LMFDB - Embedded newform 841.2.d.i.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			$-0.137526 + 0.602539i$ of defining polynomial
Character	$\chi$	$=$	841.605
Dual form			841.2.d.i.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+(-0.137526 + 0.602539i) q^{2} +(0.556829 - 0.268155i) q^{3} +(1.45780 + 0.702039i) q^{4} +(-0.857618 + 3.75747i) q^{5} +(0.0849954 + 0.372389i) q^{6} +(2.01463 - 0.970194i) q^{7} +(-1.39417 + 1.74823i) q^{8} +(-1.63232 + 2.04686i) q^{9} +(-2.14608 - 1.03350i) q^{10} +(-0.861642 - 1.08046i) q^{11} +1.00000 q^{12} +(-0.147186 - 0.184565i) q^{13} +(0.307516 + 1.34732i) q^{14} +(0.530037 + 2.32225i) q^{15} +(1.15601 + 1.44960i) q^{16} -4.38197 q^{17} +(-1.00883 - 1.26503i) q^{18} +(4.37339 + 2.10612i) q^{19} +(-3.88812 + 4.87555i) q^{20} +(0.861642 - 1.08046i) q^{21} +(0.769519 - 0.370581i) q^{22} +(0.275051 + 1.20508i) q^{23} +(-0.307516 + 1.34732i) q^{24} +(-8.87824 - 4.27553i) q^{25} +(0.131450 - 0.0633028i) q^{26} +(-0.772623 + 3.38508i) q^{27} +3.61803 q^{28} -1.47214 q^{30} +(2.24527 - 9.83719i) q^{31} +(-5.06167 + 2.43757i) q^{32} +(-0.769519 - 0.370581i) q^{33} +(0.602632 - 2.64030i) q^{34} +(1.91769 + 8.40196i) q^{35} +(-3.81657 + 1.83796i) q^{36} +(2.93552 - 3.68102i) q^{37} +(-1.87047 + 2.34549i) q^{38} +(-0.131450 - 0.0633028i) q^{39} +(-5.37326 - 6.73785i) q^{40} +3.85410 q^{41} +(0.532524 + 0.667764i) q^{42} +(1.61018 + 7.05464i) q^{43} +(-0.497572 - 2.18001i) q^{44} +(-6.29112 - 7.88881i) q^{45} -0.763932 q^{46} +(-4.36443 - 5.47282i) q^{47} +(1.03242 + 0.497187i) q^{48} +(-1.24698 + 1.56366i) q^{49} +(3.79716 - 4.76149i) q^{50} +(-2.44001 + 1.17505i) q^{51} +(-0.0849954 - 0.372389i) q^{52} +(0.445042 - 1.94986i) q^{53} +(-1.93339 - 0.931070i) q^{54} +(4.79877 - 2.31097i) q^{55} +(-1.11260 + 4.87464i) q^{56} +3.00000 q^{57} +6.09017 q^{59} +(-0.857618 + 3.75747i) q^{60} +(0.556829 - 0.268155i) q^{61} +(5.61850 + 2.70573i) q^{62} +(-1.30266 + 5.70733i) q^{63} +(0.0525301 + 0.230149i) q^{64} +(0.819729 - 0.394760i) q^{65} +(0.329118 - 0.412701i) q^{66} +(-0.952608 + 1.19453i) q^{67} +(-6.38802 - 3.07631i) q^{68} +(0.476304 + 0.597266i) q^{69} -5.32624 q^{70} +(6.52927 + 8.18745i) q^{71} +(-1.30266 - 5.70733i) q^{72} +(3.05036 + 13.3645i) q^{73} +(1.81425 + 2.27500i) q^{74} -6.09017 q^{75} +(4.89695 + 6.14058i) q^{76} +(-2.78415 - 1.34077i) q^{77} +(0.0562200 - 0.0704977i) q^{78} +(-3.79716 + 4.76149i) q^{79} +(-6.43823 + 3.10049i) q^{80} +(-1.27019 - 5.56509i) q^{81} +(-0.530037 + 2.32225i) q^{82} +(8.95948 + 4.31466i) q^{83} +(2.01463 - 0.970194i) q^{84} +(3.75805 - 16.4651i) q^{85} -4.47214 q^{86} +3.09017 q^{88} +(-1.04767 + 4.59016i) q^{89} +(5.61850 - 2.70573i) q^{90} +(-0.475589 - 0.229032i) q^{91} +(-0.445042 + 1.94986i) q^{92} +(-1.38766 - 6.07972i) q^{93} +(3.89781 - 1.87708i) q^{94} +(-11.6644 + 14.6267i) q^{95} +(-2.16484 + 2.71463i) q^{96} +(-3.20953 - 1.54563i) q^{97} +(-0.770676 - 0.966397i) q^{98} +3.61803 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 $

$2$	−0.137526	+	0.602539i	−0.0972452	+	0.426059i	−0.999992	−	0.00411419i	$-0.998690\pi$
$2$	−0.137526	+	0.602539i	−0.0972452	+	0.426059i	0.902746	+	0.430173i	$0.141548\pi$
$3$	0.556829	−	0.268155i	0.321486	−	0.154819i	−0.266180	−	0.963923i	$-0.585761\pi$
$3$	0.556829	−	0.268155i	0.321486	−	0.154819i	0.587665	+	0.809104i	$0.300047\pi$
$4$	1.45780	+	0.702039i	0.728899	+	0.351019i
$5$	−0.857618	+	3.75747i	−0.383539	+	1.68039i	0.302756	+	0.953068i	$0.402093\pi$
$5$	−0.857618	+	3.75747i	−0.383539	+	1.68039i	−0.686294	+	0.727324i	$0.740764\pi$
$6$	0.0849954	+	0.372389i	0.0346992	+	0.152027i
$7$	2.01463	−	0.970194i	0.761458	−	0.366699i	−0.0125117	−	0.999922i	$-0.503983\pi$
$7$	2.01463	−	0.970194i	0.761458	−	0.366699i	0.773969	+	0.633223i	$0.218268\pi$
$8$	−1.39417	+	1.74823i	−0.492912	+	0.618092i
$9$	−1.63232	+	2.04686i	−0.544106	+	0.682287i
$10$	−2.14608	−	1.03350i	−0.678649	−	0.326820i
$11$	−0.861642	−	1.08046i	−0.259795	−	0.325772i	0.634778	−	0.772694i	$-0.281092\pi$
$11$	−0.861642	−	1.08046i	−0.259795	−	0.325772i	−0.894573	+	0.446922i	$0.852520\pi$
$12$	1.00000			0.288675
$13$	−0.147186	−	0.184565i	−0.0408220	−	0.0511892i	0.761001	−	0.648750i	$-0.224708\pi$
$13$	−0.147186	−	0.184565i	−0.0408220	−	0.0511892i	−0.801823	+	0.597561i	$0.796137\pi$
$14$	0.307516	+	1.34732i	0.0821872	+	0.360086i
$15$	0.530037	+	2.32225i	0.136855	+	0.599601i
$16$	1.15601	+	1.44960i	0.289003	+	0.362399i
$17$	−4.38197			−1.06278			−0.531391	−	0.847126i	$-0.678331\pi$
$17$	−4.38197			−1.06278			−0.531391	+	0.847126i	$0.678331\pi$
$18$	−1.00883	−	1.26503i	−0.237783	−	0.298170i
$19$	4.37339	+	2.10612i	1.00333	+	0.483176i	0.862066	−	0.506796i	$-0.169170\pi$
$19$	4.37339	+	2.10612i	1.00333	+	0.483176i	0.141260	+	0.989973i	$0.454885\pi$
$20$	−3.88812	+	4.87555i	−0.869411	+	1.09021i
$21$	0.861642	−	1.08046i	0.188026	−	0.235777i
$22$	0.769519	−	0.370581i	0.164062	−	0.0790081i
$23$	0.275051	+	1.20508i	0.0573521	+	0.251276i	0.995475	−	0.0950275i	$-0.0302939\pi$
$23$	0.275051	+	1.20508i	0.0573521	+	0.251276i	−0.938123	+	0.346303i	$0.887437\pi$
$24$	−0.307516	+	1.34732i	−0.0627715	+	0.275020i
$25$	−8.87824	−	4.27553i	−1.77565	−	0.855107i
$26$	0.131450	−	0.0633028i	0.0257794	−	0.0124147i
$27$	−0.772623	+	3.38508i	−0.148691	+	0.651459i
$28$	3.61803			0.683744
$29$		0			0
$29$		0			0
$30$	−1.47214			−0.268774
$31$	2.24527	−	9.83719i	0.403263	−	1.76681i	−0.210775	−	0.977535i	$-0.567599\pi$
$31$	2.24527	−	9.83719i	0.403263	−	1.76681i	0.614038	−	0.789277i	$-0.289544\pi$
$32$	−5.06167	+	2.43757i	−0.894786	+	0.430906i
$33$	−0.769519	−	0.370581i	−0.133956	−	0.0645099i
$34$	0.602632	−	2.64030i	0.103351	−	0.452808i
$35$	1.91769	+	8.40196i	0.324149	+	1.42019i
$36$	−3.81657	+	1.83796i	−0.636094	+	0.306327i
$37$	2.93552	−	3.68102i	0.482596	−	0.605156i	−0.479609	−	0.877482i	$-0.659221\pi$
$37$	2.93552	−	3.68102i	0.482596	−	0.605156i	0.962205	+	0.272326i	$0.0877929\pi$
$38$	−1.87047	+	2.34549i	−0.303430	+	0.380489i
$39$	−0.131450	−	0.0633028i	−0.0210488	−	0.0101366i
$40$	−5.37326	−	6.73785i	−0.849586	−	1.06535i
$41$	3.85410			0.601910			0.300955	−	0.953638i	$-0.402695\pi$
$41$	3.85410			0.601910			0.300955	+	0.953638i	$0.402695\pi$
$42$	0.532524	+	0.667764i	0.0821702	+	0.103038i
$43$	1.61018	+	7.05464i	0.245550	+	1.07582i	0.935877	+	0.352326i	$0.114609\pi$
$43$	1.61018	+	7.05464i	0.245550	+	1.07582i	−0.690328	+	0.723497i	$0.742534\pi$
$44$	−0.497572	−	2.18001i	−0.0750118	−	0.328648i
$45$	−6.29112	−	7.88881i	−0.937825	−	1.17599i
$46$	−0.763932			−0.112636
$47$	−4.36443	−	5.47282i	−0.636617	−	0.798293i	0.353958	−	0.935261i	$-0.384836\pi$
$47$	−4.36443	−	5.47282i	−0.636617	−	0.798293i	−0.990575	+	0.136968i	$0.956264\pi$
$48$	1.03242	+	0.497187i	0.149017	+	0.0717627i
$49$	−1.24698	+	1.56366i	−0.178140	+	0.223380i
$50$	3.79716	−	4.76149i	0.536999	−	0.673376i
$51$	−2.44001	+	1.17505i	−0.341669	+	0.164539i
$52$	−0.0849954	−	0.372389i	−0.0117867	−	0.0516411i
$53$	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	$0.0275667\pi$
$54$	−1.93339	−	0.931070i	−0.263101	−	0.126703i
$55$	4.79877	−	2.31097i	0.647067	−	0.311611i
$56$	−1.11260	+	4.87464i	−0.148678	+	0.651401i
$57$	3.00000			0.397360
$58$		0			0
$59$	6.09017			0.792873			0.396436	−	0.918062i	$-0.370247\pi$
$59$	6.09017			0.792873			0.396436	+	0.918062i	$0.370247\pi$
$60$	−0.857618	+	3.75747i	−0.110718	+	0.485087i
$61$	0.556829	−	0.268155i	0.0712947	−	0.0343337i	−0.397897	−	0.917430i	$-0.630260\pi$
$61$	0.556829	−	0.268155i	0.0712947	−	0.0343337i	0.469191	+	0.883097i	$0.344545\pi$
$62$	5.61850	+	2.70573i	0.713551	+	0.343628i
$63$	−1.30266	+	5.70733i	−0.164120	+	0.719056i
$64$	0.0525301	+	0.230149i	0.00656626	+	0.0287687i
$65$	0.819729	−	0.394760i	0.101675	−	0.0489640i
$66$	0.329118	−	0.412701i	0.0405116	−	0.0507999i
$67$	−0.952608	+	1.19453i	−0.116380	+	0.145935i	−0.836609	−	0.547801i	$-0.815465\pi$
$67$	−0.952608	+	1.19453i	−0.116380	+	0.145935i	0.720229	+	0.693736i	$0.244037\pi$
$68$	−6.38802	−	3.07631i	−0.774662	−	0.373057i
$69$	0.476304	+	0.597266i	0.0573402	+	0.0719024i
$70$	−5.32624			−0.636607
$71$	6.52927	+	8.18745i	0.774882	+	0.971671i	0.999996	−	0.00266125i	$-0.000847104\pi$
$71$	6.52927	+	8.18745i	0.774882	+	0.971671i	−0.225115	+	0.974332i	$0.572276\pi$
$72$	−1.30266	−	5.70733i	−0.153520	−	0.672615i
$73$	3.05036	+	13.3645i	0.357018	+	1.56420i	0.760579	+	0.649245i	$0.224915\pi$
$73$	3.05036	+	13.3645i	0.357018	+	1.56420i	−0.403561	+	0.914953i	$0.632228\pi$
$74$	1.81425	+	2.27500i	0.210902	+	0.264463i
$75$	−6.09017			−0.703232
$76$	4.89695	+	6.14058i	0.561719	+	0.704373i
$77$	−2.78415	−	1.34077i	−0.317283	−	0.152795i
$78$	0.0562200	−	0.0704977i	0.00636567	−	0.00798229i
$79$	−3.79716	+	4.76149i	−0.427214	+	0.535709i	−0.948123	−	0.317903i	$-0.897021\pi$
$79$	−3.79716	+	4.76149i	−0.427214	+	0.535709i	0.520910	+	0.853612i	$0.325593\pi$
$80$	−6.43823	+	3.10049i	−0.719816	+	0.346645i
$81$	−1.27019	−	5.56509i	−0.141133	−	0.618343i
