LMFDB - Embedded newform 354.2.e.c.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$3$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	354.19
Dual form			354.2.e.c.205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.468408 - 0.883512i) q^{2} +(0.725995 - 0.687699i) q^{3} +(-0.561187 - 0.827689i) q^{4} +(-3.74342 + 0.823990i) q^{5} +(-0.267528 - 0.963550i) q^{6} +(-3.11942 + 2.37132i) q^{7} +(-0.994138 + 0.108119i) q^{8} +(0.0541389 - 0.998533i) q^{9} +O(q^{10})$	\(q+(0.468408 - 0.883512i) q^{2} +(0.725995 - 0.687699i) q^{3} +(-0.561187 - 0.827689i) q^{4} +(-3.74342 + 0.823990i) q^{5} +(-0.267528 - 0.963550i) q^{6} +(-3.11942 + 2.37132i) q^{7} +(-0.994138 + 0.108119i) q^{8} +(0.0541389 - 0.998533i) q^{9} +(-1.02545 + 3.69332i) q^{10} +(-1.59437 - 4.00156i) q^{11} +(-0.976621 - 0.214970i) q^{12} +(-0.0482588 - 0.890082i) q^{13} +(0.633928 + 3.86679i) q^{14} +(-2.15105 + 3.17256i) q^{15} +(-0.370138 + 0.928977i) q^{16} +(-3.20598 - 2.43712i) q^{17} +(-0.856857 - 0.515554i) q^{18} +(-5.48319 + 1.84750i) q^{19} +(2.78277 + 2.63598i) q^{20} +(-0.633928 + 3.86679i) q^{21} +(-4.28224 - 0.465722i) q^{22} +(5.68489 - 3.42049i) q^{23} +(-0.647386 + 0.762162i) q^{24} +(8.79638 - 4.06964i) q^{25} +(-0.809003 - 0.374285i) q^{26} +(-0.647386 - 0.762162i) q^{27} +(3.71329 + 1.25115i) q^{28} +(2.28795 + 4.31554i) q^{29} +(1.79543 + 3.38653i) q^{30} +(7.56437 + 2.54873i) q^{31} +(0.647386 + 0.762162i) q^{32} +(-3.90937 - 1.80867i) q^{33} +(-3.65493 + 1.69095i) q^{34} +(9.72336 - 11.4472i) q^{35} +(-0.856857 + 0.515554i) q^{36} +(-2.24539 - 0.244200i) q^{37} +(-0.936082 + 5.70985i) q^{38} +(-0.647145 - 0.613008i) q^{39} +(3.63239 - 1.22389i) q^{40} +(-4.44828 - 2.67644i) q^{41} +(3.11942 + 2.37132i) q^{42} +(-0.822975 + 2.06551i) q^{43} +(-2.41731 + 3.56526i) q^{44} +(0.620116 + 3.78254i) q^{45} +(-0.359189 - 6.62485i) q^{46} +(-1.68338 - 0.370540i) q^{47} +(0.370138 + 0.928977i) q^{48} +(2.23492 - 8.04944i) q^{49} +(0.524724 - 9.67796i) q^{50} +(-4.00353 + 0.435410i) q^{51} +(-0.709629 + 0.539446i) q^{52} +(-3.40195 - 12.2527i) q^{53} +(-0.976621 + 0.214970i) q^{54} +(9.26563 + 13.6658i) q^{55} +(2.84475 - 2.69469i) q^{56} +(-2.71024 + 5.11206i) q^{57} +4.88452 q^{58} +(-7.03804 + 3.07668i) q^{59} +3.83304 q^{60} +(-3.08810 + 5.82477i) q^{61} +(5.79505 - 5.48936i) q^{62} +(2.19896 + 3.24323i) q^{63} +(0.976621 - 0.214970i) q^{64} +(0.914071 + 3.29219i) q^{65} +(-3.42916 + 2.60678i) q^{66} +(-4.62024 + 0.502481i) q^{67} +(-0.218025 + 4.02123i) q^{68} +(1.77494 - 6.39275i) q^{69} +(-5.55926 - 13.9527i) q^{70} +(-8.48928 - 1.86863i) q^{71} +(0.0541389 + 0.998533i) q^{72} +(0.0780241 + 0.475926i) q^{73} +(-1.26751 + 1.86944i) q^{74} +(3.58744 - 9.00380i) q^{75} +(4.60625 + 3.50158i) q^{76} +(14.4625 + 8.70179i) q^{77} +(-0.844728 + 0.284622i) q^{78} +(-9.26508 - 8.77635i) q^{79} +(0.620116 - 3.78254i) q^{80} +(-0.994138 - 0.108119i) q^{81} +(-4.44828 + 2.67644i) q^{82} +(-7.39560 + 8.70677i) q^{83} +(3.55625 - 1.64530i) q^{84} +(14.0095 + 6.48148i) q^{85} +(1.43942 + 1.69461i) q^{86} +(4.62884 + 1.55964i) q^{87} +(2.01767 + 3.80572i) q^{88} +(-4.81239 - 9.07713i) q^{89} +(3.63239 + 1.22389i) q^{90} +(2.26121 + 2.66210i) q^{91} +(-6.02139 - 2.78579i) q^{92} +(7.24446 - 3.35164i) q^{93} +(-1.11589 + 1.31372i) q^{94} +(19.0036 - 11.4341i) q^{95} +(0.994138 + 0.108119i) q^{96} +(2.40640 - 14.6784i) q^{97} +(-6.06492 - 5.74500i) q^{98} +(-4.08201 + 1.37539i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{19}{29}\right)$	$1$

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 $

$2$	0.468408	−	0.883512i	0.331215	−	0.624737i
$2$	0.468408	−	0.883512i	0.331215	−	0.624737i
$3$	0.725995	−	0.687699i	0.419154	−	0.397043i
$3$	0.725995	−	0.687699i	0.419154	−	0.397043i
$4$	−0.561187	−	0.827689i	−0.280594	−	0.413844i
$5$	−3.74342	+	0.823990i	−1.67411	+	0.368499i	−0.947799	−	0.318868i	$-0.896697\pi$
$5$	−3.74342	+	0.823990i	−1.67411	+	0.368499i	−0.726310	+	0.687367i	$0.758766\pi$
$6$	−0.267528	−	0.963550i	−0.109218	−	0.393368i
$7$	−3.11942	+	2.37132i	−1.17903	+	0.896275i	−0.996219	−	0.0868731i	$-0.972313\pi$
$7$	−3.11942	+	2.37132i	−1.17903	+	0.896275i	−0.182810	+	0.983148i	$0.558519\pi$
$8$	−0.994138	+	0.108119i	−0.351481	+	0.0382258i
$9$	0.0541389	−	0.998533i	0.0180463	−	0.332844i
$10$	−1.02545	+	3.69332i	−0.324275	+	1.16793i
$11$	−1.59437	−	4.00156i	−0.480720	−	1.20652i	−0.946814	−	0.321781i	$-0.895719\pi$
$11$	−1.59437	−	4.00156i	−0.480720	−	1.20652i	0.466095	−	0.884735i	$-0.345661\pi$
$12$	−0.976621	−	0.214970i	−0.281926	−	0.0620566i
$13$	−0.0482588	−	0.890082i	−0.0133846	−	0.246864i	−0.997567	−	0.0697085i	$-0.977793\pi$
$13$	−0.0482588	−	0.890082i	−0.0133846	−	0.246864i	0.984183	−	0.177156i	$-0.0566897\pi$
$14$	0.633928	+	3.86679i	0.169424	+	1.03344i
$15$	−2.15105	+	3.17256i	−0.555399	+	0.819152i
$16$	−0.370138	+	0.928977i	−0.0925345	+	0.232244i
$17$	−3.20598	−	2.43712i	−0.777564	−	0.591089i	0.139318	−	0.990248i	$-0.455509\pi$
$17$	−3.20598	−	2.43712i	−0.777564	−	0.591089i	−0.916882	+	0.399159i	$0.869302\pi$
$18$	−0.856857	−	0.515554i	−0.201963	−	0.121517i
$19$	−5.48319	+	1.84750i	−1.25793	+	0.423846i	−0.867800	−	0.496914i	$-0.834466\pi$
$19$	−5.48319	+	1.84750i	−1.25793	+	0.423846i	−0.390130	+	0.920760i	$0.627570\pi$
$20$	2.78277	+	2.63598i	0.622246	+	0.589423i
$21$	−0.633928	+	3.86679i	−0.138334	+	0.843803i
$22$	−4.28224	−	0.465722i	−0.912977	−	0.0992922i
$23$	5.68489	−	3.42049i	1.18538	−	0.713221i	0.220367	−	0.975417i	$-0.429274\pi$
$23$	5.68489	−	3.42049i	1.18538	−	0.713221i	0.965015	+	0.262196i	$0.0844469\pi$
$24$	−0.647386	+	0.762162i	−0.132147	+	0.155576i
$25$	8.79638	−	4.06964i	1.75928	−	0.813928i
$26$	−0.809003	−	0.374285i	−0.158659	−	0.0734032i
$27$	−0.647386	−	0.762162i	−0.124590	−	0.146678i
$28$	3.71329	+	1.25115i	0.701747	+	0.236446i
$29$	2.28795	+	4.31554i	0.424862	+	0.801375i	0.999859	−	0.0167805i	$-0.00534164\pi$
$29$	2.28795	+	4.31554i	0.424862	+	0.801375i	−0.574997	+	0.818155i	$0.694997\pi$
$30$	1.79543	+	3.38653i	0.327799	+	0.618294i
$31$	7.56437	+	2.54873i	1.35860	+	0.457766i	0.901935	−	0.431873i	$-0.142147\pi$
$31$	7.56437	+	2.54873i	1.35860	+	0.457766i	0.456666	+	0.889638i	$0.349044\pi$
$32$	0.647386	+	0.762162i	0.114443	+	0.134732i
$33$	−3.90937	−	1.80867i	−0.680534	−	0.314849i
$34$	−3.65493	+	1.69095i	−0.626816	+	0.289996i
$35$	9.72336	−	11.4472i	1.64355	−	1.93493i
$36$	−0.856857	+	0.515554i	−0.142810	+	0.0859256i
$37$	−2.24539	−	0.244200i	−0.369139	−	0.0401463i	−0.0783302	−	0.996927i	$-0.524959\pi$
$37$	−2.24539	−	0.244200i	−0.369139	−	0.0401463i	−0.290809	+	0.956781i	$0.593924\pi$
$38$	−0.936082	+	5.70985i	−0.151853	+	0.926259i
$39$	−0.647145	−	0.613008i	−0.103626	−	0.0981598i
$40$	3.63239	−	1.22389i	0.574331	−	0.193515i
$41$	−4.44828	−	2.67644i	−0.694704	−	0.417989i	0.123941	−	0.992290i	$-0.460447\pi$
$41$	−4.44828	−	2.67644i	−0.694704	−	0.417989i	−0.818645	+	0.574300i	$0.805274\pi$
$42$	3.11942	+	2.37132i	0.481337	+	0.365903i
$43$	−0.822975	+	2.06551i	−0.125502	+	0.314987i	−0.978280	−	0.207286i	$-0.933537\pi$
$43$	−0.822975	+	2.06551i	−0.125502	+	0.314987i	0.852778	+	0.522274i	$0.174916\pi$
$44$	−2.41731	+	3.56526i	−0.364423	+	0.537484i
$45$	0.620116	+	3.78254i	0.0924415	+	0.563868i
$46$	−0.359189	−	6.62485i	−0.0529595	−	0.976781i
$47$	−1.68338	−	0.370540i	−0.245546	−	0.0540488i	0.0904919	−	0.995897i	$-0.471156\pi$
$47$	−1.68338	−	0.370540i	−0.245546	−	0.0540488i	−0.336038	+	0.941848i	$0.609087\pi$
$48$	0.370138	+	0.928977i	0.0534248	+	0.134086i
$49$	2.23492	−	8.04944i	0.319274	−	1.14992i
$50$	0.524724	−	9.67796i	0.0742071	−	1.36867i
$51$	−4.00353	+	0.435410i	−0.560607	+	0.0609696i
$52$	−0.709629	+	0.539446i	−0.0984078	+	0.0748077i
$53$	−3.40195	−	12.2527i	−0.467293	−	1.68304i	−0.702980	−	0.711210i	$-0.748148\pi$
$53$	−3.40195	−	12.2527i	−0.467293	−	1.68304i	0.235687	−	0.971829i	$-0.424266\pi$
$54$	−0.976621	+	0.214970i	−0.132901	+	0.0292538i
$55$	9.26563	+	13.6658i	1.24938	+	1.84269i
$56$	2.84475	−	2.69469i	0.380145	−	0.360093i
$57$	−2.71024	+	5.11206i	−0.358981	+	0.677109i
$58$	4.88452			0.641370
$59$	−7.03804	+	3.07668i	−0.916275	+	0.400549i
$59$	−7.03804	+	3.07668i	−0.916275	+	0.400549i
$60$	3.83304			0.494843
$61$	−3.08810	+	5.82477i	−0.395390	+	0.745785i	−0.998660	−	0.0517521i	$-0.983519\pi$
$61$	−3.08810	+	5.82477i	−0.395390	+	0.745785i	0.603270	+	0.797537i	$0.293864\pi$
$62$	5.79505	−	5.48936i	0.735972	−	0.697149i
$63$	2.19896	+	3.24323i	0.277043	+	0.408608i
$64$	0.976621	−	0.214970i	0.122078	−	0.0268713i
$65$	0.914071	+	3.29219i	0.113377	+	0.408346i
$66$	−3.42916	+	2.60678i	−0.422101	+	0.320873i
$67$	−4.62024	+	0.502481i	−0.564452	+	0.0613879i	−0.385897	−	0.922542i	$-0.626108\pi$
$67$	−4.62024	+	0.502481i	−0.564452	+	0.0613879i	−0.178555	+	0.983930i	$0.557142\pi$
$68$	−0.218025	+	4.02123i	−0.0264394	+	0.487646i
$69$	1.77494	−	6.39275i	0.213678	−	0.769597i
$70$	−5.55926	−	13.9527i	−0.664458	−	1.66766i
$71$	−8.48928	−	1.86863i	−1.00749	−	0.221766i	−0.319579	−	0.947559i	$-0.603542\pi$
$71$	−8.48928	−	1.86863i	−1.00749	−	0.221766i	−0.687912	+	0.725794i	$0.741473\pi$
$72$	0.0541389	+	0.998533i	0.00638033	+	0.117678i
$73$	0.0780241	+	0.475926i	0.00913203	+	0.0557029i	0.990999	−	0.133866i	$-0.0427392\pi$
$73$	0.0780241	+	0.475926i	0.00913203	+	0.0557029i	−0.981867	+	0.189569i	$0.939291\pi$
