LMFDB - Embedded newform 930.2.bg.c.691.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (of order $15$, degree $8$, 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:	$7.42608738798$
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} + 40x^{14} + 654x^{12} + 5650x^{10} + 27831x^{8} + 78445x^{6} + 119819x^{4} + 87030x^{2} + 22801 $ x^16 + 40x^14 + 654x^12 + 5650x^10 + 27831x^8 + 78445x^6 + 119819x^4 + 87030*x^2 + 22801
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			691.1
Root			$2.23655i$ of defining polynomial
Character	$\chi$	$=$	930.691
Dual form			930.2.bg.c.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(0.978148 + 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-2.70387 + 1.20384i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(0.978148 + 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-2.70387 + 1.20384i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.978148 - 0.207912i) q^{10} +(-0.0918838 + 0.874216i) q^{11} +(-0.669131 - 0.743145i) q^{12} +(-2.33680 + 2.59528i) q^{13} +(0.309379 + 2.94355i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.838261 + 7.97552i) q^{17} +(0.669131 - 0.743145i) q^{18} +(1.65932 + 1.84287i) q^{19} +(0.104528 - 0.994522i) q^{20} +(-2.89508 + 0.615369i) q^{21} +(0.803035 + 0.357534i) q^{22} +(1.80064 - 1.30824i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.74615 + 3.02442i) q^{26} +(0.809017 + 0.587785i) q^{27} +(2.89508 + 0.615369i) q^{28} +(0.877888 - 2.70186i) q^{29} +1.00000 q^{30} +(3.49214 - 4.33647i) q^{31} +1.00000 q^{32} +(-0.271636 + 0.836008i) q^{33} +(7.84421 + 1.66734i) q^{34} +(-2.39450 - 1.73970i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-2.48588 + 4.30566i) q^{37} +(2.26543 - 1.00863i) q^{38} +(-2.82533 + 2.05272i) q^{39} +(-0.913545 - 0.406737i) q^{40} +(-3.87180 + 0.822977i) q^{41} +(-0.309379 + 2.94355i) q^{42} +(2.45890 + 2.73089i) q^{43} +(0.588187 - 0.653248i) q^{44} +(0.104528 + 0.994522i) q^{45} +(-0.687785 - 2.11678i) q^{46} +(2.05322 + 6.31917i) q^{47} +(0.104528 + 0.994522i) q^{48} +(1.17779 - 1.30807i) q^{49} +(0.669131 + 0.743145i) q^{50} +(-0.838261 + 7.97552i) q^{51} +(3.41598 - 0.726089i) q^{52} +(-9.06496 - 4.03598i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-0.803035 + 0.357534i) q^{55} +(1.47988 - 2.56323i) q^{56} +(1.23991 + 2.14759i) q^{57} +(-2.29834 - 1.66984i) q^{58} +(3.74182 + 0.795347i) q^{59} +(0.309017 - 0.951057i) q^{60} +3.90546 q^{61} +(-3.04510 - 4.66126i) q^{62} -2.95976 q^{63} +(0.309017 - 0.951057i) q^{64} +(-3.41598 - 0.726089i) q^{65} +(0.711151 + 0.516682i) q^{66} +(3.84467 + 6.65917i) q^{67} +(4.00973 - 6.94505i) q^{68} +(2.03329 - 0.905281i) q^{69} +(-2.39450 + 1.73970i) q^{70} +(-8.88239 - 3.95470i) q^{71} +(-0.978148 + 0.207912i) q^{72} +(1.59395 - 15.1654i) q^{73} +(3.32675 + 3.69473i) q^{74} +(-0.669131 + 0.743145i) q^{75} +(-0.259212 - 2.46624i) q^{76} +(-0.803976 - 2.47438i) q^{77} +(1.07918 + 3.32137i) q^{78} +(0.930158 + 8.84987i) q^{79} +(-0.669131 + 0.743145i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-0.413755 + 3.93662i) q^{82} +(16.4192 - 3.49001i) q^{83} +(2.70387 + 1.20384i) q^{84} +(-6.48787 + 4.71372i) q^{85} +(3.35707 - 1.49467i) q^{86} +(1.42045 - 2.46030i) q^{87} +(-0.439516 - 0.761263i) q^{88} +(-11.8190 - 8.58700i) q^{89} +(0.978148 + 0.207912i) q^{90} +(3.19411 - 9.83045i) q^{91} -2.22572 q^{92} +(4.31743 - 3.51565i) q^{93} +6.64437 q^{94} +(-0.766307 + 2.35845i) q^{95} +(0.978148 + 0.207912i) q^{96} +(5.43339 + 3.94759i) q^{97} +(-0.880088 - 1.52436i) q^{98} +(-0.439516 + 0.761263i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 14 q^{13} - 4 q^{14} - 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} + q^{19} - 2 q^{20} - 16 q^{21} - 13 q^{22} + 3 q^{23} - 2 q^{24} - 8 q^{25} + 9 q^{26} + 4 q^{27} + 16 q^{28} + 13 q^{29} + 16 q^{30} + 9 q^{31} + 16 q^{32} + 14 q^{33} + 26 q^{34} + 7 q^{35} - 8 q^{36} - 11 q^{37} - 14 q^{38} - 7 q^{39} - 2 q^{40} + 42 q^{41} + 4 q^{42} - 18 q^{43} + 7 q^{44} - 2 q^{45} - 7 q^{46} - 37 q^{47} - 2 q^{48} + 11 q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} + 14 q^{53} + 4 q^{54} + 13 q^{55} - 9 q^{56} + 4 q^{57} - 12 q^{58} + 2 q^{59} - 4 q^{60} - 16 q^{61} + 9 q^{62} + 18 q^{63} - 4 q^{64} + 16 q^{65} - 11 q^{66} + 41 q^{67} + 16 q^{68} + 9 q^{69} + 7 q^{70} + q^{71} + 2 q^{72} - 53 q^{73} + 44 q^{74} - 2 q^{75} + 16 q^{76} - 16 q^{77} - 2 q^{78} + 30 q^{79} - 2 q^{80} + 2 q^{81} - 8 q^{82} - 11 q^{84} - 38 q^{85} + 7 q^{86} - q^{87} - 3 q^{88} - 49 q^{89} - 2 q^{90} + 2 q^{91} + 8 q^{92} + 6 q^{93} + 48 q^{94} + 2 q^{95} - 2 q^{96} + 21 q^{97} - 19 q^{98} - 3 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 + 14 * q^13 - 4 * q^14 - 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 + q^19 - 2 * q^20 - 16 * q^21 - 13 * q^22 + 3 * q^23 - 2 * q^24 - 8 * q^25 + 9 * q^26 + 4 * q^27 + 16 * q^28 + 13 * q^29 + 16 * q^30 + 9 * q^31 + 16 * q^32 + 14 * q^33 + 26 * q^34 + 7 * q^35 - 8 * q^36 - 11 * q^37 - 14 * q^38 - 7 * q^39 - 2 * q^40 + 42 * q^41 + 4 * q^42 - 18 * q^43 + 7 * q^44 - 2 * q^45 - 7 * q^46 - 37 * q^47 - 2 * q^48 + 11 * q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 + 14 * q^53 + 4 * q^54 + 13 * q^55 - 9 * q^56 + 4 * q^57 - 12 * q^58 + 2 * q^59 - 4 * q^60 - 16 * q^61 + 9 * q^62 + 18 * q^63 - 4 * q^64 + 16 * q^65 - 11 * q^66 + 41 * q^67 + 16 * q^68 + 9 * q^69 + 7 * q^70 + q^71 + 2 * q^72 - 53 * q^73 + 44 * q^74 - 2 * q^75 + 16 * q^76 - 16 * q^77 - 2 * q^78 + 30 * q^79 - 2 * q^80 + 2 * q^81 - 8 * q^82 - 11 * q^84 - 38 * q^85 + 7 * q^86 - q^87 - 3 * q^88 - 49 * q^89 - 2 * q^90 + 2 * q^91 + 8 * q^92 + 6 * q^93 + 48 * q^94 + 2 * q^95 - 2 * q^96 + 21 * q^97 - 19 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{15}\right)$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	0.978148	+	0.207912i	0.564734	+	0.120038i
$3$	0.978148	+	0.207912i	0.564734	+	0.120038i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−2.70387	+	1.20384i	−1.02197	+	0.455010i	−0.848143	−	0.529767i	$-0.822279\pi$
$7$	−2.70387	+	1.20384i	−1.02197	+	0.455010i	−0.173825	+	0.984777i	$0.555613\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.913545	+	0.406737i	0.304515	+	0.135579i
$10$	0.978148	−	0.207912i	0.309317	−	0.0657474i
$11$	−0.0918838	+	0.874216i	−0.0277040	+	0.263586i	0.971899	+	0.235400i	$0.0756399\pi$
$11$	−0.0918838	+	0.874216i	−0.0277040	+	0.263586i	−0.999603	+	0.0281864i	$0.991027\pi$
$12$	−0.669131	−	0.743145i	−0.193161	−	0.214527i
$13$	−2.33680	+	2.59528i	−0.648112	+	0.719801i	−0.974237	−	0.225525i	$-0.927590\pi$
$13$	−2.33680	+	2.59528i	−0.648112	+	0.719801i	0.326125	+	0.945327i	$0.394257\pi$
$14$	0.309379	+	2.94355i	0.0826850	+	0.786696i
$15$	0.309017	+	0.951057i	0.0797878	+	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.838261	+	7.97552i	0.203308	+	1.93435i	0.333274	+	0.942830i	$0.391847\pi$
$17$	0.838261	+	7.97552i	0.203308	+	1.93435i	−0.129966	+	0.991518i	$0.541487\pi$
$18$	0.669131	−	0.743145i	0.157716	−	0.175161i
$19$	1.65932	+	1.84287i	0.380675	+	0.422783i	0.902783	−	0.430097i	$-0.141521\pi$
$19$	1.65932	+	1.84287i	0.380675	+	0.422783i	−0.522107	+	0.852880i	$0.674854\pi$
$20$	0.104528	−	0.994522i	0.0233733	−	0.222382i
$21$	−2.89508	+	0.615369i	−0.631759	+	0.134284i
$22$	0.803035	+	0.357534i	0.171208	+	0.0762266i
$23$	1.80064	−	1.30824i	0.375460	−	0.272788i	−0.384011	−	0.923328i	$-0.625458\pi$
$23$	1.80064	−	1.30824i	0.375460	−	0.272788i	0.759471	+	0.650541i	$0.225458\pi$
$24$	−0.913545	+	0.406737i	−0.186477	+	0.0830248i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.74615	+	3.02442i	0.342448	+	0.593137i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	2.89508	+	0.615369i	0.547119	+	0.116294i
$29$	0.877888	−	2.70186i	0.163020	−	0.501723i	−0.835865	−	0.548935i	$-0.815034\pi$
$29$	0.877888	−	2.70186i	0.163020	−	0.501723i	0.998885	+	0.0472117i	$0.0150335\pi$
$30$	1.00000			0.182574
$31$	3.49214	−	4.33647i	0.627206	−	0.778853i
$31$	3.49214	−	4.33647i	0.627206	−	0.778853i
$32$	1.00000			0.176777
$33$	−0.271636	+	0.836008i	−0.0472857	+	0.145530i
$34$	7.84421	+	1.66734i	1.34527	+	0.285946i
$35$	−2.39450	−	1.73970i	−0.404744	−	0.294063i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−2.48588	+	4.30566i	−0.408675	+	0.707846i	−0.994742	−	0.102417i	$-0.967342\pi$
$37$	−2.48588	+	4.30566i	−0.408675	+	0.707846i	0.586066	+	0.810263i	$0.300676\pi$
$38$	2.26543	−	1.00863i	0.367501	−	0.163622i
$39$	−2.82533	+	2.05272i	−0.452414	+	0.328698i
$40$	−0.913545	−	0.406737i	−0.144444	−	0.0643107i
$41$	−3.87180	+	0.822977i	−0.604674	+	0.128527i	−0.500068	−	0.865986i	$-0.666692\pi$
$41$	−3.87180	+	0.822977i	−0.604674	+	0.128527i	−0.104606	+	0.994514i	$0.533358\pi$
$42$	−0.309379	+	2.94355i	−0.0477382	+	0.454199i
$43$	2.45890	+	2.73089i	0.374979	+	0.416457i	0.900866	−	0.434098i	$-0.142933\pi$
$43$	2.45890	+	2.73089i	0.374979	+	0.416457i	−0.525886	+	0.850555i	$0.676266\pi$
$44$	0.588187	−	0.653248i	0.0886725	−	0.0984808i
$45$	0.104528	+	0.994522i	0.0155822	+	0.148255i
$46$	−0.687785	−	2.11678i	−0.101408	−	0.312103i
$47$	2.05322	+	6.31917i	0.299493	+	0.921745i	0.981675	+	0.190563i	$0.0610313\pi$
$47$	2.05322	+	6.31917i	0.299493	+	0.921745i	−0.682182	+	0.731183i	$0.738969\pi$
$48$	0.104528	+	0.994522i	0.0150874	+	0.143547i
$49$	1.17779	−	1.30807i	0.168255	−	0.186867i
$50$	0.669131	+	0.743145i	0.0946294	+	0.105097i
$51$	−0.838261	+	7.97552i	−0.117380	+	1.11680i
$52$	3.41598	−	0.726089i	0.473711	−	0.100690i
$53$	−9.06496	−	4.03598i	−1.24517	−	0.554384i	−0.324928	−	0.945739i	$-0.605340\pi$
$53$	−9.06496	−	4.03598i	−1.24517	−	0.554384i	−0.920240	+	0.391354i	$0.872007\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	−0.803035	+	0.357534i	−0.108281	+	0.0482099i
