LMFDB - Embedded newform 546.2.bd.b.361.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(121,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bd (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			361.5
Root			$-2.99764i$ of defining polynomial
Character	$\chi$	$=$	546.361
Dual form			546.2.bd.b.121.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(2.59603 - 1.49882i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.521966 + 2.59375i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(2.59603 - 1.49882i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.521966 + 2.59375i) q^{7} -1.00000i q^{8} +1.00000 q^{9} -2.99764 q^{10} +0.776506i 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} +(-0.500000 + 0.866025i) q^{16} +(-1.17033 - 2.02707i) q^{17} +(-0.866025 - 0.500000i) q^{18} +2.95984i q^{19} +(2.59603 + 1.49882i) q^{20} +(0.521966 + 2.59375i) q^{21} +(0.388253 - 0.672474i) q^{22} +(-1.03995 + 1.80125i) q^{23} -1.00000i q^{24} +(1.99293 - 3.45185i) q^{25} +(-2.34005 - 2.74302i) q^{26} +1.00000 q^{27} +(-1.98527 + 1.74891i) q^{28} +(0.541131 + 0.937266i) q^{29} -2.99764 q^{30} +(-6.31977 - 3.64872i) q^{31} +(0.866025 - 0.500000i) q^{32} +0.776506i q^{33} +2.34065i q^{34} +(5.24261 + 5.95114i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-5.95195 - 3.43636i) q^{37} +(1.47992 - 2.56329i) q^{38} +(3.39805 + 1.20550i) q^{39} +(-1.49882 - 2.59603i) q^{40} +(9.81648 - 5.66755i) q^{41} +(0.844840 - 2.50724i) q^{42} +(-2.64755 + 4.58570i) q^{43} +(-0.672474 + 0.388253i) q^{44} +(2.59603 - 1.49882i) q^{45} +(1.80125 - 1.03995i) q^{46} +(7.35082 - 4.24400i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-6.45510 + 2.70770i) q^{49} +(-3.45185 + 1.99293i) q^{50} +(-1.17033 - 2.02707i) q^{51} +(0.655034 + 3.54555i) q^{52} +(2.30398 - 3.99062i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(1.16384 + 2.01584i) q^{55} +(2.59375 - 0.521966i) q^{56} +2.95984i q^{57} -1.08226i q^{58} +(-3.28379 + 1.89590i) q^{59} +(2.59603 + 1.49882i) q^{60} +13.3750 q^{61} +(3.64872 + 6.31977i) q^{62} +(0.521966 + 2.59375i) q^{63} -1.00000 q^{64} +(10.6283 - 1.96356i) q^{65} +(0.388253 - 0.672474i) q^{66} -5.34483i q^{67} +(1.17033 - 2.02707i) q^{68} +(-1.03995 + 1.80125i) q^{69} +(-1.56467 - 7.77514i) q^{70} +(-3.56761 - 2.05976i) q^{71} -1.00000i q^{72} +(-6.95039 - 4.01281i) q^{73} +(3.43636 + 5.95195i) q^{74} +(1.99293 - 3.45185i) 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} +2.99764i q^{80} +1.00000 q^{81} -11.3351 q^{82} -4.25324i q^{83} +(-1.98527 + 1.74891i) q^{84} +(-6.07642 - 3.50822i) q^{85} +(4.58570 - 2.64755i) q^{86} +(0.541131 + 0.937266i) q^{87} +0.776506 q^{88} +(-7.54364 - 4.35532i) q^{89} -2.99764 q^{90} +(-1.35310 + 9.44294i) q^{91} -2.07990 q^{92} +(-6.31977 - 3.64872i) q^{93} -8.48799 q^{94} +(4.43626 + 7.68383i) q^{95} +(0.866025 - 0.500000i) q^{96} +(2.45297 + 1.41622i) q^{97} +(6.94413 + 0.882613i) q^{98} +0.776506i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9}+O(q^{10}) $ 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9	$ 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9} - 8 q^{10} + 10 q^{12} + 8 q^{13} + 4 q^{14} - 10 q^{16} + 4 q^{17} - 6 q^{21} - 10 q^{22} + 8 q^{23} + 6 q^{25} + 2 q^{26} + 20 q^{27} - 6 q^{28} + 8 q^{29} - 8 q^{30} - 12 q^{31} + 4 q^{35} + 10 q^{36} + 6 q^{38} + 8 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} + 18 q^{43} + 6 q^{44} - 24 q^{46} + 6 q^{47} - 10 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} - 2 q^{52} + 18 q^{53} - 12 q^{55} + 2 q^{56} + 36 q^{59} + 12 q^{61} - 6 q^{63} - 20 q^{64} - 10 q^{66} - 4 q^{68} + 8 q^{69} - 42 q^{70} - 6 q^{71} - 24 q^{73} - 18 q^{74} + 6 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} + 20 q^{81} - 36 q^{82} - 6 q^{84} + 36 q^{86} + 8 q^{87} - 20 q^{88} + 18 q^{89} - 8 q^{90} - 94 q^{91} + 16 q^{92} - 12 q^{93} + 32 q^{94} + 40 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) $ 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9 - 8 * q^10 + 10 * q^12 + 8 * q^13 + 4 * q^14 - 10 * q^16 + 4 * q^17 - 6 * q^21 - 10 * q^22 + 8 * q^23 + 6 * q^25 + 2 * q^26 + 20 * q^27 - 6 * q^28 + 8 * q^29 - 8 * q^30 - 12 * q^31 + 4 * q^35 + 10 * q^36 + 6 * q^38 + 8 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 + 18 * q^43 + 6 * q^44 - 24 * q^46 + 6 * q^47 - 10 * q^48 + 4 * q^49 + 12 * q^50 + 4 * q^51 - 2 * q^52 + 18 * q^53 - 12 * q^55 + 2 * q^56 + 36 * q^59 + 12 * q^61 - 6 * q^63 - 20 * q^64 - 10 * q^66 - 4 * q^68 + 8 * q^69 - 42 * q^70 - 6 * q^71 - 24 * q^73 - 18 * q^74 + 6 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 + 20 * q^81 - 36 * q^82 - 6 * q^84 + 36 * q^86 + 8 * q^87 - 20 * q^88 + 18 * q^89 - 8 * q^90 - 94 * q^91 + 16 * q^92 - 12 * q^93 + 32 * q^94 + 40 * q^95 - 96 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.59603	−	1.49882i	1.16098	−	0.670293i	0.209443	−	0.977821i	$-0.432835\pi$
$5$	2.59603	−	1.49882i	1.16098	−	0.670293i	0.951539	+	0.307528i	$0.0995017\pi$
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	0.521966	+	2.59375i	0.197285	+	0.980346i
$7$	0.521966	+	2.59375i	0.197285	+	0.980346i
$8$		−	1.00000i		−	0.353553i
$9$	1.00000			0.333333
$10$	−2.99764			−0.947938
$11$			0.776506i			0.234125i	0.993125	+	0.117063i	$0.0373478\pi$
$11$			0.776506i			0.234125i	−0.993125	+	0.117063i	$0.962652\pi$
$12$	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
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.17033	−	2.02707i	−0.283846	−	0.491636i	0.688483	−	0.725253i	$-0.258277\pi$
$17$	−1.17033	−	2.02707i	−0.283846	−	0.491636i	−0.972329	+	0.233617i	$0.924944\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$			2.95984i			0.679033i	0.940600	+	0.339516i	$0.110263\pi$
$19$			2.95984i			0.679033i	−0.940600	+	0.339516i	$0.889737\pi$
$20$	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
$23$	−1.03995	+	1.80125i	−0.216845	+	0.375586i	−0.953842	−	0.300310i	$-0.902910\pi$
$23$	−1.03995	+	1.80125i	−0.216845	+	0.375586i	0.736997	+	0.675896i	$0.236243\pi$
$24$		−	1.00000i		−	0.204124i
$25$	1.99293	−	3.45185i	0.398586	−	0.690371i
$26$	−2.34005	−	2.74302i	−0.458922	−	0.537951i
$27$	1.00000			0.192450
$28$	−1.98527	+	1.74891i	−0.375181	+	0.330513i
$29$	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	$0.801294\pi$
$30$	−2.99764			−0.547292
$31$	−6.31977	−	3.64872i	−1.13507	−	0.655330i	−0.189861	−	0.981811i	$-0.560804\pi$
$31$	−6.31977	−	3.64872i	−1.13507	−	0.655330i	−0.945204	+	0.326481i	$0.894137\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$			0.776506i			0.135172i
$34$			2.34065i			0.401419i
$35$	5.24261	+	5.95114i	0.886163	+	1.00593i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−5.95195	−	3.43636i	−0.978495	−	0.564934i	−0.0766794	−	0.997056i	$-0.524432\pi$
$37$	−5.95195	−	3.43636i	−0.978495	−	0.564934i	−0.901815	+	0.432122i	$0.857765\pi$
$38$	1.47992	−	2.56329i	0.240074	−	0.415821i
$39$	3.39805	+	1.20550i	0.544124	+	0.193034i
$40$	−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	$-0.0125921\pi$
$42$	0.844840	−	2.50724i	0.130362	−	0.386875i
$43$	−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
$45$	2.59603	−	1.49882i	0.386994	−	0.223431i
$46$	1.80125	−	1.03995i	0.265580	−	0.153333i
$47$	7.35082	−	4.24400i	1.07223	−	0.619051i	0.143438	−	0.989659i	$-0.454184\pi$
$47$	7.35082	−	4.24400i	1.07223	−	0.619051i	0.928789	+	0.370609i	$0.120851\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−6.45510	+	2.70770i	−0.922158	+	0.386815i
$50$	−3.45185	+	1.99293i	−0.488166	+	0.281843i
$51$	−1.17033	−	2.02707i	−0.163879	−	0.283846i
$52$	0.655034	+	3.54555i	0.0908368	+	0.491679i
$53$	2.30398	−	3.99062i	0.316476	−	0.548153i	−0.663274	−	0.748377i	$-0.730834\pi$
$53$	2.30398	−	3.99062i	0.316476	−	0.548153i	0.979750	+	0.200224i	$0.0641668\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	1.16384	+	2.01584i	0.156933	+	0.271815i
