LMFDB - Embedded newform 483.2.q.d.64.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			64.3
Character	$\chi$	$=$	483.64
Dual form			483.2.q.d.400.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0618105 - 0.0181492i) q^{2} +(0.654861 - 0.755750i) q^{3} +(-1.67902 - 1.07904i) q^{4} +(-0.424340 + 2.95135i) q^{5} +(-0.0541936 + 0.0348281i) q^{6} +(0.415415 + 0.909632i) q^{7} +(0.168569 + 0.194540i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.0618105 - 0.0181492i) q^{2} +(0.654861 - 0.755750i) q^{3} +(-1.67902 - 1.07904i) q^{4} +(-0.424340 + 2.95135i) q^{5} +(-0.0541936 + 0.0348281i) q^{6} +(0.415415 + 0.909632i) q^{7} +(0.168569 + 0.194540i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.0797933 - 0.174723i) q^{10} +(-5.22740 + 1.53490i) q^{11} +(-1.91500 + 0.562296i) q^{12} +(0.149653 - 0.327694i) q^{13} +(-0.00916792 - 0.0637643i) q^{14} +(1.95260 + 2.25342i) q^{15} +(1.65132 + 3.61589i) q^{16} +(-3.74487 + 2.40668i) q^{17} +(-0.00916792 + 0.0637643i) q^{18} +(-2.77782 - 1.78519i) q^{19} +(3.89709 - 4.49748i) q^{20} +(0.959493 + 0.281733i) q^{21} +0.350966 q^{22} +(0.157333 + 4.79325i) q^{23} +0.257413 q^{24} +(-3.73293 - 1.09609i) q^{25} +(-0.0151975 + 0.0175388i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(0.284039 - 1.97554i) q^{28} +(-2.90293 + 1.86560i) q^{29} +(-0.0797933 - 0.174723i) q^{30} +(4.76100 + 5.49448i) q^{31} +(-0.109711 - 0.763056i) q^{32} +(-2.26322 + 4.95576i) q^{33} +(0.275152 - 0.0807919i) q^{34} +(-2.86092 + 0.840041i) q^{35} +(-0.829106 + 1.81549i) q^{36} +(0.108745 + 0.756341i) q^{37} +(0.139298 + 0.160759i) q^{38} +(-0.149653 - 0.327694i) q^{39} +(-0.645685 + 0.414956i) q^{40} +(0.370060 - 2.57382i) q^{41} +(-0.0541936 - 0.0348281i) q^{42} +(-0.763111 + 0.880676i) q^{43} +(10.4331 + 3.06344i) q^{44} +2.98170 q^{45} +(0.0772689 - 0.299129i) q^{46} +3.36482 q^{47} +(3.81410 + 1.11992i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(0.210841 + 0.135499i) q^{50} +(-0.633520 + 4.40623i) q^{51} +(-0.604863 + 0.388722i) q^{52} +(4.66494 + 10.2148i) q^{53} +(0.0421861 + 0.0486854i) q^{54} +(-2.31184 - 16.0792i) q^{55} +(-0.106933 + 0.234151i) q^{56} +(-3.16824 + 0.930280i) q^{57} +(0.213291 - 0.0626278i) q^{58} +(4.14385 - 9.07376i) q^{59} +(-0.846919 - 5.89045i) q^{60} +(-6.29161 - 7.26091i) q^{61} +(-0.194559 - 0.426025i) q^{62} +(0.841254 - 0.540641i) q^{63} +(1.12437 - 7.82016i) q^{64} +(0.903634 + 0.580731i) q^{65} +(0.229834 - 0.265242i) q^{66} +(-8.16946 - 2.39877i) q^{67} +8.88460 q^{68} +(3.72553 + 3.02001i) q^{69} +0.192081 q^{70} +(2.75019 + 0.807528i) q^{71} +(0.168569 - 0.194540i) q^{72} +(-8.58939 - 5.52006i) q^{73} +(0.00700538 - 0.0487235i) q^{74} +(-3.27291 + 2.10337i) q^{75} +(2.73770 + 5.99474i) q^{76} +(-3.56774 - 4.11739i) q^{77} +(0.00330273 + 0.0229710i) q^{78} +(5.60240 - 12.2676i) q^{79} +(-11.3725 + 3.33926i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-0.0695865 + 0.152373i) q^{82} +(0.333696 + 2.32091i) q^{83} +(-1.30700 - 1.50836i) q^{84} +(-5.51386 - 12.0737i) q^{85} +(0.0631519 - 0.0405852i) q^{86} +(-0.491088 + 3.41559i) q^{87} +(-1.17978 - 0.758199i) q^{88} +(-9.53851 + 11.0080i) q^{89} +(-0.184300 - 0.0541155i) q^{90} +0.360249 q^{91} +(4.90793 - 8.21771i) q^{92} +7.27024 q^{93} +(-0.207981 - 0.0610688i) q^{94} +(6.44747 - 7.44077i) q^{95} +(-0.648524 - 0.416781i) q^{96} +(-2.31779 + 16.1206i) q^{97} +(0.0541936 - 0.0348281i) q^{98} +(2.26322 + 4.95576i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9}+O(q^{10}) $ 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 22 q^{13} - q^{14} + 2 q^{15} - 27 q^{16} + q^{17} - q^{18} + 20 q^{19} - 75 q^{20} + 6 q^{21} - 16 q^{22} - 9 q^{23} - 36 q^{24} - 15 q^{25} - 16 q^{26} + 6 q^{27} - 14 q^{28} - 3 q^{29} + 17 q^{31} - 73 q^{32} - 5 q^{33} + 55 q^{34} - 2 q^{35} - 14 q^{36} + 56 q^{37} - 22 q^{38} - 22 q^{39} - 37 q^{40} - 18 q^{41} + 12 q^{42} - 19 q^{43} - 12 q^{44} + 20 q^{45} - 45 q^{46} + 42 q^{47} - 28 q^{48} - 6 q^{49} - 42 q^{50} - q^{51} + 76 q^{52} - 11 q^{53} - 10 q^{54} - 61 q^{55} + 3 q^{56} + 24 q^{57} - 78 q^{58} + 38 q^{59} + 31 q^{60} + 5 q^{61} + 69 q^{62} - 6 q^{63} - 27 q^{64} + 51 q^{65} + 49 q^{66} - 27 q^{67} + 112 q^{68} - 13 q^{69} + 22 q^{70} - 4 q^{71} + 25 q^{72} + 48 q^{73} - 62 q^{74} + 26 q^{75} - 85 q^{76} - 28 q^{77} - 6 q^{78} - 6 q^{79} + 169 q^{80} - 6 q^{81} - 200 q^{82} - 6 q^{83} + 3 q^{84} - 21 q^{85} - 180 q^{86} + 14 q^{87} + 211 q^{88} - 57 q^{89} - 22 q^{91} + 49 q^{92} - 50 q^{93} + 16 q^{94} + 56 q^{95} + 7 q^{96} - 52 q^{97} - 12 q^{98} + 5 q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9 + 5 * q^11 + 3 * q^12 + 22 * q^13 - q^14 + 2 * q^15 - 27 * q^16 + q^17 - q^18 + 20 * q^19 - 75 * q^20 + 6 * q^21 - 16 * q^22 - 9 * q^23 - 36 * q^24 - 15 * q^25 - 16 * q^26 + 6 * q^27 - 14 * q^28 - 3 * q^29 + 17 * q^31 - 73 * q^32 - 5 * q^33 + 55 * q^34 - 2 * q^35 - 14 * q^36 + 56 * q^37 - 22 * q^38 - 22 * q^39 - 37 * q^40 - 18 * q^41 + 12 * q^42 - 19 * q^43 - 12 * q^44 + 20 * q^45 - 45 * q^46 + 42 * q^47 - 28 * q^48 - 6 * q^49 - 42 * q^50 - q^51 + 76 * q^52 - 11 * q^53 - 10 * q^54 - 61 * q^55 + 3 * q^56 + 24 * q^57 - 78 * q^58 + 38 * q^59 + 31 * q^60 + 5 * q^61 + 69 * q^62 - 6 * q^63 - 27 * q^64 + 51 * q^65 + 49 * q^66 - 27 * q^67 + 112 * q^68 - 13 * q^69 + 22 * q^70 - 4 * q^71 + 25 * q^72 + 48 * q^73 - 62 * q^74 + 26 * q^75 - 85 * q^76 - 28 * q^77 - 6 * q^78 - 6 * q^79 + 169 * q^80 - 6 * q^81 - 200 * q^82 - 6 * q^83 + 3 * q^84 - 21 * q^85 - 180 * q^86 + 14 * q^87 + 211 * q^88 - 57 * q^89 - 22 * q^91 + 49 * q^92 - 50 * q^93 + 16 * q^94 + 56 * q^95 + 7 * q^96 - 52 * q^97 - 12 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	−0.0618105	−	0.0181492i	−0.0437066	−	0.0128334i	0.259806	−	0.965661i	$-0.416341\pi$
$2$	−0.0618105	−	0.0181492i	−0.0437066	−	0.0128334i	−0.303513	+	0.952827i	$0.598160\pi$
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$4$	−1.67902	−	1.07904i	−0.839508	−	0.539519i
$5$	−0.424340	+	2.95135i	−0.189771	+	1.31988i	0.642830	+	0.766009i	$0.277760\pi$
$5$	−0.424340	+	2.95135i	−0.189771	+	1.31988i	−0.832600	+	0.553874i	$0.813149\pi$
$6$	−0.0541936	+	0.0348281i	−0.0221244	+	0.0142185i
$7$	0.415415	+	0.909632i	0.157012	+	0.343809i
$7$	0.415415	+	0.909632i	0.157012	+	0.343809i
$8$	0.168569	+	0.194540i	0.0595983	+	0.0687801i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	0.0797933	−	0.174723i	0.0252329	−	0.0552523i
$11$	−5.22740	+	1.53490i	−1.57612	+	0.462791i	−0.948776	−	0.315950i	$-0.897677\pi$
$11$	−5.22740	+	1.53490i	−1.57612	+	0.462791i	−0.627346	+	0.778741i	$0.715859\pi$
$12$	−1.91500	+	0.562296i	−0.552814	+	0.162321i
$13$	0.149653	−	0.327694i	0.0415062	−	0.0908859i	−0.887743	−	0.460339i	$-0.847728\pi$
$13$	0.149653	−	0.327694i	0.0415062	−	0.0908859i	0.929249	+	0.369453i	$0.120455\pi$
$14$	−0.00916792	−	0.0637643i	−0.00245023	−	0.0170417i
$15$	1.95260	+	2.25342i	0.504158	+	0.581830i
$16$	1.65132	+	3.61589i	0.412831	+	0.903974i
$17$	−3.74487	+	2.40668i	−0.908265	+	0.583706i	−0.909230	−	0.416293i	$-0.863329\pi$
$17$	−3.74487	+	2.40668i	−0.908265	+	0.583706i	0.000965725		1.00000i	$0.499693\pi$
$18$	−0.00916792	+	0.0637643i	−0.00216090	+	0.0150294i
$19$	−2.77782	−	1.78519i	−0.637275	−	0.409552i	0.181722	−	0.983350i	$-0.441833\pi$
$19$	−2.77782	−	1.78519i	−0.637275	−	0.409552i	−0.818997	+	0.573798i	$0.805469\pi$
$20$	3.89709	−	4.49748i	0.871416	−	1.00567i
$21$	0.959493	+	0.281733i	0.209379	+	0.0614791i
$22$	0.350966			0.0748262
$23$	0.157333	+	4.79325i	0.0328061	+	0.999462i
$23$	0.157333	+	4.79325i	0.0328061	+	0.999462i
$24$	0.257413			0.0525441
$25$	−3.73293	−	1.09609i	−0.746585	−	0.219217i
$26$	−0.0151975	+	0.0175388i	−0.00298047	+	0.00343965i
$27$	−0.841254	−	0.540641i	−0.161899	−	0.104046i
$28$	0.284039	−	1.97554i	0.0536783	−	0.373341i
$29$	−2.90293	+	1.86560i	−0.539060	+	0.346433i	−0.781671	−	0.623691i	$-0.785632\pi$
$29$	−2.90293	+	1.86560i	−0.539060	+	0.346433i	0.242611	+	0.970124i	$0.421996\pi$
$30$	−0.0797933	−	0.174723i	−0.0145682	−	0.0318999i
$31$	4.76100	+	5.49448i	0.855100	+	0.986838i	0.999997	−	0.00260860i	$-0.000830345\pi$
$31$	4.76100	+	5.49448i	0.855100	+	0.986838i	−0.144896	+	0.989447i	$0.546285\pi$
$32$	−0.109711	−	0.763056i	−0.0193943	−	0.134890i
$33$	−2.26322	+	4.95576i	−0.393976	+	0.862687i
$34$	0.275152	−	0.0807919i	0.0471882	−	0.0138557i
$35$	−2.86092	+	0.840041i	−0.483583	+	0.141993i
$36$	−0.829106	+	1.81549i	−0.138184	+	0.302582i
$37$	0.108745	+	0.756341i	0.0178776	+	0.124342i	0.996806	−	0.0798630i	$-0.0254483\pi$
$37$	0.108745	+	0.756341i	0.0178776	+	0.124342i	−0.978928	+	0.204205i	$0.934539\pi$
$38$	0.139298	+	0.160759i	0.0225972	+	0.0260785i
$39$	−0.149653	−	0.327694i	−0.0239636	−	0.0524730i
$40$	−0.645685	+	0.414956i	−0.102092	+	0.0656103i
$41$	0.370060	−	2.57382i	0.0577937	−	0.401964i	−0.940305	−	0.340332i	$-0.889460\pi$
$41$	0.370060	−	2.57382i	0.0577937	−	0.401964i	0.998099	−	0.0616317i	$-0.0196304\pi$
$42$	−0.0541936	−	0.0348281i	−0.00836225	−	0.00537409i
$43$	−0.763111	+	0.880676i	−0.116373	+	0.134302i	−0.810947	−	0.585120i	$-0.801048\pi$
$43$	−0.763111	+	0.880676i	−0.116373	+	0.134302i	0.694574	+	0.719422i	$0.255593\pi$
$44$	10.4331	+	3.06344i	1.57285	+	0.461831i
$45$	2.98170			0.444485
$46$	0.0772689	−	0.299129i	0.0113927	−	0.0441041i
$47$	3.36482			0.490810			0.245405	−	0.969421i	$-0.421079\pi$
$47$	3.36482			0.490810			0.245405	+	0.969421i	$0.421079\pi$
$48$	3.81410	+	1.11992i	0.550518	+	0.161647i
$49$	−0.654861	+	0.755750i	−0.0935515	+	0.107964i
$50$	0.210841	+	0.135499i	0.0298174	+	0.0191625i
$51$	−0.633520	+	4.40623i	−0.0887105	+	0.616995i
$52$	−0.604863	+	0.388722i	−0.0838794	+	0.0539060i
$53$	4.66494	+	10.2148i	0.640778	+	1.40311i	0.899399	+	0.437129i	$0.144005\pi$
$53$	4.66494	+	10.2148i	0.640778	+	1.40311i	−0.258621	+	0.965979i	$0.583268\pi$
$54$	0.0421861	+	0.0486854i	0.00574080	+	0.00662524i
