LMFDB - Embedded newform 126.2.m.a.83.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,2,Mod(41,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.41"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.00611506547$
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} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			83.8
Root			$-1.69547 + 0.354107i$ of defining polynomial
Character	$\chi$	$=$	126.83
Dual form			126.2.m.a.41.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(1.69547 - 0.354107i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.895175 - 1.55049i) q^{5} +(1.64537 + 0.541068i) q^{6} +(-2.30191 + 1.30430i) q^{7} +1.00000i q^{8} +(2.74922 - 1.20075i) q^{9} -1.79035i q^{10} +(-2.07976 - 1.20075i) q^{11} +(1.15440 + 1.29126i) q^{12} +(-4.23601 + 2.44566i) q^{13} +(-2.64566 - 0.0213944i) q^{14} +(-2.06678 - 2.31181i) q^{15} +(-0.500000 + 0.866025i) q^{16} +3.66466 q^{17} +(2.98127 + 0.334727i) q^{18} +3.01701i q^{19} +(0.895175 - 1.55049i) q^{20} +(-3.44095 + 3.02653i) q^{21} +(-1.20075 - 2.07976i) q^{22} +(3.26178 - 1.88319i) q^{23} +(0.354107 + 1.69547i) q^{24} +(0.897324 - 1.55421i) q^{25} -4.89133 q^{26} +(4.23601 - 3.00935i) q^{27} +(-2.28052 - 1.34136i) q^{28} +(-5.68202 - 3.28052i) q^{29} +(-0.633975 - 3.03548i) q^{30} +(-4.02408 + 2.32330i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.95136 - 1.29938i) q^{33} +(3.17369 + 1.83233i) q^{34} +(4.08292 + 2.40150i) q^{35} +(2.41449 + 1.78052i) q^{36} +9.36404 q^{37} +(-1.50851 + 2.61281i) q^{38} +(-6.31599 + 5.64654i) q^{39} +(1.55049 - 0.895175i) q^{40} +(-4.04094 - 6.99911i) q^{41} +(-4.49321 + 0.900574i) q^{42} +(-3.48127 + 6.02973i) q^{43} -2.40150i q^{44} +(-4.32278 - 3.18775i) q^{45} +3.76638 q^{46} +(2.56802 - 4.44794i) q^{47} +(-0.541068 + 1.64537i) q^{48} +(3.59758 - 6.00478i) q^{49} +(1.55421 - 0.897324i) q^{50} +(6.21332 - 1.29768i) q^{51} +(-4.23601 - 2.44566i) q^{52} +(5.17317 - 0.488168i) q^{54} +4.29953i q^{55} +(-1.30430 - 2.30191i) q^{56} +(1.06834 + 5.11524i) q^{57} +(-3.28052 - 5.68202i) q^{58} +(7.29501 + 12.6353i) q^{59} +(0.968701 - 2.94579i) q^{60} +(9.81058 + 5.66414i) q^{61} -4.64661 q^{62} +(-4.76230 + 6.34984i) q^{63} -1.00000 q^{64} +(7.58394 + 4.37859i) q^{65} +(-2.77229 - 3.10098i) q^{66} +(-0.285115 - 0.493834i) q^{67} +(1.83233 + 3.17369i) q^{68} +(4.86340 - 4.34791i) q^{69} +(2.33516 + 4.12122i) q^{70} +5.96254i q^{71} +(1.20075 + 2.74922i) q^{72} -12.3814i q^{73} +(8.10950 + 4.68202i) q^{74} +(0.971027 - 2.95286i) q^{75} +(-2.61281 + 1.50851i) q^{76} +(6.35358 + 0.0513786i) q^{77} +(-8.29308 + 1.73205i) q^{78} +(-1.51831 + 2.62979i) q^{79} +1.79035 q^{80} +(6.11639 - 6.60226i) q^{81} -8.08188i q^{82} +(-7.00270 + 12.1290i) q^{83} +(-4.34152 - 1.46669i) q^{84} +(-3.28052 - 5.68202i) q^{85} +(-6.02973 + 3.48127i) q^{86} +(-10.7953 - 3.54997i) q^{87} +(1.20075 - 2.07976i) q^{88} -3.74863 q^{89} +(-2.14977 - 4.92206i) q^{90} +(6.56103 - 11.1547i) q^{91} +(3.26178 + 1.88319i) q^{92} +(-6.00000 + 5.36404i) q^{93} +(4.44794 - 2.56802i) q^{94} +(4.67784 - 2.70075i) q^{95} +(-1.29126 + 1.15440i) q^{96} +(4.77256 + 2.75544i) q^{97} +(6.11799 - 3.40150i) q^{98} +(-7.15953 - 0.803848i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{7} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 8 q^{16} - 12 q^{18} + 18 q^{21} - 48 q^{23} - 8 q^{25} + 4 q^{28} - 12 q^{29} - 24 q^{30} + 12 q^{36} - 8 q^{37} - 36 q^{39} - 12 q^{42} + 4 q^{43}+ \cdots - 72 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 8 * q^16 - 12 * q^18 + 18 * q^21 - 48 * q^23 - 8 * q^25 + 4 * q^28 - 12 * q^29 - 24 * q^30 + 12 * q^36 - 8 * q^37 - 36 * q^39 - 12 * q^42 + 4 * q^43 + 24 * q^46 - 8 * q^49 + 60 * q^50 + 12 * q^51 - 6 * q^56 + 48 * q^57 - 12 * q^58 + 24 * q^60 + 24 * q^63 - 16 * q^64 + 84 * q^65 - 28 * q^67 + 36 * q^74 + 78 * q^77 - 24 * q^78 - 4 * q^79 + 36 * q^81 + 18 * q^84 - 12 * q^85 - 24 * q^86 + 24 * q^91 - 48 * q^92 - 96 * q^93 + 12 * q^95 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.69547	−	0.354107i	0.978878	−	0.204444i
$3$	1.69547	−	0.354107i	0.978878	−	0.204444i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.895175	−	1.55049i	−0.400334	−	0.693399i	0.593432	−	0.804884i	$-0.297773\pi$
$5$	−0.895175	−	1.55049i	−0.400334	−	0.693399i	−0.993766	+	0.111485i	$0.964439\pi$
$6$	1.64537	+	0.541068i	0.671720	+	0.220890i
$7$	−2.30191	+	1.30430i	−0.870040	+	0.492981i
$7$	−2.30191	+	1.30430i	−0.870040	+	0.492981i
$8$			1.00000i			0.353553i
$9$	2.74922	−	1.20075i	0.916406	−	0.400251i
$10$		−	1.79035i		−	0.566158i
$11$	−2.07976	−	1.20075i	−0.627072	−	0.362040i	0.152545	−	0.988297i	$-0.451253\pi$
$11$	−2.07976	−	1.20075i	−0.627072	−	0.362040i	−0.779617	+	0.626256i	$0.784586\pi$
$12$	1.15440	+	1.29126i	0.333246	+	0.372756i
$13$	−4.23601	+	2.44566i	−1.17486	+	0.678305i	−0.954820	−	0.297186i	$-0.903952\pi$
$13$	−4.23601	+	2.44566i	−1.17486	+	0.678305i	−0.220039	+	0.975491i	$0.570618\pi$
$14$	−2.64566	−	0.0213944i	−0.707084	−	0.00571788i
$15$	−2.06678	−	2.31181i	−0.533640	−	0.596908i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.66466			0.888812			0.444406	−	0.895826i	$-0.353415\pi$
$17$	3.66466			0.888812			0.444406	+	0.895826i	$0.353415\pi$
$18$	2.98127	+	0.334727i	0.702692	+	0.0788958i
$19$			3.01701i			0.692150i	0.938207	+	0.346075i	$0.112486\pi$
$19$			3.01701i			0.692150i	−0.938207	+	0.346075i	$0.887514\pi$
$20$	0.895175	−	1.55049i	0.200167	−	0.346700i
$21$	−3.44095	+	3.02653i	−0.750877	+	0.660442i
$22$	−1.20075	−	2.07976i	−0.256001	−	0.443407i
$23$	3.26178	−	1.88319i	0.680129	−	0.392673i	−0.119775	−	0.992801i	$-0.538217\pi$
$23$	3.26178	−	1.88319i	0.680129	−	0.392673i	0.799904	+	0.600128i	$0.204884\pi$
$24$	0.354107	+	1.69547i	0.0722817	+	0.346086i
$25$	0.897324	−	1.55421i	0.179465	−	0.310842i
$26$	−4.89133			−0.959268
$27$	4.23601	−	3.00935i	0.815221	−	0.579150i
$28$	−2.28052	−	1.34136i	−0.430977	−	0.253493i
$29$	−5.68202	−	3.28052i	−1.05512	−	0.609176i	−0.131045	−	0.991376i	$-0.541833\pi$
$29$	−5.68202	−	3.28052i	−1.05512	−	0.609176i	−0.924080	+	0.382200i	$0.875167\pi$
$30$	−0.633975	−	3.03548i	−0.115747	−	0.554200i
$31$	−4.02408	+	2.32330i	−0.722746	+	0.417278i	−0.815763	−	0.578387i	$-0.803682\pi$
$31$	−4.02408	+	2.32330i	−0.722746	+	0.417278i	0.0930163	+	0.995665i	$0.470349\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−3.95136	−	1.29938i	−0.687844	−	0.226193i
$34$	3.17369	+	1.83233i	0.544284	+	0.314242i
$35$	4.08292	+	2.40150i	0.690140	+	0.405928i
$36$	2.41449	+	1.78052i	0.402415	+	0.296753i
$37$	9.36404			1.53944			0.769719	−	0.638382i	$-0.220396\pi$
$37$	9.36404			1.53944			0.769719	+	0.638382i	$0.220396\pi$
$38$	−1.50851	+	2.61281i	−0.244712	+	0.423853i
$39$	−6.31599	+	5.64654i	−1.01137	+	0.904170i
$40$	1.55049	−	0.895175i	0.245154	−	0.141540i
$41$	−4.04094	−	6.99911i	−0.631088	−	1.09308i	−0.987330	−	0.158683i	$-0.949275\pi$
$41$	−4.04094	−	6.99911i	−0.631088	−	1.09308i	0.356241	−	0.934394i	$-0.384058\pi$
$42$	−4.49321	+	0.900574i	−0.693318	+	0.138962i
$43$	−3.48127	+	6.02973i	−0.530888	+	0.919526i	0.468462	+	0.883484i	$0.344808\pi$
$43$	−3.48127	+	6.02973i	−0.530888	+	0.919526i	−0.999350	+	0.0360419i	$0.988525\pi$
$44$		−	2.40150i		−	0.362040i
$45$	−4.32278	−	3.18775i	−0.644402	−	0.475201i
$46$	3.76638			0.555323
$47$	2.56802	−	4.44794i	0.374584	−	0.648799i	−0.615680	−	0.787996i	$-0.711119\pi$
$47$	2.56802	−	4.44794i	0.374584	−	0.648799i	0.990265	+	0.139197i	$0.0444520\pi$
$48$	−0.541068	+	1.64537i	−0.0780965	+	0.237489i
$49$	3.59758	−	6.00478i	0.513940	−	0.857826i
$50$	1.55421	−	0.897324i	0.219799	−	0.126901i
$51$	6.21332	−	1.29768i	0.870039	−	0.181712i
$52$	−4.23601	−	2.44566i	−0.587429	−	0.339152i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	5.17317	−	0.488168i	0.703979	−	0.0664313i
$55$			4.29953i			0.579749i
$56$	−1.30430	−	2.30191i	−0.174295	−	0.307606i
$57$	1.06834	+	5.11524i	0.141506	+	0.677530i
$58$	−3.28052	−	5.68202i	−0.430753	−	0.746086i
$59$	7.29501	+	12.6353i	0.949729	+	1.64498i	0.745994	+	0.665953i	$0.231975\pi$
$59$	7.29501	+	12.6353i	0.949729	+	1.64498i	0.203735	+	0.979026i	$0.434692\pi$
$60$	0.968701	−	2.94579i	0.125059	−	0.380300i
$61$	9.81058	+	5.66414i	1.25612	+	0.725219i	0.972317	−	0.233665i	$-0.0750718\pi$
$61$	9.81058	+	5.66414i	1.25612	+	0.725219i	0.283799	+	0.958884i	$0.408405\pi$
$62$	−4.64661			−0.590120
$63$	−4.76230	+	6.34984i	−0.599994	+	0.800005i
$64$	−1.00000			−0.125000
$65$	7.58394	+	4.37859i	0.940672	+	0.543097i
$66$	−2.77229	−	3.10098i	−0.341246	−	0.381704i
$67$	−0.285115	−	0.493834i	−0.0348324	−	0.0603315i	0.848084	−	0.529862i	$-0.177756\pi$
$67$	−0.285115	−	0.493834i	−0.0348324	−	0.0603315i	−0.882916	+	0.469531i	$0.844423\pi$
$68$	1.83233	+	3.17369i	0.222203	+	0.384867i
$69$	4.86340	−	4.34791i	0.585484	−	0.523427i
$70$	2.33516	+	4.12122i	0.279105	+	0.492580i
$71$			5.96254i			0.707623i	0.935317	+	0.353811i	$0.115115\pi$
$71$			5.96254i			0.707623i	−0.935317	+	0.353811i	$0.884885\pi$
$72$	1.20075	+	2.74922i	0.141510	+	0.323998i
$73$		−	12.3814i		−	1.44913i	−0.689204	−	0.724567i	$-0.742040\pi$
$73$		−	12.3814i		−	1.44913i	0.689204	−	0.724567i	$-0.257960\pi$
