LMFDB - Embedded newform 69.2.e.b.4.1

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			4.1
Root			$-0.415415 - 0.909632i$ of defining polynomial
Character	$\chi$	$=$	69.4
Dual form			69.2.e.b.52.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.915415 + 2.00448i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-1.87023 + 2.15836i) q^{4} +(-2.61903 - 1.68315i) q^{5} +(1.44306 + 1.66538i) q^{6} +(-0.427961 - 2.97653i) q^{7} +(-1.80972 - 0.531382i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(0.915415 + 2.00448i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-1.87023 + 2.15836i) q^{4} +(-2.61903 - 1.68315i) q^{5} +(1.44306 + 1.66538i) q^{6} +(-0.427961 - 2.97653i) q^{7} +(-1.80972 - 0.531382i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.976337 - 6.79057i) q^{10} +(-2.48357 + 5.43826i) q^{11} +(-1.18639 + 2.59784i) q^{12} +(-0.0566239 + 0.393828i) q^{13} +(5.57464 - 3.58260i) q^{14} +(-2.98714 - 0.877103i) q^{15} +(0.221378 + 1.53972i) q^{16} +(0.862774 + 0.995695i) q^{17} +(1.85380 + 1.19136i) q^{18} +(1.67353 - 1.93136i) q^{19} +(8.53104 - 2.50494i) q^{20} +(-1.24921 - 2.73539i) q^{21} -13.1744 q^{22} +(2.43626 - 4.13094i) q^{23} -1.88612 q^{24} +(1.94926 + 4.26828i) q^{25} +(-0.841254 + 0.247014i) q^{26} +(0.654861 - 0.755750i) q^{27} +(7.22482 + 4.64311i) q^{28} +(-0.836577 - 0.965461i) q^{29} +(-0.976337 - 6.79057i) q^{30} +(0.575969 + 0.169120i) q^{31} +(-6.05710 + 3.89266i) q^{32} +(-0.850833 + 5.91767i) q^{33} +(-1.20605 + 2.64089i) q^{34} +(-3.88911 + 8.51595i) q^{35} +(-0.406440 + 2.82685i) q^{36} +(-6.75901 + 4.34375i) q^{37} +(5.40335 + 1.58657i) q^{38} +(0.0566239 + 0.393828i) q^{39} +(3.84532 + 4.43774i) q^{40} +(-7.15168 - 4.59610i) q^{41} +(4.33949 - 5.00804i) q^{42} +(7.26738 - 2.13390i) q^{43} +(-7.09288 - 15.5312i) q^{44} -3.11325 q^{45} +(10.5106 + 1.10192i) q^{46} +7.68323 q^{47} +(0.646201 + 1.41498i) q^{48} +(-1.96015 + 0.575552i) q^{49} +(-6.77129 + 7.81449i) q^{50} +(1.10835 + 0.712290i) q^{51} +(-0.744123 - 0.858763i) q^{52} +(0.399800 + 2.78067i) q^{53} +(2.11435 + 0.620830i) q^{54} +(15.6579 - 10.0627i) q^{55} +(-0.807187 + 5.61411i) q^{56} +(1.06162 - 2.32461i) q^{57} +(1.16943 - 2.56070i) q^{58} +(0.477417 - 3.32051i) q^{59} +(7.47975 - 4.80694i) q^{60} +(0.182679 + 0.0536394i) q^{61} +(0.188254 + 1.30933i) q^{62} +(-1.96926 - 2.27265i) q^{63} +(-10.7303 - 6.89594i) q^{64} +(0.811170 - 0.936140i) q^{65} +(-12.6407 + 3.71165i) q^{66} +(3.73947 + 8.18830i) q^{67} -3.76266 q^{68} +(1.17376 - 4.64998i) q^{69} -20.6302 q^{70} +(-5.61761 - 12.3008i) q^{71} +(-1.80972 + 0.531382i) q^{72} +(-9.37672 + 10.8213i) q^{73} +(-14.8943 - 9.57195i) q^{74} +(3.07281 + 3.54621i) q^{75} +(1.03868 + 7.22418i) q^{76} +(17.2500 + 5.06506i) q^{77} +(-0.737585 + 0.474017i) q^{78} +(-0.718701 + 4.99867i) q^{79} +(2.01178 - 4.40519i) q^{80} +(0.415415 - 0.909632i) q^{81} +(2.66604 - 18.5427i) q^{82} +(6.86519 - 4.41199i) q^{83} +(8.24028 + 2.41956i) q^{84} +(-0.583730 - 4.05993i) q^{85} +(10.9300 + 12.6139i) q^{86} +(-1.07469 - 0.690662i) q^{87} +(7.38436 - 8.52200i) q^{88} +(-0.416206 + 0.122209i) q^{89} +(-2.84991 - 6.24044i) q^{90} +1.19647 q^{91} +(4.35968 + 12.9841i) q^{92} +0.600285 q^{93} +(7.03334 + 15.4009i) q^{94} +(-7.63380 + 2.24148i) q^{95} +(-4.71506 + 5.44146i) q^{96} +(0.265546 + 0.170656i) q^{97} +(-2.94803 - 3.40221i) q^{98} +(0.850833 + 5.91767i) 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 $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$1$

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 $

$2$	0.915415	+	2.00448i	0.647296	+	1.41738i	0.893901	+	0.448265i	$0.147958\pi$
$2$	0.915415	+	2.00448i	0.647296	+	1.41738i	−0.246605	+	0.969116i	$0.579315\pi$
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$4$	−1.87023	+	2.15836i	−0.935116	+	1.07918i
$5$	−2.61903	−	1.68315i	−1.17127	−	0.752727i	−0.197505	−	0.980302i	$-0.563284\pi$
$5$	−2.61903	−	1.68315i	−1.17127	−	0.752727i	−0.973761	+	0.227575i	$0.926920\pi$
$6$	1.44306	+	1.66538i	0.589127	+	0.679889i
$7$	−0.427961	−	2.97653i	−0.161754	−	1.12502i	−0.895326	−	0.445412i	$-0.853057\pi$
$7$	−0.427961	−	2.97653i	−0.161754	−	1.12502i	0.733572	−	0.679612i	$-0.237852\pi$
$8$	−1.80972	−	0.531382i	−0.639833	−	0.187872i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	0.976337	−	6.79057i	0.308745	−	2.14737i
$11$	−2.48357	+	5.43826i	−0.748824	+	1.63970i	0.0196434	+	0.999807i	$0.493747\pi$
$11$	−2.48357	+	5.43826i	−0.748824	+	1.63970i	−0.768467	+	0.639889i	$0.778980\pi$
$12$	−1.18639	+	2.59784i	−0.342482	+	0.749931i
$13$	−0.0566239	+	0.393828i	−0.0157046	+	0.109228i	−0.996166	−	0.0874840i	$-0.972117\pi$
$13$	−0.0566239	+	0.393828i	−0.0157046	+	0.109228i	0.980461	+	0.196712i	$0.0630264\pi$
$14$	5.57464	−	3.58260i	1.48988	−	0.957491i
$15$	−2.98714	−	0.877103i	−0.771276	−	0.226467i
$16$	0.221378	+	1.53972i	0.0553446	+	0.384930i
$17$	0.862774	+	0.995695i	0.209254	+	0.241491i	0.850668	−	0.525703i	$-0.176198\pi$
$17$	0.862774	+	0.995695i	0.209254	+	0.241491i	−0.641415	+	0.767194i	$0.721652\pi$
$18$	1.85380	+	1.19136i	0.436945	+	0.280807i
$19$	1.67353	−	1.93136i	0.383935	−	0.443084i	−0.530581	−	0.847634i	$-0.678026\pi$
$19$	1.67353	−	1.93136i	0.383935	−	0.443084i	0.914516	+	0.404550i	$0.132572\pi$
$20$	8.53104	−	2.50494i	1.90760	−	0.560121i
$21$	−1.24921	−	2.73539i	−0.272600	−	0.596912i
$22$	−13.1744			−2.80878
$23$	2.43626	−	4.13094i	0.507996	−	0.861360i
$23$	2.43626	−	4.13094i	0.507996	−	0.861360i
$24$	−1.88612			−0.385003
$25$	1.94926	+	4.26828i	0.389851	+	0.853655i
$26$	−0.841254	+	0.247014i	−0.164983	+	0.0484435i
$27$	0.654861	−	0.755750i	0.126028	−	0.145444i
$28$	7.22482	+	4.64311i	1.36536	+	0.877465i
$29$	−0.836577	−	0.965461i	−0.155348	−	0.179282i	0.672740	−	0.739879i	$-0.265117\pi$
$29$	−0.836577	−	0.965461i	−0.155348	−	0.179282i	−0.828089	+	0.560597i	$0.810572\pi$
$30$	−0.976337	−	6.79057i	−0.178254	−	1.23978i
$31$	0.575969	+	0.169120i	0.103447	+	0.0303748i	0.333046	−	0.942910i	$-0.391923\pi$
$31$	0.575969	+	0.169120i	0.103447	+	0.0303748i	−0.229599	+	0.973285i	$0.573742\pi$
$32$	−6.05710	+	3.89266i	−1.07075	+	0.688132i
$33$	−0.850833	+	5.91767i	−0.148111	+	1.03013i
$34$	−1.20605	+	2.64089i	−0.206836	+	0.452908i
$35$	−3.88911	+	8.51595i	−0.657379	+	1.43946i
$36$	−0.406440	+	2.82685i	−0.0677400	+	0.471142i
$37$	−6.75901	+	4.34375i	−1.11117	+	0.714108i	−0.961549	−	0.274635i	$-0.911443\pi$
$37$	−6.75901	+	4.34375i	−1.11117	+	0.714108i	−0.149625	+	0.988743i	$0.547807\pi$
$38$	5.40335	+	1.58657i	0.876538	+	0.257375i
$39$	0.0566239	+	0.393828i	0.00906707	+	0.0630629i
$40$	3.84532	+	4.43774i	0.607999	+	0.701668i
$41$	−7.15168	−	4.59610i	−1.11690	−	0.717791i	−0.154117	−	0.988053i	$-0.549253\pi$
$41$	−7.15168	−	4.59610i	−1.11690	−	0.717791i	−0.962787	+	0.270262i	$0.912890\pi$
$42$	4.33949	−	5.00804i	0.669598	−	0.772757i
$43$	7.26738	−	2.13390i	1.10827	−	0.325416i	0.324134	−	0.946011i	$-0.394927\pi$
$43$	7.26738	−	2.13390i	1.10827	−	0.325416i	0.784131	+	0.620595i	$0.213109\pi$
$44$	−7.09288	−	15.5312i	−1.06929	−	2.34142i
$45$	−3.11325			−0.464096
$46$	10.5106	+	1.10192i	1.54970	+	0.162469i
$47$	7.68323			1.12071			0.560357	−	0.828251i	$-0.310664\pi$
$47$	7.68323			1.12071			0.560357	+	0.828251i	$0.310664\pi$
$48$	0.646201	+	1.41498i	0.0932710	+	0.204235i
$49$	−1.96015	+	0.575552i	−0.280021	+	0.0822217i
$50$	−6.77129	+	7.81449i	−0.957605	+	1.10514i
$51$	1.10835	+	0.712290i	0.155199	+	0.0997406i
$52$	−0.744123	−	0.858763i	−0.103191	−	0.119089i
$53$	0.399800	+	2.78067i	0.0549168	+	0.381954i	0.998681	+	0.0513365i	$0.0163481\pi$
$53$	0.399800	+	2.78067i	0.0549168	+	0.381954i	−0.943765	+	0.330618i	$0.892743\pi$
$54$	2.11435	+	0.620830i	0.287727	+	0.0844843i
$55$	15.6579	−	10.0627i	2.11132	−	1.35686i
$56$	−0.807187	+	5.61411i	−0.107865	+	0.750217i
$57$	1.06162	−	2.32461i	0.140614	−	0.307903i
$58$	1.16943	−	2.56070i	0.153554	−	0.336236i
$59$	0.477417	−	3.32051i	0.0621545	−	0.432294i	−0.934856	−	0.355027i	$-0.884472\pi$
$59$	0.477417	−	3.32051i	0.0621545	−	0.432294i	0.997010	−	0.0772666i	$-0.0246193\pi$
$60$	7.47975	−	4.80694i	0.965631	−	0.620573i
$61$	0.182679	+	0.0536394i	0.0233897	+	0.00686782i	0.293406	−	0.955988i	$-0.405211\pi$
$61$	0.182679	+	0.0536394i	0.0233897	+	0.00686782i	−0.270017	+	0.962856i	$0.587029\pi$
$62$	0.188254	+	1.30933i	0.0239082	+	0.166285i
$63$	−1.96926	−	2.27265i	−0.248103	−	0.286327i
$64$	−10.7303	−	6.89594i	−1.34129	−	0.861992i
$65$	0.811170	−	0.936140i	0.100613	−	0.116114i
$66$	−12.6407	+	3.71165i	−1.55596	+	0.456872i
$67$	3.73947	+	8.18830i	0.456849	+	1.00036i	0.988194	+	0.153205i	$0.0489595\pi$
$67$	3.73947	+	8.18830i	0.456849	+	1.00036i	−0.531345	+	0.847156i	$0.678313\pi$
$68$	−3.76266			−0.456289
$69$	1.17376	−	4.64998i	0.141304	−	0.559792i
$70$	−20.6302			−2.46578
$71$	−5.61761	−	12.3008i	−0.666688	−	1.45984i	−0.876156	−	0.482027i	$-0.839901\pi$
$71$	−5.61761	−	12.3008i	−0.666688	−	1.45984i	0.209469	−	0.977815i	$-0.432827\pi$
$72$	−1.80972	+	0.531382i	−0.213278	+	0.0626240i
$73$	−9.37672	+	10.8213i	−1.09746	+	1.26654i	−0.136265	+	0.990672i	$0.543510\pi$
$73$	−9.37672	+	10.8213i	−1.09746	+	1.26654i	−0.961196	+	0.275866i	$0.911035\pi$
$74$	−14.8943	−	9.57195i	−1.73142	−	1.11272i
