LMFDB - Embedded newform 546.2.bm.a.205.7

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			205.7
Root			$0.960282i$ of defining polynomial
Character	$\chi$	$=$	546.205
Dual form			546.2.bm.a.277.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(0.620092 + 0.358010i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-1.94866 - 1.78962i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(0.620092 + 0.358010i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-1.94866 - 1.78962i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.358010 + 0.620092i) q^{10} +(2.22627 + 1.28534i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(3.57509 - 0.467723i) q^{13} +(1.78962 - 1.94866i) q^{14} +(0.620092 - 0.358010i) q^{15} +1.00000 q^{16} +0.0248360 q^{17} +(0.866025 - 0.500000i) q^{18} +(5.98499 - 3.45544i) q^{19} +(-0.620092 - 0.358010i) q^{20} +(-2.52418 + 0.792781i) q^{21} +(-1.28534 + 2.22627i) q^{22} +9.39876 q^{23} +(-0.866025 - 0.500000i) q^{24} +(-2.24366 - 3.88613i) q^{25} +(0.467723 + 3.57509i) q^{26} -1.00000 q^{27} +(1.94866 + 1.78962i) q^{28} +(-2.77589 - 4.80797i) q^{29} +(0.358010 + 0.620092i) q^{30} +(-4.92140 + 2.84137i) q^{31} +1.00000i q^{32} +(2.22627 - 1.28534i) q^{33} +0.0248360i q^{34} +(-0.567647 - 1.80737i) q^{35} +(0.500000 + 0.866025i) q^{36} -4.17111i q^{37} +(3.45544 + 5.98499i) q^{38} +(1.38248 - 3.32998i) q^{39} +(0.358010 - 0.620092i) q^{40} +(4.54901 - 2.62637i) q^{41} +(-0.792781 - 2.52418i) q^{42} +(-6.37475 + 11.0414i) q^{43} +(-2.22627 - 1.28534i) q^{44} -0.716021i q^{45} +9.39876i q^{46} +(4.32056 + 2.49448i) q^{47} +(0.500000 - 0.866025i) q^{48} +(0.594548 + 6.97471i) q^{49} +(3.88613 - 2.24366i) q^{50} +(0.0124180 - 0.0215086i) q^{51} +(-3.57509 + 0.467723i) q^{52} +(-4.72462 - 8.18328i) q^{53} -1.00000i q^{54} +(0.920330 + 1.59406i) q^{55} +(-1.78962 + 1.94866i) q^{56} -6.91088i q^{57} +(4.80797 - 2.77589i) q^{58} +2.25219i q^{59} +(-0.620092 + 0.358010i) q^{60} +(0.326003 + 0.564654i) q^{61} +(-2.84137 - 4.92140i) q^{62} +(-0.575523 + 2.58240i) q^{63} -1.00000 q^{64} +(2.38433 + 0.989886i) q^{65} +(1.28534 + 2.22627i) q^{66} +(1.62475 + 0.938052i) q^{67} -0.0248360 q^{68} +(4.69938 - 8.13957i) q^{69} +(1.80737 - 0.567647i) q^{70} +(7.52246 + 4.34310i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(-13.7568 + 7.94250i) q^{73} +4.17111 q^{74} -4.48731 q^{75} +(-5.98499 + 3.45544i) q^{76} +(-2.03798 - 6.48886i) q^{77} +(3.32998 + 1.38248i) q^{78} +(-0.194223 + 0.336404i) q^{79} +(0.620092 + 0.358010i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.62637 + 4.54901i) q^{82} -8.85439i q^{83} +(2.52418 - 0.792781i) q^{84} +(0.0154006 + 0.00889156i) q^{85} +(-11.0414 - 6.37475i) q^{86} -5.55177 q^{87} +(1.28534 - 2.22627i) q^{88} +14.8382i q^{89} +0.716021 q^{90} +(-7.80367 - 5.48660i) q^{91} -9.39876 q^{92} +5.68274i q^{93} +(-2.49448 + 4.32056i) q^{94} +4.94833 q^{95} +(0.866025 + 0.500000i) q^{96} +(-1.78702 - 1.03174i) q^{97} +(-6.97471 + 0.594548i) q^{98} -2.57068i 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
$5$	0.620092	+	0.358010i	0.277314	+	0.160107i	0.632207	−	0.774800i	$-0.282149\pi$
$5$	0.620092	+	0.358010i	0.277314	+	0.160107i	−0.354893	+	0.934907i	$0.615483\pi$
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	−1.94866	−	1.78962i	−0.736524	−	0.676411i
$7$	−1.94866	−	1.78962i	−0.736524	−	0.676411i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.358010	+	0.620092i	−0.113213	+	0.196090i
$11$	2.22627	+	1.28534i	0.671247	+	0.387544i	0.796549	−	0.604574i	$-0.206657\pi$
$11$	2.22627	+	1.28534i	0.671247	+	0.387544i	−0.125302	+	0.992119i	$0.539990\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	3.57509	−	0.467723i	0.991550	−	0.129723i
$13$	3.57509	−	0.467723i	0.991550	−	0.129723i
$14$	1.78962	−	1.94866i	0.478295	−	0.520801i
$15$	0.620092	−	0.358010i	0.160107	−	0.0924379i
$16$	1.00000			0.250000
$17$	0.0248360			0.00602363			0.00301181	−	0.999995i	$-0.499041\pi$
$17$	0.0248360			0.00602363			0.00301181	+	0.999995i	$0.499041\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	5.98499	−	3.45544i	1.37305	−	0.792732i	0.381741	−	0.924269i	$-0.375325\pi$
$19$	5.98499	−	3.45544i	1.37305	−	0.792732i	0.991311	+	0.131538i	$0.0419914\pi$
$20$	−0.620092	−	0.358010i	−0.138657	−	0.0800535i
$21$	−2.52418	+	0.792781i	−0.550822	+	0.172999i
$22$	−1.28534	+	2.22627i	−0.274035	+	0.474643i
$23$	9.39876			1.95978			0.979889	−	0.199545i	$-0.0639463\pi$
$23$	9.39876			1.95978			0.979889	+	0.199545i	$0.0639463\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	−2.24366	−	3.88613i	−0.448731	−	0.777226i
$26$	0.467723	+	3.57509i	0.0917280	+	0.701132i
$27$	−1.00000			−0.192450
$28$	1.94866	+	1.78962i	0.368262	+	0.338206i
$29$	−2.77589	−	4.80797i	−0.515469	−	0.892818i	−0.999839	−	0.0179551i	$-0.994284\pi$
$29$	−2.77589	−	4.80797i	−0.515469	−	0.892818i	0.484370	−	0.874863i	$-0.339049\pi$
$30$	0.358010	+	0.620092i	0.0653634	+	0.113213i
$31$	−4.92140	+	2.84137i	−0.883909	+	0.510325i	−0.871945	−	0.489603i	$-0.837142\pi$
$31$	−4.92140	+	2.84137i	−0.883909	+	0.510325i	−0.0119639	+	0.999928i	$0.503808\pi$
$32$			1.00000i			0.176777i
$33$	2.22627	−	1.28534i	0.387544	−	0.223749i
$34$			0.0248360i			0.00425935i
$35$	−0.567647	−	1.80737i	−0.0959499	−	0.305501i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$		−	4.17111i		−	0.685726i	−0.939385	−	0.342863i	$-0.888603\pi$
$37$		−	4.17111i		−	0.685726i	0.939385	−	0.342863i	$-0.111397\pi$
$38$	3.45544	+	5.98499i	0.560546	+	0.970894i
$39$	1.38248	−	3.32998i	0.221374	−	0.533223i
$40$	0.358010	−	0.620092i	0.0566064	−	0.0980452i
$41$	4.54901	−	2.62637i	0.710436	−	0.410171i	−0.100786	−	0.994908i	$-0.532136\pi$
$41$	4.54901	−	2.62637i	0.710436	−	0.410171i	0.811223	+	0.584737i	$0.198802\pi$
$42$	−0.792781	−	2.52418i	−0.122329	−	0.389490i
$43$	−6.37475	+	11.0414i	−0.972141	+	1.68380i	−0.283075	+	0.959098i	$0.591355\pi$
$43$	−6.37475	+	11.0414i	−0.972141	+	1.68380i	−0.689065	+	0.724699i	$0.741979\pi$
$44$	−2.22627	−	1.28534i	−0.335623	−	0.193772i
$45$		−	0.716021i		−	0.106738i
$46$			9.39876i			1.38577i
$47$	4.32056	+	2.49448i	0.630219	+	0.363857i	0.780837	−	0.624735i	$-0.214793\pi$
$47$	4.32056	+	2.49448i	0.630219	+	0.363857i	−0.150618	+	0.988592i	$0.548126\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	0.594548	+	6.97471i	0.0849354	+	0.996386i
$50$	3.88613	−	2.24366i	0.549582	−	0.317301i
$51$	0.0124180	−	0.0215086i	0.00173887	−	0.00301181i
$52$	−3.57509	+	0.467723i	−0.495775	+	0.0648615i
$53$	−4.72462	−	8.18328i	−0.648977	−	1.12406i	−0.983368	−	0.181626i	$-0.941864\pi$
$53$	−4.72462	−	8.18328i	−0.648977	−	1.12406i	0.334391	−	0.942434i	$-0.391469\pi$
$54$		−	1.00000i		−	0.136083i
$55$	0.920330	+	1.59406i	0.124097	+	0.214943i
$56$	−1.78962	+	1.94866i	−0.239148	+	0.260401i
$57$		−	6.91088i		−	0.915368i
$58$	4.80797	−	2.77589i	0.631318	−	0.364492i
$59$			2.25219i			0.293210i	0.989195	+	0.146605i	$0.0468347\pi$
$59$			2.25219i			0.293210i	−0.989195	+	0.146605i	$0.953165\pi$
$60$	−0.620092	+	0.358010i	−0.0800535	+	0.0462189i
$61$	0.326003	+	0.564654i	0.0417404	+	0.0722965i	0.886141	−	0.463416i	$-0.153376\pi$
$61$	0.326003	+	0.564654i	0.0417404	+	0.0722965i	−0.844400	+	0.535713i	$0.820043\pi$
$62$	−2.84137	−	4.92140i	−0.360854	−	0.625018i
$63$	−0.575523	+	2.58240i	−0.0725091	+	0.325351i
$64$	−1.00000			−0.125000
$65$	2.38433	+	0.989886i	0.295740	+	0.122780i
$66$	1.28534	+	2.22627i	0.158214	+	0.274035i
$67$	1.62475	+	0.938052i	0.198495	+	0.114601i	0.595953	−	0.803019i	$-0.296774\pi$
$67$	1.62475	+	0.938052i	0.198495	+	0.114601i	−0.397458	+	0.917620i	$0.630108\pi$
$68$	−0.0248360			−0.00301181
$69$	4.69938	−	8.13957i	0.565739	−	0.979889i
$70$	1.80737	−	0.567647i	0.216022	−	0.0678468i
$71$	7.52246	+	4.34310i	0.892752	+	0.515431i	0.874842	−	0.484409i	$-0.160965\pi$
$71$	7.52246	+	4.34310i	0.892752	+	0.515431i	0.0179106	+	0.999840i	$0.494299\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−13.7568	+	7.94250i	−1.61011	+	0.929600i	−0.620772	+	0.783991i	$0.713181\pi$
$73$	−13.7568	+	7.94250i	−1.61011	+	0.929600i	−0.989342	+	0.145608i	$0.953486\pi$
$74$	4.17111			0.484882
$75$	−4.48731			−0.518150
$76$	−5.98499	+	3.45544i	−0.686526	+	0.396366i
$77$	−2.03798	−	6.48886i	−0.232250	−	0.739475i
$78$	3.32998	+	1.38248i	0.377046	+	0.156535i
$79$	−0.194223	+	0.336404i	−0.0218518	+	0.0378484i	−0.876744	−	0.480956i	$-0.840290\pi$
$79$	−0.194223	+	0.336404i	−0.0218518	+	0.0378484i	0.854893	+	0.518805i	$0.173623\pi$
$80$	0.620092	+	0.358010i	0.0693284	+	0.0400268i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.62637	+	4.54901i	0.290034	+	0.502354i
