LMFDB - Embedded newform 75.2.l.a.8.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [75,2,Mod(2,75)] 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("75.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(75, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	75.l (of order $20$, degree $8$, 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:	$0.598878015160$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			8.3
Character	$\chi$	$=$	75.8
Dual form			75.2.l.a.47.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.674175 + 1.32314i) q^{2} +(-0.140417 + 1.72635i) q^{3} +(-0.120624 - 0.166024i) q^{4} +(1.20181 - 1.88564i) q^{5} +(-2.18954 - 1.34965i) q^{6} +(-1.72218 + 1.72218i) q^{7} +(-2.63243 + 0.416937i) q^{8} +(-2.96057 - 0.484816i) q^{9} +(1.68474 + 2.86142i) q^{10} +(3.72206 - 1.20937i) q^{11} +(0.303553 - 0.184926i) q^{12} +(5.20313 - 2.65113i) q^{13} +(-1.11764 - 3.43974i) q^{14} +(3.08653 + 2.33952i) q^{15} +(1.34989 - 4.15452i) q^{16} +(0.120501 + 0.760813i) q^{17} +(2.63742 - 3.59040i) q^{18} +(-2.08083 + 2.86402i) q^{19} +(-0.458029 + 0.0279236i) q^{20} +(-2.73126 - 3.21491i) q^{21} +(-0.909148 + 5.74013i) q^{22} +(0.926047 + 0.471845i) q^{23} +(-0.350141 - 4.60305i) q^{24} +(-2.11130 - 4.53237i) q^{25} +8.67180i q^{26} +(1.25268 - 5.04290i) q^{27} +(0.493660 + 0.0781880i) q^{28} +(0.111964 - 0.0813465i) q^{29} +(-5.17638 + 2.50667i) q^{30} +(0.372717 + 0.270795i) q^{31} +(0.817733 + 0.817733i) q^{32} +(1.56516 + 6.59538i) q^{33} +(-1.08790 - 0.353481i) q^{34} +(1.17768 + 5.31715i) q^{35} +(0.276623 + 0.550006i) q^{36} +(-2.32130 - 4.55581i) q^{37} +(-2.38666 - 4.68409i) q^{38} +(3.84616 + 9.35468i) q^{39} +(-2.37749 + 5.46491i) q^{40} +(-6.18190 - 2.00862i) q^{41} +(6.09513 - 1.44644i) q^{42} +(-5.58451 - 5.58451i) q^{43} +(-0.649753 - 0.472073i) q^{44} +(-4.47223 + 4.99992i) q^{45} +(-1.24864 + 0.907186i) q^{46} +(-3.97607 - 0.629748i) q^{47} +(6.98261 + 2.91374i) q^{48} +1.06819i q^{49} +(7.42036 + 0.262057i) q^{50} +(-1.33035 + 0.101196i) q^{51} +(-1.06777 - 0.544057i) q^{52} +(-0.459763 + 2.90283i) q^{53} +(5.82795 + 5.05726i) q^{54} +(2.19277 - 8.47190i) q^{55} +(3.81549 - 5.25157i) q^{56} +(-4.65212 - 3.99440i) q^{57} +(0.0321498 + 0.202986i) q^{58} +(0.855253 - 2.63220i) q^{59} +(0.0161091 - 0.794640i) q^{60} +(1.24058 + 3.81812i) q^{61} +(-0.609576 + 0.310595i) q^{62} +(5.93357 - 4.26369i) q^{63} +(6.67577 - 2.16909i) q^{64} +(1.25410 - 12.9974i) q^{65} +(-9.78182 - 2.37552i) q^{66} +(1.92228 - 0.304459i) q^{67} +(0.111778 - 0.111778i) q^{68} +(-0.944601 + 1.53243i) q^{69} +(-7.82932 - 2.02645i) q^{70} +(2.08859 + 2.87469i) q^{71} +(7.99563 + 0.0418786i) q^{72} +(-5.44405 + 10.6846i) q^{73} +7.59295 q^{74} +(8.12092 - 3.00843i) q^{75} +0.726495 q^{76} +(-4.32730 + 8.49280i) q^{77} +(-14.9706 - 1.21766i) q^{78} +(0.518361 + 0.713462i) q^{79} +(-6.21164 - 7.53835i) q^{80} +(8.52991 + 2.87066i) q^{81} +(6.82537 - 6.82537i) q^{82} +(-9.43448 + 1.49428i) q^{83} +(-0.204298 + 0.841250i) q^{84} +(1.57944 + 0.687132i) q^{85} +(11.1540 - 3.62417i) q^{86} +(0.124711 + 0.204711i) q^{87} +(-9.29383 + 4.73545i) q^{88} +(-3.64270 - 11.2111i) q^{89} +(-3.60053 - 9.28821i) q^{90} +(-4.39501 + 13.5264i) q^{91} +(-0.0333656 - 0.210662i) q^{92} +(-0.519822 + 0.605416i) q^{93} +(3.51381 - 4.83635i) q^{94} +(2.89976 + 7.36572i) q^{95} +(-1.52652 + 1.29687i) q^{96} +(2.54554 - 16.0719i) q^{97} +(-1.41336 - 0.720145i) q^{98} +(-11.6057 + 1.77590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9} - 20 q^{10} - 10 q^{12} - 20 q^{13} - 10 q^{15} - 8 q^{16} - 10 q^{18} - 6 q^{21} + 20 q^{22} + 40 q^{25} - 10 q^{27} + 40 q^{28} - 10 q^{30} - 12 q^{31}+ \cdots + 120 q^{97}+O(q^{100}) $ 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9 - 20 * q^10 - 10 * q^12 - 20 * q^13 - 10 * q^15 - 8 * q^16 - 10 * q^18 - 6 * q^21 + 20 * q^22 + 40 * q^25 - 10 * q^27 + 40 * q^28 - 10 * q^30 - 12 * q^31 - 10 * q^33 + 20 * q^34 - 22 * q^36 - 20 * q^37 + 30 * q^39 - 20 * q^40 + 90 * q^42 - 20 * q^43 + 70 * q^45 - 12 * q^46 + 100 * q^48 - 16 * q^51 + 20 * q^52 + 120 * q^54 - 20 * q^55 + 70 * q^57 - 20 * q^58 + 50 * q^60 - 12 * q^61 - 20 * q^63 - 100 * q^64 - 30 * q^66 - 60 * q^67 - 80 * q^69 - 100 * q^70 - 150 * q^72 - 60 * q^73 - 90 * q^75 - 64 * q^76 - 80 * q^78 - 60 * q^79 + 14 * q^81 - 60 * q^82 - 130 * q^84 + 60 * q^85 - 60 * q^87 + 20 * q^88 - 70 * q^90 - 12 * q^91 - 20 * q^93 + 260 * q^94 + 42 * q^96 + 120 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{3}{20}\right)$

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 $

$2$	−0.674175	+	1.32314i	−0.476714	+	0.935603i	0.519967	+	0.854187i	$0.325944\pi$
$2$	−0.674175	+	1.32314i	−0.476714	+	0.935603i	−0.996680	+	0.0814164i	$0.974056\pi$
$3$	−0.140417	+	1.72635i	−0.0810696	+	0.996708i
$3$	−0.140417	+	1.72635i	−0.0810696	+	0.996708i
$4$	−0.120624	−	0.166024i	−0.0603118	−	0.0830121i
$5$	1.20181	−	1.88564i	0.537466	−	0.843285i
$5$	1.20181	−	1.88564i	0.537466	−	0.843285i
$6$	−2.18954	−	1.34965i	−0.893876	−	0.550993i
$7$	−1.72218	+	1.72218i	−0.650923	+	0.650923i	−0.953215	−	0.302292i	$-0.902248\pi$
$7$	−1.72218	+	1.72218i	−0.650923	+	0.650923i	0.302292	+	0.953215i	$0.402248\pi$
$8$	−2.63243	+	0.416937i	−0.930706	+	0.147409i
$9$	−2.96057	−	0.484816i	−0.986855	−	0.161605i
$10$	1.68474	+	2.86142i	0.532763	+	0.904860i
$11$	3.72206	−	1.20937i	1.12224	−	0.364638i	0.311619	−	0.950207i	$-0.399129\pi$
$11$	3.72206	−	1.20937i	1.12224	−	0.364638i	0.810623	+	0.585569i	$0.199129\pi$
$12$	0.303553	−	0.184926i	0.0876283	−	0.0533836i
$13$	5.20313	−	2.65113i	1.44309	−	0.735290i	0.455190	−	0.890394i	$-0.349571\pi$
$13$	5.20313	−	2.65113i	1.44309	−	0.735290i	0.987898	+	0.155104i	$0.0495714\pi$
$14$	−1.11764	−	3.43974i	−0.298702	−	0.919309i
$15$	3.08653	+	2.33952i	0.796938	+	0.604062i
$16$	1.34989	−	4.15452i	0.337471	−	1.03863i
$17$	0.120501	+	0.760813i	0.0292258	+	0.184524i	0.997983	−	0.0634883i	$-0.0202226\pi$
$17$	0.120501	+	0.760813i	0.0292258	+	0.184524i	−0.968757	+	0.248013i	$0.920223\pi$
$18$	2.63742	−	3.59040i	0.621646	−	0.846265i
$19$	−2.08083	+	2.86402i	−0.477376	+	0.657051i	−0.977998	−	0.208614i	$-0.933105\pi$
$19$	−2.08083	+	2.86402i	−0.477376	+	0.657051i	0.500622	+	0.865666i	$0.333105\pi$
$20$	−0.458029	+	0.0279236i	−0.102418	+	0.00624390i
$21$	−2.73126	−	3.21491i	−0.596011	−	0.701551i
$22$	−0.909148	+	5.74013i	−0.193831	+	1.22380i
$23$	0.926047	+	0.471845i	0.193094	+	0.0983864i	0.547864	−	0.836567i	$-0.315441\pi$
$23$	0.926047	+	0.471845i	0.193094	+	0.0983864i	−0.354770	+	0.934953i	$0.615441\pi$
$24$	−0.350141	−	4.60305i	−0.0714722	−	0.939593i
$25$	−2.11130	−	4.53237i	−0.422261	−	0.906474i
$26$			8.67180i			1.70068i
$27$	1.25268	−	5.04290i	0.241077	−	0.970506i
$28$	0.493660	+	0.0781880i	0.0932929	+	0.0147761i
$29$	0.111964	−	0.0813465i	0.0207912	−	0.0151057i	−0.577341	−	0.816503i	$-0.695910\pi$
$29$	0.111964	−	0.0813465i	0.0207912	−	0.0151057i	0.598132	+	0.801397i	$0.295910\pi$
$30$	−5.17638	+	2.50667i	−0.945073	+	0.457653i
$31$	0.372717	+	0.270795i	0.0669420	+	0.0486362i	0.620753	−	0.784006i	$-0.286827\pi$
$31$	0.372717	+	0.270795i	0.0669420	+	0.0486362i	−0.553811	+	0.832642i	$0.686827\pi$
$32$	0.817733	+	0.817733i	0.144556	+	0.144556i
$33$	1.56516	+	6.59538i	0.272459	+	1.14811i
$34$	−1.08790	−	0.353481i	−0.186574	−	0.0606215i
$35$	1.17768	+	5.31715i	0.199065	+	0.898763i
$36$	0.276623	+	0.550006i	0.0461039	+	0.0916677i
$37$	−2.32130	−	4.55581i	−0.381620	−	0.748970i	0.617679	−	0.786431i	$-0.288073\pi$
$37$	−2.32130	−	4.55581i	−0.381620	−	0.748970i	−0.999298	+	0.0374602i	$0.988073\pi$
$38$	−2.38666	−	4.68409i	−0.387168	−	0.759859i
$39$	3.84616	+	9.35468i	0.615879	+	1.49795i
$40$	−2.37749	+	5.46491i	−0.375915	+	0.864078i
$41$	−6.18190	−	2.00862i	−0.965450	−	0.313694i	−0.216472	−	0.976289i	$-0.569455\pi$
$41$	−6.18190	−	2.00862i	−0.965450	−	0.313694i	−0.748978	+	0.662595i	$0.769455\pi$
$42$	6.09513	−	1.44644i	0.940499	−	0.223191i
$43$	−5.58451	−	5.58451i	−0.851630	−	0.851630i	0.138704	−	0.990334i	$-0.455706\pi$
$43$	−5.58451	−	5.58451i	−0.851630	−	0.851630i	−0.990334	+	0.138704i	$0.955706\pi$
$44$	−0.649753	−	0.472073i	−0.0979539	−	0.0711677i
$45$	−4.47223	+	4.99992i	−0.666681	+	0.745343i
$46$	−1.24864	+	0.907186i	−0.184101	+	0.133757i
$47$	−3.97607	−	0.629748i	−0.579970	−	0.0918582i	−0.140445	−	0.990089i	$-0.544853\pi$
$47$	−3.97607	−	0.629748i	−0.579970	−	0.0918582i	−0.439525	+	0.898230i	$0.644853\pi$
$48$	6.98261	+	2.91374i	1.00785	+	0.420562i
$49$			1.06819i			0.152598i
$50$	7.42036	+	0.262057i	1.04940	+	0.0370604i
$51$	−1.33035	+	0.101196i	−0.186286	+	0.0141703i
$52$	−1.06777	−	0.544057i	−0.148073	−	0.0754471i
$53$	−0.459763	+	2.90283i	−0.0631533	+	0.398734i	0.935781	+	0.352581i	$0.114696\pi$
$53$	−0.459763	+	2.90283i	−0.0631533	+	0.398734i	−0.998934	+	0.0461526i	$0.985304\pi$
$54$	5.82795	+	5.05726i	0.793083	+	0.688206i
$55$	2.19277	−	8.47190i	0.295673	−	1.14235i
$56$	3.81549	−	5.25157i	0.509866	−	0.701770i
$57$	−4.65212	−	3.99440i	−0.616188	−	0.529071i
$58$	0.0321498	+	0.202986i	0.00422147	+	0.0266533i
$59$	0.855253	−	2.63220i	0.111344	−	0.342683i	−0.879823	−	0.475302i	$-0.842339\pi$
$59$	0.855253	−	2.63220i	0.111344	−	0.342683i	0.991167	+	0.132619i	$0.0423388\pi$
$60$	0.0161091	−	0.794640i	0.00207968	−	0.102588i
$61$	1.24058	+	3.81812i	0.158840	+	0.488860i	0.998530	−	0.0542065i	$-0.0172629\pi$
$61$	1.24058	+	3.81812i	0.158840	+	0.488860i	−0.839689	+	0.543067i	$0.817263\pi$
$62$	−0.609576	+	0.310595i	−0.0774163	+	0.0394456i
$63$	5.93357	−	4.26369i	0.747560	−	0.537174i
$64$	6.67577	−	2.16909i	0.834471	−	0.271136i
$65$	1.25410	−	12.9974i	0.155551	−	1.61213i
