LMFDB - Embedded newform 462.2.j.f.169.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(169,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("462.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.j (of order $5$, degree $4$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 4x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			169.2
Root			$0.831254 - 1.14412i$ of defining polynomial
Character	$\chi$	$=$	462.169
Dual form			462.2.j.f.421.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.0359800 - 0.0261410i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.0359800 - 0.0261410i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} -0.0444738 q^{10} +(-0.154014 - 3.31305i) q^{11} -1.00000 q^{12} +(4.52125 + 3.28488i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(0.0137431 + 0.0422971i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.18999 - 1.59112i) q^{17} +(0.309017 + 0.951057i) q^{18} +(1.10954 - 3.41481i) q^{19} +(0.0359800 + 0.0261410i) q^{20} +1.00000 q^{21} +(-1.82276 + 2.77084i) q^{22} +3.09945 q^{23} +(0.809017 + 0.587785i) q^{24} +(-1.54447 + 4.75340i) q^{25} +(-1.72696 - 5.31505i) q^{26} +(0.809017 - 0.587785i) q^{27} +(0.809017 - 0.587785i) q^{28} +(1.87573 + 5.77290i) q^{29} +(0.0137431 - 0.0422971i) q^{30} +(7.18277 + 5.21859i) q^{31} +1.00000 q^{32} +(3.19849 + 0.877312i) q^{33} -2.70698 q^{34} +(-0.0359800 - 0.0261410i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-0.777675 - 2.39344i) q^{37} +(-2.90481 + 2.11047i) q^{38} +(-4.52125 + 3.28488i) q^{39} +(-0.0137431 - 0.0422971i) q^{40} +(2.13502 - 6.57092i) q^{41} +(-0.809017 - 0.587785i) q^{42} +12.7697 q^{43} +(3.10330 - 1.17026i) q^{44} -0.0444738 q^{45} +(-2.50750 - 1.82181i) q^{46} +(3.52125 - 10.8373i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(4.04348 - 2.93776i) q^{50} +(0.836503 + 2.57449i) q^{51} +(-1.72696 + 5.31505i) q^{52} +(-6.65303 - 4.83371i) q^{53} -1.00000 q^{54} +(-0.0921479 - 0.115177i) q^{55} -1.00000 q^{56} +(2.90481 + 2.11047i) q^{57} +(1.87573 - 5.77290i) q^{58} +(-1.02285 - 3.14800i) q^{59} +(-0.0359800 + 0.0261410i) q^{60} +(-9.81713 + 7.13256i) q^{61} +(-2.74357 - 8.44385i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(-0.809017 - 0.587785i) q^{64} +0.248545 q^{65} +(-2.07196 - 2.58978i) q^{66} -1.01248 q^{67} +(2.18999 + 1.59112i) q^{68} +(-0.957782 + 2.94775i) q^{69} +(0.0137431 + 0.0422971i) q^{70} +(-2.85410 + 2.07363i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(-0.196232 - 0.603941i) q^{73} +(-0.777675 + 2.39344i) q^{74} +(-4.04348 - 2.93776i) q^{75} +3.59055 q^{76} +(-3.10330 + 1.17026i) q^{77} +5.58857 q^{78} +(5.05982 + 3.67617i) q^{79} +(-0.0137431 + 0.0422971i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-5.58956 + 4.06105i) q^{82} +(-4.43714 + 3.22377i) q^{83} +(0.309017 + 0.951057i) q^{84} +(0.0372024 - 0.114497i) q^{85} +(-10.3309 - 7.50582i) q^{86} -6.06998 q^{87} +(-3.19849 - 0.877312i) q^{88} -2.76195 q^{89} +(0.0359800 + 0.0261410i) q^{90} +(1.72696 - 5.31505i) q^{91} +(0.957782 + 2.94775i) q^{92} +(-7.18277 + 5.21859i) q^{93} +(-9.21875 + 6.69781i) q^{94} +(-0.0493454 - 0.151870i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(-9.05000 - 6.57521i) q^{97} +1.00000 q^{98} +(-1.82276 + 2.77084i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{11} - 8 q^{12} + 8 q^{13} + 2 q^{14} - 4 q^{15} - 2 q^{16} - 4 q^{17} - 2 q^{18} - 2 q^{19} - 6 q^{20} + 8 q^{21} - 6 q^{22} + 4 q^{23} + 2 q^{24} - 8 q^{25} - 12 q^{26} + 2 q^{27} + 2 q^{28} + 4 q^{29} - 4 q^{30} - 10 q^{31} + 8 q^{32} + 6 q^{33} - 4 q^{34} + 6 q^{35} - 2 q^{36} - 20 q^{37} - 12 q^{38} - 8 q^{39} + 4 q^{40} + 12 q^{41} - 2 q^{42} + 48 q^{43} - 6 q^{44} + 4 q^{45} + 4 q^{46} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 6 q^{51} - 12 q^{52} - 12 q^{53} - 8 q^{54} - 8 q^{55} - 8 q^{56} + 12 q^{57} + 4 q^{58} + 12 q^{59} + 6 q^{60} - 32 q^{61} + 20 q^{62} + 2 q^{63} - 2 q^{64} + 24 q^{65} - 4 q^{66} - 48 q^{67} - 4 q^{68} + 6 q^{69} - 4 q^{70} + 4 q^{71} - 2 q^{72} - 20 q^{74} - 2 q^{75} + 28 q^{76} + 6 q^{77} - 8 q^{78} + 40 q^{79} + 4 q^{80} - 2 q^{81} - 18 q^{82} - 32 q^{83} - 2 q^{84} - 42 q^{85} - 32 q^{86} + 16 q^{87} - 6 q^{88} + 12 q^{89} - 6 q^{90} + 12 q^{91} - 6 q^{92} + 10 q^{93} + 54 q^{95} + 2 q^{96} + 8 q^{97} + 8 q^{98} - 6 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^11 - 8 * q^12 + 8 * q^13 + 2 * q^14 - 4 * q^15 - 2 * q^16 - 4 * q^17 - 2 * q^18 - 2 * q^19 - 6 * q^20 + 8 * q^21 - 6 * q^22 + 4 * q^23 + 2 * q^24 - 8 * q^25 - 12 * q^26 + 2 * q^27 + 2 * q^28 + 4 * q^29 - 4 * q^30 - 10 * q^31 + 8 * q^32 + 6 * q^33 - 4 * q^34 + 6 * q^35 - 2 * q^36 - 20 * q^37 - 12 * q^38 - 8 * q^39 + 4 * q^40 + 12 * q^41 - 2 * q^42 + 48 * q^43 - 6 * q^44 + 4 * q^45 + 4 * q^46 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 6 * q^51 - 12 * q^52 - 12 * q^53 - 8 * q^54 - 8 * q^55 - 8 * q^56 + 12 * q^57 + 4 * q^58 + 12 * q^59 + 6 * q^60 - 32 * q^61 + 20 * q^62 + 2 * q^63 - 2 * q^64 + 24 * q^65 - 4 * q^66 - 48 * q^67 - 4 * q^68 + 6 * q^69 - 4 * q^70 + 4 * q^71 - 2 * q^72 - 20 * q^74 - 2 * q^75 + 28 * q^76 + 6 * q^77 - 8 * q^78 + 40 * q^79 + 4 * q^80 - 2 * q^81 - 18 * q^82 - 32 * q^83 - 2 * q^84 - 42 * q^85 - 32 * q^86 + 16 * q^87 - 6 * q^88 + 12 * q^89 - 6 * q^90 + 12 * q^91 - 6 * q^92 + 10 * q^93 + 54 * q^95 + 2 * q^96 + 8 * q^97 + 8 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.0359800	−	0.0261410i	0.0160908	−	0.0116906i	−0.579711	−	0.814822i	$-0.696834\pi$
$5$	0.0359800	−	0.0261410i	0.0160908	−	0.0116906i	0.595802	+	0.803132i	$0.296834\pi$
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−0.0444738			−0.0140638
$11$	−0.154014	−	3.31305i	−0.0464370	−	0.998921i
$11$	−0.154014	−	3.31305i	−0.0464370	−	0.998921i
$12$	−1.00000			−0.288675
$13$	4.52125	+	3.28488i	1.25397	+	0.911061i	0.998445	−	0.0557414i	$-0.0177522\pi$
$13$	4.52125	+	3.28488i	1.25397	+	0.911061i	0.255523	+	0.966803i	$0.417752\pi$
$14$	−0.309017	+	0.951057i	−0.0825883	+	0.254181i
$15$	0.0137431	+	0.0422971i	0.00354847	+	0.0109211i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	2.18999	−	1.59112i	0.531152	−	0.385904i	−0.289637	−	0.957137i	$-0.593535\pi$
$17$	2.18999	−	1.59112i	0.531152	−	0.385904i	0.820788	+	0.571232i	$0.193535\pi$
$18$	0.309017	+	0.951057i	0.0728360	+	0.224166i
$19$	1.10954	−	3.41481i	0.254546	−	0.783412i	−0.739373	−	0.673296i	$-0.764878\pi$
$19$	1.10954	−	3.41481i	0.254546	−	0.783412i	0.993919	−	0.110116i	$-0.0351221\pi$
$20$	0.0359800	+	0.0261410i	0.00804538	+	0.00584531i
$21$	1.00000			0.218218
$22$	−1.82276	+	2.77084i	−0.388614	+	0.590745i
$23$	3.09945			0.646279			0.323140	−	0.946351i	$-0.395262\pi$
$23$	3.09945			0.646279			0.323140	+	0.946351i	$0.395262\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	−1.54447	+	4.75340i	−0.308895	+	0.950680i
$26$	−1.72696	−	5.31505i	−0.338685	−	1.04237i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	0.809017	−	0.587785i	0.152890	−	0.111081i
$29$	1.87573	+	5.77290i	0.348314	+	1.07200i	0.959786	+	0.280734i	$0.0905778\pi$
$29$	1.87573	+	5.77290i	0.348314	+	1.07200i	−0.611472	+	0.791266i	$0.709422\pi$
$30$	0.0137431	−	0.0422971i	0.00250914	−	0.00772235i
$31$	7.18277	+	5.21859i	1.29006	+	0.937286i	0.999807	−	0.0196633i	$-0.00625943\pi$
$31$	7.18277	+	5.21859i	1.29006	+	0.937286i	0.290256	+	0.956949i	$0.406259\pi$
$32$	1.00000			0.176777
$33$	3.19849	+	0.877312i	0.556785	+	0.152720i
$34$	−2.70698			−0.464243
$35$	−0.0359800	−	0.0261410i	−0.00608174	−	0.00441864i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	−0.777675	−	2.39344i	−0.127849	−	0.393479i	0.866560	−	0.499072i	$-0.166326\pi$
$37$	−0.777675	−	2.39344i	−0.127849	−	0.393479i	−0.994409	+	0.105593i	$0.966326\pi$
$38$	−2.90481	+	2.11047i	−0.471223	+	0.342364i
$39$	−4.52125	+	3.28488i	−0.723979	+	0.526002i
$40$	−0.0137431	−	0.0422971i	−0.00217298	−	0.00668775i
$41$	2.13502	−	6.57092i	0.333434	−	1.02621i	−0.634054	−	0.773289i	$-0.718610\pi$
$41$	2.13502	−	6.57092i	0.333434	−	1.02621i	0.967488	−	0.252916i	$-0.0813898\pi$
$42$	−0.809017	−	0.587785i	−0.124834	−	0.0906972i
$43$	12.7697			1.94736			0.973678	−	0.227929i	$-0.0731953\pi$
$43$	12.7697			1.94736			0.973678	+	0.227929i	$0.0731953\pi$
$44$	3.10330	−	1.17026i	0.467840	−	0.176424i
$45$	−0.0444738			−0.00662976
$46$	−2.50750	−	1.82181i	−0.369711	−	0.268611i
$47$	3.52125	−	10.8373i	0.513627	−	1.58078i	−0.272140	−	0.962258i	$-0.587731\pi$
$47$	3.52125	−	10.8373i	0.513627	−	1.58078i	0.785767	−	0.618523i	$-0.212269\pi$
$48$	−0.309017	−	0.951057i	−0.0446028	−	0.137273i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	4.04348	−	2.93776i	0.571835	−	0.415463i
$51$	0.836503	+	2.57449i	0.117134	+	0.360501i
$52$	−1.72696	+	5.31505i	−0.239487	+	0.737064i
$53$	−6.65303	−	4.83371i	−0.913863	−	0.663961i	0.0281257	−	0.999604i	$-0.491046\pi$
$53$	−6.65303	−	4.83371i	−0.913863	−	0.663961i	−0.941989	+	0.335644i	$0.891046\pi$
$54$	−1.00000			−0.136083
$55$	−0.0921479	−	0.115177i	−0.0124252	−	0.0155305i
$56$	−1.00000			−0.133631
$57$	2.90481	+	2.11047i	0.384752	+	0.279539i
$58$	1.87573	−	5.77290i	0.246295	−	0.758018i
$59$	−1.02285	−	3.14800i	−0.133163	−	0.409835i	0.862136	−	0.506676i	$-0.169126\pi$
$59$	−1.02285	−	3.14800i	−0.133163	−	0.409835i	−0.995300	+	0.0968413i	$0.969126\pi$
$60$	−0.0359800	+	0.0261410i	−0.00464500	+	0.00337479i
