LMFDB - Embedded newform 570.2.u.b.511.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("570.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			511.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	570.511
Dual form			570.2.u.b.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.939693 - 0.342020i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(-1.59240 - 2.75811i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.939693 - 0.342020i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(-1.59240 - 2.75811i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(0.173648 + 0.984808i) q^{10} +(2.17365 - 3.76487i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(3.83022 - 3.21394i) q^{13} +(2.99273 - 1.08926i) q^{14} +(0.939693 + 0.342020i) q^{15} +(0.766044 + 0.642788i) q^{16} +(0.162504 - 0.921605i) q^{17} -1.00000 q^{18} +(-2.82635 + 3.31839i) q^{19} -1.00000 q^{20} +(0.553033 - 3.13641i) q^{21} +(3.33022 + 2.79439i) q^{22} +(5.97178 + 2.17355i) q^{23} +(0.939693 - 0.342020i) q^{24} +(0.766044 - 0.642788i) q^{25} +(2.50000 + 4.33013i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(0.553033 + 3.13641i) q^{28} +(-0.879385 - 4.98724i) q^{29} +(-0.500000 + 0.866025i) q^{30} +(2.57398 + 4.45826i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(4.08512 - 1.48686i) q^{33} +(0.879385 + 0.320070i) q^{34} +(-2.43969 - 2.04715i) q^{35} +(0.173648 - 0.984808i) q^{36} -1.98545 q^{37} +(-2.77719 - 3.35965i) q^{38} +5.00000 q^{39} +(0.173648 - 0.984808i) q^{40} +(-8.08899 - 6.78747i) q^{41} +(2.99273 + 1.08926i) q^{42} +(-4.10607 + 1.49449i) q^{43} +(-3.33022 + 2.79439i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-3.17752 + 5.50362i) q^{46} +(1.59967 + 9.07218i) q^{47} +(0.173648 + 0.984808i) q^{48} +(-1.57145 + 2.72183i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.716881 - 0.601535i) q^{51} +(-4.69846 + 1.71010i) q^{52} +(4.41875 + 1.60829i) q^{53} +(-0.766044 - 0.642788i) q^{54} +(0.754900 - 4.28125i) q^{55} -3.18479 q^{56} +(-4.29813 + 0.725293i) q^{57} +5.06418 q^{58} +(2.31655 - 13.1378i) q^{59} +(-0.766044 - 0.642788i) q^{60} +(8.21213 + 2.98897i) q^{61} +(-4.83750 + 1.76070i) q^{62} +(2.43969 - 2.04715i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.50000 - 4.33013i) q^{65} +(0.754900 + 4.28125i) q^{66} +(2.71688 + 15.4082i) q^{67} +(-0.467911 + 0.810446i) q^{68} +(3.17752 + 5.50362i) q^{69} +(2.43969 - 2.04715i) q^{70} +(-10.5963 + 3.85673i) q^{71} +(0.939693 + 0.342020i) q^{72} +(12.7023 + 10.6585i) q^{73} +(0.344770 - 1.95529i) q^{74} +1.00000 q^{75} +(3.79086 - 2.15160i) q^{76} -13.8452 q^{77} +(-0.868241 + 4.92404i) q^{78} +(-6.69459 - 5.61743i) q^{79} +(0.939693 + 0.342020i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(8.08899 - 6.78747i) q^{82} +(-2.22668 - 3.85673i) q^{83} +(-1.59240 + 2.75811i) q^{84} +(-0.162504 - 0.921605i) q^{85} +(-0.758770 - 4.30320i) q^{86} +(2.53209 - 4.38571i) q^{87} +(-2.17365 - 3.76487i) q^{88} +(9.21554 - 7.73275i) q^{89} +(-0.939693 + 0.342020i) q^{90} +(-14.9636 - 5.44632i) q^{91} +(-4.86824 - 4.08494i) q^{92} +(-0.893933 + 5.06975i) q^{93} -9.21213 q^{94} +(-1.52094 + 4.08494i) q^{95} -1.00000 q^{96} +(2.05644 - 11.6626i) q^{97} +(-2.40760 - 2.02022i) q^{98} +(4.08512 + 1.48686i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q - 6 * q^7 + 3 * q^8	$ 6 q - 6 q^{7} + 3 q^{8} + 12 q^{11} - 3 q^{12} + 6 q^{17} - 6 q^{18} - 18 q^{19} - 6 q^{20} - 9 q^{21} - 3 q^{22} + 21 q^{23} + 15 q^{26} - 3 q^{27} - 9 q^{28} + 6 q^{29} - 3 q^{30} + 3 q^{33} - 6 q^{34} - 9 q^{35} + 24 q^{37} - 6 q^{38} + 30 q^{39} - 3 q^{41} + 3 q^{44} + 3 q^{45} + 6 q^{46} + 24 q^{47} - 9 q^{49} + 3 q^{50} - 12 q^{51} + 24 q^{53} + 6 q^{55} - 12 q^{56} - 12 q^{57} + 12 q^{58} + 12 q^{59} - 24 q^{62} + 9 q^{63} - 3 q^{64} + 15 q^{65} + 6 q^{66} - 12 q^{68} - 6 q^{69} + 9 q^{70} - 36 q^{71} + 24 q^{73} + 15 q^{74} + 6 q^{75} - 9 q^{76} - 30 q^{77} - 36 q^{79} + 3 q^{82} - 6 q^{84} - 6 q^{85} + 18 q^{86} + 6 q^{87} - 12 q^{88} + 48 q^{89} - 24 q^{92} - 30 q^{93} - 6 q^{94} - 6 q^{95} - 6 q^{96} + 42 q^{97} - 18 q^{98} + 3 q^{99}+O(q^{100}) $ 6 * q - 6 * q^7 + 3 * q^8 + 12 * q^11 - 3 * q^12 + 6 * q^17 - 6 * q^18 - 18 * q^19 - 6 * q^20 - 9 * q^21 - 3 * q^22 + 21 * q^23 + 15 * q^26 - 3 * q^27 - 9 * q^28 + 6 * q^29 - 3 * q^30 + 3 * q^33 - 6 * q^34 - 9 * q^35 + 24 * q^37 - 6 * q^38 + 30 * q^39 - 3 * q^41 + 3 * q^44 + 3 * q^45 + 6 * q^46 + 24 * q^47 - 9 * q^49 + 3 * q^50 - 12 * q^51 + 24 * q^53 + 6 * q^55 - 12 * q^56 - 12 * q^57 + 12 * q^58 + 12 * q^59 - 24 * q^62 + 9 * q^63 - 3 * q^64 + 15 * q^65 + 6 * q^66 - 12 * q^68 - 6 * q^69 + 9 * q^70 - 36 * q^71 + 24 * q^73 + 15 * q^74 + 6 * q^75 - 9 * q^76 - 30 * q^77 - 36 * q^79 + 3 * q^82 - 6 * q^84 - 6 * q^85 + 18 * q^86 + 6 * q^87 - 12 * q^88 + 48 * q^89 - 24 * q^92 - 30 * q^93 - 6 * q^94 - 6 * q^95 - 6 * q^96 + 42 * q^97 - 18 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	0.939693	−	0.342020i	0.420243	−	0.152956i
$5$	0.939693	−	0.342020i	0.420243	−	0.152956i
$6$	−0.766044	+	0.642788i	−0.312736	+	0.262417i
$7$	−1.59240	−	2.75811i	−0.601869	−	1.04247i	−0.992538	−	0.121937i	$-0.961090\pi$
$7$	−1.59240	−	2.75811i	−0.601869	−	1.04247i	0.390669	−	0.920531i	$-0.372244\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$	0.173648	+	0.984808i	0.0549124	+	0.311424i
$11$	2.17365	−	3.76487i	0.655380	−	1.13515i	−0.326419	−	0.945225i	$-0.605842\pi$
$11$	2.17365	−	3.76487i	0.655380	−	1.13515i	0.981798	−	0.189926i	$-0.0608247\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	3.83022	−	3.21394i	1.06231	−	0.891386i	0.0679785	−	0.997687i	$-0.478345\pi$
$13$	3.83022	−	3.21394i	1.06231	−	0.891386i	0.994334	+	0.106301i	$0.0339006\pi$
$14$	2.99273	−	1.08926i	0.799840	−	0.291118i
$15$	0.939693	+	0.342020i	0.242628	+	0.0883092i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	0.162504	−	0.921605i	0.0394130	−	0.223522i	−0.958739	−	0.284287i	$-0.908243\pi$
$17$	0.162504	−	0.921605i	0.0394130	−	0.223522i	0.998152	+	0.0607653i	$0.0193541\pi$
$18$	−1.00000			−0.235702
$19$	−2.82635	+	3.31839i	−0.648410	+	0.761292i
$19$	−2.82635	+	3.31839i	−0.648410	+	0.761292i
$20$	−1.00000			−0.223607
$21$	0.553033	−	3.13641i	0.120682	−	0.684420i
$22$	3.33022	+	2.79439i	0.710006	+	0.595766i
$23$	5.97178	+	2.17355i	1.24520	+	0.453217i	0.878778	−	0.477231i	$-0.158360\pi$
$23$	5.97178	+	2.17355i	1.24520	+	0.453217i	0.366425	+	0.930448i	$0.380582\pi$
$24$	0.939693	−	0.342020i	0.191814	−	0.0698146i
$25$	0.766044	−	0.642788i	0.153209	−	0.128558i
$26$	2.50000	+	4.33013i	0.490290	+	0.849208i
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	0.553033	+	3.13641i	0.104513	+	0.592725i
$29$	−0.879385	−	4.98724i	−0.163298	−	0.926108i	−0.950802	−	0.309799i	$-0.899738\pi$
$29$	−0.879385	−	4.98724i	−0.163298	−	0.926108i	0.787504	−	0.616309i	$-0.211373\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	2.57398	+	4.45826i	0.462300	+	0.800727i	0.999075	−	0.0429981i	$-0.0136910\pi$
$31$	2.57398	+	4.45826i	0.462300	+	0.800727i	−0.536775	+	0.843725i	$0.680358\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	4.08512	−	1.48686i	0.711129	−	0.258830i
$34$	0.879385	+	0.320070i	0.150813	+	0.0548916i
$35$	−2.43969	−	2.04715i	−0.412383	−	0.346031i
$36$	0.173648	−	0.984808i	0.0289414	−	0.164135i
$37$	−1.98545			−0.326406			−0.163203	−	0.986592i	$-0.552183\pi$
$37$	−1.98545			−0.326406			−0.163203	+	0.986592i	$0.552183\pi$
$38$	−2.77719	−	3.35965i	−0.450520	−	0.545007i
$39$	5.00000			0.800641
$40$	0.173648	−	0.984808i	0.0274562	−	0.155712i
$41$	−8.08899	−	6.78747i	−1.26329	−	1.06002i	−0.995324	−	0.0965961i	$-0.969204\pi$
$41$	−8.08899	−	6.78747i	−1.26329	−	1.06002i	−0.267965	−	0.963429i	$-0.586351\pi$
$42$	2.99273	+	1.08926i	0.461788	+	0.168077i
$43$	−4.10607	+	1.49449i	−0.626169	+	0.227907i	−0.635563	−	0.772049i	$-0.719232\pi$
$43$	−4.10607	+	1.49449i	−0.626169	+	0.227907i	0.00939383	+	0.999956i	$0.497010\pi$
$44$	−3.33022	+	2.79439i	−0.502050	+	0.421270i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	−3.17752	+	5.50362i	−0.468500	+	0.811465i
$47$	1.59967	+	9.07218i	0.233336	+	1.32331i	0.846090	+	0.533040i	$0.178950\pi$
$47$	1.59967	+	9.07218i	0.233336	+	1.32331i	−0.612754	+	0.790274i	$0.709938\pi$
$48$	0.173648	+	0.984808i	0.0250640	+	0.142145i
$49$	−1.57145	+	2.72183i	−0.224493	+	0.388833i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	0.716881	−	0.601535i	0.100383	−	0.0842317i
$52$	−4.69846	+	1.71010i	−0.651560	+	0.237148i
$53$	4.41875	+	1.60829i	0.606962	+	0.220916i	0.627173	−	0.778880i	$-0.284212\pi$
$53$	4.41875	+	1.60829i	0.606962	+	0.220916i	−0.0202116	+	0.999796i	$0.506434\pi$
$54$	−0.766044	−	0.642788i	−0.104245	−	0.0874723i
$55$	0.754900	−	4.28125i	0.101791	−	0.577284i
$56$	−3.18479			−0.425586
$57$	−4.29813	+	0.725293i	−0.569302	+	0.0960674i
$58$	5.06418			0.664959
$59$	2.31655	−	13.1378i	0.301589	−	1.71040i	−0.337550	−	0.941307i	$-0.609598\pi$
$59$	2.31655	−	13.1378i	0.301589	−	1.71040i	0.639140	−	0.769091i	$-0.279291\pi$
$60$	−0.766044	−	0.642788i	−0.0988959	−	0.0829835i
$61$	8.21213	+	2.98897i	1.05146	+	0.382699i	0.809212	−	0.587517i	$-0.199894\pi$
$61$	8.21213	+	2.98897i	1.05146	+	0.382699i	0.242244	+	0.970215i	$0.422117\pi$
$62$	−4.83750	+	1.76070i	−0.614363	+	0.223610i
$63$	2.43969	−	2.04715i	0.307372	−	0.257916i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	2.50000	−	4.33013i	0.310087	−	0.537086i