$74$	8.10950	+	4.68202i	0.942710	+	0.544274i
$75$	0.971027	−	2.95286i	0.112125	−	0.340967i
$76$	−2.61281	+	1.50851i	−0.299710	+	0.173037i
$77$	6.35358	+	0.0513786i	0.724057	+	0.00585514i
$78$	−8.29308	+	1.73205i	−0.939007	+	0.196116i
$79$	−1.51831	+	2.62979i	−0.170824	+	0.295875i	−0.938708	−	0.344713i	$-0.887976\pi$
$79$	−1.51831	+	2.62979i	−0.170824	+	0.295875i	0.767884	+	0.640588i	$0.221309\pi$
$80$	1.79035			0.200167
$81$	6.11639	−	6.60226i	0.679599	−	0.733584i
$82$		−	8.08188i		−	0.892494i
$83$	−7.00270	+	12.1290i	−0.768646	+	1.33133i	0.169651	+	0.985504i	$0.445736\pi$
$83$	−7.00270	+	12.1290i	−0.768646	+	1.33133i	−0.938297	+	0.345830i	$0.887597\pi$
$84$	−4.34152	−	1.46669i	−0.473699	−	0.160029i
$85$	−3.28052	−	5.68202i	−0.355822	−	0.616302i
$86$	−6.02973	+	3.48127i	−0.650203	+	0.375395i
$87$	−10.7953	−	3.54997i	−1.15738	−	0.380596i
$88$	1.20075	−	2.07976i	0.128001	−	0.221704i
$89$	−3.74863			−0.397354			−0.198677	−	0.980065i	$-0.563664\pi$
$89$	−3.74863			−0.397354			−0.198677	+	0.980065i	$0.563664\pi$
$90$	−2.14977	−	4.92206i	−0.226605	−	0.518831i
$91$	6.56103	−	11.1547i	0.687783	−	1.16934i
$92$	3.26178	+	1.88319i	0.340064	+	0.196336i
$93$	−6.00000	+	5.36404i	−0.622171	+	0.556225i
$94$	4.44794	−	2.56802i	0.458770	−	0.264871i
$95$	4.67784	−	2.70075i	0.479936	−	0.277091i
$96$	−1.29126	+	1.15440i	−0.131789	+	0.117820i
$97$	4.77256	+	2.75544i	0.484580	+	0.279772i	0.722323	−	0.691556i	$-0.243074\pi$
$97$	4.77256	+	2.75544i	0.484580	+	0.279772i	−0.237743	+	0.971328i	$0.576408\pi$
$98$	6.11799	−	3.40150i	0.618010	−	0.343604i
$99$	−7.15953	−	0.803848i	−0.719560	−	0.0807897i
$100$	1.79465			0.179465
$101$	−0.125162	+	0.216787i	−0.0124541	+	0.0215711i	−0.872185	−	0.489176i	$-0.837298\pi$
$101$	−0.125162	+	0.216787i	−0.0124541	+	0.0215711i	0.859731	+	0.510747i	$0.170631\pi$
$102$	6.02973	+	1.98283i	0.597033	+	0.196330i
$103$	0.145433	−	0.0839657i	0.0143299	−	0.00827339i	−0.492818	−	0.870132i	$-0.664033\pi$
$103$	0.145433	−	0.0839657i	0.0143299	−	0.00827339i	0.507148	+	0.861859i	$0.330700\pi$
$104$	−2.44566	−	4.23601i	−0.239817	−	0.415375i
$105$	7.77285	+	2.62588i	0.758552	+	0.256260i
$106$		0			0
$107$		−	7.99080i		−	0.772500i	−0.922394	−	0.386250i	$-0.873770\pi$
$107$		−	7.99080i		−	0.772500i	0.922394	−	0.386250i	$-0.126230\pi$
$108$	4.72418	+	2.16382i	0.454585	+	0.208214i
$109$	−18.9533			−1.81540			−0.907700	−	0.419619i	$-0.862164\pi$
$109$	−18.9533			−1.81540			−0.907700	+	0.419619i	$0.862164\pi$
$110$	−2.14977	+	3.72350i	−0.204972	+	0.355022i
$111$	15.8764	−	3.31587i	1.50692	−	0.314728i
$112$	0.0213944	−	2.64566i	0.00202158	−	0.249992i
$113$	−1.00418	+	0.579764i	−0.0944653	+	0.0545396i	−0.546488	−	0.837467i	$-0.684036\pi$
$113$	−1.00418	+	0.579764i	−0.0944653	+	0.0545396i	0.452023	+	0.892006i	$0.350702\pi$
$114$	−1.63241	+	4.96410i	−0.152889	+	0.464931i
$115$	−5.83973	−	3.37157i	−0.544558	−	0.314401i
$116$		−	6.56103i		−	0.609176i
$117$	−8.70908	+	11.8101i	−0.805155	+	1.09184i
$118$			14.5900i			1.34312i
$119$	−8.43573	+	4.77984i	−0.773302	+	0.438167i
$120$	2.31181	−	2.06678i	0.211039	−	0.188670i
$121$	−2.61639	−	4.53172i	−0.237854	−	0.411974i
$122$	5.66414	+	9.81058i	0.512807	+	0.888208i
$123$	−9.32971	−	10.4358i	−0.841231	−	0.940968i
$124$	−4.02408	−	2.32330i	−0.361373	−	0.208639i
$125$	−12.1648			−1.08805
$126$	−7.29920	+	3.11797i	−0.650264	+	0.277771i
$127$	1.40150			0.124363			0.0621817	−	0.998065i	$-0.480194\pi$
$127$	1.40150			0.124363			0.0621817	+	0.998065i	$0.480194\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−3.76721	+	11.4560i	−0.331684	+	1.00864i
$130$	4.37859	+	7.58394i	0.384028	+	0.665156i
$131$	−5.24589	−	9.08614i	−0.458335	−	0.793860i	0.540538	−	0.841320i	$-0.318221\pi$
$131$	−5.24589	−	9.08614i	−0.458335	−	0.793860i	−0.998873	+	0.0474597i	$0.984887\pi$
$132$	−0.850388	−	4.07167i	−0.0740168	−	0.354393i
$133$	−3.93510	−	6.94489i	−0.341216	−	0.602198i
$134$		−	0.570231i		−	0.0492604i
$135$	−8.45794	−	3.87399i	−0.727943	−	0.333420i
$136$			3.66466i			0.314242i
$137$	−4.08812	−	2.36028i	−0.349272	−	0.201652i	0.315093	−	0.949061i	$-0.397964\pi$
$137$	−4.08812	−	2.36028i	−0.349272	−	0.201652i	−0.664365	+	0.747409i	$0.731298\pi$
$138$	6.38578	−	1.33370i	0.543594	−	0.113532i
$139$	−2.04707	+	1.18187i	−0.173630	+	0.100245i	−0.584296	−	0.811540i	$-0.698629\pi$
$139$	−2.04707	+	1.18187i	−0.173630	+	0.100245i	0.410666	+	0.911786i	$0.365296\pi$
$140$	−0.0383034	+	4.73667i	−0.00323723	+	0.400321i
$141$	2.77895	−	8.45070i	0.234030	−	0.711677i
$142$	−2.98127	+	5.16371i	−0.250182	+	0.433329i
$143$	11.7465			0.982295
$144$	−0.334727	+	2.98127i	−0.0278939	+	0.248439i
$145$			11.7465i			0.975497i
$146$	6.19070	−	10.7226i	0.512346	−	0.887410i
$147$	3.97325	−	11.4548i	0.327708	−	0.944779i
$148$	4.68202	+	8.10950i	0.384860	+	0.666597i
$149$	−15.0377	+	8.68202i	−1.23194	+	0.711259i	−0.967433	−	0.253126i	$-0.918541\pi$
$149$	−15.0377	+	8.68202i	−1.23194	+	0.711259i	−0.264503	+	0.964385i	$0.585208\pi$
$150$	2.31737	−	2.07174i	0.189212	−	0.169157i
$151$	5.61639	−	9.72787i	0.457055	−	0.791643i	−0.541749	−	0.840541i	$-0.682238\pi$
$151$	5.61639	−	9.72787i	0.457055	−	0.791643i	0.998804	+	0.0488977i	$0.0155708\pi$
$152$	−3.01701			−0.244712
$153$	10.0750	−	4.40035i	0.814512	−	0.355748i
$154$	5.47667	+	3.22128i	0.441322	+	0.259578i
$155$	7.20451	+	4.15953i	0.578680	+	0.334101i
$156$	−8.04805	−	2.64654i	−0.644359	−	0.211893i
$157$	11.9885	−	6.92154i	0.956783	−	0.552399i	0.0616014	−	0.998101i	$-0.480379\pi$
$157$	11.9885	−	6.92154i	0.956783	−	0.552399i	0.895181	+	0.445702i	$0.147046\pi$
$158$	−2.62979	+	1.51831i	−0.209215	+	0.120790i
$159$		0			0
$160$	1.55049	+	0.895175i	0.122577	+	0.0707698i
$161$	−5.05208	+	8.58930i	−0.398159	+	0.676931i
$162$	8.59808	−	2.65953i	0.675529	−	0.208952i
$163$	−4.33577			−0.339604			−0.169802	−	0.985478i	$-0.554313\pi$
$163$	−4.33577			−0.339604			−0.169802	+	0.985478i	$0.554313\pi$
$164$	4.04094	−	6.99911i	0.315544	−	0.546539i
$165$	1.52249	+	7.28972i	0.118526	+	0.567504i
$166$	−12.1290	+	7.00270i	−0.941395	+	0.543515i
$167$	−6.20756	−	10.7518i	−0.480355	−	0.832000i	0.519391	−	0.854537i	$-0.326159\pi$
$167$	−6.20756	−	10.7518i	−0.480355	−	0.832000i	−0.999746	+	0.0225370i	$0.992826\pi$
$168$	−3.02653	−	3.44095i	−0.233502	−	0.265475i
$169$	5.46254	−	9.46139i	0.420195	−	0.727799i
$170$		−	6.56103i		−	0.503208i
$171$	3.62268	+	8.29442i	0.277033	+	0.634290i
$172$	−6.96254			−0.530888
$173$	8.70908	−	15.0846i	0.662139	−	1.14686i	−0.317913	−	0.948120i	$-0.602982\pi$
$173$	8.70908	−	15.0846i	0.662139	−	1.14686i	0.980052	−	0.198739i	$-0.0636846\pi$
$174$	−7.57405	−	8.47203i	−0.574187	−	0.642263i
$175$	−0.0383954	+	4.74804i	−0.00290242	+	0.358918i
$176$	2.07976	−	1.20075i	0.156768	−	0.0905101i
$177$	16.8427	+	18.8396i	1.26597	+	1.41607i
$178$	−3.24641	−	1.87432i	−0.243329	−	0.140486i
$179$			13.1221i			0.980789i	0.871501	+	0.490395i	$0.163147\pi$
$179$			13.1221i			0.980789i	−0.871501	+	0.490395i	$0.836853\pi$
$180$	0.599278	−	5.33751i	0.0446675	−	0.397835i
$181$			13.3577i			0.992873i	0.868073	+	0.496437i	$0.165359\pi$
$181$			13.3577i			0.992873i	−0.868073	+	0.496437i	$0.834641\pi$
$182$	11.2594	−	6.37978i	0.834602	−	0.472901i
$183$	18.6392	+	6.12937i	1.37785	+	0.453096i
$184$	1.88319	+	3.26178i	0.138831	+	0.240462i
$185$	−8.38245	−	14.5188i	−0.616290	−	1.06745i
$186$	−7.87817	+	1.64539i	−0.577656	+	0.120646i
$187$	−7.62164	−	4.40035i	−0.557349	−	0.321786i
$188$	5.13604			0.374584
$189$	−5.82581	+	12.4523i	−0.423765	+	0.905772i
$190$	5.40150			0.391866
$191$	−8.01361	−	4.62666i	−0.579845	−	0.334774i	0.181227	−	0.983441i	$-0.441993\pi$
$191$	−8.01361	−	4.62666i	−0.579845	−	0.334774i	−0.761072	+	0.648668i	$0.775326\pi$
$192$	−1.69547	+	0.354107i	−0.122360	+	0.0255554i
$193$	12.2801	+	21.2698i	0.883941	+	1.53103i	0.846923	+	0.531716i	$0.178452\pi$
$193$	12.2801	+	21.2698i	0.883941	+	1.53103i	0.0370176	+	0.999315i	$0.488214\pi$
$194$	2.75544	+	4.77256i	0.197829	+	0.342650i
$195$	14.4088	+	4.73823i	1.03184	+	0.339312i
$196$	6.99908	+	0.113205i	0.499935	+	0.00808604i
$197$		−	12.4861i		−	0.889598i	−0.895630	−	0.444799i	$-0.853275\pi$
$197$		−	12.4861i		−	0.889598i	0.895630	−	0.444799i	$-0.146725\pi$
$198$	−5.79841	−	4.27592i	−0.412075	−	0.303876i
$199$			0.179145i			0.0126993i	0.999980	+	0.00634964i	$0.00202117\pi$
$199$			0.179145i			0.0126993i	−0.999980	+	0.00634964i	$0.997979\pi$
$200$	1.55421	+	0.897324i	0.109899	+	0.0634504i
$201$	−0.658274	−	0.736319i	−0.0464311	−	0.0519359i
$202$	−0.216787	+	0.125162i	−0.0152531	+	0.00880637i
$203$	17.3583	+	0.140369i	1.21831	+	0.00985198i
$204$	4.23048	+	4.73205i	0.296193	+	0.331310i
$205$	−7.23469	+	12.5309i	−0.505293	+	0.875193i
$206$	0.167931			0.0117003
$207$	6.70610	−	9.09390i	0.466107	−	0.632069i
$208$		−	4.89133i		−	0.339152i
$209$	3.62268	−	6.27467i	0.250586	−	0.434028i
$210$	5.41854	+	6.16050i	0.373915	+	0.425115i
$211$	7.56103	+	13.0961i	0.520523	+	0.901572i	0.999715	+	0.0238622i	$0.00759629\pi$
$211$	7.56103	+	13.0961i	0.520523	+	0.901572i	−0.479192	+	0.877710i	$0.659070\pi$
$212$		0			0
$213$	2.11137	+	10.1093i	0.144669	+	0.692677i