$61$	−9.81713	+	7.13256i	−1.25696	+	0.913231i	−0.998604	−	0.0528198i	$-0.983179\pi$
$61$	−9.81713	+	7.13256i	−1.25696	+	0.913231i	−0.258351	+	0.966051i	$0.583179\pi$
$62$	−2.74357	−	8.44385i	−0.348434	−	1.07237i
$63$	−0.309017	+	0.951057i	−0.0389325	+	0.119822i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.248545			0.0308282
$66$	−2.07196	−	2.58978i	−0.255041	−	0.318780i
$67$	−1.01248			−0.123694			−0.0618469	−	0.998086i	$-0.519699\pi$
$67$	−1.01248			−0.123694			−0.0618469	+	0.998086i	$0.519699\pi$
$68$	2.18999	+	1.59112i	0.265576	+	0.192952i
$69$	−0.957782	+	2.94775i	−0.115303	+	0.354867i
$70$	0.0137431	+	0.0422971i	0.00164262	+	0.00505547i
$71$	−2.85410	+	2.07363i	−0.338720	+	0.246094i	−0.744121	−	0.668044i	$-0.767132\pi$
$71$	−2.85410	+	2.07363i	−0.338720	+	0.246094i	0.405402	+	0.914139i	$0.367132\pi$
$72$	−0.809017	+	0.587785i	−0.0953436	+	0.0692712i
$73$	−0.196232	−	0.603941i	−0.0229673	−	0.0706860i	0.938916	−	0.344147i	$-0.111832\pi$
$73$	−0.196232	−	0.603941i	−0.0229673	−	0.0706860i	−0.961883	+	0.273461i	$0.911832\pi$
$74$	−0.777675	+	2.39344i	−0.0904029	+	0.278232i
$75$	−4.04348	−	2.93776i	−0.466901	−	0.339224i
$76$	3.59055			0.411864
$77$	−3.10330	+	1.17026i	−0.353654	+	0.133364i
$78$	5.58857			0.632781
$79$	5.05982	+	3.67617i	0.569274	+	0.413602i	0.834841	−	0.550491i	$-0.185559\pi$
$79$	5.05982	+	3.67617i	0.569274	+	0.413602i	−0.265567	+	0.964092i	$0.585559\pi$
$80$	−0.0137431	+	0.0422971i	−0.00153653	+	0.00472896i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−5.58956	+	4.06105i	−0.617264	+	0.448468i
$83$	−4.43714	+	3.22377i	−0.487040	+	0.353855i	−0.804045	−	0.594569i	$-0.797323\pi$
$83$	−4.43714	+	3.22377i	−0.487040	+	0.353855i	0.317005	+	0.948424i	$0.397323\pi$
$84$	0.309017	+	0.951057i	0.0337165	+	0.103769i
$85$	0.0372024	−	0.114497i	0.00403517	−	0.0124190i
$86$	−10.3309	−	7.50582i	−1.11401	−	0.809373i
$87$	−6.06998			−0.650770
$88$	−3.19849	−	0.877312i	−0.340960	−	0.0935217i
$89$	−2.76195			−0.292767			−0.146383	−	0.989228i	$-0.546763\pi$
$89$	−2.76195			−0.292767			−0.146383	+	0.989228i	$0.546763\pi$
$90$	0.0359800	+	0.0261410i	0.00379263	+	0.00275551i
$91$	1.72696	−	5.31505i	0.181035	−	0.557168i
$92$	0.957782	+	2.94775i	0.0998556	+	0.307324i
$93$	−7.18277	+	5.21859i	−0.744818	+	0.541142i
$94$	−9.21875	+	6.69781i	−0.950841	+	0.690827i
$95$	−0.0493454	−	0.151870i	−0.00506273	−	0.0155815i
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	−9.05000	−	6.57521i	−0.918888	−	0.667611i	0.0243587	−	0.999703i	$-0.492246\pi$
$97$	−9.05000	−	6.57521i	−0.918888	−	0.667611i	−0.943247	+	0.332092i	$0.892246\pi$
$98$	1.00000			0.101015
$99$	−1.82276	+	2.77084i	−0.183194	+	0.278480i
$100$	−4.99802			−0.499802
$101$	15.9771	+	11.6080i	1.58978	+	1.15504i	0.904260	+	0.426983i	$0.140423\pi$
$101$	15.9771	+	11.6080i	1.58978	+	1.15504i	0.685516	+	0.728057i	$0.259577\pi$
$102$	0.836503	−	2.57449i	0.0828262	−	0.254913i
$103$	−5.23832	−	16.1219i	−0.516147	−	1.58854i	−0.781185	−	0.624300i	$-0.785384\pi$
$103$	−5.23832	−	16.1219i	−0.516147	−	1.58854i	0.265037	−	0.964238i	$-0.414616\pi$
$104$	4.52125	−	3.28488i	0.443345	−	0.322109i
$105$	0.0359800	−	0.0261410i	0.00351129	−	0.00255110i
$106$	2.54123	+	7.82110i	0.246826	+	0.759652i
$107$	−0.126528	+	0.389412i	−0.0122319	+	0.0376459i	−0.956986	−	0.290134i	$-0.906300\pi$
$107$	−0.126528	+	0.389412i	−0.0122319	+	0.0376459i	0.944754	+	0.327779i	$0.106300\pi$
$108$	0.809017	+	0.587785i	0.0778477	+	0.0565597i
$109$	6.48263			0.620924			0.310462	−	0.950586i	$-0.399516\pi$
$109$	6.48263			0.620924			0.310462	+	0.950586i	$0.399516\pi$
$110$	0.00684958	+	0.147344i	0.000653082	+	0.0140487i
$111$	2.51661			0.238866
$112$	0.809017	+	0.587785i	0.0764449	+	0.0555405i
$113$	−3.75909	+	11.5693i	−0.353625	+	1.08835i	0.603177	+	0.797607i	$0.293901\pi$
$113$	−3.75909	+	11.5693i	−0.353625	+	1.08835i	−0.956802	+	0.290739i	$0.906099\pi$
$114$	−1.10954	−	3.41481i	−0.103918	−	0.319827i
$115$	0.111518	−	0.0810227i	0.0103991	−	0.00755541i
$116$	−4.91072	+	3.56785i	−0.455949	+	0.331266i
$117$	−1.72696	−	5.31505i	−0.159658	−	0.491376i
$118$	−1.02285	+	3.14800i	−0.0941608	+	0.289797i
$119$	−2.18999	−	1.59112i	−0.200756	−	0.145858i
$120$	0.0444738			0.00405988
$121$	−10.9526	+	1.02051i	−0.995687	+	0.0927738i
$122$	12.1346			1.09862
$123$	5.58956	+	4.06105i	0.503994	+	0.366173i
$124$	−2.74357	+	8.44385i	−0.246380	+	0.758280i
$125$	0.137404	+	0.422887i	0.0122898	+	0.0378242i
$126$	0.809017	−	0.587785i	0.0720730	−	0.0523641i
$127$	−15.2295	+	11.0648i	−1.35140	+	0.981846i	−0.352455	+	0.935829i	$0.614653\pi$
$127$	−15.2295	+	11.0648i	−1.35140	+	0.981846i	−0.998941	+	0.0460173i	$0.985347\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−3.94604	+	12.1447i	−0.347430	+	1.06928i
$130$	−0.201077	−	0.146091i	−0.0176356	−	0.0128130i
$131$	−5.73889			−0.501409			−0.250705	−	0.968064i	$-0.580662\pi$
$131$	−5.73889			−0.501409			−0.250705	+	0.968064i	$0.580662\pi$
$132$	0.154014	+	3.31305i	0.0134052	+	0.288364i
$133$	−3.59055			−0.311340
$134$	0.819111	+	0.595119i	0.0707604	+	0.0514104i
$135$	0.0137431	−	0.0422971i	0.00118282	−	0.00364035i
$136$	−0.836503	−	2.57449i	−0.0717296	−	0.220761i
$137$	−14.9119	+	10.8342i	−1.27401	+	0.925625i	−0.999355	−	0.0359172i	$-0.988565\pi$
$137$	−14.9119	+	10.8342i	−1.27401	+	0.925625i	−0.274658	+	0.961542i	$0.588565\pi$
$138$	2.50750	−	1.82181i	0.213453	−	0.155083i
$139$	1.98063	+	6.09575i	0.167995	+	0.517035i	0.999244	−	0.0388644i	$-0.0123740\pi$
$139$	1.98063	+	6.09575i	0.167995	+	0.517035i	−0.831250	+	0.555899i	$0.812374\pi$
$140$	0.0137431	−	0.0422971i	0.00116151	−	0.00357475i
$141$	9.21875	+	6.69781i	0.776359	+	0.564057i
$142$	3.52786			0.296052
$143$	10.1866	−	15.4850i	0.851848	−	1.29492i
$144$	1.00000			0.0833333
$145$	0.218398	+	0.158676i	0.0181370	+	0.0131773i
$146$	−0.196232	+	0.603941i	−0.0162403	+	0.0499825i
$147$	−0.309017	−	0.951057i	−0.0254873	−	0.0784418i
$148$	2.03598	−	1.47923i	0.167357	−	0.121592i
$149$	−9.37999	+	6.81496i	−0.768439	+	0.558303i	−0.901487	−	0.432806i	$-0.857523\pi$
$149$	−9.37999	+	6.81496i	−0.768439	+	0.558303i	0.133048	+	0.991110i	$0.457523\pi$
$150$	1.54447	+	4.75340i	0.126106	+	0.388114i
$151$	6.49663	−	19.9946i	0.528688	−	1.62713i	−0.228217	−	0.973610i	$-0.573290\pi$
$151$	6.49663	−	19.9946i	0.528688	−	1.62713i	0.756905	−	0.653524i	$-0.226710\pi$
$152$	−2.90481	−	2.11047i	−0.235612	−	0.171182i
$153$	−2.70698			−0.218846
$154$	3.19849	+	0.877312i	0.257741	+	0.0706958i
$155$	0.394855			0.0317155
$156$	−4.52125	−	3.28488i	−0.361990	−	0.263001i
$157$	4.29104	−	13.2065i	0.342462	−	1.05399i	−0.620466	−	0.784233i	$-0.713057\pi$
$157$	4.29104	−	13.2065i	0.342462	−	1.05399i	0.962928	−	0.269757i	$-0.0869435\pi$
$158$	−1.93268	−	5.94817i	−0.153756	−	0.473211i
$159$	6.65303	−	4.83371i	0.527619	−	0.383338i
$160$	0.0359800	−	0.0261410i	0.00284447	−	0.00206663i
$161$	−0.957782	−	2.94775i	−0.0754838	−	0.232315i
$162$	0.309017	−	0.951057i	0.0242787	−	0.0747221i
$163$	−10.8541	−	7.88597i	−0.850159	−	0.617677i	0.0750310	−	0.997181i	$-0.476094\pi$
$163$	−10.8541	−	7.88597i	−0.850159	−	0.617677i	−0.925190	+	0.379505i	$0.876094\pi$
$164$	6.90907			0.539508
$165$	0.138016	−	0.0520460i	0.0107445	−	0.00405178i
$166$	5.48461			0.425689
$167$	−16.6909	−	12.1266i	−1.29158	−	0.938387i	−0.291743	−	0.956497i	$-0.594235\pi$
$167$	−16.6909	−	12.1266i	−1.29158	−	0.938387i	−0.999836	+	0.0181094i	$0.994235\pi$
$168$	0.309017	−	0.951057i	0.0238412	−	0.0733756i
$169$	5.63403	+	17.3398i	0.433387	+	1.33383i
$170$	−0.0973973	+	0.0707633i	−0.00747003	+	0.00542729i
$171$	−2.90481	+	2.11047i	−0.222137	+	0.161392i
$172$	3.94604	+	12.1447i	0.300883	+	0.926023i
$173$	2.84236	−	8.74790i	0.216101	−	0.665090i	−0.782973	−	0.622056i	$-0.786298\pi$
$173$	2.84236	−	8.74790i	0.216101	−	0.665090i	0.999074	−	0.0430342i	$-0.0137024\pi$
$174$	4.91072	+	3.56785i	0.372281	+	0.270478i
$175$	4.99802			0.377815
$176$	2.07196	+	2.58978i	0.156180	+	0.195212i
$177$	3.31001			0.248795
$178$	2.23447	+	1.62344i	0.167480	+	0.121682i
$179$	−3.34251	+	10.2872i	−0.249831	+	0.768900i	0.744973	+	0.667094i	$0.232462\pi$
$179$	−3.34251	+	10.2872i	−0.249831	+	0.768900i	−0.994804	+	0.101806i	$0.967538\pi$
$180$	−0.0137431	−	0.0422971i	−0.00102435	−	0.00315264i
$181$	4.78678	−	3.47780i	0.355799	−	0.258503i	−0.395499	−	0.918466i	$-0.629428\pi$
$181$	4.78678	−	3.47780i	0.355799	−	0.258503i	0.751298	+	0.659964i	$0.229428\pi$
$182$	−4.52125	+	3.28488i	−0.335137	+	0.243491i
$183$	−3.74981	−	11.5407i	−0.277194	−	0.853115i
$184$	0.957782	−	2.94775i	0.0706086	−	0.217311i
$185$	−0.0905477	−	0.0657867i	−0.00665720	−	0.00483674i
$186$	8.87839			0.650995
$187$	−5.60876	−	7.01050i	−0.410153	−	0.512658i
$188$	11.3950			0.831066
$189$	−0.809017	−	0.587785i	−0.0588473	−	0.0427551i
$190$	−0.0493454	+	0.151870i	−0.00357989	+	0.0110178i
$191$	0.726585	+	2.23620i	0.0525739	+	0.161806i	0.973896	−	0.226994i	$-0.0728898\pi$
$191$	0.726585	+	2.23620i	0.0525739	+	0.161806i	−0.921322	+	0.388800i	$0.872890\pi$
$192$	0.809017	−	0.587785i	0.0583858	−	0.0424197i
$193$	16.4830	−	11.9756i	1.18647	−	0.862020i	0.193583	−	0.981084i	$-0.437989\pi$
$193$	16.4830	−	11.9756i	1.18647	−	0.862020i	0.992887	+	0.119064i	$0.0379893\pi$
$194$	3.45679	+	10.6389i	0.248183	+	0.763829i
$195$	−0.0768045	+	0.236380i	−0.00550009	+	0.0169275i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	18.0417			1.28542			0.642710	−	0.766109i	$-0.277810\pi$
