−8.03706	+	7.14867i	−0.416702	+	0.370641i
$373$	−3.50619	+	6.07290i	−0.181544	+	0.314443i	−0.942406	−	0.334470i	$-0.891443\pi$
$373$	−3.50619	+	6.07290i	−0.181544	+	0.314443i	0.760863	+	0.648913i	$0.224776\pi$
$374$	−9.82072	+	17.0100i	−0.507818	+	0.879566i
$375$	−3.61058	−	17.5088i	−0.186449	−	0.904151i
$376$	−2.51788	−	4.36110i	−0.129850	−	0.224906i
$377$	−1.69963			−0.0875353
$378$	−8.79851	+	0.762918i	−0.452547	+	0.0392403i
$379$	−19.0741			−0.979772			−0.489886	−	0.871787i	$-0.662962\pi$
$379$	−19.0741			−0.979772			−0.489886	+	0.871787i	$0.662962\pi$
$380$	−1.41714	−	2.45455i	−0.0726976	−	0.125916i
$381$	3.49381	+	16.9426i	0.178993	+	0.867995i
$382$	−3.93818	+	6.82112i	−0.201495	+	0.348999i
$383$	−1.60507	+	2.78007i	−0.0820155	+	0.142055i	−0.904116	−	0.427288i	$-0.859469\pi$
$383$	−1.60507	+	2.78007i	−0.0820155	+	0.142055i	0.822100	+	0.569343i	$0.192802\pi$
$384$	16.5364	−	14.7085i	0.843868	−	0.750590i
$385$	5.04325	+	8.73517i	0.257028	+	0.445185i
$386$	−42.9949			−2.18838
$387$	12.5327	+	9.34031i	0.637075	+	0.474795i
$388$	6.50680			0.330333
$389$	−2.56801	−	4.44793i	−0.130203	−	0.225519i	0.793552	−	0.608503i	$-0.208230\pi$
$389$	−2.56801	−	4.44793i	−0.130203	−	0.225519i	−0.923755	+	0.382984i	$0.874896\pi$
$390$	10.0265	+	3.32530i	0.507714	+	0.168383i
$391$	12.0796	−	20.9225i	0.610893	−	1.05810i
$392$	0.944368	−	1.63569i	0.0476978	−	0.0826150i
$393$	−26.3912	−	8.75264i	−1.33126	−	0.441512i
$394$	−9.11058	−	15.7800i	−0.458984	−	0.794984i
$395$	25.4290			1.27947
$396$	6.88303	−	2.96484i	0.345885	−	0.148989i
$397$	22.9381			1.15123			0.575615	−	0.817721i	$-0.304763\pi$
$397$	22.9381			1.15123			0.575615	+	0.817721i	$0.304763\pi$
$398$	7.44987	+	12.9036i	0.373428	+	0.646797i
$399$	1.15019	−	1.02305i	0.0575813	−	0.0512164i
$400$	19.6421	−	34.0212i	0.982107	−	1.70106i
$401$	9.10507	−	15.7705i	0.454686	−	0.787539i	−0.543984	−	0.839095i	$-0.683085\pi$
$401$	9.10507	−	15.7705i	0.454686	−	0.787539i	0.998670	+	0.0515566i	$0.0164183\pi$
$402$	7.31838	+	35.4891i	0.365008	+	1.77004i
$403$	3.49381	+	6.05146i	0.174039	+	0.301445i
$404$	3.07922			0.153197
$405$	−9.23050	−	30.9481i	−0.458667	−	1.53782i
$406$	2.88874			0.143366
$407$	6.69708	+	11.5997i	0.331962	+	0.574975i
$408$	2.71634	+	13.1724i	0.134479	+	0.652130i
$409$	7.66621	−	13.2783i	0.379070	−	0.656568i	−0.611858	−	0.790968i	$-0.709577\pi$
$409$	7.66621	−	13.2783i	0.379070	−	0.656568i	0.990927	+	0.134400i	$0.0429108\pi$
$410$	−16.5025	+	28.5831i	−0.814999	+	1.41162i
$411$	−16.8083	+	14.9504i	−0.829094	+	0.737449i
$412$	7.05494	+	12.2195i	0.347572	+	0.602013i
$413$	8.87636			0.436777
$414$	−27.5185	+	11.8535i	−1.35246	+	0.582568i
$415$	14.7527			0.724182
$416$	2.34981	+	4.07000i	0.115209	+	0.199548i
$417$	−1.82691	−	0.605896i	−0.0894644	−	0.0296708i
$418$	−2.12296	+	3.67707i	−0.103837	+	0.179851i
$419$	−5.28435	+	9.15276i	−0.258157	+	0.447142i	−0.965748	−	0.259481i	$-0.916449\pi$
$419$	−5.28435	+	9.15276i	−0.258157	+	0.447142i	0.707591	+	0.706622i	$0.249782\pi$
$420$	−5.24288	−	1.73880i	−0.255826	−	0.0848448i
$421$	18.0858	+	31.3256i	0.881449	+	1.52671i	0.849731	+	0.527217i	$0.176765\pi$
$421$	18.0858	+	31.3256i	0.881449	+	1.52671i	0.0317181	+	0.999497i	$0.489902\pi$
$422$	17.8974			0.871232
$423$	−6.41342	−	4.77975i	−0.311831	−	0.232399i
$424$	0.233531			0.0113412
$425$	16.1909	+	28.0434i	0.785374	+	1.36031i
$426$	−6.32691	+	5.62755i	−0.306540	+	0.272656i
$427$	1.93818	−	3.35702i	0.0937950	−	0.162458i
$428$	2.37890	−	4.12038i	0.114989	−	0.199166i
$429$	−0.983290	−	4.76828i	−0.0474737	−	0.230215i
$430$	15.8880	+	27.5189i	0.766190	+	1.32708i
$431$	35.0989			1.69065			0.845327	−	0.534249i	$-0.179406\pi$
$431$	35.0989			1.69065			0.845327	+	0.534249i	$0.179406\pi$
$432$	10.9709	−	23.4798i	0.527838	−	1.12967i
$433$	−41.1730			−1.97865			−0.989324	−	0.145731i	$-0.953447\pi$
$433$	−41.1730			−1.97865			−0.989324	+	0.145731i	$0.953447\pi$
$434$	−5.93818	−	10.2852i	−0.285042	−	0.493707i
$435$	2.13348	+	10.3459i	0.102292	+	0.496047i
$436$	8.38255	−	14.5190i	0.401451	−	0.695334i
$437$	2.61126	−	4.52284i	0.124914	−	0.216357i
$438$	−23.4072	+	20.8199i	−1.11844	+	0.994811i
$439$	2.33929	+	4.05178i	0.111648	+	0.193381i	0.916435	−	0.400184i	$-0.131054\pi$
$439$	2.33929	+	4.05178i	0.111648	+	0.193381i	−0.804787	+	0.593564i	$0.797720\pi$
$440$	−19.0507			−0.908209
$441$	0.349814	−	2.97954i	0.0166578	−	0.141883i
$442$	−6.98762			−0.332367
$443$	−15.0865	−	26.1306i	−0.716781	−	1.24150i	−0.962268	−	0.272102i	$-0.912281\pi$
$443$	−15.0865	−	26.1306i	−0.716781	−	1.24150i	0.245487	−	0.969400i	$-0.421052\pi$
$444$	−6.96217	−	2.30900i	−0.330410	−	0.109580i
$445$	17.2410	−	29.8623i	0.817303	−	1.41561i
$446$	4.81639	−	8.34224i	0.228063	−	0.395016i
$447$	−13.8633	−	4.59776i	−0.655711	−	0.217466i
$448$	0.993810	+	1.72133i	0.0469531	+	0.0813252i
$449$	0.333792			0.0157526			0.00787632	−	0.999969i	$-0.497493\pi$
$449$	0.333792			0.0157526			0.00787632	+	0.999969i	$0.497493\pi$
$450$	4.68292	−	39.8867i	0.220755	−	1.88028i
$451$	15.2115			0.716283
$452$	8.24357	+	14.2783i	0.387745	+	0.671594i
$453$	−19.2207	+	17.0961i	−0.903066	+	0.803244i
$454$	9.43199	−	16.3367i	0.442665	−	0.766719i
$455$	−1.79418	+	3.10761i	−0.0841125	+	0.145687i
$456$	0.587193	+	2.84748i	0.0274979	+	0.133346i
$457$	9.65452	+	16.7221i	0.451619	+	0.782227i	0.998487	−	0.0549917i	$-0.0175132\pi$
$457$	9.65452	+	16.7221i	0.451619	+	0.782227i	−0.546868	+	0.837219i	$0.684180\pi$
$458$	33.3855			1.56000
$459$	12.2396	+	17.5088i	0.571298	+	0.817241i
$460$	−18.7403			−0.873773