$66$	−9.78182	−	2.37552i	−1.20406	−	0.292406i
$67$	1.92228	−	0.304459i	0.234844	−	0.0371956i	−0.0379032	−	0.999281i	$-0.512068\pi$
$67$	1.92228	−	0.304459i	0.234844	−	0.0371956i	0.272747	+	0.962086i	$0.412068\pi$
$68$	0.111778	−	0.111778i	0.0135551	−	0.0135551i
$69$	−0.944601	+	1.53243i	−0.113717	+	0.184482i
$70$	−7.82932	−	2.02645i	−0.935782	−	0.242207i
$71$	2.08859	+	2.87469i	0.247870	+	0.341163i	0.914764	−	0.403989i	$-0.132377\pi$
$71$	2.08859	+	2.87469i	0.247870	+	0.341163i	−0.666894	+	0.745152i	$0.732377\pi$
$72$	7.99563	+	0.0418786i	0.942294	+	0.00493545i
$73$	−5.44405	+	10.6846i	−0.637178	+	1.25053i	0.316182	+	0.948698i	$0.397599\pi$
$73$	−5.44405	+	10.6846i	−0.637178	+	1.25053i	−0.953360	+	0.301834i	$0.902401\pi$
$74$	7.59295			0.882662
$75$	8.12092	−	3.00843i	0.937723	−	0.347383i
$76$	0.726495			0.0833347
$77$	−4.32730	+	8.49280i	−0.493142	+	0.967845i
$78$	−14.9706	−	1.21766i	−1.69508	−	0.137873i
$79$	0.518361	+	0.713462i	0.0583201	+	0.0802708i	0.837181	−	0.546926i	$-0.184202\pi$
$79$	0.518361	+	0.713462i	0.0583201	+	0.0802708i	−0.778861	+	0.627197i	$0.784202\pi$
$80$	−6.21164	−	7.53835i	−0.694482	−	0.842813i
$81$	8.52991	+	2.87066i	0.947767	+	0.318962i
$82$	6.82537	−	6.82537i	0.753736	−	0.753736i
$83$	−9.43448	+	1.49428i	−1.03557	+	0.164018i	−0.651000	−	0.759078i	$-0.725650\pi$
$83$	−9.43448	+	1.49428i	−1.03557	+	0.164018i	−0.384569	+	0.923096i	$0.625650\pi$
$84$	−0.204298	+	0.841250i	−0.0222907	+	0.0917879i
$85$	1.57944	+	0.687132i	0.171315	+	0.0745299i
$86$	11.1540	−	3.62417i	1.20277	−	0.390804i
$87$	0.124711	+	0.204711i	0.0133704	+	0.0219473i
$88$	−9.29383	+	4.73545i	−0.990726	+	0.504800i
$89$	−3.64270	−	11.2111i	−0.386125	−	1.18837i	−0.935661	−	0.352901i	$-0.885195\pi$
$89$	−3.64270	−	11.2111i	−0.386125	−	1.18837i	0.549535	−	0.835470i	$-0.314805\pi$
$90$	−3.60053	−	9.28821i	−0.379530	−	0.979064i
$91$	−4.39501	+	13.5264i	−0.460722	+	1.41796i
$92$	−0.0333656	−	0.210662i	−0.00347860	−	0.0219630i
$93$	−0.519822	+	0.605416i	−0.0539030	+	0.0627787i
$94$	3.51381	−	4.83635i	0.362422	−	0.498831i
$95$	2.89976	+	7.36572i	0.297509	+	0.755707i
$96$	−1.52652	+	1.29687i	−0.155799	+	0.132361i
$97$	2.54554	−	16.0719i	0.258461	−	1.63186i	−0.427356	−	0.904083i	$-0.640555\pi$
$97$	2.54554	−	16.0719i	0.258461	−	1.63186i	0.685817	−	0.727774i	$-0.259445\pi$
$98$	−1.41336	−	0.720145i	−0.142771	−	0.0727456i
$99$	−11.6057	+	1.77590i	−1.16642	+	0.178485i
$100$	−0.497811	+	0.897239i	−0.0497811	+	0.0897239i
$101$			14.8155i			1.47420i	0.675784	+	0.737100i	$0.263805\pi$
$101$			14.8155i			1.47420i	−0.675784	+	0.737100i	$0.736195\pi$
$102$	0.762992	−	1.82847i	0.0755474	−	0.181045i
$103$	8.83465	+	1.39927i	0.870504	+	0.137874i	0.575678	−	0.817677i	$-0.304738\pi$
$103$	8.83465	+	1.39927i	0.870504	+	0.137874i	0.294826	+	0.955551i	$0.404738\pi$
$104$	−12.5915	+	9.14829i	−1.23470	+	0.897063i
$105$	−9.34463	+	1.28648i	−0.911943	+	0.125547i
$106$	−3.53089	−	2.56534i	−0.342951	−	0.249168i
$107$	10.2862	+	10.2862i	0.994405	+	0.994405i	0.999984	−	0.00557906i	$-0.00177588\pi$
$107$	10.2862	+	10.2862i	0.994405	+	0.994405i	−0.00557906	+	0.999984i	$0.501776\pi$
$108$	−0.988345	+	0.400318i	−0.0951036	+	0.0385206i
$109$	9.46329	+	3.07481i	0.906419	+	0.294513i	0.724884	−	0.688871i	$-0.241893\pi$
$109$	9.46329	+	3.07481i	0.906419	+	0.294513i	0.181535	+	0.983384i	$0.441893\pi$
$110$	9.73122	+	8.61288i	0.927836	+	0.821206i
$111$	8.19087	−	3.36767i	0.777443	−	0.319645i
$112$	4.83009	+	9.47958i	0.456400	+	0.895736i
$113$	−2.20080	−	4.31931i	−0.207034	−	0.406326i	0.764018	−	0.645194i	$-0.223224\pi$
$113$	−2.20080	−	4.31931i	−0.207034	−	0.406326i	−0.971052	+	0.238868i	$0.923224\pi$
$114$	8.42150	−	3.46249i	0.788746	−	0.324292i
$115$	2.00266	−	1.17913i	0.186749	−	0.109954i
$116$	−0.0270110	−	0.00877640i	−0.00250791	−	0.000814868i
$117$	−16.6895	+	5.32627i	−1.54295	+	0.492414i
$118$	2.90618	+	2.90618i	0.267536	+	0.267536i
$119$	−1.51778	−	1.10273i	−0.139135	−	0.101087i
$120$	−9.10051	−	4.87175i	−0.830759	−	0.444728i
$121$	3.49193	−	2.53704i	0.317449	−	0.230640i
$122$	−5.88829	−	0.932613i	−0.533101	−	0.0844349i
$123$	4.33562	−	10.3901i	0.390930	−	0.936841i
$124$		−	0.0945443i		−	0.00849033i
$125$	−11.0838	−	1.46589i	−0.991367	−	0.131113i
$126$	1.64120	+	10.7254i	0.146210	+	0.955497i
$127$	10.1697	+	5.18173i	0.902417	+	0.459804i	0.842683	−	0.538410i	$-0.180975\pi$
$127$	10.1697	+	5.18173i	0.902417	+	0.459804i	0.0597340	+	0.998214i	$0.480975\pi$
$128$	−1.99244	+	12.5798i	−0.176108	+	1.11190i
$129$	10.4250	−	8.85666i	0.917868	−	0.779785i
$130$	16.3519	+	10.4219i	1.43416	+	0.914058i
$131$	−2.60417	+	3.58434i	−0.227528	+	0.313165i	−0.907483	−	0.420088i	$-0.861999\pi$
$131$	−2.60417	+	3.58434i	−0.227528	+	0.313165i	0.679956	+	0.733253i	$0.261999\pi$
$132$	0.906199	−	1.05541i	0.0788745	−	0.0918619i
$133$	−1.34879	−	8.51593i	−0.116955	−	0.738425i
$134$	−0.893109	+	2.74871i	−0.0771529	+	0.237452i
$135$	−8.00363	−	8.42271i	−0.688843	−	0.724911i
$136$	−0.634422	−	1.95255i	−0.0544012	−	0.167430i
$137$	7.38749	−	3.76412i	0.631156	−	0.321590i	−0.108983	−	0.994044i	$-0.534759\pi$
$137$	7.38749	−	3.76412i	0.631156	−	0.321590i	0.740139	+	0.672453i	$0.234759\pi$
$138$	−1.39079	−	2.28296i	−0.118392	−	0.194339i
$139$	−20.8266	+	6.76697i	−1.76649	+	0.573967i	−0.997839	−	0.0657043i	$-0.979071\pi$
$139$	−20.8266	+	6.76697i	−1.76649	+	0.573967i	−0.768649	+	0.639671i	$0.779071\pi$
$140$	0.740720	−	0.836899i	0.0626023	−	0.0707309i
$141$	1.64547	−	6.77566i	0.138574	−	0.570614i
$142$	−5.21170	+	0.825452i	−0.437356	+	0.0692704i
$143$	16.1601	−	16.1601i	1.35138	−	1.35138i
$144$	−6.01060	+	11.6453i	−0.500884	+	0.970440i
$145$	−0.0188312	−	0.308887i	−0.00156384	−	0.0256517i
$146$	−10.4669	−	14.4065i	−0.866251	−	1.19229i
$147$	−1.84406	−	0.149991i	−0.152096	−	0.0123711i
$148$	−0.476371	+	0.934931i	−0.0391575	+	0.0768508i
$149$	5.61752			0.460205			0.230103	−	0.973166i	$-0.426094\pi$
$149$	5.61752			0.460205			0.230103	+	0.973166i	$0.426094\pi$
$150$	−1.49434	+	12.7733i	−0.122013	+	1.04294i
$151$	−14.6821			−1.19482			−0.597408	−	0.801938i	$-0.703803\pi$
$151$	−14.6821			−1.19482			−0.597408	+	0.801938i	$0.703803\pi$
$152$	4.28354	−	8.40692i	0.347441	−	0.681891i
$153$	0.0121036	−	2.31086i	0.000978515	−	0.186822i
$154$	−8.31983	−	11.4513i	−0.670431	−	0.922769i
$155$	0.958558	−	0.377367i	0.0769932	−	0.0303109i
$156$	1.08917	−	1.76695i	0.0872030	−	0.141469i
$157$	−7.39864	+	7.39864i	−0.590476	+	0.590476i	−0.937760	−	0.347284i	$-0.887104\pi$
$157$	−7.39864	+	7.39864i	−0.590476	+	0.590476i	0.347284	+	0.937760i	$0.387104\pi$
$158$	−1.29348	+	0.204867i	−0.102904	+	0.0162983i
$159$	−4.94674	−	1.20132i	−0.392302	−	0.0952706i
$160$	2.52471	−	0.559193i	0.199596	−	0.0442081i
$161$	−2.40742	+	0.782219i	−0.189731	+	0.0616475i
$162$	−9.54894	+	9.35095i	−0.750236	+	0.734680i
$163$	−7.62146	+	3.88333i	−0.596959	+	0.304166i	−0.726239	−	0.687442i	$-0.758733\pi$
$163$	−7.62146	+	3.88333i	−0.596959	+	0.304166i	0.129280	+	0.991608i	$0.458733\pi$
$164$	0.412204	+	1.26863i	0.0321877	+	0.0990635i
$165$	14.3176	+	4.97508i	1.11462	+	0.387309i
$166$	4.38335	−	13.4906i	0.340214	−	1.04707i
$167$	−2.73713	−	17.2815i	−0.211805	−	1.33729i	−0.832845	−	0.553507i	$-0.813289\pi$
$167$	−2.73713	−	17.2815i	−0.211805	−	1.33729i	0.621039	−	0.783779i	$-0.286711\pi$
$168$	8.53028	+	7.32427i	0.658126	+	0.565080i
$169$	12.4029	−	17.0711i	0.954066	−	1.31316i
$170$	−1.97399	+	1.62658i	−0.151398	+	0.124753i
$171$	7.54897	−	7.47030i	0.577284	−	0.571268i
$172$	−0.253540	+	1.60079i	−0.0193322	+	0.122059i
$173$	14.9142	+	7.59919i	1.13391	+	0.577755i	0.917179	−	0.398476i	$-0.130461\pi$
$173$	14.9142	+	7.59919i	1.13391	+	0.577755i	0.216730	+	0.976232i	$0.430461\pi$
$174$	−0.354939	+	0.0269992i	−0.0269078	+	0.00204680i
$175$	11.4416	+	4.16952i	0.864904	+	0.315186i
$176$		−	17.0959i		−	1.28865i
$177$	4.42400	+	1.84607i	0.332528	+	0.138759i
$178$	17.2897	+	2.73841i	1.29591	+	0.205253i
$179$	7.83739	−	5.69420i	0.585794	−	0.425604i	−0.255014	−	0.966937i	$-0.582080\pi$
$179$	7.83739	−	5.69420i	0.585794	−	0.425604i	0.840808	+	0.541333i	$0.182080\pi$
$180$	1.36956	+	0.139391i	0.102081	+	0.0103896i
$181$	7.76955	+	5.64491i	0.577506	+	0.419583i	0.837824	−	0.545940i	$-0.183827\pi$
$181$	7.76955	+	5.64491i	0.577506	+	0.419583i	−0.260318	+	0.965523i	$0.583827\pi$
$182$	−14.9344	−	14.9344i	−1.10701	−	1.10701i
$183$	−6.76561	+	1.60555i	−0.500129	+	0.118686i
$184$	−2.63449	−	0.855997i	−0.194217	−	0.0631049i
$185$	−11.3804	−	1.09807i	−0.836703	−	0.0807320i
$186$	−0.450600	−	1.09595i	−0.0330396	−	0.0803593i
$187$	1.36862	+	2.68606i	0.100083	+	0.196424i
$188$	0.375055	+	0.736087i	0.0273537	+	0.0536847i
$189$	6.52745	+	10.8421i	0.474802	+	0.788648i
$190$	−11.7008	−	1.12899i	−0.848868	−	0.0819057i
$191$	−10.1420	−	3.29532i	−0.733847	−	0.238441i	−0.0818306	−	0.996646i	$-0.526077\pi$
$191$	−10.1420	−	3.29532i	−0.733847	−	0.238441i	−0.652016	+	0.758205i	$0.726077\pi$
$192$	2.80722	+	11.8293i	0.202593	+	0.853705i
$193$	8.82760	+	8.82760i	0.635425	+	0.635425i	0.949423	−	0.313999i	$-0.101669\pi$
$193$	8.82760	+	8.82760i	0.635425	+	0.635425i	−0.313999	+	0.949423i	$0.601669\pi$
$194$	19.5493	+	14.2034i	1.40356	+	1.01975i
$195$	22.2620	+	3.99006i	1.59421	+	0.285734i
$196$	0.177345	−	0.128849i	0.0126675	−	0.00920348i
$197$	7.55759	+	1.19701i	0.538456	+	0.0852831i	0.419739	−	0.907645i	$-0.362122\pi$
$197$	7.55759	+	1.19701i	0.538456	+	0.0852831i	0.118718	+	0.992928i	$0.462122\pi$
$198$	5.47450	−	16.5533i	0.389056	−	1.17639i
$199$			16.5759i			1.17503i	0.809212	+	0.587517i	$0.199895\pi$
$199$			16.5759i			1.17503i	−0.809212	+	0.587517i	$0.800105\pi$
$200$	7.44758	+	11.0509i	0.526623	+	0.781416i
