LMFDB - Embedded newform 160.2.u.a.43.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,2,Mod(43,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 6]))

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

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

chi := DirichletCharacter("160.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	160.u (of order $8$, degree $4$, 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:	$1.27760643234$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			43.12
Character	$\chi$	$=$	160.43
Dual form			160.2.u.a.67.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0754956 - 1.41220i) q^{2} +(-0.698571 + 1.68650i) q^{3} +(-1.98860 - 0.213229i) q^{4} +(1.86202 + 1.23810i) q^{5} +(2.32893 + 1.11384i) q^{6} +2.70081i q^{7} +(-0.451252 + 2.79220i) q^{8} +(-0.234961 - 0.234961i) q^{9} +O(q^{10})$	\(q+(0.0754956 - 1.41220i) q^{2} +(-0.698571 + 1.68650i) q^{3} +(-1.98860 - 0.213229i) q^{4} +(1.86202 + 1.23810i) q^{5} +(2.32893 + 1.11384i) q^{6} +2.70081i q^{7} +(-0.451252 + 2.79220i) q^{8} +(-0.234961 - 0.234961i) q^{9} +(1.88901 - 2.53606i) q^{10} +(0.258659 - 0.624459i) q^{11} +(1.74879 - 3.20482i) q^{12} +(1.22756 - 2.96359i) q^{13} +(3.81408 + 0.203900i) q^{14} +(-3.38881 + 2.27539i) q^{15} +(3.90907 + 0.848056i) q^{16} +(0.871815 + 0.871815i) q^{17} +(-0.349550 + 0.314073i) q^{18} +(-0.655022 - 1.58136i) q^{19} +(-3.43881 - 2.85912i) q^{20} +(-4.55492 - 1.88671i) q^{21} +(-0.862331 - 0.412422i) q^{22} +5.05482i q^{23} +(-4.39381 - 2.71159i) q^{24} +(1.93422 + 4.61073i) q^{25} +(-4.09250 - 1.95729i) q^{26} +(-4.49910 + 1.86359i) q^{27} +(0.575893 - 5.37084i) q^{28} +(-4.01808 - 9.70052i) q^{29} +(2.95746 + 4.95745i) q^{30} -8.31791i q^{31} +(1.49274 - 5.45635i) q^{32} +(0.872458 + 0.872458i) q^{33} +(1.29699 - 1.16536i) q^{34} +(-3.34388 + 5.02896i) q^{35} +(0.417144 + 0.517345i) q^{36} +(2.10924 + 5.09214i) q^{37} +(-2.28265 + 0.805634i) q^{38} +(4.14056 + 4.14056i) q^{39} +(-4.29726 + 4.64043i) q^{40} +(-2.96283 + 2.96283i) q^{41} +(-3.00828 + 6.29001i) q^{42} +(3.21452 - 1.33150i) q^{43} +(-0.647523 + 1.18665i) q^{44} +(-0.146597 - 0.728408i) q^{45} +(7.13840 + 0.381617i) q^{46} +(2.56832 - 2.56832i) q^{47} +(-4.16101 + 6.00021i) q^{48} -0.294392 q^{49} +(6.65728 - 2.38341i) q^{50} +(-2.07934 + 0.861291i) q^{51} +(-3.07305 + 5.63165i) q^{52} +(-4.76734 - 11.5094i) q^{53} +(2.29209 + 6.49431i) q^{54} +(1.25477 - 0.842508i) q^{55} +(-7.54121 - 1.21875i) q^{56} +3.12455 q^{57} +(-14.0024 + 4.94198i) q^{58} +(-1.00624 + 2.42929i) q^{59} +(7.22417 - 3.80225i) q^{60} +(9.94431 - 4.11907i) q^{61} +(-11.7465 - 0.627965i) q^{62} +(0.634587 - 0.634587i) q^{63} +(-7.59274 - 2.51997i) q^{64} +(5.95496 - 3.99842i) q^{65} +(1.29795 - 1.16622i) q^{66} +(7.76760 + 3.21745i) q^{67} +(-1.54780 - 1.91959i) q^{68} +(-8.52495 - 3.53115i) q^{69} +(6.84944 + 5.10188i) q^{70} +(11.2513 - 11.2513i) q^{71} +(0.762086 - 0.550032i) q^{72} +5.96456 q^{73} +(7.35035 - 2.59422i) q^{74} +(-9.12718 + 0.0411410i) q^{75} +(0.965385 + 3.28437i) q^{76} +(1.68655 + 0.698591i) q^{77} +(6.15988 - 5.53469i) q^{78} +2.54862i q^{79} +(6.22877 + 6.41891i) q^{80} -9.88644i q^{81} +(3.96042 + 4.40778i) q^{82} +(-15.1974 - 6.29497i) q^{83} +(8.65562 + 4.72316i) q^{84} +(0.543941 + 2.70273i) q^{85} +(-1.63765 - 4.64006i) q^{86} +19.1668 q^{87} +(1.62689 + 1.00402i) q^{88} +(-8.13681 + 8.13681i) q^{89} +(-1.03972 + 0.152032i) q^{90} +(8.00411 + 3.31541i) q^{91} +(1.07784 - 10.0520i) q^{92} +(14.0282 + 5.81065i) q^{93} +(-3.43308 - 3.82087i) q^{94} +(0.738222 - 3.75551i) q^{95} +(8.15935 + 6.32915i) q^{96} +(-6.20483 + 6.20483i) q^{97} +(-0.0222253 + 0.415739i) q^{98} +(-0.207499 + 0.0859488i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8}+O(q^{10}) $ 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8	$ 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8} - 16 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} + 16 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} + 16 q^{19} + 24 q^{20} - 8 q^{21} - 20 q^{22} - 32 q^{24} - 4 q^{25} - 8 q^{26} - 16 q^{27} + 12 q^{28} + 8 q^{30} - 24 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 8 q^{36} - 4 q^{37} - 60 q^{38} + 16 q^{40} - 8 q^{41} + 60 q^{42} - 36 q^{43} + 16 q^{44} - 4 q^{45} - 8 q^{46} - 8 q^{47} - 24 q^{48} - 40 q^{49} - 12 q^{50} + 8 q^{51} - 56 q^{52} - 4 q^{53} - 56 q^{54} - 36 q^{55} + 40 q^{56} - 8 q^{57} - 36 q^{58} + 12 q^{60} - 40 q^{61} + 40 q^{62} + 56 q^{63} + 48 q^{64} - 8 q^{65} + 72 q^{66} + 20 q^{67} + 8 q^{68} + 24 q^{69} + 60 q^{70} + 24 q^{71} + 24 q^{72} - 8 q^{73} + 8 q^{75} + 56 q^{76} + 24 q^{77} + 32 q^{78} - 8 q^{80} + 84 q^{82} - 44 q^{83} + 56 q^{84} - 4 q^{85} + 24 q^{86} - 120 q^{87} + 104 q^{88} + 148 q^{90} - 8 q^{91} + 124 q^{92} + 8 q^{93} - 32 q^{94} + 24 q^{96} - 8 q^{97} - 16 q^{98}+O(q^{100}) $ 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8 - 16 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 + 16 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 + 16 * q^19 + 24 * q^20 - 8 * q^21 - 20 * q^22 - 32 * q^24 - 4 * q^25 - 8 * q^26 - 16 * q^27 + 12 * q^28 + 8 * q^30 - 24 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 8 * q^36 - 4 * q^37 - 60 * q^38 + 16 * q^40 - 8 * q^41 + 60 * q^42 - 36 * q^43 + 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 24 * q^48 - 40 * q^49 - 12 * q^50 + 8 * q^51 - 56 * q^52 - 4 * q^53 - 56 * q^54 - 36 * q^55 + 40 * q^56 - 8 * q^57 - 36 * q^58 + 12 * q^60 - 40 * q^61 + 40 * q^62 + 56 * q^63 + 48 * q^64 - 8 * q^65 + 72 * q^66 + 20 * q^67 + 8 * q^68 + 24 * q^69 + 60 * q^70 + 24 * q^71 + 24 * q^72 - 8 * q^73 + 8 * q^75 + 56 * q^76 + 24 * q^77 + 32 * q^78 - 8 * q^80 + 84 * q^82 - 44 * q^83 + 56 * q^84 - 4 * q^85 + 24 * q^86 - 120 * q^87 + 104 * q^88 + 148 * q^90 - 8 * q^91 + 124 * q^92 + 8 * q^93 - 32 * q^94 + 24 * q^96 - 8 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{8}\right)$

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 $

$2$	0.0754956	−	1.41220i	0.0533835	−	0.998574i
$2$	0.0754956	−	1.41220i	0.0533835	−	0.998574i
$3$	−0.698571	+	1.68650i	−0.403320	+	0.973701i	0.583534	+	0.812089i	$0.301670\pi$
$3$	−0.698571	+	1.68650i	−0.403320	+	0.973701i	−0.986854	+	0.161613i	$0.948330\pi$
$4$	−1.98860	−	0.213229i	−0.994300	−	0.106615i
$5$	1.86202	+	1.23810i	0.832720	+	0.553695i
$5$	1.86202	+	1.23810i	0.832720	+	0.553695i
$6$	2.32893	+	1.11384i	0.950782	+	0.454725i
$7$			2.70081i			1.02081i	0.859934	+	0.510406i	$0.170505\pi$
$7$			2.70081i			1.02081i	−0.859934	+	0.510406i	$0.829495\pi$
$8$	−0.451252	+	2.79220i	−0.159542	+	0.987191i
$9$	−0.234961	−	0.234961i	−0.0783205	−	0.0783205i
$10$	1.88901	−	2.53606i	0.597359	−	0.801974i
$11$	0.258659	−	0.624459i	0.0779887	−	0.188281i	−0.880076	−	0.474832i	$-0.842509\pi$
$11$	0.258659	−	0.624459i	0.0779887	−	0.188281i	0.958065	+	0.286551i	$0.0925087\pi$
$12$	1.74879	−	3.20482i	0.504832	−	0.925152i
$13$	1.22756	−	2.96359i	0.340464	−	0.821952i	−0.657205	−	0.753712i	$-0.728261\pi$
$13$	1.22756	−	2.96359i	0.340464	−	0.821952i	0.997669	−	0.0682406i	$-0.0217386\pi$
$14$	3.81408	+	0.203900i	1.01936	+	0.0544944i
$15$	−3.38881	+	2.27539i	−0.874986	+	0.587504i
$16$	3.90907	+	0.848056i	0.977267	+	0.212014i
$17$	0.871815	+	0.871815i	0.211446	+	0.211446i	0.804882	−	0.593435i	$-0.202229\pi$
$17$	0.871815	+	0.871815i	0.211446	+	0.211446i	−0.593435	+	0.804882i	$0.702229\pi$
$18$	−0.349550	+	0.314073i	−0.0823898	+	0.0740278i
$19$	−0.655022	−	1.58136i	−0.150272	−	0.362790i	0.830761	−	0.556630i	$-0.187906\pi$
$19$	−0.655022	−	1.58136i	−0.150272	−	0.362790i	−0.981033	+	0.193840i	$0.937906\pi$
$20$	−3.43881	−	2.85912i	−0.768941	−	0.639319i
$21$	−4.55492	−	1.88671i	−0.993966	−	0.411714i
$22$	−0.862331	−	0.412422i	−0.183850	−	0.0879286i
$23$			5.05482i			1.05400i	0.849865	+	0.527001i	$0.176684\pi$
$23$			5.05482i			1.05400i	−0.849865	+	0.527001i	$0.823316\pi$
$24$	−4.39381	−	2.71159i	−0.896883	−	0.553500i
$25$	1.93422	+	4.61073i	0.386844	+	0.922145i
$26$	−4.09250	−	1.95729i	−0.802605	−	0.383857i
$27$	−4.49910	+	1.86359i	−0.865852	+	0.358648i
$28$	0.575893	−	5.37084i	0.108833	−	1.01499i
$29$	−4.01808	−	9.70052i	−0.746140	−	1.80134i	−0.578853	−	0.815432i	$-0.696499\pi$
$29$	−4.01808	−	9.70052i	−0.746140	−	1.80134i	−0.167287	−	0.985908i	$-0.553501\pi$
$30$	2.95746	+	4.95745i	0.539956	+	0.905102i
$31$		−	8.31791i		−	1.49394i	−0.664858	−	0.746970i	$-0.731508\pi$
$31$		−	8.31791i		−	1.49394i	0.664858	−	0.746970i	$-0.268492\pi$
$32$	1.49274	−	5.45635i	0.263882	−	0.964555i
$33$	0.872458	+	0.872458i	0.151875	+	0.151875i
$34$	1.29699	−	1.16536i	0.222432	−	0.199857i
$35$	−3.34388	+	5.02896i	−0.565218	+	0.850050i
$36$	0.417144	+	0.517345i	0.0695240	+	0.0862242i
$37$	2.10924	+	5.09214i	0.346756	+	0.837143i	0.996999	+	0.0774168i	$0.0246672\pi$
$37$	2.10924	+	5.09214i	0.346756	+	0.837143i	−0.650243	+	0.759727i	$0.725333\pi$
$38$	−2.28265	+	0.805634i	−0.370294	+	0.130691i
$39$	4.14056	+	4.14056i	0.663020	+	0.663020i
$40$	−4.29726	+	4.64043i	−0.679456	+	0.733716i
$41$	−2.96283	+	2.96283i	−0.462716	+	0.462716i	−0.899545	−	0.436829i	$-0.856102\pi$
$41$	−2.96283	+	2.96283i	−0.462716	+	0.462716i	0.436829	+	0.899545i	$0.356102\pi$
$42$	−3.00828	+	6.29001i	−0.464188	+	0.970570i
$43$	3.21452	−	1.33150i	0.490209	−	0.203051i	−0.123866	−	0.992299i	$-0.539529\pi$
$43$	3.21452	−	1.33150i	0.490209	−	0.203051i	0.614075	+	0.789248i	$0.289529\pi$
$44$	−0.647523	+	1.18665i	−0.0976178	+	0.178894i
$45$	−0.146597	−	0.728408i	−0.0218533	−	0.108585i
$46$	7.13840	+	0.381617i	1.05250	+	0.0562663i
$47$	2.56832	−	2.56832i	0.374628	−	0.374628i	−0.494532	−	0.869160i	$-0.664660\pi$
$47$	2.56832	−	2.56832i	0.374628	−	0.374628i	0.869160	+	0.494532i	$0.164660\pi$
