LMFDB - Embedded newform 570.2.u.c.541.1

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			541.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	570.541
Dual form			570.2.u.c.511.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-0.326352 + 0.565258i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(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} +(-0.326352 + 0.565258i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +(-0.173648 + 0.984808i) q^{10} +(-1.43969 - 2.49362i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-1.26604 - 1.06234i) q^{13} +(0.613341 + 0.223238i) q^{14} +(-0.939693 + 0.342020i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-1.26604 - 7.18009i) q^{17} -1.00000 q^{18} +(-3.79086 - 2.15160i) q^{19} +1.00000 q^{20} +(0.113341 + 0.642788i) q^{21} +(-2.20574 + 1.85083i) q^{22} +(-1.61334 + 0.587208i) q^{23} +(0.939693 + 0.342020i) q^{24} +(0.766044 + 0.642788i) q^{25} +(-0.826352 + 1.43128i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(0.113341 - 0.642788i) q^{28} +(0.0282185 - 0.160035i) q^{29} +(0.500000 + 0.866025i) q^{30} +(-0.471782 + 0.817150i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-2.70574 - 0.984808i) q^{33} +(-6.85117 + 2.49362i) q^{34} +(0.500000 - 0.419550i) q^{35} +(0.173648 + 0.984808i) q^{36} -7.24897 q^{37} +(-1.46064 + 4.10689i) q^{38} -1.65270 q^{39} +(-0.173648 - 0.984808i) q^{40} +(-0.309278 + 0.259515i) q^{41} +(0.613341 - 0.223238i) q^{42} +(10.6702 + 3.88365i) q^{43} +(2.20574 + 1.85083i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(0.858441 + 1.48686i) q^{46} +(1.00727 - 5.71253i) q^{47} +(0.173648 - 0.984808i) q^{48} +(3.28699 + 5.69323i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-5.58512 - 4.68647i) q^{51} +(1.55303 + 0.565258i) q^{52} +(9.93629 - 3.61651i) q^{53} +(-0.766044 + 0.642788i) q^{54} +(0.500000 + 2.83564i) q^{55} -0.652704 q^{56} +(-4.28699 + 0.788496i) q^{57} -0.162504 q^{58} +(-0.790859 - 4.48519i) q^{59} +(0.766044 - 0.642788i) q^{60} +(-10.8093 + 3.93426i) q^{61} +(0.886659 + 0.322718i) q^{62} +(0.500000 + 0.419550i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.826352 + 1.43128i) q^{65} +(-0.500000 + 2.83564i) q^{66} +(-0.396459 + 2.24843i) q^{67} +(3.64543 + 6.31407i) q^{68} +(-0.858441 + 1.48686i) q^{69} +(-0.500000 - 0.419550i) q^{70} +(4.01114 + 1.45994i) q^{71} +(0.939693 - 0.342020i) q^{72} +(8.73055 - 7.32580i) q^{73} +(1.25877 + 7.13884i) q^{74} +1.00000 q^{75} +(4.29813 + 0.725293i) q^{76} +1.87939 q^{77} +(0.286989 + 1.62760i) q^{78} +(-3.73783 + 3.13641i) q^{79} +(-0.939693 + 0.342020i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(0.309278 + 0.259515i) q^{82} +(2.14543 - 3.71599i) q^{83} +(-0.326352 - 0.565258i) q^{84} +(-1.26604 + 7.18009i) q^{85} +(1.97178 - 11.1825i) q^{86} +(-0.0812519 - 0.140732i) q^{87} +(1.43969 - 2.49362i) q^{88} +(1.91147 + 1.60392i) q^{89} +(0.939693 + 0.342020i) q^{90} +(1.01367 - 0.368946i) q^{91} +(1.31521 - 1.10359i) q^{92} +(0.163848 + 0.929228i) q^{93} -5.80066 q^{94} +(2.82635 + 3.31839i) q^{95} -1.00000 q^{96} +(-2.43717 - 13.8219i) q^{97} +(5.03596 - 4.22567i) q^{98} +(-2.70574 + 0.984808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q - 3 * q^7 + 3 * q^8	$ 6 q - 3 q^{7} + 3 q^{8} - 3 q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} - 3 q^{17} - 6 q^{18} + 9 q^{19} + 6 q^{20} - 6 q^{21} - 3 q^{22} - 3 q^{23} - 6 q^{26} - 3 q^{27} - 6 q^{28} + 15 q^{29} + 3 q^{30} + 12 q^{31} - 6 q^{33} - 15 q^{34} + 3 q^{35} - 18 q^{37} - 12 q^{39} + 18 q^{41} - 3 q^{42} + 21 q^{43} + 3 q^{44} - 3 q^{45} - 3 q^{46} + 24 q^{47} + 12 q^{49} + 3 q^{50} - 12 q^{51} - 3 q^{52} + 12 q^{53} + 3 q^{55} - 6 q^{56} - 18 q^{57} - 6 q^{58} + 27 q^{59} - 45 q^{61} + 12 q^{62} + 3 q^{63} - 3 q^{64} + 6 q^{65} - 3 q^{66} - 12 q^{67} + 6 q^{68} + 3 q^{69} - 3 q^{70} + 18 q^{71} + 15 q^{73} - 15 q^{74} + 6 q^{75} + 12 q^{76} - 6 q^{78} - 3 q^{79} - 18 q^{82} - 3 q^{83} - 3 q^{84} - 3 q^{85} - 3 q^{86} - 3 q^{87} + 3 q^{88} - 9 q^{89} - 15 q^{91} + 15 q^{92} - 3 q^{93} - 6 q^{94} + 18 q^{95} - 6 q^{96} - 24 q^{97} - 3 q^{98} - 6 q^{99}+O(q^{100}) $ 6 * q - 3 * q^7 + 3 * q^8 - 3 * q^11 - 3 * q^12 - 3 * q^13 - 3 * q^14 - 3 * q^17 - 6 * q^18 + 9 * q^19 + 6 * q^20 - 6 * q^21 - 3 * q^22 - 3 * q^23 - 6 * q^26 - 3 * q^27 - 6 * q^28 + 15 * q^29 + 3 * q^30 + 12 * q^31 - 6 * q^33 - 15 * q^34 + 3 * q^35 - 18 * q^37 - 12 * q^39 + 18 * q^41 - 3 * q^42 + 21 * q^43 + 3 * q^44 - 3 * q^45 - 3 * q^46 + 24 * q^47 + 12 * q^49 + 3 * q^50 - 12 * q^51 - 3 * q^52 + 12 * q^53 + 3 * q^55 - 6 * q^56 - 18 * q^57 - 6 * q^58 + 27 * q^59 - 45 * q^61 + 12 * q^62 + 3 * q^63 - 3 * q^64 + 6 * q^65 - 3 * q^66 - 12 * q^67 + 6 * q^68 + 3 * q^69 - 3 * q^70 + 18 * q^71 + 15 * q^73 - 15 * q^74 + 6 * q^75 + 12 * q^76 - 6 * q^78 - 3 * q^79 - 18 * q^82 - 3 * q^83 - 3 * q^84 - 3 * q^85 - 3 * q^86 - 3 * q^87 + 3 * q^88 - 9 * q^89 - 15 * q^91 + 15 * q^92 - 3 * q^93 - 6 * q^94 + 18 * q^95 - 6 * q^96 - 24 * q^97 - 3 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$	$1$

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
$7$	−0.326352	+	0.565258i	−0.123349	+	0.213647i	−0.921087	−	0.389358i	$-0.872697\pi$
$7$	−0.326352	+	0.565258i	−0.123349	+	0.213647i	0.797737	+	0.603005i	$0.206030\pi$
$8$	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
$11$	−1.43969	−	2.49362i	−0.434084	−	0.751855i	0.563137	−	0.826364i	$-0.309594\pi$
$11$	−1.43969	−	2.49362i	−0.434084	−	0.751855i	−0.997220	+	0.0745088i	$0.976261\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−1.26604	−	1.06234i	−0.351138	−	0.294639i	0.450109	−	0.892974i	$-0.351385\pi$
$13$	−1.26604	−	1.06234i	−0.351138	−	0.294639i	−0.801247	+	0.598334i	$0.795830\pi$
$14$	0.613341	+	0.223238i	0.163922	+	0.0596628i
$15$	−0.939693	+	0.342020i	−0.242628	+	0.0883092i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−1.26604	−	7.18009i	−0.307061	−	1.74143i	−0.613642	−	0.789584i	$-0.710296\pi$
$17$	−1.26604	−	7.18009i	−0.307061	−	1.74143i	0.306581	−	0.951844i	$-0.400815\pi$
$18$	−1.00000			−0.235702
$19$	−3.79086	−	2.15160i	−0.869683	−	0.493611i
$19$	−3.79086	−	2.15160i	−0.869683	−	0.493611i
$20$	1.00000			0.223607
$21$	0.113341	+	0.642788i	0.0247330	+	0.140268i
$22$	−2.20574	+	1.85083i	−0.470265	+	0.394599i
$23$	−1.61334	+	0.587208i	−0.336405	+	0.122441i	−0.504699	−	0.863296i	$-0.668396\pi$
$23$	−1.61334	+	0.587208i	−0.336405	+	0.122441i	0.168294	+	0.985737i	$0.446174\pi$
$24$	0.939693	+	0.342020i	0.191814	+	0.0698146i
$25$	0.766044	+	0.642788i	0.153209	+	0.128558i
$26$	−0.826352	+	1.43128i	−0.162061	+	0.280698i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	0.113341	−	0.642788i	0.0214194	−	0.121475i
$29$	0.0282185	−	0.160035i	0.00524004	−	0.0297178i	−0.982076	−	0.188487i	$-0.939642\pi$
$29$	0.0282185	−	0.160035i	0.00524004	−	0.0297178i	0.987316	+	0.158770i	$0.0507527\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$	−0.471782	+	0.817150i	−0.0847345	+	0.146764i	−0.905278	−	0.424820i	$-0.860338\pi$
$31$	−0.471782	+	0.817150i	−0.0847345	+	0.146764i	0.820544	+	0.571584i	$0.193671\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	−2.70574	−	0.984808i	−0.471008	−	0.171433i
$34$	−6.85117	+	2.49362i	−1.17497	+	0.427652i
$35$	0.500000	−	0.419550i	0.0845154	−	0.0709169i
$36$	0.173648	+	0.984808i	0.0289414	+	0.164135i
$37$	−7.24897			−1.19172			−0.595862	−	0.803087i	$-0.703189\pi$
$37$	−7.24897			−1.19172			−0.595862	+	0.803087i	$0.703189\pi$
$38$	−1.46064	+	4.10689i	−0.236947	+	0.666225i
$39$	−1.65270			−0.264644
$40$	−0.173648	−	0.984808i	−0.0274562	−	0.155712i
