LMFDB - Embedded newform 546.2.bd.a.121.8

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 26x^{14} + 249x^{12} + 1144x^{10} + 2766x^{8} + 3554x^{6} + 2260x^{4} + 564x^{2} + 9 $ x^16 + 26x^14 + 249x^12 + 1144x^10 + 2766x^8 + 3554x^6 + 2260x^4 + 564*x^2 + 9
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			121.8
Root			$-1.75225i$ of defining polynomial
Character	$\chi$	$=$	546.121
Dual form			546.2.bd.a.361.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(2.81905 + 1.62758i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(1.08335 + 2.41379i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(2.81905 + 1.62758i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(1.08335 + 2.41379i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +3.25515 q^{10} +2.29234i q^{11} +(-0.500000 + 0.866025i) q^{12} +(-3.57283 - 0.484638i) q^{13} +(2.14510 + 1.54873i) q^{14} +(-2.81905 - 1.62758i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.391489 + 0.678079i) q^{17} +(0.866025 - 0.500000i) q^{18} +5.18398i q^{19} +(2.81905 - 1.62758i) q^{20} +(-1.08335 - 2.41379i) q^{21} +(1.14617 + 1.98522i) q^{22} +(0.162861 + 0.282083i) q^{23} +1.00000i q^{24} +(2.79801 + 4.84630i) q^{25} +(-3.33648 + 1.36671i) q^{26} -1.00000 q^{27} +(2.63207 + 0.268687i) q^{28} +(3.35386 - 5.80906i) q^{29} -3.25515 q^{30} +(5.69921 - 3.29044i) q^{31} +(-0.866025 - 0.500000i) q^{32} -2.29234i q^{33} +0.782978i q^{34} +(-0.874616 + 8.56780i) q^{35} +(0.500000 - 0.866025i) q^{36} +(9.20750 - 5.31595i) q^{37} +(2.59199 + 4.48946i) q^{38} +(3.57283 + 0.484638i) q^{39} +(1.62758 - 2.81905i) q^{40} +(-0.818943 - 0.472817i) q^{41} +(-2.14510 - 1.54873i) q^{42} +(-4.81185 - 8.33436i) q^{43} +(1.98522 + 1.14617i) q^{44} +(2.81905 + 1.62758i) q^{45} +(0.282083 + 0.162861i) q^{46} +(2.14659 + 1.23934i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-4.65272 + 5.22993i) q^{49} +(4.84630 + 2.79801i) q^{50} +(0.391489 - 0.678079i) q^{51} +(-2.20612 + 2.85184i) q^{52} +(-6.83920 - 11.8458i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-3.73096 + 6.46221i) q^{55} +(2.41379 - 1.08335i) q^{56} -5.18398i q^{57} -6.70773i q^{58} +(0.531942 + 0.307117i) q^{59} +(-2.81905 + 1.62758i) q^{60} +0.228227 q^{61} +(3.29044 - 5.69921i) q^{62} +(1.08335 + 2.41379i) q^{63} -1.00000 q^{64} +(-9.28319 - 7.18128i) q^{65} +(-1.14617 - 1.98522i) q^{66} +9.21123i q^{67} +(0.391489 + 0.678079i) q^{68} +(-0.162861 - 0.282083i) q^{69} +(3.52646 + 7.85724i) q^{70} +(-12.7983 + 7.38911i) q^{71} -1.00000i q^{72} +(11.6734 - 6.73964i) q^{73} +(5.31595 - 9.20750i) q^{74} +(-2.79801 - 4.84630i) q^{75} +(4.48946 + 2.59199i) q^{76} +(-5.53321 + 2.48340i) q^{77} +(3.33648 - 1.36671i) q^{78} +(0.650337 - 1.12642i) q^{79} -3.25515i q^{80} +1.00000 q^{81} -0.945634 q^{82} +7.46409i q^{83} +(-2.63207 - 0.268687i) q^{84} +(-2.20725 + 1.27436i) q^{85} +(-8.33436 - 4.81185i) q^{86} +(-3.35386 + 5.80906i) q^{87} +2.29234 q^{88} +(-7.85187 + 4.53328i) q^{89} +3.25515 q^{90} +(-2.70080 - 9.14908i) q^{91} +0.325722 q^{92} +(-5.69921 + 3.29044i) q^{93} +2.47867 q^{94} +(-8.43733 + 14.6139i) q^{95} +(0.866025 + 0.500000i) q^{96} +(-4.59086 + 2.65054i) q^{97} +(-1.41441 + 6.85561i) q^{98} +2.29234i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9	$ 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9} - 8 q^{10} - 8 q^{12} - 10 q^{13} + 4 q^{14} - 8 q^{16} - 8 q^{21} + 6 q^{22} - 16 q^{23} + 2 q^{26} - 16 q^{27} + 10 q^{28} - 4 q^{29} + 8 q^{30} + 12 q^{31} + 16 q^{35} + 8 q^{36} + 30 q^{37} - 2 q^{38} + 10 q^{39} - 4 q^{40} - 18 q^{41} - 4 q^{42} - 32 q^{43} + 6 q^{44} + 12 q^{46} + 66 q^{47} + 8 q^{48} - 2 q^{49} + 36 q^{50} + 4 q^{52} + 2 q^{53} + 16 q^{55} + 2 q^{56} - 36 q^{59} - 8 q^{61} + 4 q^{62} + 8 q^{63} - 16 q^{64} - 28 q^{65} - 6 q^{66} + 16 q^{69} - 6 q^{70} - 30 q^{71} - 18 q^{73} + 6 q^{74} - 18 q^{76} - 34 q^{77} - 2 q^{78} - 24 q^{79} + 16 q^{81} - 12 q^{82} - 10 q^{84} + 72 q^{85} + 4 q^{87} + 12 q^{88} - 42 q^{89} - 8 q^{90} - 18 q^{91} - 32 q^{92} - 12 q^{93} + 48 q^{94} - 40 q^{95} - 6 q^{97} - 12 q^{98}+O(q^{100}) $ 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9 - 8 * q^10 - 8 * q^12 - 10 * q^13 + 4 * q^14 - 8 * q^16 - 8 * q^21 + 6 * q^22 - 16 * q^23 + 2 * q^26 - 16 * q^27 + 10 * q^28 - 4 * q^29 + 8 * q^30 + 12 * q^31 + 16 * q^35 + 8 * q^36 + 30 * q^37 - 2 * q^38 + 10 * q^39 - 4 * q^40 - 18 * q^41 - 4 * q^42 - 32 * q^43 + 6 * q^44 + 12 * q^46 + 66 * q^47 + 8 * q^48 - 2 * q^49 + 36 * q^50 + 4 * q^52 + 2 * q^53 + 16 * q^55 + 2 * q^56 - 36 * q^59 - 8 * q^61 + 4 * q^62 + 8 * q^63 - 16 * q^64 - 28 * q^65 - 6 * q^66 + 16 * q^69 - 6 * q^70 - 30 * q^71 - 18 * q^73 + 6 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 + 16 * q^81 - 12 * q^82 - 10 * q^84 + 72 * q^85 + 4 * q^87 + 12 * q^88 - 42 * q^89 - 8 * q^90 - 18 * q^91 - 32 * q^92 - 12 * q^93 + 48 * q^94 - 40 * q^95 - 6 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	2.81905	+	1.62758i	1.26072	+	0.727875i	0.973213	−	0.229905i	$-0.0738416\pi$
$5$	2.81905	+	1.62758i	1.26072	+	0.727875i	0.287503	+	0.957780i	$0.407175\pi$
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	1.08335	+	2.41379i	0.409467	+	0.912325i
$7$	1.08335	+	2.41379i	0.409467	+	0.912325i
$8$		−	1.00000i		−	0.353553i
$9$	1.00000			0.333333
$10$	3.25515			1.02937
$11$			2.29234i			0.691166i	0.938388	+	0.345583i	$0.112319\pi$
$11$			2.29234i			0.691166i	−0.938388	+	0.345583i	$0.887681\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−3.57283	−	0.484638i	−0.990925	−	0.134414i
$13$	−3.57283	−	0.484638i	−0.990925	−	0.134414i
$14$	2.14510	+	1.54873i	0.573302	+	0.413914i
$15$	−2.81905	−	1.62758i	−0.727875	−	0.420239i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.391489	+	0.678079i	−0.0949500	+	0.164458i	−0.909588	−	0.415512i	$-0.863602\pi$
$17$	−0.391489	+	0.678079i	−0.0949500	+	0.164458i	0.814638	+	0.579970i	$0.196936\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$			5.18398i			1.18929i	0.803990	+	0.594643i	$0.202707\pi$
$19$			5.18398i			1.18929i	−0.803990	+	0.594643i	$0.797293\pi$
$20$	2.81905	−	1.62758i	0.630358	−	0.363937i
$21$	−1.08335	−	2.41379i	−0.236406	−	0.526731i
$22$	1.14617	+	1.98522i	0.244364	+	0.423251i
$23$	0.162861	+	0.282083i	0.0339588	+	0.0588184i	0.882505	−	0.470302i	$-0.155855\pi$
$23$	0.162861	+	0.282083i	0.0339588	+	0.0588184i	−0.848546	+	0.529121i	$0.822522\pi$
$24$			1.00000i			0.204124i
$25$	2.79801	+	4.84630i	0.559603	+	0.969260i
$26$	−3.33648	+	1.36671i	−0.654338	+	0.268033i
$27$	−1.00000			−0.192450
$28$	2.63207	+	0.268687i	0.497415	+	0.0507770i
$29$	3.35386	−	5.80906i	0.622797	−	1.07872i	−0.366166	−	0.930550i	$-0.619330\pi$
$29$	3.35386	−	5.80906i	0.622797	−	1.07872i	0.988963	−	0.148166i	$-0.0473369\pi$
$30$	−3.25515			−0.594307
$31$	5.69921	−	3.29044i	1.02361	−	0.590980i	0.108461	−	0.994101i	$-0.465408\pi$
$31$	5.69921	−	3.29044i	1.02361	−	0.590980i	0.915147	+	0.403121i	$0.132075\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		−	2.29234i		−	0.399045i
$34$			0.782978i			0.134280i
$35$	−0.874616	+	8.56780i	−0.147837	+	1.44822i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	9.20750	−	5.31595i	1.51370	−	0.873937i	0.513832	−	0.857891i	$-0.328226\pi$
$37$	9.20750	−	5.31595i	1.51370	−	0.873937i	0.999871	−	0.0160459i	$-0.00510779\pi$
$38$	2.59199	+	4.48946i	0.420476	+	0.728286i
$39$	3.57283	+	0.484638i	0.572111	+	0.0776042i
$40$	1.62758	−	2.81905i	0.257343	−	0.445730i
$41$	−0.818943	−	0.472817i	−0.127897	−	0.0738416i	0.434686	−	0.900582i	$-0.356859\pi$
$41$	−0.818943	−	0.472817i	−0.127897	−	0.0738416i	−0.562584	+	0.826740i	$0.690193\pi$
$42$	−2.14510	−	1.54873i	−0.330996	−	0.238974i
$43$	−4.81185	−	8.33436i	−0.733800	−	1.27098i	−0.955248	−	0.295806i	$-0.904412\pi$
$43$	−4.81185	−	8.33436i	−0.733800	−	1.27098i	0.221448	−	0.975172i	$-0.428922\pi$
$44$	1.98522	+	1.14617i	0.299284	+	0.172791i
$45$	2.81905	+	1.62758i	0.420239	+	0.242625i
$46$	0.282083	+	0.162861i	0.0415909	+	0.0240125i
$47$	2.14659	+	1.23934i	0.313113	+	0.180776i	0.648319	−	0.761369i	$-0.275473\pi$
$47$	2.14659	+	1.23934i	0.313113	+	0.180776i	−0.335206	+	0.942145i	$0.608806\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−4.65272	+	5.22993i	−0.664674	+	0.747133i
$50$	4.84630	+	2.79801i	0.685371	+	0.395699i
$51$	0.391489	−	0.678079i	0.0548194	−	0.0949500i
$52$	−2.20612	+	2.85184i	−0.305934	+	0.395480i
$53$	−6.83920	−	11.8458i	−0.939437	−	1.62715i	−0.766525	−	0.642215i	$-0.778016\pi$
$53$	−6.83920	−	11.8458i	−0.939437	−	1.62715i	−0.172912	−	0.984937i	$-0.555318\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	−3.73096	+	6.46221i	−0.503082	+	0.871364i
$56$	2.41379	−	1.08335i	0.322556	−	0.144768i
$57$		−	5.18398i		−	0.686635i
$58$		−	6.70773i		−	0.880767i
$59$	0.531942	+	0.307117i	0.0692530	+	0.0399832i	0.534227	−	0.845341i	$-0.320603\pi$
$59$	0.531942	+	0.307117i	0.0692530	+	0.0399832i	−0.464974	+	0.885324i	$0.653936\pi$
$60$	−2.81905	+	1.62758i	−0.363937	+	0.210119i
