LMFDB - Embedded newform 43.2.g.a.38.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,2,Mod(9,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(42))

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

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

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

chi := DirichletCharacter("43.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	43.g (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.343356728692$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			38.3
Character	$\chi$	$=$	43.38
Dual form			43.2.g.a.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.377390 - 1.65345i) q^{2} +(-1.63701 - 0.504949i) q^{3} +(-0.789549 - 0.380227i) q^{4} +(0.140805 + 0.358765i) q^{5} +(-1.45270 + 2.51615i) q^{6} +(1.74586 + 3.02391i) q^{7} +(1.18819 - 1.48995i) q^{8} +(-0.0539035 - 0.0367508i) q^{9} +O(q^{10})$	\(q+(0.377390 - 1.65345i) q^{2} +(-1.63701 - 0.504949i) q^{3} +(-0.789549 - 0.380227i) q^{4} +(0.140805 + 0.358765i) q^{5} +(-1.45270 + 2.51615i) q^{6} +(1.74586 + 3.02391i) q^{7} +(1.18819 - 1.48995i) q^{8} +(-0.0539035 - 0.0367508i) q^{9} +(0.646339 - 0.0974200i) q^{10} +(-3.90633 + 1.88119i) q^{11} +(1.10050 + 1.02111i) q^{12} +(1.26408 + 0.190529i) q^{13} +(5.65876 - 1.74550i) q^{14} +(-0.0493402 - 0.658399i) q^{15} +(-3.10791 - 3.89720i) q^{16} +(0.205594 - 0.523844i) q^{17} +(-0.0811084 + 0.0752576i) q^{18} +(-6.30490 + 4.29861i) q^{19} +(0.0252397 - 0.336800i) q^{20} +(-1.33105 - 5.83172i) q^{21} +(1.63625 + 7.16888i) q^{22} +(0.553943 - 7.39185i) q^{23} +(-2.69742 + 1.83907i) q^{24} +(3.55637 - 3.29983i) q^{25} +(0.792080 - 2.01819i) q^{26} +(3.27401 + 4.10548i) q^{27} +(-0.228667 - 3.05134i) q^{28} +(3.26143 - 1.00602i) q^{29} +(-1.10725 - 0.166892i) q^{30} +(-0.717059 - 0.665333i) q^{31} +(-4.18276 + 2.01431i) q^{32} +(7.34459 - 1.10702i) q^{33} +(-0.788563 - 0.537633i) q^{34} +(-0.839048 + 1.05213i) q^{35} +(0.0285858 + 0.0495121i) q^{36} +(-2.19799 + 3.80703i) q^{37} +(4.72814 + 12.0471i) q^{38} +(-1.97309 - 0.950190i) q^{39} +(0.701843 + 0.216490i) q^{40} +(-1.07956 + 4.72986i) q^{41} -10.1448 q^{42} +(3.30784 - 5.66200i) q^{43} +3.79952 q^{44} +(0.00559502 - 0.0245134i) q^{45} +(-12.0130 - 3.70553i) q^{46} +(3.93826 + 1.89657i) q^{47} +(3.11978 + 7.94908i) q^{48} +(-2.59602 + 4.49644i) q^{49} +(-4.11398 - 7.12562i) q^{50} +(-0.601072 + 0.753721i) q^{51} +(-0.925605 - 0.631067i) q^{52} +(-9.56301 + 1.44139i) q^{53} +(8.02380 - 3.86406i) q^{54} +(-1.22493 - 1.13657i) q^{55} +(6.57987 + 0.991756i) q^{56} +(12.4917 - 3.85319i) q^{57} +(-0.432573 - 5.77229i) q^{58} +(-2.92222 - 3.66435i) q^{59} +(-0.211384 + 0.538598i) q^{60} +(3.96588 - 3.67980i) q^{61} +(-1.37071 + 0.934533i) q^{62} +(0.0170234 - 0.227161i) q^{63} +(-0.466364 - 2.04327i) q^{64} +(0.109633 + 0.480333i) q^{65} +(0.941371 - 12.5617i) q^{66} +(10.8402 - 7.39075i) q^{67} +(-0.361505 + 0.335428i) q^{68} +(-4.63932 + 11.8208i) q^{69} +(1.42300 + 1.78439i) q^{70} +(0.570335 + 7.61059i) q^{71} +(-0.118804 + 0.0366463i) q^{72} +(-2.05301 - 0.309442i) q^{73} +(5.46525 + 5.07101i) q^{74} +(-7.48805 + 3.60605i) q^{75} +(6.61247 - 0.996670i) q^{76} +(-12.5084 - 8.52811i) q^{77} +(-2.31572 + 2.90382i) q^{78} +(4.14234 + 7.17474i) q^{79} +(0.960569 - 1.66375i) q^{80} +(-3.21501 - 8.19171i) q^{81} +(7.41318 + 3.57000i) q^{82} +(-11.1319 - 3.43375i) q^{83} +(-1.16645 + 5.11053i) q^{84} +0.216885 q^{85} +(-8.11351 - 7.60614i) q^{86} -5.84697 q^{87} +(-1.83860 + 8.05544i) q^{88} +(2.60667 + 0.804052i) q^{89} +(-0.0384202 - 0.0185022i) q^{90} +(1.63075 + 4.15509i) q^{91} +(-3.24794 + 5.62560i) q^{92} +(0.837869 + 1.45123i) q^{93} +(4.62215 - 5.79599i) q^{94} +(-2.42995 - 1.65671i) q^{95} +(7.86433 - 1.18536i) q^{96} +(0.441741 - 0.212731i) q^{97} +(6.45494 + 5.98931i) q^{98} +(0.279700 + 0.0421580i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) $ 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{21}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.377390	−	1.65345i	0.266855	−	1.16917i	−0.646794	−	0.762665i	$-0.723891\pi$
$2$	0.377390	−	1.65345i	0.266855	−	1.16917i	0.913649	−	0.406504i	$-0.133252\pi$
$3$	−1.63701	−	0.504949i	−0.945125	−	0.291533i	−0.216374	−	0.976311i	$-0.569423\pi$
$3$	−1.63701	−	0.504949i	−0.945125	−	0.291533i	−0.728752	+	0.684778i	$0.759899\pi$
$4$	−0.789549	−	0.380227i	−0.394774	−	0.190113i
$5$	0.140805	+	0.358765i	0.0629698	+	0.160444i	0.958895	−	0.283760i	$-0.0915818\pi$
$5$	0.140805	+	0.358765i	0.0629698	+	0.160444i	−0.895926	+	0.444204i	$0.853487\pi$
$6$	−1.45270	+	2.51615i	−0.593062	+	1.02721i
$7$	1.74586	+	3.02391i	0.659871	+	1.14293i	0.980649	+	0.195776i	$0.0627225\pi$
$7$	1.74586	+	3.02391i	0.659871	+	1.14293i	−0.320777	+	0.947155i	$0.603944\pi$
$8$	1.18819	−	1.48995i	0.420089	−	0.526775i
$9$	−0.0539035	−	0.0367508i	−0.0179678	−	0.0122503i
$10$	0.646339	−	0.0974200i	0.204390	−	0.0308069i
$11$	−3.90633	+	1.88119i	−1.17780	+	0.567200i	−0.917270	−	0.398265i	$-0.869612\pi$
$11$	−3.90633	+	1.88119i	−1.17780	+	0.567200i	−0.260533	+	0.965465i	$0.583898\pi$
$12$	1.10050	+	1.02111i	0.317687	+	0.294770i
$13$	1.26408	+	0.190529i	0.350591	+	0.0528432i	0.321977	−	0.946747i	$-0.395653\pi$
$13$	1.26408	+	0.190529i	0.350591	+	0.0528432i	0.0286141	+	0.999591i	$0.490891\pi$
$14$	5.65876	−	1.74550i	1.51237	−	0.466504i
$15$	−0.0493402	−	0.658399i	−0.0127396	−	0.169998i
$16$	−3.10791	−	3.89720i	−0.776978	−	0.974300i
$17$	0.205594	−	0.523844i	0.0498638	−	0.127051i	−0.903772	−	0.428015i	$-0.859213\pi$
$17$	0.205594	−	0.523844i	0.0498638	−	0.127051i	0.953636	+	0.300964i	$0.0973084\pi$
$18$	−0.0811084	+	0.0752576i	−0.0191174	+	0.0177384i
$19$	−6.30490	+	4.29861i	−1.44644	+	0.986169i	−0.450830	+	0.892610i	$0.648872\pi$
$19$	−6.30490	+	4.29861i	−1.44644	+	0.986169i	−0.995614	+	0.0935586i	$0.970176\pi$
$20$	0.0252397	−	0.336800i	0.00564376	−	0.0753107i
$21$	−1.33105	−	5.83172i	−0.290460	−	1.27259i
$22$	1.63625	+	7.16888i	0.348850	+	1.52841i
$23$	0.553943	−	7.39185i	0.115505	−	1.54131i	−0.575105	−	0.818080i	$-0.695039\pi$
$23$	0.553943	−	7.39185i	0.115505	−	1.54131i	0.690610	−	0.723228i	$-0.257342\pi$
$24$	−2.69742	+	1.83907i	−0.550609	+	0.375399i
$25$	3.55637	−	3.29983i	0.711275	−	0.659966i
$26$	0.792080	−	2.01819i	0.155340	−	0.395799i
$27$	3.27401	+	4.10548i	0.630084	+	0.790100i
$28$	−0.228667	−	3.05134i	−0.0432139	−	0.576650i
$29$	3.26143	−	1.00602i	0.605633	−	0.186813i	0.0232528	−	0.999730i	$-0.492598\pi$
$29$	3.26143	−	1.00602i	0.605633	−	0.186813i	0.582380	+	0.812917i	$0.302122\pi$
$30$	−1.10725	−	0.166892i	−0.202156	−	0.0304701i
$31$	−0.717059	−	0.665333i	−0.128788	−	0.119497i	0.613150	−	0.789967i	$-0.289902\pi$
$31$	−0.717059	−	0.665333i	−0.128788	−	0.119497i	−0.741937	+	0.670469i	$0.766093\pi$
$32$	−4.18276	+	2.01431i	−0.739415	+	0.356083i
$33$	7.34459	−	1.10702i	1.27853	−	0.192707i
$34$	−0.788563	−	0.537633i	−0.135237	−	0.0922033i
$35$	−0.839048	+	1.05213i	−0.141825	+	0.177843i
$36$	0.0285858	+	0.0495121i	0.00476430	+	0.00825202i
$37$	−2.19799	+	3.80703i	−0.361348	+	0.625872i	−0.988183	−	0.153279i	$-0.951017\pi$
$37$	−2.19799	+	3.80703i	−0.361348	+	0.625872i	0.626835	+	0.779152i	$0.284350\pi$
$38$	4.72814	+	12.0471i	0.767006	+	1.95430i
$39$	−1.97309	−	0.950190i	−0.315947	−	0.152152i
$40$	0.701843	+	0.216490i	0.110971	+	0.0342301i
$41$	−1.07956	+	4.72986i	−0.168599	+	0.738679i	0.817960	+	0.575275i	$0.195105\pi$
$41$	−1.07956	+	4.72986i	−0.168599	+	0.738679i	−0.986559	+	0.163405i	$0.947752\pi$
$42$	−10.1448			−1.56538
$43$	3.30784	−	5.66200i	0.504440	−	0.863447i
$43$	3.30784	−	5.66200i	0.504440	−	0.863447i
$44$	3.79952			0.572799
$45$	0.00559502	−	0.0245134i	0.000834056	−	0.00365424i
$46$	−12.0130	−	3.70553i	−1.77122	−	0.546351i
$47$	3.93826	+	1.89657i	0.574455	+	0.276643i	0.698472	−	0.715637i	$-0.253864\pi$
$47$	3.93826	+	1.89657i	0.574455	+	0.276643i	−0.124017	+	0.992280i	$0.539578\pi$
$48$	3.11978	+	7.94908i	0.450302	+	1.14735i
$49$	−2.59602	+	4.49644i	−0.370860	+	0.642348i
$50$	−4.11398	−	7.12562i	−0.581805	−	1.00772i
$51$	−0.601072	+	0.753721i	−0.0841670	+	0.105542i
$52$	−0.925605	−	0.631067i	−0.128358	−	0.0875132i
$53$	−9.56301	+	1.44139i	−1.31358	+	0.197990i	−0.768207	−	0.640202i	$-0.778851\pi$
$53$	−9.56301	+	1.44139i	−1.31358	+	0.197990i	−0.545374	+	0.838193i	$0.683613\pi$
$54$	8.02380	−	3.86406i	1.09190	−	0.525832i
$55$	−1.22493	−	1.13657i	−0.165170	−	0.153256i
$56$	6.57987	+	0.991756i	0.879272	+	0.132529i
$57$	12.4917	−	3.85319i	1.65457	−	0.510368i
$58$	−0.432573	−	5.77229i	−0.0567997	−	0.757939i
$59$	−2.92222	−	3.66435i	−0.380441	−	0.477058i	0.554336	−	0.832293i	$-0.312972\pi$
$59$	−2.92222	−	3.66435i	−0.380441	−	0.477058i	−0.934777	+	0.355235i	$0.884401\pi$
$60$	−0.211384	+	0.538598i	−0.0272896	+	0.0695328i
$61$	3.96588	−	3.67980i	0.507779	−	0.471150i	−0.384185	−	0.923256i	$-0.625518\pi$
$61$	3.96588	−	3.67980i	0.507779	−	0.471150i	0.891964	+	0.452106i	$0.149327\pi$
$62$	−1.37071	+	0.934533i	−0.174080	+	0.118686i
$63$	0.0170234	−	0.227161i	0.00214474	−	0.0286196i
$64$	−0.466364	−	2.04327i	−0.0582955	−	0.255409i
$65$	0.109633	+	0.480333i	0.0135983	+	0.0595780i
$66$	0.941371	−	12.5617i	0.115875	−	1.54624i
$67$	10.8402	−	7.39075i	1.32435	−	0.902924i	0.325259	−	0.945625i	$-0.394549\pi$
$67$	10.8402	−	7.39075i	1.32435	−	0.902924i	0.999088	+	0.0427010i	$0.0135963\pi$
$68$	−0.361505	+	0.335428i	−0.0438390	+	0.0406766i
$69$	−4.63932	+	11.8208i	−0.558508	+	1.42306i