$201$	0.255683	+	3.36128i	0.0180345	+	0.237086i
$202$	−19.6030	−	9.98825i	−1.37927	−	0.702771i
$203$	−0.0527286	+	0.332915i	−0.00370082	+	0.0233661i
$204$	0.177273	+	0.208664i	0.0124116	+	0.0146094i
$205$	−11.2170	+	9.24287i	−0.783430	+	0.645550i
$206$	−7.80753	+	10.7461i	−0.543976	+	0.748719i
$207$	−2.51287	−	1.84589i	−0.174656	−	0.128298i
$208$	−3.99053	−	25.1952i	−0.276693	−	1.74697i
$209$	−4.28132	+	13.1765i	−0.296145	+	0.911440i
$210$	4.59772	−	13.2316i	0.317273	−	0.913066i
$211$	−7.40904	−	22.8027i	−0.510059	−	1.56980i	−0.792096	−	0.610397i	$-0.791010\pi$
$211$	−7.40904	−	22.8027i	−0.510059	−	1.56980i	0.282036	−	0.959404i	$-0.408990\pi$
$212$	0.537398	−	0.273818i	0.0369086	−	0.0188059i
$213$	−5.25599	+	3.20197i	−0.360135	+	0.219396i
$214$	−20.5448	+	6.67542i	−1.40442	+	0.456322i
$215$	−17.2419	+	3.81887i	−1.17589	+	0.260445i
$216$	−1.19502	+	13.7974i	−0.0813106	+	0.938793i
$217$	−1.10824	+	0.175529i	−0.0752325	+	0.0119157i
$218$	−10.4483	+	10.4483i	−0.707650	+	0.707650i
$219$	−17.6808	−	10.8986i	−1.19476	−	0.736461i
$220$	−1.67104	+	0.657860i	−0.112662	+	0.0443529i
$221$	2.64399	+	3.63914i	0.177854	+	0.244795i
$222$	−1.06618	+	13.1081i	−0.0715570	+	0.879757i
$223$	−1.07788	+	2.11546i	−0.0721802	+	0.141662i	−0.924277	−	0.381723i	$-0.875331\pi$
$223$	−1.07788	+	2.11546i	−0.0721802	+	0.141662i	0.852097	+	0.523385i	$0.175331\pi$
$224$	−2.81657			−0.188190
$225$	4.05328	+	14.4420i	0.270219	+	0.962799i
$226$	7.19878			0.478856
$227$	−5.52455	+	10.8425i	−0.366677	+	0.719644i	−0.998459	−	0.0555024i	$-0.982324\pi$
$227$	−5.52455	+	10.8425i	−0.366677	+	0.719644i	0.631782	+	0.775146i	$0.282324\pi$
$228$	−0.102012	+	1.25418i	−0.00675590	+	0.0830604i
$229$	−8.52530	−	11.7341i	−0.563368	−	0.775409i	0.428382	−	0.903598i	$-0.359084\pi$
$229$	−8.52530	−	11.7341i	−0.563368	−	0.775409i	−0.991750	+	0.128188i	$0.959084\pi$
$230$	0.210008	+	3.44475i	0.0138475	+	0.227140i
$231$	−14.0539	−	8.66296i	−0.924680	−	0.569981i
$232$	−0.260821	+	0.260821i	−0.0171237	+	0.0171237i
$233$	21.4020	−	3.38975i	1.40209	−	0.222070i	0.590852	−	0.806780i	$-0.298792\pi$
$233$	21.4020	−	3.38975i	1.40209	−	0.222070i	0.811242	+	0.584710i	$0.198792\pi$
$234$	4.20423	−	25.6734i	0.274839	−	1.67833i
$235$	−5.96597	+	6.74062i	−0.389177	+	0.439709i
$236$	−0.540172	+	0.175513i	−0.0351622	+	0.0114249i
$237$	−1.30447	+	0.794690i	−0.0847345	+	0.0516206i
$238$	2.48232	−	1.26481i	0.160905	−	0.0819853i
$239$	2.61133	+	8.03683i	0.168913	+	0.519859i	0.999303	−	0.0373221i	$-0.0118827\pi$
$239$	2.61133	+	8.03683i	0.168913	+	0.519859i	−0.830391	+	0.557182i	$0.811883\pi$
$240$	13.8860	−	9.66495i	0.896340	−	0.623870i
$241$	0.483477	−	1.48799i	0.0311435	−	0.0958498i	−0.934277	−	0.356549i	$-0.883953\pi$
$241$	0.483477	−	1.48799i	0.0311435	−	0.0958498i	0.965420	+	0.260699i	$0.0839532\pi$
$242$	1.00269	+	6.33073i	0.0644553	+	0.406955i
$243$	−6.15351	+	14.3225i	−0.394748	+	0.918790i
$244$	0.484257	−	0.666523i	0.0310014	−	0.0426698i
$245$	2.01422	+	1.28376i	0.128684	+	0.0820163i
$246$	10.8246	+	12.7414i	0.690150	+	0.812360i
$247$	−3.23396	+	20.4184i	−0.205772	+	1.29919i
$248$	−1.09406	−	0.557450i	−0.0694727	−	0.0353981i
$249$	−1.25488	−	16.4970i	−0.0795250	−	1.04546i
$250$	9.41201	−	13.6772i	0.595268	−	0.865023i
$251$		−	8.41068i		−	0.530878i	−0.964128	−	0.265439i	$-0.914483\pi$
$251$		−	8.41068i		−	0.530878i	0.964128	−	0.265439i	$-0.0855168\pi$
$252$	−1.42361	−	0.470815i	−0.0896787	−	0.0296586i
$253$	4.01743	+	0.636299i	0.252574	+	0.0400038i
$254$	−13.7123	+	9.96260i	−0.860389	+	0.625109i
$255$	−1.40801	+	2.63018i	−0.0881730	+	0.164709i
$256$	−3.94407	−	2.86553i	−0.246504	−	0.179096i
$257$	10.6415	+	10.6415i	0.663801	+	0.663801i	0.956274	−	0.292473i	$-0.0944781\pi$
$257$	10.6415	+	10.6415i	0.663801	+	0.663801i	−0.292473	+	0.956274i	$0.594478\pi$
$258$	4.69036	+	19.7647i	0.292009	+	1.23049i
$259$	11.8436	+	3.84823i	0.735927	+	0.239117i
$260$	−2.30916	+	1.35958i	−0.143208	+	0.0843178i
$261$	−0.370914	+	0.186550i	−0.0229590	+	0.0115471i
$262$	−2.98692	−	5.86216i	−0.184532	−	0.362165i
$263$	0.850760	+	1.66971i	0.0524601	+	0.102959i	0.915748	−	0.401753i	$-0.131599\pi$
$263$	0.850760	+	1.66971i	0.0524601	+	0.102959i	−0.863288	+	0.504711i	$0.831599\pi$
$264$	−6.87003	−	16.7093i	−0.422821	−	1.02839i
$265$	4.92115	+	4.35560i	0.302304	+	0.267562i
$266$	12.1771	+	3.95658i	0.746627	+	0.242594i
$267$	19.8657	−	4.71435i	1.21576	−	0.288514i
$268$	−0.282420	−	0.282420i	−0.0172515	−	0.0172515i
$269$	−19.0018	−	13.8056i	−1.15856	−	0.841745i	−0.168966	−	0.985622i	$-0.554043\pi$
$269$	−19.0018	−	13.8056i	−1.15856	−	0.841745i	−0.989596	+	0.143877i	$0.954043\pi$
$270$	16.5403	−	4.91156i	1.00661	−	0.298908i
$271$	0.609720	−	0.442988i	0.0370379	−	0.0269096i	−0.569112	−	0.822260i	$-0.692713\pi$
$271$	0.609720	−	0.442988i	0.0370379	−	0.0269096i	0.606150	+	0.795350i	$0.292713\pi$
$272$	3.32348	+	0.526387i	0.201515	+	0.0319169i
$273$	−22.7342	−	9.48666i	−1.37594	−	0.574159i
$274$			12.3124i			0.743818i
$275$	−13.3397	−	14.3164i	−0.804414	−	0.863311i
$276$	0.368361	−	0.0280202i	0.0221727	−	0.00168662i
$277$	8.17612	+	4.16594i	0.491255	+	0.250307i	0.682027	−	0.731327i	$-0.261099\pi$
$277$	8.17612	+	4.16594i	0.491255	+	0.250307i	−0.190771	+	0.981635i	$0.561099\pi$
$278$	5.08710	−	32.1187i	0.305104	−	1.92635i
$279$	−0.972168	−	0.982405i	−0.0582022	−	0.0588151i
$280$	−5.31709	−	13.5060i	−0.317757	−	0.807140i
$281$	14.7500	−	20.3017i	0.879913	−	1.21110i	−0.0965320	−	0.995330i	$-0.530775\pi$
$281$	14.7500	−	20.3017i	0.879913	−	1.21110i	0.976445	−	0.215766i	$-0.0692250\pi$
$282$	7.85583	+	6.74518i	0.467808	+	0.401669i
$283$	−3.69832	−	23.3503i	−0.219843	−	1.38803i	−0.812681	−	0.582709i	$-0.801993\pi$
$283$	−3.69832	−	23.3503i	−0.219843	−	1.38803i	0.592838	−	0.805322i	$-0.298007\pi$
$284$	0.225336	−	0.693512i	0.0133712	−	0.0411524i
$285$	−13.1230	+	3.97172i	−0.777338	+	0.235265i
$286$	10.4874	+	32.2769i	0.620133	+	1.90857i
$287$	14.1056	−	7.18714i	0.832624	−	0.424243i
$288$	−2.02450	−	2.81740i	−0.119295	−	0.166017i
$289$	15.6036	−	5.06993i	0.917861	−	0.298231i
$290$	0.421397	+	0.183327i	0.0247453	+	0.0107654i
$291$	27.3883	+	6.65127i	1.60553	+	0.389904i
$292$	2.43058	−	0.384966i	0.142239	−	0.0225284i
$293$	−17.4959	+	17.4959i	−1.02212	+	1.02212i	−0.0223711	+	0.999750i	$0.507122\pi$
$293$	−17.4959	+	17.4959i	−1.02212	+	1.02212i	−0.999750	+	0.0223711i	$0.992878\pi$
$294$	1.44168	−	2.33884i	0.0840806	−	0.136404i
$295$	−3.93553	−	4.77610i	−0.229136	−	0.278075i
$296$	8.01016	+	11.0250i	0.465581	+	0.640817i
$297$	−1.43620	−	20.2849i	−0.0833366	−	1.17705i
$298$	−3.78719	+	7.43278i	−0.219386	+	0.430569i
$299$	6.06926			0.350994
$300$	−1.47905	−	0.985383i	−0.0853928	−	0.0568911i
$301$	19.2351			1.10869
$302$	9.89833	−	19.4266i	0.569585	−	1.11787i
$303$	−25.5768	−	2.08035i	−1.46935	−	0.119513i
$304$	9.08974	+	12.5110i	0.521333	+	0.717553i
$305$	8.69056	+	2.24936i	0.497620	+	0.128798i
$306$	3.04944	+	1.57394i	0.174325	+	0.0899760i
$307$	−4.00162	+	4.00162i	−0.228384	+	0.228384i	−0.812017	−	0.583633i	$-0.801631\pi$
$307$	−4.00162	+	4.00162i	−0.228384	+	0.228384i	0.583633	+	0.812017i	$0.301631\pi$
$308$	1.93199	−	0.305997i	0.110085	−	0.0174358i
$309$	−3.65616	+	15.0552i	−0.207992	+	0.856461i
$310$	−0.146924	+	1.52272i	−0.00834475	+	0.0864847i
$311$	−32.7389	+	10.6375i	−1.85645	+	0.603198i	−0.860923	+	0.508735i	$0.830113\pi$
$311$	−32.7389	+	10.6375i	−1.85645	+	0.603198i	−0.995528	+	0.0944627i	$0.969887\pi$
$312$	−14.0251	−	23.0220i	−0.794014	−	1.30336i
$313$	−17.3977	+	8.86459i	−0.983378	+	0.501056i	−0.870296	−	0.492530i	$-0.836072\pi$
$313$	−17.3977	+	8.86459i	−0.983378	+	0.501056i	−0.113082	+	0.993586i	$0.536072\pi$
$314$	−4.80148	−	14.7774i	−0.270963	−	0.833939i
$315$	−0.908768	−	16.3127i	−0.0512033	−	0.919119i
$316$	0.0559255	−	0.172121i	0.00314605	−	0.00968256i
$317$	−0.459247	−	2.89957i	−0.0257939	−	0.162856i	0.971429	−	0.237330i	$-0.0762723\pi$
$317$	−0.459247	−	2.89957i	−0.0257939	−	0.162856i	−0.997223	+	0.0744738i	$0.976272\pi$
$318$	4.92448	−	5.73534i	0.276151	−	0.321622i
$319$	0.318358	−	0.438182i	0.0178246	−	0.0245335i
$320$	3.93288	−	15.1950i	0.219855	−	0.849424i
$321$	−19.2019	+	16.3132i	−1.07175	+	0.910516i
$322$	0.588036	−	3.71271i	0.0327700	−	0.206901i
$323$	−2.42973	−	1.23801i	−0.135194	−	0.0688846i
$324$	−0.552309	−	1.76244i	−0.0306838	−	0.0979134i
$325$	−23.0013	−	17.9852i	−1.27588	−	0.997638i
$326$		−	12.7023i		−	0.703516i
$327$	−6.63700	+	15.9052i	−0.367027	+	0.879559i
$328$	17.1109	+	2.71010i	0.944792	+	0.149640i
$329$	7.93206	−	5.76298i	0.437308	−	0.317723i
$330$	−16.2353	+	15.5901i	−0.893722	+	0.858207i
$331$	3.26639	+	2.37317i	0.179537	+	0.130441i	0.673924	−	0.738800i	$-0.264607\pi$
$331$	3.26639	+	2.37317i	0.179537	+	0.130441i	−0.494387	+	0.869242i	$0.664607\pi$
$332$	1.38611	+	1.38611i	0.0760725	+	0.0760725i
$333$	4.66363	+	14.6132i	0.255566	+	0.800797i
$334$	24.7112	+	8.02917i	1.35214	+	0.439337i
$335$	1.73611	−	3.99063i	0.0948540	−	0.218032i
$336$	−17.0433	+	7.00733i	−0.929788	+	0.382281i
$337$	−4.84331	−	9.50552i	−0.263832	−	0.517799i	0.720647	−	0.693302i	$-0.243845\pi$
$337$	−4.84331	−	9.50552i	−0.263832	−	0.517799i	−0.984479	+	0.175503i	$0.943845\pi$
$338$	14.2258	+	27.9196i	0.773779	+	1.51863i
$339$	7.76566	−	3.19284i	0.421773	−	0.173411i
$340$	−0.0764376	−	0.345110i	−0.00414541	−	0.0187162i
$341$	1.71476	+	0.557161i	0.0928597	+	0.0301719i
$342$	4.79495	+	15.0246i	0.259281	+	0.812440i
$343$	−13.8949	−	13.8949i	−0.750253	−	0.750253i
$344$	17.0292	+	12.3725i	0.918155	+	0.667079i
$345$	1.75438	+	3.62287i	0.0944525	+	0.195049i
$346$	−20.1096	+	14.6105i	−1.08110	+	0.785465i
