LMFDB - Embedded newform 189.2.u.a.4.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(4,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2, 12]))

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

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

chi := DirichletCharacter("189.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.u (of order $9$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			4.7
Character	$\chi$	$=$	189.4
Dual form			189.2.u.a.142.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.266701 - 1.51254i) q^{2} +(-1.44858 - 0.949540i) q^{3} +(-0.337258 + 0.122752i) q^{4} +(3.71318 - 1.35149i) q^{5} +(-1.04988 + 2.44427i) q^{6} +(2.56740 + 0.639091i) q^{7} +(-1.26026 - 2.18283i) q^{8} +(1.19675 + 2.75096i) q^{9} +O(q^{10})$	\(q+(-0.266701 - 1.51254i) q^{2} +(-1.44858 - 0.949540i) q^{3} +(-0.337258 + 0.122752i) q^{4} +(3.71318 - 1.35149i) q^{5} +(-1.04988 + 2.44427i) q^{6} +(2.56740 + 0.639091i) q^{7} +(-1.26026 - 2.18283i) q^{8} +(1.19675 + 2.75096i) q^{9} +(-3.03449 - 5.25589i) q^{10} +(-0.965994 - 0.351593i) q^{11} +(0.605101 + 0.142424i) q^{12} +(-3.84523 + 1.39955i) q^{13} +(0.281920 - 4.05374i) q^{14} +(-6.66212 - 1.56808i) q^{15} +(-3.51537 + 2.94975i) q^{16} +(0.513661 + 0.889686i) q^{17} +(3.84176 - 2.54381i) q^{18} +(-2.28787 + 3.96272i) q^{19} +(-1.08640 + 0.911600i) q^{20} +(-3.11224 - 3.36362i) q^{21} +(-0.274166 + 1.55487i) q^{22} +(0.114726 - 0.650644i) q^{23} +(-0.247105 + 4.35866i) q^{24} +(8.13099 - 6.82271i) q^{25} +(3.14240 + 5.44279i) q^{26} +(0.878570 - 5.12134i) q^{27} +(-0.944326 + 0.0996150i) q^{28} +(6.27669 + 2.28453i) q^{29} +(-0.594988 + 10.4949i) q^{30} +(-8.69005 + 3.16292i) q^{31} +(1.53751 + 1.29012i) q^{32} +(1.06546 + 1.42656i) q^{33} +(1.20869 - 1.01421i) q^{34} +(10.3970 - 1.09675i) q^{35} +(-0.741298 - 0.780881i) q^{36} +3.18970 q^{37} +(6.60394 + 2.40364i) q^{38} +(6.89903 + 1.62385i) q^{39} +(-7.62964 - 6.40203i) q^{40} +(-5.19385 + 1.89041i) q^{41} +(-4.25757 + 5.60446i) q^{42} +(0.455851 + 2.58526i) q^{43} +0.368948 q^{44} +(8.16163 + 8.59744i) q^{45} -1.01472 q^{46} +(-2.95417 - 1.07523i) q^{47} +(7.89319 - 0.934948i) q^{48} +(6.18313 + 3.28161i) q^{49} +(-12.4882 - 10.4788i) q^{50} +(0.100716 - 1.77652i) q^{51} +(1.12504 - 0.944017i) q^{52} +(2.27046 - 3.93255i) q^{53} +(-7.98054 + 0.0369978i) q^{54} -4.06209 q^{55} +(-1.84056 - 6.40963i) q^{56} +(7.07692 - 3.56787i) q^{57} +(1.78144 - 10.1030i) q^{58} +(-5.31915 - 4.46329i) q^{59} +(2.43934 - 0.288939i) q^{60} +(12.1841 + 4.43464i) q^{61} +(7.10169 + 12.3005i) q^{62} +(1.31442 + 7.82766i) q^{63} +(-3.04769 + 5.27875i) q^{64} +(-12.3866 + 10.3936i) q^{65} +(1.87357 - 1.99202i) q^{66} +(1.41867 - 8.04565i) q^{67} +(-0.282447 - 0.237001i) q^{68} +(-0.784002 + 0.833571i) q^{69} +(-4.43177 - 15.4333i) q^{70} +(0.478414 - 0.828638i) q^{71} +(4.49668 - 6.07922i) q^{72} +2.34044 q^{73} +(-0.850698 - 4.82455i) q^{74} +(-18.2568 + 2.16252i) q^{75} +(0.285173 - 1.61730i) q^{76} +(-2.25540 - 1.52004i) q^{77} +(0.616147 - 10.8681i) q^{78} +(0.996418 + 5.65097i) q^{79} +(-9.06667 + 15.7039i) q^{80} +(-6.13559 + 6.58441i) q^{81} +(4.24452 + 7.35172i) q^{82} +(-0.970385 - 0.353191i) q^{83} +(1.46252 + 0.752376i) q^{84} +(3.10972 + 2.60936i) q^{85} +(3.78873 - 1.37898i) q^{86} +(-6.92302 - 9.26929i) q^{87} +(0.449933 + 2.55170i) q^{88} +(-7.43653 + 12.8804i) q^{89} +(10.8272 - 14.6377i) q^{90} +(-10.7667 + 1.13576i) q^{91} +(0.0411755 + 0.233518i) q^{92} +(15.5915 + 3.66982i) q^{93} +(-0.838447 + 4.75507i) q^{94} +(-3.13973 + 17.8063i) q^{95} +(-1.00217 - 3.32877i) q^{96} +(-0.448435 - 2.54320i) q^{97} +(3.31451 - 10.2274i) q^{98} +(-0.188831 - 3.07818i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.266701	−	1.51254i	−0.188586	−	1.06953i	−0.921260	−	0.388946i	$-0.872839\pi$
$2$	−0.266701	−	1.51254i	−0.188586	−	1.06953i	0.732674	−	0.680580i	$-0.238272\pi$
$3$	−1.44858	−	0.949540i	−0.836336	−	0.548217i
$3$	−1.44858	−	0.949540i	−0.836336	−	0.548217i
$4$	−0.337258	+	0.122752i	−0.168629	+	0.0613759i
$5$	3.71318	−	1.35149i	1.66059	−	0.604404i	0.670131	−	0.742243i	$-0.266238\pi$
$5$	3.71318	−	1.35149i	1.66059	−	0.604404i	0.990455	+	0.137839i	$0.0440156\pi$
$6$	−1.04988	+	2.44427i	−0.428611	+	0.997870i
$7$	2.56740	+	0.639091i	0.970387	+	0.241554i
$7$	2.56740	+	0.639091i	0.970387	+	0.241554i
$8$	−1.26026	−	2.18283i	−0.445568	−	0.771747i
$9$	1.19675	+	2.75096i	0.398916	+	0.916988i
$10$	−3.03449	−	5.25589i	−0.959590	−	1.66206i
$11$	−0.965994	−	0.351593i	−0.291258	−	0.106009i	0.192259	−	0.981344i	$-0.438419\pi$
$11$	−0.965994	−	0.351593i	−0.291258	−	0.106009i	−0.483517	+	0.875335i	$0.660641\pi$
$12$	0.605101	+	0.142424i	0.174678	+	0.0411144i
$13$	−3.84523	+	1.39955i	−1.06647	+	0.388165i	−0.814857	−	0.579662i	$-0.803185\pi$
$13$	−3.84523	+	1.39955i	−1.06647	+	0.388165i	−0.251617	+	0.967827i	$0.580962\pi$
$14$	0.281920	−	4.05374i	0.0753462	−	1.08341i
$15$	−6.66212	−	1.56808i	−1.72015	−	0.404877i
$16$	−3.51537	+	2.94975i	−0.878843	+	0.737437i
$17$	0.513661	+	0.889686i	0.124581	+	0.215781i	0.921569	−	0.388214i	$-0.126908\pi$
$17$	0.513661	+	0.889686i	0.124581	+	0.215781i	−0.796988	+	0.603995i	$0.793575\pi$
$18$	3.84176	−	2.54381i	0.905512	−	0.599582i
$19$	−2.28787	+	3.96272i	−0.524874	+	0.909109i	0.474706	+	0.880144i	$0.342554\pi$
$19$	−2.28787	+	3.96272i	−0.524874	+	0.909109i	−0.999580	+	0.0289648i	$0.990779\pi$
$20$	−1.08640	+	0.911600i	−0.242927	+	0.203840i
$21$	−3.11224	−	3.36362i	−0.679146	−	0.734003i
$22$	−0.274166	+	1.55487i	−0.0584524	+	0.331500i
$23$	0.114726	−	0.650644i	0.0239221	−	0.135669i	−0.970508	−	0.241070i	$-0.922502\pi$
$23$	0.114726	−	0.650644i	0.0239221	−	0.135669i	0.994430	+	0.105401i	$0.0336127\pi$
$24$	−0.247105	+	4.35866i	−0.0504402	+	0.889708i
$25$	8.13099	−	6.82271i	1.62620	−	1.36454i
$26$	3.14240	+	5.44279i	0.616275	+	1.06742i
$27$	0.878570	−	5.12134i	0.169081	−	0.985602i
$28$	−0.944326	+	0.0996150i	−0.178461	+	0.0188255i
$29$	6.27669	+	2.28453i	1.16555	+	0.424226i	0.851078	−	0.525039i	$-0.175949\pi$
$29$	6.27669	+	2.28453i	1.16555	+	0.424226i	0.314475	+	0.949266i	$0.398172\pi$
$30$	−0.594988	+	10.4949i	−0.108629	+	1.91610i
$31$	−8.69005	+	3.16292i	−1.56078	+	0.568077i	−0.970915	−	0.239425i	$-0.923041\pi$
$31$	−8.69005	+	3.16292i	−1.56078	+	0.568077i	−0.589865	+	0.807502i	$0.700819\pi$
$32$	1.53751	+	1.29012i	0.271796	+	0.228064i
$33$	1.06546	+	1.42656i	0.185474	+	0.248332i
$34$	1.20869	−	1.01421i	0.207289	−	0.173936i
$35$	10.3970	−	1.09675i	1.75741	−	0.185385i
$36$	−0.741298	−	0.780881i	−0.123550	−	0.130147i
$37$	3.18970			0.524384			0.262192	−	0.965016i	$-0.415555\pi$
$37$	3.18970			0.524384			0.262192	+	0.965016i	$0.415555\pi$
$38$	6.60394	+	2.40364i	1.07130	+	0.389921i
$39$	6.89903	+	1.62385i	1.10473	+	0.260023i
$40$	−7.62964	−	6.40203i	−1.20635	−	1.01225i
$41$	−5.19385	+	1.89041i	−0.811143	+	0.295232i	−0.714096	−	0.700048i	$-0.753162\pi$
$41$	−5.19385	+	1.89041i	−0.811143	+	0.295232i	−0.0970471	+	0.995280i	$0.530940\pi$
$42$	−4.25757	+	5.60446i	−0.656958	+	0.864787i
$43$	0.455851	+	2.58526i	0.0695166	+	0.394248i	0.999636	+	0.0269903i	$0.00859232\pi$
$43$	0.455851	+	2.58526i	0.0695166	+	0.394248i	−0.930119	+	0.367258i	$0.880297\pi$
$44$	0.368948			0.0556209
$45$	8.16163	+	8.59744i	1.21666	+	1.28163i
$46$	−1.01472			−0.149613
$47$	−2.95417	−	1.07523i	−0.430911	−	0.156839i	0.117453	−	0.993078i	$-0.462527\pi$
$47$	−2.95417	−	1.07523i	−0.430911	−	0.156839i	−0.548364	+	0.836240i	$0.684749\pi$
$48$	7.89319	−	0.934948i	1.13928	−	0.134948i
$49$	6.18313	+	3.28161i	0.883304	+	0.468801i
$50$	−12.4882	−	10.4788i	−1.76609	−	1.48193i
$51$	0.100716	−	1.77652i	0.0141031	−	0.248763i
$52$	1.12504	−	0.944017i	0.156014	−	0.130912i
$53$	2.27046	−	3.93255i	0.311872	−	0.540178i	−0.666896	−	0.745151i	$-0.732377\pi$
$53$	2.27046	−	3.93255i	0.311872	−	0.540178i	0.978768	+	0.204973i	$0.0657107\pi$
$54$	−7.98054	+	0.0369978i	−1.08601	+	0.00503476i
$55$	−4.06209			−0.547732
$56$	−1.84056	−	6.40963i	−0.245956	−	0.856523i
$57$	7.07692	−	3.56787i	0.937361	−	0.472576i
$58$	1.78144	−	10.1030i	0.233914	−	1.32659i
$59$	−5.31915	−	4.46329i	−0.692494	−	0.581071i	0.227133	−	0.973864i	$-0.427065\pi$
$59$	−5.31915	−	4.46329i	−0.692494	−	0.581071i	−0.919627	+	0.392792i	$0.871509\pi$
$60$	2.43934	−	0.288939i	0.314917	−	0.0373019i
$61$	12.1841	+	4.43464i	1.56001	+	0.567798i	0.970739	−	0.240136i	$-0.0771922\pi$
$61$	12.1841	+	4.43464i	1.56001	+	0.567798i	0.589273	+	0.807934i	$0.299414\pi$
$62$	7.10169	+	12.3005i	0.901915	+	1.56216i
$63$	1.31442	+	7.82766i	0.165601	+	0.986193i
$64$	−3.04769	+	5.27875i	−0.380961	+	0.659844i
$65$	−12.3866	+	10.3936i	−1.53636	+	1.28916i
$66$	1.87357	−	1.99202i	0.230620	−	0.245201i
$67$	1.41867	−	8.04565i	0.173318	−	0.982933i	−0.766750	−	0.641945i	$-0.778128\pi$
$67$	1.41867	−	8.04565i	0.173318	−	0.982933i	0.940068	−	0.340987i	$-0.110761\pi$
$68$	−0.282447	−	0.237001i	−0.0342517	−	0.0287406i
$69$	−0.784002	+	0.833571i	−0.0943828	+	0.100350i
$70$	−4.43177	−	15.4333i	−0.529697	−	1.84463i
$71$	0.478414	−	0.828638i	0.0567773	−	0.0983412i	−0.836240	−	0.548364i	$-0.815251\pi$
$71$	0.478414	−	0.828638i	0.0567773	−	0.0983412i	0.893017	+	0.450023i	$0.148584\pi$
$72$	4.49668	−	6.07922i	0.529938	−	0.716443i
$73$	2.34044			0.273928			0.136964	−	0.990576i	$-0.456266\pi$
