LMFDB - Embedded newform 65.2.l.a.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(4,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("65.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.l (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:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.4
Root			$1.09445 + 0.895644i$ of defining polynomial
Character	$\chi$	$=$	65.49
Dual form			65.2.l.a.4.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09445 + 1.89564i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-1.39564 + 2.41733i) q^{4} +(-0.456850 - 2.18890i) q^{5} +(-1.89564 - 1.09445i) q^{6} +(0.866025 - 1.50000i) q^{7} -1.73205 q^{8} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(1.09445 + 1.89564i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-1.39564 + 2.41733i) q^{4} +(-0.456850 - 2.18890i) q^{5} +(-1.89564 - 1.09445i) q^{6} +(0.866025 - 1.50000i) q^{7} -1.73205 q^{8} +(-1.00000 + 1.73205i) q^{9} +(3.64938 - 3.26167i) q^{10} +(2.29129 - 1.32288i) q^{11} -2.79129i q^{12} +(-3.46410 + 1.00000i) q^{13} +3.79129 q^{14} +(1.49009 + 1.66722i) q^{15} +(0.895644 + 1.55130i) q^{16} +(-3.96863 - 2.29129i) q^{17} -4.37780 q^{18} +(-1.50000 - 0.866025i) q^{19} +(5.92889 + 1.95057i) q^{20} +1.73205i q^{21} +(5.01540 + 2.89564i) q^{22} +(3.96863 - 2.29129i) q^{23} +(1.50000 - 0.866025i) q^{24} +(-4.58258 + 2.00000i) q^{25} +(-5.68693 - 5.47225i) q^{26} -5.00000i q^{27} +(2.41733 + 4.18693i) q^{28} +(-2.29129 - 3.96863i) q^{29} +(-1.52962 + 4.64938i) q^{30} +9.66930i q^{31} +(-3.69253 + 6.39564i) q^{32} +(-1.32288 + 2.29129i) q^{33} -10.0308i q^{34} +(-3.67900 - 1.21037i) q^{35} +(-2.79129 - 4.83465i) q^{36} +(3.96863 + 6.87386i) q^{37} -3.79129i q^{38} +(2.50000 - 2.59808i) q^{39} +(0.791288 + 3.79129i) q^{40} +(-2.29129 + 1.32288i) q^{41} +(-3.28335 + 1.89564i) q^{42} +(1.22753 + 0.708712i) q^{43} +7.38505i q^{44} +(4.24814 + 1.39761i) q^{45} +(8.68693 + 5.01540i) q^{46} +8.75560 q^{47} +(-1.55130 - 0.895644i) q^{48} +(2.00000 + 3.46410i) q^{49} +(-8.80669 - 6.49803i) q^{50} +4.58258 q^{51} +(2.41733 - 9.76951i) q^{52} +1.58258i q^{53} +(9.47822 - 5.47225i) q^{54} +(-3.94242 - 4.41105i) q^{55} +(-1.50000 + 2.59808i) q^{56} +1.73205 q^{57} +(5.01540 - 8.68693i) q^{58} +(-2.91742 - 1.68438i) q^{59} +(-6.10985 + 1.27520i) q^{60} +(5.29129 - 9.16478i) q^{61} +(-18.3296 + 10.5826i) q^{62} +(1.73205 + 3.00000i) q^{63} -12.5826 q^{64} +(3.77148 + 7.12573i) q^{65} -5.79129 q^{66} +(-7.43273 - 12.8739i) q^{67} +(11.0776 - 6.39564i) q^{68} +(-2.29129 + 3.96863i) q^{69} +(-1.73205 - 8.29875i) q^{70} +(-3.08258 - 1.77973i) q^{71} +(1.73205 - 3.00000i) q^{72} +(-8.68693 + 15.0462i) q^{74} +(2.96863 - 4.02334i) q^{75} +(4.18693 - 2.41733i) q^{76} -4.58258i q^{77} +(7.66115 + 1.89564i) q^{78} +6.00000 q^{79} +(2.98647 - 2.66919i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.01540 - 2.89564i) q^{82} +11.3060 q^{83} +(-4.18693 - 2.41733i) q^{84} +(-3.20233 + 9.73371i) q^{85} +3.10260i q^{86} +(3.96863 + 2.29129i) q^{87} +(-3.96863 + 2.29129i) q^{88} +(3.70871 - 2.14123i) q^{89} +(2.00000 + 9.58258i) q^{90} +(-1.50000 + 6.06218i) q^{91} +12.7913i q^{92} +(-4.83465 - 8.37386i) q^{93} +(9.58258 + 16.5975i) q^{94} +(-1.21037 + 3.67900i) q^{95} -7.38505i q^{96} +(-2.23658 + 3.87386i) q^{97} +(-4.37780 + 7.58258i) q^{98} +5.29150i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 6 q^{6} - 8 q^{9}+O(q^{10}) $ 8 * q - 2 * q^4 - 6 * q^6 - 8 * q^9	$ 8 q - 2 q^{4} - 6 q^{6} - 8 q^{9} - 4 q^{10} + 12 q^{14} - 6 q^{15} - 2 q^{16} - 12 q^{19} + 24 q^{20} + 12 q^{24} - 18 q^{26} - 10 q^{30} + 6 q^{35} - 4 q^{36} + 20 q^{39} - 12 q^{40} + 12 q^{45} + 42 q^{46} + 16 q^{49} - 12 q^{50} + 30 q^{54} - 14 q^{55} - 12 q^{56} - 60 q^{59} + 24 q^{61} - 64 q^{64} - 24 q^{65} - 28 q^{66} + 12 q^{71} - 42 q^{74} - 8 q^{75} + 6 q^{76} + 48 q^{79} + 18 q^{80} - 4 q^{81} - 6 q^{84} + 42 q^{85} + 48 q^{89} + 16 q^{90} - 12 q^{91} + 40 q^{94} - 6 q^{95}+O(q^{100}) $ 8 * q - 2 * q^4 - 6 * q^6 - 8 * q^9 - 4 * q^10 + 12 * q^14 - 6 * q^15 - 2 * q^16 - 12 * q^19 + 24 * q^20 + 12 * q^24 - 18 * q^26 - 10 * q^30 + 6 * q^35 - 4 * q^36 + 20 * q^39 - 12 * q^40 + 12 * q^45 + 42 * q^46 + 16 * q^49 - 12 * q^50 + 30 * q^54 - 14 * q^55 - 12 * q^56 - 60 * q^59 + 24 * q^61 - 64 * q^64 - 24 * q^65 - 28 * q^66 + 12 * q^71 - 42 * q^74 - 8 * q^75 + 6 * q^76 + 48 * q^79 + 18 * q^80 - 4 * q^81 - 6 * q^84 + 42 * q^85 + 48 * q^89 + 16 * q^90 - 12 * q^91 + 40 * q^94 - 6 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.09445	+	1.89564i	0.773893	+	1.34042i	0.935414	+	0.353553i	$0.115027\pi$
$2$	1.09445	+	1.89564i	0.773893	+	1.34042i	−0.161521	+	0.986869i	$0.551640\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i	−0.728714	−	0.684819i	$-0.759881\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i	0.228714	+	0.973494i	$0.426548\pi$
$4$	−1.39564	+	2.41733i	−0.697822	+	1.20866i
$5$	−0.456850	−	2.18890i	−0.204310	−	0.978906i
$5$	−0.456850	−	2.18890i	−0.204310	−	0.978906i
$6$	−1.89564	−	1.09445i	−0.773893	−	0.446808i
$7$	0.866025	−	1.50000i	0.327327	−	0.566947i	−0.654654	−	0.755929i	$-0.727186\pi$
$7$	0.866025	−	1.50000i	0.327327	−	0.566947i	0.981981	+	0.188982i	$0.0605189\pi$
$8$	−1.73205			−0.612372
$9$	−1.00000	+	1.73205i	−0.333333	+	0.577350i
$10$	3.64938	−	3.26167i	1.15403	−	1.03143i
$11$	2.29129	−	1.32288i	0.690849	−	0.398862i	−0.113081	−	0.993586i	$-0.536072\pi$
$11$	2.29129	−	1.32288i	0.690849	−	0.398862i	0.803930	+	0.594724i	$0.202739\pi$
$12$		−	2.79129i		−	0.805775i
$13$	−3.46410	+	1.00000i	−0.960769	+	0.277350i
$13$	−3.46410	+	1.00000i	−0.960769	+	0.277350i
$14$	3.79129			1.01326
$15$	1.49009	+	1.66722i	0.384741	+	0.430474i
$16$	0.895644	+	1.55130i	0.223911	+	0.387825i
$17$	−3.96863	−	2.29129i	−0.962533	−	0.555719i	−0.0655816	−	0.997847i	$-0.520890\pi$
$17$	−3.96863	−	2.29129i	−0.962533	−	0.555719i	−0.896952	+	0.442128i	$0.854224\pi$
$18$	−4.37780			−1.03186
$19$	−1.50000	−	0.866025i	−0.344124	−	0.198680i	0.317970	−	0.948101i	$-0.396999\pi$
$19$	−1.50000	−	0.866025i	−0.344124	−	0.198680i	−0.662094	+	0.749421i	$0.730332\pi$
$20$	5.92889	+	1.95057i	1.32574	+	0.436161i
$21$			1.73205i			0.377964i
$22$	5.01540	+	2.89564i	1.06929	+	0.617353i
$23$	3.96863	−	2.29129i	0.827516	−	0.477767i	−0.0254855	−	0.999675i	$-0.508113\pi$
$23$	3.96863	−	2.29129i	0.827516	−	0.477767i	0.853001	+	0.521909i	$0.174780\pi$
$24$	1.50000	−	0.866025i	0.306186	−	0.176777i
$25$	−4.58258	+	2.00000i	−0.916515	+	0.400000i
$26$	−5.68693	−	5.47225i	−1.11530	−	1.07320i
$27$		−	5.00000i		−	0.962250i
$28$	2.41733	+	4.18693i	0.456832	+	0.791256i
$29$	−2.29129	−	3.96863i	−0.425481	−	0.736956i	0.570984	−	0.820961i	$-0.306562\pi$
$29$	−2.29129	−	3.96863i	−0.425481	−	0.736956i	−0.996465	+	0.0840058i	$0.973229\pi$
$30$	−1.52962	+	4.64938i	−0.279269	+	0.848856i
$31$			9.66930i			1.73666i	0.495988	+	0.868329i	$0.334806\pi$
$31$			9.66930i			1.73666i	−0.495988	+	0.868329i	$0.665194\pi$
$32$	−3.69253	+	6.39564i	−0.652753	+	1.13060i
$33$	−1.32288	+	2.29129i	−0.230283	+	0.398862i
$34$		−	10.0308i		−	1.72027i
$35$	−3.67900	−	1.21037i	−0.621864	−	0.204590i
$36$	−2.79129	−	4.83465i	−0.465215	−	0.805775i
$37$	3.96863	+	6.87386i	0.652438	+	1.13006i	0.982529	+	0.186107i	$0.0595872\pi$
$37$	3.96863	+	6.87386i	0.652438	+	1.13006i	−0.330091	+	0.943949i	$0.607080\pi$
$38$		−	3.79129i		−	0.615028i
$39$	2.50000	−	2.59808i	0.400320	−	0.416025i
$40$	0.791288	+	3.79129i	0.125114	+	0.599455i
$41$	−2.29129	+	1.32288i	−0.357839	+	0.206598i	−0.668132	−	0.744042i	$-0.732906\pi$
$41$	−2.29129	+	1.32288i	−0.357839	+	0.206598i	0.310293	+	0.950641i	$0.399573\pi$
$42$	−3.28335	+	1.89564i	−0.506632	+	0.292504i
$43$	1.22753	+	0.708712i	0.187196	+	0.108078i	0.590669	−	0.806914i	$-0.298864\pi$
$43$	1.22753	+	0.708712i	0.187196	+	0.108078i	−0.403473	+	0.914991i	$0.632197\pi$
$44$			7.38505i			1.11334i
$45$	4.24814	+	1.39761i	0.633275	+	0.208344i
$46$	8.68693	+	5.01540i	1.28082	+	0.739481i
$47$	8.75560			1.27714			0.638568	−	0.769565i	$-0.279527\pi$
$47$	8.75560			1.27714			0.638568	+	0.769565i	$0.279527\pi$
$48$	−1.55130	−	0.895644i	−0.223911	−	0.129275i
$49$	2.00000	+	3.46410i	0.285714	+	0.494872i
$50$	−8.80669	−	6.49803i	−1.24545	−	0.918960i
$51$	4.58258			0.641689
$52$	2.41733	−	9.76951i	0.335223	−	1.35479i
$53$			1.58258i			0.217383i	0.994076	+	0.108692i	$0.0346661\pi$
$53$			1.58258i			0.217383i	−0.994076	+	0.108692i	$0.965334\pi$
$54$	9.47822	−	5.47225i	1.28982	−	0.744679i
$55$	−3.94242	−	4.41105i	−0.531596	−	0.594785i
$56$	−1.50000	+	2.59808i	−0.200446	+	0.347183i
$57$	1.73205			0.229416
$58$	5.01540	−	8.68693i	0.658555	−	1.14065i
$59$	−2.91742	−	1.68438i	−0.379816	−	0.219287i	0.297922	−	0.954590i	$-0.403706\pi$
$59$	−2.91742	−	1.68438i	−0.379816	−	0.219287i	−0.677738	+	0.735303i	$0.737040\pi$
$60$	−6.10985	+	1.27520i	−0.788779	+	0.164628i
$61$	5.29129	−	9.16478i	0.677480	−	1.17343i	−0.298257	−	0.954485i	$-0.596405\pi$
$61$	5.29129	−	9.16478i	0.677480	−	1.17343i	0.975737	−	0.218944i	$-0.0702613\pi$
$62$	−18.3296	+	10.5826i	−2.32786	+	1.34399i
$63$	1.73205	+	3.00000i	0.218218	+	0.377964i
