LMFDB - Embedded newform 162.2.g.b.7.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

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

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			7.5
Character	$\chi$	$=$	162.7
Dual form			162.2.g.b.139.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.597159 + 0.802123i) q^{2} +(1.73136 - 0.0489119i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-0.660279 + 0.434273i) q^{5} +(1.07313 + 1.35956i) q^{6} +(-2.31933 + 2.45835i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(2.99522 - 0.169368i) q^{9} +O(q^{10})$	\(q+(0.597159 + 0.802123i) q^{2} +(1.73136 - 0.0489119i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-0.660279 + 0.434273i) q^{5} +(1.07313 + 1.35956i) q^{6} +(-2.31933 + 2.45835i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(2.99522 - 0.169368i) q^{9} +(-0.742632 - 0.270296i) q^{10} +(4.21404 - 2.11637i) q^{11} +(-0.449703 + 1.67265i) q^{12} +(-1.99428 - 4.62327i) q^{13} +(-3.35690 - 0.392366i) q^{14} +(-1.12194 + 0.784178i) q^{15} +(-0.835488 - 0.549509i) q^{16} +(2.13944 - 1.79521i) q^{17} +(1.92447 + 2.30139i) q^{18} +(-4.97401 - 4.17369i) q^{19} +(-0.226658 - 0.757092i) q^{20} +(-3.89535 + 4.36973i) q^{21} +(4.21404 + 2.11637i) q^{22} +(1.65892 + 1.75835i) q^{23} +(-1.61022 + 0.638122i) q^{24} +(-1.73302 + 4.01760i) q^{25} +(2.51753 - 4.36049i) q^{26} +(5.17751 - 0.439739i) q^{27} +(-1.68988 - 2.92696i) q^{28} +(-6.98299 + 0.816194i) q^{29} +(-1.29898 - 0.431656i) q^{30} +(-3.40578 + 0.807185i) q^{31} +(-0.0581448 - 0.998308i) q^{32} +(7.19250 - 3.87031i) q^{33} +(2.71756 + 0.644074i) q^{34} +(0.463813 - 2.63042i) q^{35} +(-0.696784 + 2.91796i) q^{36} +(-0.335520 - 1.90283i) q^{37} +(0.377541 - 6.48212i) q^{38} +(-3.67896 - 7.90700i) q^{39} +(0.471930 - 0.633912i) q^{40} +(0.912678 - 1.22594i) q^{41} +(-5.83120 - 0.515134i) q^{42} +(-0.482003 + 8.27567i) q^{43} +(0.818860 + 4.64398i) q^{44} +(-1.90413 + 1.41257i) q^{45} +(-0.419776 + 2.38067i) q^{46} +(11.9322 + 2.82797i) q^{47} +(-1.47341 - 0.910533i) q^{48} +(-0.257160 - 4.41527i) q^{49} +(-4.25750 + 1.00905i) q^{50} +(3.61634 - 3.21279i) q^{51} +(5.00101 - 0.584534i) q^{52} +(-2.74858 - 4.76068i) q^{53} +(3.44452 + 3.89041i) q^{54} +(-1.86336 + 3.22744i) q^{55} +(1.33865 - 3.10335i) q^{56} +(-8.81594 - 6.98287i) q^{57} +(-4.82464 - 5.11382i) q^{58} +(-5.27302 - 2.64821i) q^{59} +(-0.429458 - 1.29971i) q^{60} +(0.317697 + 1.06118i) q^{61} +(-2.68125 - 2.24984i) q^{62} +(-6.53053 + 7.75610i) q^{63} +(0.766044 - 0.642788i) q^{64} +(3.32454 + 2.18659i) q^{65} +(7.39953 + 3.45808i) q^{66} +(9.43341 + 1.10261i) q^{67} +(1.10619 + 2.56443i) q^{68} +(2.95819 + 2.96319i) q^{69} +(2.38689 - 1.19874i) q^{70} +(0.278197 + 0.101256i) q^{71} +(-2.75665 + 1.18358i) q^{72} +(-4.55945 + 1.65950i) q^{73} +(1.32594 - 1.40542i) q^{74} +(-2.80398 + 7.04067i) q^{75} +(5.42491 - 3.56802i) q^{76} +(-4.57097 + 15.2681i) q^{77} +(4.14547 - 7.67271i) q^{78} +(5.83110 + 7.83253i) q^{79} +0.790292 q^{80} +(8.94263 - 1.01459i) q^{81} +1.52837 q^{82} +(5.90826 + 7.93617i) q^{83} +(-3.06895 - 4.98496i) q^{84} +(-0.633021 + 2.11444i) q^{85} +(-6.92594 + 4.55526i) q^{86} +(-12.0501 + 1.75468i) q^{87} +(-3.23606 + 3.43002i) q^{88} +(-6.49122 + 2.36261i) q^{89} +(-2.27012 - 0.683816i) q^{90} +(15.9910 + 5.82025i) q^{91} +(-2.16026 + 1.08492i) q^{92} +(-5.85715 + 1.56411i) q^{93} +(4.85701 + 11.2598i) q^{94} +(5.09675 + 0.595725i) q^{95} +(-0.149499 - 1.72559i) q^{96} +(-15.2749 - 10.0465i) q^{97} +(3.38803 - 2.84289i) q^{98} +(12.2635 - 7.05270i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{8}{27}\right)$

Coefficient data

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

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

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

$2$	0.597159	+	0.802123i	0.422255	+	0.567187i
$2$	0.597159	+	0.802123i	0.422255	+	0.567187i
$3$	1.73136	−	0.0489119i	0.999601	−	0.0282393i
$3$	1.73136	−	0.0489119i	0.999601	−	0.0282393i
$4$	−0.286803	+	0.957990i	−0.143402	+	0.478995i
$5$	−0.660279	+	0.434273i	−0.295286	+	0.194213i	−0.688504	−	0.725233i	$-0.741732\pi$
$5$	−0.660279	+	0.434273i	−0.295286	+	0.194213i	0.393218	+	0.919445i	$0.371362\pi$
$6$	1.07313	+	1.35956i	0.438103	+	0.555036i
$7$	−2.31933	+	2.45835i	−0.876624	+	0.929167i	−0.997986	−	0.0634409i	$-0.979793\pi$
$7$	−2.31933	+	2.45835i	−0.876624	+	0.929167i	0.121361	+	0.992608i	$0.461274\pi$
$8$	−0.939693	+	0.342020i	−0.332232	+	0.120922i
$9$	2.99522	−	0.169368i	0.998405	−	0.0564561i
$10$	−0.742632	−	0.270296i	−0.234841	−	0.0854750i
$11$	4.21404	−	2.11637i	1.27058	−	0.638109i	0.319656	−	0.947534i	$-0.396433\pi$
$11$	4.21404	−	2.11637i	1.27058	−	0.638109i	0.950924	+	0.309425i	$0.100136\pi$
$12$	−0.449703	+	1.67265i	−0.129818	+	0.482853i
$13$	−1.99428	−	4.62327i	−0.553115	−	1.28226i	−0.933878	−	0.357592i	$-0.883598\pi$
$13$	−1.99428	−	4.62327i	−0.553115	−	1.28226i	0.380763	−	0.924673i	$-0.375661\pi$
$14$	−3.35690	−	0.392366i	−0.897170	−	0.104864i
$15$	−1.12194	+	0.784178i	−0.289684	+	0.202474i
$16$	−0.835488	−	0.549509i	−0.208872	−	0.137377i
$17$	2.13944	−	1.79521i	0.518891	−	0.435401i	−0.345354	−	0.938472i	$-0.612241\pi$
$17$	2.13944	−	1.79521i	0.518891	−	0.435401i	0.864245	+	0.503071i	$0.167797\pi$
$18$	1.92447	+	2.30139i	0.453603	+	0.542443i
$19$	−4.97401	−	4.17369i	−1.14112	−	0.957510i	−0.141641	−	0.989918i	$-0.545238\pi$
$19$	−4.97401	−	4.17369i	−1.14112	−	0.957510i	−0.999475	+	0.0324084i	$0.989682\pi$
$20$	−0.226658	−	0.757092i	−0.0506823	−	0.169291i
$21$	−3.89535	+	4.36973i	−0.850036	+	0.953552i
$22$	4.21404	+	2.11637i	0.898436	+	0.451211i
$23$	1.65892	+	1.75835i	0.345908	+	0.366641i	0.876847	−	0.480769i	$-0.159642\pi$
$23$	1.65892	+	1.75835i	0.345908	+	0.366641i	−0.530939	+	0.847410i	$0.678161\pi$
$24$	−1.61022	+	0.638122i	−0.328684	+	0.130256i
$25$	−1.73302	+	4.01760i	−0.346605	+	0.803520i
$26$	2.51753	−	4.36049i	0.493728	−	0.855162i
$27$	5.17751	−	0.439739i	0.996413	−	0.0846279i
$28$	−1.68988	−	2.92696i	−0.319357	−	0.553143i
$29$	−6.98299	+	0.816194i	−1.29671	+	0.151563i	−0.736301	−	0.676654i	$-0.763429\pi$
$29$	−6.98299	+	0.816194i	−1.29671	+	0.151563i	−0.560407	+	0.828217i	$0.689355\pi$
$30$	−1.29898	−	0.431656i	−0.237161	−	0.0788092i
$31$	−3.40578	+	0.807185i	−0.611697	+	0.144975i	−0.524776	−	0.851240i	$-0.675851\pi$
$31$	−3.40578	+	0.807185i	−0.611697	+	0.144975i	−0.0869208	+	0.996215i	$0.527703\pi$
$32$	−0.0581448	−	0.998308i	−0.0102787	−	0.176478i
$33$	7.19250	−	3.87031i	1.25205	−	0.673735i
$34$	2.71756	+	0.644074i	0.466058	+	0.110458i
$35$	0.463813	−	2.63042i	0.0783988	−	0.444622i
$36$	−0.696784	+	2.91796i	−0.116131	+	0.486327i
$37$	−0.335520	−	1.90283i	−0.0551591	−	0.312823i	0.944728	−	0.327855i	$-0.106326\pi$
$37$	−0.335520	−	1.90283i	−0.0551591	−	0.312823i	−0.999887	+	0.0150327i	$0.995215\pi$
$38$	0.377541	−	6.48212i	0.0612452	−	1.05154i
$39$	−3.67896	−	7.90700i	−0.589104	−	1.26613i
$40$	0.471930	−	0.633912i	0.0746186	−	0.100230i
$41$	0.912678	−	1.22594i	0.142536	−	0.191460i	−0.725122	−	0.688620i	$-0.758217\pi$
$41$	0.912678	−	1.22594i	0.142536	−	0.191460i	0.867658	+	0.497161i	$0.165624\pi$
$42$	−5.83120	−	0.515134i	−0.899774	−	0.0794869i
$43$	−0.482003	+	8.27567i	−0.0735048	+	1.26203i	0.736837	+	0.676070i	$0.236318\pi$
$43$	−0.482003	+	8.27567i	−0.0735048	+	1.26203i	−0.810342	+	0.585957i	$0.800719\pi$
$44$	0.818860	+	4.64398i	0.123448	+	0.700107i
$45$	−1.90413	+	1.41257i	−0.283851	+	0.210574i