$56$	1.47988	−	2.56323i	0.197757	−	0.342526i
$57$	1.23991	+	2.14759i	0.164230	+	0.284455i
$58$	−2.29834	−	1.66984i	−0.301787	−	0.219261i
$59$	3.74182	+	0.795347i	0.487143	+	0.103545i	0.444934	−	0.895563i	$-0.353227\pi$
$59$	3.74182	+	0.795347i	0.487143	+	0.103545i	0.0422090	+	0.999109i	$0.486560\pi$
$60$	0.309017	−	0.951057i	0.0398939	−	0.122781i
$61$	3.90546			0.500043			0.250021	−	0.968240i	$-0.419562\pi$
$61$	3.90546			0.500043			0.250021	+	0.968240i	$0.419562\pi$
$62$	−3.04510	−	4.66126i	−0.386728	−	0.591981i
$63$	−2.95976			−0.372895
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−3.41598	−	0.726089i	−0.423700	−	0.0900602i
$66$	0.711151	+	0.516682i	0.0875367	+	0.0635991i
$67$	3.84467	+	6.65917i	0.469702	+	0.813547i	0.999400	−	0.0346389i	$-0.0110281\pi$
$67$	3.84467	+	6.65917i	0.469702	+	0.813547i	−0.529698	+	0.848186i	$0.677695\pi$
$68$	4.00973	−	6.94505i	0.486251	−	0.842211i
$69$	2.03329	−	0.905281i	0.244780	−	0.108983i
$70$	−2.39450	+	1.73970i	−0.286197	+	0.207934i
$71$	−8.88239	−	3.95470i	−1.05415	−	0.469336i	−0.194860	−	0.980831i	$-0.562425\pi$
$71$	−8.88239	−	3.95470i	−1.05415	−	0.469336i	−0.859286	+	0.511495i	$0.829092\pi$
$72$	−0.978148	+	0.207912i	−0.115276	+	0.0245026i
$73$	1.59395	−	15.1654i	0.186557	−	1.77497i	−0.355544	−	0.934660i	$-0.615704\pi$
$73$	1.59395	−	15.1654i	0.186557	−	1.77497i	0.542101	−	0.840314i	$-0.317629\pi$
$74$	3.32675	+	3.69473i	0.386727	+	0.429504i
$75$	−0.669131	+	0.743145i	−0.0772645	+	0.0858110i
$76$	−0.259212	−	2.46624i	−0.0297337	−	0.282897i
$77$	−0.803976	−	2.47438i	−0.0916216	−	0.281982i
$78$	1.07918	+	3.32137i	0.122193	+	0.376071i
$79$	0.930158	+	8.84987i	0.104651	+	0.995688i	0.913270	+	0.407355i	$0.133549\pi$
$79$	0.930158	+	8.84987i	0.104651	+	0.995688i	−0.808619	+	0.588333i	$0.799785\pi$
$80$	−0.669131	+	0.743145i	−0.0748111	+	0.0830861i
$81$	0.669131	+	0.743145i	0.0743478	+	0.0825716i
$82$	−0.413755	+	3.93662i	−0.0456916	+	0.434727i
$83$	16.4192	−	3.49001i	1.80224	−	0.383079i	0.820252	−	0.572002i	$-0.193833\pi$
$83$	16.4192	−	3.49001i	1.80224	−	0.383079i	0.981992	+	0.188923i	$0.0604998\pi$
$84$	2.70387	+	1.20384i	0.295017	+	0.131350i
$85$	−6.48787	+	4.71372i	−0.703709	+	0.511274i
$86$	3.35707	−	1.49467i	0.362002	−	0.161174i
$87$	1.42045	−	2.46030i	0.152289	−	0.263771i
$88$	−0.439516	−	0.761263i	−0.0468525	−	0.0811510i
$89$	−11.8190	−	8.58700i	−1.25281	−	0.910220i	−0.254429	−	0.967092i	$-0.581887\pi$
$89$	−11.8190	−	8.58700i	−1.25281	−	0.910220i	−0.998382	+	0.0568716i	$0.981887\pi$
$90$	0.978148	+	0.207912i	0.103106	+	0.0219158i
$91$	3.19411	−	9.83045i	0.334834	−	1.03051i
$92$	−2.22572			−0.232047
$93$	4.31743	−	3.51565i	0.447697	−	0.364556i
$94$	6.64437			0.685314
$95$	−0.766307	+	2.35845i	−0.0786214	+	0.241972i
$96$	0.978148	+	0.207912i	0.0998318	+	0.0212199i
$97$	5.43339	+	3.94759i	0.551677	+	0.400817i	0.828403	−	0.560132i	$-0.189250\pi$
$97$	5.43339	+	3.94759i	0.551677	+	0.400817i	−0.276727	+	0.960949i	$0.589250\pi$
$98$	−0.880088	−	1.52436i	−0.0889024	−	0.153983i
$99$	−0.439516	+	0.761263i	−0.0441730	+	0.0765099i
$100$	0.913545	−	0.406737i	0.0913545	−	0.0406737i
$101$	−2.42498	+	1.76185i	−0.241295	+	0.175311i	−0.701860	−	0.712315i	$-0.747647\pi$
$101$	−2.42498	+	1.76185i	−0.241295	+	0.175311i	0.460565	+	0.887626i	$0.347647\pi$
$102$	7.32614	+	3.26181i	0.725396	+	0.322967i
$103$	−2.29784	+	0.488421i	−0.226413	+	0.0481255i	−0.319721	−	0.947512i	$-0.603589\pi$
$103$	−2.29784	+	0.488421i	−0.226413	+	0.0481255i	0.0933081	+	0.995637i	$0.470256\pi$
$104$	0.365044	−	3.47316i	0.0357955	−	0.340572i
$105$	−1.98047	−	2.19953i	−0.193274	−	0.214652i
$106$	−6.63967	+	7.37410i	−0.644902	+	0.716236i
$107$	−0.727163	−	6.91850i	−0.0702975	−	0.668836i	−0.971759	−	0.235976i	$-0.924171\pi$
$107$	−0.727163	−	6.91850i	−0.0702975	−	0.668836i	0.901461	−	0.432860i	$-0.142495\pi$
$108$	−0.309017	−	0.951057i	−0.0297352	−	0.0915155i
$109$	−2.07270	−	6.37911i	−0.198529	−	0.611008i	−0.999917	−	0.0128642i	$-0.995905\pi$
$109$	−2.07270	−	6.37911i	−0.198529	−	0.611008i	0.801389	−	0.598144i	$-0.204095\pi$
$110$	0.0918838	+	0.874216i	0.00876078	+	0.0833532i
$111$	−3.32675	+	3.69473i	−0.315761	+	0.350688i
$112$	−1.98047	−	2.19953i	−0.187136	−	0.207836i
$113$	−0.225721	+	2.14759i	−0.0212341	+	0.202029i	−0.999996	−	0.00297352i	$-0.999053\pi$
$113$	−0.225721	+	2.14759i	−0.0212341	+	0.202029i	0.978762	+	0.205002i	$0.0657202\pi$
$114$	2.42563	−	0.515584i	0.227181	−	0.0482889i
$115$	2.03329	+	0.905281i	0.189606	+	0.0844179i
$116$	−2.29834	+	1.66984i	−0.213396	+	0.155041i
$117$	−3.19037	+	1.42044i	−0.294950	+	0.131320i
$118$	1.91271	−	3.31290i	0.176079	−	0.304977i
$119$	−11.8678	−	20.5557i	−1.08792	−	1.88434i
$120$	−0.809017	−	0.587785i	−0.0738528	−	0.0536572i
$121$	10.0038	+	2.12638i	0.909438	+	0.193307i
$122$	1.20685	−	3.71431i	0.109263	−	0.336278i
$123$	−3.95830			−0.356908
$124$	−5.37411	+	1.45565i	−0.482610	+	0.130721i
$125$	−1.00000			−0.0894427
$126$	−0.914616	+	2.81490i	−0.0814805	+	0.250771i
$127$	15.9730	+	3.39517i	1.41738	+	0.301272i	0.851991	−	0.523556i	$-0.175395\pi$
$127$	15.9730	+	3.39517i	1.41738	+	0.301272i	0.565384	+	0.824828i	$0.308728\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	1.83739	+	3.18245i	0.161773	+	0.280199i
$130$	−1.74615	+	3.02442i	−0.153147	+	0.265259i
$131$	−13.3747	+	5.95480i	−1.16855	+	0.520274i	−0.896948	−	0.442135i	$-0.854221\pi$
$131$	−13.3747	+	5.95480i	−1.16855	+	0.520274i	−0.271605	+	0.962409i	$0.587555\pi$
$132$	0.711151	−	0.516682i	0.0618978	−	0.0449714i
$133$	−6.70513	−	2.98532i	−0.581408	−	0.258860i
$134$	7.52132	−	1.59871i	0.649743	−	0.138107i
$135$	−0.104528	+	0.994522i	−0.00899638	+	0.0855948i
$136$	−5.36606	−	5.95962i	−0.460136	−	0.511033i
$137$	−6.74314	+	7.48902i	−0.576106	+	0.639830i	−0.958812	−	0.284040i	$-0.908325\pi$
$137$	−6.74314	+	7.48902i	−0.576106	+	0.639830i	0.382707	+	0.923870i	$0.374992\pi$
$138$	−0.232651	−	2.21353i	−0.0198046	−	0.188428i
$139$	3.28014	+	10.0952i	0.278218	+	0.856267i	0.988350	+	0.152198i	$0.0486352\pi$
$139$	3.28014	+	10.0952i	0.278218	+	0.856267i	−0.710132	+	0.704068i	$0.751365\pi$
$140$	0.914616	+	2.81490i	0.0772992	+	0.237902i
$141$	0.694525	+	6.60797i	0.0584896	+	0.556491i
$142$	−6.50595	+	7.22559i	−0.545967	+	0.606358i
$143$	−2.05412	−	2.28133i	−0.171774	−	0.190775i
$144$	−0.104528	+	0.994522i	−0.00871071	+	0.0828768i
$145$	2.77882	−	0.590657i	0.230769	−	0.0490514i
$146$	−13.9306	−	6.20229i	−1.15290	−	0.513305i
$147$	1.42401	−	1.03461i	0.117451	−	0.0853329i
$148$	4.54192	−	2.02219i	0.373344	−	0.166223i
$149$	9.07764	−	15.7229i	0.743669	−	1.28807i	−0.207145	−	0.978310i	$-0.566417\pi$
$149$	9.07764	−	15.7229i	0.743669	−	1.28807i	0.950814	−	0.309763i	$-0.100250\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	16.3461	+	11.8761i	1.33022	+	0.966465i	0.999743	+	0.0226526i	$0.00721115\pi$
$151$	16.3461	+	11.8761i	1.33022	+	0.966465i	0.330482	+	0.943812i	$0.392789\pi$
$152$	−2.42563	−	0.515584i	−0.196745	−	0.0418194i
$153$	−2.47815	+	7.62695i	−0.200346	+	0.616603i
$154$	−2.60172			−0.209653
$155$	5.50156	+	0.856045i	0.441896	+	0.0687592i
$156$	3.49229			0.279607
$157$	1.46194	−	4.49940i	0.116676	−	0.359091i	−0.875617	−	0.483006i	$-0.839545\pi$
$157$	1.46194	−	4.49940i	0.116676	−	0.359091i	0.992293	+	0.123915i	$0.0395450\pi$
$158$	8.70416	+	1.85013i	0.692466	+	0.147188i
$159$	−8.02774	−	5.83249i	−0.636641	−	0.462547i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−3.29380	+	5.70502i	−0.259587	+	0.449619i
$162$	0.913545	−	0.406737i	0.0717749	−	0.0319562i
$163$	2.03034	−	1.47513i	0.159029	−	0.115541i	−0.505425	−	0.862870i	$-0.668664\pi$
$163$	2.03034	−	1.47513i	0.159029	−	0.115541i	0.664454	+	0.747329i	$0.268664\pi$
$164$	3.61609	+	1.60999i	0.282369	+	0.125719i
$165$	−0.859822	+	0.182761i	−0.0669371	+	0.0142279i
$166$	1.75462	−	16.6941i	0.136185	−	1.29571i
$167$	−7.13025	−	7.91894i	−0.551755	−	0.612786i	0.401166	−	0.916006i	$-0.368605\pi$
$167$	−7.13025	−	7.91894i	−0.551755	−	0.612786i	−0.952921	+	0.303219i	$0.901939\pi$
$168$	1.98047	−	2.19953i	0.152796	−	0.169697i
$169$	0.0840285	+	0.799478i	0.00646373	+	0.0614983i
$170$	2.47815	+	7.62695i	0.190065	+	0.584961i
$171$	0.766307	+	2.35845i	0.0586010	+	0.180355i
$172$	−0.384118	−	3.65464i	−0.0292888	−	0.278664i
$173$	8.35844	−	9.28299i	0.635481	−	0.705773i	−0.336275	−	0.941764i	$-0.609167\pi$
$173$	8.35844	−	9.28299i	0.635481	−	0.705773i	0.971755	+	0.235991i	$0.0758337\pi$
$174$	−1.90094	−	2.11120i	−0.144110	−	0.160050i
$175$	0.309379	−	2.94355i	0.0233869	−	0.222511i
$176$	−0.859822	+	0.182761i	−0.0648115	+	0.0137761i
$177$	3.49469	+	1.55593i	0.262677	+	0.116951i
$178$	−11.8190	+	8.58700i	−0.885871	+	0.643623i
$179$	−3.76389	+	1.67579i	−0.281326	+	0.125255i	−0.542549	−	0.840024i	$-0.682541\pi$
$179$	−3.76389	+	1.67579i	−0.281326	+	0.125255i	0.261223	+	0.965278i	$0.415874\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	−7.64407	−	13.2399i	−0.568179	−	0.984115i	−0.996746	−	0.0806051i	$-0.974315\pi$
$181$	−7.64407	−	13.2399i	−0.568179	−	0.984115i	0.428567	−	0.903510i	$-0.359019\pi$
$182$	−8.36228	−	6.07555i	−0.619854	−	0.450350i
$183$	3.82012	+	0.811991i	0.282391	+	0.0600241i
$184$	−0.687785	+	2.11678i	−0.0507042	+	0.156051i
$185$	−4.97175			−0.365530
$186$	−2.00942	−	5.19252i	−0.147338	−	0.380734i
$187$	−7.04935			−0.515500
$188$	2.05322	−	6.31917i	0.149747	−	0.460873i
$189$	−2.89508	−	0.615369i	−0.210586	−	0.0447615i
$190$	2.00622	+	1.45760i	0.145546	+	0.105746i
$191$	−12.0392	−	20.8524i	−0.871123	−	1.50883i	−0.860837	−	0.508882i	$-0.830059\pi$
$191$	−12.0392	−	20.8524i	−0.871123	−	1.50883i	−0.0102861	−	0.999947i	$-0.503274\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−1.14108	+	0.508043i	−0.0821370	+	0.0365697i	−0.447394	−	0.894337i	$-0.647648\pi$
