LMFDB - Embedded newform 845.2.n.c.484.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(484,845)]

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, 2]))

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

//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: 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			484.1
Root			$-1.09445 + 0.895644i$ of defining polynomial
Character	$\chi$	$=$	845.484
Dual form			845.2.n.c.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.89564 + 1.09445i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(1.39564 - 2.41733i) q^{4} +(2.18890 - 0.456850i) q^{5} +(1.09445 - 1.89564i) q^{6} +(-1.50000 - 0.866025i) q^{7} +1.73205i q^{8} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(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} +(-3.64938 + 3.26167i) q^{10} +(-1.32288 - 2.29129i) q^{11} +2.79129i q^{12} +3.79129 q^{14} +(-1.66722 + 1.49009i) q^{15} +(0.895644 + 1.55130i) q^{16} +(3.96863 + 2.29129i) q^{17} -4.37780i q^{18} +(0.866025 - 1.50000i) q^{19} +(1.95057 - 5.92889i) 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} +(1.52962 - 4.64938i) q^{30} -9.66930 q^{31} +(-6.39564 - 3.69253i) q^{32} +(2.29129 + 1.32288i) q^{33} -10.0308 q^{34} +(-3.67900 - 1.21037i) 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} +(-1.39761 + 4.24814i) q^{45} +(5.01540 - 8.68693i) q^{46} -8.75560i q^{47} +(-1.55130 - 0.895644i) q^{48} +(-2.00000 - 3.46410i) q^{49} +(-6.49803 + 8.80669i) q^{50} -4.58258 q^{51} +1.58258i q^{53} +(5.47225 + 9.47822i) q^{54} +(-3.94242 - 4.41105i) 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} +(-2.96863 + 4.02334i) q^{75} +(-2.41733 - 4.18693i) q^{76} +4.58258i q^{77} +6.00000 q^{79} +(2.66919 + 2.98647i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.01540 + 2.89564i) q^{82} +11.3060i q^{83} +(2.41733 - 4.18693i) q^{84} +(9.73371 + 3.20233i) 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} +(1.21037 - 3.67900i) 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}+O(q^{10}) $ 8 * q - 6 * q^2 + 2 * q^4 - 12 * q^7 - 8 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	$-0.948360\pi$
$2$	−1.89564	+	1.09445i	−1.34042	+	0.773893i	−0.353553	+	0.935414i	$0.615027\pi$
$3$	−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
$5$	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	$-0.439481\pi$
$7$	−1.50000	−	0.866025i	−0.566947	−	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$8$			1.73205i			0.612372i
$9$	−1.00000	+	1.73205i	−0.333333	+	0.577350i
$10$	−3.64938	+	3.26167i	−1.15403	+	1.03143i
$11$	−1.32288	−	2.29129i	−0.398862	−	0.690849i	0.594724	−	0.803930i	$-0.297261\pi$
$11$	−1.32288	−	2.29129i	−0.398862	−	0.690849i	−0.993586	+	0.113081i	$0.963928\pi$
$12$			2.79129i			0.805775i
$13$		0			0
$13$		0			0
$14$	3.79129			1.01326
$15$	−1.66722	+	1.49009i	−0.430474	+	0.384741i
$16$	0.895644	+	1.55130i	0.223911	+	0.387825i
$17$	3.96863	+	2.29129i	0.962533	+	0.555719i	0.896952	−	0.442128i	$-0.145776\pi$
$17$	3.96863	+	2.29129i	0.962533	+	0.555719i	0.0655816	+	0.997847i	$0.479110\pi$
$18$		−	4.37780i		−	1.03186i
$19$	0.866025	−	1.50000i	0.198680	−	0.344124i	−0.749421	−	0.662094i	$-0.769668\pi$
$19$	0.866025	−	1.50000i	0.198680	−	0.344124i	0.948101	+	0.317970i	$0.103001\pi$
$20$	1.95057	−	5.92889i	0.436161	−	1.32574i
$21$	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	$-0.825220\pi$
$23$	−3.96863	+	2.29129i	−0.827516	+	0.477767i	0.0254855	+	0.999675i	$0.491887\pi$
$24$	−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	0.570984	−	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
$31$	−9.66930			−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
$35$	−3.67900	−	1.21037i	−0.621864	−	0.204590i
$36$	2.79129	+	4.83465i	0.465215	+	0.805775i
$37$	6.87386	−	3.96863i	1.13006	−	0.652438i	0.186107	−	0.982529i	$-0.440413\pi$
$37$	6.87386	−	3.96863i	1.13006	−	0.652438i	0.943949	+	0.330091i	$0.107080\pi$
$38$			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	0.744042	−	0.668132i	$-0.232906\pi$
$41$	−1.32288	−	2.29129i	−0.206598	−	0.357839i	−0.950641	+	0.310293i	$0.899573\pi$
$42$	−3.28335	+	1.89564i	−0.506632	+	0.292504i
$43$	−1.22753	−	0.708712i	−0.187196	−	0.108078i	0.403473	−	0.914991i	$-0.367803\pi$
$43$	−1.22753	−	0.708712i	−0.187196	−	0.108078i	−0.590669	+	0.806914i	$0.701136\pi$
$44$	−7.38505			−1.11334
$45$	−1.39761	+	4.24814i	−0.208344	+	0.633275i
$46$	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
$50$	−6.49803	+	8.80669i	−0.918960	+	1.24545i
$51$	−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
$55$	−3.94242	−	4.41105i	−0.531596	−	0.594785i
$56$	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	−0.954590	−	0.297922i	$-0.903706\pi$
$59$	−1.68438	+	2.91742i	−0.219287	+	0.379816i	0.735303	+	0.677738i	$0.237040\pi$
$60$	1.27520	+	6.10985i	0.164628	+	0.788779i
$61$	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
