LMFDB - Embedded newform 546.2.bm.a.205.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$16$
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			205.1
Root			$-1.75225i$ of defining polynomial
Character	$\chi$	$=$	546.205
Dual form			546.2.bm.a.277.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-2.81905 - 1.62758i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.54873 + 2.14510i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-2.81905 - 1.62758i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.54873 + 2.14510i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.62758 + 2.81905i) q^{10} +(1.98522 + 1.14617i) 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} +1.00000 q^{16} +0.782978 q^{17} +(-0.866025 + 0.500000i) q^{18} +(-4.48946 + 2.59199i) q^{19} +(2.81905 + 1.62758i) q^{20} +(1.08335 + 2.41379i) q^{21} +(1.14617 - 1.98522i) q^{22} -0.325722 q^{23} +(0.866025 + 0.500000i) q^{24} +(2.79801 + 4.84630i) q^{25} +(0.484638 + 3.57283i) q^{26} -1.00000 q^{27} +(1.54873 - 2.14510i) q^{28} +(3.35386 + 5.80906i) q^{29} +(1.62758 + 2.81905i) q^{30} +(-5.69921 + 3.29044i) q^{31} -1.00000i q^{32} +(1.98522 - 1.14617i) q^{33} -0.782978i q^{34} +(7.85724 - 3.52646i) q^{35} +(0.500000 + 0.866025i) q^{36} -10.6319i q^{37} +(2.59199 + 4.48946i) q^{38} +(-1.36671 + 3.33648i) q^{39} +(1.62758 - 2.81905i) q^{40} +(-0.818943 + 0.472817i) q^{41} +(2.41379 - 1.08335i) q^{42} +(-4.81185 + 8.33436i) q^{43} +(-1.98522 - 1.14617i) q^{44} +3.25515i q^{45} +0.325722i q^{46} +(-2.14659 - 1.23934i) q^{47} +(0.500000 - 0.866025i) q^{48} +(-2.20290 - 6.64434i) q^{49} +(4.84630 - 2.79801i) q^{50} +(0.391489 - 0.678079i) q^{51} +(3.57283 - 0.484638i) q^{52} +(-6.83920 - 11.8458i) q^{53} +1.00000i q^{54} +(-3.73096 - 6.46221i) q^{55} +(-2.14510 - 1.54873i) q^{56} +5.18398i q^{57} +(5.80906 - 3.35386i) q^{58} +0.614234i q^{59} +(2.81905 - 1.62758i) q^{60} +(-0.114113 - 0.197650i) q^{61} +(3.29044 + 5.69921i) q^{62} +(2.63207 + 0.268687i) q^{63} -1.00000 q^{64} +(10.8608 + 4.44884i) q^{65} +(-1.14617 - 1.98522i) q^{66} +(7.97716 + 4.60562i) q^{67} -0.782978 q^{68} +(-0.162861 + 0.282083i) q^{69} +(-3.52646 - 7.85724i) q^{70} +(-12.7983 - 7.38911i) q^{71} +(0.866025 - 0.500000i) q^{72} +(-11.6734 + 6.73964i) q^{73} -10.6319 q^{74} +5.59603 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} +(-2.81905 - 1.62758i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.472817 + 0.818943i) q^{82} -7.46409i q^{83} +(-1.08335 - 2.41379i) q^{84} +(-2.20725 - 1.27436i) q^{85} +(8.33436 + 4.81185i) q^{86} +6.70773 q^{87} +(-1.14617 + 1.98522i) q^{88} +9.06656i q^{89} +3.25515 q^{90} +(4.49374 - 8.41465i) q^{91} +0.325722 q^{92} +6.58088i q^{93} +(-1.23934 + 2.14659i) q^{94} +16.8747 q^{95} +(-0.866025 - 0.500000i) q^{96} +(-4.59086 - 2.65054i) q^{97} +(-6.64434 + 2.20290i) q^{98} -2.29234i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9	$ 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9} + 4 q^{10} + 6 q^{11} - 8 q^{12} - 10 q^{13} + 4 q^{14} + 16 q^{16} + 18 q^{19} + 8 q^{21} + 6 q^{22} + 32 q^{23} - 4 q^{26} - 16 q^{27} + 2 q^{28} - 4 q^{29} - 4 q^{30} - 12 q^{31} + 6 q^{33} - 2 q^{35} + 8 q^{36} - 2 q^{38} - 14 q^{39} - 4 q^{40} - 18 q^{41} + 2 q^{42} - 32 q^{43} - 6 q^{44} - 66 q^{47} + 8 q^{48} + 22 q^{49} + 36 q^{50} + 10 q^{52} + 2 q^{53} + 16 q^{55} - 4 q^{56} + 24 q^{58} + 4 q^{61} + 4 q^{62} + 10 q^{63} - 16 q^{64} + 38 q^{65} - 6 q^{66} + 36 q^{67} + 16 q^{69} + 6 q^{70} - 30 q^{71} + 18 q^{73} - 12 q^{74} - 18 q^{76} - 34 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 6 q^{82} - 8 q^{84} + 72 q^{85} - 8 q^{87} - 6 q^{88} - 8 q^{90} - 2 q^{91} - 32 q^{92} - 24 q^{94} + 80 q^{95} - 6 q^{97} - 60 q^{98}+O(q^{100}) $ 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9 + 4 * q^10 + 6 * q^11 - 8 * q^12 - 10 * q^13 + 4 * q^14 + 16 * q^16 + 18 * q^19 + 8 * q^21 + 6 * q^22 + 32 * q^23 - 4 * q^26 - 16 * q^27 + 2 * q^28 - 4 * q^29 - 4 * q^30 - 12 * q^31 + 6 * q^33 - 2 * q^35 + 8 * q^36 - 2 * q^38 - 14 * q^39 - 4 * q^40 - 18 * q^41 + 2 * q^42 - 32 * q^43 - 6 * q^44 - 66 * q^47 + 8 * q^48 + 22 * q^49 + 36 * q^50 + 10 * q^52 + 2 * q^53 + 16 * q^55 - 4 * q^56 + 24 * q^58 + 4 * q^61 + 4 * q^62 + 10 * q^63 - 16 * q^64 + 38 * q^65 - 6 * q^66 + 36 * q^67 + 16 * q^69 + 6 * q^70 - 30 * q^71 + 18 * q^73 - 12 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 6 * q^82 - 8 * q^84 + 72 * q^85 - 8 * q^87 - 6 * q^88 - 8 * q^90 - 2 * q^91 - 32 * q^92 - 24 * q^94 + 80 * q^95 - 6 * q^97 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.00000			−0.500000
$5$	−2.81905	−	1.62758i	−1.26072	−	0.727875i	−0.287503	−	0.957780i	$-0.592825\pi$
$5$	−2.81905	−	1.62758i	−1.26072	−	0.727875i	−0.973213	+	0.229905i	$0.926158\pi$
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	−1.54873	+	2.14510i	−0.585363	+	0.810771i
$7$	−1.54873	+	2.14510i	−0.585363	+	0.810771i
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.62758	+	2.81905i	−0.514685	+	0.891461i
$11$	1.98522	+	1.14617i	0.598567	+	0.345583i	0.768478	−	0.639877i	$-0.221015\pi$
$11$	1.98522	+	1.14617i	0.598567	+	0.345583i	−0.169911	+	0.985459i	$0.554348\pi$
$12$	−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
$16$	1.00000			0.250000
$17$	0.782978			0.189900			0.0949500	−	0.995482i	$-0.469731\pi$
$17$	0.782978			0.189900			0.0949500	+	0.995482i	$0.469731\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	−4.48946	+	2.59199i	−1.02995	+	0.594643i	−0.916971	−	0.398954i	$-0.869373\pi$
$19$	−4.48946	+	2.59199i	−1.02995	+	0.594643i	−0.112981	+	0.993597i	$0.536040\pi$
$20$	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
$23$	−0.325722			−0.0679177			−0.0339588	−	0.999423i	$-0.510812\pi$
$23$	−0.325722			−0.0679177			−0.0339588	+	0.999423i	$0.510812\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	2.79801	+	4.84630i	0.559603	+	0.969260i
$26$	0.484638	+	3.57283i	0.0950454	+	0.700690i
$27$	−1.00000			−0.192450
$28$	1.54873	−	2.14510i	0.292682	−	0.405386i
$29$	3.35386	+	5.80906i	0.622797	+	1.07872i	0.988963	+	0.148166i	$0.0473369\pi$
$29$	3.35386	+	5.80906i	0.622797	+	1.07872i	−0.366166	+	0.930550i	$0.619330\pi$
$30$	1.62758	+	2.81905i	0.297154	+	0.514685i
$31$	−5.69921	+	3.29044i	−1.02361	+	0.590980i	−0.915147	−	0.403121i	$-0.867925\pi$
$31$	−5.69921	+	3.29044i	−1.02361	+	0.590980i	−0.108461	+	0.994101i	$0.534592\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.98522	−	1.14617i	0.345583	−	0.199522i
$34$		−	0.782978i		−	0.134280i
$35$	7.85724	−	3.52646i	1.32812	−	0.596081i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$		−	10.6319i		−	1.74787i	−0.486039	−	0.873937i	$-0.661559\pi$
$37$		−	10.6319i		−	1.74787i	0.486039	−	0.873937i	$-0.338441\pi$
$38$	2.59199	+	4.48946i	0.420476	+	0.728286i
$39$	−1.36671	+	3.33648i	−0.218848	+	0.534265i
$40$	1.62758	−	2.81905i	0.257343	−	0.445730i
$41$	−0.818943	+	0.472817i	−0.127897	+	0.0738416i	−0.562584	−	0.826740i	$-0.690193\pi$
$41$	−0.818943	+	0.472817i	−0.127897	+	0.0738416i	0.434686	+	0.900582i	$0.356859\pi$
$42$	2.41379	−	1.08335i	0.372455	−	0.167164i
$43$	−4.81185	+	8.33436i	−0.733800	+	1.27098i	0.221448	+	0.975172i	$0.428922\pi$
$43$	−4.81185	+	8.33436i	−0.733800	+	1.27098i	−0.955248	+	0.295806i	$0.904412\pi$
$44$	−1.98522	−	1.14617i	−0.299284	−	0.172791i
$45$			3.25515i			0.485250i
$46$			0.325722i			0.0480250i
$47$	−2.14659	−	1.23934i	−0.313113	−	0.180776i	0.335206	−	0.942145i	$-0.391194\pi$
$47$	−2.14659	−	1.23934i	−0.313113	−	0.180776i	−0.648319	+	0.761369i	$0.724527\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−2.20290	−	6.64434i	−0.314699	−	0.949191i
$50$	4.84630	−	2.79801i	0.685371	−	0.395699i
$51$	0.391489	−	0.678079i	0.0548194	−	0.0949500i
$52$	3.57283	−	0.484638i	0.495463	−	0.0672072i
$53$	−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	$-0.555318\pi$
$54$			1.00000i			0.136083i
$55$	−3.73096	−	6.46221i	−0.503082	−	0.871364i
$56$	−2.14510	−	1.54873i	−0.286651	−	0.206957i
$57$			5.18398i			0.686635i
$58$	5.80906	−	3.35386i	0.762767	−	0.440384i
$59$			0.614234i			0.0799664i	0.999200	+	0.0399832i	$0.0127304\pi$
