LMFDB - Embedded newform 546.2.cg.b.145.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(145,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 1]))

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

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

chi := DirichletCharacter("546.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.cg (of order $12$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			145.3
Character	$\chi$	$=$	546.145
Dual form			546.2.cg.b.241.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(-0.981662 + 0.263036i) q^{5} +(0.965926 - 0.258819i) q^{6} +(2.09303 - 1.61840i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(-0.981662 + 0.263036i) q^{5} +(0.965926 - 0.258819i) q^{6} +(2.09303 - 1.61840i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.508146 - 0.880134i) q^{10} +(-4.09120 + 1.09623i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.709237 - 3.53511i) q^{13} +(-0.335613 + 2.62438i) q^{14} +(0.981662 + 0.263036i) q^{15} -1.00000 q^{16} -0.895472 q^{17} +(-0.965926 - 0.258819i) q^{18} +(-0.745350 + 2.78168i) q^{19} +(0.263036 + 0.981662i) q^{20} +(-2.62182 + 0.355062i) q^{21} +(2.11776 - 3.66807i) q^{22} -1.11283i q^{23} +(-0.258819 - 0.965926i) q^{24} +(-3.43565 + 1.98358i) q^{25} +(1.99819 + 3.00120i) q^{26} -1.00000i q^{27} +(-1.61840 - 2.09303i) q^{28} +(-4.64609 - 8.04727i) q^{29} +(-0.880134 + 0.508146i) q^{30} +(1.04539 - 3.90146i) q^{31} +(0.707107 - 0.707107i) q^{32} +(4.09120 + 1.09623i) q^{33} +(0.633194 - 0.633194i) q^{34} +(-1.62895 + 2.13927i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-6.83756 - 6.83756i) q^{37} +(-1.43990 - 2.49399i) q^{38} +(-2.38177 + 2.70687i) q^{39} +(-0.880134 - 0.508146i) q^{40} +(0.375020 - 1.39959i) q^{41} +(1.60284 - 2.10497i) q^{42} +(-4.62926 - 2.67270i) q^{43} +(1.09623 + 4.09120i) q^{44} +(-0.718627 - 0.718627i) q^{45} +(0.786889 + 0.786889i) q^{46} +(-0.821480 - 3.06581i) q^{47} +(0.866025 + 0.500000i) q^{48} +(1.76155 - 6.77473i) q^{49} +(1.02677 - 3.83197i) q^{50} +(0.775501 + 0.447736i) q^{51} +(-3.53511 - 0.709237i) q^{52} +(-1.89754 - 3.28664i) q^{53} +(0.707107 + 0.707107i) q^{54} +(3.72783 - 2.15226i) q^{55} +(2.62438 + 0.335613i) q^{56} +(2.03633 - 2.03633i) q^{57} +(8.97556 + 2.40499i) q^{58} +(-5.46941 + 5.46941i) q^{59} +(0.263036 - 0.981662i) q^{60} +(2.04275 - 1.17938i) q^{61} +(2.01954 + 3.49795i) q^{62} +(2.44809 + 1.00342i) q^{63} +1.00000i q^{64} +(0.233628 + 3.65684i) q^{65} +(-3.66807 + 2.11776i) q^{66} +(1.11978 + 4.17906i) q^{67} +0.895472i q^{68} +(-0.556414 + 0.963738i) q^{69} +(-0.360846 - 2.66453i) q^{70} +(0.229950 + 0.858187i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(0.449816 + 0.120528i) q^{73} +9.66976 q^{74} +3.96715 q^{75} +(2.78168 + 0.745350i) q^{76} +(-6.78886 + 8.91566i) q^{77} +(-0.229883 - 3.59822i) q^{78} +(3.14658 - 5.45004i) q^{79} +(0.981662 - 0.263036i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.724483 + 1.25484i) q^{82} +(7.53308 + 7.53308i) q^{83} +(0.355062 + 2.62182i) q^{84} +(0.879051 - 0.235541i) q^{85} +(5.16327 - 1.38349i) q^{86} +9.29218i q^{87} +(-3.66807 - 2.11776i) q^{88} +(-9.28304 + 9.28304i) q^{89} +1.01629 q^{90} +(-4.23677 - 8.54692i) q^{91} -1.11283 q^{92} +(-2.85607 + 2.85607i) q^{93} +(2.74873 + 1.58698i) q^{94} -2.92673i q^{95} +(-0.965926 + 0.258819i) q^{96} +(8.06565 - 2.16118i) q^{97} +(3.54485 + 6.03606i) q^{98} +(-2.99497 - 2.99497i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$		−	1.00000i		−	0.500000i
$5$	−0.981662	+	0.263036i	−0.439013	+	0.117633i	−0.471554	−	0.881837i	$-0.656307\pi$
$5$	−0.981662	+	0.263036i	−0.439013	+	0.117633i	0.0325411	+	0.999470i	$0.489640\pi$
$6$	0.965926	−	0.258819i	0.394338	−	0.105662i
$7$	2.09303	−	1.61840i	0.791091	−	0.611698i
$7$	2.09303	−	1.61840i	0.791091	−	0.611698i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.508146	−	0.880134i	0.160690	−	0.278323i
$11$	−4.09120	+	1.09623i	−1.23354	+	0.330527i	−0.815958	−	0.578111i	$-0.803790\pi$
$11$	−4.09120	+	1.09623i	−1.23354	+	0.330527i	−0.417585	+	0.908638i	$0.637123\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	0.709237	−	3.53511i	0.196707	−	0.980462i
$13$	0.709237	−	3.53511i	0.196707	−	0.980462i
$14$	−0.335613	+	2.62438i	−0.0896964	+	0.701395i
$15$	0.981662	+	0.263036i	0.253464	+	0.0679155i
$16$	−1.00000			−0.250000
$17$	−0.895472			−0.217184			−0.108592	−	0.994086i	$-0.534634\pi$
$17$	−0.895472			−0.217184			−0.108592	+	0.994086i	$0.534634\pi$
$18$	−0.965926	−	0.258819i	−0.227671	−	0.0610042i
$19$	−0.745350	+	2.78168i	−0.170995	+	0.638162i	0.826204	+	0.563371i	$0.190496\pi$
$19$	−0.745350	+	2.78168i	−0.170995	+	0.638162i	−0.997199	+	0.0747911i	$0.976171\pi$
$20$	0.263036	+	0.981662i	0.0588166	+	0.219506i
$21$	−2.62182	+	0.355062i	−0.572128	+	0.0774808i
$22$	2.11776	−	3.66807i	0.451508	−	0.782035i
$23$		−	1.11283i		−	0.232041i	−0.993247	−	0.116020i	$-0.962986\pi$
$23$		−	1.11283i		−	0.232041i	0.993247	−	0.116020i	$-0.0370138\pi$
$24$	−0.258819	−	0.965926i	−0.0528312	−	0.197169i
$25$	−3.43565	+	1.98358i	−0.687131	+	0.396715i
$26$	1.99819	+	3.00120i	0.391878	+	0.588585i
$27$		−	1.00000i		−	0.192450i
$28$	−1.61840	−	2.09303i	−0.305849	−	0.395546i
$29$	−4.64609	−	8.04727i	−0.862758	−	1.49434i	−0.869257	−	0.494361i	$-0.835402\pi$
$29$	−4.64609	−	8.04727i	−0.862758	−	1.49434i	0.00649921	−	0.999979i	$-0.497931\pi$
$30$	−0.880134	+	0.508146i	−0.160690	+	0.0927743i
$31$	1.04539	−	3.90146i	0.187758	−	0.700723i	−0.806265	−	0.591554i	$-0.798515\pi$
$31$	1.04539	−	3.90146i	0.187758	−	0.700723i	0.994023	−	0.109169i	$-0.0348188\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	4.09120	+	1.09623i	0.712187	+	0.190830i
$34$	0.633194	−	0.633194i	0.108592	−	0.108592i
$35$	−1.62895	+	2.13927i	−0.275343	+	0.361602i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	−6.83756	−	6.83756i	−1.12409	−	1.12409i	−0.991120	−	0.132967i	$-0.957550\pi$
$37$	−6.83756	−	6.83756i	−1.12409	−	1.12409i	−0.132967	−	0.991120i	$-0.542450\pi$
$38$	−1.43990	−	2.49399i	−0.233583	−	0.404578i
$39$	−2.38177	+	2.70687i	−0.381389	+	0.433447i
$40$	−0.880134	−	0.508146i	−0.139161	−	0.0803449i
$41$	0.375020	−	1.39959i	0.0585683	−	0.218580i	−0.930439	−	0.366447i	$-0.880574\pi$
$41$	0.375020	−	1.39959i	0.0585683	−	0.218580i	0.989007	+	0.147867i	$0.0472408\pi$
$42$	1.60284	−	2.10497i	0.247323	−	0.324804i
$43$	−4.62926	−	2.67270i	−0.705955	−	0.407583i	0.103606	−	0.994618i	$-0.466962\pi$
$43$	−4.62926	−	2.67270i	−0.705955	−	0.407583i	−0.809562	+	0.587035i	$0.800295\pi$
$44$	1.09623	+	4.09120i	0.165263	+	0.616772i
$45$	−0.718627	−	0.718627i	−0.107127	−	0.107127i
$46$	0.786889	+	0.786889i	0.116020	+	0.116020i
$47$	−0.821480	−	3.06581i	−0.119825	−	0.447194i	0.879777	−	0.475386i	$-0.157692\pi$
$47$	−0.821480	−	3.06581i	−0.119825	−	0.447194i	−0.999603	+	0.0281923i	$0.991025\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	1.76155	−	6.77473i	0.251650	−	0.967818i
$50$	1.02677	−	3.83197i	0.145208	−	0.541923i
$51$	0.775501	+	0.447736i	0.108592	+	0.0626956i
$52$	−3.53511	−	0.709237i	−0.490231	−	0.0983534i
$53$	−1.89754	−	3.28664i	−0.260647	−	0.451454i	0.705767	−	0.708444i	$-0.250603\pi$
$53$	−1.89754	−	3.28664i	−0.260647	−	0.451454i	−0.966414	+	0.256990i	$0.917269\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	3.72783	−	2.15226i	0.502660	−	0.290211i
$56$	2.62438	+	0.335613i	0.350697	+	0.0448482i
$57$	2.03633	−	2.03633i	0.269719	−	0.269719i
$58$	8.97556	+	2.40499i	1.17855	+	0.315791i
$59$	−5.46941	+	5.46941i	−0.712057	+	0.712057i	−0.966965	−	0.254908i	$-0.917955\pi$
$59$	−5.46941	+	5.46941i	−0.712057	+	0.712057i	0.254908	+	0.966965i	$0.417955\pi$
$60$	0.263036	−	0.981662i	0.0339578	−	0.126732i
$61$	2.04275	−	1.17938i	0.261547	−	0.151004i	−0.363493	−	0.931597i	$-0.618416\pi$
$61$	2.04275	−	1.17938i	0.261547	−	0.151004i	0.625040	+	0.780593i	$0.285083\pi$
$62$	2.01954	+	3.49795i	0.256482	+	0.444240i
$63$	2.44809	+	1.00342i	0.308431	+	0.126419i
$64$			1.00000i			0.125000i
$65$	0.233628	+	3.65684i	0.0289780	+	0.453575i
$66$	−3.66807	+	2.11776i	−0.451508	+	0.260678i
$67$	1.11978	+	4.17906i	0.136802	+	0.510553i	0.999984	+	0.00565972i	$0.00180155\pi$
$67$	1.11978	+	4.17906i	0.136802	+	0.510553i	−0.863182	+	0.504893i	$0.831532\pi$
$68$			0.895472i			0.108592i
$69$	−0.556414	+	0.963738i	−0.0669844	+	0.116020i
$70$	−0.360846	−	2.66453i	−0.0431294	−	0.318473i
$71$	0.229950	+	0.858187i	0.0272901	+	0.101848i	0.978228	−	0.207535i	$-0.0665441\pi$
$71$	0.229950	+	0.858187i	0.0272901	+	0.101848i	−0.950937	+	0.309383i	$0.899877\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	0.449816	+	0.120528i	0.0526470	+	0.0141067i	0.285046	−	0.958514i	$-0.407991\pi$
$73$	0.449816	+	0.120528i	0.0526470	+	0.0141067i	−0.232399	+	0.972620i	$0.574658\pi$
$74$	9.66976			1.12409
$75$	3.96715			0.458087
$76$	2.78168	+	0.745350i	0.319081	+	0.0854975i
$77$	−6.78886	+	8.91566i	−0.773662	+	1.01603i
$78$	−0.229883	−	3.59822i	−0.0260291	−	0.407418i
