LMFDB - Embedded newform 961.2.g.j.846.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(235,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([26])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.235"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-6,-3,-14,-3,-11,-13] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			846.1
Root			$-1.14660i$ of defining polynomial
Character	$\chi$	$=$	961.846
Dual form			961.2.g.j.844.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.831304 + 2.55849i) q^{2} +(1.38815 + 0.295061i) q^{3} +(-4.23677 - 3.07819i) q^{4} +(-0.304192 - 0.526876i) q^{5} +(-1.90889 + 3.30629i) q^{6} +(-1.57758 + 0.702385i) q^{7} +(7.04481 - 5.11835i) q^{8} +(-0.900731 - 0.401031i) q^{9} +(1.60088 - 0.340278i) q^{10} +(-0.139796 + 1.33007i) q^{11} +(-4.97303 - 5.52311i) q^{12} +(-2.45615 + 2.72784i) q^{13} +(-0.485595 - 4.62012i) q^{14} +(-0.266804 - 0.821139i) q^{15} +(4.00227 + 12.3177i) q^{16} +(-0.288793 - 2.74768i) q^{17} +(1.77482 - 1.97113i) q^{18} +(-1.71811 - 1.90816i) q^{19} +(-0.333035 + 3.16861i) q^{20} +(-2.39717 + 0.509534i) q^{21} +(-3.28675 - 1.46335i) q^{22} +(-0.436271 + 0.316969i) q^{23} +(11.2895 - 5.02641i) q^{24} +(2.31493 - 4.00958i) q^{25} +(-4.93733 - 8.55171i) q^{26} +(-4.57641 - 3.32495i) q^{27} +(8.84593 + 1.88026i) q^{28} +(2.51258 - 7.73291i) q^{29} +2.32267 q^{30} -17.4262 q^{32} +(-0.586508 + 1.80509i) q^{33} +(7.27000 + 1.54529i) q^{34} +(0.849957 + 0.617530i) q^{35} +(2.58174 + 4.47170i) q^{36} +(3.87249 - 6.70735i) q^{37} +(6.31027 - 2.80951i) q^{38} +(-4.21439 + 3.06194i) q^{39} +(-4.83971 - 2.15478i) q^{40} +(0.101778 - 0.0216336i) q^{41} +(0.689139 - 6.55671i) q^{42} +(2.01054 + 2.23293i) q^{43} +(4.68648 - 5.20487i) q^{44} +(0.0627014 + 0.596564i) q^{45} +(-0.448289 - 1.37969i) q^{46} +(-2.07813 - 6.39584i) q^{47} +(1.92128 + 18.2798i) q^{48} +(-2.68849 + 2.98587i) q^{49} +(8.33407 + 9.25592i) q^{50} +(0.409845 - 3.89942i) q^{51} +(18.8030 - 3.99669i) q^{52} +(-2.55678 - 1.13835i) q^{53} +(12.3112 - 8.94464i) q^{54} +(0.743304 - 0.330940i) q^{55} +(-7.51871 + 13.0228i) q^{56} +(-1.82198 - 3.15576i) q^{57} +(17.6959 + 12.8568i) q^{58} +(-0.456044 - 0.0969352i) q^{59} +(-1.39724 + 4.30025i) q^{60} +5.11468 q^{61} +1.70266 q^{63} +(6.48190 - 19.9492i) q^{64} +(2.18437 + 0.464303i) q^{65} +(-4.13073 - 3.00115i) q^{66} +(-4.14923 - 7.18668i) q^{67} +(-7.23436 + 12.5303i) q^{68} +(-0.699136 + 0.311275i) q^{69} +(-2.28652 + 1.66125i) q^{70} +(4.34730 + 1.93554i) q^{71} +(-8.39810 + 1.78507i) q^{72} +(0.784611 - 7.46507i) q^{73} +(13.9415 + 15.4836i) q^{74} +(4.39655 - 4.88287i) q^{75} +(1.40557 + 13.3731i) q^{76} +(-0.713679 - 2.19648i) q^{77} +(-4.33049 - 13.3279i) q^{78} +(-1.01382 - 9.64582i) q^{79} +(5.27246 - 5.85566i) q^{80} +(-3.39245 - 3.76770i) q^{81} +(-0.0292592 + 0.278382i) q^{82} +(-16.3200 + 3.46892i) q^{83} +(11.7247 + 5.22018i) q^{84} +(-1.35984 + 0.987981i) q^{85} +(-7.38430 + 3.28770i) q^{86} +(5.76952 - 9.99310i) q^{87} +(5.82292 + 10.0856i) q^{88} +(-12.3911 - 9.00268i) q^{89} +(-1.57843 - 0.335505i) q^{90} +(1.95880 - 6.02855i) q^{91} +2.82407 q^{92} +18.0912 q^{94} +(-0.482726 + 1.48568i) q^{95} +(-24.1902 - 5.14178i) q^{96} +(1.03488 + 0.751881i) q^{97} +(-5.40437 - 9.36065i) q^{98} +(0.659316 - 1.14197i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 3 q^{3} - 14 q^{4} - 3 q^{5} - 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9} - 17 q^{10} + 7 q^{11} + 10 q^{12} - 8 q^{13} - 21 q^{14} - 14 q^{15} - 2 q^{16} - 9 q^{17} + 12 q^{18} - 29 q^{19}+ \cdots - 6 q^{99}+O(q^{100}) $ 16 * q - 6 * q^2 - 3 * q^3 - 14 * q^4 - 3 * q^5 - 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9 - 17 * q^10 + 7 * q^11 + 10 * q^12 - 8 * q^13 - 21 * q^14 - 14 * q^15 - 2 * q^16 - 9 * q^17 + 12 * q^18 - 29 * q^19 - 8 * q^20 + 6 * q^21 + 21 * q^22 - q^23 + 5 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 + 45 * q^28 + 14 * q^29 + 22 * q^30 - 42 * q^32 - 13 * q^33 + 17 * q^34 - 9 * q^35 + q^36 + 8 * q^37 + 23 * q^38 - 3 * q^39 - q^40 - 8 * q^41 + 51 * q^42 + 37 * q^43 + 6 * q^44 - 70 * q^45 - 34 * q^46 + 14 * q^47 - 4 * q^48 - 43 * q^49 + 3 * q^50 + 33 * q^51 + 46 * q^52 + 9 * q^53 + 46 * q^54 - 8 * q^55 - 30 * q^56 + 17 * q^57 + 15 * q^58 - 11 * q^59 + 75 * q^60 + 60 * q^61 - 46 * q^63 + 23 * q^64 - 18 * q^65 - 30 * q^66 + 13 * q^67 - 30 * q^68 - 37 * q^69 + 12 * q^70 + 31 * q^71 - 38 * q^72 + 13 * q^73 - 43 * q^74 + 17 * q^75 - 12 * q^76 - 18 * q^77 - 15 * q^78 + 12 * q^79 + 6 * q^80 - 22 * q^81 - q^82 - 44 * q^83 - 23 * q^84 - 37 * q^85 - 19 * q^86 + 15 * q^87 + 17 * q^88 - q^89 + 7 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 - 22 * q^95 - 8 * q^96 + 3 * q^97 - 10 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{15}\right)$

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 $

$2$	−0.831304	+	2.55849i	−0.587821	+	1.80913i	−0.000184800		1.00000i	$0.500059\pi$
$2$	−0.831304	+	2.55849i	−0.587821	+	1.80913i	−0.587636	+	0.809126i	$0.699941\pi$
$3$	1.38815	+	0.295061i	0.801450	+	0.170353i	0.590388	−	0.807119i	$-0.298975\pi$
$3$	1.38815	+	0.295061i	0.801450	+	0.170353i	0.211062	+	0.977473i	$0.432308\pi$
$4$	−4.23677	−	3.07819i	−2.11839	−	1.53910i
$5$	−0.304192	−	0.526876i	−0.136039	−	0.235626i	0.789955	−	0.613165i	$-0.210104\pi$
$5$	−0.304192	−	0.526876i	−0.136039	−	0.235626i	−0.925994	+	0.377539i	$0.876770\pi$
$6$	−1.90889	+	3.30629i	−0.779300	+	1.34979i
$7$	−1.57758	+	0.702385i	−0.596270	+	0.265477i	−0.682603	−	0.730790i	$-0.739152\pi$
$7$	−1.57758	+	0.702385i	−0.596270	+	0.265477i	0.0863324	+	0.996266i	$0.472485\pi$
$8$	7.04481	−	5.11835i	2.49072	−	1.80961i
$9$	−0.900731	−	0.401031i	−0.300244	−	0.133677i
$10$	1.60088	−	0.340278i	0.506243	−	0.107605i
$11$	−0.139796	+	1.33007i	−0.0421500	+	0.401030i	0.953023	+	0.302897i	$0.0979538\pi$
$11$	−0.139796	+	1.33007i	−0.0421500	+	0.401030i	−0.995173	+	0.0981331i	$0.968713\pi$
$12$	−4.97303	−	5.52311i	−1.43559	−	1.59438i
$13$	−2.45615	+	2.72784i	−0.681215	+	0.756566i	−0.980268	−	0.197671i	$-0.936662\pi$
$13$	−2.45615	+	2.72784i	−0.681215	+	0.756566i	0.299054	+	0.954236i	$0.403329\pi$
$14$	−0.485595	−	4.62012i	−0.129781	−	1.23478i
$15$	−0.266804	−	0.821139i	−0.0688885	−	0.212017i
$16$	4.00227	+	12.3177i	1.00057	+	3.07943i
$17$	−0.288793	−	2.74768i	−0.0700427	−	0.666411i	−0.972063	−	0.234719i	$-0.924583\pi$
$17$	−0.288793	−	2.74768i	−0.0700427	−	0.666411i	0.902021	−	0.431693i	$-0.142084\pi$
$18$	1.77482	−	1.97113i	0.418328	−	0.464600i
$19$	−1.71811	−	1.90816i	−0.394162	−	0.437761i	0.513099	−	0.858329i	$-0.328497\pi$
$19$	−1.71811	−	1.90816i	−0.394162	−	0.437761i	−0.907261	+	0.420568i	$0.861831\pi$
$20$	−0.333035	+	3.16861i	−0.0744688	+	0.708524i
$21$	−2.39717	+	0.509534i	−0.523106	+	0.111190i
$22$	−3.28675	−	1.46335i	−0.700737	−	0.311988i
$23$	−0.436271	+	0.316969i	−0.0909688	+	0.0660927i	−0.632340	−	0.774691i	$-0.717905\pi$
$23$	−0.436271	+	0.316969i	−0.0909688	+	0.0660927i	0.541371	+	0.840784i	$0.317905\pi$
$24$	11.2895	−	5.02641i	2.30446	−	1.02601i
$25$	2.31493	−	4.00958i	0.462987	−	0.801917i
$26$	−4.93733	−	8.55171i	−0.968290	−	1.67713i
$27$	−4.57641	−	3.32495i	−0.880730	−	0.639888i
$28$	8.84593	+	1.88026i	1.67172	+	0.355336i
$29$	2.51258	−	7.73291i	0.466574	−	1.43597i	−0.390419	−	0.920637i	$-0.627670\pi$
$29$	2.51258	−	7.73291i	0.466574	−	1.43597i	0.856993	−	0.515329i	$-0.172330\pi$
$30$	2.32267			0.424060
$31$		0			0
$31$		0			0
$32$	−17.4262			−3.08054
$33$	−0.586508	+	1.80509i	−0.102098	+	0.314225i
$34$	7.27000	+	1.54529i	1.24679	+	0.265014i
$35$	0.849957	+	0.617530i	0.143669	+	0.104382i
$36$	2.58174	+	4.47170i	0.430290	+	0.745284i
$37$	3.87249	−	6.70735i	0.636633	−	1.10268i	−0.349533	−	0.936924i	$-0.613660\pi$
$37$	3.87249	−	6.70735i	0.636633	−	1.10268i	0.986167	−	0.165757i	$-0.0530068\pi$
$38$	6.31027	−	2.80951i	1.02366	−	0.455763i
$39$	−4.21439	+	3.06194i	−0.674843	+	0.490302i
$40$	−4.83971	−	2.15478i	−0.765225	−	0.340700i
$41$	0.101778	−	0.0216336i	0.0158951	−	0.00337860i	−0.199957	−	0.979805i	$-0.564080\pi$
$41$	0.101778	−	0.0216336i	0.0158951	−	0.00337860i	0.215852	+	0.976426i	$0.430747\pi$
$42$	0.689139	−	6.55671i	0.106336	−	1.01172i
$43$	2.01054	+	2.23293i	0.306604	+	0.340519i	0.876680	−	0.481073i	$-0.159753\pi$
$43$	2.01054	+	2.23293i	0.306604	+	0.340519i	−0.570076	+	0.821592i	$0.693086\pi$
$44$	4.68648	−	5.20487i	0.706514	−	0.784663i
$45$	0.0627014	+	0.596564i	0.00934697	+	0.0889305i
$46$	−0.448289	−	1.37969i	−0.0660967	−	0.203425i
$47$	−2.07813	−	6.39584i	−0.303127	−	0.932929i	−0.980370	−	0.197169i	$-0.936825\pi$
$47$	−2.07813	−	6.39584i	−0.303127	−	0.932929i	0.677243	−	0.735760i	$-0.263175\pi$
$48$	1.92128	+	18.2798i	0.277314	+	2.63846i
$49$	−2.68849	+	2.98587i	−0.384070	+	0.426553i
$50$	8.33407	+	9.25592i	1.17862	+	1.30898i
$51$	0.409845	−	3.89942i	0.0573898	−	0.546027i
$52$	18.8030	−	3.99669i	2.60750	−	0.554242i
$53$	−2.55678	−	1.13835i	−0.351201	−	0.156365i	0.223551	−	0.974692i	$-0.428235\pi$
$53$	−2.55678	−	1.13835i	−0.351201	−	0.156365i	−0.574752	+	0.818327i	$0.694902\pi$
$54$	12.3112	−	8.94464i	1.67535	−	1.21721i
$55$	0.743304	−	0.330940i	0.100227	−	0.0446240i
$56$	−7.51871	+	13.0228i	−1.00473	+	1.74024i
$57$	−1.82198	−	3.15576i	−0.241327	−	0.417990i
$58$	17.6959	+	12.8568i	2.32358	+	1.68818i
$59$	−0.456044	−	0.0969352i	−0.0593719	−	0.0126199i	0.178130	−	0.984007i	$-0.442995\pi$
$59$	−0.456044	−	0.0969352i	−0.0593719	−	0.0126199i	−0.237502	+	0.971387i	$0.576329\pi$
$60$	−1.39724	+	4.30025i	−0.180382	+	0.555160i
$61$	5.11468			0.654867			0.327434	−	0.944874i	$-0.393816\pi$
$61$	5.11468			0.654867			0.327434	+	0.944874i	$0.393816\pi$
$62$		0			0
$63$	1.70266			0.214514
$64$	6.48190	−	19.9492i	0.810238	−	2.49365i
