LMFDB - Embedded newform 66.2.h.a.35.1

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			35.1
Root			$1.55470 + 0.763481i$ of defining polynomial
Character	$\chi$	$=$	66.35
Dual form			66.2.h.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-1.20654 - 1.24268i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.897526 - 0.291624i) q^{5} +(-1.55470 + 0.763481i) q^{6} +(0.897526 - 1.23534i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.0885088 + 2.99869i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-1.20654 - 1.24268i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.897526 - 0.291624i) q^{5} +(-1.55470 + 0.763481i) q^{6} +(0.897526 - 1.23534i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.0885088 + 2.99869i) q^{9} -0.943715i q^{10} +(-0.151841 + 3.31315i) q^{11} +(0.245684 + 1.71454i) q^{12} +(4.03112 + 1.30979i) q^{13} +(-0.897526 - 1.23534i) q^{14} +(-1.44530 - 0.763481i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.906157 + 2.78886i) q^{17} +(2.82458 + 1.01082i) q^{18} +(-4.16740 - 5.73594i) q^{19} +(-0.897526 - 0.291624i) q^{20} +(-2.61803 + 0.375151i) q^{21} +(3.10407 + 1.16823i) q^{22} -1.18465i q^{23} +(1.70654 + 0.296161i) q^{24} +(-3.32458 + 2.41545i) q^{25} +(2.49137 - 3.42908i) q^{26} +(3.83321 - 3.50806i) q^{27} +(-1.45223 + 0.471857i) q^{28} +(-5.17274 - 3.75821i) q^{29} +(-1.17274 + 1.13863i) q^{30} +(-2.68830 + 8.27372i) q^{31} +1.00000 q^{32} +(4.30039 - 3.80876i) q^{33} +2.93239 q^{34} +(0.445299 - 1.37049i) q^{35} +(1.83419 - 2.37397i) q^{36} +(-2.28642 - 1.66118i) q^{37} +(-6.74300 + 2.19093i) q^{38} +(-3.23607 - 6.58971i) q^{39} +(-0.554701 + 0.763481i) q^{40} +(5.92001 - 4.30114i) q^{41} +(-0.452227 + 2.60583i) q^{42} -5.34587i q^{43} +(2.07026 - 2.59114i) q^{44} +(0.795052 + 2.71722i) q^{45} +(-1.12667 - 0.366076i) q^{46} +(5.58154 + 7.68233i) q^{47} +(0.809017 - 1.53150i) q^{48} +(1.44261 + 4.43990i) q^{49} +(1.26988 + 3.90827i) q^{50} +(2.37235 - 4.49095i) q^{51} +(-2.49137 - 3.42908i) q^{52} +(-4.62924 - 1.50413i) q^{53} +(-2.15184 - 4.72965i) q^{54} +(0.829911 + 3.01792i) q^{55} +1.52696i q^{56} +(-2.09979 + 12.0994i) q^{57} +(-5.17274 + 3.75821i) q^{58} +(-2.74201 + 3.77405i) q^{59} +(0.720508 + 1.46719i) q^{60} +(-0.685649 + 0.222781i) q^{61} +(7.03805 + 5.11344i) q^{62} +(3.62496 + 2.80074i) q^{63} +(0.309017 - 0.951057i) q^{64} +4.00000 q^{65} +(-2.29346 - 5.26688i) q^{66} +3.89379 q^{67} +(0.906157 - 2.78886i) q^{68} +(-1.47214 + 1.42933i) q^{69} +(-1.16581 - 0.847008i) q^{70} +(-9.47214 + 3.07768i) q^{71} +(-1.69098 - 2.47802i) q^{72} +(1.03051 - 1.41838i) q^{73} +(-2.28642 + 1.66118i) q^{74} +(7.01287 + 1.21705i) q^{75} +7.09001i q^{76} +(3.95658 + 3.16121i) q^{77} +(-7.26719 + 1.04135i) q^{78} +(-1.56591 - 0.508796i) q^{79} +(0.554701 + 0.763481i) q^{80} +(-8.98433 - 0.530822i) q^{81} +(-2.26124 - 6.95939i) q^{82} +(-1.90347 - 5.85828i) q^{83} +(2.33854 + 1.23534i) q^{84} +(1.62660 + 2.23882i) q^{85} +(-5.08423 - 1.65197i) q^{86} +(1.57087 + 10.9625i) q^{87} +(-1.82458 - 2.76964i) q^{88} -17.3406i q^{89} +(2.82991 + 0.0835271i) q^{90} +(5.23607 - 3.80423i) q^{91} +(-0.696317 + 0.958399i) q^{92} +(13.5251 - 6.64191i) q^{93} +(9.03112 - 2.93439i) q^{94} +(-5.41309 - 3.93284i) q^{95} +(-1.20654 - 1.24268i) q^{96} +(3.54074 - 10.8973i) q^{97} +4.66839 q^{98} +(-9.92168 - 0.748569i) 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 $\left(\mathbb{Z}/66\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	−1.20654	−	1.24268i	−0.696598	−	0.717462i
$3$	−1.20654	−	1.24268i	−0.696598	−	0.717462i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.897526	−	0.291624i	0.401386	−	0.130418i	−0.101366	−	0.994849i	$-0.532321\pi$
$5$	0.897526	−	0.291624i	0.401386	−	0.130418i	0.502751	+	0.864431i	$0.332321\pi$
$6$	−1.55470	+	0.763481i	−0.634704	+	0.311690i
$7$	0.897526	−	1.23534i	0.339233	−	0.466914i	−0.604984	−	0.796237i	$-0.706821\pi$
$7$	0.897526	−	1.23534i	0.339233	−	0.466914i	0.944217	+	0.329323i	$0.106821\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−0.0885088	+	2.99869i	−0.0295029	+	0.999565i
$10$		−	0.943715i		−	0.298429i
$11$	−0.151841	+	3.31315i	−0.0457819	+	0.998951i
$11$	−0.151841	+	3.31315i	−0.0457819	+	0.998951i
$12$	0.245684	+	1.71454i	0.0709230	+	0.494944i
$13$	4.03112	+	1.30979i	1.11803	+	0.363270i	0.809016	−	0.587787i	$-0.200001\pi$
$13$	4.03112	+	1.30979i	1.11803	+	0.363270i	0.309015	+	0.951057i	$0.400001\pi$
$14$	−0.897526	−	1.23534i	−0.239874	−	0.330158i
$15$	−1.44530	−	0.763481i	−0.373174	−	0.197130i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.906157	+	2.78886i	0.219775	+	0.676399i	0.998780	+	0.0493808i	$0.0157248\pi$
$17$	0.906157	+	2.78886i	0.219775	+	0.676399i	−0.779005	+	0.627018i	$0.784275\pi$
$18$	2.82458	+	1.01082i	0.665759	+	0.238254i
$19$	−4.16740	−	5.73594i	−0.956067	−	1.31591i	−0.948779	−	0.315940i	$-0.897680\pi$
$19$	−4.16740	−	5.73594i	−0.956067	−	1.31591i	−0.00728837	−	0.999973i	$-0.502320\pi$
$20$	−0.897526	−	0.291624i	−0.200693	−	0.0652091i
$21$	−2.61803	+	0.375151i	−0.571302	+	0.0818646i
$22$	3.10407	+	1.16823i	0.661790	+	0.249067i
$23$		−	1.18465i		−	0.247016i	−0.992344	−	0.123508i	$-0.960586\pi$
$23$		−	1.18465i		−	0.247016i	0.992344	−	0.123508i	$-0.0394144\pi$
$24$	1.70654	+	0.296161i	0.348347	+	0.0604537i
$25$	−3.32458	+	2.41545i	−0.664915	+	0.483089i
$26$	2.49137	−	3.42908i	0.488598	−	0.672497i
$27$	3.83321	−	3.50806i	0.737701	−	0.675127i
$28$	−1.45223	+	0.471857i	−0.274445	+	0.0891726i
$29$	−5.17274	−	3.75821i	−0.960553	−	0.697883i	−0.00727378	−	0.999974i	$-0.502315\pi$
$29$	−5.17274	−	3.75821i	−0.960553	−	0.697883i	−0.953279	+	0.302091i	$0.902315\pi$
$30$	−1.17274	+	1.13863i	−0.214111	+	0.207885i
$31$	−2.68830	+	8.27372i	−0.482832	+	1.48600i	0.352264	+	0.935901i	$0.385412\pi$
$31$	−2.68830	+	8.27372i	−0.482832	+	1.48600i	−0.835096	+	0.550104i	$0.814588\pi$
$32$	1.00000			0.176777
$33$	4.30039	−	3.80876i	0.748601	−	0.663021i
$34$	2.93239			0.502900
$35$	0.445299	−	1.37049i	0.0752692	−	0.231655i
$36$	1.83419	−	2.37397i	0.305699	−	0.395662i
$37$	−2.28642	−	1.66118i	−0.375885	−	0.273097i	0.383762	−	0.923432i	$-0.374628\pi$
$37$	−2.28642	−	1.66118i	−0.375885	−	0.273097i	−0.759647	+	0.650335i	$0.774628\pi$
$38$	−6.74300	+	2.19093i	−1.09386	+	0.355416i
$39$	−3.23607	−	6.58971i	−0.518186	−	1.05520i
$40$	−0.554701	+	0.763481i	−0.0877060	+	0.120717i
$41$	5.92001	−	4.30114i	0.924551	−	0.671726i	−0.0201017	−	0.999798i	$-0.506399\pi$
$41$	5.92001	−	4.30114i	0.924551	−	0.671726i	0.944653	+	0.328072i	$0.106399\pi$
$42$	−0.452227	+	2.60583i	−0.0697802	+	0.402088i
$43$		−	5.34587i		−	0.815238i	−0.913152	−	0.407619i	$-0.866359\pi$
$43$		−	5.34587i		−	0.815238i	0.913152	−	0.407619i	$-0.133641\pi$
$44$	2.07026	−	2.59114i	0.312104	−	0.390629i
$45$	0.795052	+	2.71722i	0.118519	+	0.405059i
$46$	−1.12667	−	0.366076i	−0.166118	−	0.0539749i
$47$	5.58154	+	7.68233i	0.814151	+	1.12058i	0.990670	+	0.136286i	$0.0435165\pi$
$47$	5.58154	+	7.68233i	0.814151	+	1.12058i	−0.176518	+	0.984297i	$0.556484\pi$
$48$	0.809017	−	1.53150i	0.116772	−	0.221053i
$49$	1.44261	+	4.43990i	0.206087	+	0.634271i
$50$	1.26988	+	3.90827i	0.179587	+	0.552713i
