LMFDB - Embedded newform 126.2.m.a.41.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(41,126)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			41.5
Root			$1.69547 + 0.354107i$ of defining polynomial
Character	$\chi$	$=$	126.41
Dual form			126.2.m.a.83.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-1.69547 - 0.354107i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.895175 - 1.55049i) q^{5} +(-1.64537 + 0.541068i) q^{6} +(0.0213944 - 2.64566i) q^{7} -1.00000i q^{8} +(2.74922 + 1.20075i) q^{9} +O(q^{10})$	\(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} +(0.0213944 - 2.64566i) 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} +(-1.30430 - 2.30191i) 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} +(-0.973121 + 4.47806i) 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} +(1.39628 + 4.36468i) 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} +(-6.99908 - 0.113205i) 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} +(-2.64566 - 0.0213944i) 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} +(3.23561 - 7.24782i) 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} +(-4.73667 - 0.0383034i) 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} +(3.13229 + 5.52805i) 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} +(3.39155 + 3.08178i) 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}+O(q^{10}) $ 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	$-0.702227\pi$
$5$	0.895175	−	1.55049i	0.400334	−	0.693399i	0.993766	+	0.111485i	$0.0355607\pi$
$6$	−1.64537	+	0.541068i	−0.671720	+	0.220890i
$7$	0.0213944	−	2.64566i	0.00808631	−	0.999967i
$7$	0.0213944	−	2.64566i	0.00808631	−	0.999967i
$8$		−	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	−0.779617	−	0.626256i	$-0.784586\pi$
$11$	−2.07976	+	1.20075i	−0.627072	+	0.362040i	0.152545	+	0.988297i	$0.451253\pi$
$12$	−1.15440	+	1.29126i	−0.333246	+	0.372756i
$13$	4.23601	+	2.44566i	1.17486	+	0.678305i	0.954820	−	0.297186i	$-0.0960482\pi$
$13$	4.23601	+	2.44566i	1.17486	+	0.678305i	0.220039	+	0.975491i	$0.429382\pi$
$14$	−1.30430	−	2.30191i	−0.348590	−	0.615211i
$15$	−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	$-0.646585\pi$
$17$	−3.66466			−0.888812			−0.444406	+	0.895826i	$0.646585\pi$
$18$	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
$21$	−0.973121	+	4.47806i	−0.212352	+	0.977193i
$22$	−1.20075	+	2.07976i	−0.256001	+	0.443407i
$23$	3.26178	+	1.88319i	0.680129	+	0.392673i	0.799904	−	0.600128i	$-0.204884\pi$
$23$	3.26178	+	1.88319i	0.680129	+	0.392673i	−0.119775	+	0.992801i	$0.538217\pi$
$24$	−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	−0.924080	−	0.382200i	$-0.875167\pi$
$29$	−5.68202	+	3.28052i	−1.05512	+	0.609176i	−0.131045	+	0.991376i	$0.541833\pi$
$30$	−0.633975	+	3.03548i	−0.115747	+	0.554200i
$31$	4.02408	+	2.32330i	0.722746	+	0.417278i	0.815763	−	0.578387i	$-0.196318\pi$
$31$	4.02408	+	2.32330i	0.722746	+	0.417278i	−0.0930163	+	0.995665i	$0.529651\pi$
$32$	−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	−0.356241	−	0.934394i	$-0.615942\pi$
$41$	4.04094	−	6.99911i	0.631088	−	1.09308i	0.987330	−	0.158683i	$-0.0507248\pi$
$42$	1.39628	+	4.36468i	0.215451	+	0.673484i
$43$	−3.48127	−	6.02973i	−0.530888	−	0.919526i	−0.999350	−	0.0360419i	$-0.988525\pi$
$43$	−3.48127	−	6.02973i	−0.530888	−	0.919526i	0.468462	−	0.883484i	$-0.344808\pi$
$44$			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	$-0.288881\pi$
$47$	−2.56802	−	4.44794i	−0.374584	−	0.648799i	−0.990265	+	0.139197i	$0.955548\pi$
$48$	0.541068	+	1.64537i	0.0780965	+	0.237489i
$49$	−6.99908	−	0.113205i	−0.999869	−	0.0161721i
$50$	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
$56$	−2.64566	−	0.0213944i	−0.353542	−	0.00285894i
$57$	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	−0.203735	+	0.979026i	$0.565308\pi$
$59$	−7.29501	+	12.6353i	−0.949729	+	1.64498i	−0.745994	+	0.665953i	$0.768025\pi$
$60$	0.968701	+	2.94579i	0.125059	+	0.380300i
$61$	−9.81058	+	5.66414i	−1.25612	+	0.725219i	−0.972317	−	0.233665i	$-0.924928\pi$
$61$	−9.81058	+	5.66414i	−1.25612	+	0.725219i	−0.283799	+	0.958884i	$0.591595\pi$
$62$	4.64661			0.590120
$63$	3.23561	−	7.24782i	0.407648	−	0.913139i
$64$	−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	−0.882916	−	0.469531i	$-0.844423\pi$
$67$	−0.285115	+	0.493834i	−0.0348324	+	0.0603315i	0.848084	+	0.529862i	$0.177756\pi$
$68$	−1.83233	+	3.17369i	−0.222203	+	0.384867i
$69$	−4.86340	−	4.34791i	−0.585484	−	0.523427i
$70$	−4.73667	−	0.0383034i	−0.566140	−	0.00457813i
$71$		−	5.96254i		−	0.707623i	−0.935317	−	0.353811i	$-0.884885\pi$
$71$		−	5.96254i		−	0.707623i	0.935317	−	0.353811i	$-0.115115\pi$
$72$	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
$77$	3.13229	+	5.52805i	0.356958	+	0.629979i
$78$	−8.29308	−	1.73205i	−0.939007	−	0.196116i
$79$	−1.51831	−	2.62979i	−0.170824	−	0.295875i	0.767884	−	0.640588i	$-0.221309\pi$
$79$	−1.51831	−	2.62979i	−0.170824	−	0.295875i	−0.938708	+	0.344713i	$0.887976\pi$
$80$	−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	0.938297	+	0.345830i	$0.112403\pi$