$66$	0.754900	+	4.28125i	0.0929218	+	0.526986i
$67$	2.71688	+	15.4082i	0.331920	+	1.88241i	0.455750	+	0.890108i	$0.349371\pi$
$67$	2.71688	+	15.4082i	0.331920	+	1.88241i	−0.123830	+	0.992303i	$0.539518\pi$
$68$	−0.467911	+	0.810446i	−0.0567426	+	0.0982810i
$69$	3.17752	+	5.50362i	0.382528	+	0.662558i
$70$	2.43969	−	2.04715i	0.291599	−	0.244681i
$71$	−10.5963	+	3.85673i	−1.25755	+	0.457709i	−0.882945	−	0.469477i	$-0.844442\pi$
$71$	−10.5963	+	3.85673i	−1.25755	+	0.457709i	−0.374601	+	0.927186i	$0.622220\pi$
$72$	0.939693	+	0.342020i	0.110744	+	0.0403075i
$73$	12.7023	+	10.6585i	1.48670	+	1.24749i	0.898656	+	0.438654i	$0.144544\pi$
$73$	12.7023	+	10.6585i	1.48670	+	1.24749i	0.588039	+	0.808832i	$0.299900\pi$
$74$	0.344770	−	1.95529i	0.0400787	−	0.227298i
$75$	1.00000			0.115470
$76$	3.79086	−	2.15160i	0.434841	−	0.246806i
$77$	−13.8452			−1.57781
$78$	−0.868241	+	4.92404i	−0.0983089	+	0.557538i
$79$	−6.69459	−	5.61743i	−0.753201	−	0.632010i	0.183147	−	0.983086i	$-0.441372\pi$
$79$	−6.69459	−	5.61743i	−0.753201	−	0.632010i	−0.936347	+	0.351075i	$0.885816\pi$
$80$	0.939693	+	0.342020i	0.105061	+	0.0382390i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	8.08899	−	6.78747i	0.893280	−	0.749551i
$83$	−2.22668	−	3.85673i	−0.244410	−	0.423331i	0.717556	−	0.696501i	$-0.245261\pi$
$83$	−2.22668	−	3.85673i	−0.244410	−	0.423331i	−0.961966	+	0.273171i	$0.911928\pi$
$84$	−1.59240	+	2.75811i	−0.173745	+	0.300935i
$85$	−0.162504	−	0.921605i	−0.0176260	−	0.0999621i
$86$	−0.758770	−	4.30320i	−0.0818203	−	0.464026i
$87$	2.53209	−	4.38571i	0.271468	−	0.470197i
$88$	−2.17365	−	3.76487i	−0.231712	−	0.401336i
$89$	9.21554	−	7.73275i	0.976845	−	0.819670i	−0.00676542	−	0.999977i	$-0.502154\pi$
$89$	9.21554	−	7.73275i	0.976845	−	0.819670i	0.983610	+	0.180307i	$0.0577091\pi$
$90$	−0.939693	+	0.342020i	−0.0990523	+	0.0360521i
$91$	−14.9636	−	5.44632i	−1.56861	−	0.570929i
$92$	−4.86824	−	4.08494i	−0.507549	−	0.425884i
$93$	−0.893933	+	5.06975i	−0.0926966	+	0.525708i
$94$	−9.21213			−0.950159
$95$	−1.52094	+	4.08494i	−0.156046	+	0.419106i
$96$	−1.00000			−0.102062
$97$	2.05644	−	11.6626i	0.208800	−	1.18416i	−0.682548	−	0.730841i	$-0.739128\pi$
$97$	2.05644	−	11.6626i	0.208800	−	1.18416i	0.891348	−	0.453320i	$-0.149761\pi$
$98$	−2.40760	−	2.02022i	−0.243205	−	0.204073i
$99$	4.08512	+	1.48686i	0.410570	+	0.149435i
$100$	−0.939693	+	0.342020i	−0.0939693	+	0.0342020i
$101$	−4.84524	+	4.06564i	−0.482119	+	0.404546i	−0.851192	−	0.524855i	$-0.824120\pi$
$101$	−4.84524	+	4.06564i	−0.482119	+	0.404546i	0.369073	+	0.929400i	$0.379675\pi$
$102$	0.467911	+	0.810446i	0.0463301	+	0.0802461i
$103$	−6.65657	+	11.5295i	−0.655892	+	1.13604i	0.325778	+	0.945446i	$0.394374\pi$
$103$	−6.65657	+	11.5295i	−0.655892	+	1.13604i	−0.981669	+	0.190591i	$0.938959\pi$
$104$	−0.868241	−	4.92404i	−0.0851380	−	0.482842i
$105$	−0.553033	−	3.13641i	−0.0539705	−	0.306082i
$106$	−2.35117	+	4.07234i	−0.228366	+	0.395541i
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$	0.766044	−	0.642788i	0.0737127	−	0.0618523i
$109$	−8.59627	+	3.12879i	−0.823373	+	0.299683i	−0.719136	−	0.694869i	$-0.755462\pi$
$109$	−8.59627	+	3.12879i	−0.823373	+	0.299683i	−0.104237	+	0.994552i	$0.533240\pi$
$110$	4.08512	+	1.48686i	0.389501	+	0.141767i
$111$	−1.52094	−	1.27622i	−0.144362	−	0.121134i
$112$	0.553033	−	3.13641i	0.0522567	−	0.296363i
$113$	9.19253			0.864761			0.432380	−	0.901691i	$-0.357674\pi$
$113$	9.19253			0.864761			0.432380	+	0.901691i	$0.357674\pi$
$114$	0.0320889	−	4.35878i	0.00300540	−	0.408237i
$115$	6.35504			0.592610
$116$	−0.879385	+	4.98724i	−0.0816489	+	0.463054i
$117$	3.83022	+	3.21394i	0.354104	+	0.297129i
$118$	12.5360	+	4.56272i	1.15403	+	0.420032i
$119$	−2.80066	+	1.01936i	−0.256736	+	0.0934443i
$120$	0.766044	−	0.642788i	0.0699300	−	0.0586782i
$121$	−3.94949	−	6.84072i	−0.359045	−	0.621884i
$122$	−4.36959	+	7.56834i	−0.395604	+	0.685206i
$123$	−1.83363	−	10.3990i	−0.165332	−	0.937647i
$124$	−0.893933	−	5.06975i	−0.0802776	−	0.455277i
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$	1.59240	+	2.75811i	0.141862	+	0.245712i
$127$	−0.804063	+	0.674689i	−0.0713491	+	0.0598690i	−0.677765	−	0.735279i	$-0.737051\pi$
$127$	−0.804063	+	0.674689i	−0.0713491	+	0.0598690i	0.606416	+	0.795148i	$0.292607\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	−4.10607	−	1.49449i	−0.361519	−	0.131582i
$130$	3.83022	+	3.21394i	0.335933	+	0.281881i
$131$	−0.0444153	+	0.251892i	−0.00388058	+	0.0220079i	−0.986687	−	0.162633i	$-0.948001\pi$
$131$	−0.0444153	+	0.251892i	−0.00388058	+	0.0220079i	0.982806	+	0.184641i	$0.0591123\pi$
$132$	−4.34730			−0.378384
$133$	13.6532	+	2.51120i	1.18388	+	0.217748i
$134$	−15.6459			−1.35160
$135$	−0.173648	+	0.984808i	−0.0149453	+	0.0847588i
$136$	−0.716881	−	0.601535i	−0.0614721	−	0.0515812i
$137$	11.2071	+	4.07904i	0.957486	+	0.348496i	0.773048	−	0.634348i	$-0.218731\pi$
$137$	11.2071	+	4.07904i	0.957486	+	0.348496i	0.184438	+	0.982844i	$0.440954\pi$
$138$	−5.97178	+	2.17355i	−0.508352	+	0.185025i
$139$	−12.4042	+	10.4084i	−1.05211	+	0.882826i	−0.993314	−	0.115444i	$-0.963171\pi$
$139$	−12.4042	+	10.4084i	−1.05211	+	0.882826i	−0.0587966	+	0.998270i	$0.518726\pi$
$140$	1.59240	+	2.75811i	0.134582	+	0.233103i
$141$	−4.60607	+	7.97794i	−0.387901	+	0.671864i
$142$	−1.95811	−	11.1050i	−0.164321	−	0.931911i
$143$	−3.77450	−	21.4063i	−0.315640	−	1.79008i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−2.53209	−	4.38571i	−0.210279	−	0.364213i
$146$	−12.7023	+	10.6585i	−1.05125	+	0.882106i
$147$	−2.95336	+	1.07494i	−0.243589	+	0.0886593i
$148$	1.86571	+	0.679065i	0.153361	+	0.0558188i
$149$	−1.90167	−	1.59569i	−0.155791	−	0.130724i	0.561560	−	0.827436i	$-0.310201\pi$
$149$	−1.90167	−	1.59569i	−0.155791	−	0.130724i	−0.717351	+	0.696712i	$0.754646\pi$
$150$	−0.173648	+	0.984808i	−0.0141783	+	0.0804092i
$151$	−4.28581			−0.348774			−0.174387	−	0.984677i	$-0.555794\pi$
$151$	−4.28581			−0.348774			−0.174387	+	0.984677i	$0.555794\pi$
$152$	1.46064	+	4.10689i	0.118473	+	0.333113i
$153$	0.935822			0.0756567
$154$	2.40420	−	13.6349i	0.193736	−	1.09873i
$155$	3.94356	+	3.30904i	0.316755	+	0.265789i
$156$	−4.69846	−	1.71010i	−0.376178	−	0.136918i
$157$	−20.2062	+	7.35446i	−1.61263	+	0.586950i	−0.981958	−	0.189099i	$-0.939443\pi$
$157$	−20.2062	+	7.35446i	−1.61263	+	0.586950i	−0.630673	+	0.776049i	$0.717221\pi$
$158$	6.69459	−	5.61743i	0.532593	−	0.446899i
$159$	2.35117	+	4.07234i	0.186460	+	0.322958i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−3.51455	−	19.9320i	−0.276985	−	1.57086i
$162$	−0.173648	−	0.984808i	−0.0136431	−	0.0773738i
$163$	3.75877	−	6.51038i	0.294410	−	0.509932i	−0.680438	−	0.732806i	$-0.738210\pi$
$163$	3.75877	−	6.51038i	0.294410	−	0.509932i	0.974847	+	0.222873i	$0.0715437\pi$
$164$	5.27972	+	9.14473i	0.412276	+	0.714084i
$165$	3.33022	−	2.79439i	0.259257	−	0.217543i
$166$	4.18479	−	1.52314i	0.324803	−	0.118219i
$167$	−12.2554	−	4.46059i	−0.948349	−	0.345171i	−0.178891	−	0.983869i	$-0.557251\pi$
$167$	−12.2554	−	4.46059i	−0.948349	−	0.345171i	−0.769457	+	0.638698i	$0.779473\pi$
$168$	−2.43969	−	2.04715i	−0.188226	−	0.157941i
$169$	2.08378	−	11.8177i	0.160291	−	0.909053i
$170$	0.935822			0.0717743
$171$	−3.75877	−	2.20718i	−0.287440	−	0.168787i
$172$	4.36959			0.333178
$173$	−0.0748553	+	0.424525i	−0.00569114	+	0.0322761i	−0.987521	−	0.157487i	$-0.949661\pi$
$173$	−0.0748553	+	0.424525i	−0.00569114	+	0.0322761i	0.981830	+	0.189763i	$0.0607719\pi$
$174$	3.87939	+	3.25519i	0.294095	+	0.246775i
$175$	−2.99273	−	1.08926i	−0.226229	−	0.0823406i
$176$	4.08512	−	1.48686i	0.307928	−	0.112077i
$177$	10.2194	−	8.57510i	0.768138	−	0.644544i
$178$	6.01501	+	10.4183i	0.450844	+	0.780885i
$179$	−7.77379	+	13.4646i	−0.581040	+	1.00639i	0.414316	+	0.910133i	$0.364021\pi$
$179$	−7.77379	+	13.4646i	−0.581040	+	1.00639i	−0.995356	+	0.0962579i	$0.969313\pi$
$180$	−0.173648	−	0.984808i	−0.0129430	−	0.0734032i
$181$	−0.263518	−	1.49449i	−0.0195872	−	0.111084i	0.973447	−	0.228914i	$-0.0735174\pi$
$181$	−0.263518	−	1.49449i	−0.0195872	−	0.111084i	−0.993034	+	0.117830i	$0.962406\pi$
$182$	7.96198	−	13.7906i	0.590181	−	1.02222i
$183$	4.36959	+	7.56834i	0.323009	+	0.559468i
$184$	4.86824	−	4.08494i	0.358891	−	0.301146i
$185$	−1.86571	+	0.679065i	−0.137170	+	0.0499258i
$186$	−4.83750	−	1.76070i	−0.354702	−	0.129101i
$187$	−3.11650	−	2.61505i	−0.227901	−	0.191231i
$188$	1.59967	−	9.07218i	0.116668	−	0.661657i
$189$	3.18479			0.231660
$190$	−3.75877	−	2.20718i	−0.272690	−	0.160126i
$191$	11.5621			0.836606			0.418303	−	0.908308i	$-0.362625\pi$
$191$	11.5621			0.836606			0.418303	+	0.908308i	$0.362625\pi$
$192$	0.173648	−	0.984808i	0.0125320	−	0.0710724i
$193$	−1.63041	−	1.36808i	−0.117360	−	0.0984766i	0.582219	−	0.813032i	$-0.302185\pi$
$193$	−1.63041	−	1.36808i	−0.117360	−	0.0984766i	−0.699579	+	0.714555i	$0.746629\pi$
$194$	11.1284	+	4.05039i	0.798969	+	0.290801i
$195$	4.69846	−	1.71010i	0.336464	−	0.122463i
$196$	2.40760	−	2.02022i	0.171972	−	0.144301i
$197$	8.36618	+	14.4907i	0.596066	+	1.03242i	0.993396	+	0.114740i	$0.0366036\pi$
$197$	8.36618	+	14.4907i	0.596066	+	1.03242i	−0.397330	+	0.917676i	$0.630063\pi$
$198$	−2.17365	+	3.76487i	−0.154474	+	0.267558i
$199$	0.539830	+	3.06153i	0.0382675	+	0.217026i	0.997945	−	0.0640779i	$-0.0204106\pi$
$199$	0.539830	+	3.06153i	0.0382675	+	0.217026i	−0.959677	+	0.281104i	$0.909300\pi$
$200$	−0.173648	−	0.984808i	−0.0122788	−	0.0696364i