$461$	−19.5538	−	33.8681i	−0.910710	−	1.57740i	−0.813064	−	0.582175i	$-0.802202\pi$
$461$	−19.5538	−	33.8681i	−0.910710	−	1.57740i	−0.0976463	−	0.995221i	$-0.531131\pi$
$462$	1.67123	+	8.10430i	0.0777525	+	0.377046i
$463$	−10.9382	+	18.9455i	−0.508340	+	0.880471i	0.491613	+	0.870814i	$0.336407\pi$
$463$	−10.9382	+	18.9455i	−0.508340	+	0.880471i	−0.999953	+	0.00965741i	$0.996926\pi$
$464$	−4.23855	+	7.34138i	−0.196770	+	0.340815i
$465$	32.4505	−	28.8635i	1.50486	−	1.33851i
$466$	−7.61677	−	13.1926i	−0.352840	−	0.611137i
$467$	−12.3200			−0.570103			−0.285052	−	0.958512i	$-0.592011\pi$
$467$	−12.3200			−0.570103			−0.285052	+	0.958512i	$0.592011\pi$
$468$	2.13781	+	1.59325i	0.0988201	+	0.0736480i
$469$	−12.3090			−0.568378
$470$	−8.13045	−	14.0823i	−0.375029	−	0.649570i
$471$	−4.74907	−	1.57503i	−0.218826	−	0.0725735i
$472$	−8.38255	+	14.5190i	−0.385838	+	0.668291i
$473$	7.32258	−	12.6831i	0.336693	−	0.583169i
$474$	19.8010	+	6.56699i	0.909489	+	0.301632i
$475$	3.50000	+	6.06218i	0.160591	+	0.278152i
$476$	3.65383			0.167473
$477$	0.340671	−	0.146743i	0.0155983	−	0.00671890i
$478$	19.0741			0.872430
$479$	−6.74474	−	11.6822i	−0.308175	−	0.533775i	0.669788	−	0.742552i	$-0.266385\pi$
$479$	−6.74474	−	11.6822i	−0.308175	−	0.533775i	−0.977963	+	0.208777i	$0.933052\pi$
$480$	21.8251	−	19.4126i	0.996173	−	0.886059i
$481$	−2.38255	+	4.12669i	−0.108635	+	0.188161i
$482$	5.93701	−	10.2832i	0.270423	−	0.468387i
$483$	−2.05563	−	9.96840i	−0.0935345	−	0.453578i
$484$	1.37704	+	2.38511i	0.0625929	+	0.108414i
$485$	−26.2719			−1.19295
$486$	0.804702	−	26.4824i	0.0365020	−	1.20126i
$487$	7.54394			0.341849			0.170924	−	0.985284i	$-0.445325\pi$
$487$	7.54394			0.341849			0.170924	+	0.985284i	$0.445325\pi$
$488$	3.66071	+	6.34053i	0.165712	+	0.287022i
$489$	−3.60624	−	17.4878i	−0.163080	−	0.790826i
$490$	3.04944	−	5.28179i	0.137760	−	0.238607i
$491$	8.06979	−	13.9773i	0.364185	−	0.630786i	−0.624460	−	0.781057i	$-0.714681\pi$
$491$	8.06979	−	13.9773i	0.364185	−	0.630786i	0.988645	+	0.150270i	$0.0480143\pi$
$492$	−6.22439	+	5.53636i	−0.280617	+	0.249598i
$493$	−3.49381	−	6.05146i	−0.157353	−	0.272544i
$494$	−1.51052			−0.0679615
$495$	−27.7909	+	11.9709i	−1.24911	+	0.538050i
$496$	34.8516			1.56488
$497$	−1.43818	−	2.49100i	−0.0645111	−	0.111737i
$498$	11.4876	+	3.80987i	0.514773	+	0.170724i
$499$	15.4327	−	26.7302i	0.690862	−	1.19661i	−0.280694	−	0.959797i	$-0.590565\pi$
$499$	15.4327	−	26.7302i	0.690862	−	1.19661i	0.971556	−	0.236810i	$-0.0761019\pi$
$500$	4.58650	−	7.94406i	0.205115	−	0.355269i
$501$	−19.9778	−	6.62563i	−0.892542	−	0.296011i
$502$	−3.92649	−	6.80088i	−0.175248	−	0.303538i
$503$	24.6304			1.09822			0.549109	−	0.835751i	$-0.314967\pi$
$503$	24.6304			1.09822			0.549109	+	0.835751i	$0.314967\pi$
$504$	4.54325	+	3.38597i	0.202373	+	0.150823i
$505$	−12.4327			−0.553247
$506$	14.0371	+	24.3129i	0.624024	+	1.08084i
$507$	−15.5302	+	13.8135i	−0.689720	+	0.613480i
$508$	−4.43818	+	7.68715i	−0.196912	+	0.341062i
$509$	−6.79487	+	11.7691i	−0.301177	+	0.521654i	−0.976403	−	0.215957i	$-0.930713\pi$
$509$	−6.79487	+	11.7691i	−0.301177	+	0.521654i	0.675226	+	0.737611i	$0.264046\pi$
$510$	8.77128	+	42.5347i	0.388399	+	1.88347i
$511$	−5.32072	−	9.21576i	−0.235375	−	0.407681i
$512$	4.59937			0.203265
$513$	2.64586	+	3.78490i	0.116817	+	0.167107i
$514$	−2.42030			−0.106755
$515$	−28.4851	−	49.3376i	−1.25520	−	2.17407i
$516$	1.61980	+	7.85489i	0.0713075	+	0.345792i
$517$	−3.74721	+	6.49036i	−0.164802	+	0.285446i
$518$	4.04944	−	7.01384i	0.177922	−	0.308170i
$519$	−8.55377	+	7.60826i	−0.375469	+	0.333966i
$520$	−3.38874	−	5.86946i	−0.148606	−	0.257393i
$521$	−39.1730			−1.71620			−0.858100	−	0.513482i	$-0.828355\pi$
$521$	−39.1730			−1.71620			−0.858100	+	0.513482i	$0.828355\pi$
$522$	−1.01052	+	8.60709i	−0.0442293	+	0.376722i
$523$	19.1236			0.836219			0.418109	−	0.908397i	$-0.362693\pi$
$523$	19.1236			0.836219			0.418109	+	0.908397i	$0.362693\pi$
$524$	−7.13348	−	12.3555i	−0.311627	−	0.539754i
$525$	12.9487	+	4.29443i	0.565128	+	0.187424i
$526$	−13.8207	+	23.9382i	−0.602612	+	1.04375i
$527$	−14.3640	+	24.8791i	−0.625705	+	1.08375i
$528$	−23.0483	−	7.64396i	−1.00305	−	0.332660i
$529$	−5.76578	−	9.98663i	−0.250686	−	0.434201i
$530$	0.754090			0.0327556
$531$	−3.10507	+	26.4474i	−0.134749	+	1.14772i
$532$	0.789851			0.0342444
$533$	2.70582	+	4.68661i	0.117202	+	0.203000i
$534$	21.1371	−	18.8007i	0.914693	−	0.813585i
$535$	−9.60507	+	16.6365i	−0.415264	+	0.719258i
$536$	11.6243	−	20.1338i	0.502091	−	0.869648i
$537$	−1.34431	−	6.51899i	−0.0580114	−	0.281315i
$538$	15.8523	+	27.4570i	0.683441	+	1.18375i
$539$	−2.81089			−0.121074
$540$	7.01485	−	15.0131i	0.301871	−	0.646061i
$541$	2.53018			0.108781			0.0543906	−	0.998520i	$-0.482678\pi$
$541$	2.53018			0.108781			0.0543906	+	0.998520i	$0.482678\pi$
$542$	−3.36769	−	5.83302i	−0.144655	−	0.250550i
$543$	6.48645	+	31.4548i	0.278360	+	1.34986i
$544$	−9.66071	+	16.7328i	−0.414199	+	0.717414i
$545$	−33.8454	+	58.6220i	−1.44978	+	2.51109i
$546$	−2.19963	+	1.95649i	−0.0941354	+	0.0837299i
$547$	−8.92580	−	15.4599i	−0.381640	−	0.661019i	0.609657	−	0.792665i	$-0.291307\pi$
$547$	−8.92580	−	15.4599i	−0.381640	−	0.661019i	−0.991297	+	0.131646i	$0.957974\pi$
$548$	−11.5426			−0.493074
$549$	9.32437	+	6.94920i	0.397954	+	0.296585i
$550$	−37.6291			−1.60451
$551$	−0.755260	−	1.30815i	−0.0321752	−	0.0557290i
$552$	18.2465	+	6.05146i	0.776624	+	0.257567i
$553$	−3.54325	+	6.13709i	−0.150674	+	0.260976i
$554$	1.98329	−	3.43516i	0.0842619	−	0.145946i
$555$	28.1105	+	9.32284i	1.19322	+	0.395733i
