LMFDB - Embedded newform 841.2.d.j.645.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(190,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

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

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

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

chi := DirichletCharacter("841.190");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.d (of order $7$, degree $6$, 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:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	12.0.74049191673856.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 2x^{10} + 4x^{8} + 8x^{6} + 16x^{4} + 32x^{2} + 64 $ x^12 + 2x^10 + 4x^8 + 8x^6 + 16x^4 + 32*x^2 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			645.2
Root			$-0.881748 + 1.10568i$ of defining polynomial
Character	$\chi$	$=$	841.645
Dual form			841.2.d.j.605.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.537213 + 2.35368i) q^{2} +(-2.17513 - 1.04749i) q^{3} +(-3.44929 + 1.66109i) q^{4} +(0.222521 + 0.974928i) q^{5} +(1.29695 - 5.68230i) q^{6} +(2.54832 + 1.22721i) q^{7} +(-2.75222 - 3.45117i) q^{8} +(1.76350 + 2.21135i) q^{9} +(-2.17513 + 1.04749i) q^{10} +(-0.258258 + 0.323845i) q^{11} +9.24264 q^{12} +(-2.38699 + 2.99318i) q^{13} +(-1.51947 + 6.65722i) q^{14} +(0.537213 - 2.35368i) q^{15} +(1.87047 - 2.34549i) q^{16} +0.828427 q^{17} +(-4.25745 + 5.33868i) q^{18} +(-5.40581 + 2.60330i) q^{19} +(-2.38699 - 2.99318i) q^{20} +(-4.25745 - 5.33868i) q^{21} +(-0.900969 - 0.433884i) q^{22} +(-0.813727 + 3.56517i) q^{23} +(2.37137 + 10.3897i) q^{24} +(3.60388 - 1.73553i) q^{25} +(-8.32733 - 4.01023i) q^{26} +(0.0921712 + 0.403828i) q^{27} -10.8284 q^{28} +5.82843 q^{30} +(-2.24102 - 9.81857i) q^{31} +(-1.42874 - 0.688047i) q^{32} +(0.900969 - 0.433884i) q^{33} +(0.445042 + 1.94986i) q^{34} +(-0.629384 + 2.75751i) q^{35} +(-9.75608 - 4.69828i) q^{36} +(-2.49396 - 3.12733i) q^{37} +(-9.03143 - 11.3250i) q^{38} +(8.32733 - 4.01023i) q^{39} +(2.75222 - 3.45117i) q^{40} -4.48528 q^{41} +(10.2784 - 12.8887i) q^{42} +(-0.797913 + 3.49588i) q^{43} +(0.352871 - 1.54603i) q^{44} +(-1.76350 + 2.21135i) q^{45} -8.82843 q^{46} +(-2.02175 + 2.53520i) q^{47} +(-6.52539 + 3.14246i) q^{48} +(0.623490 + 0.781831i) q^{49} +(6.02095 + 7.55003i) q^{50} +(-1.80194 - 0.867767i) q^{51} +(3.26146 - 14.2894i) q^{52} +(-2.11067 - 9.24747i) q^{53} +(-0.900969 + 0.433884i) q^{54} +(-0.373194 - 0.179721i) q^{55} +(-2.77824 - 12.1722i) q^{56} +14.4853 q^{57} -3.65685 q^{59} +(2.05668 + 9.01091i) q^{60} +(4.35026 + 2.09498i) q^{61} +(21.9059 - 10.5493i) q^{62} +(1.78017 + 7.79942i) q^{63} +(2.18703 - 9.58201i) q^{64} +(-3.44929 - 1.66109i) q^{65} +(1.50524 + 1.88751i) q^{66} +(3.52699 + 4.42271i) q^{67} +(-2.85749 + 1.37609i) q^{68} +(5.50443 - 6.90234i) q^{69} -6.82843 q^{70} +(-5.50443 + 6.90234i) q^{71} +(2.77824 - 12.1722i) q^{72} +(-0.890084 + 3.89971i) q^{73} +(6.02095 - 7.55003i) q^{74} -9.65685 q^{75} +(14.3219 - 17.9591i) q^{76} +(-1.05555 + 0.508326i) q^{77} +(13.9124 + 17.4456i) q^{78} +(-1.50524 - 1.88751i) q^{79} +(2.70291 + 1.30165i) q^{80} +(2.11067 - 9.24747i) q^{81} +(-2.40955 - 10.5569i) q^{82} +(-6.89859 + 3.32218i) q^{83} +(23.5533 + 11.3426i) q^{84} +(0.184342 + 0.807657i) q^{85} -8.65685 q^{86} +1.82843 q^{88} +(2.77824 + 12.1722i) q^{89} +(-6.15220 - 2.96274i) q^{90} +(-9.75608 + 4.69828i) q^{91} +(-3.11529 - 13.6490i) q^{92} +(-5.41031 + 23.7041i) q^{93} +(-7.05317 - 3.39663i) q^{94} +(-3.74094 - 4.69099i) q^{95} +(2.38699 + 2.99318i) q^{96} +(-4.04110 + 1.94609i) q^{97} +(-1.50524 + 1.88751i) q^{98} -1.17157 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 6 q^{6} + 6 q^{8} - 2 q^{10} - 2 q^{11} + 60 q^{12} + 2 q^{13} - 8 q^{14} + 2 q^{15} - 6 q^{16} - 24 q^{17} + 8 q^{18} - 12 q^{19} + 2 q^{20} + 8 q^{21} - 2 q^{22}+ \cdots - 48 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 6 * q^6 + 6 * q^8 - 2 * q^10 - 2 * q^11 + 60 * q^12 + 2 * q^13 - 8 * q^14 + 2 * q^15 - 6 * q^16 - 24 * q^17 + 8 * q^18 - 12 * q^19 + 2 * q^20 + 8 * q^21 - 2 * q^22 + 4 * q^23 + 10 * q^24 + 8 * q^25 - 10 * q^26 - 2 * q^27 - 96 * q^28 + 36 * q^30 - 6 * q^31 - 6 * q^32 + 2 * q^33 + 4 * q^34 - 16 * q^36 + 8 * q^37 + 12 * q^38 + 10 * q^39 - 6 * q^40 + 48 * q^41 - 16 * q^42 - 10 * q^43 + 6 * q^44 - 72 * q^46 - 2 * q^47 - 6 * q^48 - 2 * q^49 - 8 * q^50 - 4 * q^51 + 18 * q^52 - 2 * q^53 - 2 * q^54 + 2 * q^55 - 8 * q^56 + 72 * q^57 + 24 * q^59 + 10 * q^60 + 4 * q^61 + 26 * q^62 + 16 * q^63 + 14 * q^64 - 2 * q^65 - 2 * q^66 - 12 * q^68 - 12 * q^69 - 48 * q^70 + 12 * q^71 + 8 * q^72 - 8 * q^73 - 8 * q^74 - 48 * q^75 - 12 * q^76 - 8 * q^77 - 22 * q^78 + 2 * q^79 + 6 * q^80 + 2 * q^81 - 16 * q^82 - 4 * q^83 + 24 * q^84 - 4 * q^85 - 36 * q^86 - 12 * q^88 + 8 * q^89 - 8 * q^90 - 16 * q^91 - 28 * q^92 - 26 * q^93 - 10 * q^94 + 12 * q^95 - 2 * q^96 + 8 * q^97 + 2 * q^98 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{7}\right)$

Coefficient data

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

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

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

$2$	0.537213	+	2.35368i	0.379867	+	1.66431i	0.697876	+	0.716218i	$0.254129\pi$
$2$	0.537213	+	2.35368i	0.379867	+	1.66431i	−0.318009	+	0.948088i	$0.603014\pi$
$3$	−2.17513	−	1.04749i	−1.25581	−	0.604767i	−0.316749	−	0.948510i	$-0.602591\pi$
$3$	−2.17513	−	1.04749i	−1.25581	−	0.604767i	−0.939064	+	0.343742i	$0.888305\pi$
$4$	−3.44929	+	1.66109i	−1.72465	+	0.830546i
$5$	0.222521	+	0.974928i	0.0995144	+	0.436001i	0.999999	+	0.00111393i	$0.000354575\pi$
$5$	0.222521	+	0.974928i	0.0995144	+	0.436001i	−0.900485	+	0.434887i	$0.856788\pi$
$6$	1.29695	−	5.68230i	0.529476	−	2.31979i
$7$	2.54832	+	1.22721i	0.963176	+	0.463841i	0.848287	−	0.529537i	$-0.177634\pi$
$7$	2.54832	+	1.22721i	0.963176	+	0.463841i	0.114889	+	0.993378i	$0.463349\pi$
$8$	−2.75222	−	3.45117i	−0.973056	−	1.22017i
$9$	1.76350	+	2.21135i	0.587832	+	0.737118i
$10$	−2.17513	+	1.04749i	−0.687837	+	0.331245i
$11$	−0.258258	+	0.323845i	−0.0778677	+	0.0976430i	−0.819240	−	0.573452i	$-0.805604\pi$
$11$	−0.258258	+	0.323845i	−0.0778677	+	0.0976430i	0.741372	+	0.671095i	$0.234176\pi$
$12$	9.24264			2.66812
$13$	−2.38699	+	2.99318i	−0.662031	+	0.830160i	−0.993563	−	0.113284i	$-0.963863\pi$
$13$	−2.38699	+	2.99318i	−0.662031	+	0.830160i	0.331532	+	0.943444i	$0.392434\pi$
$14$	−1.51947	+	6.65722i	−0.406095	+	1.77922i
$15$	0.537213	−	2.35368i	0.138708	−	0.607719i
$16$	1.87047	−	2.34549i	0.467617	−	0.586374i
$17$	0.828427			0.200923			0.100462	−	0.994941i	$-0.467968\pi$
$17$	0.828427			0.200923			0.100462	+	0.994941i	$0.467968\pi$
$18$	−4.25745	+	5.33868i	−1.00349	+	1.25834i
$19$	−5.40581	+	2.60330i	−1.24018	+	0.597239i	−0.934862	−	0.355012i	$-0.884477\pi$
$19$	−5.40581	+	2.60330i	−1.24018	+	0.597239i	−0.305317	+	0.952251i	$0.598762\pi$
$20$	−2.38699	−	2.99318i	−0.533746	−	0.669296i
$21$	−4.25745	−	5.33868i	−0.929053	−	1.16500i
$22$	−0.900969	−	0.433884i	−0.192087	−	0.0925043i
$23$	−0.813727	+	3.56517i	−0.169674	+	0.743389i	0.816455	+	0.577409i	$0.195936\pi$
$23$	−0.813727	+	3.56517i	−0.169674	+	0.743389i	−0.986129	+	0.165981i	$0.946921\pi$
$24$	2.37137	+	10.3897i	0.484055	+	2.12078i
$25$	3.60388	−	1.73553i	0.720775	−	0.347107i
$26$	−8.32733	−	4.01023i	−1.63312	−	0.786471i
$27$	0.0921712	+	0.403828i	0.0177384	+	0.0777168i
$28$	−10.8284			−2.04638
$29$		0			0
$29$		0			0
$30$	5.82843			1.06412
$31$	−2.24102	−	9.81857i	−0.402500	−	1.76347i	−0.617220	−	0.786791i	$-0.711741\pi$
$31$	−2.24102	−	9.81857i	−0.402500	−	1.76347i	0.214720	−	0.976676i	$-0.431116\pi$
$32$	−1.42874	−	0.688047i	−0.252569	−	0.121631i
$33$	0.900969	−	0.433884i	0.156839	−	0.0755295i
$34$	0.445042	+	1.94986i	0.0763241	+	0.334398i
$35$	−0.629384	+	2.75751i	−0.106385	+	0.466105i
$36$	−9.75608	−	4.69828i	−1.62601	−	0.783046i
$37$	−2.49396	−	3.12733i	−0.410004	−	0.514129i	0.533360	−	0.845889i	$-0.320929\pi$
$37$	−2.49396	−	3.12733i	−0.410004	−	0.514129i	−0.943364	+	0.331759i	$0.892358\pi$
$38$	−9.03143	−	11.3250i	−1.46509	−	1.83717i
$39$	8.32733	−	4.01023i	1.33344	−	0.642151i
$40$	2.75222	−	3.45117i	0.435164	−	0.545678i
$41$	−4.48528			−0.700483			−0.350242	−	0.936659i	$-0.613901\pi$
$41$	−4.48528			−0.700483			−0.350242	+	0.936659i	$0.613901\pi$
$42$	10.2784	−	12.8887i	1.58599	−	1.98877i
$43$	−0.797913	+	3.49588i	−0.121681	+	0.533117i	0.876940	+	0.480601i	$0.159581\pi$
$43$	−0.797913	+	3.49588i	−0.121681	+	0.533117i	−0.998620	+	0.0525165i	$0.983276\pi$
$44$	0.352871	−	1.54603i	0.0531973	−	0.233072i
$45$	−1.76350	+	2.21135i	−0.262886	+	0.329649i
$46$	−8.82843			−1.30168
$47$	−2.02175	+	2.53520i	−0.294903	+	0.369797i	−0.907105	−	0.420905i	$-0.861713\pi$
$47$	−2.02175	+	2.53520i	−0.294903	+	0.369797i	0.612202	+	0.790702i	$0.290284\pi$
$48$	−6.52539	+	3.14246i	−0.941859	+	0.453576i
$49$	0.623490	+	0.781831i	0.0890700	+	0.111690i
$50$	6.02095	+	7.55003i	0.851491	+	1.06774i
$51$	−1.80194	−	0.867767i	−0.252322	−	0.121512i
$52$	3.26146	−	14.2894i	0.452283	−	1.98158i
$53$	−2.11067	−	9.24747i	−0.289923	−	1.27024i	−0.884630	−	0.466294i	$-0.845589\pi$
$53$	−2.11067	−	9.24747i	−0.289923	−	1.27024i	0.594706	−	0.803943i	$-0.297268\pi$
$54$	−0.900969	+	0.433884i	−0.122606	+	0.0590441i
$55$	−0.373194	−	0.179721i	−0.0503214	−	0.0242335i
$56$	−2.77824	−	12.1722i	−0.371257	−	1.62659i
$57$	14.4853			1.91862
$58$		0			0