$64$	−12.5826			−1.57282
$65$	3.77148	+	7.12573i	0.467794	+	0.883837i
$66$	−5.79129			−0.712858
$67$	−7.43273	−	12.8739i	−0.908052	−	1.57279i	−0.816767	−	0.576968i	$-0.804236\pi$
$67$	−7.43273	−	12.8739i	−0.908052	−	1.57279i	−0.0912856	−	0.995825i	$-0.529098\pi$
$68$	11.0776	−	6.39564i	1.34335	−	0.775586i
$69$	−2.29129	+	3.96863i	−0.275839	+	0.477767i
$70$	−1.73205	−	8.29875i	−0.207020	−	0.991891i
$71$	−3.08258	−	1.77973i	−0.365834	−	0.211215i	0.305803	−	0.952095i	$-0.401075\pi$
$71$	−3.08258	−	1.77973i	−0.365834	−	0.211215i	−0.671637	+	0.740880i	$0.734409\pi$
$72$	1.73205	−	3.00000i	0.204124	−	0.353553i
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	−8.68693	+	15.0462i	−1.00984	+	1.74909i
$75$	2.96863	−	4.02334i	0.342788	−	0.464575i
$76$	4.18693	−	2.41733i	0.480274	−	0.277286i
$77$		−	4.58258i		−	0.522233i
$78$	7.66115	+	1.89564i	0.867455	+	0.214639i
$79$	6.00000			0.675053			0.337526	−	0.941316i	$-0.390410\pi$
$79$	6.00000			0.675053			0.337526	+	0.941316i	$0.390410\pi$
$80$	2.98647	−	2.66919i	0.333897	−	0.298424i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−5.01540	−	2.89564i	−0.553859	−	0.319770i
$83$	11.3060			1.24100			0.620498	−	0.784208i	$-0.286931\pi$
$83$	11.3060			1.24100			0.620498	+	0.784208i	$0.286931\pi$
$84$	−4.18693	−	2.41733i	−0.456832	−	0.263752i
$85$	−3.20233	+	9.73371i	−0.347342	+	1.05577i
$86$			3.10260i			0.334562i
$87$	3.96863	+	2.29129i	0.425481	+	0.245652i
$88$	−3.96863	+	2.29129i	−0.423057	+	0.244252i
$89$	3.70871	−	2.14123i	0.393123	−	0.226969i	−0.290390	−	0.956909i	$-0.593785\pi$
$89$	3.70871	−	2.14123i	0.393123	−	0.226969i	0.683512	+	0.729939i	$0.260452\pi$
$90$	2.00000	+	9.58258i	0.210819	+	1.01009i
$91$	−1.50000	+	6.06218i	−0.157243	+	0.635489i
$92$			12.7913i			1.33358i
$93$	−4.83465	−	8.37386i	−0.501330	−	0.868329i
$94$	9.58258	+	16.5975i	0.988367	+	1.71190i
$95$	−1.21037	+	3.67900i	−0.124181	+	0.377457i
$96$		−	7.38505i		−	0.753734i
$97$	−2.23658	+	3.87386i	−0.227090	+	0.393331i	−0.956944	−	0.290271i	$-0.906254\pi$
$97$	−2.23658	+	3.87386i	−0.227090	+	0.393331i	0.729854	+	0.683603i	$0.239588\pi$
$98$	−4.37780	+	7.58258i	−0.442225	+	0.765956i
$99$			5.29150i			0.531816i
$100$	1.56099	−	13.8689i	0.156099	−	1.38689i
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$	5.01540	+	8.68693i	0.496599	+	0.860134i
$103$			15.1652i			1.49427i	0.664674	+	0.747133i	$0.268570\pi$
$103$			15.1652i			1.49427i	−0.664674	+	0.747133i	$0.731430\pi$
$104$	6.00000	−	1.73205i	0.588348	−	0.169842i
$105$	3.79129	−	0.791288i	0.369992	−	0.0772218i
$106$	−3.00000	+	1.73205i	−0.291386	+	0.168232i
$107$	−1.22753	+	0.708712i	−0.118669	+	0.0685138i	−0.558160	−	0.829733i	$-0.688492\pi$
$107$	−1.22753	+	0.708712i	−0.118669	+	0.0685138i	0.439490	+	0.898247i	$0.355159\pi$
$108$	12.0866	+	6.97822i	1.16304	+	0.671479i
$109$		−	2.74110i		−	0.262550i	−0.991346	−	0.131275i	$-0.958093\pi$
$109$		−	2.74110i		−	0.262550i	0.991346	−	0.131275i	$-0.0419071\pi$
$110$	4.04699	−	12.3011i	0.385865	−	1.17286i
$111$	−6.87386	−	3.96863i	−0.652438	−	0.376685i
$112$	3.10260			0.293168
$113$	−14.3609	−	8.29129i	−1.35096	−	0.779979i	−0.362578	−	0.931953i	$-0.618103\pi$
$113$	−14.3609	−	8.29129i	−1.35096	−	0.779979i	−0.988384	+	0.151975i	$0.951437\pi$
$114$	1.89564	+	3.28335i	0.177543	+	0.307514i
$115$	−6.82847	−	7.64016i	−0.636758	−	0.712448i
$116$	12.7913			1.18764
$117$	1.73205	−	7.00000i	0.160128	−	0.647150i
$118$		−	7.37386i		−	0.678819i
$119$	−6.87386	+	3.96863i	−0.630126	+	0.363803i
$120$	−2.58092	−	2.88771i	−0.235605	−	0.263610i
$121$	−2.00000	+	3.46410i	−0.181818	+	0.314918i
$122$	23.1642			2.09719
$123$	1.32288	−	2.29129i	0.119280	−	0.206598i
$124$	−23.3739	−	13.4949i	−2.09903	−	1.21188i
$125$	6.47135	+	9.11710i	0.578815	+	0.815459i
$126$	−3.79129	+	6.56670i	−0.337755	+	0.585008i
$127$	−8.44178	+	4.87386i	−0.749087	+	0.432485i	−0.825364	−	0.564601i	$-0.809030\pi$
$127$	−8.44178	+	4.87386i	−0.749087	+	0.432485i	0.0762771	+	0.997087i	$0.475697\pi$
$128$	−6.38595	−	11.0608i	−0.564444	−	0.977645i
$129$	−1.41742			−0.124797
$130$	−9.38014	+	14.9481i	−0.822693	+	1.31104i
$131$	1.58258			0.138270			0.0691351	−	0.997607i	$-0.477976\pi$
$131$	1.58258			0.138270			0.0691351	+	0.997607i	$0.477976\pi$
$132$	−3.69253	−	6.39564i	−0.321393	−	0.556669i
$133$	−2.59808	+	1.50000i	−0.225282	+	0.130066i
$134$	16.2695	−	28.1796i	1.40547	−	2.43435i
$135$	−10.9445	+	2.28425i	−0.941953	+	0.196597i
$136$	6.87386	+	3.96863i	0.589429	+	0.340307i
$137$	0.0476751	−	0.0825757i	0.00407316	−	0.00705492i	−0.863982	−	0.503523i	$-0.832037\pi$
$137$	0.0476751	−	0.0825757i	0.00407316	−	0.00705492i	0.868055	+	0.496468i	$0.165370\pi$
$138$	−10.0308			−0.853879
$139$	2.87386	−	4.97768i	0.243758	−	0.422201i	−0.718024	−	0.696019i	$-0.754953\pi$
$139$	2.87386	−	4.97768i	0.243758	−	0.422201i	0.961782	+	0.273817i	$0.0882864\pi$
$140$	8.06042	−	7.20409i	0.681230	−	0.608857i
$141$	−7.58258	+	4.37780i	−0.638568	+	0.368677i
$142$		−	7.79129i		−	0.653830i
$143$	−6.61438	+	6.87386i	−0.553122	+	0.574821i
$144$	−3.58258			−0.298548
$145$	−7.64016	+	6.82847i	−0.634480	+	0.567074i
$146$		0			0
$147$	−3.46410	−	2.00000i	−0.285714	−	0.164957i
$148$	−22.1552			−1.82114
$149$	8.45644	+	4.88233i	0.692778	+	0.399976i	0.804652	−	0.593747i	$-0.202352\pi$
$149$	8.45644	+	4.88233i	0.692778	+	0.399976i	−0.111874	+	0.993722i	$0.535685\pi$
$150$	10.8758	+	1.22411i	0.888008	+	0.0999485i
$151$		−	6.20520i		−	0.504972i	−0.967601	−	0.252486i	$-0.918752\pi$
$151$		−	6.20520i		−	0.504972i	0.967601	−	0.252486i	$-0.0812482\pi$
$152$	2.59808	+	1.50000i	0.210732	+	0.121666i
$153$	7.93725	−	4.58258i	0.641689	−	0.370479i
$154$	8.68693	−	5.01540i	0.700013	−	0.404153i
$155$	21.1652	−	4.41742i	1.70003	−	0.354816i
$156$	2.79129	+	9.66930i	0.223482	+	0.774164i
$157$		−	9.16515i		−	0.731459i	−0.930721	−	0.365729i	$-0.880820\pi$
$157$		−	9.16515i		−	0.731459i	0.930721	−	0.365729i	$-0.119180\pi$
$158$	6.56670	+	11.3739i	0.522419	+	0.904856i
$159$	−0.791288	−	1.37055i	−0.0627532	−	0.108692i
$160$	15.6864	+	5.16072i	1.24012	+	0.407991i
$161$		−	7.93725i		−	0.625543i
$162$	1.09445	−	1.89564i	0.0859882	−	0.148936i
$163$	5.33918	−	9.24773i	0.418197	−	0.724338i	−0.577561	−	0.816347i	$-0.695996\pi$
$163$	5.33918	−	9.24773i	0.418197	−	0.724338i	0.995758	+	0.0920093i	$0.0293290\pi$
$164$		−	7.38505i		−	0.576676i
$165$	5.61976	+	1.84887i	0.437498	+	0.143934i
$166$	12.3739	+	21.4322i	0.960398	+	1.66346i
$167$	2.14123	+	3.70871i	0.165693	+	0.286989i	0.936901	−	0.349594i	$-0.113681\pi$
$167$	2.14123	+	3.70871i	0.165693	+	0.286989i	−0.771208	+	0.636583i	$0.780347\pi$
$168$		−	3.00000i		−	0.231455i
$169$	11.0000	−	6.92820i	0.846154	−	0.532939i
$170$	−21.9564	+	4.58258i	−1.68398	+	0.351468i
$171$	3.00000	−	1.73205i	0.229416	−	0.132453i
$172$	−3.42638	+	1.97822i	−0.261259	+	0.150838i
$173$	−6.42368	−	3.70871i	−0.488383	−	0.281968i	0.235520	−	0.971869i	$-0.424321\pi$
$173$	−6.42368	−	3.70871i	−0.488383	−	0.281968i	−0.723903	+	0.689901i	$0.757654\pi$
$174$			10.0308i			0.760433i
$175$	−0.968627	+	8.60591i	−0.0732213	+	0.650546i
$176$	4.10436	+	2.36965i	0.309377	+	0.178619i
$177$	3.36875			0.253211
$178$	8.11800	+	4.68693i	0.608470	+	0.351300i
$179$	−0.0825757	−	0.143025i	−0.00617200	−	0.0106902i	0.862923	−	0.505336i	$-0.168631\pi$
$179$	−0.0825757	−	0.143025i	−0.00617200	−	0.0106902i	−0.869095	+	0.494645i	$0.835298\pi$
$180$	−9.30738	+	8.31857i	−0.693731	+	0.620029i
$181$	−18.7477			−1.39351			−0.696754	−	0.717310i	$-0.745373\pi$
$181$	−18.7477			−1.39351			−0.696754	+	0.717310i	$0.745373\pi$
$182$	−13.1334	+	3.79129i	−0.973513	+	0.281029i
$183$			10.5826i			0.782287i
$184$	−6.87386	+	3.96863i	−0.506748	+	0.292571i
$185$	13.2331	−	11.8273i	0.972920	−	0.869557i
$186$	10.5826	−	18.3296i	0.775952	−	1.34399i
$187$	−12.1244			−0.886621
$188$	−12.2197	+	21.1652i	−0.891214	+	1.54363i
$189$	−7.50000	−	4.33013i	−0.545545	−	0.314970i
$190$	−8.29875	+	1.73205i	−0.602055	+	0.125656i
$191$	3.70871	−	6.42368i	0.268353	−	0.464801i	−0.700084	−	0.714061i	$-0.746854\pi$
$191$	3.70871	−	6.42368i	0.268353	−	0.464801i	0.968437	+	0.249260i	$0.0801873\pi$
$192$	10.8968	−	6.29129i	0.786411	−	0.454035i
$193$	0.504525	+	0.873864i	0.0363165	+	0.0629021i	0.883612	−	0.468219i	$-0.155104\pi$
$193$	0.504525	+	0.873864i	0.0363165	+	0.0629021i	−0.847296	+	0.531121i	$0.821771\pi$
$194$	−9.79129			−0.702973
$195$	−6.82906	−	4.28532i	−0.489039	−	0.306878i
$196$	−11.1652			−0.797511
$197$	9.98313	+	17.2913i	0.711269	+	1.23195i	0.964381	+	0.264516i	$0.0852123\pi$
$197$	9.98313	+	17.2913i	0.711269	+	1.23195i	−0.253113	+	0.967437i	$0.581454\pi$
$198$	−10.0308	+	5.79129i	−0.712858	+	0.411569i
$199$	0.708712	−	1.22753i	0.0502393	−	0.0870170i	−0.839812	−	0.542877i	$-0.817335\pi$
$199$	0.708712	−	1.22753i	0.0502393	−	0.0870170i	0.890051	+	0.455860i	$0.150668\pi$
$200$	7.93725	−	3.46410i	0.561249	−	0.244949i
$201$	12.8739	+	7.43273i	0.908052	+	0.524264i
$202$	9.85005	−	17.0608i	0.693047	−	1.20039i
$203$	−7.93725			−0.557086
$204$	−6.39564	+	11.0776i	−0.447785	+	0.775586i
$205$	3.94242	+	4.41105i	0.275351	+	0.308081i
$206$	−28.7477	+	16.5975i	−2.00295	+	1.15640i