$197$	18.0417			1.28542			0.642710	+	0.766109i	$0.277810\pi$
$198$	3.10330	−	1.17026i	0.220542	−	0.0831670i
$199$	2.51341			0.178171			0.0890854	−	0.996024i	$-0.471606\pi$
$199$	2.51341			0.178171			0.0890854	+	0.996024i	$0.471606\pi$
$200$	4.04348	+	2.93776i	0.285918	+	0.207731i
$201$	0.312873	−	0.962923i	0.0220683	−	0.0679193i
$202$	−6.10269	−	18.7822i	−0.429384	−	1.32151i
$203$	4.91072	−	3.56785i	0.344665	−	0.250414i
$204$	−2.18999	+	1.59112i	−0.153330	+	0.111401i
$205$	−0.0949524	−	0.292234i	−0.00663177	−	0.0204105i
$206$	−5.23832	+	16.1219i	−0.364971	+	1.12327i
$207$	−2.50750	−	1.82181i	−0.174284	−	0.126624i
$208$	−5.58857			−0.387498
$209$	−11.4843	−	3.15003i	−0.794387	−	0.217892i
$210$	−0.0444738			−0.00306898
$211$	8.38749	+	6.09387i	0.577419	+	0.419519i	0.837793	−	0.545989i	$-0.183846\pi$
$211$	8.38749	+	6.09387i	0.577419	+	0.419519i	−0.260374	+	0.965508i	$0.583846\pi$
$212$	2.54123	−	7.82110i	0.174532	−	0.537155i
$213$	−1.09017	−	3.35520i	−0.0746972	−	0.229894i
$214$	0.331254	−	0.240670i	0.0226440	−	0.0164519i
$215$	0.459453	−	0.333812i	0.0313344	−	0.0227658i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	2.74357	−	8.44385i	0.186246	−	0.573206i
$218$	−5.24456	−	3.81040i	−0.355207	−	0.258073i
$219$	0.635021			0.0429108
$220$	0.0810650	−	0.123230i	0.00546540	−	0.00830814i
$221$	15.1282			1.01763
$222$	−2.03598	−	1.47923i	−0.136646	−	0.0992792i
$223$	−0.885066	+	2.72395i	−0.0592684	+	0.182409i	−0.976307	−	0.216388i	$-0.930572\pi$
$223$	−0.885066	+	2.72395i	−0.0592684	+	0.182409i	0.917039	+	0.398797i	$0.130572\pi$
$224$	−0.309017	−	0.951057i	−0.0206471	−	0.0635451i
$225$	4.04348	−	2.93776i	0.269566	−	0.195851i
$226$	9.84142	−	7.15021i	0.654641	−	0.475625i
$227$	−0.235052	−	0.723415i	−0.0156009	−	0.0480148i	0.942953	−	0.332926i	$-0.108036\pi$
$227$	−0.235052	−	0.723415i	−0.0156009	−	0.0480148i	−0.958554	+	0.284911i	$0.908036\pi$
$228$	−1.10954	+	3.41481i	−0.0734811	+	0.226152i
$229$	2.48892	+	1.80830i	0.164472	+	0.119496i	0.666977	−	0.745078i	$-0.267588\pi$
$229$	2.48892	+	1.80830i	0.164472	+	0.119496i	−0.502505	+	0.864575i	$0.667588\pi$
$230$	−0.137844			−0.00908917
$231$	−0.154014	−	3.31305i	−0.0101334	−	0.217982i
$232$	6.06998			0.398514
$233$	6.55822	+	4.76482i	0.429643	+	0.312154i	0.781506	−	0.623898i	$-0.214452\pi$
$233$	6.55822	+	4.76482i	0.429643	+	0.312154i	−0.351863	+	0.936051i	$0.614452\pi$
$234$	−1.72696	+	5.31505i	−0.112895	+	0.347455i
$235$	−0.156603	−	0.481975i	−0.0102157	−	0.0314406i
$236$	2.67785	−	1.94557i	0.174313	−	0.126646i
$237$	−5.05982	+	3.67617i	−0.328670	+	0.238793i
$238$	0.836503	+	2.57449i	0.0542225	+	0.166880i
$239$	−4.51313	+	13.8900i	−0.291930	+	0.898469i	0.692305	+	0.721605i	$0.256595\pi$
$239$	−4.51313	+	13.8900i	−0.291930	+	0.898469i	−0.984235	+	0.176864i	$0.943405\pi$
$240$	−0.0359800	−	0.0261410i	−0.00232250	−	0.00168740i
$241$	−8.59136			−0.553418			−0.276709	−	0.960954i	$-0.589244\pi$
$241$	−8.59136			−0.553418			−0.276709	+	0.960954i	$0.589244\pi$
$242$	9.46065	+	5.61214i	0.608153	+	0.360762i
$243$	−1.00000			−0.0641500
$244$	−9.81713	−	7.13256i	−0.628478	−	0.456616i
$245$	−0.0137431	+	0.0422971i	−0.000878018	+	0.00270226i
$246$	−2.13502	−	6.57092i	−0.136124	−	0.418947i
$247$	16.2338	−	11.7945i	1.03293	−	0.750467i
$248$	7.18277	−	5.21859i	0.456106	−	0.331381i
$249$	−1.69484	−	5.21618i	−0.107406	−	0.330562i
$250$	0.137404	−	0.422887i	0.00869021	−	0.0267457i
$251$	−1.55038	−	1.12642i	−0.0978590	−	0.0710987i	0.537780	−	0.843085i	$-0.319263\pi$
$251$	−1.55038	−	1.12642i	−0.0978590	−	0.0710987i	−0.635639	+	0.771987i	$0.719263\pi$
$252$	−1.00000			−0.0629941
$253$	−0.477358	−	10.2686i	−0.0300113	−	0.645582i
$254$	18.8246			1.18116
$255$	0.0973973	+	0.0707633i	0.00609925	+	0.00443137i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	1.52848	+	4.70416i	0.0953437	+	0.293438i	0.987343	−	0.158599i	$-0.0506977\pi$
$257$	1.52848	+	4.70416i	0.0953437	+	0.293438i	−0.891999	+	0.452037i	$0.850698\pi$
$258$	10.3309	−	7.50582i	0.643172	−	0.467292i
$259$	−2.03598	+	1.47923i	−0.126510	+	0.0919146i
$260$	0.0768045	+	0.236380i	0.00476322	+	0.0146597i
$261$	1.87573	−	5.77290i	0.116105	−	0.357333i
$262$	4.64286	+	3.37324i	0.286837	+	0.208399i
$263$	−21.2209			−1.30853			−0.654267	−	0.756264i	$-0.727023\pi$
$263$	−21.2209			−1.30853			−0.654267	+	0.756264i	$0.727023\pi$
$264$	1.82276	−	2.77084i	0.112183	−	0.170533i
$265$	−0.365734			−0.0224669
$266$	2.90481	+	2.11047i	0.178106	+	0.129401i
$267$	0.853491	−	2.62677i	0.0522328	−	0.160756i
$268$	−0.312873	−	0.962923i	−0.0191117	−	0.0588199i
$269$	15.7507	−	11.4436i	0.960337	−	0.697726i	0.00710810	−	0.999975i	$-0.497737\pi$
$269$	15.7507	−	11.4436i	0.960337	−	0.697726i	0.953229	+	0.302249i	$0.0977374\pi$
$270$	−0.0359800	+	0.0261410i	−0.00218967	+	0.00159089i
$271$	1.40233	+	4.31591i	0.0851852	+	0.262173i	0.984572	−	0.174981i	$-0.0559864\pi$
$271$	1.40233	+	4.31591i	0.0851852	+	0.262173i	−0.899387	+	0.437154i	$0.855986\pi$
$272$	−0.836503	+	2.57449i	−0.0507205	+	0.156102i
$273$	4.52125	+	3.28488i	0.273638	+	0.198810i
$274$	18.4322			1.11353
$275$	15.9861	+	4.38482i	0.963999	+	0.264415i
$276$	−3.09945			−0.186565
$277$	−3.41392	−	2.48036i	−0.205123	−	0.149030i	0.480482	−	0.877005i	$-0.340462\pi$
$277$	−3.41392	−	2.48036i	−0.205123	−	0.149030i	−0.685604	+	0.727975i	$0.740462\pi$
$278$	1.98063	−	6.09575i	0.118790	−	0.365599i
$279$	−2.74357	−	8.44385i	−0.164253	−	0.505520i
$280$	−0.0359800	+	0.0261410i	−0.00215022	+	0.00156222i
$281$	−23.3286	+	16.9492i	−1.39167	+	1.01110i	−0.395985	+	0.918257i	$0.629597\pi$
$281$	−23.3286	+	16.9492i	−1.39167	+	1.01110i	−0.995680	+	0.0928472i	$0.970403\pi$
$282$	−3.52125	−	10.8373i	−0.209687	−	0.645351i
$283$	3.17288	−	9.76512i	0.188608	−	0.580476i	−0.811384	−	0.584514i	$-0.801285\pi$
$283$	3.17288	−	9.76512i	0.188608	−	0.580476i	0.999992	+	0.00403781i	$0.00128528\pi$
$284$	−2.85410	−	2.07363i	−0.169360	−	0.123047i
$285$	0.159685			0.00945893
$286$	−17.3430	+	6.54010i	−1.02551	+	0.386724i
$287$	−6.90907			−0.407830
$288$	−0.809017	−	0.587785i	−0.0476718	−	0.0346356i
$289$	−2.98889	+	9.19886i	−0.175817	+	0.541109i
$290$	−0.0834207	−	0.256742i	−0.00489863	−	0.0150764i
$291$	9.05000	−	6.57521i	0.530520	−	0.385446i
$292$	0.513743	−	0.373256i	0.0300645	−	0.0218432i
$293$	6.38445	+	19.6493i	0.372984	+	1.14793i	0.944829	+	0.327565i	$0.106228\pi$
$293$	6.38445	+	19.6493i	0.372984	+	1.14793i	−0.571845	+	0.820362i	$0.693772\pi$
$294$	−0.309017	+	0.951057i	−0.0180222	+	0.0554667i
$295$	−0.119094	−	0.0865269i	−0.00693393	−	0.00503779i
$296$	−2.51661			−0.146275
$297$	−2.07196	−	2.58978i	−0.120227	−	0.150275i
$298$	11.5943			0.671640
$299$	14.0134	+	10.1813i	0.810414	+	0.588800i
$300$	1.54447	−	4.75340i	0.0891702	−	0.274438i
$301$	−3.94604	−	12.1447i	−0.227446	−	0.700007i
$302$	−17.0084	+	12.3573i	−0.978723	+	0.711084i
$303$	−15.9771	+	11.6080i	−0.917858	+	0.666863i
$304$	1.10954	+	3.41481i	0.0636365	+	0.195853i
$305$	−0.166768	+	0.513260i	−0.00954912	+	0.0293892i
$306$	2.18999	+	1.59112i	0.125194	+	0.0909585i
$307$	28.2701			1.61346			0.806730	−	0.590920i	$-0.201235\pi$
$307$	28.2701			1.61346			0.806730	+	0.590920i	$0.201235\pi$
$308$	−2.07196	−	2.58978i	−0.118061	−	0.147567i
$309$	16.9516			0.964341
$310$	−0.319445	−	0.232090i	−0.0181432	−	0.0131818i
$311$	−6.05859	+	18.6464i	−0.343551	+	1.05734i	0.618803	+	0.785546i	$0.287618\pi$
$311$	−6.05859	+	18.6464i	−0.343551	+	1.05734i	−0.962355	+	0.271797i	$0.912382\pi$
$312$	1.72696	+	5.31505i	0.0977700	+	0.300905i
$313$	−24.3118	+	17.6635i	−1.37418	+	0.998403i	−0.376786	+	0.926300i	$0.622971\pi$
$313$	−24.3118	+	17.6635i	−1.37418	+	0.998403i	−0.997397	+	0.0721022i	$0.977029\pi$
$314$	−11.2341	+	8.16204i	−0.633976	+	0.460611i
$315$	0.0137431	+	0.0422971i	0.000774339	+	0.00238317i
$316$	−1.93268	+	5.94817i	−0.108722	+	0.334611i
$317$	3.31233	+	2.40655i	0.186039	+	0.135165i	0.676907	−	0.736069i	$-0.263320\pi$
$317$	3.31233	+	2.40655i	0.186039	+	0.135165i	−0.490867	+	0.871234i	$0.663320\pi$
$318$	−8.22359			−0.461156
$319$	18.8370	−	7.10348i	1.05467	−	0.397719i
$320$	−0.0444738			−0.00248616
$321$	−0.331254	−	0.240670i	−0.0184888	−	0.0134329i
$322$	−0.957782	+	2.94775i	−0.0533751	+	0.164272i
$323$	−3.00350	−	9.24384i	−0.167119	−	0.514341i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	−22.5973	+	16.4179i	−1.25347	+	0.910701i
$326$	4.14590	+	12.7598i	0.229620	+	0.706698i
$327$	−2.00324	+	6.16535i	−0.110780	+	0.340945i
$328$	−5.58956	−	4.06105i	−0.308632	−	0.224234i
$329$	−11.3950			−0.628227
$330$	−0.142249	−	0.0390174i	−0.00783054	−	0.00214783i
$331$	−19.9868			−1.09857			−0.549286	−	0.835634i	$-0.685100\pi$
$331$	−19.9868			−1.09857			−0.549286	+	0.835634i	$0.685100\pi$
$332$	−4.43714	−	3.22377i	−0.243520	−	0.176928i
$333$	−0.777675	+	2.39344i	−0.0426163	+	0.131160i
$334$	6.37535	+	19.6213i	0.348844	+	1.07363i
$335$	−0.0364289	+	0.0264672i	−0.00199033	+	0.00144606i
$336$	−0.809017	+	0.587785i	−0.0441355	+	0.0320663i
$337$	−1.62891	−	5.01327i	−0.0887324	−	0.273090i	0.896837	−	0.442361i	$-0.145859\pi$
$337$	−1.62891	−	5.01327i	−0.0887324	−	0.273090i	−0.985570	+	0.169270i	$0.945859\pi$
$338$	5.63403	−	17.3398i	0.306451	−	0.943159i
$339$	−9.84142	−	7.15021i	−0.534513	−	0.388346i
$340$	0.120390			0.00652905
$341$	16.1832	−	24.6006i	0.876368	−	1.33220i
$342$	3.59055			0.194155