$193$	−1.14108	+	0.508043i	−0.0821370	+	0.0365697i	0.365257	+	0.930907i	$0.380981\pi$
$194$	5.43339	−	3.94759i	0.390094	−	0.283420i
$195$	−3.19037	−	1.42044i	−0.228467	−	0.101720i
$196$	−1.72171	+	0.365961i	−0.122979	+	0.0261401i
$197$	−0.761479	+	7.24499i	−0.0542531	+	0.516184i	0.933322	+	0.359039i	$0.116896\pi$
$197$	−0.761479	+	7.24499i	−0.0542531	+	0.516184i	−0.987576	+	0.157145i	$0.949771\pi$
$198$	0.588187	+	0.653248i	0.0418006	+	0.0464243i
$199$	15.8452	−	17.5979i	1.12323	−	1.24748i	0.157621	−	0.987500i	$-0.449618\pi$
$199$	15.8452	−	17.5979i	1.12323	−	1.24748i	0.965614	−	0.259979i	$-0.0837156\pi$
$200$	−0.104528	−	0.994522i	−0.00739128	−	0.0703233i
$201$	2.37614	+	7.31301i	0.167600	+	0.515820i
$202$	0.926261	+	2.85074i	0.0651715	+	0.200577i
$203$	0.878917	+	8.36233i	0.0616879	+	0.586921i
$204$	5.36606	−	5.95962i	0.375700	−	0.417257i
$205$	−2.64862	−	2.94159i	−0.184988	−	0.205450i
$206$	−0.245556	+	2.33631i	−0.0171087	+	0.162778i
$207$	2.17708	−	0.462753i	0.151318	−	0.0321635i
$208$	−3.19037	−	1.42044i	−0.221212	−	0.0984901i
$209$	−1.76353	+	1.28128i	−0.121986	+	0.0886279i
$210$	−2.70387	+	1.20384i	−0.186585	+	0.0830730i
$211$	−5.71160	+	9.89278i	−0.393203	+	0.681047i	−0.992870	−	0.119202i	$-0.961966\pi$
$211$	−5.71160	+	9.89278i	−0.393203	+	0.681047i	0.599667	+	0.800249i	$0.295300\pi$
$212$	4.96142	+	8.59342i	0.340751	+	0.590199i
$213$	−7.86607	−	5.71503i	−0.538974	−	0.391587i
$214$	−6.80459	−	1.44636i	−0.465152	−	0.0988711i
$215$	−1.13557	+	3.49492i	−0.0774451	+	0.238351i
$216$	−1.00000			−0.0680414
$217$	−4.22188	+	15.9293i	−0.286600	+	1.08135i
$218$	−6.70740			−0.454282
$219$	4.71217	−	14.5026i	0.318419	−	0.979993i
$220$	0.859822	+	0.182761i	0.0579692	+	0.0123217i
$221$	−22.6576	−	16.4617i	−1.52411	−	1.10733i
$222$	2.48588	+	4.30566i	0.166841	+	0.288977i
$223$	−6.17667	+	10.6983i	−0.413620	+	0.716411i	−0.995283	−	0.0970192i	$-0.969069\pi$
$223$	−6.17667	+	10.6983i	−0.413620	+	0.716411i	0.581662	+	0.813430i	$0.302403\pi$
$224$	−2.70387	+	1.20384i	−0.180660	+	0.0804351i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	1.97273	+	0.878317i	0.131224	+	0.0584248i
$227$	−12.4277	+	2.64159i	−0.824855	+	0.175328i	−0.600954	−	0.799284i	$-0.705213\pi$
$227$	−12.4277	+	2.64159i	−0.824855	+	0.175328i	−0.223901	+	0.974612i	$0.571879\pi$
$228$	0.259212	−	2.46624i	0.0171667	−	0.163331i
$229$	−6.22257	−	6.91086i	−0.411199	−	0.456682i	0.501595	−	0.865102i	$-0.332747\pi$
$229$	−6.22257	−	6.91086i	−0.411199	−	0.456682i	−0.912794	+	0.408420i	$0.866080\pi$
$230$	1.48930	−	1.65403i	0.0982013	−	0.109064i
$231$	−0.271954	−	2.58747i	−0.0178933	−	0.170243i
$232$	0.877888	+	2.70186i	0.0576362	+	0.177386i
$233$	1.29441	+	3.98378i	0.0847995	+	0.260986i	0.984461	−	0.175601i	$-0.0561870\pi$
$233$	1.29441	+	3.98378i	0.0847995	+	0.260986i	−0.899662	+	0.436587i	$0.856187\pi$
$234$	0.365044	+	3.47316i	0.0238637	+	0.227048i
$235$	−4.44595	+	4.93773i	−0.290022	+	0.322102i
$236$	−2.55970	−	2.84283i	−0.166622	−	0.185053i
$237$	−0.930158	+	8.84987i	−0.0604203	+	0.574861i
$238$	−23.2170	+	4.93492i	−1.50493	+	0.319883i
$239$	−2.19268	−	0.976244i	−0.141833	−	0.0631480i	0.334593	−	0.942363i	$-0.391401\pi$
$239$	−2.19268	−	0.976244i	−0.141833	−	0.0631480i	−0.476426	+	0.879215i	$0.658068\pi$
$240$	−0.809017	+	0.587785i	−0.0522218	+	0.0379414i
$241$	13.9051	−	6.19093i	0.895704	−	0.398793i	0.0933443	−	0.995634i	$-0.470244\pi$
$241$	13.9051	−	6.19093i	0.895704	−	0.398793i	0.802360	+	0.596841i	$0.203578\pi$
$242$	5.11365	−	8.85711i	0.328718	−	0.569356i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−3.15958	−	2.29557i	−0.202272	−	0.146959i
$245$	1.72171	+	0.365961i	0.109996	+	0.0233804i
$246$	−1.22318	+	3.76457i	−0.0779873	+	0.240020i
$247$	−8.66027			−0.551040
$248$	−0.276286	+	5.56091i	−0.0175441	+	0.353118i
$249$	16.7860			1.06377
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	−2.64179	−	0.561530i	−0.166748	−	0.0354434i	0.123781	−	0.992310i	$-0.460498\pi$
$251$	−2.64179	−	0.561530i	−0.166748	−	0.0354434i	−0.290529	+	0.956866i	$0.593831\pi$
$252$	2.39450	+	1.73970i	0.150839	+	0.109591i
$253$	0.978238	+	1.69436i	0.0615013	+	0.106523i
$254$	8.16493	−	14.1421i	0.512313	−	0.887352i
$255$	−7.32614	+	3.26181i	−0.458780	+	0.204262i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	18.2684	+	8.13363i	1.13955	+	0.507362i	0.887708	−	0.460406i	$-0.152296\pi$
$257$	18.2684	+	8.13363i	1.13955	+	0.507362i	0.251845	+	0.967768i	$0.418963\pi$
$258$	3.59447	−	0.764028i	0.223782	−	0.0475663i
$259$	1.53816	−	14.6346i	0.0955763	−	0.909348i
$260$	2.33680	+	2.59528i	0.144922	+	0.160952i
$261$	1.90094	−	2.11120i	0.117665	−	0.130680i
$262$	1.53034	+	14.5602i	0.0945449	+	0.899535i
$263$	2.80872	+	8.64436i	0.173193	+	0.533034i	0.999546	−	0.0301183i	$-0.00958840\pi$
$263$	2.80872	+	8.64436i	0.173193	+	0.533034i	−0.826353	+	0.563152i	$0.809588\pi$
$264$	−0.271636	−	0.836008i	−0.0167180	−	0.0514528i
$265$	−1.03722	−	9.86847i	−0.0637158	−	0.606216i
$266$	−4.91120	+	5.45444i	−0.301125	+	0.334433i
$267$	−9.77538	−	10.8567i	−0.598243	−	0.664417i
$268$	0.803756	−	7.64723i	0.0490972	−	0.467129i
$269$	14.8011	−	3.14607i	0.902437	−	0.191819i	0.266750	−	0.963766i	$-0.414050\pi$
$269$	14.8011	−	3.14607i	0.902437	−	0.191819i	0.635687	+	0.771947i	$0.280717\pi$
$270$	0.913545	+	0.406737i	0.0555966	+	0.0247532i
$271$	3.96433	−	2.88025i	0.240816	−	0.174963i	−0.460831	−	0.887488i	$-0.652449\pi$
$271$	3.96433	−	2.88025i	0.240816	−	0.174963i	0.701647	+	0.712525i	$0.252449\pi$
$272$	−7.32614	+	3.26181i	−0.444212	+	0.197776i
$273$	5.16818	−	8.95154i	0.312792	−	0.541772i
$274$	5.03873	+	8.72734i	0.304401	+	0.527238i
$275$	−0.711151	−	0.516682i	−0.0428840	−	0.0311571i
$276$	−2.17708	−	0.462753i	−0.131045	−	0.0278544i
$277$	−8.52416	+	26.2347i	−0.512167	+	1.57629i	0.276210	+	0.961097i	$0.410921\pi$
$277$	−8.52416	+	26.2347i	−0.512167	+	1.57629i	−0.788378	+	0.615192i	$0.789079\pi$
$278$	10.6148			0.636631
$279$	4.95403	−	2.54118i	0.296590	−	0.152137i
$280$	2.95976			0.176879
$281$	−3.92589	+	12.0826i	−0.234199	+	0.720790i	0.763028	+	0.646366i	$0.223712\pi$
$281$	−3.92589	+	12.0826i	−0.234199	+	0.720790i	−0.997227	+	0.0744245i	$0.976288\pi$
$282$	6.49917	+	1.38144i	0.387020	+	0.0822636i
$283$	9.68112	+	7.03375i	0.575483	+	0.418113i	0.837093	−	0.547061i	$-0.184253\pi$
$283$	9.68112	+	7.03375i	0.575483	+	0.418113i	−0.261610	+	0.965174i	$0.584253\pi$
$284$	4.86150	+	8.42036i	0.288477	+	0.499656i
$285$	−1.23991	+	2.14759i	−0.0734460	+	0.127212i
$286$	−2.80443	+	1.24861i	−0.165830	+	0.0738321i
$287$	9.47814	−	6.88627i	0.559477	−	0.406484i
$288$	0.913545	+	0.406737i	0.0538312	+	0.0239672i
$289$	−46.2778	+	9.83664i	−2.72222	+	0.578626i
$290$	0.296955	−	2.82534i	0.0174378	−	0.165910i
$291$	4.49390	+	4.99099i	0.263437	+	0.292577i
$292$	−10.2035	+	11.3322i	−0.597116	+	0.663164i
$293$	−1.32462	−	12.6029i	−0.0773849	−	0.736268i	−0.962571	−	0.271030i	$-0.912636\pi$
$293$	−1.32462	−	12.6029i	−0.0773849	−	0.736268i	0.885186	−	0.465237i	$-0.154031\pi$
$294$	−0.543925	−	1.67403i	−0.0317223	−	0.0976313i
$295$	1.18212	+	3.63818i	0.0688255	+	0.211823i
$296$	−0.519689	−	4.94451i	−0.0302063	−	0.287394i
$297$	−0.588187	+	0.653248i	−0.0341301	+	0.0379053i
$298$	−12.1483	−	13.4920i	−0.703729	−	0.781571i
$299$	−0.812485	+	7.73028i	−0.0469872	+	0.447054i
$300$	0.978148	−	0.207912i	0.0564734	−	0.0120038i
$301$	−9.93613	−	4.42385i	−0.572709	−	0.254986i
$302$	16.3461	−	11.8761i	0.940611	−	0.683394i
$303$	−2.73830	+	1.21917i	−0.157311	+	0.0700395i
$304$	−1.23991	+	2.14759i	−0.0711138	+	0.123173i
$305$	1.95273	+	3.38223i	0.111813	+	0.193666i
$306$	6.48787	+	4.71372i	0.370887	+	0.269465i
$307$	9.01152	+	1.91546i	0.514315	+	0.109321i	0.457755	−	0.889078i	$-0.348654\pi$
$307$	9.01152	+	1.91546i	0.514315	+	0.109321i	0.0565595	+	0.998399i	$0.481987\pi$
$308$	−0.803976	+	2.47438i	−0.0458108	+	0.140991i
$309$	−2.34917			−0.133640
$310$	2.51422	−	4.96776i	0.142798	−	0.282150i
$311$	31.2399			1.77145			0.885726	−	0.464208i	$-0.153661\pi$
$311$	31.2399			1.77145			0.885726	+	0.464208i	$0.153661\pi$
$312$	1.07918	−	3.32137i	0.0610964	−	0.188035i
$313$	7.49437	+	1.59298i	0.423607	+	0.0900405i	0.414782	−	0.909921i	$-0.363858\pi$
$313$	7.49437	+	1.59298i	0.423607	+	0.0900405i	0.00882459	+	0.999961i	$0.497191\pi$
$314$	−3.82742	−	2.78078i	−0.215994	−	0.156929i
$315$	−1.47988	−	2.56323i	−0.0833818	−	0.144421i
$316$	4.44931	−	7.70643i	0.250293	−	0.433520i
$317$	−18.4334	+	8.20706i	−1.03532	+	0.460955i	−0.852795	−	0.522246i	$-0.825094\pi$
$317$	−18.4334	+	8.20706i	−1.03532	+	0.460955i	−0.182526	+	0.983201i	$0.558427\pi$
$318$	−8.02774	+	5.83249i	−0.450173	+	0.327070i
$319$	2.28135	+	1.01572i	0.127731	+	0.0568695i
$320$	0.978148	−	0.207912i	0.0546801	−	0.0116226i
$321$	0.727163	−	6.91850i	0.0405863	−	0.386153i
$322$	4.40796	+	4.89553i	0.245646	+	0.272817i
$323$	−13.3069	+	14.7788i	−0.740414	+	0.822314i
$324$	−0.104528	−	0.994522i	−0.00580714	−	0.0552512i
$325$	−1.07918	−	3.32137i	−0.0598620	−	0.184236i
$326$	−0.775521	−	2.38681i	−0.0429522	−	0.132193i
$327$	−0.701114	−	6.67065i	−0.0387717	−	0.368888i
$328$	2.64862	−	2.94159i	0.146246	−	0.162422i
$329$	−13.1589	−	14.6145i	−0.725476	−	0.805723i
$330$	−0.0918838	+	0.874216i	−0.00505804	+	0.0481240i
$331$	13.4094	−	2.85025i	0.737046	−	0.156664i	0.175932	−	0.984402i	$-0.443706\pi$
$331$	13.4094	−	2.85025i	0.737046	−	0.156664i	0.561114	+	0.827738i	$0.310373\pi$
$332$	−15.3348	−	6.82750i	−0.841607	−	0.374708i
$333$	−4.02223	+	2.92232i	−0.220417	+	0.160142i
$334$	−9.73473	+	4.33418i	−0.532661	+	0.237156i
$335$	−3.84467	+	6.65917i	−0.210057	+	0.363829i
$336$	−1.47988	−	2.56323i	−0.0807341	−	0.139835i
$337$	−23.7342	−	17.2439i	−1.29288	−	0.939335i	−0.293024	−	0.956105i	$-0.594662\pi$