$79$	3.14658	−	5.45004i	0.354018	−	0.613177i	−0.632931	−	0.774208i	$-0.718148\pi$
$79$	3.14658	−	5.45004i	0.354018	−	0.613177i	0.986949	+	0.161031i	$0.0514818\pi$
$80$	0.981662	−	0.263036i	0.109753	−	0.0294083i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.724483	+	1.25484i	0.0800057	+	0.138574i
$83$	7.53308	+	7.53308i	0.826863	+	0.826863i	0.987082	−	0.160219i	$-0.0512200\pi$
$83$	7.53308	+	7.53308i	0.826863	+	0.826863i	−0.160219	+	0.987082i	$0.551220\pi$
$84$	0.355062	+	2.62182i	0.0387404	+	0.286064i
$85$	0.879051	−	0.235541i	0.0953465	−	0.0255480i
$86$	5.16327	−	1.38349i	0.556769	−	0.149186i
$87$			9.29218i			0.996227i
$88$	−3.66807	−	2.11776i	−0.391018	−	0.225754i
$89$	−9.28304	+	9.28304i	−0.984000	+	0.984000i	−0.999874	−	0.0158739i	$-0.994947\pi$
$89$	−9.28304	+	9.28304i	−0.984000	+	0.984000i	0.0158739	+	0.999874i	$0.494947\pi$
$90$	1.01629			0.107127
$91$	−4.23677	−	8.54692i	−0.444134	−	0.895960i
$92$	−1.11283			−0.116020
$93$	−2.85607	+	2.85607i	−0.296160	+	0.296160i
$94$	2.74873	+	1.58698i	0.283509	+	0.163684i
$95$		−	2.92673i		−	0.300276i
$96$	−0.965926	+	0.258819i	−0.0985844	+	0.0264156i
$97$	8.06565	−	2.16118i	0.818943	−	0.219435i	0.175058	−	0.984558i	$-0.443989\pi$
$97$	8.06565	−	2.16118i	0.818943	−	0.219435i	0.643884	+	0.765123i	$0.277322\pi$
$98$	3.54485	+	6.03606i	0.358084	+	0.609734i
$99$	−2.99497	−	2.99497i	−0.301005	−	0.301005i
$100$	1.98358	+	3.43565i	0.198358	+	0.343565i
$101$	4.10244	−	7.10564i	0.408208	−	0.707037i	−0.586481	−	0.809963i	$-0.699487\pi$
$101$	4.10244	−	7.10564i	0.408208	−	0.707037i	0.994689	+	0.102926i	$0.0328204\pi$
$102$	−0.864960	+	0.231765i	−0.0856438	+	0.0229482i
$103$	−5.96169	+	10.3259i	−0.587423	+	1.01745i	0.407146	+	0.913363i	$0.366524\pi$
$103$	−5.96169	+	10.3259i	−0.587423	+	1.01745i	−0.994569	+	0.104083i	$0.966809\pi$
$104$	3.00120	−	1.99819i	0.294292	−	0.195939i
$105$	2.48035	−	1.03818i	0.242057	−	0.101316i
$106$	3.66577	+	0.982239i	0.356051	+	0.0954035i
$107$	1.21458			0.117418			0.0587088	−	0.998275i	$-0.481302\pi$
$107$	1.21458			0.117418			0.0587088	+	0.998275i	$0.481302\pi$
$108$	−1.00000			−0.0962250
$109$	−10.4562	−	2.80174i	−1.00152	−	0.268358i	−0.279440	−	0.960163i	$-0.590149\pi$
$109$	−10.4562	−	2.80174i	−1.00152	−	0.268358i	−0.722084	+	0.691805i	$0.756816\pi$
$110$	−1.11409	+	4.15785i	−0.106225	+	0.396436i
$111$	2.50272	+	9.34028i	0.237548	+	0.886540i
$112$	−2.09303	+	1.61840i	−0.197773	+	0.152925i
$113$	6.77909	−	11.7417i	0.637723	−	1.10457i	−0.348208	−	0.937417i	$-0.613210\pi$
$113$	6.77909	−	11.7417i	0.637723	−	1.10457i	0.985931	−	0.167152i	$-0.0534570\pi$
$114$			2.87981i			0.269719i
$115$	0.292714	+	1.09242i	0.0272957	+	0.101869i
$116$	−8.04727	+	4.64609i	−0.747170	+	0.431379i
$117$	3.41611	−	1.15334i	0.315820	−	0.106626i
$118$		−	7.73492i		−	0.712057i
$119$	−1.87425	+	1.44923i	−0.171812	+	0.132851i
$120$	0.508146	+	0.880134i	0.0463872	+	0.0803449i
$121$	6.00991	−	3.46982i	0.546356	−	0.315439i
$122$	−0.610493	+	2.27839i	−0.0552714	+	0.206276i
$123$	−1.02457	+	1.02457i	−0.0923827	+	0.0923827i
$124$	−3.90146	−	1.04539i	−0.350361	−	0.0938791i
$125$	6.44403	−	6.44403i	0.576372	−	0.576372i
$126$	−2.44059	+	1.02154i	−0.217425	+	0.0910060i
$127$	−7.87288	+	4.54541i	−0.698605	+	0.403340i	−0.806828	−	0.590787i	$-0.798817\pi$
$127$	−7.87288	+	4.54541i	−0.698605	+	0.403340i	0.108223	+	0.994127i	$0.465484\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	2.67270	+	4.62926i	0.235318	+	0.407583i
$130$	−2.75097	−	2.42057i	−0.241276	−	0.212298i
$131$	−5.46001	−	3.15234i	−0.477043	−	0.275421i	0.242140	−	0.970241i	$-0.422151\pi$
$131$	−5.46001	−	3.15234i	−0.477043	−	0.275421i	−0.719183	+	0.694820i	$0.755484\pi$
$132$	1.09623	−	4.09120i	0.0954149	−	0.356093i
$133$	2.94184	+	7.02842i	0.255090	+	0.609441i
$134$	−3.74684	−	2.16324i	−0.323678	−	0.186875i
$135$	0.263036	+	0.981662i	0.0226385	+	0.0844880i
$136$	−0.633194	−	0.633194i	−0.0542960	−	0.0542960i
$137$	16.0668	+	16.0668i	1.37268	+	1.37268i	0.856448	+	0.516233i	$0.172666\pi$
$137$	16.0668	+	16.0668i	1.37268	+	1.37268i	0.516233	+	0.856448i	$0.327334\pi$
$138$	−0.288021	−	1.07491i	−0.0245180	−	0.0915024i
$139$	13.7959	+	7.96507i	1.17015	+	0.675588i	0.953716	−	0.300708i	$-0.0972230\pi$
$139$	13.7959	+	7.96507i	1.17015	+	0.675588i	0.216437	+	0.976297i	$0.430556\pi$
$140$	2.13927	+	1.62895i	0.180801	+	0.137672i
$141$	−0.821480	+	3.06581i	−0.0691811	+	0.258187i
$142$	−0.769429	−	0.444230i	−0.0645691	−	0.0372790i
$143$	0.973674	+	15.2403i	0.0814227	+	1.27446i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	6.67761	+	6.67761i	0.554545	+	0.554545i
$146$	−0.403294	+	0.232842i	−0.0333769	+	0.0192701i
$147$	−4.91291	+	4.98631i	−0.405210	+	0.411264i
$148$	−6.83756	+	6.83756i	−0.562044	+	0.562044i
$149$	−3.43927	−	0.921550i	−0.281756	−	0.0754963i	0.115173	−	0.993345i	$-0.463258\pi$
$149$	−3.43927	−	0.921550i	−0.281756	−	0.0754963i	−0.396930	+	0.917849i	$0.629924\pi$
$150$	−2.80520	+	2.80520i	−0.229044	+	0.229044i
$151$	−1.27548	+	4.76017i	−0.103797	+	0.387377i	−0.998206	−	0.0598738i	$-0.980930\pi$
$151$	−1.27548	+	4.76017i	−0.103797	+	0.387377i	0.894409	+	0.447251i	$0.147597\pi$
$152$	−2.49399	+	1.43990i	−0.202289	+	0.116792i
$153$	−0.447736	−	0.775501i	−0.0361973	−	0.0626956i
$154$	−1.50387	−	11.1048i	−0.121185	−	0.894848i
$155$			4.10489i			0.329713i
$156$	2.70687	+	2.38177i	0.216723	+	0.190694i
$157$	9.25317	−	5.34232i	0.738483	−	0.426363i	−0.0830344	−	0.996547i	$-0.526461\pi$
$157$	9.25317	−	5.34232i	0.738483	−	0.426363i	0.821518	+	0.570183i	$0.193128\pi$
$158$	1.62879	+	6.07873i	0.129580	+	0.483598i
$159$			3.79508i			0.300969i
$160$	−0.508146	+	0.880134i	−0.0401725	+	0.0695807i
$161$	−1.80100	−	2.32918i	−0.141939	−	0.183565i
$162$	−0.258819	−	0.965926i	−0.0203347	−	0.0758903i
$163$	−6.06884	+	22.6492i	−0.475349	+	1.77402i	0.144715	+	0.989473i	$0.453773\pi$
$163$	−6.06884	+	22.6492i	−0.475349	+	1.77402i	−0.620064	+	0.784551i	$0.712893\pi$
$164$	−1.39959	−	0.375020i	−0.109290	−	0.0292841i
$165$	−4.30453			−0.335107
$166$	−10.6534			−0.826863
$167$	15.7780	+	4.22772i	1.22094	+	0.327150i	0.811046	−	0.584982i	$-0.198898\pi$
$167$	15.7780	+	4.22772i	1.22094	+	0.327150i	0.409896	+	0.912132i	$0.365565\pi$
$168$	−2.10497	−	1.60284i	−0.162402	−	0.123662i
$169$	−11.9940	−	5.01446i	−0.922613	−	0.385727i
$170$	−0.455030	+	0.788136i	−0.0348992	+	0.0604473i
$171$	−2.78168	+	0.745350i	−0.212721	+	0.0569983i
$172$	−2.67270	+	4.62926i	−0.203792	+	0.352978i
$173$	−9.26068	−	16.0400i	−0.704077	−	1.21950i	−0.967024	−	0.254686i	$-0.918028\pi$
$173$	−9.26068	−	16.0400i	−0.704077	−	1.21950i	0.262947	−	0.964810i	$-0.415306\pi$
$174$	−6.57057	−	6.57057i	−0.498113	−	0.498113i
$175$	−3.98071	+	9.71195i	−0.300913	+	0.734155i
$176$	4.09120	−	1.09623i	0.308386	−	0.0826317i
$177$	7.47136	−	2.00194i	0.561581	−	0.150475i
$178$		−	13.1282i		−	0.984000i
$179$	−19.1571	−	11.0604i	−1.43187	−	0.826691i	−0.434607	−	0.900620i	$-0.643113\pi$
$179$	−19.1571	−	11.0604i	−1.43187	−	0.826691i	−0.997263	+	0.0739299i	$0.976446\pi$
$180$	−0.718627	+	0.718627i	−0.0535633	+	0.0535633i
$181$	12.9441			0.962126			0.481063	−	0.876686i	$-0.340251\pi$
$181$	12.9441			0.962126			0.481063	+	0.876686i	$0.340251\pi$
$182$	9.03943	+	3.04773i	0.670047	+	0.225913i
$183$	−2.35876			−0.174365
$184$	0.786889	−	0.786889i	0.0580102	−	0.0580102i
$185$	8.51069	+	4.91365i	0.625719	+	0.361259i
$186$		−	4.03909i		−	0.296160i
$187$	3.66356	−	0.981647i	0.267906	−	0.0717851i
$188$	−3.06581	+	0.821480i	−0.223597	+	0.0599126i
$189$	−1.61840	−	2.09303i	−0.117721	−	0.152246i
$190$	2.06951	+	2.06951i	0.150138	+	0.150138i
$191$	−3.65123	−	6.32412i	−0.264194	−	0.457597i	0.703158	−	0.711033i	$-0.251773\pi$
$191$	−3.65123	−	6.32412i	−0.264194	−	0.457597i	−0.967352	+	0.253436i	$0.918439\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	19.9346	−	5.34146i	1.43492	−	0.384487i	0.544172	−	0.838974i	$-0.316844\pi$
$193$	19.9346	−	5.34146i	1.43492	−	0.384487i	0.890753	+	0.454487i	$0.150177\pi$
$194$	−4.17509	+	7.23146i	−0.299754	+	0.519189i
$195$	1.62609	−	3.28373i	0.116447	−	0.235153i
$196$	−6.77473	−	1.76155i	−0.483909	−	0.125825i
$197$	16.2233	+	4.34702i	1.15586	+	0.309712i	0.785312	−	0.619100i	$-0.212503\pi$
$197$	16.2233	+	4.34702i	1.15586	+	0.309712i	0.370550	+	0.928812i	$0.379169\pi$
$198$	4.23552			0.301005
$199$	4.26267			0.302172			0.151086	−	0.988521i	$-0.451723\pi$
$199$	4.26267			0.302172			0.151086	+	0.988521i	$0.451723\pi$
$200$	−3.83197	−	1.02677i	−0.270961	−	0.0726039i
$201$	1.11978	−	4.17906i	0.0789829	−	0.294768i
$202$	2.12358	+	7.92531i	0.149415	+	0.557623i
$203$	−22.7481	−	9.32393i	−1.59660	−	0.654412i
$204$	0.447736	−	0.775501i	0.0313478	−	0.0542960i
$205$			1.47257i			0.102849i
$206$	−3.08600	−	11.5171i	−0.215012	−	0.802434i
$207$	0.963738	−	0.556414i	0.0669844	−	0.0386735i
$208$	−0.709237	+	3.53511i	−0.0491767	+	0.245116i
$209$		−	12.1975i		−	0.843718i
$210$	−1.01976	+	2.48798i	−0.0703704	+	0.171687i
$211$	−7.88634	−	13.6595i	−0.542918	−	0.940362i	−0.998735	−	0.0502883i	$-0.983986\pi$
