LMFDB - Embedded newform 546.2.bm.b.205.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(205,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("546.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bm (of order $6$, degree $2$, 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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 56 x^{18} + 1306 x^{16} + 16508 x^{14} + 123139 x^{12} + 552164 x^{10} + 1447090 x^{8} + \cdots + 576 $ x^20 + 56x^18 + 1306x^16 + 16508x^14 + 123139x^12 + 552164x^10 + 1447090x^8 + 2035844x^6 + 1263505x^4 + 215520*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.6
Root			$2.99764i$ of defining polynomial
Character	$\chi$	$=$	546.205
Dual form			546.2.bm.b.277.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(-2.59603 - 1.49882i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(2.50724 - 0.844840i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(-2.59603 - 1.49882i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(2.50724 - 0.844840i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.49882 - 2.59603i) q^{10} +(-0.672474 - 0.388253i) q^{11} +(0.500000 - 0.866025i) q^{12} +(3.39805 + 1.20550i) q^{13} +(0.844840 + 2.50724i) q^{14} +(2.59603 - 1.49882i) q^{15} +1.00000 q^{16} +2.34065 q^{17} +(0.866025 - 0.500000i) q^{18} +(2.56329 - 1.47992i) q^{19} +(2.59603 + 1.49882i) q^{20} +(-0.521966 + 2.59375i) q^{21} +(0.388253 - 0.672474i) q^{22} +2.07990 q^{23} +(0.866025 + 0.500000i) q^{24} +(1.99293 + 3.45185i) q^{25} +(-1.20550 + 3.39805i) q^{26} +1.00000 q^{27} +(-2.50724 + 0.844840i) q^{28} +(0.541131 + 0.937266i) q^{29} +(1.49882 + 2.59603i) q^{30} +(6.31977 - 3.64872i) q^{31} +1.00000i q^{32} +(0.672474 - 0.388253i) q^{33} +2.34065i q^{34} +(-7.77514 - 1.56467i) q^{35} +(0.500000 + 0.866025i) q^{36} +6.87272i q^{37} +(1.47992 + 2.56329i) q^{38} +(-2.74302 + 2.34005i) q^{39} +(-1.49882 + 2.59603i) q^{40} +(9.81648 - 5.66755i) q^{41} +(-2.59375 - 0.521966i) q^{42} +(-2.64755 + 4.58570i) q^{43} +(0.672474 + 0.388253i) q^{44} +2.99764i q^{45} +2.07990i q^{46} +(-7.35082 - 4.24400i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(5.57249 - 4.23643i) q^{49} +(-3.45185 + 1.99293i) q^{50} +(-1.17033 + 2.02707i) q^{51} +(-3.39805 - 1.20550i) q^{52} +(2.30398 + 3.99062i) q^{53} +1.00000i q^{54} +(1.16384 + 2.01584i) q^{55} +(-0.844840 - 2.50724i) q^{56} +2.95984i q^{57} +(-0.937266 + 0.541131i) q^{58} -3.79180i q^{59} +(-2.59603 + 1.49882i) q^{60} +(-6.68750 - 11.5831i) q^{61} +(3.64872 + 6.31977i) q^{62} +(-1.98527 - 1.74891i) q^{63} -1.00000 q^{64} +(-7.01464 - 8.22259i) q^{65} +(0.388253 + 0.672474i) q^{66} +(4.62876 + 2.67241i) q^{67} -2.34065 q^{68} +(-1.03995 + 1.80125i) q^{69} +(1.56467 - 7.77514i) q^{70} +(-3.56761 - 2.05976i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(6.95039 - 4.01281i) q^{73} -6.87272 q^{74} -3.98586 q^{75} +(-2.56329 + 1.47992i) q^{76} +(-2.01406 - 0.405310i) q^{77} +(-2.34005 - 2.74302i) q^{78} +(-1.49451 + 2.58856i) q^{79} +(-2.59603 - 1.49882i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.66755 + 9.81648i) q^{82} -4.25324i q^{83} +(0.521966 - 2.59375i) q^{84} +(-6.07642 - 3.50822i) q^{85} +(-4.58570 - 2.64755i) q^{86} -1.08226 q^{87} +(-0.388253 + 0.672474i) q^{88} +8.71065i q^{89} -2.99764 q^{90} +(9.53819 + 0.151662i) q^{91} -2.07990 q^{92} +7.29745i q^{93} +(4.24400 - 7.35082i) q^{94} -8.87253 q^{95} +(-0.866025 - 0.500000i) q^{96} +(2.45297 + 1.41622i) q^{97} +(4.23643 + 5.57249i) q^{98} +0.776506i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9}+O(q^{10}) $ 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9	$ 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9} + 4 q^{10} + 6 q^{11} + 10 q^{12} + 8 q^{13} + 4 q^{14} + 20 q^{16} - 8 q^{17} - 12 q^{19} + 6 q^{21} - 10 q^{22} - 16 q^{23} + 6 q^{25} + 8 q^{26} + 20 q^{27} + 8 q^{29} + 4 q^{30} + 12 q^{31} - 6 q^{33} + 10 q^{35} + 10 q^{36} + 6 q^{38} - 10 q^{39} - 4 q^{40} - 18 q^{41} - 2 q^{42} + 18 q^{43} - 6 q^{44} - 6 q^{47} - 10 q^{48} - 20 q^{49} + 12 q^{50} + 4 q^{51} - 8 q^{52} + 18 q^{53} - 12 q^{55} - 4 q^{56} + 24 q^{58} - 6 q^{61} - 6 q^{63} - 20 q^{64} - 6 q^{65} - 10 q^{66} + 24 q^{67} + 8 q^{68} + 8 q^{69} + 42 q^{70} - 6 q^{71} + 24 q^{73} + 36 q^{74} - 12 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} - 10 q^{81} + 18 q^{82} - 6 q^{84} - 36 q^{86} - 16 q^{87} + 10 q^{88} - 8 q^{90} - 10 q^{91} + 16 q^{92} - 16 q^{94} - 80 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) $ 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9 + 4 * q^10 + 6 * q^11 + 10 * q^12 + 8 * q^13 + 4 * q^14 + 20 * q^16 - 8 * q^17 - 12 * q^19 + 6 * q^21 - 10 * q^22 - 16 * q^23 + 6 * q^25 + 8 * q^26 + 20 * q^27 + 8 * q^29 + 4 * q^30 + 12 * q^31 - 6 * q^33 + 10 * q^35 + 10 * q^36 + 6 * q^38 - 10 * q^39 - 4 * q^40 - 18 * q^41 - 2 * q^42 + 18 * q^43 - 6 * q^44 - 6 * q^47 - 10 * q^48 - 20 * q^49 + 12 * q^50 + 4 * q^51 - 8 * q^52 + 18 * q^53 - 12 * q^55 - 4 * q^56 + 24 * q^58 - 6 * q^61 - 6 * q^63 - 20 * q^64 - 6 * q^65 - 10 * q^66 + 24 * q^67 + 8 * q^68 + 8 * q^69 + 42 * q^70 - 6 * q^71 + 24 * q^73 + 36 * q^74 - 12 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 - 10 * q^81 + 18 * q^82 - 6 * q^84 - 36 * q^86 - 16 * q^87 + 10 * q^88 - 8 * q^90 - 10 * q^91 + 16 * q^92 - 16 * q^94 - 80 * q^95 - 96 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−1.00000			−0.500000
$5$	−2.59603	−	1.49882i	−1.16098	−	0.670293i	−0.209443	−	0.977821i	$-0.567165\pi$
$5$	−2.59603	−	1.49882i	−1.16098	−	0.670293i	−0.951539	+	0.307528i	$0.900498\pi$
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	2.50724	−	0.844840i	0.947647	−	0.319320i
$7$	2.50724	−	0.844840i	0.947647	−	0.319320i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.49882	−	2.59603i	0.473969	−	0.820938i
$11$	−0.672474	−	0.388253i	−0.202758	−	0.117063i	0.395183	−	0.918602i	$-0.370681\pi$
$11$	−0.672474	−	0.388253i	−0.202758	−	0.117063i	−0.597941	+	0.801540i	$0.704014\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	3.39805	+	1.20550i	0.942451	+	0.334345i
$13$	3.39805	+	1.20550i	0.942451	+	0.334345i
$14$	0.844840	+	2.50724i	0.225793	+	0.670088i
$15$	2.59603	−	1.49882i	0.670293	−	0.386994i
$16$	1.00000			0.250000
$17$	2.34065			0.567692			0.283846	−	0.958870i	$-0.408390\pi$
$17$	2.34065			0.567692			0.283846	+	0.958870i	$0.408390\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	2.56329	−	1.47992i	0.588060	−	0.339516i	−0.176270	−	0.984342i	$-0.556403\pi$
$19$	2.56329	−	1.47992i	0.588060	−	0.339516i	0.764330	+	0.644825i	$0.223070\pi$
$20$	2.59603	+	1.49882i	0.580491	+	0.335147i
$21$	−0.521966	+	2.59375i	−0.113902	+	0.566003i
$22$	0.388253	−	0.672474i	0.0827758	−	0.143372i
$23$	2.07990			0.433690			0.216845	−	0.976206i	$-0.430423\pi$
$23$	2.07990			0.433690			0.216845	+	0.976206i	$0.430423\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	1.99293	+	3.45185i	0.398586	+	0.690371i
$26$	−1.20550	+	3.39805i	−0.236418	+	0.666413i
$27$	1.00000			0.192450
$28$	−2.50724	+	0.844840i	−0.473824	+	0.159660i
$29$	0.541131	+	0.937266i	0.100485	+	0.174046i	0.911885	−	0.410446i	$-0.134627\pi$
$29$	0.541131	+	0.937266i	0.100485	+	0.174046i	−0.811399	+	0.584492i	$0.801294\pi$
$30$	1.49882	+	2.59603i	0.273646	+	0.473969i
$31$	6.31977	−	3.64872i	1.13507	−	0.655330i	0.189861	−	0.981811i	$-0.439196\pi$
$31$	6.31977	−	3.64872i	1.13507	−	0.655330i	0.945204	+	0.326481i	$0.105863\pi$
$32$			1.00000i			0.176777i
$33$	0.672474	−	0.388253i	0.117063	−	0.0675861i
$34$			2.34065i			0.401419i
$35$	−7.77514	−	1.56467i	−1.31424	−	0.264477i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$			6.87272i			1.12987i	0.825136	+	0.564934i	$0.191098\pi$
$37$			6.87272i			1.12987i	−0.825136	+	0.564934i	$0.808902\pi$
$38$	1.47992	+	2.56329i	0.240074	+	0.415821i
$39$	−2.74302	+	2.34005i	−0.439235	+	0.374708i
$40$	−1.49882	+	2.59603i	−0.236984	+	0.410469i
$41$	9.81648	−	5.66755i	1.53308	−	0.885122i	0.533859	−	0.845573i	$-0.320741\pi$
$41$	9.81648	−	5.66755i	1.53308	−	0.885122i	0.999218	−	0.0395490i	$-0.0125921\pi$
$42$	−2.59375	−	0.521966i	−0.400225	−	0.0805411i
$43$	−2.64755	+	4.58570i	−0.403748	+	0.699312i	−0.994175	−	0.107779i	$-0.965626\pi$
$43$	−2.64755	+	4.58570i	−0.403748	+	0.699312i	0.590427	+	0.807091i	$0.298959\pi$
$44$	0.672474	+	0.388253i	0.101379	+	0.0585313i
$45$			2.99764i			0.446862i
$46$			2.07990i			0.306665i
$47$	−7.35082	−	4.24400i	−1.07223	−	0.619051i	−0.143438	−	0.989659i	$-0.545816\pi$
$47$	−7.35082	−	4.24400i	−1.07223	−	0.619051i	−0.928789	+	0.370609i	$0.879149\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	5.57249	−	4.23643i	0.796070	−	0.605205i
$50$	−3.45185	+	1.99293i	−0.488166	+	0.281843i
$51$	−1.17033	+	2.02707i	−0.163879	+	0.283846i
$52$	−3.39805	−	1.20550i	−0.471225	−	0.167173i
$53$	2.30398	+	3.99062i	0.316476	+	0.548153i	0.979750	−	0.200224i	$-0.0641668\pi$
$53$	2.30398	+	3.99062i	0.316476	+	0.548153i	−0.663274	+	0.748377i	$0.730834\pi$
$54$			1.00000i			0.136083i
$55$	1.16384	+	2.01584i	0.156933	+	0.271815i
$56$	−0.844840	−	2.50724i	−0.112897	−	0.335044i
