LMFDB - Embedded newform 336.2.bq.a.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(37,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))

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

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

chi := DirichletCharacter("336.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bq (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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			109.1
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	336.109
Dual form			336.2.bq.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.00000 - 1.73205i) q^{4} +(3.69798 + 0.990870i) q^{5} +(1.00000 - 1.00000i) q^{6} +(0.358719 - 2.62132i) q^{7} +2.82843i q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.00000 - 1.73205i) q^{4} +(3.69798 + 0.990870i) q^{5} +(1.00000 - 1.00000i) q^{6} +(0.358719 - 2.62132i) q^{7} +2.82843i q^{8} +(0.866025 - 0.500000i) q^{9} +(-5.22973 + 1.40130i) q^{10} +(-0.624844 - 2.33195i) q^{11} +(-0.517638 + 1.93185i) q^{12} +(-2.41421 - 2.41421i) q^{13} +(1.41421 + 3.46410i) q^{14} -3.82843 q^{15} +(-2.00000 - 3.46410i) q^{16} +(3.41421 - 5.91359i) q^{17} +(-0.707107 + 1.22474i) q^{18} +(-0.732051 + 2.73205i) q^{19} +(5.41421 - 5.41421i) q^{20} +(0.331951 + 2.62484i) q^{21} +(2.41421 + 2.41421i) q^{22} +(0.210133 - 0.121320i) q^{23} +(-0.732051 - 2.73205i) q^{24} +(8.36308 + 4.82843i) q^{25} +(4.66390 + 1.24969i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-4.18154 - 3.24264i) q^{28} +(6.12132 + 6.12132i) q^{29} +(4.68885 - 2.70711i) q^{30} +(-0.207107 + 0.358719i) q^{31} +(4.89898 + 2.82843i) q^{32} +(1.20711 + 2.09077i) q^{33} +9.65685i q^{34} +(3.92392 - 9.33814i) q^{35} -2.00000i q^{36} +(-2.73205 - 0.732051i) q^{37} +(-1.03528 - 3.86370i) q^{38} +(2.95680 + 1.70711i) q^{39} +(-2.80260 + 10.4595i) q^{40} +3.41421i q^{41} +(-2.26260 - 2.98004i) q^{42} +(7.41421 - 7.41421i) q^{43} +(-4.66390 - 1.24969i) q^{44} +(3.69798 - 0.990870i) q^{45} +(-0.171573 + 0.297173i) q^{46} +(-1.12132 - 1.94218i) q^{47} +(2.82843 + 2.82843i) q^{48} +(-6.74264 - 1.88064i) q^{49} -13.6569 q^{50} +(-1.76733 + 6.59575i) q^{51} +(-6.59575 + 1.76733i) q^{52} +(0.687644 + 2.56632i) q^{53} +(0.366025 - 1.36603i) q^{54} -9.24264i q^{55} +(7.41421 + 1.01461i) q^{56} -2.82843i q^{57} +(-11.8255 - 3.16863i) q^{58} +(3.12422 + 11.6598i) q^{59} +(-3.82843 + 6.63103i) q^{60} +(-0.669251 + 2.49768i) q^{61} -0.585786i q^{62} +(-1.00000 - 2.44949i) q^{63} -8.00000 q^{64} +(-6.53553 - 11.3199i) q^{65} +(-2.95680 - 1.70711i) q^{66} +(-8.99635 + 2.41057i) q^{67} +(-6.82843 - 11.8272i) q^{68} +(-0.171573 + 0.171573i) q^{69} +(1.79725 + 14.2115i) q^{70} -3.89949i q^{71} +(1.41421 + 2.44949i) q^{72} +(3.46410 + 2.00000i) q^{73} +(3.86370 - 1.03528i) q^{74} +(-9.32780 - 2.49938i) q^{75} +(4.00000 + 4.00000i) q^{76} +(-6.33694 + 0.801401i) q^{77} -4.82843 q^{78} +(-1.37868 - 2.38794i) q^{79} +(-3.96348 - 14.7919i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-2.41421 - 4.18154i) q^{82} +(6.77817 + 6.77817i) q^{83} +(4.87832 + 2.04989i) q^{84} +(18.4853 - 18.4853i) q^{85} +(-3.83788 + 14.3232i) q^{86} +(-7.49706 - 4.32843i) q^{87} +(6.59575 - 1.76733i) q^{88} +(-13.4722 + 7.77817i) q^{89} +(-3.82843 + 3.82843i) q^{90} +(-7.19445 + 5.46240i) q^{91} -0.485281i q^{92} +(0.107206 - 0.400100i) q^{93} +(2.74666 + 1.58579i) q^{94} +(-5.41421 + 9.37769i) q^{95} +(-5.46410 - 1.46410i) q^{96} -14.3137 q^{97} +(9.58783 - 2.46447i) q^{98} +(-1.70711 - 1.70711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} + 8 q^{5} + 8 q^{6}+O(q^{10}) $ 8 * q + 8 * q^4 + 8 * q^5 + 8 * q^6	$ 8 q + 8 q^{4} + 8 q^{5} + 8 q^{6} - 4 q^{10} + 4 q^{11} - 8 q^{13} - 8 q^{15} - 16 q^{16} + 16 q^{17} + 8 q^{19} + 32 q^{20} - 12 q^{21} + 8 q^{22} + 8 q^{24} + 8 q^{26} + 32 q^{29} + 4 q^{31} + 4 q^{33} - 16 q^{35} - 8 q^{37} + 8 q^{40} - 4 q^{42} + 48 q^{43} - 8 q^{44} + 8 q^{45} - 24 q^{46} + 8 q^{47} - 20 q^{49} - 64 q^{50} + 8 q^{51} - 8 q^{52} - 16 q^{53} - 4 q^{54} + 48 q^{56} - 12 q^{58} - 20 q^{59} - 8 q^{60} - 4 q^{61} - 8 q^{63} - 64 q^{64} - 24 q^{65} - 32 q^{67} - 32 q^{68} - 24 q^{69} - 44 q^{70} - 16 q^{75} + 32 q^{76} - 8 q^{77} - 16 q^{78} - 28 q^{79} + 32 q^{80} + 4 q^{81} - 8 q^{82} - 8 q^{83} + 80 q^{85} + 8 q^{86} + 8 q^{88} - 8 q^{90} - 28 q^{91} - 4 q^{93} - 32 q^{95} - 16 q^{96} - 24 q^{97} - 8 q^{99}+O(q^{100}) $ 8 * q + 8 * q^4 + 8 * q^5 + 8 * q^6 - 4 * q^10 + 4 * q^11 - 8 * q^13 - 8 * q^15 - 16 * q^16 + 16 * q^17 + 8 * q^19 + 32 * q^20 - 12 * q^21 + 8 * q^22 + 8 * q^24 + 8 * q^26 + 32 * q^29 + 4 * q^31 + 4 * q^33 - 16 * q^35 - 8 * q^37 + 8 * q^40 - 4 * q^42 + 48 * q^43 - 8 * q^44 + 8 * q^45 - 24 * q^46 + 8 * q^47 - 20 * q^49 - 64 * q^50 + 8 * q^51 - 8 * q^52 - 16 * q^53 - 4 * q^54 + 48 * q^56 - 12 * q^58 - 20 * q^59 - 8 * q^60 - 4 * q^61 - 8 * q^63 - 64 * q^64 - 24 * q^65 - 32 * q^67 - 32 * q^68 - 24 * q^69 - 44 * q^70 - 16 * q^75 + 32 * q^76 - 8 * q^77 - 16 * q^78 - 28 * q^79 + 32 * q^80 + 4 * q^81 - 8 * q^82 - 8 * q^83 + 80 * q^85 + 8 * q^86 + 8 * q^88 - 8 * q^90 - 28 * q^91 - 4 * q^93 - 32 * q^95 - 16 * q^96 - 24 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.22474	+	0.707107i	−0.866025	+	0.500000i
$2$	−1.22474	+	0.707107i	−0.866025	+	0.500000i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	3.69798	+	0.990870i	1.65379	+	0.443130i	0.960669	−	0.277695i	$-0.0895706\pi$
$5$	3.69798	+	0.990870i	1.65379	+	0.443130i	0.693116	+	0.720826i	$0.256237\pi$
$6$	1.00000	−	1.00000i	0.408248	−	0.408248i
$7$	0.358719	−	2.62132i	0.135583	−	0.990766i
$7$	0.358719	−	2.62132i	0.135583	−	0.990766i
$8$			2.82843i			1.00000i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	−5.22973	+	1.40130i	−1.65379	+	0.443130i
$11$	−0.624844	−	2.33195i	−0.188398	−	0.703110i	−0.993878	−	0.110487i	$-0.964759\pi$
$11$	−0.624844	−	2.33195i	−0.188398	−	0.703110i	0.805480	−	0.592623i	$-0.201908\pi$
$12$	−0.517638	+	1.93185i	−0.149429	+	0.557678i
$13$	−2.41421	−	2.41421i	−0.669582	−	0.669582i	0.288037	−	0.957619i	$-0.406997\pi$
$13$	−2.41421	−	2.41421i	−0.669582	−	0.669582i	−0.957619	+	0.288037i	$0.906997\pi$
$14$	1.41421	+	3.46410i	0.377964	+	0.925820i
$15$	−3.82843			−0.988496
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	3.41421	−	5.91359i	0.828068	−	1.43426i	−0.0714831	−	0.997442i	$-0.522773\pi$
$17$	3.41421	−	5.91359i	0.828068	−	1.43426i	0.899551	−	0.436815i	$-0.143893\pi$
$18$	−0.707107	+	1.22474i	−0.166667	+	0.288675i
$19$	−0.732051	+	2.73205i	−0.167944	+	0.626775i	0.829702	+	0.558206i	$0.188510\pi$
$19$	−0.732051	+	2.73205i	−0.167944	+	0.626775i	−0.997646	+	0.0685694i	$0.978157\pi$
$20$	5.41421	−	5.41421i	1.21065	−	1.21065i
$21$	0.331951	+	2.62484i	0.0724377	+	0.572788i
$22$	2.41421	+	2.41421i	0.514712	+	0.514712i
$23$	0.210133	−	0.121320i	0.0438158	−	0.0252970i	−0.477932	−	0.878397i	$-0.658614\pi$
$23$	0.210133	−	0.121320i	0.0438158	−	0.0252970i	0.521748	+	0.853100i	$0.325280\pi$
$24$	−0.732051	−	2.73205i	−0.149429	−	0.557678i
$25$	8.36308	+	4.82843i	1.67262	+	0.965685i
$26$	4.66390	+	1.24969i	0.914667	+	0.245084i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−4.18154	−	3.24264i	−0.790237	−	0.612801i
$29$	6.12132	+	6.12132i	1.13670	+	1.13670i	0.989038	+	0.147663i	$0.0471751\pi$
$29$	6.12132	+	6.12132i	1.13670	+	1.13670i	0.147663	+	0.989038i	$0.452825\pi$
$30$	4.68885	−	2.70711i	0.856062	−	0.494248i
$31$	−0.207107	+	0.358719i	−0.0371975	+	0.0644279i	−0.884025	−	0.467440i	$-0.845176\pi$
$31$	−0.207107	+	0.358719i	−0.0371975	+	0.0644279i	0.846827	+	0.531868i	$0.178510\pi$
$32$	4.89898	+	2.82843i	0.866025	+	0.500000i
$33$	1.20711	+	2.09077i	0.210130	+	0.363956i
$34$			9.65685i			1.65614i
$35$	3.92392	−	9.33814i	0.663264	−	1.57843i
$36$		−	2.00000i		−	0.333333i
$37$	−2.73205	−	0.732051i	−0.449146	−	0.120348i	0.0271536	−	0.999631i	$-0.491356\pi$
$37$	−2.73205	−	0.732051i	−0.449146	−	0.120348i	−0.476300	+	0.879283i	$0.658022\pi$
$38$	−1.03528	−	3.86370i	−0.167944	−	0.626775i
$39$	2.95680	+	1.70711i	0.473466	+	0.273356i
$40$	−2.80260	+	10.4595i	−0.443130	+	1.65379i
$41$			3.41421i			0.533211i	0.963806	+	0.266605i	$0.0859020\pi$
$41$			3.41421i			0.533211i	−0.963806	+	0.266605i	$0.914098\pi$
$42$	−2.26260	−	2.98004i	−0.349127	−	0.459830i
$43$	7.41421	−	7.41421i	1.13066	−	1.13066i	0.140589	−	0.990068i	$-0.455100\pi$
$43$	7.41421	−	7.41421i	1.13066	−	1.13066i	0.990068	−	0.140589i	$-0.0448996\pi$
$44$	−4.66390	−	1.24969i	−0.703110	−	0.188398i
$45$	3.69798	−	0.990870i	0.551262	−	0.147710i
$46$	−0.171573	+	0.297173i	−0.0252970	+	0.0438158i
$47$	−1.12132	−	1.94218i	−0.163561	−	0.283297i	0.772582	−	0.634915i	$-0.218965\pi$
$47$	−1.12132	−	1.94218i	−0.163561	−	0.283297i	−0.936143	+	0.351618i	$0.885632\pi$
$48$	2.82843	+	2.82843i	0.408248	+	0.408248i
$49$	−6.74264	−	1.88064i	−0.963234	−	0.268662i
$50$	−13.6569			−1.93137
$51$	−1.76733	+	6.59575i	−0.247475	+	0.923590i
$52$	−6.59575	+	1.76733i	−0.914667	+	0.245084i
$53$	0.687644	+	2.56632i	0.0944552	+	0.352512i	0.996936	−	0.0782178i	$-0.0249230\pi$
$53$	0.687644	+	2.56632i	0.0944552	+	0.352512i	−0.902481	+	0.430730i	$0.858256\pi$
$54$	0.366025	−	1.36603i	0.0498097	−	0.185893i
$55$		−	9.24264i		−	1.24628i
$56$	7.41421	+	1.01461i	0.990766	+	0.135583i
$57$		−	2.82843i		−	0.374634i
$58$	−11.8255	−	3.16863i	−1.55276	−	0.416061i
$59$	3.12422	+	11.6598i	0.406739	+	1.51797i	0.800826	+	0.598898i	$0.204394\pi$