$83$	7.00270	+	12.1290i	0.768646	+	1.33133i	−0.169651	+	0.985504i	$0.554264\pi$
$84$	3.39155	+	3.08178i	0.370049	+	0.336250i
$85$	−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	$-0.436336\pi$
$89$	3.74863			0.397354			0.198677	+	0.980065i	$0.436336\pi$
$90$	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	$-0.756926\pi$
$97$	−4.77256	+	2.75544i	−0.484580	+	0.279772i	0.237743	+	0.971328i	$0.423592\pi$
$98$	−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	$-0.162702\pi$
$101$	0.125162	+	0.216787i	0.0124541	+	0.0215711i	−0.859731	+	0.510747i	$0.829369\pi$
$102$	6.02973	−	1.98283i	0.597033	−	0.196330i
$103$	−0.145433	−	0.0839657i	−0.0143299	−	0.00827339i	0.492818	−	0.870132i	$-0.335967\pi$
$103$	−0.145433	−	0.0839657i	−0.0143299	−	0.00827339i	−0.507148	+	0.861859i	$0.669300\pi$
$104$	2.44566	−	4.23601i	0.239817	−	0.415375i
$105$	6.07207	+	5.51746i	0.592573	+	0.538449i
$106$		0			0
$107$			7.99080i			0.772500i	0.922394	+	0.386250i	$0.126230\pi$
$107$			7.99080i			0.772500i	−0.922394	+	0.386250i	$0.873770\pi$
$108$	−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
$112$	−2.30191	+	1.30430i	−0.217510	+	0.123245i
$113$	−1.00418	−	0.579764i	−0.0944653	−	0.0545396i	0.452023	−	0.892006i	$-0.350702\pi$
$113$	−1.00418	−	0.579764i	−0.0944653	−	0.0545396i	−0.546488	+	0.837467i	$0.684036\pi$
$114$	−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
$119$	−0.0784032	+	9.69548i	−0.00718721	+	0.888783i
$120$	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
$126$	−0.821792	−	7.89460i	−0.0732111	−	0.703307i
$127$	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	$-0.681779\pi$
$131$	5.24589	−	9.08614i	0.458335	−	0.793860i	0.998873	+	0.0474597i	$0.0151126\pi$
$132$	0.850388	−	4.07167i	0.0740168	−	0.354393i
$133$	7.98200	+	0.0645470i	0.692127	+	0.00559694i
$134$			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	−0.664365	−	0.747409i	$-0.731298\pi$
$137$	−4.08812	+	2.36028i	−0.349272	+	0.201652i	0.315093	+	0.949061i	$0.397964\pi$
$138$	−6.38578	−	1.33370i	−0.543594	−	0.113532i
$139$	2.04707	+	1.18187i	0.173630	+	0.100245i	0.584296	−	0.811540i	$-0.301371\pi$
$139$	2.04707	+	1.18187i	0.173630	+	0.100245i	−0.410666	+	0.911786i	$0.634704\pi$
$140$	−4.12122	+	2.33516i	−0.348307	+	0.197357i
$141$	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
$147$	11.8266	+	2.67036i	0.975444	+	0.220247i
$148$	4.68202	−	8.10950i	0.384860	−	0.666597i
$149$	−15.0377	−	8.68202i	−1.23194	−	0.711259i	−0.264503	−	0.964385i	$-0.585208\pi$
$149$	−15.0377	−	8.68202i	−1.23194	−	0.711259i	−0.967433	+	0.253126i	$0.918541\pi$
$150$	−2.31737	−	2.07174i	−0.189212	−	0.169157i
$151$	5.61639	+	9.72787i	0.457055	+	0.791643i	0.998804	−	0.0488977i	$-0.0155708\pi$
$151$	5.61639	+	9.72787i	0.457055	+	0.791643i	−0.541749	+	0.840541i	$0.682238\pi$
$152$	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	$-0.519621\pi$
$157$	−11.9885	−	6.92154i	−0.956783	−	0.552399i	−0.895181	+	0.445702i	$0.852954\pi$
$158$	−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	$-0.673841\pi$
$167$	6.20756	−	10.7518i	0.480355	−	0.832000i	0.999746	+	0.0225370i	$0.00717435\pi$
$168$	4.47806	+	0.973121i	0.345490	+	0.0750779i
$169$	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	−0.980052	−	0.198739i	$-0.936315\pi$
$173$	−8.70908	−	15.0846i	−0.662139	−	1.14686i	0.317913	−	0.948120i	$-0.397018\pi$
$174$	7.57405	−	8.47203i	0.574187	−	0.642263i
$175$	4.13112	−	2.34077i	0.312283	−	0.176945i
$176$	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	$-0.836853\pi$
$179$		−	13.1221i		−	0.980789i	0.871501	−	0.490395i	$-0.163147\pi$
$180$	−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	$0.834641\pi$
$182$	0.104647	−	12.9408i	0.00775694	−	0.959237i
$183$	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
$189$	−8.05236	+	11.1427i	−0.585723	+	0.810511i
$190$	5.40150			0.391866
$191$	−8.01361	+	4.62666i	−0.579845	+	0.334774i	−0.761072	−	0.648668i	$-0.775326\pi$
$191$	−8.01361	+	4.62666i	−0.579845	+	0.334774i	0.181227	+	0.983441i	$0.441993\pi$
$192$	1.69547	+	0.354107i	0.122360	+	0.0255554i
$193$	12.2801	−	21.2698i	0.883941	−	1.53103i	0.0370176	−	0.999315i	$-0.488214\pi$
$193$	12.2801	−	21.2698i	0.883941	−	1.53103i	0.846923	−	0.531716i	$-0.178452\pi$
$194$	−2.75544	+	4.77256i	−0.197829	+	0.342650i
$195$	−14.4088	+	4.73823i	−1.03184	+	0.339312i
$196$	−3.59758	+	6.00478i	−0.256970	+	0.428913i
$197$			12.4861i			0.889598i	0.895630	+	0.444799i	$0.146725\pi$
$197$			12.4861i			0.889598i	−0.895630	+	0.444799i	$0.853275\pi$
$198$	−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
$203$	8.55758	+	15.1029i	0.600625	+	1.06002i
$204$	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
$210$	8.01730	+	1.74223i	0.553246	+	0.120225i
$211$	7.56103	−	13.0961i	0.520523	−	0.901572i	−0.479192	−	0.877710i	$-0.659070\pi$
$211$	7.56103	−	13.0961i	0.520523	−	0.901572i	0.999715	−	0.0238622i	$-0.00759629\pi$
$212$		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	$-0.575970\pi$
$223$	7.27049	−	4.19762i	0.486868	−	0.281093i	0.723274	+	0.690561i	$0.242636\pi$
$224$	−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	$-0.192313\pi$