$73$	2.34044			0.273928			0.136964	+	0.990576i	$0.456266\pi$
$74$	−0.850698	−	4.82455i	−0.0988917	−	0.560843i
$75$	−18.2568	+	2.16252i	−2.10811	+	0.249706i
$76$	0.285173	−	1.61730i	0.0327116	−	0.185517i
$77$	−2.25540	−	1.52004i	−0.257026	−	0.173225i
$78$	0.616147	−	10.8681i	0.0697649	−	1.23057i
$79$	0.996418	+	5.65097i	0.112106	+	0.635784i	0.988143	+	0.153539i	$0.0490672\pi$
$79$	0.996418	+	5.65097i	0.112106	+	0.635784i	−0.876037	+	0.482244i	$0.839822\pi$
$80$	−9.06667	+	15.7039i	−1.01368	+	1.75575i
$81$	−6.13559	+	6.58441i	−0.681732	+	0.731602i
$82$	4.24452	+	7.35172i	0.468729	+	0.811862i
$83$	−0.970385	−	0.353191i	−0.106514	−	0.0387678i	0.288214	−	0.957566i	$-0.406939\pi$
$83$	−0.970385	−	0.353191i	−0.106514	−	0.0387678i	−0.394727	+	0.918798i	$0.629161\pi$
$84$	1.46252	+	0.752376i	0.159574	+	0.0820909i
$85$	3.10972	+	2.60936i	0.337296	+	0.283025i
$86$	3.78873	−	1.37898i	0.408549	−	0.148700i
$87$	−6.92302	−	9.26929i	−0.742225	−	0.993772i
$88$	0.449933	+	2.55170i	0.0479631	+	0.272012i
$89$	−7.43653	+	12.8804i	−0.788271	+	1.36532i	0.138755	+	0.990327i	$0.455690\pi$
$89$	−7.43653	+	12.8804i	−0.788271	+	1.36532i	−0.927026	+	0.374998i	$0.877643\pi$
$90$	10.8272	−	14.6377i	1.14129	−	1.54295i
$91$	−10.7667	+	1.13576i	−1.12866	+	0.119060i
$92$	0.0411755	+	0.233518i	0.00429284	+	0.0243459i
$93$	15.5915	+	3.66982i	1.61677	+	0.380543i
$94$	−0.838447	+	4.75507i	−0.0864792	+	0.490448i
$95$	−3.13973	+	17.8063i	−0.322130	+	1.82689i
$96$	−1.00217	−	3.32877i	−0.102284	−	0.339741i
$97$	−0.448435	−	2.54320i	−0.0455316	−	0.258223i	0.953542	−	0.301261i	$-0.0974075\pi$
$97$	−0.448435	−	2.54320i	−0.0455316	−	0.258223i	−0.999073	+	0.0430380i	$0.986296\pi$
$98$	3.31451	−	10.2274i	0.334816	−	1.03313i
$99$	−0.188831	−	3.07818i	−0.0189783	−	0.309369i
$100$	−1.90474	+	3.29910i	−0.190474	+	0.329910i
$101$	−2.16311	−	12.2676i	−0.215238	−	1.22067i	−0.880494	−	0.474058i	$-0.842789\pi$
$101$	−2.16311	−	12.2676i	−0.215238	−	1.22067i	0.665256	−	0.746615i	$-0.268322\pi$
$102$	−2.71392	+	0.321463i	−0.268718	+	0.0318296i
$103$	10.4317	−	3.79681i	1.02786	−	0.374111i	0.227595	−	0.973756i	$-0.426914\pi$
$103$	10.4317	−	3.79681i	1.02786	−	0.374111i	0.800266	+	0.599645i	$0.204691\pi$
$104$	7.90096	+	6.62969i	0.774753	+	0.650095i
$105$	−16.1022	−	8.28360i	−1.57141	−	0.808397i
$106$	−6.55367	−	2.38534i	−0.636549	−	0.231685i
$107$	−3.10276	−	5.37415i	−0.299956	−	0.519538i	0.676170	−	0.736746i	$-0.263639\pi$
$107$	−3.10276	−	5.37415i	−0.299956	−	0.519538i	−0.976125	+	0.217207i	$0.930305\pi$
$108$	0.332349	+	1.83506i	0.0319803	+	0.176578i
$109$	3.36985	−	5.83675i	0.322773	−	0.559059i	−0.658286	−	0.752768i	$-0.728718\pi$
$109$	3.36985	−	5.83675i	0.322773	−	0.559059i	0.981059	+	0.193709i	$0.0620517\pi$
$110$	1.08336	+	6.14406i	0.103295	+	0.585813i
$111$	−4.62053	−	3.02875i	−0.438561	−	0.287476i
$112$	−10.9105	+	5.32655i	−1.03095	+	0.503312i
$113$	2.24063	−	12.7072i	0.210781	−	1.19540i	−0.677299	−	0.735708i	$-0.736850\pi$
$113$	2.24063	−	12.7072i	0.210781	−	1.19540i	0.888080	−	0.459689i	$-0.152039\pi$
$114$	−7.28396	−	9.75256i	−0.682205	−	0.913411i
$115$	−0.453339	−	2.57101i	−0.0422741	−	0.239748i
$116$	−2.39729			−0.222583
$117$	−8.45187	−	8.90317i	−0.781376	−	0.823099i
$118$	−5.33228	+	9.23578i	−0.490876	+	0.850222i
$119$	0.750184	+	2.61246i	0.0687693	+	0.239484i
$120$	4.97313	+	16.5185i	0.453983	+	1.50792i
$121$	−7.61696	−	6.39139i	−0.692451	−	0.581035i
$122$	3.45806	−	19.6116i	0.313078	−	1.77555i
$123$	9.31871	+	2.19337i	0.840239	+	0.197770i
$124$	2.54253	−	2.13344i	0.228326	−	0.191588i
$125$	11.0923	−	19.2124i	0.992127	−	1.71841i
$126$	11.4891	−	4.07576i	1.02353	−	0.363097i
$127$	3.75782	+	6.50873i	0.333452	+	0.577556i	0.983186	−	0.182605i	$-0.0584531\pi$
$127$	3.75782	+	6.50873i	0.333452	+	0.577556i	−0.649734	+	0.760162i	$0.725120\pi$
$128$	12.5692	+	4.57482i	1.11097	+	0.404360i
$129$	1.79447	−	4.17780i	0.157995	−	0.367834i
$130$	19.0242	+	15.9632i	1.66853	+	1.40006i
$131$	0.000374193	−	0.00212215i	3.26934e−5	−	0.000185413i	−0.984791	−	0.173741i	$-0.944414\pi$
$131$	0.000374193	−	0.00212215i	3.26934e−5	−	0.000185413i	0.984824	+	0.173555i	$0.0555256\pi$
$132$	−0.534449	−	0.350331i	−0.0465178	−	0.0304924i
$133$	−8.40643	+	8.71173i	−0.728930	+	0.755403i
$134$	−12.5477			−1.08396
$135$	−3.65914	−	20.2038i	−0.314929	−	1.73887i
$136$	1.29469	−	2.24247i	0.111019	−	0.192290i
$137$	−15.8189	+	13.2736i	−1.35150	+	1.13404i	−0.372991	+	0.927835i	$0.621668\pi$
$137$	−15.8189	+	13.2736i	−1.35150	+	1.13404i	−0.978508	+	0.206208i	$0.933888\pi$
$138$	1.46990	+	0.963519i	0.125126	+	0.0820202i
$139$	4.80878	+	4.03504i	0.407875	+	0.342248i	0.823528	−	0.567275i	$-0.192003\pi$
$139$	4.80878	+	4.03504i	0.407875	+	0.342248i	−0.415653	+	0.909523i	$0.636447\pi$
$140$	−3.37183	+	1.64613i	−0.284971	+	0.139124i
$141$	3.25837	+	4.36266i	0.274404	+	0.367402i
$142$	−1.38094	−	0.502621i	−0.115886	−	0.0421790i
$143$	4.20654			0.351768
$144$	−12.3217	−	6.14056i	−1.02681	−	0.511713i
$145$	26.3940			2.19190
$146$	−0.624198	−	3.54000i	−0.0516590	−	0.292973i
$147$	−5.84071	−	10.6248i	−0.481734	−	0.876318i
$148$	−1.07575	+	0.391542i	−0.0884263	+	0.0321845i
$149$	1.00778	+	0.845625i	0.0825602	+	0.0692763i	0.683134	−	0.730293i	$-0.260617\pi$
$149$	1.00778	+	0.845625i	0.0825602	+	0.0692763i	−0.600574	+	0.799570i	$0.705061\pi$
$150$	8.14000	+	27.0373i	0.664628	+	2.20759i
$151$	11.9386	+	4.34528i	0.971546	+	0.353614i	0.778548	−	0.627585i	$-0.215957\pi$
$151$	11.9386	+	4.34528i	0.971546	+	0.353614i	0.192998	+	0.981199i	$0.438179\pi$
$152$	11.5332			0.935470
$153$	−1.83277	+	2.47779i	−0.148171	+	0.200318i
$154$	−1.69760	+	3.81677i	−0.136797	+	0.307564i
$155$	−27.9931	+	23.4890i	−2.24846	+	1.88668i
$156$	−2.52608	+	0.299214i	−0.202248	+	0.0239563i
$157$	−16.1725	−	13.5703i	−1.29070	−	1.08303i	−0.991672	−	0.128786i	$-0.958892\pi$
$157$	−16.1725	−	13.5703i	−1.29070	−	1.08303i	−0.299031	−	0.954243i	$-0.596664\pi$
$158$	8.28156	−	3.01424i	0.658846	−	0.239800i
$159$	−7.02305	+	3.54071i	−0.556964	+	0.280797i
$160$	7.45263	+	2.71254i	0.589182	+	0.214445i
$161$	0.710369	−	1.59715i	0.0559849	−	0.125873i
$162$	11.5956	+	7.52425i	0.911032	+	0.591161i
$163$	1.90159	+	3.29365i	0.148944	+	0.257979i	0.930837	−	0.365433i	$-0.119079\pi$
$163$	1.90159	+	3.29365i	0.148944	+	0.257979i	−0.781893	+	0.623412i	$0.785746\pi$
$164$	1.51962	−	1.27511i	0.118662	−	0.0995693i
$165$	5.88424	+	3.85711i	0.458088	+	0.300276i
$166$	−0.275412	+	1.56194i	−0.0213762	+	0.121230i
$167$	−3.56546	+	20.2207i	−0.275904	+	1.56473i	0.460173	+	0.887829i	$0.347787\pi$
$167$	−3.56546	+	20.2207i	−0.275904	+	1.56473i	−0.736077	+	0.676898i	$0.763324\pi$
$168$	−3.42000	+	11.0325i	−0.263859	+	0.851178i
$169$	2.86846	−	2.40693i	0.220651	−	0.185148i
$170$	3.11740	−	5.39949i	0.239093	−	0.414122i
$171$	−13.6393	−	1.55149i	−1.04302	−	0.118645i
$172$	−0.471085	−	0.815942i	−0.0359199	−	0.0622150i
$173$	5.70462	−	4.78675i	0.433714	−	0.363930i	−0.399637	−	0.916674i	$-0.630864\pi$
$173$	5.70462	−	4.78675i	0.433714	−	0.363930i	0.833351	+	0.552744i	$0.186419\pi$
$174$	−12.1738	+	12.9435i	−0.922891	+	0.981241i
$175$	25.2359	−	12.3202i	1.90765	−	0.931320i
$176$	4.43294	−	1.61346i	0.334145	−	0.121619i
$177$	3.46711	+	11.5162i	0.260604	+	0.865608i
$178$	21.4655	+	7.81281i	1.60891	+	0.585594i
$179$	−9.27576	−	16.0661i	−0.693302	−	1.20084i	−0.970750	−	0.240094i	$-0.922822\pi$
$179$	−9.27576	−	16.0661i	−0.693302	−	1.20084i	0.277447	−	0.960741i	$-0.410512\pi$
$180$	−3.80793	−	1.89770i	−0.283826	−	0.141446i
$181$	2.32939	+	4.03463i	0.173142	+	0.299891i	0.939517	−	0.342503i	$-0.111275\pi$
$181$	2.32939	+	4.03463i	0.173142	+	0.299891i	−0.766374	+	0.642394i	$0.777941\pi$
$182$	4.58937	+	15.9821i	0.340186	+	1.18467i
$183$	−13.4387	−	17.9932i	−0.993417	−	1.33010i
$184$	−1.56483	+	0.569552i	−0.115361	+	0.0419879i
$185$	11.8440	−	4.31085i	0.870785	−	0.316940i
$186$	1.39247	−	24.5615i	0.102101	−	1.80094i
$187$	−0.183386	−	1.04003i	−0.0134105	−	0.0760546i
$188$	1.12830			0.0822901
$189$	5.52864	−	12.5871i	0.402150	−	0.915574i
$190$	27.7701			2.01466
$191$	−2.34002	−	13.2709i	−0.169318	−	0.960251i	−0.944500	−	0.328512i	$-0.893453\pi$
$191$	−2.34002	−	13.2709i	−0.169318	−	0.960251i	0.775182	−	0.631738i	$-0.217658\pi$
$192$	9.42720	−	4.75277i	0.680349	−	0.343002i
$193$	−19.9632	+	7.26601i	−1.43698	+	0.523019i	−0.938924	−	0.344124i	$-0.888176\pi$
$193$	−19.9632	+	7.26601i	−1.43698	+	0.523019i	−0.498059	+	0.867143i	$0.665954\pi$
$194$	−3.72709	+	1.35655i	−0.267589	+	0.0973946i
$195$	27.8120	−	3.29433i	1.99166	−	0.235912i
$196$	−2.48813	−	0.347758i	−0.177724	−	0.0248399i
$197$	3.33745	+	5.78063i	0.237783	+	0.411853i	0.960078	−	0.279733i	$-0.0902459\pi$
$197$	3.33745	+	5.78063i	0.237783	+	0.411853i	−0.722295	+	0.691585i	$0.756913\pi$
$198$	−4.60551	+	1.10657i	−0.327299	+	0.0786405i
$199$	5.52535	+	9.57019i	0.391682	+	0.678413i	0.992672	−	0.120844i	$-0.0385600\pi$
$199$	5.52535	+	9.57019i	0.391682	+	0.678413i	−0.600990	+	0.799257i	$0.705227\pi$
$200$	−25.1400	−	9.15019i	−1.77766	−	0.647016i
$201$	−9.69471	+	10.3077i	−0.683812	+	0.727046i
$202$	−17.9783	+	6.54358i	−1.26495	+	0.460405i
$203$	14.6548	+	9.87669i	1.02856	+	0.693208i
$204$	0.184104	+	0.611508i	0.0128898	+	0.0428141i
$205$	−16.7309	+	14.0389i	−1.16853	+	0.980516i
