LMFDB - Embedded newform 288.2.bf.a.11.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, degree $8$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.20
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.370153 - 1.36491i) q^{2} +(1.60090 + 0.661153i) q^{3} +(-1.72597 + 1.01045i) q^{4} +(-0.155947 - 1.18454i) q^{5} +(0.309839 - 2.42981i) q^{6} +(-1.23982 - 4.62708i) q^{7} +(2.01805 + 1.98178i) q^{8} +(2.12575 + 2.11688i) q^{9} +O(q^{10})$	\(q+(-0.370153 - 1.36491i) q^{2} +(1.60090 + 0.661153i) q^{3} +(-1.72597 + 1.01045i) q^{4} +(-0.155947 - 1.18454i) q^{5} +(0.309839 - 2.42981i) q^{6} +(-1.23982 - 4.62708i) q^{7} +(2.01805 + 1.98178i) q^{8} +(2.12575 + 2.11688i) q^{9} +(-1.55907 + 0.651315i) q^{10} +(0.714959 - 0.548608i) q^{11} +(-3.43117 + 0.476499i) q^{12} +(1.55287 - 2.02374i) q^{13} +(-5.85664 + 3.40497i) q^{14} +(0.533505 - 1.99943i) q^{15} +(1.95797 - 3.48803i) q^{16} -5.41926 q^{17} +(2.10250 - 3.68504i) q^{18} +(3.09852 - 1.28345i) q^{19} +(1.46608 + 1.88691i) q^{20} +(1.07438 - 8.22720i) q^{21} +(-1.01345 - 0.772789i) q^{22} +(4.48426 + 1.20155i) q^{23} +(1.92044 + 4.50688i) q^{24} +(3.45082 - 0.924644i) q^{25} +(-3.33703 - 1.37044i) q^{26} +(2.00354 + 4.79435i) q^{27} +(6.81534 + 6.73344i) q^{28} +(-3.97708 - 0.523593i) q^{29} +(-2.92653 + 0.0119070i) q^{30} +(-1.91957 + 1.10826i) q^{31} +(-5.48560 - 1.38136i) q^{32} +(1.50729 - 0.405568i) q^{33} +(2.00595 + 7.39682i) q^{34} +(-5.28761 + 2.19020i) q^{35} +(-5.80800 - 1.50570i) q^{36} +(0.235657 - 0.568926i) q^{37} +(-2.89872 - 3.75414i) q^{38} +(3.82400 - 2.21312i) q^{39} +(2.03279 - 2.69952i) q^{40} +(-2.92522 + 10.9171i) q^{41} +(-11.6271 + 1.57889i) q^{42} +(0.771590 + 1.00556i) q^{43} +(-0.679660 + 1.66931i) q^{44} +(2.17602 - 2.84816i) q^{45} +(-0.0198440 - 6.56538i) q^{46} +(4.59259 + 2.65153i) q^{47} +(5.44064 - 4.28946i) q^{48} +(-13.8105 + 7.97351i) q^{49} +(-2.53939 - 4.36781i) q^{50} +(-8.67569 - 3.58296i) q^{51} +(-0.635323 + 5.06203i) q^{52} +(-2.55243 + 6.16210i) q^{53} +(5.80226 - 4.50930i) q^{54} +(-0.761343 - 0.761343i) q^{55} +(6.66784 - 11.7947i) q^{56} +(5.80898 - 0.00607683i) q^{57} +(0.757468 + 5.62218i) q^{58} +(5.22783 - 0.688257i) q^{59} +(1.09951 + 3.99005i) q^{60} +(-1.75112 + 13.3011i) q^{61} +(2.22322 + 2.20982i) q^{62} +(7.15940 - 12.4606i) q^{63} +(0.145072 + 7.99868i) q^{64} +(-2.63937 - 1.52384i) q^{65} +(-1.11149 - 1.90720i) q^{66} +(4.89236 - 6.37585i) q^{67} +(9.35351 - 5.47591i) q^{68} +(6.38444 + 4.88835i) q^{69} +(4.94665 + 6.40642i) q^{70} +(6.14705 + 6.14705i) q^{71} +(0.0946916 + 8.48475i) q^{72} +(8.86496 - 8.86496i) q^{73} +(-0.863764 - 0.111062i) q^{74} +(6.13574 + 0.801256i) q^{75} +(-4.05111 + 5.34611i) q^{76} +(-3.42487 - 2.62800i) q^{77} +(-4.43618 - 4.40023i) q^{78} +(2.86568 - 4.96351i) q^{79} +(-4.43705 - 1.77535i) q^{80} +(0.0376598 + 8.99992i) q^{81} +(15.9836 - 0.0483107i) q^{82} +(-4.89778 - 0.644805i) q^{83} +(6.45884 + 15.2855i) q^{84} +(0.845120 + 6.41933i) q^{85} +(1.08689 - 1.42536i) q^{86} +(-6.02073 - 3.46768i) q^{87} +(2.53005 + 0.309775i) q^{88} +(3.18445 - 3.18445i) q^{89} +(-4.69295 - 1.91582i) q^{90} +(-11.2893 - 4.67619i) q^{91} +(-8.95383 + 2.45728i) q^{92} +(-3.80576 + 0.505089i) q^{93} +(1.91915 - 7.24996i) q^{94} +(-2.00350 - 3.47017i) q^{95} +(-7.86860 - 5.83824i) q^{96} +(-6.48269 + 11.2284i) q^{97} +(15.9951 + 15.8987i) q^{98} +(2.68116 + 0.347277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.370153	−	1.36491i	−0.261737	−	0.965139i
$2$	−0.370153	−	1.36491i	−0.261737	−	0.965139i
$3$	1.60090	+	0.661153i	0.924279	+	0.381717i
$3$	1.60090	+	0.661153i	0.924279	+	0.381717i
$4$	−1.72597	+	1.01045i	−0.862987	+	0.505226i
$5$	−0.155947	−	1.18454i	−0.0697418	−	0.529742i	−0.990280	−	0.139089i	$-0.955583\pi$
$5$	−0.155947	−	1.18454i	−0.0697418	−	0.529742i	0.920538	−	0.390653i	$-0.127751\pi$
$6$	0.309839	−	2.42981i	0.126491	−	0.991968i
$7$	−1.23982	−	4.62708i	−0.468609	−	1.74887i	−0.644639	−	0.764487i	$-0.722992\pi$
$7$	−1.23982	−	4.62708i	−0.468609	−	1.74887i	0.176031	−	0.984385i	$-0.443674\pi$
$8$	2.01805	+	1.98178i	0.713489	+	0.700666i
$9$	2.12575	+	2.11688i	0.708585	+	0.705626i
$10$	−1.55907	+	0.651315i	−0.493021	+	0.205964i
$11$	0.714959	−	0.548608i	0.215568	−	0.165411i	−0.495333	−	0.868703i	$-0.664954\pi$
$11$	0.714959	−	0.548608i	0.215568	−	0.165411i	0.710901	+	0.703292i	$0.248287\pi$
$12$	−3.43117	+	0.476499i	−0.990494	+	0.137553i
$13$	1.55287	−	2.02374i	0.430690	−	0.561286i	−0.526713	−	0.850043i	$-0.676576\pi$
$13$	1.55287	−	2.02374i	0.430690	−	0.561286i	0.957402	+	0.288758i	$0.0932422\pi$
$14$	−5.85664	+	3.40497i	−1.56525	+	0.910018i
$15$	0.533505	−	1.99943i	0.137750	−	0.516251i
$16$	1.95797	−	3.48803i	0.489493	−	0.872007i
$17$	−5.41926			−1.31436			−0.657182	−	0.753732i	$-0.728252\pi$
$17$	−5.41926			−1.31436			−0.657182	+	0.753732i	$0.728252\pi$
$18$	2.10250	−	3.68504i	0.495564	−	0.868571i
$19$	3.09852	−	1.28345i	0.710850	−	0.294444i	0.00219377	−	0.999998i	$-0.499302\pi$
$19$	3.09852	−	1.28345i	0.710850	−	0.294444i	0.708656	+	0.705554i	$0.249302\pi$
$20$	1.46608	+	1.88691i	0.327826	+	0.421925i
$21$	1.07438	−	8.22720i	0.234448	−	1.79532i
$22$	−1.01345	−	0.772789i	−0.216067	−	0.164759i
$23$	4.48426	+	1.20155i	0.935033	+	0.250541i	0.693999	−	0.719976i	$-0.255847\pi$
$23$	4.48426	+	1.20155i	0.935033	+	0.250541i	0.241033	+	0.970517i	$0.422514\pi$
$24$	1.92044	+	4.50688i	0.392007	+	0.919962i
$25$	3.45082	−	0.924644i	0.690163	−	0.184929i
$26$	−3.33703	−	1.37044i	−0.654446	−	0.268766i
$27$	2.00354	+	4.79435i	0.385581	+	0.922674i
$28$	6.81534	+	6.73344i	1.28798	+	1.27250i
$29$	−3.97708	−	0.523593i	−0.738526	−	0.0972287i	−0.248128	−	0.968727i	$-0.579815\pi$
$29$	−3.97708	−	0.523593i	−0.738526	−	0.0972287i	−0.490398	+	0.871499i	$0.663149\pi$
$30$	−2.92653	+	0.0119070i	−0.534309	+	0.00217391i
$31$	−1.91957	+	1.10826i	−0.344765	+	0.199050i	−0.662377	−	0.749171i	$-0.730452\pi$
$31$	−1.91957	+	1.10826i	−0.344765	+	0.199050i	0.317612	+	0.948221i	$0.397119\pi$
$32$	−5.48560	−	1.38136i	−0.969727	−	0.244192i
$33$	1.50729	−	0.405568i	0.262386	−	0.0706003i
$34$	2.00595	+	7.39682i	0.344018	+	1.26854i
$35$	−5.28761	+	2.19020i	−0.893769	+	0.370211i
$36$	−5.80800	−	1.50570i	−0.968000	−	0.250951i
$37$	0.235657	−	0.568926i	0.0387418	−	0.0935309i	−0.903324	−	0.428958i	$-0.858881\pi$
$37$	0.235657	−	0.568926i	0.0387418	−	0.0935309i	0.942066	+	0.335427i	$0.108881\pi$
$38$	−2.89872	−	3.75414i	−0.470235	−	0.609002i
$39$	3.82400	−	2.21312i	0.612330	−	0.354383i
$40$	2.03279	−	2.69952i	0.321412	−	0.426831i
$41$	−2.92522	+	10.9171i	−0.456842	+	1.70496i	0.225773	+	0.974180i	$0.427509\pi$
$41$	−2.92522	+	10.9171i	−0.456842	+	1.70496i	−0.682615	+	0.730778i	$0.739157\pi$
$42$	−11.6271	+	1.57889i	−1.79410	+	0.243628i
$43$	0.771590	+	1.00556i	0.117666	+	0.153346i	0.848473	−	0.529239i	$-0.177522\pi$
$43$	0.771590	+	1.00556i	0.117666	+	0.153346i	−0.730806	+	0.682585i	$0.760856\pi$
$44$	−0.679660	+	1.66931i	−0.102463	+	0.251659i
$45$	2.17602	−	2.84816i	0.324382	−	0.424579i
$46$	−0.0198440	−	6.56538i	−0.00292584	−	0.968013i
$47$	4.59259	+	2.65153i	0.669898	+	0.386766i	0.796038	−	0.605246i	$-0.206925\pi$
$47$	4.59259	+	2.65153i	0.669898	+	0.386766i	−0.126140	+	0.992012i	$0.540259\pi$
$48$	5.44064	−	4.28946i	0.785288	−	0.619130i
$49$	−13.8105	+	7.97351i	−1.97293	+	1.13907i
$50$	−2.53939	−	4.36781i	−0.359123	−	0.617701i
$51$	−8.67569	−	3.58296i	−1.21484	−	0.501715i
$52$	−0.635323	+	5.06203i	−0.0881035	+	0.701978i
$53$	−2.55243	+	6.16210i	−0.350603	+	0.846430i	0.645943	+	0.763386i	$0.276464\pi$
$53$	−2.55243	+	6.16210i	−0.350603	+	0.846430i	−0.996546	+	0.0830445i	$0.973536\pi$
$54$	5.80226	−	4.50930i	0.789588	−	0.613638i
$55$	−0.761343	−	0.761343i	−0.102659	−	0.102659i
$56$	6.66784	−	11.7947i	0.891028	−	1.57614i
$57$	5.80898	−	0.00607683i	0.769418	−	0.000804896i
$58$	0.757468	+	5.62218i	0.0994605	+	0.738228i
$59$	5.22783	−	0.688257i	0.680606	−	0.0896035i	0.217707	−	0.976014i	$-0.430142\pi$
$59$	5.22783	−	0.688257i	0.680606	−	0.0896035i	0.462899	+	0.886411i	$0.346809\pi$
$60$	1.09951	+	3.99005i	0.141947	+	0.515113i
$61$	−1.75112	+	13.3011i	−0.224208	+	1.70303i	0.395721	+	0.918371i	$0.370495\pi$
$61$	−1.75112	+	13.3011i	−0.224208	+	1.70303i	−0.619929	+	0.784658i	$0.712839\pi$
$62$	2.22322	+	2.20982i	0.282349	+	0.280647i
$63$	7.15940	−	12.4606i	0.902000	−	1.56989i
$64$	0.145072	+	7.99868i	0.0181341	+	0.999836i
$65$	−2.63937	−	1.52384i	−0.327374	−	0.189009i
$66$	−1.11149	−	1.90720i	−0.136815	−	0.234760i
$67$	4.89236	−	6.37585i	0.597697	−	0.778934i	−0.392328	−	0.919825i	$-0.628330\pi$
$67$	4.89236	−	6.37585i	0.597697	−	0.778934i	0.990025	+	0.140891i	$0.0449968\pi$
$68$	9.35351	−	5.47591i	1.13428	−	0.664051i
$69$	6.38444	+	4.88835i	0.768596	+	0.588488i
$70$	4.94665	+	6.40642i	0.591238	+	0.765713i
$71$	6.14705	+	6.14705i	0.729521	+	0.729521i	0.970524	−	0.241003i	$-0.0774765\pi$
$71$	6.14705	+	6.14705i	0.729521	+	0.729521i	−0.241003	+	0.970524i	$0.577476\pi$
$72$	0.0946916	+	8.48475i	0.0111595	+	0.999938i
$73$	8.86496	−	8.86496i	1.03756	−	1.03756i	0.0382983	−	0.999266i	$-0.487806\pi$
$73$	8.86496	−	8.86496i	1.03756	−	1.03756i	0.999266	−	0.0382983i	$-0.0121937\pi$
$74$	−0.863764	−	0.111062i	−0.100411	−	0.0129107i
$75$	6.13574	+	0.801256i	0.708494	+	0.0925211i
$76$	−4.05111	+	5.34611i	−0.464694	+	0.613241i
$77$	−3.42487	−	2.62800i	−0.390301	−	0.299488i