$65$	2.18437	+	0.464303i	0.270938	+	0.0575897i
$66$	−4.13073	−	3.00115i	−0.508457	−	0.369416i
$67$	−4.14923	−	7.18668i	−0.506910	−	0.877993i	−0.999968	−	0.00799701i	$-0.997454\pi$
$67$	−4.14923	−	7.18668i	−0.506910	−	0.877993i	0.493058	−	0.869996i	$-0.335879\pi$
$68$	−7.23436	+	12.5303i	−0.877294	+	1.51952i
$69$	−0.699136	+	0.311275i	−0.0841661	+	0.0374731i
$70$	−2.28652	+	1.66125i	−0.273291	+	0.198558i
$71$	4.34730	+	1.93554i	0.515929	+	0.229706i	0.648148	−	0.761514i	$-0.275544\pi$
$71$	4.34730	+	1.93554i	0.515929	+	0.229706i	−0.132219	+	0.991220i	$0.542210\pi$
$72$	−8.39810	+	1.78507i	−0.989725	+	0.210373i
$73$	0.784611	−	7.46507i	0.0918317	−	0.873720i	−0.847520	−	0.530764i	$-0.821905\pi$
$73$	0.784611	−	7.46507i	0.0918317	−	0.873720i	0.939351	−	0.342956i	$-0.111428\pi$
$74$	13.9415	+	15.4836i	1.62066	+	1.79993i
$75$	4.39655	−	4.88287i	0.507670	−	0.563825i
$76$	1.40557	+	13.3731i	0.161230	+	1.53400i
$77$	−0.713679	−	2.19648i	−0.0813313	−	0.250312i
$78$	−4.33049	−	13.3279i	−0.490332	−	1.50909i
$79$	−1.01382	−	9.64582i	−0.114063	−	1.08524i	−0.890481	−	0.455021i	$-0.849632\pi$
$79$	−1.01382	−	9.64582i	−0.114063	−	1.08524i	0.776417	−	0.630219i	$-0.217035\pi$
$80$	5.27246	−	5.85566i	0.589479	−	0.654682i
$81$	−3.39245	−	3.76770i	−0.376939	−	0.418633i
$82$	−0.0292592	+	0.278382i	−0.00323113	+	0.0307422i
$83$	−16.3200	+	3.46892i	−1.79135	+	0.380764i	−0.979234	−	0.202731i	$-0.935018\pi$
$83$	−16.3200	+	3.46892i	−1.79135	+	0.380764i	−0.812117	+	0.583495i	$0.801685\pi$
$84$	11.7247	+	5.22018i	1.27927	+	0.569568i
$85$	−1.35984	+	0.987981i	−0.147495	+	0.107162i
$86$	−7.38430	+	3.28770i	−0.796269	+	0.354522i
$87$	5.76952	−	9.99310i	0.618557	−	1.07137i
$88$	5.82292	+	10.0856i	0.620725	+	1.07513i
$89$	−12.3911	−	9.00268i	−1.31346	−	0.954282i	−0.999989	−	0.00468333i	$-0.998509\pi$
$89$	−12.3911	−	9.00268i	−1.31346	−	0.954282i	−0.313468	−	0.949599i	$-0.601491\pi$
$90$	−1.57843	−	0.335505i	−0.166381	−	0.0353653i
$91$	1.95880	−	6.02855i	0.205338	−	0.631964i
$92$	2.82407			0.294430
$93$		0			0
$94$	18.0912			1.86597
$95$	−0.482726	+	1.48568i	−0.0495266	+	0.152427i
$96$	−24.1902	−	5.14178i	−2.46890	−	0.524781i
$97$	1.03488	+	0.751881i	0.105076	+	0.0763420i	0.639082	−	0.769138i	$-0.279314\pi$
$97$	1.03488	+	0.751881i	0.105076	+	0.0763420i	−0.534007	+	0.845480i	$0.679314\pi$
$98$	−5.40437	−	9.36065i	−0.545924	−	0.945568i
$99$	0.659316	−	1.14197i	0.0662638	−	0.114772i
$100$	−22.1501	+	9.86187i	−2.21501	+	0.986187i
$101$	−6.56941	+	4.77296i	−0.653681	+	0.474927i	−0.864523	−	0.502593i	$-0.832379\pi$
$101$	−6.56941	+	4.77296i	−0.653681	+	0.474927i	0.210842	+	0.977520i	$0.432379\pi$
$102$	9.63591	+	4.29018i	0.954097	+	0.424791i
$103$	−14.8214	+	3.15038i	−1.46040	+	0.310417i	−0.868536	−	0.495625i	$-0.834939\pi$
$103$	−14.8214	+	3.15038i	−1.46040	+	0.310417i	−0.591859	+	0.806042i	$0.701606\pi$
$104$	−3.34111	+	31.7885i	−0.327623	+	3.11712i
$105$	0.997661	+	1.10801i	0.0973618	+	0.108131i
$106$	5.03792	−	5.59518i	0.489327	−	0.543452i
$107$	1.29360	+	12.3078i	0.125057	+	1.18984i	0.859487	+	0.511157i	$0.170783\pi$
$107$	1.29360	+	12.3078i	0.125057	+	1.18984i	−0.734430	+	0.678685i	$0.762550\pi$
$108$	9.15433	+	28.1741i	0.880876	+	2.71106i
$109$	2.22788	+	6.85672i	0.213392	+	0.656755i	0.999264	+	0.0383645i	$0.0122148\pi$
$109$	2.22788	+	6.85672i	0.213392	+	0.656755i	−0.785871	+	0.618390i	$0.787785\pi$
$110$	0.228796	+	2.17685i	0.0218148	+	0.207554i
$111$	7.35468	−	8.16820i	0.698075	−	0.775291i
$112$	−14.9657	−	16.6211i	−1.41413	−	1.57055i
$113$	−1.74268	+	16.5805i	−0.163937	+	1.55976i	0.535171	+	0.844744i	$0.320247\pi$
$113$	−1.74268	+	16.5805i	−0.163937	+	1.55976i	−0.699108	+	0.715016i	$0.746420\pi$
$114$	9.58859	−	2.03812i	0.898054	−	0.190887i
$115$	0.299714	+	0.133441i	0.0279484	+	0.0124434i
$116$	−34.4486	+	25.0284i	−3.19847	+	2.32383i
$117$	3.30628	−	1.47205i	0.305666	−	0.136091i
$118$	0.627119	−	1.08620i	0.0577310	−	0.0999930i
$119$	2.38553	+	4.13185i	0.218681	+	0.378767i
$120$	−6.08246	−	4.41917i	−0.555250	−	0.403413i
$121$	9.01009	+	1.91515i	0.819099	+	0.174105i
$122$	−4.25185	+	13.0859i	−0.384944	+	1.18474i
$123$	0.147667			0.0133147
$124$		0			0
$125$	−5.85866			−0.524014
$126$	−1.41542	+	4.35623i	−0.126096	+	0.388084i
$127$	−12.6273	−	2.68402i	−1.12049	−	0.238168i	−0.389818	−	0.920892i	$-0.627462\pi$
$127$	−12.6273	−	2.68402i	−1.12049	−	0.238168i	−0.730677	+	0.682724i	$0.760795\pi$
$128$	17.4553	+	12.6820i	1.54285	+	1.12095i
$129$	2.13208	+	3.69288i	0.187720	+	0.325140i
$130$	−3.00379	+	5.20272i	−0.263450	+	0.456309i
$131$	−2.22703	+	0.991536i	−0.194576	+	0.0866309i	−0.501712	−	0.865035i	$-0.667296\pi$
$131$	−2.22703	+	0.991536i	−0.194576	+	0.0866309i	0.307136	+	0.951666i	$0.400630\pi$
$132$	8.04130	−	5.84235i	0.699906	−	0.508511i
$133$	4.05072	+	1.80350i	0.351242	+	0.156383i
$134$	21.8363	−	4.64146i	1.88637	−	0.400961i
$135$	−0.359732	+	3.42262i	−0.0309608	+	0.294572i
$136$	−16.0981	−	17.8788i	−1.38040	−	1.53309i
$137$	−5.44928	+	6.05204i	−0.465564	+	0.517061i	−0.929507	−	0.368804i	$-0.879767\pi$
$137$	−5.44928	+	6.05204i	−0.465564	+	0.517061i	0.463944	+	0.885865i	$0.346434\pi$
$138$	−0.215201	−	2.04750i	−0.0183191	−	0.174294i
$139$	0.418212	+	1.28712i	0.0354723	+	0.109172i	0.967225	−	0.253921i	$-0.0817204\pi$
$139$	0.418212	+	1.28712i	0.0354723	+	0.109172i	−0.931753	+	0.363094i	$0.881720\pi$
$140$	−1.70020	−	5.23267i	−0.143693	−	0.442241i
$141$	−0.997604	−	9.49157i	−0.0840134	−	0.799334i
$142$	−8.56599	+	9.51349i	−0.718842	+	0.798354i
$143$	−3.28484	−	3.64819i	−0.274692	−	0.305077i
$144$	1.33482	−	12.7000i	0.111235	−	1.05833i
$145$	−4.83859	+	1.02847i	−0.401823	+	0.0854101i
$146$	18.4471	+	8.21316i	1.52669	+	0.679726i
$147$	−4.61305	+	3.35158i	−0.380478	+	0.276433i
$148$	−37.0534	+	16.4972i	−3.04577	+	1.35606i
$149$	4.50192	−	7.79756i	0.368812	−	0.638801i	−0.620568	−	0.784153i	$-0.713098\pi$
$149$	4.50192	−	7.79756i	0.368812	−	0.638801i	0.989380	+	0.145351i	$0.0464313\pi$
$150$	8.83789	+	15.3077i	0.721611	+	1.24987i
$151$	−2.59566	−	1.88585i	−0.211232	−	0.153469i	0.477139	−	0.878828i	$-0.341674\pi$
$151$	−2.59566	−	1.88585i	−0.211232	−	0.153469i	−0.688371	+	0.725359i	$0.741674\pi$
$152$	−21.8704	−	4.64869i	−1.77392	−	0.377059i
$153$	−0.841782	+	2.59074i	−0.0680541	+	0.209449i
$154$	6.21295			0.500654
$155$		0			0
$156$	27.2807			2.18420
$157$	−1.02803	+	3.16395i	−0.0820456	+	0.252510i	−0.983662	−	0.180027i	$-0.942382\pi$
$157$	−1.02803	+	3.16395i	−0.0820456	+	0.252510i	0.901616	+	0.432537i	$0.142382\pi$
$158$	25.5215	+	5.42477i	2.03038	+	0.431571i
$159$	−3.21332	−	2.33461i	−0.254833	−	0.185147i
$160$	5.30090	+	9.18143i	0.419073	+	0.725856i
$161$	0.465619	−	0.806476i	0.0366959	−	0.0635592i
$162$	12.4598	−	5.54745i	0.978933	−	0.435849i
$163$	−1.40797	+	1.02295i	−0.110281	+	0.0801236i	−0.641559	−	0.767074i	$-0.721712\pi$
$163$	−1.40797	+	1.02295i	−0.110281	+	0.0801236i	0.531278	+	0.847198i	$0.321712\pi$
$164$	−0.497803	−	0.221636i	−0.0388719	−	0.0173069i
$165$	1.12947	−	0.240076i	0.0879289	−	0.0186899i
$166$	4.69167	−	44.6383i	0.364144	−	3.46460i
$167$	9.37885	+	10.4163i	0.725757	+	0.806035i	0.987251	−	0.159170i	$-0.0508818\pi$
$167$	9.37885	+	10.4163i	0.725757	+	0.806035i	−0.261494	+	0.965205i	$0.584215\pi$
$168$	−14.2796	+	15.8591i	−1.10170	+	1.22356i
$169$	−0.0495237	−	0.471186i	−0.00380951	−	0.0362451i
$170$	−1.39730	−	4.30045i	−0.107168	−	0.329829i
$171$	0.782326	+	2.40775i	0.0598260	+	0.184125i
$172$	−1.64480	−	15.6492i	−0.125415	−	1.19324i
$173$	−0.00801678	+	0.00890353i	−0.000609504	+	0.000676923i	−0.743450	−	0.668792i	$-0.766812\pi$
$173$	−0.00801678	+	0.00890353i	−0.000609504	+	0.000676923i	0.742840	+	0.669469i	$0.233478\pi$
$174$	20.7710	+	23.0686i	1.57465	+	1.74882i
$175$	−0.835728	+	7.95143i	−0.0631751	+	0.601071i
$176$	−16.9429	+	3.60132i	−1.27712	+	0.271460i
$177$	−0.604457	−	0.269122i	−0.0454338	−	0.0202284i
$178$	33.3341	−	24.2186i	2.49849	−	1.81526i
$179$	9.11536	−	4.05842i	0.681314	−	0.303341i	−0.0367430	−	0.999325i	$-0.511698\pi$
$179$	9.11536	−	4.05842i	0.681314	−	0.303341i	0.718057	+	0.695984i	$0.245032\pi$
$180$	1.57069	−	2.72051i	0.117072	−	0.202775i
$181$	−9.30158	−	16.1108i	−0.691381	−	1.19751i	−0.971385	−	0.237509i	$-0.923669\pi$
$181$	−9.30158	−	16.1108i	−0.691381	−	1.19751i	0.280004	−	0.959999i	$-0.409664\pi$
$182$	13.7956	+	10.0231i	1.02260	+	0.742963i
$183$	7.09995	+	1.50914i	0.524843	+	0.111559i
$184$	−1.45108	+	4.46598i	−0.106975	+	0.329236i
$185$	−4.71192			−0.346427
$186$		0			0
$187$	3.69497			0.270203
$188$	−10.8831	+	33.4946i	−0.793728	+	2.44284i
$189$	9.55506	+	2.03099i	0.695028	+	0.147733i
$190$	−3.39980	−	2.47010i	−0.246647	−	0.179200i
$191$	−0.599059	−	1.03760i	−0.0433464	−	0.0750782i	0.843538	−	0.537069i	$-0.180469\pi$
$191$	−0.599059	−	1.03760i	−0.0433464	−	0.0750782i	−0.886885	+	0.461991i	$0.847135\pi$
$192$	14.8841	−	25.7800i	1.07417	−	1.86051i
$193$	11.6263	−	5.17636i	0.836879	−	0.372602i	0.0568780	−	0.998381i	$-0.481885\pi$
$193$	11.6263	−	5.17636i	0.836879	−	0.372602i	0.780001	+	0.625779i	$0.215219\pi$
$194$	−2.78398	+	2.02268i	−0.199878	+	0.145220i
$195$	2.89524	+	1.28905i	0.207333	+	0.0923105i
$196$	20.5816	−	4.37476i	1.47012	−	0.312483i
$197$	−0.310303	+	2.95233i	−0.0221082	+	0.210345i	0.977891	+	0.209115i	$0.0670583\pi$
$197$	−0.310303	+	2.95233i	−0.0221082	+	0.210345i	−0.999999	+	0.00123020i	$0.999608\pi$
$198$	2.37363	+	2.63618i	0.168686	+	0.187345i
$199$	8.82185	−	9.79766i	0.625365	−	0.694538i	−0.344333	−	0.938848i	$-0.611895\pi$
$199$	8.82185	−	9.79766i	0.625365	−	0.694538i	0.969697	+	0.244310i	$0.0785614\pi$
$200$	−4.21420	−	40.0954i	−0.297989	−	2.83517i
$201$	−3.63926	−	11.2005i	−0.256694	−	0.790021i
$202$	−6.75039	−	20.7755i	−0.474955	−	1.46176i