$41$	−0.309278	+	0.259515i	−0.0483011	+	0.0405294i	−0.666619	−	0.745399i	$-0.732259\pi$
$41$	−0.309278	+	0.259515i	−0.0483011	+	0.0405294i	0.618318	+	0.785928i	$0.287815\pi$
$42$	0.613341	−	0.223238i	0.0946405	−	0.0344463i
$43$	10.6702	+	3.88365i	1.62720	+	0.592251i	0.984734	−	0.174065i	$-0.0556904\pi$
$43$	10.6702	+	3.88365i	1.62720	+	0.592251i	0.642463	+	0.766317i	$0.277913\pi$
$44$	2.20574	+	1.85083i	0.332527	+	0.279024i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	0.858441	+	1.48686i	0.126570	+	0.219226i
$47$	1.00727	−	5.71253i	0.146926	−	0.833259i	−0.818875	−	0.573973i	$-0.805402\pi$
$47$	1.00727	−	5.71253i	0.146926	−	0.833259i	0.965801	−	0.259286i	$-0.0834873\pi$
$48$	0.173648	−	0.984808i	0.0250640	−	0.142145i
$49$	3.28699	+	5.69323i	0.469570	+	0.813319i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−5.58512	−	4.68647i	−0.782074	−	0.656238i
$52$	1.55303	+	0.565258i	0.215367	+	0.0783872i
$53$	9.93629	−	3.61651i	1.36485	−	0.496766i	0.447303	−	0.894383i	$-0.352385\pi$
$53$	9.93629	−	3.61651i	1.36485	−	0.496766i	0.917552	+	0.397616i	$0.130163\pi$
$54$	−0.766044	+	0.642788i	−0.104245	+	0.0874723i
$55$	0.500000	+	2.83564i	0.0674200	+	0.382358i
$56$	−0.652704			−0.0872212
$57$	−4.28699	+	0.788496i	−0.567826	+	0.104439i
$58$	−0.162504			−0.0213378
$59$	−0.790859	−	4.48519i	−0.102961	−	0.583922i	−0.992015	−	0.126119i	$-0.959748\pi$
$59$	−0.790859	−	4.48519i	−0.102961	−	0.583922i	0.889054	−	0.457802i	$-0.151363\pi$
$60$	0.766044	−	0.642788i	0.0988959	−	0.0829835i
$61$	−10.8093	+	3.93426i	−1.38399	+	0.503730i	−0.923384	−	0.383877i	$-0.874589\pi$
$61$	−10.8093	+	3.93426i	−1.38399	+	0.503730i	−0.460602	+	0.887607i	$0.652366\pi$
$62$	0.886659	+	0.322718i	0.112606	+	0.0409852i
$63$	0.500000	+	0.419550i	0.0629941	+	0.0528583i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.826352	+	1.43128i	0.102496	+	0.177529i
$66$	−0.500000	+	2.83564i	−0.0615457	+	0.349043i
$67$	−0.396459	+	2.24843i	−0.0484352	+	0.274690i	−0.999401	−	0.0346062i	$-0.988982\pi$
$67$	−0.396459	+	2.24843i	−0.0484352	+	0.274690i	0.950966	+	0.309296i	$0.100093\pi$
$68$	3.64543	+	6.31407i	0.442073	+	0.765693i
$69$	−0.858441	+	1.48686i	−0.103344	+	0.178997i
$70$	−0.500000	−	0.419550i	−0.0597614	−	0.0501458i
$71$	4.01114	+	1.45994i	0.476035	+	0.173263i	0.568884	−	0.822418i	$-0.307375\pi$
$71$	4.01114	+	1.45994i	0.476035	+	0.173263i	−0.0928491	+	0.995680i	$0.529597\pi$
$72$	0.939693	−	0.342020i	0.110744	−	0.0403075i
$73$	8.73055	−	7.32580i	1.02183	−	0.857420i	0.0319770	−	0.999489i	$-0.489820\pi$
$73$	8.73055	−	7.32580i	1.02183	−	0.857420i	0.989857	+	0.142068i	$0.0453752\pi$
$74$	1.25877	+	7.13884i	0.146329	+	0.829874i
$75$	1.00000			0.115470
$76$	4.29813	+	0.725293i	0.493030	+	0.0831968i
$77$	1.87939			0.214176
$78$	0.286989	+	1.62760i	0.0324951	+	0.184289i
$79$	−3.73783	+	3.13641i	−0.420538	+	0.352874i	−0.828368	−	0.560185i	$-0.810730\pi$
$79$	−3.73783	+	3.13641i	−0.420538	+	0.352874i	0.407830	+	0.913058i	$0.366286\pi$
$80$	−0.939693	+	0.342020i	−0.105061	+	0.0382390i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	0.309278	+	0.259515i	0.0341540	+	0.0286586i
$83$	2.14543	−	3.71599i	0.235492	−	0.407883i	−0.723924	−	0.689880i	$-0.757663\pi$
$83$	2.14543	−	3.71599i	0.235492	−	0.407883i	0.959415	+	0.281997i	$0.0909967\pi$
$84$	−0.326352	−	0.565258i	−0.0356079	−	0.0616747i
$85$	−1.26604	+	7.18009i	−0.137322	+	0.778791i
$86$	1.97178	−	11.1825i	0.212623	−	1.20584i
$87$	−0.0812519	−	0.140732i	−0.00871112	−	0.0150881i
$88$	1.43969	−	2.49362i	0.153472	−	0.265821i
$89$	1.91147	+	1.60392i	0.202616	+	0.170015i	0.738450	−	0.674309i	$-0.235558\pi$
$89$	1.91147	+	1.60392i	0.202616	+	0.170015i	−0.535834	+	0.844323i	$0.680003\pi$
$90$	0.939693	+	0.342020i	0.0990523	+	0.0360521i
$91$	1.01367	−	0.368946i	0.106262	−	0.0386760i
$92$	1.31521	−	1.10359i	0.137120	−	0.115057i
$93$	0.163848	+	0.929228i	0.0169902	+	0.0963565i
$94$	−5.80066			−0.598292
$95$	2.82635	+	3.31839i	0.289978	+	0.340460i
$96$	−1.00000			−0.102062
$97$	−2.43717	−	13.8219i	−0.247457	−	1.40340i	−0.814717	−	0.579859i	$-0.803108\pi$
$97$	−2.43717	−	13.8219i	−0.247457	−	1.40340i	0.567260	−	0.823538i	$-0.308003\pi$
$98$	5.03596	−	4.22567i	0.508709	−	0.426857i
$99$	−2.70574	+	0.984808i	−0.271937	+	0.0989769i
$100$	−0.939693	−	0.342020i	−0.0939693	−	0.0342020i
$101$	−7.01367	−	5.88517i	−0.697886	−	0.585596i	0.223285	−	0.974753i	$-0.428322\pi$
$101$	−7.01367	−	5.88517i	−0.697886	−	0.585596i	−0.921171	+	0.389157i	$0.872766\pi$
$102$	−3.64543	+	6.31407i	−0.360951	+	0.625186i
$103$	8.33022	+	14.4284i	0.820801	+	1.42167i	0.905086	+	0.425228i	$0.139806\pi$
$103$	8.33022	+	14.4284i	0.820801	+	1.42167i	−0.0842852	+	0.996442i	$0.526861\pi$
$104$	0.286989	−	1.62760i	0.0281416	−	0.159599i
$105$	0.113341	−	0.642788i	0.0110609	−	0.0627296i
$106$	−5.28699	−	9.15733i	−0.513518	−	0.889439i
$107$	3.85457	−	6.67631i	0.372635	−	0.645423i	−0.617335	−	0.786701i	$-0.711788\pi$
$107$	3.85457	−	6.67631i	0.372635	−	0.645423i	0.989970	+	0.141277i	$0.0451209\pi$
$108$	0.766044	+	0.642788i	0.0737127	+	0.0618523i
$109$	−7.71213	−	2.80699i	−0.738688	−	0.268861i	−0.0548505	−	0.998495i	$-0.517468\pi$
$109$	−7.71213	−	2.80699i	−0.738688	−	0.268861i	−0.683838	+	0.729634i	$0.739690\pi$
$110$	2.70574	−	0.984808i	0.257982	−	0.0938977i
$111$	−5.55303	+	4.65955i	−0.527071	+	0.442265i
$112$	0.113341	+	0.642788i	0.0107097	+	0.0607377i
$113$	10.0446			0.944914			0.472457	−	0.881354i	$-0.343367\pi$
$113$	10.0446			0.944914			0.472457	+	0.881354i	$0.343367\pi$
$114$	1.52094	+	4.08494i	0.142450	+	0.382590i
$115$	1.71688			0.160100
$116$	0.0282185	+	0.160035i	0.00262002	+	0.0148589i
$117$	−1.26604	+	1.06234i	−0.117046	+	0.0982131i
$118$	−4.27972	+	1.55769i	−0.393980	+	0.143397i
$119$	4.47178	+	1.62760i	0.409928	+	0.149201i
$120$	−0.766044	−	0.642788i	−0.0699300	−	0.0586782i
$121$	1.35457	−	2.34618i	0.123143	−	0.213290i
$122$	5.75150	+	9.96188i	0.520716	+	0.901907i
$123$	−0.0701076	+	0.397600i	−0.00632139	+	0.0358504i
$124$	0.163848	−	0.929228i	0.0147140	−	0.0834472i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$	0.326352	−	0.565258i	0.0290737	−	0.0503572i
$127$	2.52094	+	2.11532i	0.223698	+	0.187705i	0.747748	−	0.663983i	$-0.231135\pi$
$127$	2.52094	+	2.11532i	0.223698	+	0.187705i	−0.524050	+	0.851687i	$0.675580\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	10.6702	−	3.88365i	0.939463	−	0.341936i
$130$	1.26604	−	1.06234i	0.111039	−	0.0931732i
$131$	1.18479	+	6.71929i	0.103516	+	0.587067i	0.991803	+	0.127778i	$0.0407846\pi$
$131$	1.18479	+	6.71929i	0.103516	+	0.587067i	−0.888287	+	0.459289i	$0.848104\pi$
$132$	2.87939			0.250618
$133$	2.45336	−	1.44063i	0.212734	−	0.124919i
$134$	2.28312			0.197231
$135$	0.173648	+	0.984808i	0.0149453	+	0.0847588i
$136$	5.58512	−	4.68647i	0.478920	−	0.401862i
$137$	−9.55690	+	3.47843i	−0.816501	+	0.297182i	−0.716307	−	0.697786i	$-0.754169\pi$
$137$	−9.55690	+	3.47843i	−0.816501	+	0.297182i	−0.100195	+	0.994968i	$0.531947\pi$
$138$	1.61334	+	0.587208i	0.137337	+	0.0499865i
$139$	−4.63429	−	3.88863i	−0.393075	−	0.329829i	0.424735	−	0.905318i	$-0.360367\pi$
$139$	−4.63429	−	3.88863i	−0.393075	−	0.329829i	−0.817810	+	0.575489i	$0.804812\pi$
$140$	−0.326352	+	0.565258i	−0.0275818	+	0.0477730i
$141$	−2.90033	−	5.02352i	−0.244252	−	0.423057i
$142$	0.741230	−	4.20372i	0.0622026	−	0.352768i
$143$	−0.826352	+	4.68647i	−0.0691030	+	0.391903i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−0.0812519	+	0.140732i	−0.00674760	+	0.0116872i
$146$	−8.73055	−	7.32580i	−0.722546	−	0.606288i
$147$	6.17752	+	2.24843i	0.509513	+	0.185448i
$148$	6.81180	−	2.47929i	0.559927	−	0.203797i
$149$	11.1643	−	9.36797i	0.914616	−	0.767454i	−0.0583753	−	0.998295i	$-0.518592\pi$
