LMFDB - Embedded newform 731.2.u.b.52.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(52,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(42))

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

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

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

chi := DirichletCharacter("731.52");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.u (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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			52.14
Character	$\chi$	$=$	731.52
Dual form			731.2.u.b.239.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.251421 - 0.315272i) q^{2} +(1.17665 + 0.177352i) q^{3} +(0.408858 - 1.79132i) q^{4} +(-1.00912 - 0.688006i) q^{5} +(-0.239921 - 0.415555i) q^{6} +(1.75229 - 3.03505i) q^{7} +(-1.39418 + 0.671401i) q^{8} +(-1.51366 - 0.466903i) q^{9} +O(q^{10})$	\(q+(-0.251421 - 0.315272i) q^{2} +(1.17665 + 0.177352i) q^{3} +(0.408858 - 1.79132i) q^{4} +(-1.00912 - 0.688006i) q^{5} +(-0.239921 - 0.415555i) q^{6} +(1.75229 - 3.03505i) q^{7} +(-1.39418 + 0.671401i) q^{8} +(-1.51366 - 0.466903i) q^{9} +(0.0368048 + 0.491126i) q^{10} +(0.676310 + 2.96311i) q^{11} +(0.798778 - 2.03525i) q^{12} +(0.232626 - 3.10418i) q^{13} +(-1.39743 + 0.210628i) q^{14} +(-1.06536 - 0.988513i) q^{15} +(-2.74866 - 1.32369i) q^{16} +(-0.826239 + 0.563320i) q^{17} +(0.233365 + 0.594604i) q^{18} +(3.74305 - 1.15458i) q^{19} +(-1.64503 + 1.52636i) q^{20} +(2.60010 - 3.26043i) q^{21} +(0.764146 - 0.958209i) q^{22} +(-1.37468 + 1.27552i) q^{23} +(-1.75954 + 0.542745i) q^{24} +(-1.28174 - 3.26581i) q^{25} +(-1.03715 + 0.707116i) q^{26} +(-4.91455 - 2.36672i) q^{27} +(-4.72032 - 4.37982i) q^{28} +(-1.85533 + 0.279646i) q^{29} +(-0.0437956 + 0.584412i) q^{30} +(-0.217930 + 0.555277i) q^{31} +(0.962418 + 4.21663i) q^{32} +(0.270269 + 3.60649i) q^{33} +(0.385333 + 0.118859i) q^{34} +(-3.85640 + 1.85714i) q^{35} +(-1.45525 + 2.52056i) q^{36} +(4.35949 + 7.55086i) q^{37} +(-1.30509 - 0.889795i) q^{38} +(0.824252 - 3.61128i) q^{39} +(1.86882 + 0.281679i) q^{40} +(-5.79884 - 7.27151i) q^{41} -1.68164 q^{42} +(6.54632 - 0.381747i) q^{43} +5.58440 q^{44} +(1.20623 + 1.51257i) q^{45} +(0.747757 + 0.112706i) q^{46} +(-0.241622 + 1.05861i) q^{47} +(-2.99946 - 2.04500i) q^{48} +(-2.64101 - 4.57437i) q^{49} +(-0.707363 + 1.22519i) q^{50} +(-1.07210 + 0.516297i) q^{51} +(-5.46548 - 1.68588i) q^{52} +(-0.528914 - 7.05787i) q^{53} +(0.489460 + 2.14446i) q^{54} +(1.35616 - 3.45543i) q^{55} +(-0.405265 + 5.40788i) q^{56} +(4.60904 - 0.694701i) q^{57} +(0.554633 + 0.514625i) q^{58} +(0.257201 + 0.123862i) q^{59} +(-2.20633 + 1.50425i) q^{60} +(-2.60649 - 6.64122i) q^{61} +(0.229856 - 0.0709011i) q^{62} +(-4.06944 + 3.77589i) q^{63} +(-2.71686 + 3.40683i) q^{64} +(-2.37044 + 2.97244i) q^{65} +(1.06907 - 0.991956i) q^{66} +(8.46930 - 2.61243i) q^{67} +(0.671274 + 1.71038i) q^{68} +(-1.84373 + 1.25704i) q^{69} +(1.55508 + 0.748889i) q^{70} +(10.0834 + 9.35605i) q^{71} +(2.42379 - 0.365328i) q^{72} +(0.619698 - 8.26930i) q^{73} +(1.28451 - 3.27287i) q^{74} +(-0.928960 - 4.07004i) q^{75} +(-0.537848 - 7.17708i) q^{76} +(10.1783 + 3.13958i) q^{77} +(-1.34577 + 0.648089i) q^{78} +(-3.16831 + 5.48767i) q^{79} +(1.86303 + 3.22686i) q^{80} +(-1.43660 - 0.979457i) q^{81} +(-0.834554 + 3.65642i) q^{82} +(13.8043 + 2.08066i) q^{83} +(-4.77741 - 5.99068i) q^{84} +1.22134 q^{85} +(-1.76624 - 1.96789i) q^{86} -2.23267 q^{87} +(-2.93233 - 3.67702i) q^{88} +(14.0126 + 2.11206i) q^{89} +(0.173598 - 0.760583i) q^{90} +(-9.01371 - 6.14545i) q^{91} +(1.72281 + 2.98400i) q^{92} +(-0.354907 + 0.614718i) q^{93} +(0.394500 - 0.189981i) q^{94} +(-4.57155 - 1.41014i) q^{95} +(0.384604 + 5.13219i) q^{96} +(0.873965 + 3.82909i) q^{97} +(-0.778165 + 1.98273i) q^{98} +(0.359779 - 4.80091i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 6 q^{2} - 3 q^{3} - 54 q^{4} + q^{5} - 12 q^{6} + 49 q^{7} - 2 q^{8} + 8 q^{9}+O(q^{10}) $ 348 * q + 6 * q^2 - 3 * q^3 - 54 * q^4 + q^5 - 12 * q^6 + 49 * q^7 - 2 * q^8 + 8 * q^9	\( 348 q + 6 q^{2} - 3 q^{3} - 54 q^{4} + q^{5} - 12 q^{6} + 49 q^{7} - 2 q^{8} + 8 q^{9} - 4 q^{10} - 16 q^{11} - 12 q^{12} - 9 q^{13} - 3 q^{14} - 14 q^{15} - 30 q^{16} - 29 q^{17} - 204 q^{18} - 8 q^{19} + 61 q^{20} + 26 q^{21} + 85 q^{22} - 79 q^{23} - 12 q^{24} + 22 q^{25} - 14 q^{26} + 12 q^{27} - 15 q^{28} + 54 q^{29} - 46 q^{30} - 52 q^{31} + 33 q^{32} + 39 q^{33} + 3 q^{34} + 32 q^{35} - 161 q^{36} + 68 q^{37} - 29 q^{38} + 61 q^{39} + 107 q^{40} + 63 q^{41} - 56 q^{42} - 45 q^{43} - 74 q^{44} + 144 q^{45} - 22 q^{46} - 70 q^{47} + 168 q^{48} - 119 q^{49} + 97 q^{50} - 6 q^{51} + 27 q^{52} + 10 q^{53} - 34 q^{54} - 78 q^{55} - 44 q^{56} - 40 q^{57} - 38 q^{58} - 47 q^{59} - 72 q^{60} - 76 q^{61} - 41 q^{62} + 63 q^{63} - 112 q^{64} - 31 q^{65} - 598 q^{66} - 39 q^{67} - 20 q^{68} - 17 q^{69} - 72 q^{70} - 37 q^{71} + 245 q^{72} + 14 q^{73} + 77 q^{74} - 121 q^{75} + 152 q^{76} + 59 q^{77} + 220 q^{78} + 4 q^{79} - 42 q^{80} - 109 q^{81} + 148 q^{82} + 59 q^{83} + 390 q^{84} + 2 q^{85} + 12 q^{86} - 78 q^{87} + 344 q^{88} - 103 q^{89} - 75 q^{90} + 148 q^{91} + 28 q^{92} + 140 q^{93} + 24 q^{94} - 302 q^{95} + 22 q^{96} + 57 q^{97} - 72 q^{98} - 128 q^{99}+O(q^{100}) \) 348 * q + 6 * q^2 - 3 * q^3 - 54 * q^4 + q^5 - 12 * q^6 + 49 * q^7 - 2 * q^8 + 8 * q^9 - 4 * q^10 - 16 * q^11 - 12 * q^12 - 9 * q^13 - 3 * q^14 - 14 * q^15 - 30 * q^16 - 29 * q^17 - 204 * q^18 - 8 * q^19 + 61 * q^20 + 26 * q^21 + 85 * q^22 - 79 * q^23 - 12 * q^24 + 22 * q^25 - 14 * q^26 + 12 * q^27 - 15 * q^28 + 54 * q^29 - 46 * q^30 - 52 * q^31 + 33 * q^32 + 39 * q^33 + 3 * q^34 + 32 * q^35 - 161 * q^36 + 68 * q^37 - 29 * q^38 + 61 * q^39 + 107 * q^40 + 63 * q^41 - 56 * q^42 - 45 * q^43 - 74 * q^44 + 144 * q^45 - 22 * q^46 - 70 * q^47 + 168 * q^48 - 119 * q^49 + 97 * q^50 - 6 * q^51 + 27 * q^52 + 10 * q^53 - 34 * q^54 - 78 * q^55 - 44 * q^56 - 40 * q^57 - 38 * q^58 - 47 * q^59 - 72 * q^60 - 76 * q^61 - 41 * q^62 + 63 * q^63 - 112 * q^64 - 31 * q^65 - 598 * q^66 - 39 * q^67 - 20 * q^68 - 17 * q^69 - 72 * q^70 - 37 * q^71 + 245 * q^72 + 14 * q^73 + 77 * q^74 - 121 * q^75 + 152 * q^76 + 59 * q^77 + 220 * q^78 + 4 * q^79 - 42 * q^80 - 109 * q^81 + 148 * q^82 + 59 * q^83 + 390 * q^84 + 2 * q^85 + 12 * q^86 - 78 * q^87 + 344 * q^88 - 103 * q^89 - 75 * q^90 + 148 * q^91 + 28 * q^92 + 140 * q^93 + 24 * q^94 - 302 * q^95 + 22 * q^96 + 57 * q^97 - 72 * q^98 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{1}{21}\right)$

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 $

$2$	−0.251421	−	0.315272i	−0.177782	−	0.222931i	0.684954	−	0.728586i	$-0.259822\pi$
$2$	−0.251421	−	0.315272i	−0.177782	−	0.222931i	−0.862736	+	0.505655i	$0.831251\pi$
$3$	1.17665	+	0.177352i	0.679340	+	0.102394i	0.479643	−	0.877464i	$-0.340766\pi$
$3$	1.17665	+	0.177352i	0.679340	+	0.102394i	0.199697	+	0.979858i	$0.436004\pi$
$4$	0.408858	−	1.79132i	0.204429	−	0.895662i
$5$	−1.00912	−	0.688006i	−0.451292	−	0.307686i	0.316260	−	0.948673i	$-0.397573\pi$
$5$	−1.00912	−	0.688006i	−0.451292	−	0.307686i	−0.767552	+	0.640987i	$0.778525\pi$
$6$	−0.239921	−	0.415555i	−0.0979474	−	0.169650i
$7$	1.75229	−	3.03505i	0.662302	−	1.14714i	−0.317707	−	0.948189i	$-0.602913\pi$
$7$	1.75229	−	3.03505i	0.662302	−	1.14714i	0.980009	−	0.198952i	$-0.0637537\pi$
$8$	−1.39418	+	0.671401i	−0.492916	+	0.237376i
$9$	−1.51366	−	0.466903i	−0.504554	−	0.155634i
$10$	0.0368048	+	0.491126i	0.0116387	+	0.155308i
$11$	0.676310	+	2.96311i	0.203915	+	0.893410i	0.968525	+	0.248917i	$0.0800746\pi$
$11$	0.676310	+	2.96311i	0.203915	+	0.893410i	−0.764610	+	0.644493i	$0.777068\pi$
$12$	0.798778	−	2.03525i	0.230587	−	0.587527i
$13$	0.232626	−	3.10418i	0.0645189	−	0.860945i	−0.867245	−	0.497881i	$-0.834112\pi$
$13$	0.232626	−	3.10418i	0.0645189	−	0.860945i	0.931764	−	0.363064i	$-0.118269\pi$
$14$	−1.39743	+	0.210628i	−0.373478	+	0.0562928i
$15$	−1.06536	−	0.988513i	−0.275076	−	0.255233i
$16$	−2.74866	−	1.32369i	−0.687166	−	0.330922i
$17$	−0.826239	+	0.563320i	−0.200392	+	0.136625i
$17$	−0.826239	+	0.563320i	−0.200392	+	0.136625i
$18$	0.233365	+	0.594604i	0.0550047	+	0.140150i
$19$	3.74305	−	1.15458i	0.858716	−	0.264879i	0.166032	−	0.986120i	$-0.446904\pi$
$19$	3.74305	−	1.15458i	0.858716	−	0.264879i	0.692684	+	0.721242i	$0.256428\pi$
$20$	−1.64503	+	1.52636i	−0.367839	+	0.341305i
$21$	2.60010	−	3.26043i	0.567389	−	0.711483i
$22$	0.764146	−	0.958209i	0.162917	−	0.204291i
$23$	−1.37468	+	1.27552i	−0.286640	+	0.265963i	−0.810366	−	0.585923i	$-0.800732\pi$
$23$	−1.37468	+	1.27552i	−0.286640	+	0.265963i	0.523726	+	0.851887i	$0.324541\pi$
$24$	−1.75954	+	0.542745i	−0.359164	+	0.110787i
$25$	−1.28174	−	3.26581i	−0.256347	−	0.653162i
$26$	−1.03715	+	0.707116i	−0.203402	+	0.138677i
$27$	−4.91455	−	2.36672i	−0.945806	−	0.455476i
$28$	−4.72032	−	4.37982i	−0.892056	−	0.827707i
$29$	−1.85533	+	0.279646i	−0.344526	+	0.0519289i	−0.319026	−	0.947746i	$-0.603356\pi$
$29$	−1.85533	+	0.279646i	−0.344526	+	0.0519289i	−0.0254998	+	0.999675i	$0.508118\pi$
$30$	−0.0437956	+	0.584412i	−0.00799595	+	0.106699i
$31$	−0.217930	+	0.555277i	−0.0391414	+	0.0997307i	−0.949108	−	0.314951i	$-0.898012\pi$
$31$	−0.217930	+	0.555277i	−0.0391414	+	0.0997307i	0.909966	+	0.414682i	$0.136107\pi$
$32$	0.962418	+	4.21663i	0.170133	+	0.745401i
$33$	0.270269	+	3.60649i	0.0470478	+	0.627809i
$34$	0.385333	+	0.118859i	0.0660840	+	0.0203842i
$35$	−3.85640	+	1.85714i	−0.651850	+	0.313914i
$36$	−1.45525	+	2.52056i	−0.242541	+	0.420094i
$37$	4.35949	+	7.55086i	0.716696	+	1.24135i	0.962302	+	0.271984i	$0.0876798\pi$
$37$	4.35949	+	7.55086i	0.716696	+	1.24135i	−0.245606	+	0.969370i	$0.578987\pi$
$38$	−1.30509	−	0.889795i	−0.211713	−	0.144344i
$39$	0.824252	−	3.61128i	0.131986	−	0.578268i
$40$	1.86882	+	0.281679i	0.295486	+	0.0445374i
$41$	−5.79884	−	7.27151i	−0.905626	−	1.13562i	−0.990263	−	0.139207i	$-0.955545\pi$
$41$	−5.79884	−	7.27151i	−0.905626	−	1.13562i	0.0846372	−	0.996412i	$-0.473027\pi$
$42$	−1.68164			−0.259483