$337$	−23.7342	−	17.2439i	−1.29288	−	0.939335i	−0.999859	+	0.0167705i	$0.994662\pi$
$338$	0.786315	+	0.167136i	0.0427699	+	0.00909102i
$339$	−0.667299	+	2.05373i	−0.0362427	+	0.111544i
$340$	8.01945			0.434916
$341$	3.47014	+	3.45133i	0.187919	+	0.186900i
$342$	2.47982			0.134093
$343$	4.79243	−	14.7496i	0.258767	−	0.796402i
$344$	−3.59447	−	0.764028i	−0.193801	−	0.0411937i
$345$	1.80064	+	1.30824i	0.0969434	+	0.0704335i
$346$	−6.24575	−	10.8180i	−0.335774	−	0.581577i
$347$	−4.62123	+	8.00420i	−0.248081	+	0.429688i	−0.962993	−	0.269526i	$-0.913133\pi$
$347$	−4.62123	+	8.00420i	−0.248081	+	0.429688i	0.714913	+	0.699214i	$0.246466\pi$
$348$	−2.59530	+	1.15550i	−0.139122	+	0.0619413i
$349$	−0.458431	+	0.333070i	−0.0245393	+	0.0178288i	−0.599987	−	0.800010i	$-0.704828\pi$
$349$	−0.458431	+	0.333070i	−0.0245393	+	0.0178288i	0.575448	+	0.817838i	$0.304828\pi$
$350$	−2.70387	−	1.20384i	−0.144528	−	0.0643481i
$351$	−3.41598	+	0.726089i	−0.182331	+	0.0387558i
$352$	−0.0918838	+	0.874216i	−0.00489742	+	0.0465959i
$353$	18.2501	+	20.2688i	0.971356	+	1.07880i	0.996865	+	0.0791250i	$0.0252126\pi$
$353$	18.2501	+	20.2688i	0.971356	+	1.07880i	−0.0255091	+	0.999675i	$0.508121\pi$
$354$	2.55970	−	2.84283i	0.136046	−	0.151095i
$355$	−1.01633	−	9.66973i	−0.0539412	−	0.513216i
$356$	4.51445	+	13.8941i	0.239265	+	0.736383i
$357$	−7.33472	−	22.5740i	−0.388195	−	1.19474i
$358$	0.430667	+	4.09752i	0.0227614	+	0.216561i
$359$	3.91505	−	4.34811i	0.206629	−	0.229484i	−0.630919	−	0.775849i	$-0.717322\pi$
$359$	3.91505	−	4.34811i	0.206629	−	0.229484i	0.837548	+	0.546364i	$0.183989\pi$
$360$	−0.669131	−	0.743145i	−0.0352663	−	0.0391672i
$361$	1.34324	−	12.7801i	0.0706969	−	0.672636i
$362$	−14.9541	+	3.17858i	−0.785968	+	0.167063i
$363$	9.34311	+	4.15982i	0.490386	+	0.218334i
$364$	−8.36228	+	6.07555i	−0.438303	+	0.318446i
$365$	13.9306	−	6.20229i	0.729160	−	0.324643i
$366$	1.95273	−	3.38223i	0.102071	−	0.176792i
$367$	−6.34598	−	10.9916i	−0.331257	−	0.573755i	0.651501	−	0.758648i	$-0.274140\pi$
$367$	−6.34598	−	10.9916i	−0.331257	−	0.573755i	−0.982759	+	0.184893i	$0.940806\pi$
$368$	1.80064	+	1.30824i	0.0938650	+	0.0681969i
$369$	−3.87180	−	0.822977i	−0.201558	−	0.0428425i
$370$	−1.53636	+	4.72842i	−0.0798713	+	0.245819i
$371$	29.3692			1.52477
$372$	−5.55932	+	0.306501i	−0.288237	+	0.0158913i
$373$	22.1559			1.14719			0.573594	−	0.819140i	$-0.305549\pi$
$373$	22.1559			1.14719			0.573594	+	0.819140i	$0.305549\pi$
$374$	−2.17837	+	6.70433i	−0.112641	+	0.346673i
$375$	−0.978148	−	0.207912i	−0.0505113	−	0.0107365i
$376$	−5.37541	−	3.90546i	−0.277215	−	0.201409i
$377$	4.96064	+	8.59208i	0.255486	+	0.442515i
$378$	−1.47988	+	2.56323i	−0.0761168	+	0.131838i
$379$	30.8993	−	13.7572i	1.58719	−	0.706662i	0.592120	−	0.805850i	$-0.298291\pi$
$379$	30.8993	−	13.7572i	1.58719	−	0.706662i	0.995069	+	0.0991874i	$0.0316243\pi$
$380$	2.00622	−	1.45760i	0.102917	−	0.0747734i
$381$	14.9181	+	6.64195i	0.764276	+	0.340277i
$382$	−23.5521	+	5.00616i	−1.20503	+	0.256138i
$383$	1.77704	−	16.9074i	0.0908026	−	0.863929i	−0.850411	−	0.526118i	$-0.823647\pi$
$383$	1.77704	−	16.9074i	0.0908026	−	0.863929i	0.941214	−	0.337811i	$-0.109686\pi$
$384$	−0.669131	−	0.743145i	−0.0341464	−	0.0379235i
$385$	1.74089	−	1.93346i	0.0887240	−	0.0985380i
$386$	0.130563	+	1.24223i	0.00664551	+	0.0632278i
$387$	1.13557	+	3.49492i	0.0577241	+	0.177657i
$388$	−2.07537	−	6.38733i	−0.105361	−	0.324267i
$389$	−3.27860	−	31.1938i	−0.166231	−	1.58159i	−0.686208	−	0.727406i	$-0.740726\pi$
$389$	−3.27860	−	31.1938i	−0.166231	−	1.58159i	0.519976	−	0.854181i	$-0.325941\pi$
$390$	−2.33680	+	2.59528i	−0.118329	+	0.131417i
$391$	11.9433	+	13.2644i	0.604001	+	0.670811i
$392$	−0.183989	+	1.75053i	−0.00929283	+	0.0884153i
$393$	−14.3205	+	3.04392i	−0.722374	+	0.153545i
$394$	6.65508	+	2.96303i	0.335278	+	0.149276i
$395$	−7.19913	+	5.23047i	−0.362228	+	0.263174i
$396$	0.803035	−	0.357534i	0.0403540	−	0.0179668i
$397$	−11.3308	+	19.6255i	−0.568675	+	0.984975i	0.428022	+	0.903768i	$0.359211\pi$
$397$	−11.3308	+	19.6255i	−0.568675	+	0.984975i	−0.996697	+	0.0812062i	$0.974123\pi$
$398$	−11.8401	−	20.5077i	−0.593492	−	1.02796i
$399$	−5.93792	−	4.31415i	−0.297268	−	0.215978i
$400$	−0.978148	−	0.207912i	−0.0489074	−	0.0103956i
$401$	7.35316	−	22.6307i	0.367199	−	1.13012i	−0.581393	−	0.813623i	$-0.697492\pi$
$401$	7.35316	−	22.6307i	0.367199	−	1.13012i	0.948592	−	0.316501i	$-0.102508\pi$
$402$	7.68935			0.383510
$403$	3.09393	+	19.1965i	0.154119	+	0.956248i
$404$	2.99744			0.149128
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$	8.22465	+	1.74820i	0.408183	+	0.0867619i
$407$	−3.53567	−	2.56881i	−0.175256	−	0.127331i
$408$	−4.00973	−	6.94505i	−0.198511	−	0.343831i
$409$	1.86634	−	3.23260i	0.0922846	−	0.159842i	−0.816188	−	0.577787i	$-0.803916\pi$
$409$	1.86634	−	3.23260i	0.0922846	−	0.159842i	0.908472	+	0.417946i	$0.137250\pi$
$410$	−3.61609	+	1.60999i	−0.178586	+	0.0795116i
$411$	−8.15284	+	5.92339i	−0.402150	+	0.292179i
$412$	2.14608	+	0.955496i	0.105730	+	0.0470739i
$413$	−11.0749	+	2.35404i	−0.544959	+	0.115835i
$414$	0.232651	−	2.21353i	0.0114342	−	0.108789i
$415$	11.2321	+	12.4745i	0.551360	+	0.612347i
$416$	−2.33680	+	2.59528i	−0.114571	+	0.127244i
$417$	1.10954	+	10.5566i	0.0543346	+	0.516959i
$418$	0.673608	+	2.07315i	0.0329472	+	0.101401i
$419$	−0.160630	−	0.494367i	−0.00784727	−	0.0241514i	0.947056	−	0.321068i	$-0.104042\pi$
$419$	−0.160630	−	0.494367i	−0.00784727	−	0.0241514i	−0.954903	+	0.296916i	$0.904042\pi$
$420$	0.309379	+	2.94355i	0.0150962	+	0.143630i
$421$	7.96329	−	8.84413i	0.388107	−	0.431037i	−0.517154	−	0.855892i	$-0.673009\pi$
$421$	7.96329	−	8.84413i	0.388107	−	0.431037i	0.905261	+	0.424856i	$0.139675\pi$
$422$	7.64361	+	8.48909i	0.372085	+	0.413242i
$423$	−0.694525	+	6.60797i	−0.0337690	+	0.321290i
$424$	9.70599	−	2.06307i	0.471365	−	0.100192i
$425$	−7.32614	−	3.26181i	−0.355370	−	0.158221i
$426$	−7.86607	+	5.71503i	−0.381112	+	0.276894i
$427$	−10.5599	+	4.70156i	−0.511028	+	0.227524i
$428$	−3.47830	+	6.02460i	−0.168130	+	0.291210i
$429$	−1.53492	−	2.65856i	−0.0741065	−	0.128356i
$430$	2.97295	+	2.15998i	0.143369	+	0.104163i
$431$	15.2788	+	3.24760i	0.735952	+	0.156432i	0.560615	−	0.828077i	$-0.310565\pi$
$431$	15.2788	+	3.24760i	0.735952	+	0.156432i	0.175338	+	0.984508i	$0.443898\pi$
$432$	−0.309017	+	0.951057i	−0.0148676	+	0.0457577i
$433$	25.7677			1.23831			0.619157	−	0.785267i	$-0.287474\pi$
$433$	25.7677			1.23831			0.619157	+	0.785267i	$0.287474\pi$
$434$	13.8450	+	8.93765i	0.664581	+	0.429021i
$435$	2.84091			0.136211
$436$	−2.07270	+	6.37911i	−0.0992643	+	0.305504i
$437$	5.39877	+	1.14754i	0.258258	+	0.0548945i
$438$	−12.3366	−	8.96309i	−0.589467	−	0.428273i
$439$	6.12565	+	10.6099i	0.292361	+	0.506384i	0.974368	−	0.224962i	$-0.0722257\pi$
$439$	6.12565	+	10.6099i	0.292361	+	0.506384i	−0.682006	+	0.731346i	$0.738892\pi$
$440$	0.439516	−	0.761263i	0.0209531	−	0.0362918i
$441$	1.60800	−	0.715928i	0.0765715	−	0.0340918i
$442$	−22.6576	+	16.4617i	−1.07771	+	0.783003i
$443$	23.6602	+	10.5342i	1.12413	+	0.500496i	0.882707	−	0.469924i	$-0.155719\pi$
$443$	23.6602	+	10.5342i	1.12413	+	0.500496i	0.241425	+	0.970420i	$0.422385\pi$
$444$	4.86311	−	1.03368i	0.230793	−	0.0490565i
$445$	1.52706	−	14.5290i	0.0723898	−	0.688743i
$446$	8.26599	+	9.18031i	0.391406	+	0.434701i
$447$	12.1483	−	13.4920i	0.574593	−	0.638150i
$448$	0.309379	+	2.94355i	0.0146168	+	0.139069i
$449$	−2.63548	−	8.11117i	−0.124376	−	0.382790i	0.869411	−	0.494090i	$-0.164499\pi$
$449$	−2.63548	−	8.11117i	−0.124376	−	0.382790i	−0.993787	+	0.111300i	$0.964499\pi$
$450$	0.309017	+	0.951057i	0.0145672	+	0.0448332i
$451$	−0.363704	−	3.46041i	−0.0171261	−	0.162944i
$452$	1.44494	−	1.60476i	0.0679641	−	0.0754818i
$453$	13.5197	+	15.0151i	0.635211	+	0.705473i
$454$	−1.32807	+	12.6357i	−0.0623294	+	0.593024i
$455$	10.1105	−	2.14905i	0.473986	−	0.100749i
$456$	−2.26543	−	1.00863i	−0.106088	−	0.0472336i
$457$	1.14377	−	0.830998i	0.0535033	−	0.0388724i	−0.560712	−	0.828011i	$-0.689473\pi$
$457$	1.14377	−	0.830998i	0.0535033	−	0.0388724i	0.614215	+	0.789138i	$0.289473\pi$
$458$	−8.49550	+	3.78244i	−0.396968	+	0.176742i
$459$	−4.00973	+	6.94505i	−0.187158	+	0.324167i
$460$	−1.11286	−	1.92753i	−0.0518873	−	0.0898715i
$461$	22.9563	+	16.6787i	1.06918	+	0.776806i	0.975765	−	0.218821i	$-0.0702210\pi$
$461$	22.9563	+	16.6787i	1.06918	+	0.776806i	0.0934170	+	0.995627i	$0.470221\pi$
$462$	−2.54487	−	0.540928i	−0.118398	−	0.0251663i
$463$	−7.75266	+	23.8602i	−0.360297	+	1.10888i	0.592577	+	0.805514i	$0.298111\pi$
$463$	−7.75266	+	23.8602i	−0.360297	+	1.10888i	−0.952874	+	0.303366i	$0.901889\pi$
$464$	2.84091			0.131886
$465$	5.20336	+	1.98118i	0.241300	+	0.0918749i
$466$	4.18879			0.194042
$467$	0.164134	−	0.505153i	0.00759522	−	0.0233757i	−0.947187	−	0.320681i	$-0.896088\pi$
$467$	0.164134	−	0.505153i	0.00759522	−	0.0233757i	0.954782	+	0.297306i	$0.0960881\pi$
$468$	3.41598	+	0.726089i	0.157904	+	0.0335635i
$469$	−18.4121	−	13.3772i	−0.850192	−	0.617701i
$470$	3.32218	+	5.75419i	0.153241	+	0.265421i
$471$	2.36547	−	4.09712i	0.108995	−	0.188785i
$472$	−3.49469	+	1.55593i	−0.160856	+	0.0716177i
$473$	−2.61332	+	1.89869i	−0.120161	+	0.0873018i
$474$	8.12929	+	3.61939i	0.373391	+	0.166244i
$475$	−2.42563	+	0.515584i	−0.111296	+	0.0236566i
$476$	−2.48105	+	23.6056i	−0.113719	+	1.08196i
$477$	−6.63967	−	7.37410i	−0.304010	−	0.337637i
$478$	−1.60604	+	1.78369i	−0.0734585	+	0.0815839i
$479$	1.09768	+	10.4438i	0.0501544	+	0.477187i	0.990555	+	0.137118i	$0.0437839\pi$
$479$	1.09768	+	10.4438i	0.0501544	+	0.477187i	−0.940400	+	0.340069i	$0.889549\pi$
$480$	0.309017	+	0.951057i	0.0141046	+	0.0434096i
$481$	−5.36540	−	16.5130i	−0.244641	−	0.752929i