$347$	−24.5248	−	3.88435i	−1.31656	−	0.208523i	−0.541656	−	0.840600i	$-0.682202\pi$
$347$	−24.5248	−	3.88435i	−1.31656	−	0.208523i	−0.774905	+	0.632077i	$0.782202\pi$
$348$	0.0189439	−	0.0453980i	0.00101550	−	0.00243359i
$349$			3.68396i			0.197198i	0.995127	+	0.0985990i	$0.0314361\pi$
$349$			3.68396i			0.197198i	−0.995127	+	0.0985990i	$0.968564\pi$
$350$	−13.2305	+	12.3279i	−0.707201	+	0.658954i
$351$	−6.85152	−	29.5598i	−0.365707	−	1.57779i
$352$	4.03259	+	2.05471i	0.214938	+	0.109516i
$353$	−0.0862706	+	0.544691i	−0.00459172	+	0.0289910i	−0.989878	−	0.141922i	$-0.954672\pi$
$353$	−0.0862706	+	0.544691i	−0.00459172	+	0.0289910i	0.985286	+	0.170913i	$0.0546717\pi$
$354$	−5.42516	+	4.60901i	−0.288344	+	0.244966i
$355$	7.93073	−	0.483493i	0.420919	−	0.0256612i
$356$	−1.42191	+	1.95710i	−0.0753613	+	0.103726i
$357$	2.11683	−	2.46538i	0.112034	−	0.130482i
$358$	2.25046	+	14.2089i	0.118941	+	0.750962i
$359$	−0.0579467	+	0.178342i	−0.00305831	+	0.00941251i	−0.952574	−	0.304307i	$-0.901575\pi$
$359$	−0.0579467	+	0.178342i	−0.00305831	+	0.00941251i	0.949516	+	0.313719i	$0.101575\pi$
$360$	9.68820	−	15.0266i	0.510613	−	0.791971i
$361$	1.99857	+	6.15098i	0.105188	+	0.323736i
$362$	−12.7071	+	6.47457i	−0.667868	+	0.340296i
$363$	3.88949	+	6.38454i	0.204145	+	0.335101i
$364$	2.77586	−	0.901931i	0.145495	−	0.0472741i
$365$	13.6045	+	23.1064i	0.712094	+	1.20944i
$366$	2.43683	−	10.0343i	0.127375	−	0.524501i
$367$	20.5021	−	3.24722i	1.07020	−	0.169503i	0.403614	−	0.914929i	$-0.367754\pi$
$367$	20.5021	−	3.24722i	1.07020	−	0.169503i	0.666589	+	0.745426i	$0.267754\pi$
$368$	3.21034	−	3.21034i	0.167351	−	0.167351i
$369$	17.3281	+	8.94374i	0.902065	+	0.465592i
$370$	9.12528	−	14.3176i	0.474401	−	0.744336i
$371$	−4.20740	−	5.79099i	−0.218437	−	0.300653i
$372$	0.163217	+	0.0132756i	0.00846239	+	0.000688308i
$373$	−2.18936	+	4.29685i	−0.113361	+	0.222483i	−0.940715	−	0.339197i	$-0.889845\pi$
$373$	−2.18936	+	4.29685i	−0.113361	+	0.222483i	0.827355	+	0.561680i	$0.189845\pi$
$374$	−4.47672			−0.231486
$375$	4.08699	−	18.9287i	0.211051	−	0.977475i
$376$	10.7293			0.553322
$377$	0.366902	−	0.720086i	0.0188964	−	0.0370863i
$378$	−18.7463	+	1.32726i	−0.964205	+	0.0682670i
$379$	4.09975	+	5.64282i	0.210590	+	0.289852i	0.901225	−	0.433351i	$-0.142669\pi$
$379$	4.09975	+	5.64282i	0.210590	+	0.289852i	−0.690635	+	0.723203i	$0.742669\pi$
$380$	0.873109	−	1.36991i	0.0447895	−	0.0702749i
$381$	−10.3735	+	16.8289i	−0.531450	+	0.862171i
$382$	11.1976	−	11.1976i	0.572921	−	0.572921i
$383$	10.1039	−	1.60030i	0.516284	−	0.0817714i	0.107145	−	0.994243i	$-0.465829\pi$
$383$	10.1039	−	1.60030i	0.516284	−	0.0817714i	0.409139	+	0.912472i	$0.365829\pi$
$384$	−21.4373	−	5.20605i	−1.09397	−	0.265670i
$385$	10.8138	+	18.3665i	0.551123	+	0.936043i
$386$	−17.6315	+	5.72883i	−0.897421	+	0.291590i
$387$	13.8258	+	19.2408i	0.702807	+	0.978063i
$388$	−2.97538	+	1.51603i	−0.151052	+	0.0769650i
$389$	9.90598	+	30.4875i	0.502253	+	1.54578i	0.805340	+	0.592813i	$0.201983\pi$
$389$	9.90598	+	30.4875i	0.502253	+	1.54578i	−0.303087	+	0.952963i	$0.598017\pi$
$390$	−20.2879	+	26.7657i	−1.02732	+	1.35534i
$391$	−0.247396	+	0.761407i	−0.0125114	+	0.0385060i
$392$	−0.445366	−	2.81193i	−0.0224944	−	0.142024i
$393$	−5.82215	−	4.99901i	−0.293688	−	0.252167i
$394$	−6.67895	+	9.19278i	−0.336481	+	0.463126i
$395$	1.96831	−	0.119997i	0.0990362	−	0.00603770i
$396$	1.69477	+	1.71261i	0.0851652	+	0.0860621i
$397$	1.60445	−	10.1301i	0.0805249	−	0.508414i	−0.914152	−	0.405371i	$-0.867142\pi$
$397$	1.60445	−	10.1301i	0.0805249	−	0.508414i	0.994677	−	0.103043i	$-0.0328578\pi$
$398$	−21.9323	−	11.1751i	−1.09937	−	0.560155i
$399$	14.8909	−	1.13271i	0.745476	−	0.0567063i
$400$	−21.6798	+	2.65327i	−1.08399	+	0.132663i
$401$		−	14.6016i		−	0.729167i	−0.931171	−	0.364584i	$-0.881211\pi$
$401$		−	14.6016i		−	0.729167i	0.931171	−	0.364584i	$-0.118789\pi$
$402$	−4.61982	−	1.92778i	−0.230416	−	0.0961490i
$403$	2.65721	+	0.420860i	0.132365	+	0.0209645i
$404$	2.45974	−	1.78710i	0.122376	−	0.0889117i
$405$	15.6644	−	12.6344i	0.778369	−	0.627807i
$406$	−0.404946	−	0.294210i	−0.0200971	−	0.0146014i
$407$	−14.1497	−	14.1497i	−0.701373	−	0.701373i
$408$	3.45987	−	0.821063i	0.171289	−	0.0406487i
$409$	−15.6748	−	5.09306i	−0.775070	−	0.251835i	−0.105336	−	0.994437i	$-0.533592\pi$
$409$	−15.6748	−	5.09306i	−0.775070	−	0.251835i	−0.669734	+	0.742601i	$0.733592\pi$
$410$	−4.66741	−	21.0730i	−0.230507	−	1.04072i
$411$	5.46085	+	13.2819i	0.269364	+	0.655150i
$412$	−0.833355	−	1.63555i	−0.0410564	−	0.0805778i
$413$	3.06022	+	6.00602i	0.150584	+	0.295537i
$414$	4.13649	−	2.08043i	0.203297	−	0.102247i
$415$	−8.52079	+	19.5859i	−0.418269	+	0.961434i
$416$	6.42268	+	2.08686i	0.314898	+	0.102317i
$417$	−8.75775	−	36.9042i	−0.428869	−	1.80720i
$418$	−14.5481	−	14.5481i	−0.711570	−	0.711570i
$419$	−0.887321	−	0.644676i	−0.0433484	−	0.0314945i	0.565900	−	0.824474i	$-0.308529\pi$
$419$	−0.887321	−	0.644676i	−0.0433484	−	0.0314945i	−0.609248	+	0.792979i	$0.708529\pi$
$420$	1.34077	+	1.39626i	0.0654229	+	0.0681303i
$421$	23.5246	−	17.0916i	1.14652	−	0.832996i	0.158506	−	0.987358i	$-0.449332\pi$
$421$	23.5246	−	17.0916i	1.14652	−	0.832996i	0.988014	+	0.154362i	$0.0493324\pi$
$422$	35.1662	+	5.56977i	1.71186	+	0.271132i
$423$	11.4661	+	3.79208i	0.557502	+	0.184377i
$424$		−	7.83319i		−	0.380414i
$425$	3.19388	−	2.15246i	0.154926	−	0.104410i
$426$	−0.693210	−	9.11312i	−0.0335861	−	0.441532i
$427$	−8.71201	−	4.43899i	−0.421603	−	0.214818i
$428$	0.467000	−	2.94852i	0.0225733	−	0.142522i
$429$	25.6289	+	30.1672i	1.23737	+	1.45649i
$430$	6.57115	−	25.3881i	0.316889	−	1.22432i
$431$	−15.6969	+	21.6049i	−0.756091	+	1.04067i	0.241439	+	0.970416i	$0.422381\pi$
$431$	−15.6969	+	21.6049i	−0.756091	+	1.04067i	−0.997529	+	0.0702534i	$0.977619\pi$
$432$	−19.2598	−	12.0116i	−0.926640	−	0.577908i
$433$	4.18566	+	26.4272i	0.201150	+	1.27001i	0.857078	+	0.515187i	$0.172277\pi$
$433$	4.18566	+	26.4272i	0.201150	+	1.27001i	−0.655928	+	0.754823i	$0.727723\pi$
$434$	0.514901	−	1.58470i	0.0247160	−	0.0760681i
$435$	0.535891	+	0.0108637i	0.0256940	+	0.000520874i
$436$	−0.631004	−	1.94203i	−0.0302196	−	0.0930064i
$437$	−3.27832	+	1.67039i	−0.156823	+	0.0799055i
$438$	26.3404	−	16.0467i	1.25859	−	0.766741i
$439$	19.2932	−	6.26873i	0.920812	−	0.299190i	0.190012	−	0.981782i	$-0.439147\pi$
$439$	19.2932	−	6.26873i	0.920812	−	0.299190i	0.730800	+	0.682592i	$0.239147\pi$
$440$	−2.24007	+	23.2160i	−0.106791	+	1.10678i
$441$	0.517875	−	3.16244i	0.0246607	−	0.150592i
$442$	−6.59762	+	1.04496i	−0.313817	+	0.0497037i
$443$	12.0174	−	12.0174i	0.570962	−	0.570962i	−0.361435	−	0.932397i	$-0.617713\pi$
$443$	12.0174	−	12.0174i	0.570962	−	0.570962i	0.932397	+	0.361435i	$0.117713\pi$
$444$	−1.54713	−	0.953663i	−0.0734234	−	0.0452588i
$445$	−25.5179	−	6.60475i	−1.20967	−	0.313095i
$446$	−2.07237	−	2.85238i	−0.0981298	−	0.135064i
$447$	−0.788793	+	9.69781i	−0.0373086	+	0.458691i
$448$	−7.76132	+	15.2324i	−0.366688	+	0.719665i
$449$	−23.5930			−1.11342			−0.556711	−	0.830706i	$-0.687937\pi$
$449$	−23.5930			−1.11342			−0.556711	+	0.830706i	$0.687937\pi$
$450$	−21.8414	−	4.37335i	−1.02961	−	0.206162i
$451$	−25.4385			−1.19785
$452$	−0.451642	+	0.886396i	−0.0212434	+	0.0416926i
$453$	2.06162	−	25.3465i	0.0968632	−	1.19088i
$454$	−10.6217	−	14.6195i	−0.498501	−	0.686128i
$455$	20.2241	+	24.5436i	0.948120	+	1.15062i
$456$	13.9118	+	8.57536i	0.651480	+	0.401578i
$457$	−1.82957	+	1.82957i	−0.0855837	+	0.0855837i	−0.748603	−	0.663019i	$-0.769275\pi$
$457$	−1.82957	+	1.82957i	−0.0855837	+	0.0855837i	0.663019	+	0.748603i	$0.269275\pi$
$458$	21.2734	−	3.36937i	0.994040	−	0.157441i
$459$	3.98765	+	0.345378i	0.186128	+	0.0161209i
$460$	−0.437332	−	0.190260i	−0.0203907	−	0.00887092i
$461$	24.9186	−	8.09654i	1.16057	−	0.377094i	0.335458	−	0.942055i	$-0.391109\pi$
$461$	24.9186	−	8.09654i	1.16057	−	0.377094i	0.825117	+	0.564962i	$0.191109\pi$
$462$	20.9371	−	12.7550i	0.974084	−	0.593416i
$463$	19.1081	−	9.73607i	0.888030	−	0.452474i	0.0504107	−	0.998729i	$-0.483947\pi$
$463$	19.1081	−	9.73607i	0.888030	−	0.452474i	0.837619	+	0.546255i	$0.183947\pi$
$464$	−0.186817	−	0.574964i	−0.00867277	−	0.0266920i
$465$	0.516871	+	1.70779i	0.0239693	+	0.0791971i
$466$	−9.94359	+	30.6032i	−0.460628	+	1.41767i
$467$	4.62519	+	29.2023i	0.214028	+	1.35132i	0.827439	+	0.561556i	$0.189797\pi$
$467$	4.62519	+	29.2023i	0.214028	+	1.35132i	−0.613411	+	0.789764i	$0.710203\pi$
$468$	2.89744	+	2.12839i	0.133934	+	0.0983848i
$469$	−2.78618	+	3.83484i	−0.128654	+	0.177077i
$470$	−4.89669	−	12.4382i	−0.225868	−	0.573730i
$471$	−11.7338	−	13.8115i	−0.540663	−	0.636402i
$472$	−1.15394	+	7.28567i	−0.0531142	+	0.335350i
$473$	−27.5396	−	14.0321i	−1.26627	−	0.645197i
$474$	−0.172046	−	2.26176i	−0.00790233	−	0.103886i
$475$	17.3741	+	3.38429i	0.797177	+	0.155282i
$476$			0.385004i			0.0176467i
$477$	2.76850	−	8.37111i	0.126761	−	0.383287i
$478$	−12.3944	−	1.96307i	−0.566905	−	0.0897889i
$479$	24.4450	−	17.7603i	1.11692	−	0.811489i	0.133180	−	0.991092i	$-0.457481\pi$
$479$	24.4450	−	17.7603i	1.11692	−	0.811489i	0.983739	+	0.179603i	$0.0574813\pi$
$480$	0.610851	+	4.43706i	0.0278814	+	0.202523i
$481$	−24.1560	−	17.5504i	−1.10142	−	0.800229i
$482$	1.64287	+	1.64287i	0.0748309	+	0.0748309i
$483$	−1.01234	−	4.26589i	−0.0460631	−	0.194105i
$484$	−0.842420	−	0.273719i	−0.0382918	−	0.0124418i
$485$	−27.2467	−	24.1154i	−1.23721	−	1.09502i
$486$	−14.8022	−	17.7978i	−0.671441	−	0.807326i
$487$	−6.83736	−	13.4191i	−0.309830	−	0.608076i	0.682613	−	0.730780i	$-0.260843\pi$
$487$	−6.83736	−	13.4191i	−0.309830	−	0.608076i	−0.992443	+	0.122704i	$0.960843\pi$