$82$	−0.530037	+	2.32225i	−0.0585328	+	0.256449i
$83$	8.95948	+	4.31466i	0.983431	+	0.473595i	0.855284	−	0.518160i	$-0.173383\pi$
$83$	8.95948	+	4.31466i	0.983431	+	0.473595i	0.128147	+	0.991755i	$0.459097\pi$
$84$	2.01463	−	0.970194i	0.219814	−	0.105857i
$85$	3.75805	−	16.4651i	0.407618	−	1.78589i
$86$	−4.47214			−0.482243
$87$		0			0
$88$	3.09017			0.329413
$89$	−1.04767	+	4.59016i	−0.111053	+	0.486556i	0.888560	+	0.458760i	$0.151706\pi$
$89$	−1.04767	+	4.59016i	−0.111053	+	0.486556i	−0.999614	+	0.0277963i	$0.991151\pi$
$90$	5.61850	−	2.70573i	0.592242	−	0.285209i
$91$	−0.475589	−	0.229032i	−0.0498553	−	0.0240090i
$92$	−0.445042	+	1.94986i	−0.0463988	+	0.203287i
$93$	−1.38766	−	6.07972i	−0.143893	−	0.630437i
$94$	3.89781	−	1.87708i	0.402028	−	0.193606i
$95$	−11.6644	+	14.6267i	−1.19674	+	1.50066i
$96$	−2.16484	+	2.71463i	−0.220948	+	0.277060i
$97$	−3.20953	−	1.54563i	−0.325878	−	0.156935i	0.263790	−	0.964580i	$-0.415027\pi$
$97$	−3.20953	−	1.54563i	−0.325878	−	0.156935i	−0.589668	+	0.807645i	$0.700742\pi$
$98$	−0.770676	−	0.966397i	−0.0778500	−	0.0976208i
$99$	3.61803			0.363626
$100$	−9.94109	−	12.4657i	−0.994109	−	1.24657i
$101$	0.137526	+	0.602539i	0.0136843	+	0.0599548i	0.981309	−	0.192438i	$-0.0616395\pi$
$101$	0.137526	+	0.602539i	0.0136843	+	0.0599548i	−0.967625	+	0.252393i	$0.918782\pi$
$102$	−0.372447	−	1.63180i	−0.0368778	−	0.161572i
$103$	5.72385	+	7.17748i	0.563988	+	0.707218i	0.979289	−	0.202466i	$-0.0648955\pi$
$103$	5.72385	+	7.17748i	0.563988	+	0.707218i	−0.415302	+	0.909684i	$0.636324\pi$
$104$	0.527864			0.0517613
$105$	3.32086	+	4.16422i	0.324082	+	0.406386i
$106$	1.11366	+	0.536310i	0.108168	+	0.0520910i
$107$	4.21724	−	5.28826i	0.407696	−	0.511235i	−0.535016	−	0.844842i	$-0.679694\pi$
$107$	4.21724	−	5.28826i	0.407696	−	0.511235i	0.942712	+	0.333607i	$0.108266\pi$
$108$	−3.50279	+	4.39236i	−0.337056	+	0.422655i
$109$	12.9577	−	6.24010i	1.24112	−	0.597693i	0.306005	−	0.952030i	$-0.401008\pi$
$109$	12.9577	−	6.24010i	1.24112	−	0.597693i	0.935118	+	0.354337i	$0.115293\pi$
$110$	0.732494	+	3.20926i	0.0698405	+	0.305991i
$111$	0.647498	−	2.83687i	0.0614578	−	0.269264i
$112$	3.73533	+	1.79884i	0.352955	+	0.169974i
$113$	−7.15754	+	3.44689i	−0.673325	+	0.324256i	−0.739117	−	0.673577i	$-0.764757\pi$
$113$	−7.15754	+	3.44689i	−0.673325	+	0.324256i	0.0657920	+	0.997833i	$0.479043\pi$
$114$	−0.412577	+	1.80762i	−0.0386413	+	0.169299i
$115$	−4.76393			−0.444239
$116$		0			0
$117$	0.618034			0.0571373
$118$	−0.837554	+	3.66956i	−0.0771031	+	0.337811i
$119$	−8.82803	+	4.25136i	−0.809264	+	0.389721i
$120$	−4.79877	−	2.31097i	−0.438066	−	0.210962i
$121$	2.02275	−	8.86226i	0.183887	−	0.805660i
$122$	0.0849954	+	0.372389i	0.00769512	+	0.0337145i
$123$	2.14608	−	1.03350i	0.193505	−	0.0931872i
$124$	10.1792	−	12.7644i	0.914123	−	1.14627i
$125$	11.6644	−	14.6267i	1.04329	−	1.30825i
$126$	−3.25974	−	1.56981i	−0.290400	−	0.139849i
$127$	9.94109	+	12.4657i	0.882129	+	1.10615i	0.993664	+	0.112394i	$0.0358520\pi$
$127$	9.94109	+	12.4657i	0.882129	+	1.10615i	−0.111534	+	0.993761i	$0.535577\pi$
$128$	−11.3820			−1.00603
$129$	2.78833	+	3.49646i	0.245499	+	0.307846i
$130$	0.125125	+	0.548208i	0.0109742	+	0.0480810i
$131$	−3.18789	−	13.9670i	−0.278527	−	1.22031i	−0.899656	−	0.436599i	$-0.856183\pi$
$131$	−3.18789	−	13.9670i	−0.278527	−	1.22031i	0.621129	−	0.783708i	$-0.286674\pi$
$132$	−0.861642	−	1.08046i	−0.0749963	−	0.0940424i
$133$	10.8541			0.941170
$134$	−0.588744	−	0.738262i	−0.0508597	−	0.0637761i
$135$	−12.0567	−	5.80622i	−1.03768	−	0.499720i
$136$	6.10919	−	7.66068i	0.523858	−	0.656898i
$137$	4.45539	−	5.58689i	0.380650	−	0.477320i	−0.554189	−	0.832391i	$-0.686972\pi$
$137$	4.45539	−	5.58689i	0.380650	−	0.477320i	0.934840	+	0.355070i	$0.115543\pi$
$138$	−0.425380	+	0.204852i	−0.0362107	+	0.0174382i
$139$	−0.287452	−	1.25941i	−0.0243813	−	0.106822i	0.961273	−	0.275598i	$-0.0888757\pi$
$139$	−0.287452	−	1.25941i	−0.0243813	−	0.106822i	−0.985654	+	0.168776i	$0.946019\pi$
$140$	−3.10289	+	13.5947i	−0.262242	+	1.14896i
$141$	−3.89781	−	1.87708i	−0.328254	−	0.158079i
$142$	−5.83119	+	2.80815i	−0.489343	+	0.235655i
$143$	−0.0725948	+	0.318058i	−0.00607068	+	0.0265974i
$144$	−4.85410			−0.404508
$145$		0			0
$146$	−8.47214			−0.701159
$147$	−0.275051	+	1.20508i	−0.0226858	+	0.0993931i
$148$	6.86361	−	3.30534i	0.564185	−	0.271697i
$149$	−8.66555	−	4.17311i	−0.709909	−	0.341874i	0.0438379	−	0.999039i	$-0.486041\pi$
$149$	−8.66555	−	4.17311i	−0.709909	−	0.341874i	−0.753747	+	0.657164i	$0.771756\pi$
$150$	0.837554	−	3.66956i	0.0683860	−	0.299619i
$151$	−0.594968	−	2.60673i	−0.0484178	−	0.212132i	0.944932	−	0.327266i	$-0.106127\pi$
$151$	−0.594968	−	2.60673i	−0.0484178	−	0.212132i	−0.993350	+	0.115134i	$0.963270\pi$
$152$	−9.77921	+	4.70942i	−0.793199	+	0.381984i
$153$	7.15276	−	8.96928i	0.578266	−	0.725123i
$154$	1.19076	−	1.49317i	0.0959541	−	0.120323i
$155$	35.0374	+	16.8731i	2.81427	+	1.35528i
$156$	−0.147186	−	0.184565i	−0.0117843	−	0.0147771i
$157$	14.5623			1.16220			0.581099	−	0.813833i	$-0.302623\pi$
$157$	14.5623			1.16220			0.581099	+	0.813833i	$0.302623\pi$
$158$	−2.34677	−	2.94276i	−0.186699	−	0.234113i
$159$	−0.275051	−	1.20508i	−0.0218130	−	0.0955688i
$160$	−4.81813	−	21.1096i	−0.380907	−	1.66886i
$161$	1.72328	+	2.16093i	0.135814	+	0.170305i
$162$	3.52786			0.277175
$163$	−3.76241	−	4.71792i	−0.294695	−	0.369536i	0.612338	−	0.790596i	$-0.290229\pi$
$163$	−3.76241	−	4.71792i	−0.294695	−	0.369536i	−0.907032	+	0.421061i	$0.861658\pi$
$164$	5.61850	+	2.70573i	0.438731	+	0.211282i
$165$	2.05240	−	2.57363i	0.159779	−	0.200357i
$166$	−3.83190	+	4.80506i	−0.297413	+	0.372945i
$167$	−9.48528	+	4.56787i	−0.733993	+	0.353472i	−0.763253	−	0.646100i	$-0.776399\pi$
$167$	−9.48528	+	4.56787i	−0.733993	+	0.353472i	0.0292604	+	0.999572i	$0.490685\pi$
$168$	0.687628	+	3.01269i	0.0530516	+	0.232434i
$169$	2.88037	−	12.6197i	0.221567	−	0.970749i
$170$	9.40404	+	4.52875i	0.721257	+	0.347339i
$171$	−11.4497	+	5.51388i	−0.875580	+	0.421657i
$172$	−2.60532	+	11.4147i	−0.198654	+	0.870359i
$173$	4.09017			0.310970			0.155485	−	0.987838i	$-0.450306\pi$
$173$	4.09017			0.310970			0.155485	+	0.987838i	$0.450306\pi$
$174$		0			0
$175$	−22.0344			−1.66565
$176$	0.570167	−	2.49806i	0.0429779	−	0.188299i
$177$	3.39119	−	1.63311i	0.254897	−	0.122752i
$178$	−2.62167	−	1.26253i	−0.196502	−	0.0946305i
$179$	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	$-0.132589\pi$
$180$	−3.63293	−	15.9169i	−0.270783	−	1.18638i
$181$	−5.35560	+	2.57912i	−0.398079	+	0.191705i	−0.622203	−	0.782856i	$-0.713762\pi$
$181$	−5.35560	+	2.57912i	−0.398079	+	0.191705i	0.224124	+	0.974561i	$0.428048\pi$
$182$	0.203406	−	0.255063i	0.0150775	−	0.0189065i
$183$	0.238152	−	0.298633i	0.0176047	−	0.0220756i
$184$	−2.49022	−	1.19923i	−0.183581	−	0.0884081i
$185$	11.3138	+	14.1870i	0.831806	+	1.04305i
$186$	3.85410			0.282596
$187$	3.77568	+	4.73456i	0.276105	+	0.346225i
$188$	−2.52033	−	11.0423i	−0.183814	−	0.805340i
$189$	1.72764	+	7.56927i	0.125667	+	0.550584i
$190$	−7.20898	−	9.03977i	−0.522994	−	0.655814i
$191$	17.0344			1.23257			0.616284	−	0.787524i	$-0.288637\pi$
$191$	17.0344			1.23257			0.616284	+	0.787524i	$0.288637\pi$
$192$	0.0909659	+	0.114068i	0.00656490	+	0.00823213i
$193$	−11.2370	−	5.41146i	−0.808857	−	0.389525i	−0.0167141	−	0.999860i	$-0.505321\pi$
$193$	−11.2370	−	5.41146i	−0.808857	−	0.389525i	−0.792143	+	0.610335i	$0.791035\pi$
$194$	1.37269	−	1.72130i	0.0985535	−	0.123582i
$195$	0.350592	−	0.439628i	0.0251064	−	0.0314824i
$196$	−2.91560	+	1.40408i	−0.208257	+	0.100291i
$197$	1.40006	+	6.13405i	0.0997499	+	0.437033i	0.999999	+	0.00165687i	$0.000527397\pi$
$197$	1.40006	+	6.13405i	0.0997499	+	0.437033i	−0.900249	+	0.435376i	$0.856615\pi$
$198$	−0.497572	+	2.18001i	−0.0353609	+	0.154926i
$199$	5.27436	+	2.54000i	0.373890	+	0.180056i	0.611386	−	0.791333i	$-0.290612\pi$
$199$	5.27436	+	2.54000i	0.373890	+	0.180056i	−0.237496	+	0.971389i	$0.576327\pi$
$200$	19.8523	−	9.56039i	1.40377	−	0.676021i
$201$	−0.210120	+	0.920597i	−0.0148207	+	0.0649339i
$202$	−0.381966			−0.0268750
$203$		0			0
$204$	−4.38197			−0.306799
$205$	−3.30535	+	14.4817i	−0.230856	+	1.01144i
$206$	−5.11188	+	2.46175i	−0.356162	+	0.171518i
$207$	−2.91560	−	1.40408i	−0.202648	−	0.0975901i
$208$	0.0973961	−	0.426720i	0.00675320	−	0.0295877i
$209$	−1.49272	−	6.54002i	−0.103253	−	0.452382i
$210$	−2.96581	+	1.42826i	−0.204660	+	0.0985591i
$211$	−7.26520	+	9.11027i	−0.500157	+	0.627177i	−0.966265	−	0.257551i	$-0.917084\pi$
$211$	−7.26520	+	9.11027i	−0.500157	+	0.627177i	0.466108	+	0.884728i	$0.345656\pi$
$212$	2.01766	−	2.53006i	0.138573	−	0.173765i
$213$	5.83119	+	2.80815i	0.399547	+	0.192412i
$214$	2.60640	+	3.26832i	0.178170	+	0.223418i
$215$	−27.8885			−1.90198
$216$	−4.84073	−	6.07009i	−0.329370	−	0.413017i
$217$	−5.02059	−	21.9966i	−0.340820	−	1.49323i
$218$	1.97789	+	8.66569i	0.133959	+	0.586915i
$219$	5.28229	+	6.62378i	0.356944	+	0.447594i
