LMFDB - Embedded newform 69.2.e.a.25.1

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			25.1
Root			$-0.841254 - 0.540641i$ of defining polynomial
Character	$\chi$	$=$	69.25
Dual form			69.2.e.a.58.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.402869 - 0.258908i) q^{2} +(0.142315 + 0.989821i) q^{3} +(-0.735560 - 1.61065i) q^{4} +(3.37102 + 0.989821i) q^{5} +(0.198939 - 0.435615i) q^{6} +(0.527646 - 0.608936i) q^{7} +(-0.256983 + 1.78736i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.402869 - 0.258908i) q^{2} +(0.142315 + 0.989821i) q^{3} +(-0.735560 - 1.61065i) q^{4} +(3.37102 + 0.989821i) q^{5} +(0.198939 - 0.435615i) q^{6} +(0.527646 - 0.608936i) q^{7} +(-0.256983 + 1.78736i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(-1.10181 - 1.27155i) q^{10} +(-2.98325 + 1.91722i) q^{11} +(1.48958 - 0.957293i) q^{12} +(-4.32972 - 4.99677i) q^{13} +(-0.370231 + 0.108710i) q^{14} +(-0.500000 + 3.47758i) q^{15} +(-1.75278 + 2.02282i) q^{16} +(0.387956 - 0.849505i) q^{17} +(0.459493 + 0.134919i) q^{18} +(1.55773 + 3.41095i) q^{19} +(-0.885331 - 6.15762i) q^{20} +(0.677830 + 0.435615i) q^{21} +1.69824 q^{22} +(-4.71737 + 0.863983i) q^{23} -1.80574 q^{24} +(6.17778 + 3.97022i) q^{25} +(0.450608 + 3.13404i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-1.36890 - 0.401945i) q^{28} +(0.657326 - 1.43934i) q^{29} +(1.10181 - 1.27155i) q^{30} +(-0.0804100 + 0.559264i) q^{31} +(4.69505 - 1.37859i) q^{32} +(-2.32227 - 2.68004i) q^{33} +(-0.376239 + 0.241794i) q^{34} +(2.38145 - 1.53046i) q^{35} +(1.15954 + 1.33818i) q^{36} +(7.84580 - 2.30374i) q^{37} +(0.255563 - 1.77748i) q^{38} +(4.32972 - 4.99677i) q^{39} +(-2.63546 + 5.77086i) q^{40} +(3.65843 + 1.07421i) q^{41} +(-0.160293 - 0.350992i) q^{42} +(-0.975753 - 6.78651i) q^{43} +(5.28234 + 3.39475i) q^{44} -3.51334 q^{45} +(2.12417 + 0.873293i) q^{46} -5.69427 q^{47} +(-2.25168 - 1.44706i) q^{48} +(0.903811 + 6.28614i) q^{49} +(-1.46091 - 3.19895i) q^{50} +(0.896070 + 0.263110i) q^{51} +(-4.86328 + 10.6491i) q^{52} +(-4.57100 + 5.27521i) q^{53} +(-0.0681534 + 0.474017i) q^{54} +(-11.9543 + 3.51011i) q^{55} +(0.952791 + 1.09958i) q^{56} +(-3.15455 + 2.02730i) q^{57} +(-0.637474 + 0.409680i) q^{58} +(-0.663766 - 0.766027i) q^{59} +(5.96894 - 1.75264i) q^{60} +(1.74697 - 12.1505i) q^{61} +(0.177193 - 0.204491i) q^{62} +(-0.334716 + 0.732925i) q^{63} +(2.88789 + 0.847960i) q^{64} +(-9.64969 - 21.1299i) q^{65} +(0.241685 + 1.68096i) q^{66} +(2.09309 + 1.34515i) q^{67} -1.65362 q^{68} +(-1.52654 - 4.54639i) q^{69} -1.35566 q^{70} +(11.1508 + 7.16620i) q^{71} +(-0.256983 - 1.78736i) q^{72} +(2.78441 + 6.09701i) q^{73} +(-3.75729 - 1.10324i) q^{74} +(-3.05062 + 6.67992i) q^{75} +(4.34805 - 5.01792i) q^{76} +(-0.406637 + 2.82823i) q^{77} +(-3.03802 + 0.892042i) q^{78} +(-0.940694 - 1.08562i) q^{79} +(-7.91090 + 5.08403i) q^{80} +(0.841254 - 0.540641i) q^{81} +(-1.19575 - 1.37997i) q^{82} +(1.68020 - 0.493351i) q^{83} +(0.203039 - 1.41217i) q^{84} +(2.14867 - 2.47969i) q^{85} +(-1.36398 + 2.98671i) q^{86} +(1.51824 + 0.445795i) q^{87} +(-2.66011 - 5.82484i) q^{88} +(0.667422 + 4.64202i) q^{89} +(1.41542 + 0.909632i) q^{90} -5.32728 q^{91} +(4.86148 + 6.96252i) q^{92} -0.565015 q^{93} +(2.29404 + 1.47429i) q^{94} +(1.87491 + 13.0403i) q^{95} +(2.03274 + 4.45107i) q^{96} +(-0.762432 - 0.223870i) q^{97} +(1.26342 - 2.76650i) q^{98} +(2.32227 - 2.68004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9} - 2 q^{10} + 7 q^{11} + 14 q^{12} - 30 q^{13} + q^{14} - 5 q^{15} + 12 q^{16} - 2 q^{17} - 4 q^{18} + 10 q^{19} + 4 q^{20} - 3 q^{21} + 6 q^{22} - q^{23} - 18 q^{24} + 24 q^{25} + q^{26} + q^{27} + 9 q^{28} - 14 q^{29} + 2 q^{30} - 28 q^{31} + 23 q^{32} - 7 q^{33} - 8 q^{34} - 4 q^{35} - 3 q^{36} + 19 q^{37} - 15 q^{38} + 30 q^{39} - 13 q^{40} + 19 q^{41} + 21 q^{42} - 24 q^{43} + 54 q^{44} - 6 q^{45} + 18 q^{46} + 26 q^{47} + 10 q^{48} - 13 q^{49} - 36 q^{50} + 24 q^{51} - 57 q^{52} - q^{53} + 4 q^{54} - 24 q^{55} - 10 q^{56} + q^{57} + 10 q^{58} + 2 q^{59} + 7 q^{60} + 30 q^{61} - 24 q^{62} - 8 q^{63} + 13 q^{64} - 4 q^{65} - 28 q^{66} + 4 q^{67} - 50 q^{68} + q^{69} + 6 q^{70} - 14 q^{71} - 15 q^{72} - 26 q^{73} - 12 q^{74} - 13 q^{75} + 19 q^{76} - 43 q^{77} + 10 q^{78} + 20 q^{79} - 5 q^{80} - q^{81} + 10 q^{82} + 18 q^{83} - 42 q^{84} + 21 q^{85} + 14 q^{86} - 8 q^{87} - 38 q^{88} - 5 q^{89} + 9 q^{90} + 46 q^{91} + 52 q^{92} - 16 q^{93} - 6 q^{94} + 5 q^{95} - q^{96} + 15 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9 - 2 * q^10 + 7 * q^11 + 14 * q^12 - 30 * q^13 + q^14 - 5 * q^15 + 12 * q^16 - 2 * q^17 - 4 * q^18 + 10 * q^19 + 4 * q^20 - 3 * q^21 + 6 * q^22 - q^23 - 18 * q^24 + 24 * q^25 + q^26 + q^27 + 9 * q^28 - 14 * q^29 + 2 * q^30 - 28 * q^31 + 23 * q^32 - 7 * q^33 - 8 * q^34 - 4 * q^35 - 3 * q^36 + 19 * q^37 - 15 * q^38 + 30 * q^39 - 13 * q^40 + 19 * q^41 + 21 * q^42 - 24 * q^43 + 54 * q^44 - 6 * q^45 + 18 * q^46 + 26 * q^47 + 10 * q^48 - 13 * q^49 - 36 * q^50 + 24 * q^51 - 57 * q^52 - q^53 + 4 * q^54 - 24 * q^55 - 10 * q^56 + q^57 + 10 * q^58 + 2 * q^59 + 7 * q^60 + 30 * q^61 - 24 * q^62 - 8 * q^63 + 13 * q^64 - 4 * q^65 - 28 * q^66 + 4 * q^67 - 50 * q^68 + q^69 + 6 * q^70 - 14 * q^71 - 15 * q^72 - 26 * q^73 - 12 * q^74 - 13 * q^75 + 19 * q^76 - 43 * q^77 + 10 * q^78 + 20 * q^79 - 5 * q^80 - q^81 + 10 * q^82 + 18 * q^83 - 42 * q^84 + 21 * q^85 + 14 * q^86 - 8 * q^87 - 38 * q^88 - 5 * q^89 + 9 * q^90 + 46 * q^91 + 52 * q^92 - 16 * q^93 - 6 * q^94 + 5 * q^95 - q^96 + 15 * q^97 + 58 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.402869	−	0.258908i	−0.284871	−	0.183076i	0.390399	−	0.920646i	$-0.372337\pi$
$2$	−0.402869	−	0.258908i	−0.284871	−	0.183076i	−0.675271	+	0.737570i	$0.735973\pi$
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$4$	−0.735560	−	1.61065i	−0.367780	−	0.805326i
$5$	3.37102	+	0.989821i	1.50757	+	0.442662i	0.928099	−	0.372333i	$-0.121442\pi$
$5$	3.37102	+	0.989821i	1.50757	+	0.442662i	0.579468	+	0.814995i	$0.303260\pi$
$6$	0.198939	−	0.435615i	0.0812164	−	0.177839i
$7$	0.527646	−	0.608936i	0.199432	−	0.230156i	−0.647221	−	0.762302i	$-0.724069\pi$
$7$	0.527646	−	0.608936i	0.199432	−	0.230156i	0.846652	+	0.532146i	$0.178614\pi$
$8$	−0.256983	+	1.78736i	−0.0908573	+	0.631927i
$9$	−0.959493	+	0.281733i	−0.319831	+	0.0939109i
$10$	−1.10181	−	1.27155i	−0.348422	−	0.402101i
$11$	−2.98325	+	1.91722i	−0.899485	+	0.578064i	−0.906637	−	0.421911i	$-0.861360\pi$
$11$	−2.98325	+	1.91722i	−0.899485	+	0.578064i	0.00715262	+	0.999974i	$0.497723\pi$
$12$	1.48958	−	0.957293i	0.430004	−	0.276347i
$13$	−4.32972	−	4.99677i	−1.20085	−	1.38585i	−0.902103	−	0.431522i	$-0.857977\pi$
$13$	−4.32972	−	4.99677i	−1.20085	−	1.38585i	−0.298747	−	0.954332i	$-0.596569\pi$
$14$	−0.370231	+	0.108710i	−0.0989484	+	0.0290539i
$15$	−0.500000	+	3.47758i	−0.129099	+	0.897906i
$16$	−1.75278	+	2.02282i	−0.438196	+	0.505705i
$17$	0.387956	−	0.849505i	0.0940931	−	0.206035i	−0.856733	−	0.515760i	$-0.827510\pi$
$17$	0.387956	−	0.849505i	0.0940931	−	0.206035i	0.950826	+	0.309725i	$0.100237\pi$
$18$	0.459493	+	0.134919i	0.108304	+	0.0318008i
$19$	1.55773	+	3.41095i	0.357368	+	0.782526i	0.999868	+	0.0162408i	$0.00516984\pi$
$19$	1.55773	+	3.41095i	0.357368	+	0.782526i	−0.642500	+	0.766285i	$0.722103\pi$
$20$	−0.885331	−	6.15762i	−0.197966	−	1.37688i
$21$	0.677830	+	0.435615i	0.147915	+	0.0950590i
$22$	1.69824			0.362067
$23$	−4.71737	+	0.863983i	−0.983639	+	0.180153i
$23$	−4.71737	+	0.863983i	−0.983639	+	0.180153i
$24$	−1.80574			−0.368595
$25$	6.17778	+	3.97022i	1.23556	+	0.794043i
$26$	0.450608	+	3.13404i	0.0883714	+	0.614637i
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$	−1.36890	−	0.401945i	−0.258698	−	0.0759605i
$29$	0.657326	−	1.43934i	0.122062	−	0.267279i	−0.838730	−	0.544547i	$-0.816702\pi$
$29$	0.657326	−	1.43934i	0.122062	−	0.267279i	0.960793	+	0.277268i	$0.0894289\pi$
$30$	1.10181	−	1.27155i	0.201162	−	0.232153i
$31$	−0.0804100	+	0.559264i	−0.0144421	+	0.100447i	−0.995767	−	0.0919082i	$-0.970703\pi$
$31$	−0.0804100	+	0.559264i	−0.0144421	+	0.100447i	0.981325	+	0.192355i	$0.0616125\pi$
$32$	4.69505	−	1.37859i	0.829976	−	0.243703i
$33$	−2.32227	−	2.68004i	−0.404255	−	0.466535i
$34$	−0.376239	+	0.241794i	−0.0645245	+	0.0414674i
$35$	2.38145	−	1.53046i	0.402538	−	0.258695i
$36$	1.15954	+	1.33818i	0.193256	+	0.223030i
$37$	7.84580	−	2.30374i	1.28984	−	0.378732i	0.436321	−	0.899791i	$-0.356281\pi$
$37$	7.84580	−	2.30374i	1.28984	−	0.378732i	0.853521	+	0.521059i	$0.174463\pi$
$38$	0.255563	−	1.77748i	0.0414577	−	0.288345i
$39$	4.32972	−	4.99677i	0.693311	−	0.800123i
$40$	−2.63546	+	5.77086i	−0.416703	+	0.912453i
$41$	3.65843	+	1.07421i	0.571351	+	0.167764i	0.554631	−	0.832096i	$-0.312859\pi$
$41$	3.65843	+	1.07421i	0.571351	+	0.167764i	0.0167200	+	0.999860i	$0.494678\pi$
$42$	−0.160293	−	0.350992i	−0.0247337	−	0.0541592i
$43$	−0.975753	−	6.78651i	−0.148801	−	1.03493i	−0.918187	−	0.396148i	$-0.870347\pi$
$43$	−0.975753	−	6.78651i	−0.148801	−	1.03493i	0.769386	−	0.638785i	$-0.220562\pi$
$44$	5.28234	+	3.39475i	0.796342	+	0.511778i
$45$	−3.51334			−0.523737
$46$	2.12417	+	0.873293i	0.313192	+	0.128760i
$47$	−5.69427			−0.830594			−0.415297	−	0.909686i	$-0.636322\pi$
$47$	−5.69427			−0.830594			−0.415297	+	0.909686i	$0.636322\pi$
$48$	−2.25168	−	1.44706i	−0.325002	−	0.208866i
$49$	0.903811	+	6.28614i	0.129116	+	0.898021i
$50$	−1.46091	−	3.19895i	−0.206604	−	0.452401i
$51$	0.896070	+	0.263110i	0.125475	+	0.0368427i
$52$	−4.86328	+	10.6491i	−0.674416	+	1.47676i
$53$	−4.57100	+	5.27521i	−0.627875	+	0.724606i	−0.977182	−	0.212402i	$-0.931871\pi$
$53$	−4.57100	+	5.27521i	−0.627875	+	0.724606i	0.349308	+	0.937008i	$0.386417\pi$
$54$	−0.0681534	+	0.474017i	−0.00927450	+	0.0645055i
