LMFDB - Embedded newform 882.2.bb.a.121.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(25,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([28, 16]))

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

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

chi := DirichletCharacter("882.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.bb (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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			121.17
Character	$\chi$	$=$	882.121
Dual form			882.2.bb.a.277.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.900969 + 0.433884i) q^{2} +(0.188178 - 1.72180i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.666227 + 0.205504i) q^{5} +(0.577518 + 1.63293i) q^{6} +(-2.48496 - 0.908292i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-2.92918 - 0.648008i) q^{9} +O(q^{10})$	\(q+(-0.900969 + 0.433884i) q^{2} +(0.188178 - 1.72180i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.666227 + 0.205504i) q^{5} +(0.577518 + 1.63293i) q^{6} +(-2.48496 - 0.908292i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-2.92918 - 0.648008i) q^{9} +(0.511085 - 0.474218i) q^{10} +(0.361109 - 4.81866i) q^{11} +(-1.22883 - 1.22065i) q^{12} +(-0.329987 + 4.40337i) q^{13} +(2.63296 - 0.259839i) q^{14} +(0.228467 + 1.18578i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-2.42699 + 6.18388i) q^{17} +(2.92026 - 0.687088i) q^{18} +(3.44315 - 5.96371i) q^{19} +(-0.254716 + 0.649007i) q^{20} +(-2.03151 + 4.10767i) q^{21} +(1.76539 + 4.49815i) q^{22} +(-1.88378 - 0.283934i) q^{23} +(1.63676 + 0.566596i) q^{24} +(-3.72957 + 2.54278i) q^{25} +(-1.61324 - 4.11047i) q^{26} +(-1.66695 + 4.92151i) q^{27} +(-2.25948 + 1.37651i) q^{28} +(-3.21615 + 8.19461i) q^{29} +(-0.720332 - 0.969223i) q^{30} +2.98391 q^{31} +(0.623490 + 0.781831i) q^{32} +(-8.22881 - 1.52852i) q^{33} +(-0.496439 - 6.62452i) q^{34} +(1.84220 + 0.0944610i) q^{35} +(-2.33295 + 1.88610i) q^{36} +(5.16886 - 0.779080i) q^{37} +(-0.514613 + 6.86704i) q^{38} +(7.51961 + 1.39679i) q^{39} +(-0.0521020 - 0.695252i) q^{40} +(-4.88153 - 4.52940i) q^{41} +(0.0480745 - 4.58232i) q^{42} +(2.18524 - 2.02761i) q^{43} +(-3.54224 - 3.28671i) q^{44} +(2.08467 - 0.170237i) q^{45} +(1.82042 - 0.561525i) q^{46} +(-11.8650 + 5.71389i) q^{47} +(-1.72050 + 0.199676i) q^{48} +(5.35001 + 4.51413i) q^{49} +(2.25695 - 3.90916i) q^{50} +(10.1907 + 5.34246i) q^{51} +(3.23695 + 3.00345i) q^{52} +(2.91997 + 0.440115i) q^{53} +(-0.633499 - 5.15739i) q^{54} +(0.749673 + 3.28453i) q^{55} +(1.43847 - 2.22054i) q^{56} +(-9.62037 - 7.05064i) q^{57} +(-0.657859 - 8.77852i) q^{58} +(1.17703 + 5.15691i) q^{59} +(1.06953 + 0.560699i) q^{60} +(4.73211 + 5.93387i) q^{61} +(-2.68841 + 1.29467i) q^{62} +(6.69030 + 4.27082i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-0.685063 - 3.00146i) q^{65} +(8.07711 - 2.19320i) q^{66} -3.04976 q^{67} +(3.32155 + 5.75309i) q^{68} +(-0.843361 + 3.19005i) q^{69} +(-1.70075 + 0.714195i) q^{70} +(-8.18884 + 10.2685i) q^{71} +(1.28356 - 2.71154i) q^{72} +(-0.370444 - 4.94323i) q^{73} +(-4.31895 + 2.94461i) q^{74} +(3.67633 + 6.90006i) q^{75} +(-2.51585 - 6.41027i) q^{76} +(-5.27409 + 11.6462i) q^{77} +(-7.38098 + 2.00418i) q^{78} -8.38639 q^{79} +(0.348601 + 0.603794i) q^{80} +(8.16017 + 3.79626i) q^{81} +(6.36334 + 1.96283i) q^{82} +(-0.343227 - 4.58005i) q^{83} +(1.94488 + 4.14939i) q^{84} +(0.346118 - 4.61862i) q^{85} +(-1.08909 + 2.77495i) q^{86} +(13.5043 + 7.07960i) q^{87} +(4.61750 + 1.42431i) q^{88} +(7.27536 - 4.96025i) q^{89} +(-1.80436 + 1.05788i) q^{90} +(4.81955 - 10.6424i) q^{91} +(-1.39650 + 1.29577i) q^{92} +(0.561505 - 5.13769i) q^{93} +(8.21084 - 10.2961i) q^{94} +(-1.06835 + 4.68076i) q^{95} +(1.46348 - 0.926400i) q^{96} +(5.19497 + 8.99795i) q^{97} +(-6.77880 - 1.74581i) q^{98} +(-4.18029 + 13.8807i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 56 q^{2} - 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} - 56 q^{8} - 15 q^{9}+O(q^{10}) $ 336 * q - 56 * q^2 - 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 - 56 * q^8 - 15 * q^9	\( 336 q - 56 q^{2} - 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} - 56 q^{8} - 15 q^{9} + 2 q^{10} + 2 q^{12} - 21 q^{13} - 7 q^{15} - 56 q^{16} + 7 q^{17} + 6 q^{18} - 34 q^{19} + 2 q^{20} + 16 q^{21} - 36 q^{23} + 2 q^{24} + 32 q^{25} + 7 q^{26} + 49 q^{27} - 16 q^{29} - 7 q^{30} + 92 q^{31} - 56 q^{32} + 14 q^{33} + 7 q^{34} + 16 q^{35} - 15 q^{36} - 26 q^{37} + q^{38} + 44 q^{39} + 2 q^{40} + 3 q^{41} - 33 q^{42} - 3 q^{43} + 106 q^{45} - 36 q^{46} + 27 q^{47} + 2 q^{48} - 74 q^{49} - 164 q^{50} - 7 q^{51} + 21 q^{52} - 78 q^{53} - 28 q^{54} - 53 q^{55} - 18 q^{57} + 40 q^{58} - 16 q^{59} - 7 q^{60} - 45 q^{61} - 20 q^{62} - 50 q^{63} - 56 q^{64} - 14 q^{65} + 14 q^{66} + 86 q^{67} - 21 q^{68} - 85 q^{69} - 26 q^{70} + 7 q^{71} + 6 q^{72} + 36 q^{73} + 2 q^{74} - 35 q^{75} + 8 q^{76} - 37 q^{77} - 12 q^{78} - 2 q^{79} - 12 q^{80} + 41 q^{81} + 3 q^{82} + 191 q^{83} - 5 q^{84} + 159 q^{85} - 3 q^{86} + 72 q^{87} + 59 q^{89} + 22 q^{90} - 29 q^{91} + 27 q^{92} + 23 q^{93} + 6 q^{94} + 26 q^{95} + 2 q^{96} - 113 q^{97} - 18 q^{98} - 33 q^{99}+O(q^{100}) \) 336 * q - 56 * q^2 - 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 - 56 * q^8 - 15 * q^9 + 2 * q^10 + 2 * q^12 - 21 * q^13 - 7 * q^15 - 56 * q^16 + 7 * q^17 + 6 * q^18 - 34 * q^19 + 2 * q^20 + 16 * q^21 - 36 * q^23 + 2 * q^24 + 32 * q^25 + 7 * q^26 + 49 * q^27 - 16 * q^29 - 7 * q^30 + 92 * q^31 - 56 * q^32 + 14 * q^33 + 7 * q^34 + 16 * q^35 - 15 * q^36 - 26 * q^37 + q^38 + 44 * q^39 + 2 * q^40 + 3 * q^41 - 33 * q^42 - 3 * q^43 + 106 * q^45 - 36 * q^46 + 27 * q^47 + 2 * q^48 - 74 * q^49 - 164 * q^50 - 7 * q^51 + 21 * q^52 - 78 * q^53 - 28 * q^54 - 53 * q^55 - 18 * q^57 + 40 * q^58 - 16 * q^59 - 7 * q^60 - 45 * q^61 - 20 * q^62 - 50 * q^63 - 56 * q^64 - 14 * q^65 + 14 * q^66 + 86 * q^67 - 21 * q^68 - 85 * q^69 - 26 * q^70 + 7 * q^71 + 6 * q^72 + 36 * q^73 + 2 * q^74 - 35 * q^75 + 8 * q^76 - 37 * q^77 - 12 * q^78 - 2 * q^79 - 12 * q^80 + 41 * q^81 + 3 * q^82 + 191 * q^83 - 5 * q^84 + 159 * q^85 - 3 * q^86 + 72 * q^87 + 59 * q^89 + 22 * q^90 - 29 * q^91 + 27 * q^92 + 23 * q^93 + 6 * q^94 + 26 * q^95 + 2 * q^96 - 113 * q^97 - 18 * q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.900969	+	0.433884i	−0.637081	+	0.306802i
$2$	−0.900969	+	0.433884i	−0.637081	+	0.306802i
$3$	0.188178	−	1.72180i	0.108644	−	0.994081i
$3$	0.188178	−	1.72180i	0.108644	−	0.994081i
$4$	0.623490	−	0.781831i	0.311745	−	0.390916i
$5$	−0.666227	+	0.205504i	−0.297946	+	0.0919041i	−0.440124	−	0.897937i	$-0.645066\pi$
$5$	−0.666227	+	0.205504i	−0.297946	+	0.0919041i	0.142178	+	0.989841i	$0.454589\pi$
$6$	0.577518	+	1.63293i	0.235771	+	0.666642i
$7$	−2.48496	−	0.908292i	−0.939225	−	0.343302i
$7$	−2.48496	−	0.908292i	−0.939225	−	0.343302i
$8$	−0.222521	+	0.974928i	−0.0786730	+	0.344689i
$9$	−2.92918	−	0.648008i	−0.976393	−	0.216003i
$10$	0.511085	−	0.474218i	0.161619	−	0.149961i
$11$	0.361109	−	4.81866i	0.108878	−	1.45288i	−0.628714	−	0.777636i	$-0.716419\pi$
$11$	0.361109	−	4.81866i	0.108878	−	1.45288i	0.737593	−	0.675246i	$-0.235962\pi$
$12$	−1.22883	−	1.22065i	−0.354732	−	0.352370i
$13$	−0.329987	+	4.40337i	−0.0915219	+	1.22127i	0.742616	+	0.669718i	$0.233585\pi$
$13$	−0.329987	+	4.40337i	−0.0915219	+	1.22127i	−0.834138	+	0.551556i	$0.814034\pi$
$14$	2.63296	−	0.259839i	0.703688	−	0.0694449i
$15$	0.228467	+	1.18578i	0.0589899	+	0.306167i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	−2.42699	+	6.18388i	−0.588632	+	1.49981i	0.257198	+	0.966359i	$0.417201\pi$
$17$	−2.42699	+	6.18388i	−0.588632	+	1.49981i	−0.845830	+	0.533452i	$0.820894\pi$
$18$	2.92026	−	0.687088i	0.688312	−	0.161948i
$19$	3.44315	−	5.96371i	0.789912	−	1.36817i	−0.136108	−	0.990694i	$-0.543459\pi$
$19$	3.44315	−	5.96371i	0.789912	−	1.36817i	0.926020	−	0.377474i	$-0.123207\pi$
$20$	−0.254716	+	0.649007i	−0.0569563	+	0.145122i
$21$	−2.03151	+	4.10767i	−0.443312	+	0.896368i
$22$	1.76539	+	4.49815i	0.376383	+	0.959008i
$23$	−1.88378	−	0.283934i	−0.392795	−	0.0592043i	−0.0503243	−	0.998733i	$-0.516026\pi$
$23$	−1.88378	−	0.283934i	−0.392795	−	0.0592043i	−0.342470	+	0.939529i	$0.611264\pi$
$24$	1.63676	+	0.566596i	0.334101	+	0.115656i
$25$	−3.72957	+	2.54278i	−0.745913	+	0.508555i
$26$	−1.61324	−	4.11047i	−0.316383	−	0.806130i
$27$	−1.66695	+	4.92151i	−0.320804	+	0.947146i
$28$	−2.25948	+	1.37651i	−0.427001	+	0.260135i
$29$	−3.21615	+	8.19461i	−0.597223	+	1.52170i	0.237703	+	0.971338i	$0.423606\pi$
$29$	−3.21615	+	8.19461i	−0.597223	+	1.52170i	−0.834926	+	0.550362i	$0.814490\pi$
$30$	−0.720332	−	0.969223i	−0.131514	−	0.176955i
$31$	2.98391			0.535926			0.267963	−	0.963429i	$-0.413650\pi$
$31$	2.98391			0.535926			0.267963	+	0.963429i	$0.413650\pi$
$32$	0.623490	+	0.781831i	0.110218	+	0.138210i
$33$	−8.22881	−	1.52852i	−1.43245	−	0.266082i
$34$	−0.496439	−	6.62452i	−0.0851386	−	1.13610i
$35$	1.84220	+	0.0944610i	0.311389	+	0.0159668i
$36$	−2.33295	+	1.88610i	−0.388824	+	0.314350i
$37$	5.16886	−	0.779080i	0.849755	−	0.128080i	0.290295	−	0.956937i	$-0.406247\pi$
$37$	5.16886	−	0.779080i	0.849755	−	0.128080i	0.559460	+	0.828857i	$0.311008\pi$
$38$	−0.514613	+	6.86704i	−0.0834813	+	1.11398i
$39$	7.51961	+	1.39679i	1.20410	+	0.223665i
$40$	−0.0521020	−	0.695252i	−0.00823804	−	0.109929i
$41$	−4.88153	−	4.52940i	−0.762367	−	0.707373i	0.199799	−	0.979837i	$-0.435971\pi$
$41$	−4.88153	−	4.52940i	−0.762367	−	0.707373i	−0.962166	+	0.272464i	$0.912161\pi$
$42$	0.0480745	−	4.58232i	0.00741806	−	0.707068i
$43$	2.18524	−	2.02761i	0.333246	−	0.309207i	−0.495746	−	0.868467i	$-0.665105\pi$
$43$	2.18524	−	2.02761i	0.333246	−	0.309207i	0.828992	+	0.559261i	$0.188915\pi$
$44$	−3.54224	−	3.28671i	−0.534012	−	0.495491i
$45$	2.08467	−	0.170237i	0.310764	−	0.0253774i
$46$	1.82042	−	0.561525i	0.268406	−	0.0827923i
$47$	−11.8650	+	5.71389i	−1.73069	+	0.833456i	−0.744544	+	0.667574i	$0.767333\pi$
