LMFDB - Embedded newform 841.2.d.g.605.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(190,841)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [12,-1,1,1,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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:	12.0.4413675765625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 2x^{10} - 3x^{9} + 5x^{8} - 8x^{7} + 13x^{6} + 8x^{5} + 5x^{4} + 3x^{3} + 2x^{2} + x + 1 $ x^12 - x^11 + 2x^10 - 3x^9 + 5x^8 - 8x^7 + 13x^6 + 8x^5 + 5x^4 + 3x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			605.1
Root			$0.360046 - 1.57747i$ of defining polynomial
Character	$\chi$	$=$	841.605
Dual form			841.2.d.g.645.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.360046 + 1.57747i) q^{2} +(1.45780 - 0.702039i) q^{3} +(-0.556829 - 0.268155i) q^{4} +(0.635097 - 2.78254i) q^{5} +(0.582567 + 2.55239i) q^{6} +(-2.01463 + 0.970194i) q^{7} +(-1.39417 + 1.74823i) q^{8} +(-0.238152 + 0.298633i) q^{9} +(4.16070 + 2.00369i) q^{10} +(2.25581 + 2.82869i) q^{11} -1.00000 q^{12} +(2.64115 + 3.31189i) q^{13} +(-0.805088 - 3.52732i) q^{14} +(-1.02761 - 4.50225i) q^{15} +(-3.02648 - 3.79509i) q^{16} +6.61803 q^{17} +(-0.385338 - 0.483198i) q^{18} +(1.67049 + 0.804465i) q^{19} +(-1.09979 + 1.37910i) q^{20} +(-2.25581 + 2.82869i) q^{21} +(-5.27436 + 2.54000i) q^{22} +(-0.720093 - 3.15493i) q^{23} +(-0.805088 + 3.52732i) q^{24} +(-2.83436 - 1.36495i) q^{25} +(-6.17533 + 2.97388i) q^{26} +(-1.21766 + 5.33494i) q^{27} +1.38197 q^{28} +7.47214 q^{30} +(0.242586 - 1.06284i) q^{31} +(3.04705 - 1.46738i) q^{32} +(5.27436 + 2.54000i) q^{33} +(-2.38280 + 10.4397i) q^{34} +(1.42012 + 6.22196i) q^{35} +(0.212690 - 0.102426i) q^{36} +(5.42948 - 6.80835i) q^{37} +(-1.87047 + 2.34549i) q^{38} +(6.17533 + 2.97388i) q^{39} +(3.97909 + 4.98962i) q^{40} +2.85410 q^{41} +(-3.64997 - 4.57692i) q^{42} +(-0.615033 - 2.69463i) q^{43} +(-0.497572 - 2.18001i) q^{44} +(0.679710 + 0.852329i) q^{45} +5.23607 q^{46} +(4.36443 + 5.47282i) q^{47} +(-7.07630 - 3.40777i) q^{48} +(-1.24698 + 1.56366i) q^{49} +(3.17367 - 3.97966i) q^{50} +(9.64776 - 4.64612i) q^{51} +(-0.582567 - 2.55239i) q^{52} +(0.445042 - 1.94986i) q^{53} +(-7.97727 - 3.84165i) q^{54} +(9.30362 - 4.48039i) q^{55} +(1.11260 - 4.87464i) q^{56} +3.00000 q^{57} -5.09017 q^{59} +(-0.635097 + 2.78254i) q^{60} +(1.45780 - 0.702039i) q^{61} +(1.58925 + 0.765341i) q^{62} +(0.190056 - 0.832688i) q^{63} +(-0.942614 - 4.12986i) q^{64} +(10.8929 - 5.24573i) q^{65} +(-5.90578 + 7.40561i) q^{66} +(-6.52927 + 8.18745i) q^{67} +(-3.68512 - 1.77466i) q^{68} +(-3.26463 - 4.09372i) q^{69} -10.3262 q^{70} +(0.952608 + 1.19453i) q^{71} +(-0.190056 - 0.832688i) q^{72} +(-0.0649307 - 0.284480i) q^{73} +(8.78508 + 11.0161i) q^{74} -5.09017 q^{75} +(-0.714456 - 0.895899i) q^{76} +(-7.28899 - 3.51019i) q^{77} +(-6.91461 + 8.67064i) q^{78} +(-3.17367 + 3.97966i) q^{79} +(-12.4821 + 6.01107i) q^{80} +(1.71524 + 7.51494i) q^{81} +(-1.02761 + 4.50225i) q^{82} +(-7.15754 - 3.44689i) q^{83} +(2.01463 - 0.970194i) q^{84} +(4.20310 - 18.4150i) q^{85} +4.47214 q^{86} -8.09017 q^{88} +(-1.93776 + 8.48987i) q^{89} +(-1.58925 + 0.765341i) q^{90} +(-8.53410 - 4.10981i) q^{91} +(-0.445042 + 1.94986i) q^{92} +(-0.392512 - 1.71971i) q^{93} +(-10.2046 + 4.91427i) q^{94} +(3.29938 - 4.13729i) q^{95} +(3.41182 - 4.27829i) q^{96} +(-14.9221 - 7.18612i) q^{97} +(-2.01766 - 2.53006i) q^{98} -1.38197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} + q^{3} + q^{4} - q^{5} + 3 q^{6} + 3 q^{9} + 7 q^{10} - 5 q^{11} - 12 q^{12} - 4 q^{13} - 5 q^{14} - 7 q^{15} + 3 q^{16} + 66 q^{17} - q^{18} - 3 q^{19} + 8 q^{20} + 5 q^{21} - 5 q^{22}+ \cdots - 30 q^{99}+O(q^{100}) $ 12 * q - q^2 + q^3 + q^4 - q^5 + 3 * q^6 + 3 * q^9 + 7 * q^10 - 5 * q^11 - 12 * q^12 - 4 * q^13 - 5 * q^14 - 7 * q^15 + 3 * q^16 + 66 * q^17 - q^18 - 3 * q^19 + 8 * q^20 + 5 * q^21 - 5 * q^22 - 2 * q^23 - 5 * q^24 - 13 * q^25 - 7 * q^26 - 2 * q^27 + 30 * q^28 + 36 * q^30 - 9 * q^31 + 9 * q^32 + 5 * q^33 - 8 * q^34 + 15 * q^35 - 4 * q^36 - 4 * q^37 + 6 * q^38 + 7 * q^39 - 15 * q^40 - 6 * q^41 + 5 * q^42 - 10 * q^43 + 9 * q^45 + 36 * q^46 - 14 * q^47 - 9 * q^48 + 4 * q^49 + q^50 + 8 * q^51 - 3 * q^52 + 4 * q^53 - 11 * q^54 + 5 * q^55 + 10 * q^56 + 36 * q^57 + 6 * q^59 + q^60 + q^61 + 8 * q^62 - 5 * q^63 - 4 * q^64 + 13 * q^65 + 10 * q^66 + 12 * q^67 + 3 * q^68 + 6 * q^69 - 30 * q^70 - 12 * q^71 + 5 * q^72 - 14 * q^73 - 17 * q^74 + 6 * q^75 + 9 * q^76 - 5 * q^77 + 11 * q^78 - q^79 - 21 * q^80 + 2 * q^81 - 7 * q^82 + 2 * q^83 + 2 * q^85 - 30 * q^88 - 4 * q^89 - 8 * q^90 - 10 * q^91 - 4 * q^92 - 8 * q^93 - 7 * q^94 - 24 * q^95 - 2 * q^96 - 13 * q^97 + 2 * q^98 - 30 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{7}\right)$

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 $

$2$	−0.360046	+	1.57747i	−0.254591	+	1.11544i	0.672351	+	0.740233i	$0.265285\pi$
$2$	−0.360046	+	1.57747i	−0.254591	+	1.11544i	−0.926942	+	0.375205i	$0.877572\pi$
$3$	1.45780	−	0.702039i	0.841660	−	0.405322i	0.0371850	−	0.999308i	$-0.488161\pi$
$3$	1.45780	−	0.702039i	0.841660	−	0.405322i	0.804475	+	0.593986i	$0.202447\pi$
$4$	−0.556829	−	0.268155i	−0.278415	−	0.134077i
$5$	0.635097	−	2.78254i	0.284024	−	1.24439i	−0.608559	−	0.793509i	$-0.708252\pi$
$5$	0.635097	−	2.78254i	0.284024	−	1.24439i	0.892583	−	0.450883i	$-0.148891\pi$
$6$	0.582567	+	2.55239i	0.237832	+	1.04201i
$7$	−2.01463	+	0.970194i	−0.761458	+	0.366699i	−0.773969	−	0.633223i	$-0.781732\pi$
$7$	−2.01463	+	0.970194i	−0.761458	+	0.366699i	0.0125117	+	0.999922i	$0.496017\pi$
$8$	−1.39417	+	1.74823i	−0.492912	+	0.618092i
$9$	−0.238152	+	0.298633i	−0.0793840	+	0.0995444i
$10$	4.16070	+	2.00369i	1.31573	+	0.633622i
$11$	2.25581	+	2.82869i	0.680151	+	0.852883i	0.995368	−	0.0961367i	$-0.0306486\pi$
$11$	2.25581	+	2.82869i	0.680151	+	0.852883i	−0.315217	+	0.949020i	$0.602077\pi$
$12$	−1.00000			−0.288675
$13$	2.64115	+	3.31189i	0.732522	+	0.918553i	0.998974	−	0.0452949i	$-0.0144227\pi$
$13$	2.64115	+	3.31189i	0.732522	+	0.918553i	−0.266452	+	0.963848i	$0.585851\pi$
$14$	−0.805088	−	3.52732i	−0.215169	−	0.942717i
$15$	−1.02761	−	4.50225i	−0.265328	−	1.16248i
$16$	−3.02648	−	3.79509i	−0.756621	−	0.948772i
$17$	6.61803			1.60511			0.802555	−	0.596579i	$-0.203474\pi$
$17$	6.61803			1.60511			0.802555	+	0.596579i	$0.203474\pi$
$18$	−0.385338	−	0.483198i	−0.0908250	−	0.113891i
$19$	1.67049	+	0.804465i	0.383236	+	0.184557i	0.615575	−	0.788078i	$-0.288924\pi$
$19$	1.67049	+	0.804465i	0.383236	+	0.184557i	−0.232339	+	0.972635i	$0.574638\pi$
$20$	−1.09979	+	1.37910i	−0.245921	+	0.308376i
$21$	−2.25581	+	2.82869i	−0.492258	+	0.617271i
$22$	−5.27436	+	2.54000i	−1.12450	+	0.541530i
$23$	−0.720093	−	3.15493i	−0.150150	−	0.657849i	−0.992840	−	0.119451i	$-0.961887\pi$
$23$	−0.720093	−	3.15493i	−0.150150	−	0.657849i	0.842690	−	0.538398i	$-0.180970\pi$
$24$	−0.805088	+	3.52732i	−0.164338	+	0.720012i
$25$	−2.83436	−	1.36495i	−0.566871	−	0.272991i
$26$	−6.17533	+	2.97388i	−1.21108	+	0.583227i
$27$	−1.21766	+	5.33494i	−0.234340	+	1.02671i
$28$	1.38197			0.261167
$29$		0			0
$29$		0			0
$30$	7.47214			1.36422
$31$	0.242586	−	1.06284i	0.0435697	−	0.190891i	−0.948460	−	0.316898i	$-0.897359\pi$
$31$	0.242586	−	1.06284i	0.0435697	−	0.190891i	0.992029	+	0.126006i	$0.0402160\pi$
$32$	3.04705	−	1.46738i	0.538647	−	0.259399i
$33$	5.27436	+	2.54000i	0.918149	+	0.442157i
$34$	−2.38280	+	10.4397i	−0.408647	+	1.79040i
$35$	1.42012	+	6.22196i	0.240044	+	1.05170i
$36$	0.212690	−	0.102426i	0.0354483	−	0.0170710i
$37$	5.42948	−	6.80835i	0.892600	−	1.11929i	−0.0996489	−	0.995023i	$-0.531772\pi$
$37$	5.42948	−	6.80835i	0.892600	−	1.11929i	0.992249	−	0.124263i	$-0.0396566\pi$
$38$	−1.87047	+	2.34549i	−0.303430	+	0.380489i
$39$	6.17533	+	2.97388i	0.988845	+	0.476202i
$40$	3.97909	+	4.98962i	0.629149	+	0.788929i
$41$	2.85410			0.445736			0.222868	−	0.974849i	$-0.428458\pi$
$41$	2.85410			0.445736			0.222868	+	0.974849i	$0.428458\pi$
$42$	−3.64997	−	4.57692i	−0.563203	−	0.706234i
$43$	−0.615033	−	2.69463i	−0.0937916	−	0.410928i	0.906136	−	0.422987i	$-0.139018\pi$
$43$	−0.615033	−	2.69463i	−0.0937916	−	0.410928i	−0.999927	+	0.0120593i	$0.996161\pi$
$44$	−0.497572	−	2.18001i	−0.0750118	−	0.328648i
$45$	0.679710	+	0.852329i	0.101325	+	0.127058i
$46$	5.23607			0.772016
$47$	4.36443	+	5.47282i	0.636617	+	0.798293i	0.990575	−	0.136968i	$-0.0437359\pi$
$47$	4.36443	+	5.47282i	0.636617	+	0.798293i	−0.353958	+	0.935261i	$0.615164\pi$
$48$	−7.07630	−	3.40777i	−1.02138	−	0.491869i
$49$	−1.24698	+	1.56366i	−0.178140	+	0.223380i
$50$	3.17367	−	3.97966i	0.448825	−	0.562808i
$51$	9.64776	−	4.64612i	1.35096	−	0.650586i
$52$	−0.582567	−	2.55239i	−0.0807876	−	0.353953i
$53$	0.445042	−	1.94986i	0.0611312	−	0.267833i	−0.935121	−	0.354328i	$-0.884710\pi$
$53$	0.445042	−	1.94986i	0.0611312	−	0.267833i	0.996252	+	0.0864950i	$0.0275667\pi$
$54$	−7.97727	−	3.84165i	−1.08557	−	0.522782i
$55$	9.30362	−	4.48039i	1.25450	−	0.604135i
$56$	1.11260	−	4.87464i	0.148678	−	0.651401i
$57$	3.00000			0.397360
$58$		0			0
$59$	−5.09017			−0.662684			−0.331342	−	0.943511i	$-0.607501\pi$
$59$	−5.09017			−0.662684			−0.331342	+	0.943511i	$0.607501\pi$
$60$	−0.635097	+	2.78254i	−0.0819907	+	0.359225i
$61$	1.45780	−	0.702039i	0.186652	−	0.0898868i	−0.338224	−	0.941066i	$-0.609826\pi$