$75$	3.07281	+	3.54621i	0.354818	+	0.409481i
$76$	1.03868	+	7.22418i	0.119145	+	0.828670i
$77$	17.2500	+	5.06506i	1.96582	+	0.577218i
$78$	−0.737585	+	0.474017i	−0.0835150	+	0.0536719i
$79$	−0.718701	+	4.99867i	−0.0808602	+	0.562395i	0.908609	+	0.417649i	$0.137146\pi$
$79$	−0.718701	+	4.99867i	−0.0808602	+	0.562395i	−0.989469	+	0.144746i	$0.953763\pi$
$80$	2.01178	−	4.40519i	0.224924	−	0.492515i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	2.66604	−	18.5427i	0.294415	−	2.04770i
$83$	6.86519	−	4.41199i	0.753552	−	0.484279i	−0.106609	−	0.994301i	$-0.533999\pi$
$83$	6.86519	−	4.41199i	0.753552	−	0.484279i	0.860161	+	0.510023i	$0.170363\pi$
$84$	8.24028	+	2.41956i	0.899088	+	0.263996i
$85$	−0.583730	−	4.05993i	−0.0633144	−	0.440362i
$86$	10.9300	+	12.6139i	1.17861	+	1.36019i
$87$	−1.07469	−	0.690662i	−0.115219	−	0.0740467i
$88$	7.38436	−	8.52200i	0.787175	−	0.908449i
$89$	−0.416206	+	0.122209i	−0.0441178	+	0.0129541i	−0.303717	−	0.952762i	$-0.598228\pi$
$89$	−0.416206	+	0.122209i	−0.0441178	+	0.0129541i	0.259599	+	0.965716i	$0.416410\pi$
$90$	−2.84991	−	6.24044i	−0.300407	−	0.657800i
$91$	1.19647			0.125425
$92$	4.35968	+	12.9841i	0.454528	+	1.35369i
$93$	0.600285			0.0622466
$94$	7.03334	+	15.4009i	0.725434	+	1.58848i
$95$	−7.63380	+	2.24148i	−0.783211	+	0.229971i
$96$	−4.71506	+	5.44146i	−0.481228	+	0.555367i
$97$	0.265546	+	0.170656i	0.0269621	+	0.0173275i	0.554052	−	0.832482i	$-0.313081\pi$
$97$	0.265546	+	0.170656i	0.0269621	+	0.0173275i	−0.527090	+	0.849809i	$0.676717\pi$
$98$	−2.94803	−	3.40221i	−0.297796	−	0.343675i
$99$	0.850833	+	5.91767i	0.0855119	+	0.594748i
$100$	−12.8580	−	3.77546i	−1.28580	−	0.377546i
$101$	−0.423599	+	0.272230i	−0.0421497	+	0.0270879i	−0.561546	−	0.827446i	$-0.689793\pi$
$101$	−0.423599	+	0.272230i	−0.0421497	+	0.0270879i	0.519396	+	0.854533i	$0.326157\pi$
$102$	−0.413175	+	2.87370i	−0.0409104	+	0.284538i
$103$	6.76169	−	14.8060i	0.666249	−	1.45888i	−0.210333	−	0.977630i	$-0.567455\pi$
$103$	6.76169	−	14.8060i	0.666249	−	1.45888i	0.876582	−	0.481252i	$-0.159818\pi$
$104$	0.311746	−	0.682629i	0.0305692	−	0.0669373i
$105$	−1.33235	+	9.26669i	−0.130024	+	0.904336i
$106$	−5.20781	+	3.34686i	−0.505828	+	0.325076i
$107$	−0.412860	−	0.121227i	−0.0399127	−	0.0117194i	0.261715	−	0.965145i	$-0.415712\pi$
$107$	−0.412860	−	0.121227i	−0.0399127	−	0.0117194i	−0.301628	+	0.953426i	$0.597530\pi$
$108$	0.406440	+	2.82685i	0.0391097	+	0.272014i
$109$	3.06061	+	3.53213i	0.293153	+	0.338317i	0.883152	−	0.469088i	$-0.155417\pi$
$109$	3.06061	+	3.53213i	0.293153	+	0.338317i	−0.589999	+	0.807404i	$0.700872\pi$
$110$	34.5041	+	22.1744i	3.28983	+	2.11425i
$111$	−5.26144	+	6.07203i	−0.499394	+	0.576331i
$112$	4.48829	−	1.31788i	0.424103	−	0.124528i
$113$	−0.599543	−	1.31282i	−0.0564002	−	0.123499i	0.879334	−	0.476206i	$-0.157988\pi$
$113$	−0.599543	−	1.31282i	−0.0564002	−	0.123499i	−0.935734	+	0.352707i	$0.885261\pi$
$114$	5.63146			0.527434
$115$	−13.3336	+	6.71845i	−1.24337	+	0.626499i
$116$	3.64841			0.338746
$117$	0.165284	+	0.361922i	0.0152805	+	0.0334597i
$118$	7.09293	−	2.08267i	0.652957	−	0.191726i
$119$	2.59448	−	2.99420i	0.237836	−	0.274477i
$120$	4.93981	+	3.17463i	0.450941	+	0.289802i
$121$	−16.2031	−	18.6993i	−1.47300	−	1.69994i
$122$	0.0597080	+	0.415279i	0.00540571	+	0.0375976i
$123$	−8.15686	−	2.39507i	−0.735479	−	0.215956i
$124$	−1.44222	+	0.926857i	−0.129515	+	0.0832342i
$125$	−0.136325	+	0.948161i	−0.0121933	+	0.0848061i
$126$	2.75278	−	6.02775i	0.245237	−	0.536995i
$127$	−3.08427	+	6.75361i	−0.273685	+	0.599286i	−0.995705	−	0.0925863i	$-0.970487\pi$
$127$	−3.08427	+	6.75361i	−0.273685	+	0.599286i	0.722020	+	0.691872i	$0.243214\pi$
$128$	1.95074	−	13.5677i	0.172423	−	1.19923i
$129$	6.37181	−	4.09492i	0.561007	−	0.360537i
$130$	2.61903	+	0.769017i	0.229704	+	0.0674472i
$131$	1.79023	+	12.4513i	0.156413	+	1.08788i	0.905175	+	0.425040i	$0.139740\pi$
$131$	1.79023	+	12.4513i	0.156413	+	1.08788i	−0.748761	+	0.662840i	$0.769351\pi$
$132$	−11.1812	−	12.9038i	−0.973200	−	1.12313i
$133$	−6.46496	−	4.15478i	−0.560583	−	0.360265i
$134$	−12.9901	+	14.9914i	−1.12218	+	1.29506i
$135$	−2.98714	+	0.877103i	−0.257092	+	0.0754890i
$136$	−1.03229	−	2.26039i	−0.0885179	−	0.193827i
$137$	−12.8523			−1.09805			−0.549024	−	0.835807i	$-0.685000\pi$
$137$	−12.8523			−1.09805			−0.549024	+	0.835807i	$0.685000\pi$
$138$	10.3953	−	1.90389i	0.884903	−	0.162070i
$139$	−12.6909			−1.07643			−0.538214	−	0.842808i	$-0.680901\pi$
$139$	−12.6909			−1.07643			−0.538214	+	0.842808i	$0.680901\pi$
$140$	−11.1070	−	24.3209i	−0.938711	−	2.05549i
$141$	7.37200	−	2.16461i	0.620834	−	0.182293i
$142$	19.5144	−	22.5208i	1.63761	−	1.88990i
$143$	−2.00111	−	1.28603i	−0.167341	−	0.107543i
$144$	1.01867	+	1.17561i	0.0848893	+	0.0979675i
$145$	0.566005	+	3.93665i	0.0470042	+	0.326921i
$146$	−30.2747	−	8.88945i	−2.50555	−	0.735696i
$147$	−1.71860	+	1.10448i	−0.141748	+	0.0910957i
$148$	3.26552	−	22.7122i	0.268424	−	1.86693i
$149$	3.27547	−	7.17227i	0.268337	−	0.587576i	−0.726714	−	0.686940i	$-0.758954\pi$
$149$	3.27547	−	7.17227i	0.268337	−	0.587576i	0.995051	+	0.0993642i	$0.0316809\pi$
$150$	−4.29541	+	9.40564i	−0.350719	+	0.767967i
$151$	−1.17138	+	8.14714i	−0.0953257	+	0.663005i	0.884996	+	0.465599i	$0.154161\pi$
$151$	−1.17138	+	8.14714i	−0.0953257	+	0.663005i	−0.980322	+	0.197406i	$0.936748\pi$
$152$	−4.05492	+	2.60594i	−0.328897	+	0.211369i
$153$	1.26413	+	0.371181i	0.102198	+	0.0300082i
$154$	5.63811	+	39.2139i	0.454332	+	3.15995i
$155$	−1.22383	−	1.41237i	−0.0983001	−	0.113444i
$156$	−0.955922	−	0.614334i	−0.0765350	−	0.0491861i
$157$	0.0526905	−	0.0608081i	0.00420516	−	0.00485301i	−0.753643	−	0.657284i	$-0.771705\pi$
$157$	0.0526905	−	0.0608081i	0.00420516	−	0.00485301i	0.757848	+	0.652431i	$0.226251\pi$
$158$	−10.6776	+	3.13524i	−0.849468	+	0.249426i
$159$	1.16701	+	2.55540i	0.0925500	+	0.202656i
$160$	22.4157			1.77211
$161$	−13.3385	−	5.48374i	−1.05122	−	0.432179i
$162$	2.20362			0.173132
$163$	−1.22608	−	2.68474i	−0.0960339	−	0.210285i	0.855518	−	0.517773i	$-0.173239\pi$
$163$	−1.22608	−	2.68474i	−0.0960339	−	0.210285i	−0.951552	+	0.307488i	$0.900512\pi$
$164$	23.2953	−	6.84013i	1.81906	−	0.534124i
$165$	12.1887	−	14.0665i	0.948887	−	1.09507i
$166$	15.1282	+	9.72232i	1.17418	+	0.754599i
$167$	8.38180	+	9.67311i	0.648603	+	0.748528i	0.980871	−	0.194657i	$-0.0623594\pi$
$167$	8.38180	+	9.67311i	0.648603	+	0.748528i	−0.332268	+	0.943185i	$0.607814\pi$
$168$	0.807187	+	5.61411i	0.0622758	+	0.433138i
$169$	12.3215	+	3.61792i	0.947809	+	0.278302i
$170$	7.60370	−	4.88660i	0.583177	−	0.374785i
$171$	0.363693	−	2.52954i	0.0278123	−	0.193439i
$172$	−8.98596	+	19.6765i	−0.685173	+	1.50032i
$173$	3.29560	−	7.21636i	0.250560	−	0.548649i	−0.742001	−	0.670399i	$-0.766123\pi$
$173$	3.29560	−	7.21636i	0.250560	−	0.548649i	0.992561	+	0.121749i	$0.0388504\pi$
$174$	0.400629	−	2.78644i	0.0303716	−	0.211239i
$175$	11.8705	−	7.62868i	0.897323	−	0.576674i
$176$	−8.92321	−	2.62009i	−0.672612	−	0.197497i
$177$	−0.477417	−	3.32051i	−0.0358849	−	0.249585i
$178$	−0.625967	−	0.722405i	−0.0469182	−	0.0541465i
$179$	−6.89917	−	4.43383i	−0.515668	−	0.331400i	0.256788	−	0.966468i	$-0.417336\pi$
$179$	−6.89917	−	4.43383i	−0.515668	−	0.331400i	−0.772456	+	0.635068i	$0.780972\pi$
$180$	5.82249	−	6.71951i	0.433983	−	0.500843i
$181$	−16.9479	+	4.97635i	−1.25973	+	0.369889i	−0.842392	−	0.538864i	$-0.818853\pi$
$181$	−16.9479	+	4.97635i	−1.25973	+	0.369889i	−0.417334	+	0.908753i	$0.637035\pi$
$182$	1.09527	+	2.39831i	0.0811868	+	0.177774i
$183$	0.190391			0.0140741
$184$	−6.60406	+	6.18126i	−0.486858	+	0.455688i
$185$	25.0132			1.83901
$186$	0.549510	+	1.20326i	0.0402920	+	0.0882272i
$187$	−7.55760	+	2.21911i	−0.552667	+	0.162278i
$188$	−14.3694	+	16.5832i	−1.04800	+	1.20945i
$189$	−2.52977	−	1.62578i	−0.184014	−	0.118258i
$190$	−11.4811	−	13.2499i	−0.832927	−	0.961249i
$191$	−0.00321323	−	0.0223485i	−0.000232501	−	0.00161708i	0.989705	−	0.143123i	$-0.0457146\pi$
$191$	−0.00321323	−	0.0223485i	−0.000232501	−	0.00161708i	−0.989937	+	0.141506i	$0.954805\pi$
$192$	−12.2384	−	3.59353i	−0.883234	−	0.259341i
$193$	8.04311	−	5.16900i	0.578956	−	0.372072i	−0.218147	−	0.975916i	$-0.570001\pi$
$193$	8.04311	−	5.16900i	0.578956	−	0.372072i	0.797103	+	0.603844i	$0.206365\pi$
$194$	−0.0989917	+	0.688503i	−0.00710719	+	0.0494316i
$195$	0.514571	−	1.12675i	0.0368492	−	0.0806884i
$196$	2.42368	−	5.30713i	0.173120	−	0.379081i
$197$	−2.12712	+	14.7945i	−0.151551	+	1.05406i	0.762069	+	0.647495i	$0.224183\pi$
$197$	−2.12712	+	14.7945i	−0.151551	+	1.05406i	−0.913621	+	0.406568i	$0.866726\pi$
$198$	−11.0830	+	7.12260i	−0.787633	+	0.506181i
$199$	−2.68037	−	0.787028i	−0.190006	−	0.0557909i	0.185345	−	0.982674i	$-0.440660\pi$
$199$	−2.68037	−	0.787028i	−0.190006	−	0.0557909i	−0.375351	+	0.926883i	$0.622478\pi$
$200$	−1.25953	−	8.76019i	−0.0890619	−	0.619439i
$201$	5.89491	+	6.80309i	0.415795	+	0.479853i
$202$	−0.933449	−	0.599891i	−0.0656772	−	0.0422082i
$203$	−2.51570	+	2.90328i	−0.176568	+	0.203770i
$204$	−3.61024	+	1.06006i	−0.252768	+	0.0742193i
$205$	10.9945	+	24.0747i	0.767892	+	1.68145i
$206$	35.8681			2.49905
$207$	−0.183838	−	4.79231i	−0.0127776	−	0.333088i