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	3.94604	−	12.1447i	0.212756	−	0.654797i
$345$	0.0425962	+	0.131097i	0.00229330	+	0.00705805i
$346$	−7.44141	+	5.40650i	−0.400052	+	0.290655i
$347$	6.20793	−	4.51032i	0.333259	−	0.242127i	−0.408553	−	0.912734i	$-0.633967\pi$
$347$	6.20793	−	4.51032i	0.333259	−	0.242127i	0.741812	+	0.670608i	$0.233967\pi$
$348$	−1.87573	−	5.77290i	−0.100550	−	0.309460i
$349$	−2.96468	+	9.12433i	−0.158695	+	0.488414i	−0.998517	−	0.0544489i	$-0.982660\pi$
$349$	−2.96468	+	9.12433i	−0.158695	+	0.488414i	0.839821	+	0.542863i	$0.182660\pi$
$350$	−4.04348	−	2.93776i	−0.216133	−	0.157030i
$351$	5.58857			0.298296
$352$	−0.154014	−	3.31305i	−0.00820897	−	0.176586i
$353$	18.9953			1.01102			0.505509	−	0.862822i	$-0.331305\pi$
$353$	18.9953			1.01102			0.505509	+	0.862822i	$0.331305\pi$
$354$	−2.67785	−	1.94557i	−0.142326	−	0.103406i
$355$	−0.0484840	+	0.149218i	−0.00257326	+	0.00791968i
$356$	−0.853491	−	2.62677i	−0.0452349	−	0.139219i
$357$	2.18999	−	1.59112i	0.115907	−	0.0842112i
$358$	8.75080	−	6.35783i	0.462494	−	0.336022i
$359$	1.87248	+	5.76291i	0.0988259	+	0.304155i	0.988232	−	0.152963i	$-0.0488816\pi$
$359$	1.87248	+	5.76291i	0.0988259	+	0.304155i	−0.889406	+	0.457118i	$0.848882\pi$
$360$	−0.0137431	+	0.0422971i	−0.000724328	+	0.00222925i
$361$	4.94145	+	3.59017i	0.260076	+	0.188956i
$362$	−5.91679			−0.310979
$363$	2.41396	−	10.7319i	0.126700	−	0.563276i
$364$	5.58857			0.292921
$365$	−0.0228481	−	0.0166001i	−0.00119592	−	0.000868889i
$366$	−3.74981	+	11.5407i	−0.196006	+	0.603244i
$367$	−2.73232	−	8.40921i	−0.142626	−	0.438957i	0.854072	−	0.520154i	$-0.174126\pi$
$367$	−2.73232	−	8.40921i	−0.142626	−	0.438957i	−0.996698	+	0.0811972i	$0.974126\pi$
$368$	−2.50750	+	1.82181i	−0.130713	+	0.0949684i
$369$	−5.58956	+	4.06105i	−0.290981	+	0.211410i
$370$	0.0345861	+	0.106445i	0.00179805	+	0.00553382i
$371$	−2.54123	+	7.82110i	−0.131934	+	0.406051i
$372$	−7.18277	−	5.21859i	−0.372409	−	0.270571i
$373$	22.8998			1.18571			0.592853	−	0.805310i	$-0.298001\pi$
$373$	22.8998			1.18571			0.592853	+	0.805310i	$0.298001\pi$
$374$	0.416913	+	8.96836i	0.0215581	+	0.463743i
$375$	−0.444650			−0.0229616
$376$	−9.21875	−	6.69781i	−0.475421	−	0.345413i
$377$	−10.4826	+	32.2622i	−0.539883	+	1.66159i
$378$	0.309017	+	0.951057i	0.0158941	+	0.0489171i
$379$	−17.6432	+	12.8185i	−0.906271	+	0.658444i	−0.940069	−	0.340984i	$-0.889240\pi$
$379$	−17.6432	+	12.8185i	−0.906271	+	0.658444i	0.0337982	+	0.999429i	$0.489240\pi$
$380$	0.129188	−	0.0938606i	0.00662721	−	0.00481495i
$381$	−5.81713	−	17.9033i	−0.298021	−	0.917214i
$382$	0.726585	−	2.23620i	0.0371753	−	0.114414i
$383$	−15.1177	−	10.9836i	−0.772476	−	0.561237i	0.130235	−	0.991483i	$-0.458427\pi$
$383$	−15.1177	−	10.9836i	−0.772476	−	0.561237i	−0.902712	+	0.430246i	$0.858427\pi$
$384$	−1.00000			−0.0510310
$385$	−0.0810650	+	0.123230i	−0.00413146	+	0.00628036i
$386$	−20.3741			−1.03701
$387$	−10.3309	−	7.50582i	−0.525148	−	0.381542i
$388$	3.45679	−	10.6389i	0.175492	−	0.540109i
$389$	6.90806	+	21.2608i	0.350252	+	1.07797i	0.958711	+	0.284381i	$0.0917880\pi$
$389$	6.90806	+	21.2608i	0.350252	+	1.07797i	−0.608459	+	0.793585i	$0.708212\pi$
$390$	0.201077	−	0.146091i	0.0101819	−	0.00739760i
$391$	6.78777	−	4.93160i	0.343272	−	0.249402i
$392$	0.309017	+	0.951057i	0.0156077	+	0.0480356i
$393$	1.77341	−	5.45801i	0.0894569	−	0.275320i
$394$	−14.5961	−	10.6047i	−0.735340	−	0.534256i
$395$	0.278151			0.0139953
$396$	−3.19849	−	0.877312i	−0.160730	−	0.0440866i
$397$	−9.97135			−0.500447			−0.250224	−	0.968188i	$-0.580504\pi$
$397$	−9.97135			−0.500447			−0.250224	+	0.968188i	$0.580504\pi$
$398$	−2.03339	−	1.47734i	−0.101925	−	0.0740526i
$399$	1.10954	−	3.41481i	0.0555465	−	0.170955i
$400$	−1.54447	−	4.75340i	−0.0772237	−	0.237670i
$401$	3.53659	−	2.56948i	0.176609	−	0.128314i	−0.495969	−	0.868340i	$-0.665187\pi$
$401$	3.53659	−	2.56948i	0.176609	−	0.128314i	0.672578	+	0.740026i	$0.265187\pi$
$402$	−0.819111	+	0.595119i	−0.0408535	+	0.0296818i
$403$	15.3326	+	47.1890i	0.763774	+	2.35065i
$404$	−6.10269	+	18.7822i	−0.303620	+	0.934447i
$405$	0.0359800	+	0.0261410i	0.00178786	+	0.00129896i
$406$	−6.06998			−0.301248
$407$	−7.80980	+	2.94510i	−0.387117	+	0.145983i
$408$	2.70698			0.134016
$409$	−14.5834	−	10.5955i	−0.721102	−	0.523911i	0.165634	−	0.986187i	$-0.447033\pi$
$409$	−14.5834	−	10.5955i	−0.721102	−	0.523911i	−0.886736	+	0.462276i	$0.847033\pi$
$410$	−0.0949524	+	0.292234i	−0.00468937	+	0.0144324i
$411$	−5.69585	−	17.5300i	−0.280956	−	0.864693i
$412$	13.7141	−	9.96388i	0.675646	−	0.490885i
$413$	−2.67785	+	1.94557i	−0.131768	+	0.0957354i
$414$	0.957782	+	2.94775i	0.0470724	+	0.144874i
$415$	−0.0753758	+	0.231983i	−0.00370005	+	0.0113876i
$416$	4.52125	+	3.28488i	0.221672	+	0.161054i
$417$	−6.40945			−0.313872
$418$	7.43947	+	9.29874i	0.363876	+	0.454816i
$419$	−20.9471			−1.02334			−0.511668	−	0.859184i	$-0.670972\pi$
$419$	−20.9471			−1.02334			−0.511668	+	0.859184i	$0.670972\pi$
$420$	0.0359800	+	0.0261410i	0.00175565	+	0.00127555i
$421$	8.38524	−	25.8071i	0.408671	−	1.25776i	−0.509119	−	0.860696i	$-0.670029\pi$
$421$	8.38524	−	25.8071i	0.408671	−	1.25776i	0.917790	−	0.397065i	$-0.129971\pi$
$422$	−3.20374	−	9.86009i	−0.155955	−	0.479982i
$423$	−9.21875	+	6.69781i	−0.448231	+	0.325659i
$424$	−6.65303	+	4.83371i	−0.323099	+	0.234745i
$425$	4.18086	+	12.8674i	0.202802	+	0.624159i
$426$	−1.09017	+	3.35520i	−0.0528189	+	0.162560i
$427$	9.81713	+	7.13256i	0.475084	+	0.345169i
$428$	−0.409452			−0.0197916
$429$	11.5793	+	14.4732i	0.559054	+	0.698772i
$430$	−0.567915			−0.0273873
$431$	−4.45150	−	3.23420i	−0.214421	−	0.155786i	0.475391	−	0.879775i	$-0.342307\pi$
$431$	−4.45150	−	3.23420i	−0.214421	−	0.155786i	−0.689812	+	0.723989i	$0.742307\pi$
$432$	−0.309017	+	0.951057i	−0.0148676	+	0.0457577i
$433$	2.09072	+	6.43457i	0.100474	+	0.309226i	0.988641	−	0.150293i	$-0.0480218\pi$
$433$	2.09072	+	6.43457i	0.100474	+	0.309226i	−0.888168	+	0.459519i	$0.848022\pi$
$434$	−7.18277	+	5.21859i	−0.344784	+	0.250500i
$435$	−0.218398	+	0.158676i	−0.0104714	+	0.00760791i
$436$	2.00324	+	6.16535i	0.0959380	+	0.295267i
$437$	3.43896	−	10.5840i	0.164508	−	0.506303i
$438$	−0.513743	−	0.373256i	−0.0245476	−	0.0178349i
$439$	9.02871			0.430917			0.215458	−	0.976513i	$-0.430875\pi$
$439$	9.02871			0.430917			0.215458	+	0.976513i	$0.430875\pi$
$440$	−0.138016	+	0.0520460i	−0.00657963	+	0.00248120i
$441$	1.00000			0.0476190
$442$	−12.2389	−	8.89211i	−0.582147	−	0.422954i
$443$	−11.3408	+	34.9035i	−0.538820	+	1.65832i	0.196428	+	0.980518i	$0.437066\pi$
$443$	−11.3408	+	34.9035i	−0.538820	+	1.65832i	−0.735248	+	0.677798i	$0.762934\pi$
$444$	0.777675	+	2.39344i	0.0369068	+	0.113588i
$445$	−0.0993752	+	0.0722003i	−0.00471084	+	0.00342262i
$446$	2.31713	−	1.68350i	0.109719	−	0.0797158i
$447$	−3.58284	−	11.0268i	−0.169462	−	0.521552i
$448$	−0.309017	+	0.951057i	−0.0145997	+	0.0449332i
$449$	−11.3605	−	8.25392i	−0.536137	−	0.389527i	0.286511	−	0.958077i	$-0.407504\pi$
$449$	−11.3605	−	8.25392i	−0.536137	−	0.389527i	−0.822648	+	0.568550i	$0.807504\pi$
$450$	−4.99802			−0.235609
$451$	−22.0986	−	6.06141i	−1.04058	−	0.285421i
$452$	−12.1647			−0.572178
$453$	17.0084	+	12.3573i	0.799124	+	0.580598i
$454$	−0.235052	+	0.723415i	−0.0110315	+	0.0339516i
$455$	−0.0768045	−	0.236380i	−0.00360065	−	0.0110817i
$456$	2.90481	−	2.11047i	0.136030	−	0.0988319i
$457$	−25.1457	+	18.2694i	−1.17627	+	0.854607i	−0.991746	−	0.128221i	$-0.959073\pi$
$457$	−25.1457	+	18.2694i	−1.17627	+	0.854607i	−0.184521	+	0.982829i	$0.559073\pi$
$458$	−0.950682	−	2.92590i	−0.0444224	−	0.136718i
$459$	0.836503	−	2.57449i	0.0390446	−	0.120167i
$460$	0.111518	+	0.0810227i	0.00519956	+	0.00377770i
$461$	−15.0728			−0.702009			−0.351004	−	0.936374i	$-0.614160\pi$
$461$	−15.0728			−0.702009			−0.351004	+	0.936374i	$0.614160\pi$
$462$	−1.82276	+	2.77084i	−0.0848025	+	0.128911i
$463$	−21.6250			−1.00500			−0.502499	−	0.864578i	$-0.667586\pi$
$463$	−21.6250			−1.00500			−0.502499	+	0.864578i	$0.667586\pi$
$464$	−4.91072	−	3.56785i	−0.227974	−	0.165633i
$465$	−0.122017	+	0.375530i	−0.00565840	+	0.0174148i
$466$	−2.50502	−	7.70965i	−0.116043	−	0.357142i
$467$	27.7614	−	20.1698i	1.28464	−	0.933349i	0.284962	−	0.958539i	$-0.408019\pi$
$467$	27.7614	−	20.1698i	1.28464	−	0.933349i	0.999683	+	0.0251899i	$0.00801904\pi$
$468$	4.52125	−	3.28488i	0.208995	−	0.151844i
$469$	0.312873	+	0.962923i	0.0144471	+	0.0444636i
$470$	−0.156603	+	0.481975i	−0.00722356	+	0.0222318i
$471$	11.2341	+	8.16204i	0.517640	+	0.376087i
$472$	−3.31001			−0.152355
$473$	−1.96671	−	42.3065i	−0.0904293	−	1.94525i
$474$	6.25428			0.287268
$475$	14.5183	+	10.5482i	0.666146	+	0.483984i
$476$	0.836503	−	2.57449i	0.0383411	−	0.118002i
$477$	2.54123	+	7.82110i	0.116355	+	0.358104i
$478$	11.8155	−	8.58449i	0.540430	−	0.392645i
$479$	6.53680	−	4.74926i	0.298674	−	0.216999i	−0.428348	−	0.903614i	$-0.640904\pi$
$479$	6.53680	−	4.74926i	0.298674	−	0.216999i	0.727021	+	0.686615i	$0.240904\pi$
$480$	0.0137431	+	0.0422971i	0.000627286	+	0.00193059i
$481$	4.34609	−	13.3759i	0.198165	−	0.609888i
$482$	6.95055	+	5.04987i	0.316589	+	0.230015i
$483$	3.09945			0.141030
$484$	−4.35509	−	10.1011i	−0.197959	−	0.459143i
$485$	−0.497502			−0.0225904
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	4.20251	−	12.9340i	0.190434	−	0.586096i	−0.809565	−	0.587030i	$-0.800297\pi$