$63$	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	0.576968	−	0.816767i	$-0.304236\pi$
$67$	12.8739	−	7.43273i	1.57279	−	0.908052i	0.995825	−	0.0912856i	$-0.0290976\pi$
$68$	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	−0.740880	−	0.671637i	$-0.765591\pi$
$71$	1.77973	−	3.08258i	0.211215	−	0.365834i	0.952095	+	0.305803i	$0.0989248\pi$
$72$	−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
$75$	−2.96863	+	4.02334i	−0.342788	+	0.464575i
$76$	−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	$0.390410\pi$
$80$	2.66919	+	2.98647i	0.298424	+	0.333897i
$81$	−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
$85$	9.73371	+	3.20233i	1.05577	+	0.347342i
$86$	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	0.729939	−	0.683512i	$-0.239548\pi$
$89$	−2.14123	−	3.70871i	−0.226969	−	0.393123i	−0.956909	+	0.290390i	$0.906215\pi$
$90$	−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
$95$	1.21037	−	3.67900i	0.124181	−	0.377457i
$96$	7.38505			0.753734
$97$	−3.87386	−	2.23658i	−0.393331	−	0.227090i	0.290271	−	0.956944i	$-0.406254\pi$
$97$	−3.87386	−	2.23658i	−0.393331	−	0.227090i	−0.683603	+	0.729854i	$0.739588\pi$
$98$	7.58258	+	4.37780i	0.765956	+	0.442225i
$99$	5.29150			0.531816
$100$	1.56099	−	13.8689i	0.156099	−	1.38689i
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	0.998240	−	0.0592978i	$-0.0188862\pi$
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	−0.550474	+	0.834853i	$0.685553\pi$
$102$	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	$-0.688492\pi$
$107$	−1.22753	+	0.708712i	−0.118669	+	0.0685138i	0.439490	+	0.898247i	$0.355159\pi$
$108$	−12.0866	−	6.97822i	−1.16304	−	0.671479i
$109$	2.74110			0.262550			0.131275	−	0.991346i	$-0.458093\pi$
$109$	2.74110			0.262550			0.131275	+	0.991346i	$0.458093\pi$
$110$	12.3011	+	4.04699i	1.17286	+	0.385865i
$111$	−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	$-0.618103\pi$
$113$	−14.3609	−	8.29129i	−1.35096	−	0.779979i	−0.988384	+	0.151975i	$0.951437\pi$
$114$	−1.89564	−	3.28335i	−0.177543	−	0.307514i
$115$	−7.64016	+	6.82847i	−0.712448	+	0.636758i
$116$	−12.7913			−1.18764
$117$		0			0
$118$		−	7.37386i		−	0.678819i
$119$	−3.96863	−	6.87386i	−0.363803	−	0.630126i
$120$	−2.58092	−	2.88771i	−0.235605	−	0.263610i
$121$	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	$-0.524303\pi$
$127$	8.44178	−	4.87386i	0.749087	−	0.432485i	0.825364	+	0.564601i	$0.190970\pi$
$128$	−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	$-0.334630\pi$
$137$	−0.0825757	−	0.0476751i	−0.00705492	−	0.00407316i	−0.503523	+	0.863982i	$0.667963\pi$
$138$			10.0308i			0.853879i
$139$	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
$141$	4.37780	+	7.58258i	0.368677	+	0.638568i
$142$			7.79129i			0.653830i
$143$		0			0
$144$	−3.58258			−0.298548
$145$	−6.82847	−	7.64016i	−0.567074	−	0.634480i
$146$		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	−0.993722	−	0.111874i	$-0.964315\pi$
$149$	−4.88233	+	8.45644i	−0.399976	+	0.692778i	0.593747	+	0.804652i	$0.297648\pi$
$150$	1.22411	−	10.8758i	0.0999485	−	0.888008i
$151$	−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
$160$	−15.6864	−	5.16072i	−1.24012	−	0.407991i
$161$	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	$-0.470671\pi$
$163$	−9.24773	−	5.33918i	−0.724338	−	0.418197i	−0.816347	+	0.577561i	$0.804004\pi$
$164$	−7.38505			−0.576676
$165$	5.61976	+	1.84887i	0.437498	+	0.143934i
$166$	−12.3739	−	21.4322i	−0.960398	−	1.66346i
$167$	3.70871	−	2.14123i	0.286989	−	0.165693i	−0.349594	−	0.936901i	$-0.613681\pi$
$167$	3.70871	−	2.14123i	0.286989	−	0.165693i	0.636583	+	0.771208i	$0.280347\pi$
$168$			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	$-0.242346\pi$
$173$	6.42368	+	3.70871i	0.488383	+	0.281968i	−0.235520	+	0.971869i	$0.575679\pi$
$174$	−10.0308			−0.760433
$175$	−8.60591	−	0.968627i	−0.650546	−	0.0732213i
$176$	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	0.869095	−	0.494645i	$-0.164702\pi$
$179$	0.0825757	+	0.143025i	0.00617200	+	0.0106902i	−0.862923	+	0.505336i	$0.831369\pi$
$180$	8.31857	+	9.30738i	0.620029	+	0.693731i
$181$	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
$185$	13.2331	−	11.8273i	0.972920	−	0.869557i
$186$	−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	−0.700084	−	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
$193$	0.873864	−	0.504525i	0.0629021	−	0.0363165i	−0.468219	−	0.883612i	$-0.655104\pi$
$193$	0.873864	−	0.504525i	0.0629021	−	0.0363165i	0.531121	+	0.847296i	$0.321771\pi$
$194$	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	$-0.918546\pi$
$197$	−17.2913	+	9.98313i	−1.23195	+	0.711269i	−0.264516	+	0.964381i	$0.585212\pi$
$198$	−10.0308	+	5.79129i	−0.712858	+	0.411569i
$199$	−0.708712	+	1.22753i	−0.0502393	+	0.0870170i	−0.890051	−	0.455860i	$-0.849332\pi$
$199$	−0.708712	+	1.22753i	−0.0502393	+	0.0870170i	0.839812	+	0.542877i	$0.182665\pi$