$556$	−0.493810	−	0.855304i	−0.0209422	−	0.0362730i
$557$	41.3607			1.75251			0.876255	−	0.481847i	$-0.160034\pi$
$557$	41.3607			1.75251			0.876255	+	0.481847i	$0.160034\pi$
$558$	32.7225	−	14.0951i	1.38525	−	0.596693i
$559$	5.21015			0.220366
$560$	8.94870	+	15.4996i	0.378152	+	0.654978i
$561$	14.9560	−	13.3028i	0.631442	−	0.561644i
$562$	−23.7905	+	41.2063i	−1.00354	+	1.73818i
$563$	10.3683	−	17.9584i	0.436972	−	0.756858i	−0.560482	−	0.828166i	$-0.689384\pi$
$563$	10.3683	−	17.9584i	0.436972	−	0.756858i	0.997454	+	0.0713087i	$0.0227175\pi$
$564$	−0.828903	−	4.01961i	−0.0349031	−	0.169256i
$565$	−33.2843	−	57.6501i	−1.40028	−	2.42536i
$566$	17.5402			0.737271
$567$	8.75526	+	2.08457i	0.367686	+	0.0875436i
$568$	5.43268			0.227950
$569$	0.134164	+	0.232379i	0.00562446	+	0.00974185i	0.868824	−	0.495121i	$-0.164876\pi$
$569$	0.134164	+	0.232379i	0.00562446	+	0.00974185i	−0.863199	+	0.504863i	$0.831543\pi$
$570$	1.89610	+	9.19476i	0.0794187	+	0.385126i
$571$	−17.9684	+	31.1221i	−0.751953	+	1.30242i	0.194923	+	0.980819i	$0.437554\pi$
$571$	−17.9684	+	31.1221i	−0.751953	+	1.30242i	−0.946875	+	0.321601i	$0.895779\pi$
$572$	1.24907	−	2.16345i	0.0522263	−	0.0904585i
$573$	5.99745	−	5.33451i	0.250547	−	0.222852i
$574$	−4.59888	−	7.96550i	−0.191954	−	0.332474i
$575$	46.2843			1.93019
$576$	−5.47641	+	2.35895i	−0.228184	+	0.0982895i
$577$	5.43130			0.226108			0.113054	−	0.993589i	$-0.463937\pi$
$577$	5.43130			0.226108			0.113054	+	0.993589i	$0.463937\pi$
$578$	0.0828628	+	0.143523i	0.00344664	+	0.00596976i
$579$	41.5876	+	13.7925i	1.72832	+	0.573198i
$580$	−2.71015	+	4.69412i	−0.112533	+	0.194913i
$581$	−2.05563	+	3.56046i	−0.0852820	+	0.147713i
$582$	−20.4574	−	6.78468i	−0.847985	−	0.281234i
$583$	−0.173775	−	0.300987i	−0.00719702	−	0.0124656i
$584$	20.0989			0.831698
$585$	−8.63162	−	6.43292i	−0.356873	−	0.265968i
$586$	−52.1716			−2.15519
$587$	−17.5822	−	30.4532i	−0.725694	−	1.25694i	−0.958688	−	0.284461i	$-0.908185\pi$
$587$	−17.5822	−	30.4532i	−0.725694	−	1.25694i	0.232994	−	0.972478i	$-0.425148\pi$
$588$	1.15019	−	1.02305i	0.0474329	−	0.0421898i
$589$	−3.10507	+	5.37815i	−0.127942	+	0.221603i
$590$	−27.0679	+	46.8830i	−1.11437	+	1.93014i
$591$	3.75024	+	18.1861i	0.154264	+	0.748076i
$592$	11.8832	+	20.5824i	0.488398	+	0.845930i
$593$	−33.5068			−1.37596			−0.687980	−	0.725730i	$-0.741502\pi$
$593$	−33.5068			−1.37596			−0.687980	+	0.725730i	$0.741502\pi$
$594$	−24.7317	+	2.14448i	−1.01475	+	0.0879891i
$595$	−14.7527			−0.604802
$596$	−3.74721	−	6.49036i	−0.153492	−	0.265856i
$597$	−3.06663	−	14.8711i	−0.125509	−	0.608632i
$598$	−4.99381	+	8.64953i	−0.204212	+	0.353706i
$599$	−3.12364	+	5.41031i	−0.127629	+	0.221059i	−0.922757	−	0.385381i	$-0.874070\pi$
$599$	−3.12364	+	5.41031i	−0.127629	+	0.221059i	0.795129	+	0.606441i	$0.207403\pi$
$600$	−19.2527	+	17.1246i	−0.785989	+	0.699108i
$601$	−11.2040	−	19.4058i	−0.457019	−	0.791580i	0.541783	−	0.840519i	$-0.317750\pi$
$601$	−11.2040	−	19.4058i	−0.457019	−	0.791580i	−0.998802	+	0.0489384i	$0.984416\pi$
$602$	−8.85532			−0.360916
$603$	4.30587	−	36.6752i	0.175349	−	1.49353i
$604$	−13.1991			−0.537066
$605$	−5.55996	−	9.63014i	−0.226045	−	0.391521i
$606$	−9.68106	−	3.21072i	−0.393266	−	0.130427i
$607$	−7.47524	+	12.9475i	−0.303411	+	0.525523i	−0.976906	−	0.213669i	$-0.931459\pi$
$607$	−7.47524	+	12.9475i	−0.303411	+	0.525523i	0.673496	+	0.739191i	$0.264792\pi$
$608$	−2.08836	+	3.61715i	−0.0846943	+	0.146695i
$609$	−2.79418	−	0.926690i	−0.113226	−	0.0375514i
$610$	11.8207	+	20.4741i	0.478607	+	0.828972i
$611$	−2.66621			−0.107863
$612$	−1.27816	+	10.8867i	−0.0516666	+	0.440069i
$613$	35.1978			1.42162			0.710812	−	0.703382i	$-0.248328\pi$
$613$	35.1978			1.42162			0.710812	+	0.703382i	$0.248328\pi$
$614$	9.72500	+	16.8442i	0.392469	+	0.679776i
$615$	25.1316	−	22.3536i	1.01340	−	0.901386i
$616$	2.65452	−	4.59776i	0.106954	−	0.185249i
$617$	1.00619	−	1.74277i	0.0405077	−	0.0701614i	−0.845061	−	0.534670i	$-0.820436\pi$
$617$	1.00619	−	1.74277i	0.0405077	−	0.0701614i	0.885568	+	0.464509i	$0.153769\pi$
$618$	−9.43935	−	45.7744i	−0.379706	−	1.84131i
$619$	−19.6909	−	34.1056i	−0.791444	−	1.37082i	−0.925073	−	0.379789i	$-0.875996\pi$
$619$	−19.6909	−	34.1056i	−0.791444	−	1.37082i	0.133629	−	0.991031i	$-0.457337\pi$
$620$	22.2843			0.894958
$621$	30.4203	−	2.63774i	1.22072	−	0.105849i
$622$	20.3324			0.815256
$623$	4.80470	+	8.32199i	0.192496	+	0.333413i
$624$	−1.74474	−	8.46079i	−0.0698455	−	0.338703i
$625$	1.17240	−	2.03065i	0.0468959	−	0.0812261i
$626$	11.5098	−	19.9356i	0.460025	−	0.796787i
$627$	3.23305	−	2.87568i	0.129116	−	0.114843i
$628$	−1.28366	−	2.22337i	−0.0512237	−	0.0887220i
$629$	−19.5906			−0.781126
$630$	14.6705	+	10.9336i	0.584488	+	0.435604i
$631$	44.3832			1.76687			0.883433	−	0.468558i	$-0.155226\pi$
$631$	44.3832			1.76687			0.883433	+	0.468558i	$0.155226\pi$
$632$	−6.69227	−	11.5913i	−0.266204	−	0.461079i
$633$	−17.3116	−	5.74138i	−0.688074	−	0.228200i
$634$	25.4629	−	44.1030i	1.01126	−	1.75155i
$635$	17.9196	−	31.0377i	0.711118	−	1.23169i
$636$	0.180653	+	0.0599137i	0.00716337	+	0.00237573i
$637$	−0.500000	−	0.866025i	−0.0198107	−	0.0343132i
$638$	8.11993			0.321471
$639$	7.92511	−	3.41372i	0.313512	−	0.135045i
$640$	−45.8502			−1.81239
$641$	7.49312	+	12.9785i	0.295961	+	0.512619i	0.975208	−	0.221291i	$-0.0710270\pi$
$641$	7.49312	+	12.9785i	0.295961	+	0.512619i	−0.679247	+	0.733909i	$0.737694\pi$
$642$	−11.7756	+	10.4740i	−0.464746	+	0.413375i
$643$	5.32691	−	9.22649i	0.210073	−	0.363857i	−0.741664	−	0.670771i	$-0.765963\pi$