$78$	−4.43618	−	4.40023i	−0.502299	−	0.498228i
$79$	2.86568	−	4.96351i	0.322414	−	0.558438i	−0.658571	−	0.752518i	$-0.728839\pi$
$79$	2.86568	−	4.96351i	0.322414	−	0.558438i	0.980986	+	0.194080i	$0.0621722\pi$
$80$	−4.43705	−	1.77535i	−0.496077	−	0.198490i
$81$	0.0376598	+	8.99992i	0.00418443	+	0.999991i
$82$	15.9836	−	0.0483107i	1.76509	−	0.00533503i
$83$	−4.89778	−	0.644805i	−0.537601	−	0.0707765i	−0.143163	−	0.989699i	$-0.545727\pi$
$83$	−4.89778	−	0.644805i	−0.537601	−	0.0707765i	−0.394438	+	0.918923i	$0.629061\pi$
$84$	6.45884	+	15.2855i	0.704717	+	1.66779i
$85$	0.845120	+	6.41933i	0.0916662	+	0.696274i
$86$	1.08689	−	1.42536i	0.117202	−	0.153701i
$87$	−6.02073	−	3.46768i	−0.645490	−	0.371774i
$88$	2.53005	+	0.309775i	0.269704	+	0.0330222i
$89$	3.18445	−	3.18445i	0.337551	−	0.337551i	−0.517894	−	0.855445i	$-0.673284\pi$
$89$	3.18445	−	3.18445i	0.337551	−	0.337551i	0.855445	+	0.517894i	$0.173284\pi$
$90$	−4.69295	−	1.91582i	−0.494680	−	0.201945i
$91$	−11.2893	−	4.67619i	−1.18344	−	0.490198i
$92$	−8.95383	+	2.45728i	−0.933501	+	0.256189i
$93$	−3.80576	+	0.505089i	−0.394639	+	0.0523753i
$94$	1.91915	−	7.24996i	0.197946	−	0.747776i
$95$	−2.00350	−	3.47017i	−0.205555	−	0.356032i
$96$	−7.86860	−	5.83824i	−0.803086	−	0.595863i
$97$	−6.48269	+	11.2284i	−0.658218	+	1.14007i	0.322859	+	0.946447i	$0.395356\pi$
$97$	−6.48269	+	11.2284i	−0.658218	+	1.14007i	−0.981077	+	0.193619i	$0.937977\pi$
$98$	15.9951	+	15.8987i	1.61575	+	1.60602i
$99$	2.68116	+	0.347277i	0.269467	+	0.0349026i
$100$	−5.02171	+	5.08280i	−0.502171	+	0.508280i
$101$	0.0256902	−	0.0197128i	0.00255627	−	0.00196150i	−0.607483	−	0.794333i	$-0.707821\pi$
$101$	0.0256902	−	0.0197128i	0.00255627	−	0.00196150i	0.610039	+	0.792372i	$0.291154\pi$
$102$	−1.67910	+	13.1678i	−0.166256	+	1.30381i
$103$	9.94130	+	2.66376i	0.979546	+	0.262469i	0.712853	−	0.701313i	$-0.247403\pi$
$103$	9.94130	+	2.66376i	0.979546	+	0.262469i	0.266692	+	0.963782i	$0.414069\pi$
$104$	7.14440	−	1.00656i	0.700566	−	0.0987017i
$105$	−9.91298	+	0.0103701i	−0.967408	+	0.00101201i
$106$	9.35552	+	1.20292i	0.908689	+	0.116838i
$107$	−17.9077	−	7.41761i	−1.73120	−	0.717087i	−0.999366	−	0.0356059i	$-0.988664\pi$
$107$	−17.9077	−	7.41761i	−1.73120	−	0.717087i	−0.731836	−	0.681481i	$-0.761336\pi$
$108$	−8.30252	−	6.25045i	−0.798910	−	0.601450i
$109$	−6.92091	−	16.7085i	−0.662903	−	1.60039i	−0.793233	−	0.608918i	$-0.791604\pi$
$109$	−6.92091	−	16.7085i	−0.662903	−	1.60039i	0.130331	−	0.991471i	$-0.458396\pi$
$110$	−0.757354	+	1.32098i	−0.0722109	+	0.125950i
$111$	0.753410	−	0.754988i	0.0715106	−	0.0716603i
$112$	−18.5669	−	4.73517i	−1.75441	−	0.447431i
$113$	2.29212	+	3.97008i	0.215625	+	0.373473i	0.953466	−	0.301501i	$-0.0974878\pi$
$113$	2.29212	+	3.97008i	0.215625	+	0.373473i	−0.737841	+	0.674975i	$0.764154\pi$
$114$	−2.15850	−	7.92650i	−0.202162	−	0.742385i
$115$	0.723978	−	5.49916i	0.0675113	−	0.512799i
$116$	7.39341	−	3.11494i	0.686460	−	0.289215i
$117$	7.58505	−	1.01474i	0.701238	−	0.0938127i
$118$	−2.87451	−	6.88078i	−0.264620	−	0.633427i
$119$	6.71892	+	25.0754i	0.615923	+	2.29865i
$120$	5.03908	−	2.97767i	0.460003	−	0.271823i
$121$	−2.63681	+	9.84072i	−0.239710	+	0.894611i
$122$	18.8030	−	2.53330i	1.70234	−	0.229354i
$123$	−11.9008	+	15.5431i	−1.07306	+	1.40147i
$124$	2.19328	−	3.85246i	0.196962	−	0.345961i
$125$	−3.91950	−	9.46250i	−0.350570	−	0.846352i
$126$	−19.6577	−	5.15964i	−1.75125	−	0.459658i
$127$		−	8.57442i		−	0.760856i	−0.924810	−	0.380428i	$-0.875777\pi$
$127$		−	8.57442i		−	0.760856i	0.924810	−	0.380428i	$-0.124223\pi$
$128$	10.8638	−	3.15874i	0.960234	−	0.279196i
$129$	0.570412	+	2.11993i	0.0502220	+	0.186650i
$130$	−1.10294	+	4.16656i	−0.0967343	+	0.365432i
$131$	7.78707	+	5.97523i	0.680360	+	0.522058i	0.890138	−	0.455691i	$-0.150608\pi$
$131$	7.78707	+	5.97523i	0.680360	+	0.522058i	−0.209779	+	0.977749i	$0.567274\pi$
$132$	−2.19174	+	2.22304i	−0.190766	+	0.193491i
$133$	−9.78025	−	12.7459i	−0.848055	−	1.10521i
$134$	−10.5134	−	4.31761i	−0.908220	−	0.372985i
$135$	5.36665	−	3.12094i	0.461888	−	0.268607i
$136$	−10.9364	−	10.7398i	−0.937785	−	0.920931i
$137$	14.6659	−	3.92972i	1.25299	−	0.335739i	0.429502	−	0.903066i	$-0.358689\pi$
$137$	14.6659	−	3.92972i	1.25299	−	0.335739i	0.823492	+	0.567327i	$0.192023\pi$
$138$	4.30895	−	10.5236i	0.366802	−	0.895831i
$139$	9.71957	−	1.27961i	0.824403	−	0.108535i	0.293491	−	0.955962i	$-0.405183\pi$
$139$	9.71957	−	1.27961i	0.824403	−	0.108535i	0.530912	+	0.847427i	$0.321849\pi$
$140$	6.91318	−	9.12310i	0.584271	−	0.771043i
$141$	5.59921	+	7.28124i	0.471538	+	0.613191i
$142$	6.11484	−	10.6655i	0.513146	−	0.895032i
$143$		−	2.29881i		−	0.192236i
$144$	11.5459	−	3.26990i	0.962158	−	0.272492i
$145$			4.79266i			0.398009i
$146$	−15.3813	−	8.81851i	−1.27296	−	0.729825i
$147$	−27.3810	+	3.63392i	−2.25834	+	0.299720i
$148$	0.168135	+	1.22007i	0.0138206	+	0.100289i
$149$	−21.0056	+	2.76544i	−1.72085	+	0.226554i	−0.925273	−	0.379301i	$-0.876165\pi$
$149$	−21.0056	+	2.76544i	−1.72085	+	0.226554i	−0.795575	+	0.605855i	$0.792831\pi$
$150$	−1.17751	−	8.67134i	−0.0961436	−	0.708012i
$151$	−1.43347	+	0.384097i	−0.116654	+	0.0312574i	−0.316674	−	0.948535i	$-0.602566\pi$
$151$	−1.43347	+	0.384097i	−0.116654	+	0.0312574i	0.200020	+	0.979792i	$0.435899\pi$
$152$	8.79650	+	3.55053i	0.713491	+	0.287986i
$153$	−11.5200	−	11.4719i	−0.931338	−	0.927449i
$154$	−2.31926	+	5.64741i	−0.186891	+	0.455082i
$155$	1.61213	+	2.10097i	0.129490	+	0.168754i
$156$	−4.36387	+	7.68376i	−0.349389	+	0.615193i
$157$	−17.8346	−	13.6850i	−1.42336	−	1.09218i	−0.980706	−	0.195486i	$-0.937372\pi$
$157$	−17.8346	−	13.6850i	−1.42336	−	1.09218i	−0.442651	−	0.896694i	$-0.645962\pi$
$158$	−7.83549	−	2.07415i	−0.623358	−	0.165011i
$159$	−8.16027	+	8.17736i	−0.647152	+	0.648507i
$160$	−0.780810	+	6.71333i	−0.0617284	+	0.530735i
$161$		−	22.2387i		−	1.75266i
$162$	12.2702	−	3.38275i	0.964035	−	0.265774i
$163$	0.408455	+	0.986098i	0.0319927	+	0.0772371i	0.939068	−	0.343730i	$-0.111691\pi$
$163$	0.408455	+	0.986098i	0.0319927	+	0.0772371i	−0.907076	+	0.420968i	$0.861691\pi$
$164$	−5.98231	−	21.7984i	−0.467140	−	1.70217i
$165$	−0.715469	−	1.72220i	−0.0556992	−	0.134073i
$166$	0.932823	+	6.92372i	0.0724011	+	0.537385i
$167$	−0.711220	+	2.65431i	−0.0550358	+	0.205397i	−0.987969	−	0.154654i	$-0.950574\pi$
$167$	−0.711220	+	2.65431i	−0.0550358	+	0.205397i	0.932933	+	0.360050i	$0.117240\pi$
$168$	18.4727	−	14.4737i	1.42520	−	1.11667i
$169$	1.68052	+	6.27180i	0.129271	+	0.482446i
$170$	8.44900	−	3.52965i	0.648009	−	0.270712i
$171$	9.30361	+	3.83089i	0.711465	+	0.292956i
$172$	−2.34781	−	0.955909i	−0.179019	−	0.0728874i
$173$	0.957041	−	7.26945i	0.0727625	−	0.552686i	−0.915773	−	0.401697i	$-0.868421\pi$
$173$	0.957041	−	7.26945i	0.0727625	−	0.552686i	0.988535	−	0.150990i	$-0.0482460\pi$
$174$	−2.50449	+	9.50134i	−0.189865	+	0.720295i
$175$	−8.55680	−	14.8208i	−0.646833	−	1.12035i
$176$	−0.513687	−	3.56796i	−0.0387206	−	0.268945i
$177$	8.82428	+	2.35457i	0.663273	+	0.176980i
$178$	−5.52522	−	3.16776i	−0.414133	−	0.237434i
$179$	−2.79531	−	6.74848i	−0.208932	−	0.504405i	0.784324	−	0.620351i	$-0.213010\pi$
$179$	−2.79531	−	6.74848i	−0.208932	−	0.504405i	−0.993256	+	0.115946i	$0.963010\pi$
$180$	−0.877821	+	7.11461i	−0.0654289	+	0.530292i
$181$	−2.78704	−	1.15443i	−0.207159	−	0.0858081i	0.276691	−	0.960959i	$-0.410762\pi$
$181$	−2.78704	−	1.15443i	−0.207159	−	0.0858081i	−0.483850	+	0.875151i	$0.660762\pi$
$182$	−2.20382	+	17.1398i	−0.163358	+	1.27049i
$183$	−11.5974	+	20.1359i	−0.857305	+	1.48849i
$184$	6.66825	+	11.3116i	0.491590	+	0.833904i
$185$	−0.710666	−	0.190422i	−0.0522492	−	0.0140001i
$186$	2.09812	+	5.00758i	0.153841	+	0.367173i
$187$	−3.87455	+	2.97305i	−0.283335	+	0.217411i
$188$	−10.6059	+	0.0641139i	−0.773518	+	0.00467599i
$189$	19.6998	−	15.2147i	1.43295	−	1.10670i
$190$	−3.99488	+	4.01910i	−0.289819	+	0.291576i
$191$	8.13119	−	14.0836i	0.588352	−	1.01906i	−0.406096	−	0.913830i	$-0.633110\pi$
$191$	8.13119	−	14.0836i	0.588352	−	1.01906i	0.994448	−	0.105226i	$-0.0335566\pi$
$192$	−5.05611	+	12.9010i	−0.364893	+	0.931049i
$193$	8.29625	+	14.3695i	0.597177	+	1.03434i	0.993236	+	0.116116i	$0.0370445\pi$
$193$	8.29625	+	14.3695i	0.597177	+	1.03434i	−0.396058	+	0.918225i	$0.629622\pi$
$194$	17.7253	+	4.69211i	1.27260	+	0.336874i
$195$	−3.21787	−	4.18454i	−0.230437	−	0.299661i
$196$	15.7798	−	27.7169i	1.12713	−	1.97978i
$197$	13.0237	+	5.39459i	0.927899	+	0.384348i	0.794881	−	0.606765i	$-0.207533\pi$
$197$	13.0237	+	5.39459i	0.927899	+	0.384348i	0.133018	+	0.991114i	$0.457533\pi$
$198$	−0.518437	−	3.78810i	−0.0368437	−	0.269208i
$199$	−18.8458	+	18.8458i	−1.33594	+	1.33594i	−0.435987	+	0.899953i	$0.643601\pi$
$199$	−18.8458	+	18.8458i	−1.33594	+	1.33594i	−0.899953	+	0.435987i	$0.856399\pi$
$200$	8.79637	+	4.97279i	0.621997	+	0.351629i
$201$	12.0476	−	6.97249i	0.849771	−	0.491802i
$202$	−0.0364156	−	0.0277682i	−0.00256219	−	0.00195376i
$203$	2.50817	+	19.0514i	0.176039	+	1.33715i
$204$	18.5944	−	2.58227i	1.30187	−	0.180795i
$205$	13.3879	+	1.76255i	0.935049	+	0.123101i
$206$	−0.0439928	−	14.5550i	−0.00306512	−	1.01410i
$207$	6.98889	+	12.0468i	0.485762	+	0.837313i
$208$	−4.01839	−	9.37890i	−0.278625	−	0.650310i
$209$	1.51121	−	2.61749i	0.104532	−	0.181055i
$210$	3.68347	+	13.5265i	0.254184	+	0.933418i
$211$	−16.8643	−	12.9404i	−1.16098	−	0.890855i	−0.165541	−	0.986203i	$-0.552937\pi$