$220$	8.61803			0.581028
$221$	0.644964	+	0.808759i	0.0433850	+	0.0544030i
$222$	1.62028	+	0.780285i	0.108746	+	0.0523693i
$223$	1.66706	−	2.09043i	0.111635	−	0.139986i	−0.722875	−	0.690979i	$-0.757180\pi$
$223$	1.66706	−	2.09043i	0.111635	−	0.139986i	0.834510	+	0.550993i	$0.185751\pi$
$224$	−7.83247	+	9.82161i	−0.523329	+	0.656234i
$225$	23.2435	−	11.1935i	1.54957	−	0.746233i
$226$	−1.09254	−	4.78673i	−0.0726747	−	0.318409i
$227$	4.64814	−	20.3648i	0.308508	−	1.35166i	−0.548411	−	0.836209i	$-0.684767\pi$
$227$	4.64814	−	20.3648i	0.308508	−	1.35166i	0.856919	−	0.515452i	$-0.172376\pi$
$228$	4.37339	+	2.10612i	0.289635	+	0.139481i
$229$	−2.06484	+	0.994373i	−0.136448	+	0.0657100i	−0.500862	−	0.865527i	$-0.666984\pi$
$229$	−2.06484	+	0.994373i	−0.136448	+	0.0657100i	0.364414	+	0.931237i	$0.381269\pi$
$230$	0.655162	−	2.87045i	0.0432001	−	0.189272i
$231$	−1.90983			−0.125658
$232$		0			0
$233$	15.2361			0.998148			0.499074	−	0.866559i	$-0.333674\pi$
$233$	15.2361			0.998148			0.499074	+	0.866559i	$0.333674\pi$
$234$	−0.0849954	+	0.372389i	−0.00555633	+	0.0243439i
$235$	24.3070	−	11.7056i	1.58561	−	0.763591i
$236$	8.87824	+	4.27553i	0.577924	+	0.278314i
$237$	−0.837554	+	3.66956i	−0.0544050	+	0.238364i
$238$	−1.34753	−	5.90390i	−0.0873472	−	0.382693i
$239$	24.9953	−	12.0371i	1.61681	−	0.778614i	0.616845	−	0.787085i	$-0.288411\pi$
$239$	24.9953	−	12.0371i	1.61681	−	0.778614i	0.999964	+	0.00847060i	$0.00269631\pi$
$240$	−2.75359	+	3.45289i	−0.177743	+	0.222883i
$241$	−2.90077	+	3.63745i	−0.186855	+	0.234309i	−0.866432	−	0.499296i	$-0.833592\pi$
$241$	−2.90077	+	3.63745i	−0.186855	+	0.234309i	0.679577	+	0.733605i	$0.262164\pi$
$242$	5.06167	+	2.43757i	0.325377	+	0.156693i
$243$	−8.69411	−	10.9021i	−0.557728	−	0.699368i
$244$	1.00000			0.0640184
$245$	−4.80599	−	6.02652i	−0.307043	−	0.385020i
$246$	0.327581	+	1.43523i	0.0208858	+	0.0915067i
$247$	−0.254986	−	1.11717i	−0.0162244	−	0.0710837i
$248$	14.0674	+	17.6399i	0.893279	+	1.12014i
$249$	6.14590			0.389480
$250$	7.20898	+	9.03977i	0.455936	+	0.571726i
$251$	17.7063	+	8.52689i	1.11761	+	0.538213i	0.899153	−	0.437634i	$-0.144183\pi$
$251$	17.7063	+	8.52689i	1.11761	+	0.538213i	0.218457	+	0.975847i	$0.429898\pi$
$252$	−5.90578	+	7.40561i	−0.372029	+	0.466510i
$253$	1.06505	−	1.33553i	0.0669590	−	0.0839639i
$254$	−8.87824	+	4.27553i	−0.557070	+	0.268271i
$255$	−2.32261	−	10.1760i	−0.145447	−	0.637246i
$256$	1.46025	−	6.39778i	0.0912657	−	0.399861i
$257$	20.8848	+	10.0576i	1.30276	+	0.627374i	0.951137	−	0.308769i	$-0.0999170\pi$
$257$	20.8848	+	10.0576i	1.30276	+	0.627374i	0.351619	+	0.936143i	$0.385631\pi$
$258$	−2.49022	+	1.19923i	−0.155034	+	0.0746605i
$259$	2.34267	−	10.2639i	0.145566	−	0.637768i
$260$	1.47214			0.0912980
$261$		0			0
$262$	8.85410			0.547008
$263$	3.71793	−	16.2893i	0.229257	−	1.00444i	−0.720990	−	0.692945i	$-0.756313\pi$
$263$	3.71793	−	16.2893i	0.229257	−	1.00444i	0.950248	−	0.311496i	$-0.100830\pi$
$264$	1.72070	−	0.828644i	0.105902	−	0.0509995i
$265$	6.94485	+	3.34446i	0.426619	+	0.205449i
$266$	−1.49272	+	6.54002i	−0.0915243	+	0.400994i
$267$	0.647498	+	2.83687i	0.0396262	+	0.173614i
$268$	−2.22732	+	1.07262i	−0.136055	+	0.0655207i
$269$	−3.74094	+	4.69099i	−0.228089	+	0.286015i	−0.882686	−	0.469964i	$-0.844267\pi$
$269$	−3.74094	+	4.69099i	−0.228089	+	0.286015i	0.654597	+	0.755978i	$0.272838\pi$
$270$	5.15658	−	6.46614i	0.313819	−	0.393517i
$271$	−9.17217	−	4.41708i	−0.557170	−	0.268319i	0.134037	−	0.990976i	$-0.457206\pi$
$271$	−9.17217	−	4.41708i	−0.557170	−	0.268319i	−0.691206	+	0.722658i	$0.742920\pi$
$272$	−5.06561	−	6.35208i	−0.307148	−	0.385151i
$273$	−0.326238			−0.0197448
$274$	2.75359	+	3.45289i	0.166350	+	0.208597i
$275$	3.03030	+	13.2766i	0.182734	+	0.800609i
$276$	0.275051	+	1.20508i	0.0165561	+	0.0725371i
$277$	−13.3314	−	16.7171i	−0.801008	−	1.00443i	−0.999703	−	0.0243714i	$-0.992242\pi$
$277$	−13.3314	−	16.7171i	−0.801008	−	1.00443i	0.198695	−	0.980061i	$-0.436330\pi$
$278$	0.798374			0.0478833
$279$	16.4704	+	20.6532i	0.986055	+	1.23647i
$280$	−17.3621	−	8.36116i	−1.03759	−	0.499675i
$281$	14.4180	−	18.0795i	0.860103	−	1.07854i	−0.136032	−	0.990704i	$-0.543435\pi$
$281$	14.4180	−	18.0795i	0.860103	−	1.07854i	0.996135	−	0.0878311i	$-0.0279936\pi$
$282$	1.66706	−	2.09043i	0.0992722	−	0.124483i
$283$	4.71753	−	2.27184i	0.280428	−	0.135047i	−0.288383	−	0.957515i	$-0.593118\pi$
$283$	4.71753	−	2.27184i	0.280428	−	0.135047i	0.568811	+	0.822468i	$0.307403\pi$
$284$	3.77046	+	16.5194i	0.223735	+	0.980249i
$285$	−2.57286	+	11.2724i	−0.152403	+	0.667720i
$286$	−0.181659	−	0.0874823i	−0.0107417	−	0.00517294i
$287$	7.76458	−	3.73922i	0.458329	−	0.220719i
$288$	3.27288	−	14.3394i	0.192856	−	0.844960i
$289$	2.20163			0.129507
$290$		0			0
$291$	−2.20163			−0.129062
$292$	−4.93559	+	21.6242i	−0.288834	+	1.26546i
$293$	−7.68334	+	3.70010i	−0.448866	+	0.216162i	−0.644639	−	0.764487i	$-0.722992\pi$
$293$	−7.68334	+	3.70010i	−0.448866	+	0.216162i	0.195774	+	0.980649i	$0.437278\pi$
$294$	−0.688279	−	0.331458i	−0.0401412	−	0.0193310i
$295$	−5.22304	+	22.8836i	−0.304097	+	1.33234i
$296$	2.34267	+	10.2639i	0.136165	+	0.596578i
$297$	4.32319	−	2.08194i	0.250857	−	0.120806i
$298$	3.70619	−	4.64742i	0.214694	−	0.269218i
$299$	0.181932	−	0.228135i	0.0105214	−	0.0131934i
$300$	−8.87824	−	4.27553i	−0.512585	−	0.246848i
$301$	10.0883	+	12.6503i	0.581479	+	0.729151i
$302$	1.65248			0.0950893
$303$	0.238152	+	0.298633i	0.0136815	+	0.0171560i
$304$	2.00269	+	8.77435i	0.114862	+	0.503244i
$305$	0.530037	+	2.32225i	0.0303498	+	0.132971i
$306$	4.42065	+	5.54332i	0.252712	+	0.316890i
$307$	−19.1803			−1.09468			−0.547340	−	0.836910i	$-0.684360\pi$
$307$	−19.1803			−1.09468			−0.547340	+	0.836910i	$0.684360\pi$
$308$	−3.11745	−	3.90916i	−0.177633	−	0.222745i
$309$	5.11188	+	2.46175i	0.290805	+	0.140044i
$310$	−14.9852	+	18.7909i	−0.851104	+	1.06725i
$311$	1.30320	−	1.63416i	0.0738977	−	0.0926647i	−0.743509	−	0.668726i	$-0.766840\pi$
$311$	1.30320	−	1.63416i	0.0738977	−	0.0926647i	0.817406	+	0.576062i	$0.195411\pi$
$312$	0.293930	−	0.141549i	0.0166405	−	0.00801365i
$313$	2.87271	+	12.5862i	0.162375	+	0.711411i	0.988909	+	0.148524i	$0.0474523\pi$
$313$	2.87271	+	12.5862i	0.162375	+	0.711411i	−0.826534	+	0.562887i	$0.809691\pi$
$314$	−2.00269	+	8.77435i	−0.113018	+	0.495165i
$315$	−20.3279	−	9.78942i	−1.14535	−	0.551571i
$316$	−8.87824	+	4.27553i	−0.499440	+	0.240518i
$317$	−6.16566	+	27.0135i	−0.346298	+	1.51723i	0.439214	+	0.898383i	$0.355257\pi$
$317$	−6.16566	+	27.0135i	−0.346298	+	1.51723i	−0.785512	+	0.618847i	$0.787600\pi$
$318$	0.763932			0.0428392
$319$		0			0
$320$	−0.909830			−0.0508610
$321$	0.930213	−	4.07553i	0.0519194	−	0.227474i
$322$	−1.53904	+	0.741162i	−0.0857673	+	0.0413033i
$323$	−19.1641	−	9.22893i	−1.06632	−	0.513511i
$324$	2.05522	−	9.00450i	0.114179	−	0.500250i
$325$	0.517637	+	2.26791i	0.0287133	+	0.125801i
$326$	3.36015	−	1.61817i	0.186102	−	0.0896219i
$327$	5.54192	−	6.94934i	0.306469	−	0.384300i
$328$	−5.37326	+	6.73785i	−0.296688	+	0.372036i
$329$	−14.1024	−	6.79135i	−0.777490	−	0.374420i
$330$	1.26845	+	1.59059i	0.0698261	+	0.0875591i
$331$	21.1803			1.16418			0.582088	−	0.813126i	$-0.302236\pi$
$331$	21.1803			1.16418			0.582088	+	0.813126i	$0.302236\pi$
$332$	10.0321	+	12.5798i	0.550581	+	0.690406i
$333$	2.74285	+	12.0172i	0.150307	+	0.658538i
$334$	−1.44785	−	6.34344i	−0.0792228	−	0.347098i
$335$	−3.67145	−	4.60385i	−0.200593	−	0.251535i
$336$	2.56231			0.139785
$337$	−21.2416	−	26.6361i	−1.15710	−	1.45096i	−0.869992	−	0.493065i	$-0.835876\pi$
$337$	−21.2416	−	26.6361i	−1.15710	−	1.45096i	−0.287111	−	0.957897i	$-0.592695\pi$
$338$	7.20775	+	3.47107i	0.392050	+	0.188801i
$339$	−3.06123	+	3.83866i	−0.166263	+	0.208487i
$340$	17.0376	−	21.3645i	0.923995	−	1.15865i
$341$	−12.5634	+	6.05019i	−0.680344	+	0.327636i
$342$	−1.74770	−	7.65718i	−0.0945049	−	0.414053i
$343$	−4.47815	+	19.6200i	−0.241797	+	1.05938i
$344$	−14.5780	−	7.02039i	−0.785992	−	0.378514i
$345$	−2.65270	+	1.27747i	−0.142816	+	0.0687768i
$346$	−0.562503	+	2.46449i	−0.0302403	+	0.132492i
$347$	−32.1246			−1.72454			−0.862270	−	0.506449i	$-0.830958\pi$
$347$	−32.1246			−1.72454			−0.862270	+	0.506449i	$0.830958\pi$
$348$		0			0
$349$	4.52786			0.242371			0.121186	−	0.992630i	$-0.461330\pi$
$349$	4.52786			0.242371			0.121186	+	0.992630i	$0.461330\pi$
$350$	3.03030	−	13.2766i	0.161976	−	0.709664i
$351$	0.738488	−	0.355637i	0.0394176	−	0.0189825i
$352$	6.99506	+	3.36864i	0.372838	+	0.179549i
$353$	4.25563	−	18.6451i	0.226504	−	0.992379i	−0.725962	−	0.687735i	$-0.758605\pi$
$353$	4.25563	−	18.6451i	0.226504	−	0.992379i	0.952466	−	0.304645i	$-0.0985377\pi$
$354$	0.517637	+	2.26791i	0.0275121	+	0.120538i
$355$	−36.3637	+	17.5118i	−1.92999	+	0.929432i
$356$	−4.74977	+	5.95602i	−0.251737	+	0.315668i
$357$	−3.77568	+	4.73456i	−0.199830	+	0.250579i
$358$	8.90927	+	4.29048i	0.470870	+	0.226759i
