LMFDB - Embedded newform 570.2.u.i.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(61,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("570.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.u (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 24x^{10} + 216x^{8} + 905x^{6} + 1770x^{4} + 1395x^{2} + 361 $ x^12 + 24x^10 + 216x^8 + 905x^6 + 1770x^4 + 1395*x^2 + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			61.1
Root			$-0.918492i$ of defining polynomial
Character	$\chi$	$=$	570.61
Dual form			570.2.u.i.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(0.173648 - 0.984808i) q^{6} +(-0.814143 + 1.41014i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(0.173648 - 0.984808i) q^{6} +(-0.814143 + 1.41014i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-0.939693 + 0.342020i) q^{10} +(-0.0122091 - 0.0211467i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.900043 + 5.10440i) q^{13} +(1.24734 - 1.04664i) q^{14} +(0.766044 + 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(3.76098 + 1.36888i) q^{17} +1.00000 q^{18} +(-4.12746 - 1.40146i) q^{19} +1.00000 q^{20} +(-1.53009 - 0.556906i) q^{21} +(0.00424016 + 0.0240471i) q^{22} +(4.28392 + 3.59464i) q^{23} +(0.766044 - 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(2.59157 - 4.48873i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-1.53009 + 0.556906i) q^{28} +(-2.96978 + 1.08091i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(-2.54879 + 4.41464i) q^{31} +(0.173648 - 0.984808i) q^{32} +(0.0187054 - 0.0156957i) q^{33} +(-3.06598 - 2.57266i) q^{34} +(0.282749 + 1.60355i) q^{35} +(-0.939693 - 0.342020i) q^{36} +1.15351 q^{37} +(3.39922 + 2.72861i) q^{38} -5.18314 q^{39} +(-0.939693 - 0.342020i) q^{40} +(0.172953 + 0.980867i) q^{41} +(1.24734 + 1.04664i) q^{42} +(-2.88277 + 2.41893i) q^{43} +(0.00424016 - 0.0240471i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-2.79613 - 4.84304i) q^{46} +(-1.85268 + 0.674320i) q^{47} +(-0.939693 + 0.342020i) q^{48} +(2.17434 + 3.76607i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.695001 + 3.94154i) q^{51} +(-3.97052 + 3.33166i) q^{52} +(8.48426 + 7.11914i) q^{53} +(0.173648 + 0.984808i) q^{54} +(-0.0229455 - 0.00835149i) q^{55} +1.62829 q^{56} +(0.663440 - 4.30811i) q^{57} +3.16037 q^{58} +(-4.78016 - 1.73984i) q^{59} +(0.173648 + 0.984808i) q^{60} +(3.32108 + 2.78672i) q^{61} +(3.90498 - 3.27667i) q^{62} +(0.282749 - 1.60355i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.59157 + 4.48873i) q^{65} +(-0.0229455 + 0.00835149i) q^{66} +(-8.26361 + 3.00771i) q^{67} +(2.00117 + 3.46614i) q^{68} +(-2.79613 + 4.84304i) q^{69} +(0.282749 - 1.60355i) q^{70} +(5.16526 - 4.33417i) q^{71} +(0.766044 + 0.642788i) q^{72} +(1.30860 + 7.42142i) q^{73} +(-1.08395 - 0.394525i) q^{74} +1.00000 q^{75} +(-2.26098 - 3.72666i) q^{76} +0.0397597 q^{77} +(4.87056 + 1.77274i) q^{78} +(0.0776181 + 0.440194i) q^{79} +(0.766044 + 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(0.172953 - 0.980867i) q^{82} +(6.37237 - 11.0373i) q^{83} +(-0.814143 - 1.41014i) q^{84} +(3.76098 - 1.36888i) q^{85} +(3.53624 - 1.28709i) q^{86} +(-1.58019 - 2.73696i) q^{87} +(-0.0122091 + 0.0211467i) q^{88} +(1.87089 - 10.6103i) q^{89} +(0.766044 - 0.642788i) q^{90} +(-6.46513 - 5.42489i) q^{91} +(0.971087 + 5.50731i) q^{92} +(-4.79016 - 1.74348i) q^{93} +1.97158 q^{94} +(-4.06266 + 1.57950i) q^{95} +1.00000 q^{96} +(-5.43949 - 1.97981i) q^{97} +(-0.755141 - 4.28262i) q^{98} +(0.0187054 + 0.0156957i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q - 3 * q^7 - 6 * q^8	$ 12 q - 3 q^{7} - 6 q^{8} - 9 q^{11} - 6 q^{12} - 3 q^{13} + 3 q^{14} + 9 q^{17} + 12 q^{18} - 3 q^{19} + 12 q^{20} + 3 q^{21} - 6 q^{22} + 12 q^{23} - 9 q^{26} - 6 q^{27} + 3 q^{28} - 3 q^{29} - 6 q^{30} - 12 q^{31} + 3 q^{33} - 9 q^{34} - 6 q^{35} + 42 q^{37} + 18 q^{39} + 21 q^{41} + 3 q^{42} + 9 q^{43} - 6 q^{44} - 6 q^{45} - 3 q^{46} + 3 q^{49} - 6 q^{50} - 3 q^{52} - 18 q^{53} + 3 q^{55} + 6 q^{56} + 6 q^{58} - 15 q^{59} + 9 q^{61} + 12 q^{62} - 6 q^{63} - 6 q^{64} - 9 q^{65} + 3 q^{66} + 18 q^{67} - 6 q^{68} - 3 q^{69} - 6 q^{70} + 12 q^{71} - 9 q^{73} + 12 q^{75} + 9 q^{76} - 54 q^{77} + 6 q^{78} - 9 q^{79} + 21 q^{82} + 15 q^{83} - 3 q^{84} + 9 q^{85} - 27 q^{86} - 3 q^{87} - 9 q^{88} + 3 q^{89} - 51 q^{91} + 3 q^{92} - 15 q^{93} + 12 q^{96} - 48 q^{97} - 15 q^{98} + 3 q^{99}+O(q^{100}) $ 12 * q - 3 * q^7 - 6 * q^8 - 9 * q^11 - 6 * q^12 - 3 * q^13 + 3 * q^14 + 9 * q^17 + 12 * q^18 - 3 * q^19 + 12 * q^20 + 3 * q^21 - 6 * q^22 + 12 * q^23 - 9 * q^26 - 6 * q^27 + 3 * q^28 - 3 * q^29 - 6 * q^30 - 12 * q^31 + 3 * q^33 - 9 * q^34 - 6 * q^35 + 42 * q^37 + 18 * q^39 + 21 * q^41 + 3 * q^42 + 9 * q^43 - 6 * q^44 - 6 * q^45 - 3 * q^46 + 3 * q^49 - 6 * q^50 - 3 * q^52 - 18 * q^53 + 3 * q^55 + 6 * q^56 + 6 * q^58 - 15 * q^59 + 9 * q^61 + 12 * q^62 - 6 * q^63 - 6 * q^64 - 9 * q^65 + 3 * q^66 + 18 * q^67 - 6 * q^68 - 3 * q^69 - 6 * q^70 + 12 * q^71 - 9 * q^73 + 12 * q^75 + 9 * q^76 - 54 * q^77 + 6 * q^78 - 9 * q^79 + 21 * q^82 + 15 * q^83 - 3 * q^84 + 9 * q^85 - 27 * q^86 - 3 * q^87 - 9 * q^88 + 3 * q^89 - 51 * q^91 + 3 * q^92 - 15 * q^93 + 12 * q^96 - 48 * q^97 - 15 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$	$1$

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 $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	0.766044	−	0.642788i	0.342585	−	0.287463i
$5$	0.766044	−	0.642788i	0.342585	−	0.287463i
$6$	0.173648	−	0.984808i	0.0708916	−	0.402046i
$7$	−0.814143	+	1.41014i	−0.307717	+	0.532982i	−0.977863	−	0.209248i	$-0.932898\pi$
$7$	−0.814143	+	1.41014i	−0.307717	+	0.532982i	0.670146	+	0.742230i	$0.266232\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	−0.939693	+	0.342020i	−0.297157	+	0.108156i
$11$	−0.0122091	−	0.0211467i	−0.00368117	−	0.00637597i	0.864179	−	0.503185i	$-0.167838\pi$
$11$	−0.0122091	−	0.0211467i	−0.00368117	−	0.00637597i	−0.867860	+	0.496809i	$0.834505\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−0.900043	+	5.10440i	−0.249627	+	1.41570i	0.559870	+	0.828581i	$0.310851\pi$
$13$	−0.900043	+	5.10440i	−0.249627	+	1.41570i	−0.809497	+	0.587124i	$0.800260\pi$
$14$	1.24734	−	1.04664i	0.333365	−	0.279727i
$15$	0.766044	+	0.642788i	0.197792	+	0.165967i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	3.76098	+	1.36888i	0.912171	+	0.332003i	0.755119	−	0.655587i	$-0.227579\pi$
$17$	3.76098	+	1.36888i	0.912171	+	0.332003i	0.157052	+	0.987590i	$0.449801\pi$
$18$	1.00000			0.235702
$19$	−4.12746	−	1.40146i	−0.946904	−	0.321516i
$19$	−4.12746	−	1.40146i	−0.946904	−	0.321516i
$20$	1.00000			0.223607
$21$	−1.53009	−	0.556906i	−0.333893	−	0.121527i
$22$	0.00424016	+	0.0240471i	0.000904005	+	0.00512687i
$23$	4.28392	+	3.59464i	0.893260	+	0.749534i	0.968861	−	0.247604i	$-0.0796433\pi$
$23$	4.28392	+	3.59464i	0.893260	+	0.749534i	−0.0756015	+	0.997138i	$0.524088\pi$
$24$	0.766044	−	0.642788i	0.156368	−	0.131208i
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	2.59157	−	4.48873i	0.508249	−	0.880312i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	−1.53009	+	0.556906i	−0.289159	+	0.105245i
$29$	−2.96978	+	1.08091i	−0.551474	+	0.200720i	−0.602701	−	0.797967i	$-0.705909\pi$
$29$	−2.96978	+	1.08091i	−0.551474	+	0.200720i	0.0512271	+	0.998687i	$0.483687\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	−2.54879	+	4.41464i	−0.457777	+	0.792893i	−0.998843	−	0.0480873i	$-0.984687\pi$
$31$	−2.54879	+	4.41464i	−0.457777	+	0.792893i	0.541066	+	0.840980i	$0.318021\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	0.0187054	−	0.0156957i	0.00325619	−	0.00273226i
$34$	−3.06598	−	2.57266i	−0.525811	−	0.441208i
$35$	0.282749	+	1.60355i	0.0477933	+	0.271049i
$36$	−0.939693	−	0.342020i	−0.156615	−	0.0570034i
$37$	1.15351			0.189636			0.0948182	−	0.995495i	$-0.469773\pi$
$37$	1.15351			0.189636			0.0948182	+	0.995495i	$0.469773\pi$
$38$	3.39922	+	2.72861i	0.551426	+	0.442639i
$39$	−5.18314			−0.829967
$40$	−0.939693	−	0.342020i	−0.148578	−	0.0540781i
$41$	0.172953	+	0.980867i	0.0270108	+	0.153186i	0.995330	−	0.0965294i	$-0.0307742\pi$
$41$	0.172953	+	0.980867i	0.0270108	+	0.153186i	−0.968319	+	0.249715i	$0.919663\pi$
$42$	1.24734	+	1.04664i	0.192469	+	0.161500i
$43$	−2.88277	+	2.41893i	−0.439618	+	0.368883i	−0.835566	−	0.549390i	$-0.814860\pi$
$43$	−2.88277	+	2.41893i	−0.439618	+	0.368883i	0.395949	+	0.918273i	$0.370416\pi$
$44$	0.00424016	−	0.0240471i	0.000639228	−	0.00362524i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−2.79613	−	4.84304i	−0.412267	−	0.714068i
$47$	−1.85268	+	0.674320i	−0.270241	+	0.0983597i	−0.473586	−	0.880747i	$-0.657041\pi$
$47$	−1.85268	+	0.674320i	−0.270241	+	0.0983597i	0.203345	+	0.979107i	$0.434819\pi$
$48$	−0.939693	+	0.342020i	−0.135633	+	0.0493664i
$49$	2.17434	+	3.76607i	0.310620	+	0.538010i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−0.695001	+	3.94154i	−0.0973195	+	0.551927i
$52$	−3.97052	+	3.33166i	−0.550611	+	0.462018i
$53$	8.48426	+	7.11914i	1.16540	+	0.977889i	0.999965	−	0.00833077i	$-0.00265180\pi$
$53$	8.48426	+	7.11914i	1.16540	+	0.977889i	0.165438	+	0.986220i	$0.447096\pi$
$54$	0.173648	+	0.984808i	0.0236305	+	0.134015i
$55$	−0.0229455	−	0.00835149i	−0.00309397	−	0.00112611i
$56$	1.62829			0.217589
$57$	0.663440	−	4.30811i	0.0878748	−	0.570624i
$58$	3.16037			0.414977
$59$	−4.78016	−	1.73984i	−0.622324	−	0.226507i	0.0115628	−	0.999933i	$-0.496319\pi$
$59$	−4.78016	−	1.73984i	−0.622324	−	0.226507i	−0.633887	+	0.773426i	$0.718542\pi$
$60$	0.173648	+	0.984808i	0.0224179	+	0.127138i
