LMFDB - Embedded newform 740.2.be.a.251.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(51,740)] 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("740.51"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 0, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.be (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			251.3
Character	$\chi$	$=$	740.251
Dual form			740.2.be.a.171.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41350 + 0.0449890i) q^{2} +(-0.594790 + 1.03021i) q^{3} +(1.99595 - 0.127184i) q^{4} +(0.258819 + 0.965926i) q^{5} +(0.794386 - 1.48295i) q^{6} +(2.97366 + 1.71684i) q^{7} +(-2.81555 + 0.269570i) q^{8} +(0.792450 + 1.37256i) q^{9} +(-0.409296 - 1.35369i) q^{10} -3.31791 q^{11} +(-1.05615 + 2.13189i) q^{12} +(0.578586 + 2.15931i) q^{13} +(-4.28050 - 2.29297i) q^{14} +(-1.14905 - 0.307886i) q^{15} +(3.96765 - 0.507705i) q^{16} +(5.80783 + 1.55620i) q^{17} +(-1.18188 - 1.90446i) q^{18} +(-2.72490 + 0.730135i) q^{19} +(0.639440 + 1.89502i) q^{20} +(-3.53741 + 2.04232i) q^{21} +(4.68986 - 0.149269i) q^{22} +(0.170295 + 0.170295i) q^{23} +(1.39695 - 3.06094i) q^{24} +(-0.866025 + 0.500000i) q^{25} +(-0.914976 - 3.02615i) q^{26} -5.45410 q^{27} +(6.15364 + 3.04854i) q^{28} +(-1.18161 - 1.18161i) q^{29} +(1.63803 + 0.383502i) q^{30} +(6.10759 - 6.10759i) q^{31} +(-5.58542 + 0.896140i) q^{32} +(1.97346 - 3.41813i) q^{33} +(-8.27936 - 1.93840i) q^{34} +(-0.888704 + 3.31669i) q^{35} +(1.75626 + 2.63878i) q^{36} +(5.95044 - 1.26183i) q^{37} +(3.81880 - 1.15464i) q^{38} +(-2.56868 - 0.688275i) q^{39} +(-0.989103 - 2.64984i) q^{40} +(-6.77920 - 3.91397i) q^{41} +(4.90823 - 3.04596i) q^{42} +(4.22007 + 4.22007i) q^{43} +(-6.62239 + 0.421984i) q^{44} +(-1.12069 + 1.12069i) q^{45} +(-0.248373 - 0.233050i) q^{46} +10.5654i q^{47} +(-1.83688 + 4.38948i) q^{48} +(2.39510 + 4.14844i) q^{49} +(1.20163 - 0.745710i) q^{50} +(-5.05765 + 5.05765i) q^{51} +(1.42946 + 4.23630i) q^{52} +(-3.14124 - 5.44079i) q^{53} +(7.70936 - 0.245375i) q^{54} +(-0.858738 - 3.20485i) q^{55} +(-8.83530 - 4.03225i) q^{56} +(0.868555 - 3.24149i) q^{57} +(1.72337 + 1.61705i) q^{58} +(-1.54901 + 5.78097i) q^{59} +(-2.33260 - 0.468386i) q^{60} +(-14.7988 + 3.96533i) q^{61} +(-8.35829 + 8.90784i) q^{62} +5.44205i q^{63} +(7.85466 - 1.51797i) q^{64} +(-1.93599 + 1.11774i) q^{65} +(-2.63570 + 4.92030i) q^{66} +(-4.84754 + 8.39619i) q^{67} +(11.7901 + 2.36744i) q^{68} +(-0.276729 + 0.0741493i) q^{69} +(1.10697 - 4.72811i) q^{70} +(-4.26151 - 2.46038i) q^{71} +(-2.60118 - 3.65090i) q^{72} +3.87349i q^{73} +(-8.35417 + 2.05129i) q^{74} -1.18958i q^{75} +(-5.34591 + 1.80388i) q^{76} +(-9.86633 - 5.69633i) q^{77} +(3.66178 + 0.857313i) q^{78} +(3.33647 - 0.894004i) q^{79} +(1.51731 + 3.70105i) q^{80} +(0.866698 - 1.50117i) q^{81} +(9.75847 + 5.22740i) q^{82} +(3.99613 - 2.30716i) q^{83} +(-6.80074 + 4.52628i) q^{84} +6.01270i q^{85} +(-6.15492 - 5.77521i) q^{86} +(1.92012 - 0.514495i) q^{87} +(9.34174 - 0.894407i) q^{88} +(-0.848572 + 3.16691i) q^{89} +(1.53368 - 1.63452i) q^{90} +(-1.98668 + 7.41441i) q^{91} +(0.361560 + 0.318242i) q^{92} +(2.65935 + 9.92481i) q^{93} +(-0.475327 - 14.9342i) q^{94} +(-1.41051 - 2.44308i) q^{95} +(2.39894 - 6.28715i) q^{96} +(5.51878 - 5.51878i) q^{97} +(-3.57211 - 5.75606i) q^{98} +(-2.62928 - 4.55404i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q + 4 q^{2} - 12 q^{4} - 8 q^{8} - 152 q^{9} + 16 q^{13} - 24 q^{14} + 20 q^{16} - 60 q^{18} - 16 q^{22} - 24 q^{24} - 32 q^{29} - 56 q^{32} - 32 q^{37} + 40 q^{38} + 20 q^{42} + 12 q^{44} - 8 q^{46}+ \cdots - 36 q^{98}+O(q^{100}) $ 304 * q + 4 * q^2 - 12 * q^4 - 8 * q^8 - 152 * q^9 + 16 * q^13 - 24 * q^14 + 20 * q^16 - 60 * q^18 - 16 * q^22 - 24 * q^24 - 32 * q^29 - 56 * q^32 - 32 * q^37 + 40 * q^38 + 20 * q^42 + 12 * q^44 - 8 * q^46 + 104 * q^49 + 4 * q^50 - 40 * q^52 + 40 * q^54 + 4 * q^56 - 48 * q^57 - 12 * q^58 - 28 * q^60 - 16 * q^61 - 60 * q^62 + 24 * q^65 - 52 * q^66 - 200 * q^68 - 196 * q^72 + 20 * q^74 - 40 * q^76 + 96 * q^77 - 48 * q^78 - 152 * q^81 + 32 * q^82 - 112 * q^84 + 12 * q^88 - 8 * q^89 + 140 * q^92 - 16 * q^93 - 28 * q^94 - 132 * q^96 + 48 * q^97 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.41350	+	0.0449890i	−0.999494	+	0.0318120i
$2$	−1.41350	+	0.0449890i	−0.999494	+	0.0318120i
$3$	−0.594790	+	1.03021i	−0.343402	+	0.594790i	−0.985062	−	0.172199i	$-0.944913\pi$
$3$	−0.594790	+	1.03021i	−0.343402	+	0.594790i	0.641660	+	0.766989i	$0.278246\pi$
$4$	1.99595	−	0.127184i	0.997976	−	0.0635918i
$5$	0.258819	+	0.965926i	0.115747	+	0.431975i
$5$	0.258819	+	0.965926i	0.115747	+	0.431975i
$6$	0.794386	−	1.48295i	0.324307	−	0.605413i
$7$	2.97366	+	1.71684i	1.12394	+	0.648906i	0.942403	−	0.334479i	$-0.108560\pi$
$7$	2.97366	+	1.71684i	1.12394	+	0.648906i	0.181535	+	0.983385i	$0.441894\pi$
$8$	−2.81555	+	0.269570i	−0.995448	+	0.0953072i
$9$	0.792450	+	1.37256i	0.264150	+	0.457521i
$10$	−0.409296	−	1.35369i	−0.129431	−	0.428074i
$11$	−3.31791			−1.00039			−0.500193	−	0.865914i	$-0.666738\pi$
$11$	−3.31791			−1.00039			−0.500193	+	0.865914i	$0.666738\pi$
$12$	−1.05615	+	2.13189i	−0.304883	+	0.615424i
$13$	0.578586	+	2.15931i	0.160471	+	0.598886i	0.998575	+	0.0533747i	$0.0169978\pi$
$13$	0.578586	+	2.15931i	0.160471	+	0.598886i	−0.838104	+	0.545511i	$0.816336\pi$
$14$	−4.28050	−	2.29297i	−1.14401	−	0.612823i
$15$	−1.14905	−	0.307886i	−0.296682	−	0.0794958i
$16$	3.96765	−	0.507705i	0.991912	−	0.126926i
$17$	5.80783	+	1.55620i	1.40860	+	0.377434i	0.881427	−	0.472320i	$-0.156584\pi$
$17$	5.80783	+	1.55620i	1.40860	+	0.377434i	0.527178	+	0.849755i	$0.323250\pi$
$18$	−1.18188	−	1.90446i	−0.278571	−	0.448886i
$19$	−2.72490	+	0.730135i	−0.625135	+	0.167505i	−0.557461	−	0.830203i	$-0.688225\pi$
$19$	−2.72490	+	0.730135i	−0.625135	+	0.167505i	−0.0676742	+	0.997707i	$0.521558\pi$
$20$	0.639440	+	1.89502i	0.142983	+	0.423740i
$21$	−3.53741	+	2.04232i	−0.771925	+	0.445671i
$22$	4.68986	−	0.149269i	0.999881	−	0.0318243i
$23$	0.170295	+	0.170295i	0.0355090	+	0.0355090i	0.724638	−	0.689129i	$-0.242007\pi$
$23$	0.170295	+	0.170295i	0.0355090	+	0.0355090i	−0.689129	+	0.724638i	$0.742007\pi$
$24$	1.39695	−	3.06094i	0.285151	−	0.624811i
$25$	−0.866025	+	0.500000i	−0.173205	+	0.100000i
$26$	−0.914976	−	3.02615i	−0.179441	−	0.593478i
$27$	−5.45410			−1.04964
$28$	6.15364	+	3.04854i	1.16293	+	0.576119i
$29$	−1.18161	−	1.18161i	−0.219420	−	0.219420i	0.588834	−	0.808254i	$-0.299587\pi$
$29$	−1.18161	−	1.18161i	−0.219420	−	0.219420i	−0.808254	+	0.588834i	$0.799587\pi$
$30$	1.63803	+	0.383502i	0.299061	+	0.0700175i
$31$	6.10759	−	6.10759i	1.09696	−	1.09696i	0.102191	−	0.994765i	$-0.467415\pi$
$31$	6.10759	−	6.10759i	1.09696	−	1.09696i	0.994765	−	0.102191i	$-0.0325852\pi$
$32$	−5.58542	+	0.896140i	−0.987372	+	0.158417i
$33$	1.97346	−	3.41813i	0.343535	−	0.595020i
$34$	−8.27936	−	1.93840i	−1.41990	−	0.332433i
$35$	−0.888704	+	3.31669i	−0.150218	+	0.560622i
$36$	1.75626	+	2.63878i	0.292710	+	0.439797i
$37$	5.95044	−	1.26183i	0.978247	−	0.207443i
$37$	5.95044	−	1.26183i	0.978247	−	0.207443i
$38$	3.81880	−	1.15464i	0.619490	−	0.187307i
$39$	−2.56868	−	0.688275i	−0.411317	−	0.110212i
$40$	−0.989103	−	2.64984i	−0.156391	−	0.418977i
$41$	−6.77920	−	3.91397i	−1.05873	−	0.611260i	−0.133652	−	0.991028i	$-0.542670\pi$
$41$	−6.77920	−	3.91397i	−1.05873	−	0.611260i	−0.925082	+	0.379768i	$0.876004\pi$
$42$	4.90823	−	3.04596i	0.757357	−	0.470002i
$43$	4.22007	+	4.22007i	0.643555	+	0.643555i	0.951428	−	0.307873i	$-0.0996171\pi$
$43$	4.22007	+	4.22007i	0.643555	+	0.643555i	−0.307873	+	0.951428i	$0.599617\pi$
$44$	−6.62239	+	0.421984i	−0.998362	+	0.0636164i
$45$	−1.12069	+	1.12069i	−0.167063	+	0.167063i
$46$	−0.248373	−	0.233050i	−0.0366206	−	0.0343614i
$47$			10.5654i			1.54112i	0.637366	+	0.770562i	$0.280024\pi$
$47$			10.5654i			1.54112i	−0.637366	+	0.770562i	$0.719976\pi$
$48$	−1.83688	+	4.38948i	−0.265130	+	0.633566i
$49$	2.39510	+	4.14844i	0.342158	+	0.592634i
$50$	1.20163	−	0.745710i	0.169936	−	0.105459i
$51$	−5.05765	+	5.05765i	−0.708212	+	0.708212i
$52$	1.42946	+	4.23630i	0.198230	+	0.587469i
$53$	−3.14124	−	5.44079i	−0.431483	−	0.747350i	0.565519	−	0.824736i	$-0.308676\pi$
$53$	−3.14124	−	5.44079i	−0.431483	−	0.747350i	−0.997001	+	0.0773856i	$0.975343\pi$
$54$	7.70936	−	0.245375i	1.04911	−	0.0333912i
$55$	−0.858738	−	3.20485i	−0.115792	−	0.432142i
$56$	−8.83530	−	4.03225i	−1.18067	−	0.538833i
$57$	0.868555	−	3.24149i	0.115043	−	0.429346i
$58$	1.72337	+	1.61705i	0.226290	+	0.212329i
$59$	−1.54901	+	5.78097i	−0.201664	+	0.752618i	0.788777	+	0.614679i	$0.210715\pi$
$59$	−1.54901	+	5.78097i	−0.201664	+	0.752618i	−0.990441	+	0.137939i	$0.955952\pi$
$60$	−2.33260	−	0.468386i	−0.301137	−	0.0604683i
$61$	−14.7988	+	3.96533i	−1.89480	+	0.507709i	−0.896948	+	0.442136i	$0.854221\pi$
$61$	−14.7988	+	3.96533i	−1.89480	+	0.507709i	−0.997848	+	0.0655727i	$0.979113\pi$
$62$	−8.35829	+	8.90784i	−1.06150	+	1.13130i
$63$			5.44205i			0.685634i
$64$	7.85466	−	1.51797i	0.981833	−	0.189747i
$65$	−1.93599	+	1.11774i	−0.240130	+	0.138639i
$66$	−2.63570	+	4.92030i	−0.324432	+	0.605648i
$67$	−4.84754	+	8.39619i	−0.592222	+	1.02576i	0.401711	+	0.915766i	$0.368416\pi$
$67$	−4.84754	+	8.39619i	−0.592222	+	1.02576i	−0.993933	+	0.109991i	$0.964918\pi$
$68$	11.7901	+	2.36744i	1.42976	+	0.287095i
