LMFDB - Embedded newform 69.2.e.b.55.1

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			55.1
Root			$0.959493 - 0.281733i$ of defining polynomial
Character	$\chi$	$=$	69.55
Dual form			69.2.e.b.64.1

$q$-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 $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$

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	−0.440120	−	0.897939i	$-0.645064\pi$
$2$	−0.459493	+	0.134919i	−0.324911	+	0.0954024i	0.115210	+	0.993341i	$0.463246\pi$
$3$	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	0.756372	+	0.654142i	$0.226970\pi$
$5$	0.480602	+	3.34266i	0.214932	+	1.49488i	−0.541440	+	0.840739i	$0.682121\pi$
$6$	−0.402869	−	0.258908i	−0.164471	−	0.105699i
$7$	1.88533	−	4.12830i	0.712588	−	1.56035i	−0.111420	−	0.993773i	$-0.535540\pi$
$7$	1.88533	−	4.12830i	0.712588	−	1.56035i	0.824009	−	0.566577i	$-0.191733\pi$
$8$	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	0.136575	−	0.990630i	$-0.456390\pi$
$11$	−0.942270	−	0.276675i	−0.284105	−	0.0834208i	−0.420680	+	0.907209i	$0.638209\pi$
$12$	−1.69894	−	0.498853i	−0.490441	−	0.144007i
$13$	−0.188515	−	0.412791i	−0.0522847	−	0.114488i	0.881687	−	0.471835i	$-0.156408\pi$
$13$	−0.188515	−	0.412791i	−0.0522847	−	0.114488i	−0.933971	+	0.357348i	$0.883681\pi$
$14$	−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	0.160813	−	0.986985i	$-0.448588\pi$
$17$	−2.76321	−	1.77580i	−0.670176	−	0.430696i	−0.830989	+	0.556289i	$0.812225\pi$
$18$	−0.0681534	−	0.474017i	−0.0160639	−	0.111727i
$19$	1.41042	−	0.906424i	0.323573	−	0.207948i	−0.368762	−	0.929524i	$-0.620218\pi$
$19$	1.41042	−	0.906424i	0.323573	−	0.207948i	0.692335	+	0.721576i	$0.256582\pi$
$20$	−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	0.429303	−	0.903160i	$-0.358759\pi$
$29$	−1.15189	−	0.740277i	−0.213901	−	0.137466i	−0.643205	+	0.765694i	$0.722396\pi$
$30$	0.671822	−	1.47109i	0.122657	−	0.268582i
$31$	−4.23404	+	4.88634i	−0.760456	+	0.877613i	−0.995538	−	0.0943622i	$-0.969919\pi$
$31$	−4.23404	+	4.88634i	−0.760456	+	0.877613i	0.235082	+	0.971976i	$0.424464\pi$
$32$	−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	−0.904851	−	0.425729i	$-0.860018\pi$
$37$	0.506627	−	3.52367i	0.0832890	−	0.579288i	0.988140	−	0.153559i	$-0.0490734\pi$
$38$	−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	−0.947666	−	0.319263i	$-0.896565\pi$
$41$	−0.821738	−	5.71531i	−0.128334	−	0.892582i	0.819332	−	0.573319i	$-0.194344\pi$
$42$	−1.82839	+	1.17504i	−0.282127	+	0.181312i
$43$	7.20584	+	8.31598i	1.09888	+	1.26817i	0.960646	+	0.277775i	$0.0895970\pi$
$43$	7.20584	+	8.31598i	1.09888	+	1.26817i	0.138233	+	0.990400i	$0.455858\pi$
$44$	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	0.135229	+	0.990814i	$0.456823\pi$
$53$	−5.11162	+	11.1929i	−0.702135	+	1.53746i	−0.837364	+	0.546646i	$0.815904\pi$
$54$	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	−0.943951	−	0.330085i	$-0.892923\pi$
$59$	−4.41863	−	9.67544i	−0.575256	−	1.25964i	0.368695	−	0.929550i	$-0.379805\pi$
$60$	0.850983	−	5.91872i	0.109861	−	0.764103i
$61$	−3.65011	+	4.21246i	−0.467349	+	0.539350i	−0.939672	−	0.342076i	$-0.888870\pi$
$61$	−3.65011	+	4.21246i	−0.467349	+	0.539350i	0.472323	+	0.881425i	$0.343416\pi$
$62$	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	0.206277	−	0.978494i	$-0.433865\pi$
$67$	7.43903	−	2.18430i	0.908822	−	0.266854i	0.702545	+	0.711639i	$0.252047\pi$
$68$	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	−0.447476	−	0.894296i	$-0.647677\pi$
$71$	−2.86847	+	0.842258i	−0.340424	+	0.0999576i	0.107052	+	0.994253i	$0.465859\pi$
$72$	1.18251	+	1.36469i	0.139360	+	0.160830i
$73$	−3.27850	+	2.10697i	−0.383720	+	0.246602i	−0.718253	−	0.695782i	$-0.755058\pi$
