LMFDB - Embedded newform 57.2.i.b.28.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,2,Mod(4,57)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("57.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	57.i (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.455147291521$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			28.1
Root			$0.500000 - 0.677980i$ of defining polynomial
Character	$\chi$	$=$	57.28
Dual form			57.2.i.b.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.458021 - 2.59757i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-4.65819 + 1.69544i) q^{4} +(1.91800 + 0.698096i) q^{5} +(-2.02055 - 1.69544i) q^{6} +(-1.30802 + 2.26556i) q^{7} +(3.89993 + 6.75488i) q^{8} +(0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(-0.458021 - 2.59757i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-4.65819 + 1.69544i) q^{4} +(1.91800 + 0.698096i) q^{5} +(-2.02055 - 1.69544i) q^{6} +(-1.30802 + 2.26556i) q^{7} +(3.89993 + 6.75488i) q^{8} +(0.173648 - 0.984808i) q^{9} +(0.934866 - 5.30189i) q^{10} +(-1.86080 - 3.22300i) q^{11} +(-2.47857 + 4.29301i) q^{12} +(1.65597 + 1.38952i) q^{13} +(6.48405 + 2.36000i) q^{14} +(1.91800 - 0.698096i) q^{15} +(8.16523 - 6.85145i) q^{16} +(-0.289062 - 1.63935i) q^{17} -2.63764 q^{18} +(1.99648 + 3.87480i) q^{19} -10.1180 q^{20} +(0.454272 + 2.57630i) q^{21} +(-7.51967 + 6.30975i) q^{22} +(-6.08324 + 2.21412i) q^{23} +(7.32948 + 2.66771i) q^{24} +(-0.638820 - 0.536034i) q^{25} +(2.85091 - 4.93792i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(2.25189 - 12.7711i) q^{28} +(-0.591004 + 3.35175i) q^{29} +(-2.69184 - 4.66240i) q^{30} +(0.931902 - 1.61410i) q^{31} +(-9.58685 - 8.04432i) q^{32} +(-3.49716 - 1.27286i) q^{33} +(-4.12593 + 1.50172i) q^{34} +(-4.09038 + 3.43223i) q^{35} +(0.860798 + 4.88183i) q^{36} +0.727675 q^{37} +(9.15063 - 6.96072i) q^{38} +2.16171 q^{39} +(2.76453 + 15.6784i) q^{40} +(4.86157 - 4.07934i) q^{41} +(6.48405 - 2.36000i) q^{42} +(-6.83268 - 2.48689i) q^{43} +(14.1324 + 11.8585i) q^{44} +(1.02055 - 1.76764i) q^{45} +(8.53757 + 14.7875i) q^{46} +(0.262295 - 1.48755i) q^{47} +(1.85091 - 10.4970i) q^{48} +(0.0781505 + 0.135361i) q^{49} +(-1.09979 + 1.90489i) q^{50} +(-1.27519 - 1.07001i) q^{51} +(-10.0697 - 3.66506i) q^{52} +(-1.29527 + 0.471438i) q^{53} +(-2.02055 + 1.69544i) q^{54} +(-1.31906 - 7.48074i) q^{55} -20.4048 q^{56} +(4.02006 + 1.68496i) q^{57} +8.97710 q^{58} +(-1.27968 - 7.25745i) q^{59} +(-7.75084 + 6.50373i) q^{60} +(10.5689 - 3.84677i) q^{61} +(-4.61957 - 1.68139i) q^{62} +(2.00401 + 1.68156i) q^{63} +(-5.84573 + 10.1251i) q^{64} +(2.20613 + 3.82113i) q^{65} +(-1.70457 + 9.66710i) q^{66} +(1.15878 - 6.57179i) q^{67} +(4.12593 + 7.14633i) q^{68} +(-3.23682 + 5.60634i) q^{69} +(10.7889 + 9.05299i) q^{70} +(-5.54419 - 2.01792i) q^{71} +(7.32948 - 2.66771i) q^{72} +(-10.5104 + 8.81927i) q^{73} +(-0.333290 - 1.89018i) q^{74} -0.833921 q^{75} +(-15.8695 - 14.6646i) q^{76} +9.73587 q^{77} +(-0.990110 - 5.61519i) q^{78} +(10.2274 - 8.58178i) q^{79} +(20.4439 - 7.44098i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-12.8231 - 10.7598i) q^{82} +(-4.34610 + 7.52767i) q^{83} +(-6.48405 - 11.2307i) q^{84} +(0.590004 - 3.34608i) q^{85} +(-3.33036 + 18.8874i) q^{86} +(1.70173 + 2.94748i) q^{87} +(14.5140 - 25.1390i) q^{88} +(-5.47265 - 4.59210i) q^{89} +(-5.05900 - 1.84133i) q^{90} +(-5.31409 + 1.93417i) q^{91} +(24.5830 - 20.6276i) q^{92} +(-0.323646 - 1.83549i) q^{93} -3.98414 q^{94} +(1.12426 + 8.82562i) q^{95} -12.5147 q^{96} +(0.402070 + 2.28025i) q^{97} +(0.315814 - 0.264999i) q^{98} +(-3.49716 + 1.27286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 3 q^{6} - 9 q^{7} + 3 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 3 * q^6 - 9 * q^7 + 3 * q^8	\( 12 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 3 q^{6} - 9 q^{7} + 3 q^{8} - 18 q^{10} - 9 q^{11} - 6 q^{12} - 3 q^{13} - 3 q^{14} + 6 q^{15} + 33 q^{16} + 12 q^{17} - 9 q^{19} - 18 q^{20} - 24 q^{22} + 9 q^{23} + 30 q^{24} - 12 q^{25} - 6 q^{27} + 30 q^{28} - 6 q^{30} - 3 q^{32} - 9 q^{33} + 21 q^{34} + 30 q^{35} - 3 q^{36} - 12 q^{37} + 18 q^{38} + 6 q^{39} - 3 q^{40} - 18 q^{41} - 3 q^{42} + 15 q^{43} + 15 q^{44} - 9 q^{45} + 27 q^{46} - 9 q^{47} - 12 q^{48} - 9 q^{49} + 9 q^{50} - 15 q^{51} - 27 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 78 q^{56} - 3 q^{57} - 24 q^{58} - 30 q^{59} - 15 q^{60} + 21 q^{61} + 3 q^{62} + 9 q^{63} - 21 q^{64} + 21 q^{65} + 30 q^{66} + 3 q^{67} - 21 q^{68} - 6 q^{69} + 18 q^{70} - 30 q^{71} + 30 q^{72} - 24 q^{73} + 39 q^{74} + 30 q^{75} - 60 q^{76} + 96 q^{77} + 9 q^{78} + 24 q^{79} + 42 q^{80} - 33 q^{82} + 3 q^{83} + 3 q^{84} + 3 q^{85} + 51 q^{86} + 15 q^{87} + 42 q^{88} + 3 q^{89} - 9 q^{90} + 24 q^{91} + 69 q^{92} - 6 q^{93} + 18 q^{94} - 54 q^{95} - 42 q^{96} - 27 q^{97} - 3 q^{98} - 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 3 * q^6 - 9 * q^7 + 3 * q^8 - 18 * q^10 - 9 * q^11 - 6 * q^12 - 3 * q^13 - 3 * q^14 + 6 * q^15 + 33 * q^16 + 12 * q^17 - 9 * q^19 - 18 * q^20 - 24 * q^22 + 9 * q^23 + 30 * q^24 - 12 * q^25 - 6 * q^27 + 30 * q^28 - 6 * q^30 - 3 * q^32 - 9 * q^33 + 21 * q^34 + 30 * q^35 - 3 * q^36 - 12 * q^37 + 18 * q^38 + 6 * q^39 - 3 * q^40 - 18 * q^41 - 3 * q^42 + 15 * q^43 + 15 * q^44 - 9 * q^45 + 27 * q^46 - 9 * q^47 - 12 * q^48 - 9 * q^49 + 9 * q^50 - 15 * q^51 - 27 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 78 * q^56 - 3 * q^57 - 24 * q^58 - 30 * q^59 - 15 * q^60 + 21 * q^61 + 3 * q^62 + 9 * q^63 - 21 * q^64 + 21 * q^65 + 30 * q^66 + 3 * q^67 - 21 * q^68 - 6 * q^69 + 18 * q^70 - 30 * q^71 + 30 * q^72 - 24 * q^73 + 39 * q^74 + 30 * q^75 - 60 * q^76 + 96 * q^77 + 9 * q^78 + 24 * q^79 + 42 * q^80 - 33 * q^82 + 3 * q^83 + 3 * q^84 + 3 * q^85 + 51 * q^86 + 15 * q^87 + 42 * q^88 + 3 * q^89 - 9 * q^90 + 24 * q^91 + 69 * q^92 - 6 * q^93 + 18 * q^94 - 54 * q^95 - 42 * q^96 - 27 * q^97 - 3 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.458021	−	2.59757i	−0.323870	−	1.83676i	−0.517500	−	0.855683i	$-0.673137\pi$
$2$	−0.458021	−	2.59757i	−0.323870	−	1.83676i	0.193630	−	0.981075i	$-0.437974\pi$
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$4$	−4.65819	+	1.69544i	−2.32909	+	0.847721i
$5$	1.91800	+	0.698096i	0.857758	+	0.312198i	0.733199	−	0.680014i	$-0.238026\pi$
$5$	1.91800	+	0.698096i	0.857758	+	0.312198i	0.124559	+	0.992212i	$0.460249\pi$
$6$	−2.02055	−	1.69544i	−0.824886	−	0.692161i
$7$	−1.30802	+	2.26556i	−0.494386	+	0.856302i	−0.999979	−	0.00647005i	$-0.997941\pi$
$7$	−1.30802	+	2.26556i	−0.494386	+	0.856302i	0.505593	+	0.862772i	$0.331274\pi$
$8$	3.89993	+	6.75488i	1.37883	+	2.38821i
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$	0.934866	−	5.30189i	0.295631	−	1.67660i
$11$	−1.86080	−	3.22300i	−0.561052	−	0.971770i	−0.997405	−	0.0719948i	$-0.977064\pi$
$11$	−1.86080	−	3.22300i	−0.561052	−	0.971770i	0.436353	−	0.899775i	$-0.356270\pi$
$12$	−2.47857	+	4.29301i	−0.715502	+	1.23928i
$13$	1.65597	+	1.38952i	0.459283	+	0.385384i	0.842867	−	0.538122i	$-0.180866\pi$
$13$	1.65597	+	1.38952i	0.459283	+	0.385384i	−0.383584	+	0.923506i	$0.625310\pi$
$14$	6.48405	+	2.36000i	1.73294	+	0.630737i
$15$	1.91800	−	0.698096i	0.495227	−	0.180248i
$16$	8.16523	−	6.85145i	2.04131	−	1.71286i
$17$	−0.289062	−	1.63935i	−0.0701079	−	0.397602i	−0.999587	−	0.0287275i	$-0.990854\pi$
$17$	−0.289062	−	1.63935i	−0.0701079	−	0.397602i	0.929479	−	0.368874i	$-0.120257\pi$
$18$	−2.63764			−0.621697
$19$	1.99648	+	3.87480i	0.458023	+	0.888940i
$19$	1.99648	+	3.87480i	0.458023	+	0.888940i
$20$	−10.1180			−2.26245
$21$	0.454272	+	2.57630i	0.0991302	+	0.562195i
$22$	−7.51967	+	6.30975i	−1.60320	+	1.34524i
$23$	−6.08324	+	2.21412i	−1.26844	+	0.461675i	−0.886594	−	0.462549i	$-0.846935\pi$
$23$	−6.08324	+	2.21412i	−1.26844	+	0.461675i	−0.381849	+	0.924225i	$0.624713\pi$
$24$	7.32948	+	2.66771i	1.49612	+	0.544544i
$25$	−0.638820	−	0.536034i	−0.127764	−	0.107207i
$26$	2.85091	−	4.93792i	0.559109	−	0.968405i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	2.25189	−	12.7711i	0.425567	−	2.41351i
$29$	−0.591004	+	3.35175i	−0.109747	+	0.622405i	0.879471	+	0.475953i	$0.157897\pi$
$29$	−0.591004	+	3.35175i	−0.109747	+	0.622405i	−0.989218	+	0.146452i	$0.953215\pi$
$30$	−2.69184	−	4.66240i	−0.491460	−	0.851234i
$31$	0.931902	−	1.61410i	0.167375	−	0.289901i	−0.770121	−	0.637897i	$-0.779804\pi$
$31$	0.931902	−	1.61410i	0.167375	−	0.289901i	0.937496	+	0.347996i	$0.113138\pi$
$32$	−9.58685	−	8.04432i	−1.69473	−	1.42205i
$33$	−3.49716	−	1.27286i	−0.608777	−	0.221577i
$34$	−4.12593	+	1.50172i	−0.707592	+	0.257542i
$35$	−4.09038	+	3.43223i	−0.691400	+	0.580153i
$36$	0.860798	+	4.88183i	0.143466	+	0.813638i
$37$	0.727675			0.119629			0.0598145	−	0.998210i	$-0.480949\pi$
$37$	0.727675			0.119629			0.0598145	+	0.998210i	$0.480949\pi$
$38$	9.15063	−	6.96072i	1.48443	−	1.12918i
$39$	2.16171			0.346151
$40$	2.76453	+	15.6784i	0.437111	+	2.47898i
$41$	4.86157	−	4.07934i	0.759249	−	0.637086i	−0.178682	−	0.983907i	$-0.557183\pi$
$41$	4.86157	−	4.07934i	0.759249	−	0.637086i	0.937931	+	0.346821i	$0.112739\pi$
$42$	6.48405	−	2.36000i	1.00051	−	0.364156i
$43$	−6.83268	−	2.48689i	−1.04197	−	0.379247i	−0.236346	−	0.971669i	$-0.575950\pi$
$43$	−6.83268	−	2.48689i	−1.04197	−	0.379247i	−0.805628	+	0.592422i	$0.798172\pi$
$44$	14.1324	+	11.8585i	2.13053	+	1.78773i
$45$	1.02055	−	1.76764i	0.152134	−	0.263505i
$46$	8.53757	+	14.7875i	1.25880	+	2.18030i
$47$	0.262295	−	1.48755i	0.0382596	−	0.216981i	−0.959684	−	0.281082i	$-0.909307\pi$
$47$	0.262295	−	1.48755i	0.0382596	−	0.216981i	0.997943	+	0.0641006i	$0.0204179\pi$
$48$	1.85091	−	10.4970i	0.267156	−	1.51511i
