LMFDB - Embedded newform 546.2.bu.b.197.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(71,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.6
Character	$\chi$	$=$	546.197
Dual form			546.2.bu.b.449.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(1.01587 + 1.40286i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.99319 - 1.99319i) q^{5} +(-1.61798 + 0.618168i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.936020 + 2.85024i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(1.01587 + 1.40286i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.99319 - 1.99319i) q^{5} +(-1.61798 + 0.618168i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.936020 + 2.85024i) q^{9} +(2.44115 - 1.40940i) q^{10} +(-3.39562 - 0.909853i) q^{11} +(-0.178340 - 1.72285i) q^{12} +(-3.11895 + 1.80892i) q^{13} -1.00000i q^{14} +(0.771343 - 4.82099i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.364026 - 0.630512i) q^{17} +(-2.51086 - 1.64182i) q^{18} +(-0.985142 - 3.67660i) q^{19} +(0.729559 + 2.72275i) q^{20} +(-1.34434 - 1.09213i) q^{21} +(1.75770 - 3.04443i) q^{22} +(-2.57429 - 4.45880i) q^{23} +(1.71030 + 0.273642i) q^{24} +2.94564i q^{25} +(-0.940036 - 3.48085i) q^{26} +(-4.94935 + 1.58237i) q^{27} +(0.965926 + 0.258819i) q^{28} +(-4.47106 + 2.58137i) q^{29} +(4.45708 + 1.99282i) q^{30} +(-4.56454 + 4.56454i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-2.17311 - 5.68786i) q^{33} +(0.514811 + 0.514811i) q^{34} +(2.44115 + 1.40940i) q^{35} +(2.23574 - 2.00037i) q^{36} +(1.73320 - 6.46839i) q^{37} +3.80629 q^{38} +(-5.70609 - 2.53782i) q^{39} -2.81880 q^{40} +(2.39422 - 8.93537i) q^{41} +(1.40286 - 1.01587i) q^{42} +(9.77091 + 5.64124i) q^{43} +(2.48576 + 2.48576i) q^{44} +(7.54675 - 3.81541i) q^{45} +(4.97314 - 1.33255i) q^{46} +(-7.98109 + 7.98109i) q^{47} +(-0.706976 + 1.58120i) q^{48} +(0.866025 - 0.500000i) q^{49} +(-2.84527 - 0.762387i) q^{50} +(1.25432 - 0.129841i) q^{51} +(3.60554 - 0.00709410i) q^{52} +8.37700i q^{53} +(-0.247463 - 5.19026i) q^{54} +(4.95461 + 8.58163i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(4.15697 - 5.11696i) q^{57} +(-1.33621 - 4.98682i) q^{58} +(1.91793 + 7.15783i) q^{59} +(-3.07850 + 3.78943i) q^{60} +(-0.617982 + 1.07038i) q^{61} +(-3.22761 - 5.59039i) q^{62} +(0.166429 - 2.99538i) q^{63} -1.00000i q^{64} +(9.82218 + 2.61114i) q^{65} +(6.05649 - 0.626935i) q^{66} +(10.5323 + 2.82212i) q^{67} +(-0.630512 + 0.364026i) q^{68} +(3.63992 - 8.14091i) q^{69} +(-1.99319 + 1.99319i) q^{70} +(-4.48721 + 1.20234i) q^{71} +(1.35356 + 2.67729i) q^{72} +(-6.36810 - 6.36810i) q^{73} +(5.79940 + 3.34829i) q^{74} +(-4.13231 + 2.99238i) q^{75} +(-0.985142 + 3.67660i) q^{76} +3.51540 q^{77} +(3.92819 - 4.85483i) q^{78} -3.35978 q^{79} +(0.729559 - 2.72275i) q^{80} +(-7.24773 - 5.33576i) q^{81} +(8.01123 + 4.62529i) q^{82} +(-0.552914 - 0.552914i) q^{83} +(0.618168 + 1.61798i) q^{84} +(-1.98231 + 0.531158i) q^{85} +(-7.97792 + 7.97792i) q^{86} +(-8.16330 - 3.64993i) q^{87} +(-3.04443 + 1.75770i) q^{88} +(-7.13603 - 1.91209i) q^{89} +(1.73216 + 8.27710i) q^{90} +(2.54449 - 2.55452i) q^{91} +5.14858i q^{92} +(-11.0404 - 1.76642i) q^{93} +(-5.64349 - 9.77480i) q^{94} +(-5.36459 + 9.29175i) q^{95} +(-1.34434 - 1.09213i) q^{96} +(-2.54406 - 9.49457i) q^{97} +(0.258819 + 0.965926i) q^{98} +(5.77166 - 8.82668i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{6} - 24 q^{9}+O(q^{10}) $ 56 * q + 8 * q^6 - 24 * q^9	$ 56 q + 8 q^{6} - 24 q^{9} + 24 q^{10} + 8 q^{11} + 24 q^{13} + 4 q^{15} + 28 q^{16} - 4 q^{17} - 8 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{79} + 12 q^{81} - 4 q^{83} - 4 q^{84} + 32 q^{85} - 16 q^{86} - 144 q^{87} + 88 q^{89} - 8 q^{90} - 8 q^{91} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 q^{99}+O(q^{100}) $ 56 * q + 8 * q^6 - 24 * q^9 + 24 * q^10 + 8 * q^11 + 24 * q^13 + 4 * q^15 + 28 * q^16 - 4 * q^17 - 8 * q^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 16 * q^79 + 12 * q^81 - 4 * q^83 - 4 * q^84 + 32 * q^85 - 16 * q^86 - 144 * q^87 + 88 * q^89 - 8 * q^90 - 8 * q^91 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	1.01587	+	1.40286i	0.586512	+	0.809940i
$3$	1.01587	+	1.40286i	0.586512	+	0.809940i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−1.99319	−	1.99319i	−0.891383	−	0.891383i	0.103270	−	0.994653i	$-0.467069\pi$
$5$	−1.99319	−	1.99319i	−0.891383	−	0.891383i	−0.994653	+	0.103270i	$0.967069\pi$
$6$	−1.61798	+	0.618168i	−0.660539	+	0.252366i
$7$	−0.965926	+	0.258819i	−0.365086	+	0.0978244i
$7$	−0.965926	+	0.258819i	−0.365086	+	0.0978244i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.936020	+	2.85024i	−0.312007	+	0.950080i
$10$	2.44115	−	1.40940i	0.771960	−	0.445692i
$11$	−3.39562	−	0.909853i	−1.02382	−	0.274331i	−0.292425	−	0.956288i	$-0.594462\pi$
$11$	−3.39562	−	0.909853i	−1.02382	−	0.274331i	−0.731392	+	0.681957i	$0.761129\pi$
$12$	−0.178340	−	1.72285i	−0.0514822	−	0.497343i
$13$	−3.11895	+	1.80892i	−0.865040	+	0.501703i
$13$	−3.11895	+	1.80892i	−0.865040	+	0.501703i
$14$		−	1.00000i		−	0.267261i
$15$	0.771343	−	4.82099i	0.199160	−	1.24477i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.364026	−	0.630512i	0.0882894	−	0.152922i	−0.818499	−	0.574508i	$-0.805193\pi$
$17$	0.364026	−	0.630512i	0.0882894	−	0.152922i	0.906788	+	0.421587i	$0.138527\pi$
$18$	−2.51086	−	1.64182i	−0.591815	−	0.386981i
$19$	−0.985142	−	3.67660i	−0.226007	−	0.843470i	−0.981999	−	0.188888i	$-0.939512\pi$
$19$	−0.985142	−	3.67660i	−0.226007	−	0.843470i	0.755992	−	0.654581i	$-0.227155\pi$
$20$	0.729559	+	2.72275i	0.163134	+	0.608826i
$21$	−1.34434	−	1.09213i	−0.293359	−	0.238322i
$22$	1.75770	−	3.04443i	0.374743	−	0.649074i
$23$	−2.57429	−	4.45880i	−0.536776	−	0.929724i	−0.999075	−	0.0429994i	$-0.986309\pi$
$23$	−2.57429	−	4.45880i	−0.536776	−	0.929724i	0.462299	−	0.886724i	$-0.347025\pi$
$24$	1.71030	+	0.273642i	0.349113	+	0.0558570i
$25$			2.94564i			0.589127i
$26$	−0.940036	−	3.48085i	−0.184356	−	0.682651i
$27$	−4.94935	+	1.58237i	−0.952504	+	0.304527i
$28$	0.965926	+	0.258819i	0.182543	+	0.0489122i
$29$	−4.47106	+	2.58137i	−0.830255	+	0.479348i	−0.853940	−	0.520372i	$-0.825793\pi$
$29$	−4.47106	+	2.58137i	−0.830255	+	0.479348i	0.0236850	+	0.999719i	$0.492460\pi$
$30$	4.45708	+	1.99282i	0.813748	+	0.363838i
$31$	−4.56454	+	4.56454i	−0.819815	+	0.819815i	−0.986081	−	0.166266i	$-0.946829\pi$
$31$	−4.56454	+	4.56454i	−0.819815	+	0.819815i	0.166266	+	0.986081i	$0.446829\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−2.17311	−	5.68786i	−0.378290	−	0.990129i
$34$	0.514811	+	0.514811i	0.0882894	+	0.0882894i
$35$	2.44115	+	1.40940i	0.412630	+	0.238232i
$36$	2.23574	−	2.00037i	0.372623	−	0.333395i
$37$	1.73320	−	6.46839i	0.284936	−	1.06340i	−0.663949	−	0.747777i	$-0.731121\pi$
$37$	1.73320	−	6.46839i	0.284936	−	1.06340i	0.948886	−	0.315620i	$-0.102212\pi$
$38$	3.80629			0.617463
$39$	−5.70609	−	2.53782i	−0.913706	−	0.406376i
$40$	−2.81880			−0.445692
$41$	2.39422	−	8.93537i	0.373915	−	1.39547i	−0.481009	−	0.876716i	$-0.659729\pi$
$41$	2.39422	−	8.93537i	0.373915	−	1.39547i	0.854924	−	0.518754i	$-0.173604\pi$
$42$	1.40286	−	1.01587i	0.216466	−	0.156752i
$43$	9.77091	+	5.64124i	1.49005	+	0.860281i	0.999935	−	0.0113765i	$-0.00362134\pi$
$43$	9.77091	+	5.64124i	1.49005	+	0.860281i	0.490115	+	0.871658i	$0.336955\pi$
$44$	2.48576	+	2.48576i	0.374743	+	0.374743i
$45$	7.54675	−	3.81541i	1.12500	−	0.568768i
$46$	4.97314	−	1.33255i	0.733250	−	0.196474i
$47$	−7.98109	+	7.98109i	−1.16416	+	1.16416i	−0.180607	+	0.983555i	$0.557806\pi$
$47$	−7.98109	+	7.98109i	−1.16416	+	1.16416i	−0.983555	+	0.180607i	$0.942194\pi$
$48$	−0.706976	+	1.58120i	−0.102043	+	0.228226i
$49$	0.866025	−	0.500000i	0.123718	−	0.0714286i
$50$	−2.84527	−	0.762387i	−0.402381	−	0.107818i
$51$	1.25432	−	0.129841i	0.175640	−	0.0181813i
$52$	3.60554	−	0.00709410i	0.499999	−	0.000983775i
$53$			8.37700i			1.15067i	0.817918	+	0.575335i	$0.195128\pi$
$53$			8.37700i			1.15067i	−0.817918	+	0.575335i	$0.804872\pi$
$54$	−0.247463	−	5.19026i	−0.0336754	−	0.706304i
$55$	4.95461	+	8.58163i	0.668079	+	1.15715i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	4.15697	−	5.11696i	0.550604	−	0.677757i
$58$	−1.33621	−	4.98682i	−0.175454	−	0.654801i
$59$	1.91793	+	7.15783i	0.249694	+	0.931870i	0.970966	+	0.239218i	$0.0768911\pi$
$59$	1.91793	+	7.15783i	0.249694	+	0.931870i	−0.721272	+	0.692652i	$0.756442\pi$
$60$	−3.07850	+	3.78943i	−0.397432	+	0.489213i
$61$	−0.617982	+	1.07038i	−0.0791245	+	0.137048i	−0.902872	−	0.429909i	$-0.858546\pi$
$61$	−0.617982	+	1.07038i	−0.0791245	+	0.137048i	0.823748	+	0.566956i	$0.191879\pi$
$62$	−3.22761	−	5.59039i	−0.409907	−	0.709981i
$63$	0.166429	−	2.99538i	0.0209681	−	0.377382i
$64$		−	1.00000i		−	0.125000i
$65$	9.82218	+	2.61114i	1.21829	+	0.323872i
$66$	6.05649	−	0.626935i	0.745503	−	0.0771704i
$67$	10.5323	+	2.82212i	1.28673	+	0.344777i	0.836416	−	0.548095i	$-0.184647\pi$
$67$	10.5323	+	2.82212i	1.28673	+	0.344777i	0.450310	+	0.892872i	$0.351314\pi$
$68$	−0.630512	+	0.364026i	−0.0764608	+	0.0441447i
$69$	3.63992	−	8.14091i	0.438195	−	0.980051i
$70$	−1.99319	+	1.99319i	−0.238232	+	0.238232i
$71$	−4.48721	+	1.20234i	−0.532534	+	0.142692i	−0.515058	−	0.857155i	$-0.672230\pi$
