LMFDB - Embedded newform 75.2.l.a.8.5

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			8.5
Character	$\chi$	$=$	75.8
Dual form			75.2.l.a.47.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0231951 - 0.0455229i) q^{2} +(-1.39036 + 1.03290i) q^{3} +(1.17404 + 1.61592i) q^{4} +(-1.22804 + 1.86867i) q^{5} +(0.0147712 + 0.0872517i) q^{6} +(1.44136 - 1.44136i) q^{7} +(0.201718 - 0.0319491i) q^{8} +(0.866221 - 2.87222i) q^{9} +(0.0565829 + 0.0992477i) q^{10} +(2.86751 - 0.931709i) q^{11} +(-3.30143 - 1.03405i) q^{12} +(-2.79268 + 1.42294i) q^{13} +(-0.0321825 - 0.0990475i) q^{14} +(-0.222739 - 3.86657i) q^{15} +(-1.23123 + 3.78934i) q^{16} +(-0.952042 - 6.01096i) q^{17} +(-0.110660 - 0.106054i) q^{18} +(1.91085 - 2.63007i) q^{19} +(-4.46138 + 0.209475i) q^{20} +(-0.515229 + 3.49280i) q^{21} +(0.0240979 - 0.152148i) q^{22} +(5.12542 + 2.61153i) q^{23} +(-0.247462 + 0.252776i) q^{24} +(-1.98385 - 4.58959i) q^{25} +0.160136i q^{26} +(1.76237 + 4.88816i) q^{27} +(4.02134 + 0.636918i) q^{28} +(-0.976916 + 0.709771i) q^{29} +(-0.181184 - 0.0795457i) q^{30} +(-0.0161330 - 0.0117213i) q^{31} +(0.432772 + 0.432772i) q^{32} +(-3.02451 + 4.25727i) q^{33} +(-0.295719 - 0.0960849i) q^{34} +(0.923385 + 4.46347i) q^{35} +(5.65826 - 1.97235i) q^{36} +(1.24327 + 2.44005i) q^{37} +(-0.0754058 - 0.147992i) q^{38} +(2.41308 - 4.86298i) q^{39} +(-0.188015 + 0.416180i) q^{40} +(-10.1904 - 3.31106i) q^{41} +(0.147052 + 0.104471i) q^{42} +(-3.91319 - 3.91319i) q^{43} +(4.87212 + 3.53981i) q^{44} +(4.30349 + 5.14587i) q^{45} +(0.237769 - 0.172749i) q^{46} +(3.63479 + 0.575694i) q^{47} +(-2.20216 - 6.54030i) q^{48} +2.84495i q^{49} +(-0.254947 - 0.0161451i) q^{50} +(7.53242 + 7.37405i) q^{51} +(-5.57807 - 2.84217i) q^{52} +(-0.635421 + 4.01189i) q^{53} +(0.263401 + 0.0331531i) q^{54} +(-1.78034 + 6.50259i) q^{55} +(0.244699 - 0.336799i) q^{56} +(0.0598219 + 5.63047i) q^{57} +(0.00965120 + 0.0609353i) q^{58} +(-1.33548 + 4.11017i) q^{59} +(5.98658 - 4.89943i) q^{60} +(-3.99489 - 12.2950i) q^{61} +(-0.000907794 + 0.000462544i) q^{62} +(-2.89137 - 5.38845i) q^{63} +(-7.54893 + 2.45280i) q^{64} +(0.770505 - 6.96603i) q^{65} +(0.123650 + 0.236432i) q^{66} +(-0.920343 + 0.145768i) q^{67} +(8.59551 - 8.59551i) q^{68} +(-9.82366 + 1.66309i) q^{69} +(0.224608 + 0.0614955i) q^{70} +(-5.79154 - 7.97137i) q^{71} +(0.0829678 - 0.607055i) q^{72} +(0.0177571 - 0.0348503i) q^{73} +0.139916 q^{74} +(7.49888 + 4.33207i) q^{75} +6.49339 q^{76} +(2.79018 - 5.47604i) q^{77} +(-0.165405 - 0.222648i) q^{78} +(-6.00647 - 8.26720i) q^{79} +(-5.56902 - 6.95421i) q^{80} +(-7.49932 - 4.97596i) q^{81} +(-0.387096 + 0.387096i) q^{82} +(-2.17217 + 0.344039i) q^{83} +(-6.24900 + 3.26811i) q^{84} +(12.4016 + 5.60262i) q^{85} +(-0.268906 + 0.0873730i) q^{86} +(0.625143 - 1.99590i) q^{87} +(0.548661 - 0.279557i) q^{88} +(4.18096 + 12.8677i) q^{89} +(0.334075 - 0.0765482i) q^{90} +(-1.97429 + 6.07624i) q^{91} +(1.79740 + 11.3483i) q^{92} +(0.0345377 - 0.000366951i) q^{93} +(0.110516 - 0.152113i) q^{94} +(2.56813 + 6.80057i) q^{95} +(-1.04872 - 0.154699i) q^{96} +(-0.838657 + 5.29507i) q^{97} +(0.129510 + 0.0659889i) q^{98} +(-0.192183 - 9.04318i) 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 $

$2$	0.0231951	−	0.0455229i	0.0164014	−	0.0321896i	−0.882660	−	0.470011i	$-0.844250\pi$
$2$	0.0231951	−	0.0455229i	0.0164014	−	0.0321896i	0.899062	+	0.437822i	$0.144250\pi$
$3$	−1.39036	+	1.03290i	−0.802727	+	0.596347i
$3$	−1.39036	+	1.03290i	−0.802727	+	0.596347i
$4$	1.17404	+	1.61592i	0.587018	+	0.807961i
$5$	−1.22804	+	1.86867i	−0.549194	+	0.835695i
$5$	−1.22804	+	1.86867i	−0.549194	+	0.835695i
$6$	0.0147712	+	0.0872517i	0.00603031	+	0.0356203i
$7$	1.44136	−	1.44136i	0.544784	−	0.544784i	−0.380144	−	0.924927i	$-0.624125\pi$
$7$	1.44136	−	1.44136i	0.544784	−	0.544784i	0.924927	+	0.380144i	$0.124125\pi$
$8$	0.201718	−	0.0319491i	0.0713182	−	0.0112957i
$9$	0.866221	−	2.87222i	0.288740	−	0.957407i
$10$	0.0565829	+	0.0992477i	0.0178931	+	0.0313849i
$11$	2.86751	−	0.931709i	0.864586	−	0.280921i	0.157043	−	0.987592i	$-0.449804\pi$
$11$	2.86751	−	0.931709i	0.864586	−	0.280921i	0.707542	+	0.706671i	$0.249804\pi$
$12$	−3.30143	−	1.03405i	−0.953040	−	0.298505i
$13$	−2.79268	+	1.42294i	−0.774551	+	0.394653i	−0.796139	−	0.605114i	$-0.793128\pi$
$13$	−2.79268	+	1.42294i	−0.774551	+	0.394653i	0.0215884	+	0.999767i	$0.493128\pi$
$14$	−0.0321825	−	0.0990475i	−0.00860113	−	0.0264716i
$15$	−0.222739	−	3.86657i	−0.0575110	−	0.998345i
$16$	−1.23123	+	3.78934i	−0.307808	+	0.947334i
$17$	−0.952042	−	6.01096i	−0.230904	−	1.45787i	−0.781921	−	0.623377i	$-0.785760\pi$
$17$	−0.952042	−	6.01096i	−0.230904	−	1.45787i	0.551017	−	0.834494i	$-0.314240\pi$
$18$	−0.110660	−	0.106054i	−0.0260828	−	0.0249972i
$19$	1.91085	−	2.63007i	0.438380	−	0.603378i	−0.531471	−	0.847076i	$-0.678361\pi$
$19$	1.91085	−	2.63007i	0.438380	−	0.603378i	0.969851	+	0.243698i	$0.0783606\pi$
$20$	−4.46138	+	0.209475i	−0.997596	+	0.0468401i
$21$	−0.515229	+	3.49280i	−0.112432	+	0.762192i
$22$	0.0240979	−	0.152148i	0.00513769	−	0.0324381i
$23$	5.12542	+	2.61153i	1.06872	+	0.544542i	0.897647	−	0.440716i	$-0.145275\pi$
$23$	5.12542	+	2.61153i	1.06872	+	0.544542i	0.171077	+	0.985258i	$0.445275\pi$
$24$	−0.247462	+	0.252776i	−0.0505129	+	0.0515978i
$25$	−1.98385	−	4.58959i	−0.396771	−	0.917918i
$26$			0.160136i			0.0314053i
$27$	1.76237	+	4.88816i	0.339168	+	0.940726i
$28$	4.02134	+	0.636918i	0.759962	+	0.120366i
$29$	−0.976916	+	0.709771i	−0.181409	+	0.131801i	−0.674784	−	0.738016i	$-0.735763\pi$
$29$	−0.976916	+	0.709771i	−0.181409	+	0.131801i	0.493375	+	0.869817i	$0.335763\pi$
$30$	−0.181184	−	0.0795457i	−0.0330795	−	0.0145230i
$31$	−0.0161330	−	0.0117213i	−0.00289757	−	0.00210521i	0.586336	−	0.810068i	$-0.300570\pi$
$31$	−0.0161330	−	0.0117213i	−0.00289757	−	0.00210521i	−0.589233	+	0.807963i	$0.700570\pi$
$32$	0.432772	+	0.432772i	0.0765040	+	0.0765040i
$33$	−3.02451	+	4.25727i	−0.526500	+	0.741096i
$34$	−0.295719	−	0.0960849i	−0.0507154	−	0.0164784i
$35$	0.923385	+	4.46347i	0.156081	+	0.754465i
$36$	5.65826	−	1.97235i	0.943044	−	0.328725i
$37$	1.24327	+	2.44005i	0.204392	+	0.401142i	0.970334	−	0.241767i	$-0.0777271\pi$
$37$	1.24327	+	2.44005i	0.204392	+	0.401142i	−0.765942	+	0.642910i	$0.777727\pi$
$38$	−0.0754058	−	0.147992i	−0.0122324	−	0.0240075i
$39$	2.41308	−	4.86298i	0.386402	−	0.778700i
$40$	−0.188015	+	0.416180i	−0.0297278	+	0.0658038i
$41$	−10.1904	−	3.31106i	−1.59147	−	0.517100i	−0.626491	−	0.779428i	$-0.715510\pi$
$41$	−10.1904	−	3.31106i	−1.59147	−	0.517100i	−0.964979	+	0.262328i	$0.915510\pi$
$42$	0.147052	+	0.104471i	0.0226906	+	0.0161202i
$43$	−3.91319	−	3.91319i	−0.596755	−	0.596755i	0.342692	−	0.939448i	$-0.388661\pi$
$43$	−3.91319	−	3.91319i	−0.596755	−	0.596755i	−0.939448	+	0.342692i	$0.888661\pi$
$44$	4.87212	+	3.53981i	0.734500	+	0.533646i
$45$	4.30349	+	5.14587i	0.641526	+	0.767102i
$46$	0.237769	−	0.172749i	0.0350571	−	0.0254705i
$47$	3.63479	+	0.575694i	0.530188	+	0.0839735i	0.415789	−	0.909461i	$-0.363506\pi$
$47$	3.63479	+	0.575694i	0.530188	+	0.0839735i	0.114399	+	0.993435i	$0.463506\pi$
$48$	−2.20216	−	6.54030i	−0.317855	−	0.944011i
$49$			2.84495i			0.406422i
$50$	−0.254947	−	0.0161451i	−0.0360550	−	0.00228326i
$51$	7.53242	+	7.37405i	1.05475	+	1.03257i
$52$	−5.57807	−	2.84217i	−0.773540	−	0.394138i
$53$	−0.635421	+	4.01189i	−0.0872818	+	0.551075i	0.904835	+	0.425762i	$0.139994\pi$
$53$	−0.635421	+	4.01189i	−0.0872818	+	0.551075i	−0.992117	+	0.125314i	$0.960006\pi$
$54$	0.263401	+	0.0331531i	0.0358444	+	0.00451156i
$55$	−1.78034	+	6.50259i	−0.240062	+	0.876810i
$56$	0.244699	−	0.336799i	0.0326993	−	0.0450067i
$57$	0.0598219	+	5.63047i	0.00792360	+	0.745775i
$58$	0.00965120	+	0.0609353i	0.00126726	+	0.00800119i
$59$	−1.33548	+	4.11017i	−0.173864	+	0.535099i	−0.999580	−	0.0289879i	$-0.990772\pi$
$59$	−1.33548	+	4.11017i	−0.173864	+	0.535099i	0.825716	+	0.564087i	$0.190772\pi$
$60$	5.98658	−	4.89943i	0.772864	−	0.632513i
$61$	−3.99489	−	12.2950i	−0.511493	−	1.57421i	−0.789574	−	0.613656i	$-0.789698\pi$
$61$	−3.99489	−	12.2950i	−0.511493	−	1.57421i	0.278081	−	0.960558i	$-0.410302\pi$
$62$	−0.000907794	0	0.000462544i	−0.000115290	0	5.87432e-5i
$63$	−2.89137	−	5.38845i	−0.364279	−	0.678881i
$64$	−7.54893	+	2.45280i	−0.943617	+	0.306600i
$65$	0.770505	−	6.96603i	0.0955694	−	0.864029i
$66$	0.123650	+	0.236432i	0.0152202	+	0.0291028i
$67$	−0.920343	+	0.145768i	−0.112438	+	0.0178084i	−0.212400	−	0.977183i	$-0.568128\pi$
$67$	−0.920343	+	0.145768i	−0.112438	+	0.0178084i	0.0999620	+	0.994991i	$0.468128\pi$
$68$	8.59551	−	8.59551i	1.04236	−	1.04236i
$69$	−9.82366	+	1.66309i	−1.18263	+	0.200212i
$70$	0.224608	+	0.0614955i	0.0268458	+	0.00735012i
$71$	−5.79154	−	7.97137i	−0.687329	−	0.946028i	0.312663	−	0.949864i	$-0.398779\pi$
$71$	−5.79154	−	7.97137i	−0.687329	−	0.946028i	−0.999993	+	0.00383630i	$0.998779\pi$
$72$	0.0829678	−	0.607055i	0.00977785	−	0.0715421i
$73$	0.0177571	−	0.0348503i	0.00207831	−	0.00407891i	−0.889965	−	0.456029i	$-0.849271\pi$
$73$	0.0177571	−	0.0348503i	0.00207831	−	0.00407891i	0.892043	+	0.451950i	$0.149271\pi$
$74$	0.139916			0.0162649
$75$	7.49888	+	4.33207i	0.865896	+	0.500224i
$76$	6.49339			0.744843
$77$	2.79018	−	5.47604i	0.317971	−	0.624053i
$78$	−0.165405	−	0.222648i	−0.0187285	−	0.0252099i
$79$	−6.00647	−	8.26720i	−0.675781	−	0.930133i	0.324093	−	0.946025i	$-0.394941\pi$
$79$	−6.00647	−	8.26720i	−0.675781	−	0.930133i	−0.999874	+	0.0158924i	$0.994941\pi$