$49$	0.0781505	+	0.135361i	0.0111644	+	0.0193372i
$50$	−1.09979	+	1.90489i	−0.155534	+	0.269393i
$51$	−1.27519	−	1.07001i	−0.178562	−	0.149832i
$52$	−10.0697	−	3.66506i	−1.39641	−	0.508252i
$53$	−1.29527	+	0.471438i	−0.177918	+	0.0647570i	−0.429443	−	0.903094i	$-0.641290\pi$
$53$	−1.29527	+	0.471438i	−0.177918	+	0.0647570i	0.251525	+	0.967851i	$0.419068\pi$
$54$	−2.02055	+	1.69544i	−0.274962	+	0.230720i
$55$	−1.31906	−	7.48074i	−0.177861	−	1.00870i
$56$	−20.4048			−2.72671
$57$	4.02006	+	1.68496i	0.532470	+	0.223178i
$58$	8.97710			1.17875
$59$	−1.27968	−	7.25745i	−0.166601	−	0.944839i	−0.947399	−	0.320056i	$-0.896298\pi$
$59$	−1.27968	−	7.25745i	−0.166601	−	0.944839i	0.780798	−	0.624783i	$-0.214813\pi$
$60$	−7.75084	+	6.50373i	−1.00063	+	0.839628i
$61$	10.5689	−	3.84677i	1.35321	−	0.492529i	0.439263	−	0.898359i	$-0.355240\pi$
$61$	10.5689	−	3.84677i	1.35321	−	0.492529i	0.913949	+	0.405830i	$0.133018\pi$
$62$	−4.61957	−	1.68139i	−0.586686	−	0.213536i
$63$	2.00401	+	1.68156i	0.252481	+	0.211857i
$64$	−5.84573	+	10.1251i	−0.730717	+	1.26564i
$65$	2.20613	+	3.82113i	0.273637	+	0.473953i
$66$	−1.70457	+	9.66710i	−0.209818	+	1.18994i
$67$	1.15878	−	6.57179i	0.141568	−	0.802873i	−0.828491	−	0.560003i	$-0.810800\pi$
$67$	1.15878	−	6.57179i	0.141568	−	0.802873i	0.970059	−	0.242870i	$-0.0780888\pi$
$68$	4.12593	+	7.14633i	0.500343	+	0.866620i
$69$	−3.23682	+	5.60634i	−0.389668	+	0.674924i
$70$	10.7889	+	9.05299i	1.28952	+	1.08204i
$71$	−5.54419	−	2.01792i	−0.657975	−	0.239483i	−0.00861297	−	0.999963i	$-0.502742\pi$
$71$	−5.54419	−	2.01792i	−0.657975	−	0.239483i	−0.649362	+	0.760480i	$0.724964\pi$
$72$	7.32948	−	2.66771i	0.863787	−	0.314393i
$73$	−10.5104	+	8.81927i	−1.23015	+	1.03222i	−0.231920	+	0.972735i	$0.574501\pi$
$73$	−10.5104	+	8.81927i	−1.23015	+	1.03222i	−0.998229	+	0.0594827i	$0.981055\pi$
$74$	−0.333290	−	1.89018i	−0.0387442	−	0.219729i
$75$	−0.833921			−0.0962929
$76$	−15.8695	−	14.6646i	−1.82035	−	1.68215i
$77$	9.73587			1.10951
$78$	−0.990110	−	5.61519i	−0.112108	−	0.635795i
$79$	10.2274	−	8.58178i	1.15067	−	0.965526i	0.150934	−	0.988544i	$-0.451772\pi$
$79$	10.2274	−	8.58178i	1.15067	−	0.965526i	0.999735	+	0.0230183i	$0.00732760\pi$
$80$	20.4439	−	7.44098i	2.28570	−	0.831927i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	−12.8231	−	10.7598i	−1.41607	−	1.18822i
$83$	−4.34610	+	7.52767i	−0.477047	+	0.826269i	−0.999654	−	0.0263043i	$-0.991626\pi$
$83$	−4.34610	+	7.52767i	−0.477047	+	0.826269i	0.522607	+	0.852574i	$0.324959\pi$
$84$	−6.48405	−	11.2307i	−0.707468	−	1.22537i
$85$	0.590004	−	3.34608i	0.0639949	−	0.362933i
$86$	−3.33036	+	18.8874i	−0.359122	+	2.03668i
$87$	1.70173	+	2.94748i	0.182445	+	0.316003i
$88$	14.5140	−	25.1390i	1.54720	−	2.67982i
$89$	−5.47265	−	4.59210i	−0.580099	−	0.486761i	0.304880	−	0.952391i	$-0.401384\pi$
$89$	−5.47265	−	4.59210i	−0.580099	−	0.486761i	−0.884980	+	0.465630i	$0.845828\pi$
$90$	−5.05900	−	1.84133i	−0.533266	−	0.194093i
$91$	−5.31409	+	1.93417i	−0.557068	+	0.202756i
$92$	24.5830	−	20.6276i	2.56295	−	2.15057i
$93$	−0.323646	−	1.83549i	−0.0335605	−	0.190331i
$94$	−3.98414			−0.410933
$95$	1.12426	+	8.82562i	0.115347	+	0.905489i
$96$	−12.5147			−1.27728
$97$	0.402070	+	2.28025i	0.0408240	+	0.231524i	0.998392	−	0.0566821i	$-0.0180522\pi$
$97$	0.402070	+	2.28025i	0.0408240	+	0.231524i	−0.957568	+	0.288206i	$0.906941\pi$
$98$	0.315814	−	0.264999i	0.0319020	−	0.0267690i
$99$	−3.49716	+	1.27286i	−0.351477	+	0.127927i
$100$	3.88456	+	1.41386i	0.388456	+	0.141386i
$101$	1.68723	+	1.41576i	0.167886	+	0.140873i	0.722860	−	0.690995i	$-0.242827\pi$
$101$	1.68723	+	1.41576i	0.167886	+	0.140873i	−0.554974	+	0.831868i	$0.687272\pi$
$102$	−2.19536	+	3.80248i	−0.217373	+	0.376502i
$103$	1.33326	+	2.30928i	0.131370	+	0.227540i	0.924205	−	0.381897i	$-0.124729\pi$
$103$	1.33326	+	2.30928i	0.131370	+	0.227540i	−0.792835	+	0.609437i	$0.791396\pi$
$104$	−2.92789	+	16.6049i	−0.287104	+	1.62825i
$105$	−0.927213	+	5.25849i	−0.0904867	+	0.513176i
$106$	1.81785	+	3.14861i	0.176565	+	0.305820i
$107$	−6.25629	+	10.8362i	−0.604818	+	1.04758i	0.387262	+	0.921970i	$0.373421\pi$
$107$	−6.25629	+	10.8362i	−0.604818	+	1.04758i	−0.992080	+	0.125606i	$0.959912\pi$
$108$	3.79739	+	3.18639i	0.365404	+	0.306610i
$109$	−1.60408	−	0.583839i	−0.153643	−	0.0559216i	0.264054	−	0.964508i	$-0.414940\pi$
$109$	−1.60408	−	0.583839i	−0.153643	−	0.0559216i	−0.417697	+	0.908586i	$0.637163\pi$
$110$	−18.8276	+	6.85267i	−1.79514	+	0.653377i
$111$	0.557431	−	0.467740i	0.0529090	−	0.0443959i
$112$	4.84206	+	27.4607i	0.457532	+	2.59479i
$113$	17.7594			1.67067			0.835333	−	0.549744i	$-0.185275\pi$
$113$	17.7594			1.67067			0.835333	+	0.549744i	$0.185275\pi$
$114$	2.53552	−	11.2141i	0.237474	−	1.05030i
$115$	−13.2133			−1.23215
$116$	−2.92969	−	16.6151i	−0.272015	−	1.54267i
$117$	1.65597	−	1.38952i	0.153094	−	0.128461i
$118$	−18.2656	+	6.64813i	−1.68148	+	0.612010i
$119$	4.09216	+	1.48942i	0.375127	+	0.136535i
$120$	12.1957	+	10.2334i	1.11331	+	0.934174i
$121$	−1.42514	+	2.46842i	−0.129558	+	0.224401i
$122$	−14.8330	−	25.6916i	−1.34292	−	2.32601i
$123$	1.10203	−	6.24991i	0.0993665	−	0.563535i
$124$	−1.60436	+	9.09877i	−0.144076	+	0.817094i
$125$	−5.95380	−	10.3123i	−0.532524	−	0.922359i
$126$	3.45009	−	5.97574i	0.307359	−	0.532361i
$127$	16.6514	+	13.9722i	1.47757	+	1.23983i	0.908733	+	0.417378i	$0.137051\pi$
$127$	16.6514	+	13.9722i	1.47757	+	1.23983i	0.568837	+	0.822450i	$0.307394\pi$
$128$	5.45809	+	1.98658i	0.482432	+	0.175591i
$129$	−6.83268	+	2.48689i	−0.601584	+	0.218959i
$130$	8.91520	−	7.48074i	0.781915	−	0.656104i
$131$	1.02091	+	5.78988i	0.0891974	+	0.505864i	0.996372	+	0.0851086i	$0.0271237\pi$
$131$	1.02091	+	5.78988i	0.0891974	+	0.505864i	−0.907174	+	0.420755i	$0.861765\pi$
$132$	18.4485			1.60573
$133$	−11.3900	−	0.545190i	−0.987642	−	0.0472739i
$134$	−17.6014			−1.52053
$135$	−0.354433	−	2.01009i	−0.0305047	−	0.173001i
$136$	9.94632	−	8.34595i	0.852890	−	0.715659i
$137$	13.2894	−	4.83694i	1.13539	−	0.413248i	0.295143	−	0.955453i	$-0.404633\pi$
$137$	13.2894	−	4.83694i	1.13539	−	0.413248i	0.840246	+	0.542205i	$0.182411\pi$
$138$	16.0454	+	5.84004i	1.36587	+	0.497138i
$139$	12.3927	+	10.3987i	1.05114	+	0.882007i	0.993213	−	0.116314i	$-0.0371078\pi$
$139$	12.3927	+	10.3987i	1.05114	+	0.882007i	0.0579227	+	0.998321i	$0.481552\pi$
$140$	13.2346	−	22.9230i	1.11853	−	1.93735i
$141$	−0.755248	−	1.30813i	−0.0636034	−	0.110164i
$142$	−2.70233	+	15.3257i	−0.226774	+	1.28610i
$143$	1.39700	−	7.92280i	0.116823	−	0.662538i
$144$	−5.32948	−	9.23093i	−0.444123	−	0.769244i
$145$	−3.47340	+	6.01610i	−0.288450	+	0.499610i
$146$	27.7226	+	23.2621i	2.29434	+	1.92518i
$147$	0.146875	+	0.0534581i	0.0121140	+	0.00440915i
$148$	−3.38964	+	1.23373i	−0.278627	+	0.101412i
$149$	−9.25525	+	7.76607i	−0.758219	+	0.636222i	−0.937663	−	0.347547i	$-0.887015\pi$
$149$	−9.25525	+	7.76607i	−0.758219	+	0.636222i	0.179443	+	0.983768i	$0.442570\pi$
$150$	0.381953	+	2.16617i	0.0311864	+	0.176867i
$151$	16.9981			1.38328			0.691642	−	0.722240i	$-0.256887\pi$
$151$	16.9981			1.38328			0.691642	+	0.722240i	$0.256887\pi$
$152$	−18.3877	+	28.5974i	−1.49144	+	2.31956i
$153$	−1.66464			−0.134578
$154$	−4.45923	−	25.2896i	−0.359335	−	2.03789i
$155$	2.91419	−	2.44530i	0.234073	−	0.196411i
$156$	−10.0697	+	3.66506i	−0.806218	+	0.293439i
$157$	−13.9072	−	5.06181i	−1.10992	−	0.403976i	−0.278953	−	0.960305i	$-0.589988\pi$
$157$	−13.9072	−	5.06181i	−1.10992	−	0.403976i	−0.830963	+	0.556328i	$0.812210\pi$
$158$	−26.9761	−	22.6356i	−2.14610	−	1.80079i
$159$	−0.689196	+	1.19372i	−0.0546568	+	0.0946684i
$160$	−12.7719	−	22.1216i	−1.00971	−	1.74887i
$161$	2.94079	−	16.6781i	0.231767	−	1.31442i
$162$	−0.458021	+	2.59757i	−0.0359855	+	0.204084i
$163$	−7.32152	−	12.6812i	−0.573466	−	0.993272i	−0.996206	−	0.0870212i	$-0.972265\pi$
$163$	−7.32152	−	12.6812i	−0.573466	−	0.993272i	0.422741	−	0.906251i	$-0.361068\pi$
$164$	−15.7298	+	27.2448i	−1.22829	+	2.12746i
$165$	−5.81898	−	4.88271i	−0.453007	−	0.380118i
$166$	21.5442	+	7.84146i	1.67216	+	0.608616i
$167$	17.9384	−	6.52904i	1.38811	−	0.505232i	0.463487	−	0.886104i	$-0.346598\pi$
$167$	17.9384	−	6.52904i	1.38811	−	0.505232i	0.924628	+	0.380872i	$0.124376\pi$
$168$	−15.6310	+	13.1160i	−1.20596	+	1.01192i
$169$	−1.44597	−	8.20049i	−0.111228	−	0.630807i
$170$	−8.96190			−0.687347
$171$	4.16262	−	1.29329i	0.318323	−	0.0989005i
$172$	36.0443			2.74835
$173$	0.765696	+	4.34248i	0.0582148	+	0.330152i	0.999981	−	0.00611510i	$-0.00194651\pi$
$173$	0.765696	+	4.34248i	0.0582148	+	0.330152i	−0.941767	+	0.336267i	$0.890835\pi$
$174$	6.87685	−	5.77037i	0.521333	−	0.437450i
$175$	2.05001	−	0.746143i	0.154966	−	0.0564031i
$176$	−37.2760	−	13.5674i	−2.80979	−	1.02268i
$177$	−5.64529	−	4.73696i	−0.424326	−	0.356052i
$178$	−9.42169	+	16.3188i	−0.706185	+	1.22315i
$179$	0.297744	+	0.515707i	0.0222544	+	0.0385457i	0.876938	−	0.480603i	$-0.159582\pi$
$179$	0.297744	+	0.515707i	0.0222544	+	0.0385457i	−0.854684	+	0.519149i	$0.826249\pi$
$180$	−1.75697	+	9.96429i	−0.130957	+	0.742694i
$181$	0.0749729	−	0.425192i	0.00557269	−	0.0316043i	−0.981895	−	0.189428i	$-0.939337\pi$
$181$	0.0749729	−	0.425192i	0.00557269	−	0.0316043i	0.987467	+	0.157824i	$0.0504478\pi$
$182$	7.45811	+	12.9178i	0.552832	+	0.957533i
$183$	5.62360	−	9.74037i	0.415709	−	0.720029i
$184$	−38.6803	−	32.4567i	−2.85155	−	2.39274i
$185$	1.39568	+	0.507987i	0.102613	+	0.0373480i
$186$	−4.61957	+	1.68139i	−0.338723	+	0.123285i
$187$	−4.74574	+	3.98215i	−0.347043	+	0.291204i
$188$	1.30023	+	7.37399i	0.0948292	+	0.537803i
$189$	2.61605			0.190289
$190$	22.4102	−	6.96267i	1.62581	−	0.505125i
$191$	12.5978			0.911545			0.455772	−	0.890096i	$-0.349363\pi$