$149$	11.1643	−	9.36797i	0.914616	−	0.767454i	0.972992	+	0.230841i	$0.0741476\pi$
$150$	−0.173648	−	0.984808i	−0.0141783	−	0.0804092i
$151$	13.5449			1.10227			0.551133	−	0.834417i	$-0.314196\pi$
$151$	13.5449			1.10227			0.551133	+	0.834417i	$0.314196\pi$
$152$	−0.0320889	−	4.35878i	−0.00260275	−	0.353544i
$153$	−7.29086			−0.589431
$154$	−0.326352	−	1.85083i	−0.0262982	−	0.149144i
$155$	0.722811	−	0.606511i	0.0580576	−	0.0487161i
$156$	1.55303	−	0.565258i	0.124342	−	0.0452569i
$157$	20.6805	+	7.52709i	1.65048	+	0.600727i	0.988825	−	0.149078i	$-0.0476304\pi$
$157$	20.6805	+	7.52709i	1.65048	+	0.600727i	0.661659	+	0.749805i	$0.269853\pi$
$158$	3.73783	+	3.13641i	0.297365	+	0.249519i
$159$	5.28699	−	9.15733i	0.419285	−	0.726224i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	0.194593	−	1.10359i	0.0153361	−	0.0869751i
$162$	−0.173648	+	0.984808i	−0.0136431	+	0.0773738i
$163$	0.724155	+	1.25427i	0.0567202	+	0.0982423i	0.892991	−	0.450074i	$-0.148602\pi$
$163$	0.724155	+	1.25427i	0.0567202	+	0.0982423i	−0.836271	+	0.548316i	$0.815269\pi$
$164$	0.201867	−	0.349643i	0.0157631	−	0.0273026i
$165$	2.20574	+	1.85083i	0.171716	+	0.144087i
$166$	−4.03209	−	1.46756i	−0.312951	−	0.113905i
$167$	17.7690	−	6.46740i	1.37501	−	0.500462i	0.454348	−	0.890824i	$-0.349872\pi$
$167$	17.7690	−	6.46740i	1.37501	−	0.500462i	0.920662	+	0.390362i	$0.127650\pi$
$168$	−0.500000	+	0.419550i	−0.0385758	+	0.0323690i
$169$	−1.78312	−	10.1126i	−0.137163	−	0.777890i
$170$	7.29086			0.559183
$171$	−2.77719	+	3.35965i	−0.212377	+	0.256919i
$172$	−11.3550			−0.865813
$173$	−0.200522	−	1.13722i	−0.0152454	−	0.0864612i	0.976236	−	0.216711i	$-0.0695331\pi$
$173$	−0.200522	−	1.13722i	−0.0152454	−	0.0864612i	−0.991481	+	0.130250i	$0.958422\pi$
$174$	−0.124485	+	0.104455i	−0.00943719	+	0.00791875i
$175$	−0.613341	+	0.223238i	−0.0463642	+	0.0168752i
$176$	−2.70574	−	0.984808i	−0.203953	−	0.0742327i
$177$	−3.48886	−	2.92750i	−0.262238	−	0.220044i
$178$	1.24763	−	2.16095i	0.0935135	−	0.161970i
$179$	4.12836	+	7.15052i	0.308568	+	0.534455i	0.978049	−	0.208374i	$-0.0668170\pi$
$179$	4.12836	+	7.15052i	0.308568	+	0.534455i	−0.669482	+	0.742829i	$0.733484\pi$
$180$	0.173648	−	0.984808i	0.0129430	−	0.0734032i
$181$	0.370767	−	2.10272i	0.0275589	−	0.156294i	−0.967923	−	0.251248i	$-0.919159\pi$
$181$	0.370767	−	2.10272i	0.0275589	−	0.156294i	0.995482	+	0.0949534i	$0.0302702\pi$
$182$	−0.539363	−	0.934204i	−0.0399802	−	0.0692478i
$183$	−5.75150	+	9.96188i	−0.425163	+	0.736404i
$184$	−1.31521	−	1.10359i	−0.0969584	−	0.0813577i
$185$	6.81180	+	2.47929i	0.500814	+	0.182281i
$186$	0.886659	−	0.322718i	0.0650130	−	0.0236628i
$187$	−16.0817	+	13.4942i	−1.17601	+	0.986791i
$188$	1.00727	+	5.71253i	0.0734630	+	0.416629i
$189$	0.652704			0.0474772
$190$	2.77719	−	3.35965i	0.201478	−	0.243734i
$191$	−4.06418			−0.294074			−0.147037	−	0.989131i	$-0.546974\pi$
$191$	−4.06418			−0.294074			−0.147037	+	0.989131i	$0.546974\pi$
$192$	0.173648	+	0.984808i	0.0125320	+	0.0710724i
$193$	0.115400	−	0.0968323i	0.00830669	−	0.00697014i	−0.638625	−	0.769518i	$-0.720496\pi$
$193$	0.115400	−	0.0968323i	0.00830669	−	0.00697014i	0.646932	+	0.762548i	$0.276052\pi$
$194$	−13.1887	+	4.80028i	−0.946891	+	0.344640i
$195$	1.55303	+	0.565258i	0.111215	+	0.0404790i
$196$	−5.03596	−	4.22567i	−0.359711	−	0.301834i
$197$	−2.13563	+	3.69902i	−0.152157	+	0.263544i	−0.932020	−	0.362406i	$-0.881955\pi$
$197$	−2.13563	+	3.69902i	−0.152157	+	0.263544i	0.779863	+	0.625950i	$0.215289\pi$
$198$	1.43969	+	2.49362i	0.102314	+	0.177214i
$199$	0.222811	−	1.26363i	0.0157947	−	0.0895760i	−0.975891	−	0.218257i	$-0.929963\pi$
$199$	0.222811	−	1.26363i	0.0157947	−	0.0895760i	0.991686	+	0.128680i	$0.0410742\pi$
$200$	−0.173648	+	0.984808i	−0.0122788	+	0.0696364i
$201$	1.14156	+	1.97724i	0.0805194	+	0.139464i
$202$	−4.57785	+	7.92907i	−0.322096	+	0.557887i
$203$	0.0812519	+	0.0681784i	0.00570277	+	0.00478519i
$204$	6.85117	+	2.49362i	0.479678	+	0.174588i
$205$	0.379385	−	0.138085i	0.0264974	−	0.00964427i
$206$	12.7626	−	10.7091i	0.889215	−	0.746140i
$207$	0.298133	+	1.69080i	0.0207217	+	0.117519i
$208$	−1.65270			−0.114594
$209$	0.0923963	+	12.5506i	0.00639118	+	0.868144i
$210$	−0.652704			−0.0450408
$211$	1.17752	+	6.67804i	0.0810637	+	0.459735i	0.998137	+	0.0610160i	$0.0194341\pi$
$211$	1.17752	+	6.67804i	0.0810637	+	0.459735i	−0.917073	+	0.398719i	$0.869455\pi$
$212$	−8.10014	+	6.79682i	−0.556320	+	0.466808i
$213$	4.01114	−	1.45994i	0.274839	−	0.100033i
$214$	−7.24422	−	2.63668i	−0.495205	−	0.180240i
$215$	−8.69846	−	7.29888i	−0.593230	−	0.497779i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	−0.307934	−	0.533356i	−0.0209039	−	0.0362066i
$218$	−1.42514	+	8.08240i	−0.0965230	+	0.547409i
$219$	1.97906	−	11.2238i	0.133732	−	0.758433i
$220$	−1.43969	−	2.49362i	−0.0970641	−	0.168120i
$221$	−6.02481	+	10.4353i	−0.405273	+	0.701953i
$222$	5.55303	+	4.65955i	0.372695	+	0.312728i
$223$	26.5390	+	9.65939i	1.77718	+	0.646841i	0.999842	+	0.0177565i	$0.00565238\pi$
$223$	26.5390	+	9.65939i	1.77718	+	0.646841i	0.777337	+	0.629084i	$0.216570\pi$
$224$	0.613341	−	0.223238i	0.0409806	−	0.0149157i
$225$	0.766044	−	0.642788i	0.0510696	−	0.0428525i
$226$	−1.74422	−	9.89198i	−0.116024	−	0.658005i
$227$	−21.5645			−1.43128			−0.715642	−	0.698467i	$-0.753866\pi$
$227$	−21.5645			−1.43128			−0.715642	+	0.698467i	$0.753866\pi$
$228$	3.75877	−	2.20718i	0.248931	−	0.146174i
$229$	−11.1206			−0.734871			−0.367435	−	0.930049i	$-0.619764\pi$
$229$	−11.1206			−0.734871			−0.367435	+	0.930049i	$0.619764\pi$
$230$	−0.298133	−	1.69080i	−0.0196583	−	0.111488i
$231$	1.43969	−	1.20805i	0.0947248	−	0.0794836i
$232$	0.152704	−	0.0555796i	0.0100255	−	0.00364898i
$233$	−14.6604	−	5.33597i	−0.960438	−	0.349571i	−0.186233	−	0.982506i	$-0.559628\pi$
$233$	−14.6604	−	5.33597i	−0.960438	−	0.349571i	−0.774205	+	0.632935i	$0.781850\pi$
$234$	1.26604	+	1.06234i	0.0827639	+	0.0694472i
$235$	−2.90033	+	5.02352i	−0.189197	+	0.327698i
$236$	2.27719	+	3.94421i	0.148232	+	0.256746i
$237$	−0.847296	+	4.80526i	−0.0550378	+	0.312135i
$238$	0.826352	−	4.68647i	0.0535644	−	0.303779i
$239$	10.0064	+	17.3316i	0.647260	+	1.12109i	0.983775	+	0.179409i	$0.0574185\pi$
$239$	10.0064	+	17.3316i	0.647260	+	1.12109i	−0.336515	+	0.941678i	$0.609248\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	−21.5535	−	18.0855i	−1.38838	−	1.16499i	−0.965990	−	0.258579i	$-0.916746\pi$
$241$	−21.5535	−	18.0855i	−1.38838	−	1.16499i	−0.422393	−	0.906413i	$-0.638810\pi$
$242$	−2.54576	−	0.926581i	−0.163648	−	0.0595629i
$243$	−0.939693	+	0.342020i	−0.0602813	+	0.0219406i
$244$	8.81180	−	7.39398i	0.564118	−	0.473351i
$245$	−1.14156	−	6.47410i	−0.0729315	−	0.413615i
$246$	0.403733			0.0257411
$247$	2.51367	+	6.75119i	0.159941	+	0.429568i
$248$	−0.943563			−0.0599163
$249$	−0.745100	−	4.22567i	−0.0472188	−	0.267791i
$250$	−0.766044	+	0.642788i	−0.0484489	+	0.0406535i
$251$	−24.1250	+	8.78076i	−1.52275	+	0.554237i	−0.961834	−	0.273633i	$-0.911774\pi$
$251$	−24.1250	+	8.78076i	−1.52275	+	0.554237i	−0.560919	+	0.827870i	$0.689552\pi$
$252$	−0.613341	−	0.223238i	−0.0386368	−	0.0140627i
$253$	3.78699	+	3.17766i	0.238086	+	0.199778i
$254$	1.64543	−	2.84997i	0.103243	−	0.178823i
$255$	3.64543	+	6.31407i	0.228286	+	0.395402i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	4.07011	−	23.0827i	0.253886	−	1.43986i	−0.545029	−	0.838417i	$-0.683481\pi$
$257$	4.07011	−	23.0827i	0.253886	−	1.43986i	0.798915	−	0.601444i	$-0.205408\pi$
$258$	−5.67752	−	9.83375i	−0.353467	−	0.612223i
$259$	2.36571	−	4.09754i	0.146998	−	0.254609i