$55$	−2.31184	−	16.0792i	−0.311729	−	2.16812i
$56$	−0.106933	+	0.234151i	−0.0142895	+	0.0312897i
$57$	−3.16824	+	0.930280i	−0.419644	+	0.123219i
$58$	0.213291	−	0.0626278i	0.0280064	−	0.00822343i
$59$	4.14385	−	9.07376i	0.539483	−	1.18130i	−0.422040	−	0.906577i	$-0.638686\pi$
$59$	4.14385	−	9.07376i	0.539483	−	1.18130i	0.961523	−	0.274725i	$-0.0885869\pi$
$60$	−0.846919	−	5.89045i	−0.109337	−	0.760454i
$61$	−6.29161	−	7.26091i	−0.805558	−	0.929664i	0.193114	−	0.981176i	$-0.438141\pi$
$61$	−6.29161	−	7.26091i	−0.805558	−	0.929664i	−0.998672	+	0.0515125i	$0.983596\pi$
$62$	−0.194559	−	0.426025i	−0.0247090	−	0.0541053i
$63$	0.841254	−	0.540641i	0.105988	−	0.0681143i
$64$	1.12437	−	7.82016i	0.140546	−	0.977520i
$65$	0.903634	+	0.580731i	0.112082	+	0.0720308i
$66$	0.229834	−	0.265242i	0.0282906	−	0.0326491i
$67$	−8.16946	−	2.39877i	−0.998058	−	0.293056i	−0.258399	−	0.966038i	$-0.583195\pi$
$67$	−8.16946	−	2.39877i	−0.998058	−	0.293056i	−0.739659	+	0.672982i	$0.765013\pi$
$68$	8.88460			1.07742
$69$	3.72553	+	3.02001i	0.448501	+	0.363566i
$70$	0.192081			0.0229581
$71$	2.75019	+	0.807528i	0.326387	+	0.0958359i	0.440821	−	0.897595i	$-0.354687\pi$
$71$	2.75019	+	0.807528i	0.326387	+	0.0958359i	−0.114434	+	0.993431i	$0.536505\pi$
$72$	0.168569	−	0.194540i	0.0198661	−	0.0229267i
$73$	−8.58939	−	5.52006i	−1.00531	−	0.646075i	−0.0691361	−	0.997607i	$-0.522024\pi$
$73$	−8.58939	−	5.52006i	−1.00531	−	0.646075i	−0.936176	+	0.351533i	$0.885661\pi$
$74$	0.00700538	−	0.0487235i	0.000814359	−	0.00566399i
$75$	−3.27291	+	2.10337i	−0.377923	+	0.242877i
$76$	2.73770	+	5.99474i	0.314036	+	0.687643i
$77$	−3.56774	−	4.11739i	−0.406582	−	0.469220i
$78$	0.00330273	+	0.0229710i	0.000373961	+	0.00260095i
$79$	5.60240	−	12.2676i	0.630320	−	1.38021i	−0.277451	−	0.960740i	$-0.589490\pi$
$79$	5.60240	−	12.2676i	0.630320	−	1.38021i	0.907770	−	0.419468i	$-0.137783\pi$
$80$	−11.3725	+	3.33926i	−1.27148	+	0.373341i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	−0.0695865	+	0.152373i	−0.00768454	+	0.0168268i
$83$	0.333696	+	2.32091i	0.0366279	+	0.254753i	0.999905	−	0.0137553i	$-0.00437858\pi$
$83$	0.333696	+	2.32091i	0.0366279	+	0.254753i	−0.963278	+	0.268508i	$0.913469\pi$
$84$	−1.30700	−	1.50836i	−0.142606	−	0.164576i
$85$	−5.51386	−	12.0737i	−0.598062	−	1.30957i
$86$	0.0631519	−	0.0405852i	0.00680984	−	0.00437642i
$87$	−0.491088	+	3.41559i	−0.0526502	+	0.366190i
$88$	−1.17978	−	0.758199i	−0.125765	−	0.0808243i
$89$	−9.53851	+	11.0080i	−1.01108	+	1.16685i	−0.0251511	+	0.999684i	$0.508007\pi$
$89$	−9.53851	+	11.0080i	−1.01108	+	1.16685i	−0.985929	+	0.167165i	$0.946539\pi$
$90$	−0.184300	−	0.0541155i	−0.0194270	−	0.00570427i
$91$	0.360249			0.0377643
$92$	4.90793	−	8.21771i	0.511688	−	0.856756i
$93$	7.27024			0.753889
$94$	−0.207981	−	0.0610688i	−0.0214516	−	0.00629877i
$95$	6.44747	−	7.44077i	0.661496	−	0.763407i
$96$	−0.648524	−	0.416781i	−0.0661897	−	0.0425376i
$97$	−2.31779	+	16.1206i	−0.235336	+	1.63680i	0.439081	+	0.898447i	$0.355304\pi$
$97$	−2.31779	+	16.1206i	−0.235336	+	1.63680i	−0.674417	+	0.738351i	$0.735605\pi$
$98$	0.0541936	−	0.0348281i	0.00547438	−	0.00351817i
$99$	2.26322	+	4.95576i	0.227462	+	0.498072i
$100$	5.08492	+	5.86832i	0.508492	+	0.586832i
$101$	−0.687819	−	4.78389i	−0.0684406	−	0.476015i	−0.995001	−	0.0998680i	$-0.968158\pi$
$101$	−0.687819	−	4.78389i	−0.0684406	−	0.476015i	0.926560	−	0.376147i	$-0.122751\pi$
$102$	0.119128	−	0.260853i	0.0117954	−	0.0258283i
$103$	3.26683	−	0.959229i	0.321891	−	0.0945157i	−0.116795	−	0.993156i	$-0.537262\pi$
$103$	3.26683	−	0.959229i	0.321891	−	0.0945157i	0.438686	+	0.898640i	$0.355444\pi$
$104$	0.0889762	−	0.0261258i	0.00872484	−	0.00256184i
$105$	−1.23864	+	2.71225i	−0.120879	+	0.264688i
$106$	−0.102952	−	0.716046i	−0.00999957	−	0.0695485i
$107$	−5.48443	−	6.32937i	−0.530200	−	0.611883i	0.425955	−	0.904744i	$-0.359938\pi$
$107$	−5.48443	−	6.32937i	−0.530200	−	0.611883i	−0.956155	+	0.292861i	$0.905393\pi$
$108$	0.829106	+	1.81549i	0.0797808	+	0.174696i
$109$	−5.45263	+	3.50419i	−0.522268	+	0.335641i	−0.775068	−	0.631877i	$-0.782285\pi$
$109$	−5.45263	+	3.50419i	−0.522268	+	0.335641i	0.252801	+	0.967518i	$0.418648\pi$
$110$	−0.148929	+	1.03582i	−0.0141998	+	0.0987618i
$111$	0.642818	+	0.413114i	0.0610136	+	0.0392110i
$112$	−2.60315	+	3.00419i	−0.245974	+	0.283870i
$113$	9.91390	+	2.91098i	0.932621	+	0.273842i	0.712534	−	0.701638i	$-0.247548\pi$
$113$	9.91390	+	2.91098i	0.932621	+	0.273842i	0.220087	+	0.975480i	$0.429366\pi$
$114$	0.212715			0.0199225
$115$	−14.2133	−	1.56962i	−1.32540	−	0.146368i
$116$	6.88711			0.639453
$117$	−0.345656	−	0.101494i	−0.0319559	−	0.00938310i
$118$	−0.420815	+	0.485646i	−0.0387391	+	0.0447074i
$119$	−3.74487	−	2.40668i	−0.343292	−	0.220620i
$120$	−0.109230	+	0.759714i	−0.00997133	+	0.0693521i
$121$	15.7160	−	10.1001i	1.42873	−	0.918189i
$122$	0.257108	+	0.562988i	0.0232775	+	0.0509706i
$123$	−1.70283	−	1.96517i	−0.153539	−	0.177193i
$124$	−2.06503	−	14.3626i	−0.185445	−	1.28980i
$125$	−1.37425	+	3.00919i	−0.122917	+	0.269150i
$126$	−0.0618105	+	0.0181492i	−0.00550652	+	0.00161686i
$127$	16.3145	−	4.79037i	1.44768	−	0.425076i	0.538904	−	0.842367i	$-0.318839\pi$
$127$	16.3145	−	4.79037i	1.44768	−	0.425076i	0.908773	+	0.417291i	$0.137021\pi$
$128$	−0.851916	+	1.86544i	−0.0752995	+	0.164883i
$129$	0.165840	+	1.15344i	0.0146014	+	0.101555i
$130$	−0.0453143	−	0.0522955i	−0.00397433	−	0.00458662i
$131$	−3.24466	−	7.10481i	−0.283487	−	0.620750i	0.713299	−	0.700860i	$-0.247200\pi$
$131$	−3.24466	−	7.10481i	−0.283487	−	0.620750i	−0.996786	+	0.0801100i	$0.974473\pi$
$132$	9.14743	−	5.87870i	0.796182	−	0.511675i
$133$	0.469923	−	3.26839i	0.0407475	−	0.283405i
$134$	0.461423	+	0.296538i	0.0398609	+	0.0256170i
$135$	1.95260	−	2.25342i	0.168053	−	0.193943i
$136$	−1.09947	−	0.322832i	−0.0942784	−	0.0276826i
$137$	4.47653			0.382456			0.191228	−	0.981546i	$-0.438753\pi$
$137$	4.47653			0.382456			0.191228	+	0.981546i	$0.438753\pi$
$138$	−0.175466	−	0.254284i	−0.0149367	−	0.0216461i
$139$	13.3949			1.13614			0.568071	−	0.822980i	$-0.307690\pi$
$139$	13.3949			1.13614			0.568071	+	0.822980i	$0.307690\pi$
$140$	5.70996	+	1.67660i	0.482580	+	0.141698i
$141$	2.20349	−	2.54296i	0.185567	−	0.214156i
$142$	−0.155335	−	0.0998275i	−0.0130354	−	0.00837734i
$143$	−0.279317	+	1.94269i	−0.0233576	+	0.162456i
$144$	3.34408	−	2.14911i	0.278673	−	0.179093i
$145$	−4.27420	−	9.35920i	−0.354953	−	0.777239i
$146$	0.430730	+	0.497089i	0.0356475	+	0.0411394i
$147$	0.142315	+	0.989821i	0.0117379	+	0.0816391i
$148$	0.633536	−	1.38725i	0.0520763	−	0.114031i
$149$	22.1367	−	6.49993i	1.81351	−	0.532495i	0.814638	−	0.579970i	$-0.196936\pi$
$149$	22.1367	−	6.49993i	1.81351	−	0.532495i	0.998872	+	0.0474755i	$0.0151176\pi$
$150$	0.240475	−	0.0706099i	0.0196347	−	0.00576527i
$151$	−8.02844	+	17.5798i	−0.653345	+	1.43063i	0.235251	+	0.971935i	$0.424409\pi$
$151$	−8.02844	+	17.5798i	−0.653345	+	1.43063i	−0.888596	+	0.458691i	$0.848318\pi$
$152$	−0.120964	−	0.841324i	−0.00981149	−	0.0682404i
$153$	2.91514	+	3.36425i	0.235675	+	0.271983i
$154$	0.145797	+	0.319250i	0.0117486	+	0.0257259i
$155$	−18.2364	+	11.7198i	−1.46478	+	0.941359i
$156$	−0.102325	+	0.711684i	−0.00819253	+	0.0569803i
$157$	13.2728	+	8.52993i	1.05929	+	0.680762i	0.949683	−	0.313213i	$-0.101405\pi$
$157$	13.2728	+	8.52993i	1.05929	+	0.680762i	0.109604	+	0.993975i	$0.465042\pi$
$158$	−0.568934	+	0.656585i	−0.0452620	+	0.0522351i
$159$	10.7747	+	3.16374i	0.854489	+	0.250901i
$160$	2.29860			0.181720
$161$	−4.29474	+	2.13430i	−0.338473	+	0.168207i
$162$	0.0644200			0.00506131
$163$	4.25916	+	1.25060i	0.333603	+	0.0979548i	0.444244	−	0.895906i	$-0.353472\pi$
$163$	4.25916	+	1.25060i	0.333603	+	0.0979548i	−0.110641	+	0.993860i	$0.535290\pi$
$164$	−3.39859	+	3.92218i	−0.265385	+	0.306271i
$165$	−13.6658	−	8.78247i	−1.06388	−	0.683714i
$166$	0.0214967	−	0.149513i	0.00166847	−	0.0116044i
$167$	−1.71278	+	1.10074i	−0.132539	+	0.0851776i	−0.605230	−	0.796051i	$-0.706919\pi$
$167$	−1.71278	+	1.10074i	−0.132539	+	0.0851776i	0.472691	+	0.881228i	$0.343283\pi$
$168$	0.106933	+	0.234151i	0.00825007	+	0.0180651i
$169$	8.42820	+	9.72666i	0.648323	+	0.748205i
$170$	0.121687	+	0.846352i	0.00933297	+	0.0649123i
$171$	−1.37170	+	3.00360i	−0.104896	+	0.229691i
$172$	2.23156	−	0.655245i	0.170155	−	0.0499619i
$173$	−22.2445	+	6.53159i	−1.69122	+	0.496587i	−0.978740	−	0.205104i	$-0.934247\pi$
$173$	−22.2445	+	6.53159i	−1.69122	+	0.496587i	−0.712481	+	0.701691i	$0.752429\pi$
$174$	0.0923448	−	0.202207i	0.00700064	−	0.0153293i
$175$	−0.553679	−	3.85092i	−0.0418542	−	0.291102i
$176$	−14.1822	−	16.3671i	−1.06902	−	1.23372i
$177$	−4.14385	−	9.07376i	−0.311471	−	0.682025i
$178$	0.789367	−	0.507296i	0.0591656	−	0.0380234i
$179$	1.58143	−	10.9991i	0.118202	−	0.822111i	−0.841332	−	0.540518i	$-0.818228\pi$
$179$	1.58143	−	10.9991i	0.118202	−	0.822111i	0.959534	−	0.281593i	$-0.0908627\pi$
$180$	−5.00632	−	3.21736i	−0.373149	−	0.239808i
$181$	−14.2591	+	16.4558i	−1.05987	+	1.22315i	−0.0859380	+	0.996300i	$0.527389\pi$
$181$	−14.2591	+	16.4558i	−1.05987	+	1.22315i	−0.973929	+	0.226852i	$0.927157\pi$
$182$	−0.0222672	−	0.00653823i	−0.00165055	−	0.000484646i
$183$	−9.60756			−0.710211
$184$	−0.905955	+	0.838603i	−0.0667879	+	0.0618226i
$185$	−2.27837			−0.167509
$186$	−0.449378	−	0.131949i	−0.0329500	−	0.00967498i
$187$	15.8819	−	18.3287i	1.16140	−	1.34033i
$188$	−5.64959	−	3.63077i	−0.412039	−	0.264801i
$189$	0.142315	−	0.989821i	0.0103519	−	0.0719989i
$190$	−0.533565	+	0.342902i	−0.0387089	+	0.0248767i
$191$	4.22009	+	9.24072i	0.305355	+	0.668635i	0.998646	−	0.0520233i	$-0.0165670\pi$
$191$	4.22009	+	9.24072i	0.305355	+	0.668635i	−0.693291	+	0.720658i	$0.743840\pi$
$192$	−5.17378	−	5.97086i	−0.373385	−	0.430909i
$193$	−0.0957659	−	0.666067i	−0.00689338	−	0.0479445i	0.986084	−	0.166245i	$-0.0531644\pi$