$191$	12.5978			0.911545			0.455772	+	0.890096i	$0.349363\pi$
$192$	2.03020	+	11.5138i	0.146517	+	0.830940i
$193$	−17.4769	+	14.6649i	−1.25802	+	1.05560i	−0.262128	+	0.965033i	$0.584424\pi$
$193$	−17.4769	+	14.6649i	−1.25802	+	1.05560i	−0.995890	+	0.0905691i	$0.971131\pi$
$194$	5.73895	−	2.08881i	0.412032	−	0.149968i
$195$	4.14617	+	1.50908i	0.296914	+	0.108068i
$196$	−0.593536	−	0.498036i	−0.0423954	−	0.0355740i
$197$	−8.13872	+	14.0967i	−0.579860	+	1.00435i	0.415635	+	0.909531i	$0.363559\pi$
$197$	−8.13872	+	14.0967i	−0.579860	+	1.00435i	−0.995495	+	0.0948151i	$0.969774\pi$
$198$	4.90811	+	8.50110i	0.348805	+	0.604147i
$199$	−1.56300	+	8.86422i	−0.110798	+	0.628368i	0.877947	+	0.478758i	$0.158913\pi$
$199$	−1.56300	+	8.86422i	−0.110798	+	0.628368i	−0.988745	+	0.149610i	$0.952198\pi$
$200$	1.12949	−	6.40565i	0.0798670	−	0.452948i
$201$	−3.33659	−	5.77914i	−0.235345	−	0.407629i
$202$	2.90474	−	5.03115i	0.204377	−	0.353991i
$203$	−6.82056	−	5.72313i	−0.478709	−	0.401685i
$204$	7.75422	+	2.82231i	0.542904	+	0.197601i
$205$	12.1723	−	4.43035i	0.850149	−	0.309429i
$206$	5.38784	−	4.52093i	0.375388	−	0.314988i
$207$	1.12414	+	6.37530i	0.0781329	+	0.443114i
$208$	23.0416			1.59765
$209$	8.77344	−	13.6449i	0.606871	−	0.943835i
$210$	14.0840			0.971885
$211$	−0.284153	−	1.61151i	−0.0195619	−	0.110941i	0.973463	−	0.228843i	$-0.0734943\pi$
$211$	−0.284153	−	1.61151i	−0.0195619	−	0.110941i	−0.993025	+	0.117902i	$0.962383\pi$
$212$	5.23429	−	4.39209i	0.359493	−	0.301650i
$213$	−5.54419	+	2.01792i	−0.379882	+	0.138266i
$214$	31.0133	+	11.2879i	2.12003	+	0.771626i
$215$	−11.3690	−	9.53974i	−0.775361	−	0.650605i
$216$	3.89993	−	6.75488i	0.265357	−	0.459612i
$217$	2.43790	+	4.22256i	0.165495	+	0.286646i
$218$	−0.781856	+	4.43412i	−0.0529540	+	0.300317i
$219$	−2.38251	+	13.5119i	−0.160995	+	0.913050i
$220$	18.8276	+	32.6103i	1.26935	+	2.19859i
$221$	1.79924	−	3.11637i	0.121030	−	0.209630i
$222$	−1.47030	−	1.23373i	−0.0986802	−	0.0828025i
$223$	1.68468	+	0.613174i	0.112815	+	0.0410612i	0.397811	−	0.917468i	$-0.369770\pi$
$223$	1.68468	+	0.613174i	0.112815	+	0.0410612i	−0.284996	+	0.958529i	$0.591992\pi$
$224$	30.7647	−	11.1975i	2.05556	−	0.748161i
$225$	−0.638820	+	0.536034i	−0.0425880	+	0.0357356i
$226$	−8.13419	−	46.1313i	−0.541078	−	3.06861i
$227$	−26.1290			−1.73424			−0.867122	−	0.498097i	$-0.834032\pi$
$227$	−26.1290			−1.73424			−0.867122	+	0.498097i	$0.834032\pi$
$228$	−21.5830	−	1.03308i	−1.42937	−	0.0684173i
$229$	−16.3173			−1.07827			−0.539137	−	0.842218i	$-0.681250\pi$
$229$	−16.3173			−1.07827			−0.539137	+	0.842218i	$0.681250\pi$
$230$	6.05199	+	34.3226i	0.399057	+	2.26316i
$231$	7.45811	−	6.25810i	0.490708	−	0.411753i
$232$	−24.9456	+	9.07945i	−1.63776	+	0.596095i
$233$	−13.1519	−	4.78689i	−0.861607	−	0.313599i	−0.126844	−	0.991923i	$-0.540485\pi$
$233$	−13.1519	−	4.78689i	−0.861607	−	0.313599i	−0.734764	+	0.678323i	$0.762707\pi$
$234$	−4.36785	−	3.66506i	−0.285535	−	0.239592i
$235$	1.54154	−	2.67002i	0.100559	−	0.174173i
$236$	18.2656	+	31.6369i	1.18899	+	2.05939i
$237$	2.31836	−	13.1480i	0.150593	−	0.854058i
$238$	1.99458	−	11.3118i	0.129290	−	0.733238i
$239$	8.15839	+	14.1308i	0.527723	+	0.914042i	0.999478	+	0.0323127i	$0.0102873\pi$
$239$	8.15839	+	14.1308i	0.527723	+	0.914042i	−0.471755	+	0.881730i	$0.656379\pi$
$240$	10.8780	−	18.8412i	0.702171	−	1.21620i
$241$	−11.1851	−	9.38538i	−0.720493	−	0.604566i	0.207029	−	0.978335i	$-0.433621\pi$
$241$	−11.1851	−	9.38538i	−0.720493	−	0.604566i	−0.927522	+	0.373769i	$0.878065\pi$
$242$	7.06462	+	2.57131i	0.454131	+	0.165290i
$243$	−0.939693	+	0.342020i	−0.0602813	+	0.0219406i
$244$	−42.7100	+	35.8380i	−2.73423	+	2.29429i
$245$	0.0553982	+	0.314179i	0.00353926	+	0.0200722i
$246$	−16.7393			−1.06726
$247$	−2.07802	+	9.19069i	−0.132221	+	0.584790i
$248$	14.5374			0.923127
$249$	1.50939	+	8.56015i	0.0956534	+	0.542478i
$250$	−24.0599	+	20.1886i	−1.52168	+	1.27684i
$251$	0.622502	−	0.226572i	0.0392920	−	0.0143011i	−0.322299	−	0.946638i	$-0.604456\pi$
$251$	0.622502	−	0.226572i	0.0392920	−	0.0143011i	0.361591	+	0.932337i	$0.382234\pi$
$252$	−12.1860	−	4.43535i	−0.767648	−	0.279401i
$253$	18.4558	+	15.4862i	1.16030	+	0.973611i
$254$	28.6669	−	49.6526i	1.79872	−	3.11548i
$255$	−1.69885	−	2.94249i	−0.106386	−	0.184266i
$256$	−1.40004	+	7.94003i	−0.0875026	+	0.496252i
$257$	−1.34781	+	7.64383i	−0.0840743	+	0.476809i	0.913478	+	0.406888i	$0.133386\pi$
$257$	−1.34781	+	7.64383i	−0.0840743	+	0.476809i	−0.997553	+	0.0699213i	$0.977725\pi$
$258$	9.58938	+	16.6093i	0.597009	+	1.03405i
$259$	−0.951815	+	1.64859i	−0.0591429	+	0.102439i
$260$	−16.7551	−	14.0592i	−1.03911	−	0.871914i
$261$	3.19820	+	1.16405i	0.197964	+	0.0720530i
$262$	14.5720	−	5.30377i	0.900261	−	0.327668i
$263$	5.12608	−	4.30129i	0.316087	−	0.265229i	−0.470915	−	0.882178i	$-0.656076\pi$
$263$	5.12608	−	4.30129i	0.316087	−	0.265229i	0.787003	+	0.616950i	$0.211632\pi$
$264$	−5.04065	−	28.5870i	−0.310231	−	1.75941i
$265$	−2.81343			−0.172828
$266$	3.80071	+	29.8361i	0.233037	+	1.82937i
$267$	−7.14403			−0.437208
$268$	5.74426	+	32.5773i	0.350886	+	1.98998i
$269$	−5.38969	+	4.52249i	−0.328615	+	0.275741i	−0.792135	−	0.610345i	$-0.791031\pi$
$269$	−5.38969	+	4.52249i	−0.328615	+	0.275741i	0.463520	+	0.886086i	$0.346586\pi$
$270$	−5.05900	+	1.84133i	−0.307881	+	0.112060i
$271$	−11.9473	−	4.34847i	−0.725748	−	0.264151i	−0.0473840	−	0.998877i	$-0.515088\pi$
$271$	−11.9473	−	4.34847i	−0.725748	−	0.264151i	−0.678364	+	0.734726i	$0.737311\pi$
$272$	−13.5922	−	11.4052i	−0.824148	−	0.691542i
$273$	−2.82757	+	4.89749i	−0.171132	+	0.296410i
$274$	−18.6511	−	32.3047i	−1.12675	−	1.95160i
$275$	−0.538920	+	3.05637i	−0.0324981	+	0.184306i
$276$	5.57251	−	31.6032i	0.335425	−	1.90229i
$277$	−5.32390	−	9.22127i	−0.319882	−	0.554053i	0.660581	−	0.750755i	$-0.270310\pi$
$277$	−5.32390	−	9.22127i	−0.319882	−	0.554053i	−0.980463	+	0.196702i	$0.936977\pi$
$278$	21.3352	−	36.9537i	1.27960	−	2.21634i
$279$	−1.42776	−	1.19803i	−0.0854776	−	0.0717242i
$280$	−39.1365	−	14.2445i	−2.33885	−	0.851274i
$281$	−12.1452	+	4.42050i	−0.724523	+	0.263705i	−0.677845	−	0.735205i	$-0.737086\pi$
$281$	−12.1452	+	4.42050i	−0.724523	+	0.263705i	−0.0466784	+	0.998910i	$0.514864\pi$
$282$	−3.05203	+	2.56096i	−0.181746	+	0.152503i
$283$	0.554427	+	3.14431i	0.0329572	+	0.186910i	0.996842	−	0.0794096i	$-0.0253035\pi$
$283$	0.554427	+	3.14431i	0.0329572	+	0.186910i	−0.963885	+	0.266319i	$0.914192\pi$
$284$	29.2472			1.73550
$285$	6.53423	+	6.03815i	0.387055	+	0.357669i
$286$	−21.2199			−1.25476
$287$	2.88296	+	16.3501i	0.170176	+	0.965113i
$288$	−9.58685	+	8.04432i	−0.564911	+	0.474016i
$289$	13.3709	−	4.86659i	0.786521	−	0.286270i
$290$	17.2181	+	6.26688i	1.01108	+	0.368004i
$291$	1.77372	+	1.48833i	0.103977	+	0.0872473i
$292$	34.0068	−	58.9016i	1.99010	−	3.44695i
$293$	0.758640	+	1.31400i	0.0443203	+	0.0767649i	0.887335	−	0.461126i	$-0.152554\pi$
$293$	0.758640	+	1.31400i	0.0443203	+	0.0767649i	−0.843014	+	0.537891i	$0.819221\pi$
$294$	0.0715892	−	0.406002i	0.00417517	−	0.0236785i
$295$	2.61196	−	14.8132i	0.152074	−	0.862455i
$296$	2.83788	+	4.91536i	0.164949	+	0.285699i
$297$	−1.86080	+	3.22300i	−0.107974	+	0.187017i
$298$	24.4120	+	20.4841i	1.41415	+	1.18661i
$299$	−13.1502	−	4.78629i	−0.760496	−	0.276798i
$300$	3.88456	−	1.41386i	0.224275	−	0.0816295i
$301$	14.5715	−	12.2270i	0.839888	−	0.704750i
$302$	−7.78548	−	44.1537i	−0.448004	−	2.54076i
$303$	2.20253			0.126532
$304$	42.8497	+	17.9599i	2.45760	+	1.03007i
$305$	22.9566			1.31449
$306$	0.762442	+	4.32402i	0.0435859	+	0.247188i
$307$	18.5249	−	15.5442i	1.05727	−	0.887156i	0.0634318	−	0.997986i	$-0.479795\pi$
$307$	18.5249	−	15.5442i	1.05727	−	0.887156i	0.993839	+	0.110830i	$0.0353510\pi$
$308$	−45.3515	+	16.5066i	−2.58414	+	0.940551i
$309$	2.50571	+	0.912004i	0.142545	+	0.0518821i
$310$	−7.68658	−	6.44981i	−0.436569	−	0.366325i
$311$	−5.55236	+	9.61697i	−0.314846	+	0.545329i	−0.979405	−	0.201907i	$-0.935286\pi$
$311$	−5.55236	+	9.61697i	−0.314846	+	0.545329i	0.664559	+	0.747236i	$0.268619\pi$
$312$	8.43054	+	14.6021i	0.477285	+	0.826682i
$313$	1.86944	−	10.6021i	0.105667	−	0.599267i	−0.885285	−	0.465049i	$-0.846037\pi$
$313$	1.86944	−	10.6021i	0.105667	−	0.599267i	0.990952	−	0.134218i	$-0.0428522\pi$
$314$	−6.77860	+	38.4433i	−0.382538	+	2.16948i
$315$	2.66980	+	4.62423i	0.150426	+	0.260546i
$316$	−33.0911	+	57.3154i	−1.86152	+	3.22425i
$317$	−11.8148	−	9.91377i	−0.663583	−	0.556813i	0.247575	−	0.968869i	$-0.420366\pi$
$317$	−11.8148	−	9.91377i	−0.663583	−	0.556813i	−0.911158	+	0.412056i	$0.864811\pi$
$318$	3.41644	+	1.24348i	0.191585	+	0.0697311i
$319$	11.9024	−	4.33213i	0.666408	−	0.242553i
$320$	−18.2804	+	15.3391i	−1.02191	+	0.857483i
$321$	2.17279	+	12.3225i	0.121273	+	0.687774i
$322$	−44.6694			−2.48933
$323$	5.77506	−	4.39299i	0.321333	−	0.244432i
$324$	4.95714			0.275397
$325$	−0.313035	−	1.77531i	−0.0173641	−	0.0984765i
$326$	−29.5870	+	24.8264i	−1.63867	+	1.37501i
$327$	−1.60408	+	0.583839i	−0.0887060	+	0.0322863i
$328$	46.5153	+	16.9302i	2.56838	+	0.934812i
$329$	3.02705	+	2.53999i	0.166886	+	0.140034i
$330$	−10.0179	+	17.3516i	−0.551469	+	0.955173i
$331$	6.94517	+	12.0294i	0.381741	+	0.661194i	0.991311	−	0.131537i	$-0.0419914\pi$
$331$	6.94517	+	12.0294i	0.381741	+	0.661194i	−0.609570	+	0.792732i	$0.708658\pi$
$332$	7.48224	−	42.4339i	0.410641	−	2.32886i
$333$	0.126359	−	0.716620i	0.00692445	−	0.0392705i
$334$	−25.1758	−	43.6057i	−1.37756	−	2.38600i
$335$	6.81030	−	11.7958i	0.372086	−	0.644473i
$336$	21.3606	+	17.9237i	1.16532	+	0.977818i
$337$	25.6690	+	9.34274i	1.39828	+	0.508931i	0.927666	−	0.373410i	$-0.121811\pi$