$51$	2.37235	−	4.49095i	0.332195	−	0.628858i
$52$	−2.49137	−	3.42908i	−0.345491	−	0.475527i
$53$	−4.62924	−	1.50413i	−0.635876	−	0.206609i	−0.0266996	−	0.999644i	$-0.508500\pi$
$53$	−4.62924	−	1.50413i	−0.635876	−	0.206609i	−0.609176	+	0.793035i	$0.708500\pi$
$54$	−2.15184	−	4.72965i	−0.292829	−	0.643624i
$55$	0.829911	+	3.01792i	0.111905	+	0.406936i
$56$			1.52696i			0.204049i
$57$	−2.09979	+	12.0994i	−0.278124	+	1.60260i
$58$	−5.17274	+	3.75821i	−0.679213	+	0.493477i
$59$	−2.74201	+	3.77405i	−0.356979	+	0.491340i	−0.949304	−	0.314359i	$-0.898210\pi$
$59$	−2.74201	+	3.77405i	−0.356979	+	0.491340i	0.592325	+	0.805699i	$0.298210\pi$
$60$	0.720508	+	1.46719i	0.0930172	+	0.189414i
$61$	−0.685649	+	0.222781i	−0.0877883	+	0.0285242i	−0.352582	−	0.935781i	$-0.614696\pi$
$61$	−0.685649	+	0.222781i	−0.0877883	+	0.0285242i	0.264794	+	0.964305i	$0.414696\pi$
$62$	7.03805	+	5.11344i	0.893833	+	0.649408i
$63$	3.62496	+	2.80074i	0.456702	+	0.352861i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	4.00000			0.496139
$66$	−2.29346	−	5.26688i	−0.282305	−	0.648308i
$67$	3.89379			0.475702			0.237851	−	0.971302i	$-0.423557\pi$
$67$	3.89379			0.475702			0.237851	+	0.971302i	$0.423557\pi$
$68$	0.906157	−	2.78886i	0.109888	−	0.338199i
$69$	−1.47214	+	1.42933i	−0.177224	+	0.172071i
$70$	−1.16581	−	0.847008i	−0.139341	−	0.101237i
$71$	−9.47214	+	3.07768i	−1.12414	+	0.365254i	−0.811345	−	0.584568i	$-0.801264\pi$
$71$	−9.47214	+	3.07768i	−1.12414	+	0.365254i	−0.312791	+	0.949822i	$0.601264\pi$
$72$	−1.69098	−	2.47802i	−0.199284	−	0.292037i
$73$	1.03051	−	1.41838i	0.120612	−	0.166008i	−0.744442	−	0.667688i	$-0.767284\pi$
$73$	1.03051	−	1.41838i	0.120612	−	0.166008i	0.865054	+	0.501679i	$0.167284\pi$
$74$	−2.28642	+	1.66118i	−0.265791	+	0.193108i
$75$	7.01287	+	1.21705i	0.809777	+	0.140532i
$76$			7.09001i			0.813280i
$77$	3.95658	+	3.16121i	0.450894	+	0.360253i
$78$	−7.26719	+	1.04135i	−0.822847	+	0.117910i
$79$	−1.56591	−	0.508796i	−0.176179	−	0.0572440i	0.219599	−	0.975590i	$-0.429525\pi$
$79$	−1.56591	−	0.508796i	−0.176179	−	0.0572440i	−0.395778	+	0.918346i	$0.629525\pi$
$80$	0.554701	+	0.763481i	0.0620175	+	0.0853598i
$81$	−8.98433	−	0.530822i	−0.998259	−	0.0589802i
$82$	−2.26124	−	6.95939i	−0.249713	−	0.768537i
$83$	−1.90347	−	5.85828i	−0.208933	−	0.643029i	−0.999529	−	0.0306912i	$-0.990229\pi$
$83$	−1.90347	−	5.85828i	−0.208933	−	0.643029i	0.790596	−	0.612338i	$-0.209771\pi$
$84$	2.33854	+	1.23534i	0.255156	+	0.134786i
$85$	1.62660	+	2.23882i	0.176429	+	0.242834i
$86$	−5.08423	−	1.65197i	−0.548246	−	0.178136i
$87$	1.57087	+	10.9625i	0.168415	+	1.17530i
$88$	−1.82458	−	2.76964i	−0.194501	−	0.295245i
$89$		−	17.3406i		−	1.83811i	−0.394135	−	0.919053i	$-0.628956\pi$
$89$		−	17.3406i		−	1.83811i	0.394135	−	0.919053i	$-0.371044\pi$
$90$	2.82991	+	0.0835271i	0.298299	+	0.00880453i
$91$	5.23607	−	3.80423i	0.548889	−	0.398791i
$92$	−0.696317	+	0.958399i	−0.0725961	+	0.0999200i
$93$	13.5251	−	6.64191i	1.40249	−	0.688734i
$94$	9.03112	−	2.93439i	0.931489	−	0.302659i
$95$	−5.41309	−	3.93284i	−0.555371	−	0.403501i
$96$	−1.20654	−	1.24268i	−0.123142	−	0.126831i
$97$	3.54074	−	10.8973i	0.359507	−	1.10645i	−0.593842	−	0.804581i	$-0.702390\pi$
$97$	3.54074	−	10.8973i	0.359507	−	1.10645i	0.953350	−	0.301868i	$-0.0976103\pi$
$98$	4.66839			0.471578
$99$	−9.92168	−	0.748569i	−0.997166	−	0.0752340i
$100$	4.10940			0.410940
$101$	1.44795	−	4.45632i	0.144076	−	0.443420i	−0.852815	−	0.522213i	$-0.825107\pi$
$101$	1.44795	−	4.45632i	0.144076	−	0.443420i	0.996891	+	0.0787929i	$0.0251066\pi$
$102$	−3.53805	−	3.64402i	−0.350319	−	0.360811i
$103$	10.2430	+	7.44197i	1.00927	+	0.733279i	0.964056	−	0.265698i	$-0.0856024\pi$
$103$	10.2430	+	7.44197i	1.00927	+	0.733279i	0.0452161	+	0.998977i	$0.485602\pi$
$104$	−4.03112	+	1.30979i	−0.395284	+	0.128435i
$105$	−2.24035	+	1.10019i	−0.218636	+	0.107367i
$106$	−2.86103	+	3.93787i	−0.277888	+	0.382480i
$107$	−0.581472	+	0.422464i	−0.0562130	+	0.0408412i	−0.615537	−	0.788108i	$-0.711061\pi$
$107$	−0.581472	+	0.422464i	−0.0562130	+	0.0408412i	0.559324	+	0.828949i	$0.311061\pi$
$108$	−5.16312	+	0.584981i	−0.496821	+	0.0562898i
$109$		−	9.20929i		−	0.882090i	−0.897485	−	0.441045i	$-0.854608\pi$
$109$		−	9.20929i		−	0.882090i	0.897485	−	0.441045i	$-0.145392\pi$
$110$	3.12667	+	0.143295i	0.298116	+	0.0136626i
$111$	0.694346	+	4.84558i	0.0659044	+	0.459922i
$112$	1.45223	+	0.471857i	0.137223	+	0.0445863i
$113$	−2.88295	−	3.96804i	−0.271205	−	0.373282i	0.651591	−	0.758571i	$-0.274102\pi$
$113$	−2.88295	−	3.96804i	−0.271205	−	0.373282i	−0.922796	+	0.385289i	$0.874102\pi$
$114$	10.8583	+	5.73594i	1.01698	+	0.537220i
$115$	−0.345471	−	1.06325i	−0.0322153	−	0.0991486i
$116$	1.97581	+	6.08092i	0.183449	+	0.564599i
$117$	−4.28445	+	11.9722i	−0.396098	+	1.10683i
$118$	2.74201	+	3.77405i	0.252423	+	0.347430i
$119$	4.25849	+	1.38367i	0.390375	+	0.126841i
$120$	1.61803	−	0.231856i	0.147706	−	0.0211655i
$121$	−10.9539	−	1.00615i	−0.995808	−	0.0914678i
$122$			0.720934i			0.0652703i
$123$	−12.4877	−	2.16717i	−1.12598	−	0.195407i
$124$	7.03805	−	5.11344i	0.632035	−	0.459201i
$125$	−5.05300	+	6.95486i	−0.451954	+	0.622061i
$126$	3.78384	−	2.58207i	0.337091	−	0.230029i
$127$	−5.02793	+	1.63367i	−0.446157	+	0.144965i	−0.523474	−	0.852041i	$-0.675364\pi$
$127$	−5.02793	+	1.63367i	−0.446157	+	0.144965i	0.0773177	+	0.997007i	$0.475364\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−6.64321	+	6.45002i	−0.584902	+	0.567893i
$130$	1.23607	−	3.80423i	0.108410	−	0.333653i
$131$	10.6492			0.930421			0.465210	−	0.885200i	$-0.345979\pi$
$131$	10.6492			0.930421			0.465210	+	0.885200i	$0.345979\pi$
$132$	−5.71782	+	0.553651i	−0.497672	+	0.0481891i
$133$	−10.8262			−0.938748
$134$	1.20325	−	3.70321i	0.103945	−	0.319909i
$135$	2.41737	−	4.26643i	0.208054	−	0.367196i
$136$	−2.37235	−	1.72361i	−0.203427	−	0.147799i
$137$	0.566898	−	0.184196i	0.0484334	−	0.0157370i	−0.284700	−	0.958617i	$-0.591894\pi$
$137$	0.566898	−	0.184196i	0.0484334	−	0.0157370i	0.333133	+	0.942880i	$0.391894\pi$
$138$	0.904455	+	1.84177i	0.0769923	+	0.156782i
$139$	−3.01923	+	4.15562i	−0.256088	+	0.352475i	−0.917632	−	0.397432i	$-0.869902\pi$
$139$	−3.01923	+	4.15562i	−0.256088	+	0.352475i	0.661544	+	0.749907i	$0.269902\pi$
$140$	−1.16581	+	0.847008i	−0.0985286	+	0.0715853i
$141$	2.81231	−	16.2051i	0.236840	−	1.36472i
$142$			9.95959i			0.835790i
$143$	−4.95162	+	13.1568i	−0.414075	+	1.10023i
$144$	−2.87928	+	0.842471i	−0.239940	+	0.0702059i
$145$	−5.73865	−	1.86460i	−0.476569	−	0.154847i
$146$	−1.03051	−	1.41838i	−0.0852857	−	0.117386i
$147$	3.77680	−	7.14963i	0.311506	−	0.589692i
$148$	0.873335	+	2.68785i	0.0717877	+	0.220940i
$149$	5.36735	+	16.5190i	0.439710	+	1.35329i	0.888182	+	0.459492i	$0.151969\pi$
$149$	5.36735	+	16.5190i	0.439710	+	1.35329i	−0.448471	+	0.893797i	$0.648031\pi$
$150$	3.32458	−	6.29355i	0.271451	−	0.513866i
$151$	8.88291	+	12.2263i	0.722881	+	0.994960i	0.999423	+	0.0339586i	$0.0108114\pi$
$151$	8.88291	+	12.2263i	0.722881	+	0.994960i	−0.276542	+	0.961002i	$0.589189\pi$
$152$	6.74300	+	2.19093i	0.546929	+	0.177708i
$153$	−8.44315	+	2.47045i	−0.682588	+	0.199724i