$59$			0.614234i			0.0799664i	−0.999200	+	0.0399832i	$0.987270\pi$
$60$	2.81905	−	1.62758i	0.363937	−	0.210119i
$61$	−0.114113	−	0.197650i	−0.0146107	−	0.0253065i	0.858628	−	0.512600i	$-0.171318\pi$
$61$	−0.114113	−	0.197650i	−0.0146107	−	0.0253065i	−0.873238	+	0.487293i	$0.837984\pi$
$62$	3.29044	+	5.69921i	0.417886	+	0.723800i
$63$	2.63207	+	0.268687i	0.331610	+	0.0338513i
$64$	−1.00000			−0.125000
$65$	10.8608	+	4.44884i	1.34711	+	0.551811i
$66$	−1.14617	−	1.98522i	−0.141084	−	0.244364i
$67$	7.97716	+	4.60562i	0.974565	+	0.562665i	0.900625	−	0.434597i	$-0.143109\pi$
$67$	7.97716	+	4.60562i	0.974565	+	0.562665i	0.0739403	+	0.997263i	$0.476443\pi$
$68$	−0.782978			−0.0949500
$69$	−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	−0.999753	−	0.0222287i	$-0.992924\pi$
$71$	−12.7983	−	7.38911i	−1.51888	−	0.876926i	−0.519127	−	0.854697i	$-0.673743\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	−11.6734	+	6.73964i	−1.36627	+	0.788815i	−0.990449	−	0.137878i	$-0.955972\pi$
$73$	−11.6734	+	6.73964i	−1.36627	+	0.788815i	−0.375819	+	0.926693i	$0.622638\pi$
$74$	−10.6319			−1.23593
$75$	5.59603			0.646174
$76$	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	$0.143356\pi$
$80$	−2.81905	−	1.62758i	−0.315179	−	0.181969i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.472817	+	0.818943i	0.0522139	+	0.0904372i
$83$		−	7.46409i		−	0.819290i	−0.912245	−	0.409645i	$-0.865653\pi$
$83$		−	7.46409i		−	0.819290i	0.912245	−	0.409645i	$-0.134347\pi$
$84$	−1.08335	−	2.41379i	−0.118203	−	0.263366i
$85$	−2.20725	−	1.27436i	−0.239410	−	0.138223i
$86$	8.33436	+	4.81185i	0.898717	+	0.518875i
$87$	6.70773			0.719144
$88$	−1.14617	+	1.98522i	−0.122182	+	0.211625i
$89$			9.06656i			0.961053i	0.876980	+	0.480527i	$0.159554\pi$
$89$			9.06656i			0.961053i	−0.876980	+	0.480527i	$0.840446\pi$
$90$	3.25515			0.343123
$91$	4.49374	−	8.41465i	0.471072	−	0.882095i
$92$	0.325722			0.0339588
$93$			6.58088i			0.682405i
$94$	−1.23934	+	2.14659i	−0.127828	+	0.221404i
$95$	16.8747			1.73130
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	−4.59086	−	2.65054i	−0.466132	−	0.269121i	0.248487	−	0.968635i	$-0.420067\pi$
$97$	−4.59086	−	2.65054i	−0.466132	−	0.269121i	−0.714619	+	0.699514i	$0.753400\pi$
$98$	−6.64434	+	2.20290i	−0.671180	+	0.222526i
$99$		−	2.29234i		−	0.230389i
$100$	−2.79801	−	4.84630i	−0.279801	−	0.484630i
$101$	3.66599	−	6.34968i	0.364779	−	0.631817i	−0.623961	−	0.781455i	$-0.714478\pi$
$101$	3.66599	−	6.34968i	0.364779	−	0.631817i	0.988741	+	0.149639i	$0.0478111\pi$
$102$	−0.678079	−	0.391489i	−0.0671398	−	0.0387632i
$103$	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
$107$	17.3951			1.68165			0.840826	−	0.541306i	$-0.182070\pi$
$107$	17.3951			1.68165			0.840826	+	0.541306i	$0.182070\pi$
$108$	1.00000			0.0962250
$109$	−10.2681	+	5.92831i	−0.983510	+	0.567829i	−0.903328	−	0.428951i	$-0.858883\pi$
$109$	−10.2681	+	5.92831i	−0.983510	+	0.567829i	−0.0801817	+	0.996780i	$0.525550\pi$
$110$	−6.46221	+	3.73096i	−0.616147	+	0.355733i
$111$	−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	0.192519	+	0.981293i	$0.438334\pi$
$113$	−8.01051	+	13.8746i	−0.753565	+	1.30521i	−0.946084	+	0.323920i	$0.894999\pi$
$114$	5.18398			0.485524
$115$	0.918225	+	0.530137i	0.0856249	+	0.0494355i
$116$	−3.35386	−	5.80906i	−0.311398	−	0.539358i
$117$	2.20612	+	2.85184i	0.203956	+	0.263653i
$118$	0.614234			0.0565448
$119$	−1.21262	+	1.67957i	−0.111161	+	0.153966i
$120$	−1.62758	−	2.81905i	−0.148577	−	0.257343i
$121$	−2.87259	−	4.97548i	−0.261145	−	0.452316i
$122$	−0.197650	+	0.114113i	−0.0178944	+	0.0103314i
$123$			0.945634i			0.0852650i
$124$	5.69921	−	3.29044i	0.511804	−	0.295490i
$125$		−	1.94016i		−	0.173533i
$126$	0.268687	−	2.63207i	0.0239365	−	0.234484i
$127$	0.284508	+	0.492782i	0.0252460	+	0.0437273i	0.878372	−	0.477977i	$-0.158630\pi$
$127$	0.284508	+	0.492782i	0.0252460	+	0.0437273i	−0.853126	+	0.521704i	$0.825296\pi$
$128$			1.00000i			0.0883883i
$129$	4.81185	+	8.33436i	0.423659	+	0.733800i
$130$	4.44884	−	10.8608i	0.390189	−	0.952552i
$131$	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
$133$	1.39287	−	13.6446i	0.120777	−	1.18314i
$134$	4.60562	−	7.97716i	0.397865	−	0.689122i
$135$	2.81905	+	1.62758i	0.242625	+	0.140080i
$136$			0.782978i			0.0671398i
$137$		−	11.0183i		−	0.941359i	−0.882304	−	0.470679i	$-0.844009\pi$
$137$		−	11.0183i		−	0.941359i	0.882304	−	0.470679i	$-0.155991\pi$
$138$	0.282083	+	0.162861i	0.0240125	+	0.0138636i
$139$	6.38785	−	11.0641i	0.541811	−	0.938444i	−0.456989	−	0.889472i	$-0.651072\pi$
$139$	6.38785	−	11.0641i	0.541811	−	0.938444i	0.998800	−	0.0489716i	$-0.0155944\pi$
$140$	−7.85724	+	3.52646i	−0.664058	+	0.298040i
$141$	−2.14659	+	1.23934i	−0.180776	+	0.104371i
$142$	−7.38911	+	12.7983i	−0.620080	+	1.07401i
$143$	−7.64834	−	3.13295i	−0.639587	−	0.261991i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$		−	21.8347i		−	1.81327i
$146$	6.73964	+	11.6734i	0.557776	+	0.966097i
$147$	−6.85561	−	1.41441i	−0.565442	−	0.116658i
$148$			10.6319i			0.873937i
$149$	−10.2760	+	5.93287i	−0.841845	+	0.486040i	−0.857891	−	0.513832i	$-0.828226\pi$
$149$	−10.2760	+	5.93287i	−0.841845	+	0.486040i	0.0160456	+	0.999871i	$0.494892\pi$
$150$		−	5.59603i		−	0.456914i
$151$	−10.1344	+	5.85109i	−0.824725	+	0.476155i	−0.852043	−	0.523472i	$-0.824637\pi$
$151$	−10.1344	+	5.85109i	−0.824725	+	0.476155i	0.0273184	+	0.999627i	$0.491303\pi$
$152$	−2.59199	−	4.48946i	−0.210238	−	0.364143i
$153$	−0.391489	−	0.678079i	−0.0316500	−	0.0548194i
$154$	2.48340	+	5.53321i	0.200118	+	0.445879i
$155$	21.4218			1.72064
$156$	1.36671	−	3.33648i	0.109424	−	0.267132i
$157$	−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	$0.937756\pi$
$158$	−1.12642	−	0.650337i	−0.0896130	−	0.0517381i
$159$	−13.6784			−1.08477
$160$	−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
$163$	−0.715574	+	0.413137i	−0.0560481	+	0.0323594i	−0.527762	−	0.849392i	$-0.676969\pi$
$163$	−0.715574	+	0.413137i	−0.0560481	+	0.0323594i	0.471714	+	0.881752i	$0.343635\pi$
$164$	0.818943	−	0.472817i	0.0639487	−	0.0369208i
$165$	−7.46191			−0.580909
$166$	−7.46409			−0.579326
$167$	4.67389	−	2.69847i	0.361676	−	0.208814i	−0.308140	−	0.951341i	$-0.599706\pi$
$167$	4.67389	−	2.69847i	0.361676	−	0.208814i	0.669816	+	0.742527i	$0.266373\pi$
$168$	−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
$171$	4.48946	+	2.59199i	0.343317	+	0.198214i
$172$	4.81185	−	8.33436i	0.366900	−	0.635489i
$173$	−6.78883	−	11.7586i	−0.516145	−	0.893990i	−0.999824	−	0.0187442i	$-0.994033\pi$
$173$	−6.78883	−	11.7586i	−0.516145	−	0.893990i	0.483679	−	0.875245i	$-0.339300\pi$
$174$		−	6.70773i		−	0.508511i
$175$	−14.7292	−	1.50358i	−1.11342	−	0.113660i
$176$	1.98522	+	1.14617i	0.149642	+	0.0863957i
$177$	0.531942	+	0.307117i	0.0399832	+	0.0230843i
$178$	9.06656			0.679567
$179$	8.46923	−	14.6691i	0.633020	−	1.09642i	−0.353911	−	0.935279i	$-0.615148\pi$
$179$	8.46923	−	14.6691i	0.633020	−	1.09642i	0.986931	−	0.161143i	$-0.0515182\pi$
$180$		−	3.25515i		−	0.242625i
$181$	−12.8540			−0.955427			−0.477713	−	0.878516i	$-0.658534\pi$
$181$	−12.8540			−0.955427			−0.477713	+	0.878516i	$0.658534\pi$
$182$	−8.41465	−	4.49374i	−0.623735	−	0.333098i
$183$	−0.228227			−0.0168710
$184$		−	0.325722i		−	0.0240125i
$185$	−17.3042	+	29.9718i	−1.27223	+	2.20357i
$186$	6.58088			0.482533
$187$	1.55439	+	0.897425i	0.113668	+	0.0656262i
$188$	2.14659	+	1.23934i	0.156556	+	0.0903879i
$189$	1.54873	−	2.14510i	0.112653	−	0.156033i
$190$		−	16.8747i		−	1.22422i
$191$	10.1614	+	17.6001i	0.735253	+	1.27350i	0.954612	+	0.297852i	$0.0962701\pi$
$191$	10.1614	+	17.6001i	0.735253	+	1.27350i	−0.219359	+	0.975644i	$0.570397\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	17.0008	+	9.81539i	1.22374	+	0.706528i	0.965714	−	0.259610i	$-0.0835940\pi$
$193$	17.0008	+	9.81539i	1.22374	+	0.706528i	0.258028	+	0.966137i	$0.416927\pi$
$194$	−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	0.0964995	−	0.995333i	$-0.469235\pi$
$197$	14.1302	−	8.15806i	1.00673	−	0.581238i	0.910233	+	0.414096i	$0.135902\pi$
$198$	−2.29234			−0.162909