$69$	−0.276729	+	0.0741493i	−0.0333143	+	0.00892653i
$70$	1.10697	−	4.72811i	0.132308	−	0.565117i
$71$	−4.26151	−	2.46038i	−0.505748	−	0.291994i	0.225336	−	0.974281i	$-0.427652\pi$
$71$	−4.26151	−	2.46038i	−0.505748	−	0.291994i	−0.731084	+	0.682287i	$0.760985\pi$
$72$	−2.60118	−	3.65090i	−0.306553	−	0.430263i
$73$			3.87349i			0.453357i	0.973970	+	0.226679i	$0.0727867\pi$
$73$			3.87349i			0.453357i	−0.973970	+	0.226679i	$0.927213\pi$
$74$	−8.35417	+	2.05129i	−0.971153	+	0.238458i
$75$		−	1.18958i		−	0.137361i
$76$	−5.34591	+	1.80388i	−0.613218	+	0.206919i
$77$	−9.86633	−	5.69633i	−1.12437	−	0.649157i
$78$	3.66178	+	0.857313i	0.414615	+	0.0970715i
$79$	3.33647	−	0.894004i	0.375382	−	0.100583i	−0.0661949	−	0.997807i	$-0.521086\pi$
$79$	3.33647	−	0.894004i	0.375382	−	0.100583i	0.441577	+	0.897223i	$0.354419\pi$
$80$	1.51731	+	3.70105i	0.169640	+	0.413790i
$81$	0.866698	−	1.50117i	0.0962998	−	0.166796i
$82$	9.75847	+	5.22740i	1.07764	+	0.577270i
$83$	3.99613	−	2.30716i	0.438632	−	0.253244i	−0.264385	−	0.964417i	$-0.585169\pi$
$83$	3.99613	−	2.30716i	0.438632	−	0.253244i	0.703017	+	0.711173i	$0.251836\pi$
$84$	−6.80074	+	4.52628i	−0.742022	+	0.493857i
$85$			6.01270i			0.652169i
$86$	−6.15492	−	5.77521i	−0.663702	−	0.622756i
$87$	1.92012	−	0.514495i	0.205858	−	0.0551596i
$88$	9.34174	−	0.894407i	0.995833	−	0.0953441i
$89$	−0.848572	+	3.16691i	−0.0899484	+	0.335692i	−0.996205	−	0.0870356i	$-0.972261\pi$
$89$	−0.848572	+	3.16691i	−0.0899484	+	0.335692i	0.906257	+	0.422728i	$0.138927\pi$
$90$	1.53368	−	1.63452i	0.161664	−	0.172293i
$91$	−1.98668	+	7.41441i	−0.208261	+	0.777241i
$92$	0.361560	+	0.318242i	0.0376952	+	0.0331790i
$93$	2.65935	+	9.92481i	0.275761	+	1.02916i
$94$	−0.475327	−	14.9342i	−0.0490262	−	1.54034i
$95$	−1.41051	−	2.44308i	−0.144716	−	0.250655i
$96$	2.39894	−	6.28715i	0.244841	−	0.641680i
$97$	5.51878	−	5.51878i	0.560347	−	0.560347i	−0.369059	−	0.929406i	$-0.620320\pi$
$97$	5.51878	−	5.51878i	0.560347	−	0.560347i	0.929406	+	0.369059i	$0.120320\pi$
$98$	−3.57211	−	5.75606i	−0.360837	−	0.581450i
$99$	−2.62928	−	4.55404i	−0.264252	−	0.457698i
$100$	−1.66495	+	1.10812i	−0.166495	+	0.110812i
$101$			1.36753i			0.136074i	0.997683	+	0.0680370i	$0.0216736\pi$
$101$			1.36753i			0.136074i	−0.997683	+	0.0680370i	$0.978326\pi$
$102$	6.92143	−	7.37651i	0.685324	−	0.730383i
$103$	1.57016	−	1.57016i	0.154712	−	0.154712i	−0.625507	−	0.780219i	$-0.715108\pi$
$103$	1.57016	−	1.57016i	0.154712	−	0.154712i	0.780219	+	0.625507i	$0.215108\pi$
$104$	−2.21112	−	5.92369i	−0.216819	−	0.580866i
$105$	−2.88828	−	2.88828i	−0.281867	−	0.281867i
$106$	4.68491	+	7.54922i	0.455039	+	0.733245i
$107$	−5.97126	−	3.44751i	−0.577264	−	0.333283i	0.182781	−	0.983154i	$-0.441490\pi$
$107$	−5.97126	−	3.44751i	−0.577264	−	0.333283i	−0.760045	+	0.649870i	$0.774823\pi$
$108$	−10.8861	+	0.693673i	−1.04752	+	0.0667487i
$109$	14.2076	+	3.80691i	1.36084	+	0.364636i	0.864125	−	0.503278i	$-0.167873\pi$
$109$	14.2076	+	3.80691i	1.36084	+	0.364636i	0.496715	+	0.867914i	$0.334540\pi$
$110$	1.35801	+	4.49142i	0.129481	+	0.428240i
$111$	−2.23932	+	6.88071i	−0.212547	+	0.653088i
$112$	12.6701	+	5.30209i	1.19721	+	0.501000i
$113$	−0.0144108	+	0.0537817i	−0.00135565	+	0.00505936i	−0.966600	−	0.256288i	$-0.917500\pi$
$113$	−0.0144108	+	0.0537817i	−0.00135565	+	0.00505936i	0.965245	+	0.261348i	$0.0841670\pi$
$114$	−1.08187	+	4.62091i	−0.101326	+	0.432788i
$115$	−0.120417	+	0.208568i	−0.0112289	+	0.0194491i
$116$	−2.50873	−	2.20816i	−0.232930	−	0.205023i
$117$	−2.50529	+	2.50529i	−0.231614	+	0.231614i
$118$	1.92944	−	8.24108i	0.177619	−	0.758653i
$119$	14.5987	+	14.5987i	1.33826	+	1.33826i
$120$	3.31820	+	0.557121i	0.302908	+	0.0508580i
$121$	0.00851538			0.000774125
$122$	20.7397	−	6.27077i	1.87769	−	0.567729i
$123$	8.06440	−	4.65598i	0.727143	−	0.419816i
$124$	11.4137	−	12.9672i	1.02498	−	1.16449i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−0.244832	−	7.69232i	−0.0218114	−	0.685287i
$127$	−15.0361	+	8.68111i	−1.33424	+	0.770324i	−0.985946	−	0.167061i	$-0.946572\pi$
$127$	−15.0361	+	8.68111i	−1.33424	+	0.770324i	−0.348294	+	0.937385i	$0.613239\pi$
$128$	−11.0343	+	2.49903i	−0.975300	+	0.220885i
$129$	−6.85760	+	1.83749i	−0.603778	+	0.161782i
$130$	2.68623	−	1.66703i	0.235598	−	0.146208i
$131$	−0.143403	−	0.0384248i	−0.0125292	−	0.00335719i	0.252549	−	0.967584i	$-0.418731\pi$
$131$	−0.143403	−	0.0384248i	−0.0125292	−	0.00335719i	−0.265078	+	0.964227i	$0.585398\pi$
$132$	3.50420	−	7.07342i	0.305001	−	0.615662i
$133$	−9.35646	−	2.50706i	−0.811308	−	0.217389i
$134$	6.47425	−	12.0861i	0.559290	−	1.04408i
$135$	−1.41163	−	5.26826i	−0.121493	−	0.453420i
$136$	−16.7717	−	2.81596i	−1.43816	−	0.241466i
$137$	−10.0072			−0.854973			−0.427486	−	0.904022i	$-0.640601\pi$
$137$	−10.0072			−0.854973			−0.427486	+	0.904022i	$0.640601\pi$
$138$	0.387820	−	0.117260i	0.0330134	−	0.00998180i
$139$	3.93182	+	6.81011i	0.333492	+	0.577626i	0.983194	−	0.182564i	$-0.0584395\pi$
$139$	3.93182	+	6.81011i	0.333492	+	0.577626i	−0.649702	+	0.760189i	$0.725106\pi$
$140$	−1.35198	+	6.73298i	−0.114263	+	0.569040i
$141$	−10.8846	−	6.28420i	−0.916645	−	0.529225i
$142$	6.13433	+	3.28603i	0.514781	+	0.275757i
$143$	−1.91970	−	7.16440i	−0.160533	−	0.599118i
$144$	3.84102	+	5.04352i	0.320085	+	0.420293i
$145$	0.835528	−	1.44718i	0.0693868	−	0.120181i
$146$	−0.174264	−	5.47516i	−0.0144222	−	0.453128i
$147$	−5.69833			−0.469991
$148$	11.7163	−	3.27534i	0.963075	−	0.269232i
$149$	17.7450			1.45373			0.726865	−	0.686781i	$-0.240977\pi$
$149$	17.7450			1.45373			0.726865	+	0.686781i	$0.240977\pi$
$150$	0.0535180	+	1.68147i	0.00436972	+	0.137291i
$151$	3.73236	−	6.46464i	0.303735	−	0.526085i	−0.673244	−	0.739421i	$-0.735099\pi$
$151$	3.73236	−	6.46464i	0.303735	−	0.526085i	0.976979	+	0.213336i	$0.0684328\pi$
$152$	7.47528	−	2.79028i	0.606325	−	0.226322i
$153$	2.46642	+	9.20482i	0.199399	+	0.744166i
$154$	14.2023	+	7.60787i	1.14445	+	0.613060i
$155$	7.48024	+	4.31872i	0.600827	+	0.346888i
$156$	−5.21449	−	1.04707i	−0.417493	−	0.0838327i
$157$	−11.1702	−	19.3473i	−0.891477	−	1.54408i	−0.838105	−	0.545508i	$-0.816337\pi$
$157$	−11.1702	−	19.3473i	−0.891477	−	1.54408i	−0.0533715	−	0.998575i	$-0.516997\pi$
$158$	−4.67587	+	1.41378i	−0.371992	+	0.112474i
$159$	7.47352			0.592688
$160$	−2.31122	−	5.16316i	−0.182718	−	0.408184i
$161$	0.214030	+	0.798770i	0.0168679	+	0.0629519i
$162$	−1.15754	+	2.16089i	−0.0909449	+	0.169775i
$163$	14.0174	+	3.75596i	1.09793	+	0.294189i	0.761921	−	0.647670i	$-0.224256\pi$
$163$	14.0174	+	3.75596i	1.09793	+	0.294189i	0.336008	+	0.941859i	$0.390923\pi$
$164$	−14.0288	−	6.94990i	−1.09546	−	0.542696i
$165$	3.81243	+	1.02154i	0.296797	+	0.0795266i
$166$	−5.54472	+	3.44095i	−0.430354	+	0.267070i
$167$	21.9811	−	5.88983i	1.70095	−	0.455769i	0.727773	−	0.685818i	$-0.240556\pi$
$167$	21.9811	−	5.88983i	1.70095	−	0.455769i	0.973179	+	0.230050i	$0.0738889\pi$
$168$	9.40920	−	6.70384i	0.725936	−	0.517213i
$169$	6.93046	−	4.00130i	0.533112	−	0.307792i
$170$	−0.270505	−	8.49894i	−0.0207468	−	0.651839i
$171$	−3.16150	−	3.16150i	−0.241766	−	0.241766i
$172$	8.95979	+	7.88634i	0.683177	+	0.601328i
$173$	12.8346	−	7.41003i	0.975793	−	0.563374i	0.0747955	−	0.997199i	$-0.476170\pi$
$173$	12.8346	−	7.41003i	0.975793	−	0.563374i	0.900997	+	0.433825i	$0.142836\pi$
$174$	−2.69094	+	0.813621i	−0.204000	+	0.0616805i
$175$	−3.43369			−0.259562
$176$	−13.1643	+	1.68452i	−0.992296	+	0.126975i
$177$	−5.03426	−	5.03426i	−0.378398	−	0.378398i
$178$	1.05698	−	4.51460i	0.0792239	−	0.338384i
$179$	16.3072	−	16.3072i	1.21886	−	1.21886i	0.250828	−	0.968032i	$-0.419297\pi$
$179$	16.3072	−	16.3072i	1.21886	−	1.21886i	0.968032	−	0.250828i	$-0.0807029\pi$
$180$	−2.09432	+	2.37938i	−0.156101	+	0.177349i
$181$	8.38392	−	14.5214i	0.623172	−	1.07937i	−0.365720	−	0.930725i	$-0.619177\pi$
$181$	8.38392	−	14.5214i	0.623172	−	1.07937i	0.988891	−	0.148640i	$-0.0474896\pi$
$182$	2.47461	−	10.5696i	0.183430	−	0.783473i
$183$	4.71708	−	17.6044i	0.348697	−	1.30135i
$184$	−0.525381	−	0.433568i	−0.0387316	−	0.0319631i
$185$	2.75892	+	5.42110i	0.202840	+	0.398567i
$186$	−4.20549	−	13.9091i	−0.308361	−	1.01986i
$187$	−19.2698	−	5.16334i	−1.40915	−	0.377581i
$188$	1.34375	+	21.0880i	0.0980028	+	1.53800i
$189$	−16.2187	−	9.36384i	−1.17973	−	0.681119i
$190$	2.10367	+	3.38983i	0.152616	+	0.245924i
$191$	1.96719	+	1.96719i	0.142341	+	0.142341i	0.774686	−	0.632346i	$-0.217908\pi$
$191$	1.96719	+	1.96719i	0.142341	+	0.142341i	−0.632346	+	0.774686i	$0.717908\pi$
$192$	−3.10805	+	8.99480i	−0.224304	+	0.649144i
$193$	−0.380984	+	0.380984i	−0.0274238	+	0.0274238i	−0.720686	−	0.693262i	$-0.756173\pi$
$193$	−0.380984	+	0.380984i	−0.0274238	+	0.0274238i	0.693262	+	0.720686i	$0.256173\pi$
$194$	−7.55249	+	8.04906i	−0.542237	+	0.577889i
$195$		−	2.65929i		−	0.190436i
$196$	5.30812	+	7.97547i	0.379152	+	0.569676i
$197$	6.81142	+	11.7977i	0.485294	+	0.840554i	0.999857	−	0.0168988i	$-0.00537931\pi$
$197$	6.81142	+	11.7977i	0.485294	+	0.840554i	−0.514563	+	0.857452i	$0.672046\pi$
$198$	3.92136	+	6.31883i	0.278679	+	0.449060i
$199$	0.284624	−	0.284624i	0.0201765	−	0.0201765i	−0.696947	−	0.717123i	$-0.745459\pi$
$199$	0.284624	−	0.284624i	0.0201765	−	0.0201765i	0.717123	+	0.696947i	$0.245459\pi$
$200$	2.30355	−	1.64123i	0.162886	−	0.116052i
$201$	−5.76654	−	9.98794i	−0.406740	−	0.704495i