$203$	1.46769	+	13.9641i	0.103011	+	0.980088i
$204$	−13.7396	+	15.2593i	−0.961963	+	1.06837i
$205$	−0.0423583	−	0.0470436i	−0.00295843	−	0.00328567i
$206$	4.26085	−	40.5393i	0.296868	−	2.82451i
$207$	0.520078	−	0.110546i	0.0361479	−	0.00768347i
$208$	−43.4310	−	19.3367i	−3.01140	−	1.34076i
$209$	2.77816	−	2.01845i	0.192169	−	0.139619i
$210$	−3.66420	+	1.63141i	−0.252854	+	0.112578i
$211$	−9.16614	+	15.8762i	−0.631023	+	1.09296i	0.356320	+	0.934364i	$0.384031\pi$
$211$	−9.16614	+	15.8762i	−0.631023	+	1.09296i	−0.987343	+	0.158600i	$0.949302\pi$
$212$	7.32843	+	12.6932i	0.503318	+	0.871773i
$213$	5.46361	+	3.96954i	0.374360	+	0.271989i
$214$	−32.5648	−	6.92186i	−2.22608	−	0.473169i
$215$	0.564887	−	1.73854i	0.0385250	−	0.118568i
$216$	−49.2582			−3.35160
$217$		0			0
$218$	−19.3949			−1.31359
$219$	3.29181	−	10.1311i	0.222440	−	0.684599i
$220$	−4.16791	−	0.885916i	−0.281000	−	0.0597285i
$221$	8.20455	+	5.96096i	0.551898	+	0.400977i
$222$	14.7843	+	25.6071i	0.992256	+	1.71864i
$223$	4.69801	−	8.13718i	0.314602	−	0.544906i	−0.664751	−	0.747065i	$-0.731462\pi$
$223$	4.69801	−	8.13718i	0.314602	−	0.544906i	0.979353	+	0.202159i	$0.0647957\pi$
$224$	27.4912	−	12.2399i	1.83684	−	0.817812i
$225$	−3.69310	+	2.68320i	−0.246207	+	0.178880i
$226$	−40.9723	−	18.2420i	−2.72543	−	1.21344i
$227$	−8.27456	+	1.75881i	−0.549202	+	0.116737i	−0.474152	−	0.880443i	$-0.657245\pi$
$227$	−8.27456	+	1.75881i	−0.549202	+	0.116737i	−0.0750505	+	0.997180i	$0.523912\pi$
$228$	−1.99473	+	18.9786i	−0.132104	+	1.25689i
$229$	−15.2852	−	16.9760i	−1.01008	−	1.12180i	−0.992535	−	0.121958i	$-0.961083\pi$
$229$	−15.2852	−	16.9760i	−1.01008	−	1.12180i	−0.0175421	−	0.999846i	$-0.505584\pi$
$230$	−0.590561	+	0.655884i	−0.0389404	+	0.0432477i
$231$	−0.342601	−	3.25963i	−0.0225415	−	0.214468i
$232$	−21.8792	−	67.3372i	−1.43644	−	4.42090i
$233$	5.02260	+	15.4580i	0.329042	+	1.01269i	0.969583	+	0.244762i	$0.0787099\pi$
$233$	5.02260	+	15.4580i	0.329042	+	1.01269i	−0.640542	+	0.767923i	$0.721290\pi$
$234$	1.01770	+	9.68281i	0.0665294	+	0.632985i
$235$	−2.73766	+	3.04048i	−0.178585	+	0.198339i
$236$	1.63377	+	1.81449i	0.106349	+	0.118113i
$237$	1.43877	−	13.6890i	0.0934583	−	0.889197i
$238$	−12.5544	+	2.66852i	−0.813781	+	0.172975i
$239$	−16.6932	−	7.43230i	−1.07979	−	0.480755i	−0.211791	−	0.977315i	$-0.567930\pi$
$239$	−16.6932	−	7.43230i	−1.07979	−	0.480755i	−0.868003	+	0.496560i	$0.834596\pi$
$240$	9.04675	−	6.57285i	0.583965	−	0.424275i
$241$	16.6005	−	7.39103i	1.06933	−	0.476098i	0.204868	−	0.978790i	$-0.434323\pi$
$241$	16.6005	−	7.39103i	1.06933	−	0.476098i	0.864466	+	0.502691i	$0.167657\pi$
$242$	−12.3900	+	21.4602i	−0.796461	+	1.37951i
$243$	4.88759	+	8.46555i	0.313539	+	0.543065i
$244$	−21.6697	−	15.7440i	−1.38726	−	1.00790i
$245$	2.39100	+	0.508223i	0.152756	+	0.0324692i
$246$	−0.122756	+	0.377804i	−0.00782663	+	0.0240879i
$247$	9.42508			0.599704
$248$		0			0
$249$	−23.6782			−1.50054
$250$	4.87032	−	14.9893i	0.308026	−	0.948007i
$251$	−22.4291	−	4.76746i	−1.41571	−	0.300919i	−0.564368	−	0.825523i	$-0.690880\pi$
$251$	−22.4291	−	4.76746i	−1.41571	−	0.300919i	−0.851346	+	0.524604i	$0.824213\pi$
$252$	−7.21376	−	5.24111i	−0.454424	−	0.330159i
$253$	−0.360602	−	0.624580i	−0.0226708	−	0.0392670i
$254$	17.3642	−	30.0757i	1.08953	−	1.88712i
$255$	−2.17918	+	0.970233i	−0.136465	+	0.0607583i
$256$	−13.0179	+	9.45807i	−0.813620	+	0.591129i
$257$	0.0970122	+	0.0431926i	0.00605145	+	0.00269428i	0.409760	−	0.912193i	$-0.365612\pi$
$257$	0.0970122	+	0.0431926i	0.00605145	+	0.00269428i	−0.403709	+	0.914888i	$0.632279\pi$
$258$	−11.2206	+	2.38501i	−0.698564	+	0.148484i
$259$	−1.39803	+	13.3014i	−0.0868694	+	0.826507i
$260$	−7.82547	−	8.69107i	−0.485315	−	0.538997i
$261$	−5.36430	+	5.95765i	−0.332042	+	0.368770i
$262$	−0.685500	−	6.52209i	−0.0423503	−	0.402936i
$263$	2.25499	+	6.94015i	0.139049	+	0.427948i	0.996198	−	0.0871204i	$-0.0277665\pi$
$263$	2.25499	+	6.94015i	0.139049	+	0.427948i	−0.857149	+	0.515068i	$0.827766\pi$
$264$	5.10723	+	15.7184i	0.314328	+	0.967403i
$265$	0.177982	+	1.69338i	0.0109333	+	0.104024i
$266$	−7.98161	+	8.86448i	−0.489384	+	0.543516i
$267$	−14.5444	−	16.1532i	−0.890105	−	0.988561i
$268$	−4.54266	+	43.2205i	−0.277487	+	2.64011i
$269$	15.8649	−	3.37219i	0.967302	−	0.205606i	0.302934	−	0.953012i	$-0.402034\pi$
$269$	15.8649	−	3.37219i	0.967302	−	0.205606i	0.664368	+	0.747405i	$0.268701\pi$
$270$	−8.45770	−	3.76561i	−0.514719	−	0.229168i
$271$	−4.16291	+	3.02453i	−0.252879	+	0.183727i	−0.707002	−	0.707212i	$-0.749953\pi$
$271$	−4.16291	+	3.02453i	−0.252879	+	0.183727i	0.454123	+	0.890939i	$0.349953\pi$
$272$	32.6894	−	14.5543i	1.98209	−	0.882482i
$273$	4.49790	−	7.79058i	0.272225	−	0.471508i
$274$	−10.9541	−	18.9730i	−0.661760	−	1.14620i
$275$	5.00939	+	3.63954i	0.302078	+	0.219472i
$276$	3.92024	+	0.833274i	0.235971	+	0.0501572i
$277$	5.22944	−	16.0946i	0.314207	−	0.967029i	−0.661873	−	0.749616i	$-0.730238\pi$
$277$	5.22944	−	16.0946i	0.314207	−	0.967029i	0.976080	−	0.217413i	$-0.0697618\pi$
$278$	−3.64076			−0.218358
$279$		0			0
$280$	9.14853			0.546729
$281$	0.589193	−	1.81335i	0.0351483	−	0.108175i	−0.931943	−	0.362605i	$-0.881888\pi$
$281$	0.589193	−	1.81335i	0.0351483	−	0.108175i	0.967091	+	0.254429i	$0.0818876\pi$
$282$	25.1134	+	5.33802i	1.49548	+	0.317874i
$283$	12.3859	+	8.99888i	0.736265	+	0.534928i	0.891539	−	0.452944i	$-0.149626\pi$
$283$	12.3859	+	8.99888i	0.736265	+	0.534928i	−0.155274	+	0.987871i	$0.549626\pi$
$284$	−12.4605	−	21.5823i	−0.739396	−	1.28067i
$285$	−1.10846	+	1.91991i	−0.0656596	+	0.113726i
$286$	12.0646	−	5.37148i	0.713392	−	0.317623i
$287$	−0.145368	+	0.105616i	−0.00858081	+	0.00623433i
$288$	15.6963	+	6.98844i	0.924913	+	0.411798i
$289$	9.16214	−	1.94747i	0.538949	−	0.114557i
$290$	1.39100	−	13.2345i	0.0816822	−	0.777154i
$291$	1.21471	+	1.34908i	0.0712078	+	0.0790843i
$292$	−26.3032	+	29.2126i	−1.53928	+	1.70954i
$293$	−2.80070	−	26.6469i	−0.163619	−	1.55673i	−0.700860	−	0.713299i	$-0.747200\pi$
$293$	−2.80070	−	26.6469i	−0.163619	−	1.55673i	0.537241	−	0.843429i	$-0.319467\pi$
$294$	−4.74013	−	14.5886i	−0.276450	−	0.850826i
$295$	0.0876522	+	0.269766i	0.00510331	+	0.0157064i
$296$	−7.04963	−	67.0727i	−0.409751	−	3.89852i
$297$	5.06217	−	5.62211i	0.293737	−	0.326228i
$298$	16.2075	+	18.0003i	0.938876	+	1.04273i
$299$	0.206908	−	1.96860i	0.0119658	−	0.113847i
$300$	−33.6576	+	7.15414i	−1.94322	+	0.413045i
$301$	−4.74017	−	2.11046i	−0.273219	−	0.121645i
$302$	6.98272	−	5.07324i	0.401810	−	0.291932i
$303$	−10.5277	+	4.68721i	−0.604798	+	0.269273i
$304$	16.6278	−	28.8002i	0.953670	−	1.65181i
$305$	−1.55584	−	2.69480i	−0.0890873	−	0.154304i
$306$	−5.92860	−	4.30738i	−0.338916	−	0.246237i
$307$	−8.75565	−	1.86107i	−0.499712	−	0.106217i	−0.0488415	−	0.998807i	$-0.515553\pi$
$307$	−8.75565	−	1.86107i	−0.499712	−	0.106217i	−0.450870	+	0.892590i	$0.648886\pi$
$308$	−3.73749	+	11.5028i	−0.212963	+	0.655434i
$309$	−21.5039			−1.22331
$310$		0			0
$311$	20.6556			1.17127			0.585637	−	0.810574i	$-0.300844\pi$
$311$	20.6556			1.17127			0.585637	+	0.810574i	$0.300844\pi$
$312$	−14.0175	+	43.1415i	−0.793586	+	2.44241i
$313$	0.441458	+	0.0938349i	0.0249527	+	0.00530386i	0.220371	−	0.975416i	$-0.429273\pi$
$313$	0.441458	+	0.0938349i	0.0249527	+	0.00530386i	−0.195418	+	0.980720i	$0.562606\pi$
$314$	−7.24032	−	5.26040i	−0.408595	−	0.296862i
$315$	−0.517934	−	0.897088i	−0.0291823	−	0.0505452i
$316$	−25.3964	+	43.9879i	−1.42866	+	2.47451i
$317$	−5.09835	+	2.26993i	−0.286352	+	0.127492i	−0.544886	−	0.838510i	$-0.683427\pi$
$317$	−5.09835	+	2.26993i	−0.286352	+	0.127492i	0.258534	+	0.966002i	$0.416761\pi$
$318$	8.64432	−	6.28047i	0.484750	−	0.352191i
$319$	9.93404	+	4.42292i	0.556199	+	0.247636i
$320$	−12.4825	+	2.65324i	−0.697794	+	0.148321i
$321$	−1.83584	+	17.4668i	−0.102466	+	0.974903i
$322$	1.67629	+	1.86171i	0.0934159	+	0.103749i
$323$	−4.74683	+	5.27189i	−0.264121	+	0.293336i
$324$	2.77533	+	26.4055i	0.154185	+	1.46697i
$325$	5.25165	+	16.1629i	0.291309	+	0.896557i
$326$	−1.44676	−	4.45266i	−0.0801284	−	0.246610i
$327$	1.06949	+	10.1755i	0.0591430	+	0.562708i
$328$	0.606279	−	0.673341i	0.0334761	−	0.0371790i
$329$	7.77077	+	8.63031i	0.428416	+	0.475804i
$330$	−0.324699	+	3.08931i	−0.0178741	+	0.170061i
$331$	23.6765	−	5.03260i	1.30138	−	0.276617i	0.495454	−	0.868634i	$-0.335002\pi$
$331$	23.6765	−	5.03260i	1.30138	−	0.276617i	0.805925	+	0.592018i	$0.201668\pi$
$332$	79.8221	+	35.5391i	4.38080	+	1.95046i
$333$	−6.17793	+	4.48853i	−0.338548	+	0.245970i
$334$	−34.4466	+	15.3366i	−1.88483	+	0.839182i
$335$	−2.52433	+	4.37226i	−0.137919	+	0.238882i
$336$	−15.8704	−	27.4884i	−0.865804	−	1.49962i
$337$	8.92830	+	6.48679i	0.486355	+	0.353358i	0.803781	−	0.594925i	$-0.202818\pi$
$337$	8.92830	+	6.48679i	0.486355	+	0.353358i	−0.317426	+	0.948283i	$0.602818\pi$
$338$	1.24669	+	0.264993i	0.0678112	+	0.0144137i
$339$	−7.31135	+	22.5020i	−0.397098	+	1.22214i
$340$	8.80253			0.477384
$341$		0			0
$342$	−6.81056			−0.368273
$343$	5.87953	−	18.0953i	0.317465	−	0.977056i
$344$	25.5928	+	5.43991i	1.37987	+	0.293301i
$345$	0.376675	+	0.273670i	0.0202795	+	0.0147339i
$346$	−0.0161152	−	0.0279124i	−0.000866360	−	0.00150058i
$347$	−9.28369	+	16.0798i	−0.498375	+	0.863210i	−0.999998	−	0.00187589i	$-0.999403\pi$
$347$	−9.28369	+	16.0798i	−0.498375	+	0.863210i	0.501624	+	0.865086i	$0.332736\pi$
$348$	−55.2048	+	24.5788i	−2.95929	+	1.31756i
$349$	26.0298	−	18.9118i	1.39334	−	1.01232i	0.397855	−	0.917448i	$-0.369755\pi$
$349$	26.0298	−	18.9118i	1.39334	−	1.01232i	0.995489	−	0.0948756i	$-0.0302453\pi$
$350$	−19.6489	−	8.74825i	−1.05028	−	0.467614i
$351$	20.3103	−	4.31709i	1.08408	−	0.230429i