$227$	−1.21261	−	2.10030i	−0.0804836	−	0.139402i	−0.903458	+	0.428677i	$0.858980\pi$
$228$	−3.89576	−	3.48283i	−0.258003	−	0.230656i
$229$	−1.74915	−	1.00987i	−0.115587	−	0.0667344i	0.441092	−	0.897462i	$-0.354591\pi$
$229$	−1.74915	−	1.00987i	−0.115587	−	0.0667344i	−0.556679	+	0.830728i	$0.687925\pi$
$230$	3.37157	−	5.83973i	0.222315	−	0.385061i
$231$	−3.35318	−	10.4818i	−0.220623	−	0.689651i
$232$	3.28052	+	5.68202i	0.215376	+	0.373043i
$233$		−	12.7289i		−	0.833899i	−0.908930	−	0.416950i	$-0.863099\pi$
$233$		−	12.7289i		−	0.833899i	0.908930	−	0.416950i	$-0.136901\pi$
$234$	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
$238$	4.77984	+	8.43573i	0.309831	+	0.546807i
$239$	15.1117	+	8.72474i	0.977494	+	0.564356i	0.901513	−	0.432753i	$-0.142458\pi$
$239$	15.1117	+	8.72474i	0.977494	+	0.564356i	0.0759814	+	0.997109i	$0.475791\pi$
$240$	3.03548	+	0.633975i	0.195939	+	0.0409229i
$241$	−9.90142	+	5.71659i	−0.637807	+	0.368238i	−0.783769	−	0.621052i	$-0.786705\pi$
$241$	−9.90142	+	5.71659i	−0.637807	+	0.368238i	0.145963	+	0.989290i	$0.453372\pi$
$242$			5.23278i			0.336376i
$243$	−8.03223	−	13.3598i	−0.515268	−	0.857029i
$244$			11.3283i			0.725219i
$245$	−6.44093	+	10.7507i	−0.411496	+	0.686835i
$246$	−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	$-0.168364\pi$
$251$	27.3560			1.72669			0.863347	+	0.504611i	$0.168364\pi$
$252$	−4.65899	−	6.42603i	−0.293489	−	0.404802i
$253$	−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	$-0.868117\pi$
$257$	−1.74837	+	3.02826i	−0.109060	+	0.188898i	0.806330	+	0.591466i	$0.201451\pi$
$258$	8.99047	+	8.03754i	0.559722	+	0.500396i
$259$	0.200338	−	24.7741i	0.0124484	−	1.53939i
$260$		−	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	−0.734877	−	0.678201i	$-0.762760\pi$
$263$	−8.35150	+	4.82174i	−0.514976	+	0.297321i	0.219901	+	0.975522i	$0.429427\pi$
$264$	−1.29938	−	3.95136i	−0.0799712	−	0.243190i
$265$		0			0
$266$	6.94489	−	3.93510i	0.425818	−	0.241276i
$267$	−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	$-0.432430\pi$
$269$	6.91107			0.421376			0.210688	+	0.977553i	$0.432430\pi$
$270$	−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
$273$	−15.0740	+	16.5892i	−0.912319	+	1.00402i
$274$	−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	0.999250	−	0.0387296i	$-0.0123311\pi$
$277$	7.75718	+	13.4358i	0.466084	+	0.807281i	−0.533166	+	0.846011i	$0.678998\pi$
$278$	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	−0.105783	−	0.994389i	$-0.533735\pi$
$281$	11.7759	−	6.79883i	0.702492	−	0.405584i	0.808275	+	0.588805i	$0.200401\pi$
$282$	6.63199	+	5.92904i	0.394929	+	0.353069i
$283$	4.71796	+	2.72392i	0.280454	+	0.161920i	0.633629	−	0.773637i	$-0.281565\pi$
$283$	4.71796	+	2.72392i	0.280454	+	0.161920i	−0.353175	+	0.935557i	$0.614898\pi$
$284$	−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	0.248583	+	0.968610i	$0.420035\pi$
$293$	−12.2311	+	21.1849i	−0.714550	+	1.23764i	−0.963133	+	0.269026i	$0.913298\pi$
$294$	11.5773	−	3.60072i	0.675204	−	0.209998i
$295$	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
$301$	−16.0271	+	9.08127i	−0.923788	+	0.523435i
$302$	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	$-0.349978\pi$
$308$	6.35358	+	0.0513786i	0.362029	+	0.00292757i
$309$	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	$-0.733230\pi$
$311$	5.45501	−	9.44836i	0.309325	−	0.535767i	0.978215	+	0.207594i	$0.0665634\pi$
$312$	−5.64654	+	6.31599i	−0.319672	+	0.357573i
$313$	−2.96532	+	1.71203i	−0.167610	+	0.0967694i	−0.581458	−	0.813576i	$-0.697518\pi$
$313$	−2.96532	+	1.71203i	−0.167610	+	0.0967694i	0.413849	+	0.910346i	$0.364184\pi$
$314$	−13.8431			−0.781210
$315$	−8.34122	−	11.5048i	−0.469975	−	0.648224i
$316$	−3.03663			−0.170824
$317$	16.4953	−	9.52357i	0.926468	−	0.534897i	0.0407755	−	0.999168i	$-0.487017\pi$
$317$	16.4953	−	9.52357i	0.926468	−	0.534897i	0.885693	+	0.464272i	$0.153684\pi$
$318$		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
$322$	0.0805794	−	9.96459i	0.00449051	−	0.555305i
$323$		−	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
$329$	−11.8227	+	6.69896i	−0.651807	+	0.369326i
$330$	−2.32634	−	7.07432i	−0.128061	−	0.389429i
$331$	−0.0366251	−	0.0634366i	−0.00201310	−	0.00348679i	0.865017	−	0.501742i	$-0.167307\pi$
$331$	−0.0366251	−	0.0634366i	−0.00201310	−	0.00348679i	−0.867030	+	0.498256i	$0.833974\pi$
$332$	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
$336$	4.36468	−	1.39628i	0.238113	−	0.0761735i
$337$	1.11639	−	1.93364i	0.0608136	−	0.105332i	−0.834016	−	0.551741i	$-0.813964\pi$
$337$	1.11639	−	1.93364i	0.0608136	−	0.105332i	0.894829	+	0.446408i	$0.147297\pi$
$338$	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	0.999751	−	0.0223084i	$-0.00710156\pi$
$347$	27.5751	+	15.9205i	1.48031	+	0.854656i	0.480556	+	0.876964i	$0.340435\pi$
$348$	2.32330	−	11.1240i	0.124542	−	0.596310i
$349$	12.7613	−	7.36772i	0.683095	−	0.394385i	−0.117925	−	0.993022i	$-0.537624\pi$
$349$	12.7613	−	7.36772i	0.683095	−	0.394385i	0.801020	+	0.598637i	$0.204291\pi$
$350$	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	$-0.148363\pi$
$353$	1.07979	+	1.87025i	0.0574713	+	0.0995431i	−0.835858	+	0.548945i	$0.815030\pi$