$55$	−11.9543	+	3.51011i	−1.61192	+	0.473302i
$56$	0.952791	+	1.09958i	0.127322	+	0.146938i
$57$	−3.15455	+	2.02730i	−0.417830	+	0.268523i
$58$	−0.637474	+	0.409680i	−0.0837044	+	0.0537936i
$59$	−0.663766	−	0.766027i	−0.0864150	−	0.0997282i	0.710895	−	0.703298i	$-0.248290\pi$
$59$	−0.663766	−	0.766027i	−0.0864150	−	0.0997282i	−0.797310	+	0.603570i	$0.793745\pi$
$60$	5.96894	−	1.75264i	0.770587	−	0.226265i
$61$	1.74697	−	12.1505i	0.223677	−	1.55571i	−0.500281	−	0.865863i	$-0.666770\pi$
$61$	1.74697	−	12.1505i	0.223677	−	1.55571i	0.723958	−	0.689844i	$-0.242321\pi$
$62$	0.177193	−	0.204491i	0.0225035	−	0.0259704i
$63$	−0.334716	+	0.732925i	−0.0421702	+	0.0923399i
$64$	2.88789	+	0.847960i	0.360986	+	0.105995i
$65$	−9.64969	−	21.1299i	−1.19690	−	2.62084i
$66$	0.241685	+	1.68096i	0.0297494	+	0.206912i
$67$	2.09309	+	1.34515i	0.255712	+	0.164336i	0.662216	−	0.749313i	$-0.269616\pi$
$67$	2.09309	+	1.34515i	0.255712	+	0.164336i	−0.406504	+	0.913649i	$0.633252\pi$
$68$	−1.65362			−0.200531
$69$	−1.52654	−	4.54639i	−0.183774	−	0.547321i
$70$	−1.35566			−0.162032
$71$	11.1508	+	7.16620i	1.32336	+	0.850471i	0.995547	−	0.0942715i	$-0.0300522\pi$
$71$	11.1508	+	7.16620i	1.32336	+	0.850471i	0.327813	+	0.944743i	$0.393689\pi$
$72$	−0.256983	−	1.78736i	−0.0302858	−	0.210642i
$73$	2.78441	+	6.09701i	0.325891	+	0.713601i	0.999679	−	0.0253229i	$-0.00806139\pi$
$73$	2.78441	+	6.09701i	0.325891	+	0.713601i	−0.673789	+	0.738924i	$0.735334\pi$
$74$	−3.75729	−	1.10324i	−0.436776	−	0.128249i
$75$	−3.05062	+	6.67992i	−0.352255	+	0.771330i
$76$	4.34805	−	5.01792i	0.498756	−	0.575595i
$77$	−0.406637	+	2.82823i	−0.0463406	+	0.322306i
$78$	−3.03802	+	0.892042i	−0.343988	+	0.101004i
$79$	−0.940694	−	1.08562i	−0.105836	−	0.122142i	0.700360	−	0.713790i	$-0.253023\pi$
$79$	−0.940694	−	1.08562i	−0.105836	−	0.122142i	−0.806196	+	0.591648i	$0.798477\pi$
$80$	−7.91090	+	5.08403i	−0.884465	+	0.568411i
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$	−1.19575	−	1.37997i	−0.132048	−	0.152392i
$83$	1.68020	−	0.493351i	0.184426	−	0.0541523i	−0.188216	−	0.982128i	$-0.560270\pi$
$83$	1.68020	−	0.493351i	0.184426	−	0.0541523i	0.372641	+	0.927975i	$0.378452\pi$
$84$	0.203039	−	1.41217i	0.0221534	−	0.154080i
$85$	2.14867	−	2.47969i	0.233055	−	0.268960i
$86$	−1.36398	+	2.98671i	−0.147082	+	0.322065i
$87$	1.51824	+	0.445795i	0.162772	+	0.0477943i
$88$	−2.66011	−	5.82484i	−0.283569	−	0.620930i
$89$	0.667422	+	4.64202i	0.0707466	+	0.492053i	0.994132	+	0.108178i	$0.0345016\pi$
$89$	0.667422	+	4.64202i	0.0707466	+	0.492053i	−0.923385	+	0.383875i	$0.874589\pi$
$90$	1.41542	+	0.909632i	0.149198	+	0.0958836i
$91$	−5.32728			−0.558450
$92$	4.86148	+	6.96252i	0.506844	+	0.725893i
$93$	−0.565015			−0.0585893
$94$	2.29404	+	1.47429i	0.236613	+	0.152062i
$95$	1.87491	+	13.0403i	0.192362	+	1.33790i
$96$	2.03274	+	4.45107i	0.207465	+	0.454285i
$97$	−0.762432	−	0.223870i	−0.0774132	−	0.0227306i	0.242797	−	0.970077i	$-0.421935\pi$
$97$	−0.762432	−	0.223870i	−0.0774132	−	0.0227306i	−0.320210	+	0.947347i	$0.603753\pi$
$98$	1.26342	−	2.76650i	0.127624	−	0.279458i
$99$	2.32227	−	2.68004i	0.233397	−	0.269354i
$100$	1.85051	−	12.8706i	0.185051	−	1.28706i
$101$	12.0847	−	3.54840i	1.20248	−	0.353079i	0.381678	−	0.924295i	$-0.375346\pi$
$101$	12.0847	−	3.54840i	1.20248	−	0.353079i	0.820800	+	0.571216i	$0.193528\pi$
$102$	−0.292878	−	0.337999i	−0.0289992	−	0.0334669i
$103$	8.91245	−	5.72768i	0.878169	−	0.564365i	−0.0220720	−	0.999756i	$-0.507026\pi$
$103$	8.91245	−	5.72768i	0.878169	−	0.564365i	0.900241	+	0.435391i	$0.143390\pi$
$104$	10.0437	−	6.45468i	0.984864	−	0.632934i
$105$	1.85380	+	2.13940i	0.180912	+	0.208784i
$106$	3.20731	−	0.941751i	0.311521	−	0.0914709i
$107$	0.913569	−	6.35401i	0.0883181	−	0.614266i	−0.896806	−	0.442423i	$-0.854119\pi$
$107$	0.913569	−	6.35401i	0.0883181	−	0.614266i	0.985124	−	0.171842i	$-0.0549720\pi$
$108$	−1.15954	+	1.33818i	−0.111577	+	0.128766i
$109$	−0.487454	+	1.06738i	−0.0466896	+	0.102236i	−0.931539	−	0.363641i	$-0.881534\pi$
$109$	−0.487454	+	1.06738i	−0.0466896	+	0.102236i	0.884850	+	0.465877i	$0.154261\pi$
$110$	5.72482	+	1.68096i	0.545840	+	0.160273i
$111$	3.39686	+	7.43809i	0.322416	+	0.705992i
$112$	0.306919	+	2.13467i	0.0290011	+	0.201707i
$113$	−14.5204	−	9.33173i	−1.36597	−	0.877855i	−0.367334	−	0.930089i	$-0.619729\pi$
$113$	−14.5204	−	9.33173i	−1.36597	−	0.877855i	−0.998635	+	0.0522342i	$0.983366\pi$
$114$	1.79575			0.168188
$115$	−16.7575	−	1.75684i	−1.56265	−	0.163826i
$116$	−2.80178			−0.260139
$117$	5.56209	+	3.57454i	0.514216	+	0.330466i
$118$	0.0690802	+	0.480463i	0.00635934	+	0.0442302i
$119$	−0.312591	−	0.684478i	−0.0286552	−	0.0627460i
$120$	−6.08718	−	1.78736i	−0.555681	−	0.163163i
$121$	0.654502	−	1.43316i	0.0595002	−	0.130287i
$122$	−3.84966	+	4.44274i	−0.348531	+	0.402227i
$123$	−0.542629	+	3.77407i	−0.0489272	+	0.340296i
$124$	0.959925	−	0.281859i	0.0862038	−	0.0253117i
$125$	5.39189	+	6.22257i	0.482265	+	0.556563i
$126$	0.324607	−	0.208612i	0.0289183	−	0.0185847i
$127$	7.96136	−	5.11646i	0.706457	−	0.454012i	−0.137445	−	0.990509i	$-0.543889\pi$
$127$	7.96136	−	5.11646i	0.706457	−	0.454012i	0.843902	+	0.536497i	$0.180253\pi$
$128$	−7.35271	−	8.48548i	−0.649894	−	0.750018i
$129$	6.57857	−	1.93164i	0.579211	−	0.170072i
$130$	−1.58314	+	11.0110i	−0.138850	+	0.965725i
$131$	−8.83379	+	10.1947i	−0.771812	+	0.890718i	−0.996490	−	0.0837147i	$-0.973322\pi$
$131$	−8.83379	+	10.1947i	−0.771812	+	0.890718i	0.224678	+	0.974433i	$0.427867\pi$
$132$	−2.60844	+	5.71169i	−0.227036	+	0.497139i
$133$	2.89898	+	0.851218i	0.251374	+	0.0738100i
$134$	−0.494973	−	1.08384i	−0.0427591	−	0.0936294i
$135$	−0.500000	−	3.47758i	−0.0430331	−	0.299302i
$136$	1.41867	+	0.911725i	0.121650	+	0.0781797i
$137$	−0.768502			−0.0656576			−0.0328288	−	0.999461i	$-0.510452\pi$
$137$	−0.768502			−0.0656576			−0.0328288	+	0.999461i	$0.510452\pi$
$138$	−0.562102	+	2.22683i	−0.0478493	+	0.189561i
$139$	−14.8410			−1.25879			−0.629397	−	0.777084i	$-0.716698\pi$
$139$	−14.8410			−1.25879			−0.629397	+	0.777084i	$0.716698\pi$
$140$	−4.21674	−	2.70993i	−0.356379	−	0.229031i
$141$	−0.810379	−	5.63631i	−0.0682462	−	0.474663i
$142$	−2.63693	−	5.77408i	−0.221287	−	0.484550i
$143$	22.4966	+	6.60559i	1.88126	+	0.552387i
$144$	1.11189	−	2.43470i	0.0926574	−	0.202891i
$145$	3.64055	−	4.20142i	0.302331	−	0.348909i
$146$	0.456813	−	3.17721i	0.0378061	−	0.262947i
$147$	−6.09353	+	1.78922i	−0.502586	+	0.147573i
$148$	−9.48157	−	10.9423i	−0.779381	−	0.899453i
$149$	−7.81799	+	5.02432i	−0.640475	+	0.411608i	−0.820175	−	0.572113i	$-0.806124\pi$
$149$	−7.81799	+	5.02432i	−0.640475	+	0.411608i	0.179700	+	0.983722i	$0.442487\pi$
$150$	2.95848	−	1.90130i	0.241559	−	0.155241i
$151$	5.52469	+	6.37583i	0.449593	+	0.518857i	0.934623	−	0.355640i	$-0.115737\pi$
$151$	5.52469	+	6.37583i	0.449593	+	0.518857i	−0.485031	+	0.874497i	$0.661192\pi$
$152$	−6.49691	+	1.90766i	−0.526969	+	0.154732i
$153$	−0.132908	+	0.924394i	−0.0107450	+	0.0747328i
$154$	0.896073	−	1.03412i	0.0722076	−	0.0833320i
$155$	−0.824635	+	1.80570i	−0.0662363	+	0.145037i
$156$	−11.2328	−	3.29825i	−0.899346	−	0.264072i
$157$	3.89922	+	8.53811i	0.311192	+	0.681415i	0.999011	−	0.0444670i	$-0.0141590\pi$
$157$	3.89922	+	8.53811i	0.311192	+	0.681415i	−0.687819	+	0.725882i	$0.741432\pi$
$158$	0.0979009	+	0.680916i	0.00778858	+	0.0541707i
$159$	−5.87204	−	3.77373i	−0.465683	−	0.299276i
$160$	17.1917			1.35912
$161$	−1.96299	+	3.32845i	−0.154705	+	0.262319i
$162$	−0.478891			−0.0376253
$163$	−14.3998	−	9.25418i	−1.12788	−	0.724843i	−0.162762	−	0.986665i	$-0.552040\pi$
$163$	−14.3998	−	9.25418i	−1.12788	−	0.724843i	−0.965116	+	0.261822i	$0.915677\pi$
$164$	−0.960814	−	6.68261i	−0.0750270	−	0.521824i
$165$	−5.17565	−	11.3331i	−0.402924	−	0.882281i
$166$	−0.804632	−	0.236261i	−0.0624516	−	0.0183374i
$167$	4.44222	−	9.72711i	0.343750	−	0.752707i	−0.656249	−	0.754545i	$-0.727858\pi$
$167$	4.44222	−	9.72711i	0.343750	−	0.752707i	0.999998	+	0.00183806i	$0.000585072\pi$
$168$	−0.952791	+	1.09958i	−0.0735094	+	0.0848344i
$169$	−4.37109	+	30.4016i	−0.336237	+	2.33858i
$170$	−1.50764	+	0.442684i	−0.115631	+	0.0339523i
$171$	−2.45561	−	2.83392i	−0.187785	−	0.216715i
$172$	−10.2130	+	6.56348i	−0.778732	+	0.500461i
$173$	−20.3079	+	13.0511i	−1.54398	+	0.992255i	−0.557164	+	0.830403i	$0.688110\pi$
$173$	−20.3079	+	13.0511i	−1.54398	+	0.992255i	−0.986815	+	0.161852i	$0.948253\pi$
$174$	−0.496232	−	0.572682i	−0.0376192	−	0.0434149i
$175$	5.67729	−	1.66700i	0.429163	−	0.126014i
$176$	1.35080	−	9.39505i	0.101821	−	0.708179i
$177$	0.663766	−	0.766027i	0.0498917	−	0.0575781i
$178$	0.932974	−	2.04293i	0.0699293	−	0.153124i
$179$	−2.50104	−	0.734371i	−0.186936	−	0.0548894i	0.186925	−	0.982374i	$-0.440148\pi$
$179$	−2.50104	−	0.734371i	−0.186936	−	0.0548894i	−0.373861	+	0.927485i	$0.621966\pi$
$180$	2.58427	+	5.65876i	0.192620	+	0.421779i
$181$	1.42736	+	9.92752i	0.106095	+	0.737907i	0.971535	+	0.236895i	$0.0761296\pi$
$181$	1.42736	+	9.92752i	0.106095	+	0.737907i	−0.865440	+	0.501012i	$0.832961\pi$
$182$	2.14620	+	1.37928i	0.159087	+	0.102239i
$183$	12.2754			0.907424
$184$	−0.331964	−	8.65365i	−0.0244727	−	0.637956i
$185$	28.7287			2.11217
$186$	0.227627	+	0.146287i	0.0166904	+	0.0107263i
$187$	0.471317	+	3.27808i	0.0344661	+	0.239717i
$188$	4.18848	+	9.17148i	0.305476	+	0.668899i
$189$	−0.773100	−	0.227003i	−0.0562348	−	0.0165120i
$190$	2.62089	−	5.73895i	0.190139	−	0.416347i
$191$	16.4041	−	18.9313i	1.18696	−	1.36982i	0.274019	−	0.961724i	$-0.411647\pi$
$191$	16.4041	−	18.9313i	1.18696	−	1.36982i	0.912938	−	0.408097i	$-0.133808\pi$
$192$	−0.428340	+	2.97917i	−0.0309128	+	0.215003i
$193$	0.0958162	−	0.0281342i	0.00689700	−	0.00202514i	−0.278282	−	0.960499i	$-0.589765\pi$