$200$	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
$205$	−3.94242	−	4.41105i	−0.275351	−	0.308081i
$206$	16.5975	+	28.7477i	1.15640	+	2.00295i
$207$		−	9.16515i		−	0.637022i
$208$		0			0
$209$	−4.58258			−0.316983
$210$	−6.32091	+	5.64938i	−0.436184	+	0.389844i
$211$	−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
$213$			3.55945i			0.243890i
$214$	1.55130	−	2.68693i	0.106045	−	0.183675i
$215$	−3.01071	−	0.990505i	−0.205329	−	0.0675519i
$216$	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	$-0.760311\pi$
$223$	−7.50000	+	4.33013i	−0.502237	+	0.289967i	0.227400	+	0.973801i	$0.426978\pi$
$224$	6.39564	+	11.0776i	0.427327	+	0.740152i
$225$	−1.11847	+	9.93725i	−0.0745649	+	0.662484i
$226$	36.2976			2.41448
$227$	−5.29129	−	3.05493i	−0.351195	−	0.202763i	0.314016	−	0.949418i	$-0.398325\pi$
$227$	−5.29129	−	3.05493i	−0.351195	−	0.202763i	−0.665212	+	0.746655i	$0.731659\pi$
$228$	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	$0.442022\pi$
$230$	7.00959	−	21.3061i	0.462199	−	1.40488i
$231$	−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	$0.737322\pi$
$240$	−3.80482	−	1.25176i	−0.245600	−	0.0808010i
$241$	−0.866025	+	1.50000i	−0.0557856	+	0.0966235i	−0.892570	−	0.450910i	$-0.851100\pi$
$241$	−0.866025	+	1.50000i	−0.0557856	+	0.0966235i	0.836784	+	0.547533i	$0.184433\pi$
$242$			8.75560i			0.562832i
$243$	13.8564	+	8.00000i	0.888889	+	0.513200i
$244$	−14.7695	−	25.5815i	−0.945521	−	1.63769i
$245$	−5.96038	−	6.66888i	−0.380795	−	0.426059i
$246$	−5.79129			−0.369239
$247$		0			0
$248$		−	16.7477i		−	1.06348i
$249$	−5.65300	−	9.79129i	−0.358244	−	0.620498i
$250$	−10.2002	+	22.2456i	−0.645118	+	1.40694i
$251$	9.08258	−	15.7315i	0.573287	−	0.992962i	−0.422938	−	0.906158i	$-0.639001\pi$
$251$	9.08258	−	15.7315i	0.573287	−	0.992962i	0.996225	−	0.0868039i	$-0.0276654\pi$
$252$		−	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	$-0.668306\pi$
$257$	−0.143025	+	0.0825757i	−0.00892167	+	0.00515093i	0.495533	+	0.868589i	$0.334973\pi$
$258$	−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	$-0.756167\pi$
$263$	−7.79423	+	4.50000i	−0.480613	+	0.277482i	0.240059	+	0.970758i	$0.422833\pi$
$264$	−2.29129	+	3.96863i	−0.141019	+	0.244252i
$265$	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	−0.998816	−	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
$271$	−4.33013	−	7.50000i	−0.263036	−	0.455593i	0.704011	−	0.710189i	$-0.251391\pi$
$271$	−4.33013	−	7.50000i	−0.263036	−	0.455593i	−0.967047	+	0.254597i	$0.918057\pi$
$272$			8.20871i			0.497726i
$273$		0			0
$274$	0.208712			0.0126088
$275$	−10.6448	−	7.85425i	−0.641903	−	0.473629i
$276$	−6.39564	−	11.0776i	−0.384973	−	0.666792i
$277$	−14.3609	−	8.29129i	−0.862865	−	0.498175i	0.00210581	−	0.999998i	$-0.499330\pi$
$277$	−14.3609	−	8.29129i	−0.862865	−	0.498175i	−0.864971	+	0.501823i	$0.832663\pi$
$278$			12.5812i			0.754571i
$279$	9.66930	−	16.7477i	0.578886	−	1.00266i
$280$	2.09642	−	6.37221i	0.125285	−	0.380812i
$281$	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	$-0.669053\pi$
$283$	−0.218475	+	0.126136i	−0.0129870	+	0.00749803i	0.493492	+	0.869750i	$0.335720\pi$
$284$	−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
$290$	21.3061	+	7.00959i	1.25114	+	0.411617i
$291$	4.47315			0.262221
$292$		0			0
$293$	−20.2913	−	11.7152i	−1.18543	−	0.684408i	−0.228165	−	0.973622i	$-0.573273\pi$
$293$	−20.2913	−	11.7152i	−1.18543	−	0.684408i	−0.957264	+	0.289214i	$0.906606\pi$
$294$	−8.75560			−0.510637
$295$	−2.35411	+	7.15546i	−0.137061	+	0.416607i
$296$	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
$305$	7.39517	−	22.4781i	0.423446	−	1.28709i
$306$	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
$310$	35.2869	−	31.5381i	2.00416	−	1.79124i
$311$	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
$315$	5.77542	−	5.16184i	0.325408	−	0.290837i
$316$	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	−0.979083	−	0.203463i	$-0.934780\pi$
$331$	−5.70068	+	9.87386i	−0.313338	+	0.542717i	0.665745	+	0.746179i	$0.268114\pi$
$332$	27.3303	+	15.7792i	1.49995	+	0.865994i
$333$			15.8745i			0.869918i
$334$	−4.68693	+	8.11800i	−0.256457	+	0.444197i
$335$	24.7840	−	22.1509i	1.35409	−	1.21023i
$336$	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
$340$	21.3259	−	19.0602i	1.15656	−	1.03369i
$341$	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
$345$	3.20233	−	9.73371i	0.172408	−	0.524045i
$346$	−16.2360			−0.872853
$347$	−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
$349$	−9.16478	−	15.8739i	−0.490579	−	0.849708i	0.509362	−	0.860552i	$-0.329882\pi$
$349$	−9.16478	−	15.8739i	−0.490579	−	0.849708i	−0.999941	+	0.0108440i	$0.996548\pi$
$350$	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	$-0.513269\pi$
$353$	15.0826	−	8.70793i	0.802765	−	0.463476i	0.844437	+	0.535655i	$0.179935\pi$