$73$	−3.27850	+	2.10697i	−0.383720	+	0.246602i	0.334533	+	0.942384i	$0.391421\pi$
$74$	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	−0.996493	−	0.0836750i	$-0.973334\pi$
$79$	−3.61897	−	7.92444i	−0.407166	−	0.891570i	0.589327	−	0.807895i	$-0.299393\pi$
$80$	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	−0.843980	−	0.536375i	$-0.819793\pi$
$83$	1.06526	−	7.40902i	0.116927	−	0.813246i	0.960907	−	0.276871i	$-0.0892975\pi$
$84$	−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	0.949071	−	0.315062i	$-0.102025\pi$
$89$	4.73727	+	5.46710i	0.502150	+	0.579512i	−0.446922	+	0.894573i	$0.647480\pi$
$90$	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	0.989169	+	0.146781i	$0.0468912\pi$
$97$	0.801906	+	5.57738i	0.0814212	+	0.566297i	−0.907748	+	0.419516i	$0.862200\pi$
$98$	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	0.854435	+	0.519558i	$0.173903\pi$
$101$	−1.12323	+	7.81224i	−0.111766	+	0.777347i	−0.966201	+	0.257790i	$0.917006\pi$
$102$	0.653440	+	1.43083i	0.0647002	+	0.141674i
$103$	8.63913	+	2.53668i	0.851239	+	0.249946i	0.678117	−	0.734954i	$-0.262796\pi$
$103$	8.63913	+	2.53668i	0.851239	+	0.249946i	0.173122	+	0.984900i	$0.444615\pi$
$104$	−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	−0.629666	−	0.776866i	$-0.716808\pi$
$107$	2.36779	−	2.73258i	0.228903	−	0.264168i	0.858569	+	0.512697i	$0.171354\pi$
$108$	0.735560	−	1.61065i	0.0707793	−	0.154985i
$109$	1.07332	+	0.689779i	0.102805	+	0.0660688i	0.591033	−	0.806647i	$-0.298720\pi$
$109$	1.07332	+	0.689779i	0.102805	+	0.0660688i	−0.488228	+	0.872716i	$0.662357\pi$
$110$	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	−0.227772	−	0.973714i	$-0.573144\pi$
$113$	1.13788	−	0.334113i	0.107043	−	0.0314307i	0.334815	+	0.942284i	$0.391326\pi$
$114$	−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	0.157658	−	0.987494i	$-0.449606\pi$
$127$	−2.74514	−	0.806046i	−0.243592	−	0.0715250i	−0.401249	+	0.915969i	$0.631424\pi$
$128$	−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	−0.902504	−	0.430681i	$-0.858273\pi$
$131$	0.160212	−	0.350814i	0.0139977	−	0.0306508i	0.916502	+	0.400031i	$0.131001\pi$
$132$	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	0.660405	−	0.750909i	$-0.270385\pi$
$149$	9.88733	+	2.90318i	0.810001	+	0.237838i	0.149596	+	0.988747i	$0.452203\pi$
$150$	2.94275	+	0.864068i	0.240274	+	0.0705509i
$151$	0.207860	+	0.455151i	0.0169154	+	0.0370396i	0.917901	−	0.396809i	$-0.129882\pi$
$151$	0.207860	+	0.455151i	0.0169154	+	0.0370396i	−0.900986	+	0.433849i	$0.857155\pi$
$152$	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	−0.946556	−	0.322540i	$-0.895463\pi$
$157$	−13.1111	+	8.42597i	−1.04638	+	0.672466i	−0.0998213	+	0.995005i	$0.531827\pi$
$158$	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	−0.0164685	−	0.999864i	$-0.505242\pi$
$163$	6.51437	−	1.91279i	0.510245	−	0.149821i	0.526713	+	0.850043i	$0.323424\pi$
$164$	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	0.993750	−	0.111633i	$-0.0356080\pi$
$167$	16.8646	+	10.8382i	1.30502	+	0.838688i	0.311274	+	0.950320i	$0.399244\pi$
$168$	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	−0.120003	−	0.992774i	$-0.538290\pi$
$173$	−9.96585	−	2.92624i	−0.757690	−	0.222478i	−0.637687	+	0.770296i	$0.720109\pi$
$174$	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	−0.999893	−	0.0146436i	$-0.995339\pi$
$179$	−0.597086	−	4.15282i	−0.0446283	−	0.310396i	0.955265	−	0.295753i	$-0.0955705\pi$
$180$	5.03035	−	3.23281i	0.374940	−	0.240959i
$181$	0.398786	+	0.460224i	0.0296415	+	0.0342081i	0.770377	−	0.637589i	$-0.220068\pi$
$181$	0.398786	+	0.460224i	0.0296415	+	0.0342081i	−0.740735	+	0.671797i	$0.765523\pi$