$71$	−4.48721	+	1.20234i	−0.532534	+	0.142692i	−0.0174756	+	0.999847i	$0.505563\pi$
$72$	1.35356	+	2.67729i	0.159518	+	0.315522i
$73$	−6.36810	−	6.36810i	−0.745330	−	0.745330i	0.228268	−	0.973598i	$-0.426694\pi$
$73$	−6.36810	−	6.36810i	−0.745330	−	0.745330i	−0.973598	+	0.228268i	$0.926694\pi$
$74$	5.79940	+	3.34829i	0.674167	+	0.389230i
$75$	−4.13231	+	2.99238i	−0.477158	+	0.345530i
$76$	−0.985142	+	3.67660i	−0.113003	+	0.421735i
$77$	3.51540			0.400617
$78$	3.92819	−	4.85483i	0.444780	−	0.549701i
$79$	−3.35978			−0.378005			−0.189002	−	0.981977i	$-0.560525\pi$
$79$	−3.35978			−0.378005			−0.189002	+	0.981977i	$0.560525\pi$
$80$	0.729559	−	2.72275i	0.0815672	−	0.304413i
$81$	−7.24773	−	5.33576i	−0.805304	−	0.592862i
$82$	8.01123	+	4.62529i	0.884692	+	0.510777i
$83$	−0.552914	−	0.552914i	−0.0606901	−	0.0606901i	0.676110	−	0.736800i	$-0.263664\pi$
$83$	−0.552914	−	0.552914i	−0.0606901	−	0.0606901i	−0.736800	+	0.676110i	$0.763664\pi$
$84$	0.618168	+	1.61798i	0.0674476	+	0.176536i
$85$	−1.98231	+	0.531158i	−0.215011	+	0.0576121i
$86$	−7.97792	+	7.97792i	−0.860281	+	0.860281i
$87$	−8.16330	−	3.64993i	−0.875198	−	0.391314i
$88$	−3.04443	+	1.75770i	−0.324537	+	0.187372i
$89$	−7.13603	−	1.91209i	−0.756418	−	0.202682i	−0.140055	−	0.990144i	$-0.544728\pi$
$89$	−7.13603	−	1.91209i	−0.756418	−	0.202682i	−0.616363	+	0.787462i	$0.711395\pi$
$90$	1.73216	+	8.27710i	0.182586	+	0.872483i
$91$	2.54449	−	2.55452i	0.266735	−	0.267787i
$92$			5.14858i			0.536776i
$93$	−11.0404	−	1.76642i	−1.14483	−	0.183170i
$94$	−5.64349	−	9.77480i	−0.582081	−	1.00819i
$95$	−5.36459	+	9.29175i	−0.550396	+	0.953313i
$96$	−1.34434	−	1.09213i	−0.137206	−	0.111465i
$97$	−2.54406	−	9.49457i	−0.258310	−	0.964027i	−0.966219	−	0.257723i	$-0.917028\pi$
$97$	−2.54406	−	9.49457i	−0.258310	−	0.964027i	0.707908	−	0.706304i	$-0.249639\pi$
$98$	0.258819	+	0.965926i	0.0261447	+	0.0975732i
$99$	5.77166	−	8.82668i	0.580074	−	0.887115i
$100$	1.47282	−	2.55100i	0.147282	−	0.255100i
$101$	9.49553	+	16.4467i	0.944840	+	1.63651i	0.756071	+	0.654490i	$0.227117\pi$
$101$	9.49553	+	16.4467i	0.944840	+	1.63651i	0.188770	+	0.982021i	$0.439550\pi$
$102$	−0.199226	+	1.24519i	−0.0197263	+	0.123292i
$103$		−	11.3278i		−	1.11616i	−0.829786	−	0.558082i	$-0.811538\pi$
$103$		−	11.3278i		−	1.11616i	0.829786	−	0.558082i	$-0.188462\pi$
$104$	−0.926331	+	3.48452i	−0.0908342	+	0.341686i
$105$	0.502704	+	4.85636i	0.0490589	+	0.473932i
$106$	−8.09157	−	2.16813i	−0.785922	−	0.210587i
$107$	−3.75177	+	2.16609i	−0.362697	+	0.209403i	−0.670263	−	0.742123i	$-0.733819\pi$
$107$	−3.75177	+	2.16609i	−0.362697	+	0.209403i	0.307566	+	0.951527i	$0.400486\pi$
$108$	5.07745	+	1.10431i	0.488578	+	0.106262i
$109$	−7.29335	+	7.29335i	−0.698576	+	0.698576i	−0.964103	−	0.265527i	$-0.914454\pi$
$109$	−7.29335	+	7.29335i	−0.698576	+	0.698576i	0.265527	+	0.964103i	$0.414454\pi$
$110$	−9.57157	+	2.56469i	−0.912613	+	0.244534i
$111$	10.8349	−	4.13961i	1.02841	−	0.392914i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	−2.28140	−	1.31717i	−0.214616	−	0.123909i	0.388839	−	0.921306i	$-0.372876\pi$
$113$	−2.28140	−	1.31717i	−0.214616	−	0.123909i	−0.603455	+	0.797397i	$0.706210\pi$
$114$	3.86670	+	5.33969i	0.362149	+	0.500108i
$115$	−3.75619	+	14.0183i	−0.350267	+	1.30721i
$116$	5.16274			0.479348
$117$	−2.23645	−	10.5829i	−0.206760	−	0.978392i
$118$	−7.41033			−0.682176
$119$	−0.188434	+	0.703245i	−0.0172737	+	0.0644664i
$120$	−2.86353	−	3.95438i	−0.261404	−	0.360984i
$121$	1.17611	+	0.679026i	0.106919	+	0.0617297i
$122$	−0.873959	−	0.873959i	−0.0791245	−	0.0791245i
$123$	14.9673	−	5.71841i	1.34955	−	0.515611i
$124$	6.23527	−	1.67074i	0.559944	−	0.150037i
$125$	−4.09474	+	4.09474i	−0.366245	+	0.366245i
$126$	2.85024	+	0.936020i	0.253920	+	0.0833873i
$127$	−9.52716	+	5.50051i	−0.845398	+	0.488091i	−0.859096	−	0.511815i	$-0.828973\pi$
$127$	−9.52716	+	5.50051i	−0.845398	+	0.488091i	0.0136972	+	0.999906i	$0.495640\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	2.01211	+	19.4380i	0.177157	+	1.71142i
$130$	−5.06434	+	8.81168i	−0.444172	+	0.772836i
$131$		−	10.7166i		−	0.936309i	−0.883647	−	0.468155i	$-0.844919\pi$
$131$		−	10.7166i		−	0.936309i	0.883647	−	0.468155i	$-0.155081\pi$
$132$	−0.961963	+	6.01239i	−0.0837281	+	0.523311i
$133$	1.90315	+	3.29635i	0.165024	+	0.285830i
$134$	−5.45192	+	9.44300i	−0.470974	+	0.815751i
$135$	13.0190	+	6.71105i	1.12050	+	0.577596i
$136$	−0.188434	−	0.703245i	−0.0161581	−	0.0603028i
$137$	1.31518	+	4.90832i	0.112364	+	0.419346i	0.999076	−	0.0429746i	$-0.0136835\pi$
$137$	1.31518	+	4.90832i	0.112364	+	0.419346i	−0.886713	+	0.462321i	$0.847017\pi$
$138$	6.92144	+	5.62292i	0.589192	+	0.478654i
$139$	−8.46041	+	14.6539i	−0.717602	+	1.24292i	0.244345	+	0.969688i	$0.421427\pi$
$139$	−8.46041	+	14.6539i	−0.717602	+	1.24292i	−0.961947	+	0.273235i	$0.911906\pi$
$140$	−1.40940	−	2.44115i	−0.119116	−	0.206315i
$141$	−19.3041	−	3.08859i	−1.62570	−	0.260106i
$142$		−	4.64550i		−	0.389842i
$143$	12.2366	−	3.30460i	1.02328	−	0.276345i
$144$	−2.93639	+	0.614503i	−0.244699	+	0.0512086i
$145$	14.0568	+	3.76652i	1.16736	+	0.312793i
$146$	7.79930	−	4.50293i	0.645475	−	0.372665i
$147$	1.58120	+	0.706976i	0.130415	+	0.0583104i
$148$	−4.73519	+	4.73519i	−0.389230	+	0.389230i
$149$	14.9415	−	4.00356i	1.22405	−	0.327984i	0.411792	−	0.911278i	$-0.364903\pi$
$149$	14.9415	−	4.00356i	1.22405	−	0.327984i	0.812261	+	0.583294i	$0.198236\pi$
$150$	−1.82090	−	4.76599i	−0.148676	−	0.389141i
$151$	6.88747	+	6.88747i	0.560494	+	0.560494i	0.929448	−	0.368954i	$-0.120284\pi$
$151$	6.88747	+	6.88747i	0.560494	+	0.560494i	−0.368954	+	0.929448i	$0.620284\pi$
$152$	−3.29635	−	1.90315i	−0.267369	−	0.154366i
$153$	1.45638	+	1.62773i	0.117741	+	0.131595i
$154$	−0.909853	+	3.39562i	−0.0733180	+	0.273627i
$155$	18.1960			1.46154
$156$	3.67271	+	5.05086i	0.294052	+	0.404392i
$157$	−11.9606			−0.954562			−0.477281	−	0.878751i	$-0.658378\pi$
$157$	−11.9606			−0.954562			−0.477281	+	0.878751i	$0.658378\pi$
$158$	0.869575	−	3.24530i	0.0691797	−	0.258182i
$159$	−11.7517	+	8.50994i	−0.931974	+	0.674882i
$160$	2.44115	+	1.40940i	0.192990	+	0.111423i
$161$	3.64059	+	3.64059i	0.286919	+	0.286919i
$162$	7.02980	−	5.61978i	0.552313	−	0.441531i
$163$	19.3241	−	5.17788i	1.51358	−	0.405563i	0.595958	−	0.803016i	$-0.296773\pi$
$163$	19.3241	−	5.17788i	1.51358	−	0.405563i	0.917622	+	0.397453i	$0.130106\pi$
$164$	−6.54114	+	6.54114i	−0.510777	+	0.510777i
$165$	−7.00558	+	15.6684i	−0.545384	+	1.21979i
$166$	0.677178	−	0.390969i	0.0525592	−	0.0303451i
$167$	−15.1558	−	4.06098i	−1.17279	−	0.314248i	−0.380727	−	0.924687i	$-0.624326\pi$
$167$	−15.1558	−	4.06098i	−1.17279	−	0.314248i	−0.792063	+	0.610439i	$0.790993\pi$
$168$	−1.72285	+	0.178340i	−0.132920	+	0.0137592i
$169$	6.45565	−	11.2838i	0.496588	−	0.867986i
$170$		−	2.05224i		−	0.157399i
$171$	11.4013	+	0.633479i	0.871879	+	0.0484434i
$172$	−5.64124	−	9.77091i	−0.430141	−	0.745025i
$173$	8.54222	−	14.7956i	0.649453	−	1.12489i	−0.333801	−	0.942644i	$-0.608331\pi$
$173$	8.54222	−	14.7956i	0.649453	−	1.12489i	0.983254	−	0.182242i	$-0.0583355\pi$
$174$	5.63838	−	6.94047i	0.427444	−	0.526156i
$175$	−0.762387	−	2.84527i	−0.0576310	−	0.215082i
$176$	−0.909853	−	3.39562i	−0.0685828	−	0.255954i
$177$	−8.09304	+	9.96200i	−0.608310	+	0.748790i
$178$	3.69388	−	6.39799i	0.276868	−	0.479550i
$179$	5.32102	+	9.21627i	0.397711	+	0.688856i	0.993443	−	0.114327i	$-0.0364712\pi$
$179$	5.32102	+	9.21627i	0.397711	+	0.688856i	−0.595732	+	0.803183i	$0.703138\pi$
$180$	−8.44338	−	0.469131i	−0.629332	−	0.0349670i
$181$		−	14.4885i		−	1.07692i	−0.842650	−	0.538462i	$-0.819005\pi$
$181$		−	14.4885i		−	1.07692i	0.842650	−	0.538462i	$-0.180995\pi$
$182$	1.80892	+	3.11895i	0.134086	+	0.231192i
$183$	−2.12938	+	0.220421i	−0.157408	+	0.0162940i
$184$	−4.97314	−	1.33255i	−0.366625	−	0.0982369i
$185$	−16.3474	+	9.43815i	−1.20188	+	0.693907i
$186$	4.56369	−	10.2070i	0.334626	−	0.748413i
$187$	−1.80977	+	1.80977i	−0.132343	+	0.132343i
$188$	10.9024	−	2.92128i	0.795137	−	0.213056i
$189$	4.37116	−	2.80944i	0.317955	−	0.204356i
$190$	−7.58668	−	7.58668i	−0.550396	−	0.550396i
$191$	9.06835	+	5.23561i	0.656163	+	0.378836i	0.790813	−	0.612057i	$-0.209658\pi$
$191$	9.06835	+	5.23561i	0.656163	+	0.378836i	−0.134651	+	0.990893i	$0.542991\pi$
$192$	1.40286	−	1.01587i	0.101243	−	0.0733140i
$193$	2.90239	−	10.8319i	0.208919	−	0.779696i	−0.779300	−	0.626651i	$-0.784425\pi$
$193$	2.90239	−	10.8319i	0.208919	−	0.779696i	0.988219	−	0.153045i	$-0.0489081\pi$
$194$	9.82950			0.705717
$195$	6.31499	+	16.4317i	0.452226	+	1.17670i
$196$	−1.00000			−0.0714286
$197$	−0.725744	+	2.70851i	−0.0517071	+	0.192974i	−0.986948	−	0.161038i	$-0.948516\pi$
$197$	−0.725744	+	2.70851i	−0.0517071	+	0.192974i	0.935241	+	0.354011i	$0.115183\pi$
$198$	7.03211	+	7.85951i	0.499750	+	0.558551i
$199$	−7.15988	−	4.13376i	−0.507551	−	0.293034i	0.224276	−	0.974526i	$-0.427998\pi$
$199$	−7.15988	−	4.13376i	−0.507551	−	0.293034i	−0.731826	+	0.681491i	$0.761332\pi$
$200$	2.08288	+	2.08288i	0.147282	+	0.147282i
$201$	6.74041	+	17.6422i	0.475432	+	1.24439i
$202$	−18.3440	+	4.91525i	−1.29068	+	0.345836i
$203$	3.65061	−	3.65061i	0.256222	−	0.256222i
$204$	−1.15120	−	0.514716i	−0.0805998	−	0.0360373i