$206$	−8.52496	−	14.7657i	−0.593962	−	1.02877i
$207$	1.92720	−	0.463049i	0.133949	−	0.0321842i
$208$	9.38910	−	16.2624i	0.651017	−	1.12759i
$209$	3.60334	−	3.02356i	0.249248	−	0.209144i
$210$	−8.23479	+	26.5645i	−0.568254	+	1.83312i
$211$	−0.562697	+	3.19121i	−0.0387377	+	0.219692i	−0.998031	−	0.0627185i	$-0.980023\pi$
$211$	−0.562697	+	3.19121i	−0.0387377	+	0.219692i	0.959294	+	0.282411i	$0.0911341\pi$
$212$	−0.283003	+	1.60499i	−0.0194367	+	0.110231i
$213$	−1.47984	+	0.746072i	−0.101397	+	0.0511200i
$214$	−7.30109	+	6.12634i	−0.499092	+	0.418788i
$215$	5.18661	+	8.98346i	0.353724	+	0.612667i
$216$	−12.2862	+	4.53644i	−0.835973	+	0.308666i
$217$	−24.3323	+	2.56676i	−1.65178	+	0.174243i
$218$	−9.72705	−	3.54035i	−0.658799	−	0.239783i
$219$	−3.39031	−	2.22234i	−0.229096	−	0.150172i
$220$	1.36997	−	0.498628i	0.0923634	−	0.0336175i
$221$	−3.22030	−	2.70215i	−0.216621	−	0.181767i
$222$	−3.34880	+	7.79650i	−0.224757	+	0.523267i
$223$	−4.05086	+	3.39907i	−0.271265	+	0.227619i	−0.768265	−	0.640132i	$-0.778880\pi$
$223$	−4.05086	+	3.39907i	−0.271265	+	0.227619i	0.496999	+	0.867751i	$0.334435\pi$
$224$	3.12290	+	4.29487i	0.208657	+	0.286963i
$225$	28.4997	+	14.2030i	1.89998	+	0.946866i
$226$	−19.8178			−1.31826
$227$	23.4134	+	8.52176i	1.55400	+	0.565609i	0.969351	−	0.245678i	$-0.0790106\pi$
$227$	23.4134	+	8.52176i	1.55400	+	0.565609i	0.584648	+	0.811287i	$0.301233\pi$
$228$	−1.94878	+	2.07200i	−0.129061	+	0.137221i
$229$	−7.51971	−	6.30978i	−0.496916	−	0.416962i	0.359581	−	0.933114i	$-0.382920\pi$
$229$	−7.51971	−	6.30978i	−0.496916	−	0.416962i	−0.856497	+	0.516152i	$0.827364\pi$
$230$	−3.76785	+	1.37138i	−0.248445	+	0.0904264i
$231$	1.82378	+	4.34348i	0.119996	+	0.285780i
$232$	−2.92351	−	16.5801i	−0.191938	−	1.08853i
$233$	−13.4934			−0.883979			−0.441990	−	0.897020i	$-0.645727\pi$
$233$	−13.4934			−0.883979			−0.441990	+	0.897020i	$0.645727\pi$
$234$	−11.2123	+	15.1583i	−0.732969	+	0.990927i
$235$	−12.4226			−0.810358
$236$	2.34180	+	0.852346i	0.152438	+	0.0554830i
$237$	3.92243	−	9.13200i	0.254789	−	0.593187i
$238$	3.75137	−	1.83143i	0.243165	−	0.118714i
$239$	3.07319	+	2.57871i	0.198788	+	0.166803i	0.736748	−	0.676168i	$-0.236360\pi$
$239$	3.07319	+	2.57871i	0.198788	+	0.166803i	−0.537960	+	0.842970i	$0.680805\pi$
$240$	28.0453	−	14.1392i	1.81032	−	0.912681i
$241$	−9.43228	+	7.91462i	−0.607587	+	0.509826i	−0.893874	−	0.448318i	$-0.852023\pi$
$241$	−9.43228	+	7.91462i	−0.607587	+	0.509826i	0.286287	+	0.958144i	$0.407579\pi$
$242$	−7.63577	+	13.2255i	−0.490846	+	0.850170i
$243$	15.1400	−	3.71204i	0.971234	−	0.238127i
$244$	−4.65354			−0.297912
$245$	27.3941	+	3.82879i	1.75015	+	0.244613i
$246$	0.832245	−	14.6799i	0.0530620	−	0.935955i
$247$	3.25139	−	18.4395i	0.206881	−	1.17328i
$248$	17.8558	+	14.9828i	1.13385	+	0.951410i
$249$	1.07031	+	1.43304i	0.0678280	+	0.0908155i
$250$	−32.0179	−	11.6536i	−2.02499	−	0.737036i
$251$	−8.59559	−	14.8880i	−0.542549	−	0.939722i	−0.998757	−	0.0498487i	$-0.984126\pi$
$251$	−8.59559	−	14.8880i	−0.542549	−	0.939722i	0.456208	−	0.889873i	$-0.349207\pi$
$252$	−1.40416	−	2.47859i	−0.0884536	−	0.156137i
$253$	−0.339587	+	0.588182i	−0.0213496	+	0.0369787i
$254$	8.84249	−	7.41973i	0.554827	−	0.465555i
$255$	−2.02697	−	6.73266i	−0.126934	−	0.421616i
$256$	1.45046	−	8.22596i	0.0906537	−	0.514123i
$257$	−13.6306	−	11.4375i	−0.850256	−	0.713449i	0.109590	−	0.993977i	$-0.465046\pi$
$257$	−13.6306	−	11.4375i	−0.850256	−	0.713449i	−0.959846	+	0.280527i	$0.909491\pi$
$258$	−6.79766	−	1.59999i	−0.423204	−	0.0996107i
$259$	8.18926	+	2.03851i	0.508856	+	0.126667i
$260$	2.90164	−	5.02578i	0.179952	−	0.311686i
$261$	1.22696	+	20.0010i	0.0759469	+	1.23803i
$262$	−0.00330964			−0.000204470
$263$	0.710104	+	4.02720i	0.0437869	+	0.248328i	0.998843	−	0.0480985i	$-0.0153162\pi$
$263$	0.710104	+	4.02720i	0.0437869	+	0.248328i	−0.955056	+	0.296426i	$0.904205\pi$
$264$	1.77118	−	4.12356i	0.109008	−	0.253788i
$265$	3.11584	−	17.6708i	0.191404	−	1.08551i
$266$	15.4188	+	10.3916i	0.945389	+	0.637151i
$267$	23.0029	−	11.5970i	1.40775	−	0.709727i
$268$	0.509162	+	2.88760i	0.0311020	+	0.176388i
$269$	−4.51787	+	7.82518i	−0.275459	+	0.477110i	−0.970251	−	0.242102i	$-0.922163\pi$
$269$	−4.51787	+	7.82518i	−0.275459	+	0.477110i	0.694792	+	0.719211i	$0.255497\pi$
$270$	−29.5832	+	10.9230i	−1.80038	+	0.664752i
$271$	−14.7472	−	25.5429i	−0.895828	−	1.55162i	−0.832777	−	0.553609i	$-0.813250\pi$
$271$	−14.7472	−	25.5429i	−0.895828	−	1.55162i	−0.0630509	−	0.998010i	$-0.520083\pi$
$272$	−4.43006	−	1.61241i	−0.268612	−	0.0977667i
$273$	16.6748	+	8.57818i	1.00921	+	0.519175i
$274$	24.2958	+	20.3866i	1.46776	+	1.23160i
$275$	−10.2533	+	3.73190i	−0.618297	+	0.225042i
$276$	0.162089	−	0.377366i	0.00975659	−	0.0227148i
$277$	−1.72756	−	9.79746i	−0.103799	−	0.588672i	−0.991693	−	0.128625i	$-0.958944\pi$
$277$	−1.72756	−	9.79746i	−0.103799	−	0.588672i	0.887895	−	0.460047i	$-0.152167\pi$
$278$	4.82065	−	8.34961i	0.289123	−	0.500776i
$279$	−19.1009	−	20.1208i	−1.14354	−	1.20460i
$280$	−15.4969	−	21.3126i	−0.926116	−	1.27367i
$281$	1.64701	+	9.34066i	0.0982524	+	0.557217i	0.993702	+	0.112054i	$0.0357431\pi$
$281$	1.64701	+	9.34066i	0.0982524	+	0.557217i	−0.895450	+	0.445163i	$0.853146\pi$
$282$	5.72968	−	6.09194i	0.341198	−	0.362770i
$283$	3.98159	−	22.5807i	0.236681	−	1.34228i	−0.602364	−	0.798221i	$-0.705774\pi$
$283$	3.98159	−	22.5807i	0.236681	−	1.34228i	0.839045	−	0.544062i	$-0.183114\pi$
$284$	−0.0596322	+	0.338191i	−0.00353852	+	0.0200679i
$285$	21.4560	−	22.8125i	1.27094	−	1.35130i
$286$	−1.12189	−	6.36255i	−0.0663387	−	0.376226i
$287$	−14.5429	+	1.53410i	−0.858437	+	0.0905548i
$288$	−1.70907	+	5.77358i	−0.100708	+	0.340211i
$289$	7.97231	−	13.8084i	0.468959	−	0.812261i
$290$	−7.03932	−	39.9220i	−0.413363	−	2.34430i
$291$	−1.76528	+	4.10982i	−0.103482	+	0.240922i
$292$	−0.789331	+	0.287293i	−0.0461921	+	0.0168126i
$293$	−16.0403	−	13.4594i	−0.937083	−	0.786306i	0.0399926	−	0.999200i	$-0.487267\pi$
$293$	−16.0403	−	13.4594i	−0.937083	−	0.786306i	−0.977075	+	0.212894i	$0.931711\pi$
$294$	−14.5127	+	11.6679i	−0.846396	+	0.680488i
$295$	−25.7831	−	9.38426i	−1.50115	−	0.546373i
$296$	−4.01985	−	6.96258i	−0.233649	−	0.404692i
$297$	−2.64932	+	4.63828i	−0.153729	+	0.269141i
$298$	1.01026	−	1.74983i	0.0585231	−	0.101365i
$299$	0.469460	+	2.66244i	0.0271496	+	0.153973i
$300$	5.89179	−	2.97038i	0.340163	−	0.171495i
$301$	−0.481862	+	6.92874i	−0.0277741	+	0.399366i
$302$	3.38837	−	19.2164i	0.194979	−	1.10578i
$303$	−8.51516	+	19.8245i	−0.489183	+	1.13889i
$304$	−3.64628	−	20.6791i	−0.209128	−	1.18603i
$305$	51.2351			2.93371
$306$	4.23656	+	2.11131i	0.242188	+	0.120695i
$307$	4.45173	−	7.71062i	0.254073	−	0.440068i	−0.710570	−	0.703627i	$-0.751563\pi$
$307$	4.45173	−	7.71062i	0.254073	−	0.440068i	0.964643	+	0.263558i	$0.0848962\pi$
$308$	0.947238	+	0.235791i	0.0539739	+	0.0134354i
$309$	−18.7163	−	4.40530i	−1.06473	−	0.250609i
$310$	42.9938	+	36.0761i	2.44189	+	2.04899i
$311$	−3.25554	+	18.4631i	−0.184605	+	1.04694i	0.741858	+	0.670557i	$0.233945\pi$
$311$	−3.25554	+	18.4631i	−0.184605	+	1.04694i	−0.926462	+	0.376387i	$0.877166\pi$
$312$	−5.14998	−	17.1059i	−0.291560	−	0.968430i
$313$	−0.183264	+	0.153777i	−0.0103587	+	0.00869197i	−0.647952	−	0.761681i	$-0.724374\pi$
$313$	−0.183264	+	0.153777i	−0.0103587	+	0.00869197i	0.637594	+	0.770373i	$0.279930\pi$
$314$	−16.2124	+	28.0807i	−0.914919	+	1.58469i
$315$	15.4597	+	27.2891i	0.871054	+	1.53757i
$316$	−1.02972	−	1.78352i	−0.0579261	−	0.100331i
$317$	23.0058	+	8.37341i	1.29213	+	0.470298i	0.894426	−	0.447215i	$-0.147584\pi$
$317$	23.0058	+	8.37341i	1.29213	+	0.470298i	0.397706	+	0.917513i	$0.369806\pi$
$318$	7.22852	+	9.67832i	0.405355	+	0.542733i
$319$	−5.26002	−	4.41368i	−0.294505	−	0.247119i
$320$	−4.18246	+	23.7199i	−0.233806	+	1.32598i
$321$	−0.608375	+	10.7311i	−0.0339562	+	0.598949i
$322$	−2.60520	−	0.648500i	−0.145182	−	0.0361395i
$323$	−4.70077			−0.261558
$324$	1.26103	−	2.97380i	0.0700571	−	0.165211i
$325$	−21.7168	+	37.6146i	−1.20463	+	2.08648i
$326$	4.47462	−	3.75465i	0.247826	−	0.207951i
$327$	−10.4237	+	5.25517i	−0.576432	+	0.290611i
$328$	10.6720	+	8.95490i	0.589264	+	0.494451i
$329$	−6.89739	−	4.64854i	−0.380265	−	0.256282i
$330$	4.26470	−	9.92884i	0.234764	−	0.546565i
$331$	5.97592	+	2.17506i	0.328466	+	0.119552i	0.500989	−	0.865454i	$-0.332970\pi$
$331$	5.97592	+	2.17506i	0.328466	+	0.119552i	−0.172523	+	0.985005i	$0.555192\pi$
$332$	0.370625			0.0203407
$333$	3.81727	+	8.77476i	0.209185	+	0.480854i
$334$	31.5356			1.72555
$335$	−5.60584	−	31.7923i	−0.306280	−	1.73700i
$336$	20.8625	+	2.64408i	1.13814	+	0.144246i
$337$	−8.03107	+	2.92307i	−0.437480	+	0.159230i	−0.551365	−	0.834264i	$-0.685893\pi$
$337$	−8.03107	+	2.92307i	−0.437480	+	0.159230i	0.113885	+	0.993494i	$0.463671\pi$
$338$	−4.40559	−	3.69673i	−0.239633	−	0.201076i
$339$	−15.3118	+	16.2798i	−0.831620	+	0.884200i
$340$	−1.36908	−	0.498304i	−0.0742488	−	0.0270243i
$341$	9.50660			0.514811
$342$	1.29093	+	21.0437i	0.0698055	+	1.13791i
$343$	13.7773	+	12.3768i	0.743906	+	0.668284i
$344$	5.06869	−	4.25314i	0.273286	−	0.229314i
$345$	−1.78458	+	4.15477i	−0.0960787	+	0.223685i
$346$	−8.76157	−	7.35183i	−0.471025	−	0.395237i
$347$	−9.50707	+	3.46029i	−0.510366	+	0.185758i	−0.584351	−	0.811501i	$-0.698651\pi$