$43$	6.54632	−	0.381747i	0.998304	−	0.0582159i
$43$	6.54632	−	0.381747i	0.998304	−	0.0582159i
$44$	5.58440			0.841880
$45$	1.20623	+	1.51257i	0.179815	+	0.225480i
$46$	0.747757	+	0.112706i	0.110251	+	0.0166176i
$47$	−0.241622	+	1.05861i	−0.0352441	+	0.154415i	−0.989488	−	0.144615i	$-0.953806\pi$
$47$	−0.241622	+	1.05861i	−0.0352441	+	0.154415i	0.954244	+	0.299029i	$0.0966629\pi$
$48$	−2.99946	−	2.04500i	−0.432935	−	0.295170i
$49$	−2.64101	−	4.57437i	−0.377288	−	0.653482i
$50$	−0.707363	+	1.22519i	−0.100036	+	0.173268i
$51$	−1.07210	+	0.516297i	−0.150124	+	0.0722960i
$52$	−5.46548	−	1.68588i	−0.757926	−	0.233789i
$53$	−0.528914	−	7.05787i	−0.0726520	−	0.969473i	−0.907788	−	0.419429i	$-0.862230\pi$
$53$	−0.528914	−	7.05787i	−0.0726520	−	0.969473i	0.835136	−	0.550044i	$-0.185389\pi$
$54$	0.489460	+	2.14446i	0.0666071	+	0.291825i
$55$	1.35616	−	3.45543i	0.182864	−	0.465930i
$56$	−0.405265	+	5.40788i	−0.0541558	+	0.722659i
$57$	4.60904	−	0.694701i	0.610482	−	0.0920154i
$58$	0.554633	+	0.514625i	0.0728269	+	0.0675735i
$59$	0.257201	+	0.123862i	0.0334848	+	0.0161254i	0.450551	−	0.892751i	$-0.351227\pi$
$59$	0.257201	+	0.123862i	0.0334848	+	0.0161254i	−0.417066	+	0.908876i	$0.636942\pi$
$60$	−2.20633	+	1.50425i	−0.284836	+	0.194198i
$61$	−2.60649	−	6.64122i	−0.333726	−	0.850321i	−0.994972	−	0.100152i	$-0.968067\pi$
$61$	−2.60649	−	6.64122i	−0.333726	−	0.850321i	0.661246	−	0.750169i	$-0.270028\pi$
$62$	0.229856	−	0.0709011i	0.0291917	−	0.00900444i
$63$	−4.06944	+	3.77589i	−0.512701	+	0.475717i
$64$	−2.71686	+	3.40683i	−0.339607	+	0.425854i
$65$	−2.37044	+	2.97244i	−0.294017	+	0.368686i
$66$	1.06907	−	0.991956i	0.131594	−	0.122101i
$67$	8.46930	−	2.61243i	1.03469	−	0.319159i	0.269524	−	0.962994i	$-0.413133\pi$
$67$	8.46930	−	2.61243i	1.03469	−	0.319159i	0.765165	+	0.643834i	$0.222657\pi$
$68$	0.671274	+	1.71038i	0.0814040	+	0.207414i
$69$	−1.84373	+	1.25704i	−0.221959	+	0.151329i
$70$	1.55508	+	0.748889i	0.185868	+	0.0895094i
$71$	10.0834	+	9.35605i	1.19668	+	1.11036i	0.991292	+	0.131679i	$0.0420368\pi$
$71$	10.0834	+	9.35605i	1.19668	+	1.11036i	0.205390	+	0.978680i	$0.434154\pi$
$72$	2.42379	−	0.365328i	0.285647	−	0.0430543i
$73$	0.619698	−	8.26930i	0.0725302	−	0.967848i	−0.835648	−	0.549265i	$-0.814908\pi$
$73$	0.619698	−	8.26930i	0.0725302	−	0.967848i	0.908178	−	0.418583i	$-0.137473\pi$
$74$	1.28451	−	3.27287i	0.149321	−	0.380464i
$75$	−0.928960	−	4.07004i	−0.107267	−	0.469968i
$76$	−0.537848	−	7.17708i	−0.0616954	−	0.823268i
$77$	10.1783	+	3.13958i	1.15992	+	0.357788i
$78$	−1.34577	+	0.648089i	−0.152379	+	0.0733817i
$79$	−3.16831	+	5.48767i	−0.356463	+	0.617411i	−0.987367	−	0.158449i	$-0.949351\pi$
$79$	−3.16831	+	5.48767i	−0.356463	+	0.617411i	0.630904	+	0.775861i	$0.282684\pi$
$80$	1.86303	+	3.22686i	0.208293	+	0.360773i
$81$	−1.43660	−	0.979457i	−0.159622	−	0.108829i
$82$	−0.834554	+	3.65642i	−0.0921611	+	0.403784i
$83$	13.8043	+	2.08066i	1.51522	+	0.228382i	0.853389	−	0.521274i	$-0.174543\pi$
$83$	13.8043	+	2.08066i	1.51522	+	0.228382i	0.661827	+	0.749656i	$0.269781\pi$
$84$	−4.77741	−	5.99068i	−0.521258	−	0.653636i
$85$	1.22134			0.132473
$86$	−1.76624	−	1.96789i	−0.190458	−	0.212203i
$87$	−2.23267			−0.239368
$88$	−2.93233	−	3.67702i	−0.312587	−	0.391972i
$89$	14.0126	+	2.11206i	1.48533	+	0.223877i	0.841069	−	0.540928i	$-0.181927\pi$
$89$	14.0126	+	2.11206i	1.48533	+	0.223877i	0.644261	+	0.764806i	$0.277165\pi$
$90$	0.173598	−	0.760583i	0.0182989	−	0.0801725i
$91$	−9.01371	−	6.14545i	−0.944894	−	0.644218i
$92$	1.72281	+	2.98400i	0.179616	+	0.311103i
$93$	−0.354907	+	0.614718i	−0.0368022	+	0.0637433i
$94$	0.394500	−	0.189981i	0.0406896	−	0.0195951i
$95$	−4.57155	−	1.41014i	−0.469031	−	0.144677i
$96$	0.384604	+	5.13219i	0.0392535	+	0.523802i
$97$	0.873965	+	3.82909i	0.0887377	+	0.388785i	0.999720	−	0.0236601i	$-0.00753194\pi$
$97$	0.873965	+	3.82909i	0.0887377	+	0.388785i	−0.910982	+	0.412445i	$0.864675\pi$
$98$	−0.778165	+	1.98273i	−0.0786065	+	0.200286i
$99$	0.359779	−	4.80091i	0.0361591	−	0.482510i
$100$	−6.37417	+	0.960751i	−0.637417	+	0.0960751i
$101$	−12.0012	−	11.1355i	−1.19417	−	1.10802i	−0.991679	−	0.128739i	$-0.958907\pi$
$101$	−12.0012	−	11.1355i	−1.19417	−	1.10802i	−0.202487	−	0.979285i	$-0.564902\pi$
$102$	0.432323	+	0.208196i	0.0428063	+	0.0206144i
$103$	−3.81475	+	2.60085i	−0.375879	+	0.256270i	−0.736493	−	0.676445i	$-0.763519\pi$
$103$	−3.81475	+	2.60085i	−0.375879	+	0.256270i	0.360614	+	0.932715i	$0.382567\pi$
$104$	1.75983	+	4.48396i	0.172565	+	0.439689i
$105$	−4.86701	+	1.50127i	−0.474971	+	0.146509i
$106$	−2.09217	+	1.94125i	−0.203209	+	0.188551i
$107$	5.49827	−	6.89461i	0.531538	−	0.666527i	−0.441476	−	0.897273i	$-0.645545\pi$
$107$	5.49827	−	6.89461i	0.531538	−	0.666527i	0.973014	+	0.230746i	$0.0741165\pi$
$108$	−6.24892	+	7.83590i	−0.601303	+	0.754010i
$109$	8.21371	−	7.62121i	0.786731	−	0.729980i	−0.180583	−	0.983560i	$-0.557799\pi$
$109$	8.21371	−	7.62121i	0.786731	−	0.729980i	0.967314	+	0.253580i	$0.0816081\pi$
$110$	−1.43037	+	0.441210i	−0.136380	+	0.0420677i
$111$	3.79045	+	9.65790i	0.359773	+	0.916687i
$112$	−8.83390	+	6.02285i	−0.834725	+	0.569106i
$113$	−12.9861	−	6.25380i	−1.22163	−	0.588308i	−0.291868	−	0.956459i	$-0.594277\pi$
$113$	−12.9861	−	6.25380i	−1.22163	−	0.588308i	−0.929766	+	0.368151i	$0.879991\pi$
$114$	−1.37783	−	1.27844i	−0.129046	−	0.119737i
$115$	2.26478	−	0.341360i	0.211192	−	0.0318320i
$116$	−0.257630	+	3.43783i	−0.0239203	+	0.319195i
$117$	−1.80147	+	4.59007i	−0.166546	+	0.424352i
$118$	−0.0256157	−	0.112230i	−0.00235812	−	0.0103316i
$119$	0.261897	+	3.49477i	0.0240081	+	0.320365i
$120$	2.14899	+	0.662877i	0.196175	+	0.0605121i
$121$	1.58805	−	0.764765i	0.144368	−	0.0695241i
$122$	−1.43847	+	2.49149i	−0.130233	+	0.225569i
$123$	−5.53360	−	9.58447i	−0.498948	−	0.864203i
$124$	0.905579	+	0.617413i	0.0813234	+	0.0554453i
$125$	−2.31234	+	10.1310i	−0.206822	+	0.906147i
$126$	2.21358	+	0.333643i	0.197201	+	0.0297233i
$127$	5.26021	+	6.59610i	0.466769	+	0.585309i	0.958377	−	0.285507i	$-0.0921621\pi$
$127$	5.26021	+	6.59610i	0.466769	+	0.585309i	−0.491608	+	0.870817i	$0.663591\pi$
$128$	10.4073			0.919883
$129$	7.77044	+	0.711817i	0.684149	+	0.0626720i
$130$	1.53311			0.134462
$131$	−0.0142210	−	0.0178326i	−0.00124250	−	0.00155804i	0.781210	−	0.624269i	$-0.214603\pi$
$131$	−0.0142210	−	0.0178326i	−0.00124250	−	0.00155804i	−0.782452	+	0.622710i	$0.786031\pi$
$132$	6.57089	+	0.990403i	0.571923	+	0.0862035i
$133$	3.05470	−	13.3835i	0.264876	−	1.16050i
$134$	−2.95299	−	2.01331i	−0.255099	−	0.173924i
$135$	3.33105	+	5.76955i	0.286691	+	0.496563i
$136$	0.773710	−	1.34011i	0.0663451	−	0.114913i
$137$	0.616395	−	0.296840i	0.0526622	−	0.0253608i	−0.407367	−	0.913264i	$-0.633553\pi$
$137$	0.616395	−	0.296840i	0.0526622	−	0.0253608i	0.460030	+	0.887904i	$0.347839\pi$
$138$	0.859862	+	0.265232i	0.0731963	+	0.0225781i
$139$	1.17142	+	15.6315i	0.0993586	+	1.32585i	0.794627	+	0.607098i	$0.207667\pi$
$139$	1.17142	+	15.6315i	0.0993586	+	1.32585i	−0.695268	+	0.718750i	$0.744714\pi$
$140$	1.75003	+	7.66736i	0.147904	+	0.648011i
$141$	−0.472052	+	1.20277i	−0.0397539	+	0.101291i
$142$	0.414516	−	5.53133i	0.0347854	−	0.464179i
$143$	9.35535	−	1.41009i	0.782333	−	0.117918i
$144$	3.54252	+	3.28697i	0.295210	+	0.273915i
$145$	2.06465	+	0.994281i	0.171460	+	0.0825706i
$146$	−2.76288	+	1.88370i	−0.228658	+	0.155896i
$147$	−2.29628	−	5.85083i	−0.189394	−	0.482569i
$148$	15.3084	−	4.72203i	1.25835	−	0.388149i
$149$	0.598305	−	0.555146i	0.0490151	−	0.0454793i	−0.655285	−	0.755382i	$-0.727451\pi$
$149$	0.598305	−	0.555146i	0.0490151	−	0.0454793i	0.704300	+	0.709902i	$0.251261\pi$
$150$	−1.04961	+	1.31617i	−0.0857002	+	0.107465i
$151$	−10.4914	+	13.1558i	−0.853777	+	1.07060i	0.142947	+	0.989730i	$0.454342\pi$
$151$	−10.4914	+	13.1558i	−0.853777	+	1.07060i	−0.996724	+	0.0808727i	$0.974229\pi$
$152$	−4.44330	+	4.12278i	−0.360399	+	0.334401i
$153$	1.51366	−	0.466903i	0.122372	−	0.0377469i
$154$	−1.56921	−	3.99828i	−0.126450	−	0.322190i
$155$	0.601952	−	0.410404i	0.0483499	−	0.0329644i
$156$	−6.13198	−	2.95300i	−0.490951	−	0.236430i
$157$	15.2246	+	14.1263i	1.21505	+	1.12740i	0.988151	+	0.153487i	$0.0490502\pi$
$157$	15.2246	+	14.1263i	1.21505	+	1.12740i	0.226902	+	0.973918i	$0.427140\pi$
$158$	2.52669	−	0.380837i	0.201013	−	0.0302978i
$159$	0.629378	−	8.39846i	0.0499129	−	0.666041i
$160$	1.92987	−	4.91723i	0.152570	−	0.388741i
$161$	1.46242	+	6.40728i	0.115255	+	0.504965i
$162$	0.0523960	+	0.699175i	0.00411662	+	0.0549324i
$163$	−11.1371	−	3.43533i	−0.872321	−	0.269076i	−0.173901	−	0.984763i	$-0.555637\pi$
$163$	−11.1371	−	3.43533i	−0.872321	−	0.269076i	−0.698421	+	0.715688i	$0.746113\pi$
$164$	−15.3965	+	7.41458i	−1.20227	+	0.578981i
$165$	2.20855	−	3.82533i	0.171936	−	0.297801i
$166$	−2.81471	−	4.87522i	−0.218464	−	0.378391i
$167$	7.32507	+	4.99415i	0.566831	+	0.386459i	0.812558	−	0.582880i	$-0.198074\pi$
$167$	7.32507	+	4.99415i	0.566831	+	0.386459i	−0.245727	+	0.969339i	$0.579027\pi$
$168$	−1.43595	+	6.29132i	−0.110786	+	0.485386i
$169$	3.27298	+	0.493322i	0.251768	+	0.0379479i
$170$	−0.307071	−	0.385055i	−0.0235513	−	0.0295323i
$171$	−6.20480			−0.474493
$172$	1.99268	−	11.8827i	0.151941	−	0.906044i
$173$	7.21482			0.548533			0.274266	−	0.961654i	$-0.411565\pi$
$173$	7.21482			0.548533			0.274266	+	0.961654i	$0.411565\pi$
$174$	0.561341	+	0.703899i	0.0425551	+	0.0533625i
$175$	−12.1579	−	1.83250i	−0.919048	−	0.138524i
$176$	2.06328	−	9.03981i	0.155525	−	0.681401i
$177$	0.280669	+	0.191357i	0.0210964	+	0.0143833i
$178$	−2.85718	−	4.94879i	−0.214155	−	0.370927i
$179$	2.86985	−	4.97072i	0.214503	−	0.371529i	−0.738616	−	0.674126i	$-0.764520\pi$
$179$	2.86985	−	4.97072i	0.214503	−	0.371529i	0.953119	+	0.302597i	$0.0978536\pi$
$180$	3.20268	−	1.54233i	0.238714	−	0.114958i
$181$	9.97447	+	3.07672i	0.741397	+	0.228691i	0.642371	−	0.766394i	$-0.277951\pi$
$181$	9.97447	+	3.07672i	0.741397	+	0.228691i	0.0990262	+	0.995085i	$0.468427\pi$
$182$	0.328750	+	4.38687i	0.0243686	+	0.325176i
$183$	−1.88910	−	8.27667i	−0.139646	−	0.611829i