$70$	1.42300	+	1.78439i	0.170082	+	0.213275i
$71$	0.570335	+	7.61059i	0.0676863	+	0.903211i	0.922926	+	0.384978i	$0.125791\pi$
$71$	0.570335	+	7.61059i	0.0676863	+	0.903211i	−0.855239	+	0.518233i	$0.826590\pi$
$72$	−0.118804	+	0.0366463i	−0.0140012	+	0.00431881i
$73$	−2.05301	−	0.309442i	−0.240287	−	0.0362175i	0.0277945	−	0.999614i	$-0.491152\pi$
$73$	−2.05301	−	0.309442i	−0.240287	−	0.0362175i	−0.268082	+	0.963396i	$0.586390\pi$
$74$	5.46525	+	5.07101i	0.635323	+	0.589493i
$75$	−7.48805	+	3.60605i	−0.864646	+	0.416391i
$76$	6.61247	−	0.996670i	0.758502	−	0.114326i
$77$	−12.5084	−	8.52811i	−1.42547	−	0.971868i
$78$	−2.31572	+	2.90382i	−0.262204	+	0.328793i
$79$	4.14234	+	7.17474i	0.466049	+	0.807221i	0.999248	−	0.0387687i	$-0.0123436\pi$
$79$	4.14234	+	7.17474i	0.466049	+	0.807221i	−0.533199	+	0.845990i	$0.679010\pi$
$80$	0.960569	−	1.66375i	0.107395	−	0.186013i
$81$	−3.21501	−	8.19171i	−0.357223	−	0.910190i
$82$	7.41318	+	3.57000i	0.818649	+	0.394241i
$83$	−11.1319	−	3.43375i	−1.22189	−	0.376903i	−0.384302	−	0.923207i	$-0.625558\pi$
$83$	−11.1319	−	3.43375i	−1.22189	−	0.376903i	−0.837587	+	0.546305i	$0.816034\pi$
$84$	−1.16645	+	5.11053i	−0.127270	+	0.557605i
$85$	0.216885			0.0235245
$86$	−8.11351	−	7.60614i	−0.874902	−	0.820191i
$87$	−5.84697			−0.626861
$88$	−1.83860	+	8.05544i	−0.195995	+	0.858712i
$89$	2.60667	+	0.804052i	0.276307	+	0.0852293i	0.429812	−	0.902919i	$-0.358580\pi$
$89$	2.60667	+	0.804052i	0.276307	+	0.0852293i	−0.153505	+	0.988148i	$0.549056\pi$
$90$	−0.0384202	−	0.0185022i	−0.00404985	−	0.00195030i
$91$	1.63075	+	4.15509i	0.170949	+	0.435571i
$92$	−3.24794	+	5.62560i	−0.338621	+	0.586509i
$93$	0.837869	+	1.45123i	0.0868830	+	0.150486i
$94$	4.62215	−	5.79599i	0.476738	−	0.597811i
$95$	−2.42995	−	1.65671i	−0.249308	−	0.169975i
$96$	7.86433	−	1.18536i	0.802650	−	0.120980i
$97$	0.441741	−	0.212731i	0.0448520	−	0.0215996i	−0.411323	−	0.911490i	$-0.634933\pi$
$97$	0.441741	−	0.212731i	0.0448520	−	0.0215996i	0.456175	+	0.889890i	$0.349219\pi$
$98$	6.45494	+	5.98931i	0.652048	+	0.605012i
$99$	0.279700	+	0.0421580i	0.0281109	+	0.00423704i
$100$	−4.06261	+	1.25315i	−0.406261	+	0.125315i
$101$	0.164575	+	2.19611i	0.0163759	+	0.218521i	0.999388	+	0.0349802i	$0.0111368\pi$
$101$	0.164575	+	2.19611i	0.0163759	+	0.218521i	−0.983012	+	0.183541i	$0.941244\pi$
$102$	1.01940	+	1.27829i	0.100936	+	0.126570i
$103$	−1.86980	+	4.76417i	−0.184237	+	0.469427i	−0.992915	−	0.118823i	$-0.962088\pi$
$103$	−1.86980	+	4.76417i	−0.184237	+	0.469427i	0.808679	+	0.588250i	$0.200183\pi$
$104$	1.78584	−	1.65702i	0.175116	−	0.162484i
$105$	1.90480	−	1.29867i	0.185889	−	0.126737i
$106$	−1.22571	+	16.3560i	−0.119052	+	1.58863i
$107$	2.28640	+	10.0174i	0.221035	+	0.968418i	0.956701	+	0.291073i	$0.0940123\pi$
$107$	2.28640	+	10.0174i	0.221035	+	0.968418i	−0.735666	+	0.677345i	$0.763131\pi$
$108$	−1.02398	−	4.48634i	−0.0985323	−	0.431698i
$109$	−0.0839896	+	1.12076i	−0.00804474	+	0.107350i	−0.999781	−	0.0209470i	$-0.993332\pi$
$109$	−0.0839896	+	1.12076i	−0.00804474	+	0.107350i	0.991736	+	0.128297i	$0.0409509\pi$
$110$	−2.34155	+	1.59644i	−0.223258	+	0.152215i
$111$	5.52048	−	5.12226i	0.523981	−	0.486183i
$112$	6.35882	−	16.2020i	0.600852	−	1.53094i
$113$	9.95806	+	12.4870i	0.936776	+	1.17468i	0.984423	+	0.175815i	$0.0562562\pi$
$113$	9.95806	+	12.4870i	0.936776	+	1.17468i	−0.0476475	+	0.998864i	$0.515172\pi$
$114$	−1.65682	−	22.1087i	−0.155175	−	2.07067i
$115$	2.72993	−	0.842073i	0.254568	−	0.0785237i
$116$	−2.95757	−	0.445783i	−0.274604	−	0.0413899i
$117$	−0.0611361	−	0.0567260i	−0.00565203	−	0.00524432i
$118$	−7.16165	+	3.44887i	−0.659283	+	0.317494i
$119$	1.94299	−	0.292859i	0.178114	−	0.0268463i
$120$	−1.03960	−	0.708790i	−0.0949025	−	0.0647034i
$121$	4.86216	−	6.09695i	0.442014	−	0.554268i
$122$	−4.58770	−	7.94612i	−0.415351	−	0.719408i
$123$	4.15558	−	7.19768i	0.374696	−	0.648993i
$124$	0.313175	+	0.797957i	0.0281240	+	0.0716587i
$125$	3.42081	+	1.64738i	0.305967	+	0.147346i
$126$	−0.369176	−	0.113876i	−0.0328888	−	0.0101449i
$127$	0.749226	−	3.28258i	0.0664831	−	0.291281i	−0.930747	−	0.365665i	$-0.880842\pi$
$127$	0.749226	−	3.28258i	0.0664831	−	0.291281i	0.997230	+	0.0743833i	$0.0236988\pi$
$128$	−12.8395			−1.13486
$129$	−8.27397	+	7.59843i	−0.728482	+	0.669005i
$130$	0.835583			0.0732855
$131$	0.342281	−	1.49963i	0.0299053	−	0.131024i	−0.957772	−	0.287530i	$-0.907166\pi$
$131$	0.342281	−	1.49963i	0.0299053	−	0.131024i	0.987677	+	0.156506i	$0.0500231\pi$
$132$	−6.21983	−	1.91856i	−0.541367	−	0.166989i
$133$	−24.0060	−	11.5607i	−2.08159	−	1.00244i
$134$	−8.12927	−	20.7130i	−0.702262	−	1.78933i
$135$	−1.01191	+	1.75267i	−0.0870909	+	0.150846i
$136$	−0.536214	−	0.928750i	−0.0459800	−	0.0796397i
$137$	−1.98722	+	2.49190i	−0.169780	+	0.212897i	−0.859441	−	0.511235i	$-0.829188\pi$
$137$	−1.98722	+	2.49190i	−0.169780	+	0.212897i	0.689661	+	0.724132i	$0.257760\pi$
$138$	17.7943	+	12.1319i	1.51475	+	1.03274i
$139$	19.8520	−	2.99220i	1.68382	−	0.253795i	0.763741	−	0.645523i	$-0.223360\pi$
$139$	19.8520	−	2.99220i	1.68382	−	0.253795i	0.920081	+	0.391727i	$0.128122\pi$
$140$	1.06252	−	0.511681i	0.0897991	−	0.0432450i
$141$	−5.48929	−	5.09332i	−0.462282	−	0.428935i
$142$	12.7990	+	1.92914i	1.07407	+	0.161890i
$143$	−5.29632	+	1.63370i	−0.442900	+	0.136617i
$144$	0.0243023	+	0.324291i	0.00202519	+	0.0270243i
$145$	0.820149	+	1.02843i	0.0681097	+	0.0854069i
$146$	−1.28644	+	3.27778i	−0.106466	+	0.271271i
$147$	6.52017	−	6.04984i	0.537775	−	0.498982i
$148$	3.18296	−	2.17010i	0.261637	−	0.178381i
$149$	−0.944726	+	12.6065i	−0.0773949	+	1.03276i	0.814394	+	0.580312i	$0.197069\pi$
$149$	−0.944726	+	12.6065i	−0.0773949	+	1.03276i	−0.891789	+	0.452451i	$0.850550\pi$
$150$	3.13653	+	13.7420i	0.256097	+	1.12203i
$151$	−0.223758	−	0.980350i	−0.0182092	−	0.0797798i	0.965007	−	0.262224i	$-0.0844561\pi$
$151$	−0.223758	−	0.980350i	−0.0182092	−	0.0797798i	−0.983216	+	0.182445i	$0.941599\pi$
$152$	−1.08674	+	14.5015i	−0.0881462	+	1.17623i
$153$	−0.0303339	+	0.0206813i	−0.00245235	+	0.00167198i
$154$	−18.8214	+	17.4637i	−1.51667	+	1.40726i
$155$	0.137733	−	0.350937i	0.0110630	−	0.0281880i
$156$	1.19656	+	1.50044i	0.0958017	+	0.120132i
$157$	0.355966	+	4.75004i	0.0284092	+	0.379095i	0.993228	+	0.116180i	$0.0370648\pi$
$157$	0.355966	+	4.75004i	0.0284092	+	0.379095i	−0.964819	+	0.262915i	$0.915316\pi$
$158$	13.4264	−	4.14149i	1.06815	−	0.329479i
$159$	16.3825	+	2.46927i	1.29922	+	0.195826i
$160$	−1.31162	−	1.21700i	−0.103692	−	0.0962125i
$161$	23.3194	−	11.2300i	1.83783	−	0.885050i
$162$	−14.7579	+	2.22440i	−1.15949	+	0.174765i
$163$	−7.84688	−	5.34991i	−0.614615	−	0.419037i	0.215599	−	0.976482i	$-0.430829\pi$
$163$	−7.84688	−	5.34991i	−0.614615	−	0.419037i	−0.830214	+	0.557445i	$0.811782\pi$
$164$	2.65078	−	3.32397i	0.206991	−	0.259559i
$165$	1.43131	+	2.47911i	0.111428	+	0.192998i
$166$	−9.87862	+	17.1103i	−0.766730	+	1.32802i
$167$	−8.26817	−	21.0670i	−0.639810	−	1.63021i	−0.769494	−	0.638654i	$-0.779491\pi$
$167$	−8.26817	−	21.0670i	−0.639810	−	1.63021i	0.129684	−	0.991555i	$-0.458604\pi$
$168$	−10.2705	−	4.94601i	−0.792386	−	0.381593i
$169$	−10.8609	−	3.35013i	−0.835451	−	0.257702i
$170$	0.0818503	−	0.358610i	0.00627763	−	0.0275041i
$171$	0.497834			0.0380703
$172$	−4.76454	+	3.21269i	−0.363293	+	0.244966i
$173$	9.30235			0.707245			0.353622	−	0.935388i	$-0.384950\pi$
$173$	9.30235			0.707245			0.353622	+	0.935388i	$0.384950\pi$
$174$	−2.20659	+	9.66770i	−0.167281	+	0.732906i
$175$	16.1873	+	4.99312i	1.22365	+	0.377445i
$176$	19.4719	+	9.37718i	1.46775	+	0.706831i
$177$	2.93338	+	7.47413i	0.220486	+	0.561790i
$178$	2.31319	−	4.00657i	0.173381	−	0.300305i
$179$	−3.61481	−	6.26104i	−0.270184	−	0.467972i	0.698725	−	0.715390i	$-0.253751\pi$
$179$	−3.61481	−	6.26104i	−0.270184	−	0.467972i	−0.968909	+	0.247418i	$0.920418\pi$
$180$	−0.0137382	+	0.0172271i	−0.00102398	+	0.00128403i
$181$	−15.5329	−	10.5902i	−1.15455	−	0.787162i	−0.174259	−	0.984700i	$-0.555753\pi$
$181$	−15.5329	−	10.5902i	−1.15455	−	0.787162i	−0.980295	+	0.197538i	$0.936705\pi$
$182$	7.48567	−	1.12828i	0.554875	−	0.0836339i
$183$	−8.35028	+	4.02129i	−0.617271	+	0.297262i
$184$	−10.3553	−	9.60828i	−0.763400	−	0.708332i
$185$	−1.67532	−	0.252513i	−0.123172	−	0.0185652i
$186$	2.71575	−	0.837698i	0.199128	−	0.0614230i
$187$	0.182333	+	2.43307i	0.0133335	+	0.177924i
$188$	−2.38833	−	2.99487i	−0.174187	−	0.218423i
$189$	−6.69865	+	17.0679i	−0.487255	+	1.24151i
$190$	−3.65634	+	3.39258i	−0.265258	+	0.246124i
$191$	−5.81055	+	3.96157i	−0.420437	+	0.286649i	−0.755001	−	0.655724i	$-0.772363\pi$
$191$	−5.81055	+	3.96157i	−0.420437	+	0.286649i	0.334564	+	0.942373i	$0.391411\pi$
$192$	−0.268309	+	3.58034i	−0.0193636	+	0.258389i
$193$	0.916048	+	4.01347i	0.0659385	+	0.288896i	0.997137	−	0.0756172i	$-0.0240927\pi$
$193$	0.916048	+	4.01347i	0.0659385	+	0.288896i	−0.931198	+	0.364513i	$0.881236\pi$
$194$	−0.185033	−	0.810682i	−0.0132846	−	0.0582035i
$195$	0.0630742	−	0.841667i	0.00451684	−	0.0602730i
$196$	3.75935	−	2.56308i	0.268525	−	0.183077i
$197$	−1.32247	+	1.22707i	−0.0942220	+	0.0874252i	−0.725878	−	0.687824i	$-0.758566\pi$
$197$	−1.32247	+	1.22707i	−0.0942220	+	0.0874252i	0.631656	+	0.775249i	$0.282376\pi$
$198$	0.175262	−	0.446561i	0.0124554	−	0.0317357i
$199$	−14.1954	−	17.8005i	−1.00629	−	1.26185i	−0.964877	−	0.262704i	$-0.915386\pi$
$199$	−14.1954	−	17.8005i	−1.00629	−	1.26185i	−0.0414119	−	0.999142i	$-0.513186\pi$
$200$	−0.690916	−	9.21964i	−0.0488552	−	0.651927i