$337$	25.6690	+	9.34274i	1.39828	+	0.508931i	0.470611	+	0.882341i	$0.344034\pi$
$338$	−20.6391	+	7.51200i	−1.12262	+	0.408599i
$339$	13.6045	−	11.4155i	0.738895	−	0.620007i
$340$	2.92473	+	16.5870i	0.158616	+	0.899556i
$341$	−6.93633			−0.375623
$342$	−5.26598	−	10.2203i	−0.284752	−	0.552652i
$343$	−18.7212			−1.01085
$344$	−9.84833	−	55.8527i	−0.530987	−	3.01137i
$345$	−10.1220	+	8.49338i	−0.544951	+	0.457268i
$346$	10.9292	−	3.97789i	0.587556	−	0.213853i
$347$	8.06969	+	2.93713i	0.433204	+	0.157673i	0.549412	−	0.835552i	$-0.314852\pi$
$347$	8.06969	+	2.93713i	0.433204	+	0.157673i	−0.116208	+	0.993225i	$0.537074\pi$
$348$	−12.9243	−	10.8447i	−0.692813	−	0.581339i
$349$	16.2102	−	28.0768i	0.867710	−	1.50292i	0.00337939	−	0.999994i	$-0.498924\pi$
$349$	16.2102	−	28.0768i	0.867710	−	1.50292i	0.864331	−	0.502924i	$-0.167742\pi$
$350$	−2.87710	−	4.98329i	−0.153788	−	0.266368i
$351$	0.375377	−	2.12887i	0.0200362	−	0.113631i
$352$	−8.08764	+	45.8673i	−0.431072	+	2.44473i
$353$	8.80670	+	15.2537i	0.468733	+	0.811870i	0.999361	−	0.0357348i	$-0.0113772\pi$
$353$	8.80670	+	15.2537i	0.468733	+	0.811870i	−0.530628	+	0.847605i	$0.678044\pi$
$354$	−9.71892	+	16.8337i	−0.516555	+	0.894699i
$355$	−9.22508	−	7.74076i	−0.489617	−	0.410837i
$356$	33.2782	+	12.1123i	1.76374	+	0.641950i
$357$	4.09216	−	1.48942i	0.216580	−	0.0788287i
$358$	1.20321	−	1.00961i	0.0635917	−	0.0533597i
$359$	3.21021	+	18.2060i	0.169429	+	0.960877i	0.944380	+	0.328856i	$0.106663\pi$
$359$	3.21021	+	18.2060i	0.169429	+	0.960877i	−0.774951	+	0.632021i	$0.782226\pi$
$360$	15.9203			0.839073
$361$	−11.0282	+	15.4719i	−0.580430	+	0.814310i
$362$	−1.13880			−0.0598543
$363$	0.494946	+	2.80698i	0.0259779	+	0.147328i
$364$	21.4748	−	18.0195i	1.12558	−	0.944477i
$365$	−26.3157	+	9.57813i	−1.37743	+	0.501342i
$366$	−27.8770	−	10.1464i	−1.45715	−	0.530361i
$367$	−13.3495	−	11.2016i	−0.696840	−	0.584718i	0.224032	−	0.974582i	$-0.428078\pi$
$367$	−13.3495	−	11.2016i	−0.696840	−	0.584718i	−0.920873	+	0.389863i	$0.872522\pi$
$368$	−34.5012	+	59.7578i	−1.79850	+	3.11509i
$369$	−3.17316	−	5.49608i	−0.165188	−	0.286114i
$370$	0.680278	−	3.85805i	0.0353660	−	0.200570i
$371$	0.626165	−	3.55116i	0.0325088	−	0.184367i
$372$	4.61957	+	8.00133i	0.239513	+	0.414850i
$373$	5.83767	−	10.1111i	0.302263	−	0.523535i	−0.674385	−	0.738380i	$-0.735591\pi$
$373$	5.83767	−	10.1111i	0.302263	−	0.523535i	0.976648	+	0.214845i	$0.0689246\pi$
$374$	12.5176	+	10.5035i	0.647268	+	0.543122i
$375$	−11.1895	−	4.07264i	−0.577823	−	0.210310i
$376$	11.0711	−	4.02957i	0.570951	−	0.207809i
$377$	−5.63602	+	4.72918i	−0.290270	+	0.243565i
$378$	−1.19820	−	6.79536i	−0.0616290	−	0.349515i
$379$	−2.48283			−0.127534			−0.0637671	−	0.997965i	$-0.520311\pi$
$379$	−2.48283			−0.127534			−0.0637671	+	0.997965i	$0.520311\pi$
$380$	−20.2004	−	39.2053i	−1.03626	−	2.01119i
$381$	21.7368			1.11361
$382$	−5.77006	−	32.7236i	−0.295222	−	1.67429i
$383$	11.2940	−	9.47679i	0.577096	−	0.484241i	−0.306896	−	0.951743i	$-0.599290\pi$
$383$	11.2940	−	9.47679i	0.577096	−	0.484241i	0.883992	+	0.467502i	$0.154846\pi$
$384$	5.45809	−	1.98658i	0.278532	−	0.101377i
$385$	18.6734	+	6.79658i	0.951687	+	0.346386i
$386$	46.0979	+	38.6807i	2.34632	+	1.96880i
$387$	−3.63559	+	6.29703i	−0.184808	+	0.320096i
$388$	−5.73895	−	9.94015i	−0.291351	−	0.504635i
$389$	−4.47541	+	25.3813i	−0.226912	+	1.28688i	0.632084	+	0.774900i	$0.282200\pi$
$389$	−4.47541	+	25.3813i	−0.226912	+	1.28688i	−0.858996	+	0.511982i	$0.828911\pi$
$390$	2.02091	−	11.4612i	0.102333	−	0.580358i
$391$	5.38816	+	9.33256i	0.272491	+	0.471968i
$392$	−0.609564	+	1.05580i	−0.0307876	+	0.0533257i
$393$	4.50372	+	3.77907i	0.227183	+	0.190629i
$394$	40.3448	+	14.6843i	2.03254	+	0.739784i
$395$	25.6070	−	9.32020i	1.28843	−	0.468950i
$396$	14.1324	−	11.8585i	0.710177	−	0.595910i
$397$	6.48332	+	36.7687i	0.325388	+	1.84537i	0.506931	+	0.861986i	$0.330780\pi$
$397$	6.48332	+	36.7687i	0.325388	+	1.84537i	−0.181543	+	0.983383i	$0.558109\pi$
$398$	23.7413			1.19004
$399$	−9.07572	+	6.90374i	−0.454354	+	0.345619i
$400$	−8.88873			−0.444436
$401$	−6.08863	−	34.5303i	−0.304052	−	1.72436i	−0.627935	−	0.778266i	$-0.716100\pi$
$401$	−6.08863	−	34.5303i	−0.304052	−	1.72436i	0.323883	−	0.946097i	$-0.395012\pi$
$402$	−13.4835	+	11.3140i	−0.672495	+	0.564290i
$403$	3.78603	−	1.37800i	0.188596	−	0.0686432i
$404$	−10.2598	−	3.73426i	−0.510444	−	0.185786i
$405$	−1.56357	−	1.31199i	−0.0776945	−	0.0651934i
$406$	−11.7422	+	20.3382i	−0.582758	+	1.00937i
$407$	−1.35406	−	2.34529i	−0.0671180	−	0.116252i
$408$	2.25465	−	12.7867i	0.111622	−	0.633038i
$409$	5.53733	−	31.4038i	0.273803	−	1.55282i	−0.468934	−	0.883233i	$-0.655362\pi$
$409$	5.53733	−	31.4038i	0.273803	−	1.55282i	0.742737	−	0.669583i	$-0.233527\pi$
$410$	−17.0833	−	29.5891i	−0.843683	−	1.46130i
$411$	7.07113	−	12.2476i	0.348793	−	0.604128i
$412$	−10.1258	−	8.49658i	−0.498864	−	0.418596i
$413$	18.1161	+	6.59371i	0.891433	+	0.324455i
$414$	16.0454	−	5.84004i	0.788588	−	0.287023i
$415$	−13.5909	+	11.4041i	−0.667150	+	0.559806i
$416$	−4.69775	−	26.6423i	−0.230326	−	1.30625i
$417$	16.1775			0.792217
$418$	−39.4619	−	16.5400i	−1.93014	−	0.808996i
$419$	−26.7113			−1.30493			−0.652467	−	0.757817i	$-0.726266\pi$
$419$	−26.7113			−1.30493			−0.652467	+	0.757817i	$0.726266\pi$
$420$	−4.59632	−	26.0670i	−0.224278	−	1.27194i
$421$	−26.8637	+	22.5413i	−1.30925	+	1.09860i	−0.320789	+	0.947151i	$0.603948\pi$
$421$	−26.8637	+	22.5413i	−1.30925	+	1.09860i	−0.988466	+	0.151445i	$0.951608\pi$
$422$	−4.05587	+	1.47622i	−0.197437	+	0.0718610i
$423$	−1.41940	−	0.516620i	−0.0690137	−	0.0251189i
$424$	−8.23596	−	6.91079i	−0.399973	−	0.335618i
$425$	−0.694090	+	1.20220i	−0.0336683	+	0.0583152i
$426$	7.78104	+	13.4772i	0.376993	+	0.652971i
$427$	−5.10929	+	28.9762i	−0.247256	+	1.40226i
$428$	10.7708	−	61.0843i	0.520627	−	2.95262i
$429$	−4.02251	−	6.96719i	−0.194209	−	0.336379i
$430$	−19.5729	+	33.9012i	−0.943887	+	1.63486i
$431$	−22.0800	−	18.5273i	−1.06355	−	0.892428i	−0.0691015	−	0.997610i	$-0.522013\pi$
$431$	−22.0800	−	18.5273i	−1.06355	−	0.892428i	−0.994453	+	0.105181i	$0.966458\pi$
$432$	−10.0161	−	3.64558i	−0.481902	−	0.175398i
$433$	−6.14387	+	2.23619i	−0.295256	+	0.107464i	−0.485401	−	0.874292i	$-0.661326\pi$
$433$	−6.14387	+	2.23619i	−0.295256	+	0.107464i	0.190145	+	0.981756i	$0.439104\pi$
$434$	9.85179	−	8.26663i	0.472901	−	0.396811i
$435$	1.20630	+	6.84125i	0.0578375	+	0.328013i
$436$	8.46199			0.405256
$437$	−20.7243	−	19.1509i	−0.991378	−	0.916112i
$438$	36.1893			1.72919
$439$	1.51847	+	8.61169i	0.0724728	+	0.411014i	0.999363	+	0.0356816i	$0.0113602\pi$
$439$	1.51847	+	8.61169i	0.0724728	+	0.411014i	−0.926890	+	0.375332i	$0.877529\pi$
$440$	45.3873	−	38.0845i	2.16375	−	1.81561i
$441$	0.146875	−	0.0534581i	0.00699404	−	0.00254562i
$442$	−8.91908	−	3.24628i	−0.424238	−	0.154410i
$443$	−1.92342	−	1.61394i	−0.0913846	−	0.0766808i	0.595951	−	0.803021i	$-0.296775\pi$
$443$	−1.92342	−	1.61394i	−0.0913846	−	0.0766808i	−0.687335	+	0.726340i	$0.741220\pi$
$444$	−1.80359	+	3.12391i	−0.0855947	+	0.148254i
$445$	−7.29083	−	12.6281i	−0.345619	−	0.598629i
$446$	0.821141	−	4.65692i	0.0388821	−	0.220512i
$447$	−2.09799	+	11.8983i	−0.0992317	+	0.562771i
$448$	−15.2927	−	26.4878i	−0.722513	−	1.25143i
$449$	−0.710826	+	1.23119i	−0.0335460	+	0.0581033i	−0.882311	−	0.470667i	$-0.844013\pi$
$449$	−0.710826	+	1.23119i	−0.0335460	+	0.0581033i	0.848765	+	0.528770i	$0.177347\pi$
$450$	1.68498	+	1.41386i	0.0794306	+	0.0666502i
$451$	−22.1941	−	8.07799i	−1.04508	−	0.380378i
$452$	−82.7267	+	30.1101i	−3.89114	+	1.41626i
$453$	13.0213	−	10.9262i	0.611794	−	0.513356i
$454$	11.9676	+	67.8719i	0.561669	+	3.18538i
$455$	−11.5427			−0.541130
$456$	4.29627	+	33.7263i	0.201191	+	1.57938i
$457$	−20.5124			−0.959530			−0.479765	−	0.877397i	$-0.659278\pi$
$457$	−20.5124			−0.959530			−0.479765	+	0.877397i	$0.659278\pi$
$458$	7.47365	+	42.3852i	0.349221	+	1.98053i
$459$	−1.27519	+	1.07001i	−0.0595208	+	0.0499439i
$460$	61.5502	−	22.4025i	2.86980	−	1.04452i
$461$	−8.55174	−	3.11258i	−0.398294	−	0.144967i	0.135104	−	0.990831i	$-0.456863\pi$
$461$	−8.55174	−	3.11258i	−0.398294	−	0.144967i	−0.533398	+	0.845864i	$0.679085\pi$
$462$	−19.6718	−	16.5066i	−0.915215	−	0.767957i
$463$	−4.15877	+	7.20319i	−0.193274	+	0.334761i	−0.946333	−	0.323192i	$-0.895244\pi$
$463$	−4.15877	+	7.20319i	−0.193274	+	0.334761i	0.753059	+	0.657953i	$0.228577\pi$
$464$	18.1387	+	31.4171i	0.842066	+	1.45850i
$465$	0.660593	−	3.74641i	0.0306343	−	0.173736i
$466$	−6.41043	+	36.3554i	−0.296957	+	1.68413i
$467$	8.37956	+	14.5138i	0.387760	+	0.671620i	0.992148	−	0.125070i	$-0.0399157\pi$
$467$	8.37956	+	14.5138i	0.387760	+	0.671620i	−0.604388	+	0.796690i	$0.706582\pi$
$468$	−5.35796	+	9.28025i	−0.247672	+	0.428980i
$469$	13.3731	+	11.2214i	0.617512	+	0.518154i
$470$	−7.64161	−	2.78132i	−0.352481	−	0.128293i
$471$	−13.9072	+	5.06181i	−0.640810	+	0.233236i
$472$	44.0325	−	36.9477i	2.02676	−	1.70065i
$473$	4.69899	+	26.6493i	0.216060	+	1.22534i
$474$	−35.2148			−1.61747
$475$	0.801636	−	3.54548i	0.0367816	−	0.162678i
$476$	−21.5873			−0.989451
$477$	0.239355	+	1.35745i	0.0109593	+	0.0621534i
$478$	32.9689	−	27.6642i	1.50796	−	1.26533i
$479$	−7.01298	+	2.55252i	−0.320431	+	0.116627i	−0.497228	−	0.867620i	$-0.665649\pi$
$479$	−7.01298	+	2.55252i	−0.320431	+	0.116627i	0.176797	+	0.984247i	$0.443427\pi$
$480$	−24.0033	−	8.73650i	−1.09560	−	0.398765i
$481$	1.20501	+	1.01112i	0.0549435	+	0.0461031i
$482$	−19.2562	+	33.3527i	−0.877094	+	1.51917i
$483$	−8.46768	−	14.6665i	−0.385293	−	0.667347i
$484$	2.45352	−	13.9146i	0.111524	−	0.632481i
$485$	−0.820663	+	4.65421i	−0.0372644	+	0.211337i
$486$	1.31882	+	2.28426i	0.0598229	+	0.103616i