$201$	−7.82295	+	13.5497i	−0.551788	+	0.955725i
$202$	−3.16250	−	5.47762i	−0.222513	−	0.385404i
$203$	−12.3550	+	10.3671i	−0.867154	+	0.727628i
$204$	−0.879385	+	0.320070i	−0.0615693	+	0.0224094i
$205$	−9.92262	−	3.61154i	−0.693026	−	0.252241i
$206$	−10.1985	−	8.55753i	−0.710561	−	0.596231i
$207$	−1.10354	+	6.25849i	−0.0767014	+	0.434995i
$208$	5.00000			0.346688
$209$	6.34982	+	17.8539i	0.439226	+	1.23498i
$210$	3.18479			0.219772
$211$	−2.37851	+	13.4892i	−0.163743	+	0.928634i	0.786608	+	0.617453i	$0.211836\pi$
$211$	−2.37851	+	13.4892i	−0.163743	+	0.928634i	−0.950351	+	0.311181i	$0.899276\pi$
$212$	−3.60220	−	3.02260i	−0.247400	−	0.207593i
$213$	−10.5963	−	3.85673i	−0.726044	−	0.264258i
$214$	11.2763	−	4.10424i	0.770833	−	0.280560i
$215$	−3.34730	+	2.80872i	−0.228284	+	0.191553i
$216$	0.500000	+	0.866025i	0.0340207	+	0.0589256i
$217$	8.19759	−	14.1986i	0.556488	−	0.963866i
$218$	−1.58853	−	9.00898i	−0.107589	−	0.610165i
$219$	2.87939	+	16.3298i	0.194571	+	1.10347i
$220$	−2.17365	+	3.76487i	−0.146547	+	0.253827i
$221$	−2.33956	−	4.05223i	−0.157376	−	0.272582i
$222$	1.52094	−	1.27622i	0.102079	−	0.0856545i
$223$	6.85844	−	2.49627i	0.459275	−	0.167162i	−0.102013	−	0.994783i	$-0.532528\pi$
$223$	6.85844	−	2.49627i	0.459275	−	0.167162i	0.561288	+	0.827621i	$0.310306\pi$
$224$	2.99273	+	1.08926i	0.199960	+	0.0727795i
$225$	0.766044	+	0.642788i	0.0510696	+	0.0428525i
$226$	−1.59627	+	9.05288i	−0.106182	+	0.602188i
$227$	7.47296			0.495998			0.247999	−	0.968760i	$-0.420227\pi$
$227$	7.47296			0.495998			0.247999	+	0.968760i	$0.420227\pi$
$228$	4.28699	+	0.788496i	0.283913	+	0.0522194i
$229$	−7.19253			−0.475296			−0.237648	−	0.971351i	$-0.576376\pi$
$229$	−7.19253			−0.475296			−0.237648	+	0.971351i	$0.576376\pi$
$230$	−1.10354	+	6.25849i	−0.0727653	+	0.412673i
$231$	−10.6061	−	8.89955i	−0.697828	−	0.585547i
$232$	−4.75877	−	1.73205i	−0.312429	−	0.113715i
$233$	−14.5817	+	5.30731i	−0.955280	+	0.347694i	−0.772182	−	0.635401i	$-0.780835\pi$
$233$	−14.5817	+	5.30731i	−0.955280	+	0.347694i	−0.183098	+	0.983095i	$0.558613\pi$
$234$	−3.83022	+	3.21394i	−0.250389	+	0.210102i
$235$	4.60607	+	7.97794i	0.300467	+	0.520424i
$236$	−6.67024	+	11.5532i	−0.434196	+	0.752049i
$237$	−1.51754	−	8.60640i	−0.0985749	−	0.559046i
$238$	−0.517541	−	2.93512i	−0.0335472	−	0.190256i
$239$	−7.55943	+	13.0933i	−0.488979	+	0.846936i	−0.999920	−	0.0126797i	$-0.995964\pi$
$239$	−7.55943	+	13.0933i	−0.488979	+	0.846936i	0.510941	+	0.859616i	$0.329297\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	−4.39646	+	3.68907i	−0.283201	+	0.237634i	−0.773311	−	0.634027i	$-0.781401\pi$
$241$	−4.39646	+	3.68907i	−0.283201	+	0.237634i	0.490110	+	0.871660i	$0.336956\pi$
$242$	7.42262	−	2.70161i	0.477144	−	0.173666i
$243$	−0.939693	−	0.342020i	−0.0602813	−	0.0219406i
$244$	−6.69459	−	5.61743i	−0.428577	−	0.359619i
$245$	−0.545759	+	3.09516i	−0.0348673	+	0.197742i
$246$	10.5594			0.673245
$247$	−0.160444	+	21.7939i	−0.0102088	+	1.38671i
$248$	5.14796			0.326896
$249$	0.773318	−	4.38571i	0.0490071	−	0.277933i
$250$	0.766044	+	0.642788i	0.0484489	+	0.0406535i
$251$	22.6275	+	8.23573i	1.42823	+	0.519835i	0.936425	−	0.350869i	$-0.114114\pi$
$251$	22.6275	+	8.23573i	1.42823	+	0.519835i	0.491809	+	0.870703i	$0.336336\pi$
$252$	−2.99273	+	1.08926i	−0.188524	+	0.0686171i
$253$	21.1637	−	17.7584i	1.33055	−	1.11646i
$254$	−0.524815	−	0.909006i	−0.0329298	−	0.0570361i
$255$	0.467911	−	0.810446i	0.0293017	−	0.0507521i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	2.91353	+	16.5235i	0.181741	+	1.03071i	0.930071	+	0.367379i	$0.119745\pi$
$257$	2.91353	+	16.5235i	0.181741	+	1.03071i	−0.748330	+	0.663327i	$0.769144\pi$
$258$	2.18479	−	3.78417i	0.136019	−	0.235592i
$259$	3.16163	+	5.47610i	0.196454	+	0.340268i
$260$	−3.83022	+	3.21394i	−0.237540	+	0.199320i
$261$	4.75877	−	1.73205i	0.294560	−	0.107211i
$262$	−0.240352	−	0.0874810i	−0.0148490	−	0.00540460i
$263$	9.81773	+	8.23806i	0.605387	+	0.507980i	0.893172	−	0.449715i	$-0.148474\pi$
$263$	9.81773	+	8.23806i	0.605387	+	0.507980i	−0.287785	+	0.957695i	$0.592919\pi$
$264$	0.754900	−	4.28125i	0.0464609	−	0.263493i
$265$	4.70233			0.288862
$266$	−4.84389	+	13.0097i	−0.296998	+	0.797675i
$267$	12.0300			0.736226
$268$	2.71688	−	15.4082i	0.165960	−	0.941206i
$269$	12.8530	+	10.7849i	0.783660	+	0.657569i	0.944167	−	0.329466i	$-0.106869\pi$
$269$	12.8530	+	10.7849i	0.783660	+	0.657569i	−0.160508	+	0.987035i	$0.551313\pi$
$270$	−0.939693	−	0.342020i	−0.0571879	−	0.0208147i
$271$	3.07873	−	1.12056i	0.187019	−	0.0680694i	−0.246813	−	0.969063i	$-0.579383\pi$
$271$	3.07873	−	1.12056i	0.187019	−	0.0680694i	0.433832	+	0.900994i	$0.357161\pi$
$272$	0.716881	−	0.601535i	0.0434673	−	0.0364734i
$273$	−7.96198	−	13.7906i	−0.481881	−	0.834642i
$274$	−5.96316	+	10.3285i	−0.360248	+	0.623968i
$275$	−0.754900	−	4.28125i	−0.0455222	−	0.258169i
$276$	−1.10354	−	6.25849i	−0.0664253	−	0.376717i
$277$	4.62836	−	8.01655i	0.278091	−	0.481668i	−0.692819	−	0.721111i	$-0.743632\pi$
$277$	4.62836	−	8.01655i	0.278091	−	0.481668i	0.970910	+	0.239444i	$0.0769650\pi$
$278$	−8.09627	−	14.0231i	−0.485582	−	0.841052i
$279$	−3.94356	+	3.30904i	−0.236095	+	0.198107i
$280$	−2.99273	+	1.08926i	−0.178850	+	0.0650959i
$281$	−13.9363	−	5.07239i	−0.831369	−	0.302594i	−0.108949	−	0.994047i	$-0.534748\pi$
$281$	−13.9363	−	5.07239i	−0.831369	−	0.302594i	−0.722421	+	0.691454i	$0.756971\pi$
$282$	−7.05690	−	5.92145i	−0.420233	−	0.352617i
$283$	2.87939	−	16.3298i	0.171162	−	0.970706i	−0.771320	−	0.636448i	$-0.780403\pi$
$283$	2.87939	−	16.3298i	0.171162	−	0.970706i	0.942481	−	0.334258i	$-0.108486\pi$
$284$	11.2763			0.669126
$285$	−3.79086	+	2.15160i	−0.224551	+	0.127450i
$286$	21.7365			1.28531
$287$	−5.83972	+	33.1187i	−0.344708	+	1.95493i
$288$	−0.766044	−	0.642788i	−0.0451396	−	0.0378766i
$289$	15.1518	+	5.51481i	0.891284	+	0.324401i
$290$	4.75877	−	1.73205i	0.279445	−	0.101710i
$291$	9.07192	−	7.61224i	0.531805	−	0.446238i
$292$	−8.29086	−	14.3602i	−0.485186	−	0.840367i
$293$	0.555560	−	0.962258i	0.0324561	−	0.0562157i	−0.849341	−	0.527844i	$-0.823000\pi$
$293$	0.555560	−	0.962258i	0.0324561	−	0.0562157i	0.881797	+	0.471629i	$0.156334\pi$
$294$	−0.545759	−	3.09516i	−0.0318293	−	0.180513i
$295$	−2.31655	−	13.1378i	−0.134875	−	0.764913i
$296$	−0.992726	+	1.71945i	−0.0577010	+	0.0999411i
$297$	2.17365	+	3.76487i	0.126128	+	0.218460i
$298$	1.90167	−	1.59569i	0.110161	−	0.0924361i
$299$	29.8589	−	10.8678i	1.72679	−	0.628498i
$300$	−0.939693	−	0.342020i	−0.0542532	−	0.0197465i
$301$	10.6604	+	8.94517i	0.614458	+	0.515591i
$302$	0.744223	−	4.22070i	0.0428252	−	0.242874i
$303$	−6.32501			−0.363362
$304$	−4.29813	+	0.725293i	−0.246515	+	0.0415984i
$305$	8.73917			0.500403
$306$	−0.162504	+	0.921605i	−0.00928973	+	0.0526847i
$307$	24.3705	+	20.4493i	1.39090	+	1.16710i	0.964974	+	0.262344i	$0.0844956\pi$
$307$	24.3705	+	20.4493i	1.39090	+	1.16710i	0.425925	+	0.904759i	$0.359949\pi$
$308$	13.0103	+	4.73535i	0.741329	+	0.269822i
$309$	−12.5103	+	4.55336i	−0.711684	+	0.259032i
$310$	−3.94356	+	3.30904i	−0.223979	+	0.187941i
$311$	−2.94356	−	5.09840i	−0.166914	−	0.289104i	0.770419	−	0.637538i	$-0.220047\pi$
$311$	−2.94356	−	5.09840i	−0.166914	−	0.289104i	−0.937333	+	0.348434i	$0.886714\pi$
$312$	2.50000	−	4.33013i	0.141535	−	0.245145i
$313$	2.18210	+	12.3753i	0.123340	+	0.699495i	0.982280	+	0.187419i	$0.0600122\pi$
$313$	2.18210	+	12.3753i	0.123340	+	0.699495i	−0.858940	+	0.512076i	$0.828877\pi$
$314$	−3.73396	−	21.1763i	−0.210719	−	1.19505i
$315$	1.59240	−	2.75811i	0.0897214	−	0.155402i
$316$	4.36959	+	7.56834i	0.245808	+	0.425753i
$317$	14.2515	−	11.9584i	0.800444	−	0.671652i	−0.147863	−	0.989008i	$-0.547239\pi$
$317$	14.2515	−	11.9584i	0.800444	−	0.671652i	0.948307	+	0.317356i	$0.102795\pi$
$318$	−4.41875	+	1.60829i	−0.247791	+	0.0901886i
$319$	−20.6878	−	7.52974i	−1.15829	−	0.421584i
$320$	−0.766044	−	0.642788i	−0.0428232	−	0.0359329i
$321$	2.08378	−	11.8177i	0.116305	−	0.659599i
$322$	20.2395			1.12790
$323$	2.59896	+	3.14403i	0.144610	+	0.174939i
$324$	1.00000			0.0555556
$325$	0.868241	−	4.92404i	0.0481613	−	0.273137i
$326$	5.75877	+	4.83218i	0.318949	+	0.267630i
$327$	−8.59627	−	3.12879i	−0.475375	−	0.173022i
$328$	−9.92262	+	3.61154i	−0.547885	+	0.199414i
$329$	22.4748	−	18.8586i	1.23907	−	1.03971i
$330$	2.17365	+	3.76487i	0.119655	+	0.207249i
$331$	−0.0457595	+	0.0792577i	−0.00251517	+	0.00435640i	−0.867280	−	0.497820i	$-0.834134\pi$
$331$	−0.0457595	+	0.0792577i	−0.00251517	+	0.00435640i	0.864765	+	0.502177i	$0.167467\pi$
$332$	0.773318	+	4.38571i	0.0424414	+	0.240697i
$333$	−0.344770	−	1.95529i	−0.0188933	−	0.107149i
$334$	6.52094	−	11.2946i	0.356810	−	0.618013i
$335$	7.82295	+	13.5497i	0.427413	+	0.740302i
$336$	2.43969	−	2.04715i	0.133096	−	0.111681i
$337$	−19.6604	+	7.15582i	−1.07097	+	0.389802i	−0.816540	−	0.577288i	$-0.804111\pi$
$337$	−19.6604	+	7.15582i	−1.07097	+	0.389802i	−0.254432	+	0.967091i	$0.581889\pi$
$338$	11.2763	+	4.10424i	0.613350	+	0.223241i
$339$	7.04189	+	5.90885i	0.382463	+	0.320924i
$340$	−0.162504	+	0.921605i	−0.00881301	+	0.0499810i
$341$	22.3797			1.21193
$342$	2.82635	−	3.31839i	0.152832	−	0.179438i
$343$	−12.2841			−0.663276
$344$	−0.758770	+	4.30320i	−0.0409102	+	0.232013i
$345$	4.86824	+	4.08494i	0.262097	+	0.219926i
$346$	−0.405078	−	0.147436i	−0.0217771	−	0.00792622i