$74$	−1.26751	+	1.86944i	−0.147345	+	0.217318i
$75$	3.58744	−	9.00380i	0.414242	−	1.03967i
$76$	4.60625	+	3.50158i	0.528373	+	0.401659i
$77$	14.4625	+	8.70179i	1.64815	+	0.991660i
$78$	−0.844728	+	0.284622i	−0.0956466	+	0.0322271i
$79$	−9.26508	−	8.77635i	−1.04240	−	0.987416i	−0.0424709	−	0.999098i	$-0.513523\pi$
$79$	−9.26508	−	8.77635i	−1.04240	−	0.987416i	−0.999932	+	0.0116814i	$0.996282\pi$
$80$	0.620116	−	3.78254i	0.0693311	−	0.422901i
$81$	−0.994138	−	0.108119i	−0.110460	−	0.0120132i
$82$	−4.44828	+	2.67644i	−0.491230	+	0.295563i
$83$	−7.39560	+	8.70677i	−0.811772	+	0.955692i	−0.999649	−	0.0265004i	$-0.991564\pi$
$83$	−7.39560	+	8.70677i	−0.811772	+	0.955692i	0.187876	+	0.982193i	$0.439840\pi$
$84$	3.55625	−	1.64530i	0.388019	−	0.179517i
$85$	14.0095	+	6.48148i	1.51954	+	0.703015i
$86$	1.43942	+	1.69461i	0.155216	+	0.182735i
$87$	4.62884	+	1.55964i	0.496263	+	0.167211i
$88$	2.01767	+	3.80572i	0.215084	+	0.405691i
$89$	−4.81239	−	9.07713i	−0.510112	−	0.962174i	−0.996102	−	0.0882094i	$-0.971886\pi$
$89$	−4.81239	−	9.07713i	−0.510112	−	0.962174i	0.485990	−	0.873965i	$-0.338459\pi$
$90$	3.63239	+	1.22389i	0.382888	+	0.129010i
$91$	2.26121	+	2.66210i	0.237039	+	0.279064i
$92$	−6.02139	−	2.78579i	−0.627773	−	0.290439i
$93$	7.24446	−	3.35164i	0.751215	−	0.347549i
$94$	−1.11589	+	1.31372i	−0.115095	+	0.135500i
$95$	19.0036	−	11.4341i	1.94972	−	1.17311i
$96$	0.994138	+	0.108119i	0.101464	+	0.0110349i
$97$	2.40640	−	14.6784i	0.244333	−	1.49036i	−0.524772	−	0.851243i	$-0.675850\pi$
$97$	2.40640	−	14.6784i	0.244333	−	1.49036i	0.769105	−	0.639122i	$-0.220702\pi$
$98$	−6.06492	−	5.74500i	−0.612650	−	0.580333i
$99$	−4.08201	+	1.37539i	−0.410257	+	0.138232i
$100$	−8.30481	−	4.99684i	−0.830481	−	0.499684i
$101$	1.22204	+	0.928969i	0.121597	+	0.0924359i	0.664205	−	0.747550i	$-0.268770\pi$
$101$	1.22204	+	0.928969i	0.121597	+	0.0924359i	−0.542608	+	0.839986i	$0.682563\pi$
$102$	−1.49060	+	3.74112i	−0.147591	+	0.370426i
$103$	−0.147900	+	0.218136i	−0.0145730	+	0.0214936i	−0.834906	−	0.550393i	$-0.814478\pi$
$103$	−0.147900	+	0.218136i	−0.0145730	+	0.0214936i	0.820333	+	0.571887i	$0.193788\pi$
$104$	0.144211	+	0.879646i	0.0141410	+	0.0862564i
$105$	−0.813135	−	14.9974i	−0.0793538	−	1.46359i
$106$	−12.4189	−	2.73361i	−1.20623	−	0.265512i
$107$	−0.623527	−	1.56493i	−0.0602786	−	0.151288i	0.895753	−	0.444553i	$-0.146637\pi$
$107$	−0.623527	−	1.56493i	−0.0602786	−	0.151288i	−0.956031	+	0.293265i	$0.905258\pi$
$108$	−0.267528	+	0.963550i	−0.0257429	+	0.0927176i
$109$	−0.567900	+	10.4743i	−0.0543949	+	1.00326i	0.836190	+	0.548439i	$0.184778\pi$
$109$	−0.567900	+	10.4743i	−0.0543949	+	1.00326i	−0.890585	+	0.454816i	$0.849705\pi$
$110$	16.4140	−	1.78513i	1.56501	−	0.170205i
$111$	−1.79808	+	1.36686i	−0.170666	+	0.129737i
$112$	−1.04829	−	3.77558i	−0.0990537	−	0.356759i
$113$	20.5966	−	4.53366i	1.93757	−	0.426491i	0.941604	−	0.336723i	$-0.109318\pi$
$113$	20.5966	−	4.53366i	1.93757	−	0.426491i	0.995963	−	0.0897680i	$-0.0286126\pi$
$114$	3.24707	+	4.78907i	0.304116	+	0.448537i
$115$	−18.4625	+	17.4886i	−1.72164	+	1.63082i
$116$	2.28795	−	4.31554i	0.212431	−	0.400688i
$117$	−0.891389			−0.0824090
$118$	−0.578399	+	7.65934i	−0.0532459	+	0.705099i
$119$	15.7800			1.44655
$120$	1.79543	−	3.38653i	0.163899	−	0.309147i
$121$	−5.48452	+	5.19521i	−0.498593	+	0.472292i
$122$	3.69976	+	5.45674i	0.334961	+	0.494030i
$123$	−5.07001	+	1.11599i	−0.457148	+	0.100626i
$124$	−2.13547	−	7.69126i	−0.191771	−	0.690695i
$125$	−14.3180	+	10.8842i	−1.28064	+	0.973515i
$126$	3.89544	−	0.423655i	0.347033	−	0.0377422i
$127$	−0.969982	+	17.8903i	−0.0860720	+	1.58750i	0.562791	+	0.826599i	$0.309728\pi$
$127$	−0.969982	+	17.8903i	−0.0860720	+	1.58750i	−0.648863	+	0.760906i	$0.724755\pi$
$128$	0.267528	−	0.963550i	0.0236464	−	0.0851666i
$129$	0.822975	+	2.06551i	0.0724589	+	0.181858i
$130$	3.33685	+	0.734495i	0.292661	+	0.0644195i
$131$	−0.101029	−	1.86338i	−0.00882697	−	0.162804i	−0.999623	−	0.0274433i	$-0.991263\pi$
$131$	−0.101029	−	1.86338i	−0.00882697	−	0.162804i	0.990796	−	0.135361i	$-0.0432193\pi$
$132$	0.696874	+	4.25075i	0.0606551	+	0.369980i
$133$	12.7233	−	18.7655i	1.10325	−	1.62718i
$134$	−1.72021	+	4.31740i	−0.148604	+	0.372967i
$135$	3.05145	+	2.31966i	0.262627	+	0.199644i
$136$	3.45068	+	2.07621i	0.295894	+	0.178033i
$137$	2.37854	−	0.801422i	0.203212	−	0.0684701i	−0.215855	−	0.976425i	$-0.569254\pi$
$137$	2.37854	−	0.801422i	0.203212	−	0.0684701i	0.419067	+	0.907955i	$0.362357\pi$
$138$	−4.81668	−	4.56260i	−0.410023	−	0.388394i
$139$	0.638429	−	3.89424i	0.0541508	−	0.330305i	−0.945833	−	0.324653i	$-0.894752\pi$
$139$	0.638429	−	3.89424i	0.0541508	−	0.330305i	0.999984	−	0.00565243i	$-0.00179923\pi$
$140$	−14.9314	−	1.62388i	−1.26193	−	0.137243i
$141$	−1.47695	+	0.888650i	−0.124381	+	0.0748378i
$142$	−5.62741	+	6.62510i	−0.472241	+	0.555966i
$143$	−3.48477	+	1.61223i	−0.291411	+	0.134821i
$144$	0.907575	+	0.419889i	0.0756313	+	0.0349908i
$145$	−12.1207	−	14.2696i	−1.00657	−	1.18503i
$146$	0.457034	+	0.153993i	0.0378244	+	0.0127445i
$147$	−3.91306	−	7.38081i	−0.322743	−	0.608759i
$148$	1.05796	+	1.99552i	0.0869637	+	0.164031i
$149$	11.1977	+	3.77296i	0.917355	+	0.309093i	0.738086	−	0.674707i	$-0.235730\pi$
$149$	11.1977	+	3.77296i	0.917355	+	0.309093i	0.179269	+	0.983800i	$0.442627\pi$
$150$	−6.27458	−	7.38701i	−0.512317	−	0.603147i
$151$	2.69278	+	1.24581i	0.219136	+	0.101383i	0.526386	−	0.850246i	$-0.323547\pi$
$151$	2.69278	+	1.24581i	0.219136	+	0.101383i	−0.307250	+	0.951629i	$0.599409\pi$
$152$	5.25129	−	2.42951i	0.425936	−	0.197059i
$153$	−2.60711	+	3.06933i	−0.210773	+	0.248141i
$154$	14.4625	−	8.70179i	1.16542	−	0.701210i
$155$	−30.4167	−	3.30802i	−2.44313	−	0.265707i
$156$	−0.144211	+	0.879646i	−0.0115461	+	0.0704281i
$157$	5.31922	+	5.03863i	0.424520	+	0.402127i	0.869910	−	0.493210i	$-0.164177\pi$
$157$	5.31922	+	5.03863i	0.424520	+	0.402127i	−0.445391	+	0.895336i	$0.646935\pi$
$158$	−12.0938	+	4.07489i	−0.962135	+	0.324181i
$159$	−10.8960	−	6.55589i	−0.864107	−	0.519916i
$160$	−3.05145	−	2.31966i	−0.241239	−	0.183385i
$161$	−9.62249	+	24.1506i	−0.758358	+	1.90334i
$162$	−0.561187	+	0.827689i	−0.0440910	+	0.0650294i
$163$	−3.51473	−	21.4389i	−0.275295	−	1.67922i	−0.656182	−	0.754603i	$-0.727830\pi$
$163$	−3.51473	−	21.4389i	−0.275295	−	1.67922i	0.380887	−	0.924622i	$-0.375619\pi$
$164$	0.281056	+	5.18377i	0.0219468	+	0.404785i
$165$	16.1248	+	3.54933i	1.25531	+	0.276315i
$166$	4.22838	+	10.6124i	0.328186	+	0.823684i
$167$	−6.14610	+	22.1363i	−0.475600	+	1.71295i	0.203647	+	0.979044i	$0.434721\pi$
$167$	−6.14610	+	22.1363i	−0.475600	+	1.71295i	−0.679246	+	0.733910i	$0.737693\pi$
$168$	0.212138	−	3.91266i	0.0163668	−	0.301869i
$169$	12.1339	−	1.31964i	0.933375	−	0.101511i
$170$	12.2886	−	9.34158i	0.942495	−	0.716466i
$171$	1.54794	+	5.57517i	0.118374	+	0.426344i
$172$	2.17144	−	0.477971i	0.165571	−	0.0364449i
$173$	−6.05342	−	8.92812i	−0.460233	−	0.678792i	0.524787	−	0.851234i	$-0.324145\pi$
$173$	−6.05342	−	8.92812i	−0.460233	−	0.678792i	−0.985020	+	0.172441i	$0.944835\pi$
$174$	3.54614	−	3.35909i	0.268832	−	0.254652i
$175$	−17.7892	+	33.5539i	−1.34474	+	2.53644i
$176$	4.30749			0.324689
$177$	−2.99376	+	7.07371i	−0.225025	+	0.531693i
$178$	−10.2739			−0.770063
$179$	−11.0511	+	20.8445i	−0.825995	+	1.55799i	0.00384629	+	0.999993i	$0.498776\pi$
$179$	−11.0511	+	20.8445i	−0.825995	+	1.55799i	−0.829841	+	0.557999i	$0.811569\pi$
$180$	2.78277	−	2.63598i	0.207415	−	0.196474i
$181$	−1.50203	−	2.21533i	−0.111645	−	0.164664i	0.767762	−	0.640736i	$-0.221371\pi$
$181$	−1.50203	−	2.21533i	−0.111645	−	0.164664i	−0.879406	+	0.476072i	$0.842060\pi$
$182$	3.41117	−	0.750855i	0.252853	−	0.0556571i
$183$	1.76375	+	6.35244i	0.130380	+	0.469586i
$184$	−5.28175	+	4.01508i	−0.389376	+	0.295996i
$185$	8.60664	−	0.936029i	0.632773	−	0.0688182i
$186$	0.432148	−	7.97050i	0.0316866	−	0.584426i
$187$	−4.64078	+	16.7146i	−0.339367	+	1.22229i
$188$	0.637999	+	1.60126i	0.0465309	+	0.116784i
$189$	3.82680	+	0.842342i	0.278359	+	0.0612714i
$190$	−1.20070	−	22.1457i	−0.0871083	−	1.60662i
$191$	1.34076	+	8.17827i	0.0970140	+	0.591759i	0.989932	+	0.141541i	$0.0452056\pi$
$191$	1.34076	+	8.17827i	0.0970140	+	0.591759i	−0.892918	+	0.450218i	$0.851346\pi$
$192$	0.561187	−	0.827689i	0.0405002	−	0.0597333i
$193$	6.14025	−	15.4109i	0.441985	−	1.10930i	−0.524233	−	0.851575i	$-0.675648\pi$
$193$	6.14025	−	15.4109i	0.441985	−	1.10930i	0.966218	−	0.257725i	$-0.0829727\pi$
$194$	−11.8414	−	9.00156i	−0.850160	−	0.646275i
$195$	2.92765	+	1.76151i	0.209653	+	0.126144i
$196$	−7.91664	+	2.66743i	−0.565474	+	0.190530i
$197$	−8.26058	−	7.82484i	−0.588542	−	0.557497i	0.334402	−	0.942430i	$-0.391466\pi$
$197$	−8.26058	−	7.82484i	−0.588542	−	0.557497i	−0.922944	+	0.384934i	$0.874224\pi$
$198$	−0.696874	+	4.25075i	−0.0495247	+	0.302087i
$199$	−4.84069	−	0.526457i	−0.343148	−	0.0373196i	−0.0650772	−	0.997880i	$-0.520729\pi$
$199$	−4.84069	−	0.526457i	−0.343148	−	0.0373196i	−0.278070	+	0.960561i	$0.589695\pi$
$200$	−8.30481	+	4.99684i	−0.587239	+	0.353330i
$201$	−3.00872	+	3.54213i	−0.212218	+	0.249843i
$202$	1.39317	−	0.644548i	0.0980230	−	0.0453503i
$203$	−17.3706	−	8.03650i	−1.21918	−	0.564052i
$204$	2.60711	+	3.06933i	0.182535	+	0.214896i
$205$	18.8571	+	6.35371i	1.31704	+	0.443762i
$206$	0.123448	+	0.232848i	0.00860104	+	0.0162233i