$61$	0.228227			0.0292215			0.0146107	−	0.999893i	$-0.495349\pi$
$61$	0.228227			0.0292215			0.0146107	+	0.999893i	$0.495349\pi$
$62$	3.29044	−	5.69921i	0.417886	−	0.723800i
$63$	1.08335	+	2.41379i	0.136489	+	0.304108i
$64$	−1.00000			−0.125000
$65$	−9.28319	−	7.18128i	−1.15144	−	0.890728i
$66$	−1.14617	−	1.98522i	−0.141084	−	0.244364i
$67$			9.21123i			1.12533i	0.826685	+	0.562665i	$0.190224\pi$
$67$			9.21123i			1.12533i	−0.826685	+	0.562665i	$0.809776\pi$
$68$	0.391489	+	0.678079i	0.0474750	+	0.0822292i
$69$	−0.162861	−	0.282083i	−0.0196061	−	0.0339588i
$70$	3.52646	+	7.85724i	0.421493	+	0.939120i
$71$	−12.7983	+	7.38911i	−1.51888	+	0.876926i	−0.519127	+	0.854697i	$0.673743\pi$
$71$	−12.7983	+	7.38911i	−1.51888	+	0.876926i	−0.999753	+	0.0222287i	$0.992924\pi$
$72$		−	1.00000i		−	0.117851i
$73$	11.6734	−	6.73964i	1.36627	−	0.788815i	0.375819	−	0.926693i	$-0.377362\pi$
$73$	11.6734	−	6.73964i	1.36627	−	0.788815i	0.990449	+	0.137878i	$0.0440283\pi$
$74$	5.31595	−	9.20750i	0.617967	−	1.07035i
$75$	−2.79801	−	4.84630i	−0.323087	−	0.559603i
$76$	4.48946	+	2.59199i	0.514976	+	0.297322i
$77$	−5.53321	+	2.48340i	−0.630568	+	0.283009i
$78$	3.33648	−	1.36671i	0.377782	−	0.154749i
$79$	0.650337	−	1.12642i	0.0731687	−	0.126732i	−0.827120	−	0.562026i	$-0.810022\pi$
$79$	0.650337	−	1.12642i	0.0731687	−	0.126732i	0.900288	+	0.435294i	$0.143356\pi$
$80$		−	3.25515i		−	0.363937i
$81$	1.00000			0.111111
$82$	−0.945634			−0.104428
$83$			7.46409i			0.819290i	0.912245	+	0.409645i	$0.134347\pi$
$83$			7.46409i			0.819290i	−0.912245	+	0.409645i	$0.865653\pi$
$84$	−2.63207	−	0.268687i	−0.287183	−	0.0293161i
$85$	−2.20725	+	1.27436i	−0.239410	+	0.138223i
$86$	−8.33436	−	4.81185i	−0.898717	−	0.518875i
$87$	−3.35386	+	5.80906i	−0.359572	+	0.622797i
$88$	2.29234			0.244364
$89$	−7.85187	+	4.53328i	−0.832297	+	0.480527i	−0.854638	−	0.519224i	$-0.826221\pi$
$89$	−7.85187	+	4.53328i	−0.832297	+	0.480527i	0.0223418	+	0.999750i	$0.492888\pi$
$90$	3.25515			0.343123
$91$	−2.70080	−	9.14908i	−0.283121	−	0.959084i
$92$	0.325722			0.0339588
$93$	−5.69921	+	3.29044i	−0.590980	+	0.341203i
$94$	2.47867			0.255656
$95$	−8.43733	+	14.6139i	−0.865651	+	1.49935i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−4.59086	+	2.65054i	−0.466132	+	0.269121i	−0.714619	−	0.699514i	$-0.753400\pi$
$97$	−4.59086	+	2.65054i	−0.466132	+	0.269121i	0.248487	+	0.968635i	$0.420067\pi$
$98$	−1.41441	+	6.85561i	−0.142877	+	0.692522i
$99$			2.29234i			0.230389i
$100$	5.59603			0.559603
$101$	−7.33198			−0.729559			−0.364779	−	0.931094i	$-0.618856\pi$
$101$	−7.33198			−0.729559			−0.364779	+	0.931094i	$0.618856\pi$
$102$		−	0.782978i		−	0.0775264i
$103$	0.843858	−	1.46160i	0.0831478	−	0.144016i	−0.821453	−	0.570277i	$-0.806836\pi$
$103$	0.843858	−	1.46160i	0.0831478	−	0.144016i	0.904600	+	0.426261i	$0.140169\pi$
$104$	−0.484638	+	3.57283i	−0.0475227	+	0.350345i
$105$	0.874616	−	8.56780i	0.0853538	−	0.836132i
$106$	−11.8458	−	6.83920i	−1.15057	−	0.664282i
$107$	−8.69757	−	15.0646i	−0.840826	−	1.45635i	−0.889197	−	0.457524i	$-0.848736\pi$
$107$	−8.69757	−	15.0646i	−0.840826	−	1.45635i	0.0483713	−	0.998829i	$-0.484597\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	10.2681	−	5.92831i	0.983510	−	0.567829i	0.0801817	−	0.996780i	$-0.474450\pi$
$109$	10.2681	−	5.92831i	0.983510	−	0.567829i	0.903328	+	0.428951i	$0.141117\pi$
$110$			7.46191i			0.711465i
$111$	−9.20750	+	5.31595i	−0.873937	+	0.504568i
$112$	1.54873	−	2.14510i	0.146341	−	0.202693i
$113$	−8.01051	−	13.8746i	−0.753565	−	1.30521i	−0.946084	−	0.323920i	$-0.894999\pi$
$113$	−8.01051	−	13.8746i	−0.753565	−	1.30521i	0.192519	−	0.981293i	$-0.438334\pi$
$114$	−2.59199	−	4.48946i	−0.242762	−	0.420476i
$115$			1.06027i			0.0988711i
$116$	−3.35386	−	5.80906i	−0.311398	−	0.539358i
$117$	−3.57283	−	0.484638i	−0.330308	−	0.0448048i
$118$	0.614234			0.0565448
$119$	−2.06086	−	0.210376i	−0.188918	−	0.0192851i
$120$	−1.62758	+	2.81905i	−0.148577	+	0.257343i
$121$	5.74519			0.522290
$122$	0.197650	−	0.114113i	0.0178944	−	0.0103314i
$123$	0.818943	+	0.472817i	0.0738416	+	0.0426325i
$124$		−	6.58088i		−	0.590980i
$125$			1.94016i			0.173533i
$126$	2.14510	+	1.54873i	0.191101	+	0.137971i
$127$	0.284508	−	0.492782i	0.0252460	−	0.0437273i	−0.853126	−	0.521704i	$-0.825296\pi$
$127$	0.284508	−	0.492782i	0.0252460	−	0.0437273i	0.878372	+	0.477977i	$0.158630\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	4.81185	+	8.33436i	0.423659	+	0.733800i
$130$	−11.6301	−	1.57757i	−1.02003	−	0.138362i
$131$	4.12135	−	7.13838i	0.360084	−	0.623683i	−0.627891	−	0.778302i	$-0.716081\pi$
$131$	4.12135	−	7.13838i	0.360084	−	0.623683i	0.987974	+	0.154618i	$0.0494148\pi$
$132$	−1.98522	−	1.14617i	−0.172791	−	0.0997612i
$133$	−12.5130	+	5.61605i	−1.08502	+	0.486973i
$134$	4.60562	+	7.97716i	0.397865	+	0.689122i
$135$	−2.81905	−	1.62758i	−0.242625	−	0.140080i
$136$	0.678079	+	0.391489i	0.0581448	+	0.0335699i
$137$	−9.54214	−	5.50916i	−0.815240	−	0.470679i	0.0335320	−	0.999438i	$-0.489324\pi$
$137$	−9.54214	−	5.50916i	−0.815240	−	0.470679i	−0.848772	+	0.528758i	$0.822658\pi$
$138$	−0.282083	−	0.162861i	−0.0240125	−	0.0138636i
$139$	6.38785	+	11.0641i	0.541811	+	0.938444i	0.998800	+	0.0489716i	$0.0155944\pi$
$139$	6.38785	+	11.0641i	0.541811	+	0.938444i	−0.456989	+	0.889472i	$0.651072\pi$
$140$	6.98263	+	5.04134i	0.590140	+	0.426071i
$141$	−2.14659	−	1.23934i	−0.180776	−	0.104371i
$142$	−7.38911	+	12.7983i	−0.620080	+	1.07401i
$143$	1.11095	−	8.19014i	0.0929027	−	0.684894i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	18.9094	−	10.9173i	1.57034	−	0.906636i
$146$	6.73964	−	11.6734i	0.557776	−	0.966097i
$147$	4.65272	−	5.22993i	0.383750	−	0.431358i
$148$		−	10.6319i		−	0.873937i
$149$			11.8657i			0.972079i	0.873937	+	0.486040i	$0.161559\pi$
$149$			11.8657i			0.972079i	−0.873937	+	0.486040i	$0.838441\pi$
$150$	−4.84630	−	2.79801i	−0.395699	−	0.228457i
$151$	10.1344	−	5.85109i	0.824725	−	0.476155i	−0.0273184	−	0.999627i	$-0.508697\pi$
$151$	10.1344	−	5.85109i	0.824725	−	0.476155i	0.852043	+	0.523472i	$0.175363\pi$
$152$	5.18398			0.420476
$153$	−0.391489	+	0.678079i	−0.0316500	+	0.0548194i
$154$	−3.55020	+	4.91729i	−0.286083	+	0.396247i
$155$	21.4218			1.72064
$156$	2.20612	−	2.85184i	0.176631	−	0.228330i
$157$	−4.03718	−	6.99260i	−0.322202	−	0.558070i	0.658740	−	0.752371i	$-0.271090\pi$
$157$	−4.03718	−	6.99260i	−0.322202	−	0.558070i	−0.980942	+	0.194300i	$0.937756\pi$
$158$		−	1.30067i		−	0.103476i
$159$	6.83920	+	11.8458i	0.542384	+	0.939437i
$160$	−1.62758	−	2.81905i	−0.128671	−	0.222865i
$161$	−0.504454	+	0.698705i	−0.0397565	+	0.0550657i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$			0.826274i			0.0647188i	0.999476	+	0.0323594i	$0.0103021\pi$
$163$			0.826274i			0.0647188i	−0.999476	+	0.0323594i	$0.989698\pi$
$164$	−0.818943	+	0.472817i	−0.0639487	+	0.0369208i
$165$	3.73096	−	6.46221i	0.290455	−	0.503082i
$166$	3.73204	+	6.46409i	0.289663	+	0.501711i
$167$	4.67389	+	2.69847i	0.361676	+	0.208814i	0.669816	−	0.742527i	$-0.266373\pi$
$167$	4.67389	+	2.69847i	0.361676	+	0.208814i	−0.308140	+	0.951341i	$0.599706\pi$
$168$	−2.41379	+	1.08335i	−0.186228	+	0.0835820i
$169$	12.5303	+	3.46306i	0.963866	+	0.266389i
$170$	−1.27436	+	2.20725i	−0.0977387	+	0.169288i
$171$			5.18398i			0.396429i
$172$	−9.62369			−0.733800
$173$	13.5777			1.03229			0.516145	−	0.856501i	$-0.327367\pi$
$173$	13.5777			1.03229			0.516145	+	0.856501i	$0.327367\pi$
$174$			6.70773i			0.508511i
$175$	−8.66671	+	12.0040i	−0.655142	+	0.907419i
$176$	1.98522	−	1.14617i	0.149642	−	0.0863957i
$177$	−0.531942	−	0.307117i	−0.0399832	−	0.0230843i
$178$	−4.53328	+	7.85187i	−0.339784	+	0.588523i
$179$	−16.9385			−1.26604			−0.633020	−	0.774136i	$-0.718185\pi$
$179$	−16.9385			−1.26604			−0.633020	+	0.774136i	$0.718185\pi$
$180$	2.81905	−	1.62758i	0.210119	−	0.121312i
$181$	−12.8540			−0.955427			−0.477713	−	0.878516i	$-0.658534\pi$
$181$	−12.8540			−0.955427			−0.477713	+	0.878516i	$0.658534\pi$
$182$	−6.91350	−	6.57293i	−0.512463	−	0.487218i
$183$	−0.228227			−0.0168710
$184$	0.282083	−	0.162861i	0.0207955	−	0.0120063i
$185$	34.6085			2.54447
$186$	−3.29044	+	5.69921i	−0.241267	+	0.417886i
$187$	−1.55439	−	0.897425i	−0.113668	−	0.0656262i
$188$	2.14659	−	1.23934i	0.156556	−	0.0903879i
$189$	−1.08335	−	2.41379i	−0.0788019	−	0.175577i
$190$			16.8747i			1.22422i
$191$	−20.3228			−1.47051			−0.735253	−	0.677792i	$-0.762937\pi$
$191$	−20.3228			−1.47051			−0.735253	+	0.677792i	$0.762937\pi$
$192$	1.00000			0.0721688
$193$			19.6308i			1.41306i	0.707686	+	0.706528i	$0.249739\pi$
$193$			19.6308i			1.41306i	−0.707686	+	0.706528i	$0.750261\pi$
$194$	−2.65054	+	4.59086i	−0.190297	+	0.329605i
$195$	9.28319	+	7.18128i	0.664783	+	0.514262i
$196$	2.20290	+	6.64434i	0.157350	+	0.474596i
$197$	14.1302	+	8.15806i	1.00673	+	0.581238i	0.910233	−	0.414096i	$-0.135902\pi$
$197$	14.1302	+	8.15806i	1.00673	+	0.581238i	0.0964995	+	0.995333i	$0.469235\pi$
$198$	1.14617	+	1.98522i	0.0814547	+	0.141084i