$488$	−4.85767	−	9.53371i	−0.219896	−	0.431571i
$489$	−5.63380	−	13.7026i	−0.254769	−	0.619653i
$490$	−3.05653	+	1.79962i	−0.138080	+	0.0812987i
$491$	31.9571	+	10.3835i	1.44220	+	0.468601i	0.922584	−	0.385797i	$-0.126073\pi$
$491$	31.9571	+	10.3835i	1.44220	+	0.468601i	0.519621	+	0.854397i	$0.326073\pi$
$492$	−2.24798	+	0.533470i	−0.101347	+	0.0240507i
$493$	0.0753812	+	0.0753812i	0.00339500	+	0.00339500i
$494$	−24.8362	−	18.0446i	−1.11743	−	0.811863i
$495$	−10.5991	+	24.0185i	−0.476396	+	1.07955i
$496$	1.62815	−	1.18292i	0.0731060	−	0.0531146i
$497$	−8.54766	−	1.35382i	−0.383415	−	0.0607270i
$498$	22.6739	+	9.46149i	1.01604	+	0.423980i
$499$		−	32.3318i		−	1.44737i	−0.690131	−	0.723684i	$-0.742447\pi$
$499$		−	32.3318i		−	1.44737i	0.690131	−	0.723684i	$-0.257553\pi$
$500$	1.09360	+	2.01700i	0.0489072	+	0.0902032i
$501$	30.2183	−	2.29862i	1.35006	−	0.102695i
$502$	11.1285	+	5.67027i	0.496691	+	0.253077i
$503$	−0.102368	+	0.646326i	−0.00456436	+	0.0288182i	−0.989865	−	0.142009i	$-0.954644\pi$
$503$	−0.102368	+	0.646326i	−0.00456436	+	0.0288182i	0.985301	+	0.170827i	$0.0546439\pi$
$504$	−13.8420	+	13.6978i	−0.616574	+	0.610149i
$505$	27.9368	+	17.8055i	1.24317	+	0.792332i
$506$	−3.55037	+	4.88666i	−0.157833	+	0.217238i
$507$	27.7291	+	23.8087i	1.23149	+	1.05738i
$508$	−0.366416	−	2.31346i	−0.0162571	−	0.102643i
$509$	7.29902	−	22.4641i	0.323523	−	0.995703i	−0.648579	−	0.761147i	$-0.724636\pi$
$509$	7.29902	−	22.4641i	0.323523	−	0.995703i	0.972103	−	0.234556i	$-0.0753635\pi$
$510$	−2.53086	−	3.63620i	−0.112069	−	0.161014i
$511$	−9.02509	−	27.7764i	−0.399247	−	1.22875i
$512$	−16.2462	+	8.27787i	−0.717989	+	0.365834i
$513$	11.8364	+	14.0811i	0.522588	+	0.621696i
$514$	−21.2545	+	6.90601i	−0.937497	+	0.304611i
$515$	13.2561	−	14.9773i	0.584133	−	0.659980i
$516$	−2.72792	−	0.662476i	−0.120090	−	0.0291639i
$517$	−15.5608	+	2.46458i	−0.684361	+	0.108392i
$518$	−13.0764	+	13.0764i	−0.574545	+	0.574545i
$519$	−15.2131	+	24.6801i	−0.667779	+	1.08334i
$520$	2.11777	+	34.7377i	0.0928702	+	1.52335i
$521$	20.7338	+	28.5376i	0.908365	+	1.25026i	0.967722	+	0.252020i	$0.0810948\pi$
$521$	20.7338	+	28.5376i	0.908365	+	1.25026i	−0.0593574	+	0.998237i	$0.518905\pi$
$522$	0.00322924	−	0.616540i	0.000141340	−	0.0269852i
$523$	1.15413	−	2.26510i	0.0504664	−	0.0990460i	−0.864396	−	0.502812i	$-0.832299\pi$
$523$	1.15413	−	2.26510i	0.0504664	−	0.0990460i	0.914862	+	0.403766i	$0.132299\pi$
$524$	0.909212			0.0397191
$525$	−8.80464	+	19.1667i	−0.384266	+	0.836505i
$526$	−2.78282			−0.121337
$527$	−0.161111	+	0.316199i	−0.00701813	+	0.0137738i
$528$	29.5134	+	2.40054i	1.28441	+	0.104470i
$529$	−12.8841	−	17.7335i	−0.560180	−	0.771021i
$530$	−9.08079	+	3.57495i	−0.394444	+	0.155286i
$531$	−3.80816	+	7.37815i	−0.165260	+	0.320185i
$532$	−1.25116	+	1.25116i	−0.0542445	+	0.0542445i
$533$	−37.4903	+	5.93788i	−1.62389	+	0.257198i
$534$	−7.15521	+	29.4635i	−0.309636	+	1.27501i
$535$	31.7582	−	7.03405i	1.37303	−	0.304108i
$536$	−4.93333	+	1.60294i	−0.213087	+	0.0692363i
$537$	8.72967	+	14.3296i	0.376713	+	0.618369i
$538$	31.0774	−	15.8347i	1.33984	−	0.682683i
$539$	1.29183	+	3.97585i	0.0556432	+	0.171252i
$540$	−0.432946	+	2.34477i	−0.0186310	+	0.100903i
$541$	3.34503	−	10.2949i	0.143814	−	0.442614i	−0.853043	−	0.521841i	$-0.825245\pi$
$541$	3.34503	−	10.2949i	0.143814	−	0.442614i	0.996857	+	0.0792273i	$0.0252453\pi$
$542$	0.175078	+	1.10540i	0.00752024	+	0.0474809i
$543$	−10.8361	+	12.6203i	−0.465020	+	0.541590i
$544$	−0.523604	+	0.720680i	−0.0224494	+	0.0308989i
$545$	17.1711	−	14.1491i	0.735528	−	0.606079i
$546$	27.8790	−	23.6850i	1.19311	−	1.01362i
$547$	−3.60575	+	22.7658i	−0.154171	+	0.973396i	0.782364	+	0.622821i	$0.214014\pi$
$547$	−3.60575	+	22.7658i	−0.154171	+	0.973396i	−0.936535	+	0.350574i	$0.885986\pi$
$548$	−1.51604	−	0.772462i	−0.0647621	−	0.0329979i
$549$	−1.82174	−	11.9053i	−0.0777500	−	0.508104i
$550$	27.9359	−	7.99857i	1.19119	−	0.341060i
$551$			0.489935i			0.0208719i
$552$	1.84768	−	4.42785i	0.0786423	−	0.188462i
$553$	−2.12142	−	0.336000i	−0.0902120	−	0.0142882i
$554$	−11.0243	+	8.00960i	−0.468376	+	0.340295i
$555$	3.49366	−	19.4924i	0.148297	−	0.827404i
$556$	3.63566	+	2.64146i	0.154186	+	0.112023i
$557$	6.52436	+	6.52436i	0.276446	+	0.276446i	0.831689	−	0.555242i	$-0.187375\pi$
$557$	6.52436	+	6.52436i	0.276446	+	0.276446i	−0.555242	+	0.831689i	$0.687375\pi$
$558$	1.95527	−	0.624004i	0.0827733	−	0.0264162i
$559$	−43.8621	−	14.2517i	−1.85517	−	0.602782i
$560$	23.6800	+	2.28484i	1.00066	+	0.0965520i
$561$	−4.82925	+	1.98554i	−0.203891	+	0.0838296i
$562$	16.9179	+	33.2033i	0.713639	+	1.40060i
$563$	−4.90871	−	9.63388i	−0.206877	−	0.406020i	0.764132	−	0.645059i	$-0.223167\pi$
$563$	−4.90871	−	9.63388i	−0.206877	−	0.406020i	−0.971010	+	0.239040i	$0.923167\pi$
$564$	−1.32341	+	0.544117i	−0.0557255	+	0.0229115i
$565$	−10.7896	−	1.04107i	−0.453923	−	0.0437982i
$566$	33.3891	+	10.8488i	1.40345	+	0.456008i
$567$	−19.6338	+	9.74624i	−0.824544	+	0.409304i
$568$	−6.69663	−	6.69663i	−0.280984	−	0.280984i
$569$	−15.4318	−	11.2119i	−0.646937	−	0.470027i	0.215290	−	0.976550i	$-0.430930\pi$
$569$	−15.4318	−	11.2119i	−0.646937	−	0.470027i	−0.862226	+	0.506523i	$0.830930\pi$
$570$	3.59203	−	20.0412i	0.150453	−	0.839434i
$571$	−7.63086	+	5.54414i	−0.319342	+	0.232015i	−0.735894	−	0.677096i	$-0.763238\pi$
$571$	−7.63086	+	5.54414i	−0.319342	+	0.232015i	0.416553	+	0.909111i	$0.363238\pi$
$572$	−4.63227	−	0.733679i	−0.193685	−	0.0306767i
$573$	7.11298	−	17.0459i	0.297149	−	0.712101i
$574$			23.5090i			0.981248i
$575$	0.183409	−	5.19340i	0.00764870	−	0.216580i
$576$	−20.8157	+	3.18521i	−0.867319	+	0.132717i
$577$	5.93629	+	3.02469i	0.247131	+	0.125920i	0.573169	−	0.819437i	$-0.305714\pi$
$577$	5.93629	+	3.02469i	0.247131	+	0.125920i	−0.326038	+	0.945357i	$0.605714\pi$
$578$	−3.81134	+	24.0639i	−0.158531	+	1.00092i
$579$	−16.4791	+	14.0000i	−0.684847	+	0.581820i
$580$	−0.0490112	+	0.0403855i	−0.00203508	+	0.00167692i
$581$	13.6745	−	18.8213i	0.567313	−	0.780839i
$582$	−27.2651	+	31.7546i	−1.13017	+	1.31627i
$583$	1.79933	+	11.3605i	0.0745205	+	0.470504i
$584$	9.87633	−	30.3962i	0.408685	−	1.25780i
$585$	−10.0142	+	37.8716i	−0.414035	+	1.56580i
$586$	−11.3543	−	34.9448i	−0.469040	−	1.44356i
$587$	−14.2824	+	7.27726i	−0.589499	+	0.300365i	−0.723180	−	0.690660i	$-0.757320\pi$
$587$	−14.2824	+	7.27726i	−0.589499	+	0.300365i	0.133681	+	0.991024i	$0.457320\pi$
$588$	0.197536	+	0.324252i	0.00814624	+	0.0133719i
$589$	−1.55112	+	0.503991i	−0.0639129	+	0.0207666i
$590$	8.97270	−	1.98734i	0.369400	−	0.0818176i
$591$	−3.12766	+	12.8790i	−0.128655	+	0.529770i
$592$	−22.0607	+	3.49407i	−0.906689	+	0.143605i
$593$	−19.4509	+	19.4509i	−0.798754	+	0.798754i	−0.982899	−	0.184145i	$-0.941048\pi$
$593$	−19.4509	+	19.4509i	−0.798754	+	0.798754i	0.184145	+	0.982899i	$0.441048\pi$
$594$	27.8080	+	11.7753i	1.14098	+	0.483145i
$595$	−3.90345	+	1.53672i	−0.160026	+	0.0629994i
$596$	−0.677606	−	0.932645i	−0.0277558	−	0.0382026i
$597$	−28.6158	−	2.32753i	−1.17117	−	0.0952595i
$598$	−4.09174	+	8.03050i	−0.167324	+	0.328391i
$599$	−8.83948			−0.361171			−0.180586	−	0.983559i	$-0.557799\pi$
$599$	−8.83948			−0.361171			−0.180586	+	0.983559i	$0.557799\pi$
$600$	−20.1235	+	11.3054i	−0.821537	+	0.461541i
$601$	−18.4292			−0.751744			−0.375872	−	0.926672i	$-0.622657\pi$
$601$	−18.4292			−0.751744			−0.375872	+	0.926672i	$0.622657\pi$
$602$	−12.9678	+	25.4507i	−0.528528	+	1.03729i
$603$	−5.83864	−	0.0305810i	−0.237768	−	0.00124535i
$604$	1.77101	+	2.43759i	0.0720615	+	0.0991842i
$605$	−0.587307	−	9.63358i	−0.0238774	−	0.391661i
$606$	19.9958	−	32.4392i	0.812274	−	1.31775i
$607$	11.7369	−	11.7369i	0.476386	−	0.476386i	−0.427588	−	0.903974i	$-0.640637\pi$
$607$	11.7369	−	11.7369i	0.476386	−	0.476386i	0.903974	+	0.427588i	$0.140637\pi$
$608$	−4.04357	+	0.640439i	−0.163988	+	0.0259732i
$609$	−0.567324	−	0.137775i	−0.0229891	−	0.00558292i
$610$	−8.83518	+	9.98239i	−0.357726	+	0.404175i
$611$	−22.3576	+	7.26441i	−0.904490	+	0.293887i
$612$	−0.385119	+	0.276735i	−0.0155675	+	0.0111863i
$613$	12.8370	−	6.54078i	0.518482	−	0.264180i	−0.175109	−	0.984549i	$-0.556028\pi$
$613$	12.8370	−	6.54078i	0.518482	−	0.264180i	0.693591	+	0.720369i	$0.256028\pi$
$614$	−2.59692	−	7.99250i	−0.104803	−	0.322551i
$615$	−14.3814	−	20.6623i	−0.579913	−	0.833186i
$616$	7.85037	−	24.1610i	0.316300	−	0.973473i
$617$	2.14327	+	13.5321i	0.0862849	+	0.544782i	0.992527	+	0.122023i	$0.0389382\pi$
$617$	2.14327	+	13.5321i	0.0862849	+	0.544782i	−0.906242	+	0.422759i	$0.861062\pi$
$618$	−17.4553	−	14.9875i	−0.702155	−	0.602884i
$619$	−5.41760	+	7.45669i	−0.217752	+	0.299710i	−0.903893	−	0.427759i	$-0.859303\pi$
$619$	−5.41760	+	7.45669i	−0.217752	+	0.299710i	0.686141	+	0.727468i	$0.259303\pi$
$620$	−0.178277	−	0.113624i	−0.00715977	−	0.00456326i
$621$	3.53950	−	4.07889i	0.142035	−	0.163680i
$622$	7.99679	−	50.4897i	0.320642	−	2.02445i
$623$	25.5809	+	13.0341i	1.02488	+	0.522201i
$624$	44.0561	−	3.35122i	1.76365	−	0.134156i
$625$	−16.0848	+	19.1384i	−0.643392	+	0.765537i
$626$		−	28.9960i		−	1.15891i
$627$	−22.1461	−	9.24125i	−0.884432	−	0.369060i
$628$	2.12081	+	0.335903i	0.0846294	+	0.0134040i
$629$	3.18640	−	2.31506i	0.127050	−	0.0923073i
$630$	22.1968	+	9.79521i	0.884340	+	0.390251i
$631$	32.6151	+	23.6962i	1.29839	+	0.943333i	0.999938	−	0.0110933i	$-0.00353119\pi$
$631$	32.6151	+	23.6962i	1.29839	+	0.943333i	0.298448	+	0.954426i	$0.403531\pi$
$632$	−1.66202	−	1.66202i	−0.0661115	−	0.0661115i
$633$	40.4057	−	9.58872i	1.60598	−	0.381117i
$634$	4.14616	+	1.34717i	0.164665	+	0.0535029i
$635$	21.9930	−	12.9490i	0.872765	−	0.513866i