$205$	−22.5821	+	13.0378i	−1.57720	+	0.910597i
$206$	10.9418	+	2.93186i	0.762354	+	0.204272i
$207$	15.1182	−	3.16381i	1.05079	−	0.219900i
$208$	−3.12604	−	1.79663i	−0.216752	−	0.124574i
$209$			13.3807i			0.925559i
$210$	−4.82099	−	0.771343i	−0.332680	−	0.0532277i
$211$	−1.30347	−	2.25767i	−0.0897344	−	0.155425i	0.817664	−	0.575695i	$-0.195268\pi$
$211$	−1.30347	−	2.25767i	−0.0897344	−	0.155425i	−0.907399	+	0.420271i	$0.861935\pi$
$212$	4.18850	−	7.25470i	0.287668	−	0.498255i
$213$	−6.24513	−	5.07349i	−0.427909	−	0.347630i
$214$	−1.12125	−	4.18456i	−0.0766470	−	0.286050i
$215$	−8.23124	−	30.7194i	−0.561366	−	2.09505i
$216$	−2.38082	+	4.61863i	−0.161994	+	0.314258i
$217$	3.22761	−	5.59039i	0.219105	−	0.379501i
$218$	−5.15718	−	8.93249i	−0.349288	−	0.604985i
$219$	2.46438	−	15.4027i	0.166528	−	1.04082i
$220$		−	9.90922i		−	0.668079i
$221$	0.00516488	+	2.62503i	0.000347427	+	0.176578i
$222$	1.19426	+	11.5372i	0.0801537	+	0.774323i
$223$	17.9143	+	4.80012i	1.19963	+	0.321440i	0.802685	−	0.596403i	$-0.203404\pi$
$223$	17.9143	+	4.80012i	1.19963	+	0.321440i	0.396944	+	0.917843i	$0.370071\pi$
$224$	0.866025	−	0.500000i	0.0578638	−	0.0334077i
$225$	−8.39577	−	2.75717i	−0.559718	−	0.183812i
$226$	1.86276	−	1.86276i	0.123909	−	0.123909i
$227$	−21.1298	+	5.66172i	−1.40244	+	0.375782i	−0.879219	−	0.476418i	$-0.841935\pi$
$227$	−21.1298	+	5.66172i	−1.40244	+	0.375782i	−0.523217	+	0.852200i	$0.675268\pi$
$228$	−6.15852	+	2.35293i	−0.407858	+	0.155827i
$229$	−5.94761	−	5.94761i	−0.393029	−	0.393029i	0.482736	−	0.875766i	$-0.339643\pi$
$229$	−5.94761	−	5.94761i	−0.393029	−	0.393029i	−0.875766	+	0.482736i	$0.839643\pi$
$230$	−12.5685	−	7.25640i	−0.828740	−	0.478473i
$231$	3.57119	+	4.93161i	0.234967	+	0.324476i
$232$	−1.33621	+	4.98682i	−0.0877268	+	0.327401i
$233$	−3.84393			−0.251824			−0.125912	−	0.992041i	$-0.540186\pi$
$233$	−3.84393			−0.251824			−0.125912	+	0.992041i	$0.540186\pi$
$234$	10.8012	+	0.578819i	0.706094	+	0.0378386i
$235$	31.8157			2.07543
$236$	1.91793	−	7.15783i	0.124847	−	0.465935i
$237$	−3.41310	−	4.71329i	−0.221705	−	0.306161i
$238$	−0.630512	−	0.364026i	−0.0408700	−	0.0235963i
$239$	−10.3322	−	10.3322i	−0.668335	−	0.668335i	0.288996	−	0.957330i	$-0.406679\pi$
$239$	−10.3322	−	10.3322i	−0.668335	−	0.668335i	−0.957330	+	0.288996i	$0.906679\pi$
$240$	4.56077	−	1.74249i	0.294397	−	0.112477i
$241$	−6.36623	+	1.70583i	−0.410085	+	0.109882i	−0.457963	−	0.888971i	$-0.651421\pi$
$241$	−6.36623	+	1.70583i	−0.410085	+	0.109882i	0.0478780	+	0.998853i	$0.484754\pi$
$242$	−0.960288	+	0.960288i	−0.0617297	+	0.0617297i
$243$	0.122566	−	15.5880i	0.00786264	−	0.999969i
$244$	1.07038	−	0.617982i	0.0685238	−	0.0395623i
$245$	−2.72275	−	0.729559i	−0.173950	−	0.0466098i
$246$	1.64974	+	15.9373i	0.105184	+	1.01613i
$247$	9.72326	+	9.68507i	0.618676	+	0.616246i
$248$			6.45523i			0.409907i
$249$	0.213971	−	1.33735i	0.0135599	−	0.0847509i
$250$	−2.89542	−	5.01501i	−0.183122	−	0.317177i
$251$	−0.974313	+	1.68756i	−0.0614981	+	0.106518i	−0.895135	−	0.445795i	$-0.852921\pi$
$251$	−0.974313	+	1.68756i	−0.0614981	+	0.106518i	0.833637	+	0.552312i	$0.186254\pi$
$252$	−1.64182	+	2.51086i	−0.103425	+	0.158169i
$253$	4.68445	+	17.4826i	0.294509	+	1.09912i
$254$	−2.84727	−	10.6262i	−0.178654	−	0.666745i
$255$	−2.75890	−	2.24131i	−0.172769	−	0.140356i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.40181	−	16.2844i	−0.586469	−	1.01579i	−0.994691	−	0.102911i	$-0.967184\pi$
$257$	−9.40181	−	16.2844i	−0.586469	−	1.01579i	0.408222	−	0.912883i	$-0.366149\pi$
$258$	−19.2964	−	3.08736i	−1.20134	−	0.192211i
$259$			6.69657i			0.416105i
$260$	−7.20069	−	7.17241i	−0.446568	−	0.444814i
$261$	−3.17252	−	15.1598i	−0.196374	−	0.938368i
$262$	10.3514	+	2.77365i	0.639511	+	0.171357i
$263$	24.2157	−	13.9809i	1.49320	−	0.862100i	0.493232	−	0.869898i	$-0.335815\pi$
$263$	24.2157	−	13.9809i	1.49320	−	0.862100i	0.999970	+	0.00779731i	$0.00248199\pi$
$264$	−5.55854	−	2.48530i	−0.342105	−	0.152960i
$265$	16.6970	−	16.6970i	1.02569	−	1.02569i
$266$	−3.67660	+	0.985142i	−0.225427	+	0.0604029i
$267$	−4.56688	−	11.9533i	−0.279488	−	0.731529i
$268$	−7.71018	−	7.71018i	−0.470974	−	0.470974i
$269$	−21.6706	−	12.5115i	−1.32128	−	0.762842i	−0.337348	−	0.941380i	$-0.609530\pi$
$269$	−21.6706	−	12.5115i	−1.32128	−	0.762842i	−0.983933	+	0.178538i	$0.942863\pi$
$270$	−9.85194	+	10.8384i	−0.599570	+	0.659605i
$271$	0.320708	−	1.19690i	0.0194816	−	0.0727065i	−0.955501	−	0.294989i	$-0.904684\pi$
$271$	0.320708	−	1.19690i	0.0194816	−	0.0727065i	0.974982	+	0.222282i	$0.0713507\pi$
$272$	0.728053			0.0441447
$273$	6.16850	+	0.974496i	0.373334	+	0.0589792i
$274$	−5.08147			−0.306983
$275$	2.68010	−	10.0023i	0.161616	−	0.603159i
$276$	−7.22272	+	5.23028i	−0.434757	+	0.314826i
$277$	−17.5530	−	10.1342i	−1.05466	−	0.608908i	−0.130709	−	0.991421i	$-0.541725\pi$
$277$	−17.5530	−	10.1342i	−1.05466	−	0.608908i	−0.923950	+	0.382513i	$0.875059\pi$
$278$	−11.9648	−	11.9648i	−0.717602	−	0.717602i
$279$	−8.73753	−	17.2825i	−0.523102	−	1.03468i
$280$	2.72275	−	0.729559i	0.162716	−	0.0435995i
$281$	−12.0057	+	12.0057i	−0.716200	+	0.716200i	−0.967825	−	0.251625i	$-0.919035\pi$
$281$	−12.0057	+	12.0057i	−0.716200	+	0.716200i	0.251625	+	0.967825i	$0.419035\pi$
$282$	7.97962	−	17.8469i	0.475179	−	1.06277i
$283$	0.701167	−	0.404819i	0.0416801	−	0.0240640i	−0.479015	−	0.877807i	$-0.659006\pi$
$283$	0.701167	−	0.404819i	0.0416801	−	0.0240640i	0.520695	+	0.853743i	$0.325673\pi$
$284$	4.48721	+	1.20234i	0.266267	+	0.0713460i
$285$	−18.4847	+	1.91344i	−1.09494	+	0.113342i
$286$	0.0249386	+	12.6749i	0.00147465	+	0.749485i
$287$			9.25057i			0.546044i
$288$	0.166429	−	2.99538i	0.00980695	−	0.176504i
$289$	8.23497	+	14.2634i	0.484410	+	0.839023i
$290$	−7.27636	+	12.6030i	−0.427283	+	0.740075i
$291$	10.7351	−	13.2142i	0.629302	−	0.774630i
$292$	2.33089	+	8.69899i	0.136405	+	0.509070i
$293$	−3.34213	−	12.4730i	−0.195249	−	0.728680i	−0.992202	−	0.124638i	$-0.960223\pi$
$293$	−3.34213	−	12.4730i	−0.195249	−	0.728680i	0.796953	−	0.604041i	$-0.206444\pi$
$294$	−1.09213	+	1.34434i	−0.0636943	+	0.0784035i
$295$	10.4441	−	18.0897i	0.608080	−	1.05323i
$296$	−3.34829	−	5.79940i	−0.194615	−	0.337083i
$297$	18.2458	−	0.869931i	1.05873	−	0.0504785i
$298$			15.4686i			0.896069i
$299$	16.0947	+	9.25008i	0.930778	+	0.534946i
$300$	5.07488	−	0.525324i	0.292998	−	0.0303296i
$301$	−10.8980	−	2.92012i	−0.628153	−	0.168313i
$302$	−8.43539	+	4.87017i	−0.485402	+	0.280247i
$303$	−13.4262	+	30.0286i	−0.771316	+	1.72510i
$304$	2.69146	−	2.69146i	0.154366	−	0.154366i
$305$	3.36522	−	0.901709i	0.192692	−	0.0516317i
$306$	−1.94921	+	0.985462i	−0.111429	+	0.0563351i
$307$	2.58025	+	2.58025i	0.147263	+	0.147263i	0.776894	−	0.629631i	$-0.216794\pi$
$307$	2.58025	+	2.58025i	0.147263	+	0.147263i	−0.629631	+	0.776894i	$0.716794\pi$
$308$	−3.04443	−	1.75770i	−0.173472	−	0.100154i
$309$	15.8913	−	11.5076i	0.904026	−	0.654643i
$310$	−4.70947	+	17.5760i	−0.267480	+	0.998249i
$311$	14.3612			0.814347			0.407173	−	0.913351i	$-0.366515\pi$
$311$	14.3612			0.814347			0.407173	+	0.913351i	$0.366515\pi$
$312$	−5.82932	+	2.24031i	−0.330020	+	0.126833i
$313$	−11.0763			−0.626070			−0.313035	−	0.949742i	$-0.601346\pi$
$313$	−11.0763			−0.626070			−0.313035	+	0.949742i	$0.601346\pi$
$314$	3.09564	−	11.5531i	0.174697	−	0.651978i
$315$	−6.30210	+	5.63864i	−0.355083	+	0.317702i
$316$	2.90966	+	1.67989i	0.163681	+	0.0945012i
$317$	−12.7384	−	12.7384i	−0.715462	−	0.715462i	0.252210	−	0.967673i	$-0.418843\pi$
$317$	−12.7384	−	12.7384i	−0.715462	−	0.715462i	−0.967673	+	0.252210i	$0.918843\pi$
$318$	−5.17840	−	13.5538i	−0.290390	−	0.760062i
$319$	17.5307	−	4.69733i	0.981529	−	0.263000i
$320$	−1.99319	+	1.99319i	−0.111423	+	0.111423i
$321$	−6.85002	−	3.06274i	−0.382331	−	0.170945i
$322$	−4.45880	+	2.57429i	−0.248479	+	0.143459i
$323$	−2.67676	−	0.717235i	−0.148939	−	0.0399080i
$324$	3.60884	+	8.24477i	0.200491	+	0.458043i
$325$	−5.32841	−	9.18728i	−0.295567	−	0.509619i
$326$			20.0058i			1.10802i
$327$	−17.6406	−	2.82244i	−0.975529	−	0.156081i
$328$	−4.62529	−	8.01123i	−0.255389	−	0.442346i
$329$	5.64349	−	9.77480i	0.311135	−	0.538902i
$330$	−13.3214	−	10.8222i	−0.733317	−	0.595740i
$331$	2.54248	+	9.48865i	0.139747	+	0.521543i	0.999933	+	0.0115630i	$0.00368069\pi$
$331$	2.54248	+	9.48865i	0.139747	+	0.521543i	−0.860186	+	0.509980i	$0.829653\pi$
$332$	0.202380	+	0.755294i	0.0111071	+	0.0414521i
$333$	16.8142	+	10.9946i	0.921410	+	0.602499i
$334$	7.84522	−	13.5883i	0.429271	−	0.743520i
$335$	−15.3679	−	26.6179i	−0.839637	−	1.45429i
$336$	0.273642	−	1.71030i	0.0149284	−	0.0933044i
$337$			8.82967i			0.480983i	0.970651	+	0.240491i	$0.0773086\pi$
$337$			8.82967i			0.480983i	−0.970651	+	0.240491i	$0.922691\pi$
$338$	9.22849	+	9.15614i	0.501964	+	0.498029i
$339$	−0.469806	−	4.53855i	−0.0255164	−	0.246500i
$340$	1.98231	+	0.531158i	0.107506	+	0.0288061i
$341$	19.6525	−	11.3464i	1.06424	−	0.614440i
$342$	−3.56277	+	10.8489i	−0.192652	+	0.586639i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	10.8980	−	2.92012i	0.587583	−	0.157442i
$345$	−23.4815	+	8.97135i	−1.26420	+	0.483001i
$346$	12.0805	+	12.0805i	0.649453	+	0.649453i
$347$	2.00940	+	1.16013i	0.107870	+	0.0622788i	0.552964	−	0.833205i	$-0.313497\pi$