$193$	−0.0957659	−	0.666067i	−0.00689338	−	0.0479445i	−0.992978	+	0.118301i	$0.962255\pi$
$194$	0.435840	−	0.954356i	0.0312915	−	0.0685188i
$195$	1.03064	−	0.302624i	0.0738058	−	0.0216713i
$196$	1.91500	−	0.562296i	0.136786	−	0.0401640i
$197$	−6.95686	+	15.2334i	−0.495656	+	1.08533i	0.482201	+	0.876060i	$0.339837\pi$
$197$	−6.95686	+	15.2334i	−0.495656	+	1.08533i	−0.977857	+	0.209274i	$0.932890\pi$
$198$	−0.0499477	−	0.347394i	−0.00354963	−	0.0246882i
$199$	−11.1123	−	12.8243i	−0.787731	−	0.909090i	0.209911	−	0.977721i	$-0.432683\pi$
$199$	−11.1123	−	12.8243i	−0.787731	−	0.909090i	−0.997642	+	0.0686302i	$0.978137\pi$
$200$	−0.416025	−	0.910968i	−0.0294174	−	0.0644152i
$201$	−7.16273	+	4.60320i	−0.505220	+	0.324685i
$202$	−0.0443093	+	0.308178i	−0.00311759	+	0.0216833i
$203$	−2.90293	−	1.86560i	−0.203746	−	0.130939i
$204$	5.81818	−	6.71453i	0.407354	−	0.470111i
$205$	7.43922	+	2.18435i	0.519578	+	0.152562i
$206$	−0.219334			−0.0152817
$207$	4.72207	−	0.837882i	0.328207	−	0.0582368i
$208$	1.43203			0.0992935
$209$	17.2609	+	5.06825i	1.19396	+	0.350578i
$210$	0.125786	−	0.145165i	0.00868008	−	0.0100173i
$211$	17.8502	+	11.4716i	1.22886	+	0.789739i	0.983713	−	0.179747i	$-0.0575279\pi$
$211$	17.8502	+	11.4716i	1.22886	+	0.789739i	0.245146	+	0.969486i	$0.421164\pi$
$212$	3.18964	−	22.1844i	0.219065	−	1.52363i
$213$	2.41128	−	1.54963i	0.165218	−	0.106179i
$214$	0.224123	+	0.490760i	0.0153207	+	0.0335477i
$215$	−2.27536	−	2.62591i	−0.155179	−	0.179086i
$216$	−0.0366336	−	0.254793i	−0.00249260	−	0.0173364i
$217$	−3.02017	+	6.61325i	−0.205022	+	0.448936i
$218$	0.400629	−	0.117635i	0.0271340	−	0.00796726i
$219$	−9.79664	+	2.87655i	−0.661996	+	0.194379i
$220$	−13.4685	+	29.4918i	−0.908043	+	1.98834i
$221$	0.228225	+	1.58734i	0.0153520	+	0.106776i
$222$	−0.0322352	−	0.0372014i	−0.00216349	−	0.00249680i
$223$	4.25415	+	9.31529i	0.284879	+	0.623798i	0.996927	−	0.0783327i	$-0.0249596\pi$
$223$	4.25415	+	9.31529i	0.284879	+	0.623798i	−0.712048	+	0.702130i	$0.752232\pi$
$224$	0.648524	−	0.416781i	0.0433314	−	0.0278474i
$225$	−0.553679	+	3.85092i	−0.0369119	+	0.256728i
$226$	−0.559951	−	0.359859i	−0.0372474	−	0.0239375i
$227$	5.66236	−	6.53471i	0.375824	−	0.433724i	−0.536055	−	0.844183i	$-0.680086\pi$
$227$	5.66236	−	6.53471i	0.375824	−	0.433724i	0.911879	+	0.410459i	$0.134632\pi$
$228$	6.32334	+	1.85670i	0.418773	+	0.122963i
$229$	−0.214879			−0.0141996			−0.00709981	−	0.999975i	$-0.502260\pi$
$229$	−0.214879			−0.0141996			−0.00709981	+	0.999975i	$0.502260\pi$
$230$	0.850045	+	0.354980i	0.0560503	+	0.0234067i
$231$	−5.44809			−0.358458
$232$	−0.852278	−	0.250251i	−0.0559548	−	0.0164298i
$233$	−12.4825	+	14.4055i	−0.817753	+	0.943737i	−0.999213	−	0.0396611i	$-0.987372\pi$
$233$	−12.4825	+	14.4055i	−0.817753	+	0.943737i	0.181460	+	0.983398i	$0.441918\pi$
$234$	0.0195232	+	0.0125468i	0.00127627	+	0.000820208i
$235$	−1.42783	+	9.93076i	−0.0931412	+	0.647811i
$236$	−16.7485	+	10.7636i	−1.09024	+	0.700652i
$237$	−5.60240	−	12.2676i	−0.363915	−	0.796863i
$238$	0.187793	+	0.216725i	0.0121728	+	0.0140482i
$239$	0.913523	+	6.35369i	0.0590909	+	0.410986i	0.997801	+	0.0662788i	$0.0211127\pi$
$239$	0.913523	+	6.35369i	0.0590909	+	0.410986i	−0.938710	+	0.344707i	$0.887978\pi$
$240$	−4.92375	+	10.7815i	−0.317827	+	0.695943i
$241$	−22.8318	+	6.70402i	−1.47073	+	0.431844i	−0.916335	−	0.400413i	$-0.868867\pi$
$241$	−22.8318	+	6.70402i	−1.47073	+	0.431844i	−0.554391	+	0.832257i	$0.687049\pi$
$242$	−1.15473	+	0.339058i	−0.0742285	+	0.0217955i
$243$	−0.415415	+	0.909632i	−0.0266489	+	0.0583529i
$244$	2.72892	+	18.9801i	0.174701	+	1.21507i
$245$	−1.95260	−	2.25342i	−0.124747	−	0.143966i
$246$	0.0695865	+	0.152373i	0.00443667	+	0.00971496i
$247$	−1.00070	+	0.643113i	−0.0636733	+	0.0409203i
$248$	−0.266335	+	1.85240i	−0.0169123	+	0.117628i
$249$	1.97255	+	1.26768i	0.125005	+	0.0803359i
$250$	0.139557	−	0.161058i	0.00882638	−	0.0101862i
$251$	10.6725	+	3.13372i	0.673640	+	0.197799i	0.600623	−	0.799532i	$-0.294919\pi$
$251$	10.6725	+	3.13372i	0.673640	+	0.197799i	0.0730167	+	0.997331i	$0.476737\pi$
$252$	−1.99585			−0.125727
$253$	−8.17962	−	24.8148i	−0.514248	−	1.56009i
$254$	−1.09535			−0.0687283
$255$	−12.7355	−	3.73947i	−0.797527	−	0.234175i
$256$	−10.2610	+	11.8419i	−0.641315	+	0.740117i
$257$	13.9098	+	8.93930i	0.867671	+	0.557618i	0.897040	−	0.441950i	$-0.145713\pi$
$257$	13.9098	+	8.93930i	0.867671	+	0.557618i	−0.0293684	+	0.999569i	$0.509350\pi$
$258$	0.0106834	−	0.0743047i	0.000665119	−	0.00462601i
$259$	−0.642818	+	0.413114i	−0.0399427	+	0.0256696i
$260$	−0.890586	−	1.95011i	−0.0552318	−	0.120941i
$261$	2.25974	+	2.60788i	0.139874	+	0.161424i
$262$	0.0716073	+	0.498040i	0.00442391	+	0.0307690i
$263$	−1.83451	+	4.01701i	−0.113120	+	0.247699i	−0.957722	−	0.287697i	$-0.907110\pi$
$263$	−1.83451	+	4.01701i	−0.113120	+	0.247699i	0.844601	+	0.535396i	$0.179838\pi$
$264$	−1.34560	+	0.395104i	−0.0828160	+	0.0243170i
$265$	−32.1269	+	9.43331i	−1.97354	+	0.579484i
$266$	−0.0883648	+	0.193492i	−0.00541799	+	0.0118638i
$267$	2.07292	+	14.4174i	0.126860	+	0.882334i
$268$	11.1283	+	12.8427i	0.679768	+	0.784494i
$269$	−10.6509	−	23.3223i	−0.649398	−	1.42198i	−0.892080	−	0.451878i	$-0.850754\pi$
$269$	−10.6509	−	23.3223i	−0.649398	−	1.42198i	0.242681	−	0.970106i	$-0.421973\pi$
$270$	−0.161589	+	0.103847i	−0.00983398	+	0.00631991i
$271$	−2.50281	+	17.4074i	−0.152035	+	1.05742i	0.760768	+	0.649023i	$0.224822\pi$
$271$	−2.50281	+	17.4074i	−0.152035	+	1.05742i	−0.912803	+	0.408400i	$0.866087\pi$
$272$	−14.8863	−	9.56685i	−0.902615	−	0.580075i
$273$	0.235913	−	0.272258i	0.0142781	−	0.0164778i
$274$	−0.276697	−	0.0812456i	−0.0167159	−	0.00490822i
$275$	21.1959			1.27816
$276$	−2.99652	−	9.09063i	−0.180369	−	0.547191i
$277$	16.3136			0.980187			0.490093	−	0.871670i	$-0.336963\pi$
$277$	16.3136			0.980187			0.490093	+	0.871670i	$0.336963\pi$
$278$	−0.827947	−	0.243107i	−0.0496569	−	0.0145806i
$279$	4.76100	−	5.49448i	0.285033	−	0.328946i
$280$	−0.645685	−	0.414956i	−0.0385870	−	0.0247984i
$281$	−3.07786	+	21.4070i	−0.183610	+	1.27704i	0.664529	+	0.747262i	$0.268632\pi$
$281$	−3.07786	+	21.4070i	−0.183610	+	1.27704i	−0.848139	+	0.529773i	$0.822277\pi$
$282$	−0.182352	+	0.117190i	−0.0108589	+	0.00697858i
$283$	2.98389	+	6.53381i	0.177374	+	0.388395i	0.977348	−	0.211640i	$-0.0678805\pi$
$283$	2.98389	+	6.53381i	0.177374	+	0.388395i	−0.799974	+	0.600035i	$0.795153\pi$
$284$	−3.74626	−	4.32341i	−0.222299	−	0.256547i
$285$	−1.40117	−	9.74534i	−0.0829980	−	0.577264i
$286$	0.0525230	−	0.115009i	0.00310575	−	0.00680064i
$287$	2.49496	−	0.732587i	0.147273	−	0.0432432i
$288$	−0.739675	+	0.217188i	−0.0435858	+	0.0127979i
$289$	1.16988	−	2.56169i	0.0688167	−	0.150688i
$290$	0.0943287	+	0.656071i	0.00553917	+	0.0385258i
$291$	10.6653	+	12.3084i	0.625211	+	0.721532i
$292$	8.46536	+	18.5366i	0.495398	+	1.08477i
$293$	9.36372	−	6.01769i	0.547034	−	0.351557i	−0.237750	−	0.971326i	$-0.576410\pi$
$293$	9.36372	−	6.01769i	0.547034	−	0.351557i	0.784784	+	0.619769i	$0.212774\pi$
$294$	0.00916792	−	0.0637643i	0.000534684	−	0.00371881i
$295$	25.0214	+	16.0803i	1.45680	+	0.936231i
$296$	−0.128807	+	0.148651i	−0.00748676	+	0.00864018i
$297$	5.22740	+	1.53490i	0.303325	+	0.0890642i
$298$	−1.48625			−0.0860962
$299$	1.59426	+	0.665766i	0.0921986	+	0.0385022i
$300$	7.76489			0.448306
$301$	−1.11810	−	0.328304i	−0.0644462	−	0.0189231i
$302$	0.815302	−	0.940909i	0.0469154	−	0.0541432i
$303$	−4.06585	−	2.61296i	−0.233577	−	0.150111i
$304$	1.86800	−	12.9922i	0.107137	−	0.745155i
$305$	24.0992	−	15.4876i	1.37992	−	0.886820i
$306$	−0.119128	−	0.260853i	−0.00681008	−	0.0149120i
$307$	−1.96517	−	2.26793i	−0.112158	−	0.129437i	0.696894	−	0.717174i	$-0.254565\pi$
$307$	−1.96517	−	2.26793i	−0.112158	−	0.129437i	−0.809052	+	0.587736i	$0.800019\pi$
$308$	1.54747	+	10.7629i	0.0881753	+	0.613273i
$309$	1.41438	−	3.09707i	0.0804615	−	0.176186i
$310$	1.33991	−	0.393432i	0.0761017	−	0.0223455i
$311$	−17.2583	+	5.06750i	−0.978629	+	0.287351i	−0.731658	−	0.681672i	$-0.761253\pi$
$311$	−17.2583	+	5.06750i	−0.978629	+	0.287351i	−0.246971	+	0.969023i	$0.579435\pi$
$312$	0.0385225	−	0.0843525i	0.00218091	−	0.00477552i
$313$	−0.499688	−	3.47541i	−0.0282440	−	0.196442i	0.970814	−	0.239833i	$-0.0770928\pi$
$313$	−0.499688	−	3.47541i	−0.0282440	−	0.196442i	−0.999058	+	0.0433917i	$0.986184\pi$
$314$	−0.665589	−	0.768131i	−0.0375614	−	0.0433481i
$315$	1.23864	+	2.71225i	0.0697896	+	0.152818i
$316$	−22.6437	+	14.5522i	−1.27381	+	0.818626i
$317$	1.60880	−	11.1894i	0.0903590	−	0.628461i	−0.893440	−	0.449183i	$-0.851715\pi$
$317$	1.60880	−	11.1894i	0.0903590	−	0.628461i	0.983799	−	0.179277i	$-0.0573759\pi$
$318$	−0.608571	−	0.391105i	−0.0341269	−	0.0219321i
$319$	12.3113	−	14.2080i	0.689298	−	0.795493i
$320$	22.6029	+	6.63681i	1.26354	+	0.371009i
$321$	−8.37496			−0.467445
$322$	0.304196	−	0.0539764i	0.0169522	−	0.00300798i
$323$	14.6990			0.817872
$324$	1.91500	+	0.562296i	0.106389	+	0.0312387i
$325$	−0.917823	+	1.05922i	−0.0509117	+	0.0587552i
$326$	−0.240564	−	0.154601i	−0.0133236	−	0.00856255i
$327$	−0.922422	+	6.41558i	−0.0510100	+	0.354783i
$328$	0.563091	−	0.361877i	0.0310915	−	0.0199813i
$329$	1.39780	+	3.06075i	0.0770630	+	0.168745i
$330$	0.685295	+	0.790873i	0.0377242	+	0.0435361i
$331$	−1.39987	−	9.73632i	−0.0769439	−	0.535157i	−0.991440	−	0.130562i	$-0.958322\pi$
$331$	−1.39987	−	9.73632i	−0.0769439	−	0.535157i	0.914496	−	0.404594i	$-0.132587\pi$
$332$	1.94407	−	4.25691i	0.106694	−	0.233628i
$333$	0.733167	−	0.215277i	0.0401773	−	0.0117971i
$334$	0.125845	−	0.0369515i	0.00688595	−	0.00202190i
$335$	10.5462	−	23.0930i	0.576202	−	1.26171i
$336$	0.565718	+	3.93466i	0.0308625	+	0.214653i
$337$	−11.9966	−	13.8448i	−0.653495	−	0.754174i	0.328205	−	0.944607i	$-0.393556\pi$
$337$	−11.9966	−	13.8448i	−0.653495	−	0.754174i	−0.981700	+	0.190433i	$0.939011\pi$