$211$	−7.88634	−	13.6595i	−0.542918	−	0.940362i	0.455816	−	0.890074i	$-0.349347\pi$
$212$	−3.28664	+	1.89754i	−0.225727	+	0.130324i
$213$	0.229950	−	0.858187i	0.0157559	−	0.0588020i
$214$	−0.858835	+	0.858835i	−0.0587088	+	0.0587088i
$215$	5.24739	+	1.40603i	0.357869	+	0.0958906i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	−4.12609	−	9.85774i	−0.280097	−	0.669187i
$218$	9.37479	−	5.41254i	0.634941	−	0.366583i
$219$	−0.329288	−	0.329288i	−0.0222512	−	0.0222512i
$220$	−2.15226	−	3.72783i	−0.145106	−	0.251330i
$221$	−0.635102	+	3.16559i	−0.0427216	+	0.212941i
$222$	−8.37426	−	4.83488i	−0.562044	−	0.324496i
$223$	−7.04837	+	26.3049i	−0.471994	+	1.76151i	0.160598	+	0.987020i	$0.448658\pi$
$223$	−7.04837	+	26.3049i	−0.471994	+	1.76151i	−0.632592	+	0.774486i	$0.718009\pi$
$224$	0.335613	−	2.62438i	0.0224241	−	0.175349i
$225$	−3.43565	−	1.98358i	−0.229044	−	0.132238i
$226$	3.50912	+	13.0962i	0.233423	+	0.871146i
$227$	7.21417	+	7.21417i	0.478821	+	0.478821i	0.904754	−	0.425933i	$-0.140054\pi$
$227$	7.21417	+	7.21417i	0.478821	+	0.478821i	−0.425933	+	0.904754i	$0.640054\pi$
$228$	−2.03633	−	2.03633i	−0.134859	−	0.134859i
$229$	−6.86791	−	25.6314i	−0.453844	−	1.69377i	−0.691463	−	0.722412i	$-0.743033\pi$
$229$	−6.86791	−	25.6314i	−0.453844	−	1.69377i	0.237618	−	0.971359i	$-0.423633\pi$
$230$	−0.979439	−	0.565479i	−0.0645823	−	0.0372866i
$231$	10.3372	−	4.32675i	0.680135	−	0.284680i
$232$	2.40499	−	8.97556i	0.157896	−	0.589274i
$233$	−23.6788	−	13.6710i	−1.55125	−	0.895614i	−0.998041	−	0.0625709i	$-0.980070\pi$
$233$	−23.6788	−	13.6710i	−1.55125	−	0.895614i	−0.553208	−	0.833043i	$-0.686597\pi$
$234$	−1.60002	+	3.23109i	−0.104597	+	0.211223i
$235$	1.61283	+	2.79351i	0.105210	+	0.182228i
$236$	5.46941	+	5.46941i	0.356028	+	0.356028i
$237$	−5.45004	+	3.14658i	−0.354018	+	0.204392i
$238$	0.300532	−	2.35006i	0.0194806	−	0.152332i
$239$	19.5943	−	19.5943i	1.26745	−	1.26745i	0.320045	−	0.947402i	$-0.396302\pi$
$239$	19.5943	−	19.5943i	1.26745	−	1.26745i	0.947402	−	0.320045i	$-0.103698\pi$
$240$	−0.981662	−	0.263036i	−0.0633660	−	0.0169789i
$241$	17.7577	−	17.7577i	1.14388	−	1.14388i	0.156141	−	0.987735i	$-0.450095\pi$
$241$	17.7577	−	17.7577i	1.14388	−	1.14388i	0.987735	−	0.156141i	$-0.0499054\pi$
$242$	−1.79611	+	6.70318i	−0.115459	+	0.430897i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−1.17938	−	2.04275i	−0.0755021	−	0.130774i
$245$	0.0527446	+	7.11385i	0.00336973	+	0.454487i
$246$		−	1.44897i		−	0.0923827i
$247$	9.30492	+	4.60776i	0.592058	+	0.293185i
$248$	3.49795	−	2.01954i	0.222120	−	0.128241i
$249$	−2.75730	−	10.2904i	−0.174737	−	0.652126i
$250$			9.11324i			0.576372i
$251$	7.23404	−	12.5297i	0.456609	−	0.790869i	−0.542171	−	0.840268i	$-0.682397\pi$
$251$	7.23404	−	12.5297i	0.456609	−	0.790869i	0.998779	+	0.0493992i	$0.0157307\pi$
$252$	1.00342	−	2.44809i	0.0632093	−	0.154215i
$253$	1.21992	+	4.55281i	0.0766958	+	0.286232i
$254$	2.35288	−	8.78106i	0.147633	−	0.550972i
$255$	−0.879051	−	0.235541i	−0.0550483	−	0.0147502i
$256$	1.00000			0.0625000
$257$	12.8487			0.801482			0.400741	−	0.916191i	$-0.368753\pi$
$257$	12.8487			0.801482			0.400741	+	0.916191i	$0.368753\pi$
$258$	−5.16327	−	1.38349i	−0.321451	−	0.0861325i
$259$	−25.3771	−	3.24530i	−1.57686	−	0.201653i
$260$	3.65684	−	0.233628i	0.226787	−	0.0144890i
$261$	4.64609	−	8.04727i	0.287586	−	0.498113i
$262$	6.08985	−	1.63177i	0.376232	−	0.100811i
$263$	5.32982	−	9.23151i	0.328651	−	0.569240i	−0.653594	−	0.756846i	$-0.726739\pi$
$263$	5.32982	−	9.23151i	0.328651	−	0.569240i	0.982244	+	0.187606i	$0.0600728\pi$
$264$	2.11776	+	3.66807i	0.130339	+	0.225754i
$265$	2.72725	+	2.72725i	0.167533	+	0.167533i
$266$	−7.05004	−	2.88965i	−0.432266	−	0.177176i
$267$	12.6809	−	3.39783i	0.776056	−	0.207944i
$268$	4.17906	−	1.11978i	0.255277	−	0.0684012i
$269$			9.60406i			0.585570i	0.956178	+	0.292785i	$0.0945820\pi$
$269$			9.60406i			0.585570i	−0.956178	+	0.292785i	$0.905418\pi$
$270$	−0.880134	−	0.508146i	−0.0535633	−	0.0309248i
$271$	9.30186	−	9.30186i	0.565048	−	0.565048i	−0.365689	−	0.930737i	$-0.619167\pi$
$271$	9.30186	−	9.30186i	0.565048	−	0.565048i	0.930737	+	0.365689i	$0.119167\pi$
$272$	0.895472			0.0542960
$273$	−0.604309	+	9.52023i	−0.0365744	+	0.576191i
$274$	−22.7219			−1.37268
$275$	11.8815	−	11.8815i	0.716480	−	0.716480i
$276$	0.963738	+	0.556414i	0.0580102	+	0.0334922i
$277$			19.7086i			1.18418i	0.805873	+	0.592089i	$0.201696\pi$
$277$			19.7086i			1.18418i	−0.805873	+	0.592089i	$0.798304\pi$
$278$	−15.3873	+	4.12302i	−0.922871	+	0.247283i
$279$	3.90146	−	1.04539i	0.233574	−	0.0625860i
$280$	−2.66453	+	0.360846i	−0.159236	+	0.0215647i
$281$	−12.8366	−	12.8366i	−0.765767	−	0.765767i	0.211591	−	0.977358i	$-0.432135\pi$
$281$	−12.8366	−	12.8366i	−0.765767	−	0.765767i	−0.977358	+	0.211591i	$0.932135\pi$
$282$	−1.58698	−	2.74873i	−0.0945031	−	0.163684i
$283$	−9.67398	+	16.7558i	−0.575058	+	0.996030i	0.420977	+	0.907071i	$0.361687\pi$
$283$	−9.67398	+	16.7558i	−0.575058	+	0.996030i	−0.996035	+	0.0889589i	$0.971646\pi$
$284$	0.858187	−	0.229950i	0.0509240	−	0.0136450i
$285$	−1.46336	+	2.53462i	−0.0866822	+	0.150138i
$286$	−11.4650	−	10.0880i	−0.677941	−	0.596518i
$287$	−1.48018	−	3.53632i	−0.0873720	−	0.208743i
$288$	0.965926	+	0.258819i	0.0569177	+	0.0152511i
$289$	−16.1981			−0.952831
$290$	−9.44357			−0.554545
$291$	−8.06565	−	2.16118i	−0.472817	−	0.126691i
$292$	0.120528	−	0.449816i	0.00705336	−	0.0263235i
$293$	−2.77511	−	10.3569i	−0.162124	−	0.605054i	−0.998390	−	0.0567298i	$-0.981933\pi$
$293$	−2.77511	−	10.3569i	−0.162124	−	0.605054i	0.836266	−	0.548324i	$-0.184734\pi$
$294$	−0.0518991	−	6.99981i	−0.00302682	−	0.408237i
$295$	3.93047	−	6.80777i	0.228841	−	0.396363i
$296$		−	9.66976i		−	0.562044i
$297$	1.09623	+	4.09120i	0.0636099	+	0.237396i
$298$	3.08357	−	1.78030i	0.178626	−	0.103130i
$299$	−3.93397	−	0.789259i	−0.227507	−	0.0456440i
$300$		−	3.96715i		−	0.229044i
$301$	−14.0147	+	1.89795i	−0.807793	+	0.109396i
$302$	−2.46404	−	4.26785i	−0.141790	−	0.245587i
$303$	−7.10564	+	4.10244i	−0.408208	+	0.235679i
$304$	0.745350	−	2.78168i	0.0427487	−	0.159540i
$305$	−1.69507	+	1.69507i	−0.0970594	+	0.0970594i
$306$	0.864960	+	0.231765i	0.0494464	+	0.0132491i
$307$	−4.30658	+	4.30658i	−0.245789	+	0.245789i	−0.819240	−	0.573451i	$-0.805604\pi$
$307$	−4.30658	+	4.30658i	−0.245789	+	0.245789i	0.573451	+	0.819240i	$0.305604\pi$
$308$	8.91566	+	6.78886i	0.508017	+	0.386831i
$309$	10.3259	−	5.96169i	0.587423	−	0.339149i
$310$	−2.90260	−	2.90260i	−0.164856	−	0.164856i
$311$	0.316677	+	0.548501i	0.0179571	+	0.0311027i	0.874864	−	0.484368i	$-0.160950\pi$
$311$	0.316677	+	0.548501i	0.0179571	+	0.0311027i	−0.856907	+	0.515471i	$0.827617\pi$
$312$	−3.59822	+	0.229883i	−0.203709	+	0.0130146i
$313$	6.23316	+	3.59872i	0.352319	+	0.203411i	0.665706	−	0.746214i	$-0.268130\pi$
$313$	6.23316	+	3.59872i	0.352319	+	0.203411i	−0.313387	+	0.949625i	$0.601464\pi$
$314$	−2.76539	+	10.3206i	−0.156060	+	0.582423i
$315$	−2.66713	−	0.341081i	−0.150276	−	0.0192177i
$316$	−5.45004	−	3.14658i	−0.306589	−	0.177009i
$317$	−2.26411	−	8.44978i	−0.127165	−	0.474587i	0.872742	−	0.488181i	$-0.162339\pi$
$317$	−2.26411	−	8.44978i	−0.127165	−	0.474587i	−0.999908	+	0.0135942i	$0.995673\pi$
$318$	−2.68353	−	2.68353i	−0.150485	−	0.150485i
$319$	27.8298	+	27.8298i	1.55817	+	1.55817i
$320$	−0.263036	−	0.981662i	−0.0147041	−	0.0548766i
$321$	−1.05185	−	0.607288i	−0.0587088	−	0.0338955i
$322$	2.92048	+	0.373480i	0.162752	+	0.0208132i
$323$	0.667440	−	2.49092i	0.0371373	−	0.138598i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$	4.57546	+	13.5522i	0.253801	+	0.751742i
$326$	−11.7241	−	20.3067i	−0.649338	−	1.12469i
$327$	7.65449	+	7.65449i	0.423294	+	0.423294i
$328$	1.25484	−	0.724483i	0.0692870	−	0.0400029i
$329$	−6.68109	−	5.08734i	−0.368340	−	0.280474i
$330$	3.04376	−	3.04376i	0.167553	−	0.167553i
$331$	12.2810	+	3.29069i	0.675026	+	0.180873i	0.580018	−	0.814604i	$-0.303046\pi$
$331$	12.2810	+	3.29069i	0.675026	+	0.180873i	0.0950081	+	0.995477i	$0.469712\pi$
$332$	7.53308	−	7.53308i	0.413431	−	0.413431i
$333$	2.50272	−	9.34028i	0.137148	−	0.511844i
$334$	−14.1462	+	8.16732i	−0.774046	+	0.446896i
$335$	−2.19848	−	3.80788i	−0.120116	−	0.208047i
$336$	2.62182	−	0.355062i	0.143032	−	0.0193702i
$337$			19.1949i			1.04561i	0.852451	+	0.522807i	$0.175115\pi$
$337$			19.1949i			1.04561i	−0.852451	+	0.522807i	$0.824885\pi$
$338$	12.0268	−	4.93526i	0.654170	−	0.268443i
$339$	−11.7417	+	6.77909i	−0.637723	+	0.368190i
$340$	−0.235541	−	0.879051i	−0.0127740	−	0.0476732i
$341$			17.1076i			0.926431i
$342$	1.43990	−	2.49399i	0.0778611	−	0.134859i
$343$	−7.27725	−	17.0306i	−0.392934	−	0.919567i
$344$	−1.38349	−	5.16327i	−0.0745930	−	0.278385i
$345$	0.292714	−	1.09242i	0.0157592	−	0.0588140i
$346$	17.8903	+	4.79368i	0.961787	+	0.257710i
$347$	15.4683			0.830382			0.415191	−	0.909734i	$-0.363715\pi$
$347$	15.4683			0.830382			0.415191	+	0.909734i	$0.363715\pi$
$348$	9.29218			0.498113