$211$	−16.8643	−	12.9404i	−1.16098	−	0.890855i	−0.995444	+	0.0953480i	$0.969604\pi$
$212$	−1.82109	−	13.2147i	−0.125073	−	0.907592i
$213$	5.77667	+	13.9049i	0.395811	+	0.952751i
$214$	−3.49581	+	27.1881i	−0.238969	+	1.85854i
$215$	1.07079	−	1.07079i	0.0730274	−	0.0730274i
$216$	−5.45813	+	13.6458i	−0.371378	+	0.928482i
$217$	7.50794	+	7.50794i	0.509672	+	0.509672i
$218$	−20.2439	+	15.6311i	−1.37109	+	1.05867i
$219$	20.0530	−	8.33081i	1.35506	−	0.562944i
$220$	2.08336	+	0.544758i	0.140460	+	0.0367276i
$221$	−8.41543	+	10.9672i	−0.566083	+	0.737734i
$222$	−1.30937	−	0.748879i	−0.0878792	−	0.0502614i
$223$	5.94698	+	3.43349i	0.398239	+	0.229924i	0.685724	−	0.727862i	$-0.259486\pi$
$223$	5.94698	+	3.43349i	0.398239	+	0.229924i	−0.287485	+	0.957785i	$0.592819\pi$
$224$	0.409505	+	27.0950i	0.0273612	+	1.81036i
$225$	9.29294	+	5.33939i	0.619530	+	0.355959i
$226$	4.57037	−	4.59808i	0.304017	−	0.305860i
$227$	−1.14165	+	8.67167i	−0.0757738	+	0.575559i	0.910873	+	0.412686i	$0.135409\pi$
$227$	−1.14165	+	8.67167i	−0.0757738	+	0.575559i	−0.986647	+	0.162873i	$0.947924\pi$
$228$	−10.0200	+	5.88018i	−0.663591	+	0.389425i
$229$	4.26994	−	0.562149i	0.282166	−	0.0371478i	0.0118850	−	0.999929i	$-0.496217\pi$
$229$	4.26994	−	0.562149i	0.282166	−	0.0371478i	0.270281	+	0.962782i	$0.412883\pi$
$230$	−7.77385	+	1.04736i	−0.512593	+	0.0690609i
$231$	−3.74537	−	6.47152i	−0.246427	−	0.425795i
$232$	−6.98831	−	8.93835i	−0.458805	−	0.586831i
$233$	−2.81755	−	2.81755i	−0.184584	−	0.184584i	0.608766	−	0.793350i	$-0.291665\pi$
$233$	−2.81755	−	2.81755i	−0.184584	−	0.184584i	−0.793350	+	0.608766i	$0.791665\pi$
$234$	−4.19265	−	9.97732i	−0.274082	−	0.652238i
$235$	2.42464	−	5.85360i	0.158166	−	0.381847i
$236$	−8.32766	+	6.47039i	−0.542084	+	0.421187i
$237$	7.86930	−	6.05142i	0.511166	−	0.393082i
$238$	31.7387	−	18.4525i	2.05731	−	1.19609i
$239$	−5.92010	+	3.41797i	−0.382939	+	0.221090i	−0.679096	−	0.734049i	$-0.737628\pi$
$239$	−5.92010	+	3.41797i	−0.382939	+	0.221090i	0.296157	+	0.955139i	$0.404295\pi$
$240$	−5.92948	−	5.77571i	−0.382747	−	0.372821i
$241$	−4.93993	−	2.85207i	−0.318209	−	0.183718i	0.332385	−	0.943144i	$-0.392147\pi$
$241$	−4.93993	−	2.85207i	−0.318209	−	0.183718i	−0.650594	+	0.759426i	$0.725480\pi$
$242$	14.4077	−	0.0435477i	0.926165	−	0.00279935i
$243$	−5.89003	+	14.4329i	−0.377846	+	0.925869i
$244$	−10.4177	−	24.7267i	−0.666926	−	1.58297i
$245$	11.5986	+	15.1157i	0.741011	+	0.965704i
$246$	25.6201	+	10.4903i	1.63348	+	0.668835i
$247$	2.21424	−	8.26366i	0.140889	−	0.525804i
$248$	−6.07013	−	1.56763i	−0.385453	−	0.0995448i
$249$	−7.41454	−	4.27045i	−0.469877	−	0.270629i
$250$	−11.4647	+	8.85234i	−0.725090	+	0.559871i
$251$	4.85496	−	11.7209i	0.306442	−	0.739817i	−0.693373	−	0.720579i	$-0.743876\pi$
$251$	4.85496	−	11.7209i	0.306442	−	0.739817i	0.999815	−	0.0192376i	$-0.00612389\pi$
$252$	0.233876	+	28.7409i	0.0147328	+	1.81051i
$253$	3.86524	−	1.60104i	0.243006	−	0.100656i
$254$	−11.7033	+	3.17384i	−0.734332	+	0.199145i
$255$	−2.89120	+	10.8354i	−0.181054	+	0.678542i
$256$	−8.33268	−	13.6589i	−0.520792	−	0.853683i
$257$	13.1251	−	7.57779i	0.818722	−	0.472689i	−0.0312536	−	0.999511i	$-0.509950\pi$
$257$	13.1251	−	7.57779i	0.818722	−	0.472689i	0.849976	+	0.526822i	$0.176617\pi$
$258$	2.68238	−	1.56326i	0.166998	−	0.0973244i
$259$	−2.92464	−	0.385036i	−0.181728	−	0.0239250i
$260$	6.09525	−	0.0368464i	0.378012	−	0.00228511i
$261$	−7.34592	−	9.53202i	−0.454701	−	0.590017i
$262$	5.27326	−	12.8404i	0.325783	−	0.793284i
$263$	0.678462	−	0.181793i	0.0418358	−	0.0112099i	−0.237840	−	0.971304i	$-0.576440\pi$
$263$	0.678462	−	0.181793i	0.0418358	−	0.0112099i	0.279676	+	0.960094i	$0.409773\pi$
$264$	3.84554	+	2.16867i	0.236677	+	0.133472i
$265$	7.69730	+	2.06248i	0.472841	+	0.126697i
$266$	−13.7768	+	18.0671i	−0.844711	+	1.10776i
$267$	7.20338	−	2.99257i	0.440840	−	0.183142i
$268$	−2.00160	+	15.9481i	−0.122267	+	0.974182i
$269$	−17.0155	+	7.04803i	−1.03745	+	0.429726i	−0.835396	−	0.549648i	$-0.814762\pi$
$269$	−17.0155	+	7.04803i	−1.03745	+	0.429726i	−0.202055	+	0.979374i	$0.564762\pi$
$270$	−6.24628	−	6.16979i	−0.380137	−	0.375481i
$271$	−12.5098			−0.759916			−0.379958	−	0.925004i	$-0.624062\pi$
$271$	−12.5098			−0.759916			−0.379958	+	0.925004i	$0.624062\pi$
$272$	−10.6108	+	18.9025i	−0.643373	+	1.14613i
$273$	−14.9814	−	14.9501i	−0.906714	−	0.904819i
$274$	−10.7924	−	18.5631i	−0.651990	−	1.12144i
$275$	1.95993	−	2.55423i	0.118188	−	0.154026i
$276$	−15.9588	−	1.98600i	−0.960608	−	0.119543i
$277$	8.70831	−	6.68212i	0.523231	−	0.401490i	−0.313095	−	0.949722i	$-0.601366\pi$
$277$	8.70831	−	6.68212i	0.523231	−	0.401490i	0.836326	+	0.548232i	$0.184699\pi$
$278$	−5.34428	−	12.7927i	−0.320528	−	0.767256i
$279$	−6.42659	−	1.70760i	−0.384750	−	0.102231i
$280$	−15.0112	−	6.05895i	−0.897089	−	0.362092i
$281$	−1.62128	−	6.05068i	−0.0967172	−	0.360954i	0.900557	−	0.434738i	$-0.143159\pi$
$281$	−1.62128	−	6.05068i	−0.0967172	−	0.360954i	−0.997274	+	0.0737844i	$0.976492\pi$
$282$	7.86570	−	10.3376i	0.468396	−	0.615595i
$283$	1.44419	+	10.9697i	0.0858484	+	0.652083i	0.979225	+	0.202775i	$0.0649961\pi$
$283$	1.44419	+	10.9697i	0.0858484	+	0.652083i	−0.893377	+	0.449308i	$0.851671\pi$
$284$	−16.8210	−	4.39835i	−0.998140	−	0.260994i
$285$	−0.913094	−	6.88001i	−0.0540870	−	0.407537i
$286$	−3.13768	+	0.850911i	−0.185535	+	0.0503154i
$287$	54.1408			3.19583
$288$	−8.73687	−	14.5488i	−0.514825	−	0.857295i
$289$	12.3684			0.727554
$290$	6.54156	−	1.77402i	0.384134	−	0.104174i
$291$	−17.8018	+	13.6894i	−1.04356	+	0.802487i
$292$	−6.34307	+	24.2583i	−0.371200	+	1.41961i
$293$	−0.671066	−	5.09726i	−0.0392041	−	0.297785i	−0.999803	−	0.0198465i	$-0.993682\pi$
$293$	−0.671066	−	5.09726i	−0.0392041	−	0.297785i	0.960599	−	0.277938i	$-0.0896511\pi$
$294$	15.0951	+	36.0275i	0.880365	+	2.10117i
$295$	−1.63054	−	6.08524i	−0.0949334	−	0.354296i
$296$	1.60306	−	0.681102i	0.0931758	−	0.0395883i
$297$	4.06267	+	2.32861i	0.235740	+	0.135120i
$298$	11.5499	+	27.6472i	0.669067	+	1.60156i
$299$	9.39513	−	7.20913i	0.543334	−	0.416915i
$300$	−11.3998	+	4.81692i	−0.658165	+	0.278105i
$301$	3.69615	−	4.81692i	0.213043	−	0.277643i
$302$	1.05486	+	1.81439i	0.0607004	+	0.104406i
$303$	0.0541607	−	0.0145730i	0.00311145	−	0.000837200i
$304$	1.59012	−	13.3207i	0.0911994	−	0.763995i
$305$	16.0287			0.917802
$306$	−11.3940	+	19.9702i	−0.651352	+	1.14162i
$307$	14.4994	−	6.00584i	0.827524	−	0.342772i	0.0716017	−	0.997433i	$-0.477189\pi$
$307$	14.4994	−	6.00584i	0.827524	−	0.342772i	0.755922	+	0.654662i	$0.227189\pi$
$308$	8.56671	+	1.07519i	0.488133	+	0.0612644i
$309$	14.1539	+	10.8371i	0.805185	+	0.616503i
$310$	2.27091	−	2.97810i	0.128979	−	0.169145i
$311$	−16.2242	−	4.34726i	−0.919989	−	0.246510i	−0.232408	−	0.972618i	$-0.574661\pi$
$311$	−16.2242	−	4.34726i	−0.919989	−	0.246510i	−0.687581	+	0.726108i	$0.741327\pi$
$312$	12.1030	+	3.11213i	0.685195	+	0.176190i
$313$	25.1922	−	6.75022i	1.42395	−	0.381545i	0.537063	−	0.843542i	$-0.319534\pi$
$313$	25.1922	−	6.75022i	1.42395	−	0.381545i	0.886882	+	0.461997i	$0.152867\pi$
$314$	−12.0773	+	29.4082i	−0.681560	+	1.65960i
$315$	−15.8765	−	6.53739i	−0.894541	−	0.368340i
$316$	0.0692919	+	11.4625i	0.00389798	+	0.644817i
$317$	0.953603	+	0.125544i	0.0535597	+	0.00705127i	0.157258	−	0.987557i	$-0.449734\pi$
$317$	0.953603	+	0.125544i	0.0535597	+	0.00705127i	−0.103699	+	0.994609i	$0.533068\pi$
$318$	14.1819	+	8.11119i	0.795283	+	0.454853i
$319$	−3.13070	+	1.80751i	−0.175285	+	0.101201i
$320$	9.45213	−	1.41922i	0.528390	−	0.0793367i
$321$	−23.7642	−	23.7146i	−1.32639	−	1.32362i
$322$	−30.3539	+	8.23173i	−1.69156	+	0.458736i
$323$	−16.7917	+	6.95536i	−0.934316	+	0.387006i
$324$	−9.15899	−	15.4956i	−0.508833	−	0.860865i
$325$	3.48744	−	8.41943i	0.193448	−	0.467026i
$326$	1.19475	−	0.922512i	0.0661709	−	0.0510932i
$327$	−0.0327688	−	31.3245i	−0.00181212	−	1.73225i
$328$	−27.5385	+	16.2341i	−1.52056	+	0.896376i
$329$	6.57486	−	24.5377i	0.362484	−	1.35281i
$330$	−2.08582	+	1.61403i	−0.114820	+	0.0888493i
$331$	3.03800	+	3.95920i	0.166984	+	0.217617i	0.869348	−	0.494200i	$-0.164539\pi$
$331$	3.03800	+	3.95920i	0.166984	+	0.217617i	−0.702365	+	0.711817i	$0.747872\pi$
$332$	9.10499	−	3.83605i	0.499701	−	0.210531i
$333$	1.70530	−	0.710541i	0.0934497	−	0.0389374i
$334$	3.88616	−	0.0117460i	0.212641	−	0.000642712i
$335$	−8.31539	−	4.80089i	−0.454318	−	0.262301i
$336$	−26.5931	−	19.8561i	−1.45077	−	1.08324i
$337$	−7.62240	+	4.40080i	−0.415219	+	0.239727i	−0.693030	−	0.720909i	$-0.743724\pi$
$337$	−7.62240	+	4.40080i	−0.415219	+	0.239727i	0.277811	+	0.960636i	$0.410391\pi$
$338$	7.93841	−	4.61529i	0.431792	−	0.251039i
$339$	1.04463	+	7.87113i	0.0567366	+	0.427501i
$340$	−7.94508	−	10.2256i	−0.430882	−	0.554563i
$341$	−0.764411	+	1.84545i	−0.0413952	+	0.0999368i
$342$	1.78508	−	14.1166i	0.0965263	−	0.763340i
$343$	30.3059	+	30.3059i	1.63636	+	1.63636i
$344$	−0.435684	+	3.55839i	−0.0234905	+	0.191855i
$345$	4.79480	−	8.32494i	0.258143	−	0.448200i
$346$	−10.2764	+	1.38453i	−0.552464	+	0.0744327i
$347$	2.18082	−	0.287110i	0.117072	−	0.0154129i	−0.0717623	−	0.997422i	$-0.522862\pi$
$347$	2.18082	−	0.287110i	0.117072	−	0.0154129i	0.188835	+	0.982009i	$0.439529\pi$
$348$	13.8955	−	0.0985367i	0.744879	−	0.00528212i
$349$	−2.16918	+	16.4765i	−0.116113	+	0.881968i	0.829916	+	0.557888i	$0.188388\pi$