$359$	−14.8166	−	18.5794i	−0.781989	−	0.980583i	−0.999989	−	0.00463409i	$-0.998525\pi$
$359$	−14.8166	−	18.5794i	−0.781989	−	0.980583i	0.218001	−	0.975949i	$-0.430047\pi$
$360$	22.5623			1.18914
$361$	2.84455	+	3.56695i	0.149713	+	0.187734i
$362$	−0.817489	−	3.58165i	−0.0429663	−	0.188248i
$363$	−1.25013	−	5.47718i	−0.0656148	−	0.287477i
$364$	−0.532524	−	0.667764i	−0.0279118	−	0.0350003i
$365$	−52.8328			−2.76540
$366$	0.147186	+	0.184565i	0.00769353	+	0.00964739i
$367$	−24.5699	−	11.8322i	−1.28254	−	0.617637i	−0.336496	−	0.941685i	$-0.609242\pi$
$367$	−24.5699	−	11.8322i	−1.28254	−	0.617637i	−0.946041	+	0.324047i	$0.894956\pi$
$368$	−1.42891	+	1.79180i	−0.0744872	+	0.0934039i
$369$	−6.29112	+	7.88881i	−0.327503	+	0.410675i
$370$	−10.1042	+	4.86591i	−0.525291	+	0.252967i
$371$	−0.995144	−	4.36001i	−0.0516653	−	0.226360i
$372$	2.24527	−	9.83719i	0.116412	−	0.510034i
$373$	−18.5762	−	8.94583i	−0.961840	−	0.463198i	−0.114018	−	0.993479i	$-0.536372\pi$
$373$	−18.5762	−	8.94583i	−0.961840	−	0.463198i	−0.847822	+	0.530281i	$0.822086\pi$
$374$	−3.37201	+	1.62387i	−0.174362	+	0.0839685i
$375$	2.57286	−	11.2724i	0.132862	−	0.582105i
$376$	15.6525			0.807215
$377$		0			0
$378$	−4.79837			−0.246802
$379$	5.40543	−	23.6828i	0.277658	−	1.21650i	−0.623087	−	0.782153i	$-0.714122\pi$
$379$	5.40543	−	23.6828i	0.277658	−	1.21650i	0.900745	−	0.434348i	$-0.143021\pi$
$380$	−27.2728	+	13.1339i	−1.39906	+	0.673754i
$381$	8.87824	+	4.27553i	0.454846	+	0.219042i
$382$	−2.34267	+	10.2639i	−0.119861	+	0.525147i
$383$	6.42064	+	28.1307i	0.328079	+	1.43741i	0.822787	+	0.568350i	$0.192418\pi$
$383$	6.42064	+	28.1307i	0.328079	+	1.43741i	−0.494707	+	0.869060i	$0.664725\pi$
$384$	−6.33781	+	3.05213i	−0.323425	+	0.155753i
$385$	7.42566	−	9.31148i	0.378447	−	0.474557i
$386$	4.80599	−	6.02652i	0.244618	−	0.306742i
$387$	−17.0682	−	8.21961i	−0.867625	−	0.417826i
$388$	−3.59375	−	4.50642i	−0.182445	−	0.228779i
$389$	−19.1246			−0.969656			−0.484828	−	0.874609i	$-0.661118\pi$
$389$	−19.1246			−0.969656			−0.484828	+	0.874609i	$0.661118\pi$
$390$	0.216678	+	0.271705i	0.0109719	+	0.0137583i
$391$	−1.20526	−	5.28061i	−0.0609528	−	0.267052i
$392$	−0.995144	−	4.36001i	−0.0502624	−	0.220214i
$393$	−5.52044	−	6.92242i	−0.278469	−	0.349190i
$394$	−3.88854			−0.195902
$395$	−14.6346	−	18.3513i	−0.736349	−	0.923352i
$396$	5.27436	+	2.54000i	0.265047	+	0.127640i
$397$	−8.76360	+	10.9892i	−0.439833	+	0.551533i	−0.951499	−	0.307651i	$-0.900457\pi$
$397$	−8.76360	+	10.9892i	−0.439833	+	0.551533i	0.511666	+	0.859184i	$0.329028\pi$
$398$	−2.25581	+	2.82869i	−0.113073	+	0.141790i
$399$	6.04388	−	2.91058i	0.302573	−	0.145711i
$400$	−4.06557	−	17.8124i	−0.203279	−	0.890622i
$401$	−5.57835	+	24.4404i	−0.278570	+	1.22049i	0.621033	+	0.783784i	$0.286713\pi$
$401$	−5.57835	+	24.4404i	−0.278570	+	1.22049i	−0.899603	+	0.436709i	$0.856144\pi$
$402$	−0.525798	−	0.253211i	−0.0262244	−	0.0126290i
$403$	−2.14608	+	1.03350i	−0.106904	+	0.0514821i
$404$	−0.222521	+	0.974928i	−0.0110708	+	0.0485045i
$405$	22.0000			1.09319
$406$		0			0
$407$	−6.50658			−0.322519
$408$	1.34753	−	5.90390i	0.0667125	−	0.292287i
$409$	−24.7013	+	11.8955i	−1.22140	+	0.588196i	−0.929702	−	0.368313i	$-0.879935\pi$
$409$	−24.7013	+	11.8955i	−1.22140	+	0.588196i	−0.291700	+	0.956510i	$0.594221\pi$
$410$	−8.27120	−	3.98320i	−0.408485	−	0.196716i
$411$	0.982743	−	4.30568i	0.0484751	−	0.212383i
$412$	3.30535	+	14.4817i	0.162843	+	0.713461i
$413$	12.2694	−	5.90864i	0.603739	−	0.290745i
$414$	1.24698	−	1.56366i	0.0612857	−	0.0768498i
$415$	−23.8960	+	29.9647i	−1.17301	+	1.47091i
$416$	1.19490	+	0.575433i	0.0585847	+	0.0282129i
$417$	−0.497778	−	0.624194i	−0.0243763	−	0.0305669i
$418$	4.14590			0.202783
$419$	−10.9499	−	13.7308i	−0.534939	−	0.670792i	0.438767	−	0.898601i	$-0.355415\pi$
$419$	−10.9499	−	13.7308i	−0.534939	−	0.670792i	−0.973706	+	0.227809i	$0.926844\pi$
$420$	1.91769	+	8.40196i	0.0935738	+	0.409974i
$421$	6.90581	+	30.2563i	0.336569	+	1.47460i	0.806148	+	0.591714i	$0.201548\pi$
$421$	6.90581	+	30.2563i	0.336569	+	1.47460i	−0.469579	+	0.882890i	$0.655594\pi$
$422$	−4.49014	−	5.63046i	−0.218577	−	0.274086i
$423$	18.3262			0.891052
$424$	2.78833	+	3.49646i	0.135413	+	0.169803i
$425$	38.9041	+	18.7352i	1.88713	+	0.908793i
$426$	−2.49396	+	3.12733i	−0.120833	+	0.151519i
$427$	0.861642	−	1.08046i	0.0416978	−	0.0522873i
$428$	9.86045	−	4.74854i	0.476623	−	0.229529i
$429$	0.0448660	+	0.196571i	0.00216615	+	0.00949053i
$430$	3.83539	−	16.8039i	0.184959	−	0.810357i
$431$	−13.1512	−	6.33329i	−0.633472	−	0.305064i	0.0894526	−	0.995991i	$-0.471488\pi$
$431$	−13.1512	−	6.33329i	−0.633472	−	0.305064i	−0.722924	+	0.690927i	$0.757203\pi$
$432$	−5.80016	+	2.79321i	−0.279060	+	0.134388i
$433$	−2.31020	+	10.1217i	−0.111021	+	0.486416i	0.888594	+	0.458694i	$0.151683\pi$
$433$	−2.31020	+	10.1217i	−0.111021	+	0.486416i	−0.999616	+	0.0277224i	$0.991175\pi$
$434$	13.9443			0.669346
$435$		0			0
$436$	23.2705			1.11446
$437$	−1.33513	+	5.84957i	−0.0638677	+	0.279823i
$438$	−4.71753	+	2.27184i	−0.225413	+	0.108553i
$439$	18.8701	+	9.08738i	0.900622	+	0.433717i	0.826114	−	0.563503i	$-0.190547\pi$
$439$	18.8701	+	9.08738i	0.900622	+	0.433717i	0.0745088	+	0.997220i	$0.476261\pi$
$440$	−2.65019	+	11.6112i	−0.126343	+	0.553543i
$441$	−1.16513	−	5.10479i	−0.0554826	−	0.243085i
$442$	−0.576008	+	0.277391i	−0.0273979	+	0.0131941i
$443$	−1.19076	+	1.49317i	−0.0565747	+	0.0709424i	−0.809314	−	0.587377i	$-0.800161\pi$
$443$	−1.19076	+	1.49317i	−0.0565747	+	0.0709424i	0.752739	+	0.658319i	$0.228732\pi$
$444$	2.93552	−	3.68102i	0.139313	−	0.174694i
$445$	−16.3489	−	7.87321i	−0.775012	−	0.373226i
$446$	1.03030	+	1.29196i	0.0487862	+	0.0611760i
$447$	−5.94427			−0.281154
$448$	0.329118	+	0.412701i	0.0155494	+	0.0194983i
$449$	5.81327	+	25.4696i	0.274345	+	1.20199i	0.904826	+	0.425781i	$0.140001\pi$
$449$	5.81327	+	25.4696i	0.274345	+	1.20199i	−0.630481	+	0.776205i	$0.717142\pi$
$450$	3.54793	+	15.5445i	0.167251	+	0.732775i
$451$	−3.32086	−	4.16422i	−0.156373	−	0.196085i
$452$	−12.8541			−0.604606
$453$	−1.03030	−	1.29196i	−0.0484078	−	0.0607015i
$454$	11.6314	+	5.60137i	0.545887	+	0.262885i
$455$	1.26845	−	1.59059i	0.0594660	−	0.0745680i
$456$	−4.18250	+	5.24469i	−0.195863	+	0.245605i
$457$	−16.8555	+	8.11719i	−0.788467	+	0.379706i	−0.784376	−	0.620286i	$-0.787017\pi$
$457$	−16.8555	+	8.11719i	−0.788467	+	0.379706i	−0.00409151	+	0.999992i	$0.501302\pi$
$458$	−0.315180	−	1.38090i	−0.0147274	−	0.0645250i
$459$	3.38561	−	14.8333i	0.158027	−	0.692360i
$460$	−6.94485	−	3.34446i	−0.323805	−	0.155936i
$461$	35.1186	−	16.9122i	1.63564	−	0.787681i	0.635761	−	0.771886i	$-0.280686\pi$
$461$	35.1186	−	16.9122i	1.63564	−	0.787681i	0.999875	−	0.0157954i	$-0.00502805\pi$
$462$	0.262650	−	1.15075i	0.0122196	−	0.0535376i
$463$	10.7082			0.497652			0.248826	−	0.968548i	$-0.419955\pi$
$463$	10.7082			0.497652			0.248826	+	0.968548i	$0.419955\pi$
$464$		0			0
$465$	24.0344			1.11457
$466$	−2.09535	+	9.18032i	−0.0970651	+	0.425270i
$467$	16.1672	−	7.78573i	0.748130	−	0.360281i	−0.0206558	−	0.999787i	$-0.506575\pi$
$467$	16.1672	−	7.78573i	0.748130	−	0.360281i	0.768786	+	0.639506i	$0.220861\pi$
$468$	0.900969	+	0.433884i	0.0416473	+	0.0200563i
$469$	−0.760222	+	3.33075i	−0.0351038	+	0.153800i
$470$	3.71026	+	16.2557i	0.171142	+	0.749820i
$471$	8.10872	−	3.90495i	0.373630	−	0.179931i
$472$	−8.49071	+	10.6470i	−0.390816	+	0.490068i
$473$	6.23490	−	7.81831i	0.286681	−	0.359486i
$474$	−2.09587	−	1.00932i	−0.0962664	−	0.0463595i
$475$	−29.8233	−	37.3972i	−1.36839	−	1.71590i
$476$	−15.8541			−0.726672
$477$	3.26463	+	4.09372i	0.149477	+	0.187439i
$478$	3.81532	+	16.7160i	0.174509	+	0.764573i
$479$	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	$0.846357\pi$
$480$	−8.34352	−	10.4624i	−0.380828	−	0.477543i
$481$	−1.11146			−0.0506780
$482$	−1.79278	−	2.24807i	−0.0816587	−	0.102397i
$483$	1.53904	+	0.741162i	0.0700287	+	0.0337240i
$484$	9.17042	−	11.4993i	0.416837	−	0.522697i
$485$	8.56020	−	10.7341i	0.388699	−	0.487413i
$486$	7.76458	−	3.73922i	0.352209	−	0.169615i
$487$	−9.47100	−	41.4952i	−0.429172	−	1.88033i	−0.472613	−	0.881270i	$-0.656689\pi$
$487$	−9.47100	−	41.4952i	−0.429172	−	1.88033i	0.0434408	−	0.999056i	$-0.486168\pi$
$488$	−0.307516	+	1.34732i	−0.0139206	+	0.0609902i
$489$	−3.36015	−	1.61817i	−0.151951	−	0.0731760i
$490$	4.29215	−	2.06699i	0.193900	−	0.0933772i
$491$	3.36554	−	14.7454i	0.151885	−	0.665451i	−0.840452	−	0.541886i	$-0.817710\pi$
$491$	3.36554	−	14.7454i	0.151885	−	0.665451i	0.992337	−	0.123564i	$-0.0394326\pi$
$492$	3.85410			0.173756
$493$		0			0
$494$	0.708204			0.0318636
$495$	−3.10289	+	13.5947i	−0.139465	+	0.611035i
$496$	16.8555	−	8.11719i	0.756835	−	0.364472i
$497$	21.0975	+	10.1600i	0.946350	+	0.455738i
$498$	−0.845218	+	3.70314i	−0.0378751	+	0.165942i
$499$	−5.49336	−	24.0680i	−0.245916	−	1.07743i	−0.935529	−	0.353251i	$-0.885076\pi$
$499$	−5.49336	−	24.0680i	−0.245916	−	1.07743i	0.689612	−	0.724179i	$-0.257781\pi$
