LMFDB - Embedded newform 336.2.bq.a.37.1

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			37.1
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	336.37
Dual form			336.2.bq.a.109.1

$q$-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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

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

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	0.693116	−	0.720826i	$-0.256237\pi$
$5$	3.69798	−	0.990870i	1.65379	−	0.443130i	0.960669	+	0.277695i	$0.0895706\pi$
$6$	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	0.805480	+	0.592623i	$0.201908\pi$
$11$	−0.624844	+	2.33195i	−0.188398	+	0.703110i	−0.993878	+	0.110487i	$0.964759\pi$
$12$	−0.517638	−	1.93185i	−0.149429	−	0.557678i
$13$	−2.41421	+	2.41421i	−0.669582	+	0.669582i	−0.957619	−	0.288037i	$-0.906997\pi$
$13$	−2.41421	+	2.41421i	−0.669582	+	0.669582i	0.288037	+	0.957619i	$0.406997\pi$
$14$	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	0.899551	+	0.436815i	$0.143893\pi$
$17$	3.41421	+	5.91359i	0.828068	+	1.43426i	−0.0714831	+	0.997442i	$0.522773\pi$
$18$	−0.707107	−	1.22474i	−0.166667	−	0.288675i
$19$	−0.732051	−	2.73205i	−0.167944	−	0.626775i	−0.997646	−	0.0685694i	$-0.978157\pi$
$19$	−0.732051	−	2.73205i	−0.167944	−	0.626775i	0.829702	−	0.558206i	$-0.188510\pi$
$20$	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	0.521748	−	0.853100i	$-0.325280\pi$
$23$	0.210133	+	0.121320i	0.0438158	+	0.0252970i	−0.477932	+	0.878397i	$0.658614\pi$
$24$	−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	0.147663	−	0.989038i	$-0.452825\pi$
$29$	6.12132	−	6.12132i	1.13670	−	1.13670i	0.989038	−	0.147663i	$-0.0471751\pi$
$30$	4.68885	+	2.70711i	0.856062	+	0.494248i
$31$	−0.207107	−	0.358719i	−0.0371975	−	0.0644279i	0.846827	−	0.531868i	$-0.178510\pi$
$31$	−0.207107	−	0.358719i	−0.0371975	−	0.0644279i	−0.884025	+	0.467440i	$0.845176\pi$
$32$	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	−0.476300	−	0.879283i	$-0.658022\pi$
$37$	−2.73205	+	0.732051i	−0.449146	+	0.120348i	0.0271536	+	0.999631i	$0.491356\pi$
$38$	−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	$-0.914098\pi$
$41$		−	3.41421i		−	0.533211i	0.963806	−	0.266605i	$-0.0859020\pi$
$42$	−2.26260	+	2.98004i	−0.349127	+	0.459830i
$43$	7.41421	+	7.41421i	1.13066	+	1.13066i	0.990068	+	0.140589i	$0.0448996\pi$
$43$	7.41421	+	7.41421i	1.13066	+	1.13066i	0.140589	+	0.990068i	$0.455100\pi$
$44$	−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	−0.936143	−	0.351618i	$-0.885632\pi$
$47$	−1.12132	+	1.94218i	−0.163561	+	0.283297i	0.772582	+	0.634915i	$0.218965\pi$
$48$	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	−0.902481	−	0.430730i	$-0.858256\pi$
$53$	0.687644	−	2.56632i	0.0944552	−	0.352512i	0.996936	+	0.0782178i	$0.0249230\pi$
$54$	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	−0.394087	−	0.919073i	$-0.628939\pi$
$59$	3.12422	−	11.6598i	0.406739	−	1.51797i	0.800826	−	0.598898i	$-0.204394\pi$
$60$	−3.82843	−	6.63103i	−0.494248	−	0.856062i
$61$	−0.669251	−	2.49768i	−0.0856888	−	0.319795i	0.909755	−	0.415146i	$-0.136269\pi$
$61$	−0.669251	−	2.49768i	−0.0856888	−	0.319795i	−0.995444	+	0.0953508i	$0.969603\pi$
$62$			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	−0.336690	−	0.941616i	$-0.609307\pi$
$67$	−8.99635	−	2.41057i	−1.09908	−	0.294497i	−0.762390	+	0.647118i	$0.775974\pi$
$68$	−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	$0.0743281\pi$
$71$			3.89949i			0.462785i	−0.972860	+	0.231392i	$0.925672\pi$
$72$	1.41421	−	2.44949i	0.166667	−	0.288675i
$73$	3.46410	−	2.00000i	0.405442	−	0.234082i	−0.283387	−	0.959006i	$-0.591458\pi$