$61$	3.32108	+	2.78672i	0.425221	+	0.356802i	0.830145	−	0.557548i	$-0.188258\pi$
$61$	3.32108	+	2.78672i	0.425221	+	0.356802i	−0.404924	+	0.914350i	$0.632702\pi$
$62$	3.90498	−	3.27667i	0.495933	−	0.416137i
$63$	0.282749	−	1.60355i	0.0356230	−	0.202028i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	2.59157	+	4.48873i	0.321445	+	0.556758i
$66$	−0.0229455	+	0.00835149i	−0.00282440	+	0.00102800i
$67$	−8.26361	+	3.00771i	−1.00956	+	0.367450i	−0.793264	−	0.608877i	$-0.791620\pi$
$67$	−8.26361	+	3.00771i	−1.00956	+	0.367450i	−0.216297	+	0.976328i	$0.569398\pi$
$68$	2.00117	+	3.46614i	0.242678	+	0.420331i
$69$	−2.79613	+	4.84304i	−0.336615	+	0.583034i
$70$	0.282749	−	1.60355i	0.0337949	−	0.191661i
$71$	5.16526	−	4.33417i	0.613004	−	0.514371i	−0.282592	−	0.959240i	$-0.591194\pi$
$71$	5.16526	−	4.33417i	0.613004	−	0.514371i	0.895596	+	0.444869i	$0.146750\pi$
$72$	0.766044	+	0.642788i	0.0902792	+	0.0757532i
$73$	1.30860	+	7.42142i	0.153160	+	0.868611i	0.960449	+	0.278456i	$0.0898226\pi$
$73$	1.30860	+	7.42142i	0.153160	+	0.868611i	−0.807289	+	0.590156i	$0.799066\pi$
$74$	−1.08395	−	0.394525i	−0.126006	−	0.0458626i
$75$	1.00000			0.115470
$76$	−2.26098	−	3.72666i	−0.259352	−	0.427477i
$77$	0.0397597			0.00453103
$78$	4.87056	+	1.77274i	0.551482	+	0.200723i
$79$	0.0776181	+	0.440194i	0.00873272	+	0.0495257i	0.988863	−	0.148830i	$-0.0475509\pi$
$79$	0.0776181	+	0.440194i	0.00873272	+	0.0495257i	−0.980130	+	0.198356i	$0.936440\pi$
$80$	0.766044	+	0.642788i	0.0856464	+	0.0718658i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	0.172953	−	0.980867i	0.0190995	−	0.108319i
$83$	6.37237	−	11.0373i	0.699458	−	1.21150i	−0.269196	−	0.963085i	$-0.586758\pi$
$83$	6.37237	−	11.0373i	0.699458	−	1.21150i	0.968655	−	0.248412i	$-0.0799086\pi$
$84$	−0.814143	−	1.41014i	−0.0888303	−	0.153859i
$85$	3.76098	−	1.36888i	0.407935	−	0.148476i
$86$	3.53624	−	1.28709i	0.381322	−	0.138790i
$87$	−1.58019	−	2.73696i	−0.169414	−	0.293433i
$88$	−0.0122091	+	0.0211467i	−0.00130149	+	0.00225425i
$89$	1.87089	−	10.6103i	0.198314	−	1.12469i	−0.709306	−	0.704900i	$-0.750992\pi$
$89$	1.87089	−	10.6103i	0.198314	−	1.12469i	0.907620	−	0.419793i	$-0.137897\pi$
$90$	0.766044	−	0.642788i	0.0807482	−	0.0677558i
$91$	−6.46513	−	5.42489i	−0.677730	−	0.568683i
$92$	0.971087	+	5.50731i	0.101243	+	0.574176i
$93$	−4.79016	−	1.74348i	−0.496717	−	0.180790i
$94$	1.97158			0.203353
$95$	−4.06266	+	1.57950i	−0.416820	+	0.162053i
$96$	1.00000			0.102062
$97$	−5.43949	−	1.97981i	−0.552296	−	0.201019i	0.0507702	−	0.998710i	$-0.483832\pi$
$97$	−5.43949	−	1.97981i	−0.552296	−	0.201019i	−0.603066	+	0.797691i	$0.706055\pi$
$98$	−0.755141	−	4.28262i	−0.0762808	−	0.432610i
$99$	0.0187054	+	0.0156957i	0.00187996	+	0.00157747i
$100$	0.766044	−	0.642788i	0.0766044	−	0.0642788i
$101$	0.491489	−	2.78737i	0.0489050	−	0.277354i	−0.950542	−	0.310595i	$-0.899472\pi$
$101$	0.491489	−	2.78737i	0.0489050	−	0.277354i	0.999447	+	0.0332410i	$0.0105829\pi$
$102$	2.00117	−	3.46614i	0.198146	−	0.343199i
$103$	2.57215	+	4.45509i	0.253441	+	0.438973i	0.964471	−	0.264189i	$-0.0851042\pi$
$103$	2.57215	+	4.45509i	0.253441	+	0.438973i	−0.711030	+	0.703162i	$0.751771\pi$
$104$	4.87056	−	1.77274i	0.477597	−	0.173831i
$105$	−1.53009	+	0.556906i	−0.149321	+	0.0543485i
$106$	−5.53771	−	9.59159i	−0.537870	−	0.931618i
$107$	−3.34509	+	5.79386i	−0.323382	+	0.560114i	−0.981184	−	0.193077i	$-0.938153\pi$
$107$	−3.34509	+	5.79386i	−0.323382	+	0.560114i	0.657802	+	0.753191i	$0.271487\pi$
$108$	0.173648	−	0.984808i	0.0167093	−	0.0947632i
$109$	4.04527	−	3.39439i	0.387467	−	0.325123i	−0.428159	−	0.903704i	$-0.640838\pi$
$109$	4.04527	−	3.39439i	0.387467	−	0.325123i	0.815625	+	0.578580i	$0.196393\pi$
$110$	0.0187054	+	0.0156957i	0.00178349	+	0.00149652i
$111$	0.200305	+	1.13599i	0.0190122	+	0.107823i
$112$	−1.53009	−	0.556906i	−0.144580	−	0.0526227i
$113$	14.1801			1.33395			0.666977	−	0.745078i	$-0.267588\pi$
$113$	14.1801			1.33395			0.666977	+	0.745078i	$0.267588\pi$
$114$	−2.09689	+	3.82139i	−0.196392	+	0.357906i
$115$	5.59226			0.521481
$116$	−2.96978	−	1.08091i	−0.275737	−	0.100360i
$117$	−0.900043	−	5.10440i	−0.0832090	−	0.471902i
$118$	3.89682	+	3.26982i	0.358732	+	0.301012i
$119$	−4.99229	+	4.18903i	−0.457642	+	0.384007i
$120$	0.173648	−	0.984808i	0.0158518	−	0.0899002i
$121$	5.49970	−	9.52576i	0.499973	−	0.865978i
$122$	−2.16768	−	3.75453i	−0.196253	−	0.339919i
$123$	−0.935932	+	0.340651i	−0.0843901	+	0.0307155i
$124$	−4.79016	+	1.74348i	−0.430169	+	0.156569i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$	−0.814143	+	1.41014i	−0.0725296	+	0.125625i
$127$	2.30307	−	13.0614i	0.204364	−	1.15901i	−0.694072	−	0.719905i	$-0.744185\pi$
$127$	2.30307	−	13.0614i	0.204364	−	1.15901i	0.898437	−	0.439103i	$-0.144704\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	−2.88277	−	2.41893i	−0.253813	−	0.212975i
$130$	−0.900043	−	5.10440i	−0.0789390	−	0.447685i
$131$	−11.1254	−	4.04933i	−0.972034	−	0.353791i	−0.193296	−	0.981141i	$-0.561918\pi$
$131$	−11.1254	−	4.04933i	−0.972034	−	0.353791i	−0.778738	+	0.627349i	$0.784140\pi$
$132$	0.0244181			0.00212532
$133$	5.33659	−	4.67929i	0.462741	−	0.405746i
$134$	8.79395			0.759682
$135$	−0.939693	−	0.342020i	−0.0808759	−	0.0294364i
$136$	−0.695001	−	3.94154i	−0.0595958	−	0.337985i
$137$	−2.13895	−	1.79479i	−0.182742	−	0.153339i	0.546828	−	0.837245i	$-0.315835\pi$
$137$	−2.13895	−	1.79479i	−0.182742	−	0.153339i	−0.729570	+	0.683906i	$0.760280\pi$
$138$	4.28392	−	3.59464i	0.364672	−	0.305996i
$139$	2.15628	−	12.2289i	0.182893	−	1.03724i	−0.745739	−	0.666238i	$-0.767903\pi$
$139$	2.15628	−	12.2289i	0.182893	−	1.03724i	0.928632	−	0.371001i	$-0.120985\pi$
$140$	−0.814143	+	1.41014i	−0.0688076	+	0.119178i
$141$	−0.985790	−	1.70744i	−0.0830185	−	0.143792i
$142$	−6.33613	+	2.30616i	−0.531716	+	0.193529i
$143$	0.118930	−	0.0432869i	0.00994541	−	0.00361983i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−1.58019	+	2.73696i	−0.131227	+	0.227293i
$146$	1.30860	−	7.42142i	0.108300	−	0.614201i
$147$	−3.33129	+	2.79528i	−0.274760	+	0.230551i
$148$	0.883642	+	0.741464i	0.0726350	+	0.0609480i
$149$	−3.51381	−	19.9278i	−0.287862	−	1.63255i	−0.694879	−	0.719127i	$-0.744542\pi$
$149$	−3.51381	−	19.9278i	−0.287862	−	1.63255i	0.407017	−	0.913421i	$-0.366569\pi$
$150$	−0.939693	−	0.342020i	−0.0767256	−	0.0279258i
$151$	−8.69671			−0.707728			−0.353864	−	0.935297i	$-0.615133\pi$
$151$	−8.69671			−0.707728			−0.353864	+	0.935297i	$0.615133\pi$
$152$	0.850032	+	4.27521i	0.0689467	+	0.346766i
$153$	−4.00235			−0.323571
$154$	−0.0373619	−	0.0135986i	−0.00301070	−	0.00109581i
$155$	0.885187	+	5.02014i	0.0710999	+	0.403228i
$156$	−3.97052	−	3.33166i	−0.317896	−	0.266746i
$157$	16.1849	−	13.5807i	1.29169	−	1.08386i	0.300178	−	0.953883i	$-0.402954\pi$
$157$	16.1849	−	13.5807i	1.29169	−	1.08386i	0.991517	−	0.129978i	$-0.0414905\pi$
$158$	0.0776181	−	0.440194i	0.00617496	−	0.0350200i
$159$	−5.53771	+	9.59159i	−0.439169	+	0.760663i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−8.55666	+	3.11437i	−0.674359	+	0.245447i
$162$	−0.939693	+	0.342020i	−0.0738292	+	0.0268716i
$163$	9.28304	+	16.0787i	0.727104	+	1.25938i	0.958102	+	0.286427i	$0.0924676\pi$
$163$	9.28304	+	16.0787i	0.727104	+	1.25938i	−0.230998	+	0.972954i	$0.574199\pi$
$164$	−0.497999	+	0.862560i	−0.0388872	+	0.0673546i
$165$	0.00424016	−	0.0240471i	0.000330096	−	0.00187207i
$166$	−9.76303	+	8.19216i	−0.757758	+	0.635835i
$167$	−12.2175	−	10.2517i	−0.945420	−	0.793301i	0.0331005	−	0.999452i	$-0.489462\pi$
$167$	−12.2175	−	10.2517i	−0.945420	−	0.793301i	−0.978520	+	0.206151i	$0.933906\pi$
$168$	0.282749	+	1.60355i	0.0218145	+	0.123716i
$169$	−13.0288	−	4.74209i	−1.00221	−	0.364776i
$170$	−4.00235			−0.306966
$171$	4.35787	−	0.0947352i	0.333255	−	0.00724458i
$172$	−3.76319			−0.286940
$173$	−12.7096	−	4.62592i	−0.966294	−	0.351702i	−0.189797	−	0.981823i	$-0.560783\pi$
$173$	−12.7096	−	4.62592i	−0.966294	−	0.351702i	−0.776497	+	0.630121i	$0.783005\pi$
$174$	0.548793	+	3.11236i	0.0416039	+	0.235947i
$175$	1.24734	+	1.04664i	0.0942900	+	0.0791187i
$176$	0.0187054	−	0.0156957i	0.00140997	−	0.00118310i
$177$	0.883338	−	5.00966i	0.0663958	−	0.376549i
$178$	−5.38701	+	9.33057i	−0.403773	+	0.699356i
$179$	3.31773	+	5.74647i	0.247978	+	0.429511i	0.962965	−	0.269627i	$-0.0869004\pi$
$179$	3.31773	+	5.74647i	0.247978	+	0.429511i	−0.714986	+	0.699138i	$0.753567\pi$
$180$	−0.939693	+	0.342020i	−0.0700406	+	0.0254927i
$181$	4.02747	−	1.46588i	0.299359	−	0.108958i	−0.187974	−	0.982174i	$-0.560192\pi$
$181$	4.02747	−	1.46588i	0.299359	−	0.108958i	0.487333	+	0.873216i	$0.337970\pi$
$182$	4.21982	+	7.30893i	0.312794	+	0.541774i
$183$	−2.16768	+	3.75453i	−0.160240	+	0.277543i
$184$	0.971087	−	5.50731i	0.0715895	−	0.406004i
$185$	0.883642	−	0.741464i	0.0649667	−	0.0545135i
$186$	3.90498	+	3.27667i	0.286327	+	0.240257i
$187$	−0.0169706	−	0.0962451i	−0.00124101	−	0.00703814i
$188$	−1.85268	−	0.674320i	−0.135121	−	0.0491798i
$189$	1.62829			0.118440
$190$	4.35787	−	0.0947352i	0.316153	−	0.00687281i
$191$	0.0207854			0.00150398			0.000751989	−	1.00000i	$-0.499761\pi$
$191$	0.0207854			0.00150398			0.000751989		1.00000i	$0.499761\pi$
$192$	−0.939693	−	0.342020i	−0.0678165	−	0.0246832i
$193$	2.77709	+	15.7497i	0.199900	+	1.13369i	0.905266	+	0.424844i	$0.139671\pi$
$193$	2.77709	+	15.7497i	0.199900	+	1.13369i	−0.705367	+	0.708842i	$0.749218\pi$
$194$	4.43431	+	3.72083i	0.318365	+	0.267140i
$195$	−3.97052	+	3.33166i	−0.284334	+	0.238585i
$196$	−0.755141	+	4.28262i	−0.0539387	+	0.305901i