$184$	1.06016	−	2.70125i	0.0781564	−	0.199139i
$185$	0.795790	−	10.6191i	0.0585076	−	0.780730i
$186$	0.283035	−	0.0426606i	0.0207531	−	0.00312803i
$187$	−2.22797	−	2.06725i	−0.162925	−	0.151173i
$188$	1.79753	+	0.865645i	0.131098	+	0.0631337i
$189$	−15.7948	+	10.7687i	−1.14890	+	0.783310i
$190$	0.704807	+	1.79582i	0.0511321	+	0.130282i
$191$	17.4710	−	5.38910i	1.26416	−	0.389942i	0.411021	−	0.911626i	$-0.365172\pi$
$191$	17.4710	−	5.38910i	1.26416	−	0.389942i	0.853139	+	0.521684i	$0.174696\pi$
$192$	−3.80100	+	3.52682i	−0.274314	+	0.254526i
$193$	4.60910	−	5.77963i	0.331770	−	0.416027i	−0.587767	−	0.809031i	$-0.699993\pi$
$193$	4.60910	−	5.77963i	0.331770	−	0.416027i	0.919537	+	0.393004i	$0.128564\pi$
$194$	0.987472	−	1.23825i	0.0708964	−	0.0889012i
$195$	−3.31635	+	3.07713i	−0.237489	+	0.220358i
$196$	−9.27398	+	2.86064i	−0.662427	+	0.204332i
$197$	9.76348	+	24.8769i	0.695619	+	1.77241i	0.632709	+	0.774390i	$0.281943\pi$
$197$	9.76348	+	24.8769i	0.695619	+	1.77241i	0.0629108	+	0.998019i	$0.479962\pi$
$198$	−1.60405	+	1.09362i	−0.113995	+	0.0777204i
$199$	10.4599	+	5.03725i	0.741486	+	0.357081i	0.766190	−	0.642614i	$-0.222150\pi$
$199$	10.4599	+	5.03725i	0.741486	+	0.357081i	−0.0247041	+	0.999695i	$0.507864\pi$
$200$	3.97963	+	3.69256i	0.281403	+	0.261103i
$201$	10.4287	−	1.57188i	0.735587	−	0.110872i
$202$	−0.493354	+	6.58335i	−0.0347122	+	0.463203i
$203$	−2.40233	+	6.12103i	−0.168610	+	0.429612i
$204$	0.486518	+	2.13157i	0.0340630	+	0.149240i
$205$	0.848875	+	11.3275i	0.0592880	+	0.791144i
$206$	1.77908	+	0.548775i	0.123955	+	0.0382350i
$207$	2.67634	−	1.28886i	0.186019	−	0.0895818i
$208$	−4.74838	+	8.22443i	−0.329241	+	0.570261i
$209$	5.95261	+	10.3102i	0.411750	+	0.713173i
$210$	1.69698	+	1.15698i	0.117103	+	0.0798392i
$211$	−2.50029	+	10.9545i	−0.172127	+	0.754138i	0.812993	+	0.582273i	$0.197836\pi$
$211$	−2.50029	+	10.9545i	−0.172127	+	0.754138i	−0.985120	+	0.171865i	$0.945021\pi$
$212$	−12.8592	−	1.93821i	−0.883172	−	0.133117i
$213$	10.2054	+	12.7971i	0.699261	+	0.876845i
$214$	−3.55606			−0.243087
$215$	−6.86866	−	4.11868i	−0.468439	−	0.280891i
$216$	8.44078			0.574322
$217$	1.30342	+	1.63443i	0.0884817	+	0.110953i
$218$	−4.46786	−	0.673421i	−0.302601	−	0.0456098i
$219$	2.19574	−	9.62018i	0.148375	−	0.650072i
$220$	−5.63532	−	3.84210i	−0.379933	−	0.259034i
$221$	1.55644	+	2.69584i	0.104698	+	0.181342i
$222$	2.09187	−	3.62322i	0.140397	−	0.243175i
$223$	−21.7129	+	10.4564i	−1.45400	+	0.700211i	−0.983285	−	0.182073i	$-0.941719\pi$
$223$	−21.7129	+	10.4564i	−1.45400	+	0.700211i	−0.470718	+	0.882284i	$0.656005\pi$
$224$	14.4841	+	4.46775i	0.967760	+	0.298514i
$225$	0.415299	+	5.54178i	0.0276866	+	0.369452i
$226$	1.29334	+	5.66650i	0.0860319	+	0.376930i
$227$	1.62034	−	4.12855i	0.107546	−	0.274022i	−0.866963	−	0.498373i	$-0.833931\pi$
$227$	1.62034	−	4.12855i	0.107546	−	0.274022i	0.974508	+	0.224351i	$0.0720263\pi$
$228$	0.640008	−	8.54032i	0.0423856	−	0.565596i
$229$	−16.6465	+	2.50906i	−1.10003	+	0.165803i	−0.673875	−	0.738845i	$-0.735371\pi$
$229$	−16.6465	+	2.50906i	−1.10003	+	0.165803i	−0.426158	+	0.904649i	$0.640133\pi$
$230$	−0.677034	−	0.628196i	−0.0446423	−	0.0414220i
$231$	11.4195	+	5.49932i	0.751346	+	0.361829i
$232$	2.39890	−	1.63555i	0.157496	−	0.107379i
$233$	0.133886	+	0.341137i	0.00877119	+	0.0223486i	0.935192	−	0.354140i	$-0.115226\pi$
$233$	0.133886	+	0.341137i	0.00877119	+	0.0223486i	−0.926421	+	0.376489i	$0.877131\pi$
$234$	1.90005	−	0.586087i	0.124210	−	0.0383137i
$235$	0.972157	−	0.902030i	0.0634165	−	0.0588420i
$236$	0.327035	−	0.410089i	0.0212882	−	0.0266945i
$237$	−4.70125	+	5.89518i	−0.305379	+	0.382933i
$238$	1.03596	−	0.961228i	0.0671512	−	0.0623072i
$239$	−8.79373	+	2.71251i	−0.568819	+	0.175457i	−0.565807	−	0.824538i	$-0.691435\pi$
$239$	−8.79373	+	2.71251i	−0.568819	+	0.175457i	−0.00301249	+	0.999995i	$0.500959\pi$
$240$	1.61984	+	4.12730i	0.104561	+	0.266416i
$241$	10.7741	−	7.34568i	0.694023	−	0.473177i	−0.164218	−	0.986424i	$-0.552510\pi$
$241$	10.7741	−	7.34568i	0.694023	−	0.473177i	0.858241	+	0.513247i	$0.171558\pi$
$242$	−0.640379	−	0.308390i	−0.0411651	−	0.0198241i
$243$	10.4792	+	9.72323i	0.672238	+	0.623746i
$244$	−12.9623	+	1.95375i	−0.829824	+	0.125076i
$245$	−0.482096	+	6.43312i	−0.0308000	+	0.410997i
$246$	−1.63045	+	4.15433i	−0.103954	+	0.264870i
$247$	−2.71329	−	11.8877i	−0.172643	−	0.756396i
$248$	−0.0689800	−	0.920474i	−0.00438023	−	0.0584501i
$249$	15.8738	+	4.89643i	1.00596	+	0.310298i
$250$	3.77540	−	1.81814i	0.238777	−	0.114989i
$251$	9.90954	−	17.1638i	0.625484	−	1.08337i	−0.362962	−	0.931804i	$-0.618235\pi$
$251$	9.90954	−	17.1638i	0.625484	−	1.08337i	0.988447	−	0.151567i	$-0.0484320\pi$
$252$	5.10002	+	8.83349i	0.321271	+	0.556458i
$253$	−4.70920	−	3.21068i	−0.296065	−	0.201853i
$254$	0.757037	−	3.31680i	0.0475007	−	0.208114i
$255$	1.43709	+	0.216607i	0.0899943	+	0.0135645i
$256$	2.81710	+	3.53254i	0.176069	+	0.220784i
$257$	2.09407			0.130624			0.0653121	−	0.997865i	$-0.479196\pi$
$257$	2.09407			0.130624			0.0653121	+	0.997865i	$0.479196\pi$
$258$	−1.72924	−	2.62877i	−0.107658	−	0.163660i
$259$	30.5563			1.89868
$260$	4.35543	+	5.46153i	0.270112	+	0.338710i
$261$	2.93891	+	0.442969i	0.181914	+	0.0274191i
$262$	−0.00204665	+	0.00896697i	−0.000126443	+	0.000553981i
$263$	−1.69244	−	1.15388i	−0.104360	−	0.0711515i	0.510016	−	0.860165i	$-0.329640\pi$
$263$	−1.69244	−	1.15388i	−0.104360	−	0.0711515i	−0.614376	+	0.789014i	$0.710592\pi$
$264$	−2.79820	−	4.84663i	−0.172217	−	0.298289i
$265$	−4.32212	+	7.48613i	−0.265506	+	0.459869i
$266$	−4.98746	+	2.40183i	−0.305801	+	0.147266i
$267$	16.1134	+	4.97031i	0.986121	+	0.304178i
$268$	−1.21697	−	16.2394i	−0.0743384	−	0.991977i
$269$	−0.144540	−	0.633272i	−0.00881277	−	0.0386113i	0.970330	−	0.241783i	$-0.0777322\pi$
$269$	−0.144540	−	0.633272i	−0.00881277	−	0.0386113i	−0.979143	+	0.203172i	$0.934875\pi$
$270$	0.981481	−	2.50077i	0.0597310	−	0.152192i
$271$	1.43565	−	19.1575i	0.0872098	−	1.16373i	−0.766239	−	0.642556i	$-0.777874\pi$
$271$	1.43565	−	19.1575i	0.0872098	−	1.16373i	0.853448	−	0.521177i	$-0.174507\pi$
$272$	3.01671	−	0.454696i	0.182915	−	0.0275700i
$273$	−9.51610	−	8.82965i	−0.575940	−	0.534395i
$274$	−0.248560	−	0.119700i	−0.0150161	−	0.00723136i
$275$	8.81009	−	6.00662i	0.531268	−	0.362213i
$276$	1.49793	+	3.81667i	0.0901650	+	0.229737i
$277$	−19.3117	+	5.95686i	−1.16033	+	0.357913i	−0.814374	−	0.580340i	$-0.802920\pi$
$277$	−19.3117	+	5.95686i	−1.16033	+	0.357913i	−0.345951	+	0.938253i	$0.612444\pi$
$278$	4.63366	−	4.29941i	0.277909	−	0.257861i
$279$	0.589133	−	0.738750i	0.0352705	−	0.0442278i
$280$	4.12962	−	5.17837i	0.246792	−	0.309467i
$281$	9.23391	−	8.56782i	0.550849	−	0.511113i	−0.354913	−	0.934899i	$-0.615490\pi$
$281$	9.23391	−	8.56782i	0.550849	−	0.511113i	0.905762	+	0.423786i	$0.139299\pi$
$282$	0.497883	−	0.153576i	0.0296485	−	0.00914535i
$283$	−1.59656	−	4.06797i	−0.0949057	−	0.241816i	0.875535	−	0.483154i	$-0.160509\pi$
$283$	−1.59656	−	4.06797i	−0.0949057	−	0.241816i	−0.970441	+	0.241338i	$0.922414\pi$
$284$	20.8824	−	14.2374i	1.23914	−	0.844833i
$285$	−5.12903	−	2.47001i	−0.303817	−	0.146311i
$286$	−2.79669	−	2.59495i	−0.165372	−	0.153443i
$287$	−32.2306	+	4.85798i	−1.90251	+	0.286758i
$288$	0.511980	−	6.83190i	0.0301687	−	0.402574i
$289$	0.365341	−	0.930874i	0.0214906	−	0.0547573i
$290$	−0.205626	−	0.900909i	−0.0120748	−	0.0529032i
$291$	0.349257	+	4.66051i	0.0204738	+	0.273204i
$292$	−14.5596	−	4.49105i	−0.852037	−	0.262819i
$293$	−28.1517	+	13.5572i	−1.64464	+	0.792017i	−0.645029	+	0.764158i	$0.723155\pi$
$293$	−28.1517	+	13.5572i	−1.64464	+	0.792017i	−0.999612	+	0.0278591i	$0.991131\pi$
$294$	−1.26727	+	2.19498i	−0.0739087	+	0.128014i
$295$	−0.174329	−	0.301947i	−0.0101498	−	0.0175800i
$296$	−11.1476	−	7.60028i	−0.647939	−	0.441757i
$297$	3.68909	−	16.1630i	0.214063	−	0.937871i
$298$	−0.325448	−	0.0490535i	−0.0188527	−	0.00284159i
$299$	3.63964	+	4.56397i	0.210486	+	0.263941i
$300$	−7.67057			−0.442861
$301$	10.3124	−	20.5373i	0.594397	−	1.18375i
$302$	6.78541			0.390456
$303$	−12.1464	−	15.2310i	−0.697790	−	0.875001i
$304$	−11.8167	−	1.78108i	−0.677734	−	0.102152i
$305$	−1.93894	+	8.49506i	−0.111024	+	0.486426i
$306$	−0.527768	−	0.359826i	−0.0301705	−	0.0205699i
$307$	−12.9069	−	22.3555i	−0.736638	−	1.27589i	−0.954001	−	0.299804i	$-0.903079\pi$
$307$	−12.9069	−	22.3555i	−0.736638	−	1.27589i	0.217363	−	0.976091i	$-0.430254\pi$
$308$	9.78546	−	16.9489i	0.557579	−	0.965754i
$309$	−4.94990	+	2.38375i	−0.281590	+	0.135607i
$310$	−0.280732	−	0.0865944i	−0.0159445	−	0.00491823i
$311$	1.66219	+	22.1804i	0.0942543	+	1.25774i	0.821039	+	0.570872i	$0.193395\pi$
$311$	1.66219	+	22.1804i	0.0942543	+	1.25774i	−0.726785	+	0.686865i	$0.758986\pi$
$312$	1.27546	+	5.58817i	0.0722090	+	0.316368i
$313$	−0.496153	+	1.26418i	−0.0280442	+	0.0714555i	−0.944210	−	0.329344i	$-0.893172\pi$
$313$	−0.496153	+	1.26418i	−0.0280442	+	0.0714555i	0.916166	+	0.400800i	$0.131268\pi$
$314$	0.625861	−	8.35154i	0.0353194	−	0.471305i
$315$	6.70439	−	1.01052i	0.377749	−	0.0569366i
$316$	8.53481	+	7.91915i	0.480121	+	0.445487i
$317$	−19.7713	−	9.52135i	−1.11047	−	0.534772i	−0.213532	−	0.976936i	$-0.568497\pi$
$317$	−19.7713	−	9.52135i	−1.11047	−	0.534772i	−0.896934	+	0.442164i	$0.854211\pi$
$318$	−2.80604	+	1.91312i	−0.157355	+	0.107283i
$319$	−2.08340	−	5.30841i	−0.116648	−	0.297214i
$320$	5.08555	−	1.56869i	0.284291	−	0.0876922i
$321$	7.69232	−	7.13743i	0.429344	−	0.398373i
$322$	1.65235	−	2.07199i	0.0920821	−	0.115467i
$323$	−2.44226	+	3.06250i	−0.135891	+	0.170402i
$324$	−2.34189	+	2.17296i	−0.130105	+	0.120720i
$325$	−10.4358	+	3.21903i	−0.578875	+	0.178559i
$326$	1.71703	+	4.37492i	0.0950974	+	0.242304i
$327$	11.0163	−	7.51080i	0.609204	−	0.415348i
$328$	12.9667	+	6.24444i	0.715966	+	0.344791i
$329$	2.78955	+	2.58833i	0.153793	+	0.142699i
$330$	−1.76129	+	0.265472i	−0.0969561	+	0.0146138i
$331$	1.28301	−	17.1206i	0.0705206	−	0.941033i	−0.843961	−	0.536405i	$-0.819782\pi$
$331$	1.28301	−	17.1206i	0.0705206	−	0.941033i	0.914481	−	0.404628i	$-0.132599\pi$