$338$	−0.344420	−	0.754176i	−0.0187340	−	0.0410217i
$339$	8.69220	−	5.58614i	0.472095	−	0.303397i
$340$	−3.77009	+	26.2215i	−0.204462	+	1.42206i
$341$	−33.3212	−	21.4142i	−1.80444	−	1.15964i
$342$	0.139298	−	0.160759i	0.00753240	−	0.00869285i
$343$	−0.959493	−	0.281733i	−0.0518078	−	0.0152121i
$344$	−0.299963			−0.0161729
$345$	−10.4940	+	9.71382i	−0.564977	+	0.522974i
$346$	1.49349			0.0802905
$347$	−11.5468	−	3.39046i	−0.619867	−	0.182009i	−0.0433037	−	0.999062i	$-0.513788\pi$
$347$	−11.5468	−	3.39046i	−0.619867	−	0.182009i	−0.576563	+	0.817053i	$0.695606\pi$
$348$	4.51010	−	5.20493i	0.241767	−	0.279014i
$349$	−13.3198	−	8.56014i	−0.712995	−	0.458214i	0.133199	−	0.991089i	$-0.457475\pi$
$349$	−13.3198	−	8.56014i	−0.712995	−	0.458214i	−0.846194	+	0.532875i	$0.821111\pi$
$350$	−0.0356680	+	0.248076i	−0.00190653	+	0.0132602i
$351$	−0.303060	+	0.194765i	−0.0161762	+	0.0103958i
$352$	1.74472	+	3.82041i	0.0929939	+	0.203628i
$353$	−7.09162	−	8.18416i	−0.377449	−	0.435599i	0.534961	−	0.844877i	$-0.320326\pi$
$353$	−7.09162	−	8.18416i	−0.377449	−	0.435599i	−0.912410	+	0.409278i	$0.865781\pi$
$354$	0.0914518	+	0.636061i	0.00486061	+	0.0338063i
$355$	−3.55031	+	7.77409i	−0.188431	+	0.412606i
$356$	27.8934	−	8.19024i	1.47835	−	0.434082i
$357$	−4.27122	+	1.25414i	−0.226057	+	0.0663763i
$358$	−0.297374	+	0.651158i	−0.0157167	+	0.0344148i
$359$	3.66855	+	25.5153i	0.193619	+	1.34665i	0.822331	+	0.569010i	$0.192673\pi$
$359$	3.66855	+	25.5153i	0.193619	+	1.34665i	−0.628712	+	0.777638i	$0.716417\pi$
$360$	0.502623	+	0.580058i	0.0264906	+	0.0305717i
$361$	−3.36354	−	7.36513i	−0.177029	−	0.387638i
$362$	1.18002	−	0.758353i	0.0620205	−	0.0398581i
$363$	2.65868	−	18.4915i	0.139545	−	0.970554i
$364$	−0.604863	−	0.388722i	−0.0317034	−	0.0203746i
$365$	19.9365	−	23.0079i	1.04352	−	1.20429i
$366$	0.593848	+	0.174370i	0.0310409	+	0.00911444i
$367$	12.2185			0.637799			0.318899	−	0.947789i	$-0.396687\pi$
$367$	12.2185			0.637799			0.318899	+	0.947789i	$0.396687\pi$
$368$	−17.0721	+	8.48411i	−0.889944	+	0.442265i
$369$	−2.60029			−0.135366
$370$	0.140827	+	0.0413506i	0.00732126	+	0.00214972i
$371$	−7.35381	+	8.48675i	−0.381791	+	0.440610i
$372$	−12.2069	−	7.84487i	−0.632896	−	0.406737i
$373$	2.14476	−	14.9171i	0.111052	−	0.772380i	−0.855849	−	0.517226i	$-0.826965\pi$
$373$	2.14476	−	14.9171i	0.111052	−	0.772380i	0.966900	−	0.255154i	$-0.0821263\pi$
$374$	−1.31432	+	0.844664i	−0.0679620	+	0.0436765i
$375$	1.37425	+	3.00919i	0.0709659	+	0.155394i
$376$	0.567206	+	0.654591i	0.0292514	+	0.0337579i
$377$	0.176914	+	1.23046i	0.00911153	+	0.0633721i
$378$	−0.0267610	+	0.0585985i	−0.00137644	+	0.00301398i
$379$	21.2018	−	6.22542i	1.08906	−	0.319778i	0.312565	−	0.949896i	$-0.398812\pi$
$379$	21.2018	−	6.22542i	1.08906	−	0.319778i	0.776499	+	0.630118i	$0.216994\pi$
$380$	−18.8543	+	5.53611i	−0.967204	+	0.283997i
$381$	7.06340	−	15.4667i	0.361869	−	0.792382i
$382$	−0.0931346	−	0.647765i	−0.00476518	−	0.0331425i
$383$	−16.1204	−	18.6039i	−0.823713	−	0.950615i	0.175715	−	0.984441i	$-0.443776\pi$
$383$	−16.1204	−	18.6039i	−0.823713	−	0.950615i	−0.999428	+	0.0338258i	$0.989231\pi$
$384$	0.851916	+	1.86544i	0.0434742	+	0.0951952i
$385$	13.6658	−	8.78247i	0.696473	−	0.447596i
$386$	−0.00616924	+	0.0429080i	−0.000314006	+	0.00218396i
$387$	0.980314	+	0.630010i	0.0498322	+	0.0320252i
$388$	21.2863	−	24.5657i	1.08065	−	1.24714i
$389$	−32.3229	−	9.49087i	−1.63884	−	0.481206i	−0.672847	−	0.739782i	$-0.734929\pi$
$389$	−32.3229	−	9.49087i	−1.63884	−	0.481206i	−0.965991	+	0.258576i	$0.916747\pi$
$390$	−0.0691969			−0.00350392
$391$	−12.1250	−	17.5715i	−0.613189	−	0.888627i
$392$	−0.257413			−0.0130013
$393$	−7.49425	−	2.20051i	−0.378035	−	0.111001i
$394$	0.706481	−	0.815323i	0.0355920	−	0.0410754i
$395$	33.8285	+	21.7403i	1.70210	+	1.09387i
$396$	1.54747	−	10.7629i	0.0777633	−	0.540856i
$397$	−20.4585	+	13.1479i	−1.02678	+	0.659872i	−0.941683	−	0.336501i	$-0.890756\pi$
$397$	−20.4585	+	13.1479i	−1.02678	+	0.659872i	−0.0850973	+	0.996373i	$0.527120\pi$
$398$	0.454107	+	0.994356i	0.0227623	+	0.0498426i
$399$	−2.16235	−	2.49548i	−0.108253	−	0.124930i
$400$	−2.20094	−	15.3079i	−0.110047	−	0.765393i
$401$	−7.17114	+	15.7026i	−0.358110	+	0.784151i	0.641742	+	0.766921i	$0.278212\pi$
$401$	−7.17114	+	15.7026i	−0.358110	+	0.784151i	−0.999852	+	0.0172301i	$0.994515\pi$
$402$	0.526276	−	0.154529i	0.0262483	−	0.00770719i
$403$	2.51300	−	0.737884i	0.125182	−	0.0367566i
$404$	−4.00714	+	8.77441i	−0.199363	+	0.436543i
$405$	−0.424340	−	2.95135i	−0.0210856	−	0.146654i
$406$	0.145572	+	0.168000i	0.00722464	+	0.00833768i
$407$	−1.72937	−	3.78679i	−0.0857216	−	0.187704i
$408$	−0.963977	+	0.619511i	−0.0477240	+	0.0306703i
$409$	−2.28459	+	15.8896i	−0.112966	+	0.785693i	0.852043	+	0.523472i	$0.175364\pi$
$409$	−2.28459	+	15.8896i	−0.112966	+	0.785693i	−0.965008	+	0.262220i	$0.915545\pi$
$410$	−0.420178	−	0.270032i	−0.0207511	−	0.0133359i
$411$	2.93151	−	3.38314i	0.144601	−	0.166878i
$412$	−6.52011	−	1.91448i	−0.321223	−	0.0943195i
$413$	9.97520			0.490847
$414$	−0.307081	−	0.0339119i	−0.0150922	−	0.00166668i
$415$	−6.99140			−0.343194
$416$	−0.266467	−	0.0782418i	−0.0130646	−	0.00383612i
$417$	8.77180	−	10.1232i	0.429557	−	0.495735i
$418$	−0.974919	−	0.626542i	−0.0476848	−	0.0306452i
$419$	−0.251883	+	1.75189i	−0.0123053	+	0.0855852i	−0.995049	−	0.0993892i	$-0.968311\pi$
$419$	−0.251883	+	1.75189i	−0.0123053	+	0.0855852i	0.982743	+	0.184974i	$0.0592202\pi$
$420$	5.00632	−	3.21736i	0.244283	−	0.156991i
$421$	10.1002	+	22.1164i	0.492256	+	1.07789i	0.978909	+	0.204295i	$0.0654900\pi$
$421$	10.1002	+	22.1164i	0.492256	+	1.07789i	−0.486654	+	0.873595i	$0.661783\pi$
$422$	−0.895129	−	1.03303i	−0.0435742	−	0.0502873i
$423$	−0.478864	−	3.33057i	−0.0232832	−	0.161938i
$424$	−1.20081	+	2.62941i	−0.0583167	+	0.127696i
$425$	16.6173	−	4.87927i	0.806055	−	0.236679i
$426$	−0.177167	+	0.0520209i	−0.00858377	+	0.00252042i
$427$	3.99112	−	8.73934i	0.193144	−	0.422926i
$428$	2.37882	+	16.5450i	0.114984	+	0.799734i
$429$	1.28527	+	1.48328i	0.0620536	+	0.0716137i
$430$	0.0929833	+	0.203605i	0.00448405	+	0.00981871i
$431$	−18.8750	+	12.1302i	−0.909178	+	0.584293i	−0.909499	−	0.415707i	$-0.863534\pi$
$431$	−18.8750	+	12.1302i	−0.909178	+	0.584293i	0.000320625		1.00000i	$0.499898\pi$
$432$	0.565718	−	3.93466i	0.0272181	−	0.189306i
$433$	10.3996	+	6.68340i	0.499772	+	0.321184i	0.766125	−	0.642692i	$-0.222182\pi$
$433$	10.3996	+	6.68340i	0.499772	+	0.321184i	−0.266353	+	0.963876i	$0.585819\pi$
$434$	0.306703	−	0.353955i	0.0147222	−	0.0169904i
$435$	−9.87222	−	2.89874i	−0.473337	−	0.138984i
$436$	12.9362			0.619532
$437$	8.11984	−	13.5956i	0.388425	−	0.650367i
$438$	0.657743			0.0314282
$439$	14.0853	+	4.13581i	0.672254	+	0.197391i	0.600006	−	0.799995i	$-0.295165\pi$
$439$	14.0853	+	4.13581i	0.672254	+	0.197391i	0.0722473	+	0.997387i	$0.476983\pi$
$440$	2.73834	−	3.16021i	0.130545	−	0.150657i
$441$	0.841254	+	0.540641i	0.0400597	+	0.0257448i
$442$	0.0147022	−	0.102256i	0.000699314	−	0.00486383i
$443$	−14.0612	+	9.03661i	−0.668069	+	0.429342i	−0.830229	−	0.557422i	$-0.811790\pi$
$443$	−14.0612	+	9.03661i	−0.668069	+	0.429342i	0.162160	+	0.986765i	$0.448154\pi$
$444$	−0.633536	−	1.38725i	−0.0300663	−	0.0658359i
$445$	−28.4410	−	32.8226i	−1.34823	−	1.55594i
$446$	−0.0938861	−	0.652992i	−0.00444564	−	0.0309201i
$447$	9.58415	−	20.9864i	0.453315	−	0.992621i
$448$	7.58054	−	2.22585i	0.358147	−	0.105161i
$449$	3.28670	−	0.965061i	0.155109	−	0.0455440i	−0.203256	−	0.979126i	$-0.565152\pi$
$449$	3.28670	−	0.965061i	0.155109	−	0.0455440i	0.358365	+	0.933582i	$0.383334\pi$
$450$	0.104114	−	0.227979i	0.00490800	−	0.0107470i
$451$	2.01612	+	14.0224i	0.0949354	+	0.660290i
$452$	−13.5045	−	15.5851i	−0.635200	−	0.733060i
$453$	8.02844	+	17.5798i	0.377209	+	0.825972i
$454$	−0.468593	+	0.301147i	−0.0219922	+	0.0141335i
$455$	−0.152868	+	1.06322i	−0.00716655	+	0.0498445i
$456$	−0.715045	−	0.459531i	−0.0334850	−	0.0215195i
$457$	17.6706	−	20.3930i	0.826598	−	0.953945i	−0.172922	−	0.984936i	$-0.555321\pi$
$457$	17.6706	−	20.3930i	0.826598	−	0.953945i	0.999520	+	0.0309905i	$0.00986617\pi$
$458$	0.0132818	+	0.00389989i	0.000620618	+	0.000182230i
$459$	4.45154			0.207780
$460$	22.1707	+	17.9721i	1.03371	+	0.837955i
$461$	5.22753			0.243471			0.121735	−	0.992563i	$-0.461154\pi$
$461$	5.22753			0.243471			0.121735	+	0.992563i	$0.461154\pi$
$462$	0.336749	+	0.0988785i	0.0156670	+	0.00460025i
$463$	13.6390	−	15.7403i	0.633859	−	0.731512i	−0.344418	−	0.938817i	$-0.611924\pi$
$463$	13.6390	−	15.7403i	0.633859	−	0.731512i	0.978276	+	0.207304i	$0.0664690\pi$
$464$	−11.5395	−	7.41597i	−0.535707	−	0.344278i
$465$	−3.08505	+	21.4570i	−0.143066	+	0.995045i
$466$	1.03300	−	0.663866i	0.0478526	−	0.0307530i
$467$	−3.24027	−	7.09520i	−0.149942	−	0.328327i	0.819725	−	0.572757i	$-0.194126\pi$
$467$	−3.24027	−	7.09520i	−0.149942	−	0.328327i	−0.969667	+	0.244431i	$0.921399\pi$
$468$	0.470846	+	0.543386i	0.0217649	+	0.0251180i
$469$	−1.21172	−	8.42768i	−0.0559519	−	0.389154i
$470$	0.268490	−	0.587911i	0.0123845	−	0.0271183i
$471$	15.1383	−	4.44502i	0.697538	−	0.204816i
$472$	2.46373	−	0.723416i	0.113402	−	0.0332979i
$473$	2.63733	−	5.77495i	0.121265	−	0.265533i
$474$	0.123641	+	0.859943i	0.00567903	+	0.0394985i
$475$	8.41265	+	9.70872i	0.385999	+	0.445467i
$476$	3.69080	+	8.08172i	0.169167	+	0.370425i
$477$	9.44692	−	6.07117i	0.432545	−	0.277980i
$478$	0.0588491	−	0.409305i	0.00269170	−	0.0187212i
$479$	29.1279	+	18.7194i	1.33089	+	0.855310i	0.996206	−	0.0870218i	$-0.0277350\pi$
$479$	29.1279	+	18.7194i	1.33089	+	0.855310i	0.334681	+	0.942331i	$0.391371\pi$
$480$	1.50526	−	1.73716i	0.0687055	−	0.0792903i
$481$	0.264122	+	0.0775533i	0.0120429	+	0.00353613i
$482$	1.53292			0.0698225
$483$	−1.19945	+	4.64342i	−0.0545771	+	0.211283i
$484$	−37.2858			−1.69481