$207$			9.16515i			0.637022i
$208$	−4.65390	−	4.47822i	−0.322690	−	0.310509i
$209$	−4.58258			−0.316983
$210$	5.64938	+	6.32091i	0.389844	+	0.436184i
$211$	−9.08258	−	15.7315i	−0.625270	−	1.08300i	−0.988489	−	0.151296i	$-0.951655\pi$
$211$	−9.08258	−	15.7315i	−0.625270	−	1.08300i	0.363218	−	0.931704i	$-0.381678\pi$
$212$	−3.82560	−	2.20871i	−0.262743	−	0.151695i
$213$	3.55945			0.243890
$214$	−2.68693	−	1.55130i	−0.183675	−	0.106045i
$215$	0.990505	−	3.01071i	0.0675519	−	0.205329i
$216$			8.66025i			0.589256i
$217$	14.5040	+	8.37386i	0.984593	+	0.568455i
$218$	5.19615	−	3.00000i	0.351928	−	0.203186i
$219$		0			0
$220$	16.1652	−	3.37386i	1.08985	−	0.227466i
$221$	16.0390	+	3.96863i	1.07890	+	0.266959i
$222$		−	17.3739i		−	1.16606i
$223$	4.33013	+	7.50000i	0.289967	+	0.502237i	0.973801	−	0.227400i	$-0.0730224\pi$
$223$	4.33013	+	7.50000i	0.289967	+	0.502237i	−0.683835	+	0.729637i	$0.739689\pi$
$224$	6.39564	+	11.0776i	0.427327	+	0.740152i
$225$	1.11847	−	9.93725i	0.0745649	−	0.662484i
$226$		−	36.2976i		−	2.41448i
$227$	−3.05493	+	5.29129i	−0.202763	+	0.351195i	−0.949418	−	0.314016i	$-0.898325\pi$
$227$	−3.05493	+	5.29129i	−0.202763	+	0.351195i	0.746655	+	0.665212i	$0.231659\pi$
$228$	−2.41733	+	4.18693i	−0.160091	+	0.277286i
$229$			5.48220i			0.362274i	0.983458	+	0.181137i	$0.0579778\pi$
$229$			5.48220i			0.362274i	−0.983458	+	0.181137i	$0.942022\pi$
$230$	7.00959	−	21.3061i	0.462199	−	1.40488i
$231$	2.29129	+	3.96863i	0.150756	+	0.261116i
$232$	3.96863	+	6.87386i	0.260553	+	0.451291i
$233$		−	21.1652i		−	1.38658i	−0.720661	−	0.693288i	$-0.756162\pi$
$233$		−	21.1652i		−	1.38658i	0.720661	−	0.693288i	$-0.243838\pi$
$234$	15.1652	−	4.37780i	0.991377	−	0.286186i
$235$	−4.00000	−	19.1652i	−0.260931	−	1.25020i
$236$	8.14337	−	4.70158i	0.530088	−	0.306047i
$237$	−5.19615	+	3.00000i	−0.337526	+	0.194871i
$238$	−15.0462	−	8.68693i	−0.975301	−	0.563090i
$239$			20.9753i			1.35678i	0.734702	+	0.678390i	$0.237322\pi$
$239$			20.9753i			1.35678i	−0.734702	+	0.678390i	$0.762678\pi$
$240$	−1.25176	+	3.80482i	−0.0808010	+	0.245600i
$241$	−1.50000	−	0.866025i	−0.0966235	−	0.0557856i	0.450910	−	0.892570i	$-0.351100\pi$
$241$	−1.50000	−	0.866025i	−0.0966235	−	0.0557856i	−0.547533	+	0.836784i	$0.684433\pi$
$242$	−8.75560			−0.562832
$243$	13.8564	+	8.00000i	0.888889	+	0.513200i
$244$	14.7695	+	25.5815i	0.945521	+	1.63769i
$245$	6.66888	−	5.96038i	0.426059	−	0.380795i
$246$	5.79129			0.369239
$247$	6.06218	+	1.50000i	0.385727	+	0.0954427i
$248$		−	16.7477i		−	1.06348i
$249$	−9.79129	+	5.65300i	−0.620498	+	0.358244i
$250$	−10.2002	+	22.2456i	−0.645118	+	1.40694i
$251$	−9.08258	+	15.7315i	−0.573287	+	0.992962i	0.422938	+	0.906158i	$0.360999\pi$
$251$	−9.08258	+	15.7315i	−0.573287	+	0.992962i	−0.996225	+	0.0868039i	$0.972335\pi$
$252$	−9.66930			−0.609109
$253$	6.06218	−	10.5000i	0.381126	−	0.660129i
$254$	−18.4782	−	10.6684i	−1.15943	−	0.669395i
$255$	−2.09355	−	10.0308i	−0.131103	−	0.628153i
$256$	1.39564	−	2.41733i	0.0872277	−	0.151083i
$257$	0.143025	−	0.0825757i	0.00892167	−	0.00515093i	−0.495533	−	0.868589i	$-0.665027\pi$
$257$	0.143025	−	0.0825757i	0.00892167	−	0.00515093i	0.504454	+	0.863438i	$0.331694\pi$
$258$	−1.55130	−	2.68693i	−0.0965798	−	0.167281i
$259$	13.7477			0.854242
$260$	−22.4888	−	0.828086i	−1.39470	−	0.0513557i
$261$	9.16515			0.567309
$262$	1.73205	+	3.00000i	0.107006	+	0.185341i
$263$	−7.79423	+	4.50000i	−0.480613	+	0.277482i	−0.720672	−	0.693276i	$-0.756167\pi$
$263$	−7.79423	+	4.50000i	−0.480613	+	0.277482i	0.240059	+	0.970758i	$0.422833\pi$
$264$	2.29129	−	3.96863i	0.141019	−	0.244252i
$265$	3.46410	−	0.723000i	0.212798	−	0.0444135i
$266$	−5.68693	−	3.28335i	−0.348688	−	0.201315i
$267$	−2.14123	+	3.70871i	−0.131041	+	0.226969i
$268$	41.4938			2.53464
$269$	−7.50000	+	12.9904i	−0.457283	+	0.792038i	−0.998816	−	0.0486418i	$-0.984511\pi$
$269$	−7.50000	+	12.9904i	−0.457283	+	0.792038i	0.541533	+	0.840679i	$0.317844\pi$
$270$	−16.3083	−	18.2469i	−0.992494	−	1.11047i
$271$	7.50000	−	4.33013i	0.455593	−	0.263036i	−0.254597	−	0.967047i	$-0.581943\pi$
$271$	7.50000	−	4.33013i	0.455593	−	0.263036i	0.710189	+	0.704011i	$0.248609\pi$
$272$		−	8.20871i		−	0.497726i
$273$	−1.73205	−	6.00000i	−0.104828	−	0.363137i
$274$	0.208712			0.0126088
$275$	−7.85425	+	10.6448i	−0.473629	+	0.641903i
$276$	−6.39564	−	11.0776i	−0.384973	−	0.666792i
$277$	14.3609	+	8.29129i	0.862865	+	0.498175i	0.864971	−	0.501823i	$-0.167337\pi$
$277$	14.3609	+	8.29129i	0.862865	+	0.498175i	−0.00210581	+	0.999998i	$0.500670\pi$
$278$	12.5812			0.754571
$279$	−16.7477	−	9.66930i	−1.00266	−	0.578886i
$280$	6.37221	+	2.09642i	0.380812	+	0.125285i
$281$			17.5112i			1.04463i	0.852752	+	0.522316i	$0.174932\pi$
$281$			17.5112i			1.04463i	−0.852752	+	0.522316i	$0.825068\pi$
$282$	−16.5975	−	9.58258i	−0.988367	−	0.570634i
$283$	0.218475	−	0.126136i	0.0129870	−	0.00749803i	−0.493492	−	0.869750i	$-0.664280\pi$
$283$	0.218475	−	0.126136i	0.0129870	−	0.00749803i	0.506479	+	0.862252i	$0.330947\pi$
$284$	8.60436	−	4.96773i	0.510575	−	0.294780i
$285$	−0.791288	−	3.79129i	−0.0468718	−	0.224577i
$286$	−20.2695	−	5.01540i	−1.19856	−	0.296567i
$287$			4.58258i			0.270501i
$288$	−7.38505	−	12.7913i	−0.435168	−	0.753734i
$289$	2.00000	+	3.46410i	0.117647	+	0.203771i
$290$	−21.3061	−	7.00959i	−1.25114	−	0.411617i
$291$		−	4.47315i		−	0.262221i
$292$		0			0
$293$	11.7152	−	20.2913i	0.684408	−	1.18543i	−0.289214	−	0.957264i	$-0.593394\pi$
$293$	11.7152	−	20.2913i	0.684408	−	1.18543i	0.973622	−	0.228165i	$-0.0732727\pi$
$294$		−	8.75560i		−	0.510637i
$295$	−2.35411	+	7.15546i	−0.137061	+	0.416607i
$296$	−6.87386	−	11.9059i	−0.399535	−	0.692015i
$297$	−6.61438	−	11.4564i	−0.383805	−	0.664770i
$298$			21.3739i			1.23815i
$299$	−11.4564	+	11.9059i	−0.662543	+	0.688535i
$300$	5.58258	+	12.7913i	0.322310	+	0.738505i
$301$	2.12614	−	1.22753i	0.122548	−	0.0707534i
$302$	11.7629	−	6.79129i	0.676876	−	0.390795i
$303$	7.79423	+	4.50000i	0.447767	+	0.258518i
$304$		−	3.10260i		−	0.177946i
$305$	−22.4781	−	7.39517i	−1.28709	−	0.423446i
$306$	17.3739	+	10.0308i	0.993198	+	0.573423i
$307$	−24.2487			−1.38395			−0.691974	−	0.721923i	$-0.743259\pi$
$307$	−24.2487			−1.38395			−0.691974	+	0.721923i	$0.743259\pi$
$308$	11.0776	+	6.39564i	0.631204	+	0.364426i
$309$	−7.58258	−	13.1334i	−0.431358	−	0.747133i
$310$	31.5381	+	35.2869i	1.79124	+	2.00416i
$311$	−1.58258			−0.0897396			−0.0448698	−	0.998993i	$-0.514287\pi$
$311$	−1.58258			−0.0897396			−0.0448698	+	0.998993i	$0.514287\pi$
$312$	−4.33013	+	4.50000i	−0.245145	+	0.254762i
$313$			30.7477i			1.73796i	0.494843	+	0.868982i	$0.335225\pi$
$313$			30.7477i			1.73796i	−0.494843	+	0.868982i	$0.664775\pi$
$314$	17.3739	−	10.0308i	0.980464	−	0.566071i
$315$	5.77542	−	5.16184i	0.325408	−	0.290837i
$316$	−8.37386	+	14.5040i	−0.471067	+	0.815911i
$317$	−20.9753			−1.17809			−0.589045	−	0.808100i	$-0.700496\pi$
$317$	−20.9753			−1.17809			−0.589045	+	0.808100i	$0.700496\pi$
$318$	1.73205	−	3.00000i	0.0971286	−	0.168232i
$319$	−10.5000	−	6.06218i	−0.587887	−	0.339417i
$320$	5.74835	+	27.5420i	0.321343	+	1.53965i
$321$	0.708712	−	1.22753i	0.0395565	−	0.0685138i
$322$	15.0462	−	8.68693i	0.838492	−	0.484104i
$323$	3.96863	+	6.87386i	0.220820	+	0.382472i
$324$	2.79129			0.155072
$325$	13.8745	−	11.5108i	0.769619	−	0.638503i
$326$	23.3739			1.29456
$327$	1.37055	+	2.37386i	0.0757916	+	0.131275i
$328$	3.96863	−	2.29129i	0.219131	−	0.126515i
$329$	7.58258	−	13.1334i	0.418041	−	0.724068i
$330$	2.64575	+	12.6766i	0.145644	+	0.697821i
$331$	9.87386	+	5.70068i	0.542717	+	0.313338i	0.746179	−	0.665745i	$-0.231886\pi$
$331$	9.87386	+	5.70068i	0.542717	+	0.313338i	−0.203463	+	0.979083i	$0.565220\pi$
$332$	−15.7792	+	27.3303i	−0.865994	+	1.49995i
$333$	−15.8745			−0.869918
$334$	−4.68693	+	8.11800i	−0.256457	+	0.444197i
$335$	−24.7840	+	22.1509i	−1.35409	+	1.21023i
$336$	−2.68693	+	1.55130i	−0.146584	+	0.0846304i
$337$			3.25227i			0.177163i	0.996069	+	0.0885813i	$0.0282333\pi$
$337$			3.25227i			0.177163i	−0.996069	+	0.0885813i	$0.971767\pi$
$338$	25.1724	+	13.2695i	1.36920	+	0.721766i
$339$	16.5826			0.900642
$340$	−19.0602	−	21.3259i	−1.03369	−	1.15656i
$341$	12.7913	+	22.1552i	0.692687	+	1.19977i
$342$	6.56670	+	3.79129i	0.355087	+	0.205009i
$343$	19.0526			1.02874
$344$	−2.12614	−	1.22753i	−0.114634	−	0.0661837i
$345$	9.73371	+	3.20233i	0.524045	+	0.172408i
$346$		−	16.2360i		−	0.872853i
$347$	−13.2764	−	7.66515i	−0.712716	−	0.411487i	0.0993497	−	0.995053i	$-0.468324\pi$
$347$	−13.2764	−	7.66515i	−0.712716	−	0.411487i	−0.812066	+	0.583566i	$0.801657\pi$
$348$	−11.0776	+	6.39564i	−0.593821	+	0.342843i
$349$	15.8739	−	9.16478i	0.849708	−	0.490579i	−0.0108440	−	0.999941i	$-0.503452\pi$
$349$	15.8739	−	9.16478i	0.849708	−	0.490579i	0.860552	+	0.509362i	$0.170118\pi$
$350$	−17.3739	+	7.58258i	−0.928672	+	0.405306i
$351$	5.00000	+	17.3205i	0.266880	+	0.924500i
$352$			19.5390i			1.04143i
$353$	−8.70793	−	15.0826i	−0.463476	−	0.802765i	0.535655	−	0.844437i	$-0.320065\pi$
$353$	−8.70793	−	15.0826i	−0.463476	−	0.802765i	−0.999131	+	0.0416724i	$0.986731\pi$