$57$			2.95984i			0.392040i
$58$	−0.937266	+	0.541131i	−0.123069	+	0.0710539i
$59$		−	3.79180i		−	0.493650i	−0.969060	−	0.246825i	$-0.920613\pi$
$59$		−	3.79180i		−	0.493650i	0.969060	−	0.246825i	$-0.0793873\pi$
$60$	−2.59603	+	1.49882i	−0.335147	+	0.193497i
$61$	−6.68750	−	11.5831i	−0.856246	−	1.48306i	−0.875484	−	0.483247i	$-0.839457\pi$
$61$	−6.68750	−	11.5831i	−0.856246	−	1.48306i	0.0192379	−	0.999815i	$-0.493876\pi$
$62$	3.64872	+	6.31977i	0.463388	+	0.802612i
$63$	−1.98527	−	1.74891i	−0.250121	−	0.220342i
$64$	−1.00000			−0.125000
$65$	−7.01464	−	8.22259i	−0.870059	−	1.01989i
$66$	0.388253	+	0.672474i	0.0477906	+	0.0827758i
$67$	4.62876	+	2.67241i	0.565493	+	0.326487i	0.755347	−	0.655325i	$-0.227468\pi$
$67$	4.62876	+	2.67241i	0.565493	+	0.326487i	−0.189854	+	0.981812i	$0.560802\pi$
$68$	−2.34065			−0.283846
$69$	−1.03995	+	1.80125i	−0.125195	+	0.216845i
$70$	1.56467	−	7.77514i	0.187014	−	0.929307i
$71$	−3.56761	−	2.05976i	−0.423397	−	0.244448i	0.273133	−	0.961976i	$-0.411940\pi$
$71$	−3.56761	−	2.05976i	−0.423397	−	0.244448i	−0.696530	+	0.717528i	$0.745274\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	6.95039	−	4.01281i	0.813482	−	0.469664i	−0.0346819	−	0.999398i	$-0.511042\pi$
$73$	6.95039	−	4.01281i	0.813482	−	0.469664i	0.848163	+	0.529735i	$0.177708\pi$
$74$	−6.87272			−0.798938
$75$	−3.98586			−0.460247
$76$	−2.56329	+	1.47992i	−0.294030	+	0.169758i
$77$	−2.01406	−	0.405310i	−0.229524	−	0.0461893i
$78$	−2.34005	−	2.74302i	−0.264959	−	0.310586i
$79$	−1.49451	+	2.58856i	−0.168145	+	0.291236i	−0.937768	−	0.347263i	$-0.887111\pi$
$79$	−1.49451	+	2.58856i	−0.168145	+	0.291236i	0.769622	+	0.638499i	$0.220444\pi$
$80$	−2.59603	−	1.49882i	−0.290245	−	0.167573i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.66755	+	9.81648i	0.625876	+	1.08405i
$83$		−	4.25324i		−	0.466854i	−0.972374	−	0.233427i	$-0.925006\pi$
$83$		−	4.25324i		−	0.466854i	0.972374	−	0.233427i	$-0.0749940\pi$
$84$	0.521966	−	2.59375i	0.0569512	−	0.283002i
$85$	−6.07642	−	3.50822i	−0.659080	−	0.380520i
$86$	−4.58570	−	2.64755i	−0.494488	−	0.285493i
$87$	−1.08226			−0.116031
$88$	−0.388253	+	0.672474i	−0.0413879	+	0.0716859i
$89$			8.71065i			0.923327i	0.887055	+	0.461663i	$0.152747\pi$
$89$			8.71065i			0.923327i	−0.887055	+	0.461663i	$0.847253\pi$
$90$	−2.99764			−0.315979
$91$	9.53819	+	0.151662i	0.999874	+	0.0158985i
$92$	−2.07990			−0.216845
$93$			7.29745i			0.756710i
$94$	4.24400	−	7.35082i	0.437735	−	0.758179i
$95$	−8.87253			−0.910302
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	2.45297	+	1.41622i	0.249061	+	0.143795i	0.619334	−	0.785127i	$-0.287403\pi$
$97$	2.45297	+	1.41622i	0.249061	+	0.143795i	−0.370273	+	0.928923i	$0.620736\pi$
$98$	4.23643	+	5.57249i	0.427944	+	0.562906i
$99$			0.776506i			0.0780418i
$100$	−1.99293	−	3.45185i	−0.199293	−	0.345185i
$101$	5.80539	−	10.0552i	0.577658	−	1.00053i	−0.418090	−	0.908406i	$-0.637300\pi$
$101$	5.80539	−	10.0552i	0.577658	−	1.00053i	0.995747	−	0.0921266i	$-0.0293664\pi$
$102$	−2.02707	−	1.17033i	−0.200709	−	0.115880i
$103$	3.66662	−	6.35077i	0.361282	−	0.625760i	−0.626890	−	0.779108i	$-0.715672\pi$
$103$	3.66662	−	6.35077i	0.361282	−	0.625760i	0.988172	+	0.153348i	$0.0490057\pi$
$104$	1.20550	−	3.39805i	0.118209	−	0.333207i
$105$	5.24261	−	5.95114i	0.511627	−	0.580771i
$106$	−3.99062	+	2.30398i	−0.387603	+	0.223783i
$107$	10.9196			1.05563			0.527817	−	0.849358i	$-0.323011\pi$
$107$	10.9196			1.05563			0.527817	+	0.849358i	$0.323011\pi$
$108$	−1.00000			−0.0962250
$109$	12.1454	−	7.01217i	1.16332	−	0.671645i	0.211224	−	0.977438i	$-0.432255\pi$
$109$	12.1454	−	7.01217i	1.16332	−	0.671645i	0.952098	+	0.305793i	$0.0989216\pi$
$110$	−2.01584	+	1.16384i	−0.192202	+	0.110968i
$111$	−5.95195	−	3.43636i	−0.564934	−	0.326165i
$112$	2.50724	−	0.844840i	0.236912	−	0.0798299i
$113$	−5.08527	+	8.80794i	−0.478382	+	0.828581i	−0.999693	−	0.0247852i	$-0.992110\pi$
$113$	−5.08527	+	8.80794i	−0.478382	+	0.828581i	0.521311	+	0.853367i	$0.325443\pi$
$114$	−2.95984			−0.277214
$115$	−5.39950	−	3.11740i	−0.503506	−	0.290699i
$116$	−0.541131	−	0.937266i	−0.0502427	−	0.0870230i
$117$	−0.655034	−	3.54555i	−0.0605579	−	0.327786i
$118$	3.79180			0.349063
$119$	5.86858	−	1.97748i	0.537972	−	0.181275i
$120$	−1.49882	−	2.59603i	−0.136823	−	0.236984i
$121$	−5.19852	−	9.00410i	−0.472593	−	0.818555i
$122$	11.5831	−	6.68750i	1.04868	−	0.605457i
$123$			11.3351i			1.02205i
$124$	−6.31977	+	3.64872i	−0.567533	+	0.327665i
$125$			3.04003i			0.271909i
$126$	1.74891	−	1.98527i	0.155805	−	0.176862i
$127$	1.07357	+	1.85948i	0.0952641	+	0.165002i	0.909719	−	0.415225i	$-0.136297\pi$
$127$	1.07357	+	1.85948i	0.0952641	+	0.165002i	−0.814455	+	0.580227i	$0.802964\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−2.64755	−	4.58570i	−0.233104	−	0.403748i
$130$	8.22259	−	7.01464i	0.721169	−	0.615224i
$131$	−9.39683	+	16.2758i	−0.821005	+	1.42202i	0.0839297	+	0.996472i	$0.473253\pi$
$131$	−9.39683	+	16.2758i	−0.821005	+	1.42202i	−0.904935	+	0.425551i	$0.860080\pi$
$132$	−0.672474	+	0.388253i	−0.0585313	+	0.0337931i
$133$	5.17649	−	5.87608i	0.448859	−	0.509521i
$134$	−2.67241	+	4.62876i	−0.230861	+	0.399864i
$135$	−2.59603	−	1.49882i	−0.223431	−	0.128998i
$136$		−	2.34065i		−	0.200709i
$137$		−	18.1285i		−	1.54882i	−0.632681	−	0.774412i	$-0.718046\pi$
$137$		−	18.1285i		−	1.54882i	0.632681	−	0.774412i	$-0.281954\pi$
$138$	−1.80125	−	1.03995i	−0.153333	−	0.0885266i
$139$	−10.2597	+	17.7702i	−0.870213	+	1.50725i	−0.00843630	+	0.999964i	$0.502685\pi$
$139$	−10.2597	+	17.7702i	−0.870213	+	1.50725i	−0.861776	+	0.507288i	$0.830648\pi$
$140$	7.77514	+	1.56467i	0.657119	+	0.132239i
$141$	7.35082	−	4.24400i	0.619051	−	0.357409i
$142$	2.05976	−	3.56761i	0.172851	−	0.299387i
$143$	−1.81706	−	2.12997i	−0.151950	−	0.178117i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$		−	3.24423i		−	0.269419i
$146$	4.01281	+	6.95039i	0.332102	+	0.575218i
$147$	0.882613	+	6.94413i	0.0727967	+	0.572743i
$148$		−	6.87272i		−	0.564934i
$149$	−13.5062	+	7.79784i	−1.10648	+	0.638824i	−0.937914	−	0.346868i	$-0.887245\pi$
$149$	−13.5062	+	7.79784i	−1.10648	+	0.638824i	−0.168561	+	0.985691i	$0.553912\pi$
$150$		−	3.98586i		−	0.325444i
$151$	−6.39071	+	3.68968i	−0.520069	+	0.300262i	−0.736963	−	0.675933i	$-0.763741\pi$
$151$	−6.39071	+	3.68968i	−0.520069	+	0.300262i	0.216894	+	0.976195i	$0.430407\pi$
$152$	−1.47992	−	2.56329i	−0.120037	−	0.207911i
$153$	−1.17033	−	2.02707i	−0.0946153	−	0.163879i
$154$	0.405310	−	2.01406i	0.0326608	−	0.162298i
$155$	−21.8751			−1.75705
$156$	2.74302	−	2.34005i	0.219617	−	0.187354i
$157$	−12.3079	−	21.3179i	−0.982278	−	1.70136i	−0.653458	−	0.756963i	$-0.726682\pi$
$157$	−12.3079	−	21.3179i	−0.982278	−	1.70136i	−0.328820	−	0.944392i	$-0.606651\pi$
$158$	−2.58856	−	1.49451i	−0.205935	−	0.118897i
$159$	−4.60797			−0.365436
$160$	1.49882	−	2.59603i	0.118492	−	0.205235i
$161$	5.21481	−	1.75719i	0.410985	−	0.138486i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−9.70830	+	5.60509i	−0.760413	+	0.439025i	−0.829444	−	0.558590i	$-0.811343\pi$
$163$	−9.70830	+	5.60509i	−0.760413	+	0.439025i	0.0690310	+	0.997615i	$0.478009\pi$
$164$	−9.81648	+	5.66755i	−0.766538	+	0.442561i
$165$	−2.32769			−0.181210
$166$	4.25324			0.330116
$167$	−10.8485	+	6.26340i	−0.839485	+	0.484677i	−0.857089	−	0.515168i	$-0.827729\pi$
$167$	−10.8485	+	6.26340i	−0.839485	+	0.484677i	0.0176045	+	0.999845i	$0.494396\pi$
$168$	2.59375	+	0.521966i	0.200112	+	0.0402706i
$169$	10.0935	+	8.19270i	0.776426	+	0.630208i
$170$	3.50822	−	6.07642i	0.269068	−	0.466040i
$171$	−2.56329	−	1.47992i	−0.196020	−	0.113172i
$172$	2.64755	−	4.58570i	0.201874	−	0.349656i
$173$	3.27031	+	5.66435i	0.248637	+	0.430652i	0.963148	−	0.268972i	$-0.0866839\pi$
$173$	3.27031	+	5.66435i	0.248637	+	0.430652i	−0.714511	+	0.699625i	$0.753351\pi$
$174$		−	1.08226i		−	0.0820460i
$175$	7.91301	+	6.97092i	0.598168	+	0.526952i
$176$	−0.672474	−	0.388253i	−0.0506896	−	0.0292657i
$177$	3.28379	+	1.89590i	0.246825	+	0.142504i
$178$	−8.71065			−0.652891
$179$	−9.22443	+	15.9772i	−0.689466	+	1.19419i	0.282545	+	0.959254i	$0.408822\pi$
$179$	−9.22443	+	15.9772i	−0.689466	+	1.19419i	−0.972011	+	0.234936i	$0.924512\pi$
$180$		−	2.99764i		−	0.223431i
$181$	−14.7886			−1.09923			−0.549615	−	0.835418i	$-0.685226\pi$
$181$	−14.7886			−1.09923			−0.549615	+	0.835418i	$0.685226\pi$
$182$	−0.151662	+	9.53819i	−0.0112419	+	0.707017i
$183$	13.3750			0.988708
$184$		−	2.07990i		−	0.153333i
$185$	10.3010	−	17.8418i	0.757343	−	1.31176i
$186$	−7.29745			−0.535075
$187$	−1.57403	−	0.908766i	−0.115104	−	0.0664555i
$188$	7.35082	+	4.24400i	0.536114	+	0.309525i
$189$	2.50724	−	0.844840i	0.182375	−	0.0614531i
$190$		−	8.87253i		−	0.643681i
$191$	3.26657	+	5.65786i	0.236361	+	0.409389i	0.959667	−	0.281138i	$-0.0907120\pi$
$191$	3.26657	+	5.65786i	0.236361	+	0.409389i	−0.723307	+	0.690527i	$0.757379\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	4.65158	+	2.68559i	0.334828	+	0.193313i	0.657983	−	0.753033i	$-0.271410\pi$