$59$	−3.65685			−0.476082			−0.238041	−	0.971255i	$-0.576505\pi$
$59$	−3.65685			−0.476082			−0.238041	+	0.971255i	$0.576505\pi$
$60$	2.05668	+	9.01091i	0.265516	+	1.16330i
$61$	4.35026	+	2.09498i	0.556994	+	0.268234i	0.691132	−	0.722728i	$-0.257112\pi$
$61$	4.35026	+	2.09498i	0.556994	+	0.268234i	−0.134138	+	0.990963i	$0.542827\pi$
$62$	21.9059	−	10.5493i	2.78205	−	1.33977i
$63$	1.78017	+	7.79942i	0.224280	+	0.982635i
$64$	2.18703	−	9.58201i	0.273379	−	1.19775i
$65$	−3.44929	−	1.66109i	−0.427832	−	0.206033i
$66$	1.50524	+	1.88751i	0.185282	+	0.232336i
$67$	3.52699	+	4.42271i	0.430891	+	0.540320i	0.949117	−	0.314924i	$-0.101979\pi$
$67$	3.52699	+	4.42271i	0.430891	+	0.540320i	−0.518226	+	0.855243i	$0.673408\pi$
$68$	−2.85749	+	1.37609i	−0.346521	+	0.166876i
$69$	5.50443	−	6.90234i	0.662656	−	0.830944i
$70$	−6.82843			−0.816153
$71$	−5.50443	+	6.90234i	−0.653256	+	0.819157i	−0.992590	−	0.121509i	$-0.961227\pi$
$71$	−5.50443	+	6.90234i	−0.653256	+	0.819157i	0.339334	+	0.940666i	$0.389798\pi$
$72$	2.77824	−	12.1722i	0.327418	−	1.43451i
$73$	−0.890084	+	3.89971i	−0.104176	+	0.456427i	0.895753	+	0.444552i	$0.146637\pi$
$73$	−0.890084	+	3.89971i	−0.104176	+	0.456427i	−0.999929	+	0.0118748i	$0.996220\pi$
$74$	6.02095	−	7.55003i	0.699921	−	0.877673i
$75$	−9.65685			−1.11508
$76$	14.3219	−	17.9591i	1.64284	−	2.06005i
$77$	−1.05555	+	0.508326i	−0.120291	+	0.0579292i
$78$	13.9124	+	17.4456i	1.57527	+	1.97532i
$79$	−1.50524	−	1.88751i	−0.169352	−	0.212361i	0.689911	−	0.723894i	$-0.257649\pi$
$79$	−1.50524	−	1.88751i	−0.169352	−	0.212361i	−0.859264	+	0.511532i	$0.829078\pi$
$80$	2.70291	+	1.30165i	0.302194	+	0.145529i
$81$	2.11067	−	9.24747i	0.234519	−	1.02750i
$82$	−2.40955	−	10.5569i	−0.266090	−	1.16582i
$83$	−6.89859	+	3.32218i	−0.757218	+	0.364657i	−0.772324	−	0.635229i	$-0.780906\pi$
$83$	−6.89859	+	3.32218i	−0.757218	+	0.364657i	0.0151057	+	0.999886i	$0.495192\pi$
$84$	23.5533	+	11.3426i	2.56987	+	1.23758i
$85$	0.184342	+	0.807657i	0.0199947	+	0.0876027i
$86$	−8.65685			−0.933493
$87$		0			0
$88$	1.82843			0.194911
$89$	2.77824	+	12.1722i	0.294492	+	1.29026i	0.878201	+	0.478292i	$0.158744\pi$
$89$	2.77824	+	12.1722i	0.294492	+	1.29026i	−0.583708	+	0.811964i	$0.698399\pi$
$90$	−6.15220	−	2.96274i	−0.648499	−	0.312301i
$91$	−9.75608	+	4.69828i	−1.02271	+	0.492513i
$92$	−3.11529	−	13.6490i	−0.324792	−	1.42301i
$93$	−5.41031	+	23.7041i	−0.561023	+	2.45800i
$94$	−7.05317	−	3.39663i	−0.727479	−	0.350335i
$95$	−3.74094	−	4.69099i	−0.383812	−	0.481285i
$96$	2.38699	+	2.99318i	0.243621	+	0.305491i
$97$	−4.04110	+	1.94609i	−0.410311	+	0.197596i	−0.627641	−	0.778503i	$-0.715980\pi$
$97$	−4.04110	+	1.94609i	−0.410311	+	0.197596i	0.217330	+	0.976098i	$0.430265\pi$
$98$	−1.50524	+	1.88751i	−0.152052	+	0.190667i
$99$	−1.17157			−0.117748
$100$	−9.54794	+	11.9727i	−0.954794	+	1.19727i
$101$	0.521399	−	2.28440i	0.0518811	−	0.227306i	−0.942340	−	0.334657i	$-0.891380\pi$
$101$	0.521399	−	2.28440i	0.0518811	−	0.227306i	0.994221	+	0.107351i	$0.0342368\pi$
$102$	1.07443	−	4.70737i	0.106384	−	0.466099i
$103$	−3.01048	+	3.77502i	−0.296631	+	0.371963i	−0.907704	−	0.419611i	$-0.862167\pi$
$103$	−3.01048	+	3.77502i	−0.296631	+	0.371963i	0.611073	+	0.791574i	$0.290738\pi$
$104$	16.8995			1.65713
$105$	4.25745	−	5.33868i	0.415485	−	0.521002i
$106$	20.6317	−	9.93572i	2.00393	−	0.965042i
$107$	−9.24537	−	11.5933i	−0.893784	−	1.12077i	−0.992079	−	0.125612i	$-0.959910\pi$
$107$	−9.24537	−	11.5933i	−0.893784	−	1.12077i	0.0982954	−	0.995157i	$-0.468661\pi$
$108$	−0.988722	−	1.23982i	−0.0951398	−	0.119302i
$109$	−11.4034	−	5.49160i	−1.09225	−	0.526000i	−0.201037	−	0.979584i	$-0.564431\pi$
$109$	−11.4034	−	5.49160i	−1.09225	−	0.526000i	−0.891214	+	0.453583i	$0.850145\pi$
$110$	0.222521	−	0.974928i	0.0212165	−	0.0929557i
$111$	2.14885	+	9.41474i	0.203960	+	0.893607i
$112$	7.64497	−	3.68163i	0.722382	−	0.347881i
$113$	11.9952	+	5.77660i	1.12842	+	0.543417i	0.902483	−	0.430726i	$-0.141742\pi$
$113$	11.9952	+	5.77660i	1.12842	+	0.543417i	0.225934	+	0.974143i	$0.427457\pi$
$114$	7.78168	+	34.0938i	0.728821	+	3.19317i
$115$	−3.65685			−0.341003
$116$		0			0
$117$	−10.8284			−1.00109
$118$	−1.96451	−	8.60708i	−0.180848	−	0.792346i
$119$	2.11110	+	1.01665i	0.193524	+	0.0931964i
$120$	−9.60149	+	4.62384i	−0.876492	+	0.422097i
$121$	2.40955	+	10.5569i	0.219050	+	0.959721i
$122$	−2.59389	+	11.3646i	−0.234840	+	1.02890i
$123$	9.75608	+	4.69828i	0.879676	+	0.423630i
$124$	24.0395	+	30.1446i	2.15881	+	2.70706i
$125$	5.61141	+	7.03648i	0.501900	+	0.629362i
$126$	−17.4011	+	8.37990i	−1.55021	+	0.746541i
$127$	−2.70791	+	3.39561i	−0.240288	+	0.301311i	−0.887323	−	0.461149i	$-0.847437\pi$
$127$	−2.70791	+	3.39561i	−0.240288	+	0.301311i	0.647035	+	0.762460i	$0.276009\pi$
$128$	20.5563			1.81694
$129$	5.39746	−	6.76820i	0.475220	−	0.595907i
$130$	2.05668	−	9.01091i	0.180383	−	0.790309i
$131$	−4.74275	+	20.7793i	−0.414376	+	1.81550i	0.148447	+	0.988920i	$0.452573\pi$
$131$	−4.74275	+	20.7793i	−0.414376	+	1.81550i	−0.562822	+	0.826578i	$0.690284\pi$
$132$	−2.38699	+	2.99318i	−0.207760	+	0.260523i
$133$	−16.9706			−1.47153
$134$	−8.51491	+	10.6774i	−0.735576	+	0.922383i
$135$	−0.373194	+	0.179721i	−0.0321194	+	0.0154679i
$136$	−2.28001	−	2.85904i	−0.195509	−	0.245161i
$137$	7.48188	+	9.38198i	0.639220	+	0.801556i	0.990905	−	0.134562i	$-0.0429627\pi$
$137$	7.48188	+	9.38198i	0.639220	+	0.801556i	−0.351685	+	0.936118i	$0.614391\pi$
$138$	19.2030	+	9.24767i	1.63467	+	0.787214i
$139$	−3.11529	+	13.6490i	−0.264236	+	1.15769i	0.652370	+	0.757900i	$0.273775\pi$
$139$	−3.11529	+	13.6490i	−0.264236	+	1.15769i	−0.916606	+	0.399792i	$0.869082\pi$
$140$	−2.40955	−	10.5569i	−0.203644	−	0.892224i
$141$	7.05317	−	3.39663i	0.593984	−	0.286048i
$142$	−19.2030	−	9.24767i	−1.61148	−	0.776047i
$143$	−0.352871	−	1.54603i	−0.0295085	−	0.129285i
$144$	8.48528			0.707107
$145$		0			0
$146$	−9.65685			−0.799207
$147$	−0.537213	−	2.35368i	−0.0443086	−	0.194129i
$148$	13.7972	+	6.64437i	1.13412	+	0.546164i
$149$	7.05317	−	3.39663i	0.577818	−	0.278263i	−0.122062	−	0.992522i	$-0.538951\pi$
$149$	7.05317	−	3.39663i	0.577818	−	0.278263i	0.699881	+	0.714260i	$0.253237\pi$
$150$	−5.18779	−	22.7292i	−0.423581	−	1.85583i
$151$	3.14692	−	13.7876i	0.256093	−	1.12202i	−0.669296	−	0.742996i	$-0.733404\pi$
$151$	3.14692	−	13.7876i	0.256093	−	1.12202i	0.925389	−	0.379020i	$-0.123739\pi$
$152$	23.8624	+	11.4915i	1.93550	+	0.932086i
$153$	1.46093	+	1.83195i	0.118109	+	0.148104i
$154$	−1.76350	−	2.21135i	−0.142107	−	0.178196i
$155$	9.07372	−	4.36967i	0.728819	−	0.350981i
$156$	−22.0620	+	27.6649i	−1.76638	+	2.21497i
$157$	8.48528			0.677199			0.338600	−	0.940931i	$-0.390047\pi$
$157$	8.48528			0.677199			0.338600	+	0.940931i	$0.390047\pi$
$158$	3.63396	−	4.55685i	0.289103	−	0.362523i
$159$	−5.09562	+	22.3254i	−0.404109	+	1.77052i
$160$	0.352871	−	1.54603i	0.0278969	−	0.122224i
$161$	−6.44885	+	8.08660i	−0.508240	+	0.637313i
$162$	22.8995			1.79915
$163$	2.44965	−	3.07176i	0.191871	−	0.240599i	−0.676585	−	0.736364i	$-0.736541\pi$
$163$	2.44965	−	3.07176i	0.191871	−	0.240599i	0.868457	+	0.495765i	$0.165112\pi$
$164$	15.4711	−	7.45047i	1.20809	−	0.581784i
$165$	0.623490	+	0.781831i	0.0485386	+	0.0608655i
$166$	−11.5254	−	14.4524i	−0.894543	−	1.12172i
$167$	2.85749	+	1.37609i	0.221119	+	0.106485i	0.541164	−	0.840917i	$-0.317984\pi$
$167$	2.85749	+	1.37609i	0.221119	+	0.106485i	−0.320045	+	0.947402i	$0.603698\pi$
$168$	−6.70726	+	29.3864i	−0.517476	+	2.26721i
$169$	−0.368685	−	1.61531i	−0.0283604	−	0.124255i
$170$	−1.80194	+	0.867767i	−0.138202	+	0.0665547i
$171$	−15.2899	−	7.36325i	−1.16925	−	0.563082i
$172$	−3.05475	−	13.3837i	−0.232923	−	1.02050i
$173$	12.3431			0.938432			0.469216	−	0.883083i	$-0.344537\pi$
$173$	12.3431			0.938432			0.469216	+	0.883083i	$0.344537\pi$
$174$		0			0
$175$	11.3137			0.855236
$176$	0.276514	+	1.21149i	0.0208430	+	0.0913191i
$177$	7.95414	+	3.83051i	0.597870	+	0.287919i
$178$	−27.1571	+	13.0782i	−2.03551	+	0.980251i
$179$	1.44311	+	6.32268i	0.107863	+	0.472579i	0.999792	+	0.0204033i	$0.00649502\pi$
$179$	1.44311	+	6.32268i	0.107863	+	0.472579i	−0.891929	+	0.452176i	$0.850648\pi$
$180$	2.40955	−	10.5569i	0.179597	−	0.786868i
$181$	−7.49039	−	3.60718i	−0.556756	−	0.268120i	0.134275	−	0.990944i	$-0.457129\pi$
$181$	−7.49039	−	3.60718i	−0.556756	−	0.268120i	−0.691032	+	0.722824i	$0.742844\pi$
$182$	−16.2994	−	20.4387i	−1.20819	−	1.51502i
$183$	−7.26793	−	9.11370i	−0.537261	−	0.673704i
$184$	14.5436	−	7.00381i	1.07217	−	0.516328i
$185$	2.49396	−	3.12733i	0.183360	−	0.229926i
$186$	−58.6985			−4.30398
$187$	−0.213948	+	0.268282i	−0.0156454	+	0.0196187i
$188$	2.76242	−	12.1030i	0.201470	−	0.882699i
$189$	−0.260699	+	1.14220i	−0.0189631	+	0.0830828i
$190$	9.03143	−	11.3250i	0.655208	−	0.821605i
$191$	25.3137			1.83164			0.915818	−	0.401594i	$-0.131544\pi$
$191$	25.3137			1.83164			0.915818	+	0.401594i	$0.131544\pi$
$192$	−14.7941	+	18.5512i	−1.06767	+	1.33882i
$193$	4.65943	−	2.24386i	0.335393	−	0.161517i	−0.258605	−	0.965983i	$-0.583263\pi$
$193$	4.65943	−	2.24386i	0.335393	−	0.161517i	0.593998	+	0.804466i	$0.297549\pi$
$194$	−6.75141	−	8.46601i	−0.484723	−	0.607824i
$195$	5.76269	+	7.22619i	0.412675	+	0.517478i
$196$	−3.44929	−	1.66109i	−0.246378	−	0.118649i
$197$	−0.445042	+	1.94986i	−0.0317079	+	0.138921i	−0.988304	−	0.152495i	$-0.951269\pi$
$197$	−0.445042	+	1.94986i	−0.0317079	+	0.138921i	0.956596	+	0.291416i	$0.0941264\pi$