$73$	3.46410	−	2.00000i	0.405442	−	0.234082i	0.688830	+	0.724923i	$0.258125\pi$
$74$	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	−0.933100	−	0.359616i	$-0.882908\pi$
$79$	−1.37868	+	2.38794i	−0.155114	+	0.268665i	0.777987	+	0.628281i	$0.216241\pi$
$80$	−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	−0.229344	−	0.973345i	$-0.573658\pi$
$83$	6.77817	−	6.77817i	0.744001	−	0.744001i	0.973345	+	0.229344i	$0.0736581\pi$
$84$	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	−0.431083	−	0.902312i	$-0.641868\pi$
$89$	−13.4722	−	7.77817i	−1.42805	−	0.824485i	−0.996967	+	0.0778275i	$0.975202\pi$
$90$	−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	−0.902717	−	0.430235i	$-0.858431\pi$
$101$	0.946464	−	3.53225i	0.0941766	−	0.351472i	0.996893	+	0.0787635i	$0.0250972\pi$
$102$	−2.49938	+	9.32780i	−0.247475	+	0.923590i
$103$	5.49333	+	3.17157i	0.541273	+	0.312504i	0.745595	−	0.666399i	$-0.232165\pi$
$103$	5.49333	+	3.17157i	0.541273	+	0.312504i	−0.204321	+	0.978904i	$0.565499\pi$
$104$	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	−0.167630	−	0.985850i	$-0.553611\pi$
$107$	1.86321	−	0.499244i	0.180123	−	0.0482638i	0.347753	+	0.937586i	$0.386945\pi$
$108$	0.517638	−	1.93185i	0.0498097	−	0.185893i
$109$	17.8554	+	4.78434i	1.71024	+	0.458257i	0.975483	−	0.220075i	$-0.0706303\pi$
$109$	17.8554	+	4.78434i	1.71024	+	0.458257i	0.734755	+	0.678332i	$0.237297\pi$
$110$	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	−0.712989	−	0.701175i	$-0.752659\pi$
$131$	−5.10596	−	19.0557i	−0.446110	−	1.66491i	0.266879	−	0.963730i	$-0.414008\pi$
$132$	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	−0.741269	−	0.671208i	$-0.765776\pi$
$137$	−6.21076	+	3.58579i	−0.530621	+	0.306354i	0.210648	+	0.977562i	$0.432443\pi$
$138$	0.0888127	+	0.331453i	0.00756024	+	0.0282152i
$139$	−6.89949	−	6.89949i	−0.585208	−	0.585208i	0.351122	−	0.936330i	$-0.385800\pi$
$139$	−6.89949	−	6.89949i	−0.585208	−	0.585208i	−0.936330	+	0.351122i	$0.885800\pi$
$140$	−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	−0.602741	−	0.797937i	$-0.705925\pi$
$149$	−8.85906	+	2.37378i	−0.725762	+	0.194467i	−0.123021	+	0.992404i	$0.539258\pi$
$150$	13.1915	+	3.53465i	1.07708	+	0.288603i
$151$	−10.7510	+	6.20711i	−0.874906	+	0.505127i	−0.868975	−	0.494855i	$-0.835221\pi$
$151$	−10.7510	+	6.20711i	−0.874906	+	0.505127i	−0.00593052	+	0.999982i	$0.501888\pi$
$152$	−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	−0.278491	−	0.960439i	$-0.589834\pi$
$157$	−12.5286	−	3.35703i	−0.999891	−	0.267920i	−0.721400	+	0.692519i	$0.756501\pi$
$158$	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	−0.909944	−	0.414732i	$-0.863875\pi$
$163$	−4.20390	−	15.6892i	−0.329275	−	1.22887i	0.580668	−	0.814140i	$-0.302791\pi$
$164$	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	$-0.925425\pi$
$167$		−	6.00000i		−	0.464294i	0.972681	−	0.232147i	$-0.0745750\pi$
$168$	−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	0.905013	+	0.425384i	$0.139861\pi$
$173$	4.39230	+	16.3923i	0.333941	+	1.24628i	−0.571072	+	0.820900i	$0.693472\pi$
$174$	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	0.986761	+	0.162179i	$0.0518522\pi$
$179$	25.7201	+	6.89168i	1.92241	+	0.515109i	0.935650	+	0.352930i	$0.114814\pi$
$180$	1.98174	+	7.39595i	0.147710	+	0.551262i
$181$	9.72792	+	9.72792i	0.723071	+	0.723071i	0.969230	−	0.246159i	$-0.0791685\pi$
$181$	9.72792	+	9.72792i	0.723071	+	0.723071i	−0.246159	+	0.969230i	$0.579168\pi$
$182$	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	−0.799836	−	0.600218i	$-0.795081\pi$