$347$	17.2199	−	6.26752i	0.924411	−	0.336458i	0.164419	−	0.986391i	$-0.447425\pi$
$347$	17.2199	−	6.26752i	0.924411	−	0.336458i	0.759992	+	0.649932i	$0.225203\pi$
$348$	−3.87939	+	3.25519i	−0.207957	+	0.174497i
$349$	−2.34730	−	4.06564i	−0.125648	−	0.217629i	0.796338	−	0.604852i	$-0.206768\pi$
$349$	−2.34730	−	4.06564i	−0.125648	−	0.217629i	−0.921986	+	0.387223i	$0.873434\pi$
$350$	1.59240	−	2.75811i	0.0851172	−	0.147427i
$351$	0.868241	+	4.92404i	0.0463433	+	0.262826i
$352$	0.754900	+	4.28125i	0.0402363	+	0.228191i
$353$	−7.14796	+	12.3806i	−0.380447	+	0.658954i	−0.991126	−	0.132924i	$-0.957563\pi$
$353$	−7.14796	+	12.3806i	−0.380447	+	0.658954i	0.610679	+	0.791878i	$0.290897\pi$
$354$	6.67024	+	11.5532i	0.354520	+	0.614046i
$355$	−8.63816	+	7.24827i	−0.458466	+	0.384698i
$356$	−11.3045	+	4.11451i	−0.599139	+	0.218069i
$357$	−2.80066	−	1.01936i	−0.148227	−	0.0539501i
$358$	−11.9101	−	9.99379i	−0.629470	−	0.528188i
$359$	−3.09327	+	17.5428i	−0.163257	+	0.925875i	0.787587	+	0.616204i	$0.211330\pi$
$359$	−3.09327	+	17.5428i	−0.163257	+	0.925875i	−0.950844	+	0.309671i	$0.899781\pi$
$360$	1.00000			0.0527046
$361$	−3.02347	−	18.7579i	−0.159130	−	0.987258i
$362$	1.51754			0.0797602
$363$	1.37164	−	7.77898i	0.0719927	−	0.408291i
$364$	12.1985	+	10.2357i	0.639373	+	0.536498i
$365$	15.5817	+	5.67128i	0.815584	+	0.296848i
$366$	−8.21213	+	2.98897i	−0.429255	+	0.156236i
$367$	−26.9859	+	22.6439i	−1.40865	+	1.18200i	−0.451553	+	0.892244i	$0.649130\pi$
$367$	−26.9859	+	22.6439i	−1.40865	+	1.18200i	−0.957100	+	0.289756i	$0.906426\pi$
$368$	3.17752	+	5.50362i	0.165640	+	0.286896i
$369$	5.27972	−	9.14473i	0.274851	−	0.476056i
$370$	−0.344770	−	1.95529i	−0.0179237	−	0.101651i
$371$	−2.60055	−	14.7484i	−0.135014	−	0.765701i
$372$	2.57398	−	4.45826i	0.133455	−	0.231150i
$373$	13.4008	+	23.2109i	0.693867	+	1.20181i	0.970561	+	0.240855i	$0.0774278\pi$
$373$	13.4008	+	23.2109i	0.693867	+	1.20181i	−0.276694	+	0.960958i	$0.589239\pi$
$374$	3.11650	−	2.61505i	0.161150	−	0.135221i
$375$	0.939693	−	0.342020i	0.0485255	−	0.0176618i
$376$	8.65657	+	3.15074i	0.446429	+	0.162487i
$377$	−19.3969	−	16.2760i	−0.998993	−	0.838254i
$378$	−0.553033	+	3.13641i	−0.0284450	+	0.161319i
$379$	−32.7452			−1.68201			−0.841003	−	0.541031i	$-0.818034\pi$
$379$	−32.7452			−1.68201			−0.841003	+	0.541031i	$0.818034\pi$
$380$	2.82635	−	3.31839i	0.144989	−	0.170230i
$381$	−1.04963			−0.0537742
$382$	−2.00774	+	11.3865i	−0.102725	+	0.582582i
$383$	11.1853	+	9.38555i	0.571540	+	0.479579i	0.882157	−	0.470956i	$-0.156091\pi$
$383$	11.1853	+	9.38555i	0.571540	+	0.479579i	−0.310617	+	0.950535i	$0.600535\pi$
$384$	0.939693	+	0.342020i	0.0479535	+	0.0174536i
$385$	−13.0103	+	4.73535i	−0.663065	+	0.241336i
$386$	1.63041	−	1.36808i	0.0829859	−	0.0696335i
$387$	−2.18479	−	3.78417i	−0.111059	−	0.192360i
$388$	−5.92127	+	10.2559i	−0.300607	+	0.520667i
$389$	−0.680045	−	3.85673i	−0.0344796	−	0.195544i	0.962703	−	0.270562i	$-0.0872096\pi$
$389$	−0.680045	−	3.85673i	−0.0344796	−	0.195544i	−0.997182	+	0.0750184i	$0.976098\pi$
$390$	0.868241	+	4.92404i	0.0439651	+	0.249338i
$391$	2.97359	−	5.15041i	0.150381	−	0.260468i
$392$	1.57145	+	2.72183i	0.0793703	+	0.137473i
$393$	−0.195937	+	0.164411i	−0.00988371	+	0.00829342i
$394$	−15.7233	+	5.72281i	−0.792127	+	0.288311i
$395$	−8.21213	−	2.98897i	−0.413197	−	0.150392i
$396$	−3.33022	−	2.79439i	−0.167350	−	0.140423i
$397$	0.0603074	−	0.342020i	0.00302674	−	0.0171655i	−0.983257	−	0.182224i	$-0.941670\pi$
$397$	0.0603074	−	0.342020i	0.00302674	−	0.0171655i	0.986284	+	0.165059i	$0.0527814\pi$
$398$	−3.10876			−0.155828
$399$	8.84477	+	10.6998i	0.442792	+	0.535659i
$400$	1.00000			0.0500000
$401$	6.64321	−	37.6755i	0.331746	−	1.88142i	−0.125514	−	0.992092i	$-0.540058\pi$
$401$	6.64321	−	37.6755i	0.331746	−	1.88142i	0.457260	−	0.889333i	$-0.348831\pi$
$402$	−11.9855	−	10.0570i	−0.597780	−	0.501597i
$403$	24.1875	+	8.80352i	1.20486	+	0.438535i
$404$	5.94356	−	2.16328i	0.295703	−	0.107627i
$405$	−0.766044	+	0.642788i	−0.0380651	+	0.0319404i
$406$	−8.06418	−	13.9676i	−0.400218	−	0.693199i
$407$	−4.31567	+	7.47497i	−0.213920	+	0.370520i
$408$	−0.162504	−	0.921605i	−0.00804514	−	0.0456262i
$409$	−2.53580	−	14.3812i	−0.125387	−	0.711106i	−0.981077	−	0.193617i	$-0.937978\pi$
$409$	−2.53580	−	14.3812i	−0.125387	−	0.711106i	0.855690	−	0.517489i	$-0.173133\pi$
$410$	5.27972	−	9.14473i	0.260747	−	0.451626i
$411$	5.96316	+	10.3285i	0.294141	+	0.509467i
$412$	10.1985	−	8.55753i	0.502442	−	0.421599i
$413$	−39.9244	+	14.5313i	−1.96455	+	0.715039i
$414$	−5.97178	−	2.17355i	−0.293497	−	0.106824i
$415$	−3.41147	−	2.86257i	−0.167463	−	0.140518i
$416$	−0.868241	+	4.92404i	−0.0425690	+	0.241421i
$417$	−16.1925			−0.792952
$418$	−18.6853	+	3.15306i	−0.913926	+	0.154221i
$419$	−9.26857			−0.452799			−0.226400	−	0.974034i	$-0.572696\pi$
$419$	−9.26857			−0.452799			−0.226400	+	0.974034i	$0.572696\pi$
$420$	−0.553033	+	3.13641i	−0.0269853	+	0.153041i
$421$	4.94356	+	4.14814i	0.240935	+	0.202168i	0.755257	−	0.655429i	$-0.227512\pi$
$421$	4.94356	+	4.14814i	0.240935	+	0.202168i	−0.514322	+	0.857597i	$0.671957\pi$
$422$	−12.8712	−	4.68475i	−0.626562	−	0.228050i
$423$	−8.65657	+	3.15074i	−0.420897	+	0.153194i
$424$	3.60220	−	3.02260i	0.174938	−	0.146791i
$425$	−0.467911	−	0.810446i	−0.0226970	−	0.0393124i
$426$	5.63816	−	9.76557i	0.273170	−	0.473144i
$427$	−4.83305	−	27.4096i	−0.233888	−	1.32644i
$428$	2.08378	+	11.8177i	0.100723	+	0.571230i
$429$	10.8682	−	18.8243i	0.524724	−	0.908848i
$430$	−2.18479	−	3.78417i	−0.105360	−	0.182489i
$431$	−8.33275	+	6.99201i	−0.401374	+	0.336793i	−0.821025	−	0.570893i	$-0.806597\pi$
$431$	−8.33275	+	6.99201i	−0.401374	+	0.336793i	0.419650	+	0.907686i	$0.362153\pi$
$432$	−0.939693	+	0.342020i	−0.0452110	+	0.0164555i
$433$	−0.0145479	−	0.00529501i	−0.000699128	−	0.000254462i	0.341671	−	0.939820i	$-0.389007\pi$
$433$	−0.0145479	−	0.00529501i	−0.000699128	−	0.000254462i	−0.342370	+	0.939565i	$0.611230\pi$
$434$	12.5594	+	10.5386i	0.602872	+	0.505870i
$435$	0.879385	−	4.98724i	0.0421633	−	0.239120i
$436$	9.14796			0.438108
$437$	−24.0911	+	13.6735i	−1.15243	+	0.654092i
$438$	−16.5817			−0.792305
$439$	−0.980400	+	5.56012i	−0.0467919	+	0.265370i	−0.999224	−	0.0393798i	$-0.987462\pi$
$439$	−0.980400	+	5.56012i	−0.0467919	+	0.265370i	0.952432	+	0.304750i	$0.0985729\pi$
$440$	−3.33022	−	2.79439i	−0.158762	−	0.133217i
$441$	−2.95336	−	1.07494i	−0.140636	−	0.0511874i
$442$	4.39693	−	1.60035i	0.209140	−	0.0761209i
$443$	14.8307	−	12.4444i	0.704627	−	0.591253i	−0.218459	−	0.975846i	$-0.570103\pi$
$443$	14.8307	−	12.4444i	0.704627	−	0.591253i	0.923086	+	0.384594i	$0.125658\pi$
$444$	0.992726	+	1.71945i	0.0471127	+	0.0816016i
$445$	6.01501	−	10.4183i	0.285139	−	0.493875i
$446$	1.26739	+	7.18772i	0.0600126	+	0.340348i
$447$	−0.431074	−	2.44474i	−0.0203891	−	0.115632i
$448$	−1.59240	+	2.75811i	−0.0752337	+	0.130309i
$449$	−0.215537	−	0.373321i	−0.0101718	−	0.0176181i	0.860895	−	0.508783i	$-0.169905\pi$
$449$	−0.215537	−	0.373321i	−0.0101718	−	0.0176181i	−0.871067	+	0.491165i	$0.836571\pi$
$450$	−0.766044	+	0.642788i	−0.0361117	+	0.0303013i
$451$	−43.1366	+	15.7004i	−2.03122	+	0.739304i
$452$	−8.63816	−	3.14403i	−0.406305	−	0.147883i
$453$	−3.28312	−	2.75486i	−0.154254	−	0.129435i
$454$	−1.29767	+	7.35943i	−0.0609025	+	0.345395i
$455$	−15.9240			−0.746527
$456$	−1.52094	+	4.08494i	−0.0712248	+	0.191295i
$457$	20.8229			0.974056			0.487028	−	0.873386i	$-0.338081\pi$
$457$	20.8229			0.974056			0.487028	+	0.873386i	$0.338081\pi$
$458$	1.24897	−	7.08326i	0.0583605	−	0.330979i
$459$	0.716881	+	0.601535i	0.0334612	+	0.0280772i
$460$	−5.97178	−	2.17355i	−0.278436	−	0.101342i
$461$	26.8999	−	9.79077i	1.25285	−	0.456002i	0.371489	−	0.928437i	$-0.378847\pi$
$461$	26.8999	−	9.79077i	1.25285	−	0.456002i	0.881365	+	0.472436i	$0.156625\pi$
$462$	10.6061	−	8.89955i	0.493439	−	0.414044i
$463$	−3.38578	−	5.86435i	−0.157351	−	0.272539i	0.776562	−	0.630041i	$-0.216962\pi$
$463$	−3.38578	−	5.86435i	−0.157351	−	0.272539i	−0.933912	+	0.357502i	$0.883629\pi$
$464$	2.53209	−	4.38571i	0.117549	−	0.203601i
$465$	0.893933	+	5.06975i	0.0414552	+	0.235104i
$466$	−2.69459	−	15.2818i	−0.124825	−	0.707915i
$467$	−4.02229	+	6.96681i	−0.186129	+	0.322385i	−0.943956	−	0.330070i	$-0.892928\pi$
$467$	−4.02229	+	6.96681i	−0.186129	+	0.322385i	0.757827	+	0.652455i	$0.226261\pi$
$468$	−2.50000	−	4.33013i	−0.115563	−	0.200160i
$469$	38.1712	−	32.0294i	1.76258	−	1.47898i
$470$	−8.65657	+	3.15074i	−0.399298	+	0.145333i
$471$	−20.2062	−	7.35446i	−0.931053	−	0.338875i
$472$	−10.2194	−	8.57510i	−0.470386	−	0.394701i
$473$	−3.29860	+	18.7073i	−0.151670	+	0.860162i
$474$	8.73917			0.401403
$475$	−0.0320889	+	4.35878i	−0.00147234	+	0.199995i
$476$	2.98040			0.136606
$477$	−0.816552	+	4.63089i	−0.0373873	+	0.212034i
$478$	−11.5817	−	9.71822i	−0.529735	−	0.444501i
$479$	13.3969	+	4.87608i	0.612121	+	0.222794i	0.629431	−	0.777056i	$-0.283288\pi$
$479$	13.3969	+	4.87608i	0.612121	+	0.222794i	−0.0173099	+	0.999850i	$0.505510\pi$
$480$	−0.939693	+	0.342020i	−0.0428909	+	0.0156110i
$481$	−7.60472	+	6.38112i	−0.346746	+	0.290954i
$482$	−2.86959	−	4.97027i	−0.130706	−	0.226389i
$483$	10.1197	−	17.5279i	0.460464	−	0.797547i
$484$	1.37164	+	7.77898i	0.0623475	+	0.353590i
$485$	−2.05644	−	11.6626i	−0.0933780	−	0.529573i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−9.35117	−	16.1967i	−0.423742	−	0.733942i	0.572560	−	0.819863i	$-0.305950\pi$