$56$	2.59375	−	0.521966i	0.346605	−	0.0697507i
$57$			2.95984i			0.392040i
$58$		−	1.08226i		−	0.142108i
$59$	−3.28379	+	1.89590i	−0.427513	+	0.246825i	−0.698287	−	0.715818i	$-0.746054\pi$
$59$	−3.28379	+	1.89590i	−0.427513	+	0.246825i	0.270773	+	0.962643i	$0.412721\pi$
$60$	2.59603	+	1.49882i	0.335147	+	0.193497i
$61$	13.3750			1.71249			0.856246	−	0.516568i	$-0.172791\pi$
$61$	13.3750			1.71249			0.856246	+	0.516568i	$0.172791\pi$
$62$	3.64872	+	6.31977i	0.463388	+	0.802612i
$63$	0.521966	+	2.59375i	0.0657615	+	0.326782i
$64$	−1.00000			−0.125000
$65$	10.6283	−	1.96356i	1.31828	−	0.243549i
$66$	0.388253	−	0.672474i	0.0477906	−	0.0827758i
$67$		−	5.34483i		−	0.652975i	−0.945202	−	0.326487i	$-0.894135\pi$
$67$		−	5.34483i		−	0.652975i	0.945202	−	0.326487i	$-0.105865\pi$
$68$	1.17033	−	2.02707i	0.141923	−	0.245818i
$69$	−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	$0.745274\pi$
$72$		−	1.00000i		−	0.117851i
$73$	−6.95039	−	4.01281i	−0.813482	−	0.469664i	0.0346819	−	0.999398i	$-0.488958\pi$
$73$	−6.95039	−	4.01281i	−0.813482	−	0.469664i	−0.848163	+	0.529735i	$0.822292\pi$
$74$	3.43636	+	5.95195i	0.399469	+	0.691900i
$75$	1.99293	−	3.45185i	0.230124	−	0.398586i
$76$	−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	0.769622	−	0.638499i	$-0.220444\pi$
$79$	−1.49451	−	2.58856i	−0.168145	−	0.291236i	−0.937768	+	0.347263i	$0.887111\pi$
$80$			2.99764i			0.335147i
$81$	1.00000			0.111111
$82$	−11.3351			−1.25175
$83$		−	4.25324i		−	0.466854i	−0.972374	−	0.233427i	$-0.925006\pi$
$83$		−	4.25324i		−	0.466854i	0.972374	−	0.233427i	$-0.0749940\pi$
$84$	−1.98527	+	1.74891i	−0.216611	+	0.190822i
$85$	−6.07642	−	3.50822i	−0.659080	−	0.380520i
$86$	4.58570	−	2.64755i	0.494488	−	0.285493i
$87$	0.541131	+	0.937266i	0.0580153	+	0.100485i
$88$	0.776506			0.0827758
$89$	−7.54364	−	4.35532i	−0.799624	−	0.461663i	0.0437154	−	0.999044i	$-0.486081\pi$
$89$	−7.54364	−	4.35532i	−0.799624	−	0.461663i	−0.843340	+	0.537381i	$0.819414\pi$
$90$	−2.99764			−0.315979
$91$	−1.35310	+	9.44294i	−0.141843	+	0.989889i
$92$	−2.07990			−0.216845
$93$	−6.31977	−	3.64872i	−0.655330	−	0.378355i
$94$	−8.48799			−0.875470
$95$	4.43626	+	7.68383i	0.455151	+	0.788345i
$96$	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	$0.620736\pi$
$98$	6.94413	+	0.882613i	0.701463	+	0.0891574i
$99$			0.776506i			0.0780418i
$100$	3.98586			0.398586
$101$	−11.6108			−1.15532			−0.577658	−	0.816279i	$-0.696033\pi$
$101$	−11.6108			−1.15532			−0.577658	+	0.816279i	$0.696033\pi$
$102$			2.34065i			0.231759i
$103$	3.66662	+	6.35077i	0.361282	+	0.625760i	0.988172	−	0.153348i	$-0.0490057\pi$
$103$	3.66662	+	6.35077i	0.361282	+	0.625760i	−0.626890	+	0.779108i	$0.715672\pi$
$104$	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
$107$	−5.45978	+	9.45661i	−0.527817	+	0.914205i	0.471658	+	0.881782i	$0.343656\pi$
$107$	−5.45978	+	9.45661i	−0.527817	+	0.914205i	−0.999474	+	0.0324234i	$0.989677\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−12.1454	−	7.01217i	−1.16332	−	0.671645i	−0.211224	−	0.977438i	$-0.567745\pi$
$109$	−12.1454	−	7.01217i	−1.16332	−	0.671645i	−0.952098	+	0.305793i	$0.901078\pi$
$110$		−	2.32769i		−	0.221936i
$111$	−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	$0.325443\pi$
$114$	1.47992	−	2.56329i	0.138607	−	0.240074i
$115$			6.23481i			0.581399i
$116$	−0.541131	+	0.937266i	−0.0502427	+	0.0870230i
$117$	3.39805	+	1.20550i	0.314150	+	0.111448i
$118$	3.79180			0.349063
$119$	4.64684	−	4.09360i	0.425975	−	0.375260i
$120$	−1.49882	−	2.59603i	−0.136823	−	0.236984i
$121$	10.3970			0.945185
$122$	−11.5831	−	6.68750i	−1.04868	−	0.605457i
$123$	9.81648	−	5.66755i	0.885122	−	0.511026i
$124$		−	7.29745i		−	0.655330i
$125$			3.04003i			0.271909i
$126$	0.844840	−	2.50724i	0.0752644	−	0.223363i
$127$	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	$0.802964\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−2.64755	+	4.58570i	−0.233104	+	0.403748i
$130$	−10.1861	−	3.61366i	−0.893384	−	0.316939i
$131$	−9.39683	−	16.2758i	−0.821005	−	1.42202i	−0.904935	−	0.425551i	$-0.860080\pi$
$131$	−9.39683	−	16.2758i	−0.821005	−	1.42202i	0.0839297	−	0.996472i	$-0.473253\pi$
$132$	−0.672474	+	0.388253i	−0.0585313	+	0.0337931i
$133$	−7.67708	+	1.54493i	−0.665687	+	0.133963i
$134$	−2.67241	+	4.62876i	−0.230861	+	0.399864i
$135$	2.59603	−	1.49882i	0.223431	−	0.128998i
$136$	−2.02707	+	1.17033i	−0.173819	+	0.100355i
$137$	−15.6998	+	9.06426i	−1.34132	+	0.774412i	−0.987001	−	0.160712i	$-0.948621\pi$
$137$	−15.6998	+	9.06426i	−1.34132	+	0.774412i	−0.354320	+	0.935124i	$0.615288\pi$
$138$	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	$0.830648\pi$
$140$	−2.53253	+	7.51580i	−0.214038	+	0.635201i
$141$	7.35082	−	4.24400i	0.619051	−	0.357409i
$142$	2.05976	+	3.56761i	0.172851	+	0.299387i
$143$	−0.936077	+	2.63861i	−0.0782787	+	0.220652i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	2.80959	+	1.62212i	0.233324	+	0.134709i
$146$	4.01281	+	6.95039i	0.332102	+	0.575218i
$147$	−6.45510	+	2.70770i	−0.532408	+	0.223327i
$148$		−	6.87272i		−	0.564934i
$149$		−	15.5957i		−	1.27765i	−0.769353	−	0.638824i	$-0.779421\pi$
$149$		−	15.5957i		−	1.27765i	0.769353	−	0.638824i	$-0.220579\pi$
$150$	−3.45185	+	1.99293i	−0.281843	+	0.162722i
$151$	6.39071	+	3.68968i	0.520069	+	0.300262i	0.736963	−	0.675933i	$-0.236259\pi$
$151$	6.39071	+	3.68968i	0.520069	+	0.300262i	−0.216894	+	0.976195i	$0.569593\pi$
$152$	2.95984			0.240074
$153$	−1.17033	−	2.02707i	−0.0946153	−	0.163879i
$154$	1.94688	+	0.656023i	0.156884	+	0.0528639i
$155$	−21.8751			−1.75705
$156$	0.655034	+	3.54555i	0.0524447	+	0.283871i
$157$	−12.3079	+	21.3179i	−0.982278	+	1.70136i	−0.328820	+	0.944392i	$0.606651\pi$
$157$	−12.3079	+	21.3179i	−0.982278	+	1.70136i	−0.653458	+	0.756963i	$0.726682\pi$
$158$			2.98902i			0.237793i
$159$	2.30398	−	3.99062i	0.182718	−	0.316476i
$160$	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
$163$		−	11.2102i		−	0.878049i	−0.898475	−	0.439025i	$-0.855324\pi$
$163$		−	11.2102i		−	0.878049i	0.898475	−	0.439025i	$-0.144676\pi$
$164$	9.81648	+	5.66755i	0.766538	+	0.442561i
$165$	1.16384	+	2.01584i	0.0906051	+	0.156933i
$166$	−2.12662	+	3.68342i	−0.165058	+	0.285889i
$167$	−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
$171$			2.95984i			0.226344i
$172$	−5.29511			−0.403748
$173$	−6.54063			−0.497275			−0.248637	−	0.968597i	$-0.579983\pi$
$173$	−6.54063			−0.497275			−0.248637	+	0.968597i	$0.579983\pi$
$174$		−	1.08226i		−	0.0820460i
$175$	9.99350	+	3.36741i	0.755437	+	0.254553i
$176$	−0.672474	−	0.388253i	−0.0506896	−	0.0292657i
$177$	−3.28379	+	1.89590i	−0.246825	+	0.142504i
$178$	4.35532	+	7.54364i	0.326445	+	0.565420i
$179$	18.4489			1.37893			0.689466	−	0.724318i	$-0.257845\pi$
$179$	18.4489			1.37893			0.689466	+	0.724318i	$0.257845\pi$
$180$	2.59603	+	1.49882i	0.193497	+	0.111716i
$181$	−14.7886			−1.09923			−0.549615	−	0.835418i	$-0.685226\pi$
$181$	−14.7886			−1.09923			−0.549615	+	0.835418i	$0.685226\pi$
$182$	5.89329	−	7.50128i	0.436840	−	0.556032i
$183$	13.3750			0.988708
$184$	1.80125	+	1.03995i	0.132790	+	0.0766663i
$185$	−20.6020			−1.51469
$186$	3.64872	+	6.31977i	0.267537	+	0.463388i
$187$	1.57403	−	0.908766i	0.115104	−	0.0664555i
$188$	7.35082	+	4.24400i	0.536114	+	0.309525i
$189$	0.521966	+	2.59375i	0.0379674	+	0.188668i
$190$		−	8.87253i		−	0.643681i
$191$	−6.53314			−0.472721			−0.236361	−	0.971665i	$-0.575955\pi$
$191$	−6.53314			−0.472721			−0.236361	+	0.971665i	$0.575955\pi$
$192$	−1.00000			−0.0721688
$193$		−	5.37118i		−	0.386626i	−0.981137	−	0.193313i	$-0.938077\pi$
$193$		−	5.37118i		−	0.386626i	0.981137	−	0.193313i	$-0.0619233\pi$
$194$	−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	$0.0972952\pi$
