LMFDB - Embedded newform 261.2.x.a.101.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [261,2,Mod(2,261)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(261, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([14, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("261.2"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.x (of order $84$, degree $24$, 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:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			101.13
Character	$\chi$	$=$	261.101
Dual form			261.2.x.a.230.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.234125 + 0.536620i) q^{2} +(-1.27001 + 1.17774i) q^{3} +(1.12720 + 1.21483i) q^{4} +(-1.79123 - 0.269985i) q^{5} +(-0.334659 - 0.957252i) q^{6} +(2.59390 + 2.40679i) q^{7} +(-2.02104 + 0.707193i) q^{8} +(0.225848 - 2.99149i) q^{9} +(0.564252 - 0.898002i) q^{10} +(-0.974345 + 0.838491i) q^{11} +(-2.86231 - 0.215298i) q^{12} +(-2.06180 + 3.02410i) q^{13} +(-1.89883 + 0.828450i) q^{14} +(2.59286 - 1.76673i) q^{15} +(-0.154007 + 2.05508i) q^{16} +(-2.82385 - 2.82385i) q^{17} +(1.55242 + 0.821577i) q^{18} +(-5.81575 - 3.65428i) q^{19} +(-1.69109 - 2.48037i) q^{20} +(-6.12885 - 0.00169842i) q^{21} +(-0.221833 - 0.719165i) q^{22} +(8.33810 + 3.27246i) q^{23} +(1.73385 - 3.27841i) q^{24} +(-1.64224 - 0.506563i) q^{25} +(-1.14008 - 1.81442i) q^{26} +(3.23637 + 4.06521i) q^{27} +5.86408i q^{28} +(-1.28158 + 5.23045i) q^{29} +(0.341009 + 1.80501i) q^{30} +(3.72396 - 2.74841i) q^{31} +(-4.85287 - 2.56482i) q^{32} +(0.249901 - 2.21242i) q^{33} +(2.17647 - 0.854200i) q^{34} +(-3.99648 - 5.01143i) q^{35} +(3.88873 - 3.09763i) q^{36} +(2.62155 + 7.49197i) q^{37} +(3.32257 - 2.26529i) q^{38} +(-0.943108 - 6.26890i) q^{39} +(3.81109 - 0.721097i) q^{40} +(6.95493 + 1.86357i) q^{41} +(1.43583 - 3.28847i) q^{42} +(1.32201 - 1.79126i) q^{43} +(-2.11691 - 0.238518i) q^{44} +(-1.21220 + 5.29748i) q^{45} +(-3.70823 + 3.70823i) q^{46} +(1.08573 + 1.26165i) q^{47} +(-2.22476 - 2.79135i) q^{48} +(0.412579 + 5.50549i) q^{49} +(0.656321 - 0.762658i) q^{50} +(6.91208 + 0.260550i) q^{51} +(-5.99783 + 0.904027i) q^{52} +(6.55714 + 5.22915i) q^{53} +(-2.93919 + 0.784935i) q^{54} +(1.97166 - 1.23888i) q^{55} +(-6.94443 - 3.02983i) q^{56} +(11.6899 - 2.20848i) q^{57} +(-2.50671 - 1.91230i) q^{58} +(-7.47986 + 4.31850i) q^{59} +(5.06894 + 1.15843i) q^{60} +(13.5329 - 0.506365i) q^{61} +(0.602979 + 2.64182i) q^{62} +(7.78570 - 7.21604i) q^{63} +(-0.709949 + 0.566166i) q^{64} +(4.50962 - 4.86022i) q^{65} +(1.12872 + 0.652084i) q^{66} +(10.9354 - 0.819497i) q^{67} +(0.247461 - 6.61353i) q^{68} +(-14.4436 + 5.66407i) q^{69} +(3.62491 - 0.971292i) q^{70} +(-3.89744 + 1.87691i) q^{71} +(1.65911 + 6.20563i) q^{72} +(0.963648 - 8.55261i) q^{73} +(-4.63411 - 0.347279i) q^{74} +(2.68226 - 1.29079i) q^{75} +(-2.11617 - 11.1843i) q^{76} +(-4.54542 - 0.170078i) q^{77} +(3.58482 + 0.961615i) q^{78} +(0.335835 - 1.77493i) q^{79} +(0.830703 - 3.63955i) q^{80} +(-8.89799 - 1.35124i) q^{81} +(-2.62835 + 3.29585i) q^{82} +(-0.302531 + 0.980782i) q^{83} +(-6.90637 - 7.44743i) q^{84} +(4.29577 + 5.82057i) q^{85} +(0.651711 + 1.12880i) q^{86} +(-4.53250 - 8.15208i) q^{87} +(1.37622 - 2.38367i) q^{88} +(-2.15138 + 0.242402i) q^{89} +(-2.55893 - 1.89077i) q^{90} +(-12.6265 + 2.88191i) q^{91} +(5.42320 + 13.8181i) q^{92} +(-1.49255 + 7.87637i) q^{93} +(-0.931222 + 0.287244i) q^{94} +(9.43077 + 8.11583i) q^{95} +(9.18388 - 2.45809i) q^{96} +(-0.817727 - 1.54721i) q^{97} +(-3.05095 - 1.06757i) q^{98} +(2.28828 + 3.10411i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.234125	+	0.536620i	−0.165551	+	0.379448i	−0.979487	−	0.201507i	$-0.935416\pi$
$2$	−0.234125	+	0.536620i	−0.165551	+	0.379448i	0.813936	+	0.580955i	$0.197321\pi$
$3$	−1.27001	+	1.17774i	−0.733240	+	0.679970i
$3$	−1.27001	+	1.17774i	−0.733240	+	0.679970i
$4$	1.12720	+	1.21483i	0.563599	+	0.607416i
$5$	−1.79123	−	0.269985i	−0.801064	−	0.120741i	−0.264264	−	0.964450i	$-0.585129\pi$
$5$	−1.79123	−	0.269985i	−0.801064	−	0.120741i	−0.536800	+	0.843709i	$0.680367\pi$
$6$	−0.334659	−	0.957252i	−0.136624	−	0.390796i
$7$	2.59390	+	2.40679i	0.980401	+	0.909680i	0.995924	−	0.0901999i	$-0.0287506\pi$
$7$	2.59390	+	2.40679i	0.980401	+	0.909680i	−0.0155222	+	0.999880i	$0.504941\pi$
$8$	−2.02104	+	0.707193i	−0.714546	+	0.250030i
$9$	0.225848	−	2.99149i	0.0752828	−	0.997162i
$10$	0.564252	−	0.898002i	0.178432	−	0.283973i
$11$	−0.974345	+	0.838491i	−0.293776	+	0.252815i	−0.786810	−	0.617195i	$-0.788269\pi$
$11$	−0.974345	+	0.838491i	−0.293776	+	0.252815i	0.493034	+	0.870010i	$0.335888\pi$
$12$	−2.86231	−	0.215298i	−0.826278	−	0.0621512i
$13$	−2.06180	+	3.02410i	−0.571839	+	0.838734i	−0.997820	−	0.0659980i	$-0.978977\pi$
$13$	−2.06180	+	3.02410i	−0.571839	+	0.838734i	0.425980	+	0.904732i	$0.359929\pi$
$14$	−1.89883	+	0.828450i	−0.507483	+	0.221412i
$15$	2.59286	−	1.76673i	0.669473	−	0.456167i
$16$	−0.154007	+	2.05508i	−0.0385017	+	0.513770i
$17$	−2.82385	−	2.82385i	−0.684884	−	0.684884i	0.276213	−	0.961096i	$-0.410920\pi$
$17$	−2.82385	−	2.82385i	−0.684884	−	0.684884i	−0.961096	+	0.276213i	$0.910920\pi$
$18$	1.55242	+	0.821577i	0.365908	+	0.193647i
$19$	−5.81575	−	3.65428i	−1.33422	−	0.838349i	−0.339468	−	0.940618i	$-0.610247\pi$
$19$	−5.81575	−	3.65428i	−1.33422	−	0.838349i	−0.994757	+	0.102269i	$0.967390\pi$
$20$	−1.69109	−	2.48037i	−0.378139	−	0.554629i
$21$	−6.12885	−	0.00169842i	−1.33742	−	0.000370625i
$22$	−0.221833	−	0.719165i	−0.0472950	−	0.153326i
$23$	8.33810	+	3.27246i	1.73861	+	0.682355i	0.999966	+	0.00826369i	$0.00263044\pi$
$23$	8.33810	+	3.27246i	1.73861	+	0.682355i	0.738648	+	0.674092i	$0.235465\pi$
$24$	1.73385	−	3.27841i	0.353921	−	0.669202i
$25$	−1.64224	−	0.506563i	−0.328447	−	0.101313i
$26$	−1.14008	−	1.81442i	−0.223587	−	0.355837i
$27$	3.23637	+	4.06521i	0.622840	+	0.782350i
$28$			5.86408i			1.10821i
$29$	−1.28158	+	5.23045i	−0.237983	+	0.971269i
$29$	−1.28158	+	5.23045i	−0.237983	+	0.971269i
$30$	0.341009	+	1.80501i	0.0622595	+	0.329549i
$31$	3.72396	−	2.74841i	0.668843	−	0.493629i	−0.205676	−	0.978620i	$-0.565939\pi$
$31$	3.72396	−	2.74841i	0.668843	−	0.493629i	0.874519	+	0.484992i	$0.161177\pi$
$32$	−4.85287	−	2.56482i	−0.857874	−	0.453400i
$33$	0.249901	−	2.21242i	0.0435021	−	0.385133i
$34$	2.17647	−	0.854200i	0.373261	−	0.146494i
$35$	−3.99648	−	5.01143i	−0.675529	−	0.847086i
$36$	3.88873	−	3.09763i	0.648121	−	0.516272i
$37$	2.62155	+	7.49197i	0.430981	+	1.23167i	0.930796	+	0.365540i	$0.119116\pi$
$37$	2.62155	+	7.49197i	0.430981	+	1.23167i	−0.499815	+	0.866132i	$0.666599\pi$
$38$	3.32257	−	2.26529i	0.538992	−	0.367479i
$39$	−0.943108	−	6.26890i	−0.151018	−	1.00383i
$40$	3.81109	−	0.721097i	0.602586	−	0.114015i
$41$	6.95493	+	1.86357i	1.08618	+	0.291040i	0.757124	−	0.653271i	$-0.226604\pi$
$41$	6.95493	+	1.86357i	1.08618	+	0.291040i	0.329053	+	0.944311i	$0.393270\pi$
$42$	1.43583	−	3.28847i	0.221553	−	0.507421i
$43$	1.32201	−	1.79126i	0.201605	−	0.273165i	−0.692118	−	0.721784i	$-0.743322\pi$
$43$	1.32201	−	1.79126i	0.201605	−	0.273165i	0.893723	+	0.448620i	$0.148084\pi$
$44$	−2.11691	−	0.238518i	−0.319136	−	0.0359579i
$45$	−1.21220	+	5.29748i	−0.180705	+	0.789701i
$46$	−3.70823	+	3.70823i	−0.546748	+	0.546748i
$47$	1.08573	+	1.26165i	0.158371	+	0.184030i	0.831551	−	0.555448i	$-0.187453\pi$
$47$	1.08573	+	1.26165i	0.158371	+	0.184030i	−0.673181	+	0.739478i	$0.735072\pi$
$48$	−2.22476	−	2.79135i	−0.321117	−	0.402897i
$49$	0.412579	+	5.50549i	0.0589399	+	0.786499i
$50$	0.656321	−	0.762658i	0.0928177	−	0.107856i
$51$	6.91208	+	0.260550i	0.967884	+	0.0364843i
$52$	−5.99783	+	0.904027i	−0.831749	+	0.125366i
$53$	6.55714	+	5.22915i	0.900693	+	0.718278i	0.960011	−	0.279961i	$-0.0903214\pi$
$53$	6.55714	+	5.22915i	0.900693	+	0.718278i	−0.0593187	+	0.998239i	$0.518893\pi$
$54$	−2.93919	+	0.784935i	−0.399973	+	0.106816i
$55$	1.97166	−	1.23888i	0.265859	−	0.167050i
$56$	−6.94443	−	3.02983i	−0.927989	−	0.404877i
$57$	11.6899	−	2.20848i	1.54836	−	0.292521i
$58$	−2.50671	−	1.91230i	−0.329148	−	0.251097i
$59$	−7.47986	+	4.31850i	−0.973795	+	0.562221i	−0.900391	−	0.435082i	$-0.856719\pi$
$59$	−7.47986	+	4.31850i	−0.973795	+	0.562221i	−0.0734037	+	0.997302i	$0.523386\pi$
$60$	5.06894	+	1.15843i	0.654397	+	0.149553i
$61$	13.5329	−	0.506365i	1.73271	−	0.0648334i	0.847720	−	0.530445i	$-0.177975\pi$
$61$	13.5329	−	0.506365i	1.73271	−	0.0648334i	0.884989	+	0.465611i	$0.154165\pi$
$62$	0.602979	+	2.64182i	0.0765784	+	0.335512i
$63$	7.78570	−	7.21604i	0.980905	−	0.909136i
$64$	−0.709949	+	0.566166i	−0.0887436	+	0.0707707i
$65$	4.50962	−	4.86022i	0.559350	−	0.602836i
$66$	1.12872	+	0.652084i	0.138936	+	0.0802660i
$67$	10.9354	−	0.819497i	1.33597	−	0.100117i	0.612501	−	0.790470i	$-0.290164\pi$
$67$	10.9354	−	0.819497i	1.33597	−	0.100117i	0.723473	+	0.690352i	$0.242544\pi$
$68$	0.247461	−	6.61353i	0.0300091	−	0.802009i
$69$	−14.4436	+	5.66407i	−1.73880	+	0.681874i
$70$	3.62491	−	0.971292i	0.433260	−	0.116092i
$71$	−3.89744	+	1.87691i	−0.462541	+	0.222748i	−0.650616	−	0.759407i	$-0.725489\pi$
$71$	−3.89744	+	1.87691i	−0.462541	+	0.222748i	0.188075	+	0.982155i	$0.439775\pi$
$72$	1.65911	+	6.20563i	0.195528	+	0.731341i
$73$	0.963648	−	8.55261i	0.112786	−	1.00101i	−0.802071	−	0.597229i	$-0.796268\pi$
$73$	0.963648	−	8.55261i	0.112786	−	1.00101i	0.914857	−	0.403778i	$-0.132303\pi$
$74$	−4.63411	−	0.347279i	−0.538705	−	0.0403703i