$214$	3.99540	−	6.92024i	0.273120	−	0.473058i
$215$	12.4654			0.850131
$216$	3.00935	+	4.23601i	0.204760	+	0.288224i
$217$	6.23278	−	10.5967i	0.423109	−	0.719348i
$218$	−16.4141	−	9.47667i	−1.11170	−	0.641841i
$219$	−4.38434	−	20.9923i	−0.296266	−	1.41853i
$220$	−3.72350	+	2.14977i	−0.251039	+	0.144937i
$221$	−15.5236	+	8.96254i	−1.04423	+	0.602885i
$222$	15.4073	+	5.06658i	1.03407	+	0.340047i
$223$	−7.27049	−	4.19762i	−0.486868	−	0.281093i	0.236406	−	0.971654i	$-0.424030\pi$
$223$	−7.27049	−	4.19762i	−0.486868	−	0.281093i	−0.723274	+	0.690561i	$0.757364\pi$
$224$	1.34136	−	2.28052i	0.0896234	−	0.152373i
$225$	0.600717	−	5.35033i	0.0400478	−	0.356688i
$226$	−1.15953			−0.0771306
$227$	1.21261	−	2.10030i	0.0804836	−	0.139402i	−0.822974	−	0.568079i	$-0.807687\pi$
$227$	1.21261	−	2.10030i	0.0804836	−	0.139402i	0.903458	+	0.428677i	$0.141020\pi$
$228$	−3.89576	+	3.48283i	−0.258003	+	0.230656i
$229$	1.74915	−	1.00987i	0.115587	−	0.0667344i	−0.441092	−	0.897462i	$-0.645409\pi$
$229$	1.74915	−	1.00987i	0.115587	−	0.0667344i	0.556679	+	0.830728i	$0.312075\pi$
$230$	−3.37157	−	5.83973i	−0.222315	−	0.385061i
$231$	10.7905	−	2.16273i	0.709961	−	0.142297i
$232$	3.28052	−	5.68202i	0.215376	−	0.373043i
$233$			12.7289i			0.833899i	0.908930	+	0.416950i	$0.136901\pi$
$233$			12.7289i			0.833899i	−0.908930	+	0.416950i	$0.863099\pi$
$234$	−13.4473	+	5.87327i	−0.879079	+	0.383948i
$235$	−9.19531			−0.599836
$236$	−7.29501	+	12.6353i	−0.474864	+	0.822489i
$237$	−1.64302	+	4.99637i	−0.106726	+	0.324549i
$238$	−9.69548	−	0.0784032i	−0.628464	−	0.00508212i
$239$	15.1117	−	8.72474i	0.977494	−	0.564356i	0.0759814	−	0.997109i	$-0.475791\pi$
$239$	15.1117	−	8.72474i	0.977494	−	0.564356i	0.901513	+	0.432753i	$0.142458\pi$
$240$	3.03548	−	0.633975i	0.195939	−	0.0409229i
$241$	9.90142	+	5.71659i	0.637807	+	0.368238i	0.783769	−	0.621052i	$-0.213295\pi$
$241$	9.90142	+	5.71659i	0.637807	+	0.368238i	−0.145963	+	0.989290i	$0.546628\pi$
$242$		−	5.23278i		−	0.336376i
$243$	8.03223	−	13.3598i	0.515268	−	0.857029i
$244$			11.3283i			0.725219i
$245$	−12.5308	−	0.202676i	−0.800564	−	0.0129485i
$246$	−2.86185	−	13.7026i	−0.182465	−	0.873643i
$247$	−7.37859	−	12.7801i	−0.469489	−	0.813178i
$248$	−2.32330	−	4.02408i	−0.147530	−	0.255529i
$249$	−7.57788	+	23.0441i	−0.480228	+	1.46036i
$250$	−10.5350	−	6.08240i	−0.666293	−	0.384685i
$251$	−27.3560			−1.72669			−0.863347	−	0.504611i	$-0.831636\pi$
$251$	−27.3560			−1.72669			−0.863347	+	0.504611i	$0.831636\pi$
$252$	−7.88027	−	0.949357i	−0.496411	−	0.0598039i
$253$	−9.04499			−0.568653
$254$	1.21374	+	0.700752i	0.0761567	+	0.0439691i
$255$	−7.57405	−	8.47203i	−0.474305	−	0.530539i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.74837	+	3.02826i	0.109060	+	0.188898i	0.915390	−	0.402569i	$-0.131883\pi$
$257$	1.74837	+	3.02826i	0.109060	+	0.188898i	−0.806330	+	0.591466i	$0.798549\pi$
$258$	−8.99047	+	8.03754i	−0.559722	+	0.500396i
$259$	−21.5552	+	12.2136i	−1.33937	+	0.758914i
$260$			8.75718i			0.543097i
$261$	−19.5602	−	2.19615i	−1.21075	−	0.135938i
$262$		−	10.4918i		−	0.648184i
$263$	−8.35150	−	4.82174i	−0.514976	−	0.297321i	0.219901	−	0.975522i	$-0.429427\pi$
$263$	−8.35150	−	4.82174i	−0.514976	−	0.297321i	−0.734877	+	0.678201i	$0.762760\pi$
$264$	1.29938	−	3.95136i	0.0799712	−	0.243190i
$265$		0			0
$266$	0.0645470	−	7.98200i	0.00395763	−	0.489408i
$267$	−6.35568	+	1.32741i	−0.388961	+	0.0812365i
$268$	0.285115	−	0.493834i	0.0174162	−	0.0301657i
$269$	−6.91107			−0.421376			−0.210688	−	0.977553i	$-0.567570\pi$
$269$	−6.91107			−0.421376			−0.210688	+	0.977553i	$0.567570\pi$
$270$	−5.38779	−	7.58394i	−0.327891	−	0.461544i
$271$			20.6312i			1.25326i	0.779318	+	0.626629i	$0.215566\pi$
$271$			20.6312i			1.25326i	−0.779318	+	0.626629i	$0.784434\pi$
$272$	−1.83233	+	3.17369i	−0.111101	+	0.192433i
$273$	7.17404	−	21.2358i	0.434193	−	1.28525i
$274$	−2.36028	−	4.08812i	−0.142590	−	0.246973i
$275$	−3.73244	+	2.15493i	−0.225075	+	0.129947i
$276$	6.19710	+	2.03787i	0.373021	+	0.122665i
$277$	7.75718	−	13.4358i	0.466084	−	0.807281i	−0.533166	−	0.846011i	$-0.678998\pi$
$277$	7.75718	−	13.4358i	0.466084	−	0.807281i	0.999250	+	0.0387296i	$0.0123311\pi$
$278$	−2.36375			−0.141768
$279$	−8.27336	+	11.2192i	−0.495313	+	0.671675i
$280$	−2.40150	+	4.08292i	−0.143517	+	0.244001i
$281$	11.7759	+	6.79883i	0.702492	+	0.405584i	0.808275	−	0.588805i	$-0.200401\pi$
$281$	11.7759	+	6.79883i	0.702492	+	0.405584i	−0.105783	+	0.994389i	$0.533735\pi$
$282$	6.63199	−	5.92904i	0.394929	−	0.353069i
$283$	−4.71796	+	2.72392i	−0.280454	+	0.161920i	−0.633629	−	0.773637i	$-0.718435\pi$
$283$	−4.71796	+	2.72392i	−0.280454	+	0.161920i	0.353175	+	0.935557i	$0.385102\pi$
$284$	−5.16371	+	2.98127i	−0.306410	+	0.176906i
$285$	6.97477	−	6.23549i	0.413150	−	0.369359i
$286$	10.1728	+	5.87327i	0.601530	+	0.347294i
$287$	18.4308	+	10.8407i	1.08794	+	0.639907i
$288$	−1.78052	+	2.41449i	−0.104918	+	0.142275i
$289$	−3.57023			−0.210014
$290$	−5.87327	+	10.1728i	−0.344890	+	0.597368i
$291$	9.06743	+	2.98176i	0.531542	+	0.174794i
$292$	10.7226	−	6.19070i	0.627493	−	0.362284i
$293$	12.2311	+	21.1849i	0.714550	+	1.23764i	0.963133	+	0.269026i	$0.0867017\pi$
$293$	12.2311	+	21.1849i	0.714550	+	1.23764i	−0.248583	+	0.968610i	$0.579965\pi$
$294$	9.16835	−	7.93356i	0.534709	−	0.462694i
$295$	13.0606	−	22.6216i	0.760418	−	1.31708i
$296$			9.36404i			0.544274i
$297$	−12.4234	+	1.17234i	−0.720878	+	0.0680260i
$298$	−17.3640			−1.00587
$299$	−9.21130	+	15.9544i	−0.532703	+	0.922670i
$300$	3.04277	−	0.635497i	0.175674	−	0.0366904i
$301$	0.148959	−	18.4205i	0.00858585	−	1.06174i
$302$	9.72787	−	5.61639i	0.559776	−	0.323187i
$303$	−0.135442	+	0.411876i	−0.00778097	+	0.0236617i
$304$	−2.61281	−	1.50851i	−0.149855	−	0.0865187i
$305$		−	20.2816i		−	1.16132i
$306$	10.9253	+	1.22666i	0.624561	+	0.0701236i
$307$		−	31.2223i		−	1.78195i	−0.454053	−	0.890975i	$-0.650022\pi$
$307$		−	31.2223i		−	1.78195i	0.454053	−	0.890975i	$-0.349978\pi$
$308$	3.13229	+	5.52805i	0.178479	+	0.314990i
$309$	0.216844	−	0.193860i	0.0123358	−	0.0110283i
$310$	4.15953	+	7.20451i	0.236245	+	0.409189i
$311$	−5.45501	−	9.44836i	−0.309325	−	0.535767i	0.668889	−	0.743362i	$-0.266770\pi$
$311$	−5.45501	−	9.44836i	−0.309325	−	0.535767i	−0.978215	+	0.207594i	$0.933437\pi$
$312$	−5.64654	−	6.31599i	−0.319672	−	0.357573i
$313$	2.96532	+	1.71203i	0.167610	+	0.0967694i	0.581458	−	0.813576i	$-0.302482\pi$
$313$	2.96532	+	1.71203i	0.167610	+	0.0967694i	−0.413849	+	0.910346i	$0.635816\pi$
$314$	13.8431			0.781210
$315$	14.1084	+	1.69968i	0.794921	+	0.0957662i
$316$	−3.03663			−0.170824
$317$	16.4953	+	9.52357i	0.926468	+	0.534897i	0.885693	−	0.464272i	$-0.153684\pi$
$317$	16.4953	+	9.52357i	0.926468	+	0.534897i	0.0407755	+	0.999168i	$0.487017\pi$
$318$		0			0
$319$	7.87817	+	13.6454i	0.441093	+	0.763995i
$320$	0.895175	+	1.55049i	0.0500418	+	0.0866749i
$321$	−2.82960	−	13.5481i	−0.157933	−	0.756183i
$322$	−8.66988	+	4.91251i	−0.483153	+	0.273763i
$323$			11.0563i			0.615191i
$324$	8.77592	+	1.99582i	0.487551	+	0.110879i
$325$			8.77821i			0.486927i
$326$	−3.75489	−	2.16789i	−0.207964	−	0.120068i
$327$	−32.1348	+	6.71150i	−1.77706	+	0.371147i
$328$	6.99911	−	4.04094i	0.386461	−	0.223123i
$329$	−0.109882	+	13.5882i	−0.00605801	+	0.749144i
$330$	−2.32634	+	7.07432i	−0.128061	+	0.389429i
$331$	−0.0366251	+	0.0634366i	−0.00201310	+	0.00348679i	−0.867030	−	0.498256i	$-0.833974\pi$
$331$	−0.0366251	+	0.0634366i	−0.00201310	+	0.00348679i	0.865017	+	0.501742i	$0.167307\pi$
$332$	−14.0054			−0.768646
$333$	25.7438	−	11.2439i	1.41075	−	0.616161i
$334$		−	12.4151i		−	0.679325i
$335$	−0.510456	+	0.884136i	−0.0278892	+	0.0483055i
$336$	−0.900574	−	4.49321i	−0.0491303	−	0.245125i
$337$	1.11639	+	1.93364i	0.0608136	+	0.105332i	0.894829	−	0.446408i	$-0.147297\pi$
$337$	1.11639	+	1.93364i	0.0608136	+	0.105332i	−0.834016	+	0.551741i	$0.813964\pi$
$338$	9.46139	−	5.46254i	0.514632	−	0.297123i
$339$	−1.49726	+	1.33856i	−0.0813198	+	0.0727004i
$340$	3.28052	−	5.68202i	0.177911	−	0.308151i
$341$	11.1589			0.604286
$342$	−1.00987	+	8.99452i	−0.0546077	+	0.486368i
$343$	−0.449242	+	18.5148i	−0.0242568	+	0.999706i
$344$	−6.02973	−	3.48127i	−0.325101	−	0.187697i
$345$	−11.0950	−	3.64850i	−0.597333	−	0.196429i
$346$	15.0846	−	8.70908i	0.810952	−	0.468203i
$347$	27.5751	−	15.9205i	1.48031	−	0.854656i	0.480556	−	0.876964i	$-0.340435\pi$
$347$	27.5751	−	15.9205i	1.48031	−	0.854656i	0.999751	+	0.0223084i	$0.00710156\pi$
$348$	−2.32330	−	11.1240i	−0.124542	−	0.596310i
$349$	−12.7613	−	7.36772i	−0.683095	−	0.394385i	0.117925	−	0.993022i	$-0.462376\pi$
$349$	−12.7613	−	7.36772i	−0.683095	−	0.394385i	−0.801020	+	0.598637i	$0.795709\pi$
$350$	−2.40727	+	4.09272i	−0.128674	+	0.218765i
$351$	−10.5839	+	23.1075i	−0.564929	+	1.23339i
$352$	2.40150			0.128001
$353$	−1.07979	+	1.87025i	−0.0574713	+	0.0995431i	−0.893330	−	0.449402i	$-0.851637\pi$
$353$	−1.07979	+	1.87025i	−0.0574713	+	0.0995431i	0.835858	+	0.548945i	$0.184970\pi$
$354$	5.16642	+	24.7369i	0.274592	+	1.31475i
$355$	9.24484	−	5.33751i	0.490665	−	0.283286i