$347$	2.00940	+	1.16013i	0.107870	+	0.0622788i	−0.445094	+	0.895484i	$0.646830\pi$
$348$	5.24466	+	7.24258i	0.281143	+	0.388243i
$349$	−2.88614	+	10.7712i	−0.154491	+	0.576569i	0.844657	+	0.535308i	$0.179804\pi$
$349$	−2.88614	+	10.7712i	−0.154491	+	0.576569i	−0.999148	+	0.0412615i	$0.986862\pi$
$350$	2.94564			0.157451
$351$	12.5744	−	13.8883i	0.671172	−	0.741302i
$352$	3.51540			0.187372
$353$	8.68039	−	32.3957i	0.462011	−	1.72425i	−0.204604	−	0.978845i	$-0.565591\pi$
$353$	8.68039	−	32.3957i	0.462011	−	1.72425i	0.666615	−	0.745402i	$-0.267743\pi$
$354$	−7.52792	−	10.3956i	−0.400105	−	0.552522i
$355$	11.3404	+	6.54737i	0.601885	+	0.347498i
$356$	5.22394	+	5.22394i	0.276868	+	0.276868i
$357$	−1.17798	+	0.450059i	−0.0623452	+	0.0238196i
$358$	−10.2794	+	2.75436i	−0.543284	+	0.145572i
$359$	−1.67236	+	1.67236i	−0.0882636	+	0.0882636i	−0.749860	−	0.661596i	$-0.769879\pi$
$359$	−1.67236	+	1.67236i	−0.0882636	+	0.0882636i	0.661596	+	0.749860i	$0.269879\pi$
$360$	2.63845	−	8.03426i	0.139059	−	0.423443i
$361$	3.90761	−	2.25606i	0.205664	−	0.118740i
$362$	13.9949	+	3.74991i	0.735553	+	0.197091i
$363$	0.242195	+	2.33971i	0.0127119	+	0.122803i
$364$	−3.48085	+	0.940036i	−0.182446	+	0.0492713i
$365$			25.3857i			1.32875i
$366$	0.338212	−	2.11387i	0.0176786	−	0.110494i
$367$	−0.736212	−	1.27516i	−0.0384299	−	0.0665626i	0.846171	−	0.532912i	$-0.178902\pi$
$367$	−0.736212	−	1.27516i	−0.0384299	−	0.0665626i	−0.884601	+	0.466349i	$0.845569\pi$
$368$	2.57429	−	4.45880i	0.134194	−	0.232431i
$369$	23.2269	+	15.1878i	1.20914	+	0.790645i
$370$	−4.88555	−	18.2331i	−0.253987	−	0.947894i
$371$	−2.16813	−	8.09157i	−0.112564	−	0.420093i
$372$	8.67803	+	7.04995i	0.449935	+	0.365523i
$373$	−0.327301	+	0.566902i	−0.0169470	+	0.0293531i	−0.874375	−	0.485252i	$-0.838728\pi$
$373$	−0.327301	+	0.566902i	−0.0169470	+	0.0293531i	0.857428	+	0.514605i	$0.172061\pi$
$374$	−1.27970	−	2.21650i	−0.0661717	−	0.114613i
$375$	−9.90406	−	1.58462i	−0.511444	−	0.0818294i
$376$			11.2870i			0.582081i
$377$	9.27552	−	16.1389i	0.477713	−	0.831197i
$378$	1.58237	+	4.94935i	0.0813882	+	0.254567i
$379$	32.3766	+	8.67528i	1.66307	+	0.445619i	0.963230	−	0.268678i	$-0.0865866\pi$
$379$	32.3766	+	8.67528i	1.66307	+	0.445619i	0.699843	+	0.714297i	$0.253253\pi$
$380$	9.29175	−	5.36459i	0.476657	−	0.275198i
$381$	−17.3948	−	7.77745i	−0.891161	−	0.398451i
$382$	−7.40428	+	7.40428i	−0.378836	+	0.378836i
$383$	−14.7596	+	3.95481i	−0.754178	+	0.202081i	−0.615370	−	0.788238i	$-0.710994\pi$
$383$	−14.7596	+	3.95481i	−0.754178	+	0.202081i	−0.138807	+	0.990319i	$0.544327\pi$
$384$	0.618168	+	1.61798i	0.0315457	+	0.0825673i
$385$	−7.00688	−	7.00688i	−0.357103	−	0.357103i
$386$	9.71160	+	5.60700i	0.494308	+	0.285389i
$387$	−25.2247	+	22.5691i	−1.28224	+	1.14725i
$388$	−2.54406	+	9.49457i	−0.129155	+	0.482014i
$389$	36.4856			1.84990			0.924948	−	0.380095i	$-0.124109\pi$
$389$	36.4856			1.84990			0.924948	+	0.380095i	$0.124109\pi$
$390$	−17.5062	+	1.84697i	−0.886463	+	0.0935251i
$391$	−3.74844			−0.189567
$392$	0.258819	−	0.965926i	0.0130723	−	0.0487866i
$393$	15.0338	−	10.8866i	0.758355	−	0.549157i
$394$	−2.42839	−	1.40203i	−0.122340	−	0.0706333i
$395$	6.69669	+	6.69669i	0.336947	+	0.336947i
$396$	−9.41175	+	4.75830i	−0.472958	+	0.239114i
$397$	−5.14877	+	1.37961i	−0.258409	+	0.0692406i	−0.385698	−	0.922625i	$-0.626039\pi$
$397$	−5.14877	+	1.37961i	−0.258409	+	0.0692406i	0.127288	+	0.991866i	$0.459373\pi$
$398$	5.84602	−	5.84602i	0.293034	−	0.293034i
$399$	−2.69096	+	6.01850i	−0.134716	+	0.301302i
$400$	−2.55100	+	1.47282i	−0.127550	+	0.0736409i
$401$	22.6088	+	6.05800i	1.12903	+	0.302522i	0.774531	−	0.632536i	$-0.217986\pi$
$401$	22.6088	+	6.05800i	1.12903	+	0.302522i	0.354496	+	0.935058i	$0.384652\pi$
$402$	−18.7856	+	1.94459i	−0.936942	+	0.0969872i
$403$	5.97968	−	22.4934i	0.297869	−	1.12048i
$404$		−	18.9911i		−	0.944840i
$405$	3.81093	+	25.0813i	0.189367	+	1.24630i
$406$	2.58137	+	4.47106i	0.128111	+	0.221895i
$407$	−11.7706	+	20.3872i	−0.583446	+	1.01056i
$408$	0.795129	−	0.978751i	0.0393647	−	0.0484554i
$409$	−1.65310	−	6.16945i	−0.0817405	−	0.305060i	0.912937	−	0.408102i	$-0.133809\pi$
$409$	−1.65310	−	6.16945i	−0.0817405	−	0.305060i	−0.994677	+	0.103042i	$0.967142\pi$
$410$	−6.74884	−	25.1870i	−0.333302	−	1.24390i
$411$	−5.54963	+	6.83123i	−0.273743	+	0.336960i
$412$	−5.66391	+	9.81018i	−0.279041	+	0.483313i
$413$	−3.70516	−	6.41753i	−0.182319	−	0.315786i
$414$	−0.856874	+	15.4219i	−0.0421131	+	0.757947i
$415$			2.20413i			0.108196i
$416$	2.54449	−	2.55452i	0.124754	−	0.125246i
$417$	−29.1519	+	3.01765i	−1.42758	+	0.147775i
$418$	−12.9247	−	3.46317i	−0.632169	−	0.169389i
$419$	0.226652	−	0.130858i	0.0110727	−	0.00639281i	−0.494453	−	0.869204i	$-0.664632\pi$
$419$	0.226652	−	0.130858i	0.0110727	−	0.00639281i	0.505526	+	0.862811i	$0.331298\pi$
$420$	1.99282	−	4.45708i	0.0972399	−	0.217483i
$421$	−5.65910	+	5.65910i	−0.275808	+	0.275808i	−0.831433	−	0.555625i	$-0.812479\pi$
$421$	−5.65910	+	5.65910i	−0.275808	+	0.275808i	0.555625	+	0.831433i	$0.312479\pi$
$422$	2.51811	−	0.674724i	0.122579	−	0.0328451i
$423$	−15.2776	−	30.2185i	−0.742821	−	1.46927i
$424$	5.92344	+	5.92344i	0.287668	+	0.287668i
$425$	1.85726	+	1.07229i	0.0900903	+	0.0520137i
$426$	6.51697	−	4.71922i	0.315748	−	0.228647i
$427$	0.319891	−	1.19385i	0.0154806	−	0.0577744i
$428$	4.33217			0.209403
$429$	17.0667	+	13.8092i	0.823987	+	0.666712i
$430$	31.8031			1.53368
$431$	−3.49232	+	13.0335i	−0.168219	+	0.627802i	0.829389	+	0.558672i	$0.188689\pi$
$431$	−3.49232	+	13.0335i	−0.168219	+	0.627802i	−0.997608	+	0.0691297i	$0.977978\pi$
$432$	−3.84505	−	3.49508i	−0.184995	−	0.168157i
$433$	−28.7358	−	16.5906i	−1.38095	−	0.797294i	−0.388681	−	0.921372i	$-0.627069\pi$
$433$	−28.7358	−	16.5906i	−1.38095	−	0.797294i	−0.992272	+	0.124078i	$0.960403\pi$
$434$	4.56454	+	4.56454i	0.219105	+	0.219105i
$435$	8.99603	+	23.5461i	0.431326	+	1.12895i
$436$	9.96290	−	2.66955i	0.477136	−	0.127848i
$437$	−13.8572	+	13.8572i	−0.662878	+	0.662878i
$438$	14.2400	+	6.36692i	0.680415	+	0.304223i
$439$	−22.4807	+	12.9792i	−1.07295	+	0.619465i	−0.928985	−	0.370118i	$-0.879317\pi$
$439$	−22.4807	+	12.9792i	−1.07295	+	0.619465i	−0.143961	+	0.989583i	$0.545984\pi$
$440$	9.57157	+	2.56469i	0.456307	+	0.122267i
$441$	0.614503	+	2.93639i	0.0292620	+	0.139828i
$442$	−2.53692	−	0.674418i	−0.120669	−	0.0320788i
$443$			20.7981i			0.988147i	0.869420	+	0.494073i	$0.164493\pi$
$443$			20.7981i			0.988147i	−0.869420	+	0.494073i	$0.835507\pi$
$444$	−11.4531	−	1.83247i	−0.543542	−	0.0869650i
$445$	10.4123	+	18.0347i	0.493591	+	0.854925i
$446$	−9.27312	+	16.0615i	−0.439095	+	0.760535i
$447$	20.7950	+	16.8937i	0.983570	+	0.799044i
$448$	0.258819	+	0.965926i	0.0122281	+	0.0456357i
$449$	4.37599	+	16.3314i	0.206516	+	0.770727i	0.988982	+	0.148035i	$0.0472947\pi$
$449$	4.37599	+	16.3314i	0.206516	+	0.770727i	−0.782466	+	0.622693i	$0.786039\pi$
$450$	4.83621	−	7.39608i	0.227981	−	0.348655i
$451$	−16.2597	+	28.1627i	−0.765641	+	1.32613i
$452$	1.31717	+	2.28140i	0.0619543	+	0.107308i
$453$	−2.66537	+	16.6589i	−0.125230	+	0.782703i
$454$		−	21.8752i		−	1.02665i
$455$	−10.1633	+	0.0199969i	−0.476463	+	0.000937467i
$456$	−0.678813	−	6.55766i	−0.0317883	−	0.307090i
$457$	−9.21456	−	2.46903i	−0.431039	−	0.115496i	0.0367750	−	0.999324i	$-0.488292\pi$
$457$	−9.21456	−	2.46903i	−0.431039	−	0.115496i	−0.467814	+	0.883827i	$0.654958\pi$
$458$	7.28431	−	4.20560i	0.340373	−	0.196515i
$459$	−0.803994	+	3.69665i	−0.0375272	+	0.172545i
$460$	10.2621	−	10.2621i	0.478473	−	0.478473i
$461$	6.66260	−	1.78524i	0.310308	−	0.0831469i	−0.100304	−	0.994957i	$-0.531982\pi$
$461$	6.66260	−	1.78524i	0.310308	−	0.0831469i	0.410613	+	0.911810i	$0.365315\pi$
$462$	−5.68786	+	2.17311i	−0.264623	+	0.101102i
$463$	−17.7904	−	17.7904i	−0.826791	−	0.826791i	0.160280	−	0.987072i	$-0.448760\pi$
$463$	−17.7904	−	17.7904i	−0.826791	−	0.826791i	−0.987072	+	0.160280i	$0.948760\pi$
$464$	−4.47106	−	2.58137i	−0.207564	−	0.119837i
$465$	18.4848	+	25.5264i	0.857210	+	1.18376i
$466$	0.994882	−	3.71295i	0.0460870	−	0.171999i
$467$	−2.31231			−0.107001			−0.0535006	−	0.998568i	$-0.517038\pi$
$467$	−2.31231			−0.107001			−0.0535006	+	0.998568i	$0.517038\pi$
$468$	−3.35464	+	10.2833i	−0.155068	+	0.475346i
$469$	−10.9038			−0.503493
$470$	−8.23451	+	30.7316i	−0.379830	+	1.41754i
$471$	−12.1504	−	16.7791i	−0.559862	−	0.773138i
$472$	6.41753	+	3.70516i	0.295391	+	0.170544i
$473$	−28.0456	−	28.0456i	−1.28954	−	1.28954i
$474$	5.43607	−	2.07691i	0.249687	−	0.0953956i
$475$	10.8299	−	2.90187i	0.496911	−	0.133147i
$476$	0.514811	−	0.514811i	0.0235963	−	0.0235963i
$477$	−23.8765	−	7.84104i	−1.09323	−	0.359017i
$478$	12.6543	−	7.30597i	0.578795	−	0.334167i
$479$	34.7431	+	9.30939i	1.58745	+	0.425357i	0.941223	−	0.337785i	$-0.109678\pi$
$479$	34.7431	+	9.30939i	1.58745	+	0.425357i	0.646230	+	0.763142i	$0.276344\pi$
$480$	0.502704	+	4.85636i	0.0229452	+	0.221661i
$481$	6.29502	+	23.3098i	0.287028	+	1.06283i
$482$		−	6.59081i		−	0.300203i
$483$	−1.40887	+	8.80560i	−0.0641057	+	0.400669i
$484$	−0.679026	−	1.17611i	−0.0308648	−	0.0534595i
$485$	−13.8537	+	23.9953i	−0.629064	+	1.08957i
$486$	15.0251	+	4.15285i	0.681553	+	0.188377i