$193$	4.65158	+	2.68559i	0.334828	+	0.193313i	−0.323155	+	0.946346i	$0.604743\pi$
$194$	−1.41622	+	2.45297i	−0.101679	+	0.176113i
$195$	10.6283	−	1.96356i	0.761108	−	0.140613i
$196$	−5.57249	+	4.23643i	−0.398035	+	0.302602i
$197$	16.4198	−	9.47999i	1.16986	−	0.675421i	0.216216	−	0.976346i	$-0.430629\pi$
$197$	16.4198	−	9.47999i	1.16986	−	0.675421i	0.953648	+	0.300924i	$0.0972952\pi$
$198$	−0.776506			−0.0551839
$199$	−8.21048			−0.582026			−0.291013	−	0.956719i	$-0.593992\pi$
$199$	−8.21048			−0.582026			−0.291013	+	0.956719i	$0.593992\pi$
$200$	3.45185	−	1.99293i	0.244083	−	0.140921i
$201$	−4.62876	+	2.67241i	−0.326487	+	0.188498i
$202$	10.0552	+	5.80539i	0.707483	+	0.408466i
$203$	2.14858	+	1.89278i	0.150801	+	0.132847i
$204$	1.17033	−	2.02707i	0.0819393	−	0.141923i
$205$	−33.9786			−2.37317
$206$	6.35077	+	3.66662i	0.442479	+	0.255465i
$207$	−1.03995	−	1.80125i	−0.0722816	−	0.125195i
$208$	3.39805	+	1.20550i	0.235613	+	0.0835864i
$209$	−2.29833			−0.158979
$210$	5.95114	+	5.24261i	0.410667	+	0.361775i
$211$	−5.39098	−	9.33746i	−0.371131	−	0.642817i	0.618609	−	0.785699i	$-0.287696\pi$
$211$	−5.39098	−	9.33746i	−0.371131	−	0.642817i	−0.989740	+	0.142882i	$0.954363\pi$
$212$	−2.30398	−	3.99062i	−0.158238	−	0.274077i
$213$	3.56761	−	2.05976i	0.244448	−	0.141132i
$214$			10.9196i			0.746445i
$215$	13.7463	−	7.93642i	0.937488	−	0.541259i
$216$		−	1.00000i		−	0.0680414i
$217$	12.7626	−	14.4874i	0.866381	−	0.983470i
$218$	7.01217	+	12.1454i	0.474924	+	0.822593i
$219$			8.02562i			0.542321i
$220$	−1.16384	−	2.01584i	−0.0784663	−	0.135908i
$221$	7.95367	+	2.82166i	0.535022	+	0.189805i
$222$	3.43636	−	5.95195i	0.230633	−	0.399469i
$223$	1.45669	−	0.841020i	0.0975471	−	0.0563189i	−0.450433	−	0.892810i	$-0.648730\pi$
$223$	1.45669	−	0.841020i	0.0975471	−	0.0563189i	0.547980	+	0.836491i	$0.315397\pi$
$224$	0.844840	+	2.50724i	0.0564483	+	0.167522i
$225$	1.99293	−	3.45185i	0.132862	−	0.230124i
$226$	−8.80794	−	5.08527i	−0.585896	−	0.338267i
$227$			6.35545i			0.421826i	0.977505	+	0.210913i	$0.0676437\pi$
$227$			6.35545i			0.421826i	−0.977505	+	0.210913i	$0.932356\pi$
$228$		−	2.95984i		−	0.196020i
$229$	15.4079	+	8.89576i	1.01818	+	0.587848i	0.913577	−	0.406665i	$-0.133308\pi$
$229$	15.4079	+	8.89576i	1.01818	+	0.587848i	0.104606	+	0.994514i	$0.466642\pi$
$230$	3.11740	−	5.39950i	0.205555	−	0.356033i
$231$	1.35804	−	1.54158i	0.0893525	−	0.101428i
$232$	0.937266	−	0.541131i	0.0615345	−	0.0355270i
$233$	−5.84028	+	10.1157i	−0.382609	+	0.662699i	−0.991434	−	0.130606i	$-0.958308\pi$
$233$	−5.84028	+	10.1157i	−0.382609	+	0.662699i	0.608825	+	0.793304i	$0.291641\pi$
$234$	3.54555	−	0.655034i	0.231780	−	0.0428209i
$235$	12.7220	+	22.0351i	0.829891	+	1.43741i
$236$			3.79180i			0.246825i
$237$	−1.49451	−	2.58856i	−0.0970787	−	0.168145i
$238$	1.97748	+	5.86858i	0.128181	+	0.380403i
$239$			8.17752i			0.528960i	0.964391	+	0.264480i	$0.0852003\pi$
$239$			8.17752i			0.528960i	−0.964391	+	0.264480i	$0.914800\pi$
$240$	2.59603	−	1.49882i	0.167573	−	0.0967485i
$241$			28.9685i			1.86602i	0.359846	+	0.933012i	$0.382829\pi$
$241$			28.9685i			1.86602i	−0.359846	+	0.933012i	$0.617171\pi$
$242$	9.00410	−	5.19852i	0.578805	−	0.334173i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	6.68750	+	11.5831i	0.428123	+	0.741531i
$245$	−20.8160	+	2.64576i	−1.32989	+	0.169031i
$246$	−11.3351			−0.722699
$247$	10.4942	−	1.93879i	0.667733	−	0.123362i
$248$	−3.64872	−	6.31977i	−0.231694	−	0.401306i
$249$	3.68342	+	2.12662i	0.233427	+	0.134769i
$250$	−3.04003			−0.192269
$251$	3.11086	−	5.38817i	0.196356	−	0.340099i	−0.750988	−	0.660316i	$-0.770423\pi$
$251$	3.11086	−	5.38817i	0.196356	−	0.340099i	0.947344	+	0.320217i	$0.103756\pi$
$252$	1.98527	+	1.74891i	0.125060	+	0.110171i
$253$	−1.39868	−	0.807528i	−0.0879343	−	0.0507689i
$254$	−1.85948	+	1.07357i	−0.116674	+	0.0673619i
$255$	6.07642	−	3.50822i	0.380520	−	0.219693i
$256$	1.00000			0.0625000
$257$	9.62683			0.600505			0.300253	−	0.953860i	$-0.402929\pi$
$257$	9.62683			0.600505			0.300253	+	0.953860i	$0.402929\pi$
$258$	4.58570	−	2.64755i	0.285493	−	0.164829i
$259$	5.80635	+	17.2316i	0.360789	+	1.07072i
$260$	7.01464	+	8.22259i	0.435029	+	0.509944i
$261$	0.541131	−	0.937266i	0.0334951	−	0.0580153i
$262$	−16.2758	−	9.39683i	−1.00552	−	0.580538i
$263$	−1.48500	+	2.57210i	−0.0915691	+	0.158602i	−0.908172	−	0.418598i	$-0.862522\pi$
$263$	−1.48500	+	2.57210i	−0.0915691	+	0.158602i	0.816602	+	0.577201i	$0.195855\pi$
$264$	−0.388253	−	0.672474i	−0.0238953	−	0.0413879i
$265$		−	13.8130i		−	0.848528i
$266$	5.87608	+	5.17649i	0.360286	+	0.317391i
$267$	−7.54364	−	4.35532i	−0.461663	−	0.266541i
$268$	−4.62876	−	2.67241i	−0.282746	−	0.163244i
$269$	21.6142			1.31784			0.658920	−	0.752213i	$-0.271013\pi$
$269$	21.6142			1.31784			0.658920	+	0.752213i	$0.271013\pi$
$270$	1.49882	−	2.59603i	0.0912153	−	0.157990i
$271$			1.29946i			0.0789369i	0.999221	+	0.0394684i	$0.0125665\pi$
$271$			1.29946i			0.0789369i	−0.999221	+	0.0394684i	$0.987434\pi$
$272$	2.34065			0.141923
$273$	−4.90044	+	8.18448i	−0.296588	+	0.495347i
$274$	18.1285			1.09518
$275$		−	3.09504i		−	0.186638i
$276$	1.03995	−	1.80125i	0.0625977	−	0.108422i
$277$	−22.3327			−1.34184			−0.670921	−	0.741529i	$-0.734101\pi$
$277$	−22.3327			−1.34184			−0.670921	+	0.741529i	$0.734101\pi$
$278$	−17.7702	−	10.2597i	−1.06579	−	0.615333i
$279$	−6.31977	−	3.64872i	−0.378355	−	0.218443i
$280$	−1.56467	+	7.77514i	−0.0935068	+	0.464654i
$281$		−	29.1881i		−	1.74121i	−0.491980	−	0.870607i	$-0.663727\pi$
$281$		−	29.1881i		−	1.74121i	0.491980	−	0.870607i	$-0.336273\pi$
$282$	4.24400	+	7.35082i	0.252726	+	0.437735i
$283$	−15.6289	+	27.0700i	−0.929039	+	1.60914i	−0.144106	+	0.989562i	$0.546031\pi$
$283$	−15.6289	+	27.0700i	−0.929039	+	1.60914i	−0.784933	+	0.619581i	$0.787303\pi$
$284$	3.56761	+	2.05976i	0.211699	+	0.122224i
$285$	4.43626	−	7.68383i	0.262782	−	0.455151i
$286$	2.12997	−	1.81706i	0.125948	−	0.107445i
$287$	19.8241	−	22.5033i	1.17018	−	1.32833i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−11.5213			−0.677726
$290$	3.24423			0.190508
$291$	−2.45297	+	1.41622i	−0.143795	+	0.0830203i
$292$	−6.95039	+	4.01281i	−0.406741	+	0.234832i
$293$	22.9743	+	13.2642i	1.34217	+	0.774902i	0.987126	−	0.159947i	$-0.0511323\pi$
$293$	22.9743	+	13.2642i	1.34217	+	0.774902i	0.355045	+	0.934849i	$0.384466\pi$
$294$	−6.94413	+	0.882613i	−0.404990	+	0.0514750i
$295$	−5.68322	+	9.84363i	−0.330890	+	0.573118i
$296$	6.87272			0.399469
$297$	−0.672474	−	0.388253i	−0.0390209	−	0.0225287i
$298$	−7.79784	−	13.5062i	−0.451717	−	0.782396i
$299$	7.06762	+	2.50732i	0.408731	+	0.145002i
$300$	3.98586			0.230124
$301$	−2.76387	+	13.7342i	−0.159307	+	0.791626i
$302$	−3.68968	−	6.39071i	−0.212317	−	0.367744i
$303$	5.80539	+	10.0552i	0.333511	+	0.577658i
$304$	2.56329	−	1.47992i	0.147015	−	0.0848791i
$305$			40.0934i			2.29574i
$306$	2.02707	−	1.17033i	0.115880	−	0.0669031i
$307$			26.2517i			1.49826i	0.662421	+	0.749132i	$0.269529\pi$
$307$			26.2517i			1.49826i	−0.662421	+	0.749132i	$0.730471\pi$
$308$	2.01406	+	0.405310i	0.114762	+	0.0230947i
$309$	3.66662	+	6.35077i	0.208587	+	0.361282i
$310$		−	21.8751i		−	1.24242i
$311$	−14.7394	−	25.5294i	−0.835795	−	1.44764i	−0.893381	−	0.449299i	$-0.851674\pi$
$311$	−14.7394	−	25.5294i	−0.835795	−	1.44764i	0.0575859	−	0.998341i	$-0.481660\pi$
$312$	2.34005	+	2.74302i	0.132479	+	0.155293i
$313$	8.66910	−	15.0153i	0.490007	−	0.848717i	−0.509927	−	0.860218i	$-0.670328\pi$
$313$	8.66910	−	15.0153i	0.490007	−	0.848717i	0.999934	+	0.0115010i	$0.00366097\pi$
$314$	21.3179	−	12.3079i	1.20304	−	0.694575i
$315$	2.53253	+	7.51580i	0.142692	+	0.423468i
$316$	1.49451	−	2.58856i	0.0840726	−	0.145618i
$317$	−2.71629	−	1.56825i	−0.152562	−	0.0880818i	0.421776	−	0.906700i	$-0.361407\pi$
$317$	−2.71629	−	1.56825i	−0.152562	−	0.0880818i	−0.574338	+	0.818618i	$0.694740\pi$
$318$		−	4.60797i		−	0.258402i
$319$		−	0.840382i		−	0.0470524i
$320$	2.59603	+	1.49882i	0.145123	+	0.0837866i
$321$	−5.45978	+	9.45661i	−0.304735	+	0.527817i
$322$	1.75719	+	5.21481i	0.0979242	+	0.290610i
$323$	5.99978	−	3.46398i	0.333837	−	0.192741i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	2.61087	+	14.1321i	0.144825	+	0.783906i
$326$	−5.60509	−	9.70830i	−0.310437	−	0.537693i
$327$			14.0243i			0.775548i
$328$	−5.66755	−	9.81648i	−0.312938	−	0.542025i
$329$	−22.0158	−	4.43045i	−1.21377	−	0.244258i
$330$		−	2.32769i		−	0.128135i
$331$	−3.32718	+	1.92095i	−0.182879	+	0.105585i	−0.588644	−	0.808392i	$-0.700338\pi$
$331$	−3.32718	+	1.92095i	−0.182879	+	0.105585i	0.405766	+	0.913977i	$0.367005\pi$
$332$			4.25324i			0.233427i
$333$	5.95195	−	3.43636i	0.326165	−	0.188311i
$334$	−6.26340	−	10.8485i	−0.342718	−	0.593605i
$335$	−8.01094	−	13.8754i	−0.437685	−	0.758092i
$336$	−0.521966	+	2.59375i	−0.0284756	+	0.141501i
$337$	10.0185			0.545742			0.272871	−	0.962051i	$-0.412027\pi$
$337$	10.0185			0.545742			0.272871	+	0.962051i	$0.412027\pi$
$338$	−8.19270	+	10.0935i	−0.445624	+	0.549016i
$339$	−5.08527	−	8.80794i	−0.276194	−	0.478382i