$354$	3.68693	+	6.38595i	0.195958	+	0.339410i
$355$	2.48737	−	7.56052i	0.132016	−	0.401271i
$356$	−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	$0.843139\pi$
$360$	−7.35799	−	2.42074i	−0.387800	−	0.127584i
$361$	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	$-0.432098\pi$
$367$	22.2982	−	12.8739i	1.16396	−	0.672010i	0.952249	+	0.305323i	$0.0987644\pi$
$368$	−7.10895	−	4.10436i	−0.370580	−	0.213954i
$369$	5.29150			0.275465
$370$	−12.1410	+	36.9033i	−0.631179	+	1.91851i
$371$	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	$-0.442596\pi$
$373$	−11.2583	−	6.50000i	−0.582934	−	0.336557i	−0.762299	+	0.647225i	$0.775929\pi$
$374$	13.2695	+	22.9835i	0.686150	+	1.18845i
$375$	−4.65997	+	10.1629i	−0.240640	+	0.524810i
$376$	15.1652			0.782083
$377$		0			0
$378$		−	18.9564i		−	0.975014i
$379$	10.5353	+	18.2477i	0.541164	+	0.937323i	0.998838	+	0.0482027i	$0.0153493\pi$
$379$	10.5353	+	18.2477i	0.541164	+	0.937323i	−0.457674	+	0.889120i	$0.651317\pi$
$380$	−7.20409	−	8.06042i	−0.369562	−	0.413491i
$381$	−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	$-0.310246\pi$
$383$	2.45644	+	1.41823i	0.125518	+	0.0724680i	−0.435926	+	0.899982i	$0.643579\pi$
$384$	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	$-0.0933678\pi$
$397$	23.6216	+	13.6379i	1.18553	+	0.684468i	0.228245	+	0.973604i	$0.426701\pi$
$398$		−	3.10260i		−	0.155519i
$399$	1.50000	−	2.59808i	0.0750939	−	0.130066i
$400$	7.20696	+	5.31767i	0.360348	+	0.265883i
$401$	−6.25288	−	10.8303i	−0.312254	−	0.540840i	0.666596	−	0.745419i	$-0.267751\pi$
$401$	−6.25288	−	10.8303i	−0.312254	−	0.540840i	−0.978850	+	0.204580i	$0.934417\pi$
$402$		−	32.5390i		−	1.62290i
$403$		0			0
$404$	25.1216			1.24985
$405$	−1.49009	−	1.66722i	−0.0740434	−	0.0828448i
$406$	−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	−0.952997	−	0.302979i	$-0.902019\pi$
$409$	−4.33013	+	7.50000i	−0.214111	+	0.370851i	0.738886	+	0.673830i	$0.235352\pi$
$410$	12.3011	+	4.04699i	0.607508	+	0.199867i
$411$	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	−0.994195	−	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
$421$	−26.2668			−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
$425$	22.7691	+	2.56275i	1.10446	+	0.124311i
$426$	−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	0.963441	+	0.267922i	$0.0863369\pi$
$431$	14.8178	+	25.6652i	0.713747	+	1.23625i	−0.249693	+	0.968325i	$0.580330\pi$
$432$	7.75650	−	4.47822i	0.373185	−	0.215458i
$433$	15.3700	+	8.87386i	0.738634	+	0.426451i	0.821573	−	0.570104i	$-0.193097\pi$
$433$	15.3700	+	8.87386i	0.738634	+	0.426451i	−0.0829383	+	0.996555i	$0.526430\pi$
$434$	−36.6591			−1.75969
$435$	9.73371	+	3.20233i	0.466696	+	0.153540i
$436$	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	−0.705885	−	0.708327i	$-0.749450\pi$
$439$	−20.2477	−	35.0701i	−0.966371	−	1.67380i	−0.260487	−	0.965477i	$-0.583883\pi$
$440$	7.64016	−	6.82847i	0.364230	−	0.325535i
$441$	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
$445$	−6.38126	−	7.13978i	−0.302501	−	0.338458i
$446$	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	0.0378622	−	0.999283i	$-0.487945\pi$
$449$	18.7387	−	32.4564i	0.884336	−	1.53171i	0.846473	−	0.532431i	$-0.178721\pi$
$450$	−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	$-0.653768\pi$
$457$	1.50000	−	0.866025i	0.0701670	−	0.0405110i	0.534673	+	0.845059i	$0.320435\pi$
$458$	−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	−0.851718	−	0.524001i	$-0.824439\pi$
$461$	0.599876	−	1.03901i	0.0279390	−	0.0483917i	0.879657	+	0.475609i	$0.157772\pi$
$462$	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
$465$	16.1208	−	14.4082i	0.747586	−	0.668163i
$466$	−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
$470$	28.5579	+	31.9525i	1.31728	+	1.47386i
$471$	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
$475$	0.968627	−	8.60591i	0.0444437	−	0.394866i
$476$	−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	0.952647	+	0.304079i	$0.0983488\pi$
$479$	16.1883	+	28.0390i	0.739664	+	1.28114i	−0.212983	+	0.977056i	$0.568318\pi$
$480$	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
$485$	−9.50128	−	3.12587i	−0.431431	−	0.141938i
$486$	−35.0224			−1.58865
$487$	18.2477	+	10.5353i	0.826883	+	0.477401i	0.852784	−	0.522263i	$-0.174912\pi$
$487$	18.2477	+	10.5353i	0.826883	+	0.477401i	−0.0259009	+	0.999665i	$0.508245\pi$
$488$	15.8739	+	9.16478i	0.718576	+	0.414870i
$489$	10.6784			0.482892
$490$	18.5975	+	6.11847i	0.840150	+	0.276404i
$491$	14.2913	+	24.7532i	0.644957	+	1.11710i	0.984311	+	0.176439i	$0.0564580\pi$
$491$	14.2913	+	24.7532i	0.644957	+	1.11710i	−0.339355	+	0.940658i	$0.610209\pi$
$492$	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	$0.378842\pi$
$500$	−2.91914	−	31.0707i	−0.130548	−	1.38952i
$501$	−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	$-0.466052\pi$
$503$	−15.7315	−	9.08258i	−0.701432	−	0.404972i	−0.807881	+	0.589346i	$0.799385\pi$