$80$	−5.56902	−	6.95421i	−0.622636	−	0.777504i
$81$	−7.49932	−	4.97596i	−0.833258	−	0.552884i
$82$	−0.387096	+	0.387096i	−0.0427476	+	0.0427476i
$83$	−2.17217	+	0.344039i	−0.238427	+	0.0377632i	−0.274504	−	0.961586i	$-0.588514\pi$
$83$	−2.17217	+	0.344039i	−0.238427	+	0.0377632i	0.0360772	+	0.999349i	$0.488514\pi$
$84$	−6.24900	+	3.26811i	−0.681822	+	0.356580i
$85$	12.4016	+	5.60262i	1.34515	+	0.607690i
$86$	−0.268906	+	0.0873730i	−0.0289969	+	0.00942167i
$87$	0.625143	−	1.99590i	0.0670224	−	0.213983i
$88$	0.548661	−	0.279557i	0.0584875	−	0.0298009i
$89$	4.18096	+	12.8677i	0.443181	+	1.36397i	0.884466	+	0.466604i	$0.154523\pi$
$89$	4.18096	+	12.8677i	0.443181	+	1.36397i	−0.441285	+	0.897367i	$0.645477\pi$
$90$	0.334075	−	0.0765482i	0.0352146	−	0.00806889i
$91$	−1.97429	+	6.07624i	−0.206962	+	0.636963i
$92$	1.79740	+	11.3483i	0.187392	+	1.18314i
$93$	0.0345377		0.000366951i	0.00358139		3.80511e-5i
$94$	0.110516	−	0.152113i	0.0113989	−	0.0156892i
$95$	2.56813	+	6.80057i	0.263484	+	0.697724i
$96$	−1.04872	−	0.154699i	−0.107035	−	0.0157889i
$97$	−0.838657	+	5.29507i	−0.0851527	+	0.537633i	0.907827	+	0.419346i	$0.137740\pi$
$97$	−0.838657	+	5.29507i	−0.0851527	+	0.537633i	−0.992979	+	0.118287i	$0.962260\pi$
$98$	0.129510	+	0.0659889i	0.0130825	+	0.00666588i
$99$	−0.192183	−	9.04318i	−0.0193151	−	0.908874i
$100$	5.08730	−	8.59410i	0.508730	−	0.859410i
$101$			12.2476i			1.21869i	0.792907	+	0.609343i	$0.208567\pi$
$101$			12.2476i			1.21869i	−0.792907	+	0.609343i	$0.791433\pi$
$102$	0.510403	−	0.171856i	0.0505374	−	0.0170163i
$103$	16.5959	+	2.62854i	1.63525	+	0.258998i	0.905383	−	0.424596i	$-0.139584\pi$
$103$	16.5959	+	2.62854i	1.63525	+	0.258998i	0.729863	+	0.683593i	$0.239584\pi$
$104$	−0.517874	+	0.376257i	−0.0507817	+	0.0368951i
$105$	−5.89418	−	5.25208i	−0.575213	−	0.512551i
$106$	0.167894	+	0.121982i	0.0163073	+	0.0118480i
$107$	−3.55622	−	3.55622i	−0.343793	−	0.343793i	0.513998	−	0.857791i	$-0.328164\pi$
$107$	−3.55622	−	3.55622i	−0.343793	−	0.343793i	−0.857791	+	0.513998i	$0.828164\pi$
$108$	−5.82980	+	8.58672i	−0.560972	+	0.826257i
$109$	9.79911	+	3.18392i	0.938585	+	0.304965i	0.738069	−	0.674726i	$-0.235738\pi$
$109$	9.79911	+	3.18392i	0.938585	+	0.304965i	0.200516	+	0.979690i	$0.435738\pi$
$110$	0.254722	+	0.231875i	0.0242868	+	0.0221084i
$111$	−4.24894	−	2.10838i	−0.403291	−	0.200119i
$112$	3.68716	+	7.23645i	0.348404	+	0.683781i
$113$	−3.97267	−	7.79680i	−0.373717	−	0.733462i	0.625176	−	0.780483i	$-0.285027\pi$
$113$	−3.97267	−	7.79680i	−0.373717	−	0.733462i	−0.998894	+	0.0470217i	$0.985027\pi$
$114$	0.257703	+	0.127876i	0.0241361	+	0.0119767i
$115$	−11.1743	+	6.37066i	−1.04201	+	0.594067i
$116$	−2.29387	−	0.745324i	−0.212980	−	0.0692016i
$117$	1.66793	+	9.25379i	0.154200	+	0.855513i
$118$	0.156130	+	0.156130i	0.0143730	+	0.0143730i
$119$	−10.0362	−	7.29173i	−0.920017	−	0.668432i
$120$	−0.168464	−	0.772843i	−0.0153786	−	0.0705506i
$121$	−1.54468	+	1.12228i	−0.140425	+	0.102025i
$122$	−0.652366	−	0.103325i	−0.0590624	−	0.00935457i
$123$	17.5883	−	5.92211i	1.58589	−	0.533979i
$124$		−	0.0398309i		−	0.00357692i
$125$	11.0127	+	1.92901i	0.985003	+	0.172536i
$126$	−0.312364	+	0.00663826i	−0.0278276	+	0.000591383i
$127$	3.11066	+	1.58496i	0.276026	+	0.140642i	0.586524	−	0.809932i	$-0.300496\pi$
$127$	3.11066	+	1.58496i	0.276026	+	0.140642i	−0.310498	+	0.950574i	$0.600496\pi$
$128$	−0.254925	+	1.60954i	−0.0225324	+	0.142264i
$129$	9.48270	+	1.39881i	0.834905	+	0.123158i
$130$	−0.299242	−	0.196653i	−0.0262452	−	0.0172476i
$131$	4.58971	−	6.31720i	0.401005	−	0.551936i	−0.559991	−	0.828499i	$-0.689195\pi$
$131$	4.58971	−	6.31720i	0.401005	−	0.551936i	0.960996	+	0.276563i	$0.0891953\pi$
$132$	−10.4303	+	0.110818i	−0.907841	+	0.00964550i
$133$	−1.03664	−	6.54511i	−0.0898884	−	0.567533i
$134$	−0.0147116	+	0.0452778i	−0.00127089	+	0.00391140i
$135$	−11.2986	−	2.70955i	−0.972429	−	0.233201i
$136$	−0.384089	−	1.18210i	−0.0329353	−	0.101365i
$137$	8.83454	−	4.50142i	0.754786	−	0.384583i	−0.0338629	−	0.999426i	$-0.510781\pi$
$137$	8.83454	−	4.50142i	0.754786	−	0.384583i	0.788649	+	0.614844i	$0.210781\pi$
$138$	−0.152152	+	0.485777i	−0.0129520	+	0.0413521i
$139$	4.81723	−	1.56521i	0.408592	−	0.132760i	−0.0975070	−	0.995235i	$-0.531087\pi$
$139$	4.81723	−	1.56521i	0.408592	−	0.132760i	0.506100	+	0.862475i	$0.331087\pi$
$140$	−6.12854	+	6.73240i	−0.517956	+	0.568992i
$141$	−5.64831	+	2.95396i	−0.475674	+	0.248768i
$142$	−0.497215	+	0.0787512i	−0.0417254	+	0.00660865i
$143$	−6.68226	+	6.68226i	−0.558799	+	0.558799i
$144$	9.81730	+	6.81877i	0.818108	+	0.568231i
$145$	−0.126640	−	2.69716i	−0.0105168	−	0.223987i
$146$	−0.00117461	−	0.00161671i	−9.72113e−5	−	0.000133800i
$147$	−2.93856	−	3.95552i	−0.242368	−	0.326245i
$148$	−2.48329	+	4.87374i	−0.204125	+	0.400619i
$149$	2.08572			0.170869			0.0854344	−	0.996344i	$-0.472772\pi$
$149$	2.08572			0.170869			0.0854344	+	0.996344i	$0.472772\pi$
$150$	0.371145	−	0.240888i	0.0303039	−	0.0196684i
$151$	3.13158			0.254844			0.127422	−	0.991849i	$-0.459330\pi$
$151$	3.13158			0.254844			0.127422	+	0.991849i	$0.459330\pi$
$152$	0.301426	−	0.591583i	0.0244489	−	0.0479837i
$153$	−18.0895	−	2.47234i	−1.46245	−	0.199877i
$154$	−0.184567	−	0.254035i	−0.0148728	−	0.0204707i
$155$	0.0417151	−	0.0157530i	0.00335064	−	0.00126532i
$156$	10.6912	−	1.80996i	0.855984	−	0.144913i
$157$	4.55824	−	4.55824i	0.363787	−	0.363787i	−0.501418	−	0.865205i	$-0.667188\pi$
$157$	4.55824	−	4.55824i	0.363787	−	0.363787i	0.865205	+	0.501418i	$0.167188\pi$
$158$	−0.515668	+	0.0816737i	−0.0410243	+	0.00649761i
$159$	−3.26043	−	6.23431i	−0.258569	−	0.494413i
$160$	−1.34017	+	0.277248i	−0.105950	+	0.0219184i
$161$	11.1517	−	3.62342i	0.878881	−	0.285566i
$162$	−0.400467	+	0.225973i	−0.0314637	+	0.0177541i
$163$	−16.2906	+	8.30047i	−1.27598	+	0.650143i	−0.954905	−	0.296912i	$-0.904043\pi$
$163$	−16.2906	+	8.30047i	−1.27598	+	0.650143i	−0.321072	+	0.947055i	$0.604043\pi$
$164$	−6.61347	−	20.3542i	−0.516425	−	1.58939i
$165$	−4.24123	−	10.8799i	−0.330179	−	0.846998i
$166$	−0.0347221	+	0.106864i	−0.00269496	+	0.00829423i
$167$	−0.197736	−	1.24845i	−0.0153012	−	0.0966082i	0.978856	−	0.204551i	$-0.0655735\pi$
$167$	−0.197736	−	1.24845i	−0.0153012	−	0.0966082i	−0.994157	+	0.107943i	$0.965574\pi$
$168$	0.00766063	+	0.721024i	0.000591031	+	0.0556282i
$169$	−1.86690	+	2.56957i	−0.143608	+	0.197659i
$170$	0.542705	−	0.434605i	0.0416235	−	0.0333327i
$171$	−5.89891	−	7.76662i	−0.451101	−	0.593928i
$172$	1.72918	−	10.9176i	0.131849	−	0.832461i
$173$	−1.84621	−	0.940691i	−0.140365	−	0.0715194i	0.382398	−	0.923998i	$-0.375098\pi$
$173$	−1.84621	−	0.940691i	−0.140365	−	0.0715194i	−0.522762	+	0.852478i	$0.675098\pi$
$174$	−0.0763589	−	0.0747534i	−0.00578876	−	0.00566704i
$175$	−9.47471	−	3.75581i	−0.716221	−	0.283912i
$176$			12.0131i			0.905521i
$177$	−2.38861	−	7.09405i	−0.179539	−	0.533221i
$178$	0.682752	+	0.108137i	0.0511744	+	0.00810523i
$179$	4.10633	−	2.98343i	0.306922	−	0.222992i	−0.423653	−	0.905825i	$-0.639252\pi$
$179$	4.10633	−	2.98343i	0.306922	−	0.222992i	0.730575	+	0.682833i	$0.239252\pi$
$180$	−3.26288	+	12.9955i	−0.243201	+	0.968630i
$181$	0.846389	+	0.614938i	0.0629116	+	0.0457080i	0.618797	−	0.785551i	$-0.287621\pi$
$181$	0.846389	+	0.614938i	0.0629116	+	0.0457080i	−0.555885	+	0.831259i	$0.687621\pi$
$182$	0.230814	+	0.230814i	0.0171091	+	0.0171091i
$183$	18.2539	+	12.9682i	1.34937	+	0.958636i
$184$	1.11733	+	0.363042i	0.0823705	+	0.0267638i
$185$	−6.08643	−	0.673214i	−0.447484	−	0.0494957i
$186$	0.000784400	−	0.00158077i	5.75150e−5	−	0.000115908i
$187$	−8.33045	−	16.3494i	−0.609183	−	1.19559i
$188$	3.33709	+	6.54942i	0.243383	+	0.477665i
$189$	9.58581	+	4.50539i	0.697265	+	0.327719i
$190$	0.369150	+	0.0408313i	0.0267809	+	0.00296221i
$191$	18.0007	+	5.84879i	1.30249	+	0.423204i	0.876446	−	0.481500i	$-0.159908\pi$
$191$	18.0007	+	5.84879i	1.30249	+	0.423204i	0.426041	+	0.904704i	$0.359908\pi$
$192$	7.96226	−	11.2076i	0.574627	−	0.808839i
$193$	−7.84492	−	7.84492i	−0.564690	−	0.564690i	0.365946	−	0.930636i	$-0.380745\pi$
$193$	−7.84492	−	7.84492i	−0.564690	−	0.564690i	−0.930636	+	0.365946i	$0.880745\pi$
$194$	0.221594	+	0.160998i	0.0159095	+	0.0115590i
$195$	6.12395	+	10.4812i	0.438545	+	0.750572i
$196$	−4.59722	+	3.34008i	−0.328373	+	0.238577i
$197$	−24.8793	−	3.94049i	−1.77257	−	0.280748i	−0.817244	−	0.576291i	$-0.804499\pi$
$197$	−24.8793	−	3.94049i	−1.77257	−	0.280748i	−0.955329	+	0.295543i	$0.904499\pi$
$198$	−0.416130	−	0.201009i	−0.0295730	−	0.0142851i
$199$			16.1153i			1.14238i	0.820817	+	0.571191i	$0.193518\pi$
$199$			16.1153i			1.14238i	−0.820817	+	0.571191i	$0.806482\pi$
$200$	−0.546813	−	0.862422i	−0.0386655	−	0.0609825i
$201$	1.12905	−	1.15330i	0.0796368	−	0.0813472i
$202$	0.557548	+	0.284085i	0.0392290	+	0.0199882i
$203$	−0.385053	+	2.43113i	−0.0270254	+	0.170632i
$204$	−3.07255	+	20.8292i	−0.215121	+	1.45834i
$205$	18.7014	−	14.9764i	1.30616	−	1.04599i
$206$	0.504603	−	0.694526i	0.0351573	−	0.0483899i
$207$	11.9406	−	12.4592i	0.829932	−	0.865973i
$208$	−1.95357	−	12.3344i	−0.135456	−	0.855236i
$209$	3.02893	−	9.32209i	0.209515	−	0.644822i
$210$	−0.375806	+	0.146498i	−0.0259331	+	0.0101093i
$211$	4.91691	+	15.1327i	0.338494	+	1.04178i	0.964975	+	0.262341i	$0.0844944\pi$
$211$	4.91691	+	15.1327i	0.338494	+	1.04178i	−0.626481	+	0.779436i	$0.715506\pi$
$212$	−7.22891	+	3.68331i	−0.496484	+	0.252971i
$213$	16.2860	+	5.10100i	1.11590	+	0.349515i