$75$	2.68226	−	1.29079i	0.309720	−	0.149048i
$76$	−2.11617	−	11.1843i	−0.242742	−	1.28292i
$77$	−4.54542	−	0.170078i	−0.517999	−	0.0193821i
$78$	3.58482	+	0.961615i	0.405901	+	0.108882i
$79$	0.335835	−	1.77493i	0.0377844	−	0.199695i	−0.958588	−	0.284797i	$-0.908074\pi$
$79$	0.335835	−	1.77493i	0.0377844	−	0.199695i	0.996372	+	0.0851015i	$0.0271214\pi$
$80$	0.830703	−	3.63955i	0.0928754	−	0.406914i
$81$	−8.89799	−	1.35124i	−0.988665	−	0.150138i
$82$	−2.62835	+	3.29585i	−0.290253	+	0.363965i
$83$	−0.302531	+	0.980782i	−0.0332071	+	0.107655i	−0.970659	−	0.240460i	$-0.922702\pi$
$83$	−0.302531	+	0.980782i	−0.0332071	+	0.107655i	0.937452	+	0.348115i	$0.113178\pi$
$84$	−6.90637	−	7.44743i	−0.753546	−	0.812581i
$85$	4.29577	+	5.82057i	0.465942	+	0.631329i
$86$	0.651711	+	1.12880i	0.0702758	+	0.121721i
$87$	−4.53250	−	8.15208i	−0.485935	−	0.873995i
$88$	1.37622	−	2.38367i	0.146705	−	0.254101i
$89$	−2.15138	+	0.242402i	−0.228046	+	0.0256946i	−0.225248	−	0.974301i	$-0.572319\pi$
$89$	−2.15138	+	0.242402i	−0.228046	+	0.0256946i	−0.00279797	+	0.999996i	$0.500891\pi$
$90$	−2.55893	−	1.89077i	−0.269734	−	0.199304i
$91$	−12.6265	+	2.88191i	−1.32361	+	0.302106i
$92$	5.42320	+	13.8181i	0.565408	+	1.44064i
$93$	−1.49255	+	7.87637i	−0.154770	+	0.816741i
$94$	−0.931222	+	0.287244i	−0.0960482	+	0.0296269i
$95$	9.43077	+	8.11583i	0.967576	+	0.832667i
$96$	9.18388	−	2.45809i	0.937326	−	0.250877i
$97$	−0.817727	−	1.54721i	−0.0830276	−	0.157096i	0.839105	−	0.543969i	$-0.183079\pi$
$97$	−0.817727	−	1.54721i	−0.0830276	−	0.157096i	−0.922133	+	0.386873i	$0.873555\pi$
$98$	−3.05095	−	1.06757i	−0.308193	−	0.107841i
$99$	2.28828	+	3.10411i	0.229981	+	0.311975i
$100$	−1.23574	−	2.56604i	−0.123574	−	0.256604i
$101$	1.27105	+	0.938078i	0.126474	+	0.0933422i	0.655220	−	0.755438i	$-0.272576\pi$
$101$	1.27105	+	0.938078i	0.126474	+	0.0933422i	−0.528746	+	0.848780i	$0.677338\pi$
$102$	−1.75811	+	3.64816i	−0.174078	+	0.361221i
$103$	8.55107	+	5.83002i	0.842562	+	0.574449i	0.905875	−	0.423545i	$-0.139214\pi$
$103$	8.55107	+	5.83002i	0.842562	+	0.574449i	−0.0633131	+	0.997994i	$0.520167\pi$
$104$	2.02835	−	7.56992i	0.198896	−	0.742291i
$105$	10.9777	+	1.65774i	1.07132	+	0.161779i
$106$	−4.34126	+	2.29442i	−0.421660	+	0.222854i
$107$	1.56083	−	3.24109i	0.150891	−	0.313328i	−0.811798	−	0.583938i	$-0.801511\pi$
$107$	1.56083	−	3.24109i	0.150891	−	0.313328i	0.962689	+	0.270610i	$0.0872254\pi$
$108$	−1.29051	+	8.51394i	−0.124179	+	0.819254i
$109$	−15.2545	−	3.48174i	−1.46111	−	0.333490i	−0.583208	−	0.812323i	$-0.698203\pi$
$109$	−15.2545	−	3.48174i	−1.46111	−	0.333490i	−0.877906	+	0.478833i	$0.841060\pi$
$110$	0.203191	+	1.34808i	0.0193735	+	0.128535i
$111$	−12.1530	−	6.42736i	−1.15351	−	0.610058i
$112$	−5.34561	+	4.96000i	−0.505113	+	0.468676i
$113$	−4.36660	+	8.26201i	−0.410775	+	0.777225i	−0.999516	−	0.0310970i	$-0.990100\pi$
$113$	−4.36660	+	8.26201i	−0.410775	+	0.777225i	0.588741	+	0.808322i	$0.299624\pi$
$114$	−1.55177	+	6.79007i	−0.145337	+	0.635949i
$115$	−14.0520	−	8.11291i	−1.31035	−	0.756533i
$116$	−7.79870	+	4.33885i	−0.724091	+	0.402852i
$117$	8.58090	+	6.85082i	0.793305	+	0.633359i
$118$	−0.566172	−	5.02491i	−0.0521203	−	0.462581i
$119$	−0.528377	−	14.1212i	−0.0484362	−	1.29449i
$120$	−3.99085	+	5.40428i	−0.364313	+	0.493341i
$121$	−1.39319	+	9.24318i	−0.126653	+	0.840289i
$122$	−2.89666	+	7.38057i	−0.262251	+	0.668206i
$123$	−11.0276	+	5.82436i	−0.994328	+	0.525165i
$124$	7.53650	+	1.42598i	0.676797	+	0.128057i
$125$	10.9652	+	5.28058i	0.980761	+	0.472310i
$126$	2.04945	+	5.86742i	0.182579	+	0.522711i
$127$	−0.619721	+	1.77106i	−0.0549913	+	0.157156i	−0.968103	−	0.250554i	$-0.919387\pi$
$127$	−0.619721	+	1.77106i	−0.0549913	+	0.157156i	0.913111	+	0.407711i	$0.133673\pi$
$128$	−2.97889	−	11.1174i	−0.263299	−	0.982646i
$129$	0.430677	+	3.83190i	0.0379190	+	0.337380i
$130$	1.55228	+	3.55785i	0.136144	+	0.312044i
$131$	−3.80938	−	8.73120i	−0.332828	−	0.762849i	−0.999842	−	0.0178036i	$-0.994333\pi$
$131$	−3.80938	−	8.73120i	−0.332828	−	0.762849i	0.667014	−	0.745045i	$-0.267572\pi$
$132$	2.96940	−	2.19025i	0.258453	−	0.190637i
$133$	−6.29040	−	23.4761i	−0.545447	−	2.03564i
$134$	−2.12050	+	6.06003i	−0.183183	+	0.523507i
$135$	−4.69955	−	8.15551i	−0.404473	−	0.701915i
$136$	7.70411	+	3.71010i	0.660622	+	0.318139i
$137$	1.02757	+	0.194426i	0.0877910	+	0.0166110i	0.229622	−	0.973280i	$-0.426251\pi$
$137$	1.02757	+	0.194426i	0.0877910	+	0.0166110i	−0.141830	+	0.989891i	$0.545299\pi$
$138$	0.342149	−	9.07682i	0.0291257	−	0.772670i
$139$	−1.26551	+	3.22446i	−0.107339	+	0.273495i	−0.974444	−	0.224630i	$-0.927883\pi$
$139$	−1.26551	+	3.22446i	−0.107339	+	0.273495i	0.867105	+	0.498125i	$0.165978\pi$
$140$	1.58321	−	10.5039i	0.133806	−	0.887744i
$141$	−2.86478	−	0.323588i	−0.241258	−	0.0272510i
$142$	−0.0946987	−	2.53088i	−0.00794694	−	0.212386i
$143$	−0.526781	−	4.67531i	−0.0440517	−	0.390969i
$144$	6.11296	+	0.924845i	0.509413	+	0.0770704i
$145$	3.70775	−	9.02295i	0.307912	−	0.749315i
$146$	4.36389	+	2.51949i	0.361158	+	0.208515i
$147$	−7.00803	−	6.50611i	−0.578012	−	0.536615i
$148$	−6.14647	+	11.6297i	−0.505237	+	0.955954i
$149$	9.95683	−	9.23859i	0.815696	−	0.756855i	−0.157332	−	0.987546i	$-0.550289\pi$
$149$	9.95683	−	9.23859i	0.815696	−	0.756855i	0.973027	+	0.230691i	$0.0740987\pi$
$150$	0.0646813	+	1.74156i	0.00528120	+	0.142198i
$151$	−2.55954	−	16.9814i	−0.208292	−	1.38193i	−0.811503	−	0.584348i	$-0.801350\pi$
$151$	−2.55954	−	16.9814i	−0.208292	−	1.38193i	0.603211	−	0.797582i	$-0.293888\pi$
$152$	14.3381	+	3.27259i	1.16298	+	0.265442i
$153$	−9.08526	+	7.80974i	−0.734500	+	0.631380i
$154$	1.15546	−	2.39935i	0.0931099	−	0.193345i
$155$	−7.41251	+	3.91763i	−0.595387	+	0.314671i
$156$	6.55259	−	8.21201i	0.524627	−	0.657487i
$157$	−1.11923	+	4.17702i	−0.0893242	+	0.333362i	−0.996098	−	0.0882552i	$-0.971871\pi$
$157$	−1.11923	+	4.17702i	−0.0893242	+	0.333362i	0.906774	+	0.421618i	$0.138538\pi$
$158$	0.873837	+	0.595772i	0.0695187	+	0.0473971i
$159$	−14.4862	+	1.08156i	−1.14883	+	0.0857729i
$160$	8.00016	+	5.90439i	0.632469	+	0.466783i
$161$	13.7521	+	28.5564i	1.08381	+	2.25056i
$162$	2.80835	−	4.45848i	0.220644	−	0.350291i
$163$	−3.67650	−	1.28646i	−0.287966	−	0.100764i	0.182431	−	0.983219i	$-0.441603\pi$
$163$	−3.67650	−	1.28646i	−0.287966	−	0.100764i	−0.470397	+	0.882455i	$0.655889\pi$
$164$	5.57567	+	10.5497i	0.435386	+	0.823791i
$165$	−1.04495	+	3.89549i	−0.0813493	+	0.303264i
$166$	−0.455477	−	0.391970i	−0.0353519	−	0.0304228i
$167$	−9.41264	+	2.90341i	−0.728372	+	0.224673i	−0.636695	−	0.771116i	$-0.719699\pi$
$167$	−9.41264	+	2.90341i	−0.728372	+	0.224673i	−0.0916769	+	0.995789i	$0.529223\pi$
$168$	12.3879	−	4.33084i	0.955743	−	0.334132i
$169$	−0.144743	−	0.368799i	−0.0111341	−	0.0283692i
$170$	−4.12918	+	0.942459i	−0.316694	+	0.0722833i
$171$	−12.2452	+	16.5724i	−0.936414	+	1.26732i
$172$	3.66625	−	0.413087i	0.279549	−	0.0314976i
$173$	−3.25834	+	5.64362i	−0.247727	+	0.429076i	−0.962895	−	0.269877i	$-0.913017\pi$
$173$	−3.25834	+	5.64362i	−0.247727	+	0.429076i	0.715168	+	0.698953i	$0.246350\pi$
$174$	5.43574	−	0.523625i	0.412083	−	0.0396959i
$175$	−3.04061	−	5.26648i	−0.229848	−	0.398109i
$176$	−1.57311	−	2.13149i	−0.118578	−	0.160667i
$177$	4.41342	−	14.2939i	0.331733	−	1.07439i
$178$	0.373614	−	1.21123i	0.0280035	−	0.0907853i
$179$	15.0898	−	18.9220i	1.12786	−	1.41429i	0.230460	−	0.973082i	$-0.425977\pi$
$179$	15.0898	−	18.9220i	1.12786	−	1.41429i	0.897403	−	0.441213i	$-0.145452\pi$
$180$	−7.80194	+	4.49869i	−0.581522	+	0.335312i
$181$	−2.36553	+	10.3641i	−0.175828	+	0.770355i	0.807699	+	0.589595i	$0.200713\pi$
$181$	−2.36553	+	10.3641i	−0.175828	+	0.770355i	−0.983527	+	0.180759i	$0.942144\pi$
$182$	1.40968	−	7.45034i	0.104492	−	0.552256i
$183$	−16.5905	+	16.5813i	−1.22641	+	1.22573i
$184$	−19.1659	−	0.717137i	−1.41293	−	0.0528680i
$185$	−2.67310	−	14.1277i	−0.196530	−	1.03869i
$186$	−3.87718	−	2.64499i	−0.284288	−	0.193940i
$187$	5.11917	+	0.383629i	0.374351	+	0.0280537i
$188$	−0.308849	+	2.74111i	−0.0225251	+	0.199916i
$189$	−1.38927	+	18.3340i	−0.101055	+	1.33360i
$190$	−6.56310	+	3.16062i	−0.476137	+	0.229296i
$191$	6.01366	−	1.61136i	0.435133	−	0.116594i	−0.0346015	−	0.999401i	$-0.511016\pi$
$191$	6.01366	−	1.61136i	0.435133	−	0.116594i	0.469735	+	0.882808i	$0.344350\pi$
$192$	0.234845	−	1.55517i	0.0169485	−	0.112235i
$193$	−0.614270	+	16.4167i	−0.0442161	+	1.18170i	0.783806	+	0.621006i	$0.213276\pi$
$193$	−0.614270	+	16.4167i	−0.0442161	+	1.18170i	−0.828022	+	0.560695i	$0.810534\pi$
$194$	1.02172	−	0.0765671i	0.0733550	−	0.00549720i
$195$	−0.00318234	+	11.4837i	−0.000227892	+	0.822364i
$196$	−6.22318	+	6.70700i	−0.444513	+	0.479071i
$197$	8.02113	−	6.39664i	0.571482	−	0.455741i	−0.294616	−	0.955616i	$-0.595192\pi$
$197$	8.02113	−	6.39664i	0.571482	−	0.455741i	0.866098	+	0.499874i	$0.166620\pi$
$198$	−2.20147	+	0.501188i	−0.156452	+	0.0356179i
$199$	−4.26586	−	18.6900i	−0.302399	−	1.32490i	−0.866494	−	0.499187i	$-0.833632\pi$
$199$	−4.26586	−	18.6900i	−0.302399	−	1.32490i	0.564096	−	0.825709i	$-0.309225\pi$
$200$	3.67726	−	0.137594i	0.260022	−	0.00972933i
$201$	−12.9229	+	13.9199i	−0.911513	+	0.981832i
$202$	−0.800976	+	0.462444i	−0.0563565	+	0.0325374i
$203$	−15.9128	+	10.4828i	−1.11686	+	0.735746i
$204$	7.47476	+	8.69070i	0.523338	+	0.608471i
$205$	−11.9548	−	5.21581i	−0.834957	−	0.364288i
$206$	−5.13053	+	3.22372i	−0.357461	+	0.224608i
