LMFDB - Embedded newform 69.2.e.b.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,2,Mod(4,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, degree $10$, 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:	$0.550967773947$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			64.1
Root			$0.959493 + 0.281733i$ of defining polynomial
Character	$\chi$	$=$	69.64
Dual form			69.2.e.b.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.459493 - 0.134919i) q^{2} +(0.654861 - 0.755750i) q^{3} +(-1.48958 - 0.957293i) q^{4} +(0.480602 - 3.34266i) q^{5} +(-0.402869 + 0.258908i) q^{6} +(1.88533 + 4.12830i) q^{7} +(1.18251 + 1.36469i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.459493 - 0.134919i) q^{2} +(0.654861 - 0.755750i) q^{3} +(-1.48958 - 0.957293i) q^{4} +(0.480602 - 3.34266i) q^{5} +(-0.402869 + 0.258908i) q^{6} +(1.88533 + 4.12830i) q^{7} +(1.18251 + 1.36469i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-0.671822 + 1.47109i) q^{10} +(-0.942270 + 0.276675i) q^{11} +(-1.69894 + 0.498853i) q^{12} +(-0.188515 + 0.412791i) q^{13} +(-0.309309 - 2.15129i) q^{14} +(-2.21148 - 2.55219i) q^{15} +(1.11189 + 2.43470i) q^{16} +(-2.76321 + 1.77580i) q^{17} +(-0.0681534 + 0.474017i) q^{18} +(1.41042 + 0.906424i) q^{19} +(-3.91579 + 4.51907i) q^{20} +(4.35459 + 1.27862i) q^{21} +0.470295 q^{22} +(4.59385 + 1.37715i) q^{23} +1.80574 q^{24} +(-6.14491 - 1.80431i) q^{25} +(0.142315 - 0.164240i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(1.14365 - 7.95423i) q^{28} +(-1.15189 + 0.740277i) q^{29} +(0.671822 + 1.47109i) q^{30} +(-4.23404 - 4.88634i) q^{31} +(-0.696384 - 4.84346i) q^{32} +(-0.407958 + 0.893304i) q^{33} +(1.50926 - 0.443160i) q^{34} +(14.7056 - 4.31795i) q^{35} +(-0.735560 + 1.61065i) q^{36} +(0.506627 + 3.52367i) q^{37} +(-0.525785 - 0.606789i) q^{38} +(0.188515 + 0.412791i) q^{39} +(5.12999 - 3.29685i) q^{40} +(-0.821738 + 5.71531i) q^{41} +(-1.82839 - 1.17504i) q^{42} +(7.20584 - 8.31598i) q^{43} +(1.66844 + 0.489899i) q^{44} -3.37703 q^{45} +(-1.92504 - 1.25259i) q^{46} -10.0618 q^{47} +(2.56815 + 0.754078i) q^{48} +(-8.90436 + 10.2762i) q^{49} +(2.58011 + 1.65814i) q^{50} +(-0.467452 + 3.25120i) q^{51} +(0.675969 - 0.434419i) q^{52} +(-5.11162 - 11.1929i) q^{53} +(0.313607 + 0.361922i) q^{54} +(0.471975 + 3.28266i) q^{55} +(-3.40442 + 7.45463i) q^{56} +(1.60866 - 0.472345i) q^{57} +(0.629165 - 0.184739i) q^{58} +(-4.41863 + 9.67544i) q^{59} +(0.850983 + 5.91872i) q^{60} +(-3.65011 - 4.21246i) q^{61} +(1.28625 + 2.81649i) q^{62} +(3.81797 - 2.45366i) q^{63} +(0.428340 - 2.97917i) q^{64} +(1.28922 + 0.828529i) q^{65} +(0.307978 - 0.355426i) q^{66} +(7.43903 + 2.18430i) q^{67} +5.81597 q^{68} +(4.04911 - 2.56996i) q^{69} -7.33969 q^{70} +(-2.86847 - 0.842258i) q^{71} +(1.18251 - 1.36469i) q^{72} +(-3.27850 - 2.10697i) q^{73} +(0.242620 - 1.68746i) q^{74} +(-5.38767 + 3.46244i) q^{75} +(-1.23322 - 2.70038i) q^{76} +(-2.91869 - 3.36835i) q^{77} +(-0.0309280 - 0.215109i) q^{78} +(-3.61897 + 7.92444i) q^{79} +(8.67273 - 2.54654i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(1.14869 - 2.51528i) q^{82} +(1.06526 + 7.40902i) q^{83} +(-5.26248 - 6.07322i) q^{84} +(4.60791 + 10.0899i) q^{85} +(-4.43302 + 2.84893i) q^{86} +(-0.194866 + 1.35532i) q^{87} +(-1.49182 - 0.958732i) q^{88} +(4.73727 - 5.46710i) q^{89} +(1.55172 + 0.455627i) q^{90} -2.05954 q^{91} +(-5.52455 - 6.44903i) q^{92} -6.46556 q^{93} +(4.62333 + 1.35753i) q^{94} +(3.70772 - 4.27893i) q^{95} +(-4.11648 - 2.64550i) q^{96} +(0.801906 - 5.57738i) q^{97} +(5.47795 - 3.52046i) q^{98} +(0.407958 + 0.893304i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + q^{3} - 14 q^{4} - 3 q^{5} - 4 q^{6} + 6 q^{7} - 7 q^{8} - q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 + q^3 - 14 * q^4 - 3 * q^5 - 4 * q^6 + 6 * q^7 - 7 * q^8 - q^9	\( 10 q + 4 q^{2} + q^{3} - 14 q^{4} - 3 q^{5} - 4 q^{6} + 6 q^{7} - 7 q^{8} - q^{9} + 12 q^{10} - 15 q^{11} - 8 q^{12} + 8 q^{13} + 9 q^{14} - 8 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} - 9 q^{19} - 9 q^{20} + 5 q^{21} - 28 q^{22} + 21 q^{23} + 18 q^{24} - 4 q^{25} + q^{26} + q^{27} + 29 q^{28} - 8 q^{29} - 12 q^{30} - 23 q^{31} - q^{32} + 4 q^{33} - 15 q^{34} + 18 q^{35} + 8 q^{36} + 3 q^{37} + 3 q^{38} - 8 q^{39} - 32 q^{40} - 15 q^{41} + 13 q^{42} + 22 q^{43} - q^{44} - 14 q^{45} + 26 q^{46} + 4 q^{47} + 21 q^{48} - 29 q^{49} + 49 q^{50} - 12 q^{51} + 2 q^{52} + 29 q^{53} + 7 q^{54} + 43 q^{55} - 2 q^{56} + 20 q^{57} + 21 q^{58} - 54 q^{59} - 2 q^{60} - 30 q^{61} - 7 q^{62} + 6 q^{63} - 31 q^{64} - 9 q^{65} - 27 q^{66} + q^{67} - 30 q^{68} + q^{69} - 94 q^{70} - 3 q^{71} - 7 q^{72} - 47 q^{73} - 12 q^{74} + 15 q^{75} + 50 q^{76} + 13 q^{77} - 12 q^{78} + 18 q^{79} + 3 q^{80} - q^{81} - 28 q^{82} + 18 q^{83} + 4 q^{84} + 58 q^{85} + 8 q^{87} + 16 q^{88} + 25 q^{89} + q^{90} + 18 q^{91} - 3 q^{92} - 10 q^{93} + 39 q^{94} - 16 q^{95} - 21 q^{96} + 21 q^{97} - 27 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + q^3 - 14 * q^4 - 3 * q^5 - 4 * q^6 + 6 * q^7 - 7 * q^8 - q^9 + 12 * q^10 - 15 * q^11 - 8 * q^12 + 8 * q^13 + 9 * q^14 - 8 * q^15 + 12 * q^16 + q^17 + 4 * q^18 - 9 * q^19 - 9 * q^20 + 5 * q^21 - 28 * q^22 + 21 * q^23 + 18 * q^24 - 4 * q^25 + q^26 + q^27 + 29 * q^28 - 8 * q^29 - 12 * q^30 - 23 * q^31 - q^32 + 4 * q^33 - 15 * q^34 + 18 * q^35 + 8 * q^36 + 3 * q^37 + 3 * q^38 - 8 * q^39 - 32 * q^40 - 15 * q^41 + 13 * q^42 + 22 * q^43 - q^44 - 14 * q^45 + 26 * q^46 + 4 * q^47 + 21 * q^48 - 29 * q^49 + 49 * q^50 - 12 * q^51 + 2 * q^52 + 29 * q^53 + 7 * q^54 + 43 * q^55 - 2 * q^56 + 20 * q^57 + 21 * q^58 - 54 * q^59 - 2 * q^60 - 30 * q^61 - 7 * q^62 + 6 * q^63 - 31 * q^64 - 9 * q^65 - 27 * q^66 + q^67 - 30 * q^68 + q^69 - 94 * q^70 - 3 * q^71 - 7 * q^72 - 47 * q^73 - 12 * q^74 + 15 * q^75 + 50 * q^76 + 13 * q^77 - 12 * q^78 + 18 * q^79 + 3 * q^80 - q^81 - 28 * q^82 + 18 * q^83 + 4 * q^84 + 58 * q^85 + 8 * q^87 + 16 * q^88 + 25 * q^89 + q^90 + 18 * q^91 - 3 * q^92 - 10 * q^93 + 39 * q^94 - 16 * q^95 - 21 * q^96 + 21 * q^97 - 27 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{6}{11}\right)$	$1$

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 $

$2$	−0.459493	−	0.134919i	−0.324911	−	0.0954024i	0.115210	−	0.993341i	$-0.463246\pi$
$2$	−0.459493	−	0.134919i	−0.324911	−	0.0954024i	−0.440120	+	0.897939i	$0.645064\pi$
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$4$	−1.48958	−	0.957293i	−0.744788	−	0.478646i
$5$	0.480602	−	3.34266i	0.214932	−	1.49488i	−0.541440	−	0.840739i	$-0.682121\pi$
$5$	0.480602	−	3.34266i	0.214932	−	1.49488i	0.756372	−	0.654142i	$-0.226970\pi$
$6$	−0.402869	+	0.258908i	−0.164471	+	0.105699i
$7$	1.88533	+	4.12830i	0.712588	+	1.56035i	0.824009	+	0.566577i	$0.191733\pi$
$7$	1.88533	+	4.12830i	0.712588	+	1.56035i	−0.111420	+	0.993773i	$0.535540\pi$
$8$	1.18251	+	1.36469i	0.418079	+	0.482489i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	−0.671822	+	1.47109i	−0.212449	+	0.465198i
$11$	−0.942270	+	0.276675i	−0.284105	+	0.0834208i	−0.420680	−	0.907209i	$-0.638209\pi$
$11$	−0.942270	+	0.276675i	−0.284105	+	0.0834208i	0.136575	+	0.990630i	$0.456390\pi$
$12$	−1.69894	+	0.498853i	−0.490441	+	0.144007i
$13$	−0.188515	+	0.412791i	−0.0522847	+	0.114488i	−0.933971	−	0.357348i	$-0.883681\pi$
$13$	−0.188515	+	0.412791i	−0.0522847	+	0.114488i	0.881687	+	0.471835i	$0.156408\pi$
$14$	−0.309309	−	2.15129i	−0.0826664	−	0.574957i
$15$	−2.21148	−	2.55219i	−0.571003	−	0.658972i
$16$	1.11189	+	2.43470i	0.277972	+	0.608674i
$17$	−2.76321	+	1.77580i	−0.670176	+	0.430696i	−0.830989	−	0.556289i	$-0.812225\pi$
$17$	−2.76321	+	1.77580i	−0.670176	+	0.430696i	0.160813	+	0.986985i	$0.448588\pi$
$18$	−0.0681534	+	0.474017i	−0.0160639	+	0.111727i
$19$	1.41042	+	0.906424i	0.323573	+	0.207948i	0.692335	−	0.721576i	$-0.256582\pi$
$19$	1.41042	+	0.906424i	0.323573	+	0.207948i	−0.368762	+	0.929524i	$0.620218\pi$
$20$	−3.91579	+	4.51907i	−0.875598	+	1.01049i
$21$	4.35459	+	1.27862i	0.950250	+	0.279018i
$22$	0.470295			0.100267
$23$	4.59385	+	1.37715i	0.957884	+	0.287156i
$23$	4.59385	+	1.37715i	0.957884	+	0.287156i
$24$	1.80574			0.368595
$25$	−6.14491	−	1.80431i	−1.22898	−	0.360862i
$26$	0.142315	−	0.164240i	0.0279102	−	0.0322101i
$27$	−0.841254	−	0.540641i	−0.161899	−	0.104046i
$28$	1.14365	−	7.95423i	0.216129	−	1.50321i
$29$	−1.15189	+	0.740277i	−0.213901	+	0.137466i	−0.643205	−	0.765694i	$-0.722396\pi$
$29$	−1.15189	+	0.740277i	−0.213901	+	0.137466i	0.429303	+	0.903160i	$0.358759\pi$
$30$	0.671822	+	1.47109i	0.122657	+	0.268582i
$31$	−4.23404	−	4.88634i	−0.760456	−	0.877613i	0.235082	−	0.971976i	$-0.424464\pi$
$31$	−4.23404	−	4.88634i	−0.760456	−	0.877613i	−0.995538	+	0.0943622i	$0.969919\pi$
$32$	−0.696384	−	4.84346i	−0.123104	−	0.856211i
$33$	−0.407958	+	0.893304i	−0.0710164	+	0.155504i
$34$	1.50926	−	0.443160i	0.258837	−	0.0760013i
$35$	14.7056	−	4.31795i	2.48570	−	0.729867i
$36$	−0.735560	+	1.61065i	−0.122593	+	0.268442i
$37$	0.506627	+	3.52367i	0.0832890	+	0.579288i	0.988140	+	0.153559i	$0.0490734\pi$
$37$	0.506627	+	3.52367i	0.0832890	+	0.579288i	−0.904851	+	0.425729i	$0.860018\pi$
$38$	−0.525785	−	0.606789i	−0.0852937	−	0.0984341i
$39$	0.188515	+	0.412791i	0.0301866	+	0.0660994i
$40$	5.12999	−	3.29685i	0.811123	−	0.521277i
$41$	−0.821738	+	5.71531i	−0.128334	+	0.892582i	0.819332	+	0.573319i	$0.194344\pi$
$41$	−0.821738	+	5.71531i	−0.128334	+	0.892582i	−0.947666	+	0.319263i	$0.896565\pi$
$42$	−1.82839	−	1.17504i	−0.282127	−	0.181312i
$43$	7.20584	−	8.31598i	1.09888	−	1.26817i	0.138233	−	0.990400i	$-0.455858\pi$
$43$	7.20584	−	8.31598i	1.09888	−	1.26817i	0.960646	−	0.277775i	$-0.0895970\pi$
$44$	1.66844	+	0.489899i	0.251527	+	0.0738551i
$45$	−3.37703			−0.503418
$46$	−1.92504	−	1.25259i	−0.283831	−	0.184684i
$47$	−10.0618			−1.46767			−0.733833	−	0.679330i	$-0.762270\pi$
