LMFDB - Embedded newform 845.2.l.c.699.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(654,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, 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("845.654");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.l (of order $6$, degree $2$, not 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:	$6.74735897080$
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:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			699.1
Root			$-1.09445 - 0.895644i$ of defining polynomial
Character	$\chi$	$=$	845.699
Dual form			845.2.l.c.654.1

$q$-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} +3.79129 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} -5.00000i 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} +(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} +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} -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} +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} +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} - 10 q^{30} + 6 q^{35} - 4 q^{36} - 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} - 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} + 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 - 10 * q^30 + 6 * q^35 - 4 * q^36 - 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 - 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 + 40 * q^94 - 6 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.09445	−	1.89564i	−0.773893	−	1.34042i	−0.935414	−	0.353553i	$-0.884973\pi$
$2$	−1.09445	−	1.89564i	−0.773893	−	1.34042i	0.161521	−	0.986869i	$-0.448360\pi$
$3$	−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	−0.981981	−	0.188982i	$-0.939481\pi$
$7$	−0.866025	+	1.50000i	−0.327327	+	0.566947i	0.654654	+	0.755929i	$0.272814\pi$
$8$	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	−0.803930	−	0.594724i	$-0.797261\pi$
$11$	−2.29129	+	1.32288i	−0.690849	+	0.398862i	0.113081	+	0.993586i	$0.463928\pi$
$12$		−	2.79129i		−	0.805775i
$13$		0			0
$13$		0			0
$14$	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	0.662094	−	0.749421i	$-0.269668\pi$
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	−0.317970	+	0.948101i	$0.603001\pi$
$20$	−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
$26$		0			0
$27$		−	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	$-0.665194\pi$
$31$		−	9.66930i		−	1.73666i	0.495988	−	0.868329i	$-0.334806\pi$
$32$	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	$-0.940413\pi$
$37$	−3.96863	−	6.87386i	−0.652438	−	1.13006i	0.330091	−	0.943949i	$-0.392920\pi$
$38$		−	3.79129i		−	0.615028i
$39$		0			0
$40$	0.791288	+	3.79129i	0.125114	+	0.599455i
$41$	2.29129	−	1.32288i	0.357839	−	0.206598i	−0.310293	−	0.950641i	$-0.600427\pi$
$41$	2.29129	−	1.32288i	0.357839	−	0.206598i	0.668132	+	0.744042i	$0.267094\pi$
$42$	−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	$-0.720473\pi$
$47$	−8.75560			−1.27714			−0.638568	+	0.769565i	$0.720473\pi$
$48$	−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
$52$		0			0
$53$			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	0.677738	−	0.735303i	$-0.262960\pi$
$59$	2.91742	+	1.68438i	0.379816	+	0.219287i	−0.297922	+	0.954590i	$0.596294\pi$
$60$	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
$65$		0			0
$66$	−5.79129			−0.712858
$67$	7.43273	+	12.8739i	0.908052	+	1.57279i	0.816767	+	0.576968i	$0.195764\pi$
$67$	7.43273	+	12.8739i	0.908052	+	1.57279i	0.0912856	+	0.995825i	$0.470902\pi$
$68$	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	0.671637	−	0.740880i	$-0.265591\pi$
$71$	3.08258	+	1.77973i	0.365834	+	0.211215i	−0.305803	+	0.952095i	$0.598925\pi$