$349$	5.37886	+	1.44126i	0.287924	+	0.0771489i	0.399890	−	0.916563i	$-0.369048\pi$
$349$	5.37886	+	1.44126i	0.287924	+	0.0771489i	−0.111966	+	0.993712i	$0.535715\pi$
$350$	−4.05260	−	9.68217i	−0.216621	−	0.517534i
$351$	−3.53511	−	0.709237i	−0.188690	−	0.0378563i
$352$	−2.11776	+	3.66807i	−0.112877	+	0.195509i
$353$	−27.8499	+	7.46235i	−1.48230	+	0.397181i	−0.907129	−	0.420853i	$-0.861731\pi$
$353$	−27.8499	+	7.46235i	−1.48230	+	0.397181i	−0.575170	+	0.818034i	$0.695064\pi$
$354$	−3.86746	+	6.69863i	−0.205553	+	0.356028i
$355$	−0.451467	−	0.781964i	−0.0239614	−	0.0415024i
$356$	9.28304	+	9.28304i	0.492000	+	0.492000i
$357$	2.34776	−	0.317948i	0.124257	−	0.0168276i
$358$	21.3670	−	5.72527i	1.12928	−	0.302590i
$359$	−2.86118	+	0.766652i	−0.151007	+	0.0404623i	−0.333531	−	0.942739i	$-0.608240\pi$
$359$	−2.86118	+	0.766652i	−0.151007	+	0.0404623i	0.182523	+	0.983202i	$0.441573\pi$
$360$		−	1.01629i		−	0.0535633i
$361$	9.27227	+	5.35335i	0.488014	+	0.281755i
$362$	−9.15285	+	9.15285i	−0.481063	+	0.481063i
$363$	−6.93965			−0.364237
$364$	−8.54692	+	4.23677i	−0.447980	+	0.222067i
$365$	−0.473271			−0.0247721
$366$	1.66790	−	1.66790i	0.0871824	−	0.0871824i
$367$	−11.0391	−	6.37341i	−0.576235	−	0.332689i	0.183401	−	0.983038i	$-0.441289\pi$
$367$	−11.0391	−	6.37341i	−0.576235	−	0.332689i	−0.759636	+	0.650349i	$0.774623\pi$
$368$			1.11283i			0.0580102i
$369$	1.39959	−	0.375020i	0.0728599	−	0.0195228i
$370$	−9.49244	+	2.54349i	−0.493489	+	0.132230i
$371$	−9.29071	−	3.80805i	−0.482349	−	0.197704i
$372$	2.85607	+	2.85607i	0.148080	+	0.148080i
$373$	−7.63783	−	13.2291i	−0.395472	−	0.684978i	0.597689	−	0.801728i	$-0.296086\pi$
$373$	−7.63783	−	13.2291i	−0.395472	−	0.684978i	−0.993161	+	0.116750i	$0.962752\pi$
$374$	−1.89640	+	3.28465i	−0.0980603	+	0.169845i
$375$	−8.80272	+	2.35868i	−0.454570	+	0.121802i
$376$	1.58698	−	2.74873i	0.0818421	−	0.141755i
$377$	−31.7431	+	10.7170i	−1.63485	+	0.551954i
$378$	2.62438	+	0.335613i	0.134983	+	0.0172621i
$379$	−14.6944	−	3.93734i	−0.754799	−	0.202248i	−0.139153	−	0.990271i	$-0.544438\pi$
$379$	−14.6944	−	3.93734i	−0.754799	−	0.202248i	−0.615646	+	0.788023i	$0.711105\pi$
$380$	−2.92673			−0.150138
$381$	9.09082			0.465737
$382$	7.05364	+	1.89002i	0.360896	+	0.0967017i
$383$	3.70224	−	13.8170i	0.189176	−	0.706013i	−0.804522	−	0.593923i	$-0.797579\pi$
$383$	3.70224	−	13.8170i	0.189176	−	0.706013i	0.993698	−	0.112091i	$-0.0357548\pi$
$384$	0.258819	+	0.965926i	0.0132078	+	0.0492922i
$385$	4.31923	−	10.5379i	0.220129	−	0.537060i
$386$	−10.3189	+	17.8729i	−0.525219	+	0.909706i
$387$		−	5.34541i		−	0.271722i
$388$	−2.16118	−	8.06565i	−0.109717	−	0.409471i
$389$	−6.99902	+	4.04089i	−0.354864	+	0.204881i	−0.666826	−	0.745214i	$-0.732347\pi$
$389$	−6.99902	+	4.04089i	−0.354864	+	0.204881i	0.311961	+	0.950095i	$0.399014\pi$
$390$	1.17213	+	3.47177i	0.0593529	+	0.175800i
$391$			0.996507i			0.0503955i
$392$	6.03606	−	3.54485i	0.304867	−	0.179042i
$393$	3.15234	+	5.46001i	0.159014	+	0.275421i
$394$	−14.5454	+	8.39780i	−0.732787	+	0.423075i
$395$	−1.65533	+	6.17776i	−0.0832885	+	0.310837i
$396$	−2.99497	+	2.99497i	−0.150503	+	0.150503i
$397$	28.8453	+	7.72908i	1.44771	+	0.387912i	0.895225	−	0.445614i	$-0.147015\pi$
$397$	28.8453	+	7.72908i	1.44771	+	0.387912i	0.552481	+	0.833526i	$0.313681\pi$
$398$	−3.01416	+	3.01416i	−0.151086	+	0.151086i
$399$	0.966502	−	7.55771i	0.0483856	−	0.378359i
$400$	3.43565	−	1.98358i	0.171783	−	0.0991788i
$401$	5.58904	+	5.58904i	0.279103	+	0.279103i	0.832751	−	0.553648i	$-0.186765\pi$
$401$	5.58904	+	5.58904i	0.279103	+	0.279103i	−0.553648	+	0.832751i	$0.686765\pi$
$402$	2.16324	+	3.74684i	0.107893	+	0.186875i
$403$	−13.0506	−	6.46264i	−0.650099	−	0.321927i
$404$	−7.10564	−	4.10244i	−0.353519	−	0.204104i
$405$	0.263036	−	0.981662i	0.0130703	−	0.0487792i
$406$	22.6784	−	9.49233i	1.12551	−	0.471097i
$407$	35.4694	+	20.4783i	1.75815	+	1.01507i
$408$	0.231765	+	0.864960i	0.0114741	+	0.0428219i
$409$	4.84747	+	4.84747i	0.239692	+	0.239692i	0.816723	−	0.577030i	$-0.195789\pi$
$409$	4.84747	+	4.84747i	0.239692	+	0.239692i	−0.577030	+	0.816723i	$0.695789\pi$
$410$	−1.04127	−	1.04127i	−0.0514244	−	0.0514244i
$411$	−5.88086	−	21.9477i	−0.290082	−	1.08260i
$412$	10.3259	+	5.96169i	0.508723	+	0.293711i
$413$	−2.59594	+	20.2994i	−0.127738	+	0.998866i
$414$	−0.288021	+	1.07491i	−0.0141555	+	0.0528290i
$415$	−9.37641	−	5.41347i	−0.460270	−	0.265737i
$416$	−1.99819	−	3.00120i	−0.0979694	−	0.147146i
$417$	−7.96507	−	13.7959i	−0.390051	−	0.675588i
$418$	8.62493	+	8.62493i	0.421859	+	0.421859i
$419$	24.6906	−	14.2551i	1.20622	−	0.696409i	0.244285	−	0.969704i	$-0.421447\pi$
$419$	24.6906	−	14.2551i	1.20622	−	0.696409i	0.961930	+	0.273295i	$0.0881135\pi$
$420$	−1.03818	−	2.48035i	−0.0506581	−	0.121029i
$421$	−26.7911	+	26.7911i	−1.30572	+	1.30572i	−0.381243	+	0.924475i	$0.624504\pi$
$421$	−26.7911	+	26.7911i	−1.30572	+	1.30572i	−0.924475	+	0.381243i	$0.875496\pi$
$422$	15.2352	+	4.08227i	0.741640	+	0.198722i
$423$	2.24433	−	2.24433i	0.109123	−	0.109123i
$424$	0.982239	−	3.66577i	0.0477017	−	0.178025i
$425$	3.07653	−	1.77624i	0.149234	−	0.0861601i
$426$	0.444230	+	0.769429i	0.0215230	+	0.0372790i
$427$	2.36682	−	5.77447i	0.114539	−	0.279446i
$428$		−	1.21458i		−	0.0587088i
$429$	6.77693	−	13.6853i	0.327193	−	0.660735i
$430$	−4.70468	+	2.71625i	−0.226880	+	0.130989i
$431$	−2.12686	−	7.93755i	−0.102447	−	0.382338i	0.895596	−	0.444869i	$-0.146750\pi$
$431$	−2.12686	−	7.93755i	−0.102447	−	0.382338i	−0.998043	+	0.0625303i	$0.980083\pi$
$432$			1.00000i			0.0481125i
$433$	8.27418	−	14.3313i	0.397632	−	0.688719i	−0.595801	−	0.803132i	$-0.703165\pi$
$433$	8.27418	−	14.3313i	0.397632	−	0.688719i	0.993433	+	0.114413i	$0.0364988\pi$
$434$	9.88806	+	4.05289i	0.474642	+	0.194545i
$435$	−2.44418	−	9.12179i	−0.117189	−	0.437356i
$436$	−2.80174	+	10.4562i	−0.134179	+	0.500762i
$437$	3.09554	+	0.829447i	0.148080	+	0.0396778i
$438$	0.465684			0.0222512
$439$	−36.1411			−1.72492			−0.862460	−	0.506125i	$-0.831077\pi$
$439$	−36.1411			−1.72492			−0.862460	+	0.506125i	$0.831077\pi$
$440$	4.15785	+	1.11409i	0.198218	+	0.0531123i
$441$	6.74786	−	1.86181i	0.321327	−	0.0886578i
$442$	−1.78933	−	2.68749i	−0.0851095	−	0.127831i
$443$	9.04555	−	15.6673i	0.429767	−	0.744378i	−0.567085	−	0.823659i	$-0.691929\pi$
$443$	9.04555	−	15.6673i	0.429767	−	0.744378i	0.996852	+	0.0792809i	$0.0252624\pi$
$444$	9.34028	−	2.50272i	0.443270	−	0.118774i
$445$	6.67104	−	11.5546i	0.316238	−	0.547740i
$446$	−13.6164	−	23.5843i	−0.644756	−	1.11675i
$447$	2.51772	+	2.51772i	0.119084	+	0.119084i
$448$	1.61840	+	2.09303i	0.0764623	+	0.0988864i
$449$	−11.6055	+	3.10969i	−0.547699	+	0.146755i	−0.522049	−	0.852916i	$-0.674832\pi$
$449$	−11.6055	+	3.10969i	−0.547699	+	0.146755i	−0.0256499	+	0.999671i	$0.508166\pi$
$450$	3.83197	−	1.02677i	0.180641	−	0.0484026i
$451$			6.13713i			0.288986i
$452$	−11.7417	−	6.77909i	−0.552285	−	0.318862i
$453$	3.48468	−	3.48468i	0.163725	−	0.163725i
$454$	−10.2024			−0.478821
$455$	6.40722	+	7.27577i	0.300375	+	0.341093i
$456$	2.87981			0.134859
$457$	−10.5376	+	10.5376i	−0.492930	+	0.492930i	−0.909228	−	0.416298i	$-0.863327\pi$
$457$	−10.5376	+	10.5376i	−0.492930	+	0.492930i	0.416298	+	0.909228i	$0.363327\pi$
$458$	22.9805	+	13.2678i	1.07381	+	0.619963i
$459$			0.895472i			0.0417971i
$460$	1.09242	−	0.292714i	0.0509345	−	0.0136478i
$461$	−32.6783	+	8.75614i	−1.52198	+	0.407814i	−0.920394	−	0.390992i	$-0.872132\pi$
$461$	−32.6783	+	8.75614i	−1.52198	+	0.407814i	−0.601588	+	0.798806i	$0.705465\pi$
$462$	−4.24999	+	10.3689i	−0.197728	+	0.482407i
$463$	20.8393	+	20.8393i	0.968486	+	0.968486i	0.999518	−	0.0310326i	$-0.00987956\pi$
$463$	20.8393	+	20.8393i	0.968486	+	0.968486i	−0.0310326	+	0.999518i	$0.509880\pi$
$464$	4.64609	+	8.04727i	0.215689	+	0.373585i
$465$	2.05245	−	3.55494i	0.0951799	−	0.164856i
$466$	26.4103	−	7.07661i	1.22343	−	0.327817i
$467$	−19.7862	+	34.2707i	−0.915597	+	1.58586i	−0.109572	+	0.993979i	$0.534948\pi$
$467$	−19.7862	+	34.2707i	−0.915597	+	1.58586i	−0.806025	+	0.591882i	$0.798385\pi$
$468$	−1.15334	−	3.41611i	−0.0533130	−	0.157910i
$469$	9.10712	+	6.93465i	0.420528	+	0.320212i
$470$	−3.11575	−	0.834863i	−0.143719	−	0.0385094i
$471$	−10.6846			−0.492322
$472$	−7.73492			−0.356028
$473$	21.8691	+	5.85982i	1.00554	+	0.269435i
$474$	1.62879	−	6.07873i	0.0748128	−	0.279205i
$475$	−2.95691	−	11.0354i	−0.135673	−	0.506337i
$476$	1.44923	+	1.87425i	0.0664255	+	0.0859061i
$477$	1.89754	−	3.28664i	0.0868824	−	0.150485i
$478$			27.7105i			1.26745i
$479$	4.96278	+	18.5214i	0.226755	+	0.846262i	0.981694	+	0.190467i	$0.0610001\pi$
$479$	4.96278	+	18.5214i	0.226755	+	0.846262i	−0.754938	+	0.655796i	$0.772333\pi$
$480$	0.880134	−	0.508146i	0.0401725	−	0.0231936i
$481$	−29.0209	+	19.3220i	−1.32324	+	0.881010i
$482$			25.1132i			1.14388i
$483$	0.395123	+	2.91764i	0.0179787	+	0.132757i
$484$	−3.46982	−	6.00991i	−0.157719	−	0.273178i
$485$	−7.34928	+	4.24311i	−0.333713	+	0.192670i