$46$	−0.419776	+	2.38067i	−0.0618926	+	0.351010i
$47$	11.9322	+	2.82797i	1.74048	+	0.412502i	0.973412	−	0.229059i	$-0.0735650\pi$
$47$	11.9322	+	2.82797i	1.74048	+	0.412502i	0.767071	+	0.641562i	$0.221713\pi$
$48$	−1.47341	−	0.910533i	−0.212668	−	0.131424i
$49$	−0.257160	−	4.41527i	−0.0367372	−	0.630753i
$50$	−4.25750	+	1.00905i	−0.602101	+	0.142701i
$51$	3.61634	−	3.21279i	0.506389	−	0.449881i
$52$	5.00101	−	0.584534i	0.693515	−	0.0810603i
$53$	−2.74858	−	4.76068i	−0.377546	−	0.653929i	0.613158	−	0.789960i	$-0.289899\pi$
$53$	−2.74858	−	4.76068i	−0.377546	−	0.653929i	−0.990705	+	0.136031i	$0.956565\pi$
$54$	3.44452	+	3.89041i	0.468740	+	0.529418i
$55$	−1.86336	+	3.22744i	−0.251255	+	0.435187i
$56$	1.33865	−	3.10335i	0.178885	−	0.414702i
$57$	−8.81594	−	6.98287i	−1.16770	−	0.924904i
$58$	−4.82464	−	5.11382i	−0.633506	−	0.671477i
$59$	−5.27302	−	2.64821i	−0.686488	−	0.344767i	0.0711283	−	0.997467i	$-0.477340\pi$
$59$	−5.27302	−	2.64821i	−0.686488	−	0.344767i	−0.757617	+	0.652700i	$0.773636\pi$
$60$	−0.429458	−	1.29971i	−0.0554428	−	0.167792i
$61$	0.317697	+	1.06118i	0.0406769	+	0.135870i	0.975916	−	0.218146i	$-0.0700009\pi$
$61$	0.317697	+	1.06118i	0.0406769	+	0.135870i	−0.935239	+	0.354016i	$0.884816\pi$
$62$	−2.68125	−	2.24984i	−0.340520	−	0.285730i
$63$	−6.53053	+	7.75610i	−0.822769	+	0.977176i
$64$	0.766044	−	0.642788i	0.0957556	−	0.0803485i
$65$	3.32454	+	2.18659i	0.412359	+	0.271213i
$66$	7.39953	+	3.45808i	0.910819	+	0.425660i
$67$	9.43341	+	1.10261i	1.15247	+	0.134705i	0.670795	−	0.741643i	$-0.265953\pi$
$67$	9.43341	+	1.10261i	1.15247	+	0.134705i	0.481679	+	0.876348i	$0.340027\pi$
$68$	1.10619	+	2.56443i	0.134145	+	0.310983i
$69$	2.95819	+	2.96319i	0.356124	+	0.356727i
$70$	2.38689	−	1.19874i	0.285288	−	0.143277i
$71$	0.278197	+	0.101256i	0.0330160	+	0.0120168i	0.358475	−	0.933539i	$-0.383297\pi$
$71$	0.278197	+	0.101256i	0.0330160	+	0.0120168i	−0.325459	+	0.945556i	$0.605519\pi$
$72$	−2.75665	+	1.18358i	−0.324875	+	0.139486i
$73$	−4.55945	+	1.65950i	−0.533643	+	0.194230i	−0.594764	−	0.803900i	$-0.702755\pi$
$73$	−4.55945	+	1.65950i	−0.533643	+	0.194230i	0.0611211	+	0.998130i	$0.480532\pi$
$74$	1.32594	−	1.40542i	0.154138	−	0.163376i
$75$	−2.80398	+	7.04067i	−0.323775	+	0.812987i
$76$	5.42491	−	3.56802i	0.622280	−	0.409280i
$77$	−4.57097	+	15.2681i	−0.520911	+	1.73996i
$78$	4.14547	−	7.67271i	0.469382	−	0.868763i
$79$	5.83110	+	7.83253i	0.656050	+	0.881228i	0.998294	−	0.0583828i	$-0.0185944\pi$
$79$	5.83110	+	7.83253i	0.656050	+	0.881228i	−0.342244	+	0.939611i	$0.611187\pi$
$80$	0.790292			0.0883573
$81$	8.94263	−	1.01459i	0.993625	−	0.112732i
$82$	1.52837			0.168780
$83$	5.90826	+	7.93617i	0.648515	+	0.871107i	0.997826	−	0.0658996i	$-0.0209917\pi$
$83$	5.90826	+	7.93617i	0.648515	+	0.871107i	−0.349311	+	0.937007i	$0.613584\pi$
$84$	−3.06895	−	4.98496i	−0.334850	−	0.543904i
$85$	−0.633021	+	2.11444i	−0.0686608	+	0.229343i
$86$	−6.92594	+	4.55526i	−0.746843	+	0.491207i
$87$	−12.0501	+	1.75468i	−1.29191	+	0.188121i
$88$	−3.23606	+	3.43002i	−0.344965	+	0.365641i
$89$	−6.49122	+	2.36261i	−0.688068	+	0.250436i	−0.662308	−	0.749232i	$-0.730423\pi$
$89$	−6.49122	+	2.36261i	−0.688068	+	0.250436i	−0.0257602	+	0.999668i	$0.508201\pi$
$90$	−2.27012	−	0.683816i	−0.239292	−	0.0720805i
$91$	15.9910	+	5.82025i	1.67631	+	0.610128i
$92$	−2.16026	+	1.08492i	−0.225223	+	0.113111i
$93$	−5.85715	+	1.56411i	−0.607359	+	0.162191i
$94$	4.85701	+	11.2598i	0.500962	+	1.16136i
$95$	5.09675	+	0.595725i	0.522916	+	0.0611201i
$96$	−0.149499	−	1.72559i	−0.0152582	−	0.176117i
$97$	−15.2749	−	10.0465i	−1.55093	−	1.02006i	−0.979984	−	0.199075i	$-0.936206\pi$
$97$	−15.2749	−	10.0465i	−1.55093	−	1.02006i	−0.570946	−	0.820988i	$-0.693423\pi$
$98$	3.38803	−	2.84289i	0.342243	−	0.287176i
$99$	12.2635	−	7.05270i	1.23253	−	0.708823i
$100$	−3.35178	−	2.81248i	−0.335178	−	0.281248i
$101$	−0.312418	−	1.04355i	−0.0310867	−	0.103837i	0.941038	−	0.338300i	$-0.109852\pi$
$101$	−0.312418	−	1.04355i	−0.0310867	−	0.103837i	−0.972125	+	0.234463i	$0.924667\pi$
$102$	4.73658	+	0.982203i	0.468991	+	0.0972526i
$103$	10.9809	+	5.51483i	1.08198	+	0.543392i	0.898206	−	0.439576i	$-0.144871\pi$
$103$	10.9809	+	5.51483i	1.08198	+	0.543392i	0.183777	+	0.982968i	$0.441167\pi$
$104$	3.45526	+	3.66237i	0.338817	+	0.359125i
$105$	0.674369	−	4.57688i	0.0658117	−	0.446658i
$106$	2.17731	−	5.04758i	0.211479	−	0.490264i
$107$	−5.76622	+	9.98739i	−0.557442	+	0.965517i	0.440267	+	0.897867i	$0.354884\pi$
$107$	−5.76622	+	9.98739i	−0.557442	+	0.965517i	−0.997709	+	0.0676505i	$0.978450\pi$
$108$	−1.06366	+	5.08612i	−0.102351	+	0.489412i
$109$	−5.71238	−	9.89413i	−0.547146	−	0.947685i	−0.998468	−	0.0553242i	$-0.982381\pi$
$109$	−5.71238	−	9.89413i	−0.547146	−	0.947685i	0.451322	−	0.892361i	$-0.350953\pi$
$110$	−3.70152	+	0.432646i	−0.352926	+	0.0412512i
$111$	−0.673976	−	3.27807i	−0.0639710	−	0.311140i
$112$	3.28866	−	0.779426i	0.310749	−	0.0736488i
$113$	0.130935	+	2.24806i	0.0123173	+	0.211480i	0.998851	+	0.0479220i	$0.0152599\pi$
$113$	0.130935	+	2.24806i	0.0123173	+	0.211480i	−0.986534	+	0.163558i	$0.947703\pi$
$114$	0.336606	−	11.2414i	0.0315260	−	1.05285i
$115$	−1.85895	−	0.440580i	−0.173348	−	0.0410843i
$116$	1.22084	−	6.92372i	0.113352	−	0.642851i
$117$	−6.75634	−	13.5099i	−0.624624	−	1.24899i
$118$	−1.02464	−	5.81101i	−0.0943256	−	0.534947i
$119$	−0.548837	+	9.42316i	−0.0503118	+	0.863820i
$120$	0.786074	−	1.12061i	0.0717585	−	0.102297i
$121$	6.71034	−	9.01355i	0.610031	−	0.819414i
$122$	−0.661483	+	0.888526i	−0.0598878	+	0.0804433i
$123$	1.52021	−	2.16718i	0.137073	−	0.195408i
$124$	0.203514	−	3.49421i	0.0182761	−	0.313789i
$125$	−1.28662	−	7.29677i	−0.115079	−	0.652643i
$126$	−10.1211	−	0.606667i	−0.901660	−	0.0540462i
$127$	1.05393	−	5.97715i	0.0935214	−	0.530386i	−0.901669	−	0.432427i	$-0.857657\pi$
$127$	1.05393	−	5.97715i	0.0935214	−	0.530386i	0.995190	−	0.0979593i	$-0.0312315\pi$
$128$	0.973045	+	0.230616i	0.0860058	+	0.0203838i
$129$	−0.429742	+	14.3517i	−0.0378366	+	1.26360i
$130$	0.231368	+	3.97243i	0.0202923	+	0.348405i
$131$	1.11260	−	0.263690i	0.0972079	−	0.0230387i	−0.181724	−	0.983350i	$-0.558168\pi$
$131$	1.11260	−	0.263690i	0.0972079	−	0.0230387i	0.278932	+	0.960311i	$0.410020\pi$
$132$	1.64489	+	8.00036i	0.143169	+	0.696342i
$133$	21.7967	−	2.54767i	1.89002	−	0.220911i
$134$	4.74881	+	8.22519i	0.410235	+	0.710548i
$135$	−3.22764	+	2.53880i	−0.277791	+	0.218505i
$136$	−1.39642	+	2.41867i	−0.119742	+	0.207400i
$137$	−5.62406	+	13.0380i	−0.480496	+	1.11392i	0.489765	+	0.871855i	$0.337083\pi$
$137$	−5.62406	+	13.0380i	−0.480496	+	1.11392i	−0.970261	+	0.242061i	$0.922177\pi$
$138$	−0.610341	+	4.14233i	−0.0519556	+	0.352618i
$139$	−12.3096	−	13.0474i	−1.04409	−	1.10667i	−0.994160	−	0.107916i	$-0.965582\pi$
$139$	−12.3096	−	13.0474i	−1.04409	−	1.10667i	−0.0499277	−	0.998753i	$-0.515899\pi$
$140$	2.38689	+	1.19874i	0.201729	+	0.101312i
$141$	20.7972	+	4.31261i	1.75144	+	0.363188i
$142$	0.0849085	+	0.283614i	0.00712536	+	0.0238004i
$143$	−18.1885	−	15.2620i	−1.52100	−	1.27627i
$144$	−2.59554	−	1.50439i	−0.216295	−	0.125366i
$145$	4.25627	−	3.57144i	0.353464	−	0.296592i
$146$	−4.05384	−	2.66625i	−0.335498	−	0.220661i
$147$	−0.661197	−	7.63185i	−0.0545346	−	0.629464i
$148$	1.91912	+	0.224312i	0.157750	+	0.0184384i
$149$	−3.87440	−	8.98186i	−0.317403	−	0.735823i	−0.999987	−	0.00501621i	$-0.998403\pi$
$149$	−3.87440	−	8.98186i	−0.317403	−	0.735823i	0.682584	−	0.730807i	$-0.260856\pi$