$193$	0.0958162	−	0.0281342i	0.00689700	−	0.00202514i	0.285179	+	0.958474i	$0.407947\pi$
$194$	0.249198	+	0.287590i	0.0178914	+	0.0206478i
$195$	19.5415	−	12.5586i	1.39940	−	0.899337i
$196$	9.45998	−	6.07956i	0.675713	−	0.434254i
$197$	−10.8572	−	12.5299i	−0.773543	−	0.892716i	0.223083	−	0.974800i	$-0.428388\pi$
$197$	−10.8572	−	12.5299i	−0.773543	−	0.892716i	−0.996625	+	0.0820836i	$0.973843\pi$
$198$	−1.62945	+	0.478451i	−0.115800	+	0.0340020i
$199$	−2.85274	+	19.8412i	−0.202225	+	1.40651i	0.595437	+	0.803402i	$0.296979\pi$
$199$	−2.85274	+	19.8412i	−0.202225	+	1.40651i	−0.797662	+	0.603104i	$0.793930\pi$
$200$	−8.68379	+	10.0216i	−0.614036	+	0.708636i
$201$	−1.03358	+	2.26322i	−0.0729031	+	0.159636i
$202$	−5.78728	−	1.69930i	−0.407192	−	0.119562i
$203$	−0.529632	−	1.15973i	−0.0371729	−	0.0813973i
$204$	−0.235335	−	1.63679i	−0.0164767	−	0.114598i
$205$	11.2694	+	7.24239i	0.787087	+	0.505830i
$206$	−5.07349			−0.353487
$207$	4.28287	−	2.15802i	0.297680	−	0.149993i
$208$	17.6966			1.22704
$209$	−11.1867	−	7.18922i	−0.773797	−	0.497289i
$210$	−0.192931	−	1.34186i	−0.0133135	−	0.0925972i
$211$	−0.964715	−	2.11243i	−0.0664137	−	0.145426i	0.873514	−	0.486799i	$-0.161835\pi$
$211$	−0.964715	−	2.11243i	−0.0664137	−	0.145426i	−0.939928	+	0.341373i	$0.889108\pi$
$212$	11.8588	+	3.48205i	0.814464	+	0.239148i
$213$	−5.50633	+	12.0572i	−0.377287	+	0.826144i
$214$	−2.01316	+	2.32331i	−0.137616	+	0.158818i
$215$	3.42815	−	23.8433i	0.233798	−	1.62610i
$216$	1.73259	−	0.508735i	0.117888	−	0.0346150i
$217$	0.298128	+	0.344058i	0.0202382	+	0.0233562i
$218$	0.472733	−	0.303807i	0.0320175	−	0.0205764i
$219$	−5.63869	+	3.62377i	−0.381027	+	0.244871i
$220$	14.4467	+	16.6724i	0.973995	+	1.12405i
$221$	−5.92452	+	1.73960i	−0.398526	+	0.117018i
$222$	0.557292	−	3.87605i	0.0374030	−	0.260144i
$223$	3.01311	−	3.47732i	0.201773	−	0.232858i	−0.645841	−	0.763472i	$-0.723493\pi$
$223$	3.01311	−	3.47732i	0.201773	−	0.232858i	0.847614	+	0.530614i	$0.178038\pi$
$224$	1.63785	−	3.58640i	0.109434	−	0.239626i
$225$	−7.04607	−	2.06891i	−0.469738	−	0.137928i
$226$	3.43378	+	7.51893i	0.228412	+	0.500152i
$227$	−1.24145	−	8.63450i	−0.0823981	−	0.573092i	−0.988637	−	0.150325i	$-0.951968\pi$
$227$	−1.24145	−	8.63450i	−0.0823981	−	0.573092i	0.906239	−	0.422767i	$-0.138941\pi$
$228$	5.58564	+	3.58967i	0.369918	+	0.237732i
$229$	−9.31081			−0.615276			−0.307638	−	0.951503i	$-0.599539\pi$
$229$	−9.31081			−0.615276			−0.307638	+	0.951503i	$0.599539\pi$
$230$	6.29623	+	5.04644i	0.415161	+	0.332752i
$231$	−2.85731			−0.187997
$232$	2.40370	+	1.54476i	0.157811	+	0.101419i
$233$	0.419991	+	2.92111i	0.0275146	+	0.191368i	0.998943	−	0.0459644i	$-0.0146361\pi$
$233$	0.419991	+	2.92111i	0.0275146	+	0.191368i	−0.971429	+	0.237332i	$0.923727\pi$
$234$	−1.31532	−	2.88014i	−0.0859850	−	0.188281i
$235$	−19.1955	−	5.63631i	−1.25218	−	0.367672i
$236$	−0.745563	+	1.63255i	−0.0485320	+	0.106270i
$237$	0.940694	−	1.08562i	0.0611046	−	0.0705185i
$238$	−0.0512839	+	0.356688i	−0.00332424	+	0.0231206i
$239$	15.7671	−	4.62963i	1.01989	−	0.299466i	0.271294	−	0.962496i	$-0.412548\pi$
$239$	15.7671	−	4.62963i	1.01989	−	0.299466i	0.748592	+	0.663031i	$0.230730\pi$
$240$	−6.15812	−	7.10685i	−0.397505	−	0.458745i
$241$	−1.11201	+	0.714643i	−0.0716306	+	0.0460342i	−0.575966	−	0.817474i	$-0.695374\pi$
$241$	−1.11201	+	0.714643i	−0.0716306	+	0.0460342i	0.504335	+	0.863508i	$0.331738\pi$
$242$	−0.634735	+	0.407920i	−0.0408023	+	0.0262221i
$243$	0.654861	+	0.755750i	0.0420093	+	0.0484814i
$244$	−20.8552	+	6.12363i	−1.33511	+	0.392025i
$245$	−3.17539	+	22.0853i	−0.202868	+	1.41098i
$246$	1.19575	−	1.37997i	0.0762380	−	0.0879834i
$247$	10.2992	−	22.5521i	0.655322	−	1.43496i
$248$	−0.978940	−	0.287443i	−0.0621628	−	0.0182526i
$249$	0.727446	+	1.59288i	0.0461000	+	0.100945i
$250$	−0.561150	−	3.90288i	−0.0354902	−	0.246840i
$251$	−15.7308	−	10.1096i	−0.992920	−	0.638111i	−0.0600015	−	0.998198i	$-0.519111\pi$
$251$	−15.7308	−	10.1096i	−0.992920	−	0.638111i	−0.932919	+	0.360087i	$0.882747\pi$
$252$	1.42669			0.0898731
$253$	12.4166	−	11.6217i	0.780628	−	0.730651i
$254$	−4.53208			−0.284368
$255$	2.76024	+	1.77390i	0.172853	+	0.111086i
$256$	−0.0914606	−	0.636123i	−0.00571629	−	0.0397577i
$257$	2.62732	+	5.75302i	0.163888	+	0.358864i	0.973703	−	0.227821i	$-0.0731601\pi$
$257$	2.62732	+	5.75302i	0.163888	+	0.358864i	−0.809816	+	0.586685i	$0.800433\pi$
$258$	−3.15042	−	0.925047i	−0.196137	−	0.0575909i
$259$	2.73698	−	5.99315i	0.170068	−	0.372396i
$260$	−26.9349	+	31.0846i	−1.67043	+	1.92778i
$261$	−0.225190	+	1.56623i	−0.0139389	+	0.0969471i
$262$	6.19836	−	1.82000i	0.382936	−	0.112440i
$263$	15.9658	+	18.4255i	0.984491	+	1.13616i	0.990684	+	0.136183i	$0.0434834\pi$
$263$	15.9658	+	18.4255i	0.984491	+	1.13616i	−0.00619241	+	0.999981i	$0.501971\pi$
$264$	5.38698	−	3.46200i	0.331545	−	0.213071i
$265$	−20.6305	+	13.2584i	−1.26732	+	0.814456i
$266$	−0.947523	−	1.09350i	−0.0580964	−	0.0670468i
$267$	−4.49979	+	1.32126i	−0.275383	+	0.0808596i
$268$	0.626972	−	4.36068i	0.0382984	−	0.266371i
$269$	8.87170	−	10.2385i	0.540917	−	0.624252i	−0.417825	−	0.908527i	$-0.637208\pi$
$269$	8.87170	−	10.2385i	0.540917	−	0.624252i	0.958743	+	0.284276i	$0.0917531\pi$
$270$	−0.698939	+	1.53046i	−0.0425361	+	0.0931410i
$271$	−10.6726	−	3.13375i	−0.648312	−	0.190362i	−0.0589883	−	0.998259i	$-0.518787\pi$
$271$	−10.6726	−	3.13375i	−0.648312	−	0.190362i	−0.589324	+	0.807897i	$0.700606\pi$
$272$	1.03839	+	2.27376i	0.0629618	+	0.137867i
$273$	−0.758150	−	5.27305i	−0.0458854	−	0.319140i
$274$	0.309606	+	0.198972i	0.0187040	+	0.0120203i
$275$	−26.0417			−1.57037
$276$	−6.19979	+	5.80287i	−0.373184	+	0.349292i
$277$	−14.7239			−0.884673			−0.442337	−	0.896849i	$-0.645850\pi$
$277$	−14.7239			−0.884673			−0.442337	+	0.896849i	$0.645850\pi$
$278$	5.97896	+	3.84245i	0.358594	+	0.230455i
$279$	−0.0804100	−	0.559264i	−0.00481402	−	0.0334822i
$280$	2.12349	+	4.64980i	0.126903	+	0.277879i
$281$	−20.2215	−	5.93758i	−1.20632	−	0.354206i	−0.384051	−	0.923312i	$-0.625471\pi$
$281$	−20.2215	−	5.93758i	−1.20632	−	0.354206i	−0.822264	+	0.569106i	$0.807289\pi$
$282$	−1.13281	+	2.48051i	−0.0674579	+	0.147712i
$283$	3.85528	−	4.44924i	0.229173	−	0.264480i	−0.629504	−	0.776998i	$-0.716742\pi$
$283$	3.85528	−	4.44924i	0.229173	−	0.264480i	0.858677	+	0.512518i	$0.171287\pi$
$284$	3.34015	−	23.2313i	0.198201	−	1.37852i
$285$	−12.6407	+	3.71165i	−0.748771	+	0.219859i
$286$	−7.35293	−	8.48574i	−0.434788	−	0.501772i
$287$	2.58449	−	1.66095i	0.152557	−	0.0980426i
$288$	−4.11648	+	2.64550i	−0.242566	+	0.155887i
$289$	10.5615	+	12.1886i	0.621264	+	0.716977i
$290$	−2.55445	+	0.750054i	−0.150002	+	0.0440447i
$291$	0.113086	−	0.786531i	0.00662923	−	0.0461073i
$292$	7.77206	−	8.96944i	0.454825	−	0.524897i
$293$	−0.0808672	+	0.177074i	−0.00472431	+	0.0103448i	−0.911979	−	0.410236i	$-0.865446\pi$
$293$	−0.0808672	+	0.177074i	−0.00472431	+	0.0103448i	0.907255	+	0.420581i	$0.138174\pi$
$294$	2.91814	+	0.856844i	0.170189	+	0.0499721i
$295$	−1.47934	−	3.23930i	−0.0861305	−	0.188600i
$296$	2.10136	+	14.6153i	0.122139	+	0.849496i
$297$	2.98325	+	1.91722i	0.173106	+	0.111248i
$298$	4.45047			0.257809
$299$	24.7420	+	19.8308i	1.43087	+	1.14684i
$300$	13.0029			0.750725
$301$	−4.64740	−	2.98671i	−0.267872	−	0.172151i
$302$	−0.574971	−	3.99901i	−0.0330859	−	0.230117i
$303$	5.23212	+	11.4568i	0.300578	+	0.658173i
$304$	−9.63010	−	2.82765i	−0.552324	−	0.162177i
$305$	17.9159	−	39.2303i	1.02586	−	2.24632i
$306$	0.292878	−	0.337999i	0.0167427	−	0.0193221i
$307$	1.84026	−	12.7993i	0.105029	−	0.730492i	−0.867454	−	0.497518i	$-0.834245\pi$
$307$	1.84026	−	12.7993i	0.105029	−	0.730492i	0.972483	−	0.232975i	$-0.0748459\pi$
$308$	4.85439	−	1.42538i	0.276605	−	0.0812185i
$309$	6.93775	+	8.00660i	0.394675	+	0.455479i
$310$	0.799730	−	0.513955i	0.0454216	−	0.0291907i
$311$	−25.2289	+	16.2136i	−1.43060	+	0.919391i	−0.430744	+	0.902474i	$0.641749\pi$
$311$	−25.2289	+	16.2136i	−1.43060	+	0.919391i	−0.999857	+	0.0169172i	$0.994615\pi$
$312$	7.81835	+	9.02285i	0.442627	+	0.510819i
$313$	1.46922	−	0.431401i	0.0830451	−	0.0243843i	−0.239946	−	0.970786i	$-0.577130\pi$
$313$	1.46922	−	0.431401i	0.0830451	−	0.0243843i	0.322991	+	0.946402i	$0.395312\pi$
$314$	0.639710	−	4.44928i	0.0361009	−	0.251087i
$315$	−1.85380	+	2.13940i	−0.104450	+	0.120541i
$316$	−1.05662	+	2.31367i	−0.0594393	+	0.130154i
$317$	20.3746	+	5.98254i	1.14435	+	0.336013i	0.798334	−	0.602215i	$-0.205715\pi$
$317$	20.3746	+	5.98254i	1.14435	+	0.336013i	0.346020	+	0.938227i	$0.387533\pi$
$318$	1.38861	+	3.04064i	0.0778696	+	0.170511i
$319$	0.798568	+	5.55416i	0.0447112	+	0.310973i
$320$	8.89580	+	5.71698i	0.497290	+	0.319589i
$321$	6.41935			0.358293
$322$	1.65259	−	0.832697i	0.0920953	−	0.0464044i
$323$	3.50195			0.194854
$324$	−1.48958	−	0.957293i	−0.0827542	−	0.0531829i
$325$	−6.90982	−	48.0589i	−0.383288	−	2.66583i
$326$	3.40525	+	7.45645i	0.188599	+	0.412974i
$327$	−1.12588	−	0.330589i	−0.0622615	−	0.0182816i
$328$	−2.86016	+	6.26287i	−0.157926	+	0.345809i
$329$	−3.00456	+	3.46745i	−0.165647	+	0.191167i
$330$	−0.849122	+	5.90578i	−0.0467427	+	0.325102i
$331$	0.778568	−	0.228608i	0.0427940	−	0.0125654i	−0.260266	−	0.965537i	$-0.583810\pi$
$331$	0.778568	−	0.228608i	0.0427940	−	0.0125654i	0.303059	+	0.952972i	$0.401992\pi$
$332$	−2.03050	−	2.34332i	−0.111438	−	0.128607i
$333$	−6.87896	+	4.42084i	−0.376964	+	0.242260i
$334$	−4.30806	+	2.76862i	−0.235727	+	0.151492i
$335$	5.72441	+	6.60632i	0.312758	+	0.360942i
$336$	−2.06926	+	0.607589i	−0.112887	+	0.0331467i
$337$	2.55623	−	17.7790i	0.139247	−	0.968483i	−0.793659	−	0.608363i	$-0.791827\pi$
$337$	2.55623	−	17.7790i	0.139247	−	0.968483i	0.932906	−	0.360120i	$-0.117264\pi$
$338$	9.63219	−	11.1161i	0.523922	−	0.604639i
$339$	7.17027	−	15.7007i	0.389435	−	0.852745i
