LMFDB - Embedded newform 66.2.h.a.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [66,2,Mod(17,66)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(66, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("66.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 66 = 2 \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	66.h (of order $10$, degree $4$, 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:	$0.527012653340$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.185640625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + x^{6} + x^{5} + 4x^{4} + 3x^{3} + 9x^{2} - 81x + 81 $ x^8 - 3x^7 + x^6 + x^5 + 4x^4 + 3x^3 + 9x^2 - 81*x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.1
Root			$-1.52536 - 0.820539i$ of defining polynomial
Character	$\chi$	$=$	66.29
Dual form			66.2.h.a.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.751740 + 1.56041i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.56076 + 2.14820i) q^{5} +(1.52536 - 0.820539i) q^{6} +(1.56076 - 0.507121i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.86977 - 2.34605i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.751740 + 1.56041i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.56076 + 2.14820i) q^{5} +(1.52536 - 0.820539i) q^{6} +(1.56076 - 0.507121i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.86977 - 2.34605i) q^{9} -2.65532i q^{10} +(-2.77710 + 1.81321i) q^{11} +(-1.71634 - 0.232753i) q^{12} +(0.885446 - 1.21871i) q^{13} +(-1.56076 - 0.507121i) q^{14} +(-4.52536 + 0.820539i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(5.49344 - 3.99122i) q^{17} +(0.133706 + 2.99702i) q^{18} +(-5.21982 - 1.69602i) q^{19} +(-1.56076 + 2.14820i) q^{20} +(-0.381966 + 2.81665i) q^{21} +(3.31250 + 0.165420i) q^{22} -4.78856i q^{23} +(1.25174 + 1.19714i) q^{24} +(-0.633706 + 1.95035i) q^{25} +(-1.43268 + 0.465507i) q^{26} +(5.06639 - 1.15400i) q^{27} +(0.964601 + 1.32766i) q^{28} +(0.143392 + 0.441315i) q^{29} +(4.14339 + 1.99611i) q^{30} +(4.20067 + 3.05196i) q^{31} +1.00000 q^{32} +(-0.741699 - 5.69648i) q^{33} -6.79026 q^{34} +(3.52536 + 2.56132i) q^{35} +(1.65343 - 2.50323i) q^{36} +(0.311168 + 0.957676i) q^{37} +(3.22603 + 4.44024i) q^{38} +(1.23607 + 2.29782i) q^{39} +(2.52536 - 0.820539i) q^{40} +(-0.486479 + 1.49723i) q^{41} +(1.96460 - 2.05420i) q^{42} +3.42500i q^{43} +(-2.58263 - 2.08086i) q^{44} +(2.12151 - 7.67826i) q^{45} +(-2.81465 + 3.87403i) q^{46} +(-9.52285 - 3.09416i) q^{47} +(-0.309017 - 1.70426i) q^{48} +(-3.48433 + 2.53151i) q^{49} +(1.65906 - 1.20538i) q^{50} +(2.09831 + 11.5724i) q^{51} +(1.43268 + 0.465507i) q^{52} +(-5.77495 + 7.94853i) q^{53} +(-4.77710 - 2.04434i) q^{54} +(-8.22951 - 3.13578i) q^{55} -1.64108i q^{56} +(6.57044 - 6.87011i) q^{57} +(0.143392 - 0.441315i) q^{58} +(5.81307 - 1.88878i) q^{59} +(-2.17879 - 4.05031i) q^{60} +(-8.17223 - 11.2481i) q^{61} +(-1.60451 - 4.93818i) q^{62} +(-4.10799 - 2.71341i) q^{63} +(-0.809017 - 0.587785i) q^{64} +4.00000 q^{65} +(-2.74826 + 5.04451i) q^{66} +11.7972 q^{67} +(5.49344 + 3.99122i) q^{68} +(7.47214 + 3.59976i) q^{69} +(-1.34657 - 4.14431i) q^{70} +(-0.527864 - 0.726543i) q^{71} +(-2.80902 + 1.05329i) q^{72} +(-4.40076 + 1.42989i) q^{73} +(0.311168 - 0.957676i) q^{74} +(-2.56696 - 2.45500i) q^{75} -5.48844i q^{76} +(-3.41486 + 4.23830i) q^{77} +(0.350622 - 2.58551i) q^{78} +(-1.86762 + 2.57056i) q^{79} +(-2.52536 - 0.820539i) q^{80} +(-2.00789 + 8.77316i) q^{81} +(1.27362 - 0.925338i) q^{82} +(1.51625 - 1.10162i) q^{83} +(-2.79682 + 0.507121i) q^{84} +(17.1478 + 5.57167i) q^{85} +(2.01317 - 2.77089i) q^{86} +(-0.796426 - 0.108003i) q^{87} +(0.866294 + 3.20149i) q^{88} +12.8092i q^{89} +(-6.22951 + 4.96485i) q^{90} +(0.763932 - 2.35114i) q^{91} +(4.55420 - 1.47975i) q^{92} +(-7.92013 + 4.26049i) q^{93} +(5.88545 + 8.10062i) q^{94} +(-4.50348 - 13.8603i) q^{95} +(-0.751740 + 1.56041i) q^{96} +(2.90517 + 2.11073i) q^{97} +4.30687 q^{98} +(9.44642 + 3.12492i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 3 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 3 * q^6 - 2 * q^8 + 2 * q^9	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 3 q^{6} - 2 q^{8} + 2 q^{9} + q^{11} - 3 q^{12} - 21 q^{15} - 2 q^{16} + 10 q^{17} + 2 q^{18} - 15 q^{19} - 12 q^{21} + 6 q^{22} + 2 q^{24} - 6 q^{25} + 10 q^{26} + 20 q^{27} + 5 q^{28} - 23 q^{29} + 9 q^{30} + 13 q^{31} + 8 q^{32} + 20 q^{33} + 10 q^{34} + 13 q^{35} + 7 q^{36} + 6 q^{37} - 10 q^{38} - 8 q^{39} + 5 q^{40} - 2 q^{41} + 13 q^{42} - 9 q^{44} - 8 q^{45} - 10 q^{46} - 10 q^{47} + 2 q^{48} - 18 q^{49} - q^{50} + 15 q^{51} - 10 q^{52} - 15 q^{53} - 15 q^{54} - 14 q^{55} + 15 q^{57} - 23 q^{58} + 25 q^{59} + 4 q^{60} - 10 q^{61} - 2 q^{62} - 6 q^{63} - 2 q^{64} + 32 q^{65} - 30 q^{66} - 2 q^{67} + 10 q^{68} + 24 q^{69} - 17 q^{70} - 40 q^{71} - 18 q^{72} + 5 q^{73} + 6 q^{74} + q^{75} + 12 q^{77} - 8 q^{78} + 10 q^{79} - 5 q^{80} - 26 q^{81} + 3 q^{82} + 21 q^{83} + 8 q^{84} + 30 q^{85} - 25 q^{86} - 42 q^{87} + 6 q^{88} + 2 q^{90} + 24 q^{91} - 10 q^{92} + 27 q^{93} + 40 q^{94} - 20 q^{95} + 2 q^{96} + 9 q^{97} + 22 q^{98} + 12 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 3 * q^6 - 2 * q^8 + 2 * q^9 + q^11 - 3 * q^12 - 21 * q^15 - 2 * q^16 + 10 * q^17 + 2 * q^18 - 15 * q^19 - 12 * q^21 + 6 * q^22 + 2 * q^24 - 6 * q^25 + 10 * q^26 + 20 * q^27 + 5 * q^28 - 23 * q^29 + 9 * q^30 + 13 * q^31 + 8 * q^32 + 20 * q^33 + 10 * q^34 + 13 * q^35 + 7 * q^36 + 6 * q^37 - 10 * q^38 - 8 * q^39 + 5 * q^40 - 2 * q^41 + 13 * q^42 - 9 * q^44 - 8 * q^45 - 10 * q^46 - 10 * q^47 + 2 * q^48 - 18 * q^49 - q^50 + 15 * q^51 - 10 * q^52 - 15 * q^53 - 15 * q^54 - 14 * q^55 + 15 * q^57 - 23 * q^58 + 25 * q^59 + 4 * q^60 - 10 * q^61 - 2 * q^62 - 6 * q^63 - 2 * q^64 + 32 * q^65 - 30 * q^66 - 2 * q^67 + 10 * q^68 + 24 * q^69 - 17 * q^70 - 40 * q^71 - 18 * q^72 + 5 * q^73 + 6 * q^74 + q^75 + 12 * q^77 - 8 * q^78 + 10 * q^79 - 5 * q^80 - 26 * q^81 + 3 * q^82 + 21 * q^83 + 8 * q^84 + 30 * q^85 - 25 * q^86 - 42 * q^87 + 6 * q^88 + 2 * q^90 + 24 * q^91 - 10 * q^92 + 27 * q^93 + 40 * q^94 - 20 * q^95 + 2 * q^96 + 9 * q^97 + 22 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/66\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.751740	+	1.56041i	−0.434017	+	0.900905i
$3$	−0.751740	+	1.56041i	−0.434017	+	0.900905i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.56076	+	2.14820i	0.697992	+	0.960703i	0.999973	+	0.00738926i	$0.00235209\pi$
$5$	1.56076	+	2.14820i	0.697992	+	0.960703i	−0.301981	+	0.953314i	$0.597648\pi$
$6$	1.52536	−	0.820539i	0.622725	−	0.334983i
$7$	1.56076	−	0.507121i	0.589911	−	0.191674i	0.00117514	−	0.999999i	$-0.499626\pi$
$7$	1.56076	−	0.507121i	0.589911	−	0.191674i	0.588736	+	0.808326i	$0.299626\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−1.86977	−	2.34605i	−0.623258	−	0.782016i
$10$		−	2.65532i		−	0.839685i
$11$	−2.77710	+	1.81321i	−0.837327	+	0.546703i
$11$	−2.77710	+	1.81321i	−0.837327	+	0.546703i
$12$	−1.71634	−	0.232753i	−0.495465	−	0.0671901i
$13$	0.885446	−	1.21871i	0.245579	−	0.338010i	−0.668378	−	0.743822i	$-0.733011\pi$
$13$	0.885446	−	1.21871i	0.245579	−	0.338010i	0.913957	+	0.405812i	$0.133011\pi$
$14$	−1.56076	−	0.507121i	−0.417130	−	0.135534i
$15$	−4.52536	+	0.820539i	−1.16844	+	0.211862i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	5.49344	−	3.99122i	1.33235	−	0.968012i	0.332666	−	0.943045i	$-0.392052\pi$
$17$	5.49344	−	3.99122i	1.33235	−	0.968012i	0.999688	−	0.0249677i	$-0.00794828\pi$
$18$	0.133706	+	2.99702i	0.0315148	+	0.706404i
$19$	−5.21982	−	1.69602i	−1.19751	−	0.389094i	−0.358665	−	0.933466i	$-0.616768\pi$
$19$	−5.21982	−	1.69602i	−1.19751	−	0.389094i	−0.838844	+	0.544372i	$0.816768\pi$
$20$	−1.56076	+	2.14820i	−0.348996	+	0.480352i
