LMFDB - Embedded newform 845.2.n.d.529.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(484,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.484"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,6,0,2,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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			529.4
Root			$1.09445 + 0.895644i$ of defining polynomial
Character	$\chi$	$=$	845.529
Dual form			845.2.n.d.484.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.89564 + 1.09445i) q^{2} +(0.866025 + 0.500000i) q^{3} +(1.39564 + 2.41733i) q^{4} +(2.18890 - 0.456850i) q^{5} +(1.09445 + 1.89564i) q^{6} +(1.50000 - 0.866025i) q^{7} +1.73205i q^{8} +(-1.00000 - 1.73205i) q^{9} +(4.64938 + 1.52962i) q^{10} +(-1.32288 + 2.29129i) q^{11} +2.79129i q^{12} +3.79129 q^{14} +(2.12407 + 0.698807i) q^{15} +(0.895644 - 1.55130i) q^{16} +(-3.96863 + 2.29129i) q^{17} -4.37780i q^{18} +(0.866025 + 1.50000i) q^{19} +(4.15928 + 4.65369i) q^{20} +1.73205 q^{21} +(-5.01540 + 2.89564i) q^{22} +(3.96863 + 2.29129i) q^{23} +(-0.866025 + 1.50000i) q^{24} +(4.58258 - 2.00000i) q^{25} -5.00000i q^{27} +(4.18693 + 2.41733i) q^{28} +(-2.29129 + 3.96863i) q^{29} +(3.26167 + 3.64938i) q^{30} -9.66930 q^{31} +(6.39564 - 3.69253i) q^{32} +(-2.29129 + 1.32288i) q^{33} -10.0308 q^{34} +(2.88771 - 2.58092i) q^{35} +(2.79129 - 4.83465i) q^{36} +(-6.87386 - 3.96863i) q^{37} +3.79129i q^{38} +(0.791288 + 3.79129i) q^{40} +(-1.32288 + 2.29129i) q^{41} +(3.28335 + 1.89564i) q^{42} +(1.22753 - 0.708712i) q^{43} -7.38505 q^{44} +(-2.98019 - 3.33444i) q^{45} +(5.01540 + 8.68693i) q^{46} -8.75560i q^{47} +(1.55130 - 0.895644i) q^{48} +(-2.00000 + 3.46410i) q^{49} +(10.8758 + 1.22411i) q^{50} -4.58258 q^{51} +1.58258i q^{53} +(5.47225 - 9.47822i) q^{54} +(-1.84887 + 5.61976i) q^{55} +(1.50000 + 2.59808i) q^{56} +1.73205i q^{57} +(-8.68693 + 5.01540i) q^{58} +(-1.68438 - 2.91742i) q^{59} +(1.27520 + 6.10985i) q^{60} +(5.29129 + 9.16478i) q^{61} +(-18.3296 - 10.5826i) q^{62} +(-3.00000 - 1.73205i) q^{63} +12.5826 q^{64} -5.79129 q^{66} +(-12.8739 - 7.43273i) q^{67} +(-11.0776 - 6.39564i) q^{68} +(2.29129 + 3.96863i) q^{69} +(8.29875 - 1.73205i) q^{70} +(1.77973 + 3.08258i) q^{71} +(3.00000 - 1.73205i) q^{72} +(-8.68693 - 15.0462i) q^{74} +(4.96863 + 0.559237i) q^{75} +(-2.41733 + 4.18693i) q^{76} +4.58258i q^{77} +6.00000 q^{79} +(1.25176 - 3.80482i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.01540 + 2.89564i) q^{82} +11.3060i q^{83} +(2.41733 + 4.18693i) q^{84} +(-7.64016 + 6.82847i) q^{85} +3.10260 q^{86} +(-3.96863 + 2.29129i) q^{87} +(-3.96863 - 2.29129i) q^{88} +(-2.14123 + 3.70871i) q^{89} +(-2.00000 - 9.58258i) q^{90} +12.7913i q^{92} +(-8.37386 - 4.83465i) q^{93} +(9.58258 - 16.5975i) q^{94} +(2.58092 + 2.88771i) q^{95} +7.38505 q^{96} +(3.87386 - 2.23658i) q^{97} +(-7.58258 + 4.37780i) q^{98} +5.29150 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{2} + 2 q^{4} + 12 q^{7} - 8 q^{9} + 4 q^{10} + 12 q^{14} + 6 q^{15} - 2 q^{16} + 18 q^{20} + 6 q^{28} + 10 q^{30} + 42 q^{32} + 6 q^{35} + 4 q^{36} - 12 q^{40} + 12 q^{45} - 16 q^{49} + 42 q^{50}+ \cdots - 24 q^{98}+O(q^{100}) $ 8 * q + 6 * q^2 + 2 * q^4 + 12 * q^7 - 8 * q^9 + 4 * q^10 + 12 * q^14 + 6 * q^15 - 2 * q^16 + 18 * q^20 + 6 * q^28 + 10 * q^30 + 42 * q^32 + 6 * q^35 + 4 * q^36 - 12 * q^40 + 12 * q^45 - 16 * q^49 + 42 * q^50 - 14 * q^55 + 12 * q^56 - 42 * q^58 + 24 * q^61 - 24 * q^63 + 64 * q^64 - 28 * q^66 - 48 * q^67 + 24 * q^72 - 42 * q^74 + 8 * q^75 + 48 * q^79 - 24 * q^80 - 4 * q^81 - 42 * q^85 - 16 * q^90 - 12 * q^93 + 40 * q^94 + 6 * q^95 - 24 * q^97 - 24 * q^98

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	1.89564	+	1.09445i	1.34042	+	0.773893i	0.986869	−	0.161521i	$-0.0516399\pi$
$2$	1.89564	+	1.09445i	1.34042	+	0.773893i	0.353553	+	0.935414i	$0.384973\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i	0.728714	−	0.684819i	$-0.240119\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i	−0.228714	+	0.973494i	$0.573452\pi$
$4$	1.39564	+	2.41733i	0.697822	+	1.20866i
$5$	2.18890	−	0.456850i	0.978906	−	0.204310i
$5$	2.18890	−	0.456850i	0.978906	−	0.204310i
$6$	1.09445	+	1.89564i	0.446808	+	0.773893i
$7$	1.50000	−	0.866025i	0.566947	−	0.327327i	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	1.50000	−	0.866025i	0.566947	−	0.327327i	0.755929	+	0.654654i	$0.227186\pi$
$8$			1.73205i			0.612372i
$9$	−1.00000	−	1.73205i	−0.333333	−	0.577350i
$10$	4.64938	+	1.52962i	1.47026	+	0.483708i
$11$	−1.32288	+	2.29129i	−0.398862	+	0.690849i	−0.993586	−	0.113081i	$-0.963928\pi$
$11$	−1.32288	+	2.29129i	−0.398862	+	0.690849i	0.594724	+	0.803930i	$0.297261\pi$
$12$			2.79129i			0.805775i
$13$		0			0
$13$		0			0
$14$	3.79129			1.01326
$15$	2.12407	+	0.698807i	0.548432	+	0.180431i
$16$	0.895644	−	1.55130i	0.223911	−	0.387825i
$17$	−3.96863	+	2.29129i	−0.962533	+	0.555719i	−0.896952	−	0.442128i	$-0.854224\pi$
$17$	−3.96863	+	2.29129i	−0.962533	+	0.555719i	−0.0655816	+	0.997847i	$0.520890\pi$
$18$		−	4.37780i		−	1.03186i
$19$	0.866025	+	1.50000i	0.198680	+	0.344124i	0.948101	−	0.317970i	$-0.103001\pi$
$19$	0.866025	+	1.50000i	0.198680	+	0.344124i	−0.749421	+	0.662094i	$0.769668\pi$
$20$	4.15928	+	4.65369i	0.930044	+	1.04060i
$21$	1.73205			0.377964
$22$	−5.01540	+	2.89564i	−1.06929	+	0.617353i
$23$	3.96863	+	2.29129i	0.827516	+	0.477767i	0.853001	−	0.521909i	$-0.174780\pi$
$23$	3.96863	+	2.29129i	0.827516	+	0.477767i	−0.0254855	+	0.999675i	$0.508113\pi$
$24$	−0.866025	+	1.50000i	−0.176777	+	0.306186i
$25$	4.58258	−	2.00000i	0.916515	−	0.400000i
$26$		0			0
$27$		−	5.00000i		−	0.962250i
$28$	4.18693	+	2.41733i	0.791256	+	0.456832i
$29$	−2.29129	+	3.96863i	−0.425481	+	0.736956i	−0.996465	−	0.0840058i	$-0.973229\pi$
$29$	−2.29129	+	3.96863i	−0.425481	+	0.736956i	0.570984	+	0.820961i	$0.306562\pi$
$30$	3.26167	+	3.64938i	0.595497	+	0.666282i
$31$	−9.66930			−1.73666			−0.868329	−	0.495988i	$-0.834806\pi$
$31$	−9.66930			−1.73666			−0.868329	+	0.495988i	$0.834806\pi$
$32$	6.39564	−	3.69253i	1.13060	−	0.652753i
$33$	−2.29129	+	1.32288i	−0.398862	+	0.230283i
$34$	−10.0308			−1.72027
$35$	2.88771	−	2.58092i	0.488112	−	0.436255i
$36$	2.79129	−	4.83465i	0.465215	−	0.805775i
$37$	−6.87386	−	3.96863i	−1.13006	−	0.652438i	−0.186107	−	0.982529i	$-0.559587\pi$
$37$	−6.87386	−	3.96863i	−1.13006	−	0.652438i	−0.943949	+	0.330091i	$0.892920\pi$
$38$			3.79129i			0.615028i
$39$		0			0
$40$	0.791288	+	3.79129i	0.125114	+	0.599455i
$41$	−1.32288	+	2.29129i	−0.206598	+	0.357839i	−0.950641	−	0.310293i	$-0.899573\pi$
$41$	−1.32288	+	2.29129i	−0.206598	+	0.357839i	0.744042	+	0.668132i	$0.232906\pi$
$42$	3.28335	+	1.89564i	0.506632	+	0.292504i
$43$	1.22753	−	0.708712i	0.187196	−	0.108078i	−0.403473	−	0.914991i	$-0.632197\pi$
$43$	1.22753	−	0.708712i	0.187196	−	0.108078i	0.590669	+	0.806914i	$0.298864\pi$
$44$	−7.38505			−1.11334
$45$	−2.98019	−	3.33444i	−0.444260	−	0.497069i
$46$	5.01540	+	8.68693i	0.739481	+	1.28082i
$47$		−	8.75560i		−	1.27714i	−0.769565	−	0.638568i	$-0.779527\pi$
$47$		−	8.75560i		−	1.27714i	0.769565	−	0.638568i	$-0.220473\pi$
$48$	1.55130	−	0.895644i	0.223911	−	0.129275i
$49$	−2.00000	+	3.46410i	−0.285714	+	0.494872i
$50$	10.8758	+	1.22411i	1.53808	+	0.173116i
$51$	−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	$0.965334\pi$
$54$	5.47225	−	9.47822i	0.744679	−	1.28982i
$55$	−1.84887	+	5.61976i	−0.249301	+	0.757768i
$56$	1.50000	+	2.59808i	0.200446	+	0.347183i
$57$			1.73205i			0.229416i
$58$	−8.68693	+	5.01540i	−1.14065	+	0.658555i
$59$	−1.68438	−	2.91742i	−0.219287	−	0.379816i	0.735303	−	0.677738i	$-0.237040\pi$
$59$	−1.68438	−	2.91742i	−0.219287	−	0.379816i	−0.954590	+	0.297922i	$0.903706\pi$
$60$	1.27520	+	6.10985i	0.164628	+	0.788779i
$61$	5.29129	+	9.16478i	0.677480	+	1.17343i	0.975737	+	0.218944i	$0.0702613\pi$
$61$	5.29129	+	9.16478i	0.677480	+	1.17343i	−0.298257	+	0.954485i	$0.596405\pi$
$62$	−18.3296	−	10.5826i	−2.32786	−	1.34399i
$63$	−3.00000	−	1.73205i	−0.377964	−	0.218218i
$64$	12.5826			1.57282
$65$		0			0
$66$	−5.79129			−0.712858
$67$	−12.8739	−	7.43273i	−1.57279	−	0.908052i	−0.995825	−	0.0912856i	$-0.970902\pi$
$67$	−12.8739	−	7.43273i	−1.57279	−	0.908052i	−0.576968	−	0.816767i	$-0.695764\pi$
