LMFDB - Embedded newform 231.2.y.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(4,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("231.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.y (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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			25.1
Character	$\chi$	$=$	231.25
Dual form			231.2.y.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.50180 - 1.11387i) q^{2} +(0.978148 + 0.207912i) q^{3} +(3.68004 + 4.08710i) q^{4} +(0.150245 - 1.42949i) q^{5} +(-2.21555 - 1.60969i) q^{6} +(-2.64282 + 0.124535i) q^{7} +(-2.96170 - 9.11518i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})$	\(q+(-2.50180 - 1.11387i) q^{2} +(0.978148 + 0.207912i) q^{3} +(3.68004 + 4.08710i) q^{4} +(0.150245 - 1.42949i) q^{5} +(-2.21555 - 1.60969i) q^{6} +(-2.64282 + 0.124535i) q^{7} +(-2.96170 - 9.11518i) q^{8} +(0.913545 + 0.406737i) q^{9} +(-1.96815 + 3.40894i) q^{10} +(3.31659 + 0.0152357i) q^{11} +(2.74987 + 4.76291i) q^{12} +(3.24490 - 2.35756i) q^{13} +(6.75053 + 2.63221i) q^{14} +(0.444168 - 1.36701i) q^{15} +(-1.59381 + 15.1641i) q^{16} +(0.0162751 - 0.00724614i) q^{17} +(-1.83246 - 2.03515i) q^{18} +(3.50447 - 3.89211i) q^{19} +(6.39536 - 4.64650i) q^{20} +(-2.61096 - 0.427659i) q^{21} +(-8.28049 - 3.73238i) q^{22} +(-2.96330 - 5.13258i) q^{23} +(-1.00183 - 9.53176i) q^{24} +(2.86988 + 0.610013i) q^{25} +(-10.7441 + 2.28374i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-10.2347 - 10.3432i) q^{28} +(-1.17725 + 3.62320i) q^{29} +(-2.63390 + 2.92524i) q^{30} +(-0.833126 - 7.92666i) q^{31} +(11.2941 - 19.5619i) q^{32} +(3.24095 + 0.704461i) q^{33} -0.0487884 q^{34} +(-0.219049 + 3.79658i) q^{35} +(1.69951 + 5.23056i) q^{36} +(2.05138 - 0.436034i) q^{37} +(-13.1028 + 5.83375i) q^{38} +(3.66416 - 1.63139i) q^{39} +(-13.4750 + 2.86420i) q^{40} +(0.291768 + 0.897968i) q^{41} +(6.05575 + 3.97820i) q^{42} -0.749457 q^{43} +(12.1429 + 13.6113i) q^{44} +(0.718680 - 1.24479i) q^{45} +(1.69654 + 16.1415i) q^{46} +(-1.19873 + 1.33132i) q^{47} +(-4.71178 + 14.5014i) q^{48} +(6.96898 - 0.658247i) q^{49} +(-6.50041 - 4.72282i) q^{50} +(0.0174260 - 0.00370401i) q^{51} +(21.5770 + 4.58633i) q^{52} +(-0.000917016 - 0.00872482i) q^{53} +(-1.36928 - 2.37167i) q^{54} +(0.520080 - 4.73873i) q^{55} +(8.96240 + 23.7209i) q^{56} +(4.23710 - 3.07844i) q^{57} +(6.98104 - 7.75323i) q^{58} +(-1.86664 - 2.07312i) q^{59} +(7.22167 - 3.21529i) q^{60} +(-1.30839 + 12.4485i) q^{61} +(-6.74499 + 20.7589i) q^{62} +(-2.46499 - 0.961163i) q^{63} +(-25.3739 + 18.4352i) q^{64} +(-2.88257 - 4.99275i) q^{65} +(-7.32353 - 5.37243i) q^{66} +(-4.91687 + 8.51627i) q^{67} +(0.0895088 + 0.0398519i) q^{68} +(-1.83142 - 5.63653i) q^{69} +(4.77693 - 9.25431i) q^{70} +(3.82726 + 2.78067i) q^{71} +(1.00183 - 9.53176i) q^{72} +(-2.25789 - 2.50764i) q^{73} +(-5.61783 - 1.19411i) q^{74} +(2.68034 + 1.19336i) q^{75} +28.8041 q^{76} +(-8.76704 + 0.372766i) q^{77} -10.9842 q^{78} +(-13.4173 - 5.97376i) q^{79} +(21.4374 + 4.55667i) q^{80} +(0.669131 + 0.743145i) q^{81} +(0.270279 - 2.57153i) q^{82} +(13.3219 + 9.67889i) q^{83} +(-7.86056 - 12.2451i) q^{84} +(-0.00791300 - 0.0243537i) q^{85} +(1.87499 + 0.834802i) q^{86} +(-1.90483 + 3.29926i) q^{87} +(-9.68387 - 30.2764i) q^{88} +(2.27619 + 3.94248i) q^{89} +(-3.18453 + 2.31370i) q^{90} +(-8.28209 + 6.63471i) q^{91} +(10.0723 - 30.9994i) q^{92} +(0.833126 - 7.92666i) q^{93} +(4.48190 - 1.99547i) q^{94} +(-5.03718 - 5.59436i) q^{95} +(15.1144 - 16.7863i) q^{96} +(-2.86133 + 2.07888i) q^{97} +(-18.1682 - 6.11577i) q^{98} +(3.02366 + 1.36290i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9} - 22 q^{10} - 13 q^{11} + 30 q^{12} - 8 q^{13} - 26 q^{14} + 4 q^{17} - 5 q^{18} + 10 q^{19} + 24 q^{20} + 2 q^{21} - 38 q^{22} - 8 q^{23} + 14 q^{24} - 2 q^{25} + 4 q^{26} + 16 q^{27} - 67 q^{28} + 2 q^{29} - 3 q^{30} + 25 q^{31} + 72 q^{32} - 12 q^{33} - 56 q^{34} + 19 q^{35} - 20 q^{36} - 12 q^{37} - 37 q^{38} - 4 q^{39} - 9 q^{40} + 20 q^{41} + 9 q^{42} - 100 q^{43} - 5 q^{44} - 33 q^{46} - 18 q^{47} + 10 q^{48} + 29 q^{49} - 46 q^{50} + 6 q^{51} + 26 q^{52} - 49 q^{53} - 10 q^{54} - 24 q^{55} - 48 q^{56} + 20 q^{57} - 40 q^{58} + q^{59} + 12 q^{60} + 3 q^{61} + 4 q^{62} - 7 q^{63} - 24 q^{64} + 82 q^{65} + 11 q^{66} + 76 q^{67} - 39 q^{68} - 16 q^{69} + 59 q^{70} + 70 q^{71} - 14 q^{72} - 3 q^{73} + 32 q^{74} - 28 q^{75} + 104 q^{76} + 38 q^{77} - 12 q^{78} - 15 q^{79} - 83 q^{80} + 8 q^{81} + 42 q^{82} + 68 q^{83} + 27 q^{84} + 62 q^{85} - 47 q^{86} - 54 q^{87} - 64 q^{88} + 82 q^{89} - 16 q^{90} - 10 q^{91} + 190 q^{92} - 25 q^{93} - 6 q^{94} - 53 q^{95} + 8 q^{96} - 32 q^{97} - 152 q^{98} + 16 q^{99}+O(q^{100}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9 - 22 * q^10 - 13 * q^11 + 30 * q^12 - 8 * q^13 - 26 * q^14 + 4 * q^17 - 5 * q^18 + 10 * q^19 + 24 * q^20 + 2 * q^21 - 38 * q^22 - 8 * q^23 + 14 * q^24 - 2 * q^25 + 4 * q^26 + 16 * q^27 - 67 * q^28 + 2 * q^29 - 3 * q^30 + 25 * q^31 + 72 * q^32 - 12 * q^33 - 56 * q^34 + 19 * q^35 - 20 * q^36 - 12 * q^37 - 37 * q^38 - 4 * q^39 - 9 * q^40 + 20 * q^41 + 9 * q^42 - 100 * q^43 - 5 * q^44 - 33 * q^46 - 18 * q^47 + 10 * q^48 + 29 * q^49 - 46 * q^50 + 6 * q^51 + 26 * q^52 - 49 * q^53 - 10 * q^54 - 24 * q^55 - 48 * q^56 + 20 * q^57 - 40 * q^58 + q^59 + 12 * q^60 + 3 * q^61 + 4 * q^62 - 7 * q^63 - 24 * q^64 + 82 * q^65 + 11 * q^66 + 76 * q^67 - 39 * q^68 - 16 * q^69 + 59 * q^70 + 70 * q^71 - 14 * q^72 - 3 * q^73 + 32 * q^74 - 28 * q^75 + 104 * q^76 + 38 * q^77 - 12 * q^78 - 15 * q^79 - 83 * q^80 + 8 * q^81 + 42 * q^82 + 68 * q^83 + 27 * q^84 + 62 * q^85 - 47 * q^86 - 54 * q^87 - 64 * q^88 + 82 * q^89 - 16 * q^90 - 10 * q^91 + 190 * q^92 - 25 * q^93 - 6 * q^94 - 53 * q^95 + 8 * q^96 - 32 * q^97 - 152 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−2.50180	−	1.11387i	−1.76904	−	0.787628i	−0.986232	−	0.165368i	$-0.947119\pi$
$2$	−2.50180	−	1.11387i	−1.76904	−	0.787628i	−0.782811	−	0.622260i	$-0.786215\pi$
$3$	0.978148	+	0.207912i	0.564734	+	0.120038i
$3$	0.978148	+	0.207912i	0.564734	+	0.120038i
$4$	3.68004	+	4.08710i	1.84002	+	2.04355i
$5$	0.150245	−	1.42949i	0.0671916	−	0.639285i	−0.908159	−	0.418625i	$-0.862512\pi$
$5$	0.150245	−	1.42949i	0.0671916	−	0.639285i	0.975351	−	0.220660i	$-0.0708212\pi$
$6$	−2.21555	−	1.60969i	−0.904493	−	0.657152i
$7$	−2.64282	+	0.124535i	−0.998892	+	0.0470698i
$7$	−2.64282	+	0.124535i	−0.998892	+	0.0470698i
$8$	−2.96170	−	9.11518i	−1.04712	−	3.22270i
$9$	0.913545	+	0.406737i	0.304515	+	0.135579i
$10$	−1.96815	+	3.40894i	−0.622384	+	1.07800i
$11$	3.31659	+	0.0152357i	0.999989	+	0.00459373i
$11$	3.31659	+	0.0152357i	0.999989	+	0.00459373i
$12$	2.74987	+	4.76291i	0.793819	+	1.37493i
$13$	3.24490	−	2.35756i	0.899974	−	0.653870i	−0.0384850	−	0.999259i	$-0.512253\pi$
$13$	3.24490	−	2.35756i	0.899974	−	0.653870i	0.938459	+	0.345389i	$0.112253\pi$
$14$	6.75053	+	2.63221i	1.80416	+	0.703487i
$15$	0.444168	−	1.36701i	0.114684	−	0.352960i
$16$	−1.59381	+	15.1641i	−0.398453	+	3.79103i
$17$	0.0162751	−	0.00724614i	0.00394729	−	0.00175745i	−0.404762	−	0.914422i	$-0.632646\pi$
$17$	0.0162751	−	0.00724614i	0.00394729	−	0.00175745i	0.408709	+	0.912665i	$0.365979\pi$
$18$	−1.83246	−	2.03515i	−0.431914	−	0.479690i
$19$	3.50447	−	3.89211i	0.803981	−	0.892911i	−0.192099	−	0.981376i	$-0.561529\pi$
$19$	3.50447	−	3.89211i	0.803981	−	0.892911i	0.996079	+	0.0884645i	$0.0281960\pi$
$20$	6.39536	−	4.64650i	1.43005	−	1.03899i
$21$	−2.61096	−	0.427659i	−0.569758	−	0.0933229i
$22$	−8.28049	−	3.73238i	−1.76541	−	0.795747i
$23$	−2.96330	−	5.13258i	−0.617890	−	1.07022i	−0.989870	−	0.141976i	$-0.954654\pi$
$23$	−2.96330	−	5.13258i	−0.617890	−	1.07022i	0.371980	−	0.928241i	$-0.378679\pi$
$24$	−1.00183	−	9.53176i	−0.204497	−	1.94566i
$25$	2.86988	+	0.610013i	0.573977	+	0.122003i
$26$	−10.7441	+	2.28374i	−2.10710	+	0.447878i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−10.2347	−	10.3432i	−1.93417	−	1.95468i
$29$	−1.17725	+	3.62320i	−0.218610	+	0.672811i	0.780268	+	0.625445i	$0.215083\pi$
$29$	−1.17725	+	3.62320i	−0.218610	+	0.672811i	−0.998878	+	0.0473660i	$0.984917\pi$
$30$	−2.63390	+	2.92524i	−0.480882	+	0.534074i
$31$	−0.833126	−	7.92666i	−0.149634	−	1.42367i	−0.769342	−	0.638838i	$-0.779416\pi$
$31$	−0.833126	−	7.92666i	−0.149634	−	1.42367i	0.619708	−	0.784833i	$-0.287251\pi$
$32$	11.2941	−	19.5619i	1.99653	−	3.45809i
$33$	3.24095	+	0.704461i	0.564176	+	0.122631i
$34$	−0.0487884			−0.00836714
$35$	−0.219049	+	3.79658i	−0.0370261	+	0.641739i
$36$	1.69951	+	5.23056i	0.283252	+	0.871760i
$37$	2.05138	−	0.436034i	0.337245	−	0.0716836i	−0.0361767	−	0.999345i	$-0.511518\pi$
$37$	2.05138	−	0.436034i	0.337245	−	0.0716836i	0.373421	+	0.927662i	$0.378185\pi$
$38$	−13.1028	+	5.83375i	−2.12556	+	0.946360i
$39$	3.66416	−	1.63139i	0.586735	−	0.261231i
$40$	−13.4750	+	2.86420i	−2.13058	+	0.452869i
$41$	0.291768	+	0.897968i	0.0455664	+	0.140239i	0.971251	−	0.238056i	$-0.0765103\pi$
$41$	0.291768	+	0.897968i	0.0455664	+	0.140239i	−0.925685	+	0.378296i	$0.876510\pi$
$42$	6.05575	+	3.97820i	0.934422	+	0.613850i
$43$	−0.749457			−0.114291			−0.0571456	−	0.998366i	$-0.518200\pi$
$43$	−0.749457			−0.114291			−0.0571456	+	0.998366i	$0.518200\pi$
$44$	12.1429	+	13.6113i	1.83061	+	2.05198i
$45$	0.718680	−	1.24479i	0.107134	−	0.185562i
$46$	1.69654	+	16.1415i	0.250140	+	2.37993i
$47$	−1.19873	+	1.33132i	−0.174852	+	0.194193i	−0.824200	−	0.566298i	$-0.808375\pi$
$47$	−1.19873	+	1.33132i	−0.174852	+	0.194193i	0.649348	+	0.760491i	$0.275042\pi$
$48$	−4.71178	+	14.5014i	−0.680087	+	2.09309i
$49$	6.96898	−	0.658247i	0.995569	−	0.0940353i
$50$	−6.50041	−	4.72282i	−0.919297	−	0.667908i
$51$	0.0174260	−	0.00370401i	0.00244013	−	0.000518665i
$52$	21.5770	+	4.58633i	2.99219	+	0.636009i
$53$	−0.000917016	−	0.00872482i	−0.000125962	−	0.00119845i	0.994459	−	0.105128i	$-0.0335251\pi$