$198$	0.388253	−	0.672474i	0.0275919	−	0.0477906i
$199$	4.10524	+	7.11048i	0.291013	+	0.504049i	0.974049	−	0.226335i	$-0.0726745\pi$
$199$	4.10524	+	7.11048i	0.291013	+	0.504049i	−0.683037	+	0.730384i	$0.739341\pi$
$200$	−3.45185	−	1.99293i	−0.244083	−	0.140921i
$201$		−	5.34483i		−	0.376995i
$202$	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
$205$	16.9893	−	29.4263i	1.18658	−	2.05522i
$206$		−	7.33323i		−	0.510931i
$207$	−1.03995	+	1.80125i	−0.0722816	+	0.125195i
$208$	−2.74302	+	2.34005i	−0.190194	+	0.162253i
$209$	−2.29833			−0.158979
$210$	−1.56467	−	7.77514i	−0.107972	−	0.536536i
$211$	−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	$0.954363\pi$
$212$	4.60797			0.316476
$213$	−3.56761	−	2.05976i	−0.244448	−	0.141132i
$214$	9.45661	−	5.45978i	0.646441	−	0.373223i
$215$			15.8728i			1.08252i
$216$		−	1.00000i		−	0.0680414i
$217$	6.16518	−	18.2964i	0.418520	−	1.24204i
$218$	7.01217	+	12.1454i	0.474924	+	0.822593i
$219$	−6.95039	−	4.01281i	−0.469664	−	0.271161i
$220$	−1.16384	+	2.01584i	−0.0784663	+	0.135908i
$221$	−1.53321	−	8.29891i	−0.103135	−	0.558245i
$222$	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	$0.315397\pi$
$224$	1.74891	+	1.98527i	0.116854	+	0.132647i
$225$	1.99293	−	3.45185i	0.132862	−	0.230124i
$226$	8.80794	−	5.08527i	0.585896	−	0.338267i
$227$	5.50398	−	3.17772i	0.365312	−	0.210913i	−0.306096	−	0.952001i	$-0.599023\pi$
$227$	5.50398	−	3.17772i	0.365312	−	0.210913i	0.671408	+	0.741088i	$0.265690\pi$
$228$	−2.56329	+	1.47992i	−0.169758	+	0.0980100i
$229$	−15.4079	+	8.89576i	−1.01818	+	0.587848i	−0.913577	−	0.406665i	$-0.866692\pi$
$229$	−15.4079	+	8.89576i	−1.01818	+	0.587848i	−0.104606	+	0.994514i	$0.533358\pi$
$230$	3.11740	−	5.39950i	0.205555	−	0.356033i
$231$	−2.01406	+	0.405310i	−0.132516	+	0.0266674i
$232$	0.937266	−	0.541131i	0.0615345	−	0.0355270i
$233$	−5.84028	−	10.1157i	−0.382609	−	0.662699i	0.608825	−	0.793304i	$-0.291641\pi$
$233$	−5.84028	−	10.1157i	−0.382609	−	0.662699i	−0.991434	+	0.130606i	$0.958308\pi$
$234$	−2.34005	−	2.74302i	−0.152974	−	0.179317i
$235$	12.7220	−	22.0351i	0.829891	−	1.43741i
$236$	−3.28379	−	1.89590i	−0.213757	−	0.123412i
$237$	−1.49451	−	2.58856i	−0.0970787	−	0.168145i
$238$	−6.07108	+	1.22174i	−0.393529	+	0.0791938i
$239$			8.17752i			0.528960i	0.964391	+	0.264480i	$0.0852003\pi$
$239$			8.17752i			0.528960i	−0.964391	+	0.264480i	$0.914800\pi$
$240$			2.99764i			0.193497i
$241$	25.0874	−	14.4842i	1.61602	−	0.933012i	0.628089	−	0.778142i	$-0.283837\pi$
$241$	25.0874	−	14.4842i	1.61602	−	0.933012i	0.987935	−	0.154870i	$-0.0494959\pi$
$242$	−9.00410	−	5.19852i	−0.578805	−	0.334173i
$243$	1.00000			0.0641500
$244$	6.68750	+	11.5831i	0.428123	+	0.741531i
$245$	−12.6993	+	16.7043i	−0.811329	+	1.06720i
$246$	−11.3351			−0.722699
$247$	−3.56808	+	10.0577i	−0.227032	+	0.639955i
$248$	−3.64872	+	6.31977i	−0.231694	+	0.401306i
$249$		−	4.25324i		−	0.269538i
$250$	1.52002	−	2.63275i	0.0961343	−	0.166510i
$251$	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
$254$		−	2.14714i		−	0.134724i
$255$	−6.07642	−	3.50822i	−0.380520	−	0.219693i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.81342	+	8.33708i	−0.300253	+	0.520053i	−0.976193	−	0.216903i	$-0.930404\pi$
$257$	−4.81342	+	8.33708i	−0.300253	+	0.520053i	0.675940	+	0.736956i	$0.263738\pi$
$258$	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
$262$			18.7937i			1.16108i
$263$	2.97000			0.183138			0.0915691	−	0.995799i	$-0.470812\pi$
$263$	2.97000			0.183138			0.0915691	+	0.995799i	$0.470812\pi$
$264$	0.776506			0.0477906
$265$		−	13.8130i		−	0.848528i
$266$	7.42101	+	2.50059i	0.455012	+	0.153321i
$267$	−7.54364	−	4.35532i	−0.461663	−	0.266541i
$268$	4.62876	−	2.67241i	0.282746	−	0.163244i
$269$	−10.8071	−	18.7184i	−0.658920	−	1.14128i	−0.980895	−	0.194536i	$-0.937680\pi$
$269$	−10.8071	−	18.7184i	−0.658920	−	1.14128i	0.321975	−	0.946748i	$-0.395653\pi$
$270$	−2.99764			−0.182431
$271$	−1.12537	−	0.649732i	−0.0683613	−	0.0394684i	0.465430	−	0.885085i	$-0.345900\pi$
$271$	−1.12537	−	0.649732i	−0.0683613	−	0.0394684i	−0.533791	+	0.845616i	$0.679233\pi$
$272$	2.34065			0.141923
$273$	−1.35310	+	9.44294i	−0.0818932	+	0.571513i
$274$	18.1285			1.09518
$275$	2.68038	+	1.54752i	0.161633	+	0.0933190i
$276$	−2.07990			−0.125195
$277$	11.1664	+	19.3407i	0.670921	+	1.16207i	0.977643	+	0.210270i	$0.0674345\pi$
$277$	11.1664	+	19.3407i	0.670921	+	1.16207i	−0.306722	+	0.951799i	$0.599232\pi$
$278$	17.7702	−	10.2597i	1.06579	−	0.615333i
$279$	−6.31977	−	3.64872i	−0.378355	−	0.218443i
$280$	5.95114	−	5.24261i	0.355648	−	0.313306i
$281$		−	29.1881i		−	1.74121i	−0.491980	−	0.870607i	$-0.663727\pi$
$281$		−	29.1881i		−	1.74121i	0.491980	−	0.870607i	$-0.336273\pi$
$282$	−8.48799			−0.505453
$283$	31.2577			1.85808			0.929039	−	0.369982i	$-0.120636\pi$
$283$	31.2577			1.85808			0.929039	+	0.369982i	$0.120636\pi$
$284$		−	4.11952i		−	0.244448i
$285$	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
$289$	5.76067	−	9.97777i	0.338863	−	0.586928i
$290$	−1.62212	−	2.80959i	−0.0952539	−	0.164985i
$291$	2.45297	+	1.41622i	0.143795	+	0.0830203i
$292$		−	8.02562i		−	0.469664i
$293$	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
$296$	−3.43636	+	5.95195i	−0.199734	+	0.345950i
$297$			0.776506i			0.0450574i
$298$	−7.79784	+	13.5062i	−0.451717	+	0.782396i
$299$	−5.70522	+	4.86708i	−0.329941	+	0.281471i
$300$	3.98586			0.230124
$301$	−13.2761	−	4.47352i	−0.765221	−	0.257849i
$302$	−3.68968	−	6.39071i	−0.212317	−	0.367744i
$303$	−11.6108			−0.667022
$304$	−2.56329	−	1.47992i	−0.147015	−	0.0848791i
$305$	34.7219	−	20.0467i	1.98817	−	1.14787i
$306$			2.34065i			0.133806i
$307$			26.2517i			1.49826i	0.662421	+	0.749132i	$0.269529\pi$
$307$			26.2517i			1.49826i	−0.662421	+	0.749132i	$0.730471\pi$
$308$	−1.35804	−	1.54158i	−0.0773815	−	0.0878394i
$309$	3.66662	+	6.35077i	0.208587	+	0.361282i
$310$	18.9444	+	10.9376i	1.07597	+	0.621212i
$311$	−14.7394	+	25.5294i	−0.835795	+	1.44764i	0.0575859	+	0.998341i	$0.481660\pi$
$311$	−14.7394	+	25.5294i	−0.835795	+	1.44764i	−0.893381	+	0.449299i	$0.851674\pi$
$312$	1.20550	−	3.39805i	0.0682480	−	0.192377i
$313$	8.66910	+	15.0153i	0.490007	+	0.848717i	0.999934	−	0.0115010i	$-0.00366097\pi$
$313$	8.66910	+	15.0153i	0.490007	+	0.848717i	−0.509927	+	0.860218i	$0.670328\pi$
$314$	21.3179	−	12.3079i	1.20304	−	0.694575i
$315$	5.24261	+	5.95114i	0.295388	+	0.335309i
$316$	1.49451	−	2.58856i	0.0840726	−	0.145618i
$317$	2.71629	−	1.56825i	0.152562	−	0.0880818i	−0.421776	−	0.906700i	$-0.638593\pi$
$317$	2.71629	−	1.56825i	0.152562	−	0.0880818i	0.574338	+	0.818618i	$0.305260\pi$
$318$	−3.99062	+	2.30398i	−0.223783	+	0.129201i
$319$	−0.727792	+	0.420191i	−0.0407485	+	0.0235262i
$320$	−2.59603	+	1.49882i	−0.145123	+	0.0837866i
$321$	−5.45978	+	9.45661i	−0.304735	+	0.527817i
$322$	3.63757	+	4.12918i	0.202714	+	0.230110i
$323$	5.99978	−	3.46398i	0.333837	−	0.192741i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	10.9333	−	9.32711i	0.606470	−	0.517375i
$326$	−5.60509	+	9.70830i	−0.310437	+	0.537693i
$327$	−12.1454	−	7.01217i	−0.671645	−	0.387774i
$328$	−5.66755	−	9.81648i	−0.312938	−	0.542025i
$329$	14.8448	+	16.8510i	0.818418	+	0.929025i
$330$		−	2.32769i		−	0.128135i
$331$		−	3.84190i		−	0.211170i	−0.994410	−	0.105585i	$-0.966328\pi$
$331$		−	3.84190i		−	0.211170i	0.994410	−	0.105585i	$-0.0336715\pi$
$332$	3.68342	−	2.12662i	0.202154	−	0.116714i
$333$	−5.95195	−	3.43636i	−0.326165	−	0.188311i
$334$	12.5268			0.685436
$335$	−8.01094	−	13.8754i	−0.437685	−	0.758092i
$336$	−2.50724	−	0.844840i	−0.136781	−	0.0460898i
$337$	10.0185			0.545742			0.272871	−	0.962051i	$-0.412027\pi$
$337$	10.0185			0.545742			0.272871	+	0.962051i	$0.412027\pi$
$338$	−4.64491	−	12.1419i	−0.252650	−	0.660430i