$21$	−0.381966	+	2.81665i	−0.0833518	+	0.614643i
$22$	3.31250	+	0.165420i	0.706227	+	0.0352677i
$23$		−	4.78856i		−	0.998485i	−0.866462	−	0.499242i	$-0.833612\pi$
$23$		−	4.78856i		−	0.998485i	0.866462	−	0.499242i	$-0.166388\pi$
$24$	1.25174	+	1.19714i	0.255510	+	0.244365i
$25$	−0.633706	+	1.95035i	−0.126741	+	0.390069i
$26$	−1.43268	+	0.465507i	−0.280972	+	0.0912933i
$27$	5.06639	−	1.15400i	0.975027	−	0.222087i
$28$	0.964601	+	1.32766i	0.182292	+	0.250904i
$29$	0.143392	+	0.441315i	0.0266272	+	0.0819501i	0.963487	−	0.267755i	$-0.0862818\pi$
$29$	0.143392	+	0.441315i	0.0266272	+	0.0819501i	−0.936860	+	0.349705i	$0.886282\pi$
$30$	4.14339	+	1.99611i	0.756476	+	0.364438i
$31$	4.20067	+	3.05196i	0.754462	+	0.548149i	0.897207	−	0.441611i	$-0.145593\pi$
$31$	4.20067	+	3.05196i	0.754462	+	0.548149i	−0.142744	+	0.989760i	$0.545593\pi$
$32$	1.00000			0.176777
$33$	−0.741699	−	5.69648i	−0.129113	−	0.991630i
$34$	−6.79026			−1.16452
$35$	3.52536	+	2.56132i	0.595894	+	0.432943i
$36$	1.65343	−	2.50323i	0.275572	−	0.417205i
$37$	0.311168	+	0.957676i	0.0511557	+	0.157441i	0.973371	−	0.229236i	$-0.0736228\pi$
$37$	0.311168	+	0.957676i	0.0511557	+	0.157441i	−0.922215	+	0.386677i	$0.873623\pi$
$38$	3.22603	+	4.44024i	0.523331	+	0.720303i
$39$	1.23607	+	2.29782i	0.197929	+	0.367945i
$40$	2.52536	−	0.820539i	0.399294	−	0.129739i
$41$	−0.486479	+	1.49723i	−0.0759752	+	0.233828i	−0.981831	−	0.189759i	$-0.939229\pi$
$41$	−0.486479	+	1.49723i	−0.0759752	+	0.233828i	0.905855	+	0.423587i	$0.139229\pi$
$42$	1.96460	−	2.05420i	0.303144	−	0.316970i
$43$			3.42500i			0.522308i	0.965297	+	0.261154i	$0.0841030\pi$
$43$			3.42500i			0.522308i	−0.965297	+	0.261154i	$0.915897\pi$
$44$	−2.58263	−	2.08086i	−0.389347	−	0.313702i
$45$	2.12151	−	7.67826i	0.316257	−	1.14461i
$46$	−2.81465	+	3.87403i	−0.414997	+	0.571195i
$47$	−9.52285	−	3.09416i	−1.38905	−	0.451330i	−0.483417	−	0.875390i	$-0.660604\pi$
$47$	−9.52285	−	3.09416i	−1.38905	−	0.451330i	−0.905634	+	0.424060i	$0.860604\pi$
$48$	−0.309017	−	1.70426i	−0.0446028	−	0.245989i
$49$	−3.48433	+	2.53151i	−0.497761	+	0.361645i
$50$	1.65906	−	1.20538i	0.234627	−	0.170467i
$51$	2.09831	+	11.5724i	0.293822	+	1.62046i
$52$	1.43268	+	0.465507i	0.198677	+	0.0645541i
$53$	−5.77495	+	7.94853i	−0.793250	+	1.09181i	0.200446	+	0.979705i	$0.435761\pi$
$53$	−5.77495	+	7.94853i	−0.793250	+	1.09181i	−0.993696	+	0.112110i	$0.964239\pi$
$54$	−4.77710	−	2.04434i	−0.650081	−	0.278200i
$55$	−8.22951	−	3.13578i	−1.10967	−	0.422828i
$56$		−	1.64108i		−	0.219298i
$57$	6.57044	−	6.87011i	0.870276	−	0.909968i
$58$	0.143392	−	0.441315i	0.0188283	−	0.0579475i
$59$	5.81307	−	1.88878i	0.756798	−	0.245898i	0.0948939	−	0.995487i	$-0.469749\pi$
$59$	5.81307	−	1.88878i	0.756798	−	0.245898i	0.661904	+	0.749589i	$0.269749\pi$
$60$	−2.17879	−	4.05031i	−0.281281	−	0.522893i
$61$	−8.17223	−	11.2481i	−1.04635	−	1.44017i	−0.891934	−	0.452166i	$-0.850651\pi$
$61$	−8.17223	−	11.2481i	−1.04635	−	1.44017i	−0.154413	−	0.988006i	$-0.549349\pi$
$62$	−1.60451	−	4.93818i	−0.203773	−	0.627150i
$63$	−4.10799	−	2.71341i	−0.517558	−	0.341858i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	4.00000			0.496139
$66$	−2.74826	+	5.04451i	−0.338287	+	0.620936i
$67$	11.7972			1.44126			0.720630	−	0.693320i	$-0.243853\pi$
$67$	11.7972			1.44126			0.720630	+	0.693320i	$0.243853\pi$
$68$	5.49344	+	3.99122i	0.666177	+	0.484006i
$69$	7.47214	+	3.59976i	0.899539	+	0.433360i
$70$	−1.34657	−	4.14431i	−0.160946	−	0.495339i
$71$	−0.527864	−	0.726543i	−0.0626459	−	0.0862247i	0.776544	−	0.630062i	$-0.216971\pi$
$71$	−0.527864	−	0.726543i	−0.0626459	−	0.0862247i	−0.839190	+	0.543838i	$0.816971\pi$
$72$	−2.80902	+	1.05329i	−0.331046	+	0.124132i
$73$	−4.40076	+	1.42989i	−0.515070	+	0.167356i	−0.555007	−	0.831846i	$-0.687284\pi$
$73$	−4.40076	+	1.42989i	−0.515070	+	0.167356i	0.0399366	+	0.999202i	$0.487284\pi$
$74$	0.311168	−	0.957676i	0.0361725	−	0.111328i
$75$	−2.56696	−	2.45500i	−0.296407	−	0.283479i
$76$		−	5.48844i		−	0.629568i
$77$	−3.41486	+	4.23830i	−0.389159	+	0.482999i
$78$	0.350622	−	2.58551i	0.0397001	−	0.292752i
$79$	−1.86762	+	2.57056i	−0.210124	+	0.289211i	−0.901051	−	0.433714i	$-0.857203\pi$
$79$	−1.86762	+	2.57056i	−0.210124	+	0.289211i	0.690927	+	0.722925i	$0.257203\pi$
$80$	−2.52536	−	0.820539i	−0.282344	−	0.0917390i
$81$	−2.00789	+	8.77316i	−0.223099	+	0.974796i
$82$	1.27362	−	0.925338i	0.140648	−	0.102186i
$83$	1.51625	−	1.10162i	0.166430	−	0.120918i	−0.501453	−	0.865185i	$-0.667201\pi$
$83$	1.51625	−	1.10162i	0.166430	−	0.120918i	0.667882	+	0.744267i	$0.267201\pi$
$84$	−2.79682	+	0.507121i	−0.305159	+	0.0553314i
$85$	17.1478	+	5.57167i	1.85994	+	0.604333i
$86$	2.01317	−	2.77089i	0.217085	−	0.298792i
$87$	−0.796426	−	0.108003i	−0.0853859	−	0.0115792i
$88$	0.866294	+	3.20149i	0.0923473	+	0.341280i
$89$			12.8092i			1.35777i	0.734244	+	0.678886i	$0.237537\pi$
$89$			12.8092i			1.35777i	−0.734244	+	0.678886i	$0.762463\pi$
$90$	−6.22951	+	4.96485i	−0.656648	+	0.523341i
$91$	0.763932	−	2.35114i	0.0800818	−	0.246467i
$92$	4.55420	−	1.47975i	0.474808	−	0.154274i
$93$	−7.92013	+	4.26049i	−0.821280	+	0.441792i
$94$	5.88545	+	8.10062i	0.607037	+	0.835515i
$95$	−4.50348	−	13.8603i	−0.462047	−	1.42204i
$96$	−0.751740	+	1.56041i	−0.0767241	+	0.159259i
$97$	2.90517	+	2.11073i	0.294976	+	0.214312i	0.725423	−	0.688303i	$-0.241644\pi$
$97$	2.90517	+	2.11073i	0.294976	+	0.214312i	−0.430447	+	0.902616i	$0.641644\pi$
$98$	4.30687			0.435059
$99$	9.44642	+	3.12492i	0.949401	+	0.314066i
$100$	−2.05072			−0.205072
$101$	−9.84754	−	7.15466i	−0.979867	−	0.711915i	−0.0221881	−	0.999754i	$-0.507063\pi$
$101$	−9.84754	−	7.15466i	−0.979867	−	0.711915i	−0.957679	+	0.287839i	$0.907063\pi$
$102$	5.10451	−	10.5956i	0.505422	−	1.04912i
$103$	0.273973	+	0.843203i	0.0269954	+	0.0830833i	0.963647	−	0.267180i	$-0.0860920\pi$
$103$	0.273973	+	0.843203i	0.0269954	+	0.0830833i	−0.936651	+	0.350264i	$0.886092\pi$
$104$	−0.885446	−	1.21871i	−0.0868251	−	0.119505i
$105$	−6.64687	+	3.57556i	−0.648668	+	0.348939i
$106$	9.34406	−	3.03607i	0.907575	−	0.294889i
$107$	0.689654	−	2.12254i	0.0666713	−	0.205193i	−0.912171	−	0.409810i	$-0.865595\pi$
$107$	0.689654	−	2.12254i	0.0666713	−	0.205193i	0.978842	+	0.204617i	$0.0655949\pi$
$108$	2.66312	+	4.46182i	0.256259	+	0.429338i
$109$			4.73524i			0.453554i	0.973947	+	0.226777i	$0.0728188\pi$
$109$			4.73524i			0.453554i	−0.973947	+	0.226777i	$0.927181\pi$
$110$	4.81465	+	7.37408i	0.459059	+	0.703091i
$111$	−1.72829	−	0.234373i	−0.164042	−	0.0222457i
$112$	−0.964601	+	1.32766i	−0.0911462	+	0.125452i
$113$	−3.70508	−	1.20385i	−0.348545	−	0.113249i	0.129512	−	0.991578i	$-0.458659\pi$
$113$	−3.70508	−	1.20385i	−0.348545	−	0.113249i	−0.478057	+	0.878329i	$0.658659\pi$
$114$	−9.35375	+	1.69602i	−0.876059	+	0.158847i
$115$	10.2868	−	7.47379i	0.959248	−	0.696934i
$116$	−0.375405	+	0.272747i	−0.0348555	+	0.0253240i
$117$	−4.51474	+	0.201416i	−0.417388	+	0.0186209i
$118$	−5.81307	−	1.88878i	−0.535137	−	0.173876i
$119$	6.54989	−	9.01516i	0.600428	−	0.826418i
$120$	−0.618034	+	4.55743i	−0.0564185	+	0.416035i
$121$	4.42454	−	10.0709i	0.402231	−	0.915538i
$122$			13.9034i			1.25876i
$123$	−1.97059	−	1.88463i	−0.177682	−	0.169932i
$124$	−1.60451	+	4.93818i	−0.144089	+	0.443462i
$125$	7.44800	−	2.42000i	0.666169	−	0.216451i
$126$	1.72853	+	4.60981i	0.153990	+	0.410675i
$127$	−0.138938	−	0.191232i	−0.0123288	−	0.0169691i	0.802808	−	0.596237i	$-0.203338\pi$
$127$	−0.138938	−	0.191232i	−0.0123288	−	0.0169691i	−0.815137	+	0.579268i	$0.803338\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−5.34442	−	2.57471i	−0.470550	−	0.226691i
$130$	−3.23607	−	2.35114i	−0.283822	−	0.206209i
$131$	5.26741			0.460216			0.230108	−	0.973165i	$-0.426092\pi$
$131$	5.26741			0.460216			0.230108	+	0.973165i	$0.426092\pi$