$61$	1.45780	−	0.702039i	0.186652	−	0.0898868i	0.524876	+	0.851179i	$0.324112\pi$
$62$	1.58925	+	0.765341i	0.201835	+	0.0971985i
$63$	0.190056	−	0.832688i	0.0239448	−	0.104909i
$64$	−0.942614	−	4.12986i	−0.117827	−	0.516233i
$65$	10.8929	−	5.24573i	1.35109	−	0.650652i
$66$	−5.90578	+	7.40561i	−0.726951	+	0.911568i
$67$	−6.52927	+	8.18745i	−0.797677	+	1.00026i	0.202104	+	0.979364i	$0.435222\pi$
$67$	−6.52927	+	8.18745i	−0.797677	+	1.00026i	−0.999782	+	0.0208917i	$0.993349\pi$
$68$	−3.68512	−	1.77466i	−0.446886	−	0.215209i
$69$	−3.26463	−	4.09372i	−0.393016	−	0.492826i
$70$	−10.3262			−1.23422
$71$	0.952608	+	1.19453i	0.113054	+	0.141765i	0.835139	−	0.550040i	$-0.185387\pi$
$71$	0.952608	+	1.19453i	0.113054	+	0.141765i	−0.722085	+	0.691805i	$0.756816\pi$
$72$	−0.190056	−	0.832688i	−0.0223983	−	0.0981332i
$73$	−0.0649307	−	0.284480i	−0.00759957	−	0.0332959i	0.970986	−	0.239136i	$-0.0768643\pi$
$73$	−0.0649307	−	0.284480i	−0.00759957	−	0.0332959i	−0.978586	+	0.205841i	$0.934007\pi$
$74$	8.78508	+	11.0161i	1.02124	+	1.28060i
$75$	−5.09017			−0.587762
$76$	−0.714456	−	0.895899i	−0.0819537	−	0.102767i
$77$	−7.28899	−	3.51019i	−0.830658	−	0.400024i
$78$	−6.91461	+	8.67064i	−0.782925	+	0.981757i
$79$	−3.17367	+	3.97966i	−0.357066	+	0.447746i	−0.927626	−	0.373509i	$-0.878154\pi$
$79$	−3.17367	+	3.97966i	−0.357066	+	0.447746i	0.570561	+	0.821255i	$0.306726\pi$
$80$	−12.4821	+	6.01107i	−1.39554	+	0.672058i
$81$	1.71524	+	7.51494i	0.190582	+	0.834994i
$82$	−1.02761	+	4.50225i	−0.113480	+	0.497190i
$83$	−7.15754	−	3.44689i	−0.785642	−	0.378345i	−0.00234861	−	0.999997i	$-0.500748\pi$
$83$	−7.15754	−	3.44689i	−0.785642	−	0.378345i	−0.783294	+	0.621652i	$0.786462\pi$
$84$	2.01463	−	0.970194i	0.219814	−	0.105857i
$85$	4.20310	−	18.4150i	0.455890	−	1.99738i
$86$	4.47214			0.482243
$87$		0			0
$88$	−8.09017			−0.862415
$89$	−1.93776	+	8.48987i	−0.205402	+	0.899925i	0.762180	+	0.647366i	$0.224129\pi$
$89$	−1.93776	+	8.48987i	−0.205402	+	0.899925i	−0.967582	+	0.252559i	$0.918728\pi$
$90$	−1.58925	+	0.765341i	−0.167521	+	0.0806741i
$91$	−8.53410	−	4.10981i	−0.894617	−	0.430825i
$92$	−0.445042	+	1.94986i	−0.0463988	+	0.203287i
$93$	−0.392512	−	1.71971i	−0.0407016	−	0.178325i
$94$	−10.2046	+	4.91427i	−1.05252	+	0.506868i
$95$	3.29938	−	4.13729i	0.338509	−	0.424477i
$96$	3.41182	−	4.27829i	0.348218	−	0.436651i
$97$	−14.9221	−	7.18612i	−1.51511	−	0.729639i	−0.522691	−	0.852522i	$-0.675072\pi$
$97$	−14.9221	−	7.18612i	−1.51511	−	0.729639i	−0.992421	+	0.122883i	$0.960786\pi$
$98$	−2.01766	−	2.53006i	−0.203814	−	0.255575i
$99$	−1.38197			−0.138893
$100$	1.21223	+	1.52009i	0.121223	+	0.152009i
$101$	0.360046	+	1.57747i	0.0358260	+	0.156964i	0.989677	−	0.143317i	$-0.0457768\pi$
$101$	0.360046	+	1.57747i	0.0358260	+	0.156964i	−0.953851	+	0.300281i	$0.902920\pi$
$102$	3.85545	+	16.8918i	0.381746	+	1.67254i
$103$	−8.21781	−	10.3048i	−0.809725	−	1.01536i	−0.999438	−	0.0335230i	$-0.989327\pi$
$103$	−8.21781	−	10.3048i	−0.809725	−	1.01536i	0.189713	−	0.981840i	$-0.439244\pi$
$104$	−9.47214			−0.928819
$105$	6.43830	+	8.07338i	0.628314	+	0.787881i
$106$	2.91560	+	1.40408i	0.283188	+	0.136376i
$107$	7.00557	−	8.78471i	0.677254	−	0.849250i	−0.317844	−	0.948143i	$-0.602959\pi$
$107$	7.00557	−	8.78471i	0.677254	−	0.849250i	0.995098	+	0.0988930i	$0.0315302\pi$
$108$	2.10862	−	2.64413i	0.202902	−	0.254431i
$109$	14.9723	−	7.21029i	1.43409	−	0.690621i	0.454336	−	0.890830i	$-0.349877\pi$
$109$	14.9723	−	7.21029i	1.43409	−	0.690621i	0.979753	+	0.200209i	$0.0641622\pi$
$110$	3.71793	+	16.2893i	0.354490	+	1.55312i
$111$	3.13536	−	13.7369i	0.297595	−	1.30385i
$112$	9.77921	+	4.70942i	0.924048	+	0.444998i
$113$	−8.95948	+	4.31466i	−0.842837	+	0.405889i	−0.804914	−	0.593392i	$-0.797788\pi$
$113$	−8.95948	+	4.31466i	−0.842837	+	0.405889i	−0.0379231	+	0.999281i	$0.512074\pi$
$114$	−1.08014	+	4.73240i	−0.101164	+	0.443230i
$115$	−9.23607			−0.861268
$116$		0			0
$117$	−1.61803			−0.149587
$118$	1.83270	−	8.02957i	0.168713	−	0.739182i
$119$	−13.3329	+	6.42077i	−1.22222	+	0.588591i
$120$	9.30362	+	4.48039i	0.849300	+	0.409001i
$121$	−0.465107	+	2.03777i	−0.0422824	+	0.185251i
$122$	0.582567	+	2.55239i	0.0527432	+	0.231083i
$123$	4.16070	−	2.00369i	0.375158	−	0.180667i
$124$	−0.420084	+	0.526768i	−0.0377246	+	0.0473052i
$125$	3.29938	−	4.13729i	0.295106	−	0.370051i
$126$	1.24511	+	0.599613i	0.110923	+	0.0534177i
$127$	1.21223	+	1.52009i	0.107568	+	0.134886i	0.832701	−	0.553722i	$-0.186793\pi$
$127$	1.21223	+	1.52009i	0.107568	+	0.134886i	−0.725133	+	0.688609i	$0.758222\pi$
$128$	13.6180			1.20368
$129$	−2.78833	−	3.49646i	−0.245499	−	0.307846i
$130$	4.35302	+	19.0718i	0.381785	+	1.67271i
$131$	−0.295116	−	1.29299i	−0.0257844	−	0.112969i	0.960398	−	0.278632i	$-0.0898808\pi$
$131$	−0.295116	−	1.29299i	−0.0257844	−	0.112969i	−0.986182	+	0.165663i	$0.947024\pi$
$132$	−2.25581	−	2.82869i	−0.196343	−	0.246206i
$133$	−4.14590			−0.359495
$134$	−10.5646	−	13.2476i	−0.912641	−	1.14442i
$135$	14.0714	+	6.77641i	1.21107	+	0.583221i
$136$	−9.22664	+	11.5698i	−0.791177	+	0.992105i
$137$	−8.63789	+	10.8316i	−0.737985	+	0.925404i	−0.999205	−	0.0398756i	$-0.987304\pi$
$137$	−8.63789	+	10.8316i	−0.737985	+	0.925404i	0.261220	+	0.965279i	$0.415875\pi$
$138$	7.63313	−	3.67592i	0.649775	−	0.312915i
$139$	−3.27288	−	14.3394i	−0.277602	−	1.21626i	−0.900815	−	0.434203i	$-0.857030\pi$
$139$	−3.27288	−	14.3394i	−0.277602	−	1.21626i	0.623213	−	0.782052i	$-0.285827\pi$
$140$	0.877683	−	3.84538i	0.0741778	−	0.324994i
$141$	10.2046	+	4.91427i	0.859381	+	0.413856i
$142$	−2.22732	+	1.07262i	−0.186912	+	0.0900122i
$143$	−3.41041	+	14.9420i	−0.285193	+	1.24951i
$144$	1.85410			0.154508
$145$		0			0
$146$	0.472136			0.0390742
$147$	−0.720093	+	3.15493i	−0.0593923	+	0.260214i
$148$	−4.84898	+	2.33515i	−0.398584	+	0.191948i
$149$	−6.65092	−	3.20292i	−0.544865	−	0.262393i	0.141141	−	0.989990i	$-0.454923\pi$
$149$	−6.65092	−	3.20292i	−0.544865	−	0.262393i	−0.686005	+	0.727597i	$0.740637\pi$
$150$	1.83270	−	8.02957i	0.149639	−	0.655612i
$151$	−4.07797	−	17.8668i	−0.331861	−	1.45398i	−0.815524	−	0.578723i	$-0.803551\pi$
$151$	−4.07797	−	17.8668i	−0.331861	−	1.45398i	0.483664	−	0.875254i	$-0.339306\pi$
$152$	−3.73533	+	1.79884i	−0.302975	+	0.145905i
$153$	−1.57610	+	1.97636i	−0.127420	+	0.159780i
$154$	8.16159	−	10.2343i	0.657679	−	0.824704i
$155$	−2.80333	−	1.35001i	−0.225168	−	0.108435i
$156$	−2.64115	−	3.31189i	−0.211461	−	0.265164i
$157$	5.56231			0.443920			0.221960	−	0.975056i	$-0.428755\pi$
$157$	5.56231			0.443920			0.221960	+	0.975056i	$0.428755\pi$
$158$	−5.13510	−	6.43922i	−0.408527	−	0.512277i
$159$	−0.720093	−	3.15493i	−0.0571071	−	0.250202i
$160$	−2.14788	−	9.41047i	−0.169805	−	0.743963i
$161$	4.51161	+	5.65739i	0.355565	+	0.445864i
$162$	−12.4721			−0.979904
$163$	−14.3617	−	18.0091i	−1.12490	−	1.41058i	−0.899833	−	0.436234i	$-0.856312\pi$
$163$	−14.3617	−	18.0091i	−1.12490	−	1.41058i	−0.225065	−	0.974344i	$-0.572259\pi$
$164$	−1.58925	−	0.765341i	−0.124099	−	0.0597631i
$165$	10.4174	−	13.0630i	0.810993	−	1.01695i
$166$	8.01440	−	10.0497i	0.622038	−	0.780011i
$167$	−17.5438	+	8.44864i	−1.35758	+	0.653776i	−0.964095	−	0.265556i	$-0.914444\pi$
$167$	−17.5438	+	8.44864i	−1.35758	+	0.653776i	−0.393484	+	0.919332i	$0.628730\pi$
$168$	−1.80023	−	7.88733i	−0.138891	−	0.608521i
$169$	−1.10020	+	4.82031i	−0.0846311	+	0.370793i
$170$	27.5357	+	13.2605i	2.11189	+	1.01703i
$171$	−0.638070	+	0.307278i	−0.0487944	+	0.0234981i
$172$	−0.380111	+	1.66538i	−0.0289832	+	0.126984i
$173$	−7.09017			−0.539056			−0.269528	−	0.962993i	$-0.586868\pi$
$173$	−7.09017			−0.539056			−0.269528	+	0.962993i	$0.586868\pi$
$174$		0			0
$175$	7.03444			0.531754
$176$	3.90798	−	17.1220i	0.294575	−	1.29062i
$177$	−7.42044	+	3.57350i	−0.557754	+	0.268600i
$178$	−12.6948	−	6.11350i	−0.951516	−	0.458226i
$179$	3.56033	−	15.5988i	0.266112	−	1.16591i	−0.648383	−	0.761315i	$-0.724554\pi$
$179$	3.56033	−	15.5988i	0.266112	−	1.16591i	0.914495	−	0.404598i	$-0.132589\pi$
$180$	−0.149926	−	0.656869i	−0.0111748	−	0.0489602i
$181$	10.7614	−	5.18243i	0.799890	−	0.385207i	0.0111531	−	0.999938i	$-0.496450\pi$
$181$	10.7614	−	5.18243i	0.799890	−	0.385207i	0.788737	+	0.614731i	$0.210735\pi$
$182$	9.55575	−	11.9825i	0.708320	−	0.888205i
$183$	1.63232	−	2.04686i	0.120664	−	0.151308i
$184$	6.51947	+	3.13961i	0.480622	+	0.231455i
$185$	−15.4963	−	19.4317i	−1.13931	−	1.42865i
$186$	2.85410			0.209273
$187$	14.9290	+	18.7204i	1.09172	+	1.36897i
$188$	−0.962679	−	4.21777i	−0.0702105	−	0.307613i
$189$	−2.72278	−	11.9293i	−0.198053	−	0.867728i
$190$	5.33851	+	6.69428i	0.387296	+	0.485654i
$191$	12.0344			0.870782			0.435391	−	0.900242i	$-0.356610\pi$
$191$	12.0344			0.870782			0.435391	+	0.900242i	$0.356610\pi$
$192$	−4.27346	−	5.35875i	−0.308411	−	0.386735i
$193$	3.17850	+	1.53068i	0.228793	+	0.110181i	0.544769	−	0.838586i	$-0.316617\pi$
$193$	3.17850	+	1.53068i	0.228793	+	0.110181i	−0.315976	+	0.948767i	$0.602332\pi$
$194$	16.7085	−	20.9518i	1.19960	−	1.50425i
$195$	12.1969	−	15.2944i	0.873438	−	1.09526i
$196$	1.11366	−	0.536310i	0.0795471	−	0.0383078i
$197$	4.38549	+	19.2141i	0.312453	+	1.36895i	0.850475	+	0.526016i	$0.176315\pi$
$197$	4.38549	+	19.2141i	0.312453	+	1.36895i	−0.538022	+	0.842931i	$0.680828\pi$
$198$	0.497572	−	2.18001i	0.0353609	−	0.154926i