$487$	9.56187	−	16.5616i	0.433290	−	0.750480i	−0.563865	−	0.825867i	$-0.690686\pi$
$487$	9.56187	−	16.5616i	0.433290	−	0.750480i	0.997154	+	0.0753874i	$0.0240193\pi$
$488$	67.2026	+	56.3897i	3.04212	+	2.55264i
$489$	−13.7600	−	5.00822i	−0.622247	−	0.226479i
$490$	0.790727	−	0.287801i	0.0357214	−	0.0130015i
$491$	22.0462	−	18.4990i	0.994933	−	0.834848i	0.00865889	−	0.999963i	$-0.497244\pi$
$491$	22.0462	−	18.4990i	0.994933	−	0.834848i	0.986274	+	0.165114i	$0.0527993\pi$
$492$	5.46291	+	30.9817i	0.246287	+	1.39676i
$493$	5.66554			0.255163
$494$	24.8252	+	1.18827i	1.11694	+	0.0534628i
$495$	−7.59614			−0.341421
$496$	−3.44973	−	19.5644i	−0.154897	−	0.878467i
$497$	11.8237	−	9.92123i	0.530364	−	0.445028i
$498$	21.5442	−	7.84146i	0.965421	−	0.351384i
$499$	19.7579	+	7.19130i	0.884487	+	0.321927i	0.744019	−	0.668158i	$-0.232917\pi$
$499$	19.7579	+	7.19130i	0.884487	+	0.321927i	0.140468	+	0.990085i	$0.455139\pi$
$500$	45.2178	+	37.9422i	2.02220	+	1.69683i
$501$	9.54482	−	16.5321i	0.426431	−	0.738600i
$502$	−0.873655	−	1.51322i	−0.0389931	−	0.0675381i
$503$	−0.253809	+	1.43942i	−0.0113168	+	0.0641807i	−0.989943	−	0.141466i	$-0.954819\pi$
$503$	−0.253809	+	1.43942i	−0.0113168	+	0.0641807i	0.978626	+	0.205646i	$0.0659296\pi$
$504$	−3.54326	+	20.0948i	−0.157829	+	0.895095i
$505$	2.24779	+	3.89328i	0.100025	+	0.173249i
$506$	31.7734	−	55.0331i	1.41250	−	2.44652i
$507$	−6.37885	−	5.35249i	−0.283295	−	0.237713i
$508$	−101.254	−	36.8535i	−4.49243	−	1.63511i
$509$	3.51787	−	1.28040i	0.155927	−	0.0567528i	−0.262877	−	0.964829i	$-0.584672\pi$
$509$	3.51787	−	1.28040i	0.155927	−	0.0567528i	0.418804	+	0.908076i	$0.362449\pi$
$510$	−6.86522	+	5.76060i	−0.303997	+	0.255084i
$511$	−6.23277	−	35.3478i	−0.275721	−	1.56369i
$512$	32.8828			1.45323
$513$	2.35744	−	3.66640i	0.104083	−	0.161875i
$514$	20.4727			0.903011
$515$	0.945103	+	5.35995i	0.0416462	+	0.236187i
$516$	27.6115	−	23.1688i	1.21553	−	1.01995i
$517$	−5.28244	+	1.92265i	−0.232322	+	0.0845581i
$518$	4.71828	+	1.71731i	0.207309	+	0.0754544i
$519$	3.37785	+	2.83435i	0.148271	+	0.124414i
$520$	−17.2075	+	29.8043i	−0.754601	+	1.30701i
$521$	−9.14722	−	15.8435i	−0.400747	−	0.694114i	0.593069	−	0.805152i	$-0.297916\pi$
$521$	−9.14722	−	15.8435i	−0.400747	−	0.694114i	−0.993816	+	0.111037i	$0.964583\pi$
$522$	1.55886	−	8.84071i	0.0682293	−	0.386947i
$523$	0.206665	−	1.17205i	0.00903681	−	0.0512503i	−0.979956	−	0.199215i	$-0.936161\pi$
$523$	0.206665	−	1.17205i	0.00903681	−	0.0512503i	0.988993	+	0.147964i	$0.0472721\pi$
$524$	−14.5720	−	25.2394i	−0.636580	−	1.10259i
$525$	1.09079	−	1.88930i	0.0476059	−	0.0824558i
$526$	−13.5207	−	11.3452i	−0.589532	−	0.494676i
$527$	−2.91546	−	1.06114i	−0.126999	−	0.0462240i
$528$	−37.2760	+	13.5674i	−1.62223	+	0.590444i
$529$	14.4845	−	12.1539i	0.629759	−	0.528431i
$530$	1.28861	+	7.30808i	0.0559737	+	0.317443i
$531$	−7.36941			−0.319805
$532$	53.9813	−	16.7716i	2.34039	−	0.727139i
$533$	13.7189			0.594233
$534$	3.27212	+	18.5571i	0.141598	+	0.803044i
$535$	−19.5643	+	16.4164i	−0.845839	+	0.709743i
$536$	48.9109	−	17.8021i	2.11263	−	0.768934i
$537$	0.559575	+	0.203669i	0.0241474	+	0.00878895i
$538$	14.2161	+	11.9287i	0.612898	+	0.514282i
$539$	0.290845	−	0.503758i	0.0125276	−	0.0216984i
$540$	5.05900	+	8.76245i	0.217705	+	0.377076i
$541$	−0.498722	+	2.82839i	−0.0214417	+	0.121602i	−0.993650	−	0.112516i	$-0.964109\pi$
$541$	−0.498722	+	2.82839i	−0.0214417	+	0.121602i	0.972208	+	0.234118i	$0.0752202\pi$
$542$	−5.82331	+	33.0257i	−0.250133	+	1.41857i
$543$	−0.215876	−	0.373908i	−0.00926412	−	0.0160459i
$544$	−10.4163	+	18.0415i	−0.446595	+	0.773525i
$545$	−2.66906	−	2.23961i	−0.114330	−	0.0959343i
$546$	14.0167	+	5.10165i	0.599858	+	0.218330i
$547$	−3.94592	+	1.43620i	−0.168715	+	0.0614074i	−0.424997	−	0.905195i	$-0.639725\pi$
$547$	−3.94592	+	1.43620i	−0.168715	+	0.0614074i	0.256281	+	0.966602i	$0.417503\pi$
$548$	−53.7037	+	45.0628i	−2.29411	+	1.92499i
$549$	−1.95306	−	11.0763i	−0.0833544	−	0.472727i
$550$	8.18596			0.349050
$551$	−14.1673	+	4.40167i	−0.603547	+	0.187517i
$552$	−50.4936			−2.14915
$553$	6.06493	+	34.3959i	0.257907	+	1.46266i
$554$	−21.5144	+	18.0527i	−0.914060	+	0.766987i
$555$	1.39568	−	0.507987i	0.0592434	−	0.0215628i
$556$	−75.3579	−	27.4280i	−3.19589	−	1.16321i
$557$	13.7220	+	11.5141i	0.581420	+	0.487869i	0.885413	−	0.464805i	$-0.153876\pi$
$557$	13.7220	+	11.5141i	0.581420	+	0.487869i	−0.303993	+	0.952674i	$0.598320\pi$
$558$	−2.45802	+	4.25742i	−0.104056	+	0.180231i
$559$	−7.85911	−	13.6124i	−0.332405	−	0.575742i
$560$	−9.88312	+	56.0500i	−0.417638	+	2.36854i
$561$	−1.07577	+	6.10101i	−0.0454192	+	0.257585i
$562$	17.0453	+	29.5233i	0.719013	+	1.24537i
$563$	7.18981	−	12.4531i	0.303015	−	0.524837i	−0.673803	−	0.738911i	$-0.735340\pi$
$563$	7.18981	−	12.4531i	0.303015	−	0.524837i	0.976817	+	0.214075i	$0.0686736\pi$
$564$	5.73594	+	4.81303i	0.241527	+	0.202665i
$565$	34.0626	+	12.3978i	1.43303	+	0.521579i
$566$	7.91362	−	2.88032i	0.332634	−	0.121069i
$567$	2.00401	−	1.68156i	0.0841604	−	0.0706190i
$568$	−7.99116	−	45.3201i	−0.335302	−	1.90159i
$569$	−5.28168			−0.221420			−0.110710	−	0.993853i	$-0.535312\pi$
$569$	−5.28168			−0.221420			−0.110710	+	0.993853i	$0.535312\pi$
$570$	12.6917	−	19.7387i	0.531596	−	0.826764i
$571$	−21.5912			−0.903563			−0.451782	−	0.892129i	$-0.649211\pi$
$571$	−21.5912			−0.903563			−0.451782	+	0.892129i	$0.649211\pi$
$572$	6.92514	+	39.2744i	0.289555	+	1.64215i
$573$	9.65047	−	8.09771i	0.403154	−	0.338287i
$574$	41.1499	−	14.9773i	1.71756	−	0.625142i
$575$	5.07294	+	1.84640i	0.211556	+	0.0770002i
$576$	8.95618	+	7.51513i	0.373174	+	0.313130i
$577$	1.49922	−	2.59673i	0.0624135	−	0.108103i	−0.833130	−	0.553077i	$-0.813454\pi$
$577$	1.49922	−	2.59673i	0.0624135	−	0.108103i	0.895544	+	0.444974i	$0.146787\pi$
$578$	−18.7654	−	32.5027i	−0.780539	−	1.35193i
$579$	−3.96170	+	22.4679i	−0.164643	+	0.933735i
$580$	5.97979	−	33.9131i	0.248297	−	1.40816i
$581$	−11.3696	−	19.6927i	−0.471691	−	0.816993i
$582$	3.05363	−	5.28904i	0.126577	−	0.219238i
$583$	3.92967	+	3.29738i	0.162750	+	0.136564i
$584$	−100.563	−	36.6019i	−4.16133	−	1.51460i
$585$	4.14617	−	1.50908i	0.171423	−	0.0623929i
$586$	3.06574	−	2.57246i	0.126645	−	0.106267i
$587$	−7.63493	−	43.2998i	−0.315127	−	1.78718i	−0.571505	−	0.820599i	$-0.693640\pi$
$587$	−7.63493	−	43.2998i	−0.315127	−	1.78718i	0.256378	−	0.966577i	$-0.417471\pi$
$588$	−0.774806			−0.0319525
$589$	8.11484	+	0.388421i	0.334366	+	0.0160046i
$590$	−39.6745			−1.63337
$591$	2.82655	+	16.0301i	0.116269	+	0.659392i
$592$	5.94163	−	4.98562i	0.244200	−	0.204908i
$593$	39.4937	−	14.3745i	1.62181	−	0.590292i	0.638087	−	0.769964i	$-0.279726\pi$
$593$	39.4937	−	14.3745i	1.62181	−	0.590292i	0.983726	+	0.179673i	$0.0575038\pi$
$594$	9.22424	+	3.35735i	0.378475	+	0.137754i
$595$	6.80902	+	5.71344i	0.279142	+	0.234228i
$596$	29.9457	−	51.8676i	1.22663	−	2.12458i
$597$	4.50048	+	7.79507i	0.184193	+	0.319031i
$598$	−6.40962	+	36.3508i	−0.262109	+	1.48649i
$599$	0.357805	−	2.02921i	0.0146195	−	0.0829114i	−0.976625	−	0.214950i	$-0.931041\pi$
$599$	0.357805	−	2.02921i	0.0146195	−	0.0829114i	0.991245	+	0.132039i	$0.0421523\pi$
$600$	−3.25224	−	5.63304i	−0.132772	−	0.229968i
$601$	−1.80822	+	3.13194i	−0.0737590	+	0.127754i	−0.900546	−	0.434761i	$-0.856833\pi$
$601$	−1.80822	+	3.13194i	−0.0737590	+	0.127754i	0.826787	+	0.562515i	$0.190166\pi$
$602$	−38.4344	−	32.2503i	−1.56647	−	1.31442i
$603$	−6.27073	−	2.28236i	−0.255364	−	0.0929449i
$604$	−79.1803	+	28.8193i	−3.22180	+	1.17264i
$605$	−4.45662	+	3.73955i	−0.181187	+	0.152034i
$606$	−1.00880	−	5.72121i	−0.0409799	−	0.232408i
$607$	−22.8098			−0.925823			−0.462911	−	0.886405i	$-0.653195\pi$
$607$	−22.8098			−0.925823			−0.462911	+	0.886405i	$0.653195\pi$
$608$	12.0302	−	53.2074i	0.487891	−	2.15785i
$609$	−8.90361			−0.360792
$610$	−10.5146	−	59.6314i	−0.425725	−	2.41441i
$611$	2.50133	−	2.09887i	0.101193	−	0.0849111i
$612$	7.75422	−	2.82231i	0.313446	−	0.114085i
$613$	−18.6110	−	6.77383i	−0.751689	−	0.273593i	−0.0623729	−	0.998053i	$-0.519867\pi$
$613$	−18.6110	−	6.77383i	−0.751689	−	0.273593i	−0.689316	+	0.724460i	$0.742089\pi$
$614$	−48.8620	−	41.0001i	−1.97191	−	1.65463i
$615$	6.47673	−	11.2180i	0.261167	−	0.452355i
$616$	37.9692	+	65.7647i	1.52982	+	2.64973i
$617$	−1.73058	+	9.81460i	−0.0696705	+	0.395121i	0.929953	+	0.367679i	$0.119847\pi$
$617$	−1.73058	+	9.81460i	−0.0696705	+	0.395121i	−0.999623	+	0.0274423i	$0.991264\pi$
$618$	1.22132	−	6.92647i	0.0491288	−	0.278624i
$619$	14.9349	+	25.8681i	0.600285	+	1.03972i	0.992778	+	0.119970i	$0.0382797\pi$
$619$	14.9349	+	25.8681i	0.600285	+	1.03972i	−0.392492	+	0.919755i	$0.628387\pi$
$620$	−9.42899	+	16.3315i	−0.378677	+	0.655888i
$621$	4.95910	+	4.16118i	0.199002	+	0.166982i
$622$	27.5238	+	10.0179i	1.10361	+	0.401680i
$623$	17.5620	−	6.39206i	0.703608	−	0.256092i
$624$	17.6509	−	14.8109i	0.706601	−	0.592909i
$625$	−3.49640	−	19.8291i	−0.139856	−	0.793163i
$626$	−28.3960			−1.13493
$627$	−2.04990	−	16.0920i	−0.0818653	−	0.642654i
$628$	73.3644			2.92756
$629$	−0.210343	−	1.19292i	−0.00838693	−	0.0475647i
$630$	10.7889	−	9.05299i	0.429841	−	0.360680i
$631$	4.84455	−	1.76327i	0.192858	−	0.0701947i	−0.243785	−	0.969829i	$-0.578389\pi$
$631$	4.84455	−	1.76327i	0.192858	−	0.0701947i	0.436644	+	0.899635i	$0.356167\pi$
$632$	97.8550	+	35.6163i	3.89246	+	1.41674i
$633$	−1.25354	−	1.05184i	−0.0498236	−	0.0418069i
$634$	−20.3403	+	35.2304i	−0.807815	+	1.39918i
$635$	22.1835	+	38.4229i	0.880325	+	1.52477i
$636$	1.18652	−	6.72908i	0.0470485	−	0.266825i
$637$	−0.0586719	+	0.332745i	−0.00232466	+	0.0131838i
$638$	−16.7046	−	28.9332i	−0.661340	−	1.14547i