$356$	−1.87432	−	3.24641i	−0.0993385	−	0.172059i
$357$	−12.6099	+	11.0912i	−0.667388	+	0.587009i
$358$	−6.56103	+	11.3640i	−0.346761	+	0.600608i
$359$		−	32.6448i		−	1.72293i	−0.507820	−	0.861463i	$-0.669549\pi$
$359$		−	32.6448i		−	1.72293i	0.507820	−	0.861463i	$-0.330451\pi$
$360$	3.18775	−	4.32278i	0.168009	−	0.227831i
$361$	9.89765			0.520929
$362$	−6.67887	+	11.5681i	−0.351034	+	0.608008i
$363$	−6.04071	−	6.75690i	−0.317055	−	0.354645i
$364$	12.9408	+	0.104647i	0.678283	+	0.00548498i
$365$	−19.1972	+	11.0835i	−1.00483	+	0.580138i
$366$	13.0774	+	14.6278i	0.683564	+	0.764608i
$367$	25.7212	+	14.8501i	1.34264	+	0.775171i	0.987194	−	0.159527i	$-0.0509969\pi$
$367$	25.7212	+	14.8501i	1.34264	+	0.775171i	0.355442	+	0.934698i	$0.384330\pi$
$368$			3.76638i			0.196336i
$369$	−19.5136	−	14.3899i	−1.01584	−	0.749109i
$370$		−	16.7649i		−	0.871566i
$371$		0			0
$372$	−7.64539	−	2.51413i	−0.396395	−	0.130352i
$373$	1.00836	+	1.74653i	0.0522109	+	0.0904320i	0.890950	−	0.454102i	$-0.150040\pi$
$373$	1.00836	+	1.74653i	0.0522109	+	0.0904320i	−0.838739	+	0.544534i	$0.816707\pi$
$374$	−4.40035	−	7.62164i	−0.227537	−	0.394105i
$375$	−20.6250	+	4.30763i	−1.06507	+	0.222445i
$376$	4.44794	+	2.56802i	0.229385	+	0.132436i
$377$	32.0921			1.65283
$378$	−11.2715	+	7.87111i	−0.579741	+	0.404846i
$379$	−18.8709			−0.969332			−0.484666	−	0.874699i	$-0.661059\pi$
$379$	−18.8709			−0.969332			−0.484666	+	0.874699i	$0.661059\pi$
$380$	4.67784	+	2.70075i	0.239968	+	0.138546i
$381$	2.37620	−	0.496282i	0.121737	−	0.0254253i
$382$	−4.62666	−	8.01361i	−0.236721	−	0.410012i
$383$	−0.418256	−	0.724440i	−0.0213719	−	0.0370172i	0.855142	−	0.518394i	$-0.173470\pi$
$383$	−0.418256	−	0.724440i	−0.0213719	−	0.0370172i	−0.876514	+	0.481377i	$0.840137\pi$
$384$	−1.64537	−	0.541068i	−0.0839650	−	0.0276113i
$385$	−5.60790	−	9.89714i	−0.285805	−	0.504405i
$386$			24.5602i			1.25008i
$387$	−2.33055	+	20.7572i	−0.118468	+	1.05515i
$388$			5.51087i			0.279772i
$389$	21.4964	+	12.4109i	1.08991	+	0.629260i	0.933552	−	0.358441i	$-0.116692\pi$
$389$	21.4964	+	12.4109i	1.08991	+	0.629260i	0.156357	+	0.987701i	$0.450025\pi$
$390$	10.1093	+	11.3078i	0.511903	+	0.572595i
$391$	11.9533	−	6.90127i	0.604507	−	0.349012i
$392$	6.00478	+	3.59758i	0.303287	+	0.181705i
$393$	−12.1117	−	13.5477i	−0.610954	−	0.683389i
$394$	6.24305	−	10.8133i	0.314520	−	0.544765i
$395$	5.43662			0.273546
$396$	−2.88361	−	6.60226i	−0.144907	−	0.331776i
$397$		−	3.03390i		−	0.152267i	−0.997098	−	0.0761336i	$-0.975742\pi$
$397$		−	3.03390i		−	0.152267i	0.997098	−	0.0761336i	$-0.0242575\pi$
$398$	−0.0895727	+	0.155144i	−0.00448987	+	0.00777669i
$399$	−9.13106	−	10.3814i	−0.457125	−	0.519719i
$400$	0.897324	+	1.55421i	0.0448662	+	0.0777105i
$401$	11.3251	−	6.53854i	0.565548	−	0.326519i	−0.189822	−	0.981819i	$-0.560791\pi$
$401$	11.3251	−	6.53854i	0.565548	−	0.326519i	0.755369	+	0.655300i	$0.227458\pi$
$402$	−0.201923	−	0.966808i	−0.0100710	−	0.0482200i
$403$	11.3640	−	19.6831i	0.566083	−	0.980485i
$404$	−0.250324			−0.0124541
$405$	−15.7120	−	3.57322i	−0.780733	−	0.177555i
$406$	14.9625	+	8.80071i	0.742578	+	0.436772i
$407$	−19.4750	−	11.2439i	−0.965339	−	0.557339i
$408$	1.29768	+	6.21332i	0.0642448	+	0.307605i
$409$	4.82124	−	2.78354i	0.238395	−	0.137637i	−0.376044	−	0.926602i	$-0.622716\pi$
$409$	4.82124	−	2.78354i	0.238395	−	0.137637i	0.614439	+	0.788965i	$0.289382\pi$
$410$	−12.5309	+	7.23469i	−0.618855	+	0.357296i
$411$	−7.76707	−	2.55414i	−0.383121	−	0.125987i
$412$	0.145433	+	0.0839657i	0.00716496	+	0.00413669i
$413$	−33.2728	−	19.5705i	−1.63725	−	0.963000i
$414$	10.3546	−	4.52249i	0.508901	−	0.222268i
$415$	25.0746			1.23086
$416$	2.44566	−	4.23601i	0.119908	−	0.207688i
$417$	−3.05223	+	2.72871i	−0.149468	+	0.133625i
$418$	6.27467	−	3.62268i	0.306904	−	0.177191i
$419$	8.19938	+	14.2017i	0.400566	+	0.693800i	0.993794	−	0.111234i	$-0.0354802\pi$
$419$	8.19938	+	14.2017i	0.400566	+	0.693800i	−0.593228	+	0.805034i	$0.702147\pi$
$420$	1.61234	+	8.04442i	0.0786742	+	0.392528i
$421$	−7.72892	+	13.3869i	−0.376684	+	0.652437i	−0.990578	−	0.136952i	$-0.956269\pi$
$421$	−7.72892	+	13.3869i	−0.376684	+	0.652437i	0.613893	+	0.789389i	$0.289603\pi$
$422$			15.1221i			0.736131i
$423$	1.71917	−	15.3119i	0.0835889	−	0.744491i
$424$		0			0
$425$	3.28839	−	5.69566i	0.159510	−	0.276280i
$426$	−3.22614	+	9.81058i	−0.156307	+	0.475324i
$427$	−29.9708	−	0.242361i	−1.45039	−	0.0117287i
$428$	6.92024	−	3.99540i	0.334502	−	0.193125i
$429$	19.9159	−	4.15953i	0.961547	−	0.200824i
$430$	10.7953	+	6.23269i	0.520597	+	0.300567i
$431$			25.0266i			1.20549i	0.797935	+	0.602744i	$0.205926\pi$
$431$			25.0266i			1.20549i	−0.797935	+	0.602744i	$0.794074\pi$
$432$	0.488168	+	5.17317i	0.0234870	+	0.248894i
$433$		−	2.25168i		−	0.108209i	−0.998535	−	0.0541044i	$-0.982770\pi$
$433$		−	2.25168i		−	0.108209i	0.998535	−	0.0541044i	$-0.0172304\pi$
$434$	10.6961	−	6.06059i	0.513428	−	0.290918i
$435$	4.15953	+	19.9159i	0.199434	+	0.954893i
$436$	−9.47667	−	16.4141i	−0.453850	−	0.786091i
$437$	5.68161	+	9.84084i	0.271788	+	0.470751i
$438$	6.69919	−	20.3720i	0.320099	−	0.973412i
$439$	16.2293	+	9.37000i	0.774583	+	0.447206i	0.834507	−	0.550997i	$-0.185752\pi$
$439$	16.2293	+	9.37000i	0.774583	+	0.447206i	−0.0599239	+	0.998203i	$0.519086\pi$
$440$	−4.29953			−0.204972
$441$	2.68027	−	20.8283i	0.127632	−	0.991822i
$442$	−17.9251			−0.852609
$443$	−1.04314	−	0.602256i	−0.0495610	−	0.0286141i	0.475015	−	0.879978i	$-0.342443\pi$
$443$	−1.04314	−	0.602256i	−0.0495610	−	0.0286141i	−0.524576	+	0.851364i	$0.675776\pi$
$444$	10.8098	+	12.0914i	0.513012	+	0.573835i
$445$	3.35568	+	5.81221i	0.159074	+	0.275525i
$446$	−4.19762	−	7.27049i	−0.198763	−	0.344268i
$447$	−22.4216	+	20.0450i	−1.06050	+	0.948097i
$448$	2.30191	−	1.30430i	0.108755	−	0.0616226i
$449$		−	26.8022i		−	1.26487i	−0.774612	−	0.632436i	$-0.782055\pi$
$449$		−	26.8022i		−	1.26487i	0.774612	−	0.632436i	$-0.217945\pi$
$450$	3.19540	−	4.33316i	0.150633	−	0.204267i
$451$			19.4087i			0.913918i
$452$	−1.00418	−	0.579764i	−0.0472327	−	0.0272698i
$453$	6.07770	−	18.4821i	0.285555	−	0.868364i
$454$	2.10030	−	1.21261i	0.0985719	−	0.0569105i
$455$	−23.1686	−	0.187354i	−1.08616	−	0.00878331i
$456$	−5.11524	+	1.06834i	−0.239543	+	0.0500298i
$457$	−6.92442	+	11.9934i	−0.323911	+	0.561030i	−0.981291	−	0.192529i	$-0.938331\pi$
$457$	−6.92442	+	11.9934i	−0.323911	+	0.561030i	0.657381	+	0.753559i	$0.271664\pi$
$458$	2.01975			0.0943766
$459$	15.5236	−	11.0283i	0.724578	−	0.514755i
$460$		−	6.74314i		−	0.314401i
$461$	2.40241	−	4.16110i	0.111892	−	0.193802i	−0.804641	−	0.593761i	$-0.797642\pi$
$461$	2.40241	−	4.16110i	0.111892	−	0.193802i	0.916533	+	0.399959i	$0.130976\pi$
$462$	10.4262	+	3.52225i	0.485070	+	0.163870i
$463$	10.5194	+	18.2201i	0.488877	+	0.846760i	0.999918	−	0.0127960i	$-0.00407321\pi$
$463$	10.5194	+	18.2201i	0.488877	+	0.846760i	−0.511041	+	0.859556i	$0.670740\pi$
$464$	5.68202	−	3.28052i	0.263781	−	0.152294i
$465$	13.6879	+	4.50118i	0.634763	+	0.208737i
$466$	−6.36446	+	11.0236i	−0.294828	+	0.510657i
$467$	5.82302			0.269457			0.134729	−	0.990883i	$-0.456984\pi$
$467$	5.82302			0.269457			0.134729	+	0.990883i	$0.456984\pi$
$468$	−14.5824	−	1.63726i	−0.674070	−	0.0756823i
$469$	1.30042	+	0.764885i	0.0600478	+	0.0353191i
$470$	−7.96337	−	4.59766i	−0.367323	−	0.212074i
$471$	17.8751	−	15.9804i	0.823640	−	0.736339i
$472$	−12.6353	+	7.29501i	−0.581588	+	0.335780i
$473$	14.4804	−	8.36028i	0.665811	−	0.384406i
$474$	−3.92109	+	3.50548i	−0.180101	+	0.161012i
$475$	4.68907	+	2.70724i	0.215149	+	0.124217i
$476$	−8.35733	−	4.91564i	−0.383057	−	0.225308i
$477$		0			0
$478$	17.4495			0.798121
$479$	13.4781	−	23.3447i	0.615828	−	1.06665i	−0.374411	−	0.927263i	$-0.622155\pi$
$479$	13.4781	−	23.3447i	0.615828	−	1.06665i	0.990239	−	0.139382i	$-0.0445117\pi$
$480$	2.94579	+	0.968701i	0.134456	+	0.0442150i
$481$	−39.6662	+	22.9013i	−1.80862	+	1.04421i
$482$	5.71659	+	9.90142i	0.260383	+	0.450997i
$483$	−5.52410	+	16.3518i	−0.251355	+	0.744035i
$484$	2.61639	−	4.53172i	0.118927	−	0.205987i
$485$		−	9.86639i		−	0.448010i
$486$	13.6360	−	7.55378i	0.618541	−	0.342646i
$487$	−13.6268			−0.617487			−0.308744	−	0.951145i	$-0.599909\pi$
$487$	−13.6268			−0.617487			−0.308744	+	0.951145i	$0.599909\pi$
$488$	−5.66414	+	9.81058i	−0.256404	+	0.444104i
$489$	−7.35116	+	1.53533i	−0.332431	+	0.0694299i
$490$	−10.7507	−	6.44093i	−0.485665	−	0.290971i
$491$	−33.7430	+	19.4815i	−1.52280	+	0.879188i	−0.523162	+	0.852234i	$0.675248\pi$
$491$	−33.7430	+	19.4815i	−1.52280	+	0.879188i	−0.999637	+	0.0269544i	$0.991419\pi$
$492$	4.37285	−	13.2977i	0.197143	−	0.599506i
$493$	−20.8227	−	12.0220i	−0.937807	−	0.541443i
$494$		−	14.7572i		−	0.663957i
$495$	5.16267	+	11.8203i	0.232045	+	0.531285i
$496$		−	4.64661i		−	0.208639i
$497$	−7.77696	−	13.7252i	−0.348844	−	0.615660i
$498$	−18.0847	+	16.1678i	−0.810393	+	0.724497i
$499$	−13.0048	−	22.5250i	−0.582176	−	1.00836i	−0.995221	−	0.0976483i	$-0.968868\pi$
$499$	−13.0048	−	22.5250i	−0.582176	−	1.00836i	0.413045	−	0.910711i	$-0.364465\pi$
$500$	−6.08240	−	10.5350i	−0.272013	−	0.471141i