$349$	−2.16918	+	16.4765i	−0.116113	+	0.881968i	−0.946030	+	0.324080i	$0.894945\pi$
$350$	−17.0618	+	17.1652i	−0.911991	+	0.917521i
$351$	12.8138	+	3.39038i	0.683949	+	0.180965i
$352$	−4.67981	+	2.02183i	−0.249435	+	0.107764i
$353$	−26.2447	−	15.1524i	−1.39686	−	0.806479i	−0.402800	−	0.915288i	$-0.631963\pi$
$353$	−26.2447	−	15.1524i	−1.39686	−	0.806479i	−0.994063	+	0.108809i	$0.965296\pi$
$354$	−0.0525502	−	12.9159i	−0.00279301	−	0.686473i
$355$	6.32280	−	8.24004i	0.335580	−	0.437336i
$356$	−2.27854	+	8.71400i	−0.120763	+	0.461841i
$357$	−5.82233	+	44.5854i	−0.308150	+	2.35971i
$358$	−8.17640	+	6.31333i	−0.432136	+	0.333670i
$359$	−18.7891	−	18.7891i	−0.991652	−	0.991652i	0.00831352	−	0.999965i	$-0.497354\pi$
$359$	−18.7891	−	18.7891i	−0.991652	−	0.991652i	−0.999965	+	0.00831352i	$0.997354\pi$
$360$	10.0358	−	1.43534i	0.528931	−	0.0756492i
$361$	−5.48143	+	5.48143i	−0.288496	+	0.288496i
$362$	−0.544066	+	4.23138i	−0.0285955	+	0.222396i
$363$	−10.7275	+	14.0107i	−0.563047	+	0.735369i
$364$	24.2101	−	3.33633i	1.26896	−	0.174871i
$365$	−11.8834	−	9.11842i	−0.622003	−	0.477280i
$366$	31.7766	+	8.37609i	1.66099	+	0.437825i
$367$	−12.7357	+	22.0589i	−0.664800	+	1.15147i	0.314540	+	0.949244i	$0.398150\pi$
$367$	−12.7357	+	22.0589i	−0.664800	+	1.15147i	−0.979340	+	0.202223i	$0.935184\pi$
$368$	12.9711	−	13.2886i	0.676166	−	0.692717i
$369$	−29.3284	+	17.0147i	−1.52677	+	0.885748i
$370$	0.00314487	+	1.04048i	0.000163494	+	0.0540921i
$371$	31.6771	+	4.17037i	1.64459	+	0.216515i
$372$	6.05828	−	4.71731i	0.314107	−	0.244581i
$373$	1.50213	+	11.4098i	0.0777773	+	0.590777i	0.985307	+	0.170790i	$0.0546320\pi$
$373$	1.50213	+	11.4098i	0.0777773	+	0.590777i	−0.907530	+	0.419987i	$0.862035\pi$
$374$	5.49213	+	4.18795i	0.283991	+	0.216553i
$375$	−0.0185579	−	17.7399i	−0.000958325	−	0.916084i
$376$	4.01333	+	14.4525i	0.206972	+	0.745329i
$377$	−7.23552	+	7.23552i	−0.372648	+	0.372648i
$378$	−28.0586	−	21.2568i	−1.44318	−	1.09333i
$379$	17.9995	+	7.45564i	0.924572	+	0.382970i	0.793617	−	0.608418i	$-0.208196\pi$
$379$	17.9995	+	7.45564i	0.924572	+	0.382970i	0.130955	+	0.991388i	$0.458196\pi$
$380$	6.96444	+	3.96498i	0.357268	+	0.203399i
$381$	5.66900	−	13.7268i	0.290432	−	0.703244i
$382$	−22.2327	−	5.88527i	−1.13753	−	0.301117i
$383$	4.89477	+	8.47800i	0.250111	+	0.433205i	0.963556	−	0.267506i	$-0.0861995\pi$
$383$	4.89477	+	8.47800i	0.250111	+	0.433205i	−0.713445	+	0.700711i	$0.752866\pi$
$384$	19.4803	+	2.12581i	0.994098	+	0.108482i
$385$	−2.57886	+	4.46672i	−0.131431	+	0.227645i
$386$	16.5423	−	16.6426i	0.841980	−	0.847085i
$387$	−0.488428	+	3.77093i	−0.0248282	+	0.191687i
$388$	−0.156751	−	25.9303i	−0.00795783	−	1.31641i
$389$	24.1751	−	18.5502i	1.22573	−	0.940535i	0.226291	−	0.974060i	$-0.427340\pi$
$389$	24.1751	−	18.5502i	1.22573	−	0.940535i	0.999438	+	0.0335252i	$0.0106734\pi$
$390$	−4.52043	+	5.94103i	−0.228901	+	0.300836i
$391$	−24.3014	−	6.51154i	−1.22897	−	0.329303i
$392$	−43.6721	−	11.2785i	−2.20578	−	0.569650i
$393$	8.51577	+	14.7142i	0.429564	+	0.742232i
$394$	2.54239	−	19.7730i	0.128084	−	0.996150i
$395$	−6.32636	−	2.62046i	−0.318314	−	0.131850i
$396$	−4.97852	+	2.10980i	−0.250180	+	0.106021i
$397$	11.3447	+	27.3885i	0.569373	+	1.37459i	0.902084	+	0.431560i	$0.142037\pi$
$397$	11.3447	+	27.3885i	0.569373	+	1.37459i	−0.332711	+	0.943029i	$0.607963\pi$
$398$	32.6986	+	18.7470i	1.63903	+	0.939703i
$399$	−7.23022	−	26.8711i	−0.361964	−	1.34524i
$400$	3.53143	−	13.8470i	0.176571	−	0.692349i
$401$	6.43639	+	11.1481i	0.321418	+	0.556712i	0.980781	−	0.195113i	$-0.0625073\pi$
$401$	6.43639	+	11.1481i	0.321418	+	0.556712i	−0.659363	+	0.751825i	$0.729174\pi$
$402$	−13.9763	−	13.8630i	−0.697074	−	0.691425i
$403$	−0.738005	+	5.60571i	−0.0367627	+	0.279240i
$404$	−0.0244218	+	0.0599826i	−0.00121503	+	0.00298424i
$405$	10.6549	−	1.44812i	0.529445	−	0.0719579i
$406$	25.0751	−	10.4754i	1.24446	−	0.519884i
$407$	−0.143632	−	0.536042i	−0.00711958	−	0.0265706i
$408$	−10.4074	−	24.4239i	−0.515241	−	1.20917i
$409$	−3.59170	+	13.4044i	−0.177598	+	0.662805i	0.818496	+	0.574512i	$0.194808\pi$
$409$	−3.59170	+	13.4044i	−0.177598	+	0.662805i	−0.996094	+	0.0882936i	$0.971859\pi$
$410$	−2.54983	−	18.9257i	−0.125927	−	0.934672i
$411$	26.0768	+	3.40533i	1.28627	+	0.167972i
$412$	−19.8500	+	5.44762i	−0.977941	+	0.268385i
$413$	−9.66621	−	23.3363i	−0.475643	−	1.14830i
$414$	13.8559	−	13.9984i	0.680982	−	0.687984i
$415$			5.90217i			0.289726i
$416$	−11.3140	+	8.95638i	−0.554713	+	0.439123i
$417$	16.4061	+	4.37760i	0.803409	+	0.214372i
$418$	−4.13202	−	1.09380i	−0.202104	−	0.0534993i
$419$	−15.2863	−	11.7296i	−0.746786	−	0.573029i	0.163729	−	0.986505i	$-0.447648\pi$
$419$	−15.2863	−	11.7296i	−0.746786	−	0.573029i	−0.910515	+	0.413476i	$0.864314\pi$
$420$	17.0991	−	10.0345i	0.834349	−	0.489633i
$421$	−6.20272	−	8.08354i	−0.302302	−	0.393968i	0.617359	−	0.786682i	$-0.288203\pi$
$421$	−6.20272	−	8.08354i	−0.302302	−	0.393968i	−0.919661	+	0.392714i	$0.871536\pi$
$422$	−11.4202	+	27.8082i	−0.555926	+	1.35368i
$423$	4.14975	+	15.3585i	0.201768	+	0.746754i
$424$	−17.3629	+	7.37709i	−0.843216	+	0.358263i
$425$	−18.7009	+	5.01089i	−0.907126	+	0.243064i
$426$	16.8408	−	13.0316i	0.815939	−	0.631383i
$427$	63.7162	−	8.38840i	3.08344	−	0.405943i
$428$	38.4033	−	5.29226i	1.85630	−	0.255811i
$429$	1.51987	−	3.68017i	0.0733799	−	0.177680i
$430$	−1.85789	−	1.06518i	−0.0895956	−	0.0513676i
$431$			10.2561i			0.494018i	0.969013	+	0.247009i	$0.0794477\pi$
$431$			10.2561i			0.494018i	−0.969013	+	0.247009i	$0.920552\pi$
$432$	20.6457	+	2.39883i	0.993318	+	0.115414i
$433$		−	7.85626i		−	0.377548i	−0.982021	−	0.188774i	$-0.939549\pi$
$433$		−	7.85626i		−	0.377548i	0.982021	−	0.188774i	$-0.0604513\pi$
$434$	7.46860	−	13.0268i	0.358504	−	0.625305i
$435$	−3.16868	+	7.67256i	−0.151927	+	0.367871i
$436$	28.8285	+	21.8453i	1.38063	+	1.04620i
$437$	15.4367	−	2.03228i	0.738438	−	0.0972173i
$438$	−18.7935	−	24.2869i	−0.897988	−	1.16047i
$439$	24.0163	−	6.43516i	1.14624	−	0.307133i	0.364781	−	0.931093i	$-0.381144\pi$
$439$	24.0163	−	6.43516i	1.14624	−	0.307133i	0.781456	+	0.623960i	$0.214477\pi$
$440$	−0.0276136	−	3.04525i	−0.00131643	−	0.145176i
$441$	−46.2367	−	12.2855i	−2.20175	−	0.585022i
$442$	18.0843	+	7.42679i	0.860181	+	0.353256i
$443$	−17.3623	−	22.6270i	−0.824909	−	1.07504i	−0.995962	−	0.0897807i	$-0.971383\pi$
$443$	−17.3623	−	22.6270i	−0.824909	−	1.07504i	0.171052	−	0.985262i	$-0.445283\pi$
$444$	−0.537487	+	2.06438i	−0.0255080	+	0.0979709i
$445$	−4.26871	−	3.27549i	−0.202356	−	0.155273i
$446$	2.48513	−	9.38803i	0.117674	−	0.444536i
$447$	−35.4563	−	9.46074i	−1.67702	−	0.447478i
$448$	36.8307	−	10.5882i	1.74009	−	0.500246i
$449$			13.4706i			0.635717i	0.948138	+	0.317859i	$0.102964\pi$
$449$			13.4706i			0.635717i	−0.948138	+	0.317859i	$0.897036\pi$
$450$	3.84800	−	14.6604i	0.181396	−	0.691100i
$451$	3.89777	+	9.41005i	0.183539	+	0.443102i
$452$	−7.96772	−	4.53617i	−0.374770	−	0.213363i
$453$	−2.54879	−	0.332842i	−0.119752	−	0.0156383i
$454$	12.2587	−	1.65159i	0.575327	−	0.0775131i
$455$	−3.77858	+	14.1019i	−0.177143	+	0.661106i
$456$	11.7349	+	11.4999i	0.549536	+	0.538531i
$457$	−1.16978	−	4.36567i	−0.0547199	−	0.204218i	0.933154	−	0.359478i	$-0.117045\pi$
$457$	−1.16978	−	4.36567i	−0.0547199	−	0.204218i	−0.987874	+	0.155260i	$0.950378\pi$
$458$	−2.34781	−	5.62002i	−0.109706	−	0.262606i
$459$	−10.8577	−	25.9819i	−0.506794	−	1.21273i
$460$	4.30707	+	10.2230i	0.200818	+	0.476648i
$461$	−2.24566	+	17.0575i	−0.104591	+	0.794447i	0.856097	+	0.516816i	$0.172883\pi$
$461$	−2.24566	+	17.0575i	−0.104591	+	0.794447i	−0.960688	+	0.277631i	$0.910451\pi$
$462$	−7.44671	+	7.50755i	−0.346452	+	0.349283i
$463$	−1.87338	−	3.24479i	−0.0870635	−	0.150798i	0.819205	−	0.573501i	$-0.194415\pi$
$463$	−1.87338	−	3.24479i	−0.0870635	−	0.150798i	−0.906269	+	0.422702i	$0.861082\pi$
$464$	−9.61333	+	12.8470i	−0.446288	+	0.596407i
$465$	1.19180	+	4.42931i	0.0552683	+	0.205404i
$466$	−2.80279	+	4.88864i	−0.129837	+	0.226462i
$467$	−2.81290	−	6.79094i	−0.130166	−	0.314247i	0.845338	−	0.534232i	$-0.179399\pi$
$467$	−2.81290	−	6.79094i	−0.130166	−	0.314247i	−0.975503	+	0.219985i	$0.929399\pi$
$468$	−12.0662	+	9.41574i	−0.557762	+	0.435243i
$469$	−35.5672	−	14.7324i	−1.64234	−	0.680280i
$470$	−8.88715	−	1.14270i	−0.409933	−	0.0527088i
$471$	−19.5035	−	33.6997i	−0.898676	−	1.55280i
$472$	11.9140	+	8.97149i	0.548387	+	0.412946i
$473$	1.10331	+	0.295631i	0.0507303	+	0.0135931i
$474$	−11.1725	−	8.50096i	−0.513170	−	0.390462i
$475$	9.50570	−	7.29398i	0.436152	−	0.334671i
$476$	−36.9341	−	36.4903i	−1.69287	−	1.67253i
$477$	−18.4703	+	7.69594i	−0.845695	+	0.352373i
$478$	6.85657	+	6.81525i	0.313612	+	0.311722i
$479$	−2.97546	+	5.15366i	−0.135952	+	0.235477i	−0.925961	−	0.377619i	$-0.876743\pi$
$479$	−2.97546	+	5.15366i	−0.135952	+	0.235477i	0.790008	+	0.613096i	$0.210076\pi$
$480$	−5.68853	+	10.2311i	−0.259645	+	0.466985i
$481$	−0.785416	−	1.36038i	−0.0358119	−	0.0620280i
$482$	−2.06430	+	7.79827i	−0.0940262	+	0.355201i
$483$	14.7032	−	35.6020i	0.669019	−	1.61995i
$484$	−5.39250	−	19.6492i	−0.245114	−	0.893146i
$485$	14.3114	+	5.92797i	0.649846	+	0.269175i
$486$	21.8798	+	2.69702i	0.992488	+	0.122339i
$487$	−25.4894	+	25.4894i	−1.15504	+	1.15504i	−0.169507	+	0.985529i	$0.554217\pi$
$487$	−25.4894	+	25.4894i	−1.15504	+	1.15504i	−0.985529	+	0.169507i	$0.945783\pi$