$198$	−0.629384	−	2.75751i	−0.0447284	−	0.195968i
$199$	0.437223	−	0.210556i	0.0309939	−	0.0149259i	−0.418323	−	0.908299i	$-0.637382\pi$
$199$	0.437223	−	0.210556i	0.0309939	−	0.0149259i	0.449317	+	0.893373i	$0.351668\pi$
$200$	−15.9083	−	7.66102i	−1.12488	−	0.541716i
$201$	−3.03894	−	13.3144i	−0.214350	−	0.939129i
$202$	5.65685			0.398015
$203$		0			0
$204$	7.65685			0.536087
$205$	−0.998069	−	4.37283i	−0.0697082	−	0.305411i
$206$	−10.5025	−	5.05772i	−0.731741	−	0.352388i
$207$	−9.31885	+	4.48772i	−0.647705	+	0.311918i
$208$	2.55572	+	11.1973i	0.177207	+	0.776395i
$209$	0.553027	−	2.42297i	0.0382537	−	0.167600i
$210$	14.8527	+	7.15270i	1.02494	+	0.493583i
$211$	−12.0862	−	15.1556i	−0.832049	−	1.04336i	−0.998358	−	0.0572828i	$-0.981756\pi$
$211$	−12.0862	−	15.1556i	−0.832049	−	1.04336i	0.166309	−	0.986074i	$-0.446815\pi$
$212$	22.6412	+	28.3912i	1.55501	+	1.94992i
$213$	19.2030	−	9.24767i	1.31577	−	0.633640i
$214$	22.3203	−	27.9888i	1.52578	−	1.91327i
$215$	−3.58579			−0.244549
$216$	1.14001	−	1.42952i	0.0775676	−	0.0972666i
$217$	6.33857	−	27.7711i	0.430290	−	1.88522i
$218$	6.79943	−	29.7902i	0.460515	−	2.01765i
$219$	6.02095	−	7.55003i	0.406858	−	0.510184i
$220$	1.58579			0.106914
$221$	−1.97744	+	2.47964i	−0.133017	+	0.166798i
$222$	−21.0049	+	10.1154i	−1.40976	+	0.678904i
$223$	−1.97744	−	2.47964i	−0.132419	−	0.166049i	0.711201	−	0.702989i	$-0.248152\pi$
$223$	−1.97744	−	2.47964i	−0.132419	−	0.166049i	−0.843620	+	0.536940i	$0.819580\pi$
$224$	−2.79653	−	3.50673i	−0.186851	−	0.234304i
$225$	10.1933	+	4.90883i	0.679553	+	0.327256i
$226$	−7.15230	+	31.3363i	−0.475764	+	2.08446i
$227$	1.81180	+	7.93800i	0.120253	+	0.526863i	0.998790	+	0.0491879i	$0.0156633\pi$
$227$	1.81180	+	7.93800i	0.120253	+	0.526863i	−0.878536	+	0.477675i	$0.841480\pi$
$228$	−49.9640	+	24.0614i	−3.30895	+	1.59350i
$229$	3.16665	+	1.52498i	0.209258	+	0.100773i	0.535577	−	0.844486i	$-0.320094\pi$
$229$	3.16665	+	1.52498i	0.209258	+	0.100773i	−0.326319	+	0.945260i	$0.605808\pi$
$230$	−1.96451	−	8.60708i	−0.129536	−	0.567534i
$231$	2.82843			0.186097
$232$		0			0
$233$	18.3137			1.19977			0.599885	−	0.800086i	$-0.295213\pi$
$233$	18.3137			1.19977			0.599885	+	0.800086i	$0.295213\pi$
$234$	−5.81717	−	25.4867i	−0.380280	−	1.66612i
$235$	−2.92152	−	1.40693i	−0.190579	−	0.0917779i
$236$	12.6136	−	6.07437i	0.821073	−	0.395408i
$237$	1.29695	+	5.68230i	0.0842458	+	0.369105i
$238$	−1.25877	+	5.51503i	−0.0815938	+	0.357486i
$239$	17.7102	+	8.52879i	1.14558	+	0.551682i	0.907703	−	0.419614i	$-0.137835\pi$
$239$	17.7102	+	8.52879i	1.14558	+	0.551682i	0.237876	+	0.971296i	$0.423549\pi$
$240$	−4.51571	−	5.66252i	−0.291488	−	0.365514i
$241$	−11.4184	−	14.3182i	−0.735524	−	0.922319i	0.263580	−	0.964638i	$-0.415097\pi$
$241$	−11.4184	−	14.3182i	−0.735524	−	0.922319i	−0.999104	+	0.0423191i	$0.986525\pi$
$242$	−23.5533	+	11.3426i	−1.51406	+	0.729133i
$243$	−13.5028	+	16.9320i	−0.866207	+	1.08619i
$244$	−18.4853			−1.18340
$245$	−0.623490	+	0.781831i	−0.0398333	+	0.0499494i
$246$	−5.81717	+	25.4867i	−0.370889	+	1.62497i
$247$	5.11143	−	22.3946i	0.325233	−	1.42494i
$248$	−27.7178	+	34.7570i	−1.76008	+	2.20707i
$249$	18.4853			1.17146
$250$	−13.5471	+	16.9876i	−0.856796	+	1.07439i
$251$	−18.0834	+	8.70851i	−1.14141	+	0.549676i	−0.906444	−	0.422326i	$-0.861214\pi$
$251$	−18.0834	+	8.70851i	−1.14141	+	0.549676i	−0.234971	+	0.972002i	$0.575499\pi$
$252$	−19.0959	−	23.9455i	−1.20293	−	1.50842i
$253$	−0.944412	−	1.18425i	−0.0593746	−	0.0744535i
$254$	−9.44691	−	4.54939i	−0.592752	−	0.285454i
$255$	0.445042	−	1.94986i	0.0278696	−	0.122105i
$256$	6.66908	+	29.2191i	0.416817	+	1.82620i
$257$	16.3720	−	7.88435i	1.02126	−	0.491812i	0.153159	−	0.988202i	$-0.451055\pi$
$257$	16.3720	−	7.88435i	1.02126	−	0.491812i	0.868100	+	0.496389i	$0.165341\pi$
$258$	18.8298	+	9.06795i	1.17229	+	0.564546i
$259$	−2.51754	−	11.0301i	−0.156432	−	0.685374i
$260$	14.6569			0.908980
$261$		0			0
$262$	−51.4558			−3.17895
$263$	−0.613570	−	2.68823i	−0.0378344	−	0.165763i	0.952481	−	0.304597i	$-0.0985218\pi$
$263$	−0.613570	−	2.68823i	−0.0378344	−	0.165763i	−0.990316	+	0.138834i	$0.955665\pi$
$264$	−3.97707	−	1.91526i	−0.244772	−	0.117876i
$265$	8.54594	−	4.11551i	0.524973	−	0.252814i
$266$	−9.11681	−	39.9433i	−0.558987	−	2.44908i
$267$	6.70726	−	29.3864i	0.410477	−	1.79842i
$268$	−19.5122	−	9.39656i	−1.19189	−	0.573986i
$269$	19.6124	+	24.5932i	1.19579	+	1.49947i	0.819607	+	0.572926i	$0.194192\pi$
$269$	19.6124	+	24.5932i	1.19579	+	1.49947i	0.376182	+	0.926546i	$0.377237\pi$
$270$	−0.623490	−	0.781831i	−0.0379444	−	0.0475807i
$271$	−14.9168	+	7.18353i	−0.906128	+	0.436368i	−0.828099	−	0.560583i	$-0.810577\pi$
$271$	−14.9168	+	7.18353i	−0.906128	+	0.436368i	−0.0780298	+	0.996951i	$0.524863\pi$
$272$	1.54955	−	1.94307i	0.0939551	−	0.117816i
$273$	26.1421			1.58219
$274$	−18.0629	+	22.6501i	−1.09122	+	1.36834i
$275$	−0.368685	+	1.61531i	−0.0222325	+	0.0974071i
$276$	−7.52098	+	32.9516i	−0.452710	+	1.98345i
$277$	−10.7949	+	13.5364i	−0.648604	+	0.813324i	−0.992049	−	0.125849i	$-0.959835\pi$
$277$	−10.7949	+	13.5364i	−0.648604	+	0.813324i	0.343445	+	0.939173i	$0.388406\pi$
$278$	−33.7990			−2.02713
$279$	17.7603	−	22.2707i	1.06328	−	1.33331i
$280$	11.2488	−	5.41716i	0.672247	−	0.323737i
$281$	19.9333	+	24.9956i	1.18912	+	1.49111i	0.829947	+	0.557842i	$0.188370\pi$
$281$	19.9333	+	24.9956i	1.18912	+	1.49111i	0.359175	+	0.933270i	$0.383058\pi$
$282$	11.7836	+	14.7762i	0.701706	+	0.879911i
$283$	−10.5025	−	5.05772i	−0.624307	−	0.300650i	0.0948571	−	0.995491i	$-0.469761\pi$
$283$	−10.5025	−	5.05772i	−0.624307	−	0.300650i	−0.719164	+	0.694841i	$0.755475\pi$
$284$	7.52098	−	32.9516i	0.446288	−	1.95532i
$285$	3.22328	+	14.1221i	0.190931	+	0.836521i
$286$	3.44929	−	1.66109i	0.203961	−	0.0982224i
$287$	−11.4300	−	5.50438i	−0.674689	−	0.324913i
$288$	−0.998069	−	4.37283i	−0.0588118	−	0.257671i
$289$	−16.3137			−0.959630
$290$		0			0
$291$	10.8284			0.634774
$292$	−3.40762	−	14.9298i	−0.199416	−	0.873698i
$293$	−6.89859	−	3.32218i	−0.403020	−	0.194084i	0.221382	−	0.975187i	$-0.428943\pi$
$293$	−6.89859	−	3.32218i	−0.403020	−	0.194084i	−0.624402	+	0.781103i	$0.714657\pi$
$294$	5.25123	−	2.52886i	0.306258	−	0.147486i
$295$	−0.813727	−	3.56517i	−0.0473770	−	0.207572i
$296$	−3.92902	+	17.2142i	−0.228370	+	1.00055i
$297$	−0.154582	−	0.0744427i	−0.00896975	−	0.00431960i
$298$	11.7836	+	14.7762i	0.682608	+	0.855963i
$299$	−8.72886	−	10.9456i	−0.504803	−	0.633003i
$300$	33.3093	−	16.0409i	1.92311	−	0.926123i
$301$	−6.32352	+	7.92944i	−0.364482	+	0.457045i
$302$	34.1421			1.96466
$303$	−3.52699	+	4.42271i	−0.202620	+	0.254078i
$304$	−4.00538	+	17.5487i	−0.229724	+	1.00649i
$305$	−1.07443	+	4.70737i	−0.0615215	+	0.269543i
$306$	−3.52699	+	4.42271i	−0.201625	+	0.252829i
$307$	2.89949			0.165483			0.0827415	−	0.996571i	$-0.473632\pi$
$307$	2.89949			0.165483			0.0827415	+	0.996571i	$0.473632\pi$
$308$	2.79653	−	3.50673i	0.159347	−	0.199815i
$309$	10.5025	−	5.05772i	0.597464	−	0.287724i
$310$	15.1593	+	19.0092i	0.860993	+	1.07965i
$311$	1.67488	+	2.10023i	0.0949735	+	0.119093i	0.827047	−	0.562132i	$-0.190019\pi$
$311$	1.67488	+	2.10023i	0.0949735	+	0.119093i	−0.732074	+	0.681225i	$0.761447\pi$
$312$	−36.7586	−	17.7020i	−2.08105	−	1.00218i
$313$	−2.18703	+	9.58201i	−0.123618	+	0.541607i	0.874754	+	0.484568i	$0.161023\pi$
$313$	−2.18703	+	9.58201i	−0.123618	+	0.541607i	−0.998372	+	0.0570392i	$0.981834\pi$
$314$	4.55840	+	19.9717i	0.257246	+	1.12707i
$315$	−7.20775	+	3.47107i	−0.406111	+	0.195573i
$316$	8.32733	+	4.01023i	0.468449	+	0.225593i
$317$	6.99958	+	30.6672i	0.393136	+	1.72244i	0.653497	+	0.756929i	$0.273301\pi$
$317$	6.99958	+	30.6672i	0.393136	+	1.72244i	−0.260361	+	0.965511i	$0.583842\pi$
$318$	−55.2843			−3.10019
$319$		0			0
$320$	9.82843			0.549426
$321$	7.96602	+	34.9014i	0.444620	+	1.94801i
$322$	−22.4977	−	10.8343i	−1.25375	−	0.603773i
$323$	−4.47832	+	2.15665i	−0.249181	+	0.119999i
$324$	8.08056	+	35.4032i	0.448920	+	1.96685i
$325$	−3.40762	+	14.9298i	−0.189021	+	0.828154i
$326$	8.54594	+	4.11551i	0.473316	+	0.227937i
$327$	19.0516	+	23.8899i	1.05355	+	1.32112i
$328$	12.3445	+	15.4795i	0.681609	+	0.854711i
$329$	−8.26330	+	3.97940i	−0.455571	+	0.219391i
$330$	−1.50524	+	1.88751i	−0.0828606	+	0.103904i
$331$	−2.41421			−0.132697			−0.0663486	−	0.997797i	$-0.521135\pi$
$331$	−2.41421			−0.132697			−0.0663486	+	0.997797i	$0.521135\pi$
$332$	18.2768	−	22.9184i	1.00307	−	1.25781i
$333$	2.51754	−	11.0301i	0.137960	−	0.604443i
$334$	−1.70381	+	7.46488i	−0.0932284	+	0.408460i
$335$	−3.52699	+	4.42271i	−0.192700	+	0.241638i
$336$	−20.4853			−1.11756
$337$	13.5914	−	17.0431i	0.740373	−	0.928399i	−0.258923	−	0.965898i	$-0.583368\pi$
$337$	13.5914	−	17.0431i	0.740373	−	0.928399i	0.999297	+	0.0374991i	$0.0119391\pi$
$338$	3.60388	−	1.73553i	0.196025	−	0.0944007i
$339$	−20.0403	−	25.1297i	−1.08844	−	1.36486i
$340$	−1.97744	−	2.47964i	−0.107242	−	0.134477i
$341$	3.75846	+	1.80998i	0.203532	+	0.0980158i
$342$	9.11681	−	39.9433i	0.492981	−	2.15989i
$343$	−3.77631	−	16.5451i	−0.203901	−	0.893350i
$344$	14.2609	−	6.86770i	0.768897	−	0.370281i
$345$	7.95414	+	3.83051i	0.428236	+	0.206228i
$346$	6.63090	+	29.0519i	0.356479	+	1.56184i
$347$	2.48528			0.133417			0.0667084	−	0.997773i	$-0.478750\pi$
$347$	2.48528			0.133417			0.0667084	+	0.997773i	$0.478750\pi$
$348$		0			0
$349$	−5.14214			−0.275252			−0.137626	−	0.990484i	$-0.543947\pi$