$154$	4.22914	−	2.78606i	0.340794	−	0.224507i
$155$			8.20985i			0.659431i
$156$	−1.25530	+	7.23330i	−0.100505	+	0.579128i
$157$	3.00000	−	2.17963i	0.239426	−	0.173953i	−0.461601	−	0.887087i	$-0.652725\pi$
$157$	3.00000	−	2.17963i	0.239426	−	0.173953i	0.701028	+	0.713134i	$0.252725\pi$
$158$	−0.967787	+	1.33204i	−0.0769930	+	0.105972i
$159$	3.71623	+	7.56747i	0.294716	+	0.600140i
$160$	0.897526	−	0.291624i	0.0709556	−	0.0230549i
$161$	−1.46344	−	1.06325i	−0.115335	−	0.0837959i
$162$	−3.28115	+	8.38057i	−0.257792	+	0.658440i
$163$	3.32991	−	10.2484i	0.260819	−	0.802718i	−0.731808	−	0.681510i	$-0.761323\pi$
$163$	3.32991	−	10.2484i	0.260819	−	0.802718i	0.992627	−	0.121207i	$-0.0386766\pi$
$164$	−7.31754			−0.571404
$165$	2.74898	−	4.67256i	0.214008	−	0.363758i
$166$	−6.15976			−0.478090
$167$	4.10940	−	12.6474i	0.317995	−	0.978688i	−0.656509	−	0.754318i	$-0.727968\pi$
$167$	4.10940	−	12.6474i	0.317995	−	0.978688i	0.974504	−	0.224370i	$-0.0720325\pi$
$168$	1.89753	−	1.84235i	0.146397	−	0.142140i
$169$	4.01715	+	2.91863i	0.309012	+	0.224510i
$170$	2.63189	−	0.855153i	0.201857	−	0.0655873i
$171$	17.5692	−	11.9891i	1.34355	−	0.916828i
$172$	−3.14222	+	4.32490i	−0.239592	+	0.329771i
$173$	5.75163	−	4.17880i	0.437288	−	0.317708i	−0.347268	−	0.937766i	$-0.612891\pi$
$173$	5.75163	−	4.17880i	0.437288	−	0.317708i	0.784556	+	0.620057i	$0.212891\pi$
$174$	10.9114	+	1.89361i	0.827190	+	0.143554i
$175$			6.27490i			0.474338i
$176$	−3.19791	+	0.879409i	−0.241052	+	0.0662880i
$177$	7.99830	−	1.14612i	0.601189	−	0.0861473i
$178$	−16.4919	−	5.35856i	−1.23612	−	0.401641i
$179$	2.47537	+	3.40705i	0.185018	+	0.254655i	0.891443	−	0.453132i	$-0.149694\pi$
$179$	2.47537	+	3.40705i	0.185018	+	0.254655i	−0.706426	+	0.707787i	$0.749694\pi$
$180$	0.953930	−	2.66559i	0.0711017	−	0.198682i
$181$	2.67906	+	8.24528i	0.199133	+	0.612867i	0.999903	+	0.0138963i	$0.00442347\pi$
$181$	2.67906	+	8.24528i	0.199133	+	0.612867i	−0.800771	+	0.598971i	$0.795577\pi$
$182$	−2.00000	−	6.15537i	−0.148250	−	0.456266i
$183$	1.10411	+	0.583248i	0.0816181	+	0.0431149i
$184$	0.696317	+	0.958399i	0.0513332	+	0.0706541i
$185$	−2.53656	−	0.824179i	−0.186492	−	0.0605948i
$186$	−2.13733	−	14.9156i	−0.156717	−	1.09367i
$187$	−9.37751	+	2.57877i	−0.685751	+	0.188578i
$188$		−	9.49588i		−	0.692558i
$189$	−0.893244	−	7.88389i	−0.0649739	−	0.573468i
$190$	−5.41309	+	3.93284i	−0.392707	+	0.285318i
$191$	7.90445	−	10.8795i	0.571946	−	0.787216i	−0.420837	−	0.907136i	$-0.638264\pi$
$191$	7.90445	−	10.8795i	0.571946	−	0.787216i	0.992784	+	0.119920i	$0.0382637\pi$
$192$	−1.55470	+	0.763481i	−0.112201	+	0.0550995i
$193$	6.65520	−	2.16241i	0.479052	−	0.155653i	−0.0595300	−	0.998227i	$-0.518960\pi$
$193$	6.65520	−	2.16241i	0.479052	−	0.155653i	0.538582	+	0.842573i	$0.318960\pi$
$194$	−9.26977	−	6.73488i	−0.665531	−	0.483536i
$195$	−4.82617	−	4.97072i	−0.345609	−	0.355961i
$196$	1.44261	−	4.43990i	0.103044	−	0.317136i
$197$	−22.8937			−1.63111			−0.815554	−	0.578680i	$-0.803568\pi$
$197$	−22.8937			−1.63111			−0.815554	+	0.578680i	$0.803568\pi$
$198$	−3.77790	+	9.20475i	−0.268483	+	0.654153i
$199$	−20.8937			−1.48112			−0.740558	−	0.671993i	$-0.765439\pi$
$199$	−20.8937			−1.48112			−0.740558	+	0.671993i	$0.765439\pi$
$200$	1.26988	−	3.90827i	0.0897937	−	0.276357i
$201$	−4.69802	−	4.83873i	−0.331373	−	0.341298i
$202$	−3.79077	−	2.75416i	−0.266718	−	0.193782i
$203$	−9.28533	+	3.01699i	−0.651702	+	0.211751i
$204$	−4.55898	+	2.23882i	−0.319193	+	0.156749i
$205$	4.05905	−	5.58680i	0.283496	−	0.390199i
$206$	10.2430	−	7.44197i	0.713663	−	0.518507i
$207$	3.55239	+	0.104852i	0.246908	+	0.00728769i
$208$			4.23857i			0.293892i
$209$	19.6368	−	12.9363i	1.35830	−	0.894820i
$210$	0.354035	+	2.47068i	0.0244308	+	0.170493i
$211$	3.77185	+	1.22555i	0.259665	+	0.0843701i	0.435956	−	0.899968i	$-0.356410\pi$
$211$	3.77185	+	1.22555i	0.259665	+	0.0843701i	−0.176292	+	0.984338i	$0.556410\pi$
$212$	2.86103	+	3.93787i	0.196496	+	0.270454i
$213$	15.2531	+	8.05748i	1.04513	+	0.552089i
$214$	0.222103	+	0.683562i	0.0151826	+	0.0467273i
$215$	−1.55898	−	4.79806i	−0.106322	−	0.327225i
$216$	−1.03914	+	5.09119i	−0.0707046	+	0.346411i
$217$	7.80803	+	10.7468i	0.530044	+	0.729543i
$218$	−8.75856	−	2.84583i	−0.593204	−	0.192744i
$219$	−3.00594	+	0.430736i	−0.203123	+	0.0291065i
$220$	1.10247	−	2.92935i	0.0743288	−	0.197497i
$221$			12.4291i			0.836073i
$222$	4.82298	+	0.837003i	0.323697	+	0.0561760i
$223$	7.58582	−	5.51142i	0.507984	−	0.369072i	−0.304074	−	0.952648i	$-0.598347\pi$
$223$	7.58582	−	5.51142i	0.507984	−	0.369072i	0.812058	+	0.583576i	$0.198347\pi$
$224$	0.897526	−	1.23534i	0.0599685	−	0.0825395i
$225$	−6.94893	−	10.1832i	−0.463262	−	0.678878i
$226$	−4.66471	+	1.51566i	−0.310292	+	0.100820i
$227$	1.46877	+	1.06713i	0.0974859	+	0.0708276i	0.635460	−	0.772133i	$-0.280810\pi$
$227$	1.46877	+	1.06713i	0.0974859	+	0.0708276i	−0.537975	+	0.842961i	$0.680810\pi$
$228$	8.81061	−	8.55440i	0.583497	−	0.566529i
$229$	−5.74470	+	17.6804i	−0.379620	+	1.16835i	0.560688	+	0.828027i	$0.310537\pi$
$229$	−5.74470	+	17.6804i	−0.379620	+	1.16835i	−0.940308	+	0.340324i	$0.889463\pi$
$230$	−1.11797			−0.0737166
$231$	−0.845404	−	8.73090i	−0.0556235	−	0.574451i
$232$	6.39385			0.419777
$233$	−5.58748	+	17.1965i	−0.366048	+	1.12658i	0.583274	+	0.812275i	$0.301771\pi$
$233$	−5.58748	+	17.1965i	−0.366048	+	1.12658i	−0.949322	+	0.314305i	$0.898229\pi$
$234$	10.0622	+	7.77436i	0.657789	+	0.508226i
$235$	7.24993	+	5.26738i	0.472933	+	0.343606i
$236$	4.43667	−	1.44156i	0.288802	−	0.0938376i
$237$	1.25707	+	2.55981i	0.0816555	+	0.166278i
$238$	2.63189	−	3.62249i	0.170600	−	0.234811i
$239$	−16.1716	+	11.7494i	−1.04606	+	0.760005i	−0.971459	−	0.237209i	$-0.923767\pi$
$239$	−16.1716	+	11.7494i	−1.04606	+	0.760005i	−0.0745980	+	0.997214i	$0.523767\pi$
$240$	0.279492	−	1.61049i	0.0180411	−	0.103957i
$241$		−	1.79512i		−	0.115634i	−0.998327	−	0.0578169i	$-0.981586\pi$
$241$		−	1.79512i		−	0.115634i	0.998327	−	0.0578169i	$-0.0184140\pi$
$242$	−4.34184	+	10.1069i	−0.279104	+	0.649693i
$243$	10.1803	+	11.8051i	0.653069	+	0.757298i
$244$	0.685649	+	0.222781i	0.0438942	+	0.0142621i
$245$	2.58956	+	3.56422i	0.165441	+	0.227710i
$246$	−5.92001	+	11.2068i	−0.377446	+	0.714520i
$247$	−9.28642	−	28.5807i	−0.590881	−	1.81854i
$248$	−2.68830	−	8.27372i	−0.170707	−	0.525382i
$249$	−4.98335	+	9.43366i	−0.315807	+	0.597834i
$250$	5.05300	+	6.95486i	0.319580	+	0.439864i
$251$	12.0779	+	3.92434i	0.762348	+	0.247702i	0.664286	−	0.747478i	$-0.268736\pi$
$251$	12.0779	+	3.92434i	0.762348	+	0.247702i	0.0980620	+	0.995180i	$0.468736\pi$
$252$	−1.28642	−	4.39655i	−0.0810369	−	0.276957i
$253$	3.92491	+	0.179878i	0.246757	+	0.0113088i
$254$			5.28668i			0.331716i
$255$	0.819578	−	4.72257i	0.0513239	−	0.295739i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	3.11429	−	4.28646i	0.194264	−	0.267382i	−0.700762	−	0.713395i	$-0.747157\pi$
$257$	3.11429	−	4.28646i	0.194264	−	0.267382i	0.895026	+	0.446013i	$0.147157\pi$
$258$	4.08147	+	8.31124i	0.254101	+	0.517435i
$259$	−4.10424	+	1.33355i	−0.255025	+	0.0828627i
$260$	−3.23607	−	2.35114i	−0.200692	−	0.145812i