$201$	−21.4775	+	6.62493i	−1.51491	+	0.467286i
$202$	3.69327	+	0.556671i	0.259858	+	0.0391672i
$203$	8.73610	+	8.10592i	0.613154	+	0.568924i
$204$	0.761160	−	0.366556i	0.0532919	−	0.0256640i
$205$	−1.84891	+	0.278679i	−0.129134	+	0.0194638i
$206$	7.17169	+	4.88957i	0.499675	+	0.340673i
$207$	−0.301516	+	0.378089i	−0.0209568	+	0.0262790i
$208$	−3.18611	−	5.51850i	−0.220917	−	0.382639i
$209$	16.5425	−	28.6525i	1.14427	−	1.98194i
$210$	−1.42844	−	3.63960i	−0.0985716	−	0.251156i
$211$	7.10545	+	3.42180i	0.489159	+	0.235567i	0.662170	−	0.749353i	$-0.269635\pi$
$211$	7.10545	+	3.42180i	0.489159	+	0.235567i	−0.173011	+	0.984920i	$0.555350\pi$
$212$	8.09852	+	2.49806i	0.556209	+	0.171568i
$213$	2.90932	−	12.7466i	0.199343	−	0.873381i
$214$	17.4262			1.19123
$215$	2.49708	+	0.389499i	0.170300	+	0.0265636i
$216$	10.0071			0.680897
$217$	0.760027	−	3.32990i	0.0515940	−	0.226048i
$218$	1.82143	+	0.561838i	0.123363	+	0.0380524i
$219$	3.20454	+	1.54323i	0.216543	+	0.104282i
$220$	0.534990	+	1.36313i	0.0360690	+	0.0919024i
$221$	0.359693	−	0.623007i	0.0241956	−	0.0419080i
$222$	−6.38604	−	11.0610i	−0.428603	−	0.742363i
$223$	5.36853	−	6.73192i	0.359503	−	0.450803i	−0.568884	−	0.822418i	$-0.692625\pi$
$223$	5.36853	−	6.73192i	0.359503	−	0.450803i	0.928387	+	0.371615i	$0.121196\pi$
$224$	−13.3936	−	9.13160i	−0.894897	−	0.610131i
$225$	−0.312973	+	0.0471730i	−0.0208648	+	0.00314487i
$226$	24.4048	−	11.7527i	1.62338	−	0.781779i
$227$	5.97274	+	5.54190i	0.396425	+	0.367829i	0.853049	−	0.521831i	$-0.174751\pi$
$227$	5.97274	+	5.54190i	0.396425	+	0.367829i	−0.456624	+	0.889660i	$0.650941\pi$
$228$	−11.3279	−	1.70741i	−0.750210	−	0.113076i
$229$	−23.6766	+	7.30327i	−1.56460	+	0.482614i	−0.951565	−	0.307446i	$-0.900526\pi$
$229$	−23.6766	+	7.30327i	−1.56460	+	0.482614i	−0.613030	+	0.790060i	$0.710049\pi$
$230$	−0.362079	−	4.83161i	−0.0238748	−	0.318587i
$231$	16.1701	+	20.2767i	1.06392	+	1.33411i
$232$	2.37630	−	6.05470i	0.156011	−	0.397511i
$233$	−6.32022	+	5.86431i	−0.414051	+	0.384183i	−0.859510	−	0.511119i	$-0.829231\pi$
$233$	−6.32022	+	5.86431i	−0.414051	+	0.384183i	0.445459	+	0.895303i	$0.353041\pi$
$234$	−0.116866	+	0.0796778i	−0.00763976	+	0.00520870i
$235$	−0.125895	+	1.67996i	−0.00821251	+	0.109588i
$236$	0.913952	+	4.00429i	0.0594932	+	0.260657i
$237$	−3.15815	−	13.8368i	−0.205144	−	0.898794i
$238$	0.249037	−	3.32317i	0.0161427	−	0.215409i
$239$	2.78125	−	1.89623i	0.179904	−	0.122657i	−0.470020	−	0.882656i	$-0.655753\pi$
$239$	2.78125	−	1.89623i	0.179904	−	0.122657i	0.649924	+	0.759999i	$0.274801\pi$
$240$	−2.41257	+	2.23854i	−0.155731	+	0.144497i
$241$	−9.87013	+	25.1487i	−0.635791	+	1.61997i	0.140854	+	0.990030i	$0.455015\pi$
$241$	−9.87013	+	25.1487i	−0.635791	+	1.61997i	−0.776645	+	0.629939i	$0.783080\pi$
$242$	−8.24610	−	10.3403i	−0.530079	−	0.664698i
$243$	−0.0506572	−	0.675974i	−0.00324966	−	0.0433637i
$244$	−4.53041	+	1.39745i	−0.290030	+	0.0894624i
$245$	−1.97870	−	0.298240i	−0.126414	−	0.0190539i
$246$	−10.3328	−	9.58739i	−0.658792	−	0.611270i
$247$	−8.78888	+	4.23250i	−0.559223	+	0.269308i
$248$	−1.84331	+	0.277835i	−0.117051	+	0.0176425i
$249$	16.4892	+	11.2421i	1.04496	+	0.712441i
$250$	4.01484	−	5.03445i	0.253921	−	0.318407i
$251$	5.38285	+	9.32338i	0.339763	+	0.588486i	0.984388	−	0.176012i	$-0.0563199\pi$
$251$	5.38285	+	9.32338i	0.339763	+	0.588486i	−0.644625	+	0.764499i	$0.722987\pi$
$252$	−0.0998134	+	0.172882i	−0.00628765	+	0.0108905i
$253$	11.7416	+	29.9171i	0.738188	+	1.88087i
$254$	−5.14484	−	2.47762i	−0.322816	−	0.155460i
$255$	−0.355042	−	0.109516i	−0.0222336	−	0.00685816i
$256$	−3.91277	+	17.1430i	−0.244548	+	1.07143i
$257$	12.7546			0.795610			0.397805	−	0.917470i	$-0.369772\pi$
$257$	12.7546			0.795610			0.397805	+	0.917470i	$0.369772\pi$
$258$	9.44114	+	16.5482i	0.587780	+	1.03025i
$259$	−15.3495			−0.953772
$260$	0.0960749	−	0.420932i	0.00595831	−	0.0261051i
$261$	−0.212775	−	0.0656323i	−0.0131704	−	0.00406254i
$262$	−2.35040	−	1.13189i	−0.145208	−	0.0699286i
$263$	−5.41921	−	13.8079i	−0.334163	−	0.851433i	−0.994905	−	0.100820i	$-0.967853\pi$
$263$	−5.41921	−	13.8079i	−0.334163	−	0.851433i	0.660742	−	0.750613i	$-0.270242\pi$
$264$	7.07739	−	12.2584i	0.435583	−	0.754452i
$265$	−1.86364	−	3.22792i	−0.114482	−	0.198289i
$266$	−28.1747	+	35.3300i	−1.72750	+	2.16622i
$267$	−3.86113	−	2.63247i	−0.236297	−	0.161105i
$268$	−11.3691	+	1.71361i	−0.694476	+	0.104675i
$269$	−9.64831	+	4.64638i	−0.588268	+	0.283295i	−0.704245	−	0.709957i	$-0.748714\pi$
$269$	−9.64831	+	4.64638i	−0.588268	+	0.283295i	0.115977	+	0.993252i	$0.463000\pi$
$270$	2.51608	+	2.33458i	0.153124	+	0.142078i
$271$	−14.3276	−	2.15955i	−0.870343	−	0.131183i	−0.301338	−	0.953517i	$-0.597433\pi$
$271$	−14.3276	−	2.15955i	−0.870343	−	0.131183i	−0.569005	+	0.822334i	$0.692671\pi$
$272$	−2.68049	+	0.826822i	−0.162529	+	0.0501335i
$273$	−0.571441	−	7.62534i	−0.0345852	−	0.461507i
$274$	3.37028	+	4.22620i	0.203606	+	0.255314i
$275$	−7.68476	+	19.5804i	−0.463408	+	1.18075i
$276$	8.15754	−	7.56909i	0.491026	−	0.455606i
$277$	16.8697	−	11.5016i	1.01360	−	0.691061i	0.0618982	−	0.998082i	$-0.480285\pi$
$277$	16.8697	−	11.5016i	1.01360	−	0.691061i	0.951703	+	0.307021i	$0.0993322\pi$
$278$	2.54447	−	33.9535i	0.152607	−	2.03640i
$279$	0.0142005	+	0.0622163i	0.000850159	+	0.00372479i
$280$	0.570670	+	2.50027i	0.0341041	+	0.149420i
$281$	−0.541902	+	7.23118i	−0.0323272	+	0.431376i	0.957435	+	0.288649i	$0.0932061\pi$
$281$	−0.541902	+	7.23118i	−0.0323272	+	0.431376i	−0.989762	+	0.142727i	$0.954413\pi$
$282$	−10.4932	+	7.15412i	−0.624859	+	0.426022i
$283$	22.3431	−	20.7313i	1.32816	−	1.23235i	0.376044	−	0.926602i	$-0.377284\pi$
$283$	22.3431	−	20.7313i	1.32816	−	1.23235i	0.952113	−	0.305748i	$-0.0989065\pi$
$284$	2.44344	−	6.22579i	0.144992	−	0.369433i
$285$	3.14129	+	3.93905i	0.186074	+	0.233329i
$286$	0.702466	+	9.37376i	0.0415377	+	0.554282i
$287$	−16.1874	+	4.99316i	−0.955513	+	0.294737i
$288$	0.299493	+	0.0451413i	0.0176478	+	0.00265998i
$289$	12.2297	+	11.3475i	0.719396	+	0.667502i
$290$	2.00999	−	0.967958i	0.118030	−	0.0568405i
$291$	−0.830552	+	0.125186i	−0.0486878	+	0.00733850i
$292$	1.50330	+	1.02493i	0.0879738	+	0.0599795i
$293$	16.0151	−	20.0823i	0.935611	−	1.17322i	−0.0490592	−	0.998796i	$-0.515622\pi$
$293$	16.0151	−	20.0823i	0.935611	−	1.17322i	0.984671	−	0.174424i	$-0.0558063\pi$
$294$	−7.54248	−	13.0640i	−0.439886	−	0.761905i
$295$	0.903177	−	1.56435i	0.0525850	−	0.0910799i
$296$	3.06064	+	7.79837i	0.177896	+	0.453271i
$297$	−20.5126	−	9.87833i	−1.19026	−	0.573199i
$298$	20.4877	+	6.31962i	1.18682	+	0.366086i
$299$	2.10859	−	9.23832i	0.121943	−	0.534266i
$300$	7.28330			0.420501
$301$	22.8964	+	0.117571i	1.31973	+	0.00677671i
$302$	−1.70541			−0.0981352
$303$	0.839512	−	3.67814i	0.0482287	−	0.211304i
$304$	36.3476	+	11.2118i	2.08468	+	0.643038i
$305$	1.87860	+	0.904685i	0.107568	+	0.0518021i
$306$	0.0227479	+	0.0579606i	0.00130041	+	0.00331339i
$307$	−7.92491	+	13.7263i	−0.452298	+	0.783404i	−0.998528	−	0.0542314i	$-0.982729\pi$
$307$	−7.92491	+	13.7263i	−0.452298	+	0.783404i	0.546230	+	0.837635i	$0.316062\pi$
$308$	6.63340	+	11.4894i	0.377973	+	0.654669i
$309$	5.46653	−	6.85481i	0.310980	−	0.389957i
$310$	−0.528280	−	0.360175i	−0.0300043	−	0.0204566i
$311$	−26.7139	+	4.02647i	−1.51481	+	0.228320i	−0.853221	−	0.521550i	$-0.825354\pi$
$311$	−26.7139	+	4.02647i	−1.51481	+	0.228320i	−0.661585	+	0.749870i	$0.730116\pi$
$312$	−3.76014	+	1.81079i	−0.212876	+	0.102516i
$313$	−14.1284	−	13.1093i	−0.798586	−	0.740979i	0.171121	−	0.985250i	$-0.445261\pi$
$313$	−14.1284	−	13.1093i	−0.798586	−	0.740979i	−0.969707	+	0.244271i	$0.921452\pi$
$314$	7.98831	+	1.20404i	0.450807	+	0.0679481i
$315$	0.0838943	−	0.0258780i	0.00472691	−	0.00145806i
$316$	−0.542550	−	7.23983i	−0.0305208	−	0.407272i
$317$	−8.01912	−	10.0557i	−0.450399	−	0.564782i	0.503852	−	0.863790i	$-0.331916\pi$
$317$	−8.01912	−	10.0557i	−0.450399	−	0.564782i	−0.954251	+	0.299008i	$0.903344\pi$
$318$	10.2654	−	26.1559i	0.575657	−	1.46675i
$319$	−10.8477	+	10.0652i	−0.607356	+	0.563544i
$320$	0.667388	−	0.455018i	0.0373081	−	0.0254363i
$321$	1.31542	−	17.5530i	0.0734195	−	0.979715i
$322$	−9.76783	−	42.7956i	−0.544340	−	2.38491i
$323$	0.955553	+	4.18655i	0.0531684	+	0.232946i
$324$	−0.576300	+	7.69019i	−0.0320167	+	0.427233i
$325$	5.12424	−	3.49365i	0.284242	−	0.193793i
$326$	−11.8072	+	10.9554i	−0.653938	+	0.606766i
$327$	0.703420	−	1.79228i	0.0388992	−	0.0991135i
$328$	5.76451	+	7.22846i	0.318292	+	0.399125i
$329$	1.14059	+	15.2201i	0.0628827	+	0.839111i
$330$	4.63925	−	1.43102i	0.255382	−	0.0787750i
$331$	2.51633	+	0.379275i	0.138310	+	0.0208469i	0.217832	−	0.975986i	$-0.430101\pi$
$331$	2.51633	+	0.379275i	0.138310	+	0.0208469i	−0.0795224	+	0.996833i	$0.525340\pi$
$332$	7.48360	+	6.94377i	0.410716	+	0.381089i
$333$	0.258391	−	0.124435i	0.0141597	−	0.00681897i
$334$	−37.9536	+	5.72058i	−2.07673	+	0.313016i
$335$	4.17790	+	2.84844i	0.228263	+	0.155627i
$336$	−18.5906	+	23.3119i	−1.01420	+	1.27177i
$337$	−0.368739	−	0.638675i	−0.0200865	−	0.0347908i	0.855807	−	0.517295i	$-0.173061\pi$
$337$	−0.368739	−	0.638675i	−0.0200865	−	0.0347908i	−0.875894	+	0.482504i	$0.839727\pi$
$338$	−9.63807	+	16.6936i	−0.524242	+	0.908014i
$339$	−9.99609	−	25.4696i	−0.542913	−	1.38332i
$340$	−0.171241	−	0.0824655i	−0.00928687	−	0.00447232i
$341$	4.05269	+	1.25009i	0.219465	+	0.0676961i
$342$	0.187878	−	0.823145i	0.0101593	−	0.0445106i