$260$	−1.26604	−	1.06234i	−0.0785167	−	0.0658834i
$261$	−0.152704	−	0.0555796i	−0.00945212	−	0.00344029i
$262$	6.41147	−	2.33359i	0.396102	−	0.144169i
$263$	−15.2613	+	12.8057i	−0.941052	+	0.789636i	−0.977768	−	0.209689i	$-0.932755\pi$
$263$	−15.2613	+	12.8057i	−0.941052	+	0.789636i	0.0367162	+	0.999326i	$0.488310\pi$
$264$	−0.500000	−	2.83564i	−0.0307729	−	0.174522i
$265$	−10.5740			−0.649554
$266$	−1.84477	−	2.16593i	−0.113110	−	0.132802i
$267$	2.49525			0.152707
$268$	−0.396459	−	2.24843i	−0.0242176	−	0.137345i
$269$	−11.8216	+	9.91950i	−0.720776	+	0.604803i	−0.927600	−	0.373575i	$-0.878132\pi$
$269$	−11.8216	+	9.91950i	−0.720776	+	0.604803i	0.206824	+	0.978378i	$0.433687\pi$
$270$	0.939693	−	0.342020i	0.0571879	−	0.0208147i
$271$	21.1951	+	7.71437i	1.28751	+	0.468615i	0.892908	−	0.450238i	$-0.148661\pi$
$271$	21.1951	+	7.71437i	1.28751	+	0.468615i	0.394600	+	0.918853i	$0.370883\pi$
$272$	−5.58512	−	4.68647i	−0.338648	−	0.284159i
$273$	0.539363	−	0.934204i	0.0326437	−	0.0565406i
$274$	5.08512	+	8.80769i	0.307203	+	0.532092i
$275$	0.500000	−	2.83564i	0.0301511	−	0.170996i
$276$	0.298133	−	1.69080i	0.0179455	−	0.101774i
$277$	−9.38713	−	16.2590i	−0.564018	−	0.976907i	−0.997140	−	0.0755724i	$-0.975922\pi$
$277$	−9.38713	−	16.2590i	−0.564018	−	0.976907i	0.433123	−	0.901335i	$-0.357412\pi$
$278$	−3.02481	+	5.23913i	−0.181416	+	0.314222i
$279$	0.722811	+	0.606511i	0.0432736	+	0.0363108i
$280$	0.613341	+	0.223238i	0.0366541	+	0.0133410i
$281$	−15.9338	+	5.79942i	−0.950529	+	0.345964i	−0.770315	−	0.637663i	$-0.779901\pi$
$281$	−15.9338	+	5.79942i	−0.950529	+	0.345964i	−0.180213	+	0.983628i	$0.557679\pi$
$282$	−4.44356	+	3.72859i	−0.264610	+	0.222034i
$283$	2.87299	+	16.2935i	0.170781	+	0.968550i	0.942901	+	0.333073i	$0.108085\pi$
$283$	2.87299	+	16.2935i	0.170781	+	0.968550i	−0.772120	+	0.635477i	$0.780803\pi$
$284$	−4.26857			−0.253293
$285$	4.29813	+	0.725293i	0.254599	+	0.0429626i
$286$	4.75877			0.281392
$287$	−0.0457595	−	0.259515i	−0.00270110	−	0.0153187i
$288$	−0.766044	+	0.642788i	−0.0451396	+	0.0378766i
$289$	−33.9761	+	12.3663i	−1.99860	+	0.727429i
$290$	0.152704	+	0.0555796i	0.00896707	+	0.00326375i
$291$	−10.7515	−	9.02158i	−0.630264	−	0.528854i
$292$	−5.69846	+	9.87003i	−0.333477	+	0.577600i
$293$	−9.04576	−	15.6677i	−0.528459	−	0.915318i	−0.999449	−	0.0331794i	$-0.989437\pi$
$293$	−9.04576	−	15.6677i	−0.528459	−	0.915318i	0.470991	−	0.882138i	$-0.343897\pi$
$294$	1.14156	−	6.47410i	0.0665771	−	0.377577i
$295$	−0.790859	+	4.48519i	−0.0460456	+	0.261138i
$296$	−3.62449	−	6.27779i	−0.210669	−	0.364889i
$297$	−1.43969	+	2.49362i	−0.0835394	+	0.144695i
$298$	−11.1643	−	9.36797i	−0.646731	−	0.542672i
$299$	2.66637	+	0.970481i	0.154200	+	0.0561244i
$300$	−0.939693	+	0.342020i	−0.0542532	+	0.0197465i
$301$	−5.67752	+	4.76400i	−0.327247	+	0.274593i
$302$	−2.35204	−	13.3391i	−0.135345	−	0.767579i
$303$	−9.15570			−0.525981
$304$	−4.28699	+	0.788496i	−0.245876	+	0.0452233i
$305$	11.5030			0.658659
$306$	1.26604	+	7.18009i	0.0723749	+	0.410459i
$307$	13.9704	−	11.7226i	0.797335	−	0.669043i	−0.150214	−	0.988653i	$-0.547996\pi$
$307$	13.9704	−	11.7226i	0.797335	−	0.669043i	0.947549	+	0.319610i	$0.103552\pi$
$308$	−1.76604	+	0.642788i	−0.100630	+	0.0366262i
$309$	15.6557	+	5.69821i	0.890621	+	0.324160i
$310$	−0.722811	−	0.606511i	−0.0410529	−	0.0344475i
$311$	−11.2738	+	19.5268i	−0.639278	+	1.10726i	0.346314	+	0.938119i	$0.387433\pi$
$311$	−11.2738	+	19.5268i	−0.639278	+	1.10726i	−0.985592	+	0.169143i	$0.945900\pi$
$312$	−0.826352	−	1.43128i	−0.0467830	−	0.0810305i
$313$	4.28224	−	24.2858i	0.242047	−	1.37271i	−0.585206	−	0.810885i	$-0.698986\pi$
$313$	4.28224	−	24.2858i	0.242047	−	1.37271i	0.827253	−	0.561830i	$-0.189902\pi$
$314$	3.82160	−	21.6734i	0.215666	−	1.22310i
$315$	−0.326352	−	0.565258i	−0.0183878	−	0.0318487i
$316$	2.43969	−	4.22567i	0.137243	−	0.237713i
$317$	12.4855	+	10.4765i	0.701253	+	0.588421i	0.922130	−	0.386881i	$-0.126447\pi$
$317$	12.4855	+	10.4765i	0.701253	+	0.588421i	−0.220877	+	0.975302i	$0.570892\pi$
$318$	−9.93629	−	3.61651i	−0.557199	−	0.202804i
$319$	−0.439693	+	0.160035i	−0.0246181	+	0.00896024i
$320$	0.766044	−	0.642788i	0.0428232	−	0.0359329i
$321$	−1.33868	−	7.59202i	−0.0747177	−	0.423745i
$322$	−1.12061			−0.0624494
$323$	−10.6493	+	29.9428i	−0.592543	+	1.66606i
$324$	1.00000			0.0555556
$325$	−0.286989	−	1.62760i	−0.0159193	−	0.0902827i
$326$	1.10947	−	0.930956i	0.0614479	−	0.0515609i
$327$	−7.71213	+	2.80699i	−0.426482	+	0.155227i
$328$	−0.379385	−	0.138085i	−0.0209480	−	0.00762447i
$329$	2.90033	+	2.43367i	0.159900	+	0.134172i
$330$	1.43969	−	2.49362i	0.0792525	−	0.137269i
$331$	−3.21941	−	5.57618i	−0.176955	−	0.306494i	0.763881	−	0.645357i	$-0.223291\pi$
$331$	−3.21941	−	5.57618i	−0.176955	−	0.306494i	−0.940836	+	0.338862i	$0.889958\pi$
$332$	−0.745100	+	4.22567i	−0.0408927	+	0.231914i
$333$	−1.25877	+	7.13884i	−0.0689802	+	0.391206i
$334$	−9.45471	−	16.3760i	−0.517339	−	0.896057i
$335$	1.14156	−	1.97724i	0.0623700	−	0.108028i
$336$	0.500000	+	0.419550i	0.0272772	+	0.0228883i
$337$	18.5767	+	6.76135i	1.01194	+	0.368314i	0.794176	−	0.607688i	$-0.207903\pi$
$337$	18.5767	+	6.76135i	1.01194	+	0.368314i	0.217760	+	0.976002i	$0.430125\pi$
$338$	−9.64930	+	3.51206i	−0.524853	+	0.191031i
$339$	7.69459	−	6.45653i	0.417913	−	0.350671i
$340$	−1.26604	−	7.18009i	−0.0686609	−	0.389395i
$341$	2.71688			0.147127
$342$	3.79086	+	2.15160i	0.204986	+	0.116345i
$343$	−8.85978			−0.478383
$344$	1.97178	+	11.1825i	0.106311	+	0.602922i
$345$	1.31521	−	1.10359i	0.0708084	−	0.0594153i
$346$	−1.08512	+	0.394952i	−0.0583365	+	0.0212328i
$347$	−27.4722	−	9.99908i	−1.47479	−	0.536779i	−0.525392	−	0.850861i	$-0.676081\pi$
$347$	−27.4722	−	9.99908i	−1.47479	−	0.536779i	−0.949396	+	0.314082i	$0.898303\pi$
$348$	0.124485	+	0.104455i	0.00667310	+	0.00559940i
$349$	8.26264	−	14.3113i	0.442289	−	0.766067i	−0.555570	−	0.831470i	$-0.687500\pi$
$349$	8.26264	−	14.3113i	0.442289	−	0.766067i	0.997859	+	0.0654028i	$0.0208332\pi$
$350$	0.326352	+	0.565258i	0.0174442	+	0.0302143i
$351$	−0.286989	+	1.62760i	−0.0153183	+	0.0868746i
$352$	−0.500000	+	2.83564i	−0.0266501	+	0.151140i
$353$	−2.38413	−	4.12944i	−0.126895	−	0.219788i	0.795577	−	0.605852i	$-0.207168\pi$
$353$	−2.38413	−	4.12944i	−0.126895	−	0.219788i	−0.922472	+	0.386064i	$0.873834\pi$
$354$	−2.27719	+	3.94421i	−0.121031	+	0.209632i
$355$	−3.26991	−	2.74378i	−0.173549	−	0.145625i
$356$	−2.34477	−	0.853427i	−0.124273	−	0.0452315i
$357$	4.47178	−	1.62760i	0.236672	−	0.0861415i
$358$	6.32501	−	5.30731i	0.334287	−	0.280500i
$359$	−5.80423	−	32.9174i	−0.306335	−	1.73731i	−0.617152	−	0.786844i	$-0.711714\pi$
$359$	−5.80423	−	32.9174i	−0.306335	−	1.73731i	0.310817	−	0.950470i	$-0.399397\pi$
$360$	−1.00000			−0.0527046
$361$	9.74123	+	16.3128i	0.512696	+	0.858570i
$362$	−2.13516			−0.112222
$363$	−0.470437	−	2.66798i	−0.0246916	−	0.140033i
$364$	−0.826352	+	0.693392i	−0.0433126	+	0.0363436i
$365$	−10.7096	+	3.89798i	−0.560566	+	0.204030i
$366$	10.8093	+	3.93426i	0.565010	+	0.205647i
$367$	4.23577	+	3.55423i	0.221105	+	0.185529i	0.746611	−	0.665261i	$-0.231680\pi$
$367$	4.23577	+	3.55423i	0.221105	+	0.185529i	−0.525506	+	0.850790i	$0.676124\pi$
$368$	−0.858441	+	1.48686i	−0.0447493	+	0.0775081i
$369$	0.201867	+	0.349643i	0.0105088	+	0.0182017i
$370$	1.25877	−	7.13884i	0.0654404	−	0.371131i
$371$	−1.19846	+	6.79682i	−0.0622211	+	0.352873i
$372$	−0.471782	−	0.817150i	−0.0244607	−	0.0423672i
$373$	−6.22462	+	10.7814i	−0.322299	+	0.558238i	−0.980962	−	0.194200i	$-0.937789\pi$
$373$	−6.22462	+	10.7814i	−0.322299	+	0.558238i	0.658663	+	0.752438i	$0.271122\pi$