$150$	−7.32191	+	1.95526i	−0.597831	+	0.159647i
$151$	−5.84580	+	2.93587i	−0.475725	+	0.238918i	−0.670471	−	0.741936i	$-0.733908\pi$
$151$	−5.84580	+	2.93587i	−0.475725	+	0.238918i	0.194746	+	0.980854i	$0.437612\pi$
$152$	6.10152	+	2.22077i	0.494899	+	0.180128i
$153$	6.10404	−	5.73938i	0.493482	−	0.464001i
$154$	−14.9765	+	5.45100i	−1.20684	+	0.439254i
$155$	1.89823	−	2.01201i	0.152469	−	0.161608i
$156$	8.62996	−	1.25665i	0.690950	−	0.100612i
$157$	−6.90159	+	4.53925i	−0.550807	+	0.362271i	−0.794200	−	0.607656i	$-0.792110\pi$
$157$	−6.90159	+	4.53925i	−0.550807	+	0.362271i	0.243393	+	0.969928i	$0.421739\pi$
$158$	−2.80056	+	9.35452i	−0.222801	+	0.744206i
$159$	−4.99163	−	8.10801i	−0.395862	−	0.643007i
$160$	0.471930	+	0.633912i	0.0373093	+	0.0501151i
$161$	−8.17021			−0.643902
$162$	6.15399	+	6.56722i	0.483503	+	0.515969i
$163$	−7.72707			−0.605231			−0.302615	−	0.953113i	$-0.597860\pi$
$163$	−7.72707			−0.605231			−0.302615	+	0.953113i	$0.597860\pi$
$164$	0.912678	+	1.22594i	0.0712682	+	0.0957298i
$165$	−3.06829	+	5.67899i	−0.238866	+	0.442109i
$166$	−2.83762	+	9.47830i	−0.220242	+	0.735659i
$167$	14.2821	−	9.39346i	1.10518	−	0.726887i	0.140438	−	0.990089i	$-0.455149\pi$
$167$	14.2821	−	9.39346i	1.10518	−	0.726887i	0.964741	+	0.263202i	$0.0847786\pi$
$168$	2.16590	−	5.43849i	0.167103	−	0.419588i
$169$	−8.47631	+	8.98436i	−0.652024	+	0.691105i
$170$	−2.07405	+	0.754894i	−0.159073	+	0.0578977i
$171$	−15.6051	−	11.6587i	−1.19335	−	0.891560i
$172$	−7.78977	−	2.83524i	−0.593964	−	0.216185i
$173$	19.6916	−	9.88947i	1.49712	−	0.751882i	0.503430	−	0.864036i	$-0.332071\pi$
$173$	19.6916	−	9.88947i	1.49712	−	0.751882i	0.993691	+	0.112153i	$0.0357748\pi$
$174$	−8.60331	−	8.61788i	−0.652216	−	0.653320i
$175$	−5.85720	−	13.5785i	−0.442762	−	1.02644i
$176$	−4.68374	−	0.547451i	−0.353050	−	0.0412656i
$177$	−9.25902	−	4.32709i	−0.695951	−	0.325244i
$178$	−5.77139	−	3.79591i	−0.432584	−	0.284515i
$179$	11.9153	−	9.99811i	0.890590	−	0.747294i	−0.0777383	−	0.996974i	$-0.524770\pi$
$179$	11.9153	−	9.99811i	0.890590	−	0.747294i	0.968328	+	0.249680i	$0.0803254\pi$
$180$	−0.807118	−	2.22926i	−0.0601590	−	0.166159i
$181$	14.7326	+	12.3621i	1.09506	+	0.918868i	0.997083	−	0.0763200i	$-0.0243171\pi$
$181$	14.7326	+	12.3621i	1.09506	+	0.918868i	0.0979812	+	0.995188i	$0.468761\pi$
$182$	4.88061	+	16.3024i	0.361775	+	1.20841i
$183$	0.601952	+	1.82175i	0.0444976	+	0.134667i
$184$	−2.16026	−	1.08492i	−0.159257	−	0.0799817i
$185$	1.04788	+	1.11069i	0.0770418	+	0.0816596i
$186$	−4.75226	−	3.76414i	−0.348453	−	0.276000i
$187$	5.21637	−	12.0929i	0.381459	−	0.884321i
$188$	−6.13135	+	10.6198i	−0.447175	+	0.774529i
$189$	−10.9273	+	13.7480i	−0.794846	+	1.00002i
$190$	2.56573	+	4.44397i	0.186137	+	0.322399i
$191$	−22.0602	+	2.57847i	−1.59622	+	0.186571i	−0.867214	−	0.497936i	$-0.834091\pi$
$191$	−22.0602	+	2.57847i	−1.59622	+	0.186571i	−0.729006	+	0.684508i	$0.760017\pi$
$192$	1.29486	−	1.15037i	0.0934484	−	0.0830205i
$193$	16.8307	−	3.98896i	1.21150	−	0.287131i	0.425272	−	0.905065i	$-0.360178\pi$
$193$	16.8307	−	3.98896i	1.21150	−	0.287131i	0.786230	+	0.617934i	$0.212030\pi$
$194$	−1.06304	−	18.2517i	−0.0763217	−	1.31039i
$195$	5.86293	+	3.62316i	0.419853	+	0.259460i
$196$	4.30354	+	1.01996i	0.307396	+	0.0728541i
$197$	−1.69715	+	9.62502i	−0.120917	+	0.685754i	0.862732	+	0.505661i	$0.168751\pi$
$197$	−1.69715	+	9.62502i	−0.120917	+	0.685754i	−0.983649	+	0.180094i	$0.942360\pi$
$198$	12.9804	+	5.62525i	0.922476	+	0.399769i
$199$	3.50037	+	19.8516i	0.248135	+	1.40724i	0.813098	+	0.582126i	$0.197779\pi$
$199$	3.50037	+	19.8516i	0.248135	+	1.40724i	−0.564963	+	0.825116i	$0.691110\pi$
$200$	0.254409	−	4.36804i	0.0179894	−	0.308867i
$201$	16.3866	+	1.44760i	1.15582	+	0.102106i
$202$	0.650491	−	0.873762i	0.0457684	−	0.0614777i
$203$	14.1894	−	19.0596i	0.995898	−	1.33772i
$204$	2.04064	+	4.38585i	0.142874	+	0.307071i
$205$	−0.0702307	+	1.20581i	−0.00490512	+	0.0842177i
$206$	2.13378	+	12.1013i	0.148668	+	0.843136i
$207$	5.26662	+	4.98567i	0.366055	+	0.346528i
$208$	−0.874328	+	4.95856i	−0.0606238	+	0.343814i
$209$	−29.7937	−	7.06124i	−2.06087	−	0.488436i
$210$	4.07393	−	2.19220i	0.281128	−	0.151276i
$211$	0.248069	+	4.25918i	0.0170778	+	0.293214i	0.996023	+	0.0890924i	$0.0283967\pi$
$211$	0.248069	+	4.25918i	0.0170778	+	0.293214i	−0.978946	+	0.204121i	$0.934566\pi$
$212$	5.34898	−	1.26773i	0.367370	−	0.0870682i
$213$	0.486612	+	0.161703i	0.0333421	+	0.0110797i
$214$	−11.4545	+	1.33883i	−0.783011	+	0.0915209i
$215$	−3.27564	−	5.67358i	−0.223397	−	0.386935i
$216$	−4.71487	+	2.18403i	−0.320806	+	0.148605i
$217$	5.91479	−	10.2447i	0.401522	−	0.695457i
$218$	4.52511	−	10.4904i	0.306479	−	0.710499i
$219$	−7.81288	+	3.09621i	−0.527945	+	0.209223i
$220$	−2.55743	−	2.71072i	−0.172422	−	0.182757i
$221$	−12.5664	−	6.31107i	−0.845305	−	0.424528i
$222$	2.22694	−	2.49814i	0.149463	−	0.167664i
$223$	1.76619	+	5.89948i	0.118273	+	0.395058i	0.996540	−	0.0831112i	$-0.0264857\pi$
$223$	1.76619	+	5.89948i	0.118273	+	0.395058i	−0.878268	+	0.478169i	$0.841300\pi$
$224$	2.58904	+	2.17247i	0.172988	+	0.145154i
$225$	−4.51032	+	12.3271i	−0.300688	+	0.821806i
$226$	−1.72503	+	1.44747i	−0.114747	+	0.0962845i
$227$	−10.0236	−	6.59261i	−0.665288	−	0.437567i	0.171433	−	0.985196i	$-0.445160\pi$
$227$	−10.0236	−	6.59261i	−0.665288	−	0.437567i	−0.836721	+	0.547629i	$0.815531\pi$
$228$	9.21796	−	6.44287i	0.610474	−	0.426689i
$229$	5.33732	+	0.623843i	0.352700	+	0.0412247i	0.290598	−	0.956845i	$-0.406146\pi$
$229$	5.33732	+	0.623843i	0.352700	+	0.0412247i	0.0621016	+	0.998070i	$0.480220\pi$
$230$	−0.756690	−	1.75420i	−0.0498946	−	0.115669i
$231$	−7.16721	+	26.6582i	−0.471568	+	1.75398i
$232$	6.28271	−	3.15529i	0.412480	−	0.207155i
$233$	21.7098	+	7.90173i	1.42226	+	0.517660i	0.934702	−	0.355432i	$-0.115666\pi$
$233$	21.7098	+	7.90173i	1.42226	+	0.517660i	0.487556	+	0.873092i	$0.337888\pi$
$234$	6.80201	−	13.4870i	0.444661	−	0.881672i
$235$	−9.10667	+	3.31456i	−0.594054	+	0.216218i
$236$	4.04927	−	4.29198i	0.263585	−	0.279384i
$237$	10.4788	+	13.2757i	0.680674	+	0.862350i
$238$	−7.88628	+	5.18689i	−0.511192	+	0.336216i
$239$	5.43719	−	18.1615i	0.351703	−	1.17477i	−0.580934	−	0.813951i	$-0.697312\pi$
$239$	5.43719	−	18.1615i	0.351703	−	1.17477i	0.932636	−	0.360818i	$-0.117502\pi$
$240$	1.36828	−	0.0386547i	0.0883221	−	0.00249515i
$241$	−8.09731	−	10.8766i	−0.521594	−	0.700622i	0.460787	−	0.887511i	$-0.347567\pi$
$241$	−8.09731	−	10.8766i	−0.521594	−	0.700622i	−0.982381	+	0.186889i	$0.940160\pi$
$242$	11.2371			0.722349
$243$	15.4333	−	2.19402i	0.990046	−	0.140746i
$244$	−1.10772			−0.0709143
$245$	2.08723	+	2.80364i	0.133348	+	0.179118i
$246$	2.64616	−	0.0747554i	0.168713	−	0.00476623i
$247$	−9.37650	+	31.3197i	−0.596612	+	1.99282i
$248$	2.92432	−	1.92335i	0.185694	−	0.122133i
$249$	10.6175	+	13.4514i	0.672856	+	0.852446i
$250$	5.08459	−	5.38936i	0.321578	−	0.340853i
$251$	18.1264	−	6.59747i	1.14413	−	0.416428i	0.300725	−	0.953711i	$-0.402771\pi$
$251$	18.1264	−	6.59747i	1.14413	−	0.416428i	0.843402	+	0.537283i	$0.180549\pi$
$252$	−5.55728	−	8.48065i	−0.350076	−	0.534231i
$253$	10.7120	+	3.89887i	0.673461	+	0.245120i
$254$	5.42377	−	2.72392i	0.340318	−	0.170914i
$255$	−0.992566	+	3.69182i	−0.0621569	+	0.231190i
$256$	0.396080	+	0.918216i	0.0247550	+	0.0573885i
$257$	22.2182	+	2.59694i	1.38593	+	0.161993i	0.776137	−	0.630564i	$-0.217177\pi$
$257$	22.2182	+	2.59694i	1.38593	+	0.161993i	0.609798	+	0.792557i	$0.291251\pi$