$261$	11.7276	−	15.1788i	0.725918	−	0.939545i
$262$	3.29077	−	10.1279i	0.203304	−	0.625707i
$263$	9.51711			0.586850			0.293425	−	0.955982i	$-0.405205\pi$
$263$	9.51711			0.586850			0.293425	+	0.955982i	$0.405205\pi$
$264$	−1.24035	+	5.60906i	−0.0763383	+	0.345214i
$265$	−4.59351			−0.282177
$266$	−3.34547	+	10.2963i	−0.205124	+	0.631307i
$267$	−21.5489	+	20.9222i	−1.31877	+	1.28042i
$268$	−3.15014	−	2.28871i	−0.192425	−	0.139805i
$269$	−0.0695856	+	0.0226097i	−0.00424271	+	0.00137854i	−0.311138	−	0.950365i	$-0.600710\pi$
$269$	−0.0695856	+	0.0226097i	−0.00424271	+	0.00137854i	0.306895	+	0.951743i	$0.400710\pi$
$270$	−3.31061	−	3.61745i	−0.201477	−	0.220151i
$271$	0.00659354	−	0.00907523i	0.000400529	−	0.000551281i	−0.808817	−	0.588061i	$-0.799892\pi$
$271$	0.00659354	−	0.00907523i	0.000400529	−	0.000551281i	0.809217	+	0.587510i	$0.199892\pi$
$272$	−2.37235	+	1.72361i	−0.143845	+	0.104509i
$273$	−11.0450	−	1.91680i	−0.668472	−	0.116010i
$274$		−	0.596072i		−	0.0360100i
$275$	−7.49792	−	11.3816i	−0.452142	−	0.686335i
$276$	2.03112	−	0.291049i	0.122259	−	0.0175191i
$277$	13.2028	+	4.28984i	0.793277	+	0.257751i	0.677499	−	0.735524i	$-0.263064\pi$
$277$	13.2028	+	4.28984i	0.793277	+	0.257751i	0.115778	+	0.993275i	$0.463064\pi$
$278$	3.01923	+	4.15562i	0.181082	+	0.249237i
$279$	−24.5724	−	8.79367i	−1.47111	−	0.526463i
$280$	0.445299	+	1.37049i	0.0266117	+	0.0819023i
$281$	5.25058	+	16.1596i	0.313223	+	0.964002i	0.976480	+	0.215609i	$0.0691738\pi$
$281$	5.25058	+	16.1596i	0.313223	+	0.964002i	−0.663257	+	0.748392i	$0.730826\pi$
$282$	−14.5429	−	7.68233i	−0.866019	−	0.457476i
$283$	−13.6158	−	18.7406i	−0.809378	−	1.11401i	−0.991419	−	0.130722i	$-0.958270\pi$
$283$	−13.6158	−	18.7406i	−0.809378	−	1.11401i	0.182041	−	0.983291i	$-0.441730\pi$
$284$	9.47214	+	3.07768i	0.562068	+	0.182627i
$285$	1.64386	+	11.4719i	0.0973739	+	0.679535i
$286$	10.9827	+	8.77495i	0.649423	+	0.518874i
$287$		−	11.1736i		−	0.659557i
$288$	−0.0885088	+	2.99869i	−0.00521543	+	0.176700i
$289$	6.79665	−	4.93805i	0.399803	−	0.290474i
$290$	−3.54668	+	4.88159i	−0.208268	+	0.286657i
$291$	−17.8139	+	8.74801i	−1.04427	+	0.512818i
$292$	−1.66740	+	0.541771i	−0.0975773	+	0.0317048i
$293$	18.9457	+	13.7649i	1.10682	+	0.804151i	0.982160	−	0.188048i	$-0.0602162\pi$
$293$	18.9457	+	13.7649i	1.10682	+	0.804151i	0.124659	+	0.992200i	$0.460216\pi$
$294$	−5.63261	−	5.80131i	−0.328500	−	0.338339i
$295$	−1.36042	+	4.18695i	−0.0792068	+	0.243774i
$296$	2.82617			0.164268
$297$	11.0407	+	13.2327i	0.640646	+	0.767836i
$298$	17.3691			1.00617
$299$	1.55164	−	4.77545i	0.0897335	−	0.276171i
$300$	−4.95817	−	5.10667i	−0.286260	−	0.294834i
$301$	−6.60396	−	4.79806i	−0.380646	−	0.276555i
$302$	14.3729	−	4.67002i	0.827065	−	0.268730i
$303$	−7.28478	+	3.57740i	−0.418500	+	0.205516i
$304$	4.16740	−	5.73594i	0.239017	−	0.328978i
$305$	−0.550419	+	0.399903i	−0.0315169	+	0.0228984i
$306$	−0.259542	+	8.79333i	−0.0148370	+	0.502681i
$307$		−	4.98612i		−	0.284573i	−0.989826	−	0.142286i	$-0.954555\pi$
$307$		−	4.98612i		−	0.284573i	0.989826	−	0.142286i	$-0.0454454\pi$
$308$	−1.34282	−	4.88309i	−0.0765145	−	0.278240i
$309$	−3.11062	−	21.7078i	−0.176957	−	1.23492i
$310$	7.80803	+	2.53698i	0.443466	+	0.144091i
$311$	−8.22002	−	11.3139i	−0.466115	−	0.641552i	0.509648	−	0.860383i	$-0.329776\pi$
$311$	−8.22002	−	11.3139i	−0.466115	−	0.641552i	−0.975763	+	0.218831i	$0.929776\pi$
$312$	6.49137	+	3.42908i	0.367501	+	0.194133i
$313$	4.84018	+	14.8965i	0.273583	+	0.842002i	0.989591	+	0.143910i	$0.0459675\pi$
$313$	4.84018	+	14.8965i	0.273583	+	0.842002i	−0.716008	+	0.698092i	$0.754033\pi$
$314$	−1.14590	−	3.52671i	−0.0646668	−	0.199024i
$315$	4.07026	+	1.45661i	0.229333	+	0.0820709i
$316$	0.967787	+	1.33204i	0.0544423	+	0.0749334i
$317$	−30.4366	−	9.88946i	−1.70949	−	0.555448i	−0.719243	−	0.694758i	$-0.755511\pi$
$317$	−30.4366	−	9.88946i	−1.70949	−	0.555448i	−0.990249	+	0.139310i	$0.955511\pi$
$318$	8.34547	−	1.19586i	0.467991	−	0.0670607i
$319$	13.2369	−	16.5674i	0.741127	−	0.927595i
$320$		−	0.943715i		−	0.0527552i
$321$	1.22656	+	0.212863i	0.0684599	+	0.0118808i
$322$	−1.46344	+	1.06325i	−0.0815542	+	0.0592526i
$323$	12.2204	−	16.8200i	0.679963	−	0.935888i
$324$	6.95647	+	5.71030i	0.386470	+	0.317239i
$325$	−16.5655	+	5.38246i	−0.918888	+	0.298565i
$326$	−8.71782	−	6.33387i	−0.482835	−	0.350800i
$327$	−11.4442	+	11.1114i	−0.632866	+	0.614462i
$328$	−2.26124	+	6.95939i	−0.124856	+	0.384268i
$329$	14.4999			0.799403
$330$	−3.59439	−	4.05834i	−0.197864	−	0.223404i
$331$	5.76590			0.316923			0.158461	−	0.987365i	$-0.449347\pi$
$331$	5.76590			0.316923			0.158461	+	0.987365i	$0.449347\pi$
$332$	−1.90347	+	5.85828i	−0.104466	+	0.321515i
$333$	5.18374	−	6.70925i	0.284067	−	0.367664i
$334$	−10.7586	−	7.81655i	−0.588682	−	0.427703i
$335$	3.49477	−	1.13552i	0.190940	−	0.0620401i
$336$	−1.16581	−	2.37397i	−0.0636000	−	0.129511i
$337$	18.5288	−	25.5028i	1.00933	−	1.38922i	0.0899083	−	0.995950i	$-0.471343\pi$
$337$	18.5288	−	25.5028i	1.00933	−	1.38922i	0.919422	−	0.393273i	$-0.128657\pi$
$338$	4.01715	−	2.91863i	0.218504	−	0.158753i
$339$	−1.45260	+	8.37020i	−0.0788946	+	0.454607i
$340$		−	2.76733i		−	0.150080i
$341$	−27.0039	−	10.1630i	−1.46234	−	0.550358i
$342$	−5.97312	−	20.4141i	−0.322989	−	1.10387i
$343$	16.9451	+	5.50581i	0.914952	+	0.297286i
$344$	3.14222	+	4.32490i	0.169417	+	0.233183i
$345$	−0.904455	+	1.71217i	−0.0486942	+	0.0921800i
$346$	−2.19693	−	6.76144i	−0.118107	−	0.363497i
$347$	−9.33453	−	28.7287i	−0.501104	−	1.54224i	−0.807224	−	0.590246i	$-0.799031\pi$
$347$	−9.33453	−	28.7287i	−0.501104	−	1.54224i	0.306120	−	0.951993i	$-0.400969\pi$
$348$	5.17274	−	9.79218i	0.277288	−	0.524916i
$349$	−5.67246	−	7.80747i	−0.303640	−	0.417924i	0.629745	−	0.776802i	$-0.283160\pi$
$349$	−5.67246	−	7.80747i	−0.303640	−	0.417924i	−0.933385	+	0.358878i	$0.883160\pi$
$350$	5.96779	+	1.93905i	0.318992	+	0.103647i
$351$	20.0469	−	9.12073i	1.07003	−	0.486829i
$352$	−0.151841	+	3.31315i	−0.00809317	+	0.176591i
$353$			13.7385i			0.731224i	0.930767	+	0.365612i	$0.119140\pi$
$353$			13.7385i			0.731224i	−0.930767	+	0.365612i	$0.880860\pi$
$354$	1.38159	−	7.96100i	0.0734307	−	0.423122i
$355$	−7.60396	+	5.52460i	−0.403576	+	0.293215i
$356$	−10.1926	+	14.0289i	−0.540206	+	0.743529i
$357$	−3.41859	−	6.96140i	−0.180931	−	0.368436i
$358$	4.00523	−	1.30138i	0.211683	−	0.0687799i
$359$	23.6610	+	17.1908i	1.24878	+	0.907293i	0.998151	−	0.0607894i	$-0.0193618\pi$
$359$	23.6610	+	17.1908i	1.24878	+	0.907293i	0.250631	+	0.968083i	$0.419362\pi$
$360$	−2.24035	−	1.73095i	−0.118077	−	0.0912293i
$361$	−9.66240	+	29.7378i	−0.508547	+	1.56515i
$362$	8.66960			0.455664
$363$	11.9660	+	14.8261i	0.628053	+	0.778171i
$364$	−6.47214			−0.339232
$365$	0.511278	−	1.57355i	0.0267615	−	0.0823634i
$366$	0.895890	−	0.869837i	0.0468289	−	0.0454671i
$367$	−9.12557	−	6.63012i	−0.476351	−	0.346089i	0.323560	−	0.946208i	$-0.395120\pi$
$367$	−9.12557	−	6.63012i	−0.476351	−	0.346089i	−0.799911	+	0.600118i	$0.795120\pi$
$368$	1.12667	−	0.366076i	0.0587315	−	0.0190830i
$369$	12.3738	+	18.1330i	0.644156	+	0.943966i
$370$	−1.56768	+	2.15773i	−0.0814999	+	0.112175i