$500$	27.2728	−	13.1339i	1.21968	−	0.587365i
$501$	−4.05678	+	5.08705i	−0.181244	+	0.227273i
$502$	−7.57284	+	9.49605i	−0.337993	+	0.423829i
$503$	−12.8573	−	6.19174i	−0.573278	−	0.276076i	0.124701	−	0.992194i	$-0.460203\pi$
$503$	−12.8573	−	6.19174i	−0.573278	−	0.276076i	−0.697979	+	0.716118i	$0.745917\pi$
$504$	−8.16159	−	10.2343i	−0.363546	−	0.455872i
$505$	−2.38197			−0.105996
$506$	0.658236	+	0.825401i	0.0292621	+	0.0366936i
$507$	−1.78017	−	7.79942i	−0.0790600	−	0.346385i
$508$	5.74068	+	25.1516i	0.254701	+	1.11592i
$509$	19.6788	+	24.6764i	0.872246	+	1.09376i	0.994855	+	0.101307i	$0.0323025\pi$
$509$	19.6788	+	24.6764i	0.872246	+	1.09376i	−0.122609	+	0.992455i	$0.539126\pi$
$510$	6.45085			0.285648
$511$	19.1115	+	23.9651i	0.845443	+	1.06015i
$512$	−16.8555	−	8.11719i	−0.744915	−	0.358732i
$513$	−10.5084	+	13.1771i	−0.463955	+	0.581782i
$514$	−8.93226	+	11.2007i	−0.393985	+	0.494042i
$515$	−31.8780	+	15.3517i	−1.40471	+	0.676475i
$516$	1.61018	+	7.05464i	0.0708841	+	0.310563i
$517$	−2.15261	+	9.43122i	−0.0946719	+	0.414785i
$518$	5.86222	+	2.82310i	0.257571	+	0.124040i
$519$	2.27753	−	1.09680i	0.0999723	−	0.0481441i
$520$	−0.452706	+	1.98343i	−0.0198525	+	0.0869793i
$521$	4.09017			0.179194			0.0895968	−	0.995978i	$-0.471442\pi$
$521$	4.09017			0.179194			0.0895968	+	0.995978i	$0.471442\pi$
$522$		0			0
$523$	−20.3820			−0.891241			−0.445621	−	0.895222i	$-0.647017\pi$
$523$	−20.3820			−0.891241			−0.445621	+	0.895222i	$0.647017\pi$
$524$	5.15811	−	22.5992i	0.225333	−	0.987249i
$525$	−12.2694	+	5.90864i	−0.535482	+	0.257874i
$526$	9.30362	+	4.48039i	0.405657	+	0.195354i
$527$	−9.83871	+	43.1062i	−0.428581	+	1.87774i
$528$	−0.352382	−	1.54389i	−0.0153355	−	0.0671891i
$529$	19.3457	−	9.31641i	0.841119	−	0.405061i
$530$	−2.97026	+	3.72459i	−0.129020	+	0.161786i
$531$	−9.94109	+	12.4657i	−0.431407	+	0.540967i
$532$	15.8231	+	7.62000i	0.686018	+	0.330369i
$533$	−0.567270	−	0.711334i	−0.0245712	−	0.0308113i
$534$	−1.79837			−0.0778232
$535$	16.2537	+	20.3815i	0.702708	+	0.881168i
$536$	−0.760222	−	3.33075i	−0.0328366	−	0.143867i
$537$	−2.20041	−	9.64062i	−0.0949546	−	0.416023i
$538$	−2.31203	−	2.89919i	−0.0996786	−	0.124993i
$539$	2.76393			0.119051
$540$	−13.5001	−	16.9286i	−0.580952	−	0.728490i
$541$	13.1512	+	6.33329i	0.565415	+	0.272289i	0.694678	−	0.719321i	$-0.255547\pi$
$541$	13.1512	+	6.33329i	0.565415	+	0.272289i	−0.129263	+	0.991610i	$0.541261\pi$
$542$	3.92287	−	4.91912i	0.168502	−	0.211294i
$543$	−2.29055	+	2.87226i	−0.0982970	+	0.123261i
$544$	22.1801	−	10.6814i	0.950963	−	0.457960i
$545$	12.3342	+	54.0398i	0.528341	+	2.31481i
$546$	0.0448660	−	0.196571i	0.00192009	−	0.00841246i
$547$	−6.65092	−	3.20292i	−0.284373	−	0.136947i	0.286260	−	0.958152i	$-0.407588\pi$
$547$	−6.65092	−	3.20292i	−0.284373	−	0.136947i	−0.570633	+	0.821205i	$0.693302\pi$
$548$	10.4173	−	5.01670i	0.445004	−	0.214303i
$549$	−0.360046	+	1.57747i	−0.0153664	+	0.0673246i
$550$	−8.41641			−0.358877
$551$		0			0
$552$	−1.70820			−0.0727060
$553$	−3.03030	+	13.2766i	−0.128861	+	0.564579i
$554$	11.9061	−	5.73368i	0.505842	−	0.243601i
$555$	10.1042	+	4.86591i	0.428898	+	0.206546i
$556$	0.465107	−	2.03777i	0.0197249	−	0.0864205i
$557$	1.22533	+	5.36852i	0.0519188	+	0.227471i	0.994230	−	0.107266i	$-0.0342096\pi$
$557$	1.22533	+	5.36852i	0.0519188	+	0.227471i	−0.942312	+	0.334737i	$0.891352\pi$
$558$	−14.7094	+	7.08369i	−0.622700	+	0.299876i
$559$	1.06505	−	1.33553i	0.0450467	−	0.0564868i
$560$	−9.96257	+	12.4927i	−0.420995	+	0.527911i
$561$	3.37201	+	1.62387i	0.142366	+	0.0685600i
$562$	8.91079	+	11.1738i	0.375879	+	0.471337i
$563$	28.3951			1.19671			0.598356	−	0.801230i	$-0.295821\pi$
$563$	28.3951			1.19671			0.598356	+	0.801230i	$0.295821\pi$
$564$	−4.36443	−	5.47282i	−0.183776	−	0.230447i
$565$	−6.81315	−	29.8504i	−0.286632	−	1.25581i
$566$	0.720093	+	3.15493i	0.0302678	+	0.132612i
$567$	−7.95818	−	9.97924i	−0.334212	−	0.419089i
$568$	−23.4164			−0.982531
$569$	−1.21223	−	1.52009i	−0.0508195	−	0.0637256i	0.755772	−	0.654835i	$-0.227262\pi$
$569$	−1.21223	−	1.52009i	−0.0508195	−	0.0637256i	−0.806592	+	0.591109i	$0.798690\pi$
$570$	−6.43823	−	3.10049i	−0.269668	−	0.129865i
$571$	−21.5145	+	26.9783i	−0.900354	+	1.12901i	0.0907443	+	0.995874i	$0.471075\pi$
$571$	−21.5145	+	26.9783i	−0.900354	+	1.12901i	−0.991098	+	0.133134i	$0.957496\pi$
$572$	−0.329118	+	0.412701i	−0.0137611	+	0.0172559i
$573$	9.48528	−	4.56787i	0.396253	−	0.190825i
$574$	1.18520	+	5.19270i	0.0494693	+	0.216739i
$575$	2.71038	−	11.8750i	0.113031	−	0.495220i
$576$	−0.556829	−	0.268155i	−0.0232012	−	0.0111731i
$577$	2.49022	−	1.19923i	0.103669	−	0.0499244i	−0.381331	−	0.924439i	$-0.624534\pi$
$577$	2.49022	−	1.19923i	0.103669	−	0.0499244i	0.485000	+	0.874514i	$0.338820\pi$
$578$	−0.302780	+	1.32656i	−0.0125940	+	0.0551778i
$579$	−7.70820			−0.320342
$580$		0			0
$581$	22.2361			0.922508
$582$	0.302780	−	1.32656i	0.0125506	−	0.0549879i
$583$	−2.49022	+	1.19923i	−0.103134	+	0.0496668i
$584$	−27.6169	−	13.2996i	−1.14280	−	0.550342i
$585$	−0.530037	+	2.32225i	−0.0219143	+	0.0960130i
$586$	−1.17280	−	5.13837i	−0.0484479	−	0.212264i
$587$	−42.0014	+	20.2268i	−1.73358	+	0.834850i	−0.748421	+	0.663224i	$0.769188\pi$
$587$	−42.0014	+	20.2268i	−1.73358	+	0.834850i	−0.985162	+	0.171626i	$0.945098\pi$
$588$	−1.24698	+	1.56366i	−0.0514246	+	0.0644844i
$589$	30.5377	−	38.2931i	1.25829	−	1.57784i
$590$	−13.0700	−	6.29417i	−0.538082	−	0.259127i
$591$	2.42447	+	3.04019i	0.0997293	+	0.125057i
$592$	8.72949			0.358780
$593$	−9.00176	−	11.2878i	−0.369658	−	0.463536i	0.561860	−	0.827232i	$-0.310086\pi$
$593$	−9.00176	−	11.2878i	−0.369658	−	0.463536i	−0.931518	+	0.363696i	$0.881515\pi$
$594$	0.659899	+	2.89121i	0.0270760	+	0.118628i
$595$	−8.40327	−	36.8171i	−0.344500	−	1.50935i
$596$	−9.70294	−	12.1671i	−0.397448	−	0.498384i
$597$	3.61803			0.148076
$598$	0.112440	+	0.140995i	0.00459802	+	0.00576573i
$599$	−11.7747	−	5.67038i	−0.481099	−	0.231685i	0.177584	−	0.984106i	$-0.443172\pi$
$599$	−11.7747	−	5.67038i	−0.481099	−	0.231685i	−0.658683	+	0.752420i	$0.728886\pi$
$600$	8.49071	−	10.6470i	0.346632	−	0.434662i
$601$	18.1804	−	22.7975i	0.741593	−	0.929928i	−0.257749	−	0.966212i	$-0.582981\pi$
$601$	18.1804	−	22.7975i	0.741593	−	0.929928i	0.999342	+	0.0362840i	$0.0115521\pi$
$602$	−9.00969	+	4.33884i	−0.367207	+	0.176838i
$603$	−0.890084	−	3.89971i	−0.0362470	−	0.158809i
$604$	0.962679	−	4.21777i	0.0391708	−	0.171619i
$605$	31.5649	+	15.2009i	1.28330	+	0.618003i
$606$	−0.212690	+	0.102426i	−0.00863994	+	0.00416077i
$607$	−2.44299	+	10.7035i	−0.0991581	+	0.434440i	0.900842	+	0.434147i	$0.142950\pi$
$607$	−2.44299	+	10.7035i	−0.0991581	+	0.434440i	−1.00000		0.000292533i	$0.999907\pi$
$608$	−27.2705			−1.10597
$609$		0			0
$610$	−1.47214			−0.0596050
$611$	−0.367710	+	1.61104i	−0.0148760	+	0.0651759i
$612$	16.7241	−	8.05388i	0.676030	−	0.325559i
$613$	−24.8136	−	11.9496i	−1.00221	−	0.482640i	−0.140523	−	0.990077i	$-0.544879\pi$
$613$	−24.8136	−	11.9496i	−1.00221	−	0.482640i	−0.861689	+	0.507438i	$0.830593\pi$
$614$	2.63779	−	11.5569i	0.106452	−	0.466398i
$615$	2.04282	+	8.95017i	0.0823744	+	0.360906i
$616$	6.22554	−	2.99806i	0.250834	−	0.120795i
$617$	−8.84130	+	11.0866i	−0.355937	+	0.446331i	−0.927273	−	0.374385i	$-0.877854\pi$
$617$	−8.84130	+	11.0866i	−0.355937	+	0.446331i	0.571336	+	0.820716i	$0.306425\pi$
$618$	−2.18632	+	2.74155i	−0.0879465	+	0.110281i
$619$	−6.35699	−	3.06137i	−0.255509	−	0.123047i	0.301745	−	0.953389i	$-0.402431\pi$
$619$	−6.35699	−	3.06137i	−0.255509	−	0.123047i	−0.557254	+	0.830342i	$0.688145\pi$
$620$	39.2318	+	49.1952i	1.57559	+	1.97573i
$621$	−4.29180			−0.172224
$622$	0.805422	+	1.00997i	0.0322945	+	0.0404960i
$623$	2.34267	+	10.2639i	0.0938571	+	0.411215i
$624$	−0.0601941	−	0.263728i	−0.00240969	−	0.0105576i
$625$	14.2360	+	17.8514i	0.569441	+	0.714057i
$626$	−7.97871			−0.318894
$627$	−2.58493	−	3.24139i	−0.103232	−	0.129449i
$628$	21.2289	+	10.2233i	0.847125	+	0.407954i
$629$	−12.8633	+	16.1301i	−0.512895	+	0.643150i
$630$	8.69411	−	10.9021i	0.346382	−	0.434349i
$631$	25.4206	−	12.2419i	1.01198	−	0.487344i	0.146992	−	0.989138i	$-0.453041\pi$
$631$	25.4206	−	12.2419i	1.01198	−	0.487344i	0.864987	+	0.501794i	$0.167326\pi$
$632$	−3.03030	−	13.2766i	−0.120539	−	0.528115i
$633$	−1.60251	+	7.02107i	−0.0636942	+	0.279062i
$634$	−15.4287	−	7.43009i	−0.612754	−	0.295087i
$635$	−55.3653	+	26.6625i	−2.19711	+	1.05807i
$636$	0.445042	−	1.94986i	0.0176471	−	0.0773168i
$637$	0.472136			0.0187067
$638$		0			0
$639$	−27.4164			−1.08458
$640$	9.76138	−	42.7674i	0.385853	−	1.69053i
$641$	−9.96087	+	4.79690i	−0.393431	+	0.189466i	−0.620131	−	0.784498i	$-0.712921\pi$
$641$	−9.96087	+	4.79690i	−0.393431	+	0.189466i	0.226700	+	0.973965i	$0.427206\pi$
$642$	2.32774	+	1.12098i	0.0918684	+	0.0442415i
$643$	8.32593	−	36.4783i	0.328343	−	1.43856i	−0.493946	−	0.869493i	$-0.664446\pi$