$199$	3.92793			0.278444			0.139222	−	0.990261i	$-0.455540\pi$
$199$	3.92793			0.278444			0.139222	+	0.990261i	$0.455540\pi$
$200$	−4.84630	+	2.79801i	−0.342685	+	0.197849i
$201$	7.97716	−	4.60562i	0.562665	−	0.324855i
$202$	−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
$205$	3.07819			0.214990
$206$	−1.46160	−	0.843858i	−0.101835	−	0.0587944i
$207$	0.162861	+	0.282083i	0.0113196	+	0.0196061i
$208$	−3.57283	+	0.484638i	−0.247731	+	0.0336036i
$209$	−11.8834			−0.821994
$210$	−8.56780	−	0.874616i	−0.591235	−	0.0603543i
$211$	11.9378	+	20.6769i	0.821834	+	1.42346i	0.904315	+	0.426866i	$0.140382\pi$
$211$	11.9378	+	20.6769i	0.821834	+	1.42346i	−0.0824812	+	0.996593i	$0.526284\pi$
$212$	6.83920	+	11.8458i	0.469718	+	0.813576i
$213$	−12.7983	+	7.38911i	−0.876926	+	0.506293i
$214$		−	17.3951i		−	1.18911i
$215$	27.1296	−	15.6633i	1.85023	−	1.06823i
$216$		−	1.00000i		−	0.0680414i
$217$	1.76819	−	17.3213i	0.120033	−	1.17585i
$218$	5.92831	+	10.2681i	0.401516	+	0.695446i
$219$			13.4793i			0.910845i
$220$	3.73096	+	6.46221i	0.251541	+	0.435682i
$221$	−2.79745	+	0.379461i	−0.188177	+	0.0255253i
$222$	−5.31595	+	9.20750i	−0.356783	+	0.617967i
$223$	−2.87194	+	1.65812i	−0.192319	+	0.111036i	−0.593068	−	0.805152i	$-0.702083\pi$
$223$	−2.87194	+	1.65812i	−0.192319	+	0.111036i	0.400749	+	0.916188i	$0.368750\pi$
$224$	2.14510	+	1.54873i	0.143325	+	0.103479i
$225$	2.79801	−	4.84630i	0.186534	−	0.323087i
$226$	13.8746	+	8.01051i	0.922925	+	0.532851i
$227$		−	10.9947i		−	0.729746i	−0.931057	−	0.364873i	$-0.881112\pi$
$227$		−	10.9947i		−	0.729746i	0.931057	−	0.364873i	$-0.118888\pi$
$228$		−	5.18398i		−	0.343317i
$229$	20.2181	+	11.6729i	1.33605	+	0.771368i	0.986219	−	0.165445i	$-0.0529062\pi$
$229$	20.2181	+	11.6729i	1.33605	+	0.771368i	0.349830	+	0.936813i	$0.386240\pi$
$230$	0.530137	−	0.918225i	0.0349562	−	0.0605459i
$231$	−0.615920	+	6.03360i	−0.0405246	+	0.396982i
$232$	−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	$0.211555\pi$
$234$	2.85184	−	2.20612i	0.186431	−	0.144219i
$235$	4.03423	+	6.98749i	0.263164	+	0.455814i
$236$		−	0.614234i		−	0.0399832i
$237$	−0.650337	−	1.12642i	−0.0422440	−	0.0731687i
$238$	1.67957	+	1.21262i	0.108870	+	0.0786024i
$239$			5.59389i			0.361839i	0.983498	+	0.180919i	$0.0579073\pi$
$239$			5.59389i			0.361839i	−0.983498	+	0.180919i	$0.942093\pi$
$240$	−2.81905	+	1.62758i	−0.181969	+	0.105060i
$241$			29.2191i			1.88217i	0.338172	+	0.941084i	$0.390191\pi$
$241$			29.2191i			1.88217i	−0.338172	+	0.941084i	$0.609809\pi$
$242$	−4.97548	+	2.87259i	−0.319836	+	0.184657i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	0.114113	+	0.197650i	0.00730537	+	0.0126533i
$245$	−4.60411	+	22.3161i	−0.294146	+	1.42572i
$246$	0.945634			0.0602914
$247$	14.7839	−	11.4365i	0.940677	−	0.727687i
$248$	−3.29044	−	5.69921i	−0.208943	−	0.361900i
$249$	−6.46409	−	3.73204i	−0.409645	−	0.236509i
$250$	−1.94016			−0.122707
$251$	6.12153	−	10.6028i	0.386388	−	0.669243i	−0.605573	−	0.795790i	$-0.707056\pi$
$251$	6.12153	−	10.6028i	0.386388	−	0.669243i	0.991961	+	0.126547i	$0.0403894\pi$
$252$	−2.63207	−	0.268687i	−0.165805	−	0.0169257i
$253$	−0.646630	−	0.373332i	−0.0406533	−	0.0234712i
$254$	0.492782	−	0.284508i	0.0309199	−	0.0178516i
$255$	−2.20725	+	1.27436i	−0.138223	+	0.0798033i
$256$	1.00000			0.0625000
$257$	−4.39912			−0.274409			−0.137205	−	0.990543i	$-0.543812\pi$
$257$	−4.39912			−0.274409			−0.137205	+	0.990543i	$0.543812\pi$
$258$	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
$262$	−7.13838	−	4.12135i	−0.441011	−	0.254618i
$263$	−9.57034	+	16.5763i	−0.590132	+	1.02214i	0.404082	+	0.914723i	$0.367591\pi$
$263$	−9.57034	+	16.5763i	−0.590132	+	1.02214i	−0.994214	+	0.107416i	$0.965742\pi$
$264$	1.14617	+	1.98522i	0.0705418	+	0.122182i
$265$			44.5253i			2.73517i
$266$	−13.6446	−	1.39287i	−0.836605	−	0.0854021i
$267$	7.85187	+	4.53328i	0.480527	+	0.277432i
$268$	−7.97716	−	4.60562i	−0.487283	−	0.281333i
$269$	3.09430			0.188663			0.0943315	−	0.995541i	$-0.469929\pi$
$269$	3.09430			0.188663			0.0943315	+	0.995541i	$0.469929\pi$
$270$	1.62758	−	2.81905i	0.0990512	−	0.171562i
$271$			26.3111i			1.59828i	0.601143	+	0.799142i	$0.294712\pi$
$271$			26.3111i			1.59828i	−0.601143	+	0.799142i	$0.705288\pi$
$272$	0.782978			0.0474750
$273$	−5.04043	−	8.09902i	−0.305061	−	0.490175i
$274$	−11.0183			−0.665641
$275$			12.8280i			0.773557i
$276$	0.162861	−	0.282083i	0.00980307	−	0.0169794i
$277$	11.1939			0.672574			0.336287	−	0.941760i	$-0.390829\pi$
$277$	11.1939			0.672574			0.336287	+	0.941760i	$0.390829\pi$
$278$	−11.0641	−	6.38785i	−0.663580	−	0.383118i
$279$	5.69921	+	3.29044i	0.341203	+	0.196993i
$280$	3.52646	+	7.85724i	0.210746	+	0.469560i
$281$		−	1.85065i		−	0.110401i	−0.998475	−	0.0552003i	$-0.982420\pi$
$281$		−	1.85065i		−	0.110401i	0.998475	−	0.0552003i	$-0.0175797\pi$
$282$	1.23934	+	2.14659i	0.0738014	+	0.127828i
$283$	11.0823	−	19.1951i	0.658774	−	1.14103i	−0.322159	−	0.946686i	$-0.604409\pi$
$283$	11.0823	−	19.1951i	0.658774	−	1.14103i	0.980933	−	0.194345i	$-0.0622580\pi$
$284$	12.7983	+	7.38911i	0.759440	+	0.438463i
$285$	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
$289$	−16.3869			−0.963938
$290$	−21.8347			−1.28218
$291$	−4.59086	+	2.65054i	−0.269121	+	0.155377i
$292$	11.6734	−	6.73964i	0.683134	−	0.394408i
$293$	−12.7197	−	7.34371i	−0.743091	−	0.429024i	0.0801008	−	0.996787i	$-0.474476\pi$
$293$	−12.7197	−	7.34371i	−0.743091	−	0.429024i	−0.823192	+	0.567763i	$0.807809\pi$
$294$	−1.41441	+	6.85561i	−0.0824898	+	0.399828i
$295$	0.999713	−	1.73155i	0.0582055	−	0.100815i
$296$	10.6319			0.617967
$297$	−1.98522	−	1.14617i	−0.115194	−	0.0665075i
$298$	5.93287	+	10.2760i	0.343682	+	0.595275i
$299$	1.16375	−	0.157857i	0.0673013	−	0.00912912i
$300$	−5.59603			−0.323087
$301$	−10.4258	−	23.2295i	−0.600933	−	1.33893i
$302$	5.85109	+	10.1344i	0.336692	+	0.583168i
$303$	−3.66599	−	6.34968i	−0.210606	−	0.364779i
$304$	−4.48946	+	2.59199i	−0.257488	+	0.148661i
$305$			0.742914i			0.0425391i
$306$	−0.678079	+	0.391489i	−0.0387632	+	0.0223799i
$307$		−	1.73631i		−	0.0990965i	−0.998772	−	0.0495483i	$-0.984222\pi$
$307$		−	1.73631i		−	0.0990965i	0.998772	−	0.0495483i	$-0.0157782\pi$
$308$	5.53321	−	2.48340i	0.315284	−	0.141505i
$309$	−0.843858	−	1.46160i	−0.0480054	−	0.0831478i
$310$		−	21.4218i		−	1.21667i
$311$	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	$0.707224\pi$
$312$	−3.33648	−	1.36671i	−0.188891	−	0.0773745i
$313$	−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
$315$	−6.98263	−	5.04134i	−0.393426	−	0.284047i
$316$	−0.650337	+	1.12642i	−0.0365843	+	0.0633659i
$317$	−8.10889	−	4.68167i	−0.455441	−	0.262949i	0.254685	−	0.967024i	$-0.418028\pi$
$317$	−8.10889	−	4.68167i	−0.455441	−	0.262949i	−0.710125	+	0.704075i	$0.751362\pi$
$318$			13.6784i			0.767047i
$319$			15.3764i			0.860912i
$320$	2.81905	+	1.62758i	0.157589	+	0.0909843i
$321$	8.69757	−	15.0646i	0.485451	−	0.840826i
$322$	−0.698705	−	0.504454i	−0.0389373	−	0.0281121i
$323$	−3.51515	+	2.02947i	−0.195588	+	0.112923i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−12.3455	−	15.9590i	−0.684807	−	0.885246i
$326$	0.413137	+	0.715574i	0.0228815	+	0.0396320i
$327$			11.8566i			0.655673i
$328$	−0.472817	−	0.818943i	−0.0261070	−	0.0452186i
$329$	5.98298	−	2.68526i	0.329852	−	0.148043i
$330$			7.46191i			0.410765i
$331$	9.65401	−	5.57375i	0.530633	−	0.306361i	−0.210641	−	0.977563i	$-0.567555\pi$
$331$	9.65401	−	5.57375i	0.530633	−	0.306361i	0.741274	+	0.671203i	$0.234222\pi$
$332$			7.46409i			0.409645i
$333$	−9.20750	+	5.31595i	−0.504568	+	0.291312i
$334$	−2.69847	−	4.67389i	−0.147654	−	0.255744i
$335$	−14.9920	−	25.9669i	−0.819100	−	1.41872i
$336$	1.08335	+	2.41379i	0.0591014	+	0.131683i
$337$	7.91654			0.431241			0.215621	−	0.976477i	$-0.430823\pi$
$337$	7.91654			0.431241			0.215621	+	0.976477i	$0.430823\pi$
$338$	−3.46306	−	12.5303i	−0.188366	−	0.681556i
$339$	8.01051	+	13.8746i	0.435071	+	0.753565i
$340$	2.20725	+	1.27436i	0.119705	+	0.0691117i
$341$	−15.0856			−0.816930
$342$	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