$199$	−1.96397	+	3.40169i	−0.139222	+	0.241139i	−0.927202	−	0.374561i	$-0.877793\pi$
$199$	−1.96397	+	3.40169i	−0.139222	+	0.241139i	0.787980	+	0.615700i	$0.211127\pi$
$200$	4.84630	−	2.79801i	0.342685	−	0.197849i
$201$		−	9.21123i		−	0.649710i
$202$	−6.34968	+	3.66599i	−0.446762	+	0.257938i
$203$	17.6552	+	1.80228i	1.23915	+	0.126495i
$204$	−0.391489	−	0.678079i	−0.0274097	−	0.0474750i
$205$	−1.53909	−	2.66579i	−0.107495	−	0.186187i
$206$		−	1.68772i		−	0.117589i
$207$	0.162861	+	0.282083i	0.0113196	+	0.0196061i
$208$	1.36671	+	3.33648i	0.0947641	+	0.231343i
$209$	−11.8834			−0.821994
$210$	−3.52646	−	7.85724i	−0.243349	−	0.542201i
$211$	11.9378	−	20.6769i	0.821834	−	1.42346i	−0.0824812	−	0.996593i	$-0.526284\pi$
$211$	11.9378	−	20.6769i	0.821834	−	1.42346i	0.904315	−	0.426866i	$-0.140382\pi$
$212$	−13.6784			−0.939437
$213$	12.7983	−	7.38911i	0.876926	−	0.506293i
$214$	−15.0646	−	8.69757i	−1.02980	−	0.594554i
$215$		−	31.3266i		−	2.13646i
$216$			1.00000i			0.0680414i
$217$	14.1166	+	10.1920i	0.958299	+	0.691876i
$218$	5.92831	−	10.2681i	0.401516	−	0.695446i
$219$	−11.6734	+	6.73964i	−0.788815	+	0.455423i
$220$	3.73096	+	6.46221i	0.251541	+	0.435682i
$221$	1.72735	−	2.23293i	0.116194	−	0.150203i
$222$	−5.31595	+	9.20750i	−0.356783	+	0.617967i
$223$	−2.87194	−	1.65812i	−0.192319	−	0.111036i	0.400749	−	0.916188i	$-0.368750\pi$
$223$	−2.87194	−	1.65812i	−0.192319	−	0.111036i	−0.593068	+	0.805152i	$0.702083\pi$
$224$	0.268687	−	2.63207i	0.0179524	−	0.175863i
$225$	2.79801	+	4.84630i	0.186534	+	0.323087i
$226$	−13.8746	−	8.01051i	−0.922925	−	0.532851i
$227$	−9.52172	−	5.49737i	−0.631979	−	0.364873i	0.149539	−	0.988756i	$-0.452221\pi$
$227$	−9.52172	−	5.49737i	−0.631979	−	0.364873i	−0.781518	+	0.623883i	$0.785554\pi$
$228$	−4.48946	−	2.59199i	−0.297322	−	0.171659i
$229$	−20.2181	−	11.6729i	−1.33605	−	0.771368i	−0.349830	−	0.936813i	$-0.613760\pi$
$229$	−20.2181	−	11.6729i	−1.33605	−	0.771368i	−0.986219	+	0.165445i	$0.947094\pi$
$230$	0.530137	+	0.918225i	0.0349562	+	0.0605459i
$231$	5.53321	−	2.48340i	0.364059	−	0.163396i
$232$	−5.80906	−	3.35386i	−0.381384	−	0.220192i
$233$	−2.14547	+	3.71606i	−0.140554	+	0.243447i	−0.927705	−	0.373313i	$-0.878222\pi$
$233$	−2.14547	+	3.71606i	−0.140554	+	0.243447i	0.787151	+	0.616760i	$0.211555\pi$
$234$	−3.33648	+	1.36671i	−0.218113	+	0.0893444i
$235$	4.03423	+	6.98749i	0.263164	+	0.455814i
$236$	0.531942	−	0.307117i	0.0346265	−	0.0199916i
$237$	−0.650337	+	1.12642i	−0.0422440	+	0.0731687i
$238$	−1.88994	+	0.848237i	−0.122507	+	0.0549830i
$239$		−	5.59389i		−	0.361839i	−0.983498	−	0.180919i	$-0.942093\pi$
$239$		−	5.59389i		−	0.361839i	0.983498	−	0.180919i	$-0.0579073\pi$
$240$			3.25515i			0.210119i
$241$	25.3045	+	14.6096i	1.63001	+	0.941084i	0.984089	+	0.177677i	$0.0568582\pi$
$241$	25.3045	+	14.6096i	1.63001	+	0.941084i	0.645917	+	0.763408i	$0.276475\pi$
$242$	4.97548	−	2.87259i	0.319836	−	0.184657i
$243$	−1.00000			−0.0641500
$244$	0.114113	−	0.197650i	0.00730537	−	0.0126533i
$245$	−21.6283	+	7.17077i	−1.38178	+	0.458123i
$246$	0.945634			0.0602914
$247$	2.51235	−	18.5215i	0.159857	−	1.17849i
$248$	−3.29044	−	5.69921i	−0.208943	−	0.361900i
$249$		−	7.46409i		−	0.473017i
$250$	0.970080	+	1.68023i	0.0613533	+	0.106267i
$251$	6.12153	+	10.6028i	0.386388	+	0.669243i	0.991961	−	0.126547i	$-0.0403894\pi$
$251$	6.12153	+	10.6028i	0.386388	+	0.669243i	−0.605573	+	0.795790i	$0.707056\pi$
$252$	2.63207	+	0.268687i	0.165805	+	0.0169257i
$253$	−0.646630	+	0.373332i	−0.0406533	+	0.0234712i
$254$		−	0.569015i		−	0.0357032i
$255$	2.20725	−	1.27436i	0.138223	−	0.0798033i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.19956	+	3.80975i	0.137205	+	0.237646i	0.926438	−	0.376449i	$-0.122855\pi$
$257$	2.19956	+	3.80975i	0.137205	+	0.237646i	−0.789233	+	0.614094i	$0.789522\pi$
$258$	8.33436	+	4.81185i	0.518875	+	0.299572i
$259$	22.8065	+	16.4659i	1.41713	+	1.02314i
$260$	−10.8608	+	4.44884i	−0.673556	+	0.275905i
$261$	3.35386	−	5.80906i	0.207599	−	0.359572i
$262$		−	8.24269i		−	0.509235i
$263$	19.1407			1.18026			0.590132	−	0.807306i	$-0.299076\pi$
$263$	19.1407			1.18026			0.590132	+	0.807306i	$0.299076\pi$
$264$	−2.29234			−0.141084
$265$		−	44.5253i		−	2.73517i
$266$	−8.02856	+	11.1201i	−0.492263	+	0.681820i
$267$	7.85187	−	4.53328i	0.480527	−	0.277432i
$268$	7.97716	+	4.60562i	0.487283	+	0.281333i
$269$	−1.54715	+	2.67975i	−0.0943315	+	0.163387i	−0.909329	−	0.416077i	$-0.863405\pi$
$269$	−1.54715	+	2.67975i	−0.0943315	+	0.163387i	0.814998	+	0.579464i	$0.196738\pi$
$270$	−3.25515			−0.198102
$271$	−22.7861	+	13.1555i	−1.38415	+	0.799142i	−0.992648	−	0.121034i	$-0.961379\pi$
$271$	−22.7861	+	13.1555i	−1.38415	+	0.799142i	−0.391506	+	0.920176i	$0.628046\pi$
$272$	0.782978			0.0474750
$273$	2.70080	+	9.14908i	0.163460	+	0.553727i
$274$	−11.0183			−0.665641
$275$	−11.1094	+	6.41399i	−0.669920	+	0.386778i
$276$	−0.325722			−0.0196061
$277$	−5.59693	+	9.69416i	−0.336287	+	0.582466i	−0.983731	−	0.179647i	$-0.942504\pi$
$277$	−5.59693	+	9.69416i	−0.336287	+	0.582466i	0.647444	+	0.762113i	$0.275838\pi$
$278$	11.0641	+	6.38785i	0.663580	+	0.383118i
$279$	5.69921	−	3.29044i	0.341203	−	0.196993i
$280$	8.56780	+	0.874616i	0.512024	+	0.0522683i
$281$			1.85065i			0.110401i	0.998475	+	0.0552003i	$0.0175797\pi$
$281$			1.85065i			0.110401i	−0.998475	+	0.0552003i	$0.982420\pi$
$282$	−2.47867			−0.147603
$283$	−22.1646			−1.31755			−0.658774	−	0.752341i	$-0.728925\pi$
$283$	−22.1646			−1.31755			−0.658774	+	0.752341i	$0.728925\pi$
$284$			14.7782i			0.876926i
$285$	8.43733	−	14.6139i	0.499784	−	0.865651i
$286$	−3.13295	−	7.64834i	−0.185255	−	0.452256i
$287$	0.254079	−	2.48898i	0.0149978	−	0.146920i
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	8.19347	+	14.1915i	0.481969	+	0.834795i
$290$	10.9173	−	18.9094i	0.641088	−	1.11040i
$291$	4.59086	−	2.65054i	0.269121	−	0.155377i
$292$		−	13.4793i		−	0.788815i
$293$	−12.7197	+	7.34371i	−0.743091	+	0.429024i	−0.823192	−	0.567763i	$-0.807809\pi$
$293$	−12.7197	+	7.34371i	−0.743091	+	0.429024i	0.0801008	+	0.996787i	$0.474476\pi$
$294$	1.41441	−	6.85561i	0.0824898	−	0.399828i
$295$	0.999713	+	1.73155i	0.0582055	+	0.100815i
$296$	−5.31595	−	9.20750i	−0.308983	−	0.535175i
$297$		−	2.29234i		−	0.133015i
$298$	5.93287	+	10.2760i	0.343682	+	0.595275i
$299$	−0.445166	−	1.08676i	−0.0257446	−	0.0628492i
$300$	−5.59603			−0.323087
$301$	14.9045	−	20.6438i	0.859079	−	1.18989i
$302$	5.85109	−	10.1344i	0.336692	−	0.583168i
$303$	7.33198			0.421211
$304$	4.48946	−	2.59199i	0.257488	−	0.148661i
$305$	0.643382	+	0.371457i	0.0368400	+	0.0212696i
$306$			0.782978i			0.0447599i
$307$			1.73631i			0.0990965i	0.998772	+	0.0495483i	$0.0157782\pi$
$307$			1.73631i			0.0990965i	−0.998772	+	0.0495483i	$0.984222\pi$
$308$	−0.615920	+	6.03360i	−0.0350953	+	0.343796i
$309$	−0.843858	+	1.46160i	−0.0480054	+	0.0831478i
$310$	18.5518	−	10.7109i	1.05367	−	0.608337i
$311$	6.80544	+	11.7874i	0.385901	+	0.668400i	0.991894	−	0.127070i	$-0.0405572\pi$
$311$	6.80544	+	11.7874i	0.385901	+	0.668400i	−0.605993	+	0.795470i	$0.707224\pi$
$312$	0.484638	−	3.57283i	0.0274372	−	0.202272i
$313$	−6.42671	+	11.1314i	−0.363259	+	0.629184i	−0.988495	−	0.151252i	$-0.951669\pi$
$313$	−6.42671	+	11.1314i	−0.363259	+	0.629184i	0.625236	+	0.780436i	$0.285003\pi$
$314$	−6.99260	−	4.03718i	−0.394615	−	0.227831i
$315$	−0.874616	+	8.56780i	−0.0492790	+	0.482741i
$316$	−0.650337	−	1.12642i	−0.0365843	−	0.0633659i
$317$	8.10889	+	4.68167i	0.455441	+	0.262949i	0.710125	−	0.704075i	$-0.248638\pi$
$317$	8.10889	+	4.68167i	0.455441	+	0.262949i	−0.254685	+	0.967024i	$0.581972\pi$
$318$	11.8458	+	6.83920i	0.664282	+	0.383523i
$319$	13.3163	+	7.68819i	0.745571	+	0.430456i
$320$	−2.81905	−	1.62758i	−0.157589	−	0.0909843i
$321$	8.69757	+	15.0646i	0.485451	+	0.840826i
$322$	−0.0875171	+	0.857323i	−0.00487714	+	0.0477768i
$323$	−3.51515	−	2.02947i	−0.195588	−	0.112923i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−7.64813	−	18.6710i	−0.424242	−	1.03568i
$326$	0.413137	+	0.715574i	0.0228815	+	0.0396320i
$327$	−10.2681	+	5.92831i	−0.567829	+	0.327837i
$328$	−0.472817	+	0.818943i	−0.0261070	+	0.0452186i
$329$	−0.665986	+	6.52405i	−0.0367170	+	0.359682i
$330$		−	7.46191i		−	0.410765i
$331$		−	11.1475i		−	0.612722i	−0.951915	−	0.306361i	$-0.900889\pi$
$331$		−	11.1475i		−	0.612722i	0.951915	−	0.306361i	$-0.0991114\pi$
$332$	6.46409	+	3.73204i	0.354763	+	0.204823i
$333$	9.20750	−	5.31595i	0.504568	−	0.291312i
$334$	5.39694			0.295307
$335$	−14.9920	+	25.9669i	−0.819100	+	1.41872i
$336$	−1.54873	+	2.14510i	−0.0844899	+	0.117025i
$337$	7.91654			0.431241			0.215621	−	0.976477i	$-0.430823\pi$
$337$	7.91654			0.431241			0.215621	+	0.976477i	$0.430823\pi$
$338$	12.5830	−	3.26603i	0.684428	−	0.177648i
$339$	8.01051	+	13.8746i	0.435071	+	0.753565i
$340$			2.54871i			0.138223i
$341$	7.54279	+	13.0645i	0.408465	+	0.707483i
$342$	2.59199	+	4.48946i	0.140159	+	0.242762i
$343$	−17.6644	−	5.56483i	−0.953790	−	0.300473i