$639$	−2.95000	+	5.10956i	−0.116700	+	0.202131i
$640$	9.08182	+	7.62055i	0.358990	+	0.301229i
$641$	34.2947	+	12.4823i	1.35456	+	0.493020i	0.914368	−	0.404884i	$-0.132688\pi$
$641$	34.2947	+	12.4823i	1.35456	+	0.493020i	0.440192	+	0.897904i	$0.354910\pi$
$642$	31.0133	−	11.2879i	1.22400	−	0.445499i
$643$	9.13789	−	7.66760i	0.360363	−	0.302381i	−0.444572	−	0.895743i	$-0.646644\pi$
$643$	9.13789	−	7.66760i	0.360363	−	0.302381i	0.804936	+	0.593362i	$0.202200\pi$
$644$	14.5779	+	82.6756i	0.574451	+	3.25787i
$645$	−14.8412			−0.584372
$646$	−14.0562	−	12.9890i	−0.553033	−	0.511047i
$647$	34.5568			1.35857			0.679283	−	0.733876i	$-0.262291\pi$
$647$	34.5568			1.35857			0.679283	+	0.733876i	$0.262291\pi$
$648$	−1.35443	−	7.68137i	−0.0532071	−	0.301753i
$649$	−21.0095	+	17.6291i	−0.824695	+	0.692001i
$650$	−4.46811	+	1.62626i	−0.175254	+	0.0637871i
$651$	4.58175	+	1.66762i	0.179573	+	0.0653592i
$652$	55.6053	+	46.6584i	2.17767	+	1.82728i
$653$	−10.2308	+	17.7202i	−0.400361	+	0.693445i	−0.993769	−	0.111456i	$-0.964448\pi$
$653$	−10.2308	+	17.7202i	−0.400361	+	0.693445i	0.593409	+	0.804901i	$0.297782\pi$
$654$	2.25126	+	3.89930i	0.0880314	+	0.152475i
$655$	−2.08378	+	11.8177i	−0.0814200	+	0.461756i
$656$	11.7465	−	66.6175i	0.458622	−	2.60098i
$657$	6.86018	+	11.8822i	0.267641	+	0.463568i
$658$	5.21135	−	9.02633i	0.203160	−	0.351883i
$659$	8.84184	+	7.41919i	0.344429	+	0.289010i	0.798549	−	0.601930i	$-0.205602\pi$
$659$	8.84184	+	7.41919i	0.344429	+	0.289010i	−0.454119	+	0.890941i	$0.650046\pi$
$660$	35.3843	+	12.8788i	1.37733	+	0.501307i
$661$	5.29840	−	1.92846i	0.206084	−	0.0750084i	−0.236916	−	0.971530i	$-0.576137\pi$
$661$	5.29840	−	1.92846i	0.206084	−	0.0750084i	0.443000	+	0.896522i	$0.353914\pi$
$662$	28.0661	−	23.5502i	1.09082	−	0.915306i
$663$	−0.624869	−	3.54381i	−0.0242679	−	0.137630i
$664$	−67.7981			−2.63108
$665$	−21.4656	−	8.99702i	−0.832398	−	0.348890i
$666$	−1.91934			−0.0743730
$667$	−3.82595	−	21.6981i	−0.148142	−	0.840152i
$668$	−72.4908	+	60.8270i	−2.80475	+	2.35347i
$669$	1.68468	−	0.613174i	0.0651335	−	0.0237067i
$670$	−33.7596	−	12.2875i	−1.30425	−	0.474707i
$671$	−32.0648	−	26.9055i	−1.23785	−	1.03868i
$672$	16.3696	−	28.3529i	0.631470	−	1.09374i
$673$	−6.58001	−	11.3969i	−0.253641	−	0.439318i	0.710885	−	0.703308i	$-0.248295\pi$
$673$	−6.58001	−	11.3969i	−0.253641	−	0.439318i	−0.964525	+	0.263990i	$0.914961\pi$
$674$	12.5115	−	70.9560i	0.481923	−	2.73312i
$675$	−0.144809	+	0.821252i	−0.00557369	+	0.0316100i
$676$	20.6391	+	35.7479i	0.793810	+	1.37492i
$677$	−20.0297	+	34.6924i	−0.769804	+	1.33334i	0.167865	+	0.985810i	$0.446313\pi$
$677$	−20.0297	+	34.6924i	−0.769804	+	1.33334i	−0.937669	+	0.347529i	$0.887021\pi$
$678$	−35.8838	−	30.1101i	−1.37811	−	1.15637i
$679$	−5.69197	−	2.07171i	−0.218438	−	0.0795048i
$680$	24.9034	−	9.06408i	0.955000	−	0.347592i
$681$	−20.0160	+	16.7954i	−0.767014	+	0.643601i
$682$	3.17698	+	18.0176i	0.121653	+	0.689929i
$683$	12.5951			0.481939			0.240970	−	0.970533i	$-0.422535\pi$
$683$	12.5951			0.481939			0.240970	+	0.970533i	$0.422535\pi$
$684$	−17.1976	+	13.0819i	−0.657565	+	0.500198i
$685$	28.8658			1.10290
$686$	8.57471	+	48.6296i	0.327384	+	1.85669i
$687$	−12.4997	+	10.4885i	−0.476895	+	0.400162i
$688$	−72.8292	+	26.5077i	−2.77659	+	1.01060i
$689$	−2.79999	−	1.01911i	−0.106671	−	0.0388251i
$690$	26.6982	+	22.4025i	1.01638	+	0.852847i
$691$	−3.42606	+	5.93411i	−0.130334	+	0.225744i	−0.923805	−	0.382863i	$-0.874938\pi$
$691$	−3.42606	+	5.93411i	−0.130334	+	0.225744i	0.793472	+	0.608607i	$0.208271\pi$
$692$	−10.9292	−	18.9299i	−0.415465	−	0.719606i
$693$	1.69062	−	9.58796i	0.0642212	−	0.364216i
$694$	3.93330	−	22.3068i	0.149306	−	0.846756i
$695$	16.5100	+	28.5961i	0.626258	+	1.08471i
$696$	−13.2733	+	22.9900i	−0.503122	+	0.871432i
$697$	−8.09277	−	6.79064i	−0.306536	−	0.257214i
$698$	−80.3560	−	29.2472i	−3.04152	−	1.10702i
$699$	−13.1519	+	4.78689i	−0.497449	+	0.181057i
$700$	−8.28429	+	6.95135i	−0.313117	+	0.262736i
$701$	8.79059	+	49.8539i	0.332016	+	1.88296i	0.454912	+	0.890536i	$0.349671\pi$
$701$	8.79059	+	49.8539i	0.332016	+	1.88296i	−0.122896	+	0.992420i	$0.539218\pi$
$702$	−5.70182			−0.215201
$703$	1.45278	+	2.81959i	0.0547928	+	0.106343i
$704$	43.5109			1.63988
$705$	−0.535370	−	3.03623i	−0.0201632	−	0.114351i
$706$	35.5887	−	29.8625i	1.33940	−	1.12389i
$707$	−5.41443	+	1.97069i	−0.203631	+	0.0741155i
$708$	34.3281	+	12.4944i	1.29013	+	0.469568i
$709$	−8.05962	−	6.76282i	−0.302685	−	0.253983i	0.478776	−	0.877937i	$-0.341081\pi$
$709$	−8.05962	−	6.76282i	−0.302685	−	0.253983i	−0.781461	+	0.623954i	$0.785525\pi$
$710$	−15.8819	+	27.5082i	−0.596036	+	1.03236i
$711$	−6.67544	−	11.5622i	−0.250349	−	0.433616i
$712$	9.67611	−	54.8760i	0.362628	−	2.05656i
$713$	−2.09517	+	11.8823i	−0.0784648	+	0.444996i
$714$	−5.74317	−	9.94747i	−0.214933	−	0.372275i
$715$	8.21034	−	14.2207i	0.307049	−	0.531825i
$716$	−2.26130	−	1.89745i	−0.0845086	−	0.0709111i
$717$	15.3328	+	5.58067i	0.572613	+	0.208414i
$718$	45.8210	−	16.6775i	1.71003	−	0.622398i
$719$	19.5460	−	16.4011i	0.728944	−	0.611657i	−0.200899	−	0.979612i	$-0.564386\pi$
$719$	19.5460	−	16.4011i	0.728944	−	0.611657i	0.929844	+	0.367955i	$0.119942\pi$
$720$	−3.77788	−	21.4254i	−0.140793	−	0.798479i
$721$	−6.97575			−0.259790
$722$	45.2404	+	21.5600i	1.68367	+	0.802379i
$723$	−14.6011			−0.543019
$724$	0.371651	+	2.10774i	0.0138123	+	0.0783335i
$725$	2.17420	−	1.82437i	0.0807477	−	0.0677554i
$726$	7.06462	−	2.57131i	0.262193	−	0.0954304i
$727$	−1.74662	−	0.635719i	−0.0647787	−	0.0235775i	0.309428	−	0.950923i	$-0.399863\pi$
$727$	−1.74662	−	0.635719i	−0.0647787	−	0.0235775i	−0.374206	+	0.927346i	$0.622085\pi$
$728$	−33.7897	−	28.3529i	−1.25233	−	1.05083i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	36.9330	+	63.9698i	1.36695	+	2.36763i
$731$	−2.10183	+	11.9200i	−0.0777388	+	0.440879i
$732$	−9.68158	+	54.9070i	−0.357841	+	2.02942i
$733$	−19.9523	−	34.5584i	−0.736954	−	1.27644i	−0.953861	−	0.300250i	$-0.902930\pi$
$733$	−19.9523	−	34.5584i	−0.736954	−	1.27644i	0.216906	−	0.976192i	$-0.430403\pi$
$734$	−22.9825	+	39.8069i	−0.848300	+	1.46930i
$735$	0.244388	+	0.205066i	0.00901438	+	0.00756396i
$736$	76.1302	+	27.7091i	2.80620	+	1.02137i
$737$	−23.3371	+	8.49402i	−0.859635	+	0.312881i
$738$	−12.8231	+	10.7598i	−0.472023	+	0.396075i
$739$	−4.67575	−	26.5175i	−0.172000	−	0.975461i	−0.941550	−	0.336874i	$-0.890630\pi$
$739$	−4.67575	−	26.5175i	−0.172000	−	0.975461i	0.769550	−	0.638587i	$-0.220481\pi$
$740$	−7.36262			−0.270655
$741$	4.31581	+	8.37621i	0.158545	+	0.307708i
$742$	−9.51116			−0.349166
$743$	−4.76856	−	27.0439i	−0.174942	−	0.992143i	−0.938211	−	0.346063i	$-0.887518\pi$
$743$	−4.76856	−	27.0439i	−0.174942	−	0.992143i	0.763270	−	0.646080i	$-0.223593\pi$
$744$	11.1363	−	9.34448i	0.408277	−	0.342585i
$745$	−23.1731	+	8.43431i	−0.848996	+	0.309009i
$746$	−28.9381	−	10.5326i	−1.05950	−	0.385626i
$747$	6.65862	+	5.58724i	0.243626	+	0.204427i
$748$	15.3551	−	26.5957i	0.561437	−	0.972437i
$749$	−16.3667	−	28.3480i	−0.598028	−	1.03581i
$750$	−5.45393	+	30.9308i	−0.199150	+	1.12943i
$751$	−7.01549	+	39.7868i	−0.255999	+	1.45184i	0.537497	+	0.843266i	$0.319370\pi$
$751$	−7.01549	+	39.7868i	−0.255999	+	1.45184i	−0.793496	+	0.608576i	$0.791741\pi$
$752$	−8.05016	−	13.9433i	−0.293559	−	0.508459i
$753$	0.331226	−	0.573701i	0.0120706	−	0.0209068i
$754$	14.8658	+	12.4739i	0.541380	+	0.454272i
$755$	32.6024	+	11.8663i	1.18652	+	0.431859i
$756$	−12.1860	+	4.43535i	−0.443202	+	0.161312i
$757$	−3.31599	+	2.78244i	−0.120522	+	0.101130i	−0.701057	−	0.713106i	$-0.747288\pi$
$757$	−3.31599	+	2.78244i	−0.120522	+	0.101130i	0.580535	+	0.814235i	$0.302843\pi$
$758$	1.13719	+	6.44931i	0.0413045	+	0.234249i
$759$	24.0923			0.874495
$760$	−55.2315	+	42.0136i	−2.00346	+	1.52399i
$761$	−17.0834			−0.619272			−0.309636	−	0.950855i	$-0.600207\pi$
$761$	−17.0834			−0.619272			−0.309636	+	0.950855i	$0.600207\pi$
$762$	−9.95592	−	56.4628i	−0.360665	−	2.04543i
$763$	3.42090	−	2.87048i	0.123845	−	0.103918i
$764$	−58.6829	+	21.3588i	−2.12307	+	0.772735i
$765$	−3.19279	−	1.16208i	−0.115436	−	0.0420151i
$766$	−29.7895	−	24.9964i	−1.07634	−	0.903155i
$767$	7.96527	−	13.7962i	0.287609	−	0.498154i
$768$	4.03126	+	6.98235i	0.145466	+	0.251954i
$769$	8.47519	−	48.0652i	0.305623	−	1.73328i	−0.314933	−	0.949114i	$-0.601982\pi$
$769$	8.47519	−	48.0652i	0.305623	−	1.73328i	0.620556	−	0.784162i	$-0.286907\pi$
$770$	9.10173	−	51.6185i	0.328004	−	1.86020i
$771$	3.88087	+	6.72187i	0.139766	+	0.242082i
$772$	56.5474	−	97.9430i	2.03519	−	3.52504i
$773$	29.9386	+	25.1215i	1.07682	+	0.903557i	0.995653	−	0.0931440i	$-0.0296917\pi$
$773$	29.9386	+	25.1215i	1.07682	+	0.903557i	0.0811644	+	0.996701i	$0.474136\pi$
$774$	18.0221	+	6.55952i	0.647793	+	0.235777i
$775$	−1.46053	+	0.531590i	−0.0524638	+	0.0190953i
$776$	−13.8348	+	11.6088i	−0.496640	+	0.416730i
$777$	0.330562	+	1.87471i	0.0118588	+	0.0672548i
$778$	67.9794			2.43718
$779$	25.5126	+	10.6933i	0.914085	+	0.383127i
$780$	−21.8722			−0.783151
$781$	3.81287	+	21.6239i	0.136435	+	0.773763i
$782$	21.7741	−	18.2706i	0.778639	−	0.653356i
$783$	3.19820	−	1.16405i	0.114295	−	0.0415998i
$784$	1.56553	+	0.569808i	0.0559119	+	0.0203503i
$785$	−23.1405	−	19.4171i	−0.825918	−	0.693028i
$786$	7.75360	−	13.4296i	0.276562	−	0.479019i
$787$	19.0549	+	33.0040i	0.679232	+	1.17646i	0.975212	+	0.221270i	$0.0710203\pi$
$787$	19.0549	+	33.0040i	0.679232	+	1.17646i	−0.295980	+	0.955194i	$0.595646\pi$
$788$	14.0116	−	79.4637i	0.499142	−	2.83078i
$789$	1.16199	−	6.58996i	0.0413678	−	0.234609i
$790$	−35.9384	−	62.2472i	−1.27863	−	2.21465i
$791$	−23.2297	+	40.2351i	−0.825954	+	1.43059i
$792$	−22.2367	−	18.6588i	−0.790147	−	0.663012i