$197$	12.2517	−	21.2206i	0.872900	−	1.51191i	0.0139168	−	0.999903i	$-0.495570\pi$
$197$	12.2517	−	21.2206i	0.872900	−	1.51191i	0.858983	−	0.512004i	$-0.171097\pi$
$198$	−0.0122091	−	0.0211467i	−0.000867660	−	0.00150283i
$199$	24.5541	−	8.93697i	1.74060	−	0.633525i	0.741304	−	0.671169i	$-0.234207\pi$
$199$	24.5541	−	8.93697i	1.74060	−	0.633525i	0.999291	+	0.0376439i	$0.0119853\pi$
$200$	−0.939693	+	0.342020i	−0.0664463	+	0.0241845i
$201$	−4.39698	−	7.61579i	−0.310139	−	0.537176i
$202$	−1.41519	+	2.45117i	−0.0995721	+	0.172464i
$203$	0.893592	−	5.06781i	0.0627179	−	0.355691i
$204$	−3.06598	+	2.57266i	−0.214661	+	0.180122i
$205$	0.762979	+	0.640215i	0.0532887	+	0.0447146i
$206$	−0.893297	−	5.06614i	−0.0622390	−	0.352975i
$207$	−5.25501	−	1.91267i	−0.365248	−	0.132940i
$208$	−5.18314			−0.359386
$209$	0.0207562	+	0.104393i	0.00143573	+	0.00722099i
$210$	1.62829			0.112362
$211$	−0.639487	−	0.232754i	−0.0440241	−	0.0160235i	0.319914	−	0.947446i	$-0.396346\pi$
$211$	−0.639487	−	0.232754i	−0.0440241	−	0.0160235i	−0.363938	+	0.931423i	$0.618568\pi$
$212$	1.92323	+	10.9072i	0.132088	+	0.749107i
$213$	5.16526	+	4.33417i	0.353918	+	0.296972i
$214$	5.12497	−	4.30036i	0.350336	−	0.293967i
$215$	−0.653470	+	3.70601i	−0.0445663	+	0.252748i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	−4.15016	−	7.18829i	−0.281731	−	0.487973i
$218$	−4.96226	+	1.80611i	−0.336087	+	0.122326i
$219$	−7.08144	+	2.57743i	−0.478519	+	0.174167i
$220$	−0.0122091	−	0.0211467i	−0.000823134	−	0.00142571i
$221$	−10.3724	+	17.9655i	−0.697721	+	1.20849i
$222$	0.200305	−	1.13599i	0.0134436	−	0.0762426i
$223$	−3.53544	+	2.96659i	−0.236751	+	0.198658i	−0.753442	−	0.657514i	$-0.771608\pi$
$223$	−3.53544	+	2.96659i	−0.236751	+	0.198658i	0.516691	+	0.856172i	$0.327164\pi$
$224$	1.24734	+	1.04664i	0.0833413	+	0.0699317i
$225$	0.173648	+	0.984808i	0.0115765	+	0.0656539i
$226$	−13.3250	−	4.84989i	−0.886363	−	0.322610i
$227$	4.03671			0.267926			0.133963	−	0.990986i	$-0.457230\pi$
$227$	4.03671			0.267926			0.133963	+	0.990986i	$0.457230\pi$
$228$	3.27743	−	2.87376i	0.217053	−	0.190319i
$229$	27.7378			1.83297			0.916484	−	0.400071i	$-0.131015\pi$
$229$	27.7378			1.83297			0.916484	+	0.400071i	$0.131015\pi$
$230$	−5.25501	−	1.91267i	−0.346505	−	0.126118i
$231$	0.00690419	+	0.0391556i	0.000454263	+	0.00257625i
$232$	2.42099	+	2.03145i	0.158946	+	0.133371i
$233$	10.7339	−	9.00685i	0.703204	−	0.590059i	−0.219479	−	0.975617i	$-0.570436\pi$
$233$	10.7339	−	9.00685i	0.703204	−	0.590059i	0.922683	+	0.385559i	$0.125991\pi$
$234$	−0.900043	+	5.10440i	−0.0588376	+	0.333685i
$235$	−0.985790	+	1.70744i	−0.0643058	+	0.111381i
$236$	−2.54347	−	4.40542i	−0.165566	−	0.286769i
$237$	−0.420028	+	0.152878i	−0.0272838	+	0.00993048i
$238$	6.12395	−	2.22893i	0.396956	−	0.144480i
$239$	12.5847	+	21.7973i	0.814036	+	1.40995i	0.910018	+	0.414569i	$0.136068\pi$
$239$	12.5847	+	21.7973i	0.814036	+	1.40995i	−0.0959819	+	0.995383i	$0.530599\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	−3.95181	+	22.4118i	−0.254559	+	1.44367i	0.542644	+	0.839963i	$0.317423\pi$
$241$	−3.95181	+	22.4118i	−0.254559	+	1.44367i	−0.797203	+	0.603711i	$0.793688\pi$
$242$	−8.42603	+	7.07028i	−0.541646	+	0.454495i
$243$	0.766044	+	0.642788i	0.0491418	+	0.0412348i
$244$	0.752827	+	4.26950i	0.0481948	+	0.273327i
$245$	4.08643	+	1.48734i	0.261072	+	0.0950226i
$246$	0.995998			0.0635025
$247$	10.8685	−	19.8068i	0.691545	−	1.26028i
$248$	5.09759			0.323697
$249$	11.9761	+	4.35896i	0.758956	+	0.276238i
$250$	0.173648	+	0.984808i	0.0109825	+	0.0622847i
$251$	18.2304	+	15.2971i	1.15069	+	0.965543i	0.999736	−	0.0229974i	$-0.00732094\pi$
$251$	18.2304	+	15.2971i	1.15069	+	0.965543i	0.150954	+	0.988541i	$0.451765\pi$
$252$	1.24734	−	1.04664i	0.0785750	−	0.0659322i
$253$	0.0237121	−	0.134478i	0.00149077	−	0.00845456i
$254$	−6.63143	+	11.4860i	−0.416093	+	0.720694i
$255$	2.00117	+	3.46614i	0.125318	+	0.217058i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−23.3661	+	8.50457i	−1.45754	+	0.530500i	−0.944686	−	0.327977i	$-0.893633\pi$
$257$	−23.3661	+	8.50457i	−1.45754	+	0.530500i	−0.512852	+	0.858477i	$0.671411\pi$
$258$	1.88159	+	3.25901i	0.117143	+	0.202897i
$259$	−0.939124	+	1.62661i	−0.0583544	+	0.101073i
$260$	−0.900043	+	5.10440i	−0.0558183	+	0.316561i
$261$	2.42099	−	2.03145i	0.149855	−	0.125744i
$262$	9.06954	+	7.61025i	0.560318	+	0.470163i
$263$	1.52701	+	8.66009i	0.0941594	+	0.534004i	0.995002	+	0.0998579i	$0.0318388\pi$
$263$	1.52701	+	8.66009i	0.0941594	+	0.534004i	−0.900842	+	0.434146i	$0.857050\pi$
$264$	−0.0229455	−	0.00835149i	−0.00141220	−	0.000513998i
$265$	11.0754			0.680358
$266$	−6.61516	+	2.57188i	−0.405602	+	0.157692i
$267$	10.7740			0.659359
$268$	−8.26361	−	3.00771i	−0.504781	−	0.183725i
$269$	−3.03468	−	17.2105i	−0.185028	−	1.04935i	−0.925919	−	0.377721i	$-0.876708\pi$
$269$	−3.03468	−	17.2105i	−0.185028	−	1.04935i	0.740892	−	0.671625i	$-0.234403\pi$
$270$	0.766044	+	0.642788i	0.0466200	+	0.0391188i
$271$	−0.241002	+	0.202225i	−0.0146398	+	0.0122843i	−0.650078	−	0.759867i	$-0.725264\pi$
$271$	−0.241002	+	0.202225i	−0.0146398	+	0.0122843i	0.635438	+	0.772152i	$0.280819\pi$
$272$	−0.695001	+	3.94154i	−0.0421406	+	0.238991i
$273$	4.21982	−	7.30893i	0.255395	−	0.442357i
$274$	1.39610	+	2.41811i	0.0843413	+	0.146083i
$275$	−0.0229455	+	0.00835149i	−0.00138367	+	0.000503614i
$276$	−5.25501	+	1.91267i	−0.316314	+	0.115129i
$277$	14.6511	+	25.3765i	0.880301	+	1.52473i	0.851007	+	0.525154i	$0.175992\pi$
$277$	14.6511	+	25.3765i	0.880301	+	1.52473i	0.0292935	+	0.999571i	$0.490674\pi$
$278$	−6.20876	+	10.7539i	−0.372377	+	0.644975i
$279$	0.885187	−	5.02014i	0.0529947	−	0.300548i
$280$	1.24734	−	1.04664i	0.0745428	−	0.0625488i
$281$	−4.83990	−	4.06116i	−0.288724	−	0.242268i	0.486908	−	0.873453i	$-0.338125\pi$
$281$	−4.83990	−	4.06116i	−0.288724	−	0.242268i	−0.775633	+	0.631185i	$0.782569\pi$
$282$	0.342361	+	1.94163i	0.0203873	+	0.115622i
$283$	−27.4276	−	9.98282i	−1.63040	−	0.593417i	−0.645077	−	0.764117i	$-0.723175\pi$
$283$	−27.4276	−	9.98282i	−1.63040	−	0.593417i	−0.985323	+	0.170700i	$0.945397\pi$
$284$	6.74277			0.400110
$285$	−2.26098	−	3.72666i	−0.133929	−	0.220748i
$286$	−0.126562			−0.00748380
$287$	−1.52396	−	0.554678i	−0.0899568	−	0.0327416i
$288$	0.173648	+	0.984808i	0.0102323	+	0.0580304i
$289$	−0.751645	−	0.630705i	−0.0442144	−	0.0371003i
$290$	2.42099	−	2.03145i	0.142165	−	0.119291i
$291$	1.00518	−	5.70064i	0.0589245	−	0.334177i
$292$	−3.76795	+	6.52629i	−0.220503	+	0.381922i
$293$	3.42814	+	5.93772i	0.200274	+	0.346885i	0.948617	−	0.316427i	$-0.102483\pi$
$293$	3.42814	+	5.93772i	0.200274	+	0.346885i	−0.748343	+	0.663312i	$0.769150\pi$
$294$	4.08643	−	1.48734i	0.238325	−	0.0867433i
$295$	−4.78016	+	1.73984i	−0.278312	+	0.101297i
$296$	−0.576757	−	0.998972i	−0.0335233	−	0.0580641i
$297$	−0.0122091	+	0.0211467i	−0.000708441	+	0.00122706i
$298$	−3.51381	+	19.9278i	−0.203549	+	1.15439i
$299$	−22.2042	+	18.6315i	−1.28410	+	1.07749i
$300$	0.766044	+	0.642788i	0.0442276	+	0.0371114i
$301$	−1.06404	−	6.03445i	−0.0613300	−	0.347820i
$302$	8.17224	+	2.97445i	0.470259	+	0.171160i
$303$	2.83037			0.162601
$304$	0.663440	−	4.30811i	0.0380509	−	0.247087i
$305$	4.33536			0.248242
$306$	3.76098	+	1.36888i	0.215001	+	0.0782539i
$307$	0.216317	+	1.22680i	0.0123459	+	0.0700169i	0.990358	−	0.138530i	$-0.0442377\pi$
$307$	0.216317	+	1.22680i	0.0123459	+	0.0700169i	−0.978012	+	0.208547i	$0.933127\pi$
$308$	0.0304577	+	0.0255570i	0.00173549	+	0.00145625i
$309$	−3.94076	+	3.30669i	−0.224182	+	0.188111i
$310$	0.885187	−	5.02014i	0.0502752	−	0.285125i
$311$	8.60254	−	14.9000i	0.487805	−	0.844904i	−0.512096	−	0.858928i	$-0.671131\pi$
$311$	8.60254	−	14.9000i	0.487805	−	0.844904i	0.999902	+	0.0140245i	$0.00446428\pi$
$312$	2.59157	+	4.48873i	0.146719	+	0.254124i
$313$	−11.7387	+	4.27252i	−0.663508	+	0.241497i	−0.651750	−	0.758434i	$-0.725965\pi$
$313$	−11.7387	+	4.27252i	−0.663508	+	0.241497i	−0.0117577	+	0.999931i	$0.503743\pi$
$314$	−19.8537	+	7.22616i	−1.12041	+	0.407796i
$315$	−0.814143	−	1.41014i	−0.0458717	−	0.0794522i
$316$	−0.223492	+	0.387100i	−0.0125724	+	0.0217761i
$317$	−3.54499	+	20.1046i	−0.199106	+	1.12919i	0.707342	+	0.706872i	$0.249894\pi$
$317$	−3.54499	+	20.1046i	−0.199106	+	1.12919i	−0.906448	+	0.422317i	$0.861217\pi$
$318$	8.48426	−	7.11914i	0.475774	−	0.399222i
$319$	0.0591159	+	0.0496042i	0.00330986	+	0.00277730i
$320$	0.173648	+	0.984808i	0.00970723	+	0.0550524i
$321$	−6.28671	−	2.28818i	−0.350890	−	0.127714i
$322$	9.10580			0.507447
$323$	−13.6048	−	10.9209i	−0.756994	−	0.607653i
$324$	1.00000			0.0555556
$325$	4.87056	+	1.77274i	0.270170	+	0.0983338i
$326$	−3.22397	−	18.2840i	−0.178559	−	1.01266i
$327$	4.04527	+	3.39439i	0.223704	+	0.187710i
$328$	0.762979	−	0.640215i	0.0421285	−	0.0353500i
$329$	0.557462	−	3.16152i	0.0307339	−	0.174300i
$330$	−0.0122091	+	0.0211467i	−0.000672086	+	0.00116409i
$331$	6.39423	+	11.0751i	0.351459	+	0.608744i	0.986505	−	0.163730i	$-0.0523525\pi$
$331$	6.39423	+	11.0751i	0.351459	+	0.608744i	−0.635047	+	0.772474i	$0.719019\pi$
$332$	11.9761	−	4.35896i	0.657276	−	0.239229i
$333$	−1.08395	+	0.394525i	−0.0594000	+	0.0216198i
$334$	7.97442	+	13.8121i	0.436341	+	0.755764i
$335$	−4.39698	+	7.61579i	−0.240233	+	0.416095i
$336$	0.282749	−	1.60355i	0.0154252	−	0.0874807i
$337$	5.07464	−	4.25813i	0.276433	−	0.231955i	−0.494022	−	0.869450i	$-0.664474\pi$
$337$	5.07464	−	4.25813i	0.276433	−	0.231955i	0.770455	+	0.637495i	$0.220029\pi$
$338$	10.6212	+	8.91221i	0.577715	+	0.484760i
$339$	2.46235	+	13.9647i	0.133737	+	0.758459i