$199$	−0.769519	−	0.370581i	−0.0545498	−	0.0262698i	0.406410	−	0.913691i	$-0.366780\pi$
$199$	−0.769519	−	0.370581i	−0.0545498	−	0.0262698i	−0.460960	+	0.887421i	$0.652495\pi$
$200$	6.33781	−	3.05213i	0.448151	−	0.215818i
$201$	−3.77046	+	16.5194i	−0.265947	+	1.16519i
$202$	−2.61803			−0.184204
$203$		0			0
$204$	−6.61803			−0.463355
$205$	1.81263	−	7.94166i	0.126600	−	0.554670i
$206$	19.2143	−	9.25311i	1.33872	−	0.644695i
$207$	1.11366	+	0.536310i	0.0774046	+	0.0372761i
$208$	4.57554	−	20.0468i	0.317257	−	1.38999i
$209$	1.49272	+	6.54002i	0.103253	+	0.452382i
$210$	−15.0536	+	7.24942i	−1.03880	+	0.500257i
$211$	−12.2531	+	15.3649i	−0.843539	+	1.05777i	0.154029	+	0.988066i	$0.450775\pi$
$211$	−12.2531	+	15.3649i	−0.843539	+	1.05777i	−0.997568	+	0.0696986i	$0.977796\pi$
$212$	−0.770676	+	0.966397i	−0.0529302	+	0.0663724i
$213$	2.22732	+	1.07262i	0.152613	+	0.0734947i
$214$	11.3353	+	14.2140i	0.774862	+	0.971646i
$215$	−7.88854			−0.537994
$216$	−7.62906	−	9.56654i	−0.519092	−	0.650921i
$217$	0.542438	+	2.37658i	0.0368231	+	0.161332i
$218$	5.98326	+	26.2144i	0.405238	+	1.77546i
$219$	−0.294372	−	0.369131i	−0.0198918	−	0.0249435i
$220$	−6.38197			−0.430272
$221$	17.4792	+	21.9182i	1.17578	+	1.47438i
$222$	20.5406	+	9.89184i	1.37860	+	0.663897i
$223$	11.4262	−	14.3280i	0.765156	−	0.959476i	−0.234764	−	0.972052i	$-0.575432\pi$
$223$	11.4262	−	14.3280i	0.765156	−	0.959476i	0.999921	+	0.0125764i	$0.00400331\pi$
$224$	−4.71502	+	5.91245i	−0.315036	+	0.395042i
$225$	1.08263	−	0.521366i	0.0721752	−	0.0347577i
$226$	−3.58040	−	15.6868i	−0.238165	−	1.04347i
$227$	−3.31301	+	14.5153i	−0.219892	+	0.963411i	0.737665	+	0.675167i	$0.235929\pi$
$227$	−3.31301	+	14.5153i	−0.219892	+	0.963411i	−0.957557	+	0.288244i	$0.906929\pi$
$228$	−1.67049	−	0.804465i	−0.110631	−	0.0532770i
$229$	14.1526	−	6.81553i	0.935230	−	0.450383i	0.0967461	−	0.995309i	$-0.469157\pi$
$229$	14.1526	−	6.81553i	0.935230	−	0.450383i	0.838484	+	0.544926i	$0.183442\pi$
$230$	3.32541	−	14.5696i	0.219271	−	0.960690i
$231$	−13.0902			−0.861270
$232$		0			0
$233$	10.7639			0.705169			0.352584	−	0.935780i	$-0.385303\pi$
$233$	10.7639			0.705169			0.352584	+	0.935780i	$0.385303\pi$
$234$	0.582567	−	2.55239i	0.0380836	−	0.166855i
$235$	18.0002	−	8.66844i	1.17420	−	0.565467i
$236$	2.83436	+	1.36495i	0.184501	+	0.0888509i
$237$	−1.83270	+	8.02957i	−0.119046	+	0.521577i
$238$	−5.32810	−	23.3439i	−0.345370	−	1.51316i
$239$	−13.2827	+	6.39659i	−0.859184	+	0.413761i	−0.810978	−	0.585076i	$-0.801065\pi$
$239$	−13.2827	+	6.39659i	−0.859184	+	0.413761i	−0.0482058	+	0.998837i	$0.515350\pi$
$240$	−13.9764	+	17.5259i	−0.902173	+	1.13129i
$241$	16.6175	−	20.8377i	1.07043	−	1.34228i	0.134175	−	0.990958i	$-0.457162\pi$
$241$	16.6175	−	20.8377i	1.07043	−	1.34228i	0.936256	−	0.351319i	$-0.114267\pi$
$242$	−3.04705	−	1.46738i	−0.195872	−	0.0943268i
$243$	−2.45921	−	3.08376i	−0.157759	−	0.197823i
$244$	−1.00000			−0.0640184
$245$	3.55901	+	4.46285i	0.227377	+	0.285121i
$246$	1.66271	+	7.28479i	0.106010	+	0.464461i
$247$	1.74770	+	7.65718i	0.111204	+	0.487215i
$248$	1.51988	+	1.90587i	0.0965123	+	0.121023i
$249$	−12.8541			−0.814596
$250$	5.33851	+	6.69428i	0.337637	+	0.423383i
$251$	10.4985	+	5.05582i	0.662661	+	0.319121i	0.734810	−	0.678273i	$-0.237271\pi$
$251$	10.4985	+	5.05582i	0.662661	+	0.319121i	−0.0721491	+	0.997394i	$0.522986\pi$
$252$	−0.329118	+	0.412701i	−0.0207325	+	0.0259977i
$253$	7.29995	−	9.15384i	0.458944	−	0.575497i
$254$	−2.83436	+	1.36495i	−0.177843	+	0.0856448i
$255$	−6.80075	−	29.7960i	−0.425880	−	1.86590i
$256$	−3.01790	+	13.2223i	−0.188619	+	0.826392i
$257$	0.738488	+	0.355637i	0.0460656	+	0.0221840i	0.456775	−	0.889582i	$-0.349005\pi$
$257$	0.738488	+	0.355637i	0.0460656	+	0.0221840i	−0.410709	+	0.911766i	$0.634719\pi$
$258$	6.51947	−	3.13961i	0.405885	−	0.195464i
$259$	−4.33296	+	18.9839i	−0.269237	+	1.17960i
$260$	−7.47214			−0.463402
$261$		0			0
$262$	2.14590			0.132574
$263$	−0.732494	+	3.20926i	−0.0451675	+	0.197892i	−0.992478	−	0.122426i	$-0.960933\pi$
$263$	−0.732494	+	3.20926i	−0.0451675	+	0.197892i	0.947310	+	0.320318i	$0.103790\pi$
$264$	−11.7938	+	5.67961i	−0.725860	+	0.349556i
$265$	−5.14291	−	2.47670i	−0.315927	−	0.152142i
$266$	1.49272	−	6.54002i	0.0915243	−	0.400994i
$267$	3.13536	+	13.7369i	0.191881	+	0.840685i
$268$	5.83119	−	2.80815i	0.356197	−	0.171535i
$269$	3.74094	−	4.69099i	0.228089	−	0.286015i	−0.654597	−	0.755978i	$-0.727162\pi$
$269$	3.74094	−	4.69099i	0.228089	−	0.286015i	0.882686	+	0.469964i	$0.155733\pi$
$270$	−15.7559	+	19.7573i	−0.958874	+	1.20239i
$271$	−10.9741	−	5.28485i	−0.666630	−	0.321032i	0.0697854	−	0.997562i	$-0.477769\pi$
$271$	−10.9741	−	5.28485i	−0.666630	−	0.321032i	−0.736415	+	0.676530i	$0.763483\pi$
$272$	−20.0294	−	25.1160i	−1.21446	−	1.52288i
$273$	−15.3262			−0.927586
$274$	−13.9764	−	17.5259i	−0.844345	−	1.05878i
$275$	−2.53273	−	11.0966i	−0.152729	−	0.669150i
$276$	0.720093	+	3.15493i	0.0433445	+	0.189905i
$277$	−14.7256	−	18.4653i	−0.884776	−	1.10947i	−0.993321	−	0.115382i	$-0.963191\pi$
$277$	−14.7256	−	18.4653i	−0.884776	−	1.10947i	0.108545	−	0.994091i	$-0.465381\pi$
$278$	23.7984			1.42733
$279$	0.259626	+	0.325561i	0.0155434	+	0.0194908i
$280$	−12.8573	−	6.19174i	−0.768370	−	0.370027i
$281$	−10.6770	+	13.3886i	−0.636938	+	0.798695i	−0.990616	−	0.136672i	$-0.956359\pi$
$281$	−10.6770	+	13.3886i	−0.636938	+	0.798695i	0.353679	+	0.935367i	$0.384931\pi$
$282$	−11.4262	+	14.3280i	−0.680422	+	0.853222i
$283$	0.688279	−	0.331458i	0.0409139	−	0.0197031i	−0.413315	−	0.910588i	$-0.635629\pi$
$283$	0.688279	−	0.331458i	0.0409139	−	0.0197031i	0.454229	+	0.890885i	$0.349915\pi$
$284$	−0.210120	−	0.920597i	−0.0124683	−	0.0546274i
$285$	1.90529	−	8.34763i	0.112860	−	0.494471i
$286$	−22.3426	−	10.7596i	−1.32114	−	0.636229i
$287$	−5.74995	+	2.76903i	−0.339409	+	0.163451i
$288$	−0.287452	+	1.25941i	−0.0169383	+	0.0742113i
$289$	26.7984			1.57637
$290$		0			0
$291$	−26.7984			−1.57095
$292$	−0.0401294	+	0.175818i	−0.00234840	+	0.0102890i
$293$	15.7419	−	7.58088i	0.919649	−	0.442879i	0.0867030	−	0.996234i	$-0.472367\pi$
$293$	15.7419	−	7.58088i	0.919649	−	0.442879i	0.832946	+	0.553355i	$0.186653\pi$
$294$	−4.71753	−	2.27184i	−0.275132	−	0.132497i
$295$	−3.23275	+	14.1636i	−0.188218	+	0.824638i
$296$	4.33296	+	18.9839i	0.251848	+	1.10342i
$297$	−17.8377	+	8.59019i	−1.03505	+	0.498454i
$298$	7.44713	−	9.33841i	0.431401	−	0.540959i
$299$	8.54693	−	10.7175i	0.494281	−	0.619809i
$300$	2.83436	+	1.36495i	0.163642	+	0.0788057i
$301$	3.85338	+	4.83198i	0.222105	+	0.278511i
$302$	29.6525			1.70631
$303$	1.63232	+	2.04686i	0.0937742	+	0.117589i
$304$	−2.00269	−	8.77435i	−0.114862	−	0.503244i
$305$	−1.02761	−	4.50225i	−0.0588407	−	0.257798i
$306$	−2.55018	−	3.19782i	−0.145784	−	0.182807i
$307$	−3.18034			−0.181512			−0.0907558	−	0.995873i	$-0.528928\pi$
$307$	−3.18034			−0.181512			−0.0907558	+	0.995873i	$0.528928\pi$
$308$	3.11745	+	3.90916i	0.177633	+	0.222745i
$309$	−19.2143	−	9.25311i	−1.09306	−	0.526391i
$310$	3.13892	−	3.93609i	0.178279	−	0.223555i
$311$	5.66763	−	7.10698i	0.321382	−	0.403000i	−0.594728	−	0.803927i	$-0.702740\pi$
$311$	5.66763	−	7.10698i	0.321382	−	0.403000i	0.916110	+	0.400927i	$0.131312\pi$
$312$	−13.8085	+	6.64981i	−0.781750	+	0.376471i
$313$	5.36057	+	23.4862i	0.302997	+	1.32752i	0.865578	+	0.500775i	$0.166952\pi$
$313$	5.36057	+	23.4862i	0.302997	+	1.32752i	−0.562580	+	0.826743i	$0.690191\pi$
$314$	−2.00269	+	8.77435i	−0.113018	+	0.495165i
$315$	−2.19629	−	1.05768i	−0.123747	−	0.0595933i
$316$	2.83436	−	1.36495i	0.159445	−	0.0767847i
$317$	3.18022	−	13.9335i	0.178619	−	0.782582i	−0.803649	−	0.595103i	$-0.797111\pi$
$317$	3.18022	−	13.9335i	0.178619	−	0.782582i	0.982269	−	0.187479i	$-0.0600316\pi$
$318$	5.23607			0.293624
$319$		0			0
$320$	−12.0902			−0.675861
$321$	4.04551	−	17.7245i	0.225798	−	0.989286i
$322$	−10.5487	+	5.08000i	−0.587858	+	0.283097i
$323$	11.0553	+	5.32397i	0.615136	+	0.296234i
$324$	1.06007	−	4.64449i	0.0588930	−	0.258027i
$325$	−2.96537	−	12.9921i	−0.164489	−	0.720673i
$326$	33.5796	−	16.1711i	1.85980	−	0.895633i
$327$	16.7647	−	21.0223i	0.927092	−	1.16254i
$328$	−3.97909	+	4.98962i	−0.219709	+	0.275506i
$329$	−14.1024	−	6.79135i	−0.777490	−	0.374420i
$330$	16.8557	+	21.1364i	0.927876	+	1.16352i
$331$	1.18034			0.0648773			0.0324387	−	0.999474i	$-0.489673\pi$
$331$	1.18034			0.0648773			0.0324387	+	0.999474i	$0.489673\pi$
$332$	3.06123	+	3.83866i	0.168007	+	0.210674i
$333$	0.740158	+	3.24284i	0.0405604	+	0.177707i
$334$	−7.01087	−	30.7166i	−0.383618	−	1.68074i
$335$	18.6352	+	23.3678i	1.01815	+	1.27672i
$336$	17.5623			0.958102
$337$	−15.0067	−	18.8178i	−0.817467	−	1.02507i	−0.999130	−	0.0417105i	$-0.986719\pi$
$337$	−15.0067	−	18.8178i	−0.817467	−	1.02507i	0.181663	−	0.983361i	$-0.441852\pi$
$338$	−7.20775	−	3.47107i	−0.392050	−	0.188801i
$339$	−10.0321	+	12.5798i	−0.544867	+	0.683241i
$340$	−7.27847	+	9.12691i	−0.394731	+	0.494976i
$341$	3.55367	−	1.71136i	0.192442	−	0.0926751i
$342$	−0.254986	−	1.11717i	−0.0137881	−	0.0604095i
$343$	4.47815	−	19.6200i	0.241797	−	1.05938i
$344$	5.56829	+	2.68155i	0.300222	+	0.144579i
$345$	−13.4643	+	6.48408i	−0.724895	+	0.349091i
$346$	2.55279	−	11.1845i	0.137239	−	0.601283i
$347$	8.12461			0.436152			0.218076	−	0.975932i	$-0.430022\pi$