$132$	5.18848	−	2.46571i	0.451599	−	0.214612i
$133$	−9.00696			−0.781002
$134$	−9.54415	−	6.93423i	−0.824489	−	0.599027i
$135$	10.3864	+	9.08249i	0.893921	+	0.781696i
$136$	−2.09831	−	6.45792i	−0.179928	−	0.553762i
$137$	−0.545331	−	0.750584i	−0.0465908	−	0.0641267i	0.785086	−	0.619387i	$-0.212619\pi$
$137$	−0.545331	−	0.750584i	−0.0465908	−	0.0641267i	−0.831677	+	0.555260i	$0.812619\pi$
$138$	−3.92920	−	7.30427i	−0.334476	−	0.621781i
$139$	−8.03945	+	2.61218i	−0.681898	+	0.221562i	−0.629426	−	0.777060i	$-0.716710\pi$
$139$	−8.03945	+	2.61218i	−0.681898	+	0.221562i	−0.0524716	+	0.998622i	$0.516710\pi$
$140$	−1.34657	+	4.14431i	−0.113806	+	0.350258i
$141$	11.9869	−	12.5336i	1.00948	−	1.05552i
$142$			0.898056i			0.0753632i
$143$	−0.249191	+	4.98998i	−0.0208384	+	0.417283i
$144$	2.89165	+	0.798968i	0.240971	+	0.0665807i
$145$	−0.724231	+	0.996819i	−0.0601441	+	0.0827813i
$146$	4.40076	+	1.42989i	0.364210	+	0.118339i
$147$	−1.33089	−	7.34003i	−0.109770	−	0.605395i
$148$	−0.814648	+	0.591876i	−0.0669636	+	0.0486519i
$149$	−14.6202	+	10.6222i	−1.19774	+	0.870206i	−0.994060	−	0.108832i	$-0.965289\pi$
$149$	−14.6202	+	10.6222i	−1.19774	+	0.870206i	−0.203676	+	0.979038i	$0.565289\pi$
$150$	0.633706	+	3.49496i	0.0517419	+	0.285362i
$151$	−12.6775	−	4.11917i	−1.03168	−	0.335213i	−0.256226	−	0.966617i	$-0.582479\pi$
$151$	−12.6775	−	4.11917i	−1.03168	−	0.335213i	−0.775454	+	0.631403i	$0.782479\pi$
$152$	−3.22603	+	4.44024i	−0.261665	+	0.360151i
$153$	−19.6351	−	5.42520i	−1.58740	−	0.438602i
$154$	5.25389	−	1.42166i	0.423371	−	0.114560i
$155$			13.7872i			1.10742i
$156$	−1.80339	+	1.88563i	−0.144386	+	0.150972i
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	−0.757077	−	0.653325i	$-0.773373\pi$
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	0.996503	−	0.0835524i	$-0.0266266\pi$
$158$	3.02188	−	0.981868i	0.240408	−	0.0781132i
$159$	−8.06173	−	14.9865i	−0.639337	−	1.18851i
$160$	1.56076	+	2.14820i	0.123389	+	0.169830i
$161$	−2.42838	−	7.47379i	−0.191383	−	0.589017i
$162$	6.78115	−	5.91743i	0.532778	−	0.464917i
$163$	−5.72951	−	4.16273i	−0.448770	−	0.326050i	0.340340	−	0.940302i	$-0.389458\pi$
$163$	−5.72951	−	4.16273i	−0.448770	−	0.326050i	−0.789110	+	0.614252i	$0.789458\pi$
$164$	−1.57428			−0.122930
$165$	11.0796	−	10.4841i	0.862542	−	0.816189i
$166$	−1.87418			−0.145465
$167$	−2.05072	−	1.48993i	−0.158689	−	0.115294i	0.505607	−	0.862764i	$-0.331269\pi$
$167$	−2.05072	−	1.48993i	−0.158689	−	0.115294i	−0.664296	+	0.747470i	$0.731269\pi$
$168$	2.56076	+	1.23366i	0.197567	+	0.0951792i
$169$	3.31598	+	10.2055i	0.255075	+	0.785041i
$170$	−10.5980	−	14.5868i	−0.812826	−	1.11876i
$171$	5.78093	+	15.4171i	0.442079	+	1.17898i
$172$	−3.25737	+	1.05838i	−0.248372	+	0.0807010i
$173$	−0.293345	+	0.902823i	−0.0223026	+	0.0686404i	−0.961588	−	0.274496i	$-0.911489\pi$
$173$	−0.293345	+	0.902823i	−0.0223026	+	0.0686404i	0.939286	+	0.343136i	$0.111489\pi$
$174$	0.580840	+	0.555504i	0.0440333	+	0.0421127i
$175$			3.36538i			0.254399i
$176$	1.18094	−	3.09925i	0.0890168	−	0.233615i
$177$	−1.42264	+	10.4907i	−0.106932	+	0.788526i
$178$	7.52906	−	10.3629i	0.564327	−	0.776729i
$179$	17.6570	+	5.73709i	1.31974	+	0.428810i	0.882407	−	0.470488i	$-0.155922\pi$
$179$	17.6570	+	5.73709i	1.31974	+	0.428810i	0.437336	+	0.899298i	$0.355922\pi$
$180$	7.95804	−	0.355032i	0.593157	−	0.0264625i
$181$	−10.4196	+	7.57025i	−0.774480	+	0.562692i	−0.903317	−	0.428973i	$-0.858875\pi$
$181$	−10.4196	+	7.57025i	−0.774480	+	0.562692i	0.128837	+	0.991666i	$0.458875\pi$
$182$	−2.00000	+	1.45309i	−0.148250	+	0.107710i
$183$	23.6951	−	4.29640i	1.75159	−	0.317599i
$184$	−4.55420	−	1.47975i	−0.335740	−	0.109088i
$185$	−1.57162	+	2.16315i	−0.115548	+	0.159038i
$186$	8.91178	+	1.20853i	0.653443	+	0.0886135i
$187$	−8.01891	+	21.0448i	−0.586400	+	1.53894i
$188$		−	10.0129i		−	0.730267i
$189$	7.32218	−	4.37038i	0.532610	−	0.317899i
$190$	−4.50348	+	13.8603i	−0.326717	+	1.00553i
$191$	3.07080	−	0.997763i	0.222195	−	0.0721956i	−0.195804	−	0.980643i	$-0.562732\pi$
$191$	3.07080	−	0.997763i	0.222195	−	0.0721956i	0.417999	+	0.908448i	$0.362732\pi$
$192$	1.52536	−	0.820539i	0.110083	−	0.0592173i
$193$	5.73979	+	7.90015i	0.413159	+	0.568665i	0.963985	−	0.265955i	$-0.0856872\pi$
$193$	5.73979	+	7.90015i	0.413159	+	0.568665i	−0.550826	+	0.834620i	$0.685687\pi$
$194$	−1.10968	−	3.41524i	−0.0796702	−	0.245200i
$195$	−3.00696	+	6.24165i	−0.215333	+	0.446974i
$196$	−3.48433	−	2.53151i	−0.248881	−	0.180822i
$197$	13.9679			0.995175			0.497587	−	0.867414i	$-0.334219\pi$
$197$	13.9679			0.995175			0.497587	+	0.867414i	$0.334219\pi$
$198$	−5.80554	−	8.08058i	−0.412582	−	0.574262i
$199$	15.9679			1.13194			0.565969	−	0.824427i	$-0.308502\pi$
$199$	15.9679			1.13194			0.565969	+	0.824427i	$0.308502\pi$
$200$	1.65906	+	1.20538i	0.117314	+	0.0852333i
$201$	−8.86844	+	18.4085i	−0.625532	+	1.29844i
$202$	3.76143	+	11.5765i	0.264653	+	0.814518i
$203$	0.447600	+	0.616068i	0.0314153	+	0.0432395i
$204$	−10.3576	+	5.57167i	−0.725176	+	0.390095i
$205$	−3.97562	+	1.29176i	−0.277669	+	0.0902201i
$206$	0.273973	−	0.843203i	0.0190886	−	0.0587487i
$207$	−11.2342	+	8.95353i	−0.780831	+	0.622314i
$208$			1.50641i			0.104451i
$209$	17.5712	−	4.75461i	1.21543	−	0.328883i
$210$	7.47910	+	1.01424i	0.516107	+	0.0699893i
$211$	1.33315	−	1.83493i	0.0917782	−	0.126322i	−0.760659	−	0.649152i	$-0.775124\pi$
$211$	1.33315	−	1.83493i	0.0917782	−	0.126322i	0.852437	+	0.522830i	$0.175124\pi$
$212$	−9.34406	−	3.03607i	−0.641753	−	0.208518i
$213$	1.53052	−	0.277515i	0.104870	−	0.0190150i
$214$	−1.80554	+	1.31180i	−0.123424	+	0.0896728i
$215$	−7.35758	+	5.34560i	−0.501783	+	0.364567i
$216$	0.468081	−	5.17503i	0.0318489	−	0.352116i
$217$	8.10394	+	2.63313i	0.550131	+	0.178748i
$218$	2.78330	−	3.83089i	0.188509	−	0.259461i
$219$	1.07700	−	7.94191i	0.0727772	−	0.536665i
$220$	0.439243	−	8.79573i	0.0296138	−	0.593008i
$221$		−	10.2289i		−	0.688072i
$222$	1.26045	+	1.20547i	0.0845960	+	0.0809061i
$223$	1.36009	−	4.18592i	0.0910782	−	0.280310i	−0.895134	−	0.445798i	$-0.852920\pi$
$223$	1.36009	−	4.18592i	0.0910782	−	0.280310i	0.986212	+	0.165488i	$0.0529199\pi$
$224$	1.56076	−	0.507121i	0.104282	−	0.0338834i
$225$	5.76050	−	2.16000i	0.384033	−	0.144000i
$226$	2.28987	+	3.15173i	0.152320	+	0.209650i
$227$	−3.93483	−	12.1102i	−0.261164	−	0.803780i	−0.992552	−	0.121819i	$-0.961127\pi$
$227$	−3.93483	−	12.1102i	−0.261164	−	0.803780i	0.731388	−	0.681961i	$-0.238873\pi$
$228$	8.56424	+	4.12588i	0.567180	+	0.273243i
$229$	−5.19661	−	3.77556i	−0.343402	−	0.249496i	0.402694	−	0.915335i	$-0.368074\pi$
$229$	−5.19661	−	3.77556i	−0.343402	−	0.249496i	−0.746096	+	0.665839i	$0.768074\pi$
$230$	−12.7152			−0.838413
$231$	−4.04641	−	8.51469i	−0.266235	−	0.560225i
$232$	0.464026			0.0304648
$233$	13.5999	+	9.88087i	0.890956	+	0.647318i	0.936127	−	0.351662i	$-0.114383\pi$
$233$	13.5999	+	9.88087i	0.890956	+	0.647318i	−0.0451710	+	0.998979i	$0.514383\pi$
$234$	3.77089	+	2.49075i	0.246511	+	0.162825i
$235$	−8.21599	−	25.2862i	−0.535952	−	1.64949i
$236$	3.59268	+	4.94489i	0.233863	+	0.321885i
$237$	−2.60717	−	4.84666i	−0.169354	−	0.314824i
$238$	−10.5980	+	3.44348i	−0.686963	+	0.223208i
$239$	−3.72018	+	11.4495i	−0.240638	+	0.740608i	0.755685	+	0.654935i	$0.227304\pi$
$239$	−3.72018	+	11.4495i	−0.240638	+	0.740608i	−0.996323	+	0.0856731i	$0.972696\pi$
$240$	3.17879	−	3.32377i	0.205190	−	0.214548i
$241$		−	20.5642i		−	1.32466i	−0.749214	−	0.662328i	$-0.769568\pi$
$241$		−	20.5642i		−	1.32466i	0.749214	−	0.662328i	$-0.230432\pi$
$242$	−9.49907	+	5.54686i	−0.610623	+	0.356566i
$243$	−12.1803	−	9.72827i	−0.781369	−	0.624069i
$244$	8.17223	−	11.2481i	0.523173	−	0.720086i
$245$	−10.8764	−	3.53395i	−0.694866	−	0.225776i
$246$	0.486479	+	2.68298i	0.0310168	+	0.171061i