$340$	−5.57439	−	1.63679i	−0.302314	−	0.0887674i
$341$	−0.832348	−	1.82259i	−0.0450742	−	0.0986987i
$342$	0.255563	+	1.77748i	0.0138192	+	0.0961149i
$343$	9.04957	+	5.81580i	0.488631	+	0.314024i
$344$	12.3807			0.667521
$345$	−0.645886	−	16.8370i	−0.0347733	−	0.906473i
$346$	11.5604			0.621493
$347$	−3.92153	−	2.52021i	−0.210519	−	0.135292i	0.431133	−	0.902288i	$-0.358114\pi$
$347$	−3.92153	−	2.52021i	−0.210519	−	0.135292i	−0.641651	+	0.766996i	$0.721750\pi$
$348$	−0.398735	−	2.77326i	−0.0213744	−	0.148663i
$349$	−6.62642	−	14.5098i	−0.354704	−	0.776694i	−0.999919	−	0.0126928i	$-0.995960\pi$
$349$	−6.62642	−	14.5098i	−0.354704	−	0.776694i	0.645215	−	0.764001i	$-0.276768\pi$
$350$	−2.71881	−	0.798313i	−0.145326	−	0.0426716i
$351$	−2.74659	+	6.01419i	−0.146602	+	0.321014i
$352$	−11.3635	+	13.1141i	−0.605675	+	0.698986i
$353$	−3.97269	+	27.6307i	−0.211445	+	1.47063i	0.556891	+	0.830586i	$0.311994\pi$
$353$	−3.97269	+	27.6307i	−0.211445	+	1.47063i	−0.768336	+	0.640047i	$0.778915\pi$
$354$	−0.465741	+	0.136754i	−0.0247539	+	0.00726839i
$355$	30.4964	+	35.1947i	1.61858	+	1.86794i
$356$	6.98575	−	4.48947i	0.370244	−	0.237941i
$357$	0.633025	−	0.406821i	0.0335032	−	0.0215312i
$358$	0.817456	+	0.943394i	0.0432039	+	0.0498599i
$359$	−31.6936	+	9.30607i	−1.67272	+	0.491156i	−0.974436	−	0.224663i	$-0.927872\pi$
$359$	−31.6936	+	9.30607i	−1.67272	+	0.491156i	−0.698286	+	0.715819i	$0.746054\pi$
$360$	0.902869	−	6.27959i	0.0475854	−	0.330964i
$361$	3.23428	−	3.73256i	0.170225	−	0.196450i
$362$	1.99528	−	4.36905i	0.104869	−	0.229632i
$363$	1.51172	+	0.443880i	0.0793445	+	0.0232977i
$364$	3.91853	+	8.58039i	0.205387	+	0.449734i
$365$	3.35136	+	23.3092i	0.175418	+	1.22006i
$366$	−4.94538	−	3.17820i	−0.258499	−	0.166127i
$367$	−13.3155			−0.695066			−0.347533	−	0.937668i	$-0.612981\pi$
$367$	−13.3155			−0.695066			−0.347533	+	0.937668i	$0.612981\pi$
$368$	6.52083	−	11.0568i	0.339922	−	0.576373i
$369$	−3.81288			−0.198491
$370$	−11.5739	−	7.43809i	−0.601698	−	0.386688i
$371$	0.800398	+	5.56689i	0.0415546	+	0.289019i
$372$	0.415602	+	0.910042i	0.0215480	+	0.0471835i
$373$	23.7335	+	6.96879i	1.22888	+	0.360830i	0.830825	−	0.556533i	$-0.187869\pi$
$373$	23.7335	+	6.96879i	1.22888	+	0.360830i	0.398050	+	0.917364i	$0.369687\pi$
$374$	0.658844	−	1.44267i	0.0340680	−	0.0745985i
$375$	−5.39189	+	6.22257i	−0.278436	+	0.321332i
$376$	1.46333	−	10.1777i	0.0754656	−	0.524875i
$377$	−10.0381	+	2.94745i	−0.516988	+	0.151801i
$378$	0.252685	+	0.291614i	0.0129967	+	0.0149990i
$379$	32.2149	−	20.7033i	1.65477	−	1.06345i	0.729616	−	0.683857i	$-0.239699\pi$
$379$	32.2149	−	20.7033i	1.65477	−	1.06345i	0.925152	−	0.379597i	$-0.123938\pi$
$380$	19.6242	−	12.6117i	1.00670	−	0.646968i
$381$	6.19740	+	7.15218i	0.317502	+	0.366417i
$382$	−11.5102	+	3.37969i	−0.588911	+	0.172920i
$383$	2.38718	−	16.6032i	0.121979	−	0.848383i	−0.833330	−	0.552775i	$-0.813569\pi$
$383$	2.38718	−	16.6032i	0.121979	−	0.848383i	0.955309	−	0.295608i	$-0.0955221\pi$
$384$	7.35271	−	8.48548i	0.375216	−	0.433023i
$385$	−4.17022	+	9.13151i	−0.212534	+	0.465385i
$386$	−0.0458856	−	0.0134732i	−0.00233551	−	0.000685768i
$387$	2.84821	+	6.23671i	0.144783	+	0.317030i
$388$	0.200237	+	1.39268i	0.0101655	+	0.0707027i
$389$	1.65871	+	1.06599i	0.0841000	+	0.0540478i	0.582015	−	0.813178i	$-0.302264\pi$
$389$	1.65871	+	1.06599i	0.0841000	+	0.0540478i	−0.497915	+	0.867226i	$0.665901\pi$
$390$	−11.1242			−0.563295
$391$	−1.09617	+	4.34261i	−0.0554358	+	0.219615i
$392$	−11.4679			−0.579214
$393$	−11.3482	−	7.29301i	−0.572438	−	0.367884i
$394$	1.12994	+	7.85891i	0.0569256	+	0.395926i
$395$	−2.09653	−	4.59076i	−0.105488	−	0.230986i
$396$	−6.02478	−	1.76903i	−0.302756	−	0.0888973i
$397$	−12.0830	+	26.4580i	−0.606426	+	1.32789i	0.318565	+	0.947901i	$0.396799\pi$
$397$	−12.0830	+	26.4580i	−0.606426	+	1.32789i	−0.924992	+	0.379988i	$0.875928\pi$
$398$	6.28633	−	7.25481i	0.315105	−	0.363651i
$399$	−0.429986	+	2.99062i	−0.0215262	+	0.149718i
$400$	−18.8593	+	5.53760i	−0.942967	+	0.276880i
$401$	5.76326	+	6.65116i	0.287803	+	0.332143i	0.881179	−	0.472783i	$-0.156751\pi$
$401$	5.76326	+	6.65116i	0.287803	+	0.332143i	−0.593376	+	0.804926i	$0.702205\pi$
$402$	1.00236	−	0.644181i	0.0499934	−	0.0321288i
$403$	3.14266	−	2.01967i	0.156547	−	0.100607i
$404$	−14.6043	−	16.8543i	−0.726591	−	0.838531i
$405$	3.37102	−	0.989821i	0.167507	−	0.0491846i
$406$	−0.0868920	+	0.604347i	−0.00431238	+	0.0299932i
$407$	−18.9892	+	21.9148i	−0.941262	+	1.08627i
$408$	−0.700547	+	1.53398i	−0.0346822	+	0.0759435i
$409$	−6.24249	−	1.83296i	−0.308671	−	0.0906340i	0.123729	−	0.992316i	$-0.460515\pi$
$409$	−6.24249	−	1.83296i	−0.308671	−	0.0906340i	−0.432400	+	0.901682i	$0.642333\pi$
$410$	−2.66497	−	5.83547i	−0.131613	−	0.288193i
$411$	−0.109369	−	0.760680i	−0.00539479	−	0.0375216i
$412$	−15.7809	−	10.1418i	−0.777471	−	0.499650i
$413$	−0.816695			−0.0401869
$414$	−2.28416	−	0.239469i	−0.112261	−	0.0117693i
$415$	6.15231			0.302005
$416$	−27.2168	−	17.4912i	−1.33441	−	0.857575i
$417$	−2.11209	−	14.6899i	−0.103429	−	0.719367i
$418$	2.64541	+	5.79263i	0.129391	+	0.283327i
$419$	−8.92579	−	2.62085i	−0.436054	−	0.128037i	0.0563359	−	0.998412i	$-0.482058\pi$
$419$	−8.92579	−	2.62085i	−0.436054	−	0.128037i	−0.492389	+	0.870375i	$0.663876\pi$
$420$	2.08225	−	4.55948i	0.101603	−	0.222480i
$421$	3.18611	−	3.67697i	0.155282	−	0.179205i	−0.672778	−	0.739844i	$-0.734899\pi$
$421$	3.18611	−	3.67697i	0.155282	−	0.179205i	0.828060	+	0.560640i	$0.189445\pi$
$422$	−0.158272	+	1.10081i	−0.00770456	+	0.0535864i
$423$	5.46361	−	1.60426i	0.265650	−	0.0780018i
$424$	−8.25402	−	9.52565i	−0.400851	−	0.462607i
$425$	5.76942	−	3.70778i	0.279858	−	0.179854i
$426$	5.34003	−	3.43183i	0.258725	−	0.166273i
$427$	−6.47707	−	7.47494i	−0.313447	−	0.361738i
$428$	−10.9061	+	3.20232i	−0.527166	+	0.154790i
$429$	−3.33676	+	23.2077i	−0.161100	+	1.12048i
$430$	−7.55432	+	8.71815i	−0.364302	+	0.420427i
$431$	13.7691	−	30.1501i	0.663234	−	1.45228i	−0.216244	−	0.976339i	$-0.569381\pi$
$431$	13.7691	−	30.1501i	0.663234	−	1.45228i	0.879478	−	0.475940i	$-0.157892\pi$
$432$	2.56815	+	0.754078i	0.123560	+	0.0362806i
$433$	12.7795	+	27.9833i	0.614145	+	1.34479i	0.919702	+	0.392617i	$0.128430\pi$
$433$	12.7795	+	27.9833i	0.614145	+	1.34479i	−0.305557	+	0.952174i	$0.598843\pi$
$434$	−0.0310271	−	0.215798i	−0.00148935	−	0.0103586i
$435$	4.67676	+	3.00557i	0.224234	+	0.144106i
$436$	2.07772			0.0995048
$437$	−10.2954	−	14.7449i	−0.492495	−	0.705342i
$438$	3.20988			0.153374
$439$	26.1267	+	16.7906i	1.24696	+	0.801371i	0.986444	−	0.164099i	$-0.0524716\pi$
$439$	26.1267	+	16.7906i	1.24696	+	0.801371i	0.260514	+	0.965470i	$0.416108\pi$
$440$	−3.20175	−	22.2687i	−0.152638	−	1.06162i
$441$	−2.63821	−	5.77688i	−0.125629	−	0.275089i
$442$	2.83720	+	0.833078i	0.134952	+	0.0396255i
$443$	−1.34137	+	2.93720i	−0.0637305	+	0.139550i	−0.938817	−	0.344416i	$-0.888077\pi$
$443$	−1.34137	+	2.93720i	−0.0637305	+	0.139550i	0.875087	+	0.483966i	$0.160804\pi$
$444$	9.48157	−	10.9423i	0.449976	−	0.519300i
$445$	−2.34488	+	16.3090i	−0.111158	+	0.773120i
$446$	−2.11420	+	0.620784i	−0.100110	+	0.0293950i
$447$	−6.08579	−	7.02338i	−0.287848	−	0.332195i
$448$	2.04014	−	1.31112i	0.0963874	−	0.0619444i
$449$	17.6082	−	11.3161i	0.830982	−	0.534040i	−0.0546076	−	0.998508i	$-0.517391\pi$
$449$	17.6082	−	11.3161i	0.830982	−	0.534040i	0.885590	+	0.464468i	$0.153754\pi$
$450$	2.30299	+	2.65779i	0.108564	+	0.125289i
$451$	−12.9735	+	3.80937i	−0.610900	+	0.179376i
$452$	−4.34950	+	30.2514i	−0.204583	+	1.42291i
$453$	−5.52469	+	6.37583i	−0.259572	+	0.299562i
$454$	−1.73540	+	3.79999i	−0.0814463	+	0.178343i
$455$	−17.9584	−	5.27305i	−0.841901	−	0.247205i
$456$	−2.81285	−	6.15929i	−0.131724	−	0.288435i
$457$	0.0771726	+	0.536747i	0.00360998	+	0.0251080i	0.991547	−	0.129749i	$-0.0414173\pi$
$457$	0.0771726	+	0.536747i	0.00360998	+	0.0251080i	−0.987937	+	0.154857i	$0.950508\pi$
$458$	3.75104	+	2.41065i	0.175275	+	0.112642i
$459$	−0.933899			−0.0435907
$460$	9.49651	+	28.2828i	0.442777	+	1.31869i
$461$	2.74045			0.127636			0.0638178	−	0.997962i	$-0.479672\pi$
$461$	2.74045			0.127636			0.0638178	+	0.997962i	$0.479672\pi$
$462$	1.15112	+	0.739781i	0.0535550	+	0.0344177i
$463$	−1.60699	−	11.1768i	−0.0746831	−	0.519432i	−0.992482	−	0.122388i	$-0.960945\pi$
$463$	−1.60699	−	11.1768i	−0.0746831	−	0.519432i	0.917799	−	0.397045i	$-0.129964\pi$
$464$	1.75938	+	3.85251i	0.0816772	+	0.178848i
$465$	−1.90468	−	0.559264i	−0.0883273	−	0.0259352i
$466$	0.587097	−	1.28556i	0.0271967	−	0.0595525i
$467$	3.78682	−	4.37023i	0.175233	−	0.202230i	−0.661338	−	0.750088i	$-0.730011\pi$
$467$	3.78682	−	4.37023i	0.175233	−	0.202230i	0.836571	+	0.547858i	$0.184557\pi$
$468$	1.66609	−	11.5879i	0.0770148	−	0.535650i
$469$	1.92352	−	0.564798i	0.0888201	−	0.0260799i
$470$	6.27399	+	7.24057i	0.289398	+	0.333983i
$471$	−7.89629	+	5.07463i	−0.363842	+	0.233827i
$472$	1.53974	−	0.989532i	0.0708723	−	0.0455469i
$473$	15.9222	+	18.3751i	0.732101	+	0.844890i
$474$	−0.660052	+	0.193809i	−0.0303172	+	0.00890193i
$475$	−3.91891	+	27.2566i	−0.179812	+	1.25062i
$476$	−0.872527	+	1.00695i	−0.0399922	+	0.0461535i
$477$	2.89964	−	6.34933i	0.132765	−	0.290716i
$478$	−7.55071	−	2.21709i	−0.345361	−	0.101407i
$479$	3.47182	+	7.60222i	0.158631	+	0.347354i	0.972214	−	0.234096i	$-0.0752129\pi$
$479$	3.47182	+	7.60222i	0.158631	+	0.347354i	−0.813582	+	0.581450i	$0.802486\pi$
$480$	2.44663	+	17.0167i	0.111673	+	0.776703i
$481$	−45.4814	−	29.2291i	−2.07377	−	1.33273i
$482$	0.633020			0.0288333
$483$	−3.57394	−	1.46932i	−0.162620	−	0.0668564i
$484$	−2.78974			−0.126807
$485$	−2.34858	−	1.50934i	−0.106644	−	0.0685357i
$486$	−0.0681534	−	0.474017i	−0.00309150	−	0.0215018i
$487$	−1.44084	−	3.15501i	−0.0652909	−	0.142967i	0.874173	−	0.485614i	$-0.161404\pi$