$53$	−0.000917016	−	0.00872482i	−0.000125962	−	0.00119845i	−0.994585	+	0.103929i	$0.966858\pi$
$54$	−1.36928	−	2.37167i	−0.186336	−	0.322743i
$55$	0.520080	−	4.73873i	0.0701276	−	0.638970i
$56$	8.96240	+	23.7209i	1.19765	+	3.16984i
$57$	4.23710	−	3.07844i	0.561218	−	0.407749i
$58$	6.98104	−	7.75323i	0.916655	−	1.01805i
$59$	−1.86664	−	2.07312i	−0.243016	−	0.269897i	0.609281	−	0.792954i	$-0.291458\pi$
$59$	−1.86664	−	2.07312i	−0.243016	−	0.269897i	−0.852298	+	0.523057i	$0.824791\pi$
$60$	7.22167	−	3.21529i	0.932313	−	0.415093i
$61$	−1.30839	+	12.4485i	−0.167522	+	1.59386i	0.511196	+	0.859464i	$0.329202\pi$
$61$	−1.30839	+	12.4485i	−0.167522	+	1.59386i	−0.678718	+	0.734399i	$0.737464\pi$
$62$	−6.74499	+	20.7589i	−0.856615	+	2.63639i
$63$	−2.46499	−	0.961163i	−0.310559	−	0.121095i
$64$	−25.3739	+	18.4352i	−3.17174	+	2.30440i
$65$	−2.88257	−	4.99275i	−0.357539	−	0.619275i
$66$	−7.32353	−	5.37243i	−0.901464	−	0.661301i
$67$	−4.91687	+	8.51627i	−0.600691	+	1.04043i	0.392026	+	0.919954i	$0.371774\pi$
$67$	−4.91687	+	8.51627i	−0.600691	+	1.04043i	−0.992717	+	0.120473i	$0.961559\pi$
$68$	0.0895088	+	0.0398519i	0.0108545	+	0.00483275i
$69$	−1.83142	−	5.63653i	−0.220477	−	0.678558i
$70$	4.77693	−	9.25431i	0.570953	−	1.10610i
$71$	3.82726	+	2.78067i	0.454212	+	0.330005i	0.791257	−	0.611484i	$-0.209427\pi$
$71$	3.82726	+	2.78067i	0.454212	+	0.330005i	−0.337044	+	0.941489i	$0.609427\pi$
$72$	1.00183	−	9.53176i	0.118067	−	1.12333i
$73$	−2.25789	−	2.50764i	−0.264266	−	0.293497i	0.596379	−	0.802703i	$-0.296606\pi$
$73$	−2.25789	−	2.50764i	−0.264266	−	0.293497i	−0.860644	+	0.509206i	$0.829939\pi$
$74$	−5.61783	−	1.19411i	−0.653060	−	0.138812i
$75$	2.68034	+	1.19336i	0.309499	+	0.137798i
$76$	28.8041			3.30405
$77$	−8.76704	+	0.372766i	−0.999097	+	0.0424807i
$78$	−10.9842			−1.24371
$79$	−13.4173	−	5.97376i	−1.50956	−	0.672101i	−0.525642	−	0.850706i	$-0.676175\pi$
$79$	−13.4173	−	5.97376i	−1.50956	−	0.672101i	−0.983921	+	0.178605i	$0.942841\pi$
$80$	21.4374	+	4.55667i	2.39678	+	0.509451i
$81$	0.669131	+	0.743145i	0.0743478	+	0.0825716i
$82$	0.270279	−	2.57153i	0.0298473	−	0.283978i
$83$	13.3219	+	9.67889i	1.46226	+	1.06240i	0.982766	+	0.184853i	$0.0591808\pi$
$83$	13.3219	+	9.67889i	1.46226	+	1.06240i	0.479497	+	0.877544i	$0.340819\pi$
$84$	−7.86056	−	12.2451i	−0.857657	−	1.33605i
$85$	−0.00791300	−	0.0243537i	−0.000858285	−	0.00264153i
$86$	1.87499	+	0.834802i	0.202186	+	0.0900190i
$87$	−1.90483	+	3.29926i	−0.204219	+	0.353718i
$88$	−9.68387	−	30.2764i	−1.03230	−	3.22748i
$89$	2.27619	+	3.94248i	0.241276	+	0.417902i	0.961078	−	0.276277i	$-0.0891008\pi$
$89$	2.27619	+	3.94248i	0.241276	+	0.417902i	−0.719802	+	0.694179i	$0.755767\pi$
$90$	−3.18453	+	2.31370i	−0.335679	+	0.243885i
$91$	−8.28209	+	6.63471i	−0.868199	+	0.695507i
$92$	10.0723	−	30.9994i	1.05011	−	3.23191i
$93$	0.833126	−	7.92666i	0.0863911	−	0.821956i
$94$	4.48190	−	1.99547i	0.462273	−	0.205817i
$95$	−5.03718	−	5.59436i	−0.516804	−	0.573969i
$96$	15.1144	−	16.7863i	1.54261	−	1.71324i
$97$	−2.86133	+	2.07888i	−0.290524	+	0.211078i	−0.723495	−	0.690330i	$-0.757465\pi$
$97$	−2.86133	+	2.07888i	−0.290524	+	0.211078i	0.432971	+	0.901408i	$0.357465\pi$
$98$	−18.1682	−	6.11577i	−1.83527	−	0.617786i
$99$	3.02366	+	1.36290i	0.303889	+	0.136976i
$100$	8.06811	+	13.9744i	0.806811	+	1.39744i
$101$	1.46594	+	13.9475i	0.145867	+	1.38783i	0.785364	+	0.619034i	$0.212476\pi$
$101$	1.46594	+	13.9475i	0.145867	+	1.38783i	−0.639497	+	0.768793i	$0.720857\pi$
$102$	−0.0477223	−	0.0101437i	−0.00472521	−	0.00100437i
$103$	−1.22019	+	0.259360i	−0.120229	+	0.0255555i	−0.267633	−	0.963521i	$-0.586242\pi$
$103$	−1.22019	+	0.259360i	−0.120229	+	0.0255555i	0.147404	+	0.989076i	$0.452908\pi$
$104$	−31.1000	−	22.5955i	−3.04961	−	2.21567i
$105$	−1.00362	+	3.66807i	−0.0979429	+	0.357967i
$106$	−0.00742416	+	0.0228492i	−0.000721099	+	0.00221931i
$107$	−5.01975	+	5.57499i	−0.485277	+	0.538955i	−0.935203	−	0.354111i	$-0.884784\pi$
$107$	−5.01975	+	5.57499i	−0.485277	+	0.538955i	0.449926	+	0.893066i	$0.351450\pi$
$108$	0.574879	+	5.46961i	0.0553178	+	0.526314i
$109$	0.591490	−	1.02449i	0.0566545	−	0.0981284i	−0.836307	−	0.548261i	$-0.815290\pi$
$109$	0.591490	−	1.02449i	0.0566545	−	0.0981284i	0.892962	+	0.450133i	$0.148623\pi$
$110$	−6.57949	+	11.2761i	−0.627329	+	1.07513i
$111$	2.09721			0.199058
$112$	2.32370	−	40.2745i	0.219569	−	3.80558i
$113$	0.751424	+	2.31264i	0.0706880	+	0.217555i	0.980159	−	0.198211i	$-0.0635133\pi$
$113$	0.751424	+	2.31264i	0.0706880	+	0.217555i	−0.909471	+	0.415767i	$0.863513\pi$
$114$	−14.0294	+	2.98204i	−1.31397	+	0.279294i
$115$	−7.78217	+	3.46485i	−0.725691	+	0.323098i
$116$	−19.1407	+	8.52200i	−1.77717	+	0.791248i
$117$	3.92327	−	0.833918i	0.362707	−	0.0770957i
$118$	2.36078	+	7.26574i	0.217328	+	0.668866i
$119$	−0.0421097	+	0.0211771i	−0.00386019	+	0.00194130i
$120$	−13.7760			−1.25757
$121$	10.9995	+	0.101061i	0.999958	+	0.00918736i
$122$	17.1394	−	29.6862i	1.55172	−	2.68767i
$123$	0.0986937	+	0.939007i	0.00889891	+	0.0846674i
$124$	29.3311	−	32.5755i	2.63401	−	2.92537i
$125$	3.52403	−	10.8459i	0.315199	−	0.970083i
$126$	5.09630	+	5.15033i	0.454015	+	0.458828i
$127$	11.6971	+	8.49848i	1.03795	+	0.754118i	0.969885	−	0.243563i	$-0.0783162\pi$
$127$	11.6971	+	8.49848i	1.03795	+	0.754118i	0.0680690	+	0.997681i	$0.478316\pi$
$128$	39.8259	−	8.46525i	3.52014	−	0.748230i
$129$	−0.733080	−	0.155821i	−0.0645441	−	0.0137193i
$130$	1.65032	+	15.7017i	0.144742	+	1.37713i
$131$	−0.135061	−	0.233933i	−0.0118004	−	0.0204388i	0.860065	−	0.510185i	$-0.170423\pi$
$131$	−0.135061	−	0.233933i	−0.0118004	−	0.0204388i	−0.871865	+	0.489746i	$0.837090\pi$
$132$	9.04762	+	15.8385i	0.787495	+	1.37857i
$133$	−8.77698	+	10.7226i	−0.761061	+	0.929765i
$134$	21.7871	−	15.8292i	1.88212	−	1.36744i
$135$	0.961781	−	1.06817i	0.0827769	−	0.0919331i
$136$	−0.114252	−	0.126890i	−0.00979701	−	0.0108807i
$137$	−12.6316	+	5.62397i	−1.07919	+	0.480488i	−0.867801	−	0.496913i	$-0.834467\pi$
$137$	−12.6316	+	5.62397i	−1.07919	+	0.480488i	−0.211394	+	0.977401i	$0.567800\pi$
$138$	−1.69654	+	16.1415i	−0.144419	+	1.37405i
$139$	1.99593	−	6.14283i	0.169292	−	0.521028i	−0.830035	−	0.557712i	$-0.811679\pi$
$139$	1.99593	−	6.14283i	0.169292	−	0.521028i	0.999327	+	0.0366836i	$0.0116794\pi$
$140$	−16.3231	+	13.0763i	−1.37956	+	1.10515i
$141$	−1.44933	+	1.05300i	−0.122055	+	0.0886785i
$142$	−6.47774	−	11.2198i	−0.543600	−	0.941543i
$143$	10.7979	−	7.76962i	0.902969	−	0.649729i
$144$	−7.62383	+	13.2049i	−0.635319	+	1.10040i
$145$	5.00244	+	2.22723i	0.415430	+	0.184961i
$146$	2.85560	+	8.78862i	0.236331	+	0.727351i
$147$	6.95355	+	0.805070i	0.573519	+	0.0664011i
$148$	9.33128	+	6.77957i	0.767027	+	0.557277i
$149$	−0.922823	+	8.78007i	−0.0756006	+	0.719292i	0.889415	+	0.457100i	$0.151112\pi$
$149$	−0.922823	+	8.78007i	−0.0756006	+	0.719292i	−0.965016	+	0.262192i	$0.915555\pi$
$150$	−5.37643	−	5.97113i	−0.438984	−	0.487541i
$151$	−13.2786	−	2.82246i	−1.08060	−	0.229688i	−0.366984	−	0.930227i	$-0.619610\pi$
$151$	−13.2786	−	2.82246i	−1.08060	−	0.229688i	−0.713614	+	0.700539i	$0.752943\pi$
$152$	−45.8565	−	20.4166i	−3.71945	−	1.65601i
$153$	0.0178153			0.00144028
$154$	22.3486	+	8.83280i	1.80090	+	0.711767i
$155$	−11.4562			−0.920185
$156$	20.1519	+	8.97221i	1.61345	+	0.718352i
$157$	−4.79119	−	1.01840i	−0.382378	−	0.0812770i	0.0127123	−	0.999919i	$-0.495953\pi$
$157$	−4.79119	−	1.01840i	−0.382378	−	0.0812770i	−0.395091	+	0.918642i	$0.629287\pi$
$158$	26.9134	+	29.8904i	2.14111	+	2.37795i
$159$	0.000917016	−	0.00872482i	7.27241e−5	−	0.000691923i
$160$	−26.2666	−	19.0838i	−2.07656	−	1.50871i
$161$	8.47064	+	13.1954i	0.667580	+	1.03995i
$162$	−0.846263	−	2.60453i	−0.0664887	−	0.204631i
$163$	−15.4563	−	6.88161i	−1.21063	−	0.539009i	−0.300683	−	0.953724i	$-0.597215\pi$
$163$	−15.4563	−	6.88161i	−1.21063	−	0.539009i	−0.909951	+	0.414715i	$0.863881\pi$
$164$	−2.59637	+	4.49705i	−0.202743	+	0.351160i
$165$	1.49395	−	4.52704i	0.116304	−	0.352430i
$166$	−22.5476	−	39.0536i	−1.75003	−	3.03114i
$167$	−5.33928	+	3.87922i	−0.413166	+	0.300183i	−0.774882	−	0.632105i	$-0.782191\pi$
$167$	−5.33928	+	3.87922i	−0.413166	+	0.300183i	0.361716	+	0.932288i	$0.382191\pi$
$168$	3.83469	+	25.0660i	0.295853	+	1.93388i
$169$	0.954089	−	2.93638i	0.0733915	−	0.225876i
$170$	−0.00733021	+	0.0697423i	−0.000562201	+	0.00534899i
$171$	4.78456	−	2.13022i	0.365884	−	0.162902i
$172$	−2.75804	−	3.06311i	−0.210298	−	0.233560i
$173$	17.4395	−	19.3685i	1.32590	−	1.47256i	0.562168	−	0.827023i	$-0.309967\pi$
$173$	17.4395	−	19.3685i	1.32590	−	1.47256i	0.763730	−	0.645536i	$-0.223366\pi$
$174$	8.44047	−	6.13236i	0.639871	−	0.464893i
$175$	−7.66055	−	1.25475i	−0.579083	−	0.0948503i
$176$	−5.51706	+	50.2689i	−0.415864	+	3.78916i
$177$	−1.39483	−	2.41591i	−0.104842	−	0.181591i
$178$	−1.30316	−	12.3987i	−0.0976757	−	0.929322i
$179$	−9.01918	−	1.91709i	−0.674125	−	0.143290i	−0.141885	−	0.989883i	$-0.545316\pi$
$179$	−9.01918	−	1.91709i	−0.674125	−	0.143290i	−0.532240	+	0.846593i	$0.678650\pi$
$180$	7.73236	−	1.64356i	0.576336	−	0.122504i
$181$	−7.58362	−	5.50982i	−0.563686	−	0.409542i	0.269120	−	0.963107i	$-0.413267\pi$
$181$	−7.58362	−	5.50982i	−0.563686	−	0.409542i	−0.832806	+	0.553565i	$0.813267\pi$
$182$	28.1104	−	7.37353i	2.08368	−	0.546562i
$183$	−3.86798	+	11.9044i	−0.285929	+	0.879999i
$184$	−38.0080	+	42.2121i	−2.80199	+	3.11192i
$185$	−0.315095	−	2.99793i	−0.0231662	−	0.220412i
$186$	−10.9136	+	18.9030i	−0.800226	+	1.38603i
$187$	0.0540882	−	0.0237845i	0.00395532	−	0.00173930i
$188$	−9.85261			−0.718575
$189$	−2.21129	−	1.45266i	−0.160847	−	0.105665i
$190$	6.37063	+	19.6068i	0.462174	+	1.42243i
$191$	−5.68365	+	1.20810i	−0.411254	+	0.0874148i	−0.408893	−	0.912582i	$-0.634085\pi$
$191$	−5.68365	+	1.20810i	−0.411254	+	0.0874148i	−0.00236151	+	0.999997i	$0.500752\pi$
$192$	−28.6523	+	12.7568i	−2.06780	+	0.920645i