$643$	5.32691	−	9.22649i	0.210073	−	0.363857i	0.951737	+	0.306914i	$0.0992965\pi$
$644$	2.61126	−	4.52284i	0.102898	−	0.178225i
$645$	−6.54009	−	31.7150i	−0.257516	−	1.24878i
$646$	−3.10507	−	5.37815i	−0.122168	−	0.211600i
$647$	2.12955			0.0837213			0.0418606	−	0.999123i	$-0.486671\pi$
$647$	2.12955			0.0837213			0.0418606	+	0.999123i	$0.486671\pi$
$648$	−11.6779	+	12.3523i	−0.458751	+	0.485245i
$649$	24.9505			0.979392
$650$	−6.69344	−	11.5934i	−0.262538	−	0.454730i
$651$	2.44437	+	11.8535i	0.0958023	+	0.464575i
$652$	4.58100	−	7.93453i	0.179406	−	0.310740i
$653$	−5.58582	+	9.67492i	−0.218590	+	0.378609i	−0.954377	−	0.298604i	$-0.903479\pi$
$653$	−5.58582	+	9.67492i	−0.218590	+	0.378609i	0.735787	+	0.677213i	$0.236812\pi$
$654$	−41.4937	+	36.9071i	−1.62253	+	1.44318i
$655$	28.8022	+	49.8868i	1.12539	+	1.94924i
$656$	26.9912			1.05383
$657$	29.3200	−	12.6295i	1.14388	−	0.492723i
$658$	4.53156			0.176659
$659$	5.65452	+	9.79391i	0.220269	+	0.381517i	0.954890	−	0.296961i	$-0.0959733\pi$
$659$	5.65452	+	9.79391i	0.220269	+	0.381517i	−0.734621	+	0.678478i	$0.762640\pi$
$660$	−14.7372	−	4.88758i	−0.573644	−	0.190249i
$661$	−16.1785	+	28.0220i	−0.629271	+	1.08993i	0.358427	+	0.933558i	$0.383313\pi$
$661$	−16.1785	+	28.0220i	−0.629271	+	1.08993i	−0.987698	+	0.156372i	$0.950020\pi$
$662$	−1.77314	+	3.07117i	−0.0689151	+	0.119364i
$663$	6.75890	+	2.24159i	0.262494	+	0.0870561i
$664$	−3.88255	−	6.72477i	−0.150672	−	0.260972i
$665$	−3.18911			−0.123668
$666$	19.4814	+	14.5190i	0.754890	+	0.562600i
$667$	−9.98762			−0.386722
$668$	−5.39995	−	9.35298i	−0.208930	−	0.361878i
$669$	−7.33489	+	6.52411i	−0.283583	+	0.252237i
$670$	37.5357	−	65.0137i	1.45013	−	2.51170i
$671$	5.44801	−	9.43623i	0.210318	−	0.364282i
$672$	1.64400	+	7.97225i	0.0634185	+	0.307536i
$673$	12.0803	+	20.9237i	0.465662	+	0.806550i	0.999231	−	0.0392063i	$-0.0124830\pi$
$673$	12.0803	+	20.9237i	0.465662	+	0.806550i	−0.533569	+	0.845756i	$0.679150\pi$
$674$	−27.5489			−1.06114
$675$	−17.3251	+	37.0788i	−0.666842	+	1.42717i
$676$	−10.6648			−0.410186
$677$	−12.5371	−	21.7148i	−0.481838	−	0.834569i	0.517944	−	0.855414i	$-0.326697\pi$
$677$	−12.5371	−	21.7148i	−0.481838	−	0.834569i	−0.999783	+	0.0208457i	$0.993364\pi$
$678$	−11.0297	−	53.4865i	−0.423593	−	2.05414i
$679$	3.66071	−	6.34053i	0.140485	−	0.243327i
$680$	13.9320	−	24.1309i	0.534267	−	0.925378i
$681$	−14.3640	+	12.7762i	−0.550429	+	0.489586i
$682$	−16.6916	−	28.9107i	−0.639154	−	1.10705i
$683$	−47.6784			−1.82436			−0.912182	−	0.409785i	$-0.865604\pi$
$683$	−47.6784			−1.82436			−0.912182	+	0.409785i	$0.865604\pi$
$684$	−0.276301	+	2.35339i	−0.0105646	+	0.0899841i
$685$	46.6043			1.78066
$686$	0.849814	+	1.47192i	0.0324461	+	0.0561982i
$687$	−32.2927	−	10.7099i	−1.23204	−	0.408607i
$688$	12.9931	−	22.5047i	0.495358	−	0.857985i
$689$	0.0618219	−	0.107079i	0.00235523	−	0.00407937i
$690$	58.9195	+	19.5407i	2.24303	+	0.743900i
$691$	12.3400	+	21.3735i	0.469435	+	0.813085i	0.999389	−	0.0349408i	$-0.0111243\pi$
$691$	12.3400	+	21.3735i	0.469435	+	0.813085i	−0.529954	+	0.848026i	$0.677791\pi$
$692$	−5.87402			−0.223297
$693$	0.983290	−	8.37515i	0.0373521	−	0.318146i
$694$	19.1496			0.726910
$695$	1.99381	+	3.45338i	0.0756295	+	0.130994i
$696$	4.15452	−	3.69529i	0.157477	−	0.140070i
$697$	−11.1243	+	19.2679i	−0.421364	+	0.729824i
$698$	0.168067	−	0.291100i	0.00636142	−	0.0110183i
$699$	3.13533	+	15.2042i	0.118589	+	0.575076i
$700$	3.50000	+	6.06218i	0.132288	+	0.229129i
$701$	−29.6784			−1.12094			−0.560469	−	0.828175i	$-0.689379\pi$
$701$	−29.6784			−1.12094			−0.560469	+	0.828175i	$0.689379\pi$
$702$	−5.05996	−	7.23828i	−0.190976	−	0.273191i
$703$	−4.23491			−0.159723
$704$	2.79349	+	4.83847i	0.105284	+	0.182357i
$705$	3.34678	+	16.2296i	0.126047	+	0.611242i
$706$	10.6243	−	18.4018i	0.399849	−	0.692559i
$707$	1.73236	−	3.00054i	0.0651521	−	0.112847i
$708$	−10.2095	+	9.08094i	−0.383695	+	0.341282i
$709$	14.6291	+	25.3383i	0.549406	+	0.951599i	0.998315	+	0.0580220i	$0.0184794\pi$
$709$	14.6291	+	25.3383i	0.549406	+	0.951599i	−0.448909	+	0.893577i	$0.648187\pi$
$710$	17.5426			0.658361
$711$	−17.0462	−	12.7041i	−0.639283	−	0.476440i
$712$	−18.1496			−0.680186
$713$	20.5309	+	35.5605i	0.768887	+	1.33175i
$714$	−11.4876	−	3.80987i	−0.429913	−	0.142581i
$715$	−5.04325	+	8.73517i	−0.188607	+	0.326677i
$716$	1.70768	−	2.95778i	0.0638189	−	0.110538i
$717$	−18.4498	−	6.11887i	−0.689020	−	0.228513i
$718$	−17.0130	−	29.4674i	−0.634919	−	1.09971i
$719$	1.07413			0.0400581			0.0200291	−	0.999799i	$-0.493624\pi$
$719$	1.07413			0.0400581			0.0200291	+	0.999799i	$0.493624\pi$
$720$	−49.3120	+	21.2410i	−1.83775	+	0.791605i
$721$	15.8764			0.591266
$722$	15.4752	+	26.8039i	0.575929	+	0.997538i
$723$	−9.04147	+	8.04205i	−0.336256	+	0.299087i
$724$	−8.23972	+	14.2716i	−0.306227	+	0.530400i
$725$	6.69344	−	11.5934i	0.248588	−	0.430567i
$726$	−1.84245	−	8.93463i	−0.0683799	−	0.331595i
$727$	−12.7163	−	22.0253i	−0.471623	−	0.816875i	0.527850	−	0.849338i	$-0.322998\pi$
$727$	−12.7163	−	22.0253i	−0.471623	−	0.816875i	−0.999473	+	0.0324628i	$0.989665\pi$
$728$	1.88874			0.0700012
$729$	−9.27375	+	25.3574i	−0.343472	+	0.939163i
$730$	64.9010			2.40209
$731$	10.7101	+	18.5505i	0.396129	+	0.686116i
$732$	1.20513	+	5.84405i	0.0445429	+	0.216002i
$733$	5.69777	−	9.86883i	0.210452	−	0.364513i	−0.741404	−	0.671059i	$-0.765840\pi$
$733$	5.69777	−	9.86883i	0.210452	−	0.364513i	0.951856	+	0.306545i	$0.0991731\pi$
$734$	−25.5562	+	44.2647i	−0.943298	+	1.63384i