$207$	11.6727	−	24.2042i	0.811307	−	1.68231i
$208$	−5.89723	−	4.70288i	−0.408899	−	0.326086i
$209$	8.73062	−	1.31593i	0.603910	−	0.0910248i
$210$	−3.45974	+	5.50276i	−0.238745	+	0.379727i
$211$	8.93001	−	10.3769i	0.614767	−	0.714372i	−0.361152	−	0.932507i	$-0.617616\pi$
$211$	8.93001	−	10.3769i	0.614767	−	0.714372i	0.975919	+	0.218135i	$0.0699973\pi$
$212$	1.03867	+	13.8601i	0.0713363	+	0.951916i
$213$	2.73927	−	6.97387i	0.187692	−	0.477842i
$214$	1.37381	+	1.59639i	0.0939114	+	0.109127i
$215$	−2.85164	+	2.85164i	−0.194480	+	0.194480i
$216$	−9.41572	−	5.92721i	−0.640658	−	0.403296i
$217$	16.2744	+	1.83369i	1.10478	+	0.124479i
$218$	5.43982	−	7.37070i	0.368431	−	0.499207i
$219$	8.84893	+	11.9968i	0.597955	+	0.810670i
$220$	3.72748	+	0.998775i	0.251306	+	0.0673374i
$221$	14.3618	−	2.71740i	0.966079	−	0.182792i
$222$	6.29437	−	5.01674i	0.422451	−	0.336702i
$223$	17.7860	−	12.1263i	1.19104	−	0.812035i	0.205032	−	0.978755i	$-0.434270\pi$
$223$	17.7860	−	12.1263i	1.19104	−	0.812035i	0.986004	+	0.166721i	$0.0533178\pi$
$224$	−6.41489	−	18.3327i	−0.428613	−	1.22490i
$225$	−1.88627	+	4.79832i	−0.125751	+	0.319888i
$226$	−3.41123	−	4.27755i	−0.226912	−	0.284538i
$227$	25.1369	−	9.86550i	1.66839	−	0.654796i	0.672072	−	0.740486i	$-0.265405\pi$
$227$	25.1369	−	9.86550i	1.66839	−	0.654796i	0.996322	+	0.0856896i	$0.0273093\pi$
$228$	15.8597	+	11.7118i	1.05034	+	0.775633i
$229$	−14.6405	−	7.73771i	−0.967469	−	0.511322i	−0.0926110	−	0.995702i	$-0.529521\pi$
$229$	−14.6405	−	7.73771i	−0.967469	−	0.511322i	−0.874858	+	0.484380i	$0.839045\pi$
$230$	7.64347	−	5.64114i	0.503995	−	0.371965i
$231$	5.97304	−	5.13733i	0.392997	−	0.338012i
$232$	−1.10882	−	11.4773i	−0.0727973	−	0.753519i
$233$		−	18.9493i		−	1.24141i	−0.784044	−	0.620705i	$-0.786846\pi$
$233$		−	18.9493i		−	1.24141i	0.784044	−	0.620705i	$-0.213154\pi$
$234$	−5.68529	+	3.00074i	−0.371659	+	0.196164i
$235$	−1.60418	−	2.55303i	−0.104645	−	0.166542i
$236$	−13.6775	−	4.21896i	−0.890332	−	0.274631i
$237$	1.66390	+	2.64971i	0.108082	+	0.172117i
$238$	7.70141	+	3.02258i	0.499208	+	0.195925i
$239$	2.90929	+	9.43170i	0.188187	+	0.610086i	0.999669	+	0.0257096i	$0.00818453\pi$
$239$	2.90929	+	9.43170i	0.188187	+	0.610086i	−0.811483	+	0.584376i	$0.801339\pi$
$240$	3.23145	+	5.60061i	0.208589	+	0.361518i
$241$	1.80931	+	2.65377i	0.116548	+	0.170944i	0.880080	−	0.474826i	$-0.157489\pi$
$241$	1.80931	+	2.65377i	0.116548	+	0.170944i	−0.763532	+	0.645770i	$0.776537\pi$
$242$	−4.63390	−	2.91167i	−0.297878	−	0.187169i
$243$	12.8919	−	8.76344i	0.827019	−	0.562175i
$244$	15.8694	+	15.8694i	1.01593	+	1.01593i
$245$	0.747374	−	9.97301i	0.0477480	−	0.637152i
$246$	−0.543627	−	7.28128i	−0.0346604	−	0.464237i
$247$	23.0418	−	10.0530i	1.46611	−	0.639659i
$248$	−5.58262	+	8.18820i	−0.354497	+	0.519951i
$249$	−0.770890	−	1.60191i	−0.0488532	−	0.101517i
$250$	−5.40090	+	4.64785i	−0.341583	+	0.293956i
$251$	1.44426	−	2.29853i	0.0911610	−	0.145082i	−0.798031	−	0.602617i	$-0.794125\pi$
$251$	1.44426	−	2.29853i	0.0911610	−	0.145082i	0.889192	+	0.457535i	$0.151268\pi$
$252$	17.5423	+	1.32439i	1.10506	+	0.0834288i
$253$	−10.8681	+	3.80292i	−0.683272	+	0.239087i
$254$	−0.805295	−	0.747204i	−0.0505287	−	0.0468838i
$255$	−12.3108	−	2.33286i	−0.770932	−	0.146090i
$256$	4.86741	+	0.733644i	0.304213	+	0.0458527i
$257$	0.730713	+	0.787521i	0.0455806	+	0.0491242i	0.755431	−	0.655229i	$-0.227428\pi$
$257$	0.730713	+	0.787521i	0.0455806	+	0.0491242i	−0.709850	+	0.704353i	$0.751237\pi$
$258$	−2.15711	−	0.666035i	−0.134296	−	0.0414655i
$259$	−11.2315	+	25.7429i	−0.697893	+	1.59959i
$260$	10.9876			0.681421
$261$	15.3574	+	5.01511i	0.950597	+	0.310427i
$262$	5.57721			0.344561
$263$	−7.21655	+	16.5405i	−0.444992	+	1.01993i	0.539096	+	0.842245i	$0.318766\pi$
$263$	−7.21655	+	16.5405i	−0.444992	+	1.01993i	−0.984087	+	0.177687i	$0.943139\pi$
$264$	1.05955	+	4.64812i	0.0652106	+	0.286072i
$265$	−10.3336	−	11.1370i	−0.634787	−	0.684138i
$266$	14.0705	+	2.12078i	0.862717	+	0.130034i
$267$	2.44679	−	2.84162i	0.149741	−	0.173905i
$268$	13.3219	+	12.3610i	0.813767	+	0.755066i
$269$	4.38546	−	1.53454i	0.267386	−	0.0935625i	−0.193256	−	0.981148i	$-0.561905\pi$
$269$	4.38546	−	1.53454i	0.267386	−	0.0935625i	0.460642	+	0.887586i	$0.347619\pi$
$270$	5.47669	−	0.612465i	0.333301	−	0.0372734i
$271$	1.36275	−	2.16881i	0.0827813	−	0.131746i	−0.802767	−	0.596292i	$-0.796640\pi$
$271$	1.36275	−	2.16881i	0.0827813	−	0.131746i	0.885549	+	0.464547i	$0.153783\pi$
$272$	6.23812	−	5.36833i	0.378241	−	0.325503i
$273$	12.6416	−	18.5307i	0.765103	−	1.12153i
$274$	−0.344912	+	0.505894i	−0.0208369	+	0.0305621i
$275$	2.02485	−	0.883434i	0.122103	−	0.0532731i
$276$	−23.1617	−	11.1620i	−1.39417	−	0.671872i
$277$	−0.222034	+	2.96284i	−0.0133407	+	0.178020i	0.986553	+	0.163442i	$0.0522596\pi$
$277$	−0.222034	+	2.96284i	−0.0133407	+	0.178020i	−0.999894	+	0.0145781i	$0.995359\pi$
$278$	−1.43402	−	1.43402i	−0.0860071	−	0.0860071i
$279$	−7.38078	−	11.7609i	−0.441876	−	0.704107i
$280$	11.6211	+	7.30202i	0.694494	+	0.436379i
$281$	2.90516	+	4.26109i	0.173308	+	0.254195i	0.903058	−	0.429518i	$-0.141316\pi$
$281$	2.90516	+	4.26109i	0.173308	+	0.254195i	−0.729751	+	0.683713i	$0.760364\pi$
$282$	0.844361	−	1.46154i	0.0502810	−	0.0870335i
$283$	−4.73199	−	15.3407i	−0.281287	−	0.911911i	−0.980420	−	0.196919i	$-0.936906\pi$
$283$	−4.73199	−	15.3407i	−0.281287	−	0.911911i	0.699132	−	0.714992i	$-0.253570\pi$
$284$	−6.67332	−	2.61908i	−0.395988	−	0.155414i
$285$	−21.5355	+	0.799826i	−1.27565	+	0.0473776i
$286$	2.63220	+	0.811927i	0.155645	+	0.0480102i
$287$	13.5552	+	21.5729i	0.800136	+	1.27341i
$288$	−8.76863	+	13.9380i	−0.516696	+	0.821307i
$289$		−	1.05178i		−	0.0618692i
$290$	3.97382	+	4.10215i	0.233351	+	0.240886i
$291$	2.86074	+	1.00191i	0.167700	+	0.0587328i
$292$	11.4762	−	8.46982i	0.671594	−	0.495659i
$293$	−18.5869	−	9.82349i	−1.08586	−	0.573894i	−0.174147	−	0.984720i	$-0.555717\pi$
$293$	−18.5869	−	9.82349i	−1.08586	−	0.573894i	−0.911714	+	0.410826i	$0.865241\pi$
$294$	5.13207	−	2.23740i	0.299308	−	0.130488i
$295$	14.5641	−	5.71599i	0.847955	−	0.332798i
$296$	−10.5965	−	13.2876i	−0.615911	−	0.772328i
$297$	−6.56198	−	1.24725i	−0.380765	−	0.0723725i
$298$	2.62647	+	7.50602i	0.152147	+	0.434812i
$299$	−27.0877	+	18.4681i	−1.56652	+	1.06804i
$300$	4.59153	+	1.80351i	0.265092	+	0.104126i
$301$	7.74034	−	1.46455i	0.446146	−	0.0844153i
$302$	9.71183	+	2.60228i	0.558853	+	0.149744i
$303$	−2.71906	+	0.305601i	−0.156206	+	0.0175563i
$304$	8.40549	−	11.3890i	0.482088	−	0.653206i
$305$	−24.3773	−	2.74666i	−1.39584	−	0.157273i
$306$	−2.06378	−	6.70379i	−0.117978	−	0.383230i
$307$	−1.65888	+	1.65888i	−0.0946772	+	0.0946772i	−0.752859	−	0.658182i	$-0.771326\pi$
$307$	−1.65888	+	1.65888i	−0.0946772	+	0.0946772i	0.658182	+	0.752859i	$0.271326\pi$
$308$	−4.91698	−	5.71363i	−0.280171	−	0.325564i
$309$	−17.7262	+	2.66677i	−1.00841	+	0.151707i
$310$	−0.366824	−	4.89492i	−0.0208342	−	0.278013i
$311$	−4.21991	+	4.90363i	−0.239289	+	0.278059i	−0.864757	−	0.502191i	$-0.832527\pi$
$311$	−4.21991	+	4.90363i	−0.239289	+	0.278059i	0.625467	+	0.780250i	$0.284908\pi$
$312$	6.33938	+	12.0027i	0.358897	+	0.679521i
$313$	−19.8385	+	2.99017i	−1.12134	+	0.169014i	−0.683437	−	0.730009i	$-0.739516\pi$
$313$	−19.8385	+	2.99017i	−1.12134	+	0.169014i	−0.437900	+	0.899024i	$0.644278\pi$
$314$	−1.97943	−	1.57855i	−0.111706	−	0.0890825i
$315$	−15.8942	+	10.8236i	−0.895538	+	0.609841i
$316$	2.53480	−	1.59272i	0.142593	−	0.0895974i
$317$	−10.4430	−	4.55625i	−0.586539	−	0.255904i	0.0855997	−	0.996330i	$-0.472719\pi$
$317$	−10.4430	−	4.55625i	−0.586539	−	0.255904i	−0.672139	+	0.740425i	$0.734624\pi$
$318$	2.81120	−	8.02682i	0.157644	−	0.450122i
$319$	−3.13699	−	6.17085i	−0.175638	−	0.345501i
$320$	1.42454	−	0.822459i	0.0796343	−	0.0459769i
$321$	1.83490	+	5.95447i	0.102414	+	0.332346i
$322$	−18.5437	+	0.693855i	−1.03340	+	0.0386670i
$323$	6.10367	+	26.7419i	0.339617	+	1.48796i
$324$	−8.38826	−	12.3327i	−0.466015	−	0.685148i
$325$	4.91785	−	3.92186i	0.272793	−	0.217546i
$326$	1.55110	−	1.67169i	0.0859076	−	0.0925864i
$327$	23.4739	−	13.5440i	1.29811	−	0.748985i
$328$	−15.3741	+	1.15213i	−0.848892	+	0.0636157i
$329$	−0.220228	+	5.88571i	−0.0121415	+	0.324490i
$330$	−1.84575	−	1.47277i	−0.101605	−	0.0810735i
$331$	2.13003	−	0.570739i	0.117077	−	0.0313706i	−0.199805	−	0.979836i	$-0.564031\pi$
$331$	2.13003	−	0.570739i	0.117077	−	0.0313706i	0.316882	+	0.948465i	$0.397364\pi$
$332$	−1.53250	+	0.738012i	−0.0841067	+	0.0405037i
$333$	23.0042	−	6.15030i	1.26062	−	0.337034i
$334$	0.645703	−	5.73077i	0.0353313	−	0.313574i
$335$	−19.8092	−	1.48449i	−1.08229	−	0.0811064i
$336$	0.947375	−	12.5950i	0.0516835	−	0.687114i
$337$	6.29336	+	33.2612i	0.342821	+	1.81185i	0.551849	+	0.833944i	$0.313923\pi$
$337$	6.29336	+	33.2612i	0.342821	+	1.81185i	−0.209027	+	0.977910i	$0.567030\pi$
$338$	0.231793	+	0.00867309i	0.0126079	+	0.000471754i
$339$	−4.18489	−	15.6356i	−0.227292	−	0.849207i
$340$	−2.22882	+	11.7796i	−0.120875	+	0.638837i
$341$	−1.32390	+	5.80041i	−0.0716935	+	0.314110i
$342$	−6.02619	−	10.4510i	−0.325859	−	0.565128i
$343$	3.26315	−	4.09186i	0.176193	−	0.220940i
$344$	−1.40507	+	4.55512i	−0.0757563	+	0.245596i
$345$	27.4010	−	6.24612i	1.47522	−	0.336280i
$346$	−2.26562	−	3.06981i	−0.121800	−	0.165034i
$347$	−1.41886	−	2.45753i	−0.0761683	−	0.131927i	0.825425	−	0.564511i	$-0.190935\pi$