$636$	0.397246	+	0.966186i	0.0157518	+	0.0383117i
$637$	2.83190	+	5.55791i	0.112204	+	0.220213i
$638$	0.365148	+	0.716643i	0.0144563	+	0.0283722i
$639$	−4.78970	−	9.52330i	−0.189478	−	0.376736i
$640$	21.3264	+	18.8755i	0.843000	+	0.746120i
$641$	−41.3915	−	13.4489i	−1.63487	−	0.531201i	−0.659484	−	0.751718i	$-0.729225\pi$
$641$	−41.3915	−	13.4489i	−1.63487	−	0.531201i	−0.975383	+	0.220518i	$0.929225\pi$
$642$	−8.63927	−	36.4049i	−0.340965	−	1.43679i
$643$	19.6168	+	19.6168i	0.773612	+	0.773612i	0.978736	−	0.205124i	$-0.0657598\pi$
$643$	19.6168	+	19.6168i	0.773612	+	0.773612i	−0.205124	+	0.978736i	$0.565760\pi$
$644$	0.420259	+	0.305336i	0.0165605	+	0.0120319i
$645$	−4.17166	−	30.3018i	−0.164259	−	1.19313i
$646$	3.27612	−	2.38024i	0.128897	−	0.0936494i
$647$	26.5196	+	4.20028i	1.04259	+	0.165130i	0.654167	−	0.756350i	$-0.273019\pi$
$647$	26.5196	+	4.20028i	1.04259	+	0.165130i	0.388425	+	0.921481i	$0.373019\pi$
$648$	−23.6513	−	4.00040i	−0.929111	−	0.157150i
$649$		−	10.8315i		−	0.425173i
$650$	39.3038	−	18.3088i	1.54162	−	0.718130i
$651$	−0.147408	−	1.93786i	−0.00577737	−	0.0759508i
$652$	1.56406	+	0.796926i	0.0612531	+	0.0312100i
$653$	3.19926	−	20.1993i	0.125197	−	0.790460i	−0.842566	−	0.538594i	$-0.818956\pi$
$653$	3.19926	−	20.1993i	0.125197	−	0.790460i	0.967762	−	0.251866i	$-0.0810443\pi$
$654$	−16.5703	−	19.5046i	−0.647952	−	0.762689i
$655$	3.62906	+	9.21823i	0.141799	+	0.360186i
$656$	−16.6897	+	22.9714i	−0.651623	+	0.896883i
$657$	21.2975	−	28.9930i	0.830896	−	1.13112i
$658$	2.27765	+	14.3805i	0.0887919	+	0.560610i
$659$	−2.65726	+	8.17820i	−0.103512	+	0.318578i	−0.989378	−	0.145363i	$-0.953565\pi$
$659$	−2.65726	+	8.17820i	−0.103512	+	0.318578i	0.885866	+	0.463941i	$0.153565\pi$
$660$	−0.901054	−	2.97717i	−0.0350735	−	0.115886i
$661$	12.9264	+	39.7835i	0.502781	+	1.54740i	0.804470	+	0.593993i	$0.202449\pi$
$661$	12.9264	+	39.7835i	0.502781	+	1.54740i	−0.301689	+	0.953406i	$0.597551\pi$
$662$	−5.34217	+	2.72197i	−0.207629	+	0.105792i
$663$	−6.65370	+	4.05346i	−0.258408	+	0.157423i
$664$	24.2126	−	7.86716i	0.939632	−	0.305305i
$665$	−17.6790	−	7.69120i	−0.685562	−	0.298252i
$666$	−22.4794	−	3.68118i	−0.871060	−	0.142643i
$667$	0.142067	−	0.0225011i	0.00550084	−	0.000871248i
$668$	−2.53899	+	2.53899i	−0.0982366	+	0.0982366i
$669$	−3.50067	−	2.15784i	−0.135344	−	0.0834271i
$670$	4.10973	+	4.98751i	0.158773	+	0.192684i
$671$	9.23504	+	12.7109i	0.356515	+	0.490700i
$672$	0.395493	−	4.86238i	0.0152565	−	0.187570i
$673$	10.4947	−	20.5969i	0.404540	−	0.793954i	−0.595416	−	0.803418i	$-0.703013\pi$
$673$	10.4947	−	20.5969i	0.404540	−	0.793954i	0.999955	+	0.00946407i	$0.00301255\pi$
$674$	15.8424			0.610226
$675$	−25.5011	+	4.96949i	−0.981536	+	0.191276i
$676$	−4.33029			−0.166550
$677$	9.26592	−	18.1854i	0.356118	−	0.698921i	−0.641557	−	0.767076i	$-0.721711\pi$
$677$	9.26592	−	18.1854i	0.356118	−	0.698921i	0.997675	+	0.0681543i	$0.0217110\pi$
$678$	−1.01083	+	12.4276i	−0.0388206	+	0.477280i
$679$	23.2949	+	32.0627i	0.893976	+	1.23045i
$680$	−4.44427	−	1.15030i	−0.170430	−	0.0441120i
$681$	−17.9423	−	11.0598i	−0.687549	−	0.423811i
$682$	−1.89325	+	1.89325i	−0.0724964	+	0.0724964i
$683$	−2.14122	+	0.339136i	−0.0819315	+	0.0129767i	−0.197266	−	0.980350i	$-0.563206\pi$
$683$	−2.14122	+	0.339136i	−0.0819315	+	0.0129767i	0.115334	+	0.993327i	$0.463206\pi$
$684$	−2.15084	−	0.352216i	−0.0822393	−	0.0134673i
$685$	1.78059	−	18.4539i	0.0680327	−	0.705089i
$686$	27.7525	−	9.01733i	1.05959	−	0.344283i
$687$	21.4542	−	13.0700i	0.818529	−	0.498651i
$688$	−30.7394	+	15.6625i	−1.17193	+	0.597127i
$689$	5.30356	+	16.3227i	0.202049	+	0.621844i
$690$	−5.97633	−	0.121153i	−0.227515	−	0.00461223i
$691$	4.06682	−	12.5164i	0.154709	−	0.476146i	−0.843422	−	0.537251i	$-0.819463\pi$
$691$	4.06682	−	12.5164i	0.154709	−	0.476146i	0.998131	+	0.0611055i	$0.0194626\pi$
$692$	−0.537362	−	3.39277i	−0.0204274	−	0.128974i
$693$	16.9287	−	23.0456i	0.643068	−	0.875429i
$694$	21.6736	−	29.8311i	0.822717	−	1.13237i
$695$	−12.2695	+	47.4041i	−0.465409	+	1.79814i
$696$	−0.413645	−	0.486892i	−0.0156792	−	0.0184556i
$697$	0.783260	−	4.94531i	0.0296681	−	0.187317i
$698$	−4.87441	−	2.48363i	−0.184499	−	0.0940069i
$699$	2.84669	+	37.4234i	0.107672	+	1.41548i
$700$	−0.687888	−	2.40253i	−0.0259997	−	0.0908070i
$701$			21.8766i			0.826268i	0.910670	+	0.413134i	$0.135566\pi$
$701$			21.8766i			0.826268i	−0.910670	+	0.413134i	$0.864434\pi$
$702$	43.7310	+	10.8629i	1.65052	+	0.409996i
$703$	17.8782	+	2.83162i	0.674288	+	0.106797i
$704$	22.2243	−	16.1469i	0.837612	−	0.608560i
$705$	−10.7989	−	11.2458i	−0.406712	−	0.423543i
$706$	−0.662542	−	0.481365i	−0.0249351	−	0.0181164i
$707$	−25.5150	−	25.5150i	−0.959591	−	0.959591i
$708$	−0.227147	−	0.957171i	−0.00853671	−	0.0359727i
$709$	24.3739	+	7.91956i	0.915381	+	0.297425i	0.728570	−	0.684971i	$-0.240185\pi$
$709$	24.3739	+	7.91956i	0.915381	+	0.297425i	0.186810	+	0.982396i	$0.440185\pi$
$710$	−4.70697	+	10.8194i	−0.176649	+	0.406046i
$711$	−1.18874	−	2.36356i	−0.0445813	−	0.0886405i
$712$	14.2635	+	27.9936i	0.534546	+	1.04911i
$713$	0.217380	+	0.426633i	0.00814096	+	0.0159775i
$714$	1.83494	+	4.46296i	0.0686709	+	0.167022i
$715$	−11.0508	−	49.8937i	−0.413278	−	1.86592i
$716$	−1.89075	−	0.614342i	−0.0706606	−	0.0229590i
$717$	−14.2411	+	3.37956i	−0.531842	+	0.126212i
$718$	−0.196905	−	0.196905i	−0.00734844	−	0.00734844i
$719$	5.09685	+	3.70308i	0.190081	+	0.138102i	0.678756	−	0.734364i	$-0.262520\pi$
$719$	5.09685	+	3.70308i	0.190081	+	0.138102i	−0.488675	+	0.872466i	$0.662520\pi$
$720$	14.7352	+	25.3293i	0.549150	+	0.943967i
$721$	−17.6247	+	12.8051i	−0.656376	+	0.476885i
$722$	−9.48601	−	1.50244i	−0.353033	−	0.0559149i
$723$	2.50090	+	1.04359i	0.0930096	+	0.0388115i
$724$		−	1.97084i		−	0.0732459i
$725$	−0.605082	−	0.335715i	−0.0224722	−	0.0124681i
$726$	−11.0699	+	0.842053i	−0.410841	+	0.0312515i
$727$	−14.0192	−	7.14311i	−0.519942	−	0.264923i	0.174266	−	0.984699i	$-0.444245\pi$
$727$	−14.0192	−	7.14311i	−0.519942	−	0.264923i	−0.694207	+	0.719775i	$0.744245\pi$
$728$	5.92990	−	37.4399i	0.219777	−	1.38762i
$729$	−23.8616	−	12.6342i	−0.883763	−	0.467934i
$730$	−39.7448	+	2.42303i	−1.47102	+	0.0896802i
$731$	3.57583	−	4.92171i	0.132257	−	0.182036i
$732$	1.08265	+	0.929588i	0.0400160	+	0.0343586i
$733$	−3.48700	−	22.0161i	−0.128795	−	0.813182i	−0.964516	−	0.264026i	$-0.914949\pi$
$733$	−3.48700	−	22.0161i	−0.128795	−	0.813182i	0.835720	−	0.549155i	$-0.185051\pi$
$734$	−9.52549	+	29.3164i	−0.351592	+	1.08209i
$735$	−2.49905	+	3.29699i	−0.0921787	+	0.121611i
$736$	0.371416	+	1.14310i	0.0136906	+	0.0421353i
$737$	6.78662	−	3.45796i	0.249988	−	0.127375i
$738$	−23.5160	+	16.8979i	−0.865636	+	0.622021i
$739$	−34.2550	+	11.1301i	−1.26009	+	0.409428i	−0.861526	−	0.507713i	$-0.830491\pi$
$739$	−34.2550	+	11.1301i	−1.26009	+	0.409428i	−0.398563	+	0.917141i	$0.630491\pi$
$740$	1.19044	+	2.02188i	0.0437614	+	0.0743256i
$741$	−34.7952	−	8.45003i	−1.27823	−	0.310420i
$742$	10.4988	−	1.66285i	0.385424	−	0.0610452i
$743$	21.4863	−	21.4863i	0.788255	−	0.788255i	−0.192953	−	0.981208i	$-0.561806\pi$
$743$	21.4863	−	21.4863i	0.788255	−	0.788255i	0.981208	+	0.192953i	$0.0618065\pi$
$744$	1.11598	−	1.81045i	0.0409137	−	0.0663743i
$745$	6.75120	−	10.5926i	0.247345	−	0.388084i
$746$	−4.20934	−	5.79366i	−0.154115	−	0.212121i
$747$	28.6559	+	0.150090i	1.04846	+	0.00549152i
$748$	0.280863	−	0.551226i	0.0102694	−	0.0201548i
$749$	−35.4294			−1.29456
$750$	22.2900	+	18.1689i	0.813918	+	0.663436i
$751$	44.7068			1.63137			0.815686	−	0.578494i	$-0.196360\pi$
$751$	44.7068			1.63137			0.815686	+	0.578494i	$0.196360\pi$
$752$	−7.98354	+	15.6686i	−0.291130	+	0.571374i
$753$	14.5198	+	1.18100i	0.529130	+	0.0430380i
$754$	0.705420	+	0.970928i	0.0256899	+	0.0353591i
$755$	−17.6452	+	27.6853i	−0.642173	+	1.00757i
$756$	1.01269	−	2.39153i	0.0368311	−	0.0869791i
$757$	−33.8318	+	33.8318i	−1.22964	+	1.22964i	−0.265539	+	0.964100i	$0.585550\pi$
$757$	−33.8318	+	33.8318i	−1.22964	+	1.22964i	−0.964100	+	0.265539i	$0.914450\pi$
$758$	−10.2302	+	1.62031i	−0.371578	+	0.0588521i
$759$	−1.66259	+	6.84615i	−0.0603481	+	0.248499i
$760$	−10.7045	−	18.1808i	−0.388291	−	0.659485i
$761$	1.37065	−	0.445350i	0.0496859	−	0.0161439i	−0.284069	−	0.958804i	$-0.591684\pi$
$761$	1.37065	−	0.445350i	0.0496859	−	0.0161439i	0.333755	+	0.942660i	$0.391684\pi$
$762$	−15.2735	−	25.0712i	−0.553300	−	0.908234i
$763$	−21.5929	+	11.0021i	−0.781714	+	0.398303i
$764$	0.676257	+	2.08131i	0.0244661	+	0.0752990i
$765$	−4.34291	−	2.80004i	−0.157018	−	0.101236i
$766$	−4.69436	+	14.4477i	−0.169614	+	0.522018i
$767$	−2.52830	−	15.9630i	−0.0912915	−	0.576392i
$768$	5.50072	−	6.40647i	0.198490	−	0.231173i
$769$	−13.9798	+	19.2415i	−0.504124	+	0.693867i	−0.982915	−	0.184062i	$-0.941075\pi$
$769$	−13.9798	+	19.2415i	−0.504124	+	0.693867i	0.478791	+	0.877929i	$0.341075\pi$
$770$	−31.5919	+	1.92598i	−1.13849	+	0.0694077i
$771$	−19.8653	+	16.8768i	−0.715430	+	0.607802i
$772$	0.400778	−	2.53041i	0.0144243	−	0.0910716i
$773$	3.87030	+	1.97202i	0.139205	+	0.0709285i	0.522206	−	0.852820i	$-0.325109\pi$
$773$	3.87030	+	1.97202i	0.139205	+	0.0709285i	−0.383001	+	0.923748i	$0.625109\pi$
$774$	−34.7793	+	5.32192i	−1.25012	+	0.191293i
$775$	0.440424	−	2.26102i	0.0158205	−	0.0812183i
$776$			43.3696i			1.55688i
$777$	−8.30643	+	19.9059i	−0.297991	+	0.714120i
$778$	−47.0176	−	7.44686i	−1.68566	−	0.266983i
$779$	18.6162	−	13.5255i	0.666995	−	0.484601i
$780$	−2.02287	−	4.17732i	−0.0724304	−	0.149572i
$781$	11.2504	+	8.17389i	0.402571	+	0.292485i
$782$	−0.840661	−	0.840661i	−0.0300620	−	0.0300620i
$783$	−0.269968	−	0.666523i	−0.00964785	−	0.0238196i