$208$	−0.618920			−0.0429144
$209$	6.34689	+	13.8978i	0.439024	+	0.961328i
$210$	−19.7945	+	5.81220i	−1.36595	+	0.401080i
$211$	12.9168	−	14.9068i	0.889228	−	1.02622i	−0.110250	−	0.993904i	$-0.535165\pi$
$211$	12.9168	−	14.9068i	0.889228	−	1.02622i	0.999478	−	0.0323197i	$-0.0102895\pi$
$212$	−6.74941	−	4.33758i	−0.463551	−	0.297906i
$213$	−8.85561	−	10.2199i	−0.606776	−	0.700257i
$214$	−0.134942	−	0.938543i	−0.00922445	−	0.0641575i
$215$	−22.6252	−	6.64335i	−1.54302	−	0.453072i
$216$	−1.58671	+	1.01971i	−0.107962	+	0.0693828i
$217$	0.256898	−	1.78677i	0.0174394	−	0.121294i
$218$	−4.27835	+	9.36829i	−0.289767	+	0.634500i
$219$	−5.94818	+	13.0247i	−0.401941	+	0.880127i
$220$	−7.56492	+	52.6151i	−0.510027	+	3.54731i
$221$	−0.440986	+	0.283404i	−0.0296639	+	0.0190638i
$222$	−16.9877	−	4.98803i	−1.14014	−	0.334774i
$223$	−2.93198	−	20.3924i	−0.196340	−	1.36558i	−0.814792	−	0.579753i	$-0.803149\pi$
$223$	−2.93198	−	20.3924i	−0.196340	−	1.36558i	0.618452	−	0.785822i	$-0.287760\pi$
$224$	14.1788	+	16.3633i	0.947364	+	1.09332i
$225$	3.94742	+	2.53686i	0.263162	+	0.169124i
$226$	2.08268	−	2.40354i	0.138538	−	0.159881i
$227$	−3.73450	+	1.09655i	−0.247868	+	0.0727805i	−0.403306	−	0.915065i	$-0.632139\pi$
$227$	−3.73450	+	1.09655i	−0.247868	+	0.0727805i	0.155439	+	0.987846i	$0.450321\pi$
$228$	3.03189	+	6.63892i	0.200792	+	0.439673i
$229$	−13.4414			−0.888234			−0.444117	−	0.895969i	$-0.646483\pi$
$229$	−13.4414			−0.888234			−0.444117	+	0.895969i	$0.646483\pi$
$230$	−25.6728	−	20.5768i	−1.69281	−	1.35679i
$231$	17.9783			1.18288
$232$	1.00094	+	2.19176i	0.0657151	+	0.143896i
$233$	22.4781	−	6.60017i	1.47259	−	0.432392i	0.555651	−	0.831416i	$-0.312469\pi$
$233$	22.4781	−	6.60017i	1.47259	−	0.432392i	0.916940	+	0.399024i	$0.130651\pi$
$234$	−0.574161	+	0.662618i	−0.0375341	+	0.0433167i
$235$	−20.1226	−	12.9320i	−1.31265	−	0.843591i
$236$	6.27398	+	7.24056i	0.408401	+	0.471320i
$237$	0.718701	+	4.99867i	0.0466846	+	0.324699i
$238$	8.37683	+	2.45966i	0.542989	+	0.159436i
$239$	13.9764	−	8.98209i	0.904059	−	0.581003i	−0.00393244	−	0.999992i	$-0.501252\pi$
$239$	13.9764	−	8.98209i	0.904059	−	0.581003i	0.907991	+	0.418989i	$0.137615\pi$
$240$	0.689206	−	4.79353i	0.0444881	−	0.309421i
$241$	6.50659	−	14.2474i	0.419126	−	0.917759i	−0.575841	−	0.817562i	$-0.695325\pi$
$241$	6.50659	−	14.2474i	0.419126	−	0.917759i	0.994968	−	0.100197i	$-0.0319474\pi$
$242$	22.6499	−	49.5963i	1.45599	−	3.18817i
$243$	0.142315	−	0.989821i	0.00912950	−	0.0634971i
$244$	−0.457425	+	0.293969i	−0.0292836	+	0.0188195i
$245$	6.10243	+	1.79184i	0.389870	+	0.114476i
$246$	−2.66604	−	18.5427i	−0.169981	−	1.18224i
$247$	0.665861	+	0.768444i	0.0423677	+	0.0488949i
$248$	−0.952476	−	0.612119i	−0.0604823	−	0.0388696i
$249$	5.34410	−	6.16742i	0.338668	−	0.390844i
$250$	−2.02536	+	0.594700i	−0.128095	+	0.0376121i
$251$	5.84133	+	12.7907i	0.368701	+	0.807343i	0.999507	+	0.0314021i	$0.00999725\pi$
$251$	5.84133	+	12.7907i	0.368701	+	0.807343i	−0.630806	+	0.775941i	$0.717275\pi$
$252$	8.58816			0.541003
$253$	16.4145	+	23.5085i	1.03197	+	1.47797i
$254$	−16.3609			−1.02657
$255$	−1.70390	−	3.73102i	−0.106702	−	0.233646i
$256$	4.50498	−	1.32278i	0.281561	−	0.0826739i
$257$	−3.14220	+	3.62629i	−0.196005	+	0.226202i	−0.845241	−	0.534385i	$-0.820543\pi$
$257$	−3.14220	+	3.62629i	−0.196005	+	0.226202i	0.649236	+	0.760587i	$0.275089\pi$
$258$	14.0410	+	9.02362i	0.874156	+	0.561786i
$259$	15.8219	+	18.2595i	0.983125	+	1.13459i
$260$	0.503454	+	3.50160i	0.0312229	+	0.217160i
$261$	−1.22574	−	0.359910i	−0.0758714	−	0.0222779i
$262$	−23.3197	+	14.9866i	−1.44069	+	0.925877i
$263$	−3.14902	+	21.9019i	−0.194177	+	1.35053i	0.626626	+	0.779320i	$0.284435\pi$
$263$	−3.14902	+	21.9019i	−0.194177	+	1.35053i	−0.820803	+	0.571211i	$0.806474\pi$
$264$	4.68431	−	10.2572i	0.288300	−	0.631288i
$265$	3.63319	−	7.95558i	0.223185	−	0.488708i
$266$	2.41004	−	16.7622i	0.147769	−	1.02776i
$267$	−0.364917	+	0.234518i	−0.0223325	+	0.0143522i
$268$	−24.6670	−	7.24289i	−1.50678	−	0.442430i
$269$	−0.340830	−	2.37053i	−0.0207808	−	0.144534i	0.976789	−	0.214202i	$-0.0687150\pi$
$269$	−0.340830	−	2.37053i	−0.0207808	−	0.144534i	−0.997570	+	0.0696682i	$0.977806\pi$
$270$	−4.49261	−	5.18475i	−0.273411	−	0.315534i
$271$	−8.40291	−	5.40022i	−0.510441	−	0.328040i	0.259940	−	0.965625i	$-0.416297\pi$
$271$	−8.40291	−	5.40022i	−0.510441	−	0.328040i	−0.770380	+	0.637585i	$0.779934\pi$
$272$	−1.34209	+	1.54886i	−0.0813763	+	0.0939133i
$273$	1.14801	−	0.337086i	0.0694806	−	0.0204013i
$274$	−11.7652	−	25.7622i	−0.710762	−	1.55635i
$275$	−28.0531			−1.69167
$276$	7.84114	+	11.2299i	0.471981	+	0.675962i
$277$	12.7946			0.768754			0.384377	−	0.923176i	$-0.374416\pi$
$277$	12.7946			0.768754			0.384377	+	0.923176i	$0.374416\pi$
$278$	−11.6174	−	25.4386i	−0.696767	−	1.52571i
$279$	0.575969	−	0.169120i	0.0344824	−	0.0101249i
$280$	11.5634	−	13.3449i	0.691047	−	0.797511i
$281$	0.493916	+	0.317420i	0.0294645	+	0.0189357i	0.555290	−	0.831657i	$-0.312607\pi$
$281$	0.493916	+	0.317420i	0.0294645	+	0.0189357i	−0.525826	+	0.850592i	$0.676244\pi$
$282$	11.0874	+	12.7955i	0.660243	+	0.761961i
$283$	0.758015	+	5.27211i	0.0450593	+	0.313395i	0.999869	+	0.0161771i	$0.00514954\pi$
$283$	0.758015	+	5.27211i	0.0450593	+	0.313395i	−0.954810	+	0.297217i	$0.903941\pi$
$284$	37.0559	+	10.8806i	2.19886	+	0.645645i
$285$	−6.69307	+	4.30138i	−0.396464	+	0.254792i
$286$	0.745983	−	5.18843i	0.0441109	−	0.306798i
$287$	−10.6198	+	23.2542i	−0.626868	+	1.37265i
$288$	−2.99103	+	6.54943i	−0.176248	+	0.385929i
$289$	2.17232	−	15.1088i	0.127784	−	0.888756i
$290$	−7.37281	+	4.73822i	−0.432946	+	0.278238i
$291$	0.302869	+	0.0889303i	0.0177545	+	0.00521319i
$292$	−5.81967	−	40.4767i	−0.340570	−	2.36872i
$293$	−11.4948	−	13.2657i	−0.671533	−	0.774990i	0.313082	−	0.949726i	$-0.398638\pi$
$293$	−11.4948	−	13.2657i	−0.671533	−	0.774990i	−0.984615	+	0.174736i	$0.944093\pi$
$294$	−3.78713	−	2.43384i	−0.220870	−	0.141945i
$295$	−6.83928	+	7.89296i	−0.398199	+	0.459546i
$296$	14.5401	−	4.26936i	0.845127	−	0.248152i
$297$	2.48357	+	5.43826i	0.144111	+	0.315560i
$298$	17.3751			1.00651
$299$	1.48893	+	1.19338i	0.0861068	+	0.0690148i
$300$	−13.4009			−0.773700
$301$	−9.46177	−	20.7184i	−0.545367	−	1.19419i
$302$	−17.4031	+	5.11000i	−1.00143	+	0.294048i
$303$	−0.329744	+	0.380545i	−0.0189433	+	0.0218617i
$304$	3.34424	+	2.14921i	0.191805	+	0.123266i
$305$	−0.388159	−	0.447959i	−0.0222259	−	0.0256501i
$306$	0.413175	+	2.87370i	0.0236197	+	0.164278i
$307$	14.4658	+	4.24754i	0.825607	+	0.242420i	0.667129	−	0.744942i	$-0.267523\pi$
$307$	14.4658	+	4.24754i	0.825607	+	0.242420i	0.158478	+	0.987362i	$0.449341\pi$
$308$	−43.1938	+	27.7589i	−2.46119	+	1.58171i
$309$	2.31645	−	16.1113i	0.131778	−	0.916538i
$310$	1.71076	−	3.74604i	0.0971646	−	0.212761i
$311$	1.36422	−	2.98723i	0.0773580	−	0.169390i	−0.867001	−	0.498306i	$-0.833956\pi$
$311$	1.36422	−	2.98723i	0.0773580	−	0.169390i	0.944359	+	0.328915i	$0.106683\pi$
$312$	0.106800	−	0.742807i	0.00604633	−	0.0420532i
$313$	−25.7975	+	16.5790i	−1.45816	+	0.937101i	−0.459352	+	0.888254i	$0.651918\pi$
$313$	−25.7975	+	16.5790i	−1.45816	+	0.937101i	−0.998806	+	0.0488470i	$0.984445\pi$
$314$	0.170122	+	0.0499524i	0.00960056	+	0.00281898i
$315$	1.33235	+	9.26669i	0.0750693	+	0.522119i
$316$	−9.44481	−	10.8999i	−0.531312	−	0.613167i
$317$	−5.63055	−	3.61854i	−0.316243	−	0.203237i	0.372883	−	0.927878i	$-0.378369\pi$
$317$	−5.63055	−	3.61854i	−0.316243	−	0.203237i	−0.689127	+	0.724641i	$0.742006\pi$
$318$	−4.05394	+	4.67850i	−0.227334	+	0.262357i
$319$	7.32812	−	2.15173i	0.410296	−	0.120474i
$320$	16.4961	+	36.1213i	0.922158	+	2.01924i
$321$	−0.430290			−0.0240165
$322$	−1.21822	−	31.7566i	−0.0678887	−	1.76973i
$323$	3.36692			0.187341
$324$	1.18639	+	2.59784i	0.0659107	+	0.144324i
$325$	−1.79134	+	0.525985i	−0.0993656	+	0.0291764i
$326$	4.25913	−	4.91530i	0.235891	−	0.272233i
$327$	3.93175	+	2.52678i	0.217426	+	0.139731i
$328$	10.5003	+	12.1179i	0.579780	+	0.669101i
$329$	−3.28812	−	22.8694i	−0.181280	−	1.26083i
$330$	39.3537	+	11.5553i	2.16635	+	0.636097i
$331$	−17.4067	+	11.1866i	−0.956758	+	0.614871i	−0.923099	−	0.384563i	$-0.874352\pi$
$331$	−17.4067	+	11.1866i	−0.956758	+	0.614871i	−0.0336587	+	0.999433i	$0.510716\pi$
$332$	−3.31682	+	23.0690i	−0.182034	+	1.26608i
$333$	−3.33763	+	7.30839i	−0.182901	+	0.400497i
$334$	−11.7167	+	25.6561i	−0.641111	+	1.40384i
$335$	3.98834	−	27.7395i	0.217906	−	1.51557i
$336$	3.93519	−	2.52899i	0.214682	−	0.137968i
$337$	27.1107	+	7.96043i	1.47682	+	0.433632i	0.918308	−	0.395867i	$-0.129556\pi$
$337$	27.1107	+	7.96043i	1.47682	+	0.433632i	0.558507	+	0.829500i	$0.311374\pi$
$338$	4.02725	+	28.0101i	0.219053	+	1.52355i
$339$	−0.945120	−	1.09073i	−0.0513319	−	0.0592401i
$340$	9.85451	+	6.33311i	0.534436	+	0.343461i
$341$	−2.35018	+	2.71225i	−0.127269	+	0.146876i
$342$	5.40335	−	1.58657i	0.292179	−	0.0857916i
$343$	−6.19247	−	13.5596i	−0.334362	−	0.732150i
$344$	−14.2859			−0.770241
$345$	−10.9007	+	10.2028i	−0.586875	+	0.549302i
$346$	17.4819			0.939832
$347$	10.7181	+	23.4693i	0.575375	+	1.25990i	0.943886	+	0.330273i	$0.107141\pi$
$347$	10.7181	+	23.4693i	0.575375	+	1.25990i	−0.368510	+	0.929624i	$0.620132\pi$