$344$	−8.33436	+	4.81185i	−0.449359	+	0.259437i
$345$		−	1.06027i		−	0.0570833i
$346$	11.7586	−	6.78883i	0.632146	−	0.364970i
$347$	13.0149	−	22.5425i	0.698676	−	1.21014i	−0.270250	−	0.962790i	$-0.587106\pi$
$347$	13.0149	−	22.5425i	0.698676	−	1.21014i	0.968926	−	0.247352i	$-0.0795605\pi$
$348$	3.35386	+	5.80906i	0.179786	+	0.311398i
$349$	−12.6350	−	7.29484i	−0.676338	−	0.390484i	0.122136	−	0.992513i	$-0.461026\pi$
$349$	−12.6350	−	7.29484i	−0.676338	−	0.390484i	−0.798474	+	0.602030i	$0.794359\pi$
$350$	−1.50358	+	14.7292i	−0.0803696	+	0.787306i
$351$	3.57283	+	0.484638i	0.190704	+	0.0258681i
$352$	1.14617	−	1.98522i	0.0610910	−	0.105813i
$353$		−	10.6644i		−	0.567608i	−0.958882	−	0.283804i	$-0.908403\pi$
$353$		−	10.6644i		−	0.567608i	0.958882	−	0.283804i	$-0.0915966\pi$
$354$	−0.614234			−0.0326462
$355$	−48.1054			−2.55317
$356$			9.06656i			0.480527i
$357$	2.06086	+	0.210376i	0.109072	+	0.0111343i
$358$	−14.6691	+	8.46923i	−0.775288	+	0.447613i
$359$	14.9165	+	8.61207i	0.787265	+	0.454527i	0.838999	−	0.544133i	$-0.183141\pi$
$359$	14.9165	+	8.61207i	0.787265	+	0.454527i	−0.0517340	+	0.998661i	$0.516475\pi$
$360$	1.62758	−	2.81905i	0.0857808	−	0.148577i
$361$	−7.87365			−0.414402
$362$	−11.1318	+	6.42698i	−0.585077	+	0.337794i
$363$	−5.74519			−0.301544
$364$	−9.27374	−	2.23558i	−0.486076	−	0.117176i
$365$	43.8771			2.29663
$366$	−0.197650	+	0.114113i	−0.0103314	+	0.00596481i
$367$	17.1206			0.893690			0.446845	−	0.894611i	$-0.352547\pi$
$367$	17.1206			0.893690			0.446845	+	0.894611i	$0.352547\pi$
$368$	0.162861	−	0.282083i	0.00848971	−	0.0147046i
$369$	−0.818943	−	0.472817i	−0.0426325	−	0.0246139i
$370$	29.9718	−	17.3042i	1.55816	−	0.899604i
$371$	21.1841	−	29.3415i	1.09982	−	1.52334i
$372$			6.58088i			0.341203i
$373$	12.6004			0.652425			0.326213	−	0.945296i	$-0.394227\pi$
$373$	12.6004			0.652425			0.326213	+	0.945296i	$0.394227\pi$
$374$	−1.79485			−0.0928095
$375$		−	1.94016i		−	0.100189i
$376$	1.23934	−	2.14659i	0.0639139	−	0.110702i
$377$	−14.7981	+	19.1294i	−0.762140	+	0.985213i
$378$	−2.14510	−	1.54873i	−0.110332	−	0.0796579i
$379$	−3.10736	−	1.79403i	−0.159614	−	0.0921533i	0.418065	−	0.908417i	$-0.362708\pi$
$379$	−3.10736	−	1.79403i	−0.159614	−	0.0921533i	−0.577680	+	0.816264i	$0.696042\pi$
$380$	8.43733	+	14.6139i	0.432826	+	0.749676i
$381$	−0.284508	+	0.492782i	−0.0145758	+	0.0252460i
$382$	−17.6001	+	10.1614i	−0.900498	+	0.519903i
$383$		−	18.1845i		−	0.929185i	−0.885525	−	0.464593i	$-0.846201\pi$
$383$		−	18.1845i		−	0.929185i	0.885525	−	0.464593i	$-0.153799\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	−19.6403	−	2.00492i	−1.00096	−	0.102180i
$386$	9.81539	+	17.0008i	0.499590	+	0.865316i
$387$	−4.81185	−	8.33436i	−0.244600	−	0.423659i
$388$			5.30107i			0.269121i
$389$	13.6907	+	23.7131i	0.694148	+	1.20230i	0.970467	+	0.241234i	$0.0775522\pi$
$389$	13.6907	+	23.7131i	0.694148	+	1.20230i	−0.276319	+	0.961066i	$0.589115\pi$
$390$	11.6301	+	1.57757i	0.588914	+	0.0798835i
$391$	−0.255033			−0.0128976
$392$	5.22993	+	4.65272i	0.264152	+	0.234998i
$393$	−4.12135	+	7.13838i	−0.207894	+	0.360084i
$394$	16.3161			0.821994
$395$	3.66666	−	2.11695i	0.184490	−	0.106515i
$396$	1.98522	+	1.14617i	0.0997612	+	0.0575972i
$397$		−	16.8660i		−	0.846479i	−0.906018	−	0.423240i	$-0.860893\pi$
$397$		−	16.8660i		−	0.846479i	0.906018	−	0.423240i	$-0.139107\pi$
$398$			3.92793i			0.196890i
$399$	12.5130	−	5.61605i	0.626434	−	0.281154i
$400$	2.79801	−	4.84630i	0.139901	−	0.242315i
$401$	16.1890	−	9.34671i	0.808439	−	0.466753i	−0.0379744	−	0.999279i	$-0.512091\pi$
$401$	16.1890	−	9.34671i	0.808439	−	0.466753i	0.846414	+	0.532526i	$0.178757\pi$
$402$	−4.60562	−	7.97716i	−0.229707	−	0.397865i
$403$	−21.9570	+	8.99413i	−1.09375	+	0.448029i
$404$	−3.66599	+	6.34968i	−0.182390	+	0.315908i
$405$	2.81905	+	1.62758i	0.140080	+	0.0808750i
$406$	16.1910	−	7.26679i	0.803546	−	0.360645i
$407$	12.1860	+	21.1067i	0.604035	+	1.04622i
$408$	−0.678079	−	0.391489i	−0.0335699	−	0.0193816i
$409$	4.28358	+	2.47313i	0.211810	+	0.122288i	0.602152	−	0.798381i	$-0.294310\pi$
$409$	4.28358	+	2.47313i	0.211810	+	0.122288i	−0.390343	+	0.920670i	$0.627643\pi$
$410$	−2.66579	−	1.53909i	−0.131654	−	0.0760104i
$411$	9.54214	+	5.50916i	0.470679	+	0.271747i
$412$	−0.843858	−	1.46160i	−0.0415739	−	0.0720081i
$413$	−0.165036	+	1.61671i	−0.00812091	+	0.0795530i
$414$	0.282083	+	0.162861i	0.0138636	+	0.00800417i
$415$	−12.1484	+	21.0416i	−0.596341	+	1.03289i
$416$	2.85184	+	2.20612i	0.139823	+	0.108164i
$417$	−6.38785	−	11.0641i	−0.312815	−	0.541811i
$418$	−10.2914	+	5.94172i	−0.503367	+	0.290619i
$419$	−5.70131	+	9.87496i	−0.278527	+	0.482423i	−0.971019	−	0.239002i	$-0.923180\pi$
$419$	−5.70131	+	9.87496i	−0.278527	+	0.482423i	0.692492	+	0.721426i	$0.256513\pi$
$420$	−6.98263	−	5.04134i	−0.340717	−	0.245992i
$421$		−	9.82089i		−	0.478641i	−0.970941	−	0.239320i	$-0.923075\pi$
$421$		−	9.82089i		−	0.478641i	0.970941	−	0.239320i	$-0.0769247\pi$
$422$		−	23.8757i		−	1.16225i
$423$	2.14659	+	1.23934i	0.104371	+	0.0602586i
$424$	−11.8458	+	6.83920i	−0.575285	+	0.332141i
$425$	−4.38157			−0.212537
$426$	7.38911	−	12.7983i	0.358003	−	0.620080i
$427$	0.247249	+	0.550891i	0.0119652	+	0.0266595i
$428$	−17.3951			−0.840826
$429$	−1.11095	+	8.19014i	−0.0536374	+	0.395424i
$430$	−15.6633	−	27.1296i	−0.755351	−	1.30831i
$431$			8.61461i			0.414951i	0.978240	+	0.207476i	$0.0665247\pi$
$431$			8.61461i			0.414951i	−0.978240	+	0.207476i	$0.933475\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−11.7293	−	20.3157i	−0.563673	−	0.976310i	−0.997172	−	0.0751557i	$-0.976055\pi$
$433$	−11.7293	−	20.3157i	−0.563673	−	0.976310i	0.433499	−	0.901154i	$-0.357279\pi$
$434$	17.3213	+	1.76819i	0.831451	+	0.0848760i
$435$	−18.9094	+	10.9173i	−0.906636	+	0.523446i
$436$		−	11.8566i		−	0.567829i
$437$	−1.46231	+	0.844267i	−0.0699520	+	0.0403868i
$438$	−6.73964	+	11.6734i	−0.322032	+	0.557776i
$439$	18.6742	+	32.3447i	0.891272	+	1.54373i	0.838352	+	0.545129i	$0.183519\pi$
$439$	18.6742	+	32.3447i	0.891272	+	1.54373i	0.0529196	+	0.998599i	$0.483147\pi$
$440$	6.46221	+	3.73096i	0.308074	+	0.177866i
$441$	−4.65272	+	5.22993i	−0.221558	+	0.249044i
$442$	0.379461	−	2.79745i	0.0180491	−	0.133061i
$443$	−9.57652	+	16.5870i	−0.454994	+	0.788073i	−0.998688	−	0.0512105i	$-0.983692\pi$
$443$	−9.57652	+	16.5870i	−0.454994	+	0.788073i	0.543693	+	0.839284i	$0.317025\pi$
$444$			10.6319i			0.504568i
$445$	−29.5130			−1.39905
$446$	−3.31623			−0.157028
$447$		−	11.8657i		−	0.561230i
$448$	−1.08335	−	2.41379i	−0.0511833	−	0.114041i
$449$	−32.7190	+	18.8903i	−1.54410	+	0.891489i	−0.545530	+	0.838091i	$0.683672\pi$
$449$	−32.7190	+	18.8903i	−1.54410	+	0.891489i	−0.998573	+	0.0533973i	$0.982995\pi$
$450$	4.84630	+	2.79801i	0.228457	+	0.131900i
$451$	1.08386	−	1.87729i	0.0510368	−	0.0883984i
$452$	−16.0210			−0.753565
$453$	−10.1344	+	5.85109i	−0.476155	+	0.274908i
$454$	−10.9947			−0.516008
$455$	7.27714	−	30.1874i	0.341158	−	1.41521i
$456$	−5.18398			−0.242762
$457$	31.5850	−	18.2356i	1.47749	−	0.853027i	0.477809	−	0.878464i	$-0.341431\pi$
$457$	31.5850	−	18.2356i	1.47749	−	0.853027i	0.999676	+	0.0254372i	$0.00809780\pi$
$458$	−23.3458			−1.09088
$459$	0.391489	−	0.678079i	0.0182731	−	0.0316500i
$460$	0.918225	+	0.530137i	0.0428124	+	0.0247178i
$461$	3.03039	−	1.74960i	0.141139	−	0.0814869i	−0.427768	−	0.903889i	$-0.640700\pi$
$461$	3.03039	−	1.74960i	0.141139	−	0.0814869i	0.568907	+	0.822402i	$0.307366\pi$
$462$	3.55020	−	4.91729i	0.165170	−	0.228773i
$463$			15.8900i			0.738471i	0.929336	+	0.369236i	$0.120381\pi$
$463$			15.8900i			0.738471i	−0.929336	+	0.369236i	$0.879619\pi$
$464$	−6.70773			−0.311398
$465$	−21.4218			−0.993410
$466$			4.29093i			0.198774i
$467$	13.2374	−	22.9278i	0.612552	−	1.06097i	−0.378257	−	0.925701i	$-0.623476\pi$
$467$	13.2374	−	22.9278i	0.612552	−	1.06097i	0.990809	−	0.135270i	$-0.0431902\pi$
$468$	−2.20612	+	2.85184i	−0.101978	+	0.131827i
$469$	−22.2339	+	9.97896i	−1.02667	+	0.460786i
$470$	6.98749	+	4.03423i	0.322309	+	0.186085i
$471$	4.03718	+	6.99260i	0.186023	+	0.322202i
$472$	0.307117	−	0.531942i	0.0141362	−	0.0244846i
$473$	19.1052	−	11.0304i	0.878457	−	0.507177i
$474$			1.30067i			0.0597420i
$475$	−25.1231	+	14.5048i	−1.15273	+	0.665528i
$476$	−1.21262	+	1.67957i	−0.0555803	+	0.0769828i
$477$	−6.83920	−	11.8458i	−0.313146	−	0.542384i
$478$	−2.79694	−	4.84445i	−0.127929	−	0.221580i
$479$			5.02644i			0.229664i	0.993385	+	0.114832i	$0.0366329\pi$
$479$			5.02644i			0.229664i	−0.993385	+	0.114832i	$0.963367\pi$
$480$	1.62758	+	2.81905i	0.0742884	+	0.128671i
$481$	−35.4731	+	14.5307i	−1.61744	+	0.662542i
$482$	29.2191			1.33089
$483$	0.504454	−	0.698705i	0.0229534	−	0.0317922i
$484$	2.87259	−	4.97548i	0.130572	−	0.226158i
$485$	−17.2558			−0.783546
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	−5.33437	−	3.07980i	−0.241723	−	0.139559i	0.374245	−	0.927330i	$-0.377902\pi$
$487$	−5.33437	−	3.07980i	−0.241723	−	0.139559i	−0.615969	+	0.787771i	$0.711235\pi$