$59$	3.12422	+	11.6598i	0.406739	+	1.51797i	−0.394087	+	0.919073i	$0.628939\pi$
$60$	−3.82843	+	6.63103i	−0.494248	+	0.856062i
$61$	−0.669251	+	2.49768i	−0.0856888	+	0.319795i	−0.995444	−	0.0953508i	$-0.969603\pi$
$61$	−0.669251	+	2.49768i	−0.0856888	+	0.319795i	0.909755	+	0.415146i	$0.136269\pi$
$62$		−	0.585786i		−	0.0743950i
$63$	−1.00000	−	2.44949i	−0.125988	−	0.308607i
$64$	−8.00000			−1.00000
$65$	−6.53553	−	11.3199i	−0.810633	−	1.40406i
$66$	−2.95680	−	1.70711i	−0.363956	−	0.210130i
$67$	−8.99635	+	2.41057i	−1.09908	+	0.294497i	−0.762390	−	0.647118i	$-0.775974\pi$
$67$	−8.99635	+	2.41057i	−1.09908	+	0.294497i	−0.336690	+	0.941616i	$0.609307\pi$
$68$	−6.82843	−	11.8272i	−0.828068	−	1.43426i
$69$	−0.171573	+	0.171573i	−0.0206549	+	0.0206549i
$70$	1.79725	+	14.2115i	0.214813	+	1.69860i
$71$		−	3.89949i		−	0.462785i	−0.972860	−	0.231392i	$-0.925672\pi$
$71$		−	3.89949i		−	0.462785i	0.972860	−	0.231392i	$-0.0743281\pi$
$72$	1.41421	+	2.44949i	0.166667	+	0.288675i
$73$	3.46410	+	2.00000i	0.405442	+	0.234082i	0.688830	−	0.724923i	$-0.258125\pi$
$73$	3.46410	+	2.00000i	0.405442	+	0.234082i	−0.283387	+	0.959006i	$0.591458\pi$
$74$	3.86370	−	1.03528i	0.449146	−	0.120348i
$75$	−9.32780	−	2.49938i	−1.07708	−	0.288603i
$76$	4.00000	+	4.00000i	0.458831	+	0.458831i
$77$	−6.33694	+	0.801401i	−0.722161	+	0.0913281i
$78$	−4.82843			−0.546712
$79$	−1.37868	−	2.38794i	−0.155114	−	0.268665i	0.777987	−	0.628281i	$-0.216241\pi$
$79$	−1.37868	−	2.38794i	−0.155114	−	0.268665i	−0.933100	+	0.359616i	$0.882908\pi$
$80$	−3.96348	−	14.7919i	−0.443130	−	1.65379i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−2.41421	−	4.18154i	−0.266605	−	0.461774i
$83$	6.77817	+	6.77817i	0.744001	+	0.744001i	0.973345	−	0.229344i	$-0.0736581\pi$
$83$	6.77817	+	6.77817i	0.744001	+	0.744001i	−0.229344	+	0.973345i	$0.573658\pi$
$84$	4.87832	+	2.04989i	0.532268	+	0.223661i
$85$	18.4853	−	18.4853i	2.00501	−	2.00501i
$86$	−3.83788	+	14.3232i	−0.413849	+	1.54451i
$87$	−7.49706	−	4.32843i	−0.803769	−	0.464056i
$88$	6.59575	−	1.76733i	0.703110	−	0.188398i
$89$	−13.4722	+	7.77817i	−1.42805	+	0.824485i	−0.996967	−	0.0778275i	$-0.975202\pi$
$89$	−13.4722	+	7.77817i	−1.42805	+	0.824485i	−0.431083	+	0.902312i	$0.641868\pi$
$90$	−3.82843	+	3.82843i	−0.403552	+	0.403552i
$91$	−7.19445	+	5.46240i	−0.754184	+	0.572615i
$92$		−	0.485281i		−	0.0505941i
$93$	0.107206	−	0.400100i	0.0111168	−	0.0414884i
$94$	2.74666	+	1.58579i	0.283297	+	0.163561i
$95$	−5.41421	+	9.37769i	−0.555487	+	0.962131i
$96$	−5.46410	−	1.46410i	−0.557678	−	0.149429i
$97$	−14.3137			−1.45334			−0.726668	−	0.686988i	$-0.758932\pi$
$97$	−14.3137			−1.45334			−0.726668	+	0.686988i	$0.758932\pi$
$98$	9.58783	−	2.46447i	0.968517	−	0.248949i
$99$	−1.70711	−	1.70711i	−0.171571	−	0.171571i
$100$	16.7262	−	9.65685i	1.67262	−	0.965685i
$101$	0.946464	+	3.53225i	0.0941766	+	0.351472i	0.996893	−	0.0787635i	$-0.0250972\pi$
$101$	0.946464	+	3.53225i	0.0941766	+	0.351472i	−0.902717	+	0.430235i	$0.858431\pi$
$102$	−2.49938	−	9.32780i	−0.247475	−	0.923590i
$103$	5.49333	−	3.17157i	0.541273	−	0.312504i	−0.204321	−	0.978904i	$-0.565499\pi$
$103$	5.49333	−	3.17157i	0.541273	−	0.312504i	0.745595	+	0.666399i	$0.232165\pi$
$104$	6.82843	−	6.82843i	0.669582	−	0.669582i
$105$	−1.37333	+	10.0355i	−0.134023	+	0.979368i
$106$	−2.65685	−	2.65685i	−0.258056	−	0.258056i
$107$	1.86321	+	0.499244i	0.180123	+	0.0482638i	0.347753	−	0.937586i	$-0.386945\pi$
$107$	1.86321	+	0.499244i	0.180123	+	0.0482638i	−0.167630	+	0.985850i	$0.553611\pi$
$108$	0.517638	+	1.93185i	0.0498097	+	0.185893i
$109$	17.8554	−	4.78434i	1.71024	−	0.458257i	0.734755	−	0.678332i	$-0.237297\pi$
$109$	17.8554	−	4.78434i	1.71024	−	0.458257i	0.975483	+	0.220075i	$0.0706303\pi$
$110$	6.53553	+	11.3199i	0.623139	+	1.07931i
$111$	2.82843			0.268462
$112$	−9.79796	+	4.00000i	−0.925820	+	0.377964i
$113$	−15.8995			−1.49570			−0.747849	−	0.663868i	$-0.768913\pi$
$113$	−15.8995			−1.49570			−0.747849	+	0.663868i	$0.768913\pi$
$114$	2.00000	+	3.46410i	0.187317	+	0.324443i
$115$	0.897280	−	0.240425i	0.0836718	−	0.0224198i
$116$	16.7238	−	4.48112i	1.55276	−	0.416061i
$117$	−3.29788	−	0.883663i	−0.304889	−	0.0816947i
$118$	−12.0711	−	12.0711i	−1.11123	−	1.11123i
$119$	−14.2767	−	11.0711i	−1.30874	−	1.01488i
$120$		−	10.8284i		−	0.988496i
$121$	4.47871	−	2.58579i	0.407156	−	0.235071i
$122$	−0.946464	−	3.53225i	−0.0856888	−	0.319795i
$123$	−0.883663	−	3.29788i	−0.0796773	−	0.297360i
$124$	0.414214	+	0.717439i	0.0371975	+	0.0644279i
$125$	12.6066	+	12.6066i	1.12757	+	1.12757i
$126$	2.95680	+	2.29289i	0.263412	+	0.204267i
$127$	2.75736			0.244676			0.122338	−	0.992488i	$-0.460961\pi$
$127$	2.75736			0.244676			0.122338	+	0.992488i	$0.460961\pi$
$128$	9.79796	−	5.65685i	0.866025	−	0.500000i
$129$	−5.24264	+	9.08052i	−0.461589	+	0.799495i
$130$	16.0087	+	9.24264i	1.40406	+	0.810633i
$131$	−5.10596	+	19.0557i	−0.446110	+	1.66491i	0.266879	+	0.963730i	$0.414008\pi$
$131$	−5.10596	+	19.0557i	−0.446110	+	1.66491i	−0.712989	+	0.701175i	$0.752659\pi$
$132$	4.82843			0.420261
$133$	6.89898	+	2.89898i	0.598217	+	0.251373i
$134$	9.31371	−	9.31371i	0.804582	−	0.804582i
$135$	−3.31552	+	1.91421i	−0.285354	+	0.164749i
$136$	16.7262	+	9.65685i	1.43426	+	0.828068i
$137$	−6.21076	−	3.58579i	−0.530621	−	0.306354i	0.210648	−	0.977562i	$-0.432443\pi$
$137$	−6.21076	−	3.58579i	−0.530621	−	0.306354i	−0.741269	+	0.671208i	$0.765776\pi$
$138$	0.0888127	−	0.331453i	0.00756024	−	0.0282152i
$139$	−6.89949	+	6.89949i	−0.585208	+	0.585208i	−0.936330	−	0.351122i	$-0.885800\pi$
$139$	−6.89949	+	6.89949i	−0.585208	+	0.585208i	0.351122	+	0.936330i	$0.385800\pi$
$140$	−12.2502	−	16.1346i	−1.03533	−	1.36362i
$141$	1.58579	+	1.58579i	0.133547	+	0.133547i
$142$	2.75736	+	4.77589i	0.231392	+	0.400783i
$143$	−4.12132	+	7.13834i	−0.344642	+	0.596938i
$144$	−3.46410	−	2.00000i	−0.288675	−	0.166667i
$145$	16.5711	+	28.7019i	1.37615	+	2.38357i
$146$	−5.65685			−0.468165
$147$	6.99964	+	0.0714323i	0.577320	+	0.00589164i
$148$	−4.00000	+	4.00000i	−0.328798	+	0.328798i
$149$	−8.85906	−	2.37378i	−0.725762	−	0.194467i	−0.123021	−	0.992404i	$-0.539258\pi$
$149$	−8.85906	−	2.37378i	−0.725762	−	0.194467i	−0.602741	+	0.797937i	$0.705925\pi$
$150$	13.1915	−	3.53465i	1.07708	−	0.288603i
$151$	−10.7510	−	6.20711i	−0.874906	−	0.505127i	−0.00593052	−	0.999982i	$-0.501888\pi$
$151$	−10.7510	−	6.20711i	−0.874906	−	0.505127i	−0.868975	+	0.494855i	$0.835221\pi$
$152$	−7.72741	−	2.07055i	−0.626775	−	0.167944i
$153$		−	6.82843i		−	0.552046i
$154$	7.19445	−	5.46240i	0.579746	−	0.440173i
$155$	−1.12132	+	1.12132i	−0.0900666	+	0.0900666i
$156$	5.91359	−	3.41421i	0.473466	−	0.273356i
$157$	−12.5286	+	3.35703i	−0.999891	+	0.267920i	−0.721400	−	0.692519i	$-0.756501\pi$
$157$	−12.5286	+	3.35703i	−0.999891	+	0.267920i	−0.278491	+	0.960439i	$0.589834\pi$
$158$	3.37706	+	1.94975i	0.268665	+	0.155114i
$159$	−1.32843	−	2.30090i	−0.105351	−	0.182473i
$160$	15.3137	+	15.3137i	1.21065	+	1.21065i
$161$	−0.242641	−	0.594346i	−0.0191228	−	0.0468410i
$162$			1.41421i			0.111111i
$163$	−4.20390	+	15.6892i	−0.329275	+	1.22887i	0.580668	+	0.814140i	$0.302791\pi$
$163$	−4.20390	+	15.6892i	−0.329275	+	1.22887i	−0.909944	+	0.414732i	$0.863875\pi$
$164$	5.91359	+	3.41421i	0.461774	+	0.266605i
$165$	2.39217	+	8.92771i	0.186230	+	0.695021i
$166$	−13.0944	−	3.50864i	−1.01632	−	0.272323i
$167$			6.00000i			0.464294i	0.972681	+	0.232147i	$0.0745750\pi$
$167$			6.00000i			0.464294i	−0.972681	+	0.232147i	$0.925425\pi$
$168$	−7.42418	+	0.938900i	−0.572788	+	0.0724377i
$169$		−	1.34315i		−	0.103319i
$170$	−9.56869	+	35.7108i	−0.733885	+	2.73889i
$171$	0.732051	+	2.73205i	0.0559813	+	0.208925i
$172$	−5.42758	−	20.2560i	−0.413849	−	1.54451i
$173$	4.39230	−	16.3923i	0.333941	−	1.24628i	−0.571072	−	0.820900i	$-0.693472\pi$
$173$	4.39230	−	16.3923i	0.333941	−	1.24628i	0.905013	−	0.425384i	$-0.139861\pi$
$174$	12.2426			0.928112
$175$	15.6569	−	20.1903i	1.18355	−	1.52624i
$176$	−6.82843	+	6.82843i	−0.514712	+	0.514712i
$177$	−6.03553	−	10.4539i	−0.453659	−	0.785760i
$178$	11.0000	−	19.0526i	0.824485	−	1.42805i
$179$	25.7201	−	6.89168i	1.92241	−	0.515109i	0.935650	−	0.352930i	$-0.114814\pi$
$179$	25.7201	−	6.89168i	1.92241	−	0.515109i	0.986761	−	0.162179i	$-0.0518522\pi$
$180$	1.98174	−	7.39595i	0.147710	−	0.551262i
$181$	9.72792	−	9.72792i	0.723071	−	0.723071i	−0.246159	−	0.969230i	$-0.579168\pi$
$181$	9.72792	−	9.72792i	0.723071	−	0.723071i	0.969230	+	0.246159i	$0.0791685\pi$
$182$	4.94887	−	11.7773i	0.366834	−	0.872991i
$183$		−	2.58579i		−	0.191147i
$184$	0.343146	+	0.594346i	0.0252970	+	0.0438158i
$185$	−9.37769	−	5.41421i	−0.689462	−	0.398061i
$186$	0.151613	+	0.565826i	0.0111168	+	0.0414884i
$187$	−15.9236	−	4.26670i	−1.16445	−	0.312012i
$188$	−4.48528			−0.327123
$189$	1.59990	+	2.10721i	0.116376	+	0.153277i
$190$		−	15.3137i		−	1.11097i
$191$	1.65685	+	2.86976i	0.119886	+	0.207648i	0.919722	−	0.392570i	$-0.128414\pi$
$191$	1.65685	+	2.86976i	0.119886	+	0.207648i	−0.799836	+	0.600218i	$0.795081\pi$
$192$	7.72741	−	2.07055i	0.557678	−	0.149429i
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	−0.712123	−	0.702055i	$-0.752266\pi$
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	0.964059	+	0.265689i	$0.0855996\pi$
$194$	17.5306	−	10.1213i	1.25863	−	0.726668i
$195$	9.24264	+	9.24264i	0.661879	+	0.661879i