$793$	22.8470	+	8.31561i	0.811319	+	0.295296i
$794$	92.5397	−	33.6817i	3.28411	−	1.19532i
$795$	−2.15521	+	1.80844i	−0.0764376	+	0.0641388i
$796$	−7.74802	−	43.9412i	−0.274621	−	1.55745i
$797$	−28.1011			−0.995391			−0.497696	−	0.867352i	$-0.665820\pi$
$797$	−28.1011			−0.995391			−0.497696	+	0.867352i	$0.665820\pi$
$798$	22.0898	+	20.4127i	0.781970	+	0.722603i
$799$	−2.51444			−0.0889544
$800$	1.81225	+	10.2778i	0.0640726	+	0.363374i
$801$	−5.47265	+	4.59210i	−0.193366	+	0.162254i
$802$	−86.9062	+	31.6313i	−3.06876	+	1.11694i
$803$	47.9822	+	17.4641i	1.69326	+	0.616295i
$804$	25.3406	+	21.2633i	0.893696	+	0.749900i
$805$	17.2834	−	29.9357i	0.609159	−	1.05509i
$806$	−5.31353	−	9.20331i	−0.187161	−	0.324173i
$807$	−1.22174	+	6.92885i	−0.0430074	+	0.243907i
$808$	−2.98318	+	16.9184i	−0.104948	+	0.595188i
$809$	−5.72708	−	9.91960i	−0.201353	−	0.348754i	0.747611	−	0.664137i	$-0.231201\pi$
$809$	−5.72708	−	9.91960i	−0.201353	−	0.348754i	−0.948965	+	0.315382i	$0.897867\pi$
$810$	−2.69184	+	4.66240i	−0.0945816	+	0.163820i
$811$	8.91821	+	7.48327i	0.313161	+	0.262773i	0.785797	−	0.618485i	$-0.212253\pi$
$811$	8.91821	+	7.48327i	0.313161	+	0.262773i	−0.472636	+	0.881258i	$0.656698\pi$
$812$	41.4747	+	15.0955i	1.45548	+	0.529750i
$813$	−11.9473	+	4.34847i	−0.419011	+	0.152507i
$814$	−5.47187	+	4.59144i	−0.191789	+	0.160930i
$815$	−5.18998	−	29.4338i	−0.181797	−	1.03102i
$816$	−17.7434			−0.621142
$817$	−4.00507	−	31.4403i	−0.140120	−	1.09996i
$818$	−84.1096			−2.94082
$819$	0.982005	+	5.56923i	0.0343140	+	0.194604i
$820$	−49.1894	+	41.2748i	−1.71777	+	1.44138i
$821$	−16.5240	+	6.01425i	−0.576692	+	0.209899i	−0.613866	−	0.789410i	$-0.710387\pi$
$821$	−16.5240	+	6.01425i	−0.576692	+	0.209899i	0.0371742	+	0.999309i	$0.488164\pi$
$822$	−35.0526	−	12.7581i	−1.22260	−	0.444990i
$823$	−9.76251	−	8.19172i	−0.340300	−	0.285545i	0.456581	−	0.889682i	$-0.349074\pi$
$823$	−9.76251	−	8.19172i	−0.340300	−	0.285545i	−0.796881	+	0.604136i	$0.793518\pi$
$824$	−10.3993	+	18.0120i	−0.362275	+	0.627479i
$825$	1.55176	+	2.68772i	0.0540253	+	0.0935746i
$826$	8.83006	−	50.0777i	0.307237	−	1.74243i
$827$	6.34559	−	35.9876i	0.220658	−	1.25141i	−0.650156	−	0.759800i	$-0.725297\pi$
$827$	6.34559	−	35.9876i	0.220658	−	1.25141i	0.870814	−	0.491612i	$-0.163592\pi$
$828$	−16.0454	−	27.7914i	−0.557616	−	0.965819i
$829$	7.21702	−	12.5002i	0.250657	−	0.434151i	−0.713050	−	0.701114i	$-0.752687\pi$
$829$	7.21702	−	12.5002i	0.250657	−	0.434151i	0.963707	+	0.266962i	$0.0860199\pi$
$830$	35.8479	+	30.0799i	1.24430	+	1.04409i
$831$	−10.0057	−	3.64177i	−0.347093	−	0.126331i
$832$	−23.7494	+	8.64408i	−0.823362	+	0.299679i
$833$	0.199314	−	0.167244i	0.00690581	−	0.00579466i
$834$	−7.40965	−	42.0222i	−0.256575	−	1.45511i
$835$	38.9638			1.34840
$836$	−17.7342	+	78.4352i	−0.613352	+	2.71274i
$837$	−1.86380			−0.0644225
$838$	12.2344	+	69.3845i	0.422629	+	2.39685i
$839$	−31.0477	+	26.0521i	−1.07189	+	0.899419i	−0.995222	−	0.0976383i	$-0.968871\pi$
$839$	−31.0477	+	26.0521i	−1.07189	+	0.899419i	−0.0766635	+	0.997057i	$0.524427\pi$
$840$	−39.1365	+	14.2445i	−1.35034	+	0.491483i
$841$	16.3661	+	5.95678i	0.564349	+	0.205406i
$842$	70.8566	+	59.4558i	2.44188	+	2.04898i
$843$	−6.46234	+	11.1931i	−0.222575	+	0.385511i
$844$	4.05587	+	7.02497i	0.139609	+	0.241809i
$845$	2.95136	−	16.7380i	0.101530	−	0.575805i
$846$	−0.691839	+	3.92362i	−0.0237859	+	0.134897i
$847$	−3.72823	−	6.45749i	−0.128104	−	0.221882i
$848$	−7.34611	+	12.7238i	−0.252267	+	0.436938i
$849$	2.44584	+	2.05230i	0.0839410	+	0.0704348i
$850$	3.44070	+	1.25231i	0.118015	+	0.0429540i
$851$	−4.42662	+	1.61116i	−0.151743	+	0.0552298i
$852$	22.4046	−	18.7997i	0.767570	−	0.644068i
$853$	3.25119	+	18.4384i	0.111319	+	0.631320i	0.988507	+	0.151174i	$0.0483053\pi$
$853$	3.25119	+	18.4384i	0.111319	+	0.631320i	−0.877188	+	0.480146i	$0.840584\pi$
$854$	77.6078			2.65569
$855$	8.88676	+	0.425369i	0.303921	+	0.0145473i
$856$	−97.5965			−3.33578
$857$	−7.88756	−	44.7326i	−0.269434	−	1.52804i	−0.756105	−	0.654450i	$-0.772900\pi$
$857$	−7.88756	−	44.7326i	−0.269434	−	1.52804i	0.486671	−	0.873585i	$-0.338211\pi$
$858$	−16.2554	+	13.6399i	−0.554949	+	0.465657i
$859$	−15.4575	+	5.62608i	−0.527404	+	0.191960i	−0.591979	−	0.805953i	$-0.701653\pi$
$859$	−15.4575	+	5.62608i	−0.527404	+	0.191960i	0.0645746	+	0.997913i	$0.479431\pi$
$860$	69.1331	+	25.1624i	2.35742	+	0.858030i
$861$	12.7181	+	10.6717i	0.433431	+	0.363692i
$862$	−38.0128	+	65.8401i	−1.29472	+	2.24252i
$863$	3.35704	+	5.81456i	0.114275	+	0.197930i	0.917490	−	0.397760i	$-0.130212\pi$
$863$	3.35704	+	5.81456i	0.114275	+	0.197930i	−0.803215	+	0.595690i	$0.796879\pi$
$864$	−2.17316	+	12.3246i	−0.0739325	+	0.419292i
$865$	−1.56286	+	8.86342i	−0.0531388	+	0.301365i
$866$	8.62267	+	14.9349i	0.293010	+	0.507508i
$867$	7.11448	−	12.3226i	0.241620	−	0.418499i
$868$	−18.5153	−	15.5362i	−0.628450	−	0.527332i
$869$	−46.6901	−	16.9938i	−1.58385	−	0.576476i
$870$	17.2181	−	6.26688i	0.583748	−	0.212467i
$871$	11.0506	−	9.27252i	0.374434	−	0.314187i
$872$	−2.31206	−	13.1123i	−0.0782961	−	0.444039i
$873$	2.31543			0.0783653
$874$	−40.2536	+	62.6043i	−1.36160	+	2.11762i
$875$	31.1508			1.05309
$876$	−11.8105	−	66.9804i	−0.399038	−	2.26306i
$877$	37.2742	−	31.2768i	1.25866	−	1.05614i	0.262837	−	0.964840i	$-0.415342\pi$
$877$	37.2742	−	31.2768i	1.25866	−	1.05614i	0.995823	−	0.0913015i	$-0.0291027\pi$
$878$	21.6740	−	7.88868i	0.731461	−	0.266230i
$879$	1.42578	+	0.518941i	0.0480903	+	0.0175034i
$880$	−62.0243	−	52.0446i	−2.09084	−	1.75442i
$881$	13.7560	−	23.8260i	0.463450	−	0.802719i	−0.535680	−	0.844421i	$-0.679945\pi$
$881$	13.7560	−	23.8260i	0.463450	−	0.802719i	0.999130	+	0.0417018i	$0.0132779\pi$
$882$	−0.206133	−	0.357033i	−0.00694085	−	0.0120219i
$883$	4.46331	−	25.3127i	0.150202	−	0.851839i	−0.812840	−	0.582488i	$-0.802079\pi$
$883$	4.46331	−	25.3127i	0.150202	−	0.851839i	0.963042	−	0.269352i	$-0.0868094\pi$
$884$	−3.09756	+	17.5672i	−0.104182	+	0.590848i
$885$	−7.52084	−	13.0265i	−0.252810	−	0.437880i
$886$	−3.31136	+	5.73544i	−0.111247	+	0.192686i
$887$	−10.0837	−	8.46124i	−0.338578	−	0.284101i	0.457606	−	0.889155i	$-0.348707\pi$
$887$	−10.0837	−	8.46124i	−0.338578	−	0.284101i	−0.796184	+	0.605054i	$0.793151\pi$
$888$	5.33348	+	1.94123i	0.178980	+	0.0651433i
$889$	−53.4352	+	19.4488i	−1.79216	+	0.652292i
$890$	−29.4630	+	24.7224i	−0.987601	+	0.828696i
$891$	0.646248	+	3.66506i	0.0216501	+	0.122784i
$892$	−8.88716			−0.297564
$893$	6.28762	−	1.95351i	0.210407	−	0.0653718i
$894$	31.8676			1.06581
$895$	0.211060	+	1.19698i	0.00705496	+	0.0400107i
$896$	−11.6400	+	9.76715i	−0.388867	+	0.326298i
$897$	−13.1502	+	4.78629i	−0.439073	+	0.159809i
$898$	3.52366	+	1.28251i	0.117586	+	0.0427979i
$899$	4.85931	+	4.07745i	0.162067	+	0.135990i
$900$	2.06693	−	3.58003i	0.0688977	−	0.119334i
$901$	1.14727	+	1.98712i	0.0382210	+	0.0662006i
$902$	−10.8178	+	61.3506i	−0.360192	+	2.04275i
$903$	3.30309	−	18.7328i	0.109920	−	0.623388i
$904$	69.2606	+	119.963i	2.30357	+	3.98990i
$905$	0.440624	−	0.763182i	0.0146468	−	0.0253690i
$906$	−34.3455	−	28.8193i	−1.14105	−	0.957456i
$907$	−50.2406	−	18.2861i	−1.66821	−	0.607180i	−0.676592	−	0.736359i	$-0.736544\pi$
$907$	−50.2406	−	18.2861i	−1.66821	−	0.607180i	−0.991621	+	0.129179i	$0.958766\pi$
$908$	121.714	−	44.3002i	4.03921	−	1.47015i
$909$	1.68723	−	1.41576i	0.0559620	−	0.0469577i
$910$	5.28680	+	29.9829i	0.175256	+	0.993924i
$911$	3.55732			0.117859			0.0589297	−	0.998262i	$-0.481231\pi$
$911$	3.55732			0.117859			0.0589297	+	0.998262i	$0.481231\pi$
$912$	44.3692	−	13.7851i	1.46921	−	0.456472i
$913$	32.3489			1.07059
$914$	9.39512	+	53.2824i	0.310763	+	1.76242i
$915$	17.5858	−	14.7562i	0.581369	−	0.487827i
$916$	76.0089	−	27.6650i	2.51140	−	0.914076i
$917$	−14.4527	−	5.26035i	−0.477270	−	0.173712i
$918$	3.36349	+	2.82231i	0.111012	+	0.0931500i
$919$	1.10848	−	1.91995i	0.0365655	−	0.0633334i	−0.847163	−	0.531332i	$-0.821692\pi$
$919$	1.10848	−	1.91995i	0.0365655	−	0.0633334i	0.883729	+	0.467999i	$0.155025\pi$
$920$	−51.5312	−	89.2546i	−1.69893	−	2.94264i
$921$	4.19925	−	23.8151i	0.138370	−	0.784735i
$922$	−4.16825	+	23.6393i	−0.137274	+	0.778520i
$923$	−6.37706	−	11.0454i	−0.209903	−	0.363563i
$924$	−24.1310	+	41.7962i	−0.793853	+	1.37499i
$925$	−0.464853	−	0.390058i	−0.0152843	−	0.0128250i
$926$	20.6156	+	7.50346i	0.677470	+	0.246579i
$927$	2.50571	−	0.912004i	0.0822984	−	0.0299542i
$928$	32.6284	−	27.3785i	1.07108	−	0.898744i
$929$	−4.14615	−	23.5140i	−0.136031	−	0.771469i	−0.974136	−	0.225961i	$-0.927448\pi$
$929$	−4.14615	−	23.5140i	−0.136031	−	0.771469i	0.838106	−	0.545508i	$-0.183663\pi$
$930$	−10.0341			−0.329032
$931$	−0.368470	+	0.573062i	−0.0120761	+	0.0187813i
$932$	69.3797			2.27261
$933$	1.92832	+	10.9360i	0.0631302	+	0.358029i
$934$	33.8626	−	28.4141i	1.10802	−	0.929738i
$935$	−11.8823	+	4.32480i	−0.388592	+	0.141436i
$936$	15.8442	+	5.76683i	0.517885	+	0.188495i
$937$	−3.45271	−	2.89717i	−0.112795	−	0.0946464i	0.584646	−	0.811289i	$-0.301234\pi$
$937$	−3.45271	−	2.89717i	−0.112795	−	0.0946464i	−0.697441	+	0.716642i	$0.745678\pi$
$938$	23.0231	−	39.8771i	0.751730	−	1.30203i
$939$	−5.38283	−	9.32334i	−0.175662	−	0.304256i
$940$	−2.65390	+	15.0510i	−0.0865607	+	0.490910i
$941$	1.78879	−	10.1447i	0.0583128	−	0.330708i	−0.941670	−	0.336537i	$-0.890744\pi$
$941$	1.78879	−	10.1447i	0.0583128	−	0.330708i	0.999983	+	0.00582879i	$0.00185537\pi$
$942$	19.5182	+	33.8065i	0.635937	+	1.10148i
$943$	−20.5419	+	35.5797i	−0.668938	+	1.15863i
$944$	−60.1729	−	50.4911i	−1.95846	−	1.64334i
$945$	5.01759	+	1.82625i	0.163222	+	0.0594080i
$946$	67.0712	−	24.4119i	2.18067	−	0.793699i