$354$	3.68693	+	6.38595i	0.195958	+	0.339410i
$355$	−2.48737	+	7.56052i	−0.132016	+	0.401271i
$356$			11.9536i			0.633537i
$357$	3.96863	−	6.87386i	0.210042	−	0.363803i
$358$	0.180750	−	0.313068i	0.00955294	−	0.0165462i
$359$		−	33.3857i		−	1.76203i	−0.473088	−	0.881015i	$-0.656861\pi$
$359$		−	33.3857i		−	1.76203i	0.473088	−	0.881015i	$-0.343139\pi$
$360$	−7.35799	−	2.42074i	−0.387800	−	0.127584i
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$	−20.5185	−	35.5390i	−1.07843	−	1.86789i
$363$		−	4.00000i		−	0.209946i
$364$	−12.5608	−	12.0866i	−0.658365	−	0.633512i
$365$		0			0
$366$	−20.0608	+	11.5821i	−1.04859	+	0.605406i
$367$	22.2982	−	12.8739i	1.16396	−	0.672010i	0.211707	−	0.977333i	$-0.432098\pi$
$367$	22.2982	−	12.8739i	1.16396	−	0.672010i	0.952249	+	0.305323i	$0.0987644\pi$
$368$	7.10895	+	4.10436i	0.370580	+	0.213954i
$369$		−	5.29150i		−	0.275465i
$370$	36.9033	+	12.1410i	1.91851	+	0.631179i
$371$	2.37386	+	1.37055i	0.123245	+	0.0711554i
$372$	26.9898			1.39936
$373$	−11.2583	−	6.50000i	−0.582934	−	0.336557i	0.179364	−	0.983783i	$-0.442596\pi$
$373$	−11.2583	−	6.50000i	−0.582934	−	0.336557i	−0.762299	+	0.647225i	$0.775929\pi$
$374$	−13.2695	−	22.9835i	−0.686150	−	1.18845i
$375$	−10.1629	−	4.65997i	−0.524810	−	0.240640i
$376$	−15.1652			−0.782083
$377$	11.9059	+	11.4564i	0.613184	+	0.590037i
$378$		−	18.9564i		−	0.975014i
$379$	18.2477	−	10.5353i	0.937323	−	0.541164i	0.0482027	−	0.998838i	$-0.484651\pi$
$379$	18.2477	−	10.5353i	0.937323	−	0.541164i	0.889120	+	0.457674i	$0.151317\pi$
$380$	−7.20409	−	8.06042i	−0.369562	−	0.413491i
$381$	4.87386	−	8.44178i	0.249696	−	0.432485i
$382$	16.2360			0.830706
$383$	1.41823	−	2.45644i	0.0724680	−	0.125518i	−0.827514	−	0.561444i	$-0.810246\pi$
$383$	1.41823	−	2.45644i	0.0724680	−	0.125518i	0.899982	+	0.435926i	$0.143579\pi$
$384$	11.0608	+	6.38595i	0.564444	+	0.325882i
$385$	−10.0308	+	2.09355i	−0.511217	+	0.106697i
$386$	−1.10436	+	1.91280i	−0.0562102	+	0.0973590i
$387$	−2.45505	+	1.41742i	−0.124797	+	0.0720517i
$388$	−6.24293	−	10.8131i	−0.316937	−	0.548950i
$389$	−15.1652			−0.768904			−0.384452	−	0.923145i	$-0.625610\pi$
$389$	−15.1652			−0.768904			−0.384452	+	0.923145i	$0.625610\pi$
$390$	0.649377	−	17.6355i	0.0328825	−	0.893010i
$391$	−21.0000			−1.06202
$392$	−3.46410	−	6.00000i	−0.174964	−	0.303046i
$393$	−1.37055	+	0.791288i	−0.0691351	+	0.0399152i
$394$	−21.8521	+	37.8489i	−1.10089	+	1.90680i
$395$	−2.74110	−	13.1334i	−0.137920	−	0.660813i
$396$	−12.7913	−	7.38505i	−0.642786	−	0.371113i
$397$	−13.6379	+	23.6216i	−0.684468	+	1.18553i	0.289135	+	0.957288i	$0.406632\pi$
$397$	−13.6379	+	23.6216i	−0.684468	+	1.18553i	−0.973604	+	0.228245i	$0.926701\pi$
$398$	3.10260			0.155519
$399$	1.50000	−	2.59808i	0.0750939	−	0.130066i
$400$	−7.20696	−	5.31767i	−0.360348	−	0.265883i
$401$	10.8303	−	6.25288i	0.540840	−	0.312254i	−0.204580	−	0.978850i	$-0.565583\pi$
$401$	10.8303	−	6.25288i	0.540840	−	0.312254i	0.745419	+	0.666596i	$0.232249\pi$
$402$			32.5390i			1.62290i
$403$	−9.66930	−	33.4955i	−0.481662	−	1.66853i
$404$	25.1216			1.24985
$405$	−1.66722	+	1.49009i	−0.0828448	+	0.0740434i
$406$	−8.68693	−	15.0462i	−0.431125	−	0.746731i
$407$	18.1865	+	10.5000i	0.901473	+	0.520466i
$408$	−7.93725			−0.392953
$409$	7.50000	+	4.33013i	0.370851	+	0.214111i	0.673830	−	0.738886i	$-0.264648\pi$
$409$	7.50000	+	4.33013i	0.370851	+	0.214111i	−0.302979	+	0.952997i	$0.597981\pi$
$410$	−4.04699	+	12.3011i	−0.199867	+	0.607508i
$411$			0.0953502i			0.00470328i
$412$	−36.6591	−	21.1652i	−1.80607	−	1.04273i
$413$	−5.05313	+	2.91742i	−0.248648	+	0.143557i
$414$	−17.3739	+	10.0308i	−0.853879	+	0.492987i
$415$	−5.16515	−	24.7477i	−0.253547	−	1.21482i
$416$	6.39564	−	25.8477i	0.313572	−	1.26729i
$417$			5.74773i			0.281467i
$418$	−5.01540	−	8.68693i	−0.245311	−	0.424892i
$419$	−12.0826	−	20.9276i	−0.590272	−	1.02238i	−0.994195	−	0.107589i	$-0.965687\pi$
$419$	−12.0826	−	20.9276i	−0.590272	−	1.02238i	0.403923	−	0.914793i	$-0.367646\pi$
$420$	−3.37849	+	10.2691i	−0.164853	+	0.501083i
$421$			26.2668i			1.28017i	0.768306	+	0.640083i	$0.221100\pi$
$421$			26.2668i			1.28017i	−0.768306	+	0.640083i	$0.778900\pi$
$422$	19.8809	−	34.4347i	0.967785	−	1.67625i
$423$	−8.75560	+	15.1652i	−0.425712	+	0.737355i
$424$		−	2.74110i		−	0.133120i
$425$	22.7691	+	2.56275i	1.10446	+	0.124311i
$426$	3.89564	+	6.74745i	0.188745	+	0.326915i
$427$	−9.16478	−	15.8739i	−0.443515	−	0.768190i
$428$		−	3.95644i		−	0.191242i
$429$	2.29129	−	9.26013i	0.110624	−	0.447083i
$430$	6.79129	−	1.41742i	0.327505	−	0.0683543i
$431$	25.6652	−	14.8178i	1.23625	−	0.713747i	0.267922	−	0.963441i	$-0.413663\pi$
$431$	25.6652	−	14.8178i	1.23625	−	0.713747i	0.968325	+	0.249693i	$0.0803298\pi$
$432$	7.75650	−	4.47822i	0.373185	−	0.215458i
$433$	−15.3700	−	8.87386i	−0.738634	−	0.426451i	0.0829383	−	0.996555i	$-0.473570\pi$
$433$	−15.3700	−	8.87386i	−0.738634	−	0.426451i	−0.821573	+	0.570104i	$0.806903\pi$
$434$			36.6591i			1.75969i
$435$	3.20233	−	9.73371i	0.153540	−	0.466696i
$436$	6.62614	+	3.82560i	0.317334	+	0.183213i
$437$	−7.93725			−0.379690
$438$		0			0
$439$	20.2477	+	35.0701i	0.966371	+	1.67380i	0.705885	+	0.708327i	$0.250550\pi$
$439$	20.2477	+	35.0701i	0.966371	+	1.67380i	0.260487	+	0.965477i	$0.416117\pi$
$440$	6.82847	+	7.64016i	0.325535	+	0.364230i
$441$	−8.00000			−0.380952
$442$	10.0308	+	34.7477i	0.477117	+	1.65278i
$443$			25.9129i			1.23116i	0.788075	+	0.615579i	$0.211078\pi$
$443$			25.9129i			1.23116i	−0.788075	+	0.615579i	$0.788922\pi$
$444$	19.1869	−	11.0776i	0.910571	−	0.525719i
$445$	−6.38126	−	7.13978i	−0.302501	−	0.338458i
$446$	−9.47822	+	16.4168i	−0.448807	+	0.777356i
$447$	−9.76465			−0.461852
$448$	−10.8968	+	18.8739i	−0.514827	+	0.891706i
$449$	32.4564	+	18.7387i	1.53171	+	0.884336i	0.999283	+	0.0378622i	$0.0120548\pi$
$449$	32.4564	+	18.7387i	1.53171	+	0.884336i	0.532431	+	0.846473i	$0.321279\pi$
$450$	20.0616	−	8.75560i	0.945713	−	0.412743i
$451$	−3.50000	+	6.06218i	−0.164809	+	0.285457i
$452$	40.0855	−	23.1434i	1.88546	−	1.08857i
$453$	3.10260	+	5.37386i	0.145773	+	0.252486i
$454$	−13.3739			−0.627667
$455$	13.9548	+	0.513844i	0.654210	+	0.0240894i
$456$	−3.00000			−0.140488
$457$	−0.866025	−	1.50000i	−0.0405110	−	0.0701670i	0.845059	−	0.534673i	$-0.179565\pi$
$457$	−0.866025	−	1.50000i	−0.0405110	−	0.0701670i	−0.885570	+	0.464506i	$0.846232\pi$
$458$	−10.3923	+	6.00000i	−0.485601	+	0.280362i
$459$	−11.4564	+	19.8431i	−0.534741	+	0.926198i
$460$	27.9989	−	5.84370i	1.30545	−	0.272464i
$461$	−1.03901	−	0.599876i	−0.0483917	−	0.0279390i	0.475609	−	0.879657i	$-0.342228\pi$
$461$	−1.03901	−	0.599876i	−0.0483917	−	0.0279390i	−0.524001	+	0.851718i	$0.675561\pi$
$462$	−5.01540	+	8.68693i	−0.233338	+	0.404153i
$463$	8.22330			0.382169			0.191085	−	0.981574i	$-0.438799\pi$
$463$	8.22330			0.382169			0.191085	+	0.981574i	$0.438799\pi$
$464$	4.10436	−	7.10895i	0.190540	−	0.330025i
$465$	−16.1208	+	14.4082i	−0.747586	+	0.668163i
$466$	40.1216	−	23.1642i	1.85860	−	1.07306i
$467$			12.3303i			0.570578i	0.958441	+	0.285289i	$0.0920896\pi$
$467$			12.3303i			0.570578i	−0.958441	+	0.285289i	$0.907910\pi$
$468$	14.5040	+	13.9564i	0.670446	+	0.645137i
$469$	−25.7477			−1.18892
$470$	31.9525	−	28.5579i	1.47386	−	1.31728i
$471$	4.58258	+	7.93725i	0.211154	+	0.365729i
$472$	5.05313	+	2.91742i	0.232589	+	0.134285i
$473$	3.75015			0.172432
$474$	−11.3739	−	6.56670i	−0.522419	−	0.301619i
$475$	8.60591	+	0.968627i	0.394866	+	0.0444437i
$476$		−	22.1552i		−	1.01548i
$477$	−2.74110	−	1.58258i	−0.125506	−	0.0724612i
$478$	−39.7617	+	22.9564i	−1.81866	+	1.05000i
$479$	−28.0390	+	16.1883i	−1.28114	+	0.739664i	−0.977056	−	0.212983i	$-0.931682\pi$
$479$	−28.0390	+	16.1883i	−1.28114	+	0.739664i	−0.304079	+	0.952647i	$0.598349\pi$
$480$	−16.1652	+	3.37386i	−0.737835	+	0.153995i
$481$	−20.6216	−	19.8431i	−0.940264	−	0.904769i
$482$		−	3.79129i		−	0.172688i
$483$	3.96863	+	6.87386i	0.180579	+	0.312772i
$484$	−5.58258	−	9.66930i	−0.253753	−	0.439514i
$485$	9.50128	+	3.12587i	0.431431	+	0.141938i
$486$			35.0224i			1.58865i
$487$	10.5353	−	18.2477i	0.477401	−	0.826883i	−0.522263	−	0.852784i	$-0.674912\pi$
$487$	10.5353	−	18.2477i	0.477401	−	0.826883i	0.999665	+	0.0259009i	$0.00824545\pi$
$488$	−9.16478	+	15.8739i	−0.414870	+	0.718576i
$489$			10.6784i			0.482892i
$490$	18.5975	+	6.11847i	0.840150	+	0.276404i
$491$	−14.2913	−	24.7532i	−0.644957	−	1.11710i	−0.984311	−	0.176439i	$-0.943542\pi$
$491$	−14.2913	−	24.7532i	−0.644957	−	1.11710i	0.339355	−	0.940658i	$-0.389791\pi$
$492$	3.69253	+	6.39564i	0.166472	+	0.288338i
$493$			21.0000i			0.945792i
$494$	3.79129	+	13.1334i	0.170578	+	0.590900i
$495$	11.5826	−	2.41742i	0.520598	−	0.108655i
$496$	−15.0000	+	8.66025i	−0.673520	+	0.388857i
$497$	−5.33918	+	3.08258i	−0.239495	+	0.138272i
$498$	−21.4322	−	12.3739i	−0.960398	−	0.554486i
$499$		−	16.5975i		−	0.743006i	−0.928432	−	0.371503i	$-0.878842\pi$
$499$		−	16.5975i		−	0.743006i	0.928432	−	0.371503i	$-0.121158\pi$
$500$	−31.0707	+	2.91914i	−1.38952	+	0.130548i
$501$	−3.70871	−	2.14123i	−0.165693	−	0.0956629i
$502$	−39.7617			−1.77465