$47$	−11.8650	+	5.71389i	−1.73069	+	0.833456i	−0.986146	+	0.165882i	$0.946953\pi$
$48$	−1.72050	+	0.199676i	−0.248333	+	0.0288208i
$49$	5.35001	+	4.51413i	0.764287	+	0.644876i
$50$	2.25695	−	3.90916i	0.319182	−	0.552839i
$51$	10.1907	+	5.34246i	1.42698	+	0.748094i
$52$	3.23695	+	3.00345i	0.448884	+	0.416503i
$53$	2.91997	+	0.440115i	0.401089	+	0.0604545i	0.346489	−	0.938054i	$-0.387374\pi$
$53$	2.91997	+	0.440115i	0.401089	+	0.0604545i	0.0545997	+	0.998508i	$0.482612\pi$
$54$	−0.633499	−	5.15739i	−0.0862083	−	0.701832i
$55$	0.749673	+	3.28453i	0.101086	+	0.442886i
$56$	1.43847	−	2.22054i	0.192224	−	0.296732i
$57$	−9.62037	−	7.05064i	−1.27425	−	0.933880i
$58$	−0.657859	−	8.77852i	−0.0863811	−	1.15268i
$59$	1.17703	+	5.15691i	0.153236	+	0.671372i	0.991932	+	0.126772i	$0.0404615\pi$
$59$	1.17703	+	5.15691i	0.153236	+	0.671372i	−0.838696	+	0.544600i	$0.816681\pi$
$60$	1.06953	+	0.560699i	0.138075	+	0.0723859i
$61$	4.73211	+	5.93387i	0.605884	+	0.759755i	0.986282	−	0.165068i	$-0.0527844\pi$
$61$	4.73211	+	5.93387i	0.605884	+	0.759755i	−0.380398	+	0.924823i	$0.624213\pi$
$62$	−2.68841	+	1.29467i	−0.341428	+	0.164423i
$63$	6.69030	+	4.27082i	0.842898	+	0.538073i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	−0.685063	−	3.00146i	−0.0849716	−	0.372285i
$66$	8.07711	−	2.19320i	0.994223	−	0.269964i
$67$	−3.04976			−0.372588			−0.186294	−	0.982494i	$-0.559648\pi$
$67$	−3.04976			−0.372588			−0.186294	+	0.982494i	$0.559648\pi$
$68$	3.32155	+	5.75309i	0.402797	+	0.697664i
$69$	−0.843361	+	3.19005i	−0.101529	+	0.384037i
$70$	−1.70075	+	0.714195i	−0.203279	+	0.0853627i
$71$	−8.18884	+	10.2685i	−0.971837	+	1.21865i	0.00396557	+	0.999992i	$0.498738\pi$
$71$	−8.18884	+	10.2685i	−0.971837	+	1.21865i	−0.975803	+	0.218653i	$0.929834\pi$
$72$	1.28356	−	2.71154i	0.151270	−	0.319558i
$73$	−0.370444	−	4.94323i	−0.0433572	−	0.578562i	−0.976001	−	0.217764i	$-0.930124\pi$
$73$	−0.370444	−	4.94323i	−0.0433572	−	0.578562i	0.932644	−	0.360797i	$-0.117495\pi$
$74$	−4.31895	+	2.94461i	−0.502068	+	0.342304i
$75$	3.67633	+	6.90006i	0.424506	+	0.796750i
$76$	−2.51585	−	6.41027i	−0.288587	−	0.735308i
$77$	−5.27409	+	11.6462i	−0.601039	+	1.32720i
$78$	−7.38098	+	2.00418i	−0.835731	+	0.226928i
$79$	−8.38639			−0.943542			−0.471771	−	0.881721i	$-0.656385\pi$
$79$	−8.38639			−0.943542			−0.471771	+	0.881721i	$0.656385\pi$
$80$	0.348601	+	0.603794i	0.0389748	+	0.0675063i
$81$	8.16017	+	3.79626i	0.906686	+	0.421807i
$82$	6.36334	+	1.96283i	0.702713	+	0.216758i
$83$	−0.343227	−	4.58005i	−0.0376741	−	0.502726i	−0.983841	−	0.179046i	$-0.942699\pi$
$83$	−0.343227	−	4.58005i	−0.0376741	−	0.502726i	0.946167	−	0.323680i	$-0.104920\pi$
$84$	1.94488	+	4.14939i	0.212204	+	0.452736i
$85$	0.346118	−	4.61862i	0.0375418	−	0.500960i
$86$	−1.08909	+	2.77495i	−0.117439	+	0.299230i
$87$	13.5043	+	7.07960i	1.44781	+	0.759012i
$88$	4.61750	+	1.42431i	0.492227	+	0.151832i
$89$	7.27536	−	4.96025i	0.771186	−	0.525786i	−0.112621	−	0.993638i	$-0.535924\pi$
$89$	7.27536	−	4.96025i	0.771186	−	0.525786i	0.883807	+	0.467852i	$0.154972\pi$
$90$	−1.80436	+	1.05788i	−0.190196	+	0.111510i
$91$	4.81955	−	10.6424i	0.505226	−	1.11563i
$92$	−1.39650	+	1.29577i	−0.145596	+	0.135093i
$93$	0.561505	−	5.13769i	0.0582253	−	0.532753i
$94$	8.21084	−	10.2961i	0.846884	−	1.06196i
$95$	−1.06835	+	4.68076i	−0.109611	+	0.480236i
$96$	1.46348	−	0.926400i	0.149366	−	0.0945503i
$97$	5.19497	+	8.99795i	0.527469	+	0.913604i	0.999487	+	0.0320148i	$0.0101924\pi$
$97$	5.19497	+	8.99795i	0.527469	+	0.913604i	−0.472018	+	0.881589i	$0.656474\pi$
$98$	−6.77880	−	1.74581i	−0.684762	−	0.176353i
$99$	−4.18029	+	13.8807i	−0.420135	+	1.39507i
$100$	−0.337325	+	4.50129i	−0.0337325	+	0.450129i
$101$	−1.81521	−	1.68427i	−0.180620	−	0.167591i	0.584681	−	0.811263i	$-0.301220\pi$
$101$	−1.81521	−	1.68427i	−0.180620	−	0.167591i	−0.765301	+	0.643672i	$0.777410\pi$
$102$	−11.4995	−	0.391819i	−1.13862	−	0.0387958i
$103$	−12.9988	+	4.00959i	−1.28081	+	0.395077i	−0.859171	−	0.511688i	$-0.829020\pi$
$103$	−12.9988	+	4.00959i	−1.28081	+	0.395077i	−0.421637	+	0.906765i	$0.638544\pi$
$104$	−4.21954	−	1.30155i	−0.413760	−	0.127628i
$105$	0.509304	−	3.15413i	0.0497030	−	0.307811i
$106$	−2.82176	+	0.870399i	−0.274074	+	0.0845406i
$107$	−8.37054	+	5.70693i	−0.809210	+	0.551710i	−0.895760	−	0.444537i	$-0.853368\pi$
$107$	−8.37054	+	5.70693i	−0.809210	+	0.551710i	0.0865501	+	0.996248i	$0.472416\pi$
$108$	2.80847	+	4.37178i	0.270245	+	0.420675i
$109$	−12.2571	−	8.35674i	−1.17402	−	0.800431i	−0.190577	−	0.981672i	$-0.561036\pi$
$109$	−12.2571	−	8.35674i	−1.17402	−	0.800431i	−0.983439	+	0.181242i	$0.941988\pi$
$110$	−2.10054	−	2.63399i	−0.200278	−	0.251141i
$111$	−0.368755	−	9.04634i	−0.0350007	−	0.858641i
$112$	−0.332565	+	2.62477i	−0.0314244	+	0.248017i
$113$	−2.86139	+	1.95086i	−0.269177	+	0.183522i	−0.690385	−	0.723443i	$-0.742559\pi$
$113$	−2.86139	+	1.95086i	−0.269177	+	0.183522i	0.421208	+	0.906964i	$0.361606\pi$
$114$	11.7268	+	2.17828i	1.09832	+	0.204015i
$115$	1.31337	−	0.197959i	0.122473	−	0.0184598i
$116$	4.40157	+	7.62374i	0.408675	+	0.707846i
$117$	3.82001	−	12.6844i	0.353160	−	1.17267i
$118$	−3.29797	−	4.13552i	−0.303602	−	0.380705i
$119$	11.6477	−	13.1622i	1.06775	−	1.20658i
$120$	−1.20689	−	0.0411219i	−0.110173	−	0.00375390i
$121$	−12.2120	−	1.84066i	−1.11018	−	0.167333i
$122$	−6.83809	−	3.29305i	−0.619092	−	0.298139i
$123$	−8.71730	+	7.55268i	−0.786013	+	0.681002i
$124$	1.86044	−	2.33291i	0.167072	−	0.209502i
$125$	4.13568	−	5.18598i	0.369906	−	0.463848i
$126$	−7.88079	−	0.945066i	−0.702077	−	0.0841932i
$127$	1.95116	+	2.44668i	0.173137	+	0.217107i	0.860827	−	0.508897i	$-0.169947\pi$
$127$	1.95116	+	2.44668i	0.173137	+	0.217107i	−0.687690	+	0.726004i	$0.741375\pi$
$128$	1.00000			0.0883883
$129$	−3.07991	−	4.14409i	−0.271171	−	0.364867i
$130$	1.91950	+	2.40698i	0.168352	+	0.211106i
$131$	−3.52891	+	3.27435i	−0.308322	+	0.286081i	−0.819123	−	0.573618i	$-0.805539\pi$
$131$	−3.52891	+	3.27435i	−0.308322	+	0.286081i	0.510801	+	0.859699i	$0.329349\pi$
$132$	−6.32563	+	5.48053i	−0.550575	+	0.477019i
$133$	−13.9729	+	11.6922i	−1.21160	+	1.01384i
$134$	2.74774	−	1.32324i	0.237369	−	0.114311i
$135$	0.0991742	−	3.62141i	0.00853556	−	0.311681i
$136$	−5.48878	−	3.74219i	−0.470659	−	0.320890i
$137$	−20.9318	−	6.45661i	−1.78832	−	0.551625i	−0.790200	−	0.612849i	$-0.790024\pi$
$137$	−20.9318	−	6.45661i	−1.78832	−	0.551625i	−0.998124	+	0.0612236i	$0.980500\pi$
$138$	−0.624270	−	3.24006i	−0.0531414	−	0.275812i
$139$	−13.7861	−	12.7916i	−1.16932	−	1.08497i	−0.994958	−	0.100290i	$-0.968023\pi$
$139$	−13.7861	−	12.7916i	−1.16932	−	1.08497i	−0.174363	−	0.984681i	$-0.555787\pi$
$140$	1.22245	−	1.38140i	0.103316	−	0.116749i
$141$	7.60543	+	21.5044i	0.640493	+	1.81100i
$142$	2.92256	−	12.8046i	0.245256	−	1.07454i
$143$	21.0992	+	3.18019i	1.76440	+	0.265941i
$144$	0.0200423	+	2.99993i	0.00167019	+	0.249994i
$145$	0.458660	−	6.12040i	0.0380897	−	0.508271i
$146$	2.47855	+	4.29297i	0.205126	+	0.355289i
$147$	8.77918	−	8.36218i	0.724094	−	0.689701i
$148$	2.61362	−	4.52693i	0.214838	−	0.372111i
$149$	−3.38505	−	2.30789i	−0.277314	−	0.189070i	0.416674	−	0.909056i	$-0.363196\pi$
$149$	−3.38505	−	2.30789i	−0.277314	−	0.189070i	−0.693988	+	0.719986i	$0.744148\pi$
$150$	−6.30608	−	4.62164i	−0.514889	−	0.377355i
$151$	−7.25942	−	18.4967i	−0.590764	−	1.50524i	−0.843185	−	0.537624i	$-0.819322\pi$
$151$	−7.25942	−	18.4967i	−0.590764	−	1.50524i	0.252421	−	0.967617i	$-0.418773\pi$
$152$	5.04801	+	4.68387i	0.409448	+	0.379912i
$153$	11.1163	−	16.5410i	0.898700	−	1.33726i
$154$	−0.301290	−	12.7812i	−0.0242787	−	1.02994i
$155$	−1.98796	+	0.613204i	−0.159677	+	0.0492538i
$156$	5.78045	−	5.00819i	0.462807	−	0.400976i
$157$	2.60717	+	11.4228i	0.208075	+	0.911636i	0.965846	+	0.259116i	$0.0834311\pi$
$157$	2.60717	+	11.4228i	0.208075	+	0.911636i	−0.757771	+	0.652520i	$0.773712\pi$
$158$	7.55587	−	3.63872i	0.601113	−	0.289481i
$159$	1.30726	−	4.94479i	0.103673	−	0.392147i
$160$	−0.576055	−	0.392748i	−0.0455412	−	0.0310494i
$161$	4.42321	+	2.41658i	0.348598	+	0.190453i
$162$	−8.99920	+	0.120251i	−0.707044	+	0.00944781i
$163$	5.25254	+	1.62019i	0.411410	+	0.126903i	0.493550	−	0.869718i	$-0.335699\pi$
$163$	5.25254	+	1.62019i	0.411410	+	0.126903i	−0.0821393	+	0.996621i	$0.526175\pi$
$164$	−6.58481	+	0.992500i	−0.514187	+	0.0775013i
$165$	5.79638	−	0.672710i	0.451247	−	0.0523704i
$166$	2.29645	+	3.97756i	0.178239	+	0.308719i
$167$	13.5315	−	2.03954i	1.04710	−	0.157824i	0.397110	−	0.917771i	$-0.370013\pi$
$167$	13.5315	−	2.03954i	1.04710	−	0.157824i	0.649985	+	0.759947i	$0.274775\pi$
$168$	−3.55263	−	2.89462i	−0.274091	−	0.223325i
$169$	−6.42595	−	0.968556i	−0.494304	−	0.0745043i
$170$	1.69210	+	4.31141i	0.129778	+	0.330670i
$171$	−13.9501	+	15.2376i	−1.06679	+	1.16525i
$172$	−0.222772	−	2.97268i	−0.0169862	−	0.226665i
$173$	10.0333	−	12.5814i	0.762819	−	0.956545i	−0.237069	−	0.971493i	$-0.576187\pi$
$173$	10.0333	−	12.5814i	0.762819	−	0.956545i	0.999888	+	0.0149479i	$0.00475824\pi$
$174$	−15.2386	−	0.519221i	−1.15524	−	0.0393620i
$175$	11.5774	−	2.93115i	0.875169	−	0.221574i
$176$	−4.77820	+	0.720198i	−0.360171	+	0.0542870i
$177$	9.10064	−	1.05619i	0.684046	−	0.0793884i
$178$	−4.40270	+	7.62569i	−0.329996	+	0.571570i
$179$	4.84251	−	12.3385i	0.361946	−	0.922223i	−0.627669	−	0.778480i	$-0.715991\pi$
$179$	4.84251	−	12.3385i	0.361946	−	0.922223i	0.989615	−	0.143743i	$-0.0459139\pi$
$180$	1.16667	−	1.73600i	0.0869586	−	0.129394i
$181$	18.5582	+	8.93716i	1.37942	+	0.664294i	0.968876	−	0.247547i	$-0.0796244\pi$
$181$	18.5582	+	8.93716i	1.37942	+	0.664294i	0.410544	+	0.911841i	$0.365339\pi$
$182$	0.275324	+	11.6796i	0.0204083	+	0.865752i
$183$	11.1074	−	7.03111i	0.821083	−	0.519755i
$184$	0.695995	−	1.77337i	0.0513094	−	0.130734i
$185$	−3.28353	+	1.58126i	−0.241410	+	0.116257i
$186$	1.72326	+	4.87252i	0.126356	+	0.357271i
$187$	28.9216	+	13.9279i	2.11496	+	1.01851i
$188$	−2.93041	+	12.8390i	−0.213722	+	0.936379i
$189$	8.61246	−	10.7157i	0.626464	−	0.779450i