$347$	8.12461			0.436152			0.218076	+	0.975932i	$0.430022\pi$
$348$		0			0
$349$	13.4721			0.721147			0.360573	−	0.932731i	$-0.382581\pi$
$349$	13.4721			0.721147			0.360573	+	0.932731i	$0.382581\pi$
$350$	−2.53273	+	11.0966i	−0.135380	+	0.593138i
$351$	−20.8848	+	10.0576i	−1.11475	+	0.536834i
$352$	11.0243	+	5.30903i	0.587598	+	0.282972i
$353$	−4.70067	+	20.5950i	−0.250191	+	1.09616i	0.681188	+	0.732109i	$0.261464\pi$
$353$	−4.70067	+	20.5950i	−0.250191	+	1.09616i	−0.931379	+	0.364051i	$0.881393\pi$
$354$	−2.96537	−	12.9921i	−0.157607	−	0.690523i
$355$	3.92884	−	1.89203i	0.208521	−	0.100418i
$356$	3.35560	−	4.20779i	0.177846	−	0.223012i
$357$	−14.9290	+	18.7204i	−0.790127	+	0.990788i
$358$	23.3248	+	11.2326i	1.23275	+	0.593662i
$359$	17.6049	+	22.0758i	0.929151	+	1.16512i	0.986002	+	0.166736i	$0.0533227\pi$
$359$	17.6049	+	22.0758i	0.929151	+	1.16512i	−0.0568505	+	0.998383i	$0.518106\pi$
$360$	−2.43769			−0.128478
$361$	−9.70294	−	12.1671i	−0.510681	−	0.640374i
$362$	4.30049	+	18.8417i	0.226029	+	0.990297i
$363$	0.752558	+	3.29717i	0.0394991	+	0.173057i
$364$	3.64997	+	4.57692i	0.191311	+	0.239896i
$365$	−0.832816			−0.0435916
$366$	2.64115	+	3.31189i	0.138055	+	0.173115i
$367$	−5.64953	−	2.72067i	−0.294903	−	0.142018i	0.280582	−	0.959830i	$-0.409473\pi$
$367$	−5.64953	−	2.72067i	−0.294903	−	0.142018i	−0.575485	+	0.817812i	$0.695187\pi$
$368$	−9.79390	+	12.2812i	−0.510543	+	0.640200i
$369$	−0.679710	+	0.852329i	−0.0353843	+	0.0443705i
$370$	36.2323	−	17.4485i	1.88363	−	0.907106i
$371$	0.995144	+	4.36001i	0.0516653	+	0.226360i
$372$	−0.242586	+	1.06284i	−0.0125775	+	0.0551055i
$373$	−16.5616	−	7.97564i	−0.857526	−	0.412963i	−0.0471604	−	0.998887i	$-0.515017\pi$
$373$	−16.5616	−	7.97564i	−0.857526	−	0.412963i	−0.810366	+	0.585925i	$0.800731\pi$
$374$	−34.9059	+	16.8098i	−1.80494	+	0.869214i
$375$	1.90529	−	8.34763i	0.0983889	−	0.431070i
$376$	−15.6525			−0.807215
$377$		0			0
$378$	19.7984			1.01832
$379$	−8.39086	+	36.7628i	−0.431010	+	1.88838i	0.0273785	+	0.999625i	$0.491284\pi$
$379$	−8.39086	+	36.7628i	−0.431010	+	1.88838i	−0.458388	+	0.888752i	$0.651573\pi$
$380$	−2.94663	+	1.41902i	−0.151159	+	0.0727942i
$381$	2.83436	+	1.36495i	0.145208	+	0.0699287i
$382$	−4.33296	+	18.9839i	−0.221693	+	0.971302i
$383$	4.92793	+	21.5907i	0.251805	+	1.10323i	0.929771	+	0.368138i	$0.120004\pi$
$383$	4.92793	+	21.5907i	0.251805	+	1.10323i	−0.677966	+	0.735093i	$0.737138\pi$
$384$	19.8523	−	9.56039i	1.01309	−	0.487876i
$385$	−14.3965	+	18.0526i	−0.733713	+	0.920047i
$386$	−3.55901	+	4.46285i	−0.181149	+	0.227153i
$387$	0.951178	+	0.458063i	0.0483511	+	0.0232847i
$388$	6.38208	+	8.00288i	0.324001	+	0.406285i
$389$	−21.1246			−1.07106			−0.535530	−	0.844516i	$-0.679888\pi$
$389$	−21.1246			−1.07106			−0.535530	+	0.844516i	$0.679888\pi$
$390$	19.7350	+	24.7469i	0.999320	+	1.25311i
$391$	−4.76560	−	20.8795i	−0.241007	−	1.05592i
$392$	−0.995144	−	4.36001i	−0.0502624	−	0.220214i
$393$	−1.33795	−	1.67773i	−0.0674904	−	0.0846303i
$394$	−31.8885			−1.60652
$395$	9.05798	+	11.3583i	0.455756	+	0.571500i
$396$	0.769519	+	0.370581i	0.0386698	+	0.0186224i
$397$	−19.9169	+	24.9750i	−0.999602	+	1.25346i	−0.0323941	+	0.999475i	$0.510313\pi$
$397$	−19.9169	+	24.9750i	−0.999602	+	1.25346i	−0.967208	+	0.253986i	$0.918258\pi$
$398$	0.861642	−	1.08046i	0.0431902	−	0.0541588i
$399$	−6.04388	+	2.91058i	−0.302573	+	0.145711i
$400$	3.39801	+	14.8876i	0.169900	+	0.744382i
$401$	7.35852	−	32.2398i	0.367467	−	1.60998i	−0.366246	−	0.930518i	$-0.619357\pi$
$401$	7.35852	−	32.2398i	0.367467	−	1.60998i	0.733713	−	0.679460i	$-0.237786\pi$
$402$	−24.7013	−	11.8955i	−1.23199	−	0.593295i
$403$	4.16070	−	2.00369i	0.207259	−	0.0998109i
$404$	0.222521	−	0.974928i	0.0110708	−	0.0485045i
$405$	22.0000			1.09319
$406$		0			0
$407$	31.5066			1.56172
$408$	−5.32810	+	23.3439i	−0.263780	+	1.15570i
$409$	0.525798	−	0.253211i	0.0259991	−	0.0125205i	−0.420839	−	0.907135i	$-0.638264\pi$
$409$	0.525798	−	0.253211i	0.0259991	−	0.0125205i	0.446838	+	0.894615i	$0.352550\pi$
$410$	11.8751	+	5.71874i	0.586468	+	0.282428i
$411$	−4.98812	+	21.8544i	−0.246046	+	1.07800i
$412$	1.81263	+	7.94166i	0.0893020	+	0.391258i
$413$	10.2548	−	4.93845i	0.504606	−	0.243005i
$414$	−1.24698	+	1.56366i	−0.0612857	+	0.0768498i
$415$	−14.1369	+	17.7271i	−0.693951	+	0.870187i
$416$	12.9075	+	6.21592i	0.632842	+	0.304761i
$417$	−14.8380	−	18.6063i	−0.726622	−	0.911155i
$418$	−10.8541			−0.530891
$419$	1.59757	+	2.00329i	0.0780465	+	0.0978672i	0.819322	−	0.573334i	$-0.194350\pi$
$419$	1.59757	+	2.00329i	0.0780465	+	0.0978672i	−0.741275	+	0.671201i	$0.765779\pi$
$420$	−1.42012	−	6.22196i	−0.0692948	−	0.303600i
$421$	−0.437378	−	1.91628i	−0.0213165	−	0.0933937i	0.963151	−	0.268962i	$-0.0866807\pi$
$421$	−0.437378	−	1.91628i	−0.0213165	−	0.0933937i	−0.984467	+	0.175569i	$0.943824\pi$
$422$	−19.8260	−	24.8610i	−0.965113	−	1.21021i
$423$	−2.67376			−0.130003
$424$	2.78833	+	3.49646i	0.135413	+	0.169803i
$425$	−18.7579	−	9.03331i	−0.909890	−	0.438180i
$426$	−2.49396	+	3.12733i	−0.120833	+	0.151519i
$427$	−2.25581	+	2.82869i	−0.109166	+	0.136890i
$428$	−6.25657	+	3.01301i	−0.302423	+	0.145639i
$429$	5.51816	+	24.1766i	0.266419	+	1.16726i
$430$	2.84024	−	12.4439i	0.136969	−	0.600099i
$431$	31.1706	+	15.0110i	1.50143	+	0.723053i	0.990621	−	0.136639i	$-0.0436299\pi$
$431$	31.1706	+	15.0110i	1.50143	+	0.723053i	0.510814	+	0.859691i	$0.329344\pi$
$432$	23.9318	−	11.5250i	1.15142	−	0.554495i
$433$	2.80778	−	12.3017i	0.134933	−	0.591181i	−0.861571	−	0.507637i	$-0.830519\pi$
$433$	2.80778	−	12.3017i	0.134933	−	0.591181i	0.996504	−	0.0835436i	$-0.0266238\pi$
$434$	−3.94427			−0.189331
$435$		0			0
$436$	−10.2705			−0.491868
$437$	1.33513	−	5.84957i	0.0638677	−	0.279823i
$438$	0.688279	−	0.331458i	0.0328872	−	0.0158377i
$439$	2.75312	+	1.32583i	0.131399	+	0.0632784i	0.498428	−	0.866931i	$-0.333911\pi$
$439$	2.75312	+	1.32583i	0.131399	+	0.0632784i	−0.367029	+	0.930209i	$0.619625\pi$
$440$	−5.13805	+	22.5113i	−0.244947	+	1.07318i
$441$	−0.169991	−	0.744779i	−0.00809480	−	0.0354657i
$442$	−40.8686	+	19.6813i	−1.94392	+	0.936142i
$443$	8.16159	−	10.2343i	0.387769	−	0.486247i	−0.549185	−	0.835701i	$-0.685062\pi$
$443$	8.16159	−	10.2343i	0.387769	−	0.486247i	0.936953	+	0.349454i	$0.113633\pi$
$444$	−5.42948	+	6.80835i	−0.257672	+	0.323110i
$445$	22.3928	+	10.7838i	1.06152	+	0.511201i
$446$	18.4880	+	23.1832i	0.875433	+	1.09776i
$447$	−11.9443			−0.564945
$448$	5.90578	+	7.40561i	0.279022	+	0.349882i
$449$	3.14302	+	13.7705i	0.148328	+	0.649869i	0.993350	+	0.115136i	$0.0367305\pi$
$449$	3.14302	+	13.7705i	0.148328	+	0.649869i	−0.845021	+	0.534733i	$0.820412\pi$
$450$	0.432641	+	1.89552i	0.0203949	+	0.0893559i
$451$	6.43830	+	8.07338i	0.303168	+	0.380161i
$452$	6.14590			0.289079
$453$	−18.4880	−	23.1832i	−0.868643	−	1.08924i
$454$	−21.7045	−	10.4523i	−1.01864	−	0.490552i
$455$	−16.8557	+	21.1364i	−0.790207	+	0.990889i
$456$	−4.18250	+	5.24469i	−0.195863	+	0.245605i
$457$	−4.76774	+	2.29602i	−0.223026	+	0.107403i	−0.542060	−	0.840340i	$-0.682356\pi$
$457$	−4.76774	+	2.29602i	−0.223026	+	0.107403i	0.319035	+	0.947743i	$0.396641\pi$
$458$	5.65568	+	24.7792i	0.264273	+	1.15785i
$459$	−8.05855	+	35.3068i	−0.376141	+	1.64798i
$460$	5.14291	+	2.47670i	0.239790	+	0.115477i
$461$	7.18857	−	3.46183i	0.334805	−	0.161234i	−0.258926	−	0.965897i	$-0.583369\pi$
$461$	7.18857	−	3.46183i	0.334805	−	0.161234i	0.593731	+	0.804663i	$0.297654\pi$
$462$	4.71307	−	20.6493i	0.219272	−	0.960693i
$463$	−2.70820			−0.125861			−0.0629305	−	0.998018i	$-0.520045\pi$
$463$	−2.70820			−0.125861			−0.0629305	+	0.998018i	$0.520045\pi$
$464$		0			0
$465$	−5.03444			−0.233467
$466$	−3.87552	+	16.9797i	−0.179530	+	0.786571i
$467$	−0.0502093	+	0.0241795i	−0.00232341	+	0.00111889i	−0.435045	−	0.900409i	$-0.643268\pi$
$467$	−0.0502093	+	0.0241795i	−0.00232341	+	0.00111889i	0.432722	+	0.901528i	$0.357553\pi$
$468$	0.900969	+	0.433884i	0.0416473	+	0.0200563i
$469$	5.21064	−	22.8293i	0.240605	−	1.05416i
$470$	7.19326	+	31.5158i	0.331801	+	1.45371i
$471$	8.10872	−	3.90495i	0.373630	−	0.179931i
$472$	7.09654	−	8.89878i	0.326645	−	0.409600i
$473$	6.23490	−	7.81831i	0.286681	−	0.359486i
$474$	−12.0065	−	5.78204i	−0.551478	−	0.265578i
$475$	−3.63670	−	4.56028i	−0.166863	−	0.209240i
$476$	9.14590			0.419202
$477$	0.476304	+	0.597266i	0.0218085	+	0.0273469i
$478$	−5.30804	−	23.2560i	−0.242784	−	1.06371i
$479$	2.48786	+	10.9000i	0.113673	+	0.498035i	0.999426	+	0.0338776i	$0.0107856\pi$
$479$	2.48786	+	10.9000i	0.113673	+	0.498035i	−0.885753	+	0.464157i	$0.846357\pi$
$480$	−9.73768	−	12.2107i	−0.444462	−	0.557338i
$481$	36.8885			1.68197
$482$	26.8878	+	33.7162i	1.22470	+	1.53573i
$483$	10.5487	+	5.08000i	0.479984	+	0.231148i
$484$	0.805422	−	1.00997i	0.0366101	−	0.0459076i
$485$	−29.4727	+	36.9576i	−1.33829	+	1.67816i
$486$	5.74995	−	2.76903i	0.260823	−	0.125606i
$487$	−4.99286	−	21.8751i	−0.226248	−	0.991257i	−0.952670	−	0.304008i	$-0.901675\pi$
$487$	−4.99286	−	21.8751i	−0.226248	−	0.991257i	0.726422	−	0.687249i	$-0.241182\pi$
$488$	−0.805088	+	3.52732i	−0.0364446	+	0.159674i
$489$	−33.5796	−	16.1711i	−1.51852	−	0.731281i
$490$	−8.32141	+	4.00738i	−0.375923	+	0.181035i
$491$	5.59075	−	24.4947i	0.252307	−	1.10543i	−0.676960	−	0.736020i	$-0.736703\pi$