$345$	0.918225	−	0.530137i	0.0494355	−	0.0285416i
$346$	−11.7586	+	6.78883i	−0.632146	+	0.364970i
$347$	−26.0298			−1.39735			−0.698676	−	0.715438i	$-0.746227\pi$
$347$	−26.0298			−1.39735			−0.698676	+	0.715438i	$0.746227\pi$
$348$	−6.70773			−0.359572
$349$	−12.6350	+	7.29484i	−0.676338	+	0.390484i	−0.798474	−	0.602030i	$-0.794359\pi$
$349$	−12.6350	+	7.29484i	−0.676338	+	0.390484i	0.122136	+	0.992513i	$0.461026\pi$
$350$	−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
$353$	−9.23564	−	5.33220i	−0.491563	−	0.283804i	0.233659	−	0.972318i	$-0.424930\pi$
$353$	−9.23564	−	5.33220i	−0.491563	−	0.283804i	−0.725223	+	0.688514i	$0.758263\pi$
$354$	0.307117	−	0.531942i	0.0163231	−	0.0282724i
$355$	24.0527	+	41.6605i	1.27658	+	2.21111i
$356$		−	9.06656i		−	0.480527i
$357$	0.848237	+	1.88994i	0.0448935	+	0.100026i
$358$	−14.6691	−	8.46923i	−0.775288	−	0.447613i
$359$	−14.9165	−	8.61207i	−0.787265	−	0.454527i	0.0517340	−	0.998661i	$-0.483525\pi$
$359$	−14.9165	−	8.61207i	−0.787265	−	0.454527i	−0.838999	+	0.544133i	$0.816859\pi$
$360$	−3.25515			−0.171562
$361$	3.93682	−	6.81878i	0.207201	−	0.358883i
$362$			12.8540i			0.675589i
$363$	−5.74519			−0.301544
$364$	−4.49374	+	8.41465i	−0.235536	+	0.441047i
$365$	43.8771			2.29663
$366$			0.228227i			0.0119296i
$367$	−8.56032	+	14.8269i	−0.446845	+	0.773959i	−0.998179	−	0.0603263i	$-0.980786\pi$
$367$	−8.56032	+	14.8269i	−0.446845	+	0.773959i	0.551333	+	0.834285i	$0.314119\pi$
$368$	−0.325722			−0.0169794
$369$	0.818943	+	0.472817i	0.0426325	+	0.0246139i
$370$	29.9718	+	17.3042i	1.55816	+	0.899604i
$371$	36.0026	+	3.67520i	1.86916	+	0.190807i
$372$		−	6.58088i		−	0.341203i
$373$	−6.30021	−	10.9123i	−0.326213	−	0.565017i	0.655544	−	0.755157i	$-0.272439\pi$
$373$	−6.30021	−	10.9123i	−0.326213	−	0.565017i	−0.981757	+	0.190140i	$0.939106\pi$
$374$	0.897425	−	1.55439i	0.0464048	−	0.0803754i
$375$	−1.68023	−	0.970080i	−0.0867666	−	0.0500947i
$376$	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	−0.577680	−	0.816264i	$-0.696042\pi$
$379$	−3.10736	+	1.79403i	−0.159614	+	0.0921533i	0.418065	+	0.908417i	$0.362708\pi$
$380$	−16.8747			−0.865651
$381$	0.569015			0.0291515
$382$	17.6001	−	10.1614i	0.900498	−	0.519903i
$383$	15.7482	−	9.09226i	0.804698	−	0.464593i	−0.0404133	−	0.999183i	$-0.512867\pi$
$383$	15.7482	−	9.09226i	0.804698	−	0.464593i	0.845111	+	0.534590i	$0.179534\pi$
$384$	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
$387$	9.62369			0.489200
$388$	4.59086	+	2.65054i	0.233066	+	0.134561i
$389$	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	$0.589115\pi$
$390$	−7.18128	−	9.28319i	−0.363638	−	0.470073i
$391$	−0.255033			−0.0128976
$392$	6.64434	−	2.20290i	0.335590	−	0.111263i
$393$	−4.12135	−	7.13838i	−0.207894	−	0.360084i
$394$	−8.15806	−	14.1302i	−0.410997	−	0.711868i
$395$	−3.66666	+	2.11695i	−0.184490	+	0.106515i
$396$			2.29234i			0.115194i
$397$	14.6064	−	8.43299i	0.733073	−	0.423240i	−0.0864726	−	0.996254i	$-0.527560\pi$
$397$	14.6064	−	8.43299i	0.733073	−	0.423240i	0.819545	+	0.573015i	$0.194226\pi$
$398$		−	3.92793i		−	0.196890i
$399$	−11.1201	−	8.02856i	−0.556704	−	0.401931i
$400$	2.79801	+	4.84630i	0.139901	+	0.242315i
$401$		−	18.6934i		−	0.933505i	−0.884388	−	0.466753i	$-0.845424\pi$
$401$		−	18.6934i		−	0.933505i	0.884388	−	0.466753i	$-0.154576\pi$
$402$	−4.60562	−	7.97716i	−0.229707	−	0.397865i
$403$	18.7676	−	14.5182i	0.934882	−	0.723205i
$404$	−3.66599	+	6.34968i	−0.182390	+	0.315908i
$405$	2.81905	−	1.62758i	0.140080	−	0.0808750i
$406$	−1.80228	+	17.6552i	−0.0894455	+	0.876214i
$407$	12.1860	−	21.1067i	0.604035	−	1.04622i
$408$	0.678079	+	0.391489i	0.0335699	+	0.0193816i
$409$			4.94626i			0.244577i	0.992495	+	0.122288i	$0.0390233\pi$
$409$			4.94626i			0.244577i	−0.992495	+	0.122288i	$0.960977\pi$
$410$		−	3.07819i		−	0.152021i
$411$	−9.54214	−	5.50916i	−0.470679	−	0.271747i
$412$	−0.843858	+	1.46160i	−0.0415739	+	0.0720081i
$413$	−1.31759	−	0.951280i	−0.0648345	−	0.0468094i
$414$	0.282083	−	0.162861i	0.0138636	−	0.00800417i
$415$	−12.1484	+	21.0416i	−0.596341	+	1.03289i
$416$	0.484638	+	3.57283i	0.0237613	+	0.175172i
$417$	−6.38785	−	11.0641i	−0.312815	−	0.541811i
$418$			11.8834i			0.581238i
$419$	−5.70131	−	9.87496i	−0.278527	−	0.482423i	0.692492	−	0.721426i	$-0.256513\pi$
$419$	−5.70131	−	9.87496i	−0.278527	−	0.482423i	−0.971019	+	0.239002i	$0.923180\pi$
$420$	−0.874616	+	8.56780i	−0.0426769	+	0.418066i
$421$			9.82089i			0.478641i	0.970941	+	0.239320i	$0.0769247\pi$
$421$			9.82089i			0.478641i	−0.970941	+	0.239320i	$0.923075\pi$
$422$	20.6769	−	11.9378i	1.00654	−	0.581124i
$423$			2.47867i			0.120517i
$424$	11.8458	−	6.83920i	0.575285	−	0.332141i
$425$	2.19078	+	3.79455i	0.106269	+	0.184063i
$426$	7.38911	+	12.7983i	0.358003	+	0.620080i
$427$	0.600710	+	0.0613215i	0.0290704	+	0.00296756i
$428$	−17.3951			−0.840826
$429$	−6.53739	+	5.05718i	−0.315628	+	0.244163i
$430$	−15.6633	−	27.1296i	−0.755351	−	1.30831i
$431$	7.46047	+	4.30730i	0.359358	+	0.207476i	0.668799	−	0.743443i	$-0.266809\pi$
$431$	7.46047	+	4.30730i	0.359358	+	0.207476i	−0.309441	+	0.950919i	$0.600142\pi$
$432$	−1.00000			−0.0481125
$433$	−11.7293	+	20.3157i	−0.563673	+	0.976310i	0.433499	+	0.901154i	$0.357279\pi$
$433$	−11.7293	+	20.3157i	−0.563673	+	0.976310i	−0.997172	+	0.0751557i	$0.976055\pi$
$434$	−17.3213	−	1.76819i	−0.831451	−	0.0848760i
$435$	−18.9094	−	10.9173i	−0.906636	−	0.523446i
$436$	10.2681	−	5.92831i	0.491755	−	0.283915i
$437$	1.46231	−	0.844267i	0.0699520	−	0.0403868i
$438$	13.4793			0.644065
$439$	−37.3484			−1.78254			−0.891272	−	0.453470i	$-0.850186\pi$
$439$	−37.3484			−1.78254			−0.891272	+	0.453470i	$0.850186\pi$
$440$	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	$0.317025\pi$
$444$	9.20750	+	5.31595i	0.436968	+	0.252284i
$445$	14.7565	−	25.5590i	0.699526	−	1.21161i
$446$	1.65812	+	2.87194i	0.0785140	+	0.135990i
$447$			11.8657i			0.561230i
$448$	1.54873	−	2.14510i	0.0731704	−	0.101346i
$449$	−32.7190	−	18.8903i	−1.54410	−	0.891489i	−0.998573	−	0.0533973i	$-0.982995\pi$
$449$	−32.7190	−	18.8903i	−1.54410	−	0.891489i	−0.545530	−	0.838091i	$-0.683672\pi$
$450$	−4.84630	−	2.79801i	−0.228457	−	0.131900i
$451$	−2.16771			−0.102074
$452$	8.01051	−	13.8746i	0.376783	−	0.652607i
$453$			11.7022i			0.549816i
$454$	−10.9947			−0.516008
$455$	−26.3635	+	16.4074i	−1.23594	+	0.769189i
$456$	−5.18398			−0.242762
$457$		−	36.4712i		−	1.70605i	−0.521868	−	0.853027i	$-0.674764\pi$
$457$		−	36.4712i		−	1.70605i	0.521868	−	0.853027i	$-0.325236\pi$
$458$	11.6729	−	20.2181i	0.545439	−	0.944729i
$459$	−0.782978			−0.0365463
$460$	−0.918225	−	0.530137i	−0.0428124	−	0.0247178i
$461$	3.03039	+	1.74960i	0.141139	+	0.0814869i	0.568907	−	0.822402i	$-0.307366\pi$
$461$	3.03039	+	1.74960i	0.141139	+	0.0814869i	−0.427768	+	0.903889i	$0.640700\pi$
$462$	6.03360	+	0.615920i	0.280708	+	0.0286552i
$463$		−	15.8900i		−	0.738471i	−0.929336	−	0.369236i	$-0.879619\pi$
$463$		−	15.8900i		−	0.738471i	0.929336	−	0.369236i	$-0.120381\pi$
$464$	3.35386	+	5.80906i	0.155699	+	0.269679i
$465$	10.7109	−	18.5518i	0.496705	−	0.860319i
$466$	3.71606	+	2.14547i	0.172143	+	0.0993868i
$467$	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
$471$	−8.07436			−0.372047
$472$	−0.614234			−0.0282724
$473$	−19.1052	+	11.0304i	−0.878457	+	0.507177i
$474$	−1.12642	+	0.650337i	−0.0517381	+	0.0298710i
$475$	−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
$478$	5.59389			0.255859
$479$	4.35302	+	2.51322i	0.198895	+	0.114832i	0.596140	−	0.802881i	$-0.296700\pi$
$479$	4.35302	+	2.51322i	0.198895	+	0.114832i	−0.397245	+	0.917713i	$0.630034\pi$
$480$	1.62758	+	2.81905i	0.0742884	+	0.128671i
$481$	5.15263	+	37.9860i	0.234940	+	1.73201i
$482$	29.2191			1.33089
$483$	−0.352870	−	0.786222i	−0.0160561	−	0.0357744i
$484$	2.87259	+	4.97548i	0.130572	+	0.226158i
$485$	8.62790	+	14.9440i	0.391773	+	0.678571i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$		−	6.15960i		−	0.279118i	−0.990214	−	0.139559i	$-0.955432\pi$
$487$		−	6.15960i		−	0.279118i	0.990214	−	0.139559i	$-0.0445685\pi$
$488$	0.197650	−	0.114113i	0.00894721	−	0.00516568i