$339$	−5.08527	+	8.80794i	−0.276194	+	0.478382i
$340$		−	7.01644i		−	0.380520i
$341$	2.83325	−	4.90734i	0.153429	−	0.265747i
$342$	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
$345$			6.23481i			0.335671i
$346$	5.66435	+	3.27031i	0.304517	+	0.175813i
$347$	8.84230	+	15.3153i	0.474679	+	0.822169i	0.999580	−	0.0289951i	$-0.00923071\pi$
$347$	8.84230	+	15.3153i	0.474679	+	0.822169i	−0.524900	+	0.851164i	$0.675897\pi$
$348$	−0.541131	+	0.937266i	−0.0290077	+	0.0502427i
$349$	−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
$353$		−	26.1981i		−	1.39438i	−0.716886	−	0.697191i	$-0.754433\pi$
$353$		−	26.1981i		−	1.39438i	0.716886	−	0.697191i	$-0.245567\pi$
$354$	3.79180			0.201532
$355$	−12.3488			−0.655408
$356$		−	8.71065i		−	0.461663i
$357$	4.64684	−	4.09360i	0.245937	−	0.216656i
$358$	−15.9772	−	9.22443i	−0.844420	−	0.487526i
$359$	−0.978047	+	0.564675i	−0.0516193	+	0.0298024i	−0.525588	−	0.850740i	$-0.676154\pi$
$359$	−0.978047	+	0.564675i	−0.0516193	+	0.0298024i	0.473968	+	0.880542i	$0.342821\pi$
$360$	−1.49882	−	2.59603i	−0.0789948	−	0.136823i
$361$	10.2394			0.538914
$362$	12.8073	+	7.39432i	0.673139	+	0.388637i
$363$	10.3970			0.545703
$364$	−8.85438	+	3.54965i	−0.464095	+	0.186052i
$365$	−24.0579			−1.25925
$366$	−11.5831	−	6.68750i	−0.605457	−	0.349561i
$367$	−20.0425			−1.04621			−0.523106	−	0.852268i	$-0.675227\pi$
$367$	−20.0425			−1.04621			−0.523106	+	0.852268i	$0.675227\pi$
$368$	−1.03995	−	1.80125i	−0.0542112	−	0.0938966i
$369$	9.81648	−	5.66755i	0.511026	−	0.295041i
$370$	17.8418	+	10.3010i	0.927552	+	0.535522i
$371$	11.5533	+	3.89300i	0.599816	+	0.202114i
$372$		−	7.29745i		−	0.378355i
$373$	−1.07291			−0.0555532			−0.0277766	−	0.999614i	$-0.508843\pi$
$373$	−1.07291			−0.0555532			−0.0277766	+	0.999614i	$0.508843\pi$
$374$	−1.81753			−0.0939823
$375$			3.04003i			0.156987i
$376$	−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	$0.276614\pi$
$380$	−4.43626	+	7.68383i	−0.227576	+	0.394172i
$381$	1.07357	+	1.85948i	0.0550008	+	0.0952641i
$382$	5.65786	+	3.26657i	0.289481	+	0.167132i
$383$			31.5480i			1.61203i	0.591897	+	0.806014i	$0.298379\pi$
$383$			31.5480i			1.61203i	−0.591897	+	0.806014i	$0.701621\pi$
$384$	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
$387$	−2.64755	+	4.58570i	−0.134583	+	0.233104i
$388$			2.83244i			0.143795i
$389$	−0.542096	+	0.938937i	−0.0274853	+	0.0476060i	−0.879441	−	0.476008i	$-0.842083\pi$
$389$	−0.542096	+	0.938937i	−0.0274853	+	0.0476060i	0.851956	+	0.523614i	$0.175417\pi$
$390$	−10.1861	−	3.61366i	−0.515796	−	0.182985i
$391$	4.86833			0.246202
$392$	2.70770	+	6.45510i	0.136760	+	0.326032i
$393$	−9.39683	−	16.2758i	−0.474007	−	0.821005i
$394$	−18.9600			−0.955190
$395$	−7.75959	−	4.48000i	−0.390427	−	0.225413i
$396$	−0.672474	+	0.388253i	−0.0337931	+	0.0195104i
$397$			19.1661i			0.961921i	0.876742	+	0.480960i	$0.159712\pi$
$397$			19.1661i			0.961921i	−0.876742	+	0.480960i	$0.840288\pi$
$398$		−	8.21048i		−	0.411554i
$399$	−7.67708	+	1.54493i	−0.384335	+	0.0773434i
$400$	1.99293	+	3.45185i	0.0996465	+	0.172593i
$401$	−26.0135	−	15.0189i	−1.29905	−	0.750009i	−0.318813	−	0.947818i	$-0.603284\pi$
$401$	−26.0135	−	15.0189i	−1.29905	−	0.750009i	−0.980241	+	0.197808i	$0.936618\pi$
$402$	−2.67241	+	4.62876i	−0.133288	+	0.230861i
$403$	−17.0764	−	20.0170i	−0.850636	−	0.997120i
$404$	−5.80539	−	10.0552i	−0.288829	−	0.500266i
$405$	2.59603	−	1.49882i	0.128998	−	0.0744770i
$406$	2.80712	−	0.564904i	0.139315	−	0.0280357i
$407$	2.66835	−	4.62172i	0.132265	−	0.229090i
$408$	−2.02707	+	1.17033i	−0.100355	+	0.0579398i
$409$	3.36176	−	1.94091i	0.166228	−	0.0959719i	−0.414578	−	0.910014i	$-0.636071\pi$
$409$	3.36176	−	1.94091i	0.166228	−	0.0959719i	0.580806	+	0.814042i	$0.302737\pi$
$410$	−29.4263	+	16.9893i	−1.45326	+	0.839041i
$411$	−15.6998	+	9.06426i	−0.774412	+	0.447107i
$412$	−3.66662	+	6.35077i	−0.180641	+	0.312880i
$413$	−6.63152	−	7.52775i	−0.326316	−	0.370416i
$414$	1.80125	−	1.03995i	0.0885266	−	0.0511108i
$415$	−6.37485	−	11.0416i	−0.312929	−	0.542009i
$416$	3.54555	−	0.655034i	0.173835	−	0.0321157i
$417$	−10.2597	+	17.7702i	−0.502418	+	0.870213i
$418$	1.99041	+	1.14916i	0.0973542	+	0.0562075i
$419$	−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	$-0.482302\pi$
$420$	−2.53253	+	7.51580i	−0.123575	+	0.366734i
$421$		−	3.77781i		−	0.184119i	−0.995754	−	0.0920595i	$-0.970655\pi$
$421$		−	3.77781i		−	0.184119i	0.995754	−	0.0920595i	$-0.0293450\pi$
$422$			10.7820i			0.524858i
$423$	7.35082	−	4.24400i	0.357409	−	0.206350i
$424$	−3.99062	−	2.30398i	−0.193801	−	0.111891i
$425$	−9.32952			−0.452548
$426$	2.05976	+	3.56761i	0.0997956	+	0.172851i
$427$	6.98129	+	34.6914i	0.337848	+	1.67884i
$428$	−10.9196			−0.527817
$429$	−0.936077	+	2.63861i	−0.0451942	+	0.127393i
$430$	7.93642	−	13.7463i	0.382728	−	0.662904i
$431$		−	12.8761i		−	0.620221i	−0.950701	−	0.310110i	$-0.899634\pi$
$431$		−	12.8761i		−	0.620221i	0.950701	−	0.310110i	$-0.100366\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−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
$436$		−	14.0243i		−	0.671645i
$437$	−5.33140	−	3.07809i	−0.255036	−	0.147245i
$438$	4.01281	+	6.95039i	0.191739	+	0.332102i
$439$	16.5054	−	28.5881i	0.787758	−	1.36444i	−0.139579	−	0.990211i	$-0.544575\pi$
$439$	16.5054	−	28.5881i	0.787758	−	1.36444i	0.927337	−	0.374227i	$-0.122092\pi$
$440$	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	0.560566	−	0.828110i	$-0.310584\pi$
$443$	−9.19529	−	15.9267i	−0.436881	−	0.756700i	−0.997447	+	0.0714094i	$0.977250\pi$
$444$		−	6.87272i		−	0.326165i
$445$	−26.1114			−1.23780
$446$	−1.68204			−0.0796469
$447$		−	15.5957i		−	0.737650i
$448$	−0.521966	−	2.59375i	−0.0246606	−	0.122543i
$449$	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
$451$	4.40088	+	7.62255i	0.207230	+	0.358932i
$452$	−10.1705			−0.478382
$453$	6.39071	+	3.68968i	0.300262	+	0.173356i
$454$	−6.35545			−0.298276
$455$	10.6406	+	26.5422i	0.498838	+	1.24432i
$456$	2.95984			0.138607
$457$	23.5102	+	13.5736i	1.09976	+	0.634948i	0.936158	−	0.351579i	$-0.114355\pi$
$457$	23.5102	+	13.5736i	1.09976	+	0.634948i	0.163603	+	0.986526i	$0.447688\pi$
$458$	17.7915			0.831343
$459$	−1.17033	−	2.02707i	−0.0546262	−	0.0946153i
$460$	−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	$0.815517\pi$
$462$	1.94688	+	0.656023i	0.0905773	+	0.0305210i
$463$		−	10.1358i		−	0.471050i	−0.971868	−	0.235525i	$-0.924319\pi$
$463$		−	10.1358i		−	0.471050i	0.971868	−	0.235525i	$-0.0756810\pi$
$464$	−1.08226			−0.0502427
$465$	−21.8751			−1.01444
$466$			11.6806i			0.541091i
$467$	20.3375	+	35.2256i	0.941106	+	1.63004i	0.763365	+	0.645967i	$0.223546\pi$
$467$	20.3375	+	35.2256i	0.941106	+	1.63004i	0.177741	+	0.984077i	$0.443121\pi$
$468$	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
$471$	−12.3079	+	21.3179i	−0.567119	+	0.982278i
$472$	1.89590	+	3.28379i	0.0872658	+	0.151149i
$473$	−3.56082	−	2.05584i	−0.163727	−	0.0945276i
$474$			2.98902i			0.137290i
$475$	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
$478$	4.08876	−	7.08194i	0.187016	−	0.323920i
$479$			19.0666i			0.871175i	0.900146	+	0.435588i	$0.143459\pi$
$479$			19.0666i			0.871175i	−0.900146	+	0.435588i	$0.856541\pi$
$480$	1.49882	−	2.59603i	0.0684115	−	0.118492i
$481$	−16.0825	−	18.8520i	−0.733300	−	0.859578i
$482$	−28.9685			−1.31948
$483$	−5.21481	−	1.75719i	−0.237282	−	0.0799547i
$484$	5.19852	+	9.00410i	0.236296	+	0.409277i
$485$	8.49064			0.385540
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	−26.1114	+	15.0754i	−1.18322	+	0.683132i	−0.956757	−	0.290888i	$-0.906049\pi$
$487$	−26.1114	+	15.0754i	−1.18322	+	0.683132i	−0.226462	+	0.974020i	$0.572716\pi$
$488$		−	13.3750i		−	0.605457i
$489$		−	11.2102i		−	0.506942i
$490$	19.3501	−	8.11672i	0.874148	−	0.366676i