$47$	−10.0618			−1.46767			−0.733833	+	0.679330i	$0.762270\pi$
$48$	2.56815	+	0.754078i	0.370681	+	0.108842i
$49$	−8.90436	+	10.2762i	−1.27205	+	1.46803i
$50$	2.58011	+	1.65814i	0.364882	+	0.234496i
$51$	−0.467452	+	3.25120i	−0.0654563	+	0.455259i
$52$	0.675969	−	0.434419i	0.0937401	−	0.0602431i
$53$	−5.11162	−	11.1929i	−0.702135	−	1.53746i	−0.837364	−	0.546646i	$-0.815904\pi$
$53$	−5.11162	−	11.1929i	−0.702135	−	1.53746i	0.135229	−	0.990814i	$-0.456823\pi$
$54$	0.313607	+	0.361922i	0.0426765	+	0.0492513i
$55$	0.471975	+	3.28266i	0.0636411	+	0.442633i
$56$	−3.40442	+	7.45463i	−0.454934	+	0.996167i
$57$	1.60866	−	0.472345i	0.213072	−	0.0625637i
$58$	0.629165	−	0.184739i	0.0826134	−	0.0242575i
$59$	−4.41863	+	9.67544i	−0.575256	+	1.25964i	0.368695	+	0.929550i	$0.379805\pi$
$59$	−4.41863	+	9.67544i	−0.575256	+	1.25964i	−0.943951	+	0.330085i	$0.892923\pi$
$60$	0.850983	+	5.91872i	0.109861	+	0.764103i
$61$	−3.65011	−	4.21246i	−0.467349	−	0.539350i	0.472323	−	0.881425i	$-0.343416\pi$
$61$	−3.65011	−	4.21246i	−0.467349	−	0.539350i	−0.939672	+	0.342076i	$0.888870\pi$
$62$	1.28625	+	2.81649i	0.163354	+	0.357695i
$63$	3.81797	−	2.45366i	0.481019	−	0.309132i
$64$	0.428340	−	2.97917i	0.0535425	−	0.372396i
$65$	1.28922	+	0.828529i	0.159908	+	0.102766i
$66$	0.307978	−	0.355426i	0.0379095	−	0.0437499i
$67$	7.43903	+	2.18430i	0.908822	+	0.266854i	0.702545	−	0.711639i	$-0.252047\pi$
$67$	7.43903	+	2.18430i	0.908822	+	0.266854i	0.206277	+	0.978494i	$0.433865\pi$
$68$	5.81597			0.705290
$69$	4.04911	−	2.56996i	0.487456	−	0.309386i
$70$	−7.33969			−0.877260
$71$	−2.86847	−	0.842258i	−0.340424	−	0.0999576i	0.107052	−	0.994253i	$-0.465859\pi$
$71$	−2.86847	−	0.842258i	−0.340424	−	0.0999576i	−0.447476	+	0.894296i	$0.647677\pi$
$72$	1.18251	−	1.36469i	0.139360	−	0.160830i
$73$	−3.27850	−	2.10697i	−0.383720	−	0.246602i	0.334533	−	0.942384i	$-0.391421\pi$
$73$	−3.27850	−	2.10697i	−0.383720	−	0.246602i	−0.718253	+	0.695782i	$0.755058\pi$
$74$	0.242620	−	1.68746i	0.0282039	−	0.196163i
$75$	−5.38767	+	3.46244i	−0.622114	+	0.399809i
$76$	−1.23322	−	2.70038i	−0.141460	−	0.309754i
$77$	−2.91869	−	3.36835i	−0.332616	−	0.383859i
$78$	−0.0309280	−	0.215109i	−0.00350190	−	0.0243563i
$79$	−3.61897	+	7.92444i	−0.407166	+	0.891570i	0.589327	+	0.807895i	$0.299393\pi$
$79$	−3.61897	+	7.92444i	−0.407166	+	0.891570i	−0.996493	+	0.0836750i	$0.973334\pi$
$80$	8.67273	−	2.54654i	0.969641	−	0.284712i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	1.14869	−	2.51528i	0.126851	−	0.277766i
$83$	1.06526	+	7.40902i	0.116927	+	0.813246i	0.960907	+	0.276871i	$0.0892975\pi$
$83$	1.06526	+	7.40902i	0.116927	+	0.813246i	−0.843980	+	0.536375i	$0.819793\pi$
$84$	−5.26248	−	6.07322i	−0.574184	−	0.662643i
$85$	4.60791	+	10.0899i	0.499798	+	1.09440i
$86$	−4.43302	+	2.84893i	−0.478024	+	0.307208i
$87$	−0.194866	+	1.35532i	−0.0208918	+	0.145306i
$88$	−1.49182	−	0.958732i	−0.159028	−	0.102201i
$89$	4.73727	−	5.46710i	0.502150	−	0.579512i	−0.446922	−	0.894573i	$-0.647480\pi$
$89$	4.73727	−	5.46710i	0.502150	−	0.579512i	0.949071	+	0.315062i	$0.102025\pi$
$90$	1.55172	+	0.455627i	0.163566	+	0.0480273i
$91$	−2.05954			−0.215898
$92$	−5.52455	−	6.44903i	−0.575974	−	0.672358i
$93$	−6.46556			−0.670447
$94$	4.62333	+	1.35753i	0.476860	+	0.140019i
$95$	3.70772	−	4.27893i	0.380404	−	0.439009i
$96$	−4.11648	−	2.64550i	−0.420136	−	0.270005i
$97$	0.801906	−	5.57738i	0.0814212	−	0.566297i	−0.907748	−	0.419516i	$-0.862200\pi$
$97$	0.801906	−	5.57738i	0.0814212	−	0.566297i	0.989169	−	0.146781i	$-0.0468912\pi$
$98$	5.47795	−	3.52046i	0.553356	−	0.355620i
$99$	0.407958	+	0.893304i	0.0410014	+	0.0897804i
$100$	7.42607	+	8.57014i	0.742607	+	0.857014i
$101$	−1.12323	−	7.81224i	−0.111766	−	0.777347i	−0.966201	−	0.257790i	$-0.917006\pi$
$101$	−1.12323	−	7.81224i	−0.111766	−	0.777347i	0.854435	−	0.519558i	$-0.173903\pi$
$102$	0.653440	−	1.43083i	0.0647002	−	0.141674i
$103$	8.63913	−	2.53668i	0.851239	−	0.249946i	0.173122	−	0.984900i	$-0.444615\pi$
$103$	8.63913	−	2.53668i	0.851239	−	0.249946i	0.678117	+	0.734954i	$0.262796\pi$
$104$	−0.786250	+	0.230864i	−0.0770982	+	0.0226381i
$105$	6.36682	−	13.9414i	0.621338	−	1.36054i
$106$	0.838617	+	5.83271i	0.0814536	+	0.566523i
$107$	2.36779	+	2.73258i	0.228903	+	0.264168i	0.858569	−	0.512697i	$-0.171354\pi$
$107$	2.36779	+	2.73258i	0.228903	+	0.264168i	−0.629666	+	0.776866i	$0.716808\pi$
$108$	0.735560	+	1.61065i	0.0707793	+	0.154985i
$109$	1.07332	−	0.689779i	0.102805	−	0.0660688i	−0.488228	−	0.872716i	$-0.662357\pi$
$109$	1.07332	−	0.689779i	0.102805	−	0.0660688i	0.591033	+	0.806647i	$0.298720\pi$
$110$	0.226025	−	1.57204i	0.0215506	−	0.149888i
$111$	2.99478	+	1.92463i	0.284252	+	0.182678i
$112$	−7.95488	+	9.18042i	−0.751666	+	0.867468i
$113$	1.13788	+	0.334113i	0.107043	+	0.0314307i	0.334815	−	0.942284i	$-0.391326\pi$
$113$	1.13788	+	0.334113i	0.107043	+	0.0314307i	−0.227772	+	0.973714i	$0.573144\pi$
$114$	−0.802897			−0.0751982
$115$	6.81116	−	14.6938i	0.635144	−	1.37020i
$116$	2.42450			0.225109
$117$	0.435418	+	0.127850i	0.0402544	+	0.0118197i
$118$	3.33573	−	3.84964i	0.307079	−	0.354388i
$119$	−12.5406	−	8.05936i	−1.14960	−	0.738801i
$120$	0.867841	−	6.03596i	0.0792226	−	0.551006i
$121$	−8.44247	+	5.42564i	−0.767497	+	0.493240i
$122$	1.10886	+	2.42806i	0.100391	+	0.219827i
$123$	3.78122	+	4.36376i	0.340941	+	0.393467i
$124$	1.62927	+	11.3318i	0.146312	+	1.01763i
$125$	−1.97010	+	4.31391i	−0.176211	+	0.385848i
$126$	−2.08538	+	0.612322i	−0.185780	+	0.0545500i
$127$	−2.74514	+	0.806046i	−0.243592	+	0.0715250i	−0.401249	−	0.915969i	$-0.631424\pi$
$127$	−2.74514	+	0.806046i	−0.243592	+	0.0715250i	0.157658	+	0.987494i	$0.449606\pi$
$128$	−4.66424	+	10.2133i	−0.412264	+	0.902733i
$129$	−1.56598	−	10.8916i	−0.137877	−	0.958953i
$130$	−0.480602	−	0.554644i	−0.0421515	−	0.0486455i
$131$	0.160212	+	0.350814i	0.0139977	+	0.0306508i	0.916502	−	0.400031i	$-0.131001\pi$
$131$	0.160212	+	0.350814i	0.0139977	+	0.0306508i	−0.902504	+	0.430681i	$0.858273\pi$
$132$	1.46284	−	0.940109i	0.127324	−	0.0818260i
$133$	−1.08287	+	7.53156i	−0.0938972	+	0.653069i
$134$	−3.12348	−	2.00734i	−0.269828	−	0.173408i
$135$	−2.21148	+	2.55219i	−0.190334	+	0.219657i
$136$	−5.69093	−	1.67101i	−0.487993	−	0.143288i
$137$	20.4664			1.74856			0.874282	−	0.485419i	$-0.161333\pi$
$137$	20.4664			1.74856			0.874282	+	0.485419i	$0.161333\pi$
$138$	−2.20728	+	0.634573i	−0.187896	+	0.0540185i
$139$	10.1030			0.856927			0.428463	−	0.903559i	$-0.359055\pi$
$139$	10.1030			0.856927			0.428463	+	0.903559i	$0.359055\pi$
$140$	−26.0386	−	7.64563i	−2.20067	−	0.646174i
$141$	−6.58908	+	7.60420i	−0.554901	+	0.640390i
$142$	1.20440	+	0.774023i	0.101071	+	0.0649546i
$143$	0.0634232	−	0.441118i	0.00530371	−	0.0368881i
$144$	2.25168	−	1.44706i	0.187640	−	0.120589i
$145$	1.92089	+	4.20616i	0.159521	+	0.349303i
$146$	1.22218	+	1.41047i	0.101148	+	0.116731i
$147$	1.93510	+	13.4589i	0.159605	+	1.11007i
$148$	2.61852	−	5.73377i	0.215241	−	0.471313i
$149$	9.88733	−	2.90318i	0.810001	−	0.237838i	0.149596	−	0.988747i	$-0.452203\pi$
$149$	9.88733	−	2.90318i	0.810001	−	0.237838i	0.660405	+	0.750909i	$0.270385\pi$
$150$	2.94275	−	0.864068i	0.240274	−	0.0705509i
$151$	0.207860	−	0.455151i	0.0169154	−	0.0370396i	−0.900986	−	0.433849i	$-0.857155\pi$
$151$	0.207860	−	0.455151i	0.0169154	−	0.0370396i	0.917901	+	0.396809i	$0.129882\pi$
$152$	0.430851	+	2.99664i	0.0349467	+	0.243059i
$153$	2.15098	+	2.48236i	0.173896	+	0.200687i
$154$	0.886663	+	1.94152i	0.0714493	+	0.156452i
$155$	−18.3683	+	11.8046i	−1.47537	+	0.948165i
$156$	0.114354	−	0.795348i	0.00915562	−	0.0636788i
$157$	−13.1111	−	8.42597i	−1.04638	−	0.672466i	−0.0998213	−	0.995005i	$-0.531827\pi$
$157$	−13.1111	−	8.42597i	−1.04638	−	0.672466i	−0.946556	+	0.322540i	$0.895463\pi$
$158$	2.73205	−	3.15296i	0.217350	−	0.250836i
$159$	−11.8064	−	3.46668i	−0.936310	−	0.274925i
$160$	−16.5247			−1.30639
$161$	2.97563	+	21.5612i	0.234512	+	1.69926i
$162$	0.478891			0.0376253
$163$	6.51437	+	1.91279i	0.510245	+	0.149821i	0.526713	−	0.850043i	$-0.323424\pi$
$163$	6.51437	+	1.91279i	0.510245	+	0.149821i	−0.0164685	+	0.999864i	$0.505242\pi$
$164$	6.69527	−	7.72675i	0.522813	−	0.603358i
$165$	2.78994	+	1.79299i	0.217197	+	0.139584i
$166$	0.510142	−	3.54812i	0.0395947	−	0.275387i
$167$	16.8646	−	10.8382i	1.30502	−	0.838688i	0.311274	−	0.950320i	$-0.399244\pi$
$167$	16.8646	−	10.8382i	1.30502	−	0.838688i	0.993750	+	0.111633i	$0.0356080\pi$
$168$	3.40442	+	7.45463i	0.262656	+	0.575137i
$169$	8.37833	+	9.66911i	0.644487	+	0.743778i
$170$	−0.755977	−	5.25794i	−0.0579808	−	0.403265i
$171$	0.696474	−	1.52506i	0.0532607	−	0.116625i
$172$	−18.6945	+	5.48919i	−1.42544	+	0.418547i
$173$	−9.96585	+	2.92624i	−0.757690	+	0.222478i	−0.637687	−	0.770296i	$-0.720109\pi$
$173$	−9.96585	+	2.92624i	−0.757690	+	0.222478i	−0.120003	+	0.992774i	$0.538290\pi$
$174$	0.272399	−	0.596470i	0.0206505	−	0.0452183i
$175$	−4.13647	−	28.7698i	−0.312688	−	2.17479i
$176$	−1.72132	−	1.98651i	−0.129749	−	0.149739i
$177$	4.41863	+	9.67544i	0.332124	+	0.727251i
$178$	−2.91436	+	1.87295i	−0.218441	+	0.140383i
$179$	−0.597086	+	4.15282i	−0.0446283	+	0.310396i	0.955265	+	0.295753i	$0.0955705\pi$
$179$	−0.597086	+	4.15282i	−0.0446283	+	0.310396i	−0.999893	+	0.0146436i	$0.995339\pi$
$180$	5.03035	+	3.23281i	0.374940	+	0.240959i
$181$	0.398786	−	0.460224i	0.0296415	−	0.0342081i	−0.740735	−	0.671797i	$-0.765523\pi$
$181$	0.398786	−	0.460224i	0.0296415	−	0.0342081i	0.770377	+	0.637589i	$0.220068\pi$
$182$	0.946343	+	0.277871i	0.0701476	+	0.0205972i
$183$	−5.57388			−0.412033
$184$	3.55288	+	7.89765i	0.261922	+	0.582223i
$185$	12.0219			0.883868
$186$	2.97088	+	0.872329i	0.217835	+	0.0639623i
$187$	2.11237	−	2.43780i	0.154471	−	0.178270i
$188$	14.9878	+	9.63209i	1.09310	+	0.702493i
$189$	0.645886	−	4.49223i	0.0469813	−	0.326762i
$190$	−2.28098	+	1.46590i	−0.165480	+	0.106347i