$489$			0.826274i			0.0373654i
$490$	22.3161	+	4.60411i	1.00814	+	0.207992i
$491$	13.0021	+	22.5203i	0.586775	+	1.01632i	0.994652	+	0.103288i	$0.0329362\pi$
$491$	13.0021	+	22.5203i	0.586775	+	1.01632i	−0.407876	+	0.913037i	$0.633730\pi$
$492$		−	0.945634i		−	0.0426325i
$493$	2.62600	+	4.54837i	0.118269	+	0.204848i
$494$	−11.4365	−	14.7839i	−0.514553	−	0.665159i
$495$	−3.73096	+	6.46221i	−0.167694	+	0.290455i
$496$	−5.69921	+	3.29044i	−0.255902	+	0.147745i
$497$	35.6714	−	16.0099i	1.60008	−	0.718144i
$498$	−3.73204	+	6.46409i	−0.167237	+	0.289663i
$499$	−17.0760	−	9.85885i	−0.764428	−	0.441343i	0.0664553	−	0.997789i	$-0.478831\pi$
$499$	−17.0760	−	9.85885i	−0.764428	−	0.441343i	−0.830883	+	0.556447i	$0.812164\pi$
$500$			1.94016i			0.0867666i
$501$		−	5.39694i		−	0.241117i
$502$	−10.6028	−	6.12153i	−0.473226	−	0.273217i
$503$	−1.11315	+	1.92804i	−0.0496330	+	0.0859669i	−0.889775	−	0.456400i	$-0.849139\pi$
$503$	−1.11315	+	1.92804i	−0.0496330	+	0.0859669i	0.840142	+	0.542367i	$0.182472\pi$
$504$	−0.268687	+	2.63207i	−0.0119683	+	0.117242i
$505$	−20.6692	+	11.9334i	−0.919766	+	0.531027i
$506$	−0.373332	+	0.646630i	−0.0165966	+	0.0287462i
$507$	3.26603	−	12.5830i	0.145049	−	0.558833i
$508$	−0.284508	−	0.492782i	−0.0126230	−	0.0218636i
$509$			2.20810i			0.0978725i	0.998802	+	0.0489362i	$0.0155831\pi$
$509$			2.20810i			0.0978725i	−0.998802	+	0.0489362i	$0.984417\pi$
$510$	1.27436	+	2.20725i	0.0564295	+	0.0977387i
$511$	3.62170	−	35.4784i	0.160215	−	1.56947i
$512$		−	1.00000i		−	0.0441942i
$513$	4.48946	−	2.59199i	0.198214	−	0.114439i
$514$			4.39912i			0.194037i
$515$	−4.75775	+	2.74689i	−0.209651	+	0.121042i
$516$	−4.81185	−	8.33436i	−0.211830	−	0.366900i
$517$	−2.84098	−	4.92072i	−0.124946	−	0.216413i
$518$	16.4659	−	22.8065i	0.723470	−	1.00206i
$519$	−13.5777			−0.595993
$520$	−4.44884	+	10.8608i	−0.195095	+	0.476276i
$521$	−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	$-0.344984\pi$
$522$	−5.80906	−	3.35386i	−0.254256	−	0.146795i
$523$	14.3526			0.627594			0.313797	−	0.949490i	$-0.398399\pi$
$523$	14.3526			0.627594			0.313797	+	0.949490i	$0.398399\pi$
$524$	−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
$527$	−4.46235	+	2.57634i	−0.194383	+	0.112227i
$528$	1.98522	−	1.14617i	0.0863957	−	0.0498806i
$529$	−22.8939			−0.995387
$530$	44.5253			1.93406
$531$	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
$535$	−49.0377	−	28.3119i	−2.12009	−	1.22403i
$536$	−4.60562	+	7.97716i	−0.198932	+	0.344561i
$537$	−8.46923	−	14.6691i	−0.365474	−	0.633020i
$538$		−	3.09430i		−	0.133405i
$539$	3.24230	−	15.7154i	0.139656	−	0.676910i
$540$	−2.81905	−	1.62758i	−0.121312	−	0.0700398i
$541$	26.1094	+	15.0742i	1.12253	+	0.648093i	0.942045	−	0.335485i	$-0.108900\pi$
$541$	26.1094	+	15.0742i	1.12253	+	0.648093i	0.180484	+	0.983578i	$0.442234\pi$
$542$	26.3111			1.13016
$543$	−6.42698	+	11.1318i	−0.275808	+	0.477713i
$544$		−	0.782978i		−	0.0335699i
$545$	38.5951			1.65323
$546$	−8.09902	+	5.04043i	−0.346606	+	0.215710i
$547$	−34.0803			−1.45717			−0.728585	−	0.684955i	$-0.759822\pi$
$547$	−34.0803			−1.45717			−0.728585	+	0.684955i	$0.759822\pi$
$548$			11.0183i			0.470679i
$549$	−0.114113	+	0.197650i	−0.00487025	+	0.00843551i
$550$	12.8280			0.546987
$551$	−30.1141	−	17.3864i	−1.28290	−	0.740684i
$552$	−0.282083	−	0.162861i	−0.0120063	−	0.00693182i
$553$	1.40908	+	3.13955i	0.0599203	+	0.133507i
$554$		−	11.1939i		−	0.475581i
$555$	17.3042	+	29.9718i	0.734524	+	1.27223i
$556$	−6.38785	+	11.0641i	−0.270905	+	0.469222i
$557$	2.12822	+	1.22873i	0.0901757	+	0.0520630i	0.544410	−	0.838819i	$-0.316754\pi$
$557$	2.12822	+	1.22873i	0.0901757	+	0.0520630i	−0.454234	+	0.890882i	$0.650087\pi$
$558$	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
$562$	−1.85065			−0.0780650
$563$	−13.3196			−0.561354			−0.280677	−	0.959802i	$-0.590559\pi$
$563$	−13.3196			−0.561354			−0.280677	+	0.959802i	$0.590559\pi$
$564$	2.14659	−	1.23934i	0.0903879	−	0.0521855i
$565$	45.1640	−	26.0754i	1.90006	−	1.09700i
$566$	−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
$569$	−35.4726			−1.48709			−0.743544	−	0.668687i	$-0.766856\pi$
$569$	−35.4726			−1.48709			−0.743544	+	0.668687i	$0.766856\pi$
$570$	−14.6139	−	8.43733i	−0.612108	−	0.353401i
$571$	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	$0.796389\pi$
$572$	7.64834	+	3.13295i	0.319793	+	0.130995i
$573$	20.3228			0.848997
$574$	−2.48898	−	0.254079i	−0.103888	−	0.0106051i
$575$	−0.911374	−	1.57855i	−0.0380069	−	0.0658299i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	32.7495	−	18.9080i	1.36338	−	0.787149i	0.373309	−	0.927707i	$-0.378223\pi$
$577$	32.7495	−	18.9080i	1.36338	−	0.787149i	0.990072	+	0.140558i	$0.0448898\pi$
$578$			16.3869i			0.681607i
$579$	17.0008	−	9.81539i	0.706528	−	0.407914i
$580$			21.8347i			0.906636i
$581$	16.0112	+	11.5598i	0.664257	+	0.479583i
$582$	2.65054	+	4.59086i	0.109868	+	0.190297i
$583$		−	31.3555i		−	1.29861i
$584$	−6.73964	−	11.6734i	−0.278888	−	0.483049i
$585$	−1.57757	−	11.6301i	−0.0652246	−	0.480846i
$586$	−7.34371	+	12.7197i	−0.303366	+	0.525445i
$587$	−38.4863	+	22.2201i	−1.58850	+	0.917121i	−0.594945	+	0.803766i	$0.702826\pi$
$587$	−38.4863	+	22.2201i	−1.58850	+	0.917121i	−0.993555	+	0.113355i	$0.963840\pi$
$588$	6.85561	+	1.41441i	0.282721	+	0.0583291i
$589$	17.0576	−	29.5446i	0.702845	−	1.21736i
$590$	−1.73155	−	0.999713i	−0.0712869	−	0.0411575i
$591$		−	16.3161i		−	0.671155i
$592$		−	10.6319i		−	0.436968i
$593$	11.7799	+	6.80115i	0.483744	+	0.279290i	0.721975	−	0.691919i	$-0.243234\pi$
$593$	11.7799	+	6.80115i	0.483744	+	0.279290i	−0.238231	+	0.971208i	$0.576568\pi$
$594$	−1.14617	+	1.98522i	−0.0470279	+	0.0814547i
$595$	6.15205	−	2.76114i	0.252209	−	0.113196i
$596$	10.2760	−	5.93287i	0.420923	−	0.243020i
$597$	1.96397	−	3.40169i	0.0803798	−	0.139222i
$598$	−0.157857	−	1.16375i	−0.00645526	−	0.0475892i
$599$	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	$0.739345\pi$
$600$			5.59603i			0.228457i
$601$	5.94043	+	10.2891i	0.242315	+	0.419702i	0.961373	−	0.275248i	$-0.0887598\pi$
$601$	5.94043	+	10.2891i	0.242315	+	0.419702i	−0.719058	+	0.694950i	$0.755427\pi$
$602$	−23.2295	+	10.4258i	−0.946765	+	0.424924i
$603$		−	9.21123i		−	0.375110i
$604$	10.1344	−	5.85109i	0.412362	−	0.238078i
$605$			18.7015i			0.760323i
$606$	−6.34968	+	3.66599i	−0.257938	+	0.148921i
$607$	17.2875	+	29.9427i	0.701676	+	1.21534i	0.967878	+	0.251421i	$0.0808979\pi$
$607$	17.2875	+	29.9427i	0.701676	+	1.21534i	−0.266202	+	0.963917i	$0.585769\pi$
$608$	2.59199	+	4.48946i	0.105119	+	0.182072i
$609$	−10.3884	+	14.3887i	−0.420960	+	0.583061i
$610$	0.742914			0.0300797
$611$	8.27005	+	3.38762i	0.334570	+	0.137048i
$612$	0.391489	+	0.678079i	0.0158250	+	0.0274097i
$613$	4.41505	+	2.54903i	0.178322	+	0.102954i	0.586504	−	0.809946i	$-0.300504\pi$
$613$	4.41505	+	2.54903i	0.178322	+	0.102954i	−0.408182	+	0.912901i	$0.633837\pi$
$614$	−1.73631			−0.0700718
$615$	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	0.0747175	−	0.997205i	$-0.476194\pi$
$617$	−18.6676	−	10.7777i	−0.751528	−	0.433895i	−0.826246	+	0.563310i	$0.809528\pi$
$618$	−1.46160	+	0.843858i	−0.0587944	+	0.0339449i
$619$	8.13309	−	4.69564i	0.326897	−	0.188734i	−0.327566	−	0.944828i	$-0.606228\pi$
$619$	8.13309	−	4.69564i	0.326897	−	0.188734i	0.654462	+	0.756095i	$0.272895\pi$
$620$	−21.4218			−0.860319
$621$	0.325722			0.0130708
$622$	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
$626$	11.1314	+	6.42671i	0.444900	+	0.256863i
$627$	−5.94172	+	10.2914i	−0.237289	+	0.410997i
$628$	4.03718	+	6.99260i	0.161101	+	0.279035i
$629$		−	8.32455i		−	0.331921i
$630$	−5.04134	+	6.98263i	−0.200852	+	0.278194i
$631$	−12.1643	−	7.02306i	−0.484253	−	0.279583i	0.237934	−	0.971281i	$-0.423530\pi$
$631$	−12.1643	−	7.02306i	−0.484253	−	0.279583i	−0.722187	+	0.691698i	$0.756863\pi$
$632$	1.12642	+	0.650337i	0.0448065	+	0.0258690i
$633$	23.8757			0.948972
$634$	−4.68167	+	8.10889i	−0.185933	+	0.322045i
$635$		−	1.85223i		−	0.0735036i
$636$	13.6784			0.542384
$637$	11.0907	+	22.6715i	0.439429	+	0.898277i
$638$	15.3764			0.608756