$340$	6.07642	+	3.50822i	0.329540	+	0.190260i
$341$	−5.66651			−0.306859
$342$	1.47992	−	2.56329i	0.0800248	−	0.138607i
$343$	10.3925	−	15.3296i	0.561140	−	0.827721i
$344$	4.58570	+	2.64755i	0.247244	+	0.142746i
$345$	5.39950	−	3.11740i	0.290699	−	0.167835i
$346$	−5.66435	+	3.27031i	−0.304517	+	0.175813i
$347$	−17.6846			−0.949359			−0.474679	−	0.880159i	$-0.657436\pi$
$347$	−17.6846			−0.949359			−0.474679	+	0.880159i	$0.657436\pi$
$348$	1.08226			0.0580153
$349$	−11.2927	+	6.51984i	−0.604484	+	0.348999i	−0.770803	−	0.637073i	$-0.780145\pi$
$349$	−11.2927	+	6.51984i	−0.604484	+	0.348999i	0.166320	+	0.986072i	$0.446812\pi$
$350$	−6.97092	+	7.91301i	−0.372611	+	0.422968i
$351$	3.39805	+	1.20550i	0.181375	+	0.0643448i
$352$	0.388253	−	0.672474i	0.0206939	−	0.0358430i
$353$	22.6882	+	13.0990i	1.20757	+	0.697191i	0.962228	−	0.272246i	$-0.0877663\pi$
$353$	22.6882	+	13.0990i	1.20757	+	0.697191i	0.245342	+	0.969437i	$0.421100\pi$
$354$	−1.89590	+	3.28379i	−0.100766	+	0.174532i
$355$	6.17442	+	10.6944i	0.327704	+	0.567600i
$356$		−	8.71065i		−	0.461663i
$357$	−1.22174	+	6.07108i	−0.0646614	+	0.321315i
$358$	−15.9772	−	9.22443i	−0.844420	−	0.487526i
$359$	0.978047	+	0.564675i	0.0516193	+	0.0298024i	0.525588	−	0.850740i	$-0.323846\pi$
$359$	0.978047	+	0.564675i	0.0516193	+	0.0298024i	−0.473968	+	0.880542i	$0.657179\pi$
$360$	2.99764			0.157990
$361$	−5.11969	+	8.86756i	−0.269457	+	0.466714i
$362$		−	14.7886i		−	0.777273i
$363$	10.3970			0.545703
$364$	−9.53819	−	0.151662i	−0.499937	−	0.00794925i
$365$	−24.0579			−1.25925
$366$			13.3750i			0.699122i
$367$	10.0213	−	17.3573i	0.523106	−	0.906046i	−0.476533	−	0.879157i	$-0.658107\pi$
$367$	10.0213	−	17.3573i	0.523106	−	0.906046i	0.999638	−	0.0268892i	$-0.00856012\pi$
$368$	2.07990			0.108422
$369$	−9.81648	−	5.66755i	−0.511026	−	0.295041i
$370$	17.8418	+	10.3010i	0.927552	+	0.535522i
$371$	9.14807	+	8.05893i	0.474944	+	0.418399i
$372$		−	7.29745i		−	0.378355i
$373$	0.536455	+	0.929168i	0.0277766	+	0.0481105i	0.879580	−	0.475752i	$-0.157824\pi$
$373$	0.536455	+	0.929168i	0.0277766	+	0.0481105i	−0.851803	+	0.523862i	$0.824491\pi$
$374$	0.908766	−	1.57403i	0.0469911	−	0.0813911i
$375$	−2.63275	−	1.52002i	−0.135954	−	0.0784933i
$376$	−4.24400	+	7.35082i	−0.218867	+	0.379090i
$377$	0.708918	+	3.83721i	0.0365111	+	0.197627i
$378$	0.844840	+	2.50724i	0.0434539	+	0.128958i
$379$	5.97673	−	3.45067i	0.307004	−	0.177249i	−0.338581	−	0.940937i	$-0.609947\pi$
$379$	5.97673	−	3.45067i	0.307004	−	0.177249i	0.645585	+	0.763688i	$0.276614\pi$
$380$	8.87253			0.455151
$381$	−2.14714			−0.110002
$382$	−5.65786	+	3.26657i	−0.289481	+	0.167132i
$383$	27.3214	−	15.7740i	1.39606	−	0.806014i	0.402080	−	0.915605i	$-0.368287\pi$
$383$	27.3214	−	15.7740i	1.39606	−	0.806014i	0.993977	+	0.109591i	$0.0349540\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$	4.62109	+	4.07092i	0.235513	+	0.207473i
$386$	−2.68559	+	4.65158i	−0.136693	+	0.236759i
$387$	5.29511			0.269165
$388$	−2.45297	−	1.41622i	−0.124530	−	0.0718977i
$389$	−0.542096	−	0.938937i	−0.0274853	−	0.0476060i	0.851956	−	0.523614i	$-0.175417\pi$
$389$	−0.542096	−	0.938937i	−0.0274853	−	0.0476060i	−0.879441	+	0.476008i	$0.842083\pi$
$390$	1.96356	+	10.6283i	0.0994286	+	0.538185i
$391$	4.86833			0.246202
$392$	−4.23643	−	5.57249i	−0.213972	−	0.281453i
$393$	−9.39683	−	16.2758i	−0.474007	−	0.821005i
$394$	9.47999	+	16.4198i	0.477595	+	0.827219i
$395$	7.75959	−	4.48000i	0.390427	−	0.225413i
$396$		−	0.776506i		−	0.0390209i
$397$	16.5984	−	9.58307i	0.833048	−	0.480960i	−0.0218471	−	0.999761i	$-0.506955\pi$
$397$	16.5984	−	9.58307i	0.833048	−	0.480960i	0.854895	+	0.518801i	$0.173621\pi$
$398$		−	8.21048i		−	0.411554i
$399$	2.50059	+	7.42101i	0.125186	+	0.371515i
$400$	1.99293	+	3.45185i	0.0996465	+	0.172593i
$401$			30.0378i			1.50002i	0.661427	+	0.750009i	$0.269951\pi$
$401$			30.0378i			1.50002i	−0.661427	+	0.750009i	$0.730049\pi$
$402$	−2.67241	−	4.62876i	−0.133288	−	0.230861i
$403$	25.8735	−	4.78007i	1.28885	−	0.238112i
$404$	−5.80539	+	10.0552i	−0.288829	+	0.500266i
$405$	2.59603	−	1.49882i	0.128998	−	0.0744770i
$406$	−1.89278	+	2.14858i	−0.0939371	+	0.106632i
$407$	2.66835	−	4.62172i	0.132265	−	0.229090i
$408$	2.02707	+	1.17033i	0.100355	+	0.0579398i
$409$			3.88182i			0.191944i	0.995384	+	0.0959719i	$0.0305959\pi$
$409$			3.88182i			0.191944i	−0.995384	+	0.0959719i	$0.969404\pi$
$410$		−	33.9786i		−	1.67808i
$411$	15.6998	+	9.06426i	0.774412	+	0.447107i
$412$	−3.66662	+	6.35077i	−0.180641	+	0.312880i
$413$	−3.20346	−	9.50694i	−0.157632	−	0.467806i
$414$	1.80125	−	1.03995i	0.0885266	−	0.0511108i
$415$	−6.37485	+	11.0416i	−0.312929	+	0.542009i
$416$	−1.20550	+	3.39805i	−0.0591045	+	0.166603i
$417$	−10.2597	−	17.7702i	−0.502418	−	0.870213i
$418$		−	2.29833i		−	0.112415i
$419$	−17.1309	−	29.6717i	−0.836901	−	1.44956i	−0.892473	−	0.451101i	$-0.851032\pi$
$419$	−17.1309	−	29.6717i	−0.836901	−	1.44956i	0.0555720	−	0.998455i	$-0.482302\pi$
$420$	−5.24261	+	5.95114i	−0.255813	+	0.290386i
$421$		−	3.77781i		−	0.184119i	−0.995754	−	0.0920595i	$-0.970655\pi$
$421$		−	3.77781i		−	0.184119i	0.995754	−	0.0920595i	$-0.0293450\pi$
$422$	9.33746	−	5.39098i	0.454540	−	0.262429i
$423$			8.48799i			0.412700i
$424$	3.99062	−	2.30398i	0.193801	−	0.111891i
$425$	4.66476	+	8.07960i	0.226274	+	0.391918i
$426$	2.05976	+	3.56761i	0.0997956	+	0.172851i
$427$	−26.5530	−	23.3917i	−1.28499	−	1.13200i
$428$	−10.9196			−0.527817
$429$	2.75314	−	0.508637i	0.132923	−	0.0245572i
$430$	7.93642	+	13.7463i	0.382728	+	0.662904i
$431$	11.1510	+	6.43806i	0.537127	+	0.310110i	0.743914	−	0.668276i	$-0.232967\pi$
$431$	11.1510	+	6.43806i	0.537127	+	0.310110i	−0.206787	+	0.978386i	$0.566301\pi$
$432$	1.00000			0.0481125
$433$	−2.54694	+	4.41144i	−0.122398	+	0.212000i	−0.920713	−	0.390240i	$-0.872392\pi$
$433$	−2.54694	+	4.41144i	−0.122398	+	0.212000i	0.798315	+	0.602241i	$0.205725\pi$
$434$	14.4874	+	12.7626i	0.695418	+	0.612624i
$435$	2.80959	+	1.62212i	0.134709	+	0.0777745i
$436$	−12.1454	+	7.01217i	−0.581661	+	0.335822i
$437$	5.33140	−	3.07809i	0.255036	−	0.147245i
$438$	−8.02562			−0.383479
$439$	−33.0107			−1.57552			−0.787758	−	0.615984i	$-0.788758\pi$
$439$	−33.0107			−1.57552			−0.787758	+	0.615984i	$0.788758\pi$
$440$	2.01584	−	1.16384i	0.0961012	−	0.0554840i
$441$	−6.45510	−	2.70770i	−0.307386	−	0.128938i
$442$	−2.82166	+	7.95367i	−0.134213	+	0.378317i
$443$	−9.19529	+	15.9267i	−0.436881	+	0.756700i	−0.997447	−	0.0714094i	$-0.977250\pi$
$443$	−9.19529	+	15.9267i	−0.436881	+	0.756700i	0.560566	+	0.828110i	$0.310584\pi$
$444$	5.95195	+	3.43636i	0.282467	+	0.163082i
$445$	13.0557	−	22.6131i	0.618900	−	1.07197i
$446$	0.841020	+	1.45669i	0.0398235	+	0.0689762i
$447$		−	15.5957i		−	0.737650i
$448$	−2.50724	+	0.844840i	−0.118456	+	0.0399150i
$449$	4.04307	+	2.33427i	0.190804	+	0.110161i	0.592359	−	0.805674i	$-0.298197\pi$
$449$	4.04307	+	2.33427i	0.190804	+	0.110161i	−0.401555	+	0.915835i	$0.631530\pi$
$450$	3.45185	+	1.99293i	0.162722	+	0.0939476i
$451$	−8.80177			−0.414459
$452$	5.08527	−	8.80794i	0.239191	−	0.414291i
$453$		−	7.37936i		−	0.346713i
$454$	−6.35545			−0.298276
$455$	−24.5341	−	14.6898i	−1.15018	−	0.688666i
$456$	2.95984			0.138607
$457$		−	27.1473i		−	1.26990i	−0.772555	−	0.634948i	$-0.781022\pi$
$457$		−	27.1473i		−	1.26990i	0.772555	−	0.634948i	$-0.218978\pi$
$458$	−8.89576	+	15.4079i	−0.415672	+	0.719964i
$459$	2.34065			0.109252
$460$	5.39950	+	3.11740i	0.251753	+	0.145350i
$461$	−16.7635	−	9.67843i	−0.780756	−	0.450769i	0.0559424	−	0.998434i	$-0.482184\pi$
$461$	−16.7635	−	9.67843i	−0.780756	−	0.450769i	−0.836698	+	0.547665i	$0.815517\pi$
$462$	1.54158	+	1.35804i	0.0717206	+	0.0631817i
$463$		−	10.1358i		−	0.471050i	−0.971868	−	0.235525i	$-0.924319\pi$
$463$		−	10.1358i		−	0.471050i	0.971868	−	0.235525i	$-0.0756810\pi$
$464$	0.541131	+	0.937266i	0.0251214	+	0.0435115i
$465$	10.9376	−	18.9444i	0.507218	−	0.878527i
$466$	−10.1157	−	5.84028i	−0.468599	−	0.270546i
$467$	20.3375	−	35.2256i	0.941106	−	1.63004i	0.177741	−	0.984077i	$-0.443121\pi$
$467$	20.3375	−	35.2256i	0.941106	−	1.63004i	0.763365	−	0.645967i	$-0.223546\pi$
$468$	0.655034	+	3.54555i	0.0302789	+	0.163893i
$469$	13.8632	+	2.78982i	0.640141	+	0.128822i
$470$	−22.0351	+	12.7220i	−1.01640	+	0.586821i
$471$	24.6158			1.13424
$472$	−3.79180			−0.174532
$473$	3.56082	−	2.05584i	0.163727	−	0.0945276i
$474$	2.58856	−	1.49451i	0.118897	−	0.0686450i
$475$	10.2169	+	5.89874i	0.468785	+	0.270653i
$476$	−5.86858	+	1.97748i	−0.268986	+	0.0906376i
$477$	2.30398	−	3.99062i	0.105492	−	0.182718i
$478$	−8.17752			−0.374031
$479$	−16.5122	−	9.53330i	−0.754460	−	0.435588i	0.0728431	−	0.997343i	$-0.476793\pi$
$479$	−16.5122	−	9.53330i	−0.754460	−	0.435588i	−0.827303	+	0.561756i	$0.810126\pi$
$480$	1.49882	+	2.59603i	0.0684115	+	0.118492i
$481$	−8.28506	+	23.3539i	−0.377766	+	1.06485i
$482$	−28.9685			−1.31948
$483$	−1.08564	+	5.39475i	−0.0493983	+	0.245470i
$484$	5.19852	+	9.00410i	0.236296	+	0.409277i