$485$	−46.5939	−	13.6812i	−2.11572	−	0.621232i
$486$	0.0421861	−	0.0486854i	0.00191360	−	0.00220841i
$487$	34.0730	+	21.8974i	1.54399	+	0.992265i	0.986811	+	0.161875i	$0.0517542\pi$
$487$	34.0730	+	21.8974i	1.54399	+	0.992265i	0.557183	+	0.830390i	$0.311882\pi$
$488$	0.351960	−	2.44793i	0.0159325	−	0.110813i
$489$	3.73430	−	2.39989i	0.168871	−	0.108527i
$490$	0.0797933	+	0.174723i	0.00360469	+	0.00789318i
$491$	9.74168	+	11.2425i	0.439636	+	0.507367i	0.931718	−	0.363182i	$-0.118310\pi$
$491$	9.74168	+	11.2425i	0.439636	+	0.507367i	−0.492082	+	0.870549i	$0.663764\pi$
$492$	0.738585	+	5.13697i	0.0332980	+	0.231592i
$493$	6.38119	−	13.9729i	0.287394	−	0.629306i
$494$	0.0735261	−	0.0215892i	0.00330809	−	0.000971344i
$495$	−15.5865	+	4.57662i	−0.700563	+	0.205704i
$496$	−12.0055	+	26.2884i	−0.539064	+	1.18039i
$497$	0.407916	+	2.83712i	0.0182975	+	0.127262i
$498$	−0.0989169	−	0.114156i	−0.00443257	−	0.00511546i
$499$	13.2446	+	29.0016i	0.592909	+	1.29829i	0.933668	+	0.358138i	$0.116588\pi$
$499$	13.2446	+	29.0016i	0.592909	+	1.29829i	−0.340760	+	0.940150i	$0.610684\pi$
$500$	5.55441	−	3.56960i	0.248401	−	0.159637i
$501$	−0.289751	+	2.01526i	−0.0129451	+	0.0900352i
$502$	−0.602796	−	0.387394i	−0.0269041	−	0.0172902i
$503$	14.4861	−	16.7178i	0.645903	−	0.745412i	−0.334504	−	0.942394i	$-0.608569\pi$
$503$	14.4861	−	16.7178i	0.645903	−	0.745412i	0.980407	+	0.196983i	$0.0631142\pi$
$504$	0.246986	+	0.0725215i	0.0110016	+	0.00323037i
$505$	14.4108			0.641272
$506$	0.0552184	+	1.68227i	0.00245476	+	0.0747859i
$507$	12.8702			0.571587
$508$	−32.5613	−	9.56085i	−1.44467	−	0.424194i
$509$	21.4288	−	24.7302i	0.949817	−	1.09615i	−0.0454500	−	0.998967i	$-0.514472\pi$
$509$	21.4288	−	24.7302i	0.949817	−	1.09615i	0.995267	−	0.0971804i	$-0.0309824\pi$
$510$	0.719318	+	0.462278i	0.0318520	+	0.0204700i
$511$	1.45307	−	10.1063i	0.0642799	−	0.447076i
$512$	4.29958	−	2.76317i	0.190016	−	0.122116i
$513$	1.37170	+	3.00360i	0.0605620	+	0.132612i
$514$	−0.697533	−	0.804995i	−0.0307668	−	0.0355068i
$515$	1.44477	+	10.0486i	0.0636642	+	0.442794i
$516$	0.966159	−	2.11559i	0.0425328	−	0.0931338i
$517$	−17.5893	+	5.16468i	−0.773576	+	0.227142i
$518$	0.0472306	−	0.0138682i	0.00207519	−	0.000609332i
$519$	−9.63083	+	21.0886i	−0.422747	+	0.925686i
$520$	0.0393501	+	0.273686i	0.00172562	+	0.0120019i
$521$	−0.372589	−	0.429990i	−0.0163234	−	0.0188382i	0.747529	−	0.664229i	$-0.231240\pi$
$521$	−0.372589	−	0.429990i	−0.0163234	−	0.0188382i	−0.763853	+	0.645391i	$0.776695\pi$
$522$	−0.0923448	−	0.202207i	−0.00404182	−	0.00885035i
$523$	24.4812	−	15.7331i	1.07049	−	0.687962i	0.118148	−	0.992996i	$-0.462304\pi$
$523$	24.4812	−	15.7331i	1.07049	−	0.687962i	0.952341	+	0.305034i	$0.0986680\pi$
$524$	−2.21853	+	15.4302i	−0.0969168	+	0.674071i
$525$	−3.27291	−	2.10337i	−0.142842	−	0.0917988i
$526$	0.186297	−	0.214999i	0.00812295	−	0.00937438i
$527$	−31.0528	−	9.11792i	−1.35268	−	0.397183i
$528$	−21.6568			−0.942491
$529$	−22.9505	+	1.50827i	−0.997848	+	0.0655770i
$530$	2.15699			0.0936936
$531$	−9.57113	−	2.81034i	−0.415352	−	0.121958i
$532$	−4.31572	+	4.98061i	−0.187110	+	0.215937i
$533$	−0.788046	−	0.506446i	−0.0341340	−	0.0219366i
$534$	0.133537	−	0.928772i	0.00577872	−	0.0401919i
$535$	21.0074	−	13.5007i	0.908231	−	0.583685i
$536$	−0.910466	−	1.99364i	−0.0393261	−	0.0861122i
$537$	−7.27695	−	8.39804i	−0.314023	−	0.362402i
$538$	0.235059	+	1.63487i	0.0101341	+	0.0704842i
$539$	2.26322	−	4.95576i	0.0974837	−	0.213460i
$540$	−5.70996	+	1.67660i	−0.245718	+	0.0721492i
$541$	−4.64711	+	1.36452i	−0.199795	+	0.0586651i	−0.380099	−	0.924946i	$-0.624110\pi$
$541$	−4.64711	+	1.36452i	−0.199795	+	0.0586651i	0.180304	+	0.983611i	$0.442292\pi$
$542$	0.470630	−	1.03054i	0.0202153	−	0.0442653i
$543$	3.09879	+	21.5526i	0.132982	+	0.924909i
$544$	2.24729	+	2.59351i	0.0963516	+	0.111196i
$545$	−8.02833	−	17.5796i	−0.343896	−	0.753027i
$546$	−0.0195232	+	0.0125468i	−0.000835514	+	0.000536952i
$547$	−1.79517	+	12.4857i	−0.0767559	+	0.533849i	0.914774	+	0.403967i	$0.132369\pi$
$547$	−1.79517	+	12.4857i	−0.0767559	+	0.533849i	−0.991529	+	0.129882i	$0.958540\pi$
$548$	−7.51617	−	4.83035i	−0.321075	−	0.206342i
$549$	−6.29161	+	7.26091i	−0.268519	+	0.309888i
$550$	−1.31013	−	0.384689i	−0.0558641	−	0.0164032i
$551$	11.3943			0.485412
$552$	0.0404994	+	1.23384i	0.00172377	+	0.0525159i
$553$	13.4863			0.573495
$554$	−1.00835	−	0.296078i	−0.0428407	−	0.0125792i
$555$	−1.49202	+	1.72188i	−0.0633325	+	0.0730897i
$556$	−22.4903	−	14.4536i	−0.953800	−	0.612970i
$557$	1.98806	−	13.8272i	0.0842366	−	0.585879i	−0.903362	−	0.428879i	$-0.858909\pi$
$557$	1.98806	−	13.8272i	0.0842366	−	0.585879i	0.987599	−	0.157000i	$-0.0501822\pi$
$558$	−0.394000	+	0.253209i	−0.0166794	+	0.0107192i
$559$	0.174391	+	0.381862i	0.00737593	+	0.0161510i
$560$	−7.76180	−	8.95760i	−0.327996	−	0.378528i
$561$	−3.45147	−	24.0055i	−0.145721	−	1.01351i
$562$	0.578765	−	1.26732i	0.0244137	−	0.0534586i
$563$	30.5616	−	8.97368i	1.28802	−	0.378196i	0.435166	−	0.900350i	$-0.356690\pi$
$563$	30.5616	−	8.97368i	1.28802	−	0.378196i	0.852851	+	0.522155i	$0.174872\pi$
$564$	−6.44365	+	1.89202i	−0.271326	+	0.0796686i
$565$	−12.7982	+	28.0241i	−0.538424	+	1.17898i
$566$	−0.0658524	−	0.458014i	−0.00276798	−	0.0192518i
$567$	−0.654861	−	0.755750i	−0.0275016	−	0.0317385i
$568$	0.306501	+	0.671145i	0.0128605	+	0.0281606i
$569$	3.34587	−	2.15026i	0.140266	−	0.0901436i	−0.468626	−	0.883397i	$-0.655251\pi$
$569$	3.34587	−	2.15026i	0.140266	−	0.0901436i	0.608892	+	0.793253i	$0.291614\pi$
$570$	−0.0902632	+	0.627795i	−0.00378071	+	0.0262954i
$571$	34.4213	+	22.1213i	1.44049	+	0.925746i	0.999603	+	0.0281823i	$0.00897189\pi$
$571$	34.4213	+	22.1213i	1.44049	+	0.925746i	0.440886	+	0.897563i	$0.354664\pi$
$572$	2.56521	−	2.96041i	0.107257	−	0.123781i
$573$	9.74724	+	2.86205i	0.407197	+	0.119564i
$574$	−0.167511			−0.00699177
$575$	4.66650	−	18.0653i	0.194607	−	0.753375i
$576$	−7.90057			−0.329191
$577$	31.3165	+	9.19535i	1.30372	+	0.382808i	0.858593	−	0.512658i	$-0.171339\pi$
$577$	31.3165	+	9.19535i	1.30372	+	0.382808i	0.445130	+	0.895466i	$0.353157\pi$
$578$	−0.118804	+	0.137107i	−0.00494159	+	0.00570289i
$579$	−0.566093	−	0.363806i	−0.0235260	−	0.0151193i
$580$	−2.92248	+	20.3263i	−0.121349	+	0.844003i
$581$	−1.97255	+	1.26768i	−0.0818351	+	0.0525922i
$582$	−0.435840	−	0.954356i	−0.0180661	−	0.0395593i
$583$	−40.0642	−	46.2366i	−1.65929	−	1.91492i
$584$	−0.374038	−	2.60149i	−0.0154778	−	0.107650i
$585$	0.446219	−	0.977083i	0.0184489	−	0.0403974i
$586$	−0.687993	+	0.202013i	−0.0284207	+	0.00834508i
$587$	−35.1516	+	10.3215i	−1.45086	+	0.426012i	−0.909827	−	0.414987i	$-0.863786\pi$
$587$	−35.1516	+	10.3215i	−1.45086	+	0.426012i	−0.541036	+	0.840999i	$0.681968\pi$
$588$	0.829106	−	1.81549i	0.0341918	−	0.0748695i
$589$	−3.41645	−	23.7620i	−0.140773	−	0.979094i
$590$	−1.25474	−	1.44805i	−0.0516569	−	0.0596153i
$591$	6.95686	+	15.2334i	0.286167	+	0.626618i
$592$	−2.55528	+	1.64218i	−0.105021	+	0.0674930i
$593$	4.23419	−	29.4494i	0.173877	−	1.20934i	−0.696719	−	0.717344i	$-0.745357\pi$
$593$	4.23419	−	29.4494i	0.173877	−	1.20934i	0.870596	−	0.491998i	$-0.163733\pi$
$594$	−0.295251	−	0.189747i	−0.0121143	−	0.00778539i
$595$	8.69206	−	10.0312i	0.356340	−	0.411238i
$596$	−44.1816	−	12.9729i	−1.80975	−	0.531390i
$597$	−16.9690			−0.694494
$598$	−0.0864591	−	0.0700860i	−0.00353558	−	0.00286603i
$599$	−1.57495			−0.0643507			−0.0321753	−	0.999482i	$-0.510243\pi$
$599$	−1.57495			−0.0643507			−0.0321753	+	0.999482i	$0.510243\pi$
$600$	−0.960902	−	0.282146i	−0.0392287	−	0.0115186i
$601$	−7.37489	+	8.51107i	−0.300828	+	0.347174i	−0.885958	−	0.463766i	$-0.846498\pi$
$601$	−7.37489	+	8.51107i	−0.300828	+	0.347174i	0.585130	+	0.810939i	$0.301043\pi$
$602$	0.0631519	+	0.0405852i	0.00257388	+	0.00165413i
$603$	−1.21172	+	8.42768i	−0.0493450	+	0.343202i
$604$	32.4492	−	20.8538i	1.32034	−	0.848530i
$605$	23.1399	+	50.6694i	0.940772	+	2.06000i
$606$	0.203889	+	0.235300i	0.00828242	+	0.00955843i
$607$	−5.51745	−	38.3747i	−0.223946	−	1.55758i	−0.722901	−	0.690952i	$-0.757192\pi$
$607$	−5.51745	−	38.3747i	−0.223946	−	1.55758i	0.498954	−	0.866628i	$-0.333718\pi$
$608$	−1.05745	+	2.31548i	−0.0428851	+	0.0939052i
$609$	−3.31094	+	0.972179i	−0.134166	+	0.0393947i
$610$	−1.77068	+	0.519917i	−0.0716926	+	0.0210508i
$611$	0.503554	−	1.10263i	0.0203716	−	0.0446076i
$612$	−1.26441	−	8.79417i	−0.0511108	−	0.355483i
$613$	27.9250	+	32.2272i	1.12788	+	1.30164i	0.948113	+	0.317935i	$0.102989\pi$
$613$	27.9250	+	32.2272i	1.12788	+	1.30164i	0.179768	+	0.983709i	$0.442465\pi$
$614$	0.0803071	+	0.175848i	0.00324093	+	0.00709664i
$615$	6.52248	−	4.19174i	0.263012	−	0.169027i
$616$	0.199583	−	1.38813i	0.00804144	−	0.0559295i
$617$	30.0158	+	19.2900i	1.20839	+	0.776585i	0.980388	−	0.197076i	$-0.0631445\pi$
$617$	30.0158	+	19.2900i	1.20839	+	0.776585i	0.228002	+	0.973661i	$0.426781\pi$
$618$	−0.143633	+	0.165762i	−0.00577778	+	0.00666791i
$619$	−47.2693	−	13.8795i	−1.89991	−	0.557865i	−0.989578	−	0.143995i	$-0.954005\pi$
$619$	−47.2693	−	13.8795i	−1.89991	−	0.557865i	−0.910336	−	0.413870i	$-0.864177\pi$
$620$	43.2654			1.73758
$621$	2.45907	−	4.11740i	0.0986791	−	0.165226i
$622$	1.15872			0.0464603
$623$	−13.9757	−	4.10363i	−0.559924	−	0.164409i
$624$	0.937781	−	1.08226i	0.0375413	−	0.0433249i
$625$	−24.6626	−	15.8497i	−0.986503	−	0.633987i
$626$	−0.0321899	+	0.223886i	−0.00128657	+	0.00894827i
$627$	15.1338	−	9.72590i	0.604385	−	0.388415i
$628$	−13.0812	−	28.6438i	−0.521996	−	1.14301i
$629$	−2.22751	−	2.57068i	−0.0888167	−	0.102500i
$630$	−0.0273360	−	0.190126i	−0.00108909	−	0.00757479i
$631$	18.8986	−	41.3821i	0.752340	−	1.64739i	−0.00977495	−	0.999952i	$-0.503112\pi$
$631$	18.8986	−	41.3821i	0.752340	−	1.64739i	0.762115	−	0.647442i	$-0.224161\pi$
$632$	3.33092	−	0.978046i	0.132497	−	0.0389046i