$191$	1.65685	−	2.86976i	0.119886	−	0.207648i	0.919722	+	0.392570i	$0.128414\pi$
$192$	7.72741	+	2.07055i	0.557678	+	0.149429i
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	0.964059	−	0.265689i	$-0.0855996\pi$
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	−0.712123	+	0.702055i	$0.752266\pi$
$194$	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	0.947816	−	0.318817i	$-0.103286\pi$
$197$	8.82843	+	8.82843i	0.628999	+	0.628999i	−0.318817	+	0.947816i	$0.603286\pi$
$198$	3.29788	−	0.883663i	0.234370	−	0.0627992i
$199$	11.4069	−	6.58579i	0.808615	−	0.466854i	−0.0378598	−	0.999283i	$-0.512054\pi$
$199$	11.4069	−	6.58579i	0.808615	−	0.466854i	0.846475	+	0.532429i	$0.178721\pi$
$200$	−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	−0.872735	−	0.488194i	$-0.837656\pi$
$211$	−5.58579	+	5.58579i	−0.384541	+	0.384541i	0.488194	+	0.872735i	$0.337656\pi$
$212$	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	−0.417656	−	0.908605i	$-0.637148\pi$
$227$	−18.5870	−	4.98036i	−1.23366	−	0.330558i	−0.816004	+	0.578047i	$0.803815\pi$
$228$	−4.89898	+	2.82843i	−0.324443	+	0.187317i
$229$	−11.9628	+	3.20542i	−0.790522	+	0.211820i	−0.631419	−	0.775442i	$-0.717527\pi$
$229$	−11.9628	+	3.20542i	−0.790522	+	0.211820i	−0.159104	+	0.987262i	$0.550860\pi$
$230$	−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	0.160314	−	0.987066i	$-0.448749\pi$
$233$	−9.37769	−	5.41421i	−0.614353	−	0.354697i	−0.774667	+	0.632369i	$0.782083\pi$
$234$	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	0.936874	−	0.349667i	$-0.113705\pi$
$241$	2.57107	+	4.45322i	0.165617	+	0.286857i	−0.771257	+	0.636524i	$0.780372\pi$
$242$	−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	0.113085	−	0.993585i	$-0.463927\pi$
$251$	−13.9497	−	13.9497i	−0.880500	−	0.880500i	−0.993585	+	0.113085i	$0.963927\pi$
$252$	−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	−0.622346	−	0.782742i	$-0.713820\pi$
$257$	5.87868	−	10.1822i	0.366702	−	0.635146i	0.989048	+	0.147596i	$0.0471535\pi$
$258$			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	0.0827219	−	0.996573i	$-0.473639\pi$
$263$	16.0087	−	9.24264i	0.987140	−	0.569926i	0.904418	+	0.426647i	$0.140305\pi$
$264$	−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	−0.739332	−	0.673341i	$-0.764859\pi$
$269$	−28.1491	−	7.54254i	−1.71628	−	0.459877i	−0.976951	+	0.213464i	$0.931525\pi$
$270$	2.70711	+	4.68885i	0.164749	+	0.285354i
$271$	−0.136039	+	0.235626i	−0.00826378	+	0.0143133i	−0.870128	−	0.492826i	$-0.835964\pi$
$271$	−0.136039	+	0.235626i	−0.00826378	+	0.0143133i	0.861864	+	0.507140i	$0.169297\pi$
$272$	−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	−0.565138	−	0.824997i	$-0.691177\pi$
$277$	5.60521	−	20.9189i	0.336784	−	1.25690i	0.901922	−	0.431899i	$-0.142156\pi$
$278$	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	$-0.992134\pi$
$281$		−	0.828427i		−	0.0494198i	0.999695	−	0.0247099i	$-0.00786621\pi$
$282$	−3.06350	+	0.820863i	−0.182429	+	0.0488817i
$283$	7.10610	−	26.5203i	0.422414	−	1.57647i	−0.347094	−	0.937830i	$-0.612831\pi$
$283$	7.10610	−	26.5203i	0.422414	−	1.57647i	0.769507	−	0.638638i	$-0.220502\pi$
$284$	−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	0.675763	−	0.737119i	$-0.263814\pi$
$293$	−1.05025	−	1.05025i	−0.0613564	−	0.0613564i	−0.737119	+	0.675763i	$0.763814\pi$
$294$	−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	−0.997773	−	0.0667005i	$-0.978753\pi$
$307$	−16.3137	+	16.3137i	−0.931073	+	0.931073i	0.0667005	+	0.997773i	$0.478753\pi$
$308$	−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	0.0640825	−	0.997945i	$-0.479588\pi$