$639$			14.7782i			0.584617i
$640$	1.62758	−	2.81905i	0.0643356	−	0.111433i
$641$	20.4351			0.807139			0.403570	−	0.914949i	$-0.367769\pi$
$641$	20.4351			0.807139			0.403570	+	0.914949i	$0.367769\pi$
$642$	−15.0646	−	8.69757i	−0.594554	−	0.343266i
$643$	−3.01247	−	1.73925i	−0.118800	−	0.0685893i	0.439422	−	0.898281i	$-0.355183\pi$
$643$	−3.01247	−	1.73925i	−0.118800	−	0.0685893i	−0.558223	+	0.829691i	$0.688516\pi$
$644$	−0.504454	+	0.698705i	−0.0198783	+	0.0275328i
$645$		−	31.3266i		−	1.23348i
$646$	2.02947	+	3.51515i	0.0798485	+	0.138302i
$647$	19.5543	−	33.8690i	0.768757	−	1.33153i	−0.169480	−	0.985534i	$-0.554209\pi$
$647$	19.5543	−	33.8690i	0.768757	−	1.33153i	0.938237	−	0.345993i	$-0.112458\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−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
$653$	−10.8034			−0.422769			−0.211385	−	0.977403i	$-0.567797\pi$
$653$	−10.8034			−0.422769			−0.211385	+	0.977403i	$0.567797\pi$
$654$	11.8566			0.463631
$655$	−23.2365	+	13.4156i	−0.907926	+	0.524192i
$656$	−0.818943	+	0.472817i	−0.0319744	+	0.0184604i
$657$	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	−0.990225	−	0.139478i	$-0.955457\pi$
$659$	−9.60919	+	16.6436i	−0.374321	+	0.648343i	0.615904	+	0.787821i	$0.288791\pi$
$660$	7.46191			0.290455
$661$	−1.05336	−	0.608160i	−0.0409711	−	0.0236547i	0.479375	−	0.877610i	$-0.340864\pi$
$661$	−1.05336	−	0.608160i	−0.0409711	−	0.0236547i	−0.520346	+	0.853956i	$0.674197\pi$
$662$	−5.57375	−	9.65401i	−0.216630	−	0.375214i
$663$	−1.07010	+	2.61239i	−0.0415593	+	0.101457i
$664$	7.46409			0.289663
$665$	−26.1342	+	36.1978i	−1.01344	+	1.40369i
$666$	5.31595	+	9.20750i	0.205989	+	0.356783i
$667$	−1.09243	−	1.89214i	−0.0422989	−	0.0732638i
$668$	−4.67389	+	2.69847i	−0.180838	+	0.104407i
$669$			3.31623i			0.128213i
$670$	−25.9669	+	14.9920i	−1.00319	+	0.579191i
$671$		−	0.523173i		−	0.0201969i
$672$	2.41379	−	1.08335i	0.0931138	−	0.0417910i
$673$	−7.28073	−	12.6106i	−0.280652	−	0.486103i	0.690894	−	0.722956i	$-0.257217\pi$
$673$	−7.28073	−	12.6106i	−0.280652	−	0.486103i	−0.971545	+	0.236853i	$0.923884\pi$
$674$		−	7.91654i		−	0.304934i
$675$	−2.79801	−	4.84630i	−0.107696	−	0.186534i
$676$	−12.5303	+	3.46306i	−0.481933	+	0.133195i
$677$	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
$679$	12.7956	−	5.74290i	0.491052	−	0.220392i
$680$	1.27436	−	2.20725i	0.0488694	−	0.0846442i
$681$	−9.52172	−	5.49737i	−0.364873	−	0.210660i
$682$			15.0856i			0.577657i
$683$		−	40.4717i		−	1.54861i	−0.632814	−	0.774304i	$-0.718100\pi$
$683$		−	40.4717i		−	1.54861i	0.632814	−	0.774304i	$-0.281900\pi$
$684$	−4.48946	−	2.59199i	−0.171659	−	0.0991072i
$685$	−17.9332	+	31.0611i	−0.685191	+	1.18679i
$686$	5.56483	−	17.6644i	0.212466	−	0.674432i
$687$	20.2181	−	11.6729i	0.771368	−	0.445349i
$688$	−4.81185	+	8.33436i	−0.183450	+	0.317745i
$689$	30.1763	+	39.0087i	1.14962	+	1.48611i
$690$	−0.530137	−	0.918225i	−0.0201820	−	0.0349562i
$691$		−	26.5949i		−	1.01172i	−0.862616	−	0.505859i	$-0.831175\pi$
$691$		−	26.5949i		−	1.01172i	0.862616	−	0.505859i	$-0.168825\pi$
$692$	6.78883	+	11.7586i	0.258073	+	0.446995i
$693$	4.91729	+	3.55020i	0.186792	+	0.134861i
$694$			26.0298i			0.988077i
$695$	−36.0153	+	20.7934i	−1.36614	+	0.788740i
$696$			6.70773i			0.254256i
$697$	−0.641215	+	0.370206i	−0.0242877	+	0.0140225i
$698$	7.29484	+	12.6350i	0.276114	+	0.478243i
$699$	2.14547	+	3.71606i	0.0811490	+	0.140554i
$700$	14.7292	+	1.50358i	0.556710	+	0.0568299i
$701$	−19.9294			−0.752722			−0.376361	−	0.926473i	$-0.622825\pi$
$701$	−19.9294			−0.752722			−0.376361	+	0.926473i	$0.622825\pi$
$702$	−0.484638	−	3.57283i	−0.0182915	−	0.134848i
$703$	27.5578	+	47.7315i	1.03936	+	1.80023i
$704$	−1.98522	−	1.14617i	−0.0748209	−	0.0431979i
$705$	8.06846			0.303876
$706$	−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
$709$	−43.0189	+	24.8370i	−1.61561	+	0.932772i	−0.627571	+	0.778559i	$0.715951\pi$
$709$	−43.0189	+	24.8370i	−1.61561	+	0.932772i	−0.988038	+	0.154213i	$0.950716\pi$
$710$	41.6605	−	24.0527i	1.56349	−	0.902681i
$711$	−1.30067			−0.0487791
$712$	−9.06656			−0.339784
$713$	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
$717$	4.84445	+	2.79694i	0.180919	+	0.104454i
$718$	−8.61207	+	14.9165i	−0.321399	+	0.556680i
$719$	5.75195	+	9.96268i	0.214512	+	0.371545i	0.953121	−	0.302588i	$-0.0978507\pi$
$719$	5.75195	+	9.96268i	0.214512	+	0.371545i	−0.738610	+	0.674133i	$0.764517\pi$
$720$			3.25515i			0.121312i
$721$	1.82838	+	4.07378i	0.0680925	+	0.151716i
$722$	−6.81878	−	3.93682i	−0.253769	−	0.146513i
$723$	25.3045	+	14.6096i	0.941084	+	0.543335i
$724$	12.8540			0.477713
$725$	−18.7683	+	32.5077i	−0.697037	+	1.20730i
$726$			5.74519i			0.213224i
$727$	41.7753			1.54936			0.774679	−	0.632354i	$-0.217911\pi$
$727$	41.7753			1.54936			0.774679	+	0.632354i	$0.217911\pi$
$728$	8.41465	+	4.49374i	0.311868	+	0.166549i
$729$	1.00000			0.0370370
$730$		−	43.8771i		−	1.62397i
$731$	−3.76757	+	6.52562i	−0.139349	+	0.241359i
$732$	0.228227			0.00843551
$733$	−42.1605	−	24.3414i	−1.55723	−	0.899070i	−0.997520	−	0.0703842i	$-0.977577\pi$
$733$	−42.1605	−	24.3414i	−1.55723	−	0.899070i	−0.559714	−	0.828686i	$-0.689089\pi$
$734$	14.8269	+	8.56032i	0.547271	+	0.315967i
$735$	17.0242	+	15.1453i	0.627949	+	0.558643i
$736$			0.325722i			0.0120063i
$737$	10.5576	+	18.2863i	0.388895	+	0.673586i
$738$	0.472817	−	0.818943i	0.0174046	−	0.0301457i
$739$	3.75818	+	2.16979i	0.138247	+	0.0798168i	0.567528	−	0.823354i	$-0.307900\pi$
$739$	3.75818	+	2.16979i	0.138247	+	0.0798168i	−0.429281	+	0.903171i	$0.641233\pi$
$740$	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	−0.733740	−	0.679430i	$-0.762227\pi$
$743$	−13.9617	+	8.06082i	−0.512207	+	0.295723i	0.221534	+	0.975153i	$0.428894\pi$
$744$	−6.58088			−0.241267
$745$	38.6248			1.41510
$746$	−10.9123	+	6.30021i	−0.399527	+	0.230667i
$747$	−6.46409	+	3.73204i	−0.236509	+	0.136548i
$748$	−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
$751$	−46.0665			−1.68099			−0.840495	−	0.541819i	$-0.817736\pi$
$751$	−46.0665			−1.68099			−0.840495	+	0.541819i	$0.817736\pi$
$752$	−2.14659	−	1.23934i	−0.0782782	−	0.0451939i
$753$	−6.12153	−	10.6028i	−0.223081	−	0.386388i
$754$	−19.1294	+	14.7981i	−0.696651	+	0.538914i
$755$	38.0924			1.38632
$756$	−1.54873	+	2.14510i	−0.0563266	+	0.0780165i
$757$	−7.15268	−	12.3888i	−0.259969	−	0.450279i	0.706265	−	0.707948i	$-0.250379\pi$
$757$	−7.15268	−	12.3888i	−0.259969	−	0.450279i	−0.966233	+	0.257669i	$0.917046\pi$
$758$	1.79403	+	3.10736i	0.0651622	+	0.112864i
$759$	−0.646630	+	0.373332i	−0.0234712	+	0.0135511i
$760$			16.8747i			0.612108i
$761$	−44.1719	+	25.5026i	−1.60123	+	0.924470i	−0.609986	+	0.792412i	$0.708825\pi$
$761$	−44.1719	+	25.5026i	−1.60123	+	0.924470i	−0.991242	+	0.132058i	$0.957842\pi$
$762$		−	0.569015i		−	0.0206132i
$763$	3.18572	−	31.2075i	0.115331	−	1.12979i
$764$	−10.1614	−	17.6001i	−0.367627	−	0.636748i
$765$			2.54871i			0.0921490i
$766$	−9.09226	−	15.7482i	−0.328517	−	0.569007i
$767$	−0.297681	−	2.19455i	−0.0107486	−	0.0792408i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	38.2197	−	22.0662i	1.37824	−	0.795727i	0.386292	−	0.922377i	$-0.373756\pi$
$769$	38.2197	−	22.0662i	1.37824	−	0.795727i	0.991947	+	0.126650i	$0.0404225\pi$
$770$	2.00492	−	19.6403i	0.0722522	−	0.707787i
$771$	−2.19956	+	3.80975i	−0.0792152	+	0.137205i
$772$	−17.0008	−	9.81539i	−0.611871	−	0.353264i
$773$		−	9.87555i		−	0.355199i	−0.984103	−	0.177599i	$-0.943167\pi$
$773$		−	9.87555i		−	0.355199i	0.984103	−	0.177599i	$-0.0568331\pi$
$774$		−	9.62369i		−	0.345916i
$775$	−31.8929	−	18.4134i	−1.14563	−	0.661428i
$776$	2.65054	−	4.59086i	0.0951487	−	0.164802i
$777$	25.6631	−	11.5180i	0.920659	−	0.413207i
$778$	23.7131	−	13.6907i	0.850155	−	0.490837i
$779$	2.45107	−	4.24539i	0.0878189	−	0.152107i
$780$	−9.28319	+	7.18128i	−0.332392	+	0.257131i
$781$	−16.9383	−	29.3380i	−0.606101	−	1.04980i
$782$			0.255033i			0.00911996i
$783$	−3.35386	−	5.80906i	−0.119857	−	0.207599i
$784$	−2.20290	−	6.64434i	−0.0786749	−	0.237298i
$785$			26.2833i			0.938090i
$786$	−7.13838	+	4.12135i	−0.254618	+	0.147004i