$735$	−4.64400	+	4.13066i	−0.171296	+	0.152362i
$736$	13.8083	+	23.9168i	0.508982	+	0.881583i
$737$	−34.5994			−1.27448
$738$	25.3422	−	10.9161i	0.932861	−	0.401827i
$739$	−29.9395			−1.10134			−0.550671	−	0.834723i	$-0.685628\pi$
$739$	−29.9395			−1.10134			−0.550671	+	0.834723i	$0.685628\pi$
$740$	7.59820	+	13.1605i	0.279315	+	0.483788i
$741$	1.46108	+	0.484566i	0.0536740	+	0.0178010i
$742$	−0.105074	+	0.181994i	−0.00385740	+	0.00668121i
$743$	9.50069	−	16.4557i	0.348546	−	0.603700i	−0.637445	−	0.770496i	$-0.720009\pi$
$743$	9.50069	−	16.4557i	0.348546	−	0.603700i	0.985991	+	0.166796i	$0.0533420\pi$
$744$	−21.6971	−	7.19583i	−0.795454	−	0.263812i
$745$	15.1298	+	26.2055i	0.554311	+	0.960096i
$746$	11.9184			0.436365
$747$	−9.88942	−	7.37033i	−0.361835	−	0.269666i
$748$	10.2705			0.375527
$749$	−2.67673	−	4.63623i	−0.0978055	−	0.169404i
$750$	−22.7033	+	20.1937i	−0.829006	+	0.737370i
$751$	−0.0130684	+	0.0226352i	−0.000476873	+	0.000825969i	−0.866264	−	0.499587i	$-0.833485\pi$
$751$	−0.0130684	+	0.0226352i	−0.000476873	+	0.000825969i	0.865787	+	0.500413i	$0.166818\pi$
$752$	−6.64902	+	11.5164i	−0.242465	+	0.419961i
$753$	1.61628	+	7.83786i	0.0589006	+	0.285628i
$754$	1.44437	+	2.50172i	0.0526008	+	0.0911072i
$755$	53.2929			1.93953
$756$	2.64586	+	3.78490i	0.0962288	+	0.137655i
$757$	−13.6910			−0.497607			−0.248803	−	0.968554i	$-0.580037\pi$
$757$	−13.6910			−0.497607			−0.248803	+	0.968554i	$0.580037\pi$
$758$	16.2095	+	28.0756i	0.588754	+	1.01975i
$759$	−5.77816	−	28.0201i	−0.209734	−	1.01707i
$760$	3.01169	−	5.21640i	0.109246	−	0.189219i
$761$	7.32141	−	12.6811i	0.265401	−	0.459688i	−0.702268	−	0.711913i	$-0.747829\pi$
$761$	7.32141	−	12.6811i	0.265401	−	0.459688i	0.967669	+	0.252225i	$0.0811623\pi$
$762$	21.9691	−	19.5407i	0.795855	−	0.707883i
$763$	−9.43199	−	16.3367i	−0.341461	−	0.591428i
$764$	4.11855			0.149004
$765$	5.16071	−	43.9562i	0.186586	−	1.58924i
$766$	5.45606			0.197135
$767$	4.43818	+	7.68715i	0.160253	+	0.277567i
$768$	−29.1673	−	9.67333i	−1.05248	−	0.349056i
$769$	−24.5672	+	42.5517i	−0.885918	+	1.53445i	−0.0412592	+	0.999148i	$0.513137\pi$
$769$	−24.5672	+	42.5517i	−0.885918	+	1.53445i	−0.844658	+	0.535306i	$0.820196\pi$
$770$	8.57165	−	14.8465i	0.308901	−	0.535032i
$771$	2.34108	+	0.776418i	0.0843118	+	0.0279620i
$772$	11.2410	+	19.4700i	0.404573	+	0.700741i
$773$	12.4413			0.447484			0.223742	−	0.974648i	$-0.428173\pi$
$773$	12.4413			0.447484			0.223742	+	0.974648i	$0.428173\pi$
$774$	3.09771	−	26.3847i	0.111345	−	0.948379i
$775$	−55.0370			−1.97699
$776$	6.91411	+	11.9756i	0.248202	+	0.429898i
$777$	−6.16690	+	5.48523i	−0.221236	+	0.196781i
$778$	−4.36467	+	7.55982i	−0.156481	+	0.271033i
$779$	−2.40476	+	4.16516i	−0.0861594	+	0.149232i
$780$	−1.11559	−	5.40987i	−0.0399447	−	0.193704i
$781$	−4.04256	−	7.00193i	−0.144654	−	0.250549i
$782$	−41.0617			−1.46837
$783$	3.73855	−	8.00119i	0.133605	−	0.285939i
$784$	−4.98762			−0.178129
$785$	5.18292	+	8.97708i	0.184986	+	0.320406i
$786$	9.54442	+	46.2839i	0.340438	+	1.65089i
$787$	16.4567	−	28.5038i	0.586617	−	1.01605i	−0.408055	−	0.912957i	$-0.633793\pi$
$787$	16.4567	−	28.5038i	0.586617	−	1.01605i	0.994672	−	0.103093i	$-0.0328739\pi$
$788$	−4.76392	+	8.25135i	−0.169708	+	0.293942i
$789$	21.0476	−	18.7210i	0.749314	−	0.666487i
$790$	−21.6099	−	37.4294i	−0.768845	−	1.33168i
$791$	18.5512			0.659606
$792$	12.7706	+	9.51759i	0.453783	+	0.338193i
$793$	3.87636			0.137653
$794$	−19.4931	−	33.7631i	−0.691785	−	1.19821i
$795$	−0.729407	−	0.241908i	−0.0258694	−	0.00857958i
$796$	3.89554	−	6.74727i	0.138074	−	0.239151i
$797$	−13.1989	+	22.8612i	−0.467530	+	0.809786i	−0.999312	−	0.0370953i	$-0.988189\pi$
$797$	−13.1989	+	22.8612i	−0.467530	+	0.809786i	0.531781	+	0.846882i	$0.321523\pi$
$798$	−2.48329	−	0.823583i	−0.0879075	−	0.0291545i
$799$	−5.48074	−	9.49292i	−0.193895	−	0.335835i
$800$	−37.0159			−1.30871
$801$	−26.4764	+	11.4046i	−0.935498	+	0.402963i
$802$	−30.9505			−1.09290
$803$	−14.9560	−	25.9045i	−0.527785	−	0.914151i
$804$	14.1577	−	12.5927i	0.499303	−	0.444111i
$805$	−10.5433	+	18.2614i	−0.371601	+	0.643631i
$806$	5.93818	−	10.2852i	0.209163	−	0.362282i
$807$	−6.52537	−	31.6436i	−0.229704	−	1.11391i
$808$	3.27197	+	5.66722i	0.115108	+	0.199372i
$809$	35.5919			1.25135			0.625673	−	0.780086i	$-0.284825\pi$
$809$	35.5919			1.25135			0.625673	+	0.780086i	$0.284825\pi$
$810$	−37.7089	+	39.8867i	−1.32496	+	1.40147i
$811$	−37.8268			−1.32828			−0.664140	−	0.747608i	$-0.731202\pi$
$811$	−37.8268			−1.32828			−0.664140	+	0.747608i	$0.731202\pi$
$812$	−0.755260	−	1.30815i	−0.0265044	−	0.0459070i
$813$	1.38626	+	6.72243i	0.0486184	+	0.235766i
$814$	11.3825	−	19.7151i	0.398958	−	0.691016i
$815$	−18.4963	+	32.0365i	−0.647896	+	1.12219i
$816$	26.5378	−	23.6043i	0.929007	−	0.826317i
$817$	2.31522	+	4.01008i	0.0809994	+	0.140295i
$818$	−26.0594			−0.911146
$819$	2.75526	−	1.18682i	0.0962766	−	0.0414708i
$820$	17.2583			0.602686
$821$	9.15638	+	15.8593i	0.319560	+	0.553494i	0.980396	−	0.197036i	$-0.0631317\pi$
$821$	9.15638	+	15.8593i	0.319560	+	0.553494i	−0.660836	+	0.750530i	$0.729798\pi$
$822$	36.2898	+	12.0355i	1.26575	+	0.419786i
$823$	18.0000	−	31.1769i	0.627441	−	1.08676i	−0.360623	−	0.932712i	$-0.617436\pi$
$823$	18.0000	−	31.1769i	0.627441	−	1.08676i	0.988063	−	0.154047i	$-0.0492308\pi$
$824$	−14.9931	+	25.9688i	−0.522310	+	0.904668i
$825$	36.3974	+	12.0712i	1.26719	+	0.420265i
$826$	−7.54325	−	13.0653i	−0.262463	−	0.454600i
$827$	−28.2115			−0.981011			−0.490505	−	0.871438i	$-0.663188\pi$