$374$	16.0817	+	13.4942i	0.831566	+	0.697767i
$375$	−0.939693	−	0.342020i	−0.0485255	−	0.0176618i
$376$	5.45084	−	1.98394i	0.281105	−	0.102314i
$377$	−0.205737	+	0.172634i	−0.0105960	+	0.00889110i
$378$	−0.113341	−	0.642788i	−0.00582962	−	0.0330614i
$379$	13.2098			0.678540			0.339270	−	0.940689i	$-0.389820\pi$
$379$	13.2098			0.678540			0.339270	+	0.940689i	$0.389820\pi$
$380$	−3.79086	−	2.15160i	−0.194467	−	0.110375i
$381$	3.29086			0.168596
$382$	0.705737	+	4.00243i	0.0361086	+	0.204782i
$383$	−20.7310	+	17.3954i	−1.05931	+	0.888863i	−0.994041	−	0.109005i	$-0.965234\pi$
$383$	−20.7310	+	17.3954i	−1.05931	+	0.888863i	−0.0652644	+	0.997868i	$0.520789\pi$
$384$	0.939693	−	0.342020i	0.0479535	−	0.0174536i
$385$	−1.76604	−	0.642788i	−0.0900060	−	0.0327595i
$386$	−0.115400	−	0.0968323i	−0.00587372	−	0.00492863i
$387$	5.67752	−	9.83375i	0.288604	−	0.499878i
$388$	7.01754	+	12.1547i	0.356262	+	0.617063i
$389$	2.58424	−	14.6560i	0.131026	−	0.743088i	−0.846518	−	0.532360i	$-0.821305\pi$
$389$	2.58424	−	14.6560i	0.131026	−	0.743088i	0.977545	−	0.210728i	$-0.0675835\pi$
$390$	0.286989	−	1.62760i	0.0145323	−	0.0824165i
$391$	6.25877	+	10.8405i	0.316520	+	0.548228i
$392$	−3.28699	+	5.69323i	−0.166018	+	0.287552i
$393$	5.22668	+	4.38571i	0.263651	+	0.221230i
$394$	4.01367	+	1.46086i	0.202206	+	0.0735969i
$395$	4.58512	−	1.66885i	0.230703	−	0.0839689i
$396$	2.20574	−	1.85083i	0.110842	−	0.0930079i
$397$	−4.13041	−	23.4247i	−0.207300	−	1.17565i	−0.893780	−	0.448506i	$-0.851956\pi$
$397$	−4.13041	−	23.4247i	−0.207300	−	1.17565i	0.686480	−	0.727148i	$-0.259155\pi$
$398$	−1.28312			−0.0643169
$399$	0.953363	−	2.68058i	0.0477279	−	0.134197i
$400$	1.00000			0.0500000
$401$	0.159978	+	0.907278i	0.00798890	+	0.0453073i	0.988542	−	0.150949i	$-0.0482328\pi$
$401$	0.159978	+	0.907278i	0.00798890	+	0.0453073i	−0.980553	+	0.196256i	$0.937122\pi$
$402$	1.74897	−	1.46756i	0.0872307	−	0.0731953i
$403$	1.46538	−	0.533356i	0.0729960	−	0.0265684i
$404$	8.60354	+	3.13143i	0.428042	+	0.155795i
$405$	0.766044	+	0.642788i	0.0380651	+	0.0319404i
$406$	0.0530334	−	0.0918566i	0.00263200	−	0.00455877i
$407$	10.4363	+	18.0762i	0.517308	+	0.896003i
$408$	1.26604	−	7.18009i	0.0626785	−	0.355468i
$409$	−1.79339	+	10.1708i	−0.0886772	+	0.502913i	0.907825	+	0.419349i	$0.137742\pi$
$409$	−1.79339	+	10.1708i	−0.0886772	+	0.502913i	−0.996502	+	0.0835646i	$0.973370\pi$
$410$	−0.201867	−	0.349643i	−0.00996948	−	0.0172677i
$411$	−5.08512	+	8.80769i	−0.250831	+	0.434451i
$412$	−12.7626	−	10.7091i	−0.628770	−	0.527601i
$413$	2.79339	+	1.01671i	0.137454	+	0.0500290i
$414$	1.61334	−	0.587208i	0.0792914	−	0.0288597i
$415$	−3.28699	+	2.75811i	−0.161352	+	0.135390i
$416$	0.286989	+	1.62760i	0.0140708	+	0.0797994i
$417$	−6.04963			−0.296252
$418$	12.3439	−	2.27038i	0.603760	−	0.111048i
$419$	−0.568926			−0.0277938			−0.0138969	−	0.999903i	$-0.504424\pi$
$419$	−0.568926			−0.0277938			−0.0138969	+	0.999903i	$0.504424\pi$
$420$	0.113341	+	0.642788i	0.00553046	+	0.0313648i
$421$	−9.80381	+	8.22638i	−0.477809	+	0.400929i	−0.849633	−	0.527374i	$-0.823177\pi$
$421$	−9.80381	+	8.22638i	−0.477809	+	0.400929i	0.371825	+	0.928303i	$0.378732\pi$
$422$	6.37211	−	2.31926i	0.310190	−	0.112900i
$423$	−5.45084	−	1.98394i	−0.265029	−	0.0964626i
$424$	8.10014	+	6.79682i	0.393377	+	0.330083i
$425$	3.64543	−	6.31407i	0.176829	−	0.306277i
$426$	−2.13429	−	3.69669i	−0.103406	−	0.179105i
$427$	1.30376	−	7.39398i	0.0630933	−	0.357820i
$428$	−1.33868	+	7.59202i	−0.0647075	+	0.366974i
$429$	2.37939	+	4.12122i	0.114878	+	0.198974i
$430$	−5.67752	+	9.83375i	−0.273794	+	0.474226i
$431$	20.7324	+	17.3965i	0.998643	+	0.837961i	0.986796	−	0.161969i	$-0.0517845\pi$
$431$	20.7324	+	17.3965i	0.998643	+	0.837961i	0.0118469	+	0.999930i	$0.496229\pi$
$432$	−0.939693	−	0.342020i	−0.0452110	−	0.0164555i
$433$	23.8704	−	8.68810i	1.14714	−	0.417523i	0.302650	−	0.953102i	$-0.402129\pi$
$433$	23.8704	−	8.68810i	1.14714	−	0.417523i	0.844486	+	0.535578i	$0.179906\pi$
$434$	−0.471782	+	0.395872i	−0.0226462	+	0.0190024i
$435$	0.0282185	+	0.160035i	0.00135297	+	0.00767309i
$436$	8.20708			0.393048
$437$	7.37939	+	1.24524i	0.353004	+	0.0595680i
$438$	−11.3969			−0.544566
$439$	2.28880	+	12.9804i	0.109238	+	0.619522i	0.989442	+	0.144927i	$0.0462946\pi$
$439$	2.28880	+	12.9804i	0.109238	+	0.619522i	−0.880204	+	0.474596i	$0.842594\pi$
$440$	−2.20574	+	1.85083i	−0.105154	+	0.0882350i
$441$	6.17752	−	2.24843i	0.294168	−	0.107068i
$442$	11.3229	+	4.12122i	0.538578	+	0.196026i
$443$	−21.2049	−	17.7930i	−1.00747	−	0.845370i	−0.0194711	−	0.999810i	$-0.506198\pi$
$443$	−21.2049	−	17.7930i	−1.00747	−	0.845370i	−0.988002	+	0.154440i	$0.950643\pi$
$444$	3.62449	−	6.27779i	0.172010	−	0.297931i
$445$	−1.24763	−	2.16095i	−0.0591432	−	0.102439i
$446$	4.90420	−	27.8131i	0.232221	−	1.31699i
$447$	2.53074	−	14.3526i	0.119700	−	0.678853i
$448$	−0.326352	−	0.565258i	−0.0154187	−	0.0267059i
$449$	9.91013	−	17.1648i	0.467688	−	0.810059i	−0.531630	−	0.846976i	$-0.678420\pi$
$449$	9.91013	−	17.1648i	0.467688	−	0.810059i	0.999318	+	0.0369172i	$0.0117538\pi$
$450$	−0.766044	−	0.642788i	−0.0361117	−	0.0303013i
$451$	1.09240	+	0.397600i	0.0514389	+	0.0187222i
$452$	−9.43882	+	3.43545i	−0.443965	+	0.161590i
$453$	10.3760	−	8.70648i	0.487506	−	0.409066i
$454$	3.74463	+	21.2369i	0.175744	+	0.996696i
$455$	−1.07873			−0.0505714
$456$	−2.82635	−	3.31839i	−0.132356	−	0.155398i
$457$	7.76651			0.363302			0.181651	−	0.983363i	$-0.441856\pi$
$457$	7.76651			0.363302			0.181651	+	0.983363i	$0.441856\pi$
$458$	1.93107	+	10.9517i	0.0902332	+	0.511738i
$459$	−5.58512	+	4.68647i	−0.260691	+	0.218746i
$460$	−1.61334	+	0.587208i	−0.0752224	+	0.0273787i
$461$	25.4770	+	9.27287i	1.18658	+	0.431881i	0.858522	−	0.512776i	$-0.171383\pi$
$461$	25.4770	+	9.27287i	1.18658	+	0.431881i	0.328060	+	0.944657i	$0.393605\pi$
$462$	−1.43969	−	1.20805i	−0.0669806	−	0.0562034i
$463$	5.27197	−	9.13133i	0.245009	−	0.424369i	−0.717125	−	0.696945i	$-0.754542\pi$
$463$	5.27197	−	9.13133i	0.245009	−	0.424369i	0.962134	+	0.272576i	$0.0878756\pi$
$464$	−0.0812519	−	0.140732i	−0.00377203	−	0.00653334i
$465$	0.163848	−	0.929228i	0.00759827	−	0.0430919i
$466$	−2.70914	+	15.3643i	−0.125499	+	0.711737i
$467$	−1.79426	−	3.10775i	−0.0830286	−	0.143810i	0.821521	−	0.570178i	$-0.193126\pi$
$467$	−1.79426	−	3.10775i	−0.0830286	−	0.143810i	−0.904549	+	0.426369i	$0.859793\pi$
$468$	0.826352	−	1.43128i	0.0381981	−	0.0661611i
$469$	−1.14156	−	0.957882i	−0.0527123	−	0.0442309i
$470$	5.45084	+	1.98394i	0.251428	+	0.0915124i
$471$	20.6805	−	7.52709i	0.952908	−	0.346830i
$472$	3.48886	−	2.92750i	0.160588	−	0.134749i
$473$	−5.67752	−	32.1988i	−0.261053	−	1.48050i
$474$	4.87939			0.224118
$475$	−1.52094	−	4.08494i	−0.0697857	−	0.187430i
$476$	−4.75877			−0.218118
$477$	−1.83615	−	10.4133i	−0.0840716	−	0.476794i
$478$	15.3307	−	12.8640i	0.701209	−	0.588385i
$479$	1.07650	−	0.391815i	0.0491867	−	0.0179025i	−0.317310	−	0.948322i	$-0.602779\pi$
$479$	1.07650	−	0.391815i	0.0491867	−	0.0179025i	0.366496	+	0.930419i	$0.380557\pi$
$480$	0.939693	+	0.342020i	0.0428909	+	0.0156110i
$481$	9.17752	+	7.70085i	0.418459	+	0.351129i
$482$	−14.0680	+	24.3666i	−0.640782	+	1.10987i
$483$	−0.560307	−	0.970481i	−0.0254949	−	0.0441584i
$484$	−0.470437	+	2.66798i	−0.0213835	+	0.121272i
$485$	−2.43717	+	13.8219i	−0.110666	+	0.627618i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−1.81773	+	3.14841i	−0.0823694	+	0.142668i	−0.904267	−	0.426967i	$-0.859582\pi$
$487$	−1.81773	+	3.14841i	−0.0823694	+	0.142668i	0.821898	+	0.569635i	$0.192915\pi$
$488$	−8.81180	−	7.39398i	−0.398892	−	0.334710i