$193$	12.6860	−	5.64819i	0.913161	−	0.406566i	0.104287	−	0.994547i	$-0.466744\pi$
$193$	12.6860	−	5.64819i	0.913161	−	0.406566i	0.808874	+	0.587982i	$0.200077\pi$
$194$	9.47410	−	2.01378i	0.680201	−	0.144581i
$195$	−1.78152	−	5.48297i	−0.127578	−	0.392644i
$196$	28.3365	+	26.0606i	2.02403	+	1.86147i
$197$	−3.25404			−0.231841			−0.115920	−	0.993259i	$-0.536982\pi$
$197$	−3.25404			−0.231841			−0.115920	+	0.993259i	$0.536982\pi$
$198$	−6.04650	−	6.77768i	−0.429706	−	0.481669i
$199$	−7.16681	+	12.4133i	−0.508042	+	0.879954i	0.491915	+	0.870643i	$0.336297\pi$
$199$	−7.16681	+	12.4133i	−0.508042	+	0.879954i	−0.999957	+	0.00931074i	$0.997036\pi$
$200$	−2.93936	−	27.9662i	−0.207844	−	1.97751i
$201$	−6.58005	+	7.30789i	−0.464121	+	0.515459i
$202$	11.8683	−	36.5268i	0.835048	−	2.57001i
$203$	2.66004	−	9.72207i	0.186698	−	0.682356i
$204$	0.0792671	+	0.0575910i	0.00554981	+	0.00403217i
$205$	1.32747	−	0.282162i	0.0927145	−	0.0197071i
$206$	3.34158	+	0.710274i	0.232819	+	0.0494871i
$207$	−0.619498	−	5.89413i	−0.0430581	−	0.409670i
$208$	30.5786	+	52.9636i	2.12024	+	3.67237i
$209$	11.6822	−	12.8551i	0.808074	−	0.889208i
$210$	6.59663	−	8.05890i	0.455210	−	0.556117i
$211$	−8.63529	+	6.27391i	−0.594478	+	0.431914i	−0.843915	−	0.536478i	$-0.819755\pi$
$211$	−8.63529	+	6.27391i	−0.594478	+	0.431914i	0.249436	+	0.968391i	$0.419755\pi$
$212$	0.0322846	−	0.0358557i	0.00221731	−	0.00246258i
$213$	3.16549	+	3.51564i	0.216896	+	0.240887i
$214$	18.7683	−	8.35617i	1.28297	−	0.571216i
$215$	−0.112602	+	1.07134i	−0.00767940	+	0.0730646i
$216$	2.96170	−	9.11518i	0.201518	−	0.620209i
$217$	3.18895	+	20.8450i	0.216480	+	1.41505i
$218$	−2.62095	+	1.90423i	−0.177513	+	0.128971i
$219$	−1.68718	−	2.92228i	−0.114009	−	0.197469i
$220$	21.2816	−	15.3131i	1.43480	−	1.03241i
$221$	0.0357279	−	0.0618826i	0.00240332	−	0.00416267i
$222$	−5.24680	−	2.33603i	−0.352142	−	0.156784i
$223$	1.18867	+	3.65834i	0.0795989	+	0.244980i	0.982935	−	0.183953i	$-0.0588895\pi$
$223$	1.18867	+	3.65834i	0.0795989	+	0.244980i	−0.903336	+	0.428933i	$0.858889\pi$
$224$	−27.4121	+	53.1051i	−1.83155	+	3.54824i
$225$	2.37365	+	1.72456i	0.158244	+	0.114971i
$226$	0.696082	−	6.62277i	0.0463027	−	0.440540i
$227$	−1.04982	−	1.16594i	−0.0696788	−	0.0773862i	0.707297	−	0.706916i	$-0.249914\pi$
$227$	−1.04982	−	1.16594i	−0.0696788	−	0.0773862i	−0.776976	+	0.629530i	$0.783248\pi$
$228$	28.1746	+	5.98870i	1.86591	+	0.396611i
$229$	22.9301	+	10.2091i	1.51526	+	0.674638i	0.984899	−	0.173133i	$-0.0553889\pi$
$229$	22.9301	+	10.2091i	1.51526	+	0.674638i	0.530363	+	0.847771i	$0.322056\pi$
$230$	23.3289			1.53826
$231$	−8.65296	−	1.45815i	−0.569323	−	0.0959392i
$232$	36.5128			2.39718
$233$	−1.59624	−	0.710691i	−0.104573	−	0.0465589i	0.353783	−	0.935327i	$-0.384895\pi$
$233$	−1.59624	−	0.710691i	−0.104573	−	0.0465589i	−0.458356	+	0.888768i	$0.651562\pi$
$234$	−10.7441	−	2.28374i	−0.702366	−	0.149293i
$235$	1.72300	+	1.91359i	0.112396	+	0.124829i
$236$	1.60372	−	15.2583i	0.104393	−	0.993233i
$237$	−11.8821	−	8.63283i	−0.771823	−	0.560763i
$238$	0.128939	−	0.00607586i	0.00835787	−	0.000393840i
$239$	−6.33202	−	19.4880i	−0.409585	−	1.26057i	−0.917006	−	0.398874i	$-0.869401\pi$
$239$	−6.33202	−	19.4880i	−0.409585	−	1.26057i	0.507421	−	0.861698i	$-0.330599\pi$
$240$	20.0216	+	8.91418i	1.29239	+	0.575408i
$241$	10.8569	−	18.8047i	0.699356	−	1.21132i	−0.269334	−	0.963047i	$-0.586804\pi$
$241$	10.8569	−	18.8047i	0.699356	−	1.21132i	0.968690	−	0.248273i	$-0.0798631\pi$
$242$	−27.4061	−	12.5049i	−1.76173	−	0.803848i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−55.6931	+	40.4634i	−3.56538	+	2.59040i
$245$	0.106100	−	10.0610i	0.00677849	−	0.642771i
$246$	0.799025	−	2.45914i	0.0509439	−	0.156789i
$247$	2.19579	−	20.8915i	0.139715	−	1.32930i
$248$	−69.7854	+	31.0705i	−4.43138	+	1.97298i
$249$	11.0184	+	12.2372i	0.698262	+	0.775498i
$250$	−20.8974	+	23.2089i	−1.32167	+	1.46786i
$251$	18.9971	−	13.8022i	1.19909	−	0.871187i	0.204891	−	0.978785i	$-0.434316\pi$
$251$	18.9971	−	13.8022i	1.19909	−	0.871187i	0.994195	+	0.107598i	$0.0343159\pi$
$252$	−5.14289	−	13.6118i	−0.323972	−	0.857462i
$253$	−9.74984	−	17.0678i	−0.612967	−	1.07304i
$254$	−19.7977	−	34.2907i	−1.24222	−	2.15159i
$255$	−0.00267666	−	0.0254667i	−0.000167619	−	0.00159479i
$256$	−47.7088	−	10.1408i	−2.98180	−	0.633802i
$257$	17.3576	−	3.68947i	1.08274	−	0.230143i	0.368204	−	0.929745i	$-0.379973\pi$
$257$	17.3576	−	3.68947i	1.08274	−	0.230143i	0.714532	+	0.699603i	$0.246640\pi$
$258$	1.66046	+	1.20639i	0.103376	+	0.0751067i
$259$	−5.36712	+	1.40783i	−0.333497	+	0.0874781i
$260$	9.79792	−	30.1549i	0.607641	−	1.87013i
$261$	−2.54916	+	2.83113i	−0.157789	+	0.175242i
$262$	0.0773248	+	0.735697i	0.00477714	+	0.0454515i
$263$	−6.31971	+	10.9461i	−0.389690	+	0.674963i	−0.992408	−	0.122991i	$-0.960751\pi$
$263$	−6.31971	+	10.9461i	−0.389690	+	0.674963i	0.602718	+	0.797955i	$0.294085\pi$
$264$	−3.17743	−	31.6282i	−0.195557	−	1.94658i
$265$	−0.0126098			−0.000774612
$266$	33.9019	−	17.0493i	2.07866	−	1.04536i
$267$	1.40676	+	4.32957i	0.0860926	+	0.264966i
$268$	−52.9011	+	11.2445i	−3.23145	+	0.686866i
$269$	12.1306	−	5.40087i	0.739613	−	0.329297i	−0.00211485	−	0.999998i	$-0.500673\pi$
$269$	12.1306	−	5.40087i	0.739613	−	0.329297i	0.741728	+	0.670701i	$0.234007\pi$
$270$	−3.59599	+	1.60104i	−0.218845	+	0.0974361i
$271$	−12.9564	+	2.75398i	−0.787048	+	0.167292i	−0.583867	−	0.811849i	$-0.698461\pi$
$271$	−12.9564	+	2.75398i	−0.787048	+	0.167292i	−0.203180	+	0.979141i	$0.565128\pi$
$272$	0.0839419	+	0.258347i	0.00508973	+	0.0156646i
$273$	−9.48055	+	4.76778i	−0.573789	+	0.288559i
$274$	37.8663			2.28759
$275$	9.50893	+	2.06689i	0.573410	+	0.124638i
$276$	16.2974	−	28.2279i	0.980986	−	1.69912i
$277$	−0.871150	−	8.28844i	−0.0523423	−	0.498004i	−0.989017	−	0.147803i	$-0.952780\pi$
$277$	−0.871150	−	8.28844i	−0.0523423	−	0.498004i	0.936675	−	0.350201i	$-0.113887\pi$
$278$	−11.8358	+	13.1450i	−0.709862	+	0.788382i
$279$	2.46297	−	7.58023i	0.147454	−	0.453816i
$280$	35.2553	−	9.24766i	2.10690	−	0.552654i
$281$	3.98530	+	2.89549i	0.237743	+	0.172730i	0.700277	−	0.713871i	$-0.253060\pi$
$281$	3.98530	+	2.89549i	0.237743	+	0.172730i	−0.462534	+	0.886601i	$0.653060\pi$
$282$	4.79884	−	1.02003i	0.285767	−	0.0607417i
$283$	30.1075	+	6.39954i	1.78970	+	0.380413i	0.978808	−	0.204779i	$-0.0656477\pi$
$283$	30.1075	+	6.39954i	1.78970	+	0.380413i	0.810894	+	0.585192i	$0.198981\pi$
$284$	2.71961	+	25.8754i	0.161379	+	1.53542i
$285$	−3.76398	−	6.51940i	−0.222959	−	0.386176i
$286$	−35.6687	+	7.41053i	−2.10913	+	0.438194i
$287$	−0.882917	−	2.33683i	−0.0521170	−	0.137939i
$288$	18.2742	−	13.2770i	1.07682	−	0.782354i
$289$	−11.3750	+	12.6332i	−0.669118	+	0.743131i
$290$	−10.0343	−	11.1442i	−0.589232	−	0.654408i
$291$	−3.23103	+	1.43855i	−0.189406	+	0.0843290i
$292$	1.93985	−	18.4564i	0.113521	−	1.08008i
$293$	−2.45439	+	7.55385i	−0.143387	+	0.441300i	−0.996800	−	0.0799351i	$-0.974529\pi$
$293$	−2.45439	+	7.55385i	−0.143387	+	0.441300i	0.853413	+	0.521236i	$0.174529\pi$
$294$	−16.4997	−	9.75951i	−0.962280	−	0.569186i
$295$	−3.24395	+	2.35686i	−0.188870	+	0.137222i
$296$	−10.0501	−	17.4073i	−0.584150	−	1.01178i
$297$	2.67422	+	1.96177i	0.155174	+	0.113833i
$298$	12.0886	−	20.9381i	0.700275	−	1.21291i
$299$	−21.7160	−	9.66858i	−1.25587	−	0.559149i
$300$	4.98637	+	15.3465i	0.287888	+	0.886029i
$301$	1.98068	−	0.0933337i	0.114164	−	0.00537966i
$302$	30.0766	+	21.8519i	1.73071	+	1.25744i
$303$	−1.46594	+	13.9475i	−0.0842161	+	0.801263i
$304$	53.4350	+	59.3455i	3.06471	+	3.40370i
$305$	17.5983	+	3.74064i	1.00768	+	0.214188i
$306$	−0.0445704	−	0.0198440i	−0.00254792	−	0.00113441i
$307$	−8.09186			−0.461827			−0.230913	−	0.972974i	$-0.574171\pi$
$307$	−8.09186			−0.461827			−0.230913	+	0.972974i	$0.574171\pi$
$308$	−33.7866	−	34.4600i	−1.92517	−	1.96354i
$309$	−1.24745			−0.0709651
$310$	28.6612	+	12.7608i	1.62785	+	0.724764i
$311$	−15.3787	−	3.26884i	−0.872046	−	0.185359i	−0.249911	−	0.968269i	$-0.580401\pi$
$311$	−15.3787	−	3.26884i	−0.872046	−	0.185359i	−0.622135	+	0.782910i	$0.713735\pi$
$312$	−25.7225	−	28.5678i	−1.45625	−	1.61733i
$313$	−2.95446	+	28.1098i	−0.166996	+	1.58886i	0.514794	+	0.857314i	$0.327868\pi$
$313$	−2.95446	+	28.1098i	−0.166996	+	1.58886i	−0.681790	+	0.731548i	$0.738798\pi$
$314$	10.8522	+	7.88461i	0.612427	+	0.444954i
$315$	−1.74432	+	3.37925i	−0.0982813	+	0.190399i
$316$	−24.9608	−	76.8215i	−1.40416	−	4.32155i
$317$	8.65201	+	3.85212i	0.485945	+	0.216357i	0.635060	−	0.772463i	$-0.280976\pi$
$317$	8.65201	+	3.85212i	0.485945	+	0.216357i	−0.149114	+	0.988820i	$0.547642\pi$
$318$	−0.0120126	+	0.0208063i	−0.000673630	+	0.00116676i
$319$	−3.95965	+	11.9987i	−0.221698	+	0.671800i
$320$	22.5406	+	39.0414i	1.26006	+	2.18248i
$321$	−6.06916	+	4.40950i	−0.338747	+	0.246114i
$322$	−6.49381	−	42.4477i	−0.361886	−	2.36552i
$323$	0.0288328	−	0.0887384i	0.00160430	−	0.00493753i
$324$	−0.574879	+	5.46961i	−0.0319377	+	0.303867i
$325$	10.7506	−	4.78649i	0.596338	−	0.265507i
$326$	31.0035	+	34.4329i	1.71713	+	1.90706i
$327$	0.791568	−	0.879126i	0.0437738	−	0.0486158i
$328$	7.32101	−	5.31903i	0.404235	−	0.293694i
$329$	3.00222	−	3.66772i	0.165518	−	0.202208i
$330$	−8.78013	+	9.66170i	−0.483330	+	0.531859i
$331$	−3.06434	−	5.30759i	−0.168431	−	0.291732i	0.769437	−	0.638722i	$-0.220537\pi$
$331$	−3.06434	−	5.30759i	−0.168431	−	0.291732i	−0.937868	+	0.346991i	$0.887203\pi$
$332$	9.46637	+	90.0665i	0.519535	+	4.94304i
$333$	2.05138	+	0.436034i	0.112415	+	0.0238945i
$334$	17.6788	−	3.75775i	0.967341	−	0.205615i
$335$	11.4351	+	8.30812i	0.624768	+	0.453921i
$336$	10.6465	−	38.9113i	0.580812	−	2.12279i
$337$	−3.71490	+	11.4333i	−0.202364	+	0.622812i	0.797448	+	0.603388i	$0.206183\pi$
$337$	−3.71490	+	11.4333i	−0.202364	+	0.622812i	−0.999811	+	0.0194234i	$0.993817\pi$
$338$	−5.65771	+	6.28352i	−0.307739	+	0.341778i