$347$	−1.41886	−	2.45753i	−0.0761683	−	0.131927i	−0.901594	+	0.432584i	$0.857602\pi$
$348$	4.79438	−	14.6952i	0.257005	−	0.787748i
$349$	−13.2134	+	22.8862i	−0.707295	+	1.22507i	0.258562	+	0.965995i	$0.416751\pi$
$349$	−13.2134	+	22.8862i	−0.707295	+	1.22507i	−0.965857	+	0.259076i	$0.916582\pi$
$350$	3.53798	−	0.398635i	0.189113	−	0.0213079i
$351$	−18.9663	+	1.40547i	−1.01235	+	0.0750187i
$352$	6.87895	−	1.57007i	0.366649	−	0.0836852i
$353$	1.72127	+	4.38573i	0.0916142	+	0.233429i	0.969335	−	0.245743i	$-0.0790321\pi$
$353$	1.72127	+	4.38573i	0.0916142	+	0.233429i	−0.877721	+	0.479172i	$0.840937\pi$
$354$	6.63709	+	5.71488i	0.352757	+	0.303743i
$355$	7.48796	−	2.30973i	0.397420	−	0.122588i
$356$	−2.71951	−	2.34033i	−0.144134	−	0.124037i
$357$	17.3021	+	17.3117i	0.915726	+	0.916234i
$358$	6.62102	+	12.5276i	0.349932	+	0.662103i
$359$	−12.5299	−	4.38440i	−0.661303	−	0.231400i	−0.0213010	−	0.999773i	$-0.506781\pi$
$359$	−12.5299	−	4.38440i	−0.661303	−	0.231400i	−0.640002	+	0.768373i	$0.721067\pi$
$360$	−1.29642	−	11.5637i	−0.0683275	−	0.609459i
$361$	12.2254	+	25.3863i	0.643442	+	1.33612i
$362$	−5.00773	−	3.69588i	−0.263201	−	0.194251i
$363$	−9.11672	−	13.3797i	−0.478504	−	0.702254i
$364$	−17.7336	−	12.0905i	−0.929491	−	0.633716i
$365$	−4.03520	+	15.0596i	−0.211212	+	0.788253i
$366$	−5.01362	−	12.7849i	−0.262066	−	0.668279i
$367$	−18.6655	+	9.86501i	−0.974332	+	0.514950i	−0.877098	−	0.480312i	$-0.840523\pi$
$367$	−18.6655	+	9.86501i	−0.974332	+	0.514950i	−0.0972343	+	0.995262i	$0.531000\pi$
$368$	−8.00929	+	16.6315i	−0.417513	+	0.866975i
$369$	7.14560	−	20.3847i	0.371985	−	1.06118i
$370$	8.20702	+	1.87320i	0.426663	+	0.0973830i
$371$	4.42312	+	29.3455i	0.229637	+	1.52354i
$372$	−11.2509	+	7.06504i	−0.583330	+	0.366305i
$373$	−0.342406	+	0.317706i	−0.0177291	+	0.0164502i	−0.688988	−	0.724773i	$-0.741945\pi$
$373$	−0.342406	+	0.317706i	−0.0177291	+	0.0164502i	0.671258	+	0.741223i	$0.265754\pi$
$374$	−1.40439	+	2.65723i	−0.0726192	+	0.137402i
$375$	−20.1451	+	6.20783i	−1.04029	+	0.320571i
$376$	−3.08654	−	1.78201i	−0.159176	−	0.0919003i
$377$	−13.1750	−	14.6597i	−0.678549	−	0.755014i
$378$	−9.51312	−	5.03796i	−0.489302	−	0.259124i
$379$	1.42454	+	12.6431i	0.0731737	+	0.649435i	0.975747	+	0.218899i	$0.0702466\pi$
$379$	1.42454	+	12.6431i	0.0731737	+	0.649435i	−0.902574	+	0.430535i	$0.858325\pi$
$380$	0.770983	+	20.6049i	0.0395506	+	1.05701i
$381$	−1.29880	−	2.97913i	−0.0665396	−	0.152626i
$382$	−0.543262	+	3.60431i	−0.0277957	+	0.184413i
$383$	−4.00297	+	10.1994i	−0.204542	+	0.521165i	−0.995928	−	0.0901518i	$-0.971265\pi$
$383$	−4.00297	+	10.1994i	−0.204542	+	0.521165i	0.791386	+	0.611317i	$0.209360\pi$
$384$	16.8766	+	10.6108i	0.861231	+	0.541480i
$385$	8.09599	+	1.53184i	0.412610	+	0.0780700i
$386$	−8.66573	−	4.17319i	−0.441074	−	0.212410i
$387$	−5.05996	−	4.35933i	−0.257212	−	0.221597i
$388$	0.957864	−	2.73742i	0.0486282	−	0.138971i
$389$	−4.93448	−	18.4157i	−0.250188	−	0.933715i	−0.970704	−	0.240277i	$-0.922762\pi$
$389$	−4.93448	−	18.4157i	−0.250188	−	0.933715i	0.720516	−	0.693438i	$-0.243905\pi$
$390$	−6.16164	−	2.69033i	−0.312007	−	0.136230i
$391$	−14.3046	−	32.7864i	−0.723414	−	1.65808i
$392$	−4.72728	−	10.8350i	−0.238764	−	0.547252i
$393$	15.1211	+	6.60224i	0.762756	+	0.333039i
$394$	1.55462	+	5.80191i	0.0783205	+	0.292296i
$395$	−1.08076	+	3.08865i	−0.0543792	+	0.155407i
$396$	−1.19162	+	6.27883i	−0.0598813	+	0.315523i
$397$	−17.4974	−	8.42630i	−0.878169	−	0.422904i	−0.0602137	−	0.998186i	$-0.519178\pi$
$397$	−17.4974	−	8.42630i	−0.878169	−	0.422904i	−0.817955	+	0.575282i	$0.804892\pi$
$398$	11.0282	+	2.08664i	0.552791	+	0.104594i
$399$	35.6376	+	22.4064i	1.78411	+	1.12172i
$400$	1.29394	−	3.29691i	0.0646971	−	0.164846i
$401$	5.30567	−	35.2008i	0.264952	−	1.75784i	−0.320605	−	0.947213i	$-0.603886\pi$
$401$	5.30567	−	35.2008i	0.264952	−	1.75784i	0.585557	−	0.810631i	$-0.300876\pi$
$402$	−4.44410	−	10.1937i	−0.221652	−	0.508415i
$403$	0.633412	+	16.9283i	0.0315525	+	0.843258i
$404$	0.293120	+	2.60151i	0.0145833	+	0.129430i
$405$	15.5736	+	4.82272i	0.773856	+	0.239643i
$406$	−1.89967	−	10.9934i	−0.0942790	−	0.545595i
$407$	−8.83625	−	5.10161i	−0.437997	−	0.252878i
$408$	−14.1538	+	4.36159i	−0.700720	+	0.215931i
$409$	5.87118	−	11.1088i	0.290311	−	0.549296i	−0.695218	−	0.718798i	$-0.744692\pi$
$409$	5.87118	−	11.1088i	0.290311	−	0.549296i	0.985530	+	0.169503i	$0.0542162\pi$
$410$	5.59782	−	5.19402i	0.276457	−	0.256514i
$411$	−1.53400	+	0.963286i	−0.0756669	+	0.0475154i
$412$	2.55626	+	16.9597i	0.125938	+	0.835545i
$413$	−29.7957	−	6.80067i	−1.46615	−	0.334639i
$414$	10.2556	+	11.9306i	0.504036	+	0.586357i
$415$	0.806700	−	1.67513i	0.0395994	−	0.0822289i
$416$	17.7619	−	9.38743i	0.870848	−	0.460257i
$417$	−2.19038	−	5.58554i	−0.107263	−	0.273525i
$418$	−1.33790	+	4.99312i	−0.0654390	+	0.244222i
$419$	8.10443	+	5.52551i	0.395927	+	0.269939i	0.744876	−	0.667203i	$-0.232509\pi$
$419$	8.10443	+	5.52551i	0.395927	+	0.269939i	−0.348948	+	0.937142i	$0.613461\pi$
$420$	10.3602	+	15.2047i	0.505527	+	0.741914i
$421$	−3.24358	−	2.39387i	−0.158083	−	0.116670i	0.511907	−	0.859041i	$-0.328939\pi$
$421$	−3.24358	−	2.39387i	−0.158083	−	0.116670i	−0.669989	+	0.742371i	$0.733701\pi$
$422$	3.47769	+	7.22150i	0.169291	+	0.351537i
$423$	4.01941	−	2.96302i	0.195430	−	0.144067i
$424$	−16.9503	−	5.93115i	−0.823177	−	0.288042i
$425$	3.20697	+	6.06788i	0.155561	+	0.294335i
$426$	3.10099	+	3.10271i	0.150243	+	0.150327i
$427$	36.3217	+	31.2573i	1.75773	+	1.51265i
$428$	5.69674	−	1.75721i	0.275362	−	0.0849380i
$429$	6.17533	+	5.31728i	0.298148	+	0.256721i
$430$	−0.862608	−	2.19789i	−0.0415987	−	0.105992i
$431$	30.2968	−	6.91504i	1.45934	−	0.333086i	0.582095	−	0.813121i	$-0.302233\pi$
$431$	30.2968	−	6.91504i	1.45934	−	0.333086i	0.877249	+	0.480035i	$0.159376\pi$
$432$	−8.85274	+	6.02492i	−0.425928	+	0.289874i
$433$	−17.4126	+	1.96193i	−0.836797	+	0.0942844i	−0.519955	−	0.854194i	$-0.674051\pi$
$433$	−17.4126	+	1.96193i	−0.836797	+	0.0942844i	−0.316843	+	0.948478i	$0.602623\pi$
$434$	−4.79424	+	8.30386i	−0.230131	+	0.398598i
$435$	5.91783	+	15.8260i	0.283738	+	0.758798i
$436$	−12.9651	−	22.4562i	−0.620916	−	1.07546i
$437$	−36.5338	−	49.5015i	−1.74765	−	2.36798i
$438$	−8.50949	+	1.93976i	−0.406599	+	0.0926851i
$439$	2.94163	−	9.53652i	0.140396	−	0.455153i	−0.857880	−	0.513851i	$-0.828219\pi$
$439$	2.94163	−	9.53652i	0.140396	−	0.455153i	0.998276	+	0.0586975i	$0.0186947\pi$
$440$	−3.10868	+	3.89816i	−0.148200	+	0.185838i
$441$	16.5628	+	0.00917971i	0.788704	+	0.000437129i
$442$	−1.90424	+	8.34304i	−0.0905757	+	0.396838i
$443$	−2.02742	+	10.7152i	−0.0963257	+	0.509094i	0.900859	+	0.434111i	$0.142938\pi$
$443$	−2.02742	+	10.7152i	−0.0963257	+	0.509094i	−0.997185	+	0.0749821i	$0.976110\pi$
$444$	−5.89069	−	22.0088i	−0.279560	−	1.04449i
$445$	3.91907	+	0.146641i	0.185782	+	0.00695146i
$446$	2.34306	+	12.3834i	0.110947	+	0.586370i
$447$	−1.76460	+	23.4597i	−0.0834626	+	1.10960i
$448$	−3.20418	−	0.240120i	−0.151383	−	0.0113446i
$449$	0.405760	−	3.60122i	0.0191490	−	0.169952i	−0.980498	−	0.196530i	$-0.937033\pi$
$449$	0.405760	−	3.60122i	0.0191490	−	0.169952i	0.999647	+	0.0265783i	$0.00846113\pi$
$450$	−2.13325	−	2.13562i	−0.100563	−	0.100674i
$451$	−8.33908	+	4.01589i	−0.392672	+	0.189101i
$452$	−14.9590	+	4.00825i	−0.703611	+	0.188532i
$453$	23.2504	+	18.5521i	1.09240	+	0.871654i
$454$	−0.591146	+	15.7987i	−0.0277439	+	0.741471i
$455$	23.3950	−	1.75321i	1.09677	−	0.0821919i
$456$	−22.0638	+	12.7304i	−1.03323	+	0.596156i
$457$	9.09607	−	9.80323i	0.425496	−	0.458576i	−0.483522	−	0.875332i	$-0.660643\pi$
$457$	9.09607	−	9.80323i	0.425496	−	0.458576i	0.909018	+	0.416756i	$0.136833\pi$
$458$	7.57991	−	6.04477i	0.354186	−	0.282454i
$459$	2.34051	−	20.6185i	0.109246	−	0.962391i
$460$	−5.98355	−	26.2156i	−0.278984	−	1.22231i
$461$	18.6864	−	0.699194i	0.870311	−	0.0325647i	0.401496	−	0.915861i	$-0.368491\pi$
$461$	18.6864	−	0.699194i	0.870311	−	0.0325647i	0.468815	+	0.883296i	$0.344681\pi$
$462$	1.35836	+	4.40803i	0.0631966	+	0.205080i
$463$	−9.86520	+	5.69568i	−0.458475	+	0.264701i	−0.711403	−	0.702785i	$-0.751940\pi$
$463$	−9.86520	+	5.69568i	−0.458475	+	0.264701i	0.252928	+	0.967485i	$0.418606\pi$
$464$	−10.5516	−	3.43926i	−0.489846	−	0.159664i
$465$	4.80001	−	13.7055i	0.222595	−	0.635575i
$466$	10.1686	+	4.43651i	0.471051	+	0.205517i
$467$	−17.6805	+	11.1094i	−0.818158	+	0.514083i	−0.874898	−	0.484306i	$-0.839072\pi$
$467$	−17.6805	+	11.1094i	−0.818158	+	0.514083i	0.0567408	+	0.998389i	$0.481929\pi$
$468$	1.34979	+	18.1466i	0.0623938	+	0.838826i
$469$	30.3377	+	24.1935i	1.40087	+	1.11715i
$470$	1.74559	−	0.263105i	0.0805180	−	0.0121361i
$471$	−3.49802	−	6.62302i	−0.161180	−	0.305173i
$472$	12.0631	−	14.0176i	0.555249	−	0.645210i
$473$	0.213863	+	2.85380i	0.00983342	+	0.131218i
$474$	−1.81145	+	0.272518i	−0.0832025	+	0.0125172i
$475$	7.69971	+	8.94723i	0.353287	+	0.410527i
$476$	16.5593	−	16.5593i	0.758992	−	0.758992i
$477$	17.1238	−	18.4346i	0.784047	−	0.844063i
$478$	−5.74238	−	0.647011i	−0.262650	−	0.0295936i
$479$	−7.60424	+	10.3034i	−0.347446	+	0.470773i	−0.943120	−	0.332454i	$-0.892123\pi$
$479$	−7.60424	+	10.3034i	−0.347446	+	0.470773i	0.595673	+	0.803227i	$0.296885\pi$
$480$	−17.1141	+	1.92350i	−0.781150	+	0.0877952i
$481$	−28.0616	−	7.51908i	−1.27950	−	0.342840i
$482$	−1.84767	+	0.349598i	−0.0841591	+	0.0159238i
$483$	−51.0974	−	20.0706i	−2.32501	−	0.913243i