$491$	5.59075	−	24.4947i	0.252307	−	1.10543i	0.929267	−	0.369409i	$-0.120440\pi$
$492$	−2.85410			−0.128673
$493$		0			0
$494$	−12.7082			−0.571769
$495$	−0.877683	+	3.84538i	−0.0394489	+	0.172837i
$496$	−4.76774	+	2.29602i	−0.214078	+	0.103095i
$497$	−3.07808	−	1.48232i	−0.138071	−	0.0664913i
$498$	4.62807	−	20.2769i	0.207389	−	0.908630i
$499$	7.94109	+	34.7922i	0.355492	+	1.55751i	0.764281	+	0.644883i	$0.223094\pi$
$499$	7.94109	+	34.7922i	0.355492	+	1.55751i	−0.408790	+	0.912629i	$0.634049\pi$
$500$	−2.94663	+	1.41902i	−0.131777	+	0.0634605i
$501$	−19.6440	+	24.6328i	−0.877631	+	1.10051i
$502$	−11.7553	+	14.7407i	−0.524667	+	0.657911i
$503$	−17.3621	−	8.36116i	−0.774139	−	0.372806i	0.00473279	−	0.999989i	$-0.498494\pi$
$503$	−17.3621	−	8.36116i	−0.774139	−	0.372806i	−0.778872	+	0.627183i	$0.784208\pi$
$504$	1.19076	+	1.49317i	0.0530406	+	0.0665109i
$505$	4.61803			0.205500
$506$	11.8116	+	14.8112i	0.525088	+	0.658439i
$507$	1.78017	+	7.79942i	0.0790600	+	0.346385i
$508$	−0.267387	−	1.17150i	−0.0118634	−	0.0519769i
$509$	7.13129	+	8.94235i	0.316089	+	0.396363i	0.914341	−	0.404945i	$-0.132709\pi$
$509$	7.13129	+	8.94235i	0.316089	+	0.396363i	−0.598252	+	0.801308i	$0.704138\pi$
$510$	49.4508			2.18972
$511$	0.406812	+	0.510126i	0.0179963	+	0.0225667i
$512$	4.76774	+	2.29602i	0.210706	+	0.101471i
$513$	−6.32586	+	7.93238i	−0.279294	+	0.350223i
$514$	−0.826896	+	1.03689i	−0.0364728	+	0.0457355i
$515$	−33.8927	+	16.3219i	−1.49349	+	0.719227i
$516$	0.615033	+	2.69463i	0.0270753	+	0.118625i
$517$	−5.63562	+	24.6913i	−0.247854	+	1.08592i
$518$	−28.3864	−	13.6702i	−1.24723	−	0.600634i
$519$	−10.3360	+	4.97757i	−0.453702	+	0.218491i
$520$	−6.01573	+	26.3566i	−0.263807	+	1.15581i
$521$	−7.09017			−0.310626			−0.155313	−	0.987865i	$-0.549639\pi$
$521$	−7.09017			−0.310626			−0.155313	+	0.987865i	$0.549639\pi$
$522$		0			0
$523$	−22.6180			−0.989018			−0.494509	−	0.869173i	$-0.664652\pi$
$523$	−22.6180			−0.989018			−0.494509	+	0.869173i	$0.664652\pi$
$524$	−0.182392	+	0.799110i	−0.00796781	+	0.0349093i
$525$	10.2548	−	4.93845i	0.447556	−	0.215532i
$526$	−4.79877	−	2.31097i	−0.209237	−	0.100763i
$527$	1.60544	−	7.03389i	0.0699341	−	0.306401i
$528$	−6.32325	−	27.7039i	−0.275184	−	1.20566i
$529$	11.2872	−	5.43564i	0.490748	−	0.236332i
$530$	5.75859	−	7.22105i	0.250137	−	0.313662i
$531$	1.21223	−	1.52009i	0.0526065	−	0.0659664i
$532$	2.30856	+	1.11174i	0.100089	+	0.0482002i
$533$	7.53810	+	9.45248i	0.326511	+	0.409432i
$534$	−22.7984			−0.986582
$535$	−19.9946	−	25.0725i	−0.864443	−	1.08398i
$536$	−5.21064	−	22.8293i	−0.225065	−	0.986076i
$537$	−5.76074	−	25.2395i	−0.248594	−	1.08916i
$538$	6.05297	+	7.59018i	0.260962	+	0.327236i
$539$	−7.23607			−0.311680
$540$	−6.01822	−	7.54661i	−0.258983	−	0.324754i
$541$	31.1706	+	15.0110i	1.34013	+	0.645372i	0.960114	−	0.279609i	$-0.0902047\pi$
$541$	31.1706	+	15.0110i	1.34013	+	0.645372i	0.380014	+	0.924981i	$0.375919\pi$
$542$	12.2879	−	15.4085i	0.527809	−	0.661852i
$543$	12.0497	−	15.1099i	0.517103	−	0.648426i
$544$	20.1655	−	9.71117i	0.864587	−	0.416363i
$545$	−10.5541	−	46.2404i	−0.452087	−	1.98072i
$546$	5.51816	−	24.1766i	0.236155	−	1.03466i
$547$	−8.66555	−	4.17311i	−0.370512	−	0.178429i	0.239357	−	0.970932i	$-0.423064\pi$
$547$	−8.66555	−	4.17311i	−0.370512	−	0.178429i	−0.609869	+	0.792503i	$0.708778\pi$
$548$	7.71437	−	3.71505i	0.329542	−	0.158699i
$549$	−0.137526	+	0.602539i	−0.00586945	+	0.0257157i
$550$	18.4164			0.785278
$551$		0			0
$552$	11.7082			0.498334
$553$	2.53273	−	11.0966i	0.107702	−	0.471875i
$554$	34.4303	−	16.5808i	1.46280	−	0.704450i
$555$	−36.2323	−	17.4485i	−1.53797	−	0.740649i
$556$	−2.02275	+	8.86226i	−0.0857838	+	0.375844i
$557$	−7.23339	−	31.6916i	−0.306489	−	1.34281i	−0.860136	−	0.510064i	$-0.829622\pi$
$557$	−7.23339	−	31.6916i	−0.306489	−	1.34281i	0.553648	−	0.832751i	$-0.313235\pi$
$558$	−0.607039	+	0.292334i	−0.0256980	+	0.0123755i
$559$	7.29995	−	9.15384i	0.308755	−	0.387166i
$560$	19.3149	−	24.2201i	0.816204	−	1.02349i
$561$	34.9059	+	16.8098i	1.47373	+	0.709710i
$562$	−17.2758	−	21.6631i	−0.728735	−	0.913805i
$563$	45.3951			1.91318			0.956588	−	0.291443i	$-0.0941354\pi$
$563$	45.3951			1.91318			0.956588	+	0.291443i	$0.0941354\pi$
$564$	−4.36443	−	5.47282i	−0.183776	−	0.230447i
$565$	6.31558	+	27.6704i	0.265699	+	1.16410i
$566$	0.275051	+	1.20508i	0.0115613	+	0.0506532i
$567$	−10.7465	−	13.4757i	−0.451311	−	0.565926i
$568$	−3.41641			−0.143349
$569$	−9.94109	−	12.4657i	−0.416752	−	0.522591i	0.528499	−	0.848934i	$-0.322755\pi$
$569$	−9.94109	−	12.4657i	−0.416752	−	0.522591i	−0.945251	+	0.326343i	$0.894184\pi$
$570$	12.4821	+	6.01107i	0.522818	+	0.251776i
$571$	2.18632	−	2.74155i	0.0914945	−	0.114730i	−0.733977	−	0.679174i	$-0.762338\pi$
$571$	2.18632	−	2.74155i	0.0914945	−	0.114730i	0.825471	+	0.564444i	$0.190909\pi$
$572$	5.90578	−	7.40561i	0.246933	−	0.309644i
$573$	17.5438	−	8.44864i	0.732902	−	0.352947i
$574$	−2.29780	−	10.0673i	−0.0959085	−	0.420203i
$575$	−2.26534	+	9.92510i	−0.0944712	+	0.413905i
$576$	1.45780	+	0.702039i	0.0607416	+	0.0292516i
$577$	−6.51947	+	3.13961i	−0.271409	+	0.130704i	−0.564638	−	0.825338i	$-0.690984\pi$
$577$	−6.51947	+	3.13961i	−0.271409	+	0.130704i	0.293229	+	0.956042i	$0.405270\pi$
$578$	−9.64866	+	42.2735i	−0.401331	+	1.75835i
$579$	5.70820			0.237225
$580$		0			0
$581$	17.7639			0.736972
$582$	9.64866	−	42.2735i	0.399950	−	1.75229i
$583$	6.51947	−	3.13961i	0.270009	−	0.130029i
$584$	0.587860	+	0.283099i	0.0243258	+	0.0117147i
$585$	−1.02761	+	4.50225i	−0.0424864	+	0.186145i
$586$	6.29078	+	27.5617i	0.259870	+	1.13856i
$587$	−39.9868	+	19.2566i	−1.65043	+	0.794805i	−0.651071	+	0.759017i	$0.725680\pi$
$587$	−39.9868	+	19.2566i	−1.65043	+	0.794805i	−0.999359	+	0.0357889i	$0.988606\pi$
$588$	1.24698	−	1.56366i	0.0514246	−	0.0644844i
$589$	1.26025	−	1.58031i	0.0519278	−	0.0651153i
$590$	−21.1787	−	10.1991i	−0.871913	−	0.419891i
$591$	19.8822	+	24.9315i	0.817844	+	1.02554i
$592$	−42.2705			−1.73731
$593$	−21.5492	−	27.0219i	−0.884921	−	1.10966i	−0.993302	−	0.115547i	$-0.963138\pi$
$593$	−21.5492	−	27.0219i	−0.884921	−	1.10966i	0.108381	−	0.994109i	$-0.465433\pi$
$594$	−7.12833	−	31.2313i	−0.292479	−	1.28143i
$595$	9.39841	+	41.1771i	0.385297	+	1.68810i
$596$	2.84455	+	3.56695i	0.116517	+	0.146108i
$597$	−1.38197			−0.0565601
$598$	13.8292	+	17.3413i	0.565519	+	0.709138i
$599$	−40.6057	−	19.5547i	−1.65910	−	0.798982i	−0.998850	−	0.0479374i	$-0.984735\pi$
$599$	−40.6057	−	19.5547i	−1.65910	−	0.798982i	−0.660252	−	0.751044i	$-0.729551\pi$
$600$	7.09654	−	8.89878i	0.289715	−	0.363291i
$601$	25.0388	−	31.3976i	1.02135	−	1.28074i	0.0621344	−	0.998068i	$-0.480209\pi$
$601$	25.0388	−	31.3976i	1.02135	−	1.28074i	0.959218	−	0.282668i	$-0.0912193\pi$
$602$	−9.00969	+	4.33884i	−0.367207	+	0.176838i
$603$	−0.890084	−	3.89971i	−0.0362470	−	0.158809i
$604$	−2.52033	+	11.0423i	−0.102551	+	0.449303i
$605$	5.37478	+	2.58836i	0.218516	+	0.105232i
$606$	−3.81657	+	1.83796i	−0.155037	+	0.0746621i
$607$	−8.00602	+	35.0767i	−0.324954	+	1.42372i	0.503662	+	0.863901i	$0.331986\pi$
$607$	−8.00602	+	35.0767i	−0.324954	+	1.42372i	−0.828616	+	0.559817i	$0.810872\pi$
$608$	6.27051			0.254303
$609$		0			0
$610$	7.47214			0.302538
$611$	−6.59830	+	28.9090i	−0.266939	+	1.16953i
$612$	1.40759	−	0.677859i	0.0568984	−	0.0274008i
$613$	35.6252	+	17.1562i	1.43889	+	0.692933i	0.980627	−	0.195884i	$-0.0627577\pi$
$613$	35.6252	+	17.1562i	1.43889	+	0.692933i	0.458262	+	0.888817i	$0.348472\pi$
$614$	1.14507	−	5.01688i	0.0462113	−	0.202465i
$615$	−2.93290	−	12.8499i	−0.118266	−	0.518157i
$616$	16.2987	−	7.84903i	0.656693	−	0.316246i
$617$	−5.10036	+	6.39565i	−0.205333	+	0.257479i	−0.873826	−	0.486239i	$-0.838368\pi$
$617$	−5.10036	+	6.39565i	−0.205333	+	0.257479i	0.668493	+	0.743719i	$0.266940\pi$
$618$	21.5145	−	26.9783i	0.865440	−	1.08523i
$619$	22.4740	+	10.8229i	0.903307	+	0.435010i	0.827082	−	0.562081i	$-0.189999\pi$
$619$	22.4740	+	10.8229i	0.903307	+	0.435010i	0.0762247	+	0.997091i	$0.475713\pi$
$620$	1.19896	+	1.50345i	0.0481515	+	0.0603800i
$621$	17.7082			0.710606
$622$	9.17042	+	11.4993i	0.367700	+	0.461081i
$623$	−4.33296	−	18.9839i	−0.173596	−	0.760575i
$624$	−7.40338	−	32.4363i	−0.296373	−	1.29849i
$625$	−19.2239	−	24.1061i	−0.768958	−	0.964243i
$626$	−38.9787			−1.55790
$627$	6.76742	+	8.48608i	0.270265	+	0.338901i
$628$	−3.09726	−	1.49156i	−0.123594	−	0.0595197i
$629$	35.9325	−	45.0579i	1.43272	−	1.79658i
$630$	2.45921	−	3.08376i	0.0979774	−	0.122860i
$631$	−20.9158	+	10.0725i	−0.832645	+	0.400981i	−0.801106	−	0.598522i	$-0.795755\pi$
$631$	−20.9158	+	10.0725i	−0.832645	+	0.400981i	−0.0315383	+	0.999503i	$0.510041\pi$
$632$	−2.53273	−	11.0966i	−0.100746	−	0.441399i
$633$	−7.07580	+	31.0011i	−0.281238	+	1.23218i
$634$	20.8346	+	10.0334i	0.827446	+	0.398477i
$635$	4.99961	−	2.40769i	0.198404	−	0.0955461i
$636$	−0.445042	+	1.94986i	−0.0176471	+	0.0773168i
$637$	−8.47214			−0.335678
$638$		0			0
$639$	−0.583592			−0.0230865
$640$	8.64878	−	37.8928i	0.341873	−	1.49784i
$641$	26.0779	−	12.5584i	1.03001	−	0.496029i	0.158996	−	0.987279i	$-0.449174\pi$
$641$	26.0779	−	12.5584i	1.03001	−	0.496029i	0.871018	+	0.491250i	$0.163460\pi$
$642$	26.5033	+	12.7633i	1.04600	+	0.503727i
$643$	2.35507	−	10.3182i	0.0928749	−	0.406912i	−0.907025	−	0.421077i	$-0.861652\pi$