$784$	4.43781	+	1.44193i	0.158493	+	0.0514975i
$785$	5.05944	+	22.8430i	0.180579	+	0.815301i
$786$	10.5395	−	4.33332i	0.375933	−	0.154564i
$787$	−16.5734	−	32.5272i	−0.590779	−	1.15947i	−0.971999	−	0.234985i	$-0.924496\pi$
$787$	−16.5734	−	32.5272i	−0.590779	−	1.15947i	0.381220	−	0.924484i	$-0.375504\pi$
$788$	−0.712893	−	1.39913i	−0.0253958	−	0.0498420i
$789$	−3.00196	+	1.23425i	−0.106873	+	0.0439406i
$790$	−1.16821	+	2.68525i	−0.0415630	+	0.0955369i
$791$	11.2288	+	3.64846i	0.399250	+	0.129724i
$792$	29.8108	−	9.51380i	1.05928	−	0.338058i
$793$	16.5772	+	16.5772i	0.588675	+	0.588675i
$794$	12.3219	+	8.95235i	0.437286	+	0.317707i
$795$	−8.21029	+	7.88403i	−0.291189	+	0.279618i
$796$	2.75200	−	1.99945i	0.0975421	−	0.0708685i
$797$	23.6243	+	3.74172i	0.836816	+	0.132539i	0.560112	−	0.828417i	$-0.310758\pi$
$797$	23.6243	+	3.74172i	0.836816	+	0.132539i	0.276703	+	0.960955i	$0.410758\pi$
$798$	−8.54031	+	20.4664i	−0.302324	+	0.724502i
$799$		−	3.10093i		−	0.109703i
$800$	1.97979	−	5.43275i	0.0699961	−	0.192077i
$801$	5.34914	+	34.9572i	0.189003	+	1.23515i
$802$	19.3199	+	9.84400i	0.682211	+	0.347604i
$803$	−7.34149	+	46.3524i	−0.259076	+	1.63574i
$804$	0.527212	−	0.447899i	0.0185933	−	0.0157962i
$805$	−1.41828	+	5.47962i	−0.0499878	+	0.193131i
$806$	−2.34828	+	3.23213i	−0.0827146	+	0.113847i
$807$	26.5015	−	30.8653i	0.932898	−	1.08651i
$808$	−6.17713	−	39.0009i	−0.217311	−	1.37205i
$809$	1.75262	−	5.39400i	0.0616187	−	0.189643i	−0.915508	−	0.402299i	$-0.868211\pi$
$809$	1.75262	−	5.39400i	0.0616187	−	0.189643i	0.977127	+	0.212656i	$0.0682113\pi$
$810$	6.15654	+	29.2440i	0.216319	+	1.02753i
$811$	5.70569	+	17.5603i	0.200354	+	0.616625i	0.999872	+	0.0159840i	$0.00508808\pi$
$811$	5.70569	+	17.5603i	0.200354	+	0.616625i	−0.799518	+	0.600641i	$0.794912\pi$
$812$	0.0616323	−	0.0314032i	0.00216287	−	0.00110204i
$813$	0.679137	+	1.11479i	0.0238184	+	0.0390975i
$814$	28.2614	−	9.18267i	0.990560	−	0.321853i
$815$	−1.83698	+	19.0384i	−0.0643466	+	0.666885i
$816$	−1.37540	+	5.66357i	−0.0481486	+	0.198265i
$817$	27.6146	−	4.37372i	0.966112	−	0.153017i
$818$	17.3064	−	17.3064i	0.605104	−	0.605104i
$819$	19.5696	−	37.9152i	0.683815	−	1.32486i
$820$	2.88758	+	0.747386i	0.100839	+	0.0260999i
$821$	−15.0984	−	20.7812i	−0.526938	−	0.725268i	0.459722	−	0.888063i	$-0.347949\pi$
$821$	−15.0984	−	20.7812i	−0.526938	−	0.725268i	−0.986660	+	0.162795i	$0.947949\pi$
$822$	−21.2555	−	1.72886i	−0.741370	−	0.0603010i
$823$	−0.894443	+	1.75544i	−0.0311783	+	0.0611909i	−0.906070	−	0.423127i	$-0.860932\pi$
$823$	−0.894443	+	1.75544i	−0.0311783	+	0.0611909i	0.874892	+	0.484318i	$0.160932\pi$
$824$	−23.8400			−0.830507
$825$	26.5882	−	21.0187i	0.925683	−	0.731778i
$826$	−10.0099			−0.348290
$827$	19.2829	−	37.8448i	0.670532	−	1.31599i	−0.265511	−	0.964108i	$-0.585541\pi$
$827$	19.2829	−	37.8448i	0.670532	−	1.31599i	0.936043	−	0.351885i	$-0.114459\pi$
$828$	−0.00335136	+	0.639855i	−0.000116468	+	0.0222365i
$829$	18.3344	+	25.2352i	0.636781	+	0.876453i	0.998439	−	0.0558574i	$-0.0177892\pi$
$829$	18.3344	+	25.2352i	0.636781	+	0.876453i	−0.361658	+	0.932311i	$0.617789\pi$
$830$	−20.1704	−	24.4785i	−0.700126	−	0.849662i
$831$	−8.33993	+	13.5299i	−0.289309	+	0.469346i
$832$	28.9843	−	28.9843i	1.00485	−	1.00485i
$833$	−0.812691	+	0.128718i	−0.0281581	+	0.00445980i
$834$	54.7337	+	13.2921i	1.89527	+	0.460268i
$835$	−35.8763	−	15.6079i	−1.24155	−	0.540133i
$836$	2.70405	−	0.878600i	0.0935216	−	0.0303870i
$837$	1.83248	−	1.54036i	0.0633399	−	0.0532425i
$838$	1.45121	−	0.739427i	0.0501311	−	0.0255431i
$839$	3.12345	+	9.61299i	0.107833	+	0.331877i	0.990385	−	0.138338i	$-0.0441762\pi$
$839$	3.12345	+	9.61299i	0.107833	+	0.331877i	−0.882552	+	0.470216i	$0.844176\pi$
$840$	24.0628	−	7.28269i	0.830244	−	0.251277i
$841$	−8.95557	+	27.5624i	−0.308813	+	0.950428i
$842$	6.75497	+	42.6492i	0.232792	+	1.46979i
$843$	32.9766	+	28.3144i	1.13578	+	0.975200i
$844$	−2.89209	+	3.98062i	−0.0995499	+	0.137019i
$845$	−17.2841	−	43.9036i	−0.594590	−	1.51033i
$846$	−12.7476	+	12.6148i	−0.438272	+	0.433705i
$847$	−1.64450	+	10.3830i	−0.0565058	+	0.356763i
$848$	11.4392	+	5.82858i	0.392825	+	0.200154i
$849$	40.8301	−	3.10583i	1.40128	−	0.106592i
$850$	0.694785	+	5.67709i	0.0238309	+	0.194722i
$851$		−	5.31419i		−	0.182168i
$852$	1.16560	+	0.486389i	0.0399329	+	0.0166634i
$853$	−14.9888	−	2.37400i	−0.513208	−	0.0812842i	−0.105541	−	0.994415i	$-0.533658\pi$
$853$	−14.9888	−	2.37400i	−0.513208	−	0.0812842i	−0.407667	+	0.913131i	$0.633658\pi$
$854$	11.7468	−	8.53457i	0.401968	−	0.292047i
$855$	−5.01390	−	23.2125i	−0.171472	−	0.793852i
$856$	−31.3665	−	22.7891i	−1.07208	−	0.778914i
$857$	26.4246	+	26.4246i	0.902648	+	0.902648i	0.995665	−	0.0930163i	$-0.0296509\pi$
$857$	26.4246	+	26.4246i	0.902648	+	0.902648i	−0.0930163	+	0.995665i	$0.529651\pi$
$858$	−57.1939	+	13.5727i	−1.95257	+	0.463365i
$859$	42.0699	+	13.6693i	1.43541	+	0.466392i	0.920462	−	0.390832i	$-0.127813\pi$
$859$	42.0699	+	13.6693i	1.43541	+	0.466392i	0.514944	+	0.857224i	$0.327813\pi$
$860$	2.71381	+	2.40193i	0.0925401	+	0.0819051i
$861$	10.4269	+	25.3603i	0.355346	+	0.864277i
$862$	−18.0039	−	35.3346i	−0.613215	−	1.20350i
$863$	−24.6618	−	48.4015i	−0.839496	−	1.64760i	−0.759222	−	0.650832i	$-0.774420\pi$
$863$	−24.6618	−	48.4015i	−0.839496	−	1.64760i	−0.0802746	−	0.996773i	$-0.525580\pi$
$864$	5.14810	−	3.09939i	0.175142	−	0.105443i
$865$	32.2534	−	18.9902i	1.09665	−	0.645685i
$866$	−37.7888	−	12.2783i	−1.28412	−	0.417235i
$867$	6.56146	+	27.6492i	0.222839	+	0.939018i
$868$	0.162822	+	0.162822i	0.00552655	+	0.00552655i
$869$	2.79221	+	2.02866i	0.0947191	+	0.0688174i
$870$	−0.375658	+	0.701736i	−0.0127360	+	0.0237911i
$871$	9.19470	−	6.68034i	0.311551	−	0.226355i
$872$	−26.1935	−	4.14864i	−0.887023	−	0.140491i
$873$	−15.3282	+	46.3479i	−0.518781	+	1.56864i
$874$		−	5.46382i		−	0.184816i
$875$	21.6129	−	16.5638i	0.730648	−	0.559959i
$876$	0.323292	+	4.25008i	0.0109230	+	0.143597i
$877$	−43.2252	−	22.0243i	−1.45961	−	0.743709i	−0.469360	−	0.883007i	$-0.655515\pi$
$877$	−43.2252	−	22.0243i	−1.45961	−	0.743709i	−0.990250	+	0.139298i	$0.955515\pi$
$878$	−4.71254	+	29.7538i	−0.159041	+	1.00414i
$879$	−27.7473	−	32.6607i	−0.935894	−	1.10162i
$880$	−32.2367	−	20.5460i	−1.08670	−	0.692605i
$881$	31.2390	−	42.9968i	1.05247	−	1.44860i	0.165820	−	0.986156i	$-0.446973\pi$
$881$	31.2390	−	42.9968i	1.05247	−	1.44860i	0.886649	−	0.462443i	$-0.153027\pi$
$882$	3.83522	+	2.81726i	0.129139	+	0.0948620i
$883$	−1.48257	−	9.36055i	−0.0498923	−	0.315008i	−0.999995	−	0.00307116i	$-0.999022\pi$
$883$	−1.48257	−	9.36055i	−0.0498923	−	0.315008i	0.950103	−	0.311936i	$-0.100978\pi$
$884$	0.285258	−	0.877934i	0.00959427	−	0.0295281i
$885$	8.79784	−	6.12346i	0.295736	−	0.205838i
$886$	7.79887	+	24.0025i	0.262008	+	0.806379i
$887$	−24.1235	+	12.2915i	−0.809986	+	0.412709i	−0.809376	−	0.587291i	$-0.800194\pi$
$887$	−24.1235	+	12.2915i	−0.809986	+	0.412709i	−0.000610667		1.00000i	$0.500194\pi$
$888$	−20.1578	+	12.2802i	−0.676452	+	0.412098i
$889$	−26.4380	+	8.59022i	−0.886702	+	0.288107i
$890$	25.9426	−	29.3111i	0.869597	−	0.982510i
$891$	35.2205	+	0.368958i	1.17993	+	0.0123606i
$892$	0.481236	−	0.0762202i	0.0161130	−	0.00255204i
$893$	10.0772	−	10.0772i	0.337219	−	0.337219i
$894$	−12.2998	−	7.58170i	−0.411367	−	0.253570i
$895$	−1.31817	−	21.6219i	−0.0440615	−	0.722739i
$896$	−18.2333	−	25.0960i	−0.609131	−	0.838397i
$897$	−0.852225	+	10.4777i	−0.0284550	+	0.349839i
$898$	15.9058	−	31.2169i	0.530784	−	1.04172i
$899$	0.0637590			0.00212648
$900$	1.90880	−	2.41499i	0.0636266	−	0.0804996i
$901$	−2.26391			−0.0754218
$902$	17.1500	−	33.6588i	0.571033	−	1.12072i
$903$	−2.70092	+	33.2064i	−0.0898811	+	1.10504i
$904$	7.59433	+	10.4527i	0.252584	+	0.347652i
$905$	19.9818	−	7.86650i	0.664218	−	0.261491i
$906$	32.1472	+	19.8158i	1.06802	+	0.658335i
$907$	−5.89173	+	5.89173i	−0.195632	+	0.195632i	−0.798124	−	0.602493i	$-0.794174\pi$
$907$	−5.89173	+	5.89173i	−0.195632	+	0.195632i	0.602493	+	0.798124i	$0.294174\pi$
$908$	2.46651	−	0.390657i	0.0818541	−	0.0129644i
$909$	7.18281	−	43.8623i	0.238239	−	1.45482i
$910$	−46.1093	+	10.2126i	−1.52851	+	0.338546i
$911$	48.7073	−	15.8260i	1.61374	−	0.524337i	0.643290	−	0.765623i	$-0.277569\pi$
$911$	48.7073	−	15.8260i	1.61374	−	0.524337i	0.970454	+	0.241286i	$0.0775691\pi$
$912$	−22.8746	+	13.9353i	−0.757455	+	0.461445i
$913$	−33.3085	+	16.9715i	−1.10235	+	0.561676i
$914$	−1.18733	−	3.65423i	−0.0392735	−	0.120871i
$915$	−5.10349	+	14.6871i	−0.168716	+	0.485541i
$916$	−0.919787	+	2.83081i	−0.0303906	+	0.0935327i
$917$	−1.68802	−	10.6577i	−0.0557433	−	0.351949i
$918$	−3.14536	+	5.04339i	−0.103812	+	0.166457i
$919$	9.10877	−	12.5372i	0.300471	−	0.413562i	−0.631909	−	0.775042i	$-0.717728\pi$
$919$	9.10877	−	12.5372i	0.300471	−	0.413562i	0.932380	+	0.361480i	$0.117728\pi$
$920$	−4.78026	+	3.93896i	−0.157600	+	0.129864i
$921$	−6.34630	−	7.47008i	−0.209118	−	0.246148i
$922$	−6.08661	+	38.4293i	−0.200452	+	1.26560i
$923$	18.4883	+	9.42028i	0.608551	+	0.310072i
$924$	0.256974	+	3.37825i	0.00845383	+	0.111136i
$925$	−15.7477	+	20.1397i	−0.517780	+	0.662189i
$926$			31.8466i			1.04654i
$927$	−25.4772	−	8.42581i	−0.836780	−	0.276740i
$928$	0.158076	+	0.0250368i	0.00518911	+	0.000821874i
$929$	−33.7506	+	24.5213i	−1.10732	+	0.804517i	−0.982240	−	0.187629i	$-0.939920\pi$
$929$	−33.7506	+	24.5213i	−1.10732	+	0.804517i	−0.125083	+	0.992146i	$0.539920\pi$
$930$	−2.60812	−	0.467458i	−0.0855235	−	0.0153286i
$931$	−3.05931	−	2.22272i	−0.100265	−	0.0728467i
$932$	−3.14437	−	3.14437i	−0.102997	−	0.102997i
$933$	−13.7670	−	58.0124i	−0.450710	−	1.89924i