$491$	−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	$0.876171\pi$
$492$	9.81648	+	5.66755i	0.442561	+	0.255513i
$493$	1.26660	−	2.19382i	0.0570448	−	0.0988045i
$494$	8.11889	−	6.92617i	0.365286	−	0.311623i
$495$	1.16384	+	2.01584i	0.0523109	+	0.0906051i
$496$	6.31977	−	3.64872i	0.283766	−	0.163833i
$497$	3.48033	−	10.3286i	0.156114	−	0.463302i
$498$	−2.12662	+	3.68342i	−0.0952962	+	0.165058i
$499$	1.61575	−	0.932853i	0.0723309	−	0.0417602i	−0.463398	−	0.886150i	$-0.653370\pi$
$499$	1.61575	−	0.932853i	0.0723309	−	0.0417602i	0.535729	+	0.844390i	$0.320037\pi$
$500$	−2.63275	+	1.52002i	−0.117740	+	0.0679772i
$501$	−10.8485	+	6.26340i	−0.484677	+	0.279828i
$502$	−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	$0.257157\pi$
$504$	2.59375	−	0.521966i	0.115535	−	0.0232502i
$505$	−30.1420	+	17.4025i	−1.34130	+	0.774400i
$506$	0.807528	+	1.39868i	0.0358990	+	0.0621789i
$507$	10.0935	+	8.19270i	0.448270	+	0.363851i
$508$	−1.07357	+	1.85948i	−0.0476321	+	0.0825011i
$509$	0.557089	+	0.321635i	0.0246925	+	0.0142562i	0.512295	−	0.858809i	$-0.328795\pi$
$509$	0.557089	+	0.321635i	0.0246925	+	0.0142562i	−0.487603	+	0.873066i	$0.662129\pi$
$510$	3.50822	+	6.07642i	0.155347	+	0.269068i
$511$	6.78037	−	20.1221i	0.299946	−	0.890151i
$512$			1.00000i			0.0441942i
$513$			2.95984i			0.130680i
$514$	8.33708	−	4.81342i	0.367733	−	0.212311i
$515$	19.0373	+	10.9912i	0.838885	+	0.484330i
$516$	−5.29511			−0.233104
$517$	3.29549	+	5.70795i	0.144935	+	0.251035i
$518$	−13.6442	+	12.0198i	−0.599493	+	0.528119i
$519$	−6.54063			−0.287102
$520$	−1.96356	−	10.6283i	−0.0861077	−	0.466081i
$521$	15.8436	−	27.4419i	0.694119	−	1.20225i	−0.276358	−	0.961055i	$-0.589127\pi$
$521$	15.8436	−	27.4419i	0.694119	−	1.20225i	0.970477	−	0.241195i	$-0.0775393\pi$
$522$		−	1.08226i		−	0.0473693i
$523$	22.0710	−	38.2282i	0.965099	−	1.67160i	0.255750	−	0.966743i	$-0.417678\pi$
$523$	22.0710	−	38.2282i	0.965099	−	1.67160i	0.709349	−	0.704857i	$-0.248989\pi$
$524$	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
$527$			17.0808i			0.744051i
$528$	−0.672474	−	0.388253i	−0.0292657	−	0.0168965i
$529$	9.33700	+	16.1722i	0.405957	+	0.703137i
$530$	−6.90652	+	11.9624i	−0.300000	+	0.519615i
$531$	−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
$535$			32.7329i			1.41517i
$536$	−5.34483			−0.230861
$537$	18.4489			0.796127
$538$			21.6142i			0.931854i
$539$	−2.10255	−	5.01242i	−0.0905631	−	0.215900i
$540$	2.59603	+	1.49882i	0.111716	+	0.0644990i
$541$	36.3256	−	20.9726i	1.56176	−	0.901682i	0.564680	−	0.825310i	$-0.309000\pi$
$541$	36.3256	−	20.9726i	1.56176	−	0.901682i	0.997079	−	0.0763720i	$-0.0243337\pi$
$542$	0.649732	+	1.12537i	0.0279084	+	0.0483388i
$543$	−14.7886			−0.634641
$544$	−2.02707	−	1.17033i	−0.0869097	−	0.0501774i
$545$	−42.0400			−1.80079
$546$	5.89329	−	7.50128i	0.252209	−	0.321025i
$547$	18.9477			0.810144			0.405072	−	0.914285i	$-0.367246\pi$
$547$	18.9477			0.810144			0.405072	+	0.914285i	$0.367246\pi$
$548$	−15.6998	−	9.06426i	−0.670661	−	0.387206i
$549$	13.3750			0.570831
$550$	−1.54752	−	2.68038i	−0.0659865	−	0.114292i
$551$	−2.77415	+	1.60166i	−0.118183	+	0.0682329i
$552$	1.80125	+	1.03995i	0.0766663	+	0.0442633i
$553$	5.93401	−	5.22753i	0.252340	−	0.222297i
$554$		−	22.3327i		−	0.948826i
$555$	−20.6020			−0.874504
$556$	−20.5193			−0.870213
$557$		−	18.0617i		−	0.765298i	−0.923894	−	0.382649i	$-0.875012\pi$
$557$		−	18.0617i		−	0.765298i	0.923894	−	0.382649i	$-0.124988\pi$
$558$	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
$562$	−14.5940	+	25.2776i	−0.615612	+	1.06627i
$563$	9.79575	+	16.9667i	0.412842	+	0.715063i	0.995199	−	0.0978699i	$-0.0312029\pi$
$563$	9.79575	+	16.9667i	0.412842	+	0.715063i	−0.582357	+	0.812933i	$0.697870\pi$
$564$	7.35082	+	4.24400i	0.309525	+	0.178705i
$565$			30.4876i			1.28262i
$566$	−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
$569$	−18.3621	+	31.8041i	−0.769778	+	1.33330i	0.167905	+	0.985803i	$0.446300\pi$
$569$	−18.3621	+	31.8041i	−0.769778	+	1.33330i	−0.937683	+	0.347492i	$0.887033\pi$
$570$		−	8.87253i		−	0.371629i
$571$	4.17869	−	7.23770i	0.174873	−	0.302888i	−0.765245	−	0.643740i	$-0.777382\pi$
$571$	4.17869	−	7.23770i	0.174873	−	0.302888i	0.940117	+	0.340851i	$0.110715\pi$
$572$	−2.75314	+	0.508637i	−0.115115	+	0.0212672i
$573$	−6.53314			−0.272926
$574$	−5.91654	−	29.4004i	−0.246951	−	1.22715i
$575$	4.14510	+	7.17952i	0.172863	+	0.299407i
$576$	−1.00000			−0.0416667
$577$	−2.78965	−	1.61060i	−0.116135	−	0.0670503i	0.440808	−	0.897602i	$-0.354692\pi$
$577$	−2.78965	−	1.61060i	−0.116135	−	0.0670503i	−0.556942	+	0.830551i	$0.688025\pi$
$578$	−9.97777	+	5.76067i	−0.415021	+	0.239612i
$579$		−	5.37118i		−	0.223219i
$580$			3.24423i			0.134709i
$581$	11.0319	−	2.22005i	0.457679	−	0.0921032i
$582$	−1.41622	−	2.45297i	−0.0587042	−	0.101679i
$583$	3.09874	+	1.78906i	0.128337	+	0.0740951i
$584$	−4.01281	+	6.95039i	−0.166051	+	0.287609i
$585$	10.6283	−	1.96356i	0.439426	−	0.0811831i
$586$	−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	$0.228356\pi$
$588$	−5.57249	−	4.23643i	−0.229806	−	0.174708i
$589$	10.7996	−	18.7055i	0.444991	−	0.770746i
$590$	9.84363	−	5.68322i	0.405256	−	0.233975i
$591$	16.4198	−	9.47999i	0.675421	−	0.389955i
$592$	5.95195	−	3.43636i	0.244624	−	0.141234i
$593$	−17.1904	+	9.92487i	−0.705924	+	0.407565i	−0.809550	−	0.587051i	$-0.800289\pi$
$593$	−17.1904	+	9.92487i	−0.705924	+	0.407565i	0.103626	+	0.994616i	$0.466955\pi$
$594$	0.388253	−	0.672474i	0.0159302	−	0.0275919i
$595$	5.92777	−	17.5919i	0.243015	−	0.721197i
$596$	13.5062	−	7.79784i	0.553238	−	0.319412i
$597$	4.10524	+	7.11048i	0.168016	+	0.291013i
$598$	7.37440	−	1.36241i	0.301562	−	0.0557130i
$599$	13.2573	−	22.9622i	0.541677	−	0.938212i	−0.457131	−	0.889399i	$-0.651123\pi$
$599$	13.2573	−	22.9622i	0.541677	−	0.938212i	0.998808	−	0.0488126i	$-0.0155437\pi$
$600$	−3.45185	−	1.99293i	−0.140921	−	0.0813610i
$601$	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	$0.765921\pi$
$602$	9.26067	+	10.5122i	0.377437	+	0.428446i
$603$		−	5.34483i		−	0.217658i
$604$			7.37936i			0.300262i
$605$	26.9911	−	15.5833i	1.09734	−	0.633551i
$606$	10.0552	+	5.80539i	0.408466	+	0.235828i
$607$	−28.0621			−1.13901			−0.569503	−	0.821989i	$-0.692864\pi$
$607$	−28.0621			−1.13901			−0.569503	+	0.821989i	$0.692864\pi$
$608$	1.47992	+	2.56329i	0.0600186	+	0.103955i
$609$	−2.14858	+	1.89278i	−0.0870650	+	0.0766993i
$610$	−40.0934			−1.62334
$611$	30.0946	−	5.55992i	1.21750	−	0.224930i
$612$	1.17033	−	2.02707i	0.0473077	−	0.0819393i
$613$			30.0502i			1.21372i	0.794810	+	0.606859i	$0.207571\pi$
$613$			30.0502i			1.21372i	−0.794810	+	0.606859i	$0.792429\pi$
$614$	13.1258	−	22.7346i	0.529716	−	0.917495i
$615$	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	$0.758630\pi$
$618$		−	7.33323i		−	0.294986i
$619$	15.5989	+	9.00602i	0.626972	+	0.361982i	0.779578	−	0.626305i	$-0.215433\pi$
$619$	15.5989	+	9.00602i	0.626972	+	0.361982i	−0.152606	+	0.988287i	$0.548767\pi$
$620$	−10.9376	−	18.9444i	−0.439263	−	0.760826i
$621$	−1.03995	+	1.80125i	−0.0417318	+	0.0722816i
$622$	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
$626$		−	17.3382i		−	0.692974i
$627$	−2.29833			−0.0917864
$628$	−24.6158			−0.982278
$629$			16.0867i			0.641417i
$630$	−1.56467	−	7.77514i	−0.0623379	−	0.309769i
$631$	−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
$633$	−5.39098	−	9.33746i	−0.214272	−	0.371131i
$634$	−3.13650			−0.124566
$635$	5.57406	+	3.21818i	0.221200	+	0.127710i
$636$	4.60797			0.182718
$637$	−25.1989	+	1.41929i	−0.998418	+	0.0562344i
$638$	0.840382			0.0332710
$639$	−3.56761	−	2.05976i	−0.141132	−	0.0814828i
$640$	2.99764			0.118492
$641$	2.93631	+	5.08583i	0.115977	+	0.200878i	0.918170	−	0.396187i	$-0.129667\pi$