$207$	−3.10770	−	5.86173i	−0.216000	−	0.407419i
$208$	0.844728	+	0.284622i	0.0585713	+	0.0197350i
$209$	16.1351	+	18.9957i	1.11609	+	1.31396i
$210$	−13.6312	−	6.30649i	−0.940646	−	0.435189i
$211$	22.3758	−	10.3521i	1.54041	−	0.712670i	0.548097	−	0.836415i	$-0.315352\pi$
$211$	22.3758	−	10.3521i	1.54041	−	0.712670i	0.992314	+	0.123745i	$0.0394903\pi$
$212$	−8.23230	+	9.69181i	−0.565397	+	0.665637i
$213$	−7.44823	+	4.48145i	−0.510344	+	0.307064i
$214$	−1.67470	−	0.182135i	−0.114480	−	0.0124505i
$215$	1.37878	−	8.41020i	0.0940322	−	0.573571i
$216$	0.725995	+	0.687699i	0.0493977	+	0.0467920i
$217$	−29.6403	+	9.98698i	−2.01211	+	0.677960i
$218$	8.98816	+	5.40800i	0.608755	+	0.366276i
$219$	0.383939	+	0.291863i	0.0259442	+	0.0197223i
$220$	6.11127	−	15.3381i	0.412022	−	1.03410i
$221$	−2.01452	+	2.97120i	−0.135511	+	0.199864i
$222$	0.365405	+	2.22887i	0.0245244	+	0.149592i
$223$	−0.883907	−	16.3027i	−0.0591908	−	1.09171i	−0.865724	−	0.500522i	$-0.833142\pi$
$223$	−0.883907	−	16.3027i	−0.0591908	−	1.09171i	0.806533	−	0.591189i	$-0.201341\pi$
$224$	−3.82680	−	0.842342i	−0.255689	−	0.0562814i
$225$	−3.58744	−	9.00380i	−0.239163	−	0.600254i
$226$	5.64209	−	20.3210i	0.375306	−	1.35173i
$227$	1.09978	−	20.2842i	0.0729947	−	1.34631i	−0.701020	−	0.713141i	$-0.747272\pi$
$227$	1.09978	−	20.2842i	0.0729947	−	1.34631i	0.774015	−	0.633167i	$-0.218245\pi$
$228$	5.75215	−	0.625584i	0.380945	−	0.0414303i
$229$	19.6500	−	14.9375i	1.29851	−	0.987098i	0.299046	−	0.954239i	$-0.403332\pi$
$229$	19.6500	−	14.9375i	1.29851	−	0.987098i	0.999460	−	0.0328596i	$-0.0104614\pi$
$230$	6.80341	+	24.5037i	0.448603	+	1.61572i
$231$	16.4839	−	3.62838i	1.08456	−	0.238730i
$232$	−2.74113	−	4.04287i	−0.179964	−	0.265427i
$233$	−4.23881	+	4.01521i	−0.277694	+	0.263045i	−0.813852	−	0.581072i	$-0.802633\pi$
$233$	−4.23881	+	4.01521i	−0.277694	+	0.263045i	0.536159	+	0.844117i	$0.319875\pi$
$234$	−0.417534	+	0.787553i	−0.0272951	+	0.0514840i
$235$	6.60693			0.430988
$236$	6.49619	+	4.09872i	0.422866	+	0.266804i
$237$	−12.7619			−0.828974
$238$	7.39148	−	13.9418i	0.479118	−	0.903713i
$239$	−0.928214	+	0.879251i	−0.0600412	+	0.0568740i	−0.717132	−	0.696938i	$-0.754545\pi$
$239$	−0.928214	+	0.879251i	−0.0600412	+	0.0568740i	0.657091	+	0.753812i	$0.271787\pi$
$240$	−2.15105	−	3.17256i	−0.138850	−	0.204788i
$241$	5.43241	−	1.19576i	0.349932	−	0.0770259i	−0.0365264	−	0.999333i	$-0.511629\pi$
$241$	5.43241	−	1.19576i	0.349932	−	0.0770259i	0.386458	+	0.922307i	$0.373698\pi$
$242$	2.02104	+	7.27912i	0.129917	+	0.467919i
$243$	−0.796093	+	0.605174i	−0.0510694	+	0.0388219i
$244$	6.55410	−	0.712801i	0.419583	−	0.0456324i
$245$	−1.73358	+	31.9740i	−0.110754	+	2.04274i
$246$	−1.38884	+	5.00216i	−0.0885494	+	0.318926i
$247$	1.90904	+	4.79133i	0.121469	+	0.304865i
$248$	−7.79559	−	1.71594i	−0.495020	−	0.108962i
$249$	0.618471	+	11.4070i	0.0391940	+	0.722891i
$250$	2.90969	+	17.7483i	0.184025	+	1.12250i
$251$	−14.3248	+	21.1275i	−0.904173	+	1.33356i	0.0382977	+	0.999266i	$0.487806\pi$
$251$	−14.3248	+	21.1275i	−0.904173	+	1.33356i	−0.942471	+	0.334289i	$0.891504\pi$
$252$	1.45035	−	3.64011i	0.0913637	−	0.229306i
$253$	−22.7511	−	17.2949i	−1.43035	−	1.08732i
$254$	15.3519	+	9.23695i	0.963265	+	0.579578i
$255$	14.6281	−	4.92879i	0.916050	−	0.308653i
$256$	−0.725995	−	0.687699i	−0.0453747	−	0.0429812i
$257$	2.37627	−	14.4946i	0.148228	−	0.904150i	−0.803072	−	0.595883i	$-0.796802\pi$
$257$	2.37627	−	14.4946i	0.148228	−	0.904150i	0.951300	−	0.308268i	$-0.0997493\pi$
$258$	2.21039	+	0.240395i	0.137613	+	0.0149663i
$259$	7.58338	−	4.56277i	0.471208	−	0.283516i
$260$	2.21194	−	2.60410i	0.137179	−	0.161499i
$261$	4.43307	−	2.05096i	0.274400	−	0.126951i
$262$	−1.69364	−	0.783561i	−0.104633	−	0.0484085i
$263$	−6.15608	−	7.24750i	−0.379600	−	0.446900i	0.538871	−	0.842389i	$-0.318851\pi$
$263$	−6.15608	−	7.24750i	−0.379600	−	0.446900i	−0.918471	+	0.395488i	$0.870575\pi$
$264$	4.08201	+	1.37539i	0.251230	+	0.0846493i
$265$	22.8310	+	43.0639i	1.40250	+	2.64539i
$266$	−10.6198	−	20.0312i	−0.651145	−	1.22819i
$267$	−9.73611	−	3.28048i	−0.595840	−	0.200762i
$268$	3.00872	+	3.54213i	0.183787	+	0.216370i
$269$	−4.65521	−	2.15373i	−0.283833	−	0.131315i	0.272807	−	0.962069i	$-0.412048\pi$
$269$	−4.65521	−	2.15373i	−0.283833	−	0.131315i	−0.556640	+	0.830754i	$0.687910\pi$
$270$	3.47877	−	1.60945i	0.211711	−	0.0979480i
$271$	−6.40922	+	7.54552i	−0.389333	+	0.458358i	−0.921556	−	0.388246i	$-0.873081\pi$
$271$	−6.40922	+	7.54552i	−0.389333	+	0.458358i	0.532223	+	0.846604i	$0.321357\pi$
$272$	3.45068	−	2.07621i	0.209228	−	0.125889i
$273$	3.47235	+	0.377641i	0.210156	+	0.0228559i
$274$	0.406060	−	2.47686i	0.0245310	−	0.149632i
$275$	−30.3096	−	28.7107i	−1.82773	−	1.73132i
$276$	−6.28728	+	2.11843i	−0.378450	+	0.127515i
$277$	−20.4829	−	12.3242i	−1.23070	−	0.740487i	−0.256581	−	0.966523i	$-0.582596\pi$
$277$	−20.4829	−	12.3242i	−1.23070	−	0.740487i	−0.974119	+	0.226035i	$0.927424\pi$
$278$	−3.14157	−	2.38816i	−0.188419	−	0.143232i
$279$	2.95452	−	7.41529i	0.176882	−	0.443942i
$280$	−8.42870	+	12.4314i	−0.503711	+	0.742918i
$281$	1.38710	+	8.46095i	0.0827476	+	0.504738i	0.995385	+	0.0959669i	$0.0305943\pi$
$281$	1.38710	+	8.46095i	0.0827476	+	0.504738i	−0.912637	+	0.408771i	$0.865957\pi$
$282$	0.0933181	+	1.72115i	0.00555701	+	0.102493i
$283$	−3.61387	−	0.795474i	−0.214822	−	0.0472860i	0.106255	−	0.994339i	$-0.466114\pi$
$283$	−3.61387	−	0.795474i	−0.214822	−	0.0472860i	−0.321078	+	0.947053i	$0.604045\pi$
$284$	3.21743	+	8.07513i	0.190919	+	0.479171i
$285$	5.93330	−	21.3698i	0.351458	−	1.26584i
$286$	−0.207875	+	3.83402i	−0.0122919	+	0.226710i
$287$	20.2227	−	2.19935i	1.19371	−	0.129824i
$288$	0.796093	−	0.605174i	0.0469102	−	0.0356602i
$289$	−0.209247	−	0.753638i	−0.0123086	−	0.0443317i
$290$	−18.2848	+	4.02480i	−1.07372	+	0.236344i
$291$	−8.34729	−	12.3113i	−0.489327	−	0.721703i
$292$	0.350133	−	0.331663i	0.0204900	−	0.0194091i
$293$	1.93495	−	3.64971i	0.113041	−	0.213218i	−0.820536	−	0.571595i	$-0.806325\pi$
$293$	1.93495	−	3.64971i	0.113041	−	0.213218i	0.933577	+	0.358377i	$0.116670\pi$
$294$	−8.35394			−0.487212
$295$	23.8112	−	17.3166i	1.38634	−	1.00821i
$296$	2.25863			0.131280
$297$	−2.01767	+	3.80572i	−0.117077	+	0.220830i
$298$	8.57857	−	8.12606i	0.496943	−	0.470730i
$299$	−3.31886	−	4.89495i	−0.191935	−	0.283082i
$300$	−9.46558	+	2.08353i	−0.546495	+	0.120293i
$301$	−2.33079	−	8.39473i	−0.134344	−	0.483864i
$302$	2.36202	−	1.79556i	0.135919	−	0.103323i
$303$	1.52605	−	0.165967i	0.0876690	−	0.00953458i
$304$	0.313251	−	5.77758i	0.0179662	−	0.331367i
$305$	6.76050	−	24.3491i	0.387105	−	1.39423i
$306$	1.49060	+	3.74112i	0.0852118	+	0.213866i
$307$	9.77649	+	2.15197i	0.557974	+	0.122819i	0.484999	−	0.874514i	$-0.338820\pi$
$307$	9.77649	+	2.15197i	0.557974	+	0.122819i	0.0729745	+	0.997334i	$0.476751\pi$
$308$	−0.913785	−	16.8538i	−0.0520677	−	0.960332i
$309$	0.0426373	+	0.260076i	0.00242555	+	0.0147952i
$310$	−17.1701	+	25.3241i	−0.975198	+	1.43831i
$311$	−7.27733	+	18.2647i	−0.412659	+	1.03570i	0.564923	+	0.825144i	$0.308906\pi$
$311$	−7.27733	+	18.2647i	−0.412659	+	1.03570i	−0.977582	+	0.210553i	$0.932473\pi$
$312$	0.709629	+	0.539446i	0.0401748	+	0.0305401i
$313$	10.2143	+	6.14573i	0.577345	+	0.347377i	0.774088	−	0.633078i	$-0.218209\pi$
$313$	10.2143	+	6.14573i	0.577345	+	0.347377i	−0.196743	+	0.980455i	$0.563036\pi$
$314$	6.94326	−	2.33946i	0.391831	−	0.132023i
$315$	−10.9040	−	10.3288i	−0.614372	−	0.581964i
$316$	−2.06464	+	12.5938i	−0.116145	+	0.708455i
$317$	−19.3973	−	2.10959i	−1.08946	−	0.118486i	−0.454288	−	0.890855i	$-0.650106\pi$
$317$	−19.3973	−	2.10959i	−1.08946	−	0.118486i	−0.635174	+	0.772369i	$0.719072\pi$
$318$	−10.8960	+	6.55589i	−0.611016	+	0.367636i
$319$	13.6210	−	16.0359i	0.762632	−	0.897839i
$320$	−3.47877	+	1.60945i	−0.194469	+	0.0899710i
$321$	−1.52888	−	0.707336i	−0.0853339	−	0.0394797i
$322$	16.8301	+	19.8139i	0.937906	+	1.10419i
$323$	22.0816	+	7.44014i	1.22865	+	0.413981i
$324$	0.468408	+	0.883512i	0.0260227	+	0.0490840i
$325$	−4.04681	−	7.63310i	−0.224477	−	0.423408i
$326$	−20.5879	−	6.93686i	−1.14026	−	0.384197i
$327$	6.79088	+	7.99484i	0.375536	+	0.442115i
$328$	4.71157	+	2.17981i	0.260153	+	0.120360i
$329$	6.12984	−	2.83597i	0.337949	−	0.156352i
$330$	10.6888	−	12.5839i	0.588402	−	0.692720i
$331$	−24.9166	+	14.9918i	−1.36954	+	0.824025i	−0.994676	−	0.103055i	$-0.967138\pi$
$331$	−24.9166	+	14.9918i	−1.36954	+	0.824025i	−0.374864	+	0.927080i	$0.622311\pi$
$332$	11.3568	+	1.23513i	0.623286	+	0.0677864i
$333$	−0.365405	+	2.22887i	−0.0200241	+	0.122141i
$334$	16.6788	+	15.7990i	0.912621	+	0.864481i
$335$	16.8815	−	5.68803i	0.922333	−	0.310770i
$336$	−3.35752	−	2.02015i	−0.183168	−	0.110208i
$337$	−12.1026	−	9.20018i	−0.659272	−	0.501165i	0.221222	−	0.975224i	$-0.428996\pi$
$337$	−12.1026	−	9.20018i	−0.659272	−	0.501165i	−0.880494	+	0.474058i	$0.842789\pi$
$338$	4.51769	−	11.3386i	0.245730	−	0.616736i
$339$	11.8353	−	17.4557i	0.642803	−	0.948063i
$340$	−2.49730	−	15.2328i	−0.135435	−	0.826116i
$341$	−1.86147	−	34.3329i	−0.100804	−	1.85923i
$342$	5.65079	+	1.24383i	0.305560	+	0.0672588i
$343$	1.96369	+	4.92850i	0.106029	+	0.266114i
$344$	0.594829	−	2.14238i	0.0320711	−	0.115509i
$345$	−1.37679	+	25.3933i	−0.0741236	+	1.36713i
$346$	−10.7236	+	1.16626i	−0.576503	+	0.0626985i