$371$	−6.01298	+	4.36869i	−0.312178	+	0.226811i
$372$	−14.8461	−	2.57646i	−0.769733	−	0.133583i
$373$		−	5.73545i		−	0.296971i	−0.988915	−	0.148485i	$-0.952560\pi$
$373$		−	5.73545i		−	0.296971i	0.988915	−	0.148485i	$-0.0474398\pi$
$374$	−0.445257	+	9.71542i	−0.0230237	+	0.502373i
$375$	14.7393	−	2.11207i	0.761135	−	0.109067i
$376$	−9.03112	−	2.93439i	−0.465744	−	0.151330i
$377$	−15.9294	−	21.9250i	−0.820408	−	1.12920i
$378$	−7.77405	−	1.58673i	−0.399854	−	0.0816126i
$379$	8.34075	+	25.6702i	0.428435	+	1.31859i	0.899666	+	0.436578i	$0.143810\pi$
$379$	8.34075	+	25.6702i	0.428435	+	1.31859i	−0.471231	+	0.882010i	$0.656190\pi$
$380$	2.06761	+	6.36346i	0.106066	+	0.326439i
$381$	8.09655	+	4.27701i	0.414799	+	0.219118i
$382$	−7.90445	−	10.8795i	−0.404427	−	0.556646i
$383$	0.600988	+	0.195273i	0.0307090	+	0.00997797i	0.324331	−	0.945944i	$-0.394861\pi$
$383$	0.600988	+	0.195273i	0.0307090	+	0.00997797i	−0.293622	+	0.955922i	$0.594861\pi$
$384$	0.245684	+	1.71454i	0.0125375	+	0.0874946i
$385$	4.47301	+	1.68344i	0.227966	+	0.0857959i
$386$		−	6.99770i		−	0.356173i
$387$	16.0306	+	0.473157i	0.814883	+	0.0240519i
$388$	−9.26977	+	6.73488i	−0.470601	+	0.341912i
$389$	−15.7180	+	21.6340i	−0.796934	+	1.09688i	0.196276	+	0.980549i	$0.437115\pi$
$389$	−15.7180	+	21.6340i	−0.796934	+	1.09688i	−0.993210	+	0.116336i	$0.962885\pi$
$390$	−6.21881	+	3.05392i	−0.314901	+	0.154641i
$391$	3.30382	−	1.07347i	0.167081	−	0.0542880i
$392$	−3.77680	−	2.74401i	−0.190757	−	0.138593i
$393$	−12.8487	−	13.2335i	−0.648129	−	0.667541i
$394$	−7.07454	+	21.7732i	−0.356410	+	1.09692i
$395$	−1.55382			−0.0781814
$396$	7.58681	+	6.43742i	0.381251	+	0.323492i
$397$	36.0170			1.80764			0.903820	−	0.427913i	$-0.140751\pi$
$397$	36.0170			1.80764			0.903820	+	0.427913i	$0.140751\pi$
$398$	−6.45651	+	19.8711i	−0.323636	+	0.996048i
$399$	13.0622	+	13.4535i	0.653930	+	0.673516i
$400$	−3.32458	−	2.41545i	−0.166229	−	0.120772i
$401$	19.7141	−	6.40551i	0.984478	−	0.319876i	0.227831	−	0.973701i	$-0.426837\pi$
$401$	19.7141	−	6.40551i	0.984478	−	0.319876i	0.756646	+	0.653824i	$0.226837\pi$
$402$	−6.05367	+	2.97283i	−0.301930	+	0.148271i
$403$	−21.6737	+	29.8313i	−1.07964	+	1.48600i
$404$	−3.79077	+	2.75416i	−0.188598	+	0.137024i
$405$	−8.21847	+	2.14362i	−0.408379	+	0.106517i
$406$			9.76317i			0.484538i
$407$	5.85091	−	7.32301i	0.290019	−	0.362988i
$408$	0.720442	+	5.02768i	0.0356672	+	0.248907i
$409$	−15.7096	−	5.10437i	−0.776791	−	0.252395i	−0.106321	−	0.994332i	$-0.533907\pi$
$409$	−15.7096	−	5.10437i	−0.776791	−	0.252395i	−0.670469	+	0.741937i	$0.733907\pi$
$410$	−4.05905	−	5.58680i	−0.200462	−	0.275913i
$411$	−0.912884	−	0.482232i	−0.0450292	−	0.0237868i
$412$	−3.91248	−	12.0414i	−0.192754	−	0.593235i
$413$	2.20121	+	6.77462i	0.108314	+	0.333357i
$414$	1.19747	−	3.34612i	0.0588524	−	0.164453i
$415$	−3.41683	−	4.70286i	−0.167725	−	0.230854i
$416$	4.03112	+	1.30979i	0.197642	+	0.0642177i
$417$	8.80694	−	1.26199i	0.431278	−	0.0617999i
$418$	−6.23502	−	22.6732i	−0.304965	−	1.10898i
$419$			16.0213i			0.782693i	0.920243	+	0.391347i	$0.127991\pi$
$419$			16.0213i			0.782693i	−0.920243	+	0.391347i	$0.872009\pi$
$420$	2.45916	+	0.426773i	0.119995	+	0.0208244i
$421$	−10.5988	+	7.70048i	−0.516554	+	0.375298i	−0.815304	−	0.579033i	$-0.803430\pi$
$421$	−10.5988	+	7.70048i	−0.516554	+	0.375298i	0.298750	+	0.954331i	$0.403430\pi$
$422$	2.33113	−	3.20852i	0.113478	−	0.156189i
$423$	−23.5310	+	16.0574i	−1.14411	+	0.780736i
$424$	4.62924	−	1.50413i	0.224816	−	0.0730471i
$425$	−9.74894	−	7.08302i	−0.472893	−	0.343577i
$426$	12.3766	−	12.0167i	0.599648	−	0.582210i
$427$	−0.340178	+	1.04696i	−0.0164624	+	0.0506659i
$428$	0.718739			0.0347416
$429$	22.3241	−	9.72098i	1.07782	−	0.469333i
$430$	−5.04498			−0.243290
$431$	−3.65126	+	11.2374i	−0.175875	+	0.541287i	−0.999672	−	0.0255970i	$-0.991851\pi$
$431$	−3.65126	+	11.2374i	−0.175875	+	0.541287i	0.823797	+	0.566884i	$0.191851\pi$
$432$	4.52089	+	2.56155i	0.217512	+	0.123242i
$433$	−9.23019	−	6.70613i	−0.443575	−	0.322276i	0.343479	−	0.939160i	$-0.388395\pi$
$433$	−9.23019	−	6.70613i	−0.443575	−	0.322276i	−0.787054	+	0.616884i	$0.788395\pi$
$434$	12.6337	−	4.10493i	0.606435	−	0.197043i
$435$	4.60682	+	9.38102i	0.220880	+	0.449786i
$436$	−5.41309	+	7.45047i	−0.259240	+	0.356813i
$437$	−6.79505	+	4.93689i	−0.325051	+	0.236164i
$438$	−0.519233	+	2.99193i	−0.0248099	+	0.142960i
$439$		−	16.0229i		−	0.764733i	−0.924011	−	0.382366i	$-0.875109\pi$
$439$		−	16.0229i		−	0.764733i	0.924011	−	0.382366i	$-0.124891\pi$
$440$	−2.44530	−	1.95374i	−0.116575	−	0.0931407i
$441$	−13.4416	+	3.93298i	−0.640075	+	0.187285i
$442$	11.8208	+	3.84081i	0.562258	+	0.182689i
$443$	−2.78323	−	3.83079i	−0.132235	−	0.182006i	0.737765	−	0.675058i	$-0.235881\pi$
$443$	−2.78323	−	3.83079i	−0.132235	−	0.182006i	−0.870000	+	0.493052i	$0.835881\pi$
$444$	2.28642	−	4.32828i	0.108509	−	0.205411i
$445$	−5.05695	−	15.5637i	−0.239722	−	0.737789i
$446$	−2.89753	−	8.91767i	−0.137202	−	0.422264i
$447$	14.0519	−	26.6008i	0.664632	−	1.25817i
$448$	−0.897526	−	1.23534i	−0.0424041	−	0.0583642i
$449$	24.5951	+	7.99144i	1.16072	+	0.377139i	0.825170	−	0.564884i	$-0.191079\pi$
$449$	24.5951	+	7.99144i	1.16072	+	0.377139i	0.335546	+	0.942024i	$0.391079\pi$
$450$	−11.8321	+	3.46205i	−0.557771	+	0.163203i
$451$	13.3514	+	20.2670i	0.628694	+	0.954334i
$452$			4.90477i			0.230701i
$453$	4.47574	−	25.7901i	0.210289	−	1.21173i
$454$	1.46877	−	1.06713i	0.0689329	−	0.0500827i
$455$	3.59010	−	4.94135i	0.168307	−	0.231654i
$456$	−5.41309	−	11.0228i	−0.253491	−	0.516192i
$457$	−21.7712	+	7.07390i	−1.01841	+	0.330903i	−0.770200	−	0.637802i	$-0.779844\pi$
$457$	−21.7712	+	7.07390i	−1.01841	+	0.330903i	−0.248214	+	0.968705i	$0.579844\pi$
$458$	15.0398	+	10.9271i	0.702765	+	0.510588i
$459$	13.2570	+	7.51144i	0.618784	+	0.350604i
$460$	−0.345471	+	1.06325i	−0.0161077	+	0.0495743i
$461$	−21.2809			−0.991151			−0.495575	−	0.868565i	$-0.665043\pi$
$461$	−21.2809			−0.991151			−0.495575	+	0.868565i	$0.665043\pi$
$462$	−8.56482	−	1.89397i	−0.398471	−	0.0881154i
$463$	−20.7617			−0.964880			−0.482440	−	0.875929i	$-0.660249\pi$
$463$	−20.7617			−0.964880			−0.482440	+	0.875929i	$0.660249\pi$
$464$	1.97581	−	6.08092i	0.0917246	−	0.282299i
$465$	10.2022	−	9.90554i	0.473117	−	0.459358i
$466$	14.6282	+	10.6280i	0.677639	+	0.492334i
$467$	−3.70774	+	1.20472i	−0.171574	+	0.0557477i	−0.393544	−	0.919306i	$-0.628751\pi$
$467$	−3.70774	+	1.20472i	−0.171574	+	0.0557477i	0.221970	+	0.975053i	$0.428751\pi$
$468$	10.5033	−	7.16735i	0.485513	−	0.331311i
$469$	3.49477	−	4.81014i	0.161374	−	0.222112i
$470$	7.24993	−	5.26738i	0.334414	−	0.242966i
$471$	−6.32821	−	1.09823i	−0.291588	−	0.0506036i
$472$		−	4.66499i		−	0.214723i
$473$	17.7117	+	0.811724i	0.814383	+	0.0373231i
$474$	2.82298	−	0.404519i	0.129664	−	0.0185802i
$475$	27.7097	+	9.00342i	1.27141	+	0.413105i
$476$	−2.63189	−	3.62249i	−0.120633	−	0.166036i
$477$	4.92016	−	13.7486i	0.225279	−	0.629503i
$478$	6.17702	+	19.0109i	0.282530	+	0.869539i
$479$	−10.7639	−	33.1280i	−0.491817	−	1.51366i	−0.821860	−	0.569690i	$-0.807063\pi$
$479$	−10.7639	−	33.1280i	−0.491817	−	1.51366i	0.330043	−	0.943966i	$-0.392937\pi$