$202$	−0.0615236	−	1.93300i	−0.00432879	−	0.136005i
$203$	−1.48507	−	5.54237i	−0.104232	−	0.388998i
$204$	−9.45157	+	10.7381i	−0.661742	+	0.751815i
$205$	2.02602	−	7.56122i	0.141503	−	0.528098i
$206$	−2.14877	+	2.29005i	−0.149712	+	0.159555i
$207$	−0.0987905	+	0.368691i	−0.00686641	+	0.0256258i
$208$	3.39192	+	8.27365i	0.235187	+	0.573674i
$209$	9.04098	−	2.42252i	0.625377	−	0.167569i
$210$	4.21252	+	3.95264i	0.290691	+	0.272758i
$211$		−	22.5640i		−	1.55337i	−0.629888	−	0.776686i	$-0.716899\pi$
$211$		−	22.5640i		−	1.55337i	0.629888	−	0.776686i	$-0.283101\pi$
$212$	−6.96175	−	10.4600i	−0.478135	−	0.718399i
$213$	5.06941	−	2.92682i	0.347350	−	0.200543i
$214$	8.59547	+	4.60441i	0.587574	+	0.314751i
$215$	−2.98404	+	5.16851i	−0.203510	+	0.352490i
$216$	15.3563	−	1.47026i	1.04486	−	0.100039i
$217$	28.6477	−	7.67612i	1.94473	−	0.521089i
$218$	−20.2537	−	4.74187i	−1.37175	−	0.321160i
$219$	−3.99049	−	2.30391i	−0.269652	−	0.155684i
$220$	−2.12160	−	6.28752i	−0.143039	−	0.423904i
$221$			13.4413i			0.904161i
$222$	2.85572	−	9.82661i	0.191664	−	0.659519i
$223$			26.5109i			1.77530i	0.460518	+	0.887651i	$0.347664\pi$
$223$			26.5109i			1.77530i	−0.460518	+	0.887651i	$0.652336\pi$
$224$	−18.1477	−	6.92448i	−1.21254	−	0.462661i
$225$	−1.37256	−	0.792450i	−0.0915042	−	0.0528300i
$226$	0.0179500	−	0.0766686i	0.00119402	−	0.00509992i
$227$	−12.3647	+	3.31310i	−0.820671	+	0.219898i	−0.644640	−	0.764486i	$-0.722993\pi$
$227$	−12.3647	+	3.31310i	−0.820671	+	0.219898i	−0.176031	+	0.984385i	$0.556326\pi$
$228$	1.32133	−	6.58032i	0.0875071	−	0.435793i
$229$	−3.77314	+	6.53527i	−0.249336	+	0.431863i	−0.963342	−	0.268277i	$-0.913546\pi$
$229$	−3.77314	+	6.53527i	−0.249336	+	0.431863i	0.714006	+	0.700140i	$0.246879\pi$
$230$	0.160826	−	0.300228i	0.0106045	−	0.0197964i
$231$	11.7368	−	6.77624i	0.772224	−	0.445844i
$232$	3.64543	+	3.00837i	0.239334	+	0.197509i
$233$		−	28.6600i		−	1.87758i	−0.344487	−	0.938791i	$-0.611947\pi$
$233$		−	28.6600i		−	1.87758i	0.344487	−	0.938791i	$-0.388053\pi$
$234$	3.42852	−	3.65394i	0.224129	−	0.238865i
$235$	−10.2054	+	2.73453i	−0.665727	+	0.178381i
$236$	−2.35650	+	11.7356i	−0.153395	+	0.763919i
$237$	−1.06349	+	3.96900i	−0.0690811	+	0.257814i
$238$	−21.2921	−	19.9785i	−1.38016	−	1.29501i
$239$	−2.12599	+	7.93430i	−0.137519	+	0.513227i	0.862456	+	0.506132i	$0.168925\pi$
$239$	−2.12599	+	7.93430i	−0.137519	+	0.513227i	−0.999975	+	0.00709506i	$0.997742\pi$
$240$	−4.71533	−	0.638207i	−0.304373	−	0.0411961i
$241$	−0.393801	−	1.46969i	−0.0253670	−	0.0946709i	0.952082	−	0.305844i	$-0.0989384\pi$
$241$	−0.393801	−	1.46969i	−0.0253670	−	0.0946709i	−0.977449	+	0.211173i	$0.932272\pi$
$242$	−0.0120365		0.000383098i	−0.000773733		2.46265e-5i
$243$	−7.15015	−	12.3844i	−0.458682	−	0.794461i
$244$	−29.0334	+	9.79678i	−1.85867	+	0.627175i
$245$	−3.38719	+	3.38719i	−0.216399	+	0.216399i
$246$	−11.1895	+	6.94403i	−0.713419	+	0.442735i
$247$	−3.15318	−	5.46147i	−0.200632	−	0.347505i
$248$	−15.5498	+	18.8427i	−0.987414	+	1.19651i
$249$			5.48911i			0.347858i
$250$	1.03131	+	0.967682i	0.0652255	+	0.0612016i
$251$	−1.24326	+	1.24326i	−0.0784736	+	0.0784736i	−0.745254	−	0.666781i	$-0.767672\pi$
$251$	−1.24326	+	1.24326i	−0.0784736	+	0.0784736i	0.666781	+	0.745254i	$0.267672\pi$
$252$	0.692139	+	10.8621i	0.0436007	+	0.684246i
$253$	−0.565024	−	0.565024i	−0.0355227	−	0.0355227i
$254$	20.8630	−	12.9472i	1.30906	−	0.812379i
$255$	−6.19433	−	3.57630i	−0.387904	−	0.223956i
$256$	15.4845	−	4.02879i	0.967779	−	0.251799i
$257$	19.2236	+	5.15094i	1.19913	+	0.321307i	0.802489	−	0.596666i	$-0.203508\pi$
$257$	19.2236	+	5.15094i	1.19913	+	0.321307i	0.396643	+	0.917973i	$0.370175\pi$
$258$	9.61054	−	2.90580i	0.598326	−	0.180907i
$259$	19.8610	+	6.46374i	1.23410	+	0.401637i
$260$	−3.72198	+	2.47719i	−0.230827	+	0.153629i
$261$	0.685471	−	2.55821i	0.0424296	−	0.158349i
$262$	0.204429	+	0.0478618i	0.0126297	+	0.00295691i
$263$	−1.31479	+	2.27729i	−0.0810737	+	0.140424i	−0.903711	−	0.428142i	$-0.859168\pi$
$263$	−1.31479	+	2.27729i	−0.0810737	+	0.140424i	0.822638	+	0.568566i	$0.192502\pi$
$264$	−4.63495	+	10.1559i	−0.285262	+	0.625053i
$265$	4.44239	−	4.44239i	0.272894	−	0.272894i
$266$	13.3381	+	3.12278i	0.817813	+	0.191470i
$267$	−2.75785	−	2.75785i	−0.168778	−	0.168778i
$268$	−8.60760	+	17.3749i	−0.525793	+	1.06134i
$269$	−25.1289			−1.53214			−0.766069	−	0.642758i	$-0.777790\pi$
$269$	−25.1289			−1.53214			−0.766069	+	0.642758i	$0.777790\pi$
$270$	2.23234	+	7.38317i	0.135856	+	0.449325i
$271$	−9.03922	+	5.21880i	−0.549093	+	0.317019i	−0.748756	−	0.662845i	$-0.769349\pi$
$271$	−9.03922	+	5.21880i	−0.549093	+	0.317019i	0.199663	+	0.979865i	$0.436015\pi$
$272$	23.8335	+	3.22580i	1.44512	+	0.195593i
$273$	−6.45671	−	6.45671i	−0.390778	−	0.390778i
$274$	14.1452	−	0.450214i	0.854540	−	0.0271984i
$275$	2.87339	−	1.65895i	0.173272	−	0.100039i
$276$	−0.542907	+	0.183194i	−0.0326792	+	0.0110270i
$277$	4.58004	−	1.22722i	0.275188	−	0.0737363i	−0.118586	−	0.992944i	$-0.537836\pi$
$277$	4.58004	−	1.22722i	0.275188	−	0.0737363i	0.393774	+	0.919207i	$0.371169\pi$
$278$	−5.86399	−	9.44918i	−0.351699	−	0.566724i
$279$	13.2230	+	3.54310i	0.791641	+	0.212120i
$280$	1.60811	−	9.57787i	0.0961031	−	0.572387i
$281$	19.8712	+	5.32447i	1.18542	+	0.317631i	0.797073	−	0.603883i	$-0.206381\pi$
$281$	19.8712	+	5.32447i	1.18542	+	0.317631i	0.388344	+	0.921515i	$0.373047\pi$
$282$	15.6680	+	8.39302i	0.933016	+	0.499797i
$283$	0.505412	+	1.88622i	0.0300436	+	0.112124i	0.979319	−	0.202321i	$-0.0648483\pi$
$283$	0.505412	+	1.88622i	0.0300436	+	0.112124i	−0.949276	+	0.314445i	$0.898182\pi$
$284$	−8.81869	−	4.36882i	−0.523293	−	0.259242i
$285$	3.35584			0.198783
$286$	3.03581	+	10.0405i	0.179511	+	0.593707i
$287$	−13.4394	−	23.2777i	−0.793300	−	1.37404i
$288$	−5.65617	−	6.95620i	−0.333293	−	0.409898i
$289$	16.5866	+	9.57630i	0.975685	+	0.563312i
$290$	−1.11591	+	2.08317i	−0.0655285	+	0.122328i
$291$	2.40297	+	8.96799i	0.140864	+	0.525713i
$292$	0.492644	+	7.73129i	0.0288298	+	0.452440i
$293$	−15.6822	+	27.1624i	−0.916164	+	1.58684i	−0.110977	+	0.993823i	$0.535398\pi$
$293$	−15.6822	+	27.1624i	−0.916164	+	1.58684i	−0.805187	+	0.593020i	$0.797935\pi$
$294$	8.05458	−	0.256362i	0.469753	−	0.0149513i
$295$	−5.98490			−0.348454
$296$	−16.4136	+	5.15680i	−0.954023	+	0.299733i
$297$	18.0962			1.05005
$298$	−25.0826	+	0.798331i	−1.45299	+	0.0462460i
$299$	−0.269190	+	0.466251i	−0.0155677	+	0.0269640i
$300$	−0.151295	−	2.37434i	−0.00873503	−	0.137083i
$301$	5.30386	+	19.7943i	0.305709	+	1.14092i
$302$	−4.98485	+	9.30568i	−0.286846	+	0.535481i
$303$	−1.40884	−	0.813391i	−0.0809355	−	0.0467281i
$304$	−10.4408	+	4.28037i	−0.598819	+	0.245496i
$305$	−7.66044	−	13.2683i	−0.438635	−	0.759739i
$306$	−3.90040	−	12.9000i	−0.222971	−	0.737446i
$307$	7.28945			0.416031			0.208016	−	0.978126i	$-0.433300\pi$
$307$	7.28945			0.416031			0.208016	+	0.978126i	$0.433300\pi$
$308$	−20.4172	−	10.1148i	−1.16338	−	0.576342i
$309$	0.683672	+	2.55150i	0.0388927	+	0.145150i
$310$	−10.7676	−	5.76797i	−0.611558	−	0.327599i
$311$	8.30113	+	2.22428i	0.470714	+	0.126127i	0.486375	−	0.873750i	$-0.338319\pi$
$311$	8.30113	+	2.22428i	0.470714	+	0.126127i	−0.0156615	+	0.999877i	$0.504985\pi$
$312$	7.41778	+	1.24544i	0.419949	+	0.0705089i
$313$	−2.30492	−	0.617601i	−0.130282	−	0.0349089i	0.193089	−	0.981181i	$-0.438149\pi$
$313$	−2.30492	−	0.617601i	−0.130282	−	0.0349089i	−0.323371	+	0.946272i	$0.604816\pi$
$314$	16.6594	+	26.8448i	0.940146	+	1.51494i
$315$	−5.25661	+	1.40851i	−0.296177	+	0.0793603i
$316$	6.54573	−	2.20873i	0.368226	−	0.124251i
$317$	−11.9162	+	6.87981i	−0.669279	+	0.386408i	−0.795803	−	0.605555i	$-0.792951\pi$
$317$	−11.9162	+	6.87981i	−0.669279	+	0.386408i	0.126524	+	0.991964i	$0.459618\pi$
$318$	−10.5638	+	0.336226i	−0.592388	+	0.0188546i
$319$	3.92049	+	3.92049i	0.219505	+	0.219505i
$320$	3.49919	+	7.19414i	0.195611	+	0.402165i
$321$	7.10330	−	4.10109i	0.396467	−	0.228901i
$322$	−0.338466	−	1.11943i	−0.0188620	−	0.0623834i
$323$	−16.9620			−0.943791
$324$	1.53896	−	3.10648i	0.0854980	−	0.172582i
$325$	−1.58073	−	1.58073i	−0.0876830	−	0.0876830i
$326$	−19.9826	−	4.67841i	−1.10673	−	0.259113i
$327$	−12.3724	+	12.3724i	−0.684197	+	0.684197i
$328$	20.1423	+	9.19253i	1.11217	+	0.507572i
$329$	−18.1392	+	31.4179i	−1.00004	+	1.73213i
$330$	−5.43482	−	1.27242i	−0.299177	−	0.0700446i
$331$	7.50791	−	28.0199i	0.412672	−	1.54011i	−0.376782	−	0.926302i	$-0.622969\pi$
$331$	7.50791	−	28.0199i	0.412672	−	1.54011i	0.789454	−	0.613810i	$-0.210364\pi$
$332$	7.68264	−	5.11323i	0.421640	−	0.280625i
$333$	6.44736	+	7.16743i	0.353313	+	0.392773i
$334$	−30.8053	+	9.31417i	−1.68559	+	0.509649i
$335$	−9.36473	−	2.50927i	−0.511650	−	0.137096i
$336$	−12.9983	+	9.89918i	−0.709115	+	0.540044i
$337$	16.7861	+	9.69144i	0.914395	+	0.527926i	0.881843	−	0.471544i	$-0.156303\pi$
$337$	16.7861	+	9.69144i	0.914395	+	0.527926i	0.0325523	+	0.999470i	$0.489636\pi$
$338$	−9.61617	+	5.96763i	−0.523051	+	0.324596i
$339$	−0.0468349	−	0.0468349i	−0.00254372	−	0.00254372i
$340$	0.764717	+	12.0011i	0.0414726	+	0.650849i
$341$	−20.2644	+	20.2644i	−1.09738	+	1.09738i
$342$	4.61101	+	4.32655i	0.249335	+	0.233953i
$343$		−	7.58774i		−	0.409700i
$344$	−13.0194	−	10.7442i	−0.701961	−	0.579290i
$345$	−0.143245	−	0.248108i	−0.00771208	−	0.0133577i