$83$		−	8.85439i		−	0.971895i	−0.873988	−	0.485948i	$-0.838475\pi$
$83$		−	8.85439i		−	0.971895i	0.873988	−	0.485948i	$-0.161525\pi$
$84$	2.52418	−	0.792781i	0.275411	−	0.0864994i
$85$	0.0154006	+	0.00889156i	0.00167043	+	0.000964425i
$86$	−11.0414	−	6.37475i	−1.19062	−	0.687407i
$87$	−5.55177			−0.595212
$88$	1.28534	−	2.22627i	0.137018	−	0.237322i
$89$			14.8382i			1.57284i	0.617692	+	0.786420i	$0.288068\pi$
$89$			14.8382i			1.57284i	−0.617692	+	0.786420i	$0.711932\pi$
$90$	0.716021			0.0754752
$91$	−7.80367	−	5.48660i	−0.818047	−	0.575152i
$92$	−9.39876			−0.979889
$93$			5.68274i			0.589273i
$94$	−2.49448	+	4.32056i	−0.257286	+	0.445632i
$95$	4.94833			0.507688
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−1.78702	−	1.03174i	−0.181445	−	0.104757i	0.406527	−	0.913639i	$-0.366740\pi$
$97$	−1.78702	−	1.03174i	−0.181445	−	0.104757i	−0.587971	+	0.808882i	$0.700073\pi$
$98$	−6.97471	+	0.594548i	−0.704552	+	0.0600584i
$99$		−	2.57068i		−	0.258363i
$100$	2.24366	+	3.88613i	0.224366	+	0.388613i
$101$	−5.79514	+	10.0375i	−0.576638	+	0.998767i	0.419223	+	0.907883i	$0.362302\pi$
$101$	−5.79514	+	10.0375i	−0.576638	+	0.998767i	−0.995862	+	0.0908836i	$0.971031\pi$
$102$	0.0215086	+	0.0124180i	0.00212967	+	0.00122957i
$103$	−7.89706	+	13.6781i	−0.778120	+	1.34774i	0.154903	+	0.987930i	$0.450493\pi$
$103$	−7.89706	+	13.6781i	−0.778120	+	1.34774i	−0.933024	+	0.359814i	$0.882840\pi$
$104$	−0.467723	−	3.57509i	−0.0458640	−	0.350566i
$105$	−1.84905	−	0.412087i	−0.180449	−	0.0402155i
$106$	8.18328	−	4.72462i	0.794831	−	0.458896i
$107$	−0.482687			−0.0466631			−0.0233315	−	0.999728i	$-0.507427\pi$
$107$	−0.482687			−0.0466631			−0.0233315	+	0.999728i	$0.507427\pi$
$108$	1.00000			0.0962250
$109$	2.77524	−	1.60228i	0.265819	−	0.153471i	−0.361167	−	0.932501i	$-0.617622\pi$
$109$	2.77524	−	1.60228i	0.265819	−	0.153471i	0.626986	+	0.779030i	$0.284288\pi$
$110$	−1.59406	+	0.920330i	−0.151987	+	0.0877500i
$111$	−3.61229	−	2.08556i	−0.342863	−	0.197952i
$112$	−1.94866	−	1.78962i	−0.184131	−	0.169103i
$113$	−4.18781	+	7.25350i	−0.393956	+	0.682352i	−0.992967	−	0.118389i	$-0.962227\pi$
$113$	−4.18781	+	7.25350i	−0.393956	+	0.682352i	0.599011	+	0.800741i	$0.295560\pi$
$114$	6.91088			0.647263
$115$	5.82810	+	3.36485i	0.543473	+	0.313774i
$116$	2.77589	+	4.80797i	0.257734	+	0.446409i
$117$	−2.19260	−	2.86225i	−0.202706	−	0.264615i
$118$	−2.25219			−0.207331
$119$	−0.0483970	−	0.0444470i	−0.00443655	−	0.00407445i
$120$	−0.358010	−	0.620092i	−0.0326817	−	0.0566064i
$121$	−2.19580	−	3.80324i	−0.199619	−	0.345749i
$122$	−0.564654	+	0.326003i	−0.0511214	+	0.0295149i
$123$		−	5.25275i		−	0.473624i
$124$	4.92140	−	2.84137i	0.441955	−	0.255163i
$125$		−	6.79311i		−	0.607594i
$126$	−2.58240	−	0.575523i	−0.230058	−	0.0512717i
$127$	−11.0533	−	19.1448i	−0.980820	−	1.69883i	−0.659211	−	0.751958i	$-0.729109\pi$
$127$	−11.0533	−	19.1448i	−0.980820	−	1.69883i	−0.321610	−	0.946872i	$-0.604224\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	6.37475	+	11.0414i	0.561266	+	0.972141i
$130$	−0.989886	+	2.38433i	−0.0868187	+	0.209120i
$131$	5.57371	−	9.65394i	0.486977	−	0.843469i	−0.512911	−	0.858442i	$-0.671433\pi$
$131$	5.57371	−	9.65394i	0.486977	−	0.843469i	0.999888	+	0.0149731i	$0.00476625\pi$
$132$	−2.22627	+	1.28534i	−0.193772	+	0.111874i
$133$	−17.8466	−	3.97737i	−1.54750	−	0.344882i
$134$	−0.938052	+	1.62475i	−0.0810354	+	0.140357i
$135$	−0.620092	−	0.358010i	−0.0533690	−	0.0308126i
$136$		−	0.0248360i		−	0.00212967i
$137$		−	16.7971i		−	1.43507i	−0.696523	−	0.717534i	$-0.745271\pi$
$137$		−	16.7971i		−	1.43507i	0.696523	−	0.717534i	$-0.254729\pi$
$138$	8.13957	+	4.69938i	0.692886	+	0.400038i
$139$	−9.50946	+	16.4709i	−0.806582	+	1.39704i	0.108636	+	0.994082i	$0.465352\pi$
$139$	−9.50946	+	16.4709i	−0.806582	+	1.39704i	−0.915218	+	0.402959i	$0.867982\pi$
$140$	0.567647	+	1.80737i	0.0479749	+	0.152750i
$141$	4.32056	−	2.49448i	0.363857	−	0.210073i
$142$	−4.34310	+	7.52246i	−0.364465	+	0.631271i
$143$	8.56030	+	3.55392i	0.715848	+	0.297194i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$		−	3.97518i		−	0.330121i
$146$	−7.94250	−	13.7568i	−0.657326	−	1.13852i
$147$	6.33755	+	2.97246i	0.522712	+	0.245164i
$148$			4.17111i			0.342863i
$149$	10.6121	−	6.12689i	0.869376	−	0.501934i	0.00223492	−	0.999998i	$-0.499289\pi$
$149$	10.6121	−	6.12689i	0.869376	−	0.501934i	0.867141	+	0.498063i	$0.165955\pi$
$150$		−	4.48731i		−	0.366388i
$151$	11.5364	−	6.66053i	0.938817	−	0.542026i	0.0492279	−	0.998788i	$-0.484324\pi$
$151$	11.5364	−	6.66053i	0.938817	−	0.542026i	0.889589	+	0.456761i	$0.150991\pi$
$152$	−3.45544	−	5.98499i	−0.280273	−	0.485447i
$153$	−0.0124180	−	0.0215086i	−0.00100394	−	0.00173887i
$154$	6.48886	−	2.03798i	0.522888	−	0.164225i
$155$	−4.06896			−0.326827
$156$	−1.38248	+	3.32998i	−0.110687	+	0.266611i
$157$	−3.49931	−	6.06098i	−0.279275	−	0.483719i	0.691930	−	0.721965i	$-0.256761\pi$
$157$	−3.49931	−	6.06098i	−0.279275	−	0.483719i	−0.971205	+	0.238246i	$0.923427\pi$
$158$	−0.336404	−	0.194223i	−0.0267628	−	0.0154515i
$159$	−9.44924			−0.749374
$160$	−0.358010	+	0.620092i	−0.0283032	+	0.0490226i
$161$	−18.3150	−	16.8202i	−1.44342	−	1.32562i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	8.82738	−	5.09649i	0.691414	−	0.399188i	−0.112728	−	0.993626i	$-0.535959\pi$
$163$	8.82738	−	5.09649i	0.691414	−	0.399188i	0.804141	+	0.594438i	$0.202625\pi$
$164$	−4.54901	+	2.62637i	−0.355218	+	0.205085i
$165$	1.84066			0.143295
$166$	8.85439			0.687234
$167$	−6.33732	+	3.65885i	−0.490397	+	0.283131i	−0.724739	−	0.689023i	$-0.758040\pi$
$167$	−6.33732	+	3.65885i	−0.490397	+	0.283131i	0.234342	+	0.972154i	$0.424706\pi$
$168$	0.792781	+	2.52418i	0.0611643	+	0.194745i
$169$	12.5625	−	3.34430i	0.966344	−	0.257254i
$170$	−0.00889156	+	0.0154006i	−0.000681951	+	0.00118117i
$171$	−5.98499	−	3.45544i	−0.457684	−	0.264244i
$172$	6.37475	−	11.0414i	0.486070	−	0.841898i
$173$	−3.24254	−	5.61624i	−0.246525	−	0.426995i	0.716034	−	0.698065i	$-0.245956\pi$
$173$	−3.24254	−	5.61624i	−0.246525	−	0.426995i	−0.962559	+	0.271071i	$0.912622\pi$
$174$		−	5.55177i		−	0.420879i
$175$	−2.58255	+	11.5880i	−0.195223	+	0.875972i
$176$	2.22627	+	1.28534i	0.167812	+	0.0968861i
$177$	1.95045	+	1.12610i	0.146605	+	0.0846425i
$178$	−14.8382			−1.11217
$179$	−11.6114	+	20.1116i	−0.867878	+	1.50321i	−0.00371753	+	0.999993i	$0.501183\pi$
$179$	−11.6114	+	20.1116i	−0.867878	+	1.50321i	−0.864161	+	0.503216i	$0.832150\pi$
$180$			0.716021i			0.0533690i
$181$	−5.61910			−0.417664			−0.208832	−	0.977952i	$-0.566966\pi$
$181$	−5.61910			−0.417664			−0.208832	+	0.977952i	$0.566966\pi$
$182$	5.48660	−	7.80367i	0.406694	−	0.578446i
$183$	0.652006			0.0481977
$184$		−	9.39876i		−	0.692886i
$185$	1.49330	−	2.58647i	0.109790	−	0.190161i
$186$	−5.68274			−0.416679
$187$	0.0552918	+	0.0319228i	0.00404334	+	0.00233442i
$188$	−4.32056	−	2.49448i	−0.315109	−	0.181929i
$189$	1.94866	+	1.78962i	0.141744	+	0.130175i
$190$			4.94833i			0.358990i
$191$	11.9472	+	20.6932i	0.864472	+	1.49731i	0.867571	+	0.497314i	$0.165680\pi$
$191$	11.9472	+	20.6932i	0.864472	+	1.49731i	−0.00309854	+	0.999995i	$0.500986\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	18.1841	+	10.4986i	1.30892	+	0.755707i	0.981916	−	0.189315i	$-0.0606268\pi$
$193$	18.1841	+	10.4986i	1.30892	+	0.755707i	0.327006	+	0.945022i	$0.393960\pi$
$194$	1.03174	−	1.78702i	0.0740744	−	0.128301i
$195$	2.04943	−	1.56995i	0.146763	−	0.112426i
$196$	−0.594548	−	6.97471i	−0.0424677	−	0.498193i
$197$	−4.48984	+	2.59221i	−0.319888	+	0.184688i	−0.651343	−	0.758784i	$-0.725794\pi$
$197$	−4.48984	+	2.59221i	−0.319888	+	0.184688i	0.331455	+	0.943471i	$0.392461\pi$
$198$	2.57068			0.182690
$199$	−16.1417			−1.14426			−0.572128	−	0.820164i	$-0.693882\pi$
$199$	−16.1417			−1.14426			−0.572128	+	0.820164i	$0.693882\pi$
$200$	−3.88613	+	2.24366i	−0.274791	+	0.158651i
$201$	1.62475	−	0.938052i	0.114601	−	0.0661651i
$202$	−10.0375	−	5.79514i	−0.706235	−	0.407745i
$203$	−3.19517	+	14.3369i	−0.224257	+	1.00625i
$204$	−0.0124180	+	0.0215086i	−0.000869435	+	0.00150591i
$205$	3.76108			0.262685
$206$	−13.6781	−	7.89706i	−0.952999	−	0.550214i
$207$	−4.69938	−	8.13957i	−0.326630	−	0.565739i
$208$	3.57509	−	0.467723i	0.247888	−	0.0324308i
$209$	17.7656			1.22888
$210$	0.412087	−	1.84905i	0.0284367	−	0.127597i
$211$	7.68735	+	13.3149i	0.529219	+	0.916635i	0.999419	+	0.0340747i	$0.0108484\pi$
$211$	7.68735	+	13.3149i	0.529219	+	0.916635i	−0.470200	+	0.882560i	$0.655818\pi$
$212$	4.72462	+	8.18328i	0.324488	+	0.562030i
$213$	7.52246	−	4.34310i	0.515431	−	0.297584i
$214$		−	0.482687i		−	0.0329958i