$488$		−	0.228227i		−	0.0103314i
$489$		−	0.826274i		−	0.0373654i
$490$	−15.1453	+	17.0242i	−0.684196	+	0.769077i
$491$	13.0021	−	22.5203i	0.586775	−	1.01632i	−0.407876	−	0.913037i	$-0.633730\pi$
$491$	13.0021	−	22.5203i	0.586775	−	1.01632i	0.994652	−	0.103288i	$-0.0329362\pi$
$492$	0.818943	−	0.472817i	0.0369208	−	0.0213162i
$493$	2.62600	+	4.54837i	0.118269	+	0.204848i
$494$	−7.08498	−	17.2963i	−0.318768	−	0.778195i
$495$	−3.73096	+	6.46221i	−0.167694	+	0.290455i
$496$	−5.69921	−	3.29044i	−0.255902	−	0.147745i
$497$	−31.7007	−	22.8874i	−1.42197	−	1.02664i
$498$	−3.73204	−	6.46409i	−0.167237	−	0.289663i
$499$	17.0760	+	9.85885i	0.764428	+	0.441343i	0.830883	−	0.556447i	$-0.187836\pi$
$499$	17.0760	+	9.85885i	0.764428	+	0.441343i	−0.0664553	+	0.997789i	$0.521169\pi$
$500$	1.68023	+	0.970080i	0.0751421	+	0.0433833i
$501$	−4.67389	−	2.69847i	−0.208814	−	0.120559i
$502$	10.6028	+	6.12153i	0.473226	+	0.273217i
$503$	−1.11315	−	1.92804i	−0.0496330	−	0.0859669i	0.840142	−	0.542367i	$-0.182472\pi$
$503$	−1.11315	−	1.92804i	−0.0496330	−	0.0859669i	−0.889775	+	0.456400i	$0.849139\pi$
$504$	2.41379	−	1.08335i	0.107519	−	0.0482561i
$505$	−20.6692	−	11.9334i	−0.919766	−	0.531027i
$506$	−0.373332	+	0.646630i	−0.0165966	+	0.0287462i
$507$	−12.5303	−	3.46306i	−0.556488	−	0.153800i
$508$	−0.284508	−	0.492782i	−0.0126230	−	0.0218636i
$509$	−1.91227	+	1.10405i	−0.0847600	+	0.0489362i	−0.541781	−	0.840520i	$-0.682250\pi$
$509$	−1.91227	+	1.10405i	−0.0847600	+	0.0489362i	0.457021	+	0.889456i	$0.348916\pi$
$510$	1.27436	−	2.20725i	0.0564295	−	0.0977387i
$511$	28.9144	+	20.8757i	1.27910	+	0.923487i
$512$			1.00000i			0.0441942i
$513$		−	5.18398i		−	0.228878i
$514$	3.80975	+	2.19956i	0.168041	+	0.0970184i
$515$	4.75775	−	2.74689i	0.209651	−	0.121042i
$516$	9.62369			0.423659
$517$	−2.84098	+	4.92072i	−0.124946	+	0.216413i
$518$	27.9839	+	2.85665i	1.22954	+	0.125514i
$519$	−13.5777			−0.595993
$520$	−7.18128	+	9.28319i	−0.314920	+	0.407095i
$521$	−12.1284	−	21.0070i	−0.531355	−	0.920334i	−0.999330	−	0.0365921i	$-0.988350\pi$
$521$	−12.1284	−	21.0070i	−0.531355	−	0.920334i	0.467975	−	0.883741i	$-0.344984\pi$
$522$		−	6.70773i		−	0.293589i
$523$	−7.17629	−	12.4297i	−0.313797	−	0.543512i	0.665384	−	0.746501i	$-0.268268\pi$
$523$	−7.17629	−	12.4297i	−0.313797	−	0.543512i	−0.979181	+	0.202989i	$0.934934\pi$
$524$	−4.12135	−	7.13838i	−0.180042	−	0.311842i
$525$	8.66671	−	12.0040i	0.378246	−	0.523899i
$526$	16.5763	−	9.57034i	0.722762	−	0.417287i
$527$			5.15268i			0.224454i
$528$	−1.98522	+	1.14617i	−0.0863957	+	0.0498806i
$529$	11.4470	−	19.8267i	0.497694	−	0.862031i
$530$	−22.2627	−	38.5600i	−0.967028	−	1.67494i
$531$	0.531942	+	0.307117i	0.0230843	+	0.0133277i
$532$	−1.39287	+	13.6446i	−0.0603884	+	0.591569i
$533$	2.69680	+	2.08619i	0.116811	+	0.0903628i
$534$	4.53328	−	7.85187i	0.196174	−	0.339784i
$535$		−	56.6239i		−	2.44806i
$536$	9.21123			0.397865
$537$	16.9385			0.730948
$538$			3.09430i			0.133405i
$539$	−11.9888	−	10.6656i	−0.516393	−	0.459400i
$540$	−2.81905	+	1.62758i	−0.121312	+	0.0700398i
$541$	−26.1094	−	15.0742i	−1.12253	−	0.648093i	−0.180484	−	0.983578i	$-0.557766\pi$
$541$	−26.1094	−	15.0742i	−1.12253	−	0.648093i	−0.942045	+	0.335485i	$0.891100\pi$
$542$	−13.1555	+	22.7861i	−0.565079	+	0.978745i
$543$	12.8540			0.551616
$544$	0.678079	−	0.391489i	0.0290724	−	0.0167850i
$545$	38.5951			1.65323
$546$	6.91350	+	6.57293i	0.295871	+	0.281296i
$547$	−34.0803			−1.45717			−0.728585	−	0.684955i	$-0.759822\pi$
$547$	−34.0803			−1.45717			−0.728585	+	0.684955i	$0.759822\pi$
$548$	−9.54214	+	5.50916i	−0.407620	+	0.235340i
$549$	0.228227			0.00974049
$550$	−6.41399	+	11.1094i	−0.273494	+	0.473705i
$551$	30.1141	+	17.3864i	1.28290	+	0.740684i
$552$	−0.282083	+	0.162861i	−0.0120063	+	0.00693182i
$553$	3.42347	+	0.349474i	0.145581	+	0.0148611i
$554$			11.1939i			0.475581i
$555$	−34.6085			−1.46905
$556$	12.7757			0.541811
$557$			2.45746i			0.104126i	0.998644	+	0.0520630i	$0.0165797\pi$
$557$			2.45746i			0.104126i	−0.998644	+	0.0520630i	$0.983420\pi$
$558$	3.29044	−	5.69921i	0.139295	−	0.241267i
$559$	13.1528	+	32.1093i	0.556303	+	1.35808i
$560$	7.85724	−	3.52646i	0.332029	−	0.149020i
$561$	1.55439	+	0.897425i	0.0656262	+	0.0378893i
$562$	0.925326	+	1.60271i	0.0390325	+	0.0676063i
$563$	6.65979	−	11.5351i	0.280677	−	0.486146i	−0.690875	−	0.722974i	$-0.742774\pi$
$563$	6.65979	−	11.5351i	0.280677	−	0.486146i	0.971552	+	0.236828i	$0.0761078\pi$
$564$	−2.14659	+	1.23934i	−0.0903879	+	0.0521855i
$565$		−	52.1509i		−	2.19400i
$566$	−19.1951	+	11.0823i	−0.806830	+	0.465824i
$567$	1.08335	+	2.41379i	0.0454963	+	0.101369i
$568$	7.38911	+	12.7983i	0.310040	+	0.537005i
$569$	17.7363	+	30.7201i	0.743544	+	1.28786i	0.950872	+	0.309584i	$0.100190\pi$
$569$	17.7363	+	30.7201i	0.743544	+	1.28786i	−0.207328	+	0.978271i	$0.566477\pi$
$570$		−	16.8747i		−	0.706801i
$571$	2.76721	+	4.79294i	0.115804	+	0.200578i	0.918101	−	0.396347i	$-0.129722\pi$
$571$	2.76721	+	4.79294i	0.115804	+	0.200578i	−0.802297	+	0.596925i	$0.796389\pi$
$572$	−6.53739	−	5.05718i	−0.273342	−	0.211451i
$573$	20.3228			0.848997
$574$	−1.02445	−	2.28256i	−0.0427597	−	0.0952721i
$575$	−0.911374	+	1.57855i	−0.0380069	+	0.0658299i
$576$	−1.00000			−0.0416667
$577$	−32.7495	+	18.9080i	−1.36338	+	0.787149i	−0.990072	−	0.140558i	$-0.955110\pi$
$577$	−32.7495	+	18.9080i	−1.36338	+	0.787149i	−0.373309	+	0.927707i	$0.621777\pi$
$578$	14.1915	+	8.19347i	0.590289	+	0.340804i
$579$		−	19.6308i		−	0.815828i
$580$		−	21.8347i		−	0.906636i
$581$	−18.0167	+	8.08620i	−0.747459	+	0.335472i
$582$	2.65054	−	4.59086i	0.109868	−	0.190297i
$583$	27.1547	−	15.6778i	1.12463	−	0.649306i
$584$	−6.73964	−	11.6734i	−0.278888	−	0.483049i
$585$	−9.28319	−	7.18128i	−0.383813	−	0.296909i
$586$	−7.34371	+	12.7197i	−0.303366	+	0.525445i
$587$	−38.4863	−	22.2201i	−1.58850	−	0.917121i	−0.993555	−	0.113355i	$-0.963840\pi$
$587$	−38.4863	−	22.2201i	−1.58850	−	0.917121i	−0.594945	−	0.803766i	$-0.702826\pi$
$588$	−2.20290	−	6.64434i	−0.0908459	−	0.274008i
$589$	17.0576	+	29.5446i	0.702845	+	1.21736i
$590$	1.73155	+	0.999713i	0.0712869	+	0.0411575i
$591$	−14.1302	−	8.15806i	−0.581238	−	0.335578i
$592$	−9.20750	−	5.31595i	−0.378426	−	0.218484i
$593$	−11.7799	−	6.80115i	−0.483744	−	0.279290i	0.238231	−	0.971208i	$-0.423432\pi$
$593$	−11.7799	−	6.80115i	−0.483744	−	0.279290i	−0.721975	+	0.691919i	$0.756766\pi$
$594$	−1.14617	−	1.98522i	−0.0470279	−	0.0814547i
$595$	−5.46724	−	3.94726i	−0.224135	−	0.161822i
$596$	10.2760	+	5.93287i	0.420923	+	0.243020i
$597$	1.96397	−	3.40169i	0.0803798	−	0.139222i
$598$	−0.928907	−	0.718583i	−0.0379859	−	0.0293850i
$599$	7.12213	+	12.3359i	0.291002	+	0.504031i	0.974047	−	0.226346i	$-0.0726779\pi$
$599$	7.12213	+	12.3359i	0.291002	+	0.504031i	−0.683045	+	0.730377i	$0.739345\pi$
$600$	−4.84630	+	2.79801i	−0.197849	+	0.114228i
$601$	5.94043	−	10.2891i	0.242315	−	0.419702i	−0.719058	−	0.694950i	$-0.755427\pi$
$601$	5.94043	−	10.2891i	0.242315	−	0.419702i	0.961373	+	0.275248i	$0.0887598\pi$
$602$	2.58576	−	25.3303i	0.105388	−	1.03238i
$603$			9.21123i			0.375110i
$604$		−	11.7022i		−	0.476155i
$605$	16.1959	+	9.35074i	0.658459	+	0.380161i
$606$	6.34968	−	3.66599i	0.257938	−	0.148921i
$607$	−34.5749			−1.40335			−0.701676	−	0.712496i	$-0.747565\pi$
$607$	−34.5749			−1.40335			−0.701676	+	0.712496i	$0.747565\pi$
$608$	2.59199	−	4.48946i	0.105119	−	0.182072i
$609$	−17.6552	−	1.80228i	−0.715426	−	0.0730319i
$610$	0.742914			0.0300797
$611$	−7.06879	−	5.46826i	−0.285972	−	0.221222i
$612$	0.391489	+	0.678079i	0.0158250	+	0.0274097i
$613$			5.09806i			0.205909i	0.994686	+	0.102954i	$0.0328296\pi$
$613$			5.09806i			0.205909i	−0.994686	+	0.102954i	$0.967170\pi$
$614$	0.868156	+	1.50369i	0.0350359	+	0.0606840i
$615$	1.53909	+	2.66579i	0.0620622	+	0.107495i
$616$	2.48340	+	5.53321i	0.100059	+	0.222939i
$617$	−18.6676	+	10.7777i	−0.751528	+	0.433895i	−0.826246	−	0.563310i	$-0.809528\pi$
$617$	−18.6676	+	10.7777i	−0.751528	+	0.433895i	0.0747175	+	0.997205i	$0.476194\pi$
$618$			1.68772i			0.0678899i
$619$	−8.13309	+	4.69564i	−0.326897	+	0.188734i	−0.654462	−	0.756095i	$-0.727105\pi$
$619$	−8.13309	+	4.69564i	−0.326897	+	0.188734i	0.327566	+	0.944828i	$0.393772\pi$
$620$	10.7109	−	18.5518i	0.430159	−	0.745058i
$621$	−0.162861	−	0.282083i	−0.00653538	−	0.0113196i
$622$	11.7874	+	6.80544i	0.472630	+	0.272873i
$623$	−19.4487	−	14.0416i	−0.779194	−	0.562565i
$624$	−1.36671	−	3.33648i	−0.0547121	−	0.133566i
$625$	10.8323	−	18.7621i	0.433292	−	0.750484i
$626$			12.8534i			0.513726i
$627$	11.8834			0.474579
$628$	−8.07436			−0.322202
$629$			8.32455i			0.331921i
$630$	3.52646	+	7.85724i	0.140498	+	0.313040i
$631$	−12.1643	+	7.02306i	−0.484253	+	0.279583i	−0.722187	−	0.691698i	$-0.756863\pi$
$631$	−12.1643	+	7.02306i	−0.484253	+	0.279583i	0.237934	+	0.971281i	$0.423530\pi$
$632$	−1.12642	−	0.650337i	−0.0448065	−	0.0258690i
$633$	−11.9378	+	20.6769i	−0.474486	+	0.821834i
$634$	9.36334			0.371866