$643$	2.35507	−	10.3182i	0.0928749	−	0.406912i	0.999900	+	0.0141657i	$0.00450923\pi$
$644$	−0.995144	−	4.36001i	−0.0392142	−	0.171808i
$645$	−11.4999	+	5.53806i	−0.452808	+	0.218061i
$646$	−12.3788	+	15.5226i	−0.487039	+	0.610727i
$647$	−24.6105	+	30.8606i	−0.967538	+	1.21325i	0.00944952	+	0.999955i	$0.496992\pi$
$647$	−24.6105	+	30.8606i	−0.967538	+	1.21325i	−0.976987	+	0.213298i	$0.931579\pi$
$648$	−15.5292	−	7.47845i	−0.610043	−	0.293781i
$649$	−11.4824	−	14.3985i	−0.450725	−	0.565192i
$650$	21.5623			0.845743
$651$	2.45921	+	3.08376i	0.0963842	+	0.120862i
$652$	3.16782	+	13.8791i	0.124062	+	0.543549i
$653$	−6.23351	−	27.3108i	−0.243936	−	1.06875i	−0.937398	−	0.348261i	$-0.886772\pi$
$653$	−6.23351	−	27.3108i	−0.243936	−	1.06875i	0.693461	−	0.720494i	$-0.256085\pi$
$654$	27.1259	+	34.0148i	1.06071	+	1.33008i
$655$	−3.78522			−0.147901
$656$	−8.63789	−	10.8316i	−0.337253	−	0.422902i
$657$	0.100419	+	0.0483590i	0.00391770	+	0.00188667i
$658$	15.7907	−	19.8009i	0.615584	−	0.771918i
$659$	15.5525	−	19.5022i	0.605839	−	0.759699i	−0.380436	−	0.924807i	$-0.624226\pi$
$659$	15.5525	−	19.5022i	0.605839	−	0.759699i	0.986275	+	0.165109i	$0.0527975\pi$
$660$	−9.30362	+	4.48039i	−0.362143	+	0.174399i
$661$	−4.10570	−	17.9882i	−0.159693	−	0.699662i	−0.989848	−	0.142129i	$-0.954605\pi$
$661$	−4.10570	−	17.9882i	−0.159693	−	0.699662i	0.830155	−	0.557533i	$-0.188252\pi$
$662$	−0.424977	+	1.86195i	−0.0165172	+	0.0723666i
$663$	40.8686	+	19.6813i	1.58720	+	0.764357i
$664$	16.0047	−	7.70748i	0.621105	−	0.299108i
$665$	−2.63305	+	11.5361i	−0.102105	+	0.447352i
$666$	−5.38197			−0.208547
$667$		0			0
$668$	12.0344			0.465627
$669$	6.59830	−	28.9090i	0.255105	−	1.11769i
$670$	−43.5715	+	20.9829i	−1.68331	+	0.810641i
$671$	5.27436	+	2.54000i	0.203615	+	0.0980556i
$672$	−2.72278	+	11.9293i	−0.105034	+	0.460182i
$673$	−0.550102	−	2.41015i	−0.0212049	−	0.0929046i	0.963218	−	0.268721i	$-0.0866008\pi$
$673$	−0.550102	−	2.41015i	−0.0212049	−	0.0929046i	−0.984423	+	0.175816i	$0.943744\pi$
$674$	35.0876	−	16.8973i	1.35152	−	0.650859i
$675$	10.7332	−	13.4591i	0.413123	−	0.518039i
$676$	1.90522	−	2.38906i	0.0732775	−	0.0918871i
$677$	11.5620	+	5.56795i	0.444363	+	0.213994i	0.642665	−	0.766147i	$-0.277829\pi$
$677$	11.5620	+	5.56795i	0.444363	+	0.213994i	−0.198303	+	0.980141i	$0.563543\pi$
$678$	−16.2322	−	20.3545i	−0.623394	−	0.781712i
$679$	37.0344			1.42125
$680$	26.3338	+	33.0215i	1.00985	+	1.26632i
$681$	5.36057	+	23.4862i	0.205417	+	0.899992i
$682$	1.42012	+	6.22196i	0.0543792	+	0.238251i
$683$	8.81982	+	11.0597i	0.337481	+	0.423188i	0.921395	−	0.388628i	$-0.127051\pi$
$683$	8.81982	+	11.0597i	0.337481	+	0.423188i	−0.583914	+	0.811816i	$0.698479\pi$
$684$	0.437694			0.0167357
$685$	24.6534	+	30.9144i	0.941959	+	1.18118i
$686$	29.3376	+	14.1283i	1.12012	+	0.539419i
$687$	15.8469	−	19.8713i	0.604596	−	0.758139i
$688$	−8.36499	+	10.4894i	−0.318912	+	0.399903i
$689$	7.63313	−	3.67592i	0.290799	−	0.140041i
$690$	−5.38063	−	23.5741i	−0.204837	−	0.897450i
$691$	9.30868	−	40.7840i	0.354119	−	1.55150i	−0.413449	−	0.910527i	$-0.635676\pi$
$691$	9.30868	−	40.7840i	0.354119	−	1.55150i	0.767567	−	0.640968i	$-0.221467\pi$
$692$	3.94801	+	1.90126i	0.150081	+	0.0722752i
$693$	2.78415	−	1.34077i	0.105761	−	0.0509318i
$694$	−2.92524	+	12.8163i	−0.111040	+	0.486500i
$695$	−41.9787			−1.59234
$696$		0			0
$697$	18.8885			0.715455
$698$	−4.85059	+	21.2518i	−0.183598	+	0.804394i
$699$	15.6916	−	7.55670i	0.593512	−	0.285820i
$700$	−3.91698	−	1.88632i	−0.148048	−	0.0712962i
$701$	8.66592	−	37.9679i	0.327307	−	1.43403i	−0.496935	−	0.867788i	$-0.665541\pi$
$701$	8.66592	−	37.9679i	0.327307	−	1.43403i	0.824242	−	0.566238i	$-0.191602\pi$
$702$	−8.34600	−	36.5662i	−0.314999	−	1.38010i
$703$	14.5470	−	7.00544i	0.548649	−	0.264215i
$704$	9.55575	−	11.9825i	0.360146	−	0.451609i
$705$	20.1551	−	25.2737i	0.759084	−	0.951861i
$706$	−30.7954	−	14.8303i	−1.15900	−	0.558145i
$707$	−2.25581	−	2.82869i	−0.0848384	−	0.106384i
$708$	5.09017			0.191300
$709$	−2.17811	−	2.73127i	−0.0818008	−	0.102575i	0.739247	−	0.673434i	$-0.235182\pi$
$709$	−2.17811	−	2.73127i	−0.0818008	−	0.102575i	−0.821048	+	0.570859i	$0.806610\pi$
$710$	1.57005	+	6.87883i	0.0589228	+	0.258158i
$711$	−0.432641	−	1.89552i	−0.0162253	−	0.0710877i
$712$	−12.1407	−	15.2239i	−0.454991	−	0.570541i
$713$	−3.52786			−0.132120
$714$	−24.1556	−	30.2902i	−0.904002	−	1.13358i
$715$	39.4108	+	18.9792i	1.47388	+	0.709783i
$716$	−6.16541	+	7.73117i	−0.230412	+	0.288928i
$717$	−14.8728	+	18.6499i	−0.555434	+	0.696493i
$718$	−41.1625	+	19.8228i	−1.53617	+	0.739781i
$719$	6.56583	+	28.7668i	0.244864	+	1.07282i	0.936526	+	0.350598i	$0.114022\pi$
$719$	6.56583	+	28.7668i	0.244864	+	1.07282i	−0.691662	+	0.722222i	$0.743121\pi$
$720$	1.17754	−	5.15912i	0.0438842	−	0.192269i
$721$	26.5535	+	12.7875i	0.988903	+	0.476231i
$722$	22.6867	−	10.9253i	0.844312	−	0.406599i
$723$	9.59613	−	42.0434i	0.356884	−	1.56361i
$724$	−7.38197			−0.274349
$725$		0			0
$726$	−5.47214			−0.203090
$727$	10.2236	−	44.7924i	0.379171	−	1.66126i	−0.320847	−	0.947131i	$-0.603967\pi$
$727$	10.2236	−	44.7924i	0.379171	−	1.66126i	0.700018	−	0.714125i	$-0.253175\pi$
$728$	19.0828	−	9.18981i	0.707257	−	0.340597i
$729$	−26.5845	−	12.8024i	−0.984611	−	0.474164i
$730$	0.299852	−	1.31374i	0.0110980	−	0.0486237i
$731$	−4.07031	−	17.8332i	−0.150546	−	0.659584i
$732$	−1.45780	+	0.702039i	−0.0538818	+	0.0259481i
$733$	−23.1816	+	29.0688i	−0.856231	+	1.07368i	0.140272	+	0.990113i	$0.455202\pi$
$733$	−23.1816	+	29.0688i	−0.856231	+	1.07368i	−0.996502	+	0.0835661i	$0.973369\pi$
$734$	6.32586	−	7.93238i	0.233492	−	0.292790i
$735$	8.32141	+	4.00738i	0.306940	+	0.147814i
$736$	−6.82364	−	8.55658i	−0.251523	−	0.315400i
$737$	−37.8885			−1.39564
$738$	−1.09979	−	1.37910i	−0.0404840	−	0.0507653i
$739$	1.79550	+	7.86658i	0.0660484	+	0.289377i	0.997156	−	0.0753683i	$-0.0240133\pi$
$739$	1.79550	+	7.86658i	0.0660484	+	0.289377i	−0.931107	+	0.364745i	$0.881156\pi$
$740$	3.41807	+	14.9756i	0.125651	+	0.550512i
$741$	7.92344	+	9.93567i	0.291075	+	0.364996i
$742$	−7.23607			−0.265644
$743$	−19.1810	−	24.0522i	−0.703683	−	0.882390i	0.293610	−	0.955925i	$-0.405143\pi$
$743$	−19.1810	−	24.0522i	−0.703683	−	0.882390i	−0.997293	+	0.0735353i	$0.976572\pi$
$744$	3.55367	+	1.71136i	0.130284	+	0.0627413i
$745$	−13.1362	+	16.4723i	−0.481274	+	0.603499i
$746$	18.5442	−	23.2537i	0.678953	−	0.851380i
$747$	2.73394	−	1.31659i	0.100030	−	0.0481717i
$748$	−3.29295	−	14.4273i	−0.120402	−	0.527516i
$749$	−5.59075	+	24.4947i	−0.204282	+	0.895016i
$750$	12.4821	+	6.01107i	0.455782	+	0.219493i
$751$	−24.7515	+	11.9197i	−0.903196	+	0.434957i	−0.827042	−	0.562140i	$-0.809978\pi$
$751$	−24.7515	+	11.9197i	−0.903196	+	0.434957i	−0.0761541	+	0.997096i	$0.524264\pi$
$752$	7.56098	−	33.1268i	0.275720	−	1.20801i
$753$	18.8541			0.687082
$754$		0			0
$755$	−52.3050			−1.90357
$756$	−1.68277	+	7.37270i	−0.0612018	+	0.268143i
$757$	−42.3264	+	20.3833i	−1.53838	+	0.740844i	−0.995115	−	0.0987194i	$-0.968525\pi$
$757$	−42.3264	+	20.3833i	−1.53838	+	0.740844i	−0.543262	+	0.839563i	$0.682811\pi$
$758$	−54.9710	−	26.4726i	−1.99663	−	0.961529i
$759$	4.21550	−	18.4693i	0.153013	−	0.670393i
$760$	2.63305	+	11.5361i	0.0955107	+	0.418460i
$761$	−44.8668	+	21.6067i	−1.62642	+	0.783242i	−0.626427	+	0.779480i	$0.715483\pi$
$761$	−44.8668	+	21.6067i	−1.62642	+	0.783242i	−0.999993	+	0.00376214i	$0.998802\pi$
$762$	−3.17367	+	3.97966i	−0.114970	+	0.144168i
$763$	−23.1683	+	29.0521i	−0.838748	+	1.05176i
$764$	−6.70113	−	3.22709i	−0.242438	−	0.116752i
$765$	4.49834	+	5.64074i	0.162638	+	0.203942i
$766$	−35.8328			−1.29469
$767$	−13.4439	−	16.8581i	−0.485430	−	0.608710i
$768$	4.88306	+	21.3941i	0.176202	+	0.771992i
$769$	5.64328	+	24.7248i	0.203502	+	0.891600i	0.968784	+	0.247905i	$0.0797422\pi$
$769$	5.64328	+	24.7248i	0.203502	+	0.891600i	−0.765282	+	0.643695i	$0.777401\pi$
$770$	−23.2940	−	29.2098i	−0.839458	−	1.05265i
$771$	1.32624			0.0477633
$772$	−1.35942	−	1.70466i	−0.0489266	−	0.0613520i
$773$	−12.6136	−	6.07437i	−0.453678	−	0.218480i	0.193068	−	0.981185i	$-0.438156\pi$
$773$	−12.6136	−	6.07437i	−0.453678	−	0.218480i	−0.646746	+	0.762705i	$0.723871\pi$
$774$	−1.06505	+	1.33553i	−0.0382824	+	0.0480045i
$775$	−2.13830	+	2.68134i	−0.0768099	+	0.0963166i
$776$	33.3669	−	16.0686i	1.19780	−	0.576831i
$777$	7.01087	+	30.7166i	0.251514	+	1.10195i
$778$	7.60584	−	33.3234i	0.272683	−	1.19470i
$779$	4.76774	+	2.29602i	0.170822	+	0.0822636i
$780$	−10.8929	+	5.24573i	−0.390027	+	0.187827i
$781$	−1.23007	+	5.38927i	−0.0440152	+	0.192843i
$782$	34.6525			1.23917
$783$		0			0
$784$	9.70820			0.346722
$785$	3.53261	−	15.4774i	0.126084	−	0.552411i
$786$	3.12829	−	1.50650i	0.111582	−	0.0537352i
$787$	22.8492	+	11.0036i	0.814485	+	0.392236i	0.794274	−	0.607560i	$-0.207852\pi$
$787$	22.8492	+	11.0036i	0.814485	+	0.392236i	0.0202118	+	0.999796i	$0.493566\pi$
$788$	2.71038	−	11.8750i	0.0965533	−	0.423028i
$789$	1.18520	+	5.19270i	0.0421942	+	0.184865i
$790$	−21.1787	+	10.1991i	−0.753504	+	0.362868i
$791$	13.8640	−	17.3849i	0.492946	−	0.618134i
$792$	1.92669	−	2.41599i	0.0684619	−	0.0858485i
$793$	6.17533	+	2.97388i	0.219292	+	0.105606i
$794$	−32.2263	−	40.4105i	−1.14367	−	1.43411i
$795$	−9.23607			−0.327570
$796$	0.329118	+	0.412701i	0.0116653	+	0.0146278i