$486$	−0.258819	+	0.965926i	−0.0117403	+	0.0438153i
$487$	−2.63332	+	2.63332i	−0.119327	+	0.119327i	−0.764249	−	0.644922i	$-0.776890\pi$
$487$	−2.63332	+	2.63332i	−0.119327	+	0.119327i	0.644922	+	0.764249i	$0.276890\pi$
$488$	2.27839	+	0.610493i	0.103138	+	0.0276357i
$489$	16.5804	−	16.5804i	0.749791	−	0.749791i
$490$	−5.06755	−	4.99295i	−0.228928	−	0.225559i
$491$	−3.19473	+	1.84448i	−0.144176	+	0.0832401i	−0.570353	−	0.821400i	$-0.693194\pi$
$491$	−3.19473	+	1.84448i	−0.144176	+	0.0832401i	0.426177	+	0.904640i	$0.359860\pi$
$492$	1.02457	+	1.02457i	0.0461913	+	0.0461913i
$493$	4.16044	+	7.20610i	0.187377	+	0.324546i
$494$	−9.83775	+	3.32139i	−0.442621	+	0.149436i
$495$	3.72783	+	2.15226i	0.167553	+	0.0967370i
$496$	−1.04539	+	3.90146i	−0.0469395	+	0.175181i
$497$	1.87018	+	1.42406i	0.0838892	+	0.0638778i
$498$	9.22610	+	5.32669i	0.413431	+	0.238695i
$499$	7.22047	+	26.9472i	0.323233	+	1.20632i	0.916076	+	0.401004i	$0.131339\pi$
$499$	7.22047	+	26.9472i	0.323233	+	1.20632i	−0.592844	+	0.805318i	$0.701995\pi$
$500$	−6.44403	−	6.44403i	−0.288186	−	0.288186i
$501$	−11.5503	−	11.5503i	−0.516031	−	0.516031i
$502$	3.74461	+	13.9751i	0.167130	+	0.623739i
$503$	−12.6397	−	7.29753i	−0.563576	−	0.325381i	0.191003	−	0.981589i	$-0.438826\pi$
$503$	−12.6397	−	7.29753i	−0.563576	−	0.325381i	−0.754580	+	0.656208i	$0.772159\pi$
$504$	1.02154	+	2.44059i	0.0455030	+	0.108712i
$505$	−2.15818	+	8.05443i	−0.0960376	+	0.358417i
$506$	−4.08193	−	2.35671i	−0.181464	−	0.104768i
$507$	7.87985	+	10.3396i	0.349956	+	0.459199i
$508$	4.54541	+	7.87288i	0.201670	+	0.349303i
$509$	16.9231	+	16.9231i	0.750102	+	0.750102i	0.974498	−	0.224396i	$-0.0720408\pi$
$509$	16.9231	+	16.9231i	0.750102	+	0.750102i	−0.224396	+	0.974498i	$0.572041\pi$
$510$	0.788136	−	0.455030i	0.0348992	−	0.0201491i
$511$	1.13654	−	0.475715i	0.0502776	−	0.0210444i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	2.78168	+	0.745350i	0.122814	+	0.0329080i
$514$	−9.08543	+	9.08543i	−0.400741	+	0.400741i
$515$	3.13627	−	11.7047i	0.138201	−	0.515772i
$516$	4.62926	−	2.67270i	0.203792	−	0.117659i
$517$	6.72168	+	11.6423i	0.295619	+	0.512027i
$518$	20.2391	−	15.6496i	0.889255	−	0.687602i
$519$			18.5214i			0.812998i
$520$	−2.42057	+	2.75097i	−0.106149	+	0.120638i
$521$	−6.38446	+	3.68607i	−0.279708	+	0.161490i	−0.633291	−	0.773913i	$-0.718297\pi$
$521$	−6.38446	+	3.68607i	−0.279708	+	0.161490i	0.353583	+	0.935403i	$0.384963\pi$
$522$	2.40499	+	8.97556i	0.105264	+	0.392850i
$523$		−	33.6653i		−	1.47208i	−0.676937	−	0.736041i	$-0.736693\pi$
$523$		−	33.6653i		−	1.47208i	0.676937	−	0.736041i	$-0.263307\pi$
$524$	−3.15234	+	5.46001i	−0.137711	+	0.238522i
$525$	8.30337	−	6.42044i	0.362389	−	0.280211i
$526$	2.75892	+	10.2964i	0.120294	+	0.448945i
$527$	−0.936120	+	3.49365i	−0.0407780	+	0.152186i
$528$	−4.09120	−	1.09623i	−0.178047	−	0.0477075i
$529$	21.7616			0.946157
$530$	−3.85691			−0.167533
$531$	−7.47136	−	2.00194i	−0.324229	−	0.0868770i
$532$	7.02842	−	2.94184i	0.304721	−	0.127545i
$533$	−4.68173	−	2.31838i	−0.202788	−	0.100420i
$534$	−6.56410	+	11.3694i	−0.284056	+	0.492000i
$535$	−1.19230	+	0.319477i	−0.0515478	+	0.0138122i
$536$	−2.16324	+	3.74684i	−0.0934377	+	0.161839i
$537$	11.0604	+	19.1571i	0.477290	+	0.826691i
$538$	−6.79110	−	6.79110i	−0.292785	−	0.292785i
$539$	0.219820	+	29.6478i	0.00946831	+	1.27702i
$540$	0.981662	−	0.263036i	0.0422440	−	0.0113193i
$541$	9.31061	−	2.49477i	0.400294	−	0.107259i	−0.0530547	−	0.998592i	$-0.516896\pi$
$541$	9.31061	−	2.49477i	0.400294	−	0.107259i	0.453349	+	0.891333i	$0.350229\pi$
$542$			13.1548i			0.565048i
$543$	−11.2099	−	6.47204i	−0.481063	−	0.277742i
$544$	−0.633194	+	0.633194i	−0.0271480	+	0.0271480i
$545$	11.0014			0.471250
$546$	−6.30451	−	7.15913i	−0.269808	−	0.306383i
$547$	−7.74134			−0.330996			−0.165498	−	0.986210i	$-0.552923\pi$
$547$	−7.74134			−0.330996			−0.165498	+	0.986210i	$0.552923\pi$
$548$	16.0668	−	16.0668i	0.686341	−	0.686341i
$549$	2.04275	+	1.17938i	0.0871824	+	0.0503348i
$550$			16.8030i			0.716480i
$551$	25.8479	−	6.92592i	1.10116	−	0.295054i
$552$	−1.07491	+	0.288021i	−0.0457512	+	0.0122590i
$553$	−2.23446	−	16.4995i	−0.0950189	−	0.701631i
$554$	−13.9361	−	13.9361i	−0.592089	−	0.592089i
$555$	−4.91365	−	8.51069i	−0.208573	−	0.361259i
$556$	7.96507	−	13.7959i	0.337794	−	0.585077i
$557$	−13.4348	+	3.59983i	−0.569249	+	0.152530i	−0.531952	−	0.846774i	$-0.678541\pi$
$557$	−13.4348	+	3.59983i	−0.569249	+	0.152530i	−0.0372967	+	0.999304i	$0.511875\pi$
$558$	−2.01954	+	3.49795i	−0.0854941	+	0.148080i
$559$	−12.7315	+	14.4693i	−0.538487	+	0.611988i
$560$	1.62895	−	2.13927i	0.0688358	−	0.0904005i
$561$	−3.66356	−	0.981647i	−0.154675	−	0.0414452i
$562$	18.1537			0.765767
$563$	1.49021			0.0628050			0.0314025	−	0.999507i	$-0.490003\pi$
$563$	1.49021			0.0628050			0.0314025	+	0.999507i	$0.490003\pi$
$564$	3.06581	+	0.821480i	0.129094	+	0.0345906i
$565$	−3.56629	+	13.3096i	−0.150035	+	0.559937i
$566$	−5.00762	−	18.6887i	−0.210486	−	0.785544i
$567$	0.355062	+	2.62182i	0.0149112	+	0.110106i
$568$	−0.444230	+	0.769429i	−0.0186395	+	0.0322845i
$569$		−	1.50113i		−	0.0629308i	−0.999505	−	0.0314654i	$-0.989983\pi$
$569$		−	1.50113i		−	0.0629308i	0.999505	−	0.0314654i	$-0.0100174\pi$
$570$	−0.757493	−	2.82700i	−0.0317279	−	0.118410i
$571$	27.0036	−	15.5905i	1.13006	−	0.652443i	0.186113	−	0.982528i	$-0.440411\pi$
$571$	27.0036	−	15.5905i	1.13006	−	0.652443i	0.943951	+	0.330085i	$0.107078\pi$
$572$	15.2403	−	0.973674i	0.637230	−	0.0407114i
$573$			7.30247i			0.305065i
$574$	3.54720	+	1.45392i	0.148057	+	0.0606853i
$575$	2.20738	+	3.82329i	0.0920541	+	0.159442i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	10.9832	−	40.9897i	0.457235	−	1.70643i	−0.224197	−	0.974544i	$-0.571976\pi$
$577$	10.9832	−	40.9897i	0.457235	−	1.70643i	0.681432	−	0.731881i	$-0.261357\pi$
$578$	11.4538	−	11.4538i	0.476416	−	0.476416i
$579$	−19.9346	−	5.34146i	−0.828454	−	0.221984i
$580$	6.67761	−	6.67761i	0.277273	−	0.277273i
$581$	27.9585	+	3.57542i	1.15991	+	0.148333i
$582$	7.23146	−	4.17509i	0.299754	−	0.173063i
$583$	11.3661	+	11.3661i	0.470737	+	0.470737i
$584$	0.232842	+	0.403294i	0.00963507	+	0.0166884i
$585$	−3.05010	+	2.03075i	−0.126106	+	0.0839610i
$586$	9.28570	+	5.36110i	0.383589	+	0.221465i
$587$	−2.49601	+	9.31524i	−0.103021	+	0.384481i	−0.998113	−	0.0614008i	$-0.980443\pi$
$587$	−2.49601	+	9.31524i	−0.103021	+	0.384481i	0.895092	+	0.445882i	$0.147110\pi$
$588$	4.98631	+	4.91291i	0.205632	+	0.202605i
$589$	10.0734	+	5.81590i	0.415069	+	0.239640i
$590$	2.03456	+	7.59308i	0.0837615	+	0.312602i
$591$	−11.8763	−	11.8763i	−0.488525	−	0.488525i
$592$	6.83756	+	6.83756i	0.281022	+	0.281022i
$593$	−6.10134	−	22.7705i	−0.250552	−	0.935073i	−0.970511	−	0.241056i	$-0.922506\pi$
$593$	−6.10134	−	22.7705i	−0.250552	−	0.935073i	0.719959	−	0.694016i	$-0.244161\pi$
$594$	−3.66807	−	2.11776i	−0.150503	−	0.0868928i
$595$	1.45868	−	1.91565i	0.0598001	−	0.0785341i
$596$	−0.921550	+	3.43927i	−0.0377482	+	0.140878i
$597$	−3.69158	−	2.13133i	−0.151086	−	0.0872297i
$598$	3.33983	−	2.22365i	0.136576	−	0.0909317i
$599$	−14.5945	−	25.2784i	−0.596314	−	1.03285i	−0.993360	−	0.115048i	$-0.963298\pi$
$599$	−14.5945	−	25.2784i	−0.596314	−	1.03285i	0.397046	−	0.917799i	$-0.370035\pi$
$600$	2.80520	+	2.80520i	0.114522	+	0.114522i
$601$	−22.5127	+	12.9977i	−0.918311	+	0.530187i	−0.883096	−	0.469192i	$-0.844545\pi$
$601$	−22.5127	+	12.9977i	−0.918311	+	0.530187i	−0.0352154	+	0.999380i	$0.511212\pi$
$602$	8.56783	−	11.2519i	0.349199	−	0.458595i
$603$	−3.05928	+	3.05928i	−0.124584	+	0.124584i
$604$	4.76017	+	1.27548i	0.193688	+	0.0518987i
$605$	−4.98702	+	4.98702i	−0.202751	+	0.202751i
$606$	2.12358	−	7.92531i	0.0862645	−	0.321944i
$607$	19.9709	−	11.5302i	0.810594	−	0.467997i	−0.0365681	−	0.999331i	$-0.511643\pi$
$607$	19.9709	−	11.5302i	0.810594	−	0.467997i	0.847162	+	0.531335i	$0.178309\pi$
$608$	1.43990	+	2.49399i	0.0583958	+	0.101145i
$609$	15.0385	+	19.4488i	0.609390	+	0.788106i
$610$		−	2.39719i		−	0.0970594i
$611$	−11.4206	+	0.729638i	−0.462027	+	0.0295180i
$612$	−0.775501	+	0.447736i	−0.0313478	+	0.0180987i
$613$	−7.12247	−	26.5814i	−0.287674	−	1.07361i	−0.946863	−	0.321636i	$-0.895767\pi$
$613$	−7.12247	−	26.5814i	−0.287674	−	1.07361i	0.659190	−	0.751977i	$-0.270899\pi$
$614$		−	6.09042i		−	0.245789i
$615$	0.736286	−	1.27528i	0.0296899	−	0.0514244i
$616$	−11.1048	+	1.50387i	−0.447424	+	0.0605927i
$617$	−3.65190	−	13.6291i	−0.147020	−	0.548687i	−0.999657	−	0.0261829i	$-0.991665\pi$
$617$	−3.65190	−	13.6291i	−0.147020	−	0.548687i	0.852637	−	0.522504i	$-0.175002\pi$
$618$	−3.08600	+	11.5171i	−0.124137	+	0.463286i
$619$	7.54604	+	2.02195i	0.303301	+	0.0812692i	0.407260	−	0.913312i	$-0.366484\pi$
$619$	7.54604	+	2.02195i	0.303301	+	0.0812692i	−0.103959	+	0.994582i	$0.533151\pi$
$620$	4.10489			0.164856
$621$	−1.11283			−0.0446563
$622$	−0.611774	−	0.163924i	−0.0245299	−	0.00657276i
$623$	−4.40600	+	34.4534i	−0.176523	+	1.38034i
$624$	2.38177	−	2.70687i	0.0953471	−	0.108362i