$311$	16.9363	−	9.77817i	0.960369	−	0.554469i	0.896287	+	0.443475i	$0.146255\pi$
$312$	−4.82843	−	8.36308i	−0.273356	−	0.473466i
$313$	−3.61269	−	2.08579i	−0.204201	−	0.117896i	0.394412	−	0.918934i	$-0.370948\pi$
$313$	−3.61269	−	2.08579i	−0.204201	−	0.117896i	−0.598614	+	0.801038i	$0.704281\pi$
$314$	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	0.909859	+	0.414917i	$0.136189\pi$
$317$	5.86403	+	21.8848i	0.329356	+	1.22918i	−0.580503	+	0.814258i	$0.697144\pi$
$318$	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	−0.0401178	−	0.999195i	$-0.512773\pi$
$331$	7.72741	−	2.07055i	0.424737	−	0.113808i	0.464854	+	0.885387i	$0.346107\pi$
$332$	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	−0.998278	−	0.0586667i	$-0.981315\pi$
$347$	−1.94495	+	7.25866i	−0.104411	+	0.389665i	0.893867	+	0.448332i	$0.147982\pi$
$348$	−14.9941	−	8.65685i	−0.803769	−	0.464056i
$349$	−0.585786	+	0.585786i	−0.0313564	+	0.0313564i	−0.722611	−	0.691255i	$-0.757058\pi$
$349$	−0.585786	+	0.585786i	−0.0313564	+	0.0313564i	0.691255	+	0.722611i	$0.257058\pi$
$350$	−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	0.906744	−	0.421681i	$-0.138560\pi$
$353$	1.65685	+	2.86976i	0.0881855	+	0.152742i	−0.818559	+	0.574423i	$0.805227\pi$
$354$	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	0.664673	−	0.747134i	$-0.268571\pi$
$359$	6.63103	+	3.82843i	0.349972	+	0.202057i	−0.314701	+	0.949191i	$0.601904\pi$
$360$	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	0.979947	+	0.199260i	$0.0638537\pi$
$367$	12.6924	+	21.9839i	0.662537	+	1.14755i	−0.317409	+	0.948289i	$0.602813\pi$
$368$	−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	−0.256305	−	0.966596i	$-0.582505\pi$
$373$	0.0970804	−	0.0260126i	0.00502663	−	0.00134688i	0.261331	+	0.965249i	$0.415838\pi$
$374$	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	0.857096	−	0.515156i	$-0.172266\pi$
$379$	6.65685	+	6.65685i	0.341940	+	0.341940i	−0.515156	+	0.857096i	$0.672266\pi$
$380$	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	−0.609849	−	0.792518i	$-0.708770\pi$
$383$	7.46447	−	12.9288i	0.381416	−	0.660633i	0.991265	+	0.131885i	$0.0421031\pi$
$384$	−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	−0.170766	−	0.985312i	$-0.554624\pi$
$389$	9.26546	−	34.5792i	0.469777	−	1.75323i	0.640544	−	0.767922i	$-0.278709\pi$
$390$	−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	0.959336	−	0.282268i	$-0.0910867\pi$
$397$	−0.251200	−	0.937492i	−0.0126074	−	0.0470514i	−0.971943	+	0.235217i	$0.924420\pi$
$398$	−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	−0.393680	−	0.919247i	$-0.628798\pi$
$401$	12.0000	−	20.7846i	0.599251	−	1.03793i	0.992932	−	0.118686i	$-0.0378683\pi$
$402$	−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	0.404209	−	0.914667i	$-0.367547\pi$
$409$	28.2817	−	16.3284i	1.39844	−	0.807389i	0.994229	+	0.107278i	$0.0342134\pi$
$410$	−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	−0.958664	−	0.284540i	$-0.908159\pi$
$419$	−13.7990	+	13.7990i	−0.674125	+	0.674125i	0.284540	+	0.958664i	$0.408159\pi$
$420$	16.0087	−	12.4142i	0.781146	−	0.605752i
$421$	−1.48528	−	1.48528i	−0.0723882	−	0.0723882i	0.669986	−	0.742374i	$-0.266300\pi$
$421$	−1.48528	−	1.48528i	−0.0723882	−	0.0723882i	−0.742374	+	0.669986i	$0.766300\pi$
$422$	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	0.998952	+	0.0457752i	$0.0145758\pi$
$431$	11.1924	+	19.3858i	0.539118	+	0.933780i	−0.459833	+	0.888005i	$0.652091\pi$
$432$	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	0.402871	−	0.915257i	$-0.368012\pi$
$439$	−3.94591	−	2.27817i	−0.188328	−	0.108731i	−0.591200	+	0.806525i	$0.701345\pi$