$191$	0.608314	+	1.33202i	0.0440161	+	0.0963817i	0.930363	−	0.366641i	$-0.119492\pi$
$191$	0.608314	+	1.33202i	0.0440161	+	0.0963817i	−0.886347	+	0.463022i	$0.846765\pi$
$192$	−1.97100	−	2.27466i	−0.142245	−	0.164159i
$193$	−3.02393	−	21.0319i	−0.217667	−	1.51391i	−0.746616	−	0.665256i	$-0.768323\pi$
$193$	−3.02393	−	21.0319i	−0.217667	−	1.51391i	0.528948	−	0.848654i	$-0.322587\pi$
$194$	−1.12097	+	2.45457i	−0.0804807	+	0.176228i
$195$	1.47042	−	0.431754i	0.105299	−	0.0309185i
$196$	23.1010	−	6.78308i	1.65007	−	0.484506i
$197$	−2.52646	+	5.53217i	−0.180003	+	0.394151i	−0.978028	−	0.208473i	$-0.933151\pi$
$197$	−2.52646	+	5.53217i	−0.180003	+	0.394151i	0.798025	+	0.602624i	$0.205878\pi$
$198$	−0.0669300	−	0.465508i	−0.00475651	−	0.0330822i
$199$	−7.57550	−	8.74259i	−0.537013	−	0.619746i	0.420795	−	0.907156i	$-0.361751\pi$
$199$	−7.57550	−	8.74259i	−0.537013	−	0.619746i	−0.957808	+	0.287410i	$0.907206\pi$
$200$	−4.80409	−	10.5195i	−0.339700	−	0.743840i
$201$	6.52231	−	4.19164i	0.460048	−	0.295655i
$202$	−0.537906	+	3.74122i	−0.0378469	+	0.263231i
$203$	−5.22779	−	3.35970i	−0.366919	−	0.235804i
$204$	3.80865	−	4.39542i	0.266659	−	0.307741i
$205$	18.7094	+	5.49357i	1.30672	+	0.383688i
$206$	−4.31187			−0.300422
$207$	0.709362	−	4.74308i	0.0493041	−	0.329667i
$208$	−1.21463			−0.0842193
$209$	−1.57979	−	0.463867i	−0.109276	−	0.0320863i
$210$	−4.80647	+	5.54697i	−0.331678	+	0.382777i
$211$	−2.32817	−	1.49622i	−0.160278	−	0.103004i	0.458043	−	0.888930i	$-0.348550\pi$
$211$	−2.32817	−	1.49622i	−0.160278	−	0.103004i	−0.618321	+	0.785926i	$0.712187\pi$
$212$	−3.10072	+	21.5660i	−0.212958	+	1.48116i
$213$	−2.51498	+	1.61628i	−0.172324	+	0.110746i
$214$	−0.719307	−	1.57506i	−0.0491708	−	0.107669i
$215$	−24.3343	−	28.0833i	−1.65959	−	1.91527i
$216$	−0.256983	−	1.78736i	−0.0174855	−	0.121614i
$217$	12.1897	−	26.6918i	0.827492	−	1.81196i
$218$	−0.586246	+	0.172137i	−0.0397056	+	0.0116586i
$219$	−3.73930	+	1.09796i	−0.252679	+	0.0741932i
$220$	2.43942	−	5.34159i	0.164466	−	0.360130i
$221$	−0.212129	−	1.47539i	−0.0142694	−	0.0992456i
$222$	−1.11641	−	1.28841i	−0.0749287	−	0.0864723i
$223$	−7.66126	−	16.7758i	−0.513036	−	1.12339i	−0.972009	−	0.234942i	$-0.924510\pi$
$223$	−7.66126	−	16.7758i	−0.513036	−	1.12339i	0.458973	−	0.888450i	$-0.348217\pi$
$224$	18.6823	−	12.0064i	1.24827	−	0.802212i
$225$	−0.911432	+	6.33915i	−0.0607621	+	0.422610i
$226$	−0.477771	−	0.307045i	−0.0317809	−	0.0204243i
$227$	−4.74799	+	5.47948i	−0.315135	+	0.363686i	−0.891114	−	0.453779i	$-0.850076\pi$
$227$	−4.74799	+	5.47948i	−0.315135	+	0.363686i	0.575979	+	0.817465i	$0.304621\pi$
$228$	−2.84840	−	0.836364i	−0.188640	−	0.0553896i
$229$	9.95723			0.657992			0.328996	−	0.944331i	$-0.393290\pi$
$229$	9.95723			0.657992			0.328996	+	0.944331i	$0.393290\pi$
$230$	−5.11216	+	5.83274i	−0.337086	+	0.384600i
$231$	−4.45696			−0.293247
$232$	−2.37237	−	0.696590i	−0.155754	−	0.0457334i
$233$	−3.53680	+	4.08169i	−0.231704	+	0.267400i	−0.859681	−	0.510831i	$-0.829338\pi$
$233$	−3.53680	+	4.08169i	−0.231704	+	0.267400i	0.627977	+	0.778232i	$0.283883\pi$
$234$	−0.182822	−	0.117492i	−0.0119514	−	0.00768072i
$235$	−4.83572	+	33.6332i	−0.315448	+	2.19399i
$236$	15.8441	−	10.1824i	1.03136	−	0.662817i
$237$	3.61897	+	7.92444i	0.235078	+	0.514748i
$238$	4.67496	+	5.39519i	0.303033	+	0.349718i
$239$	2.10857	+	14.6654i	0.136392	+	0.948626i	0.936973	+	0.349402i	$0.113615\pi$
$239$	2.10857	+	14.6654i	0.136392	+	0.948626i	−0.800581	+	0.599224i	$0.795476\pi$
$240$	3.75488	−	8.22205i	0.242377	−	0.530731i
$241$	−14.0591	+	4.12814i	−0.905629	+	0.265917i	−0.701200	−	0.712965i	$-0.747352\pi$
$241$	−14.0591	+	4.12814i	−0.905629	+	0.265917i	−0.204429	+	0.978881i	$0.565534\pi$
$242$	4.61128	−	1.35399i	0.296424	−	0.0870380i
$243$	−0.415415	+	0.909632i	−0.0266489	+	0.0583529i
$244$	1.40457	+	9.76900i	0.0899184	+	0.625396i
$245$	30.0703	+	34.7030i	1.92112	+	2.21709i
$246$	−1.14869	−	2.51528i	−0.0732377	−	0.160368i
$247$	−0.640050	+	0.411335i	−0.0407254	+	0.0261726i
$248$	1.66154	−	11.5563i	0.105508	−	0.733824i
$249$	6.29696	+	4.04681i	0.399054	+	0.256456i
$250$	1.48728	−	1.71641i	0.0940636	−	0.108555i
$251$	−0.924463	−	0.271447i	−0.0583516	−	0.0171336i	0.252426	−	0.967616i	$-0.418771\pi$
$251$	−0.924463	−	0.271447i	−0.0583516	−	0.0171336i	−0.310778	+	0.950483i	$0.600590\pi$
$252$	−8.03603			−0.506222
$253$	−4.70967	−	0.0266443i	−0.296095	−	0.00167511i
$254$	1.37012			0.0859692
$255$	10.6430	+	3.12506i	0.666489	+	0.195699i
$256$	−0.420855	+	0.485693i	−0.0263035	+	0.0303558i
$257$	−0.188128	−	0.120903i	−0.0117351	−	0.00754171i	0.534760	−	0.845004i	$-0.320402\pi$
$257$	−0.188128	−	0.120903i	−0.0117351	−	0.00754171i	−0.546495	+	0.837462i	$0.684038\pi$
$258$	−0.749933	+	5.21590i	−0.0466888	+	0.324728i
$259$	−13.5916	+	8.73480i	−0.844542	+	0.542754i
$260$	−1.12724	−	2.46832i	−0.0699086	−	0.153078i
$261$	0.896674	+	1.03482i	0.0555027	+	0.0640536i
$262$	−0.0262844	−	0.182812i	−0.00162386	−	0.0112942i
$263$	−9.27832	+	20.3167i	−0.572126	+	1.25278i	0.373532	+	0.927617i	$0.378147\pi$
$263$	−9.27832	+	20.3167i	−0.572126	+	1.25278i	−0.945658	+	0.325163i	$0.894581\pi$
$264$	−1.70149	+	0.499603i	−0.104720	+	0.0307485i
$265$	−39.8706	+	11.7071i	−2.44923	+	0.719160i
$266$	1.51373	−	3.31460i	0.0928125	−	0.203231i
$267$	−1.02951	−	7.16038i	−0.0630048	−	0.438208i
$268$	−8.99000	−	10.3750i	−0.549151	−	0.633755i
$269$	−9.85399	−	21.5772i	−0.600808	−	1.31559i	−0.928686	−	0.370867i	$-0.879061\pi$
$269$	−9.85399	−	21.5772i	−0.600808	−	1.31559i	0.327878	−	0.944720i	$-0.393667\pi$
$270$	1.36050	−	0.874341i	0.0827975	−	0.0532107i
$271$	1.63660	−	11.3828i	0.0994161	−	0.691454i	−0.877772	−	0.479079i	$-0.840971\pi$
$271$	1.63660	−	11.3828i	0.0994161	−	0.691454i	0.977188	−	0.212376i	$-0.0681201\pi$
$272$	−7.39592	−	4.75307i	−0.448444	−	0.288197i
$273$	−1.34871	+	1.55649i	−0.0816277	+	0.0942033i
$274$	−9.40417	−	2.76131i	−0.568127	−	0.166817i
$275$	6.28938			0.379264
$276$	−8.49167	−	0.0480404i	−0.511138	−	0.00289169i
$277$	−6.25528			−0.375843			−0.187922	−	0.982184i	$-0.560175\pi$
$277$	−6.25528			−0.375843			−0.187922	+	0.982184i	$0.560175\pi$
$278$	−4.64227	−	1.36309i	−0.278425	−	0.0817528i
$279$	−4.23404	+	4.88634i	−0.253485	+	0.292538i
$280$	23.2821	+	14.9625i	1.39137	+	0.894180i
$281$	3.04681	−	21.1911i	0.181758	−	1.26415i	−0.670847	−	0.741596i	$-0.734069\pi$
$281$	3.04681	−	21.1911i	0.181758	−	1.26415i	0.852604	−	0.522557i	$-0.175022\pi$
$282$	4.05359	−	2.60508i	0.241388	−	0.155131i
$283$	3.01441	+	6.60063i	0.179188	+	0.392367i	0.977818	−	0.209455i	$-0.0671690\pi$
$283$	3.01441	+	6.60063i	0.179188	+	0.392367i	−0.798630	+	0.601822i	$0.794442\pi$
$284$	3.46651	+	4.00057i	0.205700	+	0.237390i
$285$	−0.805764	−	5.60421i	−0.0477293	−	0.331965i
$286$	−0.0886578	+	0.194134i	−0.00524245	+	0.0114794i
$287$	−25.1438	+	7.38288i	−1.48419	+	0.435797i
$288$	−4.69505	+	1.37859i	−0.276659	+	0.0812343i
$289$	−2.58023	+	5.64991i	−0.151778	+	0.332348i
$290$	−0.315143	−	2.19187i	−0.0185058	−	0.128711i
$291$	−3.68996	−	4.25845i	−0.216310	−	0.249634i
$292$	2.86660	+	6.27698i	0.167755	+	0.367332i
$293$	−0.329271	+	0.211609i	−0.0192362	+	0.0123624i	−0.550224	−	0.835017i	$-0.685458\pi$
$293$	−0.329271	+	0.211609i	−0.0192362	+	0.0123624i	0.530987	+	0.847380i	$0.321821\pi$
$294$	0.926704	−	6.44537i	0.0540465	−	0.375902i
$295$	30.2181	+	19.4200i	1.75937	+	1.13068i
$296$	−4.20961	+	4.85815i	−0.244679	+	0.282374i
$297$	0.942270	+	0.276675i	0.0546761	+	0.0160543i
$298$	−4.93485			−0.285868
$299$	−1.43449	+	1.63668i	−0.0829585	+	0.0946519i
$300$	11.3399			0.654710
$301$	47.9162	+	14.0695i	2.76185	+	0.810951i
$302$	−0.156919	+	0.181094i	−0.00902968	+	0.0104208i
$303$	−6.63966	−	4.26705i	−0.381439	−	0.245136i
$304$	−0.638634	+	4.44180i	−0.0366282	+	0.254754i
$305$	−15.8350	+	10.1766i	−0.906712	+	0.582709i
$306$	−0.653440	−	1.43083i	−0.0373547	−	0.0817953i
$307$	−0.843569	−	0.973531i	−0.0481450	−	0.0555623i	0.731166	−	0.682199i	$-0.238976\pi$
$307$	−0.843569	−	0.973531i	−0.0481450	−	0.0555623i	−0.779311	+	0.626637i	$0.784431\pi$
$308$	1.12312	+	7.81145i	0.0639956	+	0.445099i
$309$	3.74033	−	8.19019i	0.212780	−	0.465924i
$310$	10.0328	−	2.94588i	0.569822	−	0.167315i
$311$	1.20852	−	0.354853i	0.0685288	−	0.0201219i	−0.247288	−	0.968942i	$-0.579540\pi$
$311$	1.20852	−	0.354853i	0.0685288	−	0.0201219i	0.315817	+	0.948820i	$0.397721\pi$
$312$	−0.340409	+	0.745392i	−0.0192719	+	0.0421995i
$313$	1.48565	+	10.3330i	0.0839742	+	0.584053i	0.987750	+	0.156046i	$0.0498750\pi$
$313$	1.48565	+	10.3330i	0.0839742	+	0.584053i	−0.903776	+	0.428007i	$0.859216\pi$
$314$	4.88762	+	5.64061i	0.275824	+	0.318318i
$315$	−6.36682	−	13.9414i	−0.358730	−	0.785509i
$316$	12.9767	−	8.33965i	0.729999	−	0.469142i
$317$	3.85904	−	26.8402i	0.216745	−	1.50750i	−0.533196	−	0.845992i	$-0.679009\pi$
$317$	3.85904	−	26.8402i	0.216745	−	1.50750i	0.749941	−	0.661505i	$-0.230082\pi$
$318$	4.95724	+	3.18583i	0.277988	+	0.178652i
$319$	0.880579	−	1.01624i	0.0493029	−	0.0568986i
$320$	−9.75248	−	2.86359i	−0.545180	−	0.160079i
$321$	3.61572			0.201810
$322$	1.54174	−	10.3087i	0.0859177	−	0.574480i
$323$	−5.50692			−0.306413
$324$	1.69894	+	0.498853i	0.0943855	+	0.0277141i
$325$	1.90321	−	2.19642i	0.105571	−	0.121836i
$326$	−2.73523	−	1.75783i	−0.151491	−	0.0973571i
$327$	0.181573	−	1.26287i	0.0100410	−	0.0698368i
$328$	−8.77132	+	5.63698i	−0.484315	+	0.311250i
$329$	−18.9698	−	41.5382i	−1.04584	−	2.29007i
$330$	−1.04005	−	1.20028i	−0.0572529	−	0.0660734i
$331$	1.06491	+	7.40664i	0.0585330	+	0.407106i	0.997932	+	0.0642799i	$0.0204751\pi$
$331$	1.06491	+	7.40664i	0.0585330	+	0.407106i	−0.939399	+	0.342826i	$0.888616\pi$
$332$	5.50582	−	12.0561i	0.302171	−	0.661662i
$333$	3.41570	−	1.00294i	0.187179	−	0.0549608i
$334$	−9.21146	+	2.70473i	−0.504029	+	0.147996i
$335$	10.8766	−	23.8164i	0.594250	−	1.30123i
$336$	1.72876	+	12.0238i	0.0943116	+	0.655952i