$190$	−1.06835	−	4.68076i	−0.0775065	−	0.339578i
$191$	−2.45042	+	10.7360i	−0.177306	+	0.776830i	0.805561	+	0.592513i	$0.201864\pi$
$191$	−2.45042	+	10.7360i	−0.177306	+	0.776830i	−0.982867	+	0.184316i	$0.940993\pi$
$192$	−0.916603	+	1.46964i	−0.0661501	+	0.106062i
$193$	4.13232	−	18.1049i	0.297451	−	1.30322i	−0.576457	−	0.817128i	$-0.695565\pi$
$193$	4.13232	−	18.1049i	0.297451	−	1.30322i	0.873908	−	0.486091i	$-0.161578\pi$
$194$	−8.58457	−	5.85286i	−0.616336	−	0.420211i
$195$	−5.29681	+	0.614733i	−0.379313	+	0.0440219i
$196$	6.86497	−	1.36829i	0.490355	−	0.0977351i
$197$	−9.35051			−0.666196			−0.333098	−	0.942892i	$-0.608094\pi$
$197$	−9.35051			−0.666196			−0.333098	+	0.942892i	$0.608094\pi$
$198$	−2.25631	−	14.3199i	−0.160349	−	1.01767i
$199$	7.42321	−	2.28976i	0.526217	−	0.162317i	−0.0202532	−	0.999795i	$-0.506447\pi$
$199$	7.42321	−	2.28976i	0.526217	−	0.162317i	0.546471	+	0.837478i	$0.315971\pi$
$200$	−1.64912	−	4.20188i	−0.116610	−	0.297118i
$201$	−0.573897	+	5.25107i	−0.0404796	+	0.370382i
$202$	2.36622	+	0.729882i	0.166487	+	0.0513543i
$203$	15.4351	−	17.4420i	1.08333	−	1.22419i
$204$	10.5307	−	4.63643i	0.737296	−	0.324615i
$205$	4.18302	+	2.01443i	0.292154	+	0.140694i
$206$	9.97180	−	9.25248i	0.694768	−	0.644651i
$207$	5.33393	+	2.05239i	0.370734	+	0.142651i
$208$	4.36639	−	0.658128i	0.302755	−	0.0456330i
$209$	−27.4937	−	18.7449i	−1.90178	−	1.29661i
$210$	0.909656	+	3.06275i	0.0627723	+	0.211350i
$211$	−16.7154	+	11.3964i	−1.15074	+	0.784560i	−0.979654	−	0.200696i	$-0.935680\pi$
$211$	−16.7154	+	11.3964i	−1.15074	+	0.784560i	−0.171085	+	0.985256i	$0.554727\pi$
$212$	2.16467	−	2.00852i	0.148670	−	0.137946i
$213$	16.1393	+	16.0318i	1.10585	+	1.09848i
$214$	5.06545	−	8.77361i	0.346267	−	0.599752i
$215$	−1.03918	+	1.79992i	−0.0708718	+	0.122754i
$216$	−4.42719	−	2.72029i	−0.301232	−	0.185092i
$217$	−7.41488	−	2.71026i	−0.503355	−	0.183984i
$218$	14.6691	+	2.21101i	0.993517	+	0.149749i
$219$	−8.58096	−	0.292376i	−0.579847	−	0.0197570i
$220$	3.03537	+	1.46175i	0.204644	+	0.0985515i
$221$	−26.4290	−	12.7275i	−1.77781	−	0.856147i
$222$	4.25730	+	7.99047i	0.285731	+	0.536285i
$223$	−3.64504	−	0.549401i	−0.244090	−	0.0367906i	0.0258578	−	0.999666i	$-0.491768\pi$
$223$	−3.64504	−	0.549401i	−0.244090	−	0.0367906i	−0.269948	+	0.962875i	$0.587006\pi$
$224$	−0.839213	−	2.50913i	−0.0560723	−	0.167648i
$225$	12.5723	−	5.03145i	0.838154	−	0.335430i
$226$	1.73157	−	2.99917i	0.115183	−	0.199502i
$227$	8.14937	−	14.1151i	0.540893	−	0.936854i	−0.457960	−	0.888973i	$-0.651420\pi$
$227$	8.14937	−	14.1151i	0.540893	−	0.936854i	0.998853	−	0.0478812i	$-0.0152469\pi$
$228$	−11.5106	+	3.12551i	−0.762309	+	0.206992i
$229$	1.15810	−	1.07456i	0.0765293	−	0.0710088i	−0.640981	−	0.767557i	$-0.721472\pi$
$229$	1.15810	−	1.07456i	0.0765293	−	0.0710088i	0.717510	+	0.696548i	$0.245282\pi$
$230$	−1.09742	+	0.748206i	−0.0723615	+	0.0493352i
$231$	19.0599	+	11.2725i	1.25405	+	0.741675i
$232$	−7.27349	−	4.95898i	−0.477528	−	0.325573i
$233$	−13.5917	+	2.04861i	−0.890420	+	0.134209i	−0.578291	−	0.815831i	$-0.696280\pi$
$233$	−13.5917	+	2.04861i	−0.890420	+	0.134209i	−0.312129	+	0.950040i	$0.601042\pi$
$234$	2.06185	+	13.0857i	0.134788	+	0.855439i
$235$	6.73056	−	6.24505i	0.439054	−	0.407382i
$236$	4.76570	+	2.29504i	0.310221	+	0.149394i
$237$	−1.57813	+	14.4397i	−0.102511	+	0.937957i
$238$	−4.78337	+	16.9125i	−0.310060	+	1.09628i
$239$	−9.87005	−	3.04451i	−0.638440	−	0.196933i	−0.0413983	−	0.999143i	$-0.513181\pi$
$239$	−9.87005	−	3.04451i	−0.638440	−	0.196933i	−0.597042	+	0.802210i	$0.703657\pi$
$240$	1.10521	−	0.486600i	0.0713411	−	0.0314099i
$241$	6.43691	+	16.4010i	0.414638	+	1.05648i	0.973797	+	0.227419i	$0.0730288\pi$
$241$	6.43691	+	16.4010i	0.414638	+	1.05648i	−0.559159	+	0.829060i	$0.688876\pi$
$242$	11.8012	−	3.64020i	0.758613	−	0.234001i
$243$	8.07196	−	13.3358i	0.517817	−	0.855492i
$244$	7.58971			0.485881
$245$	−4.49199	−	1.90799i	−0.286983	−	0.121897i
$246$	4.57704	−	10.5870i	0.291821	−	0.675004i
$247$	25.1242	+	17.1294i	1.59861	+	1.08992i
$248$	−0.663982	+	2.90909i	−0.0421629	+	0.184728i
$249$	−7.95051	−	0.270895i	−0.503843	−	0.0171673i
$250$	−1.47601	+	6.46681i	−0.0933509	+	0.408997i
$251$	−1.55081	−	6.79452i	−0.0978860	−	0.428866i	0.902111	−	0.431505i	$-0.142017\pi$
$251$	−1.55081	−	6.79452i	−0.0978860	−	0.428866i	−0.999997	+	0.00263856i	$0.999160\pi$
$252$	7.51040	−	2.56787i	0.473110	−	0.161761i
$253$	−2.04843	+	8.97476i	−0.128784	+	0.564238i
$254$	−2.81951	−	1.35780i	−0.176912	−	0.0851961i
$255$	−7.88721	−	1.46507i	−0.493916	−	0.0917461i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	−2.44684	+	6.23444i	−0.152630	+	0.388894i	−0.986653	−	0.162835i	$-0.947936\pi$
$257$	−2.44684	+	6.23444i	−0.152630	+	0.388894i	0.834024	+	0.551729i	$0.186032\pi$
$258$	4.57296	+	2.39737i	0.284700	+	0.149254i
$259$	−13.5520	−	2.75886i	−0.842082	−	0.171427i
$260$	−2.77376	−	1.33577i	−0.172021	−	0.0828412i
$261$	14.7308	−	21.9194i	0.911816	−	1.35678i
$262$	1.75875	−	4.48122i	0.108656	−	0.276851i
$263$	−4.32599	+	7.49284i	−0.266752	+	0.462028i	−0.968021	−	0.250869i	$-0.919284\pi$
$263$	−4.32599	+	7.49284i	−0.266752	+	0.462028i	0.701269	+	0.712897i	$0.252617\pi$
$264$	3.32128	−	7.68237i	0.204411	−	0.472817i
$265$	−2.03581	+	0.306849i	−0.125059	+	0.0188496i
$266$	7.51607	−	16.5969i	0.460840	−	1.01762i
$267$	−7.17150	−	13.4601i	−0.438888	−	0.823745i
$268$	−1.90149	+	2.38440i	−0.116152	+	0.145650i
$269$	−1.64874	−	22.0009i	−0.100525	−	1.34142i	−0.788210	−	0.615407i	$-0.788992\pi$
$269$	−1.64874	−	22.0009i	−0.100525	−	1.34142i	0.687685	−	0.726010i	$-0.258627\pi$
$270$	1.48192	+	3.30581i	0.0901866	+	0.201185i
$271$	−9.71384	−	24.7505i	−0.590074	−	1.50348i	−0.844045	−	0.536272i	$-0.819832\pi$
$271$	−9.71384	−	24.7505i	−0.590074	−	1.50348i	0.253971	−	0.967212i	$-0.418263\pi$
$272$	6.56889	+	0.990101i	0.398298	+	0.0600337i
$273$	−17.4172	−	10.3010i	−1.05414	−	0.623442i
$274$	21.6603	−	3.26477i	1.30855	−	0.197232i
$275$	10.9060	+	18.8898i	0.657657	+	1.13909i
$276$	1.96826	+	2.64833i	0.118475	+	0.159411i
$277$	5.93466	−	0.894506i	0.356579	−	0.0537457i	0.0316900	−	0.999498i	$-0.489911\pi$
$277$	5.93466	−	0.894506i	0.356579	−	0.0537457i	0.324889	+	0.945752i	$0.394673\pi$
$278$	17.9709	+	5.54330i	1.07782	+	0.332465i
$279$	−8.74040	−	1.93360i	−0.523274	−	0.115761i
$280$	−0.502021	+	1.77499i	−0.0300015	+	0.106076i
$281$	9.52019	+	6.49076i	0.567927	+	0.387206i	0.812970	−	0.582306i	$-0.197850\pi$
$281$	9.52019	+	6.49076i	0.567927	+	0.387206i	−0.245043	+	0.969512i	$0.578802\pi$
$282$	−16.1827	−	16.0749i	−0.963663	−	0.957246i
$283$	−2.51152	+	1.20948i	−0.149294	+	0.0718964i	−0.507039	−	0.861923i	$-0.669260\pi$
$283$	−2.51152	+	1.20948i	−0.149294	+	0.0718964i	0.357745	+	0.933819i	$0.383546\pi$
$284$	2.92256	+	12.8046i	0.173422	+	0.759813i
$285$	7.85829	+	2.72030i	0.465485	+	0.161137i
$286$	−20.3895	+	6.28934i	−1.20566	+	0.371897i
$287$	8.01637	+	15.6892i	0.473191	+	0.926105i
$288$	−1.31968	−	2.69415i	−0.0777629	−	0.158754i
$289$	−19.8882	−	18.4535i	−1.16989	−	1.08550i
$290$	2.24230	+	5.71329i	0.131673	+	0.335496i
$291$	16.4702	−	7.25148i	0.965502	−	0.425089i
$292$	−4.09574	−	2.79243i	−0.239685	−	0.163415i
$293$	−0.950340	+	1.64604i	−0.0555195	+	0.0961625i	−0.892449	−	0.451148i	$-0.851015\pi$
$293$	−0.950340	+	1.64604i	−0.0555195	+	0.0961625i	0.836930	+	0.547310i	$0.184348\pi$
$294$	−4.28155	+	11.3432i	−0.249705	+	0.661549i
$295$	−1.84393	−	3.19379i	−0.107358	−	0.185949i
$296$	−0.390632	+	5.21263i	−0.0227050	+	0.302978i
$297$	23.1132	+	9.80965i	1.34116	+	0.569214i
$298$	4.05118	+	0.610617i	0.234679	+	0.0353721i
$299$	1.87189	−	8.20127i	0.108254	−	0.474291i
$300$	7.68683	+	1.42785i	0.443799	+	0.0824368i
$301$	−7.27188	+	3.05367i	−0.419144	+	0.176011i
$302$	14.5659	+	13.5152i	0.838175	+	0.777713i
$303$	−3.24155	+	2.80848i	−0.186222	+	0.161343i
$304$	−6.58036	−	2.02977i	−0.377409	−	0.116415i
$305$	−4.37209	−	2.98084i	−0.250345	−	0.170682i
$306$	−2.83858	+	19.7261i	−0.162271	+	1.12767i
$307$	−14.6665	+	7.06301i	−0.837061	+	0.403107i	−0.802759	−	0.596304i	$-0.796635\pi$
$307$	−14.6665	+	7.06301i	−0.837061	+	0.403107i	−0.0343025	+	0.999411i	$0.510921\pi$
$308$	5.81700	+	11.3847i	0.331454	+	0.648705i
$309$	4.45763	+	23.1358i	0.253586	+	1.31615i
$310$	1.52503	−	1.41502i	0.0866159	−	0.0803678i
$311$	−9.72897	−	12.1997i	−0.551679	−	0.691784i	0.425316	−	0.905045i	$-0.360163\pi$
$311$	−9.72897	−	12.1997i	−0.551679	−	0.691784i	−0.976995	+	0.213261i	$0.931592\pi$
$312$	−3.03504	+	7.02027i	−0.171825	+	0.397444i
$313$	13.2021			0.746230			0.373115	−	0.927785i	$-0.378290\pi$
$313$	13.2021			0.746230			0.373115	+	0.927785i	$0.378290\pi$
$314$	−7.30513	−	9.16035i	−0.412253	−	0.516948i
$315$	−5.33493	−	1.47046i	−0.300589	−	0.0828508i
$316$	−5.22883	+	6.55674i	−0.294144	+	0.368845i
$317$	8.03296	−	10.0730i	0.451176	−	0.565757i	−0.503274	−	0.864127i	$-0.667871\pi$
$317$	8.03296	−	10.0730i	0.451176	−	0.565757i	0.954450	+	0.298370i	$0.0964428\pi$
$318$	0.967658	+	5.02230i	0.0542636	+	0.281636i
$319$	38.3257	+	18.4567i	2.14583	+	1.03338i
$320$	0.689415	+	0.103913i	0.0385394	+	0.00580889i
$321$	8.25104	+	15.4863i	0.460528	+	0.864361i
$322$	−5.03369	−	0.258108i	−0.280516	−	0.0143838i
$323$	28.5223	+	35.7659i	1.58703	+	1.99007i
$324$	8.05582	−	4.01295i	0.447546	−	0.222942i
$325$	−9.96607	−	17.2617i	−0.552818	−	0.957509i
$326$	−5.43535	+	0.819247i	−0.301036	+	0.0453739i
$327$	−16.6951	+	19.5317i	−0.923243	+	1.08010i
$328$	5.50208	−	3.75125i	0.303801	−	0.207128i
$329$	34.6739	−	3.42186i	1.91163	−	0.188653i
$330$	−4.93048	+	3.12104i	−0.271414	+	0.171808i
$331$	−16.6625	−	20.8942i	−0.915856	−	1.14845i	−0.988520	−	0.151091i	$-0.951721\pi$
$331$	−16.6625	−	20.8942i	−0.915856	−	1.14845i	0.0726635	−	0.997357i	$-0.476850\pi$
$332$	−3.79483	−	2.58727i	−0.208268	−	0.141995i
$333$	−15.6454	−	1.06740i	−0.857361	−	0.0584931i
$334$	−11.3065	+	7.70864i	−0.618664	+	0.421798i
$335$	2.03183	−	0.626738i	0.111011	−	0.0342423i