$258$	−11.7685	+	8.22556i	−0.732674	+	0.512101i
$259$	5.45599	+	3.58846i	0.339019	+	0.222976i
$260$	−3.04822	+	2.55776i	−0.189042	+	0.158625i
$261$	−20.7773	+	3.62737i	−1.28608	+	0.224529i
$262$	0.875908	+	0.734974i	0.0541138	+	0.0454068i
$263$	4.97413	+	16.6148i	0.306718	+	1.02451i	0.962889	+	0.269898i	$0.0869899\pi$
$263$	4.97413	+	16.6148i	0.306718	+	1.02451i	−0.656171	+	0.754612i	$0.727825\pi$
$264$	−5.43501	+	6.09688i	−0.334502	+	0.375237i
$265$	3.88226	+	1.94975i	0.238485	+	0.119772i
$266$	15.0597	+	15.9623i	0.923367	+	0.978711i
$267$	−11.1231	+	4.40803i	−0.680721	+	0.269767i
$268$	−3.76182	+	8.72088i	−0.229790	+	0.532712i
$269$	−1.95957	+	3.39407i	−0.119477	+	0.206940i	−0.919560	−	0.392948i	$-0.871455\pi$
$269$	−1.95957	+	3.39407i	−0.119477	+	0.206940i	0.800084	+	0.599888i	$0.204788\pi$
$270$	−3.96384	−	1.07290i	−0.241232	−	0.0652943i
$271$	−8.05080	−	13.9444i	−0.489051	−	0.847062i	0.510869	−	0.859658i	$-0.329324\pi$
$271$	−8.05080	−	13.9444i	−0.489051	−	0.847062i	−0.999921	+	0.0125967i	$0.995990\pi$
$272$	−2.77396	+	0.324229i	−0.168196	+	0.0196593i
$273$	27.9709	+	9.29479i	1.69287	+	0.562546i
$274$	−13.8166	+	3.27459i	−0.834690	+	0.197825i
$275$	1.19970	+	20.5980i	0.0723445	+	1.24211i
$276$	−3.68713	+	1.98406i	−0.221939	+	0.119426i
$277$	−15.0423	−	3.56508i	−0.903801	−	0.214205i	−0.247664	−	0.968846i	$-0.579663\pi$
$277$	−15.0423	−	3.56508i	−0.903801	−	0.214205i	−0.656138	+	0.754641i	$0.727811\pi$
$278$	3.11485	−	17.6652i	0.186816	−	1.05949i
$279$	−10.0643	+	2.99453i	−0.602536	+	0.179278i
$280$	0.463813	+	2.63042i	0.0277182	+	0.157197i
$281$	0.924411	−	15.8715i	0.0551457	−	0.946816i	−0.851349	−	0.524599i	$-0.824215\pi$
$281$	0.924411	−	15.8715i	0.0551457	−	0.946816i	0.906495	−	0.422216i	$-0.138748\pi$
$282$	8.95997	+	19.2572i	0.533558	+	1.14675i
$283$	−7.34306	+	9.86344i	−0.436499	+	0.586320i	−0.964881	−	0.262686i	$-0.915392\pi$
$283$	−7.34306	+	9.86344i	−0.436499	+	0.586320i	0.528382	+	0.849007i	$0.322799\pi$
$284$	−0.176790	+	0.237470i	−0.0104905	+	0.0140912i
$285$	8.85345	+	0.782123i	0.524433	+	0.0463289i
$286$	1.38056	−	23.7033i	0.0816341	−	1.40160i
$287$	0.896982	+	5.08704i	0.0529472	+	0.300278i
$288$	−0.343238	−	2.98030i	−0.0202255	−	0.175616i
$289$	−1.59757	+	9.06026i	−0.0939746	+	0.532956i
$290$	5.40640	+	1.28134i	0.317475	+	0.0752429i
$291$	−26.9377	−	16.6469i	−1.57912	−	0.975859i
$292$	−0.282122	−	4.84386i	−0.0165100	−	0.283465i
$293$	1.11581	−	0.264451i	0.0651862	−	0.0154494i	−0.197893	−	0.980224i	$-0.563410\pi$
$293$	1.11581	−	0.264451i	0.0651862	−	0.0154494i	0.263080	+	0.964774i	$0.415262\pi$
$294$	5.72685	−	5.08779i	0.333996	−	0.296726i
$295$	4.63171	−	0.541369i	0.269669	−	0.0315197i
$296$	0.966090	+	1.67332i	0.0561529	+	0.0972596i
$297$	20.8876	−	12.8106i	1.21202	−	0.743346i
$298$	4.89093	−	8.47134i	0.283324	−	0.490732i
$299$	4.82097	−	11.1763i	0.278804	−	0.646340i
$300$	−5.94070	−	4.70547i	−0.342987	−	0.271670i
$301$	−19.2265	−	20.3789i	−1.10820	−	1.17462i
$302$	−5.84580	−	2.93587i	−0.336388	−	0.168940i
$303$	−0.591950	−	1.79148i	−0.0340066	−	0.102918i
$304$	1.86224	+	6.22033i	0.106807	+	0.356760i
$305$	−0.670611	−	0.562709i	−0.0383991	−	0.0322206i
$306$	8.24877	+	1.46887i	0.471551	+	0.0839698i
$307$	8.22051	−	6.89783i	0.469169	−	0.393680i	−0.377322	−	0.926082i	$-0.623155\pi$
$307$	8.22051	−	6.89783i	0.469169	−	0.393680i	0.846491	+	0.532402i	$0.178711\pi$
$308$	−13.3157	−	8.75789i	−0.758734	−	0.499027i
$309$	19.2817	+	9.01106i	1.09690	+	0.512621i
$310$	2.74742	+	0.321127i	0.156043	+	0.0182388i
$311$	−7.00067	−	16.2294i	−0.396972	−	0.920284i	−0.993087	−	0.117385i	$-0.962549\pi$
$311$	−7.00067	−	16.2294i	−0.396972	−	0.920284i	0.596115	−	0.802899i	$-0.296710\pi$
$312$	6.16144	+	6.17187i	0.348823	+	0.349413i
$313$	−21.2913	+	10.6929i	−1.20346	+	0.604399i	−0.933536	−	0.358484i	$-0.883294\pi$
$313$	−21.2913	+	10.6929i	−1.20346	+	0.604399i	−0.269921	+	0.962883i	$0.586997\pi$
$314$	−7.76238	−	2.82528i	−0.438056	−	0.159440i
$315$	0.943712	−	7.95722i	0.0531721	−	0.448339i
$316$	−9.17586	+	3.33974i	−0.516182	+	0.187875i
$317$	15.7539	−	16.6981i	0.884827	−	0.937861i	−0.113623	−	0.993524i	$-0.536246\pi$
$317$	15.7539	−	16.6981i	0.884827	−	0.937861i	0.998450	+	0.0556626i	$0.0177271\pi$
$318$	3.52283	−	8.84567i	0.197550	−	0.496041i
$319$	−27.6992	+	18.2180i	−1.55086	+	1.02001i
$320$	−0.226658	+	0.757092i	−0.0126706	+	0.0423227i
$321$	−9.49490	+	17.5738i	−0.529954	+	0.980874i
$322$	−4.87891	−	6.55351i	−0.271891	−	0.365213i
$323$	−18.1342			−1.00902
$324$	−1.59281	+	8.85793i	−0.0884894	+	0.492107i
$325$	22.0306			1.22204
$326$	−4.61428	−	6.19806i	−0.255562	−	0.343279i
$327$	−10.3741	−	16.8509i	−0.573690	−	0.931856i
$328$	−0.438341	+	1.46416i	−0.0242033	+	0.0808447i
$329$	−34.6267	+	22.7744i	−1.90903	+	1.25559i
$330$	−6.38751	+	0.930114i	−0.351621	+	0.0512011i
$331$	18.5081	−	19.6174i	1.01729	−	1.07827i	0.0203789	−	0.999792i	$-0.493513\pi$
$331$	18.5081	−	19.6174i	1.01729	−	1.07827i	0.996916	−	0.0784771i	$-0.0250058\pi$
$332$	−9.29727	+	3.38393i	−0.510254	+	0.185717i
$333$	−1.32723	−	5.64255i	−0.0727319	−	0.309210i
$334$	16.0634	+	5.84659i	0.878948	+	0.319911i
$335$	−6.70752	+	3.36864i	−0.366471	+	0.184049i
$336$	5.65572	−	1.51032i	0.308545	−	0.0823948i
$337$	−10.6524	−	24.6950i	−0.580272	−	1.34522i	−0.915208	−	0.402981i	$-0.867974\pi$
$337$	−10.6524	−	24.6950i	−0.580272	−	1.34522i	0.334937	−	0.942241i	$-0.391285\pi$
$338$	−12.2683	−	1.43395i	−0.667306	−	0.0779968i
$339$	0.336652	+	3.88579i	0.0182844	+	0.211047i
$340$	−1.84406	−	1.21286i	−0.100008	−	0.0657763i
$341$	−12.6438	+	10.6094i	−0.684700	+	0.574531i
$342$	0.0329494	−	19.4793i	0.00178170	−	1.05332i
$343$	−6.67260	−	5.59897i	−0.360286	−	0.302316i
$344$	−2.37751	−	7.94144i	−0.128187	−	0.428174i
$345$	−3.24006	−	0.671877i	−0.174439	−	0.0361726i
$346$	19.6916	+	9.88947i	1.05862	+	0.531661i
$347$	−4.24338	−	4.49772i	−0.227797	−	0.241450i	0.603387	−	0.797449i	$-0.293818\pi$
$347$	−4.24338	−	4.49772i	−0.227797	−	0.241450i	−0.831183	+	0.555998i	$0.812336\pi$
$348$	1.77506	−	12.0472i	0.0951531	−	0.645795i
$349$	4.45049	−	10.3174i	0.238229	−	0.552277i	−0.756596	−	0.653883i	$-0.773139\pi$
$349$	4.45049	−	10.3174i	0.238229	−	0.552277i	0.994825	+	0.101606i	$0.0323981\pi$
$350$	7.39396	−	12.8067i	0.395224	−	0.684548i
$351$	−12.3585	−	23.0601i	−0.659646	−	1.23086i
$352$	−2.35781	−	4.08385i	−0.125672	−	0.217670i
$353$	−18.4320	+	2.15440i	−0.981039	+	0.114667i	−0.591467	−	0.806329i	$-0.701451\pi$
$353$	−18.4320	+	2.15440i	−0.981039	+	0.114667i	−0.389572	+	0.920996i	$0.627377\pi$
$354$	−2.05824	−	10.0108i	−0.109394	−	0.532070i
$355$	−0.227661	+	0.0539565i	−0.0120830	+	0.00286372i
$356$	−0.401654	−	6.89613i	−0.0212876	−	0.365494i
$357$	−0.489329	+	16.3417i	−0.0258980	+	0.864896i
$358$	15.1350	+	3.58707i	0.799911	+	0.189582i
$359$	−2.91454	+	16.5292i	−0.153824	+	0.872378i	0.806030	+	0.591875i	$0.201612\pi$
$359$	−2.91454	+	16.5292i	−0.153824	+	0.872378i	−0.959853	+	0.280503i	$0.909499\pi$
$360$	1.30617	−	1.97863i	0.0688410	−	0.104283i
$361$	4.02177	+	22.8086i	0.211672	+	1.20045i
$362$	−1.11824	+	19.1995i	−0.0587735	+	1.00910i
$363$	11.1771	−	15.9339i	0.586648	−	0.836314i
$364$	−10.1620	+	13.6499i	−0.532634	+	0.715451i
$365$	2.28983	−	3.07578i	0.119855	−	0.160994i
$366$	−1.10181	+	1.57071i	−0.0575923	+	0.0821024i
$367$	1.03177	−	17.7149i	0.0538581	−	0.924708i	−0.857858	−	0.513887i	$-0.828205\pi$
$367$	1.03177	−	17.7149i	0.0538581	−	0.924708i	0.911716	−	0.410821i	$-0.134758\pi$
$368$	−0.419776	−	2.38067i	−0.0218823	−	0.124101i