$641$	2.93631	+	5.08583i	0.115977	+	0.200878i	−0.802193	+	0.597065i	$0.796333\pi$
$642$	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	$0.965205\pi$
$644$	−1.08564	−	5.39475i	−0.0427802	−	0.212583i
$645$			15.8728i			0.624992i
$646$	−6.92795			−0.272577
$647$	17.6983			0.695792			0.347896	−	0.937533i	$-0.386896\pi$
$647$	17.6983			0.695792			0.347896	+	0.937533i	$0.386896\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−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
$653$	8.95446	−	15.5096i	0.350415	−	0.606937i	−0.635907	−	0.771766i	$-0.719374\pi$
$653$	8.95446	−	15.5096i	0.350415	−	0.606937i	0.986322	+	0.164829i	$0.0527072\pi$
$654$	7.01217	+	12.1454i	0.274198	+	0.474924i
$655$	−48.7890	−	28.1683i	−1.90634	−	1.10063i
$656$			11.3351i			0.442561i
$657$	−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	$0.237426\pi$
$660$	−1.16384	+	2.01584i	−0.0453025	+	0.0784663i
$661$			36.7766i			1.43044i	0.698897	+	0.715222i	$0.253675\pi$
$661$			36.7766i			1.43044i	−0.698897	+	0.715222i	$0.746325\pi$
$662$	−1.92095	+	3.32718i	−0.0746599	+	0.129315i
$663$	−1.53321	−	8.29891i	−0.0595448	−	0.322303i
$664$	−4.25324			−0.165058
$665$	−17.6144	+	15.5173i	−0.683057	+	0.601734i
$666$	3.43636	+	5.95195i	0.133156	+	0.230633i
$667$	−2.25100			−0.0871590
$668$	−10.8485	−	6.26340i	−0.419742	−	0.242338i
$669$	1.45669	−	0.841020i	0.0563189	−	0.0325157i
$670$			16.0219i			0.618979i
$671$			10.3858i			0.400938i
$672$	1.74891	+	1.98527i	0.0674657	+	0.0765835i
$673$	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	$0.658062\pi$
$674$	−8.67627	−	5.00924i	−0.334197	−	0.192949i
$675$	1.99293	−	3.45185i	0.0767079	−	0.132862i
$676$	−2.04832	+	12.8376i	−0.0787815	+	0.493754i
$677$	−0.817780	−	1.41644i	−0.0314298	−	0.0544381i	0.849883	−	0.526972i	$-0.176673\pi$
$677$	−0.817780	−	1.41644i	−0.0314298	−	0.0544381i	−0.881312	+	0.472534i	$0.843339\pi$
$678$	8.80794	−	5.08527i	0.338267	−	0.195299i
$679$	−2.39296	+	7.10160i	−0.0918334	+	0.272535i
$680$	−3.50822	+	6.07642i	−0.134534	+	0.233020i
$681$	5.50398	−	3.17772i	0.210913	−	0.121771i
$682$	−4.90734	+	2.83325i	−0.187912	+	0.108491i
$683$	7.57914	−	4.37582i	0.290008	−	0.167436i	−0.347938	−	0.937518i	$-0.613118\pi$
$683$	7.57914	−	4.37582i	0.290008	−	0.167436i	0.637945	+	0.770082i	$0.279785\pi$
$684$	−2.56329	+	1.47992i	−0.0980100	+	0.0565861i
$685$	−27.1714	+	47.0623i	−1.03817	+	1.79816i
$686$	1.33532	+	18.4721i	0.0509829	+	0.705266i
$687$	−15.4079	+	8.89576i	−0.587848	+	0.339394i
$688$	−2.64755	−	4.58570i	−0.100937	−	0.174828i
$689$	12.6397	−	10.7829i	0.481536	−	0.410795i
$690$	3.11740	−	5.39950i	0.118678	−	0.205555i
$691$	35.4566	+	20.4709i	1.34883	+	0.778750i	0.988084	−	0.153913i	$-0.0491875\pi$
$691$	35.4566	+	20.4709i	1.34883	+	0.778750i	0.360750	+	0.932663i	$0.382521\pi$
$692$	−3.27031	−	5.66435i	−0.124319	−	0.215326i
$693$	−2.01406	+	0.405310i	−0.0765079	+	0.0153964i
$694$		−	17.6846i		−	0.671298i
$695$			61.5096i			2.33319i
$696$	0.937266	−	0.541131i	0.0355270	−	0.0205115i
$697$	−22.9770	−	13.2658i	−0.870315	−	0.502477i
$698$	13.0397			0.493559
$699$	−5.84028	−	10.1157i	−0.220900	−	0.382609i
$700$	2.08048	+	10.3383i	0.0786349	+	0.390752i
$701$	38.9126			1.46971			0.734854	−	0.678225i	$-0.237251\pi$
$701$	38.9126			1.46971			0.734854	+	0.678225i	$0.237251\pi$
$702$	−2.34005	−	2.74302i	−0.0883195	−	0.103529i
$703$	10.1711	−	17.6168i	0.383609	−	0.664430i
$704$		−	0.776506i		−	0.0292657i
$705$	12.7220	−	22.0351i	0.479138	−	0.829891i
$706$	−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
$709$		−	6.32654i		−	0.237598i	−0.992918	−	0.118799i	$-0.962096\pi$
$709$		−	6.32654i		−	0.237598i	0.992918	−	0.118799i	$-0.0379044\pi$
$710$	10.6944	+	6.17442i	0.401354	+	0.231722i
$711$	−1.49451	−	2.58856i	−0.0560484	−	0.0970787i
$712$	−4.35532	+	7.54364i	−0.163223	+	0.282710i
$713$	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
$717$			8.17752i			0.305395i
$718$	1.12935			0.0421470
$719$	2.32239			0.0866107			0.0433053	−	0.999062i	$-0.486211\pi$
$719$	2.32239			0.0866107			0.0433053	+	0.999062i	$0.486211\pi$
$720$			2.99764i			0.111716i
$721$	−14.5585	+	12.8252i	−0.542186	+	0.477635i
$722$	−8.86756	−	5.11969i	−0.330016	−	0.190535i
$723$	25.0874	−	14.4842i	0.933012	−	0.538675i
$724$	−7.39432	−	12.8073i	−0.274808	−	0.475981i
$725$	4.31374			0.160208
$726$	−9.00410	−	5.19852i	−0.334173	−	0.192935i
$727$	−2.78916			−0.103444			−0.0517221	−	0.998662i	$-0.516471\pi$
$727$	−2.78916			−0.103444			−0.0517221	+	0.998662i	$0.516471\pi$
$728$	9.44294	+	1.35310i	0.349979	+	0.0501492i
$729$	1.00000			0.0370370
$730$	20.8348	+	12.0290i	0.771130	+	0.445212i
$731$	12.3940			0.458409
$732$	6.68750	+	11.5831i	0.247177	+	0.428123i
$733$	−37.7543	+	21.7974i	−1.39449	+	0.805107i	−0.993808	−	0.111112i	$-0.964559\pi$
$733$	−37.7543	+	21.7974i	−1.39449	+	0.805107i	−0.400678	+	0.916219i	$0.631225\pi$
$734$	17.3573	+	10.0213i	0.640671	+	0.369892i
$735$	−12.6993	+	16.7043i	−0.468421	+	0.616149i
$736$			2.07990i			0.0766663i
$737$	4.15029			0.152878
$738$	−11.3351			−0.417251
$739$		−	40.6924i		−	1.49689i	−0.663194	−	0.748447i	$-0.730800\pi$
$739$		−	40.6924i		−	1.49689i	0.663194	−	0.748447i	$-0.269200\pi$
$740$	−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	$0.537065\pi$
$744$	−3.64872	+	6.31977i	−0.133769	+	0.231694i
$745$	−23.3751	−	40.4869i	−0.856398	−	1.48333i
$746$	0.929168	+	0.536455i	0.0340193	+	0.0196410i
$747$		−	4.25324i		−	0.155618i
$748$	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
$751$	17.9506	−	31.0913i	0.655025	−	1.13454i	−0.326863	−	0.945072i	$-0.605991\pi$
$751$	17.9506	−	31.0913i	0.655025	−	1.13454i	0.981888	−	0.189465i	$-0.0606752\pi$
$752$			8.48799i			0.309525i
$753$	3.11086	−	5.38817i	0.113366	−	0.196356i
$754$	1.30467	−	3.67758i	0.0475131	−	0.133930i
$755$	22.1207			0.805054
$756$	−1.98527	+	1.74891i	−0.0722037	+	0.0636073i
$757$	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	$0.618337\pi$
$758$	−6.90133			−0.250668
$759$	−1.39868	−	0.807528i	−0.0507689	−	0.0293114i
$760$	7.68383	−	4.43626i	0.278722	−	0.160920i
$761$			11.2214i			0.406775i	0.979098	+	0.203388i	$0.0651952\pi$
$761$			11.2214i			0.406775i	−0.979098	+	0.203388i	$0.934805\pi$
$762$		−	2.14714i		−	0.0777828i
$763$	11.8483	−	35.1624i	0.428939	−	1.27296i
$764$	−3.26657	−	5.65786i	−0.118180	−	0.204694i
$765$	−6.07642	−	3.50822i	−0.219693	−	0.126840i
$766$	15.7740	−	27.3214i	0.569938	−	0.987161i
$767$	−13.4440	+	2.48375i	−0.485435	+	0.0896832i
$768$	−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	$0.228256\pi$
$770$	6.03744	−	1.21497i	0.217574	−	0.0437846i
$771$	−4.81342	+	8.33708i	−0.173351	+	0.300253i
$772$	4.65158	−	2.68559i	0.167414	−	0.0966565i
$773$	17.8831	−	10.3248i	0.643210	−	0.371358i	−0.142640	−	0.989775i	$-0.545559\pi$
$773$	17.8831	−	10.3248i	0.643210	−	0.371358i	0.785850	+	0.618417i	$0.212226\pi$
$774$	4.58570	−	2.64755i	0.164829	−	0.0951643i
$775$	−25.1897	+	14.5433i	−0.904842	+	0.522411i
$776$	1.41622	−	2.45297i	0.0508393	−	0.0880563i
$777$	5.80635	−	17.2316i	0.208302	−	0.618178i
$778$	0.938937	−	0.542096i	0.0336625	−	0.0194351i
$779$	16.7750	+	29.0552i	0.601027	+	1.04101i
$780$	7.01464	+	8.22259i	0.251164	+	0.294416i
$781$	1.59941	−	2.77027i	0.0572315	−	0.0991279i
$782$	−4.21610	−	2.43417i	−0.150767	−	0.0870456i
$783$	0.541131	+	0.937266i	0.0193384	+	0.0334951i
$784$	0.882613	−	6.94413i	0.0315219	−	0.248005i
$785$			73.7894i			2.63366i
$786$			18.7937i			0.670348i
$787$	34.8016	−	20.0927i	1.24054	−	0.716229i	0.271339	−	0.962484i	$-0.412533\pi$
$787$	34.8016	−	20.0927i	1.24054	−	0.716229i	0.969205	+	0.246255i	$0.0792001\pi$
$788$	16.4198	+	9.47999i	0.584932	+	0.337711i
$789$	2.97000			0.105735
$790$	4.48000	+	7.75959i	0.159391	+	0.276074i
$791$	−25.5000	−	8.59248i	−0.906674	−	0.305513i
$792$	0.776506			0.0275919