$215$	−7.90587	+	4.56445i	−0.539176	+	0.311293i
$216$			1.00000i			0.0680414i
$217$	14.6751	+	3.27055i	0.996210	+	0.222019i
$218$	1.60228	+	2.77524i	0.108520	+	0.187963i
$219$			15.8850i			1.07341i
$220$	−0.920330	−	1.59406i	−0.0620486	−	0.107471i
$221$	0.0887910	−	0.0116164i	0.00597273	−	0.000781403i
$222$	2.08556	−	3.61229i	0.139973	−	0.242441i
$223$	11.0984	−	6.40769i	0.743207	−	0.429091i	−0.0800273	−	0.996793i	$-0.525501\pi$
$223$	11.0984	−	6.40769i	0.743207	−	0.429091i	0.823234	+	0.567702i	$0.192167\pi$
$224$	1.78962	−	1.94866i	0.119574	−	0.130200i
$225$	−2.24366	+	3.88613i	−0.149577	+	0.259075i
$226$	−7.25350	−	4.18781i	−0.482496	−	0.278569i
$227$			20.1537i			1.33765i	0.743422	+	0.668823i	$0.233201\pi$
$227$			20.1537i			1.33765i	−0.743422	+	0.668823i	$0.766799\pi$
$228$			6.91088i			0.457684i
$229$	−8.89145	−	5.13348i	−0.587564	−	0.339230i	0.176570	−	0.984288i	$-0.443500\pi$
$229$	−8.89145	−	5.13348i	−0.587564	−	0.339230i	−0.764134	+	0.645058i	$0.776833\pi$
$230$	−3.36485	+	5.82810i	−0.221872	+	0.384293i
$231$	−6.63851	−	1.47949i	−0.436782	−	0.0973430i
$232$	−4.80797	+	2.77589i	−0.315659	+	0.182246i
$233$	−1.56117	+	2.70402i	−0.102276	+	0.177146i	−0.912622	−	0.408805i	$-0.865946\pi$
$233$	−1.56117	+	2.70402i	−0.102276	+	0.177146i	0.810346	+	0.585951i	$0.199279\pi$
$234$	2.86225	−	2.19260i	0.187111	−	0.143335i
$235$	1.78610	+	3.09361i	0.116512	+	0.201805i
$236$		−	2.25219i		−	0.146605i
$237$	0.194223	+	0.336404i	0.0126161	+	0.0218518i
$238$	0.0444470	−	0.0483970i	0.00288107	−	0.00313711i
$239$		−	12.2325i		−	0.791253i	−0.918411	−	0.395627i	$-0.870527\pi$
$239$		−	12.2325i		−	0.791253i	0.918411	−	0.395627i	$-0.129473\pi$
$240$	0.620092	−	0.358010i	0.0400268	−	0.0231095i
$241$		−	1.88892i		−	0.121676i	−0.998148	−	0.0608382i	$-0.980623\pi$
$241$		−	1.88892i		−	0.121676i	0.998148	−	0.0608382i	$-0.0193774\pi$
$242$	3.80324	−	2.19580i	0.244482	−	0.141152i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−0.326003	−	0.564654i	−0.0208702	−	0.0361483i
$245$	−2.12834	+	4.53781i	−0.135975	+	0.289910i
$246$	5.25275			0.334903
$247$	19.7807	−	15.1528i	1.25861	−	0.964150i
$248$	2.84137	+	4.92140i	0.180427	+	0.312509i
$249$	−7.66812	−	4.42719i	−0.485948	−	0.280562i
$250$	6.79311			0.429634
$251$	−7.56052	+	13.0952i	−0.477216	+	0.826562i	−0.999659	−	0.0261123i	$-0.991687\pi$
$251$	−7.56052	+	13.0952i	−0.477216	+	0.826562i	0.522443	+	0.852674i	$0.325021\pi$
$252$	0.575523	−	2.58240i	0.0362546	−	0.162676i
$253$	20.9242	+	12.0806i	1.31549	+	0.759501i
$254$	19.1448	−	11.0533i	1.20125	−	0.693545i
$255$	0.0154006	−	0.00889156i	0.000964425	−	0.000556811i
$256$	1.00000			0.0625000
$257$	5.65409			0.352692			0.176346	−	0.984328i	$-0.443572\pi$
$257$	5.65409			0.352692			0.176346	+	0.984328i	$0.443572\pi$
$258$	−11.0414	+	6.37475i	−0.687407	+	0.396875i
$259$	−7.46469	+	8.12807i	−0.463833	+	0.505054i
$260$	−2.38433	−	0.989886i	−0.147870	−	0.0613901i
$261$	−2.77589	+	4.80797i	−0.171823	+	0.297606i
$262$	9.65394	+	5.57371i	0.596422	+	0.344345i
$263$	7.27412	−	12.5991i	0.448541	−	0.776897i	−0.549750	−	0.835329i	$-0.685277\pi$
$263$	7.27412	−	12.5991i	0.448541	−	0.776897i	0.998291	+	0.0584327i	$0.0186103\pi$
$264$	−1.28534	−	2.22627i	−0.0791072	−	0.137018i
$265$		−	6.76585i		−	0.415623i
$266$	3.97737	−	17.8466i	0.243868	−	1.09425i
$267$	12.8502	+	7.41908i	0.786420	+	0.454040i
$268$	−1.62475	−	0.938052i	−0.0992477	−	0.0573007i
$269$	3.46062			0.210998			0.105499	−	0.994419i	$-0.466356\pi$
$269$	3.46062			0.210998			0.105499	+	0.994419i	$0.466356\pi$
$270$	0.358010	−	0.620092i	0.0217878	−	0.0377376i
$271$			11.5709i			0.702880i	0.936210	+	0.351440i	$0.114308\pi$
$271$			11.5709i			0.702880i	−0.936210	+	0.351440i	$0.885692\pi$
$272$	0.0248360			0.00150591
$273$	−8.65337	+	4.01488i	−0.523726	+	0.242991i
$274$	16.7971			1.01475
$275$		−	11.5354i		−	0.695614i
$276$	−4.69938	+	8.13957i	−0.282870	+	0.489944i
$277$	4.63996			0.278788			0.139394	−	0.990237i	$-0.455485\pi$
$277$	4.63996			0.278788			0.139394	+	0.990237i	$0.455485\pi$
$278$	−16.4709	−	9.50946i	−0.987857	−	0.570340i
$279$	4.92140	+	2.84137i	0.294636	+	0.170108i
$280$	−1.80737	+	0.567647i	−0.108011	+	0.0339234i
$281$			20.9621i			1.25049i	0.780428	+	0.625246i	$0.215001\pi$
$281$			20.9621i			1.25049i	−0.780428	+	0.625246i	$0.784999\pi$
$282$	2.49448	+	4.32056i	0.148544	+	0.257286i
$283$	2.36018	−	4.08795i	0.140298	−	0.243003i	−0.787311	−	0.616556i	$-0.788527\pi$
$283$	2.36018	−	4.08795i	0.140298	−	0.243003i	0.927609	+	0.373553i	$0.121861\pi$
$284$	−7.52246	−	4.34310i	−0.446376	−	0.257715i
$285$	2.47416	−	4.28538i	0.146557	−	0.253844i
$286$	−3.55392	+	8.56030i	−0.210148	+	0.506181i
$287$	−13.5647	−	3.02308i	−0.800698	−	0.178447i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−16.9994			−0.999964
$290$	3.97518			0.233431
$291$	−1.78702	+	1.03174i	−0.104757	+	0.0604815i
$292$	13.7568	−	7.94250i	0.805057	−	0.464800i
$293$	29.0541	+	16.7744i	1.69736	+	0.979970i	0.948252	+	0.317518i	$0.102850\pi$
$293$	29.0541	+	16.7744i	1.69736	+	0.979970i	0.749105	+	0.662451i	$0.230484\pi$
$294$	−2.97246	+	6.33755i	−0.173357	+	0.369613i
$295$	−0.806308	+	1.39657i	−0.0469450	+	0.0813112i
$296$	−4.17111			−0.242441
$297$	−2.22627	−	1.28534i	−0.129181	−	0.0745830i
$298$	6.12689	+	10.6121i	0.354921	+	0.614741i
$299$	33.6014	−	4.39602i	1.94322	−	0.254228i
$300$	4.48731			0.259075
$301$	32.1821	−	10.1076i	1.85494	−	0.582590i
$302$	6.66053	+	11.5364i	0.383271	+	0.663844i
$303$	5.79514	+	10.0375i	0.332922	+	0.576638i
$304$	5.98499	−	3.45544i	0.343263	−	0.198183i
$305$			0.466850i			0.0267317i
$306$	0.0215086	−	0.0124180i	0.00122957	−	0.000709891i
$307$		−	5.49245i		−	0.313471i	−0.987641	−	0.156735i	$-0.949903\pi$
$307$		−	5.49245i		−	0.313471i	0.987641	−	0.156735i	$-0.0500970\pi$
$308$	2.03798	+	6.48886i	0.116125	+	0.369737i
$309$	7.89706	+	13.6781i	0.449248	+	0.778120i
$310$		−	4.06896i		−	0.231101i
$311$	7.45213	+	12.9075i	0.422572	+	0.731916i	0.996190	−	0.0872069i	$-0.0277941\pi$
$311$	7.45213	+	12.9075i	0.422572	+	0.731916i	−0.573619	+	0.819123i	$0.694461\pi$
$312$	−3.32998	−	1.38248i	−0.188523	−	0.0782677i
$313$	1.80173	−	3.12069i	0.101840	−	0.176392i	−0.810603	−	0.585596i	$-0.800860\pi$
$313$	1.80173	−	3.12069i	0.101840	−	0.176392i	0.912443	+	0.409205i	$0.134194\pi$
$314$	6.06098	−	3.49931i	0.342041	−	0.197477i
$315$	−1.28140	+	1.39528i	−0.0721988	+	0.0786151i
$316$	0.194223	−	0.336404i	0.0109259	−	0.0189242i
$317$	3.54331	+	2.04573i	0.199012	+	0.114900i	0.596194	−	0.802840i	$-0.296679\pi$
$317$	3.54331	+	2.04573i	0.199012	+	0.114900i	−0.397183	+	0.917740i	$0.630012\pi$
$318$		−	9.44924i		−	0.529887i
$319$		−	14.2718i		−	0.799069i
$320$	−0.620092	−	0.358010i	−0.0346642	−	0.0200134i
$321$	−0.241343	+	0.418019i	−0.0134705	+	0.0233315i
$322$	16.8202	−	18.3150i	0.937352	−	1.02065i
$323$	0.148644	−	0.0858194i	0.00827075	−	0.00477512i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−9.83890	−	12.8438i	−0.545764	−	0.712448i
$326$	5.09649	+	8.82738i	0.282268	+	0.488903i
$327$		−	3.20457i		−	0.177213i
$328$	−2.62637	−	4.54901i	−0.145017	−	0.251177i
$329$	−3.95515	−	12.5930i	−0.218054	−	0.694277i
$330$			1.84066i			0.101325i
$331$	−16.8069	+	9.70350i	−0.923793	+	0.533352i	−0.884843	−	0.465889i	$-0.845735\pi$
$331$	−16.8069	+	9.70350i	−0.923793	+	0.533352i	−0.0389501	+	0.999241i	$0.512401\pi$
$332$			8.85439i			0.485948i
$333$	−3.61229	+	2.08556i	−0.197952	+	0.114288i
$334$	−3.65885	−	6.33732i	−0.200204	−	0.346763i
$335$	0.671665	+	1.16336i	0.0366970	+	0.0635610i
$336$	−2.52418	+	0.792781i	−0.137705	+	0.0432497i
$337$	−23.0545			−1.25586			−0.627929	−	0.778271i	$-0.716097\pi$
$337$	−23.0545			−1.25586			−0.627929	+	0.778271i	$0.716097\pi$
$338$	3.34430	+	12.5625i	0.181906	+	0.683308i
$339$	4.18781	+	7.25350i	0.227451	+	0.393956i
$340$	−0.0154006	−	0.00889156i	−0.000835217	−	0.000482213i
$341$	−14.6085			−0.791095
$342$	3.45544	−	5.98499i	0.186849	−	0.323631i
$343$	11.3235	−	14.6553i	0.611410	−	0.791314i
$344$	11.0414	+	6.37475i	0.595312	+	0.343704i
$345$	5.82810	−	3.36485i	0.313774	−	0.181158i
$346$	5.61624	−	3.24254i	0.301931	−	0.174320i
$347$	−4.60157			−0.247025			−0.123513	−	0.992343i	$-0.539416\pi$
$347$	−4.60157			−0.247025			−0.123513	+	0.992343i	$0.539416\pi$
$348$	5.55177			0.297606
$349$	−3.23204	+	1.86602i	−0.173007	+	0.0998858i	−0.584003	−	0.811751i	$-0.698514\pi$
$349$	−3.23204	+	1.86602i	−0.173007	+	0.0998858i	0.410996	+	0.911637i	$0.365181\pi$
$350$	−11.5880	−	2.58255i	−0.619406	−	0.138043i
$351$	−3.57509	+	0.467723i	−0.190824	+	0.0249652i
$352$	−1.28534	+	2.22627i	−0.0685088	+	0.118661i