$336$	4.45674	+	1.06653i	0.243135	+	0.0581841i
$337$	−25.3689	−	7.82526i	−1.38193	−	0.426269i	−0.487362	−	0.873200i	$-0.662041\pi$
$337$	−25.3689	−	7.82526i	−1.38193	−	0.426269i	−0.894569	+	0.446931i	$0.852517\pi$
$338$	6.20982	−	1.91548i	0.337770	−	0.104188i
$339$	2.82054	+	5.29384i	0.153191	+	0.287522i
$340$	−3.39518	−	3.15027i	−0.184130	−	0.170847i
$341$	1.07752	−	14.3784i	0.0583507	−	0.778636i
$342$	5.95729	−	19.7813i	0.322133	−	1.06965i
$343$	−9.19439	−	16.0768i	−0.496450	−	0.868065i
$344$	1.49051	+	2.58163i	0.0803628	+	0.139192i
$345$	−0.0936981	−	2.29861i	−0.00504454	−	0.123753i
$346$	−3.58085	+	15.6887i	−0.192508	+	0.843431i
$347$	4.93643	−	6.19009i	0.265001	−	0.332301i	−0.631472	−	0.775399i	$-0.717549\pi$
$347$	4.93643	−	6.19009i	0.265001	−	0.332301i	0.896474	+	0.443097i	$0.146120\pi$
$348$	13.9548	−	6.14399i	0.748057	−	0.329353i
$349$	−13.1077	+	12.1621i	−0.701638	+	0.651025i	−0.948043	−	0.318142i	$-0.896941\pi$
$349$	−13.1077	+	12.1621i	−0.701638	+	0.651025i	0.246405	+	0.969167i	$0.420751\pi$
$350$	−9.15909	+	7.66412i	−0.489574	+	0.409664i
$351$	−21.1212	−	8.96421i	−1.12736	−	0.478474i
$352$	3.99253	−	2.72206i	0.212803	−	0.145086i
$353$	14.3185	+	4.41667i	0.762097	+	0.235076i	0.651355	−	0.758774i	$-0.274201\pi$
$353$	14.3185	+	4.41667i	0.762097	+	0.235076i	0.110742	+	0.993849i	$0.464677\pi$
$354$	−7.74113	+	4.90022i	−0.411437	+	0.260444i
$355$	3.34542	−	8.52398i	0.177556	−	0.452406i
$356$	0.658028	−	8.78077i	0.0348754	−	0.465380i
$357$	−20.4709	−	22.5319i	−1.08343	−	1.19251i
$358$	0.990529	+	13.2177i	0.0523511	+	0.698577i
$359$	−3.56178	−	1.09867i	−0.187984	−	0.0579853i	0.199334	−	0.979932i	$-0.436122\pi$
$359$	−3.56178	−	1.09867i	−0.187984	−	0.0579853i	−0.387318	+	0.921946i	$0.626598\pi$
$360$	−0.297913	+	2.07028i	−0.0157014	+	0.109113i
$361$	−14.2105	−	24.6134i	−0.747922	−	1.29544i
$362$	−20.5980			−1.08261
$363$	−5.46727	+	20.6802i	−0.286957	+	1.08543i
$364$	−5.31566	−	10.4035i	−0.278616	−	0.545293i
$365$	1.26265	+	3.21719i	0.0660903	+	0.168395i
$366$	−6.95675	+	11.1541i	−0.363635	+	0.583036i
$367$	−16.9307	+	11.5432i	−0.883777	+	0.602549i	−0.917875	−	0.396869i	$-0.870097\pi$
$367$	−16.9307	+	11.5432i	−0.883777	+	0.602549i	0.0340979	+	0.999418i	$0.489144\pi$
$368$	0.142365	+	1.89973i	0.00742128	+	0.0990302i
$369$	11.3638	+	16.4307i	0.591575	+	0.855347i
$370$	2.27227	−	2.84934i	0.118130	−	0.148130i
$371$	−6.85625	−	3.74586i	−0.355959	−	0.194475i
$372$	−3.66671	−	3.64230i	−0.190110	−	0.188844i
$373$	3.10343	+	5.37530i	0.160690	+	0.278323i	0.935116	−	0.354341i	$-0.115295\pi$
$373$	3.10343	+	5.37530i	0.160690	+	0.278323i	−0.774427	+	0.632664i	$0.781962\pi$
$374$	−32.1006			−1.65988
$375$	−8.15096	−	8.09669i	−0.420914	−	0.418111i
$376$	−2.93041	−	12.8390i	−0.151125	−	0.662120i
$377$	−35.0226	−	16.8660i	−1.80375	−	0.868642i
$378$	−3.11020	+	13.3913i	−0.159972	+	0.688774i
$379$	−18.4298	+	8.87532i	−0.946675	+	0.455895i	−0.842519	−	0.538666i	$-0.818928\pi$
$379$	−18.4298	+	8.87532i	−0.946675	+	0.455895i	−0.104156	+	0.994561i	$0.533214\pi$
$380$	2.99346	+	3.75368i	0.153561	+	0.192560i
$381$	4.57985	−	2.89909i	0.234633	−	0.148525i
$382$	−2.45042	−	10.7360i	−0.125374	−	0.549302i
$383$	−0.903889	−	12.0616i	−0.0461866	−	0.616317i	−0.971489	−	0.237086i	$-0.923808\pi$
$383$	−0.903889	−	12.0616i	−0.0461866	−	0.616317i	0.925302	−	0.379231i	$-0.123811\pi$
$384$	0.188178	−	1.72180i	0.00960290	−	0.0878651i
$385$	1.12041	−	8.84284i	0.0571014	−	0.450673i
$386$	4.13232	+	18.1049i	0.210330	+	0.921515i
$387$	−7.71486	+	4.52316i	−0.392168	+	0.229925i
$388$	10.2739	+	1.54854i	0.521578	+	0.0786152i
$389$	−15.0138	−	13.9307i	−0.761229	−	0.706317i	0.200689	−	0.979655i	$-0.435682\pi$
$389$	−15.0138	−	13.9307i	−0.761229	−	0.706317i	−0.961918	+	0.273338i	$0.911872\pi$
$390$	4.50554	−	2.85206i	0.228147	−	0.144420i
$391$	6.32773	−	10.9599i	0.320007	−	0.554268i
$392$	−5.59144	+	4.21139i	−0.282411	+	0.212707i
$393$	4.97371	+	6.69223i	0.250890	+	0.337578i
$394$	8.42451	−	4.05703i	0.424421	−	0.204390i
$395$	5.58724	−	1.72343i	0.281124	−	0.0867154i
$396$	8.24602	+	11.9228i	0.414378	+	0.599142i
$397$	18.8523	+	17.4923i	0.946167	+	0.877915i	0.992652	−	0.121004i	$-0.0386114\pi$
$397$	18.8523	+	17.4923i	0.946167	+	0.877915i	−0.0464847	+	0.998919i	$0.514802\pi$
$398$	−5.69459	+	5.28381i	−0.285444	+	0.264853i
$399$	17.5022	+	26.2586i	0.876204	+	1.31458i
$400$	3.30893	+	3.07024i	0.165446	+	0.153512i
$401$	2.30422	+	30.7476i	0.115067	+	1.53546i	0.693932	+	0.720040i	$0.255877\pi$
$401$	2.30422	+	30.7476i	0.115067	+	1.53546i	−0.578865	+	0.815423i	$0.696504\pi$
$402$	−1.76129	−	4.98006i	−0.0878453	−	0.248383i
$403$	−0.984650	+	13.1392i	−0.0490489	+	0.654512i
$404$	−2.44858	+	0.369063i	−0.121821	+	0.0183616i
$405$	−6.21667	−	0.852227i	−0.308909	−	0.0423475i
$406$	−6.33871	+	22.4118i	−0.314585	+	1.11228i
$407$	−1.88760	−	25.1883i	−0.0935651	−	1.24854i
$408$	−7.47616	+	8.74637i	−0.370125	+	0.433010i
$409$	2.12416	+	2.66361i	0.105033	+	0.131707i	0.831569	−	0.555421i	$-0.187443\pi$
$409$	2.12416	+	2.66361i	0.105033	+	0.131707i	−0.726537	+	0.687128i	$0.758871\pi$
$410$	−4.64280			−0.229291
$411$	−15.0559	+	34.8253i	−0.742651	+	1.71781i
$412$	−4.96978	+	12.6628i	−0.244844	+	0.623851i
$413$	1.75911	−	13.8838i	0.0865602	−	0.683176i
$414$	−5.69620	+	0.465160i	−0.279953	+	0.0228614i
$415$	1.16989	+	2.98082i	0.0574274	+	0.146323i
$416$	−3.64843	+	2.48746i	−0.178879	+	0.121958i
$417$	−24.6188	+	21.3298i	−1.20559	+	1.04452i
$418$	32.9041	+	4.95950i	1.60939	+	0.242577i
$419$	7.66814	+	19.5381i	0.374613	+	0.954498i	0.986531	+	0.163577i	$0.0523032\pi$
$419$	7.66814	+	19.5381i	0.374613	+	0.954498i	−0.611918	+	0.790922i	$0.709602\pi$
$420$	−2.14845	−	2.36475i	−0.104834	−	0.115388i
$421$	−0.723219	+	1.84273i	−0.0352475	+	0.0898093i	−0.947414	−	0.320011i	$-0.896313\pi$
$421$	−0.723219	+	1.84273i	−0.0352475	+	0.0898093i	0.912166	+	0.409820i	$0.134409\pi$
$422$	10.1154	−	17.5204i	0.492409	−	0.852877i
$423$	38.4574	−	9.04837i	1.86986	−	0.439947i
$424$	−1.07884	+	2.74883i	−0.0523929	+	0.133495i
$425$	−6.67258	−	29.2345i	−0.323668	−	1.41808i
$426$	−21.4970	−	7.44161i	−1.04153	−	0.360547i
$427$	−6.36938	−	19.0435i	−0.308236	−	0.921582i
$428$	−0.757083	+	10.1026i	−0.0365950	+	0.488326i
$429$	9.44604	−	35.7301i	0.456059	−	1.72507i
$430$	0.155317	−	2.07256i	0.00749004	−	0.0999476i
$431$	−14.4236	+	13.3832i	−0.694761	+	0.644644i	−0.946332	−	0.323195i	$-0.895243\pi$
$431$	−14.4236	+	13.3832i	−0.694761	+	0.644644i	0.251572	+	0.967839i	$0.419053\pi$
$432$	5.16905	+	0.530012i	0.248696	+	0.0255002i
$433$	0.0579220	−	0.253773i	0.00278356	−	0.0121956i	−0.973517	−	0.228614i	$-0.926581\pi$
$433$	0.0579220	−	0.253773i	0.00278356	−	0.0121956i	0.976301	+	0.216419i	$0.0694377\pi$
$434$	7.85651	−	0.775335i	0.377125	−	0.0372173i
$435$	−10.4518	−	1.94144i	−0.501125	−	0.0930851i
$436$	−14.1757	+	4.37263i	−0.678894	+	0.209411i
$437$	−8.17942	+	10.2567i	−0.391275	+	0.490643i
$438$	7.85803	−	3.45972i	0.375471	−	0.165312i
$439$	15.3812	−	7.40719i	0.734105	−	0.353526i	−0.0291925	−	0.999574i	$-0.509294\pi$
$439$	15.3812	−	7.40719i	0.734105	−	0.353526i	0.763297	+	0.646048i	$0.223579\pi$
$440$	−3.36900			−0.160611
$441$	−12.7459	−	16.6895i	−0.606950	−	0.794740i
$442$	29.3340			1.39528
$443$	−17.6748	+	8.51173i	−0.839755	+	0.404404i	−0.803764	−	0.594948i	$-0.797173\pi$
$443$	−17.6748	+	8.51173i	−0.839755	+	0.404404i	−0.0359901	+	0.999352i	$0.511458\pi$
$444$	−7.30263	−	5.35200i	−0.346567	−	0.253995i
$445$	−3.82769	+	4.79977i	−0.181450	+	0.227531i
$446$	3.52244	−	1.08653i	0.166792	−	0.0514487i
$447$	−4.61071	+	5.39408i	−0.218079	+	0.255131i
$448$	1.84477	+	1.89652i	0.0871574	+	0.0896024i
$449$	2.41080	−	10.5624i	0.113772	−	0.498470i	−0.885646	−	0.464362i	$-0.846284\pi$
$449$	2.41080	−	10.5624i	0.113772	−	0.498470i	0.999418	−	0.0341081i	$-0.0108591\pi$
$450$	−9.14419	+	9.98810i	−0.431061	+	0.470844i
$451$	−23.5884	+	21.8868i	−1.11073	+	1.03061i
$452$	−0.258801	+	3.45346i	−0.0121730	+	0.162437i
$453$	−33.2137	+	9.01859i	−1.56051	+	0.423731i
$454$	−1.21801	+	16.2532i	−0.0571639	+	0.762799i
$455$	−1.02385	+	8.08072i	−0.0479988	+	0.378830i
$456$	9.01460	−	7.81026i	0.422147	−	0.365749i
$457$	2.64854	+	11.6040i	0.123893	+	0.542813i	0.998335	+	0.0576818i	$0.0183709\pi$
$457$	2.64854	+	11.6040i	0.123893	+	0.542813i	−0.874442	+	0.485131i	$0.838772\pi$
$458$	−0.577177	+	1.47062i	−0.0269697	+	0.0687178i
$459$	−26.3884	−	22.2527i	−1.23170	−	1.03867i
$460$	0.664104	−	1.15026i	0.0309640	−	0.0536312i
$461$	−4.02836	+	10.2641i	−0.187620	+	0.478047i	−0.993473	−	0.114068i	$-0.963612\pi$
$461$	−4.02836	+	10.2641i	−0.187620	+	0.478047i	0.805853	+	0.592115i	$0.201707\pi$
$462$	−22.0633	−	1.88637i	−1.02648	−	0.0877620i
$463$	13.7137	+	34.9418i	0.637327	+	1.62388i	0.773940	+	0.633259i	$0.218283\pi$
$463$	13.7137	+	34.9418i	0.637327	+	1.62388i	−0.136612	+	0.990625i	$0.543621\pi$
$464$	8.70481	+	1.31204i	0.404111	+	0.0609099i
$465$	0.681724	+	3.53826i	0.0316142	+	0.164083i
$466$	11.3568	−	7.74294i	0.526094	−	0.358685i
$467$	8.05993	+	20.5364i	0.372969	+	0.950309i	0.986956	+	0.160993i	$0.0514696\pi$
$467$	8.05993	+	20.5364i	0.372969	+	0.950309i	−0.613987	+	0.789316i	$0.710435\pi$
$468$	−7.53534	−	10.8952i	−0.348321	−	0.503631i
$469$	7.57852	+	2.77007i	0.349944	+	0.127910i
$470$	−3.35440	+	8.54688i	−0.154727	+	0.394238i
$471$	20.1583	−	2.33951i	0.928846	−	0.107799i
$472$	−5.28953			−0.243470
$473$	−8.98124	−	11.2621i	−0.412958	−	0.517833i
$474$	−4.84329	−	13.6944i	−0.222460	−	0.629005i
$475$	2.32292	+	30.9972i	0.106583	+	1.42225i
$476$	−3.02841	−	17.3131i	−0.138807	−	0.793544i
$477$	−8.26792	−	3.18134i	−0.378562	−	0.145664i
$478$	10.2136	−	1.53945i	0.467158	−	0.0704127i
$479$	−1.62023	+	21.6204i	−0.0740300	+	0.987862i	0.829269	+	0.558850i	$0.188757\pi$
$479$	−1.62023	+	21.6204i	−0.0740300	+	0.987862i	−0.903299	+	0.429012i	$0.858862\pi$
$480$	−0.784633	+	0.917944i	−0.0358134	+	0.0418982i
$481$	1.72492	+	23.0175i	0.0786496	+	1.04951i
$482$	−12.9156	−	11.9839i	−0.588288	−	0.545852i