$48$	−4.16101	+	6.00021i	−0.600590	+	0.866056i
$49$	−0.294392			−0.0420559
$50$	6.65728	−	2.38341i	0.941481	−	0.337065i
$51$	−2.07934	+	0.861291i	−0.291166	+	0.120605i
$52$	−3.07305	+	5.63165i	−0.426156	+	0.780969i
$53$	−4.76734	−	11.5094i	−0.654844	−	1.58093i	−0.805664	−	0.592372i	$-0.798191\pi$
$53$	−4.76734	−	11.5094i	−0.654844	−	1.58093i	0.150820	−	0.988561i	$-0.451809\pi$
$54$	2.29209	+	6.49431i	0.311914	+	0.883764i
$55$	1.25477	−	0.842508i	0.169193	−	0.113604i
$56$	−7.54121	−	1.21875i	−1.00774	−	0.162862i
$57$	3.12455			0.413857
$58$	−14.0024	+	4.94198i	−1.83860	+	0.648914i
$59$	−1.00624	+	2.42929i	−0.131002	+	0.316266i	−0.975747	−	0.218903i	$-0.929752\pi$
$59$	−1.00624	+	2.42929i	−0.131002	+	0.316266i	0.844745	+	0.535169i	$0.179752\pi$
$60$	7.22417	−	3.80225i	0.932636	−	0.490869i
$61$	9.94431	−	4.11907i	1.27324	−	0.527393i	0.359291	−	0.933225i	$-0.383018\pi$
$61$	9.94431	−	4.11907i	1.27324	−	0.527393i	0.913947	+	0.405833i	$0.133018\pi$
$62$	−11.7465	−	0.627965i	−1.49181	−	0.0797517i
$63$	0.634587	−	0.634587i	0.0799504	−	0.0799504i
$64$	−7.59274	−	2.51997i	−0.949093	−	0.314997i
$65$	5.95496	−	3.99842i	0.738622	−	0.495943i
$66$	1.29795	−	1.16622i	0.159767	−	0.143551i
$67$	7.76760	+	3.21745i	0.948964	+	0.393074i	0.802841	−	0.596193i	$-0.203321\pi$
$67$	7.76760	+	3.21745i	0.948964	+	0.393074i	0.146123	+	0.989266i	$0.453321\pi$
$68$	−1.54780	−	1.91959i	−0.187698	−	0.232784i
$69$	−8.52495	−	3.53115i	−1.02628	−	0.425101i
$70$	6.84944	+	5.10188i	0.818664	+	0.609791i
$71$	11.2513	−	11.2513i	1.33528	−	1.33528i	0.434715	−	0.900568i	$-0.356849\pi$
$71$	11.2513	−	11.2513i	1.33528	−	1.33528i	0.900568	−	0.434715i	$-0.143151\pi$
$72$	0.762086	−	0.550032i	0.0898127	−	0.0648219i
$73$	5.96456			0.698099			0.349050	−	0.937104i	$-0.386504\pi$
$73$	5.96456			0.698099			0.349050	+	0.937104i	$0.386504\pi$
$74$	7.35035	−	2.59422i	0.854461	−	0.301572i
$75$	−9.12718	+	0.0411410i	−1.05392	+	0.00475055i
$76$	0.965385	+	3.28437i	0.110737	+	0.376743i
$77$	1.68655	+	0.698591i	0.192200	+	0.0796118i
$78$	6.15988	−	5.53469i	0.697469	−	0.626681i
$79$			2.54862i			0.286743i	0.989669	+	0.143371i	$0.0457943\pi$
$79$			2.54862i			0.286743i	−0.989669	+	0.143371i	$0.954206\pi$
$80$	6.22877	+	6.41891i	0.696398	+	0.717656i
$81$		−	9.88644i		−	1.09849i
$82$	3.96042	+	4.40778i	0.437355	+	0.486757i
$83$	−15.1974	−	6.29497i	−1.66813	−	0.690963i	−0.669478	−	0.742832i	$-0.733482\pi$
$83$	−15.1974	−	6.29497i	−1.66813	−	0.690963i	−0.998654	+	0.0518685i	$0.983482\pi$
$84$	8.65562	+	4.72316i	0.944406	+	0.515339i
$85$	0.543941	+	2.70273i	0.0589987	+	0.293152i
$86$	−1.63765	−	4.64006i	−0.176593	−	0.500350i
$87$	19.1668			2.05490
$88$	1.62689	+	1.00402i	0.173427	+	0.107029i
$89$	−8.13681	+	8.13681i	−0.862501	+	0.862501i	−0.991628	−	0.129127i	$-0.958782\pi$
$89$	−8.13681	+	8.13681i	−0.862501	+	0.862501i	0.129127	+	0.991628i	$0.458782\pi$
$90$	−1.03972	+	0.152032i	−0.109596	+	0.0160256i
$91$	8.00411	+	3.31541i	0.839058	+	0.347549i
$92$	1.07784	−	10.0520i	0.112372	−	1.04799i
$93$	14.0282	+	5.81065i	1.45465	+	0.602536i
$94$	−3.43308	−	3.82087i	−0.354095	−	0.394093i
$95$	0.738222	−	3.75551i	0.0757400	−	0.385307i
$96$	8.15935	+	6.32915i	0.832760	+	0.645967i
$97$	−6.20483	+	6.20483i	−0.630005	+	0.630005i	−0.948069	−	0.318064i	$-0.896967\pi$
$97$	−6.20483	+	6.20483i	−0.630005	+	0.630005i	0.318064	+	0.948069i	$0.396967\pi$
$98$	−0.0222253	+	0.415739i	−0.00224509	+	0.0419960i
$99$	−0.207499	+	0.0859488i	−0.0208544	+	0.00863818i
$100$	−2.86325	−	9.58133i	−0.286325	−	0.958133i
$101$	−4.44583	+	10.7332i	−0.442376	+	1.06799i	0.532736	+	0.846281i	$0.321164\pi$
$101$	−4.44583	+	10.7332i	−0.442376	+	1.06799i	−0.975113	+	0.221710i	$0.928836\pi$
$102$	1.05933	+	3.00146i	0.104889	+	0.297189i
$103$	−0.172672			−0.0170138			−0.00850691	−	0.999964i	$-0.502708\pi$
$103$	−0.172672			−0.0170138			−0.00850691	+	0.999964i	$0.502708\pi$
$104$	7.72100	+	4.76492i	0.757106	+	0.467239i
$105$	−6.14541	−	9.15254i	−0.599731	−	0.893196i
$106$	−16.6134	+	5.86351i	−1.61364	+	0.569515i
$107$	−5.48489	−	13.2417i	−0.530244	−	1.28012i	−0.931361	−	0.364096i	$-0.881378\pi$
$107$	−5.48489	−	13.2417i	−0.530244	−	1.28012i	0.401117	−	0.916027i	$-0.368622\pi$
$108$	9.34429	−	2.74659i	0.899155	−	0.264291i
$109$	−0.103842	+	0.0430126i	−0.00994622	+	0.00411986i	−0.387651	−	0.921806i	$-0.626713\pi$
$109$	−0.103842	+	0.0430126i	−0.00994622	+	0.00411986i	0.377705	+	0.925926i	$0.376713\pi$
$110$	−1.09506	−	1.83559i	−0.104410	−	0.175017i
$111$	−10.0614			−0.954982
$112$	−2.29044	+	10.5577i	−0.216426	+	0.997605i
$113$	−4.20943	+	4.20943i	−0.395989	+	0.395989i	−0.876816	−	0.480826i	$-0.840337\pi$
$113$	−4.20943	+	4.20943i	−0.395989	+	0.395989i	0.480826	+	0.876816i	$0.340337\pi$
$114$	0.235890	−	4.41248i	0.0220931	−	0.413267i
$115$	−6.25837	+	9.41216i	−0.583596	+	0.877688i
$116$	5.92193	+	20.1472i	0.549838	+	1.87062i
$117$	−0.984759	+	0.407900i	−0.0910410	+	0.0377104i
$118$	3.35466	+	1.60441i	0.308822	+	0.147698i
$119$	−2.35461	+	2.35461i	−0.215847	+	0.215847i
$120$	−4.82414	−	10.4890i	−0.440382	−	0.957510i
$121$	7.45513	+	7.45513i	0.677739	+	0.677739i
$122$	−5.06619	−	14.3543i	−0.458671	−	1.29958i
$123$	−2.92706	−	7.06656i	−0.263924	−	0.637170i
$124$	−1.77362	+	16.5410i	−0.159276	+	1.48543i
$125$	−2.10699	+	10.9800i	−0.188455	+	0.982082i
$126$	−0.848253	−	0.944070i	−0.0755684	−	0.0841044i
$127$	−6.05248	−	6.05248i	−0.537071	−	0.537071i	0.385597	−	0.922667i	$-0.373996\pi$
$127$	−6.05248	−	6.05248i	−0.537071	−	0.537071i	−0.922667	+	0.385597i	$0.873996\pi$
$128$	−4.13192	+	10.5322i	−0.365213	+	0.930924i
$129$			6.35143i			0.559212i
$130$	−5.19698	−	8.71144i	−0.455805	−	0.764044i
$131$	2.64754	+	6.39173i	0.231317	+	0.558448i	0.996333	−	0.0855634i	$-0.0272690\pi$
$131$	2.64754	+	6.39173i	0.231317	+	0.558448i	−0.765016	+	0.644011i	$0.777269\pi$
$132$	−1.54894	−	1.92101i	−0.134818	−	0.167202i
$133$	4.27097	−	1.76909i	0.370340	−	0.153400i
$134$	5.13009	−	10.7265i	0.443172	−	0.926627i
$135$	−10.6847	−	2.10030i	−0.919594	−	0.180765i
$136$	−2.82769	+	2.04087i	−0.242472	+	0.175003i
$137$			16.7223i			1.42868i	0.699799	+	0.714339i	$0.253273\pi$
$137$			16.7223i			1.42868i	−0.699799	+	0.714339i	$0.746727\pi$
$138$	−5.63028	+	11.7723i	−0.479281	+	1.00213i
$139$	6.45544	+	2.67393i	0.547543	+	0.226800i	0.639267	−	0.768985i	$-0.279238\pi$
$139$	6.45544	+	2.67393i	0.547543	+	0.226800i	−0.0917240	+	0.995784i	$0.529238\pi$
$140$	7.72196	−	9.28759i	0.652624	−	0.784944i
$141$	2.53732	+	6.12563i	0.213681	+	0.515871i
$142$	−15.0396	−	16.7385i	−1.26210	−	1.40466i
$143$	−1.53312	−	1.53312i	−0.128206	−	0.128206i
$144$	−0.719219	−	1.11774i	−0.0599349	−	0.0931450i
$145$	4.52846	−	23.0373i	0.376068	−	1.91315i
$146$	0.450298	−	8.42314i	0.0372669	−	0.697104i
$147$	0.205654	−	0.496492i	0.0169620	−	0.0409499i
$148$	−3.10863	−	10.5760i	−0.255528	−	0.869341i
$149$	−0.832989	+	2.01101i	−0.0682411	+	0.164749i	−0.954320	−	0.298785i	$-0.903419\pi$
$149$	−0.832989	+	2.01101i	−0.0682411	+	0.164749i	0.886079	+	0.463534i	$0.153419\pi$
$150$	−0.630963	+	12.8925i	−0.0515179	+	1.05267i
$151$	−9.29921	−	9.29921i	−0.756759	−	0.756759i	0.218972	−	0.975731i	$-0.429730\pi$
$151$	−9.29921	−	9.29921i	−0.756759	−	0.756759i	−0.975731	+	0.218972i	$0.929730\pi$
$152$	4.71106	−	1.11536i	0.382117	−	0.0904674i
$153$		−	0.409686i		−	0.0331211i
$154$	1.11387	−	2.32900i	0.0897586	−	0.187676i
$155$	10.2984	−	15.4881i	0.827187	−	1.24403i
$156$	−7.35103	−	9.11681i	−0.588554	−	0.729929i
$157$	−3.62587	+	8.75361i	−0.289376	+	0.698615i	−0.999988	−	0.00496954i	$-0.998418\pi$
$157$	−3.62587	+	8.75361i	−0.289376	+	0.698615i	0.710612	+	0.703584i	$0.248418\pi$
$158$	3.59916	+	0.192410i	0.286334	+	0.0153073i
$159$	22.7409			1.80347
$160$	9.53501	−	8.31166i	0.753809	−	0.657094i
$161$	−13.6521			−1.07594
$162$	−13.9616	−	0.746383i	−1.09693	−	0.0586414i
$163$	6.07590	−	14.6685i	0.475902	−	1.14893i	−0.485613	−	0.874174i	$-0.661404\pi$
$163$	6.07590	−	14.6685i	0.475902	−	1.14893i	0.961515	−	0.274754i	$-0.0885965\pi$
$164$	6.52364	−	5.26012i	0.509411	−	0.410746i
$165$	0.544343	+	2.70472i	0.0423770	+	0.210562i
$166$	−10.0371	+	20.9865i	−0.779028	+	1.62887i
$167$			3.15784i			0.244361i	0.992508	+	0.122180i	$0.0389886\pi$
$167$			3.15784i			0.244361i	−0.992508	+	0.122180i	$0.961011\pi$
$168$	7.32349	−	11.8669i	0.565020	−	0.915548i
$169$	1.91642	+	1.91642i	0.147417	+	0.147417i
$170$	3.85785	−	0.564108i	0.295884	−	0.0432651i
$171$	−0.217654	+	0.525464i	−0.0166444	+	0.0401833i
$172$	−6.67631	+	1.96239i	−0.509064	+	0.149631i
$173$	−0.112640	+	0.271938i	−0.00856388	+	0.0206750i	−0.928104	−	0.372322i	$-0.878562\pi$
$173$	−0.112640	+	0.271938i	−0.00856388	+	0.0206750i	0.919540	+	0.392997i	$0.128562\pi$
$174$	1.44701	−	27.0674i	0.109698	−	2.05197i
$175$	−12.4527	+	5.22397i	−0.941336	+	0.394895i
$176$	1.54069	−	2.22169i	0.116134	−	0.167466i
$177$	−3.39406	−	3.39406i	−0.255113	−	0.255113i
$178$	10.8765	+	12.1051i	0.815227	+	0.907314i
$179$	5.70712	+	13.7782i	0.426570	+	1.02983i	0.980367	+	0.197180i	$0.0631784\pi$
$179$	5.70712	+	13.7782i	0.426570	+	1.02983i	−0.553797	+	0.832652i	$0.686822\pi$
$180$	0.136204	+	1.47977i	0.0101521	+	0.110296i
$181$	−19.6142	−	8.12445i	−1.45791	−	0.603886i	−0.493843	−	0.869551i	$-0.664408\pi$
$181$	−19.6142	−	8.12445i	−1.45791	−	0.603886i	−0.964065	+	0.265665i	$0.914408\pi$
$182$	5.28629	−	11.0531i	0.391846	−	0.819309i
$183$			19.6486i			1.45246i
$184$	−14.1141	−	2.28100i	−1.04050	−	0.168157i
$185$	−2.37715	+	12.0931i	−0.174771	+	0.889103i
$186$	9.26485	−	19.3718i	0.679332	−	1.42041i
$187$	0.769916	−	0.318910i	0.0563018	−	0.0233210i
$188$	−5.65500	+	4.55972i	−0.412434	+	0.332552i
$189$	−5.03321	−	12.1512i	−0.366112	−	0.883872i
$190$	−5.24779	−	1.32604i	−0.380714	−	0.0962010i
$191$			18.2677i			1.32180i	0.750473	+	0.660901i	$0.229826\pi$