$484$	−12.7993	+	8.72642i	−0.581786	+	0.396655i
$485$	1.04701	+	2.99220i	0.0475425	+	0.135869i
$486$	1.68431	+	8.96982i	0.0764019	+	0.406879i
$487$	16.0848	+	20.1697i	0.728873	+	0.913978i	0.998804	−	0.0489019i	$-0.0155722\pi$
$487$	16.0848	+	20.1697i	0.728873	+	0.913978i	−0.269930	+	0.962880i	$0.587001\pi$
$488$	−26.9924	+	10.5937i	−1.22189	+	0.479556i
$489$	6.18431	−	2.69615i	0.279664	−	0.121924i
$490$	5.17674	+	2.73599i	0.233861	+	0.123599i
$491$	25.5288	−	18.8411i	1.15210	−	0.850287i	0.161470	−	0.986878i	$-0.448377\pi$
$491$	25.5288	−	18.8411i	1.15210	−	0.850287i	0.990628	+	0.136591i	$0.0436146\pi$
$492$	−19.5059	−	6.83149i	−0.879396	−	0.307987i
$493$	18.3890	−	11.1510i	0.828197	−	0.502216i
$494$			14.7184i			0.662210i
$495$	−3.26078	−	6.17799i	−0.146561	−	0.277680i
$496$	5.07468	+	8.07630i	0.227860	+	0.362637i
$497$	−14.6269	−	4.51180i	−0.656105	−	0.202382i
$498$	1.04010	−	0.0386292i	0.0466080	−	0.00173101i
$499$	−6.47222	−	2.54016i	−0.289736	−	0.113713i	0.216022	−	0.976389i	$-0.430692\pi$
$499$	−6.47222	−	2.54016i	−0.289736	−	0.113713i	−0.505758	+	0.862676i	$0.668787\pi$
$500$	5.94499	+	19.2732i	0.265868	+	0.861923i
$501$	8.53467	−	14.7730i	0.381301	−	0.660010i
$502$	0.895300	+	1.31316i	0.0399592	+	0.0586093i
$503$	−20.7948	−	13.0663i	−0.927197	−	0.582596i	−0.0183977	−	0.999831i	$-0.505856\pi$
$503$	−20.7948	−	13.0663i	−0.927197	−	0.582596i	−0.908799	+	0.417235i	$0.862999\pi$
$504$	−10.6321	+	20.0899i	−0.473590	+	0.894875i
$505$	−2.02348	−	2.02348i	−0.0900438	−	0.0900438i
$506$	0.503775	−	6.72241i	0.0223955	−	0.298847i
$507$	0.618175	+	0.297909i	0.0274541	+	0.0132306i
$508$	−2.85009	+	1.24348i	−0.126452	+	0.0551705i
$509$	−22.6715	+	33.2529i	−1.00489	+	1.47391i	−0.128859	+	0.991663i	$0.541132\pi$
$509$	−22.6715	+	33.2529i	−1.00489	+	1.47391i	−0.876035	+	0.482247i	$0.839821\pi$
$510$	4.13413	−	6.06004i	0.183062	−	0.268343i
$511$	23.0839	−	19.8653i	1.02117	−	0.878790i
$512$	10.7136	−	17.0506i	0.473480	−	0.753539i
$513$	−3.96652	−	35.4688i	−0.175126	−	1.56599i
$514$	−0.593678	+	0.207737i	−0.0261860	+	0.00916289i
$515$	−13.7430	−	12.7516i	−0.605587	−	0.561903i
$516$	−4.16966	+	4.84252i	−0.183559	+	0.213180i
$517$	−2.11576	−	0.318899i	−0.0930509	−	0.0140252i
$518$	−11.1846	−	12.0541i	−0.491423	−	0.529628i
$519$	−2.50860	−	11.0049i	−0.110115	−	0.483063i
$520$	−5.67702	+	13.0119i	−0.248954	+	0.570608i
$521$	3.70615			0.162370			0.0811848	−	0.996699i	$-0.474130\pi$
$521$	3.70615			0.162370			0.0811848	+	0.996699i	$0.474130\pi$
$522$	−6.28675	+	7.06691i	−0.275164	+	0.309310i
$523$	21.1827			0.926256			0.463128	−	0.886291i	$-0.346727\pi$
$523$	21.1827			0.926256			0.463128	+	0.886291i	$0.346727\pi$
$524$	6.31300	−	14.4696i	0.275785	−	0.632106i
$525$	10.0642	+	3.10744i	0.439236	+	0.135620i
$526$	−7.18640	−	7.74509i	−0.313342	−	0.337702i
$527$	−18.2770	−	2.75481i	−0.796158	−	0.120001i
$528$	4.50821	+	0.854293i	0.196195	+	0.0371783i
$529$	41.9547	+	38.9282i	1.82412	+	1.69253i
$530$	8.39567	−	2.93777i	0.364684	−	0.127609i
$531$	11.2294	+	23.3512i	0.487315	+	1.01336i
$532$	21.4290	−	34.1040i	0.929063	−	1.47860i
$533$	−19.9753	+	17.1901i	−0.865225	+	0.744586i
$534$	0.952019	+	1.97829i	0.0411979	+	0.0856090i
$535$	−3.67085	+	5.38415i	−0.158705	+	0.232777i
$536$	−21.5214	+	9.38968i	−0.929582	+	0.405573i
$537$	3.12105	+	41.8029i	0.134683	+	1.80393i
$538$	−0.203281	+	2.71260i	−0.00876408	+	0.116949i
$539$	−5.01830	−	5.01830i	−0.216154	−	0.216154i
$540$	4.61024	−	14.9020i	0.198393	−	0.641282i
$541$	−33.4037	−	20.9889i	−1.43614	−	0.902385i	−0.999997	−	0.00250608i	$-0.999202\pi$
$541$	−33.4037	−	20.9889i	−1.43614	−	0.902385i	−0.436140	−	0.899879i	$-0.643655\pi$
$542$	0.844771	+	1.23905i	0.0362860	+	0.0532218i
$543$	−9.20194	−	15.9484i	−0.394893	−	0.684413i
$544$	6.46111	+	20.9464i	0.277018	+	0.898070i
$545$	26.3843	+	10.3551i	1.13018	+	0.443563i
$546$	6.98427	+	11.1222i	0.298899	+	0.475988i
$547$	2.92690	+	0.902828i	0.125145	+	0.0386021i	0.356695	−	0.934221i	$-0.383904\pi$
$547$	2.92690	+	0.902828i	0.125145	+	0.0386021i	−0.231550	+	0.972823i	$0.574380\pi$
$548$	0.922078	+	1.46748i	0.0393892	+	0.0626876i
$549$	1.54160	−	40.5978i	0.0657937	−	1.73267i
$550$			1.29341i			0.0551512i
$551$	26.5668	−	25.7357i	1.13178	−	1.09638i
$552$	25.1855	−	21.6617i	1.07196	−	0.921983i
$553$	5.14300	−	3.79571i	0.218703	−	0.161410i
$554$	−1.53794	−	0.812823i	−0.0653407	−	0.0345336i
$555$	20.0336	+	14.7940i	0.850378	+	0.627972i
$556$	−5.34366	+	2.09723i	−0.226622	+	0.0889424i
$557$	9.78635	+	12.2717i	0.414661	+	0.519969i	0.944669	−	0.328024i	$-0.106383\pi$
$557$	9.78635	+	12.2717i	0.414661	+	0.519969i	−0.530008	+	0.847992i	$0.677811\pi$
$558$	8.03916	−	1.20715i	0.340325	−	0.0511028i
$559$	2.69123	+	7.69110i	0.113827	+	0.325299i
$560$	10.9144	−	7.44129i	0.461216	−	0.314452i
$561$	−6.95321	+	5.54185i	−0.293565	+	0.233977i
$562$	−2.96676	+	0.561341i	−0.125145	+	0.0236787i
$563$	26.3568	+	7.06228i	1.11081	+	0.297640i	0.767157	−	0.641459i	$-0.221670\pi$
$563$	26.3568	+	7.06228i	1.11081	+	0.297640i	0.343648	+	0.939098i	$0.388337\pi$
$564$	−2.83608	−	3.84498i	−0.119420	−	0.161903i
$565$	10.0522	−	13.6203i	0.422900	−	0.573009i
$566$	9.34002	+	1.05237i	0.392590	+	0.0442343i
$567$	−19.8283	−	24.9205i	−0.832711	−	1.04656i
$568$	6.54955	−	6.54955i	0.274813	−	0.274813i
$569$	−19.7647	−	22.9671i	−0.828581	−	0.962829i	0.171167	−	0.985242i	$-0.445246\pi$
$569$	−19.7647	−	22.9671i	−0.828581	−	0.962829i	−0.999749	+	0.0224130i	$0.992865\pi$
$570$	4.61280	−	11.7437i	0.193209	−	0.491888i
$571$	−0.146362	−	1.95307i	−0.00612506	−	0.0817333i	0.993304	−	0.115534i	$-0.0368579\pi$
$571$	−0.146362	−	1.95307i	−0.00612506	−	0.0817333i	−0.999429	+	0.0338007i	$0.989239\pi$
$572$	5.08593	−	5.90996i	0.212653	−	0.247108i
$573$	−5.73965	+	9.12898i	−0.239777	+	0.381369i
$574$	−14.7501	+	2.22322i	−0.615656	+	0.0927952i
$575$	−12.0354	−	9.59793i	−0.501912	−	0.400261i
$576$	1.53334	+	2.25167i	0.0638890	+	0.0938196i
$577$	13.6071	−	8.54991i	0.566471	−	0.355937i	−0.218148	−	0.975916i	$-0.570002\pi$
$577$	13.6071	−	8.54991i	0.566471	−	0.355937i	0.784619	+	0.619978i	$0.212859\pi$
$578$	0.564404	+	0.246247i	0.0234761	+	0.0102425i
$579$	−18.5545	−	21.5728i	−0.771100	−	0.896537i
$580$	15.1407	−	5.66637i	0.628684	−	0.235283i
$581$	−3.14527	+	1.81592i	−0.130488	+	0.0753371i
$582$	−1.20741	+	1.30056i	−0.0500489	+	0.0539099i
$583$	−10.7735	+	0.403116i	−0.446193	+	0.0166954i
$584$	4.10077	+	17.9667i	0.169691	+	0.743465i
$585$	−13.5208	−	14.5881i	−0.559016	−	0.603146i
$586$	9.62315	−	7.67421i	0.397529	−	0.317019i
$587$	9.97283	−	10.7482i	0.411623	−	0.443624i	−0.492876	−	0.870099i	$-0.664055\pi$
$587$	9.97283	−	10.7482i	0.411623	−	0.443624i	0.904499	+	0.426476i	$0.140245\pi$
$588$	0.00439157	−	15.8473i	0.000181105	−	0.653530i
$589$	−31.7011	+	2.37567i	−1.30622	+	0.0978876i
$590$	−0.342505	+	9.15365i	−0.0141007	+	0.376850i
$591$	−2.65332	+	17.5706i	−0.109143	+	0.722758i
$592$	−15.8003	+	4.23368i	−0.649389	+	0.174003i
$593$	3.15432	−	1.51904i	0.129533	−	0.0623796i	−0.367995	−	0.929828i	$-0.619956\pi$
$593$	3.15432	−	1.51904i	0.129533	−	0.0623796i	0.497527	+	0.867448i	$0.334241\pi$
$594$	2.20562	−	3.22928i	0.0904977	−	0.132499i
$595$	−2.86606	+	25.4370i	−0.117497	+	1.04281i
$596$	22.4467	+	1.68214i	0.919451	+	0.0689033i
$597$	27.4296	+	18.7123i	1.12262	+	0.765845i
$598$	−3.56844	−	18.8597i	−0.145924	−	0.771229i
$599$	43.8025	+	1.63897i	1.78972	+	0.0669666i	0.911503	−	0.411294i	$-0.134923\pi$
$599$	43.8025	+	1.63897i	1.78972	+	0.0669666i	0.878218	+	0.478261i	$0.158733\pi$
$600$	−4.50811	+	4.50561i	−0.184043	+	0.183941i
$601$	−4.34605	+	22.9694i	−0.177279	+	0.936942i	0.775057	+	0.631891i	$0.217721\pi$
$601$	−4.34605	+	22.9694i	−0.177279	+	0.936942i	−0.952336	+	0.305051i	$0.901327\pi$
$602$	−1.02630	+	4.49651i	−0.0418288	+	0.183264i
$603$	0.0182334	−	32.8983i	0.000742523	−	1.33972i
$604$	17.7445	−	22.2509i	0.722012	−	0.905375i
$605$	4.99104	−	16.1806i	0.202915	−	0.657833i
$606$	0.472608	−	1.53065i	0.0191984	−	0.0621785i
$607$	20.2804	+	27.4790i	0.823157	+	1.11534i	0.991564	+	0.129620i	$0.0413759\pi$
$607$	20.2804	+	27.4790i	0.823157	+	1.11534i	−0.168407	+	0.985718i	$0.553862\pi$
$608$	18.8505	+	32.6501i	0.764490	+	1.32413i
$609$	7.86347	−	32.0544i	0.318644	−	1.29891i
$610$	7.18125	−	12.4383i	0.290760	−	0.503611i
$611$	−6.05390	+	0.682111i	−0.244915	+	0.0275953i
$612$	−19.7284	−	2.23393i	−0.797474	−	0.0903013i
$613$	16.5394	−	3.77501i	0.668020	−	0.152471i	0.124955	−	0.992162i	$-0.460121\pi$
$613$	16.5394	−	3.77501i	0.668020	−	0.152471i	0.543064	+	0.839691i	$0.317264\pi$
$614$	−0.501803	−	1.27857i	−0.0202511	−	0.0515990i
$615$	21.3256	−	7.45550i	0.859929	−	0.300635i
$616$	9.30676	−	2.87075i	0.374980	−	0.115666i
$617$	27.2867	+	23.4821i	1.09852	+	0.945354i	0.998766	−	0.0496578i	$-0.0158131\pi$
$617$	27.2867	+	23.4821i	1.09852	+	0.945354i	0.0997552	+	0.995012i	$0.468194\pi$
$618$	2.71910	−	10.1366i	0.109378	−	0.407754i
$619$	−13.2327	−	25.0374i	−0.531865	−	1.00634i	−0.992900	−	0.118956i	$-0.962045\pi$
$619$	−13.2327	−	25.0374i	−0.531865	−	1.00634i	0.461034	−	0.887382i	$-0.347479\pi$
$620$	−13.1146	−	4.58901i	−0.526696	−	0.184299i
$621$	13.6819	+	44.4870i	0.549037	+	1.78520i
$622$	−1.64340	−	3.41255i	−0.0658943	−	0.136831i
$623$	−6.16387	−	4.54914i	−0.246950	−	0.182258i
$624$	13.0283	−	0.972707i	0.521550	−	0.0389395i
$625$	−11.1158	−	7.57863i	−0.444632	−	0.303145i
$626$	3.04010	−	11.3458i	0.121507	−	0.453469i