$337$	16.8366	+	19.4305i	0.917150	+	1.05845i	0.998093	+	0.0617284i	$0.0196613\pi$
$337$	16.8366	+	19.4305i	0.917150	+	1.05845i	−0.0809434	+	0.996719i	$0.525793\pi$
$338$	−2.54523	−	5.57329i	−0.138443	−	0.303147i
$339$	0.997660	−	0.641157i	0.0541855	−	0.0348229i
$340$	2.79517	−	19.4408i	0.151589	−	1.05433i
$341$	5.34154	+	3.43280i	0.289261	+	0.185897i
$342$	−0.525785	+	0.606789i	−0.0284312	+	0.0328114i
$343$	−28.7287	−	8.43551i	−1.55120	−	0.455475i
$344$	19.8696			1.07130
$345$	−6.64447	−	14.7699i	−0.357726	−	0.795186i
$346$	4.97404			0.267406
$347$	23.6140	+	6.93370i	1.26767	+	0.372220i	0.845342	−	0.534225i	$-0.179396\pi$
$347$	23.6140	+	6.93370i	1.26767	+	0.372220i	0.422324	+	0.906445i	$0.361215\pi$
$348$	1.58771	−	1.83231i	0.0851100	−	0.0982222i
$349$	−16.2708	−	10.4566i	−0.870956	−	0.559730i	0.0270889	−	0.999633i	$-0.491376\pi$
$349$	−16.2708	−	10.4566i	−0.870956	−	0.559730i	−0.898045	+	0.439903i	$0.855013\pi$
$350$	−1.98092	+	13.7776i	−0.105885	+	0.736443i
$351$	0.381761	−	0.245343i	0.0203769	−	0.0130954i
$352$	1.99625	+	4.37117i	0.106400	+	0.232984i
$353$	15.4031	+	17.7761i	0.819823	+	0.946126i	0.999291	−	0.0376379i	$-0.0119833\pi$
$353$	15.4031	+	17.7761i	0.819823	+	0.946126i	−0.179469	+	0.983764i	$0.557438\pi$
$354$	−0.724924	−	5.04196i	−0.0385293	−	0.267977i
$355$	−4.19397	+	9.18351i	−0.222593	+	0.487410i
$356$	−12.2901	+	3.60871i	−0.651376	+	0.191261i
$357$	−14.3032	+	4.19980i	−0.757007	+	0.222277i
$358$	0.834652	−	1.82763i	0.0441127	−	0.0965934i
$359$	0.860321	+	5.98367i	0.0454060	+	0.315806i	0.999848	+	0.0174106i	$0.00554225\pi$
$359$	0.860321	+	5.98367i	0.0454060	+	0.315806i	−0.954442	+	0.298395i	$0.903549\pi$
$360$	−3.99336	−	4.60859i	−0.210469	−	0.242894i
$361$	−6.72520	−	14.7261i	−0.353958	−	0.775059i
$362$	−0.245332	+	0.157666i	−0.0128944	+	0.00828672i
$363$	−1.42821	+	9.93343i	−0.0749617	+	0.521370i
$364$	3.06784	+	1.97158i	0.160798	+	0.103339i
$365$	−8.61852	+	9.94630i	−0.451114	+	0.520613i
$366$	2.56116	+	0.752024i	0.133874	+	0.0393089i
$367$	3.17802			0.165891			0.0829457	−	0.996554i	$-0.473567\pi$
$367$	3.17802			0.165891			0.0829457	+	0.996554i	$0.473567\pi$
$368$	1.75490	+	12.7159i	0.0914805	+	0.662861i
$369$	5.77408			0.300587
$370$	−5.52398	−	1.62199i	−0.287178	−	0.0843231i
$371$	36.5705	−	42.2046i	1.89864	−	2.19115i
$372$	9.63095	+	6.18943i	0.499341	+	0.320907i
$373$	0.0788258	−	0.548246i	0.00408145	−	0.0283871i	−0.987679	−	0.156494i	$-0.949981\pi$
$373$	0.0788258	−	0.548246i	0.00408145	−	0.0283871i	0.991760	+	0.128107i	$0.0408900\pi$
$374$	−1.29952	+	0.835153i	−0.0671967	+	0.0431847i
$375$	1.97010	+	4.31391i	0.101735	+	0.222769i
$376$	−11.8982	−	13.7312i	−0.613601	−	0.708133i
$377$	−0.0884301	−	0.615045i	−0.00455438	−	0.0316764i
$378$	−0.902869	+	1.97701i	−0.0464386	+	0.101686i
$379$	−2.23321	+	0.655730i	−0.114712	+	0.0336826i	−0.338585	−	0.940936i	$-0.609948\pi$
$379$	−2.23321	+	0.655730i	−0.114712	+	0.0336826i	0.223873	+	0.974618i	$0.428130\pi$
$380$	−9.61912	+	2.82443i	−0.493450	+	0.144890i
$381$	−1.18852	+	2.60249i	−0.0608895	+	0.133329i
$382$	−0.0998005	−	0.694128i	−0.00510624	−	0.0355147i
$383$	19.1738	+	22.1278i	0.979736	+	1.13068i	0.991416	+	0.130744i	$0.0417365\pi$
$383$	19.1738	+	22.1278i	0.979736	+	1.13068i	−0.0116804	+	0.999932i	$0.503718\pi$
$384$	4.66424	+	10.2133i	0.238021	+	0.521193i
$385$	−12.6620	+	8.13735i	−0.645313	+	0.414718i
$386$	−1.44813	+	10.0720i	−0.0737081	+	0.512651i
$387$	−9.25683	−	5.94900i	−0.470551	−	0.302405i
$388$	−6.53368	+	7.54027i	−0.331697	+	0.382799i
$389$	−9.77736	−	2.87089i	−0.495732	−	0.145560i	0.0243038	−	0.999705i	$-0.492263\pi$
$389$	−9.77736	−	2.87089i	−0.495732	−	0.145560i	−0.520035	+	0.854145i	$0.674081\pi$
$390$	−0.733899			−0.0371624
$391$	−15.1393	+	4.35242i	−0.765628	+	0.220112i
$392$	−24.5532			−1.24013
$393$	0.370044	+	0.108655i	0.0186662	+	0.00548091i
$394$	1.90729	−	2.20113i	0.0960878	−	0.110891i
$395$	24.7494	+	15.9055i	1.24528	+	0.800292i
$396$	0.247468	−	1.72118i	0.0124358	−	0.0864926i
$397$	29.0435	−	18.6651i	1.45765	−	0.936775i	0.458814	−	0.888532i	$-0.348274\pi$
$397$	29.0435	−	18.6651i	1.45765	−	0.936775i	0.998836	−	0.0482421i	$-0.0153619\pi$
$398$	2.30134	+	5.03924i	0.115356	+	0.252594i
$399$	4.98284	+	5.75051i	0.249454	+	0.287885i
$400$	−2.43951	−	16.9672i	−0.121976	−	0.848360i
$401$	3.73436	−	8.17710i	0.186485	−	0.408345i	−0.793180	−	0.608988i	$-0.791576\pi$
$401$	3.73436	−	8.17710i	0.186485	−	0.408345i	0.979664	+	0.200643i	$0.0643031\pi$
$402$	−3.56249	+	1.04604i	−0.177681	+	0.0521718i
$403$	2.81522	−	0.826623i	0.140236	−	0.0411770i
$404$	−5.80547	+	12.7122i	−0.288833	+	0.632455i
$405$	0.480602	+	3.34266i	0.0238813	+	0.166098i
$406$	1.94884	+	2.24909i	0.0967195	+	0.111620i
$407$	−1.45229	−	3.18008i	−0.0719875	−	0.157631i
$408$	−4.98963	+	3.20664i	−0.247023	+	0.158752i
$409$	−3.18911	+	22.1808i	−0.157691	+	1.09677i	0.745182	+	0.666861i	$0.232363\pi$
$409$	−3.18911	+	22.1808i	−0.157691	+	1.09677i	−0.902873	+	0.429907i	$0.858546\pi$
$410$	−7.85565	−	5.04852i	−0.387963	−	0.249329i
$411$	13.4026	−	15.4675i	0.661104	−	0.762954i
$412$	−15.2970	−	4.49160i	−0.753629	−	0.221285i
$413$	−48.2737			−2.37539
$414$	−0.965880	+	2.08371i	−0.0474704	+	0.102409i
$415$	25.2778			1.24084
$416$	2.13061	+	0.625605i	0.104462	+	0.0306728i
$417$	6.61607	−	7.63535i	0.323990	−	0.373905i
$418$	0.663316	+	0.426287i	0.0324438	+	0.0208504i
$419$	−1.45242	+	10.1018i	−0.0709555	+	0.493506i	0.923094	+	0.384575i	$0.125652\pi$
$419$	−1.45242	+	10.1018i	−0.0709555	+	0.493506i	−0.994049	+	0.108931i	$0.965257\pi$
$420$	−22.8299	+	14.6719i	−1.11398	+	0.715914i
$421$	6.66427	+	14.5927i	0.324797	+	0.711205i	0.999642	−	0.0267538i	$-0.00851702\pi$
$421$	6.66427	+	14.5927i	0.324797	+	0.711205i	−0.674846	+	0.737959i	$0.735790\pi$
$422$	0.867907	+	1.00162i	0.0422491	+	0.0487580i
$423$	1.43194	+	9.95939i	0.0696235	+	0.484242i
$424$	9.23024	−	20.2114i	0.448260	−	0.981553i
$425$	20.1838	−	5.92649i	0.979056	−	0.287477i
$426$	1.37368	−	0.403350i	0.0665552	−	0.0195424i
$427$	10.5086	−	23.0106i	0.508547	−	1.11356i
$428$	−0.911131	−	6.33706i	−0.0440412	−	0.306313i
$429$	−0.291841	−	0.336803i	−0.0140902	−	0.0162610i
$430$	7.39247	+	16.1873i	0.356497	+	0.780619i
$431$	−32.3600	+	20.7965i	−1.55873	+	1.00173i	−0.575832	+	0.817568i	$0.695322\pi$
$431$	−32.3600	+	20.7965i	−1.55873	+	1.00173i	−0.982895	+	0.184165i	$0.941042\pi$
$432$	0.380916	−	2.64933i	0.0183268	−	0.127466i
$433$	−6.54040	−	4.20326i	−0.314311	−	0.201996i	0.373968	−	0.927442i	$-0.377997\pi$
$433$	−6.54040	−	4.20326i	−0.314311	−	0.201996i	−0.688279	+	0.725446i	$0.741633\pi$
$434$	−9.20233	+	10.6201i	−0.441726	+	0.509779i
$435$	4.43672	+	1.30274i	0.212725	+	0.0624616i
$436$	−2.25911			−0.108192
$437$	5.23099	+	6.10634i	0.250232	+	0.292106i
$438$	1.86632			0.0891762
$439$	−33.5580	−	9.85352i	−1.60164	−	0.470283i	−0.645635	−	0.763646i	$-0.723407\pi$
$439$	−33.5580	−	9.85352i	−1.60164	−	0.470283i	−0.956001	+	0.293363i	$0.905226\pi$
$440$	−3.92168	+	4.52586i	−0.186959	+	0.215762i
$441$	11.4388	+	7.35128i	0.544705	+	0.350061i
$442$	−0.101587	+	0.706553i	−0.00483200	+	0.0336073i
$443$	−8.46340	+	5.43910i	−0.402108	+	0.258419i	−0.726028	−	0.687665i	$-0.758636\pi$
$443$	−8.46340	+	5.43910i	−0.402108	+	0.258419i	0.323919	+	0.946085i	$0.394999\pi$
$444$	−2.61852	−	5.73377i	−0.124270	−	0.272113i
$445$	−15.9979	−	18.4626i	−0.758373	−	0.875210i
$446$	1.25691	+	8.74203i	0.0595166	+	0.413947i
$447$	4.28074	−	9.37352i	0.202472	−	0.443352i
$448$	13.1065	−	3.84841i	0.619222	−	0.181820i
$449$	16.3702	−	4.80672i	0.772557	−	0.226843i	0.128386	−	0.991724i	$-0.459020\pi$
$449$	16.3702	−	4.80672i	0.772557	−	0.226843i	0.644172	+	0.764881i	$0.277202\pi$
$450$	1.27407	−	2.78982i	0.0600602	−	0.131514i
$451$	−0.806988	−	5.61272i	−0.0379996	−	0.264293i
$452$	−1.37512	−	1.58697i	−0.0646802	−	0.0746449i
$453$	−0.207860	−	0.455151i	−0.00976613	−	0.0213848i
$454$	2.92096	−	1.87719i	0.137087	−	0.0881007i
$455$	−0.989817	+	6.88433i	−0.0464033	+	0.322742i
$456$	2.54686	+	1.63676i	0.119267	+	0.0766485i
$457$	15.9633	−	18.4226i	0.746732	−	0.861774i	−0.247515	−	0.968884i	$-0.579614\pi$
$457$	15.9633	−	18.4226i	0.746732	−	0.861774i	0.994247	+	0.107110i	$0.0341596\pi$
$458$	−4.57528	−	1.34342i	−0.213789	−	0.0627740i
$459$	3.28463			0.153313
$460$	−24.2120	+	15.3673i	−1.12889	+	0.716503i
$461$	38.0631			1.77278			0.886388	−	0.462943i	$-0.153207\pi$
$461$	38.0631			1.77278			0.886388	+	0.462943i	$0.153207\pi$
$462$	2.04794	+	0.601331i	0.0952790	+	0.0279764i
$463$	−9.34715	+	10.7872i	−0.434399	+	0.501323i	−0.930169	−	0.367130i	$-0.880340\pi$
$463$	−9.34715	+	10.7872i	−0.434399	+	0.501323i	0.495770	+	0.868454i	$0.334886\pi$
$464$	−3.08313	−	1.98141i	−0.143131	−	0.0919845i
$465$	−3.10736	+	21.6122i	−0.144100	+	1.00224i
$466$	2.17583	−	1.39832i	0.100794	−	0.0647761i
$467$	−1.62177	−	3.55117i	−0.0750463	−	0.164329i	0.868390	−	0.495881i	$-0.165155\pi$
$467$	−1.62177	−	3.55117i	−0.0750463	−	0.164329i	−0.943437	+	0.331553i	$0.892428\pi$
$468$	−0.526198	−	0.607265i	−0.0243235	−	0.0280708i
$469$	5.00761	+	34.8287i	0.231230	+	1.60824i
$470$	6.75974	−	14.8018i	0.311804	−	0.682755i
$471$	−14.9539	+	4.39085i	−0.689037	+	0.202320i
$472$	−18.4290	+	5.41124i	−0.848263	+	0.249073i
$473$	−4.48902	+	9.82958i	−0.206405	+	0.451964i
$474$	−0.593732	−	4.12950i	−0.0272710	−	0.189674i
$475$	−7.03146	−	8.11474i	−0.322626	−	0.372330i
$476$	10.9650	+	24.0101i	0.502582	+	1.10050i
$477$	−10.3515	+	6.65250i	−0.473962	+	0.304597i
$478$	1.00977	−	7.02313i	0.0461860	−	0.321231i
$479$	15.4838	+	9.95081i	0.707471	+	0.454664i	0.844258	−	0.535936i	$-0.180041\pi$
$479$	15.4838	+	9.95081i	0.707471	+	0.454664i	−0.136787	+	0.990600i	$0.543678\pi$
$480$	−10.8214	+	12.4885i	−0.493926	+	0.570021i
$481$	−1.55005	−	0.455134i	−0.0706760	−	0.0207523i
$482$	7.01704			0.319618
$483$	18.2435	+	11.8707i	0.830107	+	0.540137i