$191$			18.2677i			1.32180i	−0.750473	+	0.660901i	$0.770174\pi$
$192$	9.55401	−	11.0448i	0.689501	−	0.797089i
$193$	−1.72215	−	1.72215i	−0.123963	−	0.123963i	0.642404	−	0.766366i	$-0.277937\pi$
$193$	−1.72215	−	1.72215i	−0.123963	−	0.123963i	−0.766366	+	0.642404i	$0.777937\pi$
$194$	8.29400	+	9.23088i	0.595475	+	0.662738i
$195$	2.58337	+	12.8362i	0.184999	+	0.919221i
$196$	0.585427	+	0.0627729i	0.0418162	+	0.00448378i
$197$	−7.05216	−	17.0254i	−0.502446	−	1.21301i	−0.948148	−	0.317830i	$-0.897046\pi$
$197$	−7.05216	−	17.0254i	−0.502446	−	1.21301i	0.445702	−	0.895181i	$-0.352954\pi$
$198$	0.105711	+	0.299518i	0.00751258	+	0.0212858i
$199$	−9.49661	−	9.49661i	−0.673197	−	0.673197i	0.285255	−	0.958452i	$-0.407922\pi$
$199$	−9.49661	−	9.49661i	−0.673197	−	0.673197i	−0.958452	+	0.285255i	$0.907922\pi$
$200$	−13.7469	+	3.32012i	−0.972051	+	0.234768i
$201$	−10.8525	+	10.8525i	−0.765473	+	0.765473i
$202$	14.8217	+	7.08869i	1.04285	+	0.498759i
$203$	26.1993	−	10.8521i	1.83883	−	0.761668i
$204$	4.31863	−	1.26939i	0.302365	−	0.0888749i
$205$	−9.18511	+	1.84856i	−0.641516	+	0.129109i
$206$	−0.0130359	+	0.243846i	−0.000908257	+	0.0169896i
$207$	1.18769	−	1.18769i	0.0825499	−	0.0825499i
$208$	7.31191	−	10.5438i	0.506989	−	0.731084i
$209$	−1.15692			−0.0800261
$210$	−13.3891	+	7.98755i	−0.923938	+	0.551194i
$211$	6.28135	−	2.60182i	0.432426	−	0.179117i	−0.155843	−	0.987782i	$-0.549809\pi$
$211$	6.28135	−	2.60182i	0.432426	−	0.179117i	0.588269	+	0.808665i	$0.299809\pi$
$212$	7.02620	+	23.9041i	0.482561	+	1.64174i
$213$	11.1155	+	26.8351i	0.761620	+	1.83871i
$214$	−19.1140	+	6.74606i	−1.30660	+	0.461151i
$215$	7.63402	+	1.50062i	0.520636	+	0.102342i
$216$	−3.17328	−	13.4033i	−0.215914	−	0.911981i
$217$	22.4651			1.52503
$218$	0.0529027	+	0.149892i	0.00358302	+	0.0101520i
$219$	−4.16667	+	10.0592i	−0.281558	+	0.679740i
$220$	−2.67489	+	1.40786i	−0.180341	+	0.0949177i
$221$	3.65391	−	1.51350i	0.245788	−	0.101809i
$222$	−0.759588	+	14.2086i	−0.0509802	+	0.953620i
$223$	−8.45074	+	8.45074i	−0.565904	+	0.565904i	−0.930978	−	0.365075i	$-0.881043\pi$
$223$	−8.45074	+	8.45074i	−0.565904	+	0.565904i	0.365075	+	0.930978i	$0.381043\pi$
$224$	14.7366	+	4.03161i	0.984629	+	0.269373i
$225$	0.628876	−	1.53781i	0.0419250	−	0.102521i
$226$	5.62674	+	6.26233i	0.374285	+	0.416564i
$227$	−13.0393	−	5.40106i	−0.865449	−	0.358481i	−0.0946127	−	0.995514i	$-0.530161\pi$
$227$	−13.0393	−	5.40106i	−0.865449	−	0.358481i	−0.770836	+	0.637034i	$0.780161\pi$
$228$	−6.21348	−	0.666246i	−0.411498	−	0.0441232i
$229$	4.62871	+	1.91727i	0.305874	+	0.126697i	0.530340	−	0.847785i	$-0.322064\pi$
$229$	4.62871	+	1.91727i	0.305874	+	0.126697i	−0.224467	+	0.974482i	$0.572064\pi$
$230$	12.8193	+	9.54862i	0.845283	+	0.629618i
$231$	−2.35635	+	2.35635i	−0.155036	+	0.155036i
$232$	28.8989	−	6.84191i	1.89731	−	0.449193i
$233$	−6.73184			−0.441018			−0.220509	−	0.975385i	$-0.570772\pi$
$233$	−6.73184			−0.441018			−0.220509	+	0.975385i	$0.570772\pi$
$234$	0.501691	+	1.42147i	0.0327966	+	0.0929243i
$235$	7.96209	−	1.60242i	0.519390	−	0.104530i
$236$	2.51901	−	4.61632i	0.163974	−	0.300497i
$237$	−4.29826	−	1.78040i	−0.279202	−	0.115649i
$238$	3.14741	+	3.50293i	0.204016	+	0.227061i
$239$		−	15.6416i		−	1.01177i	−0.862602	−	0.505884i	$-0.831166\pi$
$239$		−	15.6416i		−	1.01177i	0.862602	−	0.505884i	$-0.168834\pi$
$240$	−15.1767	+	6.02076i	−0.979654	+	0.388639i
$241$			2.53846i			0.163517i	0.996652	+	0.0817584i	$0.0260536\pi$
$241$			2.53846i			0.163517i	−0.996652	+	0.0817584i	$0.973946\pi$
$242$	11.0909	−	9.96528i	0.712953	−	0.640593i
$243$	3.17619	+	1.31562i	0.203752	+	0.0843970i
$244$	−20.6536	+	6.07077i	−1.32221	+	0.388641i
$245$	−0.548162	−	0.364486i	−0.0350208	−	0.0232862i
$246$	−10.2003	+	3.60010i	−0.650351	+	0.229534i
$247$	−5.49059			−0.349358
$248$	23.2252	+	3.75348i	1.47480	+	0.238346i
$249$	21.2329	−	21.2329i	1.34558	−	1.34558i
$250$	15.3469	+	3.80442i	0.970621	+	0.240613i
$251$	10.2862	+	4.26070i	0.649262	+	0.268933i	0.682912	−	0.730501i	$-0.260713\pi$
$251$	10.2862	+	4.26070i	0.649262	+	0.268933i	−0.0336503	+	0.999434i	$0.510713\pi$
$252$	−1.39725	+	1.12663i	−0.0880186	+	0.0709708i
$253$	3.15653	+	1.30748i	0.198449	+	0.0822003i
$254$	−9.00423	+	8.09036i	−0.564976	+	0.507634i
$255$	−4.93813	−	0.970691i	−0.309238	−	0.0607870i
$256$	14.5616	+	6.63022i	0.910100	+	0.414388i
$257$	−2.57063	+	2.57063i	−0.160352	+	0.160352i	−0.782722	−	0.622371i	$-0.786170\pi$
$257$	−2.57063	+	2.57063i	−0.160352	+	0.160352i	0.622371	+	0.782722i	$0.286170\pi$
$258$	8.96947	+	0.479505i	0.558415	+	0.0298527i
$259$	−13.7529	+	5.69665i	−0.854566	+	0.353973i
$260$	−12.6946	+	6.68149i	−0.787287	+	0.414368i
$261$	−1.33515	+	3.22334i	−0.0826438	+	0.199520i
$262$	9.22625	−	3.25630i	0.570000	−	0.201175i
$263$	1.07353			0.0661969			0.0330984	−	0.999452i	$-0.489463\pi$
$263$	1.07353			0.0661969			0.0330984	+	0.999452i	$0.489463\pi$
$264$	−2.82978	+	2.04238i	−0.174161	+	0.125700i
$265$	5.37288	−	27.3331i	0.330053	−	1.67906i
$266$	−2.17587	−	6.16501i	−0.133411	−	0.378001i
$267$	−8.03859	−	19.4069i	−0.491954	−	1.18768i
$268$	−14.7606	−	8.05450i	−0.901648	−	0.492007i
$269$	0.974714	−	0.403740i	0.0594293	−	0.0246164i	−0.352771	−	0.935710i	$-0.614760\pi$
$269$	0.974714	−	0.403740i	0.0594293	−	0.0246164i	0.412200	+	0.911093i	$0.364760\pi$
$270$	−3.77269	+	14.9304i	−0.229598	+	0.908633i
$271$	8.14790			0.494950			0.247475	−	0.968894i	$-0.420399\pi$
$271$	8.14790			0.494950			0.247475	+	0.968894i	$0.420399\pi$
$272$	2.66863	+	4.14733i	0.161810	+	0.251469i
$273$	−11.1829	+	11.1829i	−0.676819	+	0.676819i
$274$	23.6151	+	1.26246i	1.42664	+	0.0762678i
$275$	3.37951	−	0.0152332i	0.203792	−	0.000918599i
$276$	16.1998	+	8.83982i	0.975112	+	0.532095i
$277$	20.9992	−	8.69814i	1.26172	−	0.522621i	0.351282	−	0.936270i	$-0.385746\pi$
$277$	20.9992	−	8.69814i	1.26172	−	0.522621i	0.910436	+	0.413649i	$0.135746\pi$
$278$	4.26347	−	8.91448i	0.255706	−	0.534655i
$279$	−1.95439	+	1.95439i	−0.117006	+	0.117006i
$280$	−12.5329	−	11.6061i	−0.748986	−	0.693597i
$281$	−7.84595	−	7.84595i	−0.468050	−	0.468050i	0.433232	−	0.901282i	$-0.357373\pi$
$281$	−7.84595	−	7.84595i	−0.468050	−	0.468050i	−0.901282	+	0.433232i	$0.857373\pi$
$282$	8.84215	−	3.12074i	0.526542	−	0.185837i
$283$	2.15996	+	5.21462i	0.128397	+	0.309977i	0.974985	−	0.222272i	$-0.0713472\pi$
$283$	2.15996	+	5.21462i	0.128397	+	0.309977i	−0.846588	+	0.532248i	$0.821347\pi$
$284$	−24.7734	+	19.9752i	−1.47003	+	1.18531i
$285$	5.81797	+	3.86850i	0.344627	+	0.229150i
$286$	−2.28081	+	2.04933i	−0.134867	+	0.121179i
$287$	−8.00204	−	8.00204i	−0.472346	−	0.472346i
$288$	−1.63277	+	0.931295i	−0.0962117	+	0.0548771i
$289$		−	15.4799i		−	0.910581i
$290$	−32.1914	−	8.13429i	−1.89034	−	0.477662i
$291$	−6.12993	−	14.7990i	−0.359343	−	0.867531i
$292$	−11.8611	−	1.27182i	−0.694120	−	0.0744276i
$293$	−0.429806	+	0.178031i	−0.0251095	+	0.0104007i	−0.395203	−	0.918594i	$-0.629326\pi$
$293$	−0.429806	+	0.178031i	−0.0251095	+	0.0104007i	0.370093	+	0.928995i	$0.379326\pi$
$294$	−0.685618	−	0.327906i	−0.0399860	−	0.0191239i
$295$	−4.88134	+	3.27754i	−0.284203	+	0.190826i
$296$	−15.1701	+	3.59156i	−0.881743	+	0.208755i
$297$			3.29154i			0.190994i
$298$	2.77706	+	1.32817i	0.160871	+	0.0769387i
$299$	14.9804	+	6.20509i	0.866340	+	0.358850i
$300$	18.1591	+	1.86437i	1.04842	+	0.107639i
$301$	3.59612	+	8.68181i	0.207277	+	0.500411i
$302$	−13.8344	+	12.4303i	−0.796079	+	0.715282i
$303$	−14.9958	−	14.9958i	−0.861485	−	0.861485i
$304$	−1.21944	−	6.73715i	−0.0699397	−	0.386402i
$305$	23.6163	+	4.64227i	1.35227	+	0.265816i
$306$	−0.578557	−	0.0309295i	−0.0330739	−	0.00176812i
$307$	−3.06435	+	7.39799i	−0.174892	+	0.422226i	−0.986882	−	0.161446i	$-0.948384\pi$
$307$	−3.06435	+	7.39799i	−0.174892	+	0.422226i	0.811990	+	0.583671i	$0.198384\pi$
$308$	−3.20491	−	1.74884i	−0.182617	−	0.0996494i
$309$	0.120623	−	0.291211i	0.00686202	−	0.0165664i
$310$	−21.0947	−	15.7126i	−1.19810	−	0.892418i
$311$	−5.30099	−	5.30099i	−0.300592	−	0.300592i	0.540654	−	0.841245i	$-0.318177\pi$
$311$	−5.30099	−	5.30099i	−0.300592	−	0.300592i	−0.841245	+	0.540654i	$0.818177\pi$
$312$	−13.4297	+	9.69283i	−0.760307	+	0.548748i
$313$		−	23.0333i		−	1.30192i	−0.759113	−	0.650959i	$-0.774367\pi$
$313$		−	23.0333i		−	1.30192i	0.759113	−	0.650959i	$-0.225633\pi$
$314$	12.0881	+	5.78130i	0.682170	+	0.326257i
$315$	1.96729	−	0.395930i	0.110844	−	0.0223081i
$316$	0.543442	−	5.06820i	0.0305710	−	0.285108i
$317$	0.450652	−	1.08797i	0.0253111	−	0.0611064i	−0.910719	−	0.413027i	$-0.864471\pi$
$317$	0.450652	−	1.08797i	0.0253111	−	0.0611064i	0.936030	+	0.351921i	$0.114471\pi$
$318$	1.71684	−	32.1146i	0.0962754	−	1.80090i
$319$	−7.09689			−0.397350
$320$	−11.0178	−	14.0928i	−0.615916	−	0.787812i
$321$	26.1637			1.46032
$322$	−1.03067	+	19.2795i	−0.0574373	+	1.07440i
$323$	0.807598	−	1.94971i	0.0449360	−	0.108485i
$324$	−2.10808	+	19.6602i	−0.117116	+	1.09223i
$325$	16.0387	−	0.0722947i	0.889666	−	0.00401019i
$326$	−20.2562	−	9.68778i	−1.12188	−	0.536557i
$327$		−	0.205176i		−	0.0113463i
$328$	−6.93582	−	9.60978i	−0.382967	−	0.530612i
$329$	6.93655	+	6.93655i	0.382425	+	0.382425i
$330$	3.86070	−	0.564524i	0.212524	−	0.0310760i
$331$	−7.03561	+	16.9855i	−0.386712	+	0.933606i	0.603919	+	0.797045i	$0.293605\pi$
$331$	−7.03561	+	16.9855i	−0.386712	+	0.933606i	−0.990632	+	0.136561i	$0.956395\pi$
$332$	28.8793	+	15.7587i	1.58496	+	0.864872i
$333$	0.700868	−	1.69205i	0.0384074	−	0.0927236i
$334$	4.45949	+	0.238403i	0.244012	+	0.0130448i
$335$	10.4799	+	15.6080i	0.572578	+	0.852757i
$336$	−16.2055	−	11.2381i	−0.884080	−	0.613089i
$337$	−3.21523	−	3.21523i	−0.175145	−	0.175145i	0.614091	−	0.789235i	$-0.289523\pi$