$797$	4.63281	+	20.2977i	0.164103	+	0.718980i	0.988280	+	0.152649i	$0.0487805\pi$
$797$	4.63281	+	20.2977i	0.164103	+	0.718980i	−0.824178	+	0.566331i	$0.808362\pi$
$798$	−2.41526	−	10.5820i	−0.0854995	−	0.374598i
$799$	28.8839	+	36.2193i	1.02184	+	1.28135i
$800$	−10.6393			−0.376157
$801$	−2.07388	−	2.60056i	−0.0732768	−	0.0918862i
$802$	48.2078	+	23.2156i	1.70228	+	0.819773i
$803$	0.658236	−	0.825401i	0.0232286	−	0.0291278i
$804$	6.52927	−	8.18745i	0.230270	−	0.288749i
$805$	18.6072	−	8.96077i	0.655819	−	0.315826i
$806$	1.66271	+	7.28479i	0.0585663	+	0.256596i
$807$	2.16028	−	9.46480i	0.0760454	−	0.333177i
$808$	−3.25974	−	1.56981i	−0.114677	−	0.0552256i
$809$	13.5766	−	6.53814i	0.477328	−	0.229869i	−0.179720	−	0.983718i	$-0.557519\pi$
$809$	13.5766	−	6.53814i	0.477328	−	0.229869i	0.657048	+	0.753849i	$0.271805\pi$
$810$	−7.92102	+	34.7043i	−0.278316	+	1.21938i
$811$	−25.6525			−0.900780			−0.450390	−	0.892832i	$-0.648715\pi$
$811$	−25.6525			−0.900780			−0.450390	+	0.892832i	$0.648715\pi$
$812$		0			0
$813$	−19.7082			−0.691197
$814$	−11.3438	+	49.7006i	−0.397601	+	1.74200i
$815$	−59.2321	+	28.5247i	−2.07481	+	0.999175i
$816$	−46.8312	−	22.5527i	−1.63942	−	0.789503i
$817$	1.14033	−	4.99613i	0.0398952	−	0.174792i
$818$	0.210120	+	0.920597i	0.00734668	+	0.0321879i
$819$	3.25974	−	1.56981i	0.113904	−	0.0548535i
$820$	−3.13892	+	3.93609i	−0.109616	+	0.137454i
$821$	22.0818	−	27.6897i	0.770659	−	0.966376i	−0.229317	−	0.973352i	$-0.573649\pi$
$821$	22.0818	−	27.6897i	0.770659	−	0.966376i	0.999976	+	0.00697599i	$0.00222055\pi$
$822$	−32.6786	−	15.7372i	−1.13980	−	0.548897i
$823$	−2.16484	−	2.71463i	−0.0754616	−	0.0946259i	0.742668	−	0.669660i	$-0.233560\pi$
$823$	−2.16484	−	2.71463i	−0.0754616	−	0.0946259i	−0.818129	+	0.575034i	$0.804989\pi$
$824$	29.4721			1.02671
$825$	−11.4824	−	14.3985i	−0.399767	−	0.501292i
$826$	4.09804	+	17.9547i	0.142589	+	0.624723i
$827$	12.4688	+	54.6295i	0.433584	+	1.89966i	0.436592	+	0.899660i	$0.356185\pi$
$827$	12.4688	+	54.6295i	0.433584	+	1.89966i	−0.00300768	+	0.999995i	$0.500957\pi$
$828$	−0.476304	−	0.597266i	−0.0165527	−	0.0207564i
$829$	−8.20163			−0.284854			−0.142427	−	0.989805i	$-0.545491\pi$
$829$	−8.20163			−0.284854			−0.142427	+	0.989805i	$0.545491\pi$
$830$	−22.8739	−	28.6830i	−0.793965	−	0.995601i
$831$	−34.4303	−	16.5808i	−1.19437	−	0.575181i
$832$	11.1881	−	14.0294i	0.387877	−	0.486382i
$833$	−8.25255	+	10.3484i	−0.285934	+	0.358550i
$834$	34.6932	−	16.7074i	1.20133	−	0.578529i
$835$	12.3667	+	54.1821i	0.427967	+	1.87505i
$836$	0.922549	−	4.04195i	0.0319070	−	0.139794i
$837$	5.37478	+	2.58836i	0.185780	+	0.0894668i
$838$	−3.73533	+	1.79884i	−0.129035	+	0.0621398i
$839$	0.715356	−	3.13418i	0.0246968	−	0.108204i	−0.961077	−	0.276280i	$-0.910898\pi$
$839$	0.715356	−	3.13418i	0.0246968	−	0.108204i	0.985774	+	0.168076i	$0.0537554\pi$
$840$	−23.0902			−0.796687
$841$		0			0
$842$	3.18034			0.109602
$843$	−6.16566	+	27.0135i	−0.212356	+	0.930394i
$844$	10.9431	−	5.26991i	0.376676	−	0.181398i
$845$	12.7140	+	6.12273i	0.437374	+	0.210628i
$846$	0.962679	−	4.21777i	0.0330976	−	0.145010i
$847$	−1.04001	−	4.55658i	−0.0357352	−	0.156566i
$848$	−8.74679	+	4.21223i	−0.300366	+	0.144649i
$849$	0.770676	−	0.966397i	0.0264495	−	0.0331667i
$850$	21.0034	−	26.3375i	0.720412	−	0.903369i
$851$	−25.3896	−	12.2270i	−0.870345	−	0.419136i
$852$	−0.952608	−	1.19453i	−0.0326358	−	0.0409240i
$853$	45.0000			1.54077			0.770385	−	0.637579i	$-0.220064\pi$
$853$	45.0000			1.54077			0.770385	+	0.637579i	$0.220064\pi$
$854$	−3.64997	−	4.57692i	−0.124900	−	0.156619i
$855$	0.449779	+	1.97061i	0.0153821	+	0.0673934i
$856$	5.59075	+	24.4947i	0.191088	+	0.837211i
$857$	−18.5013	−	23.1999i	−0.631992	−	0.792493i	0.357984	−	0.933728i	$-0.383464\pi$
$857$	−18.5013	−	23.1999i	−0.631992	−	0.792493i	−0.989976	+	0.141235i	$0.954893\pi$
$858$	−40.1246			−1.36983
$859$	−12.0282	−	15.0829i	−0.410398	−	0.514623i	0.533077	−	0.846067i	$-0.321036\pi$
$859$	−12.0282	−	15.0829i	−0.410398	−	0.514623i	−0.943475	+	0.331444i	$0.892464\pi$
$860$	4.39257	+	2.11535i	0.149785	+	0.0721329i
$861$	−6.43830	+	8.07338i	−0.219417	+	0.275140i
$862$	−34.9022	+	43.7659i	−1.18877	+	1.49067i
$863$	22.2924	−	10.7354i	0.758841	−	0.365438i	−0.0141135	−	0.999900i	$-0.504493\pi$
$863$	22.2924	−	10.7354i	0.758841	−	0.365438i	0.772954	+	0.634462i	$0.218778\pi$
$864$	4.11810	+	18.0426i	0.140101	+	0.613821i
$865$	−4.50295	+	19.7287i	−0.153105	+	0.670796i
$866$	18.3945	+	8.85835i	0.625072	+	0.301019i
$867$	39.0666	−	18.8135i	1.32677	−	0.638940i
$868$	0.335245	−	1.46880i	0.0113790	−	0.0498545i
$869$	−18.4164			−0.624734
$870$		0			0
$871$	−44.3607			−1.50310
$872$	−8.26867	+	36.2274i	−0.280012	+	1.22681i
$873$	5.69974	−	2.74485i	0.192907	−	0.0928992i
$874$	8.74679	+	4.21223i	0.295865	+	0.142481i
$875$	−2.63305	+	11.5361i	−0.0890133	+	0.389993i
$876$	0.0649307	+	0.284480i	0.00219381	+	0.00961169i
$877$	−5.96264	+	2.87146i	−0.201344	+	0.0969622i	−0.531839	−	0.846846i	$-0.678499\pi$
$877$	−5.96264	+	2.87146i	−0.201344	+	0.0969622i	0.330495	+	0.943808i	$0.392784\pi$
$878$	−3.08270	+	3.86559i	−0.104036	+	0.130457i
$879$	17.6264	−	22.1028i	0.594523	−	0.745508i
$880$	−45.1607	−	21.7483i	−1.52237	−	0.733133i
$881$	18.2499	+	22.8846i	0.614854	+	0.771002i	0.987610	−	0.156927i	$-0.0501588\pi$
$881$	18.2499	+	22.8846i	0.614854	+	0.771002i	−0.372757	+	0.927929i	$0.621587\pi$
$882$	1.23607			0.0416206
$883$	24.7444	+	31.0285i	0.832715	+	1.04419i	0.998317	+	0.0579988i	$0.0184720\pi$
$883$	24.7444	+	31.0285i	0.832715	+	1.04419i	−0.165602	+	0.986193i	$0.552957\pi$
$884$	−3.85545	−	16.8918i	−0.129673	−	0.568134i
$885$	5.23071	+	22.9172i	0.175828	+	0.770354i
$886$	13.2057	+	16.5595i	0.443655	+	0.556326i
$887$	−20.0689			−0.673847			−0.336924	−	0.941532i	$-0.609386\pi$
$887$	−20.0689			−0.673847			−0.336924	+	0.941532i	$0.609386\pi$
$888$	19.6440	+	24.6328i	0.659210	+	0.826624i
$889$	−3.91698	−	1.88632i	−0.131371	−	0.0632651i
$890$	−25.0735	+	31.4412i	−0.840466	+	1.05391i
$891$	−17.3882	+	21.8041i	−0.582527	+	0.730466i
$892$	−10.2046	+	4.91427i	−0.341675	+	0.164542i
$893$	2.88804	+	12.6533i	0.0966444	+	0.423427i
$894$	4.30049	−	18.8417i	0.143830	−	0.630160i
$895$	−41.1433	−	19.8136i	−1.37527	−	0.662295i
$896$	−27.4353	+	13.2121i	−0.916548	+	0.441386i
$897$	4.93559	−	21.6242i	0.164795	−	0.722012i
$898$	−22.8541			−0.762651
$899$		0			0
$900$	−0.742646			−0.0247549
$901$	2.94530	−	12.9042i	0.0981222	−	0.429902i
$902$	−15.0536	+	7.24942i	−0.501229	+	0.241379i
$903$	9.00969	+	4.33884i	0.299824	+	0.144387i
$904$	4.94799	−	21.6786i	0.164568	−	0.721018i
$905$	−7.58578	−	33.2355i	−0.252160	−	1.10478i
$906$	43.2273	−	20.8172i	1.43613	−	0.691605i
$907$	−8.87604	+	11.1302i	−0.294724	+	0.369572i	−0.907043	−	0.421039i	$-0.861666\pi$
$907$	−8.87604	+	11.1302i	−0.294724	+	0.369572i	0.612318	+	0.790611i	$0.290237\pi$
$908$	5.73712	−	7.19412i	0.190393	−	0.238745i
$909$	−0.556829	−	0.268155i	−0.0184689	−	0.00889414i
$910$	−27.2731	−	34.1994i	−0.904094	−	1.13370i
$911$	−6.94427			−0.230074			−0.115037	−	0.993361i	$-0.536699\pi$
$911$	−6.94427			−0.230074			−0.115037	+	0.993361i	$0.536699\pi$
$912$	−9.07945	−	11.3853i	−0.300651	−	0.377004i
$913$	−6.39584	−	28.0220i	−0.211671	−	0.927393i
$914$	−1.90529	−	8.34763i	−0.0630215	−	0.276115i
$915$	−4.65880	−	5.84195i	−0.154015	−	0.193129i
$916$	−9.70820			−0.320768
$917$	1.84900	+	2.31857i	0.0610592	+	0.0765658i
$918$	−52.7938	−	25.4242i	−1.74246	−	0.839123i
$919$	−19.5183	+	24.4752i	−0.643850	+	0.807362i	−0.991479	−	0.130270i	$-0.958416\pi$
$919$	−19.5183	+	24.4752i	−0.643850	+	0.807362i	0.347629	+	0.937632i	$0.386987\pi$
$920$	12.8766	−	16.1468i	0.424529	−	0.532343i
$921$	−4.63629	+	2.23272i	−0.152771	+	0.0735707i
$922$	2.87271	+	12.5862i	0.0946076	+	0.414503i
$923$	−1.44019	+	6.30987i	−0.0474043	+	0.207692i
$924$	7.28899	+	3.51019i	0.239790	+	0.115477i
$925$	−24.6822	+	11.8863i	−0.811544	+	0.390819i
$926$	0.975079	−	4.27210i	0.0320431	−	0.140390i
$927$	5.03444			0.165353
$928$		0			0
$929$	27.6525			0.907248			0.453624	−	0.891193i	$-0.350131\pi$
$929$	27.6525			0.907248			0.453624	+	0.891193i	$0.350131\pi$
$930$	1.81263	−	7.94166i	0.0594386	−	0.260417i
$931$	−3.34098	+	1.60893i	−0.109496	+	0.0527305i
$932$	−5.99367	−	2.88640i	−0.196329	−	0.0945472i
$933$	3.27288	−	14.3394i	0.107149	−	0.469452i
$934$	−0.0200647	−	0.0879092i	−0.000656537	−	0.00287648i
$935$	61.5717	−	29.6514i	2.01361	−	0.969703i
$936$	2.25581	−	2.82869i	0.0737334	−	0.0924587i
$937$	−15.3706	+	19.2741i	−0.502135	+	0.629657i	−0.966709	−	0.255877i	$-0.917636\pi$
$937$	−15.3706	+	19.2741i	−0.502135	+	0.629657i	0.464575	+	0.885534i	$0.346207\pi$
$938$	34.1364	+	16.4392i	1.11459	+	0.536760i
$939$	24.3028	+	30.4748i	0.793093	+	0.994507i
$940$	−12.3475			−0.402732
$941$	0.553998	+	0.694692i	0.0180598	+	0.0226463i	0.790779	−	0.612101i	$-0.209676\pi$
$941$	0.553998	+	0.694692i	0.0180598	+	0.0226463i	−0.772720	+	0.634748i	$0.781104\pi$
$942$	3.24042	+	14.1972i	0.105579	+	0.462570i
$943$	−2.05522	−	9.00450i	−0.0669271	−	0.293227i
$944$	15.4053	+	19.3177i	0.501400	+	0.628736i
$945$	−34.9230			−1.13604
$946$	10.0883	+	12.6503i	0.327998	+	0.411297i
$947$	12.5825	+	6.05943i	0.408877	+	0.196905i	0.627005	−	0.779015i	$-0.284281\pi$
$947$	12.5825	+	6.05943i	0.408877	+	0.196905i	−0.218128	+	0.975920i	$0.569995\pi$