$488$	−29.8937	+	23.3719i	−1.35322	+	1.05800i
$489$	0.00193394	+	1.84869i	8.74557e−5	+	0.0836008i
$490$	16.3383	−	21.4262i	0.738088	−	0.967939i
$491$	−4.78779	−	36.3669i	−0.216070	−	1.64121i	−0.664422	−	0.747358i	$-0.731322\pi$
$491$	−4.78779	−	36.3669i	−0.216070	−	1.64121i	0.448352	−	0.893857i	$-0.352011\pi$
$492$	4.83496	−	38.8522i	0.217977	−	1.75159i
$493$	21.5529	+	2.83749i	0.970692	+	0.127794i
$494$	−12.0988	+	0.0365688i	−0.544350	+	0.00164531i
$495$	−0.00675808	−	3.23010i	−0.000303753	−	0.145182i
$496$	0.107189	+	8.86546i	0.00481292	+	0.398071i
$497$	20.8216	−	36.0641i	0.933978	−	1.61770i
$498$	−3.08428	+	11.7009i	−0.138210	+	0.524330i
$499$	7.70331	+	5.91096i	0.344847	+	0.264611i	0.766634	−	0.642084i	$-0.221930\pi$
$499$	7.70331	+	5.91096i	0.344847	+	0.264611i	−0.421786	+	0.906695i	$0.638597\pi$
$500$	16.3264	+	12.3716i	0.730137	+	0.553273i
$501$	−2.89349	+	3.77905i	−0.129272	+	0.168836i
$502$	−17.7951	−	2.28807i	−0.794233	−	0.102122i
$503$	−23.2112	+	23.2112i	−1.03494	+	1.03494i	−0.0355681	+	0.999367i	$0.511324\pi$
$503$	−23.2112	+	23.2112i	−1.03494	+	1.03494i	−0.999367	+	0.0355681i	$0.988676\pi$
$504$	39.1422	−	10.9577i	1.74353	−	0.488096i
$505$	−0.0273569	−	0.0273569i	−0.00121737	−	0.00121737i
$506$	−3.61601	−	4.68309i	−0.160751	−	0.208189i
$507$	−1.45627	+	11.1516i	−0.0646752	+	0.495260i
$508$	8.66404	+	14.7992i	0.384404	+	0.656609i
$509$	−14.6272	+	19.0625i	−0.648338	+	0.844930i	−0.995684	−	0.0928066i	$-0.970416\pi$
$509$	−14.6272	+	19.0625i	−0.648338	+	0.844930i	0.347346	+	0.937737i	$0.387083\pi$
$510$	15.8596	−	0.0645271i	0.702276	−	0.00285731i
$511$	−52.0098	−	30.0279i	−2.30078	−	1.32836i
$512$	−15.5589	+	16.4293i	−0.687612	+	0.726078i
$513$	12.3613	+	12.2840i	0.545766	+	0.542351i
$514$	−15.2013	−	15.1097i	−0.670501	−	0.666460i
$515$	1.60501	−	12.1913i	0.0707252	−	0.537211i
$516$	−3.12661	−	3.08257i	−0.137641	−	0.135703i
$517$	4.73817	−	0.623792i	0.208384	−	0.0274343i
$518$	0.557022	+	4.13440i	0.0244742	+	0.181655i
$519$	6.33834	−	11.0049i	0.278222	−	0.483062i
$520$	−2.30647	−	8.30585i	−0.101145	−	0.364236i
$521$	13.9854	+	13.9854i	0.612712	+	0.612712i	0.943652	−	0.330940i	$-0.107366\pi$
$521$	13.9854	+	13.9854i	0.612712	+	0.612712i	−0.330940	+	0.943652i	$0.607366\pi$
$522$	−10.2913	+	13.5548i	−0.450437	+	0.593279i
$523$	−15.0496	+	36.3331i	−0.658075	+	1.58873i	0.142698	+	0.989766i	$0.454422\pi$
$523$	−15.0496	+	36.3331i	−0.658075	+	1.58873i	−0.800773	+	0.598968i	$0.795578\pi$
$524$	−19.4780	−	2.44463i	−0.850899	−	0.106794i
$525$	−3.89975	−	29.3840i	−0.170199	−	1.28242i
$526$	−0.499267	−	0.858751i	−0.0217691	−	0.0374433i
$527$	10.4026	−	6.00597i	0.453146	−	0.261624i
$528$	1.53660	−	6.05156i	0.0668721	−	0.263361i
$529$	−1.25373	−	0.723840i	−0.0545099	−	0.0314713i
$530$	−0.0340625	−	11.2696i	−0.00147958	−	0.489519i
$531$	12.5700	+	9.60362i	0.545494	+	0.416762i
$532$	29.7595	+	12.1166i	1.29024	+	0.525320i
$533$	17.5508	+	22.8727i	0.760211	+	0.990727i
$534$	−6.75095	−	8.72428i	−0.292142	−	0.377537i
$535$	−5.99378	+	22.3691i	−0.259134	+	0.967101i
$536$	22.5086	−	3.17120i	0.972223	−	0.136975i
$537$	−0.0132351	−	12.6518i	−0.000571138	−	0.545964i
$538$	15.9183	+	20.6158i	0.686285	+	0.888809i
$539$	−5.49964	+	13.2773i	−0.236886	+	0.571894i
$540$	−6.10915	+	10.8094i	−0.262896	+	0.465162i
$541$	11.2440	−	4.65741i	0.483417	−	0.200238i	−0.127646	−	0.991820i	$-0.540742\pi$
$541$	11.2440	−	4.65741i	0.483417	−	0.200238i	0.611063	+	0.791582i	$0.290742\pi$
$542$	4.63054	+	17.0748i	0.198899	+	0.733425i
$543$	−3.69851	−	3.69078i	−0.158718	−	0.158387i
$544$	29.7279	+	7.48596i	1.27457	+	0.320958i
$545$	−18.7126	+	10.8037i	−0.801561	+	0.462781i
$546$	−14.8601	+	25.9821i	−0.635955	+	1.11193i
$547$	4.19878	+	0.552780i	0.179527	+	0.0236352i	0.219754	−	0.975555i	$-0.429475\pi$
$547$	4.19878	+	0.552780i	0.179527	+	0.0236352i	−0.0402267	+	0.999191i	$0.512808\pi$
$548$	−21.3422	+	21.6018i	−0.911694	+	0.922783i
$549$	−31.8792	+	24.5679i	−1.36057	+	1.04853i
$550$	−4.21177	−	1.72968i	−0.179590	−	0.0737536i
$551$	−12.9951	+	3.48202i	−0.553609	+	0.148339i
$552$	3.19648	+	22.5175i	0.136051	+	0.958409i
$553$	−26.5195	−	7.10587i	−1.12772	−	0.302172i
$554$	−12.3439	−	9.41267i	−0.524442	−	0.399906i
$555$	−1.01181	−	0.774705i	−0.0429487	−	0.0328844i
$556$	−15.4828	+	12.0297i	−0.656615	+	0.510174i
$557$	−6.71881	+	2.78302i	−0.284685	+	0.117921i	−0.520457	−	0.853888i	$-0.674238\pi$
$557$	−6.71881	+	2.78302i	−0.284685	+	0.117921i	0.235771	+	0.971809i	$0.424238\pi$
$558$	0.0480983	+	9.40380i	0.00203616	+	0.398095i
$559$	3.23317			0.136749
$560$	−2.71352	+	22.7317i	−0.114667	+	0.960589i
$561$	−8.16841	+	2.19788i	−0.344870	+	0.0927945i
$562$	−7.65854	+	4.45258i	−0.323056	+	0.187821i
$563$	−10.7050	+	13.9511i	−0.451163	+	0.587968i	−0.962456	−	0.271439i	$-0.912500\pi$
$563$	−10.7050	+	13.9511i	−0.451163	+	0.587968i	0.511292	+	0.859407i	$0.329167\pi$
$564$	−17.0214	−	6.90951i	−0.716732	−	0.290943i
$565$	4.34526	−	3.33423i	0.182806	−	0.140272i
$566$	14.4382	−	6.03168i	0.606881	−	0.253530i
$567$	41.5967	−	11.3326i	1.74690	−	0.475923i
$568$	0.222951	+	24.5872i	0.00935482	+	1.03166i
$569$	1.88166	+	7.02243i	0.0788831	+	0.294396i	0.994086	−	0.108598i	$-0.0346362\pi$
$569$	1.88166	+	7.02243i	0.0788831	+	0.294396i	−0.915203	+	0.402994i	$0.867970\pi$
$570$	−9.05264	+	3.79295i	−0.379173	+	0.158869i
$571$	4.57915	+	34.7821i	0.191631	+	1.45558i	0.769077	+	0.639156i	$0.220716\pi$
$571$	4.57915	+	34.7821i	0.191631	+	1.45558i	−0.577446	+	0.816429i	$0.695951\pi$
$572$	2.32284	+	3.96769i	0.0971228	+	0.165898i
$573$	22.3287	−	17.1705i	0.932793	−	0.717309i
$574$	−20.0404	−	73.8975i	−0.836469	−	3.08442i
$575$	16.5854			0.691658
$576$	−16.6238	+	17.3103i	−0.692660	+	0.721264i
$577$	−29.9660			−1.24750			−0.623750	−	0.781624i	$-0.714392\pi$
$577$	−29.9660			−1.24750			−0.623750	+	0.781624i	$0.714392\pi$
$578$	−4.57820	−	16.8818i	−0.190428	−	0.702191i
$579$	3.78101	+	28.4893i	0.157133	+	1.18397i
$580$	−4.84275	−	8.27201i	−0.201084	−	0.343476i
$581$	3.08881	+	23.4619i	0.128146	+	0.973362i
$582$	25.2742	+	19.2307i	1.04765	+	0.797139i
$583$	1.55570	+	5.80594i	0.0644303	+	0.240457i
$584$	35.4584	−	0.321528i	1.46728	−	0.0133049i
$585$	−2.38487	−	8.82653i	−0.0986021	−	0.364932i
$586$	−6.70891	+	2.80271i	−0.277143	+	0.115779i
$587$	5.85948	−	4.49614i	0.241847	−	0.185576i	−0.480725	−	0.876871i	$-0.659627\pi$
$587$	5.85948	−	4.49614i	0.241847	−	0.185576i	0.722572	+	0.691296i	$0.242960\pi$
$588$	43.5869	−	33.9392i	1.79750	−	1.39963i
$589$	−4.52543	+	5.89765i	−0.186467	+	0.243008i
$590$	−7.70228	+	4.47801i	−0.317098	+	0.184357i
$591$	17.2830	+	17.2468i	0.710926	+	0.709440i
$592$	−1.52302	−	1.93592i	−0.0625958	−	0.0795659i
$593$	14.5325			0.596778			0.298389	−	0.954444i	$-0.403551\pi$
$593$	14.5325			0.596778			0.298389	+	0.954444i	$0.403551\pi$
$594$	1.67455	−	6.40713i	0.0687075	−	0.262888i
$595$	28.6549	−	11.8693i	1.17474	−	0.486592i
$596$	33.4608	−	25.9983i	1.37061	−	1.06493i
$597$	−42.6301	+	17.7102i	−1.74473	+	0.724831i
$598$	−13.3175	−	10.1550i	−0.544592	−	0.415271i
$599$	−8.89976	−	2.38468i	−0.363634	−	0.0974355i	0.0723755	−	0.997377i	$-0.476942\pi$
$599$	−8.89976	−	2.38468i	−0.363634	−	0.0974355i	−0.436010	+	0.899942i	$0.643609\pi$
$600$	10.7943	+	13.7767i	0.440677	+	0.562431i
$601$	14.9062	−	3.99411i	0.608038	−	0.162923i	0.0583538	−	0.998296i	$-0.481415\pi$
$601$	14.9062	−	3.99411i	0.608038	−	0.162923i	0.549684	+	0.835373i	$0.314748\pi$
$602$	−7.94282	−	3.26193i	−0.323725	−	0.132946i
$603$	23.8969	−	3.19696i	0.973155	−	0.130190i
$604$	2.08602	−	2.11139i	0.0848789	−	0.0859113i
$605$	12.0679	+	1.58877i	0.490631	+	0.0645927i
$606$	−0.0399386	−	0.0685303i	−0.00162240	−	0.00278385i
$607$	−12.0050	+	6.93106i	−0.487266	+	0.281323i	−0.723440	−	0.690388i	$-0.757440\pi$
$607$	−12.0050	+	6.93106i	−0.487266	+	0.281323i	0.236174	+	0.971711i	$0.424107\pi$
$608$	−18.7702	+	2.76032i	−0.761231	+	0.111946i
$609$	−8.58058	+	32.1577i	−0.347703	+	1.30310i
$610$	−5.93307	−	21.8778i	−0.240223	−	0.885807i
$611$	12.4977	−	5.17673i	0.505605	−	0.209428i
$612$	31.4751	+	8.15980i	1.27230	+	0.329841i
$613$	−7.00821	+	16.9193i	−0.283059	+	0.683365i	−0.999904	−	0.0138677i	$-0.995586\pi$
$613$	−7.00821	+	16.9193i	−0.283059	+	0.683365i	0.716845	+	0.697233i	$0.245586\pi$
$614$	−13.5644	−	17.5673i	−0.547416	−	0.708959i
$615$	20.2673	+	11.6731i	0.817256	+	0.470704i
$616$	−1.70345	−	12.0908i	−0.0686341	−	0.487152i
$617$	3.92674	−	14.6548i	0.158085	−	0.589980i	−0.840737	−	0.541444i	$-0.817878\pi$
$617$	3.92674	−	14.6548i	0.158085	−	0.589980i	0.998821	−	0.0485361i	$-0.0154556\pi$
$618$	9.55266	−	23.3302i	0.384264	−	0.938478i
$619$	−23.4716	−	30.5888i	−0.943403	−	1.22947i	−0.973212	−	0.229911i	$-0.926156\pi$
$619$	−23.4716	−	30.5888i	−0.943403	−	1.22947i	0.0298087	−	0.999556i	$-0.490510\pi$
$620$	−4.90543	−	1.99724i	−0.197007	−	0.0802111i
$621$	3.22371	+	23.9065i	0.129363	+	0.959334i
$622$	0.0717961	+	23.7537i	0.00287876	+	0.952438i
$623$	−18.6828	−	10.7865i	−0.748512	−	0.432154i
$624$	−0.232148	−	17.6714i	−0.00929336	−	0.707424i
$625$	4.87212	−	2.81292i	0.194885	−	0.112517i
$626$	−18.5384	−	31.8865i	−0.740944	−	1.27444i
$627$	4.14985	−	3.19119i	0.165729	−	0.127444i
$628$	44.6101	+	5.59890i	1.78014	+	0.223421i
$629$	−1.27709	+	3.08316i	−0.0509208	+	0.122934i
$630$	−3.04623	+	24.0899i	−0.121365	+	0.959765i