$337$	−3.21523	−	3.21523i	−0.175145	−	0.175145i	−0.789235	+	0.614091i	$0.789523\pi$
$338$	2.85104	−	2.56167i	0.155076	−	0.139337i
$339$	−4.15861	−	10.0398i	−0.225865	−	0.545286i
$340$	−0.505381	−	5.49063i	−0.0274081	−	0.297771i
$341$	−5.19419	−	2.15150i	−0.281281	−	0.116510i
$342$	0.725627	+	0.347041i	0.0392374	+	0.0187658i
$343$			18.1106i			0.977880i
$344$	2.26724	+	9.57641i	0.122242	+	0.516326i
$345$	−11.5017	−	17.1298i	−0.619230	−	0.922238i
$346$	0.375526	+	0.179600i	0.0201884	+	0.00965538i
$347$	−18.2436	+	7.55673i	−0.979366	+	0.405667i	−0.814191	−	0.580598i	$-0.802819\pi$
$347$	−18.2436	+	7.55673i	−0.979366	+	0.405667i	−0.165175	+	0.986264i	$0.552819\pi$
$348$	−38.1152	−	4.08693i	−2.04319	−	0.219083i
$349$	−4.68825	−	11.3184i	−0.250956	−	0.605861i	0.747326	−	0.664458i	$-0.231337\pi$
$349$	−4.68825	−	11.3184i	−0.250956	−	0.605861i	−0.998282	+	0.0585964i	$0.981337\pi$
$350$	6.43714	+	17.9801i	0.344080	+	0.961075i
$351$			15.6212i			0.833796i
$352$	−3.02115	−	2.34349i	−0.161028	−	0.124908i
$353$	−23.9350	−	23.9350i	−1.27393	−	1.27393i	−0.944007	−	0.329925i	$-0.892976\pi$
$353$	−23.9350	−	23.9350i	−1.27393	−	1.27393i	−0.329925	−	0.944007i	$-0.607024\pi$
$354$	−5.04932	+	4.53684i	−0.268368	+	0.241130i
$355$	34.8803	−	7.01989i	1.85126	−	0.372577i
$356$	17.9159	−	14.4459i	0.949540	−	0.765629i
$357$	−2.32619	−	5.61591i	−0.123115	−	0.297226i
$358$	19.8884	−	7.01939i	1.05114	−	0.370986i
$359$	5.41896	+	5.41896i	0.286002	+	0.286002i	0.835497	−	0.549495i	$-0.185180\pi$
$359$	5.41896	+	5.41896i	0.286002	+	0.286002i	−0.549495	+	0.835497i	$0.685180\pi$
$360$	2.10001	−	0.0806312i	0.110680	−	0.00424964i
$361$	11.3634	−	11.3634i	0.598072	−	0.598072i
$362$	−12.9541	+	27.0857i	−0.680853	+	1.42359i
$363$	−17.7810	+	7.36514i	−0.933262	+	0.386570i
$364$	−15.2100	−	8.29974i	−0.797222	−	0.435024i
$365$	11.1061	+	7.38472i	0.581321	+	0.386534i
$366$	27.7476	+	1.48338i	1.45039	+	0.0775375i
$367$	−1.33244	+	1.33244i	−0.0695527	+	0.0695527i	−0.741027	−	0.671475i	$-0.765661\pi$
$367$	−1.33244	+	1.33244i	−0.0695527	+	0.0695527i	0.671475	+	0.741027i	$0.265661\pi$
$368$	−4.28677	+	19.7596i	−0.223463	+	1.03004i
$369$	1.39230			0.0724802
$370$	16.8984	+	4.26998i	0.878505	+	0.221986i
$371$	31.0847	−	12.8757i	1.61384	−	0.668472i
$372$	−26.6574	−	14.5463i	−1.38212	−	0.754189i
$373$	7.61514	+	18.3846i	0.394297	+	0.951917i	0.988992	+	0.147966i	$0.0472726\pi$
$373$	7.61514	+	18.3846i	0.394297	+	0.951917i	−0.594696	+	0.803951i	$0.702727\pi$
$374$	−0.392238	−	1.11135i	−0.0202821	−	0.0574665i
$375$	−17.0459	−	11.2238i	−0.880247	−	0.579592i
$376$	6.01230	+	8.33022i	0.310061	+	0.429598i
$377$	−33.6808			−1.73465
$378$	−17.5399	+	6.19051i	−0.902156	+	0.318406i
$379$	−1.22805	+	2.96478i	−0.0630807	+	0.152290i	−0.952277	−	0.305236i	$-0.901265\pi$
$379$	−1.22805	+	2.96478i	−0.0630807	+	0.152290i	0.889196	+	0.457527i	$0.151265\pi$
$380$	−2.26881	+	7.31080i	−0.116388	+	0.375036i
$381$	14.4356	−	5.97942i	0.739558	−	0.306335i
$382$	25.7976	+	1.37913i	1.31992	+	0.0705624i
$383$	−12.8700	+	12.8700i	−0.657627	+	0.657627i	−0.954818	−	0.297191i	$-0.903950\pi$
$383$	−12.8700	+	12.8700i	−0.657627	+	0.657627i	0.297191	+	0.954818i	$0.403950\pi$
$384$	−14.8761	−	14.3260i	−0.759144	−	0.731069i
$385$	2.27546	+	3.38890i	0.115968	+	0.172714i
$386$	−2.56203	+	2.30200i	−0.130404	+	0.117169i
$387$	−1.06814	−	0.442437i	−0.0542965	−	0.0224904i
$388$	13.6620	−	11.0159i	0.693582	−	0.559246i
$389$	−3.47302	−	1.43857i	−0.176089	−	0.0729386i	0.292897	−	0.956144i	$-0.405381\pi$
$389$	−3.47302	−	1.43857i	−0.176089	−	0.0729386i	−0.468986	+	0.883205i	$0.655381\pi$
$390$	18.3223	−	2.67915i	0.927786	−	0.135664i
$391$	−4.40686	+	4.40686i	−0.222865	+	0.222865i
$392$	0.132845	−	0.822000i	0.00670968	−	0.0415173i
$393$	−12.6291			−0.637056
$394$	−24.5757	+	8.67369i	−1.23810	+	0.436974i
$395$	−3.15545	+	4.74558i	−0.158768	+	0.238776i
$396$	0.430959	−	0.126673i	0.0216565	−	0.00636556i
$397$	−11.4195	−	4.73012i	−0.573129	−	0.237398i	0.0772446	−	0.997012i	$-0.475388\pi$
$397$	−11.4195	−	4.73012i	−0.573129	−	0.237398i	−0.650374	+	0.759614i	$0.725388\pi$
$398$	−14.1280	+	12.6941i	−0.708174	+	0.636299i
$399$			8.43882i			0.422470i
$400$	3.65084	+	19.6640i	0.182542	+	0.983198i
$401$		−	19.6778i		−	0.982660i	−0.870973	−	0.491330i	$-0.836511\pi$
$401$		−	19.6778i		−	0.982660i	0.870973	−	0.491330i	$-0.163489\pi$
$402$	14.5065	+	16.1451i	0.723518	+	0.805245i
$403$	−24.6509	−	10.2107i	−1.22795	−	0.508633i
$404$	11.1296	−	20.3960i	0.553718	−	1.01474i
$405$	12.2404	−	18.4087i	0.608230	−	0.914737i
$406$	−13.3474	−	37.8178i	−0.662419	−	1.87687i
$407$	3.72541			0.184662
$408$	−1.46659	−	6.19459i	−0.0726069	−	0.306678i
$409$	−5.29838	+	5.29838i	−0.261988	+	0.261988i	−0.825861	−	0.563873i	$-0.809311\pi$
$409$	−5.29838	+	5.29838i	−0.261988	+	0.261988i	0.563873	+	0.825861i	$0.309311\pi$
$410$	1.91710	+	13.1107i	0.0946787	+	0.647494i
$411$	−28.2021	−	11.6817i	−1.39111	−	0.576215i
$412$	0.343375	+	0.0368186i	0.0169169	+	0.00181392i
$413$	−6.56105	−	2.71767i	−0.322848	−	0.133728i
$414$	−1.58758	−	1.76691i	−0.0780254	−	0.0868390i
$415$	−20.5040	−	30.5373i	−1.00650	−	1.49901i
$416$	−14.3380	−	11.1219i	−0.702976	−	0.545294i
$417$	−9.01917	+	9.01917i	−0.441671	+	0.441671i
$418$	−0.0873427	+	1.63380i	−0.00427207	+	0.0799120i
$419$	−18.1722	+	7.52715i	−0.887768	+	0.367726i	−0.779504	−	0.626397i	$-0.784529\pi$
$419$	−18.1722	+	7.52715i	−0.887768	+	0.367726i	−0.108264	+	0.994122i	$0.534529\pi$
$420$	10.2692	+	19.5111i	0.501085	+	0.952045i
$421$	−12.8031	+	30.9094i	−0.623984	+	1.50643i	0.223003	+	0.974818i	$0.428414\pi$
$421$	−12.8031	+	30.9094i	−0.623984	+	1.50643i	−0.846987	+	0.531613i	$0.821586\pi$
$422$	−3.20007	−	9.06693i	−0.155777	−	0.441371i
$423$	−1.20691			−0.0586821
$424$	34.2877	−	8.11772i	1.66516	−	0.394231i
$425$	−2.33342	+	5.70598i	−0.113187	+	0.276781i
$426$	38.7357	−	13.6713i	1.87675	−	0.662377i
$427$	11.1248	+	26.8577i	0.538369	+	1.29974i
$428$	8.08374	+	27.5020i	0.390742	+	1.32936i
$429$	3.65661	−	1.51462i	0.176543	−	0.0731263i
$430$	2.69551	−	10.6674i	0.129989	−	0.514430i
$431$	20.6756			0.995910			0.497955	−	0.867203i	$-0.334084\pi$
$431$	20.6756			0.995910			0.497955	+	0.867203i	$0.334084\pi$
$432$	−19.1677	+	3.46940i	−0.922207	+	0.166922i
$433$	−21.6851	+	21.6851i	−1.04212	+	1.04212i	−0.0430440	+	0.999073i	$0.513706\pi$
$433$	−21.6851	+	21.6851i	−1.04212	+	1.04212i	−0.999073	+	0.0430440i	$0.986294\pi$
$434$	1.69602	−	31.7252i	0.0814114	−	1.52286i
$435$	35.6890	+	23.7305i	1.71116	+	1.13779i
$436$	0.215671	−	0.0633928i	0.0103288	−	0.00303596i
$437$	7.99350	−	3.31102i	0.382381	−	0.158387i
$438$	13.8911	+	6.64359i	0.663740	+	0.317443i
$439$	7.73307	−	7.73307i	0.369079	−	0.369079i	−0.498062	−	0.867141i	$-0.665955\pi$
$439$	7.73307	−	7.73307i	0.369079	−	0.369079i	0.867141	+	0.498062i	$0.165955\pi$
$440$	1.78623	+	3.88375i	0.0851552	+	0.185151i
$441$	0.0691707	+	0.0691707i	0.00329384	+	0.00329384i
$442$	−1.86150	−	5.27430i	−0.0885427	−	0.250873i
$443$	7.13735	+	17.2311i	0.339106	+	0.818674i	0.997802	+	0.0662648i	$0.0211082\pi$
$443$	7.13735	+	17.2311i	0.339106	+	0.818674i	−0.658696	+	0.752409i	$0.728892\pi$
$444$	20.0080	+	2.14538i	0.949539	+	0.101815i
$445$	−25.2251	+	5.07671i	−1.19578	+	0.240659i
$446$	11.2961	+	12.5721i	0.534887	+	0.595306i
$447$	−2.80967	−	2.80967i	−0.132893	−	0.132893i
$448$	6.80598	−	20.5066i	0.321552	−	0.968845i
$449$		−	5.31985i		−	0.251059i	−0.992090	−	0.125530i	$-0.959937\pi$
$449$		−	5.31985i		−	0.251059i	0.992090	−	0.125530i	$-0.0400630\pi$
$450$	−2.12421	−	1.00419i	−0.100136	−	0.0473382i
$451$	1.08380	+	2.61653i	0.0510342	+	0.123207i
$452$	9.26844	−	7.47329i	0.435951	−	0.351514i
$453$	22.1793	−	9.18696i	1.04207	−	0.431641i
$454$	−8.61176	+	18.0063i	−0.404170	+	0.845078i
$455$	10.7990	+	16.0832i	0.506264	+	0.753994i
$456$	−1.40996	+	8.72436i	−0.0660275	+	0.408556i
$457$		−	23.0187i		−	1.07677i	−0.842699	−	0.538384i	$-0.819035\pi$
$457$		−	23.0187i		−	1.07677i	0.842699	−	0.538384i	$-0.180965\pi$
$458$	3.05701	−	6.39190i	0.142845	−	0.298674i
$459$	−5.54709	−	2.29768i	−0.258916	−	0.107246i
$460$	14.4523	−	17.3826i	0.673844	−	0.810466i
$461$	9.54926	+	23.0539i	0.444753	+	1.07373i	0.974261	+	0.225424i	$0.0723767\pi$
$461$	9.54926	+	23.0539i	0.444753	+	1.07373i	−0.529508	+	0.848305i	$0.677623\pi$
$462$	3.14973	+	3.50552i	0.146539	+	0.163092i
$463$	25.9171	+	25.9171i	1.20447	+	1.20447i	0.972793	+	0.231676i	$0.0744210\pi$
$463$	25.9171	+	25.9171i	1.20447	+	1.20447i	0.231676	+	0.972793i	$0.425579\pi$
$464$	−7.48038	−	41.3275i	−0.347268	−	1.91858i
$465$	18.9265	+	28.1878i	0.877696	+	1.30718i
$466$	−0.508225	+	9.50669i	−0.0235430	+	0.440389i
$467$	2.21484	−	5.34710i	0.102491	−	0.247434i	−0.864313	−	0.502954i	$-0.832247\pi$
$467$	2.21484	−	5.34710i	0.102491	−	0.247434i	0.966804	+	0.255520i	$0.0822466\pi$
$468$	2.04527	−	0.601172i	0.0945426	−	0.0277892i
$469$	−8.68972	+	20.9788i	−0.401254	+	0.968713i
$470$	−1.66183	−	11.3650i	−0.0766546	−	0.524229i
$471$	−12.2300	−	12.2300i	−0.563531	−	0.563531i
$472$	−6.32898	−	3.90585i	−0.291315	−	0.179781i
$473$		−	2.35174i		−	0.108133i
$474$	−2.83877	+	5.93557i	−0.130389	+	0.272630i
$475$	6.02428	−	6.07883i	0.276413	−	0.278916i
$476$	5.18445	−	4.18031i	0.237629	−	0.191604i
$477$	−1.58412	+	3.82440i	−0.0725318	+	0.175107i
$478$	−22.0890	−	1.18087i	−1.01033	−	0.0540117i
$479$	30.8819			1.41103			0.705516	−	0.708694i	$-0.250715\pi$
$479$	30.8819			1.41103			0.705516	+	0.708694i	$0.250715\pi$
$480$	7.35673	+	21.8871i	0.335787	+	0.999004i
$481$	17.6802			0.806150
$482$	3.58481	+	0.191643i	0.163284	+	0.00872909i
$483$	9.53698	−	23.0243i	0.433948	−	1.04764i
$484$	−13.2356	−	16.4149i	−0.601619	−	0.746133i
$485$	−19.2357	+	3.87131i	−0.873448	+	0.175787i
$486$	2.09770	−	4.38608i	0.0951537	−	0.198956i