$487$	−1.44084	−	3.15501i	−0.0652909	−	0.142967i	−0.939464	+	0.342647i	$0.888677\pi$
$488$	21.2683	+	6.24493i	0.962770	+	0.282695i
$489$	7.11068	−	15.5702i	0.321556	−	0.704110i
$490$	6.99735	−	8.07537i	0.316108	−	0.364808i
$491$	−0.0523189	+	0.363886i	−0.00236112	+	0.0164219i	−0.990968	−	0.134099i	$-0.957186\pi$
$491$	−0.0523189	+	0.363886i	−0.00236112	+	0.0164219i	0.988607	+	0.150521i	$0.0480951\pi$
$492$	6.47785	−	1.90207i	0.292044	−	0.0857519i
$493$	−0.967715	−	1.11680i	−0.0435837	−	0.0502983i
$494$	−9.98815	+	6.41900i	−0.449388	+	0.288804i
$495$	10.4812	−	6.73584i	0.471094	−	0.302754i
$496$	−0.990348	−	1.14292i	−0.0444679	−	0.0513187i
$497$	10.2474	−	3.00892i	0.459661	−	0.134969i
$498$	0.119345	−	0.830066i	0.00534800	−	0.0371961i
$499$	−8.88893	+	10.2584i	−0.397923	+	0.459228i	−0.918986	−	0.394291i	$-0.870990\pi$
$499$	−8.88893	+	10.2584i	−0.397923	+	0.459228i	0.521063	+	0.853518i	$0.325536\pi$
$500$	6.05633	−	13.2615i	0.270847	−	0.593073i
$501$	10.2603	+	3.01270i	0.458396	+	0.134597i
$502$	3.72001	+	8.14567i	0.166032	+	0.363559i
$503$	2.38681	+	16.6006i	0.106423	+	0.740186i	0.971241	+	0.238100i	$0.0765247\pi$
$503$	2.38681	+	16.6006i	0.106423	+	0.740186i	−0.864818	+	0.502086i	$0.832566\pi$
$504$	−1.22398	−	0.786607i	−0.0545206	−	0.0350382i
$505$	44.2502			1.96911
$506$	−8.01124	+	1.46726i	−0.356143	+	0.0652275i
$507$	−30.7142			−1.36407
$508$	−14.0969	−	9.05952i	−0.625449	−	0.401951i
$509$	−0.426906	−	2.96920i	−0.0189223	−	0.131607i	0.978171	−	0.207804i	$-0.0666315\pi$
$509$	−0.426906	−	2.96920i	−0.0189223	−	0.131607i	−0.997093	+	0.0761963i	$0.975722\pi$
$510$	−0.652738	−	1.42930i	−0.0289037	−	0.0632904i
$511$	5.18188	+	1.52154i	0.229233	+	0.0673088i
$512$	−9.45633	+	20.7065i	−0.417915	+	0.915105i
$513$	2.45561	−	2.83392i	0.108418	−	0.125121i
$514$	0.431040	−	2.99795i	0.0190124	−	0.132234i
$515$	35.7134	−	10.4864i	1.57372	−	0.462086i
$516$	−7.95013	−	9.17494i	−0.349985	−	0.403904i
$517$	16.9874	−	10.9172i	0.747107	−	0.480137i
$518$	−2.65432	+	1.70583i	−0.116624	+	0.0749498i
$519$	−15.8083	−	18.2438i	−0.693909	−	0.800814i
$520$	40.2465	−	11.8174i	1.76492	−	0.518228i
$521$	1.30671	−	9.08839i	0.0572482	−	0.398170i	−0.940970	−	0.338491i	$-0.890083\pi$
$521$	1.30671	−	9.08839i	0.0572482	−	0.398170i	0.998218	−	0.0596783i	$-0.0190075\pi$
$522$	0.496232	−	0.572682i	0.0217195	−	0.0250656i
$523$	−3.03941	+	6.65538i	−0.132904	+	0.291019i	−0.964370	−	0.264556i	$-0.914775\pi$
$523$	−3.03941	+	6.65538i	−0.132904	+	0.291019i	0.831466	+	0.555575i	$0.187502\pi$
$524$	22.9180	+	6.72932i	1.00118	+	0.293972i
$525$	2.45800	+	5.38226i	0.107276	+	0.234901i
$526$	−1.66161	−	11.5567i	−0.0724495	−	0.503897i
$527$	0.443901	+	0.285278i	0.0193367	+	0.0124269i
$528$	9.49167			0.413072
$529$	21.5071	−	8.15145i	0.935090	−	0.354411i
$530$	11.7441			0.510130
$531$	0.852693	+	0.547993i	0.0370037	+	0.0237809i
$532$	−0.761360	−	5.29537i	−0.0330091	−	0.229584i
$533$	−10.4724	−	22.9314i	−0.453610	−	0.993268i
$534$	2.15491	+	0.632739i	0.0932521	+	0.0273813i
$535$	9.36900	−	20.5153i	0.405057	−	0.886952i
$536$	−2.94216	+	3.39543i	−0.127082	+	0.146660i
$537$	0.370961	−	2.58009i	0.0160082	−	0.111339i
$538$	−6.22496	+	1.82781i	−0.268377	+	0.0788027i
$539$	−14.7482	−	17.0204i	−0.635251	−	0.733119i
$540$	−5.23338	+	3.36329i	−0.225209	+	0.144733i
$541$	0.558457	−	0.358898i	0.0240099	−	0.0154303i	−0.528581	−	0.848883i	$-0.677276\pi$
$541$	0.558457	−	0.358898i	0.0240099	−	0.0154303i	0.552591	+	0.833453i	$0.313639\pi$
$542$	3.48829	+	4.02570i	0.149835	+	0.172919i
$543$	−9.62333	+	2.82567i	−0.412977	+	0.121261i
$544$	0.650353	−	4.52330i	0.0278836	−	0.193935i
$545$	−2.69973	+	3.11565i	−0.115644	+	0.133460i
$546$	−1.05980	+	2.32064i	−0.0453553	+	0.0993143i
$547$	17.4721	+	5.13026i	0.747052	+	0.219354i	0.633033	−	0.774124i	$-0.281810\pi$
$547$	17.4721	+	5.13026i	0.747052	+	0.219354i	0.114018	+	0.993479i	$0.463628\pi$
$548$	0.565279	+	1.23779i	0.0241475	+	0.0528757i
$549$	1.74697	+	12.1505i	0.0745590	+	0.518569i
$550$	10.4914	+	6.74240i	0.447354	+	0.287497i
$551$	5.93346			0.252774
$552$	8.51833	−	1.56013i	0.362564	−	0.0664035i
$553$	−1.15743			−0.0492188
$554$	5.93180	+	3.81214i	0.252018	+	0.161962i
$555$	4.08851	+	28.4362i	0.173548	+	1.20705i
$556$	10.9164	+	23.9036i	0.462959	+	1.01374i
$557$	24.4462	+	7.17805i	1.03582	+	0.304144i	0.755075	−	0.655639i	$-0.227601\pi$
$557$	24.4462	+	7.17805i	1.03582	+	0.304144i	0.280744	+	0.959783i	$0.409419\pi$
$558$	−0.112403	+	0.246129i	−0.00475841	+	0.0104195i
$559$	−29.6859	+	34.2593i	−1.25558	+	1.44901i
$560$	−1.07831	+	7.49980i	−0.0455669	+	0.316924i
$561$	−3.17764	+	0.933040i	−0.134160	+	0.0393930i
$562$	6.60934	+	7.62759i	0.278798	+	0.321750i
$563$	−17.8550	+	11.4747i	−0.752499	+	0.483602i	−0.859804	−	0.510624i	$-0.829414\pi$
$563$	−17.8550	+	11.4747i	−0.752499	+	0.483602i	0.107305	+	0.994226i	$0.465778\pi$
$564$	−8.48205	+	5.45108i	−0.357159	+	0.229532i
$565$	−39.7120	−	45.8301i	−1.67070	−	1.92809i
$566$	−2.70512	+	0.794295i	−0.113705	+	0.0333867i
$567$	0.114669	−	0.797537i	0.00481562	−	0.0334934i
$568$	−15.6741	+	18.0889i	−0.657672	+	0.758994i
$569$	−13.9743	+	30.5994i	−0.585833	+	1.28279i	0.352095	+	0.935964i	$0.385469\pi$
$569$	−13.9743	+	30.5994i	−0.585833	+	1.28279i	−0.937928	+	0.346831i	$0.887258\pi$
$570$	6.05353	+	1.77748i	0.253554	+	0.0744503i
$571$	−5.34091	−	11.6950i	−0.223510	−	0.489419i	0.764343	−	0.644810i	$-0.223064\pi$
$571$	−5.34091	−	11.6950i	−0.223510	−	0.489419i	−0.987853	+	0.155391i	$0.950336\pi$
$572$	−5.90827	−	41.0929i	−0.247037	−	1.71818i
$573$	21.0732	+	13.5429i	0.880344	+	0.565763i
$574$	−1.47124			−0.0614085
$575$	−32.5730	−	13.3915i	−1.35839	−	0.558463i
$576$	−3.00980			−0.125409
$577$	−9.24070	−	5.93864i	−0.384695	−	0.247229i	0.333972	−	0.942583i	$-0.391611\pi$
$577$	−9.24070	−	5.93864i	−0.384695	−	0.247229i	−0.718667	+	0.695354i	$0.755247\pi$
$578$	−1.09917	−	7.64487i	−0.0457193	−	0.317985i
$579$	0.0414839	+	0.0908370i	0.00172401	+	0.00377506i
$580$	−9.44487	−	2.77326i	−0.392177	−	0.115154i
$581$	0.586131	−	1.28345i	0.0243168	−	0.0532464i
$582$	−0.249198	+	0.287590i	−0.0103296	+	0.0119210i
$583$	3.52270	−	24.5009i	0.145895	−	1.01472i
$584$	−11.6131	+	3.40991i	−0.480553	+	0.141103i
$585$	15.2118	+	17.5553i	0.628930	+	0.725824i
$586$	0.0784249	−	0.0504006i	0.00323970	−	0.00208203i
$587$	−11.4406	+	7.35242i	−0.472204	+	0.303467i	−0.755014	−	0.655709i	$-0.772370\pi$
$587$	−11.4406	+	7.35242i	−0.472204	+	0.303467i	0.282810	+	0.959176i	$0.408733\pi$
$588$	7.36398	+	8.49848i	0.303685	+	0.350471i
$589$	−2.03288	+	0.596907i	−0.0837633	+	0.0245951i
$590$	−0.242702	+	1.68803i	−0.00999188	+	0.0694950i
$591$	10.8572	−	12.5299i	0.446605	−	0.515410i
$592$	−9.09195	+	19.9086i	−0.373677	+	0.818238i
$593$	−41.1409	−	12.0800i	−1.68945	−	0.496068i	−0.711113	−	0.703077i	$-0.751809\pi$
$593$	−41.1409	−	12.0800i	−1.68945	−	0.496068i	−0.978339	+	0.207009i	$0.933627\pi$
$594$	−0.705476	−	1.54478i	−0.0289461	−	0.0633830i
$595$	−0.376239	−	2.61680i	−0.0154243	−	0.107278i
$596$	13.8430	+	8.89638i	0.567033	+	0.364410i
$597$	−20.0452			−0.820397
$598$	−4.83344	−	14.3951i	−0.197654	−	0.588660i
$599$	−14.6628			−0.599106			−0.299553	−	0.954080i	$-0.596838\pi$
$599$	−14.6628			−0.599106			−0.299553	+	0.954080i	$0.596838\pi$
$600$	−11.1554	−	7.16917i	−0.455419	−	0.292680i
$601$	4.44759	+	30.9337i	0.181421	+	1.26181i	0.853406	+	0.521246i	$0.174533\pi$
$601$	4.44759	+	30.9337i	0.181421	+	1.26181i	−0.671985	+	0.740564i	$0.734558\pi$
$602$	1.09901	+	2.40650i	0.0447924	+	0.0980817i
$603$	−2.38728	−	0.700969i	−0.0972176	−	0.0285457i
$604$	6.20550	−	13.5881i	0.252498	−	0.552894i
$605$	3.62491	−	4.18337i	0.147374	−	0.170078i
$606$	0.858387	−	5.97021i	0.0348696	−	0.242523i
$607$	−3.74039	+	1.09828i	−0.151818	+	0.0445777i	−0.356758	−	0.934197i	$-0.616118\pi$
$607$	−3.74039	+	1.09828i	−0.151818	+	0.0445777i	0.204941	+	0.978774i	$0.434300\pi$
$608$	12.0159	+	13.8671i	0.487311	+	0.562386i
$609$	1.07255	−	0.689289i	0.0434621	−	0.0279314i
$610$	−17.3748	+	11.1661i	−0.703485	+	0.452102i
$611$	24.6546	+	28.4529i	0.997419	+	1.15108i
$612$	1.58664	−	0.465879i	0.0641360	−	0.0188320i
$613$	4.96719	−	34.5476i	0.200623	−	1.39536i	−0.601819	−	0.798633i	$-0.705557\pi$
$613$	4.96719	−	34.5476i	0.200623	−	1.39536i	0.802442	−	0.596731i	$-0.203534\pi$
$614$	−4.05522	+	4.67997i	−0.163655	+	0.188868i
$615$	−5.56487	+	12.1854i	−0.224397	+	0.491362i
$616$	−4.95055	−	1.45361i	−0.199464	−	0.0585678i
$617$	−6.31092	−	13.8190i	−0.254068	−	0.556332i	0.739023	−	0.673681i	$-0.235288\pi$
$617$	−6.31092	−	13.8190i	−0.254068	−	0.556332i	−0.993091	+	0.117349i	$0.962560\pi$
$618$	−0.722033	−	5.02185i	−0.0290444	−	0.202009i
$619$	−4.17467	−	2.68290i	−0.167794	−	0.107835i	0.454048	−	0.890977i	$-0.349979\pi$
$619$	−4.17467	−	2.68290i	−0.167794	−	0.107835i	−0.621843	+	0.783142i	$0.713616\pi$
$620$	3.51492			0.141163
$621$	2.74557	+	3.93215i	0.110176	+	0.157792i
$622$	14.3618			0.575856
$623$	3.17886	+	2.04293i	0.127358	+	0.0818482i
$624$	2.51849	+	17.5165i	0.100820	+	0.701221i
$625$	−3.23614	−	7.08616i	−0.129446	−	0.283447i
$626$	−0.703596	−	0.206594i	−0.0281214	−	0.00825718i
$627$	5.52402	−	12.0959i	0.220608	−	0.483065i
$628$	10.8838	−	12.5606i	0.434311	−	0.501222i
$629$	1.08679	−	7.55879i	0.0433332	−	0.301389i
$630$	1.30075	−	0.381934i	0.0518230	−	0.0152166i
$631$	−24.0121	−	27.7114i	−0.955905	−	1.10317i	−0.994585	−	0.103922i	$-0.966861\pi$
$631$	−24.0121	−	27.7114i	−0.955905	−	1.10317i	0.0386804	−	0.999252i	$-0.487685\pi$
$632$	2.18213	−	1.40237i	0.0868006	−	0.0557833i
$633$	1.95364	−	1.25553i	0.0776500	−	0.0499027i
$634$	−6.65939	−	7.68534i	−0.264478	−	0.305224i
$635$	31.9023	−	9.36737i	1.26600	−	0.371733i
$636$	−1.75893	+	12.2336i	−0.0697460	+	0.485094i