$346$	−17.8082	+	11.0515i	−0.957377	+	0.594131i
$347$	11.8389	−	11.8389i	0.635544	−	0.635544i	−0.313909	−	0.949453i	$-0.601639\pi$
$347$	11.8389	−	11.8389i	0.635544	−	0.635544i	0.949453	+	0.313909i	$0.101639\pi$
$348$	3.76703	−	1.27111i	0.201934	−	0.0681389i
$349$	16.8945	+	29.2622i	0.904343	+	1.56637i	0.821796	+	0.569781i	$0.192972\pi$
$349$	16.8945	+	29.2622i	0.904343	+	1.56637i	0.0825468	+	0.996587i	$0.473695\pi$
$350$	4.85351	−	0.154478i	0.259431	−	0.00825720i
$351$	−3.15567	−	11.7771i	−0.168437	−	0.628616i
$352$	18.5319	−	2.97331i	0.987754	−	0.158478i
$353$	−3.94513	+	14.7234i	−0.209978	+	0.783649i	0.777896	+	0.628393i	$0.216287\pi$
$353$	−3.94513	+	14.7234i	−0.209978	+	0.783649i	−0.987874	+	0.155256i	$0.950380\pi$
$354$	7.34240	+	6.88943i	0.390244	+	0.366169i
$355$	1.27359	−	4.75310i	0.0675951	−	0.252268i
$356$	−1.29093	+	6.42893i	−0.0684191	+	0.340733i
$357$	−23.7229	+	6.35653i	−1.25555	+	0.336423i
$358$	−22.3166	+	23.7839i	−1.17947	+	1.25702i
$359$		−	10.5691i		−	0.557817i	−0.960318	−	0.278908i	$-0.910027\pi$
$359$		−	10.5691i		−	0.557817i	0.960318	−	0.278908i	$-0.0899726\pi$
$360$	2.85326	−	3.45747i	0.150380	−	0.182225i
$361$	−9.56249	+	5.52090i	−0.503289	+	0.290574i
$362$	−11.1973	+	20.9031i	−0.588520	+	1.09864i
$363$	−0.00506486	+	0.00877260i	−0.000265836	+	0.000460442i
$364$	−3.02234	+	15.0515i	−0.158413	+	0.788911i
$365$	−3.74150	+	1.00253i	−0.195839	+	0.0524749i
$366$	−5.87558	+	25.0960i	−0.307122	+	1.31179i
$367$	−1.14405	−	0.660516i	−0.0597188	−	0.0344787i	0.469843	−	0.882750i	$-0.344310\pi$
$367$	−1.14405	−	0.660516i	−0.0597188	−	0.0344787i	−0.529562	+	0.848271i	$0.677644\pi$
$368$	0.762131	+	0.589212i	0.0397288	+	0.0307148i
$369$		−	12.4065i		−	0.645857i
$370$	−4.14362	−	7.53860i	−0.215416	−	0.391913i
$371$		−	21.5721i		−	1.11997i
$372$	6.57020	+	19.4712i	0.340649	+	1.00954i
$373$	−9.17624	−	5.29790i	−0.475128	−	0.274315i	0.243256	−	0.969962i	$-0.421784\pi$
$373$	−9.17624	−	5.29790i	−0.475128	−	0.274315i	−0.718384	+	0.695647i	$0.755118\pi$
$374$	27.4702	+	6.43143i	1.42045	+	0.332562i
$375$	1.14905	−	0.307886i	0.0593365	−	0.0158992i
$376$	−2.84811	−	29.7475i	−0.146880	−	1.53411i
$377$	1.86781	−	3.23514i	0.0961971	−	0.166618i
$378$	23.3463	+	12.5061i	1.20080	+	0.643245i
$379$	17.8105	−	10.2829i	0.914866	−	0.528198i	0.0328724	−	0.999460i	$-0.489535\pi$
$379$	17.8105	−	10.2829i	0.914866	−	0.528198i	0.881994	+	0.471261i	$0.156201\pi$
$380$	−3.12604	−	4.69688i	−0.160362	−	0.240945i
$381$		−	20.6538i		−	1.05812i
$382$	−2.86912	−	2.69212i	−0.146797	−	0.137741i
$383$	14.2796	−	3.82619i	0.729651	−	0.195509i	0.125177	−	0.992134i	$-0.460050\pi$
$383$	14.2796	−	3.82619i	0.729651	−	0.195509i	0.604474	+	0.796625i	$0.293383\pi$
$384$	3.98855	−	12.8540i	0.203540	−	0.655951i
$385$	2.94864	−	11.0045i	0.150276	−	0.560839i
$386$	0.521380	−	0.555660i	0.0265375	−	0.0282824i
$387$	−2.44812	+	9.13651i	−0.124445	+	0.464435i
$388$	10.3133	−	11.7171i	0.523579	−	0.594846i
$389$	−6.48143	−	24.1890i	−0.328621	−	1.22643i	−0.910621	−	0.413243i	$-0.864396\pi$
$389$	−6.48143	−	24.1890i	−0.328621	−	1.22643i	0.581999	−	0.813189i	$-0.302271\pi$
$390$	0.119639	+	3.75890i	0.00605814	+	0.190339i
$391$	0.724031	+	1.25406i	0.0366158	+	0.0634204i
$392$	−7.86183	−	11.0345i	−0.397082	−	0.557326i
$393$	0.124880	−	0.124880i	0.00629938	−	0.00629938i
$394$	−10.1587	−	16.3696i	−0.511788	−	0.824690i
$395$	1.72708	+	2.99140i	0.0868990	+	0.150513i
$396$	−5.82711	−	8.75524i	−0.292823	−	0.439967i
$397$		−	16.8991i		−	0.848140i	−0.905629	−	0.424070i	$-0.860601\pi$
$397$		−	16.8991i		−	0.848140i	0.905629	−	0.424070i	$-0.139399\pi$
$398$	−0.389510	+	0.415120i	−0.0195244	+	0.0208081i
$399$	8.14792	−	8.14792i	0.407906	−	0.407906i
$400$	−3.18223	+	2.42351i	−0.159112	+	0.121175i
$401$	11.2832	+	11.2832i	0.563458	+	0.563458i	0.930288	−	0.366830i	$-0.119557\pi$
$401$	11.2832	+	11.2832i	0.563458	+	0.563458i	−0.366830	+	0.930288i	$0.619557\pi$
$402$	8.60034	+	13.8585i	0.428946	+	0.691199i
$403$	16.7220	+	9.65443i	0.832981	+	0.480922i
$404$	0.173927	+	2.72952i	0.00865319	+	0.135799i
$405$	1.67433	+	0.448636i	0.0831982	+	0.0222929i
$406$	2.34849	+	7.76731i	0.116554	+	0.385485i
$407$	−19.7430	+	4.18662i	−0.978626	+	0.207523i
$408$	12.8767	−	15.6035i	0.637491	−	0.772486i
$409$	9.77735	−	36.4896i	0.483459	−	1.80429i	−0.103444	−	0.994635i	$-0.532986\pi$
$409$	9.77735	−	36.4896i	0.483459	−	1.80429i	0.586903	−	0.809658i	$-0.300347\pi$
$410$	−2.52361	+	10.7789i	−0.124632	+	0.532332i
$411$	5.95218	−	10.3095i	0.293600	−	0.508529i
$412$	2.93426	−	3.33365i	0.144560	−	0.164237i
$413$	−14.5312	+	14.5312i	−0.715036	+	0.715036i
$414$	0.123053	−	0.525588i	0.00604773	−	0.0258313i
$415$	3.26282	+	3.26282i	0.160166	+	0.160166i
$416$	−5.16669	−	11.5422i	−0.253318	−	0.565902i
$417$	−9.35442			−0.458088
$418$	−12.6704	+	3.83097i	−0.619730	+	0.187379i
$419$	18.0329	−	10.4113i	0.880964	−	0.508625i	0.00998788	−	0.999950i	$-0.496821\pi$
$419$	18.0329	−	10.4113i	0.880964	−	0.508625i	0.870976	+	0.491325i	$0.163487\pi$
$420$	−6.13221	−	5.39753i	−0.299221	−	0.263372i
$421$	12.0776	+	12.0776i	0.588624	+	0.588624i	0.937259	−	0.348635i	$-0.113355\pi$
$421$	12.0776	+	12.0776i	0.588624	+	0.588624i	−0.348635	+	0.937259i	$0.613355\pi$
$422$	1.01513	+	31.8942i	0.0494159	+	1.55259i
$423$	−14.5017	+	8.37255i	−0.705096	+	0.407087i
$424$	10.3110	+	14.4720i	0.500746	+	0.702825i
$425$	−5.80783	+	1.55620i	−0.281721	+	0.0754869i
$426$	−7.03392	+	4.36513i	−0.340795	+	0.211491i
$427$	−50.8145	−	13.6157i	−2.45909	−	0.658911i
$428$	−12.3568	−	6.12162i	−0.597290	−	0.295900i
$429$	8.52263	+	2.28363i	0.411477	+	0.110255i
$430$	3.98541	−	7.43993i	0.192194	−	0.358785i
$431$	5.17415	+	19.3102i	0.249230	+	0.930139i	0.971210	+	0.238225i	$0.0765655\pi$
$431$	5.17415	+	19.3102i	0.249230	+	0.930139i	−0.721980	+	0.691914i	$0.756768\pi$
$432$	−21.6400	+	2.76907i	−1.04115	+	0.133227i
$433$	28.2259			1.35645			0.678225	−	0.734855i	$-0.262750\pi$
$433$	28.2259			1.35645			0.678225	+	0.734855i	$0.262750\pi$
$434$	−40.1481	+	12.1390i	−1.92717	+	0.582691i
$435$	0.993927	+	1.72153i	0.0476552	+	0.0825412i
$436$	28.8418	+	5.79144i	1.38127	+	0.277360i
$437$	−0.588376	−	0.339699i	−0.0281458	−	0.0162500i
$438$	5.74420	+	3.07704i	0.274468	+	0.147027i
$439$	3.96231	+	14.7876i	0.189111	+	0.705772i	0.993713	+	0.111957i	$0.0357120\pi$
$439$	3.96231	+	14.7876i	0.189111	+	0.705772i	−0.804602	+	0.593814i	$0.797621\pi$
$440$	3.28175	+	8.79194i	0.156451	+	0.419139i
$441$	−3.79600	+	6.57486i	−0.180762	+	0.313089i
$442$	−0.604711	−	18.9993i	−0.0287632	−	0.903703i
$443$	39.6672			1.88465			0.942323	−	0.334705i	$-0.108637\pi$
$443$	39.6672			1.88465			0.942323	+	0.334705i	$0.108637\pi$
$444$	−3.59447	+	14.0184i	−0.170586	+	0.665282i
$445$	−3.27863			−0.155422
$446$	−1.19270	−	37.4731i	−0.0564759	−	1.77440i
$447$	−10.5546	+	18.2810i	−0.499214	+	0.864664i
$448$	25.9632	+	8.97129i	1.22665	+	0.423854i
$449$	−1.78409	−	6.65832i	−0.0841965	−	0.314226i	0.910964	−	0.412485i	$-0.135339\pi$
$449$	−1.78409	−	6.65832i	−0.0841965	−	0.314226i	−0.995161	+	0.0982595i	$0.968672\pi$
$450$	1.97577	+	1.05838i	0.0931385	+	0.0498923i
$451$	22.4928	+	12.9862i	1.05914	+	0.611496i
$452$	−0.0219230	+	0.109178i	−0.00103117	+	0.00513532i
$453$	4.43995	+	7.69021i	0.208607	+	0.361318i
$454$	17.3284	−	5.23933i	0.813260	−	0.245894i
$455$	−7.67596			−0.359854
$456$	−1.57165	+	9.36072i	−0.0735994	+	0.438356i
$457$	2.05184	+	7.65757i	0.0959810	+	0.358206i	0.997166	−	0.0752280i	$-0.0239685\pi$
$457$	2.05184	+	7.65757i	0.0959810	+	0.358206i	−0.901185	+	0.433434i	$0.857302\pi$
$458$	5.03931	−	9.40734i	0.235471	−	0.439576i
$459$	−31.6765	−	8.48769i	−1.47853	−	0.396171i
$460$	−0.213820	+	0.431607i	−0.00996940	+	0.0201238i
$461$	17.4961	+	4.68806i	0.814874	+	0.218345i	0.642104	−	0.766617i	$-0.278062\pi$
$461$	17.4961	+	4.68806i	0.814874	+	0.218345i	0.172770	+	0.984962i	$0.444728\pi$
$462$	−16.2851	+	10.1062i	−0.757650	+	0.470184i
$463$	−40.5450	+	10.8640i	−1.88428	+	0.504893i	−0.885062	+	0.465474i	$0.845884\pi$
$463$	−40.5450	+	10.8640i	−1.88428	+	0.504893i	−0.999223	+	0.0394189i	$0.987449\pi$
$464$	−5.28814	−	4.08832i	−0.245496	−	0.189796i
$465$	−8.89834	+	5.13746i	−0.412651	+	0.238244i
$466$	1.28939	+	40.5109i	0.0597296	+	1.87663i
$467$	14.7891	+	14.7891i	0.684358	+	0.684358i	0.960979	−	0.276621i	$-0.0892147\pi$
$467$	14.7891	+	14.7891i	0.684358	+	0.684358i	−0.276621	+	0.960979i	$0.589215\pi$
$468$	−4.68181	+	5.31908i	−0.216417	+	0.245874i
$469$	−28.8299	+	16.6449i	−1.33124	+	0.768592i
$470$	14.3023	−	4.32438i	0.659715	−	0.199469i
$471$	26.5756			1.22454
$472$	2.80293	−	16.6942i	0.129016	−	0.768412i
$473$	−14.0018	−	14.0018i	−0.643804	−	0.643804i
$474$	1.32468	−	5.65801i	0.0608445	−	0.259881i
$475$	1.99477	−	1.99477i	0.0915262	−	0.0915262i
$476$	30.9951	+	27.2817i	1.42066	+	1.25045i
$477$	4.97855	−	8.62310i	0.227952	−	0.394825i
$478$	2.64812	−	11.3108i	0.121122	−	0.517342i
$479$	7.05104	−	26.3149i	0.322170	−	1.20236i	−0.594955	−	0.803759i	$-0.702830\pi$
$479$	7.05104	−	26.3149i	0.322170	−	1.20236i	0.917126	−	0.398598i	$-0.130503\pi$
$480$	6.69382	+	0.689967i	0.305529	+	0.0314925i
$481$	6.16752	+	12.1188i	0.281215	+	0.552570i
$482$	0.622757	+	2.05968i	0.0283658	+	0.0938160i
$483$	−0.950201	−	0.254605i	−0.0432356	−	0.0115850i
$484$	0.0169963	−	0.00108302i	0.000772558	−	4.92280e-5i
$485$	6.75909	+	3.90236i	0.306915	+	0.177197i