$643$	8.32593	−	36.4783i	0.328343	−	1.43856i	0.822288	−	0.569071i	$-0.192697\pi$
$644$	0.995144	+	4.36001i	0.0392142	+	0.171808i
$645$	−15.5292	+	7.47845i	−0.611460	+	0.294464i
$646$	8.19633	−	10.2779i	0.322480	−	0.404378i
$647$	−19.0338	+	23.8676i	−0.748296	+	0.938334i	−0.999562	−	0.0295841i	$-0.990582\pi$
$647$	−19.0338	+	23.8676i	−0.748296	+	0.938334i	0.251266	+	0.967918i	$0.419153\pi$
$648$	11.4999	+	5.53806i	0.451759	+	0.217556i
$649$	−5.24754	−	6.58021i	−0.205984	−	0.258296i
$650$	−1.43769			−0.0563910
$651$	−8.69411	−	10.9021i	−0.340749	−	0.427286i
$652$	−2.17268	−	9.51913i	−0.0850887	−	0.372798i
$653$	−10.6839	−	46.8094i	−0.418095	−	1.83179i	−0.543141	−	0.839641i	$-0.682765\pi$
$653$	−10.6839	−	46.8094i	−0.418095	−	1.83179i	0.125047	−	0.992151i	$-0.460092\pi$
$654$	3.42509	+	4.29493i	0.133932	+	0.167945i
$655$	55.2148			2.15742
$656$	4.45539	+	5.58689i	0.173954	+	0.218131i
$657$	−32.3345	−	15.5715i	−1.26149	−	0.607500i
$658$	6.03149	−	7.56325i	0.235132	−	0.294846i
$659$	−4.39917	+	5.51639i	−0.171368	+	0.214888i	−0.860097	−	0.510130i	$-0.829597\pi$
$659$	−4.39917	+	5.51639i	−0.171368	+	0.214888i	0.688730	+	0.725018i	$0.258169\pi$
$660$	4.79877	−	2.31097i	0.186792	−	0.0899543i
$661$	8.33360	+	36.5119i	0.324139	+	1.42015i	0.830111	+	0.557598i	$0.188277\pi$
$661$	8.33360	+	36.5119i	0.324139	+	1.42015i	−0.505972	+	0.862550i	$0.668866\pi$
$662$	−2.91284	+	12.7620i	−0.113211	+	0.496008i
$663$	0.576008	+	0.277391i	0.0223703	+	0.0107730i
$664$	−20.0340	+	9.64787i	−0.777470	+	0.374410i
$665$	−9.30868	+	40.7840i	−0.360975	+	1.58153i
$666$	−7.61803			−0.295193
$667$		0			0
$668$	−17.0344			−0.659082
$669$	0.367710	−	1.61104i	0.0142165	−	0.0622866i
$670$	3.27891	−	1.57904i	0.126676	−	0.0610037i
$671$	−0.769519	−	0.370581i	−0.0297070	−	0.0143061i
$672$	−1.72764	+	7.56927i	−0.0666451	+	0.291991i
$673$	1.44019	+	6.30987i	0.0555151	+	0.243227i	0.995071	−	0.0991692i	$-0.0316185\pi$
$673$	1.44019	+	6.30987i	0.0555151	+	0.243227i	−0.939556	+	0.342397i	$0.888761\pi$
$674$	18.9706	−	9.13574i	0.730718	−	0.351895i
$675$	21.3326	−	26.7502i	0.821091	−	1.02962i
$676$	13.0585	−	16.3749i	0.502252	−	0.629804i
$677$	36.7891	+	17.7167i	1.41392	+	0.680908i	0.975932	−	0.218073i	$-0.0699772\pi$
$677$	36.7891	+	17.7167i	1.41392	+	0.680908i	0.437987	+	0.898981i	$0.355691\pi$
$678$	−1.89194	−	2.37242i	−0.0726597	−	0.0911123i
$679$	−7.96556			−0.305690
$680$	23.5454	+	29.5250i	0.902926	+	1.13223i
$681$	−2.87271	−	12.5862i	−0.110082	−	0.482302i
$682$	−1.91769	−	8.40196i	−0.0734323	−	0.321728i
$683$	13.0023	+	16.3044i	0.497520	+	0.623870i	0.965668	−	0.259780i	$-0.0836500\pi$
$683$	13.0023	+	16.3044i	0.497520	+	0.623870i	−0.468148	+	0.883650i	$0.655079\pi$
$684$	−20.5623			−0.786219
$685$	17.1715	+	21.5324i	0.656091	+	0.822712i
$686$	−11.2060	−	5.39651i	−0.427846	−	0.206040i
$687$	−0.883116	+	1.10739i	−0.0336930	+	0.0422496i
$688$	−8.36499	+	10.4894i	−0.318912	+	0.399903i
$689$	−0.425380	+	0.204852i	−0.0162057	+	0.00780424i
$690$	−0.404912	−	1.77404i	−0.0154148	−	0.0675365i
$691$	−2.63305	+	11.5361i	−0.100166	+	0.438856i	0.899831	+	0.436239i	$0.143690\pi$
$691$	−2.63305	+	11.5361i	−0.100166	+	0.438856i	−0.999997	+	0.00261618i	$0.999167\pi$
$692$	5.96264	+	2.87146i	0.226666	+	0.109156i
$693$	7.28899	−	3.51019i	0.276886	−	0.133341i
$694$	4.41795	−	19.3563i	0.167703	−	0.734756i
$695$	4.97871			0.188853
$696$		0			0
$697$	−16.8885			−0.639699
$698$	−0.622697	+	2.72821i	−0.0235694	+	0.103264i
$699$	8.48389	−	4.08563i	0.320890	−	0.154533i
$700$	−32.1218	−	15.4690i	−1.21409	−	0.584674i
$701$	4.68534	−	20.5278i	0.176963	−	0.775325i	−0.806059	−	0.591835i	$-0.798404\pi$
$701$	4.68534	−	20.5278i	0.176963	−	0.775325i	0.983022	−	0.183490i	$-0.0587393\pi$
$702$	0.112724	+	0.493877i	0.00425450	+	0.0186402i
$703$	20.5908	−	9.91602i	0.776598	−	0.373990i
$704$	0.203406	−	0.255063i	0.00766615	−	0.00961305i
$705$	10.3959	−	13.0361i	0.391533	−	0.490967i
$706$	10.6491	+	5.12836i	0.400786	+	0.193008i
$707$	0.861642	+	1.08046i	0.0324054	+	0.0406351i
$708$	6.09017			0.228883
$709$	−25.8789	−	32.4511i	−0.971904	−	1.21873i	−0.975784	−	0.218736i	$-0.929807\pi$
$709$	−25.8789	−	32.4511i	−0.971904	−	1.21873i	0.00388053	−	0.999992i	$-0.498765\pi$
$710$	−5.55062	−	24.3189i	−0.208311	−	0.912671i
$711$	−3.54793	−	15.5445i	−0.133058	−	0.582965i
$712$	−6.56402	−	8.23102i	−0.245997	−	0.308470i
$713$	12.4721			0.467085
$714$	−2.33350	−	2.92612i	−0.0873291	−	0.109507i
$715$	−1.13284	−	0.545546i	−0.0423657	−	0.0204022i
$716$	16.1412	−	20.2405i	0.603227	−	0.756422i
$717$	10.6903	−	13.4052i	0.399236	−	0.500626i
$718$	13.2325	−	6.37241i	0.493831	−	0.237816i
$719$	−1.89289	−	8.29330i	−0.0705929	−	0.309288i	0.927288	−	0.374348i	$-0.122133\pi$
$719$	−1.89289	−	8.29330i	−0.0705929	−	0.309288i	−0.997881	+	0.0650598i	$0.979276\pi$
$720$	4.16297	−	18.2392i	0.155145	−	0.679733i
$721$	18.4950	+	8.90671i	0.688789	+	0.331703i
$722$	−2.54043	+	1.22340i	−0.0945449	+	0.0455304i
$723$	−0.639834	+	2.80330i	−0.0237957	+	0.104256i
$724$	−9.61803			−0.357451
$725$		0			0
$726$	3.47214			0.128863
$727$	−6.24299	+	27.3523i	−0.231540	+	1.01444i	0.716824	+	0.697255i	$0.245595\pi$
$727$	−6.24299	+	27.3523i	−0.231540	+	1.01444i	−0.948363	+	0.317187i	$0.897262\pi$
$728$	1.06345	−	0.512130i	0.0394141	−	0.0189808i
$729$	7.66416	+	3.69087i	0.283858	+	0.136699i
$730$	7.26586	−	31.8338i	0.268922	−	1.17822i
$731$	−7.05574	−	30.9132i	−0.260966	−	1.14337i
$732$	0.556829	−	0.268155i	0.0205810	−	0.00991129i
$733$	9.23991	−	11.5865i	0.341284	−	0.427956i	−0.581338	−	0.813662i	$-0.697471\pi$
$733$	9.23991	−	11.5865i	0.341284	−	0.427956i	0.922622	+	0.385706i	$0.126042\pi$
$734$	10.5084	−	13.1771i	0.387871	−	0.486374i
$735$	−4.29215	−	2.06699i	−0.158319	−	0.0762422i
$736$	−4.32968	−	5.42925i	−0.159594	−	0.200125i
$737$	2.11146			0.0777765
$738$	−3.88812	−	4.87555i	−0.143124	−	0.179472i
$739$	11.1414	+	48.8136i	0.409842	+	1.79564i	0.584931	+	0.811083i	$0.301122\pi$
$739$	11.1414	+	48.8136i	0.409842	+	1.79564i	−0.175089	+	0.984553i	$0.556021\pi$
$740$	6.53337	+	28.6245i	0.240171	+	1.05226i
$741$	−0.441558	−	0.553696i	−0.0162210	−	0.0203405i
$742$	2.76393			0.101467
$743$	21.9693	+	27.5487i	0.805977	+	1.01066i	0.999562	+	0.0295793i	$0.00941674\pi$
$743$	21.9693	+	27.5487i	0.805977	+	1.01066i	−0.193586	+	0.981083i	$0.562012\pi$
$744$	12.5634	+	6.05019i	0.460595	+	0.221811i
$745$	23.1121	−	28.9816i	0.846761	−	1.06180i
$746$	7.94491	−	9.96260i	0.290884	−	0.364757i
$747$	−23.4562	+	11.2959i	−0.858218	+	0.413296i
$748$	2.18034	+	9.55271i	0.0797212	+	0.349282i
$749$	3.36554	−	14.7454i	0.122974	−	0.538785i
$750$	6.43823	+	3.10049i	0.235091	+	0.113214i
$751$	16.6930	−	8.03894i	0.609137	−	0.293345i	−0.103772	−	0.994601i	$-0.533091\pi$
$751$	16.6930	−	8.03894i	0.609137	−	0.293345i	0.712910	+	0.701256i	$0.247377\pi$
$752$	2.88804	−	12.6533i	0.105316	−	0.461419i
$753$	12.1459			0.442621
$754$		0			0
$755$	10.3050			0.375036
$756$	−2.79538	+	12.2473i	−0.101667	+	0.445432i
$757$	0.0191782	−	0.00923575i	0.000697045	−	0.000335679i	−0.433535	−	0.901137i	$-0.642734\pi$
$757$	0.0191782	−	0.00923575i	0.000697045	−	0.000335679i	0.434232	+	0.900801i	$0.357020\pi$
$758$	13.5264	+	6.51396i	0.491300	+	0.236598i
$759$	0.234922	−	1.02926i	0.00852711	−	0.0373597i
$760$	−9.30868	−	40.7840i	−0.337661	−	1.47939i
$761$	−22.7059	+	10.9346i	−0.823088	+	0.396378i	−0.797518	−	0.603295i	$-0.793854\pi$
$761$	−22.7059	+	10.9346i	−0.823088	+	0.396378i	−0.0255694	+	0.999673i	$0.508140\pi$
$762$	−3.79716	+	4.76149i	−0.137557	+	0.172490i
$763$	20.0508	−	25.1430i	0.725889	−	0.910236i
$764$	24.8328	+	11.9588i	0.898418	+	0.432656i
$765$	27.5675	+	34.5685i	0.996704	+	1.24983i
$766$	−17.8328			−0.644326
$767$	−0.896388	−	1.12403i	−0.0323667	−	0.0405865i
$768$	−0.902484	−	3.95404i	−0.0325656	−	0.142679i
$769$	4.30816	+	18.8753i	0.155356	+	0.680660i	0.991275	+	0.131807i	$0.0420780\pi$
$769$	4.30816	+	18.8753i	0.155356	+	0.680660i	−0.835919	+	0.548852i	$0.815065\pi$
$770$	4.58931	+	5.75481i	0.165387	+	0.207389i
$771$	14.3262			0.515947
$772$	−12.5822	−	15.7776i	−0.452845	−	0.567849i
$773$	12.6136	+	6.07437i	0.453678	+	0.218480i	0.646746	−	0.762705i	$-0.276129\pi$
$773$	12.6136	+	6.07437i	0.453678	+	0.218480i	−0.193068	+	0.981185i	$0.561844\pi$
$774$	7.29995	−	9.15384i	0.262391	−	0.329028i
$775$	−61.9933	+	77.7372i	−2.22687	+	2.79240i
$776$	7.17672	−	3.45613i	0.257629	−	0.124068i
$777$	−1.44785	−	6.34344i	−0.0519413	−	0.227570i
$778$	2.63012	−	11.5233i	0.0942944	−	0.413131i
$779$	16.8555	+	8.11719i	0.603911	+	0.290828i
$780$	0.819729	−	0.394760i	0.0293510	−	0.0141347i
$781$	3.22035	−	14.1093i	0.115233	−	0.504870i
$782$	3.34752			0.119707
$783$		0			0
$784$	−3.70820			−0.132436
$785$	−12.4889	+	54.7175i	−0.445748	+	1.95295i
$786$	4.93022	−	2.37427i	0.175855	−	0.0846874i
$787$	−17.4434	−	8.40028i	−0.621789	−	0.299438i	0.0963393	−	0.995349i	$-0.469287\pi$
$787$	−17.4434	−	8.40028i	−0.621789	−	0.299438i	−0.718128	+	0.695911i	$0.755001\pi$