$637$	27.4972	−	31.7334i	1.08948	−	1.25732i
$638$	1.11630	−	2.44436i	0.0441947	−	0.0967730i
$639$	−12.7181	−	3.73437i	−0.503120	−	0.147729i
$640$	−16.3870	−	35.8826i	−0.647755	−	1.41838i
$641$	−1.95454	−	13.5941i	−0.0771997	−	0.536936i	−0.991318	−	0.131488i	$-0.958025\pi$
$641$	−1.95454	−	13.5941i	−0.0771997	−	0.536936i	0.914118	−	0.405448i	$-0.132884\pi$
$642$	−2.58616	−	1.66202i	−0.102068	−	0.0655948i
$643$	−34.2265			−1.34976			−0.674880	−	0.737927i	$-0.735805\pi$
$643$	−34.2265			−1.34976			−0.674880	+	0.737927i	$0.735805\pi$
$644$	6.80487	+	0.713416i	0.268150	+	0.0281125i
$645$	24.0885			0.948483
$646$	−1.41083	−	0.906684i	−0.0555083	−	0.0356730i
$647$	5.48316	+	38.1362i	0.215565	+	1.49929i	0.754141	+	0.656712i	$0.228053\pi$
$647$	5.48316	+	38.1362i	0.215565	+	1.49929i	−0.538576	+	0.842577i	$0.681038\pi$
$648$	0.750131	+	1.64256i	0.0294679	+	0.0645257i
$649$	3.44882	+	1.01267i	0.135378	+	0.0397506i
$650$	−9.65908	+	21.1504i	−0.378860	+	0.829588i
$651$	−0.298128	+	0.344058i	−0.0116846	+	0.0134847i
$652$	−4.31336	+	30.0000i	−0.168924	+	1.17489i
$653$	−19.8816	+	5.83777i	−0.778027	+	0.228449i	−0.646552	−	0.762870i	$-0.723790\pi$
$653$	−19.8816	+	5.83777i	−0.778027	+	0.228449i	−0.131475	+	0.991319i	$0.541971\pi$
$654$	0.367991	+	0.424685i	0.0143896	+	0.0166065i
$655$	−39.8699	+	25.6228i	−1.55785	+	1.00117i
$656$	−8.58537	+	5.51748i	−0.335203	+	0.215422i
$657$	−4.38935	−	5.06558i	−0.171245	−	0.197627i
$658$	2.10819	−	0.619022i	0.0821860	−	0.0241320i
$659$	2.25543	−	15.6869i	0.0878592	−	0.611074i	−0.897555	−	0.440902i	$-0.854659\pi$
$659$	2.25543	−	15.6869i	0.0878592	−	0.611074i	0.985414	−	0.170172i	$-0.0544324\pi$
$660$	−14.4467	+	16.6724i	−0.562336	+	0.648970i
$661$	−0.0565318	+	0.123787i	−0.00219883	+	0.00481477i	−0.910728	−	0.413006i	$-0.864479\pi$
$661$	−0.0565318	+	0.123787i	−0.00219883	+	0.00481477i	0.908529	+	0.417821i	$0.137206\pi$
$662$	−0.372850	−	0.109479i	−0.0144912	−	0.00425500i
$663$	−2.56504	−	5.61665i	−0.0996178	−	0.218132i
$664$	0.450011	+	3.12990i	0.0174638	+	0.121464i
$665$	8.92998	+	5.73895i	0.346290	+	0.222547i
$666$	3.91591			0.151738
$667$	−1.85728	+	7.35782i	−0.0719141	+	0.284896i
$668$	−18.9345			−0.732598
$669$	3.87074	+	2.48757i	0.149651	+	0.0961750i
$670$	−0.595757	−	4.14358i	−0.0230161	−	0.160080i
$671$	18.0834	+	39.5972i	0.698104	+	1.52863i
$672$	3.78298	+	1.11078i	0.145932	+	0.0428494i
$673$	−8.57511	+	18.7769i	−0.330546	+	0.723795i	−0.999815	−	0.0192250i	$-0.993880\pi$
$673$	−8.57511	+	18.7769i	−0.330546	+	0.723795i	0.669269	+	0.743020i	$0.266607\pi$
$674$	−5.63295	+	6.50077i	−0.216973	+	0.250400i
$675$	1.04509	−	7.26879i	0.0402257	−	0.279776i
$676$	52.1815	−	15.3219i	2.00698	−	0.589303i
$677$	−18.5314	−	21.3864i	−0.712220	−	0.821945i	0.278129	−	0.960544i	$-0.410286\pi$
$677$	−18.5314	−	21.3864i	−0.712220	−	0.821945i	−0.990349	+	0.138599i	$0.955740\pi$
$678$	−6.95372	+	4.46888i	−0.267056	+	0.171626i
$679$	−0.538617	+	0.346148i	−0.0206702	+	0.0132839i
$680$	3.87993	+	4.47767i	0.148788	+	0.171711i
$681$	8.36993	−	2.45763i	0.320736	−	0.0941767i
$682$	−0.136556	+	0.949767i	−0.00522899	+	0.0363684i
$683$	12.7796	−	14.7484i	0.488997	−	0.564332i	−0.456601	−	0.889672i	$-0.650933\pi$
$683$	12.7796	−	14.7484i	0.488997	−	0.564332i	0.945597	+	0.325340i	$0.105479\pi$
$684$	−2.75821	+	6.03965i	−0.105463	+	0.230932i
$685$	−2.59064	−	0.760680i	−0.0989832	−	0.0290641i
$686$	−2.14003	−	4.68601i	−0.0817068	−	0.178913i
$687$	−1.32507	−	9.21604i	−0.0505545	−	0.351614i
$688$	15.4382	+	9.92150i	0.588574	+	0.378254i
$689$	46.1502			1.75818
$690$	−4.09903	+	6.95033i	−0.156047	+	0.264594i
$691$	18.2405			0.693902			0.346951	−	0.937883i	$-0.387217\pi$
$691$	18.2405			0.693902			0.346951	+	0.937883i	$0.387217\pi$
$692$	35.9584	+	23.1091i	1.36693	+	0.878474i
$693$	−0.406637	−	2.82823i	−0.0154469	−	0.107435i
$694$	0.927358	+	2.03063i	0.0352020	+	0.0770817i
$695$	−50.0292	−	14.6899i	−1.89772	−	0.557220i
$696$	−1.18696	+	2.59908i	−0.0449915	+	0.0985177i
$697$	2.33186	−	2.69111i	0.0883254	−	0.101933i
$698$	−1.08714	+	7.56120i	−0.0411487	+	0.286196i
$699$	−2.83160	+	0.831433i	−0.107101	+	0.0314477i
$700$	−6.86095	−	7.91796i	−0.259319	−	0.299271i
$701$	21.0479	−	13.5267i	0.794970	−	0.510896i	−0.0790011	−	0.996875i	$-0.525173\pi$
$701$	21.0479	−	13.5267i	0.794970	−	0.510896i	0.873971	+	0.485979i	$0.161537\pi$
$702$	2.66364	−	1.71182i	0.100533	−	0.0646083i
$703$	20.0796	+	23.1731i	0.757315	+	0.873989i
$704$	−10.2410	+	3.00704i	−0.385973	+	0.113332i
$705$	2.84713	−	19.8023i	0.107229	−	0.745796i
$706$	8.75429	−	10.1030i	0.329472	−	0.380231i
$707$	4.21572	−	9.23114i	0.158549	−	0.347173i
$708$	−1.72204	−	0.505637i	−0.0647183	−	0.0190030i
$709$	−13.2237	−	28.9559i	−0.496626	−	1.08746i	−0.977551	−	0.210698i	$-0.932426\pi$
$709$	−13.2237	−	28.9559i	−0.496626	−	1.08746i	0.480925	−	0.876762i	$-0.340301\pi$
$710$	−3.17385	−	22.0746i	−0.119113	−	0.828447i
$711$	1.20844	+	0.776619i	0.0453202	+	0.0291255i
$712$	−8.46847			−0.317369
$713$	−0.103871	−	2.70772i	−0.00389001	−	0.101405i
$714$	−0.360355			−0.0134860
$715$	69.2981	+	44.5352i	2.59160	+	1.66552i
$716$	0.656847	+	4.56847i	0.0245475	+	0.170732i
$717$	6.82639	+	14.9477i	0.254936	+	0.558232i
$718$	15.1778	+	4.45660i	0.566430	+	0.166319i
$719$	−0.758817	+	1.66158i	−0.0282991	+	0.0619664i	−0.923254	−	0.384191i	$-0.874480\pi$
$719$	−0.758817	+	1.66158i	−0.0282991	+	0.0619664i	0.894955	+	0.446157i	$0.147208\pi$
$720$	6.15812	−	7.10685i	0.229499	−	0.264857i
$721$	1.21483	−	8.44930i	0.0452425	−	0.314668i
$722$	−2.26938	+	0.666350i	−0.0844576	+	0.0247990i
$723$	−0.865624	−	0.998983i	−0.0321929	−	0.0371526i
$724$	14.9399	−	9.60127i	0.555236	−	0.356828i
$725$	9.77531	−	6.28221i	0.363046	−	0.233315i
$726$	−0.494100	−	0.570221i	−0.0183378	−	0.0211629i
$727$	35.9742	−	10.5630i	1.33421	−	0.391759i	0.464609	−	0.885516i	$-0.346195\pi$
$727$	35.9742	−	10.5630i	1.33421	−	0.391759i	0.869600	+	0.493757i	$0.164377\pi$
$728$	1.36902	−	9.52175i	0.0507393	−	0.352900i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	4.68479	−	10.2583i	0.173392	−	0.379675i
$731$	−6.14372	−	1.80396i	−0.227234	−	0.0667218i
$732$	−9.02930	−	19.7714i	−0.333732	−	0.730772i
$733$	0.471638	+	3.28031i	0.0174203	+	0.121161i	0.996676	−	0.0814675i	$-0.0259607\pi$
$733$	0.471638	+	3.28031i	0.0174203	+	0.121161i	−0.979256	+	0.202629i	$0.935052\pi$
$734$	5.36442	+	3.44751i	0.198004	+	0.127250i
$735$	−22.3125			−0.823007
$736$	−20.9572	+	10.5598i	−0.772493	+	0.389238i
$737$	−8.82318			−0.325006
$738$	1.53609	+	0.987186i	0.0565443	+	0.0363388i
$739$	0.762673	+	5.30451i	0.0280554	+	0.195129i	0.999029	−	0.0440571i	$-0.0140284\pi$
$739$	0.762673	+	5.30451i	0.0280554	+	0.195129i	−0.970974	+	0.239187i	$0.923119\pi$
$740$	−21.1317	−	46.2719i	−0.776815	−	1.70099i
$741$	23.7883	+	6.98487i	0.873884	+	0.256596i
$742$	1.11886	−	2.44996i	0.0410746	−	0.0899408i
$743$	16.8909	−	19.4931i	0.619665	−	0.715132i	−0.355978	−	0.934494i	$-0.615852\pi$
$743$	16.8909	−	19.4931i	0.619665	−	0.715132i	0.975643	+	0.219362i	$0.0703977\pi$
$744$	0.145199	−	1.00988i	0.00532327	−	0.0370241i
$745$	−31.3278	+	9.19867i	−1.14776	+	0.337013i
$746$	−7.75723	−	8.95231i	−0.284012	−	0.327768i
$747$	−1.47314	+	0.946733i	−0.0538996	+	0.0346391i
$748$	4.93317	−	3.17036i	0.180375	−	0.115920i
$749$	−3.38715	−	3.90898i	−0.123764	−	0.142831i
$750$	3.78330	−	1.11088i	0.138147	−	0.0405635i
$751$	−5.51058	+	38.3269i	−0.201084	+	1.39857i	0.599991	+	0.800007i	$0.295171\pi$
$751$	−5.51058	+	38.3269i	−0.201084	+	1.39857i	−0.801075	+	0.598564i	$0.795738\pi$
$752$	9.98081	−	11.5185i	0.363963	−	0.420036i
$753$	7.76795	−	17.0094i	0.283080	−	0.619858i
$754$	4.80716	+	1.41151i	0.175066	+	0.0514041i
$755$	12.3129	+	26.9615i	0.448113	+	0.981230i
$756$	0.203039	+	1.41217i	0.00738447	+	0.0513601i
$757$	21.7825	+	13.9987i	0.791697	+	0.508793i	0.872897	−	0.487905i	$-0.162239\pi$
$757$	21.7825	+	13.9987i	0.791697	+	0.508793i	−0.0811996	+	0.996698i	$0.525875\pi$
$758$	−18.3386			−0.666089
$759$	13.2705	+	10.6363i	0.481688	+	0.386074i
$760$	−23.7895			−0.862934
$761$	25.7260	+	16.5331i	0.932568	+	0.599325i	0.916278	−	0.400542i	$-0.131178\pi$
$761$	25.7260	+	16.5331i	0.932568	+	0.599325i	0.0162899	+	0.999867i	$0.494815\pi$
$762$	−0.644982	−	4.48595i	−0.0233652	−	0.162509i
$763$	0.392760	+	0.860025i	0.0142189	+	0.0311350i
$764$	−42.5579	−	12.4961i	−1.53969	−	0.452094i
$765$	−1.36302	+	2.98460i	−0.0492801	+	0.107908i
$766$	−5.26042	+	6.07085i	−0.190067	+	0.219349i
$767$	−0.953734	+	6.63337i	−0.0344374	+	0.239517i
$768$	0.616632	−	0.181059i	0.0222508	−	0.00653342i
$769$	9.90083	+	11.4262i	0.357033	+	0.412038i	0.905643	−	0.424040i	$-0.139388\pi$
$769$	9.90083	+	11.4262i	0.357033	+	0.412038i	−0.548610	+	0.836078i	$0.684843\pi$
$770$	4.04428	−	2.59910i	0.145746	−	0.0936651i
$771$	−5.32056	+	3.41931i	−0.191615	+	0.123144i
$772$	−0.115793	−	0.133632i	−0.00416748	−	0.00480953i
$773$	24.1446	−	7.08951i	0.868423	−	0.254992i	0.182978	−	0.983117i	$-0.441426\pi$
$773$	24.1446	−	7.08951i	0.868423	−	0.254992i	0.685444	+	0.728125i	$0.259608\pi$
$774$	0.467280	−	3.25000i	0.0167960	−	0.116819i
$775$	−2.71715	+	3.13576i	−0.0976030	+	0.112640i
$776$	0.596068	−	1.30521i	0.0213976	−	0.0468542i
$777$	6.32166	+	1.85621i	0.226788	+	0.0665911i
$778$	−0.392250	−	0.858908i	−0.0140628	−	0.0307933i
$779$	2.03476	+	14.1521i	0.0729029	+	0.507051i
$780$	−34.6014	−	22.2370i	−1.23893	−	0.796212i
$781$	−47.0049			−1.68197
$782$	1.56595	−	1.46570i	0.0559983	−	0.0524132i
$783$	−1.58233			−0.0565480
$784$	−14.2999	−	9.19000i	−0.510711	−	0.328214i
$785$	4.69317	+	32.6417i	0.167506	+	1.16503i
$786$	2.68360	+	5.87626i	0.0957208	+	0.209599i
$787$	−21.0701	−	6.18675i	−0.751070	−	0.220534i	−0.116277	−	0.993217i	$-0.537096\pi$
$787$	−21.0701	−	6.18675i	−0.751070	−	0.220534i	−0.634792	+	0.772683i	$0.718914\pi$