$482$	−1.59103	−	15.1376i	−0.0724693	−	0.689499i
$483$	−4.40796	+	4.89553i	−0.200569	+	0.222754i
$484$	−6.84340	−	7.60037i	−0.311064	−	0.345471i
$485$	−0.702017	+	6.67924i	−0.0318769	+	0.303289i
$486$	0.978148	−	0.207912i	0.0443697	−	0.00943107i
$487$	12.8257	+	5.71038i	0.581189	+	0.258762i	0.676205	−	0.736714i	$-0.263623\pi$
$487$	12.8257	+	5.71038i	0.581189	+	0.258762i	−0.0950154	+	0.995476i	$0.530290\pi$
$488$	−3.15958	+	2.29557i	−0.143028	+	0.103916i
$489$	2.29267	−	1.02076i	0.103678	−	0.0461605i
$490$	0.880088	−	1.52436i	0.0397583	−	0.0688635i
$491$	16.0982	+	27.8829i	0.726502	+	1.25834i	0.958353	+	0.285587i	$0.0921886\pi$
$491$	16.0982	+	27.8829i	0.726502	+	1.25834i	−0.231851	+	0.972751i	$0.574478\pi$
$492$	3.20233	+	2.32663i	0.144372	+	0.104893i
$493$	22.2847	+	4.73675i	1.00365	+	0.213332i
$494$	−2.67617	+	8.23640i	−0.120407	+	0.370573i
$495$	−0.879031			−0.0395095
$496$	5.20336	+	1.98118i	0.233638	+	0.0889575i
$497$	28.7777			1.29086
$498$	5.18717	−	15.9645i	0.232443	−	0.715385i
$499$	32.5696	+	6.92288i	1.45802	+	0.309911i	0.867630	−	0.497210i	$-0.165642\pi$
$499$	32.5696	+	6.92288i	1.45802	+	0.309911i	0.590386	+	0.807121i	$0.298976\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	−5.32800	−	9.22836i	−0.238037	−	0.412293i
$502$	−1.35040	+	2.33897i	−0.0602715	+	0.104393i
$503$	25.2371	−	11.2363i	1.12527	−	0.501001i	0.242190	−	0.970229i	$-0.422134\pi$
$503$	25.2371	−	11.2363i	1.12527	−	0.501001i	0.883077	+	0.469228i	$0.155468\pi$
$504$	2.39450	−	1.73970i	0.106659	−	0.0774925i
$505$	−2.73830	−	1.21917i	−0.121853	−	0.0542524i
$506$	1.91372	−	0.406774i	0.0850753	−	0.0180833i
$507$	−0.0840285	+	0.799478i	−0.00373184	+	0.0355061i
$508$	−10.9268	−	12.1354i	−0.484799	−	0.538423i
$509$	−7.20625	+	8.00335i	−0.319411	+	0.354742i	−0.881373	−	0.472421i	$-0.843380\pi$
$509$	−7.20625	+	8.00335i	−0.319411	+	0.354742i	0.561962	+	0.827163i	$0.310047\pi$
$510$	0.838261	+	7.97552i	0.0371188	+	0.353162i
$511$	13.9469	+	42.9241i	0.616975	+	1.89885i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	0.259212	+	2.46624i	0.0114445	+	0.108887i
$514$	13.3808	−	14.8609i	0.590202	−	0.655485i
$515$	−1.57190	−	1.74578i	−0.0692664	−	0.0769281i
$516$	0.384118	−	3.65464i	0.0169099	−	0.160887i
$517$	−5.71297	+	1.21433i	−0.251256	+	0.0534062i
$518$	−13.4430	−	5.98521i	−0.590651	−	0.262975i
$519$	10.1058	−	7.34232i	0.443597	−	0.322292i
$520$	3.19037	−	1.42044i	0.139907	−	0.0622906i
$521$	−19.2375	+	33.3203i	−0.842809	+	1.45979i	0.0447016	+	0.999000i	$0.485766\pi$
$521$	−19.2375	+	33.3203i	−0.842809	+	1.45979i	−0.887511	+	0.460787i	$0.847567\pi$
$522$	−1.42045	−	2.46030i	−0.0621715	−	0.107684i
$523$	−7.15308	−	5.19702i	−0.312783	−	0.227250i	0.420307	−	0.907382i	$-0.361922\pi$
$523$	−7.15308	−	5.19702i	−0.312783	−	0.227250i	−0.733090	+	0.680132i	$0.761922\pi$
$524$	14.3205	+	3.04392i	0.625595	+	0.132974i
$525$	0.914616	−	2.81490i	0.0399171	−	0.122852i
$526$	9.08922			0.396309
$527$	37.5129	+	24.2165i	1.63409	+	1.05489i
$528$	−0.879031			−0.0382549
$529$	−5.57658	+	17.1629i	−0.242460	+	0.746215i
$530$	−9.70599	−	2.06307i	−0.421601	−	0.0896142i
$531$	3.09482	+	2.24852i	0.134304	+	0.0975774i
$532$	3.66984	+	6.35635i	0.159108	+	0.275583i
$533$	6.91178	−	11.9715i	0.299382	−	0.518545i
$534$	−13.3461	+	5.94205i	−0.577540	+	0.257137i
$535$	5.62801	−	4.08899i	0.243320	−	0.176782i
$536$	−7.02457	−	3.12754i	−0.303415	−	0.135089i
$537$	−4.03005	+	0.856615i	−0.173910	+	0.0369656i
$538$	1.58170	−	15.0488i	0.0681918	−	0.648802i
$539$	1.03531	+	1.14983i	0.0445941	+	0.0495267i
$540$	0.669131	−	0.743145i	0.0287948	−	0.0319799i
$541$	−0.972127	−	9.24917i	−0.0417950	−	0.397653i	−0.995342	−	0.0964081i	$-0.969265\pi$
$541$	−0.972127	−	9.24917i	−0.0417950	−	0.397653i	0.953547	−	0.301245i	$-0.0974021\pi$
$542$	−1.51424	−	4.66035i	−0.0650422	−	0.200179i
$543$	−4.72429	−	14.5399i	−0.202739	−	0.623966i
$544$	0.838261	+	7.97552i	0.0359402	+	0.341948i
$545$	4.48812	−	4.98457i	0.192250	−	0.213515i
$546$	−6.91637	−	7.68141i	−0.295993	−	0.328734i
$547$	−2.92128	+	27.7941i	−0.124905	+	1.18839i	0.735048	+	0.678015i	$0.237160\pi$
$547$	−2.92128	+	27.7941i	−0.124905	+	1.18839i	−0.859952	+	0.510374i	$0.829507\pi$
$548$	9.85725	−	2.09522i	0.421081	−	0.0895035i
$549$	3.56782	+	1.58849i	0.152271	+	0.0677953i
$550$	−0.711151	+	0.516682i	−0.0303236	+	0.0220314i
$551$	6.43587	−	2.86543i	0.274177	−	0.122072i
$552$	−1.11286	+	1.92753i	−0.0473664	+	0.0820411i
$553$	−13.1689	−	22.8092i	−0.559998	−	0.969945i
$554$	22.3165	+	16.2139i	0.948139	+	0.688863i
$555$	−4.86311	−	1.03368i	−0.206427	−	0.0438775i
$556$	3.28014	−	10.0952i	0.139109	−	0.428133i
$557$	−14.8342			−0.628547			−0.314273	−	0.949333i	$-0.601761\pi$
$557$	−14.8342			−0.628547			−0.314273	+	0.949333i	$0.601761\pi$
$558$	−0.885929	−	5.49683i	−0.0375044	−	0.232699i
$559$	−12.8334			−0.542795
$560$	0.914616	−	2.81490i	0.0386496	−	0.118951i
$561$	−6.89531	−	1.46564i	−0.291120	−	0.0618795i
$562$	10.2781	+	7.46749i	0.433556	+	0.314997i
$563$	−0.742707	−	1.28641i	−0.0313014	−	0.0542156i	0.849950	−	0.526863i	$-0.176632\pi$
$563$	−0.742707	−	1.28641i	−0.0313014	−	0.0542156i	−0.881252	+	0.472647i	$0.843298\pi$
$564$	3.32218	−	5.75419i	0.139889	−	0.242295i
$565$	−1.97273	+	0.878317i	−0.0829935	+	0.0369511i
$566$	9.68112	−	7.03375i	0.406928	−	0.295650i
$567$	−2.70387	−	1.20384i	−0.113552	−	0.0505566i
$568$	9.51052	−	2.02152i	0.399053	−	0.0848212i
$569$	−3.92520	+	37.3458i	−0.164553	+	1.56562i	0.531144	+	0.847282i	$0.321762\pi$
$569$	−3.92520	+	37.3458i	−0.164553	+	1.56562i	−0.695697	+	0.718336i	$0.744904\pi$
$570$	1.65932	+	1.84287i	0.0695015	+	0.0771892i
$571$	20.6621	−	22.9476i	0.864682	−	0.960326i	−0.134852	−	0.990866i	$-0.543056\pi$
$571$	20.6621	−	22.9476i	0.864682	−	0.960326i	0.999534	+	0.0305396i	$0.00972257\pi$
$572$	0.320885	+	3.05302i	0.0134169	+	0.127653i
$573$	−7.44061	−	22.8998i	−0.310836	−	0.956654i
$574$	−3.62033	−	11.1422i	−0.151109	−	0.465067i
$575$	0.232651	+	2.21353i	0.00970221	+	0.0923104i
$576$	0.669131	−	0.743145i	0.0278804	−	0.0309644i
$577$	−2.63440	−	2.92579i	−0.109671	−	0.121802i	0.685810	−	0.727781i	$-0.259448\pi$
$577$	−2.63440	−	2.92579i	−0.109671	−	0.121802i	−0.795481	+	0.605979i	$0.792782\pi$
$578$	−4.94541	+	47.0525i	−0.205702	+	1.95712i
$579$	−1.22178	+	0.259696i	−0.0507753	+	0.0107926i
$580$	−2.59530	−	1.15550i	−0.107764	−	0.0479795i
$581$	−40.1941	+	29.2027i	−1.66753	+	1.21153i
$582$	6.13540	−	2.73166i	0.254321	−	0.113231i
$583$	4.36124	−	7.55389i	0.180624	−	0.312850i
$584$	7.62446	+	13.2059i	0.315502	+	0.546466i
$585$	−2.82533	−	2.05272i	−0.116813	−	0.0848695i
$586$	−12.3954	−	2.63472i	−0.512048	−	0.108839i
$587$	8.50043	−	26.1616i	0.350850	−	1.07981i	−0.607526	−	0.794299i	$-0.707838\pi$
$587$	8.50043	−	26.1616i	0.350850	−	1.07981i	0.958377	−	0.285507i	$-0.0921619\pi$
$588$	−1.76018			−0.0725885
$589$	13.7861	−	0.760067i	0.568047	−	0.0313180i
$590$	3.82541			0.157490
$591$	−2.25116	+	6.92835i	−0.0926002	+	0.284994i
$592$	−4.86311	−	1.03368i	−0.199872	−	0.0424842i
$593$	−6.48030	−	4.70821i	−0.266114	−	0.193343i	0.446724	−	0.894672i	$-0.352591\pi$
$593$	−6.48030	−	4.70821i	−0.266114	−	0.193343i	−0.712838	+	0.701329i	$0.752591\pi$
$594$	0.439516	+	0.761263i	0.0180335	+	0.0312350i
$595$	11.8678	−	20.5557i	0.486534	−	0.842701i
$596$	−16.5857	+	7.38442i	−0.679376	+	0.302478i
$597$	19.1577	−	13.9189i	0.784073	−	0.569663i
$598$	7.10086	+	3.16151i	0.290376	+	0.129284i
$599$	−44.3982	+	9.43714i	−1.81406	+	0.385591i	−0.984859	−	0.173356i	$-0.944539\pi$
$599$	−44.3982	+	9.43714i	−1.81406	+	0.385591i	−0.829203	+	0.558947i	$0.811206\pi$
$600$	0.104528	−	0.994522i	0.00426736	−	0.0406012i
$601$	−10.2423	−	11.3752i	−0.417792	−	0.464005i	0.497106	−	0.867690i	$-0.334396\pi$
$601$	−10.2423	−	11.3752i	−0.417792	−	0.464005i	−0.914898	+	0.403685i	$0.867729\pi$
$602$	−7.27776	+	8.08278i	−0.296619	+	0.329429i
$603$	0.803756	+	7.64723i	0.0327315	+	0.311419i
$604$	−6.24365	−	19.2160i	−0.254050	−	0.781887i
$605$	3.16041	+	9.72674i	0.128489	+	0.395448i
$606$	0.313318	+	2.98102i	0.0127277	+	0.121096i
$607$	10.1807	−	11.3068i	0.413222	−	0.458929i	−0.500220	−	0.865898i	$-0.666748\pi$
$607$	10.1807	−	11.3068i	0.413222	−	0.458929i	0.913442	+	0.406969i	$0.133414\pi$
$608$	1.65932	+	1.84287i	0.0672945	+	0.0747381i
$609$	−0.878917	+	8.36233i	−0.0356155	+	0.338859i
$610$	3.82012	−	0.811991i	0.154672	−	0.0328765i
$611$	−21.1980	−	9.43795i	−0.857579	−	0.381819i
$612$	6.48787	−	4.71372i	0.262257	−	0.190541i
$613$	−18.9062	+	8.41756i	−0.763612	+	0.339982i	−0.751316	−	0.659942i	$-0.770581\pi$
$613$	−18.9062	+	8.41756i	−0.763612	+	0.339982i	−0.0122961	+	0.999924i	$0.503914\pi$
$614$	4.60642	−	7.97856i	0.185900	−	0.321988i
$615$	−1.97915	−	3.42799i	−0.0798071	−	0.138230i
$616$	2.10484	+	1.52925i	0.0848063	+	0.0616154i
$617$	44.9540	+	9.55527i	1.80978	+	0.384681i	0.983836	−	0.179072i	$-0.0573096\pi$
$617$	44.9540	+	9.55527i	1.80978	+	0.384681i	0.825944	+	0.563753i	$0.190643\pi$
$618$	−0.725935	+	2.23420i	−0.0292014	+	0.0898726i
$619$	4.82990			0.194130			0.0970650	−	0.995278i	$-0.469055\pi$
$619$	4.82990			0.194130			0.0970650	+	0.995278i	$0.469055\pi$
$620$	−3.94769	−	3.92629i	−0.158543	−	0.157684i
$621$	2.22572			0.0893150
$622$	9.65366	−	29.7109i	0.387076	−	1.19130i
$623$	42.2945	+	8.98997i	1.69449	+	0.360175i
$624$	−2.82533	−	2.05272i	−0.113104	−	0.0821745i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	3.83090	−	6.63532i	0.153114	−	0.265201i
$627$	−1.99138	+	0.886621i	−0.0795282	+	0.0354082i
$628$	−3.82742	+	2.78078i	−0.152731	+	0.110965i
$629$	−36.4237	−	16.2169i	−1.45231	−	0.646610i
$630$	−2.89508	+	0.615369i	−0.115343	+	0.0245169i
$631$	4.25756	−	40.5079i	0.169491	−	1.61260i	−0.497455	−	0.867490i	$-0.665732\pi$