$485$	−4.24532	−	7.35311i	−0.192770	−	0.333888i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$		−	30.1508i		−	1.36626i	−0.730295	−	0.683132i	$-0.760617\pi$
$487$		−	30.1508i		−	1.36626i	0.730295	−	0.683132i	$-0.239383\pi$
$488$	−11.5831	+	6.68750i	−0.524342	+	0.302729i
$489$		−	11.2102i		−	0.506942i
$490$	−2.64576	−	20.8160i	−0.119523	−	0.940372i
$491$	−2.97304	−	5.14945i	−0.134171	−	0.232391i	0.791109	−	0.611675i	$-0.209504\pi$
$491$	−2.97304	−	5.14945i	−0.134171	−	0.232391i	−0.925281	+	0.379283i	$0.876171\pi$
$492$		−	11.3351i		−	0.511026i
$493$	1.26660	+	2.19382i	0.0570448	+	0.0988045i
$494$	1.93879	+	10.4942i	0.0872304	+	0.472159i
$495$	1.16384	−	2.01584i	0.0523109	−	0.0906051i
$496$	6.31977	−	3.64872i	0.283766	−	0.163833i
$497$	−10.6850	−	2.15025i	−0.479288	−	0.0964518i
$498$	−2.12662	+	3.68342i	−0.0952962	+	0.165058i
$499$	−1.61575	−	0.932853i	−0.0723309	−	0.0417602i	0.463398	−	0.886150i	$-0.346630\pi$
$499$	−1.61575	−	0.932853i	−0.0723309	−	0.0417602i	−0.535729	+	0.844390i	$0.679963\pi$
$500$		−	3.04003i		−	0.135954i
$501$		−	12.5268i		−	0.559656i
$502$	5.38817	+	3.11086i	0.240486	+	0.138845i
$503$	−6.29031	+	10.8951i	−0.280471	+	0.485790i	−0.971501	−	0.237036i	$-0.923824\pi$
$503$	−6.29031	+	10.8951i	−0.280471	+	0.485790i	0.691030	+	0.722826i	$0.257157\pi$
$504$	−1.74891	+	1.98527i	−0.0779027	+	0.0884311i
$505$	−30.1420	+	17.4025i	−1.34130	+	0.774400i
$506$	0.807528	−	1.39868i	0.0358990	−	0.0621789i
$507$	−12.1419	+	4.64491i	−0.539239	+	0.206288i
$508$	−1.07357	−	1.85948i	−0.0476321	−	0.0825011i
$509$		−	0.643271i		−	0.0285125i	−0.999898	−	0.0142562i	$-0.995462\pi$
$509$		−	0.643271i		−	0.0285125i	0.999898	−	0.0142562i	$-0.00453806\pi$
$510$	3.50822	+	6.07642i	0.155347	+	0.269068i
$511$	14.0361	−	15.9330i	0.620921	−	0.704836i
$512$			1.00000i			0.0441942i
$513$	2.56329	−	1.47992i	0.113172	−	0.0653400i
$514$			9.62683i			0.424621i
$515$	−19.0373	+	10.9912i	−0.838885	+	0.484330i
$516$	2.64755	+	4.58570i	0.116552	+	0.201874i
$517$	3.29549	+	5.70795i	0.144935	+	0.251035i
$518$	−17.2316	+	5.80635i	−0.757111	+	0.255116i
$519$	−6.54063			−0.287102
$520$	−8.22259	+	7.01464i	−0.360585	+	0.307612i
$521$	15.8436	+	27.4419i	0.694119	+	1.20225i	0.970477	+	0.241195i	$0.0775393\pi$
$521$	15.8436	+	27.4419i	0.694119	+	1.20225i	−0.276358	+	0.961055i	$0.589127\pi$
$522$	0.937266	+	0.541131i	0.0410230	+	0.0236846i
$523$	−44.1421			−1.93020			−0.965099	−	0.261886i	$-0.915656\pi$
$523$	−44.1421			−1.93020			−0.965099	+	0.261886i	$0.915656\pi$
$524$	9.39683	−	16.2758i	0.410502	−	0.711011i
$525$	−9.99350	+	3.36741i	−0.436152	+	0.146966i
$526$	−2.57210	−	1.48500i	−0.112149	−	0.0647492i
$527$	14.7924	−	8.54040i	0.644367	−	0.372026i
$528$	0.672474	−	0.388253i	0.0292657	−	0.0168965i
$529$	−18.6740			−0.811913
$530$	13.8130			0.600000
$531$	−3.28379	+	1.89590i	−0.142504	+	0.0822750i
$532$	−5.17649	+	5.87608i	−0.224429	+	0.254760i
$533$	40.1892	−	7.42487i	1.74079	−	0.321607i
$534$	4.35532	−	7.54364i	0.188473	−	0.326445i
$535$	−28.3475	−	16.3665i	−1.22557	−	0.707584i
$536$	2.67241	−	4.62876i	0.115431	−	0.199932i
$537$	−9.22443	−	15.9772i	−0.398064	−	0.689466i
$538$			21.6142i			0.931854i
$539$	−5.39216	+	0.685354i	−0.232257	+	0.0295203i
$540$	2.59603	+	1.49882i	0.111716	+	0.0644990i
$541$	−36.3256	−	20.9726i	−1.56176	−	0.901682i	−0.997079	−	0.0763720i	$-0.975666\pi$
$541$	−36.3256	−	20.9726i	−1.56176	−	0.901682i	−0.564680	−	0.825310i	$-0.691000\pi$
$542$	−1.29946			−0.0558168
$543$	7.39432	−	12.8073i	0.317321	−	0.549615i
$544$			2.34065i			0.100355i
$545$	−42.0400			−1.80079
$546$	−8.18448	−	4.90044i	−0.350263	−	0.209719i
$547$	18.9477			0.810144			0.405072	−	0.914285i	$-0.367246\pi$
$547$	18.9477			0.810144			0.405072	+	0.914285i	$0.367246\pi$
$548$			18.1285i			0.774412i
$549$	−6.68750	+	11.5831i	−0.285415	+	0.494354i
$550$	3.09504			0.131973
$551$	2.77415	+	1.60166i	0.118183	+	0.0682329i
$552$	1.80125	+	1.03995i	0.0766663	+	0.0442633i
$553$	−1.56016	+	7.75277i	−0.0663450	+	0.329681i
$554$		−	22.3327i		−	0.948826i
$555$	10.3010	+	17.8418i	0.437252	+	0.757343i
$556$	10.2597	−	17.7702i	0.435106	−	0.753626i
$557$	15.6419	+	9.03085i	0.662768	+	0.382649i	0.793331	−	0.608791i	$-0.208345\pi$
$557$	15.6419	+	9.03085i	0.662768	+	0.382649i	−0.130563	+	0.991440i	$0.541678\pi$
$558$	3.64872	−	6.31977i	0.154463	−	0.267537i
$559$	−14.5246	+	12.3908i	−0.614324	+	0.524076i
$560$	−7.77514	−	1.56467i	−0.328560	−	0.0661193i
$561$	1.57403	−	0.908766i	0.0664555	−	0.0383681i
$562$	29.1881			1.23122
$563$	−19.5915			−0.825684			−0.412842	−	0.910803i	$-0.635464\pi$
$563$	−19.5915			−0.825684			−0.412842	+	0.910803i	$0.635464\pi$
$564$	−7.35082	+	4.24400i	−0.309525	+	0.178705i
$565$	26.4031	−	15.2438i	1.11079	−	0.641312i
$566$	−27.0700	−	15.6289i	−1.13784	−	0.656930i
$567$	−0.521966	+	2.59375i	−0.0219205	+	0.108927i
$568$	−2.05976	+	3.56761i	−0.0864256	+	0.149693i
$569$	36.7242			1.53956			0.769778	−	0.638311i	$-0.220367\pi$
$569$	36.7242			1.53956			0.769778	+	0.638311i	$0.220367\pi$
$570$	7.68383	+	4.43626i	0.321840	+	0.185815i
$571$	4.17869	+	7.23770i	0.174873	+	0.302888i	0.940117	−	0.340851i	$-0.110715\pi$
$571$	4.17869	+	7.23770i	0.174873	+	0.302888i	−0.765245	+	0.643740i	$0.777382\pi$
$572$	1.81706	+	2.12997i	0.0759752	+	0.0890586i
$573$	−6.53314			−0.272926
$574$	22.5033	+	19.8241i	0.939268	+	0.827441i
$575$	4.14510	+	7.17952i	0.172863	+	0.299407i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	2.78965	−	1.61060i	0.116135	−	0.0670503i	−0.440808	−	0.897602i	$-0.645308\pi$
$577$	2.78965	−	1.61060i	0.116135	−	0.0670503i	0.556942	+	0.830551i	$0.311975\pi$
$578$		−	11.5213i		−	0.479225i
$579$	−4.65158	+	2.68559i	−0.193313	+	0.111609i
$580$			3.24423i			0.134709i
$581$	−3.59331	−	10.6639i	−0.149076	−	0.442413i
$582$	−1.41622	−	2.45297i	−0.0587042	−	0.101679i
$583$		−	3.57811i		−	0.148190i
$584$	−4.01281	−	6.95039i	−0.166051	−	0.287609i
$585$	−3.61366	+	10.1861i	−0.149406	+	0.421145i
$586$	−13.2642	+	22.9743i	−0.547939	+	0.949058i
$587$	13.5902	−	7.84629i	0.560927	−	0.323851i	−0.192591	−	0.981279i	$-0.561689\pi$
$587$	13.5902	−	7.84629i	0.560927	−	0.323851i	0.753517	+	0.657428i	$0.228356\pi$
$588$	−0.882613	−	6.94413i	−0.0363983	−	0.286371i
$589$	10.7996	−	18.7055i	0.444991	−	0.770746i
$590$	−9.84363	−	5.68322i	−0.405256	−	0.233975i
$591$			18.9600i			0.779909i
$592$			6.87272i			0.282467i
$593$	17.1904	+	9.92487i	0.705924	+	0.407565i	0.809550	−	0.587051i	$-0.199711\pi$
$593$	17.1904	+	9.92487i	0.705924	+	0.407565i	−0.103626	+	0.994616i	$0.533045\pi$
$594$	0.388253	−	0.672474i	0.0159302	−	0.0275919i
$595$	−18.1989	−	3.66235i	−0.746083	−	0.150142i
$596$	13.5062	−	7.79784i	0.553238	−	0.319412i
$597$	4.10524	−	7.11048i	0.168016	−	0.291013i
$598$	−2.50732	+	7.06762i	−0.102532	+	0.289017i
$599$	13.2573	+	22.9622i	0.541677	+	0.938212i	0.998808	+	0.0488126i	$0.0155437\pi$
$599$	13.2573	+	22.9622i	0.541677	+	0.938212i	−0.457131	+	0.889399i	$0.651123\pi$
$600$			3.98586i			0.162722i
$601$	5.15314	+	8.92551i	0.210201	+	0.364079i	0.951777	−	0.306790i	$-0.0992548\pi$
$601$	5.15314	+	8.92551i	0.210201	+	0.364079i	−0.741576	+	0.670869i	$0.765921\pi$
$602$	−13.7342	−	2.76387i	−0.559764	−	0.112647i
$603$		−	5.34483i		−	0.217658i
$604$	6.39071	−	3.68968i	0.260034	−	0.150131i
$605$			31.1666i			1.26710i
$606$	−10.0552	+	5.80539i	−0.408466	+	0.235828i
$607$	14.0311	+	24.3025i	0.569503	+	0.986408i	0.996615	+	0.0822091i	$0.0261976\pi$
$607$	14.0311	+	24.3025i	0.569503	+	0.986408i	−0.427112	+	0.904199i	$0.640469\pi$
$608$	1.47992	+	2.56329i	0.0600186	+	0.103955i
$609$	−2.71349	+	0.914338i	−0.109956	+	0.0370508i
$610$	−40.0934			−1.62334
$611$	−19.8623	−	23.2827i	−0.803544	−	0.941919i
$612$	1.17033	+	2.02707i	0.0473077	+	0.0819393i
$613$	−26.0243	−	15.0251i	−1.05111	−	0.606859i	−0.128150	−	0.991755i	$-0.540904\pi$
$613$	−26.0243	−	15.0251i	−1.05111	−	0.606859i	−0.922960	+	0.384896i	$0.874237\pi$
$614$	−26.2517			−1.05943
$615$	16.9893	−	29.4263i	0.685074	−	1.18658i
$616$	−0.405310	+	2.01406i	−0.0163304	+	0.0811489i
$617$	−12.2578	−	7.07702i	−0.493479	−	0.284910i	0.232538	−	0.972587i	$-0.425297\pi$
$617$	−12.2578	−	7.07702i	−0.493479	−	0.284910i	−0.726016	+	0.687677i	$0.758630\pi$
$618$	−6.35077	+	3.66662i	−0.255465	+	0.147493i
$619$	−15.5989	+	9.00602i	−0.626972	+	0.361982i	−0.779578	−	0.626305i	$-0.784567\pi$
$619$	−15.5989	+	9.00602i	−0.626972	+	0.361982i	0.152606	+	0.988287i	$0.451233\pi$
$620$	21.8751			0.878527
$621$	2.07990			0.0834637
$622$	25.5294	−	14.7394i	1.02364	−	0.590997i
$623$	7.35911	+	21.8397i	0.294836	+	0.874988i
$624$	−2.74302	+	2.34005i	−0.109809	+	0.0936770i
$625$	14.5211	−	25.1513i	0.580844	−	1.00605i
$626$	15.0153	+	8.66910i	0.600133	+	0.346487i
$627$	1.14916	−	1.99041i	0.0458932	−	0.0794894i
$628$	12.3079	+	21.3179i	0.491139	+	0.850678i
$629$			16.0867i			0.641417i
$630$	−7.51580	+	2.53253i	−0.299437	+	0.100898i
$631$	−2.35305	−	1.35853i	−0.0936734	−	0.0540824i	0.452432	−	0.891799i	$-0.350557\pi$
$631$	−2.35305	−	1.35853i	−0.0936734	−	0.0540824i	−0.546105	+	0.837717i	$0.683890\pi$
$632$	2.58856	+	1.49451i	0.102968	+	0.0594483i
$633$	10.7820			0.428545