$349$	−5.14214			−0.275252			−0.137626	+	0.990484i	$0.543947\pi$
$350$	6.07787	+	26.6289i	0.324876	+	1.42337i
$351$	−1.42874	−	0.688047i	−0.0762607	−	0.0367252i
$352$	0.591805	−	0.284998i	0.0315433	−	0.0151905i
$353$	−6.00151	−	26.2944i	−0.319428	−	1.39951i	−0.838558	−	0.544812i	$-0.816601\pi$
$353$	−6.00151	−	26.2944i	−0.319428	−	1.39951i	0.519130	−	0.854695i	$-0.326256\pi$
$354$	−4.74275	+	20.7793i	−0.252074	+	1.10441i
$355$	−7.95414	−	3.83051i	−0.422162	−	0.203302i
$356$	−29.8022	−	37.3708i	−1.57951	−	1.98065i
$357$	−3.52699	−	4.42271i	−0.186668	−	0.234074i
$358$	−14.1063	+	6.79325i	−0.745543	+	0.359035i
$359$	2.44965	−	3.07176i	0.129288	−	0.162121i	−0.712974	−	0.701190i	$-0.752652\pi$
$359$	2.44965	−	3.07176i	0.129288	−	0.162121i	0.842262	+	0.539069i	$0.181224\pi$
$360$	12.4853			0.658032
$361$	10.5993	−	13.2911i	0.557859	−	0.699533i
$362$	4.46623	−	19.5678i	0.234740	−	1.02846i
$363$	5.81717	−	25.4867i	0.305322	−	1.33770i
$364$	25.8473	−	32.4115i	1.35477	−	1.69882i
$365$	−4.00000			−0.209370
$366$	17.5463	−	22.0024i	0.917162	−	1.15008i
$367$	−16.2174	+	7.80991i	−0.846543	+	0.407674i	−0.806293	−	0.591516i	$-0.798530\pi$
$367$	−16.2174	+	7.80991i	−0.846543	+	0.407674i	−0.0402500	+	0.999190i	$0.512815\pi$
$368$	6.84003	+	8.57713i	0.356561	+	0.447114i
$369$	−7.90977	−	9.91854i	−0.411766	−	0.516339i
$370$	8.70053	+	4.18995i	0.452319	+	0.217825i
$371$	5.96989	−	26.1558i	0.309941	−	1.35794i
$372$	−20.7130	−	90.7495i	−1.07392	−	4.70514i
$373$	23.7078	−	11.4171i	1.22755	−	0.591155i	0.296142	−	0.955144i	$-0.404300\pi$
$373$	23.7078	−	11.4171i	1.22755	−	0.591155i	0.931403	+	0.363989i	$0.118586\pi$
$374$	−0.746387	−	0.359441i	−0.0385948	−	0.0185863i
$375$	−4.83492	−	21.1832i	−0.249674	−	1.09389i
$376$	14.3137			0.738173
$377$		0			0
$378$	−2.82843			−0.145479
$379$	1.55110	+	6.79580i	0.0796745	+	0.349077i	0.999014	−	0.0443876i	$-0.0141337\pi$
$379$	1.55110	+	6.79580i	0.0796745	+	0.349077i	−0.919340	+	0.393464i	$0.871277\pi$
$380$	20.6958	+	9.96655i	1.06167	+	0.511273i
$381$	9.44691	−	4.54939i	0.483980	−	0.233072i
$382$	13.5989	+	59.5805i	0.695778	+	3.04840i
$383$	0.782098	−	3.42660i	0.0399634	−	0.175091i	−0.951008	−	0.309167i	$-0.899950\pi$
$383$	0.782098	−	3.42660i	0.0399634	−	0.175091i	0.990971	+	0.134077i	$0.0428068\pi$
$384$	−44.7128	−	21.5325i	−2.28174	−	1.09883i
$385$	−0.730464	−	0.915973i	−0.0372279	−	0.0466823i
$386$	7.78445	+	9.76139i	0.396218	+	0.496841i
$387$	−9.13775	+	4.40051i	−0.464498	+	0.223690i
$388$	10.7063	−	13.4253i	0.543530	−	0.681565i
$389$	3.02944			0.153599			0.0767993	−	0.997047i	$-0.475530\pi$
$389$	3.02944			0.153599			0.0767993	+	0.997047i	$0.475530\pi$
$390$	−13.9124	+	17.4456i	−0.704480	+	0.883390i
$391$	−0.674113	+	2.95348i	−0.0340914	+	0.149364i
$392$	0.982255	−	4.30354i	0.0496114	−	0.217362i
$393$	32.0822	−	40.2298i	1.61833	−	2.02932i
$394$	−4.82843			−0.243253
$395$	1.50524	−	1.88751i	0.0757367	−	0.0949708i
$396$	4.04110	−	1.94609i	0.203073	−	0.0977947i
$397$	12.0603	+	15.1231i	0.605287	+	0.759006i	0.986192	−	0.165609i	$-0.0529589\pi$
$397$	12.0603	+	15.1231i	0.605287	+	0.759006i	−0.380905	+	0.924614i	$0.624387\pi$
$398$	0.730464	+	0.915973i	0.0366148	+	0.0459136i
$399$	36.9132	+	17.7765i	1.84797	+	0.889936i
$400$	2.67025	−	11.6991i	0.133513	−	0.584957i
$401$	4.15154	+	18.1891i	0.207318	+	0.908320i	0.966343	+	0.257258i	$0.0828190\pi$
$401$	4.15154	+	18.1891i	0.207318	+	0.908320i	−0.759025	+	0.651062i	$0.774324\pi$
$402$	29.7055	−	14.3054i	1.48157	−	0.713488i
$403$	34.7381	+	16.7290i	1.73043	+	0.833329i
$404$	1.99614	+	8.74565i	0.0993116	+	0.435112i
$405$	9.48528			0.471327
$406$		0			0
$407$	1.65685			0.0821272
$408$	1.96451	+	8.60708i	0.0972577	+	0.426114i
$409$	17.0919	+	8.23102i	0.845139	+	0.406998i	0.805771	−	0.592227i	$-0.201751\pi$
$409$	17.0919	+	8.23102i	0.845139	+	0.406998i	0.0393683	+	0.999225i	$0.487465\pi$
$410$	9.75608	−	4.69828i	0.481818	−	0.232031i
$411$	−6.44656	−	28.2442i	−0.317985	−	1.39318i
$412$	4.11336	−	18.0218i	0.202651	−	0.887871i
$413$	−9.31885	−	4.48772i	−0.458551	−	0.220826i
$414$	−15.5689	−	19.5228i	−0.765169	−	0.959492i
$415$	−4.77397	−	5.98637i	−0.234345	−	0.293859i
$416$	5.46984	−	2.63414i	0.268181	−	0.129149i
$417$	21.0733	−	26.4251i	1.03197	−	1.29404i
$418$	6.00000			0.293470
$419$	−5.93233	+	7.43891i	−0.289813	+	0.363414i	−0.905330	−	0.424710i	$-0.860376\pi$
$419$	−5.93233	+	7.43891i	−0.289813	+	0.363414i	0.615516	+	0.788124i	$0.288948\pi$
$420$	−5.81717	+	25.4867i	−0.283849	+	1.24362i
$421$	−8.25835	+	36.1822i	−0.402487	+	1.76341i	0.214783	+	0.976662i	$0.431096\pi$
$421$	−8.25835	+	36.1822i	−0.402487	+	1.76341i	−0.617270	+	0.786751i	$0.711762\pi$
$422$	29.1787	−	36.5889i	1.42040	−	1.78112i
$423$	−9.17157			−0.445937
$424$	−26.1056	+	32.7353i	−1.26780	+	1.58977i
$425$	2.98555	−	1.43776i	0.144820	−	0.0697418i
$426$	32.0822	+	40.2298i	1.55439	+	1.94914i
$427$	8.51491	+	10.6774i	0.412065	+	0.516714i
$428$	51.1476	+	24.6314i	2.47231	+	1.19060i
$429$	−0.851905	+	3.73244i	−0.0411304	+	0.180204i
$430$	−1.92633	−	8.43981i	−0.0928959	−	0.407004i
$431$	−17.7102	+	8.52879i	−0.853071	+	0.410817i	−0.808717	−	0.588199i	$-0.799837\pi$
$431$	−17.7102	+	8.52879i	−0.853071	+	0.410817i	−0.0443544	+	0.999016i	$0.514123\pi$
$432$	1.11958	+	0.539162i	0.0538658	+	0.0259404i
$433$	−6.81524	−	29.8595i	−0.327520	−	1.43496i	−0.823842	−	0.566819i	$-0.808174\pi$
$433$	−6.81524	−	29.8595i	−0.327520	−	1.43496i	0.496323	−	0.868138i	$-0.334683\pi$
$434$	68.7696			3.30104
$435$		0			0
$436$	48.4558			2.32061
$437$	−4.88236	−	21.3910i	−0.233555	−	1.02327i
$438$	21.0049	+	10.1154i	1.00365	+	0.483334i
$439$	0.309164	−	0.148885i	0.0147556	−	0.00710591i	−0.426491	−	0.904492i	$-0.640251\pi$
$439$	0.309164	−	0.148885i	0.0147556	−	0.00710591i	0.441247	+	0.897386i	$0.354536\pi$
$440$	0.406863	+	1.78258i	0.0193964	+	0.0849814i
$441$	−0.629384	+	2.75751i	−0.0299707	+	0.131310i
$442$	−6.89859	−	3.32218i	−0.328132	−	0.158020i
$443$	−15.1777	−	19.0322i	−0.721114	−	0.904249i	0.277286	−	0.960787i	$-0.410565\pi$
$443$	−15.1777	−	19.0322i	−0.721114	−	0.904249i	−0.998400	+	0.0565385i	$0.981994\pi$
$444$	−23.0508	−	28.9047i	−1.09394	−	1.37176i
$445$	−11.2488	+	5.41716i	−0.533247	+	0.256798i
$446$	4.77397	−	5.98637i	0.226054	−	0.283463i
$447$	−18.8995			−0.893915
$448$	17.3324	−	21.7341i	0.818878	−	1.02684i
$449$	7.78168	−	34.0938i	0.367240	−	1.60898i	−0.367085	−	0.930187i	$-0.619644\pi$
$449$	7.78168	−	34.0938i	0.367240	−	1.60898i	0.734325	−	0.678798i	$-0.237499\pi$
$450$	−6.07787	+	26.6289i	−0.286514	+	1.25530i
$451$	1.15836	−	1.45254i	0.0545450	−	0.0683973i
$452$	−50.9706			−2.39745
$453$	−21.2873	+	26.6934i	−1.00016	+	1.25417i
$454$	−17.7102	+	8.52879i	−0.831182	+	0.400276i
$455$	−6.75141	−	8.46601i	−0.316511	−	0.396892i
$456$	−39.8666	−	49.9912i	−1.86693	−	2.34105i
$457$	−0.927491	−	0.446656i	−0.0433862	−	0.0208937i	0.412065	−	0.911155i	$-0.364808\pi$
$457$	−0.927491	−	0.446656i	−0.0433862	−	0.0208937i	−0.455451	+	0.890261i	$0.650522\pi$
$458$	−1.88815	+	8.27254i	−0.0882276	+	0.386550i
$459$	0.0763571	+	0.334542i	0.00356404	+	0.0156151i
$460$	12.6136	−	6.07437i	0.588110	−	0.283219i
$461$	−12.6136	−	6.07437i	−0.587472	−	0.282912i	0.116441	−	0.993198i	$-0.462851\pi$
$461$	−12.6136	−	6.07437i	−0.587472	−	0.282912i	−0.703913	+	0.710286i	$0.748566\pi$
$462$	1.51947	+	6.65722i	0.0706920	+	0.309722i
$463$	−26.0000			−1.20832			−0.604161	−	0.796862i	$-0.706492\pi$
$463$	−26.0000			−1.20832			−0.604161	+	0.796862i	$0.706492\pi$
$464$		0			0
$465$	−24.3137			−1.12752
$466$	9.83836	+	43.1047i	0.455753	+	1.99679i
$467$	34.5570	+	16.6418i	1.59911	+	0.770089i	0.999543	−	0.0302389i	$-0.00962679\pi$
$467$	34.5570	+	16.6418i	1.59911	+	0.770089i	0.599563	+	0.800328i	$0.295341\pi$
$468$	37.3504	−	17.9870i	1.72652	−	0.831450i
$469$	3.56033	+	15.5988i	0.164401	+	0.720288i
$470$	1.74199	−	7.63215i	0.0803520	−	0.352045i
$471$	−18.4566	−	8.88823i	−0.850435	−	0.409548i
$472$	10.0645	+	12.6204i	0.463254	+	0.580902i
$473$	−0.926058	−	1.16124i	−0.0425802	−	0.0533939i
$474$	−12.6776	+	6.10521i	−0.582301	+	0.280421i
$475$	−14.9638	+	18.7640i	−0.686584	+	0.860949i
$476$	−8.97056			−0.411165
$477$	16.7273	−	20.9753i	0.765888	−	0.960393i
$478$	−10.5599	+	46.2660i	−0.482999	+	2.11616i
$479$	−1.53528	+	6.72651i	−0.0701488	+	0.307342i	−0.997815	−	0.0660682i	$-0.978954\pi$
$479$	−1.53528	+	6.72651i	−0.0701488	+	0.307342i	0.927666	+	0.373410i	$0.121812\pi$
$480$	−2.38699	+	2.99318i	−0.108950	+	0.136620i
$481$	15.3137			0.698245
$482$	27.5665	−	34.5673i	1.25562	−	1.57450i
$483$	22.4977	−	10.8343i	1.02368	−	0.492979i
$484$	−25.8473	−	32.4115i	−1.17488	−	1.47325i
$485$	−2.79653	−	3.50673i	−0.126984	−	0.159233i
$486$	−47.1065	−	22.6853i	−2.13679	−	1.02903i
$487$	2.56227	−	11.2260i	0.116107	−	0.508700i	−0.883111	−	0.469164i	$-0.844555\pi$
$487$	2.56227	−	11.2260i	0.116107	−	0.508700i	0.999218	−	0.0395351i	$-0.0125877\pi$
$488$	−4.74275	−	20.7793i	−0.214694	−	0.940636i
$489$	−8.54594	+	4.11551i	−0.386461	+	0.186110i
$490$	−2.17513	−	1.04749i	−0.0982624	−	0.0473207i
$491$	4.72693	+	20.7100i	0.213323	+	0.934631i	0.962290	+	0.272024i	$0.0876930\pi$
$491$	4.72693	+	20.7100i	0.213323	+	0.934631i	−0.748967	+	0.662607i	$0.769450\pi$
$492$	−41.4558			−1.86897
$493$		0			0
$494$	55.4558			2.49508
$495$	−0.260699	−	1.14220i	−0.0117176	−	0.0513380i
$496$	−27.2212	−	13.1090i	−1.22227	−	0.588612i
$497$	−22.4977	+	10.8343i	−1.00916	+	0.485986i
$498$	9.93053	+	43.5085i	0.444998	+	1.94966i