$633$	20.3591	−	5.97796i	0.809201	−	0.237603i
$634$	−0.302520	+	0.662426i	−0.0120146	+	0.0263083i
$635$	7.21515	+	50.1825i	0.286324	+	1.99143i
$636$	−14.6771	−	16.9383i	−0.581985	−	0.671646i
$637$	0.149653	+	0.327694i	0.00592945	+	0.0129837i
$638$	−1.01883	+	0.654762i	−0.0403358	+	0.0259223i
$639$	0.407916	−	2.83712i	0.0161369	−	0.112235i
$640$	−5.14405	−	3.30588i	−0.203336	−	0.130676i
$641$	4.07236	−	4.69976i	0.160849	−	0.185629i	−0.669604	−	0.742718i	$-0.733536\pi$
$641$	4.07236	−	4.69976i	0.160849	−	0.185629i	0.830453	+	0.557089i	$0.188082\pi$
$642$	0.517661	+	0.151999i	0.0204304	+	0.00599892i
$643$	−41.2627			−1.62724			−0.813622	−	0.581394i	$-0.802507\pi$
$643$	−41.2627			−1.62724			−0.813622	+	0.581394i	$0.802507\pi$
$644$	9.51392	+	1.05065i	0.374901	+	0.0414016i
$645$	−3.47458			−0.136811
$646$	−0.908550	−	0.266774i	−0.0357464	−	0.0104961i
$647$	−27.3811	+	31.5995i	−1.07646	+	1.24231i	−0.107736	+	0.994180i	$0.534360\pi$
$647$	−27.3811	+	31.5995i	−1.07646	+	1.24231i	−0.968728	+	0.248126i	$0.920185\pi$
$648$	−0.216549	−	0.139168i	−0.00850686	−	0.00546703i
$649$	−7.73421	+	53.7926i	−0.303594	+	2.11154i
$650$	0.0759552	−	0.0488134i	0.00297921	−	0.00191462i
$651$	3.02017	+	6.61325i	0.118370	+	0.259194i
$652$	−5.80175	−	6.69558i	−0.227214	−	0.262219i
$653$	2.70489	+	18.8129i	0.105850	+	0.736206i	0.971754	+	0.235995i	$0.0758350\pi$
$653$	2.70489	+	18.8129i	0.105850	+	0.736206i	−0.865904	+	0.500211i	$0.833256\pi$
$654$	0.173453	−	0.379809i	0.00678256	−	0.0148517i
$655$	22.3456	−	6.56126i	0.873115	−	0.256370i
$656$	9.91777	−	2.91212i	0.387224	−	0.113699i
$657$	−4.24148	+	9.28755i	−0.165476	+	0.362342i
$658$	−0.0308484	−	0.214555i	−0.00120260	−	0.00836424i
$659$	−21.3519	−	24.6414i	−0.831751	−	0.959892i	0.167913	−	0.985802i	$-0.446297\pi$
$659$	−21.3519	−	24.6414i	−0.831751	−	0.959892i	−0.999664	+	0.0259099i	$0.991752\pi$
$660$	13.4685	+	29.4918i	0.524259	+	1.14797i
$661$	−21.7640	+	13.9869i	−0.846521	+	0.544026i	−0.890488	−	0.455007i	$-0.849637\pi$
$661$	−21.7640	+	13.9869i	−0.846521	+	0.544026i	0.0439671	+	0.999033i	$0.486000\pi$
$662$	−0.0901797	+	0.627214i	−0.00350494	+	0.0243774i
$663$	1.34908	+	0.867004i	0.0523941	+	0.0336716i
$664$	−0.395257	+	0.456151i	−0.0153389	+	0.0177021i
$665$	9.44674	+	2.77381i	0.366329	+	0.107564i
$666$	−0.0492245			−0.00190741
$667$	−9.39901	−	13.6209i	−0.363931	−	0.527405i
$668$	4.06352			0.157222
$669$	9.82590	+	2.88514i	0.379891	+	0.111546i
$670$	−1.07099	+	1.23599i	−0.0413759	+	0.0477503i
$671$	44.0336	+	28.2987i	1.69990	+	1.09246i
$672$	0.109711	−	0.763056i	0.00423219	−	0.0294355i
$673$	−41.2374	+	26.5016i	−1.58958	+	1.02156i	−0.617606	+	0.786487i	$0.711897\pi$
$673$	−41.2374	+	26.5016i	−1.58958	+	1.02156i	−0.971977	+	0.235076i	$0.924466\pi$
$674$	0.490243	+	1.07348i	0.0188835	+	0.0413490i
$675$	2.54775	+	2.94026i	0.0980629	+	0.113171i
$676$	−3.65565	−	25.4256i	−0.140602	−	0.977907i
$677$	−4.21306	+	9.22532i	−0.161921	+	0.354558i	−0.973150	−	0.230170i	$-0.926072\pi$
$677$	−4.21306	+	9.22532i	−0.161921	+	0.354558i	0.811229	+	0.584728i	$0.198799\pi$
$678$	−0.638653	+	0.187526i	−0.0245273	+	0.00720187i
$679$	−15.6266	+	4.58840i	−0.599696	+	0.176087i
$680$	1.41934	−	3.10792i	0.0544291	−	0.119183i
$681$	−1.23055	−	8.55865i	−0.0471547	−	0.327968i
$682$	1.67095	+	1.92838i	0.0639839	+	0.0738414i
$683$	0.0446478	+	0.0977651i	0.00170840	+	0.00374088i	0.910484	−	0.413544i	$-0.135709\pi$
$683$	0.0446478	+	0.0977651i	0.00170840	+	0.00374088i	−0.908776	+	0.417285i	$0.862982\pi$
$684$	5.54410	−	3.56298i	0.211984	−	0.136234i
$685$	−1.89957	+	13.2118i	−0.0725789	+	0.504797i
$686$	0.0541936	+	0.0348281i	0.00206912	+	0.00132974i
$687$	−0.140716	+	0.162395i	−0.00536865	+	0.00619576i
$688$	−4.44458	−	1.30505i	−0.169448	−	0.0497544i
$689$	4.04544			0.154119
$690$	0.824937	−	0.409959i	0.0314048	−	0.0156069i
$691$	28.3238			1.07749			0.538743	−	0.842470i	$-0.318899\pi$
$691$	28.3238			1.07749			0.538743	+	0.842470i	$0.318899\pi$
$692$	44.3968	+	13.0361i	1.68771	+	0.495557i
$693$	−3.56774	+	4.11739i	−0.135527	+	0.156407i
$694$	0.652182	+	0.419132i	0.0247565	+	0.0159100i
$695$	−5.68399	+	39.5330i	−0.215606	+	1.49957i
$696$	−0.747250	+	0.480229i	−0.0283245	+	0.0182030i
$697$	4.80855	+	10.5293i	0.182137	+	0.398824i
$698$	0.667947	+	0.770852i	0.0252822	+	0.0291772i
$699$	2.71270	+	18.8672i	0.102604	+	0.713624i
$700$	−3.22565	+	7.06320i	−0.121918	+	0.266964i
$701$	−29.6418	+	8.70363i	−1.11956	+	0.328731i	−0.788595	−	0.614913i	$-0.789191\pi$
$701$	−29.6418	+	8.70363i	−1.11956	+	0.328731i	−0.330962	+	0.943644i	$0.607373\pi$
$702$	0.0222672	−	0.00653823i	0.000840420	−	0.000246770i
$703$	1.04814	−	2.29511i	0.0395314	−	0.0865616i
$704$	6.12566	+	42.6049i	0.230870	+	1.60573i
$705$	6.57014	+	7.58234i	0.247446	+	0.285568i
$706$	0.289801	+	0.634575i	0.0109068	+	0.0238825i
$707$	4.06585	−	2.61296i	0.152912	−	0.0982705i
$708$	−2.83335	+	19.7063i	−0.106484	+	0.740610i
$709$	−26.9455	−	17.3168i	−1.01196	−	0.650348i	−0.0740607	−	0.997254i	$-0.523596\pi$
$709$	−26.9455	−	17.3168i	−1.01196	−	0.650348i	−0.937900	+	0.346906i	$0.887232\pi$
$710$	0.360540	−	0.416086i	0.0135308	−	0.0156154i
$711$	−12.9400	−	3.79952i	−0.485288	−	0.142493i
$712$	−3.74940			−0.140515
$713$	−25.5874	+	23.6851i	−0.958255	+	0.887014i
$714$	0.286768			0.0107320
$715$	−5.61503	−	1.64872i	−0.209990	−	0.0616587i
$716$	−14.5237	+	16.7612i	−0.542776	+	0.626397i
$717$	5.40003	+	3.47039i	0.201668	+	0.129604i
$718$	0.236328	−	1.64370i	0.00881969	−	0.0613423i
$719$	−1.23739	+	0.795219i	−0.0461467	+	0.0296567i	−0.563511	−	0.826109i	$-0.690550\pi$
$719$	−1.23739	+	0.795219i	−0.0461467	+	0.0296567i	0.517364	+	0.855765i	$0.326913\pi$
$720$	4.92375	+	10.7815i	0.183497	+	0.401803i
$721$	2.22964	+	2.57314i	0.0830361	+	0.0958287i
$722$	0.0742311	+	0.516288i	0.00276259	+	0.0192143i
$723$	−9.88509	+	21.6453i	−0.367630	+	0.804998i
$724$	41.6976	−	12.2435i	1.54968	−	0.455027i
$725$	12.8813	−	3.78228i	0.478399	−	0.140470i
$726$	−0.499941	+	1.09472i	−0.0185546	+	0.0406288i
$727$	−2.59629	−	18.0576i	−0.0962911	−	0.669719i	−0.979604	−	0.200936i	$-0.935602\pi$
$727$	−2.59629	−	18.0576i	−0.0962911	−	0.669719i	0.883313	−	0.468783i	$-0.155307\pi$
$728$	0.0607269	+	0.0700826i	0.00225069	+	0.00259743i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	−1.64986	+	1.06030i	−0.0610640	+	0.0392434i
$731$	0.738242	−	5.13458i	0.0273049	−	0.189909i
$732$	16.1312	+	10.3669i	0.596228	+	0.383172i
$733$	28.7642	−	33.1956i	1.06243	−	1.22611i	0.0892610	−	0.996008i	$-0.471549\pi$
$733$	28.7642	−	33.1956i	1.06243	−	1.22611i	0.973167	−	0.230099i	$-0.0739051\pi$
$734$	−0.755230	−	0.221755i	−0.0278760	−	0.00818514i
$735$	−2.98170			−0.109982
$736$	3.64026	−	0.645925i	0.134182	−	0.0238091i
$737$	46.3869			1.70868
$738$	0.160725	+	0.0471932i	0.00591639	+	0.00173721i
$739$	−12.5059	+	14.4325i	−0.460036	+	0.530910i	−0.937613	−	0.347680i	$-0.886970\pi$
$739$	−12.5059	+	14.4325i	−0.460036	+	0.530910i	0.477577	+	0.878590i	$0.341515\pi$
$740$	3.82542	+	2.45845i	0.140625	+	0.0903744i
$741$	−0.169289	+	1.17743i	−0.00621899	+	0.0432540i
$742$	0.608571	−	0.391105i	0.0223413	−	0.0143579i
$743$	−15.7415	−	34.4690i	−0.577499	−	1.26455i	−0.942708	−	0.333620i	$-0.891730\pi$
$743$	−15.7415	−	34.4690i	−0.577499	−	1.26455i	0.365209	−	0.930925i	$-0.380997\pi$
$744$	1.22554	+	1.41435i	0.0449305	+	0.0518526i
$745$	9.79005	+	68.0913i	0.358680	+	2.49467i
$746$	−0.403303	+	0.883111i	−0.0147660	+	0.0323330i
$747$	2.24979	−	0.660599i	0.0823156	−	0.0241700i
$748$	−46.4434	+	13.6370i	−1.69814	+	0.498619i
$749$	3.47908	−	7.61813i	0.127123	−	0.278360i
$750$	−0.0303287	−	0.210941i	−0.00110745	−	0.00770247i
$751$	−6.11019	−	7.05153i	−0.222964	−	0.257314i	0.633236	−	0.773959i	$-0.281726\pi$
$751$	−6.11019	−	7.05153i	−0.222964	−	0.257314i	−0.856200	+	0.516645i	$0.827181\pi$
$752$	5.55641	+	12.1668i	0.202621	+	0.443679i
$753$	9.35728	−	6.01356i	0.340998	−	0.219146i
$754$	0.0113968	−	0.0792664i	0.000415047	−	0.00288671i
$755$	−48.4774	−	31.1545i	−1.76427	−	1.13383i
$756$	−1.30700	+	1.50836i	−0.0475353	+	0.0548586i
$757$	40.2340	+	11.8138i	1.46233	+	0.429379i	0.913598	−	0.406619i	$-0.133293\pi$
$757$	40.2340	+	11.8138i	1.46233	+	0.429379i	0.548732	+	0.835998i	$0.315111\pi$
$758$	−1.42348			−0.0517032
$759$	−24.1103	−	10.0685i	−0.875147	−	0.365462i
$760$	2.53437			0.0919312
$761$	−3.78003	−	1.10992i	−0.137026	−	0.0402345i	0.212500	−	0.977161i	$-0.431839\pi$
$761$	−3.78003	−	1.10992i	−0.137026	−	0.0402345i	−0.349526	+	0.936926i	$0.613658\pi$
$762$	−0.717301	+	0.827809i	−0.0259851	+	0.0299884i
$763$	−5.45263	−	3.50419i	−0.197399	−	0.126860i
$764$	2.88548	−	20.0690i	0.104393	−	0.726069i
$765$	−11.1661	+	7.17600i	−0.403710	+	0.259449i
$766$	0.658763	+	1.44249i	0.0238021	+	0.0521193i
$767$	−2.35327	−	2.71582i	−0.0849718	−	0.0980627i
$768$	2.22994	+	15.5095i	0.0804659	+	0.559653i
$769$	0.618734	−	1.35484i	0.0223121	−	0.0488568i	−0.898148	−	0.439694i	$-0.855087\pi$
$769$	0.618734	−	1.35484i	0.0223121	−	0.0488568i	0.920460	+	0.390837i	$0.127814\pi$
$770$	−1.00408	+	0.294826i	−0.0361847	+	0.0106248i
$771$	15.8649	−	4.65835i	0.571359	−	0.167766i
$772$	−0.557919	+	1.22167i	−0.0200799	+	0.0439689i
$773$	−2.18828	−	15.2198i	−0.0787070	−	0.547419i	−0.990579	−	0.136944i	$-0.956272\pi$
$773$	−2.18828	−	15.2198i	−0.0787070	−	0.547419i	0.911872	−	0.410475i	$-0.134637\pi$
$774$	−0.0491596	−	0.0567332i	−0.00176700	−	0.00203923i
$775$	−11.7500	−	25.7290i	−0.422073	−	0.924212i
$776$	−3.52680	+	2.26654i	−0.126605	+	0.0813639i
$777$	−0.108745	+	0.756341i	−0.00390122	+	0.0271336i
$778$	1.82565	+	1.17327i	0.0654526	+	0.0420638i
$779$	−5.62273	+	6.48898i	−0.201455	+	0.232492i
$780$	−2.05701	−	0.603991i	−0.0736526	−	0.0216264i
$781$	−15.6158			−0.558778
$782$	0.430546	+	1.30616i	0.0153963	+	0.0467082i
$783$	3.45072			0.123319
$784$	−3.81410	−	1.11992i	−0.136218	−	0.0399971i
$785$	−30.8070	+	35.5531i	−1.09955	+	1.26895i