$787$		−	11.5451i		−	0.411539i	−0.978600	−	0.205770i	$-0.934030\pi$
$787$		−	11.5451i		−	0.411539i	0.978600	−	0.205770i	$-0.0659698\pi$
$788$	−14.1302	+	8.15806i	−0.503366	+	0.290619i
$789$	9.57034	+	16.5763i	0.340713	+	0.590132i
$790$	2.11695	+	3.66666i	0.0753176	+	0.130454i
$791$	−17.3563	−	38.6713i	−0.617120	−	1.37499i
$792$	2.29234			0.0814547
$793$	0.503497	+	0.650868i	0.0178797	+	0.0231130i
$794$	−8.43299	−	14.6064i	−0.299276	−	0.518361i
$795$	38.5600	+	22.2627i	1.36758	+	0.789575i
$796$	−3.92793			−0.139222
$797$	−2.73081	+	4.72990i	−0.0967302	+	0.167542i	−0.910329	−	0.413884i	$-0.864172\pi$
$797$	−2.73081	+	4.72990i	−0.0967302	+	0.167542i	0.813599	+	0.581426i	$0.197505\pi$
$798$	−8.02856	+	11.1201i	−0.284208	+	0.393649i
$799$	−1.68074	−	0.970373i	−0.0594601	−	0.0343293i
$800$	4.84630	−	2.79801i	0.171343	−	0.0989247i
$801$	7.85187	−	4.53328i	0.277432	−	0.160176i
$802$	−18.6934			−0.660088
$803$	−30.8991			−1.09040
$804$	−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
$808$	6.34968	+	3.66599i	0.223381	+	0.128969i
$809$	−12.7453	+	22.0755i	−0.448101	+	0.776134i	−0.998262	−	0.0589244i	$-0.981233\pi$
$809$	−12.7453	+	22.0755i	−0.448101	+	0.776134i	0.550161	+	0.835058i	$0.314566\pi$
$810$	−1.62758	−	2.81905i	−0.0571872	−	0.0990512i
$811$			20.1506i			0.707582i	0.935324	+	0.353791i	$0.115108\pi$
$811$			20.1506i			0.707582i	−0.935324	+	0.353791i	$0.884892\pi$
$812$	17.6552	+	1.80228i	0.619577	+	0.0632475i
$813$	22.7861	+	13.1555i	0.799142	+	0.461385i
$814$	−21.1067	−	12.1860i	−0.739789	−	0.427117i
$815$	2.68965			0.0942143
$816$	0.391489	−	0.678079i	0.0137049	−	0.0237375i
$817$		−	49.8890i		−	1.74540i
$818$	4.94626			0.172942
$819$	−9.53417	+	0.315631i	−0.333151	+	0.0110290i
$820$	−3.07819			−0.107495
$821$			6.50197i			0.226920i	0.993543	+	0.113460i	$0.0361934\pi$
$821$			6.50197i			0.226920i	−0.993543	+	0.113460i	$0.963807\pi$
$822$	−5.50916	+	9.54214i	−0.192154	+	0.332821i
$823$	9.36955			0.326602			0.163301	−	0.986576i	$-0.447786\pi$
$823$	9.36955			0.326602			0.163301	+	0.986576i	$0.447786\pi$
$824$	1.46160	+	0.843858i	0.0509174	+	0.0293972i
$825$	11.1094	+	6.41399i	0.386778	+	0.223307i
$826$	−0.951280	+	1.31759i	−0.0330993	+	0.0458449i
$827$			54.1536i			1.88311i	0.336864	+	0.941553i	$0.390634\pi$
$827$			54.1536i			1.88311i	−0.336864	+	0.941553i	$0.609366\pi$
$828$	−0.162861	−	0.282083i	−0.00565981	−	0.00980307i
$829$	−24.1242	+	41.7844i	−0.837869	+	1.45123i	0.0538043	+	0.998552i	$0.482865\pi$
$829$	−24.1242	+	41.7844i	−0.837869	+	1.45123i	−0.891673	+	0.452680i	$0.850468\pi$
$830$	21.0416	+	12.1484i	0.730365	+	0.421676i
$831$	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
$835$	−17.5679			−0.607961
$836$	11.8834			0.410997
$837$	5.69921	−	3.29044i	0.196993	−	0.113734i
$838$	−9.87496	+	5.70131i	−0.341125	+	0.196949i
$839$	39.2039	+	22.6344i	1.35347	+	0.781425i	0.988733	−	0.149687i	$-0.0478265\pi$
$839$	39.2039	+	22.6344i	1.35347	+	0.781425i	0.364734	+	0.931112i	$0.381160\pi$
$840$	8.56780	+	0.874616i	0.295617	+	0.0301771i
$841$	−7.99679	+	13.8508i	−0.275751	+	0.477615i
$842$	9.82089			0.338450
$843$	−1.60271	−	0.925326i	−0.0552003	−	0.0318699i
$844$	−11.9378	−	20.6769i	−0.410917	−	0.711729i
$845$	−40.9598	−	10.6314i	−1.40906	−	0.365732i
$846$	2.47867			0.0852185
$847$	15.1218	+	1.54366i	0.519590	+	0.0530406i
$848$	−6.83920	−	11.8458i	−0.234859	−	0.406788i
$849$	−11.0823	−	19.1951i	−0.380343	−	0.658774i
$850$	3.79455	−	2.19078i	0.130152	−	0.0751433i
$851$			3.46304i			0.118712i
$852$	12.7983	−	7.38911i	0.438463	−	0.253147i
$853$			37.2246i			1.27454i	0.770639	+	0.637272i	$0.219937\pi$
$853$			37.2246i			1.27454i	−0.770639	+	0.637272i	$0.780063\pi$
$854$	0.0613215	−	0.600710i	0.00209838	−	0.0205559i
$855$	−8.43733	−	14.6139i	−0.288550	−	0.499784i
$856$			17.3951i			0.594554i
$857$	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	$0.599458\pi$
$858$	5.05718	+	6.53739i	0.172649	+	0.223183i
$859$	−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
$861$	−2.02848	−	1.46453i	−0.0691304	−	0.0499110i
$862$	4.30730	−	7.46047i	0.146707	−	0.254105i
$863$	1.46982	+	0.848602i	0.0500333	+	0.0288867i	0.524808	−	0.851221i	$-0.324137\pi$
$863$	1.46982	+	0.848602i	0.0500333	+	0.0288867i	−0.474775	+	0.880107i	$0.657470\pi$
$864$			1.00000i			0.0340207i
$865$			44.1974i			1.50276i
$866$	20.3157	+	11.7293i	0.690355	+	0.398577i
$867$	−8.19347	+	14.1915i	−0.278265	+	0.481969i
$868$	−1.76819	+	17.3213i	−0.0600164	+	0.587925i
$869$	2.58213	−	1.49079i	0.0875927	−	0.0505717i
$870$	−10.9173	+	18.9094i	−0.370132	+	0.641088i
$871$	−30.7331	−	12.5891i	−1.04135	−	0.426564i
$872$	−5.92831	−	10.2681i	−0.200758	−	0.347723i
$873$			5.30107i			0.179414i
$874$	−0.844267	−	1.46231i	−0.0285578	−	0.0494635i
$875$	4.16184	+	3.00478i	0.140696	+	0.101580i
$876$		−	13.4793i		−	0.455423i
$877$	−20.8656	+	12.0467i	−0.704580	+	0.406789i	−0.809051	−	0.587739i	$-0.800018\pi$
$877$	−20.8656	+	12.0467i	−0.704580	+	0.406789i	0.104471	+	0.994528i	$0.466685\pi$
$878$			37.3484i			1.26045i
$879$	−12.7197	+	7.34371i	−0.429024	+	0.247697i
$880$	−3.73096	−	6.46221i	−0.125771	−	0.217841i
$881$	−8.86241	−	15.3501i	−0.298582	−	0.517160i	0.677230	−	0.735772i	$-0.263180\pi$
$881$	−8.86241	−	15.3501i	−0.298582	−	0.517160i	−0.975812	+	0.218612i	$0.929847\pi$
$882$	5.22993	+	4.65272i	0.176101	+	0.156665i
$883$	−29.5760			−0.995312			−0.497656	−	0.867375i	$-0.665806\pi$
$883$	−29.5760			−0.995312			−0.497656	+	0.867375i	$0.665806\pi$
$884$	2.79745	−	0.379461i	0.0940884	−	0.0127627i
$885$	−0.999713	−	1.73155i	−0.0336050	−	0.0582055i
$886$	16.5870	+	9.57652i	0.557252	+	0.321730i
$887$	−23.5815			−0.791789			−0.395894	−	0.918296i	$-0.629565\pi$
$887$	−23.5815			−0.791789			−0.395894	+	0.918296i	$0.629565\pi$
$888$	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
$891$	−1.98522	+	1.14617i	−0.0665075	+	0.0383981i
$892$	2.87194	−	1.65812i	0.0961597	−	0.0555178i
$893$	12.8494			0.429988
$894$	11.8657			0.396850
$895$	−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
$899$	−38.2287	−	22.0714i	−1.27500	−	0.736121i
$900$	−2.79801	+	4.84630i	−0.0932671	+	0.161543i
$901$	−5.35495	−	9.27504i	−0.178399	−	0.308996i
$902$			2.16771i			0.0721770i
$903$	−25.3303	−	2.58576i	−0.842938	−	0.0860486i
$904$	−13.8746	−	8.01051i	−0.461463	−	0.266426i
$905$	36.2359	+	20.9208i	1.20452	+	0.695431i
$906$	11.7022			0.388779
$907$	−5.49141	+	9.51140i	−0.182339	+	0.315821i	−0.942677	−	0.333707i	$-0.891700\pi$
$907$	−5.49141	+	9.51140i	−0.182339	+	0.315821i	0.760337	+	0.649528i	$0.225034\pi$
$908$			10.9947i			0.364873i
$909$	−7.33198			−0.243186
$910$	16.4074	+	26.3635i	0.543899	+	0.873943i
$911$	55.4208			1.83617			0.918086	−	0.396380i	$-0.129734\pi$
$911$	55.4208			1.83617			0.918086	+	0.396380i	$0.129734\pi$
$912$			5.18398i			0.171659i
$913$	8.55511	−	14.8179i	0.283133	−	0.490400i
$914$	−36.4712			−1.20636
$915$	0.643382	+	0.371457i	0.0212696	+	0.0122800i
$916$	−20.2181	−	11.6729i	−0.668024	−	0.385684i
$917$	8.92970	+	19.8961i	0.294885	+	0.657027i
$918$			0.782978i			0.0258421i
$919$	−14.0986	−	24.4195i	−0.465070	−	0.805524i	0.534135	−	0.845399i	$-0.320637\pi$
$919$	−14.0986	−	24.4195i	−0.465070	−	0.805524i	−0.999205	+	0.0398750i	$0.987304\pi$
$920$	−0.530137	+	0.918225i	−0.0174781	+	0.0302730i
$921$	−1.50369	−	0.868156i	−0.0495483	−	0.0286067i
$922$	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
$926$	−15.8900			−0.522178
$927$	−1.68772			−0.0554318
$928$	5.80906	−	3.35386i	0.190692	−	0.110096i
$929$	17.1251	−	9.88717i	0.561856	−	0.324388i	−0.192034	−	0.981388i	$-0.561508\pi$
$929$	17.1251	−	9.88717i	0.561856	−	0.324388i	0.753890	+	0.657001i	$0.228175\pi$
$930$	−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
$933$	13.6109			0.445600
$934$	−22.9278	−	13.2374i	−0.750220	−	0.433140i
$935$	−2.92126	−	5.05977i	−0.0955353	−	0.165472i
$936$	−2.85184	+	2.20612i	−0.0932154	+	0.0721094i
$937$	−53.0303			−1.73243			−0.866213	−	0.499676i	$-0.833453\pi$
$937$	−53.0303			−1.73243			−0.866213	+	0.499676i	$0.833453\pi$
$938$	9.97896	+	22.2339i	0.325825	+	0.725964i
$939$	6.42671	+	11.1314i	0.209728	+	0.363259i