$369$	2.52603	−	3.82653i	0.131500	−	0.199201i
$370$	−0.265159	+	1.50379i	−0.0137849	+	0.0781783i
$371$	18.0783	+	4.28463i	0.938576	+	0.222447i
$372$	0.181448	−	6.05969i	0.00940766	−	0.314180i
$373$	0.331561	+	5.69268i	0.0171676	+	0.294756i	0.995953	+	0.0898703i	$0.0286452\pi$
$373$	0.331561	+	5.69268i	0.0171676	+	0.294756i	−0.978786	+	0.204886i	$0.934318\pi$
$374$	12.8150	−	3.03721i	0.662648	−	0.157050i
$375$	−2.58450	−	12.5704i	−0.133463	−	0.649133i
$376$	−12.1798	+	1.42361i	−0.628124	+	0.0734172i
$377$	17.6995	+	30.6565i	0.911573	+	1.57889i
$378$	−17.5530	−	0.555316i	−0.902826	−	0.0285624i
$379$	0.758315	−	1.31344i	0.0389520	−	0.0674669i	−0.845892	−	0.533354i	$-0.820931\pi$
$379$	0.758315	−	1.31344i	0.0389520	−	0.0674669i	0.884844	+	0.465887i	$0.154265\pi$
$380$	−2.03246	+	4.71178i	−0.104263	+	0.241709i
$381$	1.53238	−	10.4001i	0.0785063	−	0.532816i
$382$	−15.2417	−	16.1552i	−0.779832	−	0.826574i
$383$	6.65038	+	3.33995i	0.339819	+	0.170663i	0.610522	−	0.792000i	$-0.290960\pi$
$383$	6.65038	+	3.33995i	0.339819	+	0.170663i	−0.270703	+	0.962663i	$0.587256\pi$
$384$	1.69597	+	0.351686i	0.0865472	+	0.0179469i
$385$	−3.61240	−	12.0663i	−0.184105	−	0.614954i
$386$	13.2502	+	11.1183i	0.674420	+	0.565905i
$387$	−0.0420662	+	24.8691i	−0.00213835	+	1.26416i
$388$	14.0053	−	11.7518i	0.711011	−	0.596609i
$389$	−15.9106	−	10.4646i	−0.806701	−	0.530576i	0.0778798	−	0.996963i	$-0.475185\pi$
$389$	−15.9106	−	10.4646i	−0.806701	−	0.530576i	−0.884581	+	0.466387i	$0.845555\pi$
$390$	0.594880	+	6.86639i	0.0301229	+	0.347693i
$391$	6.70575	+	0.783790i	0.339125	+	0.0396380i
$392$	1.75176	+	4.06105i	0.0884775	+	0.205114i
$393$	1.91341	−	0.510962i	0.0965186	−	0.0257746i
$394$	−8.73392	+	4.38634i	−0.440009	+	0.220981i
$395$	−7.25161	−	2.63937i	−0.364868	−	0.132801i
$396$	3.23920	+	13.7710i	0.162776	+	0.692021i
$397$	18.3478	−	6.67807i	0.920851	−	0.335162i	0.162274	−	0.986746i	$-0.448117\pi$
$397$	18.3478	−	6.67807i	0.920851	−	0.335162i	0.758577	+	0.651583i	$0.225895\pi$
$398$	−13.8331	+	14.6623i	−0.693393	+	0.734954i
$399$	37.6134	−	5.47706i	1.88302	−	0.274196i
$400$	3.65563	−	2.40434i	0.182781	−	0.120217i
$401$	2.27013	−	7.58278i	0.113365	−	0.378666i	−0.882411	−	0.470479i	$-0.844081\pi$
$401$	2.27013	−	7.58278i	0.113365	−	0.378666i	0.995776	+	0.0918132i	$0.0292663\pi$
$402$	8.62422	+	14.0085i	0.430137	+	0.698680i
$403$	10.5239	+	14.1361i	0.524234	+	0.704169i
$404$	1.08931			0.0541953
$405$	−5.46403	+	4.55345i	−0.271510	+	0.226263i
$406$	23.7615			1.17926
$407$	−5.44097	−	7.30850i	−0.269699	−	0.362269i
$408$	−2.29941	+	4.25590i	−0.113838	+	0.210698i
$409$	−2.10269	+	7.02347i	−0.103971	+	0.347288i	−0.994106	−	0.108408i	$-0.965425\pi$
$409$	−2.10269	+	7.02347i	−0.103971	+	0.347288i	0.890135	+	0.455696i	$0.150610\pi$
$410$	−1.00915	+	0.663728i	−0.0498384	+	0.0327792i
$411$	−9.09956	+	22.8486i	−0.448848	+	1.12704i
$412$	−8.43251	+	8.93794i	−0.415440	+	0.440341i
$413$	18.7401	−	6.82083i	0.922139	−	0.335631i
$414$	−0.854110	+	7.20171i	−0.0419772	+	0.353945i
$415$	−7.34756	−	2.67429i	−0.360677	−	0.131276i
$416$	−4.49949	+	2.25973i	−0.220606	+	0.110792i
$417$	−21.9505	−	21.9877i	−1.07492	−	1.07674i
$418$	−12.1276	−	28.1149i	−0.593180	−	1.37514i
$419$	21.2298	+	2.48141i	1.03714	+	0.121225i	0.617586	−	0.786504i	$-0.288111\pi$
$419$	21.2298	+	2.48141i	1.03714	+	0.121225i	0.419558	+	0.907728i	$0.362185\pi$
$420$	4.19120	+	1.95870i	0.204509	+	0.0955750i
$421$	26.2023	+	17.2335i	1.27702	+	0.839910i	0.992908	−	0.118881i	$-0.0379308\pi$
$421$	26.2023	+	17.2335i	1.27702	+	0.839910i	0.284112	+	0.958791i	$0.408301\pi$
$422$	−3.26825	+	2.74238i	−0.159096	+	0.133497i
$423$	36.2183	+	6.44946i	1.76100	+	0.313583i
$424$	4.21107	+	3.53350i	0.204507	+	0.171602i
$425$	3.50471	+	11.7065i	0.170003	+	0.567851i
$426$	0.160879	+	0.486885i	0.00779463	+	0.0235897i
$427$	−3.34559	−	1.68022i	−0.161905	−	0.0813116i
$428$	−7.91404	−	8.38839i	−0.382540	−	0.405468i
$429$	−32.2374	−	25.5344i	−1.55644	−	1.23281i
$430$	2.59483	−	6.01549i	0.125134	−	0.290093i
$431$	−16.8522	+	29.1889i	−0.811744	+	1.40598i	0.0998989	+	0.994998i	$0.468148\pi$
$431$	−16.8522	+	29.1889i	−0.811744	+	1.40598i	−0.911643	+	0.410984i	$0.865185\pi$
$432$	−4.56739	−	2.47769i	−0.219749	−	0.119208i
$433$	5.47682	+	9.48613i	0.263199	+	0.455874i	0.967090	−	0.254434i	$-0.0818890\pi$
$433$	5.47682	+	9.48613i	0.263199	+	0.455874i	−0.703891	+	0.710308i	$0.748556\pi$
$434$	11.7496	−	1.37333i	0.563999	−	0.0659220i
$435$	7.19445	−	6.39162i	0.344948	−	0.306455i
$436$	11.1168	−	2.63473i	0.532398	−	0.126181i
$437$	−0.912664	−	15.6698i	−0.0436587	−	0.749590i
$438$	−7.14907	−	4.41796i	−0.341596	−	0.211098i
$439$	−8.40214	−	1.99134i	−0.401012	−	0.0950417i	0.0251604	−	0.999683i	$-0.491990\pi$
$439$	−8.40214	−	1.99134i	−0.401012	−	0.0950417i	−0.426173	+	0.904642i	$0.640138\pi$
$440$	0.647138	−	3.67010i	0.0308511	−	0.174965i
$441$	−1.51806	−	13.1811i	−0.0722885	−	0.627673i
$442$	−2.44186	−	13.8485i	−0.116148	−	0.658705i
$443$	0.271066	−	4.65403i	0.0128787	−	0.221119i	−0.985728	−	0.168347i	$-0.946157\pi$
$443$	0.271066	−	4.65403i	0.0128787	−	0.221119i	0.998607	−	0.0527726i	$-0.0168058\pi$
$444$	3.33365	+	0.294498i	0.158208	+	0.0139763i
$445$	3.26000	−	4.37894i	0.154539	−	0.207582i
$446$	−3.67741	+	4.93962i	−0.174131	+	0.233898i
$447$	−7.14730	−	15.3613i	−0.338056	−	0.726566i
$448$	−0.196515	+	3.37404i	−0.00928448	+	0.159408i
$449$	−0.0560318	−	0.317772i	−0.00264430	−	0.0149966i	0.983457	−	0.181141i	$-0.0579792\pi$
$449$	−0.0560318	−	0.317772i	−0.00264430	−	0.0149966i	−0.986101	+	0.166145i	$0.946868\pi$
$450$	−12.5812	+	3.74339i	−0.593084	+	0.176465i
$451$	1.25152	−	7.09772i	0.0589317	−	0.334218i
$452$	−2.19117	−	0.519317i	−0.103064	−	0.0244266i
$453$	−9.97759	+	5.36898i	−0.468788	+	0.252257i
$454$	−0.697579	−	11.9770i	−0.0327390	−	0.562107i
$455$	−13.0861	+	3.10146i	−0.613486	+	0.145399i
$456$	10.6726	+	3.54652i	0.499788	+	0.166081i
$457$	−2.29634	+	0.268404i	−0.107418	+	0.0125554i	−0.169632	−	0.985507i	$-0.554258\pi$
$457$	−2.29634	+	0.268404i	−0.107418	+	0.0125554i	0.0622140	+	0.998063i	$0.480184\pi$
$458$	2.68683	+	4.65372i	0.125547	+	0.217454i
$459$	10.2876	−	10.2355i	0.480182	−	0.477752i
$460$	0.955224	−	1.65450i	0.0445375	−	0.0771413i
$461$	2.43988	−	5.65627i	0.113636	−	0.263439i	−0.851901	−	0.523703i	$-0.824550\pi$
$461$	2.43988	−	5.65627i	0.113636	−	0.263439i	0.965538	+	0.260264i	$0.0838096\pi$
$462$	−25.6631	+	10.1702i	−1.19396	+	0.473159i
$463$	10.4465	+	11.0727i	0.485491	+	0.514591i	0.923092	−	0.384579i	$-0.125653\pi$
$463$	10.4465	+	11.0727i	0.485491	+	0.514591i	−0.437601	+	0.899169i	$0.644172\pi$
$464$	6.28271	+	3.15529i	0.291667	+	0.146481i
$465$	3.18811	−	3.57635i	0.147845	−	0.165849i
$466$	6.62605	+	22.1325i	0.306946	+	1.02527i
$467$	23.8215	+	19.9887i	1.10233	+	0.924965i	0.997580	−	0.0695340i	$-0.0221512\pi$
$467$	23.8215	+	19.9887i	1.10233	+	0.924965i	0.104750	+	0.994499i	$0.466596\pi$
$468$	14.8801	−	2.59782i	0.687833	−	0.120084i
$469$	−24.5898	+	20.6333i	−1.13545	+	0.952756i
$470$	−8.09681	−	5.32535i	−0.373478	−	0.245640i
$471$	−11.7271	+	8.19664i	−0.540357	+	0.377681i
$472$	5.86076	+	0.685024i	0.269763	+	0.0315308i
$473$	15.4832	+	35.8941i	0.711918	+	1.65041i
$474$	−4.39123	+	16.3330i	−0.201696	+	0.750201i
$475$	25.3883	−	12.7505i	1.16489	−	0.585032i
$476$	−8.86988	−	3.22837i	−0.406550	−	0.147972i
$477$	−9.03889	−	13.7937i	−0.413862	−	0.631572i
$478$	17.8146	−	6.48399i	0.814821	−	0.296571i