$499$	−4.22135	+	18.4949i	−0.188973	+	0.827947i	0.788186	+	0.615438i	$0.211021\pi$
$499$	−4.22135	+	18.4949i	−0.188973	+	0.827947i	−0.977159	+	0.212509i	$0.931836\pi$
$500$	−31.0436	−	14.9498i	−1.38831	−	0.668577i
$501$	−4.77397	−	5.98637i	−0.213285	−	0.267451i
$502$	−30.2117	−	37.8843i	−1.34842	−	1.69086i
$503$	−0.245134	+	0.118050i	−0.0109300	+	0.00526360i	−0.439341	−	0.898320i	$-0.644788\pi$
$503$	−0.245134	+	0.118050i	−0.0109300	+	0.00526360i	0.428411	+	0.903584i	$0.359074\pi$
$504$	22.0177	−	27.6094i	0.980748	−	1.22982i
$505$	2.34315			0.104269
$506$	2.28001	−	2.85904i	0.101359	−	0.127100i
$507$	−0.890084	+	3.89971i	−0.0395300	+	0.173192i
$508$	3.69995	−	16.2105i	0.164159	−	0.719226i
$509$	−6.55582	+	8.22074i	−0.290582	+	0.364378i	−0.905598	−	0.424136i	$-0.860578\pi$
$509$	−6.55582	+	8.22074i	−0.290582	+	0.364378i	0.615017	+	0.788514i	$0.289149\pi$
$510$	4.82843			0.213806
$511$	−7.05398	+	8.84541i	−0.312050	+	0.391298i
$512$	−28.1486	+	13.5557i	−1.24401	+	0.599082i
$513$	−1.54955	−	1.94307i	−0.0684142	−	0.0857887i
$514$	27.3525	+	34.2990i	1.20647	+	1.51286i
$515$	−4.35026	−	2.09498i	−0.191695	−	0.0923157i
$516$	−7.37482	+	32.3112i	−0.324658	+	1.42242i
$517$	−0.298878	−	1.30947i	−0.0131446	−	0.0575904i
$518$	24.6088	−	11.8510i	1.08125	−	0.520702i
$519$	−26.8480	−	12.9293i	−1.17849	−	0.567533i
$520$	3.76049	+	16.4758i	0.164908	+	0.722511i
$521$	−29.1421			−1.27674			−0.638370	−	0.769730i	$-0.720391\pi$
$521$	−29.1421			−1.27674			−0.638370	+	0.769730i	$0.720391\pi$
$522$		0			0
$523$	4.68629			0.204917			0.102459	−	0.994737i	$-0.467329\pi$
$523$	4.68629			0.204917			0.102459	+	0.994737i	$0.467329\pi$
$524$	−18.1573	−	79.5521i	−0.793204	−	3.47525i
$525$	−24.6088	−	11.8510i	−1.07402	−	0.517219i
$526$	5.99762	−	2.88830i	0.261509	−	0.125936i
$527$	−1.85652	−	8.13397i	−0.0808715	−	0.354321i
$528$	0.667563	−	2.92478i	0.0290519	−	0.127285i
$529$	8.67400	+	4.17718i	0.377131	+	0.181617i
$530$	14.2776	+	17.9035i	0.620179	+	0.777680i
$531$	−6.44885	−	8.08660i	−0.279856	−	0.350928i
$532$	58.5365	−	28.1897i	2.53788	−	1.22218i
$533$	10.7063	−	13.4253i	0.463741	−	0.581513i
$534$	72.7696			3.14905
$535$	9.24537	−	11.5933i	0.399712	−	0.501223i
$536$	5.55647	−	24.3445i	0.240003	−	1.05152i
$537$	3.48398	−	15.2643i	0.150345	−	0.658703i
$538$	−47.3485	+	59.3732i	−2.04134	+	2.55976i
$539$	−0.414214			−0.0178414
$540$	0.988722	−	1.23982i	0.0425478	−	0.0533533i
$541$	9.31885	−	4.48772i	0.400649	−	0.192942i	−0.222699	−	0.974887i	$-0.571487\pi$
$541$	9.31885	−	4.48772i	0.400649	−	0.192942i	0.623347	+	0.781945i	$0.285772\pi$
$542$	−24.9212	−	31.2502i	−1.07046	−	1.34231i
$543$	12.5141	+	15.6922i	0.537032	+	0.673416i
$544$	−1.18361	−	0.569997i	−0.0507469	−	0.0244384i
$545$	2.81642	−	12.3395i	0.120642	−	0.528567i
$546$	14.0439	+	61.5303i	0.601023	+	2.63326i
$547$	−32.2538	+	15.5326i	−1.37907	+	0.664126i	−0.968802	−	0.247838i	$-0.920280\pi$
$547$	−32.2538	+	15.5326i	−1.37907	+	0.664126i	−0.410270	+	0.911964i	$0.634566\pi$
$548$	−41.3915	−	19.9331i	−1.76816	−	0.851500i
$549$	3.03894	+	13.3144i	0.129699	+	0.568247i
$550$	−4.00000			−0.170561
$551$		0			0
$552$	−38.9706			−1.65870
$553$	−1.51947	−	6.65722i	−0.0646144	−	0.283094i
$554$	−37.6596	−	18.1359i	−1.60000	−	0.770521i
$555$	−8.70053	+	4.18995i	−0.369317	+	0.177854i
$556$	−11.9267	−	52.2542i	−0.505804	−	2.21607i
$557$	3.85266	−	16.8796i	0.163243	−	0.715212i	−0.825353	−	0.564617i	$-0.809024\pi$
$557$	3.85266	−	16.8796i	0.163243	−	0.715212i	0.988596	−	0.150595i	$-0.0481190\pi$
$558$	61.9592	+	29.8380i	2.62294	+	1.26314i
$559$	−8.55922	−	10.7329i	−0.362016	−	0.453954i
$560$	5.29049	+	6.63406i	0.223564	+	0.280340i
$561$	0.746387	−	0.359441i	0.0315125	−	0.0151756i
$562$	−48.1233	+	60.3447i	−2.02996	+	2.54549i
$563$	−0.757359			−0.0319189			−0.0159594	−	0.999873i	$-0.505080\pi$
$563$	−0.757359			−0.0319189			−0.0159594	+	0.999873i	$0.505080\pi$
$564$	−18.6863	+	23.4319i	−0.786837	+	0.986662i
$565$	−2.96258	+	12.9799i	−0.124637	+	0.546069i
$566$	6.26221	−	27.4366i	0.263221	−	1.15324i
$567$	16.7273	−	20.9753i	0.702479	−	0.880880i
$568$	38.9706			1.63517
$569$	−24.7256	+	31.0050i	−1.03655	+	1.29980i	−0.0836584	+	0.996494i	$0.526660\pi$
$569$	−24.7256	+	31.0050i	−1.03655	+	1.29980i	−0.952895	+	0.303302i	$0.901911\pi$
$570$	−31.5074	+	15.1732i	−1.31970	+	0.635534i
$571$	9.12005	+	11.4362i	0.381662	+	0.478589i	0.935142	−	0.354274i	$-0.115272\pi$
$571$	9.12005	+	11.4362i	0.381662	+	0.478589i	−0.553480	+	0.832863i	$0.686700\pi$
$572$	3.78525	+	4.74655i	0.158269	+	0.198463i
$573$	−55.0606	−	26.5158i	−2.30019	−	1.10771i
$574$	6.81524	−	29.8595i	0.284463	−	1.24631i
$575$	3.25491	+	14.2607i	0.135739	+	0.594711i
$576$	25.0460	−	12.0615i	1.04358	−	0.502564i
$577$	26.8480	+	12.9293i	1.11770	+	0.538254i	0.899180	−	0.437580i	$-0.144164\pi$
$577$	26.8480	+	12.9293i	1.11770	+	0.538254i	0.218516	+	0.975833i	$0.429879\pi$
$578$	−8.76394	−	38.3973i	−0.364532	−	1.59712i
$579$	−12.4853			−0.518871
$580$		0			0
$581$	−21.6569			−0.898478
$582$	5.81717	+	25.4867i	0.241130	+	1.05646i
$583$	3.53985	+	1.70470i	0.146605	+	0.0706015i
$584$	15.9083	−	7.66102i	0.658289	−	0.317015i
$585$	−2.40955	−	10.5569i	−0.0996227	−	0.436476i
$586$	4.11336	−	18.0218i	0.169921	−	0.744474i
$587$	−6.89859	−	3.32218i	−0.284735	−	0.137121i	0.286065	−	0.958210i	$-0.407653\pi$
$587$	−6.89859	−	3.32218i	−0.284735	−	0.137121i	−0.570800	+	0.821089i	$0.693367\pi$
$588$	5.76269	+	7.22619i	0.237649	+	0.298003i
$589$	37.6752	+	47.2433i	1.55238	+	1.94662i
$590$	7.95414	−	3.83051i	0.327467	−	0.157700i
$591$	3.01048	−	3.77502i	0.123834	−	0.155283i
$592$	−12.0000			−0.493197
$593$	−12.1489	+	15.2342i	−0.498894	+	0.625594i	−0.965980	−	0.258619i	$-0.916733\pi$
$593$	−12.1489	+	15.2342i	−0.498894	+	0.625594i	0.467085	+	0.884212i	$0.345304\pi$
$594$	0.0921712	−	0.403828i	0.00378183	−	0.0165693i
$595$	−0.521399	+	2.28440i	−0.0213753	+	0.0936512i
$596$	−18.6863	+	23.4319i	−0.765422	+	0.959809i
$597$	−1.17157			−0.0479493
$598$	21.0733	−	26.4251i	0.861752	−	1.08060i
$599$	−8.89261	+	4.28246i	−0.363342	+	0.174976i	−0.606643	−	0.794974i	$-0.707484\pi$
$599$	−8.89261	+	4.28246i	−0.363342	+	0.174976i	0.243300	+	0.969951i	$0.421770\pi$
$600$	26.5778	+	33.3275i	1.08503	+	1.36059i
$601$	−10.7063	−	13.4253i	−0.436719	−	0.547628i	0.513956	−	0.857816i	$-0.328179\pi$
$601$	−10.7063	−	13.4253i	−0.436719	−	0.547628i	−0.950675	+	0.310188i	$0.899608\pi$
$602$	−22.0605	−	10.6238i	−0.899118	−	0.432992i
$603$	−3.56033	+	15.5988i	−0.144988	+	0.635234i
$604$	12.0478	+	52.7847i	0.490216	+	2.14778i
$605$	−9.75608	+	4.69828i	−0.396641	+	0.191012i
$606$	−12.3044	−	5.92549i	−0.499832	−	0.240706i
$607$	1.71962	+	7.53417i	0.0697974	+	0.305802i	0.997762	−	0.0668661i	$-0.0213000\pi$
$607$	1.71962	+	7.53417i	0.0697974	+	0.305802i	−0.927965	+	0.372668i	$0.878443\pi$
$608$	9.51472			0.385873
$609$		0			0
$610$	−11.6569			−0.471972
$611$	−2.76242	−	12.1030i	−0.111756	−	0.489633i
$612$	−8.08220	−	3.89218i	−0.326703	−	0.157332i
$613$	8.10872	−	3.90495i	0.327508	−	0.157720i	−0.262903	−	0.964822i	$-0.584680\pi$
$613$	8.10872	−	3.90495i	0.327508	−	0.157720i	0.590411	+	0.807103i	$0.298966\pi$
$614$	1.55765	+	6.82450i	0.0628615	+	0.275414i
$615$	−2.40955	+	10.5569i	−0.0971625	+	0.425697i
$616$	4.65943	+	2.24386i	0.187734	+	0.0904078i
$617$	0.427896	+	0.536564i	0.0172264	+	0.0216013i	0.790370	−	0.612630i	$-0.209888\pi$
$617$	0.427896	+	0.536564i	0.0172264	+	0.0216013i	−0.773144	+	0.634231i	$0.781317\pi$
$618$	17.5463	+	22.0024i	0.705817	+	0.885067i
$619$	−30.2597	+	14.5723i	−1.21624	+	0.585711i	−0.928263	−	0.371925i	$-0.878698\pi$
$619$	−30.2597	+	14.5723i	−1.21624	+	0.585711i	−0.287979	+	0.957637i	$0.592983\pi$
$620$	−24.0395	+	30.1446i	−0.965449	+	1.21063i
$621$	−1.51472			−0.0607836
$622$	−4.04351	+	5.07040i	−0.162130	+	0.203304i
$623$	−7.85804	+	34.4283i	−0.314826	+	1.37934i
$624$	6.17004	−	27.0327i	0.246999	−	1.08218i
$625$	6.85839	−	8.60015i	0.274336	−	0.344006i
$626$	−23.7279			−0.948358
$627$	−3.74094	+	4.69099i	−0.149399	+	0.187340i
$628$	−29.2682	+	14.0948i	−1.16793	+	0.562445i
$629$	−2.06606	−	2.59076i	−0.0823793	−	0.103300i
$630$	−12.0419	−	15.1001i	−0.479761	−	0.601601i
$631$	33.1813	+	15.9793i	1.32093	+	0.636124i	0.955576	−	0.294746i	$-0.0952351\pi$
$631$	33.1813	+	15.9793i	1.32093	+	0.636124i	0.365350	+	0.930870i	$0.380949\pi$
$632$	−2.37137	+	10.3897i	−0.0943282	+	0.413279i
$633$	10.4138	+	45.6256i	0.413910	+	1.81346i
$634$	−68.4206	+	32.9496i	−2.71733	+	1.30860i
$635$	−3.91304	−	1.88442i	−0.155284	−	0.0747809i
$636$	−19.5082	−	85.4710i	−0.773550	−	3.38915i
$637$	−3.82843			−0.151688
$638$		0			0
$639$	−24.9706			−0.987820
$640$	4.57422	+	20.0410i	0.180812	+	0.792188i
$641$	−16.0363	−	7.72269i	−0.633397	−	0.305028i	0.0894967	−	0.995987i	$-0.471474\pi$
$641$	−16.0363	−	7.72269i	−0.633397	−	0.305028i	−0.722894	+	0.690959i	$0.757188\pi$
$642$	−77.8675	+	37.4990i	−3.07319	+	1.47997i
$643$	−7.22866	−	31.6708i	−0.285070	−	1.24897i	−0.891201	−	0.453609i	$-0.850136\pi$
$643$	−7.22866	−	31.6708i	−0.285070	−	1.24897i	0.606130	−	0.795365i	$-0.292721\pi$
$644$	8.81138	−	38.6052i	0.347217	−	1.52126i
$645$	7.79956	+	3.75607i	0.307107	+	0.147895i
$646$	−7.48188	−	9.38198i	−0.294371	−	0.369129i
$647$	24.7256	+	31.0050i	0.972065	+	1.21893i	0.975739	+	0.218938i	$0.0702593\pi$
$647$	24.7256	+	31.0050i	0.972065	+	1.21893i	−0.00367336	+	0.999993i	$0.501169\pi$
$648$	−37.7236	+	18.1667i	−1.48192	+	0.713657i