$339$	0.254177	+	2.41834i	0.0138050	+	0.131346i
$340$	0.0704159	−	0.121964i	0.00381884	−	0.00661442i
$341$	−2.64237	−	26.3022i	−0.143092	−	1.42434i
$342$	−14.3428			−0.775571
$343$	−18.3358	+	2.60751i	−0.990039	+	0.140792i
$344$	2.21967	+	6.83143i	0.119676	+	0.368326i
$345$	−8.33249	+	1.77113i	−0.448606	+	0.0953542i
$346$	−65.2042	+	29.0308i	−3.50540	+	1.56070i
$347$	−28.3079	+	12.6035i	−1.51965	+	0.676590i	−0.985635	−	0.168887i	$-0.945983\pi$
$347$	−28.3079	+	12.6035i	−1.51965	+	0.676590i	−0.534011	+	0.845478i	$0.679316\pi$
$348$	−20.4943	+	4.35619i	−1.09861	+	0.233516i
$349$	2.47954	+	7.63125i	0.132727	+	0.408491i	0.995230	−	0.0975613i	$-0.0311042\pi$
$349$	2.47954	+	7.63125i	0.132727	+	0.408491i	−0.862503	+	0.506053i	$0.831104\pi$
$350$	17.7676	+	11.6720i	0.949716	+	0.623897i
$351$	4.01092			0.214087
$352$	37.7559	−	64.7068i	2.01239	−	3.44888i
$353$	−5.97705	+	10.3526i	−0.318126	+	0.551011i	−0.980097	−	0.198519i	$-0.936387\pi$
$353$	−5.97705	+	10.3526i	−0.318126	+	0.551011i	0.661971	+	0.749530i	$0.269720\pi$
$354$	0.798561	+	7.59780i	0.0424431	+	0.403819i
$355$	4.54995	−	5.05323i	0.241486	−	0.268198i
$356$	−7.73684	+	23.8115i	−0.410051	+	1.26201i
$357$	−0.0455925	+	0.0119592i	−0.00241301	+	0.000632947i
$358$	20.4288	+	14.8424i	1.07970	+	0.784446i
$359$	20.9303	−	4.44887i	1.10466	−	0.234802i	0.380736	−	0.924684i	$-0.375671\pi$
$359$	20.9303	−	4.44887i	1.10466	−	0.234802i	0.723922	+	0.689881i	$0.242337\pi$
$360$	−13.4750	−	2.86420i	−0.710194	−	0.150956i
$361$	−0.881157	−	8.38365i	−0.0463767	−	0.441245i
$362$	12.8355	+	22.2317i	0.674618	+	1.16847i
$363$	10.7382	+	2.38578i	0.563607	+	0.125221i
$364$	−57.5952	−	9.43375i	−3.01881	−	0.494463i
$365$	−3.92387	+	2.85086i	−0.205385	+	0.149221i
$366$	22.9369	−	25.4741i	1.19893	−	1.33155i
$367$	0.306109	+	0.339969i	0.0159788	+	0.0177462i	0.751081	−	0.660210i	$-0.229533\pi$
$367$	0.306109	+	0.339969i	0.0159788	+	0.0177462i	−0.735102	+	0.677956i	$0.762866\pi$
$368$	82.5541	−	36.7554i	4.30343	−	1.91601i
$369$	−0.0986937	+	0.939007i	−0.00513779	+	0.0488828i
$370$	−2.55101	+	7.85120i	−0.132621	+	0.408165i
$371$	0.00351005	+	0.0229439i	0.000182233	+	0.00119119i
$372$	35.4630	−	25.7654i	1.83867	−	1.33587i
$373$	0.731599	+	1.26717i	0.0378808	+	0.0656114i	0.884344	−	0.466835i	$-0.154606\pi$
$373$	0.731599	+	1.26717i	0.0378808	+	0.0656114i	−0.846463	+	0.532447i	$0.821273\pi$
$374$	−0.161811		0.000743324i	−0.00836705		3.84364e-5i
$375$	5.70200	−	9.87616i	0.294450	−	0.510003i
$376$	15.6855	+	6.98363i	0.808917	+	0.360153i
$377$	4.72186	+	14.5324i	0.243188	+	0.748455i
$378$	3.91412	+	6.09736i	0.201321	+	0.313614i
$379$	−13.8141	−	10.0365i	−0.709582	−	0.515542i	0.173457	−	0.984842i	$-0.444506\pi$
$379$	−13.8141	−	10.0365i	−0.709582	−	0.515542i	−0.883039	+	0.469300i	$0.844506\pi$
$380$	4.32766	−	41.1750i	0.222004	−	2.11223i
$381$	9.67461	+	10.7447i	0.495645	+	0.550470i
$382$	15.5650	+	3.30845i	0.796377	+	0.169275i
$383$	18.6500	+	8.30353i	0.952972	+	0.424290i	0.823515	−	0.567295i	$-0.192010\pi$
$383$	18.6500	+	8.30353i	0.952972	+	0.424290i	0.129457	+	0.991585i	$0.458677\pi$
$384$	40.7156			2.07776
$385$	−0.784340	+	12.5884i	−0.0399737	+	0.641562i
$386$	−38.0294			−1.93564
$387$	−0.684663	−	0.304832i	−0.0348034	−	0.0154955i
$388$	−19.0264	−	4.04419i	−0.965920	−	0.205313i
$389$	−19.0742	−	21.1840i	−0.967100	−	1.07407i	−0.997219	−	0.0745271i	$-0.976255\pi$
$389$	−19.0742	−	21.1840i	−0.967100	−	1.07407i	0.0301189	−	0.999546i	$-0.490411\pi$
$390$	−1.65032	+	15.7017i	−0.0835670	+	0.795087i
$391$	−0.0854194	−	0.0620608i	−0.00431984	−	0.00313855i
$392$	−26.6401	−	61.5740i	−1.34553	−	3.10996i
$393$	−0.0834726	−	0.256902i	−0.00421063	−	0.0129590i
$394$	8.14097	+	3.62459i	0.410136	+	0.182604i
$395$	−10.5553	+	18.2823i	−0.531094	+	0.919881i
$396$	5.55690	+	17.3735i	0.279245	+	0.873052i
$397$	−0.959179	−	1.66135i	−0.0481398	−	0.0833806i	0.840951	−	0.541111i	$-0.181996\pi$
$397$	−0.959179	−	1.66135i	−0.0481398	−	0.0833806i	−0.889091	+	0.457730i	$0.848663\pi$
$398$	31.7568	−	23.0727i	1.59182	−	1.15653i
$399$	−10.8145	+	8.66342i	−0.541404	+	0.433713i
$400$	−13.8244	+	42.5470i	−0.691218	+	2.12735i
$401$	−2.57859	+	24.5336i	−0.128769	+	1.22515i	0.719086	+	0.694921i	$0.244561\pi$
$401$	−2.57859	+	24.5336i	−0.128769	+	1.22515i	−0.847854	+	0.530229i	$0.822106\pi$
$402$	24.6021	−	10.9536i	1.22704	−	0.546313i
$403$	−21.3910	−	23.7571i	−1.06556	−	1.18343i
$404$	−51.6101	+	57.3188i	−2.56770	+	2.85172i
$405$	1.16285	−	0.844859i	0.0577824	−	0.0419814i
$406$	−17.4841	+	21.3598i	−0.867720	+	1.06007i
$407$	6.81023	−	1.41489i	0.337570	−	0.0701336i
$408$	−0.0853733	−	0.147871i	−0.00422661	−	0.00732070i
$409$	−1.03040	−	9.80361i	−0.0509500	−	0.484757i	−0.990009	−	0.141002i	$-0.954968\pi$
$409$	−1.03040	−	9.80361i	−0.0509500	−	0.484757i	0.939059	−	0.343755i	$-0.111699\pi$
$410$	−3.63536	−	0.772720i	−0.179538	−	0.0381619i
$411$	−13.5249	+	2.87481i	−0.667134	+	0.141804i
$412$	−5.55039	−	4.03259i	−0.273448	−	0.198672i
$413$	5.19138	+	5.24641i	0.255451	+	0.258159i
$414$	−5.01546	+	15.4360i	−0.246496	+	0.758638i
$415$	15.8374	−	17.5892i	0.777426	−	0.863419i
$416$	−9.47021	−	90.1031i	−0.464315	−	4.41767i
$417$	3.22948	−	5.59362i	0.158148	−	0.273921i
$418$	−43.5456	+	19.1485i	−2.12988	+	0.936585i
$419$	39.4218			1.92588			0.962940	−	0.269716i	$-0.0869298\pi$
$419$	39.4218			1.92588			0.962940	+	0.269716i	$0.0869298\pi$
$420$	−18.6851	+	9.39679i	−0.911742	+	0.458516i
$421$	8.44162	+	25.9806i	0.411419	+	1.26622i	0.915415	+	0.402512i	$0.131863\pi$
$421$	8.44162	+	25.9806i	0.411419	+	1.26622i	−0.503995	+	0.863707i	$0.668137\pi$
$422$	28.5922	−	6.07745i	1.39184	−	0.295846i
$423$	−1.63659	+	0.728656i	−0.0795736	+	0.0354285i
$424$	−0.0768124	+	0.0341991i	−0.00373034	+	0.00166085i
$425$	0.0511279	−	0.0108676i	0.00248007	−	0.000527154i
$426$	−4.00346	−	12.3214i	−0.193968	−	0.596974i
$427$	1.90756	−	33.0620i	0.0923132	−	1.59998i
$428$	−41.2584			−1.99430
$429$	12.1774	−	5.35482i	0.587929	−	0.258533i
$430$	1.47504	−	2.55485i	0.0711330	−	0.123206i
$431$	−3.88939	−	37.0051i	−0.187345	−	1.78247i	−0.535004	−	0.844850i	$-0.679690\pi$
$431$	−3.88939	−	37.0051i	−0.187345	−	1.78247i	0.347658	−	0.937621i	$-0.386977\pi$
$432$	−10.2027	+	11.3312i	−0.490876	+	0.545173i
$433$	3.69850	−	11.3828i	0.177739	−	0.547023i	−0.822009	−	0.569474i	$-0.807147\pi$
$433$	3.69850	−	11.3828i	0.177739	−	0.547023i	0.999748	+	0.0224507i	$0.00714688\pi$
$434$	15.2406	−	55.7021i	0.731571	−	2.67379i
$435$	4.43005	+	3.21862i	0.212405	+	0.154321i
$436$	6.36391	−	1.35269i	0.304776	−	0.0647821i
$437$	−30.3614	−	6.45351i	−1.45238	−	0.308713i
$438$	0.965937	+	9.19028i	0.0461543	+	0.439128i
$439$	7.21107	+	12.4899i	0.344165	+	0.596112i	0.985202	−	0.171398i	$-0.0548285\pi$
$439$	7.21107	+	12.4899i	0.344165	+	0.596112i	−0.641036	+	0.767511i	$0.721495\pi$
$440$	−44.7347	+	9.29407i	−2.13264	+	0.443077i
$441$	6.63422	+	2.23320i	0.315915	+	0.106343i
$442$	−0.158314	+	0.115022i	−0.00753021	+	0.00547102i
$443$	−8.13939	+	9.03971i	−0.386714	+	0.429490i	−0.904799	−	0.425840i	$-0.859979\pi$
$443$	−8.13939	+	9.03971i	−0.386714	+	0.429490i	0.518084	+	0.855330i	$0.326645\pi$
$444$	7.71782	+	8.57150i	0.366271	+	0.406786i
$445$	5.97770	−	2.66145i	0.283370	−	0.126165i
$446$	1.10112	−	10.4765i	0.0521396	−	0.496075i
$447$	−2.72814	+	8.39634i	−0.129036	+	0.397133i
$448$	64.7628	−	51.8809i	3.05975	−	2.45114i
$449$	8.01581	−	5.82382i	0.378289	−	0.274843i	−0.382351	−	0.924017i	$-0.624885\pi$
$449$	8.01581	−	5.82382i	0.378289	−	0.274843i	0.760640	+	0.649174i	$0.224885\pi$
$450$	−4.01747	−	6.95847i	−0.189386	−	0.328025i
$451$	0.953992	+	2.98264i	0.0449217	+	0.140447i
$452$	−6.68674	+	11.5818i	−0.314518	+	0.544761i
$453$	−12.4016	−	5.52156i	−0.582679	−	0.259425i
$454$	1.32773	+	4.08632i	0.0623133	+	0.191780i
$455$	8.23988	+	12.8360i	0.386291	+	0.601759i
$456$	−40.6095	−	29.5046i	−1.90172	−	1.38168i
$457$	−1.74018	+	16.5567i	−0.0814021	+	0.774490i	0.875331	+	0.483524i	$0.160643\pi$
$457$	−1.74018	+	16.5567i	−0.0814021	+	0.774490i	−0.956733	+	0.290966i	$0.906023\pi$
$458$	−45.9948	−	51.0825i	−2.14920	−	2.38693i
$459$	0.0174260	+	0.00370401i	0.000813376	+	0.000172888i
$460$	−42.7999	−	19.0557i	−1.99556	−	0.888479i
$461$	−34.2505			−1.59520			−0.797602	−	0.603184i	$-0.793899\pi$
$461$	−34.2505			−1.59520			−0.797602	+	0.603184i	$0.793899\pi$
$462$	20.0238	+	13.2863i	0.931593	+	0.618136i
$463$	−33.2499			−1.54526			−0.772628	−	0.634859i	$-0.781058\pi$
$463$	−33.2499			−1.54526			−0.772628	+	0.634859i	$0.781058\pi$
$464$	−53.0664	−	23.6267i	−2.46354	−	1.09684i
$465$	−11.2059	−	2.38188i	−0.519660	−	0.110457i
$466$	3.20185	+	3.55602i	0.148323	+	0.164729i
$467$	0.323445	−	3.07737i	0.0149673	−	0.142404i	−0.984486	−	0.175462i	$-0.943858\pi$
$467$	0.323445	−	3.07737i	0.0149673	−	0.142404i	0.999453	+	0.0330583i	$0.0105247\pi$
$468$	17.8461	+	12.9660i	0.824938	+	0.599352i
$469$	11.9338	−	23.1193i	0.551053	−	1.06755i
$470$	−2.17911	−	6.70662i	−0.100515	−	0.309353i
$471$	−4.47475	−	1.99229i	−0.206186	−	0.0917998i
$472$	−13.3684	+	23.1547i	−0.615330	+	1.06578i
$473$	−2.48564	−	0.0114185i	−0.114290	−	0.000525022i
$474$	20.1107	+	34.8328i	0.923716	+	1.59992i
$475$	12.4317	−	9.03213i	0.570404	−	0.414423i
$476$	−0.241519	−	0.0941743i	−0.0110700	−	0.00431647i
$477$	0.00271097	−	0.00834350i	0.000124127	−	0.000382023i
$478$	−5.86567	+	55.8082i	−0.268290	+	2.55261i
$479$	28.4157	−	12.6515i	1.29835	−	0.578062i	0.363000	−	0.931789i	$-0.381752\pi$
$479$	28.4157	−	12.6515i	1.29835	−	0.578062i	0.935349	+	0.353727i	$0.115086\pi$
$480$	−21.7249	−	24.1279i	−0.991600	−	1.10128i
$481$	5.62855	−	6.25114i	0.256640	−	0.285027i
$482$	−48.1080	+	34.9525i	−2.19126	+	1.59204i
$483$	5.54205	+	14.6682i	0.252172	+	0.667428i
$484$	40.0657	+	45.3281i	1.82117	+	2.06037i
$485$	2.54182	+	4.40257i	0.115418	+	0.199910i
$486$	−0.286258	−	2.72356i	−0.0129849	−	0.123543i