$247$	−6.68883	+	4.85972i	−0.425600	+	0.309217i
$248$	4.20067	−	3.05196i	0.266743	−	0.193800i
$249$	0.579155	+	3.19410i	0.0367024	+	0.202418i
$250$	−7.44800	−	2.42000i	−0.471053	−	0.153054i
$251$	−9.61958	+	13.2402i	−0.607183	+	0.835715i	−0.996342	−	0.0854552i	$-0.972766\pi$
$251$	−9.61958	+	13.2402i	−0.607183	+	0.835715i	0.389159	+	0.921170i	$0.372766\pi$
$252$	1.31117	−	4.74542i	0.0825958	−	0.298934i
$253$	8.68267	+	13.2983i	0.545875	+	0.836058i
$254$			0.236376i			0.0148315i
$255$	−21.5848	+	22.5693i	−1.35169	+	1.41334i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	8.11843	−	2.63784i	0.506414	−	0.164544i	−0.0446568	−	0.999002i	$-0.514219\pi$
$257$	8.11843	−	2.63784i	0.506414	−	0.164544i	0.551071	+	0.834459i	$0.314219\pi$
$258$	2.81035	+	5.22435i	0.174965	+	0.325254i
$259$	0.971314	+	1.33690i	0.0603545	+	0.0830709i
$260$	1.23607	+	3.80423i	0.0766577	+	0.235928i
$261$	0.767236	−	1.16156i	0.0474907	−	0.0718989i
$262$	−4.26143	−	3.09611i	−0.263272	−	0.191278i
$263$	−13.5666			−0.836553			−0.418276	−	0.908320i	$-0.637366\pi$
$263$	−13.5666			−0.836553			−0.418276	+	0.908320i	$0.637366\pi$
$264$	−5.64687	−	1.05491i	−0.347541	−	0.0649253i
$265$	−26.0883			−1.60259
$266$	7.28678	+	5.29416i	0.446781	+	0.324606i
$267$	−19.9876	−	9.62919i	−1.22322	−	0.589297i
$268$	3.64554	+	11.2198i	0.222687	+	0.685360i
$269$	−6.96435	−	9.58561i	−0.424624	−	0.584445i	0.542085	−	0.840324i	$-0.317635\pi$
$269$	−6.96435	−	9.58561i	−0.424624	−	0.584445i	−0.966709	+	0.255879i	$0.917635\pi$
$270$	−3.06424	−	13.4529i	−0.186484	−	0.818716i
$271$	20.5918	−	6.69068i	1.25086	−	0.406430i	0.392632	−	0.919696i	$-0.371564\pi$
$271$	20.5918	−	6.69068i	1.25086	−	0.406430i	0.858230	+	0.513266i	$0.171564\pi$
$272$	−2.09831	+	6.45792i	−0.127229	+	0.391569i
$273$	3.09447	+	2.95950i	0.187286	+	0.179117i
$274$			0.927773i			0.0560488i
$275$	−1.77652	−	6.56534i	−0.107128	−	0.395905i
$276$	−1.11455	+	8.21881i	−0.0670883	+	0.494714i
$277$	−2.39438	+	3.29558i	−0.143864	+	0.198012i	−0.874868	−	0.484361i	$-0.839052\pi$
$277$	−2.39438	+	3.29558i	−0.143864	+	0.198012i	0.731004	+	0.682373i	$0.239052\pi$
$278$	8.03945	+	2.61218i	0.482174	+	0.156668i
$279$	−0.694243	−	15.5615i	−0.0415633	−	0.931640i
$280$	3.52536	−	2.56132i	0.210680	−	0.153068i
$281$	14.4528	−	10.5006i	0.862182	−	0.626412i	−0.0662956	−	0.997800i	$-0.521118\pi$
$281$	14.4528	−	10.5006i	0.862182	−	0.626412i	0.928478	+	0.371388i	$0.121118\pi$
$282$	−17.0646	+	3.09416i	−1.01618	+	0.184255i
$283$	2.89090	+	0.939310i	0.171846	+	0.0558362i	0.393676	−	0.919249i	$-0.371203\pi$
$283$	2.89090	+	0.939310i	0.171846	+	0.0558362i	−0.221830	+	0.975085i	$0.571203\pi$
$284$	0.527864	−	0.726543i	0.0313230	−	0.0431124i
$285$	25.0132	+	3.39205i	1.48165	+	0.200927i
$286$	3.13464	−	3.89051i	0.185355	−	0.230051i
$287$			2.58351i			0.152500i
$288$	−1.86977	−	2.34605i	−0.110177	−	0.138242i
$289$	8.99477	−	27.6830i	0.529104	−	1.62841i
$290$	1.17183	−	0.380751i	0.0688123	−	0.0223585i
$291$	−5.47755	+	2.94655i	−0.321099	+	0.172730i
$292$	−2.71982	−	3.74351i	−0.159165	−	0.219072i
$293$	7.21279	+	22.1987i	0.421376	+	1.29686i	0.906422	+	0.422373i	$0.138803\pi$
$293$	7.21279	+	22.1987i	0.421376	+	1.29686i	−0.485046	+	0.874489i	$0.661197\pi$
$294$	−3.23764	+	6.72049i	−0.188823	+	0.391947i
$295$	13.1303	+	9.53970i	0.764474	+	0.555423i
$296$	1.00696			0.0585284
$297$	−11.9774	+	12.3912i	−0.695000	+	0.719010i
$298$	18.0716			1.04686
$299$	−5.83588	−	4.24002i	−0.337498	−	0.245206i
$300$	1.54160	−	3.19996i	0.0890046	−	0.184750i
$301$	1.73689	+	5.34560i	0.100113	+	0.308115i
$302$	7.83513	+	10.7841i	0.450861	+	0.620557i
$303$	18.5670	−	9.98778i	1.06665	−	0.573783i
$304$	5.21982	−	1.69602i	0.299377	−	0.0972736i
$305$	11.4083	−	35.1111i	0.653237	−	2.01046i
$306$	12.6963	+	15.9303i	0.725797	+	0.910674i
$307$			30.0216i			1.71342i	0.515794	+	0.856712i	$0.327497\pi$
$307$			30.0216i			1.71342i	−0.515794	+	0.856712i	$0.672503\pi$
$308$	−5.08611	−	1.93802i	−0.289808	−	0.110429i
$309$	−1.52170	−	0.206358i	−0.0865666	−	0.0117393i
$310$	8.10394	−	11.1541i	0.460273	−	0.633511i
$311$	−0.470986	−	0.153033i	−0.0267071	−	0.00867768i	0.295633	−	0.955302i	$-0.404469\pi$
$311$	−0.470986	−	0.153033i	−0.0267071	−	0.00867768i	−0.322340	+	0.946624i	$0.604469\pi$
$312$	2.56732	−	0.465507i	0.145346	−	0.0263541i
$313$	22.9590	−	16.6807i	1.29772	−	0.942849i	0.297790	−	0.954632i	$-0.403751\pi$
$313$	22.9590	−	16.6807i	1.29772	−	0.942849i	0.999931	+	0.0117826i	$0.00375062\pi$
$314$	−7.85410	+	5.70634i	−0.443233	+	0.322027i
$315$	−0.582635	−	13.0598i	−0.0328278	−	0.735834i
$316$	−3.02188	−	0.981868i	−0.169994	−	0.0552344i
$317$	3.90331	−	5.37244i	0.219232	−	0.301747i	−0.685209	−	0.728347i	$-0.740289\pi$
$317$	3.90331	−	5.37244i	0.219232	−	0.301747i	0.904440	+	0.426600i	$0.140289\pi$
$318$	−2.28678	+	16.8629i	−0.128236	+	0.945626i
$319$	−1.19841	−	0.965575i	−0.0670980	−	0.0540618i
$320$		−	2.65532i		−	0.148437i
$321$	2.79359	+	2.67174i	0.155923	+	0.149122i
$322$	−2.42838	+	7.47379i	−0.135328	+	0.416498i
$323$	−35.4440	+	11.5164i	−1.97215	+	0.640792i
$324$	−8.96425	+	0.801439i	−0.498014	+	0.0445244i
$325$	1.81580	+	2.49923i	0.100722	+	0.138632i
$326$	2.18848	+	6.73544i	0.121209	+	0.373041i
$327$	−7.38893	−	3.55967i	−0.408609	−	0.196850i
$328$	1.27362	+	0.925338i	0.0703238	+	0.0510932i
$329$	−16.4320			−0.905924
$330$	−15.1260	+	1.96945i	−0.832657	+	0.108414i
$331$	7.41016			0.407299			0.203650	−	0.979044i	$-0.434720\pi$
$331$	7.41016			0.407299			0.203650	+	0.979044i	$0.434720\pi$
$332$	1.51625	+	1.10162i	0.0832149	+	0.0604591i
$333$	1.66494	−	2.52065i	0.0912382	−	0.138131i
$334$	0.783304	+	2.41076i	0.0428605	+	0.131911i
$335$	18.4126	+	25.3428i	1.00599	+	1.38462i
$336$	−1.34657	−	2.50323i	−0.0734612	−	0.136562i
$337$	−32.5392	+	10.5726i	−1.77252	+	0.575927i	−0.998370	−	0.0570720i	$-0.981824\pi$
$337$	−32.5392	+	10.5726i	−1.77252	+	0.575927i	−0.774152	+	0.632999i	$0.781824\pi$
$338$	3.31598	−	10.2055i	0.180365	−	0.555108i
$339$	4.66376	−	4.87647i	0.253301	−	0.264853i
$340$			18.0303i			0.977831i
$341$	−17.1995	−	0.858913i	−0.931406	−	0.0465127i
$342$	4.38509	−	15.8707i	0.237119	−	0.858188i
$343$	−10.9066	+	15.0117i	−0.588902	+	0.810554i
$344$	3.25737	+	1.05838i	0.175626	+	0.0570642i
$345$	3.92920	+	21.6700i	0.211541	+	1.16667i
$346$	0.767987	−	0.557975i	0.0412872	−	0.0299969i
$347$	16.9283	−	12.2991i	0.908760	−	0.660252i	−0.0319413	−	0.999490i	$-0.510169\pi$
$347$	16.9283	−	12.2991i	0.908760	−	0.660252i	0.940701	+	0.339237i	$0.110169\pi$
$348$	−0.143392	−	0.790821i	−0.00768661	−	0.0423925i
$349$	28.0113	+	9.10144i	1.49941	+	0.487189i	0.939847	−	0.341597i	$-0.110968\pi$
$349$	28.0113	+	9.10144i	1.49941	+	0.487189i	0.559566	+	0.828786i	$0.310968\pi$
$350$	1.97812	−	2.72265i	0.105735	−	0.145532i
$351$	3.07962	−	7.19627i	0.164378	−	0.384109i
$352$	−2.77710	+	1.81321i	−0.148020	+	0.0966444i
$353$		−	24.3265i		−	1.29477i	−0.762163	−	0.647385i	$-0.775863\pi$
$353$		−	24.3265i		−	1.29477i	0.762163	−	0.647385i	$-0.224137\pi$
$354$	7.31720	−	7.65092i	0.388905	−	0.406642i
$355$	0.736889	−	2.26791i	0.0391100	−	0.120368i
$356$	−12.1823	+	3.95826i	−0.645659	+	0.209787i
$357$	9.14354	+	16.9976i	0.483928	+	0.899608i
$358$	−10.9126	−	15.0199i	−0.576749	−	0.793827i
$359$	10.1134	+	31.1259i	0.533765	+	1.64276i	0.746302	+	0.665607i	$0.231827\pi$
$359$	10.1134	+	31.1259i	0.533765	+	1.64276i	−0.212537	+	0.977153i	$0.568173\pi$
$360$	−6.64687	−	4.39039i	−0.350321	−	0.231394i
$361$	8.99871	+	6.53795i	0.473617	+	0.344103i
$362$	12.8793			0.676920
$363$	12.3887	+	14.4748i	0.650237	+	0.759731i
$364$	2.47214			0.129575
$365$	−9.94022	−	7.22199i	−0.520295	−	0.378016i
$366$	−21.6951	−	10.4518i	−1.13402	−	0.546322i
$367$	−3.67822	−	11.3204i	−0.192001	−	0.590919i	−0.999998	−	0.00173292i	$-0.999448\pi$