$353$	−22.8223	−	13.1765i	−1.21471	−	0.701312i	−0.250927	−	0.968006i	$-0.580735\pi$
$353$	−22.8223	−	13.1765i	−1.21471	−	0.701312i	−0.963781	+	0.266694i	$0.914069\pi$
$354$	−1.12610	+	1.95045i	−0.0598513	+	0.103666i
$355$	3.10975	+	5.38624i	0.165048	+	0.285872i
$356$		−	14.8382i		−	0.786420i
$357$	−0.0626907	+	0.0196895i	−0.00331794	+	0.00104208i
$358$	−20.1116	−	11.6114i	−1.06293	−	0.613683i
$359$	7.11568	+	4.10824i	0.375551	+	0.216825i	0.675881	−	0.737011i	$-0.263763\pi$
$359$	7.11568	+	4.10824i	0.375551	+	0.216825i	−0.300330	+	0.953835i	$0.597097\pi$
$360$	−0.716021			−0.0377376
$361$	14.3801	−	24.9071i	0.756848	−	1.31090i
$362$		−	5.61910i		−	0.295333i
$363$	−4.39161			−0.230500
$364$	7.80367	+	5.48660i	0.409023	+	0.287576i
$365$	−11.3740			−0.595342
$366$			0.652006i			0.0340809i
$367$	−0.214399	+	0.371350i	−0.0111915	+	0.0193843i	−0.871567	−	0.490277i	$-0.836896\pi$
$367$	−0.214399	+	0.371350i	−0.0111915	+	0.0193843i	0.860375	+	0.509661i	$0.170229\pi$
$368$	9.39876			0.489944
$369$	−4.54901	−	2.62637i	−0.236812	−	0.136724i
$370$	2.58647	+	1.49330i	0.134464	+	0.0776330i
$371$	−5.43826	+	24.4017i	−0.282340	+	1.26687i
$372$		−	5.68274i		−	0.294636i
$373$	1.00753	+	1.74510i	0.0521682	+	0.0903579i	0.890930	−	0.454140i	$-0.150053\pi$
$373$	1.00753	+	1.74510i	0.0521682	+	0.0903579i	−0.838762	+	0.544498i	$0.816720\pi$
$374$	−0.0319228	+	0.0552918i	−0.00165069	+	0.00285907i
$375$	−5.88301	−	3.39656i	−0.303797	−	0.175397i
$376$	2.49448	−	4.32056i	0.128643	−	0.222816i
$377$	−12.1728	−	15.8906i	−0.626932	−	0.818406i
$378$	−1.78962	+	1.94866i	−0.0920479	+	0.100228i
$379$	15.0823	−	8.70779i	0.774727	−	0.447289i	−0.0598312	−	0.998209i	$-0.519056\pi$
$379$	15.0823	−	8.70779i	0.774727	−	0.447289i	0.834558	+	0.550920i	$0.185723\pi$
$380$	−4.94833			−0.253844
$381$	−22.1066			−1.13255
$382$	−20.6932	+	11.9472i	−1.05876	+	0.611274i
$383$	0.284342	−	0.164165i	0.0145292	−	0.00838845i	−0.492718	−	0.870189i	$-0.663997\pi$
$383$	0.284342	−	0.164165i	0.0145292	−	0.00838845i	0.507247	+	0.861801i	$0.330663\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$	1.05934	−	4.75331i	0.0539891	−	0.242251i
$386$	−10.4986	+	18.1841i	−0.534365	+	0.925548i
$387$	12.7495			0.648094
$388$	1.78702	+	1.03174i	0.0907223	+	0.0523785i
$389$	−4.30458	−	7.45575i	−0.218251	−	0.378022i	0.736022	−	0.676957i	$-0.236702\pi$
$389$	−4.30458	−	7.45575i	−0.218251	−	0.378022i	−0.954273	+	0.298935i	$0.903368\pi$
$390$	1.56995	+	2.04943i	0.0794974	+	0.103777i
$391$	0.233428			0.0118050
$392$	6.97471	−	0.594548i	0.352276	−	0.0300292i
$393$	−5.57371	−	9.65394i	−0.281156	−	0.486977i
$394$	−2.59221	−	4.48984i	−0.130594	−	0.226195i
$395$	−0.240872	+	0.139067i	−0.0121196	+	0.00699724i
$396$			2.57068i			0.129181i
$397$	−1.49677	+	0.864161i	−0.0751208	+	0.0433710i	−0.537090	−	0.843525i	$-0.680476\pi$
$397$	−1.49677	+	0.864161i	−0.0751208	+	0.0433710i	0.461969	+	0.886896i	$0.347143\pi$
$398$		−	16.1417i		−	0.809111i
$399$	−12.3678	+	13.4669i	−0.619165	+	0.674190i
$400$	−2.24366	−	3.88613i	−0.112183	−	0.194306i
$401$			13.5664i			0.677473i	0.940881	+	0.338737i	$0.110000\pi$
$401$			13.5664i			0.677473i	−0.940881	+	0.338737i	$0.890000\pi$
$402$	0.938052	+	1.62475i	0.0467858	+	0.0810354i
$403$	−16.2654	+	12.4600i	−0.810240	+	0.620677i
$404$	5.79514	−	10.0375i	0.288319	−	0.499383i
$405$	−0.620092	+	0.358010i	−0.0308126	+	0.0177897i
$406$	−14.3369	−	3.19517i	−0.711527	−	0.158574i
$407$	5.36129	−	9.28603i	0.265749	−	0.460292i
$408$	−0.0215086	−	0.0124180i	−0.00106484	−	0.000614784i
$409$			1.16202i			0.0574584i	0.999587	+	0.0287292i	$0.00914605\pi$
$409$			1.16202i			0.0574584i	−0.999587	+	0.0287292i	$0.990854\pi$
$410$			3.76108i			0.185746i
$411$	−14.5467	−	8.39853i	−0.717534	−	0.414269i
$412$	7.89706	−	13.6781i	0.389060	−	0.673872i
$413$	4.03056	−	4.38875i	0.198331	−	0.215956i
$414$	8.13957	−	4.69938i	0.400038	−	0.230962i
$415$	3.16996	−	5.49053i	0.155607	−	0.269520i
$416$	0.467723	+	3.57509i	0.0229320	+	0.175283i
$417$	9.50946	+	16.4709i	0.465680	+	0.806582i
$418$			17.7656i			0.868946i
$419$	16.6656	+	28.8657i	0.814169	+	1.41018i	0.909923	+	0.414778i	$0.136141\pi$
$419$	16.6656	+	28.8657i	0.814169	+	1.41018i	−0.0957534	+	0.995405i	$0.530526\pi$
$420$	1.84905	+	0.412087i	0.0902244	+	0.0201078i
$421$		−	17.4686i		−	0.851367i	−0.904872	−	0.425684i	$-0.860034\pi$
$421$		−	17.4686i		−	0.851367i	0.904872	−	0.425684i	$-0.139966\pi$
$422$	−13.3149	+	7.68735i	−0.648159	+	0.374214i
$423$		−	4.98896i		−	0.242571i
$424$	−8.18328	+	4.72462i	−0.397415	+	0.229448i
$425$	−0.0557236	−	0.0965161i	−0.00270299	−	0.00468172i
$426$	4.34310	+	7.52246i	0.210424	+	0.364465i
$427$	0.375245	−	1.68374i	0.0181594	−	0.0814818i
$428$	0.482687			0.0233315
$429$	7.35793	−	5.63648i	0.355244	−	0.272132i
$430$	−4.56445	−	7.90587i	−0.220118	−	0.381255i
$431$	−19.8204	−	11.4433i	−0.954715	−	0.551205i	−0.0601723	−	0.998188i	$-0.519165\pi$
$431$	−19.8204	−	11.4433i	−0.954715	−	0.551205i	−0.894542	+	0.446983i	$0.852498\pi$
$432$	−1.00000			−0.0481125
$433$	−9.81620	+	17.0022i	−0.471736	+	0.817071i	−0.999477	−	0.0323342i	$-0.989706\pi$
$433$	−9.81620	+	17.0022i	−0.471736	+	0.817071i	0.527741	+	0.849405i	$0.323039\pi$
$434$	−3.27055	+	14.6751i	−0.156991	+	0.704427i
$435$	−3.44261	−	1.98759i	−0.165060	−	0.0952977i
$436$	−2.77524	+	1.60228i	−0.132910	+	0.0767354i
$437$	56.2515	−	32.4768i	2.69088	−	1.55358i
$438$	−15.8850			−0.759015
$439$	−25.5976			−1.22171			−0.610854	−	0.791743i	$-0.709174\pi$
$439$	−25.5976			−1.22171			−0.610854	+	0.791743i	$0.709174\pi$
$440$	1.59406	−	0.920330i	0.0759937	−	0.0438750i
$441$	5.74300	−	4.00225i	0.273476	−	0.190583i
$442$	0.0116164	+	0.0887910i	0.000552535	+	0.00422336i
$443$	10.9535	−	18.9721i	0.520418	−	0.901390i	−0.479301	−	0.877651i	$-0.659110\pi$
$443$	10.9535	−	18.9721i	0.520418	−	0.901390i	0.999718	−	0.0237390i	$-0.00755706\pi$
$444$	3.61229	+	2.08556i	0.171432	+	0.0989761i
$445$	−5.31221	+	9.20102i	−0.251823	+	0.436170i
$446$	6.40769	+	11.0984i	0.303413	+	0.525527i
$447$		−	12.2538i		−	0.579584i
$448$	1.94866	+	1.78962i	0.0920655	+	0.0845514i
$449$	−23.0029	−	13.2807i	−1.08557	−	0.626756i	−0.153179	−	0.988198i	$-0.548951\pi$
$449$	−23.0029	−	13.2807i	−1.08557	−	0.626756i	−0.932394	+	0.361443i	$0.882284\pi$
$450$	−3.88613	−	2.24366i	−0.183194	−	0.105767i
$451$	13.5031			0.635837
$452$	4.18781	−	7.25350i	0.196978	−	0.341176i
$453$		−	13.3211i		−	0.625878i
$454$	−20.1537			−0.945858
$455$	−2.87473	−	6.19599i	−0.134770	−	0.290472i
$456$	−6.91088			−0.323631
$457$		−	29.2901i		−	1.37014i	−0.728480	−	0.685068i	$-0.759773\pi$
$457$		−	29.2901i		−	1.37014i	0.728480	−	0.685068i	$-0.240227\pi$
$458$	5.13348	−	8.89145i	0.239872	−	0.415470i
$459$	−0.0248360			−0.00115925
$460$	−5.82810	−	3.36485i	−0.271736	−	0.156887i
$461$	−1.95594	−	1.12927i	−0.0910974	−	0.0525951i	0.453759	−	0.891124i	$-0.350083\pi$
$461$	−1.95594	−	1.12927i	−0.0910974	−	0.0525951i	−0.544857	+	0.838529i	$0.683416\pi$
$462$	1.47949	−	6.63851i	0.0688319	−	0.308852i
$463$			2.33300i			0.108424i	0.998529	+	0.0542119i	$0.0172647\pi$
$463$			2.33300i			0.108424i	−0.998529	+	0.0542119i	$0.982735\pi$
$464$	−2.77589	−	4.80797i	−0.128867	−	0.223205i
$465$	−2.03448	+	3.52382i	−0.0943468	+	0.163413i
$466$	−2.70402	−	1.56117i	−0.125261	−	0.0723197i
$467$	−21.1203	+	36.5814i	−0.977329	+	1.69278i	−0.305305	+	0.952255i	$0.598758\pi$
$467$	−21.1203	+	36.5814i	−0.977329	+	1.69278i	−0.672025	+	0.740529i	$0.734575\pi$
$468$	2.19260	+	2.86225i	0.101353	+	0.132308i
$469$	−1.48734	−	4.73563i	−0.0686789	−	0.218671i
$470$	−3.09361	+	1.78610i	−0.142698	+	0.0823866i
$471$	−6.99861			−0.322479
$472$	2.25219			0.103666
$473$	−28.3839	+	16.3874i	−1.30509	+	0.753495i
$474$	−0.336404	+	0.194223i	−0.0154515	+	0.00892095i
$475$	−26.8566	−	15.5056i	−1.23226	−	0.711447i
$476$	0.0483970	+	0.0444470i	0.00221827	+	0.00203722i
$477$	−4.72462	+	8.18328i	−0.216326	+	0.374687i
$478$	12.2325			0.559501
$479$	16.7159	+	9.65093i	0.763769	+	0.440962i	0.830647	−	0.556799i	$-0.187971\pi$
$479$	16.7159	+	9.65093i	0.763769	+	0.440962i	−0.0668782	+	0.997761i	$0.521304\pi$
$480$	0.358010	+	0.620092i	0.0163409	+	0.0283032i
$481$	−1.95092	−	14.9121i	−0.0889545	−	0.679932i
$482$	1.88892			0.0860382
$483$	−23.7242	+	7.45116i	−1.07949	+	0.339039i
$484$	2.19580	+	3.80324i	0.0998093	+	0.172875i
$485$	−0.738745	−	1.27954i	−0.0335447	−	0.0581011i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$		−	15.0028i		−	0.679844i	−0.940454	−	0.339922i	$-0.889599\pi$
$487$		−	15.0028i		−	0.679844i	0.940454	−	0.339922i	$-0.110401\pi$
$488$	0.564654	−	0.326003i	0.0255607	−	0.0147575i
$489$		−	10.1930i		−	0.460942i