$480$	−1.44530	−	0.763481i	−0.0659686	−	0.0348480i
$481$	−7.04104	−	9.69115i	−0.321044	−	0.441879i
$482$	−1.70726	−	0.554722i	−0.0777635	−	0.0252669i
$483$	0.444421	+	3.10144i	0.0202219	+	0.141121i
$484$	8.27048	+	7.25252i	0.375931	+	0.329660i
$485$		−	10.8131i		−	0.490999i
$486$	14.3732	−	6.03410i	0.651983	−	0.273712i
$487$	−4.07454	+	2.96033i	−0.184635	+	0.134145i	−0.676263	−	0.736660i	$-0.736402\pi$
$487$	−4.07454	+	2.96033i	−0.184635	+	0.134145i	0.491628	+	0.870805i	$0.336402\pi$
$488$	0.423754	−	0.583248i	0.0191825	−	0.0264024i
$489$	−16.7532	+	8.22713i	−0.757605	+	0.372044i
$490$	4.19000	−	1.36141i	0.189285	−	0.0615024i
$491$	−11.3418	−	8.24030i	−0.511848	−	0.371879i	0.301676	−	0.953410i	$-0.402454\pi$
$491$	−11.3418	−	8.24030i	−0.511848	−	0.371879i	−0.813524	+	0.581531i	$0.802454\pi$
$492$	8.82893	+	9.09336i	0.398039	+	0.409960i
$493$	5.79383	−	17.8316i	0.260941	−	0.803094i
$494$	−30.0515			−1.35208
$495$	−9.12326	+	2.22154i	−0.410060	+	0.0998507i
$496$	−8.69951			−0.390619
$497$	−4.69951	+	14.4636i	−0.210802	+	0.648781i
$498$	7.43201	+	7.65461i	0.333036	+	0.343011i
$499$	11.2013	+	8.13820i	0.501438	+	0.364316i	0.809566	−	0.587029i	$-0.199703\pi$
$499$	11.2013	+	8.13820i	0.501438	+	0.364316i	−0.308128	+	0.951345i	$0.599703\pi$
$500$	8.17592	−	2.65652i	0.365638	−	0.118803i
$501$	−20.6749	+	10.1530i	−0.923686	+	0.453603i
$502$	7.46453	−	10.2740i	0.333158	−	0.458553i
$503$	18.2723	−	13.2756i	0.814724	−	0.591931i	−0.100473	−	0.994940i	$-0.532035\pi$
$503$	18.2723	−	13.2756i	0.814724	−	0.591931i	0.915196	+	0.403008i	$0.132035\pi$
$504$	−4.57889	−	0.135150i	−0.203960	−	0.00602004i
$505$		−	4.42191i		−	0.196773i
$506$	1.38394	−	3.67722i	0.0615235	−	0.163472i
$507$	−1.21994	−	8.51349i	−0.0541795	−	0.378098i
$508$	5.02793	+	1.63367i	0.223078	+	0.0724825i
$509$	15.1884	+	20.9050i	0.673212	+	0.926597i	0.999828	−	0.0185605i	$-0.00590832\pi$
$509$	15.1884	+	20.9050i	0.673212	+	0.926597i	−0.326616	+	0.945157i	$0.605908\pi$
$510$	−4.23817	−	2.23882i	−0.187669	−	0.0991366i
$511$	−0.827265	−	2.54606i	−0.0365960	−	0.112631i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−36.0965	−	7.36752i	−1.59370	−	0.325284i
$514$	−3.11429	−	4.28646i	−0.137366	−	0.189068i
$515$	11.3636	+	3.69226i	0.500741	+	0.162700i
$516$	9.16570	−	1.31340i	0.403497	−	0.0578191i
$517$	−26.3002	+	17.3260i	−1.15668	+	0.761995i
$518$			4.31546i			0.189610i
$519$	−12.1325	−	2.10553i	−0.532558	−	0.0924226i
$520$	−3.23607	+	2.35114i	−0.141911	+	0.103104i
$521$	16.8875	−	23.2436i	0.739854	−	1.01832i	−0.258773	−	0.965938i	$-0.583318\pi$
$521$	16.8875	−	23.2436i	0.739854	−	1.01832i	0.998627	−	0.0523840i	$-0.0166820\pi$
$522$	−10.8119	−	15.8441i	−0.473224	−	0.693477i
$523$	−3.45339	+	1.12207i	−0.151006	+	0.0490648i	−0.383545	−	0.923522i	$-0.625297\pi$
$523$	−3.45339	+	1.12207i	−0.151006	+	0.0490648i	0.232539	+	0.972587i	$0.425297\pi$
$524$	−8.61535	−	6.25942i	−0.376363	−	0.273444i
$525$	7.79770	−	7.57094i	0.340319	−	0.330423i
$526$	2.94095	−	9.05131i	0.128232	−	0.394656i
$527$	−25.5103			−1.11125
$528$	4.95124	+	2.91294i	0.215475	+	0.126769i
$529$	21.5966			0.938983
$530$	−1.41947	+	4.36869i	−0.0616579	+	0.189764i
$531$	−11.0745	−	8.55649i	−0.480594	−	0.371320i
$532$	8.75856	+	6.36346i	0.379732	+	0.275891i
$533$	29.4979	−	9.58444i	1.27770	−	0.415148i
$534$	13.2393	+	26.9595i	0.572919	+	1.16665i
$535$	−0.398686	+	0.548744i	−0.0172367	+	0.0237243i
$536$	−3.15014	+	2.28871i	−0.136065	+	0.0988572i
$537$	1.24724	−	7.18684i	0.0538223	−	0.310135i
$538$			0.0731666i			0.00315444i
$539$	−14.9291	+	4.10542i	−0.643041	+	0.176833i
$540$	−4.46344	+	2.03072i	−0.192076	+	0.0873884i
$541$	−38.8402	−	12.6199i	−1.66987	−	0.542573i	−0.686965	−	0.726691i	$-0.741057\pi$
$541$	−38.8402	−	12.6199i	−1.66987	−	0.542573i	−0.982904	+	0.184117i	$0.941057\pi$
$542$	−0.00659354	−	0.00907523i	−0.000283217	−	0.000389814i
$543$	7.01386	−	13.2775i	0.300993	−	0.569792i
$544$	0.906157	+	2.78886i	0.0388512	+	0.119572i
$545$	−2.68565	−	8.26558i	−0.115041	−	0.354058i
$546$	−5.23607	+	9.91207i	−0.224083	+	0.424198i
$547$	4.23174	+	5.82450i	0.180936	+	0.249037i	0.889845	−	0.456263i	$-0.150812\pi$
$547$	4.23174	+	5.82450i	0.180936	+	0.249037i	−0.708909	+	0.705300i	$0.750812\pi$
$548$	−0.566898	−	0.184196i	−0.0242167	−	0.00786848i
$549$	−0.607365	−	2.07577i	−0.0259217	−	0.0885917i
$550$	−13.1415	+	3.61385i	−0.560356	+	0.154095i
$551$			45.3325i			1.93123i
$552$	0.350846	−	2.02165i	0.0149330	−	0.0860471i
$553$	−2.03398	+	1.47777i	−0.0864937	+	0.0628414i
$554$	8.15976	−	11.2309i	0.346675	−	0.477157i
$555$	2.03628	+	4.14654i	0.0864353	+	0.176011i
$556$	4.88522	−	1.58730i	0.207180	−	0.0673167i
$557$	27.2935	+	19.8299i	1.15646	+	0.840219i	0.989327	−	0.145715i	$-0.0465483\pi$
$557$	27.2935	+	19.8299i	1.15646	+	0.840219i	0.167135	+	0.985934i	$0.446548\pi$
$558$	−15.9566	+	20.6524i	−0.675496	+	0.874285i
$559$	7.00197	−	21.5499i	0.296152	−	0.911462i
$560$	1.44102			0.0608941
$561$	14.5189	+	8.54185i	0.612990	+	0.360637i
$562$	16.9912			0.716731
$563$	−1.47279	+	4.53277i	−0.0620705	+	0.191033i	−0.977283	−	0.211938i	$-0.932023\pi$
$563$	−1.47279	+	4.53277i	−0.0620705	+	0.191033i	0.915213	+	0.402971i	$0.132023\pi$
$564$	−11.8003	+	11.4572i	−0.496884	+	0.482435i
$565$	−3.74470	−	2.72068i	−0.157541	−	0.114460i
$566$	−22.0309	+	7.15827i	−0.926028	+	0.300885i
$567$	−8.71941	+	10.6223i	−0.366181	+	0.446093i
$568$	5.85410	−	8.05748i	0.245633	−	0.338084i
$569$	−12.0407	+	8.74811i	−0.504774	+	0.366740i	−0.810837	−	0.585271i	$-0.800988\pi$
$569$	−12.0407	+	8.74811i	−0.504774	+	0.366740i	0.306064	+	0.952011i	$0.400988\pi$
$570$	11.4184	+	1.98160i	0.478263	+	0.0830000i
$571$			8.91378i			0.373030i	0.982452	+	0.186515i	$0.0597193\pi$
$571$			8.91378i			0.373030i	−0.982452	+	0.186515i	$0.940281\pi$
$572$	11.7393	−	7.73360i	0.490846	−	0.323358i
$573$	−23.0569	+	3.30393i	−0.963214	+	0.138024i
$574$	−10.6267	−	3.45283i	−0.443551	−	0.144119i
$575$	2.86145	+	3.93845i	0.119331	+	0.164245i
$576$	2.82458	+	1.01082i	0.117691	+	0.0421177i
$577$	−3.30341	−	10.1668i	−0.137523	−	0.423251i	0.858451	−	0.512895i	$-0.171427\pi$
$577$	−3.30341	−	10.1668i	−0.137523	−	0.423251i	−0.995974	+	0.0896439i	$0.971427\pi$
$578$	−2.59609	−	7.98994i	−0.107983	−	0.332338i
$579$	−10.7170	−	5.66126i	−0.445382	−	0.235274i
$580$	3.54668	+	4.88159i	0.147268	+	0.202697i
$581$	−8.94537	−	2.90653i	−0.371116	−	0.120583i
$582$	2.81507	+	19.6453i	0.116688	+	0.814323i
$583$	5.68632	−	15.1090i	0.235503	−	0.625750i
$584$			1.75321i			0.0725483i
$585$	−0.354035	+	11.9948i	−0.0146376	+	0.495923i
$586$	18.9457	−	13.7649i	0.782639	−	0.568621i
$587$	−16.6724	+	22.9476i	−0.688144	+	0.947150i	−0.999996	−	0.00298142i	$-0.999051\pi$
$587$	−16.6724	+	22.9476i	−0.688144	+	0.947150i	0.311851	+	0.950131i	$0.399051\pi$
$588$	−7.25795	+	3.56422i	−0.299313	+	0.146986i
$589$	58.6607	−	19.0600i	2.41707	−	0.785355i
$590$	3.56163	+	2.58768i	0.146630	+	0.106533i
$591$	27.6222	+	28.4496i	1.13623	+	1.17026i
$592$	0.873335	−	2.68785i	0.0358938	−	0.110470i
$593$	−26.8555			−1.10282			−0.551411	−	0.834234i	$-0.685910\pi$
$593$	−26.8555			−1.10282			−0.551411	+	0.834234i	$0.685910\pi$