$72$	−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
$78$		0			0
$79$	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	$-0.713069\pi$
$83$	−11.3060			−1.24100			−0.620498	+	0.784208i	$0.713069\pi$
$84$	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	−0.683512	−	0.729939i	$-0.739548\pi$
$89$	−3.70871	+	2.14123i	−0.393123	+	0.226969i	0.290390	+	0.956909i	$0.406215\pi$
$90$	2.00000	+	9.58258i	0.210819	+	1.01009i
$91$		0			0
$92$			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	−0.729854	−	0.683603i	$-0.760412\pi$
$97$	2.23658	−	3.87386i	0.227090	−	0.393331i	0.956944	+	0.290271i	$0.0937455\pi$
$98$	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	$0.731430\pi$
$104$		0			0
$105$	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	$0.0419071\pi$
$109$			2.74110i			0.262550i	−0.991346	+	0.131275i	$0.958093\pi$
$110$	−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
$117$		0			0
$118$		−	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
$130$		0			0
$131$	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	−0.868055	−	0.496468i	$-0.834630\pi$
$137$	−0.0476751	+	0.0825757i	−0.00407316	+	0.00705492i	0.863982	+	0.503523i	$0.167963\pi$
$138$	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
$143$		0			0
$144$	−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	0.111874	−	0.993722i	$-0.464315\pi$
$149$	−8.45644	−	4.88233i	−0.692778	−	0.399976i	−0.804652	+	0.593747i	$0.797648\pi$
$150$	−10.8758	−	1.22411i	−0.888008	−	0.0999485i
$151$			6.20520i			0.504972i	0.967601	+	0.252486i	$0.0812482\pi$
$151$			6.20520i			0.504972i	−0.967601	+	0.252486i	$0.918752\pi$
$152$	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
$156$		0			0
$157$		−	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	−0.995758	−	0.0920093i	$-0.970671\pi$
$163$	−5.33918	+	9.24773i	−0.418197	+	0.724338i	0.577561	+	0.816347i	$0.304004\pi$
$164$			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	0.771208	−	0.636583i	$-0.219653\pi$
$167$	−2.14123	−	3.70871i	−0.165693	−	0.286989i	−0.936901	+	0.349594i	$0.886319\pi$
$168$		−	3.00000i		−	0.231455i
$169$		0			0
$170$	−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	$0.745373\pi$
$182$		0			0
$183$			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	0.847296	−	0.531121i	$-0.178229\pi$
$193$	−0.504525	−	0.873864i	−0.0363165	−	0.0629021i	−0.883612	+	0.468219i	$0.844896\pi$
$194$	−9.79129			−0.702973
$195$		0			0
$196$	−11.1652			−0.797511
$197$	−9.98313	−	17.2913i	−0.711269	−	1.23195i	−0.964381	−	0.264516i	$-0.914788\pi$
$197$	−9.98313	−	17.2913i	−0.711269	−	1.23195i	0.253113	−	0.967437i	$-0.418546\pi$
$198$	−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
$208$		0			0
$209$	−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
$221$		0			0
$222$		−	17.3739i		−	1.16606i
$223$	−4.33013	−	7.50000i	−0.289967	−	0.502237i	0.683835	−	0.729637i	$-0.260311\pi$
$223$	−4.33013	−	7.50000i	−0.289967	−	0.502237i	−0.973801	+	0.227400i	$0.926978\pi$
$224$	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	−0.746655	−	0.665212i	$-0.768341\pi$
$227$	3.05493	−	5.29129i	0.202763	−	0.351195i	0.949418	+	0.314016i	$0.101675\pi$
$228$	2.41733	−	4.18693i	0.160091	−	0.277286i
$229$		−	5.48220i		−	0.362274i	−0.983458	−	0.181137i	$-0.942022\pi$
$229$		−	5.48220i		−	0.362274i	0.983458	−	0.181137i	$-0.0579778\pi$
$230$	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	$-0.243838\pi$
$234$		0			0
$235$	−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	$-0.762678\pi$
$239$		−	20.9753i		−	1.35678i	0.734702	−	0.678390i	$-0.237322\pi$
$240$	1.25176	−	3.80482i	0.0808010	−	0.245600i