$793$	45.4489	+	16.1235i	1.61394	+	0.572564i
$794$	9.58307	−	16.5984i	0.340090	−	0.589054i
$795$		−	13.8130i		−	0.489898i
$796$	−4.10524	+	7.11048i	−0.145506	+	0.252024i
$797$	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
$800$		−	3.98586i		−	0.140921i
$801$	−7.54364	−	4.35532i	−0.266541	−	0.153888i
$802$	15.0189	+	26.0135i	0.530337	+	0.918570i
$803$	3.11597	−	5.39702i	0.109960	−	0.190457i
$804$	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
$808$			11.6108i			0.408466i
$809$	31.2685			1.09934			0.549670	−	0.835382i	$-0.314753\pi$
$809$	31.2685			1.09934			0.549670	+	0.835382i	$0.314753\pi$
$810$	−2.99764			−0.105326
$811$		−	25.5332i		−	0.896592i	−0.893885	−	0.448296i	$-0.852031\pi$
$811$		−	25.5332i		−	0.896592i	0.893885	−	0.448296i	$-0.147969\pi$
$812$	−2.71349	−	0.914338i	−0.0952247	−	0.0320870i
$813$	−1.12537	−	0.649732i	−0.0394684	−	0.0227871i
$814$	−4.62172	+	2.66835i	−0.161991	+	0.0935257i
$815$	−16.8021	−	29.1020i	−0.588550	−	1.01940i
$816$	2.34065			0.0819393
$817$	−13.5729	−	7.83632i	−0.474856	−	0.274158i
$818$	−3.88182			−0.135725
$819$	−1.35310	+	9.44294i	−0.0472811	+	0.329963i
$820$	33.9786			1.18658
$821$	9.33912	+	5.39194i	0.325937	+	0.188180i	0.654036	−	0.756463i	$-0.273074\pi$
$821$	9.33912	+	5.39194i	0.325937	+	0.188180i	−0.328099	+	0.944643i	$0.606408\pi$
$822$	18.1285			0.632305
$823$	−7.07773	−	12.2590i	−0.246714	−	0.427321i	0.715898	−	0.698205i	$-0.246018\pi$
$823$	−7.07773	−	12.2590i	−0.246714	−	0.427321i	−0.962612	+	0.270884i	$0.912684\pi$
$824$	6.35077	−	3.66662i	0.221239	−	0.127733i
$825$	2.68038	+	1.54752i	0.0933190	+	0.0538778i
$826$	1.97919	+	9.83498i	0.0688648	+	0.342203i
$827$		−	36.2823i		−	1.26166i	−0.775921	−	0.630830i	$-0.782714\pi$
$827$		−	36.2823i		−	1.26166i	0.775921	−	0.630830i	$-0.217286\pi$
$828$	−2.07990			−0.0722816
$829$	13.4831			0.468288			0.234144	−	0.972202i	$-0.424771\pi$
$829$	13.4831			0.468288			0.234144	+	0.972202i	$0.424771\pi$
$830$			12.7497i			0.442549i
$831$	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
$835$	−18.7754	+	32.5200i	−0.649751	+	1.12540i
$836$	−1.14916	−	1.99041i	−0.0397447	−	0.0688398i
$837$	−6.31977	−	3.64872i	−0.218443	−	0.126118i
$838$			34.2619i			1.18356i
$839$	−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
$842$	−1.88890	+	3.27168i	−0.0650959	+	0.112749i
$843$		−	29.1881i		−	1.00529i
$844$	5.39098	−	9.33746i	0.185565	−	0.321409i
$845$	38.4826	+	6.14013i	1.32384	+	0.211227i
$846$	−8.48799			−0.291823
$847$	5.42690	+	26.9673i	0.186471	+	0.926609i
$848$	2.30398	+	3.99062i	0.0791191	+	0.137038i
$849$	31.2577			1.07276
$850$	8.07960	+	4.66476i	0.277128	+	0.160000i
$851$	12.3795	−	7.14730i	0.424363	−	0.245006i
$852$		−	4.11952i		−	0.141132i
$853$		−	30.2641i		−	1.03622i	−0.855313	−	0.518111i	$-0.826635\pi$
$853$		−	30.2641i		−	1.03622i	0.855313	−	0.518111i	$-0.173365\pi$
$854$	11.2997	−	33.5343i	0.386669	−	1.14752i
$855$	4.43626	+	7.68383i	0.151717	+	0.262782i
$856$	9.45661	+	5.45978i	0.323220	+	0.186611i
$857$	−18.2018	+	31.5265i	−0.621763	+	1.07693i	0.367394	+	0.930065i	$0.380250\pi$
$857$	−18.2018	+	31.5265i	−0.621763	+	1.07693i	−0.989157	+	0.146860i	$0.953083\pi$
$858$	2.12997	−	1.81706i	0.0727160	−	0.0620335i
$859$	−23.0720	−	39.9618i	−0.787205	−	1.36348i	−0.927673	−	0.373395i	$-0.878194\pi$
$859$	−23.0720	−	39.9618i	−0.787205	−	1.36348i	0.140467	−	0.990085i	$-0.455140\pi$
$860$	−13.7463	+	7.93642i	−0.468744	+	0.270630i
$861$	19.8241	+	22.5033i	0.675603	+	0.766909i
$862$	−6.43806	+	11.1510i	−0.219281	+	0.379806i
$863$	−27.1825	+	15.6938i	−0.925302	+	0.534223i	−0.885323	−	0.464977i	$-0.846062\pi$
$863$	−27.1825	+	15.6938i	−0.925302	+	0.534223i	−0.0399790	+	0.999201i	$0.512729\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	−16.9797	+	9.80323i	−0.577327	+	0.333320i
$866$	4.41144	−	2.54694i	0.149907	−	0.0865487i
$867$	5.76067	−	9.97777i	0.195643	−	0.338863i
$868$	18.9278	−	3.80902i	0.642450	−	0.129287i
$869$	2.01003	−	1.16049i	0.0681857	−	0.0393671i
$870$	−1.62212	−	2.80959i	−0.0549949	−	0.0952539i
$871$	6.44319	−	18.1620i	0.218319	−	0.615396i
$872$	−7.01217	+	12.1454i	−0.237462	+	0.411297i
$873$	2.45297	+	1.41622i	0.0830203	+	0.0479318i
$874$	3.07809	+	5.33140i	0.104118	+	0.180337i
$875$	−7.88509	+	1.58679i	−0.266565	+	0.0536434i
$876$		−	8.02562i		−	0.271161i
$877$			43.1522i			1.45715i	0.684968	+	0.728574i	$0.259816\pi$
$877$			43.1522i			1.45715i	−0.684968	+	0.728574i	$0.740184\pi$
$878$	−28.5881	+	16.5054i	−0.964803	+	0.557029i
$879$	22.9743	+	13.2642i	0.774902	+	0.447390i
$880$	−2.32769			−0.0784663
$881$	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	$0.635847\pi$
$882$	6.94413	+	0.882613i	0.233821	+	0.0297191i
$883$	11.1929			0.376671			0.188336	−	0.982105i	$-0.439691\pi$
$883$	11.1929			0.376671			0.188336	+	0.982105i	$0.439691\pi$
$884$	6.42046	−	5.47725i	0.215943	−	0.184220i
$885$	−5.68322	+	9.84363i	−0.191039	+	0.330890i
$886$			18.3906i			0.617843i
$887$	24.5172	−	42.4651i	0.823208	−	1.42584i	−0.0800736	−	0.996789i	$-0.525516\pi$
$887$	24.5172	−	42.4651i	0.823208	−	1.42584i	0.903281	−	0.429049i	$-0.141151\pi$
$888$	−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
$891$			0.776506i			0.0260139i
$892$	1.45669	+	0.841020i	0.0487736	+	0.0281594i
$893$	12.5615	+	21.7572i	0.420356	+	0.728077i
$894$	−7.79784	+	13.5062i	−0.260799	+	0.451717i
$895$	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
$899$		−	7.89775i		−	0.263405i
$900$	3.98586			0.132862
$901$	−10.7857			−0.359322
$902$		−	8.80177i		−	0.293067i
$903$	−13.2761	−	4.47352i	−0.441801	−	0.148869i
$904$	8.80794	+	5.08527i	0.292948	+	0.169133i
$905$	−38.3918	+	22.1655i	−1.27619	+	0.736807i
$906$	−3.68968	−	6.39071i	−0.122581	−	0.212317i
$907$	−41.8205			−1.38863			−0.694314	−	0.719672i	$-0.744292\pi$
$907$	−41.8205			−1.38863			−0.694314	+	0.719672i	$0.744292\pi$
$908$	5.50398	+	3.17772i	0.182656	+	0.105457i
$909$	−11.6108			−0.385105
$910$	4.05610	−	28.3066i	0.134459	−	0.938353i
$911$	7.19793			0.238478			0.119239	−	0.992866i	$-0.461955\pi$
$911$	7.19793			0.238478			0.119239	+	0.992866i	$0.461955\pi$
$912$	−2.56329	−	1.47992i	−0.0848791	−	0.0490050i
$913$	3.30267			0.109302
$914$	−13.5736	−	23.5102i	−0.448976	−	0.777649i
$915$	34.7219	−	20.0467i	1.14787	−	0.662724i
$916$	−15.4079	−	8.89576i	−0.509092	−	0.293924i
$917$	37.3105	−	32.8685i	1.23210	−	1.08541i
$918$			2.34065i			0.0772531i
$919$	−28.2156			−0.930747			−0.465373	−	0.885114i	$-0.654080\pi$
$919$	−28.2156			−0.930747			−0.465373	+	0.885114i	$0.654080\pi$
$920$	6.23481			0.205555
$921$			26.2517i			0.865023i
$922$	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
$926$	−5.06790	+	8.77785i	−0.166541	+	0.288458i
$927$	3.66662	+	6.35077i	0.120427	+	0.208587i
$928$	0.937266	+	0.541131i	0.0307673	+	0.0177635i
$929$		−	17.4840i		−	0.573631i	−0.957986	−	0.286816i	$-0.907403\pi$
$929$		−	17.4840i		−	0.573631i	0.957986	−	0.286816i	$-0.0925967\pi$
$930$	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
$933$	−14.7394	+	25.5294i	−0.482547	+	0.835795i
$934$		−	40.6750i		−	1.33093i
$935$	2.72415	−	4.71837i	0.0890894	−	0.154307i
$936$	1.20550	−	3.39805i	0.0394030	−	0.111069i
$937$	−43.3168			−1.41510			−0.707549	−	0.706664i	$-0.750199\pi$
$937$	−43.3168			−1.41510			−0.707549	+	0.706664i	$0.750199\pi$
$938$	−13.4008	−	4.51553i	−0.437550	−	0.147437i
$939$	8.66910	+	15.0153i	0.282906	+	0.490007i
$940$	25.4440			0.829891
$941$	24.7292	+	14.2774i	0.806150	+	0.465431i	0.845617	−	0.533790i	$-0.179233\pi$
$941$	24.7292	+	14.2774i	0.806150	+	0.465431i	−0.0394670	+	0.999221i	$0.512566\pi$
$942$	21.3179	−	12.3079i	0.694575	−	0.401013i
$943$			23.5759i			0.767737i
$944$		−	3.79180i		−	0.123412i
$945$	5.24261	+	5.95114i	0.170542	+	0.193590i
$946$	2.05584	+	3.56082i	0.0668411	+	0.115772i