$627$	−9.53815	+	11.9537i	−0.380917	+	0.477383i
$628$	−6.33597	+	3.34866i	−0.252833	+	0.133626i
$629$	13.7533	−	28.5590i	0.548380	−	1.13872i
$630$	−2.08693	−	11.0632i	−0.0831452	−	0.440770i
$631$	1.09042	+	0.248881i	0.0434088	+	0.00990778i	0.244170	−	0.969732i	$-0.421484\pi$
$631$	1.09042	+	0.248881i	0.0434088	+	0.00990778i	−0.200761	+	0.979640i	$0.564342\pi$
$632$	0.576482	+	3.82471i	0.0229312	+	0.152139i
$633$	0.880064	+	23.6959i	0.0349794	+	0.941829i
$634$	4.88995	−	4.53721i	0.194205	−	0.180196i
$635$	1.58822	−	3.00507i	0.0630268	−	0.119252i
$636$	−17.6428	−	16.3792i	−0.699581	−	0.649477i
$637$	−17.4998	−	10.1035i	−0.693368	−	0.400316i
$638$	4.04585	−	0.238621i	0.160177	−	0.00944709i
$639$	4.73452	+	12.0830i	0.187295	+	0.477998i
$640$	2.33437	+	20.7181i	0.0922739	+	0.818954i
$641$	1.69467	+	45.2909i	0.0669353	+	1.78888i	0.479087	+	0.877767i	$0.340968\pi$
$641$	1.69467	+	45.2909i	0.0669353	+	1.78888i	−0.412152	+	0.911115i	$0.635223\pi$
$642$	−3.62488	−	0.409444i	−0.143063	−	0.0161595i
$643$	1.46511	−	9.72037i	0.0577783	−	0.383334i	−0.941188	−	0.337883i	$-0.890289\pi$
$643$	1.46511	−	9.72037i	0.0577783	−	0.383334i	0.998967	−	0.0454513i	$-0.0144726\pi$
$644$	−19.1900	+	48.8952i	−0.756190	+	1.92674i
$645$	0.263114	−	6.98011i	0.0103601	−	0.274842i
$646$	−15.7793	−	2.98560i	−0.620827	−	0.117467i
$647$	19.9433	+	9.60419i	0.784052	+	0.377580i	0.782684	−	0.622420i	$-0.213850\pi$
$647$	19.9433	+	9.60419i	0.784052	+	0.377580i	0.00136817	+	0.999999i	$0.499564\pi$
$648$	18.9388	−	3.56167i	0.743985	−	0.139916i
$649$	3.66694	−	10.4795i	0.143940	−	0.411356i
$650$	0.953156	+	3.55723i	0.0373858	+	0.139526i
$651$	−22.8283	+	16.8383i	−0.894710	+	0.659943i
$652$	−2.58131	−	5.91643i	−0.101092	−	0.231705i
$653$	−14.9925	−	34.3631i	−0.586701	−	1.34473i	−0.916255	−	0.400596i	$-0.868803\pi$
$653$	−14.9925	−	34.3631i	−0.586701	−	1.34473i	0.329554	−	0.944137i	$-0.393102\pi$
$654$	1.77215	+	15.7676i	0.0692967	+	0.616561i
$655$	4.46621	+	16.6681i	0.174509	+	0.651277i
$656$	−4.90088	+	14.0059i	−0.191347	+	0.546839i
$657$	−25.3674	−	4.81433i	−0.989676	−	0.187825i
$658$	−3.10683	−	1.49617i	−0.121117	−	0.0583268i
$659$	34.7249	+	6.57030i	1.35269	+	0.255943i	0.811202	−	0.584766i	$-0.198814\pi$
$659$	34.7249	+	6.57030i	1.35269	+	0.255943i	0.541488	+	0.840709i	$0.317861\pi$
$660$	−5.91023	+	3.12155i	−0.230055	+	0.121506i
$661$	−7.47190	+	19.0381i	−0.290623	+	0.740496i	0.708762	+	0.705447i	$0.249254\pi$
$661$	−7.47190	+	19.0381i	−0.290623	+	0.740496i	−0.999386	+	0.0350489i	$0.988841\pi$
$662$	−0.192422	+	1.27664i	−0.00747871	+	0.0496180i
$663$	−15.0392	+	20.3656i	−0.584075	+	0.790935i
$664$	−0.0821740	−	2.19615i	−0.00318897	−	0.0852270i
$665$	4.92938	+	43.7495i	0.191153	+	1.69653i
$666$	−2.08549	+	13.7845i	−0.0808110	+	0.534137i
$667$	−27.8023	+	39.4181i	−1.07651	+	1.52627i
$668$	−14.1371	−	8.16204i	−0.546980	−	0.315799i
$669$	−8.30673	+	36.3477i	−0.321157	+	1.40528i
$670$	5.43443	−	10.2824i	0.209950	−	0.397245i
$671$	−12.7611	+	11.8406i	−0.492637	+	0.457101i
$672$	29.7381	+	15.7276i	1.14717	+	0.606706i
$673$	−0.605378	−	4.01642i	−0.0233356	−	0.154822i	0.974128	−	0.225996i	$-0.0725635\pi$
$673$	−0.605378	−	4.01642i	−0.0233356	−	0.154822i	−0.997464	+	0.0711740i	$0.977325\pi$
$674$	−19.3221	−	4.41014i	−0.744259	−	0.169872i
$675$	−3.25560	−	8.31546i	−0.125308	−	0.320062i
$676$	0.284875	−	0.591549i	0.0109567	−	0.0227519i
$677$	42.7466	−	22.5923i	1.64289	−	0.868291i	0.648650	−	0.761087i	$-0.275334\pi$
$677$	42.7466	−	22.5923i	1.64289	−	0.868291i	0.994237	−	0.107204i	$-0.0341899\pi$
$678$	9.37015	+	1.41498i	0.359858	+	0.0543419i
$679$	1.60271	−	5.98141i	0.0615065	−	0.229545i
$680$	−12.7982	−	8.72566i	−0.490788	−	0.334614i
$681$	−20.3051	+	42.1340i	−0.778092	+	1.61458i
$682$	−2.80266	−	2.06845i	−0.107319	−	0.0792052i
$683$	−19.0377	−	39.5323i	−0.728459	−	1.51266i	−0.853831	−	0.520551i	$-0.825727\pi$
$683$	−19.0377	−	39.5323i	−0.728459	−	1.51266i	0.125372	−	0.992110i	$-0.459988\pi$
$684$	−33.9355	+	3.80456i	−1.29756	+	0.145471i
$685$	−1.78812	−	0.625691i	−0.0683206	−	0.0239064i
$686$	1.43179	+	2.70908i	0.0546660	+	0.103433i
$687$	27.7065	−	7.41572i	1.05707	−	0.282927i
$688$	3.47758	+	2.99270i	0.132582	+	0.114096i
$689$	−29.3330	+	9.04802i	−1.11750	+	0.344702i
$690$	−3.06347	+	16.1663i	−0.116624	+	0.615442i
$691$	−6.47640	−	16.5016i	−0.246374	−	0.627750i	0.753174	−	0.657822i	$-0.228522\pi$
$691$	−6.47640	−	16.5016i	−0.246374	−	0.627750i	−0.999548	+	0.0300710i	$0.990427\pi$
$692$	−10.5288	+	2.40314i	−0.400247	+	0.0913537i
$693$	−1.53536	+	13.5592i	−0.0583235	+	0.515070i
$694$	1.65095	−	0.186018i	0.0626693	−	0.00706113i
$695$	3.13738	−	5.43410i	0.119008	−	0.206127i
$696$	14.9255	+	13.2703i	0.565748	+	0.503011i
$697$	−14.3772	−	24.9021i	−0.544576	−	0.943234i
$698$	−9.18762	−	12.4488i	−0.347757	−	0.471194i
$699$	22.3174	+	24.0658i	0.844122	+	0.910253i
$700$	2.97052	−	9.63020i	0.112275	−	0.363987i
$701$	28.4724	−	35.7032i	1.07539	−	1.34849i	0.141899	−	0.989881i	$-0.454679\pi$
$701$	28.4724	−	35.7032i	1.07539	−	1.34849i	0.933487	−	0.358611i	$-0.116749\pi$
$702$	3.68629	−	10.5068i	0.139130	−	0.396553i
$703$	12.1314	−	53.1513i	0.457546	−	2.00464i
$704$	0.217010	−	1.14693i	0.00817888	−	0.0432264i
$705$	5.04414	+	1.35307i	0.189973	+	0.0509596i
$706$	−2.75647	−	0.103140i	−0.103741	−	0.00388171i
$707$	1.03922	+	5.49243i	0.0390840	+	0.206564i
$708$	22.3394	−	10.7505i	0.839568	−	0.404028i
$709$	−25.9681	−	1.94604i	−0.975253	−	0.0730851i	−0.422440	−	0.906391i	$-0.638826\pi$
$709$	−25.9681	−	1.94604i	−0.975253	−	0.0730851i	−0.552812	+	0.833306i	$0.686445\pi$
$710$	−0.513671	+	4.55896i	−0.0192777	+	0.171095i
$711$	−5.23384	−	1.40551i	−0.196284	−	0.0527108i
$712$	4.17660	−	2.01134i	0.156525	−	0.0753783i
$713$	40.0448	−	10.7300i	1.49969	−	0.401841i
$714$	−13.3407	+	5.23157i	−0.499263	+	0.195786i
$715$	−0.318676	+	8.51681i	−0.0119178	+	0.318510i
$716$	39.9962	−	2.99730i	1.49473	−	0.112014i
$717$	−14.8029	−	8.55195i	−0.552826	−	0.319378i
$718$	5.28632	−	5.69730i	0.197284	−	0.212621i
$719$	17.9950	−	14.3506i	0.671101	−	0.535185i	−0.227596	−	0.973756i	$-0.573086\pi$
$719$	17.9950	−	14.3506i	0.671101	−	0.535185i	0.898697	+	0.438570i	$0.144515\pi$
$720$	−10.7000	−	3.30702i	−0.398767	−	0.123245i
$721$	8.14900	+	35.7031i	0.303485	+	1.32965i
$722$	−16.4851	+	0.616828i	−0.613511	+	0.0229560i
$723$	−5.42330	−	1.23941i	−0.201695	−	0.0460943i
$724$	−15.2570	+	8.80864i	−0.567022	+	0.327370i
$725$	4.75420	−	7.94043i	0.176567	−	0.294900i
$726$	9.31429	−	1.75969i	0.345686	−	0.0653081i
$727$	25.5756	+	11.1585i	0.948547	+	0.413847i	0.816467	−	0.577392i	$-0.195930\pi$
$727$	25.5756	+	11.1585i	0.948547	+	0.413847i	0.132080	+	0.991239i	$0.457834\pi$
$728$	23.4805	−	14.7538i	0.870245	−	0.546811i
$729$	−6.05182	+	26.3130i	−0.224142	+	0.974557i
$730$	−7.13652	−	5.69119i	−0.264135	−	0.210640i
$731$	−8.79140	+	1.32509i	−0.325162	+	0.0490102i
$732$	−38.8444	−	1.46423i	−1.43573	−	0.0541196i
$733$	−24.3536	+	28.2994i	−0.899520	+	1.04526i	0.0992190	+	0.995066i	$0.468366\pi$
$733$	−24.3536	+	28.2994i	−0.899520	+	1.04526i	−0.998739	+	0.0501960i	$0.984015\pi$
$734$	−0.923701	−	12.3259i	−0.0340944	−	0.454959i
$735$	10.7965	+	13.5460i	0.398233	+	0.499653i
$736$	−32.0704	−	37.2665i	−1.18213	−	1.37366i
$737$	−9.96773	+	9.96773i	−0.367166	+	0.367166i
$738$	9.26588	+	8.60704i	0.341082	+	0.316829i
$739$	2.57887	+	0.290569i	0.0948654	+	0.0106888i	0.159270	−	0.987235i	$-0.449086\pi$
$739$	2.57887	+	0.290569i	0.0948654	+	0.0106888i	−0.0644041	+	0.997924i	$0.520515\pi$
$740$	14.1496	−	19.1720i	0.520150	−	0.704778i
$741$	−17.4234	+	39.9047i	−0.640065	+	1.46594i
$742$	−16.7830	−	4.49698i	−0.616122	−	0.165089i
$743$	4.49542	−	0.850580i	0.164921	−	0.0312048i	−0.102795	−	0.994703i	$-0.532779\pi$
$743$	4.49542	−	0.850580i	0.164921	−	0.0312048i	0.267716	+	0.963498i	$0.413731\pi$
$744$	−2.55361	−	16.9740i	−0.0936197	−	0.622296i
$745$	−20.3293	+	13.8603i	−0.744808	+	0.507801i
$746$	−0.0903218	−	0.258125i	−0.00330692	−	0.00945063i
$747$	2.86567	+	1.12653i	0.104849	+	0.0412174i
$748$	5.30428	+	6.65136i	0.193944	+	0.243198i
$749$	11.8492	−	4.65048i	0.432962	−	0.169925i
$750$	1.38523	−	12.2637i	0.0505814	−	0.447807i
$751$	25.0618	+	13.2455i	0.914517	+	0.483337i	0.857179	−	0.515018i	$-0.172215\pi$
$751$	25.0618	+	13.2455i	0.914517	+	0.483337i	0.0573382	+	0.998355i	$0.481739\pi$
$752$	−2.75999	+	2.03697i	−0.100646	+	0.0742805i
$753$	0.872848	+	4.62012i	0.0318084	+	0.168367i
$754$	10.9513	−	3.63778i	0.398823	−	0.132480i
$755$			31.1088i			1.13216i
$756$	−23.8387	+	18.9783i	−0.867005	+	0.690235i
$757$	−6.75132	−	10.7447i	−0.245381	−	0.390521i	0.701212	−	0.712953i	$-0.252643\pi$
$757$	−6.75132	−	10.7447i	−0.245381	−	0.390521i	−0.946593	+	0.322432i	$0.895500\pi$
$758$	−7.11809	−	2.19564i	−0.258541	−	0.0797492i
$759$	9.32375	−	17.6296i	0.338431	−	0.639913i
$760$	−24.7994	−	9.73305i	−0.899569	−	0.353055i
$761$	−13.8324	−	44.8437i	−0.501425	−	1.62558i	−0.753197	−	0.657795i	$-0.771489\pi$
$761$	−13.8324	−	44.8437i	−0.501425	−	1.62558i	0.251772	−	0.967787i	$-0.418987\pi$
$762$	1.90275		0.000527286i	0.0689292		1.91016e-5i
$763$	−31.1888	−	45.7455i	−1.12911	−	1.65610i
$764$	8.73612	+	5.48927i	0.316062	+	0.198595i
$765$	18.3823	−	11.5362i	0.664615	−	0.417092i
$766$	−4.53601	−	4.53601i	−0.163893	−	0.163893i
$767$	2.36238	−	31.5237i	0.0853004	−	1.13826i
$768$	−7.04570	+	4.80082i	−0.254240	+	0.173234i
$769$	10.5381	−	4.59771i	0.380012	−	0.165798i	−0.201199	−	0.979550i	$-0.564484\pi$