$947$	−23.7033	+	19.8895i	−0.770255	+	0.646320i	−0.940774	−	0.339034i	$-0.889900\pi$
$947$	−23.7033	+	19.8895i	−0.770255	+	0.646320i	0.170520	+	0.985354i	$0.445455\pi$
$948$	11.4924	+	65.1767i	0.373256	+	2.11684i
$949$	−29.6595			−0.962787
$950$	−9.57679	−	0.458398i	−0.310712	−	0.0148724i
$951$	−15.4231			−0.500128
$952$	5.89826	+	33.4507i	0.191164	+	1.08414i
$953$	−25.3889	+	21.3038i	−0.822428	+	0.690099i	−0.953539	−	0.301269i	$-0.902590\pi$
$953$	−25.3889	+	21.3038i	−0.822428	+	0.690099i	0.131111	+	0.991368i	$0.458146\pi$
$954$	3.41644	−	1.24348i	0.110611	−	0.0402593i
$955$	24.1626	+	8.79448i	0.781884	+	0.284583i
$956$	−61.9612	−	51.9916i	−2.00397	−	1.68153i
$957$	6.33315	−	10.9693i	0.204722	−	0.354588i
$958$	9.84243	+	17.0476i	0.317994	+	0.550783i
$959$	−6.42443	+	36.4348i	−0.207456	+	1.17654i
$960$	−4.14384	+	23.5009i	−0.133742	+	0.758488i
$961$	13.7631	+	23.8384i	0.443972	+	0.768981i
$962$	2.07453	−	3.59320i	0.0668856	−	0.115849i
$963$	9.58519	+	8.04293i	0.308879	+	0.259180i
$964$	68.0145	+	24.7552i	2.19060	+	0.797313i
$965$	−43.7584	+	15.9267i	−1.40863	+	0.512700i
$966$	−34.2187	+	28.7129i	−1.10097	+	0.923823i
$967$	1.59737	+	9.05916i	0.0513681	+	0.291323i	0.999660	−	0.0260768i	$-0.00830143\pi$
$967$	1.59737	+	9.05916i	0.0513681	+	0.291323i	−0.948292	+	0.317400i	$0.897190\pi$
$968$	−22.2318			−0.714558
$969$	1.60020	−	7.07736i	0.0514057	−	0.227358i
$970$	12.4655			0.400244
$971$	−2.70340	−	15.3318i	−0.0867563	−	0.492019i	−0.996964	−	0.0778669i	$-0.975189\pi$
$971$	−2.70340	−	15.3318i	−0.0867563	−	0.492019i	0.910207	−	0.414153i	$-0.135922\pi$
$972$	3.79739	−	3.18639i	0.121801	−	0.102203i
$973$	−39.7689	+	14.4747i	−1.27493	+	0.464037i
$974$	−47.3995	−	17.2520i	−1.51878	−	0.552790i
$975$	−1.38095	−	1.15875i	−0.0442257	−	0.0371097i
$976$	59.9418	−	103.822i	1.91869	−	3.32327i
$977$	9.16601	+	15.8760i	0.293247	+	0.507918i	0.974576	−	0.224059i	$-0.0719309\pi$
$977$	9.16601	+	15.8760i	0.293247	+	0.507918i	−0.681329	+	0.731978i	$0.738598\pi$
$978$	−6.70682	+	38.0363i	−0.214461	+	1.21627i
$979$	−4.61682	+	26.1833i	−0.147554	+	0.836821i
$980$	−0.790727	−	1.36958i	−0.0252589	−	0.0437496i
$981$	−0.853515	+	1.47833i	−0.0272506	+	0.0471995i
$982$	−58.1501	−	48.7937i	−1.85564	−	1.55707i
$983$	−22.4378	−	8.16668i	−0.715654	−	0.260477i	−0.0415744	−	0.999135i	$-0.513237\pi$
$983$	−22.4378	−	8.16668i	−0.715654	−	0.260477i	−0.674080	+	0.738659i	$0.735460\pi$
$984$	46.5153	−	16.9302i	1.48285	−	0.539714i
$985$	−25.4509	+	21.3559i	−0.810934	+	0.680455i
$986$	−2.59494	−	14.7166i	−0.0826397	−	0.468673i
$987$	3.95153			0.125779
$988$	−5.90247	−	46.3351i	−0.187782	−	1.47412i
$989$	47.0711			1.49677
$990$	3.47919	+	19.7315i	0.110576	+	0.627108i
$991$	22.0435	−	18.4967i	0.700234	−	0.587566i	−0.221606	−	0.975136i	$-0.571130\pi$
$991$	22.0435	−	18.4967i	0.700234	−	0.587566i	0.921840	+	0.387570i	$0.126686\pi$
$992$	−21.9184	+	7.97763i	−0.695909	+	0.253290i
$993$	13.0526	+	4.75077i	0.414213	+	0.150761i
$994$	−31.1865	−	26.1686i	−0.989177	−	0.830018i
$995$	−9.18593	+	15.9105i	−0.291213	+	0.504396i
$996$	−21.5442	−	37.3157i	−0.682655	−	1.18239i
$997$	−3.63917	+	20.6388i	−0.115254	+	0.653636i	0.871371	+	0.490625i	$0.163232\pi$
$997$	−3.63917	+	20.6388i	−0.115254	+	0.653636i	−0.986624	+	0.163011i	$0.947880\pi$
$998$	9.63034	−	54.6164i	0.304843	−	1.72885i
$999$	−0.363837	−	0.630185i	−0.0115113	−	0.0199382i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.i.b.28.1	✓	12
3.2	odd	2		171.2.u.e.28.2		12
4.3	odd	2		912.2.bo.j.769.2		12
19.6	even	9		1083.2.a.q.1.1		6
19.13	odd	18		1083.2.a.p.1.6		6
19.17	even	9	inner	57.2.i.b.55.1	yes	12
57.17	odd	18		171.2.u.e.55.2		12
57.32	even	18		3249.2.a.bg.1.1		6
57.44	odd	18		3249.2.a.bh.1.6		6
76.55	odd	18		912.2.bo.j.625.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.i.b.28.1	✓	12	1.1	even	1	trivial
57.2.i.b.55.1	yes	12	19.17	even	9	inner
171.2.u.e.28.2		12	3.2	odd	2
171.2.u.e.55.2		12	57.17	odd	18
912.2.bo.j.625.2		12	76.55	odd	18
912.2.bo.j.769.2		12	4.3	odd	2
1083.2.a.p.1.6		6	19.13	odd	18
1083.2.a.q.1.1		6	19.6	even	9
3249.2.a.bg.1.1		6	57.32	even	18
3249.2.a.bh.1.6		6	57.44	odd	18

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.458021 - 2.59757i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-4.65819 + 1.69544i) q^{4} +(1.91800 + 0.698096i) q^{5} +(-2.02055 - 1.69544i) q^{6} +(-1.30802 + 2.26556i) q^{7} +(3.89993 + 6.75488i) q^{8} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(-0.458021 - 2.59757i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-4.65819 + 1.69544i) q^{4} +(1.91800 + 0.698096i) q^{5} +(-2.02055 - 1.69544i) q^{6} +(-1.30802 + 2.26556i) q^{7} +(3.89993 + 6.75488i) q^{8} +(0.173648 - 0.984808i) q^{9} +(0.934866 - 5.30189i) q^{10} +(-1.86080 - 3.22300i) q^{11} +(-2.47857 + 4.29301i) q^{12} +(1.65597 + 1.38952i) q^{13} +(6.48405 + 2.36000i) q^{14} +(1.91800 - 0.698096i) q^{15} +(8.16523 - 6.85145i) q^{16} +(-0.289062 - 1.63935i) q^{17} -2.63764 q^{18} +(1.99648 + 3.87480i) q^{19} -10.1180 q^{20} +(0.454272 + 2.57630i) q^{21} +(-7.51967 + 6.30975i) q^{22} +(-6.08324 + 2.21412i) q^{23} +(7.32948 + 2.66771i) q^{24} +(-0.638820 - 0.536034i) q^{25} +(2.85091 - 4.93792i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(2.25189 - 12.7711i) q^{28} +(-0.591004 + 3.35175i) q^{29} +(-2.69184 - 4.66240i) q^{30} +(0.931902 - 1.61410i) q^{31} +(-9.58685 - 8.04432i) q^{32} +(-3.49716 - 1.27286i) q^{33} +(-4.12593 + 1.50172i) q^{34} +(-4.09038 + 3.43223i) q^{35} +(0.860798 + 4.88183i) q^{36} +0.727675 q^{37} +(9.15063 - 6.96072i) q^{38} +2.16171 q^{39} +(2.76453 + 15.6784i) q^{40} +(4.86157 - 4.07934i) q^{41} +(6.48405 - 2.36000i) q^{42} +(-6.83268 - 2.48689i) q^{43} +(14.1324 + 11.8585i) q^{44} +(1.02055 - 1.76764i) q^{45} +(8.53757 + 14.7875i) q^{46} +(0.262295 - 1.48755i) q^{47} +(1.85091 - 10.4970i) q^{48} +(0.0781505 + 0.135361i) q^{49} +(-1.09979 + 1.90489i) q^{50} +(-1.27519 - 1.07001i) q^{51} +(-10.0697 - 3.66506i) q^{52} +(-1.29527 + 0.471438i) q^{53} +(-2.02055 + 1.69544i) q^{54} +(-1.31906 - 7.48074i) q^{55} -20.4048 q^{56} +(4.02006 + 1.68496i) q^{57} +8.97710 q^{58} +(-1.27968 - 7.25745i) q^{59} +(-7.75084 + 6.50373i) q^{60} +(10.5689 - 3.84677i) q^{61} +(-4.61957 - 1.68139i) q^{62} +(2.00401 + 1.68156i) q^{63} +(-5.84573 + 10.1251i) q^{64} +(2.20613 + 3.82113i) q^{65} +(-1.70457 + 9.66710i) q^{66} +(1.15878 - 6.57179i) q^{67} +(4.12593 + 7.14633i) q^{68} +(-3.23682 + 5.60634i) q^{69} +(10.7889 + 9.05299i) q^{70} +(-5.54419 - 2.01792i) q^{71} +(7.32948 - 2.66771i) q^{72} +(-10.5104 + 8.81927i) q^{73} +(-0.333290 - 1.89018i) q^{74} -0.833921 q^{75} +(-15.8695 - 14.6646i) q^{76} +9.73587 q^{77} +(-0.990110 - 5.61519i) q^{78} +(10.2274 - 8.58178i) q^{79} +(20.4439 - 7.44098i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-12.8231 - 10.7598i) q^{82} +(-4.34610 + 7.52767i) q^{83} +(-6.48405 - 11.2307i) q^{84} +(0.590004 - 3.34608i) q^{85} +(-3.33036 + 18.8874i) q^{86} +(1.70173 + 2.94748i) q^{87} +(14.5140 - 25.1390i) q^{88} +(-5.47265 - 4.59210i) q^{89} +(-5.05900 - 1.84133i) q^{90} +(-5.31409 + 1.93417i) q^{91} +(24.5830 - 20.6276i) q^{92} +(-0.323646 - 1.83549i) q^{93} -3.98414 q^{94} +(1.12426 + 8.82562i) q^{95} -12.5147 q^{96} +(0.402070 + 2.28025i) q^{97} +(0.315814 - 0.264999i) q^{98} +(-3.49716 + 1.27286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 3 q^{6} - 9 q^{7} + 3 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 3 * q^6 - 9 * q^7 + 3 * q^8	\( 12 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 3 q^{6} - 9 q^{7} + 3 q^{8} - 18 q^{10} - 9 q^{11} - 6 q^{12} - 3 q^{13} - 3 q^{14} + 6 q^{15} + 33 q^{16} + 12 q^{17} - 9 q^{19} - 18 q^{20} - 24 q^{22} + 9 q^{23} + 30 q^{24} - 12 q^{25} - 6 q^{27} + 30 q^{28} - 6 q^{30} - 3 q^{32} - 9 q^{33} + 21 q^{34} + 30 q^{35} - 3 q^{36} - 12 q^{37} + 18 q^{38} + 6 q^{39} - 3 q^{40} - 18 q^{41} - 3 q^{42} + 15 q^{43} + 15 q^{44} - 9 q^{45} + 27 q^{46} - 9 q^{47} - 12 q^{48} - 9 q^{49} + 9 q^{50} - 15 q^{51} - 27 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 78 q^{56} - 3 q^{57} - 24 q^{58} - 30 q^{59} - 15 q^{60} + 21 q^{61} + 3 q^{62} + 9 q^{63} - 21 q^{64} + 21 q^{65} + 30 q^{66} + 3 q^{67} - 21 q^{68} - 6 q^{69} + 18 q^{70} - 30 q^{71} + 30 q^{72} - 24 q^{73} + 39 q^{74} + 30 q^{75} - 60 q^{76} + 96 q^{77} + 9 q^{78} + 24 q^{79} + 42 q^{80} - 33 q^{82} + 3 q^{83} + 3 q^{84} + 3 q^{85} + 51 q^{86} + 15 q^{87} + 42 q^{88} + 3 q^{89} - 9 q^{90} + 24 q^{91} + 69 q^{92} - 6 q^{93} + 18 q^{94} - 54 q^{95} - 42 q^{96} - 27 q^{97} - 3 q^{98} - 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 3 * q^6 - 9 * q^7 + 3 * q^8 - 18 * q^10 - 9 * q^11 - 6 * q^12 - 3 * q^13 - 3 * q^14 + 6 * q^15 + 33 * q^16 + 12 * q^17 - 9 * q^19 - 18 * q^20 - 24 * q^22 + 9 * q^23 + 30 * q^24 - 12 * q^25 - 6 * q^27 + 30 * q^28 - 6 * q^30 - 3 * q^32 - 9 * q^33 + 21 * q^34 + 30 * q^35 - 3 * q^36 - 12 * q^37 + 18 * q^38 + 6 * q^39 - 3 * q^40 - 18 * q^41 - 3 * q^42 + 15 * q^43 + 15 * q^44 - 9 * q^45 + 27 * q^46 - 9 * q^47 - 12 * q^48 - 9 * q^49 + 9 * q^50 - 15 * q^51 - 27 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 78 * q^56 - 3 * q^57 - 24 * q^58 - 30 * q^59 - 15 * q^60 + 21 * q^61 + 3 * q^62 + 9 * q^63 - 21 * q^64 + 21 * q^65 + 30 * q^66 + 3 * q^67 - 21 * q^68 - 6 * q^69 + 18 * q^70 - 30 * q^71 + 30 * q^72 - 24 * q^73 + 39 * q^74 + 30 * q^75 - 60 * q^76 + 96 * q^77 + 9 * q^78 + 24 * q^79 + 42 * q^80 - 33 * q^82 + 3 * q^83 + 3 * q^84 + 3 * q^85 + 51 * q^86 + 15 * q^87 + 42 * q^88 + 3 * q^89 - 9 * q^90 + 24 * q^91 + 69 * q^92 - 6 * q^93 + 18 * q^94 - 54 * q^95 - 42 * q^96 - 27 * q^97 - 3 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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