$352$	2.43610	−	23.1780i	0.129845	−	1.23539i
$353$	−21.5550	−	23.9392i	−1.14725	−	1.27416i	−0.956245	−	0.292567i	$-0.905490\pi$
$353$	−21.5550	−	23.9392i	−1.14725	−	1.27416i	−0.191010	−	0.981588i	$-0.561176\pi$
$354$	1.19103	−	1.32278i	0.0633027	−	0.0703047i
$355$	−0.302623	−	2.87926i	−0.0160615	−	0.152815i
$356$	24.7864	+	76.2846i	1.31367	+	4.04307i
$357$	2.09233	+	6.43952i	0.110738	+	0.340815i
$358$	2.80579	+	26.6953i	0.148291	+	1.41089i
$359$	14.1603	−	15.7266i	0.747353	−	0.830019i	−0.242790	−	0.970079i	$-0.578063\pi$
$359$	14.1603	−	15.7266i	0.747353	−	0.830019i	0.990143	+	0.140059i	$0.0447293\pi$
$360$	3.49514	+	3.88175i	0.184210	+	0.204586i
$361$	1.29689	−	12.3391i	0.0682573	−	0.649425i
$362$	48.9518	−	10.4050i	2.57285	−	0.546876i
$363$	11.9423	+	5.31705i	0.626808	+	0.279073i
$364$	−26.8560	+	19.5120i	−1.40764	+	1.02271i
$365$	−4.17184	+	1.85742i	−0.218364	+	0.0972219i
$366$	−9.76334	+	16.9106i	−0.510338	+	0.883931i
$367$	6.49822	+	11.2552i	0.339204	+	0.587519i	0.984283	−	0.176597i	$-0.0565089\pi$
$367$	6.49822	+	11.2552i	0.339204	+	0.587519i	−0.645079	+	0.764116i	$0.723176\pi$
$368$	−5.65042	−	4.10527i	−0.294549	−	0.214002i
$369$	−0.100350	−	0.0213301i	−0.00522403	−	0.00111040i
$370$	3.91704	−	12.0554i	0.203637	−	0.626730i
$371$	4.83309			0.250922
$372$		0			0
$373$	−4.42592			−0.229166			−0.114583	−	0.993414i	$-0.536553\pi$
$373$	−4.42592			−0.229166			−0.114583	+	0.993414i	$0.536553\pi$
$374$	−3.07165	+	9.45355i	−0.158831	+	0.488832i
$375$	−8.13271	−	1.72866i	−0.419971	−	0.0892676i
$376$	−47.3762	−	34.4208i	−2.44324	−	1.77512i
$377$	14.9228	+	25.8471i	0.768566	+	1.33119i
$378$	−13.1394	+	22.7581i	−0.675819	+	1.17055i
$379$	−13.6627	+	6.08305i	−0.701808	+	0.312465i	−0.726438	−	0.687231i	$-0.758826\pi$
$379$	−13.6627	+	6.08305i	−0.701808	+	0.312465i	0.0246303	+	0.999697i	$0.492159\pi$
$380$	6.61840	−	4.80855i	0.339517	−	0.246673i
$381$	−16.7367	−	7.45166i	−0.857448	−	0.381760i
$382$	3.15269	−	0.670125i	0.161306	−	0.0342866i
$383$	−1.21779	+	11.5865i	−0.0622263	+	0.592044i	0.918331	+	0.395812i	$0.129537\pi$
$383$	−1.21779	+	11.5865i	−0.0622263	+	0.592044i	−0.980558	+	0.196231i	$0.937130\pi$
$384$	20.4887	+	22.7550i	1.04556	+	1.16121i
$385$	−0.940176	+	1.04417i	−0.0479158	+	0.0532159i
$386$	3.57868	+	34.0489i	0.182150	+	1.73304i
$387$	−0.915480	−	2.81756i	−0.0465365	−	0.143225i
$388$	−2.07009	−	6.37110i	−0.105093	−	0.323443i
$389$	1.50541	+	14.3230i	0.0763274	+	0.726207i	0.964031	+	0.265791i	$0.0856330\pi$
$389$	1.50541	+	14.3230i	0.0763274	+	0.726207i	−0.887703	+	0.460416i	$0.847700\pi$
$390$	−5.70484	+	6.33586i	−0.288876	+	0.320829i
$391$	0.996924	+	1.10720i	0.0504166	+	0.0559933i
$392$	−3.65716	+	34.7956i	−0.184715	+	1.75744i
$393$	−3.38402	+	0.719295i	−0.170701	+	0.0362836i
$394$	−7.29556	−	3.24819i	−0.367545	−	0.163642i
$395$	−4.77376	+	3.46834i	−0.240194	+	0.174511i
$396$	−6.30858	+	2.80876i	−0.317018	+	0.141145i
$397$	−7.89506	+	13.6746i	−0.396242	+	0.686311i	−0.993259	−	0.115918i	$-0.963019\pi$
$397$	−7.89506	+	13.6746i	−0.396242	+	0.686311i	0.597017	+	0.802229i	$0.296352\pi$
$398$	17.7336	+	30.7155i	0.888904	+	1.53963i
$399$	5.09088	+	3.69874i	0.254863	+	0.185169i
$400$	58.6540	+	12.4673i	2.93270	+	0.623365i
$401$	−9.58670	+	29.5048i	−0.478737	+	1.47340i	0.362114	+	0.932134i	$0.382055\pi$
$401$	−9.58670	+	29.5048i	−0.478737	+	1.47340i	−0.840851	+	0.541267i	$0.817945\pi$
$402$	31.6817			1.58014
$403$		0			0
$404$	42.5252			2.11571
$405$	−0.953153	+	2.93350i	−0.0473626	+	0.145767i
$406$	−36.9471	−	7.85335i	−1.83365	−	0.389755i
$407$	8.37986	+	6.08832i	0.415374	+	0.301787i
$408$	−17.0713	−	29.5684i	−0.845156	−	1.46385i
$409$	3.29291	−	5.70349i	0.162824	−	0.282019i	−0.773056	−	0.634337i	$-0.781273\pi$
$409$	3.29291	−	5.70349i	0.162824	−	0.282019i	0.935880	+	0.352318i	$0.114606\pi$
$410$	0.155573	−	0.0692657i	0.00768322	−	0.00342079i
$411$	−9.35015	+	6.79328i	−0.461209	+	0.335088i
$412$	72.4923	+	32.2757i	3.57144	+	1.59011i
$413$	0.787533	−	0.167395i	0.0387520	−	0.00823699i
$414$	−0.149512	+	1.42251i	−0.00734811	+	0.0699126i
$415$	6.79210	+	7.54339i	0.333411	+	0.370290i
$416$	42.8014	−	47.5358i	2.09851	−	2.33063i
$417$	0.200762	+	1.91012i	0.00983136	+	0.0935391i
$418$	2.85469	+	8.78583i	0.139627	+	0.429729i
$419$	−4.53389	−	13.9539i	−0.221495	−	0.681692i	−0.998628	−	0.0523559i	$-0.983327\pi$
$419$	−4.53389	−	13.9539i	−0.221495	−	0.681692i	0.777133	−	0.629336i	$-0.216673\pi$
$420$	−0.816176	−	7.76540i	−0.0398253	−	0.378913i
$421$	−17.8764	+	19.8538i	−0.871243	+	0.967613i	−0.999710	−	0.0241008i	$-0.992328\pi$
$421$	−17.8764	+	19.8538i	−0.871243	+	0.967613i	0.128467	+	0.991714i	$0.458994\pi$
$422$	−32.9993	−	36.6494i	−1.60638	−	1.78407i
$423$	−0.693091	+	6.59432i	−0.0336993	+	0.320627i
$424$	−23.8385	+	5.06703i	−1.15770	+	0.246077i
$425$	−11.6856	−	5.20277i	−0.566835	−	0.252371i
$426$	−14.6980	+	10.6787i	−0.712118	+	0.517384i
$427$	−8.06883	+	3.59247i	−0.390478	+	0.173852i
$428$	32.4052	−	56.1274i	1.56636	−	2.71302i
$429$	−3.48342	−	6.03347i	−0.168181	−	0.291299i
$430$	3.97845	+	2.89052i	0.191858	+	0.139393i
$431$	−3.90086	−	0.829154i	−0.187898	−	0.0399389i	0.113002	−	0.993595i	$-0.463954\pi$
$431$	−3.90086	−	0.829154i	−0.187898	−	0.0399389i	−0.300899	+	0.953656i	$0.597287\pi$
$432$	22.6399	−	69.6783i	1.08926	−	3.35240i
$433$	−18.0766			−0.868704			−0.434352	−	0.900743i	$-0.643023\pi$
$433$	−18.0766			−0.868704			−0.434352	+	0.900743i	$0.643023\pi$
$434$		0			0
$435$	−7.02016			−0.336591
$436$	11.6673	−	35.9082i	0.558762	−	1.71969i
$437$	1.35439	+	0.287884i	0.0647892	+	0.0137714i
$438$	23.1839	+	16.8441i	1.10777	+	0.804843i
$439$	−11.4543	−	19.8394i	−0.546684	−	0.946884i	−0.998499	−	0.0547723i	$-0.982557\pi$
$439$	−11.4543	−	19.8394i	−0.546684	−	0.946884i	0.451815	−	0.892112i	$-0.350777\pi$
$440$	3.54257	−	6.13591i	0.168885	−	0.292518i
$441$	3.61904	−	1.61130i	0.172335	−	0.0767285i
$442$	−22.0715	+	16.0359i	−1.04984	+	0.762750i
$443$	−19.6333	−	8.74131i	−0.932806	−	0.415312i	−0.116669	−	0.993171i	$-0.537222\pi$
$443$	−19.6333	−	8.74131i	−0.932806	−	0.415312i	−0.816137	+	0.577859i	$0.803888\pi$
$444$	−56.3034	+	11.9677i	−2.67204	+	0.567960i
$445$	−0.974014	+	9.26713i	−0.0461727	+	0.439304i
$446$	16.9134	+	18.7843i	0.800874	+	0.889461i
$447$	8.55011	−	9.49586i	0.404406	−	0.449139i
$448$	3.78631	+	36.0244i	0.178886	+	1.70199i
$449$	−5.80940	−	17.8795i	−0.274163	−	0.843786i	−0.989440	−	0.144945i	$-0.953700\pi$
$449$	−5.80940	−	17.8795i	−0.274163	−	0.843786i	0.715277	−	0.698841i	$-0.246300\pi$
$450$	−3.79484	−	11.6793i	−0.178890	−	0.550568i
$451$	0.0145460	+	0.138396i	0.000684944	+	0.00651681i
$452$	58.4212	−	64.8834i	2.74790	−	3.05186i
$453$	−3.04672	−	3.38373i	−0.143148	−	0.158982i
$454$	2.37877	−	22.6325i	0.111641	−	1.06220i
$455$	−3.77215	+	0.801795i	−0.176841	+	0.0375887i
$456$	−28.9878	−	12.9062i	−1.35748	−	0.604388i
$457$	3.32182	−	2.41344i	0.155388	−	0.112896i	−0.507374	−	0.861726i	$-0.669384\pi$
$457$	3.32182	−	2.41344i	0.155388	−	0.112896i	0.662763	+	0.748830i	$0.269384\pi$
$458$	56.1396	−	24.9949i	2.62323	−	1.16794i
$459$	−7.81429	+	13.5347i	−0.364740	+	0.631748i
$460$	−0.859060	−	1.48794i	−0.0400539	−	0.0693754i
$461$	−18.5063	−	13.4456i	−0.861924	−	0.626225i	0.0664836	−	0.997788i	$-0.478822\pi$
$461$	−18.5063	−	13.4456i	−0.861924	−	0.626225i	−0.928408	+	0.371563i	$0.878822\pi$
$462$	8.62453	+	1.83320i	0.401249	+	0.0852882i
$463$	5.11947	−	15.7561i	0.237922	−	0.732249i	−0.758798	−	0.651326i	$-0.774213\pi$
$463$	5.11947	−	15.7561i	0.237922	−	0.732249i	0.996720	−	0.0809233i	$-0.0257869\pi$
$464$	105.308			4.88880
$465$		0			0
$466$	−43.7244			−2.02549
$467$	11.7878	−	36.2792i	0.545476	−	1.67880i	−0.174379	−	0.984679i	$-0.555792\pi$
$467$	11.7878	−	36.2792i	0.545476	−	1.67880i	0.719855	−	0.694124i	$-0.244208\pi$
$468$	−18.5392	−	3.94063i	−0.856976	−	0.182156i
$469$	11.5936	+	8.42323i	0.535342	+	0.388949i
$470$	−5.50321	−	9.53184i	−0.253844	−	0.439671i
$471$	−2.36062	+	4.08871i	−0.108771	+	0.188398i
$472$	−3.70889	+	1.65131i	−0.170716	+	0.0760075i
$473$	−3.25101	+	2.36200i	−0.149482	+	0.108605i
$474$	33.8271	+	15.0608i	1.55373	+	0.691766i
$475$	−11.6282	+	2.47166i	−0.533540	+	0.113407i
$476$	2.61172	−	24.8488i	0.119708	−	1.13894i
$477$	1.84646	+	2.05070i	0.0845435	+	0.0938950i
$478$	32.8926	−	36.5309i	1.50447	−	1.67089i
$479$	3.52102	+	33.5002i	0.160879	+	1.53066i	0.715530	+	0.698582i	$0.246185\pi$
$479$	3.52102	+	33.5002i	0.160879	+	1.53066i	−0.554651	+	0.832083i	$0.687148\pi$
$480$	4.64938	+	14.3093i	0.212214	+	0.653128i
$481$	8.78511	+	27.0378i	0.400567	+	1.23282i
$482$	5.10980	+	48.6165i	0.232745	+	2.21442i
$483$	0.884309	−	0.982125i	0.0402375	−	0.0446882i
$484$	−32.2785	−	35.8489i	−1.46720	−	1.62949i
$485$	0.0813472	−	0.773967i	0.00369379	−	0.0351440i
$486$	−25.7221	+	5.46740i	−1.16678	+	0.248006i
$487$	18.8891	+	8.40996i	0.855946	+	0.381092i	0.787315	−	0.616550i	$-0.211470\pi$
$487$	18.8891	+	8.40996i	0.855946	+	0.381092i	0.0686306	+	0.997642i	$0.478137\pi$
$488$	36.0319	−	26.1787i	1.63109	−	1.18506i
$489$	−2.25631	+	1.00457i	−0.102034	+	0.0454284i
$490$	−3.28793	+	5.69487i	−0.148534	+	0.257268i
$491$	12.3664	+	21.4192i	0.558087	+	0.966634i	0.997656	+	0.0684258i	$0.0217976\pi$
$491$	12.3664	+	21.4192i	0.558087	+	0.966634i	−0.439570	+	0.898209i	$0.644869\pi$
$492$	−0.625630	−	0.454547i	−0.0282056	−	0.0204925i
$493$	−21.9732	−	4.67055i	−0.989624	−	0.210351i
$494$	−7.83511	+	24.1140i	−0.352518	+	1.08494i
$495$	−0.802235			−0.0360578
$496$		0			0
$497$	−8.21771			−0.368615
$498$	19.6838	−	60.5804i	0.882050	−	2.71467i
$499$	−24.0235	−	5.10635i	−1.07544	−	0.228591i	−0.364042	−	0.931383i	$-0.618604\pi$
$499$	−24.0235	−	5.10635i	−1.07544	−	0.228591i	−0.711396	+	0.702791i	$0.751937\pi$