$479$	−13.8916	+	14.7242i	−0.634722	+	0.672766i	−0.962279	−	0.272066i	$-0.912293\pi$
$479$	−13.8916	+	14.7242i	−0.634722	+	0.672766i	0.327557	+	0.944831i	$0.393775\pi$
$480$	0.848086	+	1.07445i	0.0387097	+	0.0490415i
$481$	−8.12816	+	5.34597i	−0.370612	+	0.243755i
$482$	3.88898	−	12.9901i	0.177138	−	0.591682i
$483$	−14.1456	+	0.399620i	−0.643646	+	0.0181834i
$484$	6.71034	+	9.01355i	0.305015	+	0.409707i
$485$	14.4486			0.656077
$486$	10.9760	+	11.0692i	0.497881	+	0.502110i
$487$	−31.6822			−1.43566			−0.717828	−	0.696221i	$-0.754864\pi$
$487$	−31.6822			−1.43566			−0.717828	+	0.696221i	$0.754864\pi$
$488$	−0.661483	−	0.888526i	−0.0299439	−	0.0402217i
$489$	−13.3783	+	0.377946i	−0.604989	+	0.0170913i
$490$	−1.00245	+	3.34843i	−0.0452863	+	0.151267i
$491$	3.86631	−	2.54291i	0.174484	−	0.114760i	−0.459263	−	0.888300i	$-0.651886\pi$
$491$	3.86631	−	2.54291i	0.174484	−	0.114760i	0.633747	+	0.773540i	$0.281516\pi$
$492$	1.64014	+	2.07790i	0.0739431	+	0.0936790i
$493$	−13.4745	+	14.2821i	−0.606859	+	0.643233i
$494$	−30.7215	+	11.1817i	−1.38223	+	0.503089i
$495$	−5.03454	+	9.98246i	−0.226286	+	0.448678i
$496$	3.28905	+	1.19711i	0.147682	+	0.0537520i
$497$	−0.894153	+	0.449060i	−0.0401082	+	0.0201431i
$498$	−4.44933	+	16.5491i	−0.199379	+	0.741585i
$499$	8.97778	+	20.8128i	0.401901	+	0.931711i	0.992215	+	0.124537i	$0.0397446\pi$
$499$	8.97778	+	20.8128i	0.401901	+	0.931711i	−0.590314	+	0.807174i	$0.700996\pi$
$500$	7.35924	+	0.860171i	0.329115	+	0.0384680i
$501$	24.2679	−	16.9620i	1.08421	−	0.757807i
$502$	16.1163	+	10.5999i	0.719306	+	0.473095i
$503$	15.2990	−	12.8374i	0.682150	−	0.572392i	−0.234484	−	0.972120i	$-0.575340\pi$
$503$	15.2990	−	12.8374i	0.682150	−	0.572392i	0.916634	+	0.399728i	$0.130896\pi$
$504$	3.48395	−	9.52192i	0.155187	−	0.424140i
$505$	0.659468	+	0.553359i	0.0293459	+	0.0246242i
$506$	3.26942	+	10.9206i	0.145343	+	0.485481i
$507$	−14.2361	+	15.9698i	−0.632247	+	0.709242i
$508$	5.42377	+	2.72392i	0.240641	+	0.120854i
$509$	−14.4568	−	15.3233i	−0.640785	−	0.679193i	0.322839	−	0.946454i	$-0.395363\pi$
$509$	−14.4568	−	15.3233i	−0.640785	−	0.679193i	−0.963624	+	0.267261i	$0.913881\pi$
$510$	−3.55401	+	1.40844i	−0.157374	+	0.0623667i
$511$	6.49523	−	15.0576i	0.287332	−	0.666111i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$	−27.5883	−	19.4221i	−1.21805	−	0.857505i
$514$	11.1847	+	19.3725i	0.493338	+	0.854486i
$515$	−9.64542	+	1.12739i	−0.425028	+	0.0496786i
$516$	−13.6256	−	4.52781i	−0.599832	−	0.199326i
$517$	56.2676	−	13.3357i	2.47464	−	0.586502i
$518$	0.379703	+	6.51925i	0.0166832	+	0.286440i
$519$	33.6095	−	18.0854i	1.47529	−	0.793860i
$520$	−3.87191	−	0.917659i	−0.169794	−	0.0402420i
$521$	1.13820	−	6.45504i	0.0498653	−	0.282800i	−0.949671	−	0.313249i	$-0.898583\pi$
$521$	1.13820	−	6.45504i	0.0498653	−	0.282800i	0.999536	+	0.0304487i	$0.00969363\pi$
$522$	−15.3170	−	14.4998i	−0.670405	−	0.634641i
$523$	−6.25967	−	35.5004i	−0.273716	−	1.55232i	−0.743010	−	0.669280i	$-0.766603\pi$
$523$	−6.25967	−	35.5004i	−0.273716	−	1.55232i	0.469294	−	0.883042i	$-0.344509\pi$
$524$	−0.0664838	+	1.14148i	−0.00290436	+	0.0498659i
$525$	−10.8051	−	23.2228i	−0.471572	−	1.01353i
$526$	−10.3567	+	13.9115i	−0.451575	+	0.606571i
$527$	−5.83741	+	7.84100i	−0.254282	+	0.341560i
$528$	−8.13602	−	0.718743i	−0.354075	−	0.0312793i
$529$	0.997545	−	17.1272i	0.0433715	−	0.744660i
$530$	0.754390	+	4.27836i	0.0327686	+	0.185840i
$531$	−16.2423	−	7.03887i	−0.704858	−	0.305461i
$532$	−3.81073	+	21.6117i	−0.165216	+	0.936987i
$533$	−7.48799	−	1.77469i	−0.324341	−	0.0768702i
$534$	−10.1780	−	6.28979i	−0.440446	−	0.272186i
$535$	−0.529932	−	9.09858i	−0.0229110	−	0.393366i
$536$	−9.24162	+	2.19030i	−0.399177	+	0.0946067i
$537$	20.1406	−	17.8931i	0.869132	−	0.772145i
$538$	−3.89263	+	0.454984i	−0.167823	+	0.0196157i
$539$	−10.4280	−	18.0619i	−0.449167	−	0.777980i
$540$	−1.50645	−	3.82018i	−0.0648272	−	0.164394i
$541$	−3.66022	+	6.33969i	−0.157365	+	0.272565i	−0.933918	−	0.357488i	$-0.883633\pi$
$541$	−3.66022	+	6.33969i	−0.157365	+	0.272565i	0.776552	+	0.630053i	$0.216967\pi$
$542$	6.37752	−	14.7847i	0.273938	−	0.635059i
$543$	26.1121	+	20.6827i	1.12058	+	0.887578i
$544$	−1.91657	−	2.03144i	−0.0821721	−	0.0870973i
$545$	8.06851	+	4.05216i	0.345617	+	0.173575i
$546$	9.24747	+	27.9865i	0.395755	+	1.19771i
$547$	8.55639	+	28.5803i	0.365845	+	1.22201i	0.920770	+	0.390106i	$0.127562\pi$
$547$	8.55639	+	28.5803i	0.365845	+	1.22201i	−0.554925	+	0.831900i	$0.687253\pi$
$548$	−10.8773	−	9.12715i	−0.464656	−	0.389892i
$549$	1.13130	+	3.12466i	0.0482827	+	0.133357i
$550$	−15.8057	+	13.2626i	−0.673959	+	0.565519i
$551$	38.1400	+	25.0851i	1.62482	+	1.06866i
$552$	−3.79326	−	1.77273i	−0.161452	−	0.0754525i
$553$	−32.7793	−	3.83135i	−1.39392	−	0.162926i
$554$	−6.12298	−	14.1947i	−0.260140	−	0.603073i
$555$	1.86859	+	1.87175i	0.0793171	+	0.0794514i
$556$	16.0297	−	8.05044i	0.679812	−	0.341415i
$557$	29.2909	+	10.6610i	1.24109	+	0.451721i	0.877383	−	0.479791i	$-0.159288\pi$
$557$	29.2909	+	10.6610i	1.24109	+	0.451721i	0.363711	+	0.931512i	$0.381510\pi$
$558$	−8.41199	−	6.28463i	−0.356108	−	0.266050i
$559$	39.2219	−	14.2756i	1.65891	−	0.603794i
$560$	−1.83295	+	1.94281i	−0.0774562	+	0.0820988i
$561$	8.43993	−	21.1923i	0.356334	−	0.894740i
$562$	13.2829	−	8.73632i	0.560307	−	0.368520i
$563$	−9.13725	+	30.5205i	−0.385089	+	1.28629i	0.517463	+	0.855706i	$0.326877\pi$
$563$	−9.13725	+	30.5205i	−0.385089	+	1.28629i	−0.902552	+	0.430581i	$0.858309\pi$
$564$	−10.0961	+	18.6866i	−0.425124	+	0.786848i
$565$	−1.06272	−	1.42749i	−0.0447091	−	0.0600548i
$566$	−12.2967			−0.516867
$567$	−18.2467	+	24.3372i	−0.766289	+	1.02207i
$568$	−0.296051			−0.0124220
$569$	19.9325	+	26.7740i	0.835613	+	1.12242i	0.990906	+	0.134554i	$0.0429603\pi$
$569$	19.9325	+	26.7740i	0.835613	+	1.12242i	−0.155294	+	0.987868i	$0.549632\pi$
$570$	4.65956	+	7.56861i	0.195167	+	0.317014i
$571$	−10.5506	+	35.2414i	−0.441528	+	1.47481i	0.390775	+	0.920486i	$0.372207\pi$
$571$	−10.5506	+	35.2414i	−0.441528	+	1.47481i	−0.832303	+	0.554320i	$0.812978\pi$
$572$	19.8373	−	13.0472i	0.829441	−	0.545532i
$573$	−38.0680	+	5.54326i	−1.59031	+	0.231573i
$574$	−3.54479	+	3.75726i	−0.147957	+	0.156825i
$575$	−9.93928	+	3.61760i	−0.414497	+	0.150864i
$576$	2.18560	−	2.05503i	0.0910667	−	0.0856263i
$577$	−16.1081	−	5.86287i	−0.670589	−	0.244074i	−0.0157874	−	0.999875i	$-0.505026\pi$
$577$	−16.1081	−	5.86287i	−0.670589	−	0.244074i	−0.654801	+	0.755801i	$0.727248\pi$
$578$	−8.22144	+	4.12896i	−0.341967	+	0.171742i
$579$	28.9449	−	7.72954i	1.20291	−	0.321229i
$580$	2.20069	+	5.10176i	0.0913785	+	0.211839i
$581$	−33.2130	−	3.88205i	−1.37791	−	0.161054i
$582$	−2.73323	−	31.5482i	−0.113296	−	1.30772i
$583$	−21.6580	−	14.2447i	−0.896981	−	0.589954i
$584$	3.71690	−	3.11885i	0.153806	−	0.129059i
$585$	10.3281	+	5.98623i	0.427013	+	0.247500i
$586$	0.878436	+	0.737096i	0.0362879	+	0.0304491i
$587$	−11.9434	−	39.8939i	−0.492959	−	1.64660i	−0.736299	−	0.676656i	$-0.763428\pi$
$587$	−11.9434	−	39.8939i	−0.492959	−	1.64660i	0.243341	−	0.969941i	$-0.421757\pi$
$588$	7.50087	+	1.55542i	0.309331	+	0.0641444i
$589$	20.3093	+	10.1997i	0.836831	+	0.420272i
$590$	3.20011	+	3.39192i	0.131746	+	0.139643i
$591$	−2.46760	+	16.7474i	−0.101504	+	0.688896i
$592$	−0.765298	+	1.77416i	−0.0314535	+	0.0729175i
$593$	12.3551	−	21.3996i	0.507362	−	0.878777i	−0.492602	−	0.870255i	$-0.663954\pi$
$593$	12.3551	−	21.3996i	0.507362	−	0.878777i	0.999964	−	0.00852183i	$-0.00271261\pi$