$343$	6.31287			0.340863
$344$	−4.50572	−	11.6560i	−0.242932	−	0.628451i
$345$	−4.89412			−0.263491
$346$	3.51062	−	15.3810i	0.188732	−	0.826888i
$347$	−5.00949	−	1.54522i	−0.268923	−	0.0829519i	0.157361	−	0.987541i	$-0.449701\pi$
$347$	−5.00949	−	1.54522i	−0.268923	−	0.0829519i	−0.426284	+	0.904589i	$0.640178\pi$
$348$	4.61647	+	2.22317i	0.247469	+	0.119175i
$349$	3.64385	+	9.28439i	0.195051	+	0.496982i	0.994620	−	0.103593i	$-0.0330338\pi$
$349$	3.64385	+	9.28439i	0.195051	+	0.496982i	−0.799569	+	0.600575i	$0.794939\pi$
$350$	14.3648	−	24.8806i	0.767832	−	1.32992i
$351$	3.35638	+	5.81343i	0.179151	+	0.310298i
$352$	12.5499	−	15.7371i	0.668914	−	0.838792i
$353$	20.6981	+	14.1117i	1.10165	+	0.751090i	0.970699	−	0.240299i	$-0.0772454\pi$
$353$	20.6981	+	14.1117i	1.10165	+	0.751090i	0.130948	+	0.991389i	$0.458198\pi$
$354$	13.4652	−	2.02955i	0.715665	−	0.107869i
$355$	−2.65011	+	1.27622i	−0.140653	+	0.0677349i
$356$	−1.75237	−	1.62596i	−0.0928756	−	0.0861759i
$357$	−3.32857	−	0.501701i	−0.176167	−	0.0265528i
$358$	−11.7165	+	3.61407i	−0.619238	+	0.191010i
$359$	1.02841	+	13.7231i	0.0542772	+	0.724279i	0.956262	+	0.292511i	$0.0944910\pi$
$359$	1.02841	+	13.7231i	0.0542772	+	0.724279i	−0.901985	+	0.431768i	$0.857890\pi$
$360$	−0.0298756	−	0.0374629i	−0.00157458	−	0.00197447i
$361$	14.3323	−	36.5180i	0.754330	−	1.92200i
$362$	−23.3723	+	21.6864i	−1.22842	+	1.13981i
$363$	−11.0380	+	7.52560i	−0.579346	+	0.394992i
$364$	0.292317	−	3.90070i	0.0153216	−	0.204452i
$365$	−0.178057	−	0.780120i	−0.00931995	−	0.0408334i
$366$	3.49769	+	15.3244i	0.182827	+	0.801019i
$367$	−2.05378	+	27.4058i	−0.107206	+	1.43057i	0.641222	+	0.767355i	$0.278428\pi$
$367$	−2.05378	+	27.4058i	−0.107206	+	1.43057i	−0.748429	+	0.663215i	$0.769191\pi$
$368$	−30.5291	+	20.8144i	−1.59144	+	1.08503i
$369$	0.232018	−	0.215281i	0.0120784	−	0.0112071i
$370$	−1.04977	+	2.67476i	−0.0545748	+	0.139054i
$371$	−21.0543	−	26.4012i	−1.09308	−	1.37068i
$372$	−0.109741	−	1.46440i	−0.00568983	−	0.0759255i
$373$	15.0169	−	4.63210i	0.777545	−	0.239841i	0.119515	−	0.992832i	$-0.461866\pi$
$373$	15.0169	−	4.63210i	0.777545	−	0.239841i	0.658030	+	0.752992i	$0.271390\pi$
$374$	4.09178	+	0.616736i	0.211581	+	0.0318907i
$375$	−4.76805	−	4.42410i	−0.246221	−	0.228460i
$376$	7.50520	−	3.61431i	0.387051	−	0.186394i
$377$	4.31437	−	0.650287i	0.222201	−	0.0334915i
$378$	25.6930	+	17.5172i	1.32150	+	0.900986i
$379$	−16.0442	+	20.1188i	−0.824136	+	1.03343i	0.174672	+	0.984627i	$0.444113\pi$
$379$	−16.0442	+	20.1188i	−0.824136	+	1.03343i	−0.998808	+	0.0488070i	$0.984458\pi$
$380$	1.28864	+	2.23199i	0.0661057	+	0.114498i
$381$	−2.88402	+	4.99527i	−0.147753	+	0.255916i
$382$	4.35743	+	11.1025i	0.222945	+	0.568055i
$383$	16.2586	+	7.82975i	0.830777	+	0.400081i	0.800407	−	0.599457i	$-0.204617\pi$
$383$	16.2586	+	7.82975i	0.830777	+	0.400081i	0.0303708	+	0.999539i	$0.490331\pi$
$384$	21.0183	+	6.48329i	1.07259	+	0.330849i
$385$	1.29834	−	5.68838i	0.0661694	−	0.289907i
$386$	6.98179			0.355364
$387$	−0.386387	+	0.183636i	−0.0196412	+	0.00933474i
$388$	−0.429662			−0.0218128
$389$	5.62992	−	24.6663i	0.285448	−	1.25063i	−0.605249	−	0.796036i	$-0.706927\pi$
$389$	5.62992	−	24.6663i	0.285448	−	1.25063i	0.890698	−	0.454596i	$-0.150216\pi$
$390$	−1.36785	−	0.421927i	−0.0692640	−	0.0213651i
$391$	−3.75829	−	1.80990i	−0.190065	−	0.0915304i
$392$	3.61488	+	9.21056i	0.182579	+	0.465204i
$393$	−1.31756	+	2.28207i	−0.0664619	+	0.115115i
$394$	1.52982	+	2.64973i	0.0770712	+	0.133491i
$395$	−1.99078	+	2.49636i	−0.100167	+	0.125606i
$396$	−0.204807	−	0.139635i	−0.0102920	−	0.00701694i
$397$	−2.61362	+	0.393940i	−0.131174	+	0.0197713i	−0.214301	−	0.976768i	$-0.568747\pi$
$397$	−2.61362	+	0.393940i	−0.131174	+	0.0197713i	0.0831270	+	0.996539i	$0.473509\pi$
$398$	−34.7896	+	16.7538i	−1.74384	+	0.839791i
$399$	33.4605	+	31.0468i	1.67512	+	1.55428i
$400$	−23.9130	−	3.60431i	−1.19565	−	0.180215i
$401$	28.1025	−	8.66848i	1.40337	−	0.432883i	0.501603	−	0.865098i	$-0.332744\pi$
$401$	28.1025	−	8.66848i	1.40337	−	0.432883i	0.901771	+	0.432215i	$0.142268\pi$
$402$	2.84862	+	38.0122i	0.142076	+	1.89588i
$403$	−0.779651	−	0.977651i	−0.0388372	−	0.0487003i
$404$	0.705078	−	1.79651i	0.0350789	−	0.0893797i
$405$	2.48621	−	2.30686i	0.123541	−	0.114629i
$406$	16.6997	−	11.3856i	0.828791	−	0.565060i
$407$	1.42433	−	19.0064i	0.0706014	−	0.942111i
$408$	0.408814	+	1.79113i	0.0202393	+	0.0886742i
$409$	0.0843680	+	0.369640i	0.00417173	+	0.0182775i	0.976971	−	0.213372i	$-0.0684448\pi$
$409$	0.0843680	+	0.369640i	0.00417173	+	0.0182775i	−0.972799	+	0.231650i	$0.925588\pi$
$410$	−0.236979	+	3.16226i	−0.0117035	+	0.156173i
$411$	4.51138	−	3.07581i	0.222530	−	0.151718i
$412$	3.28776	−	3.05059i	0.161976	−	0.150292i
$413$	5.97889	−	15.2340i	0.294202	−	0.749614i
$414$	0.511364	+	0.641230i	0.0251322	+	0.0315147i
$415$	−0.335522	−	4.47723i	−0.0164701	−	0.219779i
$416$	−5.67111	+	1.74931i	−0.278049	+	0.0857668i
$417$	−34.0087	−	5.12599i	−1.66541	−	0.251021i
$418$	−41.1326	−	38.1655i	−2.01186	−	1.86673i
$419$	−14.9002	+	7.17556i	−0.727922	+	0.350549i	−0.760867	−	0.648908i	$-0.775226\pi$
$419$	−14.9002	+	7.17556i	−0.727922	+	0.350549i	0.0329444	+	0.999457i	$0.489512\pi$
$420$	−1.99772	+	0.301108i	−0.0974787	+	0.0146926i
$421$	−7.57559	−	5.16495i	−0.369212	−	0.251724i	0.364473	−	0.931214i	$-0.381249\pi$
$421$	−7.57559	−	5.16495i	−0.369212	−	0.251724i	−0.733685	+	0.679489i	$0.762201\pi$
$422$	8.33932	−	10.4572i	0.405952	−	0.509047i
$423$	−0.142586	−	0.246966i	−0.00693277	−	0.0120079i
$424$	−9.21510	+	15.9610i	−0.447525	+	0.775136i
$425$	−0.997429	−	2.54141i	−0.0483824	−	0.123276i
$426$	−19.9779	−	9.62086i	−0.967933	−	0.466132i
$427$	18.0512	+	5.56807i	0.873561	+	0.269458i
$428$	2.00365	−	8.77857i	0.0968501	−	0.424328i
$429$	9.49503			0.458425
$430$	1.58639	−	3.98182i	0.0765027	−	0.192020i
$431$	9.52715			0.458907			0.229453	−	0.973320i	$-0.426306\pi$
$431$	9.52715			0.458907			0.229453	+	0.973320i	$0.426306\pi$
$432$	5.82453	−	25.5190i	0.280233	−	1.22778i
$433$	−27.5381	−	8.49437i	−1.32339	−	0.408213i	−0.449045	−	0.893509i	$-0.648236\pi$
$433$	−27.5381	−	8.49437i	−1.32339	−	0.408213i	−0.874350	+	0.485296i	$0.838712\pi$
$434$	−5.21900	−	2.51334i	−0.250520	−	0.120644i
$435$	−0.823282	−	2.09769i	−0.0394733	−	0.100576i
$436$	0.492458	−	0.852961i	0.0235844	−	0.0408494i
$437$	28.2821	+	48.9861i	1.35292	+	2.34332i
$438$	3.76102	−	4.71617i	0.179708	−	0.225347i
$439$	−5.56118	−	3.79155i	−0.265421	−	0.180961i	0.423296	−	0.905992i	$-0.360873\pi$
$439$	−5.56118	−	3.79155i	−0.265421	−	0.180961i	−0.688716	+	0.725031i	$0.741825\pi$
$440$	−3.14889	+	0.474619i	−0.150117	+	0.0226266i
$441$	0.305182	−	0.146968i	0.0145325	−	0.00699848i
$442$	−0.894368	−	0.829852i	−0.0425408	−	0.0394720i
$443$	−3.28651	−	0.495362i	−0.156147	−	0.0235354i	0.0705035	−	0.997512i	$-0.477539\pi$
$443$	−3.28651	−	0.495362i	−0.156147	−	0.0235354i	−0.226650	+	0.973976i	$0.572778\pi$
$444$	−6.30631	+	1.94524i	−0.299284	+	0.0923169i
$445$	0.0785665	+	1.04840i	0.00372441	+	0.0496988i
$446$	−9.10489	−	11.4172i	−0.431129	−	0.540619i
$447$	7.91216	−	20.1598i	0.374232	−	0.953528i
$448$	5.36447	−	4.97750i	0.253447	−	0.235165i
$449$	−3.54373	+	2.41607i	−0.167239	+	0.114022i	−0.644047	−	0.764986i	$-0.722746\pi$
$449$	−3.54373	+	2.41607i	−0.167239	+	0.114022i	0.476808	+	0.879007i	$0.341794\pi$
$450$	−0.0401143	+	0.535288i	−0.00189101	+	0.0252337i
$451$	−4.68064	−	20.5072i	−0.220403	−	0.965648i
$452$	−3.11448	−	13.6454i	−0.146493	−	0.641827i
$453$	−0.128733	+	1.71782i	−0.00604841	+	0.0807105i
$454$	11.4173	−	7.78420i	0.535841	−	0.365331i
$455$	−1.26108	+	1.17011i	−0.0591204	+	0.0548557i
$456$	9.10154	−	23.1903i	0.426219	−	1.08599i
$457$	−1.37989	−	1.73032i	−0.0645484	−	0.0809412i	0.748509	−	0.663125i	$-0.230770\pi$
$457$	−1.37989	−	1.73032i	−0.0645484	−	0.0809412i	−0.813058	+	0.582183i	$0.802199\pi$
$458$	3.14030	+	41.9044i	0.146737	+	1.95806i
$459$	2.82375	−	0.871010i	0.131801	−	0.0406553i
$460$	−2.47559	−	0.373136i	−0.115425	−	0.0173975i
$461$	−11.1729	−	10.3670i	−0.520375	−	0.482837i	0.375699	−	0.926742i	$-0.377403\pi$
$461$	−11.1729	−	10.3670i	−0.520375	−	0.482837i	−0.896074	+	0.443904i	$0.853593\pi$
$462$	39.6290	−	19.0843i	1.84371	−	0.887883i
$463$	10.6302	−	1.60224i	0.494027	−	0.0744626i	0.102697	−	0.994713i	$-0.467253\pi$
$463$	10.6302	−	1.60224i	0.494027	−	0.0744626i	0.391331	+	0.920250i	$0.372015\pi$
$464$	−14.0569	−	9.58384i	−0.652576	−	0.444918i
$465$	−0.402675	+	0.504938i	−0.0186736	+	0.0234160i
$466$	7.31117	+	12.6633i	0.338683	+	0.586617i
$467$	7.41391	−	12.8413i	0.343075	−	0.594223i	−0.641927	−	0.766766i	$-0.721865\pi$
$467$	7.41391	−	12.8413i	0.343075	−	0.594223i	0.985002	+	0.172543i	$0.0551982\pi$
$468$	0.0267012	+	0.0680335i	0.00123426	+	0.00314485i
$469$	41.2745	+	19.8767i	1.90588	+	0.917822i
$470$	2.73022	+	0.842161i	0.125936	+	0.0388460i
$471$	1.81581	−	7.95559i	0.0836682	−	0.366574i
$472$	−8.93184			−0.411121
$473$	−2.27021	+	28.3403i	−0.104384	+	1.30309i
$474$	−24.0703			−1.10559
$475$	−8.23789	+	36.0926i	−0.377981	+	1.65604i
$476$	−1.64544	−	0.507551i	−0.0754186	−	0.0232636i
$477$	0.568453	+	0.273752i	0.0260277	+	0.0125343i
$478$	−2.08571	−	5.31429i	−0.0953980	−	0.243070i
$479$	17.1592	−	29.7205i	0.784022	−	1.35797i	−0.145559	−	0.989350i	$-0.546498\pi$
$479$	17.1592	−	29.7205i	0.784022	−	1.35797i	0.929581	−	0.368617i	$-0.120169\pi$
$480$	1.53260	+	2.65454i	0.0699533	+	0.121163i