$625$	5.28702	−	9.15739i	0.211481	−	0.366296i
$626$	−6.95219	+	1.86283i	−0.277865	+	0.0744538i
$627$	−6.09875	+	10.5633i	−0.243561	+	0.421859i
$628$	−5.34232	−	9.25317i	−0.213182	−	0.369242i
$629$	6.12284	+	6.12284i	0.244134	+	0.244134i
$630$	2.12713	−	1.64477i	0.0847469	−	0.0655291i
$631$	5.31050	−	1.42295i	0.211408	−	0.0566466i	−0.151561	−	0.988448i	$-0.548430\pi$
$631$	5.31050	−	1.42295i	0.211408	−	0.0566466i	0.362969	+	0.931801i	$0.381763\pi$
$632$	6.07873	−	1.62879i	0.241799	−	0.0647898i
$633$			15.7727i			0.626908i
$634$	7.57586	+	4.37393i	0.300876	+	0.173711i
$635$	6.53291	−	6.53291i	0.259250	−	0.259250i
$636$	3.79508			0.150485
$637$	−22.7000	−	11.0322i	−0.899408	−	0.437110i
$638$	−39.3572			−1.55817
$639$	−0.628236	+	0.628236i	−0.0248526	+	0.0248526i
$640$	0.880134	+	0.508146i	0.0347904	+	0.0200862i
$641$		−	20.1284i		−	0.795026i	−0.917597	−	0.397513i	$-0.869873\pi$
$641$		−	20.1284i		−	0.795026i	0.917597	−	0.397513i	$-0.130127\pi$
$642$	1.17319	−	0.314355i	0.0463021	−	0.0124066i
$643$	−35.9273	+	9.62668i	−1.41683	+	0.379639i	−0.884359	−	0.466807i	$-0.845404\pi$
$643$	−35.9273	+	9.62668i	−1.41683	+	0.379639i	−0.532474	+	0.846446i	$0.678738\pi$
$644$	−2.32918	+	1.80100i	−0.0917827	+	0.0709695i
$645$	−3.84135	−	3.84135i	−0.151253	−	0.151253i
$646$	1.28939	+	2.23330i	0.0507305	+	0.0878679i
$647$	9.32424	−	16.1501i	0.366574	−	0.634924i	−0.622454	−	0.782657i	$-0.713864\pi$
$647$	9.32424	−	16.1501i	0.366574	−	0.634924i	0.989027	+	0.147732i	$0.0471974\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	16.3807	−	28.3722i	0.642999	−	1.11371i
$650$	−12.8182	−	6.34753i	−0.502772	−	0.248971i
$651$	−1.35557	+	10.6001i	−0.0531290	+	0.415451i
$652$	22.6492	+	6.06884i	0.887012	+	0.237674i
$653$	3.85660			0.150920			0.0754602	−	0.997149i	$-0.475957\pi$
$653$	3.85660			0.150920			0.0754602	+	0.997149i	$0.475957\pi$
$654$	−10.8251			−0.423294
$655$	6.18906	+	1.65835i	0.241827	+	0.0647973i
$656$	−0.375020	+	1.39959i	−0.0146421	+	0.0546449i
$657$	0.120528	+	0.449816i	0.00470224	+	0.0175490i
$658$	8.32153	−	1.12695i	0.324407	−	0.0439331i
$659$	13.9329	−	24.1325i	0.542748	−	0.940067i	−0.455997	−	0.889981i	$-0.650717\pi$
$659$	13.9329	−	24.1325i	0.542748	−	0.940067i	0.998745	−	0.0500858i	$-0.0159495\pi$
$660$			4.30453i			0.167553i
$661$	−8.52114	−	31.8013i	−0.331434	−	1.23693i	−0.907684	−	0.419655i	$-0.862151\pi$
$661$	−8.52114	−	31.8013i	−0.331434	−	1.23693i	0.576250	−	0.817274i	$-0.304516\pi$
$662$	−11.0109	+	6.35712i	−0.427949	+	0.247077i
$663$	2.13281	−	2.42393i	0.0828314	−	0.0941376i
$664$			10.6534i			0.413431i
$665$	−4.73662	−	6.12573i	−0.183678	−	0.237546i
$666$	4.83488	+	8.37426i	0.187348	+	0.324496i
$667$	−8.95523	+	5.17031i	−0.346748	+	0.200195i
$668$	4.22772	−	15.7780i	0.163575	−	0.610471i
$669$	19.2565	−	19.2565i	0.744500	−	0.744500i
$670$	4.24714	+	1.13802i	0.164081	+	0.0439655i
$671$	−7.06441	+	7.06441i	−0.272719	+	0.272719i
$672$	−1.60284	+	2.10497i	−0.0618309	+	0.0812011i
$673$	−41.7627	+	24.1117i	−1.60983	+	0.929438i	−0.620427	+	0.784264i	$0.713041\pi$
$673$	−41.7627	+	24.1117i	−1.60983	+	0.929438i	−0.989406	+	0.145174i	$0.953626\pi$
$674$	−13.5729	−	13.5729i	−0.522807	−	0.522807i
$675$	1.98358	+	3.43565i	0.0763479	+	0.132238i
$676$	−5.01446	+	11.9940i	−0.192864	+	0.461306i
$677$	38.4502	+	22.1992i	1.47776	+	0.853185i	0.999684	−	0.0251328i	$-0.00800086\pi$
$677$	38.4502	+	22.1992i	1.47776	+	0.853185i	0.478076	+	0.878318i	$0.341334\pi$
$678$	3.50912	−	13.0962i	0.134767	−	0.502956i
$679$	13.3840	−	17.5769i	0.513630	−	0.674539i
$680$	0.788136	+	0.455030i	0.0302236	+	0.0174496i
$681$	−2.64057	−	9.85473i	−0.101187	−	0.377634i
$682$	−12.0969	−	12.0969i	−0.463216	−	0.463216i
$683$	−9.83294	−	9.83294i	−0.376247	−	0.376247i	0.493499	−	0.869746i	$-0.335718\pi$
$683$	−9.83294	−	9.83294i	−0.376247	−	0.376247i	−0.869746	+	0.493499i	$0.835718\pi$
$684$	0.745350	+	2.78168i	0.0284992	+	0.106360i
$685$	−19.9983	−	11.5460i	−0.764097	−	0.441152i
$686$	17.1882	+	6.89667i	0.656250	+	0.263316i
$687$	−6.86791	+	25.6314i	−0.262027	+	0.977899i
$688$	4.62926	+	2.67270i	0.176489	+	0.101896i
$689$	−12.9644	+	4.37700i	−0.493905	+	0.166751i
$690$	0.565479	+	0.979439i	0.0215274	+	0.0372866i
$691$	−6.38125	−	6.38125i	−0.242754	−	0.242754i	0.575234	−	0.817989i	$-0.304911\pi$
$691$	−6.38125	−	6.38125i	−0.242754	−	0.242754i	−0.817989	+	0.575234i	$0.804911\pi$
$692$	−16.0400	+	9.26068i	−0.609748	+	0.352038i
$693$	−11.1156	−	1.42150i	−0.422247	−	0.0539982i
$694$	−10.9377	+	10.9377i	−0.415191	+	0.415191i
$695$	−15.6380	−	4.19019i	−0.593184	−	0.158943i
$696$	−6.57057	+	6.57057i	−0.249057	+	0.249057i
$697$	−0.335820	+	1.25330i	−0.0127201	+	0.0474720i
$698$	−4.82255	+	2.78430i	−0.182536	+	0.105387i
$699$	13.6710	+	23.6788i	0.517083	+	0.895614i
$700$	9.71195	+	3.98071i	0.367077	+	0.150457i
$701$			41.6879i			1.57453i	0.616615	+	0.787265i	$0.288503\pi$
$701$			41.6879i			1.57453i	−0.616615	+	0.787265i	$0.711497\pi$
$702$	3.00120	−	1.99819i	0.113273	−	0.0754169i
$703$	24.1163	−	13.9235i	0.909563	−	0.525136i
$704$	−1.09623	−	4.09120i	−0.0413159	−	0.154193i
$705$		−	3.22566i		−	0.121486i
$706$	14.4162	−	24.9695i	0.542559	−	0.939740i
$707$	−2.91324	−	21.5117i	−0.109564	−	0.809031i
$708$	−2.00194	−	7.47136i	−0.0752377	−	0.280791i
$709$	0.827388	−	3.08785i	0.0310732	−	0.115967i	−0.948647	−	0.316336i	$-0.897547\pi$
$709$	0.827388	−	3.08785i	0.0310732	−	0.115967i	0.979721	+	0.200369i	$0.0642141\pi$
$710$	0.872168	+	0.233697i	0.0327319	+	0.00877048i
$711$	6.29316			0.236012
$712$	−13.1282			−0.492000
$713$	−4.34166	−	1.16334i	−0.162596	−	0.0435676i
$714$	−1.43530	+	1.88494i	−0.0537147	+	0.0705422i
$715$	−4.96457	−	14.7047i	−0.185664	−	0.549926i
$716$	−11.0604	+	19.1571i	−0.413345	+	0.715935i
$717$	−26.7663	+	7.17200i	−0.999604	+	0.267843i
$718$	1.48106	−	2.56527i	0.0552726	−	0.0957349i
$719$	−2.51955	−	4.36399i	−0.0939634	−	0.162749i	0.815212	−	0.579163i	$-0.196620\pi$
$719$	−2.51955	−	4.36399i	−0.0939634	−	0.162749i	−0.909175	+	0.416413i	$0.863287\pi$
$720$	0.718627	+	0.718627i	0.0267816	+	0.0267816i
$721$	4.23353	+	31.2609i	0.157665	+	1.16422i
$722$	−10.3419	+	2.77110i	−0.384885	+	0.103130i
$723$	−24.2575	+	6.49978i	−0.902146	+	0.241729i
$724$		−	12.9441i		−	0.481063i
$725$	31.9247	+	18.4317i	1.18565	+	0.684538i
$726$	4.90707	−	4.90707i	0.182119	−	0.182119i
$727$	4.03230			0.149550			0.0747748	−	0.997200i	$-0.476176\pi$
$727$	4.03230			0.149550			0.0747748	+	0.997200i	$0.476176\pi$
$728$	3.04773	−	9.03943i	0.112957	−	0.335024i
$729$	−1.00000			−0.0370370
$730$	0.334653	−	0.334653i	0.0123861	−	0.0123861i
$731$	4.14537	+	2.39333i	0.153322	+	0.0885206i
$732$			2.35876i			0.0871824i
$733$	−18.7546	+	5.02527i	−0.692716	+	0.185613i	−0.587966	−	0.808886i	$-0.700071\pi$
$733$	−18.7546	+	5.02527i	−0.692716	+	0.185613i	−0.104750	+	0.994499i	$0.533404\pi$
$734$	12.3125	−	3.29912i	0.454462	−	0.121773i
$735$	3.51124	−	6.18714i	0.129514	−	0.228216i
$736$	−0.786889	−	0.786889i	−0.0290051	−	0.0290051i
$737$	−9.16245	−	15.8698i	−0.337503	−	0.584573i
$738$	−0.724483	+	1.25484i	−0.0266686	+	0.0461913i
$739$	−22.5465	+	6.04132i	−0.829387	+	0.222234i	−0.648446	−	0.761260i	$-0.724581\pi$
$739$	−22.5465	+	6.04132i	−0.829387	+	0.222234i	−0.180941	+	0.983494i	$0.557914\pi$
$740$	4.91365	−	8.51069i	0.180629	−	0.312859i
$741$	−5.75441	−	8.64290i	−0.211394	−	0.317505i
$742$	9.26222	−	3.87683i	0.340027	−	0.142323i
$743$	33.0260	+	8.84929i	1.21161	+	0.324649i	0.807392	−	0.590016i	$-0.200878\pi$
$743$	33.0260	+	8.84929i	1.21161	+	0.324649i	0.404214	+	0.914664i	$0.367545\pi$
$744$	−4.03909			−0.148080
$745$	3.61860			0.132575
$746$	14.7552	+	3.95363i	0.540225	+	0.144753i
$747$	−2.75730	+	10.2904i	−0.100884	+	0.376505i
$748$	−0.981647	−	3.66356i	−0.0358926	−	0.133953i
$749$	2.54214	−	1.96567i	0.0928879	−	0.0718241i
$750$	4.55662	−	7.89230i	0.166384	−	0.288186i
$751$		−	37.0359i		−	1.35146i	−0.737149	−	0.675730i	$-0.763829\pi$
$751$		−	37.0359i		−	1.35146i	0.737149	−	0.675730i	$-0.236171\pi$
$752$	0.821480	+	3.06581i	0.0299563	+	0.111798i
$753$	−12.5297	+	7.23404i	−0.456609	+	0.263623i
$754$	14.8677	−	30.0239i	0.541450	−	1.09340i
$755$		−	5.00838i		−	0.182273i
$756$	−2.09303	+	1.61840i	−0.0761228	+	0.0588607i
$757$	−21.9087	−	37.9470i	−0.796286	−	1.37921i	−0.922019	−	0.387144i	$-0.873461\pi$
$757$	−21.9087	−	37.9470i	−0.796286	−	1.37921i	0.125733	−	0.992064i	$-0.459872\pi$
$758$	13.1746	−	7.60636i	0.478523	−	0.276275i
$759$	1.21992	−	4.55281i	0.0442803	−	0.165256i
$760$	2.06951	−	2.06951i	0.0750689	−	0.0750689i
$761$	22.5899	+	6.05293i	0.818882	+	0.219419i	0.643857	−	0.765145i	$-0.277333\pi$
$761$	22.5899	+	6.05293i	0.818882	+	0.219419i	0.175024	+	0.984564i	$0.444000\pi$
$762$	−6.42818	+	6.42818i	−0.232868	+	0.232868i
$763$	−26.4195	+	11.0582i	−0.956451	+	0.400335i
$764$	−6.32412	+	3.65123i	−0.228799	+	0.132097i
$765$	0.643510	+	0.643510i	0.0232662	+	0.0232662i
$766$	7.15218	+	12.3879i	0.258419	+	0.447595i