$594$	22.7489	+	9.10445i	0.933398	+	0.373560i
$595$	−3.72984	−	6.46026i	−0.152908	−	0.264845i
$596$	9.71572	−	1.13561i	0.397971	−	0.0465162i
$597$	7.03138	+	34.1991i	0.287775	+	1.39967i
$598$	11.8436	−	2.80699i	0.484322	−	0.114786i
$599$	0.0200038	+	0.343453i	0.000817335	+	0.0140331i	0.998692	−	0.0511268i	$-0.0162813\pi$
$599$	0.0200038	+	0.343453i	0.000817335	+	0.0140331i	−0.997875	+	0.0651599i	$0.979244\pi$
$600$	0.226825	−	7.57509i	0.00926008	−	0.309252i
$601$	−6.54970	−	1.55231i	−0.267168	−	0.0633199i	0.0948485	−	0.995492i	$-0.469763\pi$
$601$	−6.54970	−	1.55231i	−0.267168	−	0.0633199i	−0.362016	+	0.932172i	$0.617911\pi$
$602$	4.86513	−	27.5915i	0.198288	−	1.12455i
$603$	28.4418	+	1.70483i	1.15824	+	0.0694259i
$604$	−1.13594	−	6.44223i	−0.0462207	−	0.262131i
$605$	−0.516361	+	8.86558i	−0.0209931	+	0.360437i
$606$	1.08350	−	1.54461i	0.0440141	−	0.0627456i
$607$	12.6523	−	16.9950i	0.513542	−	0.689806i	−0.467414	−	0.884039i	$-0.654814\pi$
$607$	12.6523	−	16.9950i	0.513542	−	0.689806i	0.980956	+	0.194233i	$0.0622216\pi$
$608$	−3.87741	+	5.20827i	−0.157250	+	0.211223i
$609$	23.6347	−	33.6931i	0.957725	−	1.36531i
$610$	0.0509011	−	0.873939i	0.00206093	−	0.0353848i
$611$	−10.7216	−	60.8053i	−0.433750	−	2.45992i
$612$	3.74761	+	7.49368i	0.151488	+	0.302914i
$613$	−2.40840	+	13.6587i	−0.0972744	+	0.551670i	0.896752	+	0.442533i	$0.145920\pi$
$613$	−2.40840	+	13.6587i	−0.0972744	+	0.551670i	−0.994027	+	0.109138i	$0.965191\pi$
$614$	10.4419	+	2.47477i	0.421399	+	0.0998734i
$615$	−0.0626159	+	2.09113i	−0.00252492	+	0.0843226i
$616$	−0.926693	−	15.9107i	−0.0373375	−	0.641060i
$617$	−0.935416	+	0.221698i	−0.0376584	+	0.00892521i	−0.249402	−	0.968400i	$-0.580234\pi$
$617$	−0.935416	+	0.221698i	−0.0376584	+	0.00892521i	0.211743	+	0.977325i	$0.432086\pi$
$618$	4.28624	+	20.8473i	0.172418	+	0.838602i
$619$	−18.6233	+	2.17675i	−0.748532	+	0.0874908i	−0.481802	−	0.876280i	$-0.660017\pi$
$619$	−18.6233	+	2.17675i	−0.748532	+	0.0874908i	−0.266730	+	0.963771i	$0.585943\pi$
$620$	1.38306	+	2.39553i	0.0555451	+	0.0962070i
$621$	9.36228	+	8.37438i	0.375695	+	0.336052i
$622$	8.83746	−	15.3069i	0.354350	−	0.613752i
$623$	9.24717	−	21.4373i	0.370480	−	0.858869i
$624$	−1.27124	+	8.62782i	−0.0508905	+	0.345389i
$625$	−10.9947	−	11.6537i	−0.439789	−	0.466149i
$626$	−21.2913	−	10.6929i	−0.850972	−	0.427374i
$627$	−51.9290	−	10.7683i	−2.07385	−	0.430044i
$628$	−2.36915	−	7.91352i	−0.0945395	−	0.315784i
$629$	−4.13379	−	3.46866i	−0.164825	−	0.138305i
$630$	6.94622	−	3.99475i	0.276744	−	0.159155i
$631$	−10.1754	+	8.53818i	−0.405076	+	0.339899i	−0.822452	−	0.568835i	$-0.807394\pi$
$631$	−10.1754	+	8.53818i	−0.405076	+	0.339899i	0.417375	+	0.908734i	$0.362950\pi$
$632$	−8.15833	−	5.36581i	−0.324521	−	0.213441i
$633$	0.637821	+	7.36203i	0.0253511	+	0.292615i
$634$	22.8015	+	2.66512i	0.905565	+	0.105845i
$635$	1.89982	+	4.40428i	0.0753921	+	0.174779i
$636$	9.19900	−	2.45653i	0.364764	−	0.0974077i
$637$	−19.9001	+	9.99423i	−0.788473	+	0.395986i
$638$	−31.1539	−	11.3391i	−1.23340	−	0.448919i
$639$	0.850411	+	0.256164i	0.0336417	+	0.0101337i
$640$	−0.742632	+	0.270296i	−0.0293551	+	0.0106844i
$641$	22.4005	−	23.7432i	0.884768	−	0.937799i	−0.113678	−	0.993518i	$-0.536263\pi$
$641$	22.4005	−	23.7432i	0.884768	−	0.937799i	0.998447	+	0.0557183i	$0.0177449\pi$
$642$	−19.7663	+	2.87826i	−0.780114	+	0.113596i
$643$	−20.0945	+	13.2164i	−0.792450	+	0.521202i	−0.880009	−	0.474957i	$-0.842464\pi$
$643$	−20.0945	+	13.2164i	−0.792450	+	0.521202i	0.0875592	+	0.996159i	$0.472093\pi$
$644$	2.34324	−	7.82697i	0.0923366	−	0.308426i
$645$	−5.94882	−	9.66278i	−0.234235	−	0.380472i
$646$	−10.8290	−	14.5459i	−0.426062	−	0.572300i
$647$	0.482415			0.0189657			0.00948284	−	0.999955i	$-0.496981\pi$
$647$	0.482415			0.0189657			0.00948284	+	0.999955i	$0.496981\pi$
$648$	−8.05631	+	4.01196i	−0.316482	+	0.157605i
$649$	−27.8253			−1.09224
$650$	13.1557	+	17.6712i	0.516011	+	0.693123i
$651$	9.73955	−	18.0266i	0.381723	−	0.706518i
$652$	2.21615	−	7.40245i	0.0867911	−	0.289902i
$653$	−4.36628	+	2.87175i	−0.170866	+	0.112380i	−0.632061	−	0.774918i	$-0.717791\pi$
$653$	−4.36628	+	2.87175i	−0.170866	+	0.112380i	0.461196	+	0.887298i	$0.347421\pi$
$654$	7.32150	−	18.3840i	0.286293	−	0.718870i
$655$	−0.620111	+	0.657279i	−0.0242297	+	0.0256820i
$656$	−1.43620	+	0.522733i	−0.0560740	+	0.0204093i
$657$	−13.3755	+	5.74280i	−0.521827	+	0.224048i
$658$	−38.9455	−	14.1750i	−1.51825	−	0.552599i
$659$	−18.0686	+	9.07442i	−0.703855	+	0.353489i	−0.764459	−	0.644673i	$-0.776994\pi$
$659$	−18.0686	+	9.07442i	−0.703855	+	0.353489i	0.0606040	+	0.998162i	$0.480697\pi$
$660$	−4.56042	−	4.56814i	−0.177514	−	0.177815i
$661$	−1.42505	−	3.30364i	−0.0554280	−	0.128497i	0.888252	−	0.459357i	$-0.151920\pi$
$661$	−1.42505	−	3.30364i	−0.0554280	−	0.128497i	−0.943680	+	0.330861i	$0.892661\pi$
$662$	26.7878	+	3.13105i	1.04114	+	0.121692i
$663$	−22.0656	−	10.3121i	−0.856957	−	0.400488i
$664$	−8.26627	−	5.43681i	−0.320794	−	0.210989i
$665$	−13.2856	+	11.1479i	−0.515192	+	0.432297i
$666$	3.73345	−	4.43410i	0.144668	−	0.171818i
$667$	−13.0193	−	10.9245i	−0.504111	−	0.423000i
$668$	4.90269	+	16.3761i	0.189691	+	0.633612i
$669$	3.34646	+	10.1277i	0.129382	+	0.391561i
$670$	−6.70752	−	3.36864i	−0.259134	−	0.130142i
$671$	3.58464	+	3.79949i	0.138383	+	0.146678i
$672$	4.58883	+	3.63469i	0.177018	+	0.140211i
$673$	−11.4175	+	26.4686i	−0.440111	+	1.02029i	0.543406	+	0.839470i	$0.317135\pi$
$673$	−11.4175	+	26.4686i	−0.440111	+	1.02029i	−0.983516	+	0.180821i	$0.942125\pi$
$674$	13.4473	−	23.2913i	0.517969	−	0.897149i
$675$	−7.20605	+	21.5632i	−0.277361	+	0.829969i
$676$	−6.17589	−	10.6970i	−0.237534	−	0.411421i
$677$	9.75202	−	1.13985i	0.374801	−	0.0438079i	0.0733925	−	0.997303i	$-0.476617\pi$
$677$	9.75202	−	1.13985i	0.374801	−	0.0438079i	0.301408	+	0.953495i	$0.402543\pi$
$678$	−2.91585	+	2.59047i	−0.111983	+	0.0994865i
$679$	60.1252	−	14.2499i	2.30739	−	0.546862i
$680$	−0.128335	−	2.20343i	−0.00492142	−	0.0844976i
$681$	−17.6769	−	10.9239i	−0.677379	−	0.418605i
$682$	−16.0604	−	3.80638i	−0.614984	−	0.145754i
$683$	−8.63101	+	48.9489i	−0.330256	+	1.87298i	0.139562	+	0.990213i	$0.455431\pi$
$683$	−8.63101	+	48.9489i	−0.330256	+	1.87298i	−0.469818	+	0.882763i	$0.655681\pi$
$684$	15.6445	−	11.6058i	0.598181	−	0.443759i
$685$	−1.94861	−	11.0511i	−0.0744526	−	0.422242i
$686$	0.506468	−	8.69572i	0.0193370	−	0.332004i
$687$	9.27133	+	0.819039i	0.353723	+	0.0312483i
$688$	4.95026	−	6.64936i	0.188727	−	0.253504i
$689$	−16.5284	+	22.2016i	−0.629684	+	0.845812i
$690$	−1.39590	−	3.00015i	−0.0531412	−	0.114214i
$691$	−1.03399	+	17.7529i	−0.0393348	+	0.675352i	0.919797	+	0.392394i	$0.128353\pi$
$691$	−1.03399	+	17.7529i	−0.0393348	+	0.675352i	−0.959132	+	0.282959i	$0.908684\pi$
$692$	3.82641	+	21.7006i	0.145458	+	0.824934i
$693$	−11.1051	+	46.5055i	−0.421848	+	1.76660i
$694$	1.07375	−	6.08957i	0.0407592	−	0.231157i
$695$	13.7939	+	3.26922i	0.523233	+	0.124009i
$696$	10.7233	−	5.77025i	0.406465	−	0.218721i
$697$	−0.248191	−	4.26127i	−0.00940090	−	0.161407i
$698$	10.9335	−	2.59128i	0.413838	−	0.0980813i
$699$	37.9740	+	12.6189i	1.43631	+	0.477290i
$700$	14.6879	−	1.71677i	0.555151	−	0.0648879i
$701$	−16.4310	−	28.4594i	−0.620591	−	1.07489i	−0.989376	−	0.145380i	$-0.953559\pi$
$701$	−16.4310	−	28.4594i	−0.620591	−	1.07489i	0.368785	−	0.929515i	$-0.379774\pi$
$702$	11.1171	−	23.6835i	0.419586	−	0.893877i
$703$	−6.27293	+	10.8650i	−0.236588	+	0.409782i