$347$	17.9073	−	13.6128i	0.961317	−	0.730774i	−0.00176066	−	0.999998i	$-0.500560\pi$
$347$	17.9073	−	13.6128i	0.961317	−	0.730774i	0.963077	+	0.269224i	$0.0867673\pi$
$348$	−1.30675	−	4.70648i	−0.0700491	−	0.252294i
$349$	1.53509	−	0.337900i	0.0821717	−	0.0180874i	−0.173694	−	0.984800i	$-0.555570\pi$
$349$	1.53509	−	0.337900i	0.0821717	−	0.0180874i	0.255866	+	0.966712i	$0.417639\pi$
$350$	21.3127	+	31.4339i	1.13921	+	1.68021i
$351$	−0.647145	+	0.613008i	−0.0345420	+	0.0327199i
$352$	2.01767	−	3.80572i	0.107542	−	0.202846i
$353$	28.2817			1.50528			0.752642	−	0.658430i	$-0.228779\pi$
$353$	28.2817			1.50528			0.752642	+	0.658430i	$0.228779\pi$
$354$	4.84741	+	5.95841i	0.257637	+	0.316686i
$355$	33.3187			1.76837
$356$	−4.81239	+	9.07713i	−0.255056	+	0.481087i
$357$	11.4562	−	10.8519i	0.606326	−	0.574343i
$358$	13.2400	+	19.5275i	0.699754	+	1.03206i
$359$	0.262577	−	0.0577976i	0.0138583	−	0.00305044i	−0.208036	−	0.978121i	$-0.566707\pi$
$359$	0.262577	−	0.0577976i	0.0138583	−	0.00305044i	0.221894	+	0.975071i	$0.428776\pi$
$360$	−1.02545	−	3.69332i	−0.0540458	−	0.194655i
$361$	11.5263	−	8.76207i	0.606648	−	0.461162i
$362$	−2.66083	+	0.289383i	−0.139850	+	0.0152096i
$363$	−0.408991	+	7.54340i	−0.0214665	+	0.395926i
$364$	0.934431	−	3.36551i	0.0489775	−	0.176401i
$365$	−0.684235	−	1.71730i	−0.0358145	−	0.0898877i
$366$	6.43861	+	1.41725i	0.336551	+	0.0740806i
$367$	−0.758260	−	13.9853i	−0.0395808	−	0.730025i	−0.949217	−	0.314621i	$-0.898123\pi$
$367$	−0.758260	−	13.9853i	−0.0395808	−	0.730025i	0.909637	−	0.415405i	$-0.136360\pi$
$368$	1.07336	+	6.54718i	0.0559526	+	0.341296i
$369$	−2.91334	+	4.29685i	−0.151662	+	0.223685i
$370$	3.20443	−	8.04252i	0.166590	−	0.418111i
$371$	39.6672	+	30.1542i	2.05942	+	1.56553i
$372$	−6.83961	−	4.11526i	−0.354617	−	0.213366i
$373$	−16.5769	+	5.58540i	−0.858318	+	0.289201i	−0.713841	−	0.700307i	$-0.753046\pi$
$373$	−16.5769	+	5.58540i	−0.858318	+	0.289201i	−0.144476	+	0.989508i	$0.546150\pi$
$374$	12.5937	+	11.9294i	0.651207	+	0.616856i
$375$	−2.90969	+	17.7483i	−0.150256	+	0.916521i
$376$	1.71358	+	0.186363i	0.0883709	+	0.00961091i
$377$	3.73077	−	2.24473i	0.192144	−	0.115609i
$378$	2.53673	−	2.98646i	0.130475	−	0.153607i
$379$	22.5861	−	10.4495i	1.16017	−	0.536752i	0.257160	−	0.966369i	$-0.417213\pi$
$379$	22.5861	−	10.4495i	1.16017	−	0.536752i	0.903011	+	0.429617i	$0.141351\pi$
$380$	−20.1284	−	9.31239i	−1.03257	−	0.477716i
$381$	11.5989	+	13.6553i	0.594231	+	0.699583i
$382$	7.85363	+	2.64619i	0.401826	+	0.135391i
$383$	4.25071	+	8.01768i	0.217201	+	0.409685i	0.968038	−	0.250803i	$-0.0806946\pi$
$383$	4.25071	+	8.01768i	0.217201	+	0.409685i	−0.750837	+	0.660487i	$0.770350\pi$
$384$	−0.468408	−	0.883512i	−0.0239034	−	0.0450865i
$385$	−61.3094	−	20.6575i	−3.12461	−	1.05281i
$386$	−10.7395	−	12.6436i	−0.546629	−	0.643541i
$387$	2.01793	+	0.933592i	0.102577	+	0.0474572i
$388$	−13.4996	+	6.24557i	−0.685337	+	0.317071i
$389$	−8.00609	+	9.42549i	−0.405925	+	0.477891i	−0.926700	−	0.375802i	$-0.877367\pi$
$389$	−8.00609	+	9.42549i	−0.405925	+	0.477891i	0.520775	+	0.853694i	$0.325643\pi$
$390$	2.92765	−	1.76151i	0.148247	−	0.0891974i
$391$	−26.5618	−	2.88877i	−1.34329	−	0.146091i
$392$	−1.35152	+	8.24389i	−0.0682619	+	0.416379i
$393$	−1.35479	−	1.28333i	−0.0683401	−	0.0647352i
$394$	−10.7827	+	3.63310i	−0.543223	+	0.183033i
$395$	41.9147	+	25.2193i	2.10896	+	1.26892i
$396$	3.42916	+	2.60678i	0.172322	+	0.130996i
$397$	−1.25412	+	3.14760i	−0.0629424	+	0.157974i	−0.957084	−	0.289811i	$-0.906408\pi$
$397$	−1.25412	+	3.14760i	−0.0629424	+	0.157974i	0.894141	+	0.447785i	$0.147787\pi$
$398$	−2.73255	+	4.03021i	−0.136970	+	0.202016i
$399$	−3.66795	−	22.3735i	−0.183627	−	1.12008i
$400$	0.524724	+	9.67796i	0.0262362	+	0.483898i
$401$	−14.6236	−	3.21890i	−0.730268	−	0.160744i	−0.165754	−	0.986167i	$-0.553006\pi$
$401$	−14.6236	−	3.21890i	−0.730268	−	0.160744i	−0.564515	+	0.825423i	$0.690937\pi$
$402$	1.72021	+	4.31740i	0.0857963	+	0.215332i
$403$	1.90353	−	6.85590i	0.0948217	−	0.341517i
$404$	0.0831056	−	1.53279i	0.00413466	−	0.0762593i
$405$	3.81057	−	0.414424i	0.189349	−	0.0205929i
$406$	−15.2369	+	11.5828i	−0.756194	+	0.574844i
$407$	2.60279	+	9.37439i	0.129015	+	0.464671i
$408$	3.93299	−	0.865716i	0.194712	−	0.0428593i
$409$	11.7307	+	17.3015i	0.580045	+	0.855503i	0.998611	−	0.0526836i	$-0.0167775\pi$
$409$	11.7307	+	17.3015i	0.580045	+	0.855503i	−0.418566	+	0.908186i	$0.637467\pi$
$410$	14.4464	−	13.6844i	0.713458	−	0.675823i
$411$	1.17567	−	2.21755i	0.0579915	−	0.109384i
$412$	0.263548			0.0129841
$413$	14.6588	−	26.2869i	0.721314	−	1.29349i
$414$	−6.63458			−0.326072
$415$	20.5106	−	38.6870i	1.00682	−	1.89907i
$416$	0.647145	−	0.613008i	0.0317289	−	0.0300552i
$417$	−2.21457	−	3.26625i	−0.108448	−	0.159949i
$418$	24.3407	−	5.35780i	1.19054	−	0.262059i
$419$	6.14722	+	22.1403i	0.300311	+	1.08162i	0.947621	+	0.319396i	$0.103480\pi$
$419$	6.14722	+	22.1403i	0.300311	+	1.08162i	−0.647310	+	0.762227i	$0.724106\pi$
$420$	−11.9569	+	9.08936i	−0.583435	+	0.443515i
$421$	−15.3279	+	1.66701i	−0.747038	+	0.0812453i	−0.473717	−	0.880677i	$-0.657088\pi$
$421$	−15.3279	+	1.66701i	−0.747038	+	0.0812453i	−0.273322	+	0.961923i	$0.588122\pi$
$422$	1.33476	−	24.6183i	0.0649753	−	1.19840i
$423$	−0.461133	+	1.66085i	−0.0224211	+	0.0807533i
$424$	4.70676	+	11.8131i	0.228580	+	0.573693i
$425$	−38.1192	−	8.39067i	−1.84905	−	0.407007i
$426$	0.470603	+	8.67975i	0.0228008	+	0.420535i
$427$	−4.17933	−	25.4928i	−0.202252	−	1.23368i
$428$	−0.945364	+	1.39431i	−0.0456959	+	0.0673964i
$429$	−1.42120	+	3.56695i	−0.0686162	+	0.172214i
$430$	−6.78468	−	5.15758i	−0.327186	−	0.248721i
$431$	3.40574	+	2.04917i	0.164049	+	0.0987048i	0.595211	−	0.803570i	$-0.297069\pi$
$431$	3.40574	+	2.04917i	0.164049	+	0.0987048i	−0.431162	+	0.902275i	$0.641896\pi$
$432$	0.947653	−	0.319302i	0.0455940	−	0.0153624i
$433$	−14.9556	−	14.1667i	−0.718721	−	0.680809i	0.238181	−	0.971221i	$-0.423449\pi$
$433$	−14.9556	−	14.1667i	−0.718721	−	0.680809i	−0.956902	+	0.290412i	$0.906208\pi$
$434$	−5.06015	+	30.8655i	−0.242895	+	1.48159i
$435$	−18.6128	−	2.02427i	−0.892416	−	0.0970561i
$436$	8.98816	−	5.40800i	0.430455	−	0.258996i
$437$	−24.8520	+	29.2580i	−1.18883	+	1.39960i
$438$	0.437705	−	0.202504i	0.0209143	−	0.00967601i
$439$	−13.5462	−	6.26712i	−0.646523	−	0.299113i	0.0690899	−	0.997610i	$-0.477990\pi$
$439$	−13.5462	−	6.26712i	−0.646523	−	0.299113i	−0.715613	+	0.698497i	$0.753853\pi$
$440$	−10.6888	−	12.5839i	−0.509571	−	0.599913i
$441$	−7.91664	−	2.66743i	−0.376983	−	0.127020i
$442$	1.68147	+	3.17159i	0.0799793	+	0.150857i
$443$	−9.94954	−	18.7668i	−0.472717	−	0.891639i	−0.999142	−	0.0414173i	$-0.986813\pi$
$443$	−9.94954	−	18.7668i	−0.472717	−	0.891639i	0.526425	−	0.850222i	$-0.323532\pi$
$444$	2.14039	+	0.721183i	0.101579	+	0.0342258i
$445$	25.4943	+	30.0142i	1.20854	+	1.42281i
$446$	−14.8177	−	6.85538i	−0.701637	−	0.324612i
$447$	10.7242	−	4.96153i	0.507236	−	0.234672i
$448$	−2.53673	+	2.98646i	−0.119849	+	0.141097i
$449$	19.1384	−	11.5152i	0.903199	−	0.543437i	0.0134615	−	0.999909i	$-0.495715\pi$
$449$	19.1384	−	11.5152i	0.903199	−	0.543437i	0.889737	+	0.456473i	$0.150887\pi$
$450$	−9.63536	−	1.04791i	−0.454215	−	0.0493989i
$451$	−3.61774	+	22.0673i	−0.170353	+	1.03911i
$452$	−15.3110	−	14.5034i	−0.720169	−	0.682181i
$453$	2.81170	−	0.947371i	0.132105	−	0.0445114i
$454$	−17.4062	−	10.4729i	−0.816912	−	0.491520i
$455$	−10.6582	−	8.10216i	−0.499664	−	0.379835i
$456$	2.14164	−	5.37512i	0.100292	−	0.251713i
$457$	7.75639	−	11.4398i	0.362829	−	0.535132i	−0.601834	−	0.798621i	$-0.705563\pi$
$457$	7.75639	−	11.4398i	0.362829	−	0.535132i	0.964662	+	0.263489i	$0.0848734\pi$
$458$	−3.99326	−	24.3578i	−0.186593	−	1.13817i
$459$	0.218025	+	4.02123i	0.0101765	+	0.187695i
$460$	24.8361	+	5.46683i	1.15799	+	0.254892i
$461$	−4.44843	−	11.1647i	−0.207184	−	0.519993i	0.788260	−	0.615343i	$-0.210982\pi$
$461$	−4.44843	−	11.1647i	−0.207184	−	0.519993i	−0.995444	+	0.0953498i	$0.969603\pi$
$462$	4.51548	−	16.2633i	0.210079	−	0.756637i
$463$	−0.702311	+	12.9534i	−0.0326391	+	0.601994i	0.935768	+	0.352617i	$0.114708\pi$
$463$	−0.702311	+	12.9534i	−0.0326391	+	0.601994i	−0.968407	+	0.249376i	$0.919774\pi$
$464$	−4.85589	+	0.528110i	−0.225429	+	0.0245169i
$465$	−24.3573	+	18.5160i	−1.12954	+	0.858658i
$466$	1.56200	+	5.62580i	0.0723580	+	0.260610i
$467$	−33.8880	+	7.45931i	−1.56815	+	0.345176i	−0.912238	−	0.409661i	$-0.865647\pi$
$467$	−33.8880	+	7.45931i	−1.56815	+	0.345176i	−0.655912	+	0.754837i	$0.727716\pi$
$468$	0.500236	+	0.737793i	0.0231234	+	0.0341045i
$469$	13.2209	−	12.5235i	0.610485	−	0.578282i
$470$	3.09474	−	5.83730i	0.142750	−	0.269255i
$471$	7.32679			0.337601
$472$	6.66414	−	3.81959i	0.306742	−	0.175811i
$473$	9.57739			0.440369
$474$	−5.97778	+	11.2753i	−0.274568	+	0.517891i
$475$	−40.7135	+	38.5659i	−1.86806	+	1.76952i
$476$	−8.85552	−	13.0609i	−0.405892	−	0.598646i
$477$	−12.4189	+	2.73361i	−0.568623	+	0.125163i
$478$	0.342046	+	1.23194i	0.0156448	+	0.0563475i
$479$	−8.97377	+	6.82168i	−0.410022	+	0.311690i	−0.789774	−	0.613398i	$-0.789802\pi$
$479$	−8.97377	+	6.82168i	−0.410022	+	0.311690i	0.379752	+	0.925088i	$0.376009\pi$
$480$	−3.81057	+	0.414424i	−0.173928	+	0.0189158i
$481$	−0.108999	+	2.01036i	−0.00496991	+	0.0916646i
$482$	1.48811	−	5.35970i	0.0677817	−	0.244128i