$484$	17.7696			0.807710
$485$	−18.2579	−	5.36099i	−0.829047	−	0.243430i
$486$	0.313607	−	0.361922i	0.0142255	−	0.0164171i
$487$	10.9745	+	7.05285i	0.497300	+	0.319595i	0.765135	−	0.643869i	$-0.222672\pi$
$487$	10.9745	+	7.05285i	0.497300	+	0.319595i	−0.267835	+	0.963465i	$0.586308\pi$
$488$	1.43239	−	9.96252i	0.0648414	−	0.450982i
$489$	5.71160	−	3.67062i	0.258287	−	0.165991i
$490$	−9.13499	−	20.0028i	−0.412677	−	0.903636i
$491$	−15.6987	−	18.1173i	−0.708473	−	0.817621i	0.281398	−	0.959591i	$-0.409202\pi$
$491$	−15.6987	−	18.1173i	−0.708473	−	0.817621i	−0.989871	+	0.141970i	$0.954656\pi$
$492$	−1.45502	−	10.1199i	−0.0655974	−	0.456240i
$493$	1.86833	−	4.09108i	0.0841455	−	0.184253i
$494$	0.349595	−	0.102650i	0.0157290	−	0.00461846i
$495$	3.18207	−	0.934341i	0.143024	−	0.0419955i
$496$	7.18898	−	15.7417i	0.322795	−	0.706822i
$497$	−1.93092	−	13.4298i	−0.0866135	−	0.602410i
$498$	−2.34742	−	2.70906i	−0.105190	−	0.121396i
$499$	−3.65609	−	8.00571i	−0.163669	−	0.358385i	0.809973	−	0.586467i	$-0.199482\pi$
$499$	−3.65609	−	8.00571i	−0.163669	−	0.358385i	−0.973642	+	0.228082i	$0.926754\pi$
$500$	7.06429	−	4.53994i	0.315924	−	0.203032i
$501$	2.85299	−	19.8430i	0.127462	−	0.886518i
$502$	0.388161	+	0.249456i	0.0173245	+	0.0111338i
$503$	23.6324	−	27.2732i	1.05372	−	1.21605i	0.0780145	−	0.996952i	$-0.475142\pi$
$503$	23.6324	−	27.2732i	1.05372	−	1.21605i	0.975702	−	0.219102i	$-0.0703126\pi$
$504$	7.86325	+	2.30886i	0.350257	+	0.102845i
$505$	−26.6535			−1.18606
$506$	2.16047	+	0.647668i	0.0960444	+	0.0287924i
$507$	12.7941			0.568204
$508$	4.86072	+	1.42724i	0.215659	+	0.0633233i
$509$	−22.5009	+	25.9674i	−0.997335	+	1.15099i	−0.00880523	+	0.999961i	$0.502803\pi$
$509$	−22.5009	+	25.9674i	−0.997335	+	1.15099i	−0.988530	+	0.151025i	$0.951743\pi$
$510$	−4.46874	−	2.87189i	−0.197879	−	0.127169i
$511$	2.51712	−	17.5070i	0.111351	−	0.774463i
$512$	19.1499	−	12.3069i	0.846315	−	0.543894i
$513$	−0.696474	−	1.52506i	−0.0307501	−	0.0673333i
$514$	0.0701316	+	0.0809361i	0.00309337	+	0.00356994i
$515$	−4.32726	−	30.0968i	−0.190682	−	1.32622i
$516$	−8.09382	+	17.7230i	−0.356311	+	0.780211i
$517$	9.48094	−	2.78385i	0.416971	−	0.122434i
$518$	7.42374	−	2.17981i	0.326181	−	0.0957752i
$519$	−4.31474	+	9.44796i	−0.189396	+	0.414720i
$520$	0.393826	+	2.73912i	0.0172704	+	0.120118i
$521$	−19.3174	−	22.2934i	−0.846310	−	0.976694i	0.153625	−	0.988129i	$-0.450905\pi$
$521$	−19.3174	−	22.2934i	−0.846310	−	0.976694i	−0.999935	+	0.0114355i	$0.996360\pi$
$522$	−0.272399	−	0.596470i	−0.0119226	−	0.0261068i
$523$	17.1736	−	11.0368i	0.750949	−	0.482606i	−0.108329	−	0.994115i	$-0.534550\pi$
$523$	17.1736	−	11.0368i	0.750949	−	0.482606i	0.859278	+	0.511509i	$0.170913\pi$
$524$	0.0971846	−	0.675934i	0.00424553	−	0.0295283i
$525$	−24.4516	−	15.7141i	−1.06715	−	0.685818i
$526$	7.00444	−	8.08355i	0.305408	−	0.352460i
$527$	20.3767	+	5.98315i	0.887624	+	0.260630i
$528$	−2.62853			−0.114392
$529$	19.2069	+	12.6529i	0.835083	+	0.550124i
$530$	19.8998			0.864391
$531$	10.2058	+	2.99669i	0.442894	+	0.130045i
$532$	8.82293	−	10.1822i	0.382523	−	0.441455i
$533$	−2.20432	−	1.41663i	−0.0954796	−	0.0613610i
$534$	−0.493022	+	3.42904i	−0.0213352	+	0.148389i
$535$	10.2720	−	6.60144i	0.444099	−	0.285405i
$536$	5.81583	+	12.7349i	0.251206	+	0.550063i
$537$	2.74748	+	3.17077i	0.118563	+	0.136829i
$538$	1.61665	+	11.2441i	0.0696989	+	0.484767i
$539$	5.54715	−	12.1466i	0.238933	−	0.523189i
$540$	5.73737	−	1.68464i	0.246897	−	0.0724955i
$541$	18.7902	−	5.51730i	0.807854	−	0.237207i	0.148376	−	0.988931i	$-0.452595\pi$
$541$	18.7902	−	5.51730i	0.807854	−	0.237207i	0.659478	+	0.751724i	$0.270777\pi$
$542$	−2.28776	+	5.00950i	−0.0982677	+	0.215176i
$543$	−0.0866645	−	0.602765i	−0.00371913	−	0.0258671i
$544$	10.5253	+	12.1468i	0.451268	+	0.520791i
$545$	−1.78986	−	3.91924i	−0.0766690	−	0.167882i
$546$	0.829724	−	0.533231i	0.0355089	−	0.0228202i
$547$	−6.16443	+	42.8745i	−0.263572	+	1.83318i	0.241853	+	0.970313i	$0.422245\pi$
$547$	−6.16443	+	42.8745i	−0.263572	+	1.83318i	−0.505425	+	0.862870i	$0.668664\pi$
$548$	−30.4863	−	19.5923i	−1.30231	−	0.836943i
$549$	−3.65011	+	4.21246i	−0.155783	+	0.179783i
$550$	−2.88992	−	0.848558i	−0.123227	−	0.0361827i
$551$	−2.29566			−0.0977985
$552$	8.29529	+	2.48678i	0.353071	+	0.105844i
$553$	−39.5374			−1.68130
$554$	2.87425	+	0.843957i	0.122115	+	0.0358563i
$555$	7.87268	−	9.08555i	0.334176	−	0.385660i
$556$	−15.0492	−	9.67155i	−0.638229	−	0.410165i
$557$	−5.05359	+	35.1485i	−0.214128	+	1.48929i	0.545049	+	0.838404i	$0.316511\pi$
$557$	−5.05359	+	35.1485i	−0.214128	+	1.48929i	−0.759176	+	0.650885i	$0.774398\pi$
$558$	2.60477	−	1.67399i	0.110269	−	0.0708655i
$559$	2.07435	+	4.54219i	0.0877356	+	0.192114i
$560$	26.8639	+	31.0026i	1.13521	+	1.31010i
$561$	−0.459061	−	3.19284i	−0.0193816	−	0.134802i
$562$	−4.25907	+	9.32607i	−0.179658	+	0.393397i
$563$	−13.0802	+	3.84069i	−0.551264	+	0.161866i	−0.545490	−	0.838118i	$-0.683656\pi$
$563$	−13.0802	+	3.84069i	−0.551264	+	0.161866i	−0.00577455	+	0.999983i	$0.501838\pi$
$564$	17.0944	−	5.01937i	0.719804	−	0.211353i
$565$	1.66369	−	3.64298i	0.0699921	−	0.153261i
$566$	−0.494547	−	3.43965i	−0.0207873	−	0.144579i
$567$	−2.97204	−	3.42992i	−0.124814	−	0.144043i
$568$	−2.24257	−	4.91053i	−0.0940960	−	0.206041i
$569$	−12.8326	+	8.24698i	−0.537969	+	0.345732i	−0.781244	−	0.624226i	$-0.785415\pi$
$569$	−12.8326	+	8.24698i	−0.537969	+	0.345732i	0.243275	+	0.969957i	$0.421778\pi$
$570$	−0.385873	+	2.68381i	−0.0161625	+	0.112412i
$571$	−2.37190	−	1.52433i	−0.0992610	−	0.0637912i	0.490069	−	0.871684i	$-0.336972\pi$
$571$	−2.37190	−	1.52433i	−0.0992610	−	0.0637912i	−0.589330	+	0.807893i	$0.700608\pi$
$572$	−0.516753	+	0.596364i	−0.0216065	+	0.0249352i
$573$	1.40504	+	0.412556i	0.0586962	+	0.0172348i
$574$	12.5495			0.523805
$575$	−25.7440	−	16.7512i	−1.07360	−	0.698574i
$576$	−3.00980			−0.125409
$577$	−5.15667	−	1.51414i	−0.214675	−	0.0630343i	0.172627	−	0.984987i	$-0.444775\pi$
$577$	−5.15667	−	1.51414i	−0.214675	−	0.0630343i	−0.387302	+	0.921953i	$0.626593\pi$
$578$	1.94788	−	2.24797i	0.0810211	−	0.0935033i
$579$	−17.8751	−	11.4876i	−0.742864	−	0.477410i
$580$	1.16522	−	8.10426i	0.0483830	−	0.336511i
$581$	−28.5783	+	18.3662i	−1.18563	+	0.761957i
$582$	1.12097	+	2.45457i	0.0464655	+	0.101745i
$583$	7.91332	+	9.13246i	0.327736	+	0.378228i
$584$	−1.00151	−	6.96563i	−0.0414426	−	0.288240i
$585$	0.636622	−	1.39401i	0.0263211	−	0.0576351i
$586$	0.179848	−	0.0528081i	0.00742944	−	0.00218148i
$587$	−6.92857	+	2.03441i	−0.285973	+	0.0839691i	−0.421573	−	0.906794i	$-0.638522\pi$
$587$	−6.92857	+	2.03441i	−0.285973	+	0.0839691i	0.135600	+	0.990764i	$0.456704\pi$
$588$	10.0017	−	21.9006i	0.412461	−	0.903164i
$589$	−1.54269	−	10.7297i	−0.0635655	−	0.442108i
$590$	−11.2649	−	13.0004i	−0.463767	−	0.535216i
$591$	2.52646	+	5.53217i	0.103925	+	0.227563i
$592$	−8.01576	+	5.15141i	−0.329446	+	0.211722i
$593$	0.228182	−	1.58704i	0.00937031	−	0.0651720i	−0.984600	−	0.174824i	$-0.944064\pi$
$593$	0.228182	−	1.58704i	0.00937031	−	0.0651720i	0.993970	+	0.109652i	$0.0349735\pi$
$594$	−0.395638	−	0.254261i	−0.0162332	−	0.0104325i
$595$	−32.9667	+	38.0456i	−1.35150	+	1.55972i
$596$	−17.5071	−	5.14055i	−0.717120	−	0.210565i
$597$	−11.5681			−0.473451
$598$	0.879957	−	0.558505i	0.0359841	−	0.0228390i
$599$	7.66948			0.313366			0.156683	−	0.987649i	$-0.449920\pi$
$599$	7.66948			0.313366			0.156683	+	0.987649i	$0.449920\pi$
$600$	−11.0961	−	3.25811i	−0.452997	−	0.133012i
$601$	−17.9986	+	20.7715i	−0.734177	+	0.847285i	−0.992935	−	0.118657i	$-0.962141\pi$
$601$	−17.9986	+	20.7715i	−0.734177	+	0.847285i	0.258758	+	0.965942i	$0.416687\pi$
$602$	−20.1189	−	12.9297i	−0.819986	−	0.526973i
$603$	1.10338	−	7.67417i	0.0449331	−	0.312516i
$604$	−0.745336	+	0.478999i	−0.0303273	+	0.0194902i
$605$	14.0786	+	30.8278i	0.572377	+	1.25333i
$606$	2.47517	+	2.85650i	0.100547	+	0.116037i
$607$	5.02072	+	34.9199i	0.203785	+	1.41735i	0.792923	+	0.609322i	$0.208558\pi$
$607$	5.02072	+	34.9199i	0.203785	+	1.41735i	−0.589138	+	0.808032i	$0.700533\pi$
$608$	3.40803	−	7.46255i	0.138214	−	0.302646i
$609$	−5.96256	+	1.75077i	−0.241615	+	0.0709446i
$610$	8.64911	−	2.53961i	0.350192	−	0.102826i
$611$	1.89680	−	4.15342i	0.0767364	−	0.168029i
$612$	−0.827699	−	5.75677i	−0.0334578	−	0.232704i
$613$	4.08485	+	4.71417i	0.164986	+	0.190404i	0.832222	−	0.554442i	$-0.187068\pi$
$613$	4.08485	+	4.71417i	0.164986	+	0.190404i	−0.667237	+	0.744846i	$0.732523\pi$
$614$	0.256266	+	0.561144i	0.0103421	+	0.0226459i
$615$	16.4038	−	10.5421i	0.661466	−	0.425098i
$616$	1.14537	−	7.96619i	0.0461481	−	0.320967i
$617$	27.3775	+	17.5944i	1.10218	+	0.708325i	0.959574	−	0.281455i	$-0.0908172\pi$
$617$	27.3775	+	17.5944i	1.10218	+	0.708325i	0.142601	+	0.989780i	$0.454454\pi$
$618$	−2.82367	+	3.25869i	−0.113585	+	0.131084i
$619$	35.2718	+	10.3567i	1.41769	+	0.416272i	0.898722	−	0.438519i	$-0.144497\pi$
$619$	35.2718	+	10.3567i	1.41769	+	0.416272i	0.518971	+	0.854792i	$0.326315\pi$
$620$	38.6614			1.55268
$621$	−3.12005	−	3.64216i	−0.125203	−	0.146155i
$622$	−0.603182			−0.0241854
$623$	31.5012	+	9.24957i	1.26207	+	0.370576i
$624$	−0.795412	+	0.917955i	−0.0318420	+	0.0367476i
$625$	−13.4653	−	8.65359i	−0.538610	−	0.346144i
$626$	0.711467	−	4.94836i	0.0284360	−	0.197776i
$627$	−1.38511	+	0.890154i	−0.0553158	+	0.0355493i
$628$	11.4638	+	25.1023i	0.457456	+	1.00169i
$629$	−7.65727	−	8.83696i	−0.305315	−	0.352353i
$630$	1.04455	+	7.26498i	0.0416157	+	0.289444i
$631$	−13.2756	+	29.0695i	−0.528493	+	1.15724i	0.437630	+	0.899155i	$0.355818\pi$
$631$	−13.2756	+	29.0695i	−0.528493	+	1.15724i	−0.966123	+	0.258082i	$0.916909\pi$
$632$	−15.0938	+	4.43195i	−0.600401	+	0.176294i
$633$	−2.65540	+	0.779694i	−0.105542	+	0.0309901i
$634$	−5.39446	+	11.8122i	−0.214242	+	0.469124i
$635$	1.37502	+	9.56345i	0.0545658	+	0.379514i