$947$	−42.9473	−	24.7956i	−1.39560	−	0.805750i	−0.401672	−	0.915783i	$-0.631571\pi$
$947$	−42.9473	−	24.7956i	−1.39560	−	0.805750i	−0.993928	+	0.110033i	$0.964904\pi$
$948$	1.49451	−	2.58856i	0.0485394	−	0.0840726i
$949$	−18.7804	−	22.0144i	−0.609636	−	0.714619i
$950$	−5.89874	−	10.2169i	−0.191380	−	0.331481i
$951$	2.71629	−	1.56825i	0.0880818	−	0.0508540i
$952$	−4.09360	−	4.64684i	−0.132674	−	0.150605i
$953$	−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
$955$	−16.9602	+	9.79200i	−0.548821	+	0.316862i
$956$	−7.08194	+	4.08876i	−0.229046	+	0.132240i
$957$	−0.727792	+	0.420191i	−0.0235262	+	0.0135828i
$958$	9.53330	−	16.5122i	0.308007	−	0.533484i
$959$	−31.7052	−	35.9901i	−1.02381	−	1.16218i
$960$	−2.59603	+	1.49882i	−0.0837866	+	0.0483742i
$961$	11.1264	+	19.2714i	0.358915	+	0.621659i
$962$	4.50186	+	24.3676i	0.145146	+	0.785642i
$963$	−5.45978	+	9.45661i	−0.175939	+	0.304735i
$964$	25.0874	+	14.4842i	0.808012	+	0.466506i
$965$	−8.05044	−	13.9438i	−0.259153	−	0.448866i
$966$	3.63757	+	4.12918i	0.117037	+	0.132854i
$967$			24.6124i			0.791481i	0.918362	+	0.395741i	$0.129512\pi$
$967$			24.6124i			0.791481i	−0.918362	+	0.395741i	$0.870488\pi$
$968$		−	10.3970i		−	0.334173i
$969$	5.99978	−	3.46398i	0.192741	−	0.111279i
$970$	−7.35311	−	4.24532i	−0.236094	−	0.136309i
$971$	−45.3540			−1.45548			−0.727740	−	0.685853i	$-0.759429\pi$
$971$	−45.3540			−1.45548			−0.727740	+	0.685853i	$0.759429\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−51.4468	−	17.3355i	−1.64931	−	0.555752i
$974$	30.1508			0.966095
$975$	10.9333	−	9.32711i	0.350146	−	0.298707i
$976$	−6.68750	+	11.5831i	−0.214062	+	0.370765i
$977$			7.00873i			0.224229i	0.993695	+	0.112115i	$0.0357624\pi$
$977$			7.00873i			0.224229i	−0.993695	+	0.112115i	$0.964238\pi$
$978$	−5.60509	+	9.70830i	−0.179231	+	0.310437i
$979$	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
$982$			5.94607i			0.189747i
$983$	40.9972	+	23.6698i	1.30761	+	0.754948i	0.981697	−	0.190452i	$-0.0609954\pi$
$983$	40.9972	+	23.6698i	1.30761	+	0.754948i	0.325912	+	0.945400i	$0.394329\pi$
$984$	−5.66755	−	9.81648i	−0.180675	−	0.312938i
$985$	28.4176	−	49.2207i	0.905460	−	1.56830i
$986$	−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
$990$		−	2.32769i		−	0.0739787i
$991$	−29.3301			−0.931701			−0.465850	−	0.884863i	$-0.654252\pi$
$991$	−29.3301			−0.931701			−0.465850	+	0.884863i	$0.654252\pi$
$992$	−7.29745			−0.231694
$993$		−	3.84190i		−	0.121919i
$994$	−8.17836	+	7.20467i	−0.259402	+	0.228518i
$995$	21.3147	+	12.3060i	0.675721	+	0.390128i
$996$	3.68342	−	2.12662i	0.116714	−	0.0673846i
$997$	3.74685	+	6.48974i	0.118664	+	0.205532i	0.919238	−	0.393701i	$-0.128806\pi$
$997$	3.74685	+	6.48974i	0.118664	+	0.205532i	−0.800574	+	0.599233i	$0.795472\pi$
$998$	−1.86571			−0.0590579
$999$	−5.95195	−	3.43636i	−0.188311	−	0.108722i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.b.121.5	✓	20	91.30	even	6	inner
546.2.bd.b.361.5	yes	20	1.1	even	1	trivial
546.2.bm.b.205.6	yes	20	7.2	even	3
546.2.bm.b.277.1	yes	20	13.4	even	6
1638.2.cr.b.361.6		20	3.2	odd	2
1638.2.cr.b.667.6		20	273.212	odd	6
1638.2.dt.b.1297.5		20	21.2	odd	6
1638.2.dt.b.1369.10		20	39.17	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.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(2.59603 - 1.49882i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.521966 + 2.59375i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(2.59603 - 1.49882i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.521966 + 2.59375i) q^{7} -1.00000i q^{8} +1.00000 q^{9} -2.99764 q^{10} +0.776506i 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} +(-0.500000 + 0.866025i) q^{16} +(-1.17033 - 2.02707i) q^{17} +(-0.866025 - 0.500000i) q^{18} +2.95984i q^{19} +(2.59603 + 1.49882i) q^{20} +(0.521966 + 2.59375i) q^{21} +(0.388253 - 0.672474i) q^{22} +(-1.03995 + 1.80125i) q^{23} -1.00000i q^{24} +(1.99293 - 3.45185i) q^{25} +(-2.34005 - 2.74302i) q^{26} +1.00000 q^{27} +(-1.98527 + 1.74891i) q^{28} +(0.541131 + 0.937266i) q^{29} -2.99764 q^{30} +(-6.31977 - 3.64872i) q^{31} +(0.866025 - 0.500000i) q^{32} +0.776506i q^{33} +2.34065i q^{34} +(5.24261 + 5.95114i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-5.95195 - 3.43636i) q^{37} +(1.47992 - 2.56329i) q^{38} +(3.39805 + 1.20550i) q^{39} +(-1.49882 - 2.59603i) q^{40} +(9.81648 - 5.66755i) q^{41} +(0.844840 - 2.50724i) q^{42} +(-2.64755 + 4.58570i) q^{43} +(-0.672474 + 0.388253i) q^{44} +(2.59603 - 1.49882i) q^{45} +(1.80125 - 1.03995i) q^{46} +(7.35082 - 4.24400i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-6.45510 + 2.70770i) q^{49} +(-3.45185 + 1.99293i) q^{50} +(-1.17033 - 2.02707i) q^{51} +(0.655034 + 3.54555i) q^{52} +(2.30398 - 3.99062i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(1.16384 + 2.01584i) q^{55} +(2.59375 - 0.521966i) q^{56} +2.95984i q^{57} -1.08226i q^{58} +(-3.28379 + 1.89590i) q^{59} +(2.59603 + 1.49882i) q^{60} +13.3750 q^{61} +(3.64872 + 6.31977i) q^{62} +(0.521966 + 2.59375i) q^{63} -1.00000 q^{64} +(10.6283 - 1.96356i) q^{65} +(0.388253 - 0.672474i) q^{66} -5.34483i q^{67} +(1.17033 - 2.02707i) q^{68} +(-1.03995 + 1.80125i) q^{69} +(-1.56467 - 7.77514i) q^{70} +(-3.56761 - 2.05976i) q^{71} -1.00000i q^{72} +(-6.95039 - 4.01281i) q^{73} +(3.43636 + 5.95195i) q^{74} +(1.99293 - 3.45185i) 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} +2.99764i q^{80} +1.00000 q^{81} -11.3351 q^{82} -4.25324i q^{83} +(-1.98527 + 1.74891i) q^{84} +(-6.07642 - 3.50822i) q^{85} +(4.58570 - 2.64755i) q^{86} +(0.541131 + 0.937266i) q^{87} +0.776506 q^{88} +(-7.54364 - 4.35532i) q^{89} -2.99764 q^{90} +(-1.35310 + 9.44294i) q^{91} -2.07990 q^{92} +(-6.31977 - 3.64872i) q^{93} -8.48799 q^{94} +(4.43626 + 7.68383i) q^{95} +(0.866025 - 0.500000i) q^{96} +(2.45297 + 1.41622i) q^{97} +(6.94413 + 0.882613i) q^{98} +0.776506i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9}+O(q^{10}) \) 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9	\( 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9} - 8 q^{10} + 10 q^{12} + 8 q^{13} + 4 q^{14} - 10 q^{16} + 4 q^{17} - 6 q^{21} - 10 q^{22} + 8 q^{23} + 6 q^{25} + 2 q^{26} + 20 q^{27} - 6 q^{28} + 8 q^{29} - 8 q^{30} - 12 q^{31} + 4 q^{35} + 10 q^{36} + 6 q^{38} + 8 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} + 18 q^{43} + 6 q^{44} - 24 q^{46} + 6 q^{47} - 10 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} - 2 q^{52} + 18 q^{53} - 12 q^{55} + 2 q^{56} + 36 q^{59} + 12 q^{61} - 6 q^{63} - 20 q^{64} - 10 q^{66} - 4 q^{68} + 8 q^{69} - 42 q^{70} - 6 q^{71} - 24 q^{73} - 18 q^{74} + 6 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} + 20 q^{81} - 36 q^{82} - 6 q^{84} + 36 q^{86} + 8 q^{87} - 20 q^{88} + 18 q^{89} - 8 q^{90} - 94 q^{91} + 16 q^{92} - 12 q^{93} + 32 q^{94} + 40 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) \) 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9 - 8 * q^10 + 10 * q^12 + 8 * q^13 + 4 * q^14 - 10 * q^16 + 4 * q^17 - 6 * q^21 - 10 * q^22 + 8 * q^23 + 6 * q^25 + 2 * q^26 + 20 * q^27 - 6 * q^28 + 8 * q^29 - 8 * q^30 - 12 * q^31 + 4 * q^35 + 10 * q^36 + 6 * q^38 + 8 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 + 18 * q^43 + 6 * q^44 - 24 * q^46 + 6 * q^47 - 10 * q^48 + 4 * q^49 + 12 * q^50 + 4 * q^51 - 2 * q^52 + 18 * q^53 - 12 * q^55 + 2 * q^56 + 36 * q^59 + 12 * q^61 - 6 * q^63 - 20 * q^64 - 10 * q^66 - 4 * q^68 + 8 * q^69 - 42 * q^70 - 6 * q^71 - 24 * q^73 - 18 * q^74 + 6 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 + 20 * q^81 - 36 * q^82 - 6 * q^84 + 36 * q^86 + 8 * q^87 - 20 * q^88 + 18 * q^89 - 8 * q^90 - 94 * q^91 + 16 * q^92 - 12 * q^93 + 32 * q^94 + 40 * q^95 - 96 * q^97 - 12 * q^98

Introduction

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