$483$	9.62249	+	24.1506i	0.437838	+	1.09889i
$484$	7.37786	+	1.62399i	0.335357	+	0.0738177i
$485$	3.08667	+	56.9303i	0.140158	+	2.58507i
$486$	0.161782	+	0.986827i	0.00733858	+	0.0447634i
$487$	−15.6218	+	23.0405i	−0.707892	+	1.04406i	0.288356	+	0.957523i	$0.406891\pi$
$487$	−15.6218	+	23.0405i	−0.707892	+	1.04406i	−0.996248	+	0.0865396i	$0.972419\pi$
$488$	2.44023	−	6.12451i	0.110464	−	0.277243i
$489$	−17.2952	−	13.1475i	−0.782116	−	0.594549i
$490$	27.4374	+	16.5085i	1.23950	+	0.745779i
$491$	35.6565	−	12.0141i	1.60915	−	0.542187i	0.635870	−	0.771796i	$-0.280641\pi$
$491$	35.6565	−	12.0141i	1.60915	−	0.542187i	0.973283	+	0.229609i	$0.0737448\pi$
$492$	3.76892	+	3.57011i	0.169916	+	0.160953i
$493$	3.18236	−	19.4115i	0.143326	−	0.874251i
$494$	5.12740	+	0.557639i	0.230693	+	0.0250894i
$495$	14.1474	−	8.51219i	0.635877	−	0.382595i
$496$	−5.16757	+	6.08374i	−0.232031	+	0.273168i
$497$	30.9127	−	14.3018i	1.38663	−	0.641521i
$498$	10.3679	+	4.79672i	0.464599	+	0.214946i
$499$	−26.6248	−	31.3451i	−1.19189	−	1.40320i	−0.893683	−	0.448699i	$-0.851888\pi$
$499$	−26.6248	−	31.3451i	−1.19189	−	1.40320i	−0.298206	−	0.954502i	$-0.596388\pi$
$500$	17.0438	+	5.74273i	0.762222	+	0.256823i
$501$	10.7610	+	20.2975i	0.480768	+	0.906825i
$502$	11.9565	+	22.5524i	0.533646	+	1.00656i
$503$	3.43092	+	1.15601i	0.152977	+	0.0515440i	0.394748	−	0.918789i	$-0.370832\pi$
$503$	3.43092	+	1.15601i	0.152977	+	0.0515440i	−0.241771	+	0.970333i	$0.577728\pi$
$504$	−2.53673	−	2.98646i	−0.112995	−	0.133028i
$505$	−5.34007	−	2.47058i	−0.237630	−	0.109939i
$506$	−25.9371	+	11.9998i	−1.15304	+	0.533455i
$507$	7.90162	−	9.30251i	0.350923	−	0.413139i
$508$	15.3519	−	9.23695i	0.681131	−	0.409823i
$509$	−30.1365	−	3.27755i	−1.33578	−	0.145275i	−0.587805	−	0.809003i	$-0.700008\pi$
$509$	−30.1365	−	3.27755i	−1.33578	−	0.145275i	−0.747974	+	0.663728i	$0.768973\pi$
$510$	2.49730	−	15.2328i	0.110582	−	0.674521i
$511$	−1.37196	−	1.29959i	−0.0606921	−	0.0574906i
$512$	−0.947653	+	0.319302i	−0.0418807	+	0.0141113i
$513$	4.95783	+	2.98303i	0.218894	+	0.131704i
$514$	−11.6931	−	8.88888i	−0.515761	−	0.392072i
$515$	0.373910	−	0.938443i	0.0164764	−	0.0413527i
$516$	1.24776	−	1.84031i	0.0549295	−	0.0810149i
$517$	1.20119	+	7.32692i	0.0528282	+	0.322238i
$518$	−0.479141	−	8.83724i	−0.0210523	−	0.388286i
$519$	−10.5346	−	2.31884i	−0.462418	−	0.101786i
$520$	−1.26466	−	3.17406i	−0.0554591	−	0.139192i
$521$	−7.86009	+	28.3095i	−0.344357	+	1.24026i	0.565295	+	0.824889i	$0.308763\pi$
$521$	−7.86009	+	28.3095i	−0.344357	+	1.24026i	−0.909651	+	0.415372i	$0.863651\pi$
$522$	0.264443	−	4.87736i	0.0115743	−	0.213476i
$523$	15.0179	−	1.63329i	0.656687	−	0.0714190i	0.226292	−	0.974060i	$-0.427340\pi$
$523$	15.0179	−	1.63329i	0.656687	−	0.0714190i	0.430395	+	0.902641i	$0.358374\pi$
$524$	−1.48560	+	1.12932i	−0.0648987	+	0.0493347i
$525$	10.1602	+	36.5936i	0.443426	+	1.59708i
$526$	−9.28682	+	2.04418i	−0.404924	+	0.0891306i
$527$	−18.0396	−	26.6064i	−0.785818	−	1.15900i
$528$	3.12722	−	2.96226i	0.136095	−	0.128916i
$529$	9.84487	−	18.5694i	0.428038	−	0.807365i
$530$	48.7417			2.11720
$531$	2.69113	+	7.19429i	0.116785	+	0.312206i
$532$	−22.6722			−0.982964
$533$	−2.16758	+	4.08849i	−0.0938883	+	0.177092i
$534$	−7.45882	+	7.06537i	−0.322775	+	0.305748i
$535$	3.62361	+	5.34443i	0.156663	+	0.231060i
$536$	4.53883	−	0.999071i	0.196047	−	0.0431533i
$537$	6.31174	+	22.7328i	0.272372	+	0.980994i
$538$	−4.08338	+	3.10411i	−0.176047	+	0.133828i
$539$	−35.7736	+	3.89061i	−1.54088	+	0.167581i
$540$	0.207516	−	3.82742i	0.00893009	−	0.164706i
$541$	5.56727	−	20.0515i	0.239356	−	0.862081i	−0.742083	−	0.670308i	$-0.766162\pi$
$541$	5.56727	−	20.0515i	0.239356	−	0.862081i	0.981439	−	0.191774i	$-0.0614240\pi$
$542$	3.66442	+	9.19701i	0.157401	+	0.395045i
$543$	−2.61394	−	0.575373i	−0.112175	−	0.0246916i
$544$	−0.218025	−	4.02123i	−0.00934774	−	0.172409i
$545$	−6.50482	−	39.6777i	−0.278636	−	1.69960i
$546$	1.96013	−	2.89098i	0.0838858	−	0.123722i
$547$	−1.61686	+	4.05801i	−0.0691318	+	0.173508i	−0.959483	−	0.281767i	$-0.909080\pi$
$547$	−1.61686	+	4.05801i	−0.0691318	+	0.173508i	0.890351	+	0.455275i	$0.150459\pi$
$548$	−1.99813	−	1.51894i	−0.0853560	−	0.0648859i
$549$	5.64904	+	3.39891i	0.241095	+	0.145062i
$550$	−39.5635	+	13.3305i	−1.68699	+	0.568415i
$551$	−20.5182	−	19.4359i	−0.874106	−	0.827997i
$552$	−1.07336	+	6.54718i	−0.0456851	+	0.278667i
$553$	49.7132	+	5.40664i	2.11402	+	0.229914i
$554$	−20.4829	+	12.3242i	−0.870236	+	0.523604i
$555$	5.60468	−	6.59834i	0.237905	−	0.280084i
$556$	−3.58150	+	1.65698i	−0.151889	+	0.0702715i
$557$	28.4751	+	13.1740i	1.20653	+	0.558200i	0.916968	−	0.398960i	$-0.130629\pi$
$557$	28.4751	+	13.1740i	1.20653	+	0.558200i	0.289560	+	0.957160i	$0.406491\pi$
$558$	−5.16757	−	6.08374i	−0.218761	−	0.257545i
$559$	1.87819	+	0.632836i	0.0794390	+	0.0267661i
$560$	7.03522	+	13.2698i	0.297292	+	0.560753i
$561$	8.12542	+	15.3262i	0.343055	+	0.647071i
$562$	8.12508	+	2.73766i	0.342736	+	0.115481i
$563$	−13.5661	−	15.9712i	−0.571742	−	0.673107i	0.397959	−	0.917403i	$-0.369719\pi$
$563$	−13.5661	−	15.9712i	−0.571742	−	0.673107i	−0.969701	+	0.244297i	$0.921443\pi$
$564$	1.56437	+	0.723754i	0.0658718	+	0.0304755i
$565$	−73.3662	+	33.9428i	−3.08654	+	1.42798i
$566$	−2.39558	+	2.82029i	−0.100694	+	0.118546i
$567$	3.35752	−	2.02015i	0.141003	−	0.0848384i
$568$	8.64155	+	0.939825i	0.362591	+	0.0394342i
$569$	−3.54506	+	21.6239i	−0.148617	+	0.906522i	0.802265	+	0.596968i	$0.203628\pi$
$569$	−3.54506	+	21.6239i	−0.148617	+	0.906522i	−0.950882	+	0.309554i	$0.899820\pi$
$570$	−16.1013	−	15.2519i	−0.674409	−	0.638834i
$571$	−16.5170	+	5.56521i	−0.691213	+	0.232897i	−0.642917	−	0.765936i	$-0.722276\pi$
$571$	−16.5170	+	5.56521i	−0.691213	+	0.232897i	−0.0482966	+	0.998833i	$0.515379\pi$
$572$	3.29003	+	1.97955i	0.137563	+	0.0827690i
$573$	6.59758	+	5.01535i	0.275618	+	0.209519i
$574$	7.52934	−	18.8972i	0.314269	−	0.788755i
$575$	36.0863	−	53.2233i	1.50490	−	2.21957i
$576$	−0.161782	−	0.986827i	−0.00674092	−	0.0411178i
$577$	−1.10032	−	20.2943i	−0.0458070	−	0.844861i	−0.927681	−	0.373375i	$-0.878201\pi$
$577$	−1.10032	−	20.2943i	−0.0458070	−	0.844861i	0.881874	−	0.471486i	$-0.156282\pi$
$578$	−0.763861	−	0.168139i	−0.0317724	−	0.00699364i
$579$	−6.14025	−	15.4109i	−0.255180	−	0.640454i
$580$	−5.00882	+	18.0401i	−0.207980	+	0.749076i
$581$	2.42342	−	44.6974i	0.100541	−	1.85436i
$582$	−14.7871	+	1.60820i	−0.612947	+	0.0666620i
$583$	−43.6060	+	33.1484i	−1.80597	+	1.37287i
$584$	−0.129023	−	0.464700i	−0.00533903	−	0.0192294i
$585$	3.33685	−	0.734495i	0.137962	−	0.0303676i
$586$	−2.31821	−	3.41911i	−0.0957645	−	0.141242i
$587$	12.5754	−	11.9120i	0.519042	−	0.491662i	−0.382739	−	0.923857i	$-0.625019\pi$
$587$	12.5754	−	11.9120i	0.519042	−	0.491662i	0.901781	+	0.432194i	$0.142261\pi$
$588$	−3.91306	+	7.38081i	−0.161372	+	0.304379i
$589$	−46.1856			−1.90304
$590$	−4.14602	−	29.1487i	−0.170689	−	1.20003i
$591$	−11.3783			−0.468040
$592$	1.05796	−	1.99552i	0.0434819	−	0.0820155i
$593$	−7.99340	+	7.57175i	−0.328250	+	0.310935i	−0.834021	−	0.551733i	$-0.813967\pi$
$593$	−7.99340	+	7.57175i	−0.328250	+	0.310935i	0.505771	+	0.862668i	$0.331208\pi$
$594$	2.41731	+	3.56526i	0.0991834	+	0.146285i
$595$	−59.0712	+	13.0025i	−2.42168	+	0.533052i
$596$	−3.16119	−	11.3856i	−0.129487	−	0.466372i
$597$	−3.87637	+	2.94674i	−0.158649	+	0.120602i
$598$	−5.87933	+	0.639415i	−0.240424	+	0.0261476i
$599$	−1.08150	+	19.9471i	−0.0441888	+	0.815015i	0.889501	+	0.456933i	$0.151052\pi$
$599$	−1.08150	+	19.9471i	−0.0441888	+	0.815015i	−0.933690	+	0.358082i	$0.883431\pi$
$600$	−2.59293	+	9.33889i	−0.105856	+	0.381259i
$601$	5.64548	+	14.1691i	0.230284	+	0.577969i	0.998027	−	0.0627889i	$-0.0199995\pi$
$601$	5.64548	+	14.1691i	0.230284	+	0.577969i	−0.767743	+	0.640758i	$0.778620\pi$
$602$	−8.50861	−	1.87289i	−0.346785	−	0.0763331i
$603$	0.251610	+	4.64067i	0.0102463	+	0.188983i
$604$	−0.480009	−	2.92792i	−0.0195313	−	0.119136i
$605$	16.2501	−	23.9671i	0.660659	−	0.974399i
$606$	0.568178	−	1.42602i	0.0230807	−	0.0579281i
$607$	−5.50583	−	4.18542i	−0.223475	−	0.169881i	0.487446	−	0.873153i	$-0.337929\pi$
$607$	−5.50583	−	4.18542i	−0.223475	−	0.169881i	−0.710921	+	0.703272i	$0.751722\pi$
$608$	−4.95783	−	2.98303i	−0.201067	−	0.120978i
$609$	−18.1377	+	6.11130i	−0.734976	+	0.247642i
$610$	−18.3461	−	17.3783i	−0.742811	−	0.703628i
$611$	−0.248573	+	1.51623i	−0.0100562	+	0.0613400i
$612$	4.00353	+	0.435410i	0.161833	+	0.0176004i
$613$	−23.4050	+	14.0823i	−0.945317	+	0.568779i	−0.902680	−	0.430312i	$-0.858404\pi$
$613$	−23.4050	+	14.0823i	−0.945317	+	0.568779i	−0.0426371	+	0.999091i	$0.513576\pi$
$614$	6.48068	−	7.62965i	0.261539	−	0.307908i
$615$	18.0596	−	8.35528i	0.728235	−	0.336917i
$616$	−15.3185	−	7.08711i	−0.617201	−	0.285548i
$617$	8.65847	+	10.1935i	0.348577	+	0.410376i	0.908311	−	0.418296i	$-0.137373\pi$
$617$	8.65847	+	10.1935i	0.348577	+	0.410376i	−0.559734	+	0.828672i	$0.689097\pi$
$618$	0.249752	+	0.0841513i	0.0100465	+	0.00338506i
$619$	9.65707	+	18.2152i	0.388150	+	0.732129i	0.998184	−	0.0602465i	$-0.0191887\pi$
$619$	9.65707	+	18.2152i	0.388150	+	0.732129i	−0.610033	+	0.792376i	$0.708844\pi$
$620$	14.3315	+	27.0320i	0.575566	+	1.08563i
$621$	−6.28728	−	2.11843i	−0.252300	−	0.0850098i
$622$	12.7283	+	14.9850i	0.510360	+	0.600842i