$827$	−28.2115			−0.981011			−0.490505	+	0.871438i	$0.663188\pi$
$828$	12.5625	+	9.36251i	0.436577	+	0.325370i
$829$	−11.2843			−0.391919			−0.195960	−	0.980612i	$-0.562782\pi$
$829$	−11.2843			−0.391919			−0.195960	+	0.980612i	$0.562782\pi$
$830$	−12.5371	−	21.7148i	−0.435168	−	0.753733i
$831$	−3.02035	+	2.68649i	−0.104775	+	0.0931933i
$832$	−0.993810	+	1.72133i	−0.0344542	+	0.0596764i
$833$	2.05563	−	3.56046i	0.0712234	−	0.123363i
$834$	0.660706	+	3.20397i	0.0228784	+	0.110944i
$835$	21.8028	+	37.7636i	0.754519	+	1.30686i
$836$	2.22019			0.0767868
$837$	−36.1730	+	3.13656i	−1.25032	+	0.108415i
$838$	17.9629			0.620517
$839$	1.02152	+	1.76933i	0.0352669	+	0.0610840i	0.883120	−	0.469147i	$-0.155439\pi$
$839$	1.02152	+	1.76933i	0.0352669	+	0.0610840i	−0.847853	+	0.530231i	$0.822105\pi$
$840$	−2.37085	−	11.4970i	−0.0818023	−	0.396685i
$841$	13.0556	−	22.6130i	0.450194	−	0.779759i
$842$	30.7392	−	53.2418i	1.05934	−	1.83483i
$843$	36.2305	−	32.2257i	1.24784	−	1.10991i
$844$	−4.67928	−	8.10474i	−0.161067	−	0.278977i
$845$	43.0604			1.48132
$846$	−1.58520	+	13.5019i	−0.0545004	+	0.464206i
$847$	3.09888			0.106479
$848$	−0.308344	−	0.534068i	−0.0105886	−	0.0183400i
$849$	−16.9661	−	5.62680i	−0.582275	−	0.193111i
$850$	27.5185	−	47.6634i	0.943877	−	1.63484i
$851$	−14.0007	+	24.2499i	−0.479937	+	0.831276i
$852$	4.20258	+	1.39379i	0.143978	+	0.0477503i
$853$	24.2960	+	42.0818i	0.831878	+	1.44085i	0.896547	+	0.442948i	$0.146067\pi$
$853$	24.2960	+	42.0818i	0.831878	+	1.44085i	−0.0646692	+	0.997907i	$0.520599\pi$
$854$	−6.58836			−0.225449
$855$	1.11559	−	9.50206i	0.0381525	−	0.324964i
$856$	10.1113			0.345596
$857$	22.4487	+	38.8823i	0.766833	+	1.32819i	0.939272	+	0.343173i	$0.111502\pi$
$857$	22.4487	+	38.8823i	0.766833	+	1.32819i	−0.172439	+	0.985020i	$0.555165\pi$
$858$	−6.18292	+	5.49948i	−0.211081	+	0.187749i
$859$	−14.9065	+	25.8189i	−0.508605	+	0.880929i	0.491346	+	0.870965i	$0.336505\pi$
$859$	−14.9065	+	25.8189i	−0.508605	+	0.880929i	−0.999950	+	0.00996438i	$0.996828\pi$
$860$	8.30786	−	14.3896i	0.283296	−	0.490683i
$861$	1.89307	+	9.18007i	0.0645155	+	0.312856i
$862$	−29.8275	−	51.6628i	−1.01593	−	1.75964i
$863$	−42.2595			−1.43853			−0.719265	−	0.694736i	$-0.755521\pi$
$863$	−42.2595			−1.43853			−0.719265	+	0.694736i	$0.755521\pi$
$864$	−24.3287	+	2.10954i	−0.827679	+	0.0717680i
$865$	23.7170			0.806401
$866$	34.9894	+	60.6034i	1.18899	+	2.05939i
$867$	−0.0341093	−	0.165407i	−0.00115841	−	0.00561751i
$868$	−3.10507	+	5.37815i	−0.105393	+	0.182546i
$869$	−9.95970	+	17.2507i	−0.337860	+	0.585190i
$870$	13.4153	−	11.9324i	0.454821	−	0.404546i
$871$	−6.15452	−	10.6599i	−0.208538	−	0.361198i
$872$	35.6291			1.20655
$873$	17.6113	+	13.1252i	0.596051	+	0.444221i
$874$	−8.87636			−0.300247
$875$	−5.16071	−	8.93861i	−0.174464	−	0.302180i
$876$	15.5480	+	5.15649i	0.525318	+	0.174222i
$877$	15.2658	−	26.4411i	0.515489	−	0.892853i	−0.484350	−	0.874875i	$-0.660944\pi$
$877$	15.2658	−	26.4411i	0.515489	−	0.892853i	0.999838	−	0.0179782i	$-0.00572295\pi$
$878$	3.97593	−	6.88651i	0.134181	−	0.232409i
$879$	50.4640	+	16.7364i	1.70211	+	0.564504i
$880$	25.1538	+	43.5677i	0.847935	+	1.46867i
$881$	−13.4079			−0.451724			−0.225862	−	0.974159i	$-0.572520\pi$
$881$	−13.4079			−0.451724			−0.225862	+	0.974159i	$0.572520\pi$
$882$	−4.68292	+	2.01715i	−0.157682	+	0.0679210i
$883$	−14.1250			−0.475345			−0.237672	−	0.971345i	$-0.576384\pi$
$883$	−14.1250			−0.475345			−0.237672	+	0.971345i	$0.576384\pi$
$884$	1.82691	+	3.16431i	0.0614458	+	0.106427i
$885$	41.2218	−	36.6652i	1.38565	−	1.23249i
$886$	−25.6414	+	44.4123i	−0.861441	+	1.49206i
$887$	19.9716	−	34.5918i	0.670581	−	1.16148i	−0.307159	−	0.951658i	$-0.599378\pi$
$887$	19.9716	−	34.5918i	0.670581	−	1.16148i	0.977740	−	0.209822i	$-0.0672883\pi$
$888$	−3.14833	−	15.2672i	−0.105651	−	0.512334i
$889$	4.99381	+	8.64953i	0.167487	+	0.290096i
$890$	−58.6067			−1.96450
$891$	24.6101	+	5.85949i	0.824469	+	0.196300i
$892$	−5.03699			−0.168651
$893$	−1.18478	−	2.05209i	−0.0396471	−	0.0686707i
$894$	5.01368	+	24.3129i	0.167683	+	0.813145i
$895$	−6.89493	+	11.9424i	−0.230472	+	0.399189i
$896$	6.38874	−	11.0656i	0.213433	−	0.369676i
$897$	7.60507	−	6.76443i	0.253926	−	0.225858i
$898$	−0.283662	−	0.491316i	−0.00946591	−	0.0163954i
$899$	11.8764			0.396099
$900$	−19.2868	+	8.30774i	−0.642894	+	0.276925i
$901$	0.508333			0.0169350
$902$	−12.9270	−	22.3902i	−0.430421	−	0.745511i
$903$	8.56546	+	2.84073i	0.285041	+	0.0945337i
$904$	−17.5192	+	30.3441i	−0.582679	+	1.00923i
$905$	33.2687	−	57.6231i	1.10589	−	1.91546i
$906$	41.4981	+	13.7628i	1.37868	+	0.457239i
$907$	−20.7101	−	35.8710i	−0.687669	−	1.19108i	−0.972590	−	0.232527i	$-0.925301\pi$
$907$	−20.7101	−	35.8710i	−0.687669	−	1.19108i	0.284921	−	0.958551i	$-0.408033\pi$
$908$	−9.86398			−0.327348
$909$	8.33420	+	6.21126i	0.276428	+	0.206014i
$910$	6.09888			0.202176
$911$	−0.894237	−	1.54886i	−0.0296274	−	0.0513162i	0.850832	−	0.525439i	$-0.176099\pi$
$911$	−0.894237	−	1.54886i	−0.0296274	−	0.0513162i	−0.880459	+	0.474122i	$0.842765\pi$
$912$	5.73669	−	5.10257i	0.189961	−	0.168963i
$913$	−5.77816	+	10.0081i	−0.191229	+	0.331219i
$914$	16.4091	−	28.4214i	0.542764	−	0.940096i
$915$	−4.86584	−	23.5960i	−0.160860	−	0.780058i
$916$	−8.72864	−	15.1185i	−0.288402	−	0.499528i
$917$	−16.0531			−0.530120
$918$	15.3702	−	32.8950i	0.507291	−	1.08570i
$919$	−57.4683			−1.89570			−0.947852	−	0.318711i	$-0.896750\pi$
$919$	−57.4683			−1.89570			−0.947852	+	0.318711i	$0.896750\pi$
$920$	−19.9134	−	34.4911i	−0.656526	−	1.13714i