$786$	0.423286	+	0.272030i	0.0150981	+	0.00970297i
$787$	2.40991	−	16.7613i	0.0859042	−	0.597477i	−0.900712	−	0.434417i	$-0.856955\pi$
$787$	2.40991	−	16.7613i	0.0859042	−	0.597477i	0.986616	−	0.163060i	$-0.0521364\pi$
$788$	28.1181	−	18.0704i	1.00167	−	0.643731i
$789$	1.83451	+	4.01701i	0.0653101	+	0.143009i
$790$	−1.69639	−	1.95774i	−0.0603548	−	0.0696532i
$791$	1.47046	+	10.2273i	0.0522835	+	0.363640i
$792$	−0.582581	+	1.27567i	−0.0207011	+	0.0453291i
$793$	−3.32091	+	0.975107i	−0.117929	+	0.0346271i
$794$	1.50317	−	0.441371i	0.0533456	−	0.0156637i
$795$	−13.9094	+	30.4574i	−0.493316	+	1.08021i
$796$	4.81985	+	33.5228i	0.170835	+	1.18818i
$797$	−23.0801	−	26.6359i	−0.817540	−	0.943491i	0.181665	−	0.983360i	$-0.441851\pi$
$797$	−23.0801	−	26.6359i	−0.817540	−	0.943491i	−0.999205	+	0.0398694i	$0.987306\pi$
$798$	0.0883648	+	0.193492i	0.00312808	+	0.00684954i
$799$	−12.6008	+	8.09806i	−0.445785	+	0.286489i
$800$	−0.426832	+	2.96868i	−0.0150908	+	0.104959i
$801$	12.2535	+	7.87482i	0.432954	+	0.278243i
$802$	0.728242	−	0.840436i	0.0257151	−	0.0296768i
$803$	53.3730	+	15.6717i	1.88349	+	0.553043i
$804$	16.9934			0.599310
$805$	−4.47664	−	13.5809i	−0.157781	−	0.478665i
$806$	−0.168722			−0.00594298
$807$	−24.6007	−	7.22341i	−0.865985	−	0.254276i
$808$	0.814710	−	0.940225i	0.0286614	−	0.0330770i
$809$	15.4090	+	9.90278i	0.541753	+	0.348163i	0.782724	−	0.622369i	$-0.213830\pi$
$809$	15.4090	+	9.90278i	0.541753	+	0.348163i	−0.240971	+	0.970532i	$0.577466\pi$
$810$	−0.0273360	+	0.190126i	−0.000960488	+	0.00668034i
$811$	−33.9364	+	21.8096i	−1.19167	+	0.765838i	−0.977495	−	0.210958i	$-0.932342\pi$
$811$	−33.9364	+	21.8096i	−1.19167	+	0.765838i	−0.214172	+	0.976796i	$0.568705\pi$
$812$	2.86101	+	6.26474i	0.100402	+	0.219849i
$813$	11.5166	+	13.2909i	0.403906	+	0.466133i
$814$	0.0381660	+	0.265450i	0.00133772	+	0.00930402i
$815$	−5.49830	+	12.0396i	−0.192597	+	0.421729i
$816$	−16.9786	+	4.98537i	−0.594370	+	0.174523i
$817$	3.69196	−	1.08406i	0.129165	−	0.0379263i
$818$	0.429596	−	0.940684i	0.0150205	−	0.0328903i
$819$	−0.0512687	−	0.356582i	−0.00179147	−	0.0124600i
$820$	−10.1336	−	11.6948i	−0.353880	−	0.408399i
$821$	−15.8392	−	34.6831i	−0.552794	−	1.21045i	−0.955465	−	0.295104i	$-0.904646\pi$
$821$	−15.8392	−	34.6831i	−0.552794	−	1.21045i	0.402671	−	0.915345i	$-0.368082\pi$
$822$	−0.242599	+	0.155909i	−0.00846162	+	0.00543796i
$823$	4.96902	−	34.5603i	0.173209	−	1.20470i	−0.698840	−	0.715278i	$-0.746300\pi$
$823$	4.96902	−	34.5603i	0.173209	−	1.20470i	0.872049	−	0.489418i	$-0.162791\pi$
$824$	0.737296	+	0.473832i	0.0256849	+	0.0165067i
$825$	13.8804	−	16.0188i	0.483252	−	0.557703i
$826$	−0.616572	−	0.181042i	−0.0214533	−	0.00629925i
$827$	−1.05877			−0.0368170			−0.0184085	−	0.999831i	$-0.505860\pi$
$827$	−1.05877			−0.0368170			−0.0184085	+	0.999831i	$0.505860\pi$
$828$	−8.83254	−	3.68848i	−0.306952	−	0.128183i
$829$	1.95943			0.0680539			0.0340269	−	0.999421i	$-0.489167\pi$
$829$	1.95943			0.0680539			0.0340269	+	0.999421i	$0.489167\pi$
$830$	0.432142	+	0.126888i	0.0149999	+	0.00440436i
$831$	10.6831	−	12.3290i	0.370593	−	0.427687i
$832$	−2.39435	−	1.53876i	−0.0830092	−	0.0533468i
$833$	0.633520	−	4.40623i	0.0219502	−	0.152667i
$834$	−0.725918	+	0.466519i	−0.0251365	+	0.0161542i
$835$	−2.52186	−	5.52209i	−0.0872724	−	0.191100i
$836$	−23.5124	−	27.1348i	−0.813195	−	0.938477i
$837$	−1.03466	−	7.19624i	−0.0357632	−	0.248739i
$838$	0.0473644	−	0.103713i	0.00163617	−	0.00358272i
$839$	−48.6791	+	14.2935i	−1.68059	+	0.493466i	−0.976295	−	0.216442i	$-0.930555\pi$
$839$	−48.6791	+	14.2935i	−1.68059	+	0.493466i	−0.704294	+	0.709908i	$0.748737\pi$
$840$	−0.736436	+	0.216237i	−0.0254095	+	0.00746089i
$841$	−7.10050	+	15.5479i	−0.244845	+	0.536136i
$842$	−0.222905	−	1.55034i	−0.00768182	−	0.0534283i
$843$	14.1628	+	16.3447i	0.487792	+	0.562942i
$844$	−17.5924	−	38.5221i	−0.605557	−	1.32599i
$845$	−32.2832	+	20.7471i	−1.11058	+	0.713724i
$846$	−0.0308484	+	0.214555i	−0.00106059	+	0.00737657i
$847$	15.7160	+	10.1001i	0.540009	+	0.347043i
$848$	−29.2323	+	33.7358i	−1.00384	+	1.15849i
$849$	6.89196	+	2.02366i	0.236531	+	0.0694519i
$850$	−1.11568			−0.0382674
$851$	−3.60822	+	0.640241i	−0.123688	+	0.0219472i
$852$	−5.72069			−0.195988
$853$	−12.4055	−	3.64259i	−0.424756	−	0.124720i	0.0623662	−	0.998053i	$-0.480135\pi$
$853$	−12.4055	−	3.64259i	−0.424756	−	0.124720i	−0.487123	+	0.873334i	$0.661954\pi$
$854$	−0.405306	+	0.467748i	−0.0138693	+	0.0160060i
$855$	−8.28261	−	5.32291i	−0.283259	−	0.182040i
$856$	0.306805	−	2.13388i	0.0104864	−	0.0729344i
$857$	14.6495	−	9.41466i	0.500418	−	0.321599i	−0.265966	−	0.963983i	$-0.585691\pi$
$857$	14.6495	−	9.41466i	0.500418	−	0.321599i	0.766383	+	0.642384i	$0.222054\pi$
$858$	−0.0525230	−	0.115009i	−0.00179311	−	0.00392635i
$859$	10.7339	+	12.3876i	0.366237	+	0.422660i	0.908720	−	0.417407i	$-0.137061\pi$
$859$	10.7339	+	12.3876i	0.366237	+	0.422660i	−0.542483	+	0.840067i	$0.682516\pi$
$860$	0.986916	+	6.86415i	0.0336536	+	0.234066i
$861$	1.08020	−	2.36531i	0.0368131	−	0.0806095i
$862$	1.38683	−	0.407210i	0.0472356	−	0.0138696i
$863$	0.966020	−	0.283649i	0.0328837	−	0.00965553i	−0.265249	−	0.964180i	$-0.585454\pi$
$863$	0.966020	−	0.283649i	0.0328837	−	0.00965553i	0.298133	+	0.954524i	$0.403636\pi$
$864$	−0.320244	+	0.701237i	−0.0108949	+	0.0238566i
$865$	−9.83774	−	68.4230i	−0.334493	−	2.32645i
$866$	−0.521505	−	0.601849i	−0.0177215	−	0.0204517i
$867$	−1.16988	−	2.56169i	−0.0397313	−	0.0869995i
$868$	12.2069	−	7.84487i	0.414328	−	0.266272i
$869$	−10.4565	+	72.7266i	−0.354713	+	2.46708i
$870$	0.557597	+	0.358346i	0.0189043	+	0.0121491i
$871$	−2.00864	+	2.31810i	−0.0680603	+	0.0785457i
$872$	−1.60085	−	0.470052i	−0.0542117	−	0.0159180i
$873$	16.2864			0.551210
$874$	−0.748642	+	0.692985i	−0.0253232	+	0.0234406i
$875$	−3.30813			−0.111835
$876$	19.5526	+	5.74117i	0.660622	+	0.193976i
$877$	−18.6563	+	21.5305i	−0.629977	+	0.727032i	−0.977569	−	0.210614i	$-0.932454\pi$
$877$	−18.6563	+	21.5305i	−0.629977	+	0.727032i	0.347593	+	0.937646i	$0.386999\pi$
$878$	−0.795557	−	0.511273i	−0.0268487	−	0.0172546i
$879$	1.58406	−	11.0174i	0.0534290	−	0.371607i
$880$	54.3231	−	34.9114i	1.83123	−	1.17686i
$881$	2.09037	+	4.57727i	0.0704263	+	0.154212i	0.941571	−	0.336814i	$-0.109349\pi$
$881$	2.09037	+	4.57727i	0.0704263	+	0.154212i	−0.871145	+	0.491026i	$0.836622\pi$
$882$	−0.0421861	−	0.0486854i	−0.00142048	−	0.00163932i
$883$	−4.72071	−	32.8333i	−0.158865	−	1.10493i	−0.900730	−	0.434379i	$-0.856968\pi$
$883$	−4.72071	−	32.8333i	−0.158865	−	1.10493i	0.741866	−	0.670548i	$-0.233941\pi$
$884$	1.32960	−	2.91143i	0.0447194	−	0.0979219i
$885$	28.5382	−	8.37958i	0.959302	−	0.281676i
$886$	1.03314	−	0.303357i	0.0347090	−	0.0101915i
$887$	−7.44181	+	16.2953i	−0.249871	+	0.547142i	−0.992455	−	0.122612i	$-0.960873\pi$
$887$	−7.44181	+	16.2953i	−0.249871	+	0.547142i	0.742583	+	0.669754i	$0.233600\pi$
$888$	0.0279925	+	0.194692i	0.000939365	+	0.00653343i
$889$	11.1348	+	12.8502i	0.373448	+	0.430981i
$890$	1.16225	+	2.54496i	0.0389586	+	0.0853074i
$891$	4.58323	−	2.94546i	0.153544	−	0.0986766i
$892$	2.90876	−	20.2309i	0.0973926	−	0.677381i
$893$	−9.34685	−	6.00686i	−0.312780	−	0.201012i
$894$	−0.973287	+	1.12323i	−0.0325516	+	0.0375665i
$895$	31.7911	+	9.33471i	1.06266	+	0.312025i
$896$	−2.05076			−0.0685111
$897$	1.54717	−	0.768880i	0.0516586	−	0.0256721i
$898$	−0.220667			−0.00736377
$899$	−24.0713	−	7.06798i	−0.802824	−	0.235730i
$900$	5.08492	−	5.86832i	0.169497	−	0.195611i
$901$	−42.0533	−	27.0260i	−1.40100	−	0.900368i
$902$	0.129879	−	0.903325i	0.00432448	−	0.0300774i
$903$	−0.980314	+	0.630010i	−0.0326228	+	0.0209654i
$904$	1.10488	+	2.41935i	0.0367477	+	0.0804663i
$905$	−42.5162	−	49.0663i	−1.41329	−	1.63102i
$906$	−0.177182	−	1.23233i	−0.00588648	−	0.0409414i
$907$	−1.65877	+	3.63220i	−0.0550786	+	0.120605i	−0.935170	−	0.354198i	$-0.884754\pi$
$907$	−1.65877	+	3.63220i	−0.0550786	+	0.120605i	0.880092	+	0.474804i	$0.157481\pi$
$908$	−16.5584	+	4.86198i	−0.549509	+	0.161351i
$909$	−4.63731	+	1.36164i	−0.153810	+	0.0451626i
$910$	0.0287454	−	0.0629437i	0.000952902	−	0.00208656i
$911$	0.303766	+	2.11274i	0.0100642	+	0.0699982i	0.994235	−	0.107227i	$-0.0341971\pi$
$911$	0.303766	+	2.11274i	0.0100642	+	0.0699982i	−0.984170	+	0.177225i	$0.943288\pi$
$912$	−8.59558	−	9.91983i	−0.284628	−	0.328479i
$913$	−5.30673	−	11.6201i	−0.175627	−	0.384570i
$914$	−1.46235	+	0.939795i	−0.0483702	+	0.0310857i
$915$	4.07687	−	28.3552i	0.134777	−	0.937395i
$916$	0.360786	+	0.231863i	0.0119207	+	0.00766097i
$917$	5.11488	−	5.90289i	0.168908	−	0.194930i
$918$	−0.275152	−	0.0807919i	−0.00908137	−	0.00266653i
$919$	−40.3204			−1.33005			−0.665024	−	0.746822i	$-0.731579\pi$
$919$	−40.3204			−1.33005			−0.665024	+	0.746822i	$0.731579\pi$
$920$	−2.09058	−	3.02964i	−0.0689243	−	0.0998843i
$921$	−3.00089			−0.0988829
$922$	−0.323117	−	0.0948756i	−0.0106413	−	0.00312456i
$923$	0.676195	−	0.780370i	0.0222572	−	0.0256862i
$924$	9.14743	+	5.87870i	0.300928	+	0.193395i
$925$	0.423076	−	2.94256i	0.0139107	−	0.0967508i
$926$	−1.12871	+	0.725377i	−0.0370917	+	0.0238374i
$927$	−1.41438	−	3.09707i	−0.0464545	−	0.101721i
$928$	1.74204	+	2.01042i	0.0571852	+	0.0659953i
$929$	−3.12929	−	21.7647i	−0.102669	−	0.714076i	−0.974519	−	0.224304i	$-0.927989\pi$
$929$	−3.12929	−	21.7647i	−0.102669	−	0.714076i	0.871851	−	0.489772i	$-0.162920\pi$
$930$	0.580117	−	1.27028i	0.0190228	−	0.0416541i
$931$	3.16824	−	0.930280i	0.103835	−	0.0304887i
$932$	36.5023	−	10.7181i	1.19567	−	0.351082i
$933$	−7.47203	+	16.3615i	−0.244623	+	0.535650i
$934$	0.0715105	+	0.497366i	0.00233989	+	0.0162743i
$935$	47.3551	+	54.6507i	1.54868	+	1.78727i
$936$	−0.0385225	−	0.0843525i	−0.00125915	−	0.00275715i
$937$	18.1227	−	11.6467i	0.592042	−	0.380482i	−0.210043	−	0.977692i	$-0.567360\pi$