$483$	4.99322	−	7.16112i	0.227199	−	0.325842i
$484$	−9.05313	+	8.40008i	−0.411506	+	0.381822i
$485$	−5.31014	−	4.92709i	−0.241121	−	0.223728i
$486$	−1.48640	+	15.5174i	−0.0674245	+	0.703885i
$487$	−14.4036	+	4.44293i	−0.652690	+	0.201328i	−0.603378	−	0.797455i	$-0.706179\pi$
$487$	−14.4036	+	4.44293i	−0.652690	+	0.201328i	−0.0493120	+	0.998783i	$0.515703\pi$
$488$	−6.83809	+	3.29305i	−0.309546	+	0.149069i
$489$	3.77806	−	8.73893i	0.170850	−	0.395188i
$490$	4.87499	−	0.229964i	0.220230	−	0.0103887i
$491$	10.5430	−	18.2610i	0.475798	−	0.824107i	−0.523817	−	0.851831i	$-0.675493\pi$
$491$	10.5430	−	18.2610i	0.475798	−	0.824107i	0.999616	+	0.0277240i	$0.00882595\pi$
$492$	0.469771	+	11.5245i	0.0211789	+	0.519564i
$493$	−42.8689	−	39.7765i	−1.93072	−	1.79144i
$494$	−30.0683	−	4.53206i	−1.35284	−	0.203907i
$495$	−0.0675225	−	10.1068i	−0.00303491	−	0.454266i
$496$	−0.663982	−	2.90909i	−0.0298137	−	0.130622i
$497$	29.6757	−	18.0789i	1.33114	−	0.810948i
$498$	7.28070	−	3.20553i	0.326256	−	0.143643i
$499$	1.88160	+	25.1082i	0.0842320	+	1.12400i	0.865871	+	0.500267i	$0.166765\pi$
$499$	1.88160	+	25.1082i	0.0842320	+	1.12400i	−0.781639	+	0.623731i	$0.785616\pi$
$500$	−1.47601	−	6.46681i	−0.0660090	−	0.289204i
$501$	−0.965356	−	23.6822i	−0.0431289	−	1.05804i
$502$	4.34526	+	5.44878i	0.193938	+	0.243191i
$503$	22.6468	−	10.9061i	1.00977	−	0.486280i	0.145527	−	0.989354i	$-0.453512\pi$
$503$	22.6468	−	10.9061i	1.00977	−	0.486280i	0.864243	+	0.503075i	$0.167798\pi$
$504$	−5.65247	+	5.57221i	−0.251781	+	0.248206i
$505$	1.55546	+	0.749071i	0.0692172	+	0.0333332i
$506$	−2.04843	−	8.97476i	−0.0910638	−	0.398977i
$507$	−2.87688	+	10.8819i	−0.127767	+	0.483283i
$508$	3.12942			0.138845
$509$	14.0845	+	24.3952i	0.624287	+	1.08130i	0.988678	+	0.150050i	$0.0479436\pi$
$509$	14.0845	+	24.3952i	0.624287	+	1.08130i	−0.364392	+	0.931246i	$0.618723\pi$
$510$	7.74180	−	2.10215i	0.342813	−	0.0930848i
$511$	−3.56936	+	12.6202i	−0.157899	+	0.558284i
$512$	0.623490	−	0.781831i	0.0275546	−	0.0345524i
$513$	23.6109	+	26.8867i	1.04245	+	1.18708i
$514$	−0.500498	−	6.67868i	−0.0220760	−	0.294584i
$515$	7.83615	−	5.34260i	0.345302	−	0.235423i
$516$	−5.16027	−	0.175824i	−0.227168	−	0.00774024i
$517$	23.2487	+	59.2368i	1.02248	+	2.60523i
$518$	13.4070	−	3.39436i	0.589069	−	0.149140i
$519$	−19.7746	−	19.6429i	−0.868007	−	0.862227i
$520$	3.07864			0.135007
$521$	3.00706	+	5.20838i	0.131742	+	0.228183i	0.924348	−	0.381550i	$-0.124610\pi$
$521$	3.00706	+	5.20838i	0.131742	+	0.228183i	−0.792606	+	0.609734i	$0.791276\pi$
$522$	−3.76157	+	26.1401i	−0.164639	+	1.14412i
$523$	27.5508	+	8.49830i	1.20471	+	0.371605i	0.831176	−	0.556010i	$-0.187668\pi$
$523$	27.5508	+	8.49830i	1.20471	+	0.371605i	0.373538	+	0.927615i	$0.378145\pi$
$524$	0.359750	+	4.80054i	0.0157158	+	0.209712i
$525$	−2.86824	−	20.4855i	−0.125180	−	0.894061i
$526$	0.646563	−	8.62779i	0.0281915	−	0.376189i
$527$	−7.24192	+	18.4521i	−0.315463	+	0.803787i
$528$	0.340885	+	8.36263i	0.0148351	+	0.363937i
$529$	−18.5102	−	5.70963i	−0.804790	−	0.248245i
$530$	1.70107	−	1.15977i	0.0738896	−	0.0503770i
$531$	−0.106014	−	15.8682i	−0.00460062	−	0.688622i
$532$	0.429366	+	18.2144i	0.0186154	+	0.789693i
$533$	21.5554	−	20.0005i	0.933670	−	0.866319i
$534$	12.3014	+	9.01554i	0.532334	+	0.390141i
$535$	4.40388	−	5.52229i	0.190396	−	0.238749i
$536$	0.678636	−	2.97330i	0.0293126	−	0.128427i
$537$	−20.3332	−	10.6597i	−0.877441	−	0.459998i
$538$	11.0313	+	19.1067i	0.475592	+	0.823750i
$539$	23.6840	−	24.1498i	1.02014	−	1.04021i
$540$	−2.76950	−	2.33545i	−0.119180	−	0.100502i
$541$	−0.949887	+	12.6754i	−0.0408388	+	0.544956i	0.938836	+	0.344364i	$0.111906\pi$
$541$	−0.949887	+	12.6754i	−0.0408388	+	0.544956i	−0.979675	+	0.200592i	$0.935713\pi$
$542$	19.4907	+	18.0847i	0.837197	+	0.776805i
$543$	18.8802	−	30.2717i	0.810228	−	1.29908i
$544$	−6.34796	+	1.95809i	−0.272166	+	0.0839522i
$545$	9.88334	+	3.04861i	0.423356	+	0.130588i
$546$	20.1618	+	1.72380i	0.862845	+	0.0737716i
$547$	−34.6639	+	10.6924i	−1.48212	+	0.457173i	−0.927148	−	0.374696i	$-0.877747\pi$
$547$	−34.6639	+	10.6924i	−1.48212	+	0.457173i	−0.554972	+	0.831869i	$0.687271\pi$
$548$	−18.0987	+	12.3395i	−0.773140	+	0.527118i
$549$	−10.0160	−	20.4478i	−0.427472	−	0.872691i
$550$	−18.0219	−	12.2871i	−0.768457	−	0.523925i
$551$	37.7966	+	47.3954i	1.61019	+	2.01911i
$552$	−2.92241	−	1.53207i	−0.124386	−	0.0652092i
$553$	20.8398	+	7.61729i	0.886198	+	0.323920i
$554$	−4.95883	+	3.38087i	−0.210681	+	0.143640i
$555$	2.10473	+	5.95114i	0.0893409	+	0.252612i
$556$	−18.5964	+	2.80295i	−0.788663	+	0.118872i
$557$	5.83120	+	10.0999i	0.247076	+	0.427948i	0.962713	−	0.270524i	$-0.0871970\pi$
$557$	5.83120	+	10.0999i	0.247076	+	0.427948i	−0.715637	+	0.698472i	$0.753864\pi$
$558$	8.71378	−	2.05021i	0.368884	−	0.0867921i
$559$	8.20719	+	10.2915i	0.347127	+	0.435284i
$560$	−0.317836	−	1.81703i	−0.0134310	−	0.0767837i
$561$	29.4235	−	47.1763i	1.24226	−	1.99178i
$562$	−11.3936	−	1.71731i	−0.480611	−	0.0724405i
$563$	−37.2235	−	17.9259i	−1.56878	−	0.755485i	−0.570930	−	0.820999i	$-0.693417\pi$
$563$	−37.2235	−	17.9259i	−1.56878	−	0.755485i	−0.997852	+	0.0655136i	$0.979131\pi$
$564$	21.5547	+	7.46159i	0.907617	+	0.314190i
$565$	1.50542	−	1.88774i	0.0633337	−	0.0794179i
$566$	1.73803	−	2.17942i	0.0730547	−	0.0916077i
$567$	−16.8295	−	16.8454i	−0.706775	−	0.707439i
$568$	−8.18884	−	10.2685i	−0.343596	−	0.430856i
$569$	25.9329			1.08716			0.543582	−	0.839356i	$-0.317068\pi$
$569$	25.9329			1.08716			0.543582	+	0.839356i	$0.317068\pi$
$570$	−8.26037	+	0.958674i	−0.345989	+	0.0401544i
$571$	−9.56145	−	11.9897i	−0.400134	−	0.501752i	0.540420	−	0.841395i	$-0.318265\pi$
$571$	−9.56145	−	11.9897i	−0.400134	−	0.501752i	−0.940555	+	0.339643i	$0.889694\pi$
$572$	15.6415	−	14.5132i	0.654004	−	0.606827i
$573$	18.0241	+	6.23941i	0.752968	+	0.260655i
$574$	−14.0298	−	10.6573i	−0.585592	−	0.444828i
$575$	7.74765	−	3.73107i	0.323099	−	0.155596i
$576$	2.35794	+	1.85476i	0.0982474	+	0.0772816i
$577$	−13.4672	−	9.18180i	−0.560648	−	0.382243i	0.249584	−	0.968353i	$-0.419706\pi$
$577$	−13.4672	−	9.18180i	−0.560648	−	0.382243i	−0.810232	+	0.586110i	$0.800659\pi$
$578$	25.9253	+	7.99690i	1.07835	+	0.332627i
$579$	−30.3954	−	10.5220i	−1.26319	−	0.437278i
$580$	−4.49915	−	4.17460i	−0.186817	−	0.173341i
$581$	−3.30712	+	11.6930i	−0.137202	+	0.485106i
$582$	−11.6929	+	13.6795i	−0.484685	+	0.567034i
$583$	3.17520	−	13.9114i	0.131503	−	0.576153i
$584$	4.90173	+	0.738816i	0.202835	+	0.0305724i
$585$	0.0617030	+	9.23573i	0.00255111	+	0.381850i
$586$	0.142038	−	1.89537i	0.00586754	−	0.0782968i
$587$	−4.99788	−	8.65657i	−0.206284	−	0.357295i	0.744257	−	0.667894i	$-0.232804\pi$
$587$	−4.99788	−	8.65657i	−0.206284	−	0.357295i	−0.950541	+	0.310599i	$0.899471\pi$
$588$	−1.06409	−	12.0776i	−0.0438822	−	0.498071i
$589$	10.2740	−	17.7951i	0.423334	−	0.733236i
$590$	3.04706	+	2.07745i	0.125445	+	0.0855272i
$591$	−1.75956	+	16.0997i	−0.0723785	+	0.662253i
$592$	−1.90973	−	4.86590i	−0.0784893	−	0.199987i
$593$	−0.851319	−	0.789908i	−0.0349595	−	0.0324376i	0.662500	−	0.749062i	$-0.269496\pi$
$593$	−0.851319	−	0.789908i	−0.0349595	−	0.0324376i	−0.697459	+	0.716625i	$0.745686\pi$
$594$	−25.0805	+	1.19024i	−1.02907	+	0.0488360i
$595$	−5.05515	+	11.1627i	−0.207241	+	0.457626i
$596$	−3.91492	+	1.20759i	−0.160362	+	0.0494650i
$597$	−2.54562	−	13.2121i	−0.104185	−	0.540737i
$598$	1.87189	+	8.20127i	0.0765471	+	0.335375i
$599$	32.8652	−	15.8270i	1.34284	−	0.646675i	0.382094	−	0.924123i	$-0.375203\pi$
$599$	32.8652	−	15.8270i	1.34284	−	0.646675i	0.960741	+	0.277448i	$0.0894886\pi$
$600$	−7.54512	+	2.04875i	−0.308028	+	0.0836397i
$601$	−1.95531	−	1.33311i	−0.0797589	−	0.0543787i	0.522784	−	0.852465i	$-0.324893\pi$
$601$	−1.95531	−	1.33311i	−0.0797589	−	0.0543787i	−0.602543	+	0.798086i	$0.705846\pi$
$602$	5.22680	−	5.90641i	0.213028	−	0.240727i
$603$	8.93329	+	1.97627i	0.363792	+	0.0804799i
$604$	−18.9875	−	5.85686i	−0.772590	−	0.238312i
$605$	8.51422	−	1.28331i	0.346152	−	0.0521740i
$606$	1.70198	−	3.93681i	0.0691382	−	0.159922i
$607$	16.1904	+	28.0426i	0.657147	+	1.13821i	0.981351	+	0.192225i	$0.0615704\pi$
$607$	16.1904	+	28.0426i	0.657147	+	1.13821i	−0.324203	+	0.945987i	$0.605096\pi$
$608$	6.80938	−	1.02635i	0.276157	−	0.0416239i
$609$	−27.1271	−	29.8583i	−1.09925	−	1.20992i
$610$	5.23246	+	0.788666i	0.211856	+	0.0319321i
$611$	−21.2450	−	54.1315i	−0.859483	−	2.18993i
$612$	−6.00135	−	19.0042i	−0.242590	−	0.768199i
$613$	0.184462	+	2.46147i	0.00745034	+	0.0994179i	0.999689	−	0.0249282i	$-0.00793572\pi$
$613$	0.184462	+	2.46147i	0.00745034	+	0.0994179i	−0.992239	+	0.124346i	$0.960317\pi$
$614$	10.1495	−	12.7271i	0.409602	−	0.513624i
$615$	4.25560	−	6.82324i	0.171602	−	0.275139i
$616$	−10.1806	−	7.73338i	−0.410187	−	0.311587i
$617$	−12.4896	+	1.88251i	−0.502813	+	0.0757868i	−0.395551	−	0.918444i	$-0.629446\pi$
$617$	−12.4896	+	1.88251i	−0.502813	+	0.0757868i	−0.107262	+	0.994231i	$0.534208\pi$
$618$	−14.0544	−	18.9105i	−0.565352	−	0.760693i
$619$	14.0150	−	24.2746i	0.563309	−	0.975680i	−0.433896	−	0.900963i	$-0.642861\pi$
$619$	14.0150	−	24.2746i	0.563309	−	0.975680i	0.997205	−	0.0747169i	$-0.0238053\pi$
$620$	−0.760050	+	1.93658i	−0.0305243	+	0.0777748i
$621$	4.53754	−	8.79773i	0.182085	−	0.353041i
$622$	14.0588	+	6.77035i	0.563705	+	0.271466i
$623$	−22.5843	+	5.71786i	−0.904821	+	0.229081i
$624$	−0.311506	−	7.64190i	−0.0124702	−	0.305921i
$625$	6.55602	−	16.7045i	0.262241	−	0.668179i
$626$	−11.8947	+	5.72820i	−0.475409	+	0.228945i
$627$	−37.4487	+	43.8113i	−1.49556	+	1.74965i
$628$	10.5562	+	5.08361i	0.421239	+	0.202858i
$629$	−7.72705	+	33.8544i	−0.308098	+	1.34986i
$630$	5.44461	−	0.989904i	0.216918	−	0.0394387i
$631$	5.12349	+	22.4475i	0.203963	+	0.893620i	0.968495	+	0.249034i	$0.0801131\pi$
$631$	5.12349	+	22.4475i	0.203963	+	0.893620i	−0.764532	+	0.644586i	$0.777030\pi$
$632$	1.86615	−	8.17612i	0.0742313	−	0.325229i
$633$	16.4768	+	30.9252i	0.654895	+	1.22916i
$634$	−2.86693	+	12.5608i	−0.113860	+	0.498855i