$503$	−15.7315	−	9.08258i	−0.701432	−	0.404972i	0.106448	−	0.994318i	$-0.466052\pi$
$503$	−15.7315	−	9.08258i	−0.701432	−	0.404972i	−0.807881	+	0.589346i	$0.799385\pi$
$504$	−3.00000	−	5.19615i	−0.133631	−	0.231455i
$505$	−15.0050	+	13.4109i	−0.667712	+	0.596775i
$506$	26.5390			1.17980
$507$	−6.06218	+	11.5000i	−0.269231	+	0.510733i
$508$		−	27.2087i		−	1.20719i
$509$	−25.6652	+	14.8178i	−1.13759	+	0.656787i	−0.945832	−	0.324656i	$-0.894751\pi$
$509$	−25.6652	+	14.8178i	−1.13759	+	0.656787i	−0.191756	+	0.981443i	$0.561418\pi$
$510$	16.7235	−	14.9468i	0.740531	−	0.661857i
$511$		0			0
$512$	−19.4340			−0.858868
$513$	−4.33013	+	7.50000i	−0.191180	+	0.331133i
$514$	0.313068	+	0.180750i	0.0138088	+	0.00797254i
$515$	33.1950	−	6.92820i	1.46275	−	0.305293i
$516$	1.97822	−	3.42638i	0.0870863	−	0.150838i
$517$	20.0616	−	11.5826i	0.882309	−	0.509401i
$518$	15.0462	+	26.0608i	0.661092	+	1.14505i
$519$	7.41742			0.325589
$520$	−6.53239	−	12.3421i	−0.286464	−	0.541238i
$521$	−27.4955			−1.20460			−0.602299	−	0.798271i	$-0.705748\pi$
$521$	−27.4955			−1.20460			−0.602299	+	0.798271i	$0.705748\pi$
$522$	10.0308	+	17.3739i	0.439036	+	0.760433i
$523$	15.7315	−	9.08258i	0.687890	−	0.397153i	−0.114931	−	0.993373i	$-0.536665\pi$
$523$	15.7315	−	9.08258i	0.687890	−	0.397153i	0.802821	+	0.596220i	$0.203331\pi$
$524$	−2.20871	+	3.82560i	−0.0964880	+	0.167122i
$525$	−3.46410	−	7.93725i	−0.151186	−	0.346410i
$526$	−17.0608	−	9.85005i	−0.743886	−	0.429483i
$527$	22.1552	−	38.3739i	0.965094	−	1.67159i
$528$	−4.73930			−0.206252
$529$	−1.00000	+	1.73205i	−0.0434783	+	0.0753066i
$530$	5.16184	+	5.77542i	0.224216	+	0.250868i
$531$	5.83485	−	3.36875i	0.253211	−	0.146191i
$532$		−	8.37386i		−	0.363053i
$533$	6.61438	−	6.87386i	0.286501	−	0.297740i
$534$	−9.37386			−0.405647
$535$	2.11210	+	2.36316i	0.0913139	+	0.102168i
$536$	12.8739	+	22.2982i	0.556066	+	0.963135i
$537$	0.143025	+	0.0825757i	0.00617200	+	0.00356340i
$538$	−32.8335			−1.41555
$539$	9.16515	+	5.29150i	0.394771	+	0.227921i
$540$	9.75285	−	29.6444i	0.419696	−	1.27569i
$541$			10.3923i			0.446800i	0.974727	+	0.223400i	$0.0717156\pi$
$541$			10.3923i			0.446800i	−0.974727	+	0.223400i	$0.928284\pi$
$542$	16.4168	+	9.47822i	0.705160	+	0.407124i
$543$	16.2360	−	9.37386i	0.696754	−	0.402271i
$544$	29.3085	−	16.9213i	1.25659	−	0.725494i
$545$	−6.00000	+	1.25227i	−0.257012	+	0.0536415i
$546$	9.47822	−	9.85005i	0.405630	−	0.421543i
$547$			1.25227i			0.0535433i	0.999642	+	0.0267717i	$0.00852270\pi$
$547$			1.25227i			0.0535433i	−0.999642	+	0.0267717i	$0.991477\pi$
$548$	0.133075	+	0.230493i	0.00568468	+	0.00984615i
$549$	10.5826	+	18.3296i	0.451653	+	0.782287i
$550$	−28.7747	−	3.23870i	−1.22696	−	0.138099i
$551$			7.93725i			0.338138i
$552$	3.96863	−	6.87386i	0.168916	−	0.292571i
$553$	5.19615	−	9.00000i	0.220963	−	0.382719i
$554$			36.2976i			1.54214i
$555$	−5.54661	+	16.8593i	−0.235440	+	0.715636i
$556$	8.02178	+	13.8941i	0.340199	+	0.589242i
$557$	−6.51903	−	11.2913i	−0.276220	−	0.478427i	0.694222	−	0.719761i	$-0.255749\pi$
$557$	−6.51903	−	11.2913i	−0.276220	−	0.478427i	−0.970442	+	0.241334i	$0.922415\pi$
$558$		−	42.3303i		−	1.79198i
$559$	−4.96099	−	1.22753i	−0.209827	−	0.0519188i
$560$	−1.41742	−	6.79129i	−0.0598971	−	0.286984i
$561$	10.5000	−	6.06218i	0.443310	−	0.255945i
$562$	−33.1950	+	19.1652i	−1.40025	+	0.808433i
$563$	−7.79423	−	4.50000i	−0.328488	−	0.189652i	0.326682	−	0.945134i	$-0.394069\pi$
$563$	−7.79423	−	4.50000i	−0.328488	−	0.189652i	−0.655169	+	0.755482i	$0.727403\pi$
$564$		−	24.4394i		−	1.02908i
$565$	−11.5880	+	35.2225i	−0.487511	+	1.48182i
$566$	0.478220	+	0.276100i	0.0201011	+	0.0116054i
$567$	−1.73205			−0.0727393
$568$	5.33918	+	3.08258i	0.224027	+	0.129342i
$569$	−9.87386	−	17.1020i	−0.413934	−	0.716955i	0.581382	−	0.813631i	$-0.302512\pi$
$569$	−9.87386	−	17.1020i	−0.413934	−	0.716955i	−0.995316	+	0.0966762i	$0.969179\pi$
$570$	6.32091	−	5.64938i	0.264754	−	0.236626i
$571$	29.0780			1.21688			0.608439	−	0.793601i	$-0.291796\pi$
$571$	29.0780			1.21688			0.608439	+	0.793601i	$0.291796\pi$
$572$	−7.38505	−	25.5826i	−0.308785	−	1.06966i
$573$			7.41742i			0.309867i
$574$	−8.68693	+	5.01540i	−0.362586	+	0.209339i
$575$	−13.6040	+	18.4373i	−0.567324	+	0.768887i
$576$	12.5826	−	21.7937i	0.524274	−	0.908069i
$577$	6.92820			0.288425			0.144212	−	0.989547i	$-0.453935\pi$
$577$	6.92820			0.288425			0.144212	+	0.989547i	$0.453935\pi$
$578$	−4.37780	+	7.58258i	−0.182093	+	0.315394i
$579$	−0.873864	−	0.504525i	−0.0363165	−	0.0209674i
$580$	−5.84370	−	27.9989i	−0.242647	−	1.16259i
$581$	9.79129	−	16.9590i	0.406211	−	0.703578i
$582$	8.47950	−	4.89564i	0.351487	−	0.202931i
$583$	2.09355	+	3.62614i	0.0867060	+	0.150179i
$584$		0			0
$585$	−16.1136	−	0.593336i	−0.666215	−	0.0245314i
$586$	51.2867			2.11864
$587$	9.35548	+	16.2042i	0.386142	+	0.668818i	0.991927	−	0.126811i	$-0.0404741\pi$
$587$	9.35548	+	16.2042i	0.386142	+	0.668818i	−0.605785	+	0.795628i	$0.707141\pi$
$588$	9.66930	−	5.58258i	0.398755	−	0.230222i
$589$	8.37386	−	14.5040i	0.345039	−	0.597625i
$590$	−16.1407	+	3.36875i	−0.664500	+	0.138689i
$591$	−17.2913	−	9.98313i	−0.711269	−	0.410651i
$592$	−7.10895	+	12.3131i	−0.292176	+	0.506064i
$593$	−21.1660			−0.869184			−0.434592	−	0.900627i	$-0.643107\pi$
$593$	−21.1660			−0.869184			−0.434592	+	0.900627i	$0.643107\pi$
$594$	14.4782	−	25.0770i	0.594049	−	1.02892i
$595$	11.8273	+	13.2331i	0.484870	+	0.542506i
$596$	−23.6044	+	13.6280i	−0.966872	+	0.558224i
$597$			1.41742i			0.0580113i
$598$	−35.1078	−	8.68693i	−1.43567	−	0.355235i
$599$	39.4955			1.61374			0.806870	−	0.590729i	$-0.201160\pi$
$599$	39.4955			1.61374			0.806870	+	0.590729i	$0.201160\pi$
$600$	−5.14181	+	6.96863i	−0.209914	+	0.284493i
$601$	14.4564	+	25.0393i	0.589690	+	1.02137i	0.994273	+	0.106872i	$0.0340836\pi$
$601$	14.4564	+	25.0393i	0.589690	+	1.02137i	−0.404582	+	0.914502i	$0.632583\pi$
$602$	4.65390	+	2.68693i	0.189679	+	0.109511i
$603$	29.7309			1.21074
$604$	15.0000	+	8.66025i	0.610341	+	0.352381i
$605$	8.49628	+	2.79523i	0.345423	+	0.113642i
$606$			19.7001i			0.800262i
$607$	17.1020	+	9.87386i	0.694150	+	0.400768i	0.805165	−	0.593051i	$-0.202077\pi$
$607$	17.1020	+	9.87386i	0.694150	+	0.400768i	−0.111015	+	0.993819i	$0.535410\pi$
$608$	11.0776	−	6.39564i	0.449255	−	0.259378i
$609$	6.87386	−	3.96863i	0.278543	−	0.160817i
$610$	−10.5826	−	50.7042i	−0.428476	−	2.05295i
$611$	−30.3303	+	8.75560i	−1.22703	+	0.354214i
$612$			25.5826i			1.03411i
$613$	10.8968	+	18.8739i	0.440119	+	0.762308i	0.997698	−	0.0678157i	$-0.0216030\pi$
$613$	10.8968	+	18.8739i	0.440119	+	0.762308i	−0.557579	+	0.830124i	$0.688270\pi$
$614$	−26.5390	−	45.9669i	−1.07103	−	1.85507i
$615$	−5.61976	−	1.84887i	−0.226611	−	0.0745536i
$616$			7.93725i			0.319801i
$617$	1.68438	−	2.91742i	0.0678104	−	0.117451i	−0.830127	−	0.557575i	$-0.811732\pi$
$617$	1.68438	−	2.91742i	0.0678104	−	0.117451i	0.897937	+	0.440124i	$0.145065\pi$
$618$	16.5975	−	28.7477i	0.667650	−	1.15640i
$619$		−	2.01810i		−	0.0811143i	−0.999177	−	0.0405572i	$-0.987087\pi$
$619$		−	2.01810i		−	0.0811143i	0.999177	−	0.0405572i	$-0.0129133\pi$
$620$	−18.8607	+	57.3282i	−0.757462	+	2.30236i
$621$	−11.4564	−	19.8431i	−0.459731	−	0.796278i
$622$	−1.73205	−	3.00000i	−0.0694489	−	0.120289i
$623$		−	7.41742i		−	0.297173i
$624$	6.26951	+	1.55130i	0.250981	+	0.0621017i
$625$	17.0000	−	18.3303i	0.680000	−	0.733212i
$626$	−58.2867	+	33.6519i	−2.32961	+	1.34500i
$627$	3.96863	−	2.29129i	0.158492	−	0.0915052i
$628$	22.1552	+	12.7913i	0.884087	+	0.510428i
$629$		−	36.3731i		−	1.45029i
$630$	16.1059	+	5.29875i	0.641675	+	0.211107i
$631$	−18.8739	−	10.8968i	−0.751357	−	0.433796i	0.0748272	−	0.997197i	$-0.476159\pi$
$631$	−18.8739	−	10.8968i	−0.751357	−	0.433796i	−0.826184	+	0.563401i	$0.809493\pi$
$632$	−10.3923			−0.413384
$633$	15.7315	+	9.08258i	0.625270	+	0.361000i
$634$	−22.9564	−	39.7617i	−0.911717	−	1.57914i
$635$	14.5250	+	16.2516i	0.576408	+	0.644925i
$636$	4.41742			0.175162
$637$	−10.3923	−	10.0000i	−0.411758	−	0.396214i
$638$		−	26.5390i		−	1.05069i
$639$	6.16515	−	3.55945i	0.243890	−	0.140810i
$640$	−21.2936	+	19.0313i	−0.841702	+	0.752280i
$641$	0.0825757	−	0.143025i	0.00326154	−	0.00564916i	−0.864390	−	0.502822i	$-0.832295\pi$
$641$	0.0825757	−	0.143025i	0.00326154	−	0.00564916i	0.867652	+	0.497173i	$0.165628\pi$
$642$	3.10260			0.122450
$643$	2.95958	−	5.12614i	0.116714	−	0.202155i	−0.801749	−	0.597660i	$-0.796097\pi$
$643$	2.95958	−	5.12614i	0.116714	−	0.202155i	0.918464	+	0.395505i	$0.129430\pi$
$644$	19.1869	+	11.0776i	0.756071	+	0.436518i
$645$	0.647551	+	3.10260i	0.0254973	+	0.122165i
$646$	−8.68693	+	15.0462i	−0.341783	+	0.591985i
$647$	23.3827	−	13.5000i	0.919268	−	0.530740i	0.0358667	−	0.999357i	$-0.488581\pi$
$647$	23.3827	−	13.5000i	0.919268	−	0.530740i	0.883402	+	0.468617i	$0.155247\pi$
$648$	0.866025	+	1.50000i	0.0340207	+	0.0589256i
$649$	−8.91288			−0.349861
$650$	37.0053	+	13.7031i	1.45147	+	0.537482i
$651$	−16.7477			−0.656395
$652$	14.9032	+	25.8131i	0.583654	+	1.01092i
$653$	−42.2843	+	24.4129i	−1.65471	+	0.955350i	−0.679619	+	0.733566i	$0.737855\pi$