$634$	1.56825	−	2.71629i	0.0622832	−	0.107878i
$635$		−	6.43637i		−	0.255420i
$636$	4.60797			0.182718
$637$	24.0426	−	7.67799i	0.952604	−	0.304213i
$638$	0.840382			0.0332710
$639$			4.11952i			0.162966i
$640$	−1.49882	+	2.59603i	−0.0592461	+	0.102617i
$641$	−5.87261			−0.231954			−0.115977	−	0.993252i	$-0.537000\pi$
$641$	−5.87261			−0.231954			−0.115977	+	0.993252i	$0.537000\pi$
$642$	−9.45661	−	5.45978i	−0.373223	−	0.215480i
$643$	−35.4134	−	20.4459i	−1.39657	−	0.806309i	−0.402536	−	0.915404i	$-0.631871\pi$
$643$	−35.4134	−	20.4459i	−1.39657	−	0.806309i	−0.994031	+	0.109095i	$0.965205\pi$
$644$	−5.21481	+	1.75719i	−0.205492	+	0.0692428i
$645$			15.8728i			0.624992i
$646$	3.46398	+	5.99978i	0.136288	+	0.236058i
$647$	−8.84916	+	15.3272i	−0.347896	+	0.602574i	−0.985876	−	0.167480i	$-0.946437\pi$
$647$	−8.84916	+	15.3272i	−0.347896	+	0.602574i	0.637979	+	0.770053i	$0.279771\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−1.47218	+	2.54988i	−0.0577879	+	0.100092i
$650$	−14.1321	+	2.61087i	−0.554305	+	0.102407i
$651$	6.16518	+	18.2964i	0.241632	+	0.717094i
$652$	9.70830	−	5.60509i	0.380207	−	0.219512i
$653$	−17.9089			−0.700830			−0.350415	−	0.936594i	$-0.613960\pi$
$653$	−17.9089			−0.700830			−0.350415	+	0.936594i	$0.613960\pi$
$654$	−14.0243			−0.548395
$655$	48.7890	−	28.1683i	1.90634	−	1.10063i
$656$	9.81648	−	5.66755i	0.383269	−	0.221281i
$657$	−6.95039	−	4.01281i	−0.271161	−	0.156555i
$658$	4.43045	−	22.0158i	0.172717	−	0.858264i
$659$	−5.65972	+	9.80293i	−0.220471	+	0.381868i	−0.954951	−	0.296763i	$-0.904093\pi$
$659$	−5.65972	+	9.80293i	−0.220471	+	0.381868i	0.734480	+	0.678631i	$0.237426\pi$
$660$	2.32769			0.0906051
$661$	−31.8495	−	18.3883i	−1.23880	−	0.715222i	−0.269952	−	0.962874i	$-0.587008\pi$
$661$	−31.8495	−	18.3883i	−1.23880	−	0.715222i	−0.968849	+	0.247651i	$0.920341\pi$
$662$	−1.92095	−	3.32718i	−0.0746599	−	0.129315i
$663$	−6.42046	+	5.47725i	−0.249350	+	0.212719i
$664$	−4.25324			−0.165058
$665$	−22.2455	+	7.49587i	−0.862645	+	0.290677i
$666$	3.43636	+	5.95195i	0.133156	+	0.230633i
$667$	1.12550	+	1.94942i	0.0435795	+	0.0754819i
$668$	10.8485	−	6.26340i	0.419742	−	0.242338i
$669$			1.68204i			0.0650314i
$670$	13.8754	−	8.01094i	0.536052	−	0.309490i
$671$			10.3858i			0.400938i
$672$	−2.59375	−	0.521966i	−0.100056	−	0.0201353i
$673$	13.5737	+	23.5103i	0.523226	+	0.906255i	0.999635	+	0.0270305i	$0.00860512\pi$
$673$	13.5737	+	23.5103i	0.523226	+	0.906255i	−0.476408	+	0.879224i	$0.658062\pi$
$674$			10.0185i			0.385898i
$675$	1.99293	+	3.45185i	0.0767079	+	0.132862i
$676$	−10.0935	−	8.19270i	−0.388213	−	0.315104i
$677$	−0.817780	+	1.41644i	−0.0314298	+	0.0544381i	−0.881312	−	0.472534i	$-0.843339\pi$
$677$	−0.817780	+	1.41644i	−0.0314298	+	0.0544381i	0.849883	+	0.526972i	$0.176673\pi$
$678$	8.80794	−	5.08527i	0.338267	−	0.195299i
$679$	7.34665	+	1.47844i	0.281939	+	0.0567372i
$680$	−3.50822	+	6.07642i	−0.134534	+	0.233020i
$681$	−5.50398	−	3.17772i	−0.210913	−	0.121771i
$682$		−	5.66651i		−	0.216982i
$683$			8.75164i			0.334872i	0.985883	+	0.167436i	$0.0535488\pi$
$683$			8.75164i			0.334872i	−0.985883	+	0.167436i	$0.946451\pi$
$684$	2.56329	+	1.47992i	0.0980100	+	0.0565861i
$685$	−27.1714	+	47.0623i	−1.03817	+	1.79816i
$686$	15.3296	+	10.3925i	0.585287	+	0.396786i
$687$	−15.4079	+	8.89576i	−0.587848	+	0.339394i
$688$	−2.64755	+	4.58570i	−0.100937	+	0.174828i
$689$	3.01837	+	16.3378i	0.114991	+	0.622420i
$690$	3.11740	+	5.39950i	0.118678	+	0.205555i
$691$		−	40.9418i		−	1.55750i	−0.627335	−	0.778750i	$-0.715854\pi$
$691$		−	40.9418i		−	1.55750i	0.627335	−	0.778750i	$-0.284146\pi$
$692$	−3.27031	−	5.66435i	−0.124319	−	0.215326i
$693$	0.656023	+	1.94688i	0.0249203	+	0.0739560i
$694$		−	17.6846i		−	0.671298i
$695$	53.2688	−	30.7548i	2.02060	−	1.16660i
$696$			1.08226i			0.0410230i
$697$	22.9770	−	13.2658i	0.870315	−	0.502477i
$698$	−6.51984	−	11.2927i	−0.246779	−	0.427435i
$699$	−5.84028	−	10.1157i	−0.220900	−	0.382609i
$700$	−7.91301	−	6.97092i	−0.299084	−	0.263476i
$701$	38.9126			1.46971			0.734854	−	0.678225i	$-0.237251\pi$
$701$	38.9126			1.46971			0.734854	+	0.678225i	$0.237251\pi$
$702$	−1.20550	+	3.39805i	−0.0454986	+	0.128251i
$703$	10.1711	+	17.6168i	0.383609	+	0.664430i
$704$	0.672474	+	0.388253i	0.0253448	+	0.0146328i
$705$	−25.4440			−0.958275
$706$	−13.0990	+	22.6882i	−0.492988	+	0.853881i
$707$	6.06043	−	30.1155i	0.227926	−	1.13261i
$708$	−3.28379	−	1.89590i	−0.123412	−	0.0712522i
$709$	−5.47894	+	3.16327i	−0.205766	+	0.118799i	−0.599342	−	0.800493i	$-0.704571\pi$
$709$	−5.47894	+	3.16327i	−0.205766	+	0.118799i	0.393576	+	0.919292i	$0.371238\pi$
$710$	−10.6944	+	6.17442i	−0.401354	+	0.231722i
$711$	2.98902			0.112097
$712$	8.71065			0.326445
$713$	13.1445	−	7.58899i	0.492266	−	0.284210i
$714$	−6.07108	−	1.22174i	−0.227204	−	0.0457225i
$715$	1.52471	+	8.25293i	0.0570210	+	0.308642i
$716$	9.22443	−	15.9772i	0.344733	−	0.597095i
$717$	−7.08194	−	4.08876i	−0.264480	−	0.152698i
$718$	−0.564675	+	0.978047i	−0.0210735	+	0.0365004i
$719$	−1.16120	−	2.01125i	−0.0433053	−	0.0750070i	0.843560	−	0.537034i	$-0.180455\pi$
$719$	−1.16120	−	2.01125i	−0.0433053	−	0.0750070i	−0.886866	+	0.462027i	$0.847122\pi$
$720$			2.99764i			0.111716i
$721$	3.82770	−	19.0206i	0.142551	−	0.708364i
$722$	−8.86756	−	5.11969i	−0.330016	−	0.190535i
$723$	−25.0874	−	14.4842i	−0.933012	−	0.538675i
$724$	14.7886			0.549615
$725$	−2.15687	+	3.73581i	−0.0801042	+	0.138744i
$726$			10.3970i			0.385870i
$727$	−2.78916			−0.103444			−0.0517221	−	0.998662i	$-0.516471\pi$
$727$	−2.78916			−0.103444			−0.0517221	+	0.998662i	$0.516471\pi$
$728$	0.151662	−	9.53819i	0.00562097	−	0.353509i
$729$	1.00000			0.0370370
$730$		−	24.0579i		−	0.890424i
$731$	−6.19701	+	10.7335i	−0.229205	+	0.396994i
$732$	−13.3750			−0.494354
$733$	37.7543	+	21.7974i	1.39449	+	0.805107i	0.993808	−	0.111112i	$-0.0354412\pi$
$733$	37.7543	+	21.7974i	1.39449	+	0.805107i	0.400678	+	0.916219i	$0.368775\pi$
$734$	17.3573	+	10.0213i	0.640671	+	0.369892i
$735$	8.11672	−	19.3501i	0.299390	−	0.713739i
$736$			2.07990i			0.0766663i
$737$	−2.07514	−	3.59426i	−0.0764389	−	0.132396i
$738$	5.66755	−	9.81648i	0.208625	−	0.361350i
$739$	35.2407	+	20.3462i	1.29635	+	0.748447i	0.979772	−	0.200119i	$-0.0641330\pi$
$739$	35.2407	+	20.3462i	1.29635	+	0.748447i	0.316577	+	0.948567i	$0.397466\pi$
$740$	−10.3010	+	17.8418i	−0.378672	+	0.655878i
$741$	−3.56808	+	10.0577i	−0.131077	+	0.369478i
$742$	−8.05893	+	9.14807i	−0.295853	+	0.335836i
$743$	−28.1965	+	16.2793i	−1.03443	+	0.597229i	−0.918251	−	0.395999i	$-0.870398\pi$
$743$	−28.1965	+	16.2793i	−1.03443	+	0.597229i	−0.116180	+	0.993228i	$0.537065\pi$
$744$	7.29745			0.267537
$745$	46.7502			1.71280
$746$	−0.929168	+	0.536455i	−0.0340193	+	0.0196410i
$747$	−3.68342	+	2.12662i	−0.134769	+	0.0778090i
$748$	1.57403	+	0.908766i	0.0575522	+	0.0332278i
$749$	27.3779	−	9.22528i	1.00037	−	0.337084i
$750$	1.52002	−	2.63275i	0.0555032	−	0.0961343i
$751$	−35.9011			−1.31005			−0.655025	−	0.755607i	$-0.727342\pi$
$751$	−35.9011			−1.31005			−0.655025	+	0.755607i	$0.727342\pi$
$752$	−7.35082	−	4.24400i	−0.268057	−	0.154763i
$753$	3.11086	+	5.38817i	0.113366	+	0.196356i
$754$	−3.83721	+	0.708918i	−0.139743	+	0.0258173i
$755$	22.1207			0.805054
$756$	−2.50724	+	0.844840i	−0.0911874	+	0.0307265i
$757$	17.2024	+	29.7955i	0.625233	+	1.08294i	0.988496	+	0.151249i	$0.0483296\pi$
$757$	17.2024	+	29.7955i	0.625233	+	1.08294i	−0.363262	+	0.931687i	$0.618337\pi$
$758$	3.45067	+	5.97673i	0.125334	+	0.217085i
$759$	1.39868	−	0.807528i	0.0507689	−	0.0293114i
$760$			8.87253i			0.321840i
$761$	9.71802	−	5.61070i	0.352278	−	0.203388i	−0.313410	−	0.949618i	$-0.601471\pi$
$761$	9.71802	−	5.61070i	0.352278	−	0.203388i	0.665688	+	0.746230i	$0.268138\pi$
$762$		−	2.14714i		−	0.0777828i
$763$	24.5274	−	27.8422i	0.887950	−	1.00795i
$764$	−3.26657	−	5.65786i	−0.118180	−	0.204694i
$765$			7.01644i			0.253680i
$766$	15.7740	+	27.3214i	0.569938	+	0.987161i
$767$	4.57101	−	12.8847i	0.165050	−	0.465241i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	15.5692	−	8.98887i	0.561439	−	0.324147i	−0.192284	−	0.981339i	$-0.561589\pi$
$769$	15.5692	−	8.98887i	0.561439	−	0.324147i	0.753723	+	0.657192i	$0.228256\pi$
$770$	−4.07092	+	4.62109i	−0.146706	+	0.166533i
$771$	−4.81342	+	8.33708i	−0.173351	+	0.300253i
$772$	−4.65158	−	2.68559i	−0.167414	−	0.0966565i
$773$			20.6496i			0.742715i	0.928490	+	0.371358i	$0.121108\pi$
$773$			20.6496i			0.742715i	−0.928490	+	0.371358i	$0.878892\pi$
$774$			5.29511i			0.190329i
$775$	25.1897	+	14.5433i	0.904842	+	0.522411i
$776$	1.41622	−	2.45297i	0.0508393	−	0.0880563i
$777$	−17.8261	−	3.58733i	−0.639509	−	0.128695i
$778$	0.938937	−	0.542096i	0.0336625	−	0.0194351i
$779$	16.7750	−	29.0552i	0.601027	−	1.04101i
$780$	−10.6283	+	1.96356i	−0.380554	+	0.0703066i
$781$	1.59941	+	2.77027i	0.0572315	+	0.0991279i
$782$			4.86833i			0.174091i
$783$	0.541131	+	0.937266i	0.0193384	+	0.0334951i
$784$	5.57249	−	4.23643i	0.199017	−	0.151301i
$785$			73.7894i			2.63366i
$786$	16.2758	−	9.39683i	0.580538	−	0.335174i