$367$	−3.67822	−	11.3204i	−0.192001	−	0.590919i	0.807997	−	0.589186i	$-0.200552\pi$
$368$	2.81465	+	3.87403i	0.146724	+	0.201948i
$369$	4.42217	−	1.65817i	0.230209	−	0.0863211i
$370$	2.54293	−	0.826249i	0.132201	−	0.0429547i
$371$	−4.98242	+	15.3343i	−0.258675	+	0.796118i
$372$	−6.49942	−	6.21593i	−0.336979	−	0.322281i
$373$		−	27.7804i		−	1.43841i	−0.694796	−	0.719207i	$-0.744505\pi$
$373$		−	27.7804i		−	1.43841i	0.694796	−	0.719207i	$-0.255495\pi$
$374$	18.8572	−	12.3122i	0.975084	−	0.636647i
$375$	−1.82276	+	13.4412i	−0.0941268	+	0.694099i
$376$	−5.88545	+	8.10062i	−0.303519	+	0.417758i
$377$	0.664801	+	0.216007i	0.0342390	+	0.0111249i
$378$	−8.49262	−	0.768157i	−0.436813	−	0.0395097i
$379$	6.36264	−	4.62273i	0.326827	−	0.237454i	−0.412256	−	0.911068i	$-0.635259\pi$
$379$	6.36264	−	4.62273i	0.326827	−	0.237454i	0.739083	+	0.673614i	$0.235259\pi$
$380$	11.7903	−	8.56613i	0.604828	−	0.439433i
$381$	0.402846	−	0.0730441i	0.0206384	−	0.00374216i
$382$	−3.07080	−	0.997763i	−0.157116	−	0.0510500i
$383$	7.61538	−	10.4817i	0.389128	−	0.535588i	−0.568846	−	0.822444i	$-0.692610\pi$
$383$	7.61538	−	10.4817i	0.389128	−	0.535588i	0.957974	+	0.286856i	$0.0926101\pi$
$384$	−1.71634	−	0.232753i	−0.0875867	−	0.0118776i
$385$	−14.4345	−	0.720832i	−0.735649	−	0.0367370i
$386$		−	9.76512i		−	0.497032i
$387$	8.03522	−	6.40398i	0.408453	−	0.325533i
$388$	−1.10968	+	3.41524i	−0.0563353	+	0.173382i
$389$	−24.6301	+	8.00280i	−1.24880	+	0.405758i	−0.857489	−	0.514502i	$-0.827977\pi$
$389$	−24.6301	+	8.00280i	−1.24880	+	0.405758i	−0.391306	+	0.920261i	$0.627977\pi$
$390$	6.10143	−	3.28215i	0.308958	−	0.166198i
$391$	−19.1122	−	26.3057i	−0.966546	−	1.33034i
$392$	1.33089	+	4.09607i	0.0672203	+	0.206883i
$393$	−3.95972	+	8.21934i	−0.199742	+	0.414611i
$394$	−11.3003	−	8.21015i	−0.569301	−	0.413621i
$395$	−8.43698			−0.424511
$396$	−0.0528664	+	9.94973i	−0.00265664	+	0.499993i
$397$	−17.9986			−0.903323			−0.451661	−	0.892189i	$-0.649168\pi$
$397$	−17.9986			−0.903323			−0.451661	+	0.892189i	$0.649168\pi$
$398$	−12.9183	−	9.38572i	−0.647538	−	0.470464i
$399$	6.77089	−	14.0546i	0.338969	−	0.703609i
$400$	−0.633706	−	1.95035i	−0.0316853	−	0.0975173i
$401$	2.21479	+	3.04840i	0.110601	+	0.152230i	0.860729	−	0.509063i	$-0.170008\pi$
$401$	2.21479	+	3.04840i	0.110601	+	0.152230i	−0.750128	+	0.661293i	$0.770008\pi$
$402$	17.9950	−	9.68008i	0.897508	−	0.482798i
$403$	7.43893	−	2.41706i	0.370560	−	0.120402i
$404$	3.76143	−	11.5765i	0.187138	−	0.575951i
$405$	−21.9803	+	9.37943i	−1.09221	+	0.466068i
$406$		−	0.761502i		−	0.0377927i
$407$	−2.60061	−	2.09535i	−0.128907	−	0.103863i
$408$	11.6544	+	1.58046i	0.576979	+	0.0782442i
$409$	−8.44886	+	11.6289i	−0.417769	+	0.575010i	−0.965092	−	0.261912i	$-0.915647\pi$
$409$	−8.44886	+	11.6289i	−0.417769	+	0.575010i	0.547323	+	0.836922i	$0.315647\pi$
$410$	3.97562	+	1.29176i	0.196342	+	0.0637953i
$411$	1.58117	−	0.286698i	0.0779933	−	0.0141418i
$412$	−0.717271	+	0.521128i	−0.0353374	+	0.0256741i
$413$	8.11495	−	5.89586i	0.399311	−	0.290116i
$414$	14.3514	−	0.640260i	0.705334	−	0.0314671i
$415$	4.73299	+	1.53784i	0.232333	+	0.0754896i
$416$	0.885446	−	1.21871i	0.0434126	−	0.0597523i
$417$	1.96751	−	14.5085i	0.0963492	−	0.710486i
$418$	−17.0101	−	6.48153i	−0.831990	−	0.317022i
$419$		−	31.1601i		−	1.52227i	−0.648595	−	0.761134i	$-0.724643\pi$
$419$		−	31.1601i		−	1.52227i	0.648595	−	0.761134i	$-0.275357\pi$
$420$	−5.45456	−	5.21664i	−0.266155	−	0.254546i
$421$	−3.34251	+	10.2872i	−0.162904	+	0.501367i	−0.998876	−	0.0474055i	$-0.984905\pi$
$421$	−3.34251	+	10.2872i	−0.162904	+	0.501367i	0.835972	+	0.548773i	$0.184905\pi$
$422$	−2.15709	+	0.700881i	−0.105005	+	0.0341183i
$423$	10.5465	+	28.1265i	0.512790	+	1.36756i
$424$	5.77495	+	7.94853i	0.280456	+	0.386015i
$425$	4.30303	+	13.2434i	0.208728	+	0.642398i
$426$	−1.40134	−	0.675105i	−0.0678950	−	0.0327089i
$427$	−18.4590	−	13.4113i	−0.893294	−	0.649016i
$428$	2.23177			0.107877
$429$	−7.59910	−	4.14001i	−0.366888	−	0.199881i
$430$	9.09447			0.438574
$431$	32.2249	+	23.4128i	1.55222	+	1.12775i	0.942046	+	0.335484i	$0.108900\pi$
$431$	32.2249	+	23.4128i	1.55222	+	1.12775i	0.610173	+	0.792268i	$0.291100\pi$
$432$	−3.42049	+	3.91155i	−0.164568	+	0.188195i
$433$	4.99226	+	15.3646i	0.239913	+	0.738376i	0.996432	+	0.0844037i	$0.0268985\pi$
$433$	4.99226	+	15.3646i	0.239913	+	0.738376i	−0.756519	+	0.653972i	$0.773101\pi$
$434$	−5.00851	−	6.89362i	−0.240416	−	0.330904i
$435$	−1.01102	−	1.87945i	−0.0484745	−	0.0901127i
$436$	−4.50348	+	1.46327i	−0.215678	+	0.0700779i
$437$	−8.12151	+	24.9954i	−0.388505	+	1.19569i
$438$	−5.53945	+	5.79210i	−0.264685	+	0.276757i
$439$			6.13994i			0.293043i	0.989207	+	0.146522i	$0.0468078\pi$
$439$			6.13994i			0.293043i	−0.989207	+	0.146522i	$0.953192\pi$
$440$	−5.52536	+	6.85772i	−0.263411	+	0.326929i
$441$	12.4540	+	3.44105i	0.593046	+	0.163859i
$442$	−6.01241	+	8.27537i	−0.285981	+	0.393619i
$443$	1.55768	+	0.506119i	0.0740074	+	0.0240465i	0.345787	−	0.938313i	$-0.387612\pi$
$443$	1.55768	+	0.506119i	0.0740074	+	0.0240465i	−0.271779	+	0.962360i	$0.587612\pi$
$444$	−0.311168	−	1.71612i	−0.0147674	−	0.0814436i
$445$	−27.5167	+	19.9920i	−1.30442	+	0.947714i
$446$	−3.56076	+	2.58704i	−0.168607	+	0.122500i
$447$	−5.58443	−	30.7987i	−0.264134	−	1.45673i
$448$	−1.56076	−	0.507121i	−0.0737388	−	0.0239592i
$449$	10.7458	−	14.7903i	0.507125	−	0.697997i	−0.476306	−	0.879279i	$-0.658025\pi$
$449$	10.7458	−	14.7903i	0.507125	−	0.697997i	0.983431	+	0.181282i	$0.0580247\pi$
$450$	−5.92996	−	1.63846i	−0.279541	−	0.0772376i
$451$	−1.36379	−	5.04004i	−0.0642183	−	0.237326i
$452$		−	3.89575i		−	0.183241i
$453$	15.9578	−	16.6856i	0.749763	−	0.783957i
$454$	−3.93483	+	12.1102i	−0.184671	+	0.568358i
$455$	6.24303	−	2.02848i	0.292678	−	0.0950967i
$456$	−4.50348	−	8.37184i	−0.210895	−	0.392047i
$457$	16.4490	+	22.6402i	0.769454	+	1.05906i	0.996368	+	0.0851474i	$0.0271361\pi$
$457$	16.4490	+	22.6402i	0.769454	+	1.05906i	−0.226915	+	0.973915i	$0.572864\pi$
$458$	1.98493	+	6.10899i	0.0927497	+	0.285454i
$459$	23.2260	−	26.5605i	1.08410	−	1.23974i
$460$	10.2868	+	7.47379i	0.479624	+	0.348467i
$461$	−30.3359			−1.41288			−0.706441	−	0.707772i	$-0.749700\pi$
$461$	−30.3359			−1.41288			−0.706441	+	0.707772i	$0.749700\pi$
$462$	−1.73119	+	9.26695i	−0.0805423	+	0.431138i
$463$	−10.9632			−0.509503			−0.254752	−	0.967007i	$-0.581994\pi$
$463$	−10.9632			−0.509503			−0.254752	+	0.967007i	$0.581994\pi$
$464$	−0.375405	−	0.272747i	−0.0174277	−	0.0126620i
$465$	−21.5138	−	10.3644i	−0.997678	−	0.480639i
$466$	−5.19468	−	15.9876i	−0.240639	−	0.740611i
$467$	−18.9376	−	26.0653i	−0.876326	−	1.20616i	−0.977425	−	0.211283i	$-0.932236\pi$
$467$	−18.9376	−	26.0653i	−0.876326	−	1.20616i	0.101099	−	0.994876i	$-0.467764\pi$
$468$	−1.58669	−	4.23153i	−0.0733448	−	0.195603i
$469$	18.4126	−	5.98262i	0.850215	−	0.276252i
$470$	−8.21599	+	25.2862i	−0.378975	+	1.16637i
$471$	12.1521	+	11.6221i	0.559941	+	0.535518i
$472$		−	6.11223i		−	0.281338i
$473$	−6.21025	−	9.51157i	−0.285547	−	0.437342i
$474$	−0.739548	+	5.45348i	−0.0339686	+	0.250487i
$475$	6.61566	−	9.10568i	0.303547	−	0.417797i
$476$	10.5980	+	3.44348i	0.485756	+	0.157832i
$477$	29.4455	−	1.31365i	1.34822	−	0.0601480i
$478$	9.73955	−	7.07620i	0.445477	−	0.323658i
$479$	−15.2361	+	11.0697i	−0.696154	+	0.505785i	−0.878677	−	0.477416i	$-0.841573\pi$
$479$	−15.2361	+	11.0697i	−0.696154	+	0.505785i	0.182524	+	0.983201i	$0.441573\pi$
$480$	−4.52536	+	0.820539i	−0.206553	+	0.0374523i
$481$	1.44265	+	0.468746i	0.0657793	+	0.0213730i
$482$	−12.0873	+	16.6368i	−0.550563	+	0.757785i
$483$	13.4877	+	1.82907i	0.613712	+	0.0832255i
$484$	10.9453	+	1.09591i	0.497512	+	0.0498140i
$485$			9.53523i			0.432972i
$486$	4.13597	+	15.0298i	0.187611	+	0.681764i