$948$	3.17367	−	3.97966i	0.103076	−	0.129253i
$949$	0.770676	−	0.966397i	0.0250172	−	0.0313706i
$950$	8.50307	−	4.09486i	0.275876	−	0.132855i
$951$	−5.14571	−	22.5448i	−0.166861	−	0.731066i
$952$	7.36326	−	32.2605i	0.238644	−	1.04557i
$953$	32.1026	+	15.4598i	1.03990	+	0.500792i	0.874293	−	0.485399i	$-0.161326\pi$
$953$	32.1026	+	15.4598i	1.03990	+	0.500792i	0.165612	+	0.986191i	$0.447040\pi$
$954$	−1.11366	+	0.536310i	−0.0360560	+	0.0173637i
$955$	7.64304	−	33.4864i	0.247323	−	1.08359i
$956$	9.11146			0.294686
$957$		0			0
$958$	−18.0902			−0.584467
$959$	6.89341	−	30.2020i	0.222600	−	0.975274i
$960$	−17.6250	+	8.48777i	−0.568845	+	0.273941i
$961$	26.8593	+	12.9347i	0.866428	+	0.417250i
$962$	−13.2816	+	58.1904i	−0.428216	+	1.87614i
$963$	0.955014	+	4.18419i	0.0307749	+	0.134834i
$964$	−14.8409	+	7.14699i	−0.477993	+	0.230189i
$965$	6.27785	−	7.87217i	0.202091	−	0.253414i
$966$	−11.8116	+	14.8112i	−0.380031	+	0.476543i
$967$	−14.9221	−	7.18612i	−0.479863	−	0.231090i	0.178284	−	0.983979i	$-0.442945\pi$
$967$	−14.9221	−	7.18612i	−0.479863	−	0.231090i	−0.658147	+	0.752889i	$0.728660\pi$
$968$	−2.91404	−	3.65409i	−0.0936609	−	0.117447i
$969$	19.8541			0.637806
$970$	−47.6878	−	59.7986i	−1.53116	−	1.92002i
$971$	4.11810	+	18.0426i	0.132156	+	0.579014i	0.997029	+	0.0770234i	$0.0245416\pi$
$971$	4.11810	+	18.0426i	0.132156	+	0.579014i	−0.864873	+	0.501990i	$0.832601\pi$
$972$	0.542438	+	2.37658i	0.0173987	+	0.0762287i
$973$	20.5057	+	25.7133i	0.657382	+	0.824331i
$974$	36.3050			1.16329
$975$	−13.4439	−	16.8581i	−0.430549	−	0.539891i
$976$	−7.07630	−	3.40777i	−0.226507	−	0.109080i
$977$	3.87485	−	4.85891i	0.123968	−	0.155450i	−0.715975	−	0.698126i	$-0.754017\pi$
$977$	3.87485	−	4.85891i	0.123968	−	0.155450i	0.839942	+	0.542676i	$0.182589\pi$
$978$	37.5995	−	47.1483i	1.20230	−	1.50764i
$979$	−28.3864	+	13.6702i	−0.907235	+	0.436901i
$980$	−0.785024	−	3.43941i	−0.0250767	−	0.109868i
$981$	−1.41246	+	6.18838i	−0.0450963	+	0.197580i
$982$	36.6266	+	17.6384i	1.16880	+	0.562866i
$983$	6.25657	−	3.01301i	0.199554	−	0.0961000i	−0.331438	−	0.943477i	$-0.607534\pi$
$983$	6.25657	−	3.01301i	0.199554	−	0.0961000i	0.530992	+	0.847377i	$0.321820\pi$
$984$	−2.29780	+	10.0673i	−0.0732513	+	0.320935i
$985$	56.2492			1.79225
$986$		0			0
$987$	−25.3262			−0.806143
$988$	1.08014	−	4.73240i	0.0343638	−	0.150558i
$989$	−8.05851	+	3.88077i	−0.256246	+	0.123401i
$990$	−5.74995	−	2.76903i	−0.182745	−	0.0880056i
$991$	−8.60099	+	37.6834i	−0.273219	+	1.19705i	0.632969	+	0.774177i	$0.281836\pi$
$991$	−8.60099	+	37.6834i	−0.273219	+	1.19705i	−0.906188	+	0.422875i	$0.861021\pi$
$992$	−0.820416	−	3.59448i	−0.0260482	−	0.114125i
$993$	1.72070	−	0.828644i	0.0546047	−	0.0262962i
$994$	3.44657	−	4.32186i	0.109318	−	0.137081i
$995$	−1.51988	+	1.90587i	−0.0481834	+	0.0604200i
$996$	7.15754	+	3.44689i	0.226795	+	0.109219i
$997$	−17.5139	−	21.9618i	−0.554672	−	0.695537i	0.422891	−	0.906181i	$-0.361015\pi$
$997$	−17.5139	−	21.9618i	−0.554672	−	0.695537i	−0.977563	+	0.210644i	$0.932444\pi$
$998$	−57.7426			−1.82781
$999$	29.7108	+	37.2562i	0.940009	+	1.17873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.g.605.1		12
29.2	odd	28		841.2.e.j.651.1		24
29.3	odd	28		841.2.e.j.196.1		24
29.4	even	14		841.2.d.i.574.1		12
29.5	even	14		841.2.d.i.190.2		12
29.6	even	14		841.2.a.a.1.1	✓	2
29.7	even	7	inner	841.2.d.g.645.1		12
29.8	odd	28		841.2.e.j.63.1		24
29.9	even	14		841.2.d.i.778.1		12
29.10	odd	28		841.2.e.j.267.4		24
29.11	odd	28		841.2.e.j.270.4		24
29.12	odd	4		841.2.e.j.236.1		24
29.13	even	14		841.2.d.i.571.2		12
29.14	odd	28		841.2.b.b.840.1		4
29.15	odd	28		841.2.b.b.840.4		4
29.16	even	7	inner	841.2.d.g.571.1		12
29.17	odd	4		841.2.e.j.236.4		24
29.18	odd	28		841.2.e.j.270.1		24
29.19	odd	28		841.2.e.j.267.1		24
29.20	even	7	inner	841.2.d.g.778.2		12
29.21	odd	28		841.2.e.j.63.4		24
29.22	even	14		841.2.d.i.645.2		12
29.23	even	7		841.2.a.c.1.2	yes	2
29.24	even	7	inner	841.2.d.g.190.1		12
29.25	even	7	inner	841.2.d.g.574.2		12
29.26	odd	28		841.2.e.j.196.4		24
29.27	odd	28		841.2.e.j.651.4		24
29.28	even	2		841.2.d.i.605.2		12
87.23	odd	14		7569.2.a.d.1.1		2
87.35	odd	14		7569.2.a.l.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.a.1.1	✓	2	29.6	even	14
841.2.a.c.1.2	yes	2	29.23	even	7
841.2.b.b.840.1		4	29.14	odd	28
841.2.b.b.840.4		4	29.15	odd	28
841.2.d.g.190.1		12	29.24	even	7	inner
841.2.d.g.571.1		12	29.16	even	7	inner
841.2.d.g.574.2		12	29.25	even	7	inner
841.2.d.g.605.1		12	1.1	even	1	trivial
841.2.d.g.645.1		12	29.7	even	7	inner
841.2.d.g.778.2		12	29.20	even	7	inner
841.2.d.i.190.2		12	29.5	even	14
841.2.d.i.571.2		12	29.13	even	14
841.2.d.i.574.1		12	29.4	even	14
841.2.d.i.605.2		12	29.28	even	2
841.2.d.i.645.2		12	29.22	even	14
841.2.d.i.778.1		12	29.9	even	14
841.2.e.j.63.1		24	29.8	odd	28
841.2.e.j.63.4		24	29.21	odd	28
841.2.e.j.196.1		24	29.3	odd	28
841.2.e.j.196.4		24	29.26	odd	28
841.2.e.j.236.1		24	29.12	odd	4
841.2.e.j.236.4		24	29.17	odd	4
841.2.e.j.267.1		24	29.19	odd	28
841.2.e.j.267.4		24	29.10	odd	28
841.2.e.j.270.1		24	29.18	odd	28
841.2.e.j.270.4		24	29.11	odd	28
841.2.e.j.651.1		24	29.2	odd	28
841.2.e.j.651.4		24	29.27	odd	28
7569.2.a.d.1.1		2	87.23	odd	14
7569.2.a.l.1.2		2	87.35	odd	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.360046 + 1.57747i) q^{2} +(1.45780 - 0.702039i) q^{3} +(-0.556829 - 0.268155i) q^{4} +(0.635097 - 2.78254i) q^{5} +(0.582567 + 2.55239i) q^{6} +(-2.01463 + 0.970194i) q^{7} +(-1.39417 + 1.74823i) q^{8} +(-0.238152 + 0.298633i) q^{9} +(4.16070 + 2.00369i) q^{10} +(2.25581 + 2.82869i) q^{11} -1.00000 q^{12} +(2.64115 + 3.31189i) q^{13} +(-0.805088 - 3.52732i) q^{14} +(-1.02761 - 4.50225i) q^{15} +(-3.02648 - 3.79509i) q^{16} +6.61803 q^{17} +(-0.385338 - 0.483198i) q^{18} +(1.67049 + 0.804465i) q^{19} +(-1.09979 + 1.37910i) q^{20} +(-2.25581 + 2.82869i) q^{21} +(-5.27436 + 2.54000i) q^{22} +(-0.720093 - 3.15493i) q^{23} +(-0.805088 + 3.52732i) q^{24} +(-2.83436 - 1.36495i) q^{25} +(-6.17533 + 2.97388i) q^{26} +(-1.21766 + 5.33494i) q^{27} +1.38197 q^{28} +7.47214 q^{30} +(0.242586 - 1.06284i) q^{31} +(3.04705 - 1.46738i) q^{32} +(5.27436 + 2.54000i) q^{33} +(-2.38280 + 10.4397i) q^{34} +(1.42012 + 6.22196i) q^{35} +(0.212690 - 0.102426i) q^{36} +(5.42948 - 6.80835i) q^{37} +(-1.87047 + 2.34549i) q^{38} +(6.17533 + 2.97388i) q^{39} +(3.97909 + 4.98962i) q^{40} +2.85410 q^{41} +(-3.64997 - 4.57692i) q^{42} +(-0.615033 - 2.69463i) q^{43} +(-0.497572 - 2.18001i) q^{44} +(0.679710 + 0.852329i) q^{45} +5.23607 q^{46} +(4.36443 + 5.47282i) q^{47} +(-7.07630 - 3.40777i) q^{48} +(-1.24698 + 1.56366i) q^{49} +(3.17367 - 3.97966i) q^{50} +(9.64776 - 4.64612i) q^{51} +(-0.582567 - 2.55239i) q^{52} +(0.445042 - 1.94986i) q^{53} +(-7.97727 - 3.84165i) q^{54} +(9.30362 - 4.48039i) q^{55} +(1.11260 - 4.87464i) q^{56} +3.00000 q^{57} -5.09017 q^{59} +(-0.635097 + 2.78254i) q^{60} +(1.45780 - 0.702039i) q^{61} +(1.58925 + 0.765341i) q^{62} +(0.190056 - 0.832688i) q^{63} +(-0.942614 - 4.12986i) q^{64} +(10.8929 - 5.24573i) q^{65} +(-5.90578 + 7.40561i) q^{66} +(-6.52927 + 8.18745i) q^{67} +(-3.68512 - 1.77466i) q^{68} +(-3.26463 - 4.09372i) q^{69} -10.3262 q^{70} +(0.952608 + 1.19453i) q^{71} +(-0.190056 - 0.832688i) q^{72} +(-0.0649307 - 0.284480i) q^{73} +(8.78508 + 11.0161i) q^{74} -5.09017 q^{75} +(-0.714456 - 0.895899i) q^{76} +(-7.28899 - 3.51019i) q^{77} +(-6.91461 + 8.67064i) q^{78} +(-3.17367 + 3.97966i) q^{79} +(-12.4821 + 6.01107i) q^{80} +(1.71524 + 7.51494i) q^{81} +(-1.02761 + 4.50225i) q^{82} +(-7.15754 - 3.44689i) q^{83} +(2.01463 - 0.970194i) q^{84} +(4.20310 - 18.4150i) q^{85} +4.47214 q^{86} -8.09017 q^{88} +(-1.93776 + 8.48987i) q^{89} +(-1.58925 + 0.765341i) q^{90} +(-8.53410 - 4.10981i) q^{91} +(-0.445042 + 1.94986i) q^{92} +(-0.392512 - 1.71971i) q^{93} +(-10.2046 + 4.91427i) q^{94} +(3.29938 - 4.13729i) q^{95} +(3.41182 - 4.27829i) q^{96} +(-14.9221 - 7.18612i) q^{97} +(-2.01766 - 2.53006i) q^{98} -1.38197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + q^{3} + q^{4} - q^{5} + 3 q^{6} + 3 q^{9} + 7 q^{10} - 5 q^{11} - 12 q^{12} - 4 q^{13} - 5 q^{14} - 7 q^{15} + 3 q^{16} + 66 q^{17} - q^{18} - 3 q^{19} + 8 q^{20} + 5 q^{21} - 5 q^{22}+ \cdots - 30 q^{99}+O(q^{100}) \) 12 * q - q^2 + q^3 + q^4 - q^5 + 3 * q^6 + 3 * q^9 + 7 * q^10 - 5 * q^11 - 12 * q^12 - 4 * q^13 - 5 * q^14 - 7 * q^15 + 3 * q^16 + 66 * q^17 - q^18 - 3 * q^19 + 8 * q^20 + 5 * q^21 - 5 * q^22 - 2 * q^23 - 5 * q^24 - 13 * q^25 - 7 * q^26 - 2 * q^27 + 30 * q^28 + 36 * q^30 - 9 * q^31 + 9 * q^32 + 5 * q^33 - 8 * q^34 + 15 * q^35 - 4 * q^36 - 4 * q^37 + 6 * q^38 + 7 * q^39 - 15 * q^40 - 6 * q^41 + 5 * q^42 - 10 * q^43 + 9 * q^45 + 36 * q^46 - 14 * q^47 - 9 * q^48 + 4 * q^49 + q^50 + 8 * q^51 - 3 * q^52 + 4 * q^53 - 11 * q^54 + 5 * q^55 + 10 * q^56 + 36 * q^57 + 6 * q^59 + q^60 + q^61 + 8 * q^62 - 5 * q^63 - 4 * q^64 + 13 * q^65 + 10 * q^66 + 12 * q^67 + 3 * q^68 + 6 * q^69 - 30 * q^70 - 12 * q^71 + 5 * q^72 - 14 * q^73 - 17 * q^74 + 6 * q^75 + 9 * q^76 - 5 * q^77 + 11 * q^78 - q^79 - 21 * q^80 + 2 * q^81 - 7 * q^82 + 2 * q^83 + 2 * q^85 - 30 * q^88 - 4 * q^89 - 8 * q^90 - 10 * q^91 - 4 * q^92 - 8 * q^93 - 7 * q^94 - 24 * q^95 - 2 * q^96 - 13 * q^97 + 2 * q^98 - 30 * q^99

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