$487$		−	5.84893i		−	0.265040i	−0.991180	−	0.132520i	$-0.957693\pi$
$487$		−	5.84893i		−	0.265040i	0.991180	−	0.132520i	$-0.0423069\pi$
$488$	7.01386	+	29.6252i	0.317503	+	1.34107i
$489$	20.4940	+	20.4940i	0.926772	+	0.926772i
$490$	−0.556110	+	0.746596i	−0.0251225	+	0.0337278i
$491$	−5.66495	+	13.6764i	−0.255656	+	0.617207i	−0.998642	−	0.0520993i	$-0.983409\pi$
$491$	−5.66495	+	13.6764i	−0.255656	+	0.617207i	0.742986	+	0.669307i	$0.233409\pi$
$492$	4.31396	+	14.6767i	0.194488	+	0.661677i
$493$	4.95403	−	11.9601i	0.223118	−	0.538655i
$494$	−0.414516	+	7.75380i	−0.0186499	+	0.348860i
$495$	−0.492779	−	0.0968659i	−0.0221488	−	0.00435380i
$496$	7.05405	−	32.5152i	0.316736	−	1.45998i
$497$	30.3876	+	30.3876i	1.36307	+	1.36307i
$498$	−28.3821	−	31.5881i	−1.27183	−	1.41550i
$499$	−6.93134	−	16.7337i	−0.310289	−	0.749105i	−0.999694	−	0.0247285i	$-0.992128\pi$
$499$	−6.93134	−	16.7337i	−0.310289	−	0.749105i	0.689405	−	0.724376i	$-0.257872\pi$
$500$	6.53122	−	21.3856i	0.292085	−	0.956392i
$501$	−5.32569	−	2.20597i	−0.237934	−	0.0985556i
$502$	6.79351	−	14.2045i	0.303209	−	0.633979i
$503$		−	14.7883i		−	0.659379i	−0.944089	−	0.329690i	$-0.893056\pi$
$503$		−	14.7883i		−	0.659379i	0.944089	−	0.329690i	$-0.106944\pi$
$504$	1.48553	+	2.05825i	0.0661709	+	0.0916818i
$505$	−21.5669	+	14.4810i	−0.959716	+	0.644395i
$506$	2.08472	−	4.35893i	0.0926770	−	0.193778i
$507$	−4.57079	+	1.89328i	−0.202996	+	0.0840836i
$508$	10.7454	+	13.3265i	0.476750	+	0.591269i
$509$	7.35468	+	17.7558i	0.325990	+	0.787010i	0.998882	+	0.0472694i	$0.0150519\pi$
$509$	7.35468	+	17.7558i	0.325990	+	0.787010i	−0.672892	+	0.739741i	$0.734948\pi$
$510$	−1.74361	+	6.90033i	−0.0772086	+	0.305552i
$511$			16.1092i			0.712627i
$512$	10.4625	−	20.0633i	0.462382	−	0.886681i
$513$	5.89402	+	5.89402i	0.260227	+	0.260227i
$514$	3.43617	+	3.82431i	0.151563	+	0.168683i
$515$	−0.321517	−	0.213784i	−0.0141677	−	0.00942047i
$516$	1.35431	−	12.6305i	0.0596203	−	0.556025i
$517$	−0.939490	−	2.26813i	−0.0413187	−	0.0997523i
$518$	7.00651	+	19.8519i	0.307848	+	0.872243i
$519$	−0.379936	−	0.379936i	−0.0166773	−	0.0166773i
$520$	8.47719	+	18.4317i	0.371749	+	0.808285i
$521$	1.98220	−	1.98220i	0.0868416	−	0.0868416i	−0.662352	−	0.749193i	$-0.730441\pi$
$521$	1.98220	−	1.98220i	0.0868416	−	0.0868416i	0.749193	+	0.662352i	$0.230441\pi$
$522$	4.45119	+	2.12885i	0.194824	+	0.0931770i
$523$	−14.7272	+	6.10020i	−0.643975	+	0.266743i	−0.680677	−	0.732583i	$-0.738314\pi$
$523$	−14.7272	+	6.10020i	−0.643975	+	0.266743i	0.0367029	+	0.999326i	$0.488314\pi$
$524$	−3.90200	−	13.2751i	−0.170459	−	0.579927i
$525$	−0.111114	−	24.6508i	−0.00484942	−	1.07585i
$526$	0.0810470	−	1.51604i	0.00353382	−	0.0661025i
$527$	7.25167	−	7.25167i	0.315888	−	0.315888i
$528$	2.67060	+	4.15039i	0.116223	+	0.180623i
$529$	−2.55118			−0.110921
$530$	−38.1941	−	9.65109i	−1.65904	−	0.419217i
$531$	0.807217	−	0.334360i	0.0350302	−	0.0145100i
$532$	−8.87047	+	2.60732i	−0.384584	+	0.113042i
$533$	5.14356	+	12.4177i	0.222792	+	0.537869i
$534$	−28.0132	+	9.88695i	−1.21225	+	0.427850i
$535$	6.18158	−	31.4471i	0.267253	−	1.35958i
$536$	−12.4889	+	20.2368i	−0.539438	+	0.874097i
$537$	−27.2238			−1.17479
$538$	−0.496573	−	1.40697i	−0.0214088	−	0.0606587i
$539$	−0.0761471	+	0.183835i	−0.00327989	+	0.00791835i
$540$	20.7998	+	6.45495i	0.895080	+	0.277777i
$541$	−19.8883	+	8.23801i	−0.855065	+	0.354180i	−0.766776	−	0.641915i	$-0.778140\pi$
$541$	−19.8883	+	8.23801i	−0.855065	+	0.354180i	−0.0882896	+	0.996095i	$0.528140\pi$
$542$	0.615131	−	11.5064i	0.0264221	−	0.494244i
$543$	27.4038	−	27.4038i	1.17601	−	1.17601i
$544$	6.05832	−	3.45553i	0.259748	−	0.148155i
$545$	−0.246609	−	0.0484760i	−0.0105636	−	0.00207648i
$546$	14.9482	+	16.6367i	0.639723	+	0.711985i
$547$	8.92158	+	3.69544i	0.381459	+	0.158006i	0.565169	−	0.824975i	$-0.308811\pi$
$547$	8.92158	+	3.69544i	0.381459	+	0.158006i	−0.183710	+	0.982980i	$0.558811\pi$
$548$	3.56568	−	33.2539i	0.152318	−	1.42054i
$549$	−3.30435	−	1.36871i	−0.141026	−	0.0584150i
$550$	0.233626	−	4.77369i	0.00996185	−	0.203551i
$551$	−12.7081	+	12.7081i	−0.541383	+	0.541383i
$552$	13.7066	−	22.2099i	0.583391	−	0.945317i
$553$	−6.88336			−0.292710
$554$	−10.6981	−	30.3116i	−0.454521	−	1.28782i
$555$	−18.7344	−	12.4570i	−0.795232	−	0.528768i
$556$	−12.2671	−	6.69387i	−0.520242	−	0.283883i
$557$	−24.7586	−	10.2554i	−1.04906	−	0.434533i	−0.209501	−	0.977808i	$-0.567184\pi$
$557$	−24.7586	−	10.2554i	−1.04906	−	0.434533i	−0.839555	+	0.543275i	$0.817184\pi$
$558$	2.61243	+	2.90753i	0.110593	+	0.123085i
$559$		−	11.1610i		−	0.472061i
$560$	−17.3363	+	16.8228i	−0.732591	+	0.710891i
$561$			1.52124i			0.0642270i
$562$	−11.6724	+	10.4877i	−0.492369	+	0.442397i
$563$	10.9848	+	4.55007i	0.462955	+	0.191762i	0.601955	−	0.798530i	$-0.294389\pi$
$563$	10.9848	+	4.55007i	0.462955	+	0.191762i	−0.139000	+	0.990292i	$0.544389\pi$
$564$	−3.73955	−	12.7225i	−0.157463	−	0.535712i
$565$	−13.0497	+	2.62634i	−0.549005	+	0.110491i
$566$	7.52713	−	2.65661i	0.316389	−	0.111666i
$567$	26.7014			1.12135
$568$	26.3387	+	36.4930i	1.10515	+	1.53121i
$569$	−8.67743	+	8.67743i	−0.363777	+	0.363777i	−0.865201	−	0.501425i	$-0.832809\pi$
$569$	−8.67743	+	8.67743i	−0.363777	+	0.363777i	0.501425	+	0.865201i	$0.332809\pi$
$570$	5.90232	−	7.92406i	0.247221	−	0.331902i
$571$	−22.7263	−	9.41355i	−0.951067	−	0.393945i	−0.147435	−	0.989072i	$-0.547102\pi$
$571$	−22.7263	−	9.41355i	−0.951067	−	0.393945i	−0.803632	+	0.595127i	$0.797102\pi$
$572$	2.72186	+	3.37567i	0.113807	+	0.141144i
$573$	−30.8084	−	12.7613i	−1.28704	−	0.533110i
$574$	−11.9046	+	10.6963i	−0.496888	+	0.446457i
$575$	−23.3064	+	9.77713i	−0.971943	+	0.407734i
$576$	1.19190	+	2.37610i	0.0496627	+	0.0990041i
$577$	17.4616	−	17.4616i	0.726936	−	0.726936i	−0.243072	−	0.970008i	$-0.578155\pi$
$577$	17.4616	−	17.4616i	0.726936	−	0.726936i	0.970008	+	0.243072i	$0.0781552\pi$
$578$	−21.8606	−	1.16866i	−0.909283	−	0.0486100i
$579$	4.10744	−	1.70136i	0.170700	−	0.0707061i
$580$	−13.9175	+	44.8464i	−0.577894	+	1.86215i
$581$	17.0015	−	41.0454i	0.705343	−	1.70285i
$582$	−21.3618	+	7.53941i	−0.885477	+	0.312519i
$583$	−8.42025			−0.348731
$584$	−2.69152	+	16.6542i	−0.111376	+	0.689157i
$585$	−2.33866	−	0.459711i	−0.0966917	−	0.0190067i
$586$	0.218967	+	0.620411i	0.00904545	+	0.0256290i
$587$	5.48134	+	13.2331i	0.226239	+	0.546189i	0.995714	−	0.0924879i	$-0.0294819\pi$
$587$	5.48134	+	13.2331i	0.226239	+	0.546189i	−0.769475	+	0.638677i	$0.779482\pi$
$588$	−0.514829	+	0.943472i	−0.0212312	+	0.0389081i
$589$	−13.1536	+	5.44841i	−0.541986	+	0.224498i
$590$	4.26002	+	7.14085i	0.175382	+	0.293984i
$591$	33.6398			1.38376
$592$	3.92672	+	21.6943i	0.161387	+	0.891629i
$593$	4.62969	−	4.62969i	0.190119	−	0.190119i	−0.605629	−	0.795747i	$-0.707078\pi$
$593$	4.62969	−	4.62969i	0.190119	−	0.190119i	0.795747	+	0.605629i	$0.207078\pi$
$594$	4.64830	+	0.248497i	0.190722	+	0.0101959i
$595$	−7.29956	+	1.46908i	−0.299253	+	0.0602265i
$596$	2.08529	−	3.82148i	0.0854168	−	0.156534i
$597$	22.6501	−	9.38198i	0.927007	−	0.383979i
$598$	9.89377	−	20.6868i	0.404586	−	0.845948i
$599$	−1.79569	+	1.79569i	−0.0733701	+	0.0733701i	−0.742840	−	0.669469i	$-0.766521\pi$
$599$	−1.79569	+	1.79569i	−0.0733701	+	0.0733701i	0.669469	+	0.742840i	$0.266521\pi$
$600$	4.00379	−	25.5035i	0.163454	−	1.04117i
$601$	20.4305	+	20.4305i	0.833378	+	0.833378i	0.987977	−	0.154599i	$-0.0494085\pi$
$601$	20.4305	+	20.4305i	0.833378	+	0.833378i	−0.154599	+	0.987977i	$0.549409\pi$
$602$	12.5319	−	4.42300i	0.510763	−	0.180268i
$603$	−1.06911	−	2.58106i	−0.0435376	−	0.105109i
$604$	16.5096	+	20.4753i	0.671764	+	0.833128i
$605$	4.65139	+	23.1118i	0.189106	+	0.939627i
$606$	−22.3091	+	20.0449i	−0.906245	+	0.814267i
$607$	27.5521	+	27.5521i	1.11830	+	1.11830i	0.991990	+	0.126315i	$0.0403149\pi$
$607$	27.5521	+	27.5521i	1.11830	+	1.11830i	0.126315	+	0.991990i	$0.459685\pi$
$608$	−9.60625	+	1.21346i	−0.389585	+	0.0492125i
$609$			51.7661i			2.09767i
$610$	8.33873	−	33.0004i	0.337625	−	1.33615i
$611$	−4.45869	−	10.7642i	−0.180379	−	0.435474i
$612$	−0.0873570	+	0.814701i	−0.00353120	+	0.0329323i
$613$	30.5348	−	12.6479i	1.23329	−	0.510845i	0.331679	−	0.943392i	$-0.392385\pi$
$613$	30.5348	−	12.6479i	1.23329	−	0.510845i	0.901611	+	0.432547i	$0.142385\pi$
$614$	10.2161	+	4.88598i	0.412287	+	0.197182i
$615$	3.29886	−	16.7820i	0.133023	−	0.676717i
$616$	−2.71166	+	4.39393i	−0.109256	+	0.177037i
$617$		−	4.42953i		−	0.178326i	−0.996017	−	0.0891630i	$-0.971581\pi$
$617$		−	4.42953i		−	0.178326i	0.996017	−	0.0891630i	$-0.0284192\pi$
$618$	−0.402140	−	0.192329i	−0.0161764	−	0.00773661i
$619$	−30.4815	−	12.6258i	−1.22515	−	0.507476i	−0.326109	−	0.945332i	$-0.605738\pi$
$619$	−30.4815	−	12.6258i	−1.22515	−	0.507476i	−0.899045	+	0.437856i	$0.855738\pi$
$620$	−23.7819	+	28.6037i	−0.955104	+	1.14875i
$621$	−9.42010	−	22.7421i	−0.378016	−	0.912611i
$622$	−7.88625	+	7.08585i	−0.316210	+	0.284117i
$623$	−21.9760	−	21.9760i	−0.880450	−	0.880450i
$624$	12.6743	+	19.6972i	0.507378	+	0.788517i
$625$	−17.5176	+	17.8363i	−0.700704	+	0.713453i
$626$	−32.5275	−	1.73891i	−1.30006	−	0.0695009i
$627$	0.808194	−	1.95115i	0.0322762	−	0.0779216i
$628$	9.07693	−	16.6343i	0.362209	−	0.663781i
$629$	−2.60054	+	6.27827i	−0.103690	+	0.250331i
$630$	−0.410610	−	2.80810i	−0.0163591	−	0.111877i
$631$	−23.3294	−	23.3294i	−0.928729	−	0.928729i	0.0688946	−	0.997624i	$-0.478053\pi$
$631$	−23.3294	−	23.3294i	−0.928729	−	0.928729i	−0.997624	+	0.0688946i	$0.978053\pi$
$632$	−7.11627	−	1.15007i	−0.283070	−	0.0457475i
$633$			12.4111i			0.493295i
$634$	−1.50240	−	0.718546i	−0.0596681	−	0.0285371i
$635$	−3.77625	−	18.7634i	−0.149856	−	0.744603i
$636$	−45.2225	−	4.84902i	−1.79319	−	0.192276i
$637$	−0.361383	+	0.872456i	−0.0143185	+	0.0345680i