$487$	4.20251	−	12.9340i	0.190434	−	0.586096i	1.00000		0.000933674i	$0.000297198\pi$
$488$	3.74981	+	11.5407i	0.169746	+	0.522424i
$489$	10.8541	−	7.88597i	0.490839	−	0.356616i
$490$	0.0359800	−	0.0261410i	0.00162541	−	0.00118093i
$491$	−11.1056	−	34.1795i	−0.501188	−	1.54250i	−0.807086	−	0.590434i	$-0.798957\pi$
$491$	−11.1056	−	34.1795i	−0.501188	−	1.54250i	0.305898	−	0.952064i	$-0.401043\pi$
$492$	−2.13502	+	6.57092i	−0.0962542	+	0.296240i
$493$	13.2932	+	9.65809i	0.598697	+	0.434979i
$494$	−20.0660			−0.902813
$495$	0.00684958	+	0.147344i	0.000307866	+	0.00662261i
$496$	−8.87839			−0.398651
$497$	2.85410	+	2.07363i	0.128024	+	0.0930149i
$498$	−1.69484	+	5.21618i	−0.0759475	+	0.233742i
$499$	5.70323	+	17.5527i	0.255312	+	0.785769i	0.993768	+	0.111467i	$0.0355551\pi$
$499$	5.70323	+	17.5527i	0.255312	+	0.785769i	−0.738456	+	0.674301i	$0.764445\pi$
$500$	−0.359729	+	0.261359i	−0.0160876	+	0.0116883i
$501$	16.6909	−	12.1266i	0.745694	−	0.541778i
$502$	0.592192	+	1.82258i	0.0264308	+	0.0813457i
$503$	8.45030	−	26.0074i	0.376780	−	1.15961i	−0.565489	−	0.824756i	$-0.691313\pi$
$503$	8.45030	−	26.0074i	0.376780	−	1.15961i	0.942270	−	0.334855i	$-0.108687\pi$
$504$	0.809017	+	0.587785i	0.0360365	+	0.0261820i
$505$	0.878300			0.0390838
$506$	−5.64955	+	8.58806i	−0.251153	+	0.381786i
$507$	−18.2321			−0.809717
$508$	−15.2295	−	11.0648i	−0.675698	−	0.490923i
$509$	−7.06749	+	21.7515i	−0.313261	+	0.964119i	0.663203	+	0.748439i	$0.269197\pi$
$509$	−7.06749	+	21.7515i	−0.313261	+	0.964119i	−0.976464	+	0.215679i	$0.930803\pi$
$510$	−0.0372024	−	0.114497i	−0.00164735	−	0.00507003i
$511$	−0.513743	+	0.373256i	−0.0227267	+	0.0165119i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−1.10954	−	3.41481i	−0.0489874	−	0.150768i
$514$	1.52848	−	4.70416i	0.0674182	−	0.207492i
$515$	−0.609918	−	0.443131i	−0.0268762	−	0.0195267i
$516$	−12.7697			−0.562153
$517$	−36.4468	−	9.99697i	−1.60293	−	0.439666i
$518$	2.51661			0.110573
$519$	7.44141	+	5.40650i	0.326641	+	0.237319i
$520$	0.0768045	−	0.236380i	0.00336810	−	0.0103660i
$521$	−1.63587	−	5.03468i	−0.0716686	−	0.220573i	0.908806	−	0.417219i	$-0.136995\pi$
$521$	−1.63587	−	5.03468i	−0.0716686	−	0.220573i	−0.980475	+	0.196646i	$0.936995\pi$
$522$	−4.91072	+	3.56785i	−0.214936	+	0.156160i
$523$	4.83285	−	3.51127i	0.211326	−	0.153537i	−0.477087	−	0.878856i	$-0.658308\pi$
$523$	4.83285	−	3.51127i	0.211326	−	0.153537i	0.688413	+	0.725319i	$0.258308\pi$
$524$	−1.77341	−	5.45801i	−0.0774720	−	0.238434i
$525$	−1.54447	+	4.75340i	−0.0674064	+	0.207455i
$526$	17.1680	+	12.4733i	0.748562	+	0.543862i
$527$	24.0336			1.04692
$528$	−3.10330	+	1.17026i	−0.135054	+	0.0509292i
$529$	−13.3934			−0.582323
$530$	0.295885	+	0.214973i	0.0128524	+	0.00933783i
$531$	−1.02285	+	3.14800i	−0.0443878	+	0.136612i
$532$	−1.10954	−	3.41481i	−0.0481047	−	0.148051i
$533$	31.2376	−	22.6955i	1.35305	−	0.983050i
$534$	−2.23447	+	1.62344i	−0.0966949	+	0.0702529i
$535$	0.00562716	+	0.0173186i	0.000243284	+	0.000748750i
$536$	−0.312873	+	0.962923i	−0.0135140	+	0.0415919i
$537$	−8.75080	−	6.35783i	−0.377625	−	0.274361i
$538$	−19.4689			−0.839365
$539$	2.07196	+	2.58978i	0.0892456	+	0.111550i
$540$	0.0444738			0.00191385
$541$	−2.02350	−	1.47016i	−0.0869972	−	0.0632072i	0.543436	−	0.839450i	$-0.317123\pi$
$541$	−2.02350	−	1.47016i	−0.0869972	−	0.0632072i	−0.630434	+	0.776243i	$0.717123\pi$
$542$	1.40233	−	4.31591i	0.0602350	−	0.185384i
$543$	1.82839	+	5.62720i	0.0784636	+	0.241486i
$544$	2.18999	−	1.59112i	0.0938952	−	0.0682189i
$545$	0.233245	−	0.169463i	0.00999113	−	0.00725898i
$546$	−1.72696	−	5.31505i	−0.0739072	−	0.227463i
$547$	−5.70399	+	17.5551i	−0.243885	+	0.750601i	0.751933	+	0.659240i	$0.229122\pi$
$547$	−5.70399	+	17.5551i	−0.243885	+	0.750601i	−0.995818	+	0.0913609i	$0.970878\pi$
$548$	−14.9119	−	10.8342i	−0.637007	−	0.462812i
$549$	12.1346			0.517894
$550$	−10.3557	−	12.9438i	−0.441569	−	0.551925i
$551$	21.7946			0.928479
$552$	2.50750	+	1.82181i	0.106726	+	0.0775413i
$553$	1.93268	−	5.94817i	0.0821858	−	0.252942i
$554$	1.30400	+	4.01330i	0.0554017	+	0.170509i
$555$	0.0905477	−	0.0657867i	0.00384354	−	0.00279249i
$556$	−5.18536	+	3.76738i	−0.219908	+	0.159773i
$557$	1.31730	+	4.05425i	0.0558160	+	0.171784i	0.975078	−	0.221862i	$-0.0712135\pi$
$557$	1.31730	+	4.05425i	0.0558160	+	0.171784i	−0.919262	+	0.393646i	$0.871214\pi$
$558$	−2.74357	+	8.44385i	−0.116145	+	0.357457i
$559$	57.7348	+	41.9468i	2.44192	+	1.77416i
$560$	0.0444738			0.00187936
$561$	8.40058	−	3.16788i	0.354673	−	0.133748i
$562$	28.8357			1.21636
$563$	−21.6834	−	15.7539i	−0.913845	−	0.663948i	0.0281390	−	0.999604i	$-0.491042\pi$
$563$	−21.6834	−	15.7539i	−0.913845	−	0.663948i	−0.941984	+	0.335656i	$0.891042\pi$
$564$	−3.52125	+	10.8373i	−0.148271	+	0.456332i
$565$	0.167181	+	0.514529i	0.00703335	+	0.0216464i
$566$	−8.30671	+	6.03517i	−0.349157	+	0.253677i
$567$	0.809017	−	0.587785i	0.0339755	−	0.0246847i
$568$	1.09017	+	3.35520i	0.0457425	+	0.140781i
$569$	4.37897	−	13.4771i	0.183576	−	0.564989i	−0.816345	−	0.577565i	$-0.804003\pi$
$569$	4.37897	−	13.4771i	0.183576	−	0.564989i	0.999921	+	0.0125758i	$0.00400310\pi$
$570$	−0.129188	−	0.0938606i	−0.00541109	−	0.00393139i
$571$	−2.27324			−0.0951323			−0.0475661	−	0.998868i	$-0.515146\pi$
$571$	−2.27324			−0.0951323			−0.0475661	+	0.998868i	$0.515146\pi$
$572$	17.8750	+	4.90292i	0.747390	+	0.205001i
$573$	−2.35128			−0.0982261
$574$	5.58956	+	4.06105i	0.233304	+	0.169505i
$575$	−4.78701	+	14.7329i	−0.199632	+	0.614405i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	2.77464	−	2.01589i	0.115510	−	0.0839227i	−0.528531	−	0.848914i	$-0.677257\pi$
$577$	2.77464	−	2.01589i	0.115510	−	0.0839227i	0.644040	+	0.764991i	$0.277257\pi$
$578$	7.82502	−	5.68521i	0.325478	−	0.236473i
$579$	6.29593	+	19.3769i	0.261650	+	0.805276i
$580$	−0.0834207	+	0.256742i	−0.00346385	+	0.0106606i
$581$	4.43714	+	3.22377i	0.184084	+	0.133745i
$582$	−11.1864			−0.463692
$583$	−14.9896	+	22.7862i	−0.620807	+	0.943710i
$584$	−0.635021			−0.0262774
$585$	−0.201077	−	0.146091i	−0.00831351	−	0.00604012i
$586$	6.38445	−	19.6493i	0.263739	−	0.811706i
$587$	−3.50733	−	10.7945i	−0.144763	−	0.445535i	0.852217	−	0.523188i	$-0.175257\pi$
$587$	−3.50733	−	10.7945i	−0.144763	−	0.445535i	−0.996980	+	0.0776528i	$0.975257\pi$
$588$	0.809017	−	0.587785i	0.0333633	−	0.0242399i
$589$	25.7901	−	18.7376i	1.06266	−	0.772069i
$590$	0.0454899	+	0.140004i	0.00187279	+	0.00576385i
$591$	−5.57520	+	17.1587i	−0.229333	+	0.705815i
$592$	2.03598	+	1.47923i	0.0836783	+	0.0607958i
$593$	−7.78935			−0.319870			−0.159935	−	0.987128i	$-0.551129\pi$
$593$	−7.78935			−0.319870			−0.159935	+	0.987128i	$0.551129\pi$
$594$	0.154014	+	3.31305i	0.00631927	+	0.135936i
$595$	−0.120390			−0.00493549
$596$	−9.37999	−	6.81496i	−0.384219	−	0.279152i
$597$	−0.776686	+	2.39039i	−0.0317877	+	0.0978323i
$598$	−5.35263	−	16.4737i	−0.218885	−	0.673660i
$599$	−37.4943	+	27.2412i	−1.53197	+	1.11304i	−0.576846	+	0.816853i	$0.695717\pi$
$599$	−37.4943	+	27.2412i	−1.53197	+	1.11304i	−0.955129	+	0.296192i	$0.904283\pi$
$600$	−4.04348	+	2.93776i	−0.165075	+	0.119934i
$601$	2.83589	+	8.72798i	0.115678	+	0.356022i	0.992088	−	0.125545i	$-0.0400679\pi$
$601$	2.83589	+	8.72798i	0.115678	+	0.356022i	−0.876409	+	0.481567i	$0.840068\pi$
$602$	−3.94604	+	12.1447i	−0.160829	+	0.494980i
$603$	0.819111	+	0.595119i	0.0333568	+	0.0242351i
$604$	21.0235			0.855435
$605$	−0.367396	+	0.323029i	−0.0149368	+	0.0131330i
$606$	19.7487			0.802237
$607$	11.2028	+	8.13932i	0.454708	+	0.330365i	0.791452	−	0.611231i	$-0.209326\pi$
$607$	11.2028	+	8.13932i	0.454708	+	0.330365i	−0.336744	+	0.941596i	$0.609326\pi$
$608$	1.10954	−	3.41481i	0.0449978	−	0.138489i
$609$	1.87573	+	5.77290i	0.0760083	+	0.233930i
$610$	0.436605	−	0.317212i	0.0176776	−	0.0128435i
$611$	51.5196	−	37.4312i	2.08426	−	1.51430i
$612$	−0.836503	−	2.57449i	−0.0338136	−	0.104068i
$613$	5.24781	−	16.1511i	0.211957	−	0.652336i	−0.787399	−	0.616444i	$-0.788573\pi$
$613$	5.24781	−	16.1511i	0.211957	−	0.652336i	0.999356	−	0.0358923i	$-0.0114273\pi$
$614$	−22.8710	−	16.6167i	−0.922998	−	0.670597i
$615$	0.307273			0.0123904
$616$	0.154014	+	3.31305i	0.00620540	+	0.133486i
$617$	20.2082			0.813550			0.406775	−	0.913528i	$-0.366653\pi$
$617$	20.2082			0.813550			0.406775	+	0.913528i	$0.366653\pi$
$618$	−13.7141	−	9.96388i	−0.551662	−	0.400806i
$619$	−8.24408	+	25.3727i	−0.331358	+	1.01981i	0.637131	+	0.770756i	$0.280121\pi$
$619$	−8.24408	+	25.3727i	−0.331358	+	1.01981i	−0.968488	+	0.249058i	$0.919879\pi$
$620$	0.122017	+	0.375530i	0.00490032	+	0.0150816i
$621$	2.50750	−	1.82181i	0.100623	−	0.0731067i
$622$	15.8616	−	11.5241i	0.635992	−	0.462076i
$623$	0.853491	+	2.62677i	0.0341944	+	0.105239i
$624$	1.72696	−	5.31505i	0.0691339	−	0.212772i
$625$	−20.2014	−	14.6772i	−0.808057	−	0.587088i
$626$	30.0510			1.20108
$627$	6.54471	−	9.94883i	0.261370	−	0.397318i
$628$	13.8861			0.554116
$629$	−5.51136	−	4.00424i	−0.219752	−	0.159659i
$630$	0.0137431	−	0.0422971i	0.000547540	−	0.00168516i
$631$	−12.2697	−	37.7623i	−0.488449	−	1.50329i	−0.826922	−	0.562316i	$-0.809910\pi$
$631$	−12.2697	−	37.7623i	−0.488449	−	1.50329i	0.338473	−	0.940976i	$-0.390090\pi$
$632$	5.05982	−	3.67617i	0.201269	−	0.146230i
$633$	−8.38749	+	6.09387i	−0.333373	+	0.242210i
$634$	−1.26520	−	3.89388i	−0.0502474	−	0.154646i