$241$	1.50000	+	0.866025i	0.0966235	+	0.0557856i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	1.50000	+	0.866025i	0.0966235	+	0.0557856i	−0.450910	+	0.892570i	$0.648900\pi$
$242$	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
$247$		0			0
$248$		−	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
$260$		0			0
$261$	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	−0.710189	−	0.704011i	$-0.751391\pi$
$271$	−7.50000	+	4.33013i	−0.455593	+	0.263036i	0.254597	+	0.967047i	$0.418057\pi$
$272$		−	8.20871i		−	0.497726i
$273$		0			0
$274$	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	$-0.825068\pi$
$281$		−	17.5112i		−	1.04463i	0.852752	−	0.522316i	$-0.174932\pi$
$282$	−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
$286$		0			0
$287$			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	$0.406606\pi$
$293$	−11.7152	+	20.2913i	−0.684408	+	1.18543i	−0.973622	+	0.228165i	$0.926727\pi$
$294$			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
$299$		0			0
$300$	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	$-0.256741\pi$
$307$	24.2487			1.38395			0.691974	+	0.721923i	$0.256741\pi$
$308$	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	$0.514287\pi$
$312$		0			0
$313$			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	$-0.299504\pi$
$317$	20.9753			1.17809			0.589045	+	0.808100i	$0.299504\pi$
$318$	−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
$325$		0			0
$326$	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	0.203463	−	0.979083i	$-0.434780\pi$
$331$	−9.87386	−	5.70068i	−0.542717	−	0.313338i	−0.746179	+	0.665745i	$0.768114\pi$
$332$	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	$0.971767\pi$
$338$		0			0
$339$	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	−0.860552	−	0.509362i	$-0.829882\pi$
$349$	−15.8739	+	9.16478i	−0.849708	+	0.490579i	0.0108440	+	0.999941i	$0.496548\pi$
$350$	−17.3739	+	7.58258i	−0.928672	+	0.405306i
$351$		0			0
$352$			19.5390i			1.04143i
$353$	8.70793	+	15.0826i	0.463476	+	0.802765i	0.999131	−	0.0416724i	$-0.0132686\pi$
$353$	8.70793	+	15.0826i	0.463476	+	0.802765i	−0.535655	+	0.844437i	$0.679935\pi$
$354$	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	$0.343139\pi$
$359$			33.3857i			1.76203i	−0.473088	+	0.881015i	$0.656861\pi$
$360$	−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
$364$		0			0
$365$		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
$377$		0			0
$378$		−	18.9564i		−	0.975014i
$379$	−18.2477	+	10.5353i	−0.937323	+	0.541164i	−0.889120	−	0.457674i	$-0.848683\pi$
$379$	−18.2477	+	10.5353i	−0.937323	+	0.541164i	−0.0482027	+	0.998838i	$0.515349\pi$
$380$	−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	−0.899982	−	0.435926i	$-0.856421\pi$
$383$	−1.41823	+	2.45644i	−0.0724680	+	0.125518i	0.827514	+	0.561444i	$0.189754\pi$
$384$	−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			0
$391$	−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	$-0.593368\pi$
$397$	13.6379	−	23.6216i	0.684468	−	1.18553i	0.973604	−	0.228245i	$-0.0732989\pi$
$398$	−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	−0.745419	−	0.666596i	$-0.767751\pi$
$401$	−10.8303	+	6.25288i	−0.540840	+	0.312254i	0.204580	+	0.978850i	$0.434417\pi$
$402$			32.5390i			1.62290i
$403$		0			0
$404$	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	0.302979	−	0.952997i	$-0.402019\pi$
$409$	−7.50000	−	4.33013i	−0.370851	−	0.214111i	−0.673830	+	0.738886i	$0.735352\pi$
$410$	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
$416$		0			0
$417$			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	$-0.778900\pi$
$421$		−	26.2668i		−	1.28017i	0.768306	−	0.640083i	$-0.221100\pi$