$635$	1.60408	−	0.926116i	0.0636560	−	0.0367518i
$636$	13.6784			0.542384
$637$	19.1580	−	16.4308i	0.759068	−	0.651012i
$638$	15.3764			0.608756
$639$	−12.7983	+	7.38911i	−0.506293	+	0.292309i
$640$	−3.25515			−0.128671
$641$	−10.2176	+	17.6973i	−0.403570	+	0.699003i	−0.994154	−	0.107973i	$-0.965564\pi$
$641$	−10.2176	+	17.6973i	−0.403570	+	0.699003i	0.590584	+	0.806976i	$0.298897\pi$
$642$	15.0646	+	8.69757i	0.594554	+	0.343266i
$643$	−3.01247	+	1.73925i	−0.118800	+	0.0685893i	−0.558223	−	0.829691i	$-0.688516\pi$
$643$	−3.01247	+	1.73925i	−0.118800	+	0.0685893i	0.439422	+	0.898281i	$0.355183\pi$
$644$	0.352870	+	0.786222i	0.0139050	+	0.0309815i
$645$			31.3266i			1.23348i
$646$	−4.05894			−0.159697
$647$	−39.1085			−1.53751			−0.768757	−	0.639541i	$-0.779124\pi$
$647$	−39.1085			−1.53751			−0.768757	+	0.639541i	$0.779124\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−0.704016	+	1.21939i	−0.0276350	+	0.0478653i
$650$	−15.9590	−	12.3455i	−0.625963	−	0.484232i
$651$	−14.1166	−	10.1920i	−0.553274	−	0.399455i
$652$	0.715574	+	0.413137i	0.0280240	+	0.0161797i
$653$	5.40169	+	9.35601i	0.211385	+	0.366129i	0.952148	−	0.305637i	$-0.0988694\pi$
$653$	5.40169	+	9.35601i	0.211385	+	0.366129i	−0.740763	+	0.671766i	$0.765536\pi$
$654$	−5.92831	+	10.2681i	−0.231815	+	0.401516i
$655$	23.2365	−	13.4156i	0.907926	−	0.524192i
$656$			0.945634i			0.0369208i
$657$	11.6734	−	6.73964i	0.455423	−	0.262938i
$658$	2.68526	+	5.98298i	0.104682	+	0.233241i
$659$	−9.60919	−	16.6436i	−0.374321	−	0.648343i	0.615904	−	0.787821i	$-0.288791\pi$
$659$	−9.60919	−	16.6436i	−0.374321	−	0.648343i	−0.990225	+	0.139478i	$0.955457\pi$
$660$	−3.73096	−	6.46221i	−0.145227	−	0.251541i
$661$		−	1.21632i		−	0.0473094i	−0.999720	−	0.0236547i	$-0.992470\pi$
$661$		−	1.21632i		−	0.0473094i	0.999720	−	0.0236547i	$-0.00753022\pi$
$662$	−5.57375	−	9.65401i	−0.216630	−	0.375214i
$663$	−1.72735	+	2.23293i	−0.0670846	+	0.0867199i
$664$	7.46409			0.289663
$665$	−44.4153	−	4.53399i	−1.72235	−	0.175821i
$666$	5.31595	−	9.20750i	0.205989	−	0.356783i
$667$	2.18485			0.0845978
$668$	4.67389	−	2.69847i	0.180838	−	0.104407i
$669$	2.87194	+	1.65812i	0.111036	+	0.0641065i
$670$			29.9840i			1.15838i
$671$			0.523173i			0.0201969i
$672$	−0.268687	+	2.63207i	−0.0103648	+	0.101534i
$673$	−7.28073	+	12.6106i	−0.280652	+	0.486103i	−0.971545	−	0.236853i	$-0.923884\pi$
$673$	−7.28073	+	12.6106i	−0.280652	+	0.486103i	0.690894	+	0.722956i	$0.257217\pi$
$674$	6.85592	−	3.95827i	0.264080	−	0.152467i
$675$	−2.79801	−	4.84630i	−0.107696	−	0.186534i
$676$	9.26423	−	9.11999i	0.356316	−	0.350769i
$677$	10.2682	−	17.7851i	0.394640	−	0.683536i	−0.598415	−	0.801186i	$-0.704203\pi$
$677$	10.2682	−	17.7851i	0.394640	−	0.683536i	0.993055	+	0.117650i	$0.0375360\pi$
$678$	13.8746	+	8.01051i	0.532851	+	0.307642i
$679$	−11.3713	−	8.20991i	−0.436391	−	0.315067i
$680$	1.27436	+	2.20725i	0.0488694	+	0.0846442i
$681$	9.52172	+	5.49737i	0.364873	+	0.210660i
$682$	13.0645	+	7.54279i	0.500266	+	0.288829i
$683$	−35.0496	−	20.2359i	−1.34113	−	0.774304i	−0.354160	−	0.935185i	$-0.615233\pi$
$683$	−35.0496	−	20.2359i	−1.34113	−	0.774304i	−0.986974	+	0.160881i	$0.948567\pi$
$684$	4.48946	+	2.59199i	0.171659	+	0.0991072i
$685$	−17.9332	−	31.0611i	−0.685191	−	1.18679i
$686$	−18.0803	+	4.01294i	−0.690308	+	0.153215i
$687$	20.2181	+	11.6729i	0.771368	+	0.445349i
$688$	−4.81185	+	8.33436i	−0.183450	+	0.317745i
$689$	18.6944	+	45.6377i	0.712199	+	1.73866i
$690$	−0.530137	−	0.918225i	−0.0201820	−	0.0349562i
$691$	23.0319	−	13.2975i	0.876174	−	0.505859i	0.00677902	−	0.999977i	$-0.497842\pi$
$691$	23.0319	−	13.2975i	0.876174	−	0.505859i	0.869395	+	0.494118i	$0.164509\pi$
$692$	6.78883	−	11.7586i	0.258073	−	0.446995i
$693$	−5.53321	+	2.48340i	−0.210189	+	0.0943365i
$694$		−	26.0298i		−	0.988077i
$695$			41.5869i			1.57748i
$696$	5.80906	+	3.35386i	0.220192	+	0.127128i
$697$	0.641215	−	0.370206i	0.0242877	−	0.0140225i
$698$	−14.5897			−0.552228
$699$	2.14547	−	3.71606i	0.0811490	−	0.140554i
$700$	6.06244	+	13.5076i	0.229139	+	0.510540i
$701$	−19.9294			−0.752722			−0.376361	−	0.926473i	$-0.622825\pi$
$701$	−19.9294			−0.752722			−0.376361	+	0.926473i	$0.622825\pi$
$702$	3.33648	−	1.36671i	0.125927	−	0.0515830i
$703$	27.5578	+	47.7315i	1.03936	+	1.80023i
$704$		−	2.29234i		−	0.0863957i
$705$	−4.03423	−	6.98749i	−0.151938	−	0.263164i
$706$	−5.33220	−	9.23564i	−0.200680	−	0.347588i
$707$	−7.94307	−	17.6978i	−0.298730	−	0.665595i
$708$	−0.531942	+	0.307117i	−0.0199916	+	0.0115422i
$709$			49.6739i			1.86554i	0.360467	+	0.932772i	$0.382617\pi$
$709$			49.6739i			1.86554i	−0.360467	+	0.932772i	$0.617383\pi$
$710$	−41.6605	+	24.0527i	−1.56349	+	0.902681i
$711$	0.650337	−	1.12642i	0.0243896	−	0.0422440i
$712$	4.53328	+	7.85187i	0.169892	+	0.294261i
$713$	1.85635	+	1.07177i	0.0695210	+	0.0401380i
$714$	1.88994	−	0.848237i	0.0707293	−	0.0317445i
$715$	16.4619	−	21.2802i	0.615641	−	0.795835i
$716$	−8.46923	+	14.6691i	−0.316510	+	0.548211i
$717$			5.59389i			0.208908i
$718$	17.2241			0.642799
$719$	−11.5039			−0.429023			−0.214512	−	0.976721i	$-0.568816\pi$
$719$	−11.5039			−0.429023			−0.214512	+	0.976721i	$0.568816\pi$
$720$		−	3.25515i		−	0.121312i
$721$	4.44219	+	0.453467i	0.165436	+	0.0168880i
$722$	−6.81878	+	3.93682i	−0.253769	+	0.146513i
$723$	−25.3045	−	14.6096i	−0.941084	−	0.543335i
$724$	−6.42698	+	11.1318i	−0.238857	+	0.413712i
$725$	37.5366			1.39407
$726$	−4.97548	+	2.87259i	−0.184657	+	0.106612i
$727$	41.7753			1.54936			0.774679	−	0.632354i	$-0.217911\pi$
$727$	41.7753			1.54936			0.774679	+	0.632354i	$0.217911\pi$
$728$	−9.14908	+	2.70080i	−0.339087	+	0.100098i
$729$	1.00000			0.0370370
$730$	37.9987	−	21.9386i	1.40640	−	0.811983i
$731$	7.53514			0.278697
$732$	−0.114113	+	0.197650i	−0.00421776	+	0.00730537i
$733$	42.1605	+	24.3414i	1.55723	+	0.899070i	0.997520	+	0.0703842i	$0.0224225\pi$
$733$	42.1605	+	24.3414i	1.55723	+	0.899070i	0.559714	+	0.828686i	$0.310911\pi$
$734$	14.8269	−	8.56032i	0.547271	−	0.315967i
$735$	21.6283	−	7.17077i	0.797774	−	0.264498i
$736$		−	0.325722i		−	0.0120063i
$737$	−21.1153			−0.777790
$738$	−0.945634			−0.0348093
$739$			4.33957i			0.159634i	0.996810	+	0.0798168i	$0.0254335\pi$
$739$			4.33957i			0.159634i	−0.996810	+	0.0798168i	$0.974566\pi$
$740$	17.3042	−	29.9718i	0.636116	−	1.10179i
$741$	−2.51235	+	18.5215i	−0.0922937	+	0.680404i
$742$	3.67520	−	36.0026i	0.134921	−	1.32170i
$743$	−13.9617	−	8.06082i	−0.512207	−	0.295723i	0.221534	−	0.975153i	$-0.428894\pi$
$743$	−13.9617	−	8.06082i	−0.512207	−	0.295723i	−0.733740	+	0.679430i	$0.762227\pi$
$744$	3.29044	+	5.69921i	0.120633	+	0.208943i
$745$	−19.3124	+	33.4501i	−0.707552	+	1.22552i
$746$	10.9123	−	6.30021i	0.399527	−	0.230667i
$747$			7.46409i			0.273097i
$748$	−1.55439	+	0.897425i	−0.0568340	+	0.0328131i
$749$	26.9403	−	37.3143i	0.984377	−	1.36343i
$750$	−0.970080	−	1.68023i	−0.0354223	−	0.0613533i
$751$	23.0332	+	39.8947i	0.840495	+	1.45578i	0.889477	+	0.456980i	$0.151069\pi$
$751$	23.0332	+	39.8947i	0.840495	+	1.45578i	−0.0489819	+	0.998800i	$0.515598\pi$
$752$		−	2.47867i		−	0.0903879i
$753$	−6.12153	−	10.6028i	−0.223081	−	0.386388i
$754$	−3.25082	+	23.9656i	−0.118388	+	0.872775i
$755$	38.0924			1.38632
$756$	−2.63207	−	0.268687i	−0.0957276	−	0.00977204i
$757$	−7.15268	+	12.3888i	−0.259969	+	0.450279i	−0.966233	−	0.257669i	$-0.917046\pi$
$757$	−7.15268	+	12.3888i	−0.259969	+	0.450279i	0.706265	+	0.707948i	$0.250379\pi$
$758$	−3.58807			−0.130324
$759$	0.646630	−	0.373332i	0.0234712	−	0.0135511i
$760$	14.6139	+	8.43733i	0.530101	+	0.306054i
$761$			51.0053i			1.84894i	0.381256	+	0.924470i	$0.375492\pi$
$761$			51.0053i			1.84894i	−0.381256	+	0.924470i	$0.624508\pi$
$762$			0.569015i			0.0206132i
$763$	25.4336	+	18.3627i	0.920759	+	0.664773i
$764$	−10.1614	+	17.6001i	−0.367627	+	0.636748i
$765$	−2.20725	+	1.27436i	−0.0798033	+	0.0460745i
$766$	−9.09226	−	15.7482i	−0.328517	−	0.569007i
$767$	−1.75170	−	1.35508i	−0.0632502	−	0.0489290i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	38.2197	+	22.0662i	1.37824	+	0.795727i	0.991947	−	0.126650i	$-0.0404225\pi$
$769$	38.2197	+	22.0662i	1.37824	+	0.795727i	0.386292	+	0.922377i	$0.373756\pi$
$770$	−18.0115	+	8.08384i	−0.649088	+	0.291321i
$771$	−2.19956	−	3.80975i	−0.0792152	−	0.137205i
$772$	17.0008	+	9.81539i	0.611871	+	0.353264i
$773$	−8.55247	−	4.93777i	−0.307611	−	0.177599i	0.338246	−	0.941058i	$-0.390166\pi$
$773$	−8.55247	−	4.93777i	−0.307611	−	0.177599i	−0.645857	+	0.763458i	$0.723500\pi$
$774$	−8.33436	−	4.81185i	−0.299572	−	0.172958i
$775$	31.8929	+	18.4134i	1.14563	+	0.661428i
$776$	2.65054	+	4.59086i	0.0951487	+	0.164802i
$777$	−22.8065	−	16.4659i	−0.818178	−	0.590711i
$778$	23.7131	+	13.6907i	0.850155	+	0.490837i
$779$	2.45107	−	4.24539i	0.0878189	−	0.152107i
$780$	10.8608	−	4.44884i	0.388878	−	0.159294i
$781$	−16.9383	−	29.3380i	−0.606101	−	1.04980i
$782$	−0.220865	+	0.127516i	−0.00789812	+	0.00455998i
$783$	−3.35386	+	5.80906i	−0.119857	+	0.207599i