$68$	−11.0776	−	6.39564i	−1.34335	−	0.775586i
$69$	2.29129	+	3.96863i	0.275839	+	0.477767i
$70$	8.29875	−	1.73205i	0.991891	−	0.207020i
$71$	1.77973	+	3.08258i	0.211215	+	0.365834i	0.952095	−	0.305803i	$-0.0989248\pi$
$71$	1.77973	+	3.08258i	0.211215	+	0.365834i	−0.740880	+	0.671637i	$0.765591\pi$
$72$	3.00000	−	1.73205i	0.353553	−	0.204124i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	−8.68693	−	15.0462i	−1.00984	−	1.74909i
$75$	4.96863	+	0.559237i	0.573728	+	0.0645751i
$76$	−2.41733	+	4.18693i	−0.277286	+	0.480274i
$77$			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	$0.390410\pi$
$80$	1.25176	−	3.80482i	0.139951	−	0.425392i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−5.01540	+	2.89564i	−0.553859	+	0.319770i
$83$			11.3060i			1.24100i	0.784208	+	0.620498i	$0.213069\pi$
$83$			11.3060i			1.24100i	−0.784208	+	0.620498i	$0.786931\pi$
$84$	2.41733	+	4.18693i	0.263752	+	0.456832i
$85$	−7.64016	+	6.82847i	−0.828691	+	0.740652i
$86$	3.10260			0.334562
$87$	−3.96863	+	2.29129i	−0.425481	+	0.245652i
$88$	−3.96863	−	2.29129i	−0.423057	−	0.244252i
$89$	−2.14123	+	3.70871i	−0.226969	+	0.393123i	−0.956909	−	0.290390i	$-0.906215\pi$
$89$	−2.14123	+	3.70871i	−0.226969	+	0.393123i	0.729939	+	0.683512i	$0.239548\pi$
$90$	−2.00000	−	9.58258i	−0.210819	−	1.01009i
$91$		0			0
$92$			12.7913i			1.33358i
$93$	−8.37386	−	4.83465i	−0.868329	−	0.501330i
$94$	9.58258	−	16.5975i	0.988367	−	1.71190i
$95$	2.58092	+	2.88771i	0.264797	+	0.296273i
$96$	7.38505			0.753734
$97$	3.87386	−	2.23658i	0.393331	−	0.227090i	−0.290271	−	0.956944i	$-0.593746\pi$
$97$	3.87386	−	2.23658i	0.393331	−	0.227090i	0.683603	+	0.729854i	$0.260412\pi$
$98$	−7.58258	+	4.37780i	−0.765956	+	0.442225i
$99$	5.29150			0.531816
$100$	11.2303	+	8.28629i	1.12303	+	0.828629i
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$	−8.68693	−	5.01540i	−0.860134	−	0.496599i
$103$		−	15.1652i		−	1.49427i	−0.664674	−	0.747133i	$-0.731430\pi$
$103$		−	15.1652i		−	1.49427i	0.664674	−	0.747133i	$-0.268570\pi$
$104$		0			0
$105$	3.79129	−	0.791288i	0.369992	−	0.0772218i
$106$	−1.73205	+	3.00000i	−0.168232	+	0.291386i
$107$	1.22753	+	0.708712i	0.118669	+	0.0685138i	0.558160	−	0.829733i	$-0.311508\pi$
$107$	1.22753	+	0.708712i	0.118669	+	0.0685138i	−0.439490	+	0.898247i	$0.644841\pi$
$108$	12.0866	−	6.97822i	1.16304	−	0.671479i
$109$	2.74110			0.262550			0.131275	−	0.991346i	$-0.458093\pi$
$109$	2.74110			0.262550			0.131275	+	0.991346i	$0.458093\pi$
$110$	−9.65534	+	8.62957i	−0.920601	+	0.822797i
$111$	−3.96863	−	6.87386i	−0.376685	−	0.652438i
$112$		−	3.10260i		−	0.293168i
$113$	14.3609	−	8.29129i	1.35096	−	0.779979i	0.362578	−	0.931953i	$-0.381897\pi$
$113$	14.3609	−	8.29129i	1.35096	−	0.779979i	0.988384	+	0.151975i	$0.0485632\pi$
$114$	−1.89564	+	3.28335i	−0.177543	+	0.307514i
$115$	9.73371	+	3.20233i	0.907673	+	0.298619i
$116$	−12.7913			−1.18764
$117$		0			0
$118$		−	7.37386i		−	0.678819i
$119$	−3.96863	+	6.87386i	−0.363803	+	0.630126i
$120$	−1.21037	+	3.67900i	−0.110491	+	0.335845i
$121$	2.00000	+	3.46410i	0.181818	+	0.314918i
$122$			23.1642i			2.09719i
$123$	−2.29129	+	1.32288i	−0.206598	+	0.119280i
$124$	−13.4949	−	23.3739i	−1.21188	−	2.09903i
$125$	9.11710	−	6.47135i	0.815459	−	0.578815i
$126$	−3.79129	−	6.56670i	−0.337755	−	0.585008i
$127$	−8.44178	−	4.87386i	−0.749087	−	0.432485i	0.0762771	−	0.997087i	$-0.475697\pi$
$127$	−8.44178	−	4.87386i	−0.749087	−	0.432485i	−0.825364	+	0.564601i	$0.809030\pi$
$128$	11.0608	+	6.38595i	0.977645	+	0.564444i
$129$	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	$0.477976\pi$
$132$	−6.39564	−	3.69253i	−0.556669	−	0.321393i
$133$	2.59808	+	1.50000i	0.225282	+	0.130066i
$134$	−16.2695	−	28.1796i	−1.40547	−	2.43435i
$135$	−2.28425	−	10.9445i	−0.196597	−	0.941953i
$136$	−3.96863	−	6.87386i	−0.340307	−	0.589429i
$137$	0.0825757	−	0.0476751i	0.00705492	−	0.00407316i	−0.496468	−	0.868055i	$-0.665370\pi$
$137$	0.0825757	−	0.0476751i	0.00705492	−	0.00407316i	0.503523	+	0.863982i	$0.332037\pi$
$138$			10.0308i			0.853879i
$139$	2.87386	+	4.97768i	0.243758	+	0.422201i	0.961782	−	0.273817i	$-0.0882864\pi$
$139$	2.87386	+	4.97768i	0.243758	+	0.422201i	−0.718024	+	0.696019i	$0.754953\pi$
$140$	10.2691	+	3.37849i	0.867900	+	0.285534i
$141$	4.37780	−	7.58258i	0.368677	−	0.638568i
$142$			7.79129i			0.653830i
$143$		0			0
$144$	−3.58258			−0.298548
$145$	−3.20233	+	9.73371i	−0.265939	+	0.808340i
$146$		0			0
$147$	−3.46410	+	2.00000i	−0.285714	+	0.164957i
$148$		−	22.1552i		−	1.82114i
$149$	−4.88233	−	8.45644i	−0.399976	−	0.692778i	0.593747	−	0.804652i	$-0.297648\pi$
$149$	−4.88233	−	8.45644i	−0.399976	−	0.692778i	−0.993722	+	0.111874i	$0.964315\pi$
$150$	8.80669	+	6.49803i	0.719063	+	0.530562i
$151$	−6.20520			−0.504972			−0.252486	−	0.967601i	$-0.581248\pi$
$151$	−6.20520			−0.504972			−0.252486	+	0.967601i	$0.581248\pi$
$152$	−2.59808	+	1.50000i	−0.210732	+	0.121666i
$153$	7.93725	+	4.58258i	0.641689	+	0.370479i
$154$	−5.01540	+	8.68693i	−0.404153	+	0.700013i
$155$	−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	$-0.119180\pi$
$158$	11.3739	+	6.56670i	0.904856	+	0.522419i
$159$	−0.791288	+	1.37055i	−0.0627532	+	0.108692i
$160$	12.3125	−	11.0044i	0.973389	−	0.869976i
$161$	7.93725			0.625543
$162$	−1.89564	+	1.09445i	−0.148936	+	0.0859882i
$163$	9.24773	−	5.33918i	0.724338	−	0.418197i	−0.0920093	−	0.995758i	$-0.529329\pi$
$163$	9.24773	−	5.33918i	0.724338	−	0.418197i	0.816347	+	0.577561i	$0.195996\pi$
$164$	−7.38505			−0.576676
$165$	−4.41105	+	3.94242i	−0.343399	+	0.306917i
$166$	−12.3739	+	21.4322i	−0.960398	+	1.66346i
$167$	−3.70871	−	2.14123i	−0.286989	−	0.165693i	0.349594	−	0.936901i	$-0.386319\pi$
$167$	−3.70871	−	2.14123i	−0.286989	−	0.165693i	−0.636583	+	0.771208i	$0.719653\pi$
$168$			3.00000i			0.231455i
$169$		0			0
$170$	−21.9564	+	4.58258i	−1.68398	+	0.351468i
$171$	1.73205	−	3.00000i	0.132453	−	0.229416i
$172$	3.42638	+	1.97822i	0.261259	+	0.150838i
$173$	−6.42368	+	3.70871i	−0.488383	+	0.281968i	−0.723903	−	0.689901i	$-0.757654\pi$
$173$	−6.42368	+	3.70871i	−0.488383	+	0.281968i	0.235520	+	0.971869i	$0.424321\pi$
$174$	−10.0308			−0.760433
$175$	5.14181	−	6.96863i	0.388685	−	0.526779i
$176$	2.36965	+	4.10436i	0.178619	+	0.309377i
$177$		−	3.36875i		−	0.253211i
$178$	−8.11800	+	4.68693i	−0.608470	+	0.351300i
$179$	0.0825757	−	0.143025i	0.00617200	−	0.0106902i	−0.862923	−	0.505336i	$-0.831369\pi$
$179$	0.0825757	−	0.143025i	0.00617200	−	0.0106902i	0.869095	+	0.494645i	$0.164702\pi$
$180$	3.90114	−	11.8578i	0.290774	−	0.883826i
$181$	18.7477			1.39351			0.696754	−	0.717310i	$-0.254627\pi$
$181$	18.7477			1.39351			0.696754	+	0.717310i	$0.254627\pi$
$182$		0			0
$183$			10.5826i			0.782287i
$184$	−3.96863	+	6.87386i	−0.292571	+	0.506748i
$185$	−16.8593	−	5.54661i	−1.23952	−	0.407795i
$186$	−10.5826	−	18.3296i	−0.775952	−	1.34399i
$187$		−	12.1244i		−	0.886621i
$188$	21.1652	−	12.2197i	1.54363	−	0.891214i
$189$	−4.33013	−	7.50000i	−0.314970	−	0.545545i
$190$	1.73205	+	8.29875i	0.125656	+	0.602055i
$191$	3.70871	+	6.42368i	0.268353	+	0.464801i	0.968437	−	0.249260i	$-0.0801873\pi$
$191$	3.70871	+	6.42368i	0.268353	+	0.464801i	−0.700084	+	0.714061i	$0.746854\pi$
$192$	10.8968	+	6.29129i	0.786411	+	0.454035i
$193$	−0.873864	−	0.504525i	−0.0629021	−	0.0363165i	0.468219	−	0.883612i	$-0.344896\pi$
$193$	−0.873864	−	0.504525i	−0.0629021	−	0.0363165i	−0.531121	+	0.847296i	$0.678229\pi$
$194$	9.79129			0.702973
$195$		0			0
$196$	−11.1652			−0.797511
$197$	17.2913	+	9.98313i	1.23195	+	0.711269i	0.967437	−	0.253113i	$-0.0814543\pi$
$197$	17.2913	+	9.98313i	1.23195	+	0.711269i	0.264516	+	0.964381i	$0.414788\pi$
$198$	10.0308	+	5.79129i	0.712858	+	0.411569i
$199$	−0.708712	−	1.22753i	−0.0502393	−	0.0870170i	0.839812	−	0.542877i	$-0.182665\pi$
$199$	−0.708712	−	1.22753i	−0.0502393	−	0.0870170i	−0.890051	+	0.455860i	$0.849332\pi$
$200$	3.46410	+	7.93725i	0.244949	+	0.561249i
$201$	−7.43273	−	12.8739i	−0.524264	−	0.908052i
$202$	17.0608	−	9.85005i	1.20039	−	0.693047i
$203$			7.93725i			0.557086i
$204$	−6.39564	−	11.0776i	−0.447785	−	0.775586i
$205$	−1.84887	+	5.61976i	−0.129131	+	0.392501i
$206$	16.5975	−	28.7477i	1.15640	−	2.00295i
$207$		−	9.16515i		−	0.637022i