$422$	−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
$429$		0			0
$430$	6.79129	−	1.41742i	0.327505	−	0.0683543i
$431$	−25.6652	+	14.8178i	−1.23625	+	0.713747i	−0.968325	−	0.249693i	$-0.919670\pi$
$431$	−25.6652	+	14.8178i	−1.23625	+	0.713747i	−0.267922	+	0.963441i	$0.586337\pi$
$432$	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
$442$		0			0
$443$			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	$-0.987945\pi$
$449$	−32.4564	−	18.7387i	−1.53171	−	0.884336i	−0.532431	−	0.846473i	$-0.678721\pi$
$450$	−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
$455$		0			0
$456$	−3.00000			−0.140488
$457$	0.866025	+	1.50000i	0.0405110	+	0.0701670i	0.885570	−	0.464506i	$-0.153768\pi$
$457$	0.866025	+	1.50000i	0.0405110	+	0.0701670i	−0.845059	+	0.534673i	$0.820435\pi$
$458$	−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	0.524001	−	0.851718i	$-0.324439\pi$
$461$	1.03901	+	0.599876i	0.0483917	+	0.0279390i	−0.475609	+	0.879657i	$0.657772\pi$
$462$	5.01540	−	8.68693i	0.233338	−	0.404153i
$463$	−8.22330			−0.382169			−0.191085	−	0.981574i	$-0.561201\pi$
$463$	−8.22330			−0.382169			−0.191085	+	0.981574i	$0.561201\pi$
$464$	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	$0.907910\pi$
$468$		0			0
$469$	−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	0.304079	−	0.952647i	$-0.401651\pi$
$479$	28.0390	−	16.1883i	1.28114	−	0.739664i	0.977056	+	0.212983i	$0.0683179\pi$
$480$	−16.1652	+	3.37386i	−0.737835	+	0.153995i
$481$		0			0
$482$		−	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	−0.999665	−	0.0259009i	$-0.991755\pi$
$487$	−10.5353	+	18.2477i	−0.477401	+	0.826883i	0.522263	+	0.852784i	$0.325088\pi$
$488$	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
$494$		0			0
$495$	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	$0.121158\pi$
$499$			16.5975i			0.743006i	−0.928432	+	0.371503i	$0.878842\pi$
$500$	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
$507$		0			0
$508$		−	27.2087i		−	1.20719i
$509$	25.6652	−	14.8178i	1.13759	−	0.656787i	0.191756	−	0.981443i	$-0.438582\pi$
$509$	25.6652	−	14.8178i	1.13759	−	0.656787i	0.945832	+	0.324656i	$0.105249\pi$
$510$	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
$520$		0			0
$521$	−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
$533$		0			0
$534$	−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	$-0.928284\pi$
$541$		−	10.3923i		−	0.446800i	0.974727	−	0.223400i	$-0.0717156\pi$
$542$	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
$546$		0			0
$547$			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	0.970442	−	0.241334i	$-0.0775848\pi$
$557$	6.51903	+	11.2913i	0.276220	+	0.478427i	−0.694222	+	0.719761i	$0.744251\pi$
$558$		−	42.3303i		−	1.79198i
$559$		0			0
$560$	−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	$0.291796\pi$
$572$		0			0
$573$			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	$-0.546065\pi$
$577$	−6.92820			−0.288425			−0.144212	+	0.989547i	$0.546065\pi$
$578$	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
$585$		0			0
$586$	51.2867			2.11864
$587$	−9.35548	−	16.2042i	−0.386142	−	0.668818i	0.605785	−	0.795628i	$-0.292859\pi$
$587$	−9.35548	−	16.2042i	−0.386142	−	0.668818i	−0.991927	+	0.126811i	$0.959526\pi$
$588$	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	$-0.356893\pi$
$593$	21.1660			0.869184			0.434592	+	0.900627i	$0.356893\pi$
$594$	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
$598$		0			0
$599$	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
$611$		0			0
$612$			25.5826i			1.03411i
$613$	−10.8968	−	18.8739i	−0.440119	−	0.762308i	0.557579	−	0.830124i	$-0.311730\pi$
$613$	−10.8968	−	18.8739i	−0.440119	−	0.762308i	−0.997698	+	0.0678157i	$0.978397\pi$