$489$	1.36097	+	0.495351i	0.0615451	+	0.0224006i
$490$	−6.17752	+	2.24843i	−0.279072	+	0.101574i
$491$	8.26193	−	6.93258i	0.372855	−	0.312863i	−0.437034	−	0.899445i	$-0.643971\pi$
$491$	8.26193	−	6.93258i	0.372855	−	0.312863i	0.809890	+	0.586582i	$0.199527\pi$
$492$	−0.0701076	−	0.397600i	−0.00316069	−	0.0179252i
$493$	−1.18479			−0.0533604
$494$	6.21213	−	3.64781i	0.279497	−	0.164123i
$495$	2.87939			0.129419
$496$	0.163848	+	0.929228i	0.00735699	+	0.0417236i
$497$	−2.13429	+	1.79088i	−0.0957358	+	0.0803319i
$498$	−4.03209	+	1.46756i	−0.180682	+	0.0657630i
$499$	7.66860	+	2.79114i	0.343293	+	0.124949i	0.507913	−	0.861409i	$-0.330417\pi$
$499$	7.66860	+	2.79114i	0.343293	+	0.124949i	−0.164619	+	0.986357i	$0.552639\pi$
$500$	0.766044	+	0.642788i	0.0342585	+	0.0287463i
$501$	9.45471	−	16.3760i	0.422405	−	0.731627i
$502$	12.8366	+	22.2337i	0.572926	+	0.992338i
$503$	5.01872	−	28.4626i	0.223774	−	1.26908i	−0.641242	−	0.767339i	$-0.721580\pi$
$503$	5.01872	−	28.4626i	0.223774	−	1.26908i	0.865015	−	0.501745i	$-0.167309\pi$
$504$	−0.113341	+	0.642788i	−0.00504860	+	0.0286320i
$505$	4.57785	+	7.92907i	0.203712	+	0.352839i
$506$	2.47178	−	4.28125i	0.109884	−	0.190325i
$507$	−7.86618	−	6.60051i	−0.349349	−	0.293139i
$508$	−3.09240	−	1.12554i	−0.137203	−	0.0499378i
$509$	−13.5963	+	4.94864i	−0.602644	+	0.219344i	−0.625281	−	0.780399i	$-0.715016\pi$
$509$	−13.5963	+	4.94864i	−0.602644	+	0.219344i	0.0226376	+	0.999744i	$0.492794\pi$
$510$	5.58512	−	4.68647i	0.247313	−	0.207521i
$511$	1.29174	+	7.32580i	0.0571431	+	0.324074i
$512$	−1.00000			−0.0441942
$513$	0.0320889	+	4.35878i	0.00141676	+	0.192445i
$514$	−23.4388			−1.03384
$515$	−2.89306	−	16.4073i	−0.127483	−	0.722994i
$516$	−8.69846	+	7.29888i	−0.382928	+	0.321315i
$517$	−15.6951	+	5.71253i	−0.690268	+	0.251237i
$518$	−4.44609	−	1.61824i	−0.195350	−	0.0711016i
$519$	−0.884600	−	0.742267i	−0.0388296	−	0.0325819i
$520$	−0.826352	+	1.43128i	−0.0362379	+	0.0627659i
$521$	14.3675	+	24.8853i	0.629453	+	1.09024i	0.987662	+	0.156603i	$0.0500542\pi$
$521$	14.3675	+	24.8853i	0.629453	+	1.09024i	−0.358209	+	0.933641i	$0.616612\pi$
$522$	−0.0282185	+	0.160035i	−0.00123509	+	0.00700454i
$523$	0.677519	−	3.84240i	0.0296258	−	0.168016i	−0.966405	−	0.257023i	$-0.917258\pi$
$523$	0.677519	−	3.84240i	0.0296258	−	0.168016i	0.996031	+	0.0890070i	$0.0283694\pi$
$524$	−3.41147	−	5.90885i	−0.149031	−	0.258129i
$525$	−0.326352	+	0.565258i	−0.0142432	+	0.0246699i
$526$	15.2613	+	12.8057i	0.665424	+	0.558357i
$527$	6.46451	+	2.35289i	0.281598	+	0.102493i
$528$	−2.70574	+	0.984808i	−0.117752	+	0.0428583i
$529$	−15.3610	+	12.8894i	−0.667868	+	0.560408i
$530$	1.83615	+	10.4133i	0.0797573	+	0.452326i
$531$	−4.55438			−0.197643
$532$	−1.81268	+	2.19285i	−0.0785897	+	0.0950722i
$533$	0.667252			0.0289019
$534$	−0.433296	−	2.45734i	−0.0187506	−	0.106340i
$535$	−5.90554	+	4.95534i	−0.255319	+	0.214238i
$536$	−2.14543	+	0.780873i	−0.0926684	+	0.0337286i
$537$	7.75877	+	2.82396i	0.334816	+	0.121863i
$538$	11.8216	+	9.91950i	0.509666	+	0.427660i
$539$	9.46451	−	16.3930i	0.407665	−	0.706097i
$540$	−0.500000	−	0.866025i	−0.0215166	−	0.0372678i
$541$	2.26635	−	12.8531i	0.0974380	−	0.552598i	−0.896535	−	0.442973i	$-0.853924\pi$
$541$	2.26635	−	12.8531i	0.0974380	−	0.552598i	0.993973	−	0.109625i	$-0.0349651\pi$
$542$	3.91669	−	22.2126i	0.168236	−	0.954115i
$543$	−1.06758	−	1.84911i	−0.0458143	−	0.0793527i
$544$	−3.64543	+	6.31407i	−0.156297	+	0.270713i
$545$	6.28699	+	5.27541i	0.269305	+	0.225974i
$546$	−1.01367	−	0.368946i	−0.0433811	−	0.0157894i
$547$	34.1724	−	12.4377i	1.46110	−	0.531799i	0.515435	−	0.856929i	$-0.327630\pi$
$547$	34.1724	−	12.4377i	1.46110	−	0.531799i	0.945669	+	0.325130i	$0.105408\pi$
$548$	7.79086	−	6.53731i	0.332809	−	0.279260i
$549$	1.99747	+	11.3282i	0.0852501	+	0.483477i
$550$	−2.87939			−0.122777
$551$	−0.451304	+	0.545955i	−0.0192262	+	0.0232585i
$552$	−1.71688			−0.0730753
$553$	−0.553033	−	3.13641i	−0.0235174	−	0.133374i
$554$	−14.3819	+	12.0679i	−0.611029	+	0.512714i
$555$	6.81180	−	2.47929i	0.289145	−	0.105240i
$556$	5.68479	+	2.06910i	0.241089	+	0.0877492i
$557$	−1.76083	−	1.47751i	−0.0746088	−	0.0626042i	0.604721	−	0.796438i	$-0.293285\pi$
$557$	−1.76083	−	1.47751i	−0.0746088	−	0.0626042i	−0.679329	+	0.733834i	$0.737729\pi$
$558$	0.471782	−	0.817150i	0.0199721	−	0.0345927i
$559$	−9.38326	−	16.2523i	−0.396869	−	0.687398i
$560$	0.113341	−	0.642788i	0.00478952	−	0.0271627i
$561$	−3.64543	+	20.6743i	−0.153910	+	0.872868i
$562$	8.47818	+	14.6846i	0.357630	+	0.619434i
$563$	12.4508	−	21.5655i	0.524740	−	0.908877i	−0.474845	−	0.880070i	$-0.657496\pi$
$563$	12.4508	−	21.5655i	0.524740	−	0.908877i	0.999585	−	0.0288071i	$-0.00917087\pi$
$564$	4.44356	+	3.72859i	0.187108	+	0.157002i
$565$	−9.43882	−	3.43545i	−0.397094	−	0.144530i
$566$	15.5471	−	5.65868i	0.653494	−	0.237852i
$567$	0.500000	−	0.419550i	0.0209980	−	0.0176194i
$568$	0.741230	+	4.20372i	0.0311013	+	0.176384i
$569$	6.07461			0.254661			0.127330	−	0.991860i	$-0.459359\pi$
$569$	6.07461			0.254661			0.127330	+	0.991860i	$0.459359\pi$
$570$	−0.0320889	−	4.35878i	−0.00134406	−	0.182569i
$571$	17.8557			0.747236			0.373618	−	0.927583i	$-0.378117\pi$
$571$	17.8557			0.747236			0.373618	+	0.927583i	$0.378117\pi$
$572$	−0.826352	−	4.68647i	−0.0345515	−	0.195951i
$573$	−3.11334	+	2.61240i	−0.130062	+	0.109135i
$574$	−0.247626	+	0.0901285i	−0.0103357	+	0.00376189i
$575$	−1.61334	−	0.587208i	−0.0672810	−	0.0244883i
$576$	0.766044	+	0.642788i	0.0319185	+	0.0267828i
$577$	2.57991	−	4.46853i	0.107403	−	0.186027i	−0.807314	−	0.590121i	$-0.799080\pi$
$577$	2.57991	−	4.46853i	0.107403	−	0.186027i	0.914717	+	0.404094i	$0.132413\pi$
$578$	18.0783	+	31.3126i	0.751959	+	1.30243i
$579$	0.0261591	−	0.148356i	0.00108714	−	0.00616545i
$580$	0.0282185	−	0.160035i	0.00117171	−	0.00664509i
$581$	1.40033	+	2.42544i	0.0580955	+	0.100624i
$582$	−7.01754	+	12.1547i	−0.290886	+	0.503830i
$583$	−23.3234	−	19.5707i	−0.965957	−	0.810534i
$584$	10.7096	+	3.89798i	0.443167	+	0.161299i
$585$	1.55303	−	0.565258i	0.0642100	−	0.0233705i
$586$	−13.8589	+	11.6290i	−0.572506	+	0.480390i
$587$	2.52915	+	14.3435i	0.104389	+	0.592021i	0.991462	+	0.130392i	$0.0416237\pi$
$587$	2.52915	+	14.3435i	0.104389	+	0.592021i	−0.887073	+	0.461629i	$0.847265\pi$
$588$	−6.57398			−0.271106
$589$	3.54664	−	2.08261i	0.146137	−	0.0858126i
$590$	4.55438			0.187501
$591$	0.741696	+	4.20637i	0.0305093	+	0.173027i
$592$	−5.55303	+	4.65955i	−0.228228	+	0.191506i
$593$	−42.0771	+	15.3148i	−1.72790	+	0.628904i	−0.998478	−	0.0551583i	$-0.982434\pi$
$593$	−42.0771	+	15.3148i	−1.72790	+	0.628904i	−0.729423	+	0.684063i	$0.760211\pi$
$594$	2.70574	+	0.984808i	0.111018	+	0.0404072i
$595$	−3.64543	−	3.05888i	−0.149448	−	0.125402i
$596$	−7.28699	+	12.6214i	−0.298487	+	0.516994i
$597$	−0.641559	−	1.11121i	−0.0262573	−	0.0454789i
$598$	0.492726	−	2.79439i	0.0201491	−	0.114271i
$599$	0.801947	−	4.54807i	0.0327667	−	0.185829i	−0.964031	−	0.265788i	$-0.914368\pi$
$599$	0.801947	−	4.54807i	0.0327667	−	0.185829i	0.996798	+	0.0799590i	$0.0254790\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	23.6374	−	40.9412i	0.964191	−	1.67003i	0.252419	−	0.967618i	$-0.418774\pi$
$601$	23.6374	−	40.9412i	0.964191	−	1.67003i	0.711772	−	0.702410i	$-0.247893\pi$
$602$	5.67752	+	4.76400i	0.231398	+	0.194166i
$603$	2.14543	+	0.780873i	0.0873687	+	0.0317996i
$604$	−12.7280	+	4.63262i	−0.517896	+	0.188499i
$605$	−2.07532	+	1.74140i	−0.0843738	+	0.0707981i
$606$	1.58987	+	9.01660i	0.0645841	+	0.366274i
$607$	26.4516			1.07364			0.536819	−	0.843698i	$-0.319626\pi$
$607$	26.4516			1.07364			0.536819	+	0.843698i	$0.319626\pi$