$354$	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
$357$	3.56616	−	16.4106i	0.188741	−	0.868541i
$358$	−6.56103	−	11.3640i	−0.346761	−	0.600608i
$359$			32.6448i			1.72293i	0.507820	+	0.861463i	$0.330451\pi$
$359$			32.6448i			1.72293i	−0.507820	+	0.861463i	$0.669549\pi$
$360$	−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
$364$	−6.37978	−	11.2594i	−0.334391	−	0.590153i
$365$	−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	$-0.949003\pi$
$367$	−25.7212	+	14.8501i	−1.34264	+	0.775171i	−0.355442	+	0.934698i	$0.615670\pi$
$368$		−	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	−0.838739	−	0.544534i	$-0.816707\pi$
$373$	1.00836	−	1.74653i	0.0522109	−	0.0904320i	0.890950	+	0.454102i	$0.150040\pi$
$374$	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
$378$	−1.40221	+	13.6760i	−0.0721217	+	0.703419i
$379$	−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	$-0.826530\pi$
$383$	0.418256	−	0.724440i	0.0213719	−	0.0370172i	0.876514	+	0.481377i	$0.159863\pi$
$384$	1.64537	−	0.541068i	0.0839650	−	0.0276113i
$385$	11.3751	+	0.0919857i	0.579730	+	0.00468803i
$386$		−	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	0.156357	−	0.987701i	$-0.450025\pi$
$389$	21.4964	−	12.4109i	1.08991	−	0.629260i	0.933552	+	0.358441i	$0.116692\pi$
$390$	−10.1093	+	11.3078i	−0.511903	+	0.572595i
$391$	−11.9533	−	6.90127i	−0.604507	−	0.349012i
$392$	−0.113205	+	6.99908i	−0.00571770	+	0.353507i
$393$	−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
$399$	−13.5104	−	2.93592i	−0.676364	−	0.146980i
$400$	0.897324	−	1.55421i	0.0448662	−	0.0777105i
$401$	11.3251	+	6.53854i	0.565548	+	0.326519i	0.755369	−	0.655300i	$-0.227458\pi$
$401$	11.3251	+	6.53854i	0.565548	+	0.326519i	−0.189822	+	0.981819i	$0.560791\pi$
$402$	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	$-0.377284\pi$
$409$	−4.82124	−	2.78354i	−0.238395	−	0.137637i	−0.614439	+	0.788965i	$0.710618\pi$
$410$	−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	$-0.964520\pi$
$419$	−8.19938	+	14.2017i	−0.400566	+	0.693800i	0.593228	+	0.805034i	$0.297853\pi$
$420$	7.81430	−	2.49984i	0.381299	−	0.121979i
$421$	−7.72892	−	13.3869i	−0.376684	−	0.652437i	0.613893	−	0.789389i	$-0.289603\pi$
$421$	−7.72892	−	13.3869i	−0.376684	−	0.652437i	−0.990578	+	0.136952i	$0.956269\pi$
$422$		−	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
$427$	14.7755	+	26.0767i	0.715038	+	1.26194i
$428$	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	$-0.794074\pi$
$431$		−	25.0266i		−	1.20549i	0.797935	−	0.602744i	$-0.205926\pi$
$432$	−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	$-0.0172304\pi$
$434$	0.0994112	−	12.2934i	0.00477189	−	0.590101i
$435$	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	$-0.814248\pi$
$439$	−16.2293	+	9.37000i	−0.774583	+	0.447206i	0.0599239	+	0.998203i	$0.480914\pi$
$440$	4.29953			0.204972
$441$	−19.1061	−	8.71539i	−0.909813	−	0.415019i
$442$	−17.9251			−0.852609
$443$	−1.04314	+	0.602256i	−0.0495610	+	0.0286141i	−0.524576	−	0.851364i	$-0.675776\pi$
$443$	−1.04314	+	0.602256i	−0.0495610	+	0.0286141i	0.475015	+	0.879978i	$0.342443\pi$
$444$	−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
$448$	−0.0213944	+	2.64566i	−0.00101079	+	0.124996i
$449$			26.8022i			1.26487i	0.774612	+	0.632436i	$0.217945\pi$
$449$			26.8022i			1.26487i	−0.774612	+	0.632436i	$0.782055\pi$
$450$	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
$455$	−11.4220	−	20.1583i	−0.535473	−	0.945033i
$456$	−5.11524	−	1.06834i	−0.239543	−	0.0500298i
$457$	−6.92442	−	11.9934i	−0.323911	−	0.561030i	0.657381	−	0.753559i	$-0.271664\pi$
$457$	−6.92442	−	11.9934i	−0.323911	−	0.561030i	−0.981291	+	0.192529i	$0.938331\pi$
$458$	−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	$-0.202358\pi$
$461$	−2.40241	−	4.16110i	−0.111892	−	0.193802i	−0.916533	+	0.399959i	$0.869024\pi$
$462$	−8.14483	−	7.40090i	−0.378932	−	0.344321i
$463$	10.5194	−	18.2201i	0.488877	−	0.846760i	−0.511041	−	0.859556i	$-0.670740\pi$
$463$	10.5194	−	18.2201i	0.488877	−	0.846760i	0.999918	+	0.0127960i	$0.00407321\pi$
$464$	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	$-0.543016\pi$
$467$	−5.82302			−0.269457			−0.134729	+	0.990883i	$0.543016\pi$
$468$	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	−0.990239	−	0.139382i	$-0.955488\pi$
$479$	−13.4781	−	23.3447i	−0.615828	−	1.06665i	0.374411	−	0.927263i	$-0.377845\pi$
$480$	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
$483$	−11.6072	+	12.7739i	−0.528144	+	0.581232i
$484$	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
$490$	−0.202676	+	12.5308i	−0.00915596	+	0.566084i
$491$	−33.7430	−	19.4815i	−1.52280	−	0.879188i	−0.999637	−	0.0269544i	$-0.991419\pi$
$491$	−33.7430	−	19.4815i	−1.52280	−	0.879188i	−0.523162	−	0.852234i	$-0.675248\pi$
$492$	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
$497$	−15.7749	−	0.127565i	−0.707600	−	0.00572206i
$498$	−18.0847	−	16.1678i	−0.810393	−	0.724497i
$499$	−13.0048	+	22.5250i	−0.582176	+	1.00836i	0.413045	+	0.910711i	$0.364465\pi$
$499$	−13.0048	+	22.5250i	−0.582176	+	1.00836i	−0.995221	+	0.0976483i	$0.968868\pi$