$348$	3.50062	−	1.02787i	0.187653	−	0.0550999i
$349$	−13.5165	+	15.5989i	−0.723523	+	0.834990i	−0.991726	−	0.128372i	$-0.959025\pi$
$349$	−13.5165	+	15.5989i	−0.723523	+	0.834990i	0.268203	+	0.963362i	$0.413570\pi$
$350$	26.1579	+	16.8107i	1.39820	+	0.898569i
$351$	0.260554	+	0.300696i	0.0139074	+	0.0160499i
$352$	−6.12607	−	42.6078i	−0.326521	−	2.27100i
$353$	13.0550	+	3.83330i	0.694849	+	0.204026i	0.610039	−	0.792371i	$-0.291154\pi$
$353$	13.0550	+	3.83330i	0.694849	+	0.204026i	0.0848097	+	0.996397i	$0.472972\pi$
$354$	6.21886	−	3.99662i	0.330529	−	0.212418i
$355$	−5.99147	+	41.6716i	−0.317994	+	2.21170i
$356$	0.514630	−	1.12688i	0.0272753	−	0.0597247i
$357$	1.64583	−	3.60386i	0.0871064	−	0.190737i
$358$	2.57191	−	17.8880i	0.135930	−	0.945412i
$359$	−18.5260	+	11.9059i	−0.977765	+	0.628372i	−0.928860	−	0.370432i	$-0.879210\pi$
$359$	−18.5260	+	11.9059i	−0.977765	+	0.628372i	−0.0489057	+	0.998803i	$0.515573\pi$
$360$	5.63411	+	1.65432i	0.296944	+	0.0871905i
$361$	1.77454	+	12.3422i	0.0933971	+	0.649591i
$362$	−25.4893	−	29.4163i	−1.33969	−	1.54608i
$363$	−20.8149	−	13.3769i	−1.09250	−	0.702107i
$364$	−2.23768	+	2.58242i	−0.117286	+	0.135356i
$365$	42.7718	−	12.5589i	2.23878	−	0.657364i
$366$	0.174287	+	0.381635i	0.00911013	+	0.0199484i
$367$	31.5977			1.64939			0.824694	−	0.565580i	$-0.191348\pi$
$367$	31.5977			1.64939			0.824694	+	0.565580i	$0.191348\pi$
$368$	6.89982	+	2.83666i	0.359678	+	0.147871i
$369$	−8.50121			−0.442556
$370$	22.8975	+	50.1385i	1.19038	+	2.60658i
$371$	8.10566	−	2.38004i	0.420825	−	0.123565i
$372$	−1.12267	+	1.29563i	−0.0582078	+	0.0671754i
$373$	−5.26894	−	3.38614i	−0.272816	−	0.175328i	0.397078	−	0.917785i	$-0.370024\pi$
$373$	−5.26894	−	3.38614i	−0.272816	−	0.175328i	−0.669894	+	0.742457i	$0.733660\pi$
$374$	−11.3665	−	13.1176i	−0.587748	−	0.678297i
$375$	0.136325	+	0.948161i	0.00703979	+	0.0489628i
$376$	−13.9045	−	4.08273i	−0.717070	−	0.210551i
$377$	0.427595	−	0.274799i	0.0220223	−	0.0141529i
$378$	0.943061	−	6.55914i	0.0485058	−	0.337366i
$379$	8.84183	−	19.3609i	0.454174	−	0.994503i	−0.534603	−	0.845103i	$-0.679539\pi$
$379$	8.84183	−	19.3609i	0.454174	−	0.994503i	0.988777	−	0.149399i	$-0.0477340\pi$
$380$	9.43903	−	20.6686i	0.484212	−	1.06028i
$381$	−1.05662	+	7.34898i	−0.0541325	+	0.376500i
$382$	0.0418556	−	0.0268990i	0.00214152	−	0.00137627i
$383$	7.64276	+	2.24412i	0.390527	+	0.114669i	0.471100	−	0.882080i	$-0.343857\pi$
$383$	7.64276	+	2.24412i	0.390527	+	0.114669i	−0.0805735	+	0.996749i	$0.525675\pi$
$384$	−1.95074	−	13.5677i	−0.0995482	−	0.692373i
$385$	−36.6531	−	42.2999i	−1.86801	−	2.15580i
$386$	17.7239	+	11.3905i	0.902124	+	0.579760i
$387$	4.96004	−	5.72419i	0.252133	−	0.290977i
$388$	−0.864970	+	0.253978i	−0.0439122	+	0.0128938i
$389$	−12.9484	−	28.3530i	−0.656508	−	1.43755i	−0.885741	−	0.464181i	$-0.846349\pi$
$389$	−12.9484	−	28.3530i	−0.656508	−	1.43755i	0.229233	−	0.973372i	$-0.426378\pi$
$390$	2.72960			0.138219
$391$	6.21510	−	1.13829i	0.314311	−	0.0575659i
$392$	3.85316			0.194614
$393$	5.22567	+	11.4426i	0.263600	+	0.577203i
$394$	−31.6024	+	9.27931i	−1.59211	+	0.467485i
$395$	10.2958	−	11.8820i	0.518039	−	0.597848i
$396$	−14.3637	−	9.23101i	−0.721804	−	0.463876i
$397$	17.3640	+	20.0392i	0.871476	+	1.00574i	0.999902	+	0.0140175i	$0.00446205\pi$
$397$	17.3640	+	20.0392i	0.871476	+	1.00574i	−0.128426	+	0.991719i	$0.540992\pi$
$398$	−0.876070	−	6.09320i	−0.0439134	−	0.305425i
$399$	−7.37362	−	2.16509i	−0.369143	−	0.108390i
$400$	−6.14043	+	3.94622i	−0.307022	+	0.197311i
$401$	2.30791	−	16.0519i	0.115252	−	0.801593i	−0.847420	−	0.530923i	$-0.821845\pi$
$401$	2.30791	−	16.0519i	0.115252	−	0.801593i	0.962672	−	0.270671i	$-0.0872454\pi$
$402$	−8.24036	+	18.0439i	−0.410992	+	0.899947i
$403$	−0.0992176	+	0.217256i	−0.00494238	+	0.0108223i
$404$	0.204656	−	1.42341i	0.0101820	−	0.0708175i
$405$	−2.61903	+	1.68315i	−0.130141	+	0.0836363i
$406$	−8.12247	−	2.38497i	−0.403112	−	0.118364i
$407$	−6.83597	−	47.5452i	−0.338846	−	2.35673i
$408$	−1.62730	−	1.87800i	−0.0805633	−	0.0929750i
$409$	8.55796	+	5.49986i	0.423164	+	0.271951i	0.734844	−	0.678236i	$-0.237255\pi$
$409$	8.55796	+	5.49986i	0.423164	+	0.271951i	−0.311680	+	0.950187i	$0.600892\pi$
$410$	−38.1926	+	44.0766i	−1.88620	+	2.17679i
$411$	−12.3317	+	3.62092i	−0.608278	+	0.178607i
$412$	19.3109	+	42.2849i	0.951377	+	2.08323i
$413$	−10.0879			−0.496394
$414$	9.43779	−	4.75545i	0.463842	−	0.233718i
$415$	−25.4062			−1.24714
$416$	−1.19006	−	2.60587i	−0.0583476	−	0.127763i
$417$	−12.1768	+	3.57544i	−0.596301	+	0.175090i
$418$	−22.0477	+	25.4444i	−1.07839	+	1.24453i
$419$	−9.58470	−	6.15971i	−0.468243	−	0.300922i	0.285161	−	0.958480i	$-0.407953\pi$
$419$	−9.58470	−	6.15971i	−0.468243	−	0.300922i	−0.753404	+	0.657558i	$0.771589\pi$
$420$	−17.5091	−	20.2065i	−0.854355	−	0.985978i
$421$	2.90707	+	20.2191i	0.141682	+	0.985419i	0.929318	+	0.369279i	$0.120395\pi$
$421$	2.90707	+	20.2191i	0.141682	+	0.985419i	−0.787637	+	0.616140i	$0.788696\pi$
$422$	41.7045	+	12.2455i	2.03014	+	0.596104i
$423$	6.46354	−	4.15387i	0.314268	−	0.201968i
$424$	0.754072	−	5.24469i	0.0366210	−	0.254704i
$425$	−2.56813	+	5.62342i	−0.124573	+	0.272776i
$426$	12.3791	−	27.1063i	0.599767	−	1.31331i
$427$	0.0814800	−	0.566706i	0.00394309	−	0.0274248i
$428$	1.03380	−	0.664380i	0.0499704	−	0.0321140i
$429$	−2.28236	−	0.670163i	−0.110194	−	0.0323558i
$430$	−7.39496	−	51.4331i	−0.356617	−	2.48032i
$431$	14.9007	+	17.1963i	0.717741	+	0.828317i	0.991033	−	0.133614i	$-0.0426582\pi$
$431$	14.9007	+	17.1963i	0.717741	+	0.828317i	−0.273293	+	0.961931i	$0.588113\pi$
$432$	1.30862	+	0.840996i	0.0629608	+	0.0404624i
$433$	20.1774	−	23.2860i	0.969665	−	1.11905i	−0.0231911	−	0.999731i	$-0.507383\pi$
$433$	20.1774	−	23.2860i	0.969665	−	1.11905i	0.992856	−	0.119321i	$-0.0380719\pi$
$434$	3.81671	−	1.12069i	0.183208	−	0.0537947i
$435$	1.65216	+	3.61773i	0.0792151	+	0.173457i
$436$	−13.3477			−0.639237
$437$	−3.90116	−	11.6185i	−0.186618	−	0.555791i
$438$	−31.5528			−1.50765
$439$	−12.1468	−	26.5978i	−0.579736	−	1.26944i	−0.941449	−	0.337155i	$-0.890535\pi$
$439$	−12.1468	−	26.5978i	−0.579736	−	1.26944i	0.361713	−	0.932289i	$-0.382192\pi$
$440$	−33.6837	+	9.89042i	−1.60581	+	0.471507i
$441$	−1.33782	+	1.54392i	−0.0637055	+	0.0735201i
$442$	−0.971763	−	0.624514i	−0.0462220	−	0.0297051i
$443$	18.6536	+	21.5274i	0.886260	+	1.02280i	0.999572	+	0.0292388i	$0.00930832\pi$
$443$	18.6536	+	21.5274i	0.886260	+	1.02280i	−0.113313	+	0.993559i	$0.536146\pi$
$444$	−3.26552	−	22.7122i	−0.154975	−	1.07787i
$445$	1.29575	+	0.380467i	0.0614246	+	0.0180359i
$446$	38.1921	−	24.5446i	1.80845	−	1.16222i
$447$	1.12213	−	7.80455i	0.0530747	−	0.369143i
$448$	−15.9338	+	34.8903i	−0.752804	+	1.64841i
$449$	−14.5517	+	31.8638i	−0.686737	+	1.50375i	0.168606	+	0.985684i	$0.446073\pi$
$449$	−14.5517	+	31.8638i	−0.686737	+	1.50375i	−0.855343	+	0.518062i	$0.826654\pi$
$450$	−1.47154	+	10.2348i	−0.0693692	+	0.482473i
$451$	42.7565	−	27.4779i	2.01332	−	1.29388i
$452$	3.95481	+	1.16124i	0.186019	+	0.0546200i
$453$	1.17138	+	8.14714i	0.0550363	+	0.382786i
$454$	−5.61663	−	6.48194i	−0.263601	−	0.304212i
$455$	−3.13360	−	2.01384i	−0.146906	−	0.0944104i
$456$	−3.15649	+	3.64278i	−0.147816	+	0.170589i
$457$	−4.32314	+	1.26939i	−0.202228	+	0.0593795i	−0.381278	−	0.924460i	$-0.624516\pi$
$457$	−4.32314	+	1.26939i	−0.202228	+	0.0593795i	0.179050	+	0.983840i	$0.442698\pi$
$458$	−12.3045	−	26.9431i	−0.574951	−	1.25897i
$459$	1.31749			0.0614953
$460$	10.4361	−	41.3438i	0.486586	−	1.92767i
$461$	−36.1948			−1.68576			−0.842879	−	0.538103i	$-0.819141\pi$
$461$	−36.1948			−1.68576			−0.842879	+	0.538103i	$0.819141\pi$
$462$	16.4576	+	36.0371i	0.765676	+	1.67660i
$463$	−30.4402	+	8.93805i	−1.41468	+	0.415386i	−0.897698	−	0.440612i	$-0.854761\pi$
$463$	−30.4402	+	8.93805i	−1.41468	+	0.415386i	−0.516978	+	0.855998i	$0.672943\pi$
$464$	1.30134	−	1.50183i	0.0604132	−	0.0697206i
$465$	−1.57216	−	1.01037i	−0.0729074	−	0.0468547i
$466$	33.8067	+	39.0150i	1.56607	+	1.80734i
$467$	−4.00704	−	27.8696i	−0.185424	−	1.28965i	−0.843676	−	0.536853i	$-0.819613\pi$
$467$	−4.00704	−	27.8696i	−0.185424	−	1.28965i	0.658252	−	0.752798i	$-0.271296\pi$
$468$	−1.09028	−	0.320135i	−0.0503981	−	0.0147982i
$469$	22.7724	−	14.6349i	1.05153	−	0.675779i
$470$	7.50142	−	52.1735i	0.346015	−	2.40658i
$471$	0.0334246	−	0.0731896i	0.00154012	−	0.00337240i
$472$	−2.62845	+	5.75551i	−0.120984	+	0.264919i
$473$	−6.44437	+	44.8216i	−0.296312	+	2.06090i
$474$	−9.36183	+	6.01648i	−0.430003	+	0.276346i
$475$	11.5057	+	3.37838i	0.527919	+	0.155011i
$476$	1.61027	+	11.1997i	0.0738066	+	0.513336i
$477$	1.83968	+	2.12310i	0.0842330	+	0.0972101i
$478$	30.7986	+	19.7931i	1.40870	+	0.905315i
$479$	21.7290	−	25.0766i	0.992824	−	1.14578i	0.00350736	−	0.999994i	$-0.498884\pi$
$479$	21.7290	−	25.0766i	0.992824	−	1.14578i	0.989316	−	0.145786i	$-0.0465710\pi$
$480$	21.5077	−	6.31522i	0.981686	−	0.288249i
$481$	−1.32797	−	2.90784i	−0.0605501	−	0.132586i
$482$	34.5149			1.57211
$483$	−14.3431	−	1.50372i	−0.652635	−	0.0684216i
$484$	70.6633			3.21197
$485$	−0.408234	−	0.893907i	−0.0185369	−	0.0405902i
$486$	2.11435	−	0.620830i	0.0959090	−	0.0281614i