$347$	−9.50707	+	3.46029i	−0.510366	+	0.185758i	0.0739843	+	0.997259i	$0.476429\pi$
$348$	3.47266	+	2.27633i	0.186154	+	0.122024i
$349$	18.4035	+	6.69832i	0.985116	+	0.358553i	0.783827	−	0.620979i	$-0.213265\pi$
$349$	18.4035	+	6.69832i	0.985116	+	0.358553i	0.201289	+	0.979532i	$0.435487\pi$
$350$	−25.3652	−	34.8844i	−1.35583	−	1.86465i
$351$	3.78926	+	20.9223i	0.202256	+	1.11675i
$352$	−1.03163	−	1.78683i	−0.0549858	−	0.0952382i
$353$	−0.767605	+	0.644097i	−0.0408555	+	0.0342818i	−0.662987	−	0.748631i	$-0.730711\pi$
$353$	−0.767605	+	0.644097i	−0.0408555	+	0.0342818i	0.622131	+	0.782913i	$0.286267\pi$
$354$	16.4940	−	8.31552i	0.876644	−	0.441965i
$355$	0.656546	−	3.72346i	0.0348458	−	0.197620i
$356$	0.926929	−	5.25688i	0.0491272	−	0.278614i
$357$	1.39394	−	4.49668i	0.0737750	−	0.237989i
$358$	−21.8267	+	18.3148i	−1.15358	+	0.967966i
$359$	1.26860	−	2.19728i	0.0669542	−	0.115968i	−0.830605	−	0.556862i	$-0.812005\pi$
$359$	1.26860	−	2.19728i	0.0669542	−	0.115968i	0.897559	+	0.440894i	$0.145339\pi$
$360$	8.48099	−	28.6505i	0.446987	−	1.51001i
$361$	−0.968741	−	1.67791i	−0.0509864	−	0.0883110i
$362$	5.48127	−	4.59934i	0.288089	−	0.241736i
$363$	4.96487	+	16.4910i	0.260588	+	0.865555i
$364$	3.49173	−	1.70467i	0.183017	−	0.0893492i
$365$	8.69048	−	3.16308i	0.454880	−	0.165563i
$366$	−23.6313	+	25.1254i	−1.23523	+	1.31332i
$367$	−27.0699	−	9.85264i	−1.41304	−	0.514304i	−0.481018	−	0.876711i	$-0.659733\pi$
$367$	−27.0699	−	9.85264i	−1.41304	−	0.514304i	−0.932020	+	0.362407i	$0.881955\pi$
$368$	1.51593	+	2.62567i	0.0790234	+	0.136873i
$369$	−11.4162	−	12.0257i	−0.594302	−	0.626035i
$370$	−9.67912	−	16.7647i	−0.503194	−	0.871557i
$371$	8.34245	−	8.64542i	0.433118	−	0.448848i
$372$	−5.70884	+	0.676212i	−0.295990	+	0.0350600i
$373$	−31.9072	+	11.6133i	−1.65209	+	0.601313i	−0.989091	−	0.147305i	$-0.952940\pi$
$373$	−31.9072	+	11.6133i	−1.65209	+	0.601313i	−0.663002	+	0.748618i	$0.730718\pi$
$374$	−1.52418	+	0.554755i	−0.0788134	+	0.0286857i
$375$	−34.3111	+	17.2981i	−1.77182	+	0.893270i
$376$	1.37597	+	7.80353i	0.0709604	+	0.402436i
$377$	−27.3326			−1.40770
$378$	−20.5129	−	5.00530i	−1.05507	−	0.257445i
$379$	10.2534			0.526680			0.263340	−	0.964703i	$-0.415176\pi$
$379$	10.2534			0.526680			0.263340	+	0.964703i	$0.415176\pi$
$380$	−1.12686	−	6.39073i	−0.0578066	−	0.327837i
$381$	0.736815	−	12.9966i	0.0377482	−	0.665835i
$382$	−19.4487	+	7.07875i	−0.995082	+	0.362180i
$383$	−7.96500	+	2.89902i	−0.406992	+	0.148133i	−0.537400	−	0.843327i	$-0.680594\pi$
$383$	−7.96500	+	2.89902i	−0.406992	+	0.148133i	0.130408	+	0.991460i	$0.458371\pi$
$384$	−13.8635	−	18.5619i	−0.707468	−	0.947235i
$385$	−10.4290	−	2.59604i	−0.531512	−	0.132307i
$386$	16.3143	+	28.2573i	0.830378	+	1.43826i
$387$	−6.56641	+	4.34793i	−0.333790	+	0.221018i
$388$	0.463420	+	0.802667i	0.0235266	+	0.0407493i
$389$	9.60401	+	3.49557i	0.486943	+	0.177233i	0.573812	−	0.818987i	$-0.305464\pi$
$389$	9.60401	+	3.49557i	0.486943	+	0.177233i	−0.0868692	+	0.996220i	$0.527686\pi$
$390$	−12.4003	−	41.1881i	−0.627913	−	2.08564i
$391$	0.637800	−	0.232140i	0.0322549	−	0.0117398i
$392$	−0.629136	−	17.6324i	−0.0317761	−	0.890570i
$393$	−0.00255712	+	0.00271879i	−0.000128989	+	0.000137145i
$394$	7.85332	−	6.58972i	0.395644	−	0.331985i
$395$	11.3371	+	19.6364i	0.570432	+	0.988016i
$396$	0.441537	+	1.01496i	0.0221881	+	0.0510037i
$397$	−1.77719	+	3.07819i	−0.0891948	+	0.154490i	−0.907171	−	0.420762i	$-0.861763\pi$
$397$	−1.77719	+	3.07819i	−0.0891948	+	0.154490i	0.817976	+	0.575252i	$0.195096\pi$
$398$	13.0017	−	10.9097i	0.651715	−	0.546854i
$399$	20.4495	−	4.63736i	1.02376	−	0.232158i
$400$	−8.45818	+	47.9687i	−0.422909	+	2.39844i
$401$	−0.682523	+	3.87078i	−0.0340836	+	0.193298i	−0.997096	−	0.0761611i	$-0.975734\pi$
$401$	−0.682523	+	3.87078i	−0.0340836	+	0.193298i	0.963012	+	0.269459i	$0.0868448\pi$
$402$	18.1763	+	11.9146i	0.906553	+	0.594244i
$403$	28.9886	−	24.3243i	1.44402	−	1.21168i
$404$	2.23540	+	3.87182i	0.111215	+	0.192630i
$405$	−13.8838	+	32.7413i	−0.689892	+	1.62693i
$406$	11.0304	−	24.8000i	0.547430	−	1.23081i
$407$	−3.08124	−	1.12148i	−0.152731	−	0.0555896i
$408$	−4.00477	+	2.01903i	−0.198266	+	0.0999567i
$409$	21.5696	−	7.85068i	1.06655	−	0.388191i	0.251662	−	0.967815i	$-0.419023\pi$
$409$	21.5696	−	7.85068i	1.06655	−	0.388191i	0.814884	+	0.579624i	$0.196801\pi$
$410$	25.6964	+	21.5619i	1.26906	+	1.06487i
$411$	35.5187	−	4.20719i	1.75201	−	0.207525i
$412$	−3.05209	+	2.56101i	−0.150366	+	0.126172i
$413$	−10.8039	−	14.8585i	−0.531627	−	0.731139i
$414$	−1.21437	−	2.79146i	−0.0596828	−	0.137193i
$415$	−4.08055			−0.200306
$416$	−7.71766	−	2.80900i	−0.378389	−	0.137722i
$417$	−3.13445	−	10.4112i	−0.153494	−	0.509838i
$418$	−5.53426	−	4.64380i	−0.270690	−	0.227136i
$419$	14.6795	−	5.34289i	0.717139	−	0.261017i	0.0424280	−	0.999100i	$-0.486491\pi$
$419$	14.6795	−	5.34289i	0.717139	−	0.261017i	0.674711	+	0.738082i	$0.264268\pi$
$420$	6.44742	+	0.817134i	0.314602	+	0.0398721i
$421$	4.50895	+	25.5716i	0.219753	+	1.24628i	0.872466	+	0.488676i	$0.162520\pi$
$421$	4.50895	+	25.5716i	0.219753	+	1.24628i	−0.652713	+	0.757606i	$0.726369\pi$
$422$	4.97691			0.242272
$423$	−0.577478	−	9.41360i	−0.0280780	−	0.457705i
$424$	−11.4455			−0.555841
$425$	10.2466	+	3.72947i	0.497035	+	0.180906i
$426$	1.52314	+	2.03934i	0.0737963	+	0.0988065i
$427$	28.4473	+	19.1723i	1.37666	+	0.927810i
$428$	1.70612	+	1.43160i	0.0824683	+	0.0691991i
$429$	−6.09349	−	3.99428i	−0.294197	−	0.192845i
$430$	12.2046	−	10.2408i	0.588556	−	0.493857i
$431$	−1.46799	+	2.54263i	−0.0707105	+	0.122474i	−0.899213	−	0.437511i	$-0.855860\pi$
$431$	−1.46799	+	2.54263i	−0.0707105	+	0.122474i	0.828502	+	0.559985i	$0.189193\pi$
$432$	12.0182	+	20.5950i	0.578224	+	0.990876i
$433$	12.6175			0.606360			0.303180	−	0.952933i	$-0.401952\pi$
$433$	12.6175			0.606360			0.303180	+	0.952933i	$0.401952\pi$
$434$	10.3718	+	36.1189i	0.497861	+	1.73376i
$435$	−38.2338	−	25.0622i	−1.83317	−	1.20164i
$436$	−0.420036	+	2.38214i	−0.0201161	+	0.114084i
$437$	2.31584	+	1.94322i	0.110782	+	0.0929568i
$438$	−2.45718	+	5.72067i	−0.117408	+	0.273344i
$439$	20.3014	+	7.38912i	0.968935	+	0.352664i	0.777529	−	0.628847i	$-0.216473\pi$
$439$	20.3014	+	7.38912i	0.968935	+	0.352664i	0.191406	+	0.981511i	$0.438695\pi$
$440$	5.11928	+	8.86685i	0.244052	+	0.422710i
$441$	−1.62795	+	20.9368i	−0.0775212	+	0.996991i
$442$	−3.22825	+	5.59150i	−0.153552	+	0.265960i
$443$	18.6104	−	15.6160i	0.884209	−	0.741939i	−0.0828312	−	0.996564i	$-0.526396\pi$
$443$	18.6104	−	15.6160i	0.884209	−	0.741939i	0.967040	+	0.254624i	$0.0819518\pi$
$444$	1.93009	+	0.454292i	0.0915982	+	0.0215597i
$445$	−10.2054	+	57.8778i	−0.483784	+	2.74367i
$446$	6.22160	+	5.22054i	0.294601	+	0.247200i
$447$	−0.656886	−	2.18188i	−0.0310697	−	0.103199i
$448$	−11.1983	+	11.6049i	−0.529068	+	0.548282i
$449$	16.9480	−	29.3549i	0.799827	−	1.38534i	−0.119901	−	0.992786i	$-0.538258\pi$
$449$	16.9480	−	29.3549i	0.799827	−	1.38534i	0.919728	−	0.392556i	$-0.128409\pi$
$450$	13.8816	−	46.8949i	0.654387	−	2.21065i
$451$	5.68188			0.267549
$452$	0.804167	+	4.56066i	0.0378248	+	0.214515i
$453$	−13.1679	−	17.6306i	−0.618682	−	0.828358i
$454$	6.64512	−	37.6864i	0.311871	−	1.76871i
$455$	−38.4437	+	18.7683i	−1.80227	+	0.879873i
$456$	−16.7068	−	10.9513i	−0.782367	−	0.512841i
$457$	−1.22041	−	6.92129i	−0.0570884	−	0.323764i	0.942867	−	0.333168i	$-0.108118\pi$
$457$	−1.22041	−	6.92129i	−0.0570884	−	0.323764i	−0.999956	+	0.00940397i	$0.997007\pi$
$458$	−7.53827	+	13.0567i	−0.352240	+	0.610098i
$459$	5.00767	−	1.84898i	0.233738	−	0.0863030i
$460$	0.468488	+	0.811446i	0.0218434	+	0.0378339i
$461$	−3.49395	−	1.27169i	−0.162729	−	0.0592286i	0.259371	−	0.965778i	$-0.416485\pi$
$461$	−3.49395	−	1.27169i	−0.162729	−	0.0592286i	−0.422100	+	0.906549i	$0.638707\pi$
$462$	6.08328	−	3.91694i	0.283020	−	0.182233i
$463$	5.94542	+	4.98880i	0.276307	+	0.231849i	0.770401	−	0.637559i	$-0.220056\pi$
$463$	5.94542	+	4.98880i	0.276307	+	0.231849i	−0.494094	+	0.869408i	$0.664500\pi$
$464$	−28.8037	+	10.4837i	−1.33718	+	0.486693i
$465$	62.8539	−	7.44504i	2.91478	−	0.345256i
$466$	3.59870	+	20.4092i	0.166706	+	0.945439i
$467$	−17.5196	+	30.3448i	−0.810709	+	1.40419i	0.101659	+	0.994819i	$0.467585\pi$
$467$	−17.5196	+	30.3448i	−0.810709	+	1.40419i	−0.912368	+	0.409370i	$0.865749\pi$
$468$	3.94334	+	1.96518i	0.182281	+	0.0908406i
$469$	8.78419	−	19.7498i	0.405616	−	0.911960i
$470$	3.31311	+	18.7896i	0.152822	+	0.866699i
$471$	10.5415	+	35.0141i	0.485727	+	1.61336i
$472$	−3.03912	+	17.2357i	−0.139887	+	0.793337i
$473$	0.468610	−	2.65762i	0.0215467	−	0.122197i
$474$	−14.8586	−	3.49732i	−0.682479	−	0.160637i
$475$	8.43377	+	47.8303i	0.386968	+	2.19460i
$476$	−0.573690	−	0.788986i	−0.0262950	−	0.0361631i
$477$	13.5355	+	1.53968i	0.619747	+	0.0704971i
$478$	3.08077	−	5.33606i	0.140911	−	0.244066i
$479$	−0.0169280	−	0.0960035i	−0.000773460	−	0.00438651i	0.984419	−	0.175841i	$-0.0562645\pi$
$479$	−0.0169280	−	0.0960035i	−0.000773460	−	0.00438651i	−0.985192	+	0.171454i	$0.945153\pi$
$480$	−8.22005	−	11.0059i	−0.375192	−	0.502348i
$481$	−12.2651	+	4.46415i	−0.559242	+	0.203548i
$482$	14.4868	+	12.1558i	0.659855	+	0.553684i
$483$	−2.54558	+	1.63906i	−0.115828	+	0.0745800i