$787$			40.1855i			1.43246i	0.697866	+	0.716229i	$0.254133\pi$
$787$			40.1855i			1.43246i	−0.697866	+	0.716229i	$0.745867\pi$
$788$	−16.4198	+	9.47999i	−0.584932	+	0.337711i
$789$	−1.48500	−	2.57210i	−0.0528675	−	0.0915691i
$790$	4.48000	+	7.75959i	0.159391	+	0.276074i
$791$	−5.30867	+	26.3799i	−0.188755	+	0.937959i
$792$	0.776506			0.0275919
$793$	−8.76107	−	47.4217i	−0.311115	−	1.68399i
$794$	9.58307	+	16.5984i	0.340090	+	0.589054i
$795$	11.9624	+	6.90652i	0.424264	+	0.244949i
$796$	8.21048			0.291013
$797$	0.243363	−	0.421517i	0.00862036	−	0.0149309i	−0.861683	−	0.507447i	$-0.830589\pi$
$797$	0.243363	−	0.421517i	0.00862036	−	0.0149309i	0.870303	+	0.492516i	$0.163923\pi$
$798$	−7.42101	+	2.50059i	−0.262701	+	0.0885199i
$799$	−17.2057	−	9.93373i	−0.608695	−	0.351430i
$800$	−3.45185	+	1.99293i	−0.122041	+	0.0704607i
$801$	7.54364	−	4.35532i	0.266541	−	0.153888i
$802$	−30.0378			−1.06067
$803$	−6.23194			−0.219920
$804$	4.62876	−	2.67241i	0.163244	−	0.0942488i
$805$	−16.1715	−	3.25436i	−0.569972	−	0.114701i
$806$	4.78007	+	25.8735i	0.168371	+	0.911354i
$807$	−10.8071	+	18.7184i	−0.380428	+	0.658920i
$808$	−10.0552	−	5.80539i	−0.353742	−	0.204233i
$809$	−15.6342	+	27.0793i	−0.549670	+	0.952057i	0.448626	+	0.893719i	$0.351913\pi$
$809$	−15.6342	+	27.0793i	−0.549670	+	0.952057i	−0.998297	+	0.0583377i	$0.981420\pi$
$810$	1.49882	+	2.59603i	0.0526632	+	0.0912153i
$811$		−	25.5332i		−	0.896592i	−0.893885	−	0.448296i	$-0.852031\pi$
$811$		−	25.5332i		−	0.896592i	0.893885	−	0.448296i	$-0.147969\pi$
$812$	−2.14858	−	1.89278i	−0.0754005	−	0.0664236i
$813$	−1.12537	−	0.649732i	−0.0394684	−	0.0227871i
$814$	4.62172	+	2.66835i	0.161991	+	0.0935257i
$815$	33.6041			1.17710
$816$	−1.17033	+	2.02707i	−0.0409696	+	0.0709615i
$817$			15.6726i			0.548316i
$818$	−3.88182			−0.135725
$819$	−4.63775	−	8.33614i	−0.162056	−	0.291288i
$820$	33.9786			1.18658
$821$		−	10.7839i		−	0.376360i	−0.982135	−	0.188180i	$-0.939741\pi$
$821$		−	10.7839i		−	0.376360i	0.982135	−	0.188180i	$-0.0602589\pi$
$822$	−9.06426	+	15.6998i	−0.316152	+	0.547592i
$823$	14.1555			0.493428			0.246714	−	0.969088i	$-0.420649\pi$
$823$	14.1555			0.493428			0.246714	+	0.969088i	$0.420649\pi$
$824$	−6.35077	−	3.66662i	−0.221239	−	0.127733i
$825$	2.68038	+	1.54752i	0.0933190	+	0.0538778i
$826$	9.50694	−	3.20346i	0.330789	−	0.111463i
$827$		−	36.2823i		−	1.26166i	−0.775921	−	0.630830i	$-0.782714\pi$
$827$		−	36.2823i		−	1.26166i	0.775921	−	0.630830i	$-0.217286\pi$
$828$	1.03995	+	1.80125i	0.0361408	+	0.0625977i
$829$	−6.74156	+	11.6767i	−0.234144	+	0.405549i	−0.959024	−	0.283326i	$-0.908562\pi$
$829$	−6.74156	+	11.6767i	−0.234144	+	0.405549i	0.724880	+	0.688876i	$0.241895\pi$
$830$	−11.0416	−	6.37485i	−0.383258	−	0.221274i
$831$	11.1664	−	19.3407i	0.387357	−	0.670921i
$832$	−3.39805	−	1.20550i	−0.117806	−	0.0417932i
$833$	13.0433	−	9.91602i	0.451923	−	0.343570i
$834$	17.7702	−	10.2597i	0.615333	−	0.355263i
$835$	37.5509			1.29950
$836$	2.29833			0.0794894
$837$	6.31977	−	3.64872i	0.218443	−	0.126118i
$838$	29.6717	−	17.1309i	1.02499	−	0.591778i
$839$	−18.5123	−	10.6881i	−0.639116	−	0.368994i	0.145158	−	0.989408i	$-0.453631\pi$
$839$	−18.5123	−	10.6881i	−0.639116	−	0.368994i	−0.784274	+	0.620415i	$0.786964\pi$
$840$	−5.95114	−	5.24261i	−0.205334	−	0.180887i
$841$	13.9144	−	24.1004i	0.479805	−	0.831047i
$842$	3.77781			0.130192
$843$	25.2776	+	14.5940i	0.870607	+	0.502645i
$844$	5.39098	+	9.33746i	0.185565	+	0.321409i
$845$	−13.9238	−	36.3970i	−0.478993	−	1.25209i
$846$	−8.48799			−0.291823
$847$	−20.6410	−	18.1835i	−0.709232	−	0.624793i
$848$	2.30398	+	3.99062i	0.0791191	+	0.137038i
$849$	−15.6289	−	27.0700i	−0.536381	−	0.929039i
$850$	−8.07960	+	4.66476i	−0.277128	+	0.160000i
$851$			14.2946i			0.490012i
$852$	−3.56761	+	2.05976i	−0.122224	+	0.0705662i
$853$		−	30.2641i		−	1.03622i	−0.855313	−	0.518111i	$-0.826635\pi$
$853$		−	30.2641i		−	1.03622i	0.855313	−	0.518111i	$-0.173365\pi$
$854$	23.3917	−	26.5530i	0.800447	−	0.908625i
$855$	4.43626	+	7.68383i	0.151717	+	0.262782i
$856$		−	10.9196i		−	0.373223i
$857$	−18.2018	−	31.5265i	−0.621763	−	1.07693i	−0.989157	−	0.146860i	$-0.953083\pi$
$857$	−18.2018	−	31.5265i	−0.621763	−	1.07693i	0.367394	−	0.930065i	$-0.380250\pi$
$858$	0.508637	+	2.75314i	0.0173646	+	0.0939907i
$859$	−23.0720	+	39.9618i	−0.787205	+	1.36348i	0.140467	+	0.990085i	$0.455140\pi$
$859$	−23.0720	+	39.9618i	−0.787205	+	1.36348i	−0.927673	+	0.373395i	$0.878194\pi$
$860$	−13.7463	+	7.93642i	−0.468744	+	0.270630i
$861$	9.57635	+	28.4198i	0.326361	+	0.968544i
$862$	−6.43806	+	11.1510i	−0.219281	+	0.379806i
$863$	27.1825	+	15.6938i	0.925302	+	0.534223i	0.885323	−	0.464977i	$-0.153938\pi$
$863$	27.1825	+	15.6938i	0.925302	+	0.534223i	0.0399790	+	0.999201i	$0.487271\pi$
$864$			1.00000i			0.0340207i
$865$		−	19.6065i		−	0.666640i
$866$	−4.41144	−	2.54694i	−0.149907	−	0.0865487i
$867$	5.76067	−	9.97777i	0.195643	−	0.338863i
$868$	−12.7626	+	14.4874i	−0.433191	+	0.491735i
$869$	2.01003	−	1.16049i	0.0681857	−	0.0393671i
$870$	−1.62212	+	2.80959i	−0.0549949	+	0.0952539i
$871$	12.5072	+	14.6610i	0.423789	+	0.496768i
$872$	−7.01217	−	12.1454i	−0.237462	−	0.411297i
$873$		−	2.83244i		−	0.0958636i
$874$	3.07809	+	5.33140i	0.104118	+	0.180337i
$875$	2.56834	+	7.62209i	0.0868258	+	0.257674i
$876$		−	8.02562i		−	0.271161i
$877$	37.3709	−	21.5761i	1.26193	−	0.728574i	0.288479	−	0.957486i	$-0.406850\pi$
$877$	37.3709	−	21.5761i	1.26193	−	0.728574i	0.973447	+	0.228913i	$0.0735170\pi$
$878$		−	33.0107i		−	1.11406i
$879$	−22.9743	+	13.2642i	−0.774902	+	0.447390i
$880$	1.16384	+	2.01584i	0.0392331	+	0.0679538i
$881$	17.2562	+	29.8887i	0.581378	+	1.00698i	0.995316	+	0.0966711i	$0.0308195\pi$
$881$	17.2562	+	29.8887i	0.581378	+	1.00698i	−0.413939	+	0.910305i	$0.635847\pi$
$882$	2.70770	−	6.45510i	0.0911731	−	0.217355i
$883$	11.1929			0.376671			0.188336	−	0.982105i	$-0.439691\pi$
$883$	11.1929			0.376671			0.188336	+	0.982105i	$0.439691\pi$
$884$	−7.95367	−	2.82166i	−0.267511	−	0.0949026i
$885$	−5.68322	−	9.84363i	−0.191039	−	0.330890i
$886$	−15.9267	−	9.19529i	−0.535068	−	0.308922i
$887$	−49.0344			−1.64642			−0.823208	−	0.567740i	$-0.807818\pi$
$887$	−49.0344			−1.64642			−0.823208	+	0.567740i	$0.807818\pi$
$888$	−3.43636	+	5.95195i	−0.115317	+	0.199734i
$889$	4.26267	+	3.75517i	0.142965	+	0.125944i
$890$	22.6131	+	13.0557i	0.757994	+	0.437628i
$891$	0.672474	−	0.388253i	0.0225287	−	0.0130070i
$892$	−1.45669	+	0.841020i	−0.0487736	+	0.0281594i
$893$	−25.1231			−0.840711
$894$	15.5957			0.521597
$895$	47.8939	−	27.6515i	1.60092	−	0.924289i
$896$	−0.844840	−	2.50724i	−0.0282241	−	0.0837610i
$897$	−5.70522	+	4.86708i	−0.190492	+	0.162507i
$898$	−2.33427	+	4.04307i	−0.0778955	+	0.134919i
$899$	6.83965	+	3.94887i	0.228115	+	0.131702i
$900$	−1.99293	+	3.45185i	−0.0664310	+	0.115062i
$901$	5.39283	+	9.34065i	0.179661	+	0.311182i
$902$		−	8.80177i		−	0.293067i
$903$	−10.5122	−	9.26067i	−0.349825	−	0.308176i
$904$	8.80794	+	5.08527i	0.292948	+	0.169133i
$905$	38.3918	+	22.1655i	1.27619	+	0.736807i
$906$	7.37936			0.245163
$907$	20.9103	−	36.2176i	0.694314	−	1.20259i	−0.276098	−	0.961130i	$-0.589041\pi$
$907$	20.9103	−	36.2176i	0.694314	−	1.20259i	0.970411	−	0.241457i	$-0.0776254\pi$
$908$		−	6.35545i		−	0.210913i
$909$	−11.6108			−0.385105
$910$	14.6898	−	24.5341i	0.486961	−	0.813299i
$911$	7.19793			0.238478			0.119239	−	0.992866i	$-0.461955\pi$
$911$	7.19793			0.238478			0.119239	+	0.992866i	$0.461955\pi$
$912$			2.95984i			0.0980100i
$913$	−1.65133	+	2.86019i	−0.0546512	+	0.0946586i
$914$	27.1473			0.897951
$915$	−34.7219	−	20.0467i	−1.14787	−	0.662724i
$916$	−15.4079	−	8.89576i	−0.509092	−	0.293924i
$917$	−9.80965	+	48.7461i	−0.323943	+	1.60974i
$918$			2.34065i			0.0772531i
$919$	14.1078	+	24.4354i	0.465373	+	0.806050i	0.999218	−	0.0395321i	$-0.0125867\pi$
$919$	14.1078	+	24.4354i	0.465373	+	0.806050i	−0.533845	+	0.845582i	$0.679253\pi$
$920$	−3.11740	+	5.39950i	−0.102778	+	0.178016i
$921$	−22.7346	−	13.1258i	−0.749132	−	0.432511i
$922$	9.67843	−	16.7635i	0.318742	−	0.552078i
$923$	−9.63988	−	11.2999i	−0.317301	−	0.371941i
$924$	−1.35804	+	1.54158i	−0.0446762	+	0.0507141i
$925$	−23.7236	+	13.6968i	−0.780028	+	0.450350i
$926$	10.1358			0.333083
$927$	−7.33323			−0.240855
$928$	−0.937266	+	0.541131i	−0.0307673	+	0.0177635i
$929$	−15.1416	+	8.74200i	−0.496779	+	0.286816i	−0.727382	−	0.686232i	$-0.759263\pi$
$929$	−15.1416	+	8.74200i	−0.496779	+	0.286816i	0.230603	+	0.973048i	$0.425930\pi$
$930$	18.9444	+	10.9376i	0.621212	+	0.358657i
$931$	8.01435	−	19.1060i	0.262660	−	0.626175i
$932$	5.84028	−	10.1157i	0.191305	−	0.331349i
$933$	29.4788			0.965093
$934$	35.2256	+	20.3375i	1.15262	+	0.665463i
$935$	2.72415	+	4.71837i	0.0890894	+	0.154307i
$936$	−3.54555	+	0.655034i	−0.115890	+	0.0214104i
$937$	−43.3168			−1.41510			−0.707549	−	0.706664i	$-0.750199\pi$
$937$	−43.3168			−1.41510			−0.707549	+	0.706664i	$0.750199\pi$
$938$	−2.78982	+	13.8632i	−0.0910908	+	0.452648i
$939$	8.66910	+	15.0153i	0.282906	+	0.490007i