$631$	4.25756	−	40.5079i	0.169491	−	1.61260i	0.666946	−	0.745106i	$-0.267601\pi$
$632$	−5.95434	−	6.61296i	−0.236851	−	0.263049i
$633$	−7.64361	+	8.48909i	−0.303806	+	0.337411i
$634$	2.10916	+	20.0673i	0.0837653	+	0.796974i
$635$	5.04620	+	15.5306i	0.200252	+	0.616314i
$636$	3.06632	+	9.43717i	0.121588	+	0.374208i
$637$	0.642542	+	6.11338i	0.0254585	+	0.242221i
$638$	1.67098	−	1.85581i	0.0661548	−	0.0734724i
$639$	−6.50595	−	7.22559i	−0.257371	−	0.285840i
$640$	0.104528	−	0.994522i	0.00413185	−	0.0393119i
$641$	−27.5011	+	5.84553i	−1.08623	+	0.230885i	−0.716031	−	0.698069i	$-0.754043\pi$
$641$	−27.5011	+	5.84553i	−1.08623	+	0.230885i	−0.370196	+	0.928953i	$0.620710\pi$
$642$	−6.35517	−	2.82951i	−0.250819	−	0.111672i
$643$	16.9577	−	12.3205i	0.668745	−	0.485871i	−0.200860	−	0.979620i	$-0.564374\pi$
$643$	16.9577	−	12.3205i	0.668745	−	0.485871i	0.869605	+	0.493748i	$0.164374\pi$
$644$	6.01806	−	2.67941i	0.237145	−	0.105584i
$645$	−1.83739	+	3.18245i	−0.0723470	+	0.125309i
$646$	9.94341	+	17.2225i	0.391218	+	0.677610i
$647$	−32.2298	−	23.4163i	−1.26708	−	0.920590i	−0.268001	−	0.963419i	$-0.586363\pi$
$647$	−32.2298	−	23.4163i	−1.26708	−	0.920590i	−0.999082	+	0.0428291i	$0.986363\pi$
$648$	−0.978148	−	0.207912i	−0.0384253	−	0.00816754i
$649$	−1.03912	+	3.19808i	−0.0407889	+	0.125535i
$650$	−3.49229			−0.136979
$651$	−7.44150	+	14.7034i	−0.291655	+	0.576271i
$652$	−2.50964			−0.0982851
$653$	−12.3217	+	37.9224i	−0.482187	+	1.48402i	0.353827	+	0.935311i	$0.384880\pi$
$653$	−12.3217	+	37.9224i	−0.482187	+	1.48402i	−0.836014	+	0.548708i	$0.815120\pi$
$654$	−6.56082	−	1.39455i	−0.256549	−	0.0545311i
$655$	−11.8444	−	8.60544i	−0.462798	−	0.336242i
$656$	−1.97915	−	3.42799i	−0.0772729	−	0.133841i
$657$	7.62446	−	13.2059i	0.297458	−	0.515213i
$658$	−17.9655	+	7.99877i	−0.700369	+	0.311825i
$659$	10.0842	−	7.32660i	0.392825	−	0.285404i	−0.373787	−	0.927514i	$-0.621941\pi$
$659$	10.0842	−	7.32660i	0.392825	−	0.285404i	0.766612	+	0.642111i	$0.221941\pi$
$660$	0.803035	+	0.357534i	0.0312581	+	0.0139170i
$661$	−20.3432	+	4.32407i	−0.791257	+	0.168187i	−0.585775	−	0.810474i	$-0.699210\pi$
$661$	−20.3432	+	4.32407i	−0.791257	+	0.168187i	−0.205482	+	0.978661i	$0.565876\pi$
$662$	1.43298	−	13.6339i	0.0556942	−	0.529895i
$663$	−18.7399	−	20.8127i	−0.727796	−	0.808300i
$664$	−11.2321	+	12.4745i	−0.435888	+	0.484103i
$665$	−0.767205	−	7.29947i	−0.0297509	−	0.283061i
$666$	1.53636	+	4.72842i	0.0595326	+	0.183222i
$667$	−1.95393	−	6.01358i	−0.0756565	−	0.232847i
$668$	1.11385	+	10.5976i	0.0430963	+	0.410034i
$669$	−8.26599	+	9.18031i	−0.319582	+	0.354931i
$670$	5.14518	+	5.71430i	0.198776	+	0.220763i
$671$	−0.358848	+	3.41422i	−0.0138532	+	0.131804i
$672$	−2.89508	+	0.615369i	−0.111680	+	0.0237384i
$673$	−22.8823	−	10.1879i	−0.882048	−	0.392713i	−0.0848232	−	0.996396i	$-0.527033\pi$
$673$	−22.8823	−	10.1879i	−0.882048	−	0.392713i	−0.797224	+	0.603683i	$0.793699\pi$
$674$	−23.7342	+	17.2439i	−0.914206	+	0.664210i
$675$	−0.913545	+	0.406737i	−0.0351624	+	0.0156553i
$676$	0.401941	−	0.696182i	0.0154593	−	0.0267762i
$677$	7.93110	+	13.7371i	0.304817	+	0.527958i	0.977221	−	0.212226i	$-0.0680714\pi$
$677$	7.93110	+	13.7371i	0.304817	+	0.527958i	−0.672404	+	0.740185i	$0.734738\pi$
$678$	1.74701	+	1.26928i	0.0670935	+	0.0487463i
$679$	−19.4435	−	4.13284i	−0.746172	−	0.158604i
$680$	2.47815	−	7.62695i	0.0950326	−	0.292480i
$681$	−12.7053			−0.486870
$682$	4.35475	−	2.23378i	0.166752	−	0.0855358i
$683$	−5.88130			−0.225042			−0.112521	−	0.993649i	$-0.535892\pi$
$683$	−5.88130			−0.225042			−0.112521	+	0.993649i	$0.535892\pi$
$684$	0.766307	−	2.35845i	0.0293005	−	0.0901776i
$685$	−9.85725	−	2.09522i	−0.376626	−	0.0800544i
$686$	−12.5467	−	9.11574i	−0.479037	−	0.348040i
$687$	−4.64974	−	8.05358i	−0.177399	−	0.307263i
$688$	−1.83739	+	3.18245i	−0.0700497	+	0.121330i
$689$	31.6575	−	14.0948i	1.20605	−	0.536970i
$690$	1.80064	−	1.30824i	0.0685493	−	0.0498040i
$691$	26.2828	+	11.7019i	0.999846	+	0.445160i	0.840353	−	0.542039i	$-0.182347\pi$
$691$	26.2828	+	11.7019i	0.999846	+	0.445160i	0.159493	+	0.987199i	$0.449014\pi$
$692$	−12.2185	+	2.59713i	−0.464479	+	0.0987280i
$693$	0.271954	−	2.58747i	0.0103307	−	0.0982898i
$694$	6.18441	+	6.86848i	0.234757	+	0.260724i
$695$	−7.10266	+	7.88830i	−0.269419	+	0.299220i
$696$	0.296955	+	2.82534i	0.0112561	+	0.107094i
$697$	−9.80926	−	30.1898i	−0.371552	−	1.14352i
$698$	0.175105	+	0.538918i	0.00662783	+	0.0203983i
$699$	0.437848	+	4.16585i	0.0165609	+	0.157567i
$700$	−1.98047	+	2.19953i	−0.0748546	+	0.0831344i
$701$	23.9082	+	26.5527i	0.903000	+	1.00288i	0.999971	+	0.00759590i	$0.00241787\pi$
$701$	23.9082	+	26.5527i	0.903000	+	1.00288i	−0.0969712	+	0.995287i	$0.530915\pi$
$702$	−0.365044	+	3.47316i	−0.0137777	+	0.131086i
$703$	−12.0596	+	2.56335i	−0.454838	+	0.0966787i
$704$	0.803035	+	0.357534i	0.0302655	+	0.0134751i
$705$	−5.37541	+	3.90546i	−0.202449	+	0.147088i
$706$	24.9164	−	11.0935i	0.937740	−	0.417509i
$707$	4.43586	−	7.68313i	0.166828	−	0.288954i
$708$	−1.91271	−	3.31290i	−0.0718839	−	0.124506i
$709$	−16.4340	−	11.9400i	−0.617190	−	0.448415i	0.234749	−	0.972056i	$-0.424573\pi$
$709$	−16.4340	−	11.9400i	−0.617190	−	0.448415i	−0.851939	+	0.523641i	$0.824573\pi$
$710$	−9.51052	−	2.02152i	−0.356923	−	0.0758664i
$711$	−2.74982	+	8.46309i	−0.103126	+	0.317390i
$712$	14.6091			0.547498
$713$	0.614934	−	12.3770i	0.0230294	−	0.463523i
$714$	−23.7357			−0.888285
$715$	0.948631	−	2.91959i	0.0354768	−	0.109186i
$716$	4.03005	+	0.856615i	0.150610	+	0.0320132i
$717$	−1.94179	−	1.41079i	−0.0725175	−	0.0526871i
$718$	−2.92548	−	5.06708i	−0.109178	−	0.189102i
$719$	−10.6201	+	18.3945i	−0.396062	+	0.686000i	−0.993236	−	0.116112i	$-0.962957\pi$
$719$	−10.6201	+	18.3945i	−0.396062	+	0.686000i	0.597174	+	0.802112i	$0.296290\pi$
$720$	−0.913545	+	0.406737i	−0.0340458	+	0.0151582i
$721$	5.62509	−	4.08687i	0.209489	−	0.152203i
$722$	−11.7395	−	5.22676i	−0.436899	−	0.194520i
$723$	14.8884	−	3.16462i	0.553705	−	0.117694i
$724$	−1.59805	+	15.2044i	−0.0593909	+	0.565067i
$725$	1.90094	+	2.11120i	0.0705990	+	0.0784082i
$726$	6.84340	−	7.60037i	0.253982	−	0.282076i
$727$	1.03045	+	9.80412i	0.0382174	+	0.363615i	0.996871	+	0.0790404i	$0.0251856\pi$
$727$	1.03045	+	9.80412i	0.0382174	+	0.363615i	−0.958654	+	0.284574i	$0.908148\pi$
$728$	3.19411	+	9.83045i	0.118382	+	0.364341i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−1.59395	−	15.1654i	−0.0589946	−	0.561296i
$731$	−19.7191	+	21.9002i	−0.729336	+	0.810010i
$732$	−2.61326	−	2.90232i	−0.0965890	−	0.107273i
$733$	0.378284	−	3.59913i	0.0139722	−	0.132937i	−0.985312	−	0.170763i	$-0.945377\pi$
$733$	0.378284	−	3.59913i	0.0139722	−	0.132937i	0.999284	+	0.0378263i	$0.0120434\pi$
$734$	−12.4146	+	2.63881i	−0.458232	+	0.0974001i
$735$	1.60800	+	0.715928i	0.0593120	+	0.0264074i
$736$	1.80064	−	1.30824i	0.0663726	−	0.0482225i
$737$	−6.17482	+	2.74921i	−0.227452	+	0.101268i
$738$	−1.97915	+	3.42799i	−0.0728535	+	0.126186i
$739$	1.20425	+	2.08583i	0.0442991	+	0.0767283i	0.887325	−	0.461145i	$-0.152561\pi$
$739$	1.20425	+	2.08583i	0.0442991	+	0.0767283i	−0.843026	+	0.537873i	$0.819228\pi$
$740$	4.02223	+	2.92232i	0.147860	+	0.107427i
$741$	−8.47102	−	1.80057i	−0.311191	−	0.0661456i
$742$	9.07558	−	27.9318i	0.333175	−	1.02541i
$743$	−43.0431			−1.57910			−0.789549	−	0.613688i	$-0.789685\pi$
$743$	−43.0431			−1.57910			−0.789549	+	0.613688i	$0.789685\pi$
$744$	−1.42643	+	5.38194i	−0.0522953	+	0.197312i
$745$	18.1553			0.665158
$746$	6.84654	−	21.0715i	0.250670	−	0.771482i
$747$	16.4192	+	3.49001i	0.600748	+	0.127693i
$748$	5.70304	+	4.14350i	0.208524	+	0.151502i
$749$	10.2949	+	17.8314i	0.376169	+	0.651544i
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	25.1087	−	11.1791i	0.916231	−	0.407932i	0.106217	−	0.994343i	$-0.466126\pi$
$751$	25.1087	−	11.1791i	0.916231	−	0.407932i	0.810014	+	0.586411i	$0.199459\pi$
$752$	−5.37541	+	3.90546i	−0.196021	+	0.142417i
$753$	−2.46731	−	1.09852i	−0.0899138	−	0.0400322i
$754$	9.70447	−	2.06275i	0.353416	−	0.0751209i
$755$	−2.11198	+	20.0942i	−0.0768629	+	0.731302i
$756$	1.98047	+	2.19953i	0.0720288	+	0.0799961i
$757$	−20.6794	+	22.9668i	−0.751607	+	0.834744i	−0.990673	−	0.136259i	$-0.956492\pi$
$757$	−20.6794	+	22.9668i	−0.751607	+	0.834744i	0.239067	+	0.971003i	$0.423159\pi$
$758$	−3.53552	−	33.6382i	−0.128416	−	1.22179i
$759$	0.604584	+	1.86072i	0.0219450	+	0.0675398i
$760$	−0.766307	−	2.35845i	−0.0277969	−	0.0855500i
$761$	−3.48875	−	33.1933i	−0.126467	−	1.20326i	−0.855141	−	0.518395i	$-0.826530\pi$
$761$	−3.48875	−	33.1933i	−0.126467	−	1.20326i	0.728674	−	0.684861i	$-0.240137\pi$
$762$	10.9268	−	12.1354i	0.395836	−	0.439621i
$763$	13.2838	+	14.7531i	0.480905	+	0.534099i
$764$	−2.51687	+	23.9464i	−0.0910571	+	0.866351i
$765$	−7.84421	+	1.66734i	−0.283608	+	0.0602827i
$766$	−15.5308	−	6.91475i	−0.561150	−	0.249840i
$767$	−10.8080	+	7.85249i	−0.390255	+	0.283537i
$768$	−0.913545	+	0.406737i	−0.0329647	+	0.0146768i
$769$	4.56641	−	7.90925i	0.164669	−	0.285215i	−0.771869	−	0.635782i	$-0.780678\pi$
$769$	4.56641	−	7.90925i	0.164669	−	0.285215i	0.936538	+	0.350567i	$0.114011\pi$
$770$	−1.30086	−	2.25316i	−0.0468798	−	0.0811981i
$771$	16.1781	+	11.7541i	0.582642	+	0.423314i
$772$	1.22178	+	0.259696i	0.0439727	+	0.00934668i
$773$	1.13355	−	3.48871i	0.0407709	−	0.125480i	−0.928599	−	0.371084i	$-0.878986\pi$
$773$	1.13355	−	3.48871i	0.0407709	−	0.125480i	0.969370	+	0.245604i	$0.0789862\pi$
$774$	3.67477			0.132087
$775$	2.00942	+	5.19252i	0.0721807	+	0.186521i
$776$	−6.71603			−0.241092
$777$	4.54724	−	13.9950i	0.163131	−	0.502067i
$778$	−30.6802	−	6.52127i	−1.09994	−	0.233799i
$779$	−7.94122	−	5.76963i	−0.284524	−	0.206718i
$780$	1.74615	+	3.02442i	0.0625221	+	0.108291i