$484$	3.35343	+	1.22055i	0.152429	+	0.0554796i
$485$	−5.10222	−	8.83731i	−0.231680	−	0.401282i
$486$	−9.65247	−	21.9099i	−0.437845	−	0.993853i
$487$	2.40070	−	4.15814i	0.108786	−	0.188423i	−0.806493	−	0.591244i	$-0.798637\pi$
$487$	2.40070	−	4.15814i	0.108786	−	0.188423i	0.915279	+	0.402821i	$0.131970\pi$
$488$	−5.67501	−	32.1846i	−0.256896	−	1.45693i
$489$	0.372855	−	6.57674i	0.0168611	−	0.297411i
$490$	−1.51485	−	42.4558i	−0.0684341	−	1.91796i
$491$	−0.878760	+	4.98370i	−0.0396579	+	0.224911i	−0.998195	−	0.0600567i	$-0.980872\pi$
$491$	−0.878760	+	4.98370i	−0.0396579	+	0.224911i	0.958537	+	0.284968i	$0.0919829\pi$
$492$	−3.41205	+	0.404157i	−0.153827	+	0.0182208i
$493$	1.19158	+	6.75776i	0.0536659	+	0.304354i
$494$	−28.7577			−1.29387
$495$	−4.86129	−	11.1746i	−0.218499	−	0.502263i
$496$	21.2190	−	36.7523i	0.952759	−	1.65023i
$497$	1.75786	−	1.82170i	0.0788507	−	0.0817143i
$498$	1.88208	−	2.00108i	0.0843381	−	0.0896704i
$499$	18.2063	+	15.2769i	0.815027	+	0.683889i	0.951802	−	0.306713i	$-0.0992293\pi$
$499$	18.2063	+	15.2769i	0.815027	+	0.683889i	−0.136775	+	0.990602i	$0.543674\pi$
$500$	−1.38261	+	7.84115i	−0.0618320	+	0.350667i
$501$	24.3652	−	25.9057i	1.08856	−	1.15738i
$502$	−20.2262	+	16.9718i	−0.902740	+	0.757489i
$503$	8.71394	−	15.0930i	0.388535	−	0.672963i	−0.603718	−	0.797198i	$-0.706315\pi$
$503$	8.71394	−	15.0930i	0.388535	−	0.672963i	0.992253	+	0.124236i	$0.0396478\pi$
$504$	15.4300	−	12.7340i	0.687305	−	0.567219i
$505$	−24.6116	−	42.6285i	−1.09520	−	1.89694i
$506$	0.980215	+	0.356769i	0.0435759	+	0.0158603i
$507$	−6.44066	+	0.762896i	−0.286040	+	0.0338814i
$508$	−2.06631	−	1.73384i	−0.0916777	−	0.0769267i
$509$	4.89841	−	27.7802i	0.217118	−	1.23134i	−0.660075	−	0.751200i	$-0.729476\pi$
$509$	4.89841	−	27.7802i	0.217118	−	1.23134i	0.877193	−	0.480138i	$-0.159413\pi$
$510$	−9.64281	+	4.86148i	−0.426991	+	0.215270i
$511$	6.00885	+	1.49575i	0.265816	+	0.0661682i
$512$	13.9228			0.615307
$513$	18.2844	+	15.1985i	0.807274	+	0.671030i
$514$	−13.6643	+	23.6673i	−0.602706	+	1.04392i
$515$	33.6033	−	28.1965i	1.48074	−	1.24249i
$516$	−0.0923680	+	1.62927i	−0.00406628	+	0.0717245i
$517$	2.47567	+	2.07733i	0.108880	+	0.0913611i
$518$	0.899240	−	12.9302i	0.0395103	−	0.568122i
$519$	−12.8088	+	1.51720i	−0.562243	+	0.0665977i
$520$	38.2976	+	13.9392i	1.67946	+	0.611274i
$521$	−7.47780			−0.327608			−0.163804	−	0.986493i	$-0.552376\pi$
$521$	−7.47780			−0.327608			−0.163804	+	0.986493i	$0.552376\pi$
$522$	29.9250	−	7.19010i	1.30978	−	0.314702i
$523$	−11.8867			−0.519769			−0.259884	−	0.965640i	$-0.583684\pi$
$523$	−11.8867			−0.519769			−0.259884	+	0.965640i	$0.583684\pi$
$524$	0.000134299	0	0.000761646i	5.86686e−6	0	3.32726e-5i
$525$	−48.2546	−	6.11570i	−2.10600	−	0.266911i
$526$	5.90191	−	2.14812i	0.257336	−	0.0936625i
$527$	−7.27775	−	6.10675i	−0.317024	−	0.266014i
$528$	−7.95350	−	1.87204i	−0.346131	−	0.0814699i
$529$	21.2028	+	7.71717i	0.921859	+	0.335529i
$530$	−27.5587			−1.19708
$531$	5.91268	−	19.9742i	0.256589	−	0.866807i
$532$	1.76575	−	3.97000i	0.0765552	−	0.172121i
$533$	17.3258	−	14.5381i	0.750465	−	0.629715i
$534$	−23.6759	−	31.6998i	−1.02455	−	1.37178i
$535$	−18.7842	−	15.7618i	−0.812113	−	0.681444i
$536$	−19.3502	+	7.04289i	−0.835801	+	0.304207i
$537$	−1.81875	+	32.0806i	−0.0784847	+	1.38438i
$538$	13.0408	+	4.74647i	0.562229	+	0.204635i
$539$	−4.81907	−	5.34396i	−0.207572	−	0.230181i
$540$	3.71413	+	6.36474i	0.159831	+	0.273895i
$541$	−13.5657	−	23.4965i	−0.583236	−	1.01020i	−0.995093	−	0.0989464i	$-0.968453\pi$
$541$	−13.5657	−	23.4965i	−0.583236	−	1.01020i	0.411856	−	0.911249i	$-0.364881\pi$
$542$	−34.7015	+	29.1180i	−1.49056	+	1.25073i
$543$	0.456736	−	8.05632i	0.0196004	−	0.345730i
$544$	−0.358047	+	2.03059i	−0.0153511	+	0.0870606i
$545$	4.62457	−	26.2272i	0.198095	−	1.12345i
$546$	8.52762	−	27.5091i	0.364949	−	1.17728i
$547$	6.93653	−	5.82044i	0.296585	−	0.248864i	−0.482336	−	0.875986i	$-0.660212\pi$
$547$	6.93653	−	5.82044i	0.296585	−	0.248864i	0.778921	+	0.627122i	$0.215767\pi$
$548$	3.70568	−	6.41843i	0.158299	−	0.274182i
$549$	2.38173	+	38.8251i	0.101650	+	1.65701i
$550$	8.37920	+	14.5132i	0.357290	+	0.618845i
$551$	−23.4132	+	19.6460i	−0.997437	+	0.836949i
$552$	2.80759	+	0.660830i	0.119499	+	0.0281268i
$553$	−1.05328	+	15.1451i	−0.0447898	+	0.644036i
$554$	−14.3583	+	5.22599i	−0.610025	+	0.222031i
$555$	−21.2502	−	5.00172i	−0.902021	−	0.212311i
$556$	−2.11711	−	0.770563i	−0.0897853	−	0.0326792i
$557$	−6.70466	−	11.6128i	−0.284085	−	0.492050i	0.688302	−	0.725425i	$-0.258357\pi$
$557$	−6.70466	−	11.6128i	−0.284085	−	0.492050i	−0.972387	+	0.233374i	$0.925023\pi$
$558$	−25.3392	+	34.2571i	−1.07270	+	1.45022i
$559$	−5.37105	−	9.30293i	−0.227171	−	0.393472i
$560$	−33.3141	+	34.5239i	−1.40778	+	1.45890i
$561$	−0.721903	+	1.68070i	−0.0304788	+	0.0709591i
$562$	13.6889	−	4.98234i	0.577429	−	0.210167i
$563$	33.3923	−	12.1538i	1.40732	−	0.512222i	0.476976	−	0.878916i	$-0.341733\pi$
$563$	33.3923	−	12.1538i	1.40732	−	0.512222i	0.930341	+	0.366694i	$0.119511\pi$
$564$	−1.63444	−	1.07137i	−0.0688222	−	0.0451128i
$565$	−8.85382	−	50.2125i	−0.372483	−	2.11246i
$566$	−35.2161			−1.48024
$567$	−19.9606	+	12.9836i	−0.838266	+	0.545262i
$568$	−2.41170			−0.101193
$569$	−0.123170	−	0.698533i	−0.00516356	−	0.0292840i	0.982117	−	0.188271i	$-0.0602883\pi$
$569$	−0.123170	−	0.698533i	−0.00516356	−	0.0292840i	−0.987281	+	0.158987i	$0.949177\pi$
$570$	−40.2271	−	26.3688i	−1.68493	−	1.10447i
$571$	−6.13497	+	2.23294i	−0.256740	+	0.0934458i	−0.467184	−	0.884160i	$-0.654731\pi$
$571$	−6.13497	+	2.23294i	−0.256740	+	0.0934458i	0.210444	+	0.977606i	$0.432509\pi$
$572$	−1.41869	+	0.516360i	−0.0593183	+	0.0215901i
$573$	−9.21158	+	21.4459i	−0.384819	+	0.895915i
$574$	6.19898	+	21.5875i	0.258740	+	0.901044i
$575$	−3.50632	−	6.07312i	−0.146224	−	0.253267i
$576$	−18.1690	−	2.06675i	−0.757040	−	0.0861145i
$577$	7.49345	+	12.9790i	0.311956	+	0.540324i	0.978786	−	0.204886i	$-0.0656824\pi$
$577$	7.49345	+	12.9790i	0.311956	+	0.540324i	−0.666830	+	0.745210i	$0.732349\pi$
$578$	−23.0120	−	8.37569i	−0.957174	−	0.348383i
$579$	35.8176	+	8.43049i	1.48853	+	0.350359i
$580$	−8.90159	+	3.23991i	−0.369618	+	0.134530i
$581$	−2.26565	−	1.52695i	−0.0939950	−	0.0633485i
$582$	6.68707	+	1.57395i	0.277188	+	0.0652425i
$583$	−3.57591	+	3.00054i	−0.148099	+	0.124270i
$584$	−2.94956	−	5.10878i	−0.122054	−	0.211403i
$585$	−43.4159	−	21.6365i	−1.79503	−	0.894559i
$586$	−16.0799	+	27.8512i	−0.664254	+	1.15052i
$587$	−19.4537	+	16.3236i	−0.802940	+	0.673746i	−0.948911	−	0.315542i	$-0.897814\pi$
$587$	−19.4537	+	16.3236i	−0.802940	+	0.673746i	0.145972	+	0.989289i	$0.453369\pi$
$588$	3.27404	+	2.86633i	0.135019	+	0.118206i
$589$	7.34800	−	41.6726i	0.302769	−	1.71709i
$590$	−7.31769	+	41.5007i	−0.301264	+	1.70855i
$591$	0.654391	−	11.5427i	0.0269180	−	0.474804i
$592$	−11.2130	+	9.40882i	−0.460852	+	0.386700i
$593$	19.7263	+	34.1669i	0.810060	+	1.40307i	0.912821	+	0.408359i	$0.133899\pi$
$593$	19.7263	+	34.1669i	0.810060	+	1.40307i	−0.102761	+	0.994706i	$0.532768\pi$
$594$	7.72216	+	2.77016i	0.316844	+	0.113661i
$595$	6.31628	+	8.68668i	0.258942	+	0.356119i
$596$	−0.443682	−	0.161487i	−0.0181739	−	0.00661477i
$597$	1.08339	−	19.1097i	0.0443400	−	0.782108i
$598$	3.90184	−	1.42015i	0.159558	−	0.0580744i
$599$	−1.04353	−	0.875626i	−0.0426375	−	0.0357771i	0.621220	−	0.783636i	$-0.286637\pi$
$599$	−1.04353	−	0.875626i	−0.0426375	−	0.0357771i	−0.663857	+	0.747859i	$0.731082\pi$
$600$	27.7287	+	37.1262i	1.13202	+	1.51567i
$601$	−4.73957	+	3.97697i	−0.193331	+	0.162224i	−0.734315	−	0.678809i	$-0.762496\pi$
$601$	−4.73957	+	3.97697i	−0.193331	+	0.162224i	0.540984	+	0.841033i	$0.318052\pi$
$602$	10.6085	−	1.11907i	0.432370	−	0.0456098i
$603$	23.8311	−	5.72592i	0.970476	−	0.233177i
$604$	−4.55976			−0.185534
$605$	−36.9211	−	13.4382i	−1.50105	−	0.546339i
$606$	32.2564	+	7.59228i	1.31033	+	0.308415i
$607$	1.60065	+	1.34310i	0.0649684	+	0.0545149i	0.674694	−	0.738098i	$-0.264276\pi$
$607$	1.60065	+	1.34310i	0.0649684	+	0.0545149i	−0.609725	+	0.792613i	$0.708720\pi$
$608$	−8.63001	+	3.14107i	−0.349993	+	0.127387i
$609$	−11.8503	−	28.2224i	−0.480197	−	1.14363i
$610$	−13.6645	−	77.4950i	−0.553258	−	3.13768i
$611$	12.8643			0.520434
$612$	0.313963	−	1.06063i	0.0126912	−	0.0428734i
$613$	−16.2931			−0.658071			−0.329036	−	0.944318i	$-0.606724\pi$
$613$	−16.2931			−0.658071			−0.329036	+	0.944318i	$0.606724\pi$
$614$	−12.8499	−	4.67698i	−0.518579	−	0.188747i
$615$	37.5664	−	4.44974i	1.51482	−	0.179431i
$616$	−0.475607	+	6.83879i	−0.0191628	+	0.275543i
$617$	−3.46417	−	2.90678i	−0.139462	−	0.117023i	0.570388	−	0.821375i	$-0.306793\pi$
$617$	−3.46417	−	2.90678i	−0.139462	−	0.117023i	−0.709850	+	0.704353i	$0.751237\pi$
$618$	−1.67153	+	29.4840i	−0.0672390	+	1.18602i
$619$	26.7035	−	22.4069i	1.07331	−	0.900611i	0.0779580	−	0.996957i	$-0.475160\pi$
$619$	26.7035	−	22.4069i	1.07331	−	0.900611i	0.995348	+	0.0963460i	$0.0307155\pi$
$620$	6.55758	−	11.3581i	0.263359	−	0.456150i
$621$	−3.23138	−	1.15919i	−0.129671	−	0.0465166i
$622$	28.7944			1.15455
$623$	−27.3244	+	28.3167i	−1.09473	+	1.13448i
$624$	−29.0426	+	14.6420i	−1.16263	+	0.586149i
$625$	6.00667	−	34.0655i	0.240267	−	1.36262i
$626$	0.281470	+	0.236181i	0.0112498	+	0.00943970i