$940$	−12.7220	−	22.0351i	−0.414945	−	0.718706i
$941$	−24.7292	+	14.2774i	−0.806150	+	0.465431i	−0.845617	−	0.533790i	$-0.820767\pi$
$941$	−24.7292	+	14.2774i	−0.806150	+	0.465431i	0.0394670	+	0.999221i	$0.487434\pi$
$942$			24.6158i			0.802027i
$943$	20.4173	−	11.7880i	0.664880	−	0.383869i
$944$		−	3.79180i		−	0.123412i
$945$	−7.77514	−	1.56467i	−0.252925	−	0.0508986i
$946$	2.05584	+	3.56082i	0.0668411	+	0.115772i
$947$			49.5913i			1.61150i	0.592256	+	0.805750i	$0.298238\pi$
$947$			49.5913i			1.61150i	−0.592256	+	0.805750i	$0.701762\pi$
$948$	1.49451	+	2.58856i	0.0485394	+	0.0840726i
$949$	28.4552	−	5.25705i	0.923696	−	0.170651i
$950$	−5.89874	+	10.2169i	−0.191380	+	0.331481i
$951$	2.71629	−	1.56825i	0.0880818	−	0.0508540i
$952$	−1.97748	−	5.86858i	−0.0640905	−	0.190202i
$953$	−12.1557	+	21.0543i	−0.393763	+	0.682017i	−0.992942	−	0.118598i	$-0.962160\pi$
$953$	−12.1557	+	21.0543i	−0.393763	+	0.682017i	0.599180	+	0.800615i	$0.295493\pi$
$954$	3.99062	+	2.30398i	0.129201	+	0.0745942i
$955$		−	19.5840i		−	0.633724i
$956$		−	8.17752i		−	0.264480i
$957$	0.727792	+	0.420191i	0.0235262	+	0.0135828i
$958$	9.53330	−	16.5122i	0.308007	−	0.533484i
$959$	−15.3157	−	45.4525i	−0.494570	−	1.46774i
$960$	−2.59603	+	1.49882i	−0.0837866	+	0.0483742i
$961$	11.1264	−	19.2714i	0.358915	−	0.621659i
$962$	−23.3539	−	8.28506i	−0.752959	−	0.267121i
$963$	−5.45978	−	9.45661i	−0.175939	−	0.304735i
$964$		−	28.9685i		−	0.933012i
$965$	−8.05044	−	13.9438i	−0.259153	−	0.448866i
$966$	−5.39475	−	1.08564i	−0.173573	−	0.0349299i
$967$			24.6124i			0.791481i	0.918362	+	0.395741i	$0.129512\pi$
$967$			24.6124i			0.791481i	−0.918362	+	0.395741i	$0.870488\pi$
$968$	−9.00410	+	5.19852i	−0.289403	+	0.167087i
$969$			6.92795i			0.222558i
$970$	7.35311	−	4.24532i	0.236094	−	0.136309i
$971$	22.6770	+	39.2778i	0.727740	+	1.26048i	0.957836	+	0.287315i	$0.0927627\pi$
$971$	22.6770	+	39.2778i	0.727740	+	1.26048i	−0.230096	+	0.973168i	$0.573904\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−10.7104	+	53.2220i	−0.343359	+	1.70622i
$974$	30.1508			0.966095
$975$	−13.5442	−	4.80495i	−0.433760	−	0.153882i
$976$	−6.68750	−	11.5831i	−0.214062	−	0.370765i
$977$	−6.06974	−	3.50437i	−0.194188	−	0.112115i	0.399754	−	0.916623i	$-0.369096\pi$
$977$	−6.06974	−	3.50437i	−0.194188	−	0.112115i	−0.593942	+	0.804508i	$0.702429\pi$
$978$	11.2102			0.358462
$979$	3.38193	−	5.85768i	0.108087	−	0.187212i
$980$	20.8160	−	2.64576i	0.664944	−	0.0845156i
$981$	−12.1454	−	7.01217i	−0.387774	−	0.223882i
$982$	5.14945	−	2.97304i	0.164326	−	0.0948734i
$983$	−40.9972	+	23.6698i	−1.30761	+	0.754948i	−0.981697	−	0.190452i	$-0.939005\pi$
$983$	−40.9972	+	23.6698i	−1.30761	+	0.754948i	−0.325912	+	0.945400i	$0.605671\pi$
$984$	11.3351			0.361350
$985$	−56.8352			−1.81092
$986$	−2.19382	+	1.26660i	−0.0698653	+	0.0403368i
$987$	14.8448	−	16.8510i	0.472514	−	0.536373i
$988$	−10.4942	+	1.93879i	−0.333866	+	0.0616812i
$989$	−5.50665	+	9.53781i	−0.175101	+	0.303285i
$990$	2.01584	+	1.16384i	0.0640675	+	0.0369894i
$991$	14.6650	−	25.4006i	0.465850	−	0.806877i	−0.533389	−	0.845870i	$-0.679082\pi$
$991$	14.6650	−	25.4006i	0.465850	−	0.806877i	0.999239	+	0.0389935i	$0.0124152\pi$
$992$	3.64872	+	6.31977i	0.115847	+	0.200653i
$993$		−	3.84190i		−	0.121919i
$994$	2.15025	−	10.6850i	0.0682017	−	0.338908i
$995$	21.3147	+	12.3060i	0.675721	+	0.390128i
$996$	−3.68342	−	2.12662i	−0.116714	−	0.0673846i
$997$	−7.49371			−0.237328			−0.118664	−	0.992934i	$-0.537861\pi$
$997$	−7.49371			−0.237328			−0.118664	+	0.992934i	$0.537861\pi$
$998$	0.932853	−	1.61575i	0.0295289	−	0.0511456i
$999$			6.87272i			0.217443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bm.b.205.6	yes	20
3.2	odd	2		1638.2.dt.b.1297.5		20
7.4	even	3		546.2.bd.b.361.5	yes	20
13.4	even	6		546.2.bd.b.121.5	✓	20
21.11	odd	6		1638.2.cr.b.361.6		20
39.17	odd	6		1638.2.cr.b.667.6		20
91.4	even	6	inner	546.2.bm.b.277.1	yes	20
273.95	odd	6		1638.2.dt.b.1369.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.b.121.5	✓	20	13.4	even	6
546.2.bd.b.361.5	yes	20	7.4	even	3
546.2.bm.b.205.6	yes	20	1.1	even	1	trivial
546.2.bm.b.277.1	yes	20	91.4	even	6	inner
1638.2.cr.b.361.6		20	21.11	odd	6
1638.2.cr.b.667.6		20	39.17	odd	6
1638.2.dt.b.1297.5		20	3.2	odd	2
1638.2.dt.b.1369.10		20	273.95	odd	6

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.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(-2.59603 - 1.49882i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(2.50724 - 0.844840i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(-2.59603 - 1.49882i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(2.50724 - 0.844840i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.49882 - 2.59603i) q^{10} +(-0.672474 - 0.388253i) q^{11} +(0.500000 - 0.866025i) q^{12} +(3.39805 + 1.20550i) q^{13} +(0.844840 + 2.50724i) q^{14} +(2.59603 - 1.49882i) q^{15} +1.00000 q^{16} +2.34065 q^{17} +(0.866025 - 0.500000i) q^{18} +(2.56329 - 1.47992i) q^{19} +(2.59603 + 1.49882i) q^{20} +(-0.521966 + 2.59375i) q^{21} +(0.388253 - 0.672474i) q^{22} +2.07990 q^{23} +(0.866025 + 0.500000i) q^{24} +(1.99293 + 3.45185i) q^{25} +(-1.20550 + 3.39805i) q^{26} +1.00000 q^{27} +(-2.50724 + 0.844840i) q^{28} +(0.541131 + 0.937266i) q^{29} +(1.49882 + 2.59603i) q^{30} +(6.31977 - 3.64872i) q^{31} +1.00000i q^{32} +(0.672474 - 0.388253i) q^{33} +2.34065i q^{34} +(-7.77514 - 1.56467i) q^{35} +(0.500000 + 0.866025i) q^{36} +6.87272i q^{37} +(1.47992 + 2.56329i) q^{38} +(-2.74302 + 2.34005i) q^{39} +(-1.49882 + 2.59603i) q^{40} +(9.81648 - 5.66755i) q^{41} +(-2.59375 - 0.521966i) q^{42} +(-2.64755 + 4.58570i) q^{43} +(0.672474 + 0.388253i) q^{44} +2.99764i q^{45} +2.07990i q^{46} +(-7.35082 - 4.24400i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(5.57249 - 4.23643i) q^{49} +(-3.45185 + 1.99293i) q^{50} +(-1.17033 + 2.02707i) q^{51} +(-3.39805 - 1.20550i) q^{52} +(2.30398 + 3.99062i) q^{53} +1.00000i q^{54} +(1.16384 + 2.01584i) q^{55} +(-0.844840 - 2.50724i) q^{56} +2.95984i q^{57} +(-0.937266 + 0.541131i) q^{58} -3.79180i q^{59} +(-2.59603 + 1.49882i) q^{60} +(-6.68750 - 11.5831i) q^{61} +(3.64872 + 6.31977i) q^{62} +(-1.98527 - 1.74891i) q^{63} -1.00000 q^{64} +(-7.01464 - 8.22259i) q^{65} +(0.388253 + 0.672474i) q^{66} +(4.62876 + 2.67241i) q^{67} -2.34065 q^{68} +(-1.03995 + 1.80125i) q^{69} +(1.56467 - 7.77514i) q^{70} +(-3.56761 - 2.05976i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(6.95039 - 4.01281i) q^{73} -6.87272 q^{74} -3.98586 q^{75} +(-2.56329 + 1.47992i) q^{76} +(-2.01406 - 0.405310i) q^{77} +(-2.34005 - 2.74302i) q^{78} +(-1.49451 + 2.58856i) q^{79} +(-2.59603 - 1.49882i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.66755 + 9.81648i) q^{82} -4.25324i q^{83} +(0.521966 - 2.59375i) q^{84} +(-6.07642 - 3.50822i) q^{85} +(-4.58570 - 2.64755i) q^{86} -1.08226 q^{87} +(-0.388253 + 0.672474i) q^{88} +8.71065i q^{89} -2.99764 q^{90} +(9.53819 + 0.151662i) q^{91} -2.07990 q^{92} +7.29745i q^{93} +(4.24400 - 7.35082i) q^{94} -8.87253 q^{95} +(-0.866025 - 0.500000i) q^{96} +(2.45297 + 1.41622i) q^{97} +(4.23643 + 5.57249i) q^{98} +0.776506i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9}+O(q^{10}) \) 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9	\( 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9} + 4 q^{10} + 6 q^{11} + 10 q^{12} + 8 q^{13} + 4 q^{14} + 20 q^{16} - 8 q^{17} - 12 q^{19} + 6 q^{21} - 10 q^{22} - 16 q^{23} + 6 q^{25} + 8 q^{26} + 20 q^{27} + 8 q^{29} + 4 q^{30} + 12 q^{31} - 6 q^{33} + 10 q^{35} + 10 q^{36} + 6 q^{38} - 10 q^{39} - 4 q^{40} - 18 q^{41} - 2 q^{42} + 18 q^{43} - 6 q^{44} - 6 q^{47} - 10 q^{48} - 20 q^{49} + 12 q^{50} + 4 q^{51} - 8 q^{52} + 18 q^{53} - 12 q^{55} - 4 q^{56} + 24 q^{58} - 6 q^{61} - 6 q^{63} - 20 q^{64} - 6 q^{65} - 10 q^{66} + 24 q^{67} + 8 q^{68} + 8 q^{69} + 42 q^{70} - 6 q^{71} + 24 q^{73} + 36 q^{74} - 12 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} - 10 q^{81} + 18 q^{82} - 6 q^{84} - 36 q^{86} - 16 q^{87} + 10 q^{88} - 8 q^{90} - 10 q^{91} + 16 q^{92} - 16 q^{94} - 80 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) \) 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9 + 4 * q^10 + 6 * q^11 + 10 * q^12 + 8 * q^13 + 4 * q^14 + 20 * q^16 - 8 * q^17 - 12 * q^19 + 6 * q^21 - 10 * q^22 - 16 * q^23 + 6 * q^25 + 8 * q^26 + 20 * q^27 + 8 * q^29 + 4 * q^30 + 12 * q^31 - 6 * q^33 + 10 * q^35 + 10 * q^36 + 6 * q^38 - 10 * q^39 - 4 * q^40 - 18 * q^41 - 2 * q^42 + 18 * q^43 - 6 * q^44 - 6 * q^47 - 10 * q^48 - 20 * q^49 + 12 * q^50 + 4 * q^51 - 8 * q^52 + 18 * q^53 - 12 * q^55 - 4 * q^56 + 24 * q^58 - 6 * q^61 - 6 * q^63 - 20 * q^64 - 6 * q^65 - 10 * q^66 + 24 * q^67 + 8 * q^68 + 8 * q^69 + 42 * q^70 - 6 * q^71 + 24 * q^73 + 36 * q^74 - 12 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 - 10 * q^81 + 18 * q^82 - 6 * q^84 - 36 * q^86 - 16 * q^87 + 10 * q^88 - 8 * q^90 - 10 * q^91 + 16 * q^92 - 16 * q^94 - 80 * q^95 - 96 * q^97 - 12 * q^98

Introduction

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