$608$	1.52094	+	4.08494i	0.0616824	+	0.165666i
$609$	0.106067			0.00429805
$610$	−1.99747	−	11.3282i	−0.0808753	−	0.458667i
$611$	−7.34389	+	6.16226i	−0.297102	+	0.249298i
$612$	6.85117	−	2.49362i	0.276942	−	0.100799i
$613$	−9.56583	−	3.48168i	−0.386360	−	0.140624i	0.141535	−	0.989933i	$-0.454796\pi$
$613$	−9.56583	−	3.48168i	−0.386360	−	0.140624i	−0.527895	+	0.849310i	$0.677019\pi$
$614$	−13.9704	−	11.7226i	−0.563801	−	0.473085i
$615$	0.201867	−	0.349643i	0.00814005	−	0.0140990i
$616$	0.939693	+	1.62760i	0.0378613	+	0.0655777i
$617$	−1.62613	+	9.22226i	−0.0654657	+	0.371274i	0.934420	+	0.356172i	$0.115918\pi$
$617$	−1.62613	+	9.22226i	−0.0654657	+	0.371274i	−0.999886	+	0.0151020i	$0.995193\pi$
$618$	2.89306	−	16.4073i	0.116376	−	0.660000i
$619$	−15.3803	−	26.6395i	−0.618187	−	1.07073i	−0.989816	−	0.142350i	$-0.954534\pi$
$619$	−15.3803	−	26.6395i	−0.618187	−	1.07073i	0.371629	−	0.928381i	$-0.378799\pi$
$620$	−0.471782	+	0.817150i	−0.0189472	+	0.0328175i
$621$	1.31521	+	1.10359i	0.0527775	+	0.0442855i
$622$	21.1878	+	7.71172i	0.849553	+	0.309212i
$623$	−1.53044	+	0.557035i	−0.0613158	+	0.0223171i
$624$	−1.26604	+	1.06234i	−0.0506823	+	0.0425275i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	−24.6604			−0.985630
$627$	8.13816	+	9.55493i	0.325007	+	0.381587i
$628$	−22.0077			−0.878204
$629$	9.17752	+	52.0483i	0.365932	+	2.07530i
$630$	−0.500000	+	0.419550i	−0.0199205	+	0.0167153i
$631$	−22.1853	+	8.07477i	−0.883181	+	0.321452i	−0.743493	−	0.668744i	$-0.766832\pi$
$631$	−22.1853	+	8.07477i	−0.883181	+	0.321452i	−0.139688	+	0.990196i	$0.544610\pi$
$632$	−4.58512	−	1.66885i	−0.182386	−	0.0663832i
$633$	5.19459	+	4.35878i	0.206467	+	0.173246i
$634$	8.14930	−	14.1150i	0.323650	−	0.560578i
$635$	−1.64543	−	2.84997i	−0.0652969	−	0.113098i
$636$	−1.83615	+	10.4133i	−0.0728082	+	0.412916i
$637$	1.88666	−	10.6998i	0.0747522	−	0.423941i
$638$	0.233956	+	0.405223i	0.00926239	+	0.0160429i
$639$	2.13429	−	3.69669i	0.0844310	−	0.146239i
$640$	−0.766044	−	0.642788i	−0.0302806	−	0.0254084i
$641$	−6.38490	−	2.32392i	−0.252189	−	0.0917891i	0.212833	−	0.977089i	$-0.431731\pi$
$641$	−6.38490	−	2.32392i	−0.252189	−	0.0917891i	−0.465021	+	0.885300i	$0.653953\pi$
$642$	−7.24422	+	2.63668i	−0.285907	+	0.104062i
$643$	−23.2108	+	19.4762i	−0.915344	+	0.768065i	−0.973128	−	0.230264i	$-0.926041\pi$
$643$	−23.2108	+	19.4762i	−0.915344	+	0.768065i	0.0577840	+	0.998329i	$0.481597\pi$
$644$	0.194593	+	1.10359i	0.00766803	+	0.0434875i
$645$	−11.3550			−0.447104
$646$	31.3371	+	5.28801i	1.23294	+	0.208054i
$647$	32.0597			1.26040			0.630199	−	0.776434i	$-0.282973\pi$
$647$	32.0597			1.26040			0.630199	+	0.776434i	$0.282973\pi$
$648$	−0.173648	−	0.984808i	−0.00682154	−	0.0386869i
$649$	−10.0458	+	8.42939i	−0.394331	+	0.330883i
$650$	−1.55303	+	0.565258i	−0.0609150	+	0.0221712i
$651$	−0.578726	−	0.210639i	−0.0226820	−	0.00825559i
$652$	−1.10947	−	0.930956i	−0.0434502	−	0.0364591i
$653$	17.4192	−	30.1710i	0.681667	−	1.18068i	−0.292805	−	0.956172i	$-0.594589\pi$
$653$	17.4192	−	30.1710i	0.681667	−	1.18068i	0.974472	−	0.224509i	$-0.0720778\pi$
$654$	4.10354	+	7.10754i	0.160461	+	0.277927i
$655$	1.18479	−	6.71929i	0.0462937	−	0.262544i
$656$	−0.0701076	+	0.397600i	−0.00273724	+	0.0155237i
$657$	−5.69846	−	9.87003i	−0.222318	−	0.385066i
$658$	1.89306	−	3.27887i	0.0737990	−	0.127824i
$659$	7.82501	+	6.56596i	0.304819	+	0.255774i	0.782347	−	0.622843i	$-0.214023\pi$
$659$	7.82501	+	6.56596i	0.304819	+	0.255774i	−0.477528	+	0.878617i	$0.658467\pi$
$660$	−2.70574	−	0.984808i	−0.105321	−	0.0383336i
$661$	12.6429	−	4.60164i	0.491752	−	0.178983i	−0.0842286	−	0.996446i	$-0.526843\pi$
$661$	12.6429	−	4.60164i	0.491752	−	0.178983i	0.575981	+	0.817463i	$0.304620\pi$
$662$	−4.93242	+	4.13879i	−0.191704	+	0.160859i
$663$	2.09240	+	11.8666i	0.0812619	+	0.460859i
$664$	4.29086			0.166518
$665$	−2.79813	+	0.514654i	−0.108507	+	0.0199574i
$666$	7.24897			0.280892
$667$	0.0484478	+	0.274761i	0.00187591	+	0.0106388i
$668$	−14.4855	+	12.1547i	−0.560459	+	0.470281i
$669$	26.5390	−	9.65939i	1.02606	−	0.373454i
$670$	−2.14543	−	0.780873i	−0.0828852	−	0.0301677i
$671$	25.3726	+	21.2901i	0.979498	+	0.821896i
$672$	0.326352	−	0.565258i	0.0125893	−	0.0218053i
$673$	−11.2242	−	19.4408i	−0.432659	−	0.749388i	0.564442	−	0.825473i	$-0.309091\pi$
$673$	−11.2242	−	19.4408i	−0.432659	−	0.749388i	−0.997101	+	0.0760847i	$0.975758\pi$
$674$	3.43283	−	19.4685i	0.132228	−	0.749900i
$675$	0.173648	−	0.984808i	0.00668372	−	0.0379053i
$676$	5.13429	+	8.89284i	0.197473	+	0.342032i
$677$	−12.7233	+	22.0374i	−0.488995	+	0.846965i	−0.999920	−	0.0126609i	$-0.995970\pi$
$677$	−12.7233	+	22.0374i	−0.488995	+	0.846965i	0.510925	+	0.859626i	$0.329303\pi$
$678$	−7.69459	−	6.45653i	−0.295509	−	0.247962i
$679$	8.60829	+	3.13316i	0.330356	+	0.120240i
$680$	−6.85117	+	2.49362i	−0.262730	+	0.0956260i
$681$	−16.5194	+	13.8614i	−0.633023	+	0.531169i
$682$	−0.471782	−	2.67561i	−0.0180654	−	0.102454i
$683$	11.0574			0.423099			0.211549	−	0.977367i	$-0.432149\pi$
$683$	11.0574			0.423099			0.211549	+	0.977367i	$0.432149\pi$
$684$	1.46064	−	4.10689i	0.0558489	−	0.157031i
$685$	10.1702			0.388585
$686$	1.53849	+	8.72518i	0.0587396	+	0.333129i
$687$	−8.51889	+	7.14819i	−0.325016	+	0.272721i
$688$	10.6702	−	3.88365i	0.406799	−	0.148063i
$689$	−16.4217	−	5.97702i	−0.625619	−	0.227707i
$690$	−1.31521	−	1.10359i	−0.0500691	−	0.0420130i
$691$	7.53895	−	13.0578i	0.286795	−	0.496744i	−0.686248	−	0.727368i	$-0.740743\pi$
$691$	7.53895	−	13.0578i	0.286795	−	0.496744i	0.973043	+	0.230624i	$0.0740767\pi$
$692$	0.577382	+	1.00005i	0.0219488	+	0.0380164i
$693$	0.326352	−	1.85083i	0.0123971	−	0.0703073i
$694$	−5.07667	+	28.7912i	−0.192708	+	1.09290i
$695$	3.02481	+	5.23913i	0.114738	+	0.198732i
$696$	0.0812519	−	0.140732i	0.00307985	−	0.00533445i
$697$	2.25490	+	1.89209i	0.0854104	+	0.0716679i
$698$	−15.5287	−	5.65198i	−0.587769	−	0.213931i
$699$	−14.6604	+	5.33597i	−0.554509	+	0.201825i
$700$	0.500000	−	0.419550i	0.0188982	−	0.0158575i
$701$	4.68433	+	26.5661i	0.176925	+	1.00339i	0.935899	+	0.352269i	$0.114590\pi$
$701$	4.68433	+	26.5661i	0.176925	+	1.00339i	−0.758974	+	0.651120i	$0.774299\pi$
$702$	1.65270			0.0623773
$703$	27.4798	+	15.5969i	1.03642	+	0.588248i
$704$	2.87939			0.108521
$705$	1.00727	+	5.71253i	0.0379361	+	0.215146i
$706$	−3.65270	+	3.06498i	−0.137471	+	0.115352i
$707$	5.61556	−	2.04390i	0.211195	−	0.0768687i
$708$	4.27972	+	1.55769i	0.160842	+	0.0585415i
$709$	−5.68479	−	4.77011i	−0.213497	−	0.179145i	0.529768	−	0.848143i	$-0.322279\pi$
$709$	−5.68479	−	4.77011i	−0.213497	−	0.179145i	−0.743264	+	0.668998i	$0.766724\pi$
$710$	−2.13429	+	3.69669i	−0.0800983	+	0.138734i
$711$	2.43969	+	4.22567i	0.0914956	+	0.158475i
$712$	−0.433296	+	2.45734i	−0.0162385	+	0.0920929i
$713$	0.281308	−	1.59537i	0.0105351	−	0.0597472i
$714$	−2.37939	−	4.12122i	−0.0890463	−	0.154233i
$715$	2.37939	−	4.12122i	0.0889840	−	0.154125i
$716$	−6.32501	−	5.30731i	−0.236377	−	0.198344i
$717$	18.8059	+	6.84478i	0.702318	+	0.255623i
$718$	−31.4094	+	11.4321i	−1.17219	+	0.426642i
$719$	8.05556	−	6.75942i	0.300422	−	0.252084i	−0.480098	−	0.877215i	$-0.659399\pi$
$719$	8.05556	−	6.75942i	0.300422	−	0.252084i	0.780520	+	0.625131i	$0.214954\pi$
$720$	0.173648	+	0.984808i	0.00647149	+	0.0367016i
$721$	−10.8743			−0.404981
$722$	14.3735	−	12.4259i	0.534925	−	0.462445i
$723$	−28.1361			−1.04639
$724$	0.370767	+	2.10272i	0.0137795	+	0.0781472i
$725$	0.124485	−	0.104455i	0.00462326	−	0.00387938i
$726$	−2.54576	+	0.926581i	−0.0944820	+	0.0343886i
$727$	−22.1160	−	8.04958i	−0.820238	−	0.298542i	−0.102392	−	0.994744i	$-0.532650\pi$