$635$	−0.258710	+	0.796227i	−0.0102666	+	0.0315973i
$636$	6.65303	+	4.83371i	0.263810	+	0.191669i
$637$	−5.58857			−0.221427
$638$	−19.4148	−	5.32527i	−0.768638	−	0.210829i
$639$	3.52786			0.139560
$640$	0.0359800	+	0.0261410i	0.00142224	+	0.00103331i
$641$	−3.47951	+	10.7088i	−0.137432	+	0.422973i	−0.995960	−	0.0897934i	$-0.971379\pi$
$641$	−3.47951	+	10.7088i	−0.137432	+	0.422973i	0.858528	+	0.512766i	$0.171379\pi$
$642$	0.126528	+	0.389412i	0.00499365	+	0.0153689i
$643$	21.1721	−	15.3824i	0.834947	−	0.606625i	−0.0860075	−	0.996294i	$-0.527411\pi$
$643$	21.1721	−	15.3824i	0.834947	−	0.606625i	0.920955	+	0.389670i	$0.127411\pi$
$644$	2.50750	−	1.82181i	0.0988095	−	0.0717893i
$645$	0.175495	+	0.540119i	0.00691012	+	0.0212672i
$646$	−3.00350	+	9.24384i	−0.118171	+	0.363694i
$647$	37.4234	+	27.1897i	1.47126	+	1.06894i	0.980245	+	0.197788i	$0.0633757\pi$
$647$	37.4234	+	27.1897i	1.47126	+	1.06894i	0.491020	+	0.871148i	$0.336624\pi$
$648$	1.00000			0.0392837
$649$	−10.2719	+	3.87358i	−0.403209	+	0.152051i
$650$	27.9318			1.09558
$651$	7.18277	+	5.21859i	0.281515	+	0.204532i
$652$	4.14590	−	12.7598i	0.162366	−	0.499711i
$653$	8.91856	+	27.4485i	0.349010	+	1.07414i	0.959402	+	0.282043i	$0.0910121\pi$
$653$	8.91856	+	27.4485i	0.349010	+	1.07414i	−0.610392	+	0.792100i	$0.708988\pi$
$654$	5.24456	−	3.81040i	0.205079	−	0.148998i
$655$	−0.206485	+	0.150020i	−0.00806805	+	0.00586178i
$656$	2.13502	+	6.57092i	0.0833586	+	0.256551i
$657$	−0.196232	+	0.603941i	−0.00765576	+	0.0235620i
$658$	9.21875	+	6.69781i	0.359384	+	0.261108i
$659$	−48.7813			−1.90025			−0.950124	−	0.311871i	$-0.899044\pi$
$659$	−48.7813			−1.90025			−0.950124	+	0.311871i	$0.899044\pi$
$660$	0.0921479	+	0.115177i	0.00358685	+	0.00448328i
$661$	−9.92428			−0.386010			−0.193005	−	0.981198i	$-0.561823\pi$
$661$	−9.92428			−0.386010			−0.193005	+	0.981198i	$0.561823\pi$
$662$	16.1696	+	11.7479i	0.628451	+	0.456596i
$663$	−4.67486	+	14.3877i	−0.181556	+	0.558773i
$664$	1.69484	+	5.21618i	0.0657725	+	0.202427i
$665$	−0.129188	+	0.0938606i	−0.00500970	+	0.00363976i
$666$	2.03598	−	1.47923i	0.0788926	−	0.0573188i
$667$	5.81372	+	17.8928i	0.225108	+	0.692811i
$668$	6.37535	−	19.6213i	0.246670	−	0.759171i
$669$	−2.31713	−	1.68350i	−0.0895855	−	0.0650877i
$670$	0.0450287			0.00173961
$671$	25.1425	+	31.4261i	0.970615	+	1.21319i
$672$	1.00000			0.0385758
$673$	−27.7912	−	20.1915i	−1.07127	−	0.778325i	−0.0951321	−	0.995465i	$-0.530327\pi$
$673$	−27.7912	−	20.1915i	−1.07127	−	0.778325i	−0.976141	+	0.217139i	$0.930327\pi$
$674$	−1.62891	+	5.01327i	−0.0627433	+	0.193104i
$675$	1.54447	+	4.75340i	0.0594468	+	0.182959i
$676$	−14.7501	+	10.7166i	−0.567311	+	0.412176i
$677$	19.3432	−	14.0537i	0.743421	−	0.540127i	−0.150360	−	0.988631i	$-0.548043\pi$
$677$	19.3432	−	14.0537i	0.743421	−	0.540127i	0.893780	+	0.448505i	$0.148043\pi$
$678$	3.75909	+	11.5693i	0.144367	+	0.444316i
$679$	−3.45679	+	10.6389i	−0.132660	+	0.408284i
$680$	−0.0973973	−	0.0707633i	−0.00373501	−	0.00271365i
$681$	0.760644			0.0291479
$682$	−27.5523	+	10.3901i	−1.05503	+	0.397856i
$683$	−10.8197			−0.414005			−0.207002	−	0.978340i	$-0.566371\pi$
$683$	−10.8197			−0.414005			−0.207002	+	0.978340i	$0.566371\pi$
$684$	−2.90481	−	2.11047i	−0.111068	−	0.0806959i
$685$	−0.253316	+	0.779627i	−0.00967871	+	0.0297880i
$686$	−0.309017	−	0.951057i	−0.0117983	−	0.0363115i
$687$	−2.48892	+	1.80830i	−0.0949581	+	0.0689911i
$688$	−10.3309	+	7.50582i	−0.393861	+	0.286157i
$689$	−14.2018	−	43.7088i	−0.541047	−	1.66517i
$690$	0.0425962	−	0.131097i	0.00162161	−	0.00499080i
$691$	19.7368	+	14.3396i	0.750821	+	0.545504i	0.896081	−	0.443890i	$-0.146402\pi$
$691$	19.7368	+	14.3396i	0.750821	+	0.545504i	−0.145260	+	0.989394i	$0.546402\pi$
$692$	9.19808			0.349659
$693$	3.19849	+	0.877312i	0.121501	+	0.0333263i
$694$	−7.67342			−0.291279
$695$	0.230612	+	0.167550i	0.00874762	+	0.00635552i
$696$	−1.87573	+	5.77290i	−0.0710993	+	0.218821i
$697$	−5.77946	−	17.7874i	−0.218913	−	0.673744i
$698$	7.76162	−	5.63915i	0.293782	−	0.213445i
$699$	−6.55822	+	4.76482i	−0.248055	+	0.180222i
$700$	1.54447	+	4.75340i	0.0583756	+	0.179662i
$701$	2.35891	−	7.25998i	0.0890949	−	0.274206i	−0.896575	−	0.442892i	$-0.853952\pi$
$701$	2.35891	−	7.25998i	0.0890949	−	0.274206i	0.985670	+	0.168686i	$0.0539525\pi$
$702$	−4.52125	−	3.28488i	−0.170644	−	0.123980i
$703$	−9.03601			−0.340799
$704$	−1.82276	+	2.77084i	−0.0686979	+	0.104430i
$705$	0.506778			0.0190864
$706$	−15.3675	−	11.1652i	−0.578364	−	0.420206i
$707$	6.10269	−	18.7822i	0.229515	−	0.706375i
$708$	1.02285	+	3.14800i	0.0384410	+	0.118309i
$709$	−23.4440	+	17.0331i	−0.880458	+	0.639690i	−0.933373	−	0.358909i	$-0.883149\pi$
$709$	−23.4440	+	17.0331i	−0.880458	+	0.639690i	0.0529144	+	0.998599i	$0.483149\pi$
$710$	0.126933	−	0.0922220i	0.00476370	−	0.00346103i
$711$	−1.93268	−	5.94817i	−0.0724811	−	0.223074i
$712$	−0.853491	+	2.62677i	−0.0319859	+	0.0984425i
$713$	22.2626	+	16.1747i	0.833741	+	0.605748i
$714$	−2.70698			−0.101306
$715$	−0.0382794	−	0.823440i	−0.00143157	−	0.0307949i
$716$	−10.8166			−0.404235
$717$	−11.8155	−	8.58449i	−0.441259	−	0.320594i
$718$	1.87248	−	5.76291i	0.0698805	−	0.215070i
$719$	−0.784542	−	2.41457i	−0.0292585	−	0.0900483i	0.935361	−	0.353695i	$-0.115075\pi$
$719$	−0.784542	−	2.41457i	−0.0292585	−	0.0900483i	−0.964619	+	0.263646i	$0.915075\pi$
$720$	0.0359800	−	0.0261410i	0.00134090	−	0.000974218i
$721$	−13.7141	+	9.96388i	−0.510740	+	0.371074i
$722$	−1.88747	−	5.80902i	−0.0702442	−	0.216189i
$723$	2.65488	−	8.17087i	0.0987359	−	0.303878i
$724$	4.78678	+	3.47780i	0.177899	+	0.129251i
$725$	−30.3379			−1.12672
$726$	−8.26097	+	7.26336i	−0.306593	+	0.269569i
$727$	−18.6427			−0.691421			−0.345710	−	0.938341i	$-0.612362\pi$
$727$	−18.6427			−0.691421			−0.345710	+	0.938341i	$0.612362\pi$
$728$	−4.52125	−	3.28488i	−0.167569	−	0.121746i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	0.00872719	+	0.0268595i	0.000323008	+	0.000994116i
$731$	27.9655	−	20.3181i	1.03434	−	0.751493i
$732$	9.81713	−	7.13256i	0.362852	−	0.263627i
$733$	8.74108	+	26.9023i	0.322859	+	0.993659i	0.972398	+	0.233330i	$0.0749622\pi$
$733$	8.74108	+	26.9023i	0.322859	+	0.993659i	−0.649538	+	0.760329i	$0.725038\pi$
$734$	−2.73232	+	8.40921i	−0.100852	+	0.310390i
$735$	−0.0359800	−	0.0261410i	−0.00132714	−	0.000964226i
$736$	3.09945			0.114247
$737$	0.155936	+	3.35438i	0.00574396	+	0.123560i
$738$	6.90907			0.254327
$739$	37.0567	+	26.9233i	1.36315	+	0.990390i	0.998237	+	0.0593499i	$0.0189028\pi$
$739$	37.0567	+	26.9233i	1.36315	+	0.990390i	0.364917	+	0.931040i	$0.381097\pi$
$740$	0.0345861	−	0.106445i	0.00127141	−	0.00391300i
$741$	6.20074	+	19.0839i	0.227790	+	0.701066i
$742$	6.65303	−	4.83371i	0.244240	−	0.177451i
$743$	−1.16046	+	0.843123i	−0.0425731	+	0.0309312i	−0.608868	−	0.793271i	$-0.708376\pi$
$743$	−1.16046	+	0.843123i	−0.0425731	+	0.0309312i	0.566295	+	0.824202i	$0.308376\pi$
$744$	2.74357	+	8.44385i	0.100584	+	0.309567i
$745$	−0.159342	+	0.490405i	−0.00583785	+	0.0179670i
$746$	−18.5263	−	13.4602i	−0.678297	−	0.492812i
$747$	5.48461			0.200671
$748$	4.93418	−	7.50061i	0.180411	−	0.274249i
$749$	0.409452			0.0149611
$750$	0.359729	+	0.261359i	0.0131355	+	0.00954346i
$751$	3.27181	−	10.0696i	0.119390	−	0.367445i	−0.873447	−	0.486919i	$-0.838121\pi$
$751$	3.27181	−	10.0696i	0.119390	−	0.367445i	0.992837	+	0.119474i	$0.0381207\pi$
$752$	3.52125	+	10.8373i	0.128407	+	0.395195i
$753$	1.55038	−	1.12642i	0.0564989	−	0.0410489i
$754$	27.4439	−	19.9392i	0.999448	−	0.726141i
$755$	−0.288929	−	0.889234i	−0.0105152	−	0.0323625i
$756$	0.309017	−	0.951057i	0.0112388	−	0.0345896i
$757$	19.6330	+	14.2642i	0.713574	+	0.518441i	0.884325	−	0.466873i	$-0.154619\pi$
$757$	19.6330	+	14.2642i	0.713574	+	0.518441i	−0.170751	+	0.985314i	$0.554619\pi$
$758$	21.8082			0.792110
$759$	9.91354	+	2.71918i	0.359839	+	0.0987000i
$760$	−0.159685			−0.00579239
$761$	1.25823	+	0.914160i	0.0456109	+	0.0331383i	0.610357	−	0.792126i	$-0.291026\pi$
$761$	1.25823	+	0.914160i	0.0456109	+	0.0331383i	−0.564746	+	0.825265i	$0.691026\pi$
$762$	−5.81713	+	17.9033i	−0.210732	+	0.648568i
$763$	−2.00324	−	6.16535i	−0.0725223	−	0.223201i
$764$	−1.90222	+	1.38205i	−0.0688201	+	0.0500007i
$765$	−0.0973973	+	0.0707633i	−0.00352141	+	0.00255845i
$766$	5.77443	+	17.7719i	0.208639	+	0.642124i
$767$	5.71626	−	17.5928i	0.206402	−	0.635240i
$768$	0.809017	+	0.587785i	0.0291929	+	0.0212099i
$769$	26.3090			0.948727			0.474363	−	0.880329i	$-0.342678\pi$
$769$	26.3090			0.948727			0.474363	+	0.880329i	$0.342678\pi$
$770$	0.138016	−	0.0520460i	0.00497373	−	0.00187561i
$771$	−4.94625			−0.178135
$772$	16.4830	+	11.9756i	0.593235	+	0.431010i
$773$	16.7195	−	51.4574i	0.601359	−	1.85079i	0.0812487	−	0.996694i	$-0.474109\pi$
$773$	16.7195	−	51.4574i	0.601359	−	1.85079i	0.520110	−	0.854099i	$-0.325891\pi$
$774$	3.94604	+	12.1447i	0.141838	+	0.436531i
$775$	−35.8996	+	26.0826i	−1.28955	+	0.936915i
$776$	−9.05000	+	6.57521i	−0.324876	+	0.236036i
$777$	−0.777675	−	2.39344i	−0.0278989	−	0.0858641i
$778$	6.90806	−	21.2608i	0.247666	−	0.762237i
$779$	−20.0696	−	14.5814i	−0.719067	−	0.522433i
$780$	−0.248545			−0.00889933
$781$	7.30959	+	9.13641i	0.261558	+	0.326926i
$782$	−8.39014			−0.300031
$783$	4.91072	+	3.56785i	0.175495	+	0.127504i
$784$	0.309017	−	0.951057i	0.0110363	−	0.0339663i