$490$	−4.53781	−	2.12834i	−0.204998	−	0.0961487i
$491$	14.2048	+	24.6034i	0.641052	+	1.11033i	0.985198	+	0.171418i	$0.0548350\pi$
$491$	14.2048	+	24.6034i	0.641052	+	1.11033i	−0.344147	+	0.938916i	$0.611832\pi$
$492$			5.25275i			0.236812i
$493$	−0.0689420	−	0.119411i	−0.00310499	−	0.00537800i
$494$	15.1528	+	19.7807i	0.681757	+	0.889975i
$495$	0.920330	−	1.59406i	0.0413657	−	0.0716476i
$496$	−4.92140	+	2.84137i	−0.220977	+	0.127581i
$497$	−6.88625	−	21.9255i	−0.308890	−	0.983495i
$498$	4.42719	−	7.66812i	0.198387	−	0.343617i
$499$	−3.33919	−	1.92788i	−0.149482	−	0.0863038i	0.423393	−	0.905946i	$-0.360839\pi$
$499$	−3.33919	−	1.92788i	−0.149482	−	0.0863038i	−0.572876	+	0.819642i	$0.694172\pi$
$500$			6.79311i			0.303797i
$501$			7.31771i			0.326931i
$502$	−13.0952	−	7.56052i	−0.584467	−	0.337442i
$503$	16.3872	−	28.3835i	0.730670	−	1.26556i	−0.225927	−	0.974144i	$-0.572541\pi$
$503$	16.3872	−	28.3835i	0.730670	−	1.26556i	0.956597	−	0.291413i	$-0.0941254\pi$
$504$	2.58240	+	0.575523i	0.115029	+	0.0256358i
$505$	−7.18704	+	4.14944i	−0.319819	+	0.184648i
$506$	−12.0806	+	20.9242i	−0.537048	+	0.930195i
$507$	3.38499	−	12.5516i	0.150333	−	0.557435i
$508$	11.0533	+	19.1448i	0.490410	+	0.849415i
$509$			35.6838i			1.58166i	0.612037	+	0.790829i	$0.290350\pi$
$509$			35.6838i			1.58166i	−0.612037	+	0.790829i	$0.709650\pi$
$510$	0.00889156	+	0.0154006i	0.000393725	+	0.000681951i
$511$	41.0214	+	9.14219i	1.81468	+	0.404427i
$512$			1.00000i			0.0441942i
$513$	−5.98499	+	3.45544i	−0.264244	+	0.152561i
$514$			5.65409i			0.249391i
$515$	−9.79381	+	5.65446i	−0.431567	+	0.249165i
$516$	−6.37475	−	11.0414i	−0.280633	−	0.486070i
$517$	6.41250	+	11.1068i	0.282022	+	0.488476i
$518$	−8.12807	−	7.46469i	−0.357127	−	0.327979i
$519$	−6.48507			−0.284663
$520$	0.989886	−	2.38433i	0.0434094	−	0.104560i
$521$	−0.555626	−	0.962372i	−0.0243424	−	0.0421623i	0.853598	−	0.520933i	$-0.174416\pi$
$521$	−0.555626	−	0.962372i	−0.0243424	−	0.0421623i	−0.877940	+	0.478771i	$0.841083\pi$
$522$	−4.80797	−	2.77589i	−0.210439	−	0.121497i
$523$	0.736145			0.0321894			0.0160947	−	0.999870i	$-0.494877\pi$
$523$	0.736145			0.0321894			0.0160947	+	0.999870i	$0.494877\pi$
$524$	−5.57371	+	9.65394i	−0.243488	+	0.421734i
$525$	8.74425	+	8.03057i	0.381630	+	0.350483i
$526$	12.5991	+	7.27412i	0.549349	+	0.317167i
$527$	−0.122228	+	0.0705684i	−0.00532434	+	0.00307401i
$528$	2.22627	−	1.28534i	0.0968861	−	0.0559372i
$529$	65.3367			2.84073
$530$	6.76585			0.293890
$531$	1.95045	−	1.12610i	0.0846425	−	0.0488684i
$532$	17.8466	+	3.97737i	0.773749	+	0.172441i
$533$	15.0347	−	11.5172i	0.651225	−	0.498865i
$534$	−7.41908	+	12.8502i	−0.321055	+	0.556083i
$535$	−0.299310	−	0.172807i	−0.0129403	−	0.00747109i
$536$	0.938052	−	1.62475i	0.0405177	−	0.0701787i
$537$	11.6114	+	20.1116i	0.501070	+	0.867878i
$538$			3.46062i			0.149198i
$539$	−7.64124	+	16.2918i	−0.329131	+	0.701737i
$540$	0.620092	+	0.358010i	0.0266845	+	0.0154063i
$541$	−3.31356	−	1.91309i	−0.142461	−	0.0822500i	0.427075	−	0.904216i	$-0.359544\pi$
$541$	−3.31356	−	1.91309i	−0.142461	−	0.0822500i	−0.569536	+	0.821966i	$0.692877\pi$
$542$	−11.5709			−0.497011
$543$	−2.80955	+	4.86628i	−0.120569	+	0.208832i
$544$			0.0248360i			0.00106484i
$545$	2.29454			0.0982871
$546$	−4.01488	−	8.65337i	−0.171821	−	0.370330i
$547$	−5.24598			−0.224302			−0.112151	−	0.993691i	$-0.535774\pi$
$547$	−5.24598			−0.224302			−0.112151	+	0.993691i	$0.535774\pi$
$548$			16.7971i			0.717534i
$549$	0.326003	−	0.564654i	0.0139135	−	0.0240988i
$550$	11.5354			0.491873
$551$	−33.2273	−	19.1838i	−1.41553	−	0.817257i
$552$	−8.13957	−	4.69938i	−0.346443	−	0.200019i
$553$	0.980507	−	0.307952i	0.0416954	−	0.0130955i
$554$			4.63996i			0.197133i
$555$	−1.49330	−	2.58647i	−0.0633871	−	0.109790i
$556$	9.50946	−	16.4709i	0.403291	−	0.698521i
$557$	−16.8302	−	9.71694i	−0.713120	−	0.411720i	0.0990953	−	0.995078i	$-0.468405\pi$
$557$	−16.8302	−	9.71694i	−0.713120	−	0.411720i	−0.812215	+	0.583358i	$0.801738\pi$
$558$	−2.84137	+	4.92140i	−0.120285	+	0.208339i
$559$	−17.6260	+	42.4555i	−0.745499	+	1.79568i
$560$	−0.567647	−	1.80737i	−0.0239875	−	0.0763752i
$561$	0.0552918	−	0.0319228i	0.00233442	−	0.00134778i
$562$	−20.9621			−0.884231
$563$	4.12679			0.173923			0.0869616	−	0.996212i	$-0.472284\pi$
$563$	4.12679			0.173923			0.0869616	+	0.996212i	$0.472284\pi$
$564$	−4.32056	+	2.49448i	−0.181929	+	0.105036i
$565$	−5.19366	+	2.99856i	−0.218499	+	0.126150i
$566$	4.08795	+	2.36018i	0.171829	+	0.0992057i
$567$	2.52418	−	0.792781i	0.106006	−	0.0332937i
$568$	4.34310	−	7.52246i	0.182232	−	0.315636i
$569$	−25.0534			−1.05029			−0.525147	−	0.851011i	$-0.675990\pi$
$569$	−25.0534			−1.05029			−0.525147	+	0.851011i	$0.675990\pi$
$570$	4.28538	+	2.47416i	0.179495	+	0.103631i
$571$	−15.9460	−	27.6192i	−0.667318	−	1.15583i	−0.978651	−	0.205528i	$-0.934109\pi$
$571$	−15.9460	−	27.6192i	−0.667318	−	1.15583i	0.311333	−	0.950301i	$-0.399224\pi$
$572$	−8.56030	−	3.55392i	−0.357924	−	0.148597i
$573$	23.8945			0.998206
$574$	3.02308	−	13.5647i	0.126181	−	0.566179i
$575$	−21.0876	−	36.5248i	−0.879414	−	1.52319i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−19.6398	+	11.3390i	−0.817614	+	0.472050i	−0.849593	−	0.527439i	$-0.823152\pi$
$577$	−19.6398	+	11.3390i	−0.817614	+	0.472050i	0.0319788	+	0.999489i	$0.489819\pi$
$578$		−	16.9994i		−	0.707081i
$579$	18.1841	−	10.4986i	0.755707	−	0.436308i
$580$			3.97518i			0.165060i
$581$	−15.8460	+	17.2542i	−0.657401	+	0.715824i
$582$	−1.03174	−	1.78702i	−0.0427669	−	0.0740744i
$583$		−	24.2910i		−	1.00603i
$584$	7.94250	+	13.7568i	0.328663	+	0.569261i
$585$	−0.334899	−	2.55983i	−0.0138464	−	0.105836i
$586$	−16.7744	+	29.0541i	−0.692943	+	1.20021i
$587$	−2.99085	+	1.72677i	−0.123446	+	0.0712714i	−0.560451	−	0.828187i	$-0.689372\pi$
$587$	−2.99085	+	1.72677i	−0.123446	+	0.0712714i	0.437006	+	0.899459i	$0.356039\pi$
$588$	−6.33755	−	2.97246i	−0.261356	−	0.122582i
$589$	−19.6364	+	34.0112i	−0.809102	+	1.40141i
$590$	−1.39657	−	0.806308i	−0.0574957	−	0.0331952i
$591$			5.18443i			0.213259i
$592$		−	4.17111i		−	0.171432i
$593$	−12.0235	−	6.94179i	−0.493747	−	0.285065i	0.232380	−	0.972625i	$-0.425349\pi$
$593$	−12.0235	−	6.94179i	−0.493747	−	0.285065i	−0.726128	+	0.687560i	$0.758682\pi$
$594$	1.28534	−	2.22627i	0.0527381	−	0.0913451i
$595$	−0.0140981	−	0.0448878i	−0.000577966	−	0.00184022i
$596$	−10.6121	+	6.12689i	−0.434688	+	0.250967i
$597$	−8.07086	+	13.9791i	−0.330318	+	0.572128i
$598$	4.39602	+	33.6014i	0.179767	+	1.37406i
$599$	−1.37576	−	2.38289i	−0.0562122	−	0.0973624i	0.836550	−	0.547891i	$-0.184569\pi$
$599$	−1.37576	−	2.38289i	−0.0562122	−	0.0973624i	−0.892762	+	0.450528i	$0.851236\pi$
$600$			4.48731i			0.183194i
$601$	17.0005	+	29.4457i	0.693464	+	1.20112i	0.970696	+	0.240312i	$0.0772499\pi$
$601$	17.0005	+	29.4457i	0.693464	+	1.20112i	−0.277231	+	0.960803i	$0.589417\pi$
$602$	10.1076	+	32.1821i	0.411953	+	1.31164i
$603$		−	1.87610i		−	0.0764009i
$604$	−11.5364	+	6.66053i	−0.469409	+	0.271013i
$605$		−	3.14448i		−	0.127841i
$606$	−10.0375	+	5.79514i	−0.407745	+	0.235412i
$607$	−15.4583	−	26.7746i	−0.627434	−	1.08675i	−0.988065	−	0.154039i	$-0.950772\pi$
$607$	−15.4583	−	26.7746i	−0.627434	−	1.08675i	0.360630	−	0.932709i	$-0.382562\pi$
$608$	3.45544	+	5.98499i	0.140137	+	0.242724i
$609$	10.8185	+	9.93554i	0.438388	+	0.402608i
$610$	−0.466850			−0.0189022
$611$	16.6131	+	6.89715i	0.672094	+	0.279029i
$612$	0.0124180	+	0.0215086i	0.000501969	+	0.000869435i
$613$	−5.65344	−	3.26401i	−0.228340	−	0.131832i	0.381466	−	0.924383i	$-0.375419\pi$
$613$	−5.65344	−	3.26401i	−0.228340	−	0.131832i	−0.609806	+	0.792551i	$0.708753\pi$
$614$	5.49245			0.221657
$615$	1.88054	−	3.25719i	0.0758306	−	0.131342i
$616$	−6.48886	+	2.03798i	−0.261444	+	0.0821127i
$617$	−10.8491	−	6.26373i	−0.436768	−	0.252168i	0.265458	−	0.964123i	$-0.414477\pi$
$617$	−10.8491	−	6.26373i	−0.436768	−	0.252168i	−0.702226	+	0.711954i	$0.747810\pi$
$618$	−13.6781	+	7.89706i	−0.550214	+	0.317666i
$619$	−3.04630	+	1.75878i	−0.122441	+	0.0706914i	−0.559970	−	0.828513i	$-0.689187\pi$
$619$	−3.04630	+	1.75878i	−0.122441	+	0.0706914i	0.437529	+	0.899205i	$0.355854\pi$
$620$	4.06896			0.163413
$621$	−9.39876			−0.377159
$622$	−12.9075	+	7.45213i	−0.517543	+	0.298803i
$623$	26.5546	−	28.9145i	1.06389	−	1.15844i
$624$	1.38248	−	3.32998i	0.0553436	−	0.133306i
$625$	−8.78628	+	15.2183i	−0.351451	+	0.608731i
$626$	3.12069	+	1.80173i	0.124728	+	0.0720116i
$627$	8.88282	−	15.3855i	0.354746	−	0.614438i
$628$	3.49931	+	6.06098i	0.139638	+	0.241859i
$629$		−	0.103594i		−	0.00413056i
$630$	−1.39528	−	1.28140i	−0.0555893	−	0.0510523i