$614$	−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	−0.897937	−	0.440124i	$-0.854935\pi$
$617$	−1.68438	+	2.91742i	−0.0678104	+	0.117451i	0.830127	+	0.557575i	$0.188268\pi$
$618$	−16.5975	+	28.7477i	−0.667650	+	1.15640i
$619$			2.01810i			0.0811143i	0.999177	+	0.0405572i	$0.0129133\pi$
$619$			2.01810i			0.0811143i	−0.999177	+	0.0405572i	$0.987087\pi$
$620$	−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
$624$		0			0
$625$	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	0.826184	−	0.563401i	$-0.190507\pi$
$631$	18.8739	+	10.8968i	0.751357	+	0.433796i	−0.0748272	+	0.997197i	$0.523841\pi$
$632$	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
$637$		0			0
$638$		−	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	−0.918464	−	0.395505i	$-0.870570\pi$
$643$	−2.95958	+	5.12614i	−0.116714	+	0.202155i	0.801749	+	0.597660i	$0.203903\pi$
$644$	−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
$650$		0			0
$651$	−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	−0.540778	−	0.841165i	$-0.681870\pi$
$661$	−2.12614	+	1.22753i	−0.0826971	+	0.0477452i	0.458081	+	0.888910i	$0.348537\pi$
$662$			24.9564i			0.969960i
$663$		0			0
$664$	−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
$676$		0			0
$677$		−	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	−0.728994	−	0.684520i	$-0.760012\pi$
$683$	5.96683	−	10.3348i	0.228314	−	0.395452i	0.957309	+	0.289068i	$0.0933453\pi$
$684$		−	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
$689$		0			0
$690$	4.58258	+	21.9564i	0.174456	+	0.835867i
$691$	−30.8739	+	17.8250i	−1.17450	+	0.678096i	−0.954735	−	0.297457i	$-0.903861\pi$
$691$	−30.8739	+	17.8250i	−1.17450	+	0.678096i	−0.219762	+	0.975554i	$0.570528\pi$
$692$	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	$0.517049\pi$
$702$		0			0
$703$		−	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	−0.226299	−	0.974058i	$-0.572663\pi$
$709$	−31.5000	−	18.1865i	−1.18301	−	0.683010i	−0.956708	+	0.291048i	$0.905996\pi$
$710$	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
$715$		0			0
$716$	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	$-0.291332\pi$
$728$		0			0
$729$	−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	$-0.552833\pi$
$733$	−8.94630			−0.330439			−0.165220	+	0.986257i	$0.552833\pi$
$734$	−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	$-0.312218\pi$
$739$	42.2477	−	24.3917i	1.55411	−	0.897265i	0.997801	−	0.0662878i	$-0.0211156\pi$
$740$	10.1216	+	48.4955i	0.372077	+	1.78273i
$741$		0			0
$742$			6.00000i			0.220267i
$743$	21.3845	+	37.0390i	0.784521	+	1.35883i	0.929285	+	0.369364i	$0.120424\pi$
$743$	21.3845	+	37.0390i	0.784521	+	1.35883i	−0.144764	+	0.989466i	$0.546242\pi$
$744$	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
$754$		0			0
$755$	−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	0.976721	−	0.214513i	$-0.0688164\pi$
$761$	35.2913	+	20.3754i	1.27931	+	0.738609i	0.302587	+	0.953122i	$0.402150\pi$
$762$	−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
$767$		0			0
$768$			2.79129i			0.100722i
$769$	13.5000	−	7.79423i	0.486822	−	0.281067i	−0.236433	−	0.971648i	$-0.575978\pi$
$769$	13.5000	−	7.79423i	0.486822	−	0.281067i	0.723255	+	0.690581i	$0.242645\pi$
$770$	−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	$0.381441\pi$
$773$	−17.3682	+	30.0826i	−0.624690	+	1.08200i	−0.988601	+	0.150561i	$0.951892\pi$
$774$	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
$780$		0			0
$781$	−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	$-0.638859\pi$
$787$	16.0930	−	27.8739i	0.573653	−	0.993596i	0.996187	−	0.0872487i	$-0.0278075\pi$