$785$	−0.190839	−	0.587341i	−0.00681133	−	0.0209631i
$786$	−4.64286	+	3.37324i	−0.165605	+	0.120319i
$787$	21.9999	−	15.9839i	0.784212	−	0.569763i	−0.122028	−	0.992527i	$-0.538940\pi$
$787$	21.9999	−	15.9839i	0.784212	−	0.569763i	0.906240	+	0.422763i	$0.138940\pi$
$788$	5.57520	+	17.1587i	0.198608	+	0.611254i
$789$	6.55761	−	20.1822i	0.233457	−	0.718507i
$790$	−0.225029	−	0.163493i	−0.00800618	−	0.00581683i
$791$	12.1647			0.432526
$792$	2.07196	+	2.58978i	0.0736239	+	0.0920240i
$793$	−67.8153			−2.40819
$794$	8.06699	+	5.86101i	0.286287	+	0.207999i
$795$	0.113018	−	0.347834i	0.00400834	−	0.0123364i
$796$	0.776686	+	2.39039i	0.0275289	+	0.0847253i
$797$	13.5029	−	9.81046i	0.478299	−	0.347504i	−0.322368	−	0.946614i	$-0.604479\pi$
$797$	13.5029	−	9.81046i	0.478299	−	0.347504i	0.800667	+	0.599110i	$0.204479\pi$
$798$	−2.90481	+	2.11047i	−0.102829	+	0.0747099i
$799$	−9.53195	−	29.3363i	−0.337216	−	1.03784i
$800$	−1.54447	+	4.75340i	−0.0546054	+	0.168058i
$801$	2.23447	+	1.62344i	0.0789510	+	0.0573613i
$802$	−4.37147			−0.154362
$803$	−1.97066	+	0.743143i	−0.0695432	+	0.0262249i
$804$	1.01248			0.0357073
$805$	−0.111518	−	0.0810227i	−0.00393050	−	0.00285567i
$806$	15.3326	−	47.1890i	0.540069	−	1.66216i
$807$	6.01623	+	18.5161i	0.211781	+	0.651796i
$808$	15.9771	−	11.6080i	0.562071	−	0.408368i
$809$	28.5589	−	20.7492i	1.00408	−	0.729505i	0.0411186	−	0.999154i	$-0.486908\pi$
$809$	28.5589	−	20.7492i	1.00408	−	0.729505i	0.962959	+	0.269650i	$0.0869079\pi$
$810$	−0.0137431	−	0.0422971i	−0.000482885	−	0.00148617i
$811$	−4.16091	+	12.8060i	−0.146109	+	0.449678i	−0.997152	−	0.0754185i	$-0.975971\pi$
$811$	−4.16091	+	12.8060i	−0.146109	+	0.449678i	0.851043	+	0.525096i	$0.175971\pi$
$812$	4.91072	+	3.56785i	0.172332	+	0.125207i
$813$	−4.53802			−0.159155
$814$	8.04935	+	2.20785i	0.282129	+	0.0773851i
$815$	−0.596678			−0.0209007
$816$	−2.18999	−	1.59112i	−0.0766651	−	0.0557005i
$817$	14.1685	−	43.6060i	0.495692	−	1.52558i
$818$	5.57036	+	17.1438i	0.194763	+	0.599419i
$819$	−4.52125	+	3.28488i	−0.157985	+	0.114783i
$820$	0.248589	−	0.180610i	0.00868109	−	0.00630718i
$821$	−15.8932	−	48.9142i	−0.554676	−	1.70712i	−0.696798	−	0.717268i	$-0.745392\pi$
$821$	−15.8932	−	48.9142i	−0.554676	−	1.70712i	0.142122	−	0.989849i	$-0.454608\pi$
$822$	−5.69585	+	17.5300i	−0.198666	+	0.611430i
$823$	−44.2005	−	32.1136i	−1.54073	−	1.11941i	−0.949873	−	0.312635i	$-0.898788\pi$
$823$	−44.2005	−	32.1136i	−1.54073	−	1.11941i	−0.590861	−	0.806774i	$-0.701212\pi$
$824$	−16.9516			−0.590536
$825$	−9.11020	+	13.8487i	−0.317176	+	0.482150i
$826$	3.31001			0.115170
$827$	−12.2730	−	8.91685i	−0.426774	−	0.310069i	0.353584	−	0.935403i	$-0.384963\pi$
$827$	−12.2730	−	8.91685i	−0.426774	−	0.310069i	−0.780358	+	0.625334i	$0.784963\pi$
$828$	0.957782	−	2.94775i	0.0332852	−	0.102441i
$829$	9.25973	+	28.4985i	0.321604	+	0.989794i	0.972950	+	0.231014i	$0.0742043\pi$
$829$	9.25973	+	28.4985i	0.321604	+	0.989794i	−0.651347	+	0.758780i	$0.725796\pi$
$830$	0.197337	−	0.143373i	0.00684965	−	0.00497656i
$831$	3.41392	−	2.48036i	0.118428	−	0.0860426i
$832$	−1.72696	−	5.31505i	−0.0598717	−	0.184266i
$833$	−0.836503	+	2.57449i	−0.0289831	+	0.0892009i
$834$	5.18536	+	3.76738i	0.179554	+	0.130454i
$835$	−0.917541			−0.0317528
$836$	−0.552995	−	11.8957i	−0.0191257	−	0.411420i
$837$	8.87839			0.306882
$838$	16.9466	+	12.3124i	0.585411	+	0.425326i
$839$	−5.31949	+	16.3717i	−0.183649	+	0.565214i	−0.999922	−	0.0124519i	$-0.996036\pi$
$839$	−5.31949	+	16.3717i	−0.183649	+	0.565214i	0.816273	+	0.577666i	$0.196036\pi$
$840$	−0.0137431	−	0.0422971i	−0.000474184	−	0.00145939i
$841$	−6.34648	+	4.61099i	−0.218844	+	0.159000i
$842$	−21.9528	+	15.9497i	−0.756545	+	0.549662i
$843$	−8.91072	−	27.4244i	−0.306901	−	0.944546i
$844$	−3.20374	+	9.86009i	−0.110277	+	0.339398i
$845$	0.655992	+	0.476606i	0.0225668	+	0.0163957i
$846$	11.3950			0.391768
$847$	4.35509	+	10.1011i	0.149643	+	0.347080i
$848$	8.22359			0.282399
$849$	8.30671	+	6.03517i	0.285085	+	0.207127i
$850$	4.18086	−	12.8674i	0.143402	−	0.441347i
$851$	−2.41036	−	7.41833i	−0.0826262	−	0.254297i
$852$	2.85410	−	2.07363i	0.0977799	−	0.0710413i
$853$	1.32248	−	0.960840i	0.0452809	−	0.0328985i	−0.564915	−	0.825149i	$-0.691091\pi$
$853$	1.32248	−	0.960840i	0.0452809	−	0.0328985i	0.610196	+	0.792251i	$0.291091\pi$
$854$	−3.74981	−	11.5407i	−0.128316	−	0.394916i
$855$	−0.0493454	+	0.151870i	−0.00168758	+	0.00519383i
$856$	0.331254	+	0.240670i	0.0113220	+	0.00822593i
$857$	−1.49784			−0.0511654			−0.0255827	−	0.999673i	$-0.508144\pi$
$857$	−1.49784			−0.0511654			−0.0255827	+	0.999673i	$0.508144\pi$
$858$	−0.860718	−	18.5152i	−0.0293844	−	0.632098i
$859$	−17.5329			−0.598216			−0.299108	−	0.954219i	$-0.596689\pi$
$859$	−17.5329			−0.598216			−0.299108	+	0.954219i	$0.596689\pi$
$860$	0.459453	+	0.333812i	0.0156672	+	0.0113829i
$861$	2.13502	−	6.57092i	0.0727613	−	0.223936i
$862$	1.70032	+	5.23305i	0.0579132	+	0.178238i
$863$	−23.3672	+	16.9773i	−0.795429	+	0.577913i	−0.909570	−	0.415552i	$-0.863589\pi$
$863$	−23.3672	+	16.9773i	−0.795429	+	0.577913i	0.114141	+	0.993465i	$0.463589\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$	−0.126411	−	0.389052i	−0.00429809	−	0.0132282i
$866$	2.09072	−	6.43457i	0.0710455	−	0.218656i
$867$	−7.82502	−	5.68521i	−0.265751	−	0.193080i
$868$	8.87839			0.301352
$869$	11.4000	−	17.3296i	0.386720	−	0.587866i
$870$	0.269955			0.00915233
$871$	−4.57766	−	3.32586i	−0.155108	−	0.112693i
$872$	2.00324	−	6.16535i	0.0678384	−	0.208785i
$873$	3.45679	+	10.6389i	0.116995	+	0.360073i
$874$	−9.00332	+	6.54129i	−0.304542	+	0.221262i
$875$	0.359729	−	0.261359i	0.0121611	−	0.00883553i
$876$	0.196232	+	0.603941i	0.00663008	+	0.0204053i
$877$	14.8332	−	45.6518i	0.500880	−	1.54155i	−0.306708	−	0.951804i	$-0.599227\pi$
$877$	14.8332	−	45.6518i	0.500880	−	1.54155i	0.807588	−	0.589747i	$-0.200773\pi$
$878$	−7.30438	−	5.30694i	−0.246511	−	0.179101i
$879$	−20.6605			−0.696862
$880$	0.142249	+	0.0390174i	0.00479521	+	0.00131527i
$881$	−1.08115			−0.0364248			−0.0182124	−	0.999834i	$-0.505798\pi$
$881$	−1.08115			−0.0364248			−0.0182124	+	0.999834i	$0.505798\pi$
$882$	−0.809017	−	0.587785i	−0.0272410	−	0.0197918i
$883$	−7.61441	+	23.4348i	−0.256245	+	0.788642i	0.737336	+	0.675526i	$0.236083\pi$
$883$	−7.61441	+	23.4348i	−0.256245	+	0.788642i	−0.993582	+	0.113116i	$0.963917\pi$
$884$	4.67486	+	14.3877i	0.157232	+	0.483912i
$885$	0.119094	−	0.0865269i	0.00400330	−	0.00290857i
$886$	29.6907	−	21.5716i	0.997479	−	0.724711i
$887$	10.3676	+	31.9083i	0.348111	+	1.07138i	0.959897	+	0.280353i	$0.0904514\pi$
$887$	10.3676	+	31.9083i	0.348111	+	1.07138i	−0.611786	+	0.791023i	$0.709549\pi$
$888$	0.777675	−	2.39344i	0.0260971	−	0.0803185i
$889$	15.2295	+	11.0648i	0.510779	+	0.371103i
$890$	0.122834			0.00411742
$891$	3.10330	−	1.17026i	0.103965	−	0.0392053i
$892$	−2.86413			−0.0958983
$893$	−33.1003	−	24.0488i	−1.10766	−	0.804763i
$894$	−3.58284	+	11.0268i	−0.119828	+	0.368793i
$895$	0.148654	+	0.457510i	0.00496895	+	0.0152929i
$896$	0.809017	−	0.587785i	0.0270274	−	0.0196365i
$897$	−14.0134	+	10.1813i	−0.467893	+	0.339944i
$898$	4.33934	+	13.3551i	0.144806	+	0.445666i
$899$	−16.6534	+	51.2540i	−0.555423	+	1.70942i
$900$	4.04348	+	2.93776i	0.134783	+	0.0979255i
$901$	−22.2611			−0.741625
$902$	14.3153	+	17.8930i	0.476648	+	0.595772i
$903$	12.7697			0.424948
$904$	9.84142	+	7.15021i	0.327321	+	0.237812i
$905$	0.0813153	−	0.250263i	0.00270301	−	0.00831901i
$906$	−6.49663	−	19.9946i	−0.215836	−	0.664275i
$907$	−16.3505	+	11.8794i	−0.542910	+	0.394447i	−0.825165	−	0.564892i	$-0.808918\pi$
$907$	−16.3505	+	11.8794i	−0.542910	+	0.394447i	0.282254	+	0.959340i	$0.408918\pi$
$908$	0.615374	−	0.447095i	0.0204219	−	0.0148374i
$909$	−6.10269	−	18.7822i	−0.202413	−	0.622965i
$910$	−0.0768045	+	0.236380i	−0.00254605	+	0.00783592i
$911$	−20.8882	−	15.1762i	−0.692058	−	0.502809i	0.185278	−	0.982686i	$-0.440681\pi$
$911$	−20.8882	−	15.1762i	−0.692058	−	0.502809i	−0.877336	+	0.479877i	$0.840681\pi$
$912$	−3.59055			−0.118895
$913$	11.3639	+	14.2040i	0.376090	+	0.470083i
$914$	31.0818			1.02809
$915$	−0.436605	−	0.317212i	−0.0144337	−	0.0104867i
$916$	−0.950682	+	2.92590i	−0.0314114	+	0.0966744i
$917$	1.77341	+	5.45801i	0.0585633	+	0.180239i
$918$	−2.18999	+	1.59112i	−0.0722806	+	0.0525149i
$919$	28.6686	−	20.8289i	0.945690	−	0.687084i	−0.00409394	−	0.999992i	$-0.501303\pi$
$919$	28.6686	−	20.8289i	0.945690	−	0.687084i	0.949783	+	0.312908i	$0.101303\pi$
$920$	−0.0425962	−	0.131097i	−0.00140435	−	0.00432216i
$921$	−8.73594	+	26.8865i	−0.287859	+	0.885939i
$922$	12.1941	+	8.85955i	0.401592	+	0.291774i
$923$	−19.7157			−0.648951
$924$	3.10330	−	1.17026i	0.102091	−	0.0384989i
$925$	12.5781			0.413564
$926$	17.4950	+	12.7108i	0.574921	+	0.417704i
$927$	−5.23832	+	16.1219i	−0.172049	+	0.529513i
$928$	1.87573	+	5.77290i	0.0615738	+	0.189505i
$929$	−32.9832	+	23.9637i	−1.08214	+	0.786223i	−0.978055	−	0.208345i	$-0.933192\pi$
$929$	−32.9832	+	23.9637i	−1.08214	+	0.786223i	−0.104088	+	0.994568i	$0.533192\pi$
$930$	0.319445	−	0.232090i	0.0104750	−	0.00761054i
$931$	1.10954	+	3.41481i	0.0363637	+	0.111916i
$932$	−2.50502	+	7.70965i	−0.0820545	+	0.252538i
$933$	−15.8616	−	11.5241i	−0.519286	−	0.377283i
$934$	−34.3150			−1.12282
$935$	−0.385065	−	0.105619i	−0.0125930	−	0.00345412i
$936$	−5.58857			−0.182668