$487$	−9.35117	−	16.1967i	−0.423742	−	0.733942i	−0.996302	+	0.0859203i	$0.972617\pi$
$488$	6.69459	−	5.61743i	0.303050	−	0.254289i
$489$	7.06418	−	2.57115i	0.319453	−	0.116271i
$490$	−2.95336	−	1.07494i	−0.133419	−	0.0485607i
$491$	−9.93242	−	8.33429i	−0.448244	−	0.376121i	0.390540	−	0.920586i	$-0.372288\pi$
$491$	−9.93242	−	8.33429i	−0.448244	−	0.376121i	−0.838784	+	0.544465i	$0.816733\pi$
$492$	−1.83363	+	10.3990i	−0.0826662	+	0.468824i
$493$	−4.73917			−0.213441
$494$	−21.4349	−	3.94248i	−0.964404	−	0.177381i
$495$	4.34730			0.195396
$496$	−0.893933	+	5.06975i	−0.0401388	+	0.227638i
$497$	27.5107	+	23.0842i	1.23403	+	1.03547i
$498$	4.18479	+	1.52314i	0.187525	+	0.0682535i
$499$	−36.3282	+	13.2224i	−1.62627	+	0.591915i	−0.984563	−	0.175033i	$-0.943997\pi$
$499$	−36.3282	+	13.2224i	−1.62627	+	0.591915i	−0.641709	+	0.766948i	$0.721774\pi$
$500$	−0.766044	+	0.642788i	−0.0342585	+	0.0287463i
$501$	−6.52094	−	11.2946i	−0.291334	−	0.504606i
$502$	−12.0398	+	20.8536i	−0.537364	+	0.930742i
$503$	−5.49407	−	31.1584i	−0.244968	−	1.38929i	−0.820566	−	0.571552i	$-0.806342\pi$
$503$	−5.49407	−	31.1584i	−0.244968	−	1.38929i	0.575597	−	0.817733i	$-0.304770\pi$
$504$	−0.553033	−	3.13641i	−0.0246341	−	0.139707i
$505$	−3.16250	+	5.47762i	−0.140730	+	0.243751i
$506$	13.8136	+	23.9259i	0.614090	+	1.06364i
$507$	9.19253	−	7.71345i	0.408255	−	0.342566i
$508$	0.986329	−	0.358995i	0.0437613	−	0.0159278i
$509$	−22.3533	−	8.13593i	−0.990792	−	0.360619i	−0.204765	−	0.978811i	$-0.565643\pi$
$509$	−22.3533	−	8.13593i	−0.990792	−	0.360619i	−0.786027	+	0.618192i	$0.787865\pi$
$510$	0.716881	+	0.601535i	0.0317440	+	0.0266364i
$511$	9.17024	−	52.0070i	0.405668	−	2.30066i
$512$	−1.00000			−0.0441942
$513$	−1.46064	−	4.10689i	−0.0644887	−	0.181324i
$514$	−16.7784			−0.740062
$515$	−2.31180	+	13.1109i	−0.101870	+	0.577735i
$516$	3.34730	+	2.80872i	0.147357	+	0.123647i
$517$	37.6327	+	13.6972i	1.65508	+	0.602401i
$518$	−5.94191	+	2.16268i	−0.261073	+	0.0950227i
$519$	−0.330222	+	0.277089i	−0.0144951	+	0.0121629i
$520$	−2.50000	−	4.33013i	−0.109632	−	0.189889i
$521$	−0.418281	+	0.724484i	−0.0183252	+	0.0317402i	−0.875043	−	0.484046i	$-0.839167\pi$
$521$	−0.418281	+	0.724484i	−0.0183252	+	0.0317402i	0.856717	+	0.515786i	$0.172500\pi$
$522$	0.879385	+	4.98724i	0.0384896	+	0.218286i
$523$	−2.07192	−	11.7504i	−0.0905987	−	0.513811i	−0.996007	−	0.0892698i	$-0.971547\pi$
$523$	−2.07192	−	11.7504i	−0.0905987	−	0.513811i	0.905409	−	0.424541i	$-0.139564\pi$
$524$	0.127889	−	0.221510i	0.00558684	−	0.00967670i
$525$	−1.59240	−	2.75811i	−0.0694979	−	0.120374i
$526$	−9.81773	+	8.23806i	−0.428074	+	0.359196i
$527$	4.52704	−	1.64771i	0.197201	−	0.0717752i
$528$	4.08512	+	1.48686i	0.177782	+	0.0647074i
$529$	13.3188	+	11.1758i	0.579080	+	0.485905i
$530$	−0.816552	+	4.63089i	−0.0354687	+	0.201153i
$531$	13.3405			0.578928
$532$	−11.9709	−	7.02941i	−0.519005	−	0.304764i
$533$	−52.7972			−2.28690
$534$	−2.08899	+	11.8473i	−0.0903996	+	0.512681i
$535$	−9.19253	−	7.71345i	−0.397428	−	0.333482i
$536$	14.7023	+	5.35121i	0.635044	+	0.231137i
$537$	−14.6099	+	5.31758i	−0.630465	+	0.229471i
$538$	−12.8530	+	10.7849i	−0.554131	+	0.464971i
$539$	6.83157	+	11.8326i	0.294256	+	0.509667i
$540$	0.500000	−	0.866025i	0.0215166	−	0.0372678i
$541$	−0.475652	−	2.69756i	−0.0204499	−	0.115977i	0.972874	−	0.231335i	$-0.0743095\pi$
$541$	−0.475652	−	2.69756i	−0.0204499	−	0.115977i	−0.993324	+	0.115358i	$0.963198\pi$
$542$	0.568926	+	3.22654i	0.0244374	+	0.138592i
$543$	0.758770	−	1.31423i	0.0325620	−	0.0563990i
$544$	0.467911	+	0.810446i	0.0200615	+	0.0347476i
$545$	−7.00774	+	5.88019i	−0.300179	+	0.251880i
$546$	14.9636	−	5.44632i	0.640384	−	0.233081i
$547$	20.0300	+	7.29033i	0.856422	+	0.311712i	0.732656	−	0.680599i	$-0.238280\pi$
$547$	20.0300	+	7.29033i	0.856422	+	0.311712i	0.123766	+	0.992311i	$0.460503\pi$
$548$	−9.13610	−	7.66610i	−0.390275	−	0.327479i
$549$	−1.51754	+	8.60640i	−0.0647671	+	0.367312i
$550$	4.34730			0.185369
$551$	19.0351	+	11.1776i	0.810922	+	0.476180i
$552$	6.35504			0.270488
$553$	−4.83305	+	27.4096i	−0.205522	+	1.16558i
$554$	7.09105	+	5.95010i	0.301270	+	0.252795i
$555$	−1.86571	−	0.679065i	−0.0791952	−	0.0288247i
$556$	15.2160	−	5.53817i	0.645302	−	0.234871i
$557$	25.1798	−	21.1284i	1.06690	−	0.895237i	0.0721340	−	0.997395i	$-0.477019\pi$
$557$	25.1798	−	21.1284i	1.06690	−	0.895237i	0.994768	+	0.102158i	$0.0325746\pi$
$558$	−2.57398	−	4.45826i	−0.108965	−	0.188733i
$559$	−10.9240	+	18.9209i	−0.462034	+	0.800267i
$560$	−0.553033	−	3.13641i	−0.0233699	−	0.132537i
$561$	−0.706452	−	4.00649i	−0.0298264	−	0.169154i
$562$	7.41534	−	12.8438i	0.312797	−	0.541781i
$563$	−11.9932	−	20.7728i	−0.505453	−	0.875470i	−0.999980	−	0.00630786i	$-0.997992\pi$
$563$	−11.9932	−	20.7728i	−0.505453	−	0.875470i	0.494527	−	0.869162i	$-0.335341\pi$
$564$	7.05690	−	5.92145i	0.297149	−	0.249338i
$565$	8.63816	−	3.14403i	0.363410	−	0.132270i
$566$	15.5817	+	5.67128i	0.654948	+	0.238382i
$567$	2.43969	+	2.04715i	0.102457	+	0.0859720i
$568$	−1.95811	+	11.1050i	−0.0821605	+	0.465955i
$569$	−19.4962			−0.817323			−0.408661	−	0.912686i	$-0.634004\pi$
$569$	−19.4962			−0.817323			−0.408661	+	0.912686i	$0.634004\pi$
$570$	−1.46064	−	4.10689i	−0.0611794	−	0.172019i
$571$	41.6709			1.74387			0.871936	−	0.489620i	$-0.162865\pi$
$571$	41.6709			1.74387			0.871936	+	0.489620i	$0.162865\pi$
$572$	−3.77450	+	21.4063i	−0.157820	+	0.895041i
$573$	8.85710	+	7.43199i	0.370011	+	0.310476i
$574$	−31.6015	−	11.5020i	−1.31902	−	0.480084i
$575$	5.97178	−	2.17355i	0.249041	−	0.0906433i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	−1.00000	−	1.73205i	−0.0416305	−	0.0721062i	0.844459	−	0.535620i	$-0.179922\pi$
$577$	−1.00000	−	1.73205i	−0.0416305	−	0.0721062i	−0.886090	+	0.463513i	$0.846589\pi$
$578$	−8.06212	+	13.9640i	−0.335340	+	0.580826i
$579$	−0.369585	−	2.09602i	−0.0153594	−	0.0871077i
$580$	0.879385	+	4.98724i	0.0365145	+	0.207084i
$581$	−7.09152	+	12.2829i	−0.294206	+	0.509579i
$582$	5.92127	+	10.2559i	0.245445	+	0.425123i
$583$	15.6598	−	13.1401i	0.648563	−	0.544209i
$584$	15.5817	−	5.67128i	0.644776	−	0.234679i
$585$	4.69846	+	1.71010i	0.194258	+	0.0707040i
$586$	0.851167	+	0.714214i	0.0351614	+	0.0295039i
$587$	5.36278	−	30.4138i	0.221346	−	1.25531i	−0.648204	−	0.761467i	$-0.724480\pi$
$587$	5.36278	−	30.4138i	0.221346	−	1.25531i	0.869549	−	0.493846i	$-0.164409\pi$
$588$	3.14290			0.129611
$589$	−22.0692	−	4.05914i	−0.909347	−	0.167254i
$590$	13.3405			0.549219
$591$	−2.90554	+	16.4782i	−0.119518	+	0.677821i
$592$	−1.52094	−	1.27622i	−0.0625104	−	0.0524525i
$593$	−3.57398	−	1.30082i	−0.146766	−	0.0534183i	0.267593	−	0.963532i	$-0.413772\pi$
$593$	−3.57398	−	1.30082i	−0.146766	−	0.0534183i	−0.414358	+	0.910114i	$0.635994\pi$
$594$	−4.08512	+	1.48686i	−0.167615	+	0.0610067i
$595$	−2.28312	+	1.91576i	−0.0935987	+	0.0785387i
$596$	1.24123	+	2.14987i	0.0508427	+	0.0880622i
$597$	−1.55438	+	2.69226i	−0.0636164	+	0.110187i
$598$	5.51770	+	31.2924i	0.225636	+	1.27964i
$599$	2.30272	+	13.0594i	0.0940865	+	0.533591i	0.995023	+	0.0996412i	$0.0317695\pi$
$599$	2.30272	+	13.0594i	0.0940865	+	0.533591i	−0.900937	+	0.433950i	$0.857119\pi$
$600$	0.500000	−	0.866025i	0.0204124	−	0.0353553i
$601$	3.84864	+	6.66604i	0.156989	+	0.271913i	0.933782	−	0.357843i	$-0.116488\pi$
$601$	3.84864	+	6.66604i	0.156989	+	0.271913i	−0.776792	+	0.629757i	$0.783155\pi$
$602$	−10.6604	+	8.94517i	−0.434487	+	0.364578i
$603$	−14.7023	+	5.35121i	−0.598725	+	0.217918i
$604$	4.02734	+	1.46583i	0.163870	+	0.0596439i
$605$	−6.05097	−	5.07737i	−0.246007	−	0.206424i
$606$	1.09833	−	6.22892i	0.0446164	−	0.253032i
$607$	−5.72193			−0.232246			−0.116123	−	0.993235i	$-0.537047\pi$
$607$	−5.72193			−0.232246			−0.116123	+	0.993235i	$0.537047\pi$
$608$	0.0320889	−	4.35878i	0.00130138	−	0.176772i
$609$	−16.1284			−0.653554
$610$	−1.51754	+	8.60640i	−0.0614434	+	0.348463i
$611$	35.2845	+	29.6072i	1.42746	+	1.19778i
$612$	−0.879385	−	0.320070i	−0.0355470	−	0.0129381i
$613$	−30.6377	+	11.1512i	−1.23745	+	0.450394i	−0.876142	−	0.482054i	$-0.839891\pi$
$613$	−30.6377	+	11.1512i	−1.23745	+	0.450394i	−0.361305	+	0.932448i	$0.617669\pi$
$614$	−24.3705	+	20.4493i	−0.983514	+	0.825266i
$615$	−5.27972	−	9.14473i	−0.212899	−	0.368751i
$616$	−6.92262	+	11.9903i	−0.278920	+	0.483104i
$617$	−3.09926	−	17.5768i	−0.124771	−	0.707614i	−0.981443	−	0.191753i	$-0.938583\pi$
$617$	−3.09926	−	17.5768i	−0.124771	−	0.707614i	0.856672	−	0.515862i	$-0.172528\pi$
$618$	−2.31180	−	13.1109i	−0.0929944	−	0.527397i
$619$	22.2211	−	38.4880i	0.893140	−	1.54696i	0.0570494	−	0.998371i	$-0.481831\pi$
$619$	22.2211	−	38.4880i	0.893140	−	1.54696i	0.836090	−	0.548592i	$-0.184836\pi$
$620$	−2.57398	−	4.45826i	−0.103373	−	0.179048i
$621$	−4.86824	+	4.08494i	−0.195356	+	0.163923i
$622$	5.53209	−	2.01352i	0.221817	−	0.0807346i
$623$	−36.0026	−	13.1039i	−1.44241	−	0.524995i
$624$	3.83022	+	3.21394i	0.153332	+	0.128660i
$625$	0.173648	−	0.984808i	0.00694593	−	0.0393923i
$626$	−12.5662			−0.502248
$627$	−6.61200	+	17.7584i	−0.264058	+	0.709204i
$628$	21.5030			0.858063
$629$	−0.322644	+	1.82980i	−0.0128646	+	0.0729590i
$630$	2.43969	+	2.04715i	0.0971997	+	0.0815602i
$631$	−7.71688	−	2.80872i	−0.307204	−	0.111813i	0.183818	−	0.982960i	$-0.441154\pi$
$631$	−7.71688	−	2.80872i	−0.307204	−	0.111813i	−0.491022	+	0.871147i	$0.663377\pi$