$340$	3.76098	+	1.36888i	0.203968	+	0.0742382i
$341$	0.124473			0.00674061
$342$	−4.12746	−	1.40146i	−0.223187	−	0.0757821i
$343$	−18.4789			−0.997767
$344$	3.53624	+	1.28709i	0.190661	+	0.0693950i
$345$	0.971087	+	5.50731i	0.0522815	+	0.296503i
$346$	10.3610	+	8.69388i	0.557009	+	0.467386i
$347$	−24.5071	+	20.5639i	−1.31561	+	1.10393i	−0.328395	+	0.944540i	$0.606508\pi$
$347$	−24.5071	+	20.5639i	−1.31561	+	1.10393i	−0.987216	+	0.159388i	$0.949048\pi$
$348$	0.548793	−	3.11236i	0.0294184	−	0.166840i
$349$	11.8422	−	20.5113i	0.633898	−	1.09794i	−0.352849	−	0.935680i	$-0.614787\pi$
$349$	11.8422	−	20.5113i	0.633898	−	1.09794i	0.986747	−	0.162264i	$-0.0518796\pi$
$350$	−0.814143	−	1.41014i	−0.0435178	−	0.0753750i
$351$	4.87056	−	1.77274i	0.259971	−	0.0946218i
$352$	−0.0229455	+	0.00835149i	−0.00122300	+	0.000445136i
$353$	2.89542	+	5.01502i	0.154108	+	0.266922i	0.932734	−	0.360566i	$-0.117416\pi$
$353$	2.89542	+	5.01502i	0.154108	+	0.266922i	−0.778626	+	0.627488i	$0.784083\pi$
$354$	−2.54347	+	4.40542i	−0.135184	+	0.234146i
$355$	1.17087	−	6.64033i	0.0621433	−	0.352432i
$356$	8.25337	−	6.92540i	0.437428	−	0.367046i
$357$	−4.99229	−	4.18903i	−0.264220	−	0.221707i
$358$	−1.15223	−	6.53464i	−0.0608975	−	0.345367i
$359$	−1.65256	−	0.601482i	−0.0872186	−	0.0317450i	0.298042	−	0.954553i	$-0.403666\pi$
$359$	−1.65256	−	0.601482i	−0.0872186	−	0.0317450i	−0.385261	+	0.922808i	$0.625889\pi$
$360$	1.00000			0.0527046
$361$	15.0718	+	11.5689i	0.793255	+	0.608890i
$362$	−4.28594			−0.225264
$363$	10.3361	+	3.76202i	0.542502	+	0.197455i
$364$	−1.46553	−	8.31141i	−0.0768145	−	0.435636i
$365$	5.77284	+	4.84399i	0.302164	+	0.253546i
$366$	3.32108	−	2.78672i	0.173596	−	0.145664i
$367$	−2.21101	+	12.5393i	−0.115414	+	0.654545i	0.871131	+	0.491051i	$0.163387\pi$
$367$	−2.21101	+	12.5393i	−0.115414	+	0.654545i	−0.986544	+	0.163493i	$0.947724\pi$
$368$	−2.79613	+	4.84304i	−0.145758	+	0.252461i
$369$	−0.497999	−	0.862560i	−0.0259248	−	0.0449031i
$370$	−1.08395	+	0.394525i	−0.0563518	+	0.0205104i
$371$	−16.9464	+	6.16797i	−0.879811	+	0.320225i
$372$	−2.54879	−	4.41464i	−0.132149	−	0.228888i
$373$	−0.768149	+	1.33047i	−0.0397733	+	0.0688893i	−0.885227	−	0.465160i	$-0.845997\pi$
$373$	−0.768149	+	1.33047i	−0.0397733	+	0.0688893i	0.845454	+	0.534049i	$0.179330\pi$
$374$	−0.0169706	+	0.0962451i	−0.000877529	+	0.00497671i
$375$	0.766044	−	0.642788i	0.0395584	−	0.0331934i
$376$	1.51032	+	1.26731i	0.0778887	+	0.0653564i
$377$	−2.84447	−	16.1318i	−0.146498	−	0.830830i
$378$	−1.53009	−	0.556906i	−0.0786992	−	0.0286442i
$379$	−28.5074			−1.46433			−0.732164	−	0.681128i	$-0.761490\pi$
$379$	−28.5074			−1.46433			−0.732164	+	0.681128i	$0.761490\pi$
$380$	−4.12746	−	1.40146i	−0.211734	−	0.0718932i
$381$	13.2629			0.679476
$382$	−0.0195319	−	0.00710902i	−0.000999338	−	0.000363729i
$383$	−5.95356	−	33.7643i	−0.304213	−	1.72528i	−0.627187	−	0.778869i	$-0.715794\pi$
$383$	−5.95356	−	33.7643i	−0.304213	−	1.72528i	0.322974	−	0.946408i	$-0.395317\pi$
$384$	0.766044	+	0.642788i	0.0390920	+	0.0328021i
$385$	0.0304577	−	0.0255570i	0.00155227	−	0.00130251i
$386$	2.77709	−	15.7497i	0.141350	−	0.801637i
$387$	1.88159	−	3.25901i	0.0956467	−	0.165665i
$388$	−2.89429	−	5.01306i	−0.146935	−	0.254499i
$389$	−17.1607	+	6.24597i	−0.870080	+	0.316683i	−0.738200	−	0.674582i	$-0.764324\pi$
$389$	−17.1607	+	6.24597i	−0.870080	+	0.316683i	−0.131881	+	0.991266i	$0.542102\pi$
$390$	4.87056	−	1.77274i	0.246630	−	0.0897661i
$391$	11.1911	+	19.3835i	0.565958	+	0.980268i
$392$	2.17434	−	3.76607i	0.109821	−	0.190215i
$393$	2.05590	−	11.6596i	0.103706	−	0.588148i
$394$	−18.7707	+	15.7505i	−0.945657	+	0.793500i
$395$	0.342410	+	0.287316i	0.0172285	+	0.0144564i
$396$	0.00424016	+	0.0240471i	0.000213076	+	0.00120841i
$397$	−25.1566	−	9.15624i	−1.26257	−	0.459539i	−0.377941	−	0.925830i	$-0.623368\pi$
$397$	−25.1566	−	9.15624i	−1.26257	−	0.459539i	−0.884631	+	0.466291i	$0.845590\pi$
$398$	−26.1300			−1.30978
$399$	5.53489	+	4.44296i	0.277091	+	0.222426i
$400$	1.00000			0.0500000
$401$	4.86812	+	1.77185i	0.243102	+	0.0884821i	0.460698	−	0.887557i	$-0.347599\pi$
$401$	4.86812	+	1.77185i	0.243102	+	0.0884821i	−0.217595	+	0.976039i	$0.569821\pi$
$402$	1.52705	+	8.66035i	0.0761625	+	0.431939i
$403$	−20.2400	−	16.9834i	−1.00823	−	0.846004i
$404$	2.16819	−	1.81933i	0.107872	−	0.0905149i
$405$	0.173648	−	0.984808i	0.00862865	−	0.0489355i
$406$	−2.57300	+	4.45656i	−0.127696	+	0.221175i
$407$	−0.0140833	−	0.0243930i	−0.000698084	−	0.00120912i
$408$	3.76098	−	1.36888i	0.186196	−	0.0677699i
$409$	28.7825	−	10.4760i	1.42320	−	0.518003i	0.488227	−	0.872716i	$-0.337644\pi$
$409$	28.7825	−	10.4760i	1.42320	−	0.518003i	0.934975	+	0.354713i	$0.115421\pi$
$410$	−0.497999	−	0.862560i	−0.0245944	−	0.0425988i
$411$	1.39610	−	2.41811i	0.0688644	−	0.119277i
$412$	−0.893297	+	5.06614i	−0.0440096	+	0.249591i
$413$	6.34514	−	5.32421i	0.312224	−	0.261987i
$414$	4.28392	+	3.59464i	0.210543	+	0.176667i
$415$	−2.21310	−	12.5511i	−0.108637	−	0.616110i
$416$	4.87056	+	1.77274i	0.238799	+	0.0869156i
$417$	12.4175			0.608089
$418$	0.0162000	−	0.105196i	0.000792366	−	0.00514531i
$419$	−8.92708			−0.436116			−0.218058	−	0.975936i	$-0.569972\pi$
$419$	−8.92708			−0.436116			−0.218058	+	0.975936i	$0.569972\pi$
$420$	−1.53009	−	0.556906i	−0.0746606	−	0.0271743i
$421$	−2.12993	−	12.0794i	−0.103806	−	0.588715i	−0.991690	−	0.128647i	$-0.958936\pi$
$421$	−2.12993	−	12.0794i	−0.103806	−	0.588715i	0.887884	−	0.460067i	$-0.152175\pi$
$422$	0.521314	+	0.437435i	0.0253772	+	0.0212940i
$423$	1.51032	−	1.26731i	0.0734342	−	0.0616186i
$424$	1.92323	−	10.9072i	0.0934001	−	0.529698i
$425$	2.00117	−	3.46614i	0.0970712	−	0.168132i
$426$	−3.37138	−	5.83941i	−0.163344	−	0.282920i
$427$	−6.63348	+	2.41439i	−0.321017	+	0.116841i
$428$	−6.28671	+	2.28818i	−0.303880	+	0.110603i
$429$	0.0632812	+	0.109606i	0.00305525	+	0.00529184i
$430$	1.88159	−	3.25901i	0.0907384	−	0.157164i
$431$	−3.58049	+	20.3060i	−0.172466	+	0.978105i	0.768561	+	0.639776i	$0.220973\pi$
$431$	−3.58049	+	20.3060i	−0.172466	+	0.978105i	−0.941028	+	0.338329i	$0.890138\pi$
$432$	0.766044	−	0.642788i	0.0368563	−	0.0309261i
$433$	23.2325	+	19.4944i	1.11648	+	0.936839i	0.998421	−	0.0561673i	$-0.0178880\pi$
$433$	23.2325	+	19.4944i	1.11648	+	0.936839i	0.118060	+	0.993006i	$0.462332\pi$
$434$	1.44134	+	8.17423i	0.0691864	+	0.392375i
$435$	−2.96978	−	1.08091i	−0.142390	−	0.0518257i
$436$	5.28073			0.252901
$437$	−12.6440	−	20.8405i	−0.604844	−	0.996934i
$438$	7.53591			0.360080
$439$	13.3332	+	4.85290i	0.636360	+	0.231616i	0.639997	−	0.768377i	$-0.278935\pi$
$439$	13.3332	+	4.85290i	0.636360	+	0.231616i	−0.00363707	+	0.999993i	$0.501158\pi$
$440$	0.00424016	+	0.0240471i	0.000202142	+	0.00114640i
$441$	−3.33129	−	2.79528i	−0.158633	−	0.133109i
$442$	15.8914	−	13.3345i	0.755876	−	0.634255i
$443$	4.76094	−	27.0006i	0.226199	−	1.28284i	−0.634181	−	0.773185i	$-0.718663\pi$
$443$	4.76094	−	27.0006i	0.226199	−	1.28284i	0.860380	−	0.509653i	$-0.170226\pi$
$444$	−0.576757	+	0.998972i	−0.0273717	+	0.0474091i
$445$	−5.38701	−	9.33057i	−0.255369	−	0.442311i
$446$	4.33686	−	1.57849i	0.205357	−	0.0747437i
$447$	19.0149	−	6.92085i	0.899372	−	0.327345i
$448$	−0.814143	−	1.41014i	−0.0384646	−	0.0666227i
$449$	9.93201	−	17.2027i	0.468720	−	0.811847i	−0.530640	−	0.847597i	$-0.678049\pi$
$449$	9.93201	−	17.2027i	0.468720	−	0.811847i	0.999361	+	0.0357496i	$0.0113819\pi$
$450$	0.173648	−	0.984808i	0.00818585	−	0.0464243i
$451$	0.0186305	−	0.0156328i	0.000877276	−	0.000736122i
$452$	10.8626	+	9.11481i	0.510934	+	0.428725i
$453$	−1.51017	−	8.56459i	−0.0709539	−	0.402400i
$454$	−3.79327	−	1.38064i	−0.178027	−	0.0647965i
$455$	−8.43963			−0.395656
$456$	−4.06266	+	1.57950i	−0.190251	+	0.0739669i
$457$	2.16785			0.101408			0.0507039	−	0.998714i	$-0.483854\pi$
$457$	2.16785			0.101408			0.0507039	+	0.998714i	$0.483854\pi$
$458$	−26.0650	−	9.48690i	−1.21794	−	0.443294i
$459$	−0.695001	−	3.94154i	−0.0324398	−	0.183976i
$460$	4.28392	+	3.59464i	0.199739	+	0.167601i
$461$	−23.3910	+	19.6274i	−1.08943	+	0.914140i	−0.996669	−	0.0815483i	$-0.974014\pi$
$461$	−23.3910	+	19.6274i	−1.08943	+	0.914140i	−0.0927604	+	0.995688i	$0.529569\pi$
$462$	0.00690419	−	0.0391556i	0.000321212	−	0.00182168i
$463$	3.71019	−	6.42623i	0.172427	−	0.298652i	−0.766841	−	0.641837i	$-0.778172\pi$
$463$	3.71019	−	6.42623i	0.172427	−	0.298652i	0.939268	+	0.343185i	$0.111506\pi$
$464$	−1.58019	−	2.73696i	−0.0733583	−	0.127060i
$465$	−4.79016	+	1.74348i	−0.222139	+	0.0808518i
$466$	−13.1671	+	4.79245i	−0.609956	+	0.222006i
$467$	5.15395	+	8.92689i	0.238496	+	0.413087i	0.960283	−	0.279028i	$-0.0900122\pi$
$467$	5.15395	+	8.92689i	0.238496	+	0.413087i	−0.721787	+	0.692115i	$0.756679\pi$
$468$	2.59157	−	4.48873i	0.119795	−	0.207492i
$469$	2.48648	−	14.1015i	0.114815	−	0.651148i
$470$	1.51032	−	1.26731i	0.0696658	−	0.0584565i
$471$	16.1849	+	13.5807i	0.745760	+	0.625767i
$472$	0.883338	+	5.00966i	0.0406589	+	0.230588i
$473$	0.0863482	+	0.0314282i	0.00397030	+	0.00144507i
$474$	0.446985			0.0205307
$475$	−2.09689	+	3.82139i	−0.0962120	+	0.175338i
$476$	−6.51697			−0.298705
$477$	−10.4075	−	3.78802i	−0.476526	−	0.173441i
$478$	−4.37062	−	24.7870i	−0.199907	−	1.13373i
$479$	27.1093	+	22.7474i	1.23865	+	1.03935i	0.997628	+	0.0688364i	$0.0219286\pi$
$479$	27.1093	+	22.7474i	1.23865	+	1.03935i	0.241027	+	0.970518i	$0.422516\pi$
$480$	0.766044	−	0.642788i	0.0349650	−	0.0293391i
$481$	−1.03821	+	5.88799i	−0.0473384	+	0.268469i
$482$	11.3788	−	19.7086i	0.518290	−	0.897704i
$483$	−4.55290	−	7.88586i	−0.207164	−	0.358819i