$635$	−1.80272	−	1.22907i	−0.0715386	−	0.0487742i
$636$	−3.05092	−	4.10508i	−0.120977	−	0.162777i
$637$	−21.6428	+	22.0685i	−0.857519	+	0.874384i
$638$	−42.5383			−1.68411
$639$	30.6406	−	24.7718i	1.21213	−	0.979957i
$640$	−0.666227	+	0.205504i	−0.0263349	+	0.00812325i
$641$	11.5405	+	29.4048i	0.455824	+	1.16142i	0.955443	+	0.295175i	$0.0953780\pi$
$641$	11.5405	+	29.4048i	0.455824	+	1.16142i	−0.499619	+	0.866245i	$0.666527\pi$
$642$	−14.1532	−	10.3727i	−0.558582	−	0.409377i
$643$	22.8643	+	7.05269i	0.901679	+	0.278131i	0.710727	−	0.703468i	$-0.248366\pi$
$643$	22.8643	+	7.05269i	0.901679	+	0.278131i	0.190952	+	0.981599i	$0.438842\pi$
$644$	4.64718	−	1.95149i	0.183125	−	0.0768994i
$645$	2.90355	+	2.12797i	0.114327	+	0.0837888i
$646$	−41.2160	−	19.8486i	−1.62162	−	0.780931i
$647$	−24.9431	+	23.1438i	−0.980614	+	0.909877i	−0.995941	−	0.0900054i	$-0.971312\pi$
$647$	−24.9431	+	23.1438i	−0.980614	+	0.909877i	0.0153270	+	0.999883i	$0.495121\pi$
$648$	−5.51689	+	7.11083i	−0.216724	+	0.279340i
$649$	25.2744	−	3.80951i	0.992108	−	0.149536i
$650$	16.4687	+	11.2282i	0.645956	+	0.440405i
$651$	−6.06183	+	12.2569i	−0.237582	+	0.480386i
$652$	4.54162	−	3.09643i	0.177864	−	0.121265i
$653$	−18.1692	+	16.8586i	−0.711016	+	0.659727i	−0.950340	−	0.311213i	$-0.899265\pi$
$653$	−18.1692	+	16.8586i	−0.711016	+	0.659727i	0.239324	+	0.970940i	$0.423074\pi$
$654$	6.56732	−	24.8412i	0.256802	−	0.971367i
$655$	1.67816	−	2.90666i	0.0655713	−	0.113573i
$656$	−3.32959	+	5.76702i	−0.129999	+	0.225164i
$657$	−2.11816	+	14.7197i	−0.0826372	+	0.574269i
$658$	−29.7554	+	18.1274i	−1.15999	+	0.706681i
$659$	19.9344	+	3.00463i	0.776534	+	0.117044i	0.525339	−	0.850893i	$-0.323938\pi$
$659$	19.9344	+	3.00463i	0.776534	+	0.117044i	0.251195	+	0.967937i	$0.419176\pi$
$660$	3.08804	−	4.95122i	0.120202	−	0.192726i
$661$	26.1146	+	12.5761i	1.01574	+	0.489155i	0.866252	−	0.499608i	$-0.166523\pi$
$661$	26.1146	+	12.5761i	1.01574	+	0.489155i	0.149490	+	0.988763i	$0.452237\pi$
$662$	24.0781	+	11.5954i	0.935821	+	0.450668i
$663$	−26.8876	+	43.1104i	−1.04423	+	1.67427i
$664$	4.54160	+	0.684535i	0.176248	+	0.0265651i
$665$	6.90631	−	10.6611i	0.267815	−	0.413420i
$666$	14.5591	−	5.82658i	0.564154	−	0.225775i
$667$	8.38523	−	14.5236i	0.324677	−	0.562357i
$668$	6.84215	−	11.8509i	0.264731	−	0.458527i
$669$	−1.63187	+	6.17263i	−0.0630918	+	0.238648i
$670$	−1.55869	+	1.44625i	−0.0602173	+	0.0558735i
$671$	30.3021	−	20.6597i	1.16980	−	0.797557i
$672$	−4.47813	+	0.972794i	−0.172748	+	0.0375263i
$673$	11.5286	+	7.86010i	0.444397	+	0.302985i	0.764766	−	0.644308i	$-0.222855\pi$
$673$	11.5286	+	7.86010i	0.444397	+	0.302985i	−0.320369	+	0.947293i	$0.603807\pi$
$674$	26.2518	−	3.95683i	1.01118	−	0.152411i
$675$	−6.29732	−	22.5938i	−0.242384	−	0.869635i
$676$	−4.76376	+	4.42012i	−0.183222	+	0.170005i
$677$	−33.3895	−	16.0795i	−1.28326	−	0.617986i	−0.337035	−	0.941492i	$-0.609424\pi$
$677$	−33.3895	−	16.0795i	−1.28326	−	0.617986i	−0.946226	+	0.323506i	$0.895138\pi$
$678$	−4.83813	−	3.54580i	−0.185807	−	0.136176i
$679$	−4.73650	−	27.0781i	−0.181770	−	1.03916i
$680$	4.42581	+	1.36518i	0.169722	+	0.0523523i
$681$	−22.7699	−	16.6877i	−0.872543	−	0.639475i
$682$	5.26777	+	13.4220i	0.201713	+	0.513957i
$683$	29.2582	−	9.02496i	1.11953	−	0.345331i	0.320879	−	0.947120i	$-0.396022\pi$
$683$	29.2582	−	9.02496i	1.11953	−	0.345331i	0.798655	+	0.601790i	$0.205545\pi$
$684$	3.21545	+	20.4071i	0.122946	+	0.780286i
$685$	15.2722			0.583520
$686$	15.2593	+	10.4954i	0.582603	+	0.400716i
$687$	−1.63224	−	2.19622i	−0.0622740	−	0.0837910i
$688$	−2.46303	−	1.67927i	−0.0939021	−	0.0640214i
$689$	−2.90154	+	12.7125i	−0.110540	+	0.484307i
$690$	1.08175	+	2.03033i	0.0411815	+	0.0772932i
$691$	−5.87901	+	25.7576i	−0.223648	+	0.979866i	0.731058	+	0.682315i	$0.239027\pi$
$691$	−5.87901	+	25.7576i	−0.223648	+	0.979866i	−0.954706	+	0.297551i	$0.903830\pi$
$692$	−3.58085	−	15.6887i	−0.136123	−	0.596396i
$693$	22.9956	−	30.6961i	0.873530	−	1.16605i
$694$	−1.76179	+	7.71891i	−0.0668767	+	0.293006i
$695$	11.8134	+	5.68903i	0.448108	+	0.215797i
$696$	−9.90708	+	11.5903i	−0.375527	+	0.439330i
$697$	39.8567	−	19.1940i	1.50968	−	0.727023i
$698$	6.53265	−	16.6449i	0.247264	−	0.630019i
$699$	0.969651	+	23.7876i	0.0366756	+	0.899730i
$700$	4.92672	−	10.8791i	0.186213	−	0.411192i
$701$	−0.746901	−	0.359689i	−0.0282101	−	0.0135852i	0.419726	−	0.907651i	$-0.362126\pi$
$701$	−0.746901	−	0.359689i	−0.0282101	−	0.0135852i	−0.447936	+	0.894066i	$0.647841\pi$
$702$	22.9189	−	1.08766i	0.865019	−	0.0410510i
$703$	13.1509	−	33.5080i	0.495997	−	1.26378i
$704$	−2.41609	+	4.18479i	−0.0910597	+	0.157720i
$705$	−9.48617	−	12.7639i	−0.357270	−	0.480714i
$706$	−14.8168	+	2.23328i	−0.557639	+	0.0840506i
$707$	2.98090	+	5.83406i	0.112108	+	0.219413i
$708$	4.84839	−	7.77370i	0.182214	−	0.292153i
$709$	−5.20344	+	6.52491i	−0.195419	+	0.245048i	−0.869881	−	0.493262i	$-0.835804\pi$
$709$	−5.20344	+	6.52491i	−0.195419	+	0.245048i	0.674461	+	0.738310i	$0.264376\pi$
$710$	0.684301	+	9.13136i	0.0256814	+	0.342694i
$711$	24.5652	+	5.43445i	0.921268	+	0.203808i
$712$	3.21697	+	8.19671i	0.120561	+	0.307185i
$713$	−5.62101	−	0.847232i	−0.210509	−	0.0317291i
$714$	28.2199	+	11.4186i	1.05610	+	0.427329i
$715$	−14.7104	+	2.21723i	−0.550137	+	0.0829199i
$716$	−6.62738	−	11.4790i	−0.247677	−	0.428989i
$717$	−7.09935	+	16.4213i	−0.265130	+	0.613266i
$718$	3.68575	−	0.555537i	0.137551	−	0.0207325i
$719$	−0.00698845	−	0.00215565i	−0.000260625	−	8.03922e-5i	0.294625	−	0.955613i	$-0.404805\pi$
$719$	−0.00698845	−	0.00215565i	−0.000260625	−	8.03922e-5i	−0.294885	+	0.955533i	$0.595282\pi$
$720$	−0.629850	−	1.99452i	−0.0234731	−	0.0743313i
$721$	35.9433	+	1.84303i	1.33860	+	0.0686381i
$722$	23.4826	+	16.0101i	0.873931	+	0.595836i
$723$	29.4505	−	7.99676i	1.09527	−	0.297403i
$724$	18.5582	−	8.93716i	0.689710	−	0.332147i
$725$	−8.84221	−	38.7403i	−0.328392	−	1.43878i
$726$	−4.04696	−	21.0044i	−0.150197	−	0.779545i
$727$	−11.9173	+	3.67600i	−0.441988	+	0.136335i	−0.507758	−	0.861500i	$-0.669526\pi$
$727$	−11.9173	+	3.67600i	−0.441988	+	0.136335i	0.0657705	+	0.997835i	$0.479049\pi$
$728$	9.30317	+	7.06688i	0.344798	+	0.261916i
$729$	−21.4426	−	16.4078i	−0.794170	−	0.607696i
$730$	−2.53350	−	2.35074i	−0.0937689	−	0.0870048i
$731$	7.23490	+	18.4342i	0.267593	+	0.681815i
$732$	1.42821	−	13.0679i	0.0527883	−	0.483005i
$733$	−26.9363	−	18.3649i	−0.994915	−	0.678322i	−0.0476805	−	0.998863i	$-0.515183\pi$
$733$	−26.9363	−	18.3649i	−0.994915	−	0.678322i	−0.947235	+	0.320541i	$0.896135\pi$
$734$	10.2457	−	17.7460i	0.378174	−	0.655017i
$735$	−4.13047	+	7.37526i	−0.152355	+	0.272041i
$736$	−0.952527	−	1.64983i	−0.0351106	−	0.0608134i
$737$	−1.10130	+	14.6958i	−0.0405668	+	0.541326i
$738$	−17.3674	−	9.87297i	−0.639304	−	0.363429i
$739$	5.21362	+	0.785826i	0.191786	+	0.0289071i	0.244233	−	0.969717i	$-0.421464\pi$
$739$	5.21362	+	0.785826i	0.191786	+	0.0289071i	−0.0524468	+	0.998624i	$0.516702\pi$
$740$	−0.810965	+	3.55307i	−0.0298117	+	0.130613i
$741$	34.2212	−	40.0354i	1.25715	−	1.47074i
$742$	7.80254	+	0.400084i	0.286440	+	0.0146875i
$743$	25.2214	+	23.4020i	0.925282	+	0.858536i	0.990243	−	0.139351i	$-0.0445017\pi$
$743$	25.2214	+	23.4020i	0.925282	+	0.858536i	−0.0649607	+	0.997888i	$0.520692\pi$
$744$	4.88393	+	1.69067i	0.179053	+	0.0619829i
$745$	2.72949	+	0.841937i	0.100001	+	0.0308462i
$746$	−5.12835	−	3.49645i	−0.187762	−	0.128014i
$747$	−1.96254	+	13.6382i	−0.0718054	+	0.498996i
$748$	28.9216	−	13.9279i	1.05748	−	0.509255i
$749$	25.9840	−	6.57859i	0.949434	−	0.240376i
$750$	10.8568	+	3.75830i	0.396434	+	0.137234i
$751$	26.1129	−	24.2292i	0.952872	−	0.884136i	−0.0404887	−	0.999180i	$-0.512891\pi$
$751$	26.1129	−	24.2292i	0.952872	−	0.884136i	0.993360	+	0.115044i	$0.0367010\pi$
$752$	8.21084	+	10.2961i	0.299419	+	0.375459i
$753$	−11.9906	+	1.39160i	−0.436963	+	0.0507126i
$754$	38.8721			1.41564
$755$	8.63757	+	10.8312i	0.314353	+	0.394187i
$756$	−3.00807	−	13.4146i	−0.109402	−	0.487884i
$757$	18.6746	−	23.4172i	0.678740	−	0.851113i	−0.316497	−	0.948593i	$-0.602507\pi$
$757$	18.6746	−	23.4172i	0.678740	−	0.851113i	0.995237	+	0.0974802i	$0.0310783\pi$
$758$	12.7538	−	15.9928i	0.463239	−	0.580884i
$759$	15.0673	+	5.21583i	0.546907	+	0.189323i
$760$	−4.32567	−	2.08314i	−0.156909	−	0.0755633i
$761$	−11.5142	−	1.73549i	−0.417389	−	0.0629113i	−0.0630095	−	0.998013i	$-0.520070\pi$
$761$	−11.5142	−	1.73549i	−0.417389	−	0.0629113i	−0.354380	+	0.935102i	$0.615308\pi$
$762$	−2.86843	+	4.59911i	−0.103912	+	0.166608i
$763$	22.8680	+	31.8991i	0.827876	+	1.15483i
$764$	6.86593	+	8.60960i	0.248401	+	0.311485i
$765$	−4.00675	+	13.3045i	−0.144864	+	0.481025i
$766$	6.04769	+	10.4749i	0.218512	+	0.378474i
$767$	−23.0962	+	3.48119i	−0.833954	+	0.125698i
$768$	0.577518	+	1.63293i	0.0208394	+	0.0589234i
$769$	−32.9131	+	22.4398i	−1.18688	+	0.809199i	−0.985393	−	0.170293i	$-0.945529\pi$
$769$	−32.9131	+	22.4398i	−1.18688	+	0.809199i	−0.201483	+	0.979492i	$0.564576\pi$
$770$	2.82731	+	8.45325i	0.101889	+	0.304634i
$771$	10.2740	+	5.38615i	0.370010	+	0.193977i
$772$	−11.5785	−	14.5190i	−0.416720	−	0.522550i
$773$	−21.4951	−	14.6551i	−0.773127	−	0.527109i	0.111301	−	0.993787i	$-0.464498\pi$
$773$	−21.4951	−	14.6551i	−0.773127	−	0.527109i	−0.884427	+	0.466678i	$0.845451\pi$
$774$	4.98832	−	7.42258i	0.179301	−	0.266799i
$775$	−11.1287	+	7.58741i	−0.399754	+	0.272548i
$776$	−9.92835	+	3.06249i	−0.356407	+	0.109937i
$777$	−7.30038	+	22.8147i	−0.261900	+	0.818472i
$778$	19.5713	+	6.03694i	0.701664	+	0.216435i
$779$	−43.8198	+	13.5166i	−1.57001	+	0.484283i
$780$	−2.82189	+	4.52450i	−0.101040	+	0.162003i
$781$	46.5233	+	43.1673i	1.66474	+	1.54465i
$782$	−0.945743	+	12.6201i	−0.0338197	+	0.451293i
$783$	−34.9687	−	29.4883i	−1.24968	−	1.05382i
$784$	3.21046	−	6.22036i	0.114659	−	0.222156i
$785$	−4.08439	−	7.07437i	−0.145778	−	0.252495i
$786$	−7.38480	−	3.87148i	−0.263407	−	0.138091i
$787$	2.18568	−	9.57611i	0.0779112	−	0.341351i	−0.920916	−	0.389760i	$-0.872558\pi$