$487$	−11.0476	−	41.2301i	−0.500613	−	1.86831i	−0.496000	−	0.868323i	$-0.665198\pi$
$487$	−11.0476	−	41.2301i	−0.500613	−	1.86831i	−0.00461292	−	0.999989i	$-0.501468\pi$
$488$	0.319891	+	1.19385i	0.0144808	+	0.0540430i
$489$	26.8946	+	21.8489i	1.21621	+	0.988042i
$490$	1.40940	−	2.44115i	0.0636702	−	0.110280i
$491$	−13.1604	−	22.7945i	−0.593922	−	1.02870i	−0.993698	−	0.112090i	$-0.964246\pi$
$491$	−13.1604	−	22.7945i	−0.593922	−	1.02870i	0.399777	−	0.916613i	$-0.369088\pi$
$492$	−15.8212	−	2.53135i	−0.713276	−	0.114122i
$493$			3.75874i			0.169285i
$494$	−11.8716	+	6.88527i	−0.534130	+	0.309783i
$495$	−29.0973	+	6.08924i	−1.30783	+	0.273691i
$496$	−6.23527	−	1.67074i	−0.279972	−	0.0750183i
$497$	4.02312	−	2.32275i	0.180462	−	0.104190i
$498$	1.23640	+	0.552811i	0.0554043	+	0.0247721i
$499$	−27.6807	+	27.6807i	−1.23916	+	1.23916i	−0.278812	+	0.960346i	$0.589941\pi$
$499$	−27.6807	+	27.6807i	−1.23916	+	1.23916i	−0.960346	+	0.278812i	$0.910059\pi$
$500$	5.59352	−	1.49878i	0.250150	−	0.0670275i
$501$	−9.69932	−	25.3869i	−0.433334	−	1.13420i
$502$	−1.37789	−	1.37789i	−0.0614981	−	0.0614981i
$503$	6.82482	+	3.94031i	0.304304	+	0.175690i	0.644375	−	0.764710i	$-0.277118\pi$
$503$	6.82482	+	3.94031i	0.304304	+	0.175690i	−0.340071	+	0.940400i	$0.610451\pi$
$504$	−2.00037	−	2.23574i	−0.0891036	−	0.0995876i
$505$	13.8551	−	51.7079i	0.616544	−	2.30097i
$506$	−18.0993			−0.804613
$507$	22.3877	−	2.40653i	0.994272	−	0.106878i
$508$	11.0010			0.488091
$509$	8.44901	−	31.5321i	0.374496	−	1.39764i	−0.479585	−	0.877496i	$-0.659213\pi$
$509$	8.44901	−	31.5321i	0.374496	−	1.39764i	0.854080	−	0.520141i	$-0.174121\pi$
$510$	2.87899	−	2.08480i	0.127484	−	0.0923166i
$511$	7.79930	+	4.50293i	0.345021	+	0.199198i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	10.6935	+	16.6379i	0.472132	+	0.734583i
$514$	18.1629	−	4.86673i	0.801131	−	0.214662i
$515$	−22.5785	+	22.5785i	−0.994929	+	0.994929i
$516$	7.97644	−	17.8398i	0.351143	−	0.785355i
$517$	34.3624	−	19.8391i	1.51126	−	0.872523i
$518$	−6.46839	−	1.73320i	−0.284205	−	0.0761524i
$519$	29.4339	−	3.04683i	1.29200	−	0.133741i
$520$	8.79169	−	5.09897i	0.385541	−	0.223605i
$521$			16.2159i			0.710432i	0.934784	+	0.355216i	$0.115593\pi$
$521$			16.2159i			0.710432i	−0.934784	+	0.355216i	$0.884407\pi$
$522$	15.4644	+	0.859231i	0.676856	+	0.0376075i
$523$	15.4175	+	26.7038i	0.674158	+	1.16768i	0.976714	+	0.214545i	$0.0688269\pi$
$523$	15.4175	+	26.7038i	0.674158	+	1.16768i	−0.302556	+	0.953132i	$0.597840\pi$
$524$	−5.35828	+	9.28081i	−0.234077	+	0.405434i
$525$	3.21702	−	3.95994i	0.140402	−	0.172826i
$526$	7.23706	+	27.0091i	0.315551	+	1.17765i
$527$	1.21638	+	4.53961i	0.0529865	+	0.197748i
$528$	3.83928	−	4.72590i	0.167083	−	0.205668i
$529$	−1.75392	+	3.03787i	−0.0762572	+	0.132081i
$530$	11.8066	+	20.4495i	0.512844	+	0.888272i
$531$	−22.1967	−	1.23330i	−0.963257	−	0.0535205i
$532$		−	3.80629i		−	0.165024i
$533$	8.69587	+	32.1999i	0.376660	+	1.39473i
$534$	12.7280	−	1.31753i	0.550793	−	0.0570151i
$535$	11.7954	+	3.16058i	0.509961	+	0.136644i
$536$	9.44300	−	5.45192i	0.407876	−	0.235487i
$537$	−7.52366	+	16.8272i	−0.324670	+	0.726145i
$538$	17.6940	−	17.6940i	0.762842	−	0.762842i
$539$	−3.39562	+	0.909853i	−0.146260	+	0.0391901i
$540$	−7.91924	−	12.3214i	−0.340790	−	0.530230i
$541$	−3.40827	−	3.40827i	−0.146533	−	0.146533i	0.630034	−	0.776567i	$-0.283041\pi$
$541$	−3.40827	−	3.40827i	−0.146533	−	0.146533i	−0.776567	+	0.630034i	$0.783041\pi$
$542$	1.07311	+	0.619561i	0.0460941	+	0.0266124i
$543$	20.3254	−	14.7185i	0.872245	−	0.631630i
$544$	−0.188434	+	0.703245i	−0.00807904	+	0.0301514i
$545$	29.0741			1.24540
$546$	−2.53782	+	5.70609i	−0.108608	+	0.244198i
$547$	−31.0202			−1.32633			−0.663165	−	0.748474i	$-0.730787\pi$
$547$	−31.0202			−1.32633			−0.663165	+	0.748474i	$0.730787\pi$
$548$	1.31518	−	4.90832i	0.0561818	−	0.209673i
$549$	−2.47239	−	2.76329i	−0.105519	−	0.117934i
$550$	8.96778	+	5.17755i	0.382387	+	0.220771i
$551$	13.8953	+	13.8953i	0.591959	+	0.591959i
$552$	−3.18268	−	8.33031i	−0.135464	−	0.354561i
$553$	3.24530	−	0.869575i	0.138004	−	0.0369781i
$554$	14.3320	−	14.3320i	0.608908	−	0.608908i
$555$	−29.8472	−	13.3451i	−1.26694	−	0.566468i
$556$	14.6539	−	8.46041i	0.621462	−	0.358801i
$557$	−16.1318	−	4.32251i	−0.683528	−	0.183151i	−0.0996868	−	0.995019i	$-0.531784\pi$
$557$	−16.1318	−	4.32251i	−0.683528	−	0.183151i	−0.583841	+	0.811868i	$0.698451\pi$
$558$	18.9551	−	3.96676i	0.802432	−	0.167926i
$559$	−40.6795	+	0.0800391i	−1.72056	+	0.00338529i
$560$			2.81880i			0.119116i
$561$	−4.37733	−	0.700360i	−0.184811	−	0.0295692i
$562$	−8.48932	−	14.7039i	−0.358100	−	0.620248i
$563$	1.15945	−	2.00823i	0.0488652	−	0.0846369i	−0.840558	−	0.541721i	$-0.817773\pi$
$563$	1.15945	−	2.00823i	0.0488652	−	0.0846369i	0.889423	+	0.457084i	$0.151106\pi$
$564$	15.1735	+	12.3268i	0.638921	+	0.519054i
$565$	1.92190	+	7.17264i	0.0808551	+	0.301755i
$566$	0.209550	+	0.782050i	0.00880803	+	0.0328720i
$567$	8.38177	+	3.27810i	0.352001	+	0.137667i
$568$	−2.32275	+	4.02312i	−0.0974604	+	0.168806i
$569$	−22.2778	−	38.5862i	−0.933933	−	1.61762i	−0.776526	−	0.630085i	$-0.783020\pi$
$569$	−22.2778	−	38.5862i	−0.933933	−	1.61762i	−0.157407	−	0.987534i	$-0.550313\pi$
$570$	2.93596	−	18.3501i	0.122974	−	0.768601i
$571$		−	12.9013i		−	0.539904i	−0.962874	−	0.269952i	$-0.912992\pi$
$571$		−	12.9013i		−	0.539904i	0.962874	−	0.269952i	$-0.0870079\pi$
$572$	−12.2495	−	3.25643i	−0.512178	−	0.136158i
$573$	1.86743	+	18.0403i	0.0780132	+	0.753644i
$574$	−8.93537	−	2.39422i	−0.372955	−	0.0999330i
$575$	13.1340	−	7.58292i	0.547726	−	0.316230i
$576$	2.85024	+	0.936020i	0.118760	+	0.0390008i
$577$	−15.7771	+	15.7771i	−0.656810	+	0.656810i	−0.954624	−	0.297814i	$-0.903742\pi$
$577$	−15.7771	+	15.7771i	−0.656810	+	0.656810i	0.297814	+	0.954624i	$0.403742\pi$
$578$	−15.9087	+	4.26273i	−0.661716	+	0.177306i
$579$	18.1440	−	6.93213i	0.754041	−	0.288089i
$580$	−10.2903	−	10.2903i	−0.427283	−	0.427283i
$581$	0.677178	+	0.390969i	0.0280941	+	0.0162201i
$582$	9.98549	+	13.7894i	0.413912	+	0.571589i
$583$	7.62184	−	28.4451i	0.315664	−	1.17808i
$584$	−9.00586			−0.372665
$585$	−16.6361	+	25.5515i	−0.687820	+	1.05642i
$586$	12.9130			0.533430
$587$	−7.86190	+	29.3410i	−0.324495	+	1.21103i	0.590323	+	0.807167i	$0.299000\pi$
$587$	−7.86190	+	29.3410i	−0.324495	+	1.21103i	−0.914818	+	0.403866i	$0.867666\pi$
$588$	−1.01587	−	1.40286i	−0.0418937	−	0.0578529i
$589$	21.2787	+	12.2853i	0.876773	+	0.506205i
$590$	14.7702	+	14.7702i	0.608080	+	0.608080i
$591$	−4.53692	+	1.73338i	−0.186624	+	0.0713017i
$592$	6.46839	−	1.73320i	0.265849	−	0.0712341i
$593$	−24.1780	+	24.1780i	−0.992872	+	0.992872i	−0.999975	−	0.00710251i	$-0.997739\pi$
$593$	−24.1780	+	24.1780i	−0.992872	+	0.992872i	0.00710251	+	0.999975i	$0.497739\pi$
$594$	−3.88208	+	17.8493i	−0.159284	+	0.732365i
$595$	1.77729	−	1.02612i	0.0728617	−	0.0420667i
$596$	−14.9415	−	4.00356i	−0.612027	−	0.163992i
$597$	−1.47443	−	14.2437i	−0.0603442	−	0.582954i
$598$	−13.1005	+	13.1521i	−0.535719	+	0.537831i
$599$		−	15.1141i		−	0.617547i	−0.951136	−	0.308774i	$-0.900081\pi$
$599$		−	15.1141i		−	0.617547i	0.951136	−	0.308774i	$-0.0999185\pi$
$600$	−0.806051	+	5.03792i	−0.0329069	+	0.205672i
$601$	4.71337	+	8.16379i	0.192262	+	0.333008i	0.946000	−	0.324168i	$-0.105084\pi$
$601$	4.71337	+	8.16379i	0.192262	+	0.333008i	−0.753737	+	0.657176i	$0.771751\pi$
$602$	5.64124	−	9.77091i	0.229920	−	0.398233i
$603$	−17.9022	+	27.3780i	−0.729033	+	1.11492i
$604$	−2.52099	−	9.40845i	−0.102578	−	0.382825i
$605$	−0.990780	−	3.69764i	−0.0402809	−	0.150330i
$606$	−25.5304	−	20.7407i	−1.03710	−	0.842534i
$607$	−9.49922	+	16.4531i	−0.385561	+	0.667812i	−0.991847	−	0.127435i	$-0.959326\pi$
$607$	−9.49922	+	16.4531i	−0.385561	+	0.667812i	0.606285	+	0.795247i	$0.292659\pi$
$608$	1.90315	+	3.29635i	0.0771828	+	0.133685i
$609$	8.82982	+	1.41274i	0.357802	+	0.0572472i
$610$			3.48394i			0.141060i
$611$	10.4555	−	39.3297i	0.422983	−	1.59111i
$612$	−0.447391	−	2.13785i	−0.0180847	−	0.0864173i
$613$	−38.9897	−	10.4473i	−1.57478	−	0.421961i	−0.637476	−	0.770471i	$-0.720021\pi$
$613$	−38.9897	−	10.4473i	−1.57478	−	0.421961i	−0.937305	+	0.348509i	$0.886688\pi$
$614$	−3.16015	+	1.82451i	−0.127533	+	0.0736313i
$615$	−41.2305	−	18.4348i	−1.66258	−	0.743361i
$616$	2.48576	−	2.48576i	0.100154	−	0.100154i
$617$	10.3350	−	2.76924i	0.416070	−	0.111486i	−0.0447101	−	0.999000i	$-0.514236\pi$
$617$	10.3350	−	2.76924i	0.416070	−	0.111486i	0.460780	+	0.887514i	$0.347570\pi$
$618$	7.00249	+	18.3282i	0.281682	+	0.737269i
$619$	6.05120	+	6.05120i	0.243218	+	0.243218i	0.818180	−	0.574962i	$-0.194983\pi$
$619$	6.05120	+	6.05120i	0.243218	+	0.243218i	−0.574962	+	0.818180i	$0.694983\pi$
$620$	−15.7582	−	9.09800i	−0.632865	−	0.365385i
$621$	19.7965	+	17.9947i	0.794407	+	0.722102i
$622$	−3.71694	+	13.8718i	−0.149036	+	0.556209i
$623$	7.38777			0.295985
$624$	−0.655233	−	6.21053i	−0.0262303	−	0.248620i
$625$	31.0514			1.24206
$626$	2.86676	−	10.6989i	0.114579	−	0.427613i
$627$	−18.7712	+	13.5930i	−0.749648	+	0.542852i
$628$	10.3582	+	5.98031i	0.413337	+	0.238640i
$629$	−3.44747	−	3.44747i	−0.137460	−	0.137460i
$630$	−3.81541	−	7.54675i	−0.152010	−	0.300670i
$631$	−29.7092	+	7.96056i	−1.18271	+	0.316905i	−0.795999	−	0.605298i	$-0.793054\pi$