$214$	−0.244376	+	0.0794027i	−0.0167052	+	0.00542786i
$215$	12.1180	−	2.50692i	0.826440	−	0.170970i
$216$	0.511674	+	0.929725i	0.0348150	+	0.0632598i
$217$	−0.0401481	+	0.00635884i	−0.00272543	+	0.000431666i
$218$	0.372233	−	0.372233i	0.0252108	−	0.0252108i
$219$	0.0113081	+	0.0667959i	0.000764134	+	0.00451365i
$220$	−12.5979	+	4.75738i	−0.849349	+	0.320743i
$221$	11.2120	+	15.4320i	0.754201	+	1.03807i
$222$	−0.194534	+	0.144520i	−0.0130563	+	0.00969953i
$223$	−9.88171	+	19.3939i	−0.661728	+	1.29871i	0.279240	+	0.960221i	$0.409917\pi$
$223$	−9.88171	+	19.3939i	−0.661728	+	1.29871i	−0.940969	+	0.338494i	$0.890083\pi$
$224$	1.24756			0.0833563
$225$	−14.9008	+	1.72247i	−0.993385	+	0.114832i
$226$	−0.447080			−0.0297393
$227$	−9.73935	+	19.1146i	−0.646423	+	1.26868i	0.302493	+	0.953151i	$0.402181\pi$
$227$	−9.73935	+	19.1146i	−0.646423	+	1.26868i	−0.948917	+	0.315526i	$0.897819\pi$
$228$	−9.02818	+	6.70705i	−0.597906	+	0.444185i
$229$	−6.79217	−	9.34861i	−0.448839	−	0.617774i	0.523309	−	0.852143i	$-0.324697\pi$
$229$	−6.79217	−	9.34861i	−0.448839	−	0.617774i	−0.972148	+	0.234369i	$0.924697\pi$
$230$	0.0308225	+	0.656454i	0.00203237	+	0.0432853i
$231$	1.77686	+	10.4957i	0.116909	+	0.690565i
$232$	−0.174385	+	0.174385i	−0.0114490	+	0.0114490i
$233$	−14.4364	+	2.28650i	−0.945759	+	0.149793i	−0.610219	−	0.792233i	$-0.708919\pi$
$233$	−14.4364	+	2.28650i	−0.945759	+	0.149793i	−0.335540	+	0.942026i	$0.608919\pi$
$234$	0.459947	+	0.138713i	0.0300677	+	0.00906798i
$235$	−5.53943	+	6.08524i	−0.361353	+	0.396957i
$236$	−8.20961	+	2.66746i	−0.534400	+	0.173637i
$237$	16.8904	+	5.29031i	1.09715	+	0.343642i
$238$	−0.564731	+	0.287745i	−0.0366061	+	0.0186517i
$239$	−1.25167	−	3.85226i	−0.0809640	−	0.249182i	0.902378	−	0.430945i	$-0.141820\pi$
$239$	−1.25167	−	3.85226i	−0.0809640	−	0.249182i	−0.983342	+	0.181763i	$0.941820\pi$
$240$	14.9260	+	3.91661i	0.963469	+	0.252816i
$241$	−0.611740	+	1.88274i	−0.0394057	+	0.121278i	−0.968824	−	0.247749i	$-0.920309\pi$
$241$	−0.611740	+	1.88274i	−0.0394057	+	0.121278i	0.929419	+	0.369027i	$0.120309\pi$
$242$	0.0152603	+	0.0963496i	0.000980967	+	0.00619358i
$243$	15.5665	−	0.827690i	0.998589	−	0.0530963i
$244$	15.1776	−	20.8902i	0.971648	−	1.33736i
$245$	−5.31628	−	3.49370i	−0.339644	−	0.223205i
$246$	0.138371	−	0.938036i	0.00882222	−	0.0598070i
$247$	−1.59398	+	10.0640i	−0.101422	+	0.640355i
$248$	−0.00362881	−	0.00184897i	−0.000230429	−	0.000117410i
$249$	2.66475	−	2.72199i	0.168872	−	0.172499i
$250$	0.343254	−	0.456585i	0.0217093	−	0.0288770i
$251$		−	27.0328i		−	1.70629i	−0.521671	−	0.853147i	$-0.674691\pi$
$251$		−	27.0328i		−	1.70629i	0.521671	−	0.853147i	$-0.325309\pi$
$252$	5.31274	−	10.9985i	0.334671	−	0.692839i
$253$	17.1304	+	2.71318i	1.07698	+	0.170576i
$254$	0.144304	−	0.104843i	0.00905443	−	0.00657843i
$255$	−23.0297	+	5.02002i	−1.44218	+	0.314366i
$256$	−12.7757	−	9.28206i	−0.798479	−	0.580129i
$257$	8.81239	+	8.81239i	0.549701	+	0.549701i	0.926354	−	0.376653i	$-0.122925\pi$
$257$	8.81239	+	8.81239i	0.549701	+	0.549701i	−0.376653	+	0.926354i	$0.622925\pi$
$258$	0.283630	−	0.399234i	0.0176580	−	0.0248553i
$259$	5.30900	+	1.72500i	0.329885	+	0.107186i
$260$	12.1612	−	6.93329i	0.754203	−	0.429984i
$261$	1.19240	+	3.42074i	0.0738074	+	0.211738i
$262$	−0.181119	−	0.355465i	−0.0111895	−	0.0219607i
$263$	−1.63641	−	3.21164i	−0.100906	−	0.198038i	0.835035	−	0.550198i	$-0.185448\pi$
$263$	−1.63641	−	3.21164i	−0.100906	−	0.198038i	−0.935940	+	0.352159i	$0.885448\pi$
$264$	−0.474083	+	0.955400i	−0.0291778	+	0.0588008i
$265$	−6.71658	−	6.11414i	−0.412596	−	0.375589i
$266$	−0.321997	−	0.104623i	−0.0197429	−	0.00641487i
$267$	−19.1041	−	13.5722i	−1.16915	−	0.830607i
$268$	−1.31607	−	1.31607i	−0.0803915	−	0.0803915i
$269$	10.9791	+	7.97680i	0.669409	+	0.486354i	0.869827	−	0.493356i	$-0.164230\pi$
$269$	10.9791	+	7.97680i	0.669409	+	0.486354i	−0.200418	+	0.979710i	$0.564230\pi$
$270$	−0.385418	+	0.451497i	−0.0234558	+	0.0274772i
$271$	6.66756	−	4.84427i	0.405026	−	0.294268i	−0.366559	−	0.930395i	$-0.619464\pi$
$271$	6.66756	−	4.84427i	0.405026	−	0.294268i	0.771585	+	0.636126i	$0.219464\pi$
$272$	23.9497	+	3.79326i	1.45217	+	0.230000i
$273$	−3.53119	−	10.4874i	−0.213717	−	0.634728i
$274$		−	0.506585i		−	0.0306039i
$275$	−9.96487	−	11.3123i	−0.600905	−	0.682157i
$276$	−14.2207	−	13.9217i	−0.855988	−	0.837990i
$277$	17.2075	+	8.76768i	1.03390	+	0.526799i	0.886718	−	0.462311i	$-0.152980\pi$
$277$	17.2075	+	8.76768i	1.03390	+	0.526799i	0.147182	+	0.989109i	$0.452980\pi$
$278$	0.0404830	−	0.255600i	0.00242801	−	0.0153299i
$279$	−0.0476409	+	0.0361843i	−0.00285219	+	0.00216630i
$280$	0.328868	+	0.870864i	0.0196536	+	0.0520441i
$281$	−6.10119	+	8.39756i	−0.363966	+	0.500957i	−0.951248	−	0.308426i	$-0.900198\pi$
$281$	−6.10119	+	8.39756i	−0.363966	+	0.500957i	0.587282	+	0.809382i	$0.300198\pi$
$282$	0.00345987	+	0.325645i	0.000206032	+	0.0193919i
$283$	−1.50821	−	9.52247i	−0.0896539	−	0.566052i	−0.991096	−	0.133152i	$-0.957490\pi$
$283$	−1.50821	−	9.52247i	−0.0896539	−	0.566052i	0.901442	−	0.432900i	$-0.142510\pi$
$284$	6.08164	−	18.7174i	0.360879	−	1.11067i
$285$	−10.5950	−	6.80264i	−0.627591	−	0.402954i
$286$	0.149200	+	0.459192i	0.00882241	+	0.0271526i
$287$	−19.4605	+	9.91560i	−1.14871	+	0.585299i
$288$	1.61789	−	0.868141i	0.0953353	−	0.0511557i
$289$	−19.0573	+	6.19208i	−1.12102	+	0.364240i
$290$	−0.125720	−	0.0567958i	−0.00738253	−	0.00333517i
$291$	−4.30326	−	8.22833i	−0.252262	−	0.482353i
$292$	0.0771628	−	0.0122214i	0.00451561	−	0.000715202i
$293$	−7.74605	+	7.74605i	−0.452529	+	0.452529i	−0.896193	−	0.443664i	$-0.853678\pi$
$293$	−7.74605	+	7.74605i	−0.452529	+	0.452529i	0.443664	+	0.896193i	$0.353678\pi$
$294$	−0.248227	+	0.0420233i	−0.0144769	+	0.00245085i
$295$	−6.04054	−	7.54300i	−0.351694	−	0.439171i
$296$	0.328748	+	0.452482i	0.0191081	+	0.0263000i
$297$	9.60794	+	12.3748i	0.557509	+	0.718059i
$298$	0.0483784	−	0.0949480i	0.00280249	−	0.00550019i
$299$	−18.0297			−1.04269
$300$	1.80368	+	17.2036i	0.104135	+	0.993251i
$301$	−11.2806			−0.650205
$302$	0.0726372	−	0.142558i	0.00417980	−	0.00820332i
$303$	−12.6506	−	17.0287i	−0.726760	−	0.978272i
$304$	7.61350	+	10.4791i	0.436664	+	0.601017i
$305$	27.8812	+	7.63358i	1.59647	+	0.437098i
$306$	−0.532135	+	0.766140i	−0.0304201	+	0.0437973i
$307$	−17.8437	+	17.8437i	−1.01839	+	1.01839i	−0.0185640	+	0.999828i	$0.505909\pi$
$307$	−17.8437	+	17.8437i	−1.01839	+	1.01839i	−0.999828	+	0.0185640i	$0.994091\pi$
$308$	12.1246	−	1.92035i	0.690865	−	0.109422i
$309$	−25.7894	+	13.4874i	−1.46711	+	0.767270i
$310$	0.000250462	−	0.00226439i	1.42253e−5	−	0.000128609i
$311$	−4.51681	+	1.46760i	−0.256125	+	0.0832199i	−0.434265	−	0.900785i	$-0.642992\pi$
$311$	−4.51681	+	1.46760i	−0.256125	+	0.0832199i	0.178140	+	0.984005i	$0.442992\pi$
$312$	0.331395	−	1.05805i	0.0187616	−	0.0599002i
$313$	24.0613	−	12.2599i	1.36003	−	0.692968i	0.386660	−	0.922222i	$-0.373629\pi$
$313$	24.0613	−	12.2599i	1.36003	−	0.692968i	0.973367	+	0.229254i	$0.0736287\pi$
$314$	−0.101776	−	0.313233i	−0.00574353	−	0.0176768i
$315$	13.6199	+	1.21419i	0.767397	+	0.0684117i
$316$	6.30734	−	19.4120i	0.354815	−	1.09201i
$317$	−0.606678	−	3.83042i	−0.0340745	−	0.215138i	0.964776	−	0.263073i	$-0.0847359\pi$
$317$	−0.606678	−	3.83042i	−0.0340745	−	0.215138i	−0.998850	+	0.0479351i	$0.984736\pi$
$318$	−0.359430	+	0.00381882i	−0.0201558	+	0.000214149i
$319$	−2.14001	+	2.94547i	−0.119818	+	0.164915i
$320$	4.68690	−	17.1186i	0.262005	−	0.956958i
$321$	8.61767	+	1.27121i	0.480992	+	0.0709518i
$322$	0.0937170	−	0.591706i	0.00522264	−	0.0329745i
$323$	−17.6284	−	8.98213i	−0.980872	−	0.499779i
$324$	−0.763718	−	17.9603i	−0.0424288	−	0.997793i
$325$	12.0710	+	9.99435i	0.669578	+	0.554387i
$326$			0.934125i			0.0517364i
$327$	−16.9130	+	5.69473i	−0.935292	+	0.314919i
$328$	−2.16137	−	0.342328i	−0.119342	−	0.0189019i
$329$	6.06883	−	4.40926i	0.334585	−	0.243090i
$330$	−0.593660	−	0.0592870i	−0.0326799	−	0.00326364i
$331$	14.0789	+	10.2289i	0.773845	+	0.562232i	0.903126	−	0.429377i	$-0.141267\pi$
$331$	14.0789	+	10.2289i	0.773845	+	0.562232i	−0.129280	+	0.991608i	$0.541267\pi$
$332$	−3.10615	−	3.10615i	−0.170472	−	0.170472i
$333$	8.08532	−	1.45732i	0.443073	−	0.0798607i
$334$	−0.0614197	−	0.0199565i	−0.00336074	−	0.00109197i
$335$	0.857822	−	1.89882i	0.0468678	−	0.103744i
$336$	−12.6010	−	6.25282i	−0.687444	−	0.341119i
$337$	−6.33712	−	12.4373i	−0.345205	−	0.677503i	0.651497	−	0.758651i	$-0.274141\pi$
$337$	−6.33712	−	12.4373i	−0.345205	−	0.677503i	−0.996702	+	0.0811484i	$0.974141\pi$
$338$	0.0736713	+	0.144588i	0.00400719	+	0.00786455i
$339$	13.5768	+	6.73701i	0.737391	+	0.365904i
$340$	5.50657	+	26.6178i	0.298636	+	1.44355i
$341$	−0.0571823	−	0.0185797i	−0.00309659	−	0.00100614i
$342$	−0.490385	+	0.0883883i	−0.0265170	+	0.00477949i
$343$	14.1901	+	14.1901i	0.766195	+	0.766195i
$344$	−0.914384	−	0.664339i	−0.0493003	−	0.0358188i
$345$	8.95605	−	20.3995i	0.482177	−	1.09827i
$346$	−0.0856460	+	0.0622255i	−0.00460436	+	0.00334526i
$347$	16.0196	+	2.53725i	0.859977	+	0.136207i	0.570820	−	0.821075i	$-0.306625\pi$
$347$	16.0196	+	2.53725i	0.859977	+	0.136207i	0.289156	+	0.957282i	$0.406625\pi$
$348$	3.95916	−	1.33308i	0.212233	−	0.0714604i
$349$			3.27425i			0.175267i	0.996153	+	0.0876333i	$0.0279304\pi$
$349$			3.27425i			0.175267i	−0.996153	+	0.0876333i	$0.972070\pi$
$350$	−0.390742	+	0.344200i	−0.0208860	+	0.0183983i
$351$	−11.8773	−	11.1433i	−0.633963	−	0.594786i
$352$	1.64419	+	0.837759i	0.0876358	+	0.0446527i