$788$	−12.1951	+	26.7036i	−0.434434	+	0.951277i
$789$	−15.9658	+	18.4255i	−0.568396	+	0.655964i
$790$	−0.343959	+	2.39229i	−0.0122375	+	0.0851137i
$791$	−13.3441	+	3.91818i	−0.474461	+	0.139314i
$792$	4.19341	+	4.83945i	0.149006	+	0.171962i
$793$	−68.2769	+	43.8789i	−2.42458	+	1.55819i
$794$	11.7180	−	7.53073i	0.415858	−	0.267256i
$795$	−16.0595	−	18.5336i	−0.569570	−	0.657319i
$796$	34.0556	−	9.99964i	1.20707	−	0.354428i
$797$	0.684007	−	4.75737i	0.0242288	−	0.168515i	−0.974114	−	0.226056i	$-0.927417\pi$
$797$	0.684007	−	4.75737i	0.0242288	−	0.168515i	0.998343	+	0.0575409i	$0.0183260\pi$
$798$	0.947523	−	1.09350i	0.0335420	−	0.0387095i
$799$	−2.20912	+	4.83731i	−0.0781532	+	0.171132i
$800$	34.4783	+	10.1237i	1.21899	+	0.357928i
$801$	−1.94819	−	4.26595i	−0.0688361	−	0.150730i
$802$	−0.599800	−	4.17170i	−0.0211797	−	0.147308i
$803$	−19.9959	−	12.8506i	−0.705641	−	0.453488i
$804$	4.40553			0.155371
$805$	−9.91185	+	9.27728i	−0.349347	+	0.326981i
$806$	−1.78899			−0.0630145
$807$	11.3969	+	7.32431i	0.401188	+	0.257828i
$808$	3.23669	+	22.5117i	0.113866	+	0.791957i
$809$	−12.2663	−	26.8594i	−0.431260	−	0.944327i	−0.993121	−	0.117095i	$-0.962642\pi$
$809$	−12.2663	−	26.8594i	−0.431260	−	0.944327i	0.561861	−	0.827232i	$-0.310086\pi$
$810$	−1.61435	−	0.474017i	−0.0567226	−	0.0166553i
$811$	−9.34727	+	20.4677i	−0.328227	+	0.718717i	−0.999752	−	0.0222649i	$-0.992912\pi$
$811$	−9.34727	+	20.4677i	−0.328227	+	0.718717i	0.671525	+	0.740982i	$0.265640\pi$
$812$	−1.47835	+	1.70611i	−0.0518799	+	0.0598726i
$813$	1.58299	−	11.0099i	0.0555177	−	0.386134i
$814$	13.3241	−	3.91231i	0.467009	−	0.137126i
$815$	−39.3820	−	45.4493i	−1.37949	−	1.59202i
$816$	−2.10284	+	1.35141i	−0.0736141	+	0.0473089i
$817$	21.6285	−	13.8998i	0.756685	−	0.486292i
$818$	2.04034	+	2.35467i	0.0713387	+	0.0823292i
$819$	5.11148	−	1.50087i	0.178610	−	0.0524445i
$820$	3.37566	−	23.4783i	0.117883	−	0.819896i
$821$	12.2433	−	14.1296i	0.427296	−	0.493125i	−0.500750	−	0.865592i	$-0.666942\pi$
$821$	12.2433	−	14.1296i	0.427296	−	0.493125i	0.928046	+	0.372467i	$0.121488\pi$
$822$	−0.152885	+	0.334771i	−0.00533247	+	0.0116765i
$823$	39.1112	+	11.4841i	1.36333	+	0.400310i	0.879936	−	0.475092i	$-0.157585\pi$
$823$	39.1112	+	11.4841i	1.36333	+	0.400310i	0.483396	+	0.875402i	$0.339403\pi$
$824$	7.94707	+	17.4017i	0.276849	+	0.606215i
$825$	−3.70611	−	25.7766i	−0.129030	−	0.897426i
$826$	0.329021	+	0.211449i	0.0114481	+	0.00735726i
$827$	23.5429			0.818666			0.409333	−	0.912385i	$-0.365761\pi$
$827$	23.5429			0.818666			0.409333	+	0.912385i	$0.365761\pi$
$828$	−6.62613	−	5.31085i	−0.230274	−	0.184565i
$829$	−10.5885			−0.367752			−0.183876	−	0.982949i	$-0.558865\pi$
$829$	−10.5885			−0.367752			−0.183876	+	0.982949i	$0.558865\pi$
$830$	−2.47858	−	1.59288i	−0.0860327	−	0.0552898i
$831$	−2.09543	−	14.5740i	−0.0726896	−	0.505567i
$832$	−8.26669	−	18.1015i	−0.286596	−	0.627558i
$833$	5.69075	+	1.67095i	0.197173	+	0.0578951i
$834$	−2.95244	+	6.46494i	−0.102235	+	0.223863i
$835$	24.6029	−	28.3933i	0.851420	−	0.982591i
$836$	−3.35088	+	23.3059i	−0.115893	+	0.806052i
$837$	0.542128	−	0.159183i	0.0187387	−	0.00550217i
$838$	2.91737	+	3.36682i	0.100779	+	0.116305i
$839$	33.0705	−	21.2531i	1.14172	−	0.733740i	0.173747	−	0.984790i	$-0.444412\pi$
$839$	33.0705	−	21.2531i	1.14172	−	0.733740i	0.967974	+	0.251051i	$0.0807760\pi$
$840$	−4.30027	+	2.76361i	−0.148373	+	0.0953537i
$841$	17.3513	+	20.0245i	0.598322	+	0.690500i
$842$	−2.23558	+	0.656427i	−0.0770433	+	0.0226220i
$843$	2.99932	−	20.8607i	0.103302	−	0.718481i
$844$	−2.69278	+	3.10764i	−0.0926894	+	0.106969i
$845$	−44.8272	+	98.1578i	−1.54210	+	3.37673i
$846$	−2.61648	−	0.768267i	−0.0899563	−	0.0264136i
$847$	−0.527357	−	1.15475i	−0.0181202	−	0.0396777i
$848$	−2.65883	−	18.4926i	−0.0913048	−	0.635039i
$849$	4.95261	+	3.18285i	0.169973	+	0.109235i
$850$	−3.28430			−0.112650
$851$	−35.0211	+	17.6462i	−1.20051	+	0.604904i
$852$	23.4702			0.804074
$853$	−34.9175	−	22.4401i	−1.19555	−	0.768335i	−0.217372	−	0.976089i	$-0.569748\pi$
$853$	−34.9175	−	22.4401i	−1.19555	−	0.768335i	−0.978181	+	0.207754i	$0.933385\pi$
$854$	0.674089	+	4.68839i	0.0230668	+	0.160433i
$855$	−5.47283	−	11.9838i	−0.187167	−	0.409838i
$856$	11.1221	+	3.26575i	0.380147	+	0.111621i
$857$	4.65231	−	10.1871i	0.158920	−	0.347986i	−0.813376	−	0.581738i	$-0.802373\pi$
$857$	4.65231	−	10.1871i	0.158920	−	0.347986i	0.972296	+	0.233752i	$0.0751003\pi$
$858$	7.35293	−	8.48574i	0.251025	−	0.289698i
$859$	−0.286639	+	1.99362i	−0.00978001	+	0.0680215i	−0.994127	−	0.108220i	$-0.965485\pi$
$859$	−0.286639	+	1.99362i	−0.00978001	+	0.0680215i	0.984347	+	0.176242i	$0.0563940\pi$
$860$	−40.9248	+	12.0166i	−1.39553	+	0.409763i
$861$	2.01185	+	2.32180i	0.0685637	+	0.0791268i
$862$	−13.3533	+	8.58161i	−0.454814	+	0.292291i
$863$	18.5634	−	11.9299i	0.631904	−	0.406100i	−0.185110	−	0.982718i	$-0.559264\pi$
$863$	18.5634	−	11.9299i	0.631904	−	0.406100i	0.817014	+	0.576618i	$0.195628\pi$
$864$	−3.20441	−	3.69808i	−0.109016	−	0.125811i
$865$	−81.3765	+	23.8943i	−2.76688	+	0.812431i
$866$	2.09662	−	14.5823i	0.0712461	−	0.495528i
$867$	−10.5615	+	12.1886i	−0.358687	+	0.413947i
$868$	0.334867	−	0.733255i	0.0113661	−	0.0248883i
$869$	4.88770	+	1.43516i	0.165804	+	0.0486844i
$870$	−1.10596	−	2.42170i	−0.0374954	−	0.0821034i
$871$	−2.34112	−	16.2828i	−0.0793258	−	0.551723i
$872$	−1.78252	−	1.14555i	−0.0603636	−	0.0387933i
$873$	0.794619			0.0268938
$874$	0.330128	+	8.60581i	0.0111668	+	0.291096i
$875$	6.63416			0.224275
$876$	9.98422	+	6.41647i	0.337336	+	0.216792i
$877$	7.99011	+	55.5724i	0.269807	+	1.87655i	0.450162	+	0.892947i	$0.351366\pi$
$877$	7.99011	+	55.5724i	0.269807	+	1.87655i	−0.180355	+	0.983602i	$0.557725\pi$
$878$	−6.17841	−	13.5288i	−0.208511	−	0.456576i
$879$	−0.186781	−	0.0548438i	−0.00629996	−	0.00184983i
$880$	13.8530	−	30.3339i	0.466985	−	1.02255i
$881$	26.6917	−	30.8039i	0.899267	−	1.03781i	−0.0998167	−	0.995006i	$-0.531826\pi$
$881$	26.6917	−	30.8039i	0.899267	−	1.03781i	0.999084	−	0.0428034i	$-0.0136289\pi$
$882$	−0.432827	+	3.01038i	−0.0145741	+	0.101365i
$883$	7.31464	−	2.14777i	0.246157	−	0.0722783i	−0.156326	−	0.987705i	$-0.549965\pi$
$883$	7.31464	−	2.14777i	0.246157	−	0.0722783i	0.402484	+	0.915427i	$0.368147\pi$
$884$	7.15972	+	8.26276i	0.240808	+	0.277907i
$885$	2.99580	−	1.92528i	0.100703	−	0.0647177i
$886$	1.30086	−	0.836013i	0.0437033	−	0.0280864i
$887$	−26.3936	−	30.4598i	−0.886210	−	1.02274i	−0.999574	−	0.0291872i	$-0.990708\pi$
$887$	−26.3936	−	30.4598i	−0.886210	−	1.02274i	0.113364	−	0.993554i	$-0.463837\pi$
$888$	−14.1675	+	4.15994i	−0.475429	+	0.139599i
$889$	1.08519	−	7.54764i	0.0363960	−	0.253140i
$890$	5.16721	−	5.96328i	0.173205	−	0.199890i
$891$	−1.47314	+	3.22574i	−0.0493522	+	0.108066i
$892$	−7.81707	−	2.29530i	−0.261735	−	0.0768523i
$893$	−8.87013	−	19.4229i	−0.296828	−	0.649962i
$894$	0.633367	+	4.40517i	0.0211830	+	0.147331i
$895$	−7.70415	−	4.95116i	−0.257521	−	0.165499i
$896$	−9.04675			−0.302231
$897$	−16.1078	+	27.3124i	−0.537823	+	0.911934i
$898$	−10.0236			−0.334493
$899$	0.752116	+	0.483356i	0.0250845	+	0.0161208i
$900$	1.85051	+	12.8706i	0.0616837	+	0.429019i
$901$	2.70797	+	5.92963i	0.0902156	+	0.197545i
$902$	6.21291	+	1.82428i	0.206867	+	0.0607417i
$903$	2.29491	−	5.02515i	0.0763698	−	0.167227i
$904$	20.4107	−	23.5551i	0.678848	−	0.783433i
$905$	−5.01480	+	34.8787i	−0.166698	+	1.15941i
$906$	3.87648	−	1.13824i	0.128787	−	0.0378154i
$907$	12.7271	+	14.6878i	0.422595	+	0.487701i	0.926626	−	0.375985i	$-0.122696\pi$
$907$	12.7271	+	14.6878i	0.422595	+	0.487701i	−0.504031	+	0.863686i	$0.668150\pi$
$908$	−12.9940	+	8.35074i	−0.431221	+	0.277129i
$909$	−10.5955	+	6.80933i	−0.351432	+	0.225851i
$910$	5.86963	+	6.77392i	0.194577	+	0.224553i
$911$	45.9029	−	13.4783i	1.52083	−	0.446556i	0.588602	−	0.808423i	$-0.299679\pi$
$911$	45.9029	−	13.4783i	1.52083	−	0.446556i	0.932230	+	0.361867i	$0.117860\pi$
$912$	1.42837	−	9.93450i	0.0472979	−	0.328964i
$913$	−4.06659	+	4.69310i	−0.134585	+	0.155319i
$914$	0.107878	−	0.236219i	0.00356828	−	0.00781344i
$915$	41.3807	+	12.1505i	1.36800	+	0.401682i
$916$	6.84866	+	14.9965i	0.226286	+	0.495498i
$917$	1.54683	+	10.7584i	0.0510808	+	0.355275i
$918$	0.376239	+	0.241794i	0.0124177	+	0.00798040i
$919$	50.2660			1.65812			0.829061	−	0.559158i	$-0.188876\pi$
$919$	50.2660			1.65812			0.829061	+	0.559158i	$0.188876\pi$
$920$	7.44651	−	29.5002i	0.245504	−	0.972594i
$921$	12.9309			0.426087
$922$	−1.10404	−	0.709526i	−0.0363597	−	0.0233670i
$923$	−12.4722	−	86.7457i	−0.410526	−	2.85527i
$924$	2.10172	+	4.60213i	0.0691416	+	0.151399i
$925$	57.6159	+	16.9176i	1.89440	+	0.556246i
$926$	−2.24637	+	4.91887i	−0.0738204	+	0.161644i
$927$	−6.93775	+	8.00660i	−0.227866	+	0.262971i
$928$	1.10191	−	7.66397i	0.0361721	−	0.251582i
$929$	−45.0030	+	13.2141i	−1.47650	+	0.433540i	−0.918206	−	0.396103i	$-0.870362\pi$
$929$	−45.0030	+	13.2141i	−1.47650	+	0.433540i	−0.558295	+	0.829643i	$0.688544\pi$
$930$	0.622537	+	0.718447i	0.0204138	+	0.0235588i
$931$	−20.0338	+	12.8750i	−0.656583	+	0.421960i
$932$	4.39595	−	2.82511i	0.143994	−	0.0925395i
$933$	−19.6391	−	22.6647i	−0.642954	−	0.742008i
$934$	−2.65708	+	0.780190i	−0.0869424	+	0.0255286i
$935$	−1.65590	+	11.5170i	−0.0541536	+	0.376647i
$936$	−7.81835	+	9.02285i	−0.255551	+	0.294921i
$937$	0.316944	−	0.694011i	0.0103541	−	0.0226724i	−0.904384	−	0.426719i	$-0.859669\pi$
$937$	0.316944	−	0.694011i	0.0103541	−	0.0226724i	0.914738	+	0.404047i	$0.132397\pi$
$938$	−0.921159	−	0.270477i	−0.0300769	−	0.00883138i
$939$	0.636102	+	1.39287i	0.0207584	+	0.0454546i
$940$	5.04131	+	35.0631i	0.164430	+	1.14363i
$941$	27.2858	+	17.5355i	0.889492	+	0.571642i	0.903656	−	0.428258i	$-0.140873\pi$