$182$	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	−0.886347	−	0.463022i	$-0.846765\pi$
$191$	0.608314	−	1.33202i	0.0440161	−	0.0963817i	0.930363	+	0.366641i	$0.119492\pi$
$192$	−1.97100	+	2.27466i	−0.142245	+	0.164159i
$193$	−3.02393	+	21.0319i	−0.217667	+	1.51391i	0.528948	+	0.848654i	$0.322587\pi$
$193$	−3.02393	+	21.0319i	−0.217667	+	1.51391i	−0.746616	+	0.665256i	$0.768323\pi$
$194$	−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	0.798025	−	0.602624i	$-0.205878\pi$
$197$	−2.52646	−	5.53217i	−0.180003	−	0.394151i	−0.978028	+	0.208473i	$0.933151\pi$
$198$	−0.0669300	+	0.465508i	−0.00475651	+	0.0330822i
$199$	−7.57550	+	8.74259i	−0.537013	+	0.619746i	−0.957808	−	0.287410i	$-0.907206\pi$
$199$	−7.57550	+	8.74259i	−0.537013	+	0.619746i	0.420795	+	0.907156i	$0.361751\pi$
$200$	−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	−0.618321	−	0.785926i	$-0.712187\pi$
$211$	−2.32817	+	1.49622i	−0.160278	+	0.103004i	0.458043	+	0.888930i	$0.348550\pi$
$212$	−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	0.458973	+	0.888450i	$0.348217\pi$
$223$	−7.66126	+	16.7758i	−0.513036	+	1.12339i	−0.972009	+	0.234942i	$0.924510\pi$
$224$	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	0.575979	−	0.817465i	$-0.304621\pi$
$227$	−4.74799	−	5.47948i	−0.315135	−	0.363686i	−0.891114	+	0.453779i	$0.850076\pi$
$228$	−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	0.627977	−	0.778232i	$-0.283883\pi$
$233$	−3.53680	−	4.08169i	−0.231704	−	0.267400i	−0.859681	+	0.510831i	$0.829338\pi$
$234$	−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	−0.800581	−	0.599224i	$-0.795476\pi$
$239$	2.10857	−	14.6654i	0.136392	−	0.948626i	0.936973	−	0.349402i	$-0.113615\pi$
$240$	3.75488	+	8.22205i	0.242377	+	0.530731i
$241$	−14.0591	−	4.12814i	−0.905629	−	0.265917i	−0.204429	−	0.978881i	$-0.565534\pi$
$241$	−14.0591	−	4.12814i	−0.905629	−	0.265917i	−0.701200	+	0.712965i	$0.747352\pi$
$242$	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	−0.310778	−	0.950483i	$-0.600590\pi$
$251$	−0.924463	+	0.271447i	−0.0583516	+	0.0171336i	0.252426	+	0.967616i	$0.418771\pi$
$252$	−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	−0.546495	−	0.837462i	$-0.684038\pi$
$257$	−0.188128	+	0.120903i	−0.0117351	+	0.00754171i	0.534760	+	0.845004i	$0.320402\pi$
$258$	−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	−0.945658	−	0.325163i	$-0.894581\pi$
$263$	−9.27832	−	20.3167i	−0.572126	−	1.25278i	0.373532	−	0.927617i	$-0.378147\pi$
$264$	−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	0.327878	+	0.944720i	$0.393667\pi$
$269$	−9.85399	+	21.5772i	−0.600808	+	1.31559i	−0.928686	+	0.370867i	$0.879061\pi$
$270$	1.36050	+	0.874341i	0.0827975	+	0.0532107i
$271$	1.63660	+	11.3828i	0.0994161	+	0.691454i	0.977188	+	0.212376i	$0.0681201\pi$
$271$	1.63660	+	11.3828i	0.0994161	+	0.691454i	−0.877772	+	0.479079i	$0.840971\pi$
$272$	−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	0.852604	+	0.522557i	$0.175022\pi$
$281$	3.04681	+	21.1911i	0.181758	+	1.26415i	−0.670847	+	0.741596i	$0.734069\pi$
$282$	4.05359	+	2.60508i	0.241388	+	0.155131i
$283$	3.01441	−	6.60063i	0.179188	−	0.392367i	−0.798630	−	0.601822i	$-0.794442\pi$
$283$	3.01441	−	6.60063i	0.179188	−	0.392367i	0.977818	+	0.209455i	$0.0671690\pi$
$284$	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	0.530987	−	0.847380i	$-0.321821\pi$
$293$	−0.329271	−	0.211609i	−0.0192362	−	0.0123624i	−0.550224	+	0.835017i	$0.685458\pi$
$294$	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	−0.779311	−	0.626637i	$-0.784431\pi$
$307$	−0.843569	+	0.973531i	−0.0481450	+	0.0555623i	0.731166	+	0.682199i	$0.238976\pi$
$308$	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	0.315817	−	0.948820i	$-0.397721\pi$