$631$	−29.7092	+	7.96056i	−1.18271	+	0.316905i	−0.386706	+	0.922203i	$0.626387\pi$
$632$	−2.37572	+	2.37572i	−0.0945012	+	0.0945012i
$633$	1.84304	−	4.12208i	0.0732543	−	0.163838i
$634$	15.6013	−	9.00744i	0.619609	−	0.357731i
$635$	29.9530	+	8.02589i	1.18865	+	0.318498i
$636$	14.4323	−	1.49395i	0.572277	−	0.0592390i
$637$	−1.79663	+	3.12604i	−0.0711850	+	0.123858i
$638$			18.1491i			0.718529i
$639$	0.773148	−	13.9150i	0.0305853	−	0.550470i
$640$	−1.40940	−	2.44115i	−0.0557114	−	0.0964950i
$641$	−6.26281	+	10.8475i	−0.247366	+	0.428451i	−0.962794	−	0.270236i	$-0.912898\pi$
$641$	−6.26281	+	10.8475i	−0.247366	+	0.428451i	0.715428	+	0.698687i	$0.246232\pi$
$642$	4.73129	−	5.82391i	0.186729	−	0.229851i
$643$	3.15069	+	11.7585i	0.124251	+	0.463711i	0.999812	−	0.0193970i	$-0.00617463\pi$
$643$	3.15069	+	11.7585i	0.124251	+	0.463711i	−0.875561	+	0.483108i	$0.839508\pi$
$644$	−1.33255	−	4.97314i	−0.0525098	−	0.195969i
$645$	34.7331	−	42.7541i	1.36761	−	1.68344i
$646$	1.38559	−	2.39992i	0.0545154	−	0.0944234i
$647$	15.8407	+	27.4369i	0.622763	+	1.07866i	0.988969	+	0.148123i	$0.0473231\pi$
$647$	15.8407	+	27.4369i	0.622763	+	1.07866i	−0.366206	+	0.930534i	$0.619344\pi$
$648$	−8.89788	+	1.35197i	−0.349542	+	0.0531103i
$649$		−	26.0503i		−	1.02256i
$650$	10.2533	−	2.76900i	0.402169	−	0.108609i
$651$	11.1214	−	1.15122i	0.435880	−	0.0451200i
$652$	−19.3241	−	5.17788i	−0.756790	−	0.202781i
$653$	14.7400	−	8.51013i	0.576820	−	0.333027i	−0.183049	−	0.983104i	$-0.558597\pi$
$653$	14.7400	−	8.51013i	0.576820	−	0.333027i	0.759869	+	0.650077i	$0.225263\pi$
$654$	7.29200	−	16.3090i	0.285140	−	0.637733i
$655$	−21.3602	+	21.3602i	−0.834610	+	0.834610i
$656$	8.93537	−	2.39422i	0.348867	−	0.0934788i
$657$	24.1113	−	12.1899i	0.940671	−	0.475575i
$658$	7.98109	+	7.98109i	0.311135	+	0.311135i
$659$	15.7410	+	9.08805i	0.613181	+	0.354020i	0.774209	−	0.632929i	$-0.218148\pi$
$659$	15.7410	+	9.08805i	0.613181	+	0.354020i	−0.161028	+	0.986950i	$0.551481\pi$
$660$	13.9012	−	10.0665i	0.541104	−	0.391837i
$661$	−0.642795	+	2.39894i	−0.0250018	+	0.0933081i	−0.977299	−	0.211863i	$-0.932047\pi$
$661$	−0.642795	+	2.39894i	−0.0250018	+	0.0933081i	0.952298	+	0.305171i	$0.0987136\pi$
$662$	−9.82337			−0.381796
$663$	−3.67729	+	2.67393i	−0.142814	+	0.103847i
$664$	−0.781938			−0.0303451
$665$	2.77692	−	10.3636i	0.107684	−	0.401883i
$666$	−14.9718	+	13.3956i	−0.580144	+	0.519070i
$667$	23.0196	+	13.2904i	0.891322	+	0.514605i
$668$	11.0948	+	11.0948i	0.429271	+	0.429271i
$669$	11.4647	+	30.0075i	0.443250	+	1.16016i
$670$	29.6885	−	7.95500i	1.14697	−	0.307328i
$671$	3.07232	−	3.07232i	0.118605	−	0.118605i
$672$	1.58120	+	0.706976i	0.0609960	+	0.0272722i
$673$	20.7415	−	11.9751i	0.799528	−	0.461608i	−0.0437782	−	0.999041i	$-0.513939\pi$
$673$	20.7415	−	11.9751i	0.799528	−	0.461608i	0.843306	+	0.537434i	$0.180606\pi$
$674$	−8.52880	−	2.28529i	−0.328517	−	0.0880259i
$675$	−4.66108	−	14.5790i	−0.179405	−	0.561146i
$676$	−11.2327	+	6.54425i	−0.432026	+	0.251702i
$677$			40.3255i			1.54983i	0.632063	+	0.774917i	$0.282208\pi$
$677$			40.3255i			1.54983i	−0.632063	+	0.774917i	$0.717792\pi$
$678$	4.50550	+	0.720865i	0.173033	+	0.0276847i
$679$	4.91475	+	8.51260i	0.188611	+	0.326683i
$680$	−1.02612	+	1.77729i	−0.0393498	+	0.0681559i
$681$	−29.4077	−	23.8906i	−1.12691	−	0.915489i
$682$	5.87331	+	21.9195i	0.224901	+	0.839341i
$683$	0.110006	+	0.410547i	0.00420925	+	0.0157091i	0.967999	−	0.250956i	$-0.0807449\pi$
$683$	0.110006	+	0.410547i	0.00420925	+	0.0157091i	−0.963789	+	0.266665i	$0.914078\pi$
$684$	−9.55707	−	6.24926i	−0.365424	−	0.238946i
$685$	7.16183	−	12.4046i	0.273639	−	0.473957i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$	2.30166	−	14.3856i	0.0878137	−	0.548847i
$688$			11.2825i			0.430141i
$689$	−15.1533	−	26.1274i	−0.577295	−	0.995376i
$690$	−2.58821	−	25.0033i	−0.0985314	−	0.951860i
$691$	−48.2855	−	12.9381i	−1.83687	−	0.492187i	−0.838276	−	0.545247i	$-0.816436\pi$
$691$	−48.2855	−	12.9381i	−1.83687	−	0.492187i	−0.998591	+	0.0530598i	$0.983103\pi$
$692$	−14.7956	+	8.54222i	−0.562443	+	0.324727i
$693$	−3.29049	+	10.0197i	−0.124995	+	0.380618i
$694$	−1.64066	+	1.64066i	−0.0622788	+	0.0622788i
$695$	46.0712	−	12.3447i	1.74758	−	0.468262i
$696$	−8.35322	+	3.19144i	−0.316628	+	0.120971i
$697$	−4.76230	−	4.76230i	−0.180385	−	0.180385i
$698$	−9.65720	−	5.57558i	−0.365530	−	0.211039i
$699$	−3.90493	−	5.39248i	−0.147698	−	0.203962i
$700$	−0.762387	+	2.84527i	−0.0288155	+	0.107541i
$701$	−11.2341			−0.424306			−0.212153	−	0.977236i	$-0.568047\pi$
$701$	−11.2341			−0.424306			−0.212153	+	0.977236i	$0.568047\pi$
$702$	10.1606	+	15.7405i	0.383486	+	0.594087i
$703$	−25.4891			−0.961341
$704$	−0.909853	+	3.39562i	−0.0342914	+	0.127977i
$705$	32.3206	+	44.6329i	1.21726	+	1.68097i
$706$	29.0452	+	16.7692i	1.09313	+	0.631118i
$707$	−13.4287	−	13.4287i	−0.505038	−	0.505038i
$708$	11.9898	−	4.58083i	0.450604	−	0.172158i
$709$	−38.7896	+	10.3936i	−1.45677	+	0.390341i	−0.898374	−	0.439230i	$-0.855251\pi$
$709$	−38.7896	+	10.3936i	−1.45677	+	0.390341i	−0.558400	+	0.829572i	$0.688584\pi$
$710$	−9.25938	+	9.25938i	−0.347498	+	0.347498i
$711$	3.14482	−	9.57618i	0.117940	−	0.359135i
$712$	−6.39799	+	3.69388i	−0.239775	+	0.138434i
$713$	32.1028	+	8.60191i	1.20226	+	0.322144i
$714$	−0.129841	−	1.25432i	−0.00485916	−	0.0469418i
$715$	−30.9766	−	17.8032i	−1.15846	−	0.665801i
$716$		−	10.6420i		−	0.397711i
$717$	3.99845	−	24.9908i	0.149325	−	0.933298i
$718$	−1.18254	−	2.04821i	−0.0441318	−	0.0764386i
$719$	17.8702	−	30.9520i	0.666444	−	1.15432i	−0.312447	−	0.949935i	$-0.601149\pi$
$719$	17.8702	−	30.9520i	0.666444	−	1.15432i	0.978892	−	0.204380i	$-0.0655179\pi$
$720$	7.07761	+	4.62797i	0.263767	+	0.172474i
$721$	2.93186	+	10.9418i	0.109188	+	0.407495i
$722$	1.16782	+	4.35837i	0.0434619	+	0.162202i
$723$	−8.86029	−	7.19802i	−0.329518	−	0.267697i
$724$	−7.24427	+	12.5474i	−0.269231	+	0.466322i
$725$	−7.60377	−	13.1701i	−0.282397	−	0.489126i
$726$	−2.32268	−	0.371621i	−0.0862026	−	0.0137921i
$727$			14.5192i			0.538487i	0.963072	+	0.269243i	$0.0867736\pi$
$727$			14.5192i			0.538487i	−0.963072	+	0.269243i	$0.913226\pi$
$728$	−0.00709410	−	3.60554i	−0.000262925	−	0.133630i
$729$	21.9922	−	15.6634i	0.814527	−	0.580126i
$730$	−24.5207	−	6.57031i	−0.907552	−	0.243178i
$731$	7.11374	−	4.10712i	0.263111	−	0.151907i
$732$	1.95430	+	0.873797i	0.0722331	+	0.0322965i
$733$	27.5127	−	27.5127i	1.01620	−	1.01620i	0.0163377	−	0.999867i	$-0.494799\pi$
$733$	27.5127	−	27.5127i	1.01620	−	1.01620i	0.999867	−	0.0163377i	$-0.00520068\pi$
$734$	1.42225	−	0.381091i	0.0524963	−	0.0140663i
$735$	−1.74249	−	4.56077i	−0.0642728	−	0.168227i
$736$	3.64059	+	3.64059i	0.134194	+	0.134194i
$737$	−33.1960	−	19.1657i	−1.22279	−	0.705978i
$738$	−20.6818	+	18.5046i	−0.761309	+	0.681163i
$739$	−3.19037	+	11.9066i	−0.117360	+	0.437993i	−0.999453	−	0.0330828i	$-0.989467\pi$
$739$	−3.19037	+	11.9066i	−0.117360	+	0.437993i	0.882093	+	0.471076i	$0.156134\pi$
$740$	18.8763			0.693907
$741$	−3.70922	+	23.4791i	−0.136262	+	0.862527i
$742$	8.37700			0.307530
$743$	−10.2658	+	38.3125i	−0.376616	+	1.40555i	0.474354	+	0.880334i	$0.342682\pi$
$743$	−10.2658	+	38.3125i	−0.376616	+	1.40555i	−0.850970	+	0.525215i	$0.823985\pi$
$744$	−9.05577	+	6.55767i	−0.332001	+	0.240416i
$745$	−37.7611	−	21.8014i	−1.38346	−	0.798741i
$746$	−0.462873	−	0.462873i	−0.0169470	−	0.0169470i
$747$	2.09347	−	1.05840i	0.0765962	−	0.0387248i
$748$	2.47219	−	0.662421i	0.0903922	−	0.0242205i
$749$	3.06331	−	3.06331i	0.111931	−	0.111931i
$750$	4.09398	−	9.15646i	0.149491	−	0.334347i
$751$	38.1001	−	21.9971i	1.39029	−	0.802685i	0.396944	−	0.917843i	$-0.370071\pi$
$751$	38.1001	−	21.9971i	1.39029	−	0.802685i	0.993347	+	0.115158i	$0.0367375\pi$
$752$	−10.9024	−	2.92128i	−0.397569	−	0.106528i
$753$	−3.35718	+	0.347517i	−0.122342	+	0.0126642i
$754$	13.1883	+	13.1365i	0.480290	+	0.478404i
$755$		−	27.4561i		−	0.999230i
$756$	−5.19026	+	0.247463i	−0.188768	+	0.00900013i
$757$	−11.3904	−	19.7287i	−0.413989	−	0.717051i	0.581332	−	0.813666i	$-0.302532\pi$
$757$	−11.3904	−	19.7287i	−0.413989	−	0.717051i	−0.995322	+	0.0966154i	$0.969198\pi$
$758$	−16.7594	+	29.0280i	−0.608727	+	1.05435i
$759$	−19.7668	+	24.3316i	−0.717490	+	0.883183i
$760$	2.77692	+	10.3636i	0.100729	+	0.375927i
$761$	−0.257571	−	0.961267i	−0.00933693	−	0.0348459i	0.961100	−	0.276200i	$-0.0890752\pi$
$761$	−0.257571	−	0.961267i	−0.00933693	−	0.0348459i	−0.970437	+	0.241354i	$0.922409\pi$
$762$	12.0145	−	14.7891i	0.435241	−	0.535753i
$763$	5.15718	−	8.93249i	0.186702	−	0.323378i
$764$	−5.23561	−	9.06835i	−0.189418	−	0.328081i
$765$	0.341552	−	6.14723i	0.0123489	−	0.222253i
$766$		−	15.2802i		−	0.552097i
$767$	−18.9298	−	18.8555i	−0.683517	−	0.680832i
$768$	−1.72285	+	0.178340i	−0.0621678	+	0.00643528i
$769$	22.0019	+	5.89538i	0.793408	+	0.212593i	0.632688	−	0.774407i	$-0.281952\pi$
$769$	22.0019	+	5.89538i	0.793408	+	0.212593i	0.160720	+	0.987000i	$0.448618\pi$
$770$	8.58163	−	4.95461i	0.309261	−	0.178552i
$771$	13.2937	−	29.7322i	0.478761	−	1.07078i
$772$	−7.92949	+	7.92949i	−0.285389	+	0.285389i
$773$	−33.3906	+	8.94699i	−1.20098	+	0.321801i	−0.803216	−	0.595688i	$-0.796879\pi$