$208$		0			0
$209$	−4.58258			−0.316983
$210$	8.05296	+	2.64938i	0.555707	+	0.182824i
$211$	−9.08258	+	15.7315i	−0.625270	+	1.08300i	0.363218	+	0.931704i	$0.381678\pi$
$211$	−9.08258	+	15.7315i	−0.625270	+	1.08300i	−0.988489	+	0.151296i	$0.951655\pi$
$212$	−3.82560	+	2.20871i	−0.262743	+	0.151695i
$213$			3.55945i			0.243890i
$214$	1.55130	+	2.68693i	0.106045	+	0.183675i
$215$	2.36316	−	2.11210i	0.161166	−	0.144044i
$216$	8.66025			0.589256
$217$	−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
$223$	7.50000	+	4.33013i	0.502237	+	0.289967i	0.729637	−	0.683835i	$-0.239689\pi$
$223$	7.50000	+	4.33013i	0.502237	+	0.289967i	−0.227400	+	0.973801i	$0.573022\pi$
$224$	6.39564	−	11.0776i	0.427327	−	0.740152i
$225$	−8.04668	−	5.93725i	−0.536445	−	0.395817i
$226$	36.2976			2.41448
$227$	5.29129	−	3.05493i	0.351195	−	0.202763i	−0.314016	−	0.949418i	$-0.601675\pi$
$227$	5.29129	−	3.05493i	0.351195	−	0.202763i	0.665212	+	0.746655i	$0.268341\pi$
$228$	−4.18693	+	2.41733i	−0.277286	+	0.160091i
$229$	5.48220			0.362274			0.181137	−	0.983458i	$-0.442022\pi$
$229$	5.48220			0.362274			0.181137	+	0.983458i	$0.442022\pi$
$230$	14.9468	+	16.7235i	0.985566	+	1.10272i
$231$	−2.29129	+	3.96863i	−0.150756	+	0.261116i
$232$	−6.87386	−	3.96863i	−0.451291	−	0.260553i
$233$			21.1652i			1.38658i	0.720661	+	0.693288i	$0.243838\pi$
$233$			21.1652i			1.38658i	−0.720661	+	0.693288i	$0.756162\pi$
$234$		0			0
$235$	−4.00000	−	19.1652i	−0.260931	−	1.25020i
$236$	4.70158	−	8.14337i	0.306047	−	0.530088i
$237$	5.19615	+	3.00000i	0.337526	+	0.194871i
$238$	−15.0462	+	8.68693i	−0.975301	+	0.563090i
$239$	−20.9753			−1.35678			−0.678390	−	0.734702i	$-0.737322\pi$
$239$	−20.9753			−1.35678			−0.678390	+	0.734702i	$0.737322\pi$
$240$	2.98647	−	2.66919i	0.192776	−	0.172295i
$241$	−0.866025	−	1.50000i	−0.0557856	−	0.0966235i	0.836784	−	0.547533i	$-0.184433\pi$
$241$	−0.866025	−	1.50000i	−0.0557856	−	0.0966235i	−0.892570	+	0.450910i	$0.851100\pi$
$242$			8.75560i			0.562832i
$243$	−13.8564	+	8.00000i	−0.888889	+	0.513200i
$244$	−14.7695	+	25.5815i	−0.945521	+	1.63769i
$245$	−2.79523	+	8.49628i	−0.178580	+	0.542807i
$246$	−5.79129			−0.369239
$247$		0			0
$248$		−	16.7477i		−	1.06348i
$249$	−5.65300	+	9.79129i	−0.358244	+	0.620498i
$250$	24.3654	−	2.28916i	1.54100	−	0.144779i
$251$	9.08258	+	15.7315i	0.573287	+	0.992962i	0.996225	+	0.0868039i	$0.0276654\pi$
$251$	9.08258	+	15.7315i	0.573287	+	0.992962i	−0.422938	+	0.906158i	$0.639001\pi$
$252$		−	9.66930i		−	0.609109i
$253$	−10.5000	+	6.06218i	−0.660129	+	0.381126i
$254$	−10.6684	−	18.4782i	−0.669395	−	1.15943i
$255$	−10.0308	+	2.09355i	−0.628153	+	0.131103i
$256$	1.39564	+	2.41733i	0.0872277	+	0.151083i
$257$	0.143025	+	0.0825757i	0.00892167	+	0.00515093i	0.504454	−	0.863438i	$-0.331694\pi$
$257$	0.143025	+	0.0825757i	0.00892167	+	0.00515093i	−0.495533	+	0.868589i	$0.665027\pi$
$258$	2.68693	+	1.55130i	0.167281	+	0.0965798i
$259$	−13.7477			−0.854242
$260$		0			0
$261$	9.16515			0.567309
$262$	3.00000	+	1.73205i	0.185341	+	0.107006i
$263$	7.79423	+	4.50000i	0.480613	+	0.277482i	0.720672	−	0.693276i	$-0.243833\pi$
$263$	7.79423	+	4.50000i	0.480613	+	0.277482i	−0.240059	+	0.970758i	$0.577167\pi$
$264$	−2.29129	−	3.96863i	−0.141019	−	0.244252i
$265$	0.723000	+	3.46410i	0.0444135	+	0.212798i
$266$	3.28335	+	5.68693i	0.201315	+	0.348688i
$267$	−3.70871	+	2.14123i	−0.226969	+	0.131041i
$268$		−	41.4938i		−	2.53464i
$269$	−7.50000	−	12.9904i	−0.457283	−	0.792038i	0.541533	−	0.840679i	$-0.317844\pi$
$269$	−7.50000	−	12.9904i	−0.457283	−	0.792038i	−0.998816	+	0.0486418i	$0.984511\pi$
$270$	7.64809	−	23.2469i	0.465448	−	1.41476i
$271$	−4.33013	+	7.50000i	−0.263036	+	0.455593i	−0.967047	−	0.254597i	$-0.918057\pi$
$271$	−4.33013	+	7.50000i	−0.263036	+	0.455593i	0.704011	+	0.710189i	$0.251391\pi$
$272$			8.20871i			0.497726i
$273$		0			0
$274$	0.208712			0.0126088
$275$	−1.47960	+	13.1458i	−0.0892234	+	0.792719i
$276$	−6.39564	+	11.0776i	−0.384973	+	0.666792i
$277$	14.3609	−	8.29129i	0.862865	−	0.498175i	−0.00210581	−	0.999998i	$-0.500670\pi$
$277$	14.3609	−	8.29129i	0.862865	−	0.498175i	0.864971	+	0.501823i	$0.167337\pi$
$278$			12.5812i			0.754571i
$279$	9.66930	+	16.7477i	0.578886	+	1.00266i
$280$	4.47028	+	5.00166i	0.267151	+	0.298906i
$281$	17.5112			1.04463			0.522316	−	0.852752i	$-0.325068\pi$
$281$	17.5112			1.04463			0.522316	+	0.852752i	$0.325068\pi$
$282$	16.5975	−	9.58258i	0.988367	−	0.570634i
$283$	0.218475	+	0.126136i	0.0129870	+	0.00749803i	0.506479	−	0.862252i	$-0.330947\pi$
$283$	0.218475	+	0.126136i	0.0129870	+	0.00749803i	−0.493492	+	0.869750i	$0.664280\pi$
$284$	−4.96773	+	8.60436i	−0.294780	+	0.510575i
$285$	0.791288	+	3.79129i	0.0468718	+	0.224577i
$286$		0			0
$287$			4.58258i			0.270501i
$288$	−12.7913	−	7.38505i	−0.753734	−	0.435168i
$289$	2.00000	−	3.46410i	0.117647	−	0.203771i
$290$	−16.7235	+	14.9468i	−0.982040	+	0.877709i
$291$	4.47315			0.262221
$292$		0			0
$293$	20.2913	−	11.7152i	1.18543	−	0.684408i	0.228165	−	0.973622i	$-0.426727\pi$
$293$	20.2913	−	11.7152i	1.18543	−	0.684408i	0.957264	+	0.289214i	$0.0933940\pi$
$294$	−8.75560			−0.510637
$295$	−5.01976	−	5.61645i	−0.292262	−	0.327002i
$296$	6.87386	−	11.9059i	0.399535	−	0.692015i
$297$	11.4564	+	6.61438i	0.664770	+	0.383805i
$298$		−	21.3739i		−	1.23815i
$299$		0			0
$300$	5.58258	+	12.7913i	0.322310	+	0.738505i
$301$	1.22753	−	2.12614i	0.0707534	−	0.122548i
$302$	−11.7629	−	6.79129i	−0.676876	−	0.390795i
$303$	7.79423	−	4.50000i	0.447767	−	0.258518i
$304$	3.10260			0.177946
$305$	15.7690	+	17.6435i	0.902932	+	1.01026i
$306$	10.0308	+	17.3739i	0.573423	+	0.993198i
$307$			24.2487i			1.38395i	0.721923	+	0.691974i	$0.243259\pi$
$307$			24.2487i			1.38395i	−0.721923	+	0.691974i	$0.756741\pi$
$308$	−11.0776	+	6.39564i	−0.631204	+	0.364426i
$309$	7.58258	−	13.1334i	0.431358	−	0.747133i
$310$	−44.9562	−	14.7903i	−2.55334	−	0.840035i
$311$	1.58258			0.0897396			0.0448698	−	0.998993i	$-0.485713\pi$
$311$	1.58258			0.0897396			0.0448698	+	0.998993i	$0.485713\pi$
$312$		0			0
$313$			30.7477i			1.73796i	0.494843	+	0.868982i	$0.335225\pi$
$313$			30.7477i			1.73796i	−0.494843	+	0.868982i	$0.664775\pi$
$314$	10.0308	−	17.3739i	0.566071	−	0.980464i
$315$	−7.35799	−	2.42074i	−0.414576	−	0.136393i
$316$	8.37386	+	14.5040i	0.471067	+	0.815911i
$317$		−	20.9753i		−	1.17809i	−0.808100	−	0.589045i	$-0.799504\pi$
$317$		−	20.9753i		−	1.17809i	0.808100	−	0.589045i	$-0.200496\pi$
$318$	−3.00000	+	1.73205i	−0.168232	+	0.0971286i
$319$	−6.06218	−	10.5000i	−0.339417	−	0.587887i
$320$	27.5420	−	5.74835i	1.53965	−	0.321343i
$321$	0.708712	+	1.22753i	0.0395565	+	0.0685138i
$322$	15.0462	+	8.68693i	0.838492	+	0.484104i
$323$	−6.87386	−	3.96863i	−0.382472	−	0.220820i
$324$	−2.79129			−0.155072
$325$		0			0
$326$	23.3739			1.29456
$327$	2.37386	+	1.37055i	0.131275	+	0.0757916i
$328$	−3.96863	−	2.29129i	−0.219131	−	0.126515i
$329$	−7.58258	−	13.1334i	−0.418041	−	0.724068i
$330$	−12.6766	+	2.64575i	−0.697821	+	0.145644i
$331$	−5.70068	−	9.87386i	−0.313338	−	0.542717i	0.665745	−	0.746179i	$-0.268114\pi$
$331$	−5.70068	−	9.87386i	−0.313338	−	0.542717i	−0.979083	+	0.203463i	$0.934780\pi$
$332$	−27.3303	+	15.7792i	−1.49995	+	0.865994i
$333$			15.8745i			0.869918i
$334$	−4.68693	−	8.11800i	−0.256457	−	0.444197i
$335$	−31.5753	−	10.3881i	−1.72514	−	0.567561i
$336$	1.55130	−	2.68693i	0.0846304	−	0.146584i
$337$		−	3.25227i		−	0.177163i	−0.996069	−	0.0885813i	$-0.971767\pi$
$337$		−	3.25227i		−	0.177163i	0.996069	−	0.0885813i	$-0.0282333\pi$
$338$		0			0
$339$	16.5826			0.900642
$340$	−27.1696	−	8.93864i	−1.47348	−	0.484766i
$341$	12.7913	−	22.1552i	0.692687	−	1.19977i
$342$	6.56670	−	3.79129i	0.355087	−	0.205009i
$343$			19.0526i			1.02874i
$344$	1.22753	+	2.12614i	0.0661837	+	0.114634i
$345$	6.82847	+	7.64016i	0.367633	+	0.411332i
$346$	−16.2360			−0.872853
$347$	13.2764	−	7.66515i	0.712716	−	0.411487i	−0.0993497	−	0.995053i	$-0.531676\pi$
$347$	13.2764	−	7.66515i	0.712716	−	0.411487i	0.812066	+	0.583566i	$0.198343\pi$
$348$	−11.0776	−	6.39564i	−0.593821	−	0.342843i
$349$	−9.16478	+	15.8739i	−0.490579	+	0.849708i	−0.999941	−	0.0108440i	$-0.996548\pi$
$349$	−9.16478	+	15.8739i	−0.490579	+	0.849708i	0.509362	+	0.860552i	$0.329882\pi$