$484$	10.3361	−	3.76202i	0.469821	−	0.171001i
$485$	−5.43949	+	1.97981i	−0.246994	+	0.0898986i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	2.81851	−	4.88180i	0.127719	−	0.221215i	−0.795074	−	0.606513i	$-0.792568\pi$
$487$	2.81851	−	4.88180i	0.127719	−	0.221215i	0.922792	+	0.385297i	$0.125901\pi$
$488$	0.752827	−	4.26950i	0.0340789	−	0.193271i
$489$	−14.2224	+	11.9341i	−0.643161	+	0.539676i
$490$	−3.33129	−	2.79528i	−0.150492	−	0.126278i
$491$	−1.88052	−	10.6649i	−0.0848665	−	0.481302i	−0.997385	−	0.0722670i	$-0.976977\pi$
$491$	−1.88052	−	10.6649i	−0.0848665	−	0.481302i	0.912519	−	0.409035i	$-0.134134\pi$
$492$	−0.935932	−	0.340651i	−0.0421951	−	0.0153578i
$493$	−12.6489			−0.569679
$494$	−16.9874	+	14.8951i	−0.764298	+	0.670161i
$495$	0.0244181			0.00109751
$496$	−4.79016	−	1.74348i	−0.215085	−	0.0782844i
$497$	1.90651	+	10.8124i	0.0855187	+	0.485000i
$498$	−9.76303	−	8.19216i	−0.437492	−	0.367099i
$499$	−10.3312	+	8.66890i	−0.462487	+	0.388073i	−0.844045	−	0.536272i	$-0.819832\pi$
$499$	−10.3312	+	8.66890i	−0.462487	+	0.388073i	0.381558	+	0.924345i	$0.375388\pi$
$500$	0.173648	−	0.984808i	0.00776578	−	0.0440419i
$501$	7.97442	−	13.8121i	0.356271	−	0.617079i
$502$	−11.8990	−	20.6097i	−0.531079	−	0.919856i
$503$	20.0883	−	7.31153i	0.895691	−	0.326005i	0.147166	−	0.989112i	$-0.452985\pi$
$503$	20.0883	−	7.31153i	0.895691	−	0.326005i	0.748525	+	0.663107i	$0.230762\pi$
$504$	−1.53009	+	0.556906i	−0.0681555	+	0.0248066i
$505$	−1.41519	−	2.45117i	−0.0629749	−	0.109076i
$506$	−0.0682763	+	0.118258i	−0.00303525	+	0.00525721i
$507$	2.40762	−	13.6543i	0.106926	−	0.606409i
$508$	10.1599	−	8.52520i	0.450774	−	0.378244i
$509$	6.68383	+	5.60840i	0.296255	+	0.248588i	0.778784	−	0.627293i	$-0.215837\pi$
$509$	6.68383	+	5.60840i	0.296255	+	0.248588i	−0.482528	+	0.875880i	$0.660281\pi$
$510$	−0.695001	−	3.94154i	−0.0307751	−	0.174535i
$511$	−11.5306	−	4.19680i	−0.510084	−	0.185655i
$512$	1.00000			0.0441942
$513$	0.850032	+	4.27521i	0.0375298	+	0.188755i
$514$	24.8657			1.09678
$515$	4.83405	+	1.75945i	0.213014	+	0.0775307i
$516$	−0.653470	−	3.70601i	−0.0287674	−	0.163148i
$517$	0.0368791	+	0.0309452i	0.00162194	+	0.00136097i
$518$	1.43882	−	1.20732i	0.0632182	−	0.0530464i
$519$	2.34864	−	13.3198i	0.103094	−	0.584674i
$520$	2.59157	−	4.48873i	0.113648	−	0.196844i
$521$	−5.41878	−	9.38561i	−0.237401	−	0.411191i	0.722567	−	0.691301i	$-0.242962\pi$
$521$	−5.41878	−	9.38561i	−0.237401	−	0.411191i	−0.959968	+	0.280110i	$0.909629\pi$
$522$	−2.96978	+	1.08091i	−0.129984	+	0.0473102i
$523$	−27.9920	+	10.1883i	−1.22401	+	0.445502i	−0.871541	−	0.490323i	$-0.836879\pi$
$523$	−27.9920	+	10.1883i	−1.22401	+	0.445502i	−0.352465	+	0.935825i	$0.614657\pi$
$524$	−5.91972	−	10.2533i	−0.258604	−	0.447916i
$525$	−0.814143	+	1.41014i	−0.0355321	+	0.0615434i
$526$	1.52701	−	8.66009i	0.0665807	−	0.377598i
$527$	−15.6291	+	13.1144i	−0.680814	+	0.571270i
$528$	0.0187054	+	0.0156957i	0.000814046	+	0.000683066i
$529$	1.43667	+	8.14773i	0.0624637	+	0.354249i
$530$	−10.4075	−	3.78802i	−0.452072	−	0.164541i
$531$	5.08694			0.220755
$532$	7.09586	−	0.154256i	0.307644	−	0.00668784i
$533$	−5.16240			−0.223608
$534$	−10.1243	−	3.68493i	−0.438120	−	0.159463i
$535$	1.16174	+	6.58854i	0.0502263	+	0.284847i
$536$	6.73656	+	5.65264i	0.290975	+	0.244157i
$537$	−5.08305	+	4.26519i	−0.219350	+	0.184056i
$538$	−3.03468	+	17.2105i	−0.130835	+	0.741999i
$539$	0.0530934	−	0.0919604i	0.00228689	−	0.00396101i
$540$	−0.500000	−	0.866025i	−0.0215166	−	0.0372678i
$541$	−1.35204	+	0.492103i	−0.0581288	+	0.0211572i	−0.370921	−	0.928664i	$-0.620958\pi$
$541$	−1.35204	+	0.492103i	−0.0581288	+	0.0211572i	0.312792	+	0.949822i	$0.398736\pi$
$542$	0.295633	−	0.107601i	0.0126985	−	0.00462188i
$543$	2.14297	+	3.71174i	0.0919637	+	0.159286i
$544$	2.00117	−	3.46614i	0.0857996	−	0.148609i
$545$	0.916988	−	5.20050i	0.0392795	−	0.222765i
$546$	−6.46513	+	5.42489i	−0.276682	+	0.232164i
$547$	−12.6327	−	10.6001i	−0.540135	−	0.453227i	0.331449	−	0.943473i	$-0.392462\pi$
$547$	−12.6327	−	10.6001i	−0.540135	−	0.453227i	−0.871584	+	0.490246i	$0.836907\pi$
$548$	−0.484860	−	2.74978i	−0.0207122	−	0.117465i
$549$	−4.07391	−	1.48278i	−0.173870	−	0.0632835i
$550$	0.0244181			0.00104119
$551$	13.7725	−	0.299399i	0.586728	−	0.0127548i
$552$	5.59226			0.238023
$553$	−0.683926	−	0.248929i	−0.0290835	−	0.0105855i
$554$	−5.08828	−	28.8571i	−0.216180	−	1.22602i
$555$	0.883642	+	0.741464i	0.0375085	+	0.0314734i
$556$	9.51237	−	7.98183i	0.403414	−	0.338505i
$557$	−0.258905	+	1.46832i	−0.0109701	+	0.0622148i	−0.989801	−	0.142454i	$-0.954501\pi$
$557$	−0.258905	+	1.46832i	−0.0109701	+	0.0622148i	0.978831	+	0.204669i	$0.0656118\pi$
$558$	−2.54879	+	4.41464i	−0.107899	+	0.186887i
$559$	−9.75256	−	16.8919i	−0.412489	−	0.714452i
$560$	−1.53009	+	0.556906i	−0.0646580	+	0.0235336i
$561$	0.0918360	−	0.0334256i	0.00387732	−	0.00141123i
$562$	3.15902	+	5.47158i	0.133255	+	0.230805i
$563$	4.46901	−	7.74056i	0.188346	−	0.326226i	−0.756353	−	0.654164i	$-0.773021\pi$
$563$	4.46901	−	7.74056i	0.188346	−	0.326226i	0.944699	+	0.327939i	$0.106354\pi$
$564$	0.342361	−	1.94163i	0.0144160	−	0.0817573i
$565$	10.8626	−	9.11481i	0.456993	−	0.383463i
$566$	22.3592	+	18.7616i	0.939826	+	0.788608i
$567$	0.282749	+	1.60355i	0.0118743	+	0.0673427i
$568$	−6.33613	−	2.30616i	−0.265858	−	0.0967644i
$569$	−14.9611			−0.627203			−0.313601	−	0.949555i	$-0.601536\pi$
$569$	−14.9611			−0.627203			−0.313601	+	0.949555i	$0.601536\pi$
$570$	0.850032	+	4.27521i	0.0356039	+	0.179069i
$571$	38.3385			1.60442			0.802208	−	0.597045i	$-0.203658\pi$
$571$	38.3385			1.60442			0.802208	+	0.597045i	$0.203658\pi$
$572$	0.118930	+	0.0432869i	0.00497271	+	0.00180992i
$573$	0.00360934	+	0.0204696i	0.000150783	+	0.000855130i
$574$	1.24235	+	1.04245i	0.0518546	+	0.0435112i
$575$	4.28392	−	3.59464i	0.178652	−	0.149907i
$576$	0.173648	−	0.984808i	0.00723534	−	0.0410337i
$577$	−12.7910	+	22.1546i	−0.532495	+	0.922309i	0.466785	+	0.884371i	$0.345412\pi$
$577$	−12.7910	+	22.1546i	−0.532495	+	0.922309i	−0.999280	+	0.0379381i	$0.987921\pi$
$578$	0.490601	+	0.849747i	0.0204063	+	0.0353448i
$579$	−15.0282	+	5.46981i	−0.624549	+	0.227317i
$580$	−2.96978	+	1.08091i	−0.123313	+	0.0448824i
$581$	10.3760	+	17.9718i	0.430470	+	0.745597i
$582$	−2.89429	+	5.01306i	−0.119972	+	0.207798i
$583$	0.0469616	−	0.266332i	0.00194495	−	0.0110304i
$584$	5.77284	−	4.84399i	0.238882	−	0.200446i
$585$	−3.97052	−	3.33166i	−0.164161	−	0.137747i
$586$	−1.19058	−	6.75212i	−0.0491825	−	0.278928i
$587$	9.49146	+	3.45461i	0.391755	+	0.142587i	0.530384	−	0.847757i	$-0.322048\pi$
$587$	9.49146	+	3.45461i	0.391755	+	0.142587i	−0.138630	+	0.990344i	$0.544270\pi$
$588$	−4.34869			−0.179337
$589$	16.7070	−	14.6492i	0.688399	−	0.603611i
$590$	5.08694			0.209426
$591$	23.0257	+	8.38068i	0.947152	+	0.344735i
$592$	0.200305	+	1.13599i	0.00823250	+	0.0466888i
$593$	−15.8971	−	13.3392i	−0.652815	−	0.547776i	0.255109	−	0.966912i	$-0.417889\pi$
$593$	−15.8971	−	13.3392i	−0.652815	−	0.547776i	−0.907924	+	0.419136i	$0.862333\pi$
$594$	0.0187054	−	0.0156957i	0.000767490	−	0.000644001i
$595$	−1.13166	+	6.41796i	−0.0463935	+	0.263111i
$596$	10.1176	−	17.5242i	0.414433	−	0.717819i
$597$	13.0650	+	22.6292i	0.534714	+	0.926152i
$598$	27.2374	−	9.91362i	1.11382	−	0.405398i
$599$	4.80364	−	1.74838i	0.196271	−	0.0714369i	−0.242014	−	0.970273i	$-0.577808\pi$
$599$	4.80364	−	1.74838i	0.196271	−	0.0714369i	0.438286	+	0.898836i	$0.355586\pi$
$600$	−0.500000	−	0.866025i	−0.0204124	−	0.0353553i
$601$	−19.5835	+	33.9197i	−0.798829	+	1.38361i	0.121550	+	0.992585i	$0.461214\pi$
$601$	−19.5835	+	33.9197i	−0.798829	+	1.38361i	−0.920379	+	0.391027i	$0.872120\pi$
$602$	−1.06404	+	6.03445i	−0.0433669	+	0.245946i
$603$	6.73656	−	5.65264i	0.274334	−	0.230193i
$604$	−6.66207	−	5.59014i	−0.271076	−	0.227460i
$605$	−1.91003	−	10.8323i	−0.0776536	−	0.440396i
$606$	−2.65968	−	0.968044i	−0.108042	−	0.0393241i
$607$	22.2115			0.901539			0.450769	−	0.892640i	$-0.351150\pi$
$607$	22.2115			0.901539			0.450769	+	0.892640i	$0.351150\pi$
$608$	−2.09689	+	3.82139i	−0.0850402	+	0.154978i
$609$	5.14599			0.208526
$610$	−4.07391	−	1.48278i	−0.164948	−	0.0600360i
$611$	−1.77451	−	10.0637i	−0.0717888	−	0.407135i
$612$	−3.06598	−	2.57266i	−0.123935	−	0.103994i
$613$	−31.0486	+	26.0529i	−1.25404	+	1.05227i	−0.257752	+	0.966211i	$0.582982\pi$
$613$	−31.0486	+	26.0529i	−1.25404	+	1.05227i	−0.996290	+	0.0860552i	$0.972574\pi$
$614$	0.216317	−	1.22680i	0.00872985	−	0.0495094i
$615$	−0.497999	+	0.862560i	−0.0200813	+	0.0347818i
$616$	−0.0198798	−	0.0344329i	−0.000800981	−	0.00138734i
$617$	27.3734	−	9.96311i	1.10201	−	0.401100i	0.273955	−	0.961743i	$-0.411668\pi$
$617$	27.3734	−	9.96311i	1.10201	−	0.401100i	0.828058	+	0.560643i	$0.189446\pi$
$618$	4.83405	−	1.75945i	0.194454	−	0.0707755i
$619$	−1.42019	−	2.45985i	−0.0570824	−	0.0988696i	0.836072	−	0.548620i	$-0.184846\pi$
$619$	−1.42019	−	2.45985i	−0.0570824	−	0.0988696i	−0.893155	+	0.449750i	$0.851513\pi$
$620$	−2.54879	+	4.41464i	−0.102362	+	0.177296i
$621$	0.971087	−	5.50731i	0.0389684	−	0.221001i
$622$	−13.1799	+	11.0592i	−0.528464	+	0.443434i
$623$	13.4388	+	11.2765i	0.538416	+	0.451785i
$624$	−0.900043	−	5.10440i	−0.0360305	−	0.204339i
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$	12.4920			0.499281
$627$	−0.0992024	+	0.0385684i	−0.00396176	+	0.00154027i
$628$	21.1279			0.843094
$629$	4.33834	+	1.57903i	0.172981	+	0.0629599i
$630$	0.282749	+	1.60355i	0.0112650	+	0.0638869i
$631$	13.2416	+	11.1110i	0.527139	+	0.442322i	0.867112	−	0.498113i	$-0.165974\pi$