$638$	−0.535784	+	10.0222i	−0.0212119	+	0.396783i
$639$	−5.28724			−0.209160
$640$	−20.7336	+	14.4954i	−0.819568	+	0.572982i
$641$	3.01012			0.118892			0.0594462	−	0.998232i	$-0.481067\pi$
$641$	3.01012			0.118892			0.0594462	+	0.998232i	$0.481067\pi$
$642$	1.97525	−	36.9483i	0.0779567	−	1.45823i
$643$	−18.9288	+	45.6981i	−0.746478	+	1.80216i	−0.169252	+	0.985573i	$0.554135\pi$
$643$	−18.9288	+	45.6981i	−0.746478	+	1.80216i	−0.577226	+	0.816584i	$0.695865\pi$
$644$	27.1486	+	2.91103i	1.06981	+	0.114711i
$645$	−7.86370	+	11.8265i	−0.309633	+	0.465667i
$646$	−2.69241	−	1.28768i	−0.105931	−	0.0506632i
$647$			16.2673i			0.639535i	0.947496	+	0.319767i	$0.103605\pi$
$647$			16.2673i			0.639535i	−0.947496	+	0.319767i	$0.896395\pi$
$648$	27.6049	+	4.46128i	1.08442	+	0.175256i
$649$	1.25671	+	1.25671i	0.0493304	+	0.0493304i
$650$	1.10876	−	22.6552i	0.0434890	−	0.888611i
$651$	−15.6935	+	37.8874i	−0.615076	+	1.48492i
$652$	−15.2103	+	27.8743i	−0.595682	+	1.09164i
$653$	12.3397	−	29.7907i	0.482890	−	1.16580i	−0.475340	−	0.879802i	$-0.657675\pi$
$653$	12.3397	−	29.7907i	0.482890	−	1.16580i	0.958230	−	0.285998i	$-0.0923249\pi$
$654$	−0.289749	−	0.0154899i	−0.0113301	−	0.000605703i
$655$	−2.98383	+	15.1794i	−0.116588	+	0.593109i
$656$	−14.0945	+	9.06925i	−0.550299	+	0.354095i
$657$	−1.40144	−	1.40144i	−0.0546754	−	0.0546754i
$658$	10.3195	−	9.27210i	0.402294	−	0.361464i
$659$	−14.6392	−	35.3422i	−0.570264	−	1.37674i	−0.901331	−	0.433131i	$-0.857409\pi$
$659$	−14.6392	−	35.3422i	−0.570264	−	1.37674i	0.331067	−	0.943607i	$-0.392591\pi$
$660$	−0.505754	−	5.49468i	−0.0196864	−	0.213880i
$661$	−23.6151	−	9.78169i	−0.918521	−	0.380464i	−0.127208	−	0.991876i	$-0.540602\pi$
$661$	−23.6151	−	9.78169i	−0.918521	−	0.380464i	−0.791312	+	0.611412i	$0.790602\pi$
$662$	23.4557	+	11.2180i	0.911631	+	0.436000i
$663$			7.21960i			0.280386i
$664$	24.4347	−	39.5936i	0.948250	−	1.53653i
$665$	10.1429	+	1.99380i	0.393326	+	0.0773163i
$666$	−2.33659	−	1.11751i	−0.0905410	−	0.0433025i
$667$	49.0343	−	20.3107i	1.89862	−	0.786433i
$668$	0.673343	−	6.27967i	0.0260524	−	0.242968i
$669$	−8.34873	−	20.1556i	−0.322781	−	0.779261i
$670$	22.8328	−	13.6213i	0.882107	−	0.526238i
$671$		−	7.27525i		−	0.280858i
$672$	−17.0939	+	22.0369i	−0.659410	+	0.850091i
$673$	19.1889	+	19.1889i	0.739678	+	0.739678i	0.972516	−	0.232837i	$-0.0748010\pi$
$673$	19.1889	+	19.1889i	0.739678	+	0.739678i	−0.232837	+	0.972516i	$0.574801\pi$
$674$	−4.78327	+	4.29780i	−0.184245	+	0.165545i
$675$	−17.2947	−	17.1395i	−0.665675	−	0.659701i
$676$	−3.40235	−	4.21962i	−0.130860	−	0.162293i
$677$	−14.3707	−	34.6939i	−0.552310	−	1.33339i	−0.915739	−	0.401773i	$-0.868394\pi$
$677$	−14.3707	−	34.6939i	−0.552310	−	1.33339i	0.363429	−	0.931622i	$-0.381606\pi$
$678$	−14.4921	+	5.11482i	−0.556566	+	0.196434i
$679$	−16.7581	−	16.7581i	−0.643116	−	0.643116i
$680$	−7.79201	+	0.299179i	−0.298810	+	0.0114730i
$681$	18.2178	−	18.2178i	0.698106	−	0.698106i
$682$	−3.43049	+	7.17279i	−0.131360	+	0.274660i
$683$	23.4168	−	9.69955i	0.896018	−	0.371143i	0.113330	−	0.993557i	$-0.463848\pi$
$683$	23.4168	−	9.69955i	0.896018	−	0.371143i	0.782688	+	0.622415i	$0.213848\pi$
$684$	0.544872	−	0.998528i	0.0208337	−	0.0381797i
$685$	−20.7038	+	31.1371i	−0.791052	+	1.18969i
$686$	25.5757	+	1.36727i	0.976486	+	0.0522026i
$687$	−6.46696	+	6.46696i	−0.246730	+	0.246730i
$688$	13.6950	−	2.47882i	0.522115	−	0.0945041i
$689$	−39.9613			−1.52240
$690$	−25.0590	+	14.9494i	−0.953979	+	0.569115i
$691$	32.1781	−	13.3286i	1.22411	−	0.507045i	0.325399	−	0.945577i	$-0.394501\pi$
$691$	32.1781	−	13.3286i	1.22411	−	0.507045i	0.898716	+	0.438532i	$0.144501\pi$
$692$	0.281982	−	0.516757i	0.0107193	−	0.0196442i
$693$	−0.232132	−	0.560415i	−0.00881795	−	0.0212884i
$694$	9.29428	+	26.3340i	0.352806	+	0.999625i
$695$	8.70955	+	12.9714i	0.330372	+	0.492033i
$696$	−8.64908	+	53.5176i	−0.327843	+	2.02858i
$697$	−5.16607			−0.195679
$698$	−16.3378	+	5.76623i	−0.618394	+	0.218255i
$699$	4.70267	−	11.3533i	0.177871	−	0.429420i
$700$	25.8774	−	7.73310i	0.978073	−	0.292284i
$701$	−18.1707	+	7.52654i	−0.686297	+	0.284273i	−0.698456	−	0.715653i	$-0.746129\pi$
$701$	−18.1707	+	7.52654i	−0.686297	+	0.284273i	0.0121596	+	0.999926i	$0.496129\pi$
$702$	22.0602	+	1.17933i	0.832607	+	0.0445109i
$703$	6.67093	−	6.67093i	0.251599	−	0.251599i
$704$	−3.53755	+	4.08954i	−0.133327	+	0.154130i
$705$	−2.85961	+	14.5475i	−0.107699	+	0.547890i
$706$	−35.6079	+	31.9940i	−1.34012	+	1.20411i
$707$	−28.9883	−	12.0073i	−1.09022	−	0.451583i
$708$	6.02571	+	7.47314i	0.226460	+	0.280858i
$709$	32.5315	+	13.4750i	1.22175	+	0.506064i	0.897964	−	0.440068i	$-0.145046\pi$
$709$	32.5315	+	13.4750i	1.22175	+	0.506064i	0.323782	+	0.946132i	$0.395046\pi$
$710$	−7.28015	−	49.7879i	−0.273219	−	1.86851i
$711$	0.598828	−	0.598828i	0.0224578	−	0.0224578i
$712$	−19.0478	−	26.3914i	−0.713848	−	0.989058i
$713$	42.0455			1.57462
$714$	−8.10639	+	2.86106i	−0.303374	+	0.107072i
$715$	−0.956543	−	4.75286i	−0.0357727	−	0.177747i
$716$	−8.41127	−	28.6163i	−0.314344	−	1.06944i
$717$	26.3795	+	10.9267i	0.985160	+	0.408067i
$718$	8.06174	−	7.24353i	0.300862	−	0.270326i
$719$		−	38.5177i		−	1.43647i	−0.695802	−	0.718233i	$-0.744951\pi$
$719$		−	38.5177i		−	1.43647i	0.695802	−	0.718233i	$-0.255049\pi$
$720$	0.0446745	−	2.97172i	0.00166492	−	0.110749i
$721$		−	0.466353i		−	0.0173679i
$722$	−15.1894	−	16.9052i	−0.565292	−	0.629147i
$723$	−4.28112	−	1.77330i	−0.159217	−	0.0659497i
$724$	37.2724	+	20.3386i	1.38522	+	0.755878i
$725$	36.9546	−	37.2892i	1.37246	−	1.38489i
$726$	9.05864	+	25.6663i	0.336198	+	0.952567i
$727$	−48.2210			−1.78842			−0.894210	−	0.447648i	$-0.852262\pi$
$727$	−48.2210			−1.78842			−0.894210	+	0.447648i	$0.852262\pi$
$728$	−12.8692	+	20.8530i	−0.476963	+	0.772862i
$729$	16.5347	−	16.5347i	0.612397	−	0.612397i
$730$	11.2671	−	15.1265i	0.417016	−	0.559857i
$731$	3.96328	+	1.64165i	0.146587	+	0.0607185i
$732$	4.18965	−	39.0731i	0.154854	−	1.44418i
$733$	−21.3272	−	8.83400i	−0.787737	−	0.326291i	−0.0477035	−	0.998862i	$-0.515190\pi$
$733$	−21.3272	−	8.83400i	−0.787737	−	0.326291i	−0.740033	+	0.672570i	$0.765190\pi$
$734$	1.78107	+	1.98226i	0.0657406	+	0.0731665i
$735$	0.997636	−	0.669856i	0.0367984	−	0.0247080i
$736$	27.5808	+	7.54553i	1.01664	+	0.278132i
$737$	4.01833	−	4.01833i	0.148017	−	0.148017i
$738$	0.105113	−	1.96620i	0.00386925	−	0.0723769i
$739$	38.6263	−	15.9996i	1.42089	−	0.588553i	0.465808	−	0.884886i	$-0.345764\pi$
$739$	38.6263	−	15.9996i	1.42089	−	0.588553i	0.955085	+	0.296333i	$0.0957637\pi$
$740$	7.30580	−	23.5415i	0.268567	−	0.865402i
$741$	3.83557	−	9.25989i	0.140903	−	0.340171i
$742$	−15.8363	−	44.8697i	−0.581367	−	1.64722i
$743$	34.2691			1.25721			0.628605	−	0.777725i	$-0.283626\pi$
$743$	34.2691			1.25721			0.628605	+	0.777725i	$0.283626\pi$
$744$	−22.5547	+	36.5473i	−0.826896	+	1.33989i
$745$	−4.04087	+	2.71322i	−0.148046	+	0.0994046i
$746$	26.5375	−	9.36612i	0.971608	−	0.342918i
$747$	2.09173	+	5.04988i	0.0765323	+	0.184765i
$748$	−1.59906	+	0.470015i	−0.0584673	+	0.0171855i
$749$	35.7634	−	14.8137i	1.30676	−	0.541280i
$750$	−17.1370	+	23.2248i	−0.625756	+	0.848051i
$751$	−10.1546			−0.370545			−0.185272	−	0.982687i	$-0.559317\pi$
$751$	−10.1546			−0.370545			−0.185272	+	0.982687i	$0.559317\pi$
$752$	12.2178	−	7.86165i	0.445538	−	0.286685i
$753$	−14.3713	+	14.3713i	−0.523721	+	0.523721i
$754$	−2.54275	+	47.5639i	−0.0926016	+	1.73218i
$755$	−5.80195	−	28.8287i	−0.211155	−	1.04918i
$756$	7.41804	+	25.2372i	0.269791	+	0.917867i
$757$	−12.9712	+	5.37283i	−0.471445	+	0.195279i	−0.605740	−	0.795663i	$-0.707123\pi$
$757$	−12.9712	+	5.37283i	−0.471445	+	0.195279i	0.134295	+	0.990941i	$0.457123\pi$
$758$	4.09414	+	1.95808i	0.148706	+	0.0711206i
$759$	−4.41012	+	4.41012i	−0.160077	+	0.160077i
$760$	10.1530	+	3.75595i	0.368288	+	0.136242i
$761$	9.61134	+	9.61134i	0.348411	+	0.348411i	0.859517	−	0.511107i	$-0.170764\pi$
$761$	9.61134	+	9.61134i	0.348411	+	0.348411i	−0.511107	+	0.859517i	$0.670764\pi$
$762$	−7.35430	−	20.8373i	−0.266418	−	0.754857i
$763$	−0.116169	−	0.280457i	−0.00420560	−	0.0101532i
$764$	3.89520	−	36.3271i	0.140924	−	1.31427i
$765$	0.507232	−	0.762842i	0.0183390	−	0.0275806i
$766$	17.2034	+	19.1466i	0.621583	+	0.691796i
$767$	5.96419	+	5.96419i	0.215354	+	0.215354i
$768$	−21.3542	+	19.9265i	−0.770553	+	0.719035i
$769$		−	8.93149i		−	0.322078i	−0.986948	−	0.161039i	$-0.948516\pi$
$769$		−	8.93149i		−	0.322078i	0.986948	−	0.161039i	$-0.0514845\pi$
$770$	4.95758	−	2.95754i	0.178659	−	0.106583i
$771$	−2.53960	−	6.13114i	−0.0914615	−	0.220808i
$772$	3.05745	+	3.79188i	0.110040	+	0.136473i
$773$	−37.7710	+	15.6453i	−1.35853	+	0.562721i	−0.938654	−	0.344861i	$-0.887926\pi$
$773$	−37.7710	+	15.6453i	−1.35853	+	0.562721i	−0.419875	+	0.907582i	$0.637926\pi$
$774$	−0.705448	+	1.47502i	−0.0253568	+	0.0530185i
$775$	38.3516	−	16.0887i	1.37763	−	0.577922i
$776$	−14.5252	−	20.1251i	−0.521423	−	0.722448i
$777$		−	27.1738i		−	0.974856i
$778$	−2.29375	+	4.79599i	−0.0822348	+	0.171945i
$779$	6.62602	+	2.74459i	0.237402	+	0.0983351i
$780$	−2.40023	−	26.0770i	−0.0859422	−	0.933705i
$781$	−4.11572	−	9.93622i	−0.147272	−	0.355546i
$782$	5.89066	+	6.55606i	0.210650	+	0.234444i
$783$	36.1555	+	36.1555i	1.29209	+	1.29209i
$784$	−1.15080	−	0.249661i	−0.0410999	−	0.00891645i
$785$	−17.5893	+	11.8102i	−0.627788	+	0.421524i
$786$	−0.953445	+	17.8348i	−0.0340083	+	0.636148i
$787$	−15.6155	+	37.6992i	−0.556633	+	1.34383i	0.355784	+	0.934568i	$0.384214\pi$
$787$	−15.6155	+	37.6992i	−0.556633	+	1.34383i	−0.912417	+	0.409262i	$0.865786\pi$
$788$	10.3936	+	35.3605i	0.370257	+	1.25967i
$789$	−0.749939	+	1.81051i	−0.0266985	+	0.0644560i
$790$	6.46348	+	4.81439i	0.229960	+	0.171288i