$487$	35.5733	+	7.56135i	1.61198	+	0.342637i	0.923792	−	0.382894i	$-0.125072\pi$
$487$	35.5733	+	7.56135i	1.61198	+	0.342637i	0.688189	+	0.725531i	$0.258406\pi$
$488$	117.345	−	24.9425i	5.31196	−	1.12909i
$489$	−13.6878	−	9.94479i	−0.618985	−	0.449719i
$490$	−11.4721	+	25.0524i	−0.518256	+	1.13175i
$491$	−8.69187	+	26.7508i	−0.392259	+	1.20725i	0.538818	+	0.842422i	$0.318871\pi$
$491$	−8.69187	+	26.7508i	−0.392259	+	1.20725i	−0.931076	+	0.364825i	$0.881129\pi$
$492$	−3.47462	+	3.85896i	−0.156648	+	0.173975i
$493$	0.00709437	+	0.0674985i	0.000319515	+	0.00303998i
$494$	−28.7640	+	49.8207i	−1.29415	+	2.24154i
$495$	2.40253	−	4.11751i	0.107986	−	0.185068i
$496$	121.529			5.45680
$497$	−10.4610	−	6.87217i	−0.469242	−	0.308259i
$498$	−13.9352	−	42.8881i	−0.624450	−	1.92186i
$499$	30.8093	−	6.54871i	1.37921	−	0.293161i	0.542156	−	0.840278i	$-0.317608\pi$
$499$	30.8093	−	6.54871i	1.37921	−	0.293161i	0.837056	+	0.547117i	$0.184275\pi$
$500$	57.2967	−	25.5101i	2.56239	−	1.14085i
$501$	−6.02914	+	2.68435i	−0.269362	+	0.119928i
$502$	−62.9009	+	13.3700i	−2.80741	+	0.596732i
$503$	5.36309	+	16.5059i	0.239128	+	0.735961i	0.996547	+	0.0830314i	$0.0264602\pi$
$503$	5.36309	+	16.5059i	0.239128	+	0.735961i	−0.757419	+	0.652929i	$0.773540\pi$
$504$	−1.46061	+	25.3155i	−0.0650609	+	1.12764i
$505$	20.1580			0.897019
$506$	5.38079	+	53.5604i	0.239205	+	2.38105i
$507$	1.54375	−	2.67385i	0.0685603	−	0.118750i
$508$	8.31188	+	79.0822i	0.368780	+	3.50871i
$509$	3.90300	−	4.33472i	0.172997	−	0.192133i	−0.650411	−	0.759583i	$-0.725403\pi$
$509$	3.90300	−	4.33472i	0.172997	−	0.192133i	0.823408	+	0.567450i	$0.192070\pi$
$510$	−0.0216703	+	0.0666942i	−0.000959576	+	0.00295327i
$511$	6.27947	+	6.34604i	0.277788	+	0.280732i
$512$	42.1833	+	30.6480i	1.86426	+	1.35446i
$513$	5.12290	−	1.08891i	0.226182	−	0.0480764i
$514$	−47.5349	−	10.1038i	−2.09667	−	0.445662i
$515$	0.187423	+	1.78321i	0.00825886	+	0.0785778i
$516$	−2.06091	−	3.56960i	−0.0907265	−	0.157143i
$517$	−3.99597	+	4.39718i	−0.175742	+	0.193388i
$518$	14.9956	+	2.45619i	0.658870	+	0.107919i
$519$	21.0853	−	15.3194i	0.925542	−	0.672446i
$520$	−36.9725	+	41.0622i	−1.62135	+	1.80069i
$521$	−8.56557	−	9.51303i	−0.375264	−	0.416773i	0.525697	−	0.850672i	$-0.323804\pi$
$521$	−8.56557	−	9.51303i	−0.375264	−	0.416773i	−0.900962	+	0.433898i	$0.857138\pi$
$522$	9.53102	−	4.24348i	0.417161	−	0.185732i
$523$	−0.868347	+	8.26177i	−0.0379702	+	0.361262i	0.958996	+	0.283421i	$0.0914693\pi$
$523$	−0.868347	+	8.26177i	−0.0379702	+	0.361262i	−0.996966	+	0.0778410i	$0.975197\pi$
$524$	0.459077	−	1.41289i	0.0200549	−	0.0617226i
$525$	−7.23227	−	2.82005i	−0.315642	−	0.123077i
$526$	28.0032	−	20.3455i	1.22100	−	0.887107i
$527$	−0.0709969	−	0.122970i	−0.00309267	−	0.00535667i
$528$	−15.8480	+	48.0233i	−0.689695	+	2.08995i
$529$	−6.06226	+	10.5001i	−0.263577	+	0.456528i
$530$	0.0315472	+	0.0140457i	0.00137032	+	0.000610107i
$531$	−0.862051	−	2.65312i	−0.0374098	−	0.115136i
$532$	−76.1239	+	3.58711i	−3.30039	+	0.155521i
$533$	3.06377	+	2.22596i	0.132707	+	0.0964171i
$534$	1.30316	−	12.3987i	0.0563931	−	0.536544i
$535$	7.21518	+	8.01327i	0.311939	+	0.346444i
$536$	92.1896	+	19.5955i	3.98198	+	0.846396i
$537$	−8.42351	−	3.75039i	−0.363501	−	0.161841i
$538$	−36.3642			−1.56777
$539$	23.1233	−	2.07696i	0.995990	−	0.0894609i
$540$	7.90510			0.340181
$541$	8.01613	+	3.56901i	0.344640	+	0.153444i	0.571755	−	0.820424i	$-0.306263\pi$
$541$	8.01613	+	3.56901i	0.344640	+	0.153444i	−0.227115	+	0.973868i	$0.572929\pi$
$542$	35.4820	+	7.54194i	1.52408	+	0.323954i
$543$	−6.27234	−	6.96614i	−0.269172	−	0.298946i
$544$	0.0420638	−	0.400211i	0.00180347	−	0.0171589i
$545$	−1.37563	−	0.999451i	−0.0589253	−	0.0428118i
$546$	29.0292	−	1.36791i	1.24233	−	0.0585413i
$547$	−2.97000	−	9.14073i	−0.126988	−	0.390829i	0.867270	−	0.497838i	$-0.165873\pi$
$547$	−2.97000	−	9.14073i	−0.126988	−	0.390829i	−0.994258	+	0.107009i	$0.965873\pi$
$548$	−69.4708	−	30.9304i	−2.96764	−	1.32128i
$549$	−6.25852	+	10.8401i	−0.267107	+	0.462643i
$550$	−21.4872	−	15.7627i	−0.916219	−	0.672124i
$551$	9.97626	+	17.2794i	0.425003	+	0.736127i
$552$	−45.9538	+	33.3874i	−1.95592	+	1.42106i
$553$	36.2034	+	14.1166i	1.53952	+	0.600301i
$554$	−7.05283	+	21.7064i	−0.299646	+	0.922216i
$555$	0.315095	−	2.99793i	0.0133750	−	0.127255i
$556$	32.4515	−	14.4483i	1.37625	−	0.612746i
$557$	−1.57042	−	1.74413i	−0.0665410	−	0.0739012i	0.708955	−	0.705254i	$-0.249167\pi$
$557$	−1.57042	−	1.74413i	−0.0665410	−	0.0739012i	−0.775496	+	0.631352i	$0.782500\pi$
$558$	−14.6053	+	16.2208i	−0.618291	+	0.686682i
$559$	−2.43192	+	1.76689i	−0.102859	+	0.0747315i
$560$	−57.2227	−	9.37273i	−2.41810	−	0.396070i
$561$	0.0578514	−	0.0120192i	0.00244249	−	0.000507451i
$562$	−6.74522	−	11.6831i	−0.284530	−	0.492821i
$563$	−0.124140	−	1.18111i	−0.00523188	−	0.0497780i	0.991594	−	0.129385i	$-0.0413002\pi$
$563$	−0.124140	−	1.18111i	−0.00523188	−	0.0497780i	−0.996826	+	0.0796067i	$0.974634\pi$
$564$	−9.63731	−	2.04847i	−0.405804	−	0.0862563i
$565$	3.41879	−	0.726686i	0.143829	−	0.0305719i
$566$	−68.1947	−	49.5463i	−2.86644	−	2.08259i
$567$	−1.86094	−	1.88067i	−0.0781521	−	0.0789806i
$568$	14.0111	−	43.1217i	0.587892	−	1.80935i
$569$	−7.09928	+	7.88455i	−0.297617	+	0.330538i	−0.873343	−	0.487105i	$-0.838053\pi$
$569$	−7.09928	+	7.88455i	−0.297617	+	0.330538i	0.575726	+	0.817643i	$0.304720\pi$
$570$	2.15494	+	20.5029i	0.0902604	+	0.858770i
$571$	10.0298	−	17.3721i	0.419733	−	0.726998i	−0.576180	−	0.817323i	$-0.695457\pi$
$571$	10.0298	−	17.3721i	0.419733	−	0.726998i	0.995912	+	0.0903246i	$0.0287905\pi$
$572$	71.4921	+	15.5397i	2.98924	+	0.649748i
$573$	−5.81062			−0.242742
$574$	−0.394053	+	6.82975i	−0.0164474	+	0.285068i
$575$	−5.37338	−	16.5376i	−0.224085	−	0.689664i
$576$	−30.6785	+	6.52091i	−1.27827	+	0.271705i
$577$	−21.7764	+	9.69546i	−0.906561	+	0.403627i	−0.806418	−	0.591346i	$-0.798597\pi$
$577$	−21.7764	+	9.69546i	−0.906561	+	0.403627i	−0.100143	+	0.994973i	$0.531930\pi$
$578$	42.5299	−	18.9355i	1.76901	−	0.787614i
$579$	13.5831	−	2.88719i	0.564496	−	0.119987i
$580$	9.30627	+	28.6418i	0.386422	+	1.18928i
$581$	−36.4126	−	23.9205i	−1.51065	−	0.992390i
$582$	9.68575			0.401487
$583$	−0.00290844	−	0.0289506i	−0.000120455	−	0.00119901i
$584$	−16.1704	+	28.0079i	−0.669135	+	1.15898i
$585$	−0.602621	−	5.73355i	−0.0249153	−	0.237053i
$586$	14.5544	−	16.1644i	0.601239	−	0.667743i
$587$	−11.3360	+	34.8886i	−0.467887	+	1.44001i	0.387429	+	0.921900i	$0.373363\pi$
$587$	−11.3360	+	34.8886i	−0.467887	+	1.44001i	−0.855316	+	0.518107i	$0.826637\pi$
$588$	22.2990	+	31.3826i	0.919594	+	1.29420i
$589$	−33.7711	−	24.5361i	−1.39151	−	1.01099i
$590$	10.7410	−	2.28306i	0.442199	−	0.0939922i
$591$	−3.18293	−	0.676553i	−0.130928	−	0.0278297i
$592$	3.34256	+	31.8023i	0.137378	+	1.30707i
$593$	−21.5573	−	37.3383i	−0.885252	−	1.53330i	−0.845424	−	0.534095i	$-0.820652\pi$
$593$	−21.5573	−	37.3383i	−0.885252	−	1.53330i	−0.0398279	−	0.999207i	$-0.512681\pi$
$594$	−4.50521	−	7.88671i	−0.184851	−	0.323596i
$595$	0.0239455	+	0.0633770i	0.000981670	+	0.00259820i
$596$	−39.2811	+	28.5394i	−1.60902	+	1.16902i
$597$	−9.59106	+	10.6520i	−0.392536	+	0.435955i
$598$	43.5596	+	48.3778i	1.78128	+	1.97831i
$599$	13.4109	−	5.97094i	0.547956	−	0.243966i	−0.114036	−	0.993477i	$-0.536378\pi$
$599$	13.4109	−	5.97094i	0.547956	−	0.243966i	0.661992	+	0.749511i	$0.269711\pi$
$600$	2.93936	−	27.9662i	0.119999	−	1.14171i
$601$	3.62607	−	11.1599i	0.147910	−	0.455221i	−0.849463	−	0.527647i	$-0.823074\pi$
$601$	3.62607	−	11.1599i	0.147910	−	0.455221i	0.997374	+	0.0724263i	$0.0230742\pi$
$602$	−5.05923	−	1.97273i	−0.206199	−	0.0804023i
$603$	−7.95566	+	5.78013i	−0.323980	+	0.235385i
$604$	−37.3302	−	64.6578i	−1.51894	−	2.63089i
$605$	1.79709	−	15.7085i	0.0730621	−	0.638641i
$606$	19.2033	−	33.2610i	0.780079	−	1.35114i
$607$	28.4663	+	12.6740i	1.15541	+	0.514423i	0.892789	−	0.450475i	$-0.148746\pi$
$607$	28.4663	+	12.6740i	1.15541	+	0.514423i	0.262624	+	0.964898i	$0.415412\pi$
$608$	−36.5574	−	112.512i	−1.48260	−	4.56296i
$609$	4.62325	−	8.95657i	0.187343	−	0.362938i
$610$	−39.8609	−	28.9607i	−1.61392	−	1.17258i
$611$	−0.751083	+	7.14608i	−0.0303856	+	0.289099i
$612$	0.0655611	+	0.0728130i	0.00265015	+	0.00294329i
$613$	19.8130	+	4.21139i	0.800240	+	0.170096i	0.589841	−	0.807519i	$-0.299190\pi$
$613$	19.8130	+	4.21139i	0.800240	+	0.170096i	0.210399	+	0.977616i	$0.432524\pi$
$614$	20.2443	+	9.01332i	0.816992	+	0.363748i
$615$	1.35713			0.0547246
$616$	29.3632	+	78.8091i	1.18308	+	3.17531i
$617$	4.76539			0.191847			0.0959237	−	0.995389i	$-0.469420\pi$
$617$	4.76539			0.191847			0.0959237	+	0.995389i	$0.469420\pi$
$618$	3.12088	+	1.38951i	0.125540	+	0.0558941i
$619$	−12.5187	−	2.66092i	−0.503167	−	0.106951i	−0.0506666	−	0.998716i	$-0.516135\pi$
$619$	−12.5187	−	2.66092i	−0.503167	−	0.106951i	−0.452500	+	0.891764i	$0.649468\pi$
$620$	−42.1594	−	46.8227i	−1.69316	−	1.88045i
$621$	0.619498	−	5.89413i	0.0248596	−	0.236523i
$622$	34.8334	+	25.3079i	1.39669	+	1.01476i
$623$	−6.50654	−	10.1358i	−0.260679	−	0.406082i
$624$	18.8986	+	58.1639i	0.756549	+	2.32842i
$625$	−1.57281	−	0.700261i	−0.0629125	−	0.0280105i
$626$	38.7023	−	67.0344i	1.54686	−	2.67923i
$627$	14.0996	−	10.1454i	0.563085	−	0.405167i
$628$	−13.4695	−	23.3298i	−0.537491	−	0.930961i
$629$	0.0302268	−	0.0219611i	0.00120522	−	0.000875646i
$630$	8.12801	−	6.51128i	0.323828	−	0.259415i
$631$	−10.3044	+	31.7136i	−0.410211	+	1.26250i	0.506254	+	0.862384i	$0.331030\pi$
$631$	−10.3044	+	31.7136i	−0.410211	+	1.26250i	−0.916465	+	0.400115i	$0.868970\pi$
$632$	−14.7139	+	139.993i	−0.585288	+	5.56864i
$633$	−9.75101	+	4.34143i	−0.387568	+	0.172556i
$634$	−17.3549	−	19.2745i	−0.689249	−	0.765489i
$635$	13.9059	−	15.4440i	0.551838	−	0.612878i
$636$	0.0390339	−	0.0283598i	0.00154779	−	0.00112454i
$637$	21.0618	−	18.5657i	0.834500	−	0.735602i