$631$	13.2416	+	11.1110i	0.527139	+	0.442322i	−0.339973	+	0.940435i	$0.610418\pi$
$632$	0.342410	−	0.287316i	0.0136203	−	0.0114288i
$633$	0.118172	−	0.670189i	0.00469693	−	0.0266376i
$634$	10.2074	−	17.6797i	0.405387	−	0.702151i
$635$	−6.63143	−	11.4860i	−0.263160	−	0.455807i
$636$	−10.4075	+	3.78802i	−0.412684	+	0.150205i
$637$	−21.1805	+	7.70908i	−0.839203	+	0.305445i
$638$	−0.0385852	−	0.0668315i	−0.00152760	−	0.00264588i
$639$	−3.37138	+	5.83941i	−0.133370	+	0.231003i
$640$	0.173648	−	0.984808i	0.00686405	−	0.0389279i
$641$	29.4145	−	24.6817i	1.16180	−	0.974870i	0.161876	−	0.986811i	$-0.448246\pi$
$641$	29.4145	−	24.6817i	1.16180	−	0.974870i	0.999929	+	0.0119413i	$0.00380111\pi$
$642$	5.12497	+	4.30036i	0.202267	+	0.169722i
$643$	−6.66744	−	37.8129i	−0.262938	−	1.49120i	−0.774843	−	0.632154i	$-0.782171\pi$
$643$	−6.66744	−	37.8129i	−0.262938	−	1.49120i	0.511905	−	0.859042i	$-0.328940\pi$
$644$	−8.55666	−	3.11437i	−0.337180	−	0.122723i
$645$	−3.76319			−0.148175
$646$	9.04922	+	14.9154i	0.356037	+	0.586838i
$647$	32.6398			1.28320			0.641601	−	0.767039i	$-0.278270\pi$
$647$	32.6398			1.28320			0.641601	+	0.767039i	$0.278270\pi$
$648$	−0.939693	−	0.342020i	−0.0369146	−	0.0134358i
$649$	0.0215695	+	0.122326i	0.000846675	+	0.00480173i
$650$	−3.97052	−	3.33166i	−0.155736	−	0.130678i
$651$	6.35842	−	5.33535i	0.249206	−	0.209109i
$652$	−3.22397	+	18.2840i	−0.126260	+	0.716058i
$653$	8.08062	−	13.9960i	0.316219	−	0.547707i	−0.663477	−	0.748197i	$-0.730920\pi$
$653$	8.08062	−	13.9960i	0.316219	−	0.547707i	0.979696	+	0.200489i	$0.0642532\pi$
$654$	−2.64036	−	4.57324i	−0.103246	−	0.178828i
$655$	−11.1254	+	4.04933i	−0.434707	+	0.158220i
$656$	−0.935932	+	0.340651i	−0.0365420	+	0.0133002i
$657$	−3.76795	−	6.52629i	−0.147002	−	0.254615i
$658$	−1.60515	+	2.78020i	−0.0625752	+	0.108383i
$659$	−0.954479	+	5.41312i	−0.0371812	+	0.210865i	−0.997738	−	0.0672175i	$-0.978588\pi$
$659$	−0.954479	+	5.41312i	−0.0371812	+	0.210865i	0.960557	+	0.278083i	$0.0896990\pi$
$660$	0.0187054	−	0.0156957i	0.000728105	−	0.000610953i
$661$	4.86043	+	4.07838i	0.189049	+	0.158631i	0.732400	−	0.680875i	$-0.238400\pi$
$661$	4.86043	+	4.07838i	0.189049	+	0.158631i	−0.543351	+	0.839506i	$0.682845\pi$
$662$	−2.22069	−	12.5942i	−0.0863096	−	0.489486i
$663$	−19.4937	−	7.09512i	−0.757072	−	0.275551i
$664$	−12.7447			−0.494592
$665$	1.08027	−	7.01484i	0.0418911	−	0.272024i
$666$	1.15351			0.0446977
$667$	−16.6078	−	6.04474i	−0.643057	−	0.234053i
$668$	−2.76949	−	15.7065i	−0.107155	−	0.607704i
$669$	−3.53544	−	2.96659i	−0.136688	−	0.114695i
$670$	6.73656	−	5.65264i	0.260256	−	0.218381i
$671$	0.0183826	−	0.104253i	0.000709653	−	0.00402464i
$672$	−0.814143	+	1.41014i	−0.0314062	+	0.0543972i
$673$	25.1340	+	43.5334i	0.968846	+	1.67809i	0.698906	+	0.715213i	$0.253670\pi$
$673$	25.1340	+	43.5334i	0.968846	+	1.67809i	0.269940	+	0.962877i	$0.412996\pi$
$674$	−6.22496	+	2.26570i	−0.239777	+	0.0872716i
$675$	−0.939693	+	0.342020i	−0.0361688	+	0.0131644i
$676$	−6.93247	−	12.0074i	−0.266633	−	0.461823i
$677$	−17.5836	+	30.4557i	−0.675793	+	1.17051i	0.300443	+	0.953800i	$0.402865\pi$
$677$	−17.5836	+	30.4557i	−0.675793	+	1.17051i	−0.976236	+	0.216709i	$0.930468\pi$
$678$	2.46235	−	13.9647i	0.0945661	−	0.536311i
$679$	7.22032	−	6.05857i	0.277091	−	0.232507i
$680$	−3.06598	−	2.57266i	−0.117575	−	0.0986570i
$681$	0.700968	+	3.97539i	0.0268612	+	0.152337i
$682$	−0.116967	−	0.0425724i	−0.00447889	−	0.00163018i
$683$	2.69557			0.103143			0.0515715	−	0.998669i	$-0.483577\pi$
$683$	2.69557			0.103143			0.0515715	+	0.998669i	$0.483577\pi$
$684$	3.39922	+	2.72861i	0.129972	+	0.104331i
$685$	−2.79219			−0.106684
$686$	17.3645	+	6.32016i	0.662979	+	0.241305i
$687$	4.81663	+	27.3164i	0.183766	+	1.04219i
$688$	−2.88277	−	2.41893i	−0.109904	−	0.0922208i
$689$	−43.9751	+	36.8995i	−1.67532	+	1.40576i
$690$	0.971087	−	5.50731i	0.0369686	−	0.209660i
$691$	−21.1089	+	36.5617i	−0.803020	+	1.39087i	0.114600	+	0.993412i	$0.463441\pi$
$691$	−21.1089	+	36.5617i	−0.803020	+	1.39087i	−0.917620	+	0.397459i	$0.869892\pi$
$692$	−6.76264	−	11.7132i	−0.257077	−	0.445270i
$693$	−0.0373619	+	0.0135986i	−0.00141926	+	0.000516568i
$694$	30.0624	−	10.9418i	1.14115	−	0.415346i
$695$	−6.20876	−	10.7539i	−0.235512	−	0.407918i
$696$	−1.58019	+	2.73696i	−0.0598968	+	0.103744i
$697$	−0.692219	+	3.92577i	−0.0262197	+	0.148699i
$698$	−18.1433	+	15.2240i	−0.686734	+	0.576238i
$699$	10.7339	+	9.00685i	0.405995	+	0.340670i
$700$	0.282749	+	1.60355i	0.0106869	+	0.0606084i
$701$	24.9742	+	9.08988i	0.943264	+	0.343320i	0.767454	−	0.641104i	$-0.221523\pi$
$701$	24.9742	+	9.08988i	0.943264	+	0.343320i	0.175810	+	0.984424i	$0.443746\pi$
$702$	−5.18314			−0.195625
$703$	−4.76108	−	1.61660i	−0.179567	−	0.0609712i
$704$	0.0244181			0.000920292
$705$	−1.85268	−	0.674320i	−0.0697759	−	0.0253964i
$706$	−1.00557	−	5.70287i	−0.0378451	−	0.214630i
$707$	3.53043	+	2.96239i	0.132776	+	0.111412i
$708$	3.89682	−	3.26982i	0.146452	−	0.122888i
$709$	1.97967	−	11.2272i	0.0743479	−	0.421648i	−0.924803	−	0.380446i	$-0.875770\pi$
$709$	1.97967	−	11.2272i	0.0743479	−	0.421648i	0.999151	−	0.0412015i	$-0.0131186\pi$
$710$	−3.37138	+	5.83941i	−0.126526	+	0.219149i
$711$	−0.223492	−	0.387100i	−0.00838162	−	0.0145174i
$712$	−10.1243	+	3.68493i	−0.379423	+	0.138099i
$713$	−26.7879	+	9.74999i	−1.00321	+	0.365140i
$714$	3.25848	+	5.64386i	0.121946	+	0.211216i
$715$	0.0632812	−	0.109606i	0.00236658	−	0.00409904i
$716$	−1.15223	+	6.53464i	−0.0430610	+	0.244211i
$717$	−19.2809	+	16.1786i	−0.720057	+	0.604200i
$718$	1.34718	+	1.13042i	0.0502762	+	0.0421867i
$719$	3.77346	+	21.4004i	0.140726	+	0.798099i	0.970700	+	0.240296i	$0.0772444\pi$
$719$	3.77346	+	21.4004i	0.140726	+	0.798099i	−0.829973	+	0.557803i	$0.811644\pi$
$720$	−0.939693	−	0.342020i	−0.0350203	−	0.0127463i
$721$	−8.37638			−0.311953
$722$	−10.2061	−	16.0261i	−0.379831	−	0.596429i
$723$	−22.7576			−0.846364
$724$	4.02747	+	1.46588i	0.149680	+	0.0544790i
$725$	0.548793	+	3.11236i	0.0203817	+	0.115590i
$726$	−8.42603	−	7.07028i	−0.312719	−	0.262403i
$727$	10.3172	−	8.65714i	0.382643	−	0.321076i	−0.431096	−	0.902306i	$-0.641873\pi$
$727$	10.3172	−	8.65714i	0.382643	−	0.321076i	0.813739	+	0.581230i	$0.197429\pi$
$728$	−1.46553	+	8.31141i	−0.0543160	+	0.308042i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−3.76795	−	6.52629i	−0.139458	−	0.241549i
$731$	−14.1533	+	5.15136i	−0.523477	+	0.190530i
$732$	−4.07391	+	1.48278i	−0.150576	+	0.0548051i
$733$	−5.61566	−	9.72661i	−0.207419	−	0.359261i	0.743482	−	0.668756i	$-0.233173\pi$
$733$	−5.61566	−	9.72661i	−0.207419	−	0.359261i	−0.950901	+	0.309496i	$0.899840\pi$
$734$	6.36636	−	11.0269i	0.234986	−	0.407009i
$735$	−0.755141	+	4.28262i	−0.0278538	+	0.157967i
$736$	4.28392	−	3.59464i	0.157908	−	0.132500i
$737$	0.164494	+	0.138027i	0.00605922	+	0.00508429i
$738$	0.172953	+	0.980867i	0.00636650	+	0.0361062i
$739$	−39.3128	−	14.3087i	−1.44614	−	0.526353i	−0.504632	−	0.863335i	$-0.668372\pi$
$739$	−39.3128	−	14.3087i	−1.44614	−	0.526353i	−0.941511	+	0.336981i	$0.890594\pi$
$740$	1.15351			0.0424040
$741$	21.3932	+	7.26395i	0.785899	+	0.266848i
$742$	18.0339			0.662047
$743$	23.7391	+	8.64031i	0.870902	+	0.316982i	0.738532	−	0.674218i	$-0.235519\pi$
$743$	23.7391	+	8.64031i	0.870902	+	0.316982i	0.132370	+	0.991200i	$0.457741\pi$
$744$	0.885187	+	5.02014i	0.0324525	+	0.184047i
$745$	−15.5011	−	13.0069i	−0.567915	−	0.476537i
$746$	1.17687	−	0.987514i	0.0430884	−	0.0361554i
$747$	−2.21310	+	12.5511i	−0.0809731	+	0.459221i
$748$	0.0488649	−	0.0846365i	0.00178668	−	0.00309462i
$749$	−5.44676	−	9.43407i	−0.199020	−	0.344713i
$750$	−0.939693	+	0.342020i	−0.0343127	+	0.0124888i
$751$	4.28969	−	1.56132i	0.156533	−	0.0569734i	−0.262565	−	0.964914i	$-0.584568\pi$
$751$	4.28969	−	1.56132i	0.156533	−	0.0569734i	0.419098	+	0.907941i	$0.362346\pi$
$752$	−0.985790	−	1.70744i	−0.0359481	−	0.0622639i
$753$	−11.8990	+	20.6097i	−0.433624	+	0.751059i
$754$	−2.84447	+	16.1318i	−0.103590	+	0.587486i
$755$	−6.66207	+	5.59014i	−0.242457	+	0.203446i
$756$	1.24734	+	1.04664i	0.0453653	+	0.0380660i
$757$	−1.38127	−	7.83359i	−0.0502032	−	0.284717i	0.949363	−	0.314183i	$-0.101730\pi$
$757$	−1.38127	−	7.83359i	−0.0502032	−	0.284717i	−0.999566	+	0.0294660i	$0.990619\pi$
$758$	26.7882	+	9.75011i	0.972992	+	0.354140i
$759$	0.136553			0.00495654
$760$	3.39922	+	2.72861i	0.123303	+	0.0989772i
$761$	−13.6698			−0.495528			−0.247764	−	0.968820i	$-0.579696\pi$
$761$	−13.6698			−0.495528			−0.247764	+	0.968820i	$0.579696\pi$
$762$	−12.4630	−	4.53616i	−0.451487	−	0.164328i
$763$	1.49312	+	8.46790i	0.0540545	+	0.306559i
$764$	0.0159225	+	0.0133606i	0.000576057	+	0.000483369i
$765$	−3.06598	+	2.57266i	−0.110851	+	0.0930147i
$766$	−5.95356	+	33.7643i	−0.215111	+	1.21995i
$767$	13.1832	−	22.8339i	0.476017	−	0.824485i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	9.98040	−	3.63257i	0.359902	−	0.130994i	−0.155739	−	0.987798i	$-0.549776\pi$
$769$	9.98040	−	3.63257i	0.359902	−	0.130994i	0.515641	+	0.856804i	$0.327554\pi$
$770$	−0.0373619	+	0.0135986i	−0.00134643	+	0.000490060i
$771$	−12.4328	−	21.5343i	−0.447758	−	0.775540i
$772$	−7.99632	+	13.8500i	−0.287794	+	0.498474i
$773$	0.587680	−	3.33290i	0.0211374	−	0.119876i	−0.972413	−	0.233264i	$-0.925059\pi$
$773$	0.587680	−	3.33290i	0.0211374	−	0.119876i	0.993551	+	0.113388i	$0.0361704\pi$
$774$	−2.88277	+	2.41893i	−0.103619	+	0.0869466i
$775$	3.90498	+	3.27667i	0.140271	+	0.117701i
$776$	1.00518	+	5.70064i	0.0360837	+	0.204641i
$777$	−1.76498	−	0.642399i	−0.0633182	−	0.0230459i