$649$	0.944412	−	1.18425i	0.0370714	−	0.0464861i
$650$	−36.9706			−1.45010
$651$	−42.8771	+	53.7662i	−1.68049	+	2.10726i
$652$	−3.34708	+	14.6645i	−0.131082	+	0.574306i
$653$	6.70726	−	29.3864i	0.262475	−	1.14998i	−0.656082	−	0.754690i	$-0.727787\pi$
$653$	6.70726	−	29.3864i	0.262475	−	1.14998i	0.918557	−	0.395289i	$-0.129356\pi$
$654$	−45.9946	+	57.6754i	−1.79853	+	2.25528i
$655$	−21.3137			−0.832796
$656$	−8.38958	+	10.5202i	−0.327558	+	0.410745i
$657$	−10.1933	+	4.90883i	−0.397678	+	0.191512i
$658$	−13.8054	−	17.3114i	−0.538190	−	0.674869i
$659$	8.98712	+	11.2695i	0.350088	+	0.438997i	0.925431	−	0.378915i	$-0.123703\pi$
$659$	8.98712	+	11.2695i	0.350088	+	0.438997i	−0.575343	+	0.817912i	$0.695131\pi$
$660$	−3.44929	−	1.66109i	−0.134264	−	0.0646579i
$661$	−7.41300	+	32.4785i	−0.288332	+	1.26327i	0.598481	+	0.801137i	$0.295771\pi$
$661$	−7.41300	+	32.4785i	−0.288332	+	1.26327i	−0.886813	+	0.462129i	$0.847086\pi$
$662$	−1.29695	−	5.68230i	−0.0504073	−	0.220849i
$663$	6.89859	−	3.32218i	0.267919	−	0.129023i
$664$	30.4518	+	14.6648i	1.18176	+	0.569106i
$665$	−3.77631	−	16.5451i	−0.146439	−	0.641591i
$666$	27.3137			1.05838
$667$		0			0
$668$	−12.1421			−0.469793
$669$	1.70381	+	7.46488i	0.0658731	+	0.288609i
$670$	−12.3044	−	5.92549i	−0.475360	−	0.228922i
$671$	−1.80194	+	0.867767i	−0.0695630	+	0.0334998i
$672$	2.40955	+	10.5569i	0.0929505	+	0.407243i
$673$	4.81255	−	21.0852i	0.185510	−	0.812774i	−0.793436	−	0.608654i	$-0.791710\pi$
$673$	4.81255	−	21.0852i	0.185510	−	0.812774i	0.978946	−	0.204120i	$-0.0654331\pi$
$674$	47.4157	+	22.8342i	1.82638	+	0.879540i
$675$	1.03303	+	1.29538i	0.0397614	+	0.0498592i
$676$	3.95489	+	4.95927i	0.152111	+	0.190741i
$677$	19.8213	−	9.54544i	0.761795	−	0.366861i	−0.0123051	−	0.999924i	$-0.503917\pi$
$677$	19.8213	−	9.54544i	0.761795	−	0.366861i	0.774100	+	0.633063i	$0.218203\pi$
$678$	48.3815	−	60.6685i	1.85808	−	2.32996i
$679$	−12.6863			−0.486855
$680$	2.28001	−	2.85904i	0.0874344	−	0.109639i
$681$	4.37406	−	19.1640i	0.167614	−	0.734367i
$682$	−2.24102	+	9.81857i	−0.0858132	+	0.375972i
$683$	13.0749	−	16.3954i	0.500298	−	0.627354i	−0.465998	−	0.884786i	$-0.654305\pi$
$683$	13.0749	−	16.3954i	0.500298	−	0.627354i	0.966297	+	0.257431i	$0.0828761\pi$
$684$	64.9706			2.48421
$685$	−7.48188	+	9.38198i	−0.285868	+	0.358467i
$686$	36.9132	−	17.7765i	1.40935	−	0.678708i
$687$	−5.29049	−	6.63406i	−0.201845	−	0.253105i
$688$	6.70710	+	8.41044i	0.255706	+	0.320645i
$689$	32.7175	+	15.7559i	1.24644	+	0.600253i
$690$	−4.74275	+	20.7793i	−0.180553	+	0.791056i
$691$	−10.6810	−	46.7965i	−0.406325	−	1.78022i	−0.600887	−	0.799334i	$-0.705186\pi$
$691$	−10.6810	−	46.7965i	−0.406325	−	1.78022i	0.194562	−	0.980890i	$-0.437671\pi$
$692$	−42.5751	+	20.5031i	−1.61846	+	0.779411i
$693$	−2.98555	−	1.43776i	−0.113412	−	0.0546161i
$694$	1.33513	+	5.84957i	0.0506807	+	0.222047i
$695$	−14.0000			−0.531050
$696$		0			0
$697$	−3.71573			−0.140743
$698$	−2.76242	−	12.1030i	−0.104559	−	0.458104i
$699$	−39.8347	−	19.1834i	−1.50669	−	0.725582i
$700$	−39.0243	+	18.7931i	−1.47498	+	0.710313i
$701$	8.92592	+	39.1070i	0.337127	+	1.47705i	0.805011	+	0.593260i	$0.202160\pi$
$701$	8.92592	+	39.1070i	0.337127	+	1.47705i	−0.467883	+	0.883790i	$0.654983\pi$
$702$	0.851905	−	3.73244i	0.0321531	−	0.140872i
$703$	21.6233	+	10.4132i	0.815536	+	0.392742i
$704$	2.53827	+	3.18289i	0.0956646	+	0.119960i
$705$	4.88094	+	6.12051i	0.183827	+	0.230512i
$706$	58.6645	−	28.2513i	2.20787	−	1.06325i
$707$	4.13213	−	5.18152i	0.155405	−	0.194871i
$708$	−33.7990			−1.27024
$709$	18.1698	−	22.7842i	0.682382	−	0.855680i	−0.313189	−	0.949691i	$-0.601397\pi$
$709$	18.1698	−	22.7842i	0.682382	−	0.855680i	0.995571	+	0.0940107i	$0.0299688\pi$
$710$	4.74275	−	20.7793i	0.177992	−	0.779834i
$711$	1.51947	−	6.65722i	0.0569845	−	0.249665i
$712$	34.3622	−	43.0888i	1.28778	−	1.61482i
$713$	36.8284			1.37924
$714$	8.51491	−	10.6774i	0.318662	−	0.399590i
$715$	1.42874	−	0.688047i	0.0534320	−	0.0257315i
$716$	−15.4803	−	19.4116i	−0.578525	−	0.725447i
$717$	−29.5882	−	37.1025i	−1.10499	−	1.38562i
$718$	8.54594	+	4.11551i	0.318932	+	0.153589i
$719$	4.48205	−	19.6371i	0.167152	−	0.732341i	−0.819974	−	0.572400i	$-0.806012\pi$
$719$	4.48205	−	19.6371i	0.167152	−	0.732341i	0.987127	−	0.159941i	$-0.0511305\pi$
$720$	1.88815	+	8.27254i	0.0703673	+	0.308299i
$721$	−12.3044	+	5.92549i	−0.458240	+	0.220677i
$722$	36.9772	+	17.8073i	1.37615	+	0.662719i
$723$	9.83836	+	43.1047i	0.365893	+	1.60308i
$724$	31.8284			1.18289
$725$		0			0
$726$	63.1127			2.34233
$727$	−0.292328	−	1.28077i	−0.0108418	−	0.0475012i	0.969218	−	0.246205i	$-0.0791838\pi$
$727$	−0.292328	−	1.28077i	−0.0108418	−	0.0475012i	−0.980059	+	0.198704i	$0.936327\pi$
$728$	43.0654	+	20.7392i	1.59611	+	0.768646i
$729$	21.4687	−	10.3388i	0.795136	−	0.382917i
$730$	−2.14885	−	9.41474i	−0.0795326	−	0.348455i
$731$	−0.661012	+	2.89608i	−0.0244484	+	0.107116i
$732$	40.2079	+	19.3631i	1.48613	+	0.715681i
$733$	−25.7220	−	32.2543i	−0.950063	−	1.19134i	−0.981428	−	0.191833i	$-0.938557\pi$
$733$	−25.7220	−	32.2543i	−0.950063	−	1.19134i	0.0313650	−	0.999508i	$-0.490015\pi$
$734$	−27.0943	−	33.9751i	−1.00007	−	1.25405i
$735$	2.17513	−	1.04749i	0.0802309	−	0.0386372i
$736$	3.61561	−	4.53383i	0.133273	−	0.167119i
$737$	−2.34315			−0.0863109
$738$	19.0959	−	23.9455i	0.702929	−	0.881445i
$739$	−0.905898	+	3.96900i	−0.0333240	+	0.146002i	−0.988853	−	0.148895i	$-0.952428\pi$
$739$	−0.905898	+	3.96900i	−0.0333240	+	0.146002i	0.955529	+	0.294897i	$0.0952854\pi$
$740$	−3.40762	+	14.9298i	−0.125267	+	0.548829i
$741$	−34.5762	+	43.3571i	−1.27019	+	1.59276i
$742$	64.7696			2.37777
$743$	14.7498	−	18.4957i	0.541118	−	0.678540i	−0.433825	−	0.900997i	$-0.642836\pi$
$743$	14.7498	−	18.4957i	0.541118	−	0.678540i	0.974943	+	0.222457i	$0.0714077\pi$
$744$	96.6973	−	46.5670i	3.54509	−	1.70723i
$745$	4.88094	+	6.12051i	0.178824	+	0.224238i
$746$	39.6084	+	49.6673i	1.45017	+	1.81845i
$747$	−19.5122	−	9.39656i	−0.713912	−	0.343802i
$748$	0.292328	−	1.28077i	0.0106886	−	0.0468296i
$749$	−9.33278	−	40.8896i	−0.341012	−	1.49407i
$750$	47.2611	−	22.7597i	1.72573	−	0.831068i
$751$	−22.8069	−	10.9832i	−0.832234	−	0.400783i	−0.0312816	−	0.999511i	$-0.509959\pi$
$751$	−22.8069	−	10.9832i	−0.832234	−	0.400783i	−0.800953	+	0.598728i	$0.795673\pi$
$752$	2.16467	+	9.48402i	0.0789373	+	0.345847i
$753$	48.4558			1.76583
$754$		0			0
$755$	14.1421			0.514685
$756$	−0.998069	−	4.37283i	−0.0362994	−	0.159038i
$757$	−22.9880	−	11.0704i	−0.835512	−	0.402361i	−0.0333324	−	0.999444i	$-0.510612\pi$
$757$	−22.9880	−	11.0704i	−0.835512	−	0.402361i	−0.802179	+	0.597083i	$0.796326\pi$
$758$	−15.1619	+	7.30158i	−0.550705	+	0.265205i
$759$	0.813727	+	3.56517i	0.0295364	+	0.129407i
$760$	−5.89353	+	25.8212i	−0.213781	+	0.936635i
$761$	−41.0824	−	19.7842i	−1.48923	−	0.717177i	−0.500344	−	0.865826i	$-0.666793\pi$
$761$	−41.0824	−	19.7842i	−1.48923	−	0.717177i	−0.988890	+	0.148649i	$0.952508\pi$
$762$	15.7828	+	19.7911i	0.571752	+	0.716954i
$763$	−22.3203	−	27.9888i	−0.808049	−	1.01326i
$764$	−87.3144	+	42.0484i	−3.15892	+	1.52126i
$765$	−1.46093	+	1.83195i	−0.0528199	+	0.0662341i
$766$	8.48528			0.306586
$767$	8.72886	−	10.9456i	0.315181	−	0.395224i
$768$	16.1006	−	70.5412i	0.580980	−	2.54544i
$769$	10.9286	−	47.8813i	0.394096	−	1.72665i	−0.255896	−	0.966704i	$-0.582371\pi$
$769$	10.9286	−	47.8813i	0.394096	−	1.72665i	0.649992	−	0.759941i	$-0.274772\pi$
$770$	1.76350	−	2.21135i	0.0635520	−	0.0796916i
$771$	−43.8701			−1.57994
$772$	−12.3445	+	15.4795i	−0.444287	+	0.557118i
$773$	17.5822	−	8.46712i	0.632386	−	0.304541i	−0.0900935	−	0.995933i	$-0.528717\pi$
$773$	17.5822	−	8.46712i	0.632386	−	0.304541i	0.722480	+	0.691392i	$0.243002\pi$
$774$	−15.2663	−	19.1434i	−0.548737	−	0.688094i
$775$	−25.1168	−	31.4955i	−0.902223	−	1.13135i
$776$	17.8383	+	8.59046i	0.640357	+	0.308380i
$777$	−6.07787	+	26.6289i	−0.218042	+	0.955306i
$778$	1.62745	+	7.13034i	0.0583470	+	0.255635i
$779$	24.2466	−	11.6765i	0.868724	−	0.418356i
$780$	−31.8806	−	15.3529i	−1.14151	−	0.549721i
$781$	−0.813727	−	3.56517i	−0.0291174	−	0.127572i
$782$	−7.31371			−0.261538
$783$		0			0
$784$	3.00000			0.107143
$785$	1.88815	+	8.27254i	0.0673911	+	0.295260i
$786$	111.923	+	53.8994i	3.99217	+	1.92253i
$787$	48.7273	−	23.4658i	1.73694	−	0.836467i	0.752990	−	0.658032i	$-0.228611\pi$
$787$	48.7273	−	23.4658i	1.73694	−	0.836467i	0.983952	−	0.178435i	$-0.0571036\pi$
$788$	−1.70381	−	7.46488i	−0.0606957	−	0.265925i
$789$	−1.48129	+	6.48995i	−0.0527353	+	0.231048i
$790$	5.25123	+	2.52886i	0.186830	+	0.0899728i
$791$	23.4787	+	29.4413i	0.834805	+	1.04681i
$792$	3.22442	+	4.04330i	0.114575	+	0.143672i
$793$	−16.6547	+	8.02046i	−0.591424	+	0.284815i
$794$	−29.1160	+	36.5103i	−1.03329	+	1.29570i
$795$	−22.8995			−0.812161
$796$	−1.15836	+	1.45254i	−0.0410570	+	0.0514838i
$797$	−11.5133	+	50.4429i	−0.407821	+	1.78678i	0.186397	+	0.982474i	$0.440319\pi$
$797$	−11.5133	+	50.4429i	−0.407821	+	1.78678i	−0.594218	+	0.804304i	$0.702538\pi$
$798$	−22.0099	+	96.4318i	−0.779143	+	3.41365i
$799$	−1.67488	+	2.10023i	−0.0592528	+	0.0743007i
$800$	−6.34315			−0.224264
$801$	−22.0177	+	27.6094i	−0.777958	+	0.975529i
$802$	−40.5811	+	19.5428i	−1.43297	+	0.690081i
$803$	−1.03303	−	1.29538i	−0.0364549	−	0.0457130i
$804$	32.5987	+	40.8775i	1.14967	+	1.44164i
$805$	−9.31885	−	4.48772i	−0.328446	−	0.158171i
$806$	−20.7130	+	90.7495i	−0.729583	+	3.19651i