$481$	−3.50378	+	4.39360i	−0.159758	+	0.200331i
$482$	37.8573	+	25.8107i	1.72435	+	1.17564i
$483$	−43.8446	+	6.60851i	−1.99500	+	0.300697i
$484$	−6.15713	+	2.96512i	−0.279870	+	0.134778i
$485$	0.138520	+	0.128528i	0.00628986	+	0.00583614i
$486$	−1.13681	−	0.171346i	−0.0515667	−	0.00777243i
$487$	−6.21312	+	1.91649i	−0.281543	+	0.0868446i	−0.432311	−	0.901725i	$-0.642302\pi$
$487$	−6.21312	+	1.91649i	−0.281543	+	0.0868446i	0.150768	+	0.988569i	$0.451825\pi$
$488$	−0.770474	−	10.2813i	−0.0348777	−	0.465411i
$489$	10.1439	+	12.7201i	0.458725	+	0.575223i
$490$	−1.23987	+	3.15913i	−0.0560115	+	0.142715i
$491$	5.97382	−	5.54289i	0.269595	−	0.250147i	−0.533777	−	0.845625i	$-0.679228\pi$
$491$	5.97382	−	5.54289i	0.269595	−	0.250147i	0.803372	+	0.595478i	$0.203037\pi$
$492$	−6.01778	+	4.10285i	−0.271302	+	0.184971i
$493$	0.143533	−	1.91531i	0.00646439	−	0.0862613i
$494$	3.68141	+	16.1293i	0.165634	+	0.725692i
$495$	0.0242583	+	0.106283i	0.00109033	+	0.00477705i
$496$	−0.364380	+	4.86232i	−0.0163612	+	0.218325i
$497$	−22.0180	+	15.0116i	−0.987643	+	0.673364i
$498$	24.8112	−	23.0214i	1.11182	−	1.03161i
$499$	2.88373	−	7.34763i	0.129094	−	0.328925i	−0.851684	−	0.524056i	$-0.824418\pi$
$499$	2.88373	−	7.34763i	0.129094	−	0.328925i	0.980777	+	0.195131i	$0.0625133\pi$
$500$	−2.07452	−	2.60137i	−0.0927754	−	0.116337i
$501$	2.89730	+	38.6617i	0.129442	+	1.72728i
$502$	17.4472	−	5.38175i	0.778707	−	0.240199i
$503$	−24.2178	−	3.65024i	−1.07982	−	0.162756i	−0.415044	−	0.909801i	$-0.636234\pi$
$503$	−24.2178	−	3.65024i	−1.07982	−	0.162756i	−0.664773	+	0.747045i	$0.731472\pi$
$504$	−0.318231	−	0.295275i	−0.0141751	−	0.0131526i
$505$	−0.764713	+	0.368266i	−0.0340293	+	0.0163876i
$506$	53.8977	−	8.12377i	2.39604	−	0.361146i
$507$	16.0876	+	10.9684i	0.714477	+	0.487122i
$508$	−1.83967	+	2.30688i	−0.0816223	+	0.102351i
$509$	−15.1556	−	26.2503i	−0.671760	−	1.16352i	−0.977405	−	0.211376i	$-0.932205\pi$
$509$	−15.1556	−	26.2503i	−0.671760	−	1.16352i	0.305645	−	0.952146i	$-0.401128\pi$
$510$	−0.315069	+	0.545716i	−0.0139515	+	0.0241647i
$511$	−2.64854	−	6.74837i	−0.117165	−	0.298530i
$512$	3.73249	+	1.79747i	0.164954	+	0.0794377i
$513$	−38.2902	−	11.8110i	−1.69055	−	0.521466i
$514$	4.81346	−	21.0891i	0.212313	−	0.930202i
$515$	−1.97249			−0.0869184
$516$	9.42182	−	2.85335i	0.414773	−	0.125612i
$517$	−18.9520			−0.833507
$518$	−5.79275	+	25.3797i	−0.254519	+	1.11512i
$519$	−15.2280	−	4.69722i	−0.668435	−	0.206185i
$520$	0.845935	+	0.407381i	0.0370967	+	0.0178648i
$521$	4.59482	+	11.7074i	0.201303	+	0.512911i	0.995501	−	0.0947472i	$-0.0302043\pi$
$521$	4.59482	+	11.7074i	0.201303	+	0.512911i	−0.794199	+	0.607658i	$0.792109\pi$
$522$	−0.188819	+	0.327044i	−0.00826439	+	0.0143143i
$523$	18.0801	+	31.3157i	0.790589	+	1.36934i	0.925603	+	0.378496i	$0.123559\pi$
$523$	18.0801	+	31.3157i	0.790589	+	1.36934i	−0.135014	+	0.990844i	$0.543108\pi$
$524$	−0.840448	+	1.05389i	−0.0367151	+	0.0460393i
$525$	−23.9774	−	16.3475i	−1.04646	−	0.713465i
$526$	−24.8759	+	3.74944i	−1.08464	+	0.163483i
$527$	−0.495953	+	0.238838i	−0.0216041	+	0.0104040i
$528$	−27.1406	−	25.1828i	−1.18114	−	1.09594i
$529$	−31.5895	−	4.76135i	−1.37346	−	0.207015i
$530$	−6.04053	+	1.86326i	−0.262384	+	0.0809347i
$531$	0.0228502	+	0.304915i	0.000991616	+	0.0132322i
$532$	14.5583	+	18.2555i	0.631180	+	0.791475i
$533$	−2.26582	+	5.77321i	−0.0981434	+	0.250065i
$534$	−5.80983	+	5.39073i	−0.251416	+	0.233280i
$535$	−3.27195	+	2.23078i	−0.141459	+	0.0964450i
$536$	1.86847	−	24.9330i	0.0807056	−	1.07694i
$537$	2.75596	+	12.0747i	0.118929	+	0.521060i
$538$	4.04140	+	17.7065i	0.174237	+	0.763383i
$539$	1.68226	−	22.4482i	0.0724600	−	0.966912i
$540$	1.46536	−	0.999066i	0.0630591	−	0.0429929i
$541$	3.25662	−	3.02170i	0.140013	−	0.129913i	−0.607057	−	0.794658i	$-0.707650\pi$
$541$	3.25662	−	3.02170i	0.140013	−	0.129913i	0.747070	+	0.664745i	$0.231460\pi$
$542$	−8.97782	+	22.8751i	−0.385630	+	0.982570i
$543$	20.0800	+	25.1795i	0.861715	+	1.08056i
$544$	0.195236	+	2.60524i	0.00837067	+	0.111699i
$545$	−0.413916	+	0.127676i	−0.0177302	+	0.00546905i
$546$	−12.8238	−	1.93288i	−0.548808	−	0.0827196i
$547$	−0.724131	−	0.671896i	−0.0309616	−	0.0287282i	0.664540	−	0.747252i	$-0.268627\pi$
$547$	−0.724131	−	0.671896i	−0.0309616	−	0.0287282i	−0.695502	+	0.718524i	$0.744818\pi$
$548$	2.51650	−	1.21188i	0.107499	−	0.0517690i
$549$	−0.349011	+	0.0526049i	−0.0148954	+	0.00224512i
$550$	29.4752	+	20.0959i	1.25683	+	0.856890i
$551$	−16.2385	+	20.3625i	−0.691785	+	0.867470i
$552$	12.0999	+	20.9577i	0.515007	+	0.892019i
$553$	−14.4638	+	25.0521i	−0.615065	+	1.06532i
$554$	−12.6508	−	32.2338i	−0.537483	−	1.36948i
$555$	2.61500	+	1.25932i	0.111000	+	0.0534550i
$556$	−16.8118	−	5.18576i	−0.712980	−	0.219925i
$557$	−2.10042	+	9.20253i	−0.0889976	+	0.389924i	−0.999734	−	0.0230643i	$-0.992658\pi$
$557$	−2.10042	+	9.20253i	−0.0889976	+	0.389924i	0.910736	+	0.412988i	$0.135515\pi$
$558$	0.108231			0.00458178
$559$	5.26013	−	6.52695i	0.222480	−	0.276061i
$560$	6.70806			0.283467
$561$	0.930095	−	4.07501i	0.0392687	−	0.172047i
$562$	11.7519	+	3.62499i	0.495725	+	0.152911i
$563$	24.8446	+	11.9645i	1.04708	+	0.504245i	0.876652	−	0.481125i	$-0.159772\pi$
$563$	24.8446	+	11.9645i	1.04708	+	0.504245i	0.170425	+	0.985371i	$0.445486\pi$
$564$	2.39745	+	6.10859i	0.100951	+	0.257218i
$565$	−3.07776	+	5.33083i	−0.129482	+	0.224270i
$566$	−25.8462	−	44.7670i	−1.08640	−	1.88170i
$567$	19.1581	−	24.0234i	0.804563	−	1.00889i
$568$	12.0170	+	8.19308i	0.504224	+	0.343774i
$569$	20.0473	−	3.02164i	0.840425	−	0.126674i	0.285297	−	0.958439i	$-0.407908\pi$
$569$	20.0473	−	3.02164i	0.840425	−	0.126674i	0.555127	+	0.831765i	$0.312670\pi$
$570$	7.69852	−	3.70741i	0.322456	−	0.155286i
$571$	13.1590	+	12.2098i	0.550688	+	0.510964i	0.905712	−	0.423893i	$-0.139337\pi$
$571$	13.1590	+	12.2098i	0.550688	+	0.510964i	−0.355024	+	0.934857i	$0.615527\pi$
$572$	4.80287	+	0.723917i	0.200818	+	0.0302685i
$573$	11.5123	−	3.55107i	0.480933	−	0.148348i
$574$	2.14698	+	28.6495i	0.0896134	+	1.19581i
$575$	−22.4218	−	28.1161i	−0.935055	−	1.17252i
$576$	−0.0499533	+	0.127279i	−0.00208139	+	0.00530329i
$577$	−0.766879	+	0.711560i	−0.0319256	+	0.0296226i	−0.695974	−	0.718067i	$-0.745027\pi$
$577$	−0.766879	+	0.711560i	−0.0319256	+	0.0296226i	0.664049	+	0.747689i	$0.268837\pi$
$578$	23.3780	−	15.9389i	0.972397	−	0.662969i
$579$	0.527022	−	7.03262i	0.0219023	−	0.292266i
$580$	−0.256510	−	1.12384i	−0.0106510	−	0.0466650i
$581$	−9.05140	−	39.6568i	−0.375516	−	1.64524i
$582$	−0.106453	+	1.42052i	−0.00441264	+	0.0588825i
$583$	34.6448	−	23.6204i	1.43484	−	0.978257i
$584$	−2.90043	+	2.69120i	−0.120021	+	0.111363i
$585$	0.0117430	−	0.0299208i	0.000485514	−	0.00123707i
$586$	−27.1612	−	34.0591i	−1.12202	−	1.40697i
$587$	−1.23653	−	16.5003i	−0.0510370	−	0.681042i	−0.962781	−	0.270283i	$-0.912883\pi$
$587$	−1.23653	−	16.5003i	−0.0510370	−	0.681042i	0.911744	−	0.410759i	$-0.134736\pi$
$588$	−7.44830	+	2.29750i	−0.307163	+	0.0947472i
$589$	7.38099	+	1.11251i	0.304128	+	0.0458400i
$590$	−2.24573	−	2.08373i	−0.0924551	−	0.0857858i
$591$	2.78450	−	1.34094i	0.114539	−	0.0551590i
$592$	21.6679	−	3.26592i	0.890547	−	0.134228i
$593$	−8.32969	−	5.67909i	−0.342059	−	0.233212i	0.380090	−	0.924950i	$-0.375893\pi$
$593$	−8.32969	−	5.67909i	−0.342059	−	0.233212i	−0.722149	+	0.691737i	$0.756846\pi$
$594$	−24.0746	+	30.1886i	−0.987792	+	1.23865i
$595$	0.378650	+	0.655841i	0.0155231	+	0.0268869i
$596$	5.53923	−	9.59422i	0.226896	−	0.392995i
$597$	14.2497	+	36.3075i	0.583200	+	1.48597i
$598$	−14.4794	−	6.97290i	−0.592105	−	0.285143i
$599$	32.4927	+	10.0227i	1.32761	+	0.409515i	0.875833	−	0.482614i	$-0.160312\pi$
$599$	32.4927	+	10.0227i	1.32761	+	0.409515i	0.451782	+	0.892129i	$0.350789\pi$
$600$	−3.52442	+	15.4415i	−0.143884	+	0.630396i
$601$	−27.2454			−1.11136			−0.555681	−	0.831396i	$-0.687542\pi$
$601$	−27.2454			−1.11136			−0.555681	+	0.831396i	$0.687542\pi$
$602$	8.83526	−	37.8137i	0.360098	−	1.54117i
$603$	−0.855944			−0.0348567
$604$	−0.196087	+	0.859113i	−0.00797866	+	0.0349568i
$605$	2.87199	+	0.885890i	0.116763	+	0.0360166i
$606$	−5.76481	−	2.77619i	−0.234180	−	0.112775i
$607$	−8.72876	−	22.2405i	−0.354289	−	0.902715i	−0.991272	−	0.131836i	$-0.957913\pi$
$607$	−8.72876	−	22.2405i	−0.354289	−	0.902715i	0.636982	−	0.770879i	$-0.280183\pi$
$608$	17.7132	−	30.6801i	0.718364	−	1.24424i
$609$	−10.2080	−	17.6807i	−0.413648	−	0.716459i
$610$	2.20482	−	2.76476i	0.0892705	−	0.111942i
$611$	4.61691	+	3.14776i	0.186780	+	0.127345i
$612$	0.0318137	−	0.00479514i	0.00128599	−	0.000193832i
$613$	30.1578	−	14.5232i	1.21806	−	0.586588i	0.289291	−	0.957241i	$-0.406581\pi$
$613$	30.1578	−	14.5232i	1.21806	−	0.586588i	0.928771	+	0.370654i	$0.120866\pi$
$614$	19.7051	+	18.2837i	0.795233	+	0.737868i
$615$	3.16740	+	0.477409i	0.127722	+	0.0192510i
$616$	−27.5688	+	8.50386i	−1.11078	+	0.342630i
$617$	−1.17887	−	15.7309i	−0.0474594	−	0.633302i	−0.969323	−	0.245789i	$-0.920953\pi$
$617$	−1.17887	−	15.7309i	−0.0474594	−	0.633302i	0.921864	−	0.387513i	$-0.126666\pi$
$618$	−9.27110	−	11.6256i	−0.372939	−	0.467650i
$619$	7.08652	−	18.0562i	0.284831	−	0.725738i	−0.714819	−	0.699309i	$-0.753491\pi$
$619$	7.08652	−	18.0562i	0.284831	−	0.725738i	0.999651	−	0.0264292i	$-0.00841367\pi$
$620$	−0.242182	+	0.224712i	−0.00972628	+	0.00902467i
$621$	32.1607	−	21.9268i	1.29056	−	0.879892i
$622$	−3.42397	+	45.6897i	−0.137289	+	1.83199i
$623$	2.11949	+	9.28610i	0.0849156	+	0.372040i