$631$	−17.1805	−	9.91915i	−0.683944	−	0.394875i	0.117395	−	0.993085i	$-0.462545\pi$
$631$	−17.1805	−	9.91915i	−0.683944	−	0.394875i	−0.801339	+	0.598210i	$0.795879\pi$
$632$	0.336404	+	0.194223i	0.0133814	+	0.00772577i
$633$	15.3747			0.611090
$634$	−2.04573	+	3.54331i	−0.0812463	+	0.140723i
$635$		−	15.8288i		−	0.628145i
$636$	9.44924			0.374687
$637$	5.38779	+	24.6571i	0.213472	+	0.976949i
$638$	14.2718			0.565027
$639$		−	8.68619i		−	0.343621i
$640$	0.358010	−	0.620092i	0.0141516	−	0.0245113i
$641$	3.15393			0.124573			0.0622865	−	0.998058i	$-0.480161\pi$
$641$	3.15393			0.124573			0.0622865	+	0.998058i	$0.480161\pi$
$642$	−0.418019	−	0.241343i	−0.0164979	−	0.00952506i
$643$	29.0975	+	16.7994i	1.14749	+	0.662505i	0.948275	−	0.317451i	$-0.102827\pi$
$643$	29.0975	+	16.7994i	1.14749	+	0.662505i	0.199217	+	0.979955i	$0.436160\pi$
$644$	18.3150	+	16.8202i	0.721712	+	0.662808i
$645$			9.12891i			0.359450i
$646$	0.0858194	+	0.148644i	0.00337652	+	0.00584830i
$647$	11.1506	−	19.3134i	0.438375	−	0.759288i	−0.559189	−	0.829040i	$-0.688888\pi$
$647$	11.1506	−	19.3134i	0.438375	−	0.759288i	0.997564	+	0.0697523i	$0.0222209\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−2.89483	+	5.01399i	−0.113632	+	0.196816i
$650$	12.8438	−	9.83890i	0.503776	−	0.385913i
$651$	10.1699	−	11.0737i	0.398591	−	0.434014i
$652$	−8.82738	+	5.09649i	−0.345707	+	0.199594i
$653$	−7.48348			−0.292851			−0.146426	−	0.989222i	$-0.546777\pi$
$653$	−7.48348			−0.292851			−0.146426	+	0.989222i	$0.546777\pi$
$654$	3.20457			0.125308
$655$	6.91242	−	3.99089i	0.270091	−	0.155937i
$656$	4.54901	−	2.62637i	0.177609	−	0.102543i
$657$	13.7568	+	7.94250i	0.536705	+	0.309867i
$658$	12.5930	−	3.95515i	0.490928	−	0.154188i
$659$	4.51922	−	7.82751i	0.176044	−	0.304917i	−0.764478	−	0.644650i	$-0.777003\pi$
$659$	4.51922	−	7.82751i	0.176044	−	0.304917i	0.940522	+	0.339733i	$0.110337\pi$
$660$	−1.84066			−0.0716476
$661$	−10.0667	−	5.81199i	−0.391548	−	0.226060i	0.291283	−	0.956637i	$-0.405918\pi$
$661$	−10.0667	−	5.81199i	−0.391548	−	0.226060i	−0.682831	+	0.730577i	$0.739251\pi$
$662$	−9.70350	−	16.8069i	−0.377137	−	0.653221i
$663$	0.0343354	−	0.0827034i	0.00133348	−	0.00321194i
$664$	−8.85439			−0.343617
$665$	−9.64261	−	8.85561i	−0.373924	−	0.343406i
$666$	−2.08556	−	3.61229i	−0.0808136	−	0.139973i
$667$	−26.0899	−	45.1890i	−1.01020	−	1.74973i
$668$	6.33732	−	3.65885i	0.245198	−	0.141565i
$669$		−	12.8154i		−	0.495471i
$670$	−1.16336	+	0.671665i	−0.0449444	+	0.0259487i
$671$			1.67610i			0.0647051i
$672$	−0.792781	−	2.52418i	−0.0305822	−	0.0973725i
$673$	5.44014	+	9.42260i	0.209702	+	0.363214i	0.951621	−	0.307275i	$-0.0994173\pi$
$673$	5.44014	+	9.42260i	0.209702	+	0.363214i	−0.741919	+	0.670490i	$0.766084\pi$
$674$		−	23.0545i		−	0.888025i
$675$	2.24366	+	3.88613i	0.0863584	+	0.149577i
$676$	−12.5625	+	3.34430i	−0.483172	+	0.128627i
$677$	8.71040	−	15.0869i	0.334768	−	0.579835i	−0.648672	−	0.761068i	$-0.724675\pi$
$677$	8.71040	−	15.0869i	0.334768	−	0.579835i	0.983440	+	0.181233i	$0.0580087\pi$
$678$	−7.25350	+	4.18781i	−0.278569	+	0.160832i
$679$	1.63588	+	5.20859i	0.0627794	+	0.199887i
$680$	0.00889156	−	0.0154006i	0.000340976	−	0.000590587i
$681$	17.4536	+	10.0768i	0.668823	+	0.386145i
$682$		−	14.6085i		−	0.559389i
$683$			35.6666i			1.36474i	0.731005	+	0.682372i	$0.239051\pi$
$683$			35.6666i			1.36474i	−0.731005	+	0.682372i	$0.760949\pi$
$684$	5.98499	+	3.45544i	0.228842	+	0.132122i
$685$	6.01352	−	10.4157i	0.229765	−	0.397964i
$686$	14.6553	+	11.3235i	0.559543	+	0.432332i
$687$	−8.89145	+	5.13348i	−0.339230	+	0.195855i
$688$	−6.37475	+	11.0414i	−0.243035	+	0.420949i
$689$	−20.7184	−	27.0461i	−0.789309	−	1.03038i
$690$	3.36485	+	5.82810i	0.128098	+	0.221872i
$691$			3.03038i			0.115281i	0.998337	+	0.0576406i	$0.0183578\pi$
$691$			3.03038i			0.115281i	−0.998337	+	0.0576406i	$0.981642\pi$
$692$	3.24254	+	5.61624i	0.123263	+	0.213497i
$693$	−4.60053	+	5.00938i	−0.174760	+	0.190291i
$694$		−	4.60157i		−	0.174673i
$695$	−11.7935	+	6.80897i	−0.447352	+	0.258279i
$696$			5.55177i			0.210439i
$697$	0.112979	−	0.0652287i	0.00427940	−	0.00247071i
$698$	−1.86602	−	3.23204i	−0.0706299	−	0.122335i
$699$	1.56117	+	2.70402i	0.0590488	+	0.102276i
$700$	2.58255	−	11.5880i	0.0976114	−	0.437986i
$701$	−27.7372			−1.04762			−0.523810	−	0.851835i	$-0.675490\pi$
$701$	−27.7372			−1.04762			−0.523810	+	0.851835i	$0.675490\pi$
$702$	−0.467723	−	3.57509i	−0.0176531	−	0.134933i
$703$	−14.4130	−	24.9641i	−0.543597	−	0.941538i
$704$	−2.22627	−	1.28534i	−0.0839058	−	0.0484431i
$705$	3.57220			0.134537
$706$	13.1765	−	22.8223i	0.495903	−	0.858928i
$707$	29.2560	−	9.18855i	1.10029	−	0.345571i
$708$	−1.95045	−	1.12610i	−0.0733026	−	0.0423213i
$709$	14.1175	−	8.15072i	0.530193	−	0.306107i	−0.210902	−	0.977507i	$-0.567640\pi$
$709$	14.1175	−	8.15072i	0.530193	−	0.306107i	0.741095	+	0.671400i	$0.234307\pi$
$710$	−5.38624	+	3.10975i	−0.202142	+	0.116707i
$711$	0.388445			0.0145678
$712$	14.8382			0.556083
$713$	−46.2551	+	26.7054i	−1.73227	+	1.00012i
$714$	−0.0196895	−	0.0626907i	−0.000736862	−	0.00234614i
$715$	4.03583	+	5.26843i	0.150932	+	0.197028i
$716$	11.6114	−	20.1116i	0.433939	−	0.751605i
$717$	−10.5936	−	6.11624i	−0.395627	−	0.228415i
$718$	−4.10824	+	7.11568i	−0.153318	+	0.265555i
$719$	−3.44776	−	5.97169i	−0.128580	−	0.222707i	0.794547	−	0.607203i	$-0.207708\pi$
$719$	−3.44776	−	5.97169i	−0.128580	−	0.222707i	−0.923127	+	0.384496i	$0.874375\pi$
$720$		−	0.716021i		−	0.0266845i
$721$	39.8672	−	12.5213i	1.48473	−	0.466316i
$722$	24.9071	+	14.3801i	0.926945	+	0.535172i
$723$	−1.63586	−	0.944462i	−0.0608382	−	0.0351249i
$724$	5.61910			0.208832
$725$	−12.4563	+	21.5749i	−0.462614	+	0.801271i
$726$		−	4.39161i		−	0.162988i
$727$	−26.6965			−0.990119			−0.495059	−	0.868859i	$-0.664854\pi$
$727$	−26.6965			−0.990119			−0.495059	+	0.868859i	$0.664854\pi$
$728$	−5.48660	+	7.80367i	−0.203347	+	0.289223i
$729$	1.00000			0.0370370
$730$		−	11.3740i		−	0.420970i
$731$	−0.158324	+	0.274225i	−0.00585581	+	0.0101426i
$732$	−0.652006			−0.0240988
$733$	27.0290	+	15.6052i	0.998337	+	0.576390i	0.907756	−	0.419499i	$-0.137794\pi$
$733$	27.0290	+	15.6052i	0.998337	+	0.576390i	0.0905813	+	0.995889i	$0.471128\pi$
$734$	−0.371350	−	0.214399i	−0.0137068	−	0.00791360i
$735$	2.86569	+	4.11210i	0.105703	+	0.151677i
$736$			9.39876i			0.346443i
$737$	2.41143	+	4.17672i	0.0888262	+	0.153852i
$738$	2.62637	−	4.54901i	0.0966782	−	0.167451i
$739$	18.8294	+	10.8712i	0.692651	+	0.399902i	0.804604	−	0.593811i	$-0.202377\pi$
$739$	18.8294	+	10.8712i	0.692651	+	0.399902i	−0.111953	+	0.993713i	$0.535711\pi$
$740$	−1.49330	+	2.58647i	−0.0548948	+	0.0950806i
$741$	−3.23238	−	24.7070i	−0.118744	−	0.907633i
$742$	−24.4017	−	5.43826i	−0.895814	−	0.199645i
$743$	8.60858	−	4.97016i	0.315818	−	0.182338i	−0.333709	−	0.942676i	$-0.608300\pi$
$743$	8.60858	−	4.97016i	0.315818	−	0.182338i	0.649527	+	0.760339i	$0.274967\pi$
$744$	5.68274			0.208339
$745$	8.77396			0.321453
$746$	−1.74510	+	1.00753i	−0.0638927	+	0.0368885i
$747$	−7.66812	+	4.42719i	−0.280562	+	0.161983i
$748$	−0.0552918	−	0.0319228i	−0.00202167	−	0.00116721i
$749$	0.940592	+	0.863824i	0.0343685	+	0.0315634i
$750$	3.39656	−	5.88301i	0.124025	−	0.214817i
$751$	−8.54914			−0.311963			−0.155981	−	0.987760i	$-0.549854\pi$
$751$	−8.54914			−0.311963			−0.155981	+	0.987760i	$0.549854\pi$
$752$	4.32056	+	2.49448i	0.157555	+	0.0909643i
$753$	7.56052	+	13.0952i	0.275521	+	0.477216i
$754$	15.8906	−	12.1728i	0.578701	−	0.443308i
$755$	9.53816			0.347129
$756$	−1.94866	−	1.78962i	−0.0708721	−	0.0650877i
$757$	3.50974	+	6.07905i	0.127564	+	0.220947i	0.922732	−	0.385442i	$-0.125951\pi$
$757$	3.50974	+	6.07905i	0.127564	+	0.220947i	−0.795168	+	0.606389i	$0.792618\pi$
$758$	8.70779	+	15.0823i	0.316281	+	0.547815i
$759$	20.9242	−	12.0806i	0.759501	−	0.438498i
$760$		−	4.94833i		−	0.179495i
$761$	14.0064	−	8.08661i	0.507732	−	0.293139i	−0.224169	−	0.974550i	$-0.571967\pi$
$761$	14.0064	−	8.08661i	0.507732	−	0.293139i	0.731901	+	0.681411i	$0.238633\pi$
$762$		−	22.1066i		−	0.800836i
$763$	−8.27546	−	1.84430i	−0.299592	−	0.0667682i
$764$	−11.9472	−	20.6932i	−0.432236	−	0.748655i
$765$		−	0.0177831i		−	0.000642950i
$766$	0.164165	+	0.284342i	0.00593153	+	0.0102737i
$767$	1.05340	+	8.05178i	0.0380361	+	0.290733i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	22.6397	−	13.0710i	0.816409	−	0.471354i	−0.0327678	−	0.999463i	$-0.510432\pi$
$769$	22.6397	−	13.0710i	0.816409	−	0.471354i	0.849176	+	0.528109i	$0.177099\pi$
$770$	4.75331	+	1.05934i	0.171297	+	0.0381760i