$486$	10.6639	+	17.1837i	0.483724	+	0.779467i
$487$	−22.1160	−	22.1160i	−1.00217	−	1.00217i	−0.999998	−	0.00217378i	$-0.999308\pi$
$487$	−22.1160	−	22.1160i	−1.00217	−	1.00217i	−0.00217378	−	0.999998i	$-0.500692\pi$
$488$	40.5979	−	15.1539i	1.83778	−	0.685986i
$489$	−12.2068	+	12.2068i	−0.552012	+	0.552012i
$490$	4.63540	−	4.94017i	0.209406	−	0.223174i
$491$		−	0.789415i		−	0.0356258i	−0.999841	−	0.0178129i	$-0.994330\pi$
$491$		−	0.789415i		−	0.0356258i	0.999841	−	0.0178129i	$-0.00567032\pi$
$492$	15.5040	−	10.3188i	0.698974	−	0.465207i
$493$	−5.02378	−	8.70145i	−0.226260	−	0.391893i
$494$	4.70272	+	7.57792i	0.211585	+	0.340947i
$495$	3.71836	−	3.71836i	0.167128	−	0.167128i
$496$	21.1319	−	27.3336i	0.948851	−	1.22732i
$497$	−8.44819	−	14.6327i	−0.378953	−	0.656366i
$498$	−0.246949	−	7.75885i	−0.0110661	−	0.347682i
$499$	−4.46089	−	16.6483i	−0.199697	−	0.745279i	−0.991001	−	0.133856i	$-0.957264\pi$
$499$	−4.46089	−	16.6483i	−0.199697	−	0.745279i	0.791304	−	0.611423i	$-0.209403\pi$
$500$	−1.50128	−	1.32142i	−0.0671394	−	0.0590956i
$501$	−7.00642	+	26.1483i	−0.313024	+	1.16822i
$502$	1.70141	−	1.81327i	0.0759375	−	0.0809303i
$503$	5.56824	−	20.7810i	0.248276	−	0.926577i	−0.723433	−	0.690395i	$-0.757437\pi$
$503$	5.56824	−	20.7810i	0.248276	−	0.926577i	0.971709	−	0.236183i	$-0.0758964\pi$
$504$	−1.46701	−	15.3224i	−0.0653458	−	0.682513i
$505$	−1.32093	+	0.353942i	−0.0587806	+	0.0157502i
$506$	0.824079	+	0.773240i	0.0366348	+	0.0343747i
$507$			9.51974i			0.422786i
$508$	−28.9073	+	19.2394i	−1.28255	+	0.853612i
$509$	6.18677	−	3.57193i	0.274224	−	0.158323i	−0.356582	−	0.934264i	$-0.616058\pi$
$509$	6.18677	−	3.57193i	0.274224	−	0.158323i	0.630806	+	0.775941i	$0.282725\pi$
$510$	8.91656	+	4.77641i	0.394832	+	0.211503i
$511$	−6.65017	+	11.5184i	−0.294186	+	0.509545i
$512$	−21.7060	+	6.39131i	−0.959279	+	0.282459i
$513$	14.8619	−	3.98224i	0.656169	−	0.175820i
$514$	−27.4042	−	6.41599i	−1.20875	−	0.282997i
$515$	1.92304	+	1.11027i	0.0847393	+	0.0489242i
$516$	−13.4537	+	4.53971i	−0.592268	+	0.199850i
$517$		−	35.0551i		−	1.54172i
$518$	−28.3642	−	8.24296i	−1.24625	−	0.362175i
$519$			17.6297i			0.773856i
$520$	5.14956	−	3.66895i	0.225823	−	0.160894i
$521$	−24.8622	−	14.3542i	−1.08923	−	0.628869i	−0.155861	−	0.987779i	$-0.549815\pi$
$521$	−24.8622	−	14.3542i	−1.08923	−	0.628869i	−0.933372	+	0.358910i	$0.883149\pi$
$522$	−0.853820	+	3.64686i	−0.0373707	+	0.159619i
$523$	−12.4721	+	3.34188i	−0.545366	+	0.146130i	−0.520975	−	0.853572i	$-0.674431\pi$
$523$	−12.4721	+	3.34188i	−0.545366	+	0.146130i	−0.0243912	+	0.999702i	$0.507765\pi$
$524$	−0.291113	−	0.0584555i	−0.0127173	−	0.00255364i
$525$	2.04232	−	3.53741i	0.0891343	−	0.154385i
$526$	1.75601	−	3.27810i	0.0765655	−	0.142932i
$527$	44.9765	−	25.9672i	1.95921	−	1.13115i
$528$	6.09459	−	14.5639i	0.265233	−	0.633811i
$529$		−	22.9420i		−	0.997478i
$530$	−6.07944	+	6.47916i	−0.264074	+	0.281437i
$531$	−9.16226	+	2.45502i	−0.397608	+	0.106539i
$532$	−18.9939	−	3.81398i	−0.823490	−	0.165357i
$533$	4.52914	−	16.9030i	0.196179	−	0.732150i
$534$	4.02229	+	3.77414i	0.174062	+	0.163323i
$535$	1.78456	−	6.66008i	0.0771534	−	0.287940i
$536$	11.3851	−	24.9467i	0.491764	−	1.07753i
$537$	7.10044	+	26.4992i	0.306407	+	1.14352i
$538$	35.5197	−	1.13052i	1.53136	−	0.0487404i
$539$	−7.94673	−	13.7641i	−0.342290	−	0.592864i
$540$	−3.48757	−	10.3357i	−0.150081	−	0.444776i
$541$	−16.0636	+	16.0636i	−0.690627	+	0.690627i	−0.962370	−	0.271743i	$-0.912400\pi$
$541$	−16.0636	+	16.0636i	−0.690627	+	0.690627i	0.271743	+	0.962370i	$0.412400\pi$
$542$	12.5421	−	7.78342i	0.538731	−	0.334327i
$543$	9.97334	+	17.2743i	0.427997	+	0.741313i
$544$	−33.8337	−	3.48742i	−1.45061	−	0.149522i
$545$			14.7088i			0.630054i
$546$	9.41703	+	8.83606i	0.403011	+	0.378149i
$547$	−6.62216	+	6.62216i	−0.283143	+	0.283143i	−0.834361	−	0.551218i	$-0.814163\pi$
$547$	−6.62216	+	6.62216i	−0.283143	+	0.283143i	0.551218	+	0.834361i	$0.314163\pi$
$548$	−19.9739	+	1.27275i	−0.853242	+	0.0543693i
$549$	−17.1700	−	17.1700i	−0.732798	−	0.732798i
$550$	−3.98690	+	2.47420i	−0.170002	+	0.105500i
$551$	4.08252	+	2.35705i	0.173921	+	0.100414i
$552$	0.759156	−	0.283369i	0.0323118	−	0.0120610i
$553$	11.4564	+	3.06973i	0.487175	+	0.130538i
$554$	−6.41866	+	1.94072i	−0.272703	+	0.0824533i
$555$	−7.22583	−	0.382162i	−0.306720	−	0.0162219i
$556$	8.71385	+	13.0926i	0.369550	+	0.555249i
$557$	−5.73071	+	21.3873i	−0.242818	+	0.906209i	0.731650	+	0.681681i	$0.238751\pi$
$557$	−5.73071	+	21.3873i	−0.242818	+	0.906209i	−0.974468	+	0.224528i	$0.927916\pi$
$558$	−18.8501	−	4.41327i	−0.797988	−	0.186829i
$559$	−6.67078	+	11.5541i	−0.282144	+	0.488688i
$560$	−1.84217	+	13.6106i	−0.0778457	+	0.575155i
$561$	16.7808	−	16.7808i	0.708486	−	0.708486i
$562$	−28.3274	−	6.63214i	−1.19492	−	0.279760i
$563$	5.70952	+	5.70952i	0.240628	+	0.240628i	0.817110	−	0.576482i	$-0.195575\pi$
$563$	5.70952	+	5.70952i	0.240628	+	0.240628i	−0.576482	+	0.817110i	$0.695575\pi$
$564$	−22.5243	−	11.1586i	−0.948444	−	0.469863i
$565$	−0.0556789			−0.00234243
$566$	−0.799258	−	2.64343i	−0.0335953	−	0.111112i
$567$	5.15453	−	2.97597i	0.216470	−	0.124979i
$568$	12.6618	+	5.77857i	0.531275	+	0.242463i
$569$	19.9957	+	19.9957i	0.838263	+	0.838263i	0.988630	−	0.150368i	$-0.0480457\pi$
$569$	19.9957	+	19.9957i	0.838263	+	0.838263i	−0.150368	+	0.988630i	$0.548046\pi$
$570$	−4.74347	+	0.150976i	−0.198682	+	0.00632367i
$571$	−21.7897	+	12.5803i	−0.911870	+	0.526468i	−0.881032	−	0.473056i	$-0.843151\pi$
$571$	−21.7897	+	12.5803i	−0.911870	+	0.526468i	−0.0308376	+	0.999524i	$0.509817\pi$
$572$	−4.74282	−	14.0557i	−0.198307	−	0.587696i
$573$	−3.19668	+	0.856547i	−0.133543	+	0.0357828i
$574$	20.0437	+	32.2983i	0.836610	+	1.34810i
$575$	−0.232627	−	0.0623323i	−0.00970123	−	0.00259944i
$576$	8.30794	+	9.57810i	0.346164	+	0.399088i
$577$	−21.1587	−	5.66946i	−0.880849	−	0.236023i	−0.210076	−	0.977685i	$-0.567371\pi$
$577$	−21.1587	−	5.66946i	−0.880849	−	0.236023i	−0.670774	+	0.741662i	$0.734038\pi$
$578$	−23.8760	−	12.7899i	−0.993111	−	0.531988i
$579$	−0.165887	−	0.619098i	−0.00689402	−	0.0257288i
$580$	1.48362	−	2.99476i	0.0616038	−	0.124351i
$581$	15.8442			0.657326
$582$	−3.80005	−	12.5681i	−0.157517	−	0.520966i
$583$	10.4224	+	18.0520i	0.431650	+	0.747639i
$584$	−1.04417	−	10.9060i	−0.0432082	−	0.451293i
$585$	−3.06834	−	1.77151i	−0.126860	−	0.0732429i
$586$	20.9448	−	39.0995i	0.865220	−	1.61519i
$587$	0.234681	+	0.875843i	0.00968634	+	0.0361499i	0.970600	−	0.240699i	$-0.0773766\pi$
$587$	0.234681	+	0.875843i	0.00968634	+	0.0361499i	−0.960914	+	0.276849i	$0.910710\pi$
$588$	−11.3736	+	0.724735i	−0.469039	+	0.0298875i
$589$	−12.1832	+	21.1020i	−0.502001	+	0.869491i
$590$	8.45965	−	0.269255i	0.348278	−	0.0110850i
$591$	−16.2055			−0.666604
$592$	22.9686	−	8.02755i	0.944005	−	0.329930i
$593$	30.6558			1.25888			0.629441	−	0.777049i	$-0.283284\pi$
$593$	30.6558			1.25888			0.629441	+	0.777049i	$0.283284\pi$
$594$	−25.5790	+	0.814130i	−1.04952	+	0.0334042i
$595$	−10.3229	+	17.8797i	−0.423196	+	0.732998i
$596$	35.4182	−	2.25688i	1.45079	−	0.0924453i
$597$	0.123930	+	0.462513i	0.00507212	+	0.0189294i
$598$	0.359523	−	0.671155i	0.0147020	−	0.0274456i
$599$	−19.4902	−	11.2527i	−0.796348	−	0.459772i	0.0458446	−	0.998949i	$-0.485402\pi$
$599$	−19.4902	−	11.2527i	−0.796348	−	0.459772i	−0.842193	+	0.539177i	$0.818735\pi$
$600$	0.320675	+	3.34932i	0.0130915	+	0.136736i
$601$	−18.6134	−	32.2393i	−0.759256	−	1.31507i	−0.943231	−	0.332139i	$-0.892230\pi$
$601$	−18.6134	−	32.2393i	−0.759256	−	1.31507i	0.183975	−	0.982931i	$-0.441104\pi$
$602$	−8.38751	−	27.7405i	−0.341850	−	1.13062i
$603$	−15.3657			−0.625741
$604$	6.62742	−	13.3778i	0.269666	−	0.544336i
$605$	0.00220394	+	0.00822522i	8.96030e−5	+	0.000334403i
$606$	2.02798	+	1.08634i	0.0823810	+	0.0441297i
$607$	29.1487	+	7.81037i	1.18311	+	0.317013i	0.796159	−	0.605087i	$-0.206862\pi$
$607$	29.1487	+	7.81037i	1.18311	+	0.317013i	0.386951	+	0.922100i	$0.373528\pi$
$608$	14.5654	−	6.52001i	0.590706	−	0.264421i
$609$	6.59309	+	1.76661i	0.267166	+	0.0715868i
$610$	11.4249	+	18.4100i	0.462582	+	0.745400i
$611$	−22.8140	+	6.11300i	−0.922957	+	0.247305i
$612$	6.09357	+	18.0587i	0.246318	+	0.729979i
$613$	−11.8712	+	6.85384i	−0.479473	+	0.276824i	−0.720197	−	0.693770i	$-0.755949\pi$
$613$	−11.8712	+	6.85384i	−0.479473	+	0.276824i	0.240724	+	0.970594i	$0.422615\pi$
$614$	−10.3036	+	0.327945i	−0.415820	+	0.0132348i
$615$	6.58456	+	6.58456i	0.265515	+	0.265515i
$616$	29.3147	+	13.3786i	1.18112	+	0.539041i
$617$	14.8342	−	8.56450i	0.597200	−	0.344794i	−0.170739	−	0.985316i	$-0.554615\pi$
$617$	14.8342	−	8.56450i	0.597200	−	0.344794i	0.767939	+	0.640522i	$0.221282\pi$
$618$	−1.08116	−	3.57578i	−0.0434905	−	0.143839i
$619$	1.89516			0.0761730			0.0380865	−	0.999274i	$-0.487874\pi$
$619$	1.89516			0.0761730			0.0380865	+	0.999274i	$0.487874\pi$
$620$	15.4795	+	7.66859i	0.621670	+	0.307978i
$621$	−0.928807	−	0.928807i	−0.0372718	−	0.0372718i
$622$	−11.8337	−	2.77056i	−0.474488	−	0.111089i
$623$	−7.96046	+	7.96046i	−0.318929	+	0.318929i
$624$	−10.5410	−	1.42670i	−0.421979	−	0.0571138i
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	3.28578	+	0.769282i	0.131326	+	0.0307467i
$627$	−2.88178	+	10.7550i	−0.115087	+	0.429512i
$628$	−24.7558	−	37.1956i	−0.987864	−	1.48427i
$629$	36.5228	+	1.93163i	1.45626	+	0.0770191i