$504$	3.00000	+	5.19615i	0.133631	+	0.231455i
$505$	13.4109	+	15.0050i	0.596775	+	0.667712i
$506$	−26.5390			−1.17980
$507$		0			0
$508$		−	27.2087i		−	1.20719i
$509$	−14.8178	−	25.6652i	−0.656787	−	1.13759i	−0.981443	−	0.191756i	$-0.938582\pi$
$509$	−14.8178	−	25.6652i	−0.656787	−	1.13759i	0.324656	−	0.945832i	$-0.394751\pi$
$510$	16.7235	−	14.9468i	0.740531	−	0.661857i
$511$		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	$-0.536665\pi$
$523$	15.7315	−	9.08258i	0.687890	−	0.397153i	0.802821	+	0.596220i	$0.203331\pi$
$524$	2.20871	−	3.82560i	0.0964880	−	0.167122i
$525$	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
$530$	−5.16184	−	5.77542i	−0.224216	−	0.250868i
$531$	−3.36875	−	5.83485i	−0.146191	−	0.253211i
$532$			8.37386i			0.363053i
$533$		0			0
$534$	−9.37386			−0.405647
$535$	−2.36316	+	2.11210i	−0.102168	+	0.0913139i
$536$	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
$540$	−29.6444	−	9.75285i	−1.27569	−	0.419696i
$541$	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
$550$	28.7747	+	3.23870i	1.22696	+	0.138099i
$551$	−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
$555$	−5.54661	+	16.8593i	−0.235440	+	0.715636i
$556$	−8.02178	−	13.8941i	−0.340199	−	0.589242i
$557$	−11.2913	+	6.51903i	−0.478427	+	0.276220i	−0.719761	−	0.694222i	$-0.755749\pi$
$557$	−11.2913	+	6.51903i	−0.478427	+	0.276220i	0.241334	+	0.970442i	$0.422415\pi$
$558$			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	$-0.272597\pi$
$563$	7.79423	+	4.50000i	0.328488	+	0.189652i	−0.326682	+	0.945134i	$0.605931\pi$
$564$	24.4394			1.02908
$565$	−35.2225	−	11.5880i	−1.48182	−	0.487511i
$566$	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	0.995316	−	0.0966762i	$-0.0308211\pi$
$569$	9.87386	+	17.1020i	0.413934	+	0.716955i	−0.581382	+	0.813631i	$0.697488\pi$
$570$	−5.64938	−	6.32091i	−0.236626	−	0.264754i
$571$	−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
$575$	−13.6040	+	18.4373i	−0.567324	+	0.768887i
$576$	−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	$-0.792859\pi$
$587$	−16.2042	+	9.35548i	−0.668818	+	0.386142i	0.126811	+	0.991927i	$0.459526\pi$
$588$	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
$595$	−11.8273	−	13.2331i	−0.484870	−	0.542506i
$596$	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	$0.201160\pi$
$600$	−6.96863	−	5.14181i	−0.284493	−	0.209914i
$601$	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
$603$			29.7309i			1.21074i
$604$	−8.66025	+	15.0000i	−0.352381	+	0.610341i
$605$	2.79523	−	8.49628i	0.113642	−	0.345423i
$606$	19.7001			0.800262
$607$	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
$609$	−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	$-0.811730\pi$
$613$	−18.8739	+	10.8968i	−0.762308	+	0.440119i	0.0678157	+	0.997698i	$0.478397\pi$
$614$	−26.5390	−	45.9669i	−1.07103	−	1.85507i
$615$	5.61976	+	1.84887i	0.226611	+	0.0745536i
$616$	−7.93725			−0.319801
$617$	2.91742	+	1.68438i	0.117451	+	0.0678104i	0.557575	−	0.830127i	$-0.311732\pi$
$617$	2.91742	+	1.68438i	0.117451	+	0.0678104i	−0.440124	+	0.897937i	$0.645065\pi$
$618$	−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	$0.512913\pi$
$620$	−18.8607	+	57.3282i	−0.757462	+	2.30236i
$621$	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
$630$	−5.29875	+	16.1059i	−0.211107	+	0.641675i
$631$	−10.8968	+	18.8739i	−0.433796	+	0.751357i	−0.997197	−	0.0748272i	$-0.976159\pi$
$631$	−10.8968	+	18.8739i	−0.433796	+	0.751357i	0.563401	+	0.826184i	$0.309493\pi$
$632$			10.3923i			0.413384i
$633$	15.7315	+	9.08258i	0.625270	+	0.361000i
$634$	22.9564	+	39.7617i	0.911717	+	1.57914i
$635$	16.2516	−	14.5250i	0.644925	−	0.576408i
$636$	−4.41742			−0.175162
$637$		0			0
$638$		−	26.5390i		−	1.05069i
$639$	3.55945	+	6.16515i	0.140810	+	0.243890i
$640$	−21.2936	+	19.0313i	−0.841702	+	0.752280i
$641$	−0.0825757	+	0.143025i	−0.00326154	+	0.00564916i	−0.867652	−	0.497173i	$-0.834372\pi$
$641$	−0.0825757	+	0.143025i	−0.00326154	+	0.00564916i	0.864390	+	0.502822i	$0.167705\pi$
$642$			3.10260i			0.122450i
$643$	5.12614	+	2.95958i	0.202155	+	0.116714i	0.597660	−	0.801749i	$-0.296097\pi$
$643$	5.12614	+	2.95958i	0.202155	+	0.116714i	−0.395505	+	0.918464i	$0.629430\pi$
$644$	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	$-0.844753\pi$
$647$	−23.3827	+	13.5000i	−0.919268	+	0.530740i	−0.0358667	+	0.999357i	$0.511419\pi$
$648$	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	−0.679619	+	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
$655$	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	−0.999656	−	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
$661$	−1.22753	−	2.12614i	−0.0477452	−	0.0826971i	0.841165	−	0.540778i	$-0.181870\pi$
$661$	−1.22753	−	2.12614i	−0.0477452	−	0.0826971i	−0.888910	+	0.458081i	$0.848537\pi$
$662$		−	24.9564i		−	0.969960i
$663$		0			0