$771$	2.82704	−	4.89658i	0.101813	−	0.176346i
$772$	−18.1841	−	10.4986i	−0.654461	−	0.377853i
$773$			3.49999i			0.125886i	0.998017	+	0.0629429i	$0.0200486\pi$
$773$			3.49999i			0.125886i	−0.998017	+	0.0629429i	$0.979951\pi$
$774$			12.7495i			0.458271i
$775$	22.0839	+	12.7501i	0.793276	+	0.457998i
$776$	−1.03174	+	1.78702i	−0.0370372	+	0.0641503i
$777$	3.30677	+	10.5286i	0.118630	+	0.377713i
$778$	7.45575	−	4.30458i	0.267302	−	0.154327i
$779$	18.1505	−	31.4377i	0.650311	−	1.12637i
$780$	−2.04943	+	1.56995i	−0.0733814	+	0.0562132i
$781$	11.1647	+	19.3378i	0.399505	+	0.691962i
$782$			0.233428i			0.00834737i
$783$	2.77589	+	4.80797i	0.0992020	+	0.171823i
$784$	0.594548	+	6.97471i	0.0212338	+	0.249097i
$785$		−	5.01115i		−	0.178856i
$786$	9.65394	−	5.57371i	0.344345	−	0.198807i
$787$		−	12.3184i		−	0.439102i	−0.975601	−	0.219551i	$-0.929541\pi$
$787$		−	12.3184i		−	0.439102i	0.975601	−	0.219551i	$-0.0704593\pi$
$788$	4.48984	−	2.59221i	0.159944	−	0.0923438i
$789$	−7.27412	−	12.5991i	−0.258966	−	0.448541i
$790$	−0.139067	−	0.240872i	−0.00494780	−	0.00856984i
$791$	21.1416	−	6.64003i	0.751709	−	0.236092i
$792$	−2.57068			−0.0913451
$793$	1.42959	+	1.86621i	0.0507662	+	0.0662709i
$794$	−0.864161	−	1.49677i	−0.0306679	−	0.0531184i
$795$	−5.85940	−	3.38293i	−0.207811	−	0.119980i
$796$	16.1417			0.572128
$797$	18.9472	−	32.8176i	0.671145	−	1.16246i	−0.306435	−	0.951892i	$-0.599136\pi$
$797$	18.9472	−	32.8176i	0.671145	−	1.16246i	0.977580	−	0.210566i	$-0.0675306\pi$
$798$	−13.4669	−	12.3678i	−0.476725	−	0.437816i
$799$	0.107306	+	0.0619530i	0.00379620	+	0.00219174i
$800$	3.88613	−	2.24366i	0.137395	−	0.0793253i
$801$	12.8502	−	7.41908i	0.454040	−	0.262140i
$802$	−13.5664			−0.479046
$803$	−40.8353			−1.44104
$804$	−1.62475	+	0.938052i	−0.0573007	+	0.0330826i
$805$	−5.33518	−	16.9870i	−0.188040	−	0.598713i
$806$	−12.4600	−	16.2654i	−0.438885	−	0.572926i
$807$	1.73031	−	2.99698i	0.0609098	−	0.105499i
$808$	10.0375	+	5.79514i	0.353117	+	0.203872i
$809$	−10.5325	+	18.2428i	−0.370301	+	0.641381i	−0.989612	−	0.143765i	$-0.954079\pi$
$809$	−10.5325	+	18.2428i	−0.370301	+	0.641381i	0.619310	+	0.785146i	$0.287412\pi$
$810$	−0.358010	−	0.620092i	−0.0125792	−	0.0217878i
$811$			46.4549i			1.63125i	0.578578	+	0.815627i	$0.303608\pi$
$811$			46.4549i			1.63125i	−0.578578	+	0.815627i	$0.696392\pi$
$812$	3.19517	−	14.3369i	0.112129	−	0.503126i
$813$	10.0207	+	5.78543i	0.351440	+	0.202904i
$814$	9.28603	+	5.36129i	0.325475	+	0.187913i
$815$	7.29838			0.255651
$816$	0.0124180	−	0.0215086i	0.000434718	−	0.000752953i
$817$			88.1102i			3.08259i
$818$	−1.16202			−0.0406292
$819$	−0.849699	+	9.50147i	−0.0296909	+	0.332008i
$820$	−3.76108			−0.131342
$821$			6.53079i			0.227926i	0.993485	+	0.113963i	$0.0363545\pi$
$821$			6.53079i			0.227926i	−0.993485	+	0.113963i	$0.963645\pi$
$822$	8.39853	−	14.5467i	0.292932	−	0.507373i
$823$	−7.42070			−0.258669			−0.129335	−	0.991601i	$-0.541284\pi$
$823$	−7.42070			−0.258669			−0.129335	+	0.991601i	$0.541284\pi$
$824$	13.6781	+	7.89706i	0.476499	+	0.275107i
$825$	−9.98999	−	5.76772i	−0.347807	−	0.200806i
$826$	4.38875	+	4.03056i	0.152704	+	0.140241i
$827$		−	38.3288i		−	1.33282i	−0.745584	−	0.666411i	$-0.767830\pi$
$827$		−	38.3288i		−	1.33282i	0.745584	−	0.666411i	$-0.232170\pi$
$828$	4.69938	+	8.13957i	0.163315	+	0.282870i
$829$	5.46502	−	9.46570i	0.189808	−	0.328757i	−0.755378	−	0.655289i	$-0.772547\pi$
$829$	5.46502	−	9.46570i	0.189808	−	0.328757i	0.945186	+	0.326532i	$0.105880\pi$
$830$	5.49053	+	3.16996i	0.190579	+	0.110031i
$831$	2.31998	−	4.01832i	0.0804792	−	0.139394i
$832$	−3.57509	+	0.467723i	−0.123944	+	0.0162154i
$833$	0.0147662	+	0.173224i	0.000511619	+	0.00600186i
$834$	−16.4709	+	9.50946i	−0.570340	+	0.329286i
$835$	−5.23963			−0.181325
$836$	−17.7656			−0.614438
$837$	4.92140	−	2.84137i	0.170108	−	0.0982121i
$838$	−28.8657	+	16.6656i	−0.997150	+	0.575705i
$839$	−1.82881	−	1.05586i	−0.0631375	−	0.0364525i	0.468099	−	0.883676i	$-0.344939\pi$
$839$	−1.82881	−	1.05586i	−0.0631375	−	0.0364525i	−0.531236	+	0.847224i	$0.678272\pi$
$840$	−0.412087	+	1.84905i	−0.0142183	+	0.0637983i
$841$	−0.911078	+	1.57803i	−0.0314165	+	0.0544150i
$842$	17.4686			0.602007
$843$	18.1537	+	10.4810i	0.625246	+	0.360986i
$844$	−7.68735	−	13.3149i	−0.264610	−	0.458317i
$845$	8.98718	+	2.42372i	0.309168	+	0.0833785i
$846$	4.98896			0.171524
$847$	−2.52747	+	11.3409i	−0.0868450	+	0.389677i
$848$	−4.72462	−	8.18328i	−0.162244	−	0.281015i
$849$	−2.36018	−	4.08795i	−0.0810011	−	0.140298i
$850$	0.0965161	−	0.0557236i	0.00331047	−	0.00191130i
$851$		−	39.2033i		−	1.34387i
$852$	−7.52246	+	4.34310i	−0.257715	+	0.148792i
$853$		−	1.58650i		−	0.0543207i	−0.999631	−	0.0271604i	$-0.991354\pi$
$853$		−	1.58650i		−	0.0543207i	0.999631	−	0.0271604i	$-0.00864647\pi$
$854$	1.68374	+	0.375245i	0.0576164	+	0.0128406i
$855$	−2.47416	−	4.28538i	−0.0846146	−	0.146557i
$856$			0.482687i			0.0164979i
$857$	−15.0692	−	26.1007i	−0.514756	−	0.891583i	−0.999853	−	0.0171229i	$-0.994549\pi$
$857$	−15.0692	−	26.1007i	−0.514756	−	0.891583i	0.485098	−	0.874460i	$-0.338784\pi$
$858$	5.63648	+	7.35793i	0.192426	+	0.251196i
$859$	7.96343	−	13.7931i	0.271709	−	0.470614i	−0.697591	−	0.716497i	$-0.745745\pi$
$859$	7.96343	−	13.7931i	0.271709	−	0.470614i	0.969300	+	0.245883i	$0.0790779\pi$
$860$	7.90587	−	4.56445i	0.269588	−	0.155647i
$861$	−9.40040	+	10.2358i	−0.320365	+	0.348836i
$862$	11.4433	−	19.8204i	0.389761	−	0.675085i
$863$	−19.4948	−	11.2553i	−0.663609	−	0.383135i	0.130041	−	0.991509i	$-0.458489\pi$
$863$	−19.4948	−	11.2553i	−0.663609	−	0.383135i	−0.793651	+	0.608373i	$0.791822\pi$
$864$		−	1.00000i		−	0.0340207i
$865$		−	4.64345i		−	0.157882i
$866$	−17.0022	−	9.81620i	−0.577757	−	0.333568i
$867$	−8.49969	+	14.7219i	−0.288665	+	0.499982i
$868$	−14.6751	−	3.27055i	−0.498105	−	0.111010i
$869$	−0.864786	+	0.499284i	−0.0293359	+	0.0169371i
$870$	1.98759	−	3.44261i	0.0673856	−	0.116715i
$871$	6.24738	+	2.59368i	0.211685	+	0.0878836i
$872$	−1.60228	−	2.77524i	−0.0542601	−	0.0939813i
$873$			2.06347i			0.0698380i
$874$	32.4768	+	56.2515i	1.09855	+	1.90274i
$875$	−12.1571	+	13.2375i	−0.410984	+	0.447508i
$876$		−	15.8850i		−	0.536705i
$877$	−21.6183	+	12.4813i	−0.729999	+	0.421465i	−0.818422	−	0.574618i	$-0.805151\pi$
$877$	−21.6183	+	12.4813i	−0.729999	+	0.421465i	0.0884229	+	0.996083i	$0.471817\pi$
$878$		−	25.5976i		−	0.863878i
$879$	29.0541	−	16.7744i	0.979970	−	0.565786i
$880$	0.920330	+	1.59406i	0.0310243	+	0.0537357i
$881$	21.0029	+	36.3780i	0.707605	+	1.22561i	0.965743	+	0.259500i	$0.0835576\pi$
$881$	21.0029	+	36.3780i	0.707605	+	1.22561i	−0.258138	+	0.966108i	$0.583109\pi$
$882$	4.00225	+	5.74300i	0.134763	+	0.193377i
$883$	19.4571			0.654782			0.327391	−	0.944889i	$-0.393831\pi$
$883$	19.4571			0.654782			0.327391	+	0.944889i	$0.393831\pi$
$884$	−0.0887910	+	0.0116164i	−0.00298636	+	0.000390701i
$885$	0.806308	+	1.39657i	0.0271037	+	0.0469450i
$886$	18.9721	+	10.9535i	0.637379	+	0.367991i
$887$	48.0139			1.61215			0.806075	−	0.591813i	$-0.201588\pi$
$887$	48.0139			1.61215			0.806075	+	0.591813i	$0.201588\pi$
$888$	−2.08556	+	3.61229i	−0.0699866	+	0.121220i
$889$	−12.7228	+	57.0879i	−0.426711	+	1.91467i
$890$	−9.20102	−	5.31221i	−0.308419	−	0.178066i
$891$	−2.22627	+	1.28534i	−0.0745830	+	0.0430605i
$892$	−11.0984	+	6.40769i	−0.371603	+	0.214545i
$893$	34.4781			1.15376
$894$	12.2538			0.409828
$895$	−14.4003	+	8.31401i	−0.481349	+	0.277907i
$896$	−1.78962	+	1.94866i	−0.0597869	+	0.0651001i
$897$	12.9936	−	31.2977i	0.433845	−	1.04500i
$898$	13.2807	−	23.0029i	0.443183	−	0.767616i
$899$	27.3225	+	15.7746i	0.911256	+	0.526114i
$900$	2.24366	−	3.88613i	0.0747886	−	0.129538i
$901$	−0.117341	−	0.203240i	−0.00390919	−	0.00677092i
$902$			13.5031i			0.449605i
$903$	7.33764	−	32.9243i	0.244181	−	1.09565i
$904$	7.25350	+	4.18781i	0.241248	+	0.139285i
$905$	−3.48436	−	2.01169i	−0.115824	−	0.0668710i
$906$	13.3211			0.442563
$907$	−16.4672	+	28.5220i	−0.546785	+	0.947059i	0.451707	+	0.892166i	$0.350815\pi$
$907$	−16.4672	+	28.5220i	−0.546785	+	0.947059i	−0.998492	+	0.0548929i	$0.982518\pi$
$908$		−	20.1537i		−	0.668823i
$909$	11.5903			0.384426
$910$	6.19599	−	2.87473i	0.205395	−	0.0952965i
$911$	36.6136			1.21306			0.606532	−	0.795059i	$-0.292560\pi$
$911$	36.6136			1.21306			0.606532	+	0.795059i	$0.292560\pi$
$912$		−	6.91088i		−	0.228842i
$913$	11.3809	−	19.7123i	0.376653	−	0.652381i
$914$	29.2901			0.968832
$915$	0.404304	+	0.233425i	0.0133659	+	0.00771679i
$916$	8.89145	+	5.13348i	0.293782	+	0.169615i
$917$	−28.1381	+	8.83745i	−0.929202	+	0.291838i
$918$		−	0.0248360i		−	0.000819712i