$630$	7.36685	−	2.22741i	0.293502	−	0.0887421i
$631$	−40.0376	−	10.7280i	−1.59387	−	0.427077i	−0.650687	−	0.759346i	$-0.725519\pi$
$631$	−40.0376	−	10.7280i	−1.59387	−	0.427077i	−0.943185	+	0.332269i	$0.892186\pi$
$632$	−9.15300	+	3.41653i	−0.364087	+	0.135902i
$633$	23.2456	+	13.4209i	0.923930	+	0.533431i
$634$	16.5340	−	10.2607i	0.656648	−	0.407504i
$635$	−12.2769	−	12.2769i	−0.487196	−	0.487196i
$636$	14.9168	−	0.950509i	0.591489	−	0.0376901i
$637$	−7.57201	+	7.57201i	−0.300014	+	0.300014i
$638$	−5.71798	−	5.36522i	−0.226377	−	0.212411i
$639$		−	7.79892i		−	0.308521i
$640$	−5.26975	−	10.0115i	−0.208305	−	0.395738i
$641$	−3.73063	−	6.46164i	−0.147351	−	0.255219i	0.782897	−	0.622152i	$-0.213741\pi$
$641$	−3.73063	−	6.46164i	−0.147351	−	0.255219i	−0.930248	+	0.366932i	$0.880408\pi$
$642$	−9.85599	+	6.11645i	−0.388985	+	0.241397i
$643$	22.4574	−	22.4574i	0.885634	−	0.885634i	−0.108466	−	0.994100i	$-0.534594\pi$
$643$	22.4574	−	22.4574i	0.885634	−	0.885634i	0.994100	+	0.108466i	$0.0345940\pi$
$644$	0.528783	+	1.56709i	0.0208370	+	0.0617518i
$645$	−3.54976	−	6.14836i	−0.139772	−	0.242091i
$646$	23.9757	−	0.763103i	0.943313	−	0.0300239i
$647$	4.11531	+	15.3585i	0.161790	+	0.603807i	0.998428	+	0.0560512i	$0.0178510\pi$
$647$	4.11531	+	15.3585i	0.161790	+	0.603807i	−0.836638	+	0.547756i	$0.815482\pi$
$648$	−2.03557	+	4.46024i	−0.0799645	+	0.175215i
$649$	5.13946	−	19.1807i	0.201742	−	0.752910i
$650$	2.30547	+	2.16324i	0.0904280	+	0.0848492i
$651$	−9.13136	+	34.0787i	−0.357886	+	1.33565i
$652$	28.4558	+	5.71392i	1.11442	+	0.223775i
$653$	−9.51892	+	2.55059i	−0.372504	+	0.0998121i	−0.440214	−	0.897893i	$-0.645097\pi$
$653$	−9.51892	+	2.55059i	−0.372504	+	0.0998121i	0.0677100	+	0.997705i	$0.478431\pi$
$654$	16.9318	−	18.0450i	0.662085	−	0.705616i
$655$		−	0.148462i		−	0.00580089i
$656$	−28.8846	−	12.0874i	−1.12776	−	0.471935i
$657$	−5.31660	+	3.06954i	−0.207420	+	0.119754i
$658$	24.2262	−	45.2252i	0.944435	−	1.76306i
$659$	−7.20081	+	12.4722i	−0.280504	+	0.485847i	−0.971509	−	0.237003i	$-0.923835\pi$
$659$	−7.20081	+	12.4722i	−0.280504	+	0.485847i	0.691005	+	0.722850i	$0.257168\pi$
$660$	7.73935	+	1.55406i	0.301254	+	0.0604917i
$661$	27.5547	−	7.38325i	1.07175	−	0.287175i	0.320540	−	0.947235i	$-0.396136\pi$
$661$	27.5547	−	7.38325i	1.07175	−	0.287175i	0.751213	+	0.660060i	$0.229469\pi$
$662$	−9.35182	+	39.9438i	−0.363469	+	1.55246i
$663$	−13.8473	−	7.99476i	−0.537786	−	0.310491i
$664$	−10.6294	+	7.57317i	−0.412499	+	0.293896i
$665$		−	9.68652i		−	0.375627i
$666$	−9.43579	−	9.84108i	−0.365629	−	0.381334i
$667$		−	0.402446i		−	0.0155828i
$668$	43.1242	−	14.5515i	1.66853	−	0.563013i
$669$	−27.3117	−	15.7684i	−1.05593	−	0.609642i
$670$	13.3499	+	3.12554i	0.515752	+	0.120750i
$671$	49.1012	−	13.1566i	1.89553	−	0.507905i
$672$	17.9277	−	14.5772i	0.691576	−	0.562329i
$673$	−4.26033	+	7.37910i	−0.164224	+	0.284444i	−0.936379	−	0.350990i	$-0.885845\pi$
$673$	−4.26033	+	7.37910i	−0.164224	+	0.284444i	0.772156	+	0.635433i	$0.219179\pi$
$674$	−24.1631	−	12.9436i	−0.930727	−	0.498570i
$675$	4.72339	−	2.72705i	0.181803	−	0.104964i
$676$	13.3240	−	8.86785i	0.512460	−	0.341071i
$677$			38.3906i			1.47547i	0.675090	+	0.737735i	$0.264105\pi$
$677$			38.3906i			1.47547i	−0.675090	+	0.737735i	$0.735895\pi$
$678$	0.0683080	+	0.0640939i	0.00262335	+	0.00246151i
$679$	25.8858	−	6.93609i	0.993407	−	0.266183i
$680$	−1.62084	−	16.9291i	−0.0621565	−	0.649201i
$681$	3.94120	−	14.7087i	0.151027	−	0.563641i
$682$	27.7320	−	29.5554i	1.06191	−	1.13173i
$683$	−0.417626	+	1.55860i	−0.0159800	+	0.0596382i	−0.973455	−	0.228877i	$-0.926495\pi$
$683$	−0.417626	+	1.55860i	−0.0159800	+	0.0596382i	0.957475	+	0.288515i	$0.0931614\pi$
$684$	−6.71230	−	5.90812i	−0.256651	−	0.225903i
$685$	−2.59005	−	9.66621i	−0.0989609	−	0.369327i
$686$	0.341365	+	10.7253i	0.0130334	+	0.409492i
$687$	−4.48845	−	7.77422i	−0.171245	−	0.296605i
$688$	18.8863	+	14.6012i	0.720034	+	0.556666i
$689$	9.93089	−	9.93089i	0.378337	−	0.378337i
$690$	0.213639	+	0.344256i	0.00813311	+	0.0131056i
$691$	7.68645	+	13.3133i	0.292406	+	0.506463i	0.974378	−	0.224916i	$-0.0722106\pi$
$691$	7.68645	+	13.3133i	0.292406	+	0.506463i	−0.681972	+	0.731379i	$0.738877\pi$
$692$	24.6747	−	16.4224i	0.937992	−	0.624286i
$693$		−	18.0562i		−	0.685899i
$694$	−16.2016	+	17.2668i	−0.615004	+	0.655440i
$695$	−5.56043	+	5.56043i	−0.210919	+	0.210919i
$696$	−5.26751	+	1.96619i	−0.199664	+	0.0745283i
$697$	−33.2815	−	33.2815i	−1.26063	−	1.26063i
$698$	−25.1968	−	40.6020i	−0.953715	−	1.53681i
$699$	29.5258	+	17.0467i	1.11677	+	0.644766i
$700$	−6.85347	+	0.436709i	−0.259037	+	0.0165060i
$701$	9.42320	+	2.52494i	0.355909	+	0.0953656i	0.432343	−	0.901709i	$-0.357687\pi$
$701$	9.42320	+	2.52494i	0.355909	+	0.0953656i	−0.0764341	+	0.997075i	$0.524353\pi$
$702$	4.99037	+	16.5050i	0.188349	+	0.622940i
$703$	−15.2931	+	7.78298i	−0.576789	+	0.293541i
$704$	−26.0611	+	5.03650i	−0.982213	+	0.189820i
$705$	3.25294	−	12.1401i	0.122513	−	0.457224i
$706$	4.91404	−	20.9890i	0.184942	−	0.789933i
$707$	−2.34783	+	4.06656i	−0.0882992	+	0.152939i
$708$	−10.6884	−	9.40787i	−0.401695	−	0.353569i
$709$	−0.508719	+	0.508719i	−0.0191053	+	0.0191053i	−0.716595	−	0.697490i	$-0.754300\pi$
$709$	−0.508719	+	0.508719i	−0.0191053	+	0.0191053i	0.697490	+	0.716595i	$0.254300\pi$
$710$	−1.58638	+	6.77579i	−0.0595357	+	0.254291i
$711$	3.87106	+	3.87106i	0.145176	+	0.145176i
$712$	1.53549	−	9.14536i	0.0575451	−	0.342737i
$713$	2.08019			0.0779036
$714$	33.2463	−	10.0522i	1.24421	−	0.376195i
$715$	6.42343	−	3.70857i	0.240223	−	0.138693i
$716$	30.4744	−	34.6225i	1.13888	−	1.29390i
$717$	−6.90945	−	6.90945i	−0.258038	−	0.258038i
$718$	0.475494	+	14.9394i	0.0177453	+	0.557534i
$719$	16.3294	−	9.42777i	0.608983	−	0.351596i	−0.163584	−	0.986529i	$-0.552306\pi$
$719$	16.3294	−	9.42777i	0.608983	−	0.351596i	0.772567	+	0.634933i	$0.218972\pi$
$720$	−3.87754	+	5.01550i	−0.144507	+	0.186917i
$721$	7.36482	−	1.97340i	0.274280	−	0.0734932i
$722$	13.2682	−	8.23399i	0.493790	−	0.306437i
$723$	1.74831	+	0.468458i	0.0650204	+	0.0174222i
$724$	14.8870	−	30.0503i	0.553272	−	1.11681i
$725$	1.61412	+	0.432501i	0.0599468	+	0.0160627i
$726$	0.00676450	−	0.0126279i	0.000251054	−	0.000468666i
$727$	−9.29699	−	34.6968i	−0.344806	−	1.28683i	−0.892839	−	0.450377i	$-0.851290\pi$
$727$	−9.29699	−	34.6968i	−0.344806	−	1.28683i	0.548032	−	0.836457i	$-0.315377\pi$
$728$	3.59491	−	21.4112i	0.133236	−	0.793552i
$729$	22.2115			0.822650
$730$	5.24350	−	1.58540i	0.194071	−	0.0586784i
$731$	17.9422	+	31.0767i	0.663615	+	1.14941i
$732$	7.17608	−	35.7375i	0.265236	−	1.32089i
$733$	−16.8215	−	9.71191i	−0.621317	−	0.358718i	0.156064	−	0.987747i	$-0.450119\pi$
$733$	−16.8215	−	9.71191i	−0.621317	−	0.358718i	−0.777382	+	0.629029i	$0.783453\pi$
$734$	1.64682	+	0.882168i	0.0607854	+	0.0325614i
$735$	−1.47484	−	5.50417i	−0.0544002	−	0.203024i
$736$	−1.10378	−	0.798562i	−0.0406858	−	0.0294354i
$737$	16.0837	−	27.8578i	0.592451	−	1.02615i
$738$	0.558156	+	17.5366i	0.0205460	+	0.645530i
$739$	7.17808			0.264050			0.132025	−	0.991246i	$-0.457852\pi$
$739$	7.17808			0.264050			0.132025	+	0.991246i	$0.457852\pi$
$740$	6.19615	+	10.4694i	0.227775	+	0.384862i
$741$	7.50193			0.275590
$742$	0.970506	+	30.4921i	0.0356284	+	1.11940i
$743$	16.4728	−	28.5317i	0.604328	−	1.04673i	−0.387830	−	0.921731i	$-0.626775\pi$
$743$	16.4728	−	28.5317i	0.604328	−	1.04673i	0.992157	−	0.124995i	$-0.0398915\pi$
$744$	−10.1630	−	27.2269i	−0.372592	−	0.998188i
$745$	4.59275	+	17.1404i	0.168265	+	0.627975i
$746$	13.2089	+	7.07575i	0.483614	+	0.259061i
$747$	6.33346	+	3.65662i	0.231729	+	0.133789i
$748$	−39.1184	−	7.85496i	−1.43031	−	0.287206i
$749$	−11.8377	−	20.5035i	−0.432539	−	0.749180i
$750$	−1.61032	+	0.486891i	−0.0588007	+	0.0177787i
$751$	−12.0486			−0.439659			−0.219829	−	0.975538i	$-0.570550\pi$
$751$	−12.0486			−0.439659			−0.219829	+	0.975538i	$0.570550\pi$
$752$	5.36411	+	41.9198i	0.195609	+	1.52866i
$753$	−0.541334	−	2.02029i	−0.0197273	−	0.0736233i
$754$	−2.49460	+	4.65690i	−0.0908480	+	0.169594i
$755$	7.21037	+	1.93201i	0.262412	+	0.0703132i
$756$	−33.5626	−	16.6270i	−1.22066	−	0.604719i
$757$	20.8469	+	5.58590i	0.757692	+	0.203023i	0.616927	−	0.787020i	$-0.288377\pi$
$757$	20.8469	+	5.58590i	0.757692	+	0.203023i	0.140765	+	0.990043i	$0.455044\pi$
$758$	−24.7125	+	15.3362i	−0.897600	+	0.557034i
$759$	0.918161	−	0.246021i	0.0333271	−	0.00892998i
$760$	4.62995	+	6.49839i	0.167946	+	0.235721i
$761$	−1.01649	+	0.586873i	−0.0368479	+	0.0212741i	−0.518311	−	0.855192i	$-0.673439\pi$
$761$	−1.01649	+	0.586873i	−0.0368479	+	0.0212741i	0.481463	+	0.876466i	$0.340106\pi$
$762$	0.929191	+	29.1940i	0.0336610	+	1.05759i
$763$	35.7126	+	35.7126i	1.29288	+	1.29288i
$764$	4.17661	+	3.67622i	0.151104	+	0.133001i
$765$	−8.25282	+	4.76477i	−0.298381	+	0.172270i
$766$	−20.0120	+	6.05074i	−0.723062	+	0.218622i
$767$	−13.3792			−0.483094
$768$	−5.05953	+	18.3485i	−0.182570	+	0.662094i
$769$	−19.6979	−	19.6979i	−0.710324	−	0.710324i	0.256279	−	0.966603i	$-0.417504\pi$
$769$	−19.6979	−	19.6979i	−0.710324	−	0.710324i	−0.966603	+	0.256279i	$0.917504\pi$
$770$	−3.67281	+	15.6874i	−0.132359	+	0.565336i
$771$	−16.7405	+	16.7405i	−0.602895	+	0.602895i
$772$	−0.711971	+	0.808881i	−0.0256244	+	0.0291123i
$773$	−18.6385	+	32.2828i	−0.670380	+	1.16113i	0.307417	+	0.951575i	$0.400535\pi$