$767$	15.4558	+	23.2141i	0.558078	+	0.838211i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	11.6639	−	43.5304i	0.420613	−	1.56975i	−0.352709	−	0.935733i	$-0.614739\pi$
$769$	11.6639	−	43.5304i	0.420613	−	1.56975i	0.773321	−	0.634014i	$-0.218594\pi$
$770$	4.39724	+	10.5056i	0.158466	+	0.378594i
$771$	−11.1273	−	6.42437i	−0.400741	−	0.231368i
$772$	−5.34146	−	19.9346i	−0.192243	−	0.717462i
$773$	−33.0192	−	33.0192i	−1.18762	−	1.18762i	−0.977724	−	0.209894i	$-0.932688\pi$
$773$	−33.0192	−	33.0192i	−1.18762	−	1.18762i	−0.209894	−	0.977724i	$-0.567312\pi$
$774$	3.77977	+	3.77977i	0.135861	+	0.135861i
$775$	4.14723	+	15.4777i	0.148973	+	0.555975i
$776$	7.23146	+	4.17509i	0.259594	+	0.149877i
$777$	20.3546	+	15.4991i	0.730217	+	0.556026i
$778$	2.09172	−	7.80639i	0.0749917	−	0.279873i
$779$	3.61370	+	2.08637i	0.129474	+	0.0747520i
$780$	−3.28373	−	1.62609i	−0.117576	−	0.0582234i
$781$	−1.88155	−	3.25893i	−0.0673270	−	0.116614i
$782$	−0.704637	−	0.704637i	−0.0251978	−	0.0251978i
$783$	−8.04727	+	4.64609i	−0.287586	+	0.166038i
$784$	−1.76155	+	6.77473i	−0.0629126	+	0.241955i
$785$	−7.67827	+	7.67827i	−0.274049	+	0.274049i
$786$	−6.08985	−	1.63177i	−0.217218	−	0.0582033i
$787$	15.8824	−	15.8824i	0.566145	−	0.566145i	−0.364901	−	0.931046i	$-0.618897\pi$
$787$	15.8824	−	15.8824i	0.566145	−	0.566145i	0.931046	+	0.364901i	$0.118897\pi$
$788$	4.34702	−	16.2233i	0.154856	−	0.577931i
$789$	−9.23151	+	5.32982i	−0.328651	+	0.189747i
$790$	−3.19784	−	5.53883i	−0.113774	−	0.197063i
$791$	−4.81399	−	35.5471i	−0.171166	−	1.26391i
$792$		−	4.23552i		−	0.150503i
$793$	−2.72045	−	8.05779i	−0.0966059	−	0.286141i
$794$	−25.8620	+	14.9314i	−0.917809	+	0.529897i
$795$	−0.998241	−	3.72549i	−0.0354040	−	0.132129i
$796$		−	4.26267i		−	0.151086i
$797$	−1.10641	+	1.91635i	−0.0391909	+	0.0678807i	−0.884956	−	0.465676i	$-0.845811\pi$
$797$	−1.10641	+	1.91635i	−0.0391909	+	0.0678807i	0.845765	+	0.533556i	$0.179145\pi$
$798$	4.66069	+	6.02753i	0.164987	+	0.213372i
$799$	0.735612	+	2.74534i	0.0260241	+	0.0971233i
$800$	−1.02677	+	3.83197i	−0.0363020	+	0.135481i
$801$	−12.6809	−	3.39783i	−0.448056	−	0.120056i
$802$	−7.90409			−0.279103
$803$	−1.97241			−0.0696050
$804$	−4.17906	−	1.11978i	−0.147384	−	0.0394914i
$805$	2.38064	+	1.81274i	0.0839064	+	0.0638909i
$806$	13.7980	−	4.65843i	0.486013	−	0.164086i
$807$	4.80203	−	8.31736i	0.169040	−	0.292785i
$808$	7.92531	−	2.12358i	0.278811	−	0.0747073i
$809$	−21.6687	+	37.5313i	−0.761831	+	1.31953i	0.180075	+	0.983653i	$0.442366\pi$
$809$	−21.6687	+	37.5313i	−0.761831	+	1.31953i	−0.941906	+	0.335876i	$0.890968\pi$
$810$	0.508146	+	0.880134i	0.0178544	+	0.0309248i
$811$	−6.31443	−	6.31443i	−0.221729	−	0.221729i	0.587497	−	0.809226i	$-0.300113\pi$
$811$	−6.31443	−	6.31443i	−0.221729	−	0.221729i	−0.809226	+	0.587497i	$0.800113\pi$
$812$	−9.32393	+	22.7481i	−0.327206	+	0.798302i
$813$	−12.7066	+	3.40472i	−0.445639	+	0.119409i
$814$	−39.5609	+	10.6003i	−1.38661	+	0.371541i
$815$		−	23.8302i		−	0.834736i
$816$	−0.775501	−	0.447736i	−0.0271480	−	0.0156739i
$817$	10.8850	−	10.8850i	0.380819	−	0.380819i
$818$	−6.85536			−0.239692
$819$	5.28346	−	7.94261i	0.184619	−	0.277537i
$820$	1.47257			0.0514244
$821$	−19.7288	+	19.7288i	−0.688541	+	0.688541i	−0.961909	−	0.273369i	$-0.911862\pi$
$821$	−19.7288	+	19.7288i	−0.688541	+	0.688541i	0.273369	+	0.961909i	$0.411862\pi$
$822$	19.6778	+	11.3610i	0.686341	+	0.396259i
$823$			3.02417i			0.105416i	0.998610	+	0.0527080i	$0.0167853\pi$
$823$			3.02417i			0.105416i	−0.998610	+	0.0527080i	$0.983215\pi$
$824$	−11.5171	+	3.08600i	−0.401217	+	0.107506i
$825$	−16.2304	+	4.34893i	−0.565070	+	0.151410i
$826$	−12.5182	−	16.1894i	−0.435564	−	0.563302i
$827$	17.9726	+	17.9726i	0.624969	+	0.624969i	0.946798	−	0.321829i	$-0.104297\pi$
$827$	17.9726	+	17.9726i	0.624969	+	0.624969i	−0.321829	+	0.946798i	$0.604297\pi$
$828$	−0.556414	−	0.963738i	−0.0193367	−	0.0334922i
$829$	7.65009	−	13.2503i	0.265699	−	0.460204i	−0.702048	−	0.712130i	$-0.747731\pi$
$829$	7.65009	−	13.2503i	0.265699	−	0.460204i	0.967746	+	0.251926i	$0.0810640\pi$
$830$	10.4580	−	2.80222i	0.363003	−	0.0972665i
$831$	9.85432	−	17.0682i	0.341843	−	0.592089i
$832$	3.53511	+	0.709237i	0.122558	+	0.0245884i
$833$	−1.57742	+	6.06658i	−0.0546544	+	0.210194i
$834$	15.3873	+	4.12302i	0.532820	+	0.142769i
$835$	−16.6008			−0.574493
$836$	−12.1975			−0.421859
$837$	−3.90146	−	1.04539i	−0.134854	−	0.0361341i
$838$	−7.37900	+	27.5388i	−0.254903	+	0.951312i
$839$	−11.4181	−	42.6129i	−0.394196	−	1.47116i	−0.823145	−	0.567831i	$-0.807783\pi$
$839$	−11.4181	−	42.6129i	−0.394196	−	1.47116i	0.428949	−	0.903329i	$-0.358884\pi$
$840$	2.48798	+	1.01976i	0.0858433	+	0.0351852i
$841$	−28.6723	+	49.6619i	−0.988701	+	1.71248i
$842$		−	37.8883i		−	1.30572i
$843$	4.69852	+	17.5351i	0.161826	+	0.603941i
$844$	−13.6595	+	7.88634i	−0.470181	+	0.271459i
$845$	13.0930	+	1.76766i	0.450413	+	0.0608094i
$846$			3.17396i			0.109123i
$847$	6.96336	−	16.9889i	0.239264	−	0.583745i
$848$	1.89754	+	3.28664i	0.0651618	+	0.112864i
$849$	16.7558	−	9.67398i	0.575058	−	0.332010i
$850$	−0.919448	+	3.43143i	−0.0315368	+	0.117697i
$851$	−7.60903	+	7.60903i	−0.260834	+	0.260834i
$852$	−0.858187	−	0.229950i	−0.0294010	−	0.00787797i
$853$	−22.1233	+	22.1233i	−0.757488	+	0.757488i	−0.975865	−	0.218376i	$-0.929924\pi$
$853$	−22.1233	+	22.1233i	−0.757488	+	0.757488i	0.218376	+	0.975865i	$0.429924\pi$
$854$	2.40957	+	5.75676i	0.0824538	+	0.196992i
$855$	2.53462	−	1.46336i	0.0866822	−	0.0500460i
$856$	0.858835	+	0.858835i	0.0293544	+	0.0293544i
$857$	−2.72862	−	4.72611i	−0.0932078	−	0.161441i	0.815651	−	0.578544i	$-0.196379\pi$
$857$	−2.72862	−	4.72611i	−0.0932078	−	0.161441i	−0.908859	+	0.417103i	$0.863045\pi$
$858$	4.88498	+	14.4690i	0.166771	+	0.493964i
$859$	1.26573	+	0.730767i	0.0431860	+	0.0249335i	0.521438	−	0.853289i	$-0.325396\pi$
$859$	1.26573	+	0.730767i	0.0431860	+	0.0249335i	−0.478252	+	0.878223i	$0.658729\pi$
$860$	1.40603	−	5.24739i	0.0479453	−	0.178934i
$861$	−0.486292	+	3.80263i	−0.0165728	+	0.129593i
$862$	7.11662	+	4.10878i	0.242393	+	0.139946i
$863$	6.50952	+	24.2938i	0.221587	+	0.826972i	0.983743	+	0.179580i	$0.0574738\pi$
$863$	6.50952	+	24.2938i	0.221587	+	0.826972i	−0.762157	+	0.647392i	$0.775860\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	13.3100	+	13.3100i	0.452552	+	0.452552i
$866$	4.28303	+	15.9845i	0.145543	+	0.543175i
$867$	14.0280	+	8.09906i	0.476416	+	0.275059i
$868$	−9.85774	+	4.12609i	−0.334593	+	0.140049i
$869$	−6.89878	+	25.7466i	−0.234025	+	0.873393i
$870$	8.17837	+	4.72178i	0.277273	+	0.160083i
$871$	15.5676	−	0.994584i	0.527488	−	0.0337002i
$872$	−5.41254	−	9.37479i	−0.183292	−	0.317471i
$873$	5.90446	+	5.90446i	0.199836	+	0.199836i
$874$	−2.77538	+	1.60237i	−0.0938787	+	0.0542009i
$875$	3.05853	−	23.9166i	0.103397	−	0.808529i
$876$	−0.329288	+	0.329288i	−0.0111256	+	0.0111256i
$877$	−7.18916	−	1.92633i	−0.242761	−	0.0650476i	0.135387	−	0.990793i	$-0.456772\pi$
$877$	−7.18916	−	1.92633i	−0.242761	−	0.0650476i	−0.378148	+	0.925745i	$0.623439\pi$
$878$	25.5556	−	25.5556i	0.862460	−	0.862460i
$879$	−2.77511	+	10.3569i	−0.0936022	+	0.349328i
$880$	−3.72783	+	2.15226i	−0.125665	+	0.0725528i
$881$	10.8357	+	18.7680i	0.365064	+	0.632309i	0.988786	−	0.149337i	$-0.0477139\pi$
$881$	10.8357	+	18.7680i	0.365064	+	0.632309i	−0.623723	+	0.781646i	$0.714381\pi$
$882$	−3.45496	+	6.08796i	−0.116334	+	0.204992i
$883$		−	18.1254i		−	0.609968i	−0.952357	−	0.304984i	$-0.901349\pi$
$883$		−	18.1254i		−	0.609968i	0.952357	−	0.304984i	$-0.0986512\pi$
$884$	3.16559	+	0.635102i	0.106470	+	0.0213608i
$885$	−6.80777	+	3.93047i	−0.228841	+	0.132121i
$886$	4.68232	+	17.4747i	0.157306	+	0.587073i
$887$		−	41.2369i		−	1.38460i	−0.721610	−	0.692300i	$-0.756597\pi$
$887$		−	41.2369i		−	1.38460i	0.721610	−	0.692300i	$-0.243403\pi$
$888$	−4.83488	+	8.37426i	−0.162248	+	0.281022i
$889$	−9.12188	+	22.2552i	−0.305938	+	0.746414i
$890$	3.45318	+	12.8875i	0.115751	+	0.431989i
$891$	1.09623	−	4.09120i	0.0367252	−	0.137060i
$892$	26.3049	+	7.04837i	0.880753	+	0.235997i
$893$	9.14039			0.305871
$894$	−3.56060			−0.119084
$895$	21.7151	+	5.81854i	0.725855	+	0.194492i
$896$	−2.62438	−	0.335613i	−0.0876743	−	0.0112121i
$897$	3.01229	+	2.65050i	0.100577	+	0.0884977i
$898$	6.00746	−	10.4052i	0.200472	−	0.347227i
$899$	−36.2531	+	9.71398i	−1.20911	+	0.323979i
$900$	−1.98358	+	3.43565i	−0.0661192	+	0.114522i
$901$	1.69919	+	2.94309i	0.0566084	+	0.0980486i
$902$	−4.33960	−	4.33960i	−0.144493	−	0.144493i
$903$	13.0860	+	5.36367i	0.435476	+	0.178492i
$904$	13.0962	−	3.50912i	0.435573	−	0.116711i
$905$	−12.7067	+	3.40476i	−0.422386	+	0.113178i
$906$			4.92809i			0.163725i
$907$	−38.1113	−	22.0036i	−1.26547	−	0.730617i	−0.291339	−	0.956620i	$-0.594101\pi$
$907$	−38.1113	−	22.0036i	−1.26547	−	0.730617i	−0.974127	+	0.226003i	$0.927434\pi$
$908$	7.21417	−	7.21417i	0.239411	−	0.239411i
$909$	8.20488			0.272139
$910$	−9.67533	−	0.614154i	−0.320734	−	0.0203590i
$911$	27.0222			0.895287			0.447643	−	0.894212i	$-0.352263\pi$