$788$	−2.26534	+	9.92510i	−0.0806994	+	0.353567i
$789$	−2.29780	−	10.0673i	−0.0818040	−	0.358407i
$790$	13.0700	−	6.29417i	0.465009	−	0.223936i
$791$	−11.0756	+	13.8884i	−0.393804	+	0.493815i
$792$	−5.04414	+	6.32515i	−0.179236	+	0.224754i
$793$	−0.131450	−	0.0633028i	−0.00466791	−	0.00224795i
$794$	−5.41620	−	6.79171i	−0.192214	−	0.241029i
$795$	4.76393			0.168959
$796$	5.90578	+	7.40561i	0.209325	+	0.262485i
$797$	−9.60853	−	42.0977i	−0.340352	−	1.49118i	−0.798333	−	0.602216i	$-0.794285\pi$
$797$	−9.60853	−	42.0977i	−0.340352	−	1.49118i	0.457982	−	0.888962i	$-0.348573\pi$
$798$	0.922549	+	4.04195i	0.0326579	+	0.143084i
$799$	19.1248	+	23.9817i	0.676586	+	0.848412i
$800$	55.3607			1.95730
$801$	−7.68528	−	9.63704i	−0.271546	−	0.340508i
$802$	−13.9591	−	6.72234i	−0.492913	−	0.237374i
$803$	11.8116	−	14.8112i	0.416821	−	0.522677i
$804$	−0.952608	+	1.19453i	−0.0335959	+	0.0421279i
$805$	−9.59755	+	4.62194i	−0.338269	+	0.162902i
$806$	−0.327581	−	1.43523i	−0.0115386	−	0.0505537i
$807$	−0.825153	+	3.61523i	−0.0290468	+	0.127262i
$808$	−1.24511	−	0.599613i	−0.0438028	−	0.0210943i
$809$	38.8037	−	18.6869i	1.36427	−	0.656996i	0.398683	−	0.917089i	$-0.369467\pi$
$809$	38.8037	−	18.6869i	1.36427	−	0.656996i	0.965584	+	0.260093i	$0.0837532\pi$
$810$	−3.02556	+	13.2558i	−0.106307	+	0.465763i
$811$	5.65248			0.198485			0.0992426	−	0.995063i	$-0.468358\pi$
$811$	5.65248			0.198485			0.0992426	+	0.995063i	$0.468358\pi$
$812$		0			0
$813$	−6.29180			−0.220663
$814$	0.894820	−	3.92046i	0.0313634	−	0.137412i
$815$	20.9542	−	10.0910i	0.733992	−	0.353472i
$816$	−4.52402	−	2.17865i	−0.158372	−	0.0762682i
$817$	−7.81596	+	34.2440i	−0.273446	+	1.19804i
$818$	−3.77046	−	16.5194i	−0.131831	−	0.577589i
$819$	1.24511	−	0.599613i	0.0435076	−	0.0209522i
$820$	−14.9852	+	18.7909i	−0.523307	+	0.656206i
$821$	5.35178	−	6.71092i	0.186778	−	0.234213i	−0.679622	−	0.733562i	$-0.737856\pi$
$821$	5.35178	−	6.71092i	0.186778	−	0.234213i	0.866401	+	0.499350i	$0.166428\pi$
$822$	2.45919	+	1.18428i	0.0857739	+	0.0413066i
$823$	−3.41182	−	4.27829i	−0.118929	−	0.149132i	0.718803	−	0.695214i	$-0.244690\pi$
$823$	−3.41182	−	4.27829i	−0.118929	−	0.149132i	−0.837732	+	0.546082i	$0.816119\pi$
$824$	−20.5279			−0.715122
$825$	5.24754	+	6.58021i	0.182696	+	0.229094i
$826$	1.87283	+	8.20539i	0.0651640	+	0.285502i
$827$	−6.00040	−	26.2895i	−0.208654	−	0.914175i	−0.965463	−	0.260539i	$-0.916100\pi$
$827$	−6.00040	−	26.2895i	−0.208654	−	0.914175i	0.756809	−	0.653636i	$-0.226757\pi$
$828$	−3.26463	−	4.09372i	−0.113454	−	0.142267i
$829$	32.7984			1.13913			0.569567	−	0.821945i	$-0.307111\pi$
$829$	32.7984			1.13913			0.569567	+	0.821945i	$0.307111\pi$
$830$	−14.7686	−	18.5192i	−0.512624	−	0.642810i
$831$	−11.9061	−	5.73368i	−0.413018	−	0.198899i
$832$	0.0347459	−	0.0435700i	0.00120460	−	0.00151052i
$833$	5.46422	−	6.85192i	0.189324	−	0.237405i
$834$	0.444558	−	0.214088i	0.0153938	−	0.00741326i
$835$	−9.02889	−	39.5581i	−0.312458	−	1.36897i
$836$	2.41526	−	10.5820i	0.0835337	−	0.365985i
$837$	31.5649	+	15.2009i	1.09104	+	0.525419i
$838$	9.77921	−	4.70942i	0.337817	−	0.162684i
$839$	10.7288	−	47.0059i	0.370399	−	1.62283i	−0.355258	−	0.934768i	$-0.615607\pi$
$839$	10.7288	−	47.0059i	0.370399	−	1.62283i	0.725657	−	0.688057i	$-0.241536\pi$
$840$	−11.9098			−0.410928
$841$		0			0
$842$	−19.1803			−0.660998
$843$	3.18022	−	13.9335i	0.109533	−	0.479894i
$844$	−16.9870	+	8.18049i	−0.584715	+	0.281584i
$845$	44.9480	+	21.6458i	1.54626	+	0.744639i
$846$	−2.52033	+	11.0423i	−0.0866506	+	0.379641i
$847$	−4.52301	−	19.8166i	−0.155413	−	0.680907i
$848$	3.34098	−	1.60893i	0.114730	−	0.0552509i
$849$	2.01766	−	2.53006i	0.0692458	−	0.0868314i
$850$	−16.6390	+	20.8647i	−0.570714	+	0.715652i
$851$	5.24333	+	2.52506i	0.179739	+	0.0865578i
$852$	6.52927	+	8.18745i	0.223689	+	0.280497i
$853$	−45.0000			−1.54077			−0.770385	−	0.637579i	$-0.779936\pi$
$853$	−45.0000			−1.54077			−0.770385	+	0.637579i	$0.779936\pi$
$854$	0.532524	+	0.667764i	0.0182226	+	0.0228504i
$855$	−10.8988	−	47.7507i	−0.372731	−	1.63304i
$856$	3.36554	+	14.7454i	0.115032	+	0.503988i
$857$	−28.2604	−	35.4375i	−0.965358	−	1.21052i	−0.977573	−	0.210596i	$-0.932460\pi$
$857$	−28.2604	−	35.4375i	−0.965358	−	1.21052i	0.0122147	−	0.999925i	$-0.496112\pi$
$858$	−0.124612			−0.00425418
$859$	20.3932	+	25.5723i	0.695808	+	0.872516i	0.996703	−	0.0811417i	$-0.0258566\pi$
$859$	20.3932	+	25.5723i	0.695808	+	0.872516i	−0.300894	+	0.953657i	$0.597285\pi$
$860$	−40.6559	−	19.5788i	−1.38635	−	0.667633i
$861$	3.32086	−	4.16422i	0.113174	−	0.141916i
$862$	5.62468	−	7.05313i	0.191577	−	0.240230i
$863$	−15.9856	+	7.69825i	−0.544155	+	0.262051i	−0.685705	−	0.727880i	$-0.740506\pi$
$863$	−15.9856	+	7.69825i	−0.544155	+	0.262051i	0.141550	+	0.989931i	$0.454792\pi$
$864$	−4.34062	−	19.0175i	−0.147671	−	0.646989i
$865$	−3.50780	+	15.3687i	−0.119269	+	0.522551i
$866$	−5.78098	−	2.78398i	−0.196446	−	0.0946033i
$867$	1.22593	−	0.590377i	0.0416348	−	0.0200502i
$868$	8.12348	−	35.5913i	0.275729	−	1.20805i
$869$	8.41641			0.285507
$870$		0			0
$871$	0.360680			0.0122212
$872$	−7.15606	+	31.3528i	−0.242335	+	1.06174i
$873$	8.40265	−	4.04650i	0.284387	−	0.136953i
$874$	−3.34098	−	1.60893i	−0.113010	−	0.0544228i
$875$	9.30868	−	40.7840i	0.314691	−	1.37875i
$876$	3.05036	+	13.3645i	0.103062	+	0.451545i
$877$	−3.94801	+	1.90126i	−0.133315	+	0.0642011i	−0.499352	−	0.866399i	$-0.666429\pi$
$877$	−3.94801	+	1.90126i	−0.133315	+	0.0642011i	0.366037	+	0.930600i	$0.380714\pi$
$878$	−8.07062	+	10.1202i	−0.272370	+	0.341542i
$879$	−3.28611	+	4.12065i	−0.110838	+	0.138986i
$880$	8.89742	+	4.28477i	0.299932	+	0.144440i
$881$	2.66262	+	3.33882i	0.0897059	+	0.112488i	0.824659	−	0.565631i	$-0.191367\pi$
$881$	2.66262	+	3.33882i	0.0897059	+	0.112488i	−0.734953	+	0.678118i	$0.762796\pi$
$882$	3.23607			0.108964
$883$	−12.8981	−	16.1737i	−0.434055	−	0.544288i	0.515911	−	0.856642i	$-0.327454\pi$
$883$	−12.8981	−	16.1737i	−0.434055	−	0.544288i	−0.949966	+	0.312355i	$0.898882\pi$
$884$	0.372447	+	1.63180i	0.0125268	+	0.0548833i
$885$	3.22802	+	14.1429i	0.108509	+	0.475407i
$886$	−0.735930	−	0.922827i	−0.0247240	−	0.0310030i
$887$	−38.0689			−1.27823			−0.639114	−	0.769112i	$-0.720699\pi$
$887$	−38.0689			−1.27823			−0.639114	+	0.769112i	$0.720699\pi$
$888$	4.05678	+	5.08705i	0.136137	+	0.170710i
$889$	32.1218	+	15.4690i	1.07733	+	0.518815i
$890$	6.99230	−	8.76807i	0.234382	−	0.293906i
$891$	−4.91843	+	6.16751i	−0.164773	+	0.206619i
$892$	3.89781	−	1.87708i	0.130508	−	0.0628494i
$893$	−7.56098	−	33.1268i	−0.253018	−	1.10855i
$894$	0.817489	−	3.58165i	0.0273409	−	0.119788i
$895$	55.5588	+	26.7557i	1.85713	+	0.894345i
$896$	−22.9304	+	11.0427i	−0.766052	+	0.368911i
$897$	0.0401294	−	0.175818i	0.00133988	−	0.00587041i
$898$	−16.1459			−0.538796
$899$		0			0
$900$	41.7426			1.39142
$901$	−1.95016	+	8.54420i	−0.0649692	+	0.284649i
$902$	2.96581	−	1.42826i	0.0987505	−	0.0475557i
$903$	9.00969	+	4.33884i	0.299824	+	0.144387i
$904$	3.95285	−	17.3186i	0.131470	−	0.576007i
$905$	−5.09792	−	22.3354i	−0.169460	−	0.742455i
$906$	0.920147	−	0.443119i	0.0305698	−	0.0147217i
$907$	6.08771	−	7.63375i	0.202139	−	0.253474i	−0.670421	−	0.741981i	$-0.733887\pi$
$907$	6.08771	−	7.63375i	0.202139	−	0.253474i	0.872560	+	0.488506i	$0.162458\pi$
$908$	21.0729	−	26.4246i	0.699330	−	0.876932i
$909$	−1.45780	−	0.702039i	−0.0483521	−	0.0232852i
$910$	0.783948	+	0.983039i	0.0259876	+	0.0325874i
$911$	−10.9443			−0.362600			−0.181300	−	0.983428i	$-0.558030\pi$
$911$	−10.9443			−0.362600			−0.181300	+	0.983428i	$0.558030\pi$
$912$	3.46804	+	4.34879i	0.114838	+	0.144003i
$913$	−3.05803	−	13.3981i	−0.101206	−	0.443412i
$914$	−2.57286	−	11.2724i	−0.0851025	−	0.372858i
$915$	0.917862	+	1.15096i	0.0303436	+	0.0380496i
$916$	−3.70820			−0.122523
$917$	−19.9731	−	25.0455i	−0.659571	−	0.827076i
$918$	8.47204	+	4.07992i	0.279619	+	0.134657i
$919$	19.5183	−	24.4752i	0.643850	−	0.807362i	−0.347629	−	0.937632i	$-0.613013\pi$
$919$	19.5183	−	24.4752i	0.643850	−	0.807362i	0.991479	+	0.130270i	$0.0415844\pi$
$920$	6.64171	−	8.32844i	0.218971	−	0.274581i
$921$	−10.6802	+	5.14330i	−0.351924	+	0.169478i
$922$	5.36057	+	23.4862i	0.176541	+	0.773476i
$923$	0.550102	−	2.41015i	0.0181068	−	0.0793312i
$924$	−2.78415	−	1.34077i	−0.0915917	−	0.0441082i
$925$	−41.8006	+	20.1301i	−1.37439	+	0.661873i
$926$	−1.47265	+	6.45211i	−0.0483943	+	0.212029i
$927$	−24.0344			−0.789395
$928$		0			0
$929$	−3.65248			−0.119834			−0.0599169	−	0.998203i	$-0.519084\pi$
$929$	−3.65248			−0.119834			−0.0599169	+	0.998203i	$0.519084\pi$
$930$	−3.30535	+	14.4817i	−0.108387	+	0.474873i
$931$	−8.74679	+	4.21223i	−0.286664	+	0.138050i
$932$	22.2111	+	10.6963i	0.727549	+	0.350369i
$933$	0.287452	−	1.25941i	0.00941075	−	0.0412312i
$934$	2.46779	+	10.8121i	0.0807487	+	0.353783i
$935$	−21.0281	+	10.1266i	−0.687691	+	0.331175i
$936$	−0.861642	+	1.08046i	−0.0281636	+	0.0353161i
$937$	4.14775	−	5.20112i	0.135501	−	0.169913i	−0.709451	−	0.704754i	$-0.751057\pi$