$624$	2.42911	+	10.6426i	0.0972424	+	0.426047i
$625$	1.70340	−	22.7303i	0.0681359	−	0.909210i
$626$	−27.0075	+	18.4134i	−1.07944	+	0.735947i
$627$	−41.5483	+	38.5512i	−1.65928	+	1.53959i
$628$	1.52504	−	3.88574i	0.0608557	−	0.155058i
$629$	1.54240	+	1.93411i	0.0614994	+	0.0771178i
$630$	−0.0111272	−	0.148482i	−0.000443316	−	0.00591565i
$631$	−1.52150	+	0.469320i	−0.0605699	+	0.0186833i	−0.324892	−	0.945751i	$-0.605328\pi$
$631$	−1.52150	+	0.469320i	−0.0605699	+	0.0186833i	0.264322	+	0.964434i	$0.414852\pi$
$632$	15.6119	+	2.35311i	0.621007	+	0.0936017i
$633$	−9.90382	−	9.18940i	−0.393641	−	0.365246i
$634$	−19.6529	+	9.46434i	−0.780516	+	0.375877i
$635$	1.28317	−	0.193406i	0.0509209	−	0.00767510i
$636$	−11.9959	−	8.17868i	−0.475669	−	0.324306i
$637$	−4.13827	+	5.18922i	−0.163964	+	0.205604i
$638$	12.5485	+	21.7347i	0.496802	+	0.860486i
$639$	0.248952	−	0.431198i	0.00984840	−	0.0170579i
$640$	−1.80786	−	4.60636i	−0.0714620	−	0.182082i
$641$	6.14244	+	2.95804i	0.242612	+	0.116836i	0.551239	−	0.834347i	$-0.314155\pi$
$641$	6.14244	+	2.95804i	0.242612	+	0.116836i	−0.308627	+	0.951183i	$0.599870\pi$
$642$	−28.5267	−	8.79933i	−1.12586	−	0.347282i
$643$	−3.83478	+	16.8013i	−0.151229	+	0.662578i	0.841300	+	0.540569i	$0.181791\pi$
$643$	−3.83478	+	16.8013i	−0.151229	+	0.662578i	−0.992529	+	0.122009i	$0.961066\pi$
$644$	−22.6817			−0.893786
$645$	−3.89106	−	1.89851i	−0.153210	−	0.0747539i
$646$	7.28288			0.286541
$647$	−3.00033	+	13.1453i	−0.117955	+	0.516795i	0.881084	+	0.472961i	$0.156815\pi$
$647$	−3.00033	+	13.1453i	−0.117955	+	0.516795i	−0.999039	+	0.0438349i	$0.986042\pi$
$648$	−16.0253	−	4.94314i	−0.629531	−	0.194185i
$649$	18.3085	+	8.81691i	0.718671	+	0.346094i
$650$	−3.84275	−	9.79116i	−0.150725	−	0.384041i
$651$	−2.92560	+	5.06728i	−0.114663	+	0.198602i
$652$	4.16131	+	7.20760i	0.162970	+	0.282272i
$653$	−23.9528	+	30.0358i	−0.937344	+	1.17539i	0.0469569	+	0.998897i	$0.485048\pi$
$653$	−23.9528	+	30.0358i	−0.937344	+	1.17539i	−0.984301	+	0.176496i	$0.943524\pi$
$654$	−2.69800	−	1.83946i	−0.105500	−	0.0719287i
$655$	0.586210	−	0.0883570i	0.0229051	−	0.00345239i
$656$	21.7884	−	10.4927i	0.850693	−	0.409672i
$657$	0.0992925	+	0.0921300i	0.00387377	+	0.00359433i
$658$	25.5962	+	3.85800i	0.997842	+	0.150401i
$659$	−6.80245	+	2.09828i	−0.264986	+	0.0817373i	−0.424401	−	0.905474i	$-0.639515\pi$
$659$	−6.80245	+	2.09828i	−0.264986	+	0.0817373i	0.159415	+	0.987212i	$0.449039\pi$
$660$	−0.187469	−	2.50160i	−0.00729721	−	0.0973746i
$661$	13.9581	+	17.5029i	0.542908	+	0.680785i	0.975296	−	0.220903i	$-0.0709003\pi$
$661$	13.9581	+	17.5029i	0.542908	+	0.680785i	−0.432388	+	0.901688i	$0.642329\pi$
$662$	1.57675	−	4.01750i	0.0612822	−	0.156144i
$663$	−0.903406	+	0.838238i	−0.0350854	+	0.0325545i
$664$	−18.3430	+	12.5060i	−0.711846	+	0.485328i
$665$	0.767406	−	10.2403i	0.0297587	−	0.397103i
$666$	−0.108233	−	0.474198i	−0.00419393	−	0.0183748i
$667$	−5.62969	−	24.6653i	−0.217983	−	0.955044i
$668$	−1.48209	+	19.7772i	−0.0573439	+	0.765201i
$669$	−12.1876	+	8.30936i	−0.471199	+	0.321258i
$670$	6.28647	−	5.83299i	0.242867	−	0.225348i
$671$	−8.56964	+	21.8351i	−0.330827	+	0.842935i
$672$	17.3144	+	21.7116i	0.667917	+	0.837542i
$673$	0.148095	+	1.97619i	0.00570864	+	0.0761765i	0.999330	−	0.0365873i	$-0.0116487\pi$
$673$	0.148095	+	1.97619i	0.00570864	+	0.0761765i	−0.993622	+	0.112764i	$0.964030\pi$
$674$	−1.19518	+	0.368663i	−0.0460365	+	0.0142004i
$675$	25.1910	+	3.79693i	0.969602	+	0.146144i
$676$	7.30137	+	6.77468i	0.280822	+	0.260565i
$677$	6.11443	−	2.94456i	0.234997	−	0.113168i	−0.312680	−	0.949859i	$-0.601227\pi$
$677$	6.11443	−	2.94456i	0.234997	−	0.113168i	0.547677	+	0.836690i	$0.315512\pi$
$678$	−45.8853	+	6.91609i	−1.76221	+	0.265611i
$679$	1.41450	+	0.964388i	0.0542834	+	0.0370098i
$680$	0.257701	−	0.323147i	0.00988240	−	0.0123921i
$681$	−6.97904	−	12.0880i	−0.267437	−	0.463215i
$682$	3.59641	−	6.22916i	0.137713	−	0.238527i
$683$	3.77933	+	9.62958i	0.144612	+	0.368466i	0.984767	−	0.173881i	$-0.0556310\pi$
$683$	3.77933	+	9.62958i	0.144612	+	0.368466i	−0.840154	+	0.542347i	$0.817536\pi$
$684$	−0.393064	−	0.189290i	−0.0150292	−	0.00723767i
$685$	−1.17382	−	0.362074i	−0.0448492	−	0.0138342i
$686$	2.38241	−	10.4380i	0.0909610	−	0.398526i
$687$	42.4465			1.61944
$688$	−32.3464	+	4.70570i	−1.23320	+	0.179403i
$689$	−12.3630			−0.470993
$690$	−1.84699	+	8.09220i	−0.0703138	+	0.308065i
$691$	−10.6685	−	3.29080i	−0.405850	−	0.125188i	0.0851075	−	0.996372i	$-0.472877\pi$
$691$	−10.6685	−	3.29080i	−0.405850	−	0.125188i	−0.490957	+	0.871184i	$0.663353\pi$
$692$	−7.34466	−	3.53700i	−0.279202	−	0.134457i
$693$	0.360834	+	0.919390i	0.0137070	+	0.0349247i
$694$	−4.44549	+	7.69981i	−0.168748	+	0.292281i
$695$	3.86875	+	6.70087i	0.146750	+	0.254179i
$696$	−6.94732	+	8.71167i	−0.263338	+	0.330215i
$697$	2.25576	+	1.53795i	0.0854428	+	0.0582539i
$698$	16.7265	−	2.52111i	0.633106	−	0.0954254i
$699$	13.3074	−	6.40851i	0.503332	−	0.242392i
$700$	−10.8821	−	10.0972i	−0.411306	−	0.381637i
$701$	45.9912	+	6.93206i	1.73706	+	0.261820i	0.939779	−	0.341783i	$-0.111031\pi$
$701$	45.9912	+	6.93206i	1.73706	+	0.261820i	0.797285	+	0.603603i	$0.206269\pi$
$702$	10.8789	−	3.35570i	0.410598	−	0.126653i
$703$	−2.50683	−	33.4513i	−0.0945467	−	1.26164i
$704$	5.66556	+	7.10438i	0.213529	+	0.267757i
$705$	1.05438	−	2.68653i	0.0397104	−	0.101180i
$706$	31.1443	−	28.8977i	1.17213	−	1.08758i
$707$	−6.35350	+	4.33175i	−0.238948	+	0.162912i
$708$	0.525817	−	7.01654i	0.0197614	−	0.263698i
$709$	−1.61013	−	7.05446i	−0.0604699	−	0.264936i	0.935652	−	0.352925i	$-0.114813\pi$
$709$	−1.61013	−	7.05446i	−0.0604699	−	0.264936i	−0.996121	+	0.0879894i	$0.971956\pi$
$710$	1.11005	+	4.86346i	0.0416596	+	0.182523i
$711$	0.0403908	−	0.538978i	0.00151477	−	0.0202133i
$712$	4.29522	−	2.92843i	0.160970	−	0.109748i
$713$	−5.31525	+	4.93183i	−0.199058	+	0.184699i
$714$	−2.08571	+	5.31430i	−0.0780557	+	0.198883i
$715$	−1.33186	−	1.67010i	−0.0498087	−	0.0624582i
$716$	0.473457	+	6.31784i	0.0176939	+	0.236109i
$717$	−5.51043	+	1.69974i	−0.205791	+	0.0634780i
$718$	23.0787	+	3.47855i	0.861289	+	0.129818i
$719$	26.6874	+	24.7623i	0.995274	+	0.923479i	0.997068	−	0.0765194i	$-0.0243807\pi$
$719$	26.6874	+	24.7623i	0.995274	+	0.923479i	−0.00179446	+	0.999998i	$0.500571\pi$
$720$	−0.112922	+	0.0543806i	−0.00420837	+	0.00202664i
$721$	−17.6708	+	2.66345i	−0.658095	+	0.0991919i
$722$	−54.9720	−	37.4793i	−2.04585	−	1.39483i
$723$	28.8563	−	36.1846i	1.07318	−	1.34572i
$724$	8.23734	+	14.2675i	0.306138	+	0.530247i
$725$	8.27918	−	14.3400i	0.307481	−	0.532573i
$726$	8.27759	+	21.0910i	0.307210	+	0.782759i
$727$	−38.1354	−	18.3650i	−1.41436	−	0.681121i	−0.438343	−	0.898808i	$-0.644435\pi$
$727$	−38.1354	−	18.3650i	−1.41436	−	0.681121i	−0.976019	+	0.217687i	$0.930149\pi$
$728$	8.12850	+	2.50731i	0.301262	+	0.0929271i
$729$	−6.13298	+	26.8703i	−0.227147	+	0.995197i
$730$	−1.35709			−0.0502281
$731$	−2.28593	−	2.89686i	−0.0845483	−	0.107144i
$732$	8.12195			0.300196
$733$	4.08534	−	17.8990i	0.150895	−	0.661116i	−0.841731	−	0.539898i	$-0.818463\pi$
$733$	4.08534	−	17.8990i	0.150895	−	0.661116i	0.992626	−	0.121218i	$-0.0386800\pi$
$734$	44.5391	+	13.7385i	1.64397	+	0.507097i
$735$	3.08854	+	1.48736i	0.113923	+	0.0548622i
$736$	12.5725	+	32.0342i	0.463428	+	1.18080i
$737$	−28.4422	+	49.2633i	−1.04768	+	1.81464i
$738$	−0.268396	−	0.464876i	−0.00987981	−	0.0171123i
$739$	19.5007	−	24.4531i	0.717345	−	0.899522i	−0.280839	−	0.959755i	$-0.590613\pi$
$739$	19.5007	−	24.4531i	0.717345	−	0.899522i	0.998184	+	0.0602326i	$0.0191843\pi$
$740$	1.22673	+	0.836372i	0.0450956	+	0.0307456i
$741$	16.5246	−	2.49069i	0.607048	−	0.0914977i
$742$	−51.5989	+	24.8487i	−1.89425	+	0.912225i
$743$	−17.5715	−	16.3039i	−0.644635	−	0.598134i	0.288579	−	0.957456i	$-0.406817\pi$
$743$	−17.5715	−	16.3039i	−0.644635	−	0.598134i	−0.933213	+	0.359323i	$0.883008\pi$
$744$	3.15781	+	0.475963i	0.115771	+	0.0174496i
$745$	−4.65579	+	1.43612i	−0.170575	+	0.0526153i
$746$	−1.99173	−	26.5778i	−0.0729225	−	0.973084i
$747$	0.473858	+	0.594199i	0.0173375	+	0.0217406i
$748$	0.781156	−	1.99035i	0.0285619	−	0.0727745i
$749$	−26.3000	+	24.4028i	−0.960980	+	0.891659i
$750$	−9.11446	+	6.21414i	−0.332813	+	0.226908i
$751$	−3.81330	+	50.8850i	−0.139149	+	1.85682i	0.294391	+	0.955685i	$0.404883\pi$
$751$	−3.81330	+	50.8850i	−0.139149	+	1.85682i	−0.433540	+	0.901134i	$0.642736\pi$
$752$	−4.84848	−	21.2426i	−0.176806	−	0.774637i
$753$	−4.10393	−	17.9805i	−0.149555	−	0.655245i
$754$	0.552982	−	7.37903i	0.0201384	−	0.268728i
$755$	0.320209	−	0.218315i	0.0116536	−	0.00794528i
$756$	11.7786	−	10.9289i	0.428383	−	0.397481i
$757$	8.24045	−	20.9963i	0.299504	−	0.763125i	−0.699327	−	0.714802i	$-0.746517\pi$
$757$	8.24045	−	20.9963i	0.299504	−	0.763125i	0.998832	−	0.0483232i	$-0.0153878\pi$
$758$	27.2106	+	34.1210i	0.988333	+	1.23933i
$759$	−4.11444	−	54.9033i	−0.149345	−	1.99286i
$760$	−5.35566	+	1.65200i	−0.194270	+	0.0599244i
$761$	−35.6862	−	5.37882i	−1.29362	−	0.194982i	−0.534076	−	0.845436i	$-0.679341\pi$
$761$	−35.6862	−	5.37882i	−1.29362	−	0.194982i	−0.759546	+	0.650454i	$0.774579\pi$
$762$	7.17105	+	6.65376i	0.259780	+	0.241040i
$763$	−3.53572	+	1.70271i	−0.128002	+	0.0616423i
$764$	6.09401	−	0.918524i	0.220473	−	0.0332310i
$765$	−0.0116909	−	0.00797071i	−0.000422685	−	0.000288182i
$766$	19.0820	−	23.9280i	0.689460	−	0.864555i
$767$	−2.99574	−	5.18878i	−0.108170	−	0.187356i