$940$	−4.03423	−	6.98749i	−0.131582	−	0.227907i
$941$	44.7773	−	25.8522i	1.45970	−	0.842757i	0.460702	−	0.887555i	$-0.347598\pi$
$941$	44.7773	−	25.8522i	1.45970	−	0.842757i	0.998996	+	0.0447977i	$0.0142643\pi$
$942$			8.07436i			0.263077i
$943$	0.266748	−	0.154007i	0.00868650	−	0.00501515i
$944$			0.614234i			0.0199916i
$945$	−7.85724	+	3.52646i	−0.255596	+	0.114716i
$946$	11.0304	+	19.1052i	0.358628	+	0.621163i
$947$		−	13.7512i		−	0.446855i	−0.974721	−	0.223427i	$-0.928275\pi$
$947$		−	13.7512i		−	0.446855i	0.974721	−	0.223427i	$-0.0717245\pi$
$948$	0.650337	+	1.12642i	0.0211220	+	0.0365843i
$949$	38.4408	−	29.7370i	1.24784	−	0.965303i
$950$	−14.5048	+	25.1231i	−0.470599	+	0.815102i
$951$	−8.10889	+	4.68167i	−0.262949	+	0.151814i
$952$	−1.67957	−	1.21262i	−0.0544350	−	0.0393012i
$953$	−27.8692	+	48.2709i	−0.902773	+	1.56365i	−0.0788930	+	0.996883i	$0.525139\pi$
$953$	−27.8692	+	48.2709i	−0.902773	+	1.56365i	−0.823880	+	0.566765i	$0.808195\pi$
$954$	11.8458	+	6.83920i	0.383523	+	0.221427i
$955$		−	66.1539i		−	2.14069i
$956$		−	5.59389i		−	0.180919i
$957$	13.3163	+	7.68819i	0.430456	+	0.248524i
$958$	2.51322	−	4.35302i	0.0811984	−	0.140640i
$959$	23.6354	+	17.0644i	0.763226	+	0.551037i
$960$	2.81905	−	1.62758i	0.0909843	−	0.0525298i
$961$	6.15396	−	10.6590i	0.198515	−	0.343838i
$962$	37.9860	−	5.15263i	1.22472	−	0.166127i
$963$	−8.69757	−	15.0646i	−0.280275	−	0.485451i
$964$		−	29.2191i		−	0.941084i
$965$	−31.9506	−	55.3401i	−1.02853	−	1.78146i
$966$	−0.786222	+	0.352870i	−0.0252963	+	0.0113534i
$967$		−	20.2959i		−	0.652672i	−0.945254	−	0.326336i	$-0.894186\pi$
$967$		−	20.2959i		−	0.652672i	0.945254	−	0.326336i	$-0.105814\pi$
$968$	4.97548	−	2.87259i	0.159918	−	0.0923287i
$969$			4.05894i			0.130392i
$970$	14.9440	−	8.62790i	0.479822	−	0.277025i
$971$	21.0332	+	36.4306i	0.674988	+	1.16911i	0.976472	+	0.215643i	$0.0691846\pi$
$971$	21.0332	+	36.4306i	0.674988	+	1.16911i	−0.301484	+	0.953471i	$0.597482\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	13.8405	+	30.8378i	0.443707	+	0.988615i
$974$	−6.15960			−0.197366
$975$	−19.9937	+	2.71205i	−0.640310	+	0.0868551i
$976$	−0.114113	−	0.197650i	−0.00365268	−	0.00632663i
$977$	33.1260	+	19.1253i	1.05979	+	0.611873i	0.925375	−	0.379052i	$-0.123750\pi$
$977$	33.1260	+	19.1253i	1.05979	+	0.611873i	0.134419	+	0.990925i	$0.457083\pi$
$978$	0.826274			0.0264213
$979$	−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
$982$	22.5203	−	13.0021i	0.718650	−	0.414913i
$983$	−3.57743	+	2.06543i	−0.114102	+	0.0658769i	−0.555965	−	0.831206i	$-0.687651\pi$
$983$	−3.57743	+	2.06543i	−0.114102	+	0.0658769i	0.441863	+	0.897083i	$0.354318\pi$
$984$	−0.945634			−0.0301457
$985$	−53.1115			−1.69227
$986$	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
$990$	6.46221	+	3.73096i	0.205382	+	0.118578i
$991$	−3.48675	+	6.03923i	−0.110760	+	0.191842i	−0.916077	−	0.401002i	$-0.868662\pi$
$991$	−3.48675	+	6.03923i	−0.110760	+	0.191842i	0.805317	+	0.592845i	$0.201995\pi$
$992$	3.29044	+	5.69921i	0.104472	+	0.180950i
$993$		−	11.1475i		−	0.353755i
$994$	−16.0099	−	35.6714i	−0.507804	−	1.13143i
$995$	−11.0730	−	6.39301i	−0.351038	−	0.202672i
$996$	6.46409	+	3.73204i	0.204823	+	0.118254i
$997$	29.9126			0.947341			0.473670	−	0.880702i	$-0.342929\pi$
$997$	29.9126			0.947341			0.473670	+	0.880702i	$0.342929\pi$
$998$	−9.85885	+	17.0760i	−0.312076	+	0.540532i
$999$			10.6319i			0.336378i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.a.121.8	✓	16	13.4	even	6
546.2.bd.a.361.8	yes	16	7.4	even	3
546.2.bm.a.205.1	yes	16	1.1	even	1	trivial
546.2.bm.a.277.5	yes	16	91.4	even	6	inner
1638.2.cr.a.361.1		16	21.11	odd	6
1638.2.cr.a.667.1		16	39.17	odd	6
1638.2.dt.a.1297.8		16	3.2	odd	2
1638.2.dt.a.1369.4		16	273.95	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-2.81905 - 1.62758i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.54873 + 2.14510i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-2.81905 - 1.62758i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.54873 + 2.14510i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.62758 + 2.81905i) q^{10} +(1.98522 + 1.14617i) 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} +1.00000 q^{16} +0.782978 q^{17} +(-0.866025 + 0.500000i) q^{18} +(-4.48946 + 2.59199i) q^{19} +(2.81905 + 1.62758i) q^{20} +(1.08335 + 2.41379i) q^{21} +(1.14617 - 1.98522i) q^{22} -0.325722 q^{23} +(0.866025 + 0.500000i) q^{24} +(2.79801 + 4.84630i) q^{25} +(0.484638 + 3.57283i) q^{26} -1.00000 q^{27} +(1.54873 - 2.14510i) q^{28} +(3.35386 + 5.80906i) q^{29} +(1.62758 + 2.81905i) q^{30} +(-5.69921 + 3.29044i) q^{31} -1.00000i q^{32} +(1.98522 - 1.14617i) q^{33} -0.782978i q^{34} +(7.85724 - 3.52646i) q^{35} +(0.500000 + 0.866025i) q^{36} -10.6319i q^{37} +(2.59199 + 4.48946i) q^{38} +(-1.36671 + 3.33648i) q^{39} +(1.62758 - 2.81905i) q^{40} +(-0.818943 + 0.472817i) q^{41} +(2.41379 - 1.08335i) q^{42} +(-4.81185 + 8.33436i) q^{43} +(-1.98522 - 1.14617i) q^{44} +3.25515i q^{45} +0.325722i q^{46} +(-2.14659 - 1.23934i) q^{47} +(0.500000 - 0.866025i) q^{48} +(-2.20290 - 6.64434i) q^{49} +(4.84630 - 2.79801i) q^{50} +(0.391489 - 0.678079i) q^{51} +(3.57283 - 0.484638i) q^{52} +(-6.83920 - 11.8458i) q^{53} +1.00000i q^{54} +(-3.73096 - 6.46221i) q^{55} +(-2.14510 - 1.54873i) q^{56} +5.18398i q^{57} +(5.80906 - 3.35386i) q^{58} +0.614234i q^{59} +(2.81905 - 1.62758i) q^{60} +(-0.114113 - 0.197650i) q^{61} +(3.29044 + 5.69921i) q^{62} +(2.63207 + 0.268687i) q^{63} -1.00000 q^{64} +(10.8608 + 4.44884i) q^{65} +(-1.14617 - 1.98522i) q^{66} +(7.97716 + 4.60562i) q^{67} -0.782978 q^{68} +(-0.162861 + 0.282083i) q^{69} +(-3.52646 - 7.85724i) q^{70} +(-12.7983 - 7.38911i) q^{71} +(0.866025 - 0.500000i) q^{72} +(-11.6734 + 6.73964i) q^{73} -10.6319 q^{74} +5.59603 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} +(-2.81905 - 1.62758i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.472817 + 0.818943i) q^{82} -7.46409i q^{83} +(-1.08335 - 2.41379i) q^{84} +(-2.20725 - 1.27436i) q^{85} +(8.33436 + 4.81185i) q^{86} +6.70773 q^{87} +(-1.14617 + 1.98522i) q^{88} +9.06656i q^{89} +3.25515 q^{90} +(4.49374 - 8.41465i) q^{91} +0.325722 q^{92} +6.58088i q^{93} +(-1.23934 + 2.14659i) q^{94} +16.8747 q^{95} +(-0.866025 - 0.500000i) q^{96} +(-4.59086 - 2.65054i) q^{97} +(-6.64434 + 2.20290i) q^{98} -2.29234i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9	\( 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9} + 4 q^{10} + 6 q^{11} - 8 q^{12} - 10 q^{13} + 4 q^{14} + 16 q^{16} + 18 q^{19} + 8 q^{21} + 6 q^{22} + 32 q^{23} - 4 q^{26} - 16 q^{27} + 2 q^{28} - 4 q^{29} - 4 q^{30} - 12 q^{31} + 6 q^{33} - 2 q^{35} + 8 q^{36} - 2 q^{38} - 14 q^{39} - 4 q^{40} - 18 q^{41} + 2 q^{42} - 32 q^{43} - 6 q^{44} - 66 q^{47} + 8 q^{48} + 22 q^{49} + 36 q^{50} + 10 q^{52} + 2 q^{53} + 16 q^{55} - 4 q^{56} + 24 q^{58} + 4 q^{61} + 4 q^{62} + 10 q^{63} - 16 q^{64} + 38 q^{65} - 6 q^{66} + 36 q^{67} + 16 q^{69} + 6 q^{70} - 30 q^{71} + 18 q^{73} - 12 q^{74} - 18 q^{76} - 34 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 6 q^{82} - 8 q^{84} + 72 q^{85} - 8 q^{87} - 6 q^{88} - 8 q^{90} - 2 q^{91} - 32 q^{92} - 24 q^{94} + 80 q^{95} - 6 q^{97} - 60 q^{98}+O(q^{100}) \) 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9 + 4 * q^10 + 6 * q^11 - 8 * q^12 - 10 * q^13 + 4 * q^14 + 16 * q^16 + 18 * q^19 + 8 * q^21 + 6 * q^22 + 32 * q^23 - 4 * q^26 - 16 * q^27 + 2 * q^28 - 4 * q^29 - 4 * q^30 - 12 * q^31 + 6 * q^33 - 2 * q^35 + 8 * q^36 - 2 * q^38 - 14 * q^39 - 4 * q^40 - 18 * q^41 + 2 * q^42 - 32 * q^43 - 6 * q^44 - 66 * q^47 + 8 * q^48 + 22 * q^49 + 36 * q^50 + 10 * q^52 + 2 * q^53 + 16 * q^55 - 4 * q^56 + 24 * q^58 + 4 * q^61 + 4 * q^62 + 10 * q^63 - 16 * q^64 + 38 * q^65 - 6 * q^66 + 36 * q^67 + 16 * q^69 + 6 * q^70 - 30 * q^71 + 18 * q^73 - 12 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 6 * q^82 - 8 * q^84 + 72 * q^85 - 8 * q^87 - 6 * q^88 - 8 * q^90 - 2 * q^91 - 32 * q^92 - 24 * q^94 + 80 * q^95 - 6 * q^97 - 60 * q^98

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