$500$	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	$-0.575407\pi$
$503$	−10.5271			−0.469378			−0.234689	+	0.972070i	$0.575407\pi$
$504$	−7.24782	−	3.23561i	−0.322843	−	0.144125i
$505$	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	$-0.839957\pi$
$509$	−0.469435	+	0.813086i	−0.0208074	+	0.0360394i	0.855434	+	0.517911i	$0.173290\pi$
$510$	2.32330	−	11.1240i	0.102878	−	0.492580i
$511$	−32.7571	−	0.264892i	−1.44909	−	0.0117181i
$512$			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
$518$	−12.2136	−	21.5552i	−0.536633	−	0.947080i
$519$	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	$-0.167076\pi$
$521$	39.5054			1.73076			0.865382	+	0.501112i	$0.167076\pi$
$522$	−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
$525$	−7.83306	+	2.50584i	−0.341863	+	0.109364i
$526$	−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
$546$	−4.75985	+	21.9037i	−0.203703	+	0.937390i
$547$	−12.2477	−	21.2136i	−0.523672	−	0.907026i	−0.999620	−	0.0275530i	$-0.991229\pi$
$547$	−12.2477	−	21.2136i	−0.523672	−	0.907026i	0.475949	−	0.879473i	$-0.342105\pi$
$548$			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
$553$	−6.99004	+	3.96068i	−0.297247	+	0.168425i
$554$	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	$-0.982834\pi$
$557$		−	2.54431i		−	0.107806i	0.998546	−	0.0539030i	$-0.0171662\pi$
$558$	12.7745	+	5.57943i	0.540789	+	0.236196i
$559$		−	34.0560i		−	1.44042i
$560$	−0.0383034	+	4.73667i	−0.00161861	+	0.200161i
$561$	−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	$-0.725190\pi$
$563$	7.90707	−	13.6954i	0.333243	−	0.577194i	0.983146	+	0.182823i	$0.0585236\pi$
$564$	8.70799	+	1.81871i	0.366673	+	0.0765814i
$565$	−1.79783	+	1.03798i	−0.0756354	+	0.0436681i
$566$	5.44783			0.228990
$567$	17.5982	−	16.0407i	0.739055	−	0.673645i
$568$	−5.96254			−0.250182
$569$	−5.52793	+	3.19155i	−0.231743	+	0.133797i	−0.611376	−	0.791340i	$-0.709384\pi$
$569$	−5.52793	+	3.19155i	−0.231743	+	0.133797i	0.379633	+	0.925137i	$0.376050\pi$
$570$	−9.15807	−	1.91271i	−0.383589	−	0.0801145i
$571$	3.91188	−	6.77557i	0.163707	−	0.283549i	−0.772488	−	0.635029i	$-0.780988\pi$
$571$	3.91188	−	6.77557i	0.163707	−	0.283549i	0.936195	+	0.351480i	$0.114322\pi$
$572$	−5.87327	+	10.1728i	−0.245574	+	0.425346i
$573$	15.2252	−	5.00668i	0.636040	−	0.209157i
$574$	−21.3819	−	0.172907i	−0.892465	−	0.00721698i
$575$			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
$581$	32.2392	−	18.2673i	1.33751	−	0.757855i
$582$	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	$-0.135404\pi$
$587$	2.37575	+	4.11492i	0.0980577	+	0.169841i	−0.812823	+	0.582511i	$0.802070\pi$
$588$	8.22591	−	8.90698i	0.339231	−	0.367318i
$589$	−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	$-0.523424\pi$
$593$	−3.58070			−0.147042			−0.0735208	+	0.997294i	$0.523424\pi$
$594$	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	0.209183	−	0.977877i	$-0.432920\pi$
$599$	−13.0471	−	7.53277i	−0.533091	−	0.307780i	−0.742274	+	0.670096i	$0.766253\pi$
$600$	−2.95286	+	0.971027i	−0.120550	+	0.0396420i
$601$	19.8704	−	11.4722i	0.810530	−	0.467960i	−0.0366096	−	0.999330i	$-0.511656\pi$
$601$	19.8704	−	11.4722i	0.810530	−	0.467960i	0.847140	+	0.531370i	$0.178322\pi$
$602$	−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	$-0.498851\pi$
$607$	−21.2030	−	12.2416i	−0.860605	−	0.496870i	−0.864215	+	0.503123i	$0.832184\pi$
$608$	1.50851	−	2.61281i	0.0611780	−	0.105963i
$609$	−9.16106	−	28.6368i	−0.371225	−	1.16042i
$610$	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
$616$	5.52805	−	3.13229i	0.222731	−	0.126204i
$617$	−11.7607	−	6.79005i	−0.473468	−	0.273357i	0.244222	−	0.969719i	$-0.421467\pi$
$617$	−11.7607	−	6.79005i	−0.473468	−	0.273357i	−0.717690	+	0.696362i	$0.754801\pi$
$618$	0.284722	+	0.0594656i	0.0114532	+	0.00239206i
$619$	30.7325	−	17.7434i	1.23524	−	0.713169i	0.267126	−	0.963662i	$-0.413926\pi$
$619$	30.7325	−	17.7434i	1.23524	−	0.713169i	0.968118	+	0.250493i	$0.0805926\pi$
$620$		−	8.31905i		−	0.334101i
$621$	−8.14977	−	17.7931i	−0.327039	−	0.714012i
$622$		−	10.9100i		−	0.437452i
$623$	0.0801996	−	9.91762i	0.00321313	−	0.397341i
$624$	−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
$630$	−12.9761	−	5.79286i	−0.516981	−	0.230793i
$631$	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
$637$	−29.3714	−	17.5969i	−1.16374	−	0.697216i
$638$		−	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	−0.481466	−	0.876465i	$-0.659895\pi$
$641$	0.932777	−	0.538539i	0.0368425	−	0.0212710i	0.518308	+	0.855194i	$0.326562\pi$
$642$	−4.32357	−	13.1478i	−0.170638	−	0.518903i
$643$	−33.3126	−	19.2330i	−1.31372	−	0.758477i	−0.331010	−	0.943627i	$-0.607389\pi$
$643$	−33.3126	−	19.2330i	−1.31372	−	0.758477i	−0.982710	+	0.185150i	$0.940723\pi$
$644$	−4.91251	−	8.66988i	−0.193580	−	0.341641i
$645$	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	$-0.443693\pi$
$647$	8.95210			0.351943			0.175972	+	0.984395i	$0.443693\pi$
$648$	6.60226	−	6.11639i	0.259361	−	0.240274i
$649$		−	35.0380i		−	1.37536i
$650$	4.38910	+	7.60215i	0.172155	+	0.298181i
$651$	−14.3198	+	15.7592i	−0.561238	+	0.617653i