$768$	15.0615	−	26.0874i	0.543487	−	0.941347i
$769$	−9.37295	−	23.8819i	−0.337997	−	0.861203i	−0.994292	−	0.106698i	$-0.965972\pi$
$769$	−9.37295	−	23.8819i	−0.337997	−	0.861203i	0.656294	−	0.754505i	$-0.272123\pi$
$770$	−8.91550	−	4.29348i	−0.321292	−	0.154726i
$771$	−20.8793	−	6.44043i	−0.751951	−	0.231946i
$772$	0.802762	−	3.51713i	0.0288921	−	0.126584i
$773$	−30.1582			−1.08472			−0.542358	−	0.840148i	$-0.682468\pi$
$773$	−30.1582			−1.08472			−0.542358	+	0.840148i	$0.682468\pi$
$774$	0.157815	+	0.708176i	0.00567255	+	0.0254548i
$775$	−4.74562			−0.170468
$776$	0.207915	−	0.910936i	0.00746372	−	0.0327007i
$777$	25.1272	+	7.75072i	0.901434	+	0.278055i
$778$	−38.6599	−	18.6176i	−1.38603	−	0.667475i
$779$	−13.5253	−	34.4619i	−0.484594	−	1.23472i
$780$	−0.369824	+	0.640554i	−0.0132418	+	0.0229355i
$781$	−16.5449	−	28.6566i	−0.592023	−	1.02541i
$782$	−4.41092	+	5.53112i	−0.157734	+	0.197792i
$783$	14.8082	+	10.0960i	0.529200	+	0.360803i
$784$	25.5917	−	3.85733i	0.913990	−	0.137762i
$785$	−1.65403	+	0.796537i	−0.0590347	+	0.0284296i
$786$	3.27607	+	3.03975i	0.116854	+	0.108424i
$787$	−20.5239	−	3.09348i	−0.731598	−	0.110271i	−0.227330	−	0.973818i	$-0.573000\pi$
$787$	−20.5239	−	3.09348i	−0.731598	−	0.110271i	−0.504268	+	0.863547i	$0.668238\pi$
$788$	1.51072	−	0.465995i	0.0538171	−	0.0166004i
$789$	1.89898	+	25.3401i	0.0676053	+	0.902130i
$790$	3.37632	+	4.23377i	0.120124	+	0.150631i
$791$	−20.3743	+	51.9128i	−0.724426	+	1.84581i
$792$	0.395151	−	0.366646i	0.0140411	−	0.0130282i
$793$	5.71428	−	3.89593i	0.202920	−	0.138349i
$794$	−0.334993	+	4.47018i	−0.0118885	+	0.158641i
$795$	1.42085	+	6.22516i	0.0503924	+	0.220784i
$796$	4.43976	+	19.4519i	0.157363	+	0.689453i
$797$	1.25760	−	16.7815i	0.0445463	−	0.594430i	−0.929609	−	0.368549i	$-0.879855\pi$
$797$	1.25760	−	16.7815i	0.0445463	−	0.594430i	0.974155	−	0.225881i	$-0.0725261\pi$
$798$	63.9620	−	43.6086i	2.26423	−	1.54373i
$799$	1.80319	−	1.67311i	0.0637922	−	0.0591905i
$800$	−8.22857	+	20.9661i	−0.290924	+	0.741262i
$801$	−0.110959	−	0.139139i	−0.00392055	−	0.00491622i
$802$	−3.72732	−	49.7376i	−0.131616	−	1.75630i
$803$	8.60187	−	2.65333i	0.303554	−	0.0936339i
$804$	19.4765	+	2.93561i	0.686883	+	0.103531i
$805$	7.31242	+	6.78494i	0.257729	+	0.239138i
$806$	−1.91073	+	0.920161i	−0.0673027	+	0.0324113i
$807$	18.1405	−	2.73424i	0.638577	−	0.0962499i
$808$	3.46763	+	2.36419i	0.121991	+	0.0831719i
$809$	21.2357	−	26.6287i	0.746608	−	0.936217i	−0.252903	−	0.967492i	$-0.581385\pi$
$809$	21.2357	−	26.6287i	0.746608	−	0.936217i	0.999511	+	0.0312750i	$0.00995677\pi$
$810$	−2.87602	−	4.98142i	−0.101053	−	0.175029i
$811$	−6.69823	+	11.6017i	−0.235207	+	0.407390i	−0.959333	−	0.282278i	$-0.908910\pi$
$811$	−6.69823	+	11.6017i	−0.235207	+	0.407390i	0.724126	+	0.689668i	$0.242243\pi$
$812$	−3.81549	−	9.72171i	−0.133897	−	0.341165i
$813$	22.3640	+	10.7699i	0.784339	+	0.377718i
$814$	−30.8886	−	9.52788i	−1.08265	−	0.333952i
$815$	0.814481	−	3.56848i	0.0285300	−	0.124998i
$816$	4.80548			0.168226
$817$	3.48313	+	49.9174i	0.121859	+	1.74639i
$818$	0.643023			0.0224828
$819$	0.0647995	−	0.283905i	0.00226428	−	0.00992045i
$820$	1.56577	+	0.482975i	0.0546790	+	0.0168662i
$821$	−11.8336	−	5.69878i	−0.412997	−	0.198889i	0.215836	−	0.976430i	$-0.430752\pi$
$821$	−11.8336	−	5.69878i	−0.412997	−	0.198889i	−0.628832	+	0.777541i	$0.716467\pi$
$822$	−3.38315	−	8.62014i	−0.118001	−	0.300662i
$823$	−9.61010	+	16.6452i	−0.334987	+	0.580215i	−0.983482	−	0.181004i	$-0.942065\pi$
$823$	−9.61010	+	16.6452i	−0.334987	+	0.580215i	0.648495	+	0.761219i	$0.275399\pi$
$824$	4.87667	+	8.44664i	0.169887	+	0.294253i
$825$	22.4671	−	28.1729i	0.782205	−	0.980854i
$826$	−22.9323	−	15.6350i	−0.797916	−	0.544010i
$827$	32.5196	−	4.90154i	1.13082	−	0.170443i	0.443135	−	0.896455i	$-0.353866\pi$
$827$	32.5196	−	4.90154i	1.13082	−	0.170443i	0.687682	+	0.726012i	$0.258628\pi$
$828$	0.381821	−	0.183875i	0.0132692	−	0.00639011i
$829$	8.73426	+	8.10421i	0.303353	+	0.281471i	0.817130	−	0.576453i	$-0.195564\pi$
$829$	8.73426	+	8.10421i	0.303353	+	0.281471i	−0.513777	+	0.857924i	$0.671754\pi$
$830$	−7.52952	−	1.13489i	−0.261354	−	0.0393927i
$831$	−33.4235	+	10.3098i	−1.15945	+	0.357642i
$832$	−0.200217	−	2.67171i	−0.00694127	−	0.0926248i
$833$	1.82171	+	2.28435i	0.0631184	+	0.0791480i
$834$	−21.3101	+	54.2973i	−0.737909	+	1.88016i
$835$	6.39388	−	5.93266i	0.221269	−	0.205308i
$836$	−23.9556	+	16.3326i	−0.828521	+	0.564876i
$837$	0.383854	−	5.12218i	0.0132679	−	0.177048i
$838$	6.24126	+	27.3448i	0.215601	+	0.944609i
$839$	11.8997	+	52.1359i	0.410822	+	1.79993i	0.580308	+	0.814397i	$0.302932\pi$
$839$	11.8997	+	52.1359i	0.410822	+	1.79993i	−0.169486	+	0.985533i	$0.554211\pi$
$840$	0.328319	−	4.38112i	0.0113281	−	0.151163i
$841$	−14.3361	+	9.77416i	−0.494347	+	0.337040i
$842$	−11.3990	+	10.5767i	−0.392834	+	0.364497i
$843$	4.53848	−	11.5638i	0.156313	−	0.398280i
$844$	−4.30903	−	5.40336i	−0.148323	−	0.185991i
$845$	−0.327352	−	4.36821i	−0.0112613	−	0.150271i
$846$	−0.462158	+	0.142557i	−0.0158893	+	0.00490120i
$847$	26.9253	+	4.05833i	0.925163	+	0.139446i
$848$	35.3384	+	32.7893i	1.21353	+	1.12599i
$849$	−47.0440	+	22.6552i	−1.61455	+	0.777524i
$850$	−4.57852	+	0.690101i	−0.157042	+	0.0236703i
$851$	26.9235	+	18.3561i	0.922924	+	0.629239i
$852$	−7.14364	+	8.95784i	−0.244737	+	0.306890i
$853$	−14.4537	−	25.0346i	−0.494886	−	0.857168i	0.505096	−	0.863063i	$-0.331457\pi$
$853$	−14.4537	−	25.0346i	−0.494886	−	0.857168i	−0.999983	+	0.00589491i	$0.998124\pi$
$854$	16.0189	−	27.7456i	0.548156	−	0.949434i
$855$	0.0700974	+	0.178605i	0.00239728	+	0.00610817i
$856$	17.6421	+	8.49597i	0.602993	+	0.290386i
$857$	36.3470	+	11.2116i	1.24159	+	0.382980i	0.844876	−	0.534963i	$-0.179674\pi$
$857$	36.3470	+	11.2116i	1.24159	+	0.382980i	0.396714	+	0.917942i	$0.370151\pi$
$858$	3.58333	−	15.6996i	0.122333	−	0.535976i
$859$	38.9400			1.32861			0.664307	−	0.747460i	$-0.268727\pi$
$859$	38.9400			1.32861			0.664307	+	0.747460i	$0.268727\pi$
$860$	−1.82347	−	1.25699i	−0.0621799	−	0.0428629i
$861$	29.0202			0.989005
$862$	3.59545	−	15.7527i	0.122462	−	0.536539i
$863$	−45.6356	−	14.0767i	−1.55345	−	0.479177i	−0.605035	−	0.796199i	$-0.706841\pi$
$863$	−45.6356	−	14.0767i	−1.55345	−	0.479177i	−0.948418	+	0.317022i	$0.897317\pi$
$864$	−21.9641	−	10.5774i	−0.747235	−	0.359849i
$865$	1.30982	+	3.33736i	0.0445351	+	0.113474i
$866$	−24.4376	+	42.3272i	−0.830425	+	1.43834i
$867$	−14.2902	−	24.7514i	−0.485321	−	0.840601i
$868$	−1.86619	+	2.34013i	−0.0633427	+	0.0794292i
$869$	−29.6784	−	20.2344i	−1.00677	−	0.686404i
$870$	−3.77913	+	0.569612i	−0.128124	+	0.0193116i
$871$	15.1110	−	7.27709i	0.512018	−	0.246575i
$872$	1.57008	+	1.45682i	0.0531696	+	0.0493342i
$873$	−0.0316295	−	0.00476738i	−0.00107050	−	0.000161351i
$874$	91.6696	−	28.2763i	3.10077	−	0.956461i
$875$	0.990726	+	13.2203i	0.0334926	+	0.446928i
$876$	−1.94337	−	2.43690i	−0.0656603	−	0.0823354i
$877$	−12.6609	+	32.2594i	−0.427527	+	1.08932i	0.541134	+	0.840936i	$0.317995\pi$
$877$	−12.6609	+	32.2594i	−0.427527	+	1.08932i	−0.968661	+	0.248385i	$0.920100\pi$
$878$	−8.36788	+	7.76426i	−0.282402	+	0.262031i
$879$	−36.3573	+	24.7880i	−1.22630	+	0.836079i
$880$	−0.622463	+	8.30619i	−0.0209832	+	0.280002i
$881$	11.6579	+	51.0764i	0.392763	+	1.72081i	0.654845	+	0.755763i	$0.272734\pi$
$881$	11.6579	+	51.0764i	0.392763	+	1.72081i	−0.262081	+	0.965046i	$0.584409\pi$
$882$	−0.127832	−	0.560069i	−0.00430433	−	0.0188585i
$883$	−2.16026	+	28.8267i	−0.0726985	+	0.970094i	0.834940	+	0.550341i	$0.185502\pi$
$883$	−2.16026	+	28.8267i	−0.0726985	+	0.970094i	−0.907638	+	0.419753i	$0.862117\pi$
$884$	−0.520879	+	0.355129i	−0.0175190	+	0.0119443i
$885$	−2.26842	+	2.10479i	−0.0762522	+	0.0707517i
$886$	−2.05936	+	5.24715i	−0.0691854	+	0.176282i
$887$	−28.3829	−	35.5910i	−0.953004	−	1.19503i	−0.980721	−	0.195414i	$-0.937395\pi$
$887$	−28.3829	−	35.5910i	−0.953004	−	1.19503i	0.0277167	−	0.999616i	$-0.491176\pi$
$888$	−1.07249	−	14.3114i	−0.0359906	−	0.480261i
$889$	11.2343	−	3.46531i	0.376785	−	0.116223i
$890$	1.76313	+	0.265748i	0.0591001	+	0.00890791i
$891$	27.9691	+	25.9515i	0.936999	+	0.869408i
$892$	−6.79837	+	3.27392i	−0.227626	+	0.109619i
$893$	−32.9830	+	4.97138i	−1.10373	+	0.166361i
$894$	−30.3474	−	20.6905i	−1.01497	−	0.691994i
$895$	1.73726	−	2.17845i	0.0580701	−	0.0728176i
$896$	−22.4159	−	38.8255i	−0.748862	−	1.29707i
$897$	−8.11665	+	14.0584i	−0.271007	+	0.469398i
$898$	2.65750	+	6.77120i	0.0886819	+	0.225958i
$899$	−3.00798	−	1.44856i	−0.100322	−	0.0483123i
$900$	0.265043	+	0.0817551i	0.00883478	+	0.00272517i
$901$	−1.21103	+	5.30587i	−0.0403452	+	0.176764i
$902$	−35.6742			−1.18782
$903$	−37.4221	−	11.7540i	−1.24533	−	0.391148i
$904$	30.4371			1.01232
$905$	1.61227	−	7.06382i	0.0535937	−	0.234809i
$906$	2.79176	+	0.861144i	0.0927501	+	0.0286096i
$907$	−19.7496	−	9.51092i	−0.655775	−	0.315805i	0.0762434	−	0.997089i	$-0.475707\pi$
$907$	−19.7496	−	9.51092i	−0.655775	−	0.315805i	−0.732019	+	0.681284i	$0.761422\pi$
$908$	−2.60859	−	6.64659i	−0.0865693	−	0.220575i
$909$	0.0718375	−	0.124426i	0.00238270	−	0.00412696i
$910$	1.45881	+	2.52673i	0.0483590	+	0.0837602i
$911$	−28.0122	+	35.1262i	−0.928087	+	1.16378i	0.0581272	+	0.998309i	$0.481487\pi$
$911$	−28.0122	+	35.1262i	−0.928087	+	1.16378i	−0.986214	+	0.165475i	$0.947084\pi$
$912$	−53.8399	−	36.7074i	−1.78282	−	1.21550i
$913$	49.9446	−	7.52793i	1.65292	−	0.249138i
$914$	−3.38177	+	1.62857i	−0.111859	+	0.0538684i