$937$	4.14775	−	5.20112i	0.135501	−	0.169913i	0.844952	+	0.534841i	$0.179629\pi$
$938$	−1.90236	−	0.916127i	−0.0621141	−	0.0299126i
$939$	4.97465	+	6.23801i	0.162341	+	0.203570i
$940$	43.6525			1.42379
$941$	−21.7527	−	27.2770i	−0.709116	−	0.889204i	0.288551	−	0.957464i	$-0.406826\pi$
$941$	−21.7527	−	27.2770i	−0.709116	−	0.889204i	−0.997668	+	0.0682609i	$0.978255\pi$
$942$	1.23773	+	5.42285i	0.0403274	+	0.176686i
$943$	1.06007	+	4.64449i	0.0345208	+	0.151245i
$944$	7.04032	+	8.82828i	0.229143	+	0.287336i
$945$	−29.9230			−0.973395
$946$	3.85338	+	4.83198i	0.125284	+	0.157101i
$947$	−38.7727	−	18.6719i	−1.25994	−	0.606757i	−0.319783	−	0.947491i	$-0.603610\pi$
$947$	−38.7727	−	18.6719i	−1.25994	−	0.606757i	−0.940160	+	0.340734i	$0.889324\pi$
$948$	−3.79716	+	4.76149i	−0.123326	+	0.154646i
$949$	2.01766	−	2.53006i	0.0654959	−	0.0821292i
$950$	26.6347	−	12.8266i	0.864144	−	0.416150i
$951$	3.81058	+	16.6953i	0.123567	+	0.541381i
$952$	4.87540	−	21.3605i	0.158012	−	0.692298i
$953$	−38.4094	−	18.4970i	−1.24420	−	0.599176i	−0.308250	−	0.951305i	$-0.599743\pi$
$953$	−38.4094	−	18.4970i	−1.24420	−	0.599176i	−0.935951	+	0.352129i	$0.885458\pi$
$954$	−2.91560	+	1.40408i	−0.0943959	+	0.0454587i
$955$	−14.6091	+	64.0064i	−0.472738	+	2.07120i
$956$	44.8885			1.45180
$957$		0			0
$958$	−6.90983			−0.223246
$959$	3.55560	−	15.5781i	0.114816	−	0.503043i
$960$	−0.506620	+	0.243975i	−0.0163511	+	0.00787427i
$961$	−63.7990	−	30.7240i	−2.05803	−	0.991096i
$962$	0.152854	−	0.669695i	0.00492820	−	0.0215918i
$963$	3.94045	+	17.2642i	0.126979	+	0.556332i
$964$	−6.78237	+	3.26622i	−0.218445	+	0.105198i
$965$	29.9705	−	37.5818i	0.964783	−	1.20980i
$966$	−0.658236	+	0.825401i	−0.0211784	+	0.0265569i
$967$	−3.20953	−	1.54563i	−0.103211	−	0.0497040i	0.381566	−	0.924342i	$-0.375385\pi$
$967$	−3.20953	−	1.54563i	−0.103211	−	0.0497040i	−0.484777	+	0.874638i	$0.661099\pi$
$968$	12.6732	+	15.8917i	0.407332	+	0.510778i
$969$	−13.1459			−0.422307
$970$	5.29049	+	6.63407i	0.169867	+	0.213007i
$971$	4.34062	+	19.0175i	0.139297	+	0.610301i	0.995590	+	0.0938103i	$0.0299047\pi$
$971$	4.34062	+	19.0175i	0.139297	+	0.610301i	−0.856293	+	0.516491i	$0.827238\pi$
$972$	−5.02059	−	21.9966i	−0.161035	−	0.705542i
$973$	−1.80098	−	2.25835i	−0.0577367	−	0.0723995i
$974$	26.3050			0.842865
$975$	0.896388	+	1.12403i	0.0287074	+	0.0359979i
$976$	1.03242	+	0.497187i	0.0330469	+	0.0159146i
$977$	−28.1910	+	35.3503i	−0.901909	+	1.13096i	0.0889478	+	0.996036i	$0.471650\pi$
$977$	−28.1910	+	35.3503i	−0.901909	+	1.13096i	−0.990856	+	0.134921i	$0.956922\pi$
$978$	1.43711	−	1.80208i	0.0459538	−	0.0576243i
$979$	5.86222	−	2.82310i	0.187357	−	0.0902266i
$980$	−2.77531	−	12.1594i	−0.0886541	−	0.388419i
$981$	−8.37846	+	36.7084i	−0.267504	+	1.17201i
$982$	8.42183	+	4.05574i	0.268751	+	0.129424i
$983$	9.86045	−	4.74854i	0.314499	−	0.151455i	−0.269974	−	0.962868i	$-0.587015\pi$
$983$	9.86045	−	4.74854i	0.314499	−	0.151455i	0.584474	+	0.811413i	$0.301301\pi$
$984$	−1.18520	+	5.19270i	−0.0377828	+	0.165537i
$985$	−24.2492			−0.772645
$986$		0			0
$987$	−9.67376			−0.307919
$988$	0.412577	−	1.80762i	0.0131258	−	0.0575079i
$989$	−8.05851	+	3.88077i	−0.256246	+	0.123401i
$990$	−7.76458	−	3.73922i	−0.246775	−	0.118840i
$991$	−1.63498	+	7.16331i	−0.0519368	+	0.227550i	−0.994235	−	0.107226i	$-0.965803\pi$
$991$	−1.63498	+	7.16331i	−0.0519368	+	0.227550i	0.942298	+	0.334775i	$0.108660\pi$
$992$	12.6140	+	55.2657i	0.400496	+	1.75469i
$993$	11.7938	−	5.67961i	0.374266	−	0.180237i
$994$	−9.02323	+	11.3148i	−0.286199	+	0.358883i
$995$	−14.0674	+	17.6399i	−0.445966	+	0.559223i
$996$	8.95948	+	4.31466i	0.283892	+	0.136715i
$997$	10.5431	+	13.2206i	0.333904	+	0.418702i	0.920233	−	0.391371i	$-0.127999\pi$
$997$	10.5431	+	13.2206i	0.333904	+	0.418702i	−0.586330	+	0.810073i	$0.699428\pi$
$998$	15.2574			0.482963
$999$	10.1925	+	12.7810i	0.322477	+	0.404373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.i.605.1		12
29.2	odd	28		841.2.e.j.651.2		24
29.3	odd	28		841.2.e.j.196.2		24
29.4	even	14		841.2.d.g.574.1		12
29.5	even	14		841.2.d.g.190.2		12
29.6	even	14		841.2.a.c.1.1	yes	2
29.7	even	7	inner	841.2.d.i.645.1		12
29.8	odd	28		841.2.e.j.63.2		24
29.9	even	14		841.2.d.g.778.1		12
29.10	odd	28		841.2.e.j.267.3		24
29.11	odd	28		841.2.e.j.270.3		24
29.12	odd	4		841.2.e.j.236.2		24
29.13	even	14		841.2.d.g.571.2		12
29.14	odd	28		841.2.b.b.840.2		4
29.15	odd	28		841.2.b.b.840.3		4
29.16	even	7	inner	841.2.d.i.571.1		12
29.17	odd	4		841.2.e.j.236.3		24
29.18	odd	28		841.2.e.j.270.2		24
29.19	odd	28		841.2.e.j.267.2		24
29.20	even	7	inner	841.2.d.i.778.2		12
29.21	odd	28		841.2.e.j.63.3		24
29.22	even	14		841.2.d.g.645.2		12
29.23	even	7		841.2.a.a.1.2	✓	2
29.24	even	7	inner	841.2.d.i.190.1		12
29.25	even	7	inner	841.2.d.i.574.2		12
29.26	odd	28		841.2.e.j.196.3		24
29.27	odd	28		841.2.e.j.651.3		24
29.28	even	2		841.2.d.g.605.2		12
87.23	odd	14		7569.2.a.l.1.1		2
87.35	odd	14		7569.2.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.a.1.2	✓	2	29.23	even	7
841.2.a.c.1.1	yes	2	29.6	even	14
841.2.b.b.840.2		4	29.14	odd	28
841.2.b.b.840.3		4	29.15	odd	28
841.2.d.g.190.2		12	29.5	even	14
841.2.d.g.571.2		12	29.13	even	14
841.2.d.g.574.1		12	29.4	even	14
841.2.d.g.605.2		12	29.28	even	2
841.2.d.g.645.2		12	29.22	even	14
841.2.d.g.778.1		12	29.9	even	14
841.2.d.i.190.1		12	29.24	even	7	inner
841.2.d.i.571.1		12	29.16	even	7	inner
841.2.d.i.574.2		12	29.25	even	7	inner
841.2.d.i.605.1		12	1.1	even	1	trivial
841.2.d.i.645.1		12	29.7	even	7	inner
841.2.d.i.778.2		12	29.20	even	7	inner
841.2.e.j.63.2		24	29.8	odd	28
841.2.e.j.63.3		24	29.21	odd	28
841.2.e.j.196.2		24	29.3	odd	28
841.2.e.j.196.3		24	29.26	odd	28
841.2.e.j.236.2		24	29.12	odd	4
841.2.e.j.236.3		24	29.17	odd	4
841.2.e.j.267.2		24	29.19	odd	28
841.2.e.j.267.3		24	29.10	odd	28
841.2.e.j.270.2		24	29.18	odd	28
841.2.e.j.270.3		24	29.11	odd	28
841.2.e.j.651.2		24	29.2	odd	28
841.2.e.j.651.3		24	29.27	odd	28
7569.2.a.d.1.2		2	87.35	odd	14
7569.2.a.l.1.1		2	87.23	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+(-0.137526 + 0.602539i) q^{2} +(0.556829 - 0.268155i) q^{3} +(1.45780 + 0.702039i) q^{4} +(-0.857618 + 3.75747i) q^{5} +(0.0849954 + 0.372389i) q^{6} +(2.01463 - 0.970194i) q^{7} +(-1.39417 + 1.74823i) q^{8} +(-1.63232 + 2.04686i) q^{9} +(-2.14608 - 1.03350i) q^{10} +(-0.861642 - 1.08046i) q^{11} +1.00000 q^{12} +(-0.147186 - 0.184565i) q^{13} +(0.307516 + 1.34732i) q^{14} +(0.530037 + 2.32225i) q^{15} +(1.15601 + 1.44960i) q^{16} -4.38197 q^{17} +(-1.00883 - 1.26503i) q^{18} +(4.37339 + 2.10612i) q^{19} +(-3.88812 + 4.87555i) q^{20} +(0.861642 - 1.08046i) q^{21} +(0.769519 - 0.370581i) q^{22} +(0.275051 + 1.20508i) q^{23} +(-0.307516 + 1.34732i) q^{24} +(-8.87824 - 4.27553i) q^{25} +(0.131450 - 0.0633028i) q^{26} +(-0.772623 + 3.38508i) q^{27} +3.61803 q^{28} -1.47214 q^{30} +(2.24527 - 9.83719i) q^{31} +(-5.06167 + 2.43757i) q^{32} +(-0.769519 - 0.370581i) q^{33} +(0.602632 - 2.64030i) q^{34} +(1.91769 + 8.40196i) q^{35} +(-3.81657 + 1.83796i) q^{36} +(2.93552 - 3.68102i) q^{37} +(-1.87047 + 2.34549i) q^{38} +(-0.131450 - 0.0633028i) q^{39} +(-5.37326 - 6.73785i) q^{40} +3.85410 q^{41} +(0.532524 + 0.667764i) q^{42} +(1.61018 + 7.05464i) q^{43} +(-0.497572 - 2.18001i) q^{44} +(-6.29112 - 7.88881i) q^{45} -0.763932 q^{46} +(-4.36443 - 5.47282i) q^{47} +(1.03242 + 0.497187i) q^{48} +(-1.24698 + 1.56366i) q^{49} +(3.79716 - 4.76149i) q^{50} +(-2.44001 + 1.17505i) q^{51} +(-0.0849954 - 0.372389i) q^{52} +(0.445042 - 1.94986i) q^{53} +(-1.93339 - 0.931070i) q^{54} +(4.79877 - 2.31097i) q^{55} +(-1.11260 + 4.87464i) q^{56} +3.00000 q^{57} +6.09017 q^{59} +(-0.857618 + 3.75747i) q^{60} +(0.556829 - 0.268155i) q^{61} +(5.61850 + 2.70573i) q^{62} +(-1.30266 + 5.70733i) q^{63} +(0.0525301 + 0.230149i) q^{64} +(0.819729 - 0.394760i) q^{65} +(0.329118 - 0.412701i) q^{66} +(-0.952608 + 1.19453i) q^{67} +(-6.38802 - 3.07631i) q^{68} +(0.476304 + 0.597266i) q^{69} -5.32624 q^{70} +(6.52927 + 8.18745i) q^{71} +(-1.30266 - 5.70733i) q^{72} +(3.05036 + 13.3645i) q^{73} +(1.81425 + 2.27500i) q^{74} -6.09017 q^{75} +(4.89695 + 6.14058i) q^{76} +(-2.78415 - 1.34077i) q^{77} +(0.0562200 - 0.0704977i) q^{78} +(-3.79716 + 4.76149i) q^{79} +(-6.43823 + 3.10049i) q^{80} +(-1.27019 - 5.56509i) q^{81} +(-0.530037 + 2.32225i) q^{82} +(8.95948 + 4.31466i) q^{83} +(2.01463 - 0.970194i) q^{84} +(3.75805 - 16.4651i) q^{85} -4.47214 q^{86} +3.09017 q^{88} +(-1.04767 + 4.59016i) q^{89} +(5.61850 - 2.70573i) q^{90} +(-0.475589 - 0.229032i) q^{91} +(-0.445042 + 1.94986i) q^{92} +(-1.38766 - 6.07972i) q^{93} +(3.89781 - 1.87708i) q^{94} +(-11.6644 + 14.6267i) q^{95} +(-2.16484 + 2.71463i) q^{96} +(-3.20953 - 1.54563i) q^{97} +(-0.770676 - 0.966397i) q^{98} +3.61803 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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