$773$	−33.3906	+	8.94699i	−1.20098	+	0.321801i	−0.397761	+	0.917489i	$0.630213\pi$
$774$	−15.2715	−	30.2065i	−0.548922	−	1.08575i
$775$	−13.4455	−	13.4455i	−0.482975	−	0.482975i
$776$	−8.51260	−	4.91475i	−0.305584	−	0.176429i
$777$	−9.39434	+	6.80284i	−0.337020	+	0.244051i
$778$	−9.44318	+	35.2424i	−0.338554	+	1.26350i
$779$	−35.2104			−1.26154
$780$	2.74691	−	17.3878i	0.0983552	−	0.622582i
$781$	16.3308			0.584362
$782$	0.970166	−	3.62071i	0.0346931	−	0.129476i
$783$	18.0442	−	19.8510i	0.644847	−	0.709416i
$784$	0.866025	+	0.500000i	0.0309295	+	0.0178571i
$785$	23.8398	+	23.8398i	0.850880	+	0.850880i
$786$	6.62463	+	17.3392i	0.236293	+	0.618469i
$787$	24.7212	−	6.62402i	0.881215	−	0.236121i	0.210283	−	0.977640i	$-0.432561\pi$
$787$	24.7212	−	6.62402i	0.881215	−	0.236121i	0.670931	+	0.741520i	$0.265895\pi$
$788$	1.98277	−	1.98277i	0.0706333	−	0.0706333i
$789$	44.2132	+	19.7683i	1.57403	+	0.703772i
$790$	−8.20174	+	4.73528i	−0.291805	+	0.168474i
$791$	2.54457	+	0.681816i	0.0904746	+	0.0242426i
$792$	−2.16022	−	10.3226i	−0.0767603	−	0.366797i
$793$	−0.00876806	−	4.45632i	−0.000311363	−	0.158249i
$794$		−	5.33040i		−	0.189169i
$795$	40.3855	+	6.46154i	1.43232	+	0.229167i
$796$	4.13376	+	7.15988i	0.146517	+	0.253775i
$797$	1.81152	−	3.13765i	0.0641675	−	0.111141i	−0.832157	−	0.554540i	$-0.812894\pi$
$797$	1.81152	−	3.13765i	0.0641675	−	0.111141i	0.896324	+	0.443399i	$0.146227\pi$
$798$	−5.11696	−	4.15697i	−0.181138	−	0.147155i
$799$	2.12685	+	7.93751i	0.0752425	+	0.280809i
$800$	−0.762387	−	2.84527i	−0.0269544	−	0.100595i
$801$	12.1294	−	18.5496i	0.428571	−	0.655420i
$802$	−11.7032	+	20.2705i	−0.413253	+	0.715775i
$803$	15.8296	+	27.4177i	0.558615	+	0.967549i
$804$	2.98375	−	18.6488i	0.105229	−	0.657693i
$805$		−	14.5128i		−	0.511509i
$806$	20.1793	+	11.5976i	0.710786	+	0.408510i
$807$	−4.46261	−	43.1109i	−0.157091	−	1.51758i
$808$	18.3440	+	4.91525i	0.645338	+	0.172918i
$809$	−37.6521	+	21.7385i	−1.32378	+	0.764284i	−0.984329	−	0.176341i	$-0.943574\pi$
$809$	−37.6521	+	21.7385i	−1.32378	+	0.764284i	−0.339449	+	0.940624i	$0.610241\pi$
$810$	−25.2131	−	2.81045i	−0.885896	−	0.0987493i
$811$	−13.2189	+	13.2189i	−0.464177	+	0.464177i	−0.900022	−	0.435845i	$-0.856450\pi$
$811$	−13.2189	+	13.2189i	−0.464177	+	0.464177i	0.435845	+	0.900022i	$0.356450\pi$
$812$	−4.98682	+	1.33621i	−0.175003	+	0.0468919i
$813$	2.00488	−	0.765985i	0.0703141	−	0.0268643i
$814$	−16.6461	−	16.6461i	−0.583446	−	0.583446i
$815$	−48.8372	−	28.1962i	−1.71069	−	0.987668i
$816$	0.739606	+	1.02135i	0.0258914	+	0.0357546i
$817$	11.1148	−	41.4812i	0.388859	−	1.45124i
$818$	6.38708			0.223319
$819$	4.89931	+	9.64348i	0.171196	+	0.336971i
$820$	26.0755			0.910597
$821$	−5.34016	+	19.9298i	−0.186373	+	0.695553i	0.807959	+	0.589238i	$0.200572\pi$
$821$	−5.34016	+	19.9298i	−0.186373	+	0.695553i	−0.994332	+	0.106315i	$0.966095\pi$
$822$	−5.16211	−	7.12858i	−0.180049	−	0.248638i
$823$	−12.1664	−	7.02428i	−0.424094	−	0.244851i	0.272733	−	0.962090i	$-0.412072\pi$
$823$	−12.1664	−	7.02428i	−0.424094	−	0.244851i	−0.696828	+	0.717239i	$0.745406\pi$
$824$	−8.00998	−	8.00998i	−0.279041	−	0.279041i
$825$	16.7544	−	6.40119i	0.583312	−	0.222861i
$826$	7.15783	−	1.91793i	0.249053	−	0.0667335i
$827$	−25.7758	+	25.7758i	−0.896312	+	0.896312i	−0.995108	−	0.0987955i	$-0.968501\pi$
$827$	−25.7758	+	25.7758i	−0.896312	+	0.896312i	0.0987955	+	0.995108i	$0.468501\pi$
$828$	−14.6747	−	4.81917i	−0.509980	−	0.167478i
$829$	9.54983	−	5.51359i	0.331679	−	0.191495i	−0.324907	−	0.945746i	$-0.605333\pi$
$829$	9.54983	−	5.51359i	0.331679	−	0.191495i	0.656586	+	0.754251i	$0.272000\pi$
$830$	−2.12902	−	0.570470i	−0.0738995	−	0.0198013i
$831$	−3.61467	−	34.9195i	−0.125392	−	1.21134i
$832$	1.80892	+	3.11895i	0.0627129	+	0.108130i
$833$		−	0.728053i		−	0.0252255i
$834$	4.63025	−	28.9396i	0.160332	−	1.00210i
$835$	22.1141	+	38.3028i	0.765290	+	1.32552i
$836$	6.69033	−	11.5880i	0.231390	−	0.400779i
$837$	15.3687	−	29.8143i	0.531221	−	1.03053i
$838$	0.0677368	+	0.252797i	0.00233993	+	0.00873274i
$839$	6.22071	+	23.2160i	0.214763	+	0.801505i	0.986250	+	0.165260i	$0.0528464\pi$
$839$	6.22071	+	23.2160i	0.214763	+	0.801505i	−0.771487	+	0.636245i	$0.780487\pi$
$840$	3.78943	+	3.07850i	0.130748	+	0.106218i
$841$	−1.17308	+	2.03184i	−0.0404511	+	0.0700634i
$842$	−4.00159	−	6.93096i	−0.137904	−	0.238857i
$843$	−29.0385	−	4.64607i	−1.00014	−	0.160019i
$844$			2.60693i			0.0897344i
$845$	−35.3582	+	9.62348i	−1.21636	+	0.331058i
$846$	33.1429	−	6.93588i	1.13948	−	0.238460i
$847$	−1.31178	−	0.351490i	−0.0450732	−	0.0120773i
$848$	−7.25470	+	4.18850i	−0.249127	+	0.143834i
$849$	1.28020	+	0.572395i	0.0439363	+	0.0196445i
$850$	−1.51645	+	1.51645i	−0.0520137	+	0.0520137i
$851$	−33.3030	+	8.92351i	−1.14161	+	0.305894i
$852$	2.87170	+	7.51634i	0.0983828	+	0.257505i
$853$	38.5601	+	38.5601i	1.32027	+	1.32027i	0.913552	+	0.406721i	$0.133328\pi$
$853$	38.5601	+	38.5601i	1.32027	+	1.32027i	0.406721	+	0.913552i	$0.366672\pi$
$854$	1.07038	+	0.617982i	0.0366275	+	0.0211469i
$855$	−21.4623	−	23.9876i	−0.733997	−	0.820360i
$856$	−1.12125	+	4.18456i	−0.0383235	+	0.143025i
$857$	−42.3820			−1.44774			−0.723871	−	0.689935i	$-0.757639\pi$
$857$	−42.3820			−1.44774			−0.723871	+	0.689935i	$0.757639\pi$
$858$	−17.7558	+	12.9111i	−0.606173	+	0.440776i
$859$	−20.0639			−0.684572			−0.342286	−	0.939596i	$-0.611201\pi$
$859$	−20.0639			−0.684572			−0.342286	+	0.939596i	$0.611201\pi$
$860$	−8.23124	+	30.7194i	−0.280683	+	1.04752i
$861$	−12.9772	+	9.39737i	−0.442263	+	0.320262i
$862$	−11.6855	−	6.74664i	−0.398010	−	0.229791i
$863$	3.53305	+	3.53305i	0.120266	+	0.120266i	0.764678	−	0.644412i	$-0.222898\pi$
$863$	3.53305	+	3.53305i	0.120266	+	0.120266i	−0.644412	+	0.764678i	$0.722898\pi$
$864$	4.37116	−	2.80944i	0.148710	−	0.0955790i
$865$	−46.5167	+	12.4641i	−1.58162	+	0.423793i
$866$	23.4627	−	23.4627i	0.797294	−	0.797294i
$867$	−11.6439	+	26.0422i	−0.395446	+	0.884440i
$868$	−5.59039	+	3.22761i	−0.189750	+	0.109552i
$869$	11.4085	+	3.05691i	0.387008	+	0.103698i
$870$	−25.0721	+	2.59533i	−0.850023	+	0.0879898i
$871$	−37.9547	+	10.2500i	−1.28604	+	0.347308i
$872$			10.3144i			0.349288i
$873$	29.4431	+	1.63592i	0.996498	+	0.0553674i
$874$	−9.79850	−	16.9715i	−0.331439	−	0.574069i
$875$	2.89542	−	5.01501i	0.0978831	−	0.169538i
$876$	−9.83557	+	12.1069i	−0.332313	+	0.409056i
$877$	2.43087	+	9.07214i	0.0820847	+	0.306344i	0.994746	−	0.102372i	$-0.0326432\pi$
$877$	2.43087	+	9.07214i	0.0820847	+	0.306344i	−0.912661	+	0.408716i	$0.865977\pi$
$878$	−6.71855	−	25.0740i	−0.226740	−	0.846206i
$879$	14.1027	−	17.3594i	0.475671	−	0.585520i
$880$	−4.95461	+	8.58163i	−0.167020	+	0.289287i
$881$	−17.8012	−	30.8326i	−0.599737	−	1.03878i	−0.992860	−	0.119289i	$-0.961938\pi$
$881$	−17.8012	−	30.8326i	−0.599737	−	1.03878i	0.393122	−	0.919486i	$-0.371395\pi$
$882$	−2.99538	−	0.166429i	−0.100860	−	0.00560397i
$883$			12.0709i			0.406220i	0.979156	+	0.203110i	$0.0651048\pi$
$883$			12.0709i			0.406220i	−0.979156	+	0.203110i	$0.934895\pi$
$884$	1.30804	−	2.27592i	0.0439942	−	0.0765475i
$885$	35.9872	−	3.72520i	1.20970	−	0.125221i
$886$	−20.0894	−	5.38294i	−0.674917	−	0.180843i
$887$	−8.80519	+	5.08368i	−0.295649	+	0.170693i	−0.640487	−	0.767969i	$-0.721267\pi$
$887$	−8.80519	+	5.08368i	−0.295649	+	0.170693i	0.344837	+	0.938662i	$0.387934\pi$
$888$	4.73431	−	10.5886i	0.158873	−	0.355330i
$889$	7.77889	−	7.77889i	0.260896	−	0.260896i
$890$	−20.1151	+	5.38981i	−0.674258	+	0.180667i
$891$	19.7558	+	24.7126i	0.661843	+	0.827903i
$892$	−13.1142	−	13.1142i	−0.439095	−	0.439095i
$893$	37.2058	+	21.4808i	1.24504	+	0.718826i
$894$	−21.7002	+	15.7140i	−0.725763	+	0.525556i
$895$	7.76399	−	28.9756i	0.259522	−	0.968548i
$896$	−1.00000			−0.0334077
$897$	3.37352	+	31.9754i	0.112638	+	1.06763i
$898$	−16.9075			−0.564212
$899$	8.62557	−	32.1911i	0.287679	−	1.07363i
$900$	5.89236	+	6.58567i	0.196412	+	0.219522i
$901$	5.28180	+	3.04945i	0.175962	+	0.101592i
$902$	−22.9947	−	22.9947i	−0.765641	−	0.765641i
$903$	−6.97447	−	18.2549i	−0.232096	−	0.607484i
$904$	−2.54457	+	0.681816i	−0.0846312	+	0.0226769i
$905$	−28.8785	+	28.8785i	−0.959953	+	0.959953i
$906$	−15.4014	−	6.88619i	−0.511678	−	0.228778i
$907$	26.0439	−	15.0365i	0.864774	−	0.499278i	−0.000833859	−	1.00000i	$-0.500265\pi$
$907$	26.0439	−	15.0365i	0.864774	−	0.499278i	0.865608	+	0.500722i	$0.166932\pi$
$908$	21.1298	+	5.66172i	0.701218	+	0.187891i
$909$	−55.7651	+	11.6701i	−1.84961	+	0.387071i
$910$	2.61114	−	9.82218i	0.0865585	−	0.325602i
$911$		−	0.399972i		−	0.0132517i	−0.999978	−	0.00662583i	$-0.997891\pi$
$911$		−	0.399972i		−	0.0132517i	0.999978	−	0.00662583i	$-0.00210908\pi$
$912$	6.50990	+	1.04156i	0.215564	+	0.0344896i
$913$	1.37441	+	2.38055i	0.0454864	+	0.0787848i
$914$	4.76980	−	8.26154i	0.157771	−	0.273268i
$915$	4.68360	+	3.80491i	0.154835	+	0.125787i
$916$	2.17698	+	8.12459i	0.0719293	+	0.268444i
$917$	2.77365	+	10.3514i	0.0915939	+	0.341833i
$918$	−3.36260	−	1.73336i	−0.110982	−	0.0572095i
$919$	10.9917	−	19.0382i	0.362584	−	0.628013i	−0.625802	−	0.779982i	$-0.715228\pi$
$919$	10.9917	−	19.0382i	0.362584	−	0.628013i	0.988385	+	0.151969i	$0.0485614\pi$
$920$	7.25640	+	12.5685i	0.239237	+	0.414370i
$921$	−0.998528	+	6.24092i	−0.0329026	+	0.205645i
$922$			6.89764i			0.227162i