$627$	−8.09070	+	0.958343i	−0.323111	+	0.0382725i
$628$	7.12007	+	2.59149i	0.284122	+	0.103412i
$629$	1.63843	+	2.83784i	0.0653283	+	0.113152i
$630$	37.1527	−	30.6614i	1.48020	−	1.22158i
$631$	−3.30722	+	5.72827i	−0.131658	+	0.228039i	−0.924316	−	0.381628i	$-0.875364\pi$
$631$	−3.30722	+	5.72827i	−0.131658	+	0.228039i	0.792658	+	0.609667i	$0.208697\pi$
$632$	11.0794	−	9.29669i	0.440714	−	0.369803i
$633$	3.84529	−	4.08841i	0.152837	−	0.162500i
$634$	6.52944	−	37.0303i	0.259317	−	1.47066i
$635$	22.7499	+	19.0895i	0.902803	+	0.757542i
$636$	1.93395	−	2.05622i	0.0766861	−	0.0815346i
$637$	−28.3683	−	3.96495i	−1.12399	−	0.157097i
$638$	−5.27301	+	9.13312i	−0.208760	+	0.361584i
$639$	2.85209	+	0.324430i	0.112827	+	0.0128342i
$640$	52.8546			2.08926
$641$	−1.87907	−	10.6567i	−0.0742188	−	0.420916i	−0.999166	−	0.0408213i	$-0.987003\pi$
$641$	−1.87907	−	10.6567i	−0.0742188	−	0.420916i	0.924948	−	0.380095i	$-0.124109\pi$
$642$	16.3934	−	1.94180i	0.646996	−	0.0766366i
$643$	−6.31438	+	35.8107i	−0.249015	+	1.41223i	0.561965	+	0.827161i	$0.310045\pi$
$643$	−6.31438	+	35.8107i	−0.249015	+	1.41223i	−0.810980	+	0.585073i	$0.801066\pi$
$644$	−0.0435250	+	0.625849i	−0.00171512	+	0.0246619i
$645$	1.01697	−	17.9381i	0.0400430	−	0.706313i
$646$	1.25370	+	7.11009i	0.0493262	+	0.279743i
$647$	18.3584	−	31.7976i	0.721741	−	1.25009i	−0.238560	−	0.971128i	$-0.576675\pi$
$647$	18.3584	−	31.7976i	0.721741	−	1.25009i	0.960301	−	0.278965i	$-0.0899913\pi$
$648$	22.1051	+	5.09490i	0.868370	+	0.200147i
$649$	3.56900	+	6.18169i	0.140096	+	0.242653i
$650$	62.6854	+	22.8156i	2.45872	+	0.894902i
$651$	37.6844	+	19.3863i	1.47697	+	0.759810i
$652$	−1.04563	−	0.877386i	−0.0409499	−	0.0343611i
$653$	−26.5467	+	9.66221i	−1.03885	+	0.378111i	−0.804445	−	0.594027i	$-0.797537\pi$
$653$	−26.5467	+	9.66221i	−1.03885	+	0.378111i	−0.234407	+	0.972138i	$0.575315\pi$
$654$	10.7287	+	14.3647i	0.419524	+	0.561704i
$655$	−0.00147862	−	0.00838566i	−5.77744e−5	−	0.000327655i
$656$	12.6821	−	21.9660i	0.495153	−	0.857630i
$657$	2.80091	+	6.43846i	0.109274	+	0.251188i
$658$	−5.19155	+	11.6723i	−0.202388	+	0.455035i
$659$	8.23727	+	46.7159i	0.320879	+	1.81979i	0.537182	+	0.843467i	$0.319489\pi$
$659$	8.23727	+	46.7159i	0.320879	+	1.81979i	−0.216303	+	0.976326i	$0.569400\pi$
$660$	−2.45797	−	0.578540i	−0.0956765	−	0.0225196i
$661$	−5.27750	+	29.9302i	−0.205271	+	1.16415i	0.691742	+	0.722145i	$0.256844\pi$
$661$	−5.27750	+	29.9302i	−0.205271	+	1.16415i	−0.897013	+	0.442005i	$0.854267\pi$
$662$	1.69607	−	9.61889i	0.0659196	−	0.373849i
$663$	2.09905	+	6.97208i	0.0815203	+	0.270773i
$664$	0.451979	+	2.56330i	0.0175402	+	0.0994753i
$665$	−19.4408	+	43.7094i	−0.753883	+	1.69498i
$666$	12.2541	−	8.11401i	0.474836	−	0.314411i
$667$	2.20652	−	3.82180i	0.0854367	−	0.147981i
$668$	−1.27965	−	7.25727i	−0.0495112	−	0.280792i
$669$	9.09553	−	1.07737i	0.351654	−	0.0416533i
$670$	−46.5920	+	16.9581i	−1.80001	+	0.655148i
$671$	−10.2106	−	8.56768i	−0.394174	−	0.330751i
$672$	−0.445603	−	9.18677i	−0.0171895	−	0.354387i
$673$	−36.1307	−	13.1505i	−1.39274	−	0.506915i	−0.466723	−	0.884404i	$-0.654566\pi$
$673$	−36.1307	−	13.1505i	−1.39274	−	0.506915i	−0.926014	+	0.377489i	$0.876788\pi$
$674$	6.56315	+	11.3677i	0.252803	+	0.437868i
$675$	−27.7978	−	47.6358i	−1.06994	−	1.83350i
$676$	−0.671957	+	1.16386i	−0.0258445	+	0.0447640i
$677$	−3.35615	−	19.0337i	−0.128987	−	0.731524i	−0.978859	−	0.204534i	$-0.934432\pi$
$677$	−3.35615	−	19.0337i	−0.128987	−	0.731524i	0.849872	−	0.526989i	$-0.176679\pi$
$678$	28.7076	+	18.8178i	1.10251	+	0.722692i
$679$	0.474023	−	6.81601i	0.0181913	−	0.261574i
$680$	1.77675	−	10.0765i	0.0681353	−	0.386414i
$681$	−25.8243	−	34.5763i	−0.989588	−	1.32497i
$682$	−2.53542	−	14.3791i	−0.0970864	−	0.550604i
$683$	−21.1210			−0.808172			−0.404086	−	0.914721i	$-0.632410\pi$
$683$	−21.1210			−0.808172			−0.404086	+	0.914721i	$0.632410\pi$
$684$	4.79040	−	1.15100i	0.183166	−	0.0440094i
$685$	−40.7993	+	70.6665i	−1.55886	+	2.70003i
$686$	15.0459	−	24.1397i	0.574457	−	0.921656i
$687$	4.90148	+	16.2805i	0.187003	+	0.621138i
$688$	−9.22835	−	7.74351i	−0.351828	−	0.295218i
$689$	−3.22664	+	18.2992i	−0.122925	+	0.697143i
$690$	6.76020	+	1.59117i	0.257357	+	0.0605747i
$691$	28.3169	−	23.7607i	1.07722	−	0.903898i	0.0815367	−	0.996670i	$-0.474017\pi$
$691$	28.3169	−	23.7607i	1.07722	−	0.903898i	0.995687	+	0.0927720i	$0.0295728\pi$
$692$	−1.33635	+	2.31462i	−0.0508003	+	0.0879886i
$693$	1.48243	−	8.02361i	0.0563129	−	0.304792i
$694$	7.76937	+	13.4570i	0.294921	+	0.510819i
$695$	23.3092	+	8.48385i	0.884167	+	0.321811i
$696$	−11.5085	+	26.7935i	−0.436228	+	1.01560i
$697$	−4.34975	−	3.64987i	−0.164758	−	0.138249i
$698$	5.22323	−	29.6224i	0.197702	−	1.12123i
$699$	19.5462	+	12.8125i	0.739304	+	0.484613i
$700$	−6.99866	+	7.25283i	−0.264524	+	0.274131i
$701$	29.0101			1.09569			0.547847	−	0.836578i	$-0.315447\pi$
$701$	29.0101			1.09569			0.547847	+	0.836578i	$0.315447\pi$
$702$	30.6352	−	11.3114i	1.15625	−	0.426922i
$703$	−7.29764	+	12.6399i	−0.275236	+	0.476722i
$704$	4.80002	−	4.02770i	0.180908	−	0.151800i
$705$	17.9950	+	11.7957i	0.677732	+	0.444252i
$706$	1.17894	+	0.989250i	0.0443701	+	0.0372309i
$707$	2.28654	−	32.8783i	0.0859942	−	1.23652i
$708$	−2.58294	−	3.45832i	−0.0970729	−	0.129972i
$709$	−26.4948	−	9.64331i	−0.995032	−	0.362162i	−0.207365	−	0.978264i	$-0.566489\pi$
$709$	−26.4948	−	9.64331i	−0.995032	−	0.362162i	−0.787667	+	0.616102i	$0.788711\pi$
$710$	−5.80697			−0.217932
$711$	−14.3531	+	9.50389i	−0.538285	+	0.356424i
$712$	37.4878			1.40491
$713$	1.06096	+	6.01700i	0.0397333	+	0.225339i
$714$	−7.17316	−	0.909113i	−0.268449	−	0.0340227i
$715$	15.6196	−	5.68509i	0.584142	−	0.212610i
$716$	5.10046	+	4.27979i	0.190613	+	0.159943i
$717$	−2.00316	−	6.65357i	−0.0748093	−	0.248482i
$718$	−3.66181	−	1.33279i	−0.136658	−	0.0497393i
$719$	−9.03032			−0.336774			−0.168387	−	0.985721i	$-0.553856\pi$
$719$	−9.03032			−0.336774			−0.168387	+	0.985721i	$0.553856\pi$
$720$	−54.0515	−	6.14844i	−2.01438	−	0.229139i
$721$	29.2088	−	3.08117i	1.08779	−	0.114749i
$722$	−2.27954	+	1.91276i	−0.0848356	+	0.0711855i
$723$	21.1786	−	2.50861i	0.787642	−	0.0932961i
$724$	−1.28086	−	1.07477i	−0.0476029	−	0.0399436i
$725$	66.6224	−	24.2486i	2.47429	−	0.900569i
$726$	23.6192	−	11.9077i	0.876590	−	0.441938i
$727$	−29.6742	−	10.8005i	−1.10055	−	0.400569i	−0.273033	−	0.962005i	$-0.588027\pi$
$727$	−29.6742	−	10.8005i	−1.10055	−	0.400569i	−0.827520	+	0.561436i	$0.810249\pi$
$728$	16.0480	+	22.0705i	0.594777	+	0.817988i
$729$	−25.4562	−	8.99891i	−0.942823	−	0.333293i
$730$	−7.10204	−	12.3011i	−0.262858	−	0.455284i
$731$	−2.06592	+	1.73351i	−0.0764107	+	0.0641162i
$732$	6.74100	+	4.41872i	0.249155	+	0.163321i
$733$	−4.79062	+	27.1690i	−0.176946	+	1.00351i	0.758928	+	0.651174i	$0.225723\pi$
$733$	−4.79062	+	27.1690i	−0.176946	+	1.00351i	−0.935874	+	0.352335i	$0.885388\pi$
$734$	−7.68292	+	43.5720i	−0.283582	+	1.60827i
$735$	−36.0469	−	31.5581i	−1.32961	−	1.16404i
$736$	1.01580	−	0.852360i	0.0374430	−	0.0314184i
$737$	−4.19922	+	7.27326i	−0.154680	+	0.267914i
$738$	−15.1447	+	20.4747i	−0.557484	+	0.753683i
$739$	−3.66651	−	6.35058i	−0.134875	−	0.233610i	0.790675	−	0.612236i	$-0.209730\pi$
$739$	−3.66651	−	6.35058i	−0.134875	−	0.233610i	−0.925550	+	0.378626i	$0.876397\pi$
$740$	−3.46530	+	2.90773i	−0.127387	+	0.106890i
$741$	−22.2190	+	23.6238i	−0.816234	+	0.867840i
$742$	−15.3015	−	10.3125i	−0.561735	−	0.378585i
$743$	−15.0951	+	5.49415i	−0.553784	+	0.201561i	−0.603727	−	0.797191i	$-0.706318\pi$
$743$	−15.0951	+	5.49415i	−0.553784	+	0.201561i	0.0499428	+	0.998752i	$0.484096\pi$
$744$	−11.6387	−	38.6586i	−0.426697	−	1.41729i
$745$	4.88491	+	1.77796i	0.178969	+	0.0651395i
$746$	26.0752	+	45.1636i	0.954682	+	1.65356i
$747$	−0.189690	−	3.09217i	−0.00694038	−	0.113137i
$748$	0.189514	+	0.328248i	0.00692931	+	0.0120019i
$749$	−4.53148	−	15.7806i	−0.165577	−	0.576609i
$750$	35.3149	+	47.2834i	1.28952	+	1.72654i
$751$	7.75023	−	2.82085i	0.282810	−	0.102934i	−0.196721	−	0.980460i	$-0.563029\pi$
$751$	7.75023	−	2.82085i	0.282810	−	0.102934i	0.479531	+	0.877525i	$0.340807\pi$
$752$	13.5567	−	4.93423i	0.494362	−	0.179933i
$753$	−1.68538	+	29.7282i	−0.0614187	+	1.08336i
$754$	7.28965	+	41.3416i	0.265473	+	1.50557i
$755$	50.2026			1.82706
$756$	−0.319494	+	4.92373i	−0.0116199	+	0.179074i
$757$	32.9747			1.19849			0.599243	−	0.800567i	$-0.295468\pi$
$757$	32.9747			1.19849			0.599243	+	0.800567i	$0.295468\pi$
$758$	−2.73458	−	15.5086i	−0.0993246	−	0.563298i
$759$	1.05042	−	0.529575i	0.0381278	−	0.0192223i
$760$	42.8251	−	15.5870i	1.55343	−	0.565402i
$761$	−7.91339	+	2.88024i	−0.286860	+	0.104409i	−0.481443	−	0.876478i	$-0.659887\pi$
$761$	−7.91339	+	2.88024i	−0.286860	+	0.104409i	0.194582	+	0.980886i	$0.437665\pi$
$762$	−19.8544	+	2.35175i	−0.719247	+	0.0851948i
$763$	12.3820	−	12.8316i	0.448257	−	0.464537i
$764$	2.41822	+	4.18848i	0.0874882	+	0.151534i
$765$	−3.45671	+	11.6775i	−0.124978	+	0.422200i
$766$	6.50916	+	11.2742i	0.235185	+	0.407353i
$767$	26.6999	+	9.71798i	0.964079	+	0.350896i
$768$	−9.91198	+	10.5387i	−0.357668	+	0.380281i
$769$	17.6984	−	6.44170i	0.638222	−	0.232294i	−0.00258400	−	0.999997i	$-0.500823\pi$
$769$	17.6984	−	6.44170i	0.638222	−	0.232294i	0.640806	+	0.767703i	$0.278600\pi$