$501$	−14.3320	−	16.0312i	−0.640307	−	0.716221i
$502$	−23.6910	−	13.6780i	−1.05738	−	0.610478i
$503$	10.5271			0.469378			0.234689	−	0.972070i	$-0.424593\pi$
$503$	10.5271			0.469378			0.234689	+	0.972070i	$0.424593\pi$
$504$	−6.34984	−	4.76230i	−0.282844	−	0.212130i
$505$	0.448168			0.0199432
$506$	−7.83319	−	4.52249i	−0.348228	−	0.201049i
$507$	5.91121	−	17.9758i	0.262526	−	0.798333i
$508$	0.700752	+	1.21374i	0.0310908	+	0.0538509i
$509$	0.469435	+	0.813086i	0.0208074	+	0.0360394i	0.876242	−	0.481872i	$-0.160043\pi$
$509$	0.469435	+	0.813086i	0.0208074	+	0.0360394i	−0.855434	+	0.517911i	$0.826710\pi$
$510$	−2.32330	−	11.1240i	−0.102878	−	0.492580i
$511$	16.1491	+	28.5009i	0.714395	+	1.26081i
$512$		−	1.00000i		−	0.0441942i
$513$	9.07925	+	12.7801i	0.400859	+	0.564255i
$514$			3.49673i			0.154234i
$515$	−0.260376	−	0.150328i	−0.0114735	−	0.00662424i
$516$	−11.8047	+	2.46548i	−0.519675	+	0.108537i
$517$	−10.6818	+	6.16711i	−0.469783	+	0.271229i
$518$	−24.7741	−	0.200338i	−1.08851	−	0.00880233i
$519$	9.42442	−	28.6593i	0.413686	−	1.25801i
$520$	−4.37859	+	7.58394i	−0.192014	+	0.332578i
$521$	−39.5054			−1.73076			−0.865382	−	0.501112i	$-0.832924\pi$
$521$	−39.5054			−1.73076			−0.865382	+	0.501112i	$0.832924\pi$
$522$	−15.8415	−	11.6820i	−0.693366	−	0.511308i
$523$		−	24.3292i		−	1.06384i	−0.846794	−	0.531922i	$-0.821470\pi$
$523$		−	24.3292i		−	1.06384i	0.846794	−	0.531922i	$-0.178530\pi$
$524$	5.24589	−	9.08614i	0.229168	−	0.396930i
$525$	1.61621	+	8.06374i	0.0705373	+	0.351930i
$526$	−4.82174	−	8.35150i	−0.210238	−	0.364143i
$527$	−14.7469	+	8.51413i	−0.642385	+	0.370881i
$528$	3.10098	−	2.77229i	0.134953	−	0.120649i
$529$	−4.40718	+	7.63346i	−0.191616	+	0.331889i
$530$		0			0
$531$	35.2274	+	25.9777i	1.52874	+	1.12734i
$532$	4.04690	−	6.88034i	0.175455	−	0.298301i
$533$	34.2349	+	19.7655i	1.48288	+	0.856141i
$534$	−6.16789	−	2.02826i	−0.266911	−	0.0877716i
$535$	−12.3896	+	7.15316i	−0.535651	+	0.309258i
$536$	0.493834	−	0.285115i	0.0213304	−	0.0123151i
$537$	4.64661	+	22.2480i	0.200516	+	0.960073i
$538$	−5.98517	−	3.45554i	−0.258039	−	0.148979i
$539$	−14.6924	+	8.16873i	−0.632845	+	0.351852i
$540$	−0.873992	−	9.26178i	−0.0376106	−	0.398564i
$541$	42.7281			1.83702			0.918512	−	0.395394i	$-0.129392\pi$
$541$	42.7281			1.83702			0.918512	+	0.395394i	$0.129392\pi$
$542$	−10.3156	+	17.8672i	−0.443093	+	0.767460i
$543$	4.73007	+	22.6476i	0.202987	+	0.971902i
$544$	−3.17369	+	1.83233i	−0.136071	+	0.0785606i
$545$	16.9665	+	29.3869i	0.726767	+	1.25880i
$546$	16.8308	−	14.8037i	0.720292	−	0.633541i
$547$	−12.2477	+	21.2136i	−0.523672	+	0.907026i	0.475949	+	0.879473i	$0.342105\pi$
$547$	−12.2477	+	21.2136i	−0.523672	+	0.907026i	−0.999620	+	0.0275530i	$0.991229\pi$
$548$		−	4.72056i		−	0.201652i
$549$	33.7727	+	3.79188i	1.44138	+	0.161833i
$550$	−4.30986			−0.183773
$551$	9.89735	−	17.1427i	0.421641	−	0.730304i
$552$	4.34791	+	4.86340i	0.185059	+	0.207000i
$553$	0.0649667	−	8.03389i	0.00276266	−	0.341636i
$554$	13.4358	−	7.75718i	0.570834	−	0.329571i
$555$	−19.3534	−	21.6479i	−0.821506	−	0.918903i
$556$	−2.04707	−	1.18187i	−0.0868150	−	0.0501227i
$557$			2.54431i			0.107806i	0.998546	+	0.0539030i	$0.0171662\pi$
$557$			2.54431i			0.107806i	−0.998546	+	0.0539030i	$0.982834\pi$
$558$	−12.7745	+	5.57943i	−0.540789	+	0.236196i
$559$		−	34.0560i		−	1.44042i
$560$	−4.12122	+	2.33516i	−0.174153	+	0.0986786i
$561$	−14.4804	−	4.76178i	−0.611364	−	0.201043i
$562$	6.79883	+	11.7759i	0.286791	+	0.496737i
$563$	−7.90707	−	13.6954i	−0.333243	−	0.577194i	0.649902	−	0.760018i	$-0.274810\pi$
$563$	−7.90707	−	13.6954i	−0.333243	−	0.577194i	−0.983146	+	0.182823i	$0.941476\pi$
$564$	8.70799	−	1.81871i	0.366673	−	0.0765814i
$565$	1.79783	+	1.03798i	0.0756354	+	0.0436681i
$566$	−5.44783			−0.228990
$567$	−5.46803	+	23.1754i	−0.229635	+	0.973277i
$568$	−5.96254			−0.250182
$569$	−5.52793	−	3.19155i	−0.231743	−	0.133797i	0.379633	−	0.925137i	$-0.376050\pi$
$569$	−5.52793	−	3.19155i	−0.231743	−	0.133797i	−0.611376	+	0.791340i	$0.709384\pi$
$570$	9.15807	−	1.91271i	0.383589	−	0.0801145i
$571$	3.91188	+	6.77557i	0.163707	+	0.283549i	0.936195	−	0.351480i	$-0.114322\pi$
$571$	3.91188	+	6.77557i	0.163707	+	0.283549i	−0.772488	+	0.635029i	$0.780988\pi$
$572$	5.87327	+	10.1728i	0.245574	+	0.425346i
$573$	−15.2252	−	5.00668i	−0.636040	−	0.209157i
$574$	10.5412	+	18.6038i	0.439982	+	0.776506i
$575$		−	6.75933i		−	0.281884i
$576$	−2.74922	+	1.20075i	−0.114551	+	0.0500313i
$577$			14.3197i			0.596138i	0.954544	+	0.298069i	$0.0963425\pi$
$577$			14.3197i			0.596138i	−0.954544	+	0.298069i	$0.903657\pi$
$578$	−3.09191	−	1.78512i	−0.128607	−	0.0742510i
$579$	28.3523	+	31.7137i	1.17828	+	1.31798i
$580$	−10.1728	+	5.87327i	−0.422403	+	0.243874i
$581$	0.299637	−	37.0536i	0.0124310	−	1.53724i
$582$	6.36175	+	7.11600i	0.263703	+	0.294968i
$583$		0			0
$584$	12.3814			0.512346
$585$	26.1075	+	2.93126i	1.07941	+	0.121193i
$586$			24.4622i			1.01053i
$587$	−2.37575	+	4.11492i	−0.0980577	+	0.169841i	−0.910881	−	0.412670i	$-0.864596\pi$
$587$	−2.37575	+	4.11492i	−0.0980577	+	0.169841i	0.812823	+	0.582511i	$0.197930\pi$
$588$	11.9068	−	2.28649i	0.491028	−	0.0942931i
$589$	−7.00943	−	12.1407i	−0.288819	−	0.500249i
$590$	22.6216	−	13.0606i	0.931318	−	0.537697i
$591$	−4.42141	−	21.1698i	−0.181873	−	0.870808i
$592$	−4.68202	+	8.10950i	−0.192430	+	0.333298i
$593$	3.58070			0.147042			0.0735208	−	0.997294i	$-0.476576\pi$
$593$	3.58070			0.147042			0.0735208	+	0.997294i	$0.476576\pi$
$594$	−11.3451	−	5.19642i	−0.465497	−	0.213212i
$595$	14.9625	+	8.80071i	0.613404	+	0.360794i
$596$	−15.0377	−	8.68202i	−0.615968	−	0.355629i
$597$	0.0634366	+	0.303735i	0.00259629	+	0.0124311i
$598$	−15.9544	+	9.21130i	−0.652426	+	0.376678i
$599$	−13.0471	+	7.53277i	−0.533091	+	0.307780i	−0.742274	−	0.670096i	$-0.766253\pi$
$599$	−13.0471	+	7.53277i	−0.533091	+	0.307780i	0.209183	+	0.977877i	$0.432920\pi$
$600$	2.95286	+	0.971027i	0.120550	+	0.0396420i
$601$	−19.8704	−	11.4722i	−0.810530	−	0.467960i	0.0366096	−	0.999330i	$-0.488344\pi$
$601$	−19.8704	−	11.4722i	−0.810530	−	0.467960i	−0.847140	+	0.531370i	$0.821678\pi$
$602$	9.33927	−	15.8782i	0.380640	−	0.647146i
$603$	−1.37682	−	1.01531i	−0.0560683	−	0.0413464i
$604$	11.2328			0.457055
$605$	−4.68425	+	8.11336i	−0.190442	+	0.329855i
$606$	−0.323235	+	0.288974i	−0.0131305	+	0.0117388i
$607$	21.2030	−	12.2416i	0.860605	−	0.496870i	−0.00360990	−	0.999993i	$-0.501149\pi$
$607$	21.2030	−	12.2416i	0.860605	−	0.496870i	0.864215	+	0.503123i	$0.167816\pi$
$608$	−1.50851	−	2.61281i	−0.0611780	−	0.105963i
$609$	29.4801	−	5.90869i	1.19459	−	0.239432i
$610$	10.1408	−	17.5644i	0.410589	−	0.711161i
$611$			25.1221i			1.01633i
$612$	8.84830	+	6.52499i	0.357671	+	0.263757i
$613$	−0.880086			−0.0355463			−0.0177732	−	0.999842i	$-0.505658\pi$
$613$	−0.880086			−0.0355463			−0.0177732	+	0.999842i	$0.505658\pi$
$614$	15.6111	−	27.0393i	0.630014	−	1.09122i
$615$	−7.82892	+	23.8075i	−0.315693	+	0.960011i
$616$	−0.0513786	+	6.35358i	−0.00207010	+	0.255993i
$617$	−11.7607	+	6.79005i	−0.473468	+	0.273357i	−0.717690	−	0.696362i	$-0.754801\pi$
$617$	−11.7607	+	6.79005i	−0.473468	+	0.273357i	0.244222	+	0.969719i	$0.421467\pi$
$618$	0.284722	−	0.0594656i	0.0114532	−	0.00239206i
$619$	−30.7325	−	17.7434i	−1.23524	−	0.713169i	−0.267126	−	0.963662i	$-0.586074\pi$
$619$	−30.7325	−	17.7434i	−1.23524	−	0.713169i	−0.968118	+	0.250493i	$0.919407\pi$
$620$			8.31905i			0.334101i
$621$	8.14977	−	17.7931i	0.327039	−	0.714012i
$622$		−	10.9100i		−	0.437452i
$623$	8.62901	−	4.88936i	0.345714	−	0.195888i
$624$	−1.73205	−	8.29308i	−0.0693375	−	0.331989i
$625$	6.40300	+	11.0903i	0.256120	+	0.443613i
$626$	1.71203	+	2.96532i	0.0684263	+	0.118518i
$627$	3.92024	−	11.9213i	0.156559	−	0.476091i
$628$	11.9885	+	6.92154i	0.478391	+	0.276199i
$629$	34.3161			1.36827
$630$	11.3684	+	8.52619i	0.452929	+	0.339692i
$631$	26.9822			1.07415			0.537073	−	0.843536i	$-0.319530\pi$
$631$	26.9822			1.07415			0.537073	+	0.843536i	$0.319530\pi$
$632$	−2.62979	−	1.51831i	−0.104608	−	0.0603952i
$633$	17.4569	+	19.5266i	0.693849	+	0.776112i
$634$	9.52357	+	16.4953i	0.378229	+	0.655112i
$635$	−1.25459	−	2.17302i	−0.0497869	−	0.0862335i
$636$		0			0
$637$	−0.553721	+	34.2348i	−0.0219392	+	1.35643i
$638$			15.7563i			0.623800i
$639$	7.15953	+	16.3923i	0.283227	+	0.648470i
$640$			1.79035i			0.0707698i
$641$	0.932777	+	0.538539i	0.0368425	+	0.0212710i	0.518308	−	0.855194i	$-0.326562\pi$
$641$	0.932777	+	0.538539i	0.0368425	+	0.0212710i	−0.481466	+	0.876465i	$0.659895\pi$
$642$	4.32357	−	13.1478i	0.170638	−	0.518903i
$643$	33.3126	−	19.2330i	1.31372	−	0.758477i	0.331010	−	0.943627i	$-0.392611\pi$
$643$	33.3126	−	19.2330i	1.31372	−	0.758477i	0.982710	+	0.185150i	$0.0592773\pi$
$644$	−9.96459	−	0.0805794i	−0.392660	−	0.00317527i
$645$	21.1346	−	4.41407i	0.832175	−	0.173804i
$646$	−5.52817	+	9.57507i	−0.217503	+	0.376726i
$647$	−8.95210			−0.351943			−0.175972	−	0.984395i	$-0.556307\pi$
$647$	−8.95210			−0.351943			−0.175972	+	0.984395i	$0.556307\pi$
$648$	6.60226	+	6.11639i	0.259361	+	0.240274i
$649$		−	35.0380i		−	1.37536i