$623$	36.5367	+	16.9037i	1.46381	+	0.677231i
$624$	0.809003	−	0.374285i	0.0323860	−	0.0149834i
$625$	13.2568	−	15.6071i	0.530271	−	0.624283i
$626$	10.2143	−	6.14573i	0.408245	−	0.245633i
$627$	24.7773	+	2.69470i	0.989512	+	0.107616i
$628$	1.18534	−	7.23027i	0.0473003	−	0.288519i
$629$	6.60351	+	6.25518i	0.263299	+	0.249410i
$630$	−14.2332	+	4.79572i	−0.567064	+	0.191066i
$631$	23.7829	+	14.3097i	0.946781	+	0.569659i	0.903121	−	0.429387i	$-0.141270\pi$
$631$	23.7829	+	14.3097i	0.946781	+	0.569659i	0.0436606	+	0.999046i	$0.486098\pi$
$632$	10.1597	+	7.72317i	0.404129	+	0.307211i
$633$	9.12555	−	22.9034i	0.362708	−	0.910329i
$634$	−10.9497	+	16.1496i	−0.434869	+	0.641383i
$635$	−11.1103	−	67.7701i	−0.440901	−	2.68937i
$636$	0.688442	+	12.6976i	0.0272985	+	0.503491i
$637$	−7.27251	−	1.60080i	−0.288148	−	0.0634261i
$638$	−7.78772	−	19.5457i	−0.308319	−	0.773822i
$639$	−2.32549	+	8.37566i	−0.0919950	+	0.331336i
$640$	−0.207516	+	3.82742i	−0.00820281	+	0.151292i
$641$	−38.7441	+	4.21367i	−1.53030	+	0.166430i	−0.834178	−	0.551495i	$-0.814058\pi$
$641$	−38.7441	+	4.21367i	−1.53030	+	0.166430i	−0.696120	+	0.717925i	$0.745092\pi$
$642$	−1.34108	+	1.01946i	−0.0529283	+	0.0402350i
$643$	10.9325	+	39.3752i	0.431134	+	1.55280i	0.786205	+	0.617965i	$0.212043\pi$
$643$	10.9325	+	39.3752i	0.431134	+	1.55280i	−0.355071	+	0.934839i	$0.615543\pi$
$644$	25.3892	−	5.58859i	1.00048	−	0.220221i
$645$	−4.78270	−	7.05396i	−0.188319	−	0.277749i
$646$	16.9166	−	16.0243i	0.665576	−	0.630467i
$647$	−1.47075	+	2.77412i	−0.0578210	+	0.109062i	−0.910738	−	0.412984i	$-0.864486\pi$
$647$	−1.47075	+	2.77412i	−0.0578210	+	0.109062i	0.852917	+	0.522046i	$0.174831\pi$
$648$	1.00000			0.0392837
$649$	23.5327	+	23.2578i	0.923740	+	0.912948i
$650$	−8.63950			−0.338869
$651$	−14.6507	+	27.6341i	−0.574205	+	1.08307i
$652$	−15.7723	+	14.9403i	−0.617692	+	0.585109i
$653$	−8.61781	−	12.7103i	−0.337241	−	0.497393i	0.620822	−	0.783952i	$-0.286799\pi$
$653$	−8.61781	−	12.7103i	−0.337241	−	0.497393i	−0.958063	+	0.286559i	$0.907489\pi$
$654$	10.2444	−	2.25497i	0.400589	−	0.0881764i
$655$	1.91360	+	6.89216i	0.0747705	+	0.269299i
$656$	4.13283	−	3.14169i	0.161360	−	0.122662i
$657$	0.479452	−	0.0521436i	0.0187052	−	0.00203431i
$658$	0.365659	−	6.74418i	0.0142549	−	0.262915i
$659$	9.82552	−	35.3883i	0.382748	−	1.37853i	−0.481931	−	0.876209i	$-0.660064\pi$
$659$	9.82552	−	35.3883i	0.382748	−	1.37853i	0.864679	−	0.502325i	$-0.167522\pi$
$660$	−6.11127	−	15.3381i	−0.237881	−	0.597036i
$661$	31.9079	+	7.02347i	1.24108	+	0.273181i	0.786535	−	0.617545i	$-0.211873\pi$
$661$	31.9079	+	7.02347i	1.24108	+	0.273181i	0.454540	+	0.890726i	$0.349804\pi$
$662$	1.57431	+	29.0364i	0.0611872	+	1.12853i
$663$	0.580757	+	3.54246i	0.0225547	+	0.137578i
$664$	6.41088	−	9.45534i	0.248790	−	0.366938i
$665$	−32.1662	+	80.7312i	−1.24735	+	3.13062i
$666$	1.79808	+	1.36686i	0.0696740	+	0.0529648i
$667$	27.7680	+	16.7074i	1.07518	+	0.646915i
$668$	21.7710	−	7.33552i	0.842347	−	0.283820i
$669$	−11.8531	−	11.2278i	−0.458266	−	0.434093i
$670$	2.88198	−	17.5793i	0.111341	−	0.679148i
$671$	28.2317	+	3.07038i	1.08987	+	0.118531i
$672$	−3.35752	+	2.02015i	−0.129519	+	0.0779290i
$673$	26.0044	−	30.6147i	1.00239	−	1.18011i	0.0187805	−	0.999824i	$-0.494022\pi$
$673$	26.0044	−	30.6147i	1.00239	−	1.18011i	0.983614	−	0.180287i	$-0.0577025\pi$
$674$	−13.7974	+	6.38337i	−0.531457	+	0.245878i
$675$	−8.79638	−	4.06964i	−0.338573	−	0.156640i
$676$	−7.90162	−	9.30251i	−0.303909	−	0.357789i
$677$	−8.28718	−	2.79228i	−0.318502	−	0.107316i	0.155510	−	0.987834i	$-0.450298\pi$
$677$	−8.28718	−	2.79228i	−0.318502	−	0.107316i	−0.474012	+	0.880518i	$0.657195\pi$
$678$	−9.87858	−	18.6330i	−0.379385	−	0.715596i
$679$	27.3006	+	51.4944i	1.04770	+	1.97617i
$680$	−14.6281	−	4.92879i	−0.560964	−	0.189011i
$681$	−13.1510	−	15.4825i	−0.503947	−	0.593292i
$682$	−31.2054	−	14.4372i	−1.19492	−	0.552828i
$683$	12.4113	−	5.74210i	0.474907	−	0.219715i	−0.167810	−	0.985819i	$-0.553669\pi$
$683$	12.4113	−	5.74210i	0.474907	−	0.219715i	0.642717	+	0.766104i	$0.277807\pi$
$684$	3.74582	−	4.40992i	0.143225	−	0.168618i
$685$	−8.24350	+	4.95995i	−0.314968	+	0.189510i
$686$	5.27420	+	0.573603i	0.201370	+	0.0219003i
$687$	3.99326	−	24.3578i	0.152353	−	0.929309i
$688$	−1.61420	−	1.52905i	−0.0615407	−	0.0582944i
$689$	−10.7417	+	3.61931i	−0.409228	+	0.137885i
$690$	21.7904	+	13.1108i	0.829546	+	0.499121i
$691$	15.5357	+	11.8100i	0.591007	+	0.449272i	0.857442	−	0.514581i	$-0.172053\pi$
$691$	15.5357	+	11.8100i	0.591007	+	0.449272i	−0.266435	+	0.963853i	$0.585846\pi$
$692$	−3.99261	+	10.0207i	−0.151776	+	0.380930i
$693$	9.47201	−	13.9702i	0.359812	−	0.530683i
$694$	−3.63913	−	22.1977i	−0.138140	−	0.842614i
$695$	0.818907	+	15.1039i	0.0310629	+	0.572922i
$696$	−4.77033	−	1.05003i	−0.180819	−	0.0398012i
$697$	7.73827	+	19.4216i	0.293108	+	0.735645i
$698$	0.420513	−	1.51455i	0.0159166	−	0.0573266i
$699$	−0.316096	+	5.83005i	−0.0119559	+	0.220513i
$700$	37.7553	−	4.10613i	1.42702	−	0.155197i
$701$	−9.21421	+	7.00446i	−0.348016	+	0.264555i	−0.764549	−	0.644566i	$-0.777038\pi$
$701$	−9.21421	+	7.00446i	−0.348016	+	0.264555i	0.416533	+	0.909121i	$0.363245\pi$
$702$	0.238472	+	0.858898i	0.00900054	+	0.0324170i
$703$	12.7630	−	2.80935i	0.481367	−	0.105957i
$704$	−2.41731	−	3.56526i	−0.0911057	−	0.134371i
$705$	4.79660	−	4.54358i	0.180650	−	0.171121i
$706$	13.2474	−	24.9872i	0.498572	−	0.940407i
$707$	−6.01493			−0.226215
$708$	7.53489	−	1.49177i	0.283179	−	0.0560643i
$709$	42.4938			1.59589			0.797944	−	0.602732i	$-0.205921\pi$
$709$	42.4938			1.59589			0.797944	+	0.602732i	$0.205921\pi$
$710$	15.6068	−	29.4375i	0.585711	−	1.10477i
$711$	−9.26508	+	8.77635i	−0.347468	+	0.329139i
$712$	5.76559	+	8.50361i	0.216075	+	0.318686i
$713$	51.7205	−	11.3845i	1.93695	−	0.426354i
$714$	−4.22159	−	15.2048i	−0.157989	−	0.569026i
$715$	11.7165	−	8.90667i	0.438173	−	0.333090i
$716$	23.4545	−	2.55083i	0.876535	−	0.0953290i
$717$	−0.0692187	+	1.27666i	−0.00258502	+	0.0476779i
$718$	0.0719285	−	0.259063i	0.00268435	−	0.00966814i
$719$	−11.7185	−	29.4113i	−0.437027	−	1.09686i	−0.968330	−	0.249674i	$-0.919677\pi$
$719$	−11.7185	−	29.4113i	−0.437027	−	1.09686i	0.531302	−	0.847182i	$-0.321703\pi$
$720$	−3.74342	−	0.823990i	−0.139509	−	0.0307083i
$721$	−0.0559087	−	1.03118i	−0.00208215	−	0.0384030i
$722$	−2.34238	−	14.2879i	−0.0871742	−	0.531739i
$723$	3.12158	−	4.60398i	0.116093	−	0.171224i
$724$	−0.990682	+	2.48643i	−0.0368184	+	0.0924073i
$725$	37.6884	+	28.6500i	1.39971	+	1.06403i
$726$	6.47311	+	3.89474i	0.240240	+	0.144547i
$727$	30.7712	−	10.3680i	1.14124	−	0.384528i	0.315692	−	0.948862i	$-0.397763\pi$
$727$	30.7712	−	10.3680i	1.14124	−	0.384528i	0.825547	+	0.564333i	$0.190867\pi$
$728$	−2.53578	−	2.40202i	−0.0939822	−	0.0890246i
$729$	−0.161782	+	0.986827i	−0.00599193	+	0.0365491i
$730$	−1.83776	−	0.199868i	−0.0680185	−	0.00739746i
$731$	7.67234	−	4.61629i	0.283772	−	0.170740i
$732$	4.26805	−	5.02474i	0.157752	−	0.185720i
$733$	−9.18089	+	4.24753i	−0.339104	+	0.156886i	−0.582049	−	0.813154i	$-0.697749\pi$
$733$	−9.18089	+	4.24753i	−0.339104	+	0.156886i	0.242945	+	0.970040i	$0.421887\pi$
$734$	−12.7113	−	5.88089i	−0.469184	−	0.217068i
$735$	20.7299	+	24.4052i	0.764635	+	0.900198i
$736$	6.28728	+	2.11843i	0.231752	+	0.0780865i
$737$	9.37706	+	17.6870i	0.345409	+	0.651510i
$738$	2.43169	+	4.58665i	0.0895117	+	0.168837i
$739$	−12.1848	−	4.10555i	−0.448226	−	0.151025i	0.0861308	−	0.996284i	$-0.472550\pi$
$739$	−12.1848	−	4.10555i	−0.448226	−	0.151025i	−0.534357	+	0.845259i	$0.679446\pi$
$740$	−5.60468	−	6.59834i	−0.206032	−	0.242560i
$741$	4.68095	+	2.16564i	0.171959	+	0.0795566i
$742$	45.2221	−	20.9220i	1.66015	−	0.768069i
$743$	16.8301	−	19.8140i	0.617438	−	0.726904i	−0.361202	−	0.932488i	$-0.617633\pi$
$743$	16.8301	−	19.8140i	0.617438	−	0.726904i	0.978640	+	0.205584i	$0.0659093\pi$
$744$	−6.83961	+	4.11526i	−0.250752	+	0.150873i
$745$	−45.0268	−	4.89696i	−1.64965	−	0.179411i
$746$	−2.82998	+	17.2621i	−0.103613	+	0.632011i
$747$	8.29361	+	7.85613i	0.303447	+	0.287441i
$748$	16.4388	−	5.53888i	0.601063	−	0.202522i
$749$	5.65600	+	3.40310i	0.206666	+	0.124347i
$750$	14.3180	+	10.8842i	0.522818	+	0.397436i
$751$	2.16684	−	5.43835i	0.0790690	−	0.198448i	−0.884128	−	0.467245i	$-0.845247\pi$
$751$	2.16684	−	5.43835i	0.0790690	−	0.198448i	0.963197	+	0.268797i	$0.0866259\pi$
$752$	0.967307	−	1.42667i	0.0352740	−	0.0520253i
$753$	4.12963	+	25.1896i	0.150492	+	0.917961i
$754$	−0.235721	−	4.34763i	−0.00858447	−	0.158331i
$755$	−11.1068	−	2.44479i	−0.404217	−	0.0889748i
$756$	−1.45035	−	3.64011i	−0.0527488	−	0.132390i
$757$	7.07194	−	25.4708i	0.257034	−	0.925754i	−0.716571	−	0.697514i	$-0.754289\pi$
$757$	7.07194	−	25.4708i	0.257034	−	0.925754i	0.973605	−	0.228239i	$-0.0732968\pi$
$758$	1.34731	−	24.8497i	0.0489366	−	0.902582i
$759$	−28.4109	+	3.08987i	−1.03125	+	0.112155i
$760$	−17.6559	+	13.4217i	−0.640448	+	0.486856i
$761$	10.3724	+	37.3581i	0.376000	+	1.35423i	0.873525	+	0.486780i	$0.161829\pi$
$761$	10.3724	+	37.3581i	0.376000	+	1.35423i	−0.497525	+	0.867450i	$0.665758\pi$
$762$	17.4977	−	3.85153i	0.633874	−	0.139526i
$763$	−23.0664	−	34.0204i	−0.835060	−	1.23162i
$764$	6.01665	−	5.69927i	0.217675	−	0.206192i
$765$	7.23043	−	13.6380i	0.261417	−	0.493085i
$766$	9.07479			0.327885