$921$	−4.00316	−	19.4126i	−0.131909	−	0.639666i
$922$	−33.2341	+	57.5632i	−1.09451	+	1.89574i
$923$	1.43818	−	2.49100i	0.0473382	−	0.0819922i
$924$	3.23305	−	2.87568i	0.106359	−	0.0946028i
$925$	−18.7658	−	32.5033i	−0.617015	−	1.06870i
$926$	37.1817			1.22187
$927$	−5.55377	+	47.3042i	−0.182410	+	1.55367i
$928$	7.98762			0.262206
$929$	−17.3676	−	30.0816i	−0.569813	−	0.986945i	−0.996584	−	0.0825854i	$-0.973682\pi$
$929$	−17.3676	−	30.0816i	−0.569813	−	0.986945i	0.426771	−	0.904360i	$-0.359651\pi$
$930$	−70.0617	−	23.2359i	−2.29741	−	0.761937i
$931$	0.444368	−	0.769668i	0.0145636	−	0.0252248i
$932$	−3.98281	+	6.89843i	−0.130461	+	0.225965i
$933$	−19.6669	−	6.52252i	−0.643865	−	0.213538i
$934$	10.4697	+	18.1341i	0.342580	+	0.593367i
$935$	−41.4683			−1.35616
$936$	−0.660706	+	5.62755i	−0.0215959	+	0.183942i
$937$	11.6662			0.381118			0.190559	−	0.981676i	$-0.438970\pi$
$937$	11.6662			0.381118			0.190559	+	0.981676i	$0.438970\pi$
$938$	10.4604	+	18.1179i	0.341544	+	0.591571i
$939$	−17.5283	+	15.5908i	−0.572015	+	0.508786i
$940$	−4.25141	+	7.36366i	−0.138666	+	0.240176i
$941$	25.1687	−	43.5934i	0.820475	−	1.42111i	−0.0848531	−	0.996393i	$-0.527042\pi$
$941$	25.1687	−	43.5934i	0.820475	−	1.42111i	0.905329	−	0.424712i	$-0.139625\pi$
$942$	1.71751	+	8.32874i	0.0559595	+	0.271365i
$943$	15.9004	+	27.5402i	0.517787	+	0.896833i
$944$	44.2719			1.44093
$945$	−10.6829	−	15.2819i	−0.347515	−	0.497121i
$946$	−24.8913			−0.809287
$947$	16.1941	+	28.0491i	0.526238	+	0.911472i	0.999533	+	0.0305673i	$0.00973139\pi$
$947$	16.1941	+	28.0491i	0.526238	+	0.911472i	−0.473294	+	0.880904i	$0.656935\pi$
$948$	−2.20314	−	10.6837i	−0.0715547	−	0.346991i
$949$	5.32072	−	9.21576i	0.172718	−	0.299156i
$950$	5.94870	−	10.3034i	0.193001	−	0.334288i
$951$	−38.7774	+	34.4911i	−1.25744	+	1.11845i
$952$	3.88255	+	6.72477i	0.125834	+	0.217951i
$953$	−12.5367			−0.406102			−0.203051	−	0.979168i	$-0.565086\pi$
$953$	−12.5367			−0.406102			−0.203051	+	0.979168i	$0.565086\pi$
$954$	−0.505501	−	0.376737i	−0.0163662	−	0.0121973i
$955$	−16.6291			−0.538104
$956$	−4.98693	−	8.63762i	−0.161289	−	0.279361i
$957$	−7.85414	−	2.60483i	−0.253888	−	0.0842021i
$958$	−11.4635	+	19.8555i	−0.370370	+	0.641500i
$959$	−6.49381	+	11.2476i	−0.209696	+	0.363204i
$960$	11.7255	+	3.88875i	0.378438	+	0.125509i
$961$	−8.91342	−	15.4385i	−0.287530	−	0.498016i
$962$	8.09888			0.261119
$963$	14.7502	−	6.35359i	0.475317	−	0.204741i
$964$	−6.20892			−0.199976
$965$	−45.3868	−	78.6122i	−1.46105	−	2.53062i
$966$	−12.9258	+	11.4970i	−0.415881	+	0.369910i
$967$	28.9937	−	50.2186i	0.932376	−	1.61492i	0.153127	−	0.988206i	$-0.451065\pi$
$967$	28.9937	−	50.2186i	0.932376	−	1.61492i	0.779248	−	0.626715i	$-0.215601\pi$
$968$	−2.92649	+	5.06882i	−0.0940609	+	0.162918i
$969$	1.27816	+	6.19820i	0.0410604	+	0.199115i
$970$	22.3262	+	38.6702i	0.716852	+	1.24162i
$971$	28.0370			0.899750			0.449875	−	0.893092i	$-0.351469\pi$
$971$	28.0370			0.899750			0.449875	+	0.893092i	$0.351469\pi$
$972$	−12.2028	+	6.55941i	−0.391405	+	0.210393i
$973$	−1.11126			−0.0356255
$974$	−6.41095	−	11.1041i	−0.205420	−	0.355798i
$975$	2.75526	+	13.3611i	0.0882389	+	0.427898i
$976$	9.66690	−	16.7436i	0.309430	−	0.535948i
$977$	−4.92030	+	8.52220i	−0.157414	+	0.272649i	−0.933935	−	0.357442i	$-0.883649\pi$
$977$	−4.92030	+	8.52220i	−0.157414	+	0.272649i	0.776521	+	0.630091i	$0.216982\pi$
$978$	−22.6760	+	20.1695i	−0.725100	+	0.644949i
$979$	13.5055	+	23.3922i	0.431638	+	0.747618i
$980$	−3.18911			−0.101872
$981$	51.9752	−	22.3881i	1.65944	−	0.714798i
$982$	−27.4313			−0.875368
$983$	24.3447	+	42.1663i	0.776476	+	1.34490i	0.933961	+	0.357374i	$0.116328\pi$
$983$	24.3447	+	42.1663i	0.776476	+	1.34490i	−0.157485	+	0.987521i	$0.550339\pi$
$984$	−16.8035	−	5.57289i	−0.535677	−	0.177657i
$985$	19.2348	−	33.3157i	0.612873	−	1.06153i
$986$	−5.93818	+	10.2852i	−0.189110	+	0.327548i
$987$	−4.38323	−	1.45370i	−0.139520	−	0.0462718i
$988$	0.394926	+	0.684031i	0.0125643	+	0.0217619i
$989$	30.6167			0.973554
$990$	41.2373	+	30.7331i	1.31061	+	0.976761i
$991$	2.86398			0.0909772			0.0454886	−	0.998965i	$-0.485516\pi$
$991$	2.86398			0.0909772			0.0454886	+	0.998965i	$0.485516\pi$
$992$	−16.4196	−	28.4396i	−0.521323	−	0.902958i
$993$	2.70032	−	2.40183i	0.0856920	−	0.0762198i
$994$	−2.44437	+	4.23377i	−0.0775306	+	0.134287i
$995$	−15.7286	+	27.2428i	−0.498631	+	0.863655i
$996$	−1.27816	−	6.19820i	−0.0405001	−	0.196397i
$997$	25.4203	+	44.0292i	0.805069	+	1.39442i	0.916245	+	0.400619i	$0.131205\pi$
$997$	25.4203	+	44.0292i	0.805069	+	1.39442i	−0.111176	+	0.993801i	$0.535462\pi$
$998$	−52.4596			−1.66058
$999$	−14.1862	−	20.2933i	−0.448830	−	0.642051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.f.b.22.1	✓	6
3.2	odd	2		189.2.f.a.64.3		6
4.3	odd	2		1008.2.r.k.337.1		6
7.2	even	3		441.2.g.e.67.1		6
7.3	odd	6		441.2.h.b.373.3		6
7.4	even	3		441.2.h.c.373.3		6
7.5	odd	6		441.2.g.d.67.1		6
7.6	odd	2		441.2.f.d.148.1		6
9.2	odd	6		189.2.f.a.127.3		6
9.4	even	3		567.2.a.d.1.3		3
9.5	odd	6		567.2.a.g.1.1		3
9.7	even	3	inner	63.2.f.b.43.1	yes	6
12.11	even	2		3024.2.r.g.1009.1		6
21.2	odd	6		1323.2.g.c.361.3		6
21.5	even	6		1323.2.g.b.361.3		6
21.11	odd	6		1323.2.h.d.226.1		6
21.17	even	6		1323.2.h.e.226.1		6
21.20	even	2		1323.2.f.c.442.3		6
36.7	odd	6		1008.2.r.k.673.1		6
36.11	even	6		3024.2.r.g.2017.1		6
36.23	even	6		9072.2.a.cd.1.3		3
36.31	odd	6		9072.2.a.bq.1.1		3
63.2	odd	6		1323.2.h.d.802.1		6
63.11	odd	6		1323.2.g.c.667.3		6
63.13	odd	6		3969.2.a.m.1.3		3
63.16	even	3		441.2.h.c.214.3		6
63.20	even	6		1323.2.f.c.883.3		6