$778$	18.2620			0.654724
$779$	0.660785	−	4.29087i	0.0236751	−	0.153736i
$780$	−5.18314			−0.185586
$781$	−0.154716	−	0.0563121i	−0.00553619	−	0.00201501i
$782$	−3.88663	−	22.0422i	−0.138986	−	0.788226i
$783$	2.42099	+	2.03145i	0.0865190	+	0.0725981i
$784$	−3.33129	+	2.79528i	−0.118975	+	0.0998315i
$785$	3.66882	−	20.8069i	0.130946	−	0.742630i
$786$	−5.91972	+	10.2533i	−0.211149	+	0.365722i
$787$	−15.3519	−	26.5903i	−0.547237	−	0.947842i	−0.998462	−	0.0554320i	$-0.982346\pi$
$787$	−15.3519	−	26.5903i	−0.547237	−	0.947842i	0.451226	−	0.892410i	$-0.350987\pi$
$788$	23.0257	−	8.38068i	0.820258	−	0.298549i
$789$	−8.26337	+	3.00762i	−0.294184	+	0.107074i
$790$	−0.223492	−	0.387100i	−0.00795150	−	0.0137724i
$791$	−11.5447	+	19.9959i	−0.410481	+	0.710973i
$792$	0.00424016	−	0.0240471i	0.000150668	−	0.000854478i
$793$	−17.2136	+	14.4439i	−0.611273	+	0.512919i
$794$	20.5078	+	17.2081i	0.727796	+	0.610693i
$795$	1.92323	+	10.9072i	0.0682098	+	0.386837i
$796$	24.5541	+	8.93697i	0.870298	+	0.316763i
$797$	46.4701			1.64606			0.823028	−	0.568000i	$-0.192283\pi$
$797$	46.4701			1.64606			0.823028	+	0.568000i	$0.192283\pi$
$798$	−3.68152	−	6.06806i	−0.130324	−	0.214807i
$799$	−7.89095			−0.279162
$800$	−0.939693	−	0.342020i	−0.0332232	−	0.0120922i
$801$	1.87089	+	10.6103i	0.0661046	+	0.374898i
$802$	−3.96853	−	3.32999i	−0.140134	−	0.117586i
$803$	0.140962	−	0.118281i	0.00497444	−	0.00417405i
$804$	1.52705	−	8.66035i	0.0538550	−	0.305427i
$805$	−4.55290	+	7.88586i	−0.160469	+	0.277940i
$806$	13.2108	+	22.8817i	0.465329	+	0.805973i
$807$	16.4221	−	5.97716i	0.578086	−	0.210406i
$808$	−2.65968	+	0.968044i	−0.0935672	+	0.0340557i
$809$	9.16474	+	15.8738i	0.322215	+	0.558093i	0.980945	−	0.194287i	$-0.0622392\pi$
$809$	9.16474	+	15.8738i	0.322215	+	0.558093i	−0.658730	+	0.752380i	$0.728906\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	9.17090	−	52.0107i	0.322034	−	1.82634i	−0.207715	−	0.978189i	$-0.566603\pi$
$811$	9.17090	−	52.0107i	0.322034	−	1.82634i	0.529749	−	0.848155i	$-0.322286\pi$
$812$	3.94206	−	3.30778i	0.138339	−	0.116080i
$813$	−0.241002	−	0.202225i	−0.00845231	−	0.00709233i
$814$	0.00489108	+	0.0277387i	0.000171432	+	0.000972241i
$815$	17.4464	+	6.34998i	0.611121	+	0.222430i
$816$	−4.00235			−0.140110
$817$	15.2885	−	5.94395i	0.534878	−	0.207953i
$818$	−30.6297			−1.07094
$819$	7.93066	+	2.88652i	0.277120	+	0.100863i
$820$	0.172953	+	0.980867i	0.00603979	+	0.0342533i
$821$	0.559594	+	0.469555i	0.0195300	+	0.0163876i	0.652500	−	0.757788i	$-0.273720\pi$
$821$	0.559594	+	0.469555i	0.0195300	+	0.0163876i	−0.632970	+	0.774176i	$0.718165\pi$
$822$	−2.13895	+	1.79479i	−0.0746043	+	0.0626004i
$823$	7.07008	−	40.0964i	0.246447	−	1.39767i	−0.570660	−	0.821187i	$-0.693312\pi$
$823$	7.07008	−	40.0964i	0.246447	−	1.39767i	0.817107	−	0.576486i	$-0.195576\pi$
$824$	2.57215	−	4.45509i	0.0896050	−	0.155200i
$825$	−0.0122091	−	0.0211467i	−0.000425065	−	0.000736234i
$826$	−7.78347	+	2.83295i	−0.270822	+	0.0985710i
$827$	24.0638	−	8.75851i	0.836781	−	0.304563i	0.112142	−	0.993692i	$-0.464229\pi$
$827$	24.0638	−	8.75851i	0.836781	−	0.304563i	0.724639	+	0.689129i	$0.242007\pi$
$828$	−2.79613	−	4.84304i	−0.0971723	−	0.168307i
$829$	10.5564	−	18.2842i	0.366638	−	0.635036i	−0.622399	−	0.782700i	$-0.713842\pi$
$829$	10.5564	−	18.2842i	0.366638	−	0.635036i	0.989038	+	0.147664i	$0.0471753\pi$
$830$	−2.21310	+	12.5511i	−0.0768178	+	0.435655i
$831$	−22.4468	+	18.8351i	−0.778672	+	0.653383i
$832$	−3.97052	−	3.33166i	−0.137653	−	0.115504i
$833$	3.02234	+	17.1405i	0.104718	+	0.593884i
$834$	−11.6687	−	4.24704i	−0.404052	−	0.147063i
$835$	−15.9488			−0.551932
$836$	−0.0512021	+	0.0933112i	−0.00177086	+	0.00322724i
$837$	5.09759			0.176198
$838$	8.38871	+	3.05324i	0.289783	+	0.105472i
$839$	4.90163	+	27.7985i	0.169223	+	0.959711i	0.944603	+	0.328216i	$0.106447\pi$
$839$	4.90163	+	27.7985i	0.169223	+	0.959711i	−0.775380	+	0.631495i	$0.782441\pi$
$840$	1.24734	+	1.04664i	0.0430373	+	0.0361126i
$841$	−14.5641	+	12.2207i	−0.502209	+	0.421403i
$842$	−2.12993	+	12.0794i	−0.0734021	+	0.416284i
$843$	3.15902	−	5.47158i	0.108802	−	0.188451i
$844$	−0.340264	−	0.589354i	−0.0117124	−	0.0202864i
$845$	−13.0288	+	4.74209i	−0.448204	+	0.163133i
$846$	−1.85268	+	0.674320i	−0.0636964	+	0.0231836i
$847$	8.95508	+	15.5107i	0.307700	+	0.532953i
$848$	−5.53771	+	9.59159i	−0.190166	+	0.329377i
$849$	5.06841	−	28.7444i	0.173947	−	0.986505i
$850$	−3.06598	+	2.57266i	−0.105162	+	0.0882415i
$851$	4.94156	+	4.14646i	0.169395	+	0.142139i
$852$	1.17087	+	6.64033i	0.0401133	+	0.227494i
$853$	−53.5829	−	19.5026i	−1.83464	−	0.667756i	−0.991506	−	0.130060i	$-0.958483\pi$
$853$	−53.5829	−	19.5026i	−1.83464	−	0.667756i	−0.843139	−	0.537696i	$-0.819295\pi$
$854$	7.05920			0.241561
$855$	3.27743	−	2.87376i	0.112086	−	0.0982804i
$856$	6.69018			0.228666
$857$	−21.1669	−	7.70411i	−0.723046	−	0.263167i	−0.0458278	−	0.998949i	$-0.514593\pi$
$857$	−21.1669	−	7.70411i	−0.723046	−	0.263167i	−0.677218	+	0.735782i	$0.736815\pi$
$858$	−0.0219773	−	0.124640i	−0.000750294	−	0.00425513i
$859$	−5.04714	−	4.23505i	−0.172206	−	0.144498i	0.552611	−	0.833439i	$-0.313631\pi$
$859$	−5.04714	−	4.23505i	−0.172206	−	0.144498i	−0.724817	+	0.688941i	$0.758076\pi$
$860$	−2.88277	+	2.41893i	−0.0983015	+	0.0824848i
$861$	0.281617	−	1.59713i	0.00959749	−	0.0544301i
$862$	10.3096	−	17.8568i	0.351147	−	0.608205i
$863$	2.55187	+	4.41998i	0.0868668	+	0.150458i	0.906185	−	0.422881i	$-0.138981\pi$
$863$	2.55187	+	4.41998i	0.0868668	+	0.150458i	−0.819318	+	0.573339i	$0.805648\pi$
$864$	−0.939693	+	0.342020i	−0.0319690	+	0.0116358i
$865$	−12.7096	+	4.62592i	−0.432140	+	0.157286i
$866$	−15.1639	−	26.2647i	−0.515291	−	0.892510i
$867$	0.490601	−	0.849747i	0.0166617	−	0.0288589i
$868$	1.44134	−	8.17423i	0.0489222	−	0.277451i
$869$	0.00836101	−	0.00701572i	0.000283628	−	0.000237992i
$870$	2.42099	+	2.03145i	0.0820792	+	0.0688726i
$871$	−7.91493	−	44.8878i	−0.268187	−	1.52097i
$872$	−4.96226	−	1.80611i	−0.168043	−	0.0611628i
$873$	5.78858			0.195914
$874$	4.75360	+	23.9081i	0.160793	+	0.808704i
$875$	1.62829			0.0550461
$876$	−7.08144	−	2.57743i	−0.239260	−	0.0870834i
$877$	9.41993	+	53.4231i	0.318088	+	1.80397i	0.554354	+	0.832281i	$0.312965\pi$
$877$	9.41993	+	53.4231i	0.318088	+	1.80397i	−0.236266	+	0.971688i	$0.575924\pi$
$878$	−10.8693	−	9.12046i	−0.366823	−	0.307801i
$879$	−5.25222	+	4.40713i	−0.177153	+	0.148649i
$880$	0.00424016	−	0.0240471i	0.000142936	−	0.000810629i
$881$	−0.614119	+	1.06369i	−0.0206902	+	0.0358365i	−0.876185	−	0.481975i	$-0.839920\pi$
$881$	−0.614119	+	1.06369i	−0.0206902	+	0.0358365i	0.855495	+	0.517811i	$0.173253\pi$
$882$	2.17434	+	3.76607i	0.0732139	+	0.126810i
$883$	49.7549	−	18.1093i	1.67439	−	0.609426i	0.681862	−	0.731481i	$-0.261171\pi$
$883$	49.7549	−	18.1093i	1.67439	−	0.609426i	0.992523	+	0.122055i	$0.0389484\pi$
$884$	−19.4937	+	7.09512i	−0.655643	+	0.238635i
$885$	−2.54347	−	4.40542i	−0.0854979	−	0.148087i
$886$	−13.7086	+	23.7439i	−0.460549	+	0.797694i
$887$	−0.214605	+	1.21709i	−0.00720574	+	0.0408658i	−0.988199	−	0.153178i	$-0.951049\pi$
$887$	−0.214605	+	1.21709i	−0.00720574	+	0.0408658i	0.980993	+	0.194044i	$0.0621604\pi$
$888$	0.883642	−	0.741464i	0.0296531	−	0.0248819i
$889$	16.5433	+	13.8815i	0.554844	+	0.465569i
$890$	1.87089	+	10.6103i	0.0627123	+	0.355659i
$891$	−0.0229455	−	0.00835149i	−0.000768704	−	0.000279785i
$892$	−4.61520			−0.154528
$893$	8.59189	−	0.186778i	0.287517	−	0.00625029i
$894$	−20.2352			−0.676766
$895$	6.23529	+	2.26946i	0.208423	+	0.0758596i
$896$	0.282749	+	1.60355i	0.00944597	+	0.0535708i
$897$	−22.2042	−	18.6315i	−0.741376	−	0.622088i
$898$	−15.2167	+	12.7683i	−0.507788	+	0.426085i
$899$	2.79752	−	15.8655i	0.0933026	−	0.529145i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	22.1638	+	38.3889i	0.738385	+	1.27892i
$902$	−0.0228537	+	0.00831806i	−0.000760945	+	0.000276961i
$903$	5.75800	−	2.09574i	0.191614	−	0.0697419i
$904$	−7.09007	−	12.2804i	−0.235812	−	0.408438i
$905$	2.14297	−	3.71174i	0.0712348	−	0.123382i
$906$	−1.51017	+	8.56459i	−0.0501720	+	0.284539i
$907$	−19.6155	+	16.4593i	−0.651321	+	0.546523i	−0.907471	−	0.420114i	$-0.861990\pi$
$907$	−19.6155	+	16.4593i	−0.651321	+	0.546523i	0.256151	+	0.966637i	$0.417546\pi$
$908$	3.09230	+	2.59475i	0.102622	+	0.0861098i
$909$	0.491489	+	2.78737i	0.0163017	+	0.0924513i
$910$	7.93066	+	2.88652i	0.262899	+	0.0956873i
$911$	22.7530			0.753840			0.376920	−	0.926246i	$-0.376983\pi$
$911$	22.7530			0.753840			0.376920	+	0.926246i	$0.376983\pi$
$912$	4.35787	−	0.0947352i	0.144303	−	0.00313700i
$913$	−0.311202			−0.0102993
$914$	−2.03711	−	0.741448i	−0.0673817	−	0.0245249i
$915$	0.752827	+	4.26950i	0.0248877	+	0.141145i
$916$	21.2484	+	17.8295i	0.702068	+	0.589105i
$917$	14.7678	−	12.3917i	0.487676	−	0.409208i
$918$	−0.695001	+	3.94154i	−0.0229384	+	0.130090i
$919$	−16.1288	+	27.9359i	−0.532039	+	0.921519i	0.467261	+	0.884119i	$0.345241\pi$
$919$	−16.1288	+	27.9359i	−0.532039	+	0.921519i	−0.999300	+	0.0373998i	$0.988092\pi$
$920$	−2.79613	−	4.84304i	−0.0921858	−	0.159670i
$921$	−1.17059	+	0.426062i	−0.0385724	+	0.0140392i
$922$	28.6934	−	10.4435i	0.944966	−	0.343939i
$923$	17.4744	+	30.2665i	0.575175	+	0.996233i
$924$	−0.0198798	+	0.0344329i	−0.000653998	+	0.00113276i
$925$	0.200305	−	1.13599i	0.00658600	−	0.0373511i
$926$	−5.68434	+	4.76973i	−0.186799	+	0.156743i
$927$	−3.94076	−	3.30669i	−0.129431	−	0.108606i
$928$	0.548793	+	3.11236i	0.0180150	+	0.102168i
$929$	15.5842	+	5.67219i	0.511301	+	0.186099i	0.584770	−	0.811199i	$-0.301185\pi$