$652$	−2.16789	+	3.75489i	−0.0849010	+	0.147053i
$653$	−9.85934	−	5.69229i	−0.385826	−	0.222757i	0.294524	−	0.955644i	$-0.404839\pi$
$653$	−9.85934	−	5.69229i	−0.385826	−	0.222757i	−0.680350	+	0.732887i	$0.738172\pi$
$654$	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	0.258723	−	0.965952i	$-0.416698\pi$
$659$	31.4373	−	18.1503i	1.22462	−	0.707036i	0.965900	+	0.258915i	$0.0833650\pi$
$660$	−5.55183	−	4.96337i	−0.216105	−	0.193199i
$661$	31.2425	+	18.0379i	1.21519	+	0.701593i	0.963886	−	0.266315i	$-0.0858060\pi$
$661$	31.2425	+	18.0379i	1.21519	+	0.701593i	0.251308	+	0.967907i	$0.419139\pi$
$662$	−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
$672$	3.08178	−	3.39155i	0.118882	−	0.130832i
$673$	4.78512	+	8.28806i	0.184453	+	0.319481i	0.943392	−	0.331680i	$-0.107615\pi$
$673$	4.78512	+	8.28806i	0.184453	+	0.319481i	−0.758939	+	0.651161i	$0.774282\pi$
$674$		−	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	$-0.263760\pi$
$677$	−7.81408	−	13.5344i	−0.300320	−	0.520169i	−0.976208	+	0.216835i	$0.930427\pi$
$678$	1.96594	+	0.410596i	0.0755015	+	0.0157689i
$679$	7.18786	+	12.6855i	0.275845	+	0.486826i
$680$	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	$0.0683114\pi$
$683$			11.1313i			0.425926i	−0.977060	+	0.212963i	$0.931689\pi$
$684$	5.37184	+	7.28454i	0.205397	+	0.278531i
$685$			8.45145i			0.322913i
$686$	8.86835	+	16.2589i	0.338595	+	0.620768i
$687$	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	$-0.684987\pi$
$691$	−2.61903	+	1.51210i	−0.0996324	+	0.0575228i	0.449356	+	0.893353i	$0.351654\pi$
$692$	−17.4182			−0.662139
$693$	1.97354	+	18.9589i	0.0749685	+	0.720189i
$694$	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
$700$	0.0383954	−	4.74804i	0.00145121	−	0.179459i
$701$			50.1486i			1.89409i	0.321103	+	0.947044i	$0.395946\pi$
$701$			50.1486i			1.89409i	−0.321103	+	0.947044i	$0.604054\pi$
$702$	−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
$707$	0.576224	−	0.326499i	0.0216711	−	0.0122793i
$708$	−7.89419	−	24.0060i	−0.296682	−	0.902200i
$709$	1.80385	+	3.12436i	0.0677449	+	0.117338i	0.897908	−	0.440183i	$-0.145086\pi$
$709$	1.80385	+	3.12436i	0.0677449	+	0.117338i	−0.830163	+	0.557520i	$0.811753\pi$
$710$	−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
$714$	−5.11691	−	15.9951i	−0.191496	−	0.598601i
$715$	−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	$-0.278981\pi$
$719$	34.3161			1.27977			0.639887	+	0.768469i	$0.278981\pi$
$720$	−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	$-0.803595\pi$
$727$	−19.4757	+	11.2443i	−0.722315	+	0.417029i	0.0932892	+	0.995639i	$0.470262\pi$
$728$	−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	$-0.528686\pi$
$733$	−27.0065	−	15.5922i	−0.997509	−	0.575912i	−0.907510	+	0.420030i	$0.862020\pi$
$734$	−14.8501	+	25.7212i	−0.548129	+	0.949387i
$735$	14.7273	−	15.9466i	0.543223	−	0.588200i
$736$	−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	0.466947	−	0.884285i	$-0.345354\pi$
$743$	−1.78246	−	1.02910i	−0.0653921	−	0.0377542i	−0.532340	+	0.846531i	$0.678687\pi$
$744$	−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
$749$	21.1410	+	0.170958i	0.772475	+	0.00624667i
$750$	−20.0156	+	6.58198i	−0.730866	+	0.240340i
$751$	−11.9053	+	20.6205i	−0.434429	+	0.752454i	−0.997249	−	0.0741262i	$-0.976383\pi$
$751$	−11.9053	+	20.6205i	−0.434429	+	0.752454i	0.562820	+	0.826580i	$0.309717\pi$
$752$	−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
$756$	5.62367	+	12.5449i	0.204531	+	0.456253i
$757$	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	0.494775	+	0.869021i	$0.335250\pi$
$761$	−13.9368	+	24.1392i	−0.505207	+	0.875044i	−0.999982	+	0.00602283i	$0.998083\pi$
$762$	−2.30599	+	0.758309i	−0.0835374	+	0.0274707i
$763$	−0.405495	+	50.1442i	−0.0146799	+	1.81534i
$764$			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	$-0.292052\pi$
$769$	6.21166	+	3.58631i	0.223998	+	0.129326i	−0.383802	+	0.923415i	$0.625385\pi$
$770$	9.89714	−	5.60790i	0.356668	−	0.202095i
$771$	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	$-0.487738\pi$
$773$	2.14153			0.0770255			0.0385128	+	0.999258i	$0.487738\pi$
$774$	−12.3969	−	16.8110i	−0.445598	−	0.604258i
$775$			8.33903i			0.299547i
$776$	2.75544	+	4.77256i	0.0989144	+	0.171325i
$777$	−9.11234	+	41.9327i	−0.326903	+	1.50433i
$778$	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	$-0.439420\pi$
$787$	−15.8961	−	9.17759i	−0.566633	−	0.327146i	−0.755804	+	0.654798i	$0.772753\pi$
$788$	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	$-0.978366\pi$
$797$	−12.4226	+	21.5166i	−0.440031	+	0.762156i	0.557660	+	0.830069i	$0.311699\pi$
$798$	−13.1683	+	4.21260i	−0.466152	+	0.149125i
$799$	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
$805$	−8.79511	−	15.5221i	−0.309987	−	0.547082i
$806$	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	$-0.768754\pi$
$809$		−	37.7861i		−	1.32849i	0.747516	−	0.664244i	$-0.231246\pi$
$810$	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	$-0.221536\pi$
$812$	17.3583	+	0.140369i	0.609157	+	0.00492599i
$813$	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
$819$	31.4318	−	22.7886i	1.09832	−	0.796300i