$941$	27.2858	+	17.5355i	0.889492	+	0.571642i	−0.0141648	+	0.999900i	$0.504509\pi$
$942$	4.49503			0.146456
$943$	−18.1863	−	1.90663i	−0.592226	−	0.0620884i
$944$	2.71297			0.0882997
$945$	−2.38145	−	1.53046i	−0.0774684	−	0.0497859i
$946$	−1.65707	−	11.5252i	−0.0538759	−	0.374715i
$947$	13.0693	+	28.6178i	0.424696	+	0.929954i	0.994158	+	0.107937i	$0.0344243\pi$
$947$	13.0693	+	28.6178i	0.424696	+	0.929954i	−0.569462	+	0.822018i	$0.692848\pi$
$948$	−2.44049	−	0.716593i	−0.0792634	−	0.0232738i
$949$	18.4096	−	40.3114i	0.597602	−	1.30856i
$950$	8.63577	−	9.96622i	0.280182	−	0.323347i
$951$	−3.02203	+	21.0187i	−0.0979960	+	0.681577i
$952$	1.30374	−	0.382812i	0.0422544	−	0.0124070i
$953$	3.07721	+	3.55129i	0.0996808	+	0.115038i	0.803398	−	0.595442i	$-0.203023\pi$
$953$	3.07721	+	3.55129i	0.0996808	+	0.115038i	−0.703717	+	0.710480i	$0.748478\pi$
$954$	−2.81207	+	1.80721i	−0.0910441	+	0.0585105i
$955$	74.0371	−	47.5808i	2.39578	−	1.53968i
$956$	−19.0543	−	21.9899i	−0.616261	−	0.711203i
$957$	−5.38398	+	1.58088i	−0.174039	+	0.0511026i
$958$	0.569590	−	3.96158i	0.0184026	−	0.127993i
$959$	−0.405497	+	0.467969i	−0.0130942	+	0.0151115i
$960$	−4.39279	+	9.61886i	−0.141777	+	0.310448i
$961$	29.4380	+	8.64377i	0.949612	+	0.278831i
$962$	10.7554	+	23.5510i	0.346768	+	0.759315i
$963$	0.913569	+	6.35401i	0.0294394	+	0.204755i
$964$	1.96899	+	1.26539i	0.0634168	+	0.0407555i
$965$	0.350846			0.0112941
$966$	1.05941	+	1.51727i	0.0340859	+	0.0488172i
$967$	−26.0335			−0.837180			−0.418590	−	0.908175i	$-0.637476\pi$
$967$	−26.0335			−0.837180			−0.418590	+	0.908175i	$0.637476\pi$
$968$	2.39337	+	1.53813i	0.0769259	+	0.0494373i
$969$	0.498380	+	3.46631i	0.0160103	+	0.111354i
$970$	0.555390	+	1.21613i	0.0178325	+	0.0390477i
$971$	1.29473	+	0.380168i	0.0415500	+	0.0122002i	0.302442	−	0.953168i	$-0.402198\pi$
$971$	1.29473	+	0.380168i	0.0415500	+	0.0122002i	−0.260892	+	0.965368i	$0.584016\pi$
$972$	0.735560	−	1.61065i	0.0235931	−	0.0516617i
$973$	−7.83078	+	9.03720i	−0.251043	+	0.289719i
$974$	−0.236386	+	1.64410i	−0.00757430	+	0.0526804i
$975$	46.5863	−	13.6790i	1.49196	−	0.438078i
$976$	21.5161	+	24.8309i	0.688714	+	0.794818i
$977$	−10.8844	+	6.99500i	−0.348224	+	0.223790i	−0.703047	−	0.711144i	$-0.748178\pi$
$977$	−10.8844	+	6.99500i	−0.348224	+	0.223790i	0.354823	+	0.934934i	$0.384541\pi$
$978$	−6.89593	+	4.43175i	−0.220508	+	0.141712i
$979$	−10.8909	−	12.5687i	−0.348074	−	0.401698i
$980$	37.9075	−	11.1306i	1.21091	−	0.355555i
$981$	0.166994	−	1.16147i	0.00533172	−	0.0370829i
$982$	0.115291	−	0.133053i	0.00367907	−	0.00424588i
$983$	4.04926	−	8.86663i	0.129151	−	0.282802i	−0.833999	−	0.551766i	$-0.813954\pi$
$983$	4.04926	−	8.86663i	0.129151	−	0.282802i	0.963150	+	0.268964i	$0.0866814\pi$
$984$	−6.60617	−	1.93975i	−0.210597	−	0.0618369i
$985$	−24.1975	−	52.9851i	−0.770996	−	1.68825i
$986$	0.100713	+	0.700475i	0.00320736	+	0.0223077i
$987$	−3.85975	−	2.48051i	−0.122857	−	0.0789555i
$988$	−43.8993			−1.39662
$989$	10.4664	+	31.1714i	0.332813	+	0.991193i
$990$	−5.96651			−0.189628
$991$	−17.6477	−	11.3415i	−0.560598	−	0.360274i	0.229449	−	0.973321i	$-0.426308\pi$
$991$	−17.6477	−	11.3415i	−0.560598	−	0.360274i	−0.790047	+	0.613046i	$0.789944\pi$
$992$	0.393467	+	2.73662i	0.0124926	+	0.0868879i
$993$	0.337083	+	0.738109i	0.0106970	+	0.0234232i
$994$	−4.90742	−	1.44095i	−0.155654	−	0.0457041i
$995$	−29.2559	+	64.0615i	−0.927474	+	2.03088i
$996$	2.03050	−	2.34332i	0.0643389	−	0.0742511i
$997$	1.29155	−	8.98293i	0.0409038	−	0.284492i	−0.959095	−	0.283084i	$-0.908643\pi$
$997$	1.29155	−	8.98293i	0.0409038	−	0.284492i	0.999999	−	0.00140859i	$-0.000448368\pi$
$998$	6.23705	−	1.83136i	0.197430	−	0.0579708i
$999$	−5.35482	−	6.17979i	−0.169419	−	0.195520i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.e.a.25.1	✓	10
3.2	odd	2		207.2.i.b.163.1		10
23.9	even	11		1587.2.a.o.1.3		5
23.12	even	11	inner	69.2.e.a.58.1	yes	10
23.14	odd	22		1587.2.a.p.1.3		5
69.14	even	22		4761.2.a.bq.1.3		5
69.32	odd	22		4761.2.a.br.1.3		5
69.35	odd	22		207.2.i.b.127.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.a.25.1	✓	10	1.1	even	1	trivial
69.2.e.a.58.1	yes	10	23.12	even	11	inner
207.2.i.b.127.1		10	69.35	odd	22
207.2.i.b.163.1		10	3.2	odd	2
1587.2.a.o.1.3		5	23.9	even	11
1587.2.a.p.1.3		5	23.14	odd	22
4761.2.a.bq.1.3		5	69.14	even	22
4761.2.a.br.1.3		5	69.32	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)

\(f(q)\)	\(=\)	\(q+(-0.402869 - 0.258908i) q^{2} +(0.142315 + 0.989821i) q^{3} +(-0.735560 - 1.61065i) q^{4} +(3.37102 + 0.989821i) q^{5} +(0.198939 - 0.435615i) q^{6} +(0.527646 - 0.608936i) q^{7} +(-0.256983 + 1.78736i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.402869 - 0.258908i) q^{2} +(0.142315 + 0.989821i) q^{3} +(-0.735560 - 1.61065i) q^{4} +(3.37102 + 0.989821i) q^{5} +(0.198939 - 0.435615i) q^{6} +(0.527646 - 0.608936i) q^{7} +(-0.256983 + 1.78736i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(-1.10181 - 1.27155i) q^{10} +(-2.98325 + 1.91722i) q^{11} +(1.48958 - 0.957293i) q^{12} +(-4.32972 - 4.99677i) q^{13} +(-0.370231 + 0.108710i) q^{14} +(-0.500000 + 3.47758i) q^{15} +(-1.75278 + 2.02282i) q^{16} +(0.387956 - 0.849505i) q^{17} +(0.459493 + 0.134919i) q^{18} +(1.55773 + 3.41095i) q^{19} +(-0.885331 - 6.15762i) q^{20} +(0.677830 + 0.435615i) q^{21} +1.69824 q^{22} +(-4.71737 + 0.863983i) q^{23} -1.80574 q^{24} +(6.17778 + 3.97022i) q^{25} +(0.450608 + 3.13404i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-1.36890 - 0.401945i) q^{28} +(0.657326 - 1.43934i) q^{29} +(1.10181 - 1.27155i) q^{30} +(-0.0804100 + 0.559264i) q^{31} +(4.69505 - 1.37859i) q^{32} +(-2.32227 - 2.68004i) q^{33} +(-0.376239 + 0.241794i) q^{34} +(2.38145 - 1.53046i) q^{35} +(1.15954 + 1.33818i) q^{36} +(7.84580 - 2.30374i) q^{37} +(0.255563 - 1.77748i) q^{38} +(4.32972 - 4.99677i) q^{39} +(-2.63546 + 5.77086i) q^{40} +(3.65843 + 1.07421i) q^{41} +(-0.160293 - 0.350992i) q^{42} +(-0.975753 - 6.78651i) q^{43} +(5.28234 + 3.39475i) q^{44} -3.51334 q^{45} +(2.12417 + 0.873293i) q^{46} -5.69427 q^{47} +(-2.25168 - 1.44706i) q^{48} +(0.903811 + 6.28614i) q^{49} +(-1.46091 - 3.19895i) q^{50} +(0.896070 + 0.263110i) q^{51} +(-4.86328 + 10.6491i) q^{52} +(-4.57100 + 5.27521i) q^{53} +(-0.0681534 + 0.474017i) q^{54} +(-11.9543 + 3.51011i) q^{55} +(0.952791 + 1.09958i) q^{56} +(-3.15455 + 2.02730i) q^{57} +(-0.637474 + 0.409680i) q^{58} +(-0.663766 - 0.766027i) q^{59} +(5.96894 - 1.75264i) q^{60} +(1.74697 - 12.1505i) q^{61} +(0.177193 - 0.204491i) q^{62} +(-0.334716 + 0.732925i) q^{63} +(2.88789 + 0.847960i) q^{64} +(-9.64969 - 21.1299i) q^{65} +(0.241685 + 1.68096i) q^{66} +(2.09309 + 1.34515i) q^{67} -1.65362 q^{68} +(-1.52654 - 4.54639i) q^{69} -1.35566 q^{70} +(11.1508 + 7.16620i) q^{71} +(-0.256983 - 1.78736i) q^{72} +(2.78441 + 6.09701i) q^{73} +(-3.75729 - 1.10324i) q^{74} +(-3.05062 + 6.67992i) q^{75} +(4.34805 - 5.01792i) q^{76} +(-0.406637 + 2.82823i) q^{77} +(-3.03802 + 0.892042i) q^{78} +(-0.940694 - 1.08562i) q^{79} +(-7.91090 + 5.08403i) q^{80} +(0.841254 - 0.540641i) q^{81} +(-1.19575 - 1.37997i) q^{82} +(1.68020 - 0.493351i) q^{83} +(0.203039 - 1.41217i) q^{84} +(2.14867 - 2.47969i) q^{85} +(-1.36398 + 2.98671i) q^{86} +(1.51824 + 0.445795i) q^{87} +(-2.66011 - 5.82484i) q^{88} +(0.667422 + 4.64202i) q^{89} +(1.41542 + 0.909632i) q^{90} -5.32728 q^{91} +(4.86148 + 6.96252i) q^{92} -0.565015 q^{93} +(2.29404 + 1.47429i) q^{94} +(1.87491 + 13.0403i) q^{95} +(2.03274 + 4.45107i) q^{96} +(-0.762432 - 0.223870i) q^{97} +(1.26342 - 2.76650i) q^{98} +(2.32227 - 2.68004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9} - 2 q^{10} + 7 q^{11} + 14 q^{12} - 30 q^{13} + q^{14} - 5 q^{15} + 12 q^{16} - 2 q^{17} - 4 q^{18} + 10 q^{19} + 4 q^{20} - 3 q^{21} + 6 q^{22} - q^{23} - 18 q^{24} + 24 q^{25} + q^{26} + q^{27} + 9 q^{28} - 14 q^{29} + 2 q^{30} - 28 q^{31} + 23 q^{32} - 7 q^{33} - 8 q^{34} - 4 q^{35} - 3 q^{36} + 19 q^{37} - 15 q^{38} + 30 q^{39} - 13 q^{40} + 19 q^{41} + 21 q^{42} - 24 q^{43} + 54 q^{44} - 6 q^{45} + 18 q^{46} + 26 q^{47} + 10 q^{48} - 13 q^{49} - 36 q^{50} + 24 q^{51} - 57 q^{52} - q^{53} + 4 q^{54} - 24 q^{55} - 10 q^{56} + q^{57} + 10 q^{58} + 2 q^{59} + 7 q^{60} + 30 q^{61} - 24 q^{62} - 8 q^{63} + 13 q^{64} - 4 q^{65} - 28 q^{66} + 4 q^{67} - 50 q^{68} + q^{69} + 6 q^{70} - 14 q^{71} - 15 q^{72} - 26 q^{73} - 12 q^{74} - 13 q^{75} + 19 q^{76} - 43 q^{77} + 10 q^{78} + 20 q^{79} - 5 q^{80} - q^{81} + 10 q^{82} + 18 q^{83} - 42 q^{84} + 21 q^{85} + 14 q^{86} - 8 q^{87} - 38 q^{88} - 5 q^{89} + 9 q^{90} + 46 q^{91} + 52 q^{92} - 16 q^{93} - 6 q^{94} + 5 q^{95} - q^{96} + 15 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9 - 2 * q^10 + 7 * q^11 + 14 * q^12 - 30 * q^13 + q^14 - 5 * q^15 + 12 * q^16 - 2 * q^17 - 4 * q^18 + 10 * q^19 + 4 * q^20 - 3 * q^21 + 6 * q^22 - q^23 - 18 * q^24 + 24 * q^25 + q^26 + q^27 + 9 * q^28 - 14 * q^29 + 2 * q^30 - 28 * q^31 + 23 * q^32 - 7 * q^33 - 8 * q^34 - 4 * q^35 - 3 * q^36 + 19 * q^37 - 15 * q^38 + 30 * q^39 - 13 * q^40 + 19 * q^41 + 21 * q^42 - 24 * q^43 + 54 * q^44 - 6 * q^45 + 18 * q^46 + 26 * q^47 + 10 * q^48 - 13 * q^49 - 36 * q^50 + 24 * q^51 - 57 * q^52 - q^53 + 4 * q^54 - 24 * q^55 - 10 * q^56 + q^57 + 10 * q^58 + 2 * q^59 + 7 * q^60 + 30 * q^61 - 24 * q^62 - 8 * q^63 + 13 * q^64 - 4 * q^65 - 28 * q^66 + 4 * q^67 - 50 * q^68 + q^69 + 6 * q^70 - 14 * q^71 - 15 * q^72 - 26 * q^73 - 12 * q^74 - 13 * q^75 + 19 * q^76 - 43 * q^77 + 10 * q^78 + 20 * q^79 - 5 * q^80 - q^81 + 10 * q^82 + 18 * q^83 - 42 * q^84 + 21 * q^85 + 14 * q^86 - 8 * q^87 - 38 * q^88 - 5 * q^89 + 9 * q^90 + 46 * q^91 + 52 * q^92 - 16 * q^93 - 6 * q^94 + 5 * q^95 - q^96 + 15 * q^97 + 58 * q^98 + 7 * q^99

Introduction

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