$332$	9.37112	−	23.8772i	0.514307	−	1.31043i
$333$	−3.07328	−	13.4649i	−0.168415	−	0.737872i
$334$	−0.267162	−	3.56503i	−0.0146184	−	0.195069i
$335$	−10.3439	−	3.19067i	−0.565148	−	0.174325i
$336$	−11.4626	+	5.52009i	−0.625336	+	0.301146i
$337$	−17.6636	+	30.5943i	−0.962199	+	1.66658i	−0.245239	+	0.969463i	$0.578866\pi$
$337$	−17.6636	+	30.5943i	−0.962199	+	1.66658i	−0.716960	+	0.697114i	$0.754467\pi$
$338$	−0.667365	−	1.15591i	−0.0362999	−	0.0628732i
$339$	−14.1711	−	9.66166i	−0.769666	−	0.524749i
$340$	0.499355	−	2.18782i	0.0270813	−	0.118651i
$341$	−1.79273	−	0.270211i	−0.0970820	−	0.0146328i
$342$	1.56002	+	1.95620i	0.0843560	+	0.105779i
$343$	6.02075			0.325090
$344$	−8.87042	+	4.92742i	−0.478261	+	0.265669i
$345$	2.72539			0.146730
$346$	−1.81396	−	2.27463i	−0.0975190	−	0.122285i
$347$	−25.2205	−	3.80138i	−1.35391	−	0.204069i	−0.568314	−	0.822812i	$-0.692404\pi$
$347$	−25.2205	−	3.80138i	−1.35391	−	0.204069i	−0.785593	+	0.618743i	$0.787642\pi$
$348$	−0.912846	+	3.99944i	−0.0489337	+	0.214392i
$349$	−10.0798	−	6.87230i	−0.539560	−	0.367866i	0.262665	−	0.964887i	$-0.415398\pi$
$349$	−10.0798	−	6.87230i	−0.539560	−	0.367866i	−0.802225	+	0.597021i	$0.796351\pi$
$350$	2.47900	+	4.29376i	0.132508	+	0.229511i
$351$	−8.48999	+	14.7051i	−0.453162	+	0.784900i
$352$	−11.8434	+	5.70349i	−0.631257	+	0.303997i
$353$	−26.5787	−	8.19844i	−1.41464	−	0.436359i	−0.509132	−	0.860688i	$-0.670034\pi$
$353$	−26.5787	−	8.19844i	−1.41464	−	0.436359i	−0.905508	+	0.424330i	$0.860510\pi$
$354$	−0.0102366	−	0.136598i	−0.000544071	−	0.00726012i
$355$	−3.73836	−	16.3788i	−0.198412	−	0.869298i
$356$	9.51253	−	24.2375i	0.504163	−	1.28459i
$357$	−0.311642	+	4.15858i	−0.0164939	+	0.220095i
$358$	−2.28867	+	0.344962i	−0.120960	+	0.0182318i
$359$	8.90434	+	8.26202i	0.469953	+	0.436053i	0.879259	−	0.476345i	$-0.158039\pi$
$359$	8.90434	+	8.26202i	0.469953	+	0.436053i	−0.409306	+	0.912397i	$0.634229\pi$
$360$	−2.69724	−	1.29892i	−0.142157	−	0.0684593i
$361$	−3.02113	+	2.05977i	−0.159007	+	0.108409i
$362$	−1.53779	−	3.91822i	−0.0808244	−	0.205937i
$363$	2.00422	−	0.618219i	0.105194	−	0.0324481i
$364$	−14.6938	+	13.6339i	−0.770165	+	0.714609i
$365$	−6.31467	+	7.91835i	−0.330525	+	0.414465i
$366$	−2.13444	+	2.67651i	−0.111569	+	0.139903i
$367$	16.0470	−	14.8894i	0.837645	−	0.777221i	−0.139404	−	0.990236i	$-0.544519\pi$
$367$	16.0470	−	14.8894i	0.837645	−	0.777221i	0.977049	+	0.213015i	$0.0683282\pi$
$368$	5.46691	−	1.68632i	0.284983	−	0.0879055i
$369$	5.38239	+	13.7141i	0.280196	+	0.713928i
$370$	−3.54798	+	2.41897i	−0.184450	+	0.125756i
$371$	−22.3478	−	10.7621i	−1.16024	−	0.558742i
$372$	0.956052	+	0.887086i	0.0495690	+	0.0459933i
$373$	30.9740	−	4.66858i	1.60377	−	0.241730i	0.714678	−	0.699453i	$-0.246573\pi$
$373$	30.9740	−	4.66858i	1.60377	−	0.241730i	0.889095	+	0.457724i	$0.151335\pi$
$374$	−0.0915888	+	1.22217i	−0.00473595	+	0.0631968i
$375$	−4.51758	+	11.5106i	−0.233287	+	0.594405i
$376$	−0.373890	−	1.63812i	−0.0192819	−	0.0844796i
$377$	0.436473	+	5.82433i	0.0224795	+	0.299968i
$378$	7.36623	+	2.27218i	0.378878	+	0.116868i
$379$	10.3800	−	4.99875i	0.533186	−	0.256769i	−0.147862	−	0.989008i	$-0.547239\pi$
$379$	10.3800	−	4.99875i	0.533186	−	0.256769i	0.681047	+	0.732239i	$0.261525\pi$
$380$	−4.39512	+	7.61257i	−0.225465	+	0.390517i
$381$	5.01961	+	8.69422i	0.257163	+	0.445419i
$382$	−6.09162	−	4.15320i	−0.311674	−	0.212496i
$383$	4.00444	−	17.5446i	0.204617	−	0.896487i	−0.763464	−	0.645851i	$-0.776503\pi$
$383$	4.00444	−	17.5446i	0.204617	−	0.896487i	0.968081	−	0.250637i	$-0.0806399\pi$
$384$	12.2458	+	1.84575i	0.624913	+	0.0941906i
$385$	−8.11103	−	10.1709i	−0.413376	−	0.518358i
$386$	−2.98098			−0.151728
$387$	−10.0871	−	2.47866i	−0.512759	−	0.125997i
$388$	7.21647			0.366361
$389$	−7.93762	−	9.95347i	−0.402454	−	0.504661i	0.538766	−	0.842455i	$-0.318891\pi$
$389$	−7.93762	−	9.95347i	−0.402454	−	0.504661i	−0.941220	+	0.337794i	$0.890319\pi$
$390$	1.80393	+	0.271899i	0.0913457	+	0.0137681i
$391$	0.417289	−	1.82826i	0.0211032	−	0.0924593i
$392$	6.75328	+	4.60431i	0.341092	+	0.232553i
$393$	−0.0135705	−	0.0235049i	−0.000684543	−	0.00118566i
$394$	5.38826	−	9.33274i	0.271457	−	0.470177i
$395$	6.97275	−	3.35790i	0.350837	−	0.168954i
$396$	−8.45289	−	2.60737i	−0.424774	−	0.131025i
$397$	2.72940	+	36.4213i	0.136985	+	1.82793i	0.467341	+	0.884077i	$0.345212\pi$
$397$	2.72940	+	36.4213i	0.136985	+	1.82793i	−0.330356	+	0.943856i	$0.607169\pi$
$398$	−1.04175	−	4.56420i	−0.0522181	−	0.228783i
$399$	5.96791	−	15.2060i	0.298769	−	0.761251i
$400$	−0.799848	+	10.6732i	−0.0399924	+	0.533662i
$401$	−18.2343	+	2.74838i	−0.910578	+	0.137248i	−0.587593	−	0.809157i	$-0.699924\pi$
$401$	−18.2343	+	2.74838i	−0.910578	+	0.137248i	−0.322985	+	0.946404i	$0.604686\pi$
$402$	−3.11757	−	2.89269i	−0.155490	−	0.144274i
$403$	1.67298	+	0.805667i	0.0833373	+	0.0401331i
$404$	−24.8541	+	16.9452i	−1.23654	+	0.843056i
$405$	0.775828	+	1.97678i	0.0385512	+	0.0982268i
$406$	2.53379	−	0.781570i	0.125750	−	0.0387887i
$407$	−19.4256	+	18.0244i	−0.962893	+	0.893434i
$408$	1.14806	−	1.43962i	0.0568373	−	0.0712718i
$409$	11.9118	−	14.9369i	0.588998	−	0.738580i	−0.394620	−	0.918844i	$-0.629124\pi$
$409$	11.9118	−	14.9369i	0.588998	−	0.738580i	0.983618	+	0.180264i	$0.0576952\pi$
$410$	3.35780	−	3.11559i	0.165830	−	0.153868i
$411$	0.777928	−	0.239959i	0.0383724	−	0.0118363i
$412$	3.09928	+	7.89683i	0.152690	+	0.389049i
$413$	0.826616	−	0.563577i	0.0406751	−	0.0277318i
$414$	−1.07923	−	0.519729i	−0.0530412	−	0.0255433i
$415$	−12.4987	−	11.5971i	−0.613535	−	0.569277i
$416$	13.3131	−	2.00662i	0.652726	−	0.0983826i
$417$	−1.39392	+	18.6006i	−0.0682607	+	0.910876i
$418$	1.75391	−	4.46890i	0.0857867	−	0.218581i
$419$	−4.73746	−	20.7562i	−0.231440	−	1.01401i	−0.948446	−	0.316939i	$-0.897345\pi$
$419$	−4.73746	−	20.7562i	−0.231440	−	1.01401i	0.717006	−	0.697067i	$-0.245512\pi$
$420$	0.699351	+	9.33219i	0.0341248	+	0.455364i
$421$	−30.9376	−	9.54300i	−1.50781	−	0.465097i	−0.572792	−	0.819701i	$-0.694140\pi$
$421$	−30.9376	−	9.54300i	−1.50781	−	0.465097i	−0.935017	+	0.354604i	$0.884616\pi$
$422$	4.08227	−	1.96592i	0.198722	−	0.0956994i
$423$	0.860003	−	1.48957i	0.0418148	−	0.0724253i
$424$	5.47606	+	9.48481i	0.265941	+	0.460623i
$425$	2.89872	+	1.97631i	0.140608	+	0.0958651i
$426$	1.46873	−	6.43494i	0.0711603	−	0.311774i
$427$	−24.7237	−	3.72650i	−1.19647	−	0.180338i
$428$	−10.1025	−	12.6681i	−0.488321	−	0.612336i
$429$	11.2581			0.543545
$430$	0.428422	+	3.20102i	0.0206603	+	0.154367i
$431$	22.7468			1.09568			0.547838	−	0.836584i	$-0.315451\pi$
$431$	22.7468			1.09568			0.547838	+	0.836584i	$0.315451\pi$
$432$	10.3757	+	13.0107i	0.499199	+	0.625976i
$433$	−2.31263	−	0.348573i	−0.111138	−	0.0167513i	0.0932378	−	0.995644i	$-0.470278\pi$
$433$	−2.31263	−	0.348573i	−0.111138	−	0.0167513i	−0.204376	+	0.978893i	$0.565516\pi$
$434$	0.187585	−	0.821862i	0.00900435	−	0.0394506i
$435$	2.25303	+	1.53609i	0.108025	+	0.0736500i
$436$	−10.2938	−	17.8294i	−0.492984	−	0.853874i
$437$	−3.67281	+	6.36150i	−0.175694	+	0.304312i
$438$	−3.58503	+	1.72646i	−0.171299	+	0.0824934i
$439$	−17.3228	−	5.34339i	−0.826774	−	0.255026i	−0.147641	−	0.989041i	$-0.547168\pi$
$439$	−17.3228	−	5.34339i	−0.826774	−	0.255026i	−0.679133	+	0.734015i	$0.737644\pi$
$440$	0.429255	+	5.72801i	0.0204639	+	0.273072i
$441$	1.86182	+	8.15715i	0.0886579	+	0.388436i
$442$	0.458600	−	1.16849i	0.0218134	−	0.0555795i
$443$	−0.878901	+	11.7281i	−0.0417578	+	0.557220i	0.936614	+	0.350364i	$0.113942\pi$
$443$	−0.878901	+	11.7281i	−0.0417578	+	0.557220i	−0.978371	+	0.206856i	$0.933677\pi$
$444$	18.8502	−	2.84121i	0.894590	−	0.134838i
$445$	−12.6873	−	11.7721i	−0.601433	−	0.558049i
$446$	8.75568	+	4.21652i	0.414594	+	0.199658i
$447$	0.802453	−	0.547103i	0.0379547	−	0.0258771i
$448$	5.57919	+	14.2155i	0.263592	+	0.671621i
$449$	17.2823	−	5.33088i	0.815601	−	0.251580i	0.141234	−	0.989976i	$-0.454893\pi$
$449$	17.2823	−	5.33088i	0.815601	−	0.251580i	0.674367	+	0.738397i	$0.264417\pi$
$450$	1.64275	−	1.52425i	0.0774401	−	0.0718539i
$451$	17.6245	−	22.1004i	0.829903	−	1.04067i
$452$	−16.5121	+	20.7055i	−0.776662	+	0.973904i
$453$	−14.6779	+	13.6191i	−0.689629	+	0.639882i
$454$	−1.70901	+	0.527158i	−0.0802076	+	0.0247408i
$455$	4.86781	+	12.4030i	0.228206	+	0.581460i
$456$	−5.95940	+	4.06305i	−0.279074	+	0.190270i
$457$	−16.7483	−	8.06557i	−0.783453	−	0.377291i	−0.000999281	−	1.00000i	$-0.500318\pi$
$457$	−16.7483	−	8.06557i	−0.783453	−	0.377291i	−0.782454	+	0.622708i	$0.786032\pi$
$458$	4.97632	+	4.61735i	0.232528	+	0.215755i
$459$	5.39382	−	0.812987i	0.251762	−	0.0379470i
$460$	0.314485	−	4.19652i	0.0146630	−	0.195664i
$461$	5.59541	−	14.2569i	0.260604	−	0.664008i	−0.739353	−	0.673319i	$-0.764868\pi$
$461$	5.59541	−	14.2569i	0.260604	−	0.664008i	0.999957	+	0.00931004i	$0.00296352\pi$
$462$	−1.13731	−	4.98288i	−0.0529125	−	0.231825i
$463$	−0.688900	−	9.19273i	−0.0320159	−	0.427222i	−0.990064	−	0.140616i	$-0.955092\pi$
$463$	−0.688900	−	9.19273i	−0.0320159	−	0.427222i	0.958048	−	0.286607i	$-0.0925273\pi$
$464$	5.46984	+	1.68722i	0.253931	+	0.0783273i
$465$	0.781073	−	0.376145i	0.0362214	−	0.0174433i
$466$	0.0738891	−	0.127980i	0.00342285	−	0.00592854i
$467$	6.57186	+	11.3828i	0.304110	+	0.526733i	0.977063	−	0.212952i	$-0.0683078\pi$
$467$	6.57186	+	11.3828i	0.304110	+	0.526733i	−0.672953	+	0.739685i	$0.734974\pi$
$468$	7.48575	+	5.10370i	0.346029	+	0.235919i
$469$	6.91178	−	30.2825i	0.319156	−	1.39831i
$470$	−0.528806	−	0.0797046i	−0.0243920	−	0.00367650i
$471$	15.4087	+	19.3219i	0.709995	+	0.890306i
$472$	−0.441745			−0.0203330
$473$	5.55850	+	19.1393i	0.255580	+	0.880024i
$474$	3.04058			0.139658
$475$	−8.56824	−	10.7442i	−0.393138	−	0.492979i
$476$	6.36735	+	0.959723i	0.291847	+	0.0439889i
$477$	−2.49474	+	10.9302i	−0.114226	+	0.500459i
$478$	3.06611	+	2.09044i	0.140240	+	0.0956143i
$479$	0.790324	+	1.36888i	0.0361108	+	0.0625458i	0.883516	−	0.468401i	$-0.155170\pi$
$479$	0.790324	+	1.36888i	0.0361108	+	0.0625458i	−0.847405	+	0.530947i	$0.821836\pi$