$350$	17.3739	−	7.58258i	0.928672	−	0.405306i
$351$		0			0
$352$			19.5390i			1.04143i
$353$	−15.0826	−	8.70793i	−0.802765	−	0.463476i	0.0416724	−	0.999131i	$-0.486731\pi$
$353$	−15.0826	−	8.70793i	−0.802765	−	0.463476i	−0.844437	+	0.535655i	$0.820065\pi$
$354$	3.68693	−	6.38595i	0.195958	−	0.339410i
$355$	5.30392	+	5.93438i	0.281503	+	0.314964i
$356$	−11.9536			−0.633537
$357$	−6.87386	+	3.96863i	−0.363803	+	0.210042i
$358$	0.313068	−	0.180750i	0.0165462	−	0.00955294i
$359$	−33.3857			−1.76203			−0.881015	−	0.473088i	$-0.843139\pi$
$359$	−33.3857			−1.76203			−0.881015	+	0.473088i	$0.843139\pi$
$360$	5.77542	−	5.16184i	0.304391	−	0.272053i
$361$	8.00000	−	13.8564i	0.421053	−	0.729285i
$362$	35.5390	+	20.5185i	1.86789	+	1.07843i
$363$			4.00000i			0.209946i
$364$		0			0
$365$		0			0
$366$	−11.5821	+	20.0608i	−0.605406	+	1.04859i
$367$	−22.2982	−	12.8739i	−1.16396	−	0.672010i	−0.211707	−	0.977333i	$-0.567902\pi$
$367$	−22.2982	−	12.8739i	−1.16396	−	0.672010i	−0.952249	+	0.305323i	$0.901236\pi$
$368$	7.10895	−	4.10436i	0.370580	−	0.213954i
$369$	5.29150			0.275465
$370$	−25.8887	−	28.9660i	−1.34589	−	1.50587i
$371$	1.37055	+	2.37386i	0.0711554	+	0.123245i
$372$		−	26.9898i		−	1.39936i
$373$	11.2583	−	6.50000i	0.582934	−	0.336557i	−0.179364	−	0.983783i	$-0.557404\pi$
$373$	11.2583	−	6.50000i	0.582934	−	0.336557i	0.762299	+	0.647225i	$0.224071\pi$
$374$	13.2695	−	22.9835i	0.686150	−	1.18845i
$375$	11.1313	−	1.04580i	0.574819	−	0.0540051i
$376$	15.1652			0.782083
$377$		0			0
$378$		−	18.9564i		−	0.975014i
$379$	10.5353	−	18.2477i	0.541164	−	0.937323i	−0.457674	−	0.889120i	$-0.651317\pi$
$379$	10.5353	−	18.2477i	0.541164	−	0.937323i	0.998838	−	0.0482027i	$-0.0153493\pi$
$380$	−3.37849	+	10.2691i	−0.173313	+	0.526796i
$381$	−4.87386	−	8.44178i	−0.249696	−	0.432485i
$382$			16.2360i			0.830706i
$383$	−2.45644	+	1.41823i	−0.125518	+	0.0724680i	−0.561444	−	0.827514i	$-0.689754\pi$
$383$	−2.45644	+	1.41823i	−0.125518	+	0.0724680i	0.435926	+	0.899982i	$0.356421\pi$
$384$	6.38595	+	11.0608i	0.325882	+	0.564444i
$385$	2.09355	+	10.0308i	0.106697	+	0.511217i
$386$	−1.10436	−	1.91280i	−0.0562102	−	0.0973590i
$387$	−2.45505	−	1.41742i	−0.124797	−	0.0720517i
$388$	10.8131	+	6.24293i	0.548950	+	0.316937i
$389$	15.1652			0.768904			0.384452	−	0.923145i	$-0.374390\pi$
$389$	15.1652			0.768904			0.384452	+	0.923145i	$0.374390\pi$
$390$		0			0
$391$	−21.0000			−1.06202
$392$	−6.00000	−	3.46410i	−0.303046	−	0.174964i
$393$	1.37055	+	0.791288i	0.0691351	+	0.0399152i
$394$	21.8521	+	37.8489i	1.10089	+	1.90680i
$395$	13.1334	−	2.74110i	0.660813	−	0.137920i
$396$	7.38505	+	12.7913i	0.371113	+	0.642786i
$397$	−23.6216	+	13.6379i	−1.18553	+	0.684468i	−0.957288	−	0.289135i	$-0.906632\pi$
$397$	−23.6216	+	13.6379i	−1.18553	+	0.684468i	−0.228245	+	0.973604i	$0.573299\pi$
$398$		−	3.10260i		−	0.155519i
$399$	1.50000	+	2.59808i	0.0750939	+	0.130066i
$400$	1.00175	−	8.90024i	0.0500877	−	0.445012i
$401$	−6.25288	+	10.8303i	−0.312254	+	0.540840i	−0.978850	−	0.204580i	$-0.934417\pi$
$401$	−6.25288	+	10.8303i	−0.312254	+	0.540840i	0.666596	+	0.745419i	$0.267751\pi$
$402$		−	32.5390i		−	1.62290i
$403$		0			0
$404$	25.1216			1.24985
$405$	−0.698807	+	2.12407i	−0.0347240	+	0.105546i
$406$	−8.68693	+	15.0462i	−0.431125	+	0.746731i
$407$	18.1865	−	10.5000i	0.901473	−	0.520466i
$408$		−	7.93725i		−	0.392953i
$409$	−4.33013	−	7.50000i	−0.214111	−	0.370851i	0.738886	−	0.673830i	$-0.235352\pi$
$409$	−4.33013	−	7.50000i	−0.214111	−	0.370851i	−0.952997	+	0.302979i	$0.902019\pi$
$410$	−9.65534	+	8.62957i	−0.476843	+	0.426184i
$411$	0.0953502			0.00470328
$412$	36.6591	−	21.1652i	1.80607	−	1.04273i
$413$	−5.05313	−	2.91742i	−0.248648	−	0.143557i
$414$	10.0308	−	17.3739i	0.492987	−	0.853879i
$415$	5.16515	+	24.7477i	0.253547	+	1.21482i
$416$		0			0
$417$			5.74773i			0.281467i
$418$	−8.68693	−	5.01540i	−0.424892	−	0.245311i
$419$	−12.0826	+	20.9276i	−0.590272	+	1.02238i	0.403923	+	0.914793i	$0.367646\pi$
$419$	−12.0826	+	20.9276i	−0.590272	+	1.02238i	−0.994195	+	0.107589i	$0.965687\pi$
$420$	7.20409	+	8.06042i	0.351524	+	0.393308i
$421$	−26.2668			−1.28017			−0.640083	−	0.768306i	$-0.721100\pi$
$421$	−26.2668			−1.28017			−0.640083	+	0.768306i	$0.721100\pi$
$422$	−34.4347	+	19.8809i	−1.67625	+	0.967785i
$423$	−15.1652	+	8.75560i	−0.737355	+	0.425712i
$424$	−2.74110			−0.133120
$425$	−13.6040	+	18.4373i	−0.659889	+	0.894338i
$426$	−3.89564	+	6.74745i	−0.188745	+	0.326915i
$427$	15.8739	+	9.16478i	0.768190	+	0.443515i
$428$			3.95644i			0.191242i
$429$		0			0
$430$	6.79129	−	1.41742i	0.327505	−	0.0683543i
$431$	14.8178	−	25.6652i	0.713747	−	1.23625i	−0.249693	−	0.968325i	$-0.580330\pi$
$431$	14.8178	−	25.6652i	0.713747	−	1.23625i	0.963441	−	0.267922i	$-0.0863369\pi$
$432$	−7.75650	−	4.47822i	−0.373185	−	0.215458i
$433$	−15.3700	+	8.87386i	−0.738634	+	0.426451i	−0.821573	−	0.570104i	$-0.806903\pi$
$433$	−15.3700	+	8.87386i	−0.738634	+	0.426451i	0.0829383	+	0.996555i	$0.473570\pi$
$434$	−36.6591			−1.75969
$435$	−7.64016	+	6.82847i	−0.366317	+	0.327400i
$436$	3.82560	+	6.62614i	0.183213	+	0.317334i
$437$			7.93725i			0.379690i
$438$		0			0
$439$	−20.2477	+	35.0701i	−0.966371	+	1.67380i	−0.260487	+	0.965477i	$0.583883\pi$
$439$	−20.2477	+	35.0701i	−0.966371	+	1.67380i	−0.705885	+	0.708327i	$0.749450\pi$
$440$	−9.73371	−	3.20233i	−0.464036	−	0.152665i
$441$	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	$0.788922\pi$
$444$	11.0776	−	19.1869i	0.525719	−	0.910571i
$445$	−2.99261	+	9.09622i	−0.141863	+	0.431202i
$446$	9.47822	+	16.4168i	0.448807	+	0.777356i
$447$		−	9.76465i		−	0.461852i
$448$	18.8739	−	10.8968i	0.891706	−	0.514827i
$449$	18.7387	+	32.4564i	0.884336	+	1.53171i	0.846473	+	0.532431i	$0.178721\pi$
$449$	18.7387	+	32.4564i	0.884336	+	1.53171i	0.0378622	+	0.999283i	$0.487945\pi$
$450$	−8.75560	−	20.0616i	−0.412743	−	0.945713i
$451$	−3.50000	−	6.06218i	−0.164809	−	0.285457i
$452$	40.0855	+	23.1434i	1.88546	+	1.08857i
$453$	−5.37386	−	3.10260i	−0.252486	−	0.145773i
$454$	13.3739			0.627667
$455$		0			0
$456$	−3.00000			−0.140488
$457$	−1.50000	−	0.866025i	−0.0701670	−	0.0405110i	0.464506	−	0.885570i	$-0.346232\pi$
$457$	−1.50000	−	0.866025i	−0.0701670	−	0.0405110i	−0.534673	+	0.845059i	$0.679565\pi$
$458$	10.3923	+	6.00000i	0.485601	+	0.280362i
$459$	11.4564	+	19.8431i	0.534741	+	0.926198i
$460$	5.84370	+	27.9989i	0.272464	+	1.30545i
$461$	0.599876	+	1.03901i	0.0279390	+	0.0483917i	0.879657	−	0.475609i	$-0.157772\pi$
$461$	0.599876	+	1.03901i	0.0279390	+	0.0483917i	−0.851718	+	0.524001i	$0.824439\pi$
$462$	−8.68693	+	5.01540i	−0.404153	+	0.233338i
$463$		−	8.22330i		−	0.382169i	−0.981574	−	0.191085i	$-0.938799\pi$
$463$		−	8.22330i		−	0.382169i	0.981574	−	0.191085i	$-0.0612005\pi$
$464$	4.10436	+	7.10895i	0.190540	+	0.330025i
$465$	−20.5383	−	6.75697i	−0.952440	−	0.313347i
$466$	−23.1642	+	40.1216i	−1.07306	+	1.85860i
$467$		−	12.3303i		−	0.570578i	−0.958441	−	0.285289i	$-0.907910\pi$
$467$		−	12.3303i		−	0.570578i	0.958441	−	0.285289i	$-0.0920896\pi$
$468$		0			0
$469$	−25.7477			−1.18892
$470$	13.3927	−	40.7081i	0.617761	−	1.87772i
$471$	4.58258	−	7.93725i	0.211154	−	0.365729i
$472$	5.05313	−	2.91742i	0.232589	−	0.134285i
$473$			3.75015i			0.172432i
$474$	6.56670	+	11.3739i	0.301619	+	0.522419i
$475$	6.96863	+	5.14181i	0.319743	+	0.235923i
$476$	−22.1552			−1.01548
$477$	2.74110	−	1.58258i	0.125506	−	0.0724612i
$478$	−39.7617	−	22.9564i	−1.81866	−	1.05000i
$479$	16.1883	−	28.0390i	0.739664	−	1.28114i	−0.212983	−	0.977056i	$-0.568318\pi$
$479$	16.1883	−	28.0390i	0.739664	−	1.28114i	0.952647	−	0.304079i	$-0.0983488\pi$
$480$	16.1652	−	3.37386i	0.737835	−	0.153995i
$481$		0			0
$482$		−	3.79129i		−	0.172688i
$483$	6.87386	+	3.96863i	0.312772	+	0.180579i
$484$	−5.58258	+	9.66930i	−0.253753	+	0.439514i
$485$	7.45772	−	6.66542i	0.338638	−	0.302661i
$486$	−35.0224			−1.58865
$487$	−18.2477	+	10.5353i	−0.826883	+	0.477401i	−0.852784	−	0.522263i	$-0.825088\pi$
$487$	−18.2477	+	10.5353i	−0.826883	+	0.477401i	0.0259009	+	0.999665i	$0.491755\pi$
$488$	−15.8739	+	9.16478i	−0.718576	+	0.414870i
$489$	10.6784			0.482892
$490$	−14.5975	+	13.0467i	−0.659448	+	0.589389i