$934$	−41.7570	−	13.5677i	−1.36633	−	0.443947i
$935$	6.70977	+	0.647413i	0.219433	+	0.0211727i
$936$	41.7133	−	20.9795i	1.36344	−	0.685737i
$937$	−0.368190	−	0.722614i	−0.0120282	−	0.0236068i	0.884914	−	0.465754i	$-0.154217\pi$
$937$	−0.368190	−	0.722614i	−0.0120282	−	0.0236068i	−0.896942	+	0.442147i	$0.854217\pi$
$938$	−3.19567	−	6.27186i	−0.104342	−	0.204784i
$939$	−12.8604	−	31.2793i	−0.419685	−	1.02076i
$940$	1.83874	+	0.177417i	0.0599732	+	0.00578670i
$941$	−16.0740	−	5.22276i	−0.523998	−	0.170257i	0.0350611	−	0.999385i	$-0.488837\pi$
$941$	−16.0740	−	5.22276i	−0.523998	−	0.170257i	−0.559059	+	0.829128i	$0.688837\pi$
$942$	26.1852	−	6.21404i	0.853161	−	0.202464i
$943$	−4.77697	−	4.77697i	−0.155560	−	0.155560i
$944$	−9.78102	−	7.10633i	−0.318345	−	0.231291i
$945$	28.2891	+	0.721729i	0.920245	+	0.0234778i
$946$	37.1330	−	26.9787i	1.20730	−	0.877153i
$947$	−30.9625	−	4.90398i	−1.00615	−	0.159358i	−0.368452	−	0.929647i	$-0.620112\pi$
$947$	−30.9625	−	4.90398i	−1.00615	−	0.159358i	−0.637695	+	0.770289i	$0.720112\pi$
$948$	0.289288	+	0.120716i	0.00939564	+	0.00392066i
$949$			70.0260i			2.27314i
$950$	−16.1911	+	20.7068i	−0.525308	+	0.671816i
$951$	5.07016	−	0.385673i	0.164411	−	0.0125063i
$952$	4.45523	+	2.27005i	0.144395	+	0.0735729i
$953$	−3.98191	+	25.1408i	−0.128987	+	0.814391i	0.835351	+	0.549717i	$0.185264\pi$
$953$	−3.98191	+	25.1408i	−0.128987	+	0.814391i	−0.964338	+	0.264674i	$0.914736\pi$
$954$	9.20972	+	9.30671i	0.298176	+	0.301316i
$955$	−18.4025	+	15.1638i	−0.595492	+	0.490688i
$956$	1.01932	−	1.40298i	0.0329672	−	0.0453755i
$957$	0.711752	+	0.611124i	0.0230077	+	0.0197548i
$958$	7.01924	+	44.3177i	0.226781	+	1.43184i
$959$	−6.24011	+	19.2051i	−0.201504	+	0.620165i
$960$	25.6796	+	8.92315i	0.828804	+	0.287993i
$961$	−9.51394	−	29.2809i	−0.306901	−	0.944545i
$962$	39.5071	−	20.1299i	1.27376	−	0.649013i
$963$	−25.4661	−	35.4399i	−0.820633	−	1.14204i
$964$	−0.305361	+	0.0992179i	−0.00983502	+	0.00319559i
$965$	27.2548	−	6.03661i	0.877364	−	0.194325i
$966$	6.32687	+	1.53648i	0.203564	+	0.0494355i
$967$	50.5329	−	8.00363i	1.62503	−	0.257379i	0.723572	−	0.690249i	$-0.242499\pi$
$967$	50.5329	−	8.00363i	1.62503	−	0.257379i	0.901457	+	0.432869i	$0.142499\pi$
$968$	−8.13450	+	8.13450i	−0.261453	+	0.261453i
$969$	2.47841	−	4.02072i	0.0796180	−	0.129164i
$970$	50.2771	−	19.7932i	1.61430	−	0.635522i
$971$	−18.5870	−	25.5828i	−0.596485	−	0.820991i	0.398896	−	0.916996i	$-0.369393\pi$
$971$	−18.5870	−	25.5828i	−0.596485	−	0.820991i	−0.995381	+	0.0960053i	$0.969393\pi$
$972$	3.12014	−	0.706003i	0.100079	−	0.0226450i
$973$	24.2132	−	47.5211i	0.776240	−	1.52346i
$974$	22.3649			0.716618
$975$	34.2785	−	37.1828i	1.09779	−	1.19080i
$976$	17.5371			0.561349
$977$	−20.2687	+	39.7795i	−0.648452	+	1.27266i	0.299454	+	0.954111i	$0.403195\pi$
$977$	−20.2687	+	39.7795i	−0.648452	+	1.27266i	−0.947906	+	0.318549i	$0.896805\pi$
$978$	21.9286	+	1.78362i	0.701201	+	0.0570338i
$979$	−27.1166	−	37.3229i	−0.866652	−	1.19284i
$980$	−0.0298276	−	0.489261i	−0.000952808	−	0.0156289i
$981$	−26.5260	−	13.6911i	−0.846909	−	0.437124i
$982$	−35.2835	+	35.2835i	−1.12594	+	1.12594i
$983$	−47.0740	+	7.45579i	−1.50143	+	0.237803i	−0.852371	−	0.522938i	$-0.824836\pi$
$983$	−47.0740	+	7.45579i	−1.50143	+	0.237803i	−0.649056	+	0.760740i	$0.724836\pi$
$984$	−7.08124	+	29.1589i	−0.225742	+	0.929550i
$985$	11.3399	−	12.8124i	0.361320	−	0.408236i
$986$	−0.150560	+	0.0489200i	−0.00479481	+	0.00155793i
$987$	8.83512	+	14.5027i	0.281225	+	0.461627i
$988$	3.78004	−	1.92603i	0.120259	−	0.0612751i
$989$	−2.53650	−	7.80654i	−0.0806559	−	0.248233i
$990$	−24.6343	−	30.2169i	−0.782928	−	0.960355i
$991$	1.87960	−	5.78480i	0.0597073	−	0.183760i	−0.916754	−	0.399452i	$-0.869201\pi$
$991$	1.87960	−	5.78480i	0.0597073	−	0.183760i	0.976462	+	0.215691i	$0.0692005\pi$
$992$	0.0833452	+	0.526221i	0.00264621	+	0.0167075i
$993$	−4.55559	+	5.30571i	−0.144567	+	0.168372i
$994$	7.55391	−	10.3971i	0.239595	−	0.329775i
$995$	31.2562	+	19.9211i	0.990889	+	0.631541i
$996$	−2.58754	+	2.19827i	−0.0819893	+	0.0696550i
$997$	−3.87551	+	24.4690i	−0.122739	+	0.774942i	0.847143	+	0.531365i	$0.178321\pi$
$997$	−3.87551	+	24.4690i	−0.122739	+	0.774942i	−0.969882	+	0.243577i	$0.921679\pi$
$998$	42.7795	+	21.7973i	1.35416	+	0.689980i
$999$	−25.8823	+	5.99913i	−0.818880	+	0.189804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.2.l.a.8.3	✓	64
3.2	odd	2	inner	75.2.l.a.8.6	yes	64
5.2	odd	4		375.2.l.a.107.3		64
5.3	odd	4		375.2.l.b.107.6		64
5.4	even	2		375.2.l.c.143.6		64
15.2	even	4		375.2.l.a.107.6		64
15.8	even	4		375.2.l.b.107.3		64
15.14	odd	2		375.2.l.c.143.3		64
25.3	odd	20		375.2.l.c.257.3		64
25.4	even	10		375.2.l.b.368.3		64
25.21	even	5		375.2.l.a.368.6		64
25.22	odd	20	inner	75.2.l.a.47.6	yes	64
75.29	odd	10		375.2.l.b.368.6		64
75.47	even	20	inner	75.2.l.a.47.3	yes	64
75.53	even	20		375.2.l.c.257.6		64
75.71	odd	10		375.2.l.a.368.3		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.l.a.8.3	✓	64	1.1	even	1	trivial
75.2.l.a.8.6	yes	64	3.2	odd	2	inner
75.2.l.a.47.3	yes	64	75.47	even	20	inner
75.2.l.a.47.6	yes	64	25.22	odd	20	inner
375.2.l.a.107.3		64	5.2	odd	4
375.2.l.a.107.6		64	15.2	even	4
375.2.l.a.368.3		64	75.71	odd	10
375.2.l.a.368.6		64	25.21	even	5
375.2.l.b.107.3		64	15.8	even	4
375.2.l.b.107.6		64	5.3	odd	4
375.2.l.b.368.3		64	25.4	even	10
375.2.l.b.368.6		64	75.29	odd	10
375.2.l.c.143.3		64	15.14	odd	2
375.2.l.c.143.6		64	5.4	even	2
375.2.l.c.257.3		64	25.3	odd	20
375.2.l.c.257.6		64	75.53	even	20

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	75.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.674175 + 1.32314i) q^{2} +(-0.140417 + 1.72635i) q^{3} +(-0.120624 - 0.166024i) q^{4} +(1.20181 - 1.88564i) q^{5} +(-2.18954 - 1.34965i) q^{6} +(-1.72218 + 1.72218i) q^{7} +(-2.63243 + 0.416937i) q^{8} +(-2.96057 - 0.484816i) q^{9} +(1.68474 + 2.86142i) q^{10} +(3.72206 - 1.20937i) q^{11} +(0.303553 - 0.184926i) q^{12} +(5.20313 - 2.65113i) q^{13} +(-1.11764 - 3.43974i) q^{14} +(3.08653 + 2.33952i) q^{15} +(1.34989 - 4.15452i) q^{16} +(0.120501 + 0.760813i) q^{17} +(2.63742 - 3.59040i) q^{18} +(-2.08083 + 2.86402i) q^{19} +(-0.458029 + 0.0279236i) q^{20} +(-2.73126 - 3.21491i) q^{21} +(-0.909148 + 5.74013i) q^{22} +(0.926047 + 0.471845i) q^{23} +(-0.350141 - 4.60305i) q^{24} +(-2.11130 - 4.53237i) q^{25} +8.67180i q^{26} +(1.25268 - 5.04290i) q^{27} +(0.493660 + 0.0781880i) q^{28} +(0.111964 - 0.0813465i) q^{29} +(-5.17638 + 2.50667i) q^{30} +(0.372717 + 0.270795i) q^{31} +(0.817733 + 0.817733i) q^{32} +(1.56516 + 6.59538i) q^{33} +(-1.08790 - 0.353481i) q^{34} +(1.17768 + 5.31715i) q^{35} +(0.276623 + 0.550006i) q^{36} +(-2.32130 - 4.55581i) q^{37} +(-2.38666 - 4.68409i) q^{38} +(3.84616 + 9.35468i) q^{39} +(-2.37749 + 5.46491i) q^{40} +(-6.18190 - 2.00862i) q^{41} +(6.09513 - 1.44644i) q^{42} +(-5.58451 - 5.58451i) q^{43} +(-0.649753 - 0.472073i) q^{44} +(-4.47223 + 4.99992i) q^{45} +(-1.24864 + 0.907186i) q^{46} +(-3.97607 - 0.629748i) q^{47} +(6.98261 + 2.91374i) q^{48} +1.06819i q^{49} +(7.42036 + 0.262057i) q^{50} +(-1.33035 + 0.101196i) q^{51} +(-1.06777 - 0.544057i) q^{52} +(-0.459763 + 2.90283i) q^{53} +(5.82795 + 5.05726i) q^{54} +(2.19277 - 8.47190i) q^{55} +(3.81549 - 5.25157i) q^{56} +(-4.65212 - 3.99440i) q^{57} +(0.0321498 + 0.202986i) q^{58} +(0.855253 - 2.63220i) q^{59} +(0.0161091 - 0.794640i) q^{60} +(1.24058 + 3.81812i) q^{61} +(-0.609576 + 0.310595i) q^{62} +(5.93357 - 4.26369i) q^{63} +(6.67577 - 2.16909i) q^{64} +(1.25410 - 12.9974i) q^{65} +(-9.78182 - 2.37552i) q^{66} +(1.92228 - 0.304459i) q^{67} +(0.111778 - 0.111778i) q^{68} +(-0.944601 + 1.53243i) q^{69} +(-7.82932 - 2.02645i) q^{70} +(2.08859 + 2.87469i) q^{71} +(7.99563 + 0.0418786i) q^{72} +(-5.44405 + 10.6846i) q^{73} +7.59295 q^{74} +(8.12092 - 3.00843i) q^{75} +0.726495 q^{76} +(-4.32730 + 8.49280i) q^{77} +(-14.9706 - 1.21766i) q^{78} +(0.518361 + 0.713462i) q^{79} +(-6.21164 - 7.53835i) q^{80} +(8.52991 + 2.87066i) q^{81} +(6.82537 - 6.82537i) q^{82} +(-9.43448 + 1.49428i) q^{83} +(-0.204298 + 0.841250i) q^{84} +(1.57944 + 0.687132i) q^{85} +(11.1540 - 3.62417i) q^{86} +(0.124711 + 0.204711i) q^{87} +(-9.29383 + 4.73545i) q^{88} +(-3.64270 - 11.2111i) q^{89} +(-3.60053 - 9.28821i) q^{90} +(-4.39501 + 13.5264i) q^{91} +(-0.0333656 - 0.210662i) q^{92} +(-0.519822 + 0.605416i) q^{93} +(3.51381 - 4.83635i) q^{94} +(2.89976 + 7.36572i) q^{95} +(-1.52652 + 1.29687i) q^{96} +(2.54554 - 16.0719i) q^{97} +(-1.41336 - 0.720145i) q^{98} +(-11.6057 + 1.77590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9} - 20 q^{10} - 10 q^{12} - 20 q^{13} - 10 q^{15} - 8 q^{16} - 10 q^{18} - 6 q^{21} + 20 q^{22} + 40 q^{25} - 10 q^{27} + 40 q^{28} - 10 q^{30} - 12 q^{31}+ \cdots + 120 q^{97}+O(q^{100}) \) 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9 - 20 * q^10 - 10 * q^12 - 20 * q^13 - 10 * q^15 - 8 * q^16 - 10 * q^18 - 6 * q^21 + 20 * q^22 + 40 * q^25 - 10 * q^27 + 40 * q^28 - 10 * q^30 - 12 * q^31 - 10 * q^33 + 20 * q^34 - 22 * q^36 - 20 * q^37 + 30 * q^39 - 20 * q^40 + 90 * q^42 - 20 * q^43 + 70 * q^45 - 12 * q^46 + 100 * q^48 - 16 * q^51 + 20 * q^52 + 120 * q^54 - 20 * q^55 + 70 * q^57 - 20 * q^58 + 50 * q^60 - 12 * q^61 - 20 * q^63 - 100 * q^64 - 30 * q^66 - 60 * q^67 - 80 * q^69 - 100 * q^70 - 150 * q^72 - 60 * q^73 - 90 * q^75 - 64 * q^76 - 80 * q^78 - 60 * q^79 + 14 * q^81 - 60 * q^82 - 130 * q^84 + 60 * q^85 - 60 * q^87 + 20 * q^88 - 70 * q^90 - 12 * q^91 - 20 * q^93 + 260 * q^94 + 42 * q^96 + 120 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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