$480$	3.14286	−	5.44360i	0.143451	−	0.248465i
$481$	24.4534	−	11.7761i	1.11498	−	0.536945i
$482$	−5.02473	−	1.54992i	−0.228870	−	0.0705971i
$483$	0.584417	+	7.79851i	0.0265919	+	0.354844i
$484$	−0.720655	−	3.15739i	−0.0327570	−	0.143518i
$485$	1.75250	−	4.46530i	0.0795770	−	0.202759i
$486$	0.430784	−	5.74841i	0.0195408	−	0.260753i
$487$	−9.03833	+	1.36231i	−0.409566	+	0.0617321i	−0.350594	−	0.936528i	$-0.614020\pi$
$487$	−9.03833	+	1.36231i	−0.409566	+	0.0617321i	−0.0589719	+	0.998260i	$0.518782\pi$
$488$	8.09282	+	7.50904i	0.366345	+	0.339918i
$489$	−12.4952	−	6.01736i	−0.565051	−	0.272114i
$490$	2.14939	−	1.46543i	0.0970996	−	0.0662014i
$491$	−4.00950	−	10.2160i	−0.180946	−	0.461043i	0.811406	−	0.584483i	$-0.198703\pi$
$491$	−4.00950	−	10.2160i	−0.180946	−	0.461043i	−0.992352	+	0.123440i	$0.960607\pi$
$492$	−19.4313	+	5.99378i	−0.876033	+	0.270220i
$493$	1.37541	−	1.27620i	0.0619456	−	0.0574771i
$494$	−3.06568	+	3.84424i	−0.137932	+	0.172961i
$495$	−3.66612	+	4.59716i	−0.164780	+	0.206627i
$496$	1.33403	−	1.23780i	0.0598997	−	0.0555788i
$497$	46.0651	−	14.2092i	2.06630	−	0.637370i
$498$	−2.44731	−	6.23564i	−0.109666	−	0.279426i
$499$	−1.81319	+	1.23621i	−0.0811693	+	0.0553403i	−0.603225	−	0.797571i	$-0.706118\pi$
$499$	−1.81319	+	1.23621i	−0.0811693	+	0.0553403i	0.522055	+	0.852912i	$0.325165\pi$
$500$	17.2025	+	8.28430i	0.769321	+	0.370485i
$501$	7.73334	+	7.17549i	0.345500	+	0.320577i
$502$	−7.90274	+	1.19115i	−0.352717	+	0.0531635i
$503$	−0.110959	+	1.48064i	−0.00494740	+	0.0660185i	−0.999131	−	0.0416799i	$-0.986729\pi$
$503$	−0.110959	+	1.48064i	−0.00494740	+	0.0660185i	0.994184	+	0.107698i	$0.0343481\pi$
$504$	3.13839	−	7.99649i	0.139795	−	0.356192i
$505$	4.44937	+	19.4940i	0.197994	+	0.867469i
$506$	0.171755	+	2.29191i	0.00763544	+	0.101888i
$507$	3.76367	+	1.16094i	0.167150	+	0.0515590i
$508$	13.9664	−	6.72588i	0.619660	−	0.298413i
$509$	−11.2266	+	19.4450i	−0.497610	+	0.861885i	−0.999996	−	0.00275799i	$-0.999122\pi$
$509$	−11.2266	+	19.4450i	−0.497610	+	0.861885i	0.502387	+	0.864643i	$0.332455\pi$
$510$	−0.293025	−	0.507535i	−0.0129754	−	0.0224740i
$511$	−24.0118	−	16.3710i	−1.06222	−	0.724210i
$512$	5.03711	−	22.0690i	0.222611	−	0.975322i
$513$	−21.1280	−	3.18453i	−0.932824	−	0.140601i
$514$	−0.526492	−	0.660200i	−0.0232226	−	0.0291202i
$515$	5.63894			0.248481
$516$	4.45210	−	13.6283i	0.195993	−	0.599954i
$517$	−3.30020			−0.145142
$518$	−7.68250	−	9.63355i	−0.337550	−	0.423274i
$519$	8.48934	+	1.27956i	0.372641	+	0.0561665i
$520$	1.30912	−	5.73563i	0.0574087	−	0.251524i
$521$	15.4122	+	10.5079i	0.675222	+	0.460359i	0.851758	−	0.523935i	$-0.175537\pi$
$521$	15.4122	+	10.5079i	0.675222	+	0.460359i	−0.176536	+	0.984294i	$0.556489\pi$
$522$	−0.599248	−	1.03793i	−0.0262284	−	0.0454288i
$523$	11.3374	−	19.6370i	0.495750	−	0.858665i	−0.504238	−	0.863565i	$-0.668226\pi$
$523$	11.3374	−	19.6370i	0.495750	−	0.858665i	0.999988	+	0.00490007i	$0.00155975\pi$
$524$	−0.0377583	+	0.0181834i	−0.00164948	+	0.000794347i
$525$	−13.9806	−	4.31244i	−0.610162	−	0.188210i
$526$	0.0617269	+	0.823688i	0.00269142	+	0.0359145i
$527$	−0.132736	−	0.581556i	−0.00578209	−	0.0253330i
$528$	4.03099	−	10.2708i	0.175426	−	0.446979i
$529$	−1.45599	+	19.4288i	−0.0633039	+	0.844732i
$530$	3.44684	−	0.519527i	0.149721	−	0.0225668i
$531$	−0.331484	−	0.307573i	−0.0143852	−	0.0133475i
$532$	−22.7253	−	10.9439i	−0.985265	−	0.474479i
$533$	−23.9210	+	16.3091i	−1.03614	+	0.706425i
$534$	−2.48424	−	6.32973i	−0.107503	−	0.273914i
$535$	−10.2919	+	3.17464i	−0.444960	+	0.137252i
$536$	−10.0537	+	9.32849i	−0.434255	+	0.402929i
$537$	4.25838	−	5.33984i	0.183763	−	0.230431i
$538$	−0.163312	+	0.204787i	−0.00704090	+	0.00882901i
$539$	11.7682	−	10.9193i	0.506893	−	0.470328i
$540$	11.6971	−	3.60806i	0.503361	−	0.155266i
$541$	−5.26956	−	13.4266i	−0.226556	−	0.577255i	0.771719	−	0.635963i	$-0.219397\pi$
$541$	−5.26956	−	13.4266i	−0.226556	−	0.577255i	−0.998275	+	0.0587084i	$0.981302\pi$
$542$	−6.40077	+	4.36397i	−0.274937	+	0.187449i
$543$	11.1908	+	5.38922i	0.480244	+	0.231273i
$544$	−3.17050	−	2.94179i	−0.135934	−	0.126128i
$545$	−13.5321	+	2.03963i	−0.579650	+	0.0873681i
$546$	−0.391194	+	5.22012i	−0.0167416	+	0.223400i
$547$	−3.81633	+	9.72385i	−0.163174	+	0.415762i	−0.988952	−	0.148234i	$-0.952641\pi$
$547$	−3.81633	+	9.72385i	−0.163174	+	0.415762i	0.825778	+	0.563995i	$0.190736\pi$
$548$	−0.279719	−	1.22553i	−0.0119490	−	0.0523520i
$549$	0.844535	+	11.2695i	0.0360439	+	0.480972i
$550$	−4.10876	−	1.26738i	−0.175198	−	0.0540415i
$551$	−6.62173	+	3.18885i	−0.282095	+	0.135850i
$552$	1.72652	−	2.99042i	0.0734854	−	0.127281i
$553$	11.1036	+	19.2319i	0.472172	+	0.817826i
$554$	6.73339	+	4.59075i	0.286074	+	0.195042i
$555$	2.81968	−	12.3538i	0.119689	−	0.524391i
$556$	28.4801	+	4.29268i	1.20782	+	0.182050i
$557$	11.6864	+	14.6543i	0.495170	+	0.620923i	0.965132	−	0.261763i	$-0.0843040\pi$
$557$	11.6864	+	14.6543i	0.495170	+	0.620923i	−0.469962	+	0.882686i	$0.655733\pi$
$558$	−0.381028			−0.0161302
$559$	0.337833	−	20.4098i	0.0142888	−	0.863241i
$560$	13.0582			0.551810
$561$	−2.25492	−	2.82757i	−0.0952026	−	0.119380i
$562$	−5.02279	−	0.757064i	−0.211874	−	0.0319348i
$563$	−0.538585	+	2.35969i	−0.0226986	+	0.0994493i	−0.985008	−	0.172507i	$-0.944813\pi$
$563$	−0.538585	+	2.35969i	−0.0226986	+	0.0994493i	0.962310	+	0.271956i	$0.0876705\pi$
$564$	1.96154	+	1.33736i	0.0825959	+	0.0563129i
$565$	8.80192	+	15.2454i	0.370300	+	0.641378i
$566$	−0.881109	+	1.52612i	−0.0370358	+	0.0641478i
$567$	−5.49003	+	2.64386i	−0.230560	+	0.111032i
$568$	−20.3397	−	6.27398i	−0.853437	−	0.263250i
$569$	1.74012	+	23.2203i	0.0729497	+	0.973446i	0.906829	+	0.421499i	$0.138496\pi$
$569$	1.74012	+	23.2203i	0.0729497	+	0.973446i	−0.833879	+	0.551947i	$0.813885\pi$
$570$	0.510821	+	2.23805i	0.0213959	+	0.0937417i
$571$	9.84799	−	25.0923i	0.412125	−	1.05008i	−0.562611	−	0.826722i	$-0.690203\pi$
$571$	9.84799	−	25.0923i	0.412125	−	1.05008i	0.974737	−	0.223357i	$-0.0717015\pi$
$572$	1.29908	−	17.3350i	0.0543171	−	0.724812i
$573$	21.5131	−	3.24258i	0.898723	−	0.135461i
$574$	9.63504	+	8.94001i	0.402159	+	0.373149i
$575$	5.92756	+	2.85456i	0.247196	+	0.119044i
$576$	5.70306	−	3.88828i	0.237628	−	0.162012i
$577$	7.96260	+	20.2884i	0.331488	+	0.844616i	0.995311	+	0.0967271i	$0.0308374\pi$
$577$	7.96260	+	20.2884i	0.331488	+	0.844616i	−0.663823	+	0.747889i	$0.731067\pi$
$578$	−0.385333	+	0.118859i	−0.0160277	+	0.00494390i
$579$	6.44834	−	5.98318i	0.267984	−	0.248653i
$580$	2.62523	−	3.29193i	0.109007	−	0.136690i
$581$	30.5040	−	38.2507i	1.26552	−	1.58691i
$582$	1.38152	−	1.28186i	0.0572657	−	0.0531348i
$583$	20.5555	−	6.34054i	0.851322	−	0.262598i
$584$	4.68804	+	11.9449i	0.193993	+	0.494285i
$585$	4.97589	−	3.39250i	0.205728	−	0.140263i
$586$	11.3521	+	5.46690i	0.468952	+	0.225835i
$587$	0.909111	+	0.843532i	0.0375230	+	0.0348163i	0.698711	−	0.715404i	$-0.253757\pi$
$587$	0.909111	+	0.843532i	0.0375230	+	0.0348163i	−0.661188	+	0.750220i	$0.729948\pi$
$588$	−11.4196	+	1.72123i	−0.470936	+	0.0709822i
$589$	−0.174613	+	2.33005i	−0.00719481	+	0.0960081i
$590$	−0.0513654	+	0.130877i	−0.00211468	+	0.00538812i
$591$	7.07625	+	31.0031i	0.291078	+	1.27530i
$592$	−1.98780	−	26.5254i	−0.0816982	−	1.09019i
$593$	−13.4367	−	4.14467i	−0.551779	−	0.170201i	0.00631368	−	0.999980i	$-0.497990\pi$
$593$	−13.4367	−	4.14467i	−0.551779	−	0.170201i	−0.558092	+	0.829779i	$0.688466\pi$
$594$	−6.02325	+	2.90064i	−0.247137	+	0.119015i
$595$	2.14014	−	3.70683i	0.0877371	−	0.151965i
$596$	−0.749824	−	1.29873i	−0.0307140	−	0.0531982i
$597$	11.4144	+	7.78218i	0.467158	+	0.318503i
$598$	0.523809	−	2.29496i	0.0214201	−	0.0938477i
$599$	−14.8052	−	2.23153i	−0.604925	−	0.0911778i	−0.160564	−	0.987025i	$-0.551331\pi$
$599$	−14.8052	−	2.23153i	−0.604925	−	0.0911778i	−0.444361	+	0.895848i	$0.646569\pi$
$600$	4.02776	+	5.05065i	0.164433	+	0.206192i
$601$	14.2274			0.580349			0.290175	−	0.956974i	$-0.406287\pi$
$601$	14.2274			0.580349			0.290175	+	0.956974i	$0.406287\pi$
$602$	−9.06760	+	1.91230i	−0.369568	+	0.0779397i
$603$	−14.0394			−0.571729
$604$	19.2768	+	24.1723i	0.784362	+	0.983558i
$605$	−2.12870	−	0.320849i	−0.0865438	−	0.0130444i
$606$	−1.74807	+	7.65881i	−0.0710106	+	0.311118i
$607$	24.3748	+	16.6184i	0.989341	+	0.674522i	0.945874	−	0.324533i	$-0.105207\pi$
$607$	24.3748	+	16.6184i	0.989341	+	0.674522i	0.0434672	+	0.999055i	$0.486160\pi$
$608$	8.47081	+	14.6719i	0.343537	+	0.595023i
$609$	−3.91228	+	6.77627i	−0.158534	+	0.274588i
$610$	3.16575	−	1.52454i	0.128177	−	0.0617269i
$611$	3.22992	+	0.996298i	0.130669	+	0.0403059i
$612$	−0.217501	−	2.90236i	−0.00879198	−	0.117321i
$613$	2.61106	+	11.4398i	0.105460	+	0.462049i	0.999890	+	0.0148415i	$0.00472437\pi$
$613$	2.61106	+	11.4398i	0.105460	+	0.462049i	−0.894430	+	0.447208i	$0.852418\pi$
$614$	−3.80298	+	9.68983i	−0.153476	+	0.391050i
$615$	−1.01011	+	13.4790i	−0.0407317	+	0.543527i
$616$	−16.2982	+	2.45656i	−0.656674	+	0.0989777i
$617$	16.5662	+	15.3712i	0.666930	+	0.618821i	0.939188	−	0.343404i	$-0.111580\pi$
$617$	16.5662	+	15.3712i	0.666930	+	0.618821i	−0.272258	+	0.962224i	$0.587770\pi$
$618$	1.99604	+	0.961241i	0.0802924	+	0.0386668i
$619$	−24.6224	+	16.7873i	−0.989657	+	0.674737i	−0.945952	−	0.324308i	$-0.894869\pi$
$619$	−24.6224	+	16.7873i	−0.989657	+	0.674737i	−0.0437054	+	0.999044i	$0.513916\pi$
$620$	−0.489053	−	1.24609i	−0.0196408	−	0.0500441i
$621$	9.77472	−	3.01510i	0.392246	−	0.120992i
$622$	6.57496	−	6.10067i	0.263632	−	0.244615i
$623$	30.9642	−	38.8279i	1.24056	−	1.55561i
$624$	−7.04580	+	8.83516i	−0.282058	+	0.353689i
$625$	−3.55529	+	3.29883i	−0.142212	+	0.131953i
$626$	0.523303	−	0.161418i	0.0209154	−	0.00645155i
$627$	5.17561	+	13.1872i	0.206694	+	0.526648i
$628$	31.5295	−	21.4965i	1.25817	−	0.857802i
$629$	−7.85553	−	3.78303i	−0.313221	−	0.150839i
$630$	−2.00421	−	1.85964i	−0.0798498	−	0.0740898i
$631$	−11.8704	+	1.78918i	−0.472554	+	0.0712260i	−0.381002	−	0.924574i	$-0.624421\pi$
$631$	−11.8704	+	1.78918i	−0.472554	+	0.0712260i	−0.0915520	+	0.995800i	$0.529183\pi$