$631$	−19.2059	−	19.2059i	−0.764575	−	0.764575i	0.212571	−	0.977146i	$-0.431816\pi$
$631$	−19.2059	−	19.2059i	−0.764575	−	0.764575i	−0.977146	+	0.212571i	$0.931816\pi$
$632$	15.6197	−	4.33746i	0.621318	−	0.172535i
$633$	−18.4424	−	31.8662i	−0.733020	−	1.26657i
$634$	−0.181622	−	1.34806i	−0.00721312	−	0.0535381i
$635$	−10.1567	+	1.33716i	−0.403057	+	0.0530635i
$636$	5.82159	−	22.3595i	0.230841	−	0.886611i
$637$	−5.30965	+	40.3308i	−0.210376	+	1.59797i
$638$	3.62593	+	3.60408i	0.143552	+	0.142687i
$639$	0.0545645	+	26.0797i	0.00215854	+	1.03170i
$640$	−5.43584	−	12.3760i	−0.214870	−	0.489204i
$641$	−32.6527	−	18.8520i	−1.28970	−	0.744611i	−0.311103	−	0.950376i	$-0.600698\pi$
$641$	−32.6527	−	18.8520i	−1.28970	−	0.744611i	−0.978601	+	0.205766i	$0.934032\pi$
$642$	−23.5719	+	41.2141i	−0.930309	+	1.62659i
$643$	1.11651	−	1.45506i	0.0440308	−	0.0573821i	−0.770819	−	0.637054i	$-0.780153\pi$
$643$	1.11651	−	1.45506i	0.0440308	−	0.0573821i	0.814850	+	0.579672i	$0.196819\pi$
$644$	22.4712	+	38.3835i	0.885488	+	1.51252i
$645$	2.42219	−	1.00627i	0.0953735	−	0.0396220i
$646$	15.7090	+	20.3447i	0.618060	+	0.800451i
$647$	19.0374	+	19.0374i	0.748438	+	0.748438i	0.974186	−	0.225748i	$-0.0724826\pi$
$647$	19.0374	+	19.0374i	0.748438	+	0.748438i	−0.225748	+	0.974186i	$0.572483\pi$
$648$	−17.7599	+	18.2369i	−0.697674	+	0.716415i
$649$	3.36011	−	3.36011i	0.131896	−	0.131896i
$650$	−12.7827	−	1.64358i	−0.501377	−	0.0644665i
$651$	7.05556	+	16.9834i	0.276529	+	0.665630i
$652$	−1.70139	−	1.28926i	−0.0666315	−	0.0504911i
$653$	2.81412	+	2.15935i	0.110125	+	0.0845020i	0.662356	−	0.749189i	$-0.269557\pi$
$653$	2.81412	+	2.15935i	0.110125	+	0.0845020i	−0.552231	+	0.833691i	$0.686223\pi$
$654$	−42.7430	+	11.6396i	−1.67138	+	0.455143i
$655$	5.86352	−	10.1559i	0.229107	−	0.396824i
$656$	32.3515	+	31.5786i	1.26311	+	1.23294i
$657$	37.6107	−	0.0786900i	1.46733	−	0.00306999i
$658$	−35.9256	+	0.108586i	−1.40052	+	0.00423311i
$659$	23.2164	+	3.05650i	0.904384	+	0.119064i	0.568352	−	0.822786i	$-0.307581\pi$
$659$	23.2164	+	3.05650i	0.904384	+	0.119064i	0.336033	+	0.941850i	$0.390915\pi$
$660$	2.97508	+	2.24952i	0.115805	+	0.0875625i
$661$	−4.20564	−	31.9450i	−0.163580	−	1.24252i	−0.854449	−	0.519535i	$-0.826105\pi$
$661$	−4.20564	−	31.9450i	−0.163580	−	1.24252i	0.690869	−	0.722980i	$-0.257228\pi$
$662$	4.27944	−	5.61211i	0.166325	−	0.218121i
$663$	−20.7233	+	11.9935i	−0.804824	+	0.465789i
$664$	−8.60611	−	11.0076i	−0.333982	−	0.427177i
$665$	−13.5728	+	13.5728i	−0.526329	+	0.526329i
$666$	−1.60105	−	2.06457i	−0.0620393	−	0.0800006i
$667$	−17.2051	−	7.12660i	−0.666186	−	0.275943i
$668$	−1.45450	−	5.29992i	−0.0562764	−	0.205060i
$669$	7.25045	+	9.42854i	0.280319	+	0.364528i
$670$	−3.47484	+	13.1269i	−0.134245	+	0.507134i
$671$	6.04509	+	10.4704i	0.233368	+	0.404206i
$672$	−17.2583	+	43.6470i	−0.665755	+	1.68372i
$673$	2.85420	−	4.94361i	0.110021	−	0.190562i	−0.805757	−	0.592246i	$-0.798241\pi$
$673$	2.85420	−	4.94361i	0.110021	−	0.190562i	0.915779	+	0.401684i	$0.131575\pi$
$674$	8.82816	+	8.77495i	0.340048	+	0.337998i
$675$	11.3469	+	14.6919i	0.436743	+	0.565491i
$676$	−9.23789	−	9.12687i	−0.355303	−	0.351034i
$677$	−3.08389	+	2.36635i	−0.118524	+	0.0909463i	−0.666322	−	0.745664i	$-0.732133\pi$
$677$	−3.08389	+	2.36635i	−0.118524	+	0.0909463i	0.547799	+	0.836610i	$0.315466\pi$
$678$	10.3567	−	4.33935i	0.397748	−	0.166652i
$679$	59.9919	+	16.0748i	2.30228	+	0.616893i
$680$	−11.0162	+	14.6294i	−0.422453	+	0.561011i
$681$	−7.56096	+	13.1277i	−0.289737	+	0.503053i
$682$	2.80183	+	0.360256i	0.107288	+	0.0137949i
$683$	−40.7387	−	16.8745i	−1.55882	−	0.645685i	−0.573937	−	0.818899i	$-0.694585\pi$
$683$	−40.7387	−	16.8745i	−1.55882	−	0.645685i	−0.984884	+	0.173214i	$0.944585\pi$
$684$	−19.9287	+	2.78882i	−0.761994	+	0.106633i
$685$	−6.94202	−	16.7595i	−0.265241	−	0.640348i
$686$	30.1471	−	52.5827i	1.15102	−	2.00762i
$687$	7.20741	+	1.92314i	0.274980	+	0.0733724i
$688$	5.01816	−	0.722476i	0.191316	−	0.0275441i
$689$	8.50693	+	14.7344i	0.324088	+	0.561337i
$690$	−13.1376	−	3.46299i	−0.500141	−	0.131834i
$691$	5.72504	−	43.4860i	0.217791	−	1.65429i	−0.437728	−	0.899108i	$-0.644217\pi$
$691$	5.72504	−	43.4860i	0.217791	−	1.65429i	0.655519	−	0.755179i	$-0.272450\pi$
$692$	5.69360	+	13.5139i	0.216438	+	0.513722i
$693$	−1.71729	−	12.8365i	−0.0652344	−	0.487619i
$694$	−1.19912	−	2.87035i	−0.0455178	−	0.108957i
$695$	−3.03149	−	11.3137i	−0.114991	−	0.429152i
$696$	−5.27797	−	18.9297i	−0.200061	−	0.717530i
$697$	15.8525	−	59.1624i	0.600457	−	2.24094i
$698$	23.2920	−	3.13809i	0.881613	−	0.118779i
$699$	−2.64778	−	6.37345i	−0.100148	−	0.241066i
$700$	29.7445	+	16.9341i	1.12424	+	0.640049i
$701$	−5.27727	−	12.7404i	−0.199320	−	0.481200i	0.792341	−	0.610079i	$-0.208862\pi$
$701$	−5.27727	−	12.7404i	−0.199320	−	0.481200i	−0.991660	+	0.128879i	$0.958862\pi$
$702$	−0.115484	−	18.7447i	−0.00435867	−	0.707472i
$703$		−	2.06529i		−	0.0778937i
$704$	4.49186	+	5.63915i	0.169293	+	0.212533i
$705$	7.75173	−	7.76797i	0.291947	−	0.292559i
$706$	−10.9671	+	41.4304i	−0.412753	+	1.55925i
$707$	−0.123064	−	0.0944304i	−0.00462830	−	0.00355142i
$708$	−17.6097	+	4.85259i	−0.661811	+	0.182371i
$709$	−9.44008	−	12.3025i	−0.354530	−	0.462032i	0.581709	−	0.813397i	$-0.302384\pi$
$709$	−9.44008	−	12.3025i	−0.354530	−	0.462032i	−0.936239	+	0.351365i	$0.885718\pi$
$710$	−13.5873	−	5.58001i	−0.509924	−	0.209414i
$711$	16.5989	−	4.48490i	0.622506	−	0.168197i
$712$	12.7373	−	0.115499i	0.477349	−	0.00432849i
$713$	−9.93948	+	2.66328i	−0.372236	+	0.0997404i
$714$	63.0103	−	8.55641i	2.35810	−	0.320216i
$715$	−2.72303	+	0.358494i	−0.101836	+	0.0134069i
$716$	11.6437	+	8.82318i	0.435144	+	0.329738i
$717$	−11.7373	+	1.55774i	−0.438337	+	0.0581747i
$718$	−18.6907	+	32.6004i	−0.697530	+	1.21663i
$719$		−	2.23219i		−	0.0832468i	−0.999133	−	0.0416234i	$-0.986747\pi$
$719$		−	2.23219i		−	0.0832468i	0.999133	−	0.0416234i	$-0.0132530\pi$
$720$	−5.67388	−	13.1666i	−0.211453	−	0.490691i
$721$		−	49.3018i		−	1.83609i
$722$	9.51063	+	5.45270i	0.353949	+	0.202929i
$723$	−6.02267	−	7.83192i	−0.223986	−	0.291272i
$724$	5.97685	−	0.823654i	0.222128	−	0.0306109i
$725$	−14.2083	+	1.87056i	−0.527684	+	0.0694709i
$726$	23.0941	+	9.45601i	0.857104	+	0.350945i
$727$	15.6188	−	4.18503i	0.579268	−	0.155214i	0.0427241	−	0.999087i	$-0.486396\pi$
$727$	15.6188	−	4.18503i	0.579268	−	0.155214i	0.536544	+	0.843873i	$0.319730\pi$
$728$	−13.5152	−	31.8098i	−0.500908	−	1.17895i
$729$	−18.9717	+	19.2113i	−0.702655	+	0.711531i
$730$	−8.04719	+	19.5949i	−0.297840	+	0.725241i
$731$	−4.18145	−	5.44937i	−0.154657	−	0.201552i
$732$	−0.329549	−	46.4727i	−0.0121805	−	1.71768i
$733$	−0.330246	−	0.253406i	−0.0121979	−	0.00935978i	0.602644	−	0.798010i	$-0.294114\pi$
$733$	−0.330246	−	0.253406i	−0.0121979	−	0.00935978i	−0.614842	+	0.788650i	$0.710780\pi$
$734$	34.8227	+	9.21799i	1.28533	+	0.340242i
$735$	8.57451	+	31.8671i	0.316275	+	1.17544i
$736$	−22.9391	−	12.7856i	−0.845546	−	0.471285i
$737$		−	7.24246i		−	0.266779i
$738$	34.0795	+	33.7326i	1.25448	+	1.24172i
$739$	−8.34979	−	20.1582i	−0.307152	−	0.741530i	−0.999795	−	0.0202498i	$-0.993554\pi$
$739$	−8.34979	−	20.1582i	−0.307152	−	0.741530i	0.692643	−	0.721281i	$-0.256446\pi$
$740$	1.41900	−	0.389429i	0.0521636	−	0.0143157i
$741$	9.00831	−	11.7653i	0.330929	−	0.432210i
$742$	−6.03317	−	44.7802i	−0.221485	−	1.64393i
$743$	8.01409	−	29.9090i	0.294008	−	1.09725i	−0.647993	−	0.761646i	$-0.724392\pi$
$743$	8.01409	−	29.9090i	0.294008	−	1.09725i	0.942002	−	0.335608i	$-0.108942\pi$
$744$	−8.68121	−	6.52290i	−0.318269	−	0.239141i
$745$	6.55155	+	24.4507i	0.240030	+	0.895805i
$746$	15.0174	−	6.27364i	0.549825	−	0.229694i
$747$	−9.04650	−	11.7387i	−0.330994	−	0.429496i
$748$	3.68326	−	9.04646i	0.134673	−	0.330771i
$749$	−12.1195	+	92.0568i	−0.442837	+	3.36368i
$750$	−24.2065	+	6.59180i	−0.883898	+	0.240698i
$751$	7.87620	+	13.6420i	0.287407	+	0.497803i	0.973190	−	0.230003i	$-0.0738736\pi$
$751$	7.87620	+	13.6420i	0.287407	+	0.497803i	−0.685783	+	0.727806i	$0.740540\pi$
$752$	18.2408	−	10.8275i	0.665174	−	0.394837i
$753$	15.5216	−	15.5541i	0.565638	−	0.566823i
$754$	12.5541	+	7.19761i	0.457194	+	0.262122i
$755$	0.678523	+	1.63810i	0.0246940	+	0.0596166i
$756$	−18.6277	+	46.1659i	−0.677483	+	1.67904i
$757$	26.0351	+	10.7841i	0.946261	+	0.391954i	0.801824	−	0.597560i	$-0.203863\pi$
$757$	26.0351	+	10.7841i	0.946261	+	0.391954i	0.144437	+	0.989514i	$0.453863\pi$
$758$	3.51373	−	27.3275i	0.127625	−	0.992578i
$759$	7.24640	−	0.00758053i	0.263028	−	0.000275156i
$760$	2.83395	−	10.9735i	0.102798	−	0.398051i
$761$	41.8566	+	11.2154i	1.51730	+	0.406560i	0.918852	−	0.394601i	$-0.129117\pi$
$761$	41.8566	+	11.2154i	1.51730	+	0.406560i	0.598449	+	0.801161i	$0.295784\pi$
$762$	−20.8342	−	2.65669i	−0.754745	−	0.0962417i
$763$	−68.7311	+	52.7392i	−2.48823	+	1.90929i
$764$	0.196612	+	32.5242i	0.00711316	+	1.17668i
$765$	−11.7924	+	15.4349i	−0.426356	+	0.558051i
$766$	9.75991	−	9.81909i	0.352640	−	0.354778i
$767$	6.72531	−	11.6486i	0.242837	−	0.420606i
$768$	−4.30913	−	27.3757i	−0.155492	−	0.987837i
$769$	0.306129	+	0.530231i	0.0110393	+	0.0191206i	0.871492	−	0.490409i	$-0.163153\pi$
$769$	0.306129	+	0.530231i	0.0110393	+	0.0191206i	−0.860453	+	0.509530i	$0.829819\pi$
$770$	7.05126	+	1.86656i	0.254110	+	0.0672660i
$771$	26.0220	−	3.45357i	0.937161	−	0.124377i