$500$	24.8218	+	18.0341i	1.11006	+	0.806509i
$501$	9.94584	+	17.2267i	0.444347	+	0.769632i
$502$	30.8429	−	53.4215i	1.37659	−	2.38432i
$503$	13.4649	−	5.99494i	0.600369	−	0.267301i	−0.0839669	−	0.996469i	$-0.526759\pi$
$503$	13.4649	−	5.99494i	0.600369	−	0.267301i	0.684336	+	0.729167i	$0.260092\pi$
$504$	11.9949	−	8.71479i	0.534295	−	0.388188i
$505$	4.51312	+	2.00937i	0.200831	+	0.0894157i
$506$	1.89775	−	0.403380i	0.0843654	−	0.0179324i
$507$	0.0702822	−	0.668691i	0.00312134	−	0.0296976i
$508$	45.2372	+	50.2410i	2.00708	+	2.22908i
$509$	−10.3757	+	11.5234i	−0.459896	+	0.510767i	−0.927833	−	0.372995i	$-0.878331\pi$
$509$	−10.3757	+	11.5234i	−0.459896	+	0.510767i	0.467937	+	0.883762i	$0.344997\pi$
$510$	−0.670772	−	6.38197i	−0.0297023	−	0.282598i
$511$	4.00557	+	12.3279i	0.177196	+	0.545353i
$512$	−0.0418393	−	0.128768i	−0.00184905	−	0.00569080i
$513$	1.51825	+	14.4451i	0.0670322	+	0.637769i
$514$	−0.191154	+	0.212298i	−0.00843146	+	0.00936409i
$515$	6.16841	+	6.85071i	0.271813	+	0.301878i
$516$	2.33424	−	22.2088i	0.102759	−	0.977690i
$517$	8.79740	−	1.86994i	0.386909	−	0.0822401i
$518$	−32.8692	−	14.6343i	−1.44419	−	0.642995i
$519$	−0.0137556	+	0.00999402i	−0.000603803	+	0.000438689i
$520$	17.7650	−	7.90947i	0.779045	−	0.346853i
$521$	−14.7073	+	25.4738i	−0.644337	+	1.11603i	0.340117	+	0.940383i	$0.389533\pi$
$521$	−14.7073	+	25.4738i	−0.644337	+	1.11603i	−0.984454	+	0.175642i	$0.943800\pi$
$522$	−10.7832	−	18.6771i	−0.471970	−	0.817475i
$523$	36.4268	+	26.4656i	1.59283	+	1.15726i	0.899754	+	0.436397i	$0.143746\pi$
$523$	36.4268	+	26.4656i	1.59283	+	1.15726i	0.693078	+	0.720863i	$0.256254\pi$
$524$	12.4875	+	2.65431i	0.545521	+	0.115954i
$525$	−3.50627	+	10.7912i	−0.153026	+	0.470966i
$526$	−19.6309			−0.855947
$527$		0			0
$528$	−24.5819			−1.06979
$529$	−7.01753	+	21.5977i	−0.305110	+	0.939032i
$530$	−4.48046	−	0.952352i	−0.194619	−	0.0413675i
$531$	0.371899	+	0.270201i	0.0161391	+	0.0117257i
$532$	−11.6105	−	20.1099i	−0.503378	−	0.871876i
$533$	−0.190970	+	0.330769i	−0.00827182	+	0.0143272i
$534$	53.4187	−	23.7835i	2.31165	−	1.02921i
$535$	6.09119	−	4.42551i	0.263345	−	0.191331i
$536$	−66.0146	−	29.3916i	−2.85139	−	1.26952i
$537$	13.8510	−	2.94412i	0.597714	−	0.127048i
$538$	−4.56085	+	43.3936i	−0.196632	+	1.87083i
$539$	−3.59557	−	3.99328i	−0.154872	−	0.172003i
$540$	12.0596	−	13.3935i	0.518962	−	0.576366i
$541$	−3.94895	−	37.5718i	−0.169779	−	1.61534i	−0.665188	−	0.746676i	$-0.731648\pi$
$541$	−3.94895	−	37.5718i	−0.169779	−	1.61534i	0.495409	−	0.868660i	$-0.335018\pi$
$542$	−4.27759	−	13.1651i	−0.183738	−	0.565488i
$543$	−8.15834	−	25.1088i	−0.350108	−	1.07752i
$544$	5.03256	+	47.8816i	0.215769	+	2.05291i
$545$	2.93494	−	3.25958i	0.125719	−	0.139625i
$546$	16.1930	+	17.9842i	0.692997	+	0.769651i
$547$	1.90333	−	18.1090i	0.0813807	−	0.774285i	−0.875385	−	0.483426i	$-0.839392\pi$
$547$	1.90333	−	18.1090i	0.0813807	−	0.774285i	0.956766	−	0.290859i	$-0.0939412\pi$
$548$	41.7167	−	8.86716i	1.78205	−	0.378786i
$549$	−4.60695	−	2.05115i	−0.196620	−	0.0875408i
$550$	−13.4761	+	9.79092i	−0.574621	+	0.417486i
$551$	−19.0725	+	8.49162i	−0.812516	+	0.361755i
$552$	−3.33206	+	5.77130i	−0.141822	+	0.245643i
$553$	8.37446	+	14.5050i	0.356118	+	0.616815i
$554$	36.8305	+	26.7590i	1.56478	+	1.13688i
$555$	−6.54086	−	1.39030i	−0.277644	−	0.0590151i
$556$	2.19015	−	6.74059i	0.0928831	−	0.285865i
$557$	9.19760			0.389715			0.194857	−	0.980832i	$-0.437576\pi$
$557$	9.19760			0.389715			0.194857	+	0.980832i	$0.437576\pi$
$558$		0			0
$559$	−11.0293			−0.466488
$560$	−4.20481	+	12.9411i	−0.177686	+	0.546860i
$561$	5.12919	+	1.09024i	0.216554	+	0.0460301i
$562$	4.14964	+	3.01489i	0.175042	+	0.127175i
$563$	18.0809	+	31.3170i	0.762019	+	1.31986i	0.941808	+	0.336150i	$0.109125\pi$
$563$	18.0809	+	31.3170i	0.762019	+	1.31986i	−0.179790	+	0.983705i	$0.557542\pi$
$564$	−24.9903	+	43.2844i	−1.05228	+	1.82260i
$565$	9.26596	−	4.12547i	0.389822	−	0.173560i
$566$	−33.3200	+	24.2084i	−1.40054	+	1.01755i
$567$	7.99825	+	3.56105i	0.335895	+	0.149550i
$568$	40.5327	−	8.61548i	1.70071	−	0.361498i
$569$	4.33791	−	41.2724i	0.181855	−	1.73023i	−0.399633	−	0.916675i	$-0.630863\pi$
$569$	4.33791	−	41.2724i	0.181855	−	1.73023i	0.581488	−	0.813555i	$-0.302471\pi$
$570$	−3.99061	−	4.43202i	−0.167148	−	0.185637i
$571$	21.6752	−	24.0728i	0.907080	−	1.00741i	−0.0928510	−	0.995680i	$-0.529598\pi$
$571$	21.6752	−	24.0728i	0.907080	−	1.00741i	0.999931	−	0.0117345i	$-0.00373531\pi$
$572$	2.68730	+	25.5679i	0.112361	+	1.06905i
$573$	−0.525430	−	1.61711i	−0.0219501	−	0.0675556i
$574$	−0.149373	−	0.459722i	−0.00623470	−	0.0191884i
$575$	0.260977	+	2.48303i	0.0108835	+	0.103549i
$576$	−13.8387	+	15.3695i	−0.576613	+	0.640394i
$577$	27.4227	+	30.4560i	1.14162	+	1.26790i	0.958590	+	0.284791i	$0.0919241\pi$
$577$	27.4227	+	30.4560i	1.14162	+	1.26790i	0.183031	+	0.983107i	$0.441409\pi$
$578$	−2.63393	+	25.0602i	−0.109557	+	1.04237i
$579$	17.6664	−	3.75511i	0.734190	−	0.156057i
$580$	23.6658	+	10.5367i	0.982671	+	0.437513i
$581$	23.3096	−	16.9354i	0.967046	−	0.702600i
$582$	−4.46140	+	1.98634i	−0.184931	+	0.0823365i
$583$	1.87151	−	3.24155i	0.0775100	−	0.134251i
$584$	−32.6814	−	56.6059i	−1.35237	−	2.34237i
$585$	−1.78133	−	1.29421i	−0.0736490	−	0.0535092i
$586$	70.5040	+	14.9861i	2.91249	+	0.619070i
$587$	−7.88963	+	24.2818i	−0.325640	+	1.00222i	0.645511	+	0.763751i	$0.276644\pi$
$587$	−7.88963	+	24.2818i	−0.325640	+	1.00222i	−0.971151	+	0.238466i	$0.923356\pi$
$588$	29.8612			1.23146
$589$		0			0
$590$	−0.763058			−0.0314146
$591$	−1.30187	+	4.00673i	−0.0535516	+	0.164815i
$592$	98.1181	+	20.8556i	4.03263	+	0.857162i
$593$	−36.0269	−	26.1751i	−1.47945	−	1.07488i	−0.977734	−	0.209850i	$-0.932702\pi$
$593$	−36.0269	−	26.1751i	−1.47945	−	1.07488i	−0.501716	−	0.865033i	$-0.667298\pi$
$594$	10.1759	+	17.6252i	0.417523	+	0.723170i
$595$	1.45132	−	2.51375i	0.0594982	−	0.103054i
$596$	−43.0760	+	19.1787i	−1.76446	+	0.785589i
$597$	15.1370	−	10.9977i	0.619515	−	0.450104i
$598$	4.86464	+	2.16588i	0.198930	+	0.0885694i
$599$	−18.5652	+	3.94615i	−0.758553	+	0.161235i	−0.570922	−	0.821004i	$-0.693414\pi$
$599$	−18.5652	+	3.94615i	−0.758553	+	0.161235i	−0.187631	+	0.982240i	$0.560081\pi$
$600$	5.98064	−	56.9020i	0.244159	−	2.32301i
$601$	8.59151	+	9.54184i	0.350455	+	0.389220i	0.892438	−	0.451170i	$-0.148993\pi$
$601$	8.59151	+	9.54184i	0.350455	+	0.389220i	−0.541983	+	0.840389i	$0.682326\pi$
$602$	9.34011	−	10.3732i	0.380674	−	0.422782i
$603$	0.855259	+	8.13724i	0.0348288	+	0.331374i
$604$	5.19217	+	15.9799i	0.211267	+	0.650212i
$605$	−1.73175	−	5.32977i	−0.0704056	−	0.216686i
$606$	−3.24051	−	30.8314i	−0.131637	−	1.25244i
$607$	−25.5202	+	28.3430i	−1.03583	+	1.15041i	−0.0473790	+	0.998877i	$0.515087\pi$
$607$	−25.5202	+	28.3430i	−1.03583	+	1.15041i	−0.988453	+	0.151531i	$0.951580\pi$
$608$	29.9401	+	33.2519i	1.21423	+	1.34854i
$609$	−2.08289	+	19.8174i	−0.0844029	+	0.803040i
$610$	8.18800	−	1.74041i	0.331522	−	0.0704672i
$611$	22.5510	+	10.0404i	0.912316	+	0.406189i
$612$	11.5412	−	8.38520i	0.466527	−	0.338952i
$613$	16.9393	−	7.54186i	0.684172	−	0.304613i	−0.0350577	−	0.999385i	$-0.511162\pi$
$613$	16.9393	−	7.54186i	0.684172	−	0.304613i	0.719230	+	0.694772i	$0.244495\pi$
$614$	12.0401	−	20.8541i	0.485901	−	0.841605i
$615$	−0.0449190	−	0.0778020i	−0.00181131	−	0.00313728i
$616$	−16.2701	−	11.8209i	−0.655541	−	0.476278i
$617$	−7.95777	−	1.69148i	−0.320368	−	0.0680962i	0.0449211	−	0.998991i	$-0.485696\pi$
$617$	−7.95777	−	1.69148i	−0.320368	−	0.0680962i	−0.365289	+	0.930894i	$0.619030\pi$
$618$	17.8763	−	55.0175i	0.719089	−	2.21313i
$619$	5.36063			0.215462			0.107731	−	0.994180i	$-0.465641\pi$
$619$	5.36063			0.215462			0.107731	+	0.994180i	$0.465641\pi$
$620$		0			0
$621$	3.05046			0.122411
$622$	−17.1711	+	52.8472i	−0.688499	+	2.11898i
$623$	25.8714	+	5.49913i	1.03651	+	0.220318i
$624$	−54.5833	−	39.6571i	−2.18508	−	1.58755i
$625$	−9.79252	−	16.9611i	−0.391701	−	0.678446i
$626$	−0.607062	+	1.05146i	−0.0242631	+	0.0420249i
$627$	4.45207	−	1.98219i	0.177799	−	0.0791610i
$628$	14.0948	−	10.2404i	0.562442	−	0.408638i
$629$	−19.5480	−	8.70334i	−0.779431	−	0.347025i
$630$	2.72575	−	0.579376i	0.108597	−	0.0230829i
$631$	3.03624	−	28.8879i	0.120871	−	1.15001i	−0.751010	−	0.660291i	$-0.770433\pi$
$631$	3.03624	−	28.8879i	0.120871	−	1.15001i	0.871881	−	0.489718i	$-0.162900\pi$
$632$	−56.5129	−	62.7639i	−2.24796	−	2.49661i
$633$	−17.4084	+	19.3340i	−0.691924	+	0.768459i
$634$	−1.56932	−	14.9311i	−0.0623257	−	0.592989i
$635$	2.42699	+	7.46949i	0.0963120	+	0.296418i
$636$	6.42770	+	19.7824i	0.254875	+	0.784424i
$637$	−1.54162	−	14.6675i	−0.0610812	−	0.581149i
$638$	−19.5742	+	21.7394i	−0.774950	+	0.860669i
$639$	−3.13953	−	3.48680i	−0.124198	−	0.137936i
$640$	1.37209	−	13.0546i	0.0542367	−	0.516027i
$641$	−27.0023	+	5.73951i	−1.06653	+	0.226697i	−0.707560	−	0.706653i	$-0.750204\pi$
$641$	−27.0023	+	5.73951i	−1.06653	+	0.226697i	−0.358966	+	0.933350i	$0.616871\pi$
$642$	−43.1625	−	19.2172i	−1.70349	−	0.758442i
$643$	−3.42136	+	2.48577i	−0.134925	+	0.0980291i	−0.653201	−	0.757185i	$-0.726574\pi$
$643$	−3.42136	+	2.48577i	−0.134925	+	0.0980291i	0.518275	+	0.855214i	$0.326574\pi$
$644$	−4.45521	+	1.98359i	−0.175560	+	0.0781643i
$645$	1.29713	−	2.24669i	0.0510742	−	0.0884632i
$646$	−9.54202	−	16.5273i	−0.375426	−	0.650257i
$647$	−21.2617	−	15.4475i	−0.835883	−	0.607304i	0.0853349	−	0.996352i	$-0.472804\pi$
$647$	−21.2617	−	15.4475i	−0.835883	−	0.607304i	−0.921217	+	0.389048i	$0.872804\pi$
$648$	−43.1836	−	9.17895i	−1.69641	−	0.360583i
$649$	0.192683	−	0.593018i	0.00756348	−	0.0232780i
$650$	−45.7184			−1.79322
$651$		0			0
$652$	9.11408			0.356935