$353$	4.57504	−	28.8857i	0.243505	−	1.53743i	−0.498414	−	0.866939i	$-0.666084\pi$
$353$	4.57504	−	28.8857i	0.243505	−	1.53743i	0.741919	−	0.670490i	$-0.233916\pi$
$354$	−0.378346	−	0.0558104i	−0.0201089	−	0.00296629i
$355$	22.0081	−	1.03334i	1.16807	−	0.0548442i
$356$	−15.8846	+	21.8632i	−0.841881	+	1.15875i
$357$	21.4856	−	0.228277i	1.13714	−	0.0120817i
$358$	−0.0405675	−	0.256133i	−0.00214406	−	0.0135371i
$359$	−8.54970	+	26.3133i	−0.451236	+	1.38876i	0.424262	+	0.905540i	$0.360534\pi$
$359$	−8.54970	+	26.3133i	−0.451236	+	1.38876i	−0.875498	+	0.483222i	$0.839466\pi$
$360$	1.03250	+	0.900525i	0.0544174	+	0.0474618i
$361$	2.60544	+	8.01873i	0.137129	+	0.422038i
$362$	0.0476258	−	0.0242666i	0.00250316	−	0.00127542i
$363$	0.988464	−	3.15588i	0.0518809	−	0.165640i
$364$	−12.1366	+	3.94343i	−0.636132	+	0.206692i
$365$	0.0433173	+	0.0759795i	0.00226733	+	0.00397695i
$366$	1.01375	−	0.530172i	0.0529896	−	0.0277126i
$367$	5.42920	−	0.859901i	0.283402	−	0.0448865i	−0.0131151	−	0.999914i	$-0.504175\pi$
$367$	5.42920	−	0.859901i	0.283402	−	0.0448865i	0.296517	+	0.955028i	$0.404175\pi$
$368$	−16.2065	+	16.2065i	−0.844825	+	0.844825i
$369$	−18.3372	+	26.4009i	−0.954597	+	1.37438i
$370$	−0.171822	+	0.261457i	−0.00893260	+	0.0135925i
$371$	4.86671	+	6.69846i	0.252667	+	0.347767i
$372$	0.0411415	+	0.0553794i	0.00213309	+	0.00287129i
$373$	−3.41888	+	6.70992i	−0.177023	+	0.347427i	−0.962420	−	0.271565i	$-0.912459\pi$
$373$	−3.41888	+	6.70992i	−0.177023	+	0.347427i	0.785397	+	0.618992i	$0.212459\pi$
$374$	−0.937499			−0.0484769
$375$	−17.3041	+	8.69300i	−0.893580	+	0.448904i
$376$	0.751596			0.0387606
$377$	1.71825	−	3.37226i	0.0884945	−	0.173680i
$378$	0.427442	−	0.331871i	0.0219853	−	0.0170696i
$379$	−13.4955	−	18.5749i	−0.693216	−	0.954130i	−0.999997	−	0.00234966i	$-0.999252\pi$
$379$	−13.4955	−	18.5749i	−0.693216	−	0.954130i	0.306781	−	0.951780i	$-0.400748\pi$
$380$	−7.97412	+	12.1340i	−0.409064	+	0.622461i
$381$	−5.96205	+	1.00934i	−0.305445	+	0.0517100i
$382$	0.683782	−	0.683782i	0.0349853	−	0.0349853i
$383$	7.62404	−	1.20753i	0.389570	−	0.0617019i	0.0414229	−	0.999142i	$-0.486811\pi$
$383$	7.62404	−	1.20753i	0.389570	−	0.0617019i	0.348147	+	0.937440i	$0.386811\pi$
$384$	−1.30806	−	2.50115i	−0.0667515	−	0.127636i
$385$	6.80647	+	11.9387i	0.346890	+	0.608453i
$386$	−0.539087	+	0.175160i	−0.0274388	+	0.00891542i
$387$	−14.6292	+	7.84986i	−0.743645	+	0.399031i
$388$	−9.54104	+	4.86140i	−0.484373	+	0.246800i
$389$	5.38913	+	16.5860i	0.273240	+	0.840945i	0.989680	+	0.143297i	$0.0457703\pi$
$389$	5.38913	+	16.5860i	0.273240	+	0.840945i	−0.716440	+	0.697649i	$0.754230\pi$
$390$	0.619179	−	0.0356686i	0.0313533	−	0.00180615i
$391$	10.8182	−	33.2950i	0.547099	−	1.68380i
$392$	0.0908935	+	0.573879i	0.00459082	+	0.0289853i
$393$	0.143687	+	13.5239i	0.00724806	+	0.682192i
$394$	−0.756459	+	1.04118i	−0.0381098	+	0.0524537i
$395$	22.8248	−	1.07169i	1.14844	−	0.0539227i
$396$	14.3874	−	10.9276i	0.722996	−	0.549131i
$397$	1.62336	−	10.2495i	0.0814741	−	0.514407i	−0.912874	−	0.408241i	$-0.866142\pi$
$397$	1.62336	−	10.2495i	0.0814741	−	0.514407i	0.994348	−	0.106167i	$-0.0338577\pi$
$398$	0.733615	+	0.373795i	0.0367728	+	0.0187367i
$399$	8.20178	+	8.02933i	0.410602	+	0.401969i
$400$	19.8341	−	1.86665i	0.991704	−	0.0933326i
$401$		−	14.7017i		−	0.734168i	−0.930188	−	0.367084i	$-0.880356\pi$
$401$		−	14.7017i		−	0.734168i	0.930188	−	0.367084i	$-0.119644\pi$
$402$	−0.0263130	−	0.0781483i	−0.00131238	−	0.00389768i
$403$	0.0617331	+	0.00977756i	0.00307514	+	0.000487055i
$404$	−19.7912	+	14.3792i	−0.984651	+	0.715391i
$405$	18.5079	−	7.90310i	0.919663	−	0.392708i
$406$	0.101741	+	0.0739189i	0.00504930	+	0.00366853i
$407$	5.83850	+	5.83850i	0.289404	+	0.289404i
$408$	1.75502	+	1.24683i	0.0868865	+	0.0617271i
$409$	4.73536	+	1.53861i	0.234148	+	0.0760794i	0.423741	−	0.905783i	$-0.360717\pi$
$409$	4.73536	+	1.53861i	0.234148	+	0.0760794i	−0.189593	+	0.981863i	$0.560717\pi$
$410$	−0.247986	−	1.19872i	−0.0122472	−	0.0592006i
$411$	−7.63369	+	15.3838i	−0.376542	+	0.758829i
$412$	15.2367	+	29.9037i	0.750659	+	1.47325i
$413$	3.99934	+	7.84915i	0.196795	+	0.386231i
$414$	−0.290214	−	0.832565i	−0.0142632	−	0.0409183i
$415$	2.02461	−	4.48157i	0.0993844	−	0.219992i
$416$	−1.82440	−	0.592785i	−0.0894488	−	0.0290637i
$417$	−5.08099	+	7.15195i	−0.248817	+	0.350233i
$418$	−0.354112	−	0.354112i	−0.0173202	−	0.0173202i
$419$	−19.7469	−	14.3470i	−0.964699	−	0.700895i	−0.0104616	−	0.999945i	$-0.503330\pi$
$419$	−19.7469	−	14.3470i	−0.964699	−	0.700895i	−0.954237	+	0.299051i	$0.903330\pi$
$420$	1.56698	−	15.6907i	0.0764607	−	0.765626i
$421$	−2.27800	+	1.65506i	−0.111023	+	0.0806628i	−0.641911	−	0.766779i	$-0.721858\pi$
$421$	−2.27800	+	1.65506i	−0.111023	+	0.0806628i	0.530889	+	0.847442i	$0.321858\pi$
$422$	0.802932	+	0.127172i	0.0390861	+	0.00619063i
$423$	4.80205	−	9.94124i	0.233484	−	0.483360i
$424$			0.829573i			0.0402876i
$425$	−25.6991	+	16.2943i	−1.24659	+	0.790392i
$426$	0.609968	−	0.623068i	0.0295530	−	0.0301877i
$427$	−23.4796	−	11.9635i	−1.13626	−	0.578953i
$428$	1.57144	−	9.92171i	0.0759586	−	0.479584i
$429$	2.38864	−	16.1929i	0.115325	−	0.781801i
$430$	0.166955	−	0.609794i	0.00805131	−	0.0294069i
$431$	12.9674	−	17.8481i	0.624617	−	0.859712i	−0.373062	−	0.927807i	$-0.621692\pi$
$431$	12.9674	−	17.8481i	0.624617	−	0.859712i	0.997679	+	0.0680947i	$0.0216920\pi$
$432$	−20.6927	+	0.659759i	−0.995580	+	0.0317427i
$433$	−6.30865	−	39.8312i	−0.303174	−	1.91417i	−0.395555	−	0.918442i	$-0.629448\pi$
$433$	−6.30865	−	39.8312i	−0.303174	−	1.91417i	0.0923805	−	0.995724i	$-0.470552\pi$
$434$	−0.000641766		0.00197515i	−3.08058e−5		9.48104e-5i
$435$	2.96198	+	3.61922i	0.142016	+	0.173529i
$436$	6.35954	+	19.5726i	0.304567	+	0.937360i
$437$	16.6624	−	8.48993i	0.797072	−	0.406129i
$438$	0.00330304	+	0.00103456i	0.000157825	+	4.94330e-5i
$439$	12.3771	−	4.02156i	0.590727	−	0.191939i	0.00162635	−	0.999999i	$-0.499482\pi$
$439$	12.3771	−	4.02156i	0.590727	−	0.191939i	0.589100	+	0.808060i	$0.299482\pi$
$440$	−0.151376	+	1.36857i	−0.00721659	+	0.0652442i
$441$	8.17133	+	2.46436i	0.389111	+	0.117350i
$442$	0.962572	−	0.152456i	0.0457849	−	0.00725162i
$443$	20.7027	−	20.7027i	0.983613	−	0.983613i	−0.0162549	−	0.999868i	$-0.505174\pi$
$443$	20.7027	−	20.7027i	0.983613	−	0.983613i	0.999868	+	0.0162549i	$0.00517433\pi$
$444$	−1.58142	−	9.34127i	−0.0750509	−	0.443317i
$445$	−29.1798	−	7.98914i	−1.38326	−	0.378722i
$446$	0.653662	+	0.899688i	0.0309518	+	0.0426015i
$447$	−2.89991	+	2.15435i	−0.137161	+	0.101897i
$448$	−7.34538	+	14.4161i	−0.347037	+	0.681097i
$449$	27.3773			1.29201			0.646007	−	0.763332i	$-0.276438\pi$
$449$	27.3773			1.29201			0.646007	+	0.763332i	$0.276438\pi$
$450$	−0.267213	+	0.718280i	−0.0125965	+	0.0338600i
$451$	−32.3059			−1.52123
$452$	7.93497	−	15.5733i	0.373230	−	0.732504i
$453$	−4.35403	+	3.23462i	−0.204570	+	0.151976i
$454$	0.644245	+	0.886727i	0.0302359	+	0.0416162i
$455$	−8.92999	−	11.1511i	−0.418644	−	0.522774i
$456$	0.191956	+	1.13386i	0.00898914	+	0.0530978i
$457$	−9.58199	+	9.58199i	−0.448227	+	0.448227i	−0.894765	−	0.446538i	$-0.852657\pi$
$457$	−9.58199	+	9.58199i	−0.448227	+	0.448227i	0.446538	+	0.894765i	$0.352657\pi$
$458$	−0.583121	+	0.0923573i	−0.0272475	+	0.00431557i
$459$	27.7046	−	15.2472i	1.29314	−	0.711680i
$460$	−23.4135	−	10.5774i	−1.09166	−	0.493174i
$461$	−27.6032	+	8.96881i	−1.28561	+	0.417719i	−0.870552	−	0.492077i	$-0.836238\pi$
$461$	−27.6032	+	8.96881i	−1.28561	+	0.417719i	−0.415056	+	0.909796i	$0.636238\pi$
$462$	0.519008	+	0.162561i	0.0241464	+	0.00756300i
$463$	6.38255	−	3.25207i	0.296622	−	0.151137i	−0.299346	−	0.954145i	$-0.596768\pi$
$463$	6.38255	−	3.25207i	0.296622	−	0.151137i	0.595968	+	0.803008i	$0.296768\pi$
$464$	−1.48675	−	4.57576i	−0.0690208	−	0.212424i
$465$	−0.0417278	+	0.0649902i	−0.00193508	+	0.00301385i
$466$	−0.230765	+	0.710222i	−0.0106900	+	0.0329004i
$467$	−1.33507	−	8.42928i	−0.0617795	−	0.390061i	−0.999131	−	0.0416760i	$-0.986730\pi$
$467$	−1.33507	−	8.42928i	−0.0617795	−	0.390061i	0.937352	−	0.348385i	$-0.113270\pi$
$468$	−12.9952	+	13.5595i	−0.600703	+	0.626789i
$469$	−1.11644	+	1.53665i	−0.0515525	+	0.0709560i
$470$	0.148530	+	0.393319i	0.00685120	+	0.0181424i
$471$	−1.62939	+	11.0458i	−0.0750783	+	0.508965i
$472$	−0.138074	+	0.871764i	−0.00635537	+	0.0401262i
$473$	−14.8670	−	7.57513i	−0.683587	−	0.348305i
$474$	0.632604	−	0.646191i	0.0290565	−	0.0296805i
$475$	−15.8618	−	3.55237i	−0.727788	−	0.162994i
$476$		−	24.7785i		−	1.13572i
$477$	10.9726	+	5.30025i	0.502402	+	0.242682i
$478$	−0.204399	−	0.0323735i	−0.00934897	−	0.00148073i
$479$	11.8446	−	8.60560i	0.541193	−	0.393200i	−0.283335	−	0.959021i	$-0.591441\pi$
$479$	11.8446	−	8.60560i	0.541193	−	0.393200i	0.824528	+	0.565821i	$0.191441\pi$
$480$	1.57695	−	1.76974i	0.0719776	−	0.0807772i
$481$	−6.94411	−	5.04519i	−0.316624	−	0.230041i
$482$	0.0715186	+	0.0715186i	0.00325758	+	0.00325758i
$483$	−11.7623	+	16.5566i	−0.535205	+	0.753349i
$484$	−3.62702	−	1.17849i	−0.164865	−	0.0535677i
$485$	−8.86484	−	8.06971i	−0.402532	−	0.366427i
$486$	0.323387	−	0.727829i	0.0146691	−	0.0330150i
$487$	−5.68806	−	11.1635i	−0.257751	−	0.505864i	0.725477	−	0.688246i	$-0.241619\pi$
$487$	−5.68806	−	11.1635i	−0.257751	−	0.505864i	−0.983228	+	0.182382i	$0.941619\pi$
$488$	−1.19866	−	2.35250i	−0.0542606	−	0.106492i
$489$	14.0763	−	28.3673i	0.636550	−	1.28281i
$490$	−0.282355	+	0.160976i	−0.0127555	+	0.00727213i