$773$	−18.6385	+	32.2828i	−0.670380	+	1.16113i	−0.977796	+	0.209557i	$0.932798\pi$
$774$	3.04937	−	13.0246i	0.109607	−	0.468159i
$775$	−2.23553	+	8.34312i	−0.0803027	+	0.299694i
$776$	−14.0507	+	17.0261i	−0.504391	+	0.611201i
$777$	−18.4721	+	16.6163i	−0.662682	+	0.596107i
$778$	10.2497	+	33.8995i	0.367470	+	1.21536i
$779$	21.3304	+	5.71546i	0.764241	+	0.204778i
$780$	−0.338218	−	5.30781i	−0.0121101	−	0.190050i
$781$	14.1393	+	8.16333i	0.505944	+	0.292107i
$782$	−1.07983	−	1.74003i	−0.0386148	−	0.0622235i
$783$	6.44465	+	6.44465i	0.230313	+	0.230313i
$784$	11.6091	+	15.2435i	0.414611	+	0.544412i
$785$	15.7970	−	15.7970i	0.563819	−	0.563819i
$786$	−0.170900	+	0.182136i	−0.00609580	+	0.00649659i
$787$			49.3925i			1.76065i	0.474370	+	0.880326i	$0.342676\pi$
$787$			49.3925i			1.76065i	−0.474370	+	0.880326i	$0.657324\pi$
$788$	15.0958	+	22.6814i	0.537764	+	0.807992i
$789$	−1.56405	−	2.70902i	−0.0556818	−	0.0964437i
$790$	−2.57581	−	4.15063i	−0.0916431	−	0.147673i
$791$	−0.135187	+	0.135187i	−0.00480671	+	0.00480671i
$792$	8.63049	+	12.1134i	0.306671	+	0.430429i
$793$	−17.1248	−	29.6610i	−0.608119	−	1.05329i
$794$	0.760272	+	23.8868i	0.0269810	+	0.847711i
$795$	1.93429	+	7.21886i	0.0686021	+	0.256027i
$796$	0.531896	−	0.604295i	0.0188526	−	0.0214187i
$797$	7.84495	−	29.2777i	0.277882	−	1.03707i	−0.676003	−	0.736899i	$-0.736289\pi$
$797$	7.84495	−	29.2777i	0.277882	−	1.03707i	0.953885	−	0.300172i	$-0.0970440\pi$
$798$	−11.1505	+	11.8836i	−0.394723	+	0.420676i
$799$	−16.4419	+	61.3621i	−0.581673	+	2.17083i
$800$	4.38905	−	3.56879i	0.155176	−	0.126176i
$801$	−5.01924	+	1.34490i	−0.177346	+	0.0475197i
$802$	−16.4564	−	15.4412i	−0.581097	−	0.545248i
$803$		−	12.8519i		−	0.453533i
$804$	−12.7800	−	19.2020i	−0.450717	−	0.677204i
$805$	−0.716157	+	0.413474i	−0.0252412	+	0.0145730i
$806$	−24.0708	−	12.8942i	−0.847858	−	0.454179i
$807$	14.9464	−	25.8880i	0.526140	−	0.911301i
$808$	−0.368644	−	3.85034i	−0.0129688	−	0.135455i
$809$	−21.4752	+	5.75427i	−0.755029	+	0.202309i	−0.615748	−	0.787943i	$-0.711146\pi$
$809$	−21.4752	+	5.75427i	−0.755029	+	0.202309i	−0.139281	+	0.990253i	$0.544479\pi$
$810$	−2.38685	−	0.558819i	−0.0838653	−	0.0196349i
$811$	19.7725	+	11.4157i	0.694308	+	0.400859i	0.805224	−	0.592971i	$-0.202045\pi$
$811$	19.7725	+	11.4157i	0.694308	+	0.400859i	−0.110916	+	0.993830i	$0.535378\pi$
$812$	−3.66903	−	10.8734i	−0.128758	−	0.381582i
$813$		−	12.4164i		−	0.435460i
$814$	27.7184	−	6.80600i	0.971529	−	0.238550i
$815$			14.5119i			0.508330i
$816$	−17.4992	+	22.6348i	−0.612594	+	0.792375i
$817$	−14.5805	−	8.41806i	−0.510107	−	0.294511i
$818$	−12.1786	+	52.0178i	−0.425816	+	1.81876i
$819$	−11.7511	+	3.14869i	−0.410616	+	0.110024i
$820$	3.08218	−	15.3495i	0.107634	−	0.536028i
$821$	−8.30215	+	14.3798i	−0.289747	+	0.501857i	−0.973749	−	0.227623i	$-0.926905\pi$
$821$	−8.30215	+	14.3798i	−0.289747	+	0.501857i	0.684002	+	0.729480i	$0.260238\pi$
$822$	−7.94958	+	14.8402i	−0.277274	+	0.517612i
$823$	−12.3141	+	7.10957i	−0.429244	+	0.247824i	−0.699024	−	0.715098i	$-0.746382\pi$
$823$	−12.3141	+	7.10957i	−0.429244	+	0.247824i	0.269781	+	0.962922i	$0.413049\pi$
$824$	−3.99759	+	4.84412i	−0.139263	+	0.168753i
$825$			3.94692i			0.137414i
$826$	19.8861	−	21.1936i	0.691927	−	0.737421i
$827$	25.7942	−	6.91152i	0.896951	−	0.240337i	0.219244	−	0.975670i	$-0.429641\pi$
$827$	25.7942	−	6.91152i	0.896951	−	0.240337i	0.677706	+	0.735333i	$0.262974\pi$
$828$	−0.150290	+	0.748454i	−0.00522292	+	0.0260106i
$829$	−0.957307	+	3.57272i	−0.0332486	+	0.124086i	−0.980556	−	0.196242i	$-0.937126\pi$
$829$	−0.957307	+	3.57272i	−0.0332486	+	0.124086i	0.947307	+	0.320327i	$0.103793\pi$
$830$	−4.75878	−	4.46520i	−0.165180	−	0.154989i
$831$	−1.45987	+	5.44832i	−0.0506424	+	0.189000i
$832$	7.82238	+	16.0824i	0.271192	+	0.557557i
$833$	7.45453	+	27.8207i	0.258284	+	0.963929i
$834$	13.2225	−	0.420846i	0.457856	−	0.0145727i
$835$	11.3783	+	19.7078i	0.393761	+	0.682015i
$836$	17.7372	−	5.98510i	0.613456	−	0.206999i
$837$	−33.3114	+	33.3114i	−1.15141	+	1.15141i
$838$	−25.0210	+	15.5276i	−0.864338	+	0.536393i
$839$	23.0156	+	39.8642i	0.794588	+	1.37627i	0.923101	+	0.384559i	$0.125646\pi$
$839$	23.0156	+	39.8642i	0.794588	+	1.37627i	−0.128513	+	0.991708i	$0.541020\pi$
$840$	8.91070	+	7.35351i	0.307448	+	0.253720i
$841$		−	26.2076i		−	0.903709i
$842$	−17.6150	−	16.5282i	−0.607052	−	0.569601i
$843$	−17.3045	+	17.3045i	−0.595998	+	0.595998i
$844$	−2.86978	−	45.0367i	−0.0987817	−	1.55023i
$845$	5.65870	+	5.65870i	0.194665	+	0.194665i
$846$	20.1214	−	12.4870i	0.691789	−	0.429312i
$847$	0.0253218	+	0.0146196i	0.000870068	+	0.000502334i
$848$	−15.2257	−	19.9923i	−0.522851	−	0.686539i
$849$	−2.24381	−	0.601228i	−0.0770074	−	0.0206341i
$850$	8.13934	−	2.46098i	0.279177	−	0.0844108i
$851$	1.22821	+	0.798449i	0.0421026	+	0.0273705i
$852$	9.74605	−	6.48655i	0.333894	−	0.222225i
$853$	−6.76234	+	25.2374i	−0.231538	+	0.864112i	0.748141	+	0.663540i	$0.230947\pi$
$853$	−6.76234	+	25.2374i	−0.231538	+	0.864112i	−0.979679	+	0.200572i	$0.935720\pi$
$854$	72.4388	+	16.9597i	2.47880	+	0.580349i
$855$	2.23552	−	3.87204i	0.0764532	−	0.132421i
$856$	17.7417	+	8.09698i	0.606400	+	0.276749i
$857$	−31.2698	+	31.2698i	−1.06815	+	1.06815i	−0.0706539	+	0.997501i	$0.522509\pi$
$857$	−31.2698	+	31.2698i	−1.06815	+	1.06815i	−0.997501	+	0.0706539i	$0.977491\pi$
$858$	−12.1495	−	2.84448i	−0.414776	−	0.0971091i
$859$	5.41950	+	5.41950i	0.184911	+	0.184911i	0.793492	−	0.608581i	$-0.208261\pi$
$859$	5.41950	+	5.41950i	0.184911	+	0.184911i	−0.608581	+	0.793492i	$0.708261\pi$
$860$	−5.29865	+	10.6956i	−0.180683	+	0.364718i
$861$	31.9744			1.08968
$862$	−8.18239	−	27.0621i	−0.278693	−	0.921740i
$863$	−6.29574	+	3.63484i	−0.214309	+	0.123732i	−0.603313	−	0.797505i	$-0.706153\pi$
$863$	−6.29574	+	3.63484i	−0.214309	+	0.123732i	0.389003	+	0.921236i	$0.372820\pi$
$864$	30.4635	−	4.88764i	1.03639	−	0.166281i
$865$	10.4794	+	10.4794i	0.356309	+	0.356309i
$866$	−39.8972	+	1.26985i	−1.35576	+	0.0431514i
$867$	−19.7311	+	11.3918i	−0.670105	+	0.386885i
$868$	56.2031	−	18.9647i	1.90766	−	0.643703i
$869$	−11.0701	+	2.96622i	−0.375527	+	0.100622i
$870$	−1.48236	−	2.38867i	−0.0502568	−	0.0809834i
$871$	−20.9347	−	5.60944i	−0.709346	−	0.190069i
$872$	−41.0284	−	6.88862i	−1.38940	−	0.233278i
$873$	11.9482	+	3.20152i	0.404386	+	0.108355i
$874$	0.846951	+	0.453693i	0.0286485	+	0.0153464i
$875$	−0.888704	−	3.31669i	−0.0300437	−	0.112124i
$876$	−8.25785	−	4.09097i	−0.279007	−	0.138221i
$877$	−35.1490			−1.18690			−0.593449	−	0.804871i	$-0.702234\pi$
$877$	−35.1490			−1.18690			−0.593449	+	0.804871i	$0.702234\pi$
$878$	−6.26600	−	20.7239i	−0.211467	−	0.699398i
$879$	−18.6552	−	32.3118i	−0.629226	−	1.08985i
$880$	−5.03429	−	12.2797i	−0.169706	−	0.413950i
$881$	27.6994	+	15.9923i	0.933217	+	0.538793i	0.887827	−	0.460177i	$-0.152214\pi$
$881$	27.6994	+	15.9923i	0.933217	+	0.538793i	0.0453892	+	0.998969i	$0.485547\pi$
$882$	5.06984	−	9.46433i	0.170710	−	0.318680i
$883$	−9.35604	−	34.9172i	−0.314856	−	1.17506i	−0.924124	−	0.382093i	$-0.875203\pi$
$883$	−9.35604	−	34.9172i	−0.314856	−	1.17506i	0.609268	−	0.792964i	$-0.291463\pi$
$884$	1.70951	+	26.8282i	0.0574972	+	0.902331i
$885$	3.55976	−	6.16569i	0.119660	−	0.207257i
$886$	−56.0695	+	1.78459i	−1.88369	+	0.0599544i
$887$	−16.7732			−0.563188			−0.281594	−	0.959534i	$-0.590863\pi$
$887$	−16.7732			−0.563188			−0.281594	+	0.959534i	$0.590863\pi$
$888$	4.45010	−	19.9766i	0.149336	−	0.670372i
$889$	−59.6164			−1.99947
$890$	4.63433	−	0.147502i	0.155343	−	0.00494428i
$891$	−2.87562	+	4.98073i	−0.0963371	+	0.166861i
$892$	3.37175	+	52.9145i	0.112895	+	1.77171i
$893$	−7.71418	−	28.7897i	−0.258145	−	0.963411i
$894$	14.0964	−	26.3151i	0.471455	−	0.880107i
$895$	19.9722	+	11.5310i	0.667597	+	0.385437i
$896$	−37.1026	−	11.5128i	−1.23951	−	0.384617i
$897$	−0.320223	−	0.554643i	−0.0106919	−	0.0185190i
$898$	2.82136	+	9.33126i	0.0941500	+	0.311388i
$899$	−14.4336			−0.481389
$900$	−2.84036	−	1.40712i	−0.0946786	−	0.0469041i
$901$	−9.77681	−	36.4876i	−0.325713	−	1.21558i
$902$	−32.3777	−	17.3440i	−1.07806	−	0.577494i
$903$	−23.5469	−	6.30936i	−0.783590	−	0.209962i
$904$	0.0260763	−	0.155310i	0.000867286	−	0.00516553i
$905$	16.1965	+	4.33984i	0.538389	+	0.144261i
$906$	−6.62183	−	10.6703i	−0.219996	−	0.354499i
$907$	−20.1615	+	5.40225i	−0.669451	+	0.179379i	−0.577508	−	0.816385i	$-0.695975\pi$
$907$	−20.1615	+	5.40225i	−0.669451	+	0.179379i	−0.0919435	+	0.995764i	$0.529308\pi$
$908$	−24.2579	+	8.18537i	−0.805026	+	0.271641i
$909$	−1.87702	+	1.08370i	−0.0622567	+	0.0359439i
$910$	10.8499	−	0.345333i	0.359672	−	0.0114477i
$911$	39.2309	+	39.2309i	1.29978	+	1.29978i	0.928537	+	0.371240i	$0.121067\pi$
$911$	39.2309	+	39.2309i	1.29978	+	1.29978i	0.371240	+	0.928537i	$0.378933\pi$
$912$	1.80040	−	13.3021i	0.0596172	−	0.440475i
$913$	−13.2588	+	7.65496i	−0.438801	+	0.253342i
$914$	−3.24478	−	10.7316i	−0.107328	−	0.354971i
$915$	18.2254			0.602513
$916$	−6.69982	+	13.5240i	−0.221368	+	0.446844i
$917$	−0.360463	−	0.360463i	−0.0119035	−	0.0119035i
$918$	45.1565	+	10.5722i	1.49039	+	0.348936i
$919$	−35.1073	+	35.1073i	−1.15808	+	1.15808i	−0.173196	+	0.984887i	$0.555409\pi$
$919$	−35.1073	+	35.1073i	−1.15808	+	1.15808i	−0.984887	+	0.173196i	$0.944591\pi$
$920$	0.282816	−	0.619695i	0.00932417	−	0.0204307i