63.25	even	3		441.2.g.e.79.1		6
63.34	odd	6		441.2.f.d.295.1		6
63.38	even	6		1323.2.g.b.667.3		6
63.41	even	6		3969.2.a.p.1.1		3
63.47	even	6		1323.2.h.e.802.1		6
63.52	odd	6		441.2.g.d.79.1		6
63.61	odd	6		441.2.h.b.214.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.1	✓	6	1.1	even	1	trivial
63.2.f.b.43.1	yes	6	9.7	even	3	inner
189.2.f.a.64.3		6	3.2	odd	2
189.2.f.a.127.3		6	9.2	odd	6
441.2.f.d.148.1		6	7.6	odd	2
441.2.f.d.295.1		6	63.34	odd	6
441.2.g.d.67.1		6	7.5	odd	6
441.2.g.d.79.1		6	63.52	odd	6
441.2.g.e.67.1		6	7.2	even	3
441.2.g.e.79.1		6	63.25	even	3
441.2.h.b.214.3		6	63.61	odd	6
441.2.h.b.373.3		6	7.3	odd	6
441.2.h.c.214.3		6	63.16	even	3
441.2.h.c.373.3		6	7.4	even	3
567.2.a.d.1.3		3	9.4	even	3
567.2.a.g.1.1		3	9.5	odd	6
1008.2.r.k.337.1		6	4.3	odd	2
1008.2.r.k.673.1		6	36.7	odd	6
1323.2.f.c.442.3		6	21.20	even	2
1323.2.f.c.883.3		6	63.20	even	6
1323.2.g.b.361.3		6	21.5	even	6
1323.2.g.b.667.3		6	63.38	even	6
1323.2.g.c.361.3		6	21.2	odd	6
1323.2.g.c.667.3		6	63.11	odd	6
1323.2.h.d.226.1		6	21.11	odd	6
1323.2.h.d.802.1		6	63.2	odd	6
1323.2.h.e.226.1		6	21.17	even	6
1323.2.h.e.802.1		6	63.47	even	6
3024.2.r.g.1009.1		6	12.11	even	2
3024.2.r.g.2017.1		6	36.11	even	6
3969.2.a.m.1.3		3	63.13	odd	6
3969.2.a.p.1.1		3	63.41	even	6
9072.2.a.bq.1.1		3	36.31	odd	6
9072.2.a.cd.1.3		3	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.849814 - 1.47192i) q^{2} +(0.349814 + 1.69636i) q^{3} +(-0.444368 + 0.769668i) q^{4} +(1.79418 - 3.10761i) q^{5} +(2.19963 - 1.95649i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.88874 q^{8} +(-2.75526 + 1.18682i) q^{9} -6.09888 q^{10} +(1.40545 + 2.43430i) q^{11} +(-1.46108 - 0.484566i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(0.849814 - 1.47192i) q^{14} +(5.89926 + 1.95649i) q^{15} +(2.49381 + 4.31941i) q^{16} -4.11126 q^{17} +(4.08836 + 3.04695i) q^{18} -0.888736 q^{19} +(1.59455 + 2.76185i) q^{20} +(-1.29418 + 1.15113i) q^{21} +(2.38874 - 4.13741i) q^{22} +(-2.93818 + 5.08907i) q^{23} +(-0.660706 - 3.20397i) q^{24} +(-3.93818 - 6.82112i) q^{25} +1.69963 q^{26} +(-2.97710 - 4.25874i) q^{27} -0.888736 q^{28} +(0.849814 + 1.47192i) q^{29} +(-2.13348 - 10.3459i) q^{30} +(3.49381 - 6.05146i) q^{31} +(2.34981 - 4.07000i) q^{32} +(-3.63781 + 3.23569i) q^{33} +(3.49381 + 6.05146i) q^{34} +3.58836 q^{35} +(0.310892 - 2.64802i) q^{36} +4.76509 q^{37} +(0.755260 + 1.30815i) q^{38} +(-1.64400 - 0.545231i) q^{39} +(-3.38874 + 5.86946i) q^{40} +(2.70582 - 4.68661i) q^{41} +(2.79418 + 0.926690i) q^{42} +(-2.60507 - 4.51212i) q^{43} -2.49814 q^{44} +(-1.25526 + 10.6917i) q^{45} +9.98762 q^{46} +(1.33310 + 2.30900i) q^{47} +(-6.45489 + 5.74138i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-6.69344 + 11.5934i) q^{50} +(-1.43818 - 6.97418i) q^{51} +(-0.444368 - 0.769668i) q^{52} -0.123644 q^{53} +(-3.73855 + 8.00119i) q^{54} +10.0865 q^{55} +(-0.944368 - 1.63569i) q^{56} +(-0.310892 - 1.50761i) q^{57} +(1.44437 - 2.50172i) q^{58} +(4.43818 - 7.68715i) q^{59} +(-4.12729 + 3.67107i) q^{60} +(-1.93818 - 3.35702i) q^{61} -11.8764 q^{62} +(-2.40545 - 1.79272i) q^{63} +1.98762 q^{64} +(1.79418 + 3.10761i) q^{65} +(7.85414 + 2.60483i) q^{66} +(-6.15452 + 10.6599i) q^{67} +(1.82691 - 3.16431i) q^{68} +(-9.66071 - 3.20397i) q^{69} +(-3.04944 - 5.28179i) q^{70} -2.87636 q^{71} +(5.20396 - 2.24159i) q^{72} -10.6414 q^{73} +(-4.04944 - 7.01384i) q^{74} +(10.1934 - 9.06668i) q^{75} +(0.394926 - 0.684031i) q^{76} +(-1.40545 + 2.43430i) q^{77} +(0.594554 + 2.88318i) q^{78} +(3.54325 + 6.13709i) q^{79} +17.8974 q^{80} +(6.18292 - 6.53999i) q^{81} -9.19777 q^{82} +(2.05563 + 3.56046i) q^{83} +(-0.310892 - 1.50761i) q^{84} +(-7.37636 + 12.7762i) q^{85} +(-4.42766 + 7.66893i) q^{86} +(-2.19963 + 1.95649i) q^{87} +(-2.65452 - 4.59776i) q^{88} +9.60940 q^{89} +(16.8040 - 7.23828i) q^{90} -1.00000 q^{91} +(-2.61126 - 4.52284i) q^{92} +(11.4876 + 3.80987i) q^{93} +(2.26578 - 3.92445i) q^{94} +(-1.59455 + 2.76185i) q^{95} +(7.72617 + 2.56238i) q^{96} +(-3.66071 - 6.34053i) q^{97} +1.69963 q^{98} +(-6.76145 - 5.03913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 4 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 3 q^{7} - 12 q^{8} - 4 q^{9} + 2 q^{11} - 2 q^{12} - 3 q^{13} - q^{14} + 11 q^{15} - 3 q^{16} - 24 q^{17} + 13 q^{18} - 6 q^{19} + 16 q^{20} - 2 q^{21}+ \cdots - 46 q^{99}+O(q^{100}) \) 6 * q + q^2 - 4 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 3 * q^7 - 12 * q^8 - 4 * q^9 + 2 * q^11 - 2 * q^12 - 3 * q^13 - q^14 + 11 * q^15 - 3 * q^16 - 24 * q^17 + 13 * q^18 - 6 * q^19 + 16 * q^20 - 2 * q^21 + 15 * q^22 + 15 * q^24 - 6 * q^25 - 2 * q^26 - 7 * q^27 - 6 * q^28 - q^29 - 26 * q^30 + 3 * q^31 + 8 * q^32 + 8 * q^33 + 3 * q^34 + 10 * q^35 - 11 * q^36 - 6 * q^37 - 8 * q^38 + 2 * q^39 - 21 * q^40 + 22 * q^41 + 11 * q^42 + 3 * q^43 + 46 * q^44 + 5 * q^45 + 24 * q^46 + 9 * q^47 - 14 * q^48 - 3 * q^49 - 10 * q^50 + 9 * q^51 - 3 * q^52 - 36 * q^53 - 17 * q^54 - 12 * q^55 - 6 * q^56 + 11 * q^57 + 9 * q^58 + 9 * q^59 - 20 * q^60 + 6 * q^61 - 36 * q^62 - 8 * q^63 - 24 * q^64 + 5 * q^65 - 2 * q^66 - 6 * q^68 - 39 * q^69 + 18 * q^71 - 24 * q^72 + 6 * q^73 - 6 * q^74 + 31 * q^75 + 21 * q^76 - 2 * q^77 + 10 * q^78 - 15 * q^79 + 22 * q^80 + 32 * q^81 + 18 * q^82 + 12 * q^83 + 11 * q^84 - 9 * q^85 - 34 * q^86 - q^87 + 21 * q^88 - 4 * q^89 + 73 * q^90 - 6 * q^91 - 15 * q^92 + 33 * q^93 - 24 * q^94 - 16 * q^95 + 5 * q^96 - 3 * q^97 - 2 * q^98 - 46 * q^99

Introduction

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