$311$	1.20852	+	0.354853i	0.0685288	+	0.0201219i	−0.247288	+	0.968942i	$0.579540\pi$
$312$	−0.340409	−	0.745392i	−0.0192719	−	0.0421995i
$313$	1.48565	−	10.3330i	0.0839742	−	0.584053i	−0.903776	−	0.428007i	$-0.859216\pi$
$313$	1.48565	−	10.3330i	0.0839742	−	0.584053i	0.987750	−	0.156046i	$-0.0498750\pi$
$314$	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	0.749941	+	0.661505i	$0.230082\pi$
$317$	3.85904	+	26.8402i	0.216745	+	1.50750i	−0.533196	+	0.845992i	$0.679009\pi$
$318$	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	−0.939399	−	0.342826i	$-0.888616\pi$
$331$	1.06491	−	7.40664i	0.0585330	−	0.407106i	0.997932	−	0.0642799i	$-0.0204751\pi$
$332$	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	−0.0809434	−	0.996719i	$-0.525793\pi$
$337$	16.8366	−	19.4305i	0.917150	−	1.05845i	0.998093	−	0.0617284i	$-0.0196613\pi$
$338$	−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	0.422324	−	0.906445i	$-0.361215\pi$
$347$	23.6140	−	6.93370i	1.26767	−	0.372220i	0.845342	+	0.534225i	$0.179396\pi$
$348$	1.58771	+	1.83231i	0.0851100	+	0.0982222i
$349$	−16.2708	+	10.4566i	−0.870956	+	0.559730i	−0.898045	−	0.439903i	$-0.855013\pi$
$349$	−16.2708	+	10.4566i	−0.870956	+	0.559730i	0.0270889	+	0.999633i	$0.491376\pi$
$350$	−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	−0.179469	−	0.983764i	$-0.557438\pi$
$353$	15.4031	−	17.7761i	0.819823	−	0.946126i	0.999291	+	0.0376379i	$0.0119833\pi$
$354$	−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	−0.954442	−	0.298395i	$-0.903549\pi$
$359$	0.860321	−	5.98367i	0.0454060	−	0.315806i	0.999848	−	0.0174106i	$-0.00554225\pi$
$360$	−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	0.991760	−	0.128107i	$-0.0408900\pi$
$373$	0.0788258	+	0.548246i	0.00408145	+	0.0283871i	−0.987679	+	0.156494i	$0.949981\pi$
$374$	−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	0.223873	−	0.974618i	$-0.428130\pi$
$379$	−2.23321	−	0.655730i	−0.114712	−	0.0336826i	−0.338585	+	0.940936i	$0.609948\pi$
$380$	−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	−0.0116804	−	0.999932i	$-0.503718\pi$
$383$	19.1738	−	22.1278i	0.979736	−	1.13068i	0.991416	−	0.130744i	$-0.0417365\pi$
$384$	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	−0.520035	−	0.854145i	$-0.674081\pi$
$389$	−9.77736	+	2.87089i	−0.495732	+	0.145560i	0.0243038	+	0.999705i	$0.492263\pi$
$390$	−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	0.998836	+	0.0482421i	$0.0153619\pi$
$397$	29.0435	+	18.6651i	1.45765	+	0.936775i	0.458814	+	0.888532i	$0.348274\pi$
$398$	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	0.979664	−	0.200643i	$-0.0643031\pi$
$401$	3.73436	+	8.17710i	0.186485	+	0.408345i	−0.793180	+	0.608988i	$0.791576\pi$
$402$	−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	−0.902873	−	0.429907i	$-0.858546\pi$
$409$	−3.18911	−	22.1808i	−0.157691	−	1.09677i	0.745182	−	0.666861i	$-0.232363\pi$
$410$	−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	−0.994049	−	0.108931i	$-0.965257\pi$
$419$	−1.45242	−	10.1018i	−0.0709555	−	0.493506i	0.923094	−	0.384575i	$-0.125652\pi$
$420$	−22.8299	−	14.6719i	−1.11398	−	0.715914i
$421$	6.66427	−	14.5927i	0.324797	−	0.711205i	−0.674846	−	0.737959i	$-0.735790\pi$
$421$	6.66427	−	14.5927i	0.324797	−	0.711205i	0.999642	+	0.0267538i	$0.00851702\pi$
$422$	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	−0.982895	−	0.184165i	$-0.941042\pi$
$431$	−32.3600	−	20.7965i	−1.55873	−	1.00173i	−0.575832	−	0.817568i	$-0.695322\pi$
$432$	0.380916	+	2.64933i	0.0183268	+	0.127466i
$433$	−6.54040	+	4.20326i	−0.314311	+	0.201996i	−0.688279	−	0.725446i	$-0.741633\pi$
$433$	−6.54040	+	4.20326i	−0.314311	+	0.201996i	0.373968	+	0.927442i	$0.377997\pi$