$638$	23.2714	−	25.6079i	0.921322	−	1.01383i
$639$	2.36538	+	4.09695i	0.0935729	+	0.162073i
$640$	−6.11732	−	58.2024i	−0.241808	−	2.30065i
$641$	−13.7701	−	2.92693i	−0.543887	−	0.115607i	−0.0722285	−	0.997388i	$-0.523011\pi$
$641$	−13.7701	−	2.92693i	−0.543887	−	0.115607i	−0.471658	+	0.881781i	$0.656344\pi$
$642$	20.0955	−	4.27142i	0.793105	−	0.168580i
$643$	−13.7476	−	9.98824i	−0.542154	−	0.393898i	0.282730	−	0.959199i	$-0.408760\pi$
$643$	−13.7476	−	9.98824i	−0.542154	−	0.393898i	−0.824884	+	0.565302i	$0.808760\pi$
$644$	−22.7588	+	83.1802i	−0.896823	+	3.27776i
$645$	−0.332885	+	1.02452i	−0.0131073	+	0.0403403i
$646$	−0.170978	+	0.189890i	−0.00672702	+	0.00747111i
$647$	5.09247	+	48.4516i	0.200206	+	1.90483i	0.386424	+	0.922321i	$0.373710\pi$
$647$	5.09247	+	48.4516i	0.200206	+	1.90483i	−0.186218	+	0.982508i	$0.559623\pi$
$648$	4.79213	−	8.30022i	0.188253	−	0.326063i
$649$	−6.15931	−	6.90412i	−0.241774	−	0.271010i
$650$	−32.2275			−1.26407
$651$	−1.21465	+	21.0525i	−0.0476060	+	0.825112i
$652$	−28.7542	−	88.4963i	−1.12610	−	3.46578i
$653$	−3.11609	+	0.662345i	−0.121942	+	0.0259196i	−0.268478	−	0.963286i	$-0.586521\pi$
$653$	−3.11609	+	0.662345i	−0.121942	+	0.0259196i	0.146536	+	0.989205i	$0.453187\pi$
$654$	−2.95958	+	1.31769i	−0.115729	+	0.0515258i
$655$	−0.354696	+	0.157921i	−0.0138591	+	0.00617049i
$656$	−14.0819	+	2.99321i	−0.549807	+	0.116865i
$657$	−1.04273	−	3.20921i	−0.0406809	−	0.125203i
$658$	−11.5963	+	5.83182i	−0.452073	+	0.227348i
$659$	38.6928			1.50726			0.753629	−	0.657300i	$-0.228302\pi$
$659$	38.6928			1.50726			0.753629	+	0.657300i	$0.228302\pi$
$660$	24.0003	−	10.5538i	0.934210	−	0.410805i
$661$	−0.462772	+	0.801545i	−0.0179997	+	0.0311765i	−0.874885	−	0.484331i	$-0.839063\pi$
$661$	−0.462772	+	0.801545i	−0.0179997	+	0.0311765i	0.856885	+	0.515507i	$0.172396\pi$
$662$	1.75438	+	16.6918i	0.0681860	+	0.648747i
$663$	0.0478133	−	0.0531020i	0.00185691	−	0.00206231i
$664$	48.7695	−	150.097i	1.89262	−	5.82489i
$665$	14.0091	+	14.1576i	0.543248	+	0.549007i
$666$	−4.64646	−	3.37585i	−0.180047	−	0.130812i
$667$	22.0849	−	4.69429i	0.855131	−	0.181764i
$668$	−35.5036	−	7.54651i	−1.37367	−	0.291983i
$669$	0.402079	+	3.82553i	0.0155453	+	0.147904i
$670$	−19.3543	−	33.5226i	−0.747721	−	1.29509i
$671$	−4.52904	+	41.2665i	−0.174842	+	1.59308i
$672$	−37.8542	+	46.2454i	−1.46026	+	1.78395i
$673$	2.19696	−	1.59618i	0.0846866	−	0.0615284i	−0.544636	−	0.838672i	$-0.683332\pi$
$673$	2.19696	−	1.59618i	0.0846866	−	0.0615284i	0.629323	+	0.777144i	$0.283332\pi$
$674$	22.0292	−	24.4659i	0.848534	−	0.942393i
$675$	1.96323	+	2.18039i	0.0755647	+	0.0839231i
$676$	15.5124	−	6.90656i	0.596630	−	0.265637i
$677$	1.22577	−	11.6624i	0.0471101	−	0.448223i	−0.945387	−	0.325951i	$-0.894315\pi$
$677$	1.22577	−	11.6624i	0.0471101	−	0.448223i	0.992497	−	0.122271i	$-0.0390179\pi$
$678$	2.05782	−	6.33333i	0.0790302	−	0.243230i
$679$	7.30308	−	5.85043i	0.280267	−	0.224519i
$680$	−0.198552	+	0.144257i	−0.00761414	+	0.00553200i
$681$	−0.784464	−	1.35873i	−0.0300607	−	0.0520667i
$682$	−22.6866	+	68.7462i	−0.868717	+	2.63243i
$683$	−9.95032	+	17.2345i	−0.380738	+	0.659458i	−0.991168	−	0.132612i	$-0.957663\pi$
$683$	−9.95032	+	17.2345i	−0.380738	+	0.659458i	0.610430	+	0.792070i	$0.290997\pi$
$684$	26.3138	+	11.7157i	1.00613	+	0.447960i
$685$	6.14154	+	18.9017i	0.234656	+	0.722198i
$686$	48.7770	+	13.9003i	1.86231	+	0.530715i
$687$	20.3064	+	14.7535i	0.774737	+	0.562880i
$688$	1.19450	−	11.3649i	0.0455397	−	0.433281i
$689$	−0.0235449	−	0.0261493i	−0.000896990	−	0.000996208i
$690$	22.8191	+	4.85034i	0.868707	+	0.184649i
$691$	−21.9864	−	9.78896i	−0.836400	−	0.372389i	−0.0565841	−	0.998398i	$-0.518021\pi$
$691$	−21.9864	−	9.78896i	−0.836400	−	0.372389i	−0.779816	+	0.626008i	$0.784688\pi$
$692$	143.339			5.44893
$693$	−8.16071	−	3.22534i	−0.310000	−	0.122520i
$694$	84.8594			3.22122
$695$	−8.48121	−	3.77608i	−0.321711	−	0.143235i
$696$	35.7149	+	7.59143i	1.35377	+	0.287753i
$697$	0.0112554	+	0.0125003i	0.000426327	+	0.000473484i
$698$	2.29692	−	21.8538i	0.0869399	−	0.827178i
$699$	−1.41359	−	1.02704i	−0.0534671	−	0.0388461i
$700$	−23.0629	−	35.9270i	−0.871694	−	1.35791i
$701$	2.54032	+	7.81830i	0.0959465	+	0.295293i	0.987499	−	0.157624i	$-0.0503834\pi$
$701$	2.54032	+	7.81830i	0.0959465	+	0.295293i	−0.891553	+	0.452917i	$0.850383\pi$
$702$	−10.0345	−	4.46767i	−0.378729	−	0.168621i
$703$	5.49191	−	9.51226i	0.207131	−	0.358762i
$704$	−84.4357	+	60.7554i	−3.18229	+	2.28981i
$705$	1.28749	+	2.23000i	0.0484897	+	0.0839867i
$706$	26.4848	−	19.2424i	0.996770	−	0.724196i
$707$	−5.61117	−	36.6781i	−0.211030	−	1.37942i
$708$	4.74106	−	14.5915i	0.178180	−	0.548381i
$709$	1.51172	−	14.3831i	0.0567740	−	0.540168i	−0.928759	−	0.370684i	$-0.879123\pi$
$709$	1.51172	−	14.3831i	0.0567740	−	0.540168i	0.985533	−	0.169484i	$-0.0542101\pi$
$710$	−17.0118	+	7.57412i	−0.638440	+	0.284252i
$711$	−9.82755	−	10.9146i	−0.368562	−	0.409330i
$712$	29.1950	−	32.4243i	1.09413	−	1.21515i
$713$	−38.2154	+	27.7651i	−1.43118	+	1.03981i
$714$	0.127385	+	0.0208648i	0.00476725	+	0.000780846i
$715$	−9.48423	−	16.6028i	−0.354690	−	0.620911i
$716$	−25.3557	−	43.9173i	−0.947585	−	1.64127i
$717$	−2.14188	−	20.3786i	−0.0799899	−	0.761053i
$718$	−57.3190	−	12.1835i	−2.13912	−	0.454685i
$719$	−22.8200	+	4.85055i	−0.851044	+	0.180895i	−0.612729	−	0.790293i	$-0.709928\pi$
$719$	−22.8200	+	4.85055i	−0.851044	+	0.180895i	−0.238315	+	0.971188i	$0.576595\pi$
$720$	17.7307	+	12.8821i	0.660784	+	0.480088i
$721$	3.19245	−	0.837398i	0.118893	−	0.0311863i
$722$	−7.13386	+	21.9558i	−0.265495	+	0.817109i
$723$	14.5294	−	16.1365i	0.540354	−	0.600124i
$724$	−5.38884	−	51.2714i	−0.200275	−	1.90549i
$725$	−5.58877	+	9.68003i	−0.207562	+	0.359507i
$726$	−24.2073	−	17.9297i	−0.898417	−	0.665435i
$727$	−26.9555			−0.999723			−0.499862	−	0.866105i	$-0.666616\pi$
$727$	−26.9555			−0.999723			−0.499862	+	0.866105i	$0.666616\pi$
$728$	85.0056	+	55.8427i	3.15052	+	2.06967i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	12.9922	−	2.76159i	0.480864	−	0.102211i
$731$	−0.0121975	+	0.00543067i	−0.000451141	+	0.000200861i
$732$	−62.8889	+	27.9999i	−2.32444	+	1.03491i
$733$	6.60364	−	1.40365i	0.243911	−	0.0518449i	−0.0843339	−	0.996438i	$-0.526876\pi$
$733$	6.60364	−	1.40365i	0.243911	−	0.0518449i	0.328245	+	0.944593i	$0.393543\pi$
$734$	−0.387143	−	1.19150i	−0.0142897	−	0.0439792i
$735$	2.19557	−	9.81904i	0.0809849	−	0.362181i
$736$	−133.871			−4.93455
$737$	−16.4370	+	28.1700i	−0.605464	+	1.03766i
$738$	1.29285	−	2.23928i	0.0475904	−	0.0824290i
$739$	−1.93506	−	18.4109i	−0.0711825	−	0.677256i	−0.970687	−	0.240346i	$-0.922739\pi$
$739$	−1.93506	−	18.4109i	−0.0711825	−	0.677256i	0.899505	−	0.436911i	$-0.143927\pi$
$740$	11.0933	−	12.3203i	0.407797	−	0.452904i
$741$	6.49140	−	19.9785i	0.238467	−	0.733927i
$742$	0.0167752	−	0.0613109i	0.000615837	−	0.00225080i
$743$	−13.0542	−	9.48445i	−0.478913	−	0.347951i	0.321992	−	0.946743i	$-0.395648\pi$
$743$	−13.0542	−	9.48445i	−0.478913	−	0.347951i	−0.800905	+	0.598792i	$0.795648\pi$
$744$	−74.7204	+	15.8823i	−2.73938	+	0.582274i
$745$	12.4123	+	2.63832i	0.454753	+	0.0966607i
$746$	−0.418852	−	3.98511i	−0.0153353	−	0.145905i
$747$	8.23336	+	14.2606i	0.301243	+	0.521768i
$748$	0.296257	+	0.133536i	0.0108322	+	0.00488256i
$749$	12.5720	−	15.3588i	0.459371	−	0.561199i
$750$	−25.2661	+	18.3569i	−0.922587	+	0.670299i
$751$	26.3550	−	29.2702i	0.961707	−	1.06808i	−0.0359284	−	0.999354i	$-0.511439\pi$
$751$	26.3550	−	29.2702i	0.961707	−	1.06808i	0.997635	−	0.0687294i	$-0.0218945\pi$
$752$	−18.2778	−	20.2995i	−0.666521	−	0.740247i
$753$	21.4516	−	9.55087i	0.781740	−	0.348053i
$754$	4.37409	−	41.6167i	0.159295	−	1.51559i
$755$	−6.02970	+	18.5575i	−0.219443	+	0.675377i
$756$	−2.20046	−	14.3836i	−0.0800300	−	0.523126i
$757$	18.9361	−	13.7579i	0.688244	−	0.500039i	−0.187838	−	0.982200i	$-0.560148\pi$
$757$	18.9361	−	13.7579i	0.688244	−	0.500039i	0.876082	+	0.482161i	$0.160148\pi$
$758$	23.3807	+	40.4966i	0.849226	+	1.47090i
$759$	−5.98819	−	18.7219i	−0.217357	−	0.679564i
$760$	−36.0749	+	62.4836i	−1.30858	+	2.26652i
$761$	−12.6794	−	5.64525i	−0.459630	−	0.204640i	0.163842	−	0.986487i	$-0.447611\pi$
$761$	−12.6794	−	5.64525i	−0.459630	−	0.204640i	−0.623471	+	0.781846i	$0.714278\pi$
$762$	−12.2357	−	37.6575i	−0.443252	−	1.36419i
$763$	−1.43562	+	2.78120i	−0.0519728	+	0.100686i
$764$	−25.8537	−	18.7838i	−0.935354	−	0.679574i
$765$	0.00267666	−	0.0254667i	9.67749e−5	−	0.000920751i
$766$	−37.4096	−	41.5476i	−1.35166	−	1.50118i
$767$	−10.9446	−	2.32634i	−0.395186	−	0.0839994i
$768$	−44.5579	−	19.8385i	−1.60784	−	0.715859i
$769$	−24.4963			−0.883359			−0.441680	−	0.897173i	$-0.645617\pi$
$769$	−24.4963			−0.883359			−0.441680	+	0.897173i	$0.645617\pi$
$770$	15.9841	−	30.6200i	0.576028	−	1.10347i
$771$	17.7454			0.639083
$772$	69.7699	+	31.0636i	2.51107	+	1.11800i
$773$	−4.43543	−	0.942779i	−0.159531	−	0.0339094i	0.127454	−	0.991845i	$-0.459320\pi$
$773$	−4.43543	−	0.942779i	−0.159531	−	0.0339094i	−0.286985	+	0.957935i	$0.592653\pi$
$774$	1.37335	+	1.52526i	0.0493640	+	0.0548243i
$775$	2.44439	−	23.2568i	0.0878051	−	0.835409i
$776$	27.4237	+	19.9245i	0.984455	+	0.715248i
$777$	−5.54254	+	0.261176i	−0.198838	+	0.00936963i
$778$	24.1235	+	74.2446i	0.864870	+	2.66180i
$779$	4.51748	+	2.01131i	0.161856	+	0.0720627i
$780$	15.8534	−	27.4588i	0.567642	−	0.983184i
$781$	12.6511	+	9.28065i	0.452692	+	0.332088i
$782$	0.144575	+	0.250410i	0.00516998	+	0.00895466i
$783$	−3.08208	+	2.23926i	−0.110145	+	0.0800247i
$784$	−1.12552	+	106.728i	−0.0401972	+	3.81170i
$785$	−2.17564	+	6.69592i	−0.0776518	+	0.238988i
$786$	−0.0773248	+	0.735697i	−0.00275809	+	0.0262414i
$787$	34.0456	−	15.1581i	1.21359	−	0.540327i	0.302747	−	0.953071i	$-0.402096\pi$
$787$	34.0456	−	15.1581i	1.21359	−	0.540327i	0.910847	+	0.412744i	$0.135430\pi$