$770$	−1.14518	+	16.4667i	−0.0412695	+	0.593417i
$771$	8.88469	+	29.5109i	0.319974	+	1.06281i
$772$	5.84083	−	4.90104i	0.210216	−	0.176392i
$773$	−1.56186	−	2.70522i	−0.0561763	−	0.0973002i	0.836570	−	0.547861i	$-0.184558\pi$
$773$	−1.56186	−	2.70522i	−0.0561763	−	0.0973002i	−0.892746	+	0.450560i	$0.851224\pi$
$774$	8.32769	+	8.77236i	0.299332	+	0.315316i
$775$	−49.0790	+	85.0074i	−1.76297	+	3.05355i
$776$	−4.98623	+	4.18394i	−0.178995	+	0.150195i
$777$	−9.92712	−	10.7290i	−0.356133	−	0.384900i
$778$	2.72579	−	15.4587i	0.0977242	−	0.554222i
$779$	4.39173	−	24.9068i	0.157350	−	0.892377i
$780$	−8.97542	+	4.52501i	−0.321372	+	0.162021i
$781$	−0.753489	+	0.632252i	−0.0269619	+	0.0226238i
$782$	−0.521223	−	0.902785i	−0.0186389	−	0.0322835i
$783$	17.2144	−	30.1380i	0.615191	−	1.07704i
$784$	−31.4159	+	6.70258i	−1.12200	+	0.239378i
$785$	−78.3915	−	28.5322i	−2.79791	−	1.01836i
$786$	0.00479426	+	0.00314263i	0.000171006	+	0.000112094i
$787$	28.7306	−	10.4571i	1.02413	−	0.372754i	0.225289	−	0.974292i	$-0.427667\pi$
$787$	28.7306	−	10.4571i	1.02413	−	0.372754i	0.798844	+	0.601538i	$0.205445\pi$
$788$	−1.83516	−	1.53988i	−0.0653749	−	0.0548561i
$789$	2.79535	−	6.50798i	0.0995171	−	0.231690i
$790$	26.6772	−	22.3849i	0.949134	−	0.796418i
$791$	13.8737	−	31.1927i	0.493291	−	1.10908i
$792$	−6.48117	+	4.29149i	−0.230298	+	0.152491i
$793$	−53.0571			−1.88411
$794$	5.12986	+	1.86712i	0.182052	+	0.0662615i
$795$	−21.2927	+	22.6389i	−0.755173	+	0.802918i
$796$	−3.03823	−	2.54938i	−0.107687	−	0.0903602i
$797$	23.4087	−	8.52006i	0.829178	−	0.301796i	0.107657	−	0.994188i	$-0.465665\pi$
$797$	23.4087	−	8.52006i	0.829178	−	0.301796i	0.721522	+	0.692392i	$0.243443\pi$
$798$	−12.4681	−	29.6939i	−0.441366	−	1.05115i
$799$	−0.560824	−	3.18059i	−0.0198405	−	0.112521i
$800$	21.3036			0.753195
$801$	−44.3333	−	5.04298i	−1.56644	−	0.178185i
$802$	6.03673			0.213165
$803$	−2.26085	−	0.822882i	−0.0797837	−	0.0290389i
$804$	2.00433	−	4.66638i	0.0706874	−	0.164571i
$805$	0.479207	−	6.89055i	0.0168898	−	0.242860i
$806$	−44.5227	−	37.3590i	−1.56825	−	1.31592i
$807$	13.9748	−	7.04547i	0.491936	−	0.248012i
$808$	−24.0520	+	20.1821i	−0.846148	+	0.710003i
$809$	2.94529	−	5.10138i	0.103551	−	0.179355i	−0.809594	−	0.586990i	$-0.800313\pi$
$809$	2.94529	−	5.10138i	0.103551	−	0.179355i	0.913145	+	0.407635i	$0.133646\pi$
$810$	53.2253	+	12.2677i	1.87015	+	0.431042i
$811$	−1.31810			−0.0462846			−0.0231423	−	0.999732i	$-0.507367\pi$
$811$	−1.31810			−0.0462846			−0.0231423	+	0.999732i	$0.507367\pi$
$812$	−6.15482	−	1.53209i	−0.215992	−	0.0537658i
$813$	−2.89156	+	51.0038i	−0.101411	+	1.78878i
$814$	−0.874509	+	4.95959i	−0.0306515	+	0.173833i
$815$	11.5123	+	9.65995i	0.403258	+	0.338373i
$816$	4.88623	+	6.54222i	0.171052	+	0.229023i
$817$	−11.2876	−	4.10834i	−0.394902	−	0.143733i
$818$	−17.6271	−	30.5310i	−0.616317	−	1.06749i
$819$	−16.0094	−	28.2596i	−0.559415	−	0.987469i
$820$	3.91932	−	6.78845i	0.136868	−	0.237063i
$821$	−34.0598	+	28.5795i	−1.18869	+	0.997432i	−0.188813	+	0.982013i	$0.560464\pi$
$821$	−34.0598	+	28.5795i	−1.18869	+	0.997432i	−0.999881	+	0.0154193i	$0.995092\pi$
$822$	−15.8364	−	52.6014i	−0.552359	−	1.83468i
$823$	6.28761	−	35.6588i	0.219172	−	1.24299i	−0.654346	−	0.756195i	$-0.727056\pi$
$823$	6.28761	−	35.6588i	0.219172	−	1.24299i	0.873518	−	0.486792i	$-0.161833\pi$
$824$	−21.4344	−	17.9856i	−0.746702	−	0.626557i
$825$	18.3963	+	4.32998i	0.640476	+	0.150751i
$826$	−19.5926	+	20.3042i	−0.681714	+	0.706472i
$827$	−13.8271	+	23.9493i	−0.480816	+	0.832797i	−0.999758	−	0.0220122i	$-0.992993\pi$
$827$	−13.8271	+	23.9493i	−0.480816	+	0.832797i	0.518942	+	0.854809i	$0.326326\pi$
$828$	−0.593122	+	0.392734i	−0.0206124	+	0.0136484i
$829$	12.9123			0.448463			0.224231	−	0.974536i	$-0.428013\pi$
$829$	12.9123			0.448463			0.224231	+	0.974536i	$0.428013\pi$
$830$	1.08829	+	6.17199i	0.0377750	+	0.214233i
$831$	−6.80058	+	15.8327i	−0.235910	+	0.549232i
$832$	4.33119	−	24.5634i	0.150157	−	0.851583i
$833$	0.256425	+	7.18668i	0.00888462	+	0.249004i
$834$	−14.9114	+	7.51765i	−0.516338	+	0.260315i
$835$	14.0889	+	79.9020i	0.487566	+	2.76512i
$836$	−0.844106	+	1.46203i	−0.0291940	+	0.0505655i
$837$	8.56357	+	47.2836i	0.296000	+	1.63436i
$838$	−11.9964	−	20.7783i	−0.414407	−	0.717774i
$839$	15.3223	+	5.57687i	0.528985	+	0.192535i	0.592685	−	0.805434i	$-0.298068\pi$
$839$	15.3223	+	5.57687i	0.528985	+	0.192535i	−0.0636999	+	0.997969i	$0.520290\pi$
$840$	2.21124	+	45.5879i	0.0762949	+	1.57293i
$841$	11.9625	+	10.0377i	0.412500	+	0.346129i
$842$	37.4754	−	13.6399i	1.29149	−	0.470063i
$843$	6.48351	−	15.0946i	0.223304	−	0.519885i
$844$	−0.201953	−	1.14533i	−0.00695152	−	0.0394240i
$845$	7.39820	−	12.8141i	0.254506	−	0.440817i
$846$	−14.0844	+	3.38408i	−0.484233	+	0.116347i
$847$	−15.4711	−	21.2772i	−0.531595	−	0.731094i
$848$	3.61853	+	20.5217i	0.124261	+	0.704717i
$849$	−27.2089	+	28.9292i	−0.933808	+	0.992847i
$850$	2.90818	−	16.4931i	0.0997496	−	0.565708i
$851$	0.365943	−	2.07536i	0.0125443	−	0.0711425i
$852$	0.407507	−	0.433272i	0.0139610	−	0.0148437i
$853$	−4.86497	−	27.5906i	−0.166573	−	0.944685i	−0.947427	−	0.319971i	$-0.896327\pi$
$853$	−4.86497	−	27.5906i	−0.166573	−	0.944685i	0.780854	−	0.624714i	$-0.214784\pi$
$854$	21.4118	−	48.1409i	0.732698	−	1.64735i
$855$	−52.7420	+	12.6724i	−1.80374	+	0.433386i
$856$	−7.82057	+	13.5456i	−0.267301	+	0.462980i
$857$	−1.12125	−	6.35894i	−0.0383013	−	0.217217i	0.959650	−	0.281198i	$-0.0907316\pi$
$857$	−1.12125	−	6.35894i	−0.0383013	−	0.217217i	−0.997951	+	0.0639803i	$0.979621\pi$
$858$	−4.41635	+	10.2819i	−0.150772	+	0.351019i
$859$	5.00556	−	1.82188i	0.170788	−	0.0621616i	−0.255211	−	0.966885i	$-0.582145\pi$
$859$	5.00556	−	1.82188i	0.170788	−	0.0621616i	0.425999	+	0.904724i	$0.359923\pi$
$860$	−2.85196	−	2.39308i	−0.0972510	−	0.0816033i
$861$	22.5231	+	11.5868i	0.767586	+	0.394876i
$862$	4.23734	+	1.54226i	0.144324	+	0.0525297i
$863$	−3.63727	−	6.29993i	−0.123814	−	0.214452i	0.797455	−	0.603379i	$-0.206179\pi$
$863$	−3.63727	−	6.29993i	−0.123814	−	0.214452i	−0.921269	+	0.388927i	$0.872846\pi$
$864$	7.95796	−	6.74064i	0.270735	−	0.229321i
$865$	14.7131	−	25.4838i	0.500260	−	0.866475i
$866$	−3.36512	−	19.0845i	−0.114351	−	0.648518i
$867$	−24.6602	+	12.4326i	−0.837503	+	0.422232i
$868$	7.89117	−	3.85249i	0.267844	−	0.130762i
$869$	1.02431	−	5.80914i	0.0347473	−	0.197061i
$870$	−27.7105	+	64.5141i	−0.939475	+	2.18723i
$871$	5.80519	+	32.9229i	0.196701	+	1.11555i
$872$	−16.9875			−0.575269
$873$	6.45958	−	4.27719i	0.218624	−	0.144761i
$874$	2.32156	−	4.02106i	0.0785278	−	0.136014i
$875$	40.7570	−	42.2371i	1.37784	−	1.42788i
$876$	1.41620	+	0.333336i	0.0478491	+	0.0112624i
$877$	−14.2069	−	11.9210i	−0.479732	−	0.402543i	0.370598	−	0.928793i	$-0.379153\pi$
$877$	−14.2069	−	11.9210i	−0.479732	−	0.402543i	−0.850329	+	0.526251i	$0.823597\pi$
$878$	5.76191	−	32.6774i	0.194455	−	1.10281i
$879$	10.4553	+	34.7278i	0.352650	+	1.17134i
$880$	14.2797	−	11.9821i	0.481370	−	0.403918i
$881$	11.2521	−	19.4892i	0.379093	−	0.656609i	−0.611837	−	0.790984i	$-0.709569\pi$
$881$	11.2521	−	19.4892i	0.379093	−	0.656609i	0.990931	+	0.134375i	$0.0429026\pi$
$882$	32.1019	−	3.12154i	1.08093	−	0.105108i
$883$	−27.9531	−	48.4163i	−0.940698	−	1.62934i	−0.764144	−	0.645046i	$-0.776838\pi$
$883$	−27.9531	−	48.4163i	−0.940698	−	1.62934i	−0.176555	−	0.984291i	$-0.556495\pi$
$884$	1.41777	+	0.516025i	0.0476846	+	0.0173558i
$885$	28.4380	+	38.0759i	0.955933	+	1.27991i
$886$	−28.5833	−	23.9842i	−0.960273	−	0.805765i
$887$	4.54565	−	25.7797i	0.152628	−	0.865596i	−0.808295	−	0.588778i	$-0.799609\pi$
$887$	4.54565	−	25.7797i	0.152628	−	0.865596i	0.960922	−	0.276818i	$-0.0892798\pi$
$888$	−0.788193	+	13.9028i	−0.0264500	+	0.466549i
$889$	5.48816	+	19.1121i	0.184067	+	0.641000i
$890$	90.2643			3.02566
$891$	8.24198	−	4.20327i	0.276117	−	0.140815i
$892$	0.948941	−	1.64361i	0.0317729	−	0.0550322i
$893$	11.0196	−	9.24656i	0.368757	−	0.309424i
$894$	−3.12498	+	1.57548i	−0.104515	+	0.0526918i
$895$	−56.1557	−	47.1202i	−1.87708	−	1.57506i
$896$	29.3465	+	19.7783i	0.980398	+	0.660746i
$897$	1.84805	−	4.30252i	0.0617044	−	0.143657i
$898$	−48.9204	−	17.8056i	−1.63250	−	0.594180i
$899$	−61.7706			−2.06016
$900$	−11.3552	−	1.29167i	−0.378507	−	0.0430557i
$901$	4.66499			0.155413
$902$	−1.51537	−	8.59406i	−0.0504561	−	0.286151i
$903$	7.27713	−	9.57926i	0.242168	−	0.318778i
$904$	−30.5615	+	11.1235i	−1.01646	+	0.369962i
$905$	14.1022	+	11.8332i	0.468773	+	0.393347i
$906$	−23.1551	+	24.6191i	−0.769276	+	0.817913i
$907$	−53.7846	−	19.5760i	−1.78589	−	0.650010i	−0.999478	−	0.0323031i	$-0.989716\pi$
$907$	−53.7846	−	19.5760i	−1.78589	−	0.650010i	−0.786409	−	0.617707i	$-0.788062\pi$
$908$	−8.94240			−0.296764
$909$	31.1591	−	20.6319i	1.03348	−	0.684316i
$910$	38.6408	+	53.1421i	1.28093	+	1.76164i
$911$	18.9948	−	15.9385i	0.629326	−	0.528067i	−0.271394	−	0.962468i	$-0.587485\pi$
$911$	18.9948	−	15.9385i	0.629326	−	0.528067i	0.900719	+	0.434401i	$0.143040\pi$
$912$	−14.3537	+	33.4175i	−0.475298	+	1.10656i
$913$	0.813207	+	0.682361i	0.0269132	+	0.0225829i
$914$	−10.1432	+	3.69183i	−0.335508	+	0.122115i
$915$	−74.2179	−	48.6498i	−2.45357	−	1.60831i
$916$	3.31062	+	1.20497i	0.109386	+	0.0398132i