$440$	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	0.0375516	−	0.999295i	$-0.488044\pi$
$443$	11.9912	−	3.21303i	0.569720	−	0.152656i	0.532168	+	0.846639i	$0.321377\pi$
$444$	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	−0.0618687	−	0.998084i	$-0.519706\pi$
$457$	−20.4619	−	11.8137i	−0.957169	−	0.552622i	−0.895301	+	0.445462i	$0.853039\pi$
$458$	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	−0.495825	−	0.868422i	$-0.665134\pi$
$461$	8.00000	−	8.00000i	0.372597	−	0.372597i	0.868422	+	0.495825i	$0.165134\pi$
$462$	−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	−0.985350	−	0.170543i	$-0.945448\pi$
$467$	−4.69553	−	17.5240i	−0.217283	−	0.810912i	0.768067	−	0.640369i	$-0.221219\pi$
$468$	−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	0.999617	−	0.0276792i	$-0.00881168\pi$
$479$	10.4142	+	18.0379i	0.475838	+	0.824175i	−0.523779	+	0.851854i	$0.675478\pi$
$480$	−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	−0.960362	−	0.278756i	$-0.910078\pi$
$487$	−26.4626	+	15.2782i	−1.19913	+	0.692320i	−0.238772	+	0.971076i	$0.576745\pi$
$488$	−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	0.830324	−	0.557280i	$-0.188155\pi$
$491$	6.05025	+	6.05025i	0.273044	+	0.273044i	−0.557280	+	0.830324i	$0.688155\pi$
$492$	−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	−0.954552	−	0.298043i	$-0.903666\pi$
$499$	−6.18564	−	23.0851i	−0.276907	−	1.03343i	0.677645	−	0.735389i	$-0.263001\pi$
$500$	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	$0.175649\pi$
$503$			23.5147i			1.04847i	−0.851574	+	0.524235i	$0.824351\pi$
$504$	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	0.982986	+	0.183678i	$0.0588004\pi$
$509$	5.04316	+	18.8213i	0.223534	+	0.834241i	−0.759452	+	0.650563i	$0.774533\pi$
$510$			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	−0.704562	−	0.709642i	$-0.748857\pi$
$521$	−10.0951	+	5.82843i	−0.442276	+	0.255348i	0.262287	+	0.964990i	$0.415523\pi$
$522$	−11.8255	−	3.16863i	−0.517587	−	0.138687i
$523$	26.6174	−	7.13211i	1.16390	−	0.311865i	0.375376	−	0.926873i	$-0.377514\pi$
$523$	26.6174	−	7.13211i	1.16390	−	0.311865i	0.788521	+	0.615007i	$0.210847\pi$
$524$	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	0.937543	−	0.347870i	$-0.113095\pi$
$541$	−1.12409	−	4.19516i	−0.0483284	−	0.180364i	−0.985871	+	0.167507i	$0.946428\pi$
$542$	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	−0.771652	−	0.636045i	$-0.780569\pi$
$547$	−3.17157	+	3.17157i	−0.135607	+	0.135607i	0.636045	+	0.771652i	$0.280569\pi$
$548$	−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	0.0489434	−	0.998802i	$-0.484415\pi$
$557$	−9.63082	−	2.58057i	−0.408071	−	0.109342i	−0.457015	+	0.889459i	$0.651081\pi$
$558$	−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	−0.174006	−	0.984745i	$-0.555671\pi$
$563$	−19.3872	−	5.19477i	−0.817071	−	0.218934i	−0.643066	+	0.765811i	$0.722338\pi$
$564$	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	0.370897	−	0.928674i	$-0.379050\pi$
$569$	−5.91359	−	3.41421i	−0.247911	−	0.143131i	−0.618807	+	0.785543i	$0.712384\pi$
$570$	3.96348	−	14.7919i	0.166012	−	0.619565i
$571$	1.56369	−	5.83577i	0.0654384	−	0.244219i	−0.925457	−	0.378852i	$-0.876319\pi$
$571$	1.56369	−	5.83577i	0.0654384	−	0.244219i	0.990896	+	0.134633i	$0.0429855\pi$
$572$	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	0.569587	−	0.821931i	$-0.307103\pi$
$577$	−10.2574	−	17.7663i	−0.427019	−	0.739619i	−0.996607	+	0.0823115i	$0.973770\pi$
$578$	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	0.764015	−	0.645199i	$-0.223225\pi$