$487$	−17.8460	+	20.5954i	−0.808681	+	0.933268i	−0.998824	−	0.0484885i	$-0.984560\pi$
$487$	−17.8460	+	20.5954i	−0.808681	+	0.933268i	0.190142	+	0.981757i	$0.439105\pi$
$488$	−0.302095	−	0.194145i	−0.0136752	−	0.00878852i
$489$	−1.93279	−	2.23056i	−0.0874039	−	0.100869i
$490$	1.99456	+	13.8725i	0.0901051	+	0.626695i
$491$	−0.524771	−	0.154087i	−0.0236826	−	0.00695383i	0.269870	−	0.962897i	$-0.413019\pi$
$491$	−0.524771	−	0.154087i	−0.0236826	−	0.00695383i	−0.293552	+	0.955943i	$0.594838\pi$
$492$	20.4246	−	13.1261i	0.920813	−	0.591771i
$493$	0.239527	−	1.66595i	0.0107878	−	0.0750306i
$494$	−0.930791	+	2.03815i	−0.0418783	+	0.0917007i
$495$	7.73196	−	16.9306i	0.347526	−	0.760976i
$496$	−0.132890	+	0.924271i	−0.00596694	+	0.0415010i
$497$	−34.2098	+	21.9853i	−1.53452	+	0.986175i
$498$	17.2545	+	5.06639i	0.773194	+	0.227030i
$499$	0.887321	+	6.17145i	0.0397219	+	0.276272i	0.999996	−	0.00278614i	$-0.000886857\pi$
$499$	0.887321	+	6.17145i	0.0397219	+	0.276272i	−0.960274	+	0.279058i	$0.909978\pi$
$500$	−1.79152	−	2.06752i	−0.0801190	−	0.0924622i
$501$	10.7675	+	6.91986i	0.481057	+	0.309156i
$502$	−20.2915	+	23.4176i	−0.905654	+	1.04518i
$503$	14.1498	−	4.15474i	0.630907	−	0.185251i	0.0493823	−	0.998780i	$-0.484275\pi$
$503$	14.1498	−	4.15474i	0.630907	−	0.185251i	0.581524	+	0.813529i	$0.302457\pi$
$504$	2.35617	+	5.15929i	0.104952	+	0.229813i
$505$	1.56762			0.0697583
$506$	−32.0962	+	54.4225i	−1.42685	+	2.41937i
$507$	12.8417			0.570320
$508$	−8.80843	−	19.2878i	−0.390811	−	0.855757i
$509$	−9.39815	+	2.75955i	−0.416566	+	0.122315i	−0.483297	−	0.875456i	$-0.660561\pi$
$509$	−9.39815	+	2.75955i	−0.416566	+	0.122315i	0.0667317	+	0.997771i	$0.478743\pi$
$510$	5.91898	−	6.83087i	0.262097	−	0.302476i
$511$	36.2228	+	23.2790i	1.60240	+	1.02980i
$512$	−11.1772	−	12.8992i	−0.493967	−	0.570069i
$513$	−0.363693	−	2.52954i	−0.0160575	−	0.111682i
$514$	−10.1452	−	2.97891i	−0.447487	−	0.131394i
$515$	−42.6298	+	27.3965i	−1.87849	+	1.20724i
$516$	−3.07845	+	21.4111i	−0.135521	+	0.942572i
$517$	−19.0818	+	41.7833i	−0.839217	+	1.83763i
$518$	−22.1171	+	48.4297i	−0.971769	+	2.12788i
$519$	1.12902	−	7.85252i	0.0495586	−	0.344687i
$520$	−1.96544	+	1.26311i	−0.0861902	+	0.0553911i
$521$	−5.52568	−	1.62249i	−0.242084	−	0.0710824i	0.158440	−	0.987369i	$-0.449354\pi$
$521$	−5.52568	−	1.62249i	−0.242084	−	0.0710824i	−0.400524	+	0.916286i	$0.631172\pi$
$522$	−0.400629	−	2.78644i	−0.0175351	−	0.121959i
$523$	10.9529	+	12.6404i	0.478939	+	0.552725i	0.942876	−	0.333143i	$-0.108109\pi$
$523$	10.9529	+	12.6404i	0.478939	+	0.552725i	−0.463937	+	0.885868i	$0.653564\pi$
$524$	−30.2227	−	19.4229i	−1.32028	−	0.848494i
$525$	9.24038	−	10.6640i	0.403283	−	0.465414i
$526$	−46.7846	+	13.7372i	−2.03991	+	0.598971i
$527$	0.328540	+	0.719402i	0.0143114	+	0.0313376i
$528$	−9.29992			−0.404727
$529$	−11.1293	−	20.1281i	−0.483881	−	0.875134i
$530$	19.2727			0.837152
$531$	−1.39357	−	3.05150i	−0.0604760	−	0.132424i
$532$	21.0585	−	6.18333i	0.913001	−	0.268081i
$533$	2.21503	−	2.55628i	0.0959435	−	0.110725i
$534$	−0.804136	−	0.516787i	−0.0347984	−	0.0223636i
$535$	0.877252	+	1.01240i	0.0379269	+	0.0437700i
$536$	−2.41629	−	16.8056i	−0.104368	−	0.725893i
$537$	−7.86886	−	2.31051i	−0.339566	−	0.0997057i
$538$	4.43967	−	2.85320i	0.191408	−	0.123010i
$539$	1.73817	−	12.0892i	0.0748682	−	0.520720i
$540$	3.69353	−	8.08771i	0.158944	−	0.348040i
$541$	−2.56585	+	5.61842i	−0.110314	+	0.241555i	−0.956735	−	0.290960i	$-0.906025\pi$
$541$	−2.56585	+	5.61842i	−0.110314	+	0.241555i	0.846421	+	0.532514i	$0.178753\pi$
$542$	3.13249	−	21.7869i	0.134552	−	0.935828i
$543$	−14.8594	+	9.54954i	−0.637677	+	0.409810i
$544$	−9.10181	−	2.67253i	−0.390237	−	0.114584i
$545$	−2.07073	−	14.4022i	−0.0887001	−	0.616923i
$546$	1.72659	+	1.99259i	0.0738910	+	0.0852748i
$547$	9.75579	+	6.26967i	0.417128	+	0.268072i	0.732326	−	0.680954i	$-0.238435\pi$
$547$	9.75579	+	6.26967i	0.417128	+	0.268072i	−0.315198	+	0.949026i	$0.602071\pi$
$548$	24.0368	−	27.7400i	1.02680	−	1.18499i
$549$	0.182679	−	0.0536394i	0.00779655	−	0.00228927i
$550$	−25.6802	−	56.2318i	−1.09501	−	2.39773i
$551$	−3.26469			−0.139080
$552$	−4.59509	+	7.79145i	−0.195580	+	0.331626i
$553$	15.1863			0.645787
$554$	11.7124	+	25.6465i	0.497612	+	1.08962i
$555$	24.0000	−	7.04704i	1.01874	−	0.299130i
$556$	23.7349	−	27.3915i	1.00658	−	1.16166i
$557$	−12.0874	−	7.76808i	−0.512158	−	0.329144i	0.258905	−	0.965903i	$-0.416638\pi$
$557$	−12.0874	−	7.76808i	−0.512158	−	0.329144i	−0.771063	+	0.636759i	$0.780275\pi$
$558$	0.866248	+	0.999703i	0.0366712	+	0.0423208i
$559$	0.428880	+	2.98292i	0.0181397	+	0.126164i
$560$	−13.9732	−	4.10289i	−0.590474	−	0.173379i
$561$	−6.62627	+	4.25845i	−0.279761	+	0.179792i
$562$	−0.184125	+	1.28061i	−0.00776683	+	0.0540195i
$563$	−6.06240	+	13.2748i	−0.255500	+	0.559466i	−0.993302	−	0.115551i	$-0.963137\pi$
$563$	−6.06240	+	13.2748i	−0.255500	+	0.559466i	0.737802	+	0.675017i	$0.235864\pi$
$564$	−9.11532	+	19.9598i	−0.383824	+	0.840458i
$565$	−0.639443	+	4.44742i	−0.0269016	+	0.187104i
$566$	−9.87394	+	6.34560i	−0.415033	+	0.266725i
$567$	−2.88533	−	0.847210i	−0.121173	−	0.0355795i
$568$	3.62986	+	25.2462i	0.152305	+	1.05931i
$569$	28.8440	+	33.2877i	1.20920	+	1.39549i	0.894957	+	0.446153i	$0.147206\pi$
$569$	28.8440	+	33.2877i	1.20920	+	1.39549i	0.314246	+	0.949342i	$0.398248\pi$
$570$	−14.7490	−	9.47858i	−0.617766	−	0.397014i
$571$	−1.76983	+	2.04249i	−0.0740650	+	0.0854756i	−0.791573	−	0.611075i	$-0.790737\pi$
$571$	−1.76983	+	2.04249i	−0.0740650	+	0.0854756i	0.717508	+	0.696551i	$0.245283\pi$
$572$	6.51825	−	1.91393i	0.272542	−	0.0800255i
$573$	−0.00937936	−	0.0205379i	−0.000391828	−	0.000857985i
$574$	−56.3340			−2.35134
$575$	22.3809	+	2.34639i	0.933347	+	0.0978511i
$576$	−12.7551			−0.531463
$577$	−16.0523	−	35.1497i	−0.668266	−	1.46330i	−0.874614	−	0.484820i	$-0.838885\pi$
$577$	−16.0523	−	35.1497i	−0.668266	−	1.46330i	0.206347	−	0.978479i	$-0.433842\pi$
$578$	32.2739	−	9.47648i	1.34242	−	0.394170i
$579$	6.26104	−	7.22562i	0.260200	−	0.300287i
$580$	−9.55529	−	6.14081i	−0.396762	−	0.254983i
$581$	−16.0705	−	18.5463i	−0.666715	−	0.769430i
$582$	0.0989917	+	0.688503i	0.00410334	+	0.0285394i
$583$	−16.1149	−	4.73177i	−0.667412	−	0.195970i
$584$	22.7195	−	14.6009i	0.940139	−	0.604191i
$585$	0.176284	−	1.22608i	0.00728845	−	0.0506923i
$586$	16.0683	−	35.1847i	0.663776	−	1.45347i
$587$	13.1832	−	28.8671i	0.544128	−	1.19147i	−0.415343	−	0.909665i	$-0.636338\pi$
$587$	13.1832	−	28.8671i	0.544128	−	1.19147i	0.959471	−	0.281809i	$-0.0909344\pi$
$588$	0.830317	−	5.77498i	0.0342417	−	0.238156i
$589$	1.29053	−	0.829376i	0.0531755	−	0.0341738i
$590$	−22.0820	−	6.48387i	−0.909104	−	0.266937i
$591$	2.12712	+	14.7945i	0.0874982	+	0.608564i
$592$	−8.18446	−	9.44537i	−0.336379	−	0.388202i
$593$	14.8258	+	9.52798i	0.608824	+	0.391267i	0.808416	−	0.588612i	$-0.200325\pi$
$593$	14.8258	+	9.52798i	0.608824	+	0.391267i	−0.199592	+	0.979879i	$0.563962\pi$
$594$	−8.62738	+	9.95652i	−0.353986	+	0.408521i
$595$	−11.8347	+	3.47498i	−0.485176	+	0.142460i
$596$	9.35448	+	20.4835i	0.383174	+	0.839035i
$597$	−2.79353			−0.114331
$598$	−1.02911	+	4.07696i	−0.0420836	+	0.166719i
$599$	33.4175			1.36540			0.682701	−	0.730698i	$-0.260805\pi$
$599$	33.4175			1.36540			0.682701	+	0.730698i	$0.260805\pi$
$600$	−3.67654	−	8.05049i	−0.150094	−	0.328660i
$601$	36.7785	−	10.7992i	1.50023	−	0.440507i	0.574439	−	0.818547i	$-0.305220\pi$
$601$	36.7785	−	10.7992i	1.50023	−	0.440507i	0.925789	+	0.378041i	$0.123402\pi$
$602$	32.8681	−	37.9318i	1.33960	−	1.54599i
$603$	7.57278	+	4.86673i	0.308387	+	0.198188i
$604$	−15.3937	−	17.7653i	−0.626362	−	0.722860i
$605$	10.9626	+	76.2462i	0.445691	+	3.09985i
$606$	−1.06465	−	0.312608i	−0.0432483	−	0.0126988i
$607$	−15.3194	+	9.84521i	−0.621797	+	0.399605i	−0.813264	−	0.581894i	$-0.802312\pi$
$607$	−15.3194	+	9.84521i	−0.621797	+	0.399605i	0.191467	+	0.981499i	$0.438675\pi$
$608$	−2.61862	+	18.2129i	−0.106199	+	0.738632i
$609$	−1.59585	+	3.49443i	−0.0646672	+	0.141601i
$610$	0.542598	−	1.18812i	0.0219692	−	0.0481058i
$611$	−0.435054	+	3.02587i	−0.0176004	+	0.122413i
$612$	−3.16535	+	2.03425i	−0.127952	+	0.0822295i
$613$	7.35039	+	2.15827i	0.296879	+	0.0871716i	0.426780	−	0.904355i	$-0.359648\pi$
$613$	7.35039	+	2.15827i	0.296879	+	0.0871716i	−0.129901	+	0.991527i	$0.541466\pi$
$614$	4.72810	+	32.8847i	0.190811	+	1.32712i
$615$	17.3318	+	20.0020i	0.698886	+	0.806557i
$616$	−28.5263	−	18.3327i	−1.14936	−	0.738646i
$617$	1.08898	−	1.25675i	0.0438406	−	0.0505948i	−0.733406	−	0.679791i	$-0.762070\pi$
$617$	1.08898	−	1.25675i	0.0438406	−	0.0505948i	0.777246	+	0.629196i	$0.216616\pi$
$618$	34.4152	−	10.1052i	1.38438	−	0.406492i
$619$	−6.39067	−	13.9936i	−0.256863	−	0.562451i	0.736637	−	0.676289i	$-0.236413\pi$
$619$	−6.39067	−	13.9936i	−0.256863	−	0.562451i	−0.993499	+	0.113838i	$0.963685\pi$
$620$	5.33725			0.214349
$621$	−1.52654	−	4.54639i	−0.0612580	−	0.182440i
$622$	7.23667			0.290164
$623$	0.541880	+	1.18655i	0.0217100	+	0.0475382i
$624$	−0.593849	+	0.174370i	−0.0237730	+	0.00698038i
$625$	17.3170	−	19.9849i	0.692679	−	0.799395i
$626$	−56.8477	−	36.5338i	−2.27209	−	1.46018i
$627$	10.0053	+	11.5467i	0.399571	+	0.461130i