$937$	18.1227	−	11.6467i	0.592042	−	0.380482i	0.802085	+	0.597210i	$0.203724\pi$
$938$	−0.0780589	+	0.542911i	−0.00254871	+	0.0177267i
$939$	−2.95376	−	1.89827i	−0.0963924	−	0.0619476i
$940$	13.1130	−	15.1332i	0.427699	−	0.493591i
$941$	−5.05095	−	1.48309i	−0.164656	−	0.0483475i	0.198365	−	0.980128i	$-0.436437\pi$
$941$	−5.05095	−	1.48309i	−0.164656	−	0.0483475i	−0.363022	+	0.931781i	$0.618255\pi$
$942$	−1.01638			−0.0331155
$943$	12.3952	+	1.36884i	0.403644	+	0.0445757i
$944$	39.6526			1.29058
$945$	2.86092	+	0.840041i	0.0930657	+	0.0273265i
$946$	−0.267826	+	0.309087i	−0.00870777	+	0.0100493i
$947$	39.7454	+	25.5428i	1.29155	+	0.830031i	0.992266	−	0.124132i	$-0.0396147\pi$
$947$	39.7454	+	25.5428i	1.29155	+	0.830031i	0.299287	+	0.954163i	$0.403251\pi$
$948$	−3.83063	+	26.6426i	−0.124413	+	0.865312i
$949$	−3.09431	+	1.98860i	−0.100446	+	0.0645525i
$950$	−0.343785	−	0.752784i	−0.0111539	−	0.0244235i
$951$	−7.40286	−	8.54336i	−0.240054	−	0.277037i
$952$	−0.163076	−	1.13422i	−0.00528532	−	0.0367602i
$953$	−1.44737	+	3.16930i	−0.0468850	+	0.102664i	−0.931625	−	0.363421i	$-0.881609\pi$
$953$	−1.44737	+	3.16930i	−0.0468850	+	0.102664i	0.884740	+	0.466085i	$0.154336\pi$
$954$	−0.694106	+	0.203808i	−0.0224725	+	0.00659853i
$955$	−29.0633	+	8.53376i	−0.940467	+	0.276146i
$956$	5.32205	−	11.6537i	0.172127	−	0.376907i
$957$	−2.67549	−	18.6085i	−0.0864864	−	0.601526i
$958$	−1.46067	−	1.68570i	−0.0471921	−	0.0544626i
$959$	1.85962	+	4.07200i	0.0600503	+	0.131492i
$960$	19.8175	−	12.7359i	0.639607	−	0.411051i
$961$	−3.11049	+	21.6340i	−0.100339	+	0.697870i
$962$	−0.0149180	−	0.00958722i	−0.000480976	−	0.000309104i
$963$	−5.48443	+	6.32937i	−0.176733	+	0.203961i
$964$	45.5689	+	13.3802i	1.46767	+	0.430948i
$965$	2.00643			0.0645893
$966$	0.158413	−	0.265243i	0.00509686	−	0.00853405i
$967$	8.66076			0.278511			0.139256	−	0.990256i	$-0.455529\pi$
$967$	8.66076			0.278511			0.139256	+	0.990256i	$0.455529\pi$
$968$	4.61411	+	1.35482i	0.148303	+	0.0435457i
$969$	9.62577	−	11.1087i	0.309224	−	0.356864i
$970$	2.63169	+	1.69129i	0.0844986	+	0.0543039i
$971$	0.918627	−	6.38919i	0.0294801	−	0.205039i	−0.969758	−	0.244069i	$-0.921518\pi$
$971$	0.918627	−	6.38919i	0.0294801	−	0.205039i	0.999238	+	0.0390300i	$0.0124268\pi$
$972$	1.67902	−	1.07904i	0.0538545	−	0.0346102i
$973$	5.56445	+	12.1844i	0.178388	+	0.390615i
$974$	−1.70865	−	1.97189i	−0.0547487	−	0.0631833i
$975$	0.199462	+	1.38729i	0.00638790	+	0.0444288i
$976$	15.8652	−	34.7399i	0.507832	−	1.11200i
$977$	46.7055	−	13.7140i	1.49424	−	0.438748i	0.570348	−	0.821403i	$-0.306808\pi$
$977$	46.7055	−	13.7140i	1.49424	−	0.438748i	0.923891	+	0.382655i	$0.124990\pi$
$978$	−0.274375	+	0.0805638i	−0.00877355	+	0.00257615i
$979$	32.9654	−	72.1841i	1.05358	−	2.30701i
$980$	0.846919	+	5.89045i	0.0270538	+	0.188163i
$981$	4.24452	+	4.89843i	0.135517	+	0.156395i
$982$	−0.398096	−	0.871709i	−0.0127038	−	0.0278173i
$983$	37.0611	−	23.8177i	1.18206	−	0.759667i	0.206300	−	0.978489i	$-0.433858\pi$
$983$	37.0611	−	23.8177i	1.18206	−	0.759667i	0.975765	+	0.218822i	$0.0702214\pi$
$984$	0.0952582	−	0.662535i	0.00303672	−	0.0211208i
$985$	−42.0070	−	26.9963i	−1.33845	−	0.860172i
$986$	−0.648021	+	0.747856i	−0.0206372	+	0.0238166i
$987$	3.22852	+	0.947980i	0.102765	+	0.0301745i
$988$	2.37414			0.0755315
$989$	−4.34136	−	3.51922i	−0.138047	−	0.111905i
$990$	1.04647			0.0332591
$991$	−30.6752	−	9.00705i	−0.974430	−	0.286119i	−0.244507	−	0.969648i	$-0.578626\pi$
$991$	−30.6752	−	9.00705i	−0.974430	−	0.286119i	−0.729923	+	0.683529i	$0.760444\pi$
$992$	3.67026	−	4.23571i	0.116531	−	0.134484i
$993$	−8.27494	−	5.31798i	−0.262597	−	0.168761i
$994$	0.0262779	−	0.182767i	0.000833486	−	0.00579702i
$995$	42.5644	−	27.3545i	1.34938	−	0.867194i
$996$	−1.94407	−	4.25691i	−0.0616001	−	0.134885i
$997$	26.4621	+	30.5389i	0.838063	+	0.967176i	0.999807	−	0.0196566i	$-0.00625728\pi$
$997$	26.4621	+	30.5389i	0.838063	+	0.967176i	−0.161744	+	0.986833i	$0.551712\pi$
$998$	−0.292299	−	2.03298i	−0.00925255	−	0.0643529i
$999$	0.317426	−	0.695067i	0.0100429	−	0.0219909i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.d.64.3	✓	60
23.9	even	11	inner	483.2.q.d.400.3	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.d.64.3	✓	60	1.1	even	1	trivial
483.2.q.d.400.3	yes	60	23.9	even	11	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0618105 - 0.0181492i) q^{2} +(0.654861 - 0.755750i) q^{3} +(-1.67902 - 1.07904i) q^{4} +(-0.424340 + 2.95135i) q^{5} +(-0.0541936 + 0.0348281i) q^{6} +(0.415415 + 0.909632i) q^{7} +(0.168569 + 0.194540i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.0618105 - 0.0181492i) q^{2} +(0.654861 - 0.755750i) q^{3} +(-1.67902 - 1.07904i) q^{4} +(-0.424340 + 2.95135i) q^{5} +(-0.0541936 + 0.0348281i) q^{6} +(0.415415 + 0.909632i) q^{7} +(0.168569 + 0.194540i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.0797933 - 0.174723i) q^{10} +(-5.22740 + 1.53490i) q^{11} +(-1.91500 + 0.562296i) q^{12} +(0.149653 - 0.327694i) q^{13} +(-0.00916792 - 0.0637643i) q^{14} +(1.95260 + 2.25342i) q^{15} +(1.65132 + 3.61589i) q^{16} +(-3.74487 + 2.40668i) q^{17} +(-0.00916792 + 0.0637643i) q^{18} +(-2.77782 - 1.78519i) q^{19} +(3.89709 - 4.49748i) q^{20} +(0.959493 + 0.281733i) q^{21} +0.350966 q^{22} +(0.157333 + 4.79325i) q^{23} +0.257413 q^{24} +(-3.73293 - 1.09609i) q^{25} +(-0.0151975 + 0.0175388i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(0.284039 - 1.97554i) q^{28} +(-2.90293 + 1.86560i) q^{29} +(-0.0797933 - 0.174723i) q^{30} +(4.76100 + 5.49448i) q^{31} +(-0.109711 - 0.763056i) q^{32} +(-2.26322 + 4.95576i) q^{33} +(0.275152 - 0.0807919i) q^{34} +(-2.86092 + 0.840041i) q^{35} +(-0.829106 + 1.81549i) q^{36} +(0.108745 + 0.756341i) q^{37} +(0.139298 + 0.160759i) q^{38} +(-0.149653 - 0.327694i) q^{39} +(-0.645685 + 0.414956i) q^{40} +(0.370060 - 2.57382i) q^{41} +(-0.0541936 - 0.0348281i) q^{42} +(-0.763111 + 0.880676i) q^{43} +(10.4331 + 3.06344i) q^{44} +2.98170 q^{45} +(0.0772689 - 0.299129i) q^{46} +3.36482 q^{47} +(3.81410 + 1.11992i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(0.210841 + 0.135499i) q^{50} +(-0.633520 + 4.40623i) q^{51} +(-0.604863 + 0.388722i) q^{52} +(4.66494 + 10.2148i) q^{53} +(0.0421861 + 0.0486854i) q^{54} +(-2.31184 - 16.0792i) q^{55} +(-0.106933 + 0.234151i) q^{56} +(-3.16824 + 0.930280i) q^{57} +(0.213291 - 0.0626278i) q^{58} +(4.14385 - 9.07376i) q^{59} +(-0.846919 - 5.89045i) q^{60} +(-6.29161 - 7.26091i) q^{61} +(-0.194559 - 0.426025i) q^{62} +(0.841254 - 0.540641i) q^{63} +(1.12437 - 7.82016i) q^{64} +(0.903634 + 0.580731i) q^{65} +(0.229834 - 0.265242i) q^{66} +(-8.16946 - 2.39877i) q^{67} +8.88460 q^{68} +(3.72553 + 3.02001i) q^{69} +0.192081 q^{70} +(2.75019 + 0.807528i) q^{71} +(0.168569 - 0.194540i) q^{72} +(-8.58939 - 5.52006i) q^{73} +(0.00700538 - 0.0487235i) q^{74} +(-3.27291 + 2.10337i) q^{75} +(2.73770 + 5.99474i) q^{76} +(-3.56774 - 4.11739i) q^{77} +(0.00330273 + 0.0229710i) q^{78} +(5.60240 - 12.2676i) q^{79} +(-11.3725 + 3.33926i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-0.0695865 + 0.152373i) q^{82} +(0.333696 + 2.32091i) q^{83} +(-1.30700 - 1.50836i) q^{84} +(-5.51386 - 12.0737i) q^{85} +(0.0631519 - 0.0405852i) q^{86} +(-0.491088 + 3.41559i) q^{87} +(-1.17978 - 0.758199i) q^{88} +(-9.53851 + 11.0080i) q^{89} +(-0.184300 - 0.0541155i) q^{90} +0.360249 q^{91} +(4.90793 - 8.21771i) q^{92} +7.27024 q^{93} +(-0.207981 - 0.0610688i) q^{94} +(6.44747 - 7.44077i) q^{95} +(-0.648524 - 0.416781i) q^{96} +(-2.31779 + 16.1206i) q^{97} +(0.0541936 - 0.0348281i) q^{98} +(2.26322 + 4.95576i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9}+O(q^{10}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 22 q^{13} - q^{14} + 2 q^{15} - 27 q^{16} + q^{17} - q^{18} + 20 q^{19} - 75 q^{20} + 6 q^{21} - 16 q^{22} - 9 q^{23} - 36 q^{24} - 15 q^{25} - 16 q^{26} + 6 q^{27} - 14 q^{28} - 3 q^{29} + 17 q^{31} - 73 q^{32} - 5 q^{33} + 55 q^{34} - 2 q^{35} - 14 q^{36} + 56 q^{37} - 22 q^{38} - 22 q^{39} - 37 q^{40} - 18 q^{41} + 12 q^{42} - 19 q^{43} - 12 q^{44} + 20 q^{45} - 45 q^{46} + 42 q^{47} - 28 q^{48} - 6 q^{49} - 42 q^{50} - q^{51} + 76 q^{52} - 11 q^{53} - 10 q^{54} - 61 q^{55} + 3 q^{56} + 24 q^{57} - 78 q^{58} + 38 q^{59} + 31 q^{60} + 5 q^{61} + 69 q^{62} - 6 q^{63} - 27 q^{64} + 51 q^{65} + 49 q^{66} - 27 q^{67} + 112 q^{68} - 13 q^{69} + 22 q^{70} - 4 q^{71} + 25 q^{72} + 48 q^{73} - 62 q^{74} + 26 q^{75} - 85 q^{76} - 28 q^{77} - 6 q^{78} - 6 q^{79} + 169 q^{80} - 6 q^{81} - 200 q^{82} - 6 q^{83} + 3 q^{84} - 21 q^{85} - 180 q^{86} + 14 q^{87} + 211 q^{88} - 57 q^{89} - 22 q^{91} + 49 q^{92} - 50 q^{93} + 16 q^{94} + 56 q^{95} + 7 q^{96} - 52 q^{97} - 12 q^{98} + 5 q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9 + 5 * q^11 + 3 * q^12 + 22 * q^13 - q^14 + 2 * q^15 - 27 * q^16 + q^17 - q^18 + 20 * q^19 - 75 * q^20 + 6 * q^21 - 16 * q^22 - 9 * q^23 - 36 * q^24 - 15 * q^25 - 16 * q^26 + 6 * q^27 - 14 * q^28 - 3 * q^29 + 17 * q^31 - 73 * q^32 - 5 * q^33 + 55 * q^34 - 2 * q^35 - 14 * q^36 + 56 * q^37 - 22 * q^38 - 22 * q^39 - 37 * q^40 - 18 * q^41 + 12 * q^42 - 19 * q^43 - 12 * q^44 + 20 * q^45 - 45 * q^46 + 42 * q^47 - 28 * q^48 - 6 * q^49 - 42 * q^50 - q^51 + 76 * q^52 - 11 * q^53 - 10 * q^54 - 61 * q^55 + 3 * q^56 + 24 * q^57 - 78 * q^58 + 38 * q^59 + 31 * q^60 + 5 * q^61 + 69 * q^62 - 6 * q^63 - 27 * q^64 + 51 * q^65 + 49 * q^66 - 27 * q^67 + 112 * q^68 - 13 * q^69 + 22 * q^70 - 4 * q^71 + 25 * q^72 + 48 * q^73 - 62 * q^74 + 26 * q^75 - 85 * q^76 - 28 * q^77 - 6 * q^78 - 6 * q^79 + 169 * q^80 - 6 * q^81 - 200 * q^82 - 6 * q^83 + 3 * q^84 - 21 * q^85 - 180 * q^86 + 14 * q^87 + 211 * q^88 - 57 * q^89 - 22 * q^91 + 49 * q^92 - 50 * q^93 + 16 * q^94 + 56 * q^95 + 7 * q^96 - 52 * q^97 - 12 * q^98 + 5 * q^99

Introduction

L-functions

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