$784$	6.85561	+	1.41441i	0.244843	+	0.0505145i
$785$		−	26.2833i		−	0.938090i
$786$			8.24269i			0.294007i
$787$	−9.99837	−	5.77256i	−0.356403	−	0.205770i	0.311098	−	0.950378i	$-0.399303\pi$
$787$	−9.99837	−	5.77256i	−0.356403	−	0.205770i	−0.667502	+	0.744608i	$0.732636\pi$
$788$	14.1302	−	8.15806i	0.503366	−	0.290619i
$789$	−19.1407			−0.681426
$790$	2.11695	−	3.66666i	0.0753176	−	0.130454i
$791$	24.8122	−	34.3667i	0.882219	−	1.22194i
$792$	2.29234			0.0814547
$793$	−0.815417	−	0.110608i	−0.0289563	−	0.00392779i
$794$	−8.43299	−	14.6064i	−0.299276	−	0.518361i
$795$			44.5253i			1.57915i
$796$	1.96397	+	3.40169i	0.0696110	+	0.120570i
$797$	−2.73081	−	4.72990i	−0.0967302	−	0.167542i	0.813599	−	0.581426i	$-0.197505\pi$
$797$	−2.73081	−	4.72990i	−0.0967302	−	0.167542i	−0.910329	+	0.413884i	$0.864172\pi$
$798$	8.02856	−	11.1201i	0.284208	−	0.393649i
$799$	−1.68074	+	0.970373i	−0.0594601	+	0.0343293i
$800$		−	5.59603i		−	0.197849i
$801$	−7.85187	+	4.53328i	−0.277432	+	0.160176i
$802$	9.34671	−	16.1890i	0.330044	−	0.571653i
$803$	15.4495	+	26.7594i	0.545202	+	0.944318i
$804$	−7.97716	−	4.60562i	−0.281333	−	0.162428i
$805$	−2.55927	+	1.14864i	−0.0902026	+	0.0404844i
$806$	−14.5182	+	18.7676i	−0.511383	+	0.661062i
$807$	1.54715	−	2.67975i	0.0544623	−	0.0943315i
$808$			7.33198i			0.257938i
$809$	25.4906			0.896202			0.448101	−	0.893983i	$-0.352100\pi$
$809$	25.4906			0.896202			0.448101	+	0.893983i	$0.352100\pi$
$810$	3.25515			0.114374
$811$		−	20.1506i		−	0.707582i	−0.935324	−	0.353791i	$-0.884892\pi$
$811$		−	20.1506i		−	0.707582i	0.935324	−	0.353791i	$-0.115108\pi$
$812$	10.3884	−	14.3887i	0.364562	−	0.504946i
$813$	22.7861	−	13.1555i	0.799142	−	0.461385i
$814$	21.1067	+	12.1860i	0.739789	+	0.427117i
$815$	−1.34482	+	2.32930i	−0.0471071	+	0.0815920i
$816$	−0.782978			−0.0274097
$817$	43.2052	−	24.9445i	1.51156	−	0.872698i
$818$	4.94626			0.172942
$819$	−2.70080	−	9.14908i	−0.0943737	−	0.319695i
$820$	−3.07819			−0.107495
$821$	−5.63087	+	3.25098i	−0.196519	+	0.113460i	−0.595031	−	0.803703i	$-0.702860\pi$
$821$	−5.63087	+	3.25098i	−0.196519	+	0.113460i	0.398512	+	0.917163i	$0.369527\pi$
$822$	11.0183			0.384308
$823$	−4.68477	+	8.11427i	−0.163301	+	0.282846i	−0.936051	−	0.351865i	$-0.885547\pi$
$823$	−4.68477	+	8.11427i	−0.163301	+	0.282846i	0.772750	+	0.634711i	$0.218881\pi$
$824$	−1.46160	−	0.843858i	−0.0509174	−	0.0293972i
$825$	11.1094	−	6.41399i	0.386778	−	0.223307i
$826$	0.665428	+	1.48263i	0.0231532	+	0.0515872i
$827$		−	54.1536i		−	1.88311i	−0.336864	−	0.941553i	$-0.609366\pi$
$827$		−	54.1536i		−	1.88311i	0.336864	−	0.941553i	$-0.390634\pi$
$828$	0.325722			0.0113196
$829$	48.2484			1.67574			0.837869	−	0.545872i	$-0.183801\pi$
$829$	48.2484			1.67574			0.837869	+	0.545872i	$0.183801\pi$
$830$			24.2968i			0.843353i
$831$	5.59693	−	9.69416i	0.194155	−	0.336287i
$832$	3.57283	+	0.484638i	0.123866	+	0.0168018i
$833$	−1.72482	−	5.20237i	−0.0597615	−	0.180252i
$834$	−11.0641	−	6.38785i	−0.383118	−	0.221193i
$835$	8.78393	+	15.2142i	0.303981	+	0.526510i
$836$	−5.94172	+	10.2914i	−0.205499	+	0.355934i
$837$	−5.69921	+	3.29044i	−0.196993	+	0.113734i
$838$			11.4026i			0.393897i
$839$	39.2039	−	22.6344i	1.35347	−	0.781425i	0.364734	−	0.931112i	$-0.381160\pi$
$839$	39.2039	−	22.6344i	1.35347	−	0.781425i	0.988733	+	0.149687i	$0.0478265\pi$
$840$	−8.56780	−	0.874616i	−0.295617	−	0.0301771i
$841$	−7.99679	−	13.8508i	−0.275751	−	0.477615i
$842$	−4.91045	−	8.50514i	−0.169225	−	0.293107i
$843$		−	1.85065i		−	0.0637398i
$844$	−11.9378	−	20.6769i	−0.410917	−	0.711729i
$845$	29.6870	+	30.1565i	1.02126	+	1.03741i
$846$	2.47867			0.0852185
$847$	6.22403	+	13.8677i	0.213860	+	0.476498i
$848$	−6.83920	+	11.8458i	−0.234859	+	0.406788i
$849$	22.1646			0.760687
$850$	−3.79455	+	2.19078i	−0.130152	+	0.0751433i
$851$	2.99908	+	1.73152i	0.102807	+	0.0593558i
$852$		−	14.7782i		−	0.506293i
$853$		−	37.2246i		−	1.27454i	−0.770639	−	0.637272i	$-0.780063\pi$
$853$		−	37.2246i		−	1.27454i	0.770639	−	0.637272i	$-0.219937\pi$
$854$	0.489569	+	0.353461i	0.0167527	+	0.0120952i
$855$	−8.43733	+	14.6139i	−0.288550	+	0.499784i
$856$	−15.0646	+	8.69757i	−0.514899	+	0.297277i
$857$	19.6255	+	33.9924i	0.670395	+	1.16116i	0.977792	+	0.209577i	$0.0672086\pi$
$857$	19.6255	+	33.9924i	0.670395	+	1.16116i	−0.307397	+	0.951581i	$0.599458\pi$
$858$	3.13295	+	7.64834i	0.106957	+	0.261110i
$859$	−4.49460	+	7.78487i	−0.153354	+	0.265616i	−0.932458	−	0.361277i	$-0.882341\pi$
$859$	−4.49460	+	7.78487i	−0.153354	+	0.265616i	0.779105	+	0.626894i	$0.215674\pi$
$860$	−27.1296	−	15.6633i	−0.925113	−	0.534114i
$861$	−0.254079	+	2.48898i	−0.00865900	+	0.0848242i
$862$	4.30730	+	7.46047i	0.146707	+	0.254105i
$863$	−1.46982	−	0.848602i	−0.0500333	−	0.0288867i	0.474775	−	0.880107i	$-0.342530\pi$
$863$	−1.46982	−	0.848602i	−0.0500333	−	0.0288867i	−0.524808	+	0.851221i	$0.675863\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$	38.2760	+	22.0987i	1.30142	+	0.751378i
$866$	−20.3157	−	11.7293i	−0.690355	−	0.398577i
$867$	−8.19347	−	14.1915i	−0.278265	−	0.481969i
$868$	15.8848	−	7.12937i	0.539166	−	0.241987i
$869$	2.58213	+	1.49079i	0.0875927	+	0.0505717i
$870$	−10.9173	+	18.9094i	−0.370132	+	0.641088i
$871$	4.46412	−	32.9102i	0.151261	−	1.11512i
$872$	−5.92831	−	10.2681i	−0.200758	−	0.347723i
$873$	−4.59086	+	2.65054i	−0.155377	+	0.0897071i
$874$	−0.844267	+	1.46231i	−0.0285578	+	0.0494635i
$875$	−4.68313	+	2.10187i	−0.158319	+	0.0710561i
$876$			13.4793i			0.455423i
$877$			24.0935i			0.813579i	0.913522	+	0.406789i	$0.133352\pi$
$877$			24.0935i			0.813579i	−0.913522	+	0.406789i	$0.866648\pi$
$878$	32.3447	+	18.6742i	1.09158	+	0.630224i
$879$	12.7197	−	7.34371i	0.429024	−	0.247697i
$880$	7.46191			0.251541
$881$	−8.86241	+	15.3501i	−0.298582	+	0.517160i	−0.975812	−	0.218612i	$-0.929847\pi$
$881$	−8.86241	+	15.3501i	−0.298582	+	0.517160i	0.677230	+	0.735772i	$0.263180\pi$
$882$	−1.41441	+	6.85561i	−0.0476255	+	0.230841i
$883$	−29.5760			−0.995312			−0.497656	−	0.867375i	$-0.665806\pi$
$883$	−29.5760			−0.995312			−0.497656	+	0.867375i	$0.665806\pi$
$884$	−1.07010	−	2.61239i	−0.0359914	−	0.0878643i
$885$	−0.999713	−	1.73155i	−0.0336050	−	0.0582055i
$886$			19.1530i			0.643459i
$887$	11.7907	+	20.4222i	0.395894	+	0.685709i	0.993215	−	0.116293i	$-0.0371013\pi$
$887$	11.7907	+	20.4222i	0.395894	+	0.685709i	−0.597320	+	0.802003i	$0.703768\pi$
$888$	5.31595	+	9.20750i	0.178392	+	0.308983i
$889$	1.49769	+	0.152887i	0.0502309	+	0.00512766i
$890$	−25.5590	+	14.7565i	−0.856741	+	0.494640i
$891$			2.29234i			0.0767962i
$892$	−2.87194	+	1.65812i	−0.0961597	+	0.0555178i
$893$	−6.42469	+	11.1279i	−0.214994	+	0.372381i
$894$	−5.93287	−	10.2760i	−0.198425	−	0.343682i
$895$	−47.7503	−	27.5686i	−1.59612	−	0.921518i
$896$	−2.14510	−	1.54873i	−0.0716627	−	0.0517393i
$897$	0.445166	+	1.08676i	0.0148637	+	0.0362860i
$898$	−18.8903	+	32.7190i	−0.630378	+	1.09185i
$899$		−	44.1427i		−	1.47224i
$900$	5.59603			0.186534
$901$	10.7099			0.356798
$902$		−	2.16771i		−	0.0721770i
$903$	−14.9045	+	20.6438i	−0.495989	+	0.686982i
$904$	−13.8746	+	8.01051i	−0.461463	+	0.266426i
$905$	−36.2359	−	20.9208i	−1.20452	−	0.695431i
$906$	−5.85109	+	10.1344i	−0.194389	+	0.336692i
$907$	10.9828			0.364678			0.182339	−	0.983236i	$-0.441633\pi$
$907$	10.9828			0.364678			0.182339	+	0.983236i	$0.441633\pi$
$908$	−9.52172	+	5.49737i	−0.315989	+	0.182437i
$909$	−7.33198			−0.243186
$910$	−8.79153	−	29.7817i	−0.291436	−	0.987253i
$911$	55.4208			1.83617			0.918086	−	0.396380i	$-0.129734\pi$
$911$	55.4208			1.83617			0.918086	+	0.396380i	$0.129734\pi$
$912$	−4.48946	+	2.59199i	−0.148661	+	0.0858294i
$913$	−17.1102			−0.566265
$914$	18.2356	−	31.5850i	0.603181	−	1.04474i
$915$	−0.643382	−	0.371457i	−0.0212696	−	0.0122800i
$916$	−20.2181	+	11.6729i	−0.668024	+	0.385684i
$917$	21.6954	+	2.21470i	0.716444	+	0.0731359i
$918$		−	0.782978i		−	0.0258421i
$919$	28.1972			0.930139			0.465070	−	0.885274i	$-0.346029\pi$
$919$	28.1972			0.930139			0.465070	+	0.885274i	$0.346029\pi$
$920$	1.06027			0.0349562
$921$		−	1.73631i		−	0.0572134i
$922$	1.74960	−	3.03039i	0.0576199	−	0.0998006i
$923$	49.3073	−	20.1975i	1.62297	−	0.664808i
$924$	0.615920	−	6.03360i	0.0202623	−	0.198491i
$925$	51.5254	+	29.7482i	1.69414	+	0.978115i
$926$	7.94501	+	13.7612i	0.261089	+	0.452220i
$927$	0.843858	−	1.46160i	0.0277159	−	0.0480054i
$928$	−5.80906	+	3.35386i	−0.190692	+	0.110096i
$929$		−	19.7743i		−	0.648775i	−0.945924	−	0.324388i	$-0.894842\pi$
$929$		−	19.7743i		−	0.648775i	0.945924	−	0.324388i	$-0.105158\pi$
$930$	−18.5518	+	10.7109i	−0.608337	+	0.351224i
$931$	−27.1119	−	24.1196i	−0.888556	−	0.790488i
$932$	2.14547	+	3.71606i	0.0702771	+	0.121723i
$933$	−6.80544	−	11.7874i	−0.222800	−	0.385901i
$934$		−	26.4747i		−	0.866279i
$935$	−2.92126	−	5.05977i	−0.0955353	−	0.165472i
$936$	−0.484638	+	3.57283i	−0.0158409	+	0.116782i
$937$	−53.0303			−1.73243			−0.866213	−	0.499676i	$-0.833453\pi$
$937$	−53.0303			−1.73243			−0.866213	+	0.499676i	$0.833453\pi$