$487$	−8.30030	+	25.5457i	−0.376123	+	1.15759i	0.566595	+	0.823996i	$0.308260\pi$
$487$	−8.30030	+	25.5457i	−0.376123	+	1.15759i	−0.942718	+	0.333591i	$0.891740\pi$
$488$	−13.2229	+	4.29640i	−0.598575	+	0.194489i
$489$	10.8027	−	5.81110i	0.488514	−	0.262787i
$490$	6.72197	+	9.25200i	0.303668	+	0.417963i
$491$	5.88351	+	18.1076i	0.265519	+	0.817184i	0.991573	+	0.129547i	$0.0413522\pi$
$491$	5.88351	+	18.1076i	0.265519	+	0.817184i	−0.726054	+	0.687638i	$0.758648\pi$
$492$	1.18345	−	2.45652i	0.0533540	−	0.110749i
$493$	2.54910	+	1.85203i	0.114806	+	0.0834111i
$494$	8.26785			0.371988
$495$	8.03063	+	25.1700i	0.360950	+	1.13131i
$496$	−5.19231			−0.233142
$497$	−1.19231	−	0.866266i	−0.0534825	−	0.0388573i
$498$	1.40890	−	2.92450i	0.0631343	−	0.131050i
$499$	3.28175	+	10.1002i	0.146912	+	0.452147i	0.997252	−	0.0740860i	$-0.0236039\pi$
$499$	3.28175	+	10.1002i	0.146912	+	0.452147i	−0.850340	+	0.526233i	$0.823604\pi$
$500$	4.60312	+	6.33565i	0.205858	+	0.283339i
$501$	3.86651	−	2.07992i	0.172743	−	0.0929240i
$502$	15.5648	−	5.05731i	0.694692	−	0.225719i
$503$	9.56998	−	29.4534i	0.426704	−	1.31326i	−0.474649	−	0.880175i	$-0.657425\pi$
$503$	9.56998	−	29.4534i	0.426704	−	1.31326i	0.901353	−	0.433085i	$-0.142575\pi$
$504$	−3.85005	+	3.06844i	−0.171495	+	0.136679i
$505$		−	32.3211i		−	1.43827i
$506$	0.792125	−	15.8621i	0.0352142	−	0.705157i
$507$	−18.4176	−	2.49761i	−0.817954	−	0.110923i
$508$	0.138938	−	0.191232i	0.00616438	−	0.00848454i
$509$	19.5685	+	6.35820i	0.867359	+	0.281822i	0.708699	−	0.705511i	$-0.249283\pi$
$509$	19.5685	+	6.35820i	0.867359	+	0.281822i	0.158660	+	0.987333i	$0.449283\pi$
$510$	30.7284	−	5.57167i	1.36068	−	0.246718i
$511$	−6.14339	+	4.46344i	−0.271768	+	0.197451i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−28.4028	−	2.56904i	−1.25402	−	0.113426i
$514$	−8.11843	−	2.63784i	−0.358089	−	0.116350i
$515$	−1.38376	+	1.90458i	−0.0609758	+	0.0839260i
$516$	0.797180	−	5.87847i	0.0350939	−	0.258785i
$517$	32.0563	−	8.67413i	1.40983	−	0.381488i
$518$		−	1.65250i		−	0.0726066i
$519$	−1.18826	−	1.13643i	−0.0521587	−	0.0498836i
$520$	1.23607	−	3.80423i	0.0542052	−	0.166826i
$521$	−3.64239	+	1.18348i	−0.159576	+	0.0518494i	−0.387716	−	0.921779i	$-0.626736\pi$
$521$	−3.64239	+	1.18348i	−0.159576	+	0.0518494i	0.228140	+	0.973628i	$0.426736\pi$
$522$	−1.30346	+	0.488754i	−0.0570507	+	0.0213922i
$523$	5.66137	+	7.79220i	0.247554	+	0.340729i	0.914653	−	0.404240i	$-0.132464\pi$
$523$	5.66137	+	7.79220i	0.247554	+	0.340729i	−0.667099	+	0.744969i	$0.732464\pi$
$524$	1.62772	+	5.00961i	0.0711073	+	0.218846i
$525$	−5.25138	−	2.52989i	−0.229189	−	0.110414i
$526$	10.9756	+	7.97425i	0.478560	+	0.347694i
$527$	35.2572			1.53583
$528$	3.94835	+	4.17259i	0.171830	+	0.181589i
$529$	0.0696480			0.00302817
$530$	21.1059	+	15.3343i	0.916781	+	0.666080i
$531$	−15.3003	−	10.1062i	−0.663977	−	0.438570i
$532$	−2.78330	−	8.56613i	−0.120672	−	0.371389i
$533$	1.39394	+	1.91859i	0.0603782	+	0.0831034i
$534$	10.5104	+	19.5386i	0.454831	+	0.845518i
$535$	5.63601	−	1.83125i	0.243666	−	0.0791719i
$536$	3.64554	−	11.2198i	0.157463	−	0.484623i
$537$	−22.2257	+	23.2393i	−0.959109	+	1.00285i
$538$			11.8485i			0.510824i
$539$	5.08616	−	13.3481i	0.219076	−	0.574942i
$540$	−5.42838	+	12.6847i	−0.233600	+	0.545863i
$541$	1.63935	−	2.25638i	0.0704813	−	0.0970092i	−0.772321	−	0.635232i	$-0.780904\pi$
$541$	1.63935	−	2.25638i	0.0704813	−	0.0970092i	0.842802	+	0.538223i	$0.180904\pi$
$542$	−20.5918	−	6.69068i	−0.884493	−	0.287389i
$543$	−3.97992	−	21.9497i	−0.170795	−	0.941951i
$544$	5.49344	−	3.99122i	0.235529	−	0.171122i
$545$	−10.1722	+	7.39056i	−0.435730	+	0.316577i
$546$	−0.763932	−	4.21317i	−0.0326933	−	0.180307i
$547$	−31.5016	−	10.2355i	−1.34691	−	0.437638i	−0.455259	−	0.890359i	$-0.650453\pi$
$547$	−31.5016	−	10.2355i	−1.34691	−	0.437638i	−0.891652	+	0.452721i	$0.850453\pi$
$548$	0.545331	−	0.750584i	0.0232954	−	0.0320634i
$549$	−11.1084	+	40.2039i	−0.474095	+	1.71586i
$550$	−2.42178	+	6.35569i	−0.103265	+	0.271008i
$551$		−	2.54678i		−	0.108496i
$552$	5.73259	−	5.99404i	0.243995	−	0.255123i
$553$	−1.61132	+	4.95913i	−0.0685203	+	0.210884i
$554$	3.87418	−	1.25880i	0.164598	−	0.0534812i
$555$	−2.19396	−	4.07850i	−0.0931282	−	0.173123i
$556$	−4.96866	−	6.83877i	−0.210718	−	0.290028i
$557$	−8.46752	−	26.0604i	−0.358780	−	1.10421i	−0.953785	−	0.300490i	$-0.902850\pi$
$557$	−8.46752	−	26.0604i	−0.358780	−	1.10421i	0.595004	−	0.803722i	$-0.297150\pi$
$558$	−8.58514	+	12.9976i	−0.363438	+	0.550230i
$559$	4.17409	+	3.03265i	0.176545	+	0.128268i
$560$	−4.35758			−0.184141
$561$	−26.8104	−	28.3330i	−1.13193	−	1.19622i
$562$	−17.8647			−0.753575
$563$	−17.1967	−	12.4941i	−0.724753	−	0.526564i	0.163146	−	0.986602i	$-0.447836\pi$
$563$	−17.1967	−	12.4941i	−0.724753	−	0.526564i	−0.887899	+	0.460038i	$0.847836\pi$
$564$	15.6243	+	7.52711i	0.657901	+	0.316949i
$565$	−3.19661	−	9.83817i	−0.134483	−	0.413895i
$566$	−1.78667	−	2.45914i	−0.0750995	−	0.103366i
$567$	1.31522	+	14.7110i	0.0552342	+	0.617805i
$568$	−0.854102	+	0.277515i	−0.0358373	+	0.0116443i
$569$	−11.4052	+	35.1015i	−0.478130	+	1.47153i	0.363560	+	0.931571i	$0.381561\pi$
$569$	−11.4052	+	35.1015i	−0.478130	+	1.47153i	−0.841690	+	0.539961i	$0.818439\pi$
$570$	−18.2423	−	17.4466i	−0.764087	−	0.730758i
$571$			26.4505i			1.10692i	0.832876	+	0.553460i	$0.186693\pi$
$571$			26.4505i			1.10692i	−0.832876	+	0.553460i	$0.813307\pi$
$572$	−4.82276	+	1.30499i	−0.201650	+	0.0545646i
$573$	−0.751520	+	5.54177i	−0.0313952	+	0.231511i
$574$	1.51855	−	2.09010i	0.0633831	−	0.0872393i
$575$	9.33936	+	3.03454i	0.389478	+	0.126549i
$576$	0.133706	+	2.99702i	0.00557108	+	0.124876i
$577$	19.8138	−	14.3955i	0.824858	−	0.599294i	−0.0932422	−	0.995643i	$-0.529723\pi$
$577$	19.8138	−	14.3955i	0.824858	−	0.599294i	0.918100	+	0.396349i	$0.129723\pi$
$578$	−23.5486	+	17.1091i	−0.979493	+	0.711643i
$579$	−16.6423	+	3.01759i	−0.691631	+	0.125407i
$580$	−1.17183	−	0.380751i	−0.0486576	−	0.0158098i
$581$	1.80784	−	2.48828i	0.0750018	−	0.103231i
$582$	6.16337	+	0.835815i	0.255480	+	0.0346456i
$583$	1.62524	−	32.5450i	0.0673106	−	1.34788i
$584$			4.62724i			0.191476i
$585$	−7.47910	−	9.38420i	−0.309223	−	0.387989i
$586$	7.21279	−	22.1987i	0.297958	−	0.917020i
$587$	39.3939	−	12.7999i	1.62596	−	0.528307i	0.652624	−	0.757682i	$-0.273668\pi$
$587$	39.3939	−	12.7999i	1.62596	−	0.528307i	0.973338	+	0.229375i	$0.0736683\pi$
$588$	6.56951	−	3.53395i	0.270922	−	0.145738i
$589$	−16.7505	−	23.0551i	−0.690194	−	0.949970i
$590$	−5.01532	−	15.4356i	−0.206477	−	0.635472i
$591$	−10.5003	+	21.7958i	−0.431923	+	0.896558i
$592$	−0.814648	−	0.591876i	−0.0334818	−	0.0243260i
$593$	2.94808			0.121063			0.0605316	−	0.998166i	$-0.480720\pi$
$593$	2.94808			0.121063			0.0605316	+	0.998166i	$0.480720\pi$
$594$	16.9733	−	2.98454i	0.696422	−	0.122457i
$595$	29.5891			1.21304
$596$	−14.6202	−	10.6222i	−0.598868	−	0.435103i
$597$	−12.0037	+	24.9166i	−0.491280	+	1.01977i
$598$	2.22911	+	6.86049i	0.0911550	+	0.280546i
$599$	−16.3070	−	22.4446i	−0.666284	−	0.917061i	0.333385	−	0.942791i	$-0.391809\pi$
$599$	−16.3070	−	22.4446i	−0.666284	−	0.917061i	−0.999669	+	0.0257295i	$0.991809\pi$
$600$	−3.12808	+	1.68269i	−0.127703	+	0.0686956i
$601$	4.22399	−	1.37246i	0.172300	−	0.0559836i	−0.221597	−	0.975138i	$-0.571127\pi$
$601$	4.22399	−	1.37246i	0.172300	−	0.0559836i	0.393897	+	0.919155i	$0.371127\pi$
$602$	1.73689	−	5.34560i	0.0707903	−	0.217870i
$603$	−22.0581	−	27.6769i	−0.898277	−	1.12709i
$604$		−	13.3299i		−	0.542387i
$605$	28.5400	−	6.21346i	1.16031	−	0.252613i
$606$	−20.8917	−	2.83313i	−0.848667	−	0.115088i
$607$	23.8874	−	32.8782i	0.969559	−	1.33448i	0.0272902	−	0.999628i	$-0.491312\pi$
$607$	23.8874	−	32.8782i	0.969559	−	1.33448i	0.942269	−	0.334856i	$-0.108688\pi$