$632$	−8.21213	+	2.98897i	−0.326661	+	0.118895i
$633$	−10.4927	+	8.80444i	−0.417048	+	0.349945i
$634$	9.30200	+	16.1115i	0.369430	+	0.639871i
$635$	−0.524815	+	0.909006i	−0.0208266	+	0.0360728i
$636$	−0.816552	−	4.63089i	−0.0323784	−	0.183627i
$637$	2.72880	+	15.4758i	0.108119	+	0.613173i
$638$	11.0077	−	19.0660i	0.435801	−	0.754829i
$639$	−5.63816	−	9.76557i	−0.223042	−	0.386320i
$640$	0.766044	−	0.642788i	0.0302806	−	0.0254084i
$641$	−18.6548	+	6.78980i	−0.736821	+	0.268181i	−0.683049	−	0.730372i	$-0.739347\pi$
$641$	−18.6548	+	6.78980i	−0.736821	+	0.268181i	−0.0537718	+	0.998553i	$0.517124\pi$
$642$	11.2763	+	4.10424i	0.445041	+	0.161982i
$643$	−16.8425	−	14.1326i	−0.664205	−	0.557334i	0.247139	−	0.968980i	$-0.420510\pi$
$643$	−16.8425	−	14.1326i	−0.664205	−	0.557334i	−0.911344	+	0.411646i	$0.864954\pi$
$644$	−3.51455	+	19.9320i	−0.138493	+	0.785431i
$645$	−4.36959			−0.172052
$646$	−3.54757	+	2.01352i	−0.139577	+	0.0792207i
$647$	−6.35504			−0.249842			−0.124921	−	0.992167i	$-0.539868\pi$
$647$	−6.35504			−0.249842			−0.124921	+	0.992167i	$0.539868\pi$
$648$	−0.173648	+	0.984808i	−0.00682154	+	0.0386869i
$649$	−44.4268	−	37.2785i	−1.74390	−	1.46331i
$650$	4.69846	+	1.71010i	0.184289	+	0.0670757i
$651$	15.4064	−	5.60748i	0.603825	−	0.219774i
$652$	−5.75877	+	4.83218i	−0.225531	+	0.189243i
$653$	−3.28699	−	5.69323i	−0.128630	−	0.222793i	0.794516	−	0.607243i	$-0.207725\pi$
$653$	−3.28699	−	5.69323i	−0.128630	−	0.222793i	−0.923146	+	0.384450i	$0.874391\pi$
$654$	4.57398	−	7.92236i	0.178857	−	0.309789i
$655$	0.0444153	+	0.251892i	0.00173545	+	0.00984222i
$656$	−1.83363	−	10.3990i	−0.0715911	−	0.406013i
$657$	−8.29086	+	14.3602i	−0.323457	+	0.560244i
$658$	14.6694	+	25.4081i	0.571871	+	0.990510i
$659$	7.18320	−	6.02742i	0.279818	−	0.234795i	−0.492067	−	0.870557i	$-0.663759\pi$
$659$	7.18320	−	6.02742i	0.279818	−	0.234795i	0.771885	+	0.635762i	$0.219314\pi$
$660$	−4.08512	+	1.48686i	−0.159013	+	0.0578761i
$661$	46.9172	+	17.0764i	1.82487	+	0.664197i	0.994216	+	0.107402i	$0.0342533\pi$
$661$	46.9172	+	17.0764i	1.82487	+	0.664197i	0.830650	+	0.556795i	$0.187969\pi$
$662$	−0.0701076	−	0.0588272i	−0.00272481	−	0.00228639i
$663$	0.812519	−	4.60802i	0.0315556	−	0.178961i
$664$	−4.45336			−0.172824
$665$	13.6887	−	2.30991i	0.530824	−	0.0895744i
$666$	1.98545			0.0769347
$667$	5.58853	−	31.6941i	0.216389	−	1.22720i
$668$	9.99067	+	8.38316i	0.386550	+	0.324354i
$669$	6.85844	+	2.49627i	0.265163	+	0.0965113i
$670$	−14.7023	+	5.35121i	−0.568001	+	0.206735i
$671$	29.1034	−	24.4206i	1.12352	−	0.942748i
$672$	1.59240	+	2.75811i	0.0614280	+	0.106396i
$673$	−10.7665	+	18.6481i	−0.415019	+	0.718833i	−0.995430	−	0.0954899i	$-0.969558\pi$
$673$	−10.7665	+	18.6481i	−0.415019	+	0.718833i	0.580412	+	0.814323i	$0.302892\pi$
$674$	−3.63310	−	20.6044i	−0.139942	−	0.793650i
$675$	0.173648	+	0.984808i	0.00668372	+	0.0379053i
$676$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$677$	−21.4197	−	37.1000i	−0.823225	−	1.42587i	−0.903268	−	0.429077i	$-0.858839\pi$
$677$	−21.4197	−	37.1000i	−0.823225	−	1.42587i	0.0800429	−	0.996791i	$-0.474494\pi$
$678$	−7.04189	+	5.90885i	−0.270442	+	0.226928i
$679$	−35.4415	+	12.8997i	−1.36012	+	0.495043i
$680$	−0.879385	−	0.320070i	−0.0337229	−	0.0122741i
$681$	5.72462	+	4.80353i	0.219368	+	0.184072i
$682$	−3.88619	+	22.0397i	−0.148810	+	0.843943i
$683$	−16.5134			−0.631869			−0.315934	−	0.948781i	$-0.602318\pi$
$683$	−16.5134			−0.631869			−0.315934	+	0.948781i	$0.602318\pi$
$684$	2.77719	+	3.35965i	0.106188	+	0.128459i
$685$	11.9263			0.455682
$686$	2.13310	−	12.0974i	0.0814423	−	0.461882i
$687$	−5.50980	−	4.62327i	−0.210212	−	0.176389i
$688$	−4.10607	−	1.49449i	−0.156542	−	0.0569767i
$689$	22.0937	−	8.04146i	0.841704	−	0.306355i
$690$	−4.86824	+	4.08494i	−0.185331	+	0.155511i
$691$	−17.4315	−	30.1923i	−0.663127	−	1.14857i	−0.979789	−	0.200031i	$-0.935896\pi$
$691$	−17.4315	−	30.1923i	−0.663127	−	1.14857i	0.316662	−	0.948538i	$-0.397438\pi$
$692$	0.215537	−	0.373321i	0.00819350	−	0.0141916i
$693$	−2.40420	−	13.6349i	−0.0913280	−	0.517947i
$694$	3.18210	+	18.0466i	0.120791	+	0.685040i
$695$	−8.09627	+	14.0231i	−0.307109	+	0.531928i
$696$	−2.53209	−	4.38571i	−0.0959786	−	0.166240i
$697$	−7.56986	+	6.35187i	−0.286729	+	0.240594i
$698$	4.41147	−	1.60565i	0.166977	−	0.0607746i
$699$	−14.5817	−	5.30731i	−0.551531	−	0.200741i
$700$	2.43969	+	2.04715i	0.0922117	+	0.0773748i
$701$	4.69635	−	26.6343i	0.177379	−	1.00596i	−0.757984	−	0.652273i	$-0.773815\pi$
$701$	4.69635	−	26.6343i	0.177379	−	1.00596i	0.935362	−	0.353691i	$-0.115073\pi$
$702$	−5.00000			−0.188713
$703$	5.61159	−	6.58851i	0.211645	−	0.248490i
$704$	−4.34730			−0.163845
$705$	−1.59967	+	9.07218i	−0.0602471	+	0.341678i
$706$	−10.9513	−	9.18923i	−0.412158	−	0.345841i
$707$	18.9290	+	6.88960i	0.711899	+	0.259110i
$708$	−12.5360	+	4.56272i	−0.471130	+	0.171477i
$709$	30.4165	−	25.5225i	1.14232	−	0.958517i	0.142805	−	0.989751i	$-0.454388\pi$
$709$	30.4165	−	25.5225i	1.14232	−	0.958517i	0.999512	+	0.0312334i	$0.00994353\pi$
$710$	−5.63816	−	9.76557i	−0.211596	−	0.366495i
$711$	4.36959	−	7.56834i	0.163872	−	0.283835i
$712$	−2.08899	−	11.8473i	−0.0782883	−	0.443995i
$713$	5.68098	+	32.2184i	0.212754	+	1.20659i
$714$	1.49020	−	2.58110i	0.0557693	−	0.0965953i
$715$	−10.8682	−	18.8243i	−0.406449	−	0.703991i
$716$	11.9101	−	9.99379i	0.445102	−	0.373485i
$717$	−14.2071	+	5.17095i	−0.530573	+	0.193113i
$718$	−16.7392	−	6.09256i	−0.624700	−	0.227372i
$719$	31.2540	+	26.2252i	1.16558	+	0.978036i	0.999967	−	0.00815467i	$-0.00259574\pi$
$719$	31.2540	+	26.2252i	1.16558	+	0.978036i	0.165612	+	0.986191i	$0.447040\pi$
$720$	−0.173648	+	0.984808i	−0.00647149	+	0.0367016i
$721$	42.3996			1.57904
$722$	18.9979	+	0.279737i	0.707030	+	0.0104107i
$723$	−5.73917			−0.213442
$724$	−0.263518	+	1.49449i	−0.00979358	+	0.0555421i
$725$	−3.87939	−	3.25519i	−0.144077	−	0.120895i
$726$	7.42262	+	2.70161i	0.275479	+	0.100266i
$727$	23.0060	−	8.37349i	0.853245	−	0.310556i	0.121882	−	0.992545i	$-0.461107\pi$
$727$	23.0060	−	8.37349i	0.853245	−	0.310556i	0.731363	+	0.681989i	$0.238885\pi$
$728$	−12.1985	+	10.2357i	−0.452105	+	0.379361i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−8.29086	+	14.3602i	−0.306858	+	0.531494i
$731$	0.710074	+	4.02703i	0.0262630	+	0.148945i
$732$	−1.51754	−	8.60640i	−0.0560899	−	0.318102i
$733$	−2.90286	+	5.02789i	−0.107219	+	0.185710i	−0.914643	−	0.404263i	$-0.867528\pi$
$733$	−2.90286	+	5.02789i	−0.107219	+	0.185710i	0.807423	+	0.589972i	$0.200861\pi$
$734$	−17.6138	−	30.5080i	−0.650138	−	1.12607i
$735$	−2.40760	+	2.02022i	−0.0888058	+	0.0745169i
$736$	−5.97178	+	2.17355i	−0.220123	+	0.0801181i
$737$	63.9154	+	23.2633i	2.35435	+	0.856915i
$738$	8.08899	+	6.78747i	0.297760	+	0.249850i
$739$	−3.86231	+	21.9043i	−0.142077	+	0.805761i	0.827590	+	0.561333i	$0.189711\pi$
$739$	−3.86231	+	21.9043i	−0.142077	+	0.805761i	−0.969667	+	0.244428i	$0.921400\pi$
$740$	1.98545			0.0729867
$741$	−14.1318	+	16.5920i	−0.519143	+	0.609521i
$742$	14.9760			0.549785
$743$	−7.59668	+	43.0829i	−0.278695	+	1.58056i	0.448279	+	0.893894i	$0.352037\pi$
$743$	−7.59668	+	43.0829i	−0.278695	+	1.58056i	−0.726974	+	0.686665i	$0.759074\pi$
$744$	3.94356	+	3.30904i	0.144578	+	0.121315i
$745$	−2.33275	−	0.849051i	−0.0854653	−	0.0311068i
$746$	−25.1853	+	9.16668i	−0.922098	+	0.335616i
$747$	3.41147	−	2.86257i	0.124819	−	0.104736i
$748$	2.03415	+	3.52325i	0.0743758	+	0.128823i
$749$	−19.1088	+	33.0973i	−0.698219	+	1.20935i
$750$	0.173648	+	0.984808i	0.00634073	+	0.0359601i
$751$	4.81345	+	27.2984i	0.175645	+	0.996134i	0.937396	+	0.348264i	$0.113229\pi$
$751$	4.81345	+	27.2984i	0.175645	+	0.996134i	−0.761751	+	0.647870i	$0.775660\pi$
$752$	−4.60607	+	7.97794i	−0.167966	+	0.290926i
$753$	12.0398	+	20.8536i	0.438756	+	0.759947i
$754$	19.3969	−	16.2760i	0.706394	−	0.592735i
$755$	−4.02734	+	1.46583i	−0.146570	+	0.0533471i
$756$	−2.99273	−	1.08926i	−0.108844	−	0.0396161i
$757$	12.1532	+	10.1977i	0.441714	+	0.370642i	0.836351	−	0.548195i	$-0.184685\pi$
$757$	12.1532	+	10.1977i	0.441714	+	0.370642i	−0.394636	+	0.918838i	$0.629129\pi$
$758$	5.68614	−	32.2477i	0.206530	−	1.17129i
$759$	27.6272			1.00280
$760$	2.77719	+	3.35965i	0.100739	+	0.121867i
$761$	−29.9540			−1.08583			−0.542916	−	0.839787i	$-0.682680\pi$
$761$	−29.9540			−1.08583			−0.542916	+	0.839787i	$0.682680\pi$
$762$	0.182266	−	1.03368i	0.00660281	−	0.0374464i
$763$	22.3182	+	18.7272i	0.807973	+	0.677970i
$764$	−10.8648	−	3.95448i	−0.393076	−	0.143068i
$765$	0.879385	−	0.320070i	0.0317942	−	0.0115722i
$766$	−11.1853	+	9.38555i	−0.404140	+	0.339114i
$767$	−33.3512	−	57.7660i	−1.20424	−	2.08581i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−5.88784	−	33.3916i	−0.212321	−	1.20413i	−0.885495	−	0.464648i	$-0.846181\pi$
$769$	−5.88784	−	33.3916i	−0.212321	−	1.20413i	0.673174	−	0.739484i	$-0.264930\pi$
$770$	−2.40420	−	13.6349i	−0.0866414	−	0.491368i
$771$	−8.38919	+	14.5305i	−0.302129	+	0.523303i
$772$	1.06418	+	1.84321i	0.0383006	+	0.0663386i
$773$	−26.1668	+	21.9566i	−0.941156	+	0.789724i	−0.977786	−	0.209605i	$-0.932782\pi$
$773$	−26.1668	+	21.9566i	−0.941156	+	0.789724i	0.0366302	+	0.999329i	$0.488338\pi$
$774$	4.10607	−	1.49449i	0.147590	−	0.0537182i
$775$	4.83750	+	1.76070i	0.173768	+	0.0632464i
$776$	−9.07192	−	7.61224i	−0.325663	−	0.273264i
$777$	−1.09802	+	6.22719i	−0.0393913	+	0.223399i
$778$	3.91622			0.140403