$196$	−10.0000	+	9.79796i	−0.714286	+	0.699854i
$197$	8.82843	−	8.82843i	0.628999	−	0.628999i	−0.318817	−	0.947816i	$-0.603286\pi$
$197$	8.82843	−	8.82843i	0.628999	−	0.628999i	0.947816	+	0.318817i	$0.103286\pi$
$198$	3.29788	+	0.883663i	0.234370	+	0.0627992i
$199$	11.4069	+	6.58579i	0.808615	+	0.466854i	0.846475	−	0.532429i	$-0.178721\pi$
$199$	11.4069	+	6.58579i	0.808615	+	0.466854i	−0.0378598	+	0.999283i	$0.512054\pi$
$200$	−13.6569	+	23.6544i	−0.965685	+	1.67262i
$201$	8.06591	−	4.65685i	0.568925	−	0.328469i
$202$	−3.65685	−	3.65685i	−0.257295	−	0.257295i
$203$	18.2418	−	13.8501i	1.28032	−	0.972087i
$204$	9.65685	+	9.65685i	0.676115	+	0.676115i
$205$	−3.38304	+	12.6257i	−0.236282	+	0.881816i
$206$	−4.48528	+	7.76874i	−0.312504	+	0.541273i
$207$	0.121320	−	0.210133i	0.00843235	−	0.0146053i
$208$	−3.53465	+	13.1915i	−0.245084	+	0.914667i
$209$	6.82843			0.472332
$210$	−5.41421	−	13.2621i	−0.373616	−	0.915169i
$211$	−5.58579	−	5.58579i	−0.384541	−	0.384541i	0.488194	−	0.872735i	$-0.337656\pi$
$211$	−5.58579	−	5.58579i	−0.384541	−	0.384541i	−0.872735	+	0.488194i	$0.837656\pi$
$212$	5.13265	+	1.37529i	0.352512	+	0.0944552i
$213$	1.00926	+	3.76662i	0.0691536	+	0.258085i
$214$	−2.63497	+	0.706038i	−0.180123	+	0.0482638i
$215$	34.7641	−	20.0711i	2.37089	−	1.36884i
$216$	−2.00000	−	2.00000i	−0.136083	−	0.136083i
$217$	0.866025	+	0.671573i	0.0587896	+	0.0455893i
$218$	−18.4853	+	18.4853i	−1.25198	+	1.25198i
$219$	−3.86370	−	1.03528i	−0.261085	−	0.0699575i
$220$	−16.0087	−	9.24264i	−1.07931	−	0.623139i
$221$	−22.5193	+	6.03403i	−1.51481	+	0.405893i
$222$	−3.46410	+	2.00000i	−0.232495	+	0.134231i
$223$	−10.5563			−0.706905			−0.353453	−	0.935452i	$-0.614992\pi$
$223$	−10.5563			−0.706905			−0.353453	+	0.935452i	$0.614992\pi$
$224$	9.17157	−	11.8272i	0.612801	−	0.790237i
$225$	9.65685			0.643790
$226$	19.4728	−	11.2426i	1.29531	−	0.747849i
$227$	−18.5870	+	4.98036i	−1.23366	+	0.330558i	−0.816004	−	0.578047i	$-0.803815\pi$
$227$	−18.5870	+	4.98036i	−1.23366	+	0.330558i	−0.417656	+	0.908605i	$0.637148\pi$
$228$	−4.89898	−	2.82843i	−0.324443	−	0.187317i
$229$	−11.9628	−	3.20542i	−0.790522	−	0.211820i	−0.159104	−	0.987262i	$-0.550860\pi$
$229$	−11.9628	−	3.20542i	−0.790522	−	0.211820i	−0.631419	+	0.775442i	$0.717527\pi$
$230$	−0.928932	+	0.928932i	−0.0612520	+	0.0612520i
$231$	5.91359	−	2.41421i	0.389086	−	0.158844i
$232$	−17.3137	+	17.3137i	−1.13670	+	1.13670i
$233$	−9.37769	+	5.41421i	−0.614353	+	0.354697i	−0.774667	−	0.632369i	$-0.782083\pi$
$233$	−9.37769	+	5.41421i	−0.614353	+	0.354697i	0.160314	+	0.987066i	$0.448749\pi$
$234$	4.66390	−	1.24969i	0.304889	−	0.0816947i
$235$	−2.22217	−	8.29323i	−0.144958	−	0.540991i
$236$	23.3195	+	6.24844i	1.51797	+	0.406739i
$237$	1.94975	+	1.94975i	0.126650	+	0.126650i
$238$	25.3137	+	3.46410i	1.64084	+	0.224544i
$239$	−3.07107			−0.198651			−0.0993254	−	0.995055i	$-0.531668\pi$
$239$	−3.07107			−0.198651			−0.0993254	+	0.995055i	$0.531668\pi$
$240$	7.65685	+	13.2621i	0.494248	+	0.856062i
$241$	2.57107	−	4.45322i	0.165617	−	0.286857i	−0.771257	−	0.636524i	$-0.780372\pi$
$241$	2.57107	−	4.45322i	0.165617	−	0.286857i	0.936874	+	0.349667i	$0.113705\pi$
$242$	−3.65685	+	6.33386i	−0.235071	+	0.407156i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	3.65685	+	3.65685i	0.234106	+	0.234106i
$245$	−23.0707	−	13.6356i	−1.47393	−	0.871149i
$246$	3.41421	+	3.41421i	0.217682	+	0.217682i
$247$	8.36308	−	4.82843i	0.532130	−	0.307225i
$248$	−1.01461	−	0.585786i	−0.0644279	−	0.0371975i
$249$	−8.30153	−	4.79289i	−0.526088	−	0.303737i
$250$	−24.3541	−	6.52566i	−1.54029	−	0.412719i
$251$	−13.9497	+	13.9497i	−0.880500	+	0.880500i	−0.993585	−	0.113085i	$-0.963927\pi$
$251$	−13.9497	+	13.9497i	−0.880500	+	0.880500i	0.113085	+	0.993585i	$0.463927\pi$
$252$	−5.24264	−	0.717439i	−0.330255	−	0.0451944i
$253$	−0.414214	−	0.414214i	−0.0260414	−	0.0260414i
$254$	−3.37706	+	1.94975i	−0.211896	+	0.122338i
$255$	−13.0711	+	22.6398i	−0.818542	+	1.41776i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	5.87868	+	10.1822i	0.366702	+	0.635146i	0.989048	−	0.147596i	$-0.0471535\pi$
$257$	5.87868	+	10.1822i	0.366702	+	0.635146i	−0.622346	+	0.782742i	$0.713820\pi$
$258$		−	14.8284i		−	0.923178i
$259$	−2.89898	+	6.89898i	−0.180134	+	0.428682i
$260$	−26.1421			−1.62127
$261$	8.36188	+	2.24056i	0.517587	+	0.138687i
$262$	−7.22092	−	26.9488i	−0.446110	−	1.66491i
$263$	16.0087	+	9.24264i	0.987140	+	0.569926i	0.904418	−	0.426647i	$-0.140305\pi$
$263$	16.0087	+	9.24264i	0.987140	+	0.569926i	0.0827219	+	0.996573i	$0.473639\pi$
$264$	−5.91359	+	3.41421i	−0.363956	+	0.210130i
$265$			10.1716i			0.624835i
$266$	−10.4994	+	1.32780i	−0.643758	+	0.0814129i
$267$	11.0000	−	11.0000i	0.673189	−	0.673189i
$268$	−4.82113	+	17.9927i	−0.294497	+	1.09908i
$269$	−28.1491	+	7.54254i	−1.71628	+	0.459877i	−0.976951	−	0.213464i	$-0.931525\pi$
$269$	−28.1491	+	7.54254i	−1.71628	+	0.459877i	−0.739332	+	0.673341i	$0.764859\pi$
$270$	2.70711	−	4.68885i	0.164749	−	0.285354i
$271$	−0.136039	−	0.235626i	−0.00826378	−	0.0143133i	0.861864	−	0.507140i	$-0.169297\pi$
$271$	−0.136039	−	0.235626i	−0.00826378	−	0.0143133i	−0.870128	+	0.492826i	$0.835964\pi$
$272$	−27.3137			−1.65614
$273$	5.53553	−	7.13834i	0.335026	−	0.432032i
$274$	10.1421			0.612709
$275$	6.03403	−	22.5193i	0.363866	−	1.35797i
$276$	0.125600	+	0.468746i	0.00756024	+	0.0282152i
$277$	5.60521	+	20.9189i	0.336784	+	1.25690i	0.901922	+	0.431899i	$0.142156\pi$
$277$	5.60521	+	20.9189i	0.336784	+	1.25690i	−0.565138	+	0.824997i	$0.691177\pi$
$278$	3.57144	−	13.3288i	0.214201	−	0.799408i
$279$			0.414214i			0.0247983i
$280$	26.4122	+	11.0985i	1.57843	+	0.663264i
$281$			0.828427i			0.0494198i	0.999695	+	0.0247099i	$0.00786621\pi$
$281$			0.828427i			0.0494198i	−0.999695	+	0.0247099i	$0.992134\pi$
$282$	−3.06350	−	0.820863i	−0.182429	−	0.0488817i
$283$	7.10610	+	26.5203i	0.422414	+	1.57647i	0.769507	+	0.638638i	$0.220502\pi$
$283$	7.10610	+	26.5203i	0.422414	+	1.57647i	−0.347094	+	0.937830i	$0.612831\pi$
$284$	−6.75412	−	3.89949i	−0.400783	−	0.231392i
$285$	2.80260	−	10.4595i	0.166012	−	0.619565i
$286$		−	11.6569i		−	0.689284i
$287$	8.94975	+	1.22474i	0.528287	+	0.0722944i
$288$	5.65685			0.333333
$289$	−14.8137	−	25.6581i	−0.871395	−	1.50930i
$290$	−40.5907	−	23.4350i	−2.38357	−	1.37615i
$291$	13.8260	−	3.70466i	0.810493	−	0.217171i
$292$	6.92820	−	4.00000i	0.405442	−	0.234082i
$293$	−1.05025	+	1.05025i	−0.0613564	+	0.0613564i	−0.737119	−	0.675763i	$-0.763814\pi$
$293$	−1.05025	+	1.05025i	−0.0613564	+	0.0613564i	0.675763	+	0.737119i	$0.263814\pi$
$294$	−8.62328	+	4.86200i	−0.502920	+	0.283558i
$295$			46.2132i			2.69064i
$296$	2.07055	−	7.72741i	0.120348	−	0.449146i
$297$	2.09077	+	1.20711i	0.121319	+	0.0700434i
$298$	12.5286	−	3.35703i	0.725762	−	0.194467i
$299$	−0.800199	−	0.214413i	−0.0462767	−	0.0123998i
$300$	−13.6569	+	13.6569i	−0.788479	+	0.788479i
$301$	−16.7754	−	22.0947i	−0.966918	−	1.27351i
$302$	17.5563			1.01025
$303$	−1.82843	−	3.16693i	−0.105040	−	0.181935i
$304$	10.9282	−	2.92820i	0.626775	−	0.167944i
$305$	−4.94975	+	8.57321i	−0.283422	+	0.490901i
$306$	4.82843	+	8.36308i	0.276023	+	0.478086i
$307$	−16.3137	−	16.3137i	−0.931073	−	0.931073i	0.0667005	−	0.997773i	$-0.478753\pi$
$307$	−16.3137	−	16.3137i	−0.931073	−	0.931073i	−0.997773	+	0.0667005i	$0.978753\pi$
$308$	−4.94887	+	11.7773i	−0.281988	+	0.671074i
$309$	−4.48528	+	4.48528i	−0.255159	+	0.255159i
$310$	0.580438	−	2.16622i	0.0329667	−	0.123033i
$311$	16.9363	+	9.77817i	0.960369	+	0.554469i	0.896287	−	0.443475i	$-0.146255\pi$
$311$	16.9363	+	9.77817i	0.960369	+	0.554469i	0.0640825	+	0.997945i	$0.479588\pi$
$312$	−4.82843	+	8.36308i	−0.273356	+	0.473466i
$313$	−3.61269	+	2.08579i	−0.204201	+	0.117896i	−0.598614	−	0.801038i	$-0.704281\pi$
$313$	−3.61269	+	2.08579i	−0.204201	+	0.117896i	0.394412	+	0.918934i	$0.370948\pi$
$314$	12.9706	−	12.9706i	0.731971	−	0.731971i
$315$	−1.27085	−	10.0490i	−0.0716043	−	0.566198i
$316$	−5.51472			−0.310227
$317$	5.86403	−	21.8848i	0.329356	−	1.22918i	−0.580503	−	0.814258i	$-0.697144\pi$
$317$	5.86403	−	21.8848i	0.329356	−	1.22918i	0.909859	−	0.414917i	$-0.136189\pi$
$318$	3.25397	+	1.87868i	0.182473	+	0.105351i
$319$	10.4497	−	18.0995i	0.585074	−	1.01338i
$320$	−29.5838	−	7.92696i	−1.65379	−	0.443130i
$321$	−1.92893			−0.107662
$322$	0.717439	+	0.556349i	0.0399813	+	0.0310041i
$323$	13.6569	+	13.6569i	0.759888	+	0.759888i
$324$	−1.00000	−	1.73205i	−0.0555556	−	0.0962250i
$325$	−8.53341	−	31.8471i	−0.473348	−	1.76656i
$326$	−5.94522	−	22.1879i	−0.329275	−	1.22887i
$327$	−16.0087	+	9.24264i	−0.885284	+	0.511119i
$328$	−9.65685			−0.533211
$329$	−5.49333	+	2.24264i	−0.302857	+	0.123641i
$330$	−9.24264	−	9.24264i	−0.508791	−	0.508791i
$331$	7.72741	+	2.07055i	0.424737	+	0.113808i	0.464854	−	0.885387i	$-0.346107\pi$
$331$	7.72741	+	2.07055i	0.424737	+	0.113808i	−0.0401178	+	0.999195i	$0.512773\pi$
$332$	18.5183	−	4.96197i	1.01632	−	0.272323i
$333$	−2.73205	+	0.732051i	−0.149715	+	0.0401161i
$334$	−4.24264	−	7.34847i	−0.232147	−	0.402090i
$335$	−35.6569			−1.94814
$336$	8.42883	−	6.39960i	0.459830	−	0.349127i
$337$	−7.34315			−0.400007			−0.200003	−	0.979795i	$-0.564095\pi$
$337$	−7.34315			−0.400007			−0.200003	+	0.979795i	$0.564095\pi$
$338$	0.949747	+	1.64501i	0.0516595	+	0.0894768i
$339$	15.3577	−	4.11509i	0.834118	−	0.223501i