$788$	−11.9750	−	13.2996i	−0.426592	−	0.473778i
$789$	−8.45743	+	9.39292i	−0.301092	+	0.334397i
$790$	46.7714	−	33.9814i	1.66405	−	1.20900i
$791$	−2.27388	−	6.01832i	−0.0808499	−	0.213987i
$792$	3.46788	−	31.5977i	0.123226	−	1.12277i
$793$	25.1024	+	43.4787i	0.891413	+	1.54397i
$794$	0.549146	+	5.22477i	0.0194884	+	0.185420i
$795$	−0.0123342	−	0.00262172i	−0.000437450	−	9.29828e-5i
$796$	−77.1085	+	16.3899i	−2.73304	+	0.580925i
$797$	−12.4725	−	9.06178i	−0.441798	−	0.320985i	0.344551	−	0.938768i	$-0.388031\pi$
$797$	−12.4725	−	9.06178i	−0.441798	−	0.320985i	−0.786349	+	0.617783i	$0.788031\pi$
$798$	36.7058	−	9.62814i	1.29937	−	0.340833i
$799$	−0.00986245	+	0.0303535i	−0.000348909	+	0.00107383i
$800$	44.3457	−	49.2509i	1.56786	−	1.74128i
$801$	0.475854	+	4.52745i	0.0168135	+	0.159969i
$802$	33.7785	−	58.5061i	1.19276	−	2.06592i
$803$	−7.45028	−	8.35120i	−0.262915	−	0.294708i
$804$	−54.0830			−1.90736
$805$	20.1354	−	10.1261i	0.709679	−	0.356898i
$806$	27.0536	+	83.2625i	0.952924	+	2.93280i
$807$	12.9884	−	2.76077i	0.457213	−	0.0971836i
$808$	122.792	−	54.6706i	4.31982	−	1.92331i
$809$	19.1888	−	8.54342i	0.674643	−	0.300370i	−0.0406719	−	0.999173i	$-0.512950\pi$
$809$	19.1888	−	8.54342i	0.674643	−	0.300370i	0.715315	+	0.698802i	$0.246283\pi$
$810$	−3.85028	+	0.818403i	−0.135285	+	0.0287558i
$811$	−6.79762	−	20.9209i	−0.238697	−	0.734633i	−0.996609	−	0.0822773i	$-0.973781\pi$
$811$	−6.79762	−	20.9209i	−0.238697	−	0.734633i	0.757913	−	0.652356i	$-0.226219\pi$
$812$	49.5242	−	24.9058i	1.73796	−	0.874022i
$813$	−13.2459			−0.464554
$814$	−18.6139	−	4.04596i	−0.652415	−	0.141811i
$815$	−12.1594	+	21.0607i	−0.425925	+	0.737724i
$816$	0.0283943	+	0.270154i	0.000993999	+	0.00945727i
$817$	−2.62645	+	2.91697i	−0.0918879	+	0.102052i
$818$	−8.34213	+	25.6744i	−0.291676	+	0.897686i
$819$	−10.2646	+	2.69248i	−0.358676	+	0.0940828i
$820$	6.03837	+	4.38713i	0.210869	+	0.153205i
$821$	29.9102	−	6.35761i	1.04387	−	0.221882i	0.346097	−	0.938199i	$-0.387507\pi$
$821$	29.9102	−	6.35761i	1.04387	−	0.221882i	0.697776	+	0.716316i	$0.254173\pi$
$822$	37.0388	+	7.87285i	1.29188	+	0.274597i
$823$	3.48638	+	33.1706i	0.121527	+	1.15626i	0.869987	+	0.493075i	$0.164127\pi$
$823$	3.48638	+	33.1706i	0.121527	+	1.15626i	−0.748459	+	0.663181i	$0.769206\pi$
$824$	5.97795	+	10.3541i	0.208252	+	0.360703i
$825$	8.87141	+	3.99874i	0.308863	+	0.139218i
$826$	−7.14396	−	18.9080i	−0.248570	−	0.657895i
$827$	−39.3348	+	28.5784i	−1.36781	+	0.993769i	−0.369901	+	0.929071i	$0.620609\pi$
$827$	−39.3348	+	28.5784i	−1.36781	+	0.993769i	−0.997905	+	0.0646985i	$0.979391\pi$
$828$	21.8101	−	24.2226i	0.757954	−	0.841794i
$829$	−23.3012	−	25.8786i	−0.809285	−	0.898803i	0.187221	−	0.982318i	$-0.440052\pi$
$829$	−23.3012	−	25.8786i	−0.809285	−	0.898803i	−0.996506	+	0.0835153i	$0.973385\pi$
$830$	−59.2141	+	26.3638i	−2.05535	+	0.915102i
$831$	0.871150	−	8.28844i	0.0302198	−	0.287523i
$832$	−38.8737	+	119.641i	−1.34770	+	4.14780i
$833$	0.108651	−	0.0612113i	0.00376454	−	0.00212084i
$834$	−14.3101	+	10.3969i	−0.495519	+	0.360015i
$835$	4.74308	+	8.21526i	0.164141	+	0.284301i
$836$	95.5312	+	0.438849i	3.30402	+	0.0151779i
$837$	3.98516	−	6.90250i	0.137747	−	0.238585i
$838$	−98.6256	−	43.9109i	−3.40696	−	1.51688i
$839$	−11.7043	−	36.0220i	−0.404076	−	1.24362i	−0.921664	−	0.387988i	$-0.873170\pi$
$839$	−11.7043	−	36.0220i	−0.404076	−	1.24362i	0.517588	−	0.855630i	$-0.326830\pi$
$840$	36.4075	−	1.71560i	1.25618	−	0.0591938i
$841$	11.7198	+	8.51495i	0.404132	+	0.293619i
$842$	7.81990	−	74.4014i	0.269492	−	2.56404i
$843$	3.29620	+	3.66081i	0.113527	+	0.126085i
$844$	−57.4204	−	12.2051i	−1.97649	−	0.420116i
$845$	−4.05417	−	1.80503i	−0.139468	−	0.0620950i
$846$	4.90605			0.168674
$847$	−29.0824	+	1.10274i	−0.999282	+	0.0378906i
$848$	0.133766			0.00459354
$849$	28.1190	+	12.5194i	0.965042	+	0.429664i
$850$	−0.140017	−	0.0297615i	−0.00480254	−	0.00102081i
$851$	−8.31683	−	9.23677i	−0.285097	−	0.316632i
$852$	−2.71961	+	25.8754i	−0.0931724	+	0.886476i
$853$	−40.2256	−	29.2256i	−1.37730	−	1.00067i	−0.997127	−	0.0757497i	$-0.975865\pi$
$853$	−40.2256	−	29.2256i	−1.37730	−	1.00067i	−0.380171	−	0.924916i	$-0.624135\pi$
$854$	−41.5992	+	80.5898i	−1.42350	+	2.75773i
$855$	−2.32627	−	7.15951i	−0.0795566	−	0.244850i
$856$	65.6840	+	29.2444i	2.24503	+	0.999553i
$857$	−21.2192	+	36.7527i	−0.724833	+	1.25545i	0.234210	+	0.972186i	$0.424750\pi$
$857$	−21.2192	+	36.7527i	−0.724833	+	1.25545i	−0.959043	+	0.283261i	$0.908584\pi$
$858$	−36.4300	−	0.167351i	−1.24370	−	0.00571328i
$859$	17.7102	+	30.6749i	0.604263	+	1.04661i	0.992168	+	0.124914i	$0.0398656\pi$
$859$	17.7102	+	30.6749i	0.604263	+	1.04661i	−0.387905	+	0.921699i	$0.626801\pi$
$860$	−4.79305	+	3.48235i	−0.163442	+	0.118747i
$861$	−0.377769	−	2.46934i	−0.0128743	−	0.0841547i
$862$	−31.4885	+	96.9117i	−1.07250	+	3.30083i
$863$	2.71477	−	25.8293i	0.0924117	−	0.879239i	−0.845875	−	0.533381i	$-0.820921\pi$
$863$	2.71477	−	25.8293i	0.0924117	−	0.879239i	0.938287	−	0.345858i	$-0.112412\pi$
$864$	20.6353	−	9.18743i	0.702028	−	0.312563i
$865$	−25.0668	−	27.8395i	−0.852296	−	0.946570i
$866$	−21.9320	+	24.3579i	−0.745278	+	0.827716i
$867$	−13.7530	+	9.99216i	−0.467077	+	0.339352i
$868$	−73.4601	+	89.7440i	−2.49340	+	3.04611i
$869$	−44.4086	−	20.0169i	−1.50646	−	0.679028i
$870$	−7.49798	−	12.9869i	−0.254205	−	0.440297i
$871$	4.12285	+	39.2263i	0.139697	+	1.32913i
$872$	−11.0902	−	2.35730i	−0.375563	−	0.0798283i
$873$	−3.45951	+	0.735342i	−0.117087	+	0.0248875i
$874$	68.7698	+	49.9642i	2.32617	+	1.69006i
$875$	−7.96269	+	29.1025i	−0.269188	+	0.983844i
$876$	5.73477	−	17.6498i	0.193760	−	0.596331i
$877$	−14.4227	+	16.0180i	−0.487019	+	0.540889i	−0.935697	−	0.352804i	$-0.885228\pi$
$877$	−14.4227	+	16.0180i	−0.487019	+	0.540889i	0.448678	+	0.893693i	$0.351895\pi$
$878$	−4.12845	−	39.2796i	−0.139328	−	1.32562i
$879$	−3.97129	+	6.87848i	−0.133948	+	0.232005i
$880$	71.0297	+	15.4392i	2.39441	+	0.520456i
$881$	55.3341			1.86425			0.932126	−	0.362133i	$-0.117952\pi$
$881$	55.3341			1.86425			0.932126	+	0.362133i	$0.117952\pi$
$882$	−14.1100	−	12.9767i	−0.475108	−	0.436949i
$883$	9.26599	+	28.5178i	0.311826	+	0.959700i	0.977041	+	0.213049i	$0.0683395\pi$
$883$	9.26599	+	28.5178i	0.311826	+	0.959700i	−0.665216	+	0.746651i	$0.731661\pi$
$884$	0.384401	−	0.0817069i	0.0129288	−	0.00274810i
$885$	−3.66308	+	1.63091i	−0.123133	+	0.0548223i
$886$	30.4323	−	13.5493i	1.02239	−	0.455198i
$887$	4.33957	−	0.922404i	0.145709	−	0.0309713i	−0.134480	−	0.990916i	$-0.542936\pi$
$887$	4.33957	−	0.922404i	0.145709	−	0.0309713i	0.280188	+	0.959945i	$0.409603\pi$
$888$	−6.21130	−	19.1164i	−0.208438	−	0.641505i
$889$	−31.9718	−	21.0032i	−1.07230	−	0.704426i
$890$	−17.9196			−0.600665
$891$	2.20791	+	2.47490i	0.0739677	+	0.0829123i
$892$	−10.5777	+	18.3210i	−0.354166	+	0.613434i
$893$	0.980743	+	9.33115i	0.0328193	+	0.312255i
$894$	16.1777	−	17.9672i	0.541064	−	0.600913i
$895$	−4.09553	+	12.6048i	−0.136899	+	0.421330i
$896$	−104.198	+	27.3319i	−3.48102	+	0.913093i
$897$	−19.2312	−	13.9723i	−0.642112	−	0.466522i
$898$	−26.5410	+	5.64146i	−0.885684	+	0.188258i
$899$	29.7007	+	6.31307i	0.990573	+	0.210553i
$900$	1.68670	+	16.0478i	0.0562232	+	0.534928i
$901$	−7.81458e−5	0	0.000135352i	−2.60341e−6	0	4.50925e-6i
$902$	0.935584	−	8.52460i	0.0311515	−	0.283838i
$903$	1.95680	+	0.320512i	0.0651183	+	0.0106660i
$904$	18.8547	−	13.6987i	0.627097	−	0.455613i
$905$	−9.01561	+	10.0128i	−0.299689	+	0.332838i
$906$	24.8761	+	27.6277i	0.826453	+	0.917869i
$907$	−27.5783	+	12.2787i	−0.915724	+	0.407706i	−0.809826	−	0.586671i	$-0.800438\pi$
$907$	−27.5783	+	12.2787i	−0.915724	+	0.407706i	−0.105898	+	0.994377i	$0.533772\pi$
$908$	0.901944	−	8.58142i	0.0299321	−	0.284785i
$909$	−4.33375	+	13.3379i	−0.143742	+	0.442391i
$910$	−6.31690	−	41.2913i	−0.209403	−	1.36879i
$911$	31.6179	−	22.9717i	1.04755	−	0.761087i	0.0758021	−	0.997123i	$-0.475848\pi$
$911$	31.6179	−	22.9717i	1.04755	−	0.761087i	0.971744	+	0.236036i	$0.0758483\pi$
$912$	39.9286	+	69.1584i	1.32217	+	2.29006i
$913$	44.0356	+	32.3039i	1.45737	+	1.06910i
$914$	22.7957	−	39.4833i	0.754014	−	1.30599i
$915$	16.4360	+	7.31779i	0.543358	+	0.241919i
$916$	42.6579	+	131.288i	1.40946	+	4.33786i
$917$	0.386076	+	0.601423i	0.0127493	+	0.0198608i
$918$	−0.0394706	−	0.0286771i	−0.00130273	−	0.000946485i
$919$	−2.98394	+	28.3903i	−0.0984311	+	0.936509i	0.828174	+	0.560472i	$0.189380\pi$
$919$	−2.98394	+	28.3903i	−0.0984311	+	0.936509i	−0.926605	+	0.376037i	$0.877286\pi$
$920$	54.6311	+	60.6740i	1.80114	+	2.00036i
$921$	−7.91504	−	1.68239i	−0.260809	−	0.0554367i
$922$	85.6880	+	38.1508i	2.82199	+	1.25643i
$923$	18.9747			0.624560
$924$	−25.8837	−	40.7316i	−0.851511	−	1.33997i
$925$	6.15321			0.202316
$926$	83.1848	+	37.0363i	2.73362	+	1.21709i
$927$	−1.22019	−	0.259360i	−0.0400764	−	0.00851849i
$928$	57.5808	+	63.9500i	1.89018	+	2.09926i
$929$	−4.87410	+	46.3740i	−0.159914	+	1.52148i	0.560627	+	0.828069i	$0.310560\pi$
$929$	−4.87410	+	46.3740i	−0.159914	+	1.52148i	−0.720541	+	0.693412i	$0.756106\pi$
$930$	25.3818	+	18.4409i	0.832301	+	0.604702i
$931$	21.8606	−	29.4308i	0.716453	−	0.964557i
$932$	−2.96956	−	9.13936i	−0.0972711	−	0.299370i
$933$	−14.3630	−	6.39482i	−0.470224	−	0.209357i
$934$	−4.23701	+	7.33871i	−0.138639	+	0.240130i
$935$	−0.0258731	−	0.0808918i	−0.000846142	−	0.00264545i
$936$	−19.2209	−	33.2915i	−0.628254	−	1.08817i
$937$	4.18597	−	3.04128i	0.136750	−	0.0993544i	−0.517307	−	0.855800i	$-0.673066\pi$
$937$	4.18597	−	3.04128i	0.136750	−	0.0993544i	0.654057	+	0.756445i	$0.273066\pi$
$938$	−55.6080	+	44.5471i	−1.81567	+	1.45451i
$939$	−8.73426	+	26.8813i	−0.285032	+	0.877238i
$940$	−1.48030	+	14.0842i	−0.0482822	+	0.459375i
$941$	−33.6954	+	15.0022i	−1.09844	+	0.489057i	−0.874244	−	0.485487i	$-0.838642\pi$
$941$	−33.6954	+	15.0022i	−1.09844	+	0.489057i	−0.224196	+	0.974544i	$0.571976\pi$