$632$	0.732759	−	9.77800i	0.0291476	−	0.388948i
$633$	−4.88477	+	12.4462i	−0.194152	+	0.494692i
$634$	1.96910	+	8.62720i	0.0782031	+	0.342630i
$635$	−0.770028	−	10.2753i	−0.0305576	−	0.407763i
$636$	−14.7870	−	4.56120i	−0.586344	−	0.180863i
$637$	−14.8140	+	7.13407i	−0.586954	+	0.282662i
$638$	−1.14978	+	1.99148i	−0.0455204	+	0.0788436i
$639$	−10.8945	−	18.8699i	−0.430981	−	0.746481i
$640$	−10.5022	−	7.16027i	−0.415136	−	0.283035i
$641$	0.129052	−	0.565412i	0.00509723	−	0.0223324i	−0.972315	−	0.233673i	$-0.924926\pi$
$641$	0.129052	−	0.565412i	0.00509723	−	0.0223324i	0.977413	+	0.211340i	$0.0677828\pi$
$642$	−4.18424	−	0.630673i	−0.165139	−	0.0248907i
$643$	12.8228	+	16.0793i	0.505682	+	0.634106i	0.967501	−	0.252869i	$-0.0813742\pi$
$643$	12.8228	+	16.0793i	0.505682	+	0.634106i	−0.461818	+	0.886975i	$0.652803\pi$
$644$	12.0754			0.475839
$645$	−7.35157	−	6.06442i	−0.289468	−	0.238786i
$646$	1.57955			0.0621467
$647$	−24.0274	−	30.1293i	−0.944613	−	1.18451i	−0.982695	−	0.185232i	$-0.940696\pi$
$647$	−24.0274	−	30.1293i	−0.944613	−	1.18451i	0.0380821	−	0.999275i	$-0.487875\pi$
$648$	2.66048	+	0.401003i	0.104514	+	0.0157529i
$649$	−0.193067	+	0.845884i	−0.00757856	+	0.0332038i
$650$	3.63866	+	2.48079i	0.142720	+	0.0973047i
$651$	1.24380	+	2.15432i	0.0487483	+	0.0844346i
$652$	−10.7073	+	18.5455i	−0.419328	+	0.726298i
$653$	−40.1593	+	19.3397i	−1.57155	+	0.756821i	−0.998052	−	0.0623836i	$-0.980130\pi$
$653$	−40.1593	+	19.3397i	−1.57155	+	0.756821i	−0.573502	+	0.819204i	$0.694415\pi$
$654$	−5.13768	−	1.58476i	−0.200899	−	0.0619692i
$655$	0.00208177	+	0.0277793i	8.13416e−5	+	0.00108543i
$656$	6.31385	+	27.6628i	0.246514	+	1.08005i
$657$	−4.79897	+	12.2276i	−0.187226	+	0.477043i
$658$	0.114675	−	1.53023i	0.00447049	−	0.0596545i
$659$	−30.2490	+	4.55930i	−1.17833	+	0.177605i	−0.708865	−	0.705344i	$-0.750792\pi$
$659$	−30.2490	+	4.55930i	−1.17833	+	0.177605i	−0.469468	+	0.882949i	$0.655554\pi$
$660$	−5.94941	−	5.52025i	−0.231581	−	0.214875i
$661$	37.2141	+	17.9214i	1.44746	+	0.697060i	0.982152	−	0.188089i	$-0.0602295\pi$
$661$	37.2141	+	17.9214i	1.44746	+	0.697060i	0.465308	+	0.885149i	$0.345944\pi$
$662$	−5.72022	+	3.89998i	−0.222323	+	0.151577i
$663$	1.35328	+	3.44810i	0.0525570	+	0.133913i
$664$	−20.6426	+	6.36739i	−0.801087	+	0.247103i
$665$	−12.2905	+	11.4039i	−0.476605	+	0.442224i
$666$	−3.47242	+	4.35428i	−0.134554	+	0.168725i
$667$	2.19379	−	2.75092i	0.0849438	−	0.106516i
$668$	11.9411	−	11.0797i	0.462013	−	0.428686i
$669$	−27.4030	+	8.45270i	−1.05946	+	0.326800i
$670$	1.59475	+	4.06334i	0.0616104	+	0.156981i
$671$	17.9159	−	12.2148i	0.691634	−	0.471548i
$672$	16.2504	+	7.82577i	0.626872	+	0.301886i
$673$	33.8674	+	31.4244i	1.30549	+	1.21132i	0.962279	+	0.272063i	$0.0877060\pi$
$673$	33.8674	+	31.4244i	1.30549	+	1.21132i	0.343214	+	0.939257i	$0.388485\pi$
$674$	14.0865	−	2.12320i	0.542593	−	0.0817827i
$675$	−1.43011	+	19.0835i	−0.0550450	+	0.734524i
$676$	2.22188	−	5.66126i	0.0854570	−	0.217741i
$677$	1.61108	+	7.05858i	0.0619186	+	0.271283i	0.996405	−	0.0847151i	$-0.0269980\pi$
$677$	1.61108	+	7.05858i	0.0619186	+	0.271283i	−0.934487	+	0.355998i	$0.884141\pi$
$678$	0.516850	+	6.89688i	0.0198495	+	0.264873i
$679$	13.1529	+	4.05714i	0.504762	+	0.155699i
$680$	−1.70277	+	0.820009i	−0.0652981	+	0.0314459i
$681$	2.63878	−	4.57050i	0.101118	−	0.175142i
$682$	0.365541	+	0.633136i	0.0139973	+	0.0242440i
$683$	20.3167	+	13.8517i	0.777397	+	0.530020i	0.885789	−	0.464088i	$-0.153618\pi$
$683$	20.3167	+	13.8517i	0.777397	+	0.530020i	−0.108392	+	0.994108i	$0.534570\pi$
$684$	−2.53688	+	11.1148i	−0.0970000	+	0.424985i
$685$	−0.826244	−	0.124536i	−0.0315692	−	0.00475829i
$686$	−1.51374	−	1.89818i	−0.0577950	−	0.0724727i
$687$	−20.0322			−0.764274
$688$	−18.4989	−	7.61598i	−0.705266	−	0.290357i
$689$	−22.0319			−0.839350
$690$	−0.685222	−	0.859241i	−0.0260859	−	0.0327107i
$691$	−3.45948	−	0.521432i	−0.131605	−	0.0198362i	0.0829095	−	0.996557i	$-0.473579\pi$
$691$	−3.45948	−	0.521432i	−0.131605	−	0.0198362i	−0.214514	+	0.976721i	$0.568817\pi$
$692$	2.94984	−	12.9241i	0.112136	−	0.491300i
$693$	−13.9406	−	9.50452i	−0.529558	−	0.361047i
$694$	5.14250	+	8.90707i	0.195207	+	0.338108i
$695$	9.57248	−	16.5800i	0.363105	−	0.628916i
$696$	3.11274	−	1.49902i	0.117988	−	0.0568201i
$697$	8.88741	+	2.74140i	0.336635	+	0.103838i
$698$	0.367633	+	4.90572i	0.0139151	+	0.185684i
$699$	0.0970365	+	0.425145i	0.00367026	+	0.0160804i
$700$	−8.25344	+	21.0294i	−0.311951	+	0.794838i
$701$	−2.97109	+	39.6465i	−0.112217	+	1.49743i	0.602559	+	0.798074i	$0.294148\pi$
$701$	−2.97109	+	39.6465i	−0.112217	+	1.49743i	−0.714776	+	0.699353i	$0.753471\pi$
$702$	6.77067	−	1.02051i	0.255542	−	0.0385168i
$703$	25.0359	+	23.2299i	0.944246	+	0.876133i
$704$	−11.9322	−	5.74627i	−0.449713	−	0.216571i
$705$	1.30387	−	0.888962i	0.0491065	−	0.0334802i
$706$	4.09770	+	10.4408i	0.154219	+	0.392944i
$707$	−54.8263	+	16.9117i	−2.06196	+	0.636029i
$708$	0.457536	−	0.424532i	0.0171953	−	0.0159549i
$709$	19.6740	−	24.6704i	0.738871	−	0.926515i	−0.260369	−	0.965509i	$-0.583844\pi$
$709$	19.6740	−	24.6704i	0.738871	−	0.926515i	0.999239	+	0.0389947i	$0.0124155\pi$
$710$	−4.22388	+	5.29658i	−0.158520	+	0.198777i
$711$	7.35796	−	6.82719i	0.275945	−	0.256040i
$712$	−20.9541	+	6.46347i	−0.785286	+	0.242229i
$713$	−0.408681	−	1.04130i	−0.0153052	−	0.0389970i
$714$	1.38944	−	0.947302i	0.0519984	−	0.0354519i
$715$	−10.4108	−	5.01358i	−0.389342	−	0.187497i
$716$	−7.73082	−	7.17315i	−0.288914	−	0.268073i
$717$	−10.8282	+	1.63209i	−0.404388	+	0.0609516i
$718$	0.366045	−	4.88453i	0.0136607	−	0.182289i
$719$	0.913695	−	2.32806i	0.0340751	−	0.0868219i	−0.912823	−	0.408354i	$-0.866103\pi$
$719$	0.913695	−	2.32806i	0.0340751	−	0.0868219i	0.946899	+	0.321533i	$0.104198\pi$
$720$	−1.31336	−	5.75422i	−0.0489462	−	0.214447i
$721$	1.20918	+	16.1354i	0.0450322	+	0.600913i
$722$	1.40897	+	0.434608i	0.0524362	+	0.0161744i
$723$	13.9802	−	6.73249i	0.519928	−	0.250384i
$724$	9.58954	−	16.6096i	0.356392	−	0.617290i
$725$	3.29131	+	5.70072i	0.122236	+	0.211719i
$726$	−0.698809	−	0.476440i	−0.0259352	−	0.0176823i
$727$	−1.48278	+	6.49649i	−0.0549933	+	0.240941i	−0.994953	−	0.100345i	$-0.968005\pi$
$727$	−1.48278	+	6.49649i	−0.0549933	+	0.240941i	0.939959	+	0.341286i	$0.110863\pi$
$728$	16.6928	+	2.51603i	0.618675	+	0.0932503i
$729$	13.8581	+	17.3775i	0.513263	+	0.643612i
$730$	4.08408			0.151158
$731$	−5.19378	+	4.00309i	−0.192099	+	0.148059i
$732$	−15.5986			−0.576540
$733$	−19.0950	−	23.9443i	−0.705289	−	0.884404i	0.292117	−	0.956382i	$-0.405640\pi$
$733$	−19.0950	−	23.9443i	−0.705289	−	0.884404i	−0.997406	+	0.0719783i	$0.977069\pi$
$734$	−8.72876	−	1.31565i	−0.322184	−	0.0485615i
$735$	−1.70818	+	7.48404i	−0.0630073	+	0.276053i
$736$	−6.70139	−	4.56893i	−0.247016	−	0.168413i
$737$	13.4688	+	23.3286i	0.496129	+	0.859321i
$738$	2.97043	−	5.14493i	0.109343	−	0.189387i
$739$	38.5470	−	18.5633i	1.41798	−	0.682861i	0.441256	−	0.897381i	$-0.354533\pi$
$739$	38.5470	−	18.5633i	1.41798	−	0.682861i	0.976720	+	0.214520i	$0.0688188\pi$
$740$	−18.6968	−	5.76721i	−0.687309	−	0.212007i
$741$	−1.08429	−	14.4689i	−0.0398325	−	0.531528i
$742$	2.22571	+	9.75146i	0.0817083	+	0.357987i
$743$	−9.10512	+	23.1995i	−0.334034	+	0.851106i	0.660890	+	0.750483i	$0.270179\pi$
$743$	−9.10512	+	23.1995i	−0.334034	+	0.851106i	−0.994925	+	0.100623i	$0.967916\pi$
$744$	0.0820822	−	1.09531i	0.00300928	−	0.0401560i
$745$	−0.985705	+	0.148571i	−0.0361134	+	0.00544322i
$746$	−9.25939	−	8.59146i	−0.339010	−	0.314556i
$747$	−19.9235	−	9.59467i	−0.728964	−	0.351051i
$748$	−4.61405	+	3.14580i	−0.168706	+	0.115022i
$749$	−11.2909	−	28.7689i	−0.412562	−	1.05119i
$750$	4.76478	−	1.46974i	0.173985	−	0.0536674i
$751$	−0.992021	+	0.920461i	−0.0361993	+	0.0335881i	−0.698065	−	0.716034i	$-0.745955\pi$
$751$	−0.992021	+	0.920461i	−0.0361993	+	0.0335881i	0.661866	+	0.749622i	$0.269765\pi$
$752$	2.06541	−	2.58994i	0.0753177	−	0.0944455i
$753$	14.7041	−	18.4384i	0.535848	−	0.671932i
$754$	1.72651	−	1.60197i	0.0628758	−	0.0583402i
$755$	19.6383	−	6.05762i	0.714712	−	0.220459i
$756$	12.8324	+	32.6965i	0.466711	+	1.18916i
$757$	−4.47775	+	3.05287i	−0.162746	+	0.110959i	−0.641955	−	0.766743i	$-0.721876\pi$
$757$	−4.47775	+	3.05287i	−0.162746	+	0.110959i	0.479208	+	0.877701i	$0.340924\pi$
$758$	−4.18572	−	2.01574i	−0.152032	−	0.0732149i
$759$	−4.97167	−	4.61303i	−0.180460	−	0.167442i
$760$	7.32031	−	1.10336i	0.265536	−	0.0400231i
$761$	−1.33244	+	17.7801i	−0.0483008	+	0.644529i	0.919545	+	0.392985i	$0.128558\pi$
$761$	−1.33244	+	17.7801i	−0.0483008	+	0.644529i	−0.967846	+	0.251545i	$0.919062\pi$
$762$	1.47901	−	3.76845i	0.0535789	−	0.136517i
$763$	−8.73797	−	38.2836i	−0.316336	−	1.38596i
$764$	−2.51045	−	33.4997i	−0.0908250	−	1.21198i
$765$	−1.84870	−	0.570248i	−0.0668398	−	0.0206173i
$766$	−6.53812	+	3.14859i	−0.236232	+	0.113763i
$767$	0.444321	−	0.769586i	0.0160435	−	0.0277881i
$768$	2.68825	+	4.65619i	0.0970039	+	0.168016i
$769$	−25.4412	−	17.3455i	−0.917431	−	0.625494i	0.00981259	−	0.999952i	$-0.496877\pi$
$769$	−25.4412	−	17.3455i	−0.917431	−	0.625494i	−0.927244	+	0.374458i	$0.877829\pi$
$770$	−1.16732	+	5.11436i	−0.0420673	+	0.184309i
$771$	2.46399	+	0.371386i	0.0887383	+	0.0133751i
$772$	−8.46872	−	10.6194i	−0.304796	−	0.382202i
$773$	−8.32601			−0.299466			−0.149733	−	0.988726i	$-0.547841\pi$
$773$	−8.32601			−0.299466			−0.149733	+	0.988726i	$0.547841\pi$
$774$	1.75467	+	3.80338i	0.0630703	+	0.136710i
$775$	2.09276			0.0751741
$776$	−3.78932	−	4.75165i	−0.136029	−	0.170574i
$777$	35.9541	+	5.41922i	1.28985	+	0.194413i
$778$	−1.14236	+	5.00502i	−0.0409557	+	0.179439i
$779$	−30.1009	−	20.5224i	−1.07848	−	0.735293i
$780$	4.15621	+	7.19877i	0.148816	+	0.257757i
$781$	−20.9035	+	36.2059i	−0.747985	+	1.29555i
$782$	−0.681316	+	0.328104i	−0.0243638	+	0.0117330i
$783$	9.77996	+	3.01672i	0.349507	+	0.107809i
$784$	1.20423	+	16.0693i	0.0430081	+	0.573903i
$785$	−5.64440	−	24.7297i	−0.201457	−	0.882643i
$786$	−0.00399851	+	0.0101880i	−0.000142622	+	0.000363395i