$340$	−13.5322	−	50.5027i	−0.733885	−	2.73889i
$341$	0.965926	+	0.258819i	0.0523078	+	0.0140158i
$342$	−2.82843	−	2.82843i	−0.152944	−	0.152944i
$343$	−7.34847	+	17.0000i	−0.396780	+	0.917914i
$344$	20.9706	+	20.9706i	1.13066	+	1.13066i
$345$	−0.804479	+	0.464466i	−0.0433117	+	0.0250060i
$346$	6.21166	+	23.1822i	0.333941	+	1.24628i
$347$	−1.94495	−	7.25866i	−0.104411	−	0.389665i	0.893867	−	0.448332i	$-0.147982\pi$
$347$	−1.94495	−	7.25866i	−0.104411	−	0.389665i	−0.998278	+	0.0586667i	$0.981315\pi$
$348$	−14.9941	+	8.65685i	−0.803769	+	0.464056i
$349$	−0.585786	−	0.585786i	−0.0313564	−	0.0313564i	0.691255	−	0.722611i	$-0.257058\pi$
$349$	−0.585786	−	0.585786i	−0.0313564	−	0.0313564i	−0.722611	+	0.691255i	$0.757058\pi$
$350$	−4.89898	+	35.7990i	−0.261861	+	1.91354i
$351$	3.41421			0.182237
$352$	3.53465	−	13.1915i	0.188398	−	0.703110i
$353$	1.65685	−	2.86976i	0.0881855	−	0.152742i	−0.818559	−	0.574423i	$-0.805227\pi$
$353$	1.65685	−	2.86976i	0.0881855	−	0.152742i	0.906744	+	0.421681i	$0.138560\pi$
$354$	14.7840	+	8.53553i	0.785760	+	0.453659i
$355$	3.86389	−	14.4202i	0.205074	−	0.765347i
$356$			31.1127i			1.64897i
$357$	16.6556	+	6.99876i	0.881508	+	0.370413i
$358$	−26.6274	+	26.6274i	−1.40730	+	1.40730i
$359$	6.63103	−	3.82843i	0.349972	−	0.202057i	−0.314701	−	0.949191i	$-0.601904\pi$
$359$	6.63103	−	3.82843i	0.349972	−	0.202057i	0.664673	+	0.747134i	$0.268571\pi$
$360$	2.80260	+	10.4595i	0.147710	+	0.551262i
$361$	9.52628	+	5.50000i	0.501383	+	0.289474i
$362$	−5.03554	+	18.7929i	−0.264662	+	0.987733i
$363$	−3.65685	+	3.65685i	−0.191935	+	0.191935i
$364$	2.26670	+	17.9236i	0.118808	+	0.939450i
$365$	10.8284	+	10.8284i	0.566786	+	0.566786i
$366$	1.82843	+	3.16693i	0.0955734	+	0.165538i
$367$	12.6924	−	21.9839i	0.662537	−	1.14755i	−0.317409	−	0.948289i	$-0.602813\pi$
$367$	12.6924	−	21.9839i	0.662537	−	1.14755i	0.979947	−	0.199260i	$-0.0638537\pi$
$368$	−0.840532	−	0.485281i	−0.0438158	−	0.0252970i
$369$	1.70711	+	2.95680i	0.0888684	+	0.153925i
$370$	15.3137			0.796122
$371$	6.97383	−	0.881946i	0.362063	−	0.0457884i
$372$	−0.585786	−	0.585786i	−0.0303716	−	0.0303716i
$373$	0.0970804	+	0.0260126i	0.00502663	+	0.00134688i	0.261331	−	0.965249i	$-0.415838\pi$
$373$	0.0970804	+	0.0260126i	0.00502663	+	0.00134688i	−0.256305	+	0.966596i	$0.582505\pi$
$374$	22.5193	−	6.03403i	1.16445	−	0.312012i
$375$	−15.4399	−	8.91421i	−0.797311	−	0.460328i
$376$	5.49333	−	3.17157i	0.283297	−	0.163561i
$377$		−	29.5563i		−	1.52223i
$378$	−3.44949	−	1.44949i	−0.177423	−	0.0745537i
$379$	6.65685	−	6.65685i	0.341940	−	0.341940i	−0.515156	−	0.857096i	$-0.672266\pi$
$379$	6.65685	−	6.65685i	0.341940	−	0.341940i	0.857096	+	0.515156i	$0.172266\pi$
$380$	10.8284	+	18.7554i	0.555487	+	0.962131i
$381$	−2.66340	+	0.713657i	−0.136450	+	0.0365618i
$382$	−4.05845	−	2.34315i	−0.207648	−	0.119886i
$383$	7.46447	+	12.9288i	0.381416	+	0.660633i	0.991265	−	0.131885i	$-0.0421031\pi$
$383$	7.46447	+	12.9288i	0.381416	+	0.660633i	−0.609849	+	0.792518i	$0.708770\pi$
$384$	−8.00000	+	8.00000i	−0.408248	+	0.408248i
$385$	−24.2279	−	3.31552i	−1.23477	−	0.168974i
$386$			9.89949i			0.503871i
$387$	2.71379	−	10.1280i	0.137950	−	0.514835i
$388$	−14.3137	+	24.7921i	−0.726668	+	1.25863i
$389$	9.26546	+	34.5792i	0.469777	+	1.75323i	0.640544	+	0.767922i	$0.278709\pi$
$389$	9.26546	+	34.5792i	0.469777	+	1.75323i	−0.170766	+	0.985312i	$0.554624\pi$
$390$	−17.8554	−	4.78434i	−0.904144	−	0.242265i
$391$		−	1.65685i		−	0.0837907i
$392$	5.31925	−	19.0711i	0.268662	−	0.963234i
$393$		−	19.7279i		−	0.995142i
$394$	−4.56993	+	17.0552i	−0.230230	+	0.859229i
$395$	−2.73218	−	10.1967i	−0.137471	−	0.513049i
$396$	−4.66390	+	1.24969i	−0.234370	+	0.0627992i
$397$	−0.251200	+	0.937492i	−0.0126074	+	0.0470514i	−0.971943	−	0.235217i	$-0.924420\pi$
$397$	−0.251200	+	0.937492i	−0.0126074	+	0.0470514i	0.959336	+	0.282268i	$0.0910867\pi$
$398$	−18.6274			−0.933708
$399$	−7.41421	−	1.01461i	−0.371175	−	0.0507941i
$400$		−	38.6274i		−	1.93137i
$401$	12.0000	+	20.7846i	0.599251	+	1.03793i	0.992932	+	0.118686i	$0.0378683\pi$
$401$	12.0000	+	20.7846i	0.599251	+	1.03793i	−0.393680	+	0.919247i	$0.628798\pi$
$402$	−6.58579	+	11.4069i	−0.328469	+	0.568925i
$403$	1.36603	−	0.366025i	0.0680466	−	0.0182330i
$404$	7.06450	+	1.89293i	0.351472	+	0.0941766i
$405$	2.70711	−	2.70711i	0.134517	−	0.134517i
$406$	−12.5480	+	29.8617i	−0.622748	+	1.48201i
$407$			6.82843i			0.338473i
$408$	−18.6556	−	4.99876i	−0.923590	−	0.247475i
$409$	28.2817	+	16.3284i	1.39844	+	0.807389i	0.994229	−	0.107278i	$-0.0342134\pi$
$409$	28.2817	+	16.3284i	1.39844	+	0.807389i	0.404209	+	0.914667i	$0.367547\pi$
$410$	−4.78434	−	17.8554i	−0.236282	−	0.881816i
$411$	6.92721	+	1.85614i	0.341694	+	0.0915566i
$412$		−	12.6863i		−	0.625009i
$413$	31.6847	−	4.00701i	1.55910	−	0.197172i
$414$			0.343146i			0.0168647i
$415$	18.3492	+	31.7818i	0.900729	+	1.56011i
$416$	−4.99876	−	18.6556i	−0.245084	−	0.914667i
$417$	4.87868	−	8.45012i	0.238910	−	0.413804i
$418$	−8.36308	+	4.82843i	−0.409052	+	0.236166i
$419$	−13.7990	−	13.7990i	−0.674125	−	0.674125i	0.284540	−	0.958664i	$-0.408159\pi$
$419$	−13.7990	−	13.7990i	−0.674125	−	0.674125i	−0.958664	+	0.284540i	$0.908159\pi$
$420$	16.0087	+	12.4142i	0.781146	+	0.605752i
$421$	−1.48528	+	1.48528i	−0.0723882	+	0.0723882i	−0.742374	−	0.669986i	$-0.766300\pi$
$421$	−1.48528	+	1.48528i	−0.0723882	+	0.0723882i	0.669986	+	0.742374i	$0.266300\pi$
$422$	10.7909	+	2.89142i	0.525293	+	0.140752i
$423$	−1.94218	−	1.12132i	−0.0944322	−	0.0545205i
$424$	−7.25866	+	1.94495i	−0.352512	+	0.0944552i
$425$	57.1067	−	32.9706i	2.77008	−	1.59931i
$426$	−3.89949	−	3.89949i	−0.188931	−	0.188931i
$427$	6.30714	+	2.65029i	0.305224	+	0.128256i
$428$	2.72792	−	2.72792i	0.131859	−	0.131859i
$429$	2.13335	−	7.96178i	0.102999	−	0.384398i
$430$	−28.3848	+	49.1639i	−1.36884	+	2.37089i
$431$	11.1924	−	19.3858i	0.539118	−	0.933780i	−0.459833	−	0.888005i	$-0.652091\pi$
$431$	11.1924	−	19.3858i	0.539118	−	0.933780i	0.998952	−	0.0457752i	$-0.0145758\pi$
$432$	3.86370	+	1.03528i	0.185893	+	0.0498097i
$433$	16.9706			0.815553			0.407777	−	0.913082i	$-0.366304\pi$
$433$	16.9706			0.815553			0.407777	+	0.913082i	$0.366304\pi$
$434$	−1.53553	−	0.210133i	−0.0737080	−	0.0100867i
$435$	−23.4350	−	23.4350i	−1.12362	−	1.12362i
$436$	9.56869	−	35.7108i	0.458257	−	1.71024i
$437$	0.177625	+	0.662907i	0.00849697	+	0.0317111i
$438$	5.46410	−	1.46410i	0.261085	−	0.0699575i
$439$	−3.94591	+	2.27817i	−0.188328	+	0.108731i	−0.591200	−	0.806525i	$-0.701345\pi$
$439$	−3.94591	+	2.27817i	−0.188328	+	0.108731i	0.402871	+	0.915257i	$0.368012\pi$
$440$	26.1421			1.24628
$441$	−6.77962	+	1.74264i	−0.322839	+	0.0829829i
$442$	23.3137	−	23.3137i	1.10892	−	1.10892i
$443$	11.9912	+	3.21303i	0.569720	+	0.152656i	0.532168	−	0.846639i	$-0.321377\pi$
$443$	11.9912	+	3.21303i	0.569720	+	0.152656i	0.0375516	+	0.999295i	$0.488044\pi$
$444$	2.82843	−	4.89898i	0.134231	−	0.232495i
$445$	−57.5270	+	15.4143i	−2.72704	+	0.730709i
$446$	12.9288	−	7.46447i	0.612198	−	0.353453i
$447$	9.17157			0.433801
$448$	−2.86976	+	20.9706i	−0.135583	+	0.990766i
$449$	−1.75736			−0.0829349			−0.0414675	−	0.999140i	$-0.513203\pi$
$449$	−1.75736			−0.0829349			−0.0414675	+	0.999140i	$0.513203\pi$
$450$	−11.8272	+	6.82843i	−0.557539	+	0.321895i
$451$	7.96178	−	2.13335i	0.374906	−	0.100456i
$452$	−15.8995	+	27.5387i	−0.747849	+	1.29531i
$453$	11.9912	+	3.21303i	0.563396	+	0.150962i
$454$	19.2426	−	19.2426i	0.903102	−	0.903102i
$455$	−32.0174	+	13.0711i	−1.50100	+	0.612781i
$456$	8.00000			0.374634
$457$	−20.4619	+	11.8137i	−0.957169	+	0.552622i	−0.895301	−	0.445462i	$-0.853039\pi$
$457$	−20.4619	+	11.8137i	−0.957169	+	0.552622i	−0.0618687	+	0.998084i	$0.519706\pi$
$458$	16.9179	−	4.53314i	0.790522	−	0.211820i
$459$	1.76733	+	6.59575i	0.0824918	+	0.307863i
$460$	0.480851	−	1.79456i	0.0224198	−	0.0836718i
$461$	8.00000	+	8.00000i	0.372597	+	0.372597i	0.868422	−	0.495825i	$-0.165134\pi$
$461$	8.00000	+	8.00000i	0.372597	+	0.372597i	−0.495825	+	0.868422i	$0.665134\pi$
$462$	−5.53553	+	7.13834i	−0.257536	+	0.332105i
$463$	35.7990			1.66372			0.831860	−	0.554985i	$-0.187276\pi$
$463$	35.7990			1.66372			0.831860	+	0.554985i	$0.187276\pi$
$464$	8.96224	−	33.4475i	0.416061	−	1.55276i
$465$	0.792893	−	1.37333i	0.0367695	−	0.0636867i
$466$	7.65685	−	13.2621i	0.354697	−	0.614353i
$467$	−4.69553	+	17.5240i	−0.217283	+	0.810912i	0.768067	+	0.640369i	$0.221219\pi$
$467$	−4.69553	+	17.5240i	−0.217283	+	0.810912i	−0.985350	+	0.170543i	$0.945448\pi$
$468$	−4.82843	+	4.82843i	−0.223194	+	0.223194i
$469$	3.09170	+	24.4470i	0.142761	+	1.12886i
$470$	8.58579	+	8.58579i	0.396033	+	0.396033i
$471$	11.2328	−	6.48528i	0.517582	−	0.298826i
$472$	−32.9788	+	8.83663i	−1.51797	+	0.406739i
$473$	−21.9223	−	12.6569i	−1.00799	−	0.581963i
$474$	−3.76662	−	1.00926i	−0.173007	−	0.0463570i
$475$	−19.3137	+	19.3137i	−0.886174	+	0.886174i
$476$	−33.4523	+	13.6569i	−1.53328	+	0.625961i
$477$	1.87868	+	1.87868i	0.0860188	+	0.0860188i
$478$	3.76127	−	2.17157i	0.172037	−	0.0993254i
$479$	10.4142	−	18.0379i	0.475838	−	0.824175i	−0.523779	−	0.851854i	$-0.675478\pi$
$479$	10.4142	−	18.0379i	0.475838	−	0.824175i	0.999617	+	0.0276792i	$0.00881168\pi$
$480$	−18.7554	−	10.8284i	−0.856062	−	0.494248i
$481$	4.82843	+	8.36308i	0.220157	+	0.381324i
$482$			7.27208i			0.331234i