$650$	−4.38910	+	7.60215i	−0.172155	+	0.298181i
$651$	6.81512	−	20.1734i	0.267106	−	0.790656i
$652$	−2.16789	−	3.75489i	−0.0849010	−	0.147053i
$653$	−9.85934	+	5.69229i	−0.385826	+	0.222757i	−0.680350	−	0.732887i	$-0.738172\pi$
$653$	−9.85934	+	5.69229i	−0.385826	+	0.222757i	0.294524	+	0.955644i	$0.404839\pi$
$654$	−31.1853	−	10.2550i	−1.21944	−	0.401004i
$655$	−9.39197	+	16.2674i	−0.366975	+	0.635619i
$656$	8.08188			0.315544
$657$	−14.8670	−	34.0392i	−0.580017	−	1.32799i
$658$	−6.88929	+	11.7128i	−0.268572	+	0.456614i
$659$	31.4373	+	18.1503i	1.22462	+	0.707036i	0.965900	−	0.258915i	$-0.0833650\pi$
$659$	31.4373	+	18.1503i	1.22462	+	0.707036i	0.258723	+	0.965952i	$0.416698\pi$
$660$	−5.55183	+	4.96337i	−0.216105	+	0.193199i
$661$	−31.2425	+	18.0379i	−1.21519	+	0.701593i	−0.963886	−	0.266315i	$-0.914194\pi$
$661$	−31.2425	+	18.0379i	−1.21519	+	0.701593i	−0.251308	+	0.967907i	$0.580861\pi$
$662$	−0.0634366	+	0.0366251i	−0.00246553	+	0.00142348i
$663$	−23.1460	+	20.6927i	−0.898916	+	0.803637i
$664$	−12.1290	−	7.00270i	−0.470698	−	0.271757i
$665$	−7.24536	+	12.3182i	−0.280963	+	0.477680i
$666$	27.9167	+	3.13439i	1.08175	+	0.121455i
$667$	−24.7114			−0.956828
$668$	6.20756	−	10.7518i	0.240178	−	0.416000i
$669$	−13.8133	−	4.54240i	−0.534052	−	0.175619i
$670$	−0.884136	+	0.510456i	−0.0341572	+	0.0197206i
$671$	−13.6025	−	23.5602i	−0.525117	−	0.909530i
$672$	1.46669	−	4.34152i	0.0565787	−	0.167478i
$673$	4.78512	−	8.28806i	0.184453	−	0.319481i	−0.758939	−	0.651161i	$-0.774282\pi$
$673$	4.78512	−	8.28806i	0.184453	−	0.319481i	0.943392	+	0.331680i	$0.107615\pi$
$674$			2.23278i			0.0860034i
$675$	−0.876091	−	9.28402i	−0.0337207	−	0.357342i
$676$	10.9251			0.420195
$677$	7.81408	−	13.5344i	0.300320	−	0.520169i	−0.675889	−	0.737004i	$-0.736240\pi$
$677$	7.81408	−	13.5344i	0.300320	−	0.520169i	0.976208	+	0.216835i	$0.0695733\pi$
$678$	−1.96594	+	0.410596i	−0.0755015	+	0.0157689i
$679$	−14.5799	−	0.117902i	−0.559526	−	0.00452465i
$680$	5.68202	−	3.28052i	0.217896	−	0.125802i
$681$	1.31221	−	3.99038i	0.0502839	−	0.152912i
$682$	9.66385	+	5.57943i	0.370048	+	0.213647i
$683$		−	11.1313i		−	0.425926i	−0.977060	−	0.212963i	$-0.931689\pi$
$683$		−	11.1313i		−	0.425926i	0.977060	−	0.212963i	$-0.0683114\pi$
$684$	−5.37184	+	7.28454i	−0.205397	+	0.278531i
$685$			8.45145i			0.322913i
$686$	−9.64646	+	15.8097i	−0.368304	+	0.603616i
$687$	2.60803	−	2.33159i	0.0995025	−	0.0889559i
$688$	−3.48127	−	6.02973i	−0.132722	−	0.229881i
$689$		0			0
$690$	−7.78428	−	8.70718i	−0.296342	−	0.331477i
$691$	2.61903	+	1.51210i	0.0996324	+	0.0575228i	0.548988	−	0.835830i	$-0.315013\pi$
$691$	2.61903	+	1.51210i	0.0996324	+	0.0575228i	−0.449356	+	0.893353i	$0.648346\pi$
$692$	17.4182			0.662139
$693$	17.5291	−	7.48782i	0.665874	−	0.284439i
$694$	31.8409			1.20867
$695$	3.66497	+	2.11597i	0.139020	+	0.0802633i
$696$	3.54997	−	10.7953i	0.134561	−	0.409196i
$697$	−14.8087	−	25.6494i	−0.560919	−	0.971540i
$698$	−7.36772	−	12.7613i	−0.278872	−	0.483021i
$699$	4.50739	+	21.5815i	0.170485	+	0.816286i
$700$	−4.13112	+	2.34077i	−0.156142	+	0.0884727i
$701$		−	50.1486i		−	1.89409i	−0.321103	−	0.947044i	$-0.604054\pi$
$701$		−	50.1486i		−	1.89409i	0.321103	−	0.947044i	$-0.395946\pi$
$702$	−20.7197	+	14.7197i	−0.782015	+	0.555560i
$703$			28.2514i			1.06552i
$704$	2.07976	+	1.20075i	0.0783840	+	0.0452550i
$705$	−15.5904	+	3.25612i	−0.587167	+	0.122633i
$706$	−1.87025	+	1.07979i	−0.0703876	+	0.0406383i
$707$	0.00535553	−	0.662274i	0.000201415	−	0.0249074i
$708$	−7.89419	+	24.0060i	−0.296682	+	0.902200i
$709$	1.80385	−	3.12436i	0.0677449	−	0.117338i	−0.830163	−	0.557520i	$-0.811753\pi$
$709$	1.80385	−	3.12436i	0.0677449	−	0.117338i	0.897908	+	0.440183i	$0.145086\pi$
$710$	10.6750			0.400626
$711$	−1.01644	+	9.05299i	−0.0381195	+	0.339514i
$712$		−	3.74863i		−	0.140486i
$713$	−8.75046	+	15.1562i	−0.327707	+	0.567605i
$714$	−16.4661	+	3.30030i	−0.616229	+	0.123511i
$715$	−10.5152	−	18.2129i	−0.393246	−	0.681123i
$716$	−11.3640	+	6.56103i	−0.424694	+	0.245197i
$717$	22.5319	−	20.1437i	0.841469	−	0.752279i
$718$	16.3224	−	28.2712i	0.609146	−	1.05507i
$719$	−34.3161			−1.27977			−0.639887	−	0.768469i	$-0.721019\pi$
$719$	−34.3161			−1.27977			−0.639887	+	0.768469i	$0.721019\pi$
$720$	4.92206	−	2.14977i	0.183434	−	0.0801171i
$721$	−0.225257	+	0.382970i	−0.00838899	+	0.0142626i
$722$	8.57161	+	4.94882i	0.319002	+	0.184176i
$723$	18.8118	+	6.18613i	0.699619	+	0.230065i
$724$	−11.5681	+	6.67887i	−0.429927	+	0.248218i
$725$	−10.1972	+	5.88737i	−0.378716	+	0.218651i
$726$	−1.85296	−	8.87200i	−0.0687698	−	0.329271i
$727$	19.4757	+	11.2443i	0.722315	+	0.417029i	0.815604	−	0.578610i	$-0.196405\pi$
$727$	19.4757	+	11.2443i	0.722315	+	0.417029i	−0.0932892	+	0.995639i	$0.529738\pi$
$728$	11.1547	+	6.56103i	0.413422	+	0.243168i
$729$	8.88761	−	25.4953i	0.329171	−	0.944270i
$730$	−22.1670			−0.820439
$731$	−12.7577	+	22.0970i	−0.471860	+	0.817285i
$732$	4.01142	+	19.2067i	0.148266	+	0.709901i
$733$	27.0065	−	15.5922i	0.997509	−	0.575912i	0.0899987	−	0.995942i	$-0.471314\pi$
$733$	27.0065	−	15.5922i	0.997509	−	0.575912i	0.907510	+	0.420030i	$0.137980\pi$
$734$	14.8501	+	25.7212i	0.548129	+	0.949387i
$735$	−21.3173	+	4.09361i	−0.786302	+	0.150995i
$736$	−1.88319	+	3.26178i	−0.0694154	+	0.120231i
$737$			1.36941i			0.0504429i
$738$	−9.70433	−	22.2188i	−0.357221	−	0.817886i
$739$	4.08628			0.150316			0.0751581	−	0.997172i	$-0.476054\pi$
$739$	4.08628			0.150316			0.0751581	+	0.997172i	$0.476054\pi$
$740$	8.38245	−	14.5188i	0.308145	−	0.533723i
$741$	−17.0357	−	19.0554i	−0.625821	−	0.700018i
$742$		0			0
$743$	−1.78246	+	1.02910i	−0.0653921	+	0.0377542i	−0.532340	−	0.846531i	$-0.678687\pi$
$743$	−1.78246	+	1.02910i	−0.0653921	+	0.0377542i	0.466947	+	0.884285i	$0.345354\pi$
$744$	−5.36404	−	6.00000i	−0.196655	−	0.219971i
$745$	26.9227	+	15.5439i	0.986373	+	0.569483i
$746$			2.01672i			0.0738374i
$747$	−4.68798	+	41.7538i	−0.171524	+	1.52769i
$748$		−	8.80071i		−	0.321786i
$749$	10.4224	+	18.3941i	0.380828	+	0.672106i
$750$	−20.0156	−	6.58198i	−0.730866	−	0.240340i
$751$	−11.9053	−	20.6205i	−0.434429	−	0.752454i	0.562820	−	0.826580i	$-0.309717\pi$
$751$	−11.9053	−	20.6205i	−0.434429	−	0.752454i	−0.997249	+	0.0741262i	$0.976383\pi$
$752$	2.56802	+	4.44794i	0.0936461	+	0.162200i
$753$	−46.3811	+	9.68693i	−1.69022	+	0.353011i
$754$	27.7926	+	16.0461i	1.01215	+	0.584363i
$755$	−20.1106			−0.731900
$756$	−13.6969	+	1.18085i	−0.498152	+	0.0429472i
$757$	10.0754			0.366197			0.183098	−	0.983095i	$-0.441387\pi$
$757$	10.0754			0.366197			0.183098	+	0.983095i	$0.441387\pi$
$758$	−16.3427	−	9.43544i	−0.593592	−	0.342711i
$759$	−15.3355	+	3.20289i	−0.556642	+	0.116258i
$760$	2.70075	+	4.67784i	0.0979666	+	0.169683i
$761$	13.9368	+	24.1392i	0.505207	+	0.875044i	0.999982	+	0.00602283i	$0.00191714\pi$
$761$	13.9368	+	24.1392i	0.505207	+	0.875044i	−0.494775	+	0.869021i	$0.664750\pi$
$762$	2.30599	+	0.758309i	0.0835374	+	0.0274707i
$763$	43.6289	−	24.7209i	1.57947	−	0.894957i
$764$		−	9.25333i		−	0.334774i
$765$	−15.8415	−	11.6820i	−0.572752	−	0.422364i
$766$		−	0.836511i		−	0.0302244i
$767$	−61.8035	−	35.6823i	−2.23159	−	1.28841i
$768$	−1.15440	−	1.29126i	−0.0416558	−	0.0465945i
$769$	−6.21166	+	3.58631i	−0.223998	+	0.129326i	−0.607800	−	0.794090i	$-0.707948\pi$
$769$	−6.21166	+	3.58631i	−0.223998	+	0.129326i	0.383802	+	0.923415i	$0.374615\pi$
$770$	0.0919857	−	11.3751i	0.00331494	−	0.409931i
$771$	4.03663	+	4.51521i	0.145376	+	0.162611i
$772$	−12.2801	+	21.2698i	−0.441970	+	0.765515i
$773$	−2.14153			−0.0770255			−0.0385128	−	0.999258i	$-0.512262\pi$
$773$	−2.14153			−0.0770255			−0.0385128	+	0.999258i	$0.512262\pi$
$774$	−12.3969	+	16.8110i	−0.445598	+	0.604258i
$775$			8.33903i			0.299547i
$776$	−2.75544	+	4.77256i	−0.0989144	+	0.171325i
$777$	−32.2212	+	28.3405i	−1.15593	+	1.01671i
$778$	12.4109	+	21.4964i	0.444954	+	0.770682i
$779$	21.1164	−	12.1916i	0.756573	−	0.436808i
$780$	3.10098	+	14.8475i	0.111033	+	0.531626i
$781$	7.15953	−	12.4007i	0.256188	−	0.443731i
$782$	13.8025			0.493578
$783$	−33.9413	+	3.20289i	−1.21296	+	0.114462i
$784$	3.40150	+	6.11799i	0.121482	+	0.218500i
$785$	−21.4635	−	12.3920i	−0.766066	−	0.442288i
$786$	−3.71521	−	17.7885i	−0.132517	−	0.634493i
$787$	15.8961	−	9.17759i	0.566633	−	0.327146i	−0.189170	−	0.981944i	$-0.560580\pi$
$787$	15.8961	−	9.17759i	0.566633	−	0.327146i	0.755804	+	0.654798i	$0.227247\pi$
$788$	10.8133	−	6.24305i	0.385207	−	0.222400i
$789$	−15.8671	−	5.21778i	−0.564884	−	0.185758i
$790$	4.70825	+	2.71831i	0.167512	+	0.0967131i
$791$	1.55534	−	2.64432i	0.0553017	−	0.0940212i
$792$	0.803848	−	7.15953i	0.0285635	−	0.254403i
$793$	−55.4103			−1.96768
$794$	1.51695	−	2.62744i	0.0538346	−	0.0932442i
$795$		0			0
$796$	−0.155144	+	0.0895727i	−0.00549895	+	0.00317482i
$797$	12.4226	+	21.5166i	0.440031	+	0.762156i	0.997691	−	0.0679130i	$-0.0216340\pi$
$797$	12.4226	+	21.5166i	0.440031	+	0.762156i	−0.557660	+	0.830069i	$0.688301\pi$
$798$	−2.71704	−	13.5561i	−0.0961822	−	0.479880i
$799$	9.41094	−	16.3002i	0.332935	−	0.576660i
$800$			1.79465i			0.0634504i