$653$	−4.12592	+	12.6983i	−0.161460	+	0.496922i	−0.998758	−	0.0498246i	$-0.984134\pi$
$653$	−4.12592	+	12.6983i	−0.161460	+	0.496922i	0.837298	+	0.546746i	$0.184134\pi$
$654$	−26.9231	−	5.72267i	−1.05278	−	0.223774i
$655$	1.19986	+	0.871749i	0.0468824	+	0.0340621i
$656$	0.673821	+	1.16709i	0.0263083	+	0.0455673i
$657$	−3.70045	+	6.40937i	−0.144368	+	0.250053i
$658$	−28.5404	+	12.7070i	−1.11262	+	0.495371i
$659$	12.4717	−	9.06119i	0.485827	−	0.352974i	−0.317750	−	0.948174i	$-0.602927\pi$
$659$	12.4717	−	9.06119i	0.485827	−	0.352974i	0.803577	+	0.595200i	$0.202927\pi$
$660$	−5.52429	−	2.45957i	−0.215033	−	0.0957388i
$661$	4.61985	−	0.981980i	0.179691	−	0.0381946i	−0.117187	−	0.993110i	$-0.537388\pi$
$661$	4.61985	−	0.981980i	0.179691	−	0.0381946i	0.296879	+	0.954915i	$0.404054\pi$
$662$	−6.80652	+	64.7597i	−0.264543	+	2.51696i
$663$	9.63032	+	10.6956i	0.374011	+	0.415381i
$664$	−97.2160	+	107.969i	−3.77271	+	4.19002i
$665$	−0.281978	−	2.68284i	−0.0109346	−	0.104036i
$666$	−6.34812	−	19.5375i	−0.245984	−	0.757062i
$667$	1.35493	+	4.17006i	0.0524632	+	0.161465i
$668$	−7.67274	−	73.0013i	−0.296867	−	2.82450i
$669$	8.92251	−	9.90945i	0.344964	−	0.383122i
$670$	−9.08791	−	10.0931i	−0.351096	−	0.389932i
$671$	−0.715009	+	6.80286i	−0.0276026	+	0.262621i
$672$	41.7735	−	8.87924i	1.61145	−	0.342524i
$673$	28.3866	+	12.6385i	1.09422	+	0.487180i	0.872840	−	0.488007i	$-0.162276\pi$
$673$	28.3866	+	12.6385i	1.09422	+	0.487180i	0.221384	+	0.975187i	$0.428943\pi$
$674$	−24.0185	+	17.4505i	−0.925158	+	0.672167i
$675$	−23.9258	+	10.6524i	−0.920903	+	0.410013i
$676$	−1.24058	+	2.14875i	−0.0477147	+	0.0826443i
$677$	−4.51998	−	7.82883i	−0.173717	−	0.300886i	0.766000	−	0.642841i	$-0.222244\pi$
$677$	−4.51998	−	7.82883i	−0.173717	−	0.300886i	−0.939716	+	0.341955i	$0.888911\pi$
$678$	−51.4932	−	37.4120i	−1.97759	−	1.43680i
$679$	−2.16071	−	0.459273i	−0.0829205	−	0.0176253i
$680$	−4.52297	+	13.9203i	−0.173448	+	0.533818i
$681$	−12.0053			−0.460044
$682$		0			0
$683$	7.13535			0.273027			0.136513	−	0.990638i	$-0.456410\pi$
$683$	7.13535			0.273027			0.136513	+	0.990638i	$0.456410\pi$
$684$	4.09699	−	12.6092i	0.156652	−	0.482127i
$685$	4.84630	+	1.03011i	0.185168	+	0.0393586i
$686$	41.4091	+	30.0854i	1.58101	+	1.14867i
$687$	−16.2093	−	28.0753i	−0.618423	−	1.07114i
$688$	−19.4579	+	33.7021i	−0.741826	+	1.28488i
$689$	9.38509	−	4.17851i	0.357543	−	0.159189i
$690$	−1.01331	+	0.736216i	−0.0385762	+	0.0280273i
$691$	33.3220	+	14.8359i	1.26763	+	0.564384i	0.926734	−	0.375718i	$-0.122604\pi$
$691$	33.3220	+	14.8359i	1.26763	+	0.564384i	0.340893	+	0.940102i	$0.389271\pi$
$692$	0.0613720	−	0.0130450i	0.00233301	−	0.000495898i
$693$	−0.238024	+	2.26464i	−0.00904177	+	0.0860267i
$694$	−33.4225	−	37.1194i	−1.26870	−	1.40903i
$695$	0.550938	−	0.611879i	0.0208983	−	0.0232099i
$696$	−10.5031	−	99.9299i	−0.398117	−	3.78783i
$697$	−0.0888351	−	0.273406i	−0.00336487	−	0.0103560i
$698$	26.7469	+	82.3185i	1.01238	+	3.11580i
$699$	2.41109	+	22.9400i	0.0911958	+	0.867670i
$700$	28.0168	−	31.1158i	1.05894	−	1.17607i
$701$	−1.08027	−	1.19976i	−0.0408013	−	0.0453144i	0.722399	−	0.691477i	$-0.243040\pi$
$701$	−1.08027	−	1.19976i	−0.0408013	−	0.0453144i	−0.763200	+	0.646162i	$0.776373\pi$
$702$	−5.83880	+	55.5525i	−0.220371	+	2.09669i
$703$	−19.4520	+	4.13466i	−0.733647	+	0.155942i
$704$	25.6277	+	11.4102i	0.965879	+	0.430037i
$705$	−4.69742	+	3.41287i	−0.176915	+	0.128536i
$706$	79.1669	−	35.2474i	2.97949	−	1.32655i
$707$	7.01134	−	12.1440i	0.263688	−	0.456722i
$708$	1.73254	+	3.00084i	0.0651127	+	0.112779i
$709$	9.29395	+	6.75245i	0.349042	+	0.253594i	0.748467	−	0.663172i	$-0.230790\pi$
$709$	9.29395	+	6.75245i	0.349042	+	0.253594i	−0.399425	+	0.916766i	$0.630790\pi$
$710$	7.61813	+	1.61928i	0.285903	+	0.0607706i
$711$	−2.95510	+	9.09487i	−0.110825	+	0.341084i
$712$	−133.372			−4.99833
$713$		0			0
$714$	−18.2148			−0.681672
$715$	−0.922919	+	2.84045i	−0.0345152	+	0.106227i
$716$	−51.1123	−	10.8643i	−1.91016	−	0.406016i
$717$	−20.9797	−	15.2427i	−0.783503	−	0.569248i
$718$	28.4649	+	49.3026i	1.06230	+	1.83996i
$719$	−7.08549	+	12.2724i	−0.264244	+	0.457685i	−0.967365	−	0.253386i	$-0.918456\pi$
$719$	−7.08549	+	12.2724i	−0.264244	+	0.457685i	0.703121	+	0.711070i	$0.251789\pi$
$720$	−7.09737	+	3.15995i	−0.264503	+	0.117764i
$721$	21.1692	−	15.3803i	0.788382	−	0.572793i
$722$	30.4913	+	13.5756i	1.13477	+	0.505231i
$723$	25.2249	−	5.36171i	0.938123	−	0.199404i
$724$	−10.1835	+	96.8899i	−0.378468	+	3.60089i
$725$	−25.1893	−	27.9756i	−0.935508	−	1.03899i
$726$	−23.5313	+	26.1341i	−0.873328	+	0.969929i
$727$	2.81680	+	26.8001i	0.104470	+	0.993961i	0.913678	+	0.406439i	$0.133230\pi$
$727$	2.81680	+	26.8001i	0.104470	+	0.993961i	−0.809208	+	0.587522i	$0.800104\pi$
$728$	−17.0569	−	52.4958i	−0.632172	−	1.94562i
$729$	8.98695	+	27.6590i	0.332850	+	1.02441i
$730$	−1.28413	−	12.2177i	−0.0475278	−	0.452197i
$731$	5.55476	−	6.16918i	0.205450	−	0.228175i
$732$	−25.4354	−	28.2489i	−0.940121	−	1.04411i
$733$	2.97107	−	28.2678i	0.109739	−	1.04410i	−0.791617	−	0.611017i	$-0.790761\pi$
$733$	2.97107	−	28.2678i	0.109739	−	1.04410i	0.901356	−	0.433079i	$-0.142573\pi$
$734$	−34.1984	+	7.26910i	−1.26229	+	0.268307i
$735$	3.16912	+	1.41098i	0.116895	+	0.0520449i
$736$	7.60254	−	5.52357i	0.280233	−	0.203601i
$737$	10.1388	−	4.51409i	0.373468	−	0.166279i
$738$	0.137995	−	0.239014i	0.00507965	−	0.00879822i
$739$	−0.348653	−	0.603885i	−0.0128254	−	0.0222143i	0.859541	−	0.511066i	$-0.170749\pi$
$739$	−0.348653	−	0.603885i	−0.0128254	−	0.0222143i	−0.872367	+	0.488852i	$0.837416\pi$
$740$	19.9633	+	14.5042i	0.733866	+	0.533185i
$741$	13.0834	+	2.78097i	0.480633	+	0.102162i
$742$	−4.01777	+	12.3654i	−0.147497	+	0.453949i
$743$	18.1815			0.667015			0.333508	−	0.942747i	$-0.391768\pi$
$743$	18.1815			0.667015			0.333508	+	0.942747i	$0.391768\pi$
$744$		0			0
$745$	−5.47779			−0.200691
$746$	3.67929	−	11.3237i	0.134708	−	0.414589i
$747$	16.0911	+	3.42026i	0.588741	+	0.125141i
$748$	−15.6548	−	11.3738i	−0.572395	−	0.415869i
$749$	−10.6856	−	18.5080i	−0.390443	−	0.676267i
$750$	11.1835	−	19.3704i	0.408364	−	0.707307i
$751$	−33.8615	+	15.0761i	−1.23562	+	0.550135i	−0.917432	−	0.397892i	$-0.869742\pi$
$751$	−33.8615	+	15.0761i	−1.23562	+	0.550135i	−0.318190	+	0.948027i	$0.603075\pi$
$752$	70.4650	−	51.1958i	2.56959	−	1.86692i
$753$	−29.7284	−	13.2359i	−1.08336	−	0.482344i
$754$	−78.5350	+	16.6931i	−2.86008	+	0.607928i
$755$	−0.204034	+	1.94125i	−0.00742554	+	0.0706493i
$756$	−34.2308	−	38.0172i	−1.24496	−	1.38267i
$757$	−4.28378	+	4.75762i	−0.155697	+	0.172919i	−0.815947	−	0.578127i	$-0.803784\pi$
$757$	−4.28378	+	4.75762i	−0.155697	+	0.172919i	0.660250	+	0.751046i	$0.270450\pi$
$758$	−4.20552	−	40.0129i	−0.152751	−	1.45333i
$759$	−0.316281	−	0.973412i	−0.0114803	−	0.0353326i
$760$	4.20351	+	12.9371i	0.152477	+	0.469277i
$761$	−2.23052	−	21.2219i	−0.0808561	−	0.769294i	−0.957554	−	0.288253i	$-0.906925\pi$
$761$	−2.23052	−	21.2219i	−0.0808561	−	0.769294i	0.876698	−	0.481041i	$-0.159741\pi$
$762$	32.9783	−	36.6261i	1.19468	−	1.32682i
$763$	−8.33073	−	9.25221i	−0.301593	−	0.334952i
$764$	−0.655861	+	6.24010i	−0.0237282	+	0.225759i
$765$	1.62106	−	0.344567i	0.0586096	−	0.0124579i
$766$	−28.6316	−	12.7476i	−1.03450	−	0.460591i
$767$	1.38454	−	1.00593i	0.0499928	−	0.0363219i
$768$	−20.8616	+	9.28816i	−0.752777	+	0.335158i
$769$	6.12828	−	10.6145i	0.220991	−	0.382768i	−0.734118	−	0.679022i	$-0.762404\pi$
$769$	6.12828	−	10.6145i	0.220991	−	0.382768i	0.955109	+	0.296254i	$0.0957374\pi$
$770$	−1.88993	−	3.27346i	−0.0681084	−	0.117967i
$771$	0.121923	+	0.0885824i	0.00439096	+	0.00319022i
$772$	−65.1918	−	13.8569i	−2.34630	−	0.498722i
$773$	10.7240	−	33.0050i	0.385714	−	1.18711i	−0.550247	−	0.835002i	$-0.685466\pi$
$773$	10.7240	−	33.0050i	0.385714	−	1.18711i	0.935961	−	0.352104i	$-0.114534\pi$
$774$	7.96974			0.286466
$775$		0			0
$776$	11.1389			0.399863
$777$	−5.86539	+	18.0518i	−0.210420	+	0.647605i
$778$	−37.8968	−	8.05521i	−1.35867	−	0.288793i
$779$	−0.216146	−	0.157040i	−0.00774425	−	0.00562652i
$780$	−8.29855	−	14.3735i	−0.297136	−	0.514654i
$781$	−3.18213	+	5.51161i	−0.113866	+	0.197221i
$782$	−3.66150	+	1.63020i	−0.130935	+	0.0582960i
$783$	−37.2102	+	27.0348i	−1.32978	+	0.966144i
$784$	−47.5393	−	21.1659i	−1.69783	−	0.755923i
$785$	1.97972	−	0.420804i	0.0706594	−	0.0150191i
$786$	0.972836	−	9.25592i	0.0346999	−	0.330148i
$787$	13.4617	+	14.9507i	0.479858	+	0.532936i	0.933657	−	0.358168i	$-0.116598\pi$
$787$	13.4617	+	14.9507i	0.479858	+	0.532936i	−0.453799	+	0.891104i	$0.649932\pi$
$788$	10.4025	−	11.5532i	0.370575	−	0.411565i
$789$	1.08250	+	10.2993i	0.0385382	+	0.366666i
$790$	−4.90526	−	15.0968i	−0.174521	−	0.537122i
$791$	−8.89666	−	27.3811i	−0.316329	−	0.973559i
$792$	−1.20025	−	11.4196i	−0.0426489	−	0.405777i
$793$	−12.5624	+	13.9520i	−0.446105	+	0.495450i
$794$	−28.4233	−	31.5672i	−1.00870	−	1.12028i
$795$	−0.252585	+	2.40319i	−0.00895828	+	0.0852323i
$796$	−67.5353	+	14.3551i	−2.39372	+	0.508802i
$797$	−23.9367	−	10.6573i	−0.847880	−	0.377501i	−0.0636514	−	0.997972i	$-0.520275\pi$
$797$	−23.9367	−	10.6573i	−0.847880	−	0.377501i	−0.784229	+	0.620472i	$0.786941\pi$
$798$	−13.6953	+	9.95018i	−0.484807	+	0.352233i
$799$	−16.9736	+	7.55713i	−0.600482	+	0.267352i
$800$	−40.3405	+	69.8717i	−1.42625	+	2.47034i
$801$	7.55072	+	13.0782i	0.266791	+	0.462096i
$802$	−67.5183	−	49.0549i	−2.38416	−	1.73219i
$803$	9.81935	+	2.08717i	0.346517	+	0.0736545i
$804$	−19.0586	+	58.6562i	−0.672144	+	2.06865i
$805$	−0.566550			−0.0199683
$806$		0			0
$807$	23.0179			0.810270
$808$	−21.8506	+	67.2491i	−0.768700	+	2.36582i
$809$	35.6536	+	7.57841i	1.25351	+	0.266443i	0.786380	−	0.617743i	$-0.211953\pi$