$704$	1.86776	−	4.32996i	0.0703940	−	0.163192i
$705$	−15.6048	+	6.18412i	−0.587711	+	0.232907i
$706$	−12.7349	−	13.4983i	−0.479286	−	0.508013i
$707$	3.29000	+	1.65230i	0.123733	+	0.0621412i
$708$	6.80082	−	7.62902i	0.255591	−	0.286716i
$709$	−6.31353	−	21.0887i	−0.237110	−	0.792002i	−0.990866	−	0.134848i	$-0.956945\pi$
$709$	−6.31353	−	21.0887i	−0.237110	−	0.792002i	0.753757	−	0.657154i	$-0.228240\pi$
$710$	−0.179229	−	0.150391i	−0.00672635	−	0.00564408i
$711$	18.7920	+	22.4725i	0.704755	+	0.842785i
$712$	5.29169	−	4.44026i	0.198315	−	0.166406i
$713$	−7.06922	−	4.64950i	−0.264744	−	0.174125i
$714$	−13.4003	+	9.36610i	−0.501493	+	0.350518i
$715$	18.6374	+	2.17840i	0.696998	+	0.0814674i
$716$	6.16074	+	14.2822i	0.230238	+	0.533751i
$717$	8.52542	−	31.7100i	0.318388	−	1.18423i
$718$	−14.9989	+	7.53273i	−0.559754	+	0.281119i
$719$	−24.9140	−	9.06794i	−0.929134	−	0.338177i	−0.167268	−	0.985912i	$-0.553494\pi$
$719$	−24.9140	−	9.06794i	−0.929134	−	0.338177i	−0.761866	+	0.647734i	$0.775717\pi$
$720$	2.36710	−	0.133850i	0.0882164	−	0.00498831i
$721$	−39.0258	+	14.2042i	−1.45339	+	0.528992i
$722$	−15.8936	+	16.8463i	−0.591500	+	0.626954i
$723$	−14.5514	−	18.4352i	−0.541171	−	0.685613i
$724$	−16.0681	+	10.5682i	−0.597167	+	0.392763i
$725$	8.82253	−	29.4693i	0.327661	−	1.09446i
$726$	19.4555	−	0.549629i	0.722061	−	0.0203986i
$727$	−11.5608	−	15.5288i	−0.428765	−	0.575932i	0.534268	−	0.845315i	$-0.320587\pi$
$727$	−11.5608	−	15.5288i	−0.428765	−	0.575932i	−0.963033	+	0.269383i	$0.913180\pi$
$728$	−17.0173			−0.630702
$729$	26.6133	−	4.55351i	0.985676	−	0.168649i
$730$	3.83455			0.141923
$731$	13.8253	+	18.5706i	0.511347	+	0.686859i
$732$	−1.91786	+	0.0541806i	−0.0708860	+	0.00200257i
$733$	−7.98153	+	26.6602i	−0.294805	+	0.984716i	0.674381	+	0.738384i	$0.264411\pi$
$733$	−7.98153	+	26.6602i	−0.294805	+	0.984716i	−0.969185	+	0.246332i	$0.920775\pi$
$734$	14.8256	−	9.75097i	0.547224	−	0.359915i
$735$	3.75088	+	4.75201i	0.138353	+	0.175281i
$736$	1.65892	−	1.75835i	0.0611485	−	0.0648136i
$737$	42.0862	−	15.3181i	1.55027	−	0.564251i
$738$	4.57779	−	0.258857i	0.168511	−	0.00952866i
$739$	−13.4634	−	4.90029i	−0.495261	−	0.180260i	0.0823004	−	0.996608i	$-0.473773\pi$
$739$	−13.4634	−	4.90029i	−0.495261	−	0.180260i	−0.577561	+	0.816347i	$0.695996\pi$
$740$	−1.36457	+	0.685311i	−0.0501624	+	0.0251925i
$741$	−14.7022	+	54.6843i	−0.540099	+	2.00888i
$742$	7.35879	+	17.0596i	0.270150	+	0.626277i
$743$	−11.7344	−	1.37155i	−0.430492	−	0.0503173i	−0.101912	−	0.994793i	$-0.532496\pi$
$743$	−11.7344	−	1.37155i	−0.430492	−	0.0503173i	−0.328580	+	0.944476i	$0.606570\pi$
$744$	4.96897	−	3.47305i	0.182171	−	0.127328i
$745$	6.45876	+	4.24800i	0.236631	+	0.155635i
$746$	−4.36824	+	3.66539i	−0.159933	+	0.134199i
$747$	19.0406	+	22.7699i	0.696660	+	0.833105i
$748$	10.0888	+	8.46551i	0.368883	+	0.309530i
$749$	−11.1787	−	37.3394i	−0.408460	−	1.36435i
$750$	8.53966	−	9.57961i	0.311824	−	0.349798i
$751$	−14.4113	−	7.23762i	−0.525875	−	0.264104i	0.165995	−	0.986127i	$-0.446917\pi$
$751$	−14.4113	−	7.23762i	−0.525875	−	0.264104i	−0.691870	+	0.722022i	$0.743213\pi$
$752$	−8.41517	−	8.91956i	−0.306870	−	0.325263i
$753$	31.0606	−	12.3092i	1.13191	−	0.448572i
$754$	−14.0209	+	32.5040i	−0.510610	+	1.18373i
$755$	2.58489	−	4.47717i	0.0940739	−	0.162941i
$756$	−10.0365	−	14.4112i	−0.365023	−	0.524132i
$757$	6.34606	+	10.9917i	0.230651	+	0.399500i	0.958000	−	0.286768i	$-0.0925810\pi$
$757$	6.34606	+	10.9917i	0.230651	+	0.399500i	−0.727349	+	0.686268i	$0.759248\pi$
$758$	1.50638	−	0.176070i	0.0547140	−	0.00639515i
$759$	18.7371	+	6.22640i	0.680114	+	0.226004i
$760$	−4.99313	+	1.18339i	−0.181120	+	0.0429262i
$761$	1.20661	+	20.7167i	0.0437396	+	0.750979i	0.946871	+	0.321614i	$0.104225\pi$
$761$	1.20661	+	20.7167i	0.0437396	+	0.750979i	−0.903131	+	0.429365i	$0.858737\pi$
$762$	9.25727	−	4.98138i	0.335356	−	0.180456i
$763$	37.5721	+	8.90474i	1.36020	+	0.322373i
$764$	3.85679	−	21.8729i	0.139534	−	0.791335i
$765$	−1.53792	+	6.44041i	−0.0556035	+	0.232854i
$766$	1.29228	+	7.32891i	0.0466921	+	0.264804i
$767$	−1.72749	+	29.6599i	−0.0623760	+	1.07096i

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.597159 + 0.802123i) q^{2} +(1.73136 - 0.0489119i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-0.660279 + 0.434273i) q^{5} +(1.07313 + 1.35956i) q^{6} +(-2.31933 + 2.45835i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(2.99522 - 0.169368i) q^{9} +O(q^{10})\)	\(q+(0.597159 + 0.802123i) q^{2} +(1.73136 - 0.0489119i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-0.660279 + 0.434273i) q^{5} +(1.07313 + 1.35956i) q^{6} +(-2.31933 + 2.45835i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(2.99522 - 0.169368i) q^{9} +(-0.742632 - 0.270296i) q^{10} +(4.21404 - 2.11637i) q^{11} +(-0.449703 + 1.67265i) q^{12} +(-1.99428 - 4.62327i) q^{13} +(-3.35690 - 0.392366i) q^{14} +(-1.12194 + 0.784178i) q^{15} +(-0.835488 - 0.549509i) q^{16} +(2.13944 - 1.79521i) q^{17} +(1.92447 + 2.30139i) q^{18} +(-4.97401 - 4.17369i) q^{19} +(-0.226658 - 0.757092i) q^{20} +(-3.89535 + 4.36973i) q^{21} +(4.21404 + 2.11637i) q^{22} +(1.65892 + 1.75835i) q^{23} +(-1.61022 + 0.638122i) q^{24} +(-1.73302 + 4.01760i) q^{25} +(2.51753 - 4.36049i) q^{26} +(5.17751 - 0.439739i) q^{27} +(-1.68988 - 2.92696i) q^{28} +(-6.98299 + 0.816194i) q^{29} +(-1.29898 - 0.431656i) q^{30} +(-3.40578 + 0.807185i) q^{31} +(-0.0581448 - 0.998308i) q^{32} +(7.19250 - 3.87031i) q^{33} +(2.71756 + 0.644074i) q^{34} +(0.463813 - 2.63042i) q^{35} +(-0.696784 + 2.91796i) q^{36} +(-0.335520 - 1.90283i) q^{37} +(0.377541 - 6.48212i) q^{38} +(-3.67896 - 7.90700i) q^{39} +(0.471930 - 0.633912i) q^{40} +(0.912678 - 1.22594i) q^{41} +(-5.83120 - 0.515134i) q^{42} +(-0.482003 + 8.27567i) q^{43} +(0.818860 + 4.64398i) q^{44} +(-1.90413 + 1.41257i) q^{45} +(-0.419776 + 2.38067i) q^{46} +(11.9322 + 2.82797i) q^{47} +(-1.47341 - 0.910533i) q^{48} +(-0.257160 - 4.41527i) q^{49} +(-4.25750 + 1.00905i) q^{50} +(3.61634 - 3.21279i) q^{51} +(5.00101 - 0.584534i) q^{52} +(-2.74858 - 4.76068i) q^{53} +(3.44452 + 3.89041i) q^{54} +(-1.86336 + 3.22744i) q^{55} +(1.33865 - 3.10335i) q^{56} +(-8.81594 - 6.98287i) q^{57} +(-4.82464 - 5.11382i) q^{58} +(-5.27302 - 2.64821i) q^{59} +(-0.429458 - 1.29971i) q^{60} +(0.317697 + 1.06118i) q^{61} +(-2.68125 - 2.24984i) q^{62} +(-6.53053 + 7.75610i) q^{63} +(0.766044 - 0.642788i) q^{64} +(3.32454 + 2.18659i) q^{65} +(7.39953 + 3.45808i) q^{66} +(9.43341 + 1.10261i) q^{67} +(1.10619 + 2.56443i) q^{68} +(2.95819 + 2.96319i) q^{69} +(2.38689 - 1.19874i) q^{70} +(0.278197 + 0.101256i) q^{71} +(-2.75665 + 1.18358i) q^{72} +(-4.55945 + 1.65950i) q^{73} +(1.32594 - 1.40542i) q^{74} +(-2.80398 + 7.04067i) q^{75} +(5.42491 - 3.56802i) q^{76} +(-4.57097 + 15.2681i) q^{77} +(4.14547 - 7.67271i) q^{78} +(5.83110 + 7.83253i) q^{79} +0.790292 q^{80} +(8.94263 - 1.01459i) q^{81} +1.52837 q^{82} +(5.90826 + 7.93617i) q^{83} +(-3.06895 - 4.98496i) q^{84} +(-0.633021 + 2.11444i) q^{85} +(-6.92594 + 4.55526i) q^{86} +(-12.0501 + 1.75468i) q^{87} +(-3.23606 + 3.43002i) q^{88} +(-6.49122 + 2.36261i) q^{89} +(-2.27012 - 0.683816i) q^{90} +(15.9910 + 5.82025i) q^{91} +(-2.16026 + 1.08492i) q^{92} +(-5.85715 + 1.56411i) q^{93} +(4.85701 + 11.2598i) q^{94} +(5.09675 + 0.595725i) q^{95} +(-0.149499 - 1.72559i) q^{96} +(-15.2749 - 10.0465i) q^{97} +(3.38803 - 2.84289i) q^{98} +(12.2635 - 7.05270i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more