$772$	−28.8388	−	16.4185i	−1.03793	−	0.590914i
$773$	−39.8912	−	16.5235i	−1.43479	−	0.594308i	−0.476258	−	0.879306i	$-0.658007\pi$
$773$	−39.8912	−	16.5235i	−1.43479	−	0.594308i	−0.958528	+	0.284998i	$0.908007\pi$
$774$	5.32778	−	0.729157i	0.191503	−	0.0262090i
$775$	−5.59933	+	5.59933i	−0.201134	+	0.201134i
$776$	−35.3346	+	9.81212i	−1.26844	+	0.352234i
$777$	−4.42749	−	2.55004i	−0.158835	−	0.0914821i
$778$	−34.2680	−	26.1305i	−1.22857	−	0.936826i
$779$	4.94765	+	37.5811i	0.177268	+	1.34648i
$780$	9.78224	+	3.97091i	0.350261	+	0.142181i
$781$	7.76721	+	1.02257i	0.277933	+	0.0365905i
$782$	0.107540	+	35.5795i	0.00384561	+	1.27232i
$783$	−5.45794	−	20.1166i	−0.195051	−	0.718908i
$784$	0.771181	+	63.7834i	0.0275422	+	2.27798i
$785$	−13.4291	+	23.2599i	−0.479306	+	0.830182i
$786$	16.9314	−	17.0698i	0.603925	−	0.608859i
$787$	9.50954	+	7.29693i	0.338979	+	0.260107i	0.764196	−	0.644984i	$-0.223136\pi$
$787$	9.50954	+	7.29693i	0.338979	+	0.260107i	−0.425218	+	0.905091i	$0.639802\pi$
$788$	−27.9295	+	3.84889i	−0.994947	+	0.137111i
$789$	1.20634	+	0.157534i	0.0429469	+	0.00560837i
$790$	−1.23499	+	9.60490i	−0.0439389	+	0.341727i
$791$	15.5280	−	15.5280i	0.552113	−	0.552113i
$792$	4.72250	+	6.01430i	0.167807	+	0.213709i
$793$	24.1987	+	24.1987i	0.859321	+	0.859321i
$794$	33.1836	−	25.6224i	1.17764	−	0.909306i
$795$	10.9590	+	8.39092i	0.388675	+	0.297595i
$796$	13.4846	−	51.5700i	0.477947	−	1.82785i
$797$	5.13981	−	6.69833i	0.182061	−	0.237267i	−0.693403	−	0.720550i	$-0.743889\pi$
$797$	5.13981	−	6.69833i	0.182061	−	0.237267i	0.875464	+	0.483283i	$0.160556\pi$
$798$	−34.0004	+	19.8150i	−1.20360	+	0.701444i
$799$	−24.8885	−	14.3694i	−0.880491	−	0.508352i
$800$	−20.2071	+	0.305404i	−0.714428	+	0.0107976i
$801$	13.5104	−	0.0282668i	0.477368	−	0.000998759i
$802$	12.8338	−	12.9116i	0.453177	−	0.455925i
$803$	1.47470	−	11.2015i	0.0520411	−	0.395291i
$804$	−13.7485	+	24.2079i	−0.484871	+	0.853745i
$805$	−26.3426	+	3.46808i	−0.928456	+	0.122234i
$806$	7.92448	−	1.06765i	0.279128	−	0.0376065i
$807$	−31.8999	+	0.0333708i	−1.12293	+	0.00117471i
$808$	0.0909108	+	0.0111310i	0.00319823	+	0.000391587i
$809$	17.1871	+	17.1871i	0.604266	+	0.604266i	0.941442	−	0.337176i	$-0.109472\pi$
$809$	17.1871	+	17.1871i	0.604266	+	0.604266i	−0.337176	+	0.941442i	$0.609472\pi$
$810$	−5.92050	−	14.0070i	−0.208025	−	0.492154i
$811$	0.177117	−	0.427599i	0.00621943	−	0.0150150i	−0.920739	−	0.390178i	$-0.872413\pi$
$811$	0.177117	−	0.427599i	0.00621943	−	0.0150150i	0.926959	+	0.375163i	$0.122413\pi$
$812$	−23.5796	−	30.3479i	−0.827482	−	1.06500i
$813$	−20.0269	−	8.27089i	−0.702375	−	0.290073i
$814$	−0.678485	+	0.394463i	−0.0237809	+	0.0138259i
$815$	1.10437	−	0.637610i	0.0386845	−	0.0223345i
$816$	−29.4842	+	23.2457i	−1.03216	+	0.813763i
$817$	3.68137	+	2.12544i	0.128795	+	0.0743598i
$818$	19.6253	−	0.0593179i	0.686184	−	0.00207400i
$819$	−14.0994	−	33.8385i	−0.492672	−	1.18241i
$820$	−24.8881	+	10.4857i	−0.869129	+	0.366176i
$821$	−10.1958	−	13.2874i	−0.355835	−	0.463733i	0.580797	−	0.814048i	$-0.302741\pi$
$821$	−10.1958	−	13.2874i	−0.355835	−	0.463733i	−0.936632	+	0.350316i	$0.886074\pi$
$822$	−5.00442	−	36.8530i	−0.174549	−	1.28540i
$823$	7.89285	−	29.4565i	0.275127	−	1.02679i	−0.680628	−	0.732629i	$-0.738293\pi$
$823$	7.89285	−	29.4565i	0.275127	−	1.02679i	0.955756	−	0.294161i	$-0.0950401\pi$
$824$	14.7831	+	25.0771i	0.514993	+	0.873603i
$825$	4.82638	−	2.79325i	0.168033	−	0.0972484i
$826$	−28.2740	+	21.8315i	−0.983779	+	0.759616i
$827$	21.6631	−	52.2993i	0.753299	−	1.81863i	0.213237	−	0.977000i	$-0.431599\pi$
$827$	21.6631	−	52.2993i	0.753299	−	1.81863i	0.540062	−	0.841625i	$-0.318401\pi$
$828$	−24.2354	−	13.7306i	−0.842238	−	0.477171i
$829$	−21.5086	+	8.90913i	−0.747023	+	0.309427i	−0.723526	−	0.690297i	$-0.757480\pi$
$829$	−21.5086	+	8.90913i	−0.747023	+	0.309427i	−0.0234967	+	0.999724i	$0.507480\pi$
$830$	8.05594	−	2.18470i	0.279626	−	0.0758321i
$831$	18.3590	−	4.93987i	0.636867	−	0.171362i
$832$	16.4126	+	12.1274i	0.569004	+	0.420440i
$833$	74.8429	−	43.2106i	2.59315	−	1.49716i
$834$	−0.0977012	−	24.0132i	−0.00338312	−	0.831510i
$835$	3.25504	+	0.428535i	0.112645	+	0.0148301i
$836$	0.0365409	+	6.04472i	0.00126379	+	0.209061i
$837$	−9.15933	−	6.98264i	−0.316593	−	0.241355i
$838$	−10.3516	+	25.2063i	−0.357591	+	0.870735i
$839$	−7.98934	+	2.14074i	−0.275823	+	0.0739064i	−0.394079	−	0.919077i	$-0.628936\pi$
$839$	−7.98934	+	2.14074i	−0.275823	+	0.0739064i	0.118256	+	0.992983i	$0.462270\pi$
$840$	−20.0255	−	19.6244i	−0.690944	−	0.677108i
$841$	−12.4688	−	3.34101i	−0.429959	−	0.115207i
$842$	−8.73738	+	11.4583i	−0.301110	+	0.394880i
$843$	1.40493	−	10.7584i	0.0483883	−	0.370540i
$844$	42.1830	+	5.29428i	1.45200	+	0.182237i
$845$	7.16711	−	2.96872i	0.246556	−	0.102127i
$846$	19.4269	−	11.3490i	0.667911	−	0.390187i
$847$	48.8030			1.67689
$848$	16.4960	+	20.9682i	0.566475	+	0.720050i
$849$	−4.94067	+	18.5163i	−0.169563	+	0.635477i
$850$	13.7616	+	23.6703i	0.472019	+	0.811884i
$851$	1.74034	−	2.26806i	0.0596582	−	0.0777481i
$852$	−24.0207	−	18.1625i	−0.822934	−	0.622238i
$853$	27.5219	−	21.1183i	0.942333	−	0.723077i	−0.0186095	−	0.999827i	$-0.505924\pi$
$853$	27.5219	−	21.1183i	0.942333	−	0.723077i	0.960942	+	0.276750i	$0.0892572\pi$
$854$	−35.0341	−	83.8621i	−1.19884	−	2.86970i
$855$	3.08697	−	11.6179i	0.105572	−	0.397324i
$856$	−21.4386	−	50.4583i	−0.732755	−	1.72463i
$857$	10.1959	+	38.0516i	0.348286	+	1.29982i	0.888727	+	0.458437i	$0.151591\pi$
$857$	10.1959	+	38.0516i	0.348286	+	1.29982i	−0.540441	+	0.841382i	$0.681743\pi$
$858$	−5.58569	−	0.712262i	−0.190692	−	0.0243162i
$859$	−5.04945	−	38.3544i	−0.172285	−	1.30864i	−0.831013	−	0.556254i	$-0.812238\pi$
$859$	−5.04945	−	38.3544i	−0.172285	−	1.30864i	0.658728	−	0.752382i	$-0.271095\pi$
$860$	−0.766176	+	2.93014i	−0.0261264	+	0.0999171i
$861$	86.6740	+	35.7954i	2.95384	+	1.21990i
$862$	13.9987	−	3.79631i	0.476796	−	0.129303i
$863$	−30.8184			−1.04907			−0.524535	−	0.851389i	$-0.675761\pi$
$863$	−30.8184			−1.04907			−0.524535	+	0.851389i	$0.675761\pi$
$864$	−4.36788	−	29.0675i	−0.148598	−	0.988898i
$865$	−8.76019			−0.297856
$866$	−10.7231	+	2.90801i	−0.364386	+	0.0988183i
$867$	19.8006	+	8.17741i	0.672463	+	0.277720i
$868$	−20.5449	−	5.37210i	−0.697340	−	0.182341i
$869$	−0.674171	−	5.12084i	−0.0228697	−	0.173713i
$870$	11.6453	+	1.48495i	0.394812	+	0.0503446i
$871$	−5.30587	−	19.8018i	−0.179783	−	0.670958i
$872$	19.1460	−	47.4345i	0.648364	−	1.60633i
$873$	−37.5497	+	10.1456i	−1.27086	+	0.343378i
$874$	−8.48783	−	20.3175i	−0.287105	−	0.687250i
$875$	−38.9243	+	29.8676i	−1.31588	+	1.00971i
$876$	−26.1931	+	34.6413i	−0.884981	+	1.17042i
$877$	−3.02912	+	3.94763i	−0.102286	+	0.133302i	−0.841692	−	0.539958i	$-0.818440\pi$
$877$	−3.02912	+	3.94763i	−0.102286	+	0.133302i	0.739406	+	0.673260i	$0.235107\pi$
$878$	−17.6731	−	30.3982i	−0.596440	−	1.02589i
$879$	2.29576	−	8.60387i	0.0774339	−	0.290201i
$880$	−4.14628	+	1.16490i	−0.139771	+	0.0392686i
$881$	−9.77377			−0.329287			−0.164643	−	0.986353i	$-0.552647\pi$
$881$	−9.77377			−0.329287			−0.164643	+	0.986353i	$0.552647\pi$
$882$	0.346048	+	67.6566i	0.0116520	+	2.27812i
$883$	−12.6487	+	5.23927i	−0.425663	+	0.176315i	−0.585222	−	0.810873i	$-0.698993\pi$
$883$	−12.6487	+	5.23927i	−0.425663	+	0.176315i	0.159559	+	0.987188i	$0.448993\pi$
$884$	3.44298	−	27.4325i	0.115800	−	0.922655i
$885$	1.41295	−	10.8199i	0.0474959	−	0.363707i
$886$	−24.4572	+	32.0735i	−0.821656	+	1.07753i
$887$	−3.67918	−	0.985834i	−0.123535	−	0.0331011i	0.196522	−	0.980499i	$-0.437035\pi$
$887$	−3.67918	−	0.985834i	−0.123535	−	0.0331011i	−0.320057	+	0.947398i	$0.603702\pi$
$888$	3.01664	−	0.0305103i	0.101232	−	0.00102386i
$889$	−39.6745	+	10.6308i	−1.33064	+	0.356544i
$890$	−2.89069	+	7.03885i	−0.0968962	+	0.235943i
$891$	4.96435	+	6.41392i	0.166312	+	0.214874i
$892$	−13.7337	+	0.0830215i	−0.459839	+	0.00277977i
$893$	17.6334	+	2.32148i	0.590078	+	0.0776853i
$894$	0.211149	+	51.8966i	0.00706187	+	1.73568i
$895$	−7.55792	+	4.36357i	−0.252633	+	0.145858i
$896$	−28.0850	−	46.3514i	−0.938252	−	1.54849i
$897$	19.8070	−	5.32948i	0.661336	−	0.177946i
$898$	18.3862	−	4.98618i	0.613556	−	0.166391i
$899$	8.21456	−	3.40258i	0.273971	−	0.113482i
$900$	−21.4346	+	0.174422i	−0.714486	+	0.00581407i
$901$	13.8323	−	33.3941i	0.460820	−	1.11252i
$902$	11.4011	−	8.80327i	0.379616	−	0.293117i
$903$	9.10189	−	5.26768i	0.302892	−	0.175297i
$904$	−3.24220	+	12.5543i	−0.107834	+	0.417550i
$905$	−0.932835	+	3.48139i	−0.0310085	+	0.115725i
$906$	0.489139	+	3.60207i	0.0162506	+	0.119671i
$907$	−3.53336	−	4.60477i	−0.117323	−	0.152899i	0.731000	−	0.682378i	$-0.239054\pi$
$907$	−3.53336	−	4.60477i	−0.117323	−	0.152899i	−0.848323	+	0.529479i	$0.822387\pi$
$908$	−6.79185	−	16.1207i	−0.225396	−	0.534983i
$909$	0.0963408	+	0.0124785i	0.00319542	+	0.000413886i
$910$	20.6465	−	0.0624043i	0.684424	−	0.00206868i
$911$	0.966011	+	0.557727i	0.0320054	+	0.0184783i	0.515917	−	0.856638i	$-0.327451\pi$
$911$	0.966011	+	0.557727i	0.0320054	+	0.0184783i	−0.483912	+	0.875117i	$0.660785\pi$
$912$	11.3526	−	20.2738i	0.375923	−	0.671332i
$913$	−3.85546	+	2.22595i	−0.127597	+	0.0736682i
$914$	−5.52577	+	3.21261i	−0.182776	+	0.106264i
$915$	25.6604	+	10.5974i	0.848305	+	0.350340i
$916$	−6.80179	+	5.28483i	−0.224737	+	0.174616i
$917$	17.9933	−	43.4396i	0.594191	−	1.43450i