$727$	−22.1160	−	8.04958i	−0.820238	−	0.298542i	−0.717846	+	0.696202i	$0.754872\pi$
$728$	0.826352	+	0.693392i	0.0306266	+	0.0256988i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	5.69846	+	9.87003i	0.210910	+	0.365306i
$731$	14.3760	−	81.5302i	0.531715	−	3.01550i
$732$	1.99747	−	11.3282i	0.0738288	−	0.418704i
$733$	−9.98932	−	17.3020i	−0.368964	−	0.639064i	0.620440	−	0.784254i	$-0.286954\pi$
$733$	−9.98932	−	17.3020i	−0.368964	−	0.639064i	−0.989404	+	0.145190i	$0.953621\pi$
$734$	2.76470	−	4.78860i	0.102047	−	0.176751i
$735$	−5.03596	−	4.22567i	−0.185754	−	0.155866i
$736$	1.61334	+	0.587208i	0.0594685	+	0.0216448i
$737$	6.17752	−	2.24843i	0.227552	−	0.0828221i
$738$	0.309278	−	0.259515i	0.0113847	−	0.00955287i
$739$	−6.06835	−	34.4153i	−0.223228	−	1.26599i	−0.866044	−	0.499968i	$-0.833345\pi$
$739$	−6.06835	−	34.4153i	−0.223228	−	1.26599i	0.642816	−	0.766021i	$-0.277766\pi$
$740$	−7.24897			−0.266477
$741$	6.26517	+	3.55596i	0.230157	+	0.130631i
$742$	6.90167			0.253368
$743$	1.37867	+	7.81883i	0.0505785	+	0.286845i	0.999597	−	0.0283744i	$-0.00903305\pi$
$743$	1.37867	+	7.81883i	0.0505785	+	0.286845i	−0.949019	+	0.315219i	$0.897922\pi$
$744$	−0.722811	+	0.606511i	−0.0264995	+	0.0222358i
$745$	−13.6951	+	4.98459i	−0.501748	+	0.182621i
$746$	11.6985	+	4.25789i	0.428311	+	0.155893i
$747$	−3.28699	−	2.75811i	−0.120265	−	0.100914i
$748$	10.4966	−	18.1806i	0.383794	−	0.664750i
$749$	2.51589	+	4.35765i	0.0919287	+	0.159225i
$750$	−0.173648	+	0.984808i	−0.00634073	+	0.0359601i
$751$	−2.10947	+	11.9634i	−0.0769757	+	0.436551i	0.921826	+	0.387605i	$0.126697\pi$
$751$	−2.10947	+	11.9634i	−0.0769757	+	0.436551i	−0.998801	+	0.0489462i	$0.984414\pi$
$752$	−2.90033	−	5.02352i	−0.105764	−	0.183189i
$753$	−12.8366	+	22.2337i	−0.467792	+	0.810240i
$754$	0.205737	+	0.172634i	0.00749250	+	0.00628696i
$755$	−12.7280	−	4.63262i	−0.463220	−	0.168598i
$756$	−0.613341	+	0.223238i	−0.0223070	+	0.00811908i
$757$	−41.6161	+	34.9200i	−1.51256	+	1.26919i	−0.653984	+	0.756509i	$0.726904\pi$
$757$	−41.6161	+	34.9200i	−1.51256	+	1.26919i	−0.858579	+	0.512682i	$0.828652\pi$
$758$	−2.29385	−	13.0091i	−0.0833165	−	0.472511i
$759$	4.94356			0.179440
$760$	−1.46064	+	4.10689i	−0.0529829	+	0.148973i
$761$	46.0283			1.66852			0.834262	−	0.551368i	$-0.185894\pi$
$761$	46.0283			1.66852			0.834262	+	0.551368i	$0.185894\pi$
$762$	−0.571452	−	3.24086i	−0.0207015	−	0.117404i
$763$	4.10354	−	3.44328i	0.148558	−	0.124655i
$764$	3.81908	−	1.39003i	0.138169	−	0.0502895i
$765$	6.85117	+	2.49362i	0.247704	+	0.0901570i
$766$	20.7310	+	17.3954i	0.749042	+	0.628521i
$767$	−3.76352	+	6.51860i	−0.135893	+	0.235373i

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)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-0.326352 + 0.565258i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(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} +(-0.326352 + 0.565258i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +(-0.173648 + 0.984808i) q^{10} +(-1.43969 - 2.49362i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-1.26604 - 1.06234i) q^{13} +(0.613341 + 0.223238i) q^{14} +(-0.939693 + 0.342020i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-1.26604 - 7.18009i) q^{17} -1.00000 q^{18} +(-3.79086 - 2.15160i) q^{19} +1.00000 q^{20} +(0.113341 + 0.642788i) q^{21} +(-2.20574 + 1.85083i) q^{22} +(-1.61334 + 0.587208i) q^{23} +(0.939693 + 0.342020i) q^{24} +(0.766044 + 0.642788i) q^{25} +(-0.826352 + 1.43128i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(0.113341 - 0.642788i) q^{28} +(0.0282185 - 0.160035i) q^{29} +(0.500000 + 0.866025i) q^{30} +(-0.471782 + 0.817150i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-2.70574 - 0.984808i) q^{33} +(-6.85117 + 2.49362i) q^{34} +(0.500000 - 0.419550i) q^{35} +(0.173648 + 0.984808i) q^{36} -7.24897 q^{37} +(-1.46064 + 4.10689i) q^{38} -1.65270 q^{39} +(-0.173648 - 0.984808i) q^{40} +(-0.309278 + 0.259515i) q^{41} +(0.613341 - 0.223238i) q^{42} +(10.6702 + 3.88365i) q^{43} +(2.20574 + 1.85083i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(0.858441 + 1.48686i) q^{46} +(1.00727 - 5.71253i) q^{47} +(0.173648 - 0.984808i) q^{48} +(3.28699 + 5.69323i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-5.58512 - 4.68647i) q^{51} +(1.55303 + 0.565258i) q^{52} +(9.93629 - 3.61651i) q^{53} +(-0.766044 + 0.642788i) q^{54} +(0.500000 + 2.83564i) q^{55} -0.652704 q^{56} +(-4.28699 + 0.788496i) q^{57} -0.162504 q^{58} +(-0.790859 - 4.48519i) q^{59} +(0.766044 - 0.642788i) q^{60} +(-10.8093 + 3.93426i) q^{61} +(0.886659 + 0.322718i) q^{62} +(0.500000 + 0.419550i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.826352 + 1.43128i) q^{65} +(-0.500000 + 2.83564i) q^{66} +(-0.396459 + 2.24843i) q^{67} +(3.64543 + 6.31407i) q^{68} +(-0.858441 + 1.48686i) q^{69} +(-0.500000 - 0.419550i) q^{70} +(4.01114 + 1.45994i) q^{71} +(0.939693 - 0.342020i) q^{72} +(8.73055 - 7.32580i) q^{73} +(1.25877 + 7.13884i) q^{74} +1.00000 q^{75} +(4.29813 + 0.725293i) q^{76} +1.87939 q^{77} +(0.286989 + 1.62760i) q^{78} +(-3.73783 + 3.13641i) q^{79} +(-0.939693 + 0.342020i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(0.309278 + 0.259515i) q^{82} +(2.14543 - 3.71599i) q^{83} +(-0.326352 - 0.565258i) q^{84} +(-1.26604 + 7.18009i) q^{85} +(1.97178 - 11.1825i) q^{86} +(-0.0812519 - 0.140732i) q^{87} +(1.43969 - 2.49362i) q^{88} +(1.91147 + 1.60392i) q^{89} +(0.939693 + 0.342020i) q^{90} +(1.01367 - 0.368946i) q^{91} +(1.31521 - 1.10359i) q^{92} +(0.163848 + 0.929228i) q^{93} -5.80066 q^{94} +(2.82635 + 3.31839i) q^{95} -1.00000 q^{96} +(-2.43717 - 13.8219i) q^{97} +(5.03596 - 4.22567i) q^{98} +(-2.70574 + 0.984808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q - 3 * q^7 + 3 * q^8	\( 6 q - 3 q^{7} + 3 q^{8} - 3 q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} - 3 q^{17} - 6 q^{18} + 9 q^{19} + 6 q^{20} - 6 q^{21} - 3 q^{22} - 3 q^{23} - 6 q^{26} - 3 q^{27} - 6 q^{28} + 15 q^{29} + 3 q^{30} + 12 q^{31} - 6 q^{33} - 15 q^{34} + 3 q^{35} - 18 q^{37} - 12 q^{39} + 18 q^{41} - 3 q^{42} + 21 q^{43} + 3 q^{44} - 3 q^{45} - 3 q^{46} + 24 q^{47} + 12 q^{49} + 3 q^{50} - 12 q^{51} - 3 q^{52} + 12 q^{53} + 3 q^{55} - 6 q^{56} - 18 q^{57} - 6 q^{58} + 27 q^{59} - 45 q^{61} + 12 q^{62} + 3 q^{63} - 3 q^{64} + 6 q^{65} - 3 q^{66} - 12 q^{67} + 6 q^{68} + 3 q^{69} - 3 q^{70} + 18 q^{71} + 15 q^{73} - 15 q^{74} + 6 q^{75} + 12 q^{76} - 6 q^{78} - 3 q^{79} - 18 q^{82} - 3 q^{83} - 3 q^{84} - 3 q^{85} - 3 q^{86} - 3 q^{87} + 3 q^{88} - 9 q^{89} - 15 q^{91} + 15 q^{92} - 3 q^{93} - 6 q^{94} + 18 q^{95} - 6 q^{96} - 24 q^{97} - 3 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q - 3 * q^7 + 3 * q^8 - 3 * q^11 - 3 * q^12 - 3 * q^13 - 3 * q^14 - 3 * q^17 - 6 * q^18 + 9 * q^19 + 6 * q^20 - 6 * q^21 - 3 * q^22 - 3 * q^23 - 6 * q^26 - 3 * q^27 - 6 * q^28 + 15 * q^29 + 3 * q^30 + 12 * q^31 - 6 * q^33 - 15 * q^34 + 3 * q^35 - 18 * q^37 - 12 * q^39 + 18 * q^41 - 3 * q^42 + 21 * q^43 + 3 * q^44 - 3 * q^45 - 3 * q^46 + 24 * q^47 + 12 * q^49 + 3 * q^50 - 12 * q^51 - 3 * q^52 + 12 * q^53 + 3 * q^55 - 6 * q^56 - 18 * q^57 - 6 * q^58 + 27 * q^59 - 45 * q^61 + 12 * q^62 + 3 * q^63 - 3 * q^64 + 6 * q^65 - 3 * q^66 - 12 * q^67 + 6 * q^68 + 3 * q^69 - 3 * q^70 + 18 * q^71 + 15 * q^73 - 15 * q^74 + 6 * q^75 + 12 * q^76 - 6 * q^78 - 3 * q^79 - 18 * q^82 - 3 * q^83 - 3 * q^84 - 3 * q^85 - 3 * q^86 - 3 * q^87 + 3 * q^88 - 9 * q^89 - 15 * q^91 + 15 * q^92 - 3 * q^93 - 6 * q^94 + 18 * q^95 - 6 * q^96 - 24 * q^97 - 3 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more