$923$	11.8204	−	11.8670i	0.389074	−	0.390608i
$924$	−0.626935	−	6.05649i	−0.0206247	−	0.199244i
$925$	19.0535	+	5.10538i	0.626476	+	0.167864i
$926$	21.7887	−	12.5797i	0.716022	−	0.413396i
$927$	32.2870	+	10.6031i	1.06044	+	0.348250i
$928$	3.65061	−	3.65061i	0.119837	−	0.119837i
$929$	−29.0481	+	7.78341i	−0.953036	+	0.255365i	−0.701650	−	0.712522i	$-0.747553\pi$
$929$	−29.0481	+	7.78341i	−0.953036	+	0.255365i	−0.251386	+	0.967887i	$0.580886\pi$
$930$	−29.4408	+	11.2482i	−0.965403	+	0.368843i
$931$	−2.69146	−	2.69146i	−0.0882089	−	0.0882089i
$932$	3.32894	+	1.92196i	0.109043	+	0.0629560i
$933$	14.5891	+	20.1467i	0.477624	+	0.659572i
$934$	0.598471	−	2.23352i	0.0195826	−	0.0730831i
$935$	7.21443			0.235937
$936$	−9.06467	−	5.90185i	−0.296288	−	0.192908i
$937$	−46.4528			−1.51755			−0.758773	−	0.651355i	$-0.774201\pi$
$937$	−46.4528			−1.51755			−0.758773	+	0.651355i	$0.774201\pi$
$938$	2.82212	−	10.5323i	0.0921456	−	0.343892i
$939$	−11.2521	−	15.5385i	−0.367197	−	0.507079i
$940$	−27.5532	−	15.9079i	−0.898687	−	0.518857i
$941$	22.1612	+	22.1612i	0.722433	+	0.722433i	0.969100	−	0.246667i	$-0.0793355\pi$
$941$	22.1612	+	22.1612i	0.722433	+	0.722433i	−0.246667	+	0.969100i	$0.579335\pi$
$942$	19.3521	−	7.39367i	0.630525	−	0.240899i
$943$	−46.0044	+	12.3268i	−1.49811	+	0.401417i
$944$	−5.23989	+	5.23989i	−0.170544	+	0.170544i
$945$	−14.3123	−	3.11282i	−0.465580	−	0.101260i
$946$	34.3487	−	19.8312i	1.11677	−	0.644769i
$947$	−49.3419	−	13.2211i	−1.60339	−	0.429628i	−0.657329	−	0.753603i	$-0.728314\pi$
$947$	−49.3419	−	13.2211i	−1.60339	−	0.429628i	−0.946066	+	0.323975i	$0.894981\pi$
$948$	0.599182	+	5.78838i	0.0194605	+	0.187998i
$949$	31.3811	+	8.34241i	1.01867	+	0.270806i
$950$			11.2120i			0.363764i
$951$	4.92963	−	30.8108i	0.159854	−	0.999109i
$952$	0.364026	+	0.630512i	0.0117982	+	0.0204350i
$953$	24.2831	−	42.0596i	0.786608	−	1.36245i	−0.141425	−	0.989949i	$-0.545168\pi$
$953$	24.2831	−	42.0596i	0.786608	−	1.36245i	0.928034	−	0.372497i	$-0.121498\pi$
$954$	13.7536	−	21.0335i	0.445288	−	0.680984i
$955$	−7.63938	−	28.5106i	−0.247205	−	0.922580i
$956$	3.78185	+	14.1141i	0.122314	+	0.456481i
$957$	24.3986	+	19.8212i	0.788693	+	0.640727i
$958$	−17.9844	+	31.1498i	−0.581048	+	1.00641i
$959$	−2.54074	−	4.40068i	−0.0820446	−	0.142105i
$960$	−4.82099	−	0.771343i	−0.155597	−	0.0248950i
$961$		−	10.6700i		−	0.344193i
$962$	−24.1448	+	0.0475062i	−0.778459	+	0.00153166i
$963$	−2.66213	−	12.7209i	−0.0857860	−	0.409927i
$964$	6.36623	+	1.70583i	0.205043	+	0.0549410i
$965$	−27.3751	+	15.8050i	−0.881235	+	0.508781i
$966$	−8.14091	−	3.63992i	−0.261930	−	0.117112i
$967$	−32.1856	+	32.1856i	−1.03502	+	1.03502i	−0.0356544	+	0.999364i	$0.511352\pi$
$967$	−32.1856	+	32.1856i	−1.03502	+	1.03502i	−0.999364	+	0.0356544i	$0.988648\pi$
$968$	1.31178	−	0.351490i	0.0421621	−	0.0112973i
$969$	−1.71306	−	4.48373i	−0.0550313	−	0.144038i
$970$	−19.5921	−	19.5921i	−0.629064	−	0.629064i
$971$	23.2602	+	13.4293i	0.746457	+	0.430967i	0.824412	−	0.565990i	$-0.191506\pi$
$971$	23.2602	+	13.4293i	0.746457	+	0.430967i	−0.0779555	+	0.996957i	$0.524839\pi$
$972$	−7.90013	+	13.4383i	−0.253397	+	0.431034i
$973$	4.37943	−	16.3442i	0.140398	−	0.523973i
$974$	42.6845			1.36770
$975$	7.47548	−	16.8081i	0.239407	−	0.538289i
$976$	−1.23596			−0.0395623
$977$	0.646311	−	2.41206i	0.0206773	−	0.0771688i	−0.954816	−	0.297197i	$-0.903948\pi$
$977$	0.646311	−	2.41206i	0.0206773	−	0.0771688i	0.975494	+	0.220028i	$0.0706149\pi$
$978$	−28.0653	+	20.3233i	−0.897428	+	0.649866i
$979$	22.4915	+	12.9855i	0.718832	+	0.415018i
$980$	1.99319	+	1.99319i	0.0636702	+	0.0636702i
$981$	−13.9611	−	27.6145i	−0.445743	−	0.881664i
$982$	25.4240	−	6.81234i	0.811312	−	0.217390i
$983$	3.57960	−	3.57960i	0.114172	−	0.114172i	−0.647713	−	0.761884i	$-0.724274\pi$
$983$	3.57960	−	3.57960i	0.114172	−	0.114172i	0.761884	+	0.647713i	$0.224274\pi$
$984$	6.53993	−	14.6270i	0.208485	−	0.466291i
$985$	6.84514	−	3.95204i	0.218104	−	0.125923i
$986$	−3.63067	−	0.972835i	−0.115624	−	0.0309814i
$987$	19.4457	−	2.01291i	0.618963	−	0.0640717i
$988$	−3.57805	−	13.2491i	−0.113833	−	0.421512i
$989$		−	58.0887i		−	1.84711i
$990$	1.64919	−	29.6819i	0.0524145	−	0.943352i
$991$	7.42576	+	12.8618i	0.235887	+	0.408568i	0.959530	−	0.281606i	$-0.0908671\pi$
$991$	7.42576	+	12.8618i	0.235887	+	0.408568i	−0.723643	+	0.690174i	$0.757534\pi$
$992$	3.22761	−	5.59039i	0.102477	−	0.177495i
$993$	−10.7284	+	13.2060i	−0.340456	+	0.419078i
$994$	1.20234	+	4.48721i	0.0381360	+	0.142326i
$995$	6.03164	+	22.5104i	0.191216	+	0.713628i
$996$	−0.853978	+	1.05119i	−0.0270593	+	0.0333083i
$997$	23.2453	−	40.2620i	0.736186	−	1.27511i	−0.218016	−	0.975945i	$-0.569958\pi$
$997$	23.2453	−	40.2620i	0.736186	−	1.27511i	0.954201	−	0.299166i	$-0.0967083\pi$
$998$	−19.5732	−	33.9018i	−0.619579	−	1.07314i
$999$	1.65715	+	34.7569i	0.0524300	+	1.09966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.b.197.6	yes	56
3.2	odd	2		546.2.bu.a.197.12	✓	56
13.7	odd	12		546.2.bu.a.449.12	yes	56
39.20	even	12	inner	546.2.bu.b.449.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.197.12	✓	56	3.2	odd	2
546.2.bu.a.449.12	yes	56	13.7	odd	12
546.2.bu.b.197.6	yes	56	1.1	even	1	trivial
546.2.bu.b.449.6	yes	56	39.20	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(1.01587 + 1.40286i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.99319 - 1.99319i) q^{5} +(-1.61798 + 0.618168i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.936020 + 2.85024i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(1.01587 + 1.40286i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.99319 - 1.99319i) q^{5} +(-1.61798 + 0.618168i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.936020 + 2.85024i) q^{9} +(2.44115 - 1.40940i) q^{10} +(-3.39562 - 0.909853i) q^{11} +(-0.178340 - 1.72285i) q^{12} +(-3.11895 + 1.80892i) q^{13} -1.00000i q^{14} +(0.771343 - 4.82099i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.364026 - 0.630512i) q^{17} +(-2.51086 - 1.64182i) q^{18} +(-0.985142 - 3.67660i) q^{19} +(0.729559 + 2.72275i) q^{20} +(-1.34434 - 1.09213i) q^{21} +(1.75770 - 3.04443i) q^{22} +(-2.57429 - 4.45880i) q^{23} +(1.71030 + 0.273642i) q^{24} +2.94564i q^{25} +(-0.940036 - 3.48085i) q^{26} +(-4.94935 + 1.58237i) q^{27} +(0.965926 + 0.258819i) q^{28} +(-4.47106 + 2.58137i) q^{29} +(4.45708 + 1.99282i) q^{30} +(-4.56454 + 4.56454i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-2.17311 - 5.68786i) q^{33} +(0.514811 + 0.514811i) q^{34} +(2.44115 + 1.40940i) q^{35} +(2.23574 - 2.00037i) q^{36} +(1.73320 - 6.46839i) q^{37} +3.80629 q^{38} +(-5.70609 - 2.53782i) q^{39} -2.81880 q^{40} +(2.39422 - 8.93537i) q^{41} +(1.40286 - 1.01587i) q^{42} +(9.77091 + 5.64124i) q^{43} +(2.48576 + 2.48576i) q^{44} +(7.54675 - 3.81541i) q^{45} +(4.97314 - 1.33255i) q^{46} +(-7.98109 + 7.98109i) q^{47} +(-0.706976 + 1.58120i) q^{48} +(0.866025 - 0.500000i) q^{49} +(-2.84527 - 0.762387i) q^{50} +(1.25432 - 0.129841i) q^{51} +(3.60554 - 0.00709410i) q^{52} +8.37700i q^{53} +(-0.247463 - 5.19026i) q^{54} +(4.95461 + 8.58163i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(4.15697 - 5.11696i) q^{57} +(-1.33621 - 4.98682i) q^{58} +(1.91793 + 7.15783i) q^{59} +(-3.07850 + 3.78943i) q^{60} +(-0.617982 + 1.07038i) q^{61} +(-3.22761 - 5.59039i) q^{62} +(0.166429 - 2.99538i) q^{63} -1.00000i q^{64} +(9.82218 + 2.61114i) q^{65} +(6.05649 - 0.626935i) q^{66} +(10.5323 + 2.82212i) q^{67} +(-0.630512 + 0.364026i) q^{68} +(3.63992 - 8.14091i) q^{69} +(-1.99319 + 1.99319i) q^{70} +(-4.48721 + 1.20234i) q^{71} +(1.35356 + 2.67729i) q^{72} +(-6.36810 - 6.36810i) q^{73} +(5.79940 + 3.34829i) q^{74} +(-4.13231 + 2.99238i) q^{75} +(-0.985142 + 3.67660i) q^{76} +3.51540 q^{77} +(3.92819 - 4.85483i) q^{78} -3.35978 q^{79} +(0.729559 - 2.72275i) q^{80} +(-7.24773 - 5.33576i) q^{81} +(8.01123 + 4.62529i) q^{82} +(-0.552914 - 0.552914i) q^{83} +(0.618168 + 1.61798i) q^{84} +(-1.98231 + 0.531158i) q^{85} +(-7.97792 + 7.97792i) q^{86} +(-8.16330 - 3.64993i) q^{87} +(-3.04443 + 1.75770i) q^{88} +(-7.13603 - 1.91209i) q^{89} +(1.73216 + 8.27710i) q^{90} +(2.54449 - 2.55452i) q^{91} +5.14858i q^{92} +(-11.0404 - 1.76642i) q^{93} +(-5.64349 - 9.77480i) q^{94} +(-5.36459 + 9.29175i) q^{95} +(-1.34434 - 1.09213i) q^{96} +(-2.54406 - 9.49457i) q^{97} +(0.258819 + 0.965926i) q^{98} +(5.77166 - 8.82668i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{6} - 24 q^{9}+O(q^{10}) \) 56 * q + 8 * q^6 - 24 * q^9	\( 56 q + 8 q^{6} - 24 q^{9} + 24 q^{10} + 8 q^{11} + 24 q^{13} + 4 q^{15} + 28 q^{16} - 4 q^{17} - 8 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{79} + 12 q^{81} - 4 q^{83} - 4 q^{84} + 32 q^{85} - 16 q^{86} - 144 q^{87} + 88 q^{89} - 8 q^{90} - 8 q^{91} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 q^{99}+O(q^{100}) \) 56 * q + 8 * q^6 - 24 * q^9 + 24 * q^10 + 8 * q^11 + 24 * q^13 + 4 * q^15 + 28 * q^16 - 4 * q^17 - 8 * q^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 16 * q^79 + 12 * q^81 - 4 * q^83 - 4 * q^84 + 32 * q^85 - 16 * q^86 - 144 * q^87 + 88 * q^89 - 8 * q^90 - 8 * q^91 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

Introduction

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