$820$	−14.4694			−0.505293
$821$	−5.52142	+	3.18779i	−0.192699	+	0.111255i	−0.593245	−	0.805022i	$-0.702154\pi$
$821$	−5.52142	+	3.18779i	−0.192699	+	0.111255i	0.400547	+	0.916276i	$0.368820\pi$
$822$	5.44941	−	6.09549i	0.190070	−	0.212605i
$823$	−14.0293	+	24.2995i	−0.489032	+	0.847028i	−0.999920	−	0.0126187i	$-0.995983\pi$
$823$	−14.0293	+	24.2995i	−0.489032	+	0.847028i	0.510888	+	0.859647i	$0.329317\pi$
$824$	−0.0839657	+	0.145433i	−0.00292508	+	0.00506639i
$825$	5.56516	+	4.97529i	0.193754	+	0.173217i
$826$	38.6003	+	0.312144i	1.34308	+	0.0108609i
$827$		−	0.581579i		−	0.0202235i	−0.999949	−	0.0101117i	$-0.996781\pi$
$827$		−	0.581579i		−	0.0202235i	0.999949	−	0.0101117i	$-0.00321872\pi$
$828$	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
$833$	25.6493	+	0.414857i	0.888696	+	0.0143739i
$834$	−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	$-0.129987\pi$
$839$	3.33038	+	5.76838i	0.114977	+	0.199147i	−0.802793	+	0.596257i	$0.796654\pi$
$840$	5.51746	−	6.07207i	0.190370	−	0.209506i
$841$	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	$-0.542551\pi$
$853$	19.2287	−	11.1017i	0.658378	−	0.380115i	0.791659	+	0.610964i	$0.209218\pi$
$854$	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	$-0.0825283\pi$
$857$	7.64830	+	13.2472i	0.261261	+	0.452517i	−0.705316	+	0.708893i	$0.749195\pi$
$858$	19.3274	−	6.35568i	0.659827	−	0.216979i
$859$	−3.68620	−	2.12823i	−0.125772	−	0.0726143i	0.435794	−	0.900046i	$-0.356468\pi$
$859$	−3.68620	−	2.12823i	−0.125772	−	0.0726143i	−0.561566	+	0.827432i	$0.689801\pi$
$860$	−6.23269	+	10.7953i	−0.212533	+	0.368118i
$861$	27.4101	+	24.9065i	0.934134	+	0.848813i
$862$	−12.5133	−	21.6737i	−0.426204	−	0.738208i
$863$		−	23.6624i		−	0.805476i	−0.915315	−	0.402738i	$-0.868059\pi$
$863$		−	23.6624i		−	0.805476i	0.915315	−	0.402738i	$-0.131941\pi$
$864$	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
$868$	−6.06059	−	10.6961i	−0.205710	−	0.363048i
$869$	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
$875$	0.260258	−	32.1840i	0.00879833	−	1.08802i
$876$	15.9877	+	14.2931i	0.540173	+	0.482918i
$877$	10.1962	−	17.6603i	0.344300	−	0.596344i	−0.640927	−	0.767602i	$-0.721450\pi$
$877$	10.1962	−	17.6603i	0.344300	−	0.596344i	0.985226	+	0.171258i	$0.0547831\pi$
$878$	−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	$-0.684147\pi$
$881$	−32.4586			−1.09356			−0.546780	+	0.837276i	$0.684147\pi$
$882$	−20.9040	+	2.00529i	−0.703876	+	0.0675215i
$883$	−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	$-0.781151\pi$
$887$	4.86059	−	8.41879i	0.163203	−	0.282675i	0.936016	+	0.351959i	$0.114484\pi$
$888$	−3.31587	+	15.8764i	−0.111273	+	0.532778i
$889$	0.0299843	−	3.70791i	0.00100564	−	0.124359i
$890$		−	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
$896$	1.30430	+	2.30191i	0.0435737	+	0.0769014i
$897$	−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
$903$	30.3892	−	9.72167i	1.01129	−	0.323517i
$904$	−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	0.968103	−	0.250551i	$-0.0806118\pi$
$907$	8.04314	+	13.9311i	0.267068	+	0.462575i	−0.701035	+	0.713127i	$0.747278\pi$
$908$	−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	0.0193161	−	0.999813i	$-0.493851\pi$
$911$	27.0087	−	15.5935i	0.894838	−	0.516635i	0.875522	+	0.483179i	$0.160518\pi$
$912$	−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
$924$	−10.7541	−	2.33695i	−0.353783	−	0.0768801i
$925$	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	0.829891	+	0.557926i	$0.188403\pi$
$929$	27.3744	+	47.4138i	0.898124	+	1.55560i	0.0682329	+	0.997669i	$0.478264\pi$
$930$	−9.60351	+	10.7421i	−0.314911	+	0.352247i
$931$	0.341540	−	21.1163i	0.0111935	−	0.692059i
$932$	−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	$0.600304\pi$
$938$	1.50864	+	0.0121997i	0.0492588	+	0.000398335i
$939$	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	0.455423	+	0.890275i	$0.349488\pi$
$941$	−16.6658	+	28.8660i	−0.543289	+	0.941005i	−0.998712	+	0.0507297i	$0.983845\pi$
$942$	23.4705	+	4.90192i	0.764709	+	0.159713i
$943$	26.3613	−	15.2197i	0.858443	−	0.495622i
$944$	14.5900			0.474864
$945$	10.0683	+	22.4597i	0.327523	+	0.730616i
$946$	16.7206			0.543632
$947$	−6.59497	+	3.80761i	−0.214308	+	0.123731i	−0.603312	−	0.797505i	$-0.706153\pi$
$947$	−6.59497	+	3.80761i	−0.214308	+	0.123731i	0.389004	+	0.921236i	$0.372819\pi$
$948$	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
$952$	9.69548	+	0.0784032i	0.314232	+	0.00254106i
$953$		−	55.7861i		−	1.80709i	−0.428495	−	0.903544i	$-0.640956\pi$
$953$		−	55.7861i		−	1.80709i	0.428495	−	0.903544i	$-0.359044\pi$
$954$		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
$959$	6.15705	+	10.8663i	0.198821	+	0.350891i
$960$	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
$966$	−3.66515	+	16.8661i	−0.117924	+	0.542658i
$967$	−13.3369	+	23.1003i	−0.428887	+	0.742855i	−0.996775	−	0.0802517i	$-0.974428\pi$
$967$	−13.3369	+	23.1003i	−0.428887	+	0.742855i	0.567887	+	0.823106i	$0.307761\pi$
$968$	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	$-0.455938\pi$
$971$	8.59942			0.275968			0.137984	+	0.990434i	$0.455938\pi$