$608$	−5.21982	−	1.69602i	−0.211692	−	0.0687828i
$609$	−1.29780	+	0.235317i	−0.0525895	+	0.00953553i
$610$	−29.8673	+	21.6999i	−1.20929	+	0.878602i
$611$	−12.2029	+	8.86590i	−0.493675	+	0.358676i
$612$	−0.907899	−	20.3505i	−0.0366996	−	0.822622i
$613$	−27.4583	−	8.92174i	−1.10903	−	0.360346i	−0.303459	−	0.952845i	$-0.598142\pi$
$613$	−27.4583	−	8.92174i	−1.10903	−	0.360346i	−0.805571	+	0.592499i	$0.798142\pi$
$614$	17.6463	−	24.2880i	0.712145	−	0.980184i
$615$	0.972957	−	7.17467i	0.0392334	−	0.289310i
$616$	2.97562	+	4.55743i	0.119891	+	0.183624i
$617$			31.6428i			1.27389i	0.770909	+	0.636946i	$0.219802\pi$
$617$			31.6428i			1.27389i	−0.770909	+	0.636946i	$0.780198\pi$
$618$	1.10979	+	1.06138i	0.0446422	+	0.0426950i
$619$	0.294921	−	0.907672i	0.0118539	−	0.0364824i	−0.944955	−	0.327201i	$-0.893894\pi$
$619$	0.294921	−	0.907672i	0.0118539	−	0.0364824i	0.956808	+	0.290719i	$0.0938945\pi$
$620$	−13.1124	+	4.26049i	−0.526609	+	0.171105i
$621$	−5.52600	−	24.2607i	−0.221751	−	0.973549i
$622$	0.291085	+	0.400644i	0.0116715	+	0.0160644i
$623$	6.49581	+	19.9920i	0.260249	+	0.800964i
$624$	−2.35062	−	1.13243i	−0.0941002	−	0.0453334i
$625$	25.1185	+	18.2496i	1.00474	+	0.729986i
$626$	−28.3789			−1.13425
$627$	−5.78982	+	30.9925i	−0.231223	+	1.23772i
$628$	9.70820			0.387400
$629$	5.53167	+	4.01900i	0.220562	+	0.160248i
$630$	−7.20497	+	10.9080i	−0.287053	+	0.434586i
$631$	2.19912	+	6.76820i	0.0875456	+	0.269438i	0.985239	−	0.171182i	$-0.0547587\pi$
$631$	2.19912	+	6.76820i	0.0875456	+	0.269438i	−0.897694	+	0.440620i	$0.854759\pi$
$632$	1.86762	+	2.57056i	0.0742901	+	0.102252i
$633$	1.86106	+	3.45966i	0.0739706	+	0.137509i
$634$	−6.31569	+	2.05209i	−0.250828	+	0.0814990i
$635$	0.193955	−	0.596933i	0.00769688	−	0.0236886i
$636$	11.7618	−	12.2983i	0.466387	−	0.487657i
$637$			6.48791i			0.257060i
$638$	0.401983	+	1.48557i	0.0159146	+	0.0588144i
$639$	−0.717518	+	2.59687i	−0.0283846	+	0.102730i
$640$	−1.56076	+	2.14820i	−0.0616943	+	0.0849150i
$641$	31.2374	+	10.1496i	1.23380	+	0.400887i	0.852090	−	0.523395i	$-0.175335\pi$
$641$	31.2374	+	10.1496i	1.23380	+	0.400887i	0.381712	+	0.924281i	$0.375335\pi$
$642$	−0.689654	−	3.80351i	−0.0272185	−	0.150113i
$643$	−2.66685	+	1.93758i	−0.105170	+	0.0764106i	−0.639127	−	0.769101i	$-0.720704\pi$
$643$	−2.66685	+	1.93758i	−0.105170	+	0.0764106i	0.533957	+	0.845511i	$0.320704\pi$
$644$	6.35758	−	4.61905i	0.250524	−	0.182016i
$645$	−2.81035	−	15.4994i	−0.110657	−	0.610287i
$646$	35.4440	+	11.5164i	1.39452	+	0.453108i
$647$	−3.42235	+	4.71046i	−0.134547	+	0.185187i	−0.870974	−	0.491329i	$-0.836511\pi$
$647$	−3.42235	+	4.71046i	−0.134547	+	0.185187i	0.736427	+	0.676516i	$0.236511\pi$
$648$	7.72330	+	4.62067i	0.303400	+	0.181517i
$649$	−12.7187	+	15.7856i	−0.499253	+	0.619641i
$650$		−	3.08922i		−	0.121169i
$651$	−10.2008	+	10.6661i	−0.399802	+	0.418036i
$652$	2.18848	−	6.73544i	0.0857074	−	0.263780i
$653$	−4.16347	+	1.35279i	−0.162929	+	0.0529390i	−0.389346	−	0.921092i	$-0.627299\pi$
$653$	−4.16347	+	1.35279i	−0.162929	+	0.0529390i	0.226417	+	0.974031i	$0.427299\pi$
$654$	3.88545	+	7.22293i	0.151933	+	0.282439i
$655$	8.22115	+	11.3154i	0.321227	+	0.442131i
$656$	−0.486479	−	1.49723i	−0.0189938	−	0.0584569i
$657$	11.5830	+	7.65082i	0.451897	+	0.298487i
$658$	13.2937	+	9.65847i	0.518244	+	0.376526i
$659$	−15.3805			−0.599141			−0.299570	−	0.954074i	$-0.596843\pi$
$659$	−15.3805			−0.599141			−0.299570	+	0.954074i	$0.596843\pi$
$660$	13.3948	+	7.29751i	0.521391	+	0.284055i
$661$	12.6047			0.490266			0.245133	−	0.969489i	$-0.421168\pi$
$661$	12.6047			0.490266			0.245133	+	0.969489i	$0.421168\pi$
$662$	−5.99494	−	4.35558i	−0.233000	−	0.169285i
$663$	15.9613	+	7.68949i	0.619887	+	0.298635i
$664$	−0.579155	−	1.78246i	−0.0224756	−	0.0691727i
$665$	−14.0577	−	19.3487i	−0.545133	−	0.750312i
$666$	−2.82857	+	1.06062i	−0.109605	+	0.0410983i
$667$	2.11326	−	0.686641i	0.0818259	−	0.0265868i
$668$	0.783304	−	2.41076i	0.0303069	−	0.0932751i
$669$	5.50933	+	5.26902i	0.213003	+	0.203712i
$670$		−	31.3254i		−	1.21021i
$671$	43.0903	+	16.4191i	1.66348	+	0.633854i
$672$	−0.381966	+	2.81665i	−0.0147347	+	0.108655i
$673$	−18.9461	+	26.0771i	−0.730319	+	1.00520i	0.268799	+	0.963196i	$0.413373\pi$
$673$	−18.9461	+	26.0771i	−0.730319	+	1.00520i	−0.999118	+	0.0420013i	$0.986627\pi$
$674$	32.5392	+	10.5726i	1.25336	+	0.407242i
$675$	−0.959901	+	10.6125i	−0.0369466	+	0.408476i
$676$	−8.68134	+	6.30736i	−0.333898	+	0.242591i
$677$	−7.37175	+	5.35589i	−0.283319	+	0.205844i	−0.720364	−	0.693596i	$-0.756025\pi$
$677$	−7.37175	+	5.35589i	−0.283319	+	0.205844i	0.437045	+	0.899440i	$0.356025\pi$
$678$	−6.63938	+	1.20385i	−0.254984	+	0.0462337i
$679$	5.60466	+	1.82107i	0.215087	+	0.0698861i
$680$	10.5980	−	14.5868i	0.406413	−	0.559379i
$681$	21.8548	+	2.96374i	0.837479	+	0.113571i
$682$	13.4098	+	10.8045i	0.513490	+	0.413726i
$683$			28.1535i			1.07726i	0.842541	+	0.538632i	$0.181059\pi$
$683$			28.1535i			1.07726i	−0.842541	+	0.538632i	$0.818941\pi$
$684$	−12.8762	+	10.2622i	−0.492332	+	0.392383i
$685$	0.761274	−	2.34296i	0.0290868	−	0.0895199i
$686$	17.6473	−	5.73395i	0.673776	−	0.218923i
$687$	9.79793	−	5.27062i	0.373815	−	0.201087i
$688$	−2.01317	−	2.77089i	−0.0767512	−	0.105639i
$689$	4.57357	+	14.0760i	0.174239	+	0.536253i
$690$	9.55850	−	19.8409i	0.363886	−	0.755330i
$691$	−8.68690	−	6.31140i	−0.330465	−	0.240097i	0.410163	−	0.912012i	$-0.365472\pi$
$691$	−8.68690	−	6.31140i	−0.330465	−	0.240097i	−0.740628	+	0.671915i	$0.765472\pi$
$692$	−0.949284			−0.0360864
$693$	16.3283	+	0.0867579i	0.620260	+	0.00329566i
$694$	−20.9245			−0.794285
$695$	−18.1591	−	13.1934i	−0.688814	−	0.500453i
$696$	−0.348827	+	0.724072i	−0.0132222	+	0.0274459i
$697$	3.30332	+	10.1666i	0.125122	+	0.385086i
$698$	−17.3120	−	23.8279i	−0.655268	−	0.901898i
$699$	−25.6418	+	13.7935i	−0.969862	+	0.521719i
$700$	−3.20067	+	1.03996i	−0.120974	+	0.0393068i
$701$	12.8347	−	39.5012i	0.484761	−	1.49194i	−0.347566	−	0.937656i	$-0.612992\pi$
$701$	12.8347	−	39.5012i	0.484761	−	1.49194i	0.832327	−	0.554285i	$-0.187008\pi$
$702$	−6.72133	+	4.01175i	−0.253680	+	0.151414i
$703$		−	5.52664i		−	0.208441i
$704$	3.31250	+	0.165420i	0.124844	+	0.00623450i
$705$	45.6332	+	6.18832i	1.71865	+	0.233066i
$706$	−14.2988	+	19.6806i	−0.538141	+	0.740688i
$707$	−18.9979	−	6.17279i	−0.714489	−	0.232152i
$708$	−10.4168	+	1.88878i	−0.391489	+	0.0709848i
$709$	−24.4440	+	17.7596i	−0.918015	+	0.666977i	−0.943029	−	0.332710i	$-0.892037\pi$
$709$	−24.4440	+	17.7596i	−0.918015	+	0.666977i	0.0250143	+	0.999687i	$0.492037\pi$
$710$	−1.92920	+	1.40165i	−0.0724017	+	0.0526029i
$711$	9.52270	−	0.424836i	0.357129	−	0.0159326i
$712$	12.1823	+	3.95826i	0.456550	+	0.148342i
$713$	14.6145	−	20.1152i	0.547318	−	0.753319i
$714$	2.59365	−	19.1258i	0.0970649	−	0.715764i
$715$	−11.1084	+	7.25284i	−0.415430	+	0.271241i
$716$			18.5656i			0.693830i
$717$	−15.0694	−	14.4121i	−0.562776	−	0.538229i
$718$	10.1134	−	31.1259i	0.377429	−	1.16161i
$719$	−47.7748	+	15.5230i	−1.78170	+	0.578909i	−0.999051	−	0.0435556i	$-0.986131\pi$
$719$	−47.7748	+	15.5230i	−1.78170	+	0.578909i	−0.782648	+	0.622465i	$0.786131\pi$
$720$	2.79682	+	7.45883i	0.104232	+	0.277974i
$721$	0.855212	+	1.17710i	0.0318497	+	0.0438374i
$722$	−3.43720	−	10.5786i	−0.127919	−	0.393696i
$723$	32.0886	+	15.4589i	1.19339	+	0.574924i
$724$	−10.4196	−	7.57025i	−0.387240	−	0.281346i
$725$	−0.951585			−0.0353410
$726$	−1.51456	−	18.9923i	−0.0562107	−	0.704869i
$727$	42.9707			1.59369			0.796847	−	0.604181i	$-0.206499\pi$
$727$	42.9707			1.59369			0.796847	+	0.604181i	$0.206499\pi$
$728$	−2.00000	−	1.45309i	−0.0741249	−	0.0538549i
$729$	24.3366	−	11.6932i	0.901354	−	0.433082i
$730$	3.79682	+	11.6854i	0.140527	+	0.432497i
$731$	13.6699	+	18.8150i	0.505601	+	0.695899i