$791$	−11.3689	−	11.3689i	−0.404231	−	0.404231i
$792$	−0.146352	−	0.618162i	−0.00520038	−	0.0219654i
$793$		−	34.5273i		−	1.22610i
$794$	−7.54199	+	15.7695i	−0.267655	+	0.559639i
$795$	42.3439	+	28.1555i	1.50178	+	0.998572i
$796$	16.8600	+	20.9099i	0.597587	+	0.741133i
$797$	1.56558	−	3.77965i	0.0554557	−	0.133882i	−0.893723	−	0.448619i	$-0.851916\pi$
$797$	1.56558	−	3.77965i	0.0554557	−	0.133882i	0.949179	+	0.314737i	$0.101916\pi$
$798$	11.9173	+	0.637094i	0.421867	+	0.0225529i
$799$	4.47820			0.158427
$800$	28.0450	−	3.67116i	0.991541	−	0.129795i
$801$	3.82367			0.135103
$802$	−27.7889	−	1.48558i	−0.981259	−	0.0524578i
$803$	1.54279	−	3.72462i	0.0544439	−	0.131439i
$804$	23.8953	−	19.2671i	0.842721	−	0.679499i
$805$	−25.4205	−	16.9027i	−0.895954	−	0.595741i
$806$	−16.2806	+	34.0410i	−0.573459	+	1.19904i
$807$			1.92590i			0.0677947i
$808$	−27.9630	−	17.2570i	−0.983734	−	0.607099i
$809$	15.3680	+	15.3680i	0.540308	+	0.540308i	0.923619	−	0.383311i	$-0.125216\pi$
$809$	15.3680	+	15.3680i	0.540308	+	0.540308i	−0.383311	+	0.923619i	$0.625216\pi$
$810$	−25.0727	−	18.6756i	−0.880963	−	0.656195i
$811$	−4.74017	+	11.4438i	−0.166450	+	0.401846i	−0.984992	−	0.172601i	$-0.944783\pi$
$811$	−4.74017	+	11.4438i	−0.166450	+	0.401846i	0.818542	+	0.574447i	$0.194783\pi$
$812$	−54.4139	+	15.9940i	−1.90955	+	0.561281i
$813$	−5.69189	+	13.7414i	−0.199623	+	0.481933i
$814$	0.281252	−	5.26101i	0.00985788	−	0.184398i
$815$	29.4745	−	19.7905i	1.03245	−	0.693231i
$816$	−8.85870	+	1.60345i	−0.310117	+	0.0561319i
$817$	−4.21116	−	4.21116i	−0.147330	−	0.147330i
$818$	7.08236	+	7.88237i	0.247629	+	0.275601i
$819$	−1.10166	−	2.65965i	−0.0384952	−	0.0929357i
$820$	18.6597	−	1.71752i	0.651625	−	0.0599783i
$821$	29.3799	+	12.1696i	1.02537	+	0.424720i	0.831038	−	0.556216i	$-0.187747\pi$
$821$	29.3799	+	12.1696i	1.02537	+	0.424720i	0.194328	+	0.980937i	$0.437747\pi$
$822$	−18.6260	+	38.9450i	−0.649656	+	1.35836i
$823$			0.808258i			0.0281741i	0.999901	+	0.0140871i	$0.00448420\pi$
$823$			0.808258i			0.0281741i	−0.999901	+	0.0140871i	$0.995516\pi$
$824$	0.0779184	−	0.482133i	0.00271442	−	0.0167959i
$825$	−2.33514	+	5.71019i	−0.0812992	+	0.198803i
$826$	−4.33322	+	9.06032i	−0.150772	+	0.315249i
$827$	4.94330	−	2.04758i	0.171895	−	0.0712014i	−0.295076	−	0.955474i	$-0.595345\pi$
$827$	4.94330	−	2.04758i	0.171895	−	0.0712014i	0.466972	+	0.884272i	$0.345345\pi$
$828$	−2.61508	+	2.10859i	−0.0908805	+	0.0732784i
$829$	10.1472	+	24.4974i	0.352425	+	0.850830i	0.996320	+	0.0857156i	$0.0273176\pi$
$829$	10.1472	+	24.4974i	0.352425	+	0.850830i	−0.643894	+	0.765114i	$0.722682\pi$
$830$	−44.6726	+	26.6503i	−1.55061	+	0.925046i
$831$			41.4914i			1.43932i
$832$	−16.7887	+	19.4084i	−0.582044	+	0.672864i
$833$	−0.256655	−	0.256655i	−0.00889257	−	0.00889257i
$834$	12.0559	+	13.4178i	0.417463	+	0.464619i
$835$	−3.90971	+	5.87995i	−0.135301	+	0.203484i
$836$	2.30066	+	0.246690i	0.0795700	+	0.00853196i
$837$	15.5012	+	37.4231i	0.535798	+	1.29353i
$838$	9.25791	+	26.2309i	0.319809	+	0.906133i
$839$	23.6938	+	23.6938i	0.818002	+	0.818002i	0.985818	−	0.167816i	$-0.0536715\pi$
$839$	23.6938	+	23.6938i	0.818002	+	0.818002i	−0.167816	+	0.985818i	$0.553672\pi$
$840$	28.3288	−	13.0291i	0.977437	−	0.449547i
$841$	−57.4489	+	57.4489i	−1.98100	+	1.98100i
$842$	42.6835	+	20.4140i	1.47097	+	0.703513i
$843$	18.7132	−	7.75124i	0.644515	−	0.266967i
$844$	−13.0459	+	3.83462i	−0.449058	+	0.131993i
$845$	1.19569	+	5.94111i	0.0411329	+	0.204380i
$846$	−0.0911166	+	1.70440i	−0.00313265	+	0.0585984i
$847$	−20.1349	+	20.1349i	−0.691844	+	0.691844i
$848$	−8.87525	−	49.0339i	−0.304777	−	1.68383i
$849$	−10.3033			−0.353610
$850$	7.88181	+	3.72602i	0.270344	+	0.127802i
$851$	−25.7399	+	10.6618i	−0.882351	+	0.365482i
$852$	−16.3822	−	55.7345i	−0.561245	−	1.90943i
$853$	−2.28996	−	5.52844i	−0.0784066	−	0.189290i	0.879816	−	0.475315i	$-0.157666\pi$
$853$	−2.28996	−	5.52844i	−0.0784066	−	0.189290i	−0.958222	+	0.286025i	$0.907666\pi$
$854$	38.7683	−	13.6828i	1.32662	−	0.468216i
$855$	−1.05585	+	0.708946i	−0.0361094	+	0.0242454i
$856$	39.4485	−	9.33956i	1.34832	−	0.319219i
$857$	26.9720			0.921347			0.460673	−	0.887570i	$-0.347608\pi$
$857$	26.9720			0.921347			0.460673	+	0.887570i	$0.347608\pi$
$858$	−1.86288	−	5.27819i	−0.0635976	−	0.180195i
$859$	−19.3775	+	46.7815i	−0.661153	+	1.59616i	0.134846	+	0.990867i	$0.456946\pi$
$859$	−19.3775	+	46.7815i	−0.661153	+	1.59616i	−0.795999	+	0.605298i	$0.793054\pi$
$860$	−14.8610	−	4.61193i	−0.506757	−	0.157266i
$861$	19.0854	−	7.90545i	0.650430	−	0.269417i
$862$	1.56092	−	29.1981i	0.0531651	−	0.994490i
$863$	29.0460	−	29.0460i	0.988736	−	0.988736i	−0.0112014	−	0.999937i	$-0.503566\pi$
$863$	29.0460	−	29.0460i	0.988736	−	0.988736i	0.999937	+	0.0112014i	$0.00356559\pi$
$864$	3.45240	+	27.3305i	0.117453	+	0.929803i
$865$	−0.546424	+	0.366893i	−0.0185790	+	0.0124747i
$866$	28.9864	+	32.2607i	0.984999	+	1.09626i
$867$	26.1068	+	10.8138i	0.886634	+	0.367256i
$868$	−44.6741	−	4.79022i	−1.51634	−	0.162591i
$869$	1.59151	+	0.659226i	0.0539883	+	0.0223627i
$870$	36.2064	−	48.6084i	1.22751	−	1.64798i
$871$	19.0704	−	19.0704i	0.646176	−	0.646176i
$872$	−0.0732409	−	0.309356i	−0.00248025	−	0.0104761i
$873$	2.91579			0.0986846
$874$	−4.07233	−	11.5384i	−0.137749	−	0.390291i
$875$	−29.6550	−	5.69058i	−1.00252	−	0.192377i
$876$	10.4308	−	19.1153i	0.352423	−	0.645848i
$877$	10.3784	+	4.29889i	0.350455	+	0.145163i	0.550965	−	0.834529i	$-0.314260\pi$
$877$	10.3784	+	4.29889i	0.350455	+	0.145163i	−0.200510	+	0.979692i	$0.564260\pi$
$878$	−10.3368	−	11.5044i	−0.348850	−	0.388256i
$879$		−	0.849236i		−	0.0286440i
$880$	5.61948	−	2.22930i	0.189432	−	0.0751498i
$881$		−	51.8420i		−	1.74660i	−0.487181	−	0.873301i	$-0.661975\pi$
$881$		−	51.8420i		−	1.74660i	0.487181	−	0.873301i	$-0.338025\pi$
$882$	0.102905	−	0.0924605i	0.00346498	−	0.00311331i
$883$	15.8023	+	6.54551i	0.531789	+	0.220274i	0.632386	−	0.774653i	$-0.282076\pi$
$883$	15.8023	+	6.54551i	0.531789	+	0.220274i	−0.100598	+	0.994927i	$0.532076\pi$
$884$	−7.58889	+	2.23062i	−0.255242	+	0.0750240i
$885$	−2.11761	−	10.5220i	−0.0711828	−	0.353692i
$886$	24.8725	−	8.77847i	0.835609	−	0.294919i
$887$	6.57861			0.220888			0.110444	−	0.993882i	$-0.464773\pi$
$887$	6.57861			0.220888			0.110444	+	0.993882i	$0.464773\pi$
$888$	4.54021	−	28.0933i	0.152360	−	0.942749i
$889$	16.3466	−	16.3466i	0.548248	−	0.548248i
$890$	5.26493	+	36.0060i	0.176481	+	1.20693i
$891$	−6.17368	−	2.55722i	−0.206826	−	0.0856701i
$892$	18.6071	−	15.0032i	0.623012	−	0.502344i
$893$	−5.74375	−	2.37914i	−0.192207	−	0.0796149i
$894$	−4.17993	+	3.75569i	−0.139798	+	0.125609i
$895$	−6.43203	+	32.7213i	−0.214999	+	1.09375i
$896$	−28.4455	−	11.1595i	−0.950298	−	0.372814i
$897$	−20.9298	+	20.9298i	−0.698825	+	0.698825i
$898$	−7.51267	−	0.401625i	−0.250701	−	0.0134024i
$899$	−80.6880	+	33.4221i	−2.69109	+	1.11469i
$900$	−1.57849	+	2.92399i	−0.0526163	+	0.0974665i
$901$	5.87780	−	14.1903i	0.195818	−	0.472747i
$902$	3.77687	−	1.33300i	0.125756	−	0.0443842i
$903$	−17.1540			−0.570850
$904$	−9.85404	−	13.6531i	−0.327740	−	0.454094i
$905$	−26.4630	−	39.4121i	−0.879661	−	1.31010i
$906$	−11.2994	−	32.0151i	−0.375396	−	1.06363i
$907$	−11.5043	−	27.7737i	−0.381992	−	0.922211i	−0.991580	−	0.129493i	$-0.958665\pi$
$907$	−11.5043	−	27.7737i	−0.381992	−	0.922211i	0.609588	−	0.792718i	$-0.291335\pi$
$908$	24.7783	+	13.5209i	0.822297	+	0.448707i
$909$	3.56648	−	1.47728i	0.118293	−	0.0489984i
$910$	23.5280	−	14.0361i	0.779945	−	0.465291i
$911$	−13.9591			−0.462487			−0.231243	−	0.972896i	$-0.574279\pi$
$911$	−13.9591			−0.462487			−0.231243	+	0.972896i	$0.574279\pi$
$912$	12.2141	+	2.64979i	0.404448	+	0.0877434i
$913$	−7.86190	+	7.86190i	−0.260191	+	0.260191i
$914$	−32.5069	−	1.73781i	−1.07523	−	0.0574816i
$915$	−24.3269	+	36.5860i	−0.804221	+	1.20949i
$916$	−8.79583	−	4.79967i	−0.290622	−	0.158585i
$917$	−17.2629	+	7.15051i	−0.570070	+	0.236131i
$918$	−3.66356	+	7.66012i	−0.120915	+	0.252821i
$919$	−21.9061	+	21.9061i	−0.722616	+	0.722616i	−0.969137	−	0.246521i	$-0.920712\pi$
$919$	−21.9061	+	21.9061i	−0.722616	+	0.722616i	0.246521	+	0.969137i	$0.420712\pi$
$920$	−23.4565	−	21.7219i	−0.773338	−	0.716149i
$921$	−10.3360	−	10.3360i	−0.340584	−	0.340584i
$922$	33.2776	−	11.7450i	1.09594	−	0.386800i
$923$	−19.5326	−	47.1559i	−0.642924	−	1.55215i
$924$	5.18828	−	4.18339i	0.170682	−	0.137623i
$925$	−19.3988	+	19.5744i	−0.637827	+	0.643603i
$926$	38.5567	−	34.6434i	1.26705	−	1.13845i
$927$	0.0405711	+	0.0405711i	0.00133253	+	0.00133253i
$928$	−58.9273	+	7.44372i	−1.93438	+	0.244352i
$929$		−	24.3577i		−	0.799149i	−0.916701	−	0.399575i	$-0.869158\pi$
$929$		−	24.3577i		−	0.799149i	0.916701	−	0.399575i	$-0.130842\pi$
$930$	41.2356	−	24.5999i	1.35217	−	0.806662i
$931$	0.192833	+	0.465540i	0.00631985	+	0.0152575i
$932$	13.3869	+	1.43543i	0.438504	+	0.0470190i
$933$	12.6432	−	5.23701i	0.413921	−	0.171452i
$934$	−7.38394	−	3.53147i	−0.241610	−	0.115553i
$935$	1.82844	+	0.359417i	0.0597963	+	0.0117542i
$936$	−0.694564	−	2.93371i	−0.0227025	−	0.0958912i
$937$		−	13.4082i		−	0.438028i	−0.975722	−	0.219014i	$-0.929716\pi$
$937$		−	13.4082i		−	0.438028i	0.975722	−	0.219014i	$-0.0702840\pi$
$938$	28.9702	+	13.8554i	0.945912	+	0.452395i
$939$	38.8456	+	16.0904i	1.26768	+	0.525090i
$940$	−16.1751	+	1.48883i	−0.527574	+	0.0485601i
$941$	1.85224	+	4.47169i	0.0603812	+	0.145773i	0.951191	−	0.308604i	$-0.0998618\pi$
$941$	1.85224	+	4.47169i	0.0603812	+	0.145773i	−0.890809	+	0.454377i	$0.849862\pi$
$942$	−18.1946	+	16.3479i	−0.592811	+	0.532644i
$943$	−14.9766	−	14.9766i	−0.487704	−	0.487704i
$944$	−5.99364	+	8.64289i	−0.195076	+	0.281302i
$945$	5.67252	−	28.8574i	0.184527	−	0.938732i
$946$	−3.32112	−	0.177546i	−0.107979	−	0.00577252i