$788$	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
$793$		0			0
$794$	−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
$806$		0			0
$807$		−	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	$-0.893123\pi$
$811$		−	18.7665i		−	0.658981i	0.944159	−	0.329491i	$-0.106877\pi$
$812$	−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
$819$		0			0
$820$	−16.1652	+	3.37386i	−0.564512	+	0.117820i
$821$	−20.2913	+	11.7152i	−0.708171	+	0.408863i	−0.810383	−	0.585900i	$-0.800741\pi$
$821$	−20.2913	+	11.7152i	−0.708171	+	0.408863i	0.102213	+	0.994763i	$0.467408\pi$
$822$	−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	$-0.684875\pi$
$827$	−31.5583			−1.09739			−0.548695	+	0.836023i	$0.684875\pi$
$828$	−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
$832$		0			0
$833$		−	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	0.479673	−	0.877447i	$-0.340755\pi$
$839$	−1.16970	−	0.675325i	−0.0403824	−	0.0233148i	−0.520055	+	0.854133i	$0.674089\pi$
$840$	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
$845$		0			0
$846$	−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	$-0.865258\pi$
$853$	−53.2566			−1.82347			−0.911736	+	0.410777i	$0.865258\pi$
$854$	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	$0.872985\pi$
$858$		0			0
$859$	−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	$-0.298006\pi$
$863$	34.8317			1.18569			0.592843	+	0.805318i	$0.298006\pi$
$864$	−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
$871$		0			0
$872$			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	−0.791208	−	0.611547i	$-0.790548\pi$
$877$	3.96863	−	6.87386i	0.134011	−	0.232114i	0.925219	+	0.379433i	$0.123881\pi$
$878$	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	$0.716182\pi$
$884$		0			0
$885$	−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
$897$		0			0
$898$			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
$910$		0			0
$911$	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
$923$		0			0
$924$	−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	0.709416	−	0.704790i	$-0.248959\pi$
$929$	13.8303	+	7.98493i	0.453758	+	0.261977i	−0.255658	+	0.966767i	$0.582292\pi$
$930$	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
$936$		0			0
$937$		−	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	$0.141926\pi$
$941$			26.4575i			0.862490i	−0.902235	+	0.431245i	$0.858074\pi$
$942$	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	$-0.951002\pi$
$947$	−19.2909	−	33.4129i	−0.626871	−	1.08577i	0.361305	−	0.932448i	$-0.382331\pi$
$948$		−	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
$962$		0			0
$963$		−	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	$-0.612399\pi$
$967$	−21.5076			−0.691638			−0.345819	+	0.938301i	$0.612399\pi$
$968$	−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
$975$		0			0
$976$	18.9564			0.606781
$977$	19.3863	+	33.5780i	0.620222	+	1.07426i	0.989444	+	0.144915i	$0.0462909\pi$
$977$	19.3863	+	33.5780i	0.620222	+	1.07426i	−0.369222	+	0.929341i	$0.620376\pi$
$978$	−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	$-0.515857\pi$
$983$	−3.12250			−0.0995924			−0.0497962	+	0.998759i	$0.515857\pi$
$984$	−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
$988$		0			0
$989$	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	845.2.l.c.699.1		8
5.4	even	2	inner	845.2.l.c.699.4		8
13.2	odd	12		845.2.b.f.339.1		8
13.3	even	3		845.2.d.c.844.7		8
13.4	even	6	inner	845.2.l.c.654.4		8
13.5	odd	4		845.2.n.c.484.1		8
13.6	odd	12		845.2.n.d.529.4		8
13.7	odd	12		845.2.n.c.529.2		8
13.8	odd	4		845.2.n.d.484.3		8
13.9	even	3		65.2.l.a.4.1	✓	8
13.10	even	6		845.2.d.c.844.1		8
13.11	odd	12		845.2.b.f.339.7		8