$781$	4.27341	−	7.40176i	0.152915	−	0.264856i
$782$	16.3059	−	7.25986i	0.583098	−	0.259612i
$783$	2.29834	−	1.66984i	0.0821360	−	0.0596753i
$784$	1.60800	+	0.715928i	0.0574286	+	0.0255689i
$785$	4.62756	−	0.983619i	0.165165	−	0.0351069i
$786$	−1.53034	+	14.5602i	−0.0545855	+	0.519347i
$787$	−36.0275	−	40.0126i	−1.28424	−	1.42630i	−0.851130	−	0.524955i	$-0.824082\pi$
$787$	−36.0275	−	40.0126i	−1.28424	−	1.42630i	−0.433112	−	0.901340i	$-0.642585\pi$
$788$	4.87455	−	5.41373i	0.173649	−	0.192856i
$789$	0.950082	+	9.03943i	0.0338238	+	0.321812i
$790$	2.74982	+	8.46309i	0.0978343	+	0.301103i
$791$	−1.97504	−	6.07856i	−0.0702245	−	0.216129i
$792$	−0.0918838	−	0.874216i	−0.00326495	−	0.0310639i
$793$	−9.12628	+	10.1358i	−0.324084	+	0.359931i
$794$	15.1635	+	16.8408i	0.538134	+	0.597658i
$795$	1.03722	−	9.86847i	0.0367863	−	0.349999i
$796$	−23.1628	+	4.92340i	−0.820983	+	0.174505i
$797$	−24.0552	−	10.7101i	−0.852079	−	0.379370i	−0.0662418	−	0.997804i	$-0.521101\pi$
$797$	−24.0552	−	10.7101i	−0.852079	−	0.379370i	−0.785837	+	0.618434i	$0.787768\pi$
$798$	−5.93792	+	4.31415i	−0.210200	+	0.152719i
$799$	−48.6775	+	21.6726i	−1.72209	+	0.766723i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−7.30454	−	12.6518i	−0.258093	−	0.447030i
$802$	−19.2508	−	13.9865i	−0.679771	−	0.493882i
$803$	13.1114	+	2.78690i	0.462690	+	0.0983477i
$804$	2.37614	−	7.31301i	0.0838000	−	0.257910i
$805$	−6.58759			−0.232182
$806$	19.2131	+	2.98956i	0.676752	+	0.105303i
$807$	15.1317			0.532662
$808$	0.926261	−	2.85074i	0.0325858	−	0.100289i
$809$	−6.44630	−	1.37020i	−0.226640	−	0.0481738i	0.0931918	−	0.995648i	$-0.470293\pi$
$809$	−6.44630	−	1.37020i	−0.226640	−	0.0481738i	−0.319832	+	0.947474i	$0.603626\pi$
$810$	0.809017	+	0.587785i	0.0284260	+	0.0206527i
$811$	15.7635	+	27.3032i	0.553531	+	0.958743i	0.998016	+	0.0629573i	$0.0200532\pi$
$811$	15.7635	+	27.3032i	0.553531	+	0.958743i	−0.444486	+	0.895786i	$0.646613\pi$
$812$	4.20420	−	7.28189i	0.147538	−	0.255544i
$813$	4.47654	−	1.99308i	0.156999	−	0.0699005i
$814$	−3.53567	+	2.56881i	−0.123925	+	0.0900368i
$815$	2.29267	+	1.02076i	0.0803087	+	0.0357557i
$816$	−7.84421	+	1.66734i	−0.274602	+	0.0583685i
$817$	−0.952545	+	9.06286i	−0.0333253	+	0.317069i
$818$	−2.49765	−	2.77392i	−0.0873283	−	0.0969879i
$819$	6.91637	−	7.68141i	0.241677	−	0.268410i
$820$	0.413755	+	3.93662i	0.0144490	+	0.137473i
$821$	−11.4753	−	35.3174i	−0.400491	−	1.23259i	−0.924602	−	0.380935i	$-0.875602\pi$
$821$	−11.4753	−	35.3174i	−0.400491	−	1.23259i	0.524110	−	0.851650i	$-0.324398\pi$
$822$	3.11411	+	9.58424i	0.108617	+	0.334289i
$823$	−3.60985	−	34.3455i	−0.125832	−	1.19721i	−0.857112	−	0.515130i	$-0.827744\pi$
$823$	−3.60985	−	34.3455i	−0.125832	−	1.19721i	0.731280	−	0.682077i	$-0.238923\pi$
$824$	1.57190	−	1.74578i	0.0547599	−	0.0608170i
$825$	−0.588187	−	0.653248i	−0.0204780	−	0.0227432i
$826$	−1.18350	+	11.2603i	−0.0411793	+	0.391795i
$827$	47.5200	−	10.1007i	1.65243	−	0.351235i	0.714925	−	0.699201i	$-0.246461\pi$
$827$	47.5200	−	10.1007i	1.65243	−	0.351235i	0.937507	+	0.347965i	$0.113127\pi$
$828$	−2.03329	−	0.905281i	−0.0706619	−	0.0314607i
$829$	−26.3961	+	19.1779i	−0.916773	+	0.666075i	−0.942719	−	0.333589i	$-0.891740\pi$
$829$	−26.3961	+	19.1779i	−0.916773	+	0.666075i	0.0259456	+	0.999663i	$0.491740\pi$
$830$	15.3348	−	6.82750i	0.532279	−	0.236986i
$831$	−13.7924	+	23.8891i	−0.478452	+	0.828704i
$832$	1.74615	+	3.02442i	0.0605368	+	0.104853i
$833$	11.4198	+	8.29698i	0.395673	+	0.287473i
$834$	10.3828	+	2.20693i	0.359527	+	0.0764198i
$835$	3.29288	−	10.1344i	0.113955	−	0.350717i
$836$	2.17984			0.0753914
$837$	5.37411	−	1.45565i	0.185756	−	0.0503147i
$838$	−0.519809			−0.0179565
$839$	6.24228	−	19.2118i	0.215507	−	0.663264i	−0.783610	−	0.621253i	$-0.786624\pi$
$839$	6.24228	−	19.2118i	0.215507	−	0.663264i	0.999117	−	0.0420102i	$-0.0133762\pi$
$840$	2.89508	+	0.615369i	0.0998898	+	0.0212322i
$841$	16.9321	+	12.3019i	0.583866	+	0.424204i
$842$	−5.95048	−	10.3065i	−0.205067	−	0.355186i
$843$	−6.35222	+	11.0024i	−0.218782	+	0.378942i
$844$	10.4356	−	4.64623i	0.359209	−	0.159930i
$845$	−0.650354	+	0.472510i	−0.0223729	+	0.0162548i
$846$	6.06993	+	2.70251i	0.208689	+	0.0929141i
$847$	−29.6089	+	6.29356i	−1.01737	+	0.216249i
$848$	1.03722	−	9.86847i	0.0356182	−	0.338885i
$849$	8.00717	+	8.89286i	0.274805	+	0.305202i
$850$	−5.36606	+	5.95962i	−0.184054	+	0.204413i
$851$	1.15668	+	11.0051i	0.0396506	+	0.377250i
$852$	3.00457	+	9.24711i	0.102935	+	0.316801i
$853$	10.3620	+	31.8908i	0.354787	+	1.09192i	0.956133	+	0.292933i	$0.0946312\pi$
$853$	10.3620	+	31.8908i	0.354787	+	1.09192i	−0.601346	+	0.798988i	$0.705369\pi$
$854$	1.20827	+	11.4959i	0.0413461	+	0.393382i
$855$	−1.65932	+	1.84287i	−0.0567477	+	0.0630247i
$856$	4.65488	+	5.16976i	0.159100	+	0.176699i
$857$	−2.39225	+	22.7607i	−0.0817177	+	0.777492i	0.874537	+	0.484958i	$0.161165\pi$
$857$	−2.39225	+	22.7607i	−0.0817177	+	0.777492i	−0.956255	+	0.292534i	$0.905502\pi$
$858$	−3.00275	+	0.638255i	−0.102512	+	0.0217897i
$859$	−19.7368	−	8.78737i	−0.673410	−	0.299821i	0.0413977	−	0.999143i	$-0.486819\pi$
$859$	−19.7368	−	8.78737i	−0.673410	−	0.299821i	−0.714807	+	0.699321i	$0.753486\pi$
$860$	2.97295	−	2.15998i	0.101377	−	0.0736546i
$861$	10.7028	−	4.76517i	0.364749	−	0.162397i
$862$	7.81005	−	13.5274i	0.266011	−	0.460745i
$863$	−16.5238	−	28.6201i	−0.562478	−	0.974240i	−0.997279	−	0.0737136i	$-0.976515\pi$
$863$	−16.5238	−	28.6201i	−0.562478	−	0.974240i	0.434802	−	0.900526i	$-0.356818\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	12.2185	+	2.59713i	0.415442	+	0.0883050i
$866$	7.96265	−	24.5065i	0.270582	−	0.832765i
$867$	−47.3116			−1.60679
$868$	12.7786	−	10.4055i	0.433732	−	0.353185i
$869$	−7.82216			−0.265349
$870$	0.877888	−	2.70186i	0.0297632	−	0.0916017i
$871$	−26.2667	−	5.58315i	−0.890012	−	0.189178i
$872$	5.42640	+	3.94251i	0.183761	+	0.133510i
$873$	3.35802	+	5.81626i	0.113652	+	0.196850i
$874$	2.75969	−	4.77993i	0.0933480	−	0.161683i
$875$	2.70387	−	1.20384i	0.0914077	−	0.0406973i
$876$	−12.3366	+	8.96309i	−0.416816	+	0.302835i
$877$	35.5570	+	15.8310i	1.20067	+	0.534574i	0.906919	−	0.421306i	$-0.138428\pi$
$877$	35.5570	+	15.8310i	1.20067	+	0.534574i	0.293755	+	0.955881i	$0.405095\pi$
$878$	11.9836	−	2.54719i	0.404426	−	0.0859634i
$879$	1.32462	−	12.6029i	0.0446782	−	0.425084i
$880$	−0.588187	−	0.653248i	−0.0198278	−	0.0220210i
$881$	−24.5451	+	27.2601i	−0.826946	+	0.918416i	−0.997761	−	0.0668870i	$-0.978693\pi$
$881$	−24.5451	+	27.2601i	−0.826946	+	0.918416i	0.170815	+	0.985303i	$0.445360\pi$
$882$	−0.183989	−	1.75053i	−0.00619522	−	0.0589436i
$883$	4.02753	+	12.3955i	0.135537	+	0.417141i	0.995673	−	0.0929242i	$-0.0296214\pi$
$883$	4.02753	+	12.3955i	0.135537	+	0.417141i	−0.860136	+	0.510065i	$0.829621\pi$
$884$	8.65442	+	26.6356i	0.291080	+	0.895851i
$885$	0.399864	+	3.80445i	0.0134413	+	0.127885i
$886$	17.3300	−	19.2470i	0.582214	−	0.646614i
$887$	−24.8907	−	27.6439i	−0.835749	−	0.928193i	0.162538	−	0.986702i	$-0.448032\pi$
$887$	−24.8907	−	27.6439i	−0.835749	−	0.928193i	−0.998287	+	0.0585094i	$0.981365\pi$
$888$	0.519689	−	4.94451i	0.0174396	−	0.165927i
$889$	−47.2763	+	10.0489i	−1.58559	+	0.337029i
$890$	−13.3461	−	5.94205i	−0.447361	−	0.199178i
$891$	−0.711151	+	0.516682i	−0.0238245	+	0.0173095i
$892$	11.2853	−	5.02455i	0.377861	−	0.168234i
$893$	−8.23842	+	14.2694i	−0.275688	+	0.477506i
$894$	−9.07764	−	15.7229i	−0.303602	−	0.525854i
$895$	−3.33322	−	2.42173i	−0.111417	−	0.0809494i
$896$	2.89508	+	0.615369i	0.0967179	+	0.0205580i
$897$	−2.40195	+	7.39243i	−0.0801987	+	0.246826i
$898$	−8.52859			−0.284603
$899$	−8.65084	−	13.2422i	−0.288522	−	0.441652i
$900$	1.00000			0.0333333
$901$	24.5902	−	75.6810i	0.819220	−	2.52130i
$902$	−3.40344	−	0.723423i	−0.113322	−	0.0240873i
$903$	−8.79923	−	6.39301i	−0.292820	−	0.212746i
$904$	−1.07971	−	1.87012i	−0.0359107	−	0.0621991i
$905$	7.64407	−	13.2399i	0.254097	−	0.440110i
$906$	18.4581	−	8.21806i	0.613228	−	0.273027i
$907$	−5.02139	+	3.64826i	−0.166733	+	0.121138i	−0.668023	−	0.744141i	$-0.732859\pi$
$907$	−5.02139	+	3.64826i	−0.166733	+	0.121138i	0.501290	+	0.865279i	$0.332859\pi$
$908$	11.6069	+	5.16773i	0.385189	+	0.171497i
$909$	−2.93194	+	0.623204i	−0.0972464	+	0.0206704i
$910$	1.08044	−	10.2797i	0.0358163	−	0.340770i
$911$	7.51196	+	8.34288i	0.248882	+	0.276412i	0.854622	−	0.519251i	$-0.173789\pi$
$911$	7.51196	+	8.34288i	0.248882	+	0.276412i	−0.605739	+	0.795663i	$0.707122\pi$
$912$	−1.65932	+	1.84287i	−0.0549457	+	0.0610234i
$913$	1.54236	+	14.6746i	0.0510448	+	0.485659i
$914$	−0.436881	−	1.34458i	−0.0144507	−	0.0444748i
$915$	1.20685	+	3.71431i	0.0398973	+	0.122791i
$916$	0.972060	+	9.24854i	0.0321178	+	0.305580i
$917$	28.9949	−	32.2021i	0.957496	−	1.06341i
$918$	5.36606	+	5.95962i	0.177106	+	0.196697i
$919$	−1.52036	+	14.4653i	−0.0501521	+	0.477166i	0.940404	+	0.340059i	$0.110447\pi$
$919$	−1.52036	+	14.4653i	−0.0501521	+	0.477166i	−0.990556	+	0.137107i	$0.956220\pi$
$920$	−2.17708	+	0.462753i	−0.0717762	+	0.0152565i
$921$	8.41635	+	3.74720i	0.277328	+	0.123474i
$922$	22.9563	−	16.6787i	0.756026	−	0.549285i
$923$	31.0199	−	13.8110i	1.02103	−	0.454593i
$924$	−1.30086	+	2.25316i	−0.0427952	+	0.0741234i
$925$	−2.48588	−	4.30566i	−0.0817351	−	0.141569i
$926$	20.2967	+	14.7464i	0.666992	+	0.484598i
$927$	−2.29784	−	0.488421i	−0.0754710	−	0.0160418i
$928$	0.877888	−	2.70186i	0.0288181	−	0.0886929i
$929$	14.6619			0.481041			0.240521	−	0.970644i	$-0.422682\pi$
$929$	14.6619			0.481041			0.240521	+	0.970644i	$0.422682\pi$
$930$	3.49214	−	4.33647i	0.114512	−	0.142198i
$931$	4.36493			0.143055
$932$	1.29441	−	3.98378i	0.0423997	−	0.130493i
$933$	30.5572	+	6.49514i	1.00040	+	0.212641i