$636$	14.2679	+	16.4661i	0.565760	+	0.652922i
$637$	−2.56330	−	5.61285i	−0.101562	−	0.222389i
$638$	−0.541730	+	0.348149i	−0.0214473	+	0.0137833i
$639$	−0.425460	+	2.95914i	−0.0168309	+	0.117062i
$640$	31.8978	+	20.4995i	1.26087	+	0.810312i
$641$	2.99133	−	3.45217i	0.118150	−	0.136353i	−0.693593	−	0.720367i	$-0.743973\pi$
$641$	2.99133	−	3.45217i	0.118150	−	0.136353i	0.811743	+	0.584014i	$0.198519\pi$
$642$	−1.66140	−	0.487831i	−0.0655702	−	0.0192531i
$643$	11.6990			0.461362			0.230681	−	0.973029i	$-0.425905\pi$
$643$	11.6990			0.461362			0.230681	+	0.973029i	$0.425905\pi$
$644$	16.2079	−	34.9656i	0.638682	−	1.37784i
$645$	−37.1595			−1.46316
$646$	2.53039	+	0.742990i	0.0995570	+	0.0292326i
$647$	−17.4405	+	20.1274i	−0.685656	+	0.791289i	−0.986740	−	0.162309i	$-0.948106\pi$
$647$	−17.4405	+	20.1274i	−0.685656	+	0.791289i	0.301084	+	0.953597i	$0.402651\pi$
$648$	−1.51908	−	0.976256i	−0.0596752	−	0.0383509i
$649$	1.48658	−	10.3394i	0.0583535	−	0.405857i
$650$	−1.17085	+	0.752461i	−0.0459246	+	0.0295140i
$651$	−12.1897	−	26.6918i	−0.477753	−	1.04613i
$652$	−7.87255	−	9.08541i	−0.308313	−	0.355812i
$653$	−5.73066	−	39.8576i	−0.224258	−	1.55975i	−0.721671	−	0.692236i	$-0.756626\pi$
$653$	−5.73066	−	39.8576i	−0.224258	−	1.55975i	0.497413	−	0.867514i	$-0.334283\pi$
$654$	−0.253817	+	0.555781i	−0.00992502	+	0.0217328i
$655$	1.24965	−	0.366930i	0.0488279	−	0.0143372i
$656$	−14.8287	+	4.35411i	−0.578965	+	0.169999i
$657$	−1.61894	+	3.54499i	−0.0631609	+	0.138303i
$658$	3.11221	+	21.6459i	0.121327	+	0.843844i
$659$	−32.0467	−	36.9838i	−1.24836	−	1.44069i	−0.852793	−	0.522249i	$-0.825093\pi$
$659$	−32.0467	−	36.9838i	−1.24836	−	1.44069i	−0.395568	−	0.918437i	$-0.629452\pi$
$660$	−2.43942	−	5.34159i	−0.0949543	−	0.207921i
$661$	−5.50297	+	3.53654i	−0.214041	+	0.137556i	−0.643269	−	0.765641i	$-0.722422\pi$
$661$	−5.50297	+	3.53654i	−0.214041	+	0.137556i	0.429228	+	0.903196i	$0.358786\pi$
$662$	0.509979	−	3.54698i	0.0198209	−	0.137857i
$663$	−1.25394	−	0.805860i	−0.0486991	−	0.0312970i
$664$	−8.85131	+	10.2150i	−0.343498	+	0.396417i
$665$	24.6550	+	7.23936i	0.956080	+	0.280730i
$666$	−1.70481			−0.0660600
$667$	−6.31110	+	1.81439i	−0.244367	+	0.0702534i
$668$	−35.4965			−1.37340
$669$	−17.6954	−	5.19583i	−0.684143	−	0.200883i
$670$	−8.21099	+	9.47599i	−0.317218	+	0.366089i
$671$	4.60488	+	2.95937i	0.177769	+	0.114245i
$672$	3.16049	−	21.9817i	0.121919	−	0.847962i
$673$	32.9821	−	21.1963i	1.27137	−	0.817058i	0.281570	−	0.959541i	$-0.409145\pi$
$673$	32.9821	−	21.1963i	1.27137	−	0.817058i	0.989797	+	0.142482i	$0.0455085\pi$
$674$	−5.11476	−	11.1998i	−0.197013	−	0.431399i
$675$	4.19395	+	4.84007i	0.161425	+	0.186294i
$676$	−3.22400	−	22.4234i	−0.124000	−	0.862438i
$677$	−16.0459	+	35.1357i	−0.616696	+	1.35038i	0.301203	+	0.953560i	$0.402612\pi$
$677$	−16.0459	+	35.1357i	−0.616696	+	1.35038i	−0.917899	+	0.396815i	$0.870115\pi$
$678$	−0.544922	+	0.160004i	−0.0209276	+	0.00614490i
$679$	24.5369	−	7.20470i	0.941642	−	0.276491i
$680$	−8.32067	+	18.2197i	−0.319083	+	0.698695i
$681$	1.03184	+	7.17659i	0.0395401	+	0.275008i
$682$	−1.99125	−	2.29803i	−0.0762489	−	0.0879959i
$683$	10.5331	+	23.0643i	0.403038	+	0.882531i	0.996953	+	0.0780028i	$0.0248543\pi$
$683$	10.5331	+	23.0643i	0.403038	+	0.882531i	−0.593915	+	0.804528i	$0.702418\pi$
$684$	−2.49738	+	1.60497i	−0.0954899	+	0.0613676i
$685$	9.83619	−	68.4122i	0.375821	−	2.61390i
$686$	12.0625	+	7.75211i	0.460549	+	0.295977i
$687$	6.52060	−	7.52517i	0.248776	−	0.287103i
$688$	28.2590	+	8.29758i	1.07736	+	0.316342i
$689$	5.58394			0.212731
$690$	1.06034	+	7.68314i	0.0403665	+	0.292492i
$691$	−46.4896			−1.76855			−0.884273	−	0.466970i	$-0.845346\pi$
$691$	−46.4896			−1.76855			−0.884273	+	0.466970i	$0.845346\pi$
$692$	17.6462	+	5.18138i	0.670806	+	0.196967i
$693$	−2.91869	+	3.36835i	−0.110872	+	0.127953i
$694$	−9.91498	−	6.37197i	−0.376367	−	0.241877i
$695$	4.85553	−	33.7709i	0.184181	−	1.28100i
$696$	−2.08002	+	1.33675i	−0.0788429	+	0.0506693i
$697$	−7.87865	−	17.2518i	−0.298425	−	0.653460i
$698$	6.06552	+	6.99999i	0.229583	+	0.264953i
$699$	0.768621	+	5.34587i	0.0290719	+	0.202200i
$700$	−21.3795	+	46.8146i	−0.808069	+	1.76942i
$701$	36.2960	−	10.6575i	1.37088	−	0.402526i	0.488294	−	0.872679i	$-0.337619\pi$
$701$	36.2960	−	10.6575i	1.37088	−	0.402526i	0.882585	+	0.470153i	$0.155801\pi$
$702$	−0.208518	+	0.0612263i	−0.00787000	+	0.00231084i
$703$	−2.47938	+	5.42909i	−0.0935116	+	0.204762i
$704$	0.420651	+	2.92569i	0.0158539	+	0.110266i
$705$	22.2515	+	25.6796i	0.838041	+	0.967151i
$706$	−4.67926	−	10.2462i	−0.176106	−	0.385619i
$707$	30.1336	−	19.3657i	1.13329	−	0.728322i
$708$	2.68035	−	18.6422i	0.100734	−	0.700618i
$709$	−32.8040	−	21.0818i	−1.23198	−	0.791745i	−0.247782	−	0.968816i	$-0.579702\pi$
$709$	−32.8040	−	21.0818i	−1.23198	−	0.791745i	−0.984198	+	0.177071i	$0.943338\pi$
$710$	3.16613	−	3.65391i	0.118823	−	0.137129i
$711$	8.35882	+	2.45437i	0.313480	+	0.0920461i
$712$	13.0627			0.489547
$713$	−12.7213	−	28.2781i	−0.476417	−	1.05902i
$714$	7.13886			0.267165
$715$	−1.44402	−	0.424004i	−0.0540035	−	0.0158568i
$716$	4.86487	−	5.61436i	0.181809	−	0.209818i
$717$	12.4642	+	8.01025i	0.465484	+	0.299148i
$718$	0.412001	−	2.86553i	0.0153757	−	0.106941i
$719$	6.53058	−	4.19695i	0.243550	−	0.156520i	−0.413172	−	0.910653i	$-0.635579\pi$
$719$	6.53058	−	4.19695i	0.243550	−	0.156520i	0.656721	+	0.754133i	$0.271943\pi$
$720$	−3.75488	−	8.22205i	−0.139936	−	0.306418i
$721$	26.7598	+	30.8824i	0.996587	+	1.15012i
$722$	1.10334	+	7.67391i	0.0410621	+	0.285593i
$723$	−6.08694	+	13.3285i	−0.226376	+	0.495694i
$724$	−1.03459	+	0.303783i	−0.0384503	+	0.0112900i
$725$	8.41398	−	2.47057i	0.312487	−	0.0917545i
$726$	1.99646	−	4.37165i	0.0740958	−	0.162247i
$727$	−4.82471	−	33.5566i	−0.178939	−	1.24454i	−0.859225	−	0.511598i	$-0.829054\pi$
$727$	−4.82471	−	33.5566i	−0.178939	−	1.24454i	0.680286	−	0.732947i	$-0.261855\pi$
$728$	−2.43542	−	2.81062i	−0.0902626	−	0.104169i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	5.30210	−	3.40745i	0.196239	−	0.126115i
$731$	−5.14366	+	35.7749i	−0.190245	+	1.32318i
$732$	8.30272	+	5.33583i	0.306877	+	0.197218i
$733$	18.6038	−	21.4699i	0.687146	−	0.793008i	−0.299810	−	0.953999i	$-0.596923\pi$
$733$	18.6038	−	21.4699i	0.687146	−	0.793008i	0.986956	+	0.160991i	$0.0514689\pi$
$734$	−1.46028	−	0.428776i	−0.0538999	−	0.0158264i
$735$	45.9186			1.69373
$736$	3.47110	−	23.2091i	0.127946	−	0.855500i
$737$	−7.61392			−0.280462
$738$	−2.65315	−	0.779035i	−0.0976638	−	0.0286767i
$739$	25.4735	−	29.3980i	0.937059	−	1.08142i	−0.0594739	−	0.998230i	$-0.518942\pi$
$739$	25.4735	−	29.3980i	0.937059	−	1.08142i	0.996533	−	0.0831944i	$-0.0265122\pi$
$740$	−17.9076	−	11.5085i	−0.658295	−	0.423060i
$741$	−0.108277	+	0.753084i	−0.00397766	+	0.0276652i
$742$	−22.4981	+	14.4586i	−0.825931	+	0.530794i
$743$	9.44697	+	20.6860i	0.346576	+	0.758895i	0.999998	+	0.00190149i	$0.000605264\pi$
$743$	9.44697	+	20.6860i	0.346576	+	0.758895i	−0.653422	+	0.756993i	$0.726667\pi$
$744$	−7.64557	−	8.82346i	−0.280300	−	0.323484i
$745$	−4.95247	−	34.4452i	−0.181445	−	1.26197i
$746$	−0.110189	+	0.241280i	−0.00403430	+	0.00883388i
$747$	7.18201	−	2.10883i	0.262776	−	0.0771579i
$748$	−5.48022	+	1.60914i	−0.200377	+	0.0588359i
$749$	−6.81683	+	14.9268i	−0.249082	+	0.545413i
$750$	−0.323216	−	2.24802i	−0.0118022	−	0.0820859i
$751$	2.10873	+	2.43360i	0.0769485	+	0.0888033i	0.792918	−	0.609328i	$-0.208561\pi$
$751$	2.10873	+	2.43360i	0.0769485	+	0.0888033i	−0.715970	+	0.698131i	$0.754015\pi$
$752$	−11.1876	−	24.4974i	−0.407970	−	0.893330i
$753$	−0.810540	+	0.520903i	−0.0295377	+	0.0189827i
$754$	−0.0423484	+	0.294540i	−0.00154224	+	0.0107265i
$755$	−1.42151	−	0.913552i	−0.0517342	−	0.0332476i
$756$	−5.26248	+	6.07322i	−0.191395	+	0.220881i
$757$	−33.3481	−	9.79188i	−1.21206	−	0.355892i	−0.387606	−	0.921825i	$-0.626698\pi$
$757$	−33.3481	−	9.79188i	−1.21206	−	0.355892i	−0.824451	+	0.565933i	$0.808516\pi$
$758$	1.11462			0.0404847
$759$	−3.10432	+	3.54188i	−0.112680	+	0.128562i
$760$	10.2238			0.370856
$761$	−27.7524	−	8.14883i	−1.00602	−	0.295395i	−0.263098	−	0.964769i	$-0.584744\pi$
$761$	−27.7524	−	8.14883i	−1.00602	−	0.295395i	−0.742925	+	0.669374i	$0.766562\pi$
$762$	0.897240	−	1.03547i	0.0325036	−	0.0375111i
$763$	4.87117	+	3.13051i	0.176348	+	0.113332i
$764$	0.369005	−	2.56648i	0.0133501	−	0.0928521i
$765$	9.33143	−	5.99695i	0.337379	−	0.216820i
$766$	−5.82477	−	12.7545i	−0.210457	−	0.460838i
$767$	−3.16095	−	3.64794i	−0.114135	−	0.131719i
$768$	0.0914606	+	0.636123i	0.00330030	+	0.0229541i
$769$	8.52205	−	18.6607i	0.307313	−	0.672921i	−0.691462	−	0.722413i	$-0.743033\pi$
$769$	8.52205	−	18.6607i	0.307313	−	0.672921i	0.998775	+	0.0494918i	$0.0157602\pi$
$770$	6.91597	−	2.03071i	0.249234	−	0.0731818i
$771$	−0.214570	+	0.0630035i	−0.00772755	+	0.00226901i
$772$	−15.6293	+	34.2234i	−0.562511	+	1.23173i
$773$	4.27604	+	29.7405i	0.153799	+	1.06969i	0.909777	+	0.415097i	$0.136252\pi$
$773$	4.27604	+	29.7405i	0.153799	+	1.06969i	−0.755979	+	0.654596i	$0.772839\pi$
$774$	3.45081	+	3.98245i	0.124037	+	0.143146i
$775$	17.2013	+	37.6657i	0.617890	+	1.35299i
$776$	8.55963	−	5.50094i	0.307273	−	0.197472i
$777$	−2.29929	+	15.9919i	−0.0824867	+	0.573707i
$778$	4.10529	+	2.63831i	0.147182	+	0.0945879i
$779$	−6.33949	+	7.31617i	−0.227136	+	0.262129i
$780$	−2.60362	−	0.764490i	−0.0932244	−	0.0273731i
$781$	2.93590			0.105055
$782$	7.54363	+	0.0426770i	0.269760	+	0.00152613i
$783$	1.36926			0.0489333
$784$	−34.9200	−	10.2535i	−1.24714	−	0.366195i
$785$	−34.4663	+	39.7763i	−1.23016	+	1.41968i
$786$	−0.155373	−	0.0998522i	−0.00554197	−	0.00356161i
$787$	−2.52433	+	17.5571i	−0.0899826	+	0.625843i	0.894065	+	0.447937i	$0.147841\pi$
$787$	−2.52433	+	17.5571i	−0.0899826	+	0.625843i	−0.984048	+	0.177905i	$0.943068\pi$
$788$	9.05926	−	5.82204i	0.322723	−	0.207401i