$915$	−2.61846	−	2.42957i	−0.0865635	−	0.0803192i
$916$	21.4707	+	3.23619i	0.709413	+	0.106927i
$917$	5.13233	−	1.58311i	0.169484	−	0.0522790i
$918$	−0.374522	−	4.99764i	−0.0123611	−	0.164947i
$919$	−21.8856	−	27.4436i	−0.721938	−	0.905282i	0.276508	−	0.961012i	$-0.410823\pi$
$919$	−21.8856	−	27.4436i	−0.721938	−	0.905282i	−0.998446	+	0.0557299i	$0.982251\pi$
$920$	1.98904	−	5.06800i	0.0655768	−	0.167087i
$921$	19.9042	−	18.4684i	0.655867	−	0.608555i
$922$	−21.3578	+	14.5615i	−0.703383	+	0.479558i
$923$	−0.729090	+	9.72903i	−0.0239983	+	0.320235i
$924$	−5.05736	−	22.1577i	−0.166375	−	0.728936i
$925$	4.74569	+	20.7922i	0.156037	+	0.683644i
$926$	1.36249	−	18.1812i	0.0447743	−	0.597472i
$927$	0.275876	−	0.188089i	0.00906095	−	0.00617765i
$928$	−11.6154	+	10.7775i	−0.381293	+	0.353788i
$929$	3.19040	−	8.12900i	0.104674	−	0.266704i	−0.868936	−	0.494925i	$-0.835196\pi$
$929$	3.19040	−	8.12900i	0.104674	−	0.266704i	0.973609	+	0.228221i	$0.0732908\pi$
$930$	0.682927	+	0.856363i	0.0223941	+	0.0280813i
$931$	−2.96078	−	39.5089i	−0.0970357	−	1.29485i
$932$	7.21988	−	2.22704i	0.236495	−	0.0729491i
$933$	45.7639	+	6.89780i	1.49824	+	0.225824i
$934$	−18.4345	−	17.1047i	−0.603196	−	0.559684i
$935$	−0.847226	+	0.408002i	−0.0277072	+	0.0133431i
$936$	−0.157160	+	0.0236881i	−0.00513693	+	0.000774268i
$937$	−23.8766	−	16.2788i	−0.780015	−	0.531806i	0.106606	−	0.994301i	$-0.466002\pi$
$937$	−23.8766	−	16.2788i	−0.780015	−	0.531806i	−0.886621	+	0.462496i	$0.846954\pi$
$938$	48.4418	−	60.7441i	1.58168	−	1.98337i
$939$	16.5088	+	28.5941i	0.538744	+	0.933132i
$940$	0.738165	−	1.27854i	0.0240763	−	0.0417013i
$941$	−1.16024	−	2.95624i	−0.0378226	−	0.0963705i	0.910714	−	0.413037i	$-0.135532\pi$
$941$	−1.16024	−	2.95624i	−0.0378226	−	0.0963705i	−0.948537	+	0.316666i	$0.897437\pi$
$942$	−12.4689	−	6.00472i	−0.406260	−	0.195644i
$943$	34.3644	+	10.6000i	1.11906	+	0.345184i
$944$	−5.19869	+	22.7770i	−0.169203	+	0.741327i
$945$	−7.06656			−0.229875
$946$	46.0026	+	14.4490i	1.49567	+	0.469779i
$947$	47.5288			1.54448			0.772239	−	0.635332i	$-0.219137\pi$
$947$	47.5288			1.54448			0.772239	+	0.635332i	$0.219137\pi$
$948$	−2.76759	+	12.1256i	−0.0898871	+	0.393821i
$949$	−2.53621	−	0.782316i	−0.0823288	−	0.0253951i
$950$	56.5685	+	27.2420i	1.83532	+	0.883846i
$951$	8.04974	+	20.5104i	0.261031	+	0.665096i
$952$	1.87230	−	3.24293i	0.0606817	−	0.105104i
$953$	−20.3266	−	35.2067i	−0.658443	−	1.14046i	−0.981019	−	0.193913i	$-0.937882\pi$
$953$	−20.3266	−	35.2067i	−0.658443	−	1.14046i	0.322576	−	0.946544i	$-0.395451\pi$
$954$	0.667165	−	0.836599i	0.0216003	−	0.0270859i
$955$	−2.23943	−	1.52681i	−0.0724661	−	0.0494065i
$956$	−2.91693	+	0.439657i	−0.0943403	+	0.0142195i
$957$	22.8402	−	10.9993i	0.738319	−	0.355556i
$958$	−42.6659	−	39.5881i	−1.37847	−	1.27903i
$959$	−11.0047	−	1.65869i	−0.355360	−	0.0535619i
$960$	−1.32228	+	0.407869i	−0.0426764	+	0.0131639i
$961$	−2.24513	−	29.9592i	−0.0724235	−	0.966424i
$962$	5.94232	+	7.45143i	0.191588	+	0.240244i
$963$	0.244902	−	0.624000i	0.00789186	−	0.0201081i
$964$	17.3551	−	16.1032i	0.558972	−	0.518650i
$965$	−1.31091	+	0.893761i	−0.0421996	+	0.0287712i
$966$	−5.61965	+	74.9890i	−0.180809	+	2.41273i
$967$	1.68074	+	7.36380i	0.0540490	+	0.236804i	0.994736	−	0.102472i	$-0.0326751\pi$
$967$	1.68074	+	7.36380i	0.0540490	+	0.236804i	−0.940687	+	0.339276i	$0.889818\pi$
$968$	−3.30695	−	14.4887i	−0.106289	−	0.465684i
$969$	0.549750	−	7.33591i	0.0176605	−	0.235663i
$970$	0.264791	−	0.180531i	0.00850191	−	0.00579650i
$971$	15.3469	−	14.2398i	0.492505	−	0.456978i	−0.394394	−	0.918942i	$-0.629045\pi$
$971$	15.3469	−	14.2398i	0.492505	−	0.456978i	0.886899	+	0.461964i	$0.152855\pi$
$972$	−0.217027	+	0.552975i	−0.00696114	+	0.0177367i
$973$	43.7068	+	54.8066i	1.40118	+	1.75702i
$974$	0.824064	+	10.9964i	0.0264047	+	0.352346i
$975$	−10.1525	+	3.13164i	−0.325141	+	0.100293i
$976$	−26.6665	−	4.01933i	−0.853575	−	0.128656i
$977$	−17.9851	−	16.6877i	−0.575395	−	0.533888i	0.337903	−	0.941181i	$-0.390282\pi$
$977$	−17.9851	−	16.6877i	−0.575395	−	0.533888i	−0.913298	+	0.407293i	$0.866473\pi$
$978$	24.8603	−	11.9721i	0.794946	−	0.382826i
$979$	−11.6951	+	1.76275i	−0.373777	+	0.0563378i
$980$	1.44888	+	0.987828i	0.0462827	+	0.0315550i
$981$	0.0457163	−	0.0573264i	0.00145961	−	0.00183029i
$982$	−6.91046	−	11.9693i	−0.220521	−	0.381954i
$983$	−0.981609	+	1.70020i	−0.0313085	+	0.0542279i	−0.881255	−	0.472641i	$-0.843301\pi$
$983$	−0.981609	+	1.70020i	−0.0313085	+	0.0542279i	0.849947	+	0.526869i	$0.176634\pi$
$984$	−5.78652	−	14.7438i	−0.184468	−	0.470016i
$985$	−0.626440	−	0.301678i	−0.0199600	−	0.00961225i
$986$	−3.11271	−	0.960145i	−0.0991290	−	0.0305772i
$987$	5.81823	−	25.4913i	0.185196	−	0.811397i
$988$	8.54856			0.271966
$989$	−40.0203	−	27.5875i	−1.27257	−	0.877230i
$990$	0.184888			0.00587614
$991$	−3.67174	+	16.0869i	−0.116637	+	0.511019i	0.882532	+	0.470252i	$0.155837\pi$
$991$	−3.67174	+	16.0869i	−0.116637	+	0.511019i	−0.999169	+	0.0407664i	$0.987020\pi$
$992$	4.33947	+	1.33855i	0.137778	+	0.0424990i
$993$	−3.92773	−	1.89149i	−0.124643	−	0.0600247i
$994$	16.5117	+	42.0710i	0.523718	+	1.33441i
$995$	4.38741	−	7.59922i	0.139090	−	0.240912i
$996$	−8.74445	−	15.1458i	−0.277078	−	0.479914i
$997$	−20.7198	+	25.9819i	−0.656204	+	0.822854i	−0.992924	−	0.118751i	$-0.962111\pi$
$997$	−20.7198	+	25.9819i	−0.656204	+	0.822854i	0.336720	+	0.941605i	$0.390682\pi$
$998$	−11.0607	−	7.54104i	−0.350120	−	0.238708i
$999$	−22.8259	+	3.44046i	−0.722181	+	0.108851i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.g.a.38.3	yes	36
3.2	odd	2		387.2.y.c.253.1		36
4.3	odd	2		688.2.bg.c.81.3		36
43.17	even	21	inner	43.2.g.a.17.3	✓	36
43.19	odd	42		1849.2.a.o.1.13		18
43.24	even	21		1849.2.a.n.1.6		18
129.17	odd	42		387.2.y.c.361.1		36
172.103	odd	42		688.2.bg.c.17.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.17.3	✓	36	43.17	even	21	inner
43.2.g.a.38.3	yes	36	1.1	even	1	trivial
387.2.y.c.253.1		36	3.2	odd	2
387.2.y.c.361.1		36	129.17	odd	42
688.2.bg.c.17.3		36	172.103	odd	42
688.2.bg.c.81.3		36	4.3	odd	2
1849.2.a.n.1.6		18	43.24	even	21
1849.2.a.o.1.13		18	43.19	odd	42

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.377390 - 1.65345i) q^{2} +(-1.63701 - 0.504949i) q^{3} +(-0.789549 - 0.380227i) q^{4} +(0.140805 + 0.358765i) q^{5} +(-1.45270 + 2.51615i) q^{6} +(1.74586 + 3.02391i) q^{7} +(1.18819 - 1.48995i) q^{8} +(-0.0539035 - 0.0367508i) q^{9} +O(q^{10})\)	\(q+(0.377390 - 1.65345i) q^{2} +(-1.63701 - 0.504949i) q^{3} +(-0.789549 - 0.380227i) q^{4} +(0.140805 + 0.358765i) q^{5} +(-1.45270 + 2.51615i) q^{6} +(1.74586 + 3.02391i) q^{7} +(1.18819 - 1.48995i) q^{8} +(-0.0539035 - 0.0367508i) q^{9} +(0.646339 - 0.0974200i) q^{10} +(-3.90633 + 1.88119i) q^{11} +(1.10050 + 1.02111i) q^{12} +(1.26408 + 0.190529i) q^{13} +(5.65876 - 1.74550i) q^{14} +(-0.0493402 - 0.658399i) q^{15} +(-3.10791 - 3.89720i) q^{16} +(0.205594 - 0.523844i) q^{17} +(-0.0811084 + 0.0752576i) q^{18} +(-6.30490 + 4.29861i) q^{19} +(0.0252397 - 0.336800i) q^{20} +(-1.33105 - 5.83172i) q^{21} +(1.63625 + 7.16888i) q^{22} +(0.553943 - 7.39185i) q^{23} +(-2.69742 + 1.83907i) q^{24} +(3.55637 - 3.29983i) q^{25} +(0.792080 - 2.01819i) q^{26} +(3.27401 + 4.10548i) q^{27} +(-0.228667 - 3.05134i) q^{28} +(3.26143 - 1.00602i) q^{29} +(-1.10725 - 0.166892i) q^{30} +(-0.717059 - 0.665333i) q^{31} +(-4.18276 + 2.01431i) q^{32} +(7.34459 - 1.10702i) q^{33} +(-0.788563 - 0.537633i) q^{34} +(-0.839048 + 1.05213i) q^{35} +(0.0285858 + 0.0495121i) q^{36} +(-2.19799 + 3.80703i) q^{37} +(4.72814 + 12.0471i) q^{38} +(-1.97309 - 0.950190i) q^{39} +(0.701843 + 0.216490i) q^{40} +(-1.07956 + 4.72986i) q^{41} -10.1448 q^{42} +(3.30784 - 5.66200i) q^{43} +3.79952 q^{44} +(0.00559502 - 0.0245134i) q^{45} +(-12.0130 - 3.70553i) q^{46} +(3.93826 + 1.89657i) q^{47} +(3.11978 + 7.94908i) q^{48} +(-2.59602 + 4.49644i) q^{49} +(-4.11398 - 7.12562i) q^{50} +(-0.601072 + 0.753721i) q^{51} +(-0.925605 - 0.631067i) q^{52} +(-9.56301 + 1.44139i) q^{53} +(8.02380 - 3.86406i) q^{54} +(-1.22493 - 1.13657i) q^{55} +(6.57987 + 0.991756i) q^{56} +(12.4917 - 3.85319i) q^{57} +(-0.432573 - 5.77229i) q^{58} +(-2.92222 - 3.66435i) q^{59} +(-0.211384 + 0.538598i) q^{60} +(3.96588 - 3.67980i) q^{61} +(-1.37071 + 0.934533i) q^{62} +(0.0170234 - 0.227161i) q^{63} +(-0.466364 - 2.04327i) q^{64} +(0.109633 + 0.480333i) q^{65} +(0.941371 - 12.5617i) q^{66} +(10.8402 - 7.39075i) q^{67} +(-0.361505 + 0.335428i) q^{68} +(-4.63932 + 11.8208i) q^{69} +(1.42300 + 1.78439i) q^{70} +(0.570335 + 7.61059i) q^{71} +(-0.118804 + 0.0366463i) q^{72} +(-2.05301 - 0.309442i) q^{73} +(5.46525 + 5.07101i) q^{74} +(-7.48805 + 3.60605i) q^{75} +(6.61247 - 0.996670i) q^{76} +(-12.5084 - 8.52811i) q^{77} +(-2.31572 + 2.90382i) q^{78} +(4.14234 + 7.17474i) q^{79} +(0.960569 - 1.66375i) q^{80} +(-3.21501 - 8.19171i) q^{81} +(7.41318 + 3.57000i) q^{82} +(-11.1319 - 3.43375i) q^{83} +(-1.16645 + 5.11053i) q^{84} +0.216885 q^{85} +(-8.11351 - 7.60614i) q^{86} -5.84697 q^{87} +(-1.83860 + 8.05544i) q^{88} +(2.60667 + 0.804052i) q^{89} +(-0.0384202 - 0.0185022i) q^{90} +(1.63075 + 4.15509i) q^{91} +(-3.24794 + 5.62560i) q^{92} +(0.837869 + 1.45123i) q^{93} +(4.62215 - 5.79599i) q^{94} +(-2.42995 - 1.65671i) q^{95} +(7.86433 - 1.18536i) q^{96} +(0.441741 - 0.212731i) q^{97} +(6.45494 + 5.98931i) q^{98} +(0.279700 + 0.0421580i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more