$732$	11.4083	+	21.2077i	0.421663	+	0.783859i
$733$	32.7807	−	10.6511i	1.21078	−	0.393408i	0.367066	−	0.930195i	$-0.380362\pi$
$733$	32.7807	−	10.6511i	1.21078	−	0.393408i	0.843718	+	0.536787i	$0.180362\pi$
$734$	−3.67822	+	11.3204i	−0.135765	+	0.417843i
$735$	13.6906	−	14.3150i	0.504986	−	0.528018i
$736$		−	4.78856i		−	0.176509i
$737$	−32.7620	+	21.3908i	−1.20681	+	0.787942i
$738$	−4.55226	−	1.25780i	−0.167571	−	0.0463002i
$739$	−0.669749	+	0.921830i	−0.0246371	+	0.0339101i	−0.821158	−	0.570701i	$-0.806671\pi$
$739$	−0.669749	+	0.921830i	−0.0246371	+	0.0339101i	0.796521	+	0.604611i	$0.206671\pi$
$740$	−2.54293	−	0.826249i	−0.0934801	−	0.0303735i
$741$	−2.55491	−	14.0906i	−0.0938568	−	0.517631i
$742$	13.0442	−	9.47713i	0.478866	−	0.347916i
$743$	−11.8635	+	8.61934i	−0.435230	+	0.316213i	−0.783737	−	0.621093i	$-0.786689\pi$
$743$	−11.8635	+	8.61934i	−0.435230	+	0.316213i	0.348507	+	0.937306i	$0.386689\pi$
$744$	1.60451	+	8.84906i	0.0588243	+	0.324422i
$745$	−45.6372	−	14.8284i	−1.67202	−	0.543272i
$746$	−16.3289	+	22.4748i	−0.597843	+	0.822861i
$747$	−5.41949	−	1.49741i	−0.198289	−	0.0547875i
$748$	−22.4927	−	1.12325i	−0.822416	−	0.0410699i
$749$		−	3.66250i		−	0.133825i
$750$	9.37516	−	9.80274i	0.342332	−	0.357945i
$751$	−9.49151	+	29.2119i	−0.346350	+	1.06596i	0.614507	+	0.788911i	$0.289355\pi$
$751$	−9.49151	+	29.2119i	−0.346350	+	1.06596i	−0.960857	+	0.277044i	$0.910645\pi$
$752$	9.52285	−	3.09416i	0.347263	−	0.112832i
$753$	−13.4288	−	24.9637i	−0.489372	−	0.909729i
$754$	−0.410870	−	0.565514i	−0.0149630	−	0.0205948i
$755$	−10.9377	−	33.6628i	−0.398064	−	1.22512i
$756$	6.41916	+	5.61329i	0.233463	+	0.204153i
$757$	−29.7783	−	21.6352i	−1.08231	−	0.786345i	−0.104226	−	0.994554i	$-0.533237\pi$
$757$	−29.7783	−	21.6352i	−1.08231	−	0.786345i	−0.978084	+	0.208209i	$0.933237\pi$
$758$	−7.86465			−0.285657
$759$	−27.2780	+	3.55167i	−0.990127	+	0.128918i
$760$	−14.5736			−0.528639
$761$	−14.4001	−	10.4623i	−0.522004	−	0.379258i	0.295354	−	0.955388i	$-0.404562\pi$
$761$	−14.4001	−	10.4623i	−0.522004	−	0.379258i	−0.817358	+	0.576130i	$0.804562\pi$
$762$	−0.368843	−	0.177693i	−0.0133618	−	0.00643714i
$763$	2.40134	+	7.39056i	0.0869343	+	0.267556i
$764$	1.89786	+	2.61218i	0.0686621	+	0.0945052i
$765$	−18.9912	−	50.6475i	−0.686628	−	1.83116i

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:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	66.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.751740 + 1.56041i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.56076 + 2.14820i) q^{5} +(1.52536 - 0.820539i) q^{6} +(1.56076 - 0.507121i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.86977 - 2.34605i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.751740 + 1.56041i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.56076 + 2.14820i) q^{5} +(1.52536 - 0.820539i) q^{6} +(1.56076 - 0.507121i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.86977 - 2.34605i) q^{9} -2.65532i q^{10} +(-2.77710 + 1.81321i) q^{11} +(-1.71634 - 0.232753i) q^{12} +(0.885446 - 1.21871i) q^{13} +(-1.56076 - 0.507121i) q^{14} +(-4.52536 + 0.820539i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(5.49344 - 3.99122i) q^{17} +(0.133706 + 2.99702i) q^{18} +(-5.21982 - 1.69602i) q^{19} +(-1.56076 + 2.14820i) q^{20} +(-0.381966 + 2.81665i) q^{21} +(3.31250 + 0.165420i) q^{22} -4.78856i q^{23} +(1.25174 + 1.19714i) q^{24} +(-0.633706 + 1.95035i) q^{25} +(-1.43268 + 0.465507i) q^{26} +(5.06639 - 1.15400i) q^{27} +(0.964601 + 1.32766i) q^{28} +(0.143392 + 0.441315i) q^{29} +(4.14339 + 1.99611i) q^{30} +(4.20067 + 3.05196i) q^{31} +1.00000 q^{32} +(-0.741699 - 5.69648i) q^{33} -6.79026 q^{34} +(3.52536 + 2.56132i) q^{35} +(1.65343 - 2.50323i) q^{36} +(0.311168 + 0.957676i) q^{37} +(3.22603 + 4.44024i) q^{38} +(1.23607 + 2.29782i) q^{39} +(2.52536 - 0.820539i) q^{40} +(-0.486479 + 1.49723i) q^{41} +(1.96460 - 2.05420i) q^{42} +3.42500i q^{43} +(-2.58263 - 2.08086i) q^{44} +(2.12151 - 7.67826i) q^{45} +(-2.81465 + 3.87403i) q^{46} +(-9.52285 - 3.09416i) q^{47} +(-0.309017 - 1.70426i) q^{48} +(-3.48433 + 2.53151i) q^{49} +(1.65906 - 1.20538i) q^{50} +(2.09831 + 11.5724i) q^{51} +(1.43268 + 0.465507i) q^{52} +(-5.77495 + 7.94853i) q^{53} +(-4.77710 - 2.04434i) q^{54} +(-8.22951 - 3.13578i) q^{55} -1.64108i q^{56} +(6.57044 - 6.87011i) q^{57} +(0.143392 - 0.441315i) q^{58} +(5.81307 - 1.88878i) q^{59} +(-2.17879 - 4.05031i) q^{60} +(-8.17223 - 11.2481i) q^{61} +(-1.60451 - 4.93818i) q^{62} +(-4.10799 - 2.71341i) q^{63} +(-0.809017 - 0.587785i) q^{64} +4.00000 q^{65} +(-2.74826 + 5.04451i) q^{66} +11.7972 q^{67} +(5.49344 + 3.99122i) q^{68} +(7.47214 + 3.59976i) q^{69} +(-1.34657 - 4.14431i) q^{70} +(-0.527864 - 0.726543i) q^{71} +(-2.80902 + 1.05329i) q^{72} +(-4.40076 + 1.42989i) q^{73} +(0.311168 - 0.957676i) q^{74} +(-2.56696 - 2.45500i) q^{75} -5.48844i q^{76} +(-3.41486 + 4.23830i) q^{77} +(0.350622 - 2.58551i) q^{78} +(-1.86762 + 2.57056i) q^{79} +(-2.52536 - 0.820539i) q^{80} +(-2.00789 + 8.77316i) q^{81} +(1.27362 - 0.925338i) q^{82} +(1.51625 - 1.10162i) q^{83} +(-2.79682 + 0.507121i) q^{84} +(17.1478 + 5.57167i) q^{85} +(2.01317 - 2.77089i) q^{86} +(-0.796426 - 0.108003i) q^{87} +(0.866294 + 3.20149i) q^{88} +12.8092i q^{89} +(-6.22951 + 4.96485i) q^{90} +(0.763932 - 2.35114i) q^{91} +(4.55420 - 1.47975i) q^{92} +(-7.92013 + 4.26049i) q^{93} +(5.88545 + 8.10062i) q^{94} +(-4.50348 - 13.8603i) q^{95} +(-0.751740 + 1.56041i) q^{96} +(2.90517 + 2.11073i) q^{97} +4.30687 q^{98} +(9.44642 + 3.12492i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 3 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 3 * q^6 - 2 * q^8 + 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 3 q^{6} - 2 q^{8} + 2 q^{9} + q^{11} - 3 q^{12} - 21 q^{15} - 2 q^{16} + 10 q^{17} + 2 q^{18} - 15 q^{19} - 12 q^{21} + 6 q^{22} + 2 q^{24} - 6 q^{25} + 10 q^{26} + 20 q^{27} + 5 q^{28} - 23 q^{29} + 9 q^{30} + 13 q^{31} + 8 q^{32} + 20 q^{33} + 10 q^{34} + 13 q^{35} + 7 q^{36} + 6 q^{37} - 10 q^{38} - 8 q^{39} + 5 q^{40} - 2 q^{41} + 13 q^{42} - 9 q^{44} - 8 q^{45} - 10 q^{46} - 10 q^{47} + 2 q^{48} - 18 q^{49} - q^{50} + 15 q^{51} - 10 q^{52} - 15 q^{53} - 15 q^{54} - 14 q^{55} + 15 q^{57} - 23 q^{58} + 25 q^{59} + 4 q^{60} - 10 q^{61} - 2 q^{62} - 6 q^{63} - 2 q^{64} + 32 q^{65} - 30 q^{66} - 2 q^{67} + 10 q^{68} + 24 q^{69} - 17 q^{70} - 40 q^{71} - 18 q^{72} + 5 q^{73} + 6 q^{74} + q^{75} + 12 q^{77} - 8 q^{78} + 10 q^{79} - 5 q^{80} - 26 q^{81} + 3 q^{82} + 21 q^{83} + 8 q^{84} + 30 q^{85} - 25 q^{86} - 42 q^{87} + 6 q^{88} + 2 q^{90} + 24 q^{91} - 10 q^{92} + 27 q^{93} + 40 q^{94} - 20 q^{95} + 2 q^{96} + 9 q^{97} + 22 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 3 * q^6 - 2 * q^8 + 2 * q^9 + q^11 - 3 * q^12 - 21 * q^15 - 2 * q^16 + 10 * q^17 + 2 * q^18 - 15 * q^19 - 12 * q^21 + 6 * q^22 + 2 * q^24 - 6 * q^25 + 10 * q^26 + 20 * q^27 + 5 * q^28 - 23 * q^29 + 9 * q^30 + 13 * q^31 + 8 * q^32 + 20 * q^33 + 10 * q^34 + 13 * q^35 + 7 * q^36 + 6 * q^37 - 10 * q^38 - 8 * q^39 + 5 * q^40 - 2 * q^41 + 13 * q^42 - 9 * q^44 - 8 * q^45 - 10 * q^46 - 10 * q^47 + 2 * q^48 - 18 * q^49 - q^50 + 15 * q^51 - 10 * q^52 - 15 * q^53 - 15 * q^54 - 14 * q^55 + 15 * q^57 - 23 * q^58 + 25 * q^59 + 4 * q^60 - 10 * q^61 - 2 * q^62 - 6 * q^63 - 2 * q^64 + 32 * q^65 - 30 * q^66 - 2 * q^67 + 10 * q^68 + 24 * q^69 - 17 * q^70 - 40 * q^71 - 18 * q^72 + 5 * q^73 + 6 * q^74 + q^75 + 12 * q^77 - 8 * q^78 + 10 * q^79 - 5 * q^80 - 26 * q^81 + 3 * q^82 + 21 * q^83 + 8 * q^84 + 30 * q^85 - 25 * q^86 - 42 * q^87 + 6 * q^88 + 2 * q^90 + 24 * q^91 - 10 * q^92 + 27 * q^93 + 40 * q^94 - 20 * q^95 + 2 * q^96 + 9 * q^97 + 22 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more