$491$	14.2913	−	24.7532i	0.644957	−	1.11710i	−0.339355	−	0.940658i	$-0.610209\pi$
$491$	14.2913	−	24.7532i	0.644957	−	1.11710i	0.984311	−	0.176439i	$-0.0564580\pi$
$492$	−6.39564	−	3.69253i	−0.288338	−	0.166472i
$493$		−	21.0000i		−	0.945792i
$494$		0			0
$495$	11.5826	−	2.41742i	0.520598	−	0.108655i
$496$	−8.66025	+	15.0000i	−0.388857	+	0.673520i
$497$	5.33918	+	3.08258i	0.239495	+	0.138272i
$498$	−21.4322	+	12.3739i	−0.960398	+	0.554486i
$499$	16.5975			0.743006			0.371503	−	0.928432i	$-0.378842\pi$
$499$	16.5975			0.743006			0.371503	+	0.928432i	$0.378842\pi$
$500$	28.3676	+	13.0073i	1.26864	+	0.581705i
$501$	−2.14123	−	3.70871i	−0.0956629	−	0.165693i
$502$			39.7617i			1.77465i
$503$	15.7315	−	9.08258i	0.701432	−	0.404972i	−0.106448	−	0.994318i	$-0.533948\pi$
$503$	15.7315	−	9.08258i	0.701432	−	0.404972i	0.807881	+	0.589346i	$0.200615\pi$
$504$	3.00000	−	5.19615i	0.133631	−	0.231455i
$505$	6.28926	−	19.1166i	0.279868	−	0.850678i
$506$	−26.5390			−1.17980
$507$		0			0
$508$		−	27.2087i		−	1.20719i
$509$	−14.8178	+	25.6652i	−0.656787	+	1.13759i	0.324656	+	0.945832i	$0.394751\pi$
$509$	−14.8178	+	25.6652i	−0.656787	+	1.13759i	−0.981443	+	0.191756i	$0.938582\pi$
$510$	−21.3061	−	7.00959i	−0.943451	−	0.310390i
$511$		0			0
$512$		−	19.4340i		−	0.858868i
$513$	7.50000	−	4.33013i	0.331133	−	0.191180i
$514$	0.180750	+	0.313068i	0.00797254	+	0.0138088i
$515$	−6.92820	−	33.1950i	−0.305293	−	1.46275i
$516$	1.97822	+	3.42638i	0.0870863	+	0.150838i
$517$	20.0616	+	11.5826i	0.882309	+	0.509401i
$518$	−26.0608	−	15.0462i	−1.14505	−	0.661092i
$519$	−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	$0.705748\pi$
$522$	17.3739	+	10.0308i	0.760433	+	0.439036i
$523$	−15.7315	−	9.08258i	−0.687890	−	0.397153i	0.114931	−	0.993373i	$-0.463335\pi$
$523$	−15.7315	−	9.08258i	−0.687890	−	0.397153i	−0.802821	+	0.596220i	$0.796669\pi$
$524$	2.20871	+	3.82560i	0.0964880	+	0.167122i
$525$	7.93725	−	3.46410i	0.346410	−	0.151186i
$526$	9.85005	+	17.0608i	0.429483	+	0.743886i
$527$	38.3739	−	22.1552i	1.67159	−	0.965094i
$528$			4.73930i			0.206252i
$529$	−1.00000	−	1.73205i	−0.0434783	−	0.0753066i
$530$	−2.42074	+	7.35799i	−0.105150	+	0.319611i
$531$	−3.36875	+	5.83485i	−0.146191	+	0.253211i
$532$			8.37386i			0.363053i
$533$		0			0
$534$	−9.37386			−0.405647
$535$	3.01071	+	0.990505i	0.130164	+	0.0428233i
$536$	12.8739	−	22.2982i	0.556066	−	0.963135i
$537$	0.143025	−	0.0825757i	0.00617200	−	0.00356340i
$538$		−	32.8335i		−	1.41555i
$539$	−5.29150	−	9.16515i	−0.227921	−	0.394771i
$540$	23.2684	−	20.7964i	1.00131	−	0.894935i
$541$	10.3923			0.446800			0.223400	−	0.974727i	$-0.428284\pi$
$541$	10.3923			0.446800			0.223400	+	0.974727i	$0.428284\pi$
$542$	−16.4168	+	9.47822i	−0.705160	+	0.407124i
$543$	16.2360	+	9.37386i	0.696754	+	0.402271i
$544$	−16.9213	+	29.3085i	−0.725494	+	1.25659i
$545$	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	$0.991477\pi$
$548$	0.230493	+	0.133075i	0.00984615	+	0.00568468i
$549$	10.5826	−	18.3296i	0.451653	−	0.782287i
$550$	−17.1922	+	23.3003i	−0.733077	+	0.993529i
$551$	−7.93725			−0.338138
$552$	−6.87386	+	3.96863i	−0.292571	+	0.168916i
$553$	9.00000	−	5.19615i	0.382719	−	0.220963i
$554$	36.2976			1.54214
$555$	−11.8273	−	13.2331i	−0.502039	−	0.561715i
$556$	−8.02178	+	13.8941i	−0.340199	+	0.589242i
$557$	11.2913	+	6.51903i	0.478427	+	0.276220i	0.719761	−	0.694222i	$-0.244251\pi$
$557$	11.2913	+	6.51903i	0.478427	+	0.276220i	−0.241334	+	0.970442i	$0.577585\pi$
$558$			42.3303i			1.79198i
$559$		0			0
$560$	−1.41742	−	6.79129i	−0.0598971	−	0.286984i
$561$	6.06218	−	10.5000i	0.255945	−	0.443310i
$562$	33.1950	+	19.1652i	1.40025	+	0.808433i
$563$	−7.79423	+	4.50000i	−0.328488	+	0.189652i	−0.655169	−	0.755482i	$-0.727403\pi$
$563$	−7.79423	+	4.50000i	−0.328488	+	0.189652i	0.326682	+	0.945134i	$0.394069\pi$
$564$	24.4394			1.02908
$565$	27.6468	−	24.7096i	1.16311	−	1.03954i
$566$	0.276100	+	0.478220i	0.0116054	+	0.0201011i
$567$			1.73205i			0.0727393i
$568$	−5.33918	+	3.08258i	−0.224027	+	0.129342i
$569$	9.87386	−	17.1020i	0.413934	−	0.716955i	−0.581382	−	0.813631i	$-0.697488\pi$
$569$	9.87386	−	17.1020i	0.413934	−	0.716955i	0.995316	+	0.0966762i	$0.0308211\pi$
$570$	−2.64938	+	8.05296i	−0.110970	+	0.337301i
$571$	−29.0780			−1.21688			−0.608439	−	0.793601i	$-0.708204\pi$
$571$	−29.0780			−1.21688			−0.608439	+	0.793601i	$0.708204\pi$
$572$		0			0
$573$			7.41742i			0.309867i
$574$	−5.01540	+	8.68693i	−0.209339	+	0.362586i
$575$	22.7691	+	2.56275i	0.949537	+	0.106874i
$576$	−12.5826	−	21.7937i	−0.524274	−	0.908069i
$577$			6.92820i			0.288425i	0.989547	+	0.144212i	$0.0460649\pi$
$577$			6.92820i			0.288425i	−0.989547	+	0.144212i	$0.953935\pi$
$578$	7.58258	−	4.37780i	0.315394	−	0.182093i
$579$	−0.504525	−	0.873864i	−0.0209674	−	0.0363165i
$580$	−27.9989	+	5.84370i	−1.16259	+	0.242647i
$581$	9.79129	+	16.9590i	0.406211	+	0.703578i
$582$	8.47950	+	4.89564i	0.351487	+	0.202931i
$583$	−3.62614	−	2.09355i	−0.150179	−	0.0867060i
$584$		0			0
$585$		0			0
$586$	51.2867			2.11864
$587$	16.2042	+	9.35548i	0.668818	+	0.386142i	0.795628	−	0.605785i	$-0.207141\pi$
$587$	16.2042	+	9.35548i	0.668818	+	0.386142i	−0.126811	+	0.991927i	$0.540474\pi$
$588$	−9.66930	−	5.58258i	−0.398755	−	0.230222i
$589$	−8.37386	−	14.5040i	−0.345039	−	0.597625i
$590$	−3.36875	−	16.1407i	−0.138689	−	0.664500i
$591$	9.98313	+	17.2913i	0.410651	+	0.711269i
$592$	−12.3131	+	7.10895i	−0.506064	+	0.292176i
$593$			21.1660i			0.869184i	0.900627	+	0.434592i	$0.143107\pi$
$593$			21.1660i			0.869184i	−0.900627	+	0.434592i	$0.856893\pi$
$594$	14.4782	+	25.0770i	0.594049	+	1.02892i
$595$	−5.54661	+	16.8593i	−0.227389	+	0.691163i
$596$	13.6280	−	23.6044i	0.558224	−	0.966872i
$597$		−	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	$0.201160\pi$
$600$	−0.968627	+	8.60591i	−0.0395440	+	0.351335i
$601$	14.4564	−	25.0393i	0.589690	−	1.02137i	−0.404582	−	0.914502i	$-0.632583\pi$
$601$	14.4564	−	25.0393i	0.589690	−	1.02137i	0.994273	−	0.106872i	$-0.0340836\pi$
$602$	4.65390	−	2.68693i	0.189679	−	0.109511i
$603$			29.7309i			1.21074i
$604$	−8.66025	−	15.0000i	−0.352381	−	0.610341i
$605$	5.96038	+	6.66888i	0.242324	+	0.271128i
$606$	19.7001			0.800262
$607$	−17.1020	+	9.87386i	−0.694150	+	0.400768i	−0.805165	−	0.593051i	$-0.797923\pi$
$607$	−17.1020	+	9.87386i	−0.694150	+	0.400768i	0.111015	+	0.993819i	$0.464590\pi$
$608$	11.0776	+	6.39564i	0.449255	+	0.259378i
$609$	−3.96863	+	6.87386i	−0.160817	+	0.278543i
$610$	10.5826	+	50.7042i	0.428476	+	2.05295i
$611$		0			0
$612$			25.5826i			1.03411i
$613$	18.8739	+	10.8968i	0.762308	+	0.440119i	0.830124	−	0.557579i	$-0.188270\pi$
$613$	18.8739	+	10.8968i	0.762308	+	0.440119i	−0.0678157	+	0.997698i	$0.521603\pi$
$614$	−26.5390	+	45.9669i	−1.07103	+	1.85507i
$615$	−4.41105	+	3.94242i	−0.177871	+	0.158974i
$616$	−7.93725			−0.319801
$617$	−2.91742	+	1.68438i	−0.117451	+	0.0678104i	−0.557575	−	0.830127i	$-0.688268\pi$
$617$	−2.91742	+	1.68438i	−0.117451	+	0.0678104i	0.440124	+	0.897937i	$0.354935\pi$
$618$	28.7477	−	16.5975i	1.15640	−	0.667650i
$619$	−2.01810			−0.0811143			−0.0405572	−	0.999177i	$-0.512913\pi$
$619$	−2.01810			−0.0811143			−0.0405572	+	0.999177i	$0.512913\pi$
$620$	−40.2174	−	44.9979i	−1.61517	−	1.80716i
$621$	11.4564	−	19.8431i	0.459731	−	0.796278i
$622$	3.00000	+	1.73205i	0.120289	+	0.0694489i
$623$			7.41742i			0.297173i
$624$		0			0
$625$	17.0000	−	18.3303i	0.680000	−	0.733212i
$626$	−33.6519	+	58.2867i	−1.34500	+	2.32961i
$627$	−3.96863	−	2.29129i	−0.158492	−	0.0915052i
$628$	22.1552	−	12.7913i	0.884087	−	0.510428i
$629$	36.3731			1.45029
$630$	−11.2988	−	12.6418i	−0.450153	−	0.503662i
$631$	−10.8968	−	18.8739i	−0.433796	−	0.751357i	0.563401	−	0.826184i	$-0.309493\pi$
$631$	−10.8968	−	18.8739i	−0.433796	−	0.751357i	−0.997197	+	0.0748272i	$0.976159\pi$
$632$			10.3923i			0.413384i
$633$	−15.7315	+	9.08258i	−0.625270	+	0.361000i
$634$	22.9564	−	39.7617i	0.911717	−	1.57914i
$635$	−20.7048	−	6.81178i	−0.821647	−	0.270317i
$636$	−4.41742			−0.175162
$637$		0			0
$638$		−	26.5390i		−	1.05069i
$639$	3.55945	−	6.16515i	0.140810	−	0.243890i
$640$	27.1284	+	8.92509i	1.07234	+	0.352795i
$641$	−0.0825757	−	0.143025i	−0.00326154	−	0.00564916i	0.864390	−	0.502822i	$-0.167705\pi$