$653$	−42.2843	+	24.4129i	−1.65471	+	0.955350i	−0.975096	+	0.221784i	$0.928812\pi$
$654$	−3.00000	+	5.19615i	−0.117309	+	0.203186i
$655$	−0.723000	−	3.46410i	−0.0282500	−	0.135354i
$656$	−4.10436	−	2.36965i	−0.160248	−	0.0925193i
$657$		0			0
$658$	33.1950			1.29408
$659$	−12.2477	+	21.2137i	−0.477104	+	0.826368i	−0.999656	−	0.0262396i	$-0.991647\pi$
$659$	−12.2477	+	21.2137i	−0.477104	+	0.826368i	0.522552	+	0.852607i	$0.324980\pi$
$660$	−12.3125	+	11.0044i	−0.479263	+	0.428347i
$661$	2.12614	−	1.22753i	0.0826971	−	0.0477452i	−0.458081	−	0.888910i	$-0.651463\pi$
$661$	2.12614	−	1.22753i	0.0826971	−	0.0477452i	0.540778	+	0.841165i	$0.318130\pi$
$662$			24.9564i			0.969960i
$663$	−15.8745	+	4.58258i	−0.616515	+	0.177972i
$664$	−19.5826			−0.759951
$665$	4.47028	+	5.00166i	0.173350	+	0.193956i
$666$	−17.3739	−	30.0924i	−0.673224	−	1.16606i
$667$	−18.1865	−	10.5000i	−0.704185	−	0.406562i
$668$	−11.9536			−0.462497
$669$	−7.50000	−	4.33013i	−0.289967	−	0.167412i
$670$	−69.1151	−	22.7385i	−2.67015	−	0.878464i
$671$		−	27.9989i		−	1.08088i
$672$	−11.0776	−	6.39564i	−0.427327	−	0.246717i
$673$	5.05313	−	2.91742i	0.194784	−	0.112458i	−0.399436	−	0.916761i	$-0.630794\pi$
$673$	5.05313	−	2.91742i	0.194784	−	0.112458i	0.594220	+	0.804302i	$0.297461\pi$
$674$	−6.16515	+	3.55945i	−0.237473	+	0.137105i
$675$	10.0000	+	22.9129i	0.384900	+	0.881917i
$676$	1.39564	+	36.2599i	0.0536786	+	1.39461i
$677$		−	21.1652i		−	0.813443i	−0.913552	−	0.406721i	$-0.866672\pi$
$677$		−	21.1652i		−	0.813443i	0.913552	−	0.406721i	$-0.133328\pi$
$678$	18.1488	+	31.4347i	0.697001	+	1.20724i
$679$	3.87386	+	6.70973i	0.148665	+	0.257496i
$680$	5.54661	−	16.8593i	0.212703	−	0.646524i
$681$		−	6.10985i		−	0.234130i
$682$	−27.9989	+	48.4955i	−1.07213	+	1.85699i
$683$	−5.96683	+	10.3348i	−0.228314	+	0.395452i	−0.957309	−	0.289068i	$-0.906655\pi$
$683$	−5.96683	+	10.3348i	−0.228314	+	0.395452i	0.728994	+	0.684520i	$0.239988\pi$
$684$			9.66930i			0.369715i
$685$	−0.202530	−	0.0666313i	−0.00773829	−	0.00254585i
$686$	20.8521	+	36.1169i	0.796136	+	1.37895i
$687$	−2.74110	−	4.74773i	−0.104580	−	0.181137i
$688$			2.53901i			0.0967990i
$689$	−1.58258	−	5.48220i	−0.0602913	−	0.208855i
$690$	4.58258	+	21.9564i	0.174456	+	0.835867i
$691$	30.8739	−	17.8250i	1.17450	−	0.678096i	0.219762	−	0.975554i	$-0.429472\pi$
$691$	30.8739	−	17.8250i	1.17450	−	0.678096i	0.954735	+	0.297457i	$0.0961386\pi$
$692$	17.9303	−	10.3521i	0.681609	−	0.393527i
$693$	7.93725	+	4.58258i	0.301511	+	0.174078i
$694$		−	33.5565i		−	1.27379i
$695$	−12.2086	−	4.01655i	−0.463097	−	0.152356i
$696$	−6.87386	−	3.96863i	−0.260553	−	0.150430i
$697$	12.1244			0.459243
$698$	34.7463	+	20.0608i	1.31517	+	0.759312i
$699$	10.5826	+	18.3296i	0.400270	+	0.693288i
$700$	−19.4514	−	14.3523i	−0.735195	−	0.542465i
$701$	−2.83485			−0.107071			−0.0535354	−	0.998566i	$-0.517049\pi$
$701$	−2.83485			−0.107071			−0.0535354	+	0.998566i	$0.517049\pi$
$702$	−27.3613	+	28.4347i	−1.03268	+	1.07320i
$703$		−	13.7477i		−	0.518505i
$704$	−28.8303	+	16.6452i	−1.08658	+	0.627339i
$705$	13.0467	+	14.5975i	0.491366	+	0.549774i
$706$	19.0608	−	33.0143i	0.717362	−	1.24251i
$707$	−15.5885			−0.586264
$708$	−4.70158	+	8.14337i	−0.176696	+	0.306047i
$709$	31.5000	+	18.1865i	1.18301	+	0.683010i	0.956708	−	0.291048i	$-0.0940040\pi$
$709$	31.5000	+	18.1865i	1.18301	+	0.683010i	0.226299	+	0.974058i	$0.427337\pi$
$710$	−17.0544	+	3.55945i	−0.640039	+	0.133584i
$711$	−6.00000	+	10.3923i	−0.225018	+	0.389742i
$712$	−6.42368	+	3.70871i	−0.240738	+	0.138990i
$713$	22.1552	+	38.3739i	0.829717	+	1.43711i
$714$	17.3739			0.650201
$715$	18.0680	+	11.3379i	0.675704	+	0.424013i
$716$	0.460985			0.0172278
$717$	−10.4877	−	18.1652i	−0.391669	−	0.678390i
$718$	63.2874	−	36.5390i	2.36187	−	1.36362i
$719$	15.2477	−	26.4098i	0.568644	−	0.984921i	−0.428056	−	0.903752i	$-0.640801\pi$
$719$	15.2477	−	26.4098i	0.568644	−	0.984921i	0.996700	−	0.0811686i	$-0.0258652\pi$
$720$	1.63670	+	7.84190i	0.0609962	+	0.292250i
$721$	22.7477	+	13.1334i	0.847170	+	0.489114i
$722$	17.5112	−	30.3303i	0.651700	−	1.12878i
$723$	1.73205			0.0644157
$724$	26.1652	−	45.3194i	0.972420	−	1.68428i
$725$	18.4373	+	13.6040i	0.684742	+	0.505238i
$726$	7.58258	−	4.37780i	0.281416	−	0.162475i
$727$		−	42.7477i		−	1.58543i	−0.609595	−	0.792713i	$-0.708668\pi$
$727$		−	42.7477i		−	1.58543i	0.609595	−	0.792713i	$-0.291332\pi$
$728$	2.59808	−	10.5000i	0.0962911	−	0.389156i
$729$	−13.0000			−0.481481
$730$		0			0
$731$	−3.24773	−	5.62523i	−0.120122	−	0.208057i
$732$	−25.5815	−	14.7695i	−0.945521	−	0.545897i
$733$	8.94630			0.330439			0.165220	−	0.986257i	$-0.447167\pi$
$733$	8.94630			0.330439			0.165220	+	0.986257i	$0.447167\pi$
$734$	48.8085	+	28.1796i	1.80156	+	1.04013i
$735$	−2.79523	+	8.49628i	−0.103103	+	0.313390i
$736$			33.8426i			1.24745i
$737$	−34.0610	−	19.6652i	−1.25465	−	0.724375i
$738$	10.0308	−	5.79129i	0.369239	−	0.213180i
$739$	−42.2477	+	24.3917i	−1.55411	+	0.897265i	−0.556307	+	0.830977i	$0.687782\pi$
$739$	−42.2477	+	24.3917i	−1.55411	+	0.897265i	−0.997801	+	0.0662878i	$0.978884\pi$
$740$	10.1216	+	48.4955i	0.372077	+	1.78273i
$741$	−6.00000	+	1.73205i	−0.220416	+	0.0636285i
$742$			6.00000i			0.220267i
$743$	−21.3845	−	37.0390i	−0.784521	−	1.35883i	−0.929285	−	0.369364i	$-0.879576\pi$
$743$	−21.3845	−	37.0390i	−0.784521	−	1.35883i	0.144764	−	0.989466i	$-0.453758\pi$
$744$	8.37386	+	14.5040i	0.307001	+	0.531741i
$745$	6.82361	−	20.7408i	0.249998	−	0.759884i
$746$		−	28.4557i		−	1.04184i
$747$	−11.3060	+	19.5826i	−0.413665	+	0.716489i
$748$	16.9213	−	29.3085i	0.618703	−	1.07163i
$749$			2.45505i			0.0897056i
$750$	−2.28916	−	24.3654i	−0.0835884	−	0.889697i
$751$	7.87386	+	13.6379i	0.287321	+	0.497655i	0.973169	−	0.230090i	$-0.0739019\pi$
$751$	7.87386	+	13.6379i	0.287321	+	0.497655i	−0.685848	+	0.727745i	$0.740569\pi$
$752$	7.84190	+	13.5826i	0.285965	+	0.495306i
$753$		−	18.1652i		−	0.661975i
$754$	−8.68693	+	35.1078i	−0.316359	+	1.27855i
$755$	−13.5826	+	2.83485i	−0.494321	+	0.103171i
$756$	20.9347	−	12.0866i	0.761386	−	0.439587i
$757$	−15.3700	+	8.87386i	−0.558632	+	0.322526i	−0.752596	−	0.658482i	$-0.771199\pi$
$757$	−15.3700	+	8.87386i	−0.558632	+	0.322526i	0.193965	+	0.981009i	$0.437865\pi$
$758$	39.9425	+	23.0608i	1.45078	+	0.837606i
$759$			12.1244i			0.440086i
$760$	2.09642	−	6.37221i	0.0760451	−	0.231144i
$761$	−35.2913	−	20.3754i	−1.27931	−	0.738609i	−0.302587	−	0.953122i	$-0.597850\pi$
$761$	−35.2913	−	20.3754i	−1.27931	−	0.738609i	−0.976721	+	0.214513i	$0.931184\pi$
$762$	21.3368			0.772951
$763$	−4.11165	−	2.37386i	−0.148852	−	0.0859396i
$764$	10.3521	+	17.9303i	0.374525	+	0.648697i
$765$	−13.6569	−	15.2803i	−0.493768	−	0.552461i
$766$	6.20871			0.224330
$767$	11.7906	+	2.91742i	0.425735	+	0.105342i
$768$			2.79129i			0.100722i
$769$	−13.5000	+	7.79423i	−0.486822	+	0.281067i	−0.723255	−	0.690581i	$-0.757355\pi$
$769$	−13.5000	+	7.79423i	−0.486822	+	0.281067i	0.236433	+	0.971648i	$0.424022\pi$
$770$	−14.9468	−	16.7235i	−0.538647	−	0.602675i
$771$	−0.0825757	+	0.143025i	−0.00297389	+	0.00515093i
$772$	−2.81655			−0.101370
$773$	17.3682	−	30.0826i	0.624690	−	1.08200i	−0.363911	−	0.931434i	$-0.618559\pi$
$773$	17.3682	−	30.0826i	0.624690	−	1.08200i	0.988601	−	0.150561i	$-0.0481080\pi$
$774$	−5.37386	−	3.10260i	−0.193160	−	0.111521i
$775$	−19.3386	−	44.3103i	−0.694663	−	1.59167i
$776$	3.87386	−	6.70973i	0.139064	−	0.240865i
$777$	−11.9059	+	6.87386i	−0.427121	+	0.246598i
$778$	−16.5975	−	28.7477i	−0.595049	−	1.03066i
$779$	4.58258			0.164188
$780$	19.8900	−	10.5273i	0.712174	−	0.376937i
$781$	−9.41742			−0.336982
$782$	−22.9835	−	39.8085i	−0.821887	−	1.42355i
$783$	−19.8431	+	11.4564i	−0.709136	+	0.409420i
$784$	−3.58258	+	6.20520i	−0.127949	+	0.221614i
$785$	−20.0616	+	4.18710i	−0.716030	+	0.149444i
$786$	−3.00000	−	1.73205i	−0.107006	−	0.0617802i
$787$	−16.0930	+	27.8739i	−0.573653	+	0.993596i	0.422534	+	0.906347i	$0.361141\pi$
$787$	−16.0930	+	27.8739i	−0.573653	+	0.993596i	−0.996187	+	0.0872487i	$0.972193\pi$
$788$	−55.7316			−1.98536
$789$	4.50000	−	7.79423i	0.160204	−	0.277482i
$790$	21.8963	−	19.5700i	0.779034	−	0.696270i
$791$	−24.8739	+	14.3609i	−0.884413	+	0.510616i
$792$		−	9.16515i		−	0.325669i
$793$	−9.16478	+	37.0390i	−0.325451	+	1.31529i
$794$	−59.7042			−2.11882
$795$	−2.63850	+	2.35819i	−0.0935779	+	0.0836363i
$796$	1.97822	+	3.42638i	0.0701161	+	0.121445i
$797$	17.3881	+	10.0390i	0.615918	+	0.355600i	0.775278	−	0.631620i	$-0.217610\pi$
$797$	17.3881	+	10.0390i	0.615918	+	0.355600i	−0.159360	+	0.987220i	$0.550943\pi$
$798$	6.56670			0.232459
$799$	−34.7477	−	20.0616i	−1.22929	−	0.709729i
$800$	4.13000	−	36.6936i	0.146017	−	1.29731i
$801$			8.56490i			0.302626i
$802$	23.7065	+	13.6869i	0.837104	+	0.483302i
$803$		0			0
$804$	−35.9347	+	20.7469i	−1.26732	+	0.731686i
$805$	−17.3739	+	3.62614i	−0.612348	+	0.127805i
$806$	52.9129	−	54.9887i	1.86378	−	1.93689i
$807$		−	15.0000i		−	0.528025i
$808$	7.79423	+	13.5000i	0.274200	+	0.474928i
$809$	18.4129	+	31.8920i	0.647362	+	1.12126i	0.983750	+	0.179541i	$0.0574613\pi$