$972$	−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	0.281119	−	0.959673i	$-0.409295\pi$
$977$	−12.7973	−	7.38854i	−0.409423	−	0.236380i	−0.690542	+	0.723293i	$0.742628\pi$
$978$	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	$-0.272752\pi$
$983$	−10.2568	−	17.7652i	−0.327140	−	0.566623i	−0.981943	+	0.189176i	$0.939418\pi$
$984$	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
$987$	22.4172	−	7.17137i	0.713546	−	0.228267i
$988$	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
$994$	−13.7252	+	7.77696i	−0.435338	+	0.246670i
$995$	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	$-0.666566\pi$
$997$	0.0172917	−	0.00998339i	0.000547635	−	0.000316177i	0.500274	+	0.865867i	$0.333233\pi$
$998$			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.41.5	✓	16
3.2	odd	2		378.2.m.a.125.1		16
4.3	odd	2		1008.2.cc.b.545.8		16
7.2	even	3		882.2.t.b.815.3		16
7.3	odd	6		882.2.l.a.509.6		16
7.4	even	3		882.2.l.a.509.7		16
7.5	odd	6		882.2.t.b.815.2		16
7.6	odd	2	inner	126.2.m.a.41.8	yes	16
9.2	odd	6	inner	126.2.m.a.83.8	yes	16
9.4	even	3		1134.2.d.a.1133.11		16
9.5	odd	6		1134.2.d.a.1133.6		16
9.7	even	3		378.2.m.a.251.4		16
12.11	even	2		3024.2.cc.b.881.3		16
21.2	odd	6		2646.2.t.a.2285.8		16
21.5	even	6		2646.2.t.a.2285.5		16
21.11	odd	6		2646.2.l.b.1097.1		16
21.17	even	6		2646.2.l.b.1097.4		16
21.20	even	2		378.2.m.a.125.4		16
28.27	even	2		1008.2.cc.b.545.1		16
36.7	odd	6		3024.2.cc.b.2897.6		16
36.11	even	6		1008.2.cc.b.209.1		16
63.2	odd	6		882.2.l.a.227.2		16
63.11	odd	6		882.2.t.b.803.2		16
63.13	odd	6		1134.2.d.a.1133.14		16
63.16	even	3		2646.2.l.b.521.8		16
63.20	even	6	inner	126.2.m.a.83.5	yes	16
63.25	even	3		2646.2.t.a.1979.5		16
63.34	odd	6		378.2.m.a.251.1		16
63.38	even	6		882.2.t.b.803.3		16
63.41	even	6		1134.2.d.a.1133.3		16
63.47	even	6		882.2.l.a.227.3		16
63.52	odd	6		2646.2.t.a.1979.8		16
63.61	odd	6		2646.2.l.b.521.5		16
84.83	odd	2		3024.2.cc.b.881.6		16
252.83	odd	6		1008.2.cc.b.209.8		16
252.223	even	6		3024.2.cc.b.2897.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.5	✓	16	1.1	even	1	trivial
126.2.m.a.41.8	yes	16	7.6	odd	2	inner
126.2.m.a.83.5	yes	16	63.20	even	6	inner
126.2.m.a.83.8	yes	16	9.2	odd	6	inner
378.2.m.a.125.1		16	3.2	odd	2
378.2.m.a.125.4		16	21.20	even	2
378.2.m.a.251.1		16	63.34	odd	6
378.2.m.a.251.4		16	9.7	even	3
882.2.l.a.227.2		16	63.2	odd	6
882.2.l.a.227.3		16	63.47	even	6
882.2.l.a.509.6		16	7.3	odd	6
882.2.l.a.509.7		16	7.4	even	3
882.2.t.b.803.2		16	63.11	odd	6
882.2.t.b.803.3		16	63.38	even	6
882.2.t.b.815.2		16	7.5	odd	6
882.2.t.b.815.3		16	7.2	even	3
1008.2.cc.b.209.1		16	36.11	even	6
1008.2.cc.b.209.8		16	252.83	odd	6
1008.2.cc.b.545.1		16	28.27	even	2
1008.2.cc.b.545.8		16	4.3	odd	2
1134.2.d.a.1133.3		16	63.41	even	6
1134.2.d.a.1133.6		16	9.5	odd	6
1134.2.d.a.1133.11		16	9.4	even	3
1134.2.d.a.1133.14		16	63.13	odd	6
2646.2.l.b.521.5		16	63.61	odd	6
2646.2.l.b.521.8		16	63.16	even	3
2646.2.l.b.1097.1		16	21.11	odd	6
2646.2.l.b.1097.4		16	21.17	even	6
2646.2.t.a.1979.5		16	63.25	even	3
2646.2.t.a.1979.8		16	63.52	odd	6
2646.2.t.a.2285.5		16	21.5	even	6
2646.2.t.a.2285.8		16	21.2	odd	6
3024.2.cc.b.881.3		16	12.11	even	2
3024.2.cc.b.881.6		16	84.83	odd	2
3024.2.cc.b.2897.3		16	252.223	even	6
3024.2.cc.b.2897.6		16	36.7	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.69547 - 0.354107i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.895175 - 1.55049i) q^{5} +(-1.64537 + 0.541068i) q^{6} +(0.0213944 - 2.64566i) q^{7} -1.00000i q^{8} +(2.74922 + 1.20075i) q^{9} +O(q^{10})\)	\(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} +(0.0213944 - 2.64566i) 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} +(-1.30430 - 2.30191i) 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} +(-0.973121 + 4.47806i) 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} +(1.39628 + 4.36468i) 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} +(-6.99908 - 0.113205i) 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} +(-2.64566 - 0.0213944i) 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} +(3.23561 - 7.24782i) 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} +(-4.73667 - 0.0383034i) 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} +(3.13229 + 5.52805i) 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} +(3.39155 + 3.08178i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{7} + 12 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^9	\( 16 q + 8 q^{4} + 2 q^{7} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 8 q^{16} - 12 q^{18} + 18 q^{21} - 48 q^{23} - 8 q^{25} + 4 q^{28} - 12 q^{29} - 24 q^{30} + 12 q^{36} - 8 q^{37} - 36 q^{39} - 12 q^{42} + 4 q^{43} + 24 q^{46} - 8 q^{49} + 60 q^{50} + 12 q^{51} - 6 q^{56} + 48 q^{57} - 12 q^{58} + 24 q^{60} + 24 q^{63} - 16 q^{64} + 84 q^{65} - 28 q^{67} + 36 q^{74} + 78 q^{77} - 24 q^{78} - 4 q^{79} + 36 q^{81} + 18 q^{84} - 12 q^{85} - 24 q^{86} + 24 q^{91} - 48 q^{92} - 96 q^{93} + 12 q^{95} - 72 q^{99}+O(q^{100}) \) 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

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