$434$	−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	−0.956001	−	0.293363i	$-0.905226\pi$
$439$	−33.5580	+	9.85352i	−1.60164	+	0.470283i	−0.645635	+	0.763646i	$0.723407\pi$
$440$	−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	0.323919	−	0.946085i	$-0.394999\pi$
$443$	−8.46340	−	5.43910i	−0.402108	−	0.258419i	−0.726028	+	0.687665i	$0.758636\pi$
$444$	−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	0.644172	−	0.764881i	$-0.277202\pi$
$449$	16.3702	+	4.80672i	0.772557	+	0.226843i	0.128386	+	0.991724i	$0.459020\pi$
$450$	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	0.994247	−	0.107110i	$-0.0341596\pi$
$457$	15.9633	+	18.4226i	0.746732	+	0.861774i	−0.247515	+	0.968884i	$0.579614\pi$
$458$	−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	0.495770	−	0.868454i	$-0.334886\pi$
$463$	−9.34715	−	10.7872i	−0.434399	−	0.501323i	−0.930169	+	0.367130i	$0.880340\pi$
$464$	−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	−0.943437	−	0.331553i	$-0.892428\pi$
$467$	−1.62177	+	3.55117i	−0.0750463	+	0.164329i	0.868390	+	0.495881i	$0.165155\pi$
$468$	−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	−0.136787	−	0.990600i	$-0.543678\pi$
$479$	15.4838	−	9.95081i	0.707471	−	0.454664i	0.844258	+	0.535936i	$0.180041\pi$
$480$	−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	−0.267835	−	0.963465i	$-0.586308\pi$
$487$	10.9745	−	7.05285i	0.497300	−	0.319595i	0.765135	+	0.643869i	$0.222672\pi$
$488$	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	−0.989871	−	0.141970i	$-0.954656\pi$
$491$	−15.6987	+	18.1173i	−0.708473	+	0.817621i	0.281398	+	0.959591i	$0.409202\pi$
$492$	−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	−0.973642	−	0.228082i	$-0.926754\pi$
$499$	−3.65609	+	8.00571i	−0.163669	+	0.358385i	0.809973	+	0.586467i	$0.199482\pi$
$500$	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	0.975702	+	0.219102i	$0.0703126\pi$
$503$	23.6324	+	27.2732i	1.05372	+	1.21605i	0.0780145	+	0.996952i	$0.475142\pi$
$504$	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	−0.988530	−	0.151025i	$-0.951743\pi$
$509$	−22.5009	−	25.9674i	−0.997335	−	1.15099i	−0.00880523	−	0.999961i	$-0.502803\pi$
$510$	−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	−0.999935	−	0.0114355i	$-0.996360\pi$
$521$	−19.3174	+	22.2934i	−0.846310	+	0.976694i	0.153625	+	0.988129i	$0.450905\pi$
$522$	−0.272399	+	0.596470i	−0.0119226	+	0.0261068i
$523$	17.1736	+	11.0368i	0.750949	+	0.482606i	0.859278	−	0.511509i	$-0.170913\pi$
$523$	17.1736	+	11.0368i	0.750949	+	0.482606i	−0.108329	+	0.994115i	$0.534550\pi$
$524$	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	0.659478	−	0.751724i	$-0.270777\pi$
$541$	18.7902	+	5.51730i	0.807854	+	0.237207i	0.148376	+	0.988931i	$0.452595\pi$
$542$	−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	−0.505425	−	0.862870i	$-0.668664\pi$
$547$	−6.16443	−	42.8745i	−0.263572	−	1.83318i	0.241853	−	0.970313i	$-0.422245\pi$
$548$	−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	−0.759176	−	0.650885i	$-0.774398\pi$
$557$	−5.05359	−	35.1485i	−0.214128	−	1.48929i	0.545049	−	0.838404i	$-0.316511\pi$
$558$	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	−0.00577455	−	0.999983i	$-0.501838\pi$
$563$	−13.0802	−	3.84069i	−0.551264	−	0.161866i	−0.545490	+	0.838118i	$0.683656\pi$
$564$	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	0.243275	−	0.969957i	$-0.421778\pi$
$569$	−12.8326	−	8.24698i	−0.537969	−	0.345732i	−0.781244	+	0.624226i	$0.785415\pi$
$570$	−0.385873	−	2.68381i	−0.0161625	−	0.112412i
$571$	−2.37190	+	1.52433i	−0.0992610	+	0.0637912i	−0.589330	−	0.807893i	$-0.700608\pi$
$571$	−2.37190	+	1.52433i	−0.0992610	+	0.0637912i	0.490069	+	0.871684i	$0.336972\pi$