$491$	34.7580	+	11.2936i	1.56861	+	0.509672i	0.959090	−	0.283101i	$-0.0913631\pi$
$491$	34.7580	+	11.2936i	1.56861	+	0.509672i	0.609518	+	0.792772i	$0.291363\pi$
$492$	30.2190	+	21.4686i	1.36238	+	0.967880i
$493$	5.19647	+	5.19647i	0.234037	+	0.234037i
$494$	0.421169	+	0.305997i	0.0189493	+	0.0137675i
$495$	17.1347	+	10.7462i	0.770149	+	0.483007i
$496$	0.0642794	−	0.0467017i	0.00288623	−	0.00209697i
$497$	−19.8373	−	3.14193i	−0.889826	−	0.140935i
$498$	−0.0621035	−	0.184444i	−0.00278293	−	0.00826513i
$499$		−	8.39246i		−	0.375698i	−0.982198	−	0.187849i	$-0.939848\pi$
$499$		−	8.39246i		−	0.375698i	0.982198	−	0.187849i	$-0.0601515\pi$
$500$	9.81214	+	20.0603i	0.438812	+	0.897126i
$501$	1.56446	+	1.53156i	0.0698948	+	0.0684251i
$502$	−1.23061	−	0.627027i	−0.0549248	−	0.0279856i
$503$	−5.88019	+	37.1261i	−0.262185	+	1.65537i	0.407857	+	0.913046i	$0.366276\pi$
$503$	−5.88019	+	37.1261i	−0.262185	+	1.65537i	−0.670042	+	0.742323i	$0.733724\pi$
$504$	−0.755399	−	0.994573i	−0.0336482	−	0.0443018i
$505$	−22.8868	−	15.0405i	−1.01845	−	0.669296i
$506$	0.520852	−	0.716891i	0.0231547	−	0.0318697i
$507$	−0.0584458	−	5.50096i	−0.00259567	−	0.244306i
$508$	1.09085	+	6.88738i	0.0483988	+	0.305578i
$509$	−4.05260	+	12.4726i	−0.179628	+	0.552839i	−0.999815	−	0.0192578i	$-0.993870\pi$
$509$	−4.05260	+	12.4726i	−0.179628	+	0.552839i	0.820186	+	0.572096i	$0.193870\pi$
$510$	−0.305651	+	1.16482i	−0.0135345	+	0.0515791i
$511$	−0.0246374	−	0.0758262i	−0.00108990	−	0.00335436i
$512$	−3.62285	+	1.84593i	−0.160109	+	0.0815794i
$513$	16.2238	+	4.70541i	0.716298	+	0.207749i
$514$	0.605569	−	0.196761i	0.0267105	−	0.00867877i
$515$	−25.2923	+	27.7844i	−1.11451	+	1.22433i
$516$	8.87266	+	16.9655i	0.390597	+	0.746867i
$517$	10.9592	−	1.73576i	0.481983	−	0.0763386i
$518$	0.201670	−	0.201670i	0.00886086	−	0.00886086i
$519$	3.53855	−	0.599055i	0.155325	−	0.0262956i
$520$	−0.0671330	−	1.42979i	−0.00294398	−	0.0627006i
$521$	−10.1668	−	13.9934i	−0.445415	−	0.613061i	0.525990	−	0.850491i	$-0.323695\pi$
$521$	−10.1668	−	13.9934i	−0.445415	−	0.613061i	−0.971405	+	0.237430i	$0.923695\pi$
$522$	0.183380	+	0.0250630i	0.00802631	+	0.00109698i
$523$	−5.13521	+	10.0784i	−0.224547	+	0.440698i	−0.975604	−	0.219540i	$-0.929545\pi$
$523$	−5.13521	+	10.0784i	−0.224547	+	0.440698i	0.751057	+	0.660238i	$0.229545\pi$
$524$	15.5966			0.681340
$525$	17.0527	−	4.56453i	0.744240	−	0.199212i
$526$	−0.184160			−0.00802976
$527$	−0.0550970	+	0.108134i	−0.00240006	+	0.00471039i
$528$	−12.4084	−	16.7026i	−0.540005	−	0.726886i
$529$	5.93077	+	8.16301i	0.257860	+	0.354913i
$530$	−0.434125	+	0.163940i	−0.0188572	+	0.00712111i
$531$	10.6485	+	7.39610i	0.462106	+	0.320963i
$532$	9.35933	−	9.35933i	0.405778	−	0.405778i
$533$	33.1699	−	5.25360i	1.43675	−	0.227559i
$534$	−1.06097	+	0.554867i	−0.0459126	+	0.0240114i
$535$	11.0126	−	2.27823i	0.476115	−	0.0984967i
$536$	−0.180993	+	0.0588082i	−0.00781770	+	0.00254013i
$537$	−2.62771	+	8.38949i	−0.113394	+	0.362033i
$538$	0.617789	−	0.314779i	0.0266348	−	0.0135711i
$539$	2.65067	+	8.15791i	0.114172	+	0.351386i
$540$	−8.88654	−	21.4388i	−0.382416	−	0.922578i
$541$	−9.85115	+	30.3187i	−0.423534	+	1.30350i	0.480857	+	0.876799i	$0.340326\pi$
$541$	−9.85115	+	30.3187i	−0.423534	+	1.30350i	−0.904391	+	0.426705i	$0.859674\pi$
$542$	−0.0658705	−	0.415890i	−0.00282938	−	0.0178640i
$543$	−1.81196	+	0.0192515i	−0.0777586	+	0.000826159i
$544$	2.18936	−	3.01339i	0.0938679	−	0.129198i
$545$	−17.9834	+	14.4013i	−0.770323	+	0.616885i
$546$	−0.559325	−	0.0825069i	−0.0239369	−	0.00353097i
$547$	2.95981	−	18.6875i	0.126552	−	0.799020i	−0.840007	−	0.542576i	$-0.817449\pi$
$547$	2.95981	−	18.6875i	0.126552	−	0.799020i	0.966559	−	0.256444i	$-0.0825510\pi$
$548$	17.6460	+	8.99110i	0.753801	+	0.384081i
$549$	−38.7744	+	0.824023i	−1.65485	+	0.0351685i
$550$	−0.746105	+	0.191240i	−0.0318140	+	0.00815452i
$551$			3.92562i			0.167237i
$552$	−1.92848	+	0.649332i	−0.0820815	+	0.0276374i
$553$	−20.5735	−	3.25853i	−0.874876	−	0.138567i
$554$	0.798260	−	0.579970i	0.0339148	−	0.0246406i
$555$	9.15772	−	5.35069i	0.388724	−	0.227124i
$556$	8.18487	+	5.94666i	0.347116	+	0.252194i
$557$	−27.8152	−	27.8152i	−1.17857	−	1.17857i	−0.980109	−	0.198459i	$-0.936406\pi$
$557$	−27.8152	−	27.8152i	−1.17857	−	1.17857i	−0.198459	−	0.980109i	$-0.563594\pi$
$558$	0.000542180		0.00300805i	2.29523e−5		0.000127341i
$559$	16.4965	+	5.36005i	0.697729	+	0.226706i
$560$	−18.0505	−	1.99655i	−0.762773	−	0.0843695i
$561$	28.4697	+	14.1271i	1.20199	+	0.596446i
$562$	0.240764	+	0.472526i	0.0101560	+	0.0199323i
$563$	18.6793	+	36.6601i	0.787237	+	1.54504i	0.837584	+	0.546309i	$0.183967\pi$
$563$	18.6793	+	36.6601i	0.787237	+	1.54504i	−0.0503464	+	0.998732i	$0.516033\pi$
$564$	−11.4047	−	5.65917i	−0.480224	−	0.238294i
$565$	19.4482	+	2.15115i	0.818193	+	0.0904995i
$566$	−0.468474	−	0.152216i	−0.0196914	−	0.00639813i
$567$	−17.9814	+	3.63708i	−0.755148	+	0.152743i
$568$	−1.42294	−	1.42294i	−0.0597052	−	0.0597052i
$569$	7.49851	+	5.44798i	0.314354	+	0.228391i	0.733762	−	0.679406i	$-0.237763\pi$
$569$	7.49851	+	5.44798i	0.314354	+	0.228391i	−0.419409	+	0.907798i	$0.637763\pi$
$570$	−0.555427	+	0.324526i	−0.0232643	+	0.0135929i
$571$	6.86662	−	4.98889i	0.287359	−	0.208779i	−0.434762	−	0.900545i	$-0.643167\pi$
$571$	6.86662	−	4.98889i	0.287359	−	0.208779i	0.722121	+	0.691767i	$0.243167\pi$
$572$	−18.6432	−	2.95280i	−0.779513	−	0.123463i
$573$	−31.0688	+	10.4611i	−1.29792	+	0.437017i
$574$			1.11589i			0.0465763i
$575$	1.81777	−	28.7045i	0.0758063	−	1.19706i
$576$	0.505937	+	23.8069i	0.0210807	+	0.991953i
$577$	23.4083	+	11.9271i	0.974498	+	0.496532i	0.867343	−	0.497711i	$-0.165826\pi$
$577$	23.4083	+	11.9271i	0.974498	+	0.496532i	0.107155	+	0.994242i	$0.465826\pi$
$578$	−0.160153	+	1.01117i	−0.00666150	+	0.0420590i
$579$	19.0103	+	2.80425i	0.790043	+	0.116540i
$580$	4.20972	−	3.37120i	0.174799	−	0.139982i
$581$	−2.63501	+	3.62677i	−0.109318	+	0.150464i
$582$	−0.474392	+	0.00504025i	−0.0196642	+	0.000208925i
$583$	1.91584	+	12.0961i	0.0793460	+	0.500971i
$584$	0.00246850	−	0.00759726i	0.000102147	−	0.000314377i
$585$	−19.3406	−	8.24718i	−0.799633	−	0.340979i
$586$	0.172952	+	0.532293i	0.00714460	+	0.0219888i
$587$	29.1195	−	14.8371i	1.20189	−	0.612395i	0.265759	−	0.964040i	$-0.414378\pi$
$587$	29.1195	−	14.8371i	1.20189	−	0.612395i	0.936133	+	0.351645i	$0.114378\pi$
$588$	2.94183	−	9.39240i	0.121319	−	0.387336i
$589$	−0.0616556	+	0.0200331i	−0.00254047	+	0.000825450i
$590$	−0.483490	+	0.100022i	−0.0199050	+	0.00411786i
$591$	38.6613	−	20.2192i	1.59032	−	0.831705i
$592$	−10.7769	+	1.70690i	−0.442929	+	0.0701531i
$593$	−4.77949	+	4.77949i	−0.196270	+	0.196270i	−0.798399	−	0.602129i	$-0.794319\pi$
$593$	−4.77949	+	4.77949i	−0.196270	+	0.196270i	0.602129	+	0.798399i	$0.294319\pi$
$594$	0.786194	−	0.150347i	0.0322579	−	0.00616880i
$595$	25.9507	−	9.79984i	1.06387	−	0.401754i
$596$	2.44871	+	3.37036i	0.100303	+	0.138055i
$597$	−16.6455	−	22.4061i	−0.681256	−	0.917021i
$598$	−0.418201	+	0.820766i	−0.0171015	+	0.0335636i
$599$	−26.7065			−1.09120			−0.545598	−	0.838047i	$-0.683697\pi$
$599$	−26.7065			−1.09120			−0.545598	+	0.838047i	$0.683697\pi$
$600$	1.65107	+	0.634275i	0.0674046	+	0.0258942i
$601$	12.6263			0.515039			0.257520	−	0.966273i	$-0.417095\pi$
$601$	12.6263			0.515039			0.257520	+	0.966273i	$0.417095\pi$
$602$	−0.261655	+	0.513527i	−0.0106643	+	0.0209298i
$603$	−0.378542	+	2.76970i	−0.0154154	+	0.112791i
$604$	3.67658	+	5.06038i	0.149598	+	0.205904i
$605$	−0.200240	−	4.26469i	−0.00814090	−	0.173384i
$606$	−1.06863	+	0.180912i	−0.0434100	+	0.00734905i
$607$	27.3885	−	27.3885i	1.11167	−	1.11167i	0.118742	−	0.992925i	$-0.462114\pi$
$607$	27.3885	−	27.3885i	1.11167	−	1.11167i	0.992925	−	0.118742i	$-0.0378861\pi$
$608$	1.96518	−	0.311254i	0.0796987	−	0.0126230i
$609$	−1.97576	−	3.77787i	−0.0800617	−	0.153087i
$610$	0.994209	−	1.09217i	0.0402543	−	0.0442207i
$611$	−10.9700	+	3.56436i	−0.443798	+	0.144199i
$612$	−17.2426	−	32.1338i	−0.696991	−	1.29893i
$613$	−30.2547	+	15.4155i	−1.22198	+	0.622628i	−0.941429	−	0.337212i	$-0.890516\pi$
$613$	−30.2547	+	15.4155i	−1.22198	+	0.622628i	−0.280547	+	0.959840i	$0.590516\pi$
$614$	0.398410	+	1.22618i	0.0160785	+	0.0494846i
$615$	−10.5326	+	40.1394i	−0.424717	+	1.61857i
$616$	0.387877	−	1.19376i	0.0156280	−	0.0480981i
$617$	2.87470	+	18.1501i	0.115731	+	0.730697i	0.975498	+	0.220010i	$0.0706090\pi$
$617$	2.87470	+	18.1501i	0.115731	+	0.730697i	−0.859767	+	0.510687i	$0.829391\pi$
$618$	0.0157973	+	1.48685i	0.000635459	+	0.0598099i
$619$	1.95042	−	2.68452i	0.0783938	−	0.107900i	−0.768019	−	0.640427i	$-0.778757\pi$
$619$	1.95042	−	2.68452i	0.0783938	−	0.107900i	0.846413	+	0.532527i	$0.178757\pi$
$620$	0.0744308	+	0.0489138i	0.00298921	+	0.00196442i
$621$	−3.73270	+	29.6563i	−0.149788	+	1.19007i
$622$	−0.0379583	+	0.239659i	−0.00152199	+	0.00960946i
$623$	24.5733	+	12.5207i	0.984507	+	0.501631i
$624$	15.4564	+	15.1314i	0.618752	+	0.605742i
$625$	−17.1286	+	18.2101i	−0.685146	+	0.728406i
$626$		−	1.37971i		−	0.0551443i
$627$	5.41750	+	16.0897i	0.216354	+	0.642560i
$628$	12.7173	+	2.01422i	0.507476	+	0.0803763i
$629$	13.4834	−	9.79627i	0.537619	−	0.390603i
$630$	0.371189	−	0.591856i	0.0147885	−	0.0235801i
$631$	16.0880	+	11.6886i	0.640454	+	0.465317i	0.860006	−	0.510284i	$-0.170460\pi$
$631$	16.0880	+	11.6886i	0.640454	+	0.465317i	−0.219552	+	0.975601i	$0.570460\pi$
$632$	−1.47575	−	1.47575i	−0.0587020	−	0.0587020i
$633$	−22.4669	−	15.9612i	−0.892979	−	0.634402i