$807$	−16.8985	−	74.0371i	−0.594855	−	2.60623i
$808$	−9.31885	+	4.48772i	−0.327836	+	0.157878i
$809$	−32.6910	−	15.7432i	−1.14935	−	0.553500i	−0.240515	−	0.970646i	$-0.577316\pi$
$809$	−32.6910	−	15.7432i	−1.14935	−	0.553500i	−0.908840	+	0.417146i	$0.863030\pi$
$810$	5.09562	+	22.3254i	0.179042	+	0.784433i
$811$	10.8284			0.380238			0.190119	−	0.981761i	$-0.439113\pi$
$811$	10.8284			0.380238			0.190119	+	0.981761i	$0.439113\pi$
$812$		0			0
$813$	39.9706			1.40183
$814$	0.890084	+	3.89971i	0.0311974	+	0.136685i
$815$	3.53985	+	1.70470i	0.123995	+	0.0597130i
$816$	−5.40581	+	2.60330i	−0.189241	+	0.0911338i
$817$	−4.78748	−	20.9753i	−0.167493	−	0.733833i
$818$	−10.1912	+	44.6507i	−0.356328	+	1.56118i
$819$	−27.5943	−	13.2887i	−0.964225	−	0.464346i
$820$	10.7063	+	13.4253i	0.373880	+	0.468831i
$821$	−0.926058	−	1.16124i	−0.0323196	−	0.0405275i	0.765409	−	0.643544i	$-0.222537\pi$
$821$	−0.926058	−	1.16124i	−0.0323196	−	0.0405275i	−0.797729	+	0.603017i	$0.793965\pi$
$822$	63.0148	−	30.3463i	2.19789	−	1.05845i
$823$	−33.8457	+	42.4412i	−1.17979	+	1.47941i	−0.336713	+	0.941607i	$0.609315\pi$
$823$	−33.8457	+	42.4412i	−1.17979	+	1.47941i	−0.843074	+	0.537798i	$0.819256\pi$
$824$	21.3137			0.742498
$825$	2.49396	−	3.12733i	0.0868285	−	0.108880i
$826$	5.55647	−	24.3445i	0.193334	−	0.847053i
$827$	−7.32083	+	32.0746i	−0.254570	+	1.11534i	0.672394	+	0.740194i	$0.265266\pi$
$827$	−7.32083	+	32.0746i	−0.254570	+	1.11534i	−0.926964	+	0.375151i	$0.877591\pi$
$828$	24.6889	−	30.9589i	0.858000	−	1.07590i
$829$	−29.7990			−1.03496			−0.517481	−	0.855695i	$-0.673130\pi$
$829$	−29.7990			−1.03496			−0.517481	+	0.855695i	$0.673130\pi$
$830$	11.5254	−	14.4524i	0.400052	−	0.501649i
$831$	37.6596	−	18.1359i	1.30640	−	0.629127i
$832$	23.4603	+	29.4183i	0.813340	+	1.01990i
$833$	0.516516	+	0.647690i	0.0178962	+	0.0224411i
$834$	73.5172	+	35.4040i	2.54569	+	1.22594i
$835$	−0.705741	+	3.09205i	−0.0244232	+	0.107005i
$836$	2.11722	+	9.27616i	0.0732257	+	0.320823i
$837$	3.75846	−	1.80998i	0.129911	−	0.0625620i
$838$	−20.6958	−	9.96655i	−0.714923	−	0.344289i
$839$	1.76435	+	7.73014i	0.0609122	+	0.266874i	0.996209	−	0.0869898i	$-0.0277248\pi$
$839$	1.76435	+	7.73014i	0.0609122	+	0.266874i	−0.935297	+	0.353864i	$0.884868\pi$
$840$	−30.1421			−1.04000
$841$		0			0
$842$	−89.5980			−3.08775
$843$	−17.1750	−	75.2486i	−0.591539	−	2.59170i
$844$	66.8638	+	32.1999i	2.30155	+	1.10837i
$845$	1.49277	−	0.718882i	0.0513530	−	0.0247303i
$846$	−4.92709	−	21.5870i	−0.169397	−	0.742176i
$847$	−6.81524	+	29.8595i	−0.234174	+	1.02599i
$848$	−25.6378	−	12.3465i	−0.880407	−	0.423982i
$849$	17.5463	+	22.0024i	0.602189	+	0.755121i
$850$	4.98792	+	6.25465i	0.171084	+	0.214533i
$851$	13.1788	−	6.34660i	0.451765	−	0.217559i
$852$	−50.8755	+	63.7959i	−1.74297	+	2.18561i
$853$	−22.9706			−0.786497			−0.393249	−	0.919432i	$-0.628649\pi$
$853$	−22.9706			−0.786497			−0.393249	+	0.919432i	$0.628649\pi$
$854$	−20.5568	+	25.7774i	−0.703440	+	0.882085i
$855$	3.77631	−	16.5451i	0.129147	−	0.565830i
$856$	−14.5653	+	63.8147i	−0.497832	+	2.18114i
$857$	−3.84791	+	4.82513i	−0.131442	+	0.164823i	−0.843197	−	0.537605i	$-0.819329\pi$
$857$	−3.84791	+	4.82513i	−0.131442	+	0.164823i	0.711755	+	0.702428i	$0.247901\pi$
$858$	−9.24264			−0.315539
$859$	12.3002	−	15.4239i	0.419676	−	0.526257i	−0.526385	−	0.850247i	$-0.676453\pi$
$859$	12.3002	−	15.4239i	0.419676	−	0.526257i	0.946061	+	0.323989i	$0.105024\pi$
$860$	12.3684	−	5.95632i	0.421760	−	0.203109i
$861$	19.0959	+	23.9455i	0.650786	+	0.816060i
$862$	−29.5882	−	37.1025i	−1.00778	−	1.26372i
$863$	−15.4180	−	7.42492i	−0.524835	−	0.252747i	0.152654	−	0.988280i	$-0.451218\pi$
$863$	−15.4180	−	7.42492i	−0.524835	−	0.252747i	−0.677490	+	0.735532i	$0.736932\pi$
$864$	0.146164	−	0.640386i	0.00497259	−	0.0217864i
$865$	2.74661	+	12.0337i	0.0933875	+	0.409157i
$866$	66.6187	−	32.0819i	2.26379	−	1.09019i
$867$	35.4845	+	17.0884i	1.20512	+	0.580353i
$868$	24.2668	+	106.320i	0.823667	+	3.60872i
$869$	1.00000			0.0339227
$870$		0			0
$871$	−21.6569			−0.733815
$872$	12.4323	+	54.4693i	0.421009	+	1.84456i
$873$	−11.4300	−	5.50438i	−0.386845	−	0.186295i
$874$	47.7248	−	22.9831i	1.61432	−	0.777414i
$875$	5.66446	+	24.8176i	0.191494	+	0.838988i
$876$	−8.22672	+	36.0436i	−0.277955	+	1.21780i
$877$	33.4639	+	16.1154i	1.13000	+	0.544177i	0.902967	−	0.429711i	$-0.141384\pi$
$877$	33.4639	+	16.1154i	1.13000	+	0.544177i	0.227029	+	0.973888i	$0.427099\pi$
$878$	0.516516	+	0.647690i	0.0174316	+	0.0218585i
$879$	11.5254	+	14.4524i	0.388742	+	0.487467i
$880$	−1.11958	+	0.539162i	−0.0377411	+	0.0181751i
$881$	8.72886	−	10.9456i	0.294083	−	0.368768i	−0.612737	−	0.790287i	$-0.709931\pi$
$881$	8.72886	−	10.9456i	0.294083	−	0.368768i	0.906820	+	0.421519i	$0.138503\pi$
$882$	−6.82843			−0.229925
$883$	23.9585	−	30.0430i	0.806267	−	1.01103i	−0.193287	−	0.981142i	$-0.561915\pi$
$883$	23.9585	−	30.0430i	0.806267	−	1.01103i	0.999553	−	0.0298842i	$-0.00951387\pi$
$884$	2.70188	−	11.8377i	0.0908740	−	0.398145i
$885$	−1.96451	+	8.60708i	−0.0660363	+	0.289324i
$886$	36.6422	−	45.9479i	1.23102	−	1.54365i
$887$	17.1005			0.574179			0.287089	−	0.957904i	$-0.407312\pi$
$887$	17.1005			0.574179			0.287089	+	0.957904i	$0.407312\pi$
$888$	26.5778	−	33.3275i	0.891891	−	1.11840i
$889$	−11.0677	+	5.32995i	−0.371200	+	0.178761i
$890$	−18.7933	−	23.5661i	−0.629953	−	0.789936i
$891$	2.44965	+	3.07176i	0.0820663	+	0.102908i
$892$	10.9397	+	5.26828i	0.366288	+	0.176395i
$893$	4.32933	−	18.9680i	0.144876	−	0.634741i
$894$	−10.1531	−	44.4834i	−0.339569	−	1.48775i
$895$	−5.84304	+	2.81386i	−0.195311	+	0.0940569i
$896$	52.3843	+	25.2269i	1.75004	+	0.842772i
$897$	7.52098	+	32.9516i	0.251118	+	1.10022i
$898$	84.4264			2.81735
$899$		0			0
$900$	−43.3137			−1.44379
$901$	−1.74854	−	7.66085i	−0.0582523	−	0.255220i
$902$	4.04110	+	1.94609i	0.134554	+	0.0647977i
$903$	22.0605	−	10.6238i	0.734127	−	0.353537i
$904$	−13.0775	−	57.2961i	−0.434950	−	1.90564i
$905$	1.84997	−	8.10527i	0.0614952	−	0.269428i
$906$	−74.2636	−	35.7635i	−2.46724	−	1.18816i
$907$	13.8940	+	17.4225i	0.461343	+	0.578506i	0.957028	−	0.289997i	$-0.0936542\pi$
$907$	13.8940	+	17.4225i	0.461343	+	0.578506i	−0.495684	+	0.868503i	$0.665083\pi$
$908$	−19.4352	−	24.3709i	−0.644978	−	0.808777i
$909$	5.97110	−	2.87553i	0.198049	−	0.0953753i
$910$	16.2994	−	20.4387i	0.540318	−	0.677538i
$911$	−15.4437			−0.511671			−0.255835	−	0.966720i	$-0.582351\pi$
$911$	−15.4437			−0.511671			−0.255835	+	0.966720i	$0.582351\pi$
$912$	27.0943	−	33.9751i	0.897181	−	1.12503i
$913$	0.705741	−	3.09205i	0.0233566	−	0.102332i
$914$	0.553027	−	2.42297i	0.0182925	−	0.0801447i
$915$	7.26793	−	9.11370i	0.240270	−	0.301289i
$916$	−13.4558			−0.444594
$917$	−37.5866	+	47.1321i	−1.24122	+	1.55644i
$918$	−0.746387	+	0.359441i	−0.0246344	+	0.0118633i
$919$	5.07654	+	6.36578i	0.167460	+	0.209988i	0.858479	−	0.512848i	$-0.171410\pi$
$919$	5.07654	+	6.36578i	0.167460	+	0.209988i	−0.691020	+	0.722836i	$0.742838\pi$
$920$	10.0645	+	12.6204i	0.331815	+	0.416083i
$921$	−6.30678	−	3.03719i	−0.207816	−	0.100079i
$922$	7.52098	−	32.9516i	0.247690	−	1.08520i
$923$	−7.52098	−	32.9516i	−0.247556	−	1.08461i
$924$	−9.75608	+	4.69828i	−0.320951	+	0.154562i
$925$	−14.4155	−	6.94214i	−0.473979	−	0.228256i
$926$	−13.9675	−	61.1958i	−0.459002	−	2.01102i
$927$	−13.6569			−0.448550
$928$		0			0
$929$	18.6863			0.613077			0.306539	−	0.951858i	$-0.400829\pi$
$929$	18.6863			0.613077			0.306539	+	0.951858i	$0.400829\pi$
$930$	−13.0616	−	57.2268i	−0.428308	−	1.87654i
$931$	−5.40581	−	2.60330i	−0.177168	−	0.0853198i
$932$	−63.1694	+	30.4208i	−2.06918	+	0.996465i
$933$	−1.44311	−	6.32268i	−0.0472453	−	0.206995i
$934$	−20.6050	+	90.2764i	−0.674216	+	2.95393i
$935$	−0.309164	−	0.148885i	−0.0101107	−	0.00486907i
$936$	29.8022	+	37.3708i	0.974115	+	1.22150i
$937$	−10.3670	−	12.9998i	−0.338676	−	0.424686i	0.583105	−	0.812397i	$-0.301837\pi$
$937$	−10.3670	−	12.9998i	−0.338676	−	0.424686i	−0.921781	+	0.387710i	$0.873266\pi$
$938$	−34.8021	+	16.7598i	−1.13633	+	0.547227i
$939$	14.7941	−	18.5512i	0.482788	−	0.605397i
$940$	12.4142			0.404907
$941$	−35.2883	+	44.2501i	−1.15036	+	1.44251i	−0.273436	+	0.961890i	$0.588160\pi$
$941$	−35.2883	+	44.2501i	−1.15036	+	1.44251i	−0.876928	+	0.480621i	$0.840411\pi$
$942$	11.0050	−	48.2159i	0.358561	−	1.57096i
$943$	3.64979	−	15.9908i	0.118854	−	0.520732i
$944$	−6.84003	+	8.57713i	−0.222624	+	0.279162i
$945$	−1.17157			−0.0381113
$946$	2.23570	−	2.80348i	0.0726889	−	0.0911490i
$947$	−2.35624	+	1.13470i	−0.0765674	+	0.0368729i	−0.471776	−	0.881719i	$-0.656387\pi$
$947$	−2.35624	+	1.13470i	−0.0765674	+	0.0368729i	0.395208	+	0.918592i	$0.370672\pi$
$948$	−13.9124	−	17.4456i	−0.451853	−	0.566605i
$949$	−9.54794	−	11.9727i	−0.309939	−	0.388652i
$950$	−52.2032	−	25.1397i	−1.69369	−	0.815640i
$951$	16.8985	−	74.0371i	0.547971	−	2.40082i
$952$	−2.30157	−	10.0838i	−0.0745942	−	0.326819i
$953$	32.0992	−	15.4582i	1.03979	−	0.500739i	0.165538	−	0.986203i	$-0.447064\pi$
$953$	32.0992	−	15.4582i	1.03979	−	0.500739i	0.874256	+	0.485465i	$0.161350\pi$
$954$	58.3554	+	28.1025i	1.88932	+	0.909851i
$955$	5.63283	+	24.6790i	0.182274	+	0.798595i
$956$	−75.2548			−2.43392
$957$		0			0
$958$	−16.6569			−0.538159
$959$	7.55261	+	33.0902i	0.243887	+	1.06854i
$960$	−21.3781	−	10.2952i	−0.689976	−	0.332275i
$961$	−63.4520	+	30.5569i	−2.04684	+	0.985706i
$962$	8.22672	+	36.0436i	0.265240	+	1.16209i