$938$	−14.2657	+	19.7590i	−0.465791	+	0.645154i
$939$	6.42671	−	11.1314i	0.209728	−	0.363259i
$940$	8.06846			0.263164
$941$	−44.7773	+	25.8522i	−1.45970	+	0.842757i	−0.998996	−	0.0447977i	$-0.985736\pi$
$941$	−44.7773	+	25.8522i	−1.45970	+	0.842757i	−0.460702	+	0.887555i	$0.652402\pi$
$942$	6.99260	+	4.03718i	0.227831	+	0.131538i
$943$		−	0.308014i		−	0.0100303i
$944$		−	0.614234i		−	0.0199916i
$945$	0.874616	−	8.56780i	0.0284513	−	0.278711i
$946$	11.0304	−	19.1052i	0.358628	−	0.621163i
$947$	11.9089	−	6.87561i	0.386987	−	0.223427i	−0.293867	−	0.955846i	$-0.594942\pi$
$947$	11.9089	−	6.87561i	0.386987	−	0.223427i	0.680854	+	0.732419i	$0.261609\pi$
$948$	0.650337	+	1.12642i	0.0211220	+	0.0365843i
$949$	−44.9734	+	18.4222i	−1.45990	+	0.598011i
$950$	−14.5048	+	25.1231i	−0.470599	+	0.815102i
$951$	−8.10889	−	4.68167i	−0.262949	−	0.151814i
$952$	−0.210376	+	2.06086i	−0.00681832	+	0.0667927i
$953$	−27.8692	−	48.2709i	−0.902773	−	1.56365i	−0.823880	−	0.566765i	$-0.808195\pi$
$953$	−27.8692	−	48.2709i	−0.902773	−	1.56365i	−0.0788930	−	0.996883i	$-0.525139\pi$
$954$	−11.8458	−	6.83920i	−0.383523	−	0.221427i
$955$	−57.2909	−	33.0769i	−1.85389	−	1.07034i
$956$	−4.84445	−	2.79694i	−0.156681	−	0.0904597i
$957$	−13.3163	−	7.68819i	−0.430456	−	0.248524i
$958$	2.51322	+	4.35302i	0.0811984	+	0.140640i
$959$	2.96048	−	29.0010i	0.0955987	−	0.936492i
$960$	2.81905	+	1.62758i	0.0909843	+	0.0525298i
$961$	6.15396	−	10.6590i	0.198515	−	0.343838i
$962$	−23.4553	+	30.3205i	−0.756229	+	0.977573i
$963$	−8.69757	−	15.0646i	−0.280275	−	0.485451i
$964$	25.3045	−	14.6096i	0.815003	−	0.470542i
$965$	−31.9506	+	55.3401i	−1.02853	+	1.78146i
$966$	0.0875171	−	0.857323i	0.00281582	−	0.0275839i
$967$			20.2959i			0.652672i	0.945254	+	0.326336i	$0.105814\pi$
$967$			20.2959i			0.652672i	−0.945254	+	0.326336i	$0.894186\pi$
$968$		−	5.74519i		−	0.184657i
$969$	3.51515	+	2.02947i	0.112923	+	0.0651960i
$970$	−14.9440	+	8.62790i	−0.479822	+	0.277025i
$971$	−42.0664			−1.34998			−0.674988	−	0.737829i	$-0.735851\pi$
$971$	−42.0664			−1.34998			−0.674988	+	0.737829i	$0.735851\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−19.7861	+	27.4052i	−0.634312	+	0.878569i
$974$	−6.15960			−0.197366
$975$	7.64813	+	18.6710i	0.244936	+	0.597952i
$976$	−0.114113	−	0.197650i	−0.00365268	−	0.00632663i
$977$			38.2506i			1.22375i	0.790956	+	0.611873i	$0.209584\pi$
$977$			38.2506i			1.22375i	−0.790956	+	0.611873i	$0.790416\pi$
$978$	−0.413137	−	0.715574i	−0.0132107	−	0.0228815i
$979$	−10.3918	−	17.9991i	−0.332124	−	0.575255i
$980$	−4.60411	+	22.3161i	−0.147073	+	0.712861i
$981$	10.2681	−	5.92831i	0.327837	−	0.189276i
$982$		−	26.0042i		−	0.829826i
$983$	3.57743	−	2.06543i	0.114102	−	0.0658769i	−0.441863	−	0.897083i	$-0.645682\pi$
$983$	3.57743	−	2.06543i	0.114102	−	0.0658769i	0.555965	+	0.831206i	$0.312349\pi$
$984$	0.472817	−	0.818943i	0.0150729	−	0.0261070i
$985$	26.5557	+	45.9959i	0.846136	+	1.46555i
$986$	4.54837	+	2.62600i	0.144850	+	0.0836289i
$987$	0.665986	−	6.52405i	0.0211986	−	0.207663i
$988$	−14.7839	−	11.4365i	−0.470339	−	0.363844i
$989$	1.56732	−	2.71468i	0.0498380	−	0.0863219i
$990$			7.46191i			0.237155i
$991$	6.97350			0.221521			0.110760	−	0.993847i	$-0.464671\pi$
$991$	6.97350			0.221521			0.110760	+	0.993847i	$0.464671\pi$
$992$	−6.58088			−0.208943
$993$			11.1475i			0.353755i
$994$	−38.8973	−	3.97071i	−1.23375	−	0.125943i
$995$	−11.0730	+	6.39301i	−0.351038	+	0.202672i
$996$	−6.46409	−	3.73204i	−0.204823	−	0.118254i
$997$	−14.9563	+	25.9050i	−0.473670	+	0.820421i	−0.999546	−	0.0301406i	$-0.990405\pi$
$997$	−14.9563	+	25.9050i	−0.473670	+	0.820421i	0.525875	+	0.850562i	$0.323738\pi$
$998$	19.7177			0.624153
$999$	−9.20750	+	5.31595i	−0.291312	+	0.168189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bd.a.121.8	✓	16
3.2	odd	2		1638.2.cr.a.667.1		16
7.4	even	3		546.2.bm.a.277.5	yes	16
13.10	even	6		546.2.bm.a.205.1	yes	16
21.11	odd	6		1638.2.dt.a.1369.4		16
39.23	odd	6		1638.2.dt.a.1297.8		16
91.88	even	6	inner	546.2.bd.a.361.8	yes	16
273.179	odd	6		1638.2.cr.a.361.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.a.121.8	✓	16	1.1	even	1	trivial
546.2.bd.a.361.8	yes	16	91.88	even	6	inner
546.2.bm.a.205.1	yes	16	13.10	even	6
546.2.bm.a.277.5	yes	16	7.4	even	3
1638.2.cr.a.361.1		16	273.179	odd	6
1638.2.cr.a.667.1		16	3.2	odd	2
1638.2.dt.a.1297.8		16	39.23	odd	6
1638.2.dt.a.1369.4		16	21.11	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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(2.81905 + 1.62758i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(1.08335 + 2.41379i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(2.81905 + 1.62758i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(1.08335 + 2.41379i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +3.25515 q^{10} +2.29234i q^{11} +(-0.500000 + 0.866025i) q^{12} +(-3.57283 - 0.484638i) q^{13} +(2.14510 + 1.54873i) q^{14} +(-2.81905 - 1.62758i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.391489 + 0.678079i) q^{17} +(0.866025 - 0.500000i) q^{18} +5.18398i q^{19} +(2.81905 - 1.62758i) q^{20} +(-1.08335 - 2.41379i) q^{21} +(1.14617 + 1.98522i) q^{22} +(0.162861 + 0.282083i) q^{23} +1.00000i q^{24} +(2.79801 + 4.84630i) q^{25} +(-3.33648 + 1.36671i) q^{26} -1.00000 q^{27} +(2.63207 + 0.268687i) q^{28} +(3.35386 - 5.80906i) q^{29} -3.25515 q^{30} +(5.69921 - 3.29044i) q^{31} +(-0.866025 - 0.500000i) q^{32} -2.29234i q^{33} +0.782978i q^{34} +(-0.874616 + 8.56780i) q^{35} +(0.500000 - 0.866025i) q^{36} +(9.20750 - 5.31595i) q^{37} +(2.59199 + 4.48946i) q^{38} +(3.57283 + 0.484638i) q^{39} +(1.62758 - 2.81905i) q^{40} +(-0.818943 - 0.472817i) q^{41} +(-2.14510 - 1.54873i) q^{42} +(-4.81185 - 8.33436i) q^{43} +(1.98522 + 1.14617i) q^{44} +(2.81905 + 1.62758i) q^{45} +(0.282083 + 0.162861i) q^{46} +(2.14659 + 1.23934i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-4.65272 + 5.22993i) q^{49} +(4.84630 + 2.79801i) q^{50} +(0.391489 - 0.678079i) q^{51} +(-2.20612 + 2.85184i) q^{52} +(-6.83920 - 11.8458i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-3.73096 + 6.46221i) q^{55} +(2.41379 - 1.08335i) q^{56} -5.18398i q^{57} -6.70773i q^{58} +(0.531942 + 0.307117i) q^{59} +(-2.81905 + 1.62758i) q^{60} +0.228227 q^{61} +(3.29044 - 5.69921i) q^{62} +(1.08335 + 2.41379i) q^{63} -1.00000 q^{64} +(-9.28319 - 7.18128i) q^{65} +(-1.14617 - 1.98522i) q^{66} +9.21123i q^{67} +(0.391489 + 0.678079i) q^{68} +(-0.162861 - 0.282083i) q^{69} +(3.52646 + 7.85724i) q^{70} +(-12.7983 + 7.38911i) q^{71} -1.00000i q^{72} +(11.6734 - 6.73964i) q^{73} +(5.31595 - 9.20750i) q^{74} +(-2.79801 - 4.84630i) q^{75} +(4.48946 + 2.59199i) q^{76} +(-5.53321 + 2.48340i) q^{77} +(3.33648 - 1.36671i) q^{78} +(0.650337 - 1.12642i) q^{79} -3.25515i q^{80} +1.00000 q^{81} -0.945634 q^{82} +7.46409i q^{83} +(-2.63207 - 0.268687i) q^{84} +(-2.20725 + 1.27436i) q^{85} +(-8.33436 - 4.81185i) q^{86} +(-3.35386 + 5.80906i) q^{87} +2.29234 q^{88} +(-7.85187 + 4.53328i) q^{89} +3.25515 q^{90} +(-2.70080 - 9.14908i) q^{91} +0.325722 q^{92} +(-5.69921 + 3.29044i) q^{93} +2.47867 q^{94} +(-8.43733 + 14.6139i) q^{95} +(0.866025 + 0.500000i) q^{96} +(-4.59086 + 2.65054i) q^{97} +(-1.41441 + 6.85561i) q^{98} +2.29234i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9	\( 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9} - 8 q^{10} - 8 q^{12} - 10 q^{13} + 4 q^{14} - 8 q^{16} - 8 q^{21} + 6 q^{22} - 16 q^{23} + 2 q^{26} - 16 q^{27} + 10 q^{28} - 4 q^{29} + 8 q^{30} + 12 q^{31} + 16 q^{35} + 8 q^{36} + 30 q^{37} - 2 q^{38} + 10 q^{39} - 4 q^{40} - 18 q^{41} - 4 q^{42} - 32 q^{43} + 6 q^{44} + 12 q^{46} + 66 q^{47} + 8 q^{48} - 2 q^{49} + 36 q^{50} + 4 q^{52} + 2 q^{53} + 16 q^{55} + 2 q^{56} - 36 q^{59} - 8 q^{61} + 4 q^{62} + 8 q^{63} - 16 q^{64} - 28 q^{65} - 6 q^{66} + 16 q^{69} - 6 q^{70} - 30 q^{71} - 18 q^{73} + 6 q^{74} - 18 q^{76} - 34 q^{77} - 2 q^{78} - 24 q^{79} + 16 q^{81} - 12 q^{82} - 10 q^{84} + 72 q^{85} + 4 q^{87} + 12 q^{88} - 42 q^{89} - 8 q^{90} - 18 q^{91} - 32 q^{92} - 12 q^{93} + 48 q^{94} - 40 q^{95} - 6 q^{97} - 12 q^{98}+O(q^{100}) \) 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9 - 8 * q^10 - 8 * q^12 - 10 * q^13 + 4 * q^14 - 8 * q^16 - 8 * q^21 + 6 * q^22 - 16 * q^23 + 2 * q^26 - 16 * q^27 + 10 * q^28 - 4 * q^29 + 8 * q^30 + 12 * q^31 + 16 * q^35 + 8 * q^36 + 30 * q^37 - 2 * q^38 + 10 * q^39 - 4 * q^40 - 18 * q^41 - 4 * q^42 - 32 * q^43 + 6 * q^44 + 12 * q^46 + 66 * q^47 + 8 * q^48 - 2 * q^49 + 36 * q^50 + 4 * q^52 + 2 * q^53 + 16 * q^55 + 2 * q^56 - 36 * q^59 - 8 * q^61 + 4 * q^62 + 8 * q^63 - 16 * q^64 - 28 * q^65 - 6 * q^66 + 16 * q^69 - 6 * q^70 - 30 * q^71 - 18 * q^73 + 6 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 + 16 * q^81 - 12 * q^82 - 10 * q^84 + 72 * q^85 + 4 * q^87 + 12 * q^88 - 42 * q^89 - 8 * q^90 - 18 * q^91 - 32 * q^92 - 12 * q^93 + 48 * q^94 - 40 * q^95 - 6 * q^97 - 12 * q^98

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