$917$	0.00231695	−	0.00520928i	7.65125e−5	−	0.000172026i
$918$	−4.13221	−	7.08117i	−0.136383	−	0.233714i
$919$	29.6758	+	51.4000i	0.978914	+	1.69553i	0.666361	+	0.745629i	$0.267851\pi$
$919$	29.6758	+	51.4000i	0.978914	+	1.69553i	0.312553	+	0.949900i	$0.398816\pi$
$920$	−5.04076	+	4.22970i	−0.166189	+	0.139449i
$921$	−13.7702	+	6.94233i	−0.453744	+	0.228757i
$922$	−0.991644	+	5.62389i	−0.0326580	+	0.185213i
$923$	−0.679893	+	3.85587i	−0.0223790	+	0.126917i
$924$	−1.14825	−	1.24100i	−0.0377747	−	0.0408259i
$925$	25.9354	−	21.7624i	0.852752	−	0.715544i
$926$	5.96010	−	10.3232i	0.195861	−	0.339241i
$927$	22.9289	+	24.1533i	0.753085	+	0.793298i
$928$	6.70314	+	11.6102i	0.220041	+	0.381123i
$929$	−11.0422	+	9.26550i	−0.362282	+	0.303991i	−0.805700	−	0.592324i	$-0.798210\pi$
$929$	−11.0422	+	9.26550i	−0.362282	+	0.303991i	0.443417	+	0.896315i	$0.353766\pi$
$930$	−28.0241	−	93.0834i	−0.918948	−	3.05232i
$931$	−27.1503	+	16.9941i	−0.889815	+	0.556958i
$932$	4.55074	−	1.65633i	0.149064	−	0.0542550i
$933$	22.2473	−	23.6539i	0.728344	−	0.774394i
$934$	50.5702	+	18.4060i	1.65471	+	0.602264i
$935$	−2.08653	−	3.61398i	−0.0682370	−	0.118190i
$936$	−8.78258	+	29.6693i	−0.287068	+	0.969771i
$937$	23.3307	+	40.4100i	0.762181	+	1.32014i	0.941724	+	0.336386i	$0.109205\pi$
$937$	23.3307	+	40.4100i	0.762181	+	1.32014i	−0.179543	+	0.983750i	$0.557462\pi$
$938$	−32.2151	−	8.01913i	−1.05186	−	0.261834i
$939$	0.411489	−	0.0487408i	0.0134284	−	0.00159060i
$940$	4.18960	−	1.52489i	0.136650	−	0.0497364i
$941$	−16.1680	+	5.88468i	−0.527063	+	0.191835i	−0.591826	−	0.806066i	$-0.701593\pi$
$941$	−16.1680	+	5.88468i	−0.527063	+	0.191835i	0.0647636	+	0.997901i	$0.479371\pi$
$942$	50.1487	−	25.2827i	1.63393	−	0.823756i
$943$	0.634112	+	3.59623i	0.0206495	+	0.117109i
$944$	31.8644			1.03710
$945$	3.51761	−	54.2100i	0.114428	−	1.76345i
$946$	−4.14473			−0.134757
$947$	4.74284	+	26.8980i	0.154122	+	0.874068i	0.959584	+	0.281421i	$0.0908058\pi$
$947$	4.74284	+	26.8980i	0.154122	+	0.874068i	−0.805463	+	0.592647i	$0.798083\pi$
$948$	−0.201902	+	3.56132i	−0.00655747	+	0.115666i
$949$	−8.99952	+	3.27556i	−0.292137	+	0.106329i
$950$	70.0958	−	25.5128i	2.27421	−	0.827744i
$951$	−25.3747	−	33.9744i	−0.822832	−	1.10170i
$952$	4.75713	−	4.92990i	0.154180	−	0.159779i
$953$	−5.96599	−	10.3334i	−0.193257	−	0.334732i	0.753071	−	0.657940i	$-0.228572\pi$
$953$	−5.96599	−	10.3334i	−0.193257	−	0.334732i	−0.946328	+	0.323208i	$0.895239\pi$
$954$	−1.28110	−	20.8836i	−0.0414773	−	0.676130i
$955$	−26.6244	−	46.1149i	−0.861546	−	1.49224i
$956$	−1.35300	−	0.492451i	−0.0437590	−	0.0159270i
$957$	3.42858	+	11.3882i	0.110830	+	0.368127i
$958$	−0.140694	+	0.0512085i	−0.00454563	+	0.00165447i
$959$	−49.0966	+	23.9691i	−1.58541	+	0.774001i
$960$	28.5816	−	30.3887i	0.922467	−	0.980790i
$961$	41.7656	−	35.0455i	1.34728	−	1.13050i
$962$	10.0233	+	17.3609i	0.323165	+	0.559738i
$963$	11.0709	−	14.9671i	0.356753	−	0.482308i
$964$	2.20958	−	3.82710i	0.0711656	−	0.123263i
$965$	−64.3071	+	53.9601i	−2.07012	+	1.73704i
$966$	3.15806	+	3.41314i	0.101609	+	0.109816i
$967$	−9.08541	+	51.5259i	−0.292167	+	1.65696i	0.386331	+	0.922360i	$0.373742\pi$
$967$	−9.08541	+	51.5259i	−0.292167	+	1.65696i	−0.678499	+	0.734602i	$0.737369\pi$
$968$	−4.35199	+	24.6813i	−0.139878	+	0.793288i
$969$	6.80942	+	4.46357i	0.218750	+	0.143390i
$970$	−12.0060	+	10.0742i	−0.385489	+	0.323464i
$971$	−26.6903	−	46.2290i	−0.856533	−	1.48356i	−0.875215	−	0.483734i	$-0.839280\pi$
$971$	−26.6903	−	46.2290i	−0.856533	−	1.48356i	0.0186820	−	0.999825i	$-0.494053\pi$
$972$	−4.65044	+	3.11038i	−0.149163	+	0.0997655i
$973$	9.76731	+	13.4328i	0.313126	+	0.430637i
$974$	−6.92961	−	2.52217i	−0.222039	−	0.0808156i
$975$	67.1750	−	33.8666i	2.15132	−	1.08460i
$976$	−55.9127	+	20.3505i	−1.78972	+	0.651405i
$977$	−18.7298	−	15.7162i	−0.599220	−	0.502805i	0.291975	−	0.956426i	$-0.405688\pi$
$977$	−18.7298	−	15.7162i	−0.599220	−	0.502805i	−0.891195	+	0.453621i	$0.850132\pi$
$978$	−10.0470	+	1.19007i	−0.321268	+	0.0380542i
$979$	11.7123	−	9.82780i	0.374327	−	0.314098i
$980$	−9.70887	+	2.07139i	−0.310139	+	0.0661681i
$981$	20.0895	+	2.28521i	0.641409	+	0.0729612i
$982$	7.77240			0.248027
$983$	34.8743	+	12.6932i	1.11232	+	0.404850i	0.831843	−	0.555012i	$-0.187286\pi$
$983$	34.8743	+	12.6932i	1.11232	+	0.404850i	0.280474	+	0.959862i	$0.409508\pi$
$984$	−6.95622	−	23.1054i	−0.221756	−	0.736572i
$985$	20.2050	+	16.9540i	0.643785	+	0.540200i
$986$	9.90358	−	3.60461i	0.315394	−	0.114794i
$987$	5.57742	+	13.2831i	0.177531	+	0.422806i
$988$	1.16693	+	6.61799i	0.0371250	+	0.210546i
$989$	1.73438			0.0551502
$990$	−15.6056	+	10.3332i	−0.495978	+	0.328410i
$991$	24.0175			0.762941			0.381470	−	0.924381i	$-0.375418\pi$
$991$	24.0175			0.762941			0.381470	+	0.924381i	$0.375418\pi$
$992$	−17.4416	−	6.34822i	−0.553771	−	0.201556i
$993$	−6.59127	−	8.82510i	−0.209168	−	0.280056i
$994$	−3.22421	−	2.17298i	−0.102266	−	0.0689227i
$995$	33.4507	+	28.0684i	1.06046	+	0.889829i
$996$	−0.536878	−	0.351923i	−0.0170116	−	0.0111511i
$997$	39.5326	−	33.1718i	1.25201	−	1.05056i	0.255525	−	0.966802i	$-0.417752\pi$
$997$	39.5326	−	33.1718i	1.25201	−	1.05056i	0.996486	−	0.0837594i	$-0.0266927\pi$
$998$	18.2513	−	31.6121i	0.577734	−	1.00066i
$999$	2.80238	−	16.3356i	0.0886633	−	0.516834i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.u.a.4.7	✓	132
3.2	odd	2		567.2.u.a.550.16		132
7.2	even	3		189.2.w.a.58.7	yes	132
21.2	odd	6		567.2.w.a.226.16		132
27.7	even	9		189.2.w.a.88.7	yes	132
27.20	odd	18		567.2.w.a.424.16		132
189.128	odd	18		567.2.u.a.100.16		132
189.142	even	9	inner	189.2.u.a.142.7	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.4.7	✓	132	1.1	even	1	trivial
189.2.u.a.142.7	yes	132	189.142	even	9	inner
189.2.w.a.58.7	yes	132	7.2	even	3
189.2.w.a.88.7	yes	132	27.7	even	9
567.2.u.a.100.16		132	189.128	odd	18
567.2.u.a.550.16		132	3.2	odd	2
567.2.w.a.226.16		132	21.2	odd	6
567.2.w.a.424.16		132	27.20	odd	18

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.266701 - 1.51254i) q^{2} +(-1.44858 - 0.949540i) q^{3} +(-0.337258 + 0.122752i) q^{4} +(3.71318 - 1.35149i) q^{5} +(-1.04988 + 2.44427i) q^{6} +(2.56740 + 0.639091i) q^{7} +(-1.26026 - 2.18283i) q^{8} +(1.19675 + 2.75096i) q^{9} +O(q^{10})\)	\(q+(-0.266701 - 1.51254i) q^{2} +(-1.44858 - 0.949540i) q^{3} +(-0.337258 + 0.122752i) q^{4} +(3.71318 - 1.35149i) q^{5} +(-1.04988 + 2.44427i) q^{6} +(2.56740 + 0.639091i) q^{7} +(-1.26026 - 2.18283i) q^{8} +(1.19675 + 2.75096i) q^{9} +(-3.03449 - 5.25589i) q^{10} +(-0.965994 - 0.351593i) q^{11} +(0.605101 + 0.142424i) q^{12} +(-3.84523 + 1.39955i) q^{13} +(0.281920 - 4.05374i) q^{14} +(-6.66212 - 1.56808i) q^{15} +(-3.51537 + 2.94975i) q^{16} +(0.513661 + 0.889686i) q^{17} +(3.84176 - 2.54381i) q^{18} +(-2.28787 + 3.96272i) q^{19} +(-1.08640 + 0.911600i) q^{20} +(-3.11224 - 3.36362i) q^{21} +(-0.274166 + 1.55487i) q^{22} +(0.114726 - 0.650644i) q^{23} +(-0.247105 + 4.35866i) q^{24} +(8.13099 - 6.82271i) q^{25} +(3.14240 + 5.44279i) q^{26} +(0.878570 - 5.12134i) q^{27} +(-0.944326 + 0.0996150i) q^{28} +(6.27669 + 2.28453i) q^{29} +(-0.594988 + 10.4949i) q^{30} +(-8.69005 + 3.16292i) q^{31} +(1.53751 + 1.29012i) q^{32} +(1.06546 + 1.42656i) q^{33} +(1.20869 - 1.01421i) q^{34} +(10.3970 - 1.09675i) q^{35} +(-0.741298 - 0.780881i) q^{36} +3.18970 q^{37} +(6.60394 + 2.40364i) q^{38} +(6.89903 + 1.62385i) q^{39} +(-7.62964 - 6.40203i) q^{40} +(-5.19385 + 1.89041i) q^{41} +(-4.25757 + 5.60446i) q^{42} +(0.455851 + 2.58526i) q^{43} +0.368948 q^{44} +(8.16163 + 8.59744i) q^{45} -1.01472 q^{46} +(-2.95417 - 1.07523i) q^{47} +(7.89319 - 0.934948i) q^{48} +(6.18313 + 3.28161i) q^{49} +(-12.4882 - 10.4788i) q^{50} +(0.100716 - 1.77652i) q^{51} +(1.12504 - 0.944017i) q^{52} +(2.27046 - 3.93255i) q^{53} +(-7.98054 + 0.0369978i) q^{54} -4.06209 q^{55} +(-1.84056 - 6.40963i) q^{56} +(7.07692 - 3.56787i) q^{57} +(1.78144 - 10.1030i) q^{58} +(-5.31915 - 4.46329i) q^{59} +(2.43934 - 0.288939i) q^{60} +(12.1841 + 4.43464i) q^{61} +(7.10169 + 12.3005i) q^{62} +(1.31442 + 7.82766i) q^{63} +(-3.04769 + 5.27875i) q^{64} +(-12.3866 + 10.3936i) q^{65} +(1.87357 - 1.99202i) q^{66} +(1.41867 - 8.04565i) q^{67} +(-0.282447 - 0.237001i) q^{68} +(-0.784002 + 0.833571i) q^{69} +(-4.43177 - 15.4333i) q^{70} +(0.478414 - 0.828638i) q^{71} +(4.49668 - 6.07922i) q^{72} +2.34044 q^{73} +(-0.850698 - 4.82455i) q^{74} +(-18.2568 + 2.16252i) q^{75} +(0.285173 - 1.61730i) q^{76} +(-2.25540 - 1.52004i) q^{77} +(0.616147 - 10.8681i) q^{78} +(0.996418 + 5.65097i) q^{79} +(-9.06667 + 15.7039i) q^{80} +(-6.13559 + 6.58441i) q^{81} +(4.24452 + 7.35172i) q^{82} +(-0.970385 - 0.353191i) q^{83} +(1.46252 + 0.752376i) q^{84} +(3.10972 + 2.60936i) q^{85} +(3.78873 - 1.37898i) q^{86} +(-6.92302 - 9.26929i) q^{87} +(0.449933 + 2.55170i) q^{88} +(-7.43653 + 12.8804i) q^{89} +(10.8272 - 14.6377i) q^{90} +(-10.7667 + 1.13576i) q^{91} +(0.0411755 + 0.233518i) q^{92} +(15.5915 + 3.66982i) q^{93} +(-0.838447 + 4.75507i) q^{94} +(-3.13973 + 17.8063i) q^{95} +(-1.00217 - 3.32877i) q^{96} +(-0.448435 - 2.54320i) q^{97} +(3.31451 - 10.2274i) q^{98} +(-0.188831 - 3.07818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Introduction

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