$641$	−0.0825757	−	0.143025i	−0.00326154	−	0.00564916i	−0.867652	+	0.497173i	$0.834372\pi$
$642$			3.10260i			0.122450i
$643$	−5.12614	+	2.95958i	−0.202155	+	0.116714i	−0.597660	−	0.801749i	$-0.703903\pi$
$643$	−5.12614	+	2.95958i	−0.202155	+	0.116714i	0.395505	+	0.918464i	$0.370570\pi$
$644$	11.0776	+	19.1869i	0.436518	+	0.756071i
$645$	3.10260	−	0.647551i	0.122165	−	0.0254973i
$646$	−8.68693	−	15.0462i	−0.341783	−	0.591985i
$647$	23.3827	+	13.5000i	0.919268	+	0.530740i	0.883402	−	0.468617i	$-0.155247\pi$
$647$	23.3827	+	13.5000i	0.919268	+	0.530740i	0.0358667	+	0.999357i	$0.488581\pi$
$648$	−1.50000	−	0.866025i	−0.0589256	−	0.0340207i
$649$	8.91288			0.349861
$650$		0			0
$651$	−16.7477			−0.656395
$652$	25.8131	+	14.9032i	1.01092	+	0.583654i
$653$	42.2843	+	24.4129i	1.65471	+	0.955350i	0.975096	+	0.221784i	$0.0711880\pi$
$653$	42.2843	+	24.4129i	1.65471	+	0.955350i	0.679619	+	0.733566i	$0.262145\pi$
$654$	3.00000	+	5.19615i	0.117309	+	0.203186i
$655$	3.46410	−	0.723000i	0.135354	−	0.0282500i
$656$	2.36965	+	4.10436i	0.0925193	+	0.160248i
$657$		0			0
$658$		−	33.1950i		−	1.29408i
$659$	−12.2477	−	21.2137i	−0.477104	−	0.826368i	0.522552	−	0.852607i	$-0.324980\pi$
$659$	−12.2477	−	21.2137i	−0.477104	−	0.826368i	−0.999656	+	0.0262396i	$0.991647\pi$
$660$	−15.6864	−	5.16072i	−0.610591	−	0.200881i
$661$	−1.22753	+	2.12614i	−0.0477452	+	0.0826971i	−0.888910	−	0.458081i	$-0.848537\pi$
$661$	−1.22753	+	2.12614i	−0.0477452	+	0.0826971i	0.841165	+	0.540778i	$0.181870\pi$
$662$		−	24.9564i		−	0.969960i
$663$		0			0
$664$	−19.5826			−0.759951
$665$	6.37221	+	2.09642i	0.247104	+	0.0812957i
$666$	−17.3739	+	30.0924i	−0.673224	+	1.16606i
$667$	−18.1865	+	10.5000i	−0.704185	+	0.406562i
$668$		−	11.9536i		−	0.462497i
$669$	4.33013	+	7.50000i	0.167412	+	0.289967i
$670$	−48.4862	−	54.2497i	−1.87319	−	2.09585i
$671$	−27.9989			−1.08088
$672$	11.0776	−	6.39564i	0.427327	−	0.246717i
$673$	5.05313	+	2.91742i	0.194784	+	0.112458i	0.594220	−	0.804302i	$-0.297461\pi$
$673$	5.05313	+	2.91742i	0.194784	+	0.112458i	−0.399436	+	0.916761i	$0.630794\pi$
$674$	3.55945	−	6.16515i	0.137105	−	0.237473i
$675$	−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	$-0.133328\pi$
$678$	31.4347	+	18.1488i	1.20724	+	0.697001i
$679$	3.87386	−	6.70973i	0.148665	−	0.257496i
$680$	−11.8273	−	13.2331i	−0.453555	−	0.507468i
$681$	6.10985			0.234130
$682$	48.4955	−	27.9989i	1.85699	−	1.07213i
$683$	−10.3348	+	5.96683i	−0.395452	+	0.228314i	−0.684520	−	0.728994i	$-0.739988\pi$
$683$	−10.3348	+	5.96683i	−0.395452	+	0.228314i	0.289068	+	0.957309i	$0.406655\pi$
$684$	9.66930			0.369715
$685$	0.158970	−	0.142081i	0.00607392	−	0.00542863i
$686$	−20.8521	+	36.1169i	−0.796136	+	1.37895i
$687$	4.74773	+	2.74110i	0.181137	+	0.104580i
$688$		−	2.53901i		−	0.0967990i
$689$		0			0
$690$	4.58258	+	21.9564i	0.174456	+	0.835867i
$691$	17.8250	−	30.8739i	0.678096	−	1.17450i	−0.297457	−	0.954735i	$-0.596139\pi$
$691$	17.8250	−	30.8739i	0.678096	−	1.17450i	0.975554	−	0.219762i	$-0.0705281\pi$
$692$	−17.9303	−	10.3521i	−0.681609	−	0.393527i
$693$	7.93725	−	4.58258i	0.301511	−	0.174078i
$694$	33.5565			1.27379
$695$	8.56466	+	9.58272i	0.324876	+	0.363493i
$696$	−3.96863	−	6.87386i	−0.150430	−	0.260553i
$697$		−	12.1244i		−	0.459243i
$698$	−34.7463	+	20.0608i	−1.31517	+	0.759312i
$699$	−10.5826	+	18.3296i	−0.400270	+	0.693288i
$700$	24.0216	+	2.70372i	0.907931	+	0.102191i
$701$	2.83485			0.107071			0.0535354	−	0.998566i	$-0.482951\pi$
$701$	2.83485			0.107071			0.0535354	+	0.998566i	$0.482951\pi$
$702$		0			0
$703$		−	13.7477i		−	0.518505i
$704$	−16.6452	+	28.8303i	−0.627339	+	1.08658i
$705$	6.11847	−	18.5975i	0.230435	−	0.700423i
$706$	−19.0608	−	33.0143i	−0.717362	−	1.24251i
$707$		−	15.5885i		−	0.586264i
$708$	8.14337	−	4.70158i	0.306047	−	0.176696i
$709$	18.1865	+	31.5000i	0.683010	+	1.18301i	0.974058	+	0.226299i	$0.0726626\pi$
$709$	18.1865	+	31.5000i	0.683010	+	1.18301i	−0.291048	+	0.956708i	$0.594004\pi$
$710$	3.55945	+	17.0544i	0.133584	+	0.640039i
$711$	−6.00000	−	10.3923i	−0.225018	−	0.389742i
$712$	−6.42368	−	3.70871i	−0.240738	−	0.138990i
$713$	−38.3739	−	22.1552i	−1.43711	−	0.829717i
$714$	−17.3739			−0.650201
$715$		0			0
$716$	0.460985			0.0172278
$717$	−18.1652	−	10.4877i	−0.678390	−	0.391669i
$718$	−63.2874	−	36.5390i	−2.36187	−	1.36362i
$719$	−15.2477	−	26.4098i	−0.568644	−	0.984921i	−0.996700	−	0.0811686i	$-0.974135\pi$
$719$	−15.2477	−	26.4098i	−0.568644	−	0.984921i	0.428056	−	0.903752i	$-0.359199\pi$
$720$	−7.84190	+	1.63670i	−0.292250	+	0.0609962i
$721$	−13.1334	−	22.7477i	−0.489114	−	0.847170i
$722$	30.3303	−	17.5112i	1.12878	−	0.651700i
$723$		−	1.73205i		−	0.0644157i
$724$	26.1652	+	45.3194i	0.972420	+	1.68428i
$725$	−2.56275	+	22.7691i	−0.0951780	+	0.845623i
$726$	−4.37780	+	7.58258i	−0.162475	+	0.281416i
$727$			42.7477i			1.58543i	0.609595	+	0.792713i	$0.291332\pi$
$727$			42.7477i			1.58543i	−0.609595	+	0.792713i	$0.708668\pi$
$728$		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
$733$			8.94630i			0.330439i	0.986257	+	0.165220i	$0.0528333\pi$
$733$			8.94630i			0.330439i	−0.986257	+	0.165220i	$0.947167\pi$
$734$	−28.1796	−	48.8085i	−1.04013	−	1.80156i
$735$	−6.66888	+	5.96038i	−0.245985	+	0.219852i
$736$	33.8426			1.24745
$737$	34.0610	−	19.6652i	1.25465	−	0.724375i
$738$	10.0308	+	5.79129i	0.369239	+	0.213180i
$739$	24.3917	−	42.2477i	0.897265	−	1.55411i	0.0662878	−	0.997801i	$-0.478884\pi$
$739$	24.3917	−	42.2477i	0.897265	−	1.55411i	0.830977	−	0.556307i	$-0.187782\pi$
$740$	−10.1216	−	48.4955i	−0.372077	−	1.78273i
$741$		0			0
$742$			6.00000i			0.220267i
$743$	−37.0390	−	21.3845i	−1.35883	−	0.784521i	−0.369364	−	0.929285i	$-0.620424\pi$
$743$	−37.0390	−	21.3845i	−1.35883	−	0.784521i	−0.989466	+	0.144764i	$0.953758\pi$
$744$	8.37386	−	14.5040i	0.307001	−	0.531741i
$745$	−14.5503	−	16.2798i	−0.533080	−	0.596446i
$746$	28.4557			1.04184
$747$	19.5826	−	11.3060i	0.716489	−	0.413665i
$748$	29.3085	−	16.9213i	1.07163	−	0.618703i
$749$	2.45505			0.0897056
$750$	22.2456	+	10.2002i	0.812294	+	0.372459i
$751$	−7.87386	+	13.6379i	−0.287321	+	0.497655i	−0.973169	−	0.230090i	$-0.926098\pi$
$751$	−7.87386	+	13.6379i	−0.287321	+	0.497655i	0.685848	+	0.727745i	$0.259431\pi$
$752$	−13.5826	−	7.84190i	−0.495306	−	0.285965i
$753$			18.1652i			0.661975i
$754$		0			0
$755$	−13.5826	+	2.83485i	−0.494321	+	0.103171i
$756$	12.0866	−	20.9347i	0.439587	−	0.761386i
$757$	15.3700	+	8.87386i	0.558632	+	0.322526i	0.752596	−	0.658482i	$-0.228801\pi$
$757$	15.3700	+	8.87386i	0.558632	+	0.322526i	−0.193965	+	0.981009i	$0.562135\pi$
$758$	39.9425	−	23.0608i	1.45078	−	0.837606i
$759$	−12.1244			−0.440086
$760$	−5.00166	+	4.47028i	−0.181429	+	0.162154i
$761$	−20.3754	−	35.2913i	−0.738609	−	1.27931i	−0.953122	−	0.302587i	$-0.902150\pi$
$761$	−20.3754	−	35.2913i	−0.738609	−	1.27931i	0.214513	−	0.976721i	$-0.431184\pi$
$762$		−	21.3368i		−	0.772951i
$763$	4.11165	−	2.37386i	0.148852	−	0.0859396i
$764$	−10.3521	+	17.9303i	−0.374525	+	0.648697i
$765$	19.4674	+	6.40467i	0.703846	+	0.231561i
$766$	−6.20871			−0.224330
$767$		0			0
$768$			2.79129i			0.100722i
$769$	−7.79423	+	13.5000i	−0.281067	+	0.486822i	−0.971648	−	0.236433i	$-0.924022\pi$
$769$	−7.79423	+	13.5000i	−0.281067	+	0.486822i	0.690581	+	0.723255i	$0.257355\pi$
$770$	−7.00959	+	21.3061i	−0.252608	+	0.767819i
$771$	0.0825757	+	0.143025i	0.00297389	+	0.00515093i
$772$		−	2.81655i		−	0.101370i
$773$	−30.0826	+	17.3682i	−1.08200	+	0.624690i	−0.931434	−	0.363911i	$-0.881441\pi$
$773$	−30.0826	+	17.3682i	−1.08200	+	0.624690i	−0.150561	+	0.988601i	$0.548108\pi$
$774$	−3.10260	−	5.37386i	−0.111521	−	0.193160i
$775$	−44.3103	+	19.3386i	−1.59167	+	0.694663i
$776$	3.87386	+	6.70973i	0.139064	+	0.240865i
$777$	−11.9059	−	6.87386i	−0.427121	−	0.246598i
$778$	28.7477	+	16.5975i	1.03066	+	0.595049i
$779$	−4.58258			−0.164188
$780$		0			0
$781$	−9.41742			−0.336982
$782$	−39.8085	−	22.9835i	−1.42355	−	0.821887i
$783$	19.8431	+	11.4564i	0.709136	+	0.409420i
$784$	3.58258	+	6.20520i	0.127949	+	0.221614i
$785$	−4.18710	−	20.0616i	−0.149444	−	0.716030i
$786$	1.73205	+	3.00000i	0.0617802	+	0.107006i
$787$	−27.8739	+	16.0930i	−0.993596	+	0.573653i	−0.906347	−	0.422534i	$-0.861141\pi$