$572$	−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	−0.387302	−	0.921953i	$-0.626593\pi$
$577$	−5.15667	+	1.51414i	−0.214675	+	0.0630343i	0.172627	+	0.984987i	$0.444775\pi$
$578$	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	0.135600	−	0.990764i	$-0.456704\pi$
$587$	−6.92857	−	2.03441i	−0.285973	−	0.0839691i	−0.421573	+	0.906794i	$0.638522\pi$
$588$	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	0.993970	−	0.109652i	$-0.0349735\pi$
$593$	0.228182	+	1.58704i	0.00937031	+	0.0651720i	−0.984600	+	0.174824i	$0.944064\pi$
$594$	−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	0.258758	−	0.965942i	$-0.416687\pi$
$601$	−17.9986	−	20.7715i	−0.734177	−	0.847285i	−0.992935	+	0.118657i	$0.962141\pi$
$602$	−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	−0.589138	−	0.808032i	$-0.700533\pi$
$607$	5.02072	−	34.9199i	0.203785	−	1.41735i	0.792923	−	0.609322i	$-0.208558\pi$
$608$	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	−0.667237	−	0.744846i	$-0.732523\pi$
$613$	4.08485	−	4.71417i	0.164986	−	0.190404i	0.832222	+	0.554442i	$0.187068\pi$
$614$	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	0.142601	−	0.989780i	$-0.454454\pi$
$617$	27.3775	−	17.5944i	1.10218	−	0.708325i	0.959574	+	0.281455i	$0.0908172\pi$
$618$	−2.82367	−	3.25869i	−0.113585	−	0.131084i
$619$	35.2718	−	10.3567i	1.41769	−	0.416272i	0.518971	−	0.854792i	$-0.326315\pi$
$619$	35.2718	−	10.3567i	1.41769	−	0.416272i	0.898722	+	0.438519i	$0.144497\pi$
$620$	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	−0.966123	−	0.258082i	$-0.916909\pi$
$631$	−13.2756	−	29.0695i	−0.528493	−	1.15724i	0.437630	−	0.899155i	$-0.355818\pi$
$632$	−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	0.811743	−	0.584014i	$-0.198519\pi$
$641$	2.99133	+	3.45217i	0.118150	+	0.136353i	−0.693593	+	0.720367i	$0.743973\pi$
$642$	−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	0.301084	−	0.953597i	$-0.402651\pi$
$647$	−17.4405	−	20.1274i	−0.685656	−	0.791289i	−0.986740	+	0.162309i	$0.948106\pi$
$648$	−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	0.497413	+	0.867514i	$0.334283\pi$
$653$	−5.73066	+	39.8576i	−0.224258	+	1.55975i	−0.721671	+	0.692236i	$0.756626\pi$
$654$	−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	−0.395568	+	0.918437i	$0.629452\pi$
$659$	−32.0467	+	36.9838i	−1.24836	+	1.44069i	−0.852793	+	0.522249i	$0.825093\pi$
$660$	−2.43942	+	5.34159i	−0.0949543	+	0.207921i
$661$	−5.50297	−	3.53654i	−0.214041	−	0.137556i	0.429228	−	0.903196i	$-0.358786\pi$
$661$	−5.50297	−	3.53654i	−0.214041	−	0.137556i	−0.643269	+	0.765641i	$0.722422\pi$
$662$	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	0.989797	−	0.142482i	$-0.0455085\pi$
$673$	32.9821	+	21.1963i	1.27137	+	0.817058i	0.281570	+	0.959541i	$0.409145\pi$
$674$	−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	−0.917899	−	0.396815i	$-0.870115\pi$
$677$	−16.0459	−	35.1357i	−0.616696	−	1.35038i	0.301203	−	0.953560i	$-0.402612\pi$
$678$	−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	−0.593915	−	0.804528i	$-0.702418\pi$
$683$	10.5331	−	23.0643i	0.403038	−	0.882531i	0.996953	−	0.0780028i	$-0.0248543\pi$
$684$	−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	0.882585	−	0.470153i	$-0.155801\pi$
$701$	36.2960	+	10.6575i	1.37088	+	0.402526i	0.488294	+	0.872679i	$0.337619\pi$
$702$	−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	−0.984198	−	0.177071i	$-0.943338\pi$
$709$	−32.8040	+	21.0818i	−1.23198	+	0.791745i	−0.247782	+	0.968816i	$0.579702\pi$
$710$	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	0.656721	−	0.754133i	$-0.271943\pi$
$719$	6.53058	+	4.19695i	0.243550	+	0.156520i	−0.413172	+	0.910653i	$0.635579\pi$