$483$	0.388201	+	0.511294i	0.0176638	+	0.0232647i
$484$		−	10.3431i		−	0.470143i
$485$	−52.9318	−	14.1830i	−2.40351	−	0.644018i
$486$	−0.366025	−	1.36603i	−0.0166032	−	0.0619642i
$487$	−26.4626	−	15.2782i	−1.19913	−	0.692320i	−0.238772	−	0.971076i	$-0.576745\pi$
$487$	−26.4626	−	15.2782i	−1.19913	−	0.692320i	−0.960362	+	0.278756i	$0.910078\pi$
$488$	−7.06450	−	1.89293i	−0.319795	−	0.0856888i
$489$		−	16.2426i		−	0.734518i
$490$	37.8975	+	0.386750i	1.71204	+	0.0174716i
$491$	6.05025	−	6.05025i	0.273044	−	0.273044i	−0.557280	−	0.830324i	$-0.688155\pi$
$491$	6.05025	−	6.05025i	0.273044	−	0.273044i	0.830324	+	0.557280i	$0.188155\pi$
$492$	−6.59575	−	1.76733i	−0.297360	−	0.0796773i
$493$	57.0985	−	15.2995i	2.57159	−	0.689054i
$494$	−6.82843	+	11.8272i	−0.307225	+	0.532130i
$495$	−4.62132	−	8.00436i	−0.207713	−	0.359769i
$496$	1.65685			0.0743950
$497$	−10.2218	−	1.39882i	−0.458512	−	0.0627459i
$498$	13.5563			0.607475
$499$	−6.18564	+	23.0851i	−0.276907	+	1.03343i	0.677645	+	0.735389i	$0.263001\pi$
$499$	−6.18564	+	23.0851i	−0.276907	+	1.03343i	−0.954552	+	0.298043i	$0.903666\pi$
$500$	34.4419	−	9.22867i	1.54029	−	0.412719i
$501$	−1.55291	−	5.79555i	−0.0693791	−	0.258926i
$502$	7.22092	−	26.9488i	0.322285	−	1.20279i
$503$		−	23.5147i		−	1.04847i	−0.851574	−	0.524235i	$-0.824351\pi$
$503$		−	23.5147i		−	1.04847i	0.851574	−	0.524235i	$-0.175649\pi$
$504$	6.92820	−	2.82843i	0.308607	−	0.125988i
$505$			14.0000i			0.622992i
$506$	0.800199	+	0.214413i	0.0355732	+	0.00953181i
$507$	0.347632	+	1.29738i	0.0154389	+	0.0576186i
$508$	2.75736	−	4.77589i	0.122338	−	0.211896i
$509$	5.04316	−	18.8213i	0.223534	−	0.834241i	−0.759452	−	0.650563i	$-0.774533\pi$
$509$	5.04316	−	18.8213i	0.223534	−	0.834241i	0.982986	−	0.183678i	$-0.0588004\pi$
$510$		−	36.9706i		−	1.63708i
$511$	6.48528	−	8.36308i	0.286892	−	0.369961i
$512$		−	22.6274i		−	1.00000i
$513$	−1.41421	−	2.44949i	−0.0624391	−	0.108148i
$514$	−14.3998	−	8.31371i	−0.635146	−	0.366702i
$515$	23.4568	−	6.28523i	1.03363	−	0.276960i
$516$	10.4853	+	18.1610i	0.461589	+	0.799495i
$517$	−3.82843	+	3.82843i	−0.168374	+	0.168374i
$518$	−1.32780	−	10.4994i	−0.0583404	−	0.461316i
$519$			16.9706i			0.744925i
$520$	32.0174	−	18.4853i	1.40406	−	0.810633i
$521$	−10.0951	−	5.82843i	−0.442276	−	0.255348i	0.262287	−	0.964990i	$-0.415523\pi$
$521$	−10.0951	−	5.82843i	−0.442276	−	0.255348i	−0.704562	+	0.709642i	$0.748857\pi$
$522$	−11.8255	+	3.16863i	−0.517587	+	0.138687i
$523$	26.6174	+	7.13211i	1.16390	+	0.311865i	0.788521	−	0.615007i	$-0.210847\pi$
$523$	26.6174	+	7.13211i	1.16390	+	0.311865i	0.375376	+	0.926873i	$0.377514\pi$
$524$	27.8995	+	27.8995i	1.21880	+	1.21880i
$525$	−9.89774	+	23.5546i	−0.431973	+	1.02801i
$526$	−26.1421			−1.13985
$527$	1.41421	+	2.44949i	0.0616041	+	0.106701i
$528$	4.82843	−	8.36308i	0.210130	−	0.363956i
$529$	−11.4706	+	19.8676i	−0.498720	+	0.863809i
$530$	−7.19239	−	12.4576i	−0.312417	−	0.541123i
$531$	8.53553	+	8.53553i	0.370411	+	0.370411i
$532$	11.9202	−	9.05040i	0.516804	−	0.392385i
$533$	8.24264	−	8.24264i	0.357028	−	0.357028i
$534$	−5.69402	+	21.2504i	−0.246404	+	0.919593i
$535$	6.39540	+	3.69239i	0.276497	+	0.159636i
$536$	−6.81811	−	25.4455i	−0.294497	−	1.09908i
$537$	−23.0600	+	13.3137i	−0.995113	+	0.574529i
$538$	29.1421	−	29.1421i	1.25641	−	1.25641i
$539$	−0.172453	+	16.8986i	−0.00742807	+	0.727875i
$540$			7.65685i			0.329499i
$541$	−1.12409	+	4.19516i	−0.0483284	+	0.180364i	−0.985871	−	0.167507i	$-0.946428\pi$
$541$	−1.12409	+	4.19516i	−0.0483284	+	0.180364i	0.937543	+	0.347870i	$0.113095\pi$
$542$	0.333226	+	0.192388i	0.0143133	+	0.00826378i
$543$	−6.87868	+	11.9142i	−0.295192	+	0.511288i
$544$	33.4523	−	19.3137i	1.43426	−	0.828068i
$545$	70.7696			3.03143
$546$	−1.73205	+	12.6569i	−0.0741249	+	0.541663i
$547$	−3.17157	−	3.17157i	−0.135607	−	0.135607i	0.636045	−	0.771652i	$-0.280569\pi$
$547$	−3.17157	−	3.17157i	−0.135607	−	0.135607i	−0.771652	+	0.636045i	$0.780569\pi$
$548$	−12.4215	+	7.17157i	−0.530621	+	0.306354i
$549$	0.669251	+	2.49768i	0.0285629	+	0.106598i
$550$	8.53341	+	31.8471i	0.363866	+	1.35797i
$551$	−21.2049	+	12.2426i	−0.903358	+	0.521554i
$552$	−0.485281	−	0.485281i	−0.0206549	−	0.0206549i
$553$	−6.75412	+	2.75736i	−0.287215	+	0.117255i
$554$	−21.6569	−	21.6569i	−0.920112	−	0.920112i
$555$	10.4595	+	2.80260i	0.443979	+	0.118964i
$556$	5.05078	+	18.8498i	0.214201	+	0.799408i
$557$	−9.63082	+	2.58057i	−0.408071	+	0.109342i	−0.457015	−	0.889459i	$-0.651081\pi$
$557$	−9.63082	+	2.58057i	−0.408071	+	0.109342i	0.0489434	+	0.998802i	$0.484415\pi$
$558$	−0.292893	−	0.507306i	−0.0123992	−	0.0214760i
$559$	−35.7990			−1.51414
$560$	−40.1961	+	5.08340i	−1.69860	+	0.214813i
$561$	16.4853			0.696009
$562$	−0.585786	−	1.01461i	−0.0247099	−	0.0427988i
$563$	−19.3872	+	5.19477i	−0.817071	+	0.218934i	−0.643066	−	0.765811i	$-0.722338\pi$
$563$	−19.3872	+	5.19477i	−0.817071	+	0.218934i	−0.174006	+	0.984745i	$0.555671\pi$
$564$	4.33245	−	1.16088i	0.182429	−	0.0488817i
$565$	−58.7960	−	15.7543i	−2.47356	−	0.662790i
$566$	−27.4558	−	27.4558i	−1.15406	−	1.15406i
$567$	−2.09077	−	1.62132i	−0.0878041	−	0.0680891i
$568$	11.0294			0.462785
$569$	−5.91359	+	3.41421i	−0.247911	+	0.143131i	−0.618807	−	0.785543i	$-0.712384\pi$
$569$	−5.91359	+	3.41421i	−0.247911	+	0.143131i	0.370897	+	0.928674i	$0.379050\pi$
$570$	3.96348	+	14.7919i	0.166012	+	0.619565i
$571$	1.56369	+	5.83577i	0.0654384	+	0.244219i	0.990896	−	0.134633i	$-0.0429855\pi$
$571$	1.56369	+	5.83577i	0.0654384	+	0.244219i	−0.925457	+	0.378852i	$0.876319\pi$
$572$	8.24264	+	14.2767i	0.344642	+	0.596938i
$573$	−2.34315	−	2.34315i	−0.0978863	−	0.0978863i
$574$	−11.8272	+	4.82843i	−0.493657	+	0.201535i
$575$	2.34315			0.0977159
$576$	−6.92820	+	4.00000i	−0.288675	+	0.166667i
$577$	−10.2574	+	17.7663i	−0.427019	+	0.739619i	−0.996607	−	0.0823115i	$-0.973770\pi$
$577$	−10.2574	+	17.7663i	−0.427019	+	0.739619i	0.569587	+	0.821931i	$0.307103\pi$
$578$	36.2860	+	20.9497i	1.50930	+	0.871395i
$579$	−1.81173	+	6.76148i	−0.0752931	+	0.280998i
$580$	66.2843			2.75230
$581$	20.1992	−	15.3363i	0.838005	−	0.636257i
$582$	−14.3137	+	14.3137i	−0.593322	+	0.593322i
$583$	5.55487	−	3.20711i	0.230059	−	0.132825i
$584$	−5.65685	+	9.79796i	−0.234082	+	0.405442i
$585$	−11.3199	−	6.53553i	−0.468019	−	0.270211i
$586$	0.543651	−	2.02893i	0.0224580	−	0.0838144i
$587$	2.87868	−	2.87868i	0.118816	−	0.118816i	−0.645199	−	0.764015i	$-0.723225\pi$
$587$	2.87868	−	2.87868i	0.118816	−	0.118816i	0.764015	+	0.645199i	$0.223225\pi$
$588$	7.12336	−	12.0523i	0.293762	−	0.497028i
$589$	−0.828427	−	0.828427i	−0.0341347	−	0.0341347i
$590$	−32.6777	−	56.5994i	−1.34532	−	2.33016i
$591$	−6.24264	+	10.8126i	−0.256788	+	0.444770i
$592$	2.92820	+	10.9282i	0.120348	+	0.449146i
$593$	−8.29289	−	14.3637i	−0.340548	−	0.589847i	0.643986	−	0.765037i	$-0.277279\pi$
$593$	−8.29289	−	14.3637i	−0.340548	−	0.589847i	−0.984535	+	0.175190i	$0.943946\pi$
$594$	−3.41421			−0.140087
$595$	−41.8248	−	55.0869i	−1.71465	−	2.25834i
$596$	−12.9706	+	12.9706i	−0.531295	+	0.531295i
$597$	−12.7228	−	3.40905i	−0.520708	−	0.139523i
$598$	1.13165	−	0.303225i	0.0462767	−	0.0123998i
$599$	−16.1828	−	9.34315i	−0.661211	−	0.381751i	0.131527	−	0.991313i	$-0.458012\pi$
$599$	−16.1828	−	9.34315i	−0.661211	−	0.381751i	−0.792738	+	0.609562i	$0.791345\pi$
$600$	7.06931	−	26.3830i	0.288603	−	1.07708i
$601$		−	3.34315i		−	0.136370i	−0.997673	−	0.0681849i	$-0.978279\pi$
$601$		−	3.34315i		−	0.136370i	0.997673	−	0.0681849i	$-0.0217208\pi$
$602$	36.1689	+	15.1983i	1.47413	+	0.619437i
$603$	−6.58579	+	6.58579i	−0.268194	+	0.268194i
$604$	−21.5020	+	12.4142i	−0.874906	+	0.505127i
$605$	19.1244	−	5.12436i	0.777516	−	0.208335i
$606$	4.47871	+	2.58579i	0.181935	+	0.105040i
$607$	−7.96447	−	13.7949i	−0.323268	−	0.559916i	0.657893	−	0.753112i	$-0.271448\pi$
$607$	−7.96447	−	13.7949i	−0.323268	−	0.559916i	−0.981160	+	0.193196i	$0.938115\pi$
$608$	−11.3137	+	11.3137i	−0.458831	+	0.458831i
$609$	−14.0355	+	18.0995i	−0.568749	+	0.733428i
$610$		−	14.0000i		−	0.566843i
$611$	−1.98174	+	7.39595i	−0.0801726	+	0.299208i
$612$	−11.8272	−	6.82843i	−0.478086	−	0.276023i
$613$	−6.06004	−	22.6164i	−0.244763	−	0.913468i	−0.973502	−	0.228677i	$-0.926560\pi$
$613$	−6.06004	−	22.6164i	−0.244763	−	0.913468i	0.728740	−	0.684791i	$-0.240106\pi$
$614$	31.5157	+	8.44460i	1.27187	+	0.340796i
$615$		−	13.0711i		−	0.527076i
$616$	−2.26670	−	17.9236i	−0.0913281	−	0.722161i
$617$			32.2426i			1.29804i	0.760771	+	0.649020i	$0.224821\pi$
$617$			32.2426i			1.29804i	−0.760771	+	0.649020i	$0.775179\pi$
$618$	2.32175	−	8.66490i	0.0933946	−	0.348553i
$619$	−6.43684	−	24.0226i	−0.258719	−	0.965551i	−0.965984	−	0.258603i	$-0.916738\pi$
$619$	−6.43684	−	24.0226i	−0.258719	−	0.965551i	0.707265	−	0.706948i	$-0.249929\pi$
$620$	0.820863	+	3.06350i	0.0329667	+	0.123033i
$621$	−0.0628000	+	0.234373i	−0.00252008	+	0.00940506i
$622$	−27.6569			−1.10894
$623$	15.5563	+	38.1051i	0.623252	+	1.52665i
$624$		−	13.6569i		−	0.546712i
$625$	9.98528	+	17.2950i	0.399411	+	0.691801i
$626$	2.94975	−	5.10911i	0.117896	−	0.204201i
$627$	−6.59575	+	1.76733i	−0.263409	+	0.0705802i
$628$	−6.71406	+	25.0572i	−0.267920	+	0.999891i
$629$	−13.6569	+	13.6569i	−0.544534	+	0.544534i
$630$	8.66220	+	11.4089i	0.345110	+	0.454540i
$631$		−	8.75736i		−	0.348625i	−0.984690	−	0.174312i	$-0.944230\pi$