$918$	−31.4440	+	24.4371i	−1.03781	+	0.806543i
$919$	−14.8682	−	14.8682i	−0.490457	−	0.490457i	0.417993	−	0.908450i	$-0.362734\pi$
$919$	−14.8682	−	14.8682i	−0.490457	−	0.490457i	−0.908450	+	0.417993i	$0.862734\pi$
$920$	12.3592	−	9.66282i	0.407470	−	0.318574i
$921$	27.1828	−	0.0284362i	0.895705	−	0.000937005i
$922$	24.1132	−	3.24874i	0.794127	−	0.106992i
$923$	21.9857	−	2.89447i	0.723667	−	0.0952725i
$924$	13.0036	+	7.38517i	0.427786	+	0.242954i
$925$	0.287155	−	2.18116i	0.00944160	−	0.0717161i
$926$	−3.73542	+	3.75807i	−0.122754	+	0.123498i
$927$	15.4939	+	26.7070i	0.508887	+	0.877174i
$928$	21.0934	+	8.36601i	0.692425	+	0.274628i
$929$	16.7941	+	9.69609i	0.550997	+	0.318118i	0.749524	−	0.661977i	$-0.230282\pi$
$929$	16.7941	+	9.69609i	0.550997	+	0.318118i	−0.198527	+	0.980095i	$0.563616\pi$
$930$	5.60447	−	3.26622i	0.183778	−	0.107104i
$931$	−32.5586	+	42.4312i	−1.06707	+	1.39063i
$932$	7.71002	+	2.01602i	0.252550	+	0.0660370i
$933$	−23.0991	−	17.6862i	−0.756230	−	0.579020i
$934$	−8.22784	+	6.35305i	−0.269223	+	0.207878i
$935$	4.12592	+	4.12592i	0.134932	+	0.134932i
$936$	17.3180	+	12.9841i	0.566057	+	0.424399i
$937$	22.5258	−	22.5258i	0.735887	−	0.735887i	−0.235892	−	0.971779i	$-0.575801\pi$
$937$	22.5258	−	22.5258i	0.735887	−	0.735887i	0.971779	+	0.235892i	$0.0758013\pi$
$938$	−6.94318	+	53.9994i	−0.226703	+	1.76314i
$939$	44.7930	+	5.84945i	1.46177	+	0.190890i
$940$	1.72992	+	12.5532i	0.0564236	+	0.409439i
$941$	28.2164	+	21.6512i	0.919828	+	0.705809i	0.955947	−	0.293538i	$-0.0948329\pi$
$941$	28.2164	+	21.6512i	0.919828	+	0.705809i	−0.0361190	+	0.999347i	$0.511500\pi$
$942$	−38.7778	+	39.0947i	−1.26345	+	1.27377i
$943$	−26.2349	+	45.4401i	−0.854325	+	1.47973i
$944$	7.83530	−	19.5824i	0.255017	−	0.637354i
$945$	−21.0945	−	20.9625i	−0.686204	−	0.681911i
$946$	−0.00488243	−	1.61535i	−0.000158742	−	0.0525196i
$947$	−8.88425	−	1.16963i	−0.288699	−	0.0380080i	−0.0152143	−	0.999884i	$-0.504843\pi$
$947$	−8.88425	−	1.16963i	−0.288699	−	0.0380080i	−0.273485	+	0.961876i	$0.588176\pi$
$948$	−7.46755	+	18.3961i	−0.242535	+	0.597479i
$949$	−4.17425	−	31.7066i	−0.135502	−	1.02924i
$950$	−13.4742	−	10.2746i	−0.437161	−	0.333351i
$951$	1.44362	+	0.831461i	0.0468125	+	0.0269620i
$952$	−36.1348	+	63.9188i	−1.17114	+	2.07162i
$953$	−24.9238	+	24.9238i	−0.807360	+	0.807360i	−0.984234	−	0.176874i	$-0.943402\pi$
$953$	−24.9238	+	24.9238i	−0.807360	+	0.807360i	0.176874	+	0.984234i	$0.443402\pi$
$954$	17.3411	+	22.3616i	0.561439	+	0.723984i
$955$	−17.9507	−	7.43540i	−0.580870	−	0.240604i
$956$	6.76424	−	11.8813i	0.218771	−	0.384269i
$957$	−6.20697	+	0.823770i	−0.200643	+	0.0266287i
$958$	8.13567	+	2.15361i	0.262851	+	0.0695800i
$959$	−36.3663	−	62.9882i	−1.17433	−	2.03400i
$960$	16.0702	+	3.97728i	0.518664	+	0.128366i
$961$	−13.0435	+	22.5920i	−0.420758	+	0.728775i
$962$	−1.56608	+	1.57557i	−0.0504923	+	0.0507985i
$963$	−22.3652	−	53.6764i	−0.720708	−	1.72970i
$964$	11.4081	−	0.0689628i	0.367429	−	0.00222114i
$965$	15.7275	−	12.0681i	0.506286	−	0.388487i
$966$	−54.0360	−	6.89043i	−1.73858	−	0.221696i
$967$	18.0621	+	4.83972i	0.580837	+	0.155635i	0.537262	−	0.843415i	$-0.319459\pi$
$967$	18.0621	+	4.83972i	0.580837	+	0.155635i	0.0435748	+	0.999050i	$0.486125\pi$
$968$	−24.8234	+	14.6335i	−0.797854	+	0.470338i
$969$	−31.4804	+	0.0329319i	−1.01130	+	0.00105793i
$970$	2.79377	−	21.7280i	0.0897024	−	0.697645i
$971$	15.9790	+	6.61874i	0.512792	+	0.212405i	0.624047	−	0.781386i	$-0.285487\pi$
$971$	15.9790	+	6.61874i	0.512792	+	0.212405i	−0.111255	+	0.993792i	$0.535487\pi$
$972$	−4.41767	−	30.8623i	−0.141697	−	0.989910i
$973$	−17.9714	−	43.3868i	−0.576136	−	1.39092i
$974$	44.2258	+	25.3559i	1.41709	+	0.812454i
$975$	11.1496	−	11.1729i	0.357072	−	0.357820i
$976$	42.9659	+	32.1511i	1.37530	+	1.02913i
$977$	−28.3312	−	49.0712i	−0.906397	−	1.56993i	−0.819031	−	0.573749i	$-0.805488\pi$
$977$	−28.3312	−	49.0712i	−0.906397	−	1.56993i	−0.0873657	−	0.996176i	$-0.527845\pi$
$978$	2.52259	−	0.686939i	0.0806636	−	0.0219659i
$979$	0.529738	−	4.02376i	0.0169305	−	0.128600i
$980$	−35.2926	−	14.3694i	−1.12738	−	0.459012i
$981$	20.6578	−	50.1690i	0.659553	−	1.60177i
$982$	−47.8654	+	19.9962i	−1.52745	+	0.638105i
$983$	4.65479	+	17.3719i	0.148465	+	0.554078i	0.999577	+	0.0290935i	$0.00926205\pi$
$983$	4.65479	+	17.3719i	0.148465	+	0.554078i	−0.851112	+	0.524984i	$0.824071\pi$
$984$	−54.8195	+	7.78193i	−1.74758	+	0.248079i
$985$	4.35909	−	16.2683i	0.138892	−	0.518352i
$986$	−4.10492	−	30.4681i	−0.130727	−	0.970301i
$987$	26.7489	−	34.9354i	0.851426	−	1.11201i
$988$	4.52831	+	16.5002i	0.144065	+	0.524943i
$989$	2.25178	+	5.43628i	0.0716025	+	0.172864i
$990$	−4.40630	+	1.20485i	−0.140041	+	0.0382927i
$991$			45.0139i			1.42991i	0.699169	+	0.714956i	$0.253553\pi$
$991$			45.0139i			1.42991i	−0.699169	+	0.714956i	$0.746447\pi$
$992$	12.0609	−	3.42787i	0.382934	−	0.108835i
$993$	2.24589	+	8.34686i	0.0712713	+	0.264880i
$994$	−56.9316	−	15.0705i	−1.80576	−	0.478007i
$995$	25.2625	+	19.3846i	0.800874	+	0.614532i
$996$	17.1124	−	0.121348i	0.542227	−	0.00384506i
$997$	−7.88254	−	10.2727i	−0.249643	−	0.325341i	0.651676	−	0.758498i	$-0.274066\pi$
$997$	−7.88254	−	10.2727i	−0.249643	−	0.325341i	−0.901319	+	0.433157i	$0.857400\pi$
$998$	5.21654	−	12.7023i	0.165127	−	0.402084i
$999$	3.19978	−	0.0100420i	0.101237	−	0.000317715i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.20	✓	368
3.2	odd	2		864.2.bn.a.683.27		368
9.4	even	3		864.2.bn.a.395.42		368
9.5	odd	6	inner	288.2.bf.a.203.5	yes	368
32.3	odd	8	inner	288.2.bf.a.227.5	yes	368
96.35	even	8		864.2.bn.a.35.42		368
288.67	odd	24		864.2.bn.a.611.27		368
288.131	even	24	inner	288.2.bf.a.131.20	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.20	✓	368	1.1	even	1	trivial
288.2.bf.a.131.20	yes	368	288.131	even	24	inner
288.2.bf.a.203.5	yes	368	9.5	odd	6	inner
288.2.bf.a.227.5	yes	368	32.3	odd	8	inner
864.2.bn.a.35.42		368	96.35	even	8
864.2.bn.a.395.42		368	9.4	even	3
864.2.bn.a.611.27		368	288.67	odd	24
864.2.bn.a.683.27		368	3.2	odd	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.370153 - 1.36491i) q^{2} +(1.60090 + 0.661153i) q^{3} +(-1.72597 + 1.01045i) q^{4} +(-0.155947 - 1.18454i) q^{5} +(0.309839 - 2.42981i) q^{6} +(-1.23982 - 4.62708i) q^{7} +(2.01805 + 1.98178i) q^{8} +(2.12575 + 2.11688i) q^{9} +O(q^{10})\)	\(q+(-0.370153 - 1.36491i) q^{2} +(1.60090 + 0.661153i) q^{3} +(-1.72597 + 1.01045i) q^{4} +(-0.155947 - 1.18454i) q^{5} +(0.309839 - 2.42981i) q^{6} +(-1.23982 - 4.62708i) q^{7} +(2.01805 + 1.98178i) q^{8} +(2.12575 + 2.11688i) q^{9} +(-1.55907 + 0.651315i) q^{10} +(0.714959 - 0.548608i) q^{11} +(-3.43117 + 0.476499i) q^{12} +(1.55287 - 2.02374i) q^{13} +(-5.85664 + 3.40497i) q^{14} +(0.533505 - 1.99943i) q^{15} +(1.95797 - 3.48803i) q^{16} -5.41926 q^{17} +(2.10250 - 3.68504i) q^{18} +(3.09852 - 1.28345i) q^{19} +(1.46608 + 1.88691i) q^{20} +(1.07438 - 8.22720i) q^{21} +(-1.01345 - 0.772789i) q^{22} +(4.48426 + 1.20155i) q^{23} +(1.92044 + 4.50688i) q^{24} +(3.45082 - 0.924644i) q^{25} +(-3.33703 - 1.37044i) q^{26} +(2.00354 + 4.79435i) q^{27} +(6.81534 + 6.73344i) q^{28} +(-3.97708 - 0.523593i) q^{29} +(-2.92653 + 0.0119070i) q^{30} +(-1.91957 + 1.10826i) q^{31} +(-5.48560 - 1.38136i) q^{32} +(1.50729 - 0.405568i) q^{33} +(2.00595 + 7.39682i) q^{34} +(-5.28761 + 2.19020i) q^{35} +(-5.80800 - 1.50570i) q^{36} +(0.235657 - 0.568926i) q^{37} +(-2.89872 - 3.75414i) q^{38} +(3.82400 - 2.21312i) q^{39} +(2.03279 - 2.69952i) q^{40} +(-2.92522 + 10.9171i) q^{41} +(-11.6271 + 1.57889i) q^{42} +(0.771590 + 1.00556i) q^{43} +(-0.679660 + 1.66931i) q^{44} +(2.17602 - 2.84816i) q^{45} +(-0.0198440 - 6.56538i) q^{46} +(4.59259 + 2.65153i) q^{47} +(5.44064 - 4.28946i) q^{48} +(-13.8105 + 7.97351i) q^{49} +(-2.53939 - 4.36781i) q^{50} +(-8.67569 - 3.58296i) q^{51} +(-0.635323 + 5.06203i) q^{52} +(-2.55243 + 6.16210i) q^{53} +(5.80226 - 4.50930i) q^{54} +(-0.761343 - 0.761343i) q^{55} +(6.66784 - 11.7947i) q^{56} +(5.80898 - 0.00607683i) q^{57} +(0.757468 + 5.62218i) q^{58} +(5.22783 - 0.688257i) q^{59} +(1.09951 + 3.99005i) q^{60} +(-1.75112 + 13.3011i) q^{61} +(2.22322 + 2.20982i) q^{62} +(7.15940 - 12.4606i) q^{63} +(0.145072 + 7.99868i) q^{64} +(-2.63937 - 1.52384i) q^{65} +(-1.11149 - 1.90720i) q^{66} +(4.89236 - 6.37585i) q^{67} +(9.35351 - 5.47591i) q^{68} +(6.38444 + 4.88835i) q^{69} +(4.94665 + 6.40642i) q^{70} +(6.14705 + 6.14705i) q^{71} +(0.0946916 + 8.48475i) q^{72} +(8.86496 - 8.86496i) q^{73} +(-0.863764 - 0.111062i) q^{74} +(6.13574 + 0.801256i) q^{75} +(-4.05111 + 5.34611i) q^{76} +(-3.42487 - 2.62800i) q^{77} +(-4.43618 - 4.40023i) q^{78} +(2.86568 - 4.96351i) q^{79} +(-4.43705 - 1.77535i) q^{80} +(0.0376598 + 8.99992i) q^{81} +(15.9836 - 0.0483107i) q^{82} +(-4.89778 - 0.644805i) q^{83} +(6.45884 + 15.2855i) q^{84} +(0.845120 + 6.41933i) q^{85} +(1.08689 - 1.42536i) q^{86} +(-6.02073 - 3.46768i) q^{87} +(2.53005 + 0.309775i) q^{88} +(3.18445 - 3.18445i) q^{89} +(-4.69295 - 1.91582i) q^{90} +(-11.2893 - 4.67619i) q^{91} +(-8.95383 + 2.45728i) q^{92} +(-3.80576 + 0.505089i) q^{93} +(1.91915 - 7.24996i) q^{94} +(-2.00350 - 3.47017i) q^{95} +(-7.86860 - 5.83824i) q^{96} +(-6.48269 + 11.2284i) q^{97} +(15.9951 + 15.8987i) q^{98} +(2.68116 + 0.347277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

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