$720$	−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	0.680286	+	0.732947i	$0.261855\pi$
$727$	−4.82471	+	33.5566i	−0.178939	+	1.24454i	−0.859225	+	0.511598i	$0.829054\pi$
$728$	−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	0.986956	−	0.160991i	$-0.0514689\pi$
$733$	18.6038	+	21.4699i	0.687146	+	0.793008i	−0.299810	+	0.953999i	$0.596923\pi$
$734$	−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	0.996533	+	0.0831944i	$0.0265122\pi$
$739$	25.4735	+	29.3980i	0.937059	+	1.08142i	−0.0594739	+	0.998230i	$0.518942\pi$
$740$	−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	−0.653422	−	0.756993i	$-0.726667\pi$
$743$	9.44697	−	20.6860i	0.346576	−	0.758895i	0.999998	−	0.00190149i	$-0.000605264\pi$
$744$	−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	−0.715970	−	0.698131i	$-0.754015\pi$
$751$	2.10873	−	2.43360i	0.0769485	−	0.0888033i	0.792918	+	0.609328i	$0.208561\pi$
$752$	−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	−0.824451	−	0.565933i	$-0.808516\pi$
$757$	−33.3481	+	9.79188i	−1.21206	+	0.355892i	−0.387606	+	0.921825i	$0.626698\pi$
$758$	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	−0.742925	−	0.669374i	$-0.766562\pi$
$761$	−27.7524	+	8.14883i	−1.00602	+	0.295395i	−0.263098	+	0.964769i	$0.584744\pi$
$762$	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	0.998775	−	0.0494918i	$-0.0157602\pi$
$769$	8.52205	+	18.6607i	0.307313	+	0.672921i	−0.691462	+	0.722413i	$0.743033\pi$
$770$	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	−0.755979	−	0.654596i	$-0.772839\pi$
$773$	4.27604	−	29.7405i	0.153799	−	1.06969i	0.909777	−	0.415097i	$-0.136252\pi$
$774$	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	−0.984048	−	0.177905i	$-0.943068\pi$
$787$	−2.52433	−	17.5571i	−0.0899826	−	0.625843i	0.894065	−	0.447937i	$-0.147841\pi$
$788$	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	−0.981735	−	0.190252i	$-0.939069\pi$
$797$	−18.4548	+	21.2980i	−0.653704	+	0.754414i	0.328031	+	0.944667i	$0.393615\pi$
$798$	−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	−0.319268	−	0.947664i	$-0.603437\pi$
$809$	11.6653	−	7.49681i	0.410129	−	0.263574i	0.729397	+	0.684091i	$0.239801\pi$
$810$	0.230156	+	1.60077i	0.00808686	+	0.0562453i
$811$	−28.7636	−	18.4852i	−1.01003	−	0.649105i	−0.0726267	−	0.997359i	$-0.523138\pi$
$811$	−28.7636	−	18.4852i	−1.01003	−	0.649105i	−0.937400	+	0.348254i	$0.886775\pi$
$812$	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	−0.681752	−	0.731584i	$-0.738782\pi$
$821$	9.10007	−	19.9264i	0.317595	−	0.695435i	0.999346	+	0.0361483i	$0.0115089\pi$
$822$	−8.24528	−	5.29892i	−0.287587	−	0.184821i
$823$	−7.94565	−	55.2632i	−0.276968	−	1.92635i	−0.366599	−	0.930379i	$-0.619478\pi$
$823$	−7.94565	−	55.2632i	−0.276968	−	1.92635i	0.0896310	−	0.995975i	$-0.471431\pi$
$824$	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	0.199241	−	0.979951i	$-0.436152\pi$
$839$	−4.71989	−	1.38588i	−0.162949	−	0.0478460i	−0.362189	+	0.932105i	$0.617971\pi$
$840$	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	−0.346348	−	0.938106i	$-0.612578\pi$
$853$	−3.81247	+	1.11944i	−0.130537	+	0.0383290i	0.215812	+	0.976435i	$0.430760\pi$
$854$	−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	−0.0489622	−	0.998801i	$-0.515591\pi$
$857$	−28.6259	−	18.3968i	−0.977843	−	0.628421i	−0.928881	+	0.370379i	$0.879228\pi$
$858$	0.0886578	−	0.194134i	0.00302673	−	0.00662761i
$859$	−23.4721	+	27.0883i	−0.800858	+	0.924240i	−0.998428	−	0.0560492i	$-0.982150\pi$
$859$	−23.4721	+	27.0883i	−0.800858	+	0.924240i	0.197570	+	0.980289i	$0.436695\pi$
$860$	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	0.424049	−	0.905639i	$-0.360609\pi$