$631$		−	8.75736i		−	0.348625i	0.984690	−	0.174312i	$-0.0557703\pi$
$632$	6.75412	−	3.89949i	0.268665	−	0.155114i
$633$	6.84116	+	3.94975i	0.271912	+	0.156988i
$634$	8.29298	+	30.9498i	0.329356	+	1.22918i
$635$	10.1967	+	2.73218i	0.404642	+	0.108423i
$636$	−5.31371			−0.210702
$637$	11.7379	+	20.8184i	0.465073	+	0.824856i
$638$			29.5563i			1.17015i
$639$	−1.94975	−	3.37706i	−0.0771308	−	0.133594i
$640$	41.8378	−	11.2104i	1.65379	−	0.443130i
$641$	20.2635	−	35.0973i	0.800358	−	1.38626i	−0.119022	−	0.992892i	$-0.537976\pi$
$641$	20.2635	−	35.0973i	0.800358	−	1.38626i	0.919380	−	0.393370i	$-0.128691\pi$
$642$	2.36245	−	1.36396i	0.0932385	−	0.0538312i
$643$	16.9289	+	16.9289i	0.667612	+	0.667612i	0.957163	−	0.289551i	$-0.0935059\pi$
$643$	16.9289	+	16.9289i	0.667612	+	0.667612i	−0.289551	+	0.957163i	$0.593506\pi$
$644$	−1.27208	−	0.174080i	−0.0501269	−	0.00685971i
$645$	−28.3848	+	28.3848i	−1.11765	+	1.11765i
$646$	−26.3830	−	7.06931i	−1.03803	−	0.278138i
$647$	−9.88500	−	5.70711i	−0.388619	−	0.224370i	0.292942	−	0.956130i	$-0.405366\pi$
$647$	−9.88500	−	5.70711i	−0.388619	−	0.224370i	−0.681562	+	0.731761i	$0.738699\pi$
$648$	2.44949	+	1.41421i	0.0962250	+	0.0555556i
$649$	25.2378	−	14.5711i	0.990671	−	0.571964i
$650$	32.9706	+	32.9706i	1.29321	+	1.29321i
$651$	−1.01033	−	0.424546i	−0.0395980	−	0.0166393i
$652$	22.9706	+	22.9706i	0.899597	+	0.899597i
$653$	−4.52552	+	16.8895i	−0.177097	+	0.660937i	0.819087	+	0.573669i	$0.194480\pi$
$653$	−4.52552	+	16.8895i	−0.177097	+	0.660937i	−0.996185	+	0.0872679i	$0.972186\pi$
$654$	13.0711	−	22.6398i	0.511119	−	0.885284i
$655$	−37.7635	+	65.4082i	−1.47554	+	2.55571i
$656$	11.8272	−	6.82843i	0.461774	−	0.266605i
$657$	4.00000			0.156055
$658$	5.14214	−	6.63103i	0.200461	−	0.258504i
$659$	−21.4142	−	21.4142i	−0.834179	−	0.834179i	0.153906	−	0.988085i	$-0.450815\pi$
$659$	−21.4142	−	21.4142i	−0.834179	−	0.834179i	−0.988085	+	0.153906i	$0.950815\pi$
$660$	17.8554	+	4.78434i	0.695021	+	0.186230i
$661$	0.0888127	+	0.331453i	0.00345441	+	0.0128920i	0.967632	−	0.252367i	$-0.0812091\pi$
$661$	0.0888127	+	0.331453i	0.00345441	+	0.0128920i	−0.964177	+	0.265259i	$0.914542\pi$
$662$	−10.9282	+	2.92820i	−0.424737	+	0.113808i
$663$	20.1903	−	11.6569i	0.784125	−	0.452715i
$664$	−19.1716	+	19.1716i	−0.744001	+	0.744001i
$665$	22.6398	+	17.5563i	0.877932	+	0.680806i
$666$	2.82843	−	2.82843i	0.109599	−	0.109599i
$667$	2.02893	+	0.543651i	0.0785606	+	0.0210502i
$668$	10.3923	+	6.00000i	0.402090	+	0.232147i
$669$	10.1967	−	2.73218i	0.394225	−	0.105632i
$670$	43.6705	−	25.2132i	1.68714	−	0.974071i
$671$	6.24264			0.240994
$672$	−5.79796	+	13.7980i	−0.223661	+	0.532268i
$673$	36.9411			1.42398			0.711988	−	0.702192i	$-0.247795\pi$
$673$	36.9411			1.42398			0.711988	+	0.702192i	$0.247795\pi$
$674$	8.99348	−	5.19239i	0.346416	−	0.200003i
$675$	−9.32780	+	2.49938i	−0.359027	+	0.0962011i
$676$	−2.32640	−	1.34315i	−0.0894768	−	0.0516595i
$677$	30.2752	+	8.11220i	1.16357	+	0.311777i	0.788390	−	0.615175i	$-0.210915\pi$
$677$	30.2752	+	8.11220i	1.16357	+	0.311777i	0.375178	+	0.926953i	$0.377581\pi$
$678$	−15.8995	+	15.8995i	−0.610616	+	0.610616i
$679$	−5.13461	+	37.5208i	−0.197048	+	1.43992i
$680$	52.2843	+	52.2843i	2.00501	+	2.00501i
$681$	16.6646	−	9.62132i	0.638589	−	0.368690i
$682$	−1.36603	+	0.366025i	−0.0523078	+	0.0140158i
$683$	−3.51626	−	13.1229i	−0.134546	−	0.502132i	−0.999999	−	0.00114290i	$-0.999636\pi$
$683$	−3.51626	−	13.1229i	−0.134546	−	0.502132i	0.865453	−	0.500989i	$-0.167030\pi$
$684$	5.46410	+	1.46410i	0.208925	+	0.0559813i
$685$	−19.4142	−	19.4142i	−0.741779	−	0.741779i
$686$	−3.02082	−	26.0168i	−0.115335	−	0.993327i
$687$	12.3848			0.472509
$688$	−40.5120	−	10.8552i	−1.54451	−	0.413849i
$689$	4.53553	−	7.85578i	0.172790	−	0.299281i
$690$	0.656854	−	1.13770i	0.0250060	−	0.0433117i
$691$	3.95270	−	14.7517i	0.150368	−	0.561181i	−0.849090	−	0.528249i	$-0.822849\pi$
$691$	3.95270	−	14.7517i	0.150368	−	0.561181i	0.999458	−	0.0329321i	$-0.0104845\pi$
$692$	−24.0000	−	24.0000i	−0.912343	−	0.912343i
$693$	−5.08725	+	3.86250i	−0.193249	+	0.146724i
$694$	7.51472	+	7.51472i	0.285255	+	0.285255i
$695$	−32.3507	+	18.6777i	−1.22713	+	0.708484i
$696$	12.2426	−	21.2049i	0.464056	−	0.803769i
$697$	20.1903	+	11.6569i	0.764761	+	0.441535i
$698$	1.13165	+	0.303225i	0.0428337	+	0.0114772i
$699$	7.65685	−	7.65685i	0.289609	−	0.289609i
$700$	−19.3137	−	47.3087i	−0.729990	−	1.78810i
$701$	−20.1213	−	20.1213i	−0.759972	−	0.759972i	0.216345	−	0.976317i	$-0.430586\pi$
$701$	−20.1213	−	20.1213i	−0.759972	−	0.759972i	−0.976317	+	0.216345i	$0.930586\pi$
$702$	−4.18154	+	2.41421i	−0.157822	+	0.0911186i
$703$	4.00000	−	6.92820i	0.150863	−	0.261302i
$704$	4.99876	+	18.6556i	0.188398	+	0.703110i
$705$	4.29289	+	7.43551i	0.161680	+	0.280037i
$706$			4.68629i			0.176371i
$707$	9.59867	−	1.21390i	0.360995	−	0.0456533i
$708$	−24.1421			−0.907317
$709$	−13.4259	−	3.59745i	−0.504220	−	0.135105i	−0.00226194	−	0.999997i	$-0.500720\pi$
$709$	−13.4259	−	3.59745i	−0.504220	−	0.135105i	−0.501958	+	0.864892i	$0.667387\pi$
$710$	5.46437	+	20.3933i	0.205074	+	0.765347i
$711$	−2.38794	−	1.37868i	−0.0895549	−	0.0517045i
$712$	−22.0000	−	38.1051i	−0.824485	−	1.42805i
$713$			0.100505i			0.00376394i
$714$	−25.3477	+	3.20560i	−0.948615	+	0.119967i
$715$	−22.3137	+	22.3137i	−0.834485	+	0.834485i
$716$	13.7834	−	51.4402i	0.515109	−	1.92241i
$717$	2.96642	−	0.794851i	0.110783	−	0.0296842i
$718$	−5.41421	+	9.37769i	−0.202057	+	0.349972i
$719$	−16.4350	−	28.4663i	−0.612923	−	1.06161i	−0.990745	−	0.135736i	$-0.956660\pi$
$719$	−16.4350	−	28.4663i	−0.612923	−	1.06161i	0.377822	−	0.925878i	$-0.376673\pi$
$720$	−10.8284	−	10.8284i	−0.403552	−	0.403552i
$721$	−6.34315	−	15.5375i	−0.236231	−	0.578646i
$722$	−15.5563			−0.578947
$723$	−1.33088	+	4.96692i	−0.0494961	+	0.184722i
$724$	−7.12133	−	26.5772i	−0.264662	−	0.987733i
$725$	21.6367	+	80.7494i	0.803569	+	2.99896i
$726$	1.89293	−	7.06450i	0.0702531	−	0.262188i
$727$			14.5563i			0.539865i	0.962879	+	0.269933i	$0.0870014\pi$
$727$			14.5563i			0.539865i	−0.962879	+	0.269933i	$0.912999\pi$
$728$	−15.4500	−	20.3490i	−0.572615	−	0.754184i
$729$		−	1.00000i		−	0.0370370i
$730$	−20.9189	−	5.60521i	−0.774244	−	0.207458i
$731$	−18.5309	−	69.1583i	−0.685391	−	2.55791i
$732$	−4.47871	−	2.58579i	−0.165538	−	0.0955734i
$733$	−10.8704	+	40.5689i	−0.401507	+	1.49845i	0.408900	+	0.912579i	$0.365912\pi$
$733$	−10.8704	+	40.5689i	−0.401507	+	1.49845i	−0.810407	+	0.585867i	$0.800754\pi$
$734$			35.8995i			1.32507i
$735$	25.8137	+	7.19988i	0.952153	+	0.265572i
$736$	1.37258			0.0505941
$737$	11.2426	+	19.4728i	0.414128	+	0.717291i
$738$	−4.18154	−	2.41421i	−0.153925	−	0.0888684i
$739$	−12.8198	+	3.43507i	−0.471586	+	0.126361i	−0.486782	−	0.873524i	$-0.661829\pi$
$739$	−12.8198	+	3.43507i	−0.471586	+	0.126361i	0.0151963	+	0.999885i	$0.495163\pi$
$740$	−18.7554	+	10.8284i	−0.689462	+	0.398061i
$741$	−6.82843	+	6.82843i	−0.250849	+	0.250849i
$742$	−7.91753	+	6.01140i	−0.290662	+	0.220685i
$743$		−	5.31371i		−	0.194941i	−0.995238	−	0.0974705i	$-0.968925\pi$
$743$		−	5.31371i		−	0.194941i	0.995238	−	0.0974705i	$-0.0310752\pi$
$744$	1.13165	+	0.303225i	0.0414884	+	0.0111168i
$745$	−30.4085	−	17.5563i	−1.11408	−	0.643215i
$746$	−0.137292	+	0.0367874i	−0.00502663	+	0.00134688i
$747$	9.25916	+	2.48098i	0.338775	+	0.0907745i
$748$	−23.3137	+	23.3137i	−0.852434	+	0.852434i
$749$	1.97705	−	4.70497i	0.0722397	−	0.171916i
$750$	25.2132			0.920656
$751$	−15.0355	−	26.0423i	−0.548654	−	0.950297i	−0.998367	−	0.0571241i	$-0.981807\pi$
$751$	−15.0355	−	26.0423i	−0.548654	−	0.950297i	0.449713	−	0.893173i	$-0.351526\pi$
$752$	−4.48528	+	7.76874i	−0.163561	+	0.283297i
$753$	9.86396	−	17.0849i	0.359463	−	0.622608i
$754$	20.8995	+	36.1990i	0.761115	+	1.31829i
$755$	−33.6066	−	33.6066i	−1.22307	−	1.22307i
$756$	5.24969	−	0.663902i	0.190929	−	0.0241459i
$757$	12.3137	−	12.3137i	0.447549	−	0.447549i	−0.446990	−	0.894539i	$-0.647504\pi$
$757$	12.3137	−	12.3137i	0.447549	−	0.447549i	0.894539	+	0.446990i	$0.147504\pi$
$758$	−3.44584	+	12.8601i	−0.125159	+	0.467098i
$759$	0.507306	+	0.292893i	0.0184140	+	0.0106314i
$760$	−26.5241	−	15.3137i	−0.962131	−	0.555487i
$761$	−30.9158	+	17.8492i	−1.12070	+	0.647035i	−0.941579	−	0.336793i	$-0.890658\pi$
$761$	−30.9158	+	17.8492i	−1.12070	+	0.647035i	−0.179118	+	0.983828i	$0.557324\pi$
$762$	2.75736	−	2.75736i	0.0998886	−	0.0998886i
$763$	−6.13621	−	48.5210i	−0.222146	−	1.75658i
$764$	6.62742			0.239772
$765$	6.76608	−	25.2514i	0.244628	−	0.912965i
$766$	−18.2841	−	10.5563i	−0.660633	−	0.381416i
$767$	20.6066	−	35.6917i	0.744061	−	1.28875i
$768$	4.14110	−	15.4548i	0.149429	−	0.557678i
$769$	14.1716			0.511040			0.255520	−	0.966804i	$-0.417753\pi$
$769$	14.1716			0.511040			0.255520	+	0.966804i	$0.417753\pi$
$770$	32.0174	−	13.0711i	1.15383	−	0.471049i
$771$	−8.31371	−	8.31371i	−0.299411	−	0.299411i
$772$	−7.00000	−	12.1244i	−0.251936	−	0.436365i
$773$	6.76608	+	25.2514i	0.243359	+	0.908228i	0.974201	+	0.225682i	$0.0724610\pi$
$773$	6.76608	+	25.2514i	0.243359	+	0.908228i	−0.730842	+	0.682547i	$0.760872\pi$
$774$	3.83788	+	14.3232i	0.137950	+	0.514835i
$775$	−3.46410	+	2.00000i	−0.124434	+	0.0718421i
$776$		−	40.4853i		−	1.45334i
$777$	1.01461	−	7.41421i	0.0363990	−	0.265983i
$778$	−35.7990	−	35.7990i	−1.28346	−	1.28346i
$779$	−9.32780	−	2.49938i	−0.334203	−	0.0895495i