$634$	−0.188444	−	0.0612291i	−0.00748405	−	0.00243172i
$635$	−6.78176	+	3.86640i	−0.269126	+	0.153433i
$636$	6.24630	−	12.5879i	0.247682	−	0.499143i
$637$	−4.04820	−	7.94505i	−0.160396	−	0.314794i
$638$	0.0844488	+	0.165740i	0.00334336	+	0.00656171i
$639$	−27.9123	+	9.72963i	−1.10419	+	0.384898i
$640$	−2.69463	−	2.45294i	−0.106515	−	0.0969610i
$641$	−39.9060	−	12.9663i	−1.57619	−	0.512136i	−0.615121	−	0.788433i	$-0.710893\pi$
$641$	−39.9060	−	12.9663i	−1.57619	−	0.512136i	−0.961072	+	0.276296i	$0.910893\pi$
$642$	0.257757	−	0.362816i	0.0101728	−	0.0143192i
$643$	−18.4566	−	18.4566i	−0.727857	−	0.727857i	0.242335	−	0.970193i	$-0.422087\pi$
$643$	−18.4566	−	18.4566i	−0.727857	−	0.727857i	−0.970193	+	0.242335i	$0.922087\pi$
$644$	18.9477	+	13.7663i	0.746645	+	0.542469i
$645$	−14.2590	+	16.0022i	−0.561448	+	0.630088i
$646$	−0.817785	+	0.594156i	−0.0321753	+	0.0233768i
$647$	−0.715984	−	0.113401i	−0.0281482	−	0.00445824i	0.142344	−	0.989817i	$-0.454536\pi$
$647$	−0.715984	−	0.113401i	−0.0281482	−	0.00445824i	−0.170493	+	0.985359i	$0.554536\pi$
$648$	−1.67173	−	0.764146i	−0.0656717	−	0.0300185i
$649$			13.0302i			0.511481i
$650$	0.734960	−	0.317687i	0.0288275	−	0.0124607i
$651$	0.0492524	−	0.0503102i	0.00193035	−	0.00197181i
$652$	−32.5386	−	16.5793i	−1.27431	−	0.649294i
$653$	3.58799	−	22.6537i	0.140409	−	0.886507i	−0.812436	−	0.583050i	$-0.801859\pi$
$653$	3.58799	−	22.6537i	0.140409	−	0.886507i	0.952845	−	0.303457i	$-0.0981408\pi$
$654$	−0.133058	+	0.902019i	−0.00520299	+	0.0352717i
$655$	6.16843	+	16.3344i	0.241020	+	0.638238i
$656$	25.0934	−	34.5381i	0.979733	−	1.34849i
$657$	−0.0847161	−	0.0811904i	−0.00330509	−	0.00316754i
$658$	−0.0599554	−	0.378544i	−0.00233731	−	0.0147572i
$659$	6.79306	−	20.9069i	0.264620	−	0.814416i	−0.727161	−	0.686467i	$-0.759161\pi$
$659$	6.79306	−	20.9069i	0.264620	−	0.814416i	0.991781	−	0.127949i	$-0.0408395\pi$
$660$	12.6017	−	19.6269i	0.490521	−	0.763975i
$661$	−3.85456	−	11.8631i	−0.149925	−	0.461421i	0.847687	−	0.530497i	$-0.177995\pi$
$661$	−3.85456	−	11.8631i	−0.149925	−	0.461421i	−0.997611	+	0.0690762i	$0.977995\pi$
$662$	0.792210	−	0.403651i	0.0307901	−	0.0156884i
$663$	−31.5285	−	9.87516i	−1.22447	−	0.383520i
$664$	−0.427176	+	0.138798i	−0.0165776	+	0.00538640i
$665$	13.5037	+	6.10049i	0.523650	+	0.236567i
$666$	0.121198	−	0.401870i	0.00469633	−	0.0155721i
$667$	−6.86070	+	1.08663i	−0.265647	+	0.0420744i
$668$	1.78525	−	1.78525i	0.0690736	−	0.0690736i
$669$	−6.29291	−	37.1715i	−0.243298	−	1.43713i
$670$	−0.0665428	−	0.0830939i	−0.00257077	−	0.00321020i
$671$	−22.9107	−	31.5339i	−0.884459	−	1.21735i
$672$	−1.73456	+	1.28861i	−0.0669123	+	0.0497093i
$673$	5.83674	−	11.4552i	0.224990	−	0.441567i	−0.750724	−	0.660616i	$-0.770295\pi$
$673$	5.83674	−	11.4552i	0.224990	−	0.441567i	0.975714	+	0.219048i	$0.0702953\pi$
$674$	−0.713172			−0.0274704
$675$	18.9383	−	17.7859i	0.728937	−	0.684581i
$676$	−6.34403			−0.244001
$677$	13.0973	−	25.7050i	0.503371	−	0.987922i	−0.489863	−	0.871799i	$-0.662953\pi$
$677$	13.0973	−	25.7050i	0.503371	−	0.987922i	0.993235	−	0.116123i	$-0.0370466\pi$
$678$	0.621603	−	0.461790i	0.0238725	−	0.0177349i
$679$	6.42331	+	8.84092i	0.246504	+	0.339283i
$680$	2.68064	+	0.733931i	0.102798	+	0.0281450i
$681$	−6.20225	−	36.6360i	−0.237671	−	1.40389i
$682$	−0.00217215	+	0.00217215i	−8.31758e−5	+	8.31758e-5i
$683$	−20.5763	+	3.25897i	−0.787331	+	0.124701i	−0.537137	−	0.843495i	$-0.680494\pi$
$683$	−20.5763	+	3.25897i	−0.787331	+	0.124701i	−0.250194	+	0.968196i	$0.580494\pi$
$684$	5.62471	−	18.6505i	0.215066	−	0.713119i
$685$	−2.43746	+	22.0368i	−0.0931307	+	0.841981i
$686$	0.975118	−	0.316835i	0.0372302	−	0.0120968i
$687$	19.0998	+	5.98232i	0.728703	+	0.228240i
$688$	19.6464	−	10.0103i	0.749013	−	0.381641i
$689$	−3.93416	−	12.1081i	−0.149880	−	0.461282i
$690$	−0.720908	−	0.880873i	−0.0274445	−	0.0335343i
$691$	−3.21593	+	9.89763i	−0.122340	+	0.376524i	−0.993407	−	0.114640i	$-0.963428\pi$
$691$	−3.21593	+	9.89763i	−0.122340	+	0.376524i	0.871067	+	0.491164i	$0.163428\pi$
$692$	−0.647434	−	4.08774i	−0.0246117	−	0.155392i
$693$	−13.3115	−	12.7575i	−0.505662	−	0.484617i
$694$	0.487079	−	0.670407i	0.0184893	−	0.0254483i
$695$	−2.99087	+	10.9240i	−0.113450	+	0.414369i
$696$	0.0623358	−	0.422583i	0.00236283	−	0.0160179i
$697$	−10.2009	+	64.4062i	−0.386388	+	2.43956i
$698$	0.149053	+	0.0759465i	0.00564175	+	0.00287462i
$699$	17.7101	−	18.0905i	0.669857	−	0.684244i
$700$	−5.05456	−	19.7198i	−0.191044	−	0.745340i
$701$			29.3464i			1.10840i	0.832384	+	0.554199i	$0.186975\pi$
$701$			29.3464i			1.10840i	−0.832384	+	0.554199i	$0.813025\pi$
$702$	−0.782771	+	0.282219i	−0.0295438	+	0.0106517i
$703$	8.79321	+	1.39271i	0.331642	+	0.0525270i
$704$	−19.3613	+	14.0668i	−0.729707	+	0.530163i
$705$	1.41635	−	14.1824i	0.0533429	−	0.534140i
$706$	−1.20884	−	0.878275i	−0.0454953	−	0.0330543i
$707$	17.6533	+	17.6533i	0.663920	+	0.663920i
$708$	8.65911	−	12.1885i	0.325429	−	0.458071i
$709$	−18.4297	−	5.98817i	−0.692141	−	0.224890i	−0.0582380	−	0.998303i	$-0.518548\pi$
$709$	−18.4297	−	5.98817i	−0.692141	−	0.224890i	−0.633903	+	0.773412i	$0.718548\pi$
$710$	0.463438	−	1.02584i	0.0173925	−	0.0384991i
$711$	−28.9482	+	10.0907i	−1.08564	+	0.378431i
$712$	1.25449	+	2.46207i	0.0470139	+	0.0922700i
$713$	−0.0520778	−	0.102208i	−0.00195033	−	0.00382774i
$714$	0.487969	−	0.983383i	0.0182618	−	0.0368022i
$715$	−4.28088	−	20.6930i	−0.160096	−	0.773875i
$716$	9.64197	+	3.13287i	0.360337	+	0.117081i
$717$	5.71929	+	4.06318i	0.213591	+	0.151742i
$718$	0.999546	+	0.999546i	0.0373027	+	0.0373027i
$719$	23.3742	+	16.9824i	0.871712	+	0.633336i	0.931046	−	0.364903i	$-0.118898\pi$
$719$	23.3742	+	16.9824i	0.871712	+	0.633336i	−0.0593341	+	0.998238i	$0.518898\pi$
$720$	−24.7980	+	9.97160i	−0.924168	+	0.371620i
$721$	27.7094	−	20.1321i	1.03195	−	0.749758i
$722$	0.425469	+	0.0673877i	0.0158343	+	0.00250791i
$723$	−1.09415	−	3.24957i	−0.0406919	−	0.120853i
$724$			2.08966i			0.0776615i
$725$	5.19562	+	3.07556i	0.192960	+	0.114223i
$726$	−0.120737	−	0.118199i	−0.00448097	−	0.00438676i
$727$	23.3536	+	11.8992i	0.866136	+	0.441318i	0.829826	−	0.558022i	$-0.188440\pi$
$727$	23.3536	+	11.8992i	0.866136	+	0.441318i	0.0363101	+	0.999341i	$0.488440\pi$
$728$	−0.204121	+	1.28877i	−0.00756521	+	0.0477649i
$729$	−20.7881	+	17.2294i	−0.769931	+	0.638128i
$730$	0.00446356		0.000209577i	0.000165204		7.75680e-6i
$731$	−19.7965	+	27.2475i	−0.732199	+	1.00779i
$732$	0.475156	+	44.7220i	0.0175623	+	1.65297i
$733$	6.31509	+	39.8719i	0.233253	+	1.47270i	0.774893	+	0.632092i	$0.217804\pi$
$733$	6.31509	+	39.8719i	0.233253	+	1.47270i	−0.541640	+	0.840610i	$0.682196\pi$
$734$	0.0867856	−	0.267099i	0.00320332	−	0.00985879i
$735$	11.0002	−	0.633682i	0.405749	−	0.0233737i
$736$	1.08794	+	3.34834i	0.0401020	+	0.123421i
$737$	−2.50327	+	1.27548i	−0.0922093	+	0.0469830i
$738$	0.776514	+	1.44713i	0.0285839	+	0.0532698i
$739$	15.4065	−	5.00589i	0.566739	−	0.184145i	−0.0116122	−	0.999933i	$-0.503696\pi$
$739$	15.4065	−	5.00589i	0.566739	−	0.184145i	0.578351	+	0.815788i	$0.303696\pi$
$740$	−6.05783	−	10.6256i	−0.222690	−	0.390604i
$741$	−8.17891	−	15.6390i	−0.300460	−	0.574513i
$742$	0.417817	−	0.0661757i	0.0153385	−	0.00242939i
$743$	3.57440	−	3.57440i	0.131132	−	0.131132i	−0.638494	−	0.769626i	$-0.720442\pi$
$743$	3.57440	−	3.57440i	0.131132	−	0.131132i	0.769626	+	0.638494i	$0.220442\pi$
$744$	0.00695516	−	0.00117747i	0.000254989	−	4.31681e-5i
$745$	−2.56134	+	3.89752i	−0.0938402	+	0.142794i
$746$	0.226154	+	0.311274i	0.00828009	+	0.0113966i
$747$	−0.893427	+	6.53698i	−0.0326888	+	0.239176i
$748$	16.6392	−	32.6562i	0.608388	−	1.19403i
$749$	−10.2516			−0.374585
$750$	−0.00563940	+	0.989368i	−0.000205922	+	0.0361266i
$751$	5.81393			0.212153			0.106077	−	0.994358i	$-0.466171\pi$
$751$	5.81393			0.212153			0.106077	+	0.994358i	$0.466171\pi$
$752$	−6.65676	+	13.0646i	−0.242747	+	0.476418i
$753$	27.9222	+	37.5854i	1.01754	+	1.36969i
$754$	−0.113660	−	0.156440i	−0.00413926	−	0.00569720i
$755$	−3.84569	+	5.85188i	−0.139959	+	0.212972i
$756$	3.97373	+	20.7794i	0.144523	+	0.755740i
$757$	−3.51235	+	3.51235i	−0.127658	+	0.127658i	−0.768049	−	0.640391i	$-0.778772\pi$
$757$	−3.51235	+	3.51235i	−0.127658	+	0.127658i	0.640391	+	0.768049i	$0.278772\pi$
$758$	−1.15861	+	0.183506i	−0.0420827	+	0.00666525i
$759$	−26.6199	+	13.9217i	−0.966240	+	0.505326i
$760$	0.735310	+	1.28975i	0.0266725	+	0.0467842i
$761$	16.5920	−	5.39106i	0.601459	−	0.195426i	0.00756785	−	0.999971i	$-0.497591\pi$
$761$	16.5920	−	5.39106i	0.601459	−	0.195426i	0.593891	+	0.804546i	$0.297591\pi$
$762$	−0.0923422	+	0.294822i	−0.00334520	+	0.0106803i
$763$	18.7133	−	9.53488i	0.677465	−	0.345186i
$764$	11.6823	+	35.9545i	0.422651	+	1.30079i
$765$	26.8345	−	30.7672i	0.970204	−	1.11239i
$766$	0.121870	−	0.375077i	0.00440334	−	0.0135521i
$767$	−2.11898	−	13.3787i	−0.0765119	−	0.483077i
$768$	27.3503	−	0.290587i	0.986918	−	0.0104857i
$769$	2.97500	−	4.09474i	0.107281	−	0.147660i	−0.752000	−	0.659163i	$-0.770911\pi$
$769$	2.97500	−	4.09474i	0.107281	−	0.147660i	0.859282	+	0.511502i	$0.170911\pi$
$770$	0.701362	−	0.0329310i	0.0252753	−	0.00118675i
$771$	−21.3548	−	3.15007i	−0.769073	−	0.113447i
$772$	3.46656	−	21.8870i	0.124764	−	0.787731i
$773$	−4.71165	−	2.40071i	−0.169466	−	0.0863474i	0.367200	−	0.930142i	$-0.380317\pi$
$773$	−4.71165	−	2.40071i	−0.169466	−	0.0863474i	−0.536666	+	0.843795i	$0.680317\pi$
$774$	0.0180224	+	0.848043i	0.000647801	+	0.0304823i