$947$	−18.0901	+	43.6734i	−0.587850	+	1.41919i	0.297704	+	0.954658i	$0.403779\pi$
$947$	−18.0901	+	43.6734i	−0.587850	+	1.41919i	−0.885554	+	0.464536i	$0.846221\pi$
$948$	8.16788	+	4.45701i	0.265281	+	0.144757i
$949$	7.32186	−	17.6765i	0.237677	−	0.573804i
$950$	−8.12970	−	8.96639i	−0.263762	−	0.290908i
$951$	1.52005	+	1.52005i	0.0492909	+	0.0492909i
$952$	−5.51201	−	7.63706i	−0.178645	−	0.247518i
$953$			0.0771644i			0.00249960i	0.999999	+	0.00124980i	$0.000397824\pi$
$953$			0.0771644i			0.00249960i	−0.999999	+	0.00124980i	$0.999602\pi$
$954$	5.28121	+	2.52581i	0.170985	+	0.0817762i
$955$	−22.6172	+	34.0147i	−0.731875	+	1.10069i
$956$	−3.33524	+	31.1048i	−0.107869	+	1.00600i
$957$	4.95768	−	11.9689i	0.160259	−	0.386900i
$958$	2.33145	−	43.6114i	0.0753257	−	1.40902i
$959$	−45.1637			−1.45841
$960$	31.4643	−	8.73677i	1.01550	−	0.281978i
$961$	−38.1876			−1.23186
$962$	1.33478	−	24.9680i	0.0430351	−	0.805000i
$963$	−1.82255	+	4.40003i	−0.0587309	+	0.141789i
$964$	0.541275	−	5.04799i	0.0174333	−	0.162585i
$965$	−1.07448	−	5.33886i	−0.0345887	−	0.171864i
$966$	−31.7949	−	15.2063i	−1.02298	−	0.489256i
$967$		−	19.1182i		−	0.614800i	−0.951580	−	0.307400i	$-0.900541\pi$
$967$		−	19.1182i		−	0.614800i	0.951580	−	0.307400i	$-0.0994589\pi$
$968$	−24.1803	+	17.4521i	−0.777186	+	0.560930i
$969$	2.72403	+	2.72403i	0.0875084	+	0.0875084i
$970$	4.01484	+	27.4569i	0.128909	+	0.881587i
$971$	−6.55027	+	15.8137i	−0.210208	+	0.507487i	−0.993455	−	0.114223i	$-0.963562\pi$
$971$	−6.55027	+	15.8137i	−0.210208	+	0.507487i	0.783247	+	0.621711i	$0.213562\pi$
$972$	−6.03564	−	3.29350i	−0.193593	−	0.105639i
$973$	−7.22179	+	17.4349i	−0.231520	+	0.558938i
$974$	−8.25984	−	0.441568i	−0.264662	−	0.0141488i
$975$	−11.0822	+	27.0997i	−0.354916	+	0.867886i
$976$	42.3662	−	7.66838i	1.35611	−	0.245459i
$977$	41.8163	+	41.8163i	1.33782	+	1.33782i	0.898168	+	0.439653i	$0.144899\pi$
$977$	41.8163	+	41.8163i	1.33782	+	1.33782i	0.439653	+	0.898168i	$0.355101\pi$
$978$	30.4888	−	27.3944i	0.974925	−	0.875976i
$979$	2.97644	+	7.18577i	0.0951275	+	0.229658i
$980$	1.01236	+	0.841702i	0.0323386	+	0.0268872i
$981$	0.0345051	+	0.0142925i	0.00110166	+	0.000456323i
$982$	18.8861	+	9.03254i	0.602680	+	0.288240i
$983$		−	4.73187i		−	0.150923i	−0.997149	−	0.0754617i	$-0.975957\pi$
$983$		−	4.73187i		−	0.150923i	0.997149	−	0.0754617i	$-0.0240431\pi$
$984$	21.0521	−	4.98414i	0.671115	−	0.158889i
$985$	7.94792	−	40.4329i	0.253242	−	1.28830i
$986$	−16.5160	−	7.89899i	−0.525976	−	0.251555i
$987$	−16.5442	+	6.85282i	−0.526607	+	0.218128i
$988$	10.9186	+	1.17076i	0.347367	+	0.0372467i
$989$	6.73047	+	16.2488i	0.214017	+	0.516682i
$990$	−0.173996	+	0.688589i	−0.00552997	+	0.0218848i
$991$		−	57.2898i		−	1.81987i	−0.414751	−	0.909935i	$-0.636131\pi$
$991$		−	57.2898i		−	1.81987i	0.414751	−	0.909935i	$-0.363869\pi$
$992$	−45.3854	−	12.4165i	−1.44099	−	0.394223i
$993$	−23.7311	−	23.7311i	−0.753085	−	0.753085i
$994$	45.2075	−	40.6192i	1.43389	−	1.28836i
$995$	−5.92511	−	29.4406i	−0.187839	−	0.933330i
$996$	−46.7513	+	37.6964i	−1.48137	+	1.19446i
$997$	7.66278	+	18.4996i	0.242683	+	0.585887i	0.997547	−	0.0699928i	$-0.0222976\pi$
$997$	7.66278	+	18.4996i	0.242683	+	0.585887i	−0.754865	+	0.655880i	$0.772298\pi$
$998$	−24.1546	+	8.52509i	−0.764601	+	0.269857i
$999$	−18.9793	−	18.9793i	−0.600479	−	0.600479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.2.u.a.43.12	✓	88
4.3	odd	2		640.2.u.a.463.18		88
5.2	odd	4		160.2.ba.a.107.22	yes	88
5.3	odd	4		800.2.bb.b.107.1		88
5.4	even	2		800.2.v.b.43.11		88
20.7	even	4		640.2.ba.a.207.5		88
32.3	odd	8		160.2.ba.a.3.22	yes	88
32.29	even	8		640.2.ba.a.303.5		88
160.3	even	8		800.2.v.b.707.11		88
160.67	even	8	inner	160.2.u.a.67.12	yes	88
160.99	odd	8		800.2.bb.b.643.1		88
160.157	odd	8		640.2.u.a.47.18		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.u.a.43.12	✓	88	1.1	even	1	trivial
160.2.u.a.67.12	yes	88	160.67	even	8	inner
160.2.ba.a.3.22	yes	88	32.3	odd	8
160.2.ba.a.107.22	yes	88	5.2	odd	4
640.2.u.a.47.18		88	160.157	odd	8
640.2.u.a.463.18		88	4.3	odd	2
640.2.ba.a.207.5		88	20.7	even	4
640.2.ba.a.303.5		88	32.29	even	8
800.2.v.b.43.11		88	5.4	even	2
800.2.v.b.707.11		88	160.3	even	8
800.2.bb.b.107.1		88	5.3	odd	4
800.2.bb.b.643.1		88	160.99	odd	8

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	160.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0754956 - 1.41220i) q^{2} +(-0.698571 + 1.68650i) q^{3} +(-1.98860 - 0.213229i) q^{4} +(1.86202 + 1.23810i) q^{5} +(2.32893 + 1.11384i) q^{6} +2.70081i q^{7} +(-0.451252 + 2.79220i) q^{8} +(-0.234961 - 0.234961i) q^{9} +O(q^{10})\)	\(q+(0.0754956 - 1.41220i) q^{2} +(-0.698571 + 1.68650i) q^{3} +(-1.98860 - 0.213229i) q^{4} +(1.86202 + 1.23810i) q^{5} +(2.32893 + 1.11384i) q^{6} +2.70081i q^{7} +(-0.451252 + 2.79220i) q^{8} +(-0.234961 - 0.234961i) q^{9} +(1.88901 - 2.53606i) q^{10} +(0.258659 - 0.624459i) q^{11} +(1.74879 - 3.20482i) q^{12} +(1.22756 - 2.96359i) q^{13} +(3.81408 + 0.203900i) q^{14} +(-3.38881 + 2.27539i) q^{15} +(3.90907 + 0.848056i) q^{16} +(0.871815 + 0.871815i) q^{17} +(-0.349550 + 0.314073i) q^{18} +(-0.655022 - 1.58136i) q^{19} +(-3.43881 - 2.85912i) q^{20} +(-4.55492 - 1.88671i) q^{21} +(-0.862331 - 0.412422i) q^{22} +5.05482i q^{23} +(-4.39381 - 2.71159i) q^{24} +(1.93422 + 4.61073i) q^{25} +(-4.09250 - 1.95729i) q^{26} +(-4.49910 + 1.86359i) q^{27} +(0.575893 - 5.37084i) q^{28} +(-4.01808 - 9.70052i) q^{29} +(2.95746 + 4.95745i) q^{30} -8.31791i q^{31} +(1.49274 - 5.45635i) q^{32} +(0.872458 + 0.872458i) q^{33} +(1.29699 - 1.16536i) q^{34} +(-3.34388 + 5.02896i) q^{35} +(0.417144 + 0.517345i) q^{36} +(2.10924 + 5.09214i) q^{37} +(-2.28265 + 0.805634i) q^{38} +(4.14056 + 4.14056i) q^{39} +(-4.29726 + 4.64043i) q^{40} +(-2.96283 + 2.96283i) q^{41} +(-3.00828 + 6.29001i) q^{42} +(3.21452 - 1.33150i) q^{43} +(-0.647523 + 1.18665i) q^{44} +(-0.146597 - 0.728408i) q^{45} +(7.13840 + 0.381617i) q^{46} +(2.56832 - 2.56832i) q^{47} +(-4.16101 + 6.00021i) q^{48} -0.294392 q^{49} +(6.65728 - 2.38341i) q^{50} +(-2.07934 + 0.861291i) q^{51} +(-3.07305 + 5.63165i) q^{52} +(-4.76734 - 11.5094i) q^{53} +(2.29209 + 6.49431i) q^{54} +(1.25477 - 0.842508i) q^{55} +(-7.54121 - 1.21875i) q^{56} +3.12455 q^{57} +(-14.0024 + 4.94198i) q^{58} +(-1.00624 + 2.42929i) q^{59} +(7.22417 - 3.80225i) q^{60} +(9.94431 - 4.11907i) q^{61} +(-11.7465 - 0.627965i) q^{62} +(0.634587 - 0.634587i) q^{63} +(-7.59274 - 2.51997i) q^{64} +(5.95496 - 3.99842i) q^{65} +(1.29795 - 1.16622i) q^{66} +(7.76760 + 3.21745i) q^{67} +(-1.54780 - 1.91959i) q^{68} +(-8.52495 - 3.53115i) q^{69} +(6.84944 + 5.10188i) q^{70} +(11.2513 - 11.2513i) q^{71} +(0.762086 - 0.550032i) q^{72} +5.96456 q^{73} +(7.35035 - 2.59422i) q^{74} +(-9.12718 + 0.0411410i) q^{75} +(0.965385 + 3.28437i) q^{76} +(1.68655 + 0.698591i) q^{77} +(6.15988 - 5.53469i) q^{78} +2.54862i q^{79} +(6.22877 + 6.41891i) q^{80} -9.88644i q^{81} +(3.96042 + 4.40778i) q^{82} +(-15.1974 - 6.29497i) q^{83} +(8.65562 + 4.72316i) q^{84} +(0.543941 + 2.70273i) q^{85} +(-1.63765 - 4.64006i) q^{86} +19.1668 q^{87} +(1.62689 + 1.00402i) q^{88} +(-8.13681 + 8.13681i) q^{89} +(-1.03972 + 0.152032i) q^{90} +(8.00411 + 3.31541i) q^{91} +(1.07784 - 10.0520i) q^{92} +(14.0282 + 5.81065i) q^{93} +(-3.43308 - 3.82087i) q^{94} +(0.738222 - 3.75551i) q^{95} +(8.15935 + 6.32915i) q^{96} +(-6.20483 + 6.20483i) q^{97} +(-0.0222253 + 0.415739i) q^{98} +(-0.207499 + 0.0859488i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8}+O(q^{10}) \) 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8	\( 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8} - 16 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} + 16 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} + 16 q^{19} + 24 q^{20} - 8 q^{21} - 20 q^{22} - 32 q^{24} - 4 q^{25} - 8 q^{26} - 16 q^{27} + 12 q^{28} + 8 q^{30} - 24 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 8 q^{36} - 4 q^{37} - 60 q^{38} + 16 q^{40} - 8 q^{41} + 60 q^{42} - 36 q^{43} + 16 q^{44} - 4 q^{45} - 8 q^{46} - 8 q^{47} - 24 q^{48} - 40 q^{49} - 12 q^{50} + 8 q^{51} - 56 q^{52} - 4 q^{53} - 56 q^{54} - 36 q^{55} + 40 q^{56} - 8 q^{57} - 36 q^{58} + 12 q^{60} - 40 q^{61} + 40 q^{62} + 56 q^{63} + 48 q^{64} - 8 q^{65} + 72 q^{66} + 20 q^{67} + 8 q^{68} + 24 q^{69} + 60 q^{70} + 24 q^{71} + 24 q^{72} - 8 q^{73} + 8 q^{75} + 56 q^{76} + 24 q^{77} + 32 q^{78} - 8 q^{80} + 84 q^{82} - 44 q^{83} + 56 q^{84} - 4 q^{85} + 24 q^{86} - 120 q^{87} + 104 q^{88} + 148 q^{90} - 8 q^{91} + 124 q^{92} + 8 q^{93} - 32 q^{94} + 24 q^{96} - 8 q^{97} - 16 q^{98}+O(q^{100}) \) 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8 - 16 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 + 16 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 + 16 * q^19 + 24 * q^20 - 8 * q^21 - 20 * q^22 - 32 * q^24 - 4 * q^25 - 8 * q^26 - 16 * q^27 + 12 * q^28 + 8 * q^30 - 24 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 8 * q^36 - 4 * q^37 - 60 * q^38 + 16 * q^40 - 8 * q^41 + 60 * q^42 - 36 * q^43 + 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 24 * q^48 - 40 * q^49 - 12 * q^50 + 8 * q^51 - 56 * q^52 - 4 * q^53 - 56 * q^54 - 36 * q^55 + 40 * q^56 - 8 * q^57 - 36 * q^58 + 12 * q^60 - 40 * q^61 + 40 * q^62 + 56 * q^63 + 48 * q^64 - 8 * q^65 + 72 * q^66 + 20 * q^67 + 8 * q^68 + 24 * q^69 + 60 * q^70 + 24 * q^71 + 24 * q^72 - 8 * q^73 + 8 * q^75 + 56 * q^76 + 24 * q^77 + 32 * q^78 - 8 * q^80 + 84 * q^82 - 44 * q^83 + 56 * q^84 - 4 * q^85 + 24 * q^86 - 120 * q^87 + 104 * q^88 + 148 * q^90 - 8 * q^91 + 124 * q^92 + 8 * q^93 - 32 * q^94 + 24 * q^96 - 8 * q^97 - 16 * q^98

Introduction

L-functions

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