$779$	45.3858	−	7.65868i	1.62612	−	0.274401i
$780$	−5.00000			−0.179029
$781$	−8.51249	+	48.2767i	−0.304601	+	1.72748i
$782$	4.55581	+	3.82278i	0.162915	+	0.136702i
$783$	4.75877	+	1.73205i	0.170065	+	0.0618984i
$784$	−2.95336	+	1.07494i	−0.105477	+	0.0383906i
$785$	−16.4722	+	13.8219i	−0.587920	+	0.493323i
$786$	−0.127889	−	0.221510i	−0.00456164	−	0.00790099i
$787$	24.3773	−	42.2228i	0.868958	−	1.50508i	0.00589493	−	0.999983i	$-0.498124\pi$
$787$	24.3773	−	42.2228i	0.868958	−	1.50508i	0.863063	−	0.505096i	$-0.168543\pi$
$788$	−2.90554	−	16.4782i	−0.103506	−	0.587010i
$789$	2.22550	+	12.6214i	0.0792299	+	0.449335i
$790$	4.36959	−	7.56834i	0.155463	−	0.269270i
$791$	−14.6382	−	25.3540i	−0.520473	−	0.901486i
$792$	3.33022	−	2.79439i	0.118334	−	0.0992943i
$793$	41.0607	−	14.9449i	1.45811	−	0.530708i
$794$	0.326352	+	0.118782i	0.0115818	+	0.00421543i
$795$	3.60220	+	3.02260i	0.127757	+	0.107201i
$796$	0.539830	−	3.06153i	0.0191338	−	0.108513i
$797$	−39.4971			−1.39906			−0.699530	−	0.714603i	$-0.746607\pi$
$797$	−39.4971			−1.39906			−0.699530	+	0.714603i	$0.746607\pi$
$798$	−12.0731	+	6.85240i	−0.427383	+	0.242572i
$799$	8.62092			0.304986
$800$	−0.173648	+	0.984808i	−0.00613939	+	0.0348182i
$801$	9.21554	+	7.73275i	0.325615	+	0.273223i
$802$	35.9495	+	13.0846i	1.26942	+	0.462032i
$803$	67.7383	−	24.6547i	2.39043	−	0.870047i
$804$	11.9855	−	10.0570i	0.422694	−	0.354683i
$805$	−10.1197	−	17.5279i	−0.356674	−	0.617777i
$806$	−12.8699	+	22.2913i	−0.453323	+	0.785178i
$807$	2.91353	+	16.5235i	0.102561	+	0.581654i
$808$	1.09833	+	6.22892i	0.0386390	+	0.219133i
$809$	−11.5719	+	20.0432i	−0.406847	+	0.704680i	−0.994535	−	0.104408i	$-0.966705\pi$
$809$	−11.5719	+	20.0432i	−0.406847	+	0.704680i	0.587688	+	0.809088i	$0.300038\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	33.0369	−	27.7212i	1.16008	−	0.973425i	0.160176	−	0.987089i	$-0.448794\pi$
$811$	33.0369	−	27.7212i	1.16008	−	0.973425i	0.999907	+	0.0136640i	$0.00434952\pi$
$812$	15.1557	−	5.51622i	0.531861	−	0.193581i
$813$	3.07873	+	1.12056i	0.107976	+	0.0392999i
$814$	−6.61200	−	5.54812i	−0.231750	−	0.194462i
$815$	1.30541	−	7.40333i	0.0457264	−	0.259327i
$816$	0.935822			0.0327603
$817$	6.64590	−	17.8495i	0.232510	−	0.624475i
$818$	14.6031			0.510585
$819$	2.76517	−	15.6820i	0.0966228	−	0.547975i
$820$	8.08899	+	6.78747i	0.282480	+	0.237029i
$821$	6.85978	+	2.49676i	0.239408	+	0.0871374i	0.458938	−	0.888468i	$-0.348230\pi$
$821$	6.85978	+	2.49676i	0.239408	+	0.0871374i	−0.219530	+	0.975606i	$0.570452\pi$
$822$	−11.2071	+	4.07904i	−0.390892	+	0.142273i
$823$	−21.1668	+	17.7611i	−0.737830	+	0.619113i	−0.932254	−	0.361805i	$-0.882161\pi$
$823$	−21.1668	+	17.7611i	−0.737830	+	0.619113i	0.194424	+	0.980918i	$0.437716\pi$
$824$	6.65657	+	11.5295i	0.231893	+	0.401650i
$825$	2.17365	−	3.76487i	0.0756767	−	0.131076i
$826$	−7.37774	−	41.8412i	−0.256704	−	1.45584i
$827$	−0.331815	−	1.88182i	−0.0115383	−	0.0654371i	0.978495	−	0.206271i	$-0.0661328\pi$
$827$	−0.331815	−	1.88182i	−0.0115383	−	0.0654371i	−0.990033	+	0.140834i	$0.955022\pi$
$828$	3.17752	−	5.50362i	0.110426	−	0.191264i
$829$	−2.49020	−	4.31315i	−0.0864882	−	0.149802i	0.819536	−	0.573027i	$-0.194231\pi$
$829$	−2.49020	−	4.31315i	−0.0864882	−	0.149802i	−0.906024	+	0.423225i	$0.860898\pi$
$830$	3.41147	−	2.86257i	0.118414	−	0.0993611i
$831$	8.69846	−	3.16598i	0.301746	−	0.109827i
$832$	−4.69846	−	1.71010i	−0.162890	−	0.0592871i
$833$	2.25309	+	1.89057i	0.0780649	+	0.0655042i
$834$	2.81180	−	15.9465i	0.0973648	−	0.552183i
$835$	−13.0419			−0.451333
$836$	0.139500	−	18.9489i	0.00482470	−	0.655362i
$837$	−5.14796			−0.177939
$838$	1.60947	−	9.12776i	0.0555982	−	0.315313i
$839$	−38.1070	−	31.9756i	−1.31560	−	1.10392i	−0.987218	−	0.159374i	$-0.949052\pi$
$839$	−38.1070	−	31.9756i	−1.31560	−	1.10392i	−0.328381	−	0.944545i	$-0.606503\pi$
$840$	−2.99273	−	1.08926i	−0.103259	−	0.0375832i
$841$	3.15183	−	1.14717i	0.108684	−	0.0395576i
$842$	−4.94356	+	4.14814i	−0.170366	+	0.142954i
$843$	−7.41534	−	12.8438i	−0.255398	−	0.442362i
$844$	6.84864	−	11.8622i	0.235740	−	0.408314i
$845$	−2.08378	−	11.8177i	−0.0716841	−	0.406541i
$846$	−1.59967	−	9.07218i	−0.0549978	−	0.311908i
$847$	−12.5783	+	21.7863i	−0.432196	+	0.748585i
$848$	2.35117	+	4.07234i	0.0807394	+	0.139845i
$849$	12.7023	−	10.6585i	0.435943	−	0.365800i
$850$	0.879385	−	0.320070i	0.0301627	−	0.0109783i
$851$	−11.8567	−	4.31548i	−0.406442	−	0.147933i
$852$	8.63816	+	7.24827i	0.295938	+	0.248322i
$853$	8.00939	−	45.4235i	0.274236	−	1.55527i	−0.467141	−	0.884183i	$-0.654716\pi$
$853$	8.00939	−	45.4235i	0.274236	−	1.55527i	0.741377	−	0.671088i	$-0.234173\pi$
$854$	27.8324			0.952407
$855$	−4.28699	−	0.788496i	−0.146612	−	0.0269660i
$856$	−12.0000			−0.410152
$857$	−6.40467	+	36.3227i	−0.218779	+	1.24076i	0.655447	+	0.755241i	$0.272480\pi$
$857$	−6.40467	+	36.3227i	−0.218779	+	1.24076i	−0.874227	+	0.485518i	$0.838631\pi$
$858$	16.6511	+	13.9719i	0.568460	+	0.476994i
$859$	28.5403	+	10.3878i	0.973782	+	0.354428i	0.779420	−	0.626502i	$-0.215514\pi$
$859$	28.5403	+	10.3878i	0.973782	+	0.354428i	0.194363	+	0.980930i	$0.437736\pi$
$860$	4.10607	−	1.49449i	0.140016	−	0.0509616i
$861$	−25.7618	+	21.6167i	−0.877959	+	0.736695i
$862$	−5.43882	−	9.42030i	−0.185247	−	0.320857i
$863$	−0.739885	+	1.28152i	−0.0251860	+	0.0436234i	−0.878344	−	0.478030i	$-0.841351\pi$
$863$	−0.739885	+	1.28152i	−0.0251860	+	0.0436234i	0.853158	+	0.521653i	$0.174684\pi$
$864$	−0.173648	−	0.984808i	−0.00590763	−	0.0335038i
$865$	0.0748553	+	0.424525i	0.00254516	+	0.0144343i
$866$	0.00774079	−	0.0134074i	0.000263043	−	0.000455603i
$867$	8.06212	+	13.9640i	0.273804	+	0.474242i
$868$	−12.5594	+	10.5386i	−0.426295	+	0.357704i
$869$	−35.7006	+	12.9939i	−1.21106	+	0.440789i
$870$	4.75877	+	1.73205i	0.161337	+	0.0587220i
$871$	59.9273	+	50.2849i	2.03056	+	1.70384i
$872$	−1.58853	+	9.00898i	−0.0537943	+	0.305082i
$873$	11.8425			0.400810
$874$	−9.28240	−	26.0994i	−0.313982	−	0.882827i
$875$	−3.18479			−0.107666
$876$	2.87939	−	16.3298i	0.0972854	−	0.551733i
$877$	23.5390	+	19.7515i	0.794854	+	0.666962i	0.946942	−	0.321405i	$-0.104155\pi$
$877$	23.5390	+	19.7515i	0.794854	+	0.666962i	−0.152088	+	0.988367i	$0.548600\pi$
$878$	−5.30541	−	1.93101i	−0.179049	−	0.0651684i
$879$	1.04411	−	0.380025i	0.0352170	−	0.0128179i
$880$	3.33022	−	2.79439i	0.112262	−	0.0941988i
$881$	12.7677	+	22.1143i	0.430155	+	0.745049i	0.996886	−	0.0788529i	$-0.0251257\pi$
$881$	12.7677	+	22.1143i	0.430155	+	0.745049i	−0.566732	+	0.823902i	$0.691792\pi$
$882$	1.57145	−	2.72183i	0.0529135	−	0.0916489i
$883$	7.80066	+	44.2397i	0.262513	+	1.48879i	0.776024	+	0.630703i	$0.217233\pi$
$883$	7.80066	+	44.2397i	0.262513	+	1.48879i	−0.513511	+	0.858083i	$0.671656\pi$
$884$	0.812519	+	4.60802i	0.0273280	+	0.154985i
$885$	6.67024	−	11.5532i	0.224218	−	0.388357i
$886$	9.68004	+	16.7663i	0.325207	+	0.563276i
$887$	41.7825	−	35.0596i	1.40292	−	1.17719i	0.443131	−	0.896457i	$-0.353868\pi$
$887$	41.7825	−	35.0596i	1.40292	−	1.17719i	0.959787	−	0.280731i	$-0.0905769\pi$
$888$	−1.86571	+	0.679065i	−0.0626093	+	0.0227879i
$889$	3.14125	+	1.14332i	0.105354	+	0.0383458i
$890$	9.21554	+	7.73275i	0.308906	+	0.259202i
$891$	−0.754900	+	4.28125i	−0.0252901	+	0.143427i
$892$	−7.29860			−0.244375
$893$	−34.6263	−	20.3328i	−1.15872	−	0.680413i
$894$	2.48246			0.0830259
$895$	−2.69981	+	15.3114i	−0.0902446	+	0.511803i
$896$	−2.43969	−	2.04715i	−0.0815044	−	0.0683903i
$897$	29.8589	+	10.8678i	0.996960	+	0.362864i
$898$	0.405078	−	0.147436i	0.0135176	−	0.00492001i
$899$	19.9709	−	16.7576i	0.666067	−	0.558897i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	2.20027	−	3.81099i	0.0733018	−	0.126962i
$902$	−7.97131	−	45.2076i	−0.265416	−	1.50525i
$903$	2.41653	+	13.7048i	0.0804170	+	0.456067i
$904$	4.59627	−	7.96097i	0.152870	−	0.264778i
$905$	−0.758770	−	1.31423i	−0.0252224	−	0.0436865i
$906$	3.28312	−	2.75486i	0.109074	−	0.0915242i
$907$	41.7229	−	15.1859i	1.38539	−	0.504239i	0.461579	−	0.887099i	$-0.347283\pi$
$907$	41.7229	−	15.1859i	1.38539	−	0.504239i	0.923806	+	0.382860i	$0.125061\pi$
$908$	−7.02229	−	2.55590i	−0.233043	−	0.0848207i
$909$	−4.84524	−	4.06564i	−0.160706	−	0.134849i
$910$	2.76517	−	15.6820i	0.0916644	−	0.519855i
$911$	−21.5776			−0.714898			−0.357449	−	0.933933i	$-0.616353\pi$
$911$	−21.5776			−0.714898			−0.357449	+	0.933933i	$0.616353\pi$
$912$	−3.75877	−	2.20718i	−0.124465	−	0.0730870i
$913$	−19.3601			−0.640725
$914$	−3.61587	+	20.5066i	−0.119602	+	0.678298i
$915$	6.69459	+	5.61743i	0.221316	+	0.185707i
$916$	6.75877	+	2.45999i	0.223316	+	0.0812804i
$917$	0.765472	−	0.278609i	0.0252781	−	0.00920048i
$918$	−0.716881	+	0.601535i	−0.0236606	+	0.0198536i
$919$	21.2645	+	36.8311i	0.701450	+	1.21495i	0.967958	+	0.251114i	$0.0807968\pi$
$919$	21.2645	+	36.8311i	0.701450	+	1.21495i	−0.266508	+	0.963833i	$0.585870\pi$
$920$	3.17752	−	5.50362i	0.104760	−	0.181449i
$921$	5.52435	+	31.3301i	0.182033	+	1.03236i
$922$	4.97090	+	28.1914i	0.163708	+	0.928434i
$923$	−28.1908	+	48.8279i	−0.927911	+	1.60719i
$924$	6.92262	+	11.9903i	0.227737	+	0.394453i
$925$	−1.52094	+	1.27622i	−0.0500083	+	0.0419620i
$926$	6.36319	−	2.31601i	0.209107	−	0.0761089i
$927$	−12.5103	−	4.55336i	−0.410891	−	0.149552i
$928$	3.87939	+	3.25519i	0.127347	+	0.106857i
$929$	8.68820	−	49.2732i	0.285050	−	1.61660i	−0.420055	−	0.907499i	$-0.637989\pi$
$929$	8.68820	−	49.2732i	0.285050	−	1.61660i	0.705105	−	0.709103i	$-0.250900\pi$