$911$	27.0222			0.895287			0.447643	+	0.894212i	$0.352263\pi$
$912$	−2.03633	+	2.03633i	−0.0674297	+	0.0674297i
$913$	−39.0773	−	22.5613i	−1.29327	−	0.746671i
$914$		−	14.9025i		−	0.492930i
$915$	2.31551	−	0.620438i	0.0765483	−	0.0205111i
$916$	−25.6314	+	6.86791i	−0.846885	+	0.226922i
$917$	−16.5297	+	2.23855i	−0.545859	+	0.0739234i
$918$	−0.633194	−	0.633194i	−0.0208985	−	0.0208985i
$919$	−15.9973	−	27.7081i	−0.527701	−	0.914005i	−0.999479	−	0.0322873i	$-0.989721\pi$
$919$	−15.9973	−	27.7081i	−0.527701	−	0.914005i	0.471778	−	0.881718i	$-0.343612\pi$
$920$	−0.565479	+	0.979439i	−0.0186433	+	0.0322912i
$921$	5.88289	−	1.57632i	0.193848	−	0.0519414i
$922$	16.9156	−	29.2986i	0.557084	−	0.964898i
$923$	3.19687	−	0.204242i	0.105226	−	0.00672270i
$924$	−4.32675	−	10.3372i	−0.142340	−	0.340067i
$925$	37.0543	+	9.92867i	1.21834	+	0.326453i
$926$	−29.4713			−0.968486
$927$	−11.9234			−0.391615
$928$	−8.97556	−	2.40499i	−0.294637	−	0.0789478i
$929$	11.2325	−	41.9204i	0.368527	−	1.37536i	−0.494048	−	0.869435i	$-0.664483\pi$
$929$	11.2325	−	41.9204i	0.368527	−	1.37536i	0.862575	−	0.505929i	$-0.168850\pi$
$930$	1.06242	+	3.96502i	0.0348383	+	0.130018i
$931$	17.5322	+	9.94962i	0.574594	+	0.326086i
$932$	−13.6710	+	23.6788i	−0.447807	+	0.775624i
$933$		−	0.633355i		−	0.0207351i
$934$	−10.2421	−	38.2240i	−0.335132	−	1.25073i
$935$	−3.33817	+	1.92729i	−0.109170	+	0.0630292i
$936$	3.23109	+	1.60002i	0.105611	+	0.0522984i
$937$			14.3005i			0.467178i	0.972335	+	0.233589i	$0.0750471\pi$
$937$			14.3005i			0.467178i	−0.972335	+	0.233589i	$0.924953\pi$
$938$	−11.3432	+	1.53617i	−0.370370	+	0.0501576i
$939$	−3.59872	−	6.23316i	−0.117440	−	0.203411i
$940$	2.79351	−	1.61283i	0.0911142	−	0.0526048i
$941$	−1.29859	+	4.84640i	−0.0423328	+	0.157988i	−0.983857	−	0.178958i	$-0.942727\pi$
$941$	−1.29859	+	4.84640i	−0.0423328	+	0.157988i	0.941524	+	0.336946i	$0.109394\pi$
$942$	7.55518	−	7.55518i	0.246161	−	0.246161i
$943$	−1.55751	−	0.417333i	−0.0507194	−	0.0135902i
$944$	5.46941	−	5.46941i	0.178014	−	0.178014i
$945$	2.13927	+	1.62895i	0.0695903	+	0.0529898i
$946$	−19.6073	+	11.3203i	−0.637489	+	0.368055i
$947$	32.1004	+	32.1004i	1.04312	+	1.04312i	0.999027	+	0.0440947i	$0.0140403\pi$
$947$	32.1004	+	32.1004i	1.04312	+	1.04312i	0.0440947	+	0.999027i	$0.485960\pi$
$948$	3.14658	+	5.45004i	0.102196	+	0.177009i
$949$	0.745105	−	1.50467i	0.0241871	−	0.0488435i
$950$	9.89403	+	5.71232i	0.321005	+	0.185332i
$951$	−2.26411	+	8.44978i	−0.0734188	+	0.274003i
$952$	−2.35006	−	0.300532i	−0.0761658	−	0.00974031i
$953$	40.9867	+	23.6637i	1.32769	+	0.766542i	0.984942	−	0.172885i	$-0.0553091\pi$
$953$	40.9867	+	23.6637i	1.32769	+	0.766542i	0.342748	+	0.939427i	$0.388642\pi$
$954$	0.982239	+	3.66577i	0.0318012	+	0.118684i
$955$	5.24775	+	5.24775i	0.169813	+	0.169813i
$956$	−19.5943	−	19.5943i	−0.633724	−	0.633724i
$957$	−10.1864	−	38.0162i	−0.329280	−	1.22889i
$958$	−16.6058	−	9.58736i	−0.536509	−	0.309753i
$959$	59.6309	+	7.62578i	1.92558	+	0.246249i
$960$	−0.263036	+	0.981662i	−0.00848944	+	0.0316830i
$961$	12.7182	+	7.34288i	0.410266	+	0.236867i
$962$	6.85815	−	34.1837i	0.221116	−	1.10213i
$963$	0.607288	+	1.05185i	0.0195696	+	0.0338955i
$964$	−17.7577	−	17.7577i	−0.571938	−	0.571938i
$965$	−18.1641	+	10.4870i	−0.584722	+	0.337589i
$966$	−2.34247	−	1.78369i	−0.0753679	−	0.0573891i
$967$	5.00087	−	5.00087i	0.160817	−	0.160817i	−0.622111	−	0.782929i	$-0.713725\pi$
$967$	5.00087	−	5.00087i	0.160817	−	0.160817i	0.782929	+	0.622111i	$0.213725\pi$
$968$	6.70318	+	1.79611i	0.215449	+	0.0577293i
$969$	−1.82348	+	1.82348i	−0.0585786	+	0.0585786i
$970$	2.19639	−	8.19705i	0.0705219	−	0.263191i
$971$	−9.65115	+	5.57209i	−0.309720	+	0.178817i	−0.646801	−	0.762659i	$-0.723894\pi$
$971$	−9.65115	+	5.57209i	−0.309720	+	0.178817i	0.337081	+	0.941476i	$0.390560\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	41.7659	−	5.65618i	1.33895	−	0.181329i
$974$		−	3.72408i		−	0.119327i
$975$	2.81365	−	14.0243i	0.0901089	−	0.449137i
$976$	−2.04275	+	1.17938i	−0.0653868	+	0.0377511i
$977$	−1.67668	−	6.25745i	−0.0536417	−	0.200194i	0.933905	−	0.357522i	$-0.116378\pi$
$977$	−1.67668	−	6.25745i	−0.0536417	−	0.200194i	−0.987546	+	0.157329i	$0.949712\pi$
$978$			23.4482i			0.749791i
$979$	27.8024	−	48.1551i	0.888568	−	1.53905i
$980$	7.11385	−	0.0527446i	0.227243	−	0.00168487i
$981$	−2.80174	−	10.4562i	−0.0894526	−	0.333841i
$982$	0.954772	−	3.56326i	0.0304680	−	0.113708i
$983$	9.28727	+	2.48852i	0.296218	+	0.0793713i	0.403867	−	0.914818i	$-0.367666\pi$
$983$	9.28727	+	2.48852i	0.296218	+	0.0793713i	−0.107649	+	0.994189i	$0.534332\pi$
$984$	−1.44897			−0.0461913
$985$	−17.0692			−0.543871
$986$	−8.03736	−	2.15360i	−0.255962	−	0.0685847i
$987$	3.24232	+	7.74631i	0.103204	+	0.246568i
$988$	4.60776	−	9.30492i	0.146592	−	0.296029i
$989$	−2.97426	+	5.15157i	−0.0945760	+	0.163810i
$990$	−4.15785	+	1.11409i	−0.132145	+	0.0354082i
$991$	−7.96164	+	13.7900i	−0.252910	+	0.438053i	−0.964326	−	0.264718i	$-0.914721\pi$
$991$	−7.96164	+	13.7900i	−0.252910	+	0.438053i	0.711416	+	0.702771i	$0.248054\pi$
$992$	−2.01954	−	3.49795i	−0.0641206	−	0.111060i
$993$	−8.99033	−	8.99033i	−0.285299	−	0.285299i
$994$	−2.32938	+	0.315458i	−0.0738835	+	0.0100057i
$995$	−4.18450	+	1.12123i	−0.132658	+	0.0355455i
$996$	−10.2904	+	2.75730i	−0.326063	+	0.0873683i
$997$			28.7699i			0.911151i	0.890197	+	0.455576i	$0.150567\pi$
$997$			28.7699i			0.911151i	−0.890197	+	0.455576i	$0.849433\pi$
$998$	−24.1602	−	13.9489i	−0.764777	−	0.441544i
$999$	−6.83756	+	6.83756i	−0.216331	+	0.216331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.cg.b.145.3	yes	40
7.3	odd	6		546.2.by.b.535.3	yes	40
13.7	odd	12		546.2.by.b.397.3	✓	40
91.59	even	12	inner	546.2.cg.b.241.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.3	✓	40	13.7	odd	12
546.2.by.b.535.3	yes	40	7.3	odd	6
546.2.cg.b.145.3	yes	40	1.1	even	1	trivial
546.2.cg.b.241.3	yes	40	91.59	even	12	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(-0.981662 + 0.263036i) q^{5} +(0.965926 - 0.258819i) q^{6} +(2.09303 - 1.61840i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(-0.981662 + 0.263036i) q^{5} +(0.965926 - 0.258819i) q^{6} +(2.09303 - 1.61840i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.508146 - 0.880134i) q^{10} +(-4.09120 + 1.09623i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.709237 - 3.53511i) q^{13} +(-0.335613 + 2.62438i) q^{14} +(0.981662 + 0.263036i) q^{15} -1.00000 q^{16} -0.895472 q^{17} +(-0.965926 - 0.258819i) q^{18} +(-0.745350 + 2.78168i) q^{19} +(0.263036 + 0.981662i) q^{20} +(-2.62182 + 0.355062i) q^{21} +(2.11776 - 3.66807i) q^{22} -1.11283i q^{23} +(-0.258819 - 0.965926i) q^{24} +(-3.43565 + 1.98358i) q^{25} +(1.99819 + 3.00120i) q^{26} -1.00000i q^{27} +(-1.61840 - 2.09303i) q^{28} +(-4.64609 - 8.04727i) q^{29} +(-0.880134 + 0.508146i) q^{30} +(1.04539 - 3.90146i) q^{31} +(0.707107 - 0.707107i) q^{32} +(4.09120 + 1.09623i) q^{33} +(0.633194 - 0.633194i) q^{34} +(-1.62895 + 2.13927i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-6.83756 - 6.83756i) q^{37} +(-1.43990 - 2.49399i) q^{38} +(-2.38177 + 2.70687i) q^{39} +(-0.880134 - 0.508146i) q^{40} +(0.375020 - 1.39959i) q^{41} +(1.60284 - 2.10497i) q^{42} +(-4.62926 - 2.67270i) q^{43} +(1.09623 + 4.09120i) q^{44} +(-0.718627 - 0.718627i) q^{45} +(0.786889 + 0.786889i) q^{46} +(-0.821480 - 3.06581i) q^{47} +(0.866025 + 0.500000i) q^{48} +(1.76155 - 6.77473i) q^{49} +(1.02677 - 3.83197i) q^{50} +(0.775501 + 0.447736i) q^{51} +(-3.53511 - 0.709237i) q^{52} +(-1.89754 - 3.28664i) q^{53} +(0.707107 + 0.707107i) q^{54} +(3.72783 - 2.15226i) q^{55} +(2.62438 + 0.335613i) q^{56} +(2.03633 - 2.03633i) q^{57} +(8.97556 + 2.40499i) q^{58} +(-5.46941 + 5.46941i) q^{59} +(0.263036 - 0.981662i) q^{60} +(2.04275 - 1.17938i) q^{61} +(2.01954 + 3.49795i) q^{62} +(2.44809 + 1.00342i) q^{63} +1.00000i q^{64} +(0.233628 + 3.65684i) q^{65} +(-3.66807 + 2.11776i) q^{66} +(1.11978 + 4.17906i) q^{67} +0.895472i q^{68} +(-0.556414 + 0.963738i) q^{69} +(-0.360846 - 2.66453i) q^{70} +(0.229950 + 0.858187i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(0.449816 + 0.120528i) q^{73} +9.66976 q^{74} +3.96715 q^{75} +(2.78168 + 0.745350i) q^{76} +(-6.78886 + 8.91566i) q^{77} +(-0.229883 - 3.59822i) q^{78} +(3.14658 - 5.45004i) q^{79} +(0.981662 - 0.263036i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.724483 + 1.25484i) q^{82} +(7.53308 + 7.53308i) q^{83} +(0.355062 + 2.62182i) q^{84} +(0.879051 - 0.235541i) q^{85} +(5.16327 - 1.38349i) q^{86} +9.29218i q^{87} +(-3.66807 - 2.11776i) q^{88} +(-9.28304 + 9.28304i) q^{89} +1.01629 q^{90} +(-4.23677 - 8.54692i) q^{91} -1.11283 q^{92} +(-2.85607 + 2.85607i) q^{93} +(2.74873 + 1.58698i) q^{94} -2.92673i q^{95} +(-0.965926 + 0.258819i) q^{96} +(8.06565 - 2.16118i) q^{97} +(3.54485 + 6.03606i) q^{98} +(-2.99497 - 2.99497i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

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