$769$	10.5381	−	4.59771i	0.380012	−	0.165798i	0.581211	+	0.813753i	$0.302579\pi$
$770$	−2.71749	+	3.98583i	−0.0979317	+	0.143639i
$771$	−1.85551	−	0.139568i	−0.0668245	−	0.00502643i
$772$	−20.6359	+	17.7587i	−0.742704	+	0.639149i
$773$	−23.2548	+	37.0098i	−0.836416	+	1.33115i	0.105196	+	0.994451i	$0.466453\pi$
$773$	−23.2548	+	37.0098i	−0.836416	+	1.33115i	−0.941613	+	0.336698i	$0.890690\pi$
$774$	3.52397	−	1.69465i	0.126666	−	0.0609128i
$775$	−7.50787	+	2.62712i	−0.269691	+	0.0943688i
$776$	2.74684	+	2.54869i	0.0986057	+	0.0914927i
$777$	−16.0544	−	45.9216i	−0.575948	−	1.64743i
$778$	11.0375	+	1.66364i	0.395715	+	0.0596445i
$779$	−33.6381	−	36.2533i	−1.20521	−	1.29891i
$780$	−13.9543	+	12.9405i	−0.499645	+	0.463346i
$781$	2.22368	−	5.09673i	0.0795695	−	0.182375i
$782$	20.9429			0.748918
$783$	−25.4105	+	11.7178i	−0.908097	+	0.418759i
$784$	−11.3778			−0.406348
$785$	3.13253	−	7.17984i	0.111805	−	0.256260i
$786$	−7.08311	+	6.56852i	−0.252646	+	0.234291i
$787$	6.05694	+	6.52783i	0.215906	+	0.232692i	0.831713	−	0.555205i	$-0.187360\pi$
$787$	6.05694	+	6.52783i	0.215906	+	0.232692i	−0.615807	+	0.787897i	$0.711170\pi$
$788$	16.8122	+	2.53404i	0.598911	+	0.0902713i
$789$	−10.3154	−	29.5058i	−0.367237	−	1.05044i
$790$	−1.40440	−	1.30309i	−0.0499662	−	0.0463619i
$791$	−31.2114	+	10.9213i	−1.10975	+	0.388318i
$792$	−6.81991	−	4.65528i	−0.242335	−	0.165418i
$793$	−26.3708	+	41.9688i	−0.936453	+	1.49036i
$794$	8.61830	−	7.41665i	0.305852	−	0.263207i
$795$	26.2402	+	1.97374i	0.930644	+	0.0700015i
$796$	17.8967	−	26.2496i	0.634331	−	0.930392i
$797$	−36.7249	+	16.0229i	−1.30086	+	0.567560i	−0.932180	−	0.361996i	$-0.882095\pi$
$797$	−36.7249	+	16.0229i	−1.30086	+	0.567560i	−0.368682	+	0.929556i	$0.620191\pi$
$798$	−20.3674	+	13.8780i	−0.720998	+	0.491275i
$799$	0.496748	−	6.62864i	0.0175737	−	0.234504i
$800$	6.67032	+	6.67032i	0.235831	+	0.235831i
$801$	0.239258	+	6.49057i	0.00845376	+	0.229333i
$802$	17.6473	+	11.0885i	0.623147	+	0.391549i
$803$	6.23237	+	9.14120i	0.219935	+	0.322586i
$804$	−31.4770	−	0.00872286i	−1.11011	−	0.000307632i
$805$	−16.9233	−	54.8641i	−0.596470	−	1.93371i
$806$	−9.23236	−	3.62343i	−0.325196	−	0.127630i
$807$	−3.76229	+	7.11382i	−0.132439	+	0.250418i
$808$	−3.23225	−	0.997016i	−0.113710	−	0.0350749i
$809$	0.548274	+	0.872572i	0.0192763	+	0.0306780i	0.856223	−	0.516606i	$-0.172805\pi$
$809$	0.548274	+	0.872572i	0.0192763	+	0.0306780i	−0.836947	+	0.547284i	$0.815662\pi$
$810$	−6.23413	+	7.22797i	−0.219045	+	0.253965i
$811$		−	5.29060i		−	0.185778i	−0.995676	−	0.0928891i	$-0.970390\pi$
$811$		−	5.29060i		−	0.185778i	0.995676	−	0.0928891i	$-0.0296102\pi$
$812$	−30.6717	−	7.51526i	−1.07637	−	0.263734i
$813$	0.823587	+	4.35937i	0.0288845	+	0.152890i
$814$	4.80642	−	3.54730i	0.168465	−	0.124333i
$815$	6.23815	+	3.29696i	0.218513	+	0.115487i
$816$	−1.59996	+	14.1647i	−0.0560097	+	0.495865i
$817$	−14.2342	+	5.58653i	−0.497993	+	0.195448i
$818$	4.58663	+	5.75145i	0.160368	+	0.201095i
$819$	5.76952	+	38.4227i	0.201603	+	1.34260i
$820$	−7.13907	−	20.4023i	−0.249307	−	0.712479i
$821$	−29.0659	+	19.8168i	−1.01441	+	0.691611i	−0.951892	−	0.306433i	$-0.900864\pi$
$821$	−29.0659	+	19.8168i	−1.01441	+	0.691611i	−0.0625149	+	0.998044i	$0.519912\pi$
$822$	−0.157770	−	1.04871i	−0.00550286	−	0.0365779i
$823$	13.1045	−	2.47951i	0.456795	−	0.0864303i	0.0475784	−	0.998868i	$-0.484850\pi$
$823$	13.1045	−	2.47951i	0.456795	−	0.0864303i	0.409217	+	0.912437i	$0.365802\pi$
$824$	−21.4050	−	5.73546i	−0.745679	−	0.199804i
$825$	−1.53113	+	3.50672i	−0.0533069	+	0.122088i
$826$	10.6253	−	14.3968i	0.369701	−	0.500928i
$827$	−47.5270	−	5.35500i	−1.65267	−	0.186212i	−0.764149	−	0.645039i	$-0.776841\pi$
$827$	−47.5270	−	5.35500i	−1.65267	−	0.186212i	−0.888525	+	0.458828i	$0.848270\pi$
$828$	42.5615	−	13.1026i	1.47911	−	0.455348i
$829$	39.4991	−	39.4991i	1.37186	−	1.37186i	0.514174	−	0.857686i	$-0.328098\pi$
$829$	39.4991	−	39.4991i	1.37186	−	1.37186i	0.857686	−	0.514174i	$-0.171902\pi$
$830$	0.710040	+	0.825082i	0.0246459	+	0.0286390i
$831$	−3.20748	−	4.02434i	−0.111266	−	0.139603i
$832$	−0.248371	−	3.31428i	−0.00861070	−	0.114902i
$833$	14.3816	−	16.7117i	0.498293	−	0.579027i
$834$	3.51014	+	0.132314i	0.121546	+	0.00458166i
$835$	17.6441	−	2.65942i	0.610600	−	0.0920331i
$836$	11.4398	+	9.12292i	0.395653	+	0.315523i
$837$	23.2250	+	6.24381i	0.802772	+	0.215818i
$838$	−4.86255	+	3.05534i	−0.167974	+	0.105545i
$839$	18.2703	+	7.97124i	0.630760	+	0.275198i	0.690853	−	0.722995i	$-0.257235\pi$
$839$	18.2703	+	7.97124i	0.630760	+	0.275198i	−0.0600932	+	0.998193i	$0.519140\pi$
$840$	−23.3588	+	4.41302i	−0.805955	+	0.152264i
$841$	−25.7151	−	13.4064i	−0.886728	−	0.462291i
$842$	2.04401	−	1.18011i	0.0704411	−	0.0406692i
$843$	−8.70805	−	1.99010i	−0.299921	−	0.0685425i
$844$	22.6720	−	0.848327i	0.780403	−	0.0292006i
$845$	0.159698	+	0.699684i	0.00549379	+	0.0240699i
$846$	0.648971	+	2.85061i	0.0223121	+	0.0980060i
$847$	−25.8601	+	20.6228i	−0.888565	+	0.708607i
$848$	−11.7561	+	12.6701i	−0.403708	+	0.435094i
$849$	24.0771	+	13.9098i	0.826323	+	0.477383i
$850$	−4.00698	+	0.300282i	−0.137438	+	0.0102996i
$851$	−2.65842	+	71.0477i	−0.0911294	+	2.43548i
$852$	11.5598	−	4.53318i	0.396032	−	0.155304i
$853$	1.54122	−	0.412969i	0.0527704	−	0.0141398i	−0.232337	−	0.972635i	$-0.574637\pi$
$853$	1.54122	−	0.412969i	0.0527704	−	0.0141398i	0.285108	+	0.958496i	$0.407971\pi$
$854$	−25.2771	+	12.1728i	−0.864965	+	0.416545i
$855$	26.4083	−	26.3791i	0.903146	−	0.902145i
$856$	−0.862419	+	7.65418i	−0.0294769	+	0.261614i
$857$	−4.58909	−	0.343904i	−0.156760	−	0.0117476i	−0.00388120	−	0.999992i	$-0.501235\pi$
$857$	−4.58909	−	0.343904i	−0.156760	−	0.0117476i	−0.152879	+	0.988245i	$0.548854\pi$
$858$	−4.29916	+	2.06890i	−0.146771	+	0.0706310i
$859$	7.08136	+	37.4259i	0.241613	+	1.27696i	0.867655	+	0.497166i	$0.165626\pi$
$859$	7.08136	+	37.4259i	0.241613	+	1.27696i	−0.626042	+	0.779789i	$0.715326\pi$
$860$	−6.67863	−	0.249897i	−0.227740	−	0.00852141i
$861$	−42.6225	−	11.4333i	−1.45257	−	0.389647i
$862$	−3.38248	+	17.8768i	−0.115208	+	0.608888i
$863$	−1.48533	+	6.50765i	−0.0505612	+	0.221523i	−0.993896	−	0.110319i	$-0.964813\pi$
$863$	−1.48533	+	6.50765i	−0.0505612	+	0.221523i	0.943335	+	0.331842i	$0.107670\pi$
$864$	−5.27917	−	28.0286i	−0.179601	−	0.953553i
$865$	7.36015	−	9.22934i	0.250253	−	0.313807i
$866$	3.02392	−	9.80331i	0.102757	−	0.333130i
$867$	1.23872	+	1.33577i	0.0420691	+	0.0453650i
$868$	16.1169	+	21.8376i	0.547042	+	0.741216i
$869$	1.16105	+	2.01099i	0.0393858	+	0.0682182i
$870$	−9.87806	−	0.529634i	−0.334898	−	0.0179563i
$871$	−20.0684	+	34.7594i	−0.679991	+	1.17778i
$872$	33.2922	−	3.75113i	1.12742	−	0.127029i
$873$	−4.81315	+	2.09678i	−0.162901	+	0.0709653i
$874$	35.1170	−	8.01523i	1.18785	−	0.271119i
$875$	15.7335	+	40.0883i	0.531889	+	1.35523i
$876$	−4.59962	+	24.2728i	−0.155407	+	0.820100i
$877$	−22.2970	+	6.87772i	−0.752916	+	0.232244i	−0.647376	−	0.762171i	$-0.724134\pi$
$877$	−22.2970	+	6.87772i	−0.752916	+	0.232244i	−0.105541	+	0.994415i	$0.533657\pi$
$878$	4.42878	+	3.81127i	0.149464	+	0.128624i
$879$	35.1751	−	9.41470i	1.18643	−	0.317550i
$880$	2.24234	+	4.24271i	0.0755892	+	0.143022i
$881$	5.99551	+	2.09792i	0.201994	+	0.0706808i	0.429380	−	0.903124i	$-0.358732\pi$
$881$	5.99551	+	2.09792i	0.201994	+	0.0706808i	−0.227386	+	0.973805i	$0.573018\pi$
$882$	−3.88269	+	8.88577i	−0.130737	+	0.299200i
$883$	−13.4568	−	27.9434i	−0.452859	−	0.940371i	−0.994980	−	0.100071i	$-0.968093\pi$
$883$	−13.4568	−	27.9434i	−0.452859	−	0.940371i	0.542121	−	0.840300i	$-0.317621\pi$
$884$	19.4898	+	14.3841i	0.655512	+	0.483790i
$885$	−11.7646	+	24.4121i	−0.395462	+	0.820605i
$886$	−5.27531	−	3.59665i	−0.177228	−	0.120832i
$887$	−7.38642	+	27.5665i	−0.248012	+	0.925592i	0.723834	+	0.689974i	$0.242378\pi$
$887$	−7.38642	+	27.5665i	−0.248012	+	0.925592i	−0.971846	+	0.235618i	$0.924289\pi$
$888$	29.1071	+	4.39544i	0.976770	+	0.147501i
$889$	−5.87006	+	3.10242i	−0.196875	+	0.104052i
$890$	−0.996243	+	2.06872i	−0.0333941	+	0.0693437i
$891$	9.80271	−	6.14431i	0.328403	−	0.205842i
$892$	34.7797	+	7.93824i	1.16451	+	0.265792i
$893$	−1.70395	−	11.3050i	−0.0570206	−	0.378307i
$894$	−12.1758	−	6.43942i	−0.407220	−	0.215366i
$895$	−32.1380	+	29.8197i	−1.07425	+	0.996762i
$896$	19.0302	−	36.0069i	0.635754	−	1.20291i
$897$	12.6510	−	55.3570i	0.422405	−	1.84832i
$898$	1.83749	+	1.06088i	0.0613178	+	0.0354019i
$899$	9.60286	+	23.0003i	0.320273	+	0.767102i
$900$	−7.95536	+	3.11716i	−0.265179	+	0.103905i
$901$	−3.75006	−	33.2827i	−0.124933	−	1.10881i
$902$	−0.202620	−	5.41514i	−0.00674652	−	0.180304i
$903$	−8.10544	+	10.9761i	−0.269732	+	0.365262i
$904$	2.98224	−	19.7859i	0.0991879	−	0.658069i
$905$	7.03536	−	17.9258i	0.233863	−	0.595874i
$906$	−15.3989	+	8.13311i	−0.511595	+	0.270205i
$907$	−31.4200	−	5.94498i	−1.04328	−	0.197400i	−0.364094	−	0.931362i	$-0.618621\pi$
$907$	−31.4200	−	5.94498i	−1.04328	−	0.197400i	−0.679190	+	0.733962i	$0.737669\pi$
$908$	40.3192	+	19.4167i	1.33804	+	0.644366i
$909$	3.09331	−	3.59047i	0.102599	−	0.119088i
$910$	−4.53655	+	12.9647i	−0.150385	+	0.429776i
$911$	8.67377	+	32.3709i	0.287375	+	1.07250i	0.947086	+	0.320979i	$0.104012\pi$
$911$	8.67377	+	32.3709i	0.287375	+	1.07250i	−0.659712	+	0.751519i	$0.729322\pi$
$912$	2.73829	+	24.3637i	0.0906739	+	0.806762i
$913$	−0.527608	−	1.20929i	−0.0174613	−	0.0400216i