$664$	−19.5826			−0.759951
$665$	−5.00166	+	4.47028i	−0.193956	+	0.173350i
$666$	−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
$670$	−22.7385	+	69.1151i	−0.878464	+	2.67015i
$671$	−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	$-0.702539\pi$
$673$	−5.05313	+	2.91742i	−0.194784	+	0.112458i	0.399436	+	0.916761i	$0.369206\pi$
$674$	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
$680$	−5.54661	+	16.8593i	−0.212703	+	0.646524i
$681$	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	$-0.260012\pi$
$683$	10.3348	+	5.96683i	0.395452	+	0.228314i	−0.289068	+	0.957309i	$0.593345\pi$
$684$	9.66930			0.369715
$685$	−0.202530	−	0.0666313i	−0.00773829	−	0.00254585i
$686$	−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	0.975554	+	0.219762i	$0.0705281\pi$
$691$	17.8250	+	30.8739i	0.678096	+	1.17450i	−0.297457	+	0.954735i	$0.596139\pi$
$692$	17.9303	−	10.3521i	0.681609	−	0.393527i
$693$	−7.93725	−	4.58258i	−0.301511	−	0.174078i
$694$	33.5565			1.27379
$695$	4.01655	−	12.2086i	0.152356	−	0.463097i
$696$	−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
$700$	−14.3523	+	19.4514i	−0.542465	+	0.735195i
$701$	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
$705$	13.0467	+	14.5975i	0.491366	+	0.549774i
$706$	−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	−0.291048	−	0.956708i	$-0.594004\pi$
$709$	18.1865	−	31.5000i	0.683010	−	1.18301i	0.974058	−	0.226299i	$-0.0726626\pi$
$710$	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	0.428056	+	0.903752i	$0.359199\pi$
$719$	−15.2477	+	26.4098i	−0.568644	+	0.984921i	−0.996700	+	0.0811686i	$0.974135\pi$
$720$	−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
$725$	−18.4373	−	13.6040i	−0.684742	−	0.505238i
$726$	−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
$735$	8.49628	+	2.79523i	0.313390	+	0.103103i
$736$	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	0.830977	+	0.556307i	$0.187782\pi$
$739$	24.3917	+	42.2477i	0.897265	+	1.55411i	0.0662878	+	0.997801i	$0.478884\pi$
$740$	−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	$-0.379576\pi$
$743$	37.0390	−	21.3845i	1.35883	−	0.784521i	0.989466	+	0.144764i	$0.0462424\pi$
$744$	8.37386	+	14.5040i	0.307001	+	0.531741i
$745$	−6.82361	+	20.7408i	−0.249998	+	0.759884i
$746$	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
$750$	−2.28916	−	24.3654i	−0.0835884	−	0.889697i
$751$	−7.87386	−	13.6379i	−0.287321	−	0.497655i	0.685848	−	0.727745i	$-0.259431\pi$
$751$	−7.87386	−	13.6379i	−0.287321	−	0.497655i	−0.973169	+	0.230090i	$0.926098\pi$
$752$	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	$-0.771199\pi$
$757$	−15.3700	+	8.87386i	−0.558632	+	0.322526i	0.193965	+	0.981009i	$0.437865\pi$
$758$	−39.9425	−	23.0608i	−1.45078	−	0.837606i
$759$	−12.1244			−0.440086
$760$	6.37221	+	2.09642i	0.231144	+	0.0760451i
$761$	−20.3754	+	35.2913i	−0.738609	+	1.27931i	0.214513	+	0.976721i	$0.431184\pi$
$761$	−20.3754	+	35.2913i	−0.738609	+	1.27931i	−0.953122	+	0.302587i	$0.902150\pi$
$762$		−	21.3368i		−	0.772951i
$763$	−4.11165	−	2.37386i	−0.148852	−	0.0859396i
$764$	−10.3521	−	17.9303i	−0.374525	−	0.648697i
$765$	−15.2803	+	13.6569i	−0.552461	+	0.493768i
$766$	−6.20871			−0.224330
$767$		0			0
$768$			2.79129i			0.100722i
$769$	−7.79423	−	13.5000i	−0.281067	−	0.486822i	0.690581	−	0.723255i	$-0.257355\pi$
$769$	−7.79423	−	13.5000i	−0.281067	−	0.486822i	−0.971648	+	0.236433i	$0.924022\pi$
$770$	−14.9468	−	16.7235i	−0.538647	−	0.602675i
$771$	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	$-0.118559\pi$
$773$	30.0826	+	17.3682i	1.08200	+	0.624690i	0.150561	+	0.988601i	$0.451892\pi$
$774$	−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	$-0.138859\pi$
$787$	27.8739	+	16.0930i	0.993596	+	0.573653i	0.0872487	+	0.996187i	$0.472193\pi$
$788$			55.7316i			1.98536i
$789$	4.50000	−	7.79423i	0.160204	−	0.277482i
$790$	−21.8963	+	19.5700i	−0.779034	+	0.696270i
$791$	14.3609	+	24.8739i	0.510616	+	0.884413i
$792$			9.16515i			0.325669i
$793$		0			0
$794$	−59.7042			−2.11882
$795$	−2.35819	−	2.63850i	−0.0836363	−	0.0935779i
$796$	1.97822	+	3.42638i	0.0701161	+	0.121445i
$797$	−17.3881	−	10.0390i	−0.615918	−	0.355600i	0.159360	−	0.987220i	$-0.449057\pi$
$797$	−17.3881	−	10.0390i	−0.615918	−	0.355600i	−0.775278	+	0.631620i	$0.782390\pi$
$798$			6.56670i			0.232459i
$799$	20.0616	−	34.7477i	0.709729	−	1.22929i
$800$	−36.6936	−	4.13000i	−1.29731	−	0.146017i
$801$	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	0.983750	+	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
$811$	−18.7665			−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
$815$	−22.6816	−	7.46211i	−0.794501	−	0.261386i
$816$	−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	0.994763	−	0.102213i	$-0.0325922\pi$
$821$	11.7152	+	20.2913i	0.408863	+	0.708171i	−0.585900	+	0.810383i	$0.699259\pi$
$822$	−0.180750	+	0.104356i	−0.00630438	+	0.00363984i