$934$	−0.429708	−	0.312201i	−0.0140605	−	0.0102155i
$935$	−3.52468	−	6.10492i	−0.115269	−	0.199652i
$936$	1.74615	−	3.02442i	0.0570746	−	0.0988561i
$937$	19.7067	−	8.77397i	0.643789	−	0.286633i	−0.0587566	−	0.998272i	$-0.518714\pi$
$937$	19.7067	−	8.77397i	0.643789	−	0.286633i	0.702545	+	0.711639i	$0.252047\pi$
$938$	−18.4121	+	13.3772i	−0.601177	+	0.436781i
$939$	6.99941	+	3.11634i	0.228417	+	0.101698i
$940$	6.49917	−	1.38144i	0.211980	−	0.0450577i
$941$	2.99455	−	28.4912i	0.0976194	−	0.928787i	−0.830629	−	0.556826i	$-0.812019\pi$
$941$	2.99455	−	28.4912i	0.0976194	−	0.928787i	0.928248	−	0.371961i	$-0.121314\pi$
$942$	−3.16562	−	3.51578i	−0.103142	−	0.114550i
$943$	−5.89508	+	6.54715i	−0.191970	+	0.213205i
$944$	0.399864	+	3.80445i	0.0130145	+	0.123824i
$945$	−0.914616	−	2.81490i	−0.0297525	−	0.0915687i
$946$	0.998199	+	3.07214i	0.0324543	+	0.0998839i
$947$	−0.332191	−	3.16059i	−0.0107948	−	0.102705i	0.987798	−	0.155742i	$-0.0497767\pi$
$947$	−0.332191	−	3.16059i	−0.0107948	−	0.102705i	−0.998593	+	0.0530364i	$0.983110\pi$
$948$	5.95434	−	6.61296i	0.193388	−	0.214779i
$949$	35.6337	+	39.5752i	1.15672	+	1.28467i
$950$	−0.259212	+	2.46624i	−0.00840995	+	0.0800153i
$951$	−19.7369	+	4.19521i	−0.640013	+	0.136039i
$952$	21.6836	+	9.65416i	0.702770	+	0.312893i
$953$	20.6426	−	14.9977i	0.668679	−	0.485824i	−0.200904	−	0.979611i	$-0.564388\pi$
$953$	20.6426	−	14.9977i	0.668679	−	0.485824i	0.869583	+	0.493787i	$0.164388\pi$
$954$	−9.06496	+	4.03598i	−0.293489	+	0.130670i
$955$	12.0392	−	20.8524i	0.389578	−	0.674769i
$956$	1.20009	+	2.07862i	0.0388138	+	0.0672274i
$957$	2.02031	+	1.46784i	0.0653075	+	0.0474486i
$958$	10.2718	+	2.18334i	0.331867	+	0.0705405i
$959$	9.21701	−	28.3671i	0.297633	−	0.916020i
$960$	1.00000			0.0322749
$961$	−6.60995	−	30.2871i	−0.213224	−	0.977003i
$962$	−17.3628			−0.559800
$963$	2.14971	−	6.61612i	0.0692734	−	0.213202i
$964$	−14.8884	−	3.16462i	−0.479522	−	0.101926i
$965$	−1.01052	−	0.734186i	−0.0325298	−	0.0236343i
$966$	3.29380	+	5.70502i	0.105976	+	0.183556i
$967$	19.8583	−	34.3955i	0.638599	−	1.10609i	−0.347142	−	0.937813i	$-0.612848\pi$
$967$	19.8583	−	34.3955i	0.638599	−	1.10609i	0.985740	−	0.168273i	$-0.0538189\pi$
$968$	−9.34311	+	4.15982i	−0.300299	+	0.133702i
$969$	−16.0888	+	11.6892i	−0.516846	+	0.375510i
$970$	6.13540	+	2.73166i	0.196996	+	0.0877082i
$971$	−33.4915	+	7.11883i	−1.07479	+	0.228454i	−0.711118	−	0.703072i	$-0.751811\pi$
$971$	−33.4915	+	7.11883i	−1.07479	+	0.228454i	−0.363674	+	0.931526i	$0.618478\pi$
$972$	0.104528	−	0.994522i	0.00335275	−	0.0318993i
$973$	−21.0222	−	23.3475i	−0.673940	−	0.748486i
$974$	9.39427	−	10.4334i	0.301012	−	0.334307i
$975$	−0.365044	−	3.47316i	−0.0116908	−	0.111230i
$976$	1.20685	+	3.71431i	0.0386304	+	0.118892i
$977$	−10.8280	−	33.3252i	−0.346419	−	1.06617i	−0.960820	−	0.277173i	$-0.910602\pi$
$977$	−10.8280	−	33.3252i	−0.346419	−	1.06617i	0.614401	−	0.788994i	$-0.289398\pi$
$978$	−0.262329	−	2.49589i	−0.00838835	−	0.0798098i
$979$	8.59286	−	9.54334i	0.274629	−	0.305007i
$980$	−1.17779	−	1.30807i	−0.0376231	−	0.0417846i
$981$	0.701114	−	6.67065i	0.0223848	−	0.212978i
$982$	31.4929	−	6.69401i	1.00498	−	0.213615i
$983$	−37.2035	−	16.5641i	−1.18661	−	0.528311i	−0.284019	−	0.958819i	$-0.591668\pi$
$983$	−37.2035	−	16.5641i	−1.18661	−	0.528311i	−0.902587	+	0.430507i	$0.858335\pi$
$984$	3.20233	−	2.32663i	0.102087	−	0.0741703i
$985$	−6.65508	+	2.96303i	−0.212049	+	0.0944101i
$986$	11.3913	−	19.7302i	0.362771	−	0.628339i
$987$	−9.83286	−	17.0310i	−0.312983	−	0.542103i
$988$	7.00630	+	5.09038i	0.222900	+	0.161946i
$989$	8.00028	+	1.70051i	0.254394	+	0.0540731i
$990$	−0.271636	+	0.836008i	−0.00863315	+	0.0265701i
$991$	−48.7166			−1.54753			−0.773767	−	0.633470i	$-0.781630\pi$
$991$	−48.7166			−1.54753			−0.773767	+	0.633470i	$0.781630\pi$
$992$	3.49214	−	4.33647i	0.110875	−	0.137683i
$993$	13.7090			0.435041
$994$	8.89280	−	27.3692i	0.282063	−	0.868099i
$995$	23.1628	+	4.92340i	0.734309	+	0.156082i
$996$	−13.5802	−	9.86659i	−0.430305	−	0.312635i
$997$	15.4584	+	26.7747i	0.489573	+	0.847964i	0.999928	−	0.0119991i	$-0.00381951\pi$
$997$	15.4584	+	26.7747i	0.489573	+	0.847964i	−0.510356	+	0.859964i	$0.670486\pi$
$998$	16.6486	−	28.8362i	0.527003	−	0.912796i
$999$	−4.54192	+	2.02219i	−0.143700	+	0.0639794i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.c.691.1	✓	16
31.7	even	15	inner	930.2.bg.c.751.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.c.691.1	✓	16	1.1	even	1	trivial
930.2.bg.c.751.1	yes	16	31.7	even	15	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.978148 + 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-2.70387 + 1.20384i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.978148 + 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-2.70387 + 1.20384i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.978148 - 0.207912i) q^{10} +(-0.0918838 + 0.874216i) q^{11} +(-0.669131 - 0.743145i) q^{12} +(-2.33680 + 2.59528i) q^{13} +(0.309379 + 2.94355i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.838261 + 7.97552i) q^{17} +(0.669131 - 0.743145i) q^{18} +(1.65932 + 1.84287i) q^{19} +(0.104528 - 0.994522i) q^{20} +(-2.89508 + 0.615369i) q^{21} +(0.803035 + 0.357534i) q^{22} +(1.80064 - 1.30824i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.74615 + 3.02442i) q^{26} +(0.809017 + 0.587785i) q^{27} +(2.89508 + 0.615369i) q^{28} +(0.877888 - 2.70186i) q^{29} +1.00000 q^{30} +(3.49214 - 4.33647i) q^{31} +1.00000 q^{32} +(-0.271636 + 0.836008i) q^{33} +(7.84421 + 1.66734i) q^{34} +(-2.39450 - 1.73970i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-2.48588 + 4.30566i) q^{37} +(2.26543 - 1.00863i) q^{38} +(-2.82533 + 2.05272i) q^{39} +(-0.913545 - 0.406737i) q^{40} +(-3.87180 + 0.822977i) q^{41} +(-0.309379 + 2.94355i) q^{42} +(2.45890 + 2.73089i) q^{43} +(0.588187 - 0.653248i) q^{44} +(0.104528 + 0.994522i) q^{45} +(-0.687785 - 2.11678i) q^{46} +(2.05322 + 6.31917i) q^{47} +(0.104528 + 0.994522i) q^{48} +(1.17779 - 1.30807i) q^{49} +(0.669131 + 0.743145i) q^{50} +(-0.838261 + 7.97552i) q^{51} +(3.41598 - 0.726089i) q^{52} +(-9.06496 - 4.03598i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-0.803035 + 0.357534i) q^{55} +(1.47988 - 2.56323i) q^{56} +(1.23991 + 2.14759i) q^{57} +(-2.29834 - 1.66984i) q^{58} +(3.74182 + 0.795347i) q^{59} +(0.309017 - 0.951057i) q^{60} +3.90546 q^{61} +(-3.04510 - 4.66126i) q^{62} -2.95976 q^{63} +(0.309017 - 0.951057i) q^{64} +(-3.41598 - 0.726089i) q^{65} +(0.711151 + 0.516682i) q^{66} +(3.84467 + 6.65917i) q^{67} +(4.00973 - 6.94505i) q^{68} +(2.03329 - 0.905281i) q^{69} +(-2.39450 + 1.73970i) q^{70} +(-8.88239 - 3.95470i) q^{71} +(-0.978148 + 0.207912i) q^{72} +(1.59395 - 15.1654i) q^{73} +(3.32675 + 3.69473i) q^{74} +(-0.669131 + 0.743145i) q^{75} +(-0.259212 - 2.46624i) q^{76} +(-0.803976 - 2.47438i) q^{77} +(1.07918 + 3.32137i) q^{78} +(0.930158 + 8.84987i) q^{79} +(-0.669131 + 0.743145i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-0.413755 + 3.93662i) q^{82} +(16.4192 - 3.49001i) q^{83} +(2.70387 + 1.20384i) q^{84} +(-6.48787 + 4.71372i) q^{85} +(3.35707 - 1.49467i) q^{86} +(1.42045 - 2.46030i) q^{87} +(-0.439516 - 0.761263i) q^{88} +(-11.8190 - 8.58700i) q^{89} +(0.978148 + 0.207912i) q^{90} +(3.19411 - 9.83045i) q^{91} -2.22572 q^{92} +(4.31743 - 3.51565i) q^{93} +6.64437 q^{94} +(-0.766307 + 2.35845i) q^{95} +(0.978148 + 0.207912i) q^{96} +(5.43339 + 3.94759i) q^{97} +(-0.880088 - 1.52436i) q^{98} +(-0.439516 + 0.761263i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 14 q^{13} - 4 q^{14} - 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} + q^{19} - 2 q^{20} - 16 q^{21} - 13 q^{22} + 3 q^{23} - 2 q^{24} - 8 q^{25} + 9 q^{26} + 4 q^{27} + 16 q^{28} + 13 q^{29} + 16 q^{30} + 9 q^{31} + 16 q^{32} + 14 q^{33} + 26 q^{34} + 7 q^{35} - 8 q^{36} - 11 q^{37} - 14 q^{38} - 7 q^{39} - 2 q^{40} + 42 q^{41} + 4 q^{42} - 18 q^{43} + 7 q^{44} - 2 q^{45} - 7 q^{46} - 37 q^{47} - 2 q^{48} + 11 q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} + 14 q^{53} + 4 q^{54} + 13 q^{55} - 9 q^{56} + 4 q^{57} - 12 q^{58} + 2 q^{59} - 4 q^{60} - 16 q^{61} + 9 q^{62} + 18 q^{63} - 4 q^{64} + 16 q^{65} - 11 q^{66} + 41 q^{67} + 16 q^{68} + 9 q^{69} + 7 q^{70} + q^{71} + 2 q^{72} - 53 q^{73} + 44 q^{74} - 2 q^{75} + 16 q^{76} - 16 q^{77} - 2 q^{78} + 30 q^{79} - 2 q^{80} + 2 q^{81} - 8 q^{82} - 11 q^{84} - 38 q^{85} + 7 q^{86} - q^{87} - 3 q^{88} - 49 q^{89} - 2 q^{90} + 2 q^{91} + 8 q^{92} + 6 q^{93} + 48 q^{94} + 2 q^{95} - 2 q^{96} + 21 q^{97} - 19 q^{98} - 3 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 + 14 * q^13 - 4 * q^14 - 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 + q^19 - 2 * q^20 - 16 * q^21 - 13 * q^22 + 3 * q^23 - 2 * q^24 - 8 * q^25 + 9 * q^26 + 4 * q^27 + 16 * q^28 + 13 * q^29 + 16 * q^30 + 9 * q^31 + 16 * q^32 + 14 * q^33 + 26 * q^34 + 7 * q^35 - 8 * q^36 - 11 * q^37 - 14 * q^38 - 7 * q^39 - 2 * q^40 + 42 * q^41 + 4 * q^42 - 18 * q^43 + 7 * q^44 - 2 * q^45 - 7 * q^46 - 37 * q^47 - 2 * q^48 + 11 * q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 + 14 * q^53 + 4 * q^54 + 13 * q^55 - 9 * q^56 + 4 * q^57 - 12 * q^58 + 2 * q^59 - 4 * q^60 - 16 * q^61 + 9 * q^62 + 18 * q^63 - 4 * q^64 + 16 * q^65 - 11 * q^66 + 41 * q^67 + 16 * q^68 + 9 * q^69 + 7 * q^70 + q^71 + 2 * q^72 - 53 * q^73 + 44 * q^74 - 2 * q^75 + 16 * q^76 - 16 * q^77 - 2 * q^78 + 30 * q^79 - 2 * q^80 + 2 * q^81 - 8 * q^82 - 11 * q^84 - 38 * q^85 + 7 * q^86 - q^87 - 3 * q^88 - 49 * q^89 - 2 * q^90 + 2 * q^91 + 8 * q^92 + 6 * q^93 + 48 * q^94 + 2 * q^95 - 2 * q^96 + 21 * q^97 - 19 * q^98 - 3 * q^99

Introduction

L-functions

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