$594$	15.9968	−	6.41121i	0.656355	−	0.263055i
$595$	4.22562			0.173233
$596$	5.36735	−	16.5190i	0.219855	−	0.676645i
$597$	25.2091	+	25.9642i	1.03174	+	1.06264i
$598$	−4.06224	−	2.95139i	−0.166117	−	0.120691i
$599$	15.8754	−	5.15824i	0.648653	−	0.210760i	0.0338328	−	0.999428i	$-0.489229\pi$
$599$	15.8754	−	5.15824i	0.648653	−	0.210760i	0.614820	+	0.788667i	$0.289229\pi$
$600$	−6.38889	+	3.13745i	−0.260826	+	0.128086i
$601$	4.76046	−	6.55221i	0.194183	−	0.267270i	−0.700812	−	0.713346i	$-0.747179\pi$
$601$	4.76046	−	6.55221i	0.194183	−	0.267270i	0.894995	+	0.446076i	$0.147179\pi$
$602$	−6.60396	+	4.79806i	−0.269157	+	0.195554i
$603$	−0.344634	+	11.6763i	−0.0140346	+	0.475495i
$604$		−	15.1125i		−	0.614919i
$605$	−10.1248	+	2.29137i	−0.411632	+	0.0931576i
$606$	1.15119	+	8.03372i	0.0467639	+	0.326348i
$607$	4.80362	+	1.56079i	0.194973	+	0.0633505i	0.404876	−	0.914372i	$-0.367315\pi$
$607$	4.80362	+	1.56079i	0.194973	+	0.0633505i	−0.209903	+	0.977722i	$0.567315\pi$
$608$	−4.16740	−	5.73594i	−0.169010	−	0.232623i
$609$	14.9523	+	7.89857i	0.605898	+	0.320066i
$610$	0.210241	+	0.647057i	0.00851243	+	0.0261986i
$611$	12.4376	+	38.2790i	0.503172	+	1.54860i
$612$	8.28275	+	2.96413i	0.334810	+	0.119818i
$613$	17.6683	+	24.3183i	0.713616	+	0.982208i	0.999712	+	0.0240072i	$0.00764247\pi$
$613$	17.6683	+	24.3183i	0.713616	+	0.982208i	−0.286096	+	0.958201i	$0.592358\pi$
$614$	−4.74208	−	1.54079i	−0.191375	−	0.0621814i
$615$	−11.8400	+	1.69662i	−0.477436	+	0.0684141i
$616$	−5.05905	−	0.231856i	−0.203835	−	0.00934174i
$617$		−	1.33268i		−	0.0536518i	−0.999640	−	0.0268259i	$-0.991460\pi$
$617$		−	1.33268i		−	0.0536518i	0.999640	−	0.0268259i	$-0.00853997\pi$
$618$	−21.6066	−	3.74971i	−0.869145	−	0.150836i
$619$	1.11705	−	0.811583i	0.0448980	−	0.0326203i	−0.565110	−	0.825016i	$-0.691166\pi$
$619$	1.11705	−	0.811583i	0.0448980	−	0.0326203i	0.610008	+	0.792395i	$0.291166\pi$
$620$	4.82563	−	6.64191i	0.193802	−	0.266745i
$621$	−4.15581	−	4.54099i	−0.166767	−	0.182224i
$622$	−13.3003	+	4.32152i	−0.533293	+	0.173277i
$623$	−21.4216	−	15.5637i	−0.858237	−	0.623546i
$624$	5.26719	−	5.11402i	0.210856	−	0.204724i
$625$	3.84238	−	11.8256i	0.153695	−	0.473025i
$626$	15.6631			0.626025
$627$	−39.7683	−	8.79409i	−1.58819	−	0.351202i
$628$	−3.70820			−0.147973
$629$	2.56095	−	7.88181i	0.102112	−	0.314268i
$630$	2.64310	−	3.42093i	0.105304	−	0.136293i
$631$	14.7715	+	10.7321i	0.588046	+	0.427240i	0.841616	−	0.540077i	$-0.181605\pi$
$631$	14.7715	+	10.7321i	0.588046	+	0.427240i	−0.253570	+	0.967317i	$0.581605\pi$
$632$	1.56591	−	0.508796i	0.0622887	−	0.0202388i
$633$	−3.02793	−	6.16587i	−0.120349	−	0.245071i
$634$	−18.8109	+	25.8910i	−0.747075	+	1.02826i
$635$	−4.03628	+	2.93253i	−0.160175	+	0.116374i
$636$	1.44156	−	8.30656i	0.0571615	−	0.329376i
$637$			19.7873i			0.784001i
$638$	−11.6661	−	17.7087i	−0.461864	−	0.701094i
$639$	−8.39066	−	28.6764i	−0.331930	−	1.13442i
$640$	−0.897526	−	0.291624i	−0.0354778	−	0.0115274i
$641$	−12.4155	−	17.0884i	−0.490381	−	0.674952i	0.490077	−	0.871679i	$-0.336969\pi$
$641$	−12.4155	−	17.0884i	−0.490381	−	0.674952i	−0.980458	+	0.196727i	$0.936969\pi$
$642$	0.581472	−	1.10075i	0.0229489	−	0.0434431i
$643$	−0.228154	−	0.702185i	−0.00899751	−	0.0276915i	0.946457	−	0.322830i	$-0.104634\pi$
$643$	−0.228154	−	0.702185i	−0.00899751	−	0.0276915i	−0.955454	+	0.295139i	$0.904634\pi$
$644$	0.558984	+	1.72037i	0.0220270	+	0.0677923i
$645$	−4.08147	+	7.72638i	−0.160708	+	0.304226i
$646$	−12.2204	−	16.8200i	−0.480806	−	0.661773i
$647$	34.1070	+	11.0820i	1.34088	+	0.435680i	0.889616	−	0.456709i	$-0.150972\pi$
$647$	34.1070	+	11.0820i	1.34088	+	0.435680i	0.451268	+	0.892388i	$0.350972\pi$
$648$	7.58049	−	4.85141i	0.297790	−	0.190582i
$649$	−12.0876	−	9.65774i	−0.474482	−	0.379100i
$650$			17.4180i			0.683190i
$651$	3.93415	−	22.6694i	0.154192	−	0.888484i
$652$	−8.71782	+	6.33387i	−0.341416	+	0.248053i
$653$	−9.84112	+	13.5451i	−0.385113	+	0.530062i	−0.956930	−	0.290319i	$-0.906239\pi$
$653$	−9.84112	+	13.5451i	−0.385113	+	0.530062i	0.571817	+	0.820381i	$0.306239\pi$
$654$	7.03112	+	14.3177i	0.274939	+	0.559866i
$655$	9.55789	−	3.10555i	0.373458	−	0.121344i
$656$	5.92001	+	4.30114i	0.231138	+	0.167931i
$657$	4.16207	+	3.21572i	0.162378	+	0.125457i
$658$	4.48070	−	13.7902i	0.174676	−	0.537597i
$659$	36.3989			1.41790			0.708951	−	0.705258i	$-0.249169\pi$
$659$	36.3989			1.41790			0.708951	+	0.705258i	$0.249169\pi$
$660$	−4.97043	+	2.16437i	−0.193474	+	0.0842479i
$661$	−16.8578			−0.655694			−0.327847	−	0.944731i	$-0.606323\pi$
$661$	−16.8578			−0.655694			−0.327847	+	0.944731i	$0.606323\pi$
$662$	1.78176	−	5.48370i	0.0692501	−	0.213130i
$663$	15.4454	−	14.9963i	0.599851	−	0.582407i
$664$	4.98335	+	3.62061i	0.193391	+	0.140507i
$665$	−9.71677	+	3.15717i	−0.376800	+	0.122430i
$666$	−4.77901	−	7.00331i	−0.185183	−	0.271373i
$667$	−4.45215	+	6.12786i	−0.172388	+	0.237272i
$668$	−10.7586	+	7.81655i	−0.416261	+	0.302431i
$669$	−16.0016	−	2.77698i	−0.618656	−	0.107364i
$670$		−	3.67462i		−	0.141963i
$671$	−0.633996	−	2.30548i	−0.0244751	−	0.0890022i
$672$	−2.61803	+	0.375151i	−0.100993	+	0.0144718i
$673$	−9.70460	−	3.15322i	−0.374085	−	0.121548i	0.115940	−	0.993256i	$-0.463012\pi$
$673$	−9.70460	−	3.15322i	−0.374085	−	0.121548i	−0.490024	+	0.871709i	$0.663012\pi$
$674$	−18.5288	−	25.5028i	−0.713704	−	0.982329i
$675$	−4.27025	+	20.9217i	−0.164362	+	0.805278i
$676$	−1.53442	−	4.72245i	−0.0590160	−	0.181633i
$677$	−9.68951	−	29.8213i	−0.372398	−	1.14612i	−0.945217	−	0.326442i	$-0.894150\pi$
$677$	−9.68951	−	29.8213i	−0.372398	−	1.14612i	0.572819	−	0.819682i	$-0.305850\pi$
$678$	7.51165	+	3.96804i	0.288483	+	0.152392i
$679$	−10.2839	−	14.1546i	−0.394660	−	0.543203i
$680$	−2.63189	−	0.855153i	−0.100928	−	0.0327936i
$681$	−0.446041	−	3.11275i	−0.0170923	−	0.119281i
$682$	−18.0103	+	22.5417i	−0.689648	+	0.863165i
$683$		−	46.5132i		−	1.77978i	−0.456178	−	0.889889i	$-0.650782\pi$
$683$		−	46.5132i		−	1.77978i	0.456178	−	0.889889i	$-0.349218\pi$
$684$	−21.2608	−	0.627528i	−0.812925	−	0.0239941i
$685$	0.455089	−	0.330642i	0.0173881	−	0.0126332i
$686$	10.4727	−	14.4144i	0.399849	−	0.550345i
$687$	28.9023	−	14.1933i	1.10269	−	0.541508i
$688$	5.08423	−	1.65197i	0.193834	−	0.0629806i
$689$	−16.6909	−	12.1267i	−0.635874	−	0.461990i
$690$	1.34888	+	1.38928i	0.0513508	+	0.0528888i
$691$	9.08650	−	27.9654i	0.345667	−	1.06385i	−0.615559	−	0.788091i	$-0.711070\pi$
$691$	9.08650	−	27.9654i	0.345667	−	1.06385i	0.961226	−	0.275762i	$-0.0889301\pi$
$692$	−7.10940			−0.270259
$693$	−9.82970	+	11.5848i	−0.373399	+	0.440069i
$694$	−30.2072			−1.14665
$695$	−1.49796	+	4.61025i	−0.0568210	+	0.174877i
$696$	−7.71446	−	7.94551i	−0.292416	−	0.301174i
$697$	17.3598	+	12.6126i	0.657548	+	0.477737i
$698$	−9.17824	+	2.98219i	−0.347401	+	0.112878i
$699$	28.1113	−	13.8049i	1.06327	−	0.522148i
$700$	3.68830	−	5.07650i	0.139404	−	0.191874i
$701$	22.1405	−	16.0860i	0.836236	−	0.607561i	−0.0850807	−	0.996374i	$-0.527115\pi$
$701$	22.1405	−	16.0860i	0.836236	−	0.607561i	0.921317	+	0.388813i	$0.127115\pi$
$702$	−2.47948	−	21.8842i	−0.0935820	−	0.825967i
$703$			20.0376i			0.755731i