$767$	3.07814	+	6.11596i	0.111145	+	0.220834i
$768$	−1.00000			−0.0360844
$769$	−5.65831	+	10.6727i	−0.204044	+	0.384867i	−0.964323	−	0.264729i	$-0.914717\pi$
$769$	−5.65831	+	10.6727i	−0.204044	+	0.384867i	0.760279	+	0.649597i	$0.225062\pi$
$770$	−46.9690	+	44.4914i	−1.69265	+	1.60336i
$771$	−8.24279	−	12.1572i	−0.296857	−	0.437831i
$772$	−16.2012	+	3.56616i	−0.583096	+	0.128349i
$773$	−13.4084	−	48.2926i	−0.482265	−	1.73696i	−0.658467	−	0.752609i	$-0.728795\pi$
$773$	−13.4084	−	48.2926i	−0.482265	−	1.73696i	0.176202	−	0.984354i	$-0.443619\pi$
$774$	1.77005	−	1.34556i	0.0636233	−	0.0483652i
$775$	76.9114	−	8.36462i	2.76274	−	0.300466i
$776$	−0.805280	+	14.8525i	−0.0289079	+	0.533174i
$777$	2.36768	−	8.52763i	0.0849402	−	0.305927i
$778$	4.57742	+	11.4885i	0.164108	+	0.411881i
$779$	29.3354	+	6.45722i	1.05105	+	0.231354i
$780$	−0.184978	−	3.41172i	−0.00662327	−	0.122159i
$781$	6.05758	+	36.9496i	0.216757	+	1.32216i
$782$	−14.9940	+	22.1145i	−0.536185	+	0.790814i
$783$	1.80795	−	4.53761i	0.0646108	−	0.162161i
$784$	6.65051	+	5.05559i	0.237518	+	0.180557i
$785$	−24.0639	−	14.4787i	−0.858876	−	0.516769i
$786$	−1.76843	+	0.595853i	−0.0630777	+	0.0212534i
$787$	−18.4099	−	17.4388i	−0.656242	−	0.621625i	0.285333	−	0.958428i	$-0.407896\pi$
$787$	−18.4099	−	17.4388i	−0.656242	−	0.621625i	−0.941575	+	0.336803i	$0.890654\pi$
$788$	−1.84080	+	11.2284i	−0.0655758	+	0.399995i
$789$	−9.45339	−	1.02812i	−0.336550	−	0.0366020i
$790$	41.9147	−	25.2193i	1.49126	−	0.897261i
$791$	−53.4987	+	62.9836i	−1.90220	+	2.23944i
$792$	3.90937	−	1.80867i	0.138914	−	0.0642682i
$793$	5.33355	+	2.46756i	0.189400	+	0.0876257i
$794$	2.19350	+	2.58239i	0.0778445	+	0.0916457i
$795$	46.1902	+	15.5633i	1.63820	+	0.551974i
$796$	2.28079	+	4.30203i	0.0808405	+	0.152481i
$797$	13.4228	+	25.3180i	0.475458	+	0.896809i	0.998996	+	0.0448067i	$0.0142672\pi$
$797$	13.4228	+	25.3180i	0.475458	+	0.896809i	−0.523537	+	0.852003i	$0.675388\pi$
$798$	−21.4854	−	7.23927i	−0.760574	−	0.256267i
$799$	4.49383	+	5.29055i	0.158980	+	0.187166i
$800$	8.79638	+	4.06964i	0.310999	+	0.143883i
$801$	−9.32436	+	4.31391i	−0.329460	+	0.152424i
$802$	−9.69376	+	11.4124i	−0.342299	+	0.402985i
$803$	1.78005	−	1.07102i	0.0628165	−	0.0377954i
$804$	4.62024	+	0.502481i	0.162943	+	0.0177211i
$805$	16.1212	−	98.3349i	0.568197	−	3.46585i
$806$	−5.16564	−	4.89316i	−0.181952	−	0.172354i
$807$	−4.86078	+	1.63779i	−0.171108	+	0.0576528i
$808$	−1.31531	−	0.791398i	−0.0462726	−	0.0278413i
$809$	−21.6488	−	16.4570i	−0.761131	−	0.578597i	0.150981	−	0.988537i	$-0.451757\pi$
$809$	−21.6488	−	16.4570i	−0.761131	−	0.578597i	−0.912113	+	0.409940i	$0.865550\pi$
$810$	1.41875	−	3.56080i	0.0498499	−	0.125114i
$811$	−3.78168	+	5.57756i	−0.132793	+	0.195855i	−0.888272	−	0.459318i	$-0.848094\pi$
$811$	−3.78168	+	5.57756i	−0.132793	+	0.195855i	0.755479	+	0.655173i	$0.227404\pi$
$812$	3.09644	+	18.8874i	0.108664	+	0.662819i
$813$	0.535983	+	9.88563i	0.0187978	+	0.346704i
$814$	9.50155	+	2.09145i	0.333029	+	0.0733053i
$815$	30.8226	+	77.3588i	1.07967	+	2.70976i
$816$	1.07737	−	3.88035i	0.0377156	−	0.135839i
$817$	0.696491	−	12.8460i	0.0243672	−	0.449426i
$818$	20.7808	−	2.26005i	0.726584	−	0.0790208i
$819$	2.78062	−	2.11377i	0.0971626	−	0.0738611i
$820$	−5.32349	−	19.1735i	−0.185904	−	0.669566i
$821$	23.6068	−	5.19625i	0.823883	−	0.181350i	0.217030	−	0.976165i	$-0.430363\pi$
$821$	23.6068	−	5.19625i	0.823883	−	0.181350i	0.606852	+	0.794815i	$0.292432\pi$
$822$	−1.40854	−	2.07743i	−0.0491283	−	0.0724589i
$823$	−10.7980	+	10.2284i	−0.376395	+	0.356540i	−0.852389	−	0.522908i	$-0.824847\pi$
$823$	−10.7980	+	10.2284i	−0.376395	+	0.356540i	0.475994	+	0.879449i	$0.342088\pi$
$824$	0.123448	−	0.232848i	0.00430052	−	0.00811164i
$825$	−41.7490			−1.45351
$826$	−16.3585	−	25.2643i	−0.569184	−	0.879056i
$827$	−41.8657			−1.45581			−0.727907	−	0.685675i	$-0.759507\pi$
$827$	−41.8657			−1.45581			−0.727907	+	0.685675i	$0.759507\pi$
$828$	−3.10770	+	5.86173i	−0.108000	+	0.203709i
$829$	−3.36878	+	3.19108i	−0.117003	+	0.110831i	−0.743964	−	0.668219i	$-0.767057\pi$
$829$	−3.36878	+	3.19108i	−0.117003	+	0.110831i	0.626962	+	0.779050i	$0.284298\pi$
$830$	−24.5731	−	36.2427i	−0.852946	−	1.25800i
$831$	−23.3458	+	5.13881i	−0.809858	+	0.178263i
$832$	−0.238472	−	0.858898i	−0.00826752	−	0.0297769i
$833$	−26.7825	+	20.3596i	−0.927960	+	0.705417i
$834$	−3.92310	+	0.426662i	−0.135846	+	0.0147741i
$835$	4.76741	−	87.9297i	0.164983	−	3.04293i
$836$	6.66773	−	24.0150i	0.230608	−	0.830575i
$837$	−2.95452	−	7.41529i	−0.102123	−	0.256310i
$838$	22.4406	+	4.93955i	0.775198	+	0.170634i
$839$	−0.900636	−	16.6113i	−0.0310934	−	0.573484i	−0.972024	−	0.234883i	$-0.924529\pi$
$839$	−0.900636	−	16.6113i	−0.0310934	−	0.573484i	0.940930	−	0.338601i	$-0.109954\pi$
$840$	2.42987	+	14.8216i	0.0838385	+	0.511392i
$841$	2.88530	−	4.25549i	0.0994930	−	0.146741i
$842$	−5.70691	+	14.3233i	−0.196673	+	0.493612i
$843$	6.82562	+	5.18870i	0.235087	+	0.178708i
$844$	−21.1253	−	12.7107i	−0.727164	−	0.437520i
$845$	−44.3349	+	14.9382i	−1.52517	+	0.513888i
$846$	1.25138	+	1.18537i	0.0430234	+	0.0407540i
$847$	4.78900	−	29.2116i	0.164552	−	1.00372i
$848$	12.6417	+	1.37486i	0.434117	+	0.0472130i
$849$	−3.17070	+	1.90775i	−0.108818	+	0.0654738i
$850$	−25.2686	+	29.7485i	−0.866706	+	1.02037i
$851$	−13.6001	+	6.29205i	−0.466204	+	0.215689i
$852$	7.88910	+	3.64989i	0.270276	+	0.125043i
$853$	−11.9647	−	14.0859i	−0.409663	−	0.482293i	0.518176	−	0.855274i	$-0.326611\pi$
$853$	−11.9647	−	14.0859i	−0.409663	−	0.482293i	−0.927839	+	0.372981i	$0.878336\pi$
$854$	−24.4808	−	8.24854i	−0.837716	−	0.282259i
$855$	−10.3885	−	19.5947i	−0.355278	−	0.670125i
$856$	0.789071	+	1.48835i	0.0269699	+	0.0508706i
$857$	−33.5272	−	11.2966i	−1.14527	−	0.385886i	−0.318220	−	0.948017i	$-0.603085\pi$
$857$	−33.5272	−	11.2966i	−1.14527	−	0.385886i	−0.827048	+	0.562131i	$0.809982\pi$
$858$	2.48574	+	2.92644i	0.0848617	+	0.0999069i
$859$	14.4015	+	6.66284i	0.491372	+	0.227333i	0.649897	−	0.760022i	$-0.274812\pi$
$859$	14.4015	+	6.66284i	0.491372	+	0.227333i	−0.158525	+	0.987355i	$0.550674\pi$
$860$	−7.73479	+	3.57849i	−0.263754	+	0.122026i
$861$	13.1691	−	15.5039i	0.448802	−	0.528371i
$862$	3.40574	−	2.04917i	0.116000	−	0.0697948i
$863$	19.4857	+	2.11919i	0.663300	+	0.0721382i	0.433575	−	0.901117i	$-0.357252\pi$
$863$	19.4857	+	2.11919i	0.663300	+	0.0721382i	0.229725	+	0.973256i	$0.426217\pi$
$864$	0.161782	−	0.986827i	0.00550394	−	0.0335725i
$865$	30.0172	+	28.4338i	1.02061	+	0.966778i
$866$	−19.5218	+	6.57766i	−0.663378	+	0.223518i
$867$	−0.670189	−	0.403239i	−0.0227608	−	0.0136947i
$868$	24.8999	+	18.9284i	0.845156	+	0.642471i
$869$	−20.3471	+	51.0675i	−0.690229	+	1.73235i
$870$	−10.5069	+	15.4965i	−0.356216	+	0.525379i
$871$	0.670217	+	4.08814i	0.0227094	+	0.138521i
$872$	−0.567900	−	10.4743i	−0.0192315	−	0.354704i
$873$	−14.5266	−	3.19754i	−0.491650	−	0.108220i
$874$	14.2089	+	35.6617i	0.480624	+	1.20628i
$875$	18.8537	−	67.9049i	0.637372	−	2.29561i
$876$	0.0261101	−	0.481572i	0.000882178	−	0.0162708i
$877$	−45.9643	+	4.99892i	−1.55210	+	0.168802i	−0.843626	−	0.536931i	$-0.819584\pi$
$877$	−45.9643	+	4.99892i	−1.55210	+	0.168802i	−0.708479	+	0.705732i	$0.750618\pi$
$878$	−11.8822	+	9.03262i	−0.401005	+	0.304836i
$879$	−1.10514	−	3.98034i	−0.0372753	−	0.134253i
$880$	−16.1248	+	3.54933i	−0.543566	+	0.119648i
$881$	−10.6730	−	15.7414i	−0.359581	−	0.530343i	0.604271	−	0.796779i	$-0.293464\pi$
$881$	−10.6730	−	15.7414i	−0.359581	−	0.530343i	−0.963853	+	0.266436i	$0.914154\pi$
$882$	−6.06492	+	5.74500i	−0.204217	+	0.193444i
$883$	−9.08887	+	17.1434i	−0.305865	+	0.576922i	−0.988027	−	0.154278i	$-0.950695\pi$
$883$	−9.08887	+	17.1434i	−0.305865	+	0.576922i	0.682163	+	0.731200i	$0.261040\pi$
$884$	3.58975			0.120736
$885$	5.37824	−	28.9467i	0.180788	−	0.973033i
$886$	−21.2412			−0.713611
$887$	22.7700	−	42.9488i	0.764543	−	1.44208i	−0.128311	−	0.991734i	$-0.540956\pi$
$887$	22.7700	−	42.9488i	0.764543	−	1.44208i	0.892854	−	0.450346i	$-0.148699\pi$
$888$	1.63975	−	1.55326i	0.0550265	−	0.0521238i
$889$	−39.3978	−	58.1074i	−1.32136	−	1.94886i
$890$	38.4596	−	8.46560i	1.28917	−	0.283768i
$891$	1.15238	+	4.15048i	0.0386060	+	0.139046i
$892$	−12.9975	+	9.88047i	−0.435190	+	0.330823i
$893$	9.91486	−	1.07831i	0.331788	−	0.0360841i
$894$	0.639721	−	11.7990i	0.0213955	−	0.394616i
$895$	24.1931	−	87.1358i	0.808687	−	2.91263i
$896$	1.45035	+	3.64011i	0.0484529	+	0.121608i
$897$	−5.77573	−	1.27133i	−0.192846	−	0.0424486i
$898$	−1.20923	−	22.3029i	−0.0403524	−	0.744256i
$899$	6.30777	+	38.4757i	0.210376	+	1.28324i
$900$	−5.43912	+	8.02211i	−0.181304	+	0.267404i
$901$	−18.9548	+	47.5729i	−0.631475	+	1.58488i
$902$	17.8021	+	13.5328i	0.592745	+	0.450593i
$903$	−7.46519	−	4.49166i	−0.248426	−	0.149473i
$904$	−19.9857	+	6.73397i	−0.664715	+	0.223968i
$905$	7.44813	+	7.05525i	0.247584	+	0.234524i
$906$	0.480009	−	2.92792i	0.0159472	−	0.0972738i
$907$	8.69441	+	0.945574i	0.288693	+	0.0313973i	0.251320	−	0.967904i	$-0.419135\pi$
$907$	8.69441	+	0.945574i	0.288693	+	0.0313973i	0.0373733	+	0.999301i	$0.488101\pi$
$908$	−17.4062	+	10.4729i	−0.577644	+	0.347557i
$909$	0.993767	−	1.16995i	0.0329612	−	0.0388049i
$910$	−12.1507	+	5.62153i	−0.402793	+	0.186352i
$911$	26.4319	+	12.2287i	0.875727	+	0.405155i	0.805653	−	0.592387i	$-0.201814\pi$