$823$	35.1455	+	20.2913i	1.22510	+	0.707310i	0.966000	−	0.258542i	$-0.0832419\pi$
$823$	35.1455	+	20.2913i	1.22510	+	0.707310i	0.259096	+	0.965851i	$0.416575\pi$
$824$	26.2668			0.915048
$825$	13.1458	+	1.47960i	0.457676	+	0.0515131i
$826$	−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	0.835659	−	0.549248i	$-0.185086\pi$
$829$	−1.66515	−	2.88413i	−0.0578331	−	0.100170i	−0.893492	+	0.449078i	$0.851752\pi$
$830$	−36.8765	−	41.2599i	−1.28000	−	1.43215i
$831$	16.5826			0.575243
$832$		0			0
$833$		−	18.3303i		−	0.635107i
$834$	−6.29060	−	10.8956i	−0.217826	−	0.377285i
$835$	7.13978	−	6.38126i	0.247082	−	0.220833i
$836$	−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	−0.854133	−	0.520055i	$-0.825911\pi$
$839$	0.675325	−	1.16970i	0.0233148	−	0.0403824i	0.877447	+	0.479673i	$0.159245\pi$
$840$	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
$855$	5.16184	+	5.77542i	0.176531	+	0.197515i
$856$	−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	$0.726246\pi$
$860$	−6.59625	+	5.89547i	−0.224930	+	0.201034i
$861$	−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
$865$	15.7551	+	5.18335i	0.535690	+	0.176239i
$866$	−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
$875$	−19.2800	+	1.81139i	−0.651783	+	0.0612360i
$876$		0			0
$877$	−6.87386	−	3.96863i	−0.232114	−	0.134011i	0.379433	−	0.925219i	$-0.376119\pi$
$877$	−6.87386	−	3.96863i	−0.232114	−	0.134011i	−0.611547	+	0.791208i	$0.709452\pi$
$878$	76.7650	+	44.3203i	2.59069	+	1.49574i
$879$	23.4304			0.790286
$880$	3.31186	−	10.0666i	0.111643	−	0.339345i
$881$	−9.24773	−	16.0175i	−0.311564	−	0.539644i	0.667137	−	0.744935i	$-0.267519\pi$
$881$	−9.24773	−	16.0175i	−0.311564	−	0.539644i	−0.978701	+	0.205290i	$0.934186\pi$
$882$	−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	$-0.669314\pi$
$887$	−0.429076	+	0.247727i	−0.0144070	+	0.00831786i	0.492779	+	0.870154i	$0.335981\pi$
$888$	−11.9059	−	6.87386i	−0.399535	−	0.230672i
$889$	−16.8836			−0.566256
$890$	19.9107	+	6.55052i	0.667409	+	0.219574i
$891$	−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
$895$	0.246091	+	0.275344i	0.00822592	+	0.00920372i
$896$	22.1216			0.739030
$897$		0			0
$898$			82.0345i			2.73753i
$899$	22.1552	+	38.3739i	0.738916	+	1.27984i
$900$	22.4606	+	16.5726i	0.748686	+	0.552419i
$901$	−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	$-0.477357\pi$
$907$	29.2264	−	16.8739i	0.970446	−	0.560287i	0.899372	+	0.437184i	$0.144024\pi$
$908$	−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	−0.403051	−	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
$921$	−12.1244	−	21.0000i	−0.399511	−	0.691974i
$922$			2.62614i			0.0864872i
$923$		0			0
$924$	−12.7913			−0.420802
$925$	23.5627	−	31.9343i	0.774738	−	1.04999i
$926$	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	−0.704790	−	0.709416i	$-0.748959\pi$
$929$	7.98493	−	13.8303i	0.261977	−	0.453758i	0.966767	+	0.255658i	$0.0822922\pi$
$930$	−14.7903	+	44.9562i	−0.484995	+	1.47417i
$931$	−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
$940$	−51.9110	−	17.0784i	−1.69315	−	0.557037i
$941$	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
$945$	−6.05184	+	18.3950i	−0.196866	+	0.598389i
$946$	−4.10436	−	7.10895i	−0.133444	−	0.231132i
$947$	33.4129	−	19.2909i	1.08577	−	0.626871i	0.153325	−	0.988176i	$-0.451002\pi$
$947$	33.4129	−	19.2909i	1.08577	−	0.626871i	0.932448	+	0.361305i	$0.117669\pi$
$948$			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	−0.995777	−	0.0918100i	$-0.970735\pi$
$953$	−48.5650	−	28.0390i	−1.57317	−	0.908273i	−0.577398	−	0.816463i	$-0.695932\pi$
$954$	6.92820			0.224309
$955$	5.18335	−	15.7551i	0.167729	−	0.509824i
$956$	−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
$960$	−20.9779	+	18.7492i	−0.677059	+	0.605129i
$961$	62.4955			2.01598
$962$		0			0
$963$		−	2.83485i		−	0.0913517i
$964$	2.41733	+	4.18693i	0.0778568	+	0.134852i
$965$	1.68231	−	1.50358i	0.0541554	−	0.0484020i
$966$	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	0.409203	+	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
$973$	−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	$-0.453709\pi$
$977$	33.5780	−	19.3863i	1.07426	−	0.620222i	0.929341	+	0.369222i	$0.120376\pi$
$978$	−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
$985$	−33.2881	+	29.7516i	−1.06065	+	0.947965i
$986$	22.9835	+	39.8085i	0.731943	+	1.26776i
$987$		−	15.1652i		−	0.482712i
$988$		0			0
$989$	6.49545			0.206543
$990$	−19.3107	+	17.2591i	−0.613734	+	0.548531i
$991$	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
$993$		−	11.4014i		−	0.361811i
$994$	6.74745	−	11.6869i	0.214016	−	0.370687i
$995$	−0.990505	+	3.01071i	−0.0314011	+	0.0954458i
$996$	−31.5583			−0.999963
$997$	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
$999$	−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.c.484.1		8
5.4	even	2		845.2.n.d.484.4		8