$780$	25.2514	−	6.76608i	0.904144	−	0.242265i
$781$	−9.09343	+	2.43658i	−0.325389	+	0.0871876i
$782$	1.17157	+	2.02922i	0.0418954	+	0.0725649i
$783$	−8.65685			−0.309371
$784$	6.97056	+	27.1185i	0.248949	+	0.968517i
$785$	−49.6569			−1.77233
$786$	13.9497	+	24.1617i	0.497571	+	0.861818i
$787$	−49.7427	+	13.3285i	−1.77314	+	0.475111i	−0.989305	−	0.145862i	$-0.953404\pi$
$787$	−49.7427	+	13.3285i	−1.77314	+	0.475111i	−0.783832	+	0.620973i	$0.786738\pi$
$788$	−6.46286	−	24.1197i	−0.230230	−	0.859229i
$789$	−17.8554	−	4.78434i	−0.635669	−	0.170327i
$790$	10.5563	+	10.5563i	0.375578	+	0.375578i
$791$	−5.70346	+	41.6777i	−0.202792	+	1.48189i
$792$	4.82843	−	4.82843i	0.171571	−	0.171571i
$793$	7.64564	−	4.41421i	0.271505	−	0.156753i
$794$	−0.355251	−	1.32581i	−0.0126074	−	0.0470514i
$795$	−2.63260	−	9.82498i	−0.0933686	−	0.348456i
$796$	22.8138	−	13.1716i	0.808615	−	0.466854i
$797$	−2.26346	−	2.26346i	−0.0801757	−	0.0801757i	0.665882	−	0.746057i	$-0.268056\pi$
$797$	−2.26346	−	2.26346i	−0.0801757	−	0.0801757i	−0.746057	+	0.665882i	$0.768056\pi$
$798$	9.79796	−	4.00000i	0.346844	−	0.141598i
$799$	−15.3137			−0.541760
$800$	27.3137	+	47.3087i	0.965685	+	1.67262i
$801$	−7.77817	+	13.4722i	−0.274828	+	0.476017i
$802$	−29.3939	−	16.9706i	−1.03793	−	0.599251i
$803$	2.49938	−	9.32780i	0.0882011	−	0.329171i
$804$		−	18.6274i		−	0.656938i
$805$	−0.308360	−	2.43830i	−0.0108683	−	0.0859389i
$806$	−1.41421	+	1.41421i	−0.0498135	+	0.0498135i
$807$	25.2378	−	14.5711i	0.888414	−	0.512926i
$808$	−9.99071	+	2.67700i	−0.351472	+	0.0941766i
$809$	15.2913	+	8.82843i	0.537613	+	0.310391i	0.744111	−	0.668056i	$-0.232873\pi$
$809$	15.2913	+	8.82843i	0.537613	+	0.310391i	−0.206498	+	0.978447i	$0.566207\pi$
$810$	−1.40130	+	5.22973i	−0.0492367	+	0.183754i
$811$	15.5563	−	15.5563i	0.546257	−	0.546257i	−0.379099	−	0.925356i	$-0.623766\pi$
$811$	15.5563	−	15.5563i	0.546257	−	0.546257i	0.925356	+	0.379099i	$0.123766\pi$
$812$	−5.74731	−	45.4458i	−0.201691	−	1.59483i
$813$	0.192388	+	0.192388i	0.00674735	+	0.00674735i
$814$	−4.82843	−	8.36308i	−0.169236	−	0.293126i
$815$	−31.0919	+	53.8527i	−1.08910	+	1.88638i
$816$	26.3830	−	7.06931i	0.923590	−	0.247475i
$817$	14.8284	+	25.6836i	0.518781	+	0.898555i
$818$	−46.1838			−1.61478
$819$	−3.49938	+	8.32780i	−0.122278	+	0.290997i
$820$	18.4853	+	18.4853i	0.645534	+	0.645534i
$821$	−4.82963	−	1.29410i	−0.168555	−	0.0451642i	0.173554	−	0.984824i	$-0.444475\pi$
$821$	−4.82963	−	1.29410i	−0.168555	−	0.0451642i	−0.342110	+	0.939660i	$0.611141\pi$
$822$	−9.79655	+	2.62498i	−0.341694	+	0.0915566i
$823$	−15.8856	−	9.17157i	−0.553738	−	0.319701i	0.196890	−	0.980426i	$-0.436916\pi$
$823$	−15.8856	−	9.17157i	−0.553738	−	0.319701i	−0.750628	+	0.660725i	$0.770249\pi$
$824$	8.97056	+	15.5375i	0.312504	+	0.541273i
$825$			23.3137i			0.811679i
$826$	−35.9723	+	27.3120i	−1.25164	+	0.950306i
$827$	−29.9497	+	29.9497i	−1.04145	+	1.04145i	−0.0423520	+	0.999103i	$0.513485\pi$
$827$	−29.9497	+	29.9497i	−1.04145	+	1.04145i	−0.999103	+	0.0423520i	$0.986515\pi$
$828$	−0.242641	−	0.420266i	−0.00843235	−	0.0146053i
$829$	40.7062	−	10.9072i	1.41378	−	0.378822i	0.530510	−	0.847679i	$-0.322001\pi$
$829$	40.7062	−	10.9072i	1.41378	−	0.378822i	0.883274	+	0.468857i	$0.155334\pi$
$830$	−44.9463	−	25.9497i	−1.56011	−	0.900729i
$831$	−10.8284	−	18.7554i	−0.375634	−	0.650617i
$832$	19.3137	+	19.3137i	0.669582	+	0.669582i
$833$	−34.1421	+	33.4523i	−1.18295	+	1.15905i
$834$			13.7990i			0.477820i
$835$	−5.94522	+	22.1879i	−0.205743	+	0.767843i
$836$	6.82843	−	11.8272i	0.236166	−	0.409052i
$837$	−0.107206	−	0.400100i	−0.00370559	−	0.0138295i
$838$	26.6576	+	7.14288i	0.920872	+	0.246747i
$839$			19.7990i			0.683537i	0.939784	+	0.341769i	$0.111026\pi$
$839$			19.7990i			0.683537i	−0.939784	+	0.341769i	$0.888974\pi$
$840$	−28.3848	−	3.88437i	−0.979368	−	0.134023i
$841$			45.9411i			1.58418i
$842$	0.768838	−	2.86934i	0.0264959	−	0.0988841i
$843$	−0.214413	−	0.800199i	−0.00738477	−	0.0275603i
$844$	−15.2607	+	4.08908i	−0.525293	+	0.140752i
$845$	1.33088	−	4.96692i	0.0457838	−	0.170867i
$846$	3.17157			0.109041
$847$	−5.17157	−	12.6677i	−0.177697	−	0.435268i
$848$	7.51472	−	7.51472i	0.258056	−	0.258056i
$849$	−13.7279	−	23.7775i	−0.471141	−	0.816040i
$850$	−46.6274	+	80.7611i	−1.59931	+	2.77008i
$851$	−0.662907	+	0.177625i	−0.0227241	+	0.00608892i
$852$	7.53325	+	2.01853i	0.258085	+	0.0691536i
$853$	5.07107	−	5.07107i	0.173630	−	0.173630i	−0.614942	−	0.788572i	$-0.710821\pi$
$853$	5.07107	−	5.07107i	0.173630	−	0.173630i	0.788572	+	0.614942i	$0.210821\pi$
$854$	−9.59867	+	1.21390i	−0.328460	+	0.0415387i
$855$			10.8284i			0.370324i
$856$	−1.41208	+	5.26994i	−0.0482638	+	0.180123i
$857$	6.71807	+	3.87868i	0.229485	+	0.132493i	0.610334	−	0.792144i	$-0.291035\pi$
$857$	6.71807	+	3.87868i	0.229485	+	0.132493i	−0.380850	+	0.924637i	$0.624368\pi$
$858$	3.01702	+	11.2597i	0.102999	+	0.384398i
$859$	−41.9751	−	11.2472i	−1.43217	−	0.383750i	−0.542387	−	0.840129i	$-0.682479\pi$
$859$	−41.9751	−	11.2472i	−1.43217	−	0.383750i	−0.889785	+	0.456379i	$0.849146\pi$
$860$		−	80.2843i		−	2.73767i
$861$	−8.96178	+	1.13335i	−0.305417	+	0.0386245i
$862$			31.6569i			1.07824i
$863$	18.1924	+	31.5101i	0.619276	+	1.07262i	0.989618	+	0.143722i	$0.0459072\pi$
$863$	18.1924	+	31.5101i	0.619276	+	1.07262i	−0.370342	+	0.928895i	$0.620759\pi$
$864$	−5.46410	+	1.46410i	−0.185893	+	0.0498097i
$865$	32.4853	−	56.2662i	1.10453	−	1.91311i
$866$	−20.7846	+	12.0000i	−0.706290	+	0.407777i
$867$	20.9497	+	20.9497i	0.711491	+	0.711491i
$868$	2.02922	−	0.828427i	0.0688763	−	0.0281186i
$869$	−4.70711	+	4.70711i	−0.159678	+	0.159678i
$870$	45.2730	+	12.1309i	1.53490	+	0.411275i
$871$	27.5387	+	15.8995i	0.933114	+	0.538734i
$872$	13.5322	+	50.5027i	0.458257	+	1.71024i
$873$	−12.3960	+	7.15685i	−0.419542	+	0.242223i
$874$	−0.686292	−	0.686292i	−0.0232142	−	0.0232142i
$875$	37.5682	−	28.5237i	1.27004	−	0.964277i
$876$	−5.65685	+	5.65685i	−0.191127	+	0.191127i
$877$	11.4616	−	42.7753i	0.387031	−	1.44442i	−0.447909	−	0.894079i	$-0.647831\pi$
$877$	11.4616	−	42.7753i	0.387031	−	1.44442i	0.834940	−	0.550341i	$-0.185502\pi$
$878$	3.22183	−	5.58037i	0.108731	−	0.188328i
$879$	0.742641	−	1.28629i	0.0250486	−	0.0433855i
$880$	−32.0174	+	18.4853i	−1.07931	+	0.623139i
$881$	33.5147			1.12914			0.564570	−	0.825385i	$-0.309042\pi$
$881$	33.5147			1.12914			0.564570	+	0.825385i	$0.309042\pi$
$882$	7.07107	−	6.92820i	0.238095	−	0.233285i
$883$	−19.0000	−	19.0000i	−0.639401	−	0.639401i	0.311007	−	0.950408i	$-0.399334\pi$
$883$	−19.0000	−	19.0000i	−0.639401	−	0.639401i	−0.950408	+	0.311007i	$0.899334\pi$
$884$	−12.0681	+	45.0386i	−0.405893	+	1.51481i
$885$	−11.9609	−	44.6385i	−0.402060	−	1.50051i
$886$	−16.9581	+	4.54392i	−0.569720	+	0.152656i
$887$	−12.0373	+	6.94975i	−0.404174	+	0.233350i	−0.688283	−	0.725442i	$-0.741635\pi$
$887$	−12.0373	+	6.94975i	−0.404174	+	0.233350i	0.284110	+	0.958792i	$0.408302\pi$
$888$			8.00000i			0.268462i
$889$	0.989118	−	7.22792i	0.0331740	−	0.242417i
$890$	59.5563	−	59.5563i	1.99633	−	1.99633i
$891$	−2.33195	−	0.624844i	−0.0781233	−	0.0209331i
$892$	−10.5563	+	18.2841i	−0.353453	+	0.612198i
$893$	6.12701	−	1.64173i	0.205033	−	0.0549383i
$894$	−11.2328	+	6.48528i	−0.375682	+	0.216900i
$895$	101.941			3.40752
$896$	−11.3137	−	27.7128i	−0.377964	−	0.925820i
$897$	0.828427			0.0276604
$898$	2.15232	−	1.24264i	0.0718237	−	0.0414675i
$899$	−3.46360	+	0.928070i	−0.115518	+	0.0309529i
$900$	9.65685	−	16.7262i	0.321895	−	0.557539i
$901$	17.5240	+	4.69553i	0.583808	+	0.156431i
$902$	−8.24264	+	8.24264i	−0.274450	+	0.274450i
$903$	21.9223	+	17.0000i	0.729529	+	0.565725i
$904$		−	44.9706i		−	1.49570i
$905$	45.6127	−	26.3345i	1.51622	−	0.875389i
$906$	−16.9581	+	4.54392i	−0.563396	+	0.150962i
$907$	7.30973	+	27.2803i	0.242716	+	0.905827i	0.974518	+	0.224310i	$0.0720129\pi$
$907$	7.30973	+	27.2803i	0.242716	+	0.905827i	−0.731802	+	0.681517i	$0.761320\pi$
$908$	−9.96072	+	37.1739i	−0.330558	+	1.23366i
$909$	2.58579	+	2.58579i	0.0857651	+	0.0857651i
$910$	29.9706	−	38.6485i	0.993514	−	1.28118i
$911$	−38.7279			−1.28311			−0.641557	−	0.767076i	$-0.721711\pi$
$911$	−38.7279			−1.28311			−0.641557	+	0.767076i	$0.721711\pi$
$912$	−9.79796	+	5.65685i	−0.324443	+	0.187317i
$913$	11.5711	−	20.0417i	0.382946	−	0.663283i
$914$	16.7071	−	28.9376i	0.552622	−	0.957169i
$915$	2.56218	−	9.56218i	0.0847030	−	0.316116i
$916$	−17.5147	+	17.5147i	−0.578703	+	0.578703i
$917$	48.1195	+	20.2200i	1.58905	+	0.667724i
$918$	−6.82843	−	6.82843i	−0.225372	−	0.225372i
$919$	47.3087	−	27.3137i	1.56057	−	0.900996i	0.563372	−	0.826203i	$-0.309504\pi$
$919$	47.3087	−	27.3137i	1.56057	−	0.900996i	0.997199	−	0.0747927i	$-0.0238295\pi$
$920$	0.680026	+	2.53789i	0.0224198	+	0.0836718i
$921$	19.9801	+	11.5355i	0.658368	+	0.380109i
$922$	−15.4548	−	4.14110i	−0.508977	−	0.136380i
$923$	−9.41421	+	9.41421i	−0.309873	+	0.309873i
$924$	1.73205	−	12.6569i	0.0569803	−	0.416380i
$925$	−19.3137	−	19.3137i	−0.635031	−	0.635031i
$926$	−43.8446	+	25.3137i	−1.44082	+	0.831860i
$927$	3.17157	−	5.49333i	0.104168	−	0.180424i
$928$	12.6745	+	47.3019i	0.416061	+	1.55276i
$929$	−11.8284	−	20.4874i	−0.388078	−	0.672171i	0.604113	−	0.796899i	$-0.293528\pi$
$929$	−11.8284	−	20.4874i	−0.388078	−	0.672171i	−0.992191	+	0.124728i	$0.960194\pi$
$930$			2.24264i			0.0735391i