$921$	−4.33569	+	7.50964i	−0.142866	+	0.247451i
$922$	−24.9416	−	5.83944i	−0.821408	−	0.192312i
$923$	2.84709	−	10.6255i	0.0937131	−	0.349742i
$924$	22.5642	−	15.0178i	0.742309	−	0.494049i
$925$	−4.52232	+	4.06800i	−0.148693	+	0.133755i
$926$	56.8215	−	17.1803i	1.86727	−	0.564580i
$927$	3.39941	+	0.910868i	0.111651	+	0.0299168i
$928$	7.65871	+	5.54092i	0.251409	+	0.181890i
$929$	45.4936	+	26.2657i	1.49260	+	0.861751i	0.999964	−	0.00848584i	$-0.00270116\pi$
$929$	45.4936	+	26.2657i	1.49260	+	0.861751i	0.492633	+	0.870237i	$0.336034\pi$
$930$	12.3467	−	7.66212i	0.404863	−	0.251251i
$931$	−9.55534	−	9.55534i	−0.313164	−	0.313164i
$932$	−3.64509	−	57.2041i	−0.119399	−	1.87378i
$933$	−7.22890	+	7.22890i	−0.236663	+	0.236663i
$934$	−21.5697	−	20.2390i	−0.705782	−	0.662241i
$935$		−	19.9496i		−	0.652422i
$936$	6.37843	−	7.72913i	0.208486	−	0.252635i
$937$	25.1486	+	43.5587i	0.821569	+	1.42300i	0.904513	+	0.426445i	$0.140234\pi$
$937$	25.1486	+	43.5587i	0.821569	+	1.42300i	−0.0829444	+	0.996554i	$0.526432\pi$
$938$	40.0021	−	24.8246i	1.30612	−	0.810552i
$939$	2.00720	−	2.00720i	0.0655025	−	0.0655025i
$940$	−20.0217	+	6.75595i	−0.653036	+	0.220355i
$941$	−22.5576	−	39.0708i	−0.735355	−	1.27367i	−0.954567	−	0.297996i	$-0.903682\pi$
$941$	−22.5576	−	39.0708i	−0.735355	−	1.27367i	0.219212	−	0.975677i	$-0.429651\pi$
$942$	−37.5646	+	1.19561i	−1.22392	+	0.0389551i
$943$	−0.487934	−	1.82100i	−0.0158893	−	0.0592998i
$944$	−3.21089	+	23.7233i	−0.104505	+	0.772128i
$945$	4.84708	−	18.0896i	0.157676	−	0.588453i
$946$	20.4215	+	19.1616i	0.663959	+	0.622997i
$947$	−2.80777	+	10.4787i	−0.0912402	+	0.340513i	−0.996423	−	0.0845103i	$-0.973067\pi$
$947$	−2.80777	+	10.4787i	−0.0912402	+	0.340513i	0.905182	+	0.425023i	$0.139734\pi$
$948$	−1.61788	+	8.05718i	−0.0525464	+	0.261685i
$949$	−8.36407	+	2.24115i	−0.271509	+	0.0727507i
$950$	−2.72986	+	2.90934i	−0.0885682	+	0.0943915i
$951$		−	16.3682i		−	0.530774i
$952$	−45.0389	−	37.1681i	−1.45972	−	1.20463i
$953$	27.4554	−	15.8514i	0.889366	−	0.513476i	0.0156312	−	0.999878i	$-0.495024\pi$
$953$	27.4554	−	15.8514i	0.889366	−	0.513476i	0.873735	+	0.486402i	$0.161691\pi$
$954$	−6.64923	+	12.4127i	−0.215277	+	0.401877i
$955$	−1.39101	+	2.40931i	−0.0450121	+	0.0779633i
$956$	−3.23426	+	16.1069i	−0.104603	+	0.520933i
$957$	−6.37078	+	1.70705i	−0.205938	+	0.0551810i
$958$	−8.78276	+	37.5132i	−0.283758	+	1.21200i
$959$	−29.7580	−	17.1808i	−0.960936	−	0.554797i
$960$	−9.49273	−	0.674119i	−0.306377	−	0.0217571i
$961$		−	43.6053i		−	1.40662i
$962$	−9.26299	−	16.8524i	−0.298651	−	0.543344i
$963$		−	10.9279i		−	0.352147i
$964$	−0.972929	−	2.88334i	−0.0313359	−	0.0928661i
$965$	−0.466608	−	0.269396i	−0.0150207	−	0.00867218i
$966$	1.35456	+	0.317136i	0.0435823	+	0.0102037i
$967$	−28.5989	+	7.66305i	−0.919679	+	0.246427i	−0.687448	−	0.726234i	$-0.741269\pi$
$967$	−28.5989	+	7.66305i	−0.919679	+	0.246427i	−0.232231	+	0.972661i	$0.574602\pi$
$968$	−0.0239755	+	0.00229549i	−0.000770601	+	7.37797e-5i
$969$	10.0888	−	17.4744i	0.324100	−	0.561357i
$970$	−9.72953	−	5.21190i	−0.312396	−	0.167344i
$971$	35.7358	−	20.6320i	1.14682	−	0.662114i	0.198706	−	0.980059i	$-0.436326\pi$
$971$	35.7358	−	20.6320i	1.14682	−	0.662114i	0.948109	+	0.317945i	$0.102993\pi$
$972$	−15.8465	−	23.8093i	−0.508275	−	0.763685i
$973$			27.0013i			0.865621i
$974$	32.2559	+	30.2659i	1.03355	+	0.969783i
$975$	2.56868	−	0.688275i	0.0822635	−	0.0220424i
$976$	−56.7033	+	23.2465i	−1.81503	+	0.744102i
$977$	10.8566	−	40.5174i	0.347333	−	1.29626i	−0.542530	−	0.840037i	$-0.682533\pi$
$977$	10.8566	−	40.5174i	0.347333	−	1.29626i	0.889863	−	0.456228i	$-0.150800\pi$
$978$	16.7052	−	17.8035i	0.534172	−	0.569293i
$979$	2.81548	−	10.5075i	0.0899832	−	0.335822i
$980$	−6.32987	+	7.19146i	−0.202200	+	0.229723i
$981$	6.03357	+	22.5176i	0.192637	+	0.718931i
$982$	0.0355150	+	1.11584i	0.00113333	+	0.0356078i
$983$	−15.0226	−	26.0198i	−0.479145	−	0.829904i	0.520569	−	0.853820i	$-0.325720\pi$
$983$	−15.0226	−	26.0198i	−0.479145	−	0.829904i	−0.999714	+	0.0239157i	$0.992387\pi$
$984$	−21.4506	+	15.2831i	−0.683821	+	0.487207i
$985$	−9.63281	+	9.63281i	−0.306927	+	0.306927i
$986$	7.49257	+	12.0735i	0.238612	+	0.384497i
$987$	−21.5780	−	37.3741i	−0.686834	−	1.18963i
$988$	−6.98821	−	10.4998i	−0.222325	−	0.334043i
$989$			1.43732i			0.0457040i
$990$	−5.08860	+	5.42317i	−0.161726	+	0.172360i
$991$	6.59064	−	6.59064i	0.209359	−	0.209359i	−0.594636	−	0.803995i	$-0.702704\pi$
$991$	6.59064	−	6.59064i	0.209359	−	0.209359i	0.803995	+	0.594636i	$0.202704\pi$
$992$	−28.6402	+	39.5867i	−0.909328	+	1.25688i
$993$	24.4006	+	24.4006i	0.774331	+	0.774331i
$994$	12.5998	+	20.3032i	0.399642	+	0.643979i
$995$	0.348592	+	0.201260i	0.0110511	+	0.00638036i
$996$	0.698125	+	10.9560i	0.0221209	+	0.347154i
$997$	45.5835	+	12.2141i	1.44364	+	0.386823i	0.893808	−	0.448450i	$-0.148024\pi$
$997$	45.5835	+	12.2141i	1.44364	+	0.386823i	0.549835	+	0.835273i	$0.314690\pi$
$998$	7.05445	+	23.3316i	0.223305	+	0.738549i
$999$	−32.4543	+	6.88213i	−1.02681	+	0.217741i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.be.a.251.3	yes	304
4.3	odd	2	inner	740.2.be.a.251.63	yes	304
37.23	odd	12	inner	740.2.be.a.171.63	yes	304
148.23	even	12	inner	740.2.be.a.171.3	✓	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.be.a.171.3	✓	304	148.23	even	12	inner
740.2.be.a.171.63	yes	304	37.23	odd	12	inner
740.2.be.a.251.3	yes	304	1.1	even	1	trivial
740.2.be.a.251.63	yes	304	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41350 + 0.0449890i) q^{2} +(-0.594790 + 1.03021i) q^{3} +(1.99595 - 0.127184i) q^{4} +(0.258819 + 0.965926i) q^{5} +(0.794386 - 1.48295i) q^{6} +(2.97366 + 1.71684i) q^{7} +(-2.81555 + 0.269570i) q^{8} +(0.792450 + 1.37256i) q^{9} +(-0.409296 - 1.35369i) q^{10} -3.31791 q^{11} +(-1.05615 + 2.13189i) q^{12} +(0.578586 + 2.15931i) q^{13} +(-4.28050 - 2.29297i) q^{14} +(-1.14905 - 0.307886i) q^{15} +(3.96765 - 0.507705i) q^{16} +(5.80783 + 1.55620i) q^{17} +(-1.18188 - 1.90446i) q^{18} +(-2.72490 + 0.730135i) q^{19} +(0.639440 + 1.89502i) q^{20} +(-3.53741 + 2.04232i) q^{21} +(4.68986 - 0.149269i) q^{22} +(0.170295 + 0.170295i) q^{23} +(1.39695 - 3.06094i) q^{24} +(-0.866025 + 0.500000i) q^{25} +(-0.914976 - 3.02615i) q^{26} -5.45410 q^{27} +(6.15364 + 3.04854i) q^{28} +(-1.18161 - 1.18161i) q^{29} +(1.63803 + 0.383502i) q^{30} +(6.10759 - 6.10759i) q^{31} +(-5.58542 + 0.896140i) q^{32} +(1.97346 - 3.41813i) q^{33} +(-8.27936 - 1.93840i) q^{34} +(-0.888704 + 3.31669i) q^{35} +(1.75626 + 2.63878i) q^{36} +(5.95044 - 1.26183i) q^{37} +(3.81880 - 1.15464i) q^{38} +(-2.56868 - 0.688275i) q^{39} +(-0.989103 - 2.64984i) q^{40} +(-6.77920 - 3.91397i) q^{41} +(4.90823 - 3.04596i) q^{42} +(4.22007 + 4.22007i) q^{43} +(-6.62239 + 0.421984i) q^{44} +(-1.12069 + 1.12069i) q^{45} +(-0.248373 - 0.233050i) q^{46} +10.5654i q^{47} +(-1.83688 + 4.38948i) q^{48} +(2.39510 + 4.14844i) q^{49} +(1.20163 - 0.745710i) q^{50} +(-5.05765 + 5.05765i) q^{51} +(1.42946 + 4.23630i) q^{52} +(-3.14124 - 5.44079i) q^{53} +(7.70936 - 0.245375i) q^{54} +(-0.858738 - 3.20485i) q^{55} +(-8.83530 - 4.03225i) q^{56} +(0.868555 - 3.24149i) q^{57} +(1.72337 + 1.61705i) q^{58} +(-1.54901 + 5.78097i) q^{59} +(-2.33260 - 0.468386i) q^{60} +(-14.7988 + 3.96533i) q^{61} +(-8.35829 + 8.90784i) q^{62} +5.44205i q^{63} +(7.85466 - 1.51797i) q^{64} +(-1.93599 + 1.11774i) q^{65} +(-2.63570 + 4.92030i) q^{66} +(-4.84754 + 8.39619i) q^{67} +(11.7901 + 2.36744i) q^{68} +(-0.276729 + 0.0741493i) q^{69} +(1.10697 - 4.72811i) q^{70} +(-4.26151 - 2.46038i) q^{71} +(-2.60118 - 3.65090i) q^{72} +3.87349i q^{73} +(-8.35417 + 2.05129i) q^{74} -1.18958i q^{75} +(-5.34591 + 1.80388i) q^{76} +(-9.86633 - 5.69633i) q^{77} +(3.66178 + 0.857313i) q^{78} +(3.33647 - 0.894004i) q^{79} +(1.51731 + 3.70105i) q^{80} +(0.866698 - 1.50117i) q^{81} +(9.75847 + 5.22740i) q^{82} +(3.99613 - 2.30716i) q^{83} +(-6.80074 + 4.52628i) q^{84} +6.01270i q^{85} +(-6.15492 - 5.77521i) q^{86} +(1.92012 - 0.514495i) q^{87} +(9.34174 - 0.894407i) q^{88} +(-0.848572 + 3.16691i) q^{89} +(1.53368 - 1.63452i) q^{90} +(-1.98668 + 7.41441i) q^{91} +(0.361560 + 0.318242i) q^{92} +(2.65935 + 9.92481i) q^{93} +(-0.475327 - 14.9342i) q^{94} +(-1.41051 - 2.44308i) q^{95} +(2.39894 - 6.28715i) q^{96} +(5.51878 - 5.51878i) q^{97} +(-3.57211 - 5.75606i) q^{98} +(-2.62928 - 4.55404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q + 4 q^{2} - 12 q^{4} - 8 q^{8} - 152 q^{9} + 16 q^{13} - 24 q^{14} + 20 q^{16} - 60 q^{18} - 16 q^{22} - 24 q^{24} - 32 q^{29} - 56 q^{32} - 32 q^{37} + 40 q^{38} + 20 q^{42} + 12 q^{44} - 8 q^{46}+ \cdots - 36 q^{98}+O(q^{100}) \) 304 * q + 4 * q^2 - 12 * q^4 - 8 * q^8 - 152 * q^9 + 16 * q^13 - 24 * q^14 + 20 * q^16 - 60 * q^18 - 16 * q^22 - 24 * q^24 - 32 * q^29 - 56 * q^32 - 32 * q^37 + 40 * q^38 + 20 * q^42 + 12 * q^44 - 8 * q^46 + 104 * q^49 + 4 * q^50 - 40 * q^52 + 40 * q^54 + 4 * q^56 - 48 * q^57 - 12 * q^58 - 28 * q^60 - 16 * q^61 - 60 * q^62 + 24 * q^65 - 52 * q^66 - 200 * q^68 - 196 * q^72 + 20 * q^74 - 40 * q^76 + 96 * q^77 - 48 * q^78 - 152 * q^81 + 32 * q^82 - 112 * q^84 + 12 * q^88 - 8 * q^89 + 140 * q^92 - 16 * q^93 - 28 * q^94 - 132 * q^96 + 48 * q^97 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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