$587$	2.87868	+	2.87868i	0.118816	+	0.118816i	−0.645199	+	0.764015i	$0.723225\pi$
$588$	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	−0.984535	−	0.175190i	$-0.943946\pi$
$593$	−8.29289	+	14.3637i	−0.340548	+	0.589847i	0.643986	+	0.765037i	$0.277279\pi$
$594$	−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	−0.792738	−	0.609562i	$-0.791345\pi$
$599$	−16.1828	+	9.34315i	−0.661211	+	0.381751i	0.131527	+	0.991313i	$0.458012\pi$
$600$	7.06931	+	26.3830i	0.288603	+	1.07708i
$601$			3.34315i			0.136370i	0.997673	+	0.0681849i	$0.0217208\pi$
$601$			3.34315i			0.136370i	−0.997673	+	0.0681849i	$0.978279\pi$
$602$	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	−0.981160	−	0.193196i	$-0.938115\pi$
$607$	−7.96447	+	13.7949i	−0.323268	+	0.559916i	0.657893	+	0.753112i	$0.271448\pi$
$608$	−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	0.728740	+	0.684791i	$0.240106\pi$
$613$	−6.06004	+	22.6164i	−0.244763	+	0.913468i	−0.973502	+	0.228677i	$0.926560\pi$
$614$	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	$-0.775179\pi$
$617$		−	32.2426i		−	1.29804i	0.760771	−	0.649020i	$-0.224821\pi$
$618$	2.32175	+	8.66490i	0.0933946	+	0.348553i
$619$	−6.43684	+	24.0226i	−0.258719	+	0.965551i	0.707265	+	0.706948i	$0.249929\pi$
$619$	−6.43684	+	24.0226i	−0.258719	+	0.965551i	−0.965984	+	0.258603i	$0.916738\pi$
$620$	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	$0.0557703\pi$
$631$			8.75736i			0.348625i	−0.984690	+	0.174312i	$0.944230\pi$
$632$	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	0.919380	+	0.393370i	$0.128691\pi$
$641$	20.2635	+	35.0973i	0.800358	+	1.38626i	−0.119022	+	0.992892i	$0.537976\pi$
$642$	2.36245	+	1.36396i	0.0932385	+	0.0538312i
$643$	16.9289	−	16.9289i	0.667612	−	0.667612i	−0.289551	−	0.957163i	$-0.593506\pi$
$643$	16.9289	−	16.9289i	0.667612	−	0.667612i	0.957163	+	0.289551i	$0.0935059\pi$
$644$	−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	−0.681562	−	0.731761i	$-0.738699\pi$
$647$	−9.88500	+	5.70711i	−0.388619	+	0.224370i	0.292942	+	0.956130i	$0.405366\pi$
$648$	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	−0.996185	−	0.0872679i	$-0.972186\pi$
$653$	−4.52552	−	16.8895i	−0.177097	−	0.660937i	0.819087	−	0.573669i	$-0.194480\pi$
$654$	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	−0.988085	−	0.153906i	$-0.950815\pi$
$659$	−21.4142	+	21.4142i	−0.834179	+	0.834179i	0.153906	+	0.988085i	$0.450815\pi$
$660$	17.8554	−	4.78434i	0.695021	−	0.186230i
$661$	0.0888127	−	0.331453i	0.00345441	−	0.0128920i	−0.964177	−	0.265259i	$-0.914542\pi$
$661$	0.0888127	−	0.331453i	0.00345441	−	0.0128920i	0.967632	+	0.252367i	$0.0812091\pi$
$662$	−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	0.375178	−	0.926953i	$-0.377581\pi$
$677$	30.2752	−	8.11220i	1.16357	−	0.311777i	0.788390	+	0.615175i	$0.210915\pi$
$678$	−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	0.865453	+	0.500989i	$0.167030\pi$
$683$	−3.51626	+	13.1229i	−0.134546	+	0.502132i	−0.999999	+	0.00114290i	$0.999636\pi$
$684$	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	0.999458	+	0.0329321i	$0.0104845\pi$
$691$	3.95270	+	14.7517i	0.150368	+	0.561181i	−0.849090	+	0.528249i	$0.822849\pi$
$692$	−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	−0.976317	−	0.216345i	$-0.930586\pi$
$701$	−20.1213	+	20.1213i	−0.759972	+	0.759972i	0.216345	+	0.976317i	$0.430586\pi$
$702$	−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	−0.501958	−	0.864892i	$-0.667387\pi$
$709$	−13.4259	+	3.59745i	−0.504220	+	0.135105i	−0.00226194	+	0.999997i	$0.500720\pi$
$710$	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	0.377822	+	0.925878i	$0.376673\pi$