$787$	−2.09813	+	27.9976i	−0.0747902	+	0.998006i	0.825977	+	0.563704i	$0.190624\pi$
$787$	−2.09813	+	27.9976i	−0.0747902	+	0.998006i	−0.900767	+	0.434302i	$0.856995\pi$
$788$	48.5545	−	7.31842i	1.72968	−	0.260708i
$789$	−1.78676	−	1.65788i	−0.0636105	−	0.0590219i
$790$	−2.81175	−	1.35407i	−0.100038	−	0.0481755i
$791$	−41.7360	+	28.4551i	−1.48396	+	1.01175i
$792$	2.72174	+	6.93488i	0.0967128	+	0.246420i
$793$	−21.2219	+	6.54608i	−0.753611	+	0.232458i
$794$	10.7964	−	10.0176i	0.383150	−	0.355511i
$795$	−6.41331	+	8.04203i	−0.227457	+	0.285222i
$796$	13.3000	−	16.6776i	0.471405	−	0.591123i
$797$	16.5240	−	15.3321i	0.585312	−	0.543090i	−0.330961	−	0.943644i	$-0.607373\pi$
$797$	16.5240	−	15.3321i	0.585312	−	0.543090i	0.916273	+	0.400554i	$0.131182\pi$
$798$	−6.29448	+	1.94159i	−0.222822	+	0.0687315i
$799$	−0.396701	−	1.01078i	−0.0140343	−	0.0357587i
$800$	12.5371	−	8.54767i	0.443255	−	0.302206i
$801$	−20.2242	−	9.73945i	−0.714586	−	0.344127i
$802$	5.45098	+	5.05777i	0.192481	+	0.178596i
$803$	24.9219	−	3.75637i	0.879475	−	0.132560i
$804$	1.44813	−	19.3239i	0.0510715	−	0.681502i
$805$	2.93249	−	7.47187i	0.103357	−	0.263349i
$806$	−0.166619	−	0.730007i	−0.00586891	−	0.0257134i
$807$	−0.0577616	−	0.770775i	−0.00203330	−	0.0271326i
$808$	24.2082	+	7.46724i	0.851642	+	0.262697i
$809$	32.9062	−	15.8468i	1.15692	−	0.557143i	0.245814	−	0.969317i	$-0.420945\pi$
$809$	32.9062	−	15.8468i	1.15692	−	0.557143i	0.911105	+	0.412174i	$0.135230\pi$
$810$	0.428163	−	0.741600i	0.0150441	−	0.0260572i
$811$	19.2998	+	33.4282i	0.677706	+	1.17382i	0.975670	+	0.219245i	$0.0703593\pi$
$811$	19.2998	+	33.4282i	0.677706	+	1.17382i	−0.297964	+	0.954577i	$0.596307\pi$
$812$	9.98254	+	6.80598i	0.350319	+	0.238843i
$813$	5.08688	−	22.2871i	0.178405	−	0.781642i
$814$	10.5666	+	1.59266i	0.370359	+	0.0558226i
$815$	8.87509	+	11.1290i	0.310881	+	0.389832i
$816$	3.63026			0.127085
$817$	24.0625	−	8.98714i	0.841839	−	0.314420i
$818$	−7.70404			−0.269365
$819$	10.7744	+	13.5107i	0.376488	+	0.472100i
$820$	20.6382	+	3.11071i	0.720717	+	0.108631i
$821$	7.84725	−	34.3810i	0.273871	−	1.19991i	−0.631531	−	0.775351i	$-0.717573\pi$
$821$	7.84725	−	34.3810i	0.273871	−	1.19991i	0.905402	−	0.424556i	$-0.139570\pi$
$822$	−0.271240	−	0.184928i	−0.00946058	−	0.00645011i
$823$	−22.8440	−	39.5669i	−0.796291	−	1.37922i	−0.922016	−	0.387152i	$-0.873459\pi$
$823$	−22.8440	−	39.5669i	−0.796291	−	1.37922i	0.125725	−	0.992065i	$-0.459874\pi$
$824$	3.57223	−	6.18728i	0.124444	−	0.215544i
$825$	11.4317	−	5.50521i	0.398001	−	0.191667i
$826$	−0.385509	−	0.118914i	−0.0134136	−	0.00413754i
$827$	4.04410	+	53.9647i	0.140627	+	1.87654i	0.408051	+	0.912959i	$0.366208\pi$
$827$	4.04410	+	53.9647i	0.140627	+	1.87654i	−0.267424	+	0.963579i	$0.586173\pi$
$828$	−1.21452	−	5.32115i	−0.0422074	−	0.184923i
$829$	8.95575	−	22.8189i	0.311046	−	0.792532i	−0.686795	−	0.726851i	$-0.740983\pi$
$829$	8.95575	−	22.8189i	0.311046	−	0.792532i	0.997841	−	0.0656808i	$-0.0209219\pi$
$830$	−0.513803	+	6.85622i	−0.0178344	+	0.237983i
$831$	−23.7796	+	3.58419i	−0.824904	+	0.124334i
$832$	9.94341	+	9.22614i	0.344726	+	0.319859i
$833$	4.75894	+	2.29179i	0.164888	+	0.0794057i
$834$	6.21472	−	4.23712i	0.215198	−	0.146720i
$835$	−3.95587	−	10.0794i	−0.136898	−	0.348812i
$836$	20.9027	−	6.44763i	0.722935	−	0.222996i
$837$	2.38522	−	2.21316i	0.0824452	−	0.0764979i
$838$	−5.35275	+	6.71213i	−0.184908	+	0.231867i
$839$	28.6011	−	35.8647i	0.987420	−	1.23819i	0.0162327	−	0.999868i	$-0.494833\pi$
$839$	28.6011	−	35.8647i	0.987420	−	1.23819i	0.971187	−	0.238317i	$-0.0765958\pi$
$840$	5.77752	−	5.36075i	0.199343	−	0.184963i
$841$	−24.3476	+	7.51023i	−0.839571	+	0.258973i
$842$	4.76973	+	12.1531i	0.164376	+	0.418823i
$843$	12.3846	−	8.44369i	0.426549	−	0.290816i
$844$	18.6008	+	8.95766i	0.640265	+	0.308335i
$845$	−2.96342	−	2.74965i	−0.101945	−	0.0945908i
$846$	−0.685842	+	0.103374i	−0.0235797	+	0.00355407i
$847$	0.461621	−	6.15990i	0.0158615	−	0.211657i
$848$	−7.88860	+	20.0998i	−0.270896	+	0.690231i
$849$	−1.15714	−	5.06974i	−0.0397128	−	0.173993i
$850$	−0.105723	−	1.41077i	−0.00362625	−	0.0483890i
$851$	−15.6241	−	4.81941i	−0.535589	−	0.165207i
$852$	27.0964	−	13.0489i	0.928306	−	0.447049i
$853$	−8.52373	+	14.7635i	−0.291847	+	0.505494i	−0.974246	−	0.225486i	$-0.927603\pi$
$853$	−8.52373	+	14.7635i	−0.291847	+	0.505494i	0.682400	+	0.730979i	$0.260936\pi$
$854$	5.04121	+	8.73162i	0.172507	+	0.298790i
$855$	6.26138	+	4.26894i	0.214135	+	0.145995i
$856$	−3.03652	+	13.3039i	−0.103786	+	0.454716i
$857$	−36.4988	−	5.50131i	−1.24678	−	0.187921i	−0.507695	−	0.861537i	$-0.669502\pi$
$857$	−36.4988	−	5.50131i	−1.24678	−	0.187921i	−0.739082	+	0.673616i	$0.764740\pi$
$858$	−2.83052	−	3.54935i	−0.0966322	−	0.121173i
$859$	−33.2972			−1.13609			−0.568043	−	0.822999i	$-0.692299\pi$
$859$	−33.2972			−1.13609			−0.568043	+	0.822999i	$0.692299\pi$
$860$	−10.1862	+	10.6200i	−0.347346	+	0.362140i
$861$	−38.7858			−1.32182
$862$	−5.71903	−	7.17144i	−0.194791	−	0.244260i
$863$	−22.5870	−	3.40445i	−0.768872	−	0.115889i	−0.247119	−	0.968985i	$-0.579484\pi$
$863$	−22.5870	−	3.40445i	−0.768872	−	0.115889i	−0.521753	+	0.853096i	$0.674722\pi$
$864$	5.24974	−	23.0006i	0.178600	−	0.782497i
$865$	−7.28062	−	4.96384i	−0.247548	−	0.168776i
$866$	0.471548	+	0.816746i	0.0160239	+	0.0277541i
$867$	0.594971	−	1.03052i	0.0202063	−	0.0349983i
$868$	3.46071	−	1.66659i	0.117464	−	0.0565678i
$869$	−18.4033	−	5.67667i	−0.624290	−	0.192568i
$870$	−0.0821731	−	1.09652i	−0.00278593	−	0.0371757i
$871$	−6.13928	−	26.8980i	−0.208022	−	0.911402i
$872$	−6.33449	+	16.1400i	−0.214513	+	0.546570i
$873$	0.464926	−	6.20400i	0.0157354	−	0.209974i
$874$	2.92903	−	0.441480i	0.0990758	−	0.0149333i
$875$	26.6963	+	24.7705i	0.902499	+	0.837397i
$876$	−16.3351	−	7.86658i	−0.551912	−	0.265787i
$877$	−7.30031	+	4.97727i	−0.246514	+	0.168070i	−0.680274	−	0.732958i	$-0.738139\pi$
$877$	−7.30031	+	4.97727i	−0.246514	+	0.168070i	0.433760	+	0.901029i	$0.357187\pi$
$878$	2.67071	+	6.80485i	0.0901319	+	0.229652i
$879$	−35.5292	+	10.9593i	−1.19837	+	0.369648i
$880$	−8.30153	+	7.70270i	−0.279845	+	0.259658i
$881$	−3.70180	+	4.64191i	−0.124717	+	0.156390i	−0.840270	−	0.542169i	$-0.817603\pi$
$881$	−3.70180	+	4.64191i	−0.124717	+	0.156390i	0.715553	+	0.698559i	$0.246175\pi$
$882$	2.10362	−	2.63786i	0.0708326	−	0.0888213i
$883$	−35.5591	+	32.9940i	−1.19666	+	1.11034i	−0.205361	+	0.978686i	$0.565837\pi$
$883$	−35.5591	+	32.9940i	−1.19666	+	1.11034i	−0.991296	+	0.131650i	$0.957973\pi$
$884$	5.46548	−	1.68588i	0.183824	−	0.0567022i
$885$	−0.151574	−	0.386204i	−0.00509511	−	0.0129821i
$886$	3.91852	−	2.67160i	0.131645	−	0.0897542i
$887$	9.11980	+	4.39187i	0.306213	+	0.147464i	0.580679	−	0.814132i	$-0.302787\pi$
$887$	9.11980	+	4.39187i	0.306213	+	0.147464i	−0.274466	+	0.961597i	$0.588501\pi$
$888$	−11.7689	−	10.9199i	−0.394938	−	0.366449i
$889$	29.2369	−	4.40675i	0.980574	−	0.147798i
$890$	−0.521556	+	6.95968i	−0.0174826	+	0.233289i
$891$	1.93065	−	4.91921i	0.0646792	−	0.164800i
$892$	9.85327	+	43.1700i	0.329912	+	1.44544i
$893$	0.317850	+	4.24142i	0.0106365	+	0.141934i
$894$	−0.374240	−	0.115438i	−0.0125165	−	0.00386081i
$895$	−6.31591	+	3.04158i	−0.211118	+	0.101669i
$896$	18.2365	−	31.5866i	0.609240	−	1.05523i
$897$	3.47317	+	6.01570i	0.115966	+	0.200858i
$898$	−6.02580	−	4.10832i	−0.201084	−	0.137097i
$899$	0.249051	−	1.09117i	0.00830633	−	0.0363924i
$900$	10.0969	+	1.52186i	0.336564	+	0.0507288i
$901$	4.41285	+	5.53354i	0.147013	+	0.184349i
$902$	−11.3988			−0.379538
$903$	15.7764	−	22.3364i	0.525007	−	0.743308i
$904$	22.3038			0.741813
$905$	−7.94863	−	9.96727i	−0.264221	−	0.331323i
$906$	7.98407	+	1.20340i	0.265253	+	0.0399804i
$907$	0.859461	−	3.76555i	0.0285379	−	0.125033i	−0.958652	−	0.284579i	$-0.908146\pi$
$907$	0.859461	−	3.76555i	0.0285379	−	0.125033i	0.987190	+	0.159547i	$0.0510032\pi$
$908$	−6.73309	−	4.59054i	−0.223445	−	0.152343i
$909$	12.9666	+	22.4588i	0.430074	+	0.744911i
$910$	2.68644	−	4.65305i	0.0890547	−	0.154247i
$911$	−42.7895	+	20.6063i	−1.41768	+	0.682718i	−0.976662	−	0.214781i	$-0.931096\pi$
$911$	−42.7895	+	20.6063i	−1.41768	+	0.682718i	−0.441017	+	0.897499i	$0.645382\pi$
$912$	−13.5883	−	4.19143i	−0.449953	−	0.138792i
$913$	3.17075	+	42.3107i	0.104937	+	1.40028i
$914$	1.66803	+	7.30813i	0.0551736	+	0.241731i
$915$	−3.78807	+	9.65186i	−0.125230	+	0.319081i
$916$	−2.31153	+	30.8452i	−0.0763750	+	1.01915i
$917$	−0.0790420	+	0.0119137i	−0.00261020	+	0.000393424i
$918$	−1.61243	−	1.49612i	−0.0532181	−	0.0493792i
$919$	−39.3747	−	18.9619i	−1.29885	−	0.625495i	−0.348687	−	0.937239i	$-0.613372\pi$
$919$	−39.3747	−	18.9619i	−1.29885	−	0.625495i	−0.950166	+	0.311745i	$0.899087\pi$
$920$	−2.92831	+	1.99649i	−0.0965436	+	0.0658223i
$921$	−11.2222	−	28.5937i	−0.369784	−	0.942194i
$922$	−5.90159	+	1.82040i	−0.194359	+	0.0599517i
$923$	31.3885	−	29.1243i	1.03317	−	0.958639i
$924$	14.5200	−	18.2075i	0.477673	−	0.598983i
$925$	19.0720	−	23.9155i	0.627082	−	0.786336i
$926$	−2.72501	+	2.52844i	−0.0895493	+	0.0830896i
$927$	6.98859	−	2.15569i	0.229535	−	0.0708023i
$928$	−2.96476	−	7.55409i	−0.0973231	−	0.247975i
$929$	−1.21448	+	0.828016i	−0.0398457	+	0.0271663i	−0.583079	−	0.812415i	$-0.698152\pi$
$929$	−1.21448	+	0.828016i	−0.0398457	+	0.0271663i	0.543233	+	0.839582i	$0.317200\pi$
$930$	−0.314966	−	0.151680i	−0.0103282	−	0.00497378i
$931$	−15.1669	−	14.0729i	−0.497076	−	0.461219i
$932$	0.665828	−	0.100357i	0.0218099	−	0.00328731i
$933$	−1.97792	+	26.3934i	−0.0647540	+	0.864082i
$934$	1.93637	−	4.93380i	0.0633601	−	0.161439i
$935$	0.826005	+	3.61896i	0.0270132	+	0.118353i
$936$	−0.570206	−	7.60887i	−0.0186378	−	0.248704i
$937$	52.0378	+	16.0515i	1.70000	+	0.524381i	0.984673	−	0.174409i	$-0.0558014\pi$
$937$	52.0378	+	16.0515i	1.70000	+	0.524381i	0.715327	+	0.698789i	$0.246278\pi$
$938$	−11.2850	+	5.43456i	−0.368468	+	0.177445i
$939$	−0.808004	+	1.39950i	−0.0263682	+	0.0456711i
$940$	−1.21835	−	2.11025i	−0.0397383	−	0.0688288i
$941$	7.76408	+	5.29346i	0.253102	+	0.172562i	0.683224	−	0.730209i	$-0.260577\pi$