$911$	26.4319	+	12.2287i	0.875727	+	0.405155i	0.0700738	+	0.997542i	$0.477677\pi$
$912$	−3.74582	−	4.40992i	−0.124037	−	0.146027i
$913$	46.6320	+	15.7121i	1.54329	+	0.519996i
$914$	−6.47406	−	12.2114i	−0.214143	−	0.403916i
$915$	−11.8368	−	22.3266i	−0.391312	−	0.738093i
$916$	−23.3909	−	7.88132i	−0.772858	−	0.260406i
$917$	4.73382	+	5.57308i	0.156324	+	0.184039i
$918$	3.65493	+	1.69095i	0.120631	+	0.0558097i
$919$	35.3848	−	16.3707i	1.16724	−	0.540021i	0.262058	−	0.965052i	$-0.415599\pi$
$919$	35.3848	−	16.3707i	1.16724	−	0.540021i	0.905179	+	0.425031i	$0.139737\pi$
$920$	16.4634	−	19.3822i	0.542783	−	0.639014i
$921$	8.57760	−	5.16097i	0.282642	−	0.170060i
$922$	−11.9478	−	1.29941i	−0.393481	−	0.0427937i
$923$	−1.25355	+	7.64633i	−0.0412612	+	0.251682i
$924$	−12.2537	−	11.6073i	−0.403118	−	0.381854i
$925$	−20.7451	+	6.98983i	−0.682094	+	0.229824i
$926$	11.1155	+	6.68796i	0.365277	+	0.219780i
$927$	0.209809	+	0.159493i	0.00689103	+	0.00523842i
$928$	−1.80795	+	4.53761i	−0.0593488	+	0.148954i
$929$	−13.8133	+	20.3731i	−0.453199	+	0.668419i	−0.983814	−	0.179194i	$-0.942651\pi$
$929$	−13.8133	+	20.3731i	−0.453199	+	0.668419i	0.530614	+	0.847613i	$0.321961\pi$
$930$	4.94990	+	30.1930i	0.162314	+	0.990069i
$931$	2.61688	+	48.2656i	0.0857649	+	1.58184i
$932$	5.70211	+	1.25513i	0.186779	+	0.0411131i
$933$	7.27733	+	18.2647i	0.238249	+	0.597960i
$934$	−9.28303	+	33.4345i	−0.303750	+	1.09401i
$935$	3.59976	−	66.3937i	0.117725	−	2.17131i
$936$	0.886164	−	0.0963761i	0.0289652	−	0.00315015i
$937$	6.13638	−	4.66475i	0.200467	−	0.152391i	−0.500125	−	0.865953i	$-0.666713\pi$
$937$	6.13638	−	4.66475i	0.200467	−	0.152391i	0.700592	+	0.713562i	$0.252919\pi$
$938$	−4.87189	−	17.5470i	−0.159073	−	0.572929i
$939$	11.6419	−	2.56258i	0.379920	−	0.0836268i
$940$	−3.70772	−	5.46848i	−0.120933	−	0.178362i
$941$	30.0773	−	28.4907i	0.980491	−	0.928770i	−0.0169794	−	0.999856i	$-0.505405\pi$
$941$	30.0773	−	28.4907i	0.980491	−	0.928770i	0.997470	+	0.0710856i	$0.0226463\pi$
$942$	3.43193	−	6.47331i	0.111818	−	0.210912i
$943$	−34.4427			−1.12161
$944$	−0.253112	−	7.67697i	−0.00823809	−	0.249864i
$945$	−15.0194			−0.488582
$946$	4.48613	−	8.46174i	0.145857	−	0.275115i
$947$	10.7337	−	10.1675i	0.348798	−	0.330399i	−0.493164	−	0.869936i	$-0.664160\pi$
$947$	10.7337	−	10.1675i	0.348798	−	0.330399i	0.841961	+	0.539538i	$0.181401\pi$
$948$	7.16181	+	10.5629i	0.232605	+	0.343066i
$949$	0.419848	−	0.0924155i	0.0136288	−	0.00299993i
$950$	15.0029	+	54.0355i	0.486758	+	1.75314i
$951$	−15.5331	+	11.8080i	−0.503696	+	0.382900i
$952$	−15.6875	+	1.70612i	−0.508434	+	0.0552956i
$953$	−0.200900	+	3.70539i	−0.00650780	+	0.120029i	0.993474	+	0.114056i	$0.0363842\pi$
$953$	−0.200900	+	3.70539i	−0.00650780	+	0.120029i	−0.999982	+	0.00597363i	$0.998099\pi$
$954$	−3.40195	+	12.2527i	−0.110142	+	0.396696i
$955$	−11.7578	−	29.5100i	−0.380475	−	0.954920i
$956$	1.24865	+	0.274848i	0.0403842	+	0.00888923i
$957$	−1.13909	−	21.0092i	−0.0368214	−	0.679131i
$958$	1.82365	+	11.1238i	0.0589194	+	0.359392i
$959$	−5.51922	+	8.14024i	−0.178225	+	0.262862i
$960$	−1.41875	+	3.56080i	−0.0457901	+	0.114924i
$961$	26.0447	+	19.7987i	0.840152	+	0.638667i
$962$	1.72512	+	1.03797i	0.0556202	+	0.0334656i
$963$	−1.59640	+	0.537889i	−0.0514432	+	0.0173332i
$964$	−4.03832	−	3.82530i	−0.130065	−	0.123204i
$965$	−10.2872	+	62.7489i	−0.331156	+	2.01996i
$966$	25.8446	+	2.81077i	0.831537	+	0.0904351i
$967$	−35.6127	+	21.4275i	−1.14523	+	0.689061i	−0.956143	−	0.292900i	$-0.905380\pi$
$967$	−35.6127	+	21.4275i	−1.14523	+	0.689061i	−0.189085	+	0.981961i	$0.560552\pi$
$968$	4.89067	−	5.75774i	0.157192	−	0.185061i
$969$	21.1477	−	9.78396i	0.679362	−	0.314306i
$970$	51.7444	+	23.9395i	1.66141	+	0.768651i
$971$	−22.8141	−	26.8588i	−0.732139	−	0.861940i	0.262545	−	0.964920i	$-0.415438\pi$
$971$	−22.8141	−	26.8588i	−0.732139	−	0.861940i	−0.994683	+	0.102979i	$0.967162\pi$
$972$	0.947653	+	0.319302i	0.0303960	+	0.0102416i
$973$	7.24297	+	13.6617i	0.232199	+	0.437974i
$974$	13.0391	+	24.5944i	0.417801	+	0.788056i
$975$	−8.18725	−	2.75861i	−0.262202	−	0.0883461i
$976$	−4.26805	−	5.02474i	−0.136617	−	0.160838i
$977$	−19.1895	−	8.87800i	−0.613926	−	0.284032i	0.0881803	−	0.996105i	$-0.471895\pi$
$977$	−19.1895	−	8.87800i	−0.613926	−	0.284032i	−0.702106	+	0.712072i	$0.747757\pi$
$978$	−19.7172	+	9.12213i	−0.630485	+	0.291694i
$979$	−28.6500	+	33.7293i	−0.915657	+	1.07799i
$980$	27.4374	−	16.5085i	0.876455	−	0.527346i
$981$	10.4282	+	1.13413i	0.332946	+	0.0362101i
$982$	6.08722	−	37.1304i	0.194251	−	1.18488i
$983$	−2.18900	−	2.07353i	−0.0698182	−	0.0661353i	0.651995	−	0.758223i	$-0.273932\pi$
$983$	−2.18900	−	2.07353i	−0.0698182	−	0.0661353i	−0.721813	+	0.692088i	$0.756691\pi$
$984$	4.91963	−	1.65762i	0.156832	−	0.0528429i
$985$	37.3704	+	22.4850i	1.19072	+	0.716433i
$986$	−15.6597	−	11.9042i	−0.498706	−	0.379106i
$987$	2.49994	−	6.27439i	0.0795741	−	0.199716i
$988$	2.89440	−	4.26892i	0.0920831	−	0.135812i
$989$	2.38653	+	14.5572i	0.0758872	+	0.462891i
$990$	−0.893875	−	16.4866i	−0.0284092	−	0.523977i
$991$	8.93375	+	1.96647i	0.283790	+	0.0624669i	0.354584	−	0.935024i	$-0.384622\pi$
$991$	8.93375	+	1.96647i	0.283790	+	0.0624669i	−0.0707944	+	0.997491i	$0.522553\pi$
$992$	2.95452	+	7.41529i	0.0938061	+	0.235436i
$993$	−7.77947	+	28.0191i	−0.246874	+	0.889160i
$994$	1.84401	−	34.0108i	0.0584886	−	1.07876i
$995$	18.5546	−	2.01793i	0.588219	−	0.0639727i
$996$	9.09439	−	6.91338i	0.288167	−	0.219059i
$997$	5.25719	+	18.9347i	0.166497	+	0.599668i	0.998960	+	0.0455876i	$0.0145160\pi$
$997$	5.25719	+	18.9347i	0.166497	+	0.599668i	−0.832463	+	0.554080i	$0.813070\pi$
$998$	−40.1651	+	8.84100i	−1.27140	+	0.279857i
$999$	1.26751	+	1.86944i	0.0401023	+	0.0591464i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.c.19.1	✓	84
59.28	even	29	inner	354.2.e.c.205.1	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.c.19.1	✓	84	1.1	even	1	trivial
354.2.e.c.205.1	yes	84	59.28	even	29	inner

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.468408 - 0.883512i) q^{2} +(0.725995 - 0.687699i) q^{3} +(-0.561187 - 0.827689i) q^{4} +(-3.74342 + 0.823990i) q^{5} +(-0.267528 - 0.963550i) q^{6} +(-3.11942 + 2.37132i) q^{7} +(-0.994138 + 0.108119i) q^{8} +(0.0541389 - 0.998533i) q^{9} +O(q^{10})\)	\(q+(0.468408 - 0.883512i) q^{2} +(0.725995 - 0.687699i) q^{3} +(-0.561187 - 0.827689i) q^{4} +(-3.74342 + 0.823990i) q^{5} +(-0.267528 - 0.963550i) q^{6} +(-3.11942 + 2.37132i) q^{7} +(-0.994138 + 0.108119i) q^{8} +(0.0541389 - 0.998533i) q^{9} +(-1.02545 + 3.69332i) q^{10} +(-1.59437 - 4.00156i) q^{11} +(-0.976621 - 0.214970i) q^{12} +(-0.0482588 - 0.890082i) q^{13} +(0.633928 + 3.86679i) q^{14} +(-2.15105 + 3.17256i) q^{15} +(-0.370138 + 0.928977i) q^{16} +(-3.20598 - 2.43712i) q^{17} +(-0.856857 - 0.515554i) q^{18} +(-5.48319 + 1.84750i) q^{19} +(2.78277 + 2.63598i) q^{20} +(-0.633928 + 3.86679i) q^{21} +(-4.28224 - 0.465722i) q^{22} +(5.68489 - 3.42049i) q^{23} +(-0.647386 + 0.762162i) q^{24} +(8.79638 - 4.06964i) q^{25} +(-0.809003 - 0.374285i) q^{26} +(-0.647386 - 0.762162i) q^{27} +(3.71329 + 1.25115i) q^{28} +(2.28795 + 4.31554i) q^{29} +(1.79543 + 3.38653i) q^{30} +(7.56437 + 2.54873i) q^{31} +(0.647386 + 0.762162i) q^{32} +(-3.90937 - 1.80867i) q^{33} +(-3.65493 + 1.69095i) q^{34} +(9.72336 - 11.4472i) q^{35} +(-0.856857 + 0.515554i) q^{36} +(-2.24539 - 0.244200i) q^{37} +(-0.936082 + 5.70985i) q^{38} +(-0.647145 - 0.613008i) q^{39} +(3.63239 - 1.22389i) q^{40} +(-4.44828 - 2.67644i) q^{41} +(3.11942 + 2.37132i) q^{42} +(-0.822975 + 2.06551i) q^{43} +(-2.41731 + 3.56526i) q^{44} +(0.620116 + 3.78254i) q^{45} +(-0.359189 - 6.62485i) q^{46} +(-1.68338 - 0.370540i) q^{47} +(0.370138 + 0.928977i) q^{48} +(2.23492 - 8.04944i) q^{49} +(0.524724 - 9.67796i) q^{50} +(-4.00353 + 0.435410i) q^{51} +(-0.709629 + 0.539446i) q^{52} +(-3.40195 - 12.2527i) q^{53} +(-0.976621 + 0.214970i) q^{54} +(9.26563 + 13.6658i) q^{55} +(2.84475 - 2.69469i) q^{56} +(-2.71024 + 5.11206i) q^{57} +4.88452 q^{58} +(-7.03804 + 3.07668i) q^{59} +3.83304 q^{60} +(-3.08810 + 5.82477i) q^{61} +(5.79505 - 5.48936i) q^{62} +(2.19896 + 3.24323i) q^{63} +(0.976621 - 0.214970i) q^{64} +(0.914071 + 3.29219i) q^{65} +(-3.42916 + 2.60678i) q^{66} +(-4.62024 + 0.502481i) q^{67} +(-0.218025 + 4.02123i) q^{68} +(1.77494 - 6.39275i) q^{69} +(-5.55926 - 13.9527i) q^{70} +(-8.48928 - 1.86863i) q^{71} +(0.0541389 + 0.998533i) q^{72} +(0.0780241 + 0.475926i) q^{73} +(-1.26751 + 1.86944i) q^{74} +(3.58744 - 9.00380i) q^{75} +(4.60625 + 3.50158i) q^{76} +(14.4625 + 8.70179i) q^{77} +(-0.844728 + 0.284622i) q^{78} +(-9.26508 - 8.77635i) q^{79} +(0.620116 - 3.78254i) q^{80} +(-0.994138 - 0.108119i) q^{81} +(-4.44828 + 2.67644i) q^{82} +(-7.39560 + 8.70677i) q^{83} +(3.55625 - 1.64530i) q^{84} +(14.0095 + 6.48148i) q^{85} +(1.43942 + 1.69461i) q^{86} +(4.62884 + 1.55964i) q^{87} +(2.01767 + 3.80572i) q^{88} +(-4.81239 - 9.07713i) q^{89} +(3.63239 + 1.22389i) q^{90} +(2.26121 + 2.66210i) q^{91} +(-6.02139 - 2.78579i) q^{92} +(7.24446 - 3.35164i) q^{93} +(-1.11589 + 1.31372i) q^{94} +(19.0036 - 11.4341i) q^{95} +(0.994138 + 0.108119i) q^{96} +(2.40640 - 14.6784i) q^{97} +(-6.06492 - 5.74500i) q^{98} +(-4.08201 + 1.37539i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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