$930$	−5.14796			−0.168808
$931$	−4.59064	−	12.9076i	−0.150452	−	0.423028i
$932$	15.5175			0.508294
$933$	1.02229	−	5.79769i	0.0334682	−	0.189808i
$934$	−6.16250	−	5.17095i	−0.201643	−	0.169199i
$935$	−3.82295	−	1.39144i	−0.125024	−	0.0455049i
$936$	4.69846	−	1.71010i	0.153574	−	0.0558964i
$937$	−43.5003	+	36.5011i	−1.42109	+	1.19244i	−0.470341	+	0.882484i	$0.655869\pi$
$937$	−43.5003	+	36.5011i	−1.42109	+	1.19244i	−0.950752	+	0.309954i	$0.899686\pi$
$938$	24.9145	+	43.1531i	0.813486	+	1.40900i
$939$	−6.28312	+	10.8827i	−0.205042	+	0.355143i
$940$	−1.59967	−	9.07218i	−0.0521755	−	0.295902i
$941$	1.08915	+	6.17690i	0.0355054	+	0.201361i	0.997400	−	0.0720577i	$-0.0229566\pi$
$941$	1.08915	+	6.17690i	0.0355054	+	0.201361i	−0.961895	+	0.273419i	$0.911845\pi$
$942$	10.7515	−	18.6221i	0.350303	−	0.606742i
$943$	−33.5528	−	58.1151i	−1.09263	−	1.89249i
$944$	10.2194	−	8.57510i	0.332613	−	0.279096i
$945$	2.99273	−	1.08926i	0.0973534	−	0.0354337i
$946$	−17.8503	−	6.49697i	−0.580363	−	0.211235i
$947$	−21.2722	−	17.8495i	−0.691253	−	0.580030i	0.228017	−	0.973657i	$-0.426776\pi$
$947$	−21.2722	−	17.8495i	−0.691253	−	0.580030i	−0.919270	+	0.393627i	$0.871220\pi$
$948$	−1.51754	+	8.60640i	−0.0492874	+	0.279523i
$949$	82.9086			2.69133
$950$	−4.28699	−	0.788496i	−0.139088	−	0.0255822i
$951$	18.6040			0.603276
$952$	−0.517541	+	2.93512i	−0.0167736	+	0.0951278i
$953$	11.7246	+	9.83813i	0.379798	+	0.318688i	0.812623	−	0.582790i	$-0.198039\pi$
$953$	11.7246	+	9.83813i	0.379798	+	0.318688i	−0.432825	+	0.901478i	$0.642483\pi$
$954$	−4.41875	−	1.60829i	−0.143062	−	0.0520704i
$955$	10.8648	−	3.95448i	0.351578	−	0.127964i
$956$	11.5817	−	9.71822i	0.374580	−	0.314310i
$957$	−11.0077	−	19.0660i	−0.355830	−	0.616315i
$958$	−7.12836	+	12.3467i	−0.230307	+	0.398903i
$959$	−6.59566	−	37.4058i	−0.212985	−	1.20790i
$960$	−0.173648	−	0.984808i	−0.00560447	−	0.0317845i
$961$	2.24928	−	3.89586i	0.0725573	−	0.125673i
$962$	−4.96363	−	8.59726i	−0.160034	−	0.277187i
$963$	9.19253	−	7.71345i	0.296225	−	0.248562i
$964$	5.39306	−	1.96291i	0.173699	−	0.0632211i
$965$	−2.00000	−	0.727940i	−0.0643823	−	0.0234332i
$966$	15.5043	+	13.0097i	0.498844	+	0.418580i
$967$	−6.19665	+	35.1430i	−0.199271	+	1.13012i	0.706933	+	0.707280i	$0.250078\pi$
$967$	−6.19665	+	35.1430i	−0.199271	+	1.13012i	−0.906204	+	0.422841i	$0.861033\pi$
$968$	−7.89899			−0.253883
$969$	−0.0300295	+	4.07904i	−0.000964686	+	0.131038i
$970$	11.8425			0.380241
$971$	9.78952	−	55.5191i	0.314160	−	1.78169i	−0.262728	−	0.964870i	$-0.584622\pi$
$971$	9.78952	−	55.5191i	0.314160	−	1.78169i	0.576889	−	0.816823i	$-0.304267\pi$
$972$	0.766044	+	0.642788i	0.0245709	+	0.0206174i
$973$	48.4598	+	17.6379i	1.55355	+	0.565446i
$974$	17.5744	−	6.39657i	0.563122	−	0.204959i
$975$	3.83022	−	3.21394i	0.122665	−	0.102928i
$976$	4.36959	+	7.56834i	0.139867	+	0.242257i
$977$	7.34730	−	12.7259i	0.235061	−	0.407137i	−0.724230	−	0.689559i	$-0.757804\pi$
$977$	7.34730	−	12.7259i	0.235061	−	0.407137i	0.959290	+	0.282422i	$0.0911377\pi$
$978$	1.30541	+	7.40333i	0.0417423	+	0.236732i
$979$	−9.08147	−	51.5036i	−0.290245	−	1.64606i
$980$	1.57145	−	2.72183i	0.0501982	−	0.0869458i
$981$	−4.57398	−	7.92236i	−0.146036	−	0.252942i
$982$	9.93242	−	8.33429i	0.316956	−	0.265958i
$983$	16.1001	−	5.85997i	0.513515	−	0.186904i	−0.0722480	−	0.997387i	$-0.523017\pi$
$983$	16.1001	−	5.85997i	0.513515	−	0.186904i	0.585763	+	0.810483i	$0.300795\pi$
$984$	−9.92262	−	3.61154i	−0.316322	−	0.115132i
$985$	12.8177	+	10.7554i	0.408407	+	0.342694i
$986$	0.822948	−	4.66717i	0.0262080	−	0.148633i
$987$	29.3387			0.933862
$988$	7.60472	−	20.4247i	0.241938	−	0.649796i
$989$	−27.7689			−0.882999
$990$	−0.754900	+	4.28125i	−0.0239923	+	0.136067i
$991$	8.49794	+	7.13062i	0.269946	+	0.226512i	0.767704	−	0.640804i	$-0.221399\pi$
$991$	8.49794	+	7.13062i	0.269946	+	0.226512i	−0.497758	+	0.867316i	$0.665843\pi$
$992$	−4.83750	−	1.76070i	−0.153591	−	0.0559024i
$993$	−0.0859997	+	0.0313013i	−0.00272912	+	0.000993317i
$994$	−27.5107	+	23.0842i	−0.872587	+	0.732188i
$995$	1.55438	+	2.69226i	0.0492771	+	0.0853504i
$996$	−2.22668	+	3.85673i	−0.0705551	+	0.122205i
$997$	−5.49778	−	31.1795i	−0.174116	−	0.987463i	−0.939159	−	0.343483i	$-0.888393\pi$
$997$	−5.49778	−	31.1795i	−0.174116	−	0.987463i	0.765042	−	0.643980i	$-0.222718\pi$
$998$	−6.71317	−	38.0723i	−0.212502	−	1.20516i
$999$	0.992726	−	1.71945i	0.0314085	−	0.0544011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.u.b.511.1	✓	6
19.9	even	9	inner	570.2.u.b.541.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.b.511.1	✓	6	1.1	even	1	trivial
570.2.u.b.541.1	yes	6	19.9	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.939693 - 0.342020i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(-1.59240 - 2.75811i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.939693 - 0.342020i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(-1.59240 - 2.75811i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(0.173648 + 0.984808i) q^{10} +(2.17365 - 3.76487i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(3.83022 - 3.21394i) q^{13} +(2.99273 - 1.08926i) q^{14} +(0.939693 + 0.342020i) q^{15} +(0.766044 + 0.642788i) q^{16} +(0.162504 - 0.921605i) q^{17} -1.00000 q^{18} +(-2.82635 + 3.31839i) q^{19} -1.00000 q^{20} +(0.553033 - 3.13641i) q^{21} +(3.33022 + 2.79439i) q^{22} +(5.97178 + 2.17355i) q^{23} +(0.939693 - 0.342020i) q^{24} +(0.766044 - 0.642788i) q^{25} +(2.50000 + 4.33013i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(0.553033 + 3.13641i) q^{28} +(-0.879385 - 4.98724i) q^{29} +(-0.500000 + 0.866025i) q^{30} +(2.57398 + 4.45826i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(4.08512 - 1.48686i) q^{33} +(0.879385 + 0.320070i) q^{34} +(-2.43969 - 2.04715i) q^{35} +(0.173648 - 0.984808i) q^{36} -1.98545 q^{37} +(-2.77719 - 3.35965i) q^{38} +5.00000 q^{39} +(0.173648 - 0.984808i) q^{40} +(-8.08899 - 6.78747i) q^{41} +(2.99273 + 1.08926i) q^{42} +(-4.10607 + 1.49449i) q^{43} +(-3.33022 + 2.79439i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-3.17752 + 5.50362i) q^{46} +(1.59967 + 9.07218i) q^{47} +(0.173648 + 0.984808i) q^{48} +(-1.57145 + 2.72183i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.716881 - 0.601535i) q^{51} +(-4.69846 + 1.71010i) q^{52} +(4.41875 + 1.60829i) q^{53} +(-0.766044 - 0.642788i) q^{54} +(0.754900 - 4.28125i) q^{55} -3.18479 q^{56} +(-4.29813 + 0.725293i) q^{57} +5.06418 q^{58} +(2.31655 - 13.1378i) q^{59} +(-0.766044 - 0.642788i) q^{60} +(8.21213 + 2.98897i) q^{61} +(-4.83750 + 1.76070i) q^{62} +(2.43969 - 2.04715i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.50000 - 4.33013i) q^{65} +(0.754900 + 4.28125i) q^{66} +(2.71688 + 15.4082i) q^{67} +(-0.467911 + 0.810446i) q^{68} +(3.17752 + 5.50362i) q^{69} +(2.43969 - 2.04715i) q^{70} +(-10.5963 + 3.85673i) q^{71} +(0.939693 + 0.342020i) q^{72} +(12.7023 + 10.6585i) q^{73} +(0.344770 - 1.95529i) q^{74} +1.00000 q^{75} +(3.79086 - 2.15160i) q^{76} -13.8452 q^{77} +(-0.868241 + 4.92404i) q^{78} +(-6.69459 - 5.61743i) q^{79} +(0.939693 + 0.342020i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(8.08899 - 6.78747i) q^{82} +(-2.22668 - 3.85673i) q^{83} +(-1.59240 + 2.75811i) q^{84} +(-0.162504 - 0.921605i) q^{85} +(-0.758770 - 4.30320i) q^{86} +(2.53209 - 4.38571i) q^{87} +(-2.17365 - 3.76487i) q^{88} +(9.21554 - 7.73275i) q^{89} +(-0.939693 + 0.342020i) q^{90} +(-14.9636 - 5.44632i) q^{91} +(-4.86824 - 4.08494i) q^{92} +(-0.893933 + 5.06975i) q^{93} -9.21213 q^{94} +(-1.52094 + 4.08494i) q^{95} -1.00000 q^{96} +(2.05644 - 11.6626i) q^{97} +(-2.40760 - 2.02022i) q^{98} +(4.08512 + 1.48686i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q - 6 * q^7 + 3 * q^8	\( 6 q - 6 q^{7} + 3 q^{8} + 12 q^{11} - 3 q^{12} + 6 q^{17} - 6 q^{18} - 18 q^{19} - 6 q^{20} - 9 q^{21} - 3 q^{22} + 21 q^{23} + 15 q^{26} - 3 q^{27} - 9 q^{28} + 6 q^{29} - 3 q^{30} + 3 q^{33} - 6 q^{34} - 9 q^{35} + 24 q^{37} - 6 q^{38} + 30 q^{39} - 3 q^{41} + 3 q^{44} + 3 q^{45} + 6 q^{46} + 24 q^{47} - 9 q^{49} + 3 q^{50} - 12 q^{51} + 24 q^{53} + 6 q^{55} - 12 q^{56} - 12 q^{57} + 12 q^{58} + 12 q^{59} - 24 q^{62} + 9 q^{63} - 3 q^{64} + 15 q^{65} + 6 q^{66} - 12 q^{68} - 6 q^{69} + 9 q^{70} - 36 q^{71} + 24 q^{73} + 15 q^{74} + 6 q^{75} - 9 q^{76} - 30 q^{77} - 36 q^{79} + 3 q^{82} - 6 q^{84} - 6 q^{85} + 18 q^{86} + 6 q^{87} - 12 q^{88} + 48 q^{89} - 24 q^{92} - 30 q^{93} - 6 q^{94} - 6 q^{95} - 6 q^{96} + 42 q^{97} - 18 q^{98} + 3 q^{99}+O(q^{100}) \) 6 * q - 6 * q^7 + 3 * q^8 + 12 * q^11 - 3 * q^12 + 6 * q^17 - 6 * q^18 - 18 * q^19 - 6 * q^20 - 9 * q^21 - 3 * q^22 + 21 * q^23 + 15 * q^26 - 3 * q^27 - 9 * q^28 + 6 * q^29 - 3 * q^30 + 3 * q^33 - 6 * q^34 - 9 * q^35 + 24 * q^37 - 6 * q^38 + 30 * q^39 - 3 * q^41 + 3 * q^44 + 3 * q^45 + 6 * q^46 + 24 * q^47 - 9 * q^49 + 3 * q^50 - 12 * q^51 + 24 * q^53 + 6 * q^55 - 12 * q^56 - 12 * q^57 + 12 * q^58 + 12 * q^59 - 24 * q^62 + 9 * q^63 - 3 * q^64 + 15 * q^65 + 6 * q^66 - 12 * q^68 - 6 * q^69 + 9 * q^70 - 36 * q^71 + 24 * q^73 + 15 * q^74 + 6 * q^75 - 9 * q^76 - 30 * q^77 - 36 * q^79 + 3 * q^82 - 6 * q^84 - 6 * q^85 + 18 * q^86 + 6 * q^87 - 12 * q^88 + 48 * q^89 - 24 * q^92 - 30 * q^93 - 6 * q^94 - 6 * q^95 - 6 * q^96 + 42 * q^97 - 18 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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