$787$	−27.8739	+	16.0930i	−0.993596	+	0.573653i	−0.0872487	+	0.996187i	$0.527807\pi$
$788$			55.7316i			1.98536i
$789$	4.50000	+	7.79423i	0.160204	+	0.277482i
$790$	27.8963	+	9.17771i	0.992504	+	0.326528i
$791$	14.3609	−	24.8739i	0.510616	−	0.884413i
$792$			9.16515i			0.325669i
$793$		0			0
$794$	−59.7042			−2.11882
$795$	−1.10591	+	3.36150i	−0.0392227	+	0.119220i
$796$	1.97822	−	3.42638i	0.0701161	−	0.121445i
$797$	17.3881	−	10.0390i	0.615918	−	0.355600i	−0.159360	−	0.987220i	$-0.550943\pi$
$797$	17.3881	−	10.0390i	0.615918	−	0.355600i	0.775278	+	0.631620i	$0.217610\pi$
$798$			6.56670i			0.232459i
$799$	20.0616	+	34.7477i	0.709729	+	1.22929i
$800$	21.9235	−	29.7126i	0.775112	−	1.05050i
$801$	8.56490			0.302626
$802$	−23.7065	+	13.6869i	−0.837104	+	0.483302i
$803$		0			0
$804$	20.7469	−	35.9347i	0.731686	−	1.26732i
$805$	17.3739	−	3.62614i	0.612348	−	0.127805i
$806$		0			0
$807$		−	15.0000i		−	0.528025i
$808$	13.5000	+	7.79423i	0.474928	+	0.274200i
$809$	18.4129	−	31.8920i	0.647362	−	1.12126i	−0.336388	−	0.941723i	$-0.609205\pi$
$809$	18.4129	−	31.8920i	0.647362	−	1.12126i	0.983750	−	0.179541i	$-0.0574613\pi$
$810$	−3.64938	+	3.26167i	−0.128226	+	0.114603i
$811$	−18.7665			−0.658981			−0.329491	−	0.944159i	$-0.606877\pi$
$811$	−18.7665			−0.658981			−0.329491	+	0.944159i	$0.606877\pi$
$812$	−19.1869	+	11.0776i	−0.673329	+	0.388747i
$813$	−7.50000	+	4.33013i	−0.263036	+	0.151864i
$814$	45.9669			1.61114
$815$	17.8032	−	15.9118i	0.623617	−	0.557365i
$816$	−4.10436	+	7.10895i	−0.143681	+	0.248863i
$817$	2.12614	+	1.22753i	0.0743841	+	0.0429457i
$818$		−	18.9564i		−	0.662796i
$819$		0			0
$820$	−16.1652	+	3.37386i	−0.564512	+	0.117820i
$821$	11.7152	−	20.2913i	0.408863	−	0.708171i	−0.585900	−	0.810383i	$-0.699259\pi$
$821$	11.7152	−	20.2913i	0.408863	−	0.708171i	0.994763	+	0.102213i	$0.0325922\pi$
$822$	0.180750	+	0.104356i	0.00630438	+	0.00363984i
$823$	−35.1455	+	20.2913i	−1.22510	+	0.707310i	−0.966000	−	0.258542i	$-0.916758\pi$
$823$	−35.1455	+	20.2913i	−1.22510	+	0.707310i	−0.259096	+	0.965851i	$0.583425\pi$
$824$	26.2668			0.915048
$825$	−7.85425	+	10.6448i	−0.273450	+	0.370603i
$826$	−6.38595	−	11.0608i	−0.222196	−	0.384854i
$827$		−	31.5583i		−	1.09739i	−0.836023	−	0.548695i	$-0.815125\pi$
$827$		−	31.5583i		−	1.09739i	0.836023	−	0.548695i	$-0.184875\pi$
$828$	22.1552	−	12.7913i	0.769945	−	0.444528i
$829$	−1.66515	+	2.88413i	−0.0578331	+	0.100170i	−0.893492	−	0.449078i	$-0.851752\pi$
$829$	−1.66515	+	2.88413i	−0.0578331	+	0.100170i	0.835659	+	0.549248i	$0.185086\pi$
$830$	−17.2939	+	52.5659i	−0.600279	+	1.82459i
$831$	16.5826			0.575243
$832$		0			0
$833$		−	18.3303i		−	0.635107i
$834$	−6.29060	+	10.8956i	−0.217826	+	0.377285i
$835$	−9.09622	−	2.99261i	−0.314788	−	0.103563i
$836$	−6.39564	−	11.0776i	−0.221198	−	0.383126i
$837$			48.3465i			1.67110i
$838$	−45.8085	+	26.4476i	−1.58243	+	0.913616i
$839$	0.675325	+	1.16970i	0.0233148	+	0.0403824i	0.877447	−	0.479673i	$-0.159245\pi$
$839$	0.675325	+	1.16970i	0.0233148	+	0.0403824i	−0.854133	+	0.520055i	$0.825911\pi$
$840$	1.37055	+	6.56670i	0.0472885	+	0.226573i
$841$	4.00000	+	6.92820i	0.137931	+	0.238904i
$842$	−49.7925	−	28.7477i	−1.71596	−	0.990712i
$843$	15.1652	+	8.75560i	0.522316	+	0.301559i
$844$	−50.7042			−1.74531
$845$		0			0
$846$	−38.3303			−1.31782
$847$	6.00000	+	3.46410i	0.206162	+	0.119028i
$848$	2.45505	+	1.41742i	0.0843068	+	0.0486746i
$849$	0.126136	+	0.218475i	0.00432899	+	0.00749803i
$850$	−45.9669	+	20.0616i	−1.57665	+	0.688108i
$851$	−18.1865	−	31.5000i	−0.623426	−	1.07981i
$852$	−8.60436	+	4.96773i	−0.294780	+	0.170192i
$853$		−	53.2566i		−	1.82347i	−0.410777	−	0.911736i	$-0.634742\pi$
$853$		−	53.2566i		−	1.82347i	0.410777	−	0.911736i	$-0.365258\pi$
$854$	20.0608	+	34.7463i	0.686466	+	1.18899i
$855$	2.42074	−	7.35799i	0.0827875	−	0.251638i
$856$	−1.22753	+	2.12614i	−0.0419560	+	0.0726698i
$857$		−	22.7477i		−	0.777048i	−0.921439	−	0.388524i	$-0.872985\pi$
$857$		−	22.7477i		−	0.777048i	0.921439	−	0.388524i	$-0.127015\pi$
$858$		0			0
$859$	−38.2432			−1.30484			−0.652420	−	0.757857i	$-0.726246\pi$
$859$	−38.2432			−1.30484			−0.652420	+	0.757857i	$0.726246\pi$
$860$	8.40375	+	2.76479i	0.286566	+	0.0942784i
$861$	−2.29129	+	3.96863i	−0.0780869	+	0.135250i
$862$	56.1785	−	32.4347i	1.91345	−	1.10473i
$863$		−	34.8317i		−	1.18569i	−0.805318	−	0.592843i	$-0.798006\pi$
$863$		−	34.8317i		−	1.18569i	0.805318	−	0.592843i	$-0.201994\pi$
$864$	−18.4626	−	31.9782i	−0.628112	−	1.08792i
$865$	−12.3665	+	11.0527i	−0.420473	+	0.375802i
$866$	−38.8480			−1.32011
$867$	3.46410	−	2.00000i	0.117647	−	0.0679236i
$868$	−40.4847	−	23.3739i	−1.37414	−	0.793361i
$869$	−7.93725	+	13.7477i	−0.269253	+	0.466360i
$870$	−21.9564	+	4.58258i	−0.744393	+	0.155364i
$871$		0			0
$872$			4.74773i			0.160778i
$873$	−7.74773	−	4.47315i	−0.262221	−	0.151393i
$874$	−8.68693	+	15.0462i	−0.293840	+	0.508946i
$875$	8.07130	−	17.6027i	0.272860	−	0.595079i
$876$		0			0
$877$	6.87386	−	3.96863i	0.232114	−	0.134011i	−0.379433	−	0.925219i	$-0.623881\pi$
$877$	6.87386	−	3.96863i	0.232114	−	0.134011i	0.611547	+	0.791208i	$0.290548\pi$
$878$	−76.7650	+	44.3203i	−2.59069	+	1.49574i
$879$	23.4304			0.790286
$880$	7.06201	+	7.90145i	0.238060	+	0.266358i
$881$	−9.24773	+	16.0175i	−0.311564	+	0.539644i	−0.978701	−	0.205290i	$-0.934186\pi$
$881$	−9.24773	+	16.0175i	−0.311564	+	0.539644i	0.667137	+	0.744935i	$0.267519\pi$
$882$	15.1652	+	8.75560i	0.510637	+	0.294817i
$883$		−	46.2432i		−	1.55621i	−0.628136	−	0.778103i	$-0.716182\pi$
$883$		−	46.2432i		−	1.55621i	0.628136	−	0.778103i	$-0.283818\pi$
$884$		0			0
$885$	−1.53901	−	7.37386i	−0.0517334	−	0.247870i
$886$	−28.3604	+	49.1216i	−0.952785	+	1.65027i
$887$	0.429076	+	0.247727i	0.0144070	+	0.00831786i	0.507186	−	0.861837i	$-0.330686\pi$
$887$	0.429076	+	0.247727i	0.0144070	+	0.00831786i	−0.492779	+	0.870154i	$0.664019\pi$
$888$	11.9059	−	6.87386i	0.399535	−	0.230672i
$889$	−16.8836			−0.566256
$890$	−15.6283	+	13.9679i	−0.523861	+	0.468206i
$891$	−1.32288	−	2.29129i	−0.0443180	−	0.0767610i
$892$			24.1733i			0.809381i
$893$	13.1334	−	7.58258i	0.439493	−	0.253741i
$894$	10.6869	−	18.5103i	0.357424	−	0.619077i
$895$	0.115409	−	0.350793i	0.00385769	−	0.0117257i
$896$	22.1216			0.739030
$897$		0			0
$898$			82.0345i			2.73753i
$899$	22.1552	−	38.3739i	0.738916	−	1.27984i
$900$	3.12198	−	27.7377i	0.104066	−	0.924591i
$901$	−3.62614	−	6.28065i	−0.120804	−	0.209239i
$902$		−	15.3223i		−	0.510177i
$903$	2.12614	−	1.22753i	0.0707534	−	0.0408495i
$904$	14.3609	+	24.8739i	0.477637	+	0.827292i
$905$	41.0369	−	8.56490i	1.36411	−	0.284707i
$906$	−6.79129	−	11.7629i	−0.225625	−	0.390795i
$907$	−29.2264	−	16.8739i	−0.970446	−	0.560287i	−0.0710740	−	0.997471i	$-0.522643\pi$
$907$	−29.2264	−	16.8739i	−0.970446	−	0.560287i	−0.899372	+	0.437184i	$0.855976\pi$
$908$	14.7695	+	8.52718i	0.490143	+	0.282984i
$909$	−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	$0.283851\pi$
$912$	2.68693	+	1.55130i	0.0889732	+	0.0513687i
$913$	−25.9053	−	14.9564i	−0.857341	−	0.494986i
$914$	−1.89564	−	3.28335i	−0.0627023	−	0.108604i
$915$	4.83465	+	23.1642i	0.159829	+	0.765785i
$916$	7.65120	+	13.2523i	0.252803	+	0.437867i
$917$	2.37386	−	1.37055i	0.0783919	−	0.0452596i
$918$			50.1540i			1.65533i
$919$	17.9174	+	31.0339i	0.591041	+	1.02371i	0.994093	+	0.108536i	$0.0346163\pi$
$919$	17.9174	+	31.0339i	0.591041	+	1.02371i	−0.403051	+	0.915177i	$0.632050\pi$
$920$	−5.54661	+	16.8593i	−0.182866	+	0.555834i
$921$	−12.1244	+	21.0000i	−0.399511	+	0.691974i
$922$			2.62614i			0.0864872i
$923$		0			0
$924$	−12.7913			−0.420802
$925$	−39.4373	−	4.43881i	−1.29669	−	0.145947i
$926$	9.00000	−	15.5885i	0.295758	−	0.512268i
$927$	−26.2668	+	15.1652i	−0.862715	+	0.498089i
$928$			33.8426i			1.11094i
$929$	7.98493	+	13.8303i	0.261977	+	0.453758i	0.966767	−	0.255658i	$-0.0822922\pi$
$929$	7.98493	+	13.8303i	0.261977	+	0.453758i	−0.704790	+	0.709416i	$0.748959\pi$
$930$	−31.5381	−	35.2869i	−1.03417	−	1.15710i
$931$	−6.92820			−0.227063
$932$	−51.1631	+	29.5390i	−1.67590	+	0.967583i
$933$	1.37055	+	0.791288i	0.0448698	+	0.0259056i
$934$	13.4949	−	23.3739i	0.441567	−	0.764816i
$935$	−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	$-0.125378\pi$