$801$	−10.3058	+	4.50118i	−0.364138	+	0.159041i
$802$	13.0771			0.461768
$803$	−14.8670	+	25.7504i	−0.524645	+	0.908712i
$804$	0.308534	−	0.938241i	0.0108811	−	0.0330892i
$805$	17.8401	+	0.144265i	0.628781	+	0.00508468i
$806$	19.6831	−	11.3640i	0.693307	−	0.400281i
$807$	−11.7175	+	2.44726i	−0.412475	+	0.0861475i
$808$	−0.216787	−	0.125162i	−0.00762654	−	0.00440319i
$809$			37.7861i			1.32849i	0.747516	+	0.664244i	$0.231246\pi$
$809$			37.7861i			1.32849i	−0.747516	+	0.664244i	$0.768754\pi$
$810$	−11.8203	−	10.9505i	−0.415325	−	0.384760i
$811$		−	36.5165i		−	1.28227i	−0.767429	−	0.641134i	$-0.778464\pi$
$811$		−	36.5165i		−	1.28227i	0.767429	−	0.641134i	$-0.221536\pi$
$812$	8.55758	+	15.1029i	0.300312	+	0.530008i
$813$	7.30565	+	34.9795i	0.256220	+	1.22679i
$814$	−11.2439	−	19.4750i	−0.394098	−	0.682598i
$815$	3.88128	+	6.72257i	0.135955	+	0.235481i
$816$	−1.98283	+	6.02973i	−0.0694131	+	0.211083i
$817$	−18.1918	−	10.5030i	−0.636449	−	0.367454i
$818$	5.56709			0.194649
$819$	4.64361	−	38.5450i	0.162261	−	1.34687i
$820$	−14.4694			−0.505293
$821$	−5.52142	−	3.18779i	−0.192699	−	0.111255i	0.400547	−	0.916276i	$-0.368820\pi$
$821$	−5.52142	−	3.18779i	−0.192699	−	0.111255i	−0.593245	+	0.805022i	$0.702154\pi$
$822$	−5.44941	−	6.09549i	−0.190070	−	0.212605i
$823$	−14.0293	−	24.2995i	−0.489032	−	0.847028i	0.510888	−	0.859647i	$-0.329317\pi$
$823$	−14.0293	−	24.2995i	−0.489032	−	0.847028i	−0.999920	+	0.0126187i	$0.995983\pi$
$824$	0.0839657	+	0.145433i	0.00292508	+	0.00506639i
$825$	−5.56516	+	4.97529i	−0.193754	+	0.173217i
$826$	−19.0298	−	33.5849i	−0.662132	−	1.16857i
$827$			0.581579i			0.0202235i	0.999949	+	0.0101117i	$0.00321872\pi$
$827$			0.581579i			0.0202235i	−0.999949	+	0.0101117i	$0.996781\pi$
$828$	11.2286	+	1.26071i	0.390221	+	0.0438127i
$829$		−	51.9246i		−	1.80342i	−0.432346	−	0.901708i	$-0.642314\pi$
$829$		−	51.9246i		−	1.80342i	0.432346	−	0.901708i	$-0.357686\pi$
$830$	21.7152	+	12.5373i	0.753746	+	0.435175i
$831$	8.39433	−	25.5269i	0.291196	−	0.885518i
$832$	4.23601	−	2.44566i	0.146857	−	0.0847881i
$833$	13.1839	−	22.0055i	0.456796	−	0.762446i
$834$	−4.00766	+	0.837019i	−0.138774	+	0.0289836i
$835$	−11.1137	+	19.2495i	−0.384606	+	0.666156i
$836$	7.24536			0.250586
$837$	−10.0544	+	21.9514i	−0.347532	+	0.758752i
$838$			16.3988i			0.566486i
$839$	−3.33038	+	5.76838i	−0.114977	+	0.199147i	−0.917771	−	0.397111i	$-0.870013\pi$
$839$	−3.33038	+	5.76838i	−0.114977	+	0.199147i	0.802793	+	0.596257i	$0.203346\pi$
$840$	−2.62588	+	7.77285i	−0.0906015	+	0.268189i
$841$	7.02357	+	12.1652i	0.242192	+	0.419489i
$842$	−13.3869	+	7.72892i	−0.461342	+	0.266356i
$843$	22.3732	+	7.35726i	0.770574	+	0.253397i
$844$	−7.56103	+	13.0961i	−0.260261	+	0.450786i
$845$	−19.5597			−0.672874
$846$	9.14481	−	12.4009i	0.314405	−	0.426353i
$847$	11.9334	+	7.01904i	0.410038	+	0.241177i
$848$		0			0
$849$	−7.03459	+	6.28897i	−0.241427	+	0.215837i
$850$	5.69566	−	3.28839i	0.195360	−	0.112791i
$851$	30.5435	−	17.6343i	1.04702	−	0.604495i
$852$	−7.69921	+	6.88314i	−0.263771	+	0.235813i
$853$	−19.2287	−	11.1017i	−0.658378	−	0.380115i	0.133281	−	0.991078i	$-0.457449\pi$
$853$	−19.2287	−	11.1017i	−0.658378	−	0.380115i	−0.791659	+	0.610964i	$0.790782\pi$
$854$	−25.8343	−	15.1953i	−0.884033	−	0.519973i
$855$	9.61746	−	13.0419i	0.328910	−	0.446023i
$856$	7.99080			0.273120
$857$	−7.64830	+	13.2472i	−0.261261	+	0.452517i	−0.966577	−	0.256375i	$-0.917472\pi$
$857$	−7.64830	+	13.2472i	−0.261261	+	0.452517i	0.705316	+	0.708893i	$0.250805\pi$
$858$	19.3274	+	6.35568i	0.659827	+	0.216979i
$859$	3.68620	−	2.12823i	0.125772	−	0.0726143i	−0.435794	−	0.900046i	$-0.643532\pi$
$859$	3.68620	−	2.12823i	0.125772	−	0.0726143i	0.561566	+	0.827432i	$0.310199\pi$
$860$	6.23269	+	10.7953i	0.212533	+	0.368118i
$861$	35.0877	+	11.8536i	1.19578	+	0.403969i
$862$	−12.5133	+	21.6737i	−0.426204	+	0.738208i
$863$			23.6624i			0.805476i	0.915315	+	0.402738i	$0.131941\pi$
$863$			23.6624i			0.805476i	−0.915315	+	0.402738i	$0.868059\pi$
$864$	−2.16382	+	4.72418i	−0.0736146	+	0.160720i
$865$	−31.1846			−1.06031
$866$	1.12584	−	1.95001i	0.0382576	−	0.0662641i
$867$	−6.05321	+	1.26424i	−0.205578	+	0.0429359i
$868$	12.2934	+	0.0994112i	0.417264	+	0.00337424i
$869$	6.31546	−	3.64623i	0.214237	−	0.123690i
$870$	−6.35568	+	19.3274i	−0.215478	+	0.655261i
$871$	2.41551	+	1.39459i	0.0818463	+	0.0472540i
$872$		−	18.9533i		−	0.641841i
$873$	16.4294	+	1.84464i	0.556051	+	0.0624315i
$874$			11.3632i			0.384367i
$875$	28.0023	−	15.8666i	0.946649	−	0.536389i
$876$	15.9877	−	14.2931i	0.540173	−	0.482918i
$877$	10.1962	+	17.6603i	0.344300	+	0.596344i	0.985226	−	0.171258i	$-0.0547831\pi$
$877$	10.1962	+	17.6603i	0.344300	+	0.596344i	−0.640927	+	0.767602i	$0.721450\pi$
$878$	9.37000	+	16.2293i	0.316222	+	0.547713i
$879$	28.2392	+	31.5872i	0.952484	+	1.06541i
$880$	−3.72350	−	2.14977i	−0.125519	−	0.0724686i
$881$	32.4586			1.09356			0.546780	−	0.837276i	$-0.315853\pi$
$881$	32.4586			1.09356			0.546780	+	0.837276i	$0.315853\pi$
$882$	12.7353	−	16.6977i	0.428820	−	0.562239i
$883$	−24.8311			−0.835632			−0.417816	−	0.908532i	$-0.637204\pi$
$883$	−24.8311			−0.835632			−0.417816	+	0.908532i	$0.637204\pi$
$884$	−15.5236	−	8.96254i	−0.522114	−	0.301443i
$885$	14.1334	−	42.9791i	0.475088	−	1.44473i
$886$	−0.602256	−	1.04314i	−0.0202332	−	0.0350449i
$887$	−4.86059	−	8.41879i	−0.163203	−	0.282675i	0.772813	−	0.634634i	$-0.218849\pi$
$887$	−4.86059	−	8.41879i	−0.163203	−	0.282675i	−0.936016	+	0.351959i	$0.885516\pi$
$888$	3.31587	+	15.8764i	0.111273	+	0.532778i
$889$	−3.22614	+	1.82799i	−0.108201	+	0.0613088i
$890$			6.71136i			0.224965i
$891$	−20.6483	+	6.38687i	−0.691745	+	0.213968i
$892$		−	8.39524i		−	0.281093i
$893$	13.4195	+	7.74775i	0.449066	+	0.259269i
$894$	−29.4402	+	6.14872i	−0.984626	+	0.205644i
$895$	20.3456	−	11.7465i	0.680079	−	0.392644i
$896$	2.64566	+	0.0213944i	0.0883855	+	0.000714735i
$897$	−9.96789	+	30.3120i	−0.332818	+	1.01209i
$898$	13.4011	−	23.2114i	0.447200	−	0.774573i
$899$	30.4865			1.01678
$900$	4.93388	−	2.15493i	0.164463	−	0.0718309i
$901$		0			0
$902$	−9.70433	+	16.8084i	−0.323119	+	0.559658i
$903$	−6.27028	−	31.2842i	−0.208662	−	1.04107i
$904$	−0.579764	−	1.00418i	−0.0192827	−	0.0333985i
$905$	20.7110	−	11.9575i	0.688458	−	0.397481i
$906$	14.5045	−	12.9671i	0.481879	−	0.430803i
$907$	8.04314	−	13.9311i	0.267068	−	0.462575i	−0.701035	−	0.713127i	$-0.747278\pi$
$907$	8.04314	−	13.9311i	0.267068	−	0.462575i	0.968103	+	0.250551i	$0.0806118\pi$
$908$	2.42522			0.0804836
$909$	−0.0837902	+	0.746284i	−0.00277915	+	0.0247527i
$910$	−19.9709	−	11.7465i	−0.662029	−	0.389394i
$911$	27.0087	+	15.5935i	0.894838	+	0.516635i	0.875522	−	0.483179i	$-0.160518\pi$
$911$	27.0087	+	15.5935i	0.894838	+	0.516635i	0.0193161	+	0.999813i	$0.493851\pi$
$912$	−4.96410	−	1.63241i	−0.164378	−	0.0540545i
$913$	29.1279	−	16.8170i	0.963993	−	0.556562i
$914$	−11.9934	+	6.92442i	−0.396708	+	0.229039i
$915$	−7.18184	−	34.3868i	−0.237424	−	1.13679i
$916$	1.74915	+	1.00987i	0.0577936	+	0.0333672i
$917$	23.9267	+	14.0733i	0.790128	+	0.464740i
$918$	18.9579	−	1.78897i	0.625705	−	0.0590449i
$919$	25.7664			0.849955			0.424977	−	0.905204i	$-0.360282\pi$
$919$	25.7664			0.849955			0.424977	+	0.905204i	$0.360282\pi$
$920$	3.37157	−	5.83973i	0.111157	−	0.192530i
$921$	−11.0560	−	52.9363i	−0.364308	−	1.74431i
$922$	4.16110	−	2.40241i	0.137039	−	0.0791193i
$923$	−14.5824	−	25.2574i	−0.479984	−	0.831357i
$924$	7.26822	+	8.26346i	0.239107	+	0.271848i
$925$	8.40258	−	14.5537i	0.276275	−	0.478522i
$926$			21.0388i			0.691377i
$927$	0.299004	−	0.405469i	0.00982060	−	0.0133173i
$928$	6.56103			0.215376
$929$	−27.3744	+	47.4138i	−0.898124	+	1.55560i	−0.0682329	+	0.997669i	$0.521736\pi$
$929$	−27.3744	+	47.4138i	−0.898124	+	1.55560i	−0.829891	+	0.557926i	$0.811597\pi$
$930$	9.60351	+	10.7421i	0.314911	+	0.352247i
$931$	18.1165	+	10.8539i	0.593744	+	0.355723i
$932$	−11.0236	+	6.36446i	−0.361089	+	0.208475i
$933$	−12.5945	−	14.0877i	−0.412326	−	0.461212i
$934$	5.04288	+	2.91151i	0.165008	+	0.0952675i
$935$			15.7563i			0.515288i
$936$	−11.8101	−	8.70908i	−0.386024	−	0.284665i
$937$			58.2065i			1.90152i	0.309924	+	0.950761i	$0.399696\pi$
$937$			58.2065i			1.90152i	−0.309924	+	0.950761i	$0.600304\pi$
$938$	0.743755	+	1.31262i	0.0242844	+	0.0428586i
$939$	5.63384	+	1.85265i	0.183853	+	0.0604588i
$940$	−4.59766	−	7.96337i	−0.149959	−	0.259737i
$941$	16.6658	+	28.8660i	0.543289	+	0.941005i	0.998712	+	0.0507297i	$0.0161547\pi$
$941$	16.6658	+	28.8660i	0.543289	+	0.941005i	−0.455423	+	0.890275i	$0.650512\pi$
$942$	23.4705	−	4.90192i	0.764709	−	0.159713i
$943$	−26.3613	−	15.2197i	−0.858443	−	0.495622i
$944$	−14.5900			−0.474864
$945$	24.5223	−	2.11414i	0.797710	−	0.0687730i
$946$	16.7206			0.543632
$947$	−6.59497	−	3.80761i	−0.214308	−	0.123731i	0.389004	−	0.921236i	$-0.372819\pi$
$947$	−6.59497	−	3.80761i	−0.214308	−	0.123731i	−0.603312	+	0.797505i	$0.706153\pi$
$948$	−5.14850	+	1.07529i	−0.167215	+	0.0349238i
$949$	30.2808	+	52.4478i	0.982955	+	1.70253i
$950$	2.70724	+	4.68907i	0.0878344	+	0.152134i