$809$	18.4129	+	31.8920i	0.647362	+	1.12126i	−0.336388	+	0.941723i	$0.609205\pi$
$810$	−4.64938	−	1.52962i	−0.163362	−	0.0537453i
$811$			18.7665i			0.658981i	0.944159	+	0.329491i	$0.106877\pi$
$811$			18.7665i			0.658981i	−0.944159	+	0.329491i	$0.893123\pi$
$812$	11.0776	−	19.1869i	0.388747	−	0.673329i
$813$	−4.33013	+	7.50000i	−0.151864	+	0.263036i
$814$			45.9669i			1.61114i
$815$	−22.6816	−	7.46211i	−0.794501	−	0.261386i
$816$	4.10436	+	7.10895i	0.143681	+	0.248863i
$817$	−1.22753	−	2.12614i	−0.0429457	−	0.0743841i
$818$			18.9564i			0.662796i
$819$	−9.00000	−	8.66025i	−0.314485	−	0.302614i
$820$	−16.1652	+	3.37386i	−0.564512	+	0.117820i
$821$	20.2913	−	11.7152i	0.708171	−	0.408863i	−0.102213	−	0.994763i	$-0.532592\pi$
$821$	20.2913	−	11.7152i	0.708171	−	0.408863i	0.810383	+	0.585900i	$0.199259\pi$
$822$	−0.180750	+	0.104356i	−0.00630438	+	0.00363984i
$823$	−35.1455	−	20.2913i	−1.22510	−	0.707310i	−0.259096	−	0.965851i	$-0.583425\pi$
$823$	−35.1455	−	20.2913i	−1.22510	−	0.707310i	−0.966000	+	0.258542i	$0.916758\pi$
$824$		−	26.2668i		−	0.915048i
$825$	1.47960	−	13.1458i	0.0515131	−	0.457676i
$826$	−11.0608	−	6.38595i	−0.384854	−	0.222196i
$827$	31.5583			1.09739			0.548695	−	0.836023i	$-0.315125\pi$
$827$	31.5583			1.09739			0.548695	+	0.836023i	$0.315125\pi$
$828$	−22.1552	−	12.7913i	−0.769945	−	0.444528i
$829$	1.66515	+	2.88413i	0.0578331	+	0.100170i	0.893492	−	0.449078i	$-0.148248\pi$
$829$	1.66515	+	2.88413i	0.0578331	+	0.100170i	−0.835659	+	0.549248i	$0.814914\pi$
$830$	41.2599	−	36.8765i	1.43215	−	1.28000i
$831$	−16.5826			−0.575243
$832$	43.5873	−	12.5826i	1.51112	−	0.436222i
$833$		−	18.3303i		−	0.635107i
$834$	−10.8956	+	6.29060i	−0.377285	+	0.217826i
$835$	7.13978	−	6.38126i	0.247082	−	0.220833i
$836$	6.39564	−	11.0776i	0.221198	−	0.383126i
$837$	48.3465			1.67110
$838$	26.4476	−	45.8085i	0.913616	−	1.58243i
$839$	1.16970	+	0.675325i	0.0403824	+	0.0233148i	0.520055	−	0.854133i	$-0.325911\pi$
$839$	1.16970	+	0.675325i	0.0403824	+	0.0233148i	−0.479673	+	0.877447i	$0.659245\pi$
$840$	−6.56670	+	1.37055i	−0.226573	+	0.0472885i
$841$	4.00000	−	6.92820i	0.137931	−	0.238904i
$842$	−49.7925	+	28.7477i	−1.71596	+	0.990712i
$843$	−8.75560	−	15.1652i	−0.301559	−	0.522316i
$844$	50.7042			1.74531
$845$	−20.1905	−	20.9128i	−0.694574	−	0.719421i
$846$	−38.3303			−1.31782
$847$	3.46410	+	6.00000i	0.119028	+	0.206162i
$848$	−2.45505	+	1.41742i	−0.0843068	+	0.0486746i
$849$	−0.126136	+	0.218475i	−0.00432899	+	0.00749803i
$850$	20.0616	+	45.9669i	0.688108	+	1.57665i
$851$	31.5000	+	18.1865i	1.07981	+	0.623426i
$852$	−4.96773	+	8.60436i	−0.170192	+	0.294780i
$853$	53.2566			1.82347			0.911736	−	0.410777i	$-0.134742\pi$
$853$	53.2566			1.82347			0.911736	+	0.410777i	$0.134742\pi$
$854$	20.0608	−	34.7463i	0.686466	−	1.18899i
$855$	−5.16184	−	5.77542i	−0.176531	−	0.197515i
$856$	2.12614	−	1.22753i	0.0726698	−	0.0419560i
$857$			22.7477i			0.777048i	0.921439	+	0.388524i	$0.127015\pi$
$857$			22.7477i			0.777048i	−0.921439	+	0.388524i	$0.872985\pi$
$858$	20.0616	−	5.79129i	0.684892	−	0.197711i
$859$	−38.2432			−1.30484			−0.652420	−	0.757857i	$-0.726246\pi$
$859$	−38.2432			−1.30484			−0.652420	+	0.757857i	$0.726246\pi$
$860$	5.89547	+	6.59625i	0.201034	+	0.224930i
$861$	−2.29129	−	3.96863i	−0.0780869	−	0.135250i
$862$	56.1785	+	32.4347i	1.91345	+	1.10473i
$863$	−34.8317			−1.18569			−0.592843	−	0.805318i	$-0.701994\pi$
$863$	−34.8317			−1.18569			−0.592843	+	0.805318i	$0.701994\pi$
$864$	31.9782	+	18.4626i	1.08792	+	0.628112i
$865$	−5.18335	+	15.7551i	−0.176239	+	0.535690i
$866$		−	38.8480i		−	1.32011i
$867$	−3.46410	−	2.00000i	−0.117647	−	0.0679236i
$868$	−40.4847	+	23.3739i	−1.37414	+	0.793361i
$869$	13.7477	−	7.93725i	0.466360	−	0.269253i
$870$	21.9564	−	4.58258i	0.744393	−	0.155364i
$871$	38.6216	+	37.1636i	1.30864	+	1.25924i
$872$			4.74773i			0.160778i
$873$	−4.47315	−	7.74773i	−0.151393	−	0.262221i
$874$	−8.68693	−	15.0462i	−0.293840	−	0.508946i
$875$	19.2800	−	1.81139i	0.651783	−	0.0612360i
$876$		0			0
$877$	−3.96863	+	6.87386i	−0.134011	+	0.232114i	−0.925219	−	0.379433i	$-0.876119\pi$
$877$	−3.96863	+	6.87386i	−0.134011	+	0.232114i	0.791208	+	0.611547i	$0.209452\pi$
$878$	−44.3203	+	76.7650i	−1.49574	+	2.59069i
$879$			23.4304i			0.790286i
$880$	3.31186	−	10.0666i	0.111643	−	0.339345i
$881$	9.24773	+	16.0175i	0.311564	+	0.539644i	0.978701	−	0.205290i	$-0.0658139\pi$
$881$	9.24773	+	16.0175i	0.311564	+	0.539644i	−0.667137	+	0.744935i	$0.732481\pi$
$882$	−8.75560	−	15.1652i	−0.294817	−	0.510637i
$883$			46.2432i			1.55621i	0.628136	+	0.778103i	$0.283818\pi$
$883$			46.2432i			1.55621i	−0.628136	+	0.778103i	$0.716182\pi$
$884$	−31.9782	+	33.2327i	−1.07554	+	1.11774i
$885$	−1.53901	−	7.37386i	−0.0517334	−	0.247870i
$886$	−49.1216	+	28.3604i	−1.65027	+	0.952785i
$887$	−0.429076	+	0.247727i	−0.0144070	+	0.00831786i	−0.507186	−	0.861837i	$-0.669314\pi$
$887$	−0.429076	+	0.247727i	−0.0144070	+	0.00831786i	0.492779	+	0.870154i	$0.335981\pi$
$888$	11.9059	+	6.87386i	0.399535	+	0.230672i
$889$			16.8836i			0.566256i
$890$	6.55052	−	19.9107i	0.219574	−	0.667409i
$891$	−2.29129	−	1.32288i	−0.0767610	−	0.0443180i
$892$	−24.1733			−0.809381
$893$	−13.1334	−	7.58258i	−0.439493	−	0.253741i
$894$	−10.6869	−	18.5103i	−0.357424	−	0.619077i
$895$	−0.275344	+	0.246091i	−0.00920372	+	0.00822592i
$896$	−22.1216			−0.739030
$897$	3.96863	−	16.0390i	0.132509	−	0.535527i
$898$			82.0345i			2.73753i
$899$	38.3739	−	22.1552i	1.27984	−	0.738916i
$900$	22.4606	+	16.5726i	0.748686	+	0.552419i
$901$	3.62614	−	6.28065i	0.120804	−	0.209239i
$902$	−15.3223			−0.510177
$903$	−1.22753	+	2.12614i	−0.0408495	+	0.0707534i
$904$	24.8739	+	14.3609i	0.827292	+	0.477637i
$905$	8.56490	+	41.0369i	0.284707	+	1.36411i
$906$	−6.79129	+	11.7629i	−0.225625	+	0.390795i
$907$	−29.2264	+	16.8739i	−0.970446	+	0.560287i	−0.899372	−	0.437184i	$-0.855976\pi$
$907$	−29.2264	+	16.8739i	−0.970446	+	0.560287i	−0.0710740	+	0.997471i	$0.522643\pi$
$908$	−8.52718	−	14.7695i	−0.282984	−	0.490143i
$909$	18.0000			0.597022
$910$	14.2988	+	27.0157i	0.473999	+	0.895561i
$911$	37.9129			1.25611			0.628055	−	0.778169i	$-0.283851\pi$
$911$	37.9129			1.25611			0.628055	+	0.778169i	$0.283851\pi$
$912$	1.55130	+	2.68693i	0.0513687	+	0.0889732i
$913$	25.9053	−	14.9564i	0.857341	−	0.494986i
$914$	1.89564	−	3.28335i	0.0627023	−	0.108604i
$915$	23.1642	−	4.83465i	0.765785	−	0.159829i
$916$	−13.2523	−	7.65120i	−0.437867	−	0.252803i
$917$	1.37055	−	2.37386i	0.0452596	−	0.0783919i
$918$	−50.1540			−1.65533
$919$	17.9174	−	31.0339i	0.591041	−	1.02371i	−0.403051	−	0.915177i	$-0.632050\pi$
$919$	17.9174	−	31.0339i	0.591041	−	1.02371i	0.994093	−	0.108536i	$-0.0346163\pi$
$920$	11.8273	+	13.2331i	0.389933	+	0.436284i
$921$	21.0000	−	12.1244i	0.691974	−	0.399511i
$922$		−	2.62614i		−	0.0864872i
$923$	12.4581	+	3.08258i	0.410063	+	0.101464i
$924$	−12.7913			−0.420802
$925$	−31.9343	−	23.5627i	−1.04999	−	0.774738i
$926$	9.00000	+	15.5885i	0.295758	+	0.512268i
$927$	−26.2668	−	15.1652i	−0.862715	−	0.498089i
$928$	33.8426			1.11094
$929$	−13.8303	−	7.98493i	−0.453758	−	0.261977i	0.255658	−	0.966767i	$-0.417708\pi$
$929$	−13.8303	−	7.98493i	−0.453758	−	0.261977i	−0.709416	+	0.704790i	$0.751041\pi$
$930$	−44.9562	−	14.7903i	−1.47417	−	0.484995i
$931$		−	6.92820i		−	0.227063i
$932$	51.1631	+	29.5390i	1.67590	+	0.967583i
$933$	1.37055	−	0.791288i	0.0448698	−	0.0259056i
$934$	−23.3739	+	13.4949i	−0.764816	+	0.441567i
$935$	5.53901	+	26.5390i	0.181145	+	0.867919i
$936$	−3.00000	+	12.1244i	−0.0980581	+	0.396297i
$937$		−	23.4955i		−	0.767563i	−0.923424	−	0.383782i	$-0.874622\pi$
$937$		−	23.4955i		−	0.767563i	0.923424	−	0.383782i	$-0.125378\pi$
$938$	−28.1796	−	48.8085i	−0.920097	−	1.59365i
$939$	−15.3739	−	26.6283i	−0.501707	−	0.868982i
$940$	51.9110	+	17.0784i	1.69315	+	0.557037i
$941$		−	26.4575i		−	0.862490i	−0.902235	−	0.431245i	$-0.858074\pi$
$941$		−	26.4575i		−	0.862490i	0.902235	−	0.431245i	$-0.141926\pi$
$942$	−10.0308	+	17.3739i	−0.326821	+	0.566071i
$943$	−6.06218	+	10.5000i	−0.197412	+	0.341927i
$944$		−	6.03440i		−	0.196403i
$945$	−6.05184	+	18.3950i	−0.196866	+	0.598389i
$946$	4.10436	+	7.10895i	0.133444	+	0.231132i
$947$	19.2909	+	33.4129i	0.626871	+	1.08577i	0.988176	+	0.153325i	$0.0489981\pi$
$947$	19.2909	+	33.4129i	0.626871	+	1.08577i	−0.361305	+	0.932448i	$0.617669\pi$
$948$		−	16.7477i		−	0.543941i
$949$		0			0
$950$	7.58258	+	17.3739i	0.246011	+	0.563683i
$951$	18.1652	−	10.4877i	0.589045	−	0.340086i
$952$	11.9059	−	6.87386i	0.385872	−	0.222783i
$953$	48.5650	+	28.0390i	1.57317	+	0.908273i	0.995777	+	0.0918100i	$0.0292652\pi$
$953$	48.5650	+	28.0390i	1.57317	+	0.908273i	0.577398	+	0.816463i	$0.304068\pi$
$954$		−	6.92820i		−	0.224309i
$955$	−15.7551	−	5.18335i	−0.509824	−	0.167729i
$956$	−50.7042	−	29.2741i	−1.63989	−	0.946791i
$957$	12.1244			0.391925
$958$	−61.3746	−	35.4347i	−1.98292	−	1.14484i
$959$	−0.0825757	−	0.143025i	−0.00266651	−	0.00461853i
$960$	−18.7492	−	20.9779i	−0.605129	−	0.677059i
$961$	−62.4955			−2.01598
$962$	15.0462	−	60.8085i	0.485109	−	1.96055i
$963$		−	2.83485i		−	0.0913517i