$938$	−48.8085	−	28.1796i	−1.59365	−	0.920097i
$939$	−15.3739	+	26.6283i	−0.501707	+	0.868982i
$940$	40.7458	−	36.4170i	1.32898	−	1.18779i
$941$	26.4575			0.862490			0.431245	−	0.902235i	$-0.358074\pi$
$941$	26.4575			0.862490			0.431245	+	0.902235i	$0.358074\pi$
$942$	17.3739	−	10.0308i	0.566071	−	0.326821i
$943$	−10.5000	+	6.06218i	−0.341927	+	0.197412i
$944$	−6.03440			−0.196403
$945$	−12.9046	−	14.4385i	−0.419787	−	0.469686i
$946$	−4.10436	+	7.10895i	−0.133444	+	0.231132i
$947$	−33.4129	−	19.2909i	−1.08577	−	0.626871i	−0.153325	−	0.988176i	$-0.548998\pi$
$947$	−33.4129	−	19.2909i	−1.08577	−	0.626871i	−0.932448	+	0.361305i	$0.882331\pi$
$948$			16.7477i			0.543941i
$949$		0			0
$950$	7.58258	+	17.3739i	0.246011	+	0.563683i
$951$	10.4877	−	18.1652i	0.340086	−	0.589045i
$952$	−11.9059	−	6.87386i	−0.385872	−	0.222783i
$953$	48.5650	−	28.0390i	1.57317	−	0.908273i	0.577398	−	0.816463i	$-0.304068\pi$
$953$	48.5650	−	28.0390i	1.57317	−	0.908273i	0.995777	−	0.0918100i	$-0.0292652\pi$
$954$	6.92820			0.224309
$955$	11.0527	+	12.3665i	0.357656	+	0.400170i
$956$	−29.2741	−	50.7042i	−0.946791	−	1.63989i
$957$		−	12.1244i		−	0.391925i
$958$	61.3746	−	35.4347i	1.98292	−	1.14484i
$959$	0.0825757	−	0.143025i	0.00266651	−	0.00461853i
$960$	26.7263	+	8.79279i	0.862586	+	0.283786i
$961$	62.4955			2.01598
$962$		0			0
$963$		−	2.83485i		−	0.0913517i
$964$	2.41733	−	4.18693i	0.0778568	−	0.134852i
$965$	−2.14329	−	0.705131i	−0.0689951	−	0.0226990i
$966$	8.68693	+	15.0462i	0.279497	+	0.484104i
$967$			21.5076i			0.691638i	0.938301	+	0.345819i	$0.112399\pi$
$967$			21.5076i			0.691638i	−0.938301	+	0.345819i	$0.887601\pi$
$968$	−6.00000	+	3.46410i	−0.192847	+	0.111340i
$969$	−3.96863	−	6.87386i	−0.127491	−	0.220820i
$970$	21.4322	−	4.47315i	0.688145	−	0.143624i
$971$	−18.2477	−	31.6060i	−0.585597	−	1.01428i	−0.994801	−	0.101841i	$-0.967527\pi$
$971$	−18.2477	−	31.6060i	−0.585597	−	1.01428i	0.409203	−	0.912443i	$-0.365807\pi$
$972$	−38.6772	−	22.3303i	−1.24057	−	0.716245i
$973$	8.62159	+	4.97768i	0.276396	+	0.159577i
$974$	−46.1216			−1.47783
$975$		0			0
$976$	18.9564			0.606781
$977$	−33.5780	−	19.3863i	−1.07426	−	0.620222i	−0.144915	−	0.989444i	$-0.546291\pi$
$977$	−33.5780	−	19.3863i	−1.07426	−	0.620222i	−0.929341	+	0.369222i	$0.879624\pi$
$978$	20.2424	+	11.6869i	0.647279	+	0.373707i
$979$	−5.66515	−	9.81233i	−0.181059	−	0.313603i
$980$	−24.4394	+	5.10080i	−0.780688	+	0.162939i
$981$	−2.74110	−	4.74773i	−0.0875166	−	0.151583i
$982$	54.1824	−	31.2822i	1.72903	−	0.998256i
$983$		−	3.12250i		−	0.0995924i	−0.998759	−	0.0497962i	$-0.984143\pi$
$983$		−	3.12250i		−	0.0995924i	0.998759	−	0.0497962i	$-0.0158572\pi$
$984$	−2.29129	−	3.96863i	−0.0730436	−	0.126515i
$985$	42.4097	+	13.9526i	1.35129	+	0.444565i
$986$	22.9835	−	39.8085i	0.731943	−	1.26776i
$987$		−	15.1652i		−	0.482712i
$988$		0			0
$989$	6.49545			0.206543
$990$	24.6022	+	8.09398i	0.781909	+	0.257244i
$991$	6.50000	−	11.2583i	0.206479	−	0.357633i	−0.744124	−	0.668042i	$-0.767133\pi$
$991$	6.50000	−	11.2583i	0.206479	−	0.357633i	0.950603	+	0.310409i	$0.100466\pi$
$992$	−61.8414	+	35.7042i	−1.96347	+	1.13361i
$993$		−	11.4014i		−	0.361811i
$994$	6.74745	+	11.6869i	0.214016	+	0.370687i
$995$	−2.11210	−	2.36316i	−0.0669579	−	0.0749171i
$996$	−31.5583			−0.999963
$997$	−15.7315	+	9.08258i	−0.498221	+	0.287648i	−0.727979	−	0.685600i	$-0.759540\pi$
$997$	−15.7315	+	9.08258i	−0.498221	+	0.287648i	0.229758	+	0.973248i	$0.426207\pi$
$998$	31.4630	+	18.1652i	0.995943	+	0.575008i
$999$	−19.8431	+	34.3693i	−0.627809	+	1.08740i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.l.a.4.1	✓	8	13.8	odd	4
65.2.l.a.4.4	yes	8	65.34	odd	4
65.2.l.a.49.1	yes	8	65.54	odd	12
65.2.l.a.49.4	yes	8	13.2	odd	12
325.2.n.b.101.1		4	65.2	even	12
325.2.n.b.251.1		4	65.47	even	4
325.2.n.c.101.2		4	65.28	even	12
325.2.n.c.251.2		4	65.8	even	4
585.2.bf.a.199.1		8	195.164	even	4
585.2.bf.a.199.4		8	39.8	even	4
585.2.bf.a.244.1		8	39.2	even	12
585.2.bf.a.244.4		8	195.119	even	12
845.2.b.f.339.1		8	13.9	even	3
845.2.b.f.339.2		8	65.4	even	6
845.2.b.f.339.7		8	13.4	even	6
845.2.b.f.339.8		8	65.9	even	6
845.2.d.c.844.1		8	13.6	odd	12
845.2.d.c.844.2		8	65.59	odd	12
845.2.d.c.844.7		8	13.7	odd	12
845.2.d.c.844.8		8	65.19	odd	12
845.2.l.c.654.1		8	65.44	odd	4
845.2.l.c.654.4		8	13.5	odd	4
845.2.l.c.699.1		8	13.11	odd	12
845.2.l.c.699.4		8	65.24	odd	12
845.2.n.c.484.1		8	13.3	even	3
845.2.n.c.484.2		8	65.49	even	6
845.2.n.c.529.1		8	5.4	even	2
845.2.n.c.529.2		8	13.12	even	2
845.2.n.d.484.3		8	13.10	even	6	inner
845.2.n.d.484.4		8	65.29	even	6	inner
845.2.n.d.529.3		8	65.64	even	2	inner
845.2.n.d.529.4		8	1.1	even	1	trivial
1040.2.df.b.49.2		8	260.119	even	12
1040.2.df.b.49.3		8	52.15	even	12
1040.2.df.b.849.2		8	52.47	even	4
1040.2.df.b.849.3		8	260.99	even	4
4225.2.a.bj.1.1		4	65.17	odd	12
4225.2.a.bj.1.4		4	65.22	odd	12
4225.2.a.bk.1.1		4	65.48	odd	12
4225.2.a.bk.1.4		4	65.43	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.89564 + 1.09445i) q^{2} +(0.866025 + 0.500000i) q^{3} +(1.39564 + 2.41733i) q^{4} +(2.18890 - 0.456850i) q^{5} +(1.09445 + 1.89564i) q^{6} +(1.50000 - 0.866025i) q^{7} +1.73205i q^{8} +(-1.00000 - 1.73205i) q^{9} +(4.64938 + 1.52962i) q^{10} +(-1.32288 + 2.29129i) q^{11} +2.79129i q^{12} +3.79129 q^{14} +(2.12407 + 0.698807i) q^{15} +(0.895644 - 1.55130i) q^{16} +(-3.96863 + 2.29129i) q^{17} -4.37780i q^{18} +(0.866025 + 1.50000i) q^{19} +(4.15928 + 4.65369i) q^{20} +1.73205 q^{21} +(-5.01540 + 2.89564i) q^{22} +(3.96863 + 2.29129i) q^{23} +(-0.866025 + 1.50000i) q^{24} +(4.58258 - 2.00000i) q^{25} -5.00000i q^{27} +(4.18693 + 2.41733i) q^{28} +(-2.29129 + 3.96863i) q^{29} +(3.26167 + 3.64938i) q^{30} -9.66930 q^{31} +(6.39564 - 3.69253i) q^{32} +(-2.29129 + 1.32288i) q^{33} -10.0308 q^{34} +(2.88771 - 2.58092i) q^{35} +(2.79129 - 4.83465i) q^{36} +(-6.87386 - 3.96863i) q^{37} +3.79129i q^{38} +(0.791288 + 3.79129i) q^{40} +(-1.32288 + 2.29129i) q^{41} +(3.28335 + 1.89564i) q^{42} +(1.22753 - 0.708712i) q^{43} -7.38505 q^{44} +(-2.98019 - 3.33444i) q^{45} +(5.01540 + 8.68693i) q^{46} -8.75560i q^{47} +(1.55130 - 0.895644i) q^{48} +(-2.00000 + 3.46410i) q^{49} +(10.8758 + 1.22411i) q^{50} -4.58258 q^{51} +1.58258i q^{53} +(5.47225 - 9.47822i) q^{54} +(-1.84887 + 5.61976i) q^{55} +(1.50000 + 2.59808i) q^{56} +1.73205i q^{57} +(-8.68693 + 5.01540i) q^{58} +(-1.68438 - 2.91742i) q^{59} +(1.27520 + 6.10985i) q^{60} +(5.29129 + 9.16478i) q^{61} +(-18.3296 - 10.5826i) q^{62} +(-3.00000 - 1.73205i) q^{63} +12.5826 q^{64} -5.79129 q^{66} +(-12.8739 - 7.43273i) q^{67} +(-11.0776 - 6.39564i) q^{68} +(2.29129 + 3.96863i) q^{69} +(8.29875 - 1.73205i) q^{70} +(1.77973 + 3.08258i) q^{71} +(3.00000 - 1.73205i) q^{72} +(-8.68693 - 15.0462i) q^{74} +(4.96863 + 0.559237i) q^{75} +(-2.41733 + 4.18693i) q^{76} +4.58258i q^{77} +6.00000 q^{79} +(1.25176 - 3.80482i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.01540 + 2.89564i) q^{82} +11.3060i q^{83} +(2.41733 + 4.18693i) q^{84} +(-7.64016 + 6.82847i) q^{85} +3.10260 q^{86} +(-3.96863 + 2.29129i) q^{87} +(-3.96863 - 2.29129i) q^{88} +(-2.14123 + 3.70871i) q^{89} +(-2.00000 - 9.58258i) q^{90} +12.7913i q^{92} +(-8.37386 - 4.83465i) q^{93} +(9.58258 - 16.5975i) q^{94} +(2.58092 + 2.88771i) q^{95} +7.38505 q^{96} +(3.87386 - 2.23658i) q^{97} +(-7.58258 + 4.37780i) q^{98} +5.29150 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{2} + 2 q^{4} + 12 q^{7} - 8 q^{9} + 4 q^{10} + 12 q^{14} + 6 q^{15} - 2 q^{16} + 18 q^{20} + 6 q^{28} + 10 q^{30} + 42 q^{32} + 6 q^{35} + 4 q^{36} - 12 q^{40} + 12 q^{45} - 16 q^{49} + 42 q^{50}+ \cdots - 24 q^{98}+O(q^{100}) \) 8 * q + 6 * q^2 + 2 * q^4 + 12 * q^7 - 8 * q^9 + 4 * q^10 + 12 * q^14 + 6 * q^15 - 2 * q^16 + 18 * q^20 + 6 * q^28 + 10 * q^30 + 42 * q^32 + 6 * q^35 + 4 * q^36 - 12 * q^40 + 12 * q^45 - 16 * q^49 + 42 * q^50 - 14 * q^55 + 12 * q^56 - 42 * q^58 + 24 * q^61 - 24 * q^63 + 64 * q^64 - 28 * q^66 - 48 * q^67 + 24 * q^72 - 42 * q^74 + 8 * q^75 + 48 * q^79 - 24 * q^80 - 4 * q^81 - 42 * q^85 - 16 * q^90 - 12 * q^93 + 40 * q^94 + 6 * q^95 - 24 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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