$789$	9.27832	+	20.3167i	0.330317	+	0.723293i
$790$	−9.22623	−	10.6476i	−0.328254	−	0.378826i
$791$	0.765970	+	5.32744i	0.0272347	+	0.189422i
$792$	−0.736666	+	1.61307i	−0.0261763	+	0.0573181i
$793$	2.42696	−	0.712621i	0.0861840	−	0.0253059i
$794$	−15.8635	+	4.65796i	−0.562976	+	0.165305i
$795$	−17.2621	+	37.7987i	−0.612223	+	1.34058i
$796$	2.91507	+	20.2747i	0.103322	+	0.718619i
$797$	−18.4548	−	21.2980i	−0.653704	−	0.754414i	0.328031	−	0.944667i	$-0.393615\pi$
$797$	−18.4548	−	21.2980i	−0.653704	−	0.754414i	−0.981735	+	0.190252i	$0.939069\pi$
$798$	−1.51373	−	3.31460i	−0.0535853	−	0.117336i
$799$	27.8028	−	17.8678i	0.983594	−	0.632117i
$800$	−4.45988	+	31.0191i	−0.157680	+	1.09669i
$801$	−6.08564	−	3.91100i	−0.215025	−	0.138188i
$802$	−2.81916	+	3.25348i	−0.0995480	+	0.114884i
$803$	3.67218	+	1.07825i	0.129589	+	0.0380506i
$804$	−13.7281			−0.484153
$805$	73.5017	+	0.415825i	2.59060	+	0.0146559i
$806$	−1.40510			−0.0494926
$807$	−22.7600	−	6.68293i	−0.801189	−	0.235250i
$808$	9.33303	−	10.7709i	0.328335	−	0.378919i
$809$	11.6653	+	7.49681i	0.410129	+	0.263574i	0.729397	−	0.684091i	$-0.239801\pi$
$809$	11.6653	+	7.49681i	0.410129	+	0.263574i	−0.319268	+	0.947664i	$0.603437\pi$
$810$	0.230156	−	1.60077i	0.00808686	−	0.0562453i
$811$	−28.7636	+	18.4852i	−1.01003	+	0.649105i	−0.937400	−	0.348254i	$-0.886775\pi$
$811$	−28.7636	+	18.4852i	−1.01003	+	0.649105i	−0.0726267	+	0.997359i	$0.523138\pi$
$812$	4.57098	+	10.0090i	0.160410	+	0.351249i
$813$	−7.53079	−	8.69099i	−0.264116	−	0.304806i
$814$	0.238265	+	1.65717i	0.00835117	+	0.0580836i
$815$	9.52462	−	20.8560i	0.333633	−	0.730554i
$816$	−8.43543	+	2.47687i	−0.295299	+	0.0867077i
$817$	17.7011	−	5.19751i	0.619282	−	0.181838i
$818$	4.45799	−	9.76163i	0.155870	−	0.341307i
$819$	0.293103	+	2.03857i	0.0102418	+	0.0712336i
$820$	−22.6101	−	26.0935i	−0.789580	−	0.911223i
$821$	9.10007	+	19.9264i	0.317595	+	0.695435i	0.999346	−	0.0361483i	$-0.0115089\pi$
$821$	9.10007	+	19.9264i	0.317595	+	0.695435i	−0.681752	+	0.731584i	$0.738782\pi$
$822$	−8.24528	+	5.29892i	−0.287587	+	0.184821i
$823$	−7.94565	+	55.2632i	−0.276968	+	1.92635i	0.0896310	+	0.995975i	$0.471431\pi$
$823$	−7.94565	+	55.2632i	−0.276968	+	1.92635i	−0.366599	+	0.930379i	$0.619478\pi$
$824$	13.6776	+	8.79006i	0.476482	+	0.306216i
$825$	4.11867	−	4.75319i	0.143394	−	0.165485i
$826$	22.1814	+	6.51306i	0.771791	+	0.226618i
$827$	−14.1505			−0.492060			−0.246030	−	0.969262i	$-0.579126\pi$
$827$	−14.1505			−0.492060			−0.246030	+	0.969262i	$0.579126\pi$
$828$	−5.59716	+	6.38611i	−0.194515	+	0.221933i
$829$	−14.1731			−0.492253			−0.246126	−	0.969238i	$-0.579158\pi$
$829$	−14.1731			−0.492253			−0.246126	+	0.969238i	$0.579158\pi$
$830$	−11.6150	−	3.41046i	−0.403161	−	0.118379i
$831$	−4.09633	+	4.72742i	−0.142100	+	0.163992i
$832$	1.14902	+	0.738433i	0.0398353	+	0.0256006i
$833$	6.35610	−	44.2076i	0.220226	−	1.53170i
$834$	−4.07019	+	2.61575i	−0.140939	+	0.0905762i
$835$	−28.1233	−	61.5815i	−0.973248	−	2.13112i
$836$	1.90915	+	2.20328i	0.0660295	+	0.0762021i
$837$	0.920145	+	6.39975i	0.0318049	+	0.221208i
$838$	2.03031	−	4.44575i	0.0701358	−	0.153576i
$839$	−4.71989	+	1.38588i	−0.162949	+	0.0478460i	−0.362189	−	0.932105i	$-0.617971\pi$
$839$	−4.71989	+	1.38588i	−0.162949	+	0.0478460i	0.199241	+	0.979951i	$0.436152\pi$
$840$	26.5544	−	7.79709i	0.916215	−	0.269025i
$841$	−11.2682	+	24.6739i	−0.388558	+	0.850824i
$842$	−1.09335	−	7.60439i	−0.0376792	−	0.262064i
$843$	−14.0199	−	16.1798i	−0.482871	−	0.557263i
$844$	2.03566	+	4.45748i	0.0700703	+	0.153433i
$845$	36.3472	−	23.3589i	1.25038	−	0.803571i
$846$	0.685746	−	4.76947i	0.0235764	−	0.163978i
$847$	−38.3155	−	24.6239i	−1.31654	−	0.846087i
$848$	21.5677	−	24.8905i	0.740639	−	0.854743i
$849$	6.96244	+	2.04436i	0.238950	+	0.0701622i
$850$	−10.0739			−0.345532
$851$	−2.52526	+	16.8849i	−0.0865649	+	0.578807i
$852$	5.29351			0.181353
$853$	−3.81247	−	1.11944i	−0.130537	−	0.0383290i	0.215812	−	0.976435i	$-0.430760\pi$
$853$	−3.81247	−	1.11944i	−0.130537	−	0.0383290i	−0.346348	+	0.938106i	$0.612578\pi$
$854$	−7.93321	+	9.15541i	−0.271469	+	0.313292i
$855$	−4.76304	−	3.06102i	−0.162893	−	0.104685i
$856$	−0.929180	+	6.46259i	−0.0317587	+	0.220887i
$857$	−28.6259	+	18.3968i	−0.977843	+	0.628421i	−0.928881	−	0.370379i	$-0.879228\pi$
$857$	−28.6259	+	18.3968i	−0.977843	+	0.628421i	−0.0489622	+	0.998801i	$0.515591\pi$
$858$	0.0886578	+	0.194134i	0.00302673	+	0.00662761i
$859$	−23.4721	−	27.0883i	−0.800858	−	0.924240i	0.197570	−	0.980289i	$-0.436695\pi$
$859$	−23.4721	−	27.0883i	−0.800858	−	0.924240i	−0.998428	+	0.0560492i	$0.982150\pi$
$860$	9.36389	+	65.1273i	0.319306	+	2.22082i
$861$	−10.8861	+	23.8371i	−0.370996	+	0.812368i
$862$	17.6751	−	5.18986i	0.602015	−	0.176767i
$863$	8.55323	−	2.51146i	0.291155	−	0.0854909i	−0.132893	−	0.991130i	$-0.542427\pi$
$863$	8.55323	−	2.51146i	0.291155	−	0.0854909i	0.424049	+	0.905639i	$0.360609\pi$
$864$	−2.03274	+	4.45107i	−0.0691551	+	0.151428i
$865$	4.99181	+	34.7188i	0.169726	+	1.18047i
$866$	2.43817	+	2.81379i	0.0828522	+	0.0956166i
$867$	2.58023	+	5.64991i	0.0876292	+	0.191881i
$868$	−43.7094	+	28.0903i	−1.48359	+	0.953447i
$869$	1.21755	−	8.46825i	0.0413026	−	0.287266i
$870$	−1.86288	−	1.19720i	−0.0631575	−	0.0405889i
$871$	−2.30403	+	2.65899i	−0.0780690	+	0.0900964i
$872$	2.21054	+	0.649072i	0.0748582	+	0.0219804i
$873$	−5.63473			−0.190707
$874$	−1.57974	−	3.51158i	−0.0534355	−	0.118781i
$875$	−21.5234			−0.727624
$876$	6.62105	+	1.94411i	0.223704	+	0.0656855i
$877$	27.3868	−	31.6060i	0.924785	−	1.06726i	−0.0727683	−	0.997349i	$-0.523183\pi$
$877$	27.3868	−	31.6060i	0.924785	−	1.06726i	0.997553	−	0.0699099i	$-0.0222712\pi$
$878$	14.0902	+	9.05525i	0.475523	+	0.305600i
$879$	−0.0557027	+	0.387421i	−0.00187881	+	0.0130674i
$880$	−7.46749	+	4.79906i	−0.251729	+	0.161776i
$881$	16.5934	+	36.3344i	0.559045	+	1.22414i	0.952428	+	0.304763i	$0.0985773\pi$
$881$	16.5934	+	36.3344i	0.559045	+	1.22414i	−0.393383	+	0.919375i	$0.628695\pi$
$882$	−4.26422	−	4.92118i	−0.143584	−	0.165705i
$883$	−7.73017	−	53.7645i	−0.260141	−	1.80932i	−0.531738	−	0.846909i	$-0.678461\pi$
$883$	−7.73017	−	53.7645i	−0.260141	−	1.80932i	0.271597	−	0.962411i	$-0.412448\pi$
$884$	−1.09640	+	2.40078i	−0.0368759	+	0.0807469i
$885$	34.4653	−	10.1199i	1.15854	−	0.340177i
$886$	4.62271	−	1.35735i	0.155303	−	0.0456011i
$887$	17.4644	−	38.2417i	0.586397	−	1.28403i	−0.351198	−	0.936301i	$-0.614226\pi$
$887$	17.4644	−	38.2417i	0.586397	−	1.28403i	0.937595	−	0.347729i	$-0.113047\pi$
$888$	0.914836	+	6.36283i	0.0306999	+	0.213522i
$889$	−8.50310	−	9.81309i	−0.285185	−	0.329121i
$890$	4.85997	+	10.6418i	0.162907	+	0.356715i
$891$	0.826153	−	0.530936i	0.0276772	−	0.0177870i
$892$	−4.64734	+	32.3230i	−0.155604	+	1.08225i
$893$	−14.1914	−	9.12026i	−0.474897	−	0.305198i
$894$	−3.23164	+	3.72951i	−0.108082	+	0.124734i
$895$	13.5945	+	3.99170i	0.454414	+	0.133428i
$896$	−50.9570			−1.70235
$897$	0.297535	+	2.15591i	0.00993439	+	0.0719838i
$898$	−8.17051			−0.272654
$899$	8.49442	+	2.49419i	0.283305	+	0.0831858i
$900$	7.42607	−	8.57014i	0.247536	−	0.285671i
$901$	34.0008	+	21.8510i	1.13273	+	0.727963i
$902$	−0.386459	+	2.68788i	−0.0128677	+	0.0894968i
$903$	42.0115	−	26.9991i	1.39805	−	0.898475i
$904$	0.889596	+	1.94794i	0.0295875	+	0.0647876i
$905$	−1.34671	−	1.55419i	−0.0447662	−	0.0516630i
$906$	0.0341018	+	0.237183i	0.00113296	+	0.00787988i
$907$	−4.45205	+	9.74862i	−0.147828	+	0.323698i	−0.969031	−	0.246938i	$-0.920576\pi$
$907$	−4.45205	+	9.74862i	−0.147828	+	0.323698i	0.821204	+	0.570635i	$0.193303\pi$
$908$	12.3180	−	3.61688i	0.408786	−	0.120030i
$909$	−7.57287	+	2.22360i	−0.251176	+	0.0737520i
$910$	1.38364	−	3.02975i	0.0458673	−	0.100435i
$911$	−0.661955	−	4.60400i	−0.0219316	−	0.152537i	0.975913	−	0.218160i	$-0.0700056\pi$
$911$	−0.661955	−	4.60400i	−0.0219316	−	0.152537i	−0.997844	+	0.0656231i	$0.979097\pi$
$912$	2.93867	+	3.39140i	0.0973091	+	0.112301i
$913$	−3.05365	−	6.68657i	−0.101061	−	0.221293i
$914$	−9.82059	+	6.31131i	−0.324836	+	0.208760i
$915$	−2.67881	+	18.6316i	−0.0885589	+	0.615941i
$916$	−14.8320	−	9.53198i	−0.490065	−	0.314945i
$917$	−1.14621	+	1.32280i	−0.0378513	+	0.0436828i
$918$	−1.50926	−	0.443160i	−0.0498131	−	0.0146265i
$919$	45.2701			1.49332			0.746661	−	0.665205i	$-0.231656\pi$
$919$	45.2701			1.49332			0.746661	+	0.665205i	$0.231656\pi$
$920$	28.1067	−	8.08043i	0.926649	−	0.266404i
$921$	−1.28817			−0.0424465
$922$	−17.4897	−	5.13545i	−0.575994	−	0.169127i
$923$	0.888426	−	1.02530i	0.0292429	−	0.0337481i
$924$	6.63899	+	4.26662i	0.218407	+	0.140361i
$925$	3.24461	−	22.5668i	0.106682	−	0.741991i
$926$	5.75035	−	3.69553i	0.188968	−	0.121443i
$927$	−3.74033	−	8.19019i	−0.122849	−	0.269001i
$928$	4.38766	+	5.06363i	0.144032	+	0.166222i
$929$	4.77406	+	33.2043i	0.156632	+	1.08940i	0.904784	+	0.425871i	$0.140032\pi$
$929$	4.77406	+	33.2043i	0.156632	+	1.08940i	−0.748152	+	0.663528i	$0.769059\pi$
$930$	4.34371	−	9.51139i	0.142436	−	0.311891i
$931$	−21.8735	+	6.42264i	−0.716875	+	0.210493i
$932$	9.17571	−	2.69423i	0.300560	−	0.0882525i
$933$	0.523231	−	1.14572i	0.0171298	−	0.0375091i
$934$	0.266068	+	1.85055i	0.00870602	+	0.0605517i
$935$	−7.13352	−	8.23252i	−0.233291	−	0.269232i
$936$	0.340409	+	0.745392i	0.0111266	+	0.0243639i
$937$	3.73421	−	2.39983i	0.121991	−	0.0783991i	−0.478222	−	0.878239i	$-0.658719\pi$
$937$	3.73421	−	2.39983i	0.121991	−	0.0783991i	0.600214	+	0.799840i	$0.295082\pi$
$938$	2.39810	−	16.6792i	0.0783008	−	0.544594i
$939$	8.78202	+	5.64386i	0.286591	+	0.184181i
$940$	39.4000	−	45.4700i	1.28508	−	1.48307i
$941$	−17.2470	−	5.06418i	−0.562236	−	0.165087i	−0.0117490	−	0.999931i	$-0.503740\pi$
$941$	−17.2470	−	5.06418i	−0.562236	−	0.165087i	−0.550487	+	0.834843i	$0.685558\pi$
$942$	7.46360			0.243177
$943$	−11.6458	+	25.1236i	−0.379239	+	0.818138i
$944$	−28.4698			−0.926613