$704$	3.10407	+	1.16823i	0.116989	+	0.0440293i
$705$	−2.20168	−	15.3647i	−0.0829200	−	0.578667i
$706$	13.0660	+	4.24542i	0.491747	+	0.159778i
$707$	−4.20549	−	5.78836i	−0.158164	−	0.217694i
$708$	−7.14443	−	3.77405i	−0.268504	−	0.141838i
$709$	13.1638	+	40.5141i	0.494378	+	1.52154i	0.817924	+	0.575327i	$0.195125\pi$
$709$	13.1638	+	40.5141i	0.494378	+	1.52154i	−0.323546	+	0.946213i	$0.604875\pi$
$710$	2.90445	+	8.93899i	0.109002	+	0.335474i
$711$	1.66432	−	4.65066i	0.0624169	−	0.174413i
$712$	10.1926	+	14.0289i	0.381983	+	0.525754i
$713$	9.80143	+	3.18468i	0.367066	+	0.119267i
$714$	−7.67708	+	1.10009i	−0.287308	+	0.0411697i
$715$	−0.607365	+	13.2526i	−0.0227142	+	0.495619i
$716$		−	4.21134i		−	0.157385i
$717$	34.1125	+	5.92004i	1.27396	+	0.221088i
$718$	23.6610	−	17.1908i	0.883022	−	0.641553i
$719$	−9.60723	+	13.2232i	−0.358289	+	0.493143i	−0.949671	−	0.313249i	$-0.898583\pi$
$719$	−9.60723	+	13.2232i	−0.358289	+	0.493143i	0.591382	+	0.806392i	$0.298583\pi$
$720$	−2.33854	+	1.59581i	−0.0871523	+	0.0594721i
$721$	18.3867	−	5.97420i	0.684757	−	0.222491i
$722$	25.2965	+	18.3790i	0.941438	+	0.683995i
$723$	−2.23076	+	2.16589i	−0.0829628	+	0.0805502i
$724$	2.67906	−	8.24528i	0.0995663	−	0.306434i
$725$	26.2749			0.975826
$726$	17.7982	−	6.79883i	0.660553	−	0.252328i
$727$	−21.6566			−0.803197			−0.401599	−	0.915816i	$-0.631545\pi$
$727$	−21.6566			−0.803197			−0.401599	+	0.915816i	$0.631545\pi$
$728$	−2.00000	+	6.15537i	−0.0741249	+	0.228133i
$729$	2.38697	−	26.8943i	0.0884061	−	0.996085i
$730$	−1.33854	−	0.972508i	−0.0495417	−	0.0359941i
$731$	14.9089	−	4.84420i	0.551426	−	0.179169i
$732$	−0.550419	−	1.12084i	−0.0203441	−	0.0414273i
$733$	−16.0834	+	22.1368i	−0.594052	+	0.817643i	−0.995148	−	0.0983933i	$-0.968630\pi$
$733$	−16.0834	+	22.1368i	−0.594052	+	0.817643i	0.401095	+	0.916036i	$0.368630\pi$
$734$	−9.12557	+	6.63012i	−0.336831	+	0.244722i
$735$	1.30478	−	7.51839i	0.0481274	−	0.277320i
$736$		−	1.18465i		−	0.0436666i
$737$	−0.591238	+	12.9007i	−0.0217785	+	0.475203i
$738$	21.0692	−	6.16481i	0.775569	−	0.226930i
$739$	−47.3897	−	15.3979i	−1.74326	−	0.566420i	−0.748003	−	0.663696i	$-0.768987\pi$
$739$	−47.3897	−	15.3979i	−1.74326	−	0.566420i	−0.995257	+	0.0972762i	$0.968987\pi$
$740$	1.56768	+	2.15773i	0.0576291	+	0.0793197i
$741$	−24.3122	+	46.0238i	−0.893130	+	1.69073i
$742$	2.29675	+	7.06868i	0.0843165	+	0.259499i
$743$	6.29906	+	19.3865i	0.231090	+	0.711222i	0.997616	+	0.0690089i	$0.0219837\pi$
$743$	6.29906	+	19.3865i	0.231090	+	0.711222i	−0.766526	+	0.642213i	$0.778016\pi$
$744$	−7.03805	+	13.3233i	−0.258027	+	0.488456i
$745$	9.63467	+	13.2610i	0.352987	+	0.485845i
$746$	−5.45474	−	1.77235i	−0.199712	−	0.0648904i
$747$	17.7357	−	5.18941i	0.648914	−	0.189871i
$748$	9.10233	+	3.42570i	0.332814	+	0.125256i
$749$			1.09749i			0.0401013i
$750$	2.54600	−	14.6706i	0.0929669	−	0.535694i
$751$	15.4668	−	11.2373i	0.564390	−	0.410053i	−0.268673	−	0.963231i	$-0.586585\pi$
$751$	15.4668	−	11.2373i	0.564390	−	0.410053i	0.833063	+	0.553178i	$0.186585\pi$
$752$	−5.58154	+	7.68233i	−0.203538	+	0.280146i
$753$	−9.69577	−	19.7438i	−0.353333	−	0.719504i
$754$	−25.7744	+	8.37461i	−0.938648	+	0.304985i
$755$	11.5381	+	8.38293i	0.419915	+	0.305086i
$756$	−3.91138	+	6.90323i	−0.142256	+	0.251068i
$757$	5.81223	−	17.8882i	0.211249	−	0.650158i	−0.788150	−	0.615484i	$-0.788961\pi$
$757$	5.81223	−	17.8882i	0.211249	−	0.650158i	0.999399	−	0.0346742i	$-0.0110394\pi$
$758$	26.9912			0.980365
$759$	−4.51204	−	5.09443i	−0.163777	−	0.184916i
$760$	6.69094			0.242706
$761$	−7.25897	+	22.3408i	−0.263138	+	0.809854i	0.728979	+	0.684536i	$0.239995\pi$
$761$	−7.25897	+	22.3408i	−0.263138	+	0.809854i	−0.992117	+	0.125318i	$0.960005\pi$
$762$	6.56965	−	6.37860i	0.237993	−	0.231072i
$763$	−11.3766	−	8.26558i	−0.411860	−	0.299234i
$764$	−12.7897	+	4.15562i	−0.462714	+	0.150345i
$765$	−6.85751	+	4.67952i	−0.247934	+	0.169188i

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)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-1.20654 - 1.24268i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.897526 - 0.291624i) q^{5} +(-1.55470 + 0.763481i) q^{6} +(0.897526 - 1.23534i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.0885088 + 2.99869i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-1.20654 - 1.24268i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.897526 - 0.291624i) q^{5} +(-1.55470 + 0.763481i) q^{6} +(0.897526 - 1.23534i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.0885088 + 2.99869i) q^{9} -0.943715i q^{10} +(-0.151841 + 3.31315i) q^{11} +(0.245684 + 1.71454i) q^{12} +(4.03112 + 1.30979i) q^{13} +(-0.897526 - 1.23534i) q^{14} +(-1.44530 - 0.763481i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.906157 + 2.78886i) q^{17} +(2.82458 + 1.01082i) q^{18} +(-4.16740 - 5.73594i) q^{19} +(-0.897526 - 0.291624i) q^{20} +(-2.61803 + 0.375151i) q^{21} +(3.10407 + 1.16823i) q^{22} -1.18465i q^{23} +(1.70654 + 0.296161i) q^{24} +(-3.32458 + 2.41545i) q^{25} +(2.49137 - 3.42908i) q^{26} +(3.83321 - 3.50806i) q^{27} +(-1.45223 + 0.471857i) q^{28} +(-5.17274 - 3.75821i) q^{29} +(-1.17274 + 1.13863i) q^{30} +(-2.68830 + 8.27372i) q^{31} +1.00000 q^{32} +(4.30039 - 3.80876i) q^{33} +2.93239 q^{34} +(0.445299 - 1.37049i) q^{35} +(1.83419 - 2.37397i) q^{36} +(-2.28642 - 1.66118i) q^{37} +(-6.74300 + 2.19093i) q^{38} +(-3.23607 - 6.58971i) q^{39} +(-0.554701 + 0.763481i) q^{40} +(5.92001 - 4.30114i) q^{41} +(-0.452227 + 2.60583i) q^{42} -5.34587i q^{43} +(2.07026 - 2.59114i) q^{44} +(0.795052 + 2.71722i) q^{45} +(-1.12667 - 0.366076i) q^{46} +(5.58154 + 7.68233i) q^{47} +(0.809017 - 1.53150i) q^{48} +(1.44261 + 4.43990i) q^{49} +(1.26988 + 3.90827i) q^{50} +(2.37235 - 4.49095i) q^{51} +(-2.49137 - 3.42908i) q^{52} +(-4.62924 - 1.50413i) q^{53} +(-2.15184 - 4.72965i) q^{54} +(0.829911 + 3.01792i) q^{55} +1.52696i q^{56} +(-2.09979 + 12.0994i) q^{57} +(-5.17274 + 3.75821i) q^{58} +(-2.74201 + 3.77405i) q^{59} +(0.720508 + 1.46719i) q^{60} +(-0.685649 + 0.222781i) q^{61} +(7.03805 + 5.11344i) q^{62} +(3.62496 + 2.80074i) q^{63} +(0.309017 - 0.951057i) q^{64} +4.00000 q^{65} +(-2.29346 - 5.26688i) q^{66} +3.89379 q^{67} +(0.906157 - 2.78886i) q^{68} +(-1.47214 + 1.42933i) q^{69} +(-1.16581 - 0.847008i) q^{70} +(-9.47214 + 3.07768i) q^{71} +(-1.69098 - 2.47802i) q^{72} +(1.03051 - 1.41838i) q^{73} +(-2.28642 + 1.66118i) q^{74} +(7.01287 + 1.21705i) q^{75} +7.09001i q^{76} +(3.95658 + 3.16121i) q^{77} +(-7.26719 + 1.04135i) q^{78} +(-1.56591 - 0.508796i) q^{79} +(0.554701 + 0.763481i) q^{80} +(-8.98433 - 0.530822i) q^{81} +(-2.26124 - 6.95939i) q^{82} +(-1.90347 - 5.85828i) q^{83} +(2.33854 + 1.23534i) q^{84} +(1.62660 + 2.23882i) q^{85} +(-5.08423 - 1.65197i) q^{86} +(1.57087 + 10.9625i) q^{87} +(-1.82458 - 2.76964i) q^{88} -17.3406i q^{89} +(2.82991 + 0.0835271i) q^{90} +(5.23607 - 3.80423i) q^{91} +(-0.696317 + 0.958399i) q^{92} +(13.5251 - 6.64191i) q^{93} +(9.03112 - 2.93439i) q^{94} +(-5.41309 - 3.93284i) q^{95} +(-1.20654 - 1.24268i) q^{96} +(3.54074 - 10.8973i) q^{97} +4.66839 q^{98} +(-9.92168 - 0.748569i) 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