13.12	even	2		65.2.l.a.49.4	yes	8
39.35	odd	6		585.2.bf.a.199.4		8
39.38	odd	2		585.2.bf.a.244.1		8
52.35	odd	6		1040.2.df.b.849.2		8
52.51	odd	2		1040.2.df.b.49.3		8
65.2	even	12		4225.2.a.bj.1.4		4
65.4	even	6	inner	845.2.l.c.654.1		8
65.9	even	6		65.2.l.a.4.4	yes	8
65.12	odd	4		325.2.n.b.101.1		4
65.19	odd	12		845.2.n.c.529.1		8
65.22	odd	12		325.2.n.b.251.1		4
65.24	odd	12		845.2.b.f.339.2		8
65.28	even	12		4225.2.a.bk.1.1		4
65.29	even	6		845.2.d.c.844.2		8
65.34	odd	4		845.2.n.c.484.2		8
65.37	even	12		4225.2.a.bj.1.1		4
65.38	odd	4		325.2.n.c.101.2		4
65.44	odd	4		845.2.n.d.484.4		8
65.48	odd	12		325.2.n.c.251.2		4
65.49	even	6		845.2.d.c.844.8		8
65.54	odd	12		845.2.b.f.339.8		8
65.59	odd	12		845.2.n.d.529.3		8
65.63	even	12		4225.2.a.bk.1.4		4
65.64	even	2		65.2.l.a.49.1	yes	8
195.74	odd	6		585.2.bf.a.199.1		8
195.194	odd	2		585.2.bf.a.244.4		8
260.139	odd	6		1040.2.df.b.849.3		8
260.259	odd	2		1040.2.df.b.49.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.l.a.4.1	✓	8	13.9	even	3
65.2.l.a.4.4	yes	8	65.9	even	6
65.2.l.a.49.1	yes	8	65.64	even	2
65.2.l.a.49.4	yes	8	13.12	even	2
325.2.n.b.101.1		4	65.12	odd	4
325.2.n.b.251.1		4	65.22	odd	12
325.2.n.c.101.2		4	65.38	odd	4
325.2.n.c.251.2		4	65.48	odd	12
585.2.bf.a.199.1		8	195.74	odd	6
585.2.bf.a.199.4		8	39.35	odd	6
585.2.bf.a.244.1		8	39.38	odd	2
585.2.bf.a.244.4		8	195.194	odd	2
845.2.b.f.339.1		8	13.2	odd	12
845.2.b.f.339.2		8	65.24	odd	12
845.2.b.f.339.7		8	13.11	odd	12
845.2.b.f.339.8		8	65.54	odd	12
845.2.d.c.844.1		8	13.10	even	6
845.2.d.c.844.2		8	65.29	even	6
845.2.d.c.844.7		8	13.3	even	3
845.2.d.c.844.8		8	65.49	even	6
845.2.l.c.654.1		8	65.4	even	6	inner
845.2.l.c.654.4		8	13.4	even	6	inner
845.2.l.c.699.1		8	1.1	even	1	trivial
845.2.l.c.699.4		8	5.4	even	2	inner
845.2.n.c.484.1		8	13.5	odd	4
845.2.n.c.484.2		8	65.34	odd	4
845.2.n.c.529.1		8	65.19	odd	12
845.2.n.c.529.2		8	13.7	odd	12
845.2.n.d.484.3		8	13.8	odd	4
845.2.n.d.484.4		8	65.44	odd	4
845.2.n.d.529.3		8	65.59	odd	12
845.2.n.d.529.4		8	13.6	odd	12
1040.2.df.b.49.2		8	260.259	odd	2
1040.2.df.b.49.3		8	52.51	odd	2
1040.2.df.b.849.2		8	52.35	odd	6
1040.2.df.b.849.3		8	260.139	odd	6
4225.2.a.bj.1.1		4	65.37	even	12
4225.2.a.bj.1.4		4	65.2	even	12
4225.2.a.bk.1.1		4	65.28	even	12
4225.2.a.bk.1.4		4	65.63	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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.l (of order \(6\), degree \(2\), not 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} +3.79129 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} -5.00000i 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} +(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} +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} -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} +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} +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	\( 8 q - 2 q^{4} + 6 q^{6} - 8 q^{9} - 4 q^{10} + 12 q^{14} + 6 q^{15} - 2 q^{16} + 12 q^{19} - 24 q^{20} - 12 q^{24} - 10 q^{30} + 6 q^{35} - 4 q^{36} - 12 q^{40} - 12 q^{45} - 42 q^{46} + 16 q^{49} + 12 q^{50} - 30 q^{54} - 14 q^{55} - 12 q^{56} + 60 q^{59} + 24 q^{61} - 64 q^{64} - 28 q^{66} - 12 q^{71} - 42 q^{74} - 8 q^{75} - 6 q^{76} + 48 q^{79} - 18 q^{80} - 4 q^{81} + 6 q^{84} - 42 q^{85} - 48 q^{89} + 16 q^{90} + 40 q^{94} - 6 q^{95}+O(q^{100}) \) 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 - 10 * q^30 + 6 * q^35 - 4 * q^36 - 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 - 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 + 40 * q^94 - 6 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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