$945$	−14.7056	−	4.31795i	−0.478373	−	0.140463i
$946$	3.38887	−	3.91097i	0.110182	−	0.127156i
$947$	−2.72766	−	1.75296i	−0.0886370	−	0.0569635i	0.495572	−	0.868567i	$-0.334959\pi$
$947$	−2.72766	−	1.75296i	−0.0886370	−	0.0569635i	−0.584209	+	0.811604i	$0.698595\pi$
$948$	2.19528	−	15.2685i	0.0712993	−	0.495897i
$949$	1.48778	−	0.956141i	0.0482955	−	0.0310376i
$950$	2.13607	+	4.67734i	0.0693033	+	0.151753i
$951$	−17.7573	−	20.4931i	−0.575821	−	0.664533i
$952$	−3.83087	−	26.6443i	−0.124159	−	0.863545i
$953$	5.50230	−	12.0484i	0.178237	−	0.390285i	−0.799335	−	0.600886i	$-0.794815\pi$
$953$	5.50230	−	12.0484i	0.178237	−	0.390285i	0.977572	+	0.210601i	$0.0675420\pi$
$954$	5.65399	−	1.66016i	0.183055	−	0.0537497i
$955$	4.74485	−	1.39321i	0.153540	−	0.0450833i
$956$	10.8982	−	23.8637i	0.352473	−	0.771809i
$957$	−0.191368	−	1.33099i	−0.00618605	−	0.0430249i
$958$	−5.77212	−	6.66138i	−0.186489	−	0.215220i
$959$	38.5860	+	84.4915i	1.24601	+	2.72837i
$960$	−8.55067	+	5.49518i	−0.275972	+	0.177356i
$961$	−1.53749	+	10.6935i	−0.0495966	+	0.344952i
$962$	0.650829	+	0.418262i	0.0209836	+	0.0134853i
$963$	2.36779	−	2.73258i	0.0763011	−	0.0880562i
$964$	24.8940	+	7.30954i	0.801782	+	0.235424i
$965$	−71.7557			−2.30990
$966$	−6.78116	−	7.91592i	−0.218180	−	0.254690i
$967$	31.9173			1.02639			0.513196	−	0.858272i	$-0.328461\pi$
$967$	31.9173			1.02639			0.513196	+	0.858272i	$0.328461\pi$
$968$	−17.3876	−	5.10545i	−0.558858	−	0.164095i
$969$	−3.60627	+	4.16185i	−0.115850	+	0.133698i
$970$	7.66606	+	4.92668i	0.246142	+	0.158186i
$971$	7.94033	−	55.2262i	0.254817	−	1.77229i	−0.313603	−	0.949554i	$-0.601536\pi$
$971$	7.94033	−	55.2262i	0.254817	−	1.77229i	0.568420	−	0.822738i	$-0.307555\pi$
$972$	1.48958	−	0.957293i	0.0477782	−	0.0307052i
$973$	19.0475	+	41.7083i	0.610636	+	1.33711i
$974$	−4.09112	−	4.72140i	−0.131088	−	0.151284i
$975$	−0.413607	−	2.87670i	−0.0132460	−	0.0921282i
$976$	6.19753	−	13.5707i	0.198378	−	0.434388i
$977$	20.0943	−	5.90022i	0.642874	−	0.188765i	0.0559840	−	0.998432i	$-0.482170\pi$
$977$	20.0943	−	5.90022i	0.642874	−	0.188765i	0.586890	+	0.809667i	$0.300352\pi$
$978$	−3.11968	+	0.916019i	−0.0997562	+	0.0292911i
$979$	−2.95118	+	6.46217i	−0.0943200	+	0.206532i
$980$	−11.5711	−	80.4788i	−0.369625	−	2.57080i
$981$	−0.835507	−	0.964226i	−0.0266757	−	0.0307854i
$982$	4.76907	+	10.4428i	0.152187	+	0.333244i
$983$	19.0495	−	12.2424i	0.607585	−	0.390471i	−0.200366	−	0.979721i	$-0.564213\pi$
$983$	19.0495	−	12.2424i	0.607585	−	0.390471i	0.807951	+	0.589250i	$0.200577\pi$
$984$	−1.48384	+	10.3204i	−0.0473032	+	0.329001i
$985$	17.2779	+	11.1039i	0.550521	+	0.353798i
$986$	−1.41045	+	1.62775i	−0.0449179	+	0.0518380i
$987$	−43.8150	−	12.8653i	−1.39465	−	0.409506i
$988$	1.34717			0.0428592
$989$	44.5549	−	28.2788i	1.41676	−	0.899214i
$990$	−1.58820			−0.0504764
$991$	−36.8257	−	10.8130i	−1.16981	−	0.343486i	−0.361570	−	0.932345i	$-0.617759\pi$
$991$	−36.8257	−	10.8130i	−1.16981	−	0.343486i	−0.808236	+	0.588859i	$0.799577\pi$
$992$	−20.7183	+	23.9102i	−0.657806	+	0.759149i
$993$	6.29494	+	4.04551i	0.199764	+	0.128380i
$994$	−0.924700	+	6.43143i	−0.0293297	+	0.203993i
$995$	−32.8643	+	21.1206i	−1.04187	+	0.669568i
$996$	−5.50582	−	12.0561i	−0.174459	−	0.382011i
$997$	31.2609	+	36.0770i	0.990044	+	1.14257i	0.989785	+	0.142571i	$0.0455371\pi$
$997$	31.2609	+	36.0770i	0.990044	+	1.14257i	0.000259238		1.00000i	$0.499917\pi$
$998$	0.599821	+	4.17185i	0.0189870	+	0.132057i
$999$	1.47884	−	3.23820i	0.0467884	−	0.102452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.e.b.64.1	yes	10
3.2	odd	2		207.2.i.a.64.1		10
23.3	even	11		1587.2.a.q.1.3		5
23.9	even	11	inner	69.2.e.b.55.1	✓	10
23.20	odd	22		1587.2.a.r.1.3		5
69.20	even	22		4761.2.a.bm.1.3		5
69.26	odd	22		4761.2.a.bp.1.3		5
69.32	odd	22		207.2.i.a.55.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.b.55.1	✓	10	23.9	even	11	inner
69.2.e.b.64.1	yes	10	1.1	even	1	trivial
207.2.i.a.55.1		10	69.32	odd	22
207.2.i.a.64.1		10	3.2	odd	2
1587.2.a.q.1.3		5	23.3	even	11
1587.2.a.r.1.3		5	23.20	odd	22
4761.2.a.bm.1.3		5	69.20	even	22
4761.2.a.bp.1.3		5	69.26	odd	22

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.459493 - 0.134919i) q^{2} +(0.654861 - 0.755750i) q^{3} +(-1.48958 - 0.957293i) q^{4} +(0.480602 - 3.34266i) q^{5} +(-0.402869 + 0.258908i) q^{6} +(1.88533 + 4.12830i) q^{7} +(1.18251 + 1.36469i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.459493 - 0.134919i) q^{2} +(0.654861 - 0.755750i) q^{3} +(-1.48958 - 0.957293i) q^{4} +(0.480602 - 3.34266i) q^{5} +(-0.402869 + 0.258908i) q^{6} +(1.88533 + 4.12830i) q^{7} +(1.18251 + 1.36469i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-0.671822 + 1.47109i) q^{10} +(-0.942270 + 0.276675i) q^{11} +(-1.69894 + 0.498853i) q^{12} +(-0.188515 + 0.412791i) q^{13} +(-0.309309 - 2.15129i) q^{14} +(-2.21148 - 2.55219i) q^{15} +(1.11189 + 2.43470i) q^{16} +(-2.76321 + 1.77580i) q^{17} +(-0.0681534 + 0.474017i) q^{18} +(1.41042 + 0.906424i) q^{19} +(-3.91579 + 4.51907i) q^{20} +(4.35459 + 1.27862i) q^{21} +0.470295 q^{22} +(4.59385 + 1.37715i) q^{23} +1.80574 q^{24} +(-6.14491 - 1.80431i) q^{25} +(0.142315 - 0.164240i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(1.14365 - 7.95423i) q^{28} +(-1.15189 + 0.740277i) q^{29} +(0.671822 + 1.47109i) q^{30} +(-4.23404 - 4.88634i) q^{31} +(-0.696384 - 4.84346i) q^{32} +(-0.407958 + 0.893304i) q^{33} +(1.50926 - 0.443160i) q^{34} +(14.7056 - 4.31795i) q^{35} +(-0.735560 + 1.61065i) q^{36} +(0.506627 + 3.52367i) q^{37} +(-0.525785 - 0.606789i) q^{38} +(0.188515 + 0.412791i) q^{39} +(5.12999 - 3.29685i) q^{40} +(-0.821738 + 5.71531i) q^{41} +(-1.82839 - 1.17504i) q^{42} +(7.20584 - 8.31598i) q^{43} +(1.66844 + 0.489899i) q^{44} -3.37703 q^{45} +(-1.92504 - 1.25259i) q^{46} -10.0618 q^{47} +(2.56815 + 0.754078i) q^{48} +(-8.90436 + 10.2762i) q^{49} +(2.58011 + 1.65814i) q^{50} +(-0.467452 + 3.25120i) q^{51} +(0.675969 - 0.434419i) q^{52} +(-5.11162 - 11.1929i) q^{53} +(0.313607 + 0.361922i) q^{54} +(0.471975 + 3.28266i) q^{55} +(-3.40442 + 7.45463i) q^{56} +(1.60866 - 0.472345i) q^{57} +(0.629165 - 0.184739i) q^{58} +(-4.41863 + 9.67544i) q^{59} +(0.850983 + 5.91872i) q^{60} +(-3.65011 - 4.21246i) q^{61} +(1.28625 + 2.81649i) q^{62} +(3.81797 - 2.45366i) q^{63} +(0.428340 - 2.97917i) q^{64} +(1.28922 + 0.828529i) q^{65} +(0.307978 - 0.355426i) q^{66} +(7.43903 + 2.18430i) q^{67} +5.81597 q^{68} +(4.04911 - 2.56996i) q^{69} -7.33969 q^{70} +(-2.86847 - 0.842258i) q^{71} +(1.18251 - 1.36469i) q^{72} +(-3.27850 - 2.10697i) q^{73} +(0.242620 - 1.68746i) q^{74} +(-5.38767 + 3.46244i) q^{75} +(-1.23322 - 2.70038i) q^{76} +(-2.91869 - 3.36835i) q^{77} +(-0.0309280 - 0.215109i) q^{78} +(-3.61897 + 7.92444i) q^{79} +(8.67273 - 2.54654i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(1.14869 - 2.51528i) q^{82} +(1.06526 + 7.40902i) q^{83} +(-5.26248 - 6.07322i) q^{84} +(4.60791 + 10.0899i) q^{85} +(-4.43302 + 2.84893i) q^{86} +(-0.194866 + 1.35532i) q^{87} +(-1.49182 - 0.958732i) q^{88} +(4.73727 - 5.46710i) q^{89} +(1.55172 + 0.455627i) q^{90} -2.05954 q^{91} +(-5.52455 - 6.44903i) q^{92} -6.46556 q^{93} +(4.62333 + 1.35753i) q^{94} +(3.70772 - 4.27893i) q^{95} +(-4.11648 - 2.64550i) q^{96} +(0.801906 - 5.57738i) q^{97} +(5.47795 - 3.52046i) q^{98} +(0.407958 + 0.893304i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + q^{3} - 14 q^{4} - 3 q^{5} - 4 q^{6} + 6 q^{7} - 7 q^{8} - q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + q^3 - 14 * q^4 - 3 * q^5 - 4 * q^6 + 6 * q^7 - 7 * q^8 - q^9	\( 10 q + 4 q^{2} + q^{3} - 14 q^{4} - 3 q^{5} - 4 q^{6} + 6 q^{7} - 7 q^{8} - q^{9} + 12 q^{10} - 15 q^{11} - 8 q^{12} + 8 q^{13} + 9 q^{14} - 8 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} - 9 q^{19} - 9 q^{20} + 5 q^{21} - 28 q^{22} + 21 q^{23} + 18 q^{24} - 4 q^{25} + q^{26} + q^{27} + 29 q^{28} - 8 q^{29} - 12 q^{30} - 23 q^{31} - q^{32} + 4 q^{33} - 15 q^{34} + 18 q^{35} + 8 q^{36} + 3 q^{37} + 3 q^{38} - 8 q^{39} - 32 q^{40} - 15 q^{41} + 13 q^{42} + 22 q^{43} - q^{44} - 14 q^{45} + 26 q^{46} + 4 q^{47} + 21 q^{48} - 29 q^{49} + 49 q^{50} - 12 q^{51} + 2 q^{52} + 29 q^{53} + 7 q^{54} + 43 q^{55} - 2 q^{56} + 20 q^{57} + 21 q^{58} - 54 q^{59} - 2 q^{60} - 30 q^{61} - 7 q^{62} + 6 q^{63} - 31 q^{64} - 9 q^{65} - 27 q^{66} + q^{67} - 30 q^{68} + q^{69} - 94 q^{70} - 3 q^{71} - 7 q^{72} - 47 q^{73} - 12 q^{74} + 15 q^{75} + 50 q^{76} + 13 q^{77} - 12 q^{78} + 18 q^{79} + 3 q^{80} - q^{81} - 28 q^{82} + 18 q^{83} + 4 q^{84} + 58 q^{85} + 8 q^{87} + 16 q^{88} + 25 q^{89} + q^{90} + 18 q^{91} - 3 q^{92} - 10 q^{93} + 39 q^{94} - 16 q^{95} - 21 q^{96} + 21 q^{97} - 27 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + q^3 - 14 * q^4 - 3 * q^5 - 4 * q^6 + 6 * q^7 - 7 * q^8 - q^9 + 12 * q^10 - 15 * q^11 - 8 * q^12 + 8 * q^13 + 9 * q^14 - 8 * q^15 + 12 * q^16 + q^17 + 4 * q^18 - 9 * q^19 - 9 * q^20 + 5 * q^21 - 28 * q^22 + 21 * q^23 + 18 * q^24 - 4 * q^25 + q^26 + q^27 + 29 * q^28 - 8 * q^29 - 12 * q^30 - 23 * q^31 - q^32 + 4 * q^33 - 15 * q^34 + 18 * q^35 + 8 * q^36 + 3 * q^37 + 3 * q^38 - 8 * q^39 - 32 * q^40 - 15 * q^41 + 13 * q^42 + 22 * q^43 - q^44 - 14 * q^45 + 26 * q^46 + 4 * q^47 + 21 * q^48 - 29 * q^49 + 49 * q^50 - 12 * q^51 + 2 * q^52 + 29 * q^53 + 7 * q^54 + 43 * q^55 - 2 * q^56 + 20 * q^57 + 21 * q^58 - 54 * q^59 - 2 * q^60 - 30 * q^61 - 7 * q^62 + 6 * q^63 - 31 * q^64 - 9 * q^65 - 27 * q^66 + q^67 - 30 * q^68 + q^69 - 94 * q^70 - 3 * q^71 - 7 * q^72 - 47 * q^73 - 12 * q^74 + 15 * q^75 + 50 * q^76 + 13 * q^77 - 12 * q^78 + 18 * q^79 + 3 * q^80 - q^81 - 28 * q^82 + 18 * q^83 + 4 * q^84 + 58 * q^85 + 8 * q^87 + 16 * q^88 + 25 * q^89 + q^90 + 18 * q^91 - 3 * q^92 - 10 * q^93 + 39 * q^94 - 16 * q^95 - 21 * q^96 + 21 * q^97 - 27 * q^98 - 4 * q^99

Introduction

L-functions

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