$719$	−16.4350	+	28.4663i	−0.612923	+	1.06161i	−0.990745	+	0.135736i	$0.956660\pi$
$720$	−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	$-0.912999\pi$
$727$		−	14.5563i		−	0.539865i	0.962879	−	0.269933i	$-0.0870014\pi$
$728$	−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	−0.810407	−	0.585867i	$-0.800754\pi$
$733$	−10.8704	−	40.5689i	−0.401507	−	1.49845i	0.408900	−	0.912579i	$-0.365912\pi$
$734$		−	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	0.0151963	−	0.999885i	$-0.495163\pi$
$739$	−12.8198	−	3.43507i	−0.471586	−	0.126361i	−0.486782	+	0.873524i	$0.661829\pi$
$740$	−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	$0.0310752\pi$
$743$			5.31371i			0.194941i	−0.995238	+	0.0974705i	$0.968925\pi$
$744$	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	0.449713	+	0.893173i	$0.351526\pi$
$751$	−15.0355	+	26.0423i	−0.548654	+	0.950297i	−0.998367	+	0.0571241i	$0.981807\pi$
$752$	−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	0.894539	−	0.446990i	$-0.147504\pi$
$757$	12.3137	+	12.3137i	0.447549	+	0.447549i	−0.446990	+	0.894539i	$0.647504\pi$
$758$	−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	−0.179118	−	0.983828i	$-0.557324\pi$
$761$	−30.9158	−	17.8492i	−1.12070	−	0.647035i	−0.941579	+	0.336793i	$0.890658\pi$
$762$	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	−0.730842	−	0.682547i	$-0.760872\pi$
$773$	6.76608	−	25.2514i	0.243359	−	0.908228i	0.974201	−	0.225682i	$-0.0724610\pi$
$774$	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	−0.783832	−	0.620973i	$-0.786738\pi$
$787$	−49.7427	−	13.3285i	−1.77314	−	0.475111i	−0.989305	+	0.145862i	$0.953404\pi$
$788$	−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	−0.746057	−	0.665882i	$-0.768056\pi$
$797$	−2.26346	+	2.26346i	−0.0801757	+	0.0801757i	0.665882	+	0.746057i	$0.268056\pi$
$798$	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	−0.206498	−	0.978447i	$-0.566207\pi$
$809$	15.2913	−	8.82843i	0.537613	−	0.310391i	0.744111	+	0.668056i	$0.232873\pi$
$810$	−1.40130	−	5.22973i	−0.0492367	−	0.183754i
$811$	15.5563	+	15.5563i	0.546257	+	0.546257i	0.925356	−	0.379099i	$-0.123766\pi$
$811$	15.5563	+	15.5563i	0.546257	+	0.546257i	−0.379099	+	0.925356i	$0.623766\pi$
$812$	−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	−0.342110	−	0.939660i	$-0.611141\pi$
$821$	−4.82963	+	1.29410i	−0.168555	+	0.0451642i	0.173554	+	0.984824i	$0.444475\pi$
$822$	−9.79655	−	2.62498i	−0.341694	−	0.0915566i
$823$	−15.8856	+	9.17157i	−0.553738	+	0.319701i	−0.750628	−	0.660725i	$-0.770249\pi$
$823$	−15.8856	+	9.17157i	−0.553738	+	0.319701i	0.196890	+	0.980426i	$0.436916\pi$
$824$	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	−0.999103	−	0.0423520i	$-0.986515\pi$
$827$	−29.9497	−	29.9497i	−1.04145	−	1.04145i	−0.0423520	−	0.999103i	$-0.513485\pi$
$828$	−0.242641	+	0.420266i	−0.00843235	+	0.0146053i
$829$	40.7062	+	10.9072i	1.41378	+	0.378822i	0.883274	−	0.468857i	$-0.155334\pi$
$829$	40.7062	+	10.9072i	1.41378	+	0.378822i	0.530510	+	0.847679i	$0.322001\pi$
$830$	−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	$-0.888974\pi$
$839$		−	19.7990i		−	0.683537i	0.939784	−	0.341769i	$-0.111026\pi$
$840$	−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	0.788572	−	0.614942i	$-0.210821\pi$
$853$	5.07107	+	5.07107i	0.173630	+	0.173630i	−0.614942	+	0.788572i	$0.710821\pi$
$854$	−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	−0.380850	−	0.924637i	$-0.624368\pi$
$857$	6.71807	−	3.87868i	0.229485	−	0.132493i	0.610334	+	0.792144i	$0.291035\pi$
$858$	3.01702	−	11.2597i	0.102999	−	0.384398i