$628$	0.0327024	+	0.227450i	0.00130497	+	0.00907626i
$629$	−10.1565	−	2.98223i	−0.404968	−	0.118909i
$630$	−17.3552	+	11.1535i	−0.691449	+	0.444367i
$631$	−1.78897	+	12.4426i	−0.0712180	+	0.495332i	0.922727	+	0.385454i	$0.125955\pi$
$631$	−1.78897	+	12.4426i	−0.0712180	+	0.495332i	−0.993945	+	0.109878i	$0.964954\pi$
$632$	3.95685	−	8.66430i	0.157395	−	0.344648i
$633$	8.19384	−	17.9420i	0.325676	−	0.713131i
$634$	2.09899	−	14.5988i	0.0833615	−	0.579792i
$635$	19.4451	−	12.4966i	0.771656	−	0.495913i
$636$	−7.69805	−	2.26035i	−0.305248	−	0.0896288i
$637$	−0.115677	−	0.804551i	−0.00458329	−	0.0318775i
$638$	11.0214	+	12.7193i	0.436340	+	0.503563i
$639$	−11.3762	−	7.31102i	−0.450035	−	0.289220i
$640$	−27.9455	+	32.2508i	−1.10464	+	1.27482i
$641$	4.03168	−	1.18381i	0.159242	−	0.0467576i	−0.201140	−	0.979563i	$-0.564465\pi$
$641$	4.03168	−	1.18381i	0.159242	−	0.0467576i	0.360382	+	0.932805i	$0.382646\pi$
$642$	−0.393894	−	0.862508i	−0.0155458	−	0.0340405i
$643$	−23.2446			−0.916678			−0.458339	−	0.888778i	$-0.651555\pi$
$643$	−23.2446			−0.916678			−0.458339	+	0.888778i	$0.651555\pi$
$644$	36.7820	−	18.5334i	1.44941	−	0.730320i
$645$	−23.5803			−0.928474
$646$	3.08213	+	6.74893i	0.121265	+	0.265533i
$647$	−47.5298	+	13.9560i	−1.86859	+	0.548667i	−0.870152	+	0.492784i	$0.835979\pi$
$647$	−47.5298	+	13.9560i	−1.86859	+	0.548667i	−0.998437	+	0.0558835i	$0.982202\pi$
$648$	−1.23515	+	1.42544i	−0.0485212	+	0.0559964i
$649$	16.8721	+	10.8430i	0.662287	+	0.425626i
$650$	−2.69414	−	3.10921i	−0.105673	−	0.121953i
$651$	−0.256898	−	1.78677i	−0.0100686	−	0.0700290i
$652$	8.08768	+	2.37476i	0.316738	+	0.0930027i
$653$	23.6782	−	15.2170i	0.926598	−	0.595488i	0.0120330	−	0.999928i	$-0.496170\pi$
$653$	23.6782	−	15.2170i	0.926598	−	0.595488i	0.914565	+	0.404439i	$0.132533\pi$
$654$	−1.46570	+	10.1942i	−0.0573133	+	0.398623i
$655$	16.2688	−	35.6237i	0.635674	−	1.39193i
$656$	5.49349	−	12.0291i	0.214485	−	0.469656i
$657$	−2.03776	+	14.1729i	−0.0795004	+	0.552937i
$658$	42.8312	−	27.5259i	1.66973	−	1.07307i
$659$	14.3070	+	4.20090i	0.557320	+	0.163644i	0.548249	−	0.836315i	$-0.315294\pi$
$659$	14.3070	+	4.20090i	0.557320	+	0.163644i	0.00907087	+	0.999959i	$0.497113\pi$
$660$	7.56492	+	52.6151i	0.294464	+	2.04804i
$661$	−17.4317	−	20.1173i	−0.678015	−	0.782471i	0.307593	−	0.951518i	$-0.400476\pi$
$661$	−17.4317	−	20.1173i	−0.678015	−	0.782471i	−0.985608	+	0.169047i	$0.945931\pi$
$662$	−38.3576	−	24.6510i	−1.49081	−	0.958086i
$663$	−0.343278	+	0.396164i	−0.0133318	+	0.0153858i
$664$	−14.7685	+	4.33643i	−0.573130	+	0.168286i
$665$	9.93882	+	21.7630i	0.385411	+	0.843932i
$666$	−17.7048			−0.686048
$667$	−6.02638	+	1.10373i	−0.233342	+	0.0427365i
$668$	−36.5540			−1.41432
$669$	−8.55841	−	18.7403i	−0.330887	−	0.724542i
$670$	59.2543	−	17.3986i	2.28919	−	0.672167i
$671$	−0.745401	+	0.860238i	−0.0287759	+	0.0332091i
$672$	18.2146	+	11.7058i	0.702642	+	0.451561i
$673$	−27.3534	−	31.5675i	−1.05439	−	1.21684i	−0.975511	−	0.219952i	$-0.929410\pi$
$673$	−27.3534	−	31.5675i	−1.05439	−	1.21684i	−0.0788835	−	0.996884i	$-0.525136\pi$
$674$	8.86105	+	61.6300i	0.341315	+	2.37390i
$675$	4.50224	+	1.32198i	0.173291	+	0.0508829i
$676$	−30.8529	+	19.8279i	−1.18665	+	0.762613i
$677$	5.42984	−	37.7653i	0.208686	−	1.45144i	−0.568767	−	0.822498i	$-0.692580\pi$
$677$	5.42984	−	37.7653i	0.208686	−	1.45144i	0.777453	−	0.628941i	$-0.216511\pi$
$678$	1.32116	−	2.89294i	0.0507389	−	0.111103i
$679$	0.394320	−	0.863441i	0.0151326	−	0.0331358i
$680$	−1.10099	+	7.65753i	−0.0422209	+	0.293653i
$681$	−3.27430	+	2.10426i	−0.125471	+	0.0806355i
$682$	−7.58803	−	2.22805i	−0.290561	−	0.0853163i
$683$	−4.27715	−	29.7482i	−0.163661	−	1.13828i	−0.891660	−	0.452706i	$-0.850459\pi$
$683$	−4.27715	−	29.7482i	−0.163661	−	1.13828i	0.727999	−	0.685578i	$-0.240450\pi$
$684$	4.77948	+	5.51581i	0.182748	+	0.210902i
$685$	33.6606	+	21.6324i	1.28611	+	0.826530i
$686$	21.5113	−	24.8253i	0.821304	−	0.947836i
$687$	−12.8969	+	3.78689i	−0.492049	+	0.144479i
$688$	4.89445	+	10.7173i	0.186599	+	0.408595i
$689$	−1.11774			−0.0425826
$690$	−30.4300	−	12.5104i	−1.15845	−	0.476264i
$691$	−0.898924			−0.0341967			−0.0170983	−	0.999854i	$-0.505443\pi$
$691$	−0.898924			−0.0341967			−0.0170983	+	0.999854i	$0.505443\pi$
$692$	9.41197	+	20.6093i	0.357790	+	0.783450i
$693$	17.2500	−	5.06506i	0.655274	−	0.192406i
$694$	−37.2322	+	42.9682i	−1.41331	+	1.63105i
$695$	33.2378	+	21.3607i	1.26078	+	0.810256i
$696$	1.57789	+	1.82098i	0.0598096	+	0.0690240i
$697$	−1.59397	−	11.0863i	−0.0603758	−	0.419923i
$698$	−43.6409	−	12.8141i	−1.65183	−	0.485022i
$699$	19.7081	−	12.6656i	0.745430	−	0.479058i
$700$	−5.73505	+	39.8882i	−0.216765	+	1.50763i
$701$	−9.94289	+	21.7719i	−0.375538	+	0.822313i	0.623638	+	0.781714i	$0.285654\pi$
$701$	−9.94289	+	21.7719i	−0.375538	+	0.822313i	−0.999175	+	0.0405997i	$0.987073\pi$
$702$	−0.364223	+	0.797537i	−0.0137467	+	0.0301011i
$703$	−2.92207	+	20.3235i	−0.110208	+	0.766514i
$704$	64.1513	−	41.2275i	2.41779	−	1.55382i
$705$	−22.9509	−	6.73898i	−0.864380	−	0.253805i
$706$	4.26700	+	29.6776i	0.160590	+	1.11693i
$707$	0.991587	+	1.14435i	0.0372925	+	0.0430378i
$708$	8.05974	+	5.17968i	0.302904	+	0.194664i
$709$	2.92841	−	3.37956i	0.109979	−	0.126922i	−0.698091	−	0.716009i	$-0.745967\pi$
$709$	2.92841	−	3.37956i	0.109979	−	0.126922i	0.808070	+	0.589087i	$0.200512\pi$
$710$	−89.0145	+	26.1370i	−3.34065	+	0.980905i
$711$	2.09788	+	4.59371i	0.0786766	+	0.172278i
$712$	0.818157			0.0306617
$713$	2.10183	−	1.96727i	0.0787143	−	0.0736749i
$714$	8.73048			0.326730
$715$	3.07637	+	6.73632i	0.115050	+	0.251924i
$716$	22.4729	−	6.59863i	0.839850	−	0.246602i
$717$	10.8797	−	12.5559i	0.406311	−	0.468907i
$718$	−40.8242	−	26.2361i	−1.52355	−	0.979123i
$719$	−3.21986	−	3.71591i	−0.120080	−	0.138580i	0.692526	−	0.721393i	$-0.256498\pi$
$719$	−3.21986	−	3.71591i	−0.120080	−	0.138580i	−0.812607	+	0.582812i	$0.801952\pi$
$720$	−0.689206	−	4.79353i	−0.0256852	−	0.178644i
$721$	−46.9644	−	13.7900i	−1.74905	−	0.513566i
$722$	−23.1153	+	14.8553i	−0.860262	+	0.552857i
$723$	2.22906	−	15.5034i	0.0828996	−	0.576579i
$724$	20.9557	−	45.8866i	0.778812	−	1.70536i
$725$	2.49015	−	5.45267i	0.0924819	−	0.202507i
$726$	7.75950	−	53.9685i	0.287982	−	2.00296i
$727$	−24.0803	+	15.4755i	−0.893089	+	0.573954i	−0.904733	−	0.425978i	$-0.859930\pi$
$727$	−24.0803	+	15.4755i	−0.893089	+	0.573954i	0.0116439	+	0.999932i	$0.496294\pi$
$728$	−2.16528	−	0.635785i	−0.0802508	−	0.0235638i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	64.3280	+	74.2385i	2.38089	+	2.74769i
$731$	8.39482	+	5.39502i	0.310494	+	0.199542i
$732$	−0.356076	+	0.410933i	−0.0131609	+	0.0151885i
$733$	−12.0199	+	3.52937i	−0.443966	+	0.130360i	−0.496072	−	0.868281i	$-0.665225\pi$
$733$	−12.0199	+	3.52937i	−0.443966	+	0.130360i	0.0521061	+	0.998642i	$0.483407\pi$
$734$	28.9250	+	63.3370i	1.06764	+	2.33781i
$735$	6.36006			0.234594
$736$	1.32365	+	34.5050i	0.0487905	+	1.27187i
$737$	−53.8173			−1.98239
$738$	−7.78214	−	17.0405i	−0.286465	−	0.627270i
$739$	−5.50796	+	1.61728i	−0.202614	+	0.0594927i	−0.381465	−	0.924383i	$-0.624580\pi$
$739$	−5.50796	+	1.61728i	−0.202614	+	0.0594927i	0.178851	+	0.983876i	$0.442762\pi$
$740$	−46.7805	+	53.9876i	−1.71969	+	1.98462i
$741$	0.855384	+	0.549722i	0.0314233	+	0.0201945i
$742$	12.1908	+	14.0689i	0.447538	+	0.516486i
$743$	0.838499	+	5.83189i	0.0307615	+	0.213951i	0.999405	−	0.0345057i	$-0.0109857\pi$
$743$	0.838499	+	5.83189i	0.0307615	+	0.213951i	−0.968643	+	0.248457i	$0.920077\pi$
$744$	−1.08635	−	0.318981i	−0.0398275	−	0.0116944i
$745$	−20.6506	+	13.2713i	−0.756578	+	0.486223i
$746$	1.96419	−	13.6612i	0.0719140	−	0.500173i
$747$	3.39006	−	7.42320i	0.124036	−	0.271601i
$748$	9.34482	−	20.4623i	0.341680	−	0.748175i
$749$	−0.184147	+	1.28077i	−0.00672860	+	0.0467984i
$750$	−1.77578	+	1.14122i	−0.0648421	+	0.0416715i
$751$	27.9337	+	8.20207i	1.01931	+	0.299298i	0.748359	−	0.663294i	$-0.230842\pi$
$751$	27.9337	+	8.20207i	1.01931	+	0.299298i	0.270956	+	0.962592i	$0.412660\pi$
$752$	1.70090	+	11.8300i	0.0620255	+	0.431397i
$753$	9.20827	+	10.6269i	0.335568	+	0.387266i
$754$	0.942256	+	0.605551i	0.0343149	+	0.0220529i
$755$	16.7807	−	19.3660i	0.610713	−	0.704801i
$756$	8.24028	−	2.41956i	0.299696	−	0.0879987i
$757$	−8.82046	−	19.3141i	−0.320585	−	0.701983i	0.678895	−	0.734236i	$-0.262459\pi$
$757$	−8.82046	−	19.3141i	−0.320585	−	0.701983i	−0.999480	+	0.0322524i	$0.989732\pi$
$758$	46.9025			1.70357
$759$	22.3727	+	17.9317i	0.812076	+	0.650881i
$760$	15.0061			0.544330
$761$	4.56385	+	9.99345i	0.165440	+	0.362262i	0.974135	−	0.225965i	$-0.0725534\pi$
$761$	4.56385	+	9.99345i	0.165440	+	0.362262i	−0.808696	+	0.588227i	$0.799826\pi$
$762$	−15.6981	+	4.60939i	−0.568683	+	0.166980i
$763$	9.20368	−	10.6216i	0.333196	−	0.384528i
$764$	0.0542456	+	0.0348615i	0.00196254	+	0.00126125i
$765$	−2.68603	−	3.09984i	−0.0971136	−	0.112075i
$766$	2.49801	+	17.3741i	0.0902568	+	0.627750i
$767$	1.28068	+	0.376040i	0.0462425	+	0.0135780i
$768$	3.94983	−	2.53840i	0.142527	−	0.0915966i
$769$	−6.66647	+	46.3663i	−0.240399	+	1.67201i	0.409743	+	0.912201i	$0.365618\pi$
$769$	−6.66647	+	46.3663i	−0.240399	+	1.67201i	−0.650143	+	0.759812i	$0.725291\pi$