$931$	10.0740	−	17.0445i	0.330160	−	0.558611i
$932$			21.6569i			0.709394i
$933$	−18.8900	−	5.06156i	−0.618430	−	0.165708i
$934$	−6.64048	−	24.7826i	−0.217283	−	0.810912i
$935$	−54.6572	−	31.5563i	−1.78748	−	1.03200i
$936$	2.49938	−	9.32780i	0.0816947	−	0.304889i
$937$		−	27.0000i		−	0.882052i	−0.897494	−	0.441026i	$-0.854615\pi$
$937$		−	27.0000i		−	0.882052i	0.897494	−	0.441026i	$-0.145385\pi$
$938$	−21.0732	−	27.7552i	−0.688065	−	0.906240i
$939$	2.94975	−	2.94975i	0.0962614	−	0.0962614i
$940$	−16.5865	−	4.44433i	−0.540991	−	0.144958i
$941$	−17.8838	+	4.79196i	−0.582997	+	0.156213i	−0.538251	−	0.842785i	$-0.680915\pi$
$941$	−17.8838	+	4.79196i	−0.582997	+	0.156213i	−0.0447462	+	0.998998i	$0.514248\pi$
$942$	−9.17157	+	15.8856i	−0.298826	+	0.517582i
$943$	0.414214	+	0.717439i	0.0134886	+	0.0233630i
$944$	34.1421	−	34.1421i	1.11123	−	1.11123i
$945$	3.82843	+	9.37769i	0.124539	+	0.305056i
$946$	35.7990			1.16393
$947$	11.7648	−	43.9070i	0.382306	−	1.42678i	−0.460064	−	0.887886i	$-0.652174\pi$
$947$	11.7648	−	43.9070i	0.382306	−	1.42678i	0.842370	−	0.538899i	$-0.181160\pi$
$948$	5.32681	−	1.42731i	0.173007	−	0.0463570i
$949$	−3.53465	−	13.1915i	−0.114740	−	0.428214i
$950$	9.99751	−	37.3112i	0.324362	−	1.21054i
$951$			22.6569i			0.734699i
$952$	31.3137	−	40.3805i	1.01488	−	1.30874i
$953$		−	35.2548i		−	1.14202i	−0.820944	−	0.571008i	$-0.806553\pi$
$953$		−	35.2548i		−	1.14202i	0.820944	−	0.571008i	$-0.193447\pi$
$954$	−3.62933	−	0.972476i	−0.117504	−	0.0314851i
$955$	3.28345	+	12.2540i	0.106250	+	0.396531i
$956$	−3.07107	+	5.31925i	−0.0993254	+	0.172037i
$957$	−5.40919	+	20.1874i	−0.174854	+	0.652565i
$958$			29.4558i			0.951675i
$959$	−11.6274	+	14.9941i	−0.375469	+	0.484185i
$960$	30.6274			0.988496
$961$	15.4142	+	26.6982i	0.497233	+	0.861232i
$962$	−11.8272	−	6.82843i	−0.381324	−	0.220157i
$963$	1.86321	−	0.499244i	0.0600410	−	0.0160879i
$964$	−5.14214	−	8.90644i	−0.165617	−	0.286857i
$965$	18.9497	−	18.9497i	0.610014	−	0.610014i
$966$	−0.836987	−	0.351705i	−0.0269296	−	0.0113159i
$967$		−	41.1838i		−	1.32438i	−0.749336	−	0.662190i	$-0.769627\pi$
$967$		−	41.1838i		−	1.32438i	0.749336	−	0.662190i	$-0.230373\pi$
$968$	7.31371	+	12.6677i	0.235071	+	0.407156i
$969$	−16.7262	−	9.65685i	−0.537322	−	0.310223i
$970$	74.8568	−	20.0578i	2.40351	−	0.644018i
$971$	−11.1910	−	2.99862i	−0.359137	−	0.0962304i	0.0747390	−	0.997203i	$-0.476188\pi$
$971$	−11.1910	−	2.99862i	−0.359137	−	0.0962304i	−0.433876	+	0.900973i	$0.642854\pi$
$972$	1.41421	+	1.41421i	0.0453609	+	0.0453609i
$973$	15.6108	+	20.5608i	0.500459	+	0.659148i
$974$	43.2132			1.38464
$975$	16.4853	+	28.5533i	0.527952	+	0.914439i
$976$	9.99071	−	2.67700i	0.319795	−	0.0856888i
$977$	5.34315	−	9.25460i	0.170942	−	0.296081i	−0.767807	−	0.640681i	$-0.778652\pi$
$977$	5.34315	−	9.25460i	0.170942	−	0.296081i	0.938750	+	0.344600i	$0.111985\pi$
$978$	11.4853	+	19.8931i	0.367259	+	0.636111i
$979$	26.5563	+	26.5563i	0.848745	+	0.848745i
$980$	−46.6883	+	26.3239i	−1.49140	+	0.840887i
$981$	13.0711	−	13.0711i	0.417327	−	0.417327i
$982$	−3.13184	+	11.6882i	−0.0999411	+	0.372985i
$983$	28.9376	+	16.7071i	0.922965	+	0.532874i	0.884580	−	0.466389i	$-0.154445\pi$
$983$	28.9376	+	16.7071i	0.922965	+	0.532874i	0.0383851	+	0.999263i	$0.487779\pi$
$984$	9.32780	−	2.49938i	0.297360	−	0.0796773i
$985$	41.3951	−	23.8995i	1.31896	−	0.761501i
$986$	−59.1127	+	59.1127i	−1.88253	+	1.88253i
$987$	4.72571	−	3.58800i	0.150421	−	0.114207i
$988$		−	19.3137i		−	0.614451i
$989$	0.658476	−	2.45747i	0.0209383	−	0.0781429i
$990$	11.3199	+	6.53553i	0.359769	+	0.207713i
$991$	−0.278175	+	0.481813i	−0.00883651	+	0.0153053i	−0.870410	−	0.492328i	$-0.836146\pi$
$991$	−0.278175	+	0.481813i	−0.00883651	+	0.0153053i	0.861573	+	0.507633i	$0.169479\pi$
$992$	−2.02922	+	1.17157i	−0.0644279	+	0.0371975i
$993$	−8.00000			−0.253872
$994$	13.5082	−	5.51472i	0.428456	−	0.174916i
$995$	35.6569	+	35.6569i	1.13040	+	1.13040i
$996$	−16.6031	+	9.58579i	−0.526088	+	0.303737i
$997$	−2.53617	−	9.46510i	−0.0803212	−	0.299763i	0.914066	−	0.405566i	$-0.132925\pi$
$997$	−2.53617	−	9.46510i	−0.0803212	−	0.299763i	−0.994387	+	0.105803i	$0.966259\pi$
$998$	−8.74782	−	32.6473i	−0.276907	−	1.03343i
$999$	2.44949	−	1.41421i	0.0774984	−	0.0447437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bq.a.109.1	yes	8
7.2	even	3	inner	336.2.bq.a.205.2	yes	8
16.5	even	4	inner	336.2.bq.a.277.2	yes	8
112.37	even	12	inner	336.2.bq.a.37.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bq.a.37.1	✓	8	112.37	even	12	inner
336.2.bq.a.109.1	yes	8	1.1	even	1	trivial
336.2.bq.a.205.2	yes	8	7.2	even	3	inner
336.2.bq.a.277.2	yes	8	16.5	even	4	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bq (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.00000 - 1.73205i) q^{4} +(3.69798 + 0.990870i) q^{5} +(1.00000 - 1.00000i) q^{6} +(0.358719 - 2.62132i) q^{7} +2.82843i q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.00000 - 1.73205i) q^{4} +(3.69798 + 0.990870i) q^{5} +(1.00000 - 1.00000i) q^{6} +(0.358719 - 2.62132i) q^{7} +2.82843i q^{8} +(0.866025 - 0.500000i) q^{9} +(-5.22973 + 1.40130i) q^{10} +(-0.624844 - 2.33195i) q^{11} +(-0.517638 + 1.93185i) q^{12} +(-2.41421 - 2.41421i) q^{13} +(1.41421 + 3.46410i) q^{14} -3.82843 q^{15} +(-2.00000 - 3.46410i) q^{16} +(3.41421 - 5.91359i) q^{17} +(-0.707107 + 1.22474i) q^{18} +(-0.732051 + 2.73205i) q^{19} +(5.41421 - 5.41421i) q^{20} +(0.331951 + 2.62484i) q^{21} +(2.41421 + 2.41421i) q^{22} +(0.210133 - 0.121320i) q^{23} +(-0.732051 - 2.73205i) q^{24} +(8.36308 + 4.82843i) q^{25} +(4.66390 + 1.24969i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-4.18154 - 3.24264i) q^{28} +(6.12132 + 6.12132i) q^{29} +(4.68885 - 2.70711i) q^{30} +(-0.207107 + 0.358719i) q^{31} +(4.89898 + 2.82843i) q^{32} +(1.20711 + 2.09077i) q^{33} +9.65685i q^{34} +(3.92392 - 9.33814i) q^{35} -2.00000i q^{36} +(-2.73205 - 0.732051i) q^{37} +(-1.03528 - 3.86370i) q^{38} +(2.95680 + 1.70711i) q^{39} +(-2.80260 + 10.4595i) q^{40} +3.41421i q^{41} +(-2.26260 - 2.98004i) q^{42} +(7.41421 - 7.41421i) q^{43} +(-4.66390 - 1.24969i) q^{44} +(3.69798 - 0.990870i) q^{45} +(-0.171573 + 0.297173i) q^{46} +(-1.12132 - 1.94218i) q^{47} +(2.82843 + 2.82843i) q^{48} +(-6.74264 - 1.88064i) q^{49} -13.6569 q^{50} +(-1.76733 + 6.59575i) q^{51} +(-6.59575 + 1.76733i) q^{52} +(0.687644 + 2.56632i) q^{53} +(0.366025 - 1.36603i) q^{54} -9.24264i q^{55} +(7.41421 + 1.01461i) q^{56} -2.82843i q^{57} +(-11.8255 - 3.16863i) q^{58} +(3.12422 + 11.6598i) q^{59} +(-3.82843 + 6.63103i) q^{60} +(-0.669251 + 2.49768i) q^{61} -0.585786i q^{62} +(-1.00000 - 2.44949i) q^{63} -8.00000 q^{64} +(-6.53553 - 11.3199i) q^{65} +(-2.95680 - 1.70711i) q^{66} +(-8.99635 + 2.41057i) q^{67} +(-6.82843 - 11.8272i) q^{68} +(-0.171573 + 0.171573i) q^{69} +(1.79725 + 14.2115i) q^{70} -3.89949i q^{71} +(1.41421 + 2.44949i) q^{72} +(3.46410 + 2.00000i) q^{73} +(3.86370 - 1.03528i) q^{74} +(-9.32780 - 2.49938i) q^{75} +(4.00000 + 4.00000i) q^{76} +(-6.33694 + 0.801401i) q^{77} -4.82843 q^{78} +(-1.37868 - 2.38794i) q^{79} +(-3.96348 - 14.7919i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-2.41421 - 4.18154i) q^{82} +(6.77817 + 6.77817i) q^{83} +(4.87832 + 2.04989i) q^{84} +(18.4853 - 18.4853i) q^{85} +(-3.83788 + 14.3232i) q^{86} +(-7.49706 - 4.32843i) q^{87} +(6.59575 - 1.76733i) q^{88} +(-13.4722 + 7.77817i) q^{89} +(-3.82843 + 3.82843i) q^{90} +(-7.19445 + 5.46240i) q^{91} -0.485281i q^{92} +(0.107206 - 0.400100i) q^{93} +(2.74666 + 1.58579i) q^{94} +(-5.41421 + 9.37769i) q^{95} +(-5.46410 - 1.46410i) q^{96} -14.3137 q^{97} +(9.58783 - 2.46447i) q^{98} +(-1.70711 - 1.70711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} + 8 q^{5} + 8 q^{6}+O(q^{10}) \) 8 * q + 8 * q^4 + 8 * q^5 + 8 * q^6	\( 8 q + 8 q^{4} + 8 q^{5} + 8 q^{6} - 4 q^{10} + 4 q^{11} - 8 q^{13} - 8 q^{15} - 16 q^{16} + 16 q^{17} + 8 q^{19} + 32 q^{20} - 12 q^{21} + 8 q^{22} + 8 q^{24} + 8 q^{26} + 32 q^{29} + 4 q^{31} + 4 q^{33} - 16 q^{35} - 8 q^{37} + 8 q^{40} - 4 q^{42} + 48 q^{43} - 8 q^{44} + 8 q^{45} - 24 q^{46} + 8 q^{47} - 20 q^{49} - 64 q^{50} + 8 q^{51} - 8 q^{52} - 16 q^{53} - 4 q^{54} + 48 q^{56} - 12 q^{58} - 20 q^{59} - 8 q^{60} - 4 q^{61} - 8 q^{63} - 64 q^{64} - 24 q^{65} - 32 q^{67} - 32 q^{68} - 24 q^{69} - 44 q^{70} - 16 q^{75} + 32 q^{76} - 8 q^{77} - 16 q^{78} - 28 q^{79} + 32 q^{80} + 4 q^{81} - 8 q^{82} - 8 q^{83} + 80 q^{85} + 8 q^{86} + 8 q^{88} - 8 q^{90} - 28 q^{91} - 4 q^{93} - 32 q^{95} - 16 q^{96} - 24 q^{97} - 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^4 + 8 * q^5 + 8 * q^6 - 4 * q^10 + 4 * q^11 - 8 * q^13 - 8 * q^15 - 16 * q^16 + 16 * q^17 + 8 * q^19 + 32 * q^20 - 12 * q^21 + 8 * q^22 + 8 * q^24 + 8 * q^26 + 32 * q^29 + 4 * q^31 + 4 * q^33 - 16 * q^35 - 8 * q^37 + 8 * q^40 - 4 * q^42 + 48 * q^43 - 8 * q^44 + 8 * q^45 - 24 * q^46 + 8 * q^47 - 20 * q^49 - 64 * q^50 + 8 * q^51 - 8 * q^52 - 16 * q^53 - 4 * q^54 + 48 * q^56 - 12 * q^58 - 20 * q^59 - 8 * q^60 - 4 * q^61 - 8 * q^63 - 64 * q^64 - 24 * q^65 - 32 * q^67 - 32 * q^68 - 24 * q^69 - 44 * q^70 - 16 * q^75 + 32 * q^76 - 8 * q^77 - 16 * q^78 - 28 * q^79 + 32 * q^80 + 4 * q^81 - 8 * q^82 - 8 * q^83 + 80 * q^85 + 8 * q^86 + 8 * q^88 - 8 * q^90 - 28 * q^91 - 4 * q^93 - 32 * q^95 - 16 * q^96 - 24 * q^97 - 8 * q^99

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