$914$	3.13099	+	7.17631i	0.103564	+	0.237371i
$915$	34.1942	−	25.2219i	1.13043	−	0.833809i
$916$	−7.10269	−	26.5076i	−0.234680	−	0.875836i
$917$	11.1330	−	31.8162i	0.367643	−	1.05066i
$918$	10.5164	+	6.08328i	0.347091	+	0.200778i
$919$	2.37687	+	1.14464i	0.0784057	+	0.0377582i	0.472676	−	0.881236i	$-0.343288\pi$
$919$	2.37687	+	1.14464i	0.0784057	+	0.0377582i	−0.394270	+	0.918995i	$0.629003\pi$
$920$	34.1370	+	6.45907i	1.12546	+	0.212949i
$921$	0.153061	−	4.06052i	0.00504353	−	0.133799i
$922$	−3.99974	+	10.1912i	−0.131725	+	0.335629i
$923$	2.35977	−	15.6561i	0.0776728	−	0.515325i
$924$	12.9738	+	1.46544i	0.426806	+	0.0482093i
$925$	−0.510057	−	13.6316i	−0.0167706	−	0.448203i
$926$	−0.746725	−	6.62737i	−0.0245389	−	0.217789i
$927$	19.3717	−	24.2637i	0.636249	−	0.796925i
$928$	19.6345	−	22.0957i	0.644533	−	0.725326i
$929$	−8.30673	−	4.79589i	−0.272535	−	0.157348i	0.357504	−	0.933912i	$-0.383628\pi$
$929$	−8.30673	−	4.79589i	−0.272535	−	0.157348i	−0.630039	+	0.776563i	$0.716961\pi$
$930$	6.23082	+	5.78457i	0.204317	+	0.189684i
$931$	17.7191	−	33.5262i	0.580721	−	1.09878i
$932$	23.0202	−	21.3596i	0.754052	−	0.699658i
$933$	−0.415878	−	11.1976i	−0.0136152	−	0.366594i
$934$	−1.82208	−	12.0887i	−0.0596204	−	0.395555i
$935$	−9.06606	−	2.06927i	−0.296492	−	0.0676723i
$936$	−22.1872	−	7.77744i	−0.725211	−	0.254214i
$937$	−5.49690	+	11.4144i	−0.179576	+	0.372893i	−0.971254	−	0.238045i	$-0.923493\pi$
$937$	−5.49690	+	11.4144i	−0.179576	+	0.372893i	0.791678	+	0.610938i	$0.209208\pi$
$938$	−20.0856	+	10.6155i	−0.655817	+	0.346609i
$939$	21.6734	−	27.1621i	0.707285	−	0.886403i
$940$	1.29328	−	4.82658i	0.0421821	−	0.157426i
$941$	27.9758	+	19.0736i	0.911986	+	0.621781i	0.925755	−	0.378124i	$-0.123431\pi$
$941$	27.9758	+	19.0736i	0.911986	+	0.621781i	−0.0137692	+	0.999905i	$0.504383\pi$
$942$	4.37302	−	0.326494i	0.142481	−	0.0106377i
$943$	51.8924	+	38.2983i	1.68985	+	1.24717i
$944$	−7.72290	−	16.0368i	−0.251359	−	0.521952i
$945$	7.43841	−	32.4654i	0.241972	−	1.05610i
$946$	−1.58148	−	0.553383i	−0.0514182	−	0.0179920i
$947$	0.835381	+	1.58062i	0.0271462	+	0.0513632i	0.897315	−	0.441390i	$-0.145514\pi$
$947$	0.835381	+	1.58062i	0.0271462	+	0.0513632i	−0.870169	+	0.492753i	$0.835991\pi$
$948$	−1.34340	+	5.00810i	−0.0436318	+	0.162656i
$949$	23.8771	+	20.5479i	0.775084	+	0.667013i
$950$	−6.60396	+	2.03705i	−0.214261	+	0.0660907i
$951$	18.6288	−	6.51272i	0.604081	−	0.211189i
$952$	11.0543	+	28.1658i	0.358270	+	0.912858i
$953$	12.7383	−	2.90744i	0.412635	−	0.0941812i	−0.0111637	−	0.999938i	$-0.503554\pi$
$953$	12.7383	−	2.90744i	0.412635	−	0.0941812i	0.423799	+	0.905756i	$0.360696\pi$
$954$	5.88326	+	13.5050i	0.190478	+	0.437241i
$955$	−11.2069	+	1.26272i	−0.362647	+	0.0408605i
$956$	−8.17857	+	14.1657i	−0.264514	+	0.458151i
$957$	11.2517	+	4.14247i	0.363715	+	0.133907i
$958$	−3.74866	−	6.49287i	−0.121114	−	0.209775i
$959$	2.19746	+	2.97746i	0.0709598	+	0.0961471i
$960$	−0.840536	+	2.72227i	−0.0271282	+	0.0878610i
$961$	−2.82327	+	9.15283i	−0.0910733	+	0.295253i
$962$	10.6048	−	13.2980i	0.341913	−	0.428745i
$963$	−9.34317	−	5.40119i	−0.301079	−	0.174051i
$964$	−1.18443	+	5.18933i	−0.0381480	+	0.167137i
$965$	5.53257	−	29.2403i	0.178100	−	0.941280i
$966$	22.7335	−	22.7209i	0.731437	−	0.731032i
$967$	−17.2340	−	0.644851i	−0.554208	−	0.0207370i	−0.241179	−	0.970481i	$-0.577534\pi$
$967$	−17.2340	−	0.644851i	−0.554208	−	0.0207370i	−0.313029	+	0.949744i	$0.601344\pi$
$968$	−3.72102	−	19.6661i	−0.119598	−	0.632092i
$969$	−39.2468	−	26.7739i	−1.26079	−	0.860103i
$970$	−1.85081	−	0.138699i	−0.0594258	−	0.00445335i
$971$	−2.65467	+	23.5608i	−0.0851923	+	0.756102i	0.876393	+	0.481596i	$0.159943\pi$
$971$	−2.65467	+	23.5608i	−0.0851923	+	0.756102i	−0.961585	+	0.274506i	$0.911486\pi$
$972$	25.1779	+	5.78340i	0.807581	+	0.185503i
$973$	−11.0432	+	5.31812i	−0.354029	+	0.170491i
$974$	−14.5893	+	3.90920i	−0.467473	+	0.125259i
$975$	−1.62679	+	10.7728i	−0.0520988	+	0.345004i
$976$	−1.04354	+	27.8891i	−0.0334028	+	0.892709i
$977$	−45.2855	+	3.39368i	−1.44881	+	0.108573i	−0.775763	−	0.631024i	$-0.782635\pi$
$977$	−45.2855	+	3.39368i	−1.44881	+	0.108573i	−0.673049	+	0.739598i	$0.735016\pi$
$978$	−0.00109458	+	3.94986i	−3.50008e−5	+	0.126303i
$979$	1.89293	−	2.04010i	0.0604984	−	0.0652018i
$980$	12.9580	−	10.3336i	0.413927	−	0.330096i
$981$	−13.8608	+	44.8472i	−0.442540	+	1.43186i
$982$	4.13359	+	18.1104i	0.131908	+	0.577927i
$983$	−41.2564	+	1.54371i	−1.31587	+	0.0492366i	−0.686081	−	0.727526i	$-0.740670\pi$
$983$	−41.2564	+	1.54371i	−1.31587	+	0.0492366i	−0.629794	+	0.776762i	$0.716861\pi$
$984$	18.1683	−	19.5699i	0.579185	−	0.623866i
$985$	−16.0947	+	9.29229i	−0.512820	+	0.296077i
$986$	1.67854	+	12.4786i	0.0534556	+	0.397400i
$987$	−6.65215	−	7.73428i	−0.211740	−	0.246185i
$988$	38.1854	+	16.6601i	1.21484	+	0.530029i
$989$	16.8849	−	10.6095i	0.536908	−	0.337362i
$990$	4.07867	−	0.303381i	0.129629	−	0.00964207i
$991$	−15.2058	−	12.1262i	−0.483028	−	0.385202i	0.351482	−	0.936195i	$-0.385678\pi$
$991$	−15.2058	−	12.1262i	−0.483028	−	0.385202i	−0.834510	+	0.550993i	$0.814249\pi$
$992$	−25.1211	+	3.78639i	−0.797595	+	0.120218i
$993$	−2.03297	+	3.23347i	−0.0645144	+	0.102611i
$994$	5.84564	−	6.79276i	0.185412	−	0.215453i
$995$	2.59515	+	34.6298i	0.0822716	+	1.09784i
$996$	1.07710	−	2.74217i	0.0341292	−	0.0868889i
$997$	−6.74063	−	7.83275i	−0.213478	−	0.248066i	0.641016	−	0.767528i	$-0.278513\pi$
$997$	−6.74063	−	7.83275i	−0.213478	−	0.248066i	−0.854494	+	0.519462i	$0.826132\pi$
$998$	2.87841	−	2.87841i	0.0911144	−	0.0911144i
$999$	−21.9721	+	34.9039i	−0.695166	+	1.10431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.101.13	yes	672
3.2	odd	2		783.2.be.a.710.16		672
9.4	even	3		783.2.be.a.449.13		672
9.5	odd	6	inner	261.2.x.a.14.16	✓	672
29.27	odd	28	inner	261.2.x.a.56.16	yes	672
87.56	even	28		783.2.be.a.143.13		672
261.85	odd	84		783.2.be.a.665.16		672
261.230	even	84	inner	261.2.x.a.230.13	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.14.16	✓	672	9.5	odd	6	inner
261.2.x.a.56.16	yes	672	29.27	odd	28	inner
261.2.x.a.101.13	yes	672	1.1	even	1	trivial
261.2.x.a.230.13	yes	672	261.230	even	84	inner
783.2.be.a.143.13		672	87.56	even	28
783.2.be.a.449.13		672	9.4	even	3
783.2.be.a.665.16		672	261.85	odd	84
783.2.be.a.710.16		672	3.2	odd	2

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.234125 + 0.536620i) q^{2} +(-1.27001 + 1.17774i) q^{3} +(1.12720 + 1.21483i) q^{4} +(-1.79123 - 0.269985i) q^{5} +(-0.334659 - 0.957252i) q^{6} +(2.59390 + 2.40679i) q^{7} +(-2.02104 + 0.707193i) q^{8} +(0.225848 - 2.99149i) q^{9} +(0.564252 - 0.898002i) q^{10} +(-0.974345 + 0.838491i) q^{11} +(-2.86231 - 0.215298i) q^{12} +(-2.06180 + 3.02410i) q^{13} +(-1.89883 + 0.828450i) q^{14} +(2.59286 - 1.76673i) q^{15} +(-0.154007 + 2.05508i) q^{16} +(-2.82385 - 2.82385i) q^{17} +(1.55242 + 0.821577i) q^{18} +(-5.81575 - 3.65428i) q^{19} +(-1.69109 - 2.48037i) q^{20} +(-6.12885 - 0.00169842i) q^{21} +(-0.221833 - 0.719165i) q^{22} +(8.33810 + 3.27246i) q^{23} +(1.73385 - 3.27841i) q^{24} +(-1.64224 - 0.506563i) q^{25} +(-1.14008 - 1.81442i) q^{26} +(3.23637 + 4.06521i) q^{27} +5.86408i q^{28} +(-1.28158 + 5.23045i) q^{29} +(0.341009 + 1.80501i) q^{30} +(3.72396 - 2.74841i) q^{31} +(-4.85287 - 2.56482i) q^{32} +(0.249901 - 2.21242i) q^{33} +(2.17647 - 0.854200i) q^{34} +(-3.99648 - 5.01143i) q^{35} +(3.88873 - 3.09763i) q^{36} +(2.62155 + 7.49197i) q^{37} +(3.32257 - 2.26529i) q^{38} +(-0.943108 - 6.26890i) q^{39} +(3.81109 - 0.721097i) q^{40} +(6.95493 + 1.86357i) q^{41} +(1.43583 - 3.28847i) q^{42} +(1.32201 - 1.79126i) q^{43} +(-2.11691 - 0.238518i) q^{44} +(-1.21220 + 5.29748i) q^{45} +(-3.70823 + 3.70823i) q^{46} +(1.08573 + 1.26165i) q^{47} +(-2.22476 - 2.79135i) q^{48} +(0.412579 + 5.50549i) q^{49} +(0.656321 - 0.762658i) q^{50} +(6.91208 + 0.260550i) q^{51} +(-5.99783 + 0.904027i) q^{52} +(6.55714 + 5.22915i) q^{53} +(-2.93919 + 0.784935i) q^{54} +(1.97166 - 1.23888i) q^{55} +(-6.94443 - 3.02983i) q^{56} +(11.6899 - 2.20848i) q^{57} +(-2.50671 - 1.91230i) q^{58} +(-7.47986 + 4.31850i) q^{59} +(5.06894 + 1.15843i) q^{60} +(13.5329 - 0.506365i) q^{61} +(0.602979 + 2.64182i) q^{62} +(7.78570 - 7.21604i) q^{63} +(-0.709949 + 0.566166i) q^{64} +(4.50962 - 4.86022i) q^{65} +(1.12872 + 0.652084i) q^{66} +(10.9354 - 0.819497i) q^{67} +(0.247461 - 6.61353i) q^{68} +(-14.4436 + 5.66407i) q^{69} +(3.62491 - 0.971292i) q^{70} +(-3.89744 + 1.87691i) q^{71} +(1.65911 + 6.20563i) q^{72} +(0.963648 - 8.55261i) q^{73} +(-4.63411 - 0.347279i) q^{74} +(2.68226 - 1.29079i) q^{75} +(-2.11617 - 11.1843i) q^{76} +(-4.54542 - 0.170078i) q^{77} +(3.58482 + 0.961615i) q^{78} +(0.335835 - 1.77493i) q^{79} +(0.830703 - 3.63955i) q^{80} +(-8.89799 - 1.35124i) q^{81} +(-2.62835 + 3.29585i) q^{82} +(-0.302531 + 0.980782i) q^{83} +(-6.90637 - 7.44743i) q^{84} +(4.29577 + 5.82057i) q^{85} +(0.651711 + 1.12880i) q^{86} +(-4.53250 - 8.15208i) q^{87} +(1.37622 - 2.38367i) q^{88} +(-2.15138 + 0.242402i) q^{89} +(-2.55893 - 1.89077i) q^{90} +(-12.6265 + 2.88191i) q^{91} +(5.42320 + 13.8181i) q^{92} +(-1.49255 + 7.87637i) q^{93} +(-0.931222 + 0.287244i) q^{94} +(9.43077 + 8.11583i) q^{95} +(9.18388 - 2.45809i) q^{96} +(-0.817727 - 1.54721i) q^{97} +(-3.05095 - 1.06757i) q^{98} +(2.28828 + 3.10411i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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