$809$	35.6536	+	7.57841i	1.25351	+	0.266443i	0.467135	+	0.884186i	$0.345286\pi$
$810$	−6.71298	−	4.87727i	−0.235870	−	0.171370i
$811$	9.55322	+	16.5467i	0.335459	+	0.581032i	0.983573	−	0.180511i	$-0.0577753\pi$
$811$	9.55322	+	16.5467i	0.335459	+	0.581032i	−0.648114	+	0.761543i	$0.724442\pi$
$812$	36.7660	−	63.6805i	1.29023	−	2.23475i
$813$	−6.67117	+	2.97020i	−0.233968	+	0.104169i
$814$	−22.5431	+	16.3785i	−0.790136	+	0.574067i
$815$	0.967260	+	0.430652i	0.0338816	+	0.0150851i
$816$	49.6723	−	10.5582i	1.73888	−	0.369610i
$817$	0.806448	−	7.67284i	0.0282141	−	0.268439i
$818$	11.8549	+	13.1662i	0.414497	+	0.460346i
$819$	−4.18199	+	4.64457i	−0.146130	+	0.162294i
$820$	0.0346529	+	0.329700i	0.00121013	+	0.0115136i
$821$	−12.1937	−	37.5285i	−0.425565	−	1.30975i	−0.902453	−	0.430789i	$-0.858235\pi$
$821$	−12.1937	−	37.5285i	−0.425565	−	1.30975i	0.476888	−	0.878964i	$-0.341765\pi$
$822$	−9.60773	−	29.5696i	−0.335108	−	1.03136i
$823$	−3.30184	−	31.4149i	−0.115095	−	1.09506i	−0.887781	−	0.460267i	$-0.847754\pi$
$823$	−3.30184	−	31.4149i	−0.115095	−	1.09506i	0.772686	−	0.634789i	$-0.218913\pi$
$824$	−88.2891	+	98.0550i	−3.07570	+	3.41591i
$825$	5.87992	+	6.53031i	0.204712	+	0.227356i
$826$	−0.226400	+	2.15405i	−0.00787746	+	0.0749491i
$827$	19.3965	−	4.12286i	0.674483	−	0.143366i	0.142078	−	0.989855i	$-0.454622\pi$
$827$	19.3965	−	4.12286i	0.674483	−	0.143366i	0.532405	+	0.846490i	$0.321288\pi$
$828$	−2.54373	−	1.13254i	−0.0884008	−	0.0393586i
$829$	7.28104	−	5.28999i	0.252881	−	0.183729i	−0.454122	−	0.890940i	$-0.650047\pi$
$829$	7.28104	−	5.28999i	0.252881	−	0.183729i	0.707003	+	0.707211i	$0.250047\pi$
$830$	−24.9460	+	11.1067i	−0.865888	+	0.385518i
$831$	12.0081	−	20.7987i	0.416558	−	0.721499i
$832$	38.4977	+	66.6800i	1.33467	+	2.31171i
$833$	8.98066	+	6.52483i	0.311161	+	0.226072i
$834$	−5.05392	−	1.07424i	−0.175003	−	0.0371981i
$835$	2.63511	−	8.11003i	0.0911917	−	0.280659i
$836$	−17.9836			−0.621976
$837$		0			0
$838$	39.4699			1.36347
$839$	−9.84070	+	30.2866i	−0.339739	+	1.04561i	0.624602	+	0.780944i	$0.285261\pi$
$839$	−9.84070	+	30.2866i	−0.339739	+	1.04561i	−0.964340	+	0.264665i	$0.914739\pi$
$840$	12.6995	+	2.69937i	0.438176	+	0.0931372i
$841$	−30.0234	−	21.8133i	−1.03529	−	0.752183i
$842$	−35.9349	−	62.2411i	−1.23840	−	2.14497i
$843$	1.35294	−	2.34336i	0.0465976	−	0.0807095i
$844$	87.7049	−	39.0487i	3.01893	−	1.34411i
$845$	−0.233192	+	0.169424i	−0.00802205	+	0.00582836i
$846$	−16.2953	−	7.25515i	−0.560245	−	0.249437i
$847$	−15.5593	+	3.30724i	−0.534625	+	0.113638i
$848$	3.78898	−	36.0498i	0.130114	−	1.23795i
$849$	14.5383	+	16.1464i	0.498953	+	0.554143i
$850$	23.0255	−	25.5724i	0.789769	−	0.877127i
$851$	0.436570	+	4.15368i	0.0149654	+	0.142386i
$852$	−10.9290	−	33.6361i	−0.374422	−	1.15235i
$853$	−15.1702	−	46.6890i	−0.519417	−	1.59860i	−0.775099	−	0.631839i	$-0.782300\pi$
$853$	−15.1702	−	46.6890i	−0.519417	−	1.59860i	0.255683	−	0.966761i	$-0.417700\pi$
$854$	−2.48366	−	23.6304i	−0.0849891	−	0.808617i
$855$	1.03061	−	1.14461i	0.0352461	−	0.0391447i
$856$	72.1090	+	80.0851i	2.46463	+	2.73725i
$857$	−2.01118	+	19.1351i	−0.0687005	+	0.653641i	0.904938	+	0.425544i	$0.139917\pi$
$857$	−2.01118	+	19.1351i	−0.0687005	+	0.653641i	−0.973638	+	0.228098i	$0.926749\pi$
$858$	18.3323	−	3.89666i	0.625856	−	0.133030i
$859$	−4.24081	−	1.88813i	−0.144695	−	0.0644222i	0.333112	−	0.942887i	$-0.391901\pi$
$859$	−4.24081	−	1.88813i	−0.144695	−	0.0644222i	−0.477806	+	0.878465i	$0.658568\pi$
$860$	−7.74487	+	5.62698i	−0.264098	+	0.191878i
$861$	−0.232956	+	0.103719i	−0.00793913	+	0.00353473i
$862$	5.36418	−	9.29104i	0.182705	−	0.316454i
$863$	−19.2652	−	33.3683i	−0.655795	−	1.13587i	−0.981694	−	0.190466i	$-0.939000\pi$
$863$	−19.2652	−	33.3683i	−0.655795	−	1.13587i	0.325899	−	0.945405i	$-0.394333\pi$
$864$	79.7493	+	57.9413i	2.71313	+	1.97120i
$865$	0.00712969	+	0.00151546i	0.000242417	+	5.15273e-5i
$866$	15.0271	−	46.2487i	0.510642	−	1.57159i
$867$	13.2931			0.451456
$868$		0			0
$869$	12.9713			0.440022
$870$	5.83589	−	17.9610i	0.197855	−	0.608935i
$871$	29.7953	+	6.33318i	1.00957	+	0.214592i
$872$	50.7901	+	36.9012i	1.71997	+	1.24963i
$873$	−0.630617	−	1.09226i	−0.0213431	−	0.0369674i
$874$	−1.86246	+	3.22587i	−0.0629986	+	0.109117i
$875$	9.24251	−	4.11503i	0.312454	−	0.139113i
$876$	−45.1323	+	32.7905i	−1.52488	+	1.10789i
$877$	−8.45792	−	3.76571i	−0.285604	−	0.127159i	0.258935	−	0.965895i	$-0.416628\pi$
$877$	−8.45792	−	3.76571i	−0.285604	−	0.127159i	−0.544538	+	0.838736i	$0.683295\pi$
$878$	60.2810	−	12.8131i	2.03438	−	0.432422i
$879$	3.97465	−	37.8163i	0.134062	−	1.27551i
$880$	7.05134	+	7.83131i	0.237701	+	0.263993i
$881$	11.9634	−	13.2867i	0.403058	−	0.447642i	−0.507109	−	0.861882i	$-0.669286\pi$
$881$	11.9634	−	13.2867i	0.403058	−	0.447642i	0.910168	+	0.414240i	$0.135953\pi$
$882$	1.11397	+	10.5987i	0.0375094	+	0.356878i
$883$	14.9303	+	45.9509i	0.502446	+	1.54637i	0.805022	+	0.593244i	$0.202153\pi$
$883$	14.9303	+	45.9509i	0.502446	+	1.54637i	−0.302577	+	0.953125i	$0.597847\pi$
$884$	−16.4118	−	50.5104i	−0.551990	−	1.69885i
$885$	0.0420773	+	0.400338i	0.00141441	+	0.0134572i
$886$	38.6858	−	42.9649i	1.29967	−	1.44343i
$887$	15.7327	+	17.4730i	0.528254	+	0.586685i	0.946926	−	0.321452i	$-0.104171\pi$
$887$	15.7327	+	17.4730i	0.528254	+	0.586685i	−0.418672	+	0.908138i	$0.637504\pi$
$888$	10.0046	−	95.1872i	0.335732	−	3.19427i
$889$	21.8059	−	4.63498i	0.731346	−	0.155452i
$890$	−22.9001	−	10.1958i	−0.767615	−	0.341764i
$891$	5.48554	−	3.98548i	0.183772	−	0.133518i
$892$	−44.9522	+	20.0140i	−1.50511	+	0.670119i
$893$	−8.63379	+	14.9542i	−0.288919	+	0.500422i
$894$	17.1873	+	29.7693i	0.574830	+	0.995635i
$895$	−4.91110	−	3.56812i	−0.164160	−	0.119269i
$896$	−36.4449	−	7.74661i	−1.21754	−	0.258796i
$897$	0.868078	−	2.67167i	0.0289843	−	0.0892044i
$898$	50.5739			1.68767
$899$		0			0
$900$	23.9062			0.796874
$901$	−2.38945	+	7.35398i	−0.0796042	+	0.244996i
$902$	−0.366177	−	0.0778332i	−0.0121923	−	0.00259156i
$903$	−5.95736	−	4.32827i	−0.198249	−	0.144036i
$904$	72.5879	+	125.726i	2.41424	+	4.18158i
$905$	−5.65893	+	9.80156i	−0.188109	+	0.325815i
$906$	11.1900	−	4.98211i	0.371763	−	0.165519i
$907$	10.1792	−	7.39560i	0.337994	−	0.245567i	−0.405821	−	0.913952i	$-0.633014\pi$
$907$	10.1792	−	7.39560i	0.337994	−	0.245567i	0.743815	+	0.668386i	$0.233014\pi$
$908$	40.4714	+	18.0190i	1.34309	+	0.597982i
$909$	7.83138	−	1.66461i	0.259750	−	0.0552117i
$910$	1.08442	−	10.3175i	0.0359481	−	0.342023i
$911$	31.6395	+	35.1392i	1.04826	+	1.16421i	0.986101	+	0.166148i	$0.0531330\pi$
$911$	31.6395	+	35.1392i	1.04826	+	1.16421i	0.0621624	+	0.998066i	$0.480200\pi$
$912$	31.5797	−	35.0729i	1.04571	−	1.16138i
$913$	−2.33243	−	22.1916i	−0.0771922	−	0.734435i
$914$	3.41333	+	10.5051i	0.112903	+	0.347479i
$915$	−1.36462	−	4.19986i	−0.0451129	−	0.138843i
$916$	12.5047	+	118.974i	0.413167	+	3.93102i
$917$	2.81688	−	3.12846i	0.0930215	−	0.103311i
$918$	−28.1325	−	31.2443i	−0.928510	−	1.03121i
$919$	2.41794	−	23.0052i	0.0797605	−	0.758870i	−0.879415	−	0.476057i	$-0.842066\pi$
$919$	2.41794	−	23.0052i	0.0797605	−	0.758870i	0.959175	−	0.282813i	$-0.0912677\pi$
$920$	2.79442	−	0.593973i	0.0921294	−	0.0195827i
$921$	−11.6051	−	5.16690i	−0.382399	−	0.170255i
$922$	49.7848	−	36.1708i	1.63958	−	1.19122i
$923$	−15.9575	+	7.10472i	−0.525246	+	0.233855i
$924$	−8.58224	+	14.8649i	−0.282335	+	0.489019i
$925$	−17.9291	−	31.0541i	−0.589506	−	1.02105i
$926$	36.0560	+	26.1962i	1.18488	+	0.860862i
$927$	14.6135	+	3.10619i	0.479970	+	0.102021i
$928$	−43.7846	+	134.755i	−1.43730	+	4.42355i
$929$	−1.68694			−0.0553468			−0.0276734	−	0.999617i	$-0.508810\pi$
$929$	−1.68694			−0.0553468			−0.0276734	+	0.999617i	$0.508810\pi$
$930$		0			0
$931$	10.3166			0.338114
$932$	26.3030	−	80.9524i	0.861585	−	2.65169i
$933$	28.6732	+	6.09467i	0.938717	+	0.199531i
$934$	83.0208	+	60.3181i	2.71652	+	1.97367i
$935$	−1.12398	−	1.94679i	−0.0367581	−	0.0636669i
$936$	15.7576	−	27.2930i	0.515055	−	0.892101i
$937$	18.0212	−	8.02355i	0.588727	−	0.262118i	−0.0906798	−	0.995880i	$-0.528904\pi$
$937$	18.0212	−	8.02355i	0.588727	−	0.262118i	0.679407	+	0.733762i	$0.262237\pi$
$938$	−31.1885	+	22.6598i	−1.01834	+	0.739868i
$939$	0.585124	+	0.260514i	0.0190948	+	0.00850156i
$940$	20.9580	−	4.45477i	0.683575	−	0.145298i
$941$	−0.922282	+	8.77493i	−0.0300655	+	0.286054i	0.969151	+	0.246469i	$0.0792704\pi$
$941$	−0.922282	+	8.77493i	−0.0300655	+	0.286054i	−0.999216	+	0.0395854i	$0.987396\pi$
$942$	−8.49853	−	9.43857i	−0.276897	−	0.307525i
$943$	−0.0375456	+	0.0416987i	−0.00122265	+	0.00135789i
$944$	−0.631192	−	6.00539i	−0.0205436	−	0.195459i
$945$	−1.83649	−	5.65214i	−0.0597411	−	0.183864i
$946$	−3.34057	−	10.2812i	−0.108611	−	0.334271i
$947$	1.62659	+	15.4759i	0.0528569	+	0.502900i	0.988638	+	0.150318i	$0.0480297\pi$
$947$	1.62659	+	15.4759i	0.0528569	+	0.502900i	−0.935781	+	0.352582i	$0.885304\pi$
$948$	−48.2332	+	53.5684i	−1.56654	+	1.73982i
$949$	18.4364	+	20.4757i	0.598470	+	0.664668i
$950$	3.34288	−	31.8054i	0.108457	−	1.03190i
$951$	−7.74706	+	1.64669i	−0.251216	+	0.0533975i
$952$	37.9539	+	16.8982i	1.23009	+	0.547672i
$953$	7.80840	−	5.67314i	0.252939	−	0.183771i	−0.454089	−	0.890956i	$-0.650035\pi$
$953$	7.80840	−	5.67314i	0.252939	−	0.183771i	0.707028	+	0.707185i	$0.250035\pi$
$954$	−6.78166	+	3.01939i	−0.219564	+	0.0977563i
$955$	−0.364458	+	0.631260i	−0.0117936	+	0.0204271i
$956$	47.8473	+	82.8739i	1.54749	+	2.68033i
$957$	12.4849	+	9.07083i	0.403580	+	0.293218i
$958$	−88.6370	−	18.8404i	−2.86373	−	0.608705i
$959$	4.34583	−	13.3751i	0.140334	−	0.431904i
$960$	−18.1105			−0.584514
$961$		0			0
$962$	−76.4790			−2.46578
$963$	3.77063	−	11.6048i	0.121507	−	0.373960i