$863$	8.55323	+	2.51146i	0.291155	+	0.0854909i	−0.132893	+	0.991130i	$0.542427\pi$
$864$	−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	0.997553	+	0.0699099i	$0.0222712\pi$
$877$	27.3868	+	31.6060i	0.924785	+	1.06726i	−0.0727683	+	0.997349i	$0.523183\pi$
$878$	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	−0.393383	−	0.919375i	$-0.628695\pi$
$881$	16.5934	−	36.3344i	0.559045	−	1.22414i	0.952428	−	0.304763i	$-0.0985773\pi$
$882$	−4.26422	+	4.92118i	−0.143584	+	0.165705i
$883$	−7.73017	+	53.7645i	−0.260141	+	1.80932i	0.271597	+	0.962411i	$0.412448\pi$
$883$	−7.73017	+	53.7645i	−0.260141	+	1.80932i	−0.531738	+	0.846909i	$0.678461\pi$
$884$	−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	0.937595	+	0.347729i	$0.113047\pi$
$887$	17.4644	+	38.2417i	0.586397	+	1.28403i	−0.351198	+	0.936301i	$0.614226\pi$
$888$	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	0.821204	−	0.570635i	$-0.193303\pi$
$907$	−4.45205	−	9.74862i	−0.147828	−	0.323698i	−0.969031	+	0.246938i	$0.920576\pi$
$908$	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	−0.997844	−	0.0656231i	$-0.979097\pi$
$911$	−0.661955	+	4.60400i	−0.0219316	+	0.152537i	0.975913	+	0.218160i	$0.0700056\pi$
$912$	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	−0.748152	−	0.663528i	$-0.769059\pi$
$929$	4.77406	−	33.2043i	0.156632	−	1.08940i	0.904784	−	0.425871i	$-0.140032\pi$
$930$	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	0.600214	−	0.799840i	$-0.295082\pi$
$937$	3.73421	+	2.39983i	0.121991	+	0.0783991i	−0.478222	+	0.878239i	$0.658719\pi$
$938$	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	−0.550487	−	0.834843i	$-0.685558\pi$
$941$	−17.2470	+	5.06418i	−0.562236	+	0.165087i	−0.0117490	+	0.999931i	$0.503740\pi$
$942$	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	−0.584209	−	0.811604i	$-0.698595\pi$
$947$	−2.72766	+	1.75296i	−0.0886370	+	0.0569635i	0.495572	+	0.868567i	$0.334959\pi$
$948$	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	0.977572	−	0.210601i	$-0.0675420\pi$
$953$	5.50230	+	12.0484i	0.178237	+	0.390285i	−0.799335	+	0.600886i	$0.794815\pi$
$954$	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	0.568420	+	0.822738i	$0.307555\pi$
$971$	7.94033	+	55.2262i	0.254817	+	1.77229i	−0.313603	+	0.949554i	$0.601536\pi$
$972$	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	0.586890	−	0.809667i	$-0.300352\pi$
$977$	20.0943	+	5.90022i	0.642874	+	0.188765i	0.0559840	+	0.998432i	$0.482170\pi$
$978$	−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	0.807951	−	0.589250i	$-0.200577\pi$
$983$	19.0495	+	12.2424i	0.607585	+	0.390471i	−0.200366	+	0.979721i	$0.564213\pi$
$984$	−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	−0.808236	−	0.588859i	$-0.799577\pi$
$991$	−36.8257	+	10.8130i	−1.16981	+	0.343486i	−0.361570	+	0.932345i	$0.617759\pi$
$992$	−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	0.000259238	−	1.00000i	$-0.499917\pi$
$997$	31.2609	−	36.0770i	0.990044	−	1.14257i	0.989785	−	0.142571i	$-0.0455371\pi$
$998$	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.55.1	✓	10
3.2	odd	2		207.2.i.a.55.1		10
23.8	even	11		1587.2.a.q.1.3		5
23.15	odd	22		1587.2.a.r.1.3		5
23.18	even	11	inner	69.2.e.b.64.1	yes	10
69.8	odd	22		4761.2.a.bp.1.3		5
69.38	even	22		4761.2.a.bm.1.3		5
69.41	odd	22		207.2.i.a.64.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.b.55.1	✓	10	1.1	even	1	trivial
69.2.e.b.64.1	yes	10	23.18	even	11	inner
207.2.i.a.55.1		10	3.2	odd	2
207.2.i.a.64.1		10	69.41	odd	22
1587.2.a.q.1.3		5	23.8	even	11
1587.2.a.r.1.3		5	23.15	odd	22
4761.2.a.bm.1.3		5	69.38	even	22
4761.2.a.bp.1.3		5	69.8	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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