$942$	8.97579	+	9.96862i	0.292447	+	0.324795i
$943$	3.74430	−	4.15847i	0.121931	−	0.135418i
$944$	34.4121	−	25.0019i	1.12002	−	0.813741i
$945$	−2.40879	+	2.94274i	−0.0783579	+	0.0957275i
$946$	6.20587	+	2.79726i	0.201770	+	0.0909468i
$947$	−12.7623	−	22.1050i	−0.414719	−	0.718315i	0.580679	−	0.814132i	$-0.302787\pi$
$947$	−12.7623	−	22.1050i	−0.414719	−	0.718315i	−0.995399	+	0.0958170i	$0.969454\pi$
$948$	−8.44328	−	80.3324i	−0.274225	−	2.60908i
$949$	−13.2385	−	2.81394i	−0.429741	−	0.0913443i
$950$	−41.1622	+	8.74930i	−1.33548	+	0.283865i
$951$	7.66204	+	5.56680i	0.248459	+	0.180516i
$952$	0.317749	+	0.321118i	0.0102983	+	0.0104075i
$953$	−3.88343	+	11.9520i	−0.125797	+	0.387163i	−0.994045	−	0.108967i	$-0.965246\pi$
$953$	−3.88343	+	11.9520i	−0.125797	+	0.387163i	0.868249	+	0.496129i	$0.165246\pi$
$954$	−0.0160759	+	0.0178541i	−0.000520477	+	0.000578049i
$955$	0.873017	+	8.30620i	0.0282502	+	0.268782i
$956$	56.3472	−	97.5962i	1.82240	−	3.15649i
$957$	−6.36780	+	10.9133i	−0.205842	+	0.352776i
$958$	−85.1828			−2.75213
$959$	32.6828	−	16.4362i	1.05538	−	0.530753i
$960$	13.9308	+	42.8747i	0.449616	+	1.38377i
$961$	−31.8153	+	6.76255i	−1.02630	+	0.218147i
$962$	−21.0445	+	9.36962i	−0.678502	+	0.302089i
$963$	−6.85332	+	3.05129i	−0.220845	+	0.0983266i
$964$	116.811	−	24.8289i	3.76223	−	0.799686i
$965$	−6.16799	−	18.9831i	−0.198555	−	0.611088i
$966$	2.47346	−	42.8702i	0.0795822	−	1.37933i
$967$	32.6669			1.05050			0.525249	−	0.850949i	$-0.323972\pi$
$967$	32.6669			1.05050			0.525249	+	0.850949i	$0.323972\pi$
$968$	−31.6561	−	100.562i	−1.01747	−	3.23219i
$969$	0.0466525	−	0.0808045i	0.00149869	−	0.00259582i
$970$	−1.45524	−	13.8456i	−0.0467248	−	0.444557i
$971$	9.04759	−	10.0484i	0.290351	−	0.322467i	−0.580268	−	0.814426i	$-0.697052\pi$
$971$	9.04759	−	10.0484i	0.290351	−	0.322467i	0.870619	+	0.491958i	$0.163719\pi$
$972$	−1.69951	+	5.23056i	−0.0545119	+	0.167770i
$973$	−4.50988	+	16.4830i	−0.144580	+	0.528419i
$974$	−80.5751	−	58.5413i	−2.58179	−	1.87578i
$975$	11.5109	−	2.44671i	0.368643	−	0.0783575i
$976$	−186.685	−	39.6811i	−5.97563	−	1.27016i
$977$	−0.856992	−	8.15373i	−0.0274176	−	0.260861i	−0.999641	−	0.0268049i	$-0.991467\pi$
$977$	−0.856992	−	8.15373i	−0.0274176	−	0.260861i	0.972223	−	0.234056i	$-0.0752000\pi$
$978$	23.1670	+	40.1264i	0.740799	+	1.28310i
$979$	7.48913	+	13.1103i	0.239354	+	0.419006i
$980$	41.5106	−	36.5911i	1.32601	−	1.16886i
$981$	0.957051	−	0.695338i	0.0305563	−	0.0222004i
$982$	51.5424	−	57.2436i	1.64478	−	1.82672i
$983$	−11.8771	−	13.1909i	−0.378822	−	0.420724i	0.523339	−	0.852125i	$-0.324686\pi$
$983$	−11.8771	−	13.1909i	−0.378822	−	0.420724i	−0.902160	+	0.431401i	$0.858020\pi$
$984$	8.26692	−	3.68067i	0.263540	−	0.117335i
$985$	−0.488903	+	4.65160i	−0.0155777	+	0.148212i
$986$	0.0574361	−	0.176770i	0.00182914	−	0.00562951i
$987$	3.69918	−	2.96338i	0.117746	−	0.0943253i
$988$	93.4664	−	67.9073i	2.97356	−	2.16042i
$989$	2.22086	+	3.84665i	0.0706194	+	0.122316i
$990$	−10.5970	+	7.62508i	−0.336796	+	0.242341i
$991$	−22.0581	+	38.2057i	−0.700698	+	1.21365i	0.267523	+	0.963551i	$0.413795\pi$
$991$	−22.0581	+	38.2057i	−0.700698	+	1.21365i	−0.968222	+	0.250094i	$0.919539\pi$
$992$	−164.470	−	73.2268i	−5.22193	−	2.32495i
$993$	−1.89387	−	5.82872i	−0.0601000	−	0.184969i
$994$	18.5168	+	28.8451i	0.587316	+	0.914912i
$995$	16.6678	+	12.1099i	0.528405	+	0.383909i
$996$	−9.46637	+	90.0665i	−0.299953	+	2.85387i
$997$	−17.0668	−	18.9546i	−0.540510	−	0.600298i	0.409579	−	0.912275i	$-0.365676\pi$
$997$	−17.0668	−	18.9546i	−0.540510	−	0.600298i	−0.950090	+	0.311977i	$0.899009\pi$
$998$	−84.3732	−	17.9341i	−2.67079	−	0.567693i
$999$	1.91589	+	0.853011i	0.0606162	+	0.0269881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.y.a.25.1	yes	64
3.2	odd	2		693.2.by.d.487.8		64
7.2	even	3	inner	231.2.y.a.58.8	yes	64
11.4	even	5	inner	231.2.y.a.4.8	✓	64
21.2	odd	6		693.2.by.d.289.1		64
33.26	odd	10		693.2.by.d.235.1		64
77.37	even	15	inner	231.2.y.a.37.1	yes	64
231.191	odd	30		693.2.by.d.37.8		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.a.4.8	✓	64	11.4	even	5	inner
231.2.y.a.25.1	yes	64	1.1	even	1	trivial
231.2.y.a.37.1	yes	64	77.37	even	15	inner
231.2.y.a.58.8	yes	64	7.2	even	3	inner
693.2.by.d.37.8		64	231.191	odd	30
693.2.by.d.235.1		64	33.26	odd	10
693.2.by.d.289.1		64	21.2	odd	6
693.2.by.d.487.8		64	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.50180 - 1.11387i) q^{2} +(0.978148 + 0.207912i) q^{3} +(3.68004 + 4.08710i) q^{4} +(0.150245 - 1.42949i) q^{5} +(-2.21555 - 1.60969i) q^{6} +(-2.64282 + 0.124535i) q^{7} +(-2.96170 - 9.11518i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\)	\(q+(-2.50180 - 1.11387i) q^{2} +(0.978148 + 0.207912i) q^{3} +(3.68004 + 4.08710i) q^{4} +(0.150245 - 1.42949i) q^{5} +(-2.21555 - 1.60969i) q^{6} +(-2.64282 + 0.124535i) q^{7} +(-2.96170 - 9.11518i) q^{8} +(0.913545 + 0.406737i) q^{9} +(-1.96815 + 3.40894i) q^{10} +(3.31659 + 0.0152357i) q^{11} +(2.74987 + 4.76291i) q^{12} +(3.24490 - 2.35756i) q^{13} +(6.75053 + 2.63221i) q^{14} +(0.444168 - 1.36701i) q^{15} +(-1.59381 + 15.1641i) q^{16} +(0.0162751 - 0.00724614i) q^{17} +(-1.83246 - 2.03515i) q^{18} +(3.50447 - 3.89211i) q^{19} +(6.39536 - 4.64650i) q^{20} +(-2.61096 - 0.427659i) q^{21} +(-8.28049 - 3.73238i) q^{22} +(-2.96330 - 5.13258i) q^{23} +(-1.00183 - 9.53176i) q^{24} +(2.86988 + 0.610013i) q^{25} +(-10.7441 + 2.28374i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-10.2347 - 10.3432i) q^{28} +(-1.17725 + 3.62320i) q^{29} +(-2.63390 + 2.92524i) q^{30} +(-0.833126 - 7.92666i) q^{31} +(11.2941 - 19.5619i) q^{32} +(3.24095 + 0.704461i) q^{33} -0.0487884 q^{34} +(-0.219049 + 3.79658i) q^{35} +(1.69951 + 5.23056i) q^{36} +(2.05138 - 0.436034i) q^{37} +(-13.1028 + 5.83375i) q^{38} +(3.66416 - 1.63139i) q^{39} +(-13.4750 + 2.86420i) q^{40} +(0.291768 + 0.897968i) q^{41} +(6.05575 + 3.97820i) q^{42} -0.749457 q^{43} +(12.1429 + 13.6113i) q^{44} +(0.718680 - 1.24479i) q^{45} +(1.69654 + 16.1415i) q^{46} +(-1.19873 + 1.33132i) q^{47} +(-4.71178 + 14.5014i) q^{48} +(6.96898 - 0.658247i) q^{49} +(-6.50041 - 4.72282i) q^{50} +(0.0174260 - 0.00370401i) q^{51} +(21.5770 + 4.58633i) q^{52} +(-0.000917016 - 0.00872482i) q^{53} +(-1.36928 - 2.37167i) q^{54} +(0.520080 - 4.73873i) q^{55} +(8.96240 + 23.7209i) q^{56} +(4.23710 - 3.07844i) q^{57} +(6.98104 - 7.75323i) q^{58} +(-1.86664 - 2.07312i) q^{59} +(7.22167 - 3.21529i) q^{60} +(-1.30839 + 12.4485i) q^{61} +(-6.74499 + 20.7589i) q^{62} +(-2.46499 - 0.961163i) q^{63} +(-25.3739 + 18.4352i) q^{64} +(-2.88257 - 4.99275i) q^{65} +(-7.32353 - 5.37243i) q^{66} +(-4.91687 + 8.51627i) q^{67} +(0.0895088 + 0.0398519i) q^{68} +(-1.83142 - 5.63653i) q^{69} +(4.77693 - 9.25431i) q^{70} +(3.82726 + 2.78067i) q^{71} +(1.00183 - 9.53176i) q^{72} +(-2.25789 - 2.50764i) q^{73} +(-5.61783 - 1.19411i) q^{74} +(2.68034 + 1.19336i) q^{75} +28.8041 q^{76} +(-8.76704 + 0.372766i) q^{77} -10.9842 q^{78} +(-13.4173 - 5.97376i) q^{79} +(21.4374 + 4.55667i) q^{80} +(0.669131 + 0.743145i) q^{81} +(0.270279 - 2.57153i) q^{82} +(13.3219 + 9.67889i) q^{83} +(-7.86056 - 12.2451i) q^{84} +(-0.00791300 - 0.0243537i) q^{85} +(1.87499 + 0.834802i) q^{86} +(-1.90483 + 3.29926i) q^{87} +(-9.68387 - 30.2764i) q^{88} +(2.27619 + 3.94248i) q^{89} +(-3.18453 + 2.31370i) q^{90} +(-8.28209 + 6.63471i) q^{91} +(10.0723 - 30.9994i) q^{92} +(0.833126 - 7.92666i) q^{93} +(4.48190 - 1.99547i) q^{94} +(-5.03718 - 5.59436i) q^{95} +(15.1144 - 16.7863i) q^{96} +(-2.86133 + 2.07888i) q^{97} +(-18.1682 - 6.11577i) q^{98} +(3.02366 + 1.36290i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9} - 22 q^{10} - 13 q^{11} + 30 q^{12} - 8 q^{13} - 26 q^{14} + 4 q^{17} - 5 q^{18} + 10 q^{19} + 24 q^{20} + 2 q^{21} - 38 q^{22} - 8 q^{23} + 14 q^{24} - 2 q^{25} + 4 q^{26} + 16 q^{27} - 67 q^{28} + 2 q^{29} - 3 q^{30} + 25 q^{31} + 72 q^{32} - 12 q^{33} - 56 q^{34} + 19 q^{35} - 20 q^{36} - 12 q^{37} - 37 q^{38} - 4 q^{39} - 9 q^{40} + 20 q^{41} + 9 q^{42} - 100 q^{43} - 5 q^{44} - 33 q^{46} - 18 q^{47} + 10 q^{48} + 29 q^{49} - 46 q^{50} + 6 q^{51} + 26 q^{52} - 49 q^{53} - 10 q^{54} - 24 q^{55} - 48 q^{56} + 20 q^{57} - 40 q^{58} + q^{59} + 12 q^{60} + 3 q^{61} + 4 q^{62} - 7 q^{63} - 24 q^{64} + 82 q^{65} + 11 q^{66} + 76 q^{67} - 39 q^{68} - 16 q^{69} + 59 q^{70} + 70 q^{71} - 14 q^{72} - 3 q^{73} + 32 q^{74} - 28 q^{75} + 104 q^{76} + 38 q^{77} - 12 q^{78} - 15 q^{79} - 83 q^{80} + 8 q^{81} + 42 q^{82} + 68 q^{83} + 27 q^{84} + 62 q^{85} - 47 q^{86} - 54 q^{87} - 64 q^{88} + 82 q^{89} - 16 q^{90} - 10 q^{91} + 190 q^{92} - 25 q^{93} - 6 q^{94} - 53 q^{95} + 8 q^{96} - 32 q^{97} - 152 q^{98} + 16 q^{99}+O(q^{100}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9 - 22 * q^10 - 13 * q^11 + 30 * q^12 - 8 * q^13 - 26 * q^14 + 4 * q^17 - 5 * q^18 + 10 * q^19 + 24 * q^20 + 2 * q^21 - 38 * q^22 - 8 * q^23 + 14 * q^24 - 2 * q^25 + 4 * q^26 + 16 * q^27 - 67 * q^28 + 2 * q^29 - 3 * q^30 + 25 * q^31 + 72 * q^32 - 12 * q^33 - 56 * q^34 + 19 * q^35 - 20 * q^36 - 12 * q^37 - 37 * q^38 - 4 * q^39 - 9 * q^40 + 20 * q^41 + 9 * q^42 - 100 * q^43 - 5 * q^44 - 33 * q^46 - 18 * q^47 + 10 * q^48 + 29 * q^49 - 46 * q^50 + 6 * q^51 + 26 * q^52 - 49 * q^53 - 10 * q^54 - 24 * q^55 - 48 * q^56 + 20 * q^57 - 40 * q^58 + q^59 + 12 * q^60 + 3 * q^61 + 4 * q^62 - 7 * q^63 - 24 * q^64 + 82 * q^65 + 11 * q^66 + 76 * q^67 - 39 * q^68 - 16 * q^69 + 59 * q^70 + 70 * q^71 - 14 * q^72 - 3 * q^73 + 32 * q^74 - 28 * q^75 + 104 * q^76 + 38 * q^77 - 12 * q^78 - 15 * q^79 - 83 * q^80 + 8 * q^81 + 42 * q^82 + 68 * q^83 + 27 * q^84 + 62 * q^85 - 47 * q^86 - 54 * q^87 - 64 * q^88 + 82 * q^89 - 16 * q^90 - 10 * q^91 + 190 * q^92 - 25 * q^93 - 6 * q^94 - 53 * q^95 + 8 * q^96 - 32 * q^97 - 152 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

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