$919$	−9.96198	−	17.2547i	−0.328615	−	0.569179i	0.653622	−	0.756821i	$-0.273249\pi$
$919$	−9.96198	−	17.2547i	−0.328615	−	0.569179i	−0.982237	+	0.187643i	$0.939915\pi$
$920$	3.36485	−	5.82810i	0.110936	−	0.192147i
$921$	−4.75660	−	2.74622i	−0.156735	−	0.0904912i
$922$	1.12927	−	1.95594i	0.0371904	−	0.0644156i
$923$	28.9248	+	12.0085i	0.952072	+	0.395265i
$924$	6.63851	+	1.47949i	0.218391	+	0.0486715i
$925$	−16.2095	+	9.35854i	−0.532964	+	0.307707i
$926$	−2.33300			−0.0766673
$927$	15.7941			0.518747
$928$	4.80797	−	2.77589i	0.157829	−	0.0911229i
$929$	−3.88404	+	2.24245i	−0.127431	+	0.0735724i	−0.562361	−	0.826892i	$-0.690107\pi$
$929$	−3.88404	+	2.24245i	−0.127431	+	0.0735724i	0.434929	+	0.900465i	$0.356773\pi$
$930$	−3.52382	−	2.03448i	−0.115551	−	0.0667132i
$931$	27.6590	+	39.6891i	0.906488	+	1.30076i
$932$	1.56117	−	2.70402i	0.0511378	−	0.0885732i
$933$	14.9043			0.487944
$934$	−36.5814	−	21.1203i	−1.19698	−	0.691076i
$935$	0.0228573	+	0.0395901i	0.000747515	+	0.00129473i
$936$	−2.86225	+	2.19260i	−0.0935557	+	0.0716675i
$937$	−1.54887			−0.0505995			−0.0252997	−	0.999680i	$-0.508054\pi$
$937$	−1.54887			−0.0505995			−0.0252997	+	0.999680i	$0.508054\pi$
$938$	4.73563	−	1.48734i	0.154624	−	0.0485633i
$939$	−1.80173	−	3.12069i	−0.0587972	−	0.101840i
$940$	−1.78610	−	3.09361i	−0.0582561	−	0.100903i
$941$	−0.0220362	+	0.0127226i	−0.000718359	+	0.000414745i	−0.500359	−	0.865818i	$-0.666799\pi$
$941$	−0.0220362	+	0.0127226i	−0.000718359	+	0.000414745i	0.499641	+	0.866233i	$0.333465\pi$
$942$		−	6.99861i		−	0.228027i
$943$	42.7551	−	24.6847i	1.39230	−	0.803843i
$944$			2.25219i			0.0733026i
$945$	0.567647	+	1.80737i	0.0184656	+	0.0587936i
$946$	−16.3874	−	28.3839i	−0.532802	−	0.922840i
$947$		−	6.83433i		−	0.222086i	−0.993816	−	0.111043i	$-0.964581\pi$
$947$		−	6.83433i		−	0.222086i	0.993816	−	0.111043i	$-0.0354191\pi$
$948$	−0.194223	−	0.336404i	−0.00630806	−	0.0109259i
$949$	−45.4669	+	34.8295i	−1.47592	+	1.13061i
$950$	15.5056	−	26.8566i	0.503069	−	0.871342i
$951$	3.54331	−	2.04573i	0.114900	−	0.0663373i
$952$	−0.0444470	+	0.0483970i	−0.00144054	+	0.00156856i
$953$	23.9163	−	41.4242i	0.774724	−	1.34186i	−0.160225	−	0.987081i	$-0.551222\pi$
$953$	23.9163	−	41.4242i	0.774724	−	1.34186i	0.934949	−	0.354782i	$-0.115445\pi$
$954$	−8.18328	−	4.72462i	−0.264944	−	0.152965i
$955$			17.1089i			0.553632i
$956$			12.2325i			0.395627i
$957$	−12.3598	−	7.13591i	−0.399534	−	0.230671i
$958$	−9.65093	+	16.7159i	−0.311807	+	0.540066i
$959$	−30.0603	+	32.7317i	−0.970697	+	1.05696i
$960$	−0.620092	+	0.358010i	−0.0200134	+	0.0115547i
$961$	0.646777	−	1.12025i	0.0208638	−	0.0361371i
$962$	14.9121	−	1.95092i	0.480785	−	0.0629003i
$963$	0.241343	+	0.418019i	0.00777718	+	0.0134705i
$964$			1.88892i			0.0608382i
$965$	7.51722	+	13.0202i	0.241988	+	0.419136i
$966$	−7.45116	−	23.7242i	−0.239737	−	0.763313i
$967$		−	14.3721i		−	0.462175i	−0.972933	−	0.231088i	$-0.925772\pi$
$967$		−	14.3721i		−	0.462175i	0.972933	−	0.231088i	$-0.0742284\pi$
$968$	−3.80324	+	2.19580i	−0.122241	+	0.0705758i
$969$		−	0.171639i		−	0.00551383i
$970$	1.27954	−	0.738745i	0.0410837	−	0.0237197i
$971$	4.07935	+	7.06564i	0.130913	+	0.226747i	0.924029	−	0.382323i	$-0.124876\pi$
$971$	4.07935	+	7.06564i	0.130913	+	0.226747i	−0.793116	+	0.609071i	$0.791543\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	48.0072	−	15.0778i	1.53904	−	0.483373i
$974$	15.0028			0.480722
$975$	−16.0425	+	2.09882i	−0.513772	+	0.0672160i
$976$	0.326003	+	0.564654i	0.0104351	+	0.0180741i
$977$	−12.3071	−	7.10549i	−0.393738	−	0.227325i	0.290040	−	0.957014i	$-0.406331\pi$
$977$	−12.3071	−	7.10549i	−0.393738	−	0.227325i	−0.683779	+	0.729690i	$0.739665\pi$
$978$	10.1930			0.325936
$979$	−19.0721	+	33.0338i	−0.609546	+	1.05576i
$980$	2.12834	−	4.53781i	0.0679874	−	0.144955i
$981$	−2.77524	−	1.60228i	−0.0886065	−	0.0511570i
$982$	−24.6034	+	14.2048i	−0.785125	+	0.453292i
$983$	3.80375	−	2.19610i	0.121321	−	0.0700447i	−0.438111	−	0.898921i	$-0.644352\pi$
$983$	3.80375	−	2.19610i	0.121321	−	0.0700447i	0.559432	+	0.828876i	$0.311019\pi$
$984$	−5.25275			−0.167451
$985$	−3.71216			−0.118279
$986$	0.119411	−	0.0689420i	0.00380282	−	0.00219556i
$987$	−12.8835	−	2.87126i	−0.410085	−	0.0913933i
$988$	−19.7807	+	15.1528i	−0.629307	+	0.482075i
$989$	−59.9148	+	103.775i	−1.90518	+	3.29987i
$990$	1.59406	+	0.920330i	0.0506625	+	0.0292500i
$991$	6.73641	−	11.6678i	0.213989	−	0.370640i	−0.738970	−	0.673738i	$-0.764688\pi$
$991$	6.73641	−	11.6678i	0.213989	−	0.370640i	0.952959	+	0.303098i	$0.0980210\pi$
$992$	−2.84137	−	4.92140i	−0.0902136	−	0.156255i
$993$			19.4070i			0.615862i
$994$	21.9255	−	6.88625i	0.695436	−	0.218418i
$995$	−10.0094	−	5.77890i	−0.317318	−	0.183204i
$996$	7.66812	+	4.42719i	0.242974	+	0.140281i
$997$	−16.8369			−0.533229			−0.266615	−	0.963803i	$-0.585905\pi$
$997$	−16.8369			−0.533229			−0.266615	+	0.963803i	$0.585905\pi$
$998$	1.92788	−	3.33919i	0.0610260	−	0.105700i
$999$			4.17111i			0.131968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bm.a.205.7	yes	16
3.2	odd	2		1638.2.dt.a.1297.2		16
7.4	even	3		546.2.bd.a.361.2	yes	16
13.4	even	6		546.2.bd.a.121.2	✓	16
21.11	odd	6		1638.2.cr.a.361.7		16
39.17	odd	6		1638.2.cr.a.667.7		16
91.4	even	6	inner	546.2.bm.a.277.3	yes	16
273.95	odd	6		1638.2.dt.a.1369.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.a.121.2	✓	16	13.4	even	6
546.2.bd.a.361.2	yes	16	7.4	even	3
546.2.bm.a.205.7	yes	16	1.1	even	1	trivial
546.2.bm.a.277.3	yes	16	91.4	even	6	inner
1638.2.cr.a.361.7		16	21.11	odd	6
1638.2.cr.a.667.7		16	39.17	odd	6
1638.2.dt.a.1297.2		16	3.2	odd	2
1638.2.dt.a.1369.6		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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(0.620092 + 0.358010i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-1.94866 - 1.78962i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(0.620092 + 0.358010i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-1.94866 - 1.78962i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.358010 + 0.620092i) q^{10} +(2.22627 + 1.28534i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(3.57509 - 0.467723i) q^{13} +(1.78962 - 1.94866i) q^{14} +(0.620092 - 0.358010i) q^{15} +1.00000 q^{16} +0.0248360 q^{17} +(0.866025 - 0.500000i) q^{18} +(5.98499 - 3.45544i) q^{19} +(-0.620092 - 0.358010i) q^{20} +(-2.52418 + 0.792781i) q^{21} +(-1.28534 + 2.22627i) q^{22} +9.39876 q^{23} +(-0.866025 - 0.500000i) q^{24} +(-2.24366 - 3.88613i) q^{25} +(0.467723 + 3.57509i) q^{26} -1.00000 q^{27} +(1.94866 + 1.78962i) q^{28} +(-2.77589 - 4.80797i) q^{29} +(0.358010 + 0.620092i) q^{30} +(-4.92140 + 2.84137i) q^{31} +1.00000i q^{32} +(2.22627 - 1.28534i) q^{33} +0.0248360i q^{34} +(-0.567647 - 1.80737i) q^{35} +(0.500000 + 0.866025i) q^{36} -4.17111i q^{37} +(3.45544 + 5.98499i) q^{38} +(1.38248 - 3.32998i) q^{39} +(0.358010 - 0.620092i) q^{40} +(4.54901 - 2.62637i) q^{41} +(-0.792781 - 2.52418i) q^{42} +(-6.37475 + 11.0414i) q^{43} +(-2.22627 - 1.28534i) q^{44} -0.716021i q^{45} +9.39876i q^{46} +(4.32056 + 2.49448i) q^{47} +(0.500000 - 0.866025i) q^{48} +(0.594548 + 6.97471i) q^{49} +(3.88613 - 2.24366i) q^{50} +(0.0124180 - 0.0215086i) q^{51} +(-3.57509 + 0.467723i) q^{52} +(-4.72462 - 8.18328i) q^{53} -1.00000i q^{54} +(0.920330 + 1.59406i) q^{55} +(-1.78962 + 1.94866i) q^{56} -6.91088i q^{57} +(4.80797 - 2.77589i) q^{58} +2.25219i q^{59} +(-0.620092 + 0.358010i) q^{60} +(0.326003 + 0.564654i) q^{61} +(-2.84137 - 4.92140i) q^{62} +(-0.575523 + 2.58240i) q^{63} -1.00000 q^{64} +(2.38433 + 0.989886i) q^{65} +(1.28534 + 2.22627i) q^{66} +(1.62475 + 0.938052i) q^{67} -0.0248360 q^{68} +(4.69938 - 8.13957i) q^{69} +(1.80737 - 0.567647i) q^{70} +(7.52246 + 4.34310i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(-13.7568 + 7.94250i) q^{73} +4.17111 q^{74} -4.48731 q^{75} +(-5.98499 + 3.45544i) q^{76} +(-2.03798 - 6.48886i) q^{77} +(3.32998 + 1.38248i) q^{78} +(-0.194223 + 0.336404i) q^{79} +(0.620092 + 0.358010i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.62637 + 4.54901i) q^{82} -8.85439i q^{83} +(2.52418 - 0.792781i) q^{84} +(0.0154006 + 0.00889156i) q^{85} +(-11.0414 - 6.37475i) q^{86} -5.55177 q^{87} +(1.28534 - 2.22627i) q^{88} +14.8382i q^{89} +0.716021 q^{90} +(-7.80367 - 5.48660i) q^{91} -9.39876 q^{92} +5.68274i q^{93} +(-2.49448 + 4.32056i) q^{94} +4.94833 q^{95} +(0.866025 + 0.500000i) q^{96} +(-1.78702 - 1.03174i) q^{97} +(-6.97471 + 0.594548i) q^{98} -2.57068i 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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