$963$	9.33278	−	40.8896i	0.300745	−	1.31765i
$964$	63.1694	+	30.4208i	2.03455	+	0.979787i
$965$	3.22442	+	4.04330i	0.103798	+	0.130158i
$966$	37.5866	+	47.1321i	1.20933	+	1.51645i
$967$	31.7525	−	15.2912i	1.02109	−	0.491732i	0.153048	−	0.988219i	$-0.451091\pi$
$967$	31.7525	−	15.2912i	1.02109	−	0.491732i	0.868044	+	0.496487i	$0.165377\pi$
$968$	29.8022	−	37.3708i	0.957878	−	1.20114i
$969$	12.0000			0.385496
$970$	6.75141	−	8.46601i	0.216775	−	0.271827i
$971$	3.48398	−	15.2643i	0.111806	−	0.489855i	−0.887757	−	0.460312i	$-0.847738\pi$
$971$	3.48398	−	15.2643i	0.111806	−	0.489855i	0.999564	−	0.0295431i	$-0.00940522\pi$
$972$	18.4496	−	80.8329i	0.591771	−	2.59272i
$973$	−24.6889	+	30.9589i	−0.791491	+	0.992498i
$974$	27.7990			0.890737
$975$	23.0508	−	28.9047i	0.738215	−	0.925693i
$976$	13.0508	−	6.28493i	0.417746	−	0.201176i
$977$	22.5526	+	28.2801i	0.721522	+	0.904760i	0.998423	−	0.0561387i	$-0.0178789\pi$
$977$	22.5526	+	28.2801i	0.721522	+	0.904760i	−0.276901	+	0.960898i	$0.589307\pi$
$978$	−14.2776	−	17.9035i	−0.456547	−	0.572492i
$979$	−4.65943	−	2.24386i	−0.148916	−	0.0717141i
$980$	0.851905	−	3.73244i	0.0272131	−	0.119228i
$981$	−7.96602	−	34.9014i	−0.254336	−	1.11432i
$982$	−46.2055	+	22.2514i	−1.47448	+	0.710071i
$983$	19.7042	+	9.48906i	0.628468	+	0.302654i	0.720873	−	0.693067i	$-0.243741\pi$
$983$	19.7042	+	9.48906i	0.628468	+	0.302654i	−0.0924051	+	0.995721i	$0.529455\pi$
$984$	−10.6363	−	46.6006i	−0.339072	−	1.48557i
$985$	−2.00000			−0.0637253
$986$		0			0
$987$	22.1421			0.704792
$988$	19.5687	+	85.7363i	0.622565	+	2.72763i
$989$	−11.8141	−	5.68939i	−0.375668	−	0.180912i
$990$	2.54832	−	1.22721i	0.0809911	−	0.0390032i
$991$	2.85459	+	12.5068i	0.0906792	+	0.397291i	0.999816	−	0.0192072i	$-0.00611423\pi$
$991$	2.85459	+	12.5068i	0.0906792	+	0.397291i	−0.909136	+	0.416499i	$0.863257\pi$
$992$	−3.55378	+	15.5701i	−0.112833	+	0.494353i
$993$	5.25123	+	2.52886i	0.166643	+	0.0802509i
$994$	−37.5866	−	47.1321i	−1.19218	−	1.49494i
$995$	0.302568	+	0.379408i	0.00959205	+	0.0120281i
$996$	−63.7612	+	30.7058i	−2.02035	+	0.972949i
$997$	17.6350	−	22.1135i	0.558505	−	0.700343i	−0.419776	−	0.907628i	$-0.637891\pi$
$997$	17.6350	−	22.1135i	0.558505	−	0.700343i	0.978281	+	0.207285i	$0.0664628\pi$
$998$	−45.7990			−1.44974
$999$	1.03303	−	1.29538i	0.0326837	−	0.0409840i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.j.645.2		12
29.2	odd	28		841.2.b.a.840.4		4
29.3	odd	28		841.2.e.k.63.1		24
29.4	even	14		841.2.d.f.605.1		12
29.5	even	14		841.2.a.d.1.2		2
29.6	even	14		841.2.d.f.571.1		12
29.7	even	7	inner	841.2.d.j.778.1		12
29.8	odd	28		841.2.e.k.651.1		24
29.9	even	14		841.2.d.f.190.1		12
29.10	odd	28		841.2.e.k.236.4		24
29.11	odd	28		841.2.e.k.267.4		24
29.12	odd	4		841.2.e.k.196.1		24
29.13	even	14		841.2.d.f.574.2		12
29.14	odd	28		841.2.e.k.270.1		24
29.15	odd	28		841.2.e.k.270.4		24
29.16	even	7	inner	841.2.d.j.574.1		12
29.17	odd	4		841.2.e.k.196.4		24
29.18	odd	28		841.2.e.k.267.1		24
29.19	odd	28		841.2.e.k.236.1		24
29.20	even	7	inner	841.2.d.j.190.2		12
29.21	odd	28		841.2.e.k.651.4		24
29.22	even	14		841.2.d.f.778.2		12
29.23	even	7	inner	841.2.d.j.571.2		12
29.24	even	7		29.2.a.a.1.1	✓	2
29.25	even	7	inner	841.2.d.j.605.2		12
29.26	odd	28		841.2.e.k.63.4		24
29.27	odd	28		841.2.b.a.840.1		4
29.28	even	2		841.2.d.f.645.1		12
87.5	odd	14		7569.2.a.c.1.1		2
87.53	odd	14		261.2.a.d.1.2		2
116.111	odd	14		464.2.a.h.1.1		2
145.24	even	14		725.2.a.b.1.2		2
145.53	odd	28		725.2.b.b.349.4		4
145.82	odd	28		725.2.b.b.349.1		4
203.111	odd	14		1421.2.a.j.1.1		2
232.53	even	14		1856.2.a.r.1.1		2
232.227	odd	14		1856.2.a.w.1.2		2
319.285	odd	14		3509.2.a.j.1.2		2
348.227	even	14		4176.2.a.bq.1.2		2
377.285	even	14		4901.2.a.g.1.2		2
435.314	odd	14		6525.2.a.o.1.1		2
493.169	even	14		8381.2.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.a.a.1.1	✓	2	29.24	even	7
261.2.a.d.1.2		2	87.53	odd	14
464.2.a.h.1.1		2	116.111	odd	14
725.2.a.b.1.2		2	145.24	even	14
725.2.b.b.349.1		4	145.82	odd	28
725.2.b.b.349.4		4	145.53	odd	28
841.2.a.d.1.2		2	29.5	even	14
841.2.b.a.840.1		4	29.27	odd	28
841.2.b.a.840.4		4	29.2	odd	28
841.2.d.f.190.1		12	29.9	even	14
841.2.d.f.571.1		12	29.6	even	14
841.2.d.f.574.2		12	29.13	even	14
841.2.d.f.605.1		12	29.4	even	14
841.2.d.f.645.1		12	29.28	even	2
841.2.d.f.778.2		12	29.22	even	14
841.2.d.j.190.2		12	29.20	even	7	inner
841.2.d.j.571.2		12	29.23	even	7	inner
841.2.d.j.574.1		12	29.16	even	7	inner
841.2.d.j.605.2		12	29.25	even	7	inner
841.2.d.j.645.2		12	1.1	even	1	trivial
841.2.d.j.778.1		12	29.7	even	7	inner
841.2.e.k.63.1		24	29.3	odd	28
841.2.e.k.63.4		24	29.26	odd	28
841.2.e.k.196.1		24	29.12	odd	4
841.2.e.k.196.4		24	29.17	odd	4
841.2.e.k.236.1		24	29.19	odd	28
841.2.e.k.236.4		24	29.10	odd	28
841.2.e.k.267.1		24	29.18	odd	28
841.2.e.k.267.4		24	29.11	odd	28
841.2.e.k.270.1		24	29.14	odd	28
841.2.e.k.270.4		24	29.15	odd	28
841.2.e.k.651.1		24	29.8	odd	28
841.2.e.k.651.4		24	29.21	odd	28
1421.2.a.j.1.1		2	203.111	odd	14
1856.2.a.r.1.1		2	232.53	even	14
1856.2.a.w.1.2		2	232.227	odd	14
3509.2.a.j.1.2		2	319.285	odd	14
4176.2.a.bq.1.2		2	348.227	even	14
4901.2.a.g.1.2		2	377.285	even	14
6525.2.a.o.1.1		2	435.314	odd	14
7569.2.a.c.1.1		2	87.5	odd	14
8381.2.a.e.1.1		2	493.169	even	14

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.d (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.537213 + 2.35368i) q^{2} +(-2.17513 - 1.04749i) q^{3} +(-3.44929 + 1.66109i) q^{4} +(0.222521 + 0.974928i) q^{5} +(1.29695 - 5.68230i) q^{6} +(2.54832 + 1.22721i) q^{7} +(-2.75222 - 3.45117i) q^{8} +(1.76350 + 2.21135i) q^{9} +(-2.17513 + 1.04749i) q^{10} +(-0.258258 + 0.323845i) q^{11} +9.24264 q^{12} +(-2.38699 + 2.99318i) q^{13} +(-1.51947 + 6.65722i) q^{14} +(0.537213 - 2.35368i) q^{15} +(1.87047 - 2.34549i) q^{16} +0.828427 q^{17} +(-4.25745 + 5.33868i) q^{18} +(-5.40581 + 2.60330i) q^{19} +(-2.38699 - 2.99318i) q^{20} +(-4.25745 - 5.33868i) q^{21} +(-0.900969 - 0.433884i) q^{22} +(-0.813727 + 3.56517i) q^{23} +(2.37137 + 10.3897i) q^{24} +(3.60388 - 1.73553i) q^{25} +(-8.32733 - 4.01023i) q^{26} +(0.0921712 + 0.403828i) q^{27} -10.8284 q^{28} +5.82843 q^{30} +(-2.24102 - 9.81857i) q^{31} +(-1.42874 - 0.688047i) q^{32} +(0.900969 - 0.433884i) q^{33} +(0.445042 + 1.94986i) q^{34} +(-0.629384 + 2.75751i) q^{35} +(-9.75608 - 4.69828i) q^{36} +(-2.49396 - 3.12733i) q^{37} +(-9.03143 - 11.3250i) q^{38} +(8.32733 - 4.01023i) q^{39} +(2.75222 - 3.45117i) q^{40} -4.48528 q^{41} +(10.2784 - 12.8887i) q^{42} +(-0.797913 + 3.49588i) q^{43} +(0.352871 - 1.54603i) q^{44} +(-1.76350 + 2.21135i) q^{45} -8.82843 q^{46} +(-2.02175 + 2.53520i) q^{47} +(-6.52539 + 3.14246i) q^{48} +(0.623490 + 0.781831i) q^{49} +(6.02095 + 7.55003i) q^{50} +(-1.80194 - 0.867767i) q^{51} +(3.26146 - 14.2894i) q^{52} +(-2.11067 - 9.24747i) q^{53} +(-0.900969 + 0.433884i) q^{54} +(-0.373194 - 0.179721i) q^{55} +(-2.77824 - 12.1722i) q^{56} +14.4853 q^{57} -3.65685 q^{59} +(2.05668 + 9.01091i) q^{60} +(4.35026 + 2.09498i) q^{61} +(21.9059 - 10.5493i) q^{62} +(1.78017 + 7.79942i) q^{63} +(2.18703 - 9.58201i) q^{64} +(-3.44929 - 1.66109i) q^{65} +(1.50524 + 1.88751i) q^{66} +(3.52699 + 4.42271i) q^{67} +(-2.85749 + 1.37609i) q^{68} +(5.50443 - 6.90234i) q^{69} -6.82843 q^{70} +(-5.50443 + 6.90234i) q^{71} +(2.77824 - 12.1722i) q^{72} +(-0.890084 + 3.89971i) q^{73} +(6.02095 - 7.55003i) q^{74} -9.65685 q^{75} +(14.3219 - 17.9591i) q^{76} +(-1.05555 + 0.508326i) q^{77} +(13.9124 + 17.4456i) q^{78} +(-1.50524 - 1.88751i) q^{79} +(2.70291 + 1.30165i) q^{80} +(2.11067 - 9.24747i) q^{81} +(-2.40955 - 10.5569i) q^{82} +(-6.89859 + 3.32218i) q^{83} +(23.5533 + 11.3426i) q^{84} +(0.184342 + 0.807657i) q^{85} -8.65685 q^{86} +1.82843 q^{88} +(2.77824 + 12.1722i) q^{89} +(-6.15220 - 2.96274i) q^{90} +(-9.75608 + 4.69828i) q^{91} +(-3.11529 - 13.6490i) q^{92} +(-5.41031 + 23.7041i) q^{93} +(-7.05317 - 3.39663i) q^{94} +(-3.74094 - 4.69099i) q^{95} +(2.38699 + 2.99318i) q^{96} +(-4.04110 + 1.94609i) q^{97} +(-1.50524 + 1.88751i) q^{98} -1.17157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 6 q^{6} + 6 q^{8} - 2 q^{10} - 2 q^{11} + 60 q^{12} + 2 q^{13} - 8 q^{14} + 2 q^{15} - 6 q^{16} - 24 q^{17} + 8 q^{18} - 12 q^{19} + 2 q^{20} + 8 q^{21} - 2 q^{22}+ \cdots - 48 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 6 * q^6 + 6 * q^8 - 2 * q^10 - 2 * q^11 + 60 * q^12 + 2 * q^13 - 8 * q^14 + 2 * q^15 - 6 * q^16 - 24 * q^17 + 8 * q^18 - 12 * q^19 + 2 * q^20 + 8 * q^21 - 2 * q^22 + 4 * q^23 + 10 * q^24 + 8 * q^25 - 10 * q^26 - 2 * q^27 - 96 * q^28 + 36 * q^30 - 6 * q^31 - 6 * q^32 + 2 * q^33 + 4 * q^34 - 16 * q^36 + 8 * q^37 + 12 * q^38 + 10 * q^39 - 6 * q^40 + 48 * q^41 - 16 * q^42 - 10 * q^43 + 6 * q^44 - 72 * q^46 - 2 * q^47 - 6 * q^48 - 2 * q^49 - 8 * q^50 - 4 * q^51 + 18 * q^52 - 2 * q^53 - 2 * q^54 + 2 * q^55 - 8 * q^56 + 72 * q^57 + 24 * q^59 + 10 * q^60 + 4 * q^61 + 26 * q^62 + 16 * q^63 + 14 * q^64 - 2 * q^65 - 2 * q^66 - 12 * q^68 - 12 * q^69 - 48 * q^70 + 12 * q^71 + 8 * q^72 - 8 * q^73 - 8 * q^74 - 48 * q^75 - 12 * q^76 - 8 * q^77 - 22 * q^78 + 2 * q^79 + 6 * q^80 + 2 * q^81 - 16 * q^82 - 4 * q^83 + 24 * q^84 - 4 * q^85 - 36 * q^86 - 12 * q^88 + 8 * q^89 - 8 * q^90 - 16 * q^91 - 28 * q^92 - 26 * q^93 - 10 * q^94 + 12 * q^95 - 2 * q^96 + 8 * q^97 + 2 * q^98 - 48 * q^99

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