$859$	−41.9751	+	11.2472i	−1.43217	+	0.383750i	−0.889785	−	0.456379i	$-0.849146\pi$
$859$	−41.9751	+	11.2472i	−1.43217	+	0.383750i	−0.542387	+	0.840129i	$0.682479\pi$
$860$			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	−0.370342	−	0.928895i	$-0.620759\pi$
$863$	18.1924	−	31.5101i	0.619276	−	1.07262i	0.989618	−	0.143722i	$-0.0459072\pi$
$864$	−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	0.834940	+	0.550341i	$0.185502\pi$
$877$	11.4616	+	42.7753i	0.387031	+	1.44442i	−0.447909	+	0.894079i	$0.647831\pi$
$878$	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	−0.950408	−	0.311007i	$-0.899334\pi$
$883$	−19.0000	+	19.0000i	−0.639401	+	0.639401i	0.311007	+	0.950408i	$0.399334\pi$
$884$	−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	0.284110	−	0.958792i	$-0.408302\pi$
$887$	−12.0373	−	6.94975i	−0.404174	−	0.233350i	−0.688283	+	0.725442i	$0.741635\pi$
$888$		−	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	−0.731802	−	0.681517i	$-0.761320\pi$
$907$	7.30973	−	27.2803i	0.242716	−	0.905827i	0.974518	−	0.224310i	$-0.0720129\pi$
$908$	−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	0.997199	+	0.0747927i	$0.0238295\pi$
$919$	47.3087	+	27.3137i	1.56057	+	0.900996i	0.563372	+	0.826203i	$0.309504\pi$
$920$	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	−0.992191	−	0.124728i	$-0.960194\pi$
$929$	−11.8284	+	20.4874i	−0.388078	+	0.672171i	0.604113	+	0.796899i	$0.293528\pi$
$930$		−	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	$0.145385\pi$
$937$			27.0000i			0.882052i	−0.897494	+	0.441026i	$0.854615\pi$
$938$	−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	−0.0447462	−	0.998998i	$-0.514248\pi$
$941$	−17.8838	−	4.79196i	−0.582997	−	0.156213i	−0.538251	+	0.842785i	$0.680915\pi$
$942$	−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	0.842370	+	0.538899i	$0.181160\pi$
$947$	11.7648	+	43.9070i	0.382306	+	1.42678i	−0.460064	+	0.887886i	$0.652174\pi$
$948$	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	$0.193447\pi$
$953$			35.2548i			1.14202i	−0.820944	+	0.571008i	$0.806553\pi$
$954$	−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	$0.230373\pi$
$967$			41.1838i			1.32438i	−0.749336	+	0.662190i	$0.769627\pi$
$968$	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	−0.433876	−	0.900973i	$-0.642854\pi$
$971$	−11.1910	+	2.99862i	−0.359137	+	0.0962304i	0.0747390	+	0.997203i	$0.476188\pi$
$972$	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	0.938750	−	0.344600i	$-0.111985\pi$
$977$	5.34315	+	9.25460i	0.170942	+	0.296081i	−0.767807	+	0.640681i	$0.778652\pi$
$978$	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	0.0383851	−	0.999263i	$-0.487779\pi$
$983$	28.9376	−	16.7071i	0.922965	−	0.532874i	0.884580	+	0.466389i	$0.154445\pi$
$984$	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	0.861573	−	0.507633i	$-0.169479\pi$
$991$	−0.278175	−	0.481813i	−0.00883651	−	0.0153053i	−0.870410	+	0.492328i	$0.836146\pi$
$992$	−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	−0.994387	−	0.105803i	$-0.966259\pi$
$997$	−2.53617	+	9.46510i	−0.0803212	+	0.299763i	0.914066	+	0.405566i	$0.132925\pi$
$998$	−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.37.1	✓	8
7.4	even	3	inner	336.2.bq.a.277.2	yes	8
16.13	even	4	inner	336.2.bq.a.205.2	yes	8
112.109	even	12	inner	336.2.bq.a.109.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bq.a.37.1	✓	8	1.1	even	1	trivial
336.2.bq.a.109.1	yes	8	112.109	even	12	inner
336.2.bq.a.205.2	yes	8	16.13	even	4	inner
336.2.bq.a.277.2	yes	8	7.4	even	3	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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