$770$	51.2365	−	112.192i	1.84644	−	4.04313i
$771$	−1.99327	+	4.36466i	−0.0717860	+	0.157189i
$772$	−3.88592	+	27.0272i	−0.139857	+	0.972729i
$773$	34.1685	−	21.9588i	1.22896	−	0.789802i	0.245228	−	0.969465i	$-0.421137\pi$
$773$	34.1685	−	21.9588i	1.22896	−	0.789802i	0.983728	+	0.179663i	$0.0575008\pi$
$774$	16.0145	+	4.70229i	0.575630	+	0.169020i
$775$	0.400862	+	2.78805i	0.0143994	+	0.100150i
$776$	−0.389881	−	0.449946i	−0.0139959	−	0.0161521i
$777$	20.3253	+	13.0623i	0.729166	+	0.468606i
$778$	44.9798	−	51.9095i	1.61260	−	1.86104i
$779$	−20.8453	+	6.12073i	−0.746860	+	0.219298i
$780$	1.46957	+	3.21792i	0.0526192	+	0.115220i
$781$	80.8469			2.89293
$782$	7.97107	+	11.4160i	0.285045	+	0.408236i
$783$	−1.27749			−0.0456537
$784$	−1.32012	−	2.89067i	−0.0471473	−	0.103238i
$785$	−0.240347	+	0.0705723i	−0.00857836	+	0.00251883i
$786$	−18.1528	+	20.9495i	−0.647490	+	0.747243i
$787$	−5.26443	−	3.38324i	−0.187657	−	0.120600i	0.443439	−	0.896304i	$-0.353758\pi$
$787$	−5.26443	−	3.38324i	−0.187657	−	0.120600i	−0.631096	+	0.775705i	$0.717395\pi$
$788$	−27.9536	−	32.2602i	−0.995806	−	1.14922i
$789$	3.14902	+	21.9019i	0.112108	+	0.779730i
$790$	33.2422	+	9.76078i	1.18270	+	0.347273i
$791$	−3.65106	+	2.34639i	−0.129817	+	0.0834281i
$792$	1.60477	−	11.1615i	0.0570232	−	0.396605i
$793$	−0.0314687	+	0.0689068i	−0.00111748	+	0.00244695i
$794$	−24.2728	+	53.1500i	−0.861409	+	1.88622i
$795$	1.24468	−	8.65692i	0.0441441	−	0.307029i
$796$	6.71160	−	4.31328i	0.237886	−	0.152880i
$797$	−46.9806	−	13.7947i	−1.66414	−	0.488635i	−0.691775	−	0.722113i	$-0.743171\pi$
$797$	−46.9806	−	13.7947i	−1.66414	−	0.488635i	−0.972362	+	0.233478i	$0.924989\pi$
$798$	−2.41004	−	16.7622i	−0.0853146	−	0.593376i
$799$	6.62889	+	7.65015i	0.234513	+	0.270643i
$800$	−28.4218	−	18.2656i	−1.00486	−	0.645786i
$801$	−0.284064	+	0.327827i	−0.0100369	+	0.0115832i
$802$	34.2884	−	10.0680i	1.21077	−	0.355513i
$803$	−35.5613	−	77.8684i	−1.25493	−	2.74792i
$804$	−25.7084			−0.906664
$805$	25.7040	+	36.8127i	0.905946	+	1.29748i
$806$	−0.526311			−0.0185385
$807$	−0.994879	−	2.17848i	−0.0350214	−	0.0766862i
$808$	0.911254	−	0.267568i	0.0320578	−	0.00941302i
$809$	−34.5027	+	39.8182i	−1.21305	+	1.39993i	−0.321563	+	0.946888i	$0.604208\pi$
$809$	−34.5027	+	39.8182i	−1.21305	+	1.39993i	−0.891487	+	0.453046i	$0.850337\pi$
$810$	−5.77134	−	3.70901i	−0.202784	−	0.130321i
$811$	−32.7679	−	37.8162i	−1.15064	−	1.32791i	−0.936323	−	0.351141i	$-0.885794\pi$
$811$	−32.7679	−	37.8162i	−1.15064	−	1.32791i	−0.214314	−	0.976765i	$-0.568752\pi$
$812$	−1.56137	−	10.8596i	−0.0547935	−	0.381097i
$813$	−9.58396	−	2.81410i	−0.336124	−	0.0986949i
$814$	89.0456	−	57.2261i	3.12105	−	2.00578i
$815$	−1.30768	+	9.09508i	−0.0458059	+	0.318587i
$816$	−0.851365	+	1.86423i	−0.0298037	+	0.0652611i
$817$	8.04088	−	17.6071i	0.281315	−	0.615993i
$818$	−3.19028	+	22.1889i	−0.111546	+	0.775817i
$819$	1.00654	−	0.646863i	0.0351713	−	0.0226032i
$820$	−72.5242	−	21.2950i	−2.53265	−	0.743654i
$821$	2.53131	+	17.6056i	0.0883432	+	0.614441i	0.985108	+	0.171934i	$0.0550016\pi$
$821$	2.53131	+	17.6056i	0.0883432	+	0.614441i	−0.896765	+	0.442507i	$0.854089\pi$
$822$	−18.5467	−	21.4040i	−0.646890	−	0.746551i
$823$	−6.20749	−	3.98931i	−0.216380	−	0.139059i	0.427961	−	0.903797i	$-0.359232\pi$
$823$	−6.20749	−	3.98931i	−0.216380	−	0.139059i	−0.644341	+	0.764738i	$0.722868\pi$
$824$	−20.1044	+	23.2018i	−0.700371	+	0.808271i
$825$	−26.9167	+	7.90347i	−0.937121	+	0.275163i
$826$	−9.23464	−	20.2210i	−0.321314	−	0.703580i
$827$	37.1158			1.29064			0.645321	−	0.763912i	$-0.276724\pi$
$827$	37.1158			1.29064			0.645321	+	0.763912i	$0.276724\pi$
$828$	10.6874	+	8.56593i	0.371411	+	0.297687i
$829$	−47.1158			−1.63640			−0.818200	−	0.574933i	$-0.805028\pi$
$829$	−47.1158			−1.63640			−0.818200	+	0.574933i	$0.805028\pi$
$830$	−23.2572	−	50.9261i	−0.807269	−	1.76767i
$831$	12.2763	−	3.60466i	0.425862	−	0.125044i
$832$	3.32340	−	3.83541i	0.115218	−	0.132969i
$833$	−2.26424	−	1.45514i	−0.0784513	−	0.0504176i
$834$	−18.3137	−	21.1352i	−0.634153	−	0.731851i
$835$	−5.67090	−	39.4420i	−0.196250	−	1.36495i
$836$	−41.8665	−	12.2931i	−1.44798	−	0.425167i
$837$	0.504992	−	0.324538i	0.0174551	−	0.0112177i
$838$	3.57304	−	24.8510i	0.123429	−	0.858465i
$839$	−8.46878	+	18.5440i	−0.292375	+	0.640211i	−0.997635	−	0.0687374i	$-0.978103\pi$
$839$	−8.46878	+	18.5440i	−0.292375	+	0.640211i	0.705260	+	0.708949i	$0.250830\pi$
$840$	7.33533	−	16.0621i	0.253093	−	0.554196i
$841$	3.89488	−	27.0895i	0.134306	−	0.934119i
$842$	−37.8676	+	24.3360i	−1.30500	+	0.838675i
$843$	0.563336	+	0.165410i	0.0194023	+	0.00569704i
$844$	8.01681	+	55.7582i	0.275950	+	1.91928i
$845$	−26.1809	−	30.2144i	−0.900651	−	1.03941i
$846$	14.2432	+	9.15352i	0.489690	+	0.314705i
$847$	−48.7249	+	56.2315i	−1.67421	+	1.93214i
$848$	−4.19295	+	1.23116i	−0.143986	+	0.0422782i
$849$	2.21264	+	4.84500i	0.0759375	+	0.166280i
$850$	−13.6229			−0.467263
$851$	1.47704	+	38.5035i	0.0506322	+	1.31988i
$852$	38.6203			1.32311
$853$	−6.68087	−	14.6291i	−0.228749	−	0.500889i	0.760101	−	0.649804i	$-0.225149\pi$
$853$	−6.68087	−	14.6291i	−0.228749	−	0.500889i	−0.988850	+	0.148915i	$0.952422\pi$
$854$	1.21054	−	0.355446i	0.0414238	−	0.0121631i
$855$	−5.21012	+	6.01280i	−0.178182	+	0.205633i
$856$	0.682745	+	0.438773i	0.0233357	+	0.0149970i
$857$	21.3906	+	24.6860i	0.730688	+	0.843259i	0.992549	−	0.121847i	$-0.0388817\pi$
$857$	21.3906	+	24.6860i	0.730688	+	0.843259i	−0.261861	+	0.965106i	$0.584336\pi$
$858$	−0.745983	−	5.18843i	−0.0254675	−	0.177130i
$859$	−38.6173	−	11.3391i	−1.31760	−	0.386884i	−0.453977	−	0.891014i	$-0.649995\pi$
$859$	−38.6173	−	11.3391i	−1.31760	−	0.386884i	−0.863628	+	0.504130i	$0.831813\pi$
$860$	56.6530	−	36.4087i	1.93185	−	1.24153i
$861$	−3.63819	+	25.3041i	−0.123989	+	0.862363i
$862$	−20.8293	+	45.6099i	−0.709450	+	1.55348i
$863$	3.04816	−	6.67455i	0.103761	−	0.227204i	−0.850630	−	0.525765i	$-0.823779\pi$
$863$	3.04816	−	6.67455i	0.103761	−	0.227204i	0.954391	+	0.298561i	$0.0965065\pi$
$864$	−1.02468	+	7.12680i	−0.0348603	+	0.242459i
$865$	−20.7775	+	13.3529i	−0.706455	+	0.454011i
$866$	65.1470	+	19.1289i	2.21378	+	0.650026i
$867$	−2.17232	−	15.1088i	−0.0737760	−	0.513123i
$868$	3.37603	+	3.89615i	0.114590	+	0.132244i
$869$	−25.3991	−	16.3230i	−0.861606	−	0.553721i
$870$	−5.73925	+	6.62345i	−0.194579	+	0.224556i
$871$	−3.43652	+	1.00905i	−0.116442	+	0.0341905i
$872$	−3.66194	−	8.01852i	−0.124009	−	0.271541i
$873$	0.315655			0.0106833
$874$	19.7180	−	18.4556i	0.666970	−	0.624269i
$875$	2.88057			0.0973812
$876$	−16.9875	−	37.1975i	−0.573956	−	1.25679i
$877$	8.67530	−	2.54730i	0.292944	−	0.0860162i	−0.131958	−	0.991255i	$-0.542127\pi$
$877$	8.67530	−	2.54730i	0.292944	−	0.0860162i	0.424903	+	0.905239i	$0.360308\pi$
$878$	42.1954	−	48.6961i	1.42403	−	1.64341i
$879$	−14.7666	−	9.48989i	−0.498063	−	0.320086i
$880$	18.9601	+	21.8812i	0.639146	+	0.737614i
$881$	−5.86295	−	40.7777i	−0.197528	−	1.37384i	−0.811428	−	0.584452i	$-0.801310\pi$
$881$	−5.86295	−	40.7777i	−0.197528	−	1.37384i	0.613901	−	0.789383i	$-0.289600\pi$
$882$	−4.31942	−	1.26830i	−0.145442	−	0.0427057i
$883$	−8.94234	+	5.74690i	−0.300934	+	0.193398i	−0.682390	−	0.730989i	$-0.739059\pi$
$883$	−8.94234	+	5.74690i	−0.300934	+	0.193398i	0.381456	+	0.924387i	$0.375423\pi$
$884$	0.213056	−	1.48184i	0.00716585	−	0.0498396i
$885$	−4.33854	+	9.50008i	−0.145839	+	0.319342i
$886$	−26.0755	+	57.0973i	−0.876022	+	1.91822i
$887$	1.56339	−	10.8736i	0.0524935	−	0.365101i	−0.946595	−	0.322424i	$-0.895502\pi$
$887$	1.56339	−	10.8736i	0.0524935	−	0.365101i	0.999089	−	0.0426767i	$-0.0135885\pi$
$888$	12.7483	−	8.19284i	0.427805	−	0.274934i
$889$	21.4223	+	6.29015i	0.718481	+	0.210965i
$890$	0.423513	+	2.94560i	0.0141962	+	0.0987366i
$891$	3.91510	+	4.51827i	0.131161	+	0.151368i
$892$	49.4976	+	31.8102i	1.65730	+	1.06508i
$893$	12.8581	−	14.8391i	0.430281	−	0.496570i
$894$	16.6713	−	4.89513i	0.557571	−	0.163718i
$895$	10.6064	+	23.2247i	0.354531	+	0.776315i
$896$	−41.2195			−1.37705
$897$	1.76483	+	0.725558i	0.0589259	+	0.0242257i
$898$	−77.1911			−2.57590
$899$	−0.318564	−	0.697557i	−0.0106247	−	0.0232648i
$900$	−12.8580	+	3.77546i	−0.428601	+	0.125849i
$901$	−2.42376	+	2.79717i	−0.0807472	+	0.0931873i
$902$	94.2188	+	60.5508i	3.13714	+	2.01612i
$903$	−14.9155	−	17.2135i	−0.496358	−	0.572828i
$904$	0.387399	+	2.69442i	0.0128847	+	0.0896149i
$905$	52.7629	+	15.4926i	1.75390	+	0.514991i
$906$	−15.2585	+	9.80603i	−0.506929	+	0.325783i
$907$	1.93048	−	13.4268i	0.0641005	−	0.445829i	−0.932344	−	0.361573i	$-0.882240\pi$
$907$	1.93048	−	13.4268i	0.0641005	−	0.445829i	0.996444	−	0.0842554i	$-0.0268512\pi$
$908$	4.61763	−	10.1112i	0.153242	−	0.335552i
$909$	−0.209175	+	0.458030i	−0.00693790	+	0.0151919i
$910$	1.16816	−	8.12474i	0.0387242	−	0.269333i
$911$	3.17718	−	2.04185i	0.105265	−	0.0676495i	−0.486949	−	0.873430i	$-0.661890\pi$
$911$	3.17718	−	2.04185i	0.105265	−	0.0676495i	0.592214	+	0.805781i	$0.298254\pi$
$912$	3.81428	+	1.11997i	0.126303	+	0.0370860i
$913$	6.94336	+	48.2921i	0.229792	+	1.59824i
$914$	−6.50194	−	7.50363i	−0.215065	−	0.248198i
$915$	−0.498640	−	0.320457i	−0.0164845	−	0.0105940i