$775$	−0.0217905	+	0.0972971i	−0.000782736	+	0.00349502i
$776$			1.09491i			0.0393049i
$777$	−9.16320	+	3.08531i	−0.328728	+	0.110685i
$778$	0.880046	+	0.139386i	0.0315512	+	0.00499722i
$779$	−28.1806	+	20.4744i	−1.00968	+	0.733572i
$780$	−9.74701	+	22.2011i	−0.348999	+	0.794927i
$781$	−24.0343	−	17.4619i	−0.860014	−	0.624837i
$782$	−1.26476	−	1.26476i	−0.0452275	−	0.0452275i
$783$	−5.19116	−	3.52444i	−0.185517	−	0.125953i
$784$	−10.7805	−	3.50279i	−0.385017	−	0.125100i
$785$	2.92016	+	14.1155i	0.104225	+	0.503805i
$786$	0.618982	+	0.307148i	0.0220783	+	0.0109556i
$787$	14.6311	+	28.7152i	0.521543	+	1.02359i	0.990128	+	0.140167i	$0.0447639\pi$
$787$	14.6311	+	28.7152i	0.521543	+	1.02359i	−0.468585	+	0.883418i	$0.655236\pi$
$788$	−22.8416	−	44.8292i	−0.813699	−	1.59697i
$789$	5.59253	+	2.77509i	0.199099	+	0.0987959i
$790$	0.480637	−	1.06391i	0.0171003	−	0.0378523i
$791$	−16.9641	−	5.51196i	−0.603173	−	0.195983i
$792$	−0.327688	−	1.81804i	−0.0116439	−	0.0646011i
$793$	28.6515	+	28.6515i	1.01745	+	1.01745i
$794$	−0.428933	−	0.311638i	−0.0152223	−	0.0110596i
$795$	15.6538	+	1.56330i	0.555183	+	0.0554444i
$796$	−26.0410	+	18.9199i	−0.923000	+	0.670599i
$797$	27.1310	+	4.29713i	0.961030	+	0.152212i	0.617188	−	0.786816i	$-0.288272\pi$
$797$	27.1310	+	4.29713i	0.961030	+	0.152212i	0.343841	+	0.939028i	$0.388272\pi$
$798$	0.555759	−	0.187128i	0.0196737	−	0.00662425i
$799$		−	22.3966i		−	0.792336i
$800$	1.12769	−	2.84480i	0.0398698	−	0.100579i
$801$	40.5805	−	0.862405i	1.43384	−	0.0304716i
$802$	−0.669264	−	0.341007i	−0.0236325	−	0.0120414i
$803$	0.0184483	−	0.116478i	0.000651025	−	0.00411041i
$804$	3.18918	+	0.470440i	0.112474	+	0.0165912i
$805$	−6.92377	+	25.2886i	−0.244031	+	0.891307i
$806$	0.00187701	−	0.00258348i	6.61147e−5	−	9.09991e-5i
$807$	−23.5042	+	0.249724i	−0.827388	+	0.00879072i
$808$	0.391301	+	2.47057i	0.0137659	+	0.0869145i
$809$	−1.47285	+	4.53298i	−0.0517828	+	0.159371i	−0.973604	−	0.228245i	$-0.926701\pi$
$809$	−1.47285	+	4.53298i	−0.0517828	+	0.159371i	0.921821	+	0.387616i	$0.126701\pi$
$810$	0.0695190	−	1.02584i	0.00244265	−	0.0360445i
$811$	−17.2310	−	53.0316i	−0.605062	−	1.86219i	−0.496363	−	0.868115i	$-0.665331\pi$
$811$	−17.2310	−	53.0316i	−0.605062	−	1.86219i	−0.108700	−	0.994075i	$-0.534669\pi$
$812$	−4.38058	+	2.23202i	−0.153728	+	0.0783284i
$813$	−4.26667	+	13.6222i	−0.149639	+	0.477753i
$814$	0.401210	−	0.130361i	0.0140624	−	0.00456915i
$815$	4.49459	−	40.6350i	0.157439	−	1.42338i
$816$	−37.2169	+	19.4637i	−1.30285	+	0.681367i
$817$	−17.7695	+	2.81441i	−0.621675	+	0.0984636i
$818$	0.179879	−	0.179879i	0.00628932	−	0.00628932i
$819$	15.7421	+	10.9340i	0.550075	+	0.382064i
$820$	46.1568	+	12.6373i	1.61186	+	0.441312i
$821$	11.9603	+	16.4619i	0.417416	+	0.574524i	0.965008	−	0.262222i	$-0.0844552\pi$
$821$	11.9603	+	16.4619i	0.417416	+	0.574524i	−0.547591	+	0.836746i	$0.684455\pi$
$822$	0.523253	+	0.704337i	0.0182506	+	0.0245666i
$823$	12.2207	−	23.9846i	0.425989	−	0.836050i	−0.573865	−	0.818950i	$-0.694557\pi$
$823$	12.2207	−	23.9846i	0.425989	−	0.836050i	0.999854	−	0.0170998i	$-0.00544330\pi$
$824$	3.43168			0.119548
$825$	25.5393	+	5.43545i	0.889165	+	0.189238i
$826$	0.450081			0.0156603
$827$	−8.46369	+	16.6109i	−0.294311	+	0.577618i	−0.990057	−	0.140670i	$-0.955074\pi$
$827$	−8.46369	+	16.6109i	−0.294311	+	0.577618i	0.695745	+	0.718289i	$0.255074\pi$
$828$	34.1518	+	4.66762i	1.18686	+	0.162211i
$829$	−20.7919	−	28.6176i	−0.722132	−	0.993930i	−0.999450	−	0.0331514i	$-0.989446\pi$
$829$	−20.7919	−	28.6176i	−0.722132	−	0.993930i	0.277318	−	0.960778i	$-0.410554\pi$
$830$	−0.157053	−	0.196117i	−0.00545139	−	0.00680731i
$831$	−32.9809	+	5.58347i	−1.14409	+	0.193688i
$832$	17.5916	−	17.5916i	0.609879	−	0.609879i
$833$	17.1009	−	2.70851i	0.592510	−	0.0938444i
$834$	0.207724	+	0.397192i	0.00719289	+	0.0137536i
$835$	2.57577	+	1.16364i	0.0891383	+	0.0402695i
$836$	18.6198	−	6.04995i	0.643981	−	0.209242i
$837$	0.0288633	−	0.0995178i	0.000997662	−	0.00343984i
$838$	−1.11115	+	0.566157i	−0.0383839	+	0.0195576i
$839$	−8.42816	−	25.9392i	−0.290972	−	0.895520i	−0.984545	−	0.175134i	$-0.943964\pi$
$839$	−8.42816	−	25.9392i	−0.290972	−	0.895520i	0.693572	−	0.720387i	$-0.256036\pi$
$840$	−1.35676	−	0.871128i	−0.0468128	−	0.0300568i
$841$	−8.51090	+	26.1939i	−0.293479	+	0.903237i
$842$	0.0225049	+	0.142090i	0.000775570	+	0.00489676i
$843$	−0.191006	−	17.9776i	−0.00657859	−	0.619182i
$844$	−18.6806	+	25.7117i	−0.643013	+	0.885032i
$845$	−2.50905	−	6.64414i	−0.0863140	−	0.228565i
$846$	−0.341170	−	0.449191i	−0.0117297	−	0.0154435i
$847$	−0.608837	+	3.84405i	−0.0209199	+	0.132083i
$848$	−14.4201	−	7.34738i	−0.495187	−	0.252310i
$849$	11.9328	+	11.6819i	0.409531	+	0.400920i
$850$	0.145673	+	1.54785i	0.00499654	+	0.0530907i
$851$			15.7531i			0.540011i
$852$	10.8775	+	32.3057i	0.372658	+	1.10677i
$853$	−47.8254	−	7.57479i	−1.63751	−	0.259356i	−0.731260	−	0.682099i	$-0.761067\pi$
$853$	−47.8254	−	7.57479i	−1.63751	−	0.259356i	−0.906250	+	0.422743i	$0.861067\pi$
$854$	−1.08922	+	0.791367i	−0.0372725	+	0.0270800i
$855$	21.7573	−	1.48543i	0.744085	−	0.0508007i
$856$	−0.830973	−	0.603737i	−0.0284021	−	0.0206353i
$857$	27.4824	+	27.4824i	0.938780	+	0.938780i	0.998231	−	0.0594514i	$-0.0189351\pi$
$857$	27.4824	+	27.4824i	0.938780	+	0.938780i	−0.0594514	+	0.998231i	$0.518935\pi$
$858$	−0.681744	−	0.484334i	−0.0232743	−	0.0165349i
$859$	−28.7211	−	9.33206i	−0.979953	−	0.318406i	−0.225126	−	0.974330i	$-0.572279\pi$
$859$	−28.7211	−	9.33206i	−0.979953	−	0.318406i	−0.754827	+	0.655924i	$0.772279\pi$
$860$	18.2779	+	16.6385i	0.623273	+	0.567369i
$861$	16.8153	−	33.8871i	0.573062	−	1.15487i
$862$	−0.511717	−	1.00430i	−0.0174291	−	0.0342066i
$863$	−16.3635	−	32.1153i	−0.557021	−	1.09322i	−0.982153	−	0.188085i	$-0.939772\pi$
$863$	−16.3635	−	32.1153i	−0.557021	−	1.09322i	0.425131	−	0.905132i	$-0.360228\pi$
$864$	−1.35275	+	2.87816i	−0.0460216	+	0.0979170i
$865$	4.02505	−	2.29475i	0.136856	−	0.0780240i
$866$	−1.95956	−	0.636700i	−0.0665886	−	0.0216360i
$867$	20.1007	−	28.2936i	0.682655	−	0.960899i
$868$	−0.0574107	−	0.0574107i	−0.00194865	−	0.00194865i
$869$	−24.9262	−	18.1100i	−0.845564	−	0.614338i
$870$	0.233461	−	0.0508897i	0.00791507	−	0.00172532i
$871$	2.36280	−	1.71668i	0.0800606	−	0.0581674i
$872$	2.07838	+	0.329184i	0.0703830	+	0.0111476i
$873$	14.4822	+	6.99551i	0.490147	+	0.236762i
$874$		−	0.955447i		−	0.0323185i
$875$	18.6536	−	13.0928i	0.630608	−	0.442619i
$876$	−0.0946608	+	0.0966939i	−0.00319829	+	0.00326698i
$877$	−36.9183	−	18.8108i	−1.24664	−	0.635195i	−0.298915	−	0.954280i	$-0.596625\pi$
$877$	−36.9183	−	18.8108i	−1.24664	−	0.635195i	−0.947726	+	0.319085i	$0.896625\pi$
$878$	0.104015	−	0.656722i	0.00351032	−	0.0221633i
$879$	2.76890	−	18.7707i	0.0933927	−	0.633122i
$880$	−22.4485	−	14.7525i	−0.756739	−	0.497307i
$881$	−7.72042	+	10.6262i	−0.260107	+	0.358007i	−0.919019	−	0.394213i	$-0.871017\pi$
$881$	−7.72042	+	10.6262i	−0.260107	+	0.358007i	0.658912	+	0.752220i	$0.271017\pi$
$882$	0.301719	−	0.314822i	0.0101594	−	0.0106006i
$883$	1.28990	+	8.14408i	0.0434084	+	0.274070i	0.999840	−	0.0178865i	$-0.00569375\pi$
$883$	1.28990	+	8.14408i	0.0434084	+	0.274070i	−0.956432	+	0.291957i	$0.905694\pi$
$884$	−11.7736	+	36.2354i	−0.395989	+	1.21873i
$885$	16.1897	+	4.24822i	0.544212	+	0.142802i
$886$	−0.462245	−	1.42265i	−0.0155294	−	0.0477947i
$887$	−7.79789	+	3.97322i	−0.261827	+	0.133408i	−0.579977	−	0.814633i	$-0.696939\pi$
$887$	−7.79789	+	3.97322i	−0.261827	+	0.133408i	0.318150	+	0.948040i	$0.396939\pi$
$888$	−0.924450	−	0.289550i	−0.0310225	−	0.00971667i
$889$	6.76808	−	2.19908i	0.226994	−	0.0737548i
$890$	−1.04052	+	1.14304i	−0.0348782	+	0.0383148i
$891$	−26.1405	−	7.28140i	−0.875740	−	0.243936i
$892$	−42.9406	+	6.80112i	−1.43776	+	0.227718i
$893$	8.45966	−	8.45966i	0.283092	−	0.283092i
$894$	0.0308085	+	0.181982i	0.00103039	+	0.00608640i
$895$	0.532312	+	11.3371i	0.0177932	+	0.378959i
$896$	1.95248	+	2.68736i	0.0652279	+	0.0897785i
$897$	25.0679	−	18.6230i	0.836992	−	0.621803i
$898$	0.635018	−	1.24629i	0.0211908	−	0.0415893i
$899$	0.0240800			0.000803114
$900$	−20.2774	−	22.0562i	−0.675914	−	0.735208i
$901$	24.7202			0.823551
$902$	−0.749338	+	1.47066i	−0.0249502	+	0.0489676i
$903$	15.6842	−	11.6518i	0.521937	−	0.387748i
$904$	−1.05046	−	1.44584i	−0.0349378	−	0.0480878i
$905$	−2.18851	+	0.826456i	−0.0727486	+	0.0274723i
$906$	0.0462571	+	0.273235i	0.00153679	+	0.00907763i
$907$	−22.7174	+	22.7174i	−0.754317	+	0.754317i	−0.975282	−	0.220964i	$-0.929080\pi$
$907$	−22.7174	+	22.7174i	−0.754317	+	0.754317i	0.220964	+	0.975282i	$0.429080\pi$
$908$	−42.3220	+	6.70314i	−1.40450	+	0.222452i
$909$	35.1780	+	10.6092i	1.16678	+	0.351884i
$910$	−0.714764	+	0.147867i	−0.0236942	+	0.00490176i
$911$	32.0727	−	10.4210i	1.06262	−	0.345265i	0.275008	−	0.961442i	$-0.411320\pi$
$911$	32.0727	−	10.4210i	1.06262	−	0.345265i	0.787607	+	0.616177i	$0.211320\pi$
$912$	−21.4094	−	6.70573i	−0.708937	−	0.222049i
$913$	−5.90818	+	3.01037i	−0.195532	+	0.0996286i
$914$	0.213945	+	0.658455i	0.00707667	+	0.0217798i
$915$	−46.6497	+	18.1851i	−1.54219	+	0.601181i
$916$	7.13239	−	21.9512i	0.235661	−	0.725289i
$917$	−2.48993	−	15.7208i	−0.0822248	−	0.519147i
$918$	−0.0514874	−	1.61486i	−0.00169934	−	0.0532982i
$919$	−21.7602	+	29.9504i	−0.717804	+	0.987972i	0.281790	+	0.959476i	$0.409072\pi$
$919$	−21.7602	+	29.9504i	−0.717804	+	0.987972i	−0.999594	+	0.0284959i	$0.990928\pi$
$920$	−2.05052	+	1.64209i	−0.0676038	+	0.0541380i