$937$	−5.91802	−	4.29969i	−0.193333	−	0.140465i	0.486908	−	0.873453i	$-0.338125\pi$
$937$	−5.91802	−	4.29969i	−0.193333	−	0.140465i	−0.680241	+	0.732989i	$0.738125\pi$
$938$	0.312873	−	0.962923i	0.0102156	−	0.0314405i
$939$	−9.28627	−	28.5802i	−0.303046	−	0.932680i
$940$	0.409992	−	0.297877i	0.0133725	−	0.00971567i
$941$	5.96607	−	4.33460i	0.194488	−	0.141304i	−0.486279	−	0.873803i	$-0.661646\pi$
$941$	5.96607	−	4.33460i	0.194488	−	0.141304i	0.680768	+	0.732499i	$0.261646\pi$
$942$	−4.29104	−	13.2065i	−0.139810	−	0.430290i
$943$	6.61738	−	20.3662i	0.215492	−	0.663215i
$944$	2.67785	+	1.94557i	0.0871566	+	0.0633230i
$945$	−0.0444738			−0.00144673
$946$	−23.2760	+	35.3827i	−0.756769	+	1.15039i
$947$	5.35736			0.174091			0.0870453	−	0.996204i	$-0.472258\pi$
$947$	5.35736			0.174091			0.0870453	+	0.996204i	$0.472258\pi$
$948$	−5.05982	−	3.67617i	−0.164335	−	0.119397i
$949$	1.09666	−	3.37517i	0.0355990	−	0.109563i
$950$	−5.54551	−	17.0673i	−0.179920	−	0.553737i
$951$	−3.31233	+	2.40655i	−0.107410	+	0.0780377i
$952$	−2.18999	+	1.59112i	−0.0709781	+	0.0515686i
$953$	−5.55598	−	17.0995i	−0.179976	−	0.553909i	0.819850	−	0.572578i	$-0.194057\pi$
$953$	−5.55598	−	17.0995i	−0.179976	−	0.553909i	−0.999826	+	0.0186700i	$0.994057\pi$
$954$	2.54123	−	7.82110i	0.0822753	−	0.253217i
$955$	0.0845991	+	0.0614648i	0.00273756	+	0.00198896i
$956$	−14.6048			−0.472353
$957$	0.934862	+	20.1101i	0.0302198	+	0.650068i
$958$	−8.07993			−0.261051
$959$	14.9119	+	10.8342i	0.481532	+	0.349853i
$960$	0.0137431	−	0.0422971i	0.000443558	−	0.00136513i
$961$	14.7790	+	45.4850i	0.476741	+	1.46726i
$962$	−11.3782	+	8.26676i	−0.366848	+	0.266531i
$963$	0.331254	−	0.240670i	0.0106745	−	0.00775548i
$964$	−2.65488	−	8.17087i	−0.0855078	−	0.263166i
$965$	0.280004	−	0.861763i	0.00901364	−	0.0277411i
$966$	−2.50750	−	1.82181i	−0.0806776	−	0.0586157i
$967$	33.2965			1.07074			0.535372	−	0.844616i	$-0.320171\pi$
$967$	33.2965			1.07074			0.535372	+	0.844616i	$0.320171\pi$
$968$	−2.41396	+	10.7319i	−0.0775877	+	0.344935i
$969$	9.71955			0.312237
$970$	0.402488	+	0.292424i	0.0129231	+	0.00938918i
$971$	−3.68059	+	11.3277i	−0.118116	+	0.363523i	−0.992584	−	0.121560i	$-0.961210\pi$
$971$	−3.68059	+	11.3277i	−0.118116	+	0.363523i	0.874468	+	0.485083i	$0.161210\pi$
$972$	−0.309017	−	0.951057i	−0.00991172	−	0.0305052i
$973$	5.18536	−	3.76738i	0.166235	−	0.120777i
$974$	−11.0023	+	7.99366i	−0.352537	+	0.256133i
$975$	−8.63140	−	26.5647i	−0.276426	−	0.850752i
$976$	3.74981	−	11.5407i	0.120029	−	0.369410i
$977$	−2.98786	−	2.17081i	−0.0955900	−	0.0694502i	0.538964	−	0.842329i	$-0.318816\pi$
$977$	−2.98786	−	2.17081i	−0.0955900	−	0.0694502i	−0.634554	+	0.772879i	$0.718816\pi$
$978$	−13.4164			−0.429009
$979$	0.425380	+	9.15048i	0.0135952	+	0.292451i
$980$	−0.0444738			−0.00142066
$981$	−5.24456	−	3.81040i	−0.167446	−	0.121657i
$982$	−11.1056	+	34.1795i	−0.354393	+	1.09071i
$983$	−14.1609	−	43.5828i	−0.451663	−	1.39008i	−0.875009	−	0.484107i	$-0.839145\pi$
$983$	−14.1609	−	43.5828i	−0.451663	−	1.39008i	0.423346	−	0.905968i	$-0.360855\pi$
$984$	5.58956	−	4.06105i	0.178189	−	0.129462i
$985$	0.649142	−	0.471630i	0.0206834	−	0.0150274i
$986$	−5.07756	−	15.6271i	−0.161702	−	0.497669i
$987$	3.52125	−	10.8373i	0.112083	−	0.344955i
$988$	16.2338	+	11.7945i	0.516465	+	0.375233i
$989$	39.5789			1.25854
$990$	0.0810650	−	0.123230i	0.00257641	−	0.00391649i
$991$	−25.4738			−0.809203			−0.404601	−	0.914493i	$-0.632590\pi$
$991$	−25.4738			−0.809203			−0.404601	+	0.914493i	$0.632590\pi$
$992$	7.18277	+	5.21859i	0.228053	+	0.165690i
$993$	6.17625	−	19.0085i	0.195997	−	0.603218i
$994$	−1.09017	−	3.35520i	−0.0345781	−	0.106420i
$995$	0.0904325	−	0.0657031i	0.00286690	−	0.00208293i
$996$	4.43714	−	3.22377i	0.140596	−	0.102149i
$997$	−1.37235	−	4.22366i	−0.0434628	−	0.133765i	0.926970	−	0.375134i	$-0.122403\pi$
$997$	−1.37235	−	4.22366i	−0.0434628	−	0.133765i	−0.970433	+	0.241370i	$0.922403\pi$
$998$	5.70323	−	17.5527i	0.180533	−	0.555622i
$999$	−2.03598	−	1.47923i	−0.0644156	−	0.0468006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.j.f.169.2	✓	8
11.3	even	5	inner	462.2.j.f.421.2	yes	8
11.5	even	5		5082.2.a.cc.1.2		4
11.6	odd	10		5082.2.a.bx.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.j.f.169.2	✓	8	1.1	even	1	trivial
462.2.j.f.421.2	yes	8	11.3	even	5	inner
5082.2.a.bx.1.2		4	11.6	odd	10
5082.2.a.cc.1.2		4	11.5	even	5

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.0359800 - 0.0261410i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.0359800 - 0.0261410i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} -0.0444738 q^{10} +(-0.154014 - 3.31305i) q^{11} -1.00000 q^{12} +(4.52125 + 3.28488i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(0.0137431 + 0.0422971i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.18999 - 1.59112i) q^{17} +(0.309017 + 0.951057i) q^{18} +(1.10954 - 3.41481i) q^{19} +(0.0359800 + 0.0261410i) q^{20} +1.00000 q^{21} +(-1.82276 + 2.77084i) q^{22} +3.09945 q^{23} +(0.809017 + 0.587785i) q^{24} +(-1.54447 + 4.75340i) q^{25} +(-1.72696 - 5.31505i) q^{26} +(0.809017 - 0.587785i) q^{27} +(0.809017 - 0.587785i) q^{28} +(1.87573 + 5.77290i) q^{29} +(0.0137431 - 0.0422971i) q^{30} +(7.18277 + 5.21859i) q^{31} +1.00000 q^{32} +(3.19849 + 0.877312i) q^{33} -2.70698 q^{34} +(-0.0359800 - 0.0261410i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-0.777675 - 2.39344i) q^{37} +(-2.90481 + 2.11047i) q^{38} +(-4.52125 + 3.28488i) q^{39} +(-0.0137431 - 0.0422971i) q^{40} +(2.13502 - 6.57092i) q^{41} +(-0.809017 - 0.587785i) q^{42} +12.7697 q^{43} +(3.10330 - 1.17026i) q^{44} -0.0444738 q^{45} +(-2.50750 - 1.82181i) q^{46} +(3.52125 - 10.8373i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(4.04348 - 2.93776i) q^{50} +(0.836503 + 2.57449i) q^{51} +(-1.72696 + 5.31505i) q^{52} +(-6.65303 - 4.83371i) q^{53} -1.00000 q^{54} +(-0.0921479 - 0.115177i) q^{55} -1.00000 q^{56} +(2.90481 + 2.11047i) q^{57} +(1.87573 - 5.77290i) q^{58} +(-1.02285 - 3.14800i) q^{59} +(-0.0359800 + 0.0261410i) q^{60} +(-9.81713 + 7.13256i) q^{61} +(-2.74357 - 8.44385i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(-0.809017 - 0.587785i) q^{64} +0.248545 q^{65} +(-2.07196 - 2.58978i) q^{66} -1.01248 q^{67} +(2.18999 + 1.59112i) q^{68} +(-0.957782 + 2.94775i) q^{69} +(0.0137431 + 0.0422971i) q^{70} +(-2.85410 + 2.07363i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(-0.196232 - 0.603941i) q^{73} +(-0.777675 + 2.39344i) q^{74} +(-4.04348 - 2.93776i) q^{75} +3.59055 q^{76} +(-3.10330 + 1.17026i) q^{77} +5.58857 q^{78} +(5.05982 + 3.67617i) q^{79} +(-0.0137431 + 0.0422971i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-5.58956 + 4.06105i) q^{82} +(-4.43714 + 3.22377i) q^{83} +(0.309017 + 0.951057i) q^{84} +(0.0372024 - 0.114497i) q^{85} +(-10.3309 - 7.50582i) q^{86} -6.06998 q^{87} +(-3.19849 - 0.877312i) q^{88} -2.76195 q^{89} +(0.0359800 + 0.0261410i) q^{90} +(1.72696 - 5.31505i) q^{91} +(0.957782 + 2.94775i) q^{92} +(-7.18277 + 5.21859i) q^{93} +(-9.21875 + 6.69781i) q^{94} +(-0.0493454 - 0.151870i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(-9.05000 - 6.57521i) q^{97} +1.00000 q^{98} +(-1.82276 + 2.77084i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{11} - 8 q^{12} + 8 q^{13} + 2 q^{14} - 4 q^{15} - 2 q^{16} - 4 q^{17} - 2 q^{18} - 2 q^{19} - 6 q^{20} + 8 q^{21} - 6 q^{22} + 4 q^{23} + 2 q^{24} - 8 q^{25} - 12 q^{26} + 2 q^{27} + 2 q^{28} + 4 q^{29} - 4 q^{30} - 10 q^{31} + 8 q^{32} + 6 q^{33} - 4 q^{34} + 6 q^{35} - 2 q^{36} - 20 q^{37} - 12 q^{38} - 8 q^{39} + 4 q^{40} + 12 q^{41} - 2 q^{42} + 48 q^{43} - 6 q^{44} + 4 q^{45} + 4 q^{46} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 6 q^{51} - 12 q^{52} - 12 q^{53} - 8 q^{54} - 8 q^{55} - 8 q^{56} + 12 q^{57} + 4 q^{58} + 12 q^{59} + 6 q^{60} - 32 q^{61} + 20 q^{62} + 2 q^{63} - 2 q^{64} + 24 q^{65} - 4 q^{66} - 48 q^{67} - 4 q^{68} + 6 q^{69} - 4 q^{70} + 4 q^{71} - 2 q^{72} - 20 q^{74} - 2 q^{75} + 28 q^{76} + 6 q^{77} - 8 q^{78} + 40 q^{79} + 4 q^{80} - 2 q^{81} - 18 q^{82} - 32 q^{83} - 2 q^{84} - 42 q^{85} - 32 q^{86} + 16 q^{87} - 6 q^{88} + 12 q^{89} - 6 q^{90} + 12 q^{91} - 6 q^{92} + 10 q^{93} + 54 q^{95} + 2 q^{96} + 8 q^{97} + 8 q^{98} - 6 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^11 - 8 * q^12 + 8 * q^13 + 2 * q^14 - 4 * q^15 - 2 * q^16 - 4 * q^17 - 2 * q^18 - 2 * q^19 - 6 * q^20 + 8 * q^21 - 6 * q^22 + 4 * q^23 + 2 * q^24 - 8 * q^25 - 12 * q^26 + 2 * q^27 + 2 * q^28 + 4 * q^29 - 4 * q^30 - 10 * q^31 + 8 * q^32 + 6 * q^33 - 4 * q^34 + 6 * q^35 - 2 * q^36 - 20 * q^37 - 12 * q^38 - 8 * q^39 + 4 * q^40 + 12 * q^41 - 2 * q^42 + 48 * q^43 - 6 * q^44 + 4 * q^45 + 4 * q^46 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 6 * q^51 - 12 * q^52 - 12 * q^53 - 8 * q^54 - 8 * q^55 - 8 * q^56 + 12 * q^57 + 4 * q^58 + 12 * q^59 + 6 * q^60 - 32 * q^61 + 20 * q^62 + 2 * q^63 - 2 * q^64 + 24 * q^65 - 4 * q^66 - 48 * q^67 - 4 * q^68 + 6 * q^69 - 4 * q^70 + 4 * q^71 - 2 * q^72 - 20 * q^74 - 2 * q^75 + 28 * q^76 + 6 * q^77 - 8 * q^78 + 40 * q^79 + 4 * q^80 - 2 * q^81 - 18 * q^82 - 32 * q^83 - 2 * q^84 - 42 * q^85 - 32 * q^86 + 16 * q^87 - 6 * q^88 + 12 * q^89 - 6 * q^90 + 12 * q^91 - 6 * q^92 + 10 * q^93 + 54 * q^95 + 2 * q^96 + 8 * q^97 + 8 * q^98 - 6 * q^99

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