$964$	4.18693	−	2.41733i	0.134852	−	0.0778568i
$965$	1.68231	−	1.50358i	0.0541554	−	0.0484020i
$966$	−8.68693	+	15.0462i	−0.279497	+	0.484104i
$967$	21.5076			0.691638			0.345819	−	0.938301i	$-0.387601\pi$
$967$	21.5076			0.691638			0.345819	+	0.938301i	$0.387601\pi$
$968$	3.46410	−	6.00000i	0.111340	−	0.192847i
$969$	−6.87386	−	3.96863i	−0.220820	−	0.127491i
$970$	4.47315	+	21.4322i	0.143624	+	0.688145i
$971$	−18.2477	+	31.6060i	−0.585597	+	1.01428i	0.409203	+	0.912443i	$0.365807\pi$
$971$	−18.2477	+	31.6060i	−0.585597	+	1.01428i	−0.994801	+	0.101841i	$0.967527\pi$
$972$	−38.6772	+	22.3303i	−1.24057	+	0.716245i
$973$	−4.97768	−	8.62159i	−0.159577	−	0.276396i
$974$	46.1216			1.47783
$975$	−6.26029	+	16.9059i	−0.200490	+	0.541421i
$976$	18.9564			0.606781
$977$	−19.3863	−	33.5780i	−0.620222	−	1.07426i	−0.989444	−	0.144915i	$-0.953709\pi$
$977$	−19.3863	−	33.5780i	−0.620222	−	1.07426i	0.369222	−	0.929341i	$-0.379624\pi$
$978$	−20.2424	+	11.6869i	−0.647279	+	0.373707i
$979$	5.66515	−	9.81233i	0.181059	−	0.313603i
$980$	5.10080	+	24.4394i	0.162939	+	0.780688i
$981$	4.74773	+	2.74110i	0.151583	+	0.0875166i
$982$	31.2822	−	54.1824i	0.998256	−	1.72903i
$983$	3.12250			0.0995924			0.0497962	−	0.998759i	$-0.484143\pi$
$983$	3.12250			0.0995924			0.0497962	+	0.998759i	$0.484143\pi$
$984$	−2.29129	+	3.96863i	−0.0730436	+	0.126515i
$985$	33.2881	−	29.7516i	1.06065	−	0.947965i
$986$	−39.8085	+	22.9835i	−1.26776	+	0.731943i
$987$			15.1652i			0.482712i
$988$	−12.0866	+	12.5608i	−0.384527	+	0.399612i
$989$	6.49545			0.206543
$990$	17.2591	+	19.3107i	0.548531	+	0.613734i
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	0.950603	−	0.310409i	$-0.100466\pi$
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	−0.744124	+	0.668042i	$0.767133\pi$
$992$	−61.8414	−	35.7042i	−1.96347	−	1.13361i
$993$	−11.4014			−0.361811
$994$	−11.6869	−	6.74745i	−0.370687	−	0.214016i
$995$	−3.01071	−	0.990505i	−0.0954458	−	0.0314011i
$996$		−	31.5583i		−	0.999963i
$997$	15.7315	+	9.08258i	0.498221	+	0.287648i	0.727979	−	0.685600i	$-0.240460\pi$
$997$	15.7315	+	9.08258i	0.498221	+	0.287648i	−0.229758	+	0.973248i	$0.573793\pi$
$998$	31.4630	−	18.1652i	0.995943	−	0.575008i
$999$	34.3693	−	19.8431i	1.08740	−	0.627809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.l.a.49.4	yes	8
3.2	odd	2		585.2.bf.a.244.1		8
4.3	odd	2		1040.2.df.b.49.3		8
5.2	odd	4		325.2.n.b.101.1		4
5.3	odd	4		325.2.n.c.101.2		4
5.4	even	2	inner	65.2.l.a.49.1	yes	8
13.2	odd	12		845.2.b.f.339.7		8
13.3	even	3		845.2.d.c.844.1		8
13.4	even	6	inner	65.2.l.a.4.1	✓	8
13.5	odd	4		845.2.n.d.484.3		8
13.6	odd	12		845.2.n.c.529.2		8
13.7	odd	12		845.2.n.d.529.4		8
13.8	odd	4		845.2.n.c.484.1		8
13.9	even	3		845.2.l.c.654.4		8
13.10	even	6		845.2.d.c.844.7		8
13.11	odd	12		845.2.b.f.339.1		8
13.12	even	2		845.2.l.c.699.1		8
15.14	odd	2		585.2.bf.a.244.4		8
20.19	odd	2		1040.2.df.b.49.2		8
39.17	odd	6		585.2.bf.a.199.4		8
52.43	odd	6		1040.2.df.b.849.2		8
65.2	even	12		4225.2.a.bj.1.1		4
65.4	even	6	inner	65.2.l.a.4.4	yes	8
65.9	even	6		845.2.l.c.654.1		8
65.17	odd	12		325.2.n.b.251.1		4
65.19	odd	12		845.2.n.d.529.3		8
65.24	odd	12		845.2.b.f.339.8		8
65.28	even	12		4225.2.a.bk.1.4		4
65.29	even	6		845.2.d.c.844.8		8
65.34	odd	4		845.2.n.d.484.4		8
65.37	even	12		4225.2.a.bj.1.4		4
65.43	odd	12		325.2.n.c.251.2		4
65.44	odd	4		845.2.n.c.484.2		8
65.49	even	6		845.2.d.c.844.2		8
65.54	odd	12		845.2.b.f.339.2		8
65.59	odd	12		845.2.n.c.529.1		8
65.63	even	12		4225.2.a.bk.1.1		4
65.64	even	2		845.2.l.c.699.4		8
195.134	odd	6		585.2.bf.a.199.1		8
260.199	odd	6		1040.2.df.b.849.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.l.a.4.1	✓	8	13.4	even	6	inner
65.2.l.a.4.4	yes	8	65.4	even	6	inner
65.2.l.a.49.1	yes	8	5.4	even	2	inner
65.2.l.a.49.4	yes	8	1.1	even	1	trivial
325.2.n.b.101.1		4	5.2	odd	4
325.2.n.b.251.1		4	65.17	odd	12
325.2.n.c.101.2		4	5.3	odd	4
325.2.n.c.251.2		4	65.43	odd	12
585.2.bf.a.199.1		8	195.134	odd	6
585.2.bf.a.199.4		8	39.17	odd	6
585.2.bf.a.244.1		8	3.2	odd	2
585.2.bf.a.244.4		8	15.14	odd	2
845.2.b.f.339.1		8	13.11	odd	12
845.2.b.f.339.2		8	65.54	odd	12
845.2.b.f.339.7		8	13.2	odd	12
845.2.b.f.339.8		8	65.24	odd	12
845.2.d.c.844.1		8	13.3	even	3
845.2.d.c.844.2		8	65.49	even	6
845.2.d.c.844.7		8	13.10	even	6
845.2.d.c.844.8		8	65.29	even	6
845.2.l.c.654.1		8	65.9	even	6
845.2.l.c.654.4		8	13.9	even	3
845.2.l.c.699.1		8	13.12	even	2
845.2.l.c.699.4		8	65.64	even	2
845.2.n.c.484.1		8	13.8	odd	4
845.2.n.c.484.2		8	65.44	odd	4
845.2.n.c.529.1		8	65.59	odd	12
845.2.n.c.529.2		8	13.6	odd	12
845.2.n.d.484.3		8	13.5	odd	4
845.2.n.d.484.4		8	65.34	odd	4
845.2.n.d.529.3		8	65.19	odd	12
845.2.n.d.529.4		8	13.7	odd	12
1040.2.df.b.49.2		8	20.19	odd	2
1040.2.df.b.49.3		8	4.3	odd	2
1040.2.df.b.849.2		8	52.43	odd	6
1040.2.df.b.849.3		8	260.199	odd	6
4225.2.a.bj.1.1		4	65.2	even	12
4225.2.a.bj.1.4		4	65.37	even	12
4225.2.a.bk.1.1		4	65.63	even	12
4225.2.a.bk.1.4		4	65.28	even	12

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09445 + 1.89564i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-1.39564 + 2.41733i) q^{4} +(-0.456850 - 2.18890i) q^{5} +(-1.89564 - 1.09445i) q^{6} +(0.866025 - 1.50000i) q^{7} -1.73205 q^{8} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(1.09445 + 1.89564i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-1.39564 + 2.41733i) q^{4} +(-0.456850 - 2.18890i) q^{5} +(-1.89564 - 1.09445i) q^{6} +(0.866025 - 1.50000i) q^{7} -1.73205 q^{8} +(-1.00000 + 1.73205i) q^{9} +(3.64938 - 3.26167i) q^{10} +(2.29129 - 1.32288i) q^{11} -2.79129i q^{12} +(-3.46410 + 1.00000i) q^{13} +3.79129 q^{14} +(1.49009 + 1.66722i) q^{15} +(0.895644 + 1.55130i) q^{16} +(-3.96863 - 2.29129i) q^{17} -4.37780 q^{18} +(-1.50000 - 0.866025i) q^{19} +(5.92889 + 1.95057i) q^{20} +1.73205i q^{21} +(5.01540 + 2.89564i) q^{22} +(3.96863 - 2.29129i) q^{23} +(1.50000 - 0.866025i) q^{24} +(-4.58258 + 2.00000i) q^{25} +(-5.68693 - 5.47225i) q^{26} -5.00000i q^{27} +(2.41733 + 4.18693i) q^{28} +(-2.29129 - 3.96863i) q^{29} +(-1.52962 + 4.64938i) q^{30} +9.66930i q^{31} +(-3.69253 + 6.39564i) q^{32} +(-1.32288 + 2.29129i) q^{33} -10.0308i q^{34} +(-3.67900 - 1.21037i) q^{35} +(-2.79129 - 4.83465i) q^{36} +(3.96863 + 6.87386i) q^{37} -3.79129i q^{38} +(2.50000 - 2.59808i) q^{39} +(0.791288 + 3.79129i) q^{40} +(-2.29129 + 1.32288i) q^{41} +(-3.28335 + 1.89564i) q^{42} +(1.22753 + 0.708712i) q^{43} +7.38505i q^{44} +(4.24814 + 1.39761i) q^{45} +(8.68693 + 5.01540i) q^{46} +8.75560 q^{47} +(-1.55130 - 0.895644i) q^{48} +(2.00000 + 3.46410i) q^{49} +(-8.80669 - 6.49803i) q^{50} +4.58258 q^{51} +(2.41733 - 9.76951i) q^{52} +1.58258i q^{53} +(9.47822 - 5.47225i) q^{54} +(-3.94242 - 4.41105i) q^{55} +(-1.50000 + 2.59808i) q^{56} +1.73205 q^{57} +(5.01540 - 8.68693i) q^{58} +(-2.91742 - 1.68438i) q^{59} +(-6.10985 + 1.27520i) q^{60} +(5.29129 - 9.16478i) q^{61} +(-18.3296 + 10.5826i) q^{62} +(1.73205 + 3.00000i) q^{63} -12.5826 q^{64} +(3.77148 + 7.12573i) q^{65} -5.79129 q^{66} +(-7.43273 - 12.8739i) q^{67} +(11.0776 - 6.39564i) q^{68} +(-2.29129 + 3.96863i) q^{69} +(-1.73205 - 8.29875i) q^{70} +(-3.08258 - 1.77973i) q^{71} +(1.73205 - 3.00000i) q^{72} +(-8.68693 + 15.0462i) q^{74} +(2.96863 - 4.02334i) q^{75} +(4.18693 - 2.41733i) q^{76} -4.58258i q^{77} +(7.66115 + 1.89564i) q^{78} +6.00000 q^{79} +(2.98647 - 2.66919i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.01540 - 2.89564i) q^{82} +11.3060 q^{83} +(-4.18693 - 2.41733i) q^{84} +(-3.20233 + 9.73371i) q^{85} +3.10260i q^{86} +(3.96863 + 2.29129i) q^{87} +(-3.96863 + 2.29129i) q^{88} +(3.70871 - 2.14123i) q^{89} +(2.00000 + 9.58258i) q^{90} +(-1.50000 + 6.06218i) q^{91} +12.7913i q^{92} +(-4.83465 - 8.37386i) q^{93} +(9.58258 + 16.5975i) q^{94} +(-1.21037 + 3.67900i) q^{95} -7.38505i q^{96} +(-2.23658 + 3.87386i) q^{97} +(-4.37780 + 7.58258i) q^{98} +5.29150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 6 q^{6} - 8 q^{9}+O(q^{10}) \) 8 * q - 2 * q^4 - 6 * q^6 - 8 * q^9	\( 8 q - 2 q^{4} - 6 q^{6} - 8 q^{9} - 4 q^{10} + 12 q^{14} - 6 q^{15} - 2 q^{16} - 12 q^{19} + 24 q^{20} + 12 q^{24} - 18 q^{26} - 10 q^{30} + 6 q^{35} - 4 q^{36} + 20 q^{39} - 12 q^{40} + 12 q^{45} + 42 q^{46} + 16 q^{49} - 12 q^{50} + 30 q^{54} - 14 q^{55} - 12 q^{56} - 60 q^{59} + 24 q^{61} - 64 q^{64} - 24 q^{65} - 28 q^{66} + 12 q^{71} - 42 q^{74} - 8 q^{75} + 6 q^{76} + 48 q^{79} + 18 q^{80} - 4 q^{81} - 6 q^{84} + 42 q^{85} + 48 q^{89} + 16 q^{90} - 12 q^{91} + 40 q^{94} - 6 q^{95}+O(q^{100}) \) 8 * q - 2 * q^4 - 6 * q^6 - 8 * q^9 - 4 * q^10 + 12 * q^14 - 6 * q^15 - 2 * q^16 - 12 * q^19 + 24 * q^20 + 12 * q^24 - 18 * q^26 - 10 * q^30 + 6 * q^35 - 4 * q^36 + 20 * q^39 - 12 * q^40 + 12 * q^45 + 42 * q^46 + 16 * q^49 - 12 * q^50 + 30 * q^54 - 14 * q^55 - 12 * q^56 - 60 * q^59 + 24 * q^61 - 64 * q^64 - 24 * q^65 - 28 * q^66 + 12 * q^71 - 42 * q^74 - 8 * q^75 + 6 * q^76 + 48 * q^79 + 18 * q^80 - 4 * q^81 - 6 * q^84 + 42 * q^85 + 48 * q^89 + 16 * q^90 - 12 * q^91 + 40 * q^94 - 6 * q^95

Introduction

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