$921$	6.37839	−	43.2400i	0.210175	−	1.42481i
$922$	−0.231971	+	1.46461i	−0.00763956	+	0.0482343i
$923$	27.5167	+	14.0205i	0.905724	+	0.461490i
$924$	−14.8741	+	15.1936i	−0.489322	+	0.499832i
$925$	8.73238	−	10.5468i	0.287119	−	0.346777i
$926$		−	0.365984i		−	0.0120270i
$927$	21.9255	−	45.3903i	0.720127	−	1.49081i
$928$	−0.729951	−	0.115613i	−0.0239618	−	0.00379518i
$929$	21.0087	−	15.2637i	0.689272	−	0.500785i	−0.187149	−	0.982332i	$-0.559925\pi$
$929$	21.0087	−	15.2637i	0.689272	−	0.500785i	0.876421	+	0.481546i	$0.159925\pi$
$930$	0.00199066	+	0.00340702i	6.52764e−5	+	0.000111721i
$931$	7.48241	+	5.43629i	0.245226	+	0.178167i
$932$	−20.6436	−	20.6436i	−0.676205	−	0.676205i
$933$	4.76411	−	6.70592i	0.155970	−	0.219542i
$934$	−0.414692	−	0.134742i	−0.0135692	−	0.00440888i
$935$	40.7818	+	4.51083i	1.33371	+	0.147520i
$936$	0.632102	+	1.81337i	0.0206609	+	0.0592719i
$937$	−11.4061	−	22.3857i	−0.372621	−	0.731310i	0.626210	−	0.779655i	$-0.284605\pi$
$937$	−11.4061	−	22.3857i	−0.372621	−	0.731310i	−0.998831	+	0.0483450i	$0.984605\pi$
$938$	0.0440569	+	0.0864664i	0.00143851	+	0.00282323i
$939$	−20.7907	+	41.8987i	−0.678480	+	1.36731i
$940$	−16.3368	−	1.80699i	−0.532847	−	0.0589376i
$941$	−37.5058	−	12.1864i	−1.22265	−	0.397264i	−0.374606	−	0.927184i	$-0.622222\pi$
$941$	−37.5058	−	12.1864i	−1.22265	−	0.397264i	−0.848047	+	0.529920i	$0.822222\pi$
$942$	0.465045	+	0.330384i	0.0151520	+	0.0107645i
$943$	−43.5831	−	43.5831i	−1.41926	−	1.41926i
$944$	−13.9305	−	10.1211i	−0.453401	−	0.329415i
$945$	−20.1908	+	12.3799i	−0.656807	+	0.402719i
$946$	−0.689684	+	0.501085i	−0.0224236	+	0.0162917i
$947$	27.4747	+	4.35156i	0.892808	+	0.141407i	0.585949	−	0.810348i	$-0.300722\pi$
$947$	27.4747	+	4.35156i	0.892808	+	0.141407i	0.306859	+	0.951755i	$0.400722\pi$
$948$	11.2812	+	33.5046i	0.366397	+	1.08818i
$949$			0.122593i			0.00397954i
$950$	−0.529629	+	0.639677i	−0.0171834	+	0.0207538i
$951$	4.79995	+	4.69903i	0.155649	+	0.152377i
$952$	−2.25745	−	1.15023i	−0.0731644	−	0.0372791i
$953$	−1.49150	+	9.41698i	−0.0483145	+	0.305046i	−0.999998	−	0.00203511i	$-0.999352\pi$
$953$	−1.49150	+	9.41698i	−0.0483145	+	0.305046i	0.951683	+	0.307081i	$0.0993522\pi$
$954$	0.495794	−	0.376566i	0.0160519	−	0.0121918i
$955$	−33.0350	+	26.4549i	−1.06899	+	0.856060i
$956$	4.75543	−	6.54529i	0.153802	−	0.211690i
$957$	−0.0669960	−	6.30571i	−0.00216567	−	0.203835i
$958$	−0.117016	−	0.738808i	−0.00378060	−	0.0238698i
$959$	6.24559	−	19.2220i	0.201681	−	0.620709i
$960$	11.1654	+	28.6422i	0.360361	+	0.924422i
$961$	−9.57940	−	29.4824i	−0.309013	−	0.951044i
$962$	−0.390741	+	0.199093i	−0.0125980	+	0.00641900i
$963$	−13.2947	+	7.13379i	−0.428417	+	0.229883i
$964$	−3.76057	+	1.22188i	−0.121120	+	0.0393542i
$965$	24.2934	−	5.02572i	0.782033	−	0.161784i
$966$	0.480874	+	0.919486i	0.0154719	+	0.0295840i
$967$	61.1082	−	9.67859i	1.96511	−	0.311242i	0.966624	−	0.256201i	$-0.0824708\pi$
$967$	61.1082	−	9.67859i	1.96511	−	0.311242i	0.998484	−	0.0550419i	$-0.0175292\pi$
$968$	−0.275735	+	0.275735i	−0.00886245	+	0.00886245i
$969$	33.7876	−	5.72004i	1.08541	−	0.183754i
$970$	−0.572977	+	0.216376i	−0.0183972	+	0.00694740i
$971$	15.4537	+	21.2702i	0.495933	+	0.682594i	0.981469	−	0.191623i	$-0.0613752\pi$
$971$	15.4537	+	21.2702i	0.495933	+	0.682594i	−0.485535	+	0.874217i	$0.661375\pi$
$972$	19.6131	+	24.1825i	0.629090	+	0.775653i
$973$	4.68734	−	9.19942i	0.150269	−	0.294920i
$974$	−0.640128			−0.0205110
$975$	−27.1063	−	1.42761i	−0.868095	−	0.0457200i
$976$	51.5085			1.64875
$977$	−8.85510	+	17.3791i	−0.283300	+	0.556007i	−0.988176	−	0.153323i	$-0.951002\pi$
$977$	−8.85510	+	17.3791i	−0.283300	+	0.556007i	0.704876	+	0.709330i	$0.251002\pi$
$978$	−0.964861	−	1.29877i	−0.0308528	−	0.0415302i
$979$	23.9779	+	33.0027i	0.766336	+	1.05477i
$980$	−0.595946	−	12.6924i	−0.0190368	−	0.405445i
$981$	17.6331	−	25.3873i	0.562983	−	0.810553i
$982$	1.32033	−	1.32033i	0.0421335	−	0.0421335i
$983$	−54.7775	+	8.67590i	−1.74713	+	0.276718i	−0.946562	−	0.322523i	$-0.895469\pi$
$983$	−54.7775	+	8.67590i	−1.74713	+	0.276718i	−0.800569	+	0.599241i	$0.795469\pi$
$984$	3.35868	−	1.75653i	0.107071	−	0.0559961i
$985$	37.9161	−	41.6521i	1.20811	−	1.32714i
$986$	0.357091	−	0.116026i	0.0113721	−	0.00369502i
$987$	−3.88353	+	12.3990i	−0.123614	+	0.394664i
$988$	−18.1340	+	9.23973i	−0.576919	+	0.293955i
$989$	−9.83731	−	30.2761i	−0.312808	−	0.962725i
$990$	0.886641	−	0.530763i	0.0281793	−	0.0168688i
$991$	−8.12909	+	25.0188i	−0.258229	+	0.794748i	0.734947	+	0.678124i	$0.237207\pi$
$991$	−8.12909	+	25.0188i	−0.258229	+	0.794748i	−0.993176	+	0.116623i	$0.962793\pi$
$992$	−0.00190925	−	0.0120546i	−6.06189e−5	−	0.000382733i
$993$	−30.1402	+	0.320230i	−0.956471	+	0.0101622i
$994$	−0.603158	+	0.830176i	−0.0191310	+	0.0263316i
$995$	−30.1141	−	19.7902i	−0.954683	−	0.627390i
$996$	7.52703	+	1.11032i	0.238503	+	0.0351820i
$997$	3.96330	−	25.0233i	0.125519	−	0.792496i	−0.841959	−	0.539541i	$-0.818598\pi$
$997$	3.96330	−	25.0233i	0.125519	−	0.792496i	0.967478	−	0.252955i	$-0.0814023\pi$
$998$	−0.382049	−	0.194664i	−0.0120935	−	0.00616197i
$999$	−9.73626	+	10.3776i	−0.308042	+	0.328332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.2.l.a.8.5	yes	64
3.2	odd	2	inner	75.2.l.a.8.4	✓	64
5.2	odd	4		375.2.l.a.107.5		64
5.3	odd	4		375.2.l.b.107.4		64
5.4	even	2		375.2.l.c.143.4		64
15.2	even	4		375.2.l.a.107.4		64
15.8	even	4		375.2.l.b.107.5		64
15.14	odd	2		375.2.l.c.143.5		64
25.3	odd	20		375.2.l.c.257.5		64
25.4	even	10		375.2.l.b.368.5		64
25.21	even	5		375.2.l.a.368.4		64
25.22	odd	20	inner	75.2.l.a.47.4	yes	64
75.29	odd	10		375.2.l.b.368.4		64
75.47	even	20	inner	75.2.l.a.47.5	yes	64
75.53	even	20		375.2.l.c.257.4		64
75.71	odd	10		375.2.l.a.368.5		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.l.a.8.4	✓	64	3.2	odd	2	inner
75.2.l.a.8.5	yes	64	1.1	even	1	trivial
75.2.l.a.47.4	yes	64	25.22	odd	20	inner
75.2.l.a.47.5	yes	64	75.47	even	20	inner
375.2.l.a.107.4		64	15.2	even	4
375.2.l.a.107.5		64	5.2	odd	4
375.2.l.a.368.4		64	25.21	even	5
375.2.l.a.368.5		64	75.71	odd	10
375.2.l.b.107.4		64	5.3	odd	4
375.2.l.b.107.5		64	15.8	even	4
375.2.l.b.368.4		64	75.29	odd	10
375.2.l.b.368.5		64	25.4	even	10
375.2.l.c.143.4		64	5.4	even	2
375.2.l.c.143.5		64	15.14	odd	2
375.2.l.c.257.4		64	75.53	even	20
375.2.l.c.257.5		64	25.3	odd	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+(0.0231951 - 0.0455229i) q^{2} +(-1.39036 + 1.03290i) q^{3} +(1.17404 + 1.61592i) q^{4} +(-1.22804 + 1.86867i) q^{5} +(0.0147712 + 0.0872517i) q^{6} +(1.44136 - 1.44136i) q^{7} +(0.201718 - 0.0319491i) q^{8} +(0.866221 - 2.87222i) q^{9} +(0.0565829 + 0.0992477i) q^{10} +(2.86751 - 0.931709i) q^{11} +(-3.30143 - 1.03405i) q^{12} +(-2.79268 + 1.42294i) q^{13} +(-0.0321825 - 0.0990475i) q^{14} +(-0.222739 - 3.86657i) q^{15} +(-1.23123 + 3.78934i) q^{16} +(-0.952042 - 6.01096i) q^{17} +(-0.110660 - 0.106054i) q^{18} +(1.91085 - 2.63007i) q^{19} +(-4.46138 + 0.209475i) q^{20} +(-0.515229 + 3.49280i) q^{21} +(0.0240979 - 0.152148i) q^{22} +(5.12542 + 2.61153i) q^{23} +(-0.247462 + 0.252776i) q^{24} +(-1.98385 - 4.58959i) q^{25} +0.160136i q^{26} +(1.76237 + 4.88816i) q^{27} +(4.02134 + 0.636918i) q^{28} +(-0.976916 + 0.709771i) q^{29} +(-0.181184 - 0.0795457i) q^{30} +(-0.0161330 - 0.0117213i) q^{31} +(0.432772 + 0.432772i) q^{32} +(-3.02451 + 4.25727i) q^{33} +(-0.295719 - 0.0960849i) q^{34} +(0.923385 + 4.46347i) q^{35} +(5.65826 - 1.97235i) q^{36} +(1.24327 + 2.44005i) q^{37} +(-0.0754058 - 0.147992i) q^{38} +(2.41308 - 4.86298i) q^{39} +(-0.188015 + 0.416180i) q^{40} +(-10.1904 - 3.31106i) q^{41} +(0.147052 + 0.104471i) q^{42} +(-3.91319 - 3.91319i) q^{43} +(4.87212 + 3.53981i) q^{44} +(4.30349 + 5.14587i) q^{45} +(0.237769 - 0.172749i) q^{46} +(3.63479 + 0.575694i) q^{47} +(-2.20216 - 6.54030i) q^{48} +2.84495i q^{49} +(-0.254947 - 0.0161451i) q^{50} +(7.53242 + 7.37405i) q^{51} +(-5.57807 - 2.84217i) q^{52} +(-0.635421 + 4.01189i) q^{53} +(0.263401 + 0.0331531i) q^{54} +(-1.78034 + 6.50259i) q^{55} +(0.244699 - 0.336799i) q^{56} +(0.0598219 + 5.63047i) q^{57} +(0.00965120 + 0.0609353i) q^{58} +(-1.33548 + 4.11017i) q^{59} +(5.98658 - 4.89943i) q^{60} +(-3.99489 - 12.2950i) q^{61} +(-0.000907794 + 0.000462544i) q^{62} +(-2.89137 - 5.38845i) q^{63} +(-7.54893 + 2.45280i) q^{64} +(0.770505 - 6.96603i) q^{65} +(0.123650 + 0.236432i) q^{66} +(-0.920343 + 0.145768i) q^{67} +(8.59551 - 8.59551i) q^{68} +(-9.82366 + 1.66309i) q^{69} +(0.224608 + 0.0614955i) q^{70} +(-5.79154 - 7.97137i) q^{71} +(0.0829678 - 0.607055i) q^{72} +(0.0177571 - 0.0348503i) q^{73} +0.139916 q^{74} +(7.49888 + 4.33207i) q^{75} +6.49339 q^{76} +(2.79018 - 5.47604i) q^{77} +(-0.165405 - 0.222648i) q^{78} +(-6.00647 - 8.26720i) q^{79} +(-5.56902 - 6.95421i) q^{80} +(-7.49932 - 4.97596i) q^{81} +(-0.387096 + 0.387096i) q^{82} +(-2.17217 + 0.344039i) q^{83} +(-6.24900 + 3.26811i) q^{84} +(12.4016 + 5.60262i) q^{85} +(-0.268906 + 0.0873730i) q^{86} +(0.625143 - 1.99590i) q^{87} +(0.548661 - 0.279557i) q^{88} +(4.18096 + 12.8677i) q^{89} +(0.334075 - 0.0765482i) q^{90} +(-1.97429 + 6.07624i) q^{91} +(1.79740 + 11.3483i) q^{92} +(0.0345377 - 0.000366951i) q^{93} +(0.110516 - 0.152113i) q^{94} +(2.56813 + 6.80057i) q^{95} +(-1.04872 - 0.154699i) q^{96} +(-0.838657 + 5.29507i) q^{97} +(0.129510 + 0.0659889i) q^{98} +(-0.192183 - 9.04318i) 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

Related objects

Downloads

Learn more