$941$	7.76408	+	5.29346i	0.253102	+	0.172562i	−0.430122	+	0.902771i	$0.641530\pi$
$942$	2.21758	−	9.71586i	0.0722527	−	0.316560i
$943$	17.2465	+	2.59949i	0.561622	+	0.0846509i
$944$	−0.543006	−	0.680908i	−0.0176733	−	0.0221617i
$945$	23.3478			0.759504
$946$	4.63655	−	6.56445i	0.150747	−	0.213429i
$947$	−33.0835			−1.07507			−0.537535	−	0.843242i	$-0.680644\pi$
$947$	−33.0835			−1.07507			−0.537535	+	0.843242i	$0.680644\pi$
$948$	8.63803	+	10.8317i	0.280550	+	0.351799i
$949$	−25.5252	−	3.84731i	−0.828584	−	0.124889i
$950$	−1.23312	+	5.40265i	−0.0400077	+	0.175285i
$951$	−21.5753	−	14.7098i	−0.699627	−	0.476998i
$952$	−2.71152	−	4.69650i	−0.0878810	−	0.152214i
$953$	−2.79196	+	4.83581i	−0.0904404	+	0.156647i	−0.907697	−	0.419627i	$-0.862161\pi$
$953$	−2.79196	+	4.83581i	−0.0904404	+	0.156647i	0.817256	+	0.576275i	$0.195494\pi$
$954$	4.07321	−	1.96156i	0.131875	−	0.0635077i
$955$	−21.3381	−	6.58193i	−0.690484	−	0.212986i
$956$	1.26359	+	16.8614i	0.0408674	+	0.545338i
$957$	−1.50998	−	6.61565i	−0.0488107	−	0.213854i
$958$	0.232866	−	0.593333i	0.00752356	−	0.0191697i
$959$	0.179176	−	2.39094i	0.00578590	−	0.0772075i
$960$	6.26214	−	0.943865i	0.202110	−	0.0304631i
$961$	22.4638	+	20.8433i	0.724638	+	0.672366i
$962$	−9.86077	−	4.74870i	−0.317924	−	0.153104i
$963$	−11.5416	+	7.86895i	−0.371924	+	0.253574i
$964$	−8.75340	−	22.3033i	−0.281928	−	0.718341i
$965$	−8.62755	+	2.66125i	−0.277731	+	0.0856686i
$966$	2.31172	−	2.14496i	0.0743783	−	0.0690129i
$967$	−16.0081	+	20.0735i	−0.514786	+	0.645522i	−0.969493	−	0.245120i	$-0.921173\pi$
$967$	−16.0081	+	20.0735i	−0.514786	+	0.645522i	0.454706	+	0.890641i	$0.349744\pi$
$968$	−1.70056	+	2.13244i	−0.0546581	+	0.0685391i
$969$	−3.41683	+	3.17035i	−0.109764	+	0.101846i
$970$	−1.84840	+	0.570156i	−0.0593486	+	0.0183066i
$971$	−3.02144	−	7.69849i	−0.0969625	−	0.247056i	0.874160	−	0.485638i	$-0.161413\pi$
$971$	−3.02144	−	7.69849i	−0.0969625	−	0.247056i	−0.971122	+	0.238582i	$0.923317\pi$
$972$	21.7019	−	14.7961i	0.696090	−	0.474586i
$973$	49.4951	+	23.8356i	1.58674	+	0.764134i
$974$	2.70193	+	2.50702i	0.0865753	+	0.0803301i
$975$	−12.8502	+	1.93686i	−0.411537	+	0.0620292i
$976$	−1.62654	+	21.7047i	−0.0520643	+	0.694749i
$977$	−13.2577	+	33.7799i	−0.424150	+	1.08072i	0.545909	+	0.837845i	$0.316185\pi$
$977$	−13.2577	+	33.7799i	−0.424150	+	1.08072i	−0.970058	+	0.242872i	$0.921911\pi$
$978$	1.24445	+	5.45227i	0.0397930	+	0.174344i
$979$	3.21859	+	42.9492i	0.102867	+	1.37266i
$980$	11.3267	+	3.49382i	0.361818	+	0.111606i
$981$	−15.9912	+	7.70093i	−0.510558	+	0.245872i
$982$	−2.21276	+	3.83261i	−0.0706119	+	0.122303i
$983$	0.999886	+	1.73185i	0.0318914	+	0.0552375i	0.881531	−	0.472127i	$-0.156514\pi$
$983$	0.999886	+	1.73185i	0.0318914	+	0.0552375i	−0.849639	+	0.527364i	$0.823180\pi$
$984$	14.1498	+	9.64720i	0.451080	+	0.307541i
$985$	7.26297	−	31.8211i	0.231417	−	1.01391i
$986$	−0.748158	−	0.112767i	−0.0238262	−	0.00359122i
$987$	2.82329	+	3.54029i	0.0898663	+	0.112689i
$988$	−22.4041			−0.712769
$989$	−8.51216	+	8.87471i	−0.270671	+	0.282199i
$990$	2.37110			0.0753584
$991$	−10.3784	−	13.0141i	−0.329680	−	0.413405i	0.589172	−	0.808007i	$-0.299454\pi$
$991$	−10.3784	−	13.0141i	−0.329680	−	0.413405i	−0.918852	+	0.394602i	$0.870882\pi$
$992$	−2.55114	−	0.384522i	−0.0809987	−	0.0122086i
$993$	4.54602	−	19.9174i	0.144264	−	0.632061i
$994$	−16.0615	−	10.9506i	−0.509440	−	0.347330i
$995$	−7.08968	−	12.2797i	−0.224758	−	0.389292i
$996$	15.2612	−	26.4332i	0.483570	−	0.837568i
$997$	−18.0929	+	8.71307i	−0.573007	+	0.275946i	−0.697866	−	0.716229i	$-0.745867\pi$
$997$	−18.0929	+	8.71307i	−0.573007	+	0.275946i	0.124858	+	0.992175i	$0.460152\pi$
$998$	0.845615	+	0.260838i	0.0267675	+	0.00825667i
$999$	−3.55415	−	47.4268i	−0.112448	−	1.50052i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.u.b.52.14	✓	348
43.24	even	21	inner	731.2.u.b.239.14	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.u.b.52.14	✓	348	1.1	even	1	trivial
731.2.u.b.239.14	yes	348	43.24	even	21	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.u (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.251421 - 0.315272i) q^{2} +(1.17665 + 0.177352i) q^{3} +(0.408858 - 1.79132i) q^{4} +(-1.00912 - 0.688006i) q^{5} +(-0.239921 - 0.415555i) q^{6} +(1.75229 - 3.03505i) q^{7} +(-1.39418 + 0.671401i) q^{8} +(-1.51366 - 0.466903i) q^{9} +O(q^{10})\)	\(q+(-0.251421 - 0.315272i) q^{2} +(1.17665 + 0.177352i) q^{3} +(0.408858 - 1.79132i) q^{4} +(-1.00912 - 0.688006i) q^{5} +(-0.239921 - 0.415555i) q^{6} +(1.75229 - 3.03505i) q^{7} +(-1.39418 + 0.671401i) q^{8} +(-1.51366 - 0.466903i) q^{9} +(0.0368048 + 0.491126i) q^{10} +(0.676310 + 2.96311i) q^{11} +(0.798778 - 2.03525i) q^{12} +(0.232626 - 3.10418i) q^{13} +(-1.39743 + 0.210628i) q^{14} +(-1.06536 - 0.988513i) q^{15} +(-2.74866 - 1.32369i) q^{16} +(-0.826239 + 0.563320i) q^{17} +(0.233365 + 0.594604i) q^{18} +(3.74305 - 1.15458i) q^{19} +(-1.64503 + 1.52636i) q^{20} +(2.60010 - 3.26043i) q^{21} +(0.764146 - 0.958209i) q^{22} +(-1.37468 + 1.27552i) q^{23} +(-1.75954 + 0.542745i) q^{24} +(-1.28174 - 3.26581i) q^{25} +(-1.03715 + 0.707116i) q^{26} +(-4.91455 - 2.36672i) q^{27} +(-4.72032 - 4.37982i) q^{28} +(-1.85533 + 0.279646i) q^{29} +(-0.0437956 + 0.584412i) q^{30} +(-0.217930 + 0.555277i) q^{31} +(0.962418 + 4.21663i) q^{32} +(0.270269 + 3.60649i) q^{33} +(0.385333 + 0.118859i) q^{34} +(-3.85640 + 1.85714i) q^{35} +(-1.45525 + 2.52056i) q^{36} +(4.35949 + 7.55086i) q^{37} +(-1.30509 - 0.889795i) q^{38} +(0.824252 - 3.61128i) q^{39} +(1.86882 + 0.281679i) q^{40} +(-5.79884 - 7.27151i) q^{41} -1.68164 q^{42} +(6.54632 - 0.381747i) q^{43} +5.58440 q^{44} +(1.20623 + 1.51257i) q^{45} +(0.747757 + 0.112706i) q^{46} +(-0.241622 + 1.05861i) q^{47} +(-2.99946 - 2.04500i) q^{48} +(-2.64101 - 4.57437i) q^{49} +(-0.707363 + 1.22519i) q^{50} +(-1.07210 + 0.516297i) q^{51} +(-5.46548 - 1.68588i) q^{52} +(-0.528914 - 7.05787i) q^{53} +(0.489460 + 2.14446i) q^{54} +(1.35616 - 3.45543i) q^{55} +(-0.405265 + 5.40788i) q^{56} +(4.60904 - 0.694701i) q^{57} +(0.554633 + 0.514625i) q^{58} +(0.257201 + 0.123862i) q^{59} +(-2.20633 + 1.50425i) q^{60} +(-2.60649 - 6.64122i) q^{61} +(0.229856 - 0.0709011i) q^{62} +(-4.06944 + 3.77589i) q^{63} +(-2.71686 + 3.40683i) q^{64} +(-2.37044 + 2.97244i) q^{65} +(1.06907 - 0.991956i) q^{66} +(8.46930 - 2.61243i) q^{67} +(0.671274 + 1.71038i) q^{68} +(-1.84373 + 1.25704i) q^{69} +(1.55508 + 0.748889i) q^{70} +(10.0834 + 9.35605i) q^{71} +(2.42379 - 0.365328i) q^{72} +(0.619698 - 8.26930i) q^{73} +(1.28451 - 3.27287i) q^{74} +(-0.928960 - 4.07004i) q^{75} +(-0.537848 - 7.17708i) q^{76} +(10.1783 + 3.13958i) q^{77} +(-1.34577 + 0.648089i) q^{78} +(-3.16831 + 5.48767i) q^{79} +(1.86303 + 3.22686i) q^{80} +(-1.43660 - 0.979457i) q^{81} +(-0.834554 + 3.65642i) q^{82} +(13.8043 + 2.08066i) q^{83} +(-4.77741 - 5.99068i) q^{84} +1.22134 q^{85} +(-1.76624 - 1.96789i) q^{86} -2.23267 q^{87} +(-2.93233 - 3.67702i) q^{88} +(14.0126 + 2.11206i) q^{89} +(0.173598 - 0.760583i) q^{90} +(-9.01371 - 6.14545i) q^{91} +(1.72281 + 2.98400i) q^{92} +(-0.354907 + 0.614718i) q^{93} +(0.394500 - 0.189981i) q^{94} +(-4.57155 - 1.41014i) q^{95} +(0.384604 + 5.13219i) q^{96} +(0.873965 + 3.82909i) q^{97} +(-0.778165 + 1.98273i) q^{98} +(0.359779 - 4.80091i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 6 q^{2} - 3 q^{3} - 54 q^{4} + q^{5} - 12 q^{6} + 49 q^{7} - 2 q^{8} + 8 q^{9}+O(q^{10}) \) 348 * q + 6 * q^2 - 3 * q^3 - 54 * q^4 + q^5 - 12 * q^6 + 49 * q^7 - 2 * q^8 + 8 * q^9	\( 348 q + 6 q^{2} - 3 q^{3} - 54 q^{4} + q^{5} - 12 q^{6} + 49 q^{7} - 2 q^{8} + 8 q^{9} - 4 q^{10} - 16 q^{11} - 12 q^{12} - 9 q^{13} - 3 q^{14} - 14 q^{15} - 30 q^{16} - 29 q^{17} - 204 q^{18} - 8 q^{19} + 61 q^{20} + 26 q^{21} + 85 q^{22} - 79 q^{23} - 12 q^{24} + 22 q^{25} - 14 q^{26} + 12 q^{27} - 15 q^{28} + 54 q^{29} - 46 q^{30} - 52 q^{31} + 33 q^{32} + 39 q^{33} + 3 q^{34} + 32 q^{35} - 161 q^{36} + 68 q^{37} - 29 q^{38} + 61 q^{39} + 107 q^{40} + 63 q^{41} - 56 q^{42} - 45 q^{43} - 74 q^{44} + 144 q^{45} - 22 q^{46} - 70 q^{47} + 168 q^{48} - 119 q^{49} + 97 q^{50} - 6 q^{51} + 27 q^{52} + 10 q^{53} - 34 q^{54} - 78 q^{55} - 44 q^{56} - 40 q^{57} - 38 q^{58} - 47 q^{59} - 72 q^{60} - 76 q^{61} - 41 q^{62} + 63 q^{63} - 112 q^{64} - 31 q^{65} - 598 q^{66} - 39 q^{67} - 20 q^{68} - 17 q^{69} - 72 q^{70} - 37 q^{71} + 245 q^{72} + 14 q^{73} + 77 q^{74} - 121 q^{75} + 152 q^{76} + 59 q^{77} + 220 q^{78} + 4 q^{79} - 42 q^{80} - 109 q^{81} + 148 q^{82} + 59 q^{83} + 390 q^{84} + 2 q^{85} + 12 q^{86} - 78 q^{87} + 344 q^{88} - 103 q^{89} - 75 q^{90} + 148 q^{91} + 28 q^{92} + 140 q^{93} + 24 q^{94} - 302 q^{95} + 22 q^{96} + 57 q^{97} - 72 q^{98} - 128 q^{99}+O(q^{100}) \) 348 * q + 6 * q^2 - 3 * q^3 - 54 * q^4 + q^5 - 12 * q^6 + 49 * q^7 - 2 * q^8 + 8 * q^9 - 4 * q^10 - 16 * q^11 - 12 * q^12 - 9 * q^13 - 3 * q^14 - 14 * q^15 - 30 * q^16 - 29 * q^17 - 204 * q^18 - 8 * q^19 + 61 * q^20 + 26 * q^21 + 85 * q^22 - 79 * q^23 - 12 * q^24 + 22 * q^25 - 14 * q^26 + 12 * q^27 - 15 * q^28 + 54 * q^29 - 46 * q^30 - 52 * q^31 + 33 * q^32 + 39 * q^33 + 3 * q^34 + 32 * q^35 - 161 * q^36 + 68 * q^37 - 29 * q^38 + 61 * q^39 + 107 * q^40 + 63 * q^41 - 56 * q^42 - 45 * q^43 - 74 * q^44 + 144 * q^45 - 22 * q^46 - 70 * q^47 + 168 * q^48 - 119 * q^49 + 97 * q^50 - 6 * q^51 + 27 * q^52 + 10 * q^53 - 34 * q^54 - 78 * q^55 - 44 * q^56 - 40 * q^57 - 38 * q^58 - 47 * q^59 - 72 * q^60 - 76 * q^61 - 41 * q^62 + 63 * q^63 - 112 * q^64 - 31 * q^65 - 598 * q^66 - 39 * q^67 - 20 * q^68 - 17 * q^69 - 72 * q^70 - 37 * q^71 + 245 * q^72 + 14 * q^73 + 77 * q^74 - 121 * q^75 + 152 * q^76 + 59 * q^77 + 220 * q^78 + 4 * q^79 - 42 * q^80 - 109 * q^81 + 148 * q^82 + 59 * q^83 + 390 * q^84 + 2 * q^85 + 12 * q^86 - 78 * q^87 + 344 * q^88 - 103 * q^89 - 75 * q^90 + 148 * q^91 + 28 * q^92 + 140 * q^93 + 24 * q^94 - 302 * q^95 + 22 * q^96 + 57 * q^97 - 72 * q^98 - 128 * q^99

Introduction

L-functions

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