$916$	25.1386	−	29.0114i	0.830602	−	0.958565i
$917$	36.2957	−	10.6574i	1.19859	−	0.351938i
$918$	1.20605	+	2.64089i	0.0398057	+	0.0871623i
$919$	−18.2612			−0.602382			−0.301191	−	0.953564i	$-0.597384\pi$
$919$	−18.2612			−0.602382			−0.301191	+	0.953564i	$0.597384\pi$
$920$	27.7002	−	5.07328i	0.913249	−	0.167261i
$921$	15.0765			0.496788
$922$	−33.1332	−	72.5516i	−1.09118	−	2.38936i
$923$	5.16250	−	1.51585i	0.169926	−	0.0498947i
$924$	−33.6235	+	38.8036i	−1.10613	+	1.27654i
$925$	−31.7154	−	20.3822i	−1.04279	−	0.670163i
$926$	−45.7816	−	52.8347i	−1.50448	−	1.73626i
$927$	−2.31645	−	16.1113i	−0.0760822	−	0.529164i
$928$	8.82544	+	2.59138i	0.289709	+	0.0850663i
$929$	4.53409	−	2.91389i	0.148759	−	0.0956015i	−0.464144	−	0.885760i	$-0.653638\pi$
$929$	4.53409	−	2.91389i	0.148759	−	0.0956015i	0.612903	+	0.790158i	$0.290002\pi$
$930$	0.586080	−	4.07628i	0.0192183	−	0.133666i
$931$	−2.16878	+	4.74896i	−0.0710788	+	0.155641i
$932$	−27.7937	+	60.8598i	−0.910414	+	1.99353i
$933$	0.467362	−	3.25057i	0.0153007	−	0.106419i
$934$	52.1959	−	33.5443i	1.70790	−	1.09760i
$935$	23.5287	+	6.90865i	0.769470	+	0.225937i
$936$	−0.106800	−	0.742807i	−0.00349085	−	0.0242794i
$937$	−4.43568	−	5.11905i	−0.144908	−	0.167232i	0.678656	−	0.734456i	$-0.262563\pi$
$937$	−4.43568	−	5.11905i	−0.144908	−	0.167232i	−0.823563	+	0.567224i	$0.808017\pi$
$938$	50.1816	+	32.2498i	1.63849	+	1.05299i
$939$	−20.0816	+	23.1754i	−0.655339	+	0.756302i
$940$	65.5459	−	19.2460i	2.13787	−	0.627735i
$941$	1.31435	+	2.87802i	0.0428465	+	0.0938207i	0.929845	−	0.367952i	$-0.119941\pi$
$941$	1.31435	+	2.87802i	0.0428465	+	0.0938207i	−0.886998	+	0.461773i	$0.847214\pi$
$942$	0.177304			0.00577689
$943$	−36.4096	+	18.3458i	−1.18566	+	0.597422i
$944$	5.21835			0.169843
$945$	3.88911	+	8.51595i	0.126513	+	0.277024i
$946$	−95.7432	+	28.1127i	−3.11288	+	0.914024i
$947$	10.1676	−	11.7340i	0.330402	−	0.381305i	−0.566105	−	0.824333i	$-0.691550\pi$
$947$	10.1676	−	11.7340i	0.330402	−	0.381305i	0.896508	+	0.443028i	$0.146096\pi$
$948$	−12.1331	−	7.79746i	−0.394064	−	0.253250i
$949$	−3.73078	−	4.30555i	−0.121106	−	0.139764i
$950$	3.76061	+	26.1556i	0.122010	+	0.848600i
$951$	−6.42194	−	1.88565i	−0.208246	−	0.0611464i
$952$	−6.28636	+	4.04000i	−0.203742	+	0.130937i
$953$	−1.54155	+	10.7217i	−0.0499356	+	0.347310i	0.949502	+	0.313762i	$0.101590\pi$
$953$	−1.54155	+	10.7217i	−0.0499356	+	0.347310i	−0.999437	+	0.0335474i	$0.989320\pi$
$954$	−2.57164	+	5.63111i	−0.0832600	+	0.182314i
$955$	−0.0292003	+	0.0639397i	−0.000944899	+	0.00206904i
$956$	−6.75251	+	46.9647i	−0.218392	+	1.51895i
$957$	6.42507	−	4.12914i	0.207693	−	0.133476i
$958$	70.1566	+	20.5998i	2.26666	+	0.665550i
$959$	5.50029	+	38.2554i	0.177614	+	1.23533i
$960$	26.0044	+	30.0107i	0.839289	+	0.968591i
$961$	−25.7757	−	16.5650i	−0.831475	−	0.534356i
$962$	4.61307	−	5.32377i	0.148731	−	0.171645i
$963$	−0.412860	+	0.121227i	−0.0133042	+	0.00390648i
$964$	18.5823	+	40.6896i	0.598496	+	1.31052i
$965$	−29.7653			−0.958181
$966$	−10.1157	−	30.1270i	−0.325469	−	0.969322i
$967$	32.6916			1.05129			0.525646	−	0.850703i	$-0.323824\pi$
$967$	32.6916			1.05129			0.525646	+	0.850703i	$0.323824\pi$
$968$	19.3865	+	42.4506i	0.623106	+	1.36441i
$969$	3.23054	−	0.948572i	0.103780	−	0.0304725i
$970$	1.41811	−	1.63659i	0.0455329	−	0.0525478i
$971$	47.4661	+	30.5046i	1.52326	+	0.978940i	0.991220	+	0.132221i	$0.0422110\pi$
$971$	47.4661	+	30.5046i	1.52326	+	0.978940i	0.532041	+	0.846719i	$0.321425\pi$
$972$	1.87023	+	2.15836i	0.0599877	+	0.0692295i
$973$	5.43120	+	37.7749i	0.174116	+	1.21101i
$974$	−57.6196	−	16.9187i	−1.84625	−	0.542109i
$975$	−1.57059	+	1.00936i	−0.0502992	+	0.0323253i
$976$	−0.0421485	+	0.293149i	−0.00134914	+	0.00938348i
$977$	20.5183	−	44.9288i	0.656439	−	1.43740i	−0.229365	−	0.973340i	$-0.573665\pi$
$977$	20.5183	−	44.9288i	0.656439	−	1.43740i	0.885804	−	0.464060i	$-0.153608\pi$
$978$	2.70181	−	5.91613i	0.0863942	−	0.189177i
$979$	0.369072	−	2.56695i	0.0117956	−	0.0820401i
$980$	−15.2804	+	9.82011i	−0.488114	+	0.313692i
$981$	4.48436	+	1.31673i	0.143175	+	0.0420399i
$982$	−0.171520	−	1.19295i	−0.00547341	−	0.0380684i
$983$	−11.1189	−	12.8318i	−0.354636	−	0.409272i	0.550199	−	0.835033i	$-0.314552\pi$
$983$	−11.1189	−	12.8318i	−0.354636	−	0.409272i	−0.904836	+	0.425761i	$0.860006\pi$
$984$	13.4889	+	8.66882i	0.430012	+	0.276352i
$985$	30.4723	−	35.1669i	0.970929	−	1.12051i
$986$	3.55863	−	1.04491i	0.113330	−	0.0332766i
$987$	−9.59798	−	21.0166i	−0.305507	−	0.668967i
$988$	−2.90389			−0.0923852
$989$	8.89026	−	35.2198i	0.282694	−	1.11992i
$990$	41.0151			1.30354
$991$	15.5283	+	34.0022i	0.493272	+	1.08012i	0.978598	+	0.205782i	$0.0659738\pi$
$991$	15.5283	+	34.0022i	0.493272	+	1.08012i	−0.485326	+	0.874334i	$0.661299\pi$
$992$	−4.14703	+	1.21768i	−0.131668	+	0.0386613i
$993$	−13.5500	+	15.6375i	−0.429995	+	0.496241i
$994$	−75.3852	−	48.4471i	−2.39107	−	1.53665i
$995$	5.69529	+	6.57271i	0.180553	+	0.208369i
$996$	3.31682	+	23.0690i	0.105097	+	0.730969i
$997$	37.2528	+	10.9384i	1.17981	+	0.346423i	0.812100	−	0.583518i	$-0.198324\pi$
$997$	37.2528	+	10.9384i	1.17981	+	0.346423i	0.367709	+	0.929941i	$0.380142\pi$
$998$	−11.5583	+	7.42805i	−0.365871	+	0.235131i
$999$	−1.14342	+	7.95267i	−0.0361762	+	0.251611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.e.b.4.1	✓	10
3.2	odd	2		207.2.i.a.73.1		10
23.6	even	11	inner	69.2.e.b.52.1	yes	10
23.11	odd	22		1587.2.a.r.1.5		5
23.12	even	11		1587.2.a.q.1.5		5
69.11	even	22		4761.2.a.bm.1.1		5
69.29	odd	22		207.2.i.a.190.1		10
69.35	odd	22		4761.2.a.bp.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.b.4.1	✓	10	1.1	even	1	trivial
69.2.e.b.52.1	yes	10	23.6	even	11	inner
207.2.i.a.73.1		10	3.2	odd	2
207.2.i.a.190.1		10	69.29	odd	22
1587.2.a.q.1.5		5	23.12	even	11
1587.2.a.r.1.5		5	23.11	odd	22
4761.2.a.bm.1.1		5	69.11	even	22
4761.2.a.bp.1.1		5	69.35	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)

\(f(q)\)	\(=\)	\(q+(0.915415 + 2.00448i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-1.87023 + 2.15836i) q^{4} +(-2.61903 - 1.68315i) q^{5} +(1.44306 + 1.66538i) q^{6} +(-0.427961 - 2.97653i) q^{7} +(-1.80972 - 0.531382i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.915415 + 2.00448i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-1.87023 + 2.15836i) q^{4} +(-2.61903 - 1.68315i) q^{5} +(1.44306 + 1.66538i) q^{6} +(-0.427961 - 2.97653i) q^{7} +(-1.80972 - 0.531382i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.976337 - 6.79057i) q^{10} +(-2.48357 + 5.43826i) q^{11} +(-1.18639 + 2.59784i) q^{12} +(-0.0566239 + 0.393828i) q^{13} +(5.57464 - 3.58260i) q^{14} +(-2.98714 - 0.877103i) q^{15} +(0.221378 + 1.53972i) q^{16} +(0.862774 + 0.995695i) q^{17} +(1.85380 + 1.19136i) q^{18} +(1.67353 - 1.93136i) q^{19} +(8.53104 - 2.50494i) q^{20} +(-1.24921 - 2.73539i) q^{21} -13.1744 q^{22} +(2.43626 - 4.13094i) q^{23} -1.88612 q^{24} +(1.94926 + 4.26828i) q^{25} +(-0.841254 + 0.247014i) q^{26} +(0.654861 - 0.755750i) q^{27} +(7.22482 + 4.64311i) q^{28} +(-0.836577 - 0.965461i) q^{29} +(-0.976337 - 6.79057i) q^{30} +(0.575969 + 0.169120i) q^{31} +(-6.05710 + 3.89266i) q^{32} +(-0.850833 + 5.91767i) q^{33} +(-1.20605 + 2.64089i) q^{34} +(-3.88911 + 8.51595i) q^{35} +(-0.406440 + 2.82685i) q^{36} +(-6.75901 + 4.34375i) q^{37} +(5.40335 + 1.58657i) q^{38} +(0.0566239 + 0.393828i) q^{39} +(3.84532 + 4.43774i) q^{40} +(-7.15168 - 4.59610i) q^{41} +(4.33949 - 5.00804i) q^{42} +(7.26738 - 2.13390i) q^{43} +(-7.09288 - 15.5312i) q^{44} -3.11325 q^{45} +(10.5106 + 1.10192i) q^{46} +7.68323 q^{47} +(0.646201 + 1.41498i) q^{48} +(-1.96015 + 0.575552i) q^{49} +(-6.77129 + 7.81449i) q^{50} +(1.10835 + 0.712290i) q^{51} +(-0.744123 - 0.858763i) q^{52} +(0.399800 + 2.78067i) q^{53} +(2.11435 + 0.620830i) q^{54} +(15.6579 - 10.0627i) q^{55} +(-0.807187 + 5.61411i) q^{56} +(1.06162 - 2.32461i) q^{57} +(1.16943 - 2.56070i) q^{58} +(0.477417 - 3.32051i) q^{59} +(7.47975 - 4.80694i) q^{60} +(0.182679 + 0.0536394i) q^{61} +(0.188254 + 1.30933i) q^{62} +(-1.96926 - 2.27265i) q^{63} +(-10.7303 - 6.89594i) q^{64} +(0.811170 - 0.936140i) q^{65} +(-12.6407 + 3.71165i) q^{66} +(3.73947 + 8.18830i) q^{67} -3.76266 q^{68} +(1.17376 - 4.64998i) q^{69} -20.6302 q^{70} +(-5.61761 - 12.3008i) q^{71} +(-1.80972 + 0.531382i) q^{72} +(-9.37672 + 10.8213i) q^{73} +(-14.8943 - 9.57195i) q^{74} +(3.07281 + 3.54621i) q^{75} +(1.03868 + 7.22418i) q^{76} +(17.2500 + 5.06506i) q^{77} +(-0.737585 + 0.474017i) q^{78} +(-0.718701 + 4.99867i) q^{79} +(2.01178 - 4.40519i) q^{80} +(0.415415 - 0.909632i) q^{81} +(2.66604 - 18.5427i) q^{82} +(6.86519 - 4.41199i) q^{83} +(8.24028 + 2.41956i) q^{84} +(-0.583730 - 4.05993i) q^{85} +(10.9300 + 12.6139i) q^{86} +(-1.07469 - 0.690662i) q^{87} +(7.38436 - 8.52200i) q^{88} +(-0.416206 + 0.122209i) q^{89} +(-2.84991 - 6.24044i) q^{90} +1.19647 q^{91} +(4.35968 + 12.9841i) q^{92} +0.600285 q^{93} +(7.03334 + 15.4009i) q^{94} +(-7.63380 + 2.24148i) q^{95} +(-4.71506 + 5.44146i) q^{96} +(0.265546 + 0.170656i) q^{97} +(-2.94803 - 3.40221i) q^{98} +(0.850833 + 5.91767i) 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

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