13.2	odd	12		845.2.d.c.844.1		8
13.3	even	3		845.2.b.f.339.1		8
13.4	even	6	inner	845.2.n.c.529.2		8
13.5	odd	4		65.2.l.a.49.4	yes	8
13.6	odd	12		845.2.l.c.654.4		8
13.7	odd	12		65.2.l.a.4.1	✓	8
13.8	odd	4		845.2.l.c.699.1		8
13.9	even	3		845.2.n.d.529.4		8
13.10	even	6		845.2.b.f.339.7		8
13.11	odd	12		845.2.d.c.844.7		8
13.12	even	2		845.2.n.d.484.3		8
39.5	even	4		585.2.bf.a.244.1		8
39.20	even	12		585.2.bf.a.199.4		8
52.7	even	12		1040.2.df.b.849.2		8
52.31	even	4		1040.2.df.b.49.3		8
65.3	odd	12		4225.2.a.bk.1.1		4
65.4	even	6		845.2.n.d.529.3		8
65.7	even	12		325.2.n.b.251.1		4
65.9	even	6	inner	845.2.n.c.529.1		8
65.18	even	4		325.2.n.c.101.2		4
65.19	odd	12		845.2.l.c.654.1		8
65.23	odd	12		4225.2.a.bk.1.4		4
65.24	odd	12		845.2.d.c.844.2		8
65.29	even	6		845.2.b.f.339.8		8
65.33	even	12		325.2.n.c.251.2		4
65.34	odd	4		845.2.l.c.699.4		8
65.42	odd	12		4225.2.a.bj.1.4		4
65.44	odd	4		65.2.l.a.49.1	yes	8
65.49	even	6		845.2.b.f.339.2		8
65.54	odd	12		845.2.d.c.844.8		8
65.57	even	4		325.2.n.b.101.1		4
65.59	odd	12		65.2.l.a.4.4	yes	8
65.62	odd	12		4225.2.a.bj.1.1		4
65.64	even	2	inner	845.2.n.c.484.2		8
195.44	even	4		585.2.bf.a.244.4		8
195.59	even	12		585.2.bf.a.199.1		8
260.59	even	12		1040.2.df.b.849.3		8
260.239	even	4		1040.2.df.b.49.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.l.a.4.1	✓	8	13.7	odd	12
65.2.l.a.4.4	yes	8	65.59	odd	12
65.2.l.a.49.1	yes	8	65.44	odd	4
65.2.l.a.49.4	yes	8	13.5	odd	4
325.2.n.b.101.1		4	65.57	even	4
325.2.n.b.251.1		4	65.7	even	12
325.2.n.c.101.2		4	65.18	even	4
325.2.n.c.251.2		4	65.33	even	12
585.2.bf.a.199.1		8	195.59	even	12
585.2.bf.a.199.4		8	39.20	even	12
585.2.bf.a.244.1		8	39.5	even	4
585.2.bf.a.244.4		8	195.44	even	4
845.2.b.f.339.1		8	13.3	even	3
845.2.b.f.339.2		8	65.49	even	6
845.2.b.f.339.7		8	13.10	even	6
845.2.b.f.339.8		8	65.29	even	6
845.2.d.c.844.1		8	13.2	odd	12
845.2.d.c.844.2		8	65.24	odd	12
845.2.d.c.844.7		8	13.11	odd	12
845.2.d.c.844.8		8	65.54	odd	12
845.2.l.c.654.1		8	65.19	odd	12
845.2.l.c.654.4		8	13.6	odd	12
845.2.l.c.699.1		8	13.8	odd	4
845.2.l.c.699.4		8	65.34	odd	4
845.2.n.c.484.1		8	1.1	even	1	trivial
845.2.n.c.484.2		8	65.64	even	2	inner
845.2.n.c.529.1		8	65.9	even	6	inner
845.2.n.c.529.2		8	13.4	even	6	inner
845.2.n.d.484.3		8	13.12	even	2
845.2.n.d.484.4		8	5.4	even	2
845.2.n.d.529.3		8	65.4	even	6
845.2.n.d.529.4		8	13.9	even	3
1040.2.df.b.49.2		8	260.239	even	4
1040.2.df.b.49.3		8	52.31	even	4
1040.2.df.b.849.2		8	52.7	even	12
1040.2.df.b.849.3		8	260.59	even	12
4225.2.a.bj.1.1		4	65.62	odd	12
4225.2.a.bj.1.4		4	65.42	odd	12
4225.2.a.bk.1.1		4	65.3	odd	12
4225.2.a.bk.1.4		4	65.23	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.89564 + 1.09445i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(1.39564 - 2.41733i) q^{4} +(2.18890 - 0.456850i) q^{5} +(1.09445 - 1.89564i) q^{6} +(-1.50000 - 0.866025i) q^{7} +1.73205i q^{8} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(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} +(-3.64938 + 3.26167i) q^{10} +(-1.32288 - 2.29129i) q^{11} +2.79129i q^{12} +3.79129 q^{14} +(-1.66722 + 1.49009i) q^{15} +(0.895644 + 1.55130i) q^{16} +(3.96863 + 2.29129i) q^{17} -4.37780i q^{18} +(0.866025 - 1.50000i) q^{19} +(1.95057 - 5.92889i) 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} +(1.52962 - 4.64938i) q^{30} -9.66930 q^{31} +(-6.39564 - 3.69253i) q^{32} +(2.29129 + 1.32288i) q^{33} -10.0308 q^{34} +(-3.67900 - 1.21037i) 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} +(-1.39761 + 4.24814i) q^{45} +(5.01540 - 8.68693i) q^{46} -8.75560i q^{47} +(-1.55130 - 0.895644i) q^{48} +(-2.00000 - 3.46410i) q^{49} +(-6.49803 + 8.80669i) q^{50} -4.58258 q^{51} +1.58258i q^{53} +(5.47225 + 9.47822i) q^{54} +(-3.94242 - 4.41105i) 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} +(-2.96863 + 4.02334i) q^{75} +(-2.41733 - 4.18693i) q^{76} +4.58258i q^{77} +6.00000 q^{79} +(2.66919 + 2.98647i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.01540 + 2.89564i) q^{82} +11.3060i q^{83} +(2.41733 - 4.18693i) q^{84} +(9.73371 + 3.20233i) 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} +(1.21037 - 3.67900i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} + 2 q^{4} - 12 q^{7} - 8 q^{9}+O(q^{10}) \) 8 * q - 6 * q^2 + 2 * q^4 - 12 * q^7 - 8 * q^9	\( 8 q - 6 q^{2} + 2 q^{4} - 12 q^{7} - 8 q^{9} + 4 q^{10} + 12 q^{14} - 6 q^{15} - 2 q^{16} - 18 q^{20} - 6 q^{28} + 10 q^{30} - 42 q^{32} + 6 q^{35} + 4 q^{36} - 12 q^{40} - 12 q^{45} - 16 q^{49} - 42 q^{50} - 14 q^{55} + 12 q^{56} + 42 q^{58} + 24 q^{61} + 24 q^{63} + 64 q^{64} - 28 q^{66} + 48 q^{67} - 24 q^{72} - 42 q^{74} + 8 q^{75} + 48 q^{79} + 24 q^{80} - 4 q^{81} + 42 q^{85} - 16 q^{90} + 12 q^{93} + 40 q^{94} + 6 q^{95} + 24 q^{97} + 24 q^{98}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

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