$787$	2.18568	−	9.57611i	0.0779112	−	0.341351i	0.998828	+	0.0484088i	$0.0154150\pi$
$788$	−5.82995	+	7.31052i	−0.207683	+	0.260426i
$789$	12.0871	+	8.85847i	0.430312	+	0.315370i
$790$	−4.28616	+	3.97697i	−0.152495	+	0.141494i
$791$	8.88237	−	2.24883i	0.315821	−	0.0799591i
$792$	−12.6025	−	7.16423i	−0.447810	−	0.254570i
$793$	−27.6906	+	18.8791i	−0.983320	+	0.670416i
$794$	−24.5749	−	7.58036i	−0.872132	−	0.269017i
$795$	0.145238	+	3.56300i	0.00515106	+	0.126366i
$796$	2.83809	−	7.23134i	0.100593	−	0.256308i
$797$	1.66483	−	22.2157i	0.0589715	−	0.786919i	−0.886814	−	0.462127i	$-0.847086\pi$
$797$	1.66483	−	22.2157i	0.0589715	−	0.786919i	0.945785	−	0.324793i	$-0.105294\pi$
$798$	−27.1621	−	16.0643i	−0.961528	−	0.568671i
$799$	−6.53768	−	87.2393i	−0.231287	−	3.08631i
$800$	−4.31337	−	1.33050i	−0.152501	−	0.0470402i
$801$	−24.5251	+	9.81498i	−0.866552	+	0.346795i
$802$	−15.4169	−	26.7029i	−0.544391	−	0.942912i
$803$	−23.9535			−0.845302
$804$	3.74764	+	3.72268i	0.132169	+	0.131289i
$805$	−3.44348	−	0.701007i	−0.121367	−	0.0247072i
$806$	−4.81376	−	12.2653i	−0.169558	−	0.432026i
$807$	−38.1913	−	1.30128i	−1.34440	−	0.0458072i
$808$	2.04596	−	1.39491i	0.0719766	−	0.0490728i
$809$	−2.42169	−	32.3153i	−0.0851422	−	1.13614i	−0.862150	−	0.506653i	$-0.830883\pi$
$809$	−2.42169	−	32.3153i	−0.0851422	−	1.13614i	0.777008	−	0.629491i	$-0.216736\pi$
$810$	5.97080	−	1.92948i	0.209792	−	0.0677952i
$811$	−6.85556	+	8.59660i	−0.240731	+	0.301867i	−0.887490	−	0.460827i	$-0.847553\pi$
$811$	−6.85556	+	8.59660i	−0.240731	+	0.301867i	0.646759	+	0.762695i	$0.276124\pi$
$812$	−4.01312	−	22.9426i	−0.140833	−	0.805126i
$813$	−44.4432	+	12.0678i	−1.55869	+	0.423236i
$814$	12.6295	+	21.8749i	0.442663	+	0.766715i
$815$	−3.83234			−0.134241
$816$	2.94087	−	11.1240i	0.102951	−	0.389418i
$817$	−4.56794	−	20.0135i	−0.159812	−	0.700182i
$818$	−3.06949	−	1.47819i	−0.107322	−	0.0516837i
$819$	−21.0137	+	28.0505i	−0.734278	+	0.980165i
$820$	4.18302	−	2.01443i	0.146077	−	0.0703471i
$821$	−3.39905	−	4.26227i	−0.118628	−	0.148754i	0.718972	−	0.695039i	$-0.244613\pi$
$821$	−3.39905	−	4.26227i	−0.118628	−	0.148754i	−0.837599	+	0.546285i	$0.816042\pi$
$822$	−1.54528	−	37.9091i	−0.0538979	−	1.32223i
$823$	−1.84762	−	8.09494i	−0.0644039	−	0.282172i	0.932463	−	0.361264i	$-0.117655\pi$
$823$	−1.84762	−	8.09494i	−0.0644039	−	0.282172i	−0.996867	+	0.0790926i	$0.974798\pi$
$824$	−1.01656	−	13.5651i	−0.0354137	−	0.472562i
$825$	34.5766	−	15.2233i	1.20380	−	0.530007i
$826$	4.43904	+	13.2721i	0.154454	+	0.461795i
$827$	2.88825	+	12.6542i	0.100434	+	0.440031i	0.999995	+	0.00323509i	$0.00102976\pi$
$827$	2.88825	+	12.6542i	0.100434	+	0.440031i	−0.899561	+	0.436796i	$0.856113\pi$
$828$	4.93028	−	2.89058i	0.171339	−	0.100455i
$829$	13.2790	+	2.00149i	0.461198	+	0.0695145i	0.375532	−	0.926809i	$-0.377460\pi$
$829$	13.2790	+	2.00149i	0.461198	+	0.0695145i	0.0856663	+	0.996324i	$0.472698\pi$
$830$	−2.34736	−	2.17803i	−0.0814780	−	0.0756006i
$831$	−0.423388	−	10.3866i	−0.0146872	−	0.360308i
$832$	2.20786	−	3.82412i	0.0765437	−	0.132578i
$833$	−40.8993	+	22.1280i	−1.41708	+	0.766691i
$834$	12.9262	−	29.8992i	0.447596	−	1.03532i
$835$	−8.59589	+	4.13956i	−0.297473	+	0.143255i
$836$	−31.7974	+	9.80821i	−1.09974	+	0.339224i
$837$	−4.97401	+	14.6853i	−0.171927	+	0.507600i
$838$	−15.3860	−	14.2761i	−0.531501	−	0.493161i
$839$	32.5520	−	30.2038i	1.12382	−	1.04275i	0.125101	−	0.992144i	$-0.460075\pi$
$839$	32.5520	−	30.2038i	1.12382	−	1.04275i	0.998719	−	0.0506080i	$-0.0161159\pi$
$840$	2.96171	+	1.19839i	0.102189	+	0.0413485i
$841$	−35.5495	−	32.9851i	−1.22584	−	1.13742i
$842$	−0.147934	−	1.97404i	−0.00509813	−	0.0680298i
$843$	12.9673	−	15.1704i	0.446616	−	0.522497i
$844$	−1.51185	+	20.1742i	−0.0520399	+	0.694424i
$845$	4.48018	−	0.675279i	0.154123	−	0.0232303i
$846$	−30.7230	+	24.8383i	−1.05628	+	0.853959i
$847$	28.6744	+	15.6660i	0.985263	+	0.538290i
$848$	−0.220675	−	2.94470i	−0.00757800	−	0.101121i
$849$	1.60988	+	4.55193i	0.0552508	+	0.156222i
$850$	18.6962	+	23.4442i	0.641273	+	0.804131i
$851$	−9.95819			−0.341362
$852$	22.5969	−	2.62253i	0.774157	−	0.0898463i
$853$	−0.719198	+	1.83249i	−0.0246249	+	0.0627432i	−0.942657	−	0.333762i	$-0.891682\pi$
$853$	−0.719198	+	1.83249i	−0.0246249	+	0.0627432i	0.918033	+	0.396505i	$0.129777\pi$
$854$	14.0013	+	14.3941i	0.479115	+	0.492555i
$855$	6.16257	−	13.0185i	0.210755	−	0.445223i
$856$	−3.70123	−	9.43058i	−0.126505	−	0.322331i
$857$	43.2843	−	29.5107i	1.47856	−	1.00807i	0.487728	−	0.872995i	$-0.337826\pi$
$857$	43.2843	−	29.5107i	1.47856	−	1.00807i	0.990836	−	0.135072i	$-0.0431267\pi$
$858$	6.99212	+	36.2902i	0.238707	+	1.23893i
$859$	−51.8465	−	7.81460i	−1.76898	−	0.266631i	−0.817852	−	0.575428i	$-0.804835\pi$
$859$	−51.8465	−	7.81460i	−1.76898	−	0.266631i	−0.951128	+	0.308798i	$0.900073\pi$
$860$	0.759313	+	1.93470i	0.0258924	+	0.0659727i
$861$	28.5222	−	10.8502i	0.972032	−	0.369774i
$862$	7.18849	−	18.3160i	0.244841	−	0.623844i
$863$	8.84764	−	15.3246i	0.301177	−	0.521654i	−0.675226	−	0.737611i	$-0.735954\pi$
$863$	8.84764	−	15.3246i	0.301177	−	0.521654i	0.976403	+	0.215957i	$0.0692871\pi$
$864$	−4.88712	+	1.76524i	−0.166263	+	0.0600548i
$865$	−4.09895	+	10.4439i	−0.139368	+	0.355105i
$866$	0.0579220	+	0.253773i	0.00196827	+	0.00862356i
$867$	−35.5158	+	30.7709i	−1.20618	+	1.04503i
$868$	−6.74207	+	4.10737i	−0.228841	+	0.139413i
$869$	−3.02840	+	40.4112i	−0.102731	+	1.37086i
$870$	10.2591	−	2.78568i	0.347816	−	0.0944433i
$871$	1.00638	−	13.4292i	0.0340999	−	0.455032i
$872$	10.8747	−	10.0902i	0.368263	−	0.341698i
$873$	−9.38625	−	29.7230i	−0.317676	−	1.00597i
$874$	2.91920	−	12.7899i	0.0987434	−	0.432623i
$875$	−14.9874	+	9.13052i	−0.506665	+	0.308668i
$876$	−5.57873	+	6.52657i	−0.188488	+	0.220512i
$877$	−23.4329	+	7.22808i	−0.791272	+	0.244075i	−0.663941	−	0.747785i	$-0.731117\pi$
$877$	−23.4329	+	7.22808i	−0.791272	+	0.244075i	−0.127331	+	0.991860i	$0.540641\pi$
$878$	−10.6441	+	13.3473i	−0.359222	+	0.450450i
$879$	2.65531	+	1.94604i	0.0895614	+	0.0656383i
$880$	3.03537	−	1.46175i	0.102322	−	0.0492757i
$881$	56.2248			1.89426			0.947130	−	0.320850i	$-0.103968\pi$
$881$	56.2248			1.89426			0.947130	+	0.320850i	$0.103968\pi$
$882$	18.7250	+	9.50651i	0.630504	+	0.320101i
$883$	−51.6551			−1.73833			−0.869166	−	0.494520i	$-0.835344\pi$
$883$	−51.6551			−1.73833			−0.869166	+	0.494520i	$0.835344\pi$
$884$	−26.4290	+	12.7275i	−0.888904	+	0.428074i
$885$	−5.84604	+	2.57388i	−0.196513	+	0.0865201i
$886$	12.2313	−	15.3376i	0.410920	−	0.515277i
$887$	4.82845	−	1.48938i	0.162123	−	0.0500085i	−0.212631	−	0.977133i	$-0.568203\pi$
$887$	4.82845	−	1.48938i	0.162123	−	0.0500085i	0.374754	+	0.927124i	$0.377727\pi$
$888$	8.90158	+	1.65349i	0.298718	+	0.0554875i
$889$	−2.62625	−	7.85210i	−0.0880815	−	0.263351i
$890$	1.36609	−	5.98521i	0.0457913	−	0.200625i
$891$	21.2396	−	37.9503i	0.711554	−	1.27138i
$892$	−2.70218	+	2.50726i	−0.0904758	+	0.0839493i
$893$	−6.77703	+	90.4332i	−0.226785	+	3.02623i
$894$	1.81370	−	6.86041i	0.0606593	−	0.229446i
$895$	−0.690599	+	9.21540i	−0.0230842	+	0.308037i
$896$	−2.48496	−	0.908292i	−0.0830165	−	0.0303439i
$897$	−13.7687	−	4.76630i	−0.459723	−	0.159142i
$898$	2.41080	+	10.5624i	0.0804493	+	0.352471i
$899$	−9.59668	+	24.4519i	−0.320067	+	0.815518i
$900$	3.90496	−	12.9665i	0.130165	−	0.432216i
$901$	−9.80838	+	16.9886i	−0.326764	+	0.565973i
$902$	11.7561	−	29.9540i	0.391434	−	0.997359i
$903$	3.88940	+	13.0953i	0.129431	+	0.435786i
$904$	−1.26523	−	3.22375i	−0.0420809	−	0.107220i
$905$	−14.2006	−	2.14040i	−0.472044	−	0.0711491i
$906$	26.0115	−	22.5363i	0.864173	−	0.748720i
$907$	19.9836	−	13.6246i	0.663546	−	0.452398i	−0.184137	−	0.982901i	$-0.558949\pi$
$907$	19.9836	−	13.6246i	0.663546	−	0.452398i	0.847683	+	0.530502i	$0.177997\pi$
$908$	−5.95460	−	15.1721i	−0.197610	−	0.503503i
$909$	4.22565	+	6.10978i	0.140156	+	0.202649i
$910$	−2.58364	−	7.72471i	−0.0856468	−	0.256072i
$911$	−0.212524	+	0.541502i	−0.00704123	+	0.0179408i	−0.934351	−	0.356354i	$-0.884020\pi$
$911$	−0.212524	+	0.541502i	−0.00704123	+	0.0179408i	0.927310	+	0.374294i	$0.122115\pi$
$912$	−4.73313	+	10.9481i	−0.156730	+	0.362527i
$913$	−22.1937			−0.734503
$914$	−7.42104	−	9.30569i	−0.245466	−	0.307805i
$915$	−5.95514	+	6.96693i	−0.196871	+	0.230320i
$916$	−0.118061	−	1.57541i	−0.00390085	−	0.0520532i
$917$	11.7432	−	4.93133i	0.387796	−	0.162847i
$918$	33.4302	+	8.59947i	1.10336	+	0.283825i
$919$	18.8125	−	2.83552i	0.620566	−	0.0935353i	0.168769	−	0.985656i	$-0.446021\pi$
$919$	18.8125	−	2.83552i	0.620566	−	0.0935353i	0.451798	+	0.892120i	$0.350783\pi$
$920$	−0.0992571	+	1.32449i	−0.00327241	+	0.0436673i
$921$	9.40117	+	26.5818i	0.309779	+	0.875902i
$922$	−0.823997	−	10.9955i	−0.0271369	−	0.362117i
$923$	−42.5137	−	39.4470i	−1.39936	−	1.29841i
$924$	20.6968	−	7.87335i	0.680876	−	0.259014i
$925$	−17.2966	+	16.0489i	−0.568708	+	0.527684i
$926$	−27.5163	−	25.5314i	−0.904240	−	0.839012i
$927$	40.6740	−	3.32150i	1.33591	−	0.109092i
$928$	−8.41204	+	2.59477i	−0.276139	+	0.0851775i
$929$	−0.518568	+	0.249729i	−0.0170137	+	0.00819334i	−0.442371	−	0.896832i	$-0.645863\pi$
$929$	−0.518568	+	0.249729i	−0.0170137	+	0.00819334i	0.425358	+	0.905025i	$0.360148\pi$
$930$	−2.14940	−	2.89207i	−0.0704818	−	0.0948347i
$931$	45.3418	−	16.3631i	1.48602	−	0.536278i
$932$	−6.87259	+	11.9037i	−0.225119	+	0.389918i
$933$	−22.8363	+	14.4556i	−0.747626	+	0.473255i
$934$	−16.1721	−	15.0055i	−0.529168	−	0.490997i
$935$	−22.1306	−	3.33565i	−0.723748	−	0.109088i
$936$	11.5164	+	6.54678i	0.376424	+	0.213988i
$937$	9.01575	+	39.5006i	0.294532	+	1.29043i	0.878144	+	0.478396i	$0.158782\pi$
$937$	9.01575	+	39.5006i	0.294532	+	1.29043i	−0.583612	+	0.812032i	$0.698361\pi$
$938$	−8.02990	+	0.792446i	−0.262186	+	0.0258743i
$939$	2.48435	−	22.7314i	0.0810737	−	0.741812i
$940$	−0.686139	−	9.15589i	−0.0223794	−	0.298632i
$941$	−3.28731	−	14.4026i	−0.107163	−	0.469513i	−0.999824	−	0.0187829i	$-0.994021\pi$