$951$	31.3396	+	10.3058i	1.01626	+	0.334188i
$952$	−4.77984	−	8.43573i	−0.154915	−	0.273404i
$953$			55.7861i			1.80709i	0.428495	+	0.903544i	$0.359044\pi$
$953$			55.7861i			1.80709i	−0.428495	+	0.903544i	$0.640956\pi$
$954$		0			0
$955$			16.5667i			0.536085i
$956$	15.1117	+	8.72474i	0.488747	+	0.282178i
$957$	18.1891	+	20.3456i	0.587970	+	0.657680i
$958$	23.3447	−	13.4781i	0.754232	−	0.435456i
$959$	12.4890	+	0.100993i	0.403291	+	0.00326125i
$960$	2.06678	+	2.31181i	0.0667050	+	0.0746135i
$961$	−4.70451	+	8.14845i	−0.151758	+	0.262853i
$962$	−45.8026			−1.47673
$963$	−9.59497	−	21.9684i	−0.309194	−	0.707923i
$964$			11.4332i			0.368238i
$965$	21.9857	−	38.0803i	0.707744	−	1.22585i
$966$	−12.9599	+	11.3991i	−0.416979	+	0.366759i
$967$	−13.3369	−	23.1003i	−0.428887	−	0.742855i	0.567887	−	0.823106i	$-0.307761\pi$
$967$	−13.3369	−	23.1003i	−0.428887	−	0.742855i	−0.996775	+	0.0802517i	$0.974428\pi$
$968$	4.53172	−	2.61639i	0.145655	−	0.0840939i
$969$	3.91512	+	18.7456i	0.125772	+	0.602197i
$970$	4.93320	−	8.54455i	0.158395	−	0.274349i
$971$	−8.59942			−0.275968			−0.137984	−	0.990434i	$-0.544062\pi$
$971$	−8.59942			−0.275968			−0.137984	+	0.990434i	$0.544062\pi$
$972$	15.5860	+	0.276237i	0.499921	+	0.00886031i
$973$	3.17064	−	5.39057i	0.101646	−	0.172814i
$974$	−11.8011	−	6.81338i	−0.378132	−	0.218315i
$975$	3.10842	+	14.8832i	0.0995492	+	0.476643i
$976$	−9.81058	+	5.66414i	−0.314029	+	0.181305i
$977$	−12.7973	+	7.38854i	−0.409423	+	0.236380i	−0.690542	−	0.723293i	$-0.742628\pi$
$977$	−12.7973	+	7.38854i	−0.409423	+	0.236380i	0.281119	+	0.959673i	$0.409295\pi$
$978$	−7.13396	−	2.34595i	−0.228119	−	0.0750152i
$979$	7.79627	+	4.50118i	0.249170	+	0.143858i
$980$	−6.08988	−	10.9533i	−0.194534	−	0.349891i
$981$	−52.1068	+	22.7583i	−1.66364	+	0.726615i
$982$	−38.9630			−1.24336
$983$	10.2568	−	17.7652i	0.327140	−	0.566623i	−0.654803	−	0.755800i	$-0.727248\pi$
$983$	10.2568	−	17.7652i	0.327140	−	0.566623i	0.981943	+	0.189176i	$0.0605818\pi$
$984$	10.4358	−	9.32971i	0.332682	−	0.297420i
$985$	−19.3596	+	11.1772i	−0.616847	+	0.356137i
$986$	−12.0220	−	20.8227i	−0.382858	−	0.663130i
$987$	4.62539	+	23.0773i	0.147228	+	0.734560i
$988$	7.37859	−	12.7801i	0.234744	−	0.406589i
$989$			26.2236i			0.833861i
$990$	−1.43917	+	12.8181i	−0.0457398	+	0.407385i
$991$	−9.29294			−0.295200			−0.147600	−	0.989047i	$-0.547155\pi$
$991$	−9.29294			−0.295200			−0.147600	+	0.989047i	$0.547155\pi$
$992$	2.32330	−	4.02408i	0.0737650	−	0.127765i
$993$	−0.0396334	+	0.120524i	−0.00125773	+	0.00382471i
$994$	0.127565	−	15.7749i	0.00404610	−	0.500349i
$995$	0.277763	−	0.160366i	0.00880567	−	0.00508396i
$996$	−23.7457	+	4.95940i	−0.752411	+	0.157145i
$997$	−0.0172917	−	0.00998339i	−0.000547635	−	0.000316177i	0.499726	−	0.866183i	$-0.333434\pi$
$997$	−0.0172917	−	0.00998339i	−0.000547635	−	0.000316177i	−0.500274	+	0.865867i	$0.666767\pi$
$998$		−	26.0097i		−	0.823322i
$999$	39.6662	−	28.1797i	1.25498	−	0.891566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.m.a.83.8	yes	16
3.2	odd	2		378.2.m.a.251.4		16
4.3	odd	2		1008.2.cc.b.209.1		16
7.2	even	3		882.2.l.a.227.2		16
7.3	odd	6		882.2.t.b.803.3		16
7.4	even	3		882.2.t.b.803.2		16
7.5	odd	6		882.2.l.a.227.3		16
7.6	odd	2	inner	126.2.m.a.83.5	yes	16
9.2	odd	6		1134.2.d.a.1133.11		16
9.4	even	3		378.2.m.a.125.1		16
9.5	odd	6	inner	126.2.m.a.41.5	✓	16
9.7	even	3		1134.2.d.a.1133.6		16
12.11	even	2		3024.2.cc.b.2897.6		16
21.2	odd	6		2646.2.l.b.521.8		16
21.5	even	6		2646.2.l.b.521.5		16
21.11	odd	6		2646.2.t.a.1979.5		16
21.17	even	6		2646.2.t.a.1979.8		16
21.20	even	2		378.2.m.a.251.1		16
28.27	even	2		1008.2.cc.b.209.8		16
36.23	even	6		1008.2.cc.b.545.8		16
36.31	odd	6		3024.2.cc.b.881.3		16
63.4	even	3		2646.2.l.b.1097.1		16
63.5	even	6		882.2.t.b.815.2		16
63.13	odd	6		378.2.m.a.125.4		16
63.20	even	6		1134.2.d.a.1133.14		16
63.23	odd	6		882.2.t.b.815.3		16
63.31	odd	6		2646.2.l.b.1097.4		16
63.32	odd	6		882.2.l.a.509.7		16
63.34	odd	6		1134.2.d.a.1133.3		16
63.40	odd	6		2646.2.t.a.2285.5		16
63.41	even	6	inner	126.2.m.a.41.8	yes	16
63.58	even	3		2646.2.t.a.2285.8		16
63.59	even	6		882.2.l.a.509.6		16
84.83	odd	2		3024.2.cc.b.2897.3		16
252.139	even	6		3024.2.cc.b.881.6		16
252.167	odd	6		1008.2.cc.b.545.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.5	✓	16	9.5	odd	6	inner
126.2.m.a.41.8	yes	16	63.41	even	6	inner
126.2.m.a.83.5	yes	16	7.6	odd	2	inner
126.2.m.a.83.8	yes	16	1.1	even	1	trivial
378.2.m.a.125.1		16	9.4	even	3
378.2.m.a.125.4		16	63.13	odd	6
378.2.m.a.251.1		16	21.20	even	2
378.2.m.a.251.4		16	3.2	odd	2
882.2.l.a.227.2		16	7.2	even	3
882.2.l.a.227.3		16	7.5	odd	6
882.2.l.a.509.6		16	63.59	even	6
882.2.l.a.509.7		16	63.32	odd	6
882.2.t.b.803.2		16	7.4	even	3
882.2.t.b.803.3		16	7.3	odd	6
882.2.t.b.815.2		16	63.5	even	6
882.2.t.b.815.3		16	63.23	odd	6
1008.2.cc.b.209.1		16	4.3	odd	2
1008.2.cc.b.209.8		16	28.27	even	2
1008.2.cc.b.545.1		16	252.167	odd	6
1008.2.cc.b.545.8		16	36.23	even	6
1134.2.d.a.1133.3		16	63.34	odd	6
1134.2.d.a.1133.6		16	9.7	even	3
1134.2.d.a.1133.11		16	9.2	odd	6
1134.2.d.a.1133.14		16	63.20	even	6
2646.2.l.b.521.5		16	21.5	even	6
2646.2.l.b.521.8		16	21.2	odd	6
2646.2.l.b.1097.1		16	63.4	even	3
2646.2.l.b.1097.4		16	63.31	odd	6
2646.2.t.a.1979.5		16	21.11	odd	6
2646.2.t.a.1979.8		16	21.17	even	6
2646.2.t.a.2285.5		16	63.40	odd	6
2646.2.t.a.2285.8		16	63.58	even	3
3024.2.cc.b.881.3		16	36.31	odd	6
3024.2.cc.b.881.6		16	252.139	even	6
3024.2.cc.b.2897.3		16	84.83	odd	2
3024.2.cc.b.2897.6		16	12.11	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.69547 - 0.354107i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.895175 - 1.55049i) q^{5} +(1.64537 + 0.541068i) q^{6} +(-2.30191 + 1.30430i) q^{7} +1.00000i q^{8} +(2.74922 - 1.20075i) q^{9} -1.79035i q^{10} +(-2.07976 - 1.20075i) q^{11} +(1.15440 + 1.29126i) q^{12} +(-4.23601 + 2.44566i) q^{13} +(-2.64566 - 0.0213944i) q^{14} +(-2.06678 - 2.31181i) q^{15} +(-0.500000 + 0.866025i) q^{16} +3.66466 q^{17} +(2.98127 + 0.334727i) q^{18} +3.01701i q^{19} +(0.895175 - 1.55049i) q^{20} +(-3.44095 + 3.02653i) q^{21} +(-1.20075 - 2.07976i) q^{22} +(3.26178 - 1.88319i) q^{23} +(0.354107 + 1.69547i) q^{24} +(0.897324 - 1.55421i) q^{25} -4.89133 q^{26} +(4.23601 - 3.00935i) q^{27} +(-2.28052 - 1.34136i) q^{28} +(-5.68202 - 3.28052i) q^{29} +(-0.633975 - 3.03548i) q^{30} +(-4.02408 + 2.32330i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.95136 - 1.29938i) q^{33} +(3.17369 + 1.83233i) q^{34} +(4.08292 + 2.40150i) q^{35} +(2.41449 + 1.78052i) q^{36} +9.36404 q^{37} +(-1.50851 + 2.61281i) q^{38} +(-6.31599 + 5.64654i) q^{39} +(1.55049 - 0.895175i) q^{40} +(-4.04094 - 6.99911i) q^{41} +(-4.49321 + 0.900574i) q^{42} +(-3.48127 + 6.02973i) q^{43} -2.40150i q^{44} +(-4.32278 - 3.18775i) q^{45} +3.76638 q^{46} +(2.56802 - 4.44794i) q^{47} +(-0.541068 + 1.64537i) q^{48} +(3.59758 - 6.00478i) q^{49} +(1.55421 - 0.897324i) q^{50} +(6.21332 - 1.29768i) q^{51} +(-4.23601 - 2.44566i) q^{52} +(5.17317 - 0.488168i) q^{54} +4.29953i q^{55} +(-1.30430 - 2.30191i) q^{56} +(1.06834 + 5.11524i) q^{57} +(-3.28052 - 5.68202i) q^{58} +(7.29501 + 12.6353i) q^{59} +(0.968701 - 2.94579i) q^{60} +(9.81058 + 5.66414i) q^{61} -4.64661 q^{62} +(-4.76230 + 6.34984i) q^{63} -1.00000 q^{64} +(7.58394 + 4.37859i) q^{65} +(-2.77229 - 3.10098i) q^{66} +(-0.285115 - 0.493834i) q^{67} +(1.83233 + 3.17369i) q^{68} +(4.86340 - 4.34791i) q^{69} +(2.33516 + 4.12122i) q^{70} +5.96254i q^{71} +(1.20075 + 2.74922i) q^{72} -12.3814i q^{73} +(8.10950 + 4.68202i) q^{74} +(0.971027 - 2.95286i) q^{75} +(-2.61281 + 1.50851i) q^{76} +(6.35358 + 0.0513786i) q^{77} +(-8.29308 + 1.73205i) q^{78} +(-1.51831 + 2.62979i) q^{79} +1.79035 q^{80} +(6.11639 - 6.60226i) q^{81} -8.08188i q^{82} +(-7.00270 + 12.1290i) q^{83} +(-4.34152 - 1.46669i) q^{84} +(-3.28052 - 5.68202i) q^{85} +(-6.02973 + 3.48127i) q^{86} +(-10.7953 - 3.54997i) q^{87} +(1.20075 - 2.07976i) q^{88} -3.74863 q^{89} +(-2.14977 - 4.92206i) q^{90} +(6.56103 - 11.1547i) q^{91} +(3.26178 + 1.88319i) q^{92} +(-6.00000 + 5.36404i) q^{93} +(4.44794 - 2.56802i) q^{94} +(4.67784 - 2.70075i) q^{95} +(-1.29126 + 1.15440i) q^{96} +(4.77256 + 2.75544i) q^{97} +(6.11799 - 3.40150i) q^{98} +(-7.15953 - 0.803848i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{7} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 8 q^{16} - 12 q^{18} + 18 q^{21} - 48 q^{23} - 8 q^{25} + 4 q^{28} - 12 q^{29} - 24 q^{30} + 12 q^{36} - 8 q^{37} - 36 q^{39} - 12 q^{42} + 4 q^{43}+ \cdots - 72 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 8 * q^16 - 12 * q^18 + 18 * q^21 - 48 * q^23 - 8 * q^25 + 4 * q^28 - 12 * q^29 - 24 * q^30 + 12 * q^36 - 8 * q^37 - 36 * q^39 - 12 * q^42 + 4 * q^43 + 24 * q^46 - 8 * q^49 + 60 * q^50 + 12 * q^51 - 6 * q^56 + 48 * q^57 - 12 * q^58 + 24 * q^60 + 24 * q^63 - 16 * q^64 + 84 * q^65 - 28 * q^67 + 36 * q^74 + 78 * q^77 - 24 * q^78 - 4 * q^79 + 36 * q^81 + 18 * q^84 - 12 * q^85 - 24 * q^86 + 24 * q^91 - 48 * q^92 - 96 * q^93 + 12 * q^95 - 72 * q^99

Introduction

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