$964$	−93.0837	−	19.7856i	−2.99802	−	0.637250i
$965$	−6.26392	−	4.55100i	−0.201643	−	0.146502i
$966$	1.77763	+	3.07894i	0.0571942	+	0.0990633i
$967$	14.1988	−	24.5930i	0.456602	−	0.790858i	−0.542177	−	0.840264i	$-0.682400\pi$
$967$	14.1988	−	24.5930i	0.456602	−	0.790858i	0.998779	+	0.0494066i	$0.0157330\pi$
$968$	73.2768	−	32.6249i	2.35521	−	1.04861i
$969$	−8.14485	+	5.91758i	−0.261650	+	0.190100i
$970$	1.91256	+	0.851528i	0.0614087	+	0.0273409i
$971$	21.6435	−	4.60048i	0.694574	−	0.147636i	0.152921	−	0.988238i	$-0.451132\pi$
$971$	21.6435	−	4.60048i	0.694574	−	0.147636i	0.541653	+	0.840602i	$0.317799\pi$
$972$	5.35102	−	50.9115i	0.171634	−	1.63299i
$973$	−1.56382	−	1.73680i	−0.0501338	−	0.0556792i
$974$	−37.2194	+	41.3363i	−1.19259	+	1.32450i
$975$	2.52105	+	23.9861i	0.0807381	+	0.768171i
$976$	20.4703	+	63.0012i	0.655240	+	2.01662i
$977$	−6.15324	−	18.9377i	−0.196859	−	0.605871i	−0.999950	−	0.0100140i	$-0.996812\pi$
$977$	−6.15324	−	18.9377i	−0.196859	−	0.605871i	0.803090	−	0.595857i	$-0.203188\pi$
$978$	−0.694513	−	6.60785i	−0.0222081	−	0.211296i
$979$	13.7064	−	15.2225i	0.438058	−	0.486513i
$980$	−8.56572	−	9.51319i	−0.273622	−	0.303888i
$981$	0.743036	−	7.06951i	0.0237233	−	0.225712i
$982$	−65.0810	+	13.8334i	−2.07682	+	0.441441i
$983$	22.7750	+	10.1401i	0.726411	+	0.323419i	0.736414	−	0.676531i	$-0.236518\pi$
$983$	22.7750	+	10.1401i	0.726411	+	0.323419i	−0.0100033	+	0.999950i	$0.503184\pi$
$984$	1.04028	−	0.755810i	0.0331630	−	0.0240944i
$985$	1.64990	−	0.734585i	0.0525703	−	0.0234058i
$986$	30.2160	−	52.3356i	0.962273	−	1.66671i
$987$	8.24054	+	14.2730i	0.262299	+	0.454316i
$988$	−39.9319	−	29.0122i	−1.27040	−	0.923002i
$989$	−1.58491	−	0.336883i	−0.0503972	−	0.0107123i
$990$	0.666901	−	2.05251i	0.0211955	−	0.0652330i
$991$	42.0512			1.33580			0.667900	−	0.744251i	$-0.267193\pi$
$991$	42.0512			1.33580			0.667900	+	0.744251i	$0.267193\pi$
$992$		0			0
$993$	34.3515			1.09011
$994$	6.83142	−	21.0249i	0.216679	−	0.666871i
$995$	−7.84569	−	1.66765i	−0.248725	−	0.0528681i
$996$	100.319	+	72.8860i	3.17873	+	2.30948i
$997$	−7.23233	−	12.5268i	−0.229050	−	0.396727i	0.728477	−	0.685071i	$-0.240229\pi$
$997$	−7.23233	−	12.5268i	−0.229050	−	0.396727i	−0.957527	+	0.288344i	$0.906895\pi$
$998$	33.0353	−	57.2189i	1.04572	−	1.81123i
$999$	−40.0237	+	17.8197i	−1.26629	+	0.563790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.j.846.1		16
31.2	even	5		961.2.c.i.439.1		16
31.3	odd	30		961.2.g.s.732.2		16
31.4	even	5		961.2.g.l.547.1		16
31.5	even	3		961.2.d.n.628.1		16
31.6	odd	6		31.2.g.a.14.1	✓	16
31.7	even	15	inner	961.2.g.j.844.1		16
31.8	even	5		961.2.g.m.235.2		16
31.9	even	15		961.2.d.q.388.4		16
31.10	even	15		961.2.a.j.1.1		8
31.11	odd	30		961.2.d.o.531.1		16
31.12	odd	30		961.2.c.j.521.1		16
31.13	odd	30		961.2.d.p.374.4		16
31.14	even	15		961.2.g.n.338.2		16
31.15	odd	10		961.2.g.t.816.2		16
31.16	even	5		961.2.g.n.816.2		16
31.17	odd	30		961.2.g.t.338.2		16
31.18	even	15		961.2.d.q.374.4		16
31.19	even	15		961.2.c.i.521.1		16
31.20	even	15		961.2.d.n.531.1		16
31.21	odd	30		961.2.a.i.1.1		8
31.22	odd	30		961.2.d.p.388.4		16
31.23	odd	10		961.2.g.s.235.2		16
31.24	odd	30		961.2.g.k.844.1		16
31.25	even	3		961.2.g.l.448.1		16
31.26	odd	6		961.2.d.o.628.1		16
31.27	odd	10		31.2.g.a.20.1	yes	16
31.28	even	15		961.2.g.m.732.2		16
31.29	odd	10		961.2.c.j.439.1		16
31.30	odd	2		961.2.g.k.846.1		16
93.41	odd	30		8649.2.a.be.1.8		8
93.68	even	6		279.2.y.c.262.2		16
93.83	even	30		8649.2.a.bf.1.8		8
93.89	even	10		279.2.y.c.82.2		16
124.27	even	10		496.2.bg.c.113.1		16
124.99	even	6		496.2.bg.c.417.1		16
155.27	even	20		775.2.ck.a.299.4		32
155.37	even	12		775.2.ck.a.324.1		32
155.58	even	20		775.2.ck.a.299.1		32
155.68	even	12		775.2.ck.a.324.4		32
155.89	odd	10		775.2.bl.a.51.2		16
155.99	odd	6		775.2.bl.a.76.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.14.1	✓	16	31.6	odd	6
31.2.g.a.20.1	yes	16	31.27	odd	10
279.2.y.c.82.2		16	93.89	even	10
279.2.y.c.262.2		16	93.68	even	6
496.2.bg.c.113.1		16	124.27	even	10
496.2.bg.c.417.1		16	124.99	even	6
775.2.bl.a.51.2		16	155.89	odd	10
775.2.bl.a.76.2		16	155.99	odd	6
775.2.ck.a.299.1		32	155.58	even	20
775.2.ck.a.299.4		32	155.27	even	20
775.2.ck.a.324.1		32	155.37	even	12
775.2.ck.a.324.4		32	155.68	even	12
961.2.a.i.1.1		8	31.21	odd	30
961.2.a.j.1.1		8	31.10	even	15
961.2.c.i.439.1		16	31.2	even	5
961.2.c.i.521.1		16	31.19	even	15
961.2.c.j.439.1		16	31.29	odd	10
961.2.c.j.521.1		16	31.12	odd	30
961.2.d.n.531.1		16	31.20	even	15
961.2.d.n.628.1		16	31.5	even	3
961.2.d.o.531.1		16	31.11	odd	30
961.2.d.o.628.1		16	31.26	odd	6
961.2.d.p.374.4		16	31.13	odd	30
961.2.d.p.388.4		16	31.22	odd	30
961.2.d.q.374.4		16	31.18	even	15
961.2.d.q.388.4		16	31.9	even	15
961.2.g.j.844.1		16	31.7	even	15	inner
961.2.g.j.846.1		16	1.1	even	1	trivial
961.2.g.k.844.1		16	31.24	odd	30
961.2.g.k.846.1		16	31.30	odd	2
961.2.g.l.448.1		16	31.25	even	3
961.2.g.l.547.1		16	31.4	even	5
961.2.g.m.235.2		16	31.8	even	5
961.2.g.m.732.2		16	31.28	even	15
961.2.g.n.338.2		16	31.14	even	15
961.2.g.n.816.2		16	31.16	even	5
961.2.g.s.235.2		16	31.23	odd	10
961.2.g.s.732.2		16	31.3	odd	30
961.2.g.t.338.2		16	31.17	odd	30
961.2.g.t.816.2		16	31.15	odd	10
8649.2.a.be.1.8		8	93.41	odd	30
8649.2.a.bf.1.8		8	93.83	even	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.831304 + 2.55849i) q^{2} +(1.38815 + 0.295061i) q^{3} +(-4.23677 - 3.07819i) q^{4} +(-0.304192 - 0.526876i) q^{5} +(-1.90889 + 3.30629i) q^{6} +(-1.57758 + 0.702385i) q^{7} +(7.04481 - 5.11835i) q^{8} +(-0.900731 - 0.401031i) q^{9} +(1.60088 - 0.340278i) q^{10} +(-0.139796 + 1.33007i) q^{11} +(-4.97303 - 5.52311i) q^{12} +(-2.45615 + 2.72784i) q^{13} +(-0.485595 - 4.62012i) q^{14} +(-0.266804 - 0.821139i) q^{15} +(4.00227 + 12.3177i) q^{16} +(-0.288793 - 2.74768i) q^{17} +(1.77482 - 1.97113i) q^{18} +(-1.71811 - 1.90816i) q^{19} +(-0.333035 + 3.16861i) q^{20} +(-2.39717 + 0.509534i) q^{21} +(-3.28675 - 1.46335i) q^{22} +(-0.436271 + 0.316969i) q^{23} +(11.2895 - 5.02641i) q^{24} +(2.31493 - 4.00958i) q^{25} +(-4.93733 - 8.55171i) q^{26} +(-4.57641 - 3.32495i) q^{27} +(8.84593 + 1.88026i) q^{28} +(2.51258 - 7.73291i) q^{29} +2.32267 q^{30} -17.4262 q^{32} +(-0.586508 + 1.80509i) q^{33} +(7.27000 + 1.54529i) q^{34} +(0.849957 + 0.617530i) q^{35} +(2.58174 + 4.47170i) q^{36} +(3.87249 - 6.70735i) q^{37} +(6.31027 - 2.80951i) q^{38} +(-4.21439 + 3.06194i) q^{39} +(-4.83971 - 2.15478i) q^{40} +(0.101778 - 0.0216336i) q^{41} +(0.689139 - 6.55671i) q^{42} +(2.01054 + 2.23293i) q^{43} +(4.68648 - 5.20487i) q^{44} +(0.0627014 + 0.596564i) q^{45} +(-0.448289 - 1.37969i) q^{46} +(-2.07813 - 6.39584i) q^{47} +(1.92128 + 18.2798i) q^{48} +(-2.68849 + 2.98587i) q^{49} +(8.33407 + 9.25592i) q^{50} +(0.409845 - 3.89942i) q^{51} +(18.8030 - 3.99669i) q^{52} +(-2.55678 - 1.13835i) q^{53} +(12.3112 - 8.94464i) q^{54} +(0.743304 - 0.330940i) q^{55} +(-7.51871 + 13.0228i) q^{56} +(-1.82198 - 3.15576i) q^{57} +(17.6959 + 12.8568i) q^{58} +(-0.456044 - 0.0969352i) q^{59} +(-1.39724 + 4.30025i) q^{60} +5.11468 q^{61} +1.70266 q^{63} +(6.48190 - 19.9492i) q^{64} +(2.18437 + 0.464303i) q^{65} +(-4.13073 - 3.00115i) q^{66} +(-4.14923 - 7.18668i) q^{67} +(-7.23436 + 12.5303i) q^{68} +(-0.699136 + 0.311275i) q^{69} +(-2.28652 + 1.66125i) q^{70} +(4.34730 + 1.93554i) q^{71} +(-8.39810 + 1.78507i) q^{72} +(0.784611 - 7.46507i) q^{73} +(13.9415 + 15.4836i) q^{74} +(4.39655 - 4.88287i) q^{75} +(1.40557 + 13.3731i) q^{76} +(-0.713679 - 2.19648i) q^{77} +(-4.33049 - 13.3279i) q^{78} +(-1.01382 - 9.64582i) q^{79} +(5.27246 - 5.85566i) q^{80} +(-3.39245 - 3.76770i) q^{81} +(-0.0292592 + 0.278382i) q^{82} +(-16.3200 + 3.46892i) q^{83} +(11.7247 + 5.22018i) q^{84} +(-1.35984 + 0.987981i) q^{85} +(-7.38430 + 3.28770i) q^{86} +(5.76952 - 9.99310i) q^{87} +(5.82292 + 10.0856i) q^{88} +(-12.3911 - 9.00268i) q^{89} +(-1.57843 - 0.335505i) q^{90} +(1.95880 - 6.02855i) q^{91} +2.82407 q^{92} +18.0912 q^{94} +(-0.482726 + 1.48568i) q^{95} +(-24.1902 - 5.14178i) q^{96} +(1.03488 + 0.751881i) q^{97} +(-5.40437 - 9.36065i) q^{98} +(0.659316 - 1.14197i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 3 q^{3} - 14 q^{4} - 3 q^{5} - 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9} - 17 q^{10} + 7 q^{11} + 10 q^{12} - 8 q^{13} - 21 q^{14} - 14 q^{15} - 2 q^{16} - 9 q^{17} + 12 q^{18} - 29 q^{19}+ \cdots - 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 3 * q^3 - 14 * q^4 - 3 * q^5 - 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9 - 17 * q^10 + 7 * q^11 + 10 * q^12 - 8 * q^13 - 21 * q^14 - 14 * q^15 - 2 * q^16 - 9 * q^17 + 12 * q^18 - 29 * q^19 - 8 * q^20 + 6 * q^21 + 21 * q^22 - q^23 + 5 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 + 45 * q^28 + 14 * q^29 + 22 * q^30 - 42 * q^32 - 13 * q^33 + 17 * q^34 - 9 * q^35 + q^36 + 8 * q^37 + 23 * q^38 - 3 * q^39 - q^40 - 8 * q^41 + 51 * q^42 + 37 * q^43 + 6 * q^44 - 70 * q^45 - 34 * q^46 + 14 * q^47 - 4 * q^48 - 43 * q^49 + 3 * q^50 + 33 * q^51 + 46 * q^52 + 9 * q^53 + 46 * q^54 - 8 * q^55 - 30 * q^56 + 17 * q^57 + 15 * q^58 - 11 * q^59 + 75 * q^60 + 60 * q^61 - 46 * q^63 + 23 * q^64 - 18 * q^65 - 30 * q^66 + 13 * q^67 - 30 * q^68 - 37 * q^69 + 12 * q^70 + 31 * q^71 - 38 * q^72 + 13 * q^73 - 43 * q^74 + 17 * q^75 - 12 * q^76 - 18 * q^77 - 15 * q^78 + 12 * q^79 + 6 * q^80 - 22 * q^81 - q^82 - 44 * q^83 - 23 * q^84 - 37 * q^85 - 19 * q^86 + 15 * q^87 + 17 * q^88 - q^89 + 7 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 - 22 * q^95 - 8 * q^96 + 3 * q^97 - 10 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

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