$929$	15.5842	+	5.67219i	0.511301	+	0.186099i	−0.0734687	+	0.997298i	$0.523407\pi$
$930$	5.09759			0.167156
$931$	−3.69652	−	18.5916i	−0.121149	−	0.609314i
$932$	14.0122			0.458984
$933$	16.1675	+	5.88448i	0.529300	+	0.192649i
$934$	−1.78995	−	10.1513i	−0.0585688	−	0.332160i
$935$	−0.0748654	−	0.0628195i	−0.00244836	−	0.00205442i
$936$	−3.97052	+	3.33166i	−0.129780	+	0.108899i
$937$	−3.76459	+	21.3500i	−0.122984	+	0.697475i	0.859501	+	0.511134i	$0.170774\pi$
$937$	−3.76459	+	21.3500i	−0.122984	+	0.697475i	−0.982485	+	0.186342i	$0.940337\pi$
$938$	−7.15953	+	12.4007i	−0.233767	+	0.404896i
$939$	−6.24601	−	10.8184i	−0.203831	−	0.353045i
$940$	−1.85268	+	0.674320i	−0.0604277	+	0.0219939i
$941$	−45.2881	+	16.4835i	−1.47635	+	0.537348i	−0.949817	−	0.312807i	$-0.898731\pi$
$941$	−45.2881	+	16.4835i	−1.47635	+	0.537348i	−0.526534	+	0.850154i	$0.676509\pi$
$942$	−10.5639	−	18.2973i	−0.344192	−	0.596157i
$943$	−2.78494	+	4.82366i	−0.0906902	+	0.157080i
$944$	0.883338	−	5.00966i	0.0287502	−	0.163051i
$945$	1.24734	−	1.04664i	0.0405759	−	0.0340473i
$946$	−0.0703917	−	0.0590657i	−0.00228863	−	0.00192039i
$947$	−0.607634	−	3.44606i	−0.0197454	−	0.111982i	0.973342	−	0.229358i	$-0.0736627\pi$
$947$	−0.607634	−	3.44606i	−0.0197454	−	0.111982i	−0.993088	+	0.117376i	$0.962552\pi$
$948$	−0.420028	−	0.152878i	−0.0136419	−	0.00496524i
$949$	−39.0597			−1.26793
$950$	3.27743	−	2.87376i	0.106334	−	0.0932369i
$951$	−20.4148			−0.661994
$952$	6.12395	+	2.22893i	0.198478	+	0.0722402i
$953$	−7.10861	−	40.3149i	−0.230270	−	1.30593i	−0.852349	−	0.522973i	$-0.824823\pi$
$953$	−7.10861	−	40.3149i	−0.230270	−	1.30593i	0.622079	−	0.782955i	$-0.286288\pi$
$954$	8.48426	+	7.11914i	0.274688	+	0.230491i
$955$	0.0159225	−	0.0133606i	0.000515241	−	0.000432339i
$956$	−4.37062	+	24.7870i	−0.141356	+	0.801669i
$957$	−0.0385852	+	0.0668315i	−0.00124728	+	0.00216036i
$958$	−17.6943	−	30.6475i	−0.571678	−	0.990175i
$959$	4.27230	−	1.55499i	0.137960	−	0.0502133i
$960$	−0.939693	+	0.342020i	−0.0303284	+	0.0110387i
$961$	2.50731	+	4.34278i	0.0808808	+	0.140090i
$962$	2.98941	−	5.17781i	0.0963824	−	0.166939i
$963$	1.16174	−	6.58854i	0.0374365	−	0.212313i
$964$	−17.4333	+	14.6283i	−0.561489	+	0.471146i
$965$	12.2511	+	10.2799i	0.394376	+	0.330921i
$966$	1.58121	+	8.96747i	0.0508745	+	0.288523i
$967$	54.6326	+	19.8846i	1.75687	+	0.639447i	0.999902	−	0.0140107i	$-0.00445988\pi$
$967$	54.6326	+	19.8846i	1.75687	+	0.639447i	0.756963	+	0.653457i	$0.226682\pi$
$968$	−10.9994			−0.353534
$969$	8.39249	−	15.2945i	0.269606	−	0.491332i
$970$	5.78858			0.185860
$971$	21.4135	+	7.79388i	0.687192	+	0.250117i	0.661932	−	0.749564i	$-0.269737\pi$
$971$	21.4135	+	7.79388i	0.687192	+	0.250117i	0.0252595	+	0.999681i	$0.491959\pi$
$972$	0.173648	+	0.984808i	0.00556977	+	0.0315877i
$973$	15.4889	+	12.9967i	0.496550	+	0.416655i
$974$	−4.31820	+	3.62340i	−0.138364	+	0.116101i
$975$	−0.900043	+	5.10440i	−0.0288244	+	0.163472i
$976$	−2.16768	+	3.75453i	−0.0693858	+	0.120180i
$977$	2.74475	+	4.75405i	0.0878125	+	0.152096i	0.906586	−	0.422021i	$-0.138679\pi$
$977$	2.74475	+	4.75405i	0.0878125	+	0.152096i	−0.818774	+	0.574116i	$0.805346\pi$
$978$	17.4464	−	6.34998i	0.557875	−	0.203050i
$979$	−0.247215	+	0.0899790i	−0.00790104	+	0.00287574i
$980$	2.17434	+	3.76607i	0.0694568	+	0.120303i
$981$	−2.64036	+	4.57324i	−0.0843003	+	0.146012i
$982$	−1.88052	+	10.6649i	−0.0600096	+	0.340332i
$983$	47.0479	−	39.4779i	1.50059	−	1.25915i	0.620636	−	0.784099i	$-0.286874\pi$
$983$	47.0479	−	39.4779i	1.50059	−	1.25915i	0.879959	−	0.475050i	$-0.157570\pi$
$984$	0.762979	+	0.640215i	0.0243229	+	0.0204093i
$985$	−4.25498	−	24.1312i	−0.135575	−	0.768884i
$986$	11.8861	+	4.32619i	0.378530	+	0.137774i
$987$	3.21030			0.102185
$988$	21.0573	−	8.18677i	0.669922	−	0.260456i
$989$	−21.0447			−0.669183
$990$	−0.0229455	−	0.00835149i	−0.000729257	−	0.000265428i
$991$	−4.04023	−	22.9133i	−0.128342	−	0.727865i	−0.979266	−	0.202576i	$-0.935069\pi$
$991$	−4.04023	−	22.9133i	−0.128342	−	0.727865i	0.850924	−	0.525288i	$-0.176043\pi$
$992$	3.90498	+	3.27667i	0.123983	+	0.104034i
$993$	−9.79652	+	8.22026i	−0.310883	+	0.260862i
$994$	1.90651	−	10.8124i	0.0604708	−	0.342947i
$995$	13.0650	−	22.6292i	0.414188	−	0.717394i
$996$	6.37237	+	11.0373i	0.201916	+	0.349729i
$997$	−15.5581	+	5.66270i	−0.492731	+	0.179339i	−0.576422	−	0.817152i	$-0.695551\pi$
$997$	−15.5581	+	5.66270i	−0.492731	+	0.179339i	0.0836907	+	0.996492i	$0.473329\pi$
$998$	12.6731	−	4.61262i	0.401159	−	0.146010i
$999$	−0.576757	−	0.998972i	−0.0182478	−	0.0316061i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.u.i.61.1	✓	12
19.5	even	9	inner	570.2.u.i.271.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.i.61.1	✓	12	1.1	even	1	trivial
570.2.u.i.271.1	yes	12	19.5	even	9	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(0.173648 - 0.984808i) q^{6} +(-0.814143 + 1.41014i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(0.173648 - 0.984808i) q^{6} +(-0.814143 + 1.41014i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-0.939693 + 0.342020i) q^{10} +(-0.0122091 - 0.0211467i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.900043 + 5.10440i) q^{13} +(1.24734 - 1.04664i) q^{14} +(0.766044 + 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(3.76098 + 1.36888i) q^{17} +1.00000 q^{18} +(-4.12746 - 1.40146i) q^{19} +1.00000 q^{20} +(-1.53009 - 0.556906i) q^{21} +(0.00424016 + 0.0240471i) q^{22} +(4.28392 + 3.59464i) q^{23} +(0.766044 - 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(2.59157 - 4.48873i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-1.53009 + 0.556906i) q^{28} +(-2.96978 + 1.08091i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(-2.54879 + 4.41464i) q^{31} +(0.173648 - 0.984808i) q^{32} +(0.0187054 - 0.0156957i) q^{33} +(-3.06598 - 2.57266i) q^{34} +(0.282749 + 1.60355i) q^{35} +(-0.939693 - 0.342020i) q^{36} +1.15351 q^{37} +(3.39922 + 2.72861i) q^{38} -5.18314 q^{39} +(-0.939693 - 0.342020i) q^{40} +(0.172953 + 0.980867i) q^{41} +(1.24734 + 1.04664i) q^{42} +(-2.88277 + 2.41893i) q^{43} +(0.00424016 - 0.0240471i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-2.79613 - 4.84304i) q^{46} +(-1.85268 + 0.674320i) q^{47} +(-0.939693 + 0.342020i) q^{48} +(2.17434 + 3.76607i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.695001 + 3.94154i) q^{51} +(-3.97052 + 3.33166i) q^{52} +(8.48426 + 7.11914i) q^{53} +(0.173648 + 0.984808i) q^{54} +(-0.0229455 - 0.00835149i) q^{55} +1.62829 q^{56} +(0.663440 - 4.30811i) q^{57} +3.16037 q^{58} +(-4.78016 - 1.73984i) q^{59} +(0.173648 + 0.984808i) q^{60} +(3.32108 + 2.78672i) q^{61} +(3.90498 - 3.27667i) q^{62} +(0.282749 - 1.60355i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.59157 + 4.48873i) q^{65} +(-0.0229455 + 0.00835149i) q^{66} +(-8.26361 + 3.00771i) q^{67} +(2.00117 + 3.46614i) q^{68} +(-2.79613 + 4.84304i) q^{69} +(0.282749 - 1.60355i) q^{70} +(5.16526 - 4.33417i) q^{71} +(0.766044 + 0.642788i) q^{72} +(1.30860 + 7.42142i) q^{73} +(-1.08395 - 0.394525i) q^{74} +1.00000 q^{75} +(-2.26098 - 3.72666i) q^{76} +0.0397597 q^{77} +(4.87056 + 1.77274i) q^{78} +(0.0776181 + 0.440194i) q^{79} +(0.766044 + 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(0.172953 - 0.980867i) q^{82} +(6.37237 - 11.0373i) q^{83} +(-0.814143 - 1.41014i) q^{84} +(3.76098 - 1.36888i) q^{85} +(3.53624 - 1.28709i) q^{86} +(-1.58019 - 2.73696i) q^{87} +(-0.0122091 + 0.0211467i) q^{88} +(1.87089 - 10.6103i) q^{89} +(0.766044 - 0.642788i) q^{90} +(-6.46513 - 5.42489i) q^{91} +(0.971087 + 5.50731i) q^{92} +(-4.79016 - 1.74348i) q^{93} +1.97158 q^{94} +(-4.06266 + 1.57950i) q^{95} +1.00000 q^{96} +(-5.43949 - 1.97981i) q^{97} +(-0.755141 - 4.28262i) q^{98} +(0.0187054 + 0.0156957i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q - 3 * q^7 - 6 * q^8	\( 12 q - 3 q^{7} - 6 q^{8} - 9 q^{11} - 6 q^{12} - 3 q^{13} + 3 q^{14} + 9 q^{17} + 12 q^{18} - 3 q^{19} + 12 q^{20} + 3 q^{21} - 6 q^{22} + 12 q^{23} - 9 q^{26} - 6 q^{27} + 3 q^{28} - 3 q^{29} - 6 q^{30} - 12 q^{31} + 3 q^{33} - 9 q^{34} - 6 q^{35} + 42 q^{37} + 18 q^{39} + 21 q^{41} + 3 q^{42} + 9 q^{43} - 6 q^{44} - 6 q^{45} - 3 q^{46} + 3 q^{49} - 6 q^{50} - 3 q^{52} - 18 q^{53} + 3 q^{55} + 6 q^{56} + 6 q^{58} - 15 q^{59} + 9 q^{61} + 12 q^{62} - 6 q^{63} - 6 q^{64} - 9 q^{65} + 3 q^{66} + 18 q^{67} - 6 q^{68} - 3 q^{69} - 6 q^{70} + 12 q^{71} - 9 q^{73} + 12 q^{75} + 9 q^{76} - 54 q^{77} + 6 q^{78} - 9 q^{79} + 21 q^{82} + 15 q^{83} - 3 q^{84} + 9 q^{85} - 27 q^{86} - 3 q^{87} - 9 q^{88} + 3 q^{89} - 51 q^{91} + 3 q^{92} - 15 q^{93} + 12 q^{96} - 48 q^{97} - 15 q^{98} + 3 q^{99}+O(q^{100}) \) 12 * q - 3 * q^7 - 6 * q^8 - 9 * q^11 - 6 * q^12 - 3 * q^13 + 3 * q^14 + 9 * q^17 + 12 * q^18 - 3 * q^19 + 12 * q^20 + 3 * q^21 - 6 * q^22 + 12 * q^23 - 9 * q^26 - 6 * q^27 + 3 * q^28 - 3 * q^29 - 6 * q^30 - 12 * q^31 + 3 * q^33 - 9 * q^34 - 6 * q^35 + 42 * q^37 + 18 * q^39 + 21 * q^41 + 3 * q^42 + 9 * q^43 - 6 * q^44 - 6 * q^45 - 3 * q^46 + 3 * q^49 - 6 * q^50 - 3 * q^52 - 18 * q^53 + 3 * q^55 + 6 * q^56 + 6 * q^58 - 15 * q^59 + 9 * q^61 + 12 * q^62 - 6 * q^63 - 6 * q^64 - 9 * q^65 + 3 * q^66 + 18 * q^67 - 6 * q^68 - 3 * q^69 - 6 * q^70 + 12 * q^71 - 9 * q^73 + 12 * q^75 + 9 * q^76 - 54 * q^77 + 6 * q^78 - 9 * q^79 + 21 * q^82 + 15 * q^83 - 3 * q^84 + 9 * q^85 - 27 * q^86 - 3 * q^87 - 9 * q^88 + 3 * q^89 - 51 * q^91 + 3 * q^92 - 15 * q^93 + 12 * q^96 - 48 * q^97 - 15 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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