$941$	−3.28731	−	14.4026i	−0.107163	−	0.469513i	0.892660	−	0.450730i	$-0.148836\pi$
$942$	−17.1469	+	10.8542i	−0.558677	+	0.353649i
$943$	7.90966	+	9.91840i	0.257574	+	0.322988i
$944$	4.76570	−	2.29504i	0.155110	−	0.0746972i
$945$	−3.53574	+	8.90896i	−0.115018	+	0.289809i
$946$	12.9783	+	6.25000i	0.421960	+	0.203205i
$947$	11.7698	+	51.5671i	0.382469	+	1.67570i	0.689720	+	0.724076i	$0.257733\pi$
$947$	11.7698	+	51.5671i	0.382469	+	1.67570i	−0.307252	+	0.951628i	$0.599409\pi$
$948$	10.3054	+	10.2368i	0.334705	+	0.332476i
$949$	21.8891			0.710551
$950$	−15.5421	−	26.9196i	−0.504251	−	0.873388i
$951$	−15.8321	−	15.7267i	−0.513390	−	0.509972i
$952$	10.2404	+	14.2846i	0.331892	+	0.462966i
$953$	10.8234	−	13.5721i	0.350605	−	0.439645i	−0.574990	−	0.818160i	$-0.694994\pi$
$953$	10.8234	−	13.5721i	0.350605	−	0.439645i	0.925595	+	0.378516i	$0.123565\pi$
$954$	8.82948	−	0.721028i	0.285865	−	0.0233441i
$955$	−0.573752	−	7.65618i	−0.0185662	−	0.247748i
$956$	−8.53417	+	5.81850i	−0.276015	+	0.188184i
$957$	38.9907	−	62.5159i	1.26039	−	2.02085i
$958$	−7.92097	−	20.1823i	−0.255915	−	0.652061i
$959$	46.1501	+	35.0566i	1.49026	+	1.13204i
$960$	0.308649	−	1.16748i	0.00996160	−	0.0376802i
$961$	−22.0963			−0.712784
$962$	−11.5410	−	19.9896i	−0.372097	−	0.644491i
$963$	28.2169	−	11.2925i	0.909278	−	0.363894i
$964$	16.8361	+	5.19326i	0.542256	+	0.167264i
$965$	0.967559	+	12.9112i	0.0311468	+	0.415626i
$966$	−1.39164	+	8.61842i	−0.0447752	+	0.277293i
$967$	4.11826	−	54.9543i	0.132434	−	1.76721i	−0.396011	−	0.918246i	$-0.629606\pi$
$967$	4.11826	−	54.9543i	0.132434	−	1.76721i	0.528446	−	0.848967i	$-0.322775\pi$
$968$	4.51193	−	11.4962i	0.145019	−	0.369502i
$969$	66.9489	−	42.3794i	2.15071	−	1.36142i
$970$	6.92206	+	2.13517i	0.222254	+	0.0685563i
$971$	−37.1251	+	25.3114i	−1.19140	+	0.812283i	−0.986057	−	0.166407i	$-0.946783\pi$
$971$	−37.1251	+	25.3114i	−1.19140	+	0.812283i	−0.205343	+	0.978690i	$0.565831\pi$
$972$	−5.39356	−	14.6256i	−0.172999	−	0.469118i
$973$	22.6393	+	44.3084i	0.725783	+	1.42046i
$974$	11.0495	−	10.2524i	0.354049	−	0.328509i
$975$	−31.5966	+	13.9113i	−1.01190	+	0.445518i
$976$	4.73211	−	5.93387i	0.151471	−	0.189939i
$977$	9.28175	−	40.6660i	0.296950	−	1.30102i	−0.577694	−	0.816254i	$-0.696047\pi$
$977$	9.28175	−	40.6660i	0.296950	−	1.30102i	0.874643	−	0.484767i	$-0.161096\pi$
$978$	0.387766	+	9.51274i	0.0123994	+	0.304184i
$979$	−21.2746	−	36.8487i	−0.679939	−	1.17769i
$980$	−4.29244	+	2.32237i	−0.137117	+	0.0741854i
$981$	30.4880	+	32.4211i	0.973406	+	1.03513i
$982$	−1.57576	+	21.0270i	−0.0502844	+	0.670999i
$983$	−20.6916	−	19.1990i	−0.659959	−	0.612352i	0.277385	−	0.960759i	$-0.410532\pi$
$983$	−20.6916	−	19.1990i	−0.659959	−	0.612352i	−0.937343	+	0.348407i	$0.886723\pi$
$984$	−5.42353	−	10.1794i	−0.172896	−	0.324506i
$985$	6.22956	−	1.92156i	0.198490	−	0.0612261i
$986$	55.8819	+	17.2373i	1.77964	+	0.548947i
$987$	0.633101	−	60.3454i	0.0201518	−	1.92081i
$988$	29.0570	−	8.96289i	0.924425	−	0.285147i
$989$	−4.69221	+	3.19909i	−0.149203	+	0.101725i
$990$	4.44600	+	9.07660i	0.141303	+	0.288473i
$991$	−10.2488	−	6.98748i	−0.325563	−	0.221965i	0.389498	−	0.921027i	$-0.372649\pi$
$991$	−10.2488	−	6.98748i	−0.325563	−	0.221965i	−0.715061	+	0.699063i	$0.753601\pi$
$992$	1.86044	+	2.33291i	0.0590689	+	0.0740700i
$993$	−39.1111	+	24.7577i	−1.24115	+	0.785663i
$994$	−18.8928	+	29.1643i	−0.599242	+	0.925036i
$995$	−4.47499	+	3.05100i	−0.141867	+	0.0967231i
$996$	−5.16886	+	6.04706i	−0.163782	+	0.191608i
$997$	48.7317	−	7.34512i	1.54335	−	0.232622i	0.678479	−	0.734620i	$-0.262639\pi$
$997$	48.7317	−	7.34512i	1.54335	−	0.232622i	0.864869	+	0.501998i	$0.167401\pi$
$998$	−12.5893	−	21.8053i	−0.398508	−	0.690236i
$999$	−4.78195	+	26.7373i	−0.151294	+	0.845931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bb.a.121.17	yes	336
9.7	even	3		882.2.y.b.709.21	yes	336
49.32	even	21		882.2.y.b.571.21	✓	336
441.277	even	21	inner	882.2.bb.a.277.17	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.y.b.571.21	✓	336	49.32	even	21
882.2.y.b.709.21	yes	336	9.7	even	3
882.2.bb.a.121.17	yes	336	1.1	even	1	trivial
882.2.bb.a.277.17	yes	336	441.277	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.900969 + 0.433884i) q^{2} +(0.188178 - 1.72180i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.666227 + 0.205504i) q^{5} +(0.577518 + 1.63293i) q^{6} +(-2.48496 - 0.908292i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-2.92918 - 0.648008i) q^{9} +O(q^{10})\)	\(q+(-0.900969 + 0.433884i) q^{2} +(0.188178 - 1.72180i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.666227 + 0.205504i) q^{5} +(0.577518 + 1.63293i) q^{6} +(-2.48496 - 0.908292i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-2.92918 - 0.648008i) q^{9} +(0.511085 - 0.474218i) q^{10} +(0.361109 - 4.81866i) q^{11} +(-1.22883 - 1.22065i) q^{12} +(-0.329987 + 4.40337i) q^{13} +(2.63296 - 0.259839i) q^{14} +(0.228467 + 1.18578i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-2.42699 + 6.18388i) q^{17} +(2.92026 - 0.687088i) q^{18} +(3.44315 - 5.96371i) q^{19} +(-0.254716 + 0.649007i) q^{20} +(-2.03151 + 4.10767i) q^{21} +(1.76539 + 4.49815i) q^{22} +(-1.88378 - 0.283934i) q^{23} +(1.63676 + 0.566596i) q^{24} +(-3.72957 + 2.54278i) q^{25} +(-1.61324 - 4.11047i) q^{26} +(-1.66695 + 4.92151i) q^{27} +(-2.25948 + 1.37651i) q^{28} +(-3.21615 + 8.19461i) q^{29} +(-0.720332 - 0.969223i) q^{30} +2.98391 q^{31} +(0.623490 + 0.781831i) q^{32} +(-8.22881 - 1.52852i) q^{33} +(-0.496439 - 6.62452i) q^{34} +(1.84220 + 0.0944610i) q^{35} +(-2.33295 + 1.88610i) q^{36} +(5.16886 - 0.779080i) q^{37} +(-0.514613 + 6.86704i) q^{38} +(7.51961 + 1.39679i) q^{39} +(-0.0521020 - 0.695252i) q^{40} +(-4.88153 - 4.52940i) q^{41} +(0.0480745 - 4.58232i) q^{42} +(2.18524 - 2.02761i) q^{43} +(-3.54224 - 3.28671i) q^{44} +(2.08467 - 0.170237i) q^{45} +(1.82042 - 0.561525i) q^{46} +(-11.8650 + 5.71389i) q^{47} +(-1.72050 + 0.199676i) q^{48} +(5.35001 + 4.51413i) q^{49} +(2.25695 - 3.90916i) q^{50} +(10.1907 + 5.34246i) q^{51} +(3.23695 + 3.00345i) q^{52} +(2.91997 + 0.440115i) q^{53} +(-0.633499 - 5.15739i) q^{54} +(0.749673 + 3.28453i) q^{55} +(1.43847 - 2.22054i) q^{56} +(-9.62037 - 7.05064i) q^{57} +(-0.657859 - 8.77852i) q^{58} +(1.17703 + 5.15691i) q^{59} +(1.06953 + 0.560699i) q^{60} +(4.73211 + 5.93387i) q^{61} +(-2.68841 + 1.29467i) q^{62} +(6.69030 + 4.27082i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-0.685063 - 3.00146i) q^{65} +(8.07711 - 2.19320i) q^{66} -3.04976 q^{67} +(3.32155 + 5.75309i) q^{68} +(-0.843361 + 3.19005i) q^{69} +(-1.70075 + 0.714195i) q^{70} +(-8.18884 + 10.2685i) q^{71} +(1.28356 - 2.71154i) q^{72} +(-0.370444 - 4.94323i) q^{73} +(-4.31895 + 2.94461i) q^{74} +(3.67633 + 6.90006i) q^{75} +(-2.51585 - 6.41027i) q^{76} +(-5.27409 + 11.6462i) q^{77} +(-7.38098 + 2.00418i) q^{78} -8.38639 q^{79} +(0.348601 + 0.603794i) q^{80} +(8.16017 + 3.79626i) q^{81} +(6.36334 + 1.96283i) q^{82} +(-0.343227 - 4.58005i) q^{83} +(1.94488 + 4.14939i) q^{84} +(0.346118 - 4.61862i) q^{85} +(-1.08909 + 2.77495i) q^{86} +(13.5043 + 7.07960i) q^{87} +(4.61750 + 1.42431i) q^{88} +(7.27536 - 4.96025i) q^{89} +(-1.80436 + 1.05788i) q^{90} +(4.81955 - 10.6424i) q^{91} +(-1.39650 + 1.29577i) q^{92} +(0.561505 - 5.13769i) q^{93} +(8.21084 - 10.2961i) q^{94} +(-1.06835 + 4.68076i) q^{95} +(1.46348 - 0.926400i) q^{96} +(5.19497 + 8.99795i) q^{97} +(-6.77880 - 1.74581i) q^{98} +(-4.18029 + 13.8807i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 56 q^{2} - 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} - 56 q^{8} - 15 q^{9}+O(q^{10}) \) 336 * q - 56 * q^2 - 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 - 56 * q^8 - 15 * q^9	\( 336 q - 56 q^{2} - 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} - 56 q^{8} - 15 q^{9} + 2 q^{10} + 2 q^{12} - 21 q^{13} - 7 q^{15} - 56 q^{16} + 7 q^{17} + 6 q^{18} - 34 q^{19} + 2 q^{20} + 16 q^{21} - 36 q^{23} + 2 q^{24} + 32 q^{25} + 7 q^{26} + 49 q^{27} - 16 q^{29} - 7 q^{30} + 92 q^{31} - 56 q^{32} + 14 q^{33} + 7 q^{34} + 16 q^{35} - 15 q^{36} - 26 q^{37} + q^{38} + 44 q^{39} + 2 q^{40} + 3 q^{41} - 33 q^{42} - 3 q^{43} + 106 q^{45} - 36 q^{46} + 27 q^{47} + 2 q^{48} - 74 q^{49} - 164 q^{50} - 7 q^{51} + 21 q^{52} - 78 q^{53} - 28 q^{54} - 53 q^{55} - 18 q^{57} + 40 q^{58} - 16 q^{59} - 7 q^{60} - 45 q^{61} - 20 q^{62} - 50 q^{63} - 56 q^{64} - 14 q^{65} + 14 q^{66} + 86 q^{67} - 21 q^{68} - 85 q^{69} - 26 q^{70} + 7 q^{71} + 6 q^{72} + 36 q^{73} + 2 q^{74} - 35 q^{75} + 8 q^{76} - 37 q^{77} - 12 q^{78} - 2 q^{79} - 12 q^{80} + 41 q^{81} + 3 q^{82} + 191 q^{83} - 5 q^{84} + 159 q^{85} - 3 q^{86} + 72 q^{87} + 59 q^{89} + 22 q^{90} - 29 q^{91} + 27 q^{92} + 23 q^{93} + 6 q^{94} + 26 q^{95} + 2 q^{96} - 113 q^{97} - 18 q^{98} - 33 q^{99}+O(q^{100}) \) 336 * q - 56 * q^2 - 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 - 56 * q^8 - 15 * q^9 + 2 * q^10 + 2 * q^12 - 21 * q^13 - 7 * q^15 - 56 * q^16 + 7 * q^17 + 6 * q^18 - 34 * q^19 + 2 * q^20 + 16 * q^21 - 36 * q^23 + 2 * q^24 + 32 * q^25 + 7 * q^26 + 49 * q^27 - 16 * q^29 - 7 * q^30 + 92 * q^31 - 56 * q^32 + 14 * q^33 + 7 * q^34 + 16 * q^35 - 15 * q^36 - 26 * q^37 + q^38 + 44 * q^39 + 2 * q^40 + 3 * q^41 - 33 * q^42 - 3 * q^43 + 106 * q^45 - 36 * q^46 + 27 * q^47 + 2 * q^48 - 74 * q^49 - 164 * q^50 - 7 * q^51 + 21 * q^52 - 78 * q^53 - 28 * q^54 - 53 * q^55 - 18 * q^57 + 40 * q^58 - 16 * q^59 - 7 * q^60 - 45 * q^61 - 20 * q^62 - 50 * q^63 - 56 * q^64 - 14 * q^65 + 14 * q^66 + 86 * q^67 - 21 * q^68 - 85 * q^69 - 26 * q^70 + 7 * q^71 + 6 * q^72 + 36 * q^73 + 2 * q^74 - 35 * q^75 + 8 * q^76 - 37 * q^77 - 12 * q^78 - 2 * q^79 - 12 * q^80 + 41 * q^81 + 3 * q^82 + 191 * q^83 - 5 * q^84 + 159 * q^85 - 3 * q^86 + 72 * q^87 + 59 * q^89 + 22 * q^90 - 29 * q^91 + 27 * q^92 + 23 * q^93 + 6 * q